1,1,29,0,0.945783," ","integrate((b*x)^p*(c*x)^m,x, algorithm=""fricas"")","\frac{\left(b x\right)^{p} x e^{\left(m \log\left(b x\right) + m \log\left(\frac{c}{b}\right)\right)}}{m + p + 1}"," ",0,"(b*x)^p*x*e^(m*log(b*x) + m*log(c/b))/(m + p + 1)","A",0
2,1,12,0,0.783866," ","integrate(x^3*(b*x^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{5} \, \sqrt{b x^{2}} x^{4}"," ",0,"1/5*sqrt(b*x^2)*x^4","A",0
3,1,12,0,0.930306," ","integrate(x^2*(b*x^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{b x^{2}} x^{3}"," ",0,"1/4*sqrt(b*x^2)*x^3","A",0
4,1,12,0,0.946530," ","integrate(x*(b*x^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{3} \, \sqrt{b x^{2}} x^{2}"," ",0,"1/3*sqrt(b*x^2)*x^2","A",0
5,1,10,0,1.030116," ","integrate((b*x^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{b x^{2}} x"," ",0,"1/2*sqrt(b*x^2)*x","A",0
6,1,7,0,0.863824," ","integrate((b*x^2)^(1/2)/x,x, algorithm=""fricas"")","\sqrt{b x^{2}}"," ",0,"sqrt(b*x^2)","A",0
7,1,13,0,0.952107," ","integrate((b*x^2)^(1/2)/x^2,x, algorithm=""fricas"")","\frac{\sqrt{b x^{2}} \log\left(x\right)}{x}"," ",0,"sqrt(b*x^2)*log(x)/x","A",0
8,1,12,0,0.871308," ","integrate((b*x^2)^(1/2)/x^3,x, algorithm=""fricas"")","-\frac{\sqrt{b x^{2}}}{x^{2}}"," ",0,"-sqrt(b*x^2)/x^2","A",0
9,1,12,0,0.959501," ","integrate((b*x^2)^(1/2)/x^4,x, algorithm=""fricas"")","-\frac{\sqrt{b x^{2}}}{2 \, x^{3}}"," ",0,"-1/2*sqrt(b*x^2)/x^3","A",0
10,1,12,0,0.853378," ","integrate((b*x^2)^(1/2)/x^5,x, algorithm=""fricas"")","-\frac{\sqrt{b x^{2}}}{3 \, x^{4}}"," ",0,"-1/3*sqrt(b*x^2)/x^4","A",0
11,1,5,0,0.773575," ","integrate(x^2*(x^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{4} \, x^{4}"," ",0,"1/4*x^4","A",0
12,1,13,0,0.510063," ","integrate(x^2*(b*x^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{6} \, \sqrt{b x^{2}} b x^{5}"," ",0,"1/6*sqrt(b*x^2)*b*x^5","A",0
13,1,13,0,0.950843," ","integrate(x*(b*x^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{5} \, \sqrt{b x^{2}} b x^{4}"," ",0,"1/5*sqrt(b*x^2)*b*x^4","A",0
14,1,13,0,0.895236," ","integrate((b*x^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{b x^{2}} b x^{3}"," ",0,"1/4*sqrt(b*x^2)*b*x^3","A",0
15,1,13,0,0.994900," ","integrate((b*x^2)^(3/2)/x,x, algorithm=""fricas"")","\frac{1}{3} \, \sqrt{b x^{2}} b x^{2}"," ",0,"1/3*sqrt(b*x^2)*b*x^2","A",0
16,1,11,0,1.023510," ","integrate((b*x^2)^(3/2)/x^2,x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{b x^{2}} b x"," ",0,"1/2*sqrt(b*x^2)*b*x","A",0
17,1,9,0,0.980765," ","integrate((b*x^2)^(3/2)/x^3,x, algorithm=""fricas"")","\sqrt{b x^{2}} b"," ",0,"sqrt(b*x^2)*b","A",0
18,1,14,0,0.963278," ","integrate((b*x^2)^(3/2)/x^4,x, algorithm=""fricas"")","\frac{\sqrt{b x^{2}} b \log\left(x\right)}{x}"," ",0,"sqrt(b*x^2)*b*log(x)/x","A",0
19,1,13,0,1.041075," ","integrate((b*x^2)^(3/2)/x^5,x, algorithm=""fricas"")","-\frac{\sqrt{b x^{2}} b}{x^{2}}"," ",0,"-sqrt(b*x^2)*b/x^2","A",0
20,1,13,0,0.834343," ","integrate((b*x^2)^(3/2)/x^6,x, algorithm=""fricas"")","-\frac{\sqrt{b x^{2}} b}{2 \, x^{3}}"," ",0,"-1/2*sqrt(b*x^2)*b/x^3","A",0
21,1,13,0,0.983512," ","integrate((b*x^2)^(3/2)/x^7,x, algorithm=""fricas"")","-\frac{\sqrt{b x^{2}} b}{3 \, x^{4}}"," ",0,"-1/3*sqrt(b*x^2)*b/x^4","A",0
22,1,5,0,0.838901," ","integrate((x^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{6} \, x^{6}"," ",0,"1/6*x^6","A",0
23,1,15,0,0.773266," ","integrate(x*(b*x^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{7} \, \sqrt{b x^{2}} b^{2} x^{6}"," ",0,"1/7*sqrt(b*x^2)*b^2*x^6","A",0
24,1,15,0,0.711381," ","integrate((b*x^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{6} \, \sqrt{b x^{2}} b^{2} x^{5}"," ",0,"1/6*sqrt(b*x^2)*b^2*x^5","A",0
25,1,15,0,0.992787," ","integrate((b*x^2)^(5/2)/x,x, algorithm=""fricas"")","\frac{1}{5} \, \sqrt{b x^{2}} b^{2} x^{4}"," ",0,"1/5*sqrt(b*x^2)*b^2*x^4","A",0
26,1,15,0,1.082375," ","integrate((b*x^2)^(5/2)/x^2,x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{b x^{2}} b^{2} x^{3}"," ",0,"1/4*sqrt(b*x^2)*b^2*x^3","A",0
27,1,15,0,1.029334," ","integrate((b*x^2)^(5/2)/x^3,x, algorithm=""fricas"")","\frac{1}{3} \, \sqrt{b x^{2}} b^{2} x^{2}"," ",0,"1/3*sqrt(b*x^2)*b^2*x^2","A",0
28,1,13,0,0.972300," ","integrate((b*x^2)^(5/2)/x^4,x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{b x^{2}} b^{2} x"," ",0,"1/2*sqrt(b*x^2)*b^2*x","A",0
29,1,11,0,0.889695," ","integrate((b*x^2)^(5/2)/x^5,x, algorithm=""fricas"")","\sqrt{b x^{2}} b^{2}"," ",0,"sqrt(b*x^2)*b^2","A",0
30,1,16,0,0.656736," ","integrate((b*x^2)^(5/2)/x^6,x, algorithm=""fricas"")","\frac{\sqrt{b x^{2}} b^{2} \log\left(x\right)}{x}"," ",0,"sqrt(b*x^2)*b^2*log(x)/x","A",0
31,1,15,0,0.825079," ","integrate((b*x^2)^(5/2)/x^7,x, algorithm=""fricas"")","-\frac{\sqrt{b x^{2}} b^{2}}{x^{2}}"," ",0,"-sqrt(b*x^2)*b^2/x^2","A",0
32,1,15,0,1.065098," ","integrate((b*x^2)^(5/2)/x^8,x, algorithm=""fricas"")","-\frac{\sqrt{b x^{2}} b^{2}}{2 \, x^{3}}"," ",0,"-1/2*sqrt(b*x^2)*b^2/x^3","A",0
33,1,15,0,0.858576," ","integrate((b*x^2)^(5/2)/x^9,x, algorithm=""fricas"")","-\frac{\sqrt{b x^{2}} b^{2}}{3 \, x^{4}}"," ",0,"-1/3*sqrt(b*x^2)*b^2/x^4","A",0
34,1,5,0,0.848801," ","integrate((x^2)^(7/2),x, algorithm=""fricas"")","\frac{1}{8} \, x^{8}"," ",0,"1/8*x^8","A",0
35,1,15,0,0.971852," ","integrate(x^3/(b*x^2)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{b x^{2}} x^{2}}{3 \, b}"," ",0,"1/3*sqrt(b*x^2)*x^2/b","A",0
36,1,11,0,1.032844," ","integrate(x/(b*x^2)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{b x^{2}}}{b}"," ",0,"sqrt(b*x^2)/b","A",0
37,1,15,0,0.893302," ","integrate(1/x/(b*x^2)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{b x^{2}}}{b x^{2}}"," ",0,"-sqrt(b*x^2)/(b*x^2)","A",0
38,1,15,0,0.857716," ","integrate(1/x^3/(b*x^2)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{b x^{2}}}{3 \, b x^{4}}"," ",0,"-1/3*sqrt(b*x^2)/(b*x^4)","A",0
39,1,13,0,1.040064," ","integrate(x^2/(b*x^2)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{b x^{2}} x}{2 \, b}"," ",0,"1/2*sqrt(b*x^2)*x/b","A",0
40,1,16,0,0.831759," ","integrate(1/(b*x^2)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{b x^{2}} \log\left(x\right)}{b x}"," ",0,"sqrt(b*x^2)*log(x)/(b*x)","A",0
41,1,15,0,0.819393," ","integrate(1/x^2/(b*x^2)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{b x^{2}}}{2 \, b x^{3}}"," ",0,"-1/2*sqrt(b*x^2)/(b*x^3)","A",0
42,1,15,0,1.131185," ","integrate(x^5/(b*x^2)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{b x^{2}} x^{2}}{3 \, b^{2}}"," ",0,"1/3*sqrt(b*x^2)*x^2/b^2","A",0
43,1,11,0,0.686314," ","integrate(x^3/(b*x^2)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{b x^{2}}}{b^{2}}"," ",0,"sqrt(b*x^2)/b^2","A",0
44,1,15,0,1.037193," ","integrate(x/(b*x^2)^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{b x^{2}}}{b^{2} x^{2}}"," ",0,"-sqrt(b*x^2)/(b^2*x^2)","A",0
45,1,15,0,0.555407," ","integrate(1/x/(b*x^2)^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{b x^{2}}}{3 \, b^{2} x^{4}}"," ",0,"-1/3*sqrt(b*x^2)/(b^2*x^4)","A",0
46,1,15,0,0.578183," ","integrate(1/x^3/(b*x^2)^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{b x^{2}}}{5 \, b^{2} x^{6}}"," ",0,"-1/5*sqrt(b*x^2)/(b^2*x^6)","A",0
47,1,15,0,0.912262," ","integrate(x^6/(b*x^2)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{b x^{2}} x^{3}}{4 \, b^{2}}"," ",0,"1/4*sqrt(b*x^2)*x^3/b^2","A",0
48,1,13,0,1.002084," ","integrate(x^4/(b*x^2)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{b x^{2}} x}{2 \, b^{2}}"," ",0,"1/2*sqrt(b*x^2)*x/b^2","A",0
49,1,16,0,0.858430," ","integrate(x^2/(b*x^2)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{b x^{2}} \log\left(x\right)}{b^{2} x}"," ",0,"sqrt(b*x^2)*log(x)/(b^2*x)","A",0
50,1,15,0,0.965548," ","integrate(1/(b*x^2)^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{b x^{2}}}{2 \, b^{2} x^{3}}"," ",0,"-1/2*sqrt(b*x^2)/(b^2*x^3)","A",0
51,1,15,0,0.656844," ","integrate(1/x^2/(b*x^2)^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{b x^{2}}}{4 \, b^{2} x^{5}}"," ",0,"-1/4*sqrt(b*x^2)/(b^2*x^5)","A",0
52,1,15,0,1.064909," ","integrate(x^7/(b*x^2)^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{b x^{2}} x^{2}}{3 \, b^{3}}"," ",0,"1/3*sqrt(b*x^2)*x^2/b^3","A",0
53,1,11,0,0.888464," ","integrate(x^5/(b*x^2)^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{b x^{2}}}{b^{3}}"," ",0,"sqrt(b*x^2)/b^3","A",0
54,1,15,0,1.008131," ","integrate(x^3/(b*x^2)^(5/2),x, algorithm=""fricas"")","-\frac{\sqrt{b x^{2}}}{b^{3} x^{2}}"," ",0,"-sqrt(b*x^2)/(b^3*x^2)","A",0
55,1,15,0,1.038318," ","integrate(x/(b*x^2)^(5/2),x, algorithm=""fricas"")","-\frac{\sqrt{b x^{2}}}{3 \, b^{3} x^{4}}"," ",0,"-1/3*sqrt(b*x^2)/(b^3*x^4)","A",0
56,1,15,0,1.122600," ","integrate(1/x/(b*x^2)^(5/2),x, algorithm=""fricas"")","-\frac{\sqrt{b x^{2}}}{5 \, b^{3} x^{6}}"," ",0,"-1/5*sqrt(b*x^2)/(b^3*x^6)","A",0
57,1,13,0,1.029757," ","integrate(x^6/(b*x^2)^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{b x^{2}} x}{2 \, b^{3}}"," ",0,"1/2*sqrt(b*x^2)*x/b^3","A",0
58,1,16,0,1.152129," ","integrate(x^4/(b*x^2)^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{b x^{2}} \log\left(x\right)}{b^{3} x}"," ",0,"sqrt(b*x^2)*log(x)/(b^3*x)","A",0
59,1,15,0,0.821704," ","integrate(x^2/(b*x^2)^(5/2),x, algorithm=""fricas"")","-\frac{\sqrt{b x^{2}}}{2 \, b^{3} x^{3}}"," ",0,"-1/2*sqrt(b*x^2)/(b^3*x^3)","A",0
60,1,15,0,1.108917," ","integrate(1/(b*x^2)^(5/2),x, algorithm=""fricas"")","-\frac{\sqrt{b x^{2}}}{4 \, b^{3} x^{5}}"," ",0,"-1/4*sqrt(b*x^2)/(b^3*x^5)","A",0
61,1,15,0,0.964598," ","integrate(1/x^2/(b*x^2)^(5/2),x, algorithm=""fricas"")","-\frac{\sqrt{b x^{2}}}{6 \, b^{3} x^{7}}"," ",0,"-1/6*sqrt(b*x^2)/(b^3*x^7)","A",0
62,1,22,0,1.107462," ","integrate((c*x)^m*(b*x^2)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{b x^{2}} \left(c x\right)^{m} b x^{3}}{m + 4}"," ",0,"sqrt(b*x^2)*(c*x)^m*b*x^3/(m + 4)","A",0
63,1,19,0,0.638047," ","integrate((c*x)^m*(b*x^2)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{b x^{2}} \left(c x\right)^{m} x}{m + 2}"," ",0,"sqrt(b*x^2)*(c*x)^m*x/(m + 2)","A",0
64,1,22,0,0.785159," ","integrate((c*x)^m/(b*x^2)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{b x^{2}} \left(c x\right)^{m}}{b m x}"," ",0,"sqrt(b*x^2)*(c*x)^m/(b*m*x)","A",0
65,1,29,0,1.093238," ","integrate((c*x)^m/(b*x^2)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{b x^{2}} \left(c x\right)^{m}}{{\left(b^{2} m - 2 \, b^{2}\right)} x^{3}}"," ",0,"sqrt(b*x^2)*(c*x)^m/((b^2*m - 2*b^2)*x^3)","A",0
66,1,24,0,0.998255," ","integrate(x^m*(b*x^2)^p,x, algorithm=""fricas"")","\frac{x x^{m} e^{\left(p \log\left(b\right) + 2 \, p \log\left(x\right)\right)}}{m + 2 \, p + 1}"," ",0,"x*x^m*e^(p*log(b) + 2*p*log(x))/(m + 2*p + 1)","A",0
67,1,32,0,0.906885," ","integrate((c*x)^m*(b*x^2)^p,x, algorithm=""fricas"")","\frac{\left(c x\right)^{m} x e^{\left(2 \, p \log\left(c x\right) + p \log\left(\frac{b}{c^{2}}\right)\right)}}{m + 2 \, p + 1}"," ",0,"(c*x)^m*x*e^(2*p*log(c*x) + p*log(b/c^2))/(m + 2*p + 1)","A",0
68,1,2,0,0.760285," ","integrate(x^(-1-2*p)*(x^2)^p,x, algorithm=""fricas"")","\log\left(x\right)"," ",0,"log(x)","A",0
69,1,17,0,1.188745," ","integrate(x^3*(b*x^2)^p,x, algorithm=""fricas"")","\frac{\left(b x^{2}\right)^{p} x^{4}}{2 \, {\left(p + 2\right)}}"," ",0,"1/2*(b*x^2)^p*x^4/(p + 2)","A",0
70,1,18,0,0.966373," ","integrate(x^2*(b*x^2)^p,x, algorithm=""fricas"")","\frac{\left(b x^{2}\right)^{p} x^{3}}{2 \, p + 3}"," ",0,"(b*x^2)^p*x^3/(2*p + 3)","A",0
71,1,17,0,1.080584," ","integrate(x*(b*x^2)^p,x, algorithm=""fricas"")","\frac{\left(b x^{2}\right)^{p} x^{2}}{2 \, {\left(p + 1\right)}}"," ",0,"1/2*(b*x^2)^p*x^2/(p + 1)","A",0
72,1,16,0,1.249232," ","integrate((b*x^2)^p,x, algorithm=""fricas"")","\frac{\left(b x^{2}\right)^{p} x}{2 \, p + 1}"," ",0,"(b*x^2)^p*x/(2*p + 1)","A",0
73,1,12,0,1.096184," ","integrate((b*x^2)^p/x,x, algorithm=""fricas"")","\frac{\left(b x^{2}\right)^{p}}{2 \, p}"," ",0,"1/2*(b*x^2)^p/p","A",0
74,1,18,0,0.929138," ","integrate((b*x^2)^p/x^2,x, algorithm=""fricas"")","\frac{\left(b x^{2}\right)^{p}}{{\left(2 \, p - 1\right)} x}"," ",0,"(b*x^2)^p/((2*p - 1)*x)","A",0
75,1,17,0,0.872378," ","integrate((b*x^2)^p/x^3,x, algorithm=""fricas"")","\frac{\left(b x^{2}\right)^{p}}{2 \, {\left(p - 1\right)} x^{2}}"," ",0,"1/2*(b*x^2)^p/((p - 1)*x^2)","A",0
76,1,18,0,1.008335," ","integrate((b*x^2)^p/x^4,x, algorithm=""fricas"")","\frac{\left(b x^{2}\right)^{p}}{{\left(2 \, p - 3\right)} x^{3}}"," ",0,"(b*x^2)^p/((2*p - 3)*x^3)","A",0
77,1,10,0,0.953216," ","integrate((b*x^3)^(1/2),x, algorithm=""fricas"")","\frac{2}{5} \, \sqrt{b x^{3}} x"," ",0,"2/5*sqrt(b*x^3)*x","A",0
78,1,10,0,0.922967," ","integrate((b*x^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{b x^{2}} x"," ",0,"1/2*sqrt(b*x^2)*x","A",0
79,1,8,0,0.939272," ","integrate((b*x)^(1/2),x, algorithm=""fricas"")","\frac{2}{3} \, \sqrt{b x} x"," ",0,"2/3*sqrt(b*x)*x","A",0
80,1,10,0,0.967290," ","integrate((b/x)^(1/2),x, algorithm=""fricas"")","2 \, x \sqrt{\frac{b}{x}}"," ",0,"2*x*sqrt(b/x)","A",0
81,1,11,0,1.178969," ","integrate((b/x^2)^(1/2),x, algorithm=""fricas"")","x \sqrt{\frac{b}{x^{2}}} \log\left(x\right)"," ",0,"x*sqrt(b/x^2)*log(x)","A",0
82,1,10,0,1.110822," ","integrate((b/x^3)^(1/2),x, algorithm=""fricas"")","-2 \, x \sqrt{\frac{b}{x^{3}}}"," ",0,"-2*x*sqrt(b/x^3)","A",0
83,1,13,0,1.030569," ","integrate((b*x^3)^(3/2),x, algorithm=""fricas"")","\frac{2}{11} \, \sqrt{b x^{3}} b x^{4}"," ",0,"2/11*sqrt(b*x^3)*b*x^4","A",0
84,1,13,0,1.057240," ","integrate((b*x^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{b x^{2}} b x^{3}"," ",0,"1/4*sqrt(b*x^2)*b*x^3","A",0
85,1,11,0,1.160577," ","integrate((b*x)^(3/2),x, algorithm=""fricas"")","\frac{2}{5} \, \sqrt{b x} b x^{2}"," ",0,"2/5*sqrt(b*x)*b*x^2","A",0
86,1,10,0,0.764142," ","integrate((b/x)^(3/2),x, algorithm=""fricas"")","-2 \, b \sqrt{\frac{b}{x}}"," ",0,"-2*b*sqrt(b/x)","A",0
87,1,13,0,1.116467," ","integrate((b/x^2)^(3/2),x, algorithm=""fricas"")","-\frac{b \sqrt{\frac{b}{x^{2}}}}{2 \, x}"," ",0,"-1/2*b*sqrt(b/x^2)/x","A",0
88,1,13,0,0.888944," ","integrate((b/x^3)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, b \sqrt{\frac{b}{x^{3}}}}{7 \, x^{2}}"," ",0,"-2/7*b*sqrt(b/x^3)/x^2","A",0
89,1,15,0,1.202138," ","integrate(1/(b*x^3)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{b x^{3}}}{b x^{2}}"," ",0,"-2*sqrt(b*x^3)/(b*x^2)","A",0
90,1,16,0,0.654022," ","integrate(1/(b*x^2)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{b x^{2}} \log\left(x\right)}{b x}"," ",0,"sqrt(b*x^2)*log(x)/(b*x)","A",0
91,1,10,0,1.143235," ","integrate(1/(b*x)^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{b x}}{b}"," ",0,"2*sqrt(b*x)/b","A",0
92,1,15,0,1.113140," ","integrate(1/(b/x)^(1/2),x, algorithm=""fricas"")","\frac{2 \, x^{2} \sqrt{\frac{b}{x}}}{3 \, b}"," ",0,"2/3*x^2*sqrt(b/x)/b","A",0
93,1,15,0,1.109562," ","integrate(1/(b/x^2)^(1/2),x, algorithm=""fricas"")","\frac{x^{3} \sqrt{\frac{b}{x^{2}}}}{2 \, b}"," ",0,"1/2*x^3*sqrt(b/x^2)/b","A",0
94,1,15,0,0.982460," ","integrate(1/(b/x^3)^(1/2),x, algorithm=""fricas"")","\frac{2 \, x^{4} \sqrt{\frac{b}{x^{3}}}}{5 \, b}"," ",0,"2/5*x^4*sqrt(b/x^3)/b","A",0
95,1,15,0,0.934000," ","integrate(1/(b*x^3)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{b x^{3}}}{7 \, b^{2} x^{5}}"," ",0,"-2/7*sqrt(b*x^3)/(b^2*x^5)","A",0
96,1,15,0,1.102069," ","integrate(1/(b*x^2)^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{b x^{2}}}{2 \, b^{2} x^{3}}"," ",0,"-1/2*sqrt(b*x^2)/(b^2*x^3)","A",0
97,1,13,0,1.140781," ","integrate(1/(b*x)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{b x}}{b^{2} x}"," ",0,"-2*sqrt(b*x)/(b^2*x)","A",0
98,1,15,0,0.918370," ","integrate(1/(b/x)^(3/2),x, algorithm=""fricas"")","\frac{2 \, x^{3} \sqrt{\frac{b}{x}}}{5 \, b^{2}}"," ",0,"2/5*x^3*sqrt(b/x)/b^2","A",0
99,1,15,0,1.093844," ","integrate(1/(b/x^2)^(3/2),x, algorithm=""fricas"")","\frac{x^{5} \sqrt{\frac{b}{x^{2}}}}{4 \, b^{2}}"," ",0,"1/4*x^5*sqrt(b/x^2)/b^2","A",0
100,1,15,0,0.605965," ","integrate(1/(b/x^3)^(3/2),x, algorithm=""fricas"")","\frac{2 \, x^{7} \sqrt{\frac{b}{x^{3}}}}{11 \, b^{2}}"," ",0,"2/11*x^7*sqrt(b/x^3)/b^2","A",0
101,-2,0,0,0.000000," ","integrate((b*x^n)^(1/3),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
102,1,10,0,1.617484," ","integrate((b*x^3)^(1/3),x, algorithm=""fricas"")","\frac{1}{2} \, \left(b x^{3}\right)^{\frac{1}{3}} x"," ",0,"1/2*(b*x^3)^(1/3)*x","A",0
103,1,10,0,0.954059," ","integrate((b*x^2)^(1/3),x, algorithm=""fricas"")","\frac{3}{5} \, \left(b x^{2}\right)^{\frac{1}{3}} x"," ",0,"3/5*(b*x^2)^(1/3)*x","A",0
104,1,8,0,0.976106," ","integrate((b*x)^(1/3),x, algorithm=""fricas"")","\frac{3}{4} \, \left(b x\right)^{\frac{1}{3}} x"," ",0,"3/4*(b*x)^(1/3)*x","A",0
105,1,10,0,1.194573," ","integrate((b/x)^(1/3),x, algorithm=""fricas"")","\frac{3}{2} \, x \left(\frac{b}{x}\right)^{\frac{1}{3}}"," ",0,"3/2*x*(b/x)^(1/3)","A",0
106,1,10,0,1.239464," ","integrate((b/x^2)^(1/3),x, algorithm=""fricas"")","3 \, x \left(\frac{b}{x^{2}}\right)^{\frac{1}{3}}"," ",0,"3*x*(b/x^2)^(1/3)","A",0
107,1,11,0,1.235441," ","integrate((b/x^3)^(1/3),x, algorithm=""fricas"")","x \left(\frac{b}{x^{3}}\right)^{\frac{1}{3}} \log\left(x\right)"," ",0,"x*(b/x^3)^(1/3)*log(x)","A",0
108,1,10,0,1.300729," ","integrate((b/x^4)^(1/3),x, algorithm=""fricas"")","-3 \, x \left(\frac{b}{x^{4}}\right)^{\frac{1}{3}}"," ",0,"-3*x*(b/x^4)^(1/3)","A",0
109,-2,0,0,0.000000," ","integrate((b*x^n)^(2/3),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
110,1,10,0,1.211154," ","integrate((b*x^2)^(2/3),x, algorithm=""fricas"")","\frac{3}{7} \, \left(b x^{2}\right)^{\frac{2}{3}} x"," ",0,"3/7*(b*x^2)^(2/3)*x","A",0
111,1,8,0,1.219024," ","integrate((b*x)^(2/3),x, algorithm=""fricas"")","\frac{3}{5} \, \left(b x\right)^{\frac{2}{3}} x"," ",0,"3/5*(b*x)^(2/3)*x","A",0
112,1,10,0,1.235315," ","integrate((b/x)^(2/3),x, algorithm=""fricas"")","3 \, x \left(\frac{b}{x}\right)^{\frac{2}{3}}"," ",0,"3*x*(b/x)^(2/3)","A",0
113,1,10,0,1.262793," ","integrate((b/x^2)^(2/3),x, algorithm=""fricas"")","-3 \, x \left(\frac{b}{x^{2}}\right)^{\frac{2}{3}}"," ",0,"-3*x*(b/x^2)^(2/3)","A",0
114,1,10,0,1.281926," ","integrate((b/x^3)^(2/3),x, algorithm=""fricas"")","-x \left(\frac{b}{x^{3}}\right)^{\frac{2}{3}}"," ",0,"-x*(b/x^3)^(2/3)","A",0
115,1,10,0,1.147447," ","integrate((b/x^4)^(2/3),x, algorithm=""fricas"")","-\frac{3}{5} \, x \left(\frac{b}{x^{4}}\right)^{\frac{2}{3}}"," ",0,"-3/5*x*(b/x^4)^(2/3)","A",0
116,-2,0,0,0.000000," ","integrate(1/(b*x^n)^(1/3),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
117,1,15,0,1.294322," ","integrate(1/(b*x^4)^(1/3),x, algorithm=""fricas"")","-\frac{3 \, \left(b x^{4}\right)^{\frac{2}{3}}}{b x^{3}}"," ",0,"-3*(b*x^4)^(2/3)/(b*x^3)","A",0
118,1,16,0,1.203834," ","integrate(1/(b*x^3)^(1/3),x, algorithm=""fricas"")","\frac{\left(b x^{3}\right)^{\frac{2}{3}} \log\left(x\right)}{b x^{2}}"," ",0,"(b*x^3)^(2/3)*log(x)/(b*x^2)","A",0
119,1,15,0,1.105104," ","integrate(1/(b*x^2)^(1/3),x, algorithm=""fricas"")","\frac{3 \, \left(b x^{2}\right)^{\frac{2}{3}}}{b x}"," ",0,"3*(b*x^2)^(2/3)/(b*x)","A",0
120,1,10,0,0.956508," ","integrate(1/(b*x)^(1/3),x, algorithm=""fricas"")","\frac{3 \, \left(b x\right)^{\frac{2}{3}}}{2 \, b}"," ",0,"3/2*(b*x)^(2/3)/b","A",0
121,1,15,0,0.867254," ","integrate(1/(b/x)^(1/3),x, algorithm=""fricas"")","\frac{3 \, x^{2} \left(\frac{b}{x}\right)^{\frac{2}{3}}}{4 \, b}"," ",0,"3/4*x^2*(b/x)^(2/3)/b","A",0
122,1,15,0,1.073654," ","integrate(1/(b/x^2)^(1/3),x, algorithm=""fricas"")","\frac{3 \, x^{3} \left(\frac{b}{x^{2}}\right)^{\frac{2}{3}}}{5 \, b}"," ",0,"3/5*x^3*(b/x^2)^(2/3)/b","A",0
123,1,15,0,0.930707," ","integrate(1/(b/x^3)^(1/3),x, algorithm=""fricas"")","\frac{x^{4} \left(\frac{b}{x^{3}}\right)^{\frac{2}{3}}}{2 \, b}"," ",0,"1/2*x^4*(b/x^3)^(2/3)/b","A",0
124,-2,0,0,0.000000," ","integrate(1/(b*x^n)^(2/3),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
125,1,15,0,1.254459," ","integrate(1/(b*x^3)^(2/3),x, algorithm=""fricas"")","-\frac{\left(b x^{3}\right)^{\frac{1}{3}}}{b x^{2}}"," ",0,"-(b*x^3)^(1/3)/(b*x^2)","A",0
126,1,15,0,1.269830," ","integrate(1/(b*x^2)^(2/3),x, algorithm=""fricas"")","-\frac{3 \, \left(b x^{2}\right)^{\frac{1}{3}}}{b x}"," ",0,"-3*(b*x^2)^(1/3)/(b*x)","A",0
127,1,10,0,1.219373," ","integrate(1/(b*x)^(2/3),x, algorithm=""fricas"")","\frac{3 \, \left(b x\right)^{\frac{1}{3}}}{b}"," ",0,"3*(b*x)^(1/3)/b","A",0
128,1,15,0,0.942605," ","integrate(1/(b/x)^(2/3),x, algorithm=""fricas"")","\frac{3 \, x^{2} \left(\frac{b}{x}\right)^{\frac{1}{3}}}{5 \, b}"," ",0,"3/5*x^2*(b/x)^(1/3)/b","A",0
129,1,15,0,1.308953," ","integrate(1/(b/x^2)^(2/3),x, algorithm=""fricas"")","\frac{3 \, x^{3} \left(\frac{b}{x^{2}}\right)^{\frac{1}{3}}}{7 \, b}"," ",0,"3/7*x^3*(b/x^2)^(1/3)/b","A",0
130,1,15,0,1.139132," ","integrate(1/(b/x^3)^(2/3),x, algorithm=""fricas"")","\frac{x^{4} \left(\frac{b}{x^{3}}\right)^{\frac{1}{3}}}{3 \, b}"," ",0,"1/3*x^4*(b/x^3)^(1/3)/b","A",0
131,-2,0,0,0.000000," ","integrate(x^2*(b*x^n)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
132,-2,0,0,0.000000," ","integrate(x*(b*x^n)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
133,-2,0,0,0.000000," ","integrate((b*x^n)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
134,1,12,0,1.072445," ","integrate((b*x^n)^(1/2)/x,x, algorithm=""fricas"")","\frac{2 \, \sqrt{b x^{n}}}{n}"," ",0,"2*sqrt(b*x^n)/n","A",0
135,-2,0,0,0.000000," ","integrate((b*x^n)^(1/2)/x^2,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
136,-2,0,0,0.000000," ","integrate((b*x^n)^(1/2)/x^3,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
137,-2,0,0,0.000000," ","integrate(x*(b*x^n)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
138,-2,0,0,0.000000," ","integrate((b*x^n)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
139,1,16,0,1.032140," ","integrate((b*x^n)^(3/2)/x,x, algorithm=""fricas"")","\frac{2 \, \sqrt{b x^{n}} b x^{n}}{3 \, n}"," ",0,"2/3*sqrt(b*x^n)*b*x^n/n","A",0
140,-2,0,0,0.000000," ","integrate((b*x^n)^(3/2)/x^2,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
141,-2,0,0,0.000000," ","integrate((b*x^n)^(3/2)/x^3,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
142,-2,0,0,0.000000," ","integrate((b*x^n)^(3/2)/x^4,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
143,-2,0,0,0.000000," ","integrate(x^2/(b*x^n)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
144,-2,0,0,0.000000," ","integrate(x/(b*x^n)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
145,-2,0,0,0.000000," ","integrate(1/(b*x^n)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
146,1,20,0,1.546829," ","integrate(1/x/(b*x^n)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{b x^{n}}}{b n x^{n}}"," ",0,"-2*sqrt(b*x^n)/(b*n*x^n)","A",0
147,-2,0,0,0.000000," ","integrate(1/x^2/(b*x^n)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
148,-2,0,0,0.000000," ","integrate(1/x^3/(b*x^n)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
149,-2,0,0,0.000000," ","integrate(x^2/(b*x^n)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
150,-2,0,0,0.000000," ","integrate(x/(b*x^n)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
151,-2,0,0,0.000000," ","integrate(1/(b*x^n)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
152,1,22,0,1.318551," ","integrate(1/x/(b*x^n)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{b x^{n}}}{3 \, b^{2} n x^{2 \, n}}"," ",0,"-2/3*sqrt(b*x^n)/(b^2*n*x^(2*n))","A",0
153,-2,0,0,0.000000," ","integrate(1/x^2/(b*x^n)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
154,-2,0,0,0.000000," ","integrate(1/x^3/(b*x^n)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
155,-2,0,0,0.000000," ","integrate(1/x^4/(b*x^n)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
156,-2,0,0,0.000000," ","integrate(x^m/(a*x^n)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
157,-2,0,0,0.000000," ","integrate((c*x)^m/(a*x^n)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
158,-2,0,0,0.000000," ","integrate(x^m*(b*x^n)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
159,-2,0,0,0.000000," ","integrate(x^m*(b*x^n)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
160,-2,0,0,0.000000," ","integrate(x^m/(b*x^n)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
161,-2,0,0,0.000000," ","integrate(x^m/(b*x^n)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
162,-2,0,0,0.000000," ","integrate((c*x)^m*(b*x^n)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
163,-2,0,0,0.000000," ","integrate((c*x)^m*(b*x^n)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
164,-2,0,0,0.000000," ","integrate((c*x)^m*(b*x^n)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
165,-2,0,0,0.000000," ","integrate((c*x)^m/(b*x^n)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
166,-2,0,0,0.000000," ","integrate((c*x)^m/(b*x^n)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
167,-2,0,0,0.000000," ","integrate((c*x)^m/(b*x^n)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
168,1,110,0,11.557832," ","integrate(x^(-1-3/2*n)*(b*x^n)^(3/2),x, algorithm=""fricas"")","\left[\frac{1}{2} \, b^{\frac{3}{2}} \log\left(\frac{b x^{4} + {\left(x^{4} - 1\right)} \sqrt{b} x^{\frac{1}{3}} x^{-\frac{1}{2} \, n - \frac{1}{3}} \sqrt{\frac{b}{x^{\frac{2}{3}} x^{-n - \frac{2}{3}}}} + b}{x^{2}}\right), -\sqrt{-b} b \arctan\left(\frac{{\left(x^{2} + 1\right)} \sqrt{-b} x^{\frac{1}{3}} x^{-\frac{1}{2} \, n - \frac{1}{3}} \sqrt{\frac{b}{x^{\frac{2}{3}} x^{-n - \frac{2}{3}}}}}{b x^{2} - b}\right)\right]"," ",0,"[1/2*b^(3/2)*log((b*x^4 + (x^4 - 1)*sqrt(b)*x^(1/3)*x^(-1/2*n - 1/3)*sqrt(b/(x^(2/3)*x^(-n - 2/3))) + b)/x^2), -sqrt(-b)*b*arctan((x^2 + 1)*sqrt(-b)*x^(1/3)*x^(-1/2*n - 1/3)*sqrt(b/(x^(2/3)*x^(-n - 2/3)))/(b*x^2 - b))]","B",0
169,1,27,0,0.652828," ","integrate(x^(-1-1/2*n)*(b*x^n)^(1/2),x, algorithm=""fricas"")","x x^{-\frac{1}{2} \, n - 1} \sqrt{\frac{b}{x^{2} x^{-n - 2}}} \log\left(x\right)"," ",0,"x*x^(-1/2*n - 1)*sqrt(b/(x^2*x^(-n - 2)))*log(x)","A",0
170,1,30,0,1.168981," ","integrate(x^(-1+1/2*n)/(b*x^n)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{b x^{2} x^{n - 2}} \log\left(x\right)}{b x x^{\frac{1}{2} \, n - 1}}"," ",0,"sqrt(b*x^2*x^(n - 2))*log(x)/(b*x*x^(1/2*n - 1))","A",0
171,1,20,0,1.070036," ","integrate(x^(-1+3/2*n)/(b*x^n)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{b x^{n}} \log\left(x\right)}{b^{2} x^{\frac{1}{2} \, n}}"," ",0,"sqrt(b*x^n)*log(x)/(b^2*x^(1/2*n))","A",0
172,1,24,0,0.797261," ","integrate(x^m*(b*x^n)^p,x, algorithm=""fricas"")","\frac{x x^{m} e^{\left(n p \log\left(x\right) + p \log\left(b\right)\right)}}{n p + m + 1}"," ",0,"x*x^m*e^(n*p*log(x) + p*log(b))/(n*p + m + 1)","A",0
173,1,29,0,0.613845," ","integrate((c*x)^m*(b*x^n)^p,x, algorithm=""fricas"")","\frac{x e^{\left(n p \log\left(x\right) + p \log\left(b\right) + m \log\left(c\right) + m \log\left(x\right)\right)}}{n p + m + 1}"," ",0,"x*e^(n*p*log(x) + p*log(b) + m*log(c) + m*log(x))/(n*p + m + 1)","A",0
174,1,22,0,0.818244," ","integrate(x^2*(b*x^n)^p,x, algorithm=""fricas"")","\frac{x^{3} e^{\left(n p \log\left(x\right) + p \log\left(b\right)\right)}}{n p + 3}"," ",0,"x^3*e^(n*p*log(x) + p*log(b))/(n*p + 3)","A",0
175,1,22,0,0.891931," ","integrate(x*(b*x^n)^p,x, algorithm=""fricas"")","\frac{x^{2} e^{\left(n p \log\left(x\right) + p \log\left(b\right)\right)}}{n p + 2}"," ",0,"x^2*e^(n*p*log(x) + p*log(b))/(n*p + 2)","A",0
176,1,20,0,0.872176," ","integrate((b*x^n)^p,x, algorithm=""fricas"")","\frac{x e^{\left(n p \log\left(x\right) + p \log\left(b\right)\right)}}{n p + 1}"," ",0,"x*e^(n*p*log(x) + p*log(b))/(n*p + 1)","A",0
177,1,18,0,0.839284," ","integrate((b*x^n)^p/x,x, algorithm=""fricas"")","\frac{e^{\left(n p \log\left(x\right) + p \log\left(b\right)\right)}}{n p}"," ",0,"e^(n*p*log(x) + p*log(b))/(n*p)","A",0
178,1,22,0,0.568842," ","integrate((b*x^n)^p/x^2,x, algorithm=""fricas"")","\frac{e^{\left(n p \log\left(x\right) + p \log\left(b\right)\right)}}{{\left(n p - 1\right)} x}"," ",0,"e^(n*p*log(x) + p*log(b))/((n*p - 1)*x)","A",0
179,1,22,0,0.866662," ","integrate((b*x^n)^p/x^3,x, algorithm=""fricas"")","\frac{e^{\left(n p \log\left(x\right) + p \log\left(b\right)\right)}}{{\left(n p - 2\right)} x^{2}}"," ",0,"e^(n*p*log(x) + p*log(b))/((n*p - 2)*x^2)","A",0
180,1,14,0,0.838778," ","integrate(x^m/((a*x^n)^(1/n)),x, algorithm=""fricas"")","\frac{x^{m}}{a^{\left(\frac{1}{n}\right)} m}"," ",0,"x^m/(a^(1/n)*m)","A",0
181,1,21,0,0.770767," ","integrate((c*x)^m/((a*x^n)^(1/n)),x, algorithm=""fricas"")","\frac{e^{\left(m \log\left(c\right) + m \log\left(x\right)\right)}}{a^{\left(\frac{1}{n}\right)} m}"," ",0,"e^(m*log(c) + m*log(x))/(a^(1/n)*m)","A",0
182,1,12,0,0.907857," ","integrate(x^2/((a*x^n)^(1/n)),x, algorithm=""fricas"")","\frac{x^{2}}{2 \, a^{\left(\frac{1}{n}\right)}}"," ",0,"1/2*x^2/a^(1/n)","A",0
183,1,9,0,0.962867," ","integrate(x/((a*x^n)^(1/n)),x, algorithm=""fricas"")","\frac{x}{a^{\left(\frac{1}{n}\right)}}"," ",0,"x/a^(1/n)","A",0
184,1,10,0,0.931502," ","integrate(1/((a*x^n)^(1/n)),x, algorithm=""fricas"")","\frac{\log\left(x\right)}{a^{\left(\frac{1}{n}\right)}}"," ",0,"log(x)/a^(1/n)","A",0
185,1,12,0,0.980779," ","integrate(1/x/((a*x^n)^(1/n)),x, algorithm=""fricas"")","-\frac{1}{a^{\left(\frac{1}{n}\right)} x}"," ",0,"-1/(a^(1/n)*x)","A",0
186,1,12,0,0.582210," ","integrate(1/x^2/((a*x^n)^(1/n)),x, algorithm=""fricas"")","-\frac{1}{2 \, a^{\left(\frac{1}{n}\right)} x^{2}}"," ",0,"-1/2/(a^(1/n)*x^2)","A",0
187,1,14,0,0.661572," ","integrate(x^m/((a*x^n)^((1+m)/n)),x, algorithm=""fricas"")","\frac{\log\left(x\right)}{a^{\frac{m + 1}{n}}}"," ",0,"log(x)/a^((m + 1)/n)","A",0
188,1,6,0,0.870771," ","integrate(x^(-n*p-1)*(a*x^n)^p,x, algorithm=""fricas"")","a^{p} \log\left(x\right)"," ",0,"a^p*log(x)","A",0
189,1,31,0,0.813613," ","integrate(x^m*(a*(b*x^n)^p)^q,x, algorithm=""fricas"")","\frac{x x^{m} e^{\left(n p q \log\left(x\right) + p q \log\left(b\right) + q \log\left(a\right)\right)}}{n p q + m + 1}"," ",0,"x*x^m*e^(n*p*q*log(x) + p*q*log(b) + q*log(a))/(n*p*q + m + 1)","A",0
190,1,29,0,0.973423," ","integrate(x^2*(a*(b*x^n)^p)^q,x, algorithm=""fricas"")","\frac{x^{3} e^{\left(n p q \log\left(x\right) + p q \log\left(b\right) + q \log\left(a\right)\right)}}{n p q + 3}"," ",0,"x^3*e^(n*p*q*log(x) + p*q*log(b) + q*log(a))/(n*p*q + 3)","A",0
191,1,29,0,0.924197," ","integrate(x*(a*(b*x^n)^p)^q,x, algorithm=""fricas"")","\frac{x^{2} e^{\left(n p q \log\left(x\right) + p q \log\left(b\right) + q \log\left(a\right)\right)}}{n p q + 2}"," ",0,"x^2*e^(n*p*q*log(x) + p*q*log(b) + q*log(a))/(n*p*q + 2)","A",0
192,1,27,0,0.926290," ","integrate((a*(b*x^n)^p)^q,x, algorithm=""fricas"")","\frac{x e^{\left(n p q \log\left(x\right) + p q \log\left(b\right) + q \log\left(a\right)\right)}}{n p q + 1}"," ",0,"x*e^(n*p*q*log(x) + p*q*log(b) + q*log(a))/(n*p*q + 1)","A",0
193,1,27,0,0.943879," ","integrate((a*(b*x^n)^p)^q/x,x, algorithm=""fricas"")","\frac{e^{\left(n p q \log\left(x\right) + p q \log\left(b\right) + q \log\left(a\right)\right)}}{n p q}"," ",0,"e^(n*p*q*log(x) + p*q*log(b) + q*log(a))/(n*p*q)","A",0
194,1,29,0,0.584908," ","integrate((a*(b*x^n)^p)^q/x^2,x, algorithm=""fricas"")","\frac{e^{\left(n p q \log\left(x\right) + p q \log\left(b\right) + q \log\left(a\right)\right)}}{{\left(n p q - 1\right)} x}"," ",0,"e^(n*p*q*log(x) + p*q*log(b) + q*log(a))/((n*p*q - 1)*x)","A",0
195,1,29,0,0.946861," ","integrate((a*(b*x^n)^p)^q/x^3,x, algorithm=""fricas"")","\frac{e^{\left(n p q \log\left(x\right) + p q \log\left(b\right) + q \log\left(a\right)\right)}}{{\left(n p q - 2\right)} x^{2}}"," ",0,"e^(n*p*q*log(x) + p*q*log(b) + q*log(a))/((n*p*q - 2)*x^2)","A",0
196,1,21,0,0.686959," ","integrate(x^2/((a*(b*x^m)^n)^(1/m/n)),x, algorithm=""fricas"")","\frac{1}{2} \, x^{2} e^{\left(-\frac{n \log\left(b\right) + \log\left(a\right)}{m n}\right)}"," ",0,"1/2*x^2*e^(-(n*log(b) + log(a))/(m*n))","A",0
197,1,18,0,0.749980," ","integrate(x/((a*(b*x^m)^n)^(1/m/n)),x, algorithm=""fricas"")","x e^{\left(-\frac{n \log\left(b\right) + \log\left(a\right)}{m n}\right)}"," ",0,"x*e^(-(n*log(b) + log(a))/(m*n))","A",0
198,1,19,0,0.854348," ","integrate(1/((a*(b*x^m)^n)^(1/m/n)),x, algorithm=""fricas"")","e^{\left(-\frac{n \log\left(b\right) + \log\left(a\right)}{m n}\right)} \log\left(x\right)"," ",0,"e^(-(n*log(b) + log(a))/(m*n))*log(x)","A",0
199,1,21,0,0.814003," ","integrate(1/x/((a*(b*x^m)^n)^(1/m/n)),x, algorithm=""fricas"")","-\frac{e^{\left(-\frac{n \log\left(b\right) + \log\left(a\right)}{m n}\right)}}{x}"," ",0,"-e^(-(n*log(b) + log(a))/(m*n))/x","A",0
200,1,21,0,0.796014," ","integrate(1/x^2/((a*(b*x^m)^n)^(1/m/n)),x, algorithm=""fricas"")","-\frac{e^{\left(-\frac{n \log\left(b\right) + \log\left(a\right)}{m n}\right)}}{2 \, x^{2}}"," ",0,"-1/2*e^(-(n*log(b) + log(a))/(m*n))/x^2","A",0
201,1,16,0,0.896784," ","integrate(x^(-n*p*q+2)*(a*(b*x^n)^p)^q,x, algorithm=""fricas"")","\frac{1}{3} \, x^{3} e^{\left(p q \log\left(b\right) + q \log\left(a\right)\right)}"," ",0,"1/3*x^3*e^(p*q*log(b) + q*log(a))","A",0
202,1,16,0,1.250737," ","integrate(x^(-n*p*q+1)*(a*(b*x^n)^p)^q,x, algorithm=""fricas"")","\frac{1}{2} \, x^{2} e^{\left(p q \log\left(b\right) + q \log\left(a\right)\right)}"," ",0,"1/2*x^2*e^(p*q*log(b) + q*log(a))","A",0
203,1,13,0,0.865545," ","integrate((a*(b*x^n)^p)^q/(x^(n*p*q)),x, algorithm=""fricas"")","x e^{\left(p q \log\left(b\right) + q \log\left(a\right)\right)}"," ",0,"x*e^(p*q*log(b) + q*log(a))","A",0
204,1,14,0,0.728455," ","integrate(x^(-n*p*q-1)*(a*(b*x^n)^p)^q,x, algorithm=""fricas"")","e^{\left(p q \log\left(b\right) + q \log\left(a\right)\right)} \log\left(x\right)"," ",0,"e^(p*q*log(b) + q*log(a))*log(x)","A",0
205,1,16,0,0.699315," ","integrate(x^(-n*p*q-2)*(a*(b*x^n)^p)^q,x, algorithm=""fricas"")","-\frac{e^{\left(p q \log\left(b\right) + q \log\left(a\right)\right)}}{x}"," ",0,"-e^(p*q*log(b) + q*log(a))/x","A",0
206,1,13,0,0.750843," ","integrate(x^3*(b*x^3+a),x, algorithm=""fricas"")","\frac{1}{7} x^{7} b + \frac{1}{4} x^{4} a"," ",0,"1/7*x^7*b + 1/4*x^4*a","A",0
207,1,13,0,0.799537," ","integrate(x^2*(b*x^3+a),x, algorithm=""fricas"")","\frac{1}{6} x^{6} b + \frac{1}{3} x^{3} a"," ",0,"1/6*x^6*b + 1/3*x^3*a","A",0
208,1,13,0,0.799144," ","integrate(x*(b*x^3+a),x, algorithm=""fricas"")","\frac{1}{5} x^{5} b + \frac{1}{2} x^{2} a"," ",0,"1/5*x^5*b + 1/2*x^2*a","A",0
209,1,10,0,0.644388," ","integrate(b*x^3+a,x, algorithm=""fricas"")","\frac{1}{4} x^{4} b + x a"," ",0,"1/4*x^4*b + x*a","A",0
210,1,11,0,0.860419," ","integrate((b*x^3+a)/x,x, algorithm=""fricas"")","\frac{1}{3} \, b x^{3} + a \log\left(x\right)"," ",0,"1/3*b*x^3 + a*log(x)","A",0
211,1,14,0,0.972695," ","integrate((b*x^3+a)/x^2,x, algorithm=""fricas"")","\frac{b x^{3} - 2 \, a}{2 \, x}"," ",0,"1/2*(b*x^3 - 2*a)/x","A",0
212,1,15,0,0.982009," ","integrate((b*x^3+a)/x^3,x, algorithm=""fricas"")","\frac{2 \, b x^{3} - a}{2 \, x^{2}}"," ",0,"1/2*(2*b*x^3 - a)/x^2","A",0
213,1,17,0,0.643201," ","integrate((b*x^3+a)/x^4,x, algorithm=""fricas"")","\frac{3 \, b x^{3} \log\left(x\right) - a}{3 \, x^{3}}"," ",0,"1/3*(3*b*x^3*log(x) - a)/x^3","A",0
214,1,13,0,0.712743," ","integrate((b*x^3+a)/x^5,x, algorithm=""fricas"")","-\frac{4 \, b x^{3} + a}{4 \, x^{4}}"," ",0,"-1/4*(4*b*x^3 + a)/x^4","A",0
215,1,15,0,0.680554," ","integrate((b*x^3+a)/x^6,x, algorithm=""fricas"")","-\frac{5 \, b x^{3} + 2 \, a}{10 \, x^{5}}"," ",0,"-1/10*(5*b*x^3 + 2*a)/x^5","A",0
216,1,13,0,0.772105," ","integrate((b*x^3+a)/x^7,x, algorithm=""fricas"")","-\frac{2 \, b x^{3} + a}{6 \, x^{6}}"," ",0,"-1/6*(2*b*x^3 + a)/x^6","A",0
217,1,15,0,0.803643," ","integrate((b*x^3+a)/x^8,x, algorithm=""fricas"")","-\frac{7 \, b x^{3} + 4 \, a}{28 \, x^{7}}"," ",0,"-1/28*(7*b*x^3 + 4*a)/x^7","A",0
218,1,24,0,0.871900," ","integrate(x^4*(b*x^3+a)^2,x, algorithm=""fricas"")","\frac{1}{11} x^{11} b^{2} + \frac{1}{4} x^{8} b a + \frac{1}{5} x^{5} a^{2}"," ",0,"1/11*x^11*b^2 + 1/4*x^8*b*a + 1/5*x^5*a^2","A",0
219,1,24,0,0.836686," ","integrate(x^3*(b*x^3+a)^2,x, algorithm=""fricas"")","\frac{1}{10} x^{10} b^{2} + \frac{2}{7} x^{7} b a + \frac{1}{4} x^{4} a^{2}"," ",0,"1/10*x^10*b^2 + 2/7*x^7*b*a + 1/4*x^4*a^2","A",0
220,1,24,0,0.455356," ","integrate(x^2*(b*x^3+a)^2,x, algorithm=""fricas"")","\frac{1}{9} x^{9} b^{2} + \frac{1}{3} x^{6} b a + \frac{1}{3} x^{3} a^{2}"," ",0,"1/9*x^9*b^2 + 1/3*x^6*b*a + 1/3*x^3*a^2","A",0
221,1,24,0,0.689368," ","integrate(x*(b*x^3+a)^2,x, algorithm=""fricas"")","\frac{1}{8} x^{8} b^{2} + \frac{2}{5} x^{5} b a + \frac{1}{2} x^{2} a^{2}"," ",0,"1/8*x^8*b^2 + 2/5*x^5*b*a + 1/2*x^2*a^2","A",0
222,1,21,0,0.776649," ","integrate((b*x^3+a)^2,x, algorithm=""fricas"")","\frac{1}{7} x^{7} b^{2} + \frac{1}{2} x^{4} b a + x a^{2}"," ",0,"1/7*x^7*b^2 + 1/2*x^4*b*a + x*a^2","A",0
223,1,22,0,0.857490," ","integrate((b*x^3+a)^2/x,x, algorithm=""fricas"")","\frac{1}{6} \, b^{2} x^{6} + \frac{2}{3} \, a b x^{3} + a^{2} \log\left(x\right)"," ",0,"1/6*b^2*x^6 + 2/3*a*b*x^3 + a^2*log(x)","A",0
224,1,25,0,0.687675," ","integrate((b*x^3+a)^2/x^2,x, algorithm=""fricas"")","\frac{b^{2} x^{6} + 5 \, a b x^{3} - 5 \, a^{2}}{5 \, x}"," ",0,"1/5*(b^2*x^6 + 5*a*b*x^3 - 5*a^2)/x","A",0
225,1,25,0,0.815700," ","integrate((b*x^3+a)^2/x^3,x, algorithm=""fricas"")","\frac{b^{2} x^{6} + 8 \, a b x^{3} - 2 \, a^{2}}{4 \, x^{2}}"," ",0,"1/4*(b^2*x^6 + 8*a*b*x^3 - 2*a^2)/x^2","A",0
226,1,27,0,0.815225," ","integrate((b*x^3+a)^2/x^4,x, algorithm=""fricas"")","\frac{b^{2} x^{6} + 6 \, a b x^{3} \log\left(x\right) - a^{2}}{3 \, x^{3}}"," ",0,"1/3*(b^2*x^6 + 6*a*b*x^3*log(x) - a^2)/x^3","A",0
227,1,26,0,0.793861," ","integrate((b*x^3+a)^2/x^5,x, algorithm=""fricas"")","\frac{2 \, b^{2} x^{6} - 8 \, a b x^{3} - a^{2}}{4 \, x^{4}}"," ",0,"1/4*(2*b^2*x^6 - 8*a*b*x^3 - a^2)/x^4","A",0
228,1,26,0,0.762470," ","integrate((b*x^3+a)^2/x^6,x, algorithm=""fricas"")","\frac{5 \, b^{2} x^{6} - 5 \, a b x^{3} - a^{2}}{5 \, x^{5}}"," ",0,"1/5*(5*b^2*x^6 - 5*a*b*x^3 - a^2)/x^5","A",0
229,1,28,0,0.879135," ","integrate((b*x^3+a)^2/x^7,x, algorithm=""fricas"")","\frac{6 \, b^{2} x^{6} \log\left(x\right) - 4 \, a b x^{3} - a^{2}}{6 \, x^{6}}"," ",0,"1/6*(6*b^2*x^6*log(x) - 4*a*b*x^3 - a^2)/x^6","A",0
230,1,26,0,0.725613," ","integrate((b*x^3+a)^2/x^8,x, algorithm=""fricas"")","-\frac{14 \, b^{2} x^{6} + 7 \, a b x^{3} + 2 \, a^{2}}{14 \, x^{7}}"," ",0,"-1/14*(14*b^2*x^6 + 7*a*b*x^3 + 2*a^2)/x^7","A",0
231,1,26,0,0.781338," ","integrate((b*x^3+a)^2/x^9,x, algorithm=""fricas"")","-\frac{20 \, b^{2} x^{6} + 16 \, a b x^{3} + 5 \, a^{2}}{40 \, x^{8}}"," ",0,"-1/40*(20*b^2*x^6 + 16*a*b*x^3 + 5*a^2)/x^8","A",0
232,1,24,0,0.552732," ","integrate((b*x^3+a)^2/x^10,x, algorithm=""fricas"")","-\frac{3 \, b^{2} x^{6} + 3 \, a b x^{3} + a^{2}}{9 \, x^{9}}"," ",0,"-1/9*(3*b^2*x^6 + 3*a*b*x^3 + a^2)/x^9","A",0
233,1,26,0,0.733093," ","integrate((b*x^3+a)^2/x^11,x, algorithm=""fricas"")","-\frac{35 \, b^{2} x^{6} + 40 \, a b x^{3} + 14 \, a^{2}}{140 \, x^{10}}"," ",0,"-1/140*(35*b^2*x^6 + 40*a*b*x^3 + 14*a^2)/x^10","A",0
234,1,26,0,0.715793," ","integrate((b*x^3+a)^2/x^12,x, algorithm=""fricas"")","-\frac{44 \, b^{2} x^{6} + 55 \, a b x^{3} + 20 \, a^{2}}{220 \, x^{11}}"," ",0,"-1/220*(44*b^2*x^6 + 55*a*b*x^3 + 20*a^2)/x^11","A",0
235,1,26,0,0.815880," ","integrate((b*x^3+a)^2/x^13,x, algorithm=""fricas"")","-\frac{6 \, b^{2} x^{6} + 8 \, a b x^{3} + 3 \, a^{2}}{36 \, x^{12}}"," ",0,"-1/36*(6*b^2*x^6 + 8*a*b*x^3 + 3*a^2)/x^12","A",0
236,1,35,0,0.693531," ","integrate(x^14*(b*x^3+a)^3,x, algorithm=""fricas"")","\frac{1}{24} x^{24} b^{3} + \frac{1}{7} x^{21} b^{2} a + \frac{1}{6} x^{18} b a^{2} + \frac{1}{15} x^{15} a^{3}"," ",0,"1/24*x^24*b^3 + 1/7*x^21*b^2*a + 1/6*x^18*b*a^2 + 1/15*x^15*a^3","A",0
237,1,35,0,0.703868," ","integrate(x^11*(b*x^3+a)^3,x, algorithm=""fricas"")","\frac{1}{21} x^{21} b^{3} + \frac{1}{6} x^{18} b^{2} a + \frac{1}{5} x^{15} b a^{2} + \frac{1}{12} x^{12} a^{3}"," ",0,"1/21*x^21*b^3 + 1/6*x^18*b^2*a + 1/5*x^15*b*a^2 + 1/12*x^12*a^3","A",0
238,1,35,0,0.633573," ","integrate(x^8*(b*x^3+a)^3,x, algorithm=""fricas"")","\frac{1}{18} x^{18} b^{3} + \frac{1}{5} x^{15} b^{2} a + \frac{1}{4} x^{12} b a^{2} + \frac{1}{9} x^{9} a^{3}"," ",0,"1/18*x^18*b^3 + 1/5*x^15*b^2*a + 1/4*x^12*b*a^2 + 1/9*x^9*a^3","A",0
239,1,35,0,0.703657," ","integrate(x^5*(b*x^3+a)^3,x, algorithm=""fricas"")","\frac{1}{15} x^{15} b^{3} + \frac{1}{4} x^{12} b^{2} a + \frac{1}{3} x^{9} b a^{2} + \frac{1}{6} x^{6} a^{3}"," ",0,"1/15*x^15*b^3 + 1/4*x^12*b^2*a + 1/3*x^9*b*a^2 + 1/6*x^6*a^3","A",0
240,1,35,0,0.567591," ","integrate(x^2*(b*x^3+a)^3,x, algorithm=""fricas"")","\frac{1}{12} x^{12} b^{3} + \frac{1}{3} x^{9} b^{2} a + \frac{1}{2} x^{6} b a^{2} + \frac{1}{3} x^{3} a^{3}"," ",0,"1/12*x^12*b^3 + 1/3*x^9*b^2*a + 1/2*x^6*b*a^2 + 1/3*x^3*a^3","B",0
241,1,32,0,0.705040," ","integrate((b*x^3+a)^3/x,x, algorithm=""fricas"")","\frac{1}{9} \, b^{3} x^{9} + \frac{1}{2} \, a b^{2} x^{6} + a^{2} b x^{3} + a^{3} \log\left(x\right)"," ",0,"1/9*b^3*x^9 + 1/2*a*b^2*x^6 + a^2*b*x^3 + a^3*log(x)","A",0
242,1,38,0,0.839681," ","integrate((b*x^3+a)^3/x^4,x, algorithm=""fricas"")","\frac{b^{3} x^{9} + 6 \, a b^{2} x^{6} + 18 \, a^{2} b x^{3} \log\left(x\right) - 2 \, a^{3}}{6 \, x^{3}}"," ",0,"1/6*(b^3*x^9 + 6*a*b^2*x^6 + 18*a^2*b*x^3*log(x) - 2*a^3)/x^3","A",0
243,1,39,0,0.629146," ","integrate((b*x^3+a)^3/x^7,x, algorithm=""fricas"")","\frac{2 \, b^{3} x^{9} + 18 \, a b^{2} x^{6} \log\left(x\right) - 6 \, a^{2} b x^{3} - a^{3}}{6 \, x^{6}}"," ",0,"1/6*(2*b^3*x^9 + 18*a*b^2*x^6*log(x) - 6*a^2*b*x^3 - a^3)/x^6","A",0
244,1,39,0,0.830243," ","integrate((b*x^3+a)^3/x^10,x, algorithm=""fricas"")","\frac{18 \, b^{3} x^{9} \log\left(x\right) - 18 \, a b^{2} x^{6} - 9 \, a^{2} b x^{3} - 2 \, a^{3}}{18 \, x^{9}}"," ",0,"1/18*(18*b^3*x^9*log(x) - 18*a*b^2*x^6 - 9*a^2*b*x^3 - 2*a^3)/x^9","A",0
245,1,35,0,0.761832," ","integrate((b*x^3+a)^3/x^13,x, algorithm=""fricas"")","-\frac{4 \, b^{3} x^{9} + 6 \, a b^{2} x^{6} + 4 \, a^{2} b x^{3} + a^{3}}{12 \, x^{12}}"," ",0,"-1/12*(4*b^3*x^9 + 6*a*b^2*x^6 + 4*a^2*b*x^3 + a^3)/x^12","B",0
246,1,37,0,0.804394," ","integrate((b*x^3+a)^3/x^16,x, algorithm=""fricas"")","-\frac{10 \, b^{3} x^{9} + 20 \, a b^{2} x^{6} + 15 \, a^{2} b x^{3} + 4 \, a^{3}}{60 \, x^{15}}"," ",0,"-1/60*(10*b^3*x^9 + 20*a*b^2*x^6 + 15*a^2*b*x^3 + 4*a^3)/x^15","A",0
247,1,37,0,0.816141," ","integrate((b*x^3+a)^3/x^19,x, algorithm=""fricas"")","-\frac{20 \, b^{3} x^{9} + 45 \, a b^{2} x^{6} + 36 \, a^{2} b x^{3} + 10 \, a^{3}}{180 \, x^{18}}"," ",0,"-1/180*(20*b^3*x^9 + 45*a*b^2*x^6 + 36*a^2*b*x^3 + 10*a^3)/x^18","A",0
248,1,37,0,0.749889," ","integrate((b*x^3+a)^3/x^22,x, algorithm=""fricas"")","-\frac{35 \, b^{3} x^{9} + 84 \, a b^{2} x^{6} + 70 \, a^{2} b x^{3} + 20 \, a^{3}}{420 \, x^{21}}"," ",0,"-1/420*(35*b^3*x^9 + 84*a*b^2*x^6 + 70*a^2*b*x^3 + 20*a^3)/x^21","A",0
249,1,35,0,0.631280," ","integrate(x^4*(b*x^3+a)^3,x, algorithm=""fricas"")","\frac{1}{14} x^{14} b^{3} + \frac{3}{11} x^{11} b^{2} a + \frac{3}{8} x^{8} b a^{2} + \frac{1}{5} x^{5} a^{3}"," ",0,"1/14*x^14*b^3 + 3/11*x^11*b^2*a + 3/8*x^8*b*a^2 + 1/5*x^5*a^3","A",0
250,1,35,0,0.708684," ","integrate(x^3*(b*x^3+a)^3,x, algorithm=""fricas"")","\frac{1}{13} x^{13} b^{3} + \frac{3}{10} x^{10} b^{2} a + \frac{3}{7} x^{7} b a^{2} + \frac{1}{4} x^{4} a^{3}"," ",0,"1/13*x^13*b^3 + 3/10*x^10*b^2*a + 3/7*x^7*b*a^2 + 1/4*x^4*a^3","A",0
251,1,35,0,0.693264," ","integrate(x*(b*x^3+a)^3,x, algorithm=""fricas"")","\frac{1}{11} x^{11} b^{3} + \frac{3}{8} x^{8} b^{2} a + \frac{3}{5} x^{5} b a^{2} + \frac{1}{2} x^{2} a^{3}"," ",0,"1/11*x^11*b^3 + 3/8*x^8*b^2*a + 3/5*x^5*b*a^2 + 1/2*x^2*a^3","A",0
252,1,32,0,0.692744," ","integrate((b*x^3+a)^3,x, algorithm=""fricas"")","\frac{1}{10} x^{10} b^{3} + \frac{3}{7} x^{7} b^{2} a + \frac{3}{4} x^{4} b a^{2} + x a^{3}"," ",0,"1/10*x^10*b^3 + 3/7*x^7*b^2*a + 3/4*x^4*b*a^2 + x*a^3","A",0
253,1,37,0,0.851461," ","integrate((b*x^3+a)^3/x^2,x, algorithm=""fricas"")","\frac{5 \, b^{3} x^{9} + 24 \, a b^{2} x^{6} + 60 \, a^{2} b x^{3} - 40 \, a^{3}}{40 \, x}"," ",0,"1/40*(5*b^3*x^9 + 24*a*b^2*x^6 + 60*a^2*b*x^3 - 40*a^3)/x","A",0
254,1,37,0,0.754650," ","integrate((b*x^3+a)^3/x^3,x, algorithm=""fricas"")","\frac{4 \, b^{3} x^{9} + 21 \, a b^{2} x^{6} + 84 \, a^{2} b x^{3} - 14 \, a^{3}}{28 \, x^{2}}"," ",0,"1/28*(4*b^3*x^9 + 21*a*b^2*x^6 + 84*a^2*b*x^3 - 14*a^3)/x^2","A",0
255,1,37,0,0.738892," ","integrate((b*x^3+a)^3/x^5,x, algorithm=""fricas"")","\frac{4 \, b^{3} x^{9} + 30 \, a b^{2} x^{6} - 60 \, a^{2} b x^{3} - 5 \, a^{3}}{20 \, x^{4}}"," ",0,"1/20*(4*b^3*x^9 + 30*a*b^2*x^6 - 60*a^2*b*x^3 - 5*a^3)/x^4","A",0
256,1,37,0,0.753479," ","integrate((b*x^3+a)^3/x^6,x, algorithm=""fricas"")","\frac{5 \, b^{3} x^{9} + 60 \, a b^{2} x^{6} - 30 \, a^{2} b x^{3} - 4 \, a^{3}}{20 \, x^{5}}"," ",0,"1/20*(5*b^3*x^9 + 60*a*b^2*x^6 - 30*a^2*b*x^3 - 4*a^3)/x^5","A",0
257,1,37,0,0.753320," ","integrate((b*x^3+a)^3/x^8,x, algorithm=""fricas"")","\frac{14 \, b^{3} x^{9} - 84 \, a b^{2} x^{6} - 21 \, a^{2} b x^{3} - 4 \, a^{3}}{28 \, x^{7}}"," ",0,"1/28*(14*b^3*x^9 - 84*a*b^2*x^6 - 21*a^2*b*x^3 - 4*a^3)/x^7","A",0
258,1,57,0,0.768855," ","integrate(x^17*(b*x^3+a)^5,x, algorithm=""fricas"")","\frac{1}{33} x^{33} b^{5} + \frac{1}{6} x^{30} b^{4} a + \frac{10}{27} x^{27} b^{3} a^{2} + \frac{5}{12} x^{24} b^{2} a^{3} + \frac{5}{21} x^{21} b a^{4} + \frac{1}{18} x^{18} a^{5}"," ",0,"1/33*x^33*b^5 + 1/6*x^30*b^4*a + 10/27*x^27*b^3*a^2 + 5/12*x^24*b^2*a^3 + 5/21*x^21*b*a^4 + 1/18*x^18*a^5","A",0
259,1,57,0,0.763725," ","integrate(x^14*(b*x^3+a)^5,x, algorithm=""fricas"")","\frac{1}{30} x^{30} b^{5} + \frac{5}{27} x^{27} b^{4} a + \frac{5}{12} x^{24} b^{3} a^{2} + \frac{10}{21} x^{21} b^{2} a^{3} + \frac{5}{18} x^{18} b a^{4} + \frac{1}{15} x^{15} a^{5}"," ",0,"1/30*x^30*b^5 + 5/27*x^27*b^4*a + 5/12*x^24*b^3*a^2 + 10/21*x^21*b^2*a^3 + 5/18*x^18*b*a^4 + 1/15*x^15*a^5","A",0
260,1,57,0,0.772714," ","integrate(x^11*(b*x^3+a)^5,x, algorithm=""fricas"")","\frac{1}{27} x^{27} b^{5} + \frac{5}{24} x^{24} b^{4} a + \frac{10}{21} x^{21} b^{3} a^{2} + \frac{5}{9} x^{18} b^{2} a^{3} + \frac{1}{3} x^{15} b a^{4} + \frac{1}{12} x^{12} a^{5}"," ",0,"1/27*x^27*b^5 + 5/24*x^24*b^4*a + 10/21*x^21*b^3*a^2 + 5/9*x^18*b^2*a^3 + 1/3*x^15*b*a^4 + 1/12*x^12*a^5","A",0
261,1,57,0,0.702326," ","integrate(x^8*(b*x^3+a)^5,x, algorithm=""fricas"")","\frac{1}{24} x^{24} b^{5} + \frac{5}{21} x^{21} b^{4} a + \frac{5}{9} x^{18} b^{3} a^{2} + \frac{2}{3} x^{15} b^{2} a^{3} + \frac{5}{12} x^{12} b a^{4} + \frac{1}{9} x^{9} a^{5}"," ",0,"1/24*x^24*b^5 + 5/21*x^21*b^4*a + 5/9*x^18*b^3*a^2 + 2/3*x^15*b^2*a^3 + 5/12*x^12*b*a^4 + 1/9*x^9*a^5","A",0
262,1,57,0,0.459829," ","integrate(x^5*(b*x^3+a)^5,x, algorithm=""fricas"")","\frac{1}{21} x^{21} b^{5} + \frac{5}{18} x^{18} b^{4} a + \frac{2}{3} x^{15} b^{3} a^{2} + \frac{5}{6} x^{12} b^{2} a^{3} + \frac{5}{9} x^{9} b a^{4} + \frac{1}{6} x^{6} a^{5}"," ",0,"1/21*x^21*b^5 + 5/18*x^18*b^4*a + 2/3*x^15*b^3*a^2 + 5/6*x^12*b^2*a^3 + 5/9*x^9*b*a^4 + 1/6*x^6*a^5","A",0
263,1,57,0,0.762645," ","integrate(x^2*(b*x^3+a)^5,x, algorithm=""fricas"")","\frac{1}{18} x^{18} b^{5} + \frac{1}{3} x^{15} b^{4} a + \frac{5}{6} x^{12} b^{3} a^{2} + \frac{10}{9} x^{9} b^{2} a^{3} + \frac{5}{6} x^{6} b a^{4} + \frac{1}{3} x^{3} a^{5}"," ",0,"1/18*x^18*b^5 + 1/3*x^15*b^4*a + 5/6*x^12*b^3*a^2 + 10/9*x^9*b^2*a^3 + 5/6*x^6*b*a^4 + 1/3*x^3*a^5","B",0
264,1,55,0,0.774837," ","integrate((b*x^3+a)^5/x,x, algorithm=""fricas"")","\frac{1}{15} \, b^{5} x^{15} + \frac{5}{12} \, a b^{4} x^{12} + \frac{10}{9} \, a^{2} b^{3} x^{9} + \frac{5}{3} \, a^{3} b^{2} x^{6} + \frac{5}{3} \, a^{4} b x^{3} + a^{5} \log\left(x\right)"," ",0,"1/15*b^5*x^15 + 5/12*a*b^4*x^12 + 10/9*a^2*b^3*x^9 + 5/3*a^3*b^2*x^6 + 5/3*a^4*b*x^3 + a^5*log(x)","A",0
265,1,61,0,0.840739," ","integrate((b*x^3+a)^5/x^4,x, algorithm=""fricas"")","\frac{3 \, b^{5} x^{15} + 20 \, a b^{4} x^{12} + 60 \, a^{2} b^{3} x^{9} + 120 \, a^{3} b^{2} x^{6} + 180 \, a^{4} b x^{3} \log\left(x\right) - 12 \, a^{5}}{36 \, x^{3}}"," ",0,"1/36*(3*b^5*x^15 + 20*a*b^4*x^12 + 60*a^2*b^3*x^9 + 120*a^3*b^2*x^6 + 180*a^4*b*x^3*log(x) - 12*a^5)/x^3","A",0
266,1,61,0,0.734213," ","integrate((b*x^3+a)^5/x^7,x, algorithm=""fricas"")","\frac{2 \, b^{5} x^{15} + 15 \, a b^{4} x^{12} + 60 \, a^{2} b^{3} x^{9} + 180 \, a^{3} b^{2} x^{6} \log\left(x\right) - 30 \, a^{4} b x^{3} - 3 \, a^{5}}{18 \, x^{6}}"," ",0,"1/18*(2*b^5*x^15 + 15*a*b^4*x^12 + 60*a^2*b^3*x^9 + 180*a^3*b^2*x^6*log(x) - 30*a^4*b*x^3 - 3*a^5)/x^6","A",0
267,1,61,0,0.777669," ","integrate((b*x^3+a)^5/x^10,x, algorithm=""fricas"")","\frac{3 \, b^{5} x^{15} + 30 \, a b^{4} x^{12} + 180 \, a^{2} b^{3} x^{9} \log\left(x\right) - 60 \, a^{3} b^{2} x^{6} - 15 \, a^{4} b x^{3} - 2 \, a^{5}}{18 \, x^{9}}"," ",0,"1/18*(3*b^5*x^15 + 30*a*b^4*x^12 + 180*a^2*b^3*x^9*log(x) - 60*a^3*b^2*x^6 - 15*a^4*b*x^3 - 2*a^5)/x^9","A",0
268,1,61,0,0.842798," ","integrate((b*x^3+a)^5/x^13,x, algorithm=""fricas"")","\frac{12 \, b^{5} x^{15} + 180 \, a b^{4} x^{12} \log\left(x\right) - 120 \, a^{2} b^{3} x^{9} - 60 \, a^{3} b^{2} x^{6} - 20 \, a^{4} b x^{3} - 3 \, a^{5}}{36 \, x^{12}}"," ",0,"1/36*(12*b^5*x^15 + 180*a*b^4*x^12*log(x) - 120*a^2*b^3*x^9 - 60*a^3*b^2*x^6 - 20*a^4*b*x^3 - 3*a^5)/x^12","A",0
269,1,61,0,0.583523," ","integrate((b*x^3+a)^5/x^16,x, algorithm=""fricas"")","\frac{180 \, b^{5} x^{15} \log\left(x\right) - 300 \, a b^{4} x^{12} - 300 \, a^{2} b^{3} x^{9} - 200 \, a^{3} b^{2} x^{6} - 75 \, a^{4} b x^{3} - 12 \, a^{5}}{180 \, x^{15}}"," ",0,"1/180*(180*b^5*x^15*log(x) - 300*a*b^4*x^12 - 300*a^2*b^3*x^9 - 200*a^3*b^2*x^6 - 75*a^4*b*x^3 - 12*a^5)/x^15","A",0
270,1,57,0,0.872704," ","integrate((b*x^3+a)^5/x^19,x, algorithm=""fricas"")","-\frac{6 \, b^{5} x^{15} + 15 \, a b^{4} x^{12} + 20 \, a^{2} b^{3} x^{9} + 15 \, a^{3} b^{2} x^{6} + 6 \, a^{4} b x^{3} + a^{5}}{18 \, x^{18}}"," ",0,"-1/18*(6*b^5*x^15 + 15*a*b^4*x^12 + 20*a^2*b^3*x^9 + 15*a^3*b^2*x^6 + 6*a^4*b*x^3 + a^5)/x^18","B",0
271,1,59,0,1.066915," ","integrate((b*x^3+a)^5/x^22,x, algorithm=""fricas"")","-\frac{21 \, b^{5} x^{15} + 70 \, a b^{4} x^{12} + 105 \, a^{2} b^{3} x^{9} + 84 \, a^{3} b^{2} x^{6} + 35 \, a^{4} b x^{3} + 6 \, a^{5}}{126 \, x^{21}}"," ",0,"-1/126*(21*b^5*x^15 + 70*a*b^4*x^12 + 105*a^2*b^3*x^9 + 84*a^3*b^2*x^6 + 35*a^4*b*x^3 + 6*a^5)/x^21","A",0
272,1,59,0,0.741307," ","integrate((b*x^3+a)^5/x^25,x, algorithm=""fricas"")","-\frac{56 \, b^{5} x^{15} + 210 \, a b^{4} x^{12} + 336 \, a^{2} b^{3} x^{9} + 280 \, a^{3} b^{2} x^{6} + 120 \, a^{4} b x^{3} + 21 \, a^{5}}{504 \, x^{24}}"," ",0,"-1/504*(56*b^5*x^15 + 210*a*b^4*x^12 + 336*a^2*b^3*x^9 + 280*a^3*b^2*x^6 + 120*a^4*b*x^3 + 21*a^5)/x^24","A",0
273,1,59,0,0.640703," ","integrate((b*x^3+a)^5/x^28,x, algorithm=""fricas"")","-\frac{126 \, b^{5} x^{15} + 504 \, a b^{4} x^{12} + 840 \, a^{2} b^{3} x^{9} + 720 \, a^{3} b^{2} x^{6} + 315 \, a^{4} b x^{3} + 56 \, a^{5}}{1512 \, x^{27}}"," ",0,"-1/1512*(126*b^5*x^15 + 504*a*b^4*x^12 + 840*a^2*b^3*x^9 + 720*a^3*b^2*x^6 + 315*a^4*b*x^3 + 56*a^5)/x^27","A",0
274,1,59,0,0.644511," ","integrate((b*x^3+a)^5/x^31,x, algorithm=""fricas"")","-\frac{252 \, b^{5} x^{15} + 1050 \, a b^{4} x^{12} + 1800 \, a^{2} b^{3} x^{9} + 1575 \, a^{3} b^{2} x^{6} + 700 \, a^{4} b x^{3} + 126 \, a^{5}}{3780 \, x^{30}}"," ",0,"-1/3780*(252*b^5*x^15 + 1050*a*b^4*x^12 + 1800*a^2*b^3*x^9 + 1575*a^3*b^2*x^6 + 700*a^4*b*x^3 + 126*a^5)/x^30","A",0
275,1,57,0,0.658068," ","integrate(x^4*(b*x^3+a)^5,x, algorithm=""fricas"")","\frac{1}{20} x^{20} b^{5} + \frac{5}{17} x^{17} b^{4} a + \frac{5}{7} x^{14} b^{3} a^{2} + \frac{10}{11} x^{11} b^{2} a^{3} + \frac{5}{8} x^{8} b a^{4} + \frac{1}{5} x^{5} a^{5}"," ",0,"1/20*x^20*b^5 + 5/17*x^17*b^4*a + 5/7*x^14*b^3*a^2 + 10/11*x^11*b^2*a^3 + 5/8*x^8*b*a^4 + 1/5*x^5*a^5","A",0
276,1,56,0,0.754897," ","integrate(x^3*(b*x^3+a)^5,x, algorithm=""fricas"")","\frac{1}{19} x^{19} b^{5} + \frac{5}{16} x^{16} b^{4} a + \frac{10}{13} x^{13} b^{3} a^{2} + x^{10} b^{2} a^{3} + \frac{5}{7} x^{7} b a^{4} + \frac{1}{4} x^{4} a^{5}"," ",0,"1/19*x^19*b^5 + 5/16*x^16*b^4*a + 10/13*x^13*b^3*a^2 + x^10*b^2*a^3 + 5/7*x^7*b*a^4 + 1/4*x^4*a^5","A",0
277,1,56,0,0.815284," ","integrate(x*(b*x^3+a)^5,x, algorithm=""fricas"")","\frac{1}{17} x^{17} b^{5} + \frac{5}{14} x^{14} b^{4} a + \frac{10}{11} x^{11} b^{3} a^{2} + \frac{5}{4} x^{8} b^{2} a^{3} + x^{5} b a^{4} + \frac{1}{2} x^{2} a^{5}"," ",0,"1/17*x^17*b^5 + 5/14*x^14*b^4*a + 10/11*x^11*b^3*a^2 + 5/4*x^8*b^2*a^3 + x^5*b*a^4 + 1/2*x^2*a^5","A",0
278,1,53,0,1.057136," ","integrate((b*x^3+a)^5,x, algorithm=""fricas"")","\frac{1}{16} x^{16} b^{5} + \frac{5}{13} x^{13} b^{4} a + x^{10} b^{3} a^{2} + \frac{10}{7} x^{7} b^{2} a^{3} + \frac{5}{4} x^{4} b a^{4} + x a^{5}"," ",0,"1/16*x^16*b^5 + 5/13*x^13*b^4*a + x^10*b^3*a^2 + 10/7*x^7*b^2*a^3 + 5/4*x^4*b*a^4 + x*a^5","A",0
279,1,59,0,0.857226," ","integrate((b*x^3+a)^5/x^2,x, algorithm=""fricas"")","\frac{22 \, b^{5} x^{15} + 140 \, a b^{4} x^{12} + 385 \, a^{2} b^{3} x^{9} + 616 \, a^{3} b^{2} x^{6} + 770 \, a^{4} b x^{3} - 308 \, a^{5}}{308 \, x}"," ",0,"1/308*(22*b^5*x^15 + 140*a*b^4*x^12 + 385*a^2*b^3*x^9 + 616*a^3*b^2*x^6 + 770*a^4*b*x^3 - 308*a^5)/x","A",0
280,1,59,0,1.034303," ","integrate((b*x^3+a)^5/x^3,x, algorithm=""fricas"")","\frac{14 \, b^{5} x^{15} + 91 \, a b^{4} x^{12} + 260 \, a^{2} b^{3} x^{9} + 455 \, a^{3} b^{2} x^{6} + 910 \, a^{4} b x^{3} - 91 \, a^{5}}{182 \, x^{2}}"," ",0,"1/182*(14*b^5*x^15 + 91*a*b^4*x^12 + 260*a^2*b^3*x^9 + 455*a^3*b^2*x^6 + 910*a^4*b*x^3 - 91*a^5)/x^2","A",0
281,1,59,0,0.667344," ","integrate((b*x^3+a)^5/x^5,x, algorithm=""fricas"")","\frac{8 \, b^{5} x^{15} + 55 \, a b^{4} x^{12} + 176 \, a^{2} b^{3} x^{9} + 440 \, a^{3} b^{2} x^{6} - 440 \, a^{4} b x^{3} - 22 \, a^{5}}{88 \, x^{4}}"," ",0,"1/88*(8*b^5*x^15 + 55*a*b^4*x^12 + 176*a^2*b^3*x^9 + 440*a^3*b^2*x^6 - 440*a^4*b*x^3 - 22*a^5)/x^4","A",0
282,1,59,0,0.989500," ","integrate((b*x^3+a)^5/x^6,x, algorithm=""fricas"")","\frac{7 \, b^{5} x^{15} + 50 \, a b^{4} x^{12} + 175 \, a^{2} b^{3} x^{9} + 700 \, a^{3} b^{2} x^{6} - 175 \, a^{4} b x^{3} - 14 \, a^{5}}{70 \, x^{5}}"," ",0,"1/70*(7*b^5*x^15 + 50*a*b^4*x^12 + 175*a^2*b^3*x^9 + 700*a^3*b^2*x^6 - 175*a^4*b*x^3 - 14*a^5)/x^5","A",0
283,1,59,0,0.793032," ","integrate((b*x^3+a)^5/x^8,x, algorithm=""fricas"")","\frac{7 \, b^{5} x^{15} + 56 \, a b^{4} x^{12} + 280 \, a^{2} b^{3} x^{9} - 560 \, a^{3} b^{2} x^{6} - 70 \, a^{4} b x^{3} - 8 \, a^{5}}{56 \, x^{7}}"," ",0,"1/56*(7*b^5*x^15 + 56*a*b^4*x^12 + 280*a^2*b^3*x^9 - 560*a^3*b^2*x^6 - 70*a^4*b*x^3 - 8*a^5)/x^7","A",0
284,1,59,0,0.676624," ","integrate((b*x^3+a)^5/x^9,x, algorithm=""fricas"")","\frac{8 \, b^{5} x^{15} + 70 \, a b^{4} x^{12} + 560 \, a^{2} b^{3} x^{9} - 280 \, a^{3} b^{2} x^{6} - 56 \, a^{4} b x^{3} - 7 \, a^{5}}{56 \, x^{8}}"," ",0,"1/56*(8*b^5*x^15 + 70*a*b^4*x^12 + 560*a^2*b^3*x^9 - 280*a^3*b^2*x^6 - 56*a^4*b*x^3 - 7*a^5)/x^8","A",0
285,1,90,0,0.904556," ","integrate(x^20*(b*x^3+a)^8,x, algorithm=""fricas"")","\frac{1}{45} x^{45} b^{8} + \frac{4}{21} x^{42} b^{7} a + \frac{28}{39} x^{39} b^{6} a^{2} + \frac{14}{9} x^{36} b^{5} a^{3} + \frac{70}{33} x^{33} b^{4} a^{4} + \frac{28}{15} x^{30} b^{3} a^{5} + \frac{28}{27} x^{27} b^{2} a^{6} + \frac{1}{3} x^{24} b a^{7} + \frac{1}{21} x^{21} a^{8}"," ",0,"1/45*x^45*b^8 + 4/21*x^42*b^7*a + 28/39*x^39*b^6*a^2 + 14/9*x^36*b^5*a^3 + 70/33*x^33*b^4*a^4 + 28/15*x^30*b^3*a^5 + 28/27*x^27*b^2*a^6 + 1/3*x^24*b*a^7 + 1/21*x^21*a^8","A",0
286,1,90,0,0.668384," ","integrate(x^17*(b*x^3+a)^8,x, algorithm=""fricas"")","\frac{1}{42} x^{42} b^{8} + \frac{8}{39} x^{39} b^{7} a + \frac{7}{9} x^{36} b^{6} a^{2} + \frac{56}{33} x^{33} b^{5} a^{3} + \frac{7}{3} x^{30} b^{4} a^{4} + \frac{56}{27} x^{27} b^{3} a^{5} + \frac{7}{6} x^{24} b^{2} a^{6} + \frac{8}{21} x^{21} b a^{7} + \frac{1}{18} x^{18} a^{8}"," ",0,"1/42*x^42*b^8 + 8/39*x^39*b^7*a + 7/9*x^36*b^6*a^2 + 56/33*x^33*b^5*a^3 + 7/3*x^30*b^4*a^4 + 56/27*x^27*b^3*a^5 + 7/6*x^24*b^2*a^6 + 8/21*x^21*b*a^7 + 1/18*x^18*a^8","A",0
287,1,90,0,0.611166," ","integrate(x^14*(b*x^3+a)^8,x, algorithm=""fricas"")","\frac{1}{39} x^{39} b^{8} + \frac{2}{9} x^{36} b^{7} a + \frac{28}{33} x^{33} b^{6} a^{2} + \frac{28}{15} x^{30} b^{5} a^{3} + \frac{70}{27} x^{27} b^{4} a^{4} + \frac{7}{3} x^{24} b^{3} a^{5} + \frac{4}{3} x^{21} b^{2} a^{6} + \frac{4}{9} x^{18} b a^{7} + \frac{1}{15} x^{15} a^{8}"," ",0,"1/39*x^39*b^8 + 2/9*x^36*b^7*a + 28/33*x^33*b^6*a^2 + 28/15*x^30*b^5*a^3 + 70/27*x^27*b^4*a^4 + 7/3*x^24*b^3*a^5 + 4/3*x^21*b^2*a^6 + 4/9*x^18*b*a^7 + 1/15*x^15*a^8","A",0
288,1,90,0,0.812737," ","integrate(x^11*(b*x^3+a)^8,x, algorithm=""fricas"")","\frac{1}{36} x^{36} b^{8} + \frac{8}{33} x^{33} b^{7} a + \frac{14}{15} x^{30} b^{6} a^{2} + \frac{56}{27} x^{27} b^{5} a^{3} + \frac{35}{12} x^{24} b^{4} a^{4} + \frac{8}{3} x^{21} b^{3} a^{5} + \frac{14}{9} x^{18} b^{2} a^{6} + \frac{8}{15} x^{15} b a^{7} + \frac{1}{12} x^{12} a^{8}"," ",0,"1/36*x^36*b^8 + 8/33*x^33*b^7*a + 14/15*x^30*b^6*a^2 + 56/27*x^27*b^5*a^3 + 35/12*x^24*b^4*a^4 + 8/3*x^21*b^3*a^5 + 14/9*x^18*b^2*a^6 + 8/15*x^15*b*a^7 + 1/12*x^12*a^8","A",0
289,1,90,0,0.848832," ","integrate(x^8*(b*x^3+a)^8,x, algorithm=""fricas"")","\frac{1}{33} x^{33} b^{8} + \frac{4}{15} x^{30} b^{7} a + \frac{28}{27} x^{27} b^{6} a^{2} + \frac{7}{3} x^{24} b^{5} a^{3} + \frac{10}{3} x^{21} b^{4} a^{4} + \frac{28}{9} x^{18} b^{3} a^{5} + \frac{28}{15} x^{15} b^{2} a^{6} + \frac{2}{3} x^{12} b a^{7} + \frac{1}{9} x^{9} a^{8}"," ",0,"1/33*x^33*b^8 + 4/15*x^30*b^7*a + 28/27*x^27*b^6*a^2 + 7/3*x^24*b^5*a^3 + 10/3*x^21*b^4*a^4 + 28/9*x^18*b^3*a^5 + 28/15*x^15*b^2*a^6 + 2/3*x^12*b*a^7 + 1/9*x^9*a^8","A",0
290,1,90,0,0.870737," ","integrate(x^5*(b*x^3+a)^8,x, algorithm=""fricas"")","\frac{1}{30} x^{30} b^{8} + \frac{8}{27} x^{27} b^{7} a + \frac{7}{6} x^{24} b^{6} a^{2} + \frac{8}{3} x^{21} b^{5} a^{3} + \frac{35}{9} x^{18} b^{4} a^{4} + \frac{56}{15} x^{15} b^{3} a^{5} + \frac{7}{3} x^{12} b^{2} a^{6} + \frac{8}{9} x^{9} b a^{7} + \frac{1}{6} x^{6} a^{8}"," ",0,"1/30*x^30*b^8 + 8/27*x^27*b^7*a + 7/6*x^24*b^6*a^2 + 8/3*x^21*b^5*a^3 + 35/9*x^18*b^4*a^4 + 56/15*x^15*b^3*a^5 + 7/3*x^12*b^2*a^6 + 8/9*x^9*b*a^7 + 1/6*x^6*a^8","B",0
291,1,90,0,0.636202," ","integrate(x^2*(b*x^3+a)^8,x, algorithm=""fricas"")","\frac{1}{27} x^{27} b^{8} + \frac{1}{3} x^{24} b^{7} a + \frac{4}{3} x^{21} b^{6} a^{2} + \frac{28}{9} x^{18} b^{5} a^{3} + \frac{14}{3} x^{15} b^{4} a^{4} + \frac{14}{3} x^{12} b^{3} a^{5} + \frac{28}{9} x^{9} b^{2} a^{6} + \frac{4}{3} x^{6} b a^{7} + \frac{1}{3} x^{3} a^{8}"," ",0,"1/27*x^27*b^8 + 1/3*x^24*b^7*a + 4/3*x^21*b^6*a^2 + 28/9*x^18*b^5*a^3 + 14/3*x^15*b^4*a^4 + 14/3*x^12*b^3*a^5 + 28/9*x^9*b^2*a^6 + 4/3*x^6*b*a^7 + 1/3*x^3*a^8","B",0
292,1,88,0,0.983377," ","integrate((b*x^3+a)^8/x,x, algorithm=""fricas"")","\frac{1}{24} \, b^{8} x^{24} + \frac{8}{21} \, a b^{7} x^{21} + \frac{14}{9} \, a^{2} b^{6} x^{18} + \frac{56}{15} \, a^{3} b^{5} x^{15} + \frac{35}{6} \, a^{4} b^{4} x^{12} + \frac{56}{9} \, a^{5} b^{3} x^{9} + \frac{14}{3} \, a^{6} b^{2} x^{6} + \frac{8}{3} \, a^{7} b x^{3} + a^{8} \log\left(x\right)"," ",0,"1/24*b^8*x^24 + 8/21*a*b^7*x^21 + 14/9*a^2*b^6*x^18 + 56/15*a^3*b^5*x^15 + 35/6*a^4*b^4*x^12 + 56/9*a^5*b^3*x^9 + 14/3*a^6*b^2*x^6 + 8/3*a^7*b*x^3 + a^8*log(x)","A",0
293,1,94,0,0.957503," ","integrate((b*x^3+a)^8/x^4,x, algorithm=""fricas"")","\frac{15 \, b^{8} x^{24} + 140 \, a b^{7} x^{21} + 588 \, a^{2} b^{6} x^{18} + 1470 \, a^{3} b^{5} x^{15} + 2450 \, a^{4} b^{4} x^{12} + 2940 \, a^{5} b^{3} x^{9} + 2940 \, a^{6} b^{2} x^{6} + 2520 \, a^{7} b x^{3} \log\left(x\right) - 105 \, a^{8}}{315 \, x^{3}}"," ",0,"1/315*(15*b^8*x^24 + 140*a*b^7*x^21 + 588*a^2*b^6*x^18 + 1470*a^3*b^5*x^15 + 2450*a^4*b^4*x^12 + 2940*a^5*b^3*x^9 + 2940*a^6*b^2*x^6 + 2520*a^7*b*x^3*log(x) - 105*a^8)/x^3","A",0
294,1,94,0,0.815129," ","integrate((b*x^3+a)^8/x^7,x, algorithm=""fricas"")","\frac{5 \, b^{8} x^{24} + 48 \, a b^{7} x^{21} + 210 \, a^{2} b^{6} x^{18} + 560 \, a^{3} b^{5} x^{15} + 1050 \, a^{4} b^{4} x^{12} + 1680 \, a^{5} b^{3} x^{9} + 2520 \, a^{6} b^{2} x^{6} \log\left(x\right) - 240 \, a^{7} b x^{3} - 15 \, a^{8}}{90 \, x^{6}}"," ",0,"1/90*(5*b^8*x^24 + 48*a*b^7*x^21 + 210*a^2*b^6*x^18 + 560*a^3*b^5*x^15 + 1050*a^4*b^4*x^12 + 1680*a^5*b^3*x^9 + 2520*a^6*b^2*x^6*log(x) - 240*a^7*b*x^3 - 15*a^8)/x^6","A",0
295,1,94,0,0.867972," ","integrate((b*x^3+a)^8/x^10,x, algorithm=""fricas"")","\frac{3 \, b^{8} x^{24} + 30 \, a b^{7} x^{21} + 140 \, a^{2} b^{6} x^{18} + 420 \, a^{3} b^{5} x^{15} + 1050 \, a^{4} b^{4} x^{12} + 2520 \, a^{5} b^{3} x^{9} \log\left(x\right) - 420 \, a^{6} b^{2} x^{6} - 60 \, a^{7} b x^{3} - 5 \, a^{8}}{45 \, x^{9}}"," ",0,"1/45*(3*b^8*x^24 + 30*a*b^7*x^21 + 140*a^2*b^6*x^18 + 420*a^3*b^5*x^15 + 1050*a^4*b^4*x^12 + 2520*a^5*b^3*x^9*log(x) - 420*a^6*b^2*x^6 - 60*a^7*b*x^3 - 5*a^8)/x^9","A",0
296,1,94,0,0.970161," ","integrate((b*x^3+a)^8/x^13,x, algorithm=""fricas"")","\frac{3 \, b^{8} x^{24} + 32 \, a b^{7} x^{21} + 168 \, a^{2} b^{6} x^{18} + 672 \, a^{3} b^{5} x^{15} + 2520 \, a^{4} b^{4} x^{12} \log\left(x\right) - 672 \, a^{5} b^{3} x^{9} - 168 \, a^{6} b^{2} x^{6} - 32 \, a^{7} b x^{3} - 3 \, a^{8}}{36 \, x^{12}}"," ",0,"1/36*(3*b^8*x^24 + 32*a*b^7*x^21 + 168*a^2*b^6*x^18 + 672*a^3*b^5*x^15 + 2520*a^4*b^4*x^12*log(x) - 672*a^5*b^3*x^9 - 168*a^6*b^2*x^6 - 32*a^7*b*x^3 - 3*a^8)/x^12","A",0
297,1,94,0,0.971517," ","integrate((b*x^3+a)^8/x^16,x, algorithm=""fricas"")","\frac{5 \, b^{8} x^{24} + 60 \, a b^{7} x^{21} + 420 \, a^{2} b^{6} x^{18} + 2520 \, a^{3} b^{5} x^{15} \log\left(x\right) - 1050 \, a^{4} b^{4} x^{12} - 420 \, a^{5} b^{3} x^{9} - 140 \, a^{6} b^{2} x^{6} - 30 \, a^{7} b x^{3} - 3 \, a^{8}}{45 \, x^{15}}"," ",0,"1/45*(5*b^8*x^24 + 60*a*b^7*x^21 + 420*a^2*b^6*x^18 + 2520*a^3*b^5*x^15*log(x) - 1050*a^4*b^4*x^12 - 420*a^5*b^3*x^9 - 140*a^6*b^2*x^6 - 30*a^7*b*x^3 - 3*a^8)/x^15","A",0
298,1,94,0,0.876143," ","integrate((b*x^3+a)^8/x^19,x, algorithm=""fricas"")","\frac{15 \, b^{8} x^{24} + 240 \, a b^{7} x^{21} + 2520 \, a^{2} b^{6} x^{18} \log\left(x\right) - 1680 \, a^{3} b^{5} x^{15} - 1050 \, a^{4} b^{4} x^{12} - 560 \, a^{5} b^{3} x^{9} - 210 \, a^{6} b^{2} x^{6} - 48 \, a^{7} b x^{3} - 5 \, a^{8}}{90 \, x^{18}}"," ",0,"1/90*(15*b^8*x^24 + 240*a*b^7*x^21 + 2520*a^2*b^6*x^18*log(x) - 1680*a^3*b^5*x^15 - 1050*a^4*b^4*x^12 - 560*a^5*b^3*x^9 - 210*a^6*b^2*x^6 - 48*a^7*b*x^3 - 5*a^8)/x^18","A",0
299,1,94,0,1.044236," ","integrate((b*x^3+a)^8/x^22,x, algorithm=""fricas"")","\frac{105 \, b^{8} x^{24} + 2520 \, a b^{7} x^{21} \log\left(x\right) - 2940 \, a^{2} b^{6} x^{18} - 2940 \, a^{3} b^{5} x^{15} - 2450 \, a^{4} b^{4} x^{12} - 1470 \, a^{5} b^{3} x^{9} - 588 \, a^{6} b^{2} x^{6} - 140 \, a^{7} b x^{3} - 15 \, a^{8}}{315 \, x^{21}}"," ",0,"1/315*(105*b^8*x^24 + 2520*a*b^7*x^21*log(x) - 2940*a^2*b^6*x^18 - 2940*a^3*b^5*x^15 - 2450*a^4*b^4*x^12 - 1470*a^5*b^3*x^9 - 588*a^6*b^2*x^6 - 140*a^7*b*x^3 - 15*a^8)/x^21","A",0
300,1,94,0,0.632998," ","integrate((b*x^3+a)^8/x^25,x, algorithm=""fricas"")","\frac{2520 \, b^{8} x^{24} \log\left(x\right) - 6720 \, a b^{7} x^{21} - 11760 \, a^{2} b^{6} x^{18} - 15680 \, a^{3} b^{5} x^{15} - 14700 \, a^{4} b^{4} x^{12} - 9408 \, a^{5} b^{3} x^{9} - 3920 \, a^{6} b^{2} x^{6} - 960 \, a^{7} b x^{3} - 105 \, a^{8}}{2520 \, x^{24}}"," ",0,"1/2520*(2520*b^8*x^24*log(x) - 6720*a*b^7*x^21 - 11760*a^2*b^6*x^18 - 15680*a^3*b^5*x^15 - 14700*a^4*b^4*x^12 - 9408*a^5*b^3*x^9 - 3920*a^6*b^2*x^6 - 960*a^7*b*x^3 - 105*a^8)/x^24","A",0
301,1,90,0,0.993038," ","integrate((b*x^3+a)^8/x^28,x, algorithm=""fricas"")","-\frac{9 \, b^{8} x^{24} + 36 \, a b^{7} x^{21} + 84 \, a^{2} b^{6} x^{18} + 126 \, a^{3} b^{5} x^{15} + 126 \, a^{4} b^{4} x^{12} + 84 \, a^{5} b^{3} x^{9} + 36 \, a^{6} b^{2} x^{6} + 9 \, a^{7} b x^{3} + a^{8}}{27 \, x^{27}}"," ",0,"-1/27*(9*b^8*x^24 + 36*a*b^7*x^21 + 84*a^2*b^6*x^18 + 126*a^3*b^5*x^15 + 126*a^4*b^4*x^12 + 84*a^5*b^3*x^9 + 36*a^6*b^2*x^6 + 9*a^7*b*x^3 + a^8)/x^27","B",0
302,1,92,0,0.878241," ","integrate((b*x^3+a)^8/x^31,x, algorithm=""fricas"")","-\frac{45 \, b^{8} x^{24} + 240 \, a b^{7} x^{21} + 630 \, a^{2} b^{6} x^{18} + 1008 \, a^{3} b^{5} x^{15} + 1050 \, a^{4} b^{4} x^{12} + 720 \, a^{5} b^{3} x^{9} + 315 \, a^{6} b^{2} x^{6} + 80 \, a^{7} b x^{3} + 9 \, a^{8}}{270 \, x^{30}}"," ",0,"-1/270*(45*b^8*x^24 + 240*a*b^7*x^21 + 630*a^2*b^6*x^18 + 1008*a^3*b^5*x^15 + 1050*a^4*b^4*x^12 + 720*a^5*b^3*x^9 + 315*a^6*b^2*x^6 + 80*a^7*b*x^3 + 9*a^8)/x^30","B",0
303,1,92,0,0.969918," ","integrate((b*x^3+a)^8/x^34,x, algorithm=""fricas"")","-\frac{165 \, b^{8} x^{24} + 990 \, a b^{7} x^{21} + 2772 \, a^{2} b^{6} x^{18} + 4620 \, a^{3} b^{5} x^{15} + 4950 \, a^{4} b^{4} x^{12} + 3465 \, a^{5} b^{3} x^{9} + 1540 \, a^{6} b^{2} x^{6} + 396 \, a^{7} b x^{3} + 45 \, a^{8}}{1485 \, x^{33}}"," ",0,"-1/1485*(165*b^8*x^24 + 990*a*b^7*x^21 + 2772*a^2*b^6*x^18 + 4620*a^3*b^5*x^15 + 4950*a^4*b^4*x^12 + 3465*a^5*b^3*x^9 + 1540*a^6*b^2*x^6 + 396*a^7*b*x^3 + 45*a^8)/x^33","A",0
304,1,92,0,1.094175," ","integrate((b*x^3+a)^8/x^37,x, algorithm=""fricas"")","-\frac{495 \, b^{8} x^{24} + 3168 \, a b^{7} x^{21} + 9240 \, a^{2} b^{6} x^{18} + 15840 \, a^{3} b^{5} x^{15} + 17325 \, a^{4} b^{4} x^{12} + 12320 \, a^{5} b^{3} x^{9} + 5544 \, a^{6} b^{2} x^{6} + 1440 \, a^{7} b x^{3} + 165 \, a^{8}}{5940 \, x^{36}}"," ",0,"-1/5940*(495*b^8*x^24 + 3168*a*b^7*x^21 + 9240*a^2*b^6*x^18 + 15840*a^3*b^5*x^15 + 17325*a^4*b^4*x^12 + 12320*a^5*b^3*x^9 + 5544*a^6*b^2*x^6 + 1440*a^7*b*x^3 + 165*a^8)/x^36","A",0
305,1,92,0,0.791797," ","integrate((b*x^3+a)^8/x^40,x, algorithm=""fricas"")","-\frac{1287 \, b^{8} x^{24} + 8580 \, a b^{7} x^{21} + 25740 \, a^{2} b^{6} x^{18} + 45045 \, a^{3} b^{5} x^{15} + 50050 \, a^{4} b^{4} x^{12} + 36036 \, a^{5} b^{3} x^{9} + 16380 \, a^{6} b^{2} x^{6} + 4290 \, a^{7} b x^{3} + 495 \, a^{8}}{19305 \, x^{39}}"," ",0,"-1/19305*(1287*b^8*x^24 + 8580*a*b^7*x^21 + 25740*a^2*b^6*x^18 + 45045*a^3*b^5*x^15 + 50050*a^4*b^4*x^12 + 36036*a^5*b^3*x^9 + 16380*a^6*b^2*x^6 + 4290*a^7*b*x^3 + 495*a^8)/x^39","A",0
306,1,92,0,0.867240," ","integrate((b*x^3+a)^8/x^43,x, algorithm=""fricas"")","-\frac{3003 \, b^{8} x^{24} + 20592 \, a b^{7} x^{21} + 63063 \, a^{2} b^{6} x^{18} + 112112 \, a^{3} b^{5} x^{15} + 126126 \, a^{4} b^{4} x^{12} + 91728 \, a^{5} b^{3} x^{9} + 42042 \, a^{6} b^{2} x^{6} + 11088 \, a^{7} b x^{3} + 1287 \, a^{8}}{54054 \, x^{42}}"," ",0,"-1/54054*(3003*b^8*x^24 + 20592*a*b^7*x^21 + 63063*a^2*b^6*x^18 + 112112*a^3*b^5*x^15 + 126126*a^4*b^4*x^12 + 91728*a^5*b^3*x^9 + 42042*a^6*b^2*x^6 + 11088*a^7*b*x^3 + 1287*a^8)/x^42","A",0
307,1,92,0,0.579314," ","integrate((b*x^3+a)^8/x^46,x, algorithm=""fricas"")","-\frac{6435 \, b^{8} x^{24} + 45045 \, a b^{7} x^{21} + 140140 \, a^{2} b^{6} x^{18} + 252252 \, a^{3} b^{5} x^{15} + 286650 \, a^{4} b^{4} x^{12} + 210210 \, a^{5} b^{3} x^{9} + 97020 \, a^{6} b^{2} x^{6} + 25740 \, a^{7} b x^{3} + 3003 \, a^{8}}{135135 \, x^{45}}"," ",0,"-1/135135*(6435*b^8*x^24 + 45045*a*b^7*x^21 + 140140*a^2*b^6*x^18 + 252252*a^3*b^5*x^15 + 286650*a^4*b^4*x^12 + 210210*a^5*b^3*x^9 + 97020*a^6*b^2*x^6 + 25740*a^7*b*x^3 + 3003*a^8)/x^45","A",0
308,1,89,0,0.771898," ","integrate(x^4*(b*x^3+a)^8,x, algorithm=""fricas"")","\frac{1}{29} x^{29} b^{8} + \frac{4}{13} x^{26} b^{7} a + \frac{28}{23} x^{23} b^{6} a^{2} + \frac{14}{5} x^{20} b^{5} a^{3} + \frac{70}{17} x^{17} b^{4} a^{4} + 4 x^{14} b^{3} a^{5} + \frac{28}{11} x^{11} b^{2} a^{6} + x^{8} b a^{7} + \frac{1}{5} x^{5} a^{8}"," ",0,"1/29*x^29*b^8 + 4/13*x^26*b^7*a + 28/23*x^23*b^6*a^2 + 14/5*x^20*b^5*a^3 + 70/17*x^17*b^4*a^4 + 4*x^14*b^3*a^5 + 28/11*x^11*b^2*a^6 + x^8*b*a^7 + 1/5*x^5*a^8","A",0
309,1,90,0,0.895282," ","integrate(x^3*(b*x^3+a)^8,x, algorithm=""fricas"")","\frac{1}{28} x^{28} b^{8} + \frac{8}{25} x^{25} b^{7} a + \frac{14}{11} x^{22} b^{6} a^{2} + \frac{56}{19} x^{19} b^{5} a^{3} + \frac{35}{8} x^{16} b^{4} a^{4} + \frac{56}{13} x^{13} b^{3} a^{5} + \frac{14}{5} x^{10} b^{2} a^{6} + \frac{8}{7} x^{7} b a^{7} + \frac{1}{4} x^{4} a^{8}"," ",0,"1/28*x^28*b^8 + 8/25*x^25*b^7*a + 14/11*x^22*b^6*a^2 + 56/19*x^19*b^5*a^3 + 35/8*x^16*b^4*a^4 + 56/13*x^13*b^3*a^5 + 14/5*x^10*b^2*a^6 + 8/7*x^7*b*a^7 + 1/4*x^4*a^8","A",0
310,1,90,0,0.868580," ","integrate(x*(b*x^3+a)^8,x, algorithm=""fricas"")","\frac{1}{26} x^{26} b^{8} + \frac{8}{23} x^{23} b^{7} a + \frac{7}{5} x^{20} b^{6} a^{2} + \frac{56}{17} x^{17} b^{5} a^{3} + 5 x^{14} b^{4} a^{4} + \frac{56}{11} x^{11} b^{3} a^{5} + \frac{7}{2} x^{8} b^{2} a^{6} + \frac{8}{5} x^{5} b a^{7} + \frac{1}{2} x^{2} a^{8}"," ",0,"1/26*x^26*b^8 + 8/23*x^23*b^7*a + 7/5*x^20*b^6*a^2 + 56/17*x^17*b^5*a^3 + 5*x^14*b^4*a^4 + 56/11*x^11*b^3*a^5 + 7/2*x^8*b^2*a^6 + 8/5*x^5*b*a^7 + 1/2*x^2*a^8","A",0
311,1,87,0,0.890280," ","integrate((b*x^3+a)^8,x, algorithm=""fricas"")","\frac{1}{25} x^{25} b^{8} + \frac{4}{11} x^{22} b^{7} a + \frac{28}{19} x^{19} b^{6} a^{2} + \frac{7}{2} x^{16} b^{5} a^{3} + \frac{70}{13} x^{13} b^{4} a^{4} + \frac{28}{5} x^{10} b^{3} a^{5} + 4 x^{7} b^{2} a^{6} + 2 x^{4} b a^{7} + x a^{8}"," ",0,"1/25*x^25*b^8 + 4/11*x^22*b^7*a + 28/19*x^19*b^6*a^2 + 7/2*x^16*b^5*a^3 + 70/13*x^13*b^4*a^4 + 28/5*x^10*b^3*a^5 + 4*x^7*b^2*a^6 + 2*x^4*b*a^7 + x*a^8","A",0
312,1,92,0,0.736527," ","integrate((b*x^3+a)^8/x^2,x, algorithm=""fricas"")","\frac{935 \, b^{8} x^{24} + 8602 \, a b^{7} x^{21} + 35420 \, a^{2} b^{6} x^{18} + 86020 \, a^{3} b^{5} x^{15} + 136850 \, a^{4} b^{4} x^{12} + 150535 \, a^{5} b^{3} x^{9} + 120428 \, a^{6} b^{2} x^{6} + 86020 \, a^{7} b x^{3} - 21505 \, a^{8}}{21505 \, x}"," ",0,"1/21505*(935*b^8*x^24 + 8602*a*b^7*x^21 + 35420*a^2*b^6*x^18 + 86020*a^3*b^5*x^15 + 136850*a^4*b^4*x^12 + 150535*a^5*b^3*x^9 + 120428*a^6*b^2*x^6 + 86020*a^7*b*x^3 - 21505*a^8)/x","A",0
313,1,92,0,0.731444," ","integrate((b*x^3+a)^8/x^3,x, algorithm=""fricas"")","\frac{494 \, b^{8} x^{24} + 4576 \, a b^{7} x^{21} + 19019 \, a^{2} b^{6} x^{18} + 46816 \, a^{3} b^{5} x^{15} + 76076 \, a^{4} b^{4} x^{12} + 86944 \, a^{5} b^{3} x^{9} + 76076 \, a^{6} b^{2} x^{6} + 86944 \, a^{7} b x^{3} - 5434 \, a^{8}}{10868 \, x^{2}}"," ",0,"1/10868*(494*b^8*x^24 + 4576*a*b^7*x^21 + 19019*a^2*b^6*x^18 + 46816*a^3*b^5*x^15 + 76076*a^4*b^4*x^12 + 86944*a^5*b^3*x^9 + 76076*a^6*b^2*x^6 + 86944*a^7*b*x^3 - 5434*a^8)/x^2","A",0
314,1,92,0,0.892719," ","integrate((b*x^3+a)^8/x^5,x, algorithm=""fricas"")","\frac{187 \, b^{8} x^{24} + 1760 \, a b^{7} x^{21} + 7480 \, a^{2} b^{6} x^{18} + 19040 \, a^{3} b^{5} x^{15} + 32725 \, a^{4} b^{4} x^{12} + 41888 \, a^{5} b^{3} x^{9} + 52360 \, a^{6} b^{2} x^{6} - 29920 \, a^{7} b x^{3} - 935 \, a^{8}}{3740 \, x^{4}}"," ",0,"1/3740*(187*b^8*x^24 + 1760*a*b^7*x^21 + 7480*a^2*b^6*x^18 + 19040*a^3*b^5*x^15 + 32725*a^4*b^4*x^12 + 41888*a^5*b^3*x^9 + 52360*a^6*b^2*x^6 - 29920*a^7*b*x^3 - 935*a^8)/x^4","A",0
315,1,92,0,0.571941," ","integrate((b*x^3+a)^8/x^6,x, algorithm=""fricas"")","\frac{130 \, b^{8} x^{24} + 1235 \, a b^{7} x^{21} + 5320 \, a^{2} b^{6} x^{18} + 13832 \, a^{3} b^{5} x^{15} + 24700 \, a^{4} b^{4} x^{12} + 34580 \, a^{5} b^{3} x^{9} + 69160 \, a^{6} b^{2} x^{6} - 9880 \, a^{7} b x^{3} - 494 \, a^{8}}{2470 \, x^{5}}"," ",0,"1/2470*(130*b^8*x^24 + 1235*a*b^7*x^21 + 5320*a^2*b^6*x^18 + 13832*a^3*b^5*x^15 + 24700*a^4*b^4*x^12 + 34580*a^5*b^3*x^9 + 69160*a^6*b^2*x^6 - 9880*a^7*b*x^3 - 494*a^8)/x^5","A",0
316,1,92,0,0.991787," ","integrate((b*x^3+a)^8/x^8,x, algorithm=""fricas"")","\frac{77 \, b^{8} x^{24} + 748 \, a b^{7} x^{21} + 3332 \, a^{2} b^{6} x^{18} + 9163 \, a^{3} b^{5} x^{15} + 18326 \, a^{4} b^{4} x^{12} + 36652 \, a^{5} b^{3} x^{9} - 36652 \, a^{6} b^{2} x^{6} - 2618 \, a^{7} b x^{3} - 187 \, a^{8}}{1309 \, x^{7}}"," ",0,"1/1309*(77*b^8*x^24 + 748*a*b^7*x^21 + 3332*a^2*b^6*x^18 + 9163*a^3*b^5*x^15 + 18326*a^4*b^4*x^12 + 36652*a^5*b^3*x^9 - 36652*a^6*b^2*x^6 - 2618*a^7*b*x^3 - 187*a^8)/x^7","A",0
317,1,92,0,0.655125," ","integrate((b*x^3+a)^8/x^9,x, algorithm=""fricas"")","\frac{65 \, b^{8} x^{24} + 640 \, a b^{7} x^{21} + 2912 \, a^{2} b^{6} x^{18} + 8320 \, a^{3} b^{5} x^{15} + 18200 \, a^{4} b^{4} x^{12} + 58240 \, a^{5} b^{3} x^{9} - 14560 \, a^{6} b^{2} x^{6} - 1664 \, a^{7} b x^{3} - 130 \, a^{8}}{1040 \, x^{8}}"," ",0,"1/1040*(65*b^8*x^24 + 640*a*b^7*x^21 + 2912*a^2*b^6*x^18 + 8320*a^3*b^5*x^15 + 18200*a^4*b^4*x^12 + 58240*a^5*b^3*x^9 - 14560*a^6*b^2*x^6 - 1664*a^7*b*x^3 - 130*a^8)/x^8","A",0
318,1,33,0,0.668588," ","integrate(x^8/(b*x^3+a),x, algorithm=""fricas"")","\frac{b^{2} x^{6} - 2 \, a b x^{3} + 2 \, a^{2} \log\left(b x^{3} + a\right)}{6 \, b^{3}}"," ",0,"1/6*(b^2*x^6 - 2*a*b*x^3 + 2*a^2*log(b*x^3 + a))/b^3","A",0
319,1,22,0,1.078033," ","integrate(x^5/(b*x^3+a),x, algorithm=""fricas"")","\frac{b x^{3} - a \log\left(b x^{3} + a\right)}{3 \, b^{2}}"," ",0,"1/3*(b*x^3 - a*log(b*x^3 + a))/b^2","A",0
320,1,13,0,0.942596," ","integrate(x^2/(b*x^3+a),x, algorithm=""fricas"")","\frac{\log\left(b x^{3} + a\right)}{3 \, b}"," ",0,"1/3*log(b*x^3 + a)/b","A",0
321,1,18,0,1.089887," ","integrate(1/x/(b*x^3+a),x, algorithm=""fricas"")","-\frac{\log\left(b x^{3} + a\right) - 3 \, \log\left(x\right)}{3 \, a}"," ",0,"-1/3*(log(b*x^3 + a) - 3*log(x))/a","A",0
322,1,33,0,1.038633," ","integrate(1/x^4/(b*x^3+a),x, algorithm=""fricas"")","\frac{b x^{3} \log\left(b x^{3} + a\right) - 3 \, b x^{3} \log\left(x\right) - a}{3 \, a^{2} x^{3}}"," ",0,"1/3*(b*x^3*log(b*x^3 + a) - 3*b*x^3*log(x) - a)/(a^2*x^3)","A",0
323,1,123,0,0.706308," ","integrate(x^4/(b*x^3+a),x, algorithm=""fricas"")","\frac{3 \, x^{2} - 2 \, \sqrt{3} \left(\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} b x \left(\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}} - \sqrt{3} a}{3 \, a}\right) - \left(\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}} \log\left(a x^{2} - b x \left(\frac{a^{2}}{b^{2}}\right)^{\frac{2}{3}} + a \left(\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}}\right) + 2 \, \left(\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}} \log\left(a x + b \left(\frac{a^{2}}{b^{2}}\right)^{\frac{2}{3}}\right)}{6 \, b}"," ",0,"1/6*(3*x^2 - 2*sqrt(3)*(a^2/b^2)^(1/3)*arctan(1/3*(2*sqrt(3)*b*x*(a^2/b^2)^(1/3) - sqrt(3)*a)/a) - (a^2/b^2)^(1/3)*log(a*x^2 - b*x*(a^2/b^2)^(2/3) + a*(a^2/b^2)^(1/3)) + 2*(a^2/b^2)^(1/3)*log(a*x + b*(a^2/b^2)^(2/3)))/b","A",0
324,1,106,0,1.056264," ","integrate(x^3/(b*x^3+a),x, algorithm=""fricas"")","\frac{2 \, \sqrt{3} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} b x \left(-\frac{a}{b}\right)^{\frac{2}{3}} - \sqrt{3} a}{3 \, a}\right) - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right) + 2 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left(x - \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right) + 6 \, x}{6 \, b}"," ",0,"1/6*(2*sqrt(3)*(-a/b)^(1/3)*arctan(1/3*(2*sqrt(3)*b*x*(-a/b)^(2/3) - sqrt(3)*a)/a) - (-a/b)^(1/3)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3)) + 2*(-a/b)^(1/3)*log(x - (-a/b)^(1/3)) + 6*x)/b","A",0
325,1,304,0,1.149239," ","integrate(x/(b*x^3+a),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{\frac{1}{3}} a b \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \log\left(\frac{2 \, b^{2} x^{3} - a b + 3 \, \sqrt{\frac{1}{3}} {\left(a b x + 2 \, \left(-a b^{2}\right)^{\frac{2}{3}} x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} - 3 \, \left(-a b^{2}\right)^{\frac{2}{3}} x}{b x^{3} + a}\right) + \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} b x + \left(-a b^{2}\right)^{\frac{2}{3}}\right) - 2 \, \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b x - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{6 \, a b^{2}}, \frac{6 \, \sqrt{\frac{1}{3}} a b \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, b x + \left(-a b^{2}\right)^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}}}{b}\right) + \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} b x + \left(-a b^{2}\right)^{\frac{2}{3}}\right) - 2 \, \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b x - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{6 \, a b^{2}}\right]"," ",0,"[1/6*(3*sqrt(1/3)*a*b*sqrt((-a*b^2)^(1/3)/a)*log((2*b^2*x^3 - a*b + 3*sqrt(1/3)*(a*b*x + 2*(-a*b^2)^(2/3)*x^2 + (-a*b^2)^(1/3)*a)*sqrt((-a*b^2)^(1/3)/a) - 3*(-a*b^2)^(2/3)*x)/(b*x^3 + a)) + (-a*b^2)^(2/3)*log(b^2*x^2 + (-a*b^2)^(1/3)*b*x + (-a*b^2)^(2/3)) - 2*(-a*b^2)^(2/3)*log(b*x - (-a*b^2)^(1/3)))/(a*b^2), 1/6*(6*sqrt(1/3)*a*b*sqrt(-(-a*b^2)^(1/3)/a)*arctan(sqrt(1/3)*(2*b*x + (-a*b^2)^(1/3))*sqrt(-(-a*b^2)^(1/3)/a)/b) + (-a*b^2)^(2/3)*log(b^2*x^2 + (-a*b^2)^(1/3)*b*x + (-a*b^2)^(2/3)) - 2*(-a*b^2)^(2/3)*log(b*x - (-a*b^2)^(1/3)))/(a*b^2)]","A",0
326,1,299,0,0.699067," ","integrate(1/(b*x^3+a),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{\frac{1}{3}} a b \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \log\left(\frac{2 \, a b x^{3} - 3 \, \left(a^{2} b\right)^{\frac{1}{3}} a x - a^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, a b x^{2} + \left(a^{2} b\right)^{\frac{2}{3}} x - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{b x^{3} + a}\right) - \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(a^{2} b\right)^{\frac{2}{3}} x + \left(a^{2} b\right)^{\frac{1}{3}} a\right) + 2 \, \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(a^{2} b\right)^{\frac{2}{3}}\right)}{6 \, a^{2} b}, \frac{6 \, \sqrt{\frac{1}{3}} a b \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(a^{2} b\right)^{\frac{2}{3}} x - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{a^{2}}\right) - \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(a^{2} b\right)^{\frac{2}{3}} x + \left(a^{2} b\right)^{\frac{1}{3}} a\right) + 2 \, \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(a^{2} b\right)^{\frac{2}{3}}\right)}{6 \, a^{2} b}\right]"," ",0,"[1/6*(3*sqrt(1/3)*a*b*sqrt(-(a^2*b)^(1/3)/b)*log((2*a*b*x^3 - 3*(a^2*b)^(1/3)*a*x - a^2 + 3*sqrt(1/3)*(2*a*b*x^2 + (a^2*b)^(2/3)*x - (a^2*b)^(1/3)*a)*sqrt(-(a^2*b)^(1/3)/b))/(b*x^3 + a)) - (a^2*b)^(2/3)*log(a*b*x^2 - (a^2*b)^(2/3)*x + (a^2*b)^(1/3)*a) + 2*(a^2*b)^(2/3)*log(a*b*x + (a^2*b)^(2/3)))/(a^2*b), 1/6*(6*sqrt(1/3)*a*b*sqrt((a^2*b)^(1/3)/b)*arctan(sqrt(1/3)*(2*(a^2*b)^(2/3)*x - (a^2*b)^(1/3)*a)*sqrt((a^2*b)^(1/3)/b)/a^2) - (a^2*b)^(2/3)*log(a*b*x^2 - (a^2*b)^(2/3)*x + (a^2*b)^(1/3)*a) + 2*(a^2*b)^(2/3)*log(a*b*x + (a^2*b)^(2/3)))/(a^2*b)]","A",0
327,1,103,0,1.123183," ","integrate(1/x^2/(b*x^3+a),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} x \left(\frac{b}{a}\right)^{\frac{1}{3}} \arctan\left(\frac{2}{3} \, \sqrt{3} x \left(\frac{b}{a}\right)^{\frac{1}{3}} - \frac{1}{3} \, \sqrt{3}\right) + x \left(\frac{b}{a}\right)^{\frac{1}{3}} \log\left(b x^{2} - a x \left(\frac{b}{a}\right)^{\frac{2}{3}} + a \left(\frac{b}{a}\right)^{\frac{1}{3}}\right) - 2 \, x \left(\frac{b}{a}\right)^{\frac{1}{3}} \log\left(b x + a \left(\frac{b}{a}\right)^{\frac{2}{3}}\right) + 6}{6 \, a x}"," ",0,"-1/6*(2*sqrt(3)*x*(b/a)^(1/3)*arctan(2/3*sqrt(3)*x*(b/a)^(1/3) - 1/3*sqrt(3)) + x*(b/a)^(1/3)*log(b*x^2 - a*x*(b/a)^(2/3) + a*(b/a)^(1/3)) - 2*x*(b/a)^(1/3)*log(b*x + a*(b/a)^(2/3)) + 6)/(a*x)","A",0
328,1,143,0,0.938640," ","integrate(1/x^3/(b*x^3+a),x, algorithm=""fricas"")","\frac{2 \, \sqrt{3} x^{2} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} a x \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}} - \sqrt{3} b}{3 \, b}\right) - x^{2} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b^{2} x^{2} + a b x \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} + a^{2} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}}\right) + 2 \, x^{2} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b x - a \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}}\right) - 3}{6 \, a x^{2}}"," ",0,"1/6*(2*sqrt(3)*x^2*(-b^2/a^2)^(1/3)*arctan(1/3*(2*sqrt(3)*a*x*(-b^2/a^2)^(2/3) - sqrt(3)*b)/b) - x^2*(-b^2/a^2)^(1/3)*log(b^2*x^2 + a*b*x*(-b^2/a^2)^(1/3) + a^2*(-b^2/a^2)^(2/3)) + 2*x^2*(-b^2/a^2)^(1/3)*log(b*x - a*(-b^2/a^2)^(1/3)) - 3)/(a*x^2)","A",0
329,1,56,0,1.007939," ","integrate(x^8/(b*x^3+a)^2,x, algorithm=""fricas"")","\frac{b^{2} x^{6} + a b x^{3} - a^{2} - 2 \, {\left(a b x^{3} + a^{2}\right)} \log\left(b x^{3} + a\right)}{3 \, {\left(b^{4} x^{3} + a b^{3}\right)}}"," ",0,"1/3*(b^2*x^6 + a*b*x^3 - a^2 - 2*(a*b*x^3 + a^2)*log(b*x^3 + a))/(b^4*x^3 + a*b^3)","A",0
330,1,35,0,1.189832," ","integrate(x^5/(b*x^3+a)^2,x, algorithm=""fricas"")","\frac{{\left(b x^{3} + a\right)} \log\left(b x^{3} + a\right) + a}{3 \, {\left(b^{3} x^{3} + a b^{2}\right)}}"," ",0,"1/3*((b*x^3 + a)*log(b*x^3 + a) + a)/(b^3*x^3 + a*b^2)","A",0
331,1,15,0,1.078724," ","integrate(x^2/(b*x^3+a)^2,x, algorithm=""fricas"")","-\frac{1}{3 \, {\left(b^{2} x^{3} + a b\right)}}"," ",0,"-1/3/(b^2*x^3 + a*b)","A",0
332,1,47,0,1.289359," ","integrate(1/x/(b*x^3+a)^2,x, algorithm=""fricas"")","-\frac{{\left(b x^{3} + a\right)} \log\left(b x^{3} + a\right) - 3 \, {\left(b x^{3} + a\right)} \log\left(x\right) - a}{3 \, {\left(a^{2} b x^{3} + a^{3}\right)}}"," ",0,"-1/3*((b*x^3 + a)*log(b*x^3 + a) - 3*(b*x^3 + a)*log(x) - a)/(a^2*b*x^3 + a^3)","A",0
333,1,73,0,0.920998," ","integrate(1/x^4/(b*x^3+a)^2,x, algorithm=""fricas"")","-\frac{2 \, a b x^{3} + a^{2} - 2 \, {\left(b^{2} x^{6} + a b x^{3}\right)} \log\left(b x^{3} + a\right) + 6 \, {\left(b^{2} x^{6} + a b x^{3}\right)} \log\left(x\right)}{3 \, {\left(a^{3} b x^{6} + a^{4} x^{3}\right)}}"," ",0,"-1/3*(2*a*b*x^3 + a^2 - 2*(b^2*x^6 + a*b*x^3)*log(b*x^3 + a) + 6*(b^2*x^6 + a*b*x^3)*log(x))/(a^3*b*x^6 + a^4*x^3)","A",0
334,1,400,0,0.802003," ","integrate(x^4/(b*x^3+a)^2,x, algorithm=""fricas"")","\left[-\frac{3 \, a b^{2} x^{2} - 3 \, \sqrt{\frac{1}{3}} {\left(a b^{2} x^{3} + a^{2} b\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \log\left(\frac{2 \, b^{2} x^{3} - a b + 3 \, \sqrt{\frac{1}{3}} {\left(a b x + 2 \, \left(-a b^{2}\right)^{\frac{2}{3}} x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} - 3 \, \left(-a b^{2}\right)^{\frac{2}{3}} x}{b x^{3} + a}\right) - {\left(b x^{3} + a\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} b x + \left(-a b^{2}\right)^{\frac{2}{3}}\right) + 2 \, {\left(b x^{3} + a\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b x - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{9 \, {\left(a b^{4} x^{3} + a^{2} b^{3}\right)}}, -\frac{3 \, a b^{2} x^{2} - 6 \, \sqrt{\frac{1}{3}} {\left(a b^{2} x^{3} + a^{2} b\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, b x + \left(-a b^{2}\right)^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}}}{b}\right) - {\left(b x^{3} + a\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} b x + \left(-a b^{2}\right)^{\frac{2}{3}}\right) + 2 \, {\left(b x^{3} + a\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b x - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{9 \, {\left(a b^{4} x^{3} + a^{2} b^{3}\right)}}\right]"," ",0,"[-1/9*(3*a*b^2*x^2 - 3*sqrt(1/3)*(a*b^2*x^3 + a^2*b)*sqrt((-a*b^2)^(1/3)/a)*log((2*b^2*x^3 - a*b + 3*sqrt(1/3)*(a*b*x + 2*(-a*b^2)^(2/3)*x^2 + (-a*b^2)^(1/3)*a)*sqrt((-a*b^2)^(1/3)/a) - 3*(-a*b^2)^(2/3)*x)/(b*x^3 + a)) - (b*x^3 + a)*(-a*b^2)^(2/3)*log(b^2*x^2 + (-a*b^2)^(1/3)*b*x + (-a*b^2)^(2/3)) + 2*(b*x^3 + a)*(-a*b^2)^(2/3)*log(b*x - (-a*b^2)^(1/3)))/(a*b^4*x^3 + a^2*b^3), -1/9*(3*a*b^2*x^2 - 6*sqrt(1/3)*(a*b^2*x^3 + a^2*b)*sqrt(-(-a*b^2)^(1/3)/a)*arctan(sqrt(1/3)*(2*b*x + (-a*b^2)^(1/3))*sqrt(-(-a*b^2)^(1/3)/a)/b) - (b*x^3 + a)*(-a*b^2)^(2/3)*log(b^2*x^2 + (-a*b^2)^(1/3)*b*x + (-a*b^2)^(2/3)) + 2*(b*x^3 + a)*(-a*b^2)^(2/3)*log(b*x - (-a*b^2)^(1/3)))/(a*b^4*x^3 + a^2*b^3)]","A",0
335,1,391,0,1.258312," ","integrate(x^3/(b*x^3+a)^2,x, algorithm=""fricas"")","\left[-\frac{6 \, a^{2} b x - 3 \, \sqrt{\frac{1}{3}} {\left(a b^{2} x^{3} + a^{2} b\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \log\left(\frac{2 \, a b x^{3} - 3 \, \left(a^{2} b\right)^{\frac{1}{3}} a x - a^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, a b x^{2} + \left(a^{2} b\right)^{\frac{2}{3}} x - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{b x^{3} + a}\right) + {\left(b x^{3} + a\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(a^{2} b\right)^{\frac{2}{3}} x + \left(a^{2} b\right)^{\frac{1}{3}} a\right) - 2 \, {\left(b x^{3} + a\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(a^{2} b\right)^{\frac{2}{3}}\right)}{18 \, {\left(a^{2} b^{3} x^{3} + a^{3} b^{2}\right)}}, -\frac{6 \, a^{2} b x - 6 \, \sqrt{\frac{1}{3}} {\left(a b^{2} x^{3} + a^{2} b\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(a^{2} b\right)^{\frac{2}{3}} x - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{a^{2}}\right) + {\left(b x^{3} + a\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(a^{2} b\right)^{\frac{2}{3}} x + \left(a^{2} b\right)^{\frac{1}{3}} a\right) - 2 \, {\left(b x^{3} + a\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(a^{2} b\right)^{\frac{2}{3}}\right)}{18 \, {\left(a^{2} b^{3} x^{3} + a^{3} b^{2}\right)}}\right]"," ",0,"[-1/18*(6*a^2*b*x - 3*sqrt(1/3)*(a*b^2*x^3 + a^2*b)*sqrt(-(a^2*b)^(1/3)/b)*log((2*a*b*x^3 - 3*(a^2*b)^(1/3)*a*x - a^2 + 3*sqrt(1/3)*(2*a*b*x^2 + (a^2*b)^(2/3)*x - (a^2*b)^(1/3)*a)*sqrt(-(a^2*b)^(1/3)/b))/(b*x^3 + a)) + (b*x^3 + a)*(a^2*b)^(2/3)*log(a*b*x^2 - (a^2*b)^(2/3)*x + (a^2*b)^(1/3)*a) - 2*(b*x^3 + a)*(a^2*b)^(2/3)*log(a*b*x + (a^2*b)^(2/3)))/(a^2*b^3*x^3 + a^3*b^2), -1/18*(6*a^2*b*x - 6*sqrt(1/3)*(a*b^2*x^3 + a^2*b)*sqrt((a^2*b)^(1/3)/b)*arctan(sqrt(1/3)*(2*(a^2*b)^(2/3)*x - (a^2*b)^(1/3)*a)*sqrt((a^2*b)^(1/3)/b)/a^2) + (b*x^3 + a)*(a^2*b)^(2/3)*log(a*b*x^2 - (a^2*b)^(2/3)*x + (a^2*b)^(1/3)*a) - 2*(b*x^3 + a)*(a^2*b)^(2/3)*log(a*b*x + (a^2*b)^(2/3)))/(a^2*b^3*x^3 + a^3*b^2)]","A",0
336,1,402,0,0.784381," ","integrate(x/(b*x^3+a)^2,x, algorithm=""fricas"")","\left[\frac{6 \, a b^{2} x^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(a b^{2} x^{3} + a^{2} b\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \log\left(\frac{2 \, b^{2} x^{3} - a b + 3 \, \sqrt{\frac{1}{3}} {\left(a b x + 2 \, \left(-a b^{2}\right)^{\frac{2}{3}} x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} - 3 \, \left(-a b^{2}\right)^{\frac{2}{3}} x}{b x^{3} + a}\right) + {\left(b x^{3} + a\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} b x + \left(-a b^{2}\right)^{\frac{2}{3}}\right) - 2 \, {\left(b x^{3} + a\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b x - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{18 \, {\left(a^{2} b^{3} x^{3} + a^{3} b^{2}\right)}}, \frac{6 \, a b^{2} x^{2} + 6 \, \sqrt{\frac{1}{3}} {\left(a b^{2} x^{3} + a^{2} b\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, b x + \left(-a b^{2}\right)^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}}}{b}\right) + {\left(b x^{3} + a\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} b x + \left(-a b^{2}\right)^{\frac{2}{3}}\right) - 2 \, {\left(b x^{3} + a\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b x - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{18 \, {\left(a^{2} b^{3} x^{3} + a^{3} b^{2}\right)}}\right]"," ",0,"[1/18*(6*a*b^2*x^2 + 3*sqrt(1/3)*(a*b^2*x^3 + a^2*b)*sqrt((-a*b^2)^(1/3)/a)*log((2*b^2*x^3 - a*b + 3*sqrt(1/3)*(a*b*x + 2*(-a*b^2)^(2/3)*x^2 + (-a*b^2)^(1/3)*a)*sqrt((-a*b^2)^(1/3)/a) - 3*(-a*b^2)^(2/3)*x)/(b*x^3 + a)) + (b*x^3 + a)*(-a*b^2)^(2/3)*log(b^2*x^2 + (-a*b^2)^(1/3)*b*x + (-a*b^2)^(2/3)) - 2*(b*x^3 + a)*(-a*b^2)^(2/3)*log(b*x - (-a*b^2)^(1/3)))/(a^2*b^3*x^3 + a^3*b^2), 1/18*(6*a*b^2*x^2 + 6*sqrt(1/3)*(a*b^2*x^3 + a^2*b)*sqrt(-(-a*b^2)^(1/3)/a)*arctan(sqrt(1/3)*(2*b*x + (-a*b^2)^(1/3))*sqrt(-(-a*b^2)^(1/3)/a)/b) + (b*x^3 + a)*(-a*b^2)^(2/3)*log(b^2*x^2 + (-a*b^2)^(1/3)*b*x + (-a*b^2)^(2/3)) - 2*(b*x^3 + a)*(-a*b^2)^(2/3)*log(b*x - (-a*b^2)^(1/3)))/(a^2*b^3*x^3 + a^3*b^2)]","A",0
337,1,389,0,1.233113," ","integrate(1/(b*x^3+a)^2,x, algorithm=""fricas"")","\left[\frac{3 \, a^{2} b x + 3 \, \sqrt{\frac{1}{3}} {\left(a b^{2} x^{3} + a^{2} b\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \log\left(\frac{2 \, a b x^{3} - 3 \, \left(a^{2} b\right)^{\frac{1}{3}} a x - a^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, a b x^{2} + \left(a^{2} b\right)^{\frac{2}{3}} x - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{b x^{3} + a}\right) - {\left(b x^{3} + a\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(a^{2} b\right)^{\frac{2}{3}} x + \left(a^{2} b\right)^{\frac{1}{3}} a\right) + 2 \, {\left(b x^{3} + a\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(a^{2} b\right)^{\frac{2}{3}}\right)}{9 \, {\left(a^{3} b^{2} x^{3} + a^{4} b\right)}}, \frac{3 \, a^{2} b x + 6 \, \sqrt{\frac{1}{3}} {\left(a b^{2} x^{3} + a^{2} b\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(a^{2} b\right)^{\frac{2}{3}} x - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{a^{2}}\right) - {\left(b x^{3} + a\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(a^{2} b\right)^{\frac{2}{3}} x + \left(a^{2} b\right)^{\frac{1}{3}} a\right) + 2 \, {\left(b x^{3} + a\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(a^{2} b\right)^{\frac{2}{3}}\right)}{9 \, {\left(a^{3} b^{2} x^{3} + a^{4} b\right)}}\right]"," ",0,"[1/9*(3*a^2*b*x + 3*sqrt(1/3)*(a*b^2*x^3 + a^2*b)*sqrt(-(a^2*b)^(1/3)/b)*log((2*a*b*x^3 - 3*(a^2*b)^(1/3)*a*x - a^2 + 3*sqrt(1/3)*(2*a*b*x^2 + (a^2*b)^(2/3)*x - (a^2*b)^(1/3)*a)*sqrt(-(a^2*b)^(1/3)/b))/(b*x^3 + a)) - (b*x^3 + a)*(a^2*b)^(2/3)*log(a*b*x^2 - (a^2*b)^(2/3)*x + (a^2*b)^(1/3)*a) + 2*(b*x^3 + a)*(a^2*b)^(2/3)*log(a*b*x + (a^2*b)^(2/3)))/(a^3*b^2*x^3 + a^4*b), 1/9*(3*a^2*b*x + 6*sqrt(1/3)*(a*b^2*x^3 + a^2*b)*sqrt((a^2*b)^(1/3)/b)*arctan(sqrt(1/3)*(2*(a^2*b)^(2/3)*x - (a^2*b)^(1/3)*a)*sqrt((a^2*b)^(1/3)/b)/a^2) - (b*x^3 + a)*(a^2*b)^(2/3)*log(a*b*x^2 - (a^2*b)^(2/3)*x + (a^2*b)^(1/3)*a) + 2*(b*x^3 + a)*(a^2*b)^(2/3)*log(a*b*x + (a^2*b)^(2/3)))/(a^3*b^2*x^3 + a^4*b)]","A",0
338,1,146,0,0.908009," ","integrate(1/x^2/(b*x^3+a)^2,x, algorithm=""fricas"")","-\frac{12 \, b x^{3} + 4 \, \sqrt{3} {\left(b x^{4} + a x\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}} \arctan\left(\frac{2}{3} \, \sqrt{3} x \left(\frac{b}{a}\right)^{\frac{1}{3}} - \frac{1}{3} \, \sqrt{3}\right) + 2 \, {\left(b x^{4} + a x\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}} \log\left(b x^{2} - a x \left(\frac{b}{a}\right)^{\frac{2}{3}} + a \left(\frac{b}{a}\right)^{\frac{1}{3}}\right) - 4 \, {\left(b x^{4} + a x\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}} \log\left(b x + a \left(\frac{b}{a}\right)^{\frac{2}{3}}\right) + 9 \, a}{9 \, {\left(a^{2} b x^{4} + a^{3} x\right)}}"," ",0,"-1/9*(12*b*x^3 + 4*sqrt(3)*(b*x^4 + a*x)*(b/a)^(1/3)*arctan(2/3*sqrt(3)*x*(b/a)^(1/3) - 1/3*sqrt(3)) + 2*(b*x^4 + a*x)*(b/a)^(1/3)*log(b*x^2 - a*x*(b/a)^(2/3) + a*(b/a)^(1/3)) - 4*(b*x^4 + a*x)*(b/a)^(1/3)*log(b*x + a*(b/a)^(2/3)) + 9*a)/(a^2*b*x^4 + a^3*x)","A",0
339,1,187,0,0.996126," ","integrate(1/x^3/(b*x^3+a)^2,x, algorithm=""fricas"")","-\frac{15 \, b x^{3} - 10 \, \sqrt{3} {\left(b x^{5} + a x^{2}\right)} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} a x \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}} - \sqrt{3} b}{3 \, b}\right) + 5 \, {\left(b x^{5} + a x^{2}\right)} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b^{2} x^{2} + a b x \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} + a^{2} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}}\right) - 10 \, {\left(b x^{5} + a x^{2}\right)} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b x - a \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}}\right) + 9 \, a}{18 \, {\left(a^{2} b x^{5} + a^{3} x^{2}\right)}}"," ",0,"-1/18*(15*b*x^3 - 10*sqrt(3)*(b*x^5 + a*x^2)*(-b^2/a^2)^(1/3)*arctan(1/3*(2*sqrt(3)*a*x*(-b^2/a^2)^(2/3) - sqrt(3)*b)/b) + 5*(b*x^5 + a*x^2)*(-b^2/a^2)^(1/3)*log(b^2*x^2 + a*b*x*(-b^2/a^2)^(1/3) + a^2*(-b^2/a^2)^(2/3)) - 10*(b*x^5 + a*x^2)*(-b^2/a^2)^(1/3)*log(b*x - a*(-b^2/a^2)^(1/3)) + 9*a)/(a^2*b*x^5 + a^3*x^2)","A",0
340,1,91,0,0.987478," ","integrate(x^11/(b*x^3+a)^3,x, algorithm=""fricas"")","\frac{2 \, b^{3} x^{9} + 4 \, a b^{2} x^{6} - 4 \, a^{2} b x^{3} - 5 \, a^{3} - 6 \, {\left(a b^{2} x^{6} + 2 \, a^{2} b x^{3} + a^{3}\right)} \log\left(b x^{3} + a\right)}{6 \, {\left(b^{6} x^{6} + 2 \, a b^{5} x^{3} + a^{2} b^{4}\right)}}"," ",0,"1/6*(2*b^3*x^9 + 4*a*b^2*x^6 - 4*a^2*b*x^3 - 5*a^3 - 6*(a*b^2*x^6 + 2*a^2*b*x^3 + a^3)*log(b*x^3 + a))/(b^6*x^6 + 2*a*b^5*x^3 + a^2*b^4)","A",0
341,1,69,0,0.564821," ","integrate(x^8/(b*x^3+a)^3,x, algorithm=""fricas"")","\frac{4 \, a b x^{3} + 3 \, a^{2} + 2 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \log\left(b x^{3} + a\right)}{6 \, {\left(b^{5} x^{6} + 2 \, a b^{4} x^{3} + a^{2} b^{3}\right)}}"," ",0,"1/6*(4*a*b*x^3 + 3*a^2 + 2*(b^2*x^6 + 2*a*b*x^3 + a^2)*log(b*x^3 + a))/(b^5*x^6 + 2*a*b^4*x^3 + a^2*b^3)","A",0
342,1,36,0,0.912157," ","integrate(x^5/(b*x^3+a)^3,x, algorithm=""fricas"")","-\frac{2 \, b x^{3} + a}{6 \, {\left(b^{4} x^{6} + 2 \, a b^{3} x^{3} + a^{2} b^{2}\right)}}"," ",0,"-1/6*(2*b*x^3 + a)/(b^4*x^6 + 2*a*b^3*x^3 + a^2*b^2)","B",0
343,1,26,0,0.944485," ","integrate(x^2/(b*x^3+a)^3,x, algorithm=""fricas"")","-\frac{1}{6 \, {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}}"," ",0,"-1/6/(b^3*x^6 + 2*a*b^2*x^3 + a^2*b)","A",0
344,1,90,0,0.977772," ","integrate(1/x/(b*x^3+a)^3,x, algorithm=""fricas"")","\frac{2 \, a b x^{3} + 3 \, a^{2} - 2 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \log\left(b x^{3} + a\right) + 6 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \log\left(x\right)}{6 \, {\left(a^{3} b^{2} x^{6} + 2 \, a^{4} b x^{3} + a^{5}\right)}}"," ",0,"1/6*(2*a*b*x^3 + 3*a^2 - 2*(b^2*x^6 + 2*a*b*x^3 + a^2)*log(b*x^3 + a) + 6*(b^2*x^6 + 2*a*b*x^3 + a^2)*log(x))/(a^3*b^2*x^6 + 2*a^4*b*x^3 + a^5)","A",0
345,1,119,0,0.914087," ","integrate(1/x^4/(b*x^3+a)^3,x, algorithm=""fricas"")","-\frac{6 \, a b^{2} x^{6} + 9 \, a^{2} b x^{3} + 2 \, a^{3} - 6 \, {\left(b^{3} x^{9} + 2 \, a b^{2} x^{6} + a^{2} b x^{3}\right)} \log\left(b x^{3} + a\right) + 18 \, {\left(b^{3} x^{9} + 2 \, a b^{2} x^{6} + a^{2} b x^{3}\right)} \log\left(x\right)}{6 \, {\left(a^{4} b^{2} x^{9} + 2 \, a^{5} b x^{6} + a^{6} x^{3}\right)}}"," ",0,"-1/6*(6*a*b^2*x^6 + 9*a^2*b*x^3 + 2*a^3 - 6*(b^3*x^9 + 2*a*b^2*x^6 + a^2*b*x^3)*log(b*x^3 + a) + 18*(b^3*x^9 + 2*a*b^2*x^6 + a^2*b*x^3)*log(x))/(a^4*b^2*x^9 + 2*a^5*b*x^6 + a^6*x^3)","A",0
346,1,510,0,0.977870," ","integrate(x^7/(b*x^3+a)^3,x, algorithm=""fricas"")","\left[-\frac{24 \, a b^{3} x^{5} + 15 \, a^{2} b^{2} x^{2} - 15 \, \sqrt{\frac{1}{3}} {\left(a b^{3} x^{6} + 2 \, a^{2} b^{2} x^{3} + a^{3} b\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \log\left(\frac{2 \, b^{2} x^{3} - a b + 3 \, \sqrt{\frac{1}{3}} {\left(a b x + 2 \, \left(-a b^{2}\right)^{\frac{2}{3}} x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} - 3 \, \left(-a b^{2}\right)^{\frac{2}{3}} x}{b x^{3} + a}\right) - 5 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} b x + \left(-a b^{2}\right)^{\frac{2}{3}}\right) + 10 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b x - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{54 \, {\left(a b^{6} x^{6} + 2 \, a^{2} b^{5} x^{3} + a^{3} b^{4}\right)}}, -\frac{24 \, a b^{3} x^{5} + 15 \, a^{2} b^{2} x^{2} - 30 \, \sqrt{\frac{1}{3}} {\left(a b^{3} x^{6} + 2 \, a^{2} b^{2} x^{3} + a^{3} b\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, b x + \left(-a b^{2}\right)^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}}}{b}\right) - 5 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} b x + \left(-a b^{2}\right)^{\frac{2}{3}}\right) + 10 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b x - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{54 \, {\left(a b^{6} x^{6} + 2 \, a^{2} b^{5} x^{3} + a^{3} b^{4}\right)}}\right]"," ",0,"[-1/54*(24*a*b^3*x^5 + 15*a^2*b^2*x^2 - 15*sqrt(1/3)*(a*b^3*x^6 + 2*a^2*b^2*x^3 + a^3*b)*sqrt((-a*b^2)^(1/3)/a)*log((2*b^2*x^3 - a*b + 3*sqrt(1/3)*(a*b*x + 2*(-a*b^2)^(2/3)*x^2 + (-a*b^2)^(1/3)*a)*sqrt((-a*b^2)^(1/3)/a) - 3*(-a*b^2)^(2/3)*x)/(b*x^3 + a)) - 5*(b^2*x^6 + 2*a*b*x^3 + a^2)*(-a*b^2)^(2/3)*log(b^2*x^2 + (-a*b^2)^(1/3)*b*x + (-a*b^2)^(2/3)) + 10*(b^2*x^6 + 2*a*b*x^3 + a^2)*(-a*b^2)^(2/3)*log(b*x - (-a*b^2)^(1/3)))/(a*b^6*x^6 + 2*a^2*b^5*x^3 + a^3*b^4), -1/54*(24*a*b^3*x^5 + 15*a^2*b^2*x^2 - 30*sqrt(1/3)*(a*b^3*x^6 + 2*a^2*b^2*x^3 + a^3*b)*sqrt(-(-a*b^2)^(1/3)/a)*arctan(sqrt(1/3)*(2*b*x + (-a*b^2)^(1/3))*sqrt(-(-a*b^2)^(1/3)/a)/b) - 5*(b^2*x^6 + 2*a*b*x^3 + a^2)*(-a*b^2)^(2/3)*log(b^2*x^2 + (-a*b^2)^(1/3)*b*x + (-a*b^2)^(2/3)) + 10*(b^2*x^6 + 2*a*b*x^3 + a^2)*(-a*b^2)^(2/3)*log(b*x - (-a*b^2)^(1/3)))/(a*b^6*x^6 + 2*a^2*b^5*x^3 + a^3*b^4)]","B",0
347,1,503,0,0.968577," ","integrate(x^6/(b*x^3+a)^3,x, algorithm=""fricas"")","\left[-\frac{21 \, a^{2} b^{2} x^{4} + 12 \, a^{3} b x - 6 \, \sqrt{\frac{1}{3}} {\left(a b^{3} x^{6} + 2 \, a^{2} b^{2} x^{3} + a^{3} b\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \log\left(\frac{2 \, a b x^{3} - 3 \, \left(a^{2} b\right)^{\frac{1}{3}} a x - a^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, a b x^{2} + \left(a^{2} b\right)^{\frac{2}{3}} x - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{b x^{3} + a}\right) + 2 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(a^{2} b\right)^{\frac{2}{3}} x + \left(a^{2} b\right)^{\frac{1}{3}} a\right) - 4 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(a^{2} b\right)^{\frac{2}{3}}\right)}{54 \, {\left(a^{2} b^{5} x^{6} + 2 \, a^{3} b^{4} x^{3} + a^{4} b^{3}\right)}}, -\frac{21 \, a^{2} b^{2} x^{4} + 12 \, a^{3} b x - 12 \, \sqrt{\frac{1}{3}} {\left(a b^{3} x^{6} + 2 \, a^{2} b^{2} x^{3} + a^{3} b\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(a^{2} b\right)^{\frac{2}{3}} x - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{a^{2}}\right) + 2 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(a^{2} b\right)^{\frac{2}{3}} x + \left(a^{2} b\right)^{\frac{1}{3}} a\right) - 4 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(a^{2} b\right)^{\frac{2}{3}}\right)}{54 \, {\left(a^{2} b^{5} x^{6} + 2 \, a^{3} b^{4} x^{3} + a^{4} b^{3}\right)}}\right]"," ",0,"[-1/54*(21*a^2*b^2*x^4 + 12*a^3*b*x - 6*sqrt(1/3)*(a*b^3*x^6 + 2*a^2*b^2*x^3 + a^3*b)*sqrt(-(a^2*b)^(1/3)/b)*log((2*a*b*x^3 - 3*(a^2*b)^(1/3)*a*x - a^2 + 3*sqrt(1/3)*(2*a*b*x^2 + (a^2*b)^(2/3)*x - (a^2*b)^(1/3)*a)*sqrt(-(a^2*b)^(1/3)/b))/(b*x^3 + a)) + 2*(b^2*x^6 + 2*a*b*x^3 + a^2)*(a^2*b)^(2/3)*log(a*b*x^2 - (a^2*b)^(2/3)*x + (a^2*b)^(1/3)*a) - 4*(b^2*x^6 + 2*a*b*x^3 + a^2)*(a^2*b)^(2/3)*log(a*b*x + (a^2*b)^(2/3)))/(a^2*b^5*x^6 + 2*a^3*b^4*x^3 + a^4*b^3), -1/54*(21*a^2*b^2*x^4 + 12*a^3*b*x - 12*sqrt(1/3)*(a*b^3*x^6 + 2*a^2*b^2*x^3 + a^3*b)*sqrt((a^2*b)^(1/3)/b)*arctan(sqrt(1/3)*(2*(a^2*b)^(2/3)*x - (a^2*b)^(1/3)*a)*sqrt((a^2*b)^(1/3)/b)/a^2) + 2*(b^2*x^6 + 2*a*b*x^3 + a^2)*(a^2*b)^(2/3)*log(a*b*x^2 - (a^2*b)^(2/3)*x + (a^2*b)^(1/3)*a) - 4*(b^2*x^6 + 2*a*b*x^3 + a^2)*(a^2*b)^(2/3)*log(a*b*x + (a^2*b)^(2/3)))/(a^2*b^5*x^6 + 2*a^3*b^4*x^3 + a^4*b^3)]","B",0
348,1,512,0,0.943652," ","integrate(x^4/(b*x^3+a)^3,x, algorithm=""fricas"")","\left[\frac{6 \, a b^{3} x^{5} - 3 \, a^{2} b^{2} x^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(a b^{3} x^{6} + 2 \, a^{2} b^{2} x^{3} + a^{3} b\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \log\left(\frac{2 \, b^{2} x^{3} - a b + 3 \, \sqrt{\frac{1}{3}} {\left(a b x + 2 \, \left(-a b^{2}\right)^{\frac{2}{3}} x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} - 3 \, \left(-a b^{2}\right)^{\frac{2}{3}} x}{b x^{3} + a}\right) + {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} b x + \left(-a b^{2}\right)^{\frac{2}{3}}\right) - 2 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b x - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{54 \, {\left(a^{2} b^{5} x^{6} + 2 \, a^{3} b^{4} x^{3} + a^{4} b^{3}\right)}}, \frac{6 \, a b^{3} x^{5} - 3 \, a^{2} b^{2} x^{2} + 6 \, \sqrt{\frac{1}{3}} {\left(a b^{3} x^{6} + 2 \, a^{2} b^{2} x^{3} + a^{3} b\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, b x + \left(-a b^{2}\right)^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}}}{b}\right) + {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} b x + \left(-a b^{2}\right)^{\frac{2}{3}}\right) - 2 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b x - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{54 \, {\left(a^{2} b^{5} x^{6} + 2 \, a^{3} b^{4} x^{3} + a^{4} b^{3}\right)}}\right]"," ",0,"[1/54*(6*a*b^3*x^5 - 3*a^2*b^2*x^2 + 3*sqrt(1/3)*(a*b^3*x^6 + 2*a^2*b^2*x^3 + a^3*b)*sqrt((-a*b^2)^(1/3)/a)*log((2*b^2*x^3 - a*b + 3*sqrt(1/3)*(a*b*x + 2*(-a*b^2)^(2/3)*x^2 + (-a*b^2)^(1/3)*a)*sqrt((-a*b^2)^(1/3)/a) - 3*(-a*b^2)^(2/3)*x)/(b*x^3 + a)) + (b^2*x^6 + 2*a*b*x^3 + a^2)*(-a*b^2)^(2/3)*log(b^2*x^2 + (-a*b^2)^(1/3)*b*x + (-a*b^2)^(2/3)) - 2*(b^2*x^6 + 2*a*b*x^3 + a^2)*(-a*b^2)^(2/3)*log(b*x - (-a*b^2)^(1/3)))/(a^2*b^5*x^6 + 2*a^3*b^4*x^3 + a^4*b^3), 1/54*(6*a*b^3*x^5 - 3*a^2*b^2*x^2 + 6*sqrt(1/3)*(a*b^3*x^6 + 2*a^2*b^2*x^3 + a^3*b)*sqrt(-(-a*b^2)^(1/3)/a)*arctan(sqrt(1/3)*(2*b*x + (-a*b^2)^(1/3))*sqrt(-(-a*b^2)^(1/3)/a)/b) + (b^2*x^6 + 2*a*b*x^3 + a^2)*(-a*b^2)^(2/3)*log(b^2*x^2 + (-a*b^2)^(1/3)*b*x + (-a*b^2)^(2/3)) - 2*(b^2*x^6 + 2*a*b*x^3 + a^2)*(-a*b^2)^(2/3)*log(b*x - (-a*b^2)^(1/3)))/(a^2*b^5*x^6 + 2*a^3*b^4*x^3 + a^4*b^3)]","A",0
349,1,503,0,0.692939," ","integrate(x^3/(b*x^3+a)^3,x, algorithm=""fricas"")","\left[\frac{3 \, a^{2} b^{2} x^{4} - 6 \, a^{3} b x + 3 \, \sqrt{\frac{1}{3}} {\left(a b^{3} x^{6} + 2 \, a^{2} b^{2} x^{3} + a^{3} b\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \log\left(\frac{2 \, a b x^{3} - 3 \, \left(a^{2} b\right)^{\frac{1}{3}} a x - a^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, a b x^{2} + \left(a^{2} b\right)^{\frac{2}{3}} x - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{b x^{3} + a}\right) - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(a^{2} b\right)^{\frac{2}{3}} x + \left(a^{2} b\right)^{\frac{1}{3}} a\right) + 2 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(a^{2} b\right)^{\frac{2}{3}}\right)}{54 \, {\left(a^{3} b^{4} x^{6} + 2 \, a^{4} b^{3} x^{3} + a^{5} b^{2}\right)}}, \frac{3 \, a^{2} b^{2} x^{4} - 6 \, a^{3} b x + 6 \, \sqrt{\frac{1}{3}} {\left(a b^{3} x^{6} + 2 \, a^{2} b^{2} x^{3} + a^{3} b\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(a^{2} b\right)^{\frac{2}{3}} x - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{a^{2}}\right) - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(a^{2} b\right)^{\frac{2}{3}} x + \left(a^{2} b\right)^{\frac{1}{3}} a\right) + 2 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(a^{2} b\right)^{\frac{2}{3}}\right)}{54 \, {\left(a^{3} b^{4} x^{6} + 2 \, a^{4} b^{3} x^{3} + a^{5} b^{2}\right)}}\right]"," ",0,"[1/54*(3*a^2*b^2*x^4 - 6*a^3*b*x + 3*sqrt(1/3)*(a*b^3*x^6 + 2*a^2*b^2*x^3 + a^3*b)*sqrt(-(a^2*b)^(1/3)/b)*log((2*a*b*x^3 - 3*(a^2*b)^(1/3)*a*x - a^2 + 3*sqrt(1/3)*(2*a*b*x^2 + (a^2*b)^(2/3)*x - (a^2*b)^(1/3)*a)*sqrt(-(a^2*b)^(1/3)/b))/(b*x^3 + a)) - (b^2*x^6 + 2*a*b*x^3 + a^2)*(a^2*b)^(2/3)*log(a*b*x^2 - (a^2*b)^(2/3)*x + (a^2*b)^(1/3)*a) + 2*(b^2*x^6 + 2*a*b*x^3 + a^2)*(a^2*b)^(2/3)*log(a*b*x + (a^2*b)^(2/3)))/(a^3*b^4*x^6 + 2*a^4*b^3*x^3 + a^5*b^2), 1/54*(3*a^2*b^2*x^4 - 6*a^3*b*x + 6*sqrt(1/3)*(a*b^3*x^6 + 2*a^2*b^2*x^3 + a^3*b)*sqrt((a^2*b)^(1/3)/b)*arctan(sqrt(1/3)*(2*(a^2*b)^(2/3)*x - (a^2*b)^(1/3)*a)*sqrt((a^2*b)^(1/3)/b)/a^2) - (b^2*x^6 + 2*a*b*x^3 + a^2)*(a^2*b)^(2/3)*log(a*b*x^2 - (a^2*b)^(2/3)*x + (a^2*b)^(1/3)*a) + 2*(b^2*x^6 + 2*a*b*x^3 + a^2)*(a^2*b)^(2/3)*log(a*b*x + (a^2*b)^(2/3)))/(a^3*b^4*x^6 + 2*a^4*b^3*x^3 + a^5*b^2)]","B",0
350,1,514,0,1.084488," ","integrate(x/(b*x^3+a)^3,x, algorithm=""fricas"")","\left[\frac{12 \, a b^{3} x^{5} + 21 \, a^{2} b^{2} x^{2} + 6 \, \sqrt{\frac{1}{3}} {\left(a b^{3} x^{6} + 2 \, a^{2} b^{2} x^{3} + a^{3} b\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \log\left(\frac{2 \, b^{2} x^{3} - a b + 3 \, \sqrt{\frac{1}{3}} {\left(a b x + 2 \, \left(-a b^{2}\right)^{\frac{2}{3}} x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} - 3 \, \left(-a b^{2}\right)^{\frac{2}{3}} x}{b x^{3} + a}\right) + 2 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} b x + \left(-a b^{2}\right)^{\frac{2}{3}}\right) - 4 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b x - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{54 \, {\left(a^{3} b^{4} x^{6} + 2 \, a^{4} b^{3} x^{3} + a^{5} b^{2}\right)}}, \frac{12 \, a b^{3} x^{5} + 21 \, a^{2} b^{2} x^{2} + 12 \, \sqrt{\frac{1}{3}} {\left(a b^{3} x^{6} + 2 \, a^{2} b^{2} x^{3} + a^{3} b\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, b x + \left(-a b^{2}\right)^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}}}{b}\right) + 2 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} b x + \left(-a b^{2}\right)^{\frac{2}{3}}\right) - 4 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b x - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{54 \, {\left(a^{3} b^{4} x^{6} + 2 \, a^{4} b^{3} x^{3} + a^{5} b^{2}\right)}}\right]"," ",0,"[1/54*(12*a*b^3*x^5 + 21*a^2*b^2*x^2 + 6*sqrt(1/3)*(a*b^3*x^6 + 2*a^2*b^2*x^3 + a^3*b)*sqrt((-a*b^2)^(1/3)/a)*log((2*b^2*x^3 - a*b + 3*sqrt(1/3)*(a*b*x + 2*(-a*b^2)^(2/3)*x^2 + (-a*b^2)^(1/3)*a)*sqrt((-a*b^2)^(1/3)/a) - 3*(-a*b^2)^(2/3)*x)/(b*x^3 + a)) + 2*(b^2*x^6 + 2*a*b*x^3 + a^2)*(-a*b^2)^(2/3)*log(b^2*x^2 + (-a*b^2)^(1/3)*b*x + (-a*b^2)^(2/3)) - 4*(b^2*x^6 + 2*a*b*x^3 + a^2)*(-a*b^2)^(2/3)*log(b*x - (-a*b^2)^(1/3)))/(a^3*b^4*x^6 + 2*a^4*b^3*x^3 + a^5*b^2), 1/54*(12*a*b^3*x^5 + 21*a^2*b^2*x^2 + 12*sqrt(1/3)*(a*b^3*x^6 + 2*a^2*b^2*x^3 + a^3*b)*sqrt(-(-a*b^2)^(1/3)/a)*arctan(sqrt(1/3)*(2*b*x + (-a*b^2)^(1/3))*sqrt(-(-a*b^2)^(1/3)/a)/b) + 2*(b^2*x^6 + 2*a*b*x^3 + a^2)*(-a*b^2)^(2/3)*log(b^2*x^2 + (-a*b^2)^(1/3)*b*x + (-a*b^2)^(2/3)) - 4*(b^2*x^6 + 2*a*b*x^3 + a^2)*(-a*b^2)^(2/3)*log(b*x - (-a*b^2)^(1/3)))/(a^3*b^4*x^6 + 2*a^4*b^3*x^3 + a^5*b^2)]","B",0
351,1,499,0,0.949862," ","integrate(1/(b*x^3+a)^3,x, algorithm=""fricas"")","\left[\frac{15 \, a^{2} b^{2} x^{4} + 24 \, a^{3} b x + 15 \, \sqrt{\frac{1}{3}} {\left(a b^{3} x^{6} + 2 \, a^{2} b^{2} x^{3} + a^{3} b\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \log\left(\frac{2 \, a b x^{3} - 3 \, \left(a^{2} b\right)^{\frac{1}{3}} a x - a^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, a b x^{2} + \left(a^{2} b\right)^{\frac{2}{3}} x - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{b x^{3} + a}\right) - 5 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(a^{2} b\right)^{\frac{2}{3}} x + \left(a^{2} b\right)^{\frac{1}{3}} a\right) + 10 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(a^{2} b\right)^{\frac{2}{3}}\right)}{54 \, {\left(a^{4} b^{3} x^{6} + 2 \, a^{5} b^{2} x^{3} + a^{6} b\right)}}, \frac{15 \, a^{2} b^{2} x^{4} + 24 \, a^{3} b x + 30 \, \sqrt{\frac{1}{3}} {\left(a b^{3} x^{6} + 2 \, a^{2} b^{2} x^{3} + a^{3} b\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(a^{2} b\right)^{\frac{2}{3}} x - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{a^{2}}\right) - 5 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(a^{2} b\right)^{\frac{2}{3}} x + \left(a^{2} b\right)^{\frac{1}{3}} a\right) + 10 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(a^{2} b\right)^{\frac{2}{3}}\right)}{54 \, {\left(a^{4} b^{3} x^{6} + 2 \, a^{5} b^{2} x^{3} + a^{6} b\right)}}\right]"," ",0,"[1/54*(15*a^2*b^2*x^4 + 24*a^3*b*x + 15*sqrt(1/3)*(a*b^3*x^6 + 2*a^2*b^2*x^3 + a^3*b)*sqrt(-(a^2*b)^(1/3)/b)*log((2*a*b*x^3 - 3*(a^2*b)^(1/3)*a*x - a^2 + 3*sqrt(1/3)*(2*a*b*x^2 + (a^2*b)^(2/3)*x - (a^2*b)^(1/3)*a)*sqrt(-(a^2*b)^(1/3)/b))/(b*x^3 + a)) - 5*(b^2*x^6 + 2*a*b*x^3 + a^2)*(a^2*b)^(2/3)*log(a*b*x^2 - (a^2*b)^(2/3)*x + (a^2*b)^(1/3)*a) + 10*(b^2*x^6 + 2*a*b*x^3 + a^2)*(a^2*b)^(2/3)*log(a*b*x + (a^2*b)^(2/3)))/(a^4*b^3*x^6 + 2*a^5*b^2*x^3 + a^6*b), 1/54*(15*a^2*b^2*x^4 + 24*a^3*b*x + 30*sqrt(1/3)*(a*b^3*x^6 + 2*a^2*b^2*x^3 + a^3*b)*sqrt((a^2*b)^(1/3)/b)*arctan(sqrt(1/3)*(2*(a^2*b)^(2/3)*x - (a^2*b)^(1/3)*a)*sqrt((a^2*b)^(1/3)/b)/a^2) - 5*(b^2*x^6 + 2*a*b*x^3 + a^2)*(a^2*b)^(2/3)*log(a*b*x^2 - (a^2*b)^(2/3)*x + (a^2*b)^(1/3)*a) + 10*(b^2*x^6 + 2*a*b*x^3 + a^2)*(a^2*b)^(2/3)*log(a*b*x + (a^2*b)^(2/3)))/(a^4*b^3*x^6 + 2*a^5*b^2*x^3 + a^6*b)]","B",0
352,1,35,0,0.975012," ","integrate(x^8/(-b*x^3+a),x, algorithm=""fricas"")","-\frac{b^{2} x^{6} + 2 \, a b x^{3} + 2 \, a^{2} \log\left(b x^{3} - a\right)}{6 \, b^{3}}"," ",0,"-1/6*(b^2*x^6 + 2*a*b*x^3 + 2*a^2*log(b*x^3 - a))/b^3","A",0
353,1,23,0,0.784863," ","integrate(x^5/(-b*x^3+a),x, algorithm=""fricas"")","-\frac{b x^{3} + a \log\left(b x^{3} - a\right)}{3 \, b^{2}}"," ",0,"-1/3*(b*x^3 + a*log(b*x^3 - a))/b^2","A",0
354,1,15,0,0.922639," ","integrate(x^2/(-b*x^3+a),x, algorithm=""fricas"")","-\frac{\log\left(b x^{3} - a\right)}{3 \, b}"," ",0,"-1/3*log(b*x^3 - a)/b","A",0
355,1,20,0,1.006310," ","integrate(1/x/(-b*x^3+a),x, algorithm=""fricas"")","-\frac{\log\left(b x^{3} - a\right) - 3 \, \log\left(x\right)}{3 \, a}"," ",0,"-1/3*(log(b*x^3 - a) - 3*log(x))/a","A",0
356,1,33,0,0.936420," ","integrate(1/x^4/(-b*x^3+a),x, algorithm=""fricas"")","-\frac{b x^{3} \log\left(b x^{3} - a\right) - 3 \, b x^{3} \log\left(x\right) + a}{3 \, a^{2} x^{3}}"," ",0,"-1/3*(b*x^3*log(b*x^3 - a) - 3*b*x^3*log(x) + a)/(a^2*x^3)","A",0
357,1,130,0,1.006621," ","integrate(x^4/(-b*x^3+a),x, algorithm=""fricas"")","-\frac{3 \, x^{2} + 2 \, \sqrt{3} \left(-\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} b x \left(-\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}} - \sqrt{3} a}{3 \, a}\right) + \left(-\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}} \log\left(a x^{2} + b x \left(-\frac{a^{2}}{b^{2}}\right)^{\frac{2}{3}} - a \left(-\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}}\right) - 2 \, \left(-\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}} \log\left(a x - b \left(-\frac{a^{2}}{b^{2}}\right)^{\frac{2}{3}}\right)}{6 \, b}"," ",0,"-1/6*(3*x^2 + 2*sqrt(3)*(-a^2/b^2)^(1/3)*arctan(1/3*(2*sqrt(3)*b*x*(-a^2/b^2)^(1/3) - sqrt(3)*a)/a) + (-a^2/b^2)^(1/3)*log(a*x^2 + b*x*(-a^2/b^2)^(2/3) - a*(-a^2/b^2)^(1/3)) - 2*(-a^2/b^2)^(1/3)*log(a*x - b*(-a^2/b^2)^(2/3)))/b","A",0
358,1,103,0,0.952578," ","integrate(x^3/(-b*x^3+a),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} b x \left(-\frac{a}{b}\right)^{\frac{2}{3}} + \sqrt{3} a}{3 \, a}\right) + \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left(x^{2} - x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right) - 2 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left(x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right) + 6 \, x}{6 \, b}"," ",0,"-1/6*(2*sqrt(3)*(-a/b)^(1/3)*arctan(1/3*(2*sqrt(3)*b*x*(-a/b)^(2/3) + sqrt(3)*a)/a) + (-a/b)^(1/3)*log(x^2 - x*(-a/b)^(1/3) + (-a/b)^(2/3)) - 2*(-a/b)^(1/3)*log(x + (-a/b)^(1/3)) + 6*x)/b","A",0
359,1,307,0,1.002984," ","integrate(x/(-b*x^3+a),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{\frac{1}{3}} a b \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \log\left(\frac{2 \, b^{2} x^{3} + a b + 3 \, \sqrt{\frac{1}{3}} {\left(a b x - 2 \, \left(-a b^{2}\right)^{\frac{2}{3}} x^{2} - \left(-a b^{2}\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} - 3 \, \left(-a b^{2}\right)^{\frac{2}{3}} x}{b x^{3} - a}\right) + \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} x^{2} - \left(-a b^{2}\right)^{\frac{1}{3}} b x + \left(-a b^{2}\right)^{\frac{2}{3}}\right) - 2 \, \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b x + \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{6 \, a b^{2}}, \frac{6 \, \sqrt{\frac{1}{3}} a b \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \arctan\left(-\frac{\sqrt{\frac{1}{3}} {\left(2 \, b x - \left(-a b^{2}\right)^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}}}{b}\right) + \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} x^{2} - \left(-a b^{2}\right)^{\frac{1}{3}} b x + \left(-a b^{2}\right)^{\frac{2}{3}}\right) - 2 \, \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b x + \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{6 \, a b^{2}}\right]"," ",0,"[1/6*(3*sqrt(1/3)*a*b*sqrt((-a*b^2)^(1/3)/a)*log((2*b^2*x^3 + a*b + 3*sqrt(1/3)*(a*b*x - 2*(-a*b^2)^(2/3)*x^2 - (-a*b^2)^(1/3)*a)*sqrt((-a*b^2)^(1/3)/a) - 3*(-a*b^2)^(2/3)*x)/(b*x^3 - a)) + (-a*b^2)^(2/3)*log(b^2*x^2 - (-a*b^2)^(1/3)*b*x + (-a*b^2)^(2/3)) - 2*(-a*b^2)^(2/3)*log(b*x + (-a*b^2)^(1/3)))/(a*b^2), 1/6*(6*sqrt(1/3)*a*b*sqrt(-(-a*b^2)^(1/3)/a)*arctan(-sqrt(1/3)*(2*b*x - (-a*b^2)^(1/3))*sqrt(-(-a*b^2)^(1/3)/a)/b) + (-a*b^2)^(2/3)*log(b^2*x^2 - (-a*b^2)^(1/3)*b*x + (-a*b^2)^(2/3)) - 2*(-a*b^2)^(2/3)*log(b*x + (-a*b^2)^(1/3)))/(a*b^2)]","A",0
360,1,320,0,0.825944," ","integrate(1/(-b*x^3+a),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{\frac{1}{3}} a b \sqrt{\frac{\left(-a^{2} b\right)^{\frac{1}{3}}}{b}} \log\left(\frac{2 \, a b x^{3} + 3 \, \left(-a^{2} b\right)^{\frac{1}{3}} a x + a^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, a b x^{2} - \left(-a^{2} b\right)^{\frac{2}{3}} x + \left(-a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(-a^{2} b\right)^{\frac{1}{3}}}{b}}}{b x^{3} - a}\right) + \left(-a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} + \left(-a^{2} b\right)^{\frac{2}{3}} x - \left(-a^{2} b\right)^{\frac{1}{3}} a\right) - 2 \, \left(-a^{2} b\right)^{\frac{2}{3}} \log\left(a b x - \left(-a^{2} b\right)^{\frac{2}{3}}\right)}{6 \, a^{2} b}, \frac{6 \, \sqrt{\frac{1}{3}} a b \sqrt{-\frac{\left(-a^{2} b\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(-a^{2} b\right)^{\frac{2}{3}} x - \left(-a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{-\frac{\left(-a^{2} b\right)^{\frac{1}{3}}}{b}}}{a^{2}}\right) + \left(-a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} + \left(-a^{2} b\right)^{\frac{2}{3}} x - \left(-a^{2} b\right)^{\frac{1}{3}} a\right) - 2 \, \left(-a^{2} b\right)^{\frac{2}{3}} \log\left(a b x - \left(-a^{2} b\right)^{\frac{2}{3}}\right)}{6 \, a^{2} b}\right]"," ",0,"[1/6*(3*sqrt(1/3)*a*b*sqrt((-a^2*b)^(1/3)/b)*log((2*a*b*x^3 + 3*(-a^2*b)^(1/3)*a*x + a^2 + 3*sqrt(1/3)*(2*a*b*x^2 - (-a^2*b)^(2/3)*x + (-a^2*b)^(1/3)*a)*sqrt((-a^2*b)^(1/3)/b))/(b*x^3 - a)) + (-a^2*b)^(2/3)*log(a*b*x^2 + (-a^2*b)^(2/3)*x - (-a^2*b)^(1/3)*a) - 2*(-a^2*b)^(2/3)*log(a*b*x - (-a^2*b)^(2/3)))/(a^2*b), 1/6*(6*sqrt(1/3)*a*b*sqrt(-(-a^2*b)^(1/3)/b)*arctan(sqrt(1/3)*(2*(-a^2*b)^(2/3)*x - (-a^2*b)^(1/3)*a)*sqrt(-(-a^2*b)^(1/3)/b)/a^2) + (-a^2*b)^(2/3)*log(a*b*x^2 + (-a^2*b)^(2/3)*x - (-a^2*b)^(1/3)*a) - 2*(-a^2*b)^(2/3)*log(a*b*x - (-a^2*b)^(2/3)))/(a^2*b)]","A",0
361,1,111,0,0.719958," ","integrate(1/x^2/(-b*x^3+a),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} x \left(-\frac{b}{a}\right)^{\frac{1}{3}} \arctan\left(\frac{2}{3} \, \sqrt{3} x \left(-\frac{b}{a}\right)^{\frac{1}{3}} - \frac{1}{3} \, \sqrt{3}\right) + x \left(-\frac{b}{a}\right)^{\frac{1}{3}} \log\left(b x^{2} + a x \left(-\frac{b}{a}\right)^{\frac{2}{3}} - a \left(-\frac{b}{a}\right)^{\frac{1}{3}}\right) - 2 \, x \left(-\frac{b}{a}\right)^{\frac{1}{3}} \log\left(b x - a \left(-\frac{b}{a}\right)^{\frac{2}{3}}\right) + 6}{6 \, a x}"," ",0,"-1/6*(2*sqrt(3)*x*(-b/a)^(1/3)*arctan(2/3*sqrt(3)*x*(-b/a)^(1/3) - 1/3*sqrt(3)) + x*(-b/a)^(1/3)*log(b*x^2 + a*x*(-b/a)^(2/3) - a*(-b/a)^(1/3)) - 2*x*(-b/a)^(1/3)*log(b*x - a*(-b/a)^(2/3)) + 6)/(a*x)","A",0
362,1,141,0,1.008793," ","integrate(1/x^3/(-b*x^3+a),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} x^{2} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} a x \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}} + \sqrt{3} b}{3 \, b}\right) + x^{2} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b^{2} x^{2} - a b x \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} + a^{2} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}}\right) - 2 \, x^{2} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b x + a \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}}\right) + 3}{6 \, a x^{2}}"," ",0,"-1/6*(2*sqrt(3)*x^2*(-b^2/a^2)^(1/3)*arctan(1/3*(2*sqrt(3)*a*x*(-b^2/a^2)^(2/3) + sqrt(3)*b)/b) + x^2*(-b^2/a^2)^(1/3)*log(b^2*x^2 - a*b*x*(-b^2/a^2)^(1/3) + a^2*(-b^2/a^2)^(2/3)) - 2*x^2*(-b^2/a^2)^(1/3)*log(b*x + a*(-b^2/a^2)^(1/3)) + 3)/(a*x^2)","A",0
363,1,446,0,1.091816," ","integrate(1/(b*x^3+a+1),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{\frac{1}{3}} {\left(a + 1\right)} b \sqrt{-\frac{\left({\left(a^{2} + 2 \, a + 1\right)} b\right)^{\frac{1}{3}}}{b}} \log\left(\frac{2 \, {\left(a + 1\right)} b x^{3} - 3 \, \left({\left(a^{2} + 2 \, a + 1\right)} b\right)^{\frac{1}{3}} {\left(a + 1\right)} x - a^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, {\left(a + 1\right)} b x^{2} + \left({\left(a^{2} + 2 \, a + 1\right)} b\right)^{\frac{2}{3}} x - \left({\left(a^{2} + 2 \, a + 1\right)} b\right)^{\frac{1}{3}} {\left(a + 1\right)}\right)} \sqrt{-\frac{\left({\left(a^{2} + 2 \, a + 1\right)} b\right)^{\frac{1}{3}}}{b}} - 2 \, a - 1}{b x^{3} + a + 1}\right) - \left({\left(a^{2} + 2 \, a + 1\right)} b\right)^{\frac{2}{3}} \log\left({\left(a + 1\right)} b x^{2} - \left({\left(a^{2} + 2 \, a + 1\right)} b\right)^{\frac{2}{3}} x + \left({\left(a^{2} + 2 \, a + 1\right)} b\right)^{\frac{1}{3}} {\left(a + 1\right)}\right) + 2 \, \left({\left(a^{2} + 2 \, a + 1\right)} b\right)^{\frac{2}{3}} \log\left({\left(a + 1\right)} b x + \left({\left(a^{2} + 2 \, a + 1\right)} b\right)^{\frac{2}{3}}\right)}{6 \, {\left(a^{2} + 2 \, a + 1\right)} b}, \frac{6 \, \sqrt{\frac{1}{3}} {\left(a + 1\right)} b \sqrt{\frac{\left({\left(a^{2} + 2 \, a + 1\right)} b\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left({\left(a^{2} + 2 \, a + 1\right)} b\right)^{\frac{2}{3}} x - \left({\left(a^{2} + 2 \, a + 1\right)} b\right)^{\frac{1}{3}} {\left(a + 1\right)}\right)} \sqrt{\frac{\left({\left(a^{2} + 2 \, a + 1\right)} b\right)^{\frac{1}{3}}}{b}}}{a^{2} + 2 \, a + 1}\right) - \left({\left(a^{2} + 2 \, a + 1\right)} b\right)^{\frac{2}{3}} \log\left({\left(a + 1\right)} b x^{2} - \left({\left(a^{2} + 2 \, a + 1\right)} b\right)^{\frac{2}{3}} x + \left({\left(a^{2} + 2 \, a + 1\right)} b\right)^{\frac{1}{3}} {\left(a + 1\right)}\right) + 2 \, \left({\left(a^{2} + 2 \, a + 1\right)} b\right)^{\frac{2}{3}} \log\left({\left(a + 1\right)} b x + \left({\left(a^{2} + 2 \, a + 1\right)} b\right)^{\frac{2}{3}}\right)}{6 \, {\left(a^{2} + 2 \, a + 1\right)} b}\right]"," ",0,"[1/6*(3*sqrt(1/3)*(a + 1)*b*sqrt(-((a^2 + 2*a + 1)*b)^(1/3)/b)*log((2*(a + 1)*b*x^3 - 3*((a^2 + 2*a + 1)*b)^(1/3)*(a + 1)*x - a^2 + 3*sqrt(1/3)*(2*(a + 1)*b*x^2 + ((a^2 + 2*a + 1)*b)^(2/3)*x - ((a^2 + 2*a + 1)*b)^(1/3)*(a + 1))*sqrt(-((a^2 + 2*a + 1)*b)^(1/3)/b) - 2*a - 1)/(b*x^3 + a + 1)) - ((a^2 + 2*a + 1)*b)^(2/3)*log((a + 1)*b*x^2 - ((a^2 + 2*a + 1)*b)^(2/3)*x + ((a^2 + 2*a + 1)*b)^(1/3)*(a + 1)) + 2*((a^2 + 2*a + 1)*b)^(2/3)*log((a + 1)*b*x + ((a^2 + 2*a + 1)*b)^(2/3)))/((a^2 + 2*a + 1)*b), 1/6*(6*sqrt(1/3)*(a + 1)*b*sqrt(((a^2 + 2*a + 1)*b)^(1/3)/b)*arctan(sqrt(1/3)*(2*((a^2 + 2*a + 1)*b)^(2/3)*x - ((a^2 + 2*a + 1)*b)^(1/3)*(a + 1))*sqrt(((a^2 + 2*a + 1)*b)^(1/3)/b)/(a^2 + 2*a + 1)) - ((a^2 + 2*a + 1)*b)^(2/3)*log((a + 1)*b*x^2 - ((a^2 + 2*a + 1)*b)^(2/3)*x + ((a^2 + 2*a + 1)*b)^(1/3)*(a + 1)) + 2*((a^2 + 2*a + 1)*b)^(2/3)*log((a + 1)*b*x + ((a^2 + 2*a + 1)*b)^(2/3)))/((a^2 + 2*a + 1)*b)]","B",0
364,1,467,0,1.148913," ","integrate(1/(-b*x^3+a+1),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{\frac{1}{3}} {\left(a + 1\right)} b \sqrt{\frac{\left(-{\left(a^{2} + 2 \, a + 1\right)} b\right)^{\frac{1}{3}}}{b}} \log\left(\frac{2 \, {\left(a + 1\right)} b x^{3} + 3 \, \left(-{\left(a^{2} + 2 \, a + 1\right)} b\right)^{\frac{1}{3}} {\left(a + 1\right)} x + a^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, {\left(a + 1\right)} b x^{2} - \left(-{\left(a^{2} + 2 \, a + 1\right)} b\right)^{\frac{2}{3}} x + \left(-{\left(a^{2} + 2 \, a + 1\right)} b\right)^{\frac{1}{3}} {\left(a + 1\right)}\right)} \sqrt{\frac{\left(-{\left(a^{2} + 2 \, a + 1\right)} b\right)^{\frac{1}{3}}}{b}} + 2 \, a + 1}{b x^{3} - a - 1}\right) + \left(-{\left(a^{2} + 2 \, a + 1\right)} b\right)^{\frac{2}{3}} \log\left({\left(a + 1\right)} b x^{2} + \left(-{\left(a^{2} + 2 \, a + 1\right)} b\right)^{\frac{2}{3}} x - \left(-{\left(a^{2} + 2 \, a + 1\right)} b\right)^{\frac{1}{3}} {\left(a + 1\right)}\right) - 2 \, \left(-{\left(a^{2} + 2 \, a + 1\right)} b\right)^{\frac{2}{3}} \log\left({\left(a + 1\right)} b x - \left(-{\left(a^{2} + 2 \, a + 1\right)} b\right)^{\frac{2}{3}}\right)}{6 \, {\left(a^{2} + 2 \, a + 1\right)} b}, \frac{6 \, \sqrt{\frac{1}{3}} {\left(a + 1\right)} b \sqrt{-\frac{\left(-{\left(a^{2} + 2 \, a + 1\right)} b\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(-{\left(a^{2} + 2 \, a + 1\right)} b\right)^{\frac{2}{3}} x - \left(-{\left(a^{2} + 2 \, a + 1\right)} b\right)^{\frac{1}{3}} {\left(a + 1\right)}\right)} \sqrt{-\frac{\left(-{\left(a^{2} + 2 \, a + 1\right)} b\right)^{\frac{1}{3}}}{b}}}{a^{2} + 2 \, a + 1}\right) + \left(-{\left(a^{2} + 2 \, a + 1\right)} b\right)^{\frac{2}{3}} \log\left({\left(a + 1\right)} b x^{2} + \left(-{\left(a^{2} + 2 \, a + 1\right)} b\right)^{\frac{2}{3}} x - \left(-{\left(a^{2} + 2 \, a + 1\right)} b\right)^{\frac{1}{3}} {\left(a + 1\right)}\right) - 2 \, \left(-{\left(a^{2} + 2 \, a + 1\right)} b\right)^{\frac{2}{3}} \log\left({\left(a + 1\right)} b x - \left(-{\left(a^{2} + 2 \, a + 1\right)} b\right)^{\frac{2}{3}}\right)}{6 \, {\left(a^{2} + 2 \, a + 1\right)} b}\right]"," ",0,"[1/6*(3*sqrt(1/3)*(a + 1)*b*sqrt((-(a^2 + 2*a + 1)*b)^(1/3)/b)*log((2*(a + 1)*b*x^3 + 3*(-(a^2 + 2*a + 1)*b)^(1/3)*(a + 1)*x + a^2 + 3*sqrt(1/3)*(2*(a + 1)*b*x^2 - (-(a^2 + 2*a + 1)*b)^(2/3)*x + (-(a^2 + 2*a + 1)*b)^(1/3)*(a + 1))*sqrt((-(a^2 + 2*a + 1)*b)^(1/3)/b) + 2*a + 1)/(b*x^3 - a - 1)) + (-(a^2 + 2*a + 1)*b)^(2/3)*log((a + 1)*b*x^2 + (-(a^2 + 2*a + 1)*b)^(2/3)*x - (-(a^2 + 2*a + 1)*b)^(1/3)*(a + 1)) - 2*(-(a^2 + 2*a + 1)*b)^(2/3)*log((a + 1)*b*x - (-(a^2 + 2*a + 1)*b)^(2/3)))/((a^2 + 2*a + 1)*b), 1/6*(6*sqrt(1/3)*(a + 1)*b*sqrt(-(-(a^2 + 2*a + 1)*b)^(1/3)/b)*arctan(sqrt(1/3)*(2*(-(a^2 + 2*a + 1)*b)^(2/3)*x - (-(a^2 + 2*a + 1)*b)^(1/3)*(a + 1))*sqrt(-(-(a^2 + 2*a + 1)*b)^(1/3)/b)/(a^2 + 2*a + 1)) + (-(a^2 + 2*a + 1)*b)^(2/3)*log((a + 1)*b*x^2 + (-(a^2 + 2*a + 1)*b)^(2/3)*x - (-(a^2 + 2*a + 1)*b)^(1/3)*(a + 1)) - 2*(-(a^2 + 2*a + 1)*b)^(2/3)*log((a + 1)*b*x - (-(a^2 + 2*a + 1)*b)^(2/3)))/((a^2 + 2*a + 1)*b)]","B",0
365,1,446,0,1.171452," ","integrate(1/(b*x^3+a-1),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{\frac{1}{3}} {\left(a - 1\right)} b \sqrt{-\frac{\left({\left(a^{2} - 2 \, a + 1\right)} b\right)^{\frac{1}{3}}}{b}} \log\left(\frac{2 \, {\left(a - 1\right)} b x^{3} - 3 \, \left({\left(a^{2} - 2 \, a + 1\right)} b\right)^{\frac{1}{3}} {\left(a - 1\right)} x - a^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, {\left(a - 1\right)} b x^{2} + \left({\left(a^{2} - 2 \, a + 1\right)} b\right)^{\frac{2}{3}} x - \left({\left(a^{2} - 2 \, a + 1\right)} b\right)^{\frac{1}{3}} {\left(a - 1\right)}\right)} \sqrt{-\frac{\left({\left(a^{2} - 2 \, a + 1\right)} b\right)^{\frac{1}{3}}}{b}} + 2 \, a - 1}{b x^{3} + a - 1}\right) - \left({\left(a^{2} - 2 \, a + 1\right)} b\right)^{\frac{2}{3}} \log\left({\left(a - 1\right)} b x^{2} - \left({\left(a^{2} - 2 \, a + 1\right)} b\right)^{\frac{2}{3}} x + \left({\left(a^{2} - 2 \, a + 1\right)} b\right)^{\frac{1}{3}} {\left(a - 1\right)}\right) + 2 \, \left({\left(a^{2} - 2 \, a + 1\right)} b\right)^{\frac{2}{3}} \log\left({\left(a - 1\right)} b x + \left({\left(a^{2} - 2 \, a + 1\right)} b\right)^{\frac{2}{3}}\right)}{6 \, {\left(a^{2} - 2 \, a + 1\right)} b}, \frac{6 \, \sqrt{\frac{1}{3}} {\left(a - 1\right)} b \sqrt{\frac{\left({\left(a^{2} - 2 \, a + 1\right)} b\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left({\left(a^{2} - 2 \, a + 1\right)} b\right)^{\frac{2}{3}} x - \left({\left(a^{2} - 2 \, a + 1\right)} b\right)^{\frac{1}{3}} {\left(a - 1\right)}\right)} \sqrt{\frac{\left({\left(a^{2} - 2 \, a + 1\right)} b\right)^{\frac{1}{3}}}{b}}}{a^{2} - 2 \, a + 1}\right) - \left({\left(a^{2} - 2 \, a + 1\right)} b\right)^{\frac{2}{3}} \log\left({\left(a - 1\right)} b x^{2} - \left({\left(a^{2} - 2 \, a + 1\right)} b\right)^{\frac{2}{3}} x + \left({\left(a^{2} - 2 \, a + 1\right)} b\right)^{\frac{1}{3}} {\left(a - 1\right)}\right) + 2 \, \left({\left(a^{2} - 2 \, a + 1\right)} b\right)^{\frac{2}{3}} \log\left({\left(a - 1\right)} b x + \left({\left(a^{2} - 2 \, a + 1\right)} b\right)^{\frac{2}{3}}\right)}{6 \, {\left(a^{2} - 2 \, a + 1\right)} b}\right]"," ",0,"[1/6*(3*sqrt(1/3)*(a - 1)*b*sqrt(-((a^2 - 2*a + 1)*b)^(1/3)/b)*log((2*(a - 1)*b*x^3 - 3*((a^2 - 2*a + 1)*b)^(1/3)*(a - 1)*x - a^2 + 3*sqrt(1/3)*(2*(a - 1)*b*x^2 + ((a^2 - 2*a + 1)*b)^(2/3)*x - ((a^2 - 2*a + 1)*b)^(1/3)*(a - 1))*sqrt(-((a^2 - 2*a + 1)*b)^(1/3)/b) + 2*a - 1)/(b*x^3 + a - 1)) - ((a^2 - 2*a + 1)*b)^(2/3)*log((a - 1)*b*x^2 - ((a^2 - 2*a + 1)*b)^(2/3)*x + ((a^2 - 2*a + 1)*b)^(1/3)*(a - 1)) + 2*((a^2 - 2*a + 1)*b)^(2/3)*log((a - 1)*b*x + ((a^2 - 2*a + 1)*b)^(2/3)))/((a^2 - 2*a + 1)*b), 1/6*(6*sqrt(1/3)*(a - 1)*b*sqrt(((a^2 - 2*a + 1)*b)^(1/3)/b)*arctan(sqrt(1/3)*(2*((a^2 - 2*a + 1)*b)^(2/3)*x - ((a^2 - 2*a + 1)*b)^(1/3)*(a - 1))*sqrt(((a^2 - 2*a + 1)*b)^(1/3)/b)/(a^2 - 2*a + 1)) - ((a^2 - 2*a + 1)*b)^(2/3)*log((a - 1)*b*x^2 - ((a^2 - 2*a + 1)*b)^(2/3)*x + ((a^2 - 2*a + 1)*b)^(1/3)*(a - 1)) + 2*((a^2 - 2*a + 1)*b)^(2/3)*log((a - 1)*b*x + ((a^2 - 2*a + 1)*b)^(2/3)))/((a^2 - 2*a + 1)*b)]","A",0
366,1,467,0,1.103997," ","integrate(1/(-b*x^3+a-1),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{\frac{1}{3}} {\left(a - 1\right)} b \sqrt{\frac{\left(-{\left(a^{2} - 2 \, a + 1\right)} b\right)^{\frac{1}{3}}}{b}} \log\left(\frac{2 \, {\left(a - 1\right)} b x^{3} + 3 \, \left(-{\left(a^{2} - 2 \, a + 1\right)} b\right)^{\frac{1}{3}} {\left(a - 1\right)} x + a^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, {\left(a - 1\right)} b x^{2} - \left(-{\left(a^{2} - 2 \, a + 1\right)} b\right)^{\frac{2}{3}} x + \left(-{\left(a^{2} - 2 \, a + 1\right)} b\right)^{\frac{1}{3}} {\left(a - 1\right)}\right)} \sqrt{\frac{\left(-{\left(a^{2} - 2 \, a + 1\right)} b\right)^{\frac{1}{3}}}{b}} - 2 \, a + 1}{b x^{3} - a + 1}\right) + \left(-{\left(a^{2} - 2 \, a + 1\right)} b\right)^{\frac{2}{3}} \log\left({\left(a - 1\right)} b x^{2} + \left(-{\left(a^{2} - 2 \, a + 1\right)} b\right)^{\frac{2}{3}} x - \left(-{\left(a^{2} - 2 \, a + 1\right)} b\right)^{\frac{1}{3}} {\left(a - 1\right)}\right) - 2 \, \left(-{\left(a^{2} - 2 \, a + 1\right)} b\right)^{\frac{2}{3}} \log\left({\left(a - 1\right)} b x - \left(-{\left(a^{2} - 2 \, a + 1\right)} b\right)^{\frac{2}{3}}\right)}{6 \, {\left(a^{2} - 2 \, a + 1\right)} b}, \frac{6 \, \sqrt{\frac{1}{3}} {\left(a - 1\right)} b \sqrt{-\frac{\left(-{\left(a^{2} - 2 \, a + 1\right)} b\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(-{\left(a^{2} - 2 \, a + 1\right)} b\right)^{\frac{2}{3}} x - \left(-{\left(a^{2} - 2 \, a + 1\right)} b\right)^{\frac{1}{3}} {\left(a - 1\right)}\right)} \sqrt{-\frac{\left(-{\left(a^{2} - 2 \, a + 1\right)} b\right)^{\frac{1}{3}}}{b}}}{a^{2} - 2 \, a + 1}\right) + \left(-{\left(a^{2} - 2 \, a + 1\right)} b\right)^{\frac{2}{3}} \log\left({\left(a - 1\right)} b x^{2} + \left(-{\left(a^{2} - 2 \, a + 1\right)} b\right)^{\frac{2}{3}} x - \left(-{\left(a^{2} - 2 \, a + 1\right)} b\right)^{\frac{1}{3}} {\left(a - 1\right)}\right) - 2 \, \left(-{\left(a^{2} - 2 \, a + 1\right)} b\right)^{\frac{2}{3}} \log\left({\left(a - 1\right)} b x - \left(-{\left(a^{2} - 2 \, a + 1\right)} b\right)^{\frac{2}{3}}\right)}{6 \, {\left(a^{2} - 2 \, a + 1\right)} b}\right]"," ",0,"[1/6*(3*sqrt(1/3)*(a - 1)*b*sqrt((-(a^2 - 2*a + 1)*b)^(1/3)/b)*log((2*(a - 1)*b*x^3 + 3*(-(a^2 - 2*a + 1)*b)^(1/3)*(a - 1)*x + a^2 + 3*sqrt(1/3)*(2*(a - 1)*b*x^2 - (-(a^2 - 2*a + 1)*b)^(2/3)*x + (-(a^2 - 2*a + 1)*b)^(1/3)*(a - 1))*sqrt((-(a^2 - 2*a + 1)*b)^(1/3)/b) - 2*a + 1)/(b*x^3 - a + 1)) + (-(a^2 - 2*a + 1)*b)^(2/3)*log((a - 1)*b*x^2 + (-(a^2 - 2*a + 1)*b)^(2/3)*x - (-(a^2 - 2*a + 1)*b)^(1/3)*(a - 1)) - 2*(-(a^2 - 2*a + 1)*b)^(2/3)*log((a - 1)*b*x - (-(a^2 - 2*a + 1)*b)^(2/3)))/((a^2 - 2*a + 1)*b), 1/6*(6*sqrt(1/3)*(a - 1)*b*sqrt(-(-(a^2 - 2*a + 1)*b)^(1/3)/b)*arctan(sqrt(1/3)*(2*(-(a^2 - 2*a + 1)*b)^(2/3)*x - (-(a^2 - 2*a + 1)*b)^(1/3)*(a - 1))*sqrt(-(-(a^2 - 2*a + 1)*b)^(1/3)/b)/(a^2 - 2*a + 1)) + (-(a^2 - 2*a + 1)*b)^(2/3)*log((a - 1)*b*x^2 + (-(a^2 - 2*a + 1)*b)^(2/3)*x - (-(a^2 - 2*a + 1)*b)^(1/3)*(a - 1)) - 2*(-(a^2 - 2*a + 1)*b)^(2/3)*log((a - 1)*b*x - (-(a^2 - 2*a + 1)*b)^(2/3)))/((a^2 - 2*a + 1)*b)]","B",0
367,1,6,0,0.914318," ","integrate(x^(1/2)/(x^3+1),x, algorithm=""fricas"")","\frac{2}{3} \, \arctan\left(x^{\frac{3}{2}}\right)"," ",0,"2/3*arctan(x^(3/2))","A",0
368,1,57,0,1.090049," ","integrate(x^11*(b*x^3+a)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, b^{4} x^{12} + 5 \, a b^{3} x^{9} - 6 \, a^{2} b^{2} x^{6} + 8 \, a^{3} b x^{3} - 16 \, a^{4}\right)} \sqrt{b x^{3} + a}}{945 \, b^{4}}"," ",0,"2/945*(35*b^4*x^12 + 5*a*b^3*x^9 - 6*a^2*b^2*x^6 + 8*a^3*b*x^3 - 16*a^4)*sqrt(b*x^3 + a)/b^4","A",0
369,1,46,0,0.923506," ","integrate(x^8*(b*x^3+a)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, b^{3} x^{9} + 3 \, a b^{2} x^{6} - 4 \, a^{2} b x^{3} + 8 \, a^{3}\right)} \sqrt{b x^{3} + a}}{315 \, b^{3}}"," ",0,"2/315*(15*b^3*x^9 + 3*a*b^2*x^6 - 4*a^2*b*x^3 + 8*a^3)*sqrt(b*x^3 + a)/b^3","A",0
370,1,34,0,1.030627," ","integrate(x^5*(b*x^3+a)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, b^{2} x^{6} + a b x^{3} - 2 \, a^{2}\right)} \sqrt{b x^{3} + a}}{45 \, b^{2}}"," ",0,"2/45*(3*b^2*x^6 + a*b*x^3 - 2*a^2)*sqrt(b*x^3 + a)/b^2","A",0
371,1,14,0,1.059676," ","integrate(x^2*(b*x^3+a)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(b x^{3} + a\right)}^{\frac{3}{2}}}{9 \, b}"," ",0,"2/9*(b*x^3 + a)^(3/2)/b","A",0
372,1,84,0,0.959111," ","integrate((b*x^3+a)^(1/2)/x,x, algorithm=""fricas"")","\left[\frac{1}{3} \, \sqrt{a} \log\left(\frac{b x^{3} - 2 \, \sqrt{b x^{3} + a} \sqrt{a} + 2 \, a}{x^{3}}\right) + \frac{2}{3} \, \sqrt{b x^{3} + a}, \frac{2}{3} \, \sqrt{-a} \arctan\left(\frac{\sqrt{b x^{3} + a} \sqrt{-a}}{a}\right) + \frac{2}{3} \, \sqrt{b x^{3} + a}\right]"," ",0,"[1/3*sqrt(a)*log((b*x^3 - 2*sqrt(b*x^3 + a)*sqrt(a) + 2*a)/x^3) + 2/3*sqrt(b*x^3 + a), 2/3*sqrt(-a)*arctan(sqrt(b*x^3 + a)*sqrt(-a)/a) + 2/3*sqrt(b*x^3 + a)]","A",0
373,1,108,0,0.952758," ","integrate((b*x^3+a)^(1/2)/x^4,x, algorithm=""fricas"")","\left[\frac{\sqrt{a} b x^{3} \log\left(\frac{b x^{3} - 2 \, \sqrt{b x^{3} + a} \sqrt{a} + 2 \, a}{x^{3}}\right) - 2 \, \sqrt{b x^{3} + a} a}{6 \, a x^{3}}, \frac{\sqrt{-a} b x^{3} \arctan\left(\frac{\sqrt{b x^{3} + a} \sqrt{-a}}{a}\right) - \sqrt{b x^{3} + a} a}{3 \, a x^{3}}\right]"," ",0,"[1/6*(sqrt(a)*b*x^3*log((b*x^3 - 2*sqrt(b*x^3 + a)*sqrt(a) + 2*a)/x^3) - 2*sqrt(b*x^3 + a)*a)/(a*x^3), 1/3*(sqrt(-a)*b*x^3*arctan(sqrt(b*x^3 + a)*sqrt(-a)/a) - sqrt(b*x^3 + a)*a)/(a*x^3)]","A",0
374,1,133,0,0.991799," ","integrate((b*x^3+a)^(1/2)/x^7,x, algorithm=""fricas"")","\left[\frac{\sqrt{a} b^{2} x^{6} \log\left(\frac{b x^{3} + 2 \, \sqrt{b x^{3} + a} \sqrt{a} + 2 \, a}{x^{3}}\right) - 2 \, {\left(a b x^{3} + 2 \, a^{2}\right)} \sqrt{b x^{3} + a}}{24 \, a^{2} x^{6}}, -\frac{\sqrt{-a} b^{2} x^{6} \arctan\left(\frac{\sqrt{b x^{3} + a} \sqrt{-a}}{a}\right) + {\left(a b x^{3} + 2 \, a^{2}\right)} \sqrt{b x^{3} + a}}{12 \, a^{2} x^{6}}\right]"," ",0,"[1/24*(sqrt(a)*b^2*x^6*log((b*x^3 + 2*sqrt(b*x^3 + a)*sqrt(a) + 2*a)/x^3) - 2*(a*b*x^3 + 2*a^2)*sqrt(b*x^3 + a))/(a^2*x^6), -1/12*(sqrt(-a)*b^2*x^6*arctan(sqrt(b*x^3 + a)*sqrt(-a)/a) + (a*b*x^3 + 2*a^2)*sqrt(b*x^3 + a))/(a^2*x^6)]","A",0
375,1,159,0,0.747891," ","integrate((b*x^3+a)^(1/2)/x^10,x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{a} b^{3} x^{9} \log\left(\frac{b x^{3} - 2 \, \sqrt{b x^{3} + a} \sqrt{a} + 2 \, a}{x^{3}}\right) + 2 \, {\left(3 \, a b^{2} x^{6} - 2 \, a^{2} b x^{3} - 8 \, a^{3}\right)} \sqrt{b x^{3} + a}}{144 \, a^{3} x^{9}}, \frac{3 \, \sqrt{-a} b^{3} x^{9} \arctan\left(\frac{\sqrt{b x^{3} + a} \sqrt{-a}}{a}\right) + {\left(3 \, a b^{2} x^{6} - 2 \, a^{2} b x^{3} - 8 \, a^{3}\right)} \sqrt{b x^{3} + a}}{72 \, a^{3} x^{9}}\right]"," ",0,"[1/144*(3*sqrt(a)*b^3*x^9*log((b*x^3 - 2*sqrt(b*x^3 + a)*sqrt(a) + 2*a)/x^3) + 2*(3*a*b^2*x^6 - 2*a^2*b*x^3 - 8*a^3)*sqrt(b*x^3 + a))/(a^3*x^9), 1/72*(3*sqrt(-a)*b^3*x^9*arctan(sqrt(b*x^3 + a)*sqrt(-a)/a) + (3*a*b^2*x^6 - 2*a^2*b*x^3 - 8*a^3)*sqrt(b*x^3 + a))/(a^3*x^9)]","A",0
376,0,0,0,1.067691," ","integrate(x^6*(b*x^3+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b x^{3} + a} x^{6}, x\right)"," ",0,"integral(sqrt(b*x^3 + a)*x^6, x)","F",0
377,0,0,0,0.855573," ","integrate(x^3*(b*x^3+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b x^{3} + a} x^{3}, x\right)"," ",0,"integral(sqrt(b*x^3 + a)*x^3, x)","F",0
378,0,0,0,1.044496," ","integrate((b*x^3+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b x^{3} + a}, x\right)"," ",0,"integral(sqrt(b*x^3 + a), x)","F",0
379,0,0,0,0.705270," ","integrate((b*x^3+a)^(1/2)/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{3} + a}}{x^{3}}, x\right)"," ",0,"integral(sqrt(b*x^3 + a)/x^3, x)","F",0
380,0,0,0,1.305347," ","integrate((b*x^3+a)^(1/2)/x^6,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{3} + a}}{x^{6}}, x\right)"," ",0,"integral(sqrt(b*x^3 + a)/x^6, x)","F",0
381,0,0,0,1.031787," ","integrate((b*x^3+a)^(1/2)/x^9,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{3} + a}}{x^{9}}, x\right)"," ",0,"integral(sqrt(b*x^3 + a)/x^9, x)","F",0
382,0,0,0,0.678557," ","integrate(x^7*(b*x^3+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b x^{3} + a} x^{7}, x\right)"," ",0,"integral(sqrt(b*x^3 + a)*x^7, x)","F",0
383,0,0,0,0.998463," ","integrate(x^4*(b*x^3+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b x^{3} + a} x^{4}, x\right)"," ",0,"integral(sqrt(b*x^3 + a)*x^4, x)","F",0
384,0,0,0,1.051327," ","integrate(x*(b*x^3+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b x^{3} + a} x, x\right)"," ",0,"integral(sqrt(b*x^3 + a)*x, x)","F",0
385,0,0,0,1.052246," ","integrate((b*x^3+a)^(1/2)/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{3} + a}}{x^{2}}, x\right)"," ",0,"integral(sqrt(b*x^3 + a)/x^2, x)","F",0
386,0,0,0,1.035127," ","integrate((b*x^3+a)^(1/2)/x^5,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{3} + a}}{x^{5}}, x\right)"," ",0,"integral(sqrt(b*x^3 + a)/x^5, x)","F",0
387,1,68,0,0.836561," ","integrate(x^11*(b*x^3+a)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(105 \, b^{5} x^{15} + 140 \, a b^{4} x^{12} + 5 \, a^{2} b^{3} x^{9} - 6 \, a^{3} b^{2} x^{6} + 8 \, a^{4} b x^{3} - 16 \, a^{5}\right)} \sqrt{b x^{3} + a}}{3465 \, b^{4}}"," ",0,"2/3465*(105*b^5*x^15 + 140*a*b^4*x^12 + 5*a^2*b^3*x^9 - 6*a^3*b^2*x^6 + 8*a^4*b*x^3 - 16*a^5)*sqrt(b*x^3 + a)/b^4","A",0
388,1,57,0,0.837577," ","integrate(x^8*(b*x^3+a)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, b^{4} x^{12} + 50 \, a b^{3} x^{9} + 3 \, a^{2} b^{2} x^{6} - 4 \, a^{3} b x^{3} + 8 \, a^{4}\right)} \sqrt{b x^{3} + a}}{945 \, b^{3}}"," ",0,"2/945*(35*b^4*x^12 + 50*a*b^3*x^9 + 3*a^2*b^2*x^6 - 4*a^3*b*x^3 + 8*a^4)*sqrt(b*x^3 + a)/b^3","A",0
389,1,45,0,0.920487," ","integrate(x^5*(b*x^3+a)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, b^{3} x^{9} + 8 \, a b^{2} x^{6} + a^{2} b x^{3} - 2 \, a^{3}\right)} \sqrt{b x^{3} + a}}{105 \, b^{2}}"," ",0,"2/105*(5*b^3*x^9 + 8*a*b^2*x^6 + a^2*b*x^3 - 2*a^3)*sqrt(b*x^3 + a)/b^2","A",0
390,1,32,0,0.927161," ","integrate(x^2*(b*x^3+a)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \sqrt{b x^{3} + a}}{15 \, b}"," ",0,"2/15*(b^2*x^6 + 2*a*b*x^3 + a^2)*sqrt(b*x^3 + a)/b","B",0
391,1,103,0,0.603809," ","integrate((b*x^3+a)^(3/2)/x,x, algorithm=""fricas"")","\left[\frac{1}{3} \, a^{\frac{3}{2}} \log\left(\frac{b x^{3} - 2 \, \sqrt{b x^{3} + a} \sqrt{a} + 2 \, a}{x^{3}}\right) + \frac{2}{9} \, {\left(b x^{3} + 4 \, a\right)} \sqrt{b x^{3} + a}, \frac{2}{3} \, \sqrt{-a} a \arctan\left(\frac{\sqrt{b x^{3} + a} \sqrt{-a}}{a}\right) + \frac{2}{9} \, {\left(b x^{3} + 4 \, a\right)} \sqrt{b x^{3} + a}\right]"," ",0,"[1/3*a^(3/2)*log((b*x^3 - 2*sqrt(b*x^3 + a)*sqrt(a) + 2*a)/x^3) + 2/9*(b*x^3 + 4*a)*sqrt(b*x^3 + a), 2/3*sqrt(-a)*a*arctan(sqrt(b*x^3 + a)*sqrt(-a)/a) + 2/9*(b*x^3 + 4*a)*sqrt(b*x^3 + a)]","A",0
392,1,121,0,1.127212," ","integrate((b*x^3+a)^(3/2)/x^4,x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{a} b x^{3} \log\left(\frac{b x^{3} - 2 \, \sqrt{b x^{3} + a} \sqrt{a} + 2 \, a}{x^{3}}\right) + 2 \, {\left(2 \, b x^{3} - a\right)} \sqrt{b x^{3} + a}}{6 \, x^{3}}, \frac{3 \, \sqrt{-a} b x^{3} \arctan\left(\frac{\sqrt{b x^{3} + a} \sqrt{-a}}{a}\right) + {\left(2 \, b x^{3} - a\right)} \sqrt{b x^{3} + a}}{3 \, x^{3}}\right]"," ",0,"[1/6*(3*sqrt(a)*b*x^3*log((b*x^3 - 2*sqrt(b*x^3 + a)*sqrt(a) + 2*a)/x^3) + 2*(2*b*x^3 - a)*sqrt(b*x^3 + a))/x^3, 1/3*(3*sqrt(-a)*b*x^3*arctan(sqrt(b*x^3 + a)*sqrt(-a)/a) + (2*b*x^3 - a)*sqrt(b*x^3 + a))/x^3]","A",0
393,1,138,0,1.123472," ","integrate((b*x^3+a)^(3/2)/x^7,x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{a} b^{2} x^{6} \log\left(\frac{b x^{3} - 2 \, \sqrt{b x^{3} + a} \sqrt{a} + 2 \, a}{x^{3}}\right) - 2 \, {\left(5 \, a b x^{3} + 2 \, a^{2}\right)} \sqrt{b x^{3} + a}}{24 \, a x^{6}}, \frac{3 \, \sqrt{-a} b^{2} x^{6} \arctan\left(\frac{\sqrt{b x^{3} + a} \sqrt{-a}}{a}\right) - {\left(5 \, a b x^{3} + 2 \, a^{2}\right)} \sqrt{b x^{3} + a}}{12 \, a x^{6}}\right]"," ",0,"[1/24*(3*sqrt(a)*b^2*x^6*log((b*x^3 - 2*sqrt(b*x^3 + a)*sqrt(a) + 2*a)/x^3) - 2*(5*a*b*x^3 + 2*a^2)*sqrt(b*x^3 + a))/(a*x^6), 1/12*(3*sqrt(-a)*b^2*x^6*arctan(sqrt(b*x^3 + a)*sqrt(-a)/a) - (5*a*b*x^3 + 2*a^2)*sqrt(b*x^3 + a))/(a*x^6)]","A",0
394,0,0,0,0.754192," ","integrate(x^6*(b*x^3+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{9} + a x^{6}\right)} \sqrt{b x^{3} + a}, x\right)"," ",0,"integral((b*x^9 + a*x^6)*sqrt(b*x^3 + a), x)","F",0
395,0,0,0,1.039912," ","integrate(x^3*(b*x^3+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{6} + a x^{3}\right)} \sqrt{b x^{3} + a}, x\right)"," ",0,"integral((b*x^6 + a*x^3)*sqrt(b*x^3 + a), x)","F",0
396,0,0,0,0.909832," ","integrate((b*x^3+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{3} + a\right)}^{\frac{3}{2}}, x\right)"," ",0,"integral((b*x^3 + a)^(3/2), x)","F",0
397,0,0,0,1.154497," ","integrate((b*x^3+a)^(3/2)/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{3} + a\right)}^{\frac{3}{2}}}{x^{3}}, x\right)"," ",0,"integral((b*x^3 + a)^(3/2)/x^3, x)","F",0
398,0,0,0,0.780898," ","integrate((b*x^3+a)^(3/2)/x^6,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{3} + a\right)}^{\frac{3}{2}}}{x^{6}}, x\right)"," ",0,"integral((b*x^3 + a)^(3/2)/x^6, x)","F",0
399,0,0,0,0.983864," ","integrate(x^7*(b*x^3+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{10} + a x^{7}\right)} \sqrt{b x^{3} + a}, x\right)"," ",0,"integral((b*x^10 + a*x^7)*sqrt(b*x^3 + a), x)","F",0
400,0,0,0,1.040477," ","integrate(x^4*(b*x^3+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{7} + a x^{4}\right)} \sqrt{b x^{3} + a}, x\right)"," ",0,"integral((b*x^7 + a*x^4)*sqrt(b*x^3 + a), x)","F",0
401,0,0,0,0.727613," ","integrate(x*(b*x^3+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{4} + a x\right)} \sqrt{b x^{3} + a}, x\right)"," ",0,"integral((b*x^4 + a*x)*sqrt(b*x^3 + a), x)","F",0
402,0,0,0,1.073926," ","integrate((b*x^3+a)^(3/2)/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{3} + a\right)}^{\frac{3}{2}}}{x^{2}}, x\right)"," ",0,"integral((b*x^3 + a)^(3/2)/x^2, x)","F",0
403,0,0,0,1.056480," ","integrate((b*x^3+a)^(3/2)/x^5,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{3} + a\right)}^{\frac{3}{2}}}{x^{5}}, x\right)"," ",0,"integral((b*x^3 + a)^(3/2)/x^5, x)","F",0
404,1,46,0,0.970788," ","integrate(x^11/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, b^{3} x^{9} - 6 \, a b^{2} x^{6} + 8 \, a^{2} b x^{3} - 16 \, a^{3}\right)} \sqrt{b x^{3} + a}}{105 \, b^{4}}"," ",0,"2/105*(5*b^3*x^9 - 6*a*b^2*x^6 + 8*a^2*b*x^3 - 16*a^3)*sqrt(b*x^3 + a)/b^4","A",0
405,1,35,0,1.062858," ","integrate(x^8/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, b^{2} x^{6} - 4 \, a b x^{3} + 8 \, a^{2}\right)} \sqrt{b x^{3} + a}}{45 \, b^{3}}"," ",0,"2/45*(3*b^2*x^6 - 4*a*b*x^3 + 8*a^2)*sqrt(b*x^3 + a)/b^3","A",0
406,1,23,0,0.867092," ","integrate(x^5/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{b x^{3} + a} {\left(b x^{3} - 2 \, a\right)}}{9 \, b^{2}}"," ",0,"2/9*sqrt(b*x^3 + a)*(b*x^3 - 2*a)/b^2","A",0
407,1,14,0,1.104769," ","integrate(x^2/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{b x^{3} + a}}{3 \, b}"," ",0,"2/3*sqrt(b*x^3 + a)/b","A",0
408,1,63,0,0.935568," ","integrate(1/x/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{b x^{3} - 2 \, \sqrt{b x^{3} + a} \sqrt{a} + 2 \, a}{x^{3}}\right)}{3 \, \sqrt{a}}, \frac{2 \, \sqrt{-a} \arctan\left(\frac{\sqrt{b x^{3} + a} \sqrt{-a}}{a}\right)}{3 \, a}\right]"," ",0,"[1/3*log((b*x^3 - 2*sqrt(b*x^3 + a)*sqrt(a) + 2*a)/x^3)/sqrt(a), 2/3*sqrt(-a)*arctan(sqrt(b*x^3 + a)*sqrt(-a)/a)/a]","A",0
409,1,107,0,0.872857," ","integrate(1/x^4/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a} b x^{3} \log\left(\frac{b x^{3} + 2 \, \sqrt{b x^{3} + a} \sqrt{a} + 2 \, a}{x^{3}}\right) - 2 \, \sqrt{b x^{3} + a} a}{6 \, a^{2} x^{3}}, -\frac{\sqrt{-a} b x^{3} \arctan\left(\frac{\sqrt{b x^{3} + a} \sqrt{-a}}{a}\right) + \sqrt{b x^{3} + a} a}{3 \, a^{2} x^{3}}\right]"," ",0,"[1/6*(sqrt(a)*b*x^3*log((b*x^3 + 2*sqrt(b*x^3 + a)*sqrt(a) + 2*a)/x^3) - 2*sqrt(b*x^3 + a)*a)/(a^2*x^3), -1/3*(sqrt(-a)*b*x^3*arctan(sqrt(b*x^3 + a)*sqrt(-a)/a) + sqrt(b*x^3 + a)*a)/(a^2*x^3)]","A",0
410,1,137,0,0.810912," ","integrate(1/x^7/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{a} b^{2} x^{6} \log\left(\frac{b x^{3} - 2 \, \sqrt{b x^{3} + a} \sqrt{a} + 2 \, a}{x^{3}}\right) + 2 \, {\left(3 \, a b x^{3} - 2 \, a^{2}\right)} \sqrt{b x^{3} + a}}{24 \, a^{3} x^{6}}, \frac{3 \, \sqrt{-a} b^{2} x^{6} \arctan\left(\frac{\sqrt{b x^{3} + a} \sqrt{-a}}{a}\right) + {\left(3 \, a b x^{3} - 2 \, a^{2}\right)} \sqrt{b x^{3} + a}}{12 \, a^{3} x^{6}}\right]"," ",0,"[1/24*(3*sqrt(a)*b^2*x^6*log((b*x^3 - 2*sqrt(b*x^3 + a)*sqrt(a) + 2*a)/x^3) + 2*(3*a*b*x^3 - 2*a^2)*sqrt(b*x^3 + a))/(a^3*x^6), 1/12*(3*sqrt(-a)*b^2*x^6*arctan(sqrt(b*x^3 + a)*sqrt(-a)/a) + (3*a*b*x^3 - 2*a^2)*sqrt(b*x^3 + a))/(a^3*x^6)]","A",0
411,0,0,0,1.054250," ","integrate(x^6/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{6}}{\sqrt{b x^{3} + a}}, x\right)"," ",0,"integral(x^6/sqrt(b*x^3 + a), x)","F",0
412,0,0,0,0.987076," ","integrate(x^3/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3}}{\sqrt{b x^{3} + a}}, x\right)"," ",0,"integral(x^3/sqrt(b*x^3 + a), x)","F",0
413,0,0,0,1.072802," ","integrate(1/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{b x^{3} + a}}, x\right)"," ",0,"integral(1/sqrt(b*x^3 + a), x)","F",0
414,0,0,0,1.085700," ","integrate(1/x^3/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{3} + a}}{b x^{6} + a x^{3}}, x\right)"," ",0,"integral(sqrt(b*x^3 + a)/(b*x^6 + a*x^3), x)","F",0
415,0,0,0,0.732339," ","integrate(1/x^6/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{3} + a}}{b x^{9} + a x^{6}}, x\right)"," ",0,"integral(sqrt(b*x^3 + a)/(b*x^9 + a*x^6), x)","F",0
416,0,0,0,0.954684," ","integrate(x^7/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{7}}{\sqrt{b x^{3} + a}}, x\right)"," ",0,"integral(x^7/sqrt(b*x^3 + a), x)","F",0
417,0,0,0,1.127518," ","integrate(x^4/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{4}}{\sqrt{b x^{3} + a}}, x\right)"," ",0,"integral(x^4/sqrt(b*x^3 + a), x)","F",0
418,0,0,0,0.941475," ","integrate(x/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{\sqrt{b x^{3} + a}}, x\right)"," ",0,"integral(x/sqrt(b*x^3 + a), x)","F",0
419,0,0,0,0.834564," ","integrate(1/x^2/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{3} + a}}{b x^{5} + a x^{2}}, x\right)"," ",0,"integral(sqrt(b*x^3 + a)/(b*x^5 + a*x^2), x)","F",0
420,0,0,0,1.236027," ","integrate(1/x^5/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{3} + a}}{b x^{8} + a x^{5}}, x\right)"," ",0,"integral(sqrt(b*x^3 + a)/(b*x^8 + a*x^5), x)","F",0
421,1,57,0,0.719241," ","integrate(x^11/(b*x^3+a)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(b^{3} x^{9} - 2 \, a b^{2} x^{6} + 8 \, a^{2} b x^{3} + 16 \, a^{3}\right)} \sqrt{b x^{3} + a}}{15 \, {\left(b^{5} x^{3} + a b^{4}\right)}}"," ",0,"2/15*(b^3*x^9 - 2*a*b^2*x^6 + 8*a^2*b*x^3 + 16*a^3)*sqrt(b*x^3 + a)/(b^5*x^3 + a*b^4)","A",0
422,1,46,0,0.853161," ","integrate(x^8/(b*x^3+a)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(b^{2} x^{6} - 4 \, a b x^{3} - 8 \, a^{2}\right)} \sqrt{b x^{3} + a}}{9 \, {\left(b^{4} x^{3} + a b^{3}\right)}}"," ",0,"2/9*(b^2*x^6 - 4*a*b*x^3 - 8*a^2)*sqrt(b*x^3 + a)/(b^4*x^3 + a*b^3)","A",0
423,1,35,0,0.618850," ","integrate(x^5/(b*x^3+a)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(b x^{3} + 2 \, a\right)} \sqrt{b x^{3} + a}}{3 \, {\left(b^{3} x^{3} + a b^{2}\right)}}"," ",0,"2/3*(b*x^3 + 2*a)*sqrt(b*x^3 + a)/(b^3*x^3 + a*b^2)","A",0
424,1,24,0,0.951499," ","integrate(x^2/(b*x^3+a)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{b x^{3} + a}}{3 \, {\left(b^{2} x^{3} + a b\right)}}"," ",0,"-2/3*sqrt(b*x^3 + a)/(b^2*x^3 + a*b)","A",0
425,1,129,0,1.246658," ","integrate(1/x/(b*x^3+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(b x^{3} + a\right)} \sqrt{a} \log\left(\frac{b x^{3} - 2 \, \sqrt{b x^{3} + a} \sqrt{a} + 2 \, a}{x^{3}}\right) + 2 \, \sqrt{b x^{3} + a} a}{3 \, {\left(a^{2} b x^{3} + a^{3}\right)}}, \frac{2 \, {\left({\left(b x^{3} + a\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{b x^{3} + a} \sqrt{-a}}{a}\right) + \sqrt{b x^{3} + a} a\right)}}{3 \, {\left(a^{2} b x^{3} + a^{3}\right)}}\right]"," ",0,"[1/3*((b*x^3 + a)*sqrt(a)*log((b*x^3 - 2*sqrt(b*x^3 + a)*sqrt(a) + 2*a)/x^3) + 2*sqrt(b*x^3 + a)*a)/(a^2*b*x^3 + a^3), 2/3*((b*x^3 + a)*sqrt(-a)*arctan(sqrt(b*x^3 + a)*sqrt(-a)/a) + sqrt(b*x^3 + a)*a)/(a^2*b*x^3 + a^3)]","A",0
426,1,173,0,1.026487," ","integrate(1/x^4/(b*x^3+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{2} x^{6} + a b x^{3}\right)} \sqrt{a} \log\left(\frac{b x^{3} + 2 \, \sqrt{b x^{3} + a} \sqrt{a} + 2 \, a}{x^{3}}\right) - 2 \, {\left(3 \, a b x^{3} + a^{2}\right)} \sqrt{b x^{3} + a}}{6 \, {\left(a^{3} b x^{6} + a^{4} x^{3}\right)}}, -\frac{3 \, {\left(b^{2} x^{6} + a b x^{3}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{b x^{3} + a} \sqrt{-a}}{a}\right) + {\left(3 \, a b x^{3} + a^{2}\right)} \sqrt{b x^{3} + a}}{3 \, {\left(a^{3} b x^{6} + a^{4} x^{3}\right)}}\right]"," ",0,"[1/6*(3*(b^2*x^6 + a*b*x^3)*sqrt(a)*log((b*x^3 + 2*sqrt(b*x^3 + a)*sqrt(a) + 2*a)/x^3) - 2*(3*a*b*x^3 + a^2)*sqrt(b*x^3 + a))/(a^3*b*x^6 + a^4*x^3), -1/3*(3*(b^2*x^6 + a*b*x^3)*sqrt(-a)*arctan(sqrt(b*x^3 + a)*sqrt(-a)/a) + (3*a*b*x^3 + a^2)*sqrt(b*x^3 + a))/(a^3*b*x^6 + a^4*x^3)]","A",0
427,1,203,0,0.678606," ","integrate(1/x^7/(b*x^3+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(b^{3} x^{9} + a b^{2} x^{6}\right)} \sqrt{a} \log\left(\frac{b x^{3} - 2 \, \sqrt{b x^{3} + a} \sqrt{a} + 2 \, a}{x^{3}}\right) + 2 \, {\left(15 \, a b^{2} x^{6} + 5 \, a^{2} b x^{3} - 2 \, a^{3}\right)} \sqrt{b x^{3} + a}}{24 \, {\left(a^{4} b x^{9} + a^{5} x^{6}\right)}}, \frac{15 \, {\left(b^{3} x^{9} + a b^{2} x^{6}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{b x^{3} + a} \sqrt{-a}}{a}\right) + {\left(15 \, a b^{2} x^{6} + 5 \, a^{2} b x^{3} - 2 \, a^{3}\right)} \sqrt{b x^{3} + a}}{12 \, {\left(a^{4} b x^{9} + a^{5} x^{6}\right)}}\right]"," ",0,"[1/24*(15*(b^3*x^9 + a*b^2*x^6)*sqrt(a)*log((b*x^3 - 2*sqrt(b*x^3 + a)*sqrt(a) + 2*a)/x^3) + 2*(15*a*b^2*x^6 + 5*a^2*b*x^3 - 2*a^3)*sqrt(b*x^3 + a))/(a^4*b*x^9 + a^5*x^6), 1/12*(15*(b^3*x^9 + a*b^2*x^6)*sqrt(-a)*arctan(sqrt(b*x^3 + a)*sqrt(-a)/a) + (15*a*b^2*x^6 + 5*a^2*b*x^3 - 2*a^3)*sqrt(b*x^3 + a))/(a^4*b*x^9 + a^5*x^6)]","A",0
428,0,0,0,0.816329," ","integrate(x^6/(b*x^3+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{3} + a} x^{6}}{b^{2} x^{6} + 2 \, a b x^{3} + a^{2}}, x\right)"," ",0,"integral(sqrt(b*x^3 + a)*x^6/(b^2*x^6 + 2*a*b*x^3 + a^2), x)","F",0
429,0,0,0,1.019517," ","integrate(x^3/(b*x^3+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{3} + a} x^{3}}{b^{2} x^{6} + 2 \, a b x^{3} + a^{2}}, x\right)"," ",0,"integral(sqrt(b*x^3 + a)*x^3/(b^2*x^6 + 2*a*b*x^3 + a^2), x)","F",0
430,0,0,0,1.008605," ","integrate(1/(b*x^3+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{3} + a}}{b^{2} x^{6} + 2 \, a b x^{3} + a^{2}}, x\right)"," ",0,"integral(sqrt(b*x^3 + a)/(b^2*x^6 + 2*a*b*x^3 + a^2), x)","F",0
431,0,0,0,0.975774," ","integrate(1/x^3/(b*x^3+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{3} + a}}{b^{2} x^{9} + 2 \, a b x^{6} + a^{2} x^{3}}, x\right)"," ",0,"integral(sqrt(b*x^3 + a)/(b^2*x^9 + 2*a*b*x^6 + a^2*x^3), x)","F",0
432,0,0,0,1.027098," ","integrate(1/x^6/(b*x^3+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{3} + a}}{b^{2} x^{12} + 2 \, a b x^{9} + a^{2} x^{6}}, x\right)"," ",0,"integral(sqrt(b*x^3 + a)/(b^2*x^12 + 2*a*b*x^9 + a^2*x^6), x)","F",0
433,0,0,0,0.724985," ","integrate(x^7/(b*x^3+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{3} + a} x^{7}}{b^{2} x^{6} + 2 \, a b x^{3} + a^{2}}, x\right)"," ",0,"integral(sqrt(b*x^3 + a)*x^7/(b^2*x^6 + 2*a*b*x^3 + a^2), x)","F",0
434,0,0,0,0.768845," ","integrate(x^4/(b*x^3+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{3} + a} x^{4}}{b^{2} x^{6} + 2 \, a b x^{3} + a^{2}}, x\right)"," ",0,"integral(sqrt(b*x^3 + a)*x^4/(b^2*x^6 + 2*a*b*x^3 + a^2), x)","F",0
435,0,0,0,0.723207," ","integrate(x/(b*x^3+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{3} + a} x}{b^{2} x^{6} + 2 \, a b x^{3} + a^{2}}, x\right)"," ",0,"integral(sqrt(b*x^3 + a)*x/(b^2*x^6 + 2*a*b*x^3 + a^2), x)","F",0
436,0,0,0,0.707569," ","integrate(1/x^2/(b*x^3+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{3} + a}}{b^{2} x^{8} + 2 \, a b x^{5} + a^{2} x^{2}}, x\right)"," ",0,"integral(sqrt(b*x^3 + a)/(b^2*x^8 + 2*a*b*x^5 + a^2*x^2), x)","F",0
437,0,0,0,1.009601," ","integrate(1/x^5/(b*x^3+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{3} + a}}{b^{2} x^{11} + 2 \, a b x^{8} + a^{2} x^{5}}, x\right)"," ",0,"integral(sqrt(b*x^3 + a)/(b^2*x^11 + 2*a*b*x^8 + a^2*x^5), x)","F",0
438,1,26,0,0.953124," ","integrate(x^11/(x^3+1)^(1/2),x, algorithm=""fricas"")","\frac{2}{105} \, {\left(5 \, x^{9} - 6 \, x^{6} + 8 \, x^{3} - 16\right)} \sqrt{x^{3} + 1}"," ",0,"2/105*(5*x^9 - 6*x^6 + 8*x^3 - 16)*sqrt(x^3 + 1)","A",0
439,1,21,0,0.671914," ","integrate(x^8/(x^3+1)^(1/2),x, algorithm=""fricas"")","\frac{2}{45} \, {\left(3 \, x^{6} - 4 \, x^{3} + 8\right)} \sqrt{x^{3} + 1}"," ",0,"2/45*(3*x^6 - 4*x^3 + 8)*sqrt(x^3 + 1)","A",0
440,1,14,0,0.633871," ","integrate(x^5/(x^3+1)^(1/2),x, algorithm=""fricas"")","\frac{2}{9} \, \sqrt{x^{3} + 1} {\left(x^{3} - 2\right)}"," ",0,"2/9*sqrt(x^3 + 1)*(x^3 - 2)","A",0
441,1,9,0,0.995466," ","integrate(x^2/(x^3+1)^(1/2),x, algorithm=""fricas"")","\frac{2}{3} \, \sqrt{x^{3} + 1}"," ",0,"2/3*sqrt(x^3 + 1)","A",0
442,1,25,0,0.809920," ","integrate(1/x/(x^3+1)^(1/2),x, algorithm=""fricas"")","-\frac{1}{3} \, \log\left(\sqrt{x^{3} + 1} + 1\right) + \frac{1}{3} \, \log\left(\sqrt{x^{3} + 1} - 1\right)"," ",0,"-1/3*log(sqrt(x^3 + 1) + 1) + 1/3*log(sqrt(x^3 + 1) - 1)","B",0
443,1,44,0,1.082340," ","integrate(1/x^4/(x^3+1)^(1/2),x, algorithm=""fricas"")","\frac{x^{3} \log\left(\sqrt{x^{3} + 1} + 1\right) - x^{3} \log\left(\sqrt{x^{3} + 1} - 1\right) - 2 \, \sqrt{x^{3} + 1}}{6 \, x^{3}}"," ",0,"1/6*(x^3*log(sqrt(x^3 + 1) + 1) - x^3*log(sqrt(x^3 + 1) - 1) - 2*sqrt(x^3 + 1))/x^3","A",0
444,1,52,0,0.945042," ","integrate(1/x^7/(x^3+1)^(1/2),x, algorithm=""fricas"")","-\frac{3 \, x^{6} \log\left(\sqrt{x^{3} + 1} + 1\right) - 3 \, x^{6} \log\left(\sqrt{x^{3} + 1} - 1\right) - 2 \, {\left(3 \, x^{3} - 2\right)} \sqrt{x^{3} + 1}}{24 \, x^{6}}"," ",0,"-1/24*(3*x^6*log(sqrt(x^3 + 1) + 1) - 3*x^6*log(sqrt(x^3 + 1) - 1) - 2*(3*x^3 - 2)*sqrt(x^3 + 1))/x^6","A",0
445,1,57,0,1.144984," ","integrate(1/x^10/(x^3+1)^(1/2),x, algorithm=""fricas"")","\frac{15 \, x^{9} \log\left(\sqrt{x^{3} + 1} + 1\right) - 15 \, x^{9} \log\left(\sqrt{x^{3} + 1} - 1\right) - 2 \, {\left(15 \, x^{6} - 10 \, x^{3} + 8\right)} \sqrt{x^{3} + 1}}{144 \, x^{9}}"," ",0,"1/144*(15*x^9*log(sqrt(x^3 + 1) + 1) - 15*x^9*log(sqrt(x^3 + 1) - 1) - 2*(15*x^6 - 10*x^3 + 8)*sqrt(x^3 + 1))/x^9","A",0
446,0,0,0,0.628316," ","integrate(x^6/(x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{6}}{\sqrt{x^{3} + 1}}, x\right)"," ",0,"integral(x^6/sqrt(x^3 + 1), x)","F",0
447,0,0,0,0.955406," ","integrate(x^3/(x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3}}{\sqrt{x^{3} + 1}}, x\right)"," ",0,"integral(x^3/sqrt(x^3 + 1), x)","F",0
448,0,0,0,0.784312," ","integrate(1/(x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{x^{3} + 1}}, x\right)"," ",0,"integral(1/sqrt(x^3 + 1), x)","F",0
449,0,0,0,0.933563," ","integrate(1/x^3/(x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{3} + 1}}{x^{6} + x^{3}}, x\right)"," ",0,"integral(sqrt(x^3 + 1)/(x^6 + x^3), x)","F",0
450,0,0,0,1.301291," ","integrate(1/x^6/(x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{3} + 1}}{x^{9} + x^{6}}, x\right)"," ",0,"integral(sqrt(x^3 + 1)/(x^9 + x^6), x)","F",0
451,0,0,0,1.247921," ","integrate(x^7/(x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{7}}{\sqrt{x^{3} + 1}}, x\right)"," ",0,"integral(x^7/sqrt(x^3 + 1), x)","F",0
452,0,0,0,1.009771," ","integrate(x^4/(x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{4}}{\sqrt{x^{3} + 1}}, x\right)"," ",0,"integral(x^4/sqrt(x^3 + 1), x)","F",0
453,0,0,0,1.105840," ","integrate(x/(x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{\sqrt{x^{3} + 1}}, x\right)"," ",0,"integral(x/sqrt(x^3 + 1), x)","F",0
454,0,0,0,1.144056," ","integrate(1/x^2/(x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{3} + 1}}{x^{5} + x^{2}}, x\right)"," ",0,"integral(sqrt(x^3 + 1)/(x^5 + x^2), x)","F",0
455,0,0,0,1.126868," ","integrate(1/x^5/(x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{3} + 1}}{x^{8} + x^{5}}, x\right)"," ",0,"integral(sqrt(x^3 + 1)/(x^8 + x^5), x)","F",0
456,1,28,0,1.089950," ","integrate(x^11/(-x^3+1)^(1/2),x, algorithm=""fricas"")","-\frac{2}{105} \, {\left(5 \, x^{9} + 6 \, x^{6} + 8 \, x^{3} + 16\right)} \sqrt{-x^{3} + 1}"," ",0,"-2/105*(5*x^9 + 6*x^6 + 8*x^3 + 16)*sqrt(-x^3 + 1)","A",0
457,1,23,0,0.828545," ","integrate(x^8/(-x^3+1)^(1/2),x, algorithm=""fricas"")","-\frac{2}{45} \, {\left(3 \, x^{6} + 4 \, x^{3} + 8\right)} \sqrt{-x^{3} + 1}"," ",0,"-2/45*(3*x^6 + 4*x^3 + 8)*sqrt(-x^3 + 1)","A",0
458,1,16,0,0.641153," ","integrate(x^5/(-x^3+1)^(1/2),x, algorithm=""fricas"")","-\frac{2}{9} \, {\left(x^{3} + 2\right)} \sqrt{-x^{3} + 1}"," ",0,"-2/9*(x^3 + 2)*sqrt(-x^3 + 1)","A",0
459,1,11,0,1.111495," ","integrate(x^2/(-x^3+1)^(1/2),x, algorithm=""fricas"")","-\frac{2}{3} \, \sqrt{-x^{3} + 1}"," ",0,"-2/3*sqrt(-x^3 + 1)","A",0
460,1,29,0,1.070355," ","integrate(1/x/(-x^3+1)^(1/2),x, algorithm=""fricas"")","-\frac{1}{3} \, \log\left(\sqrt{-x^{3} + 1} + 1\right) + \frac{1}{3} \, \log\left(\sqrt{-x^{3} + 1} - 1\right)"," ",0,"-1/3*log(sqrt(-x^3 + 1) + 1) + 1/3*log(sqrt(-x^3 + 1) - 1)","B",0
461,1,50,0,1.114394," ","integrate(1/x^4/(-x^3+1)^(1/2),x, algorithm=""fricas"")","-\frac{x^{3} \log\left(\sqrt{-x^{3} + 1} + 1\right) - x^{3} \log\left(\sqrt{-x^{3} + 1} - 1\right) + 2 \, \sqrt{-x^{3} + 1}}{6 \, x^{3}}"," ",0,"-1/6*(x^3*log(sqrt(-x^3 + 1) + 1) - x^3*log(sqrt(-x^3 + 1) - 1) + 2*sqrt(-x^3 + 1))/x^3","A",0
462,1,58,0,1.172662," ","integrate(1/x^7/(-x^3+1)^(1/2),x, algorithm=""fricas"")","-\frac{3 \, x^{6} \log\left(\sqrt{-x^{3} + 1} + 1\right) - 3 \, x^{6} \log\left(\sqrt{-x^{3} + 1} - 1\right) + 2 \, {\left(3 \, x^{3} + 2\right)} \sqrt{-x^{3} + 1}}{24 \, x^{6}}"," ",0,"-1/24*(3*x^6*log(sqrt(-x^3 + 1) + 1) - 3*x^6*log(sqrt(-x^3 + 1) - 1) + 2*(3*x^3 + 2)*sqrt(-x^3 + 1))/x^6","A",0
463,1,63,0,1.008296," ","integrate(1/x^10/(-x^3+1)^(1/2),x, algorithm=""fricas"")","-\frac{15 \, x^{9} \log\left(\sqrt{-x^{3} + 1} + 1\right) - 15 \, x^{9} \log\left(\sqrt{-x^{3} + 1} - 1\right) + 2 \, {\left(15 \, x^{6} + 10 \, x^{3} + 8\right)} \sqrt{-x^{3} + 1}}{144 \, x^{9}}"," ",0,"-1/144*(15*x^9*log(sqrt(-x^3 + 1) + 1) - 15*x^9*log(sqrt(-x^3 + 1) - 1) + 2*(15*x^6 + 10*x^3 + 8)*sqrt(-x^3 + 1))/x^9","A",0
464,0,0,0,0.846833," ","integrate(x^6/(-x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{3} + 1} x^{6}}{x^{3} - 1}, x\right)"," ",0,"integral(-sqrt(-x^3 + 1)*x^6/(x^3 - 1), x)","F",0
465,0,0,0,1.073295," ","integrate(x^3/(-x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{3} + 1} x^{3}}{x^{3} - 1}, x\right)"," ",0,"integral(-sqrt(-x^3 + 1)*x^3/(x^3 - 1), x)","F",0
466,0,0,0,1.056135," ","integrate(1/(-x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{3} + 1}}{x^{3} - 1}, x\right)"," ",0,"integral(-sqrt(-x^3 + 1)/(x^3 - 1), x)","F",0
467,0,0,0,1.163832," ","integrate(1/x^3/(-x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{3} + 1}}{x^{6} - x^{3}}, x\right)"," ",0,"integral(-sqrt(-x^3 + 1)/(x^6 - x^3), x)","F",0
468,0,0,0,0.860586," ","integrate(1/x^6/(-x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{3} + 1}}{x^{9} - x^{6}}, x\right)"," ",0,"integral(-sqrt(-x^3 + 1)/(x^9 - x^6), x)","F",0
469,0,0,0,1.012532," ","integrate(x^7/(-x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{3} + 1} x^{7}}{x^{3} - 1}, x\right)"," ",0,"integral(-sqrt(-x^3 + 1)*x^7/(x^3 - 1), x)","F",0
470,0,0,0,1.109279," ","integrate(x^4/(-x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{3} + 1} x^{4}}{x^{3} - 1}, x\right)"," ",0,"integral(-sqrt(-x^3 + 1)*x^4/(x^3 - 1), x)","F",0
471,0,0,0,1.018207," ","integrate(x/(-x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{3} + 1} x}{x^{3} - 1}, x\right)"," ",0,"integral(-sqrt(-x^3 + 1)*x/(x^3 - 1), x)","F",0
472,0,0,0,0.880037," ","integrate(1/x^2/(-x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{3} + 1}}{x^{5} - x^{2}}, x\right)"," ",0,"integral(-sqrt(-x^3 + 1)/(x^5 - x^2), x)","F",0
473,0,0,0,1.087557," ","integrate(1/x^5/(-x^3+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{3} + 1}}{x^{8} - x^{5}}, x\right)"," ",0,"integral(-sqrt(-x^3 + 1)/(x^8 - x^5), x)","F",0
474,1,26,0,0.698034," ","integrate(x^11/(x^3-1)^(1/2),x, algorithm=""fricas"")","\frac{2}{105} \, {\left(5 \, x^{9} + 6 \, x^{6} + 8 \, x^{3} + 16\right)} \sqrt{x^{3} - 1}"," ",0,"2/105*(5*x^9 + 6*x^6 + 8*x^3 + 16)*sqrt(x^3 - 1)","A",0
475,1,21,0,1.022650," ","integrate(x^8/(x^3-1)^(1/2),x, algorithm=""fricas"")","\frac{2}{45} \, {\left(3 \, x^{6} + 4 \, x^{3} + 8\right)} \sqrt{x^{3} - 1}"," ",0,"2/45*(3*x^6 + 4*x^3 + 8)*sqrt(x^3 - 1)","A",0
476,1,14,0,1.093181," ","integrate(x^5/(x^3-1)^(1/2),x, algorithm=""fricas"")","\frac{2}{9} \, {\left(x^{3} + 2\right)} \sqrt{x^{3} - 1}"," ",0,"2/9*(x^3 + 2)*sqrt(x^3 - 1)","A",0
477,1,9,0,1.052473," ","integrate(x^2/(x^3-1)^(1/2),x, algorithm=""fricas"")","\frac{2}{3} \, \sqrt{x^{3} - 1}"," ",0,"2/3*sqrt(x^3 - 1)","A",0
478,1,10,0,1.109047," ","integrate(1/x/(x^3-1)^(1/2),x, algorithm=""fricas"")","\frac{2}{3} \, \arctan\left(\sqrt{x^{3} - 1}\right)"," ",0,"2/3*arctan(sqrt(x^3 - 1))","A",0
479,1,25,0,1.148538," ","integrate(1/x^4/(x^3-1)^(1/2),x, algorithm=""fricas"")","\frac{x^{3} \arctan\left(\sqrt{x^{3} - 1}\right) + \sqrt{x^{3} - 1}}{3 \, x^{3}}"," ",0,"1/3*(x^3*arctan(sqrt(x^3 - 1)) + sqrt(x^3 - 1))/x^3","A",0
480,1,34,0,1.185738," ","integrate(1/x^7/(x^3-1)^(1/2),x, algorithm=""fricas"")","\frac{3 \, x^{6} \arctan\left(\sqrt{x^{3} - 1}\right) + {\left(3 \, x^{3} + 2\right)} \sqrt{x^{3} - 1}}{12 \, x^{6}}"," ",0,"1/12*(3*x^6*arctan(sqrt(x^3 - 1)) + (3*x^3 + 2)*sqrt(x^3 - 1))/x^6","A",0
481,1,39,0,1.178011," ","integrate(1/x^10/(x^3-1)^(1/2),x, algorithm=""fricas"")","\frac{15 \, x^{9} \arctan\left(\sqrt{x^{3} - 1}\right) + {\left(15 \, x^{6} + 10 \, x^{3} + 8\right)} \sqrt{x^{3} - 1}}{72 \, x^{9}}"," ",0,"1/72*(15*x^9*arctan(sqrt(x^3 - 1)) + (15*x^6 + 10*x^3 + 8)*sqrt(x^3 - 1))/x^9","A",0
482,0,0,0,1.274849," ","integrate(x^6/(x^3-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{6}}{\sqrt{x^{3} - 1}}, x\right)"," ",0,"integral(x^6/sqrt(x^3 - 1), x)","F",0
483,0,0,0,1.243532," ","integrate(x^3/(x^3-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3}}{\sqrt{x^{3} - 1}}, x\right)"," ",0,"integral(x^3/sqrt(x^3 - 1), x)","F",0
484,0,0,0,1.293095," ","integrate(1/(x^3-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{x^{3} - 1}}, x\right)"," ",0,"integral(1/sqrt(x^3 - 1), x)","F",0
485,0,0,0,0.942860," ","integrate(1/x^3/(x^3-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{3} - 1}}{x^{6} - x^{3}}, x\right)"," ",0,"integral(sqrt(x^3 - 1)/(x^6 - x^3), x)","F",0
486,0,0,0,1.172678," ","integrate(1/x^6/(x^3-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{3} - 1}}{x^{9} - x^{6}}, x\right)"," ",0,"integral(sqrt(x^3 - 1)/(x^9 - x^6), x)","F",0
487,0,0,0,1.063096," ","integrate(x^7/(x^3-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{7}}{\sqrt{x^{3} - 1}}, x\right)"," ",0,"integral(x^7/sqrt(x^3 - 1), x)","F",0
488,0,0,0,0.738731," ","integrate(x^4/(x^3-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{4}}{\sqrt{x^{3} - 1}}, x\right)"," ",0,"integral(x^4/sqrt(x^3 - 1), x)","F",0
489,0,0,0,0.863820," ","integrate(x/(x^3-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{\sqrt{x^{3} - 1}}, x\right)"," ",0,"integral(x/sqrt(x^3 - 1), x)","F",0
490,0,0,0,1.244283," ","integrate(1/x^2/(x^3-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{3} - 1}}{x^{5} - x^{2}}, x\right)"," ",0,"integral(sqrt(x^3 - 1)/(x^5 - x^2), x)","F",0
491,0,0,0,1.006999," ","integrate(1/x^5/(x^3-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{3} - 1}}{x^{8} - x^{5}}, x\right)"," ",0,"integral(sqrt(x^3 - 1)/(x^8 - x^5), x)","F",0
492,1,28,0,1.183926," ","integrate(x^11/(-x^3-1)^(1/2),x, algorithm=""fricas"")","-\frac{2}{105} \, {\left(5 \, x^{9} - 6 \, x^{6} + 8 \, x^{3} - 16\right)} \sqrt{-x^{3} - 1}"," ",0,"-2/105*(5*x^9 - 6*x^6 + 8*x^3 - 16)*sqrt(-x^3 - 1)","A",0
493,1,23,0,1.278910," ","integrate(x^8/(-x^3-1)^(1/2),x, algorithm=""fricas"")","-\frac{2}{45} \, {\left(3 \, x^{6} - 4 \, x^{3} + 8\right)} \sqrt{-x^{3} - 1}"," ",0,"-2/45*(3*x^6 - 4*x^3 + 8)*sqrt(-x^3 - 1)","A",0
494,1,16,0,1.169970," ","integrate(x^5/(-x^3-1)^(1/2),x, algorithm=""fricas"")","-\frac{2}{9} \, {\left(x^{3} - 2\right)} \sqrt{-x^{3} - 1}"," ",0,"-2/9*(x^3 - 2)*sqrt(-x^3 - 1)","A",0
495,1,11,0,1.275522," ","integrate(x^2/(-x^3-1)^(1/2),x, algorithm=""fricas"")","-\frac{2}{3} \, \sqrt{-x^{3} - 1}"," ",0,"-2/3*sqrt(-x^3 - 1)","A",0
496,1,12,0,1.020699," ","integrate(1/x/(-x^3-1)^(1/2),x, algorithm=""fricas"")","\frac{2}{3} \, \arctan\left(\sqrt{-x^{3} - 1}\right)"," ",0,"2/3*arctan(sqrt(-x^3 - 1))","A",0
497,1,31,0,1.044754," ","integrate(1/x^4/(-x^3-1)^(1/2),x, algorithm=""fricas"")","-\frac{x^{3} \arctan\left(\sqrt{-x^{3} - 1}\right) - \sqrt{-x^{3} - 1}}{3 \, x^{3}}"," ",0,"-1/3*(x^3*arctan(sqrt(-x^3 - 1)) - sqrt(-x^3 - 1))/x^3","A",0
498,1,39,0,1.143241," ","integrate(1/x^7/(-x^3-1)^(1/2),x, algorithm=""fricas"")","\frac{3 \, x^{6} \arctan\left(\sqrt{-x^{3} - 1}\right) - {\left(3 \, x^{3} - 2\right)} \sqrt{-x^{3} - 1}}{12 \, x^{6}}"," ",0,"1/12*(3*x^6*arctan(sqrt(-x^3 - 1)) - (3*x^3 - 2)*sqrt(-x^3 - 1))/x^6","A",0
499,1,44,0,1.089767," ","integrate(1/x^10/(-x^3-1)^(1/2),x, algorithm=""fricas"")","-\frac{15 \, x^{9} \arctan\left(\sqrt{-x^{3} - 1}\right) - {\left(15 \, x^{6} - 10 \, x^{3} + 8\right)} \sqrt{-x^{3} - 1}}{72 \, x^{9}}"," ",0,"-1/72*(15*x^9*arctan(sqrt(-x^3 - 1)) - (15*x^6 - 10*x^3 + 8)*sqrt(-x^3 - 1))/x^9","A",0
500,0,0,0,1.258232," ","integrate(x^6/(-x^3-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{3} - 1} x^{6}}{x^{3} + 1}, x\right)"," ",0,"integral(-sqrt(-x^3 - 1)*x^6/(x^3 + 1), x)","F",0
501,0,0,0,1.084341," ","integrate(x^3/(-x^3-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{3} - 1} x^{3}}{x^{3} + 1}, x\right)"," ",0,"integral(-sqrt(-x^3 - 1)*x^3/(x^3 + 1), x)","F",0
502,0,0,0,1.132281," ","integrate(1/(-x^3-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{3} - 1}}{x^{3} + 1}, x\right)"," ",0,"integral(-sqrt(-x^3 - 1)/(x^3 + 1), x)","F",0
503,0,0,0,1.322578," ","integrate(1/x^3/(-x^3-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{3} - 1}}{x^{6} + x^{3}}, x\right)"," ",0,"integral(-sqrt(-x^3 - 1)/(x^6 + x^3), x)","F",0
504,0,0,0,0.770748," ","integrate(1/x^6/(-x^3-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{3} - 1}}{x^{9} + x^{6}}, x\right)"," ",0,"integral(-sqrt(-x^3 - 1)/(x^9 + x^6), x)","F",0
505,0,0,0,1.278608," ","integrate(x^7/(-x^3-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{3} - 1} x^{7}}{x^{3} + 1}, x\right)"," ",0,"integral(-sqrt(-x^3 - 1)*x^7/(x^3 + 1), x)","F",0
506,0,0,0,1.161220," ","integrate(x^4/(-x^3-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{3} - 1} x^{4}}{x^{3} + 1}, x\right)"," ",0,"integral(-sqrt(-x^3 - 1)*x^4/(x^3 + 1), x)","F",0
507,0,0,0,1.125731," ","integrate(x/(-x^3-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{3} - 1} x}{x^{3} + 1}, x\right)"," ",0,"integral(-sqrt(-x^3 - 1)*x/(x^3 + 1), x)","F",0
508,0,0,0,1.108290," ","integrate(1/x^2/(-x^3-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{3} - 1}}{x^{5} + x^{2}}, x\right)"," ",0,"integral(-sqrt(-x^3 - 1)/(x^5 + x^2), x)","F",0
509,0,0,0,1.125691," ","integrate(1/x^5/(-x^3-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{3} - 1}}{x^{8} + x^{5}}, x\right)"," ",0,"integral(-sqrt(-x^3 - 1)/(x^8 + x^5), x)","F",0
510,1,57,0,1.090600," ","integrate(x^11*(b*x^3+a)^(1/3),x, algorithm=""fricas"")","\frac{{\left(140 \, b^{4} x^{12} + 14 \, a b^{3} x^{9} - 18 \, a^{2} b^{2} x^{6} + 27 \, a^{3} b x^{3} - 81 \, a^{4}\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{1820 \, b^{4}}"," ",0,"1/1820*(140*b^4*x^12 + 14*a*b^3*x^9 - 18*a^2*b^2*x^6 + 27*a^3*b*x^3 - 81*a^4)*(b*x^3 + a)^(1/3)/b^4","A",0
511,1,46,0,0.762376," ","integrate(x^8*(b*x^3+a)^(1/3),x, algorithm=""fricas"")","\frac{{\left(14 \, b^{3} x^{9} + 2 \, a b^{2} x^{6} - 3 \, a^{2} b x^{3} + 9 \, a^{3}\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{140 \, b^{3}}"," ",0,"1/140*(14*b^3*x^9 + 2*a*b^2*x^6 - 3*a^2*b*x^3 + 9*a^3)*(b*x^3 + a)^(1/3)/b^3","A",0
512,1,34,0,1.131236," ","integrate(x^5*(b*x^3+a)^(1/3),x, algorithm=""fricas"")","\frac{{\left(4 \, b^{2} x^{6} + a b x^{3} - 3 \, a^{2}\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{28 \, b^{2}}"," ",0,"1/28*(4*b^2*x^6 + a*b*x^3 - 3*a^2)*(b*x^3 + a)^(1/3)/b^2","A",0
513,1,14,0,1.050226," ","integrate(x^2*(b*x^3+a)^(1/3),x, algorithm=""fricas"")","\frac{{\left(b x^{3} + a\right)}^{\frac{4}{3}}}{4 \, b}"," ",0,"1/4*(b*x^3 + a)^(4/3)/b","A",0
514,1,100,0,1.262164," ","integrate((b*x^3+a)^(1/3)/x,x, algorithm=""fricas"")","-\frac{1}{3} \, \sqrt{3} a^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} a^{\frac{2}{3}} + \sqrt{3} a}{3 \, a}\right) - \frac{1}{6} \, a^{\frac{1}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + a^{\frac{2}{3}}\right) + \frac{1}{3} \, a^{\frac{1}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} - a^{\frac{1}{3}}\right) + {\left(b x^{3} + a\right)}^{\frac{1}{3}}"," ",0,"-1/3*sqrt(3)*a^(1/3)*arctan(1/3*(2*sqrt(3)*(b*x^3 + a)^(1/3)*a^(2/3) + sqrt(3)*a)/a) - 1/6*a^(1/3)*log((b*x^3 + a)^(2/3) + (b*x^3 + a)^(1/3)*a^(1/3) + a^(2/3)) + 1/3*a^(1/3)*log((b*x^3 + a)^(1/3) - a^(1/3)) + (b*x^3 + a)^(1/3)","A",0
515,1,155,0,1.240683," ","integrate((b*x^3+a)^(1/3)/x^4,x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} {\left(a^{2}\right)}^{\frac{1}{6}} a b x^{3} \arctan\left(\frac{{\left(a^{2}\right)}^{\frac{1}{6}} {\left(\sqrt{3} {\left(a^{2}\right)}^{\frac{1}{3}} a + 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(a^{2}\right)}^{\frac{2}{3}}\right)}}{3 \, a^{2}}\right) + {\left(a^{2}\right)}^{\frac{2}{3}} b x^{3} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} a + {\left(a^{2}\right)}^{\frac{1}{3}} a + {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(a^{2}\right)}^{\frac{2}{3}}\right) - 2 \, {\left(a^{2}\right)}^{\frac{2}{3}} b x^{3} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} a - {\left(a^{2}\right)}^{\frac{2}{3}}\right) + 6 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} a^{2}}{18 \, a^{2} x^{3}}"," ",0,"-1/18*(2*sqrt(3)*(a^2)^(1/6)*a*b*x^3*arctan(1/3*(a^2)^(1/6)*(sqrt(3)*(a^2)^(1/3)*a + 2*sqrt(3)*(b*x^3 + a)^(1/3)*(a^2)^(2/3))/a^2) + (a^2)^(2/3)*b*x^3*log((b*x^3 + a)^(2/3)*a + (a^2)^(1/3)*a + (b*x^3 + a)^(1/3)*(a^2)^(2/3)) - 2*(a^2)^(2/3)*b*x^3*log((b*x^3 + a)^(1/3)*a - (a^2)^(2/3)) + 6*(b*x^3 + a)^(1/3)*a^2)/(a^2*x^3)","A",0
516,1,181,0,1.226357," ","integrate(x^4*(b*x^3+a)^(1/3),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} a^{2} {\left(b^{2}\right)}^{\frac{1}{6}} b \arctan\left(\frac{{\left(\sqrt{3} {\left(b^{2}\right)}^{\frac{1}{3}} b x + 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b^{2}\right)}^{\frac{2}{3}}\right)} {\left(b^{2}\right)}^{\frac{1}{6}}}{3 \, b^{2} x}\right) - 2 \, a^{2} {\left(b^{2}\right)}^{\frac{2}{3}} \log\left(-\frac{{\left(b^{2}\right)}^{\frac{2}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}} b}{x}\right) + a^{2} {\left(b^{2}\right)}^{\frac{2}{3}} \log\left(\frac{{\left(b^{2}\right)}^{\frac{1}{3}} b x^{2} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b^{2}\right)}^{\frac{2}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}} b}{x^{2}}\right) - 3 \, {\left(3 \, b^{3} x^{5} + a b^{2} x^{2}\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{54 \, b^{3}}"," ",0,"-1/54*(2*sqrt(3)*a^2*(b^2)^(1/6)*b*arctan(1/3*(sqrt(3)*(b^2)^(1/3)*b*x + 2*sqrt(3)*(b*x^3 + a)^(1/3)*(b^2)^(2/3))*(b^2)^(1/6)/(b^2*x)) - 2*a^2*(b^2)^(2/3)*log(-((b^2)^(2/3)*x - (b*x^3 + a)^(1/3)*b)/x) + a^2*(b^2)^(2/3)*log(((b^2)^(1/3)*b*x^2 + (b*x^3 + a)^(1/3)*(b^2)^(2/3)*x + (b*x^3 + a)^(2/3)*b)/x^2) - 3*(3*b^3*x^5 + a*b^2*x^2)*(b*x^3 + a)^(1/3))/b^3","A",0
517,1,193,0,1.240422," ","integrate(x*(b*x^3+a)^(1/3),x, algorithm=""fricas"")","\frac{6 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{2} x^{2} + 2 \, \sqrt{3} a b \sqrt{-\left(-b^{2}\right)^{\frac{1}{3}}} \arctan\left(-\frac{{\left(\sqrt{3} \left(-b^{2}\right)^{\frac{1}{3}} b x - 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b^{2}\right)^{\frac{2}{3}}\right)} \sqrt{-\left(-b^{2}\right)^{\frac{1}{3}}}}{3 \, b^{2} x}\right) - 2 \, \left(-b^{2}\right)^{\frac{2}{3}} a \log\left(-\frac{\left(-b^{2}\right)^{\frac{2}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}} b}{x}\right) + \left(-b^{2}\right)^{\frac{2}{3}} a \log\left(-\frac{\left(-b^{2}\right)^{\frac{1}{3}} b x^{2} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b^{2}\right)^{\frac{2}{3}} x - {\left(b x^{3} + a\right)}^{\frac{2}{3}} b}{x^{2}}\right)}{18 \, b^{2}}"," ",0,"1/18*(6*(b*x^3 + a)^(1/3)*b^2*x^2 + 2*sqrt(3)*a*b*sqrt(-(-b^2)^(1/3))*arctan(-1/3*(sqrt(3)*(-b^2)^(1/3)*b*x - 2*sqrt(3)*(b*x^3 + a)^(1/3)*(-b^2)^(2/3))*sqrt(-(-b^2)^(1/3))/(b^2*x)) - 2*(-b^2)^(2/3)*a*log(-((-b^2)^(2/3)*x - (b*x^3 + a)^(1/3)*b)/x) + (-b^2)^(2/3)*a*log(-((-b^2)^(1/3)*b*x^2 - (b*x^3 + a)^(1/3)*(-b^2)^(2/3)*x - (b*x^3 + a)^(2/3)*b)/x^2))/b^2","B",0
518,-1,0,0,0.000000," ","integrate((b*x^3+a)^(1/3)/x^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
519,1,17,0,1.244808," ","integrate((b*x^3+a)^(1/3)/x^5,x, algorithm=""fricas"")","-\frac{{\left(b x^{3} + a\right)}^{\frac{4}{3}}}{4 \, a x^{4}}"," ",0,"-1/4*(b*x^3 + a)^(4/3)/(a*x^4)","A",0
520,1,38,0,1.179754," ","integrate((b*x^3+a)^(1/3)/x^8,x, algorithm=""fricas"")","\frac{{\left(3 \, b^{2} x^{6} - a b x^{3} - 4 \, a^{2}\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{28 \, a^{2} x^{7}}"," ",0,"1/28*(3*b^2*x^6 - a*b*x^3 - 4*a^2)*(b*x^3 + a)^(1/3)/(a^2*x^7)","A",0
521,1,49,0,1.164757," ","integrate((b*x^3+a)^(1/3)/x^11,x, algorithm=""fricas"")","-\frac{{\left(9 \, b^{3} x^{9} - 3 \, a b^{2} x^{6} + 2 \, a^{2} b x^{3} + 14 \, a^{3}\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{140 \, a^{3} x^{10}}"," ",0,"-1/140*(9*b^3*x^9 - 3*a*b^2*x^6 + 2*a^2*b*x^3 + 14*a^3)*(b*x^3 + a)^(1/3)/(a^3*x^10)","A",0
522,1,60,0,0.888200," ","integrate((b*x^3+a)^(1/3)/x^14,x, algorithm=""fricas"")","\frac{{\left(81 \, b^{4} x^{12} - 27 \, a b^{3} x^{9} + 18 \, a^{2} b^{2} x^{6} - 14 \, a^{3} b x^{3} - 140 \, a^{4}\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{1820 \, a^{4} x^{13}}"," ",0,"1/1820*(81*b^4*x^12 - 27*a*b^3*x^9 + 18*a^2*b^2*x^6 - 14*a^3*b*x^3 - 140*a^4)*(b*x^3 + a)^(1/3)/(a^4*x^13)","A",0
523,0,0,0,1.049552," ","integrate(x^3*(b*x^3+a)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} x^{3}, x\right)"," ",0,"integral((b*x^3 + a)^(1/3)*x^3, x)","F",0
524,0,0,0,1.072106," ","integrate((b*x^3+a)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{3} + a\right)}^{\frac{1}{3}}, x\right)"," ",0,"integral((b*x^3 + a)^(1/3), x)","F",0
525,0,0,0,0.914977," ","integrate((b*x^3+a)^(1/3)/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x^{3}}, x\right)"," ",0,"integral((b*x^3 + a)^(1/3)/x^3, x)","F",0
526,0,0,0,0.623193," ","integrate((b*x^3+a)^(1/3)/x^6,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x^{6}}, x\right)"," ",0,"integral((b*x^3 + a)^(1/3)/x^6, x)","F",0
527,1,57,0,0.717660," ","integrate(x^11*(b*x^3+a)^(2/3),x, algorithm=""fricas"")","\frac{{\left(220 \, b^{4} x^{12} + 40 \, a b^{3} x^{9} - 45 \, a^{2} b^{2} x^{6} + 54 \, a^{3} b x^{3} - 81 \, a^{4}\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{3080 \, b^{4}}"," ",0,"1/3080*(220*b^4*x^12 + 40*a*b^3*x^9 - 45*a^2*b^2*x^6 + 54*a^3*b*x^3 - 81*a^4)*(b*x^3 + a)^(2/3)/b^4","A",0
528,1,46,0,0.963084," ","integrate(x^8*(b*x^3+a)^(2/3),x, algorithm=""fricas"")","\frac{{\left(20 \, b^{3} x^{9} + 5 \, a b^{2} x^{6} - 6 \, a^{2} b x^{3} + 9 \, a^{3}\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{220 \, b^{3}}"," ",0,"1/220*(20*b^3*x^9 + 5*a*b^2*x^6 - 6*a^2*b*x^3 + 9*a^3)*(b*x^3 + a)^(2/3)/b^3","A",0
529,1,35,0,1.041111," ","integrate(x^5*(b*x^3+a)^(2/3),x, algorithm=""fricas"")","\frac{{\left(5 \, b^{2} x^{6} + 2 \, a b x^{3} - 3 \, a^{2}\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{40 \, b^{2}}"," ",0,"1/40*(5*b^2*x^6 + 2*a*b*x^3 - 3*a^2)*(b*x^3 + a)^(2/3)/b^2","A",0
530,1,14,0,0.772362," ","integrate(x^2*(b*x^3+a)^(2/3),x, algorithm=""fricas"")","\frac{{\left(b x^{3} + a\right)}^{\frac{5}{3}}}{5 \, b}"," ",0,"1/5*(b*x^3 + a)^(5/3)/b","A",0
531,1,122,0,0.699342," ","integrate((b*x^3+a)^(2/3)/x,x, algorithm=""fricas"")","\frac{1}{3} \, \sqrt{3} {\left(a^{2}\right)}^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} a + 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(a^{2}\right)}^{\frac{1}{3}}}{3 \, a}\right) - \frac{1}{6} \, {\left(a^{2}\right)}^{\frac{1}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} a + {\left(a^{2}\right)}^{\frac{1}{3}} a + {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(a^{2}\right)}^{\frac{2}{3}}\right) + \frac{1}{3} \, {\left(a^{2}\right)}^{\frac{1}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} a - {\left(a^{2}\right)}^{\frac{2}{3}}\right) + \frac{1}{2} \, {\left(b x^{3} + a\right)}^{\frac{2}{3}}"," ",0,"1/3*sqrt(3)*(a^2)^(1/3)*arctan(1/3*(sqrt(3)*a + 2*sqrt(3)*(b*x^3 + a)^(1/3)*(a^2)^(1/3))/a) - 1/6*(a^2)^(1/3)*log((b*x^3 + a)^(2/3)*a + (a^2)^(1/3)*a + (b*x^3 + a)^(1/3)*(a^2)^(2/3)) + 1/3*(a^2)^(1/3)*log((b*x^3 + a)^(1/3)*a - (a^2)^(2/3)) + 1/2*(b*x^3 + a)^(2/3)","A",0
532,1,290,0,0.729707," ","integrate((b*x^3+a)^(2/3)/x^4,x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{\frac{1}{3}} a b x^{3} \sqrt{-\frac{1}{a^{\frac{2}{3}}}} \log\left(\frac{2 \, b x^{3} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} a^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} a - a^{\frac{4}{3}}\right)} \sqrt{-\frac{1}{a^{\frac{2}{3}}}} - 3 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} a^{\frac{2}{3}} + 3 \, a}{x^{3}}\right) - a^{\frac{2}{3}} b x^{3} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + a^{\frac{2}{3}}\right) + 2 \, a^{\frac{2}{3}} b x^{3} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} - a^{\frac{1}{3}}\right) - 3 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} a}{9 \, a x^{3}}, \frac{6 \, \sqrt{\frac{1}{3}} a^{\frac{2}{3}} b x^{3} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} + a^{\frac{1}{3}}\right)}}{a^{\frac{1}{3}}}\right) - a^{\frac{2}{3}} b x^{3} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + a^{\frac{2}{3}}\right) + 2 \, a^{\frac{2}{3}} b x^{3} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} - a^{\frac{1}{3}}\right) - 3 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} a}{9 \, a x^{3}}\right]"," ",0,"[1/9*(3*sqrt(1/3)*a*b*x^3*sqrt(-1/a^(2/3))*log((2*b*x^3 + 3*sqrt(1/3)*(2*(b*x^3 + a)^(2/3)*a^(2/3) - (b*x^3 + a)^(1/3)*a - a^(4/3))*sqrt(-1/a^(2/3)) - 3*(b*x^3 + a)^(1/3)*a^(2/3) + 3*a)/x^3) - a^(2/3)*b*x^3*log((b*x^3 + a)^(2/3) + (b*x^3 + a)^(1/3)*a^(1/3) + a^(2/3)) + 2*a^(2/3)*b*x^3*log((b*x^3 + a)^(1/3) - a^(1/3)) - 3*(b*x^3 + a)^(2/3)*a)/(a*x^3), 1/9*(6*sqrt(1/3)*a^(2/3)*b*x^3*arctan(sqrt(1/3)*(2*(b*x^3 + a)^(1/3) + a^(1/3))/a^(1/3)) - a^(2/3)*b*x^3*log((b*x^3 + a)^(2/3) + (b*x^3 + a)^(1/3)*a^(1/3) + a^(2/3)) + 2*a^(2/3)*b*x^3*log((b*x^3 + a)^(1/3) - a^(1/3)) - 3*(b*x^3 + a)^(2/3)*a)/(a*x^3)]","A",0
533,0,0,0,0.869009," ","integrate(x^4*(b*x^3+a)^(2/3),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} x^{4}, x\right)"," ",0,"integral((b*x^3 + a)^(2/3)*x^4, x)","F",0
534,0,0,0,0.960026," ","integrate(x*(b*x^3+a)^(2/3),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} x, x\right)"," ",0,"integral((b*x^3 + a)^(2/3)*x, x)","F",0
535,0,0,0,1.116312," ","integrate((b*x^3+a)^(2/3)/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}, x\right)"," ",0,"integral((b*x^3 + a)^(2/3)/x^2, x)","F",0
536,0,0,0,0.780447," ","integrate((b*x^3+a)^(2/3)/x^5,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{5}}, x\right)"," ",0,"integral((b*x^3 + a)^(2/3)/x^5, x)","F",0
537,1,345,0,0.972670," ","integrate(x^3*(b*x^3+a)^(2/3),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{\frac{1}{3}} a^{2} b \sqrt{-\frac{1}{b^{\frac{2}{3}}}} \log\left(3 \, b x^{3} - 3 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{2}{3}} x^{2} - 3 \, \sqrt{\frac{1}{3}} {\left(b^{\frac{4}{3}} x^{3} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} b x^{2} - 2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} b^{\frac{2}{3}} x\right)} \sqrt{-\frac{1}{b^{\frac{2}{3}}}} + 2 \, a\right) + 2 \, a^{2} b^{\frac{2}{3}} \log\left(-\frac{b^{\frac{1}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) - a^{2} b^{\frac{2}{3}} \log\left(\frac{b^{\frac{2}{3}} x^{2} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right) + 3 \, {\left(3 \, b^{2} x^{4} + 2 \, a b x\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{54 \, b^{2}}, \frac{6 \, \sqrt{\frac{1}{3}} a^{2} b^{\frac{2}{3}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(b^{\frac{1}{3}} x + 2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right)}}{b^{\frac{1}{3}} x}\right) + 2 \, a^{2} b^{\frac{2}{3}} \log\left(-\frac{b^{\frac{1}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) - a^{2} b^{\frac{2}{3}} \log\left(\frac{b^{\frac{2}{3}} x^{2} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right) + 3 \, {\left(3 \, b^{2} x^{4} + 2 \, a b x\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{54 \, b^{2}}\right]"," ",0,"[1/54*(3*sqrt(1/3)*a^2*b*sqrt(-1/b^(2/3))*log(3*b*x^3 - 3*(b*x^3 + a)^(1/3)*b^(2/3)*x^2 - 3*sqrt(1/3)*(b^(4/3)*x^3 + (b*x^3 + a)^(1/3)*b*x^2 - 2*(b*x^3 + a)^(2/3)*b^(2/3)*x)*sqrt(-1/b^(2/3)) + 2*a) + 2*a^2*b^(2/3)*log(-(b^(1/3)*x - (b*x^3 + a)^(1/3))/x) - a^2*b^(2/3)*log((b^(2/3)*x^2 + (b*x^3 + a)^(1/3)*b^(1/3)*x + (b*x^3 + a)^(2/3))/x^2) + 3*(3*b^2*x^4 + 2*a*b*x)*(b*x^3 + a)^(2/3))/b^2, 1/54*(6*sqrt(1/3)*a^2*b^(2/3)*arctan(sqrt(1/3)*(b^(1/3)*x + 2*(b*x^3 + a)^(1/3))/(b^(1/3)*x)) + 2*a^2*b^(2/3)*log(-(b^(1/3)*x - (b*x^3 + a)^(1/3))/x) - a^2*b^(2/3)*log((b^(2/3)*x^2 + (b*x^3 + a)^(1/3)*b^(1/3)*x + (b*x^3 + a)^(2/3))/x^2) + 3*(3*b^2*x^4 + 2*a*b*x)*(b*x^3 + a)^(2/3))/b^2]","A",0
538,1,362,0,0.844421," ","integrate((b*x^3+a)^(2/3),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{\frac{1}{3}} a b \sqrt{\frac{\left(-b\right)^{\frac{1}{3}}}{b}} \log\left(3 \, b x^{3} - 3 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b\right)^{\frac{2}{3}} x^{2} - 3 \, \sqrt{\frac{1}{3}} {\left(\left(-b\right)^{\frac{1}{3}} b x^{3} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} b x^{2} + 2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} \left(-b\right)^{\frac{2}{3}} x\right)} \sqrt{\frac{\left(-b\right)^{\frac{1}{3}}}{b}} + 2 \, a\right) + 3 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} b x - 2 \, a \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) + a \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{2}{3}} x^{2} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{9 \, b}, -\frac{6 \, \sqrt{\frac{1}{3}} a b \sqrt{-\frac{\left(-b\right)^{\frac{1}{3}}}{b}} \arctan\left(-\frac{\sqrt{\frac{1}{3}} {\left(\left(-b\right)^{\frac{1}{3}} x - 2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-b\right)^{\frac{1}{3}}}{b}}}{x}\right) - 3 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} b x + 2 \, a \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) - a \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{2}{3}} x^{2} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{9 \, b}\right]"," ",0,"[1/9*(3*sqrt(1/3)*a*b*sqrt((-b)^(1/3)/b)*log(3*b*x^3 - 3*(b*x^3 + a)^(1/3)*(-b)^(2/3)*x^2 - 3*sqrt(1/3)*((-b)^(1/3)*b*x^3 - (b*x^3 + a)^(1/3)*b*x^2 + 2*(b*x^3 + a)^(2/3)*(-b)^(2/3)*x)*sqrt((-b)^(1/3)/b) + 2*a) + 3*(b*x^3 + a)^(2/3)*b*x - 2*a*(-b)^(2/3)*log(((-b)^(1/3)*x + (b*x^3 + a)^(1/3))/x) + a*(-b)^(2/3)*log(((-b)^(2/3)*x^2 - (b*x^3 + a)^(1/3)*(-b)^(1/3)*x + (b*x^3 + a)^(2/3))/x^2))/b, -1/9*(6*sqrt(1/3)*a*b*sqrt(-(-b)^(1/3)/b)*arctan(-sqrt(1/3)*((-b)^(1/3)*x - 2*(b*x^3 + a)^(1/3))*sqrt(-(-b)^(1/3)/b)/x) - 3*(b*x^3 + a)^(2/3)*b*x + 2*a*(-b)^(2/3)*log(((-b)^(1/3)*x + (b*x^3 + a)^(1/3))/x) - a*(-b)^(2/3)*log(((-b)^(2/3)*x^2 - (b*x^3 + a)^(1/3)*(-b)^(1/3)*x + (b*x^3 + a)^(2/3))/x^2))/b]","B",0
539,-1,0,0,0.000000," ","integrate((b*x^3+a)^(2/3)/x^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
540,1,17,0,1.099906," ","integrate((b*x^3+a)^(2/3)/x^6,x, algorithm=""fricas"")","-\frac{{\left(b x^{3} + a\right)}^{\frac{5}{3}}}{5 \, a x^{5}}"," ",0,"-1/5*(b*x^3 + a)^(5/3)/(a*x^5)","A",0
541,1,38,0,1.201273," ","integrate((b*x^3+a)^(2/3)/x^9,x, algorithm=""fricas"")","\frac{{\left(3 \, b^{2} x^{6} - 2 \, a b x^{3} - 5 \, a^{2}\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{40 \, a^{2} x^{8}}"," ",0,"1/40*(3*b^2*x^6 - 2*a*b*x^3 - 5*a^2)*(b*x^3 + a)^(2/3)/(a^2*x^8)","A",0
542,1,49,0,0.915429," ","integrate((b*x^3+a)^(2/3)/x^12,x, algorithm=""fricas"")","-\frac{{\left(9 \, b^{3} x^{9} - 6 \, a b^{2} x^{6} + 5 \, a^{2} b x^{3} + 20 \, a^{3}\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{220 \, a^{3} x^{11}}"," ",0,"-1/220*(9*b^3*x^9 - 6*a*b^2*x^6 + 5*a^2*b*x^3 + 20*a^3)*(b*x^3 + a)^(2/3)/(a^3*x^11)","A",0
543,1,33,0,1.180124," ","integrate(x^8*(-x^3+1)^(6/5),x, algorithm=""fricas"")","-\frac{5}{5544} \, {\left(88 \, x^{12} - 121 \, x^{9} + 3 \, x^{6} + 5 \, x^{3} + 25\right)} {\left(-x^{3} + 1\right)}^{\frac{1}{5}}"," ",0,"-5/5544*(88*x^12 - 121*x^9 + 3*x^6 + 5*x^3 + 25)*(-x^3 + 1)^(1/5)","A",0
544,1,46,0,1.282408," ","integrate(x^11/(b*x^3+a)^(1/3),x, algorithm=""fricas"")","\frac{{\left(40 \, b^{3} x^{9} - 45 \, a b^{2} x^{6} + 54 \, a^{2} b x^{3} - 81 \, a^{3}\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{440 \, b^{4}}"," ",0,"1/440*(40*b^3*x^9 - 45*a*b^2*x^6 + 54*a^2*b*x^3 - 81*a^3)*(b*x^3 + a)^(2/3)/b^4","A",0
545,1,35,0,0.840071," ","integrate(x^8/(b*x^3+a)^(1/3),x, algorithm=""fricas"")","\frac{{\left(5 \, b^{2} x^{6} - 6 \, a b x^{3} + 9 \, a^{2}\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{40 \, b^{3}}"," ",0,"1/40*(5*b^2*x^6 - 6*a*b*x^3 + 9*a^2)*(b*x^3 + a)^(2/3)/b^3","A",0
546,1,24,0,1.189420," ","integrate(x^5/(b*x^3+a)^(1/3),x, algorithm=""fricas"")","\frac{{\left(2 \, b x^{3} - 3 \, a\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{10 \, b^{2}}"," ",0,"1/10*(2*b*x^3 - 3*a)*(b*x^3 + a)^(2/3)/b^2","A",0
547,1,14,0,1.013697," ","integrate(x^2/(b*x^3+a)^(1/3),x, algorithm=""fricas"")","\frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}{2 \, b}"," ",0,"1/2*(b*x^3 + a)^(2/3)/b","A",0
548,1,236,0,0.918401," ","integrate(1/x/(b*x^3+a)^(1/3),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{\frac{1}{3}} a \sqrt{-\frac{1}{a^{\frac{2}{3}}}} \log\left(\frac{2 \, b x^{3} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} a^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} a - a^{\frac{4}{3}}\right)} \sqrt{-\frac{1}{a^{\frac{2}{3}}}} - 3 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} a^{\frac{2}{3}} + 3 \, a}{x^{3}}\right) - a^{\frac{2}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + a^{\frac{2}{3}}\right) + 2 \, a^{\frac{2}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} - a^{\frac{1}{3}}\right)}{6 \, a}, \frac{6 \, \sqrt{\frac{1}{3}} a^{\frac{2}{3}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} + a^{\frac{1}{3}}\right)}}{a^{\frac{1}{3}}}\right) - a^{\frac{2}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + a^{\frac{2}{3}}\right) + 2 \, a^{\frac{2}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} - a^{\frac{1}{3}}\right)}{6 \, a}\right]"," ",0,"[1/6*(3*sqrt(1/3)*a*sqrt(-1/a^(2/3))*log((2*b*x^3 + 3*sqrt(1/3)*(2*(b*x^3 + a)^(2/3)*a^(2/3) - (b*x^3 + a)^(1/3)*a - a^(4/3))*sqrt(-1/a^(2/3)) - 3*(b*x^3 + a)^(1/3)*a^(2/3) + 3*a)/x^3) - a^(2/3)*log((b*x^3 + a)^(2/3) + (b*x^3 + a)^(1/3)*a^(1/3) + a^(2/3)) + 2*a^(2/3)*log((b*x^3 + a)^(1/3) - a^(1/3)))/a, 1/6*(6*sqrt(1/3)*a^(2/3)*arctan(sqrt(1/3)*(2*(b*x^3 + a)^(1/3) + a^(1/3))/a^(1/3)) - a^(2/3)*log((b*x^3 + a)^(2/3) + (b*x^3 + a)^(1/3)*a^(1/3) + a^(2/3)) + 2*a^(2/3)*log((b*x^3 + a)^(1/3) - a^(1/3)))/a]","A",0
549,1,344,0,0.705781," ","integrate(1/x^4/(b*x^3+a)^(1/3),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{\frac{1}{3}} a b x^{3} \sqrt{\frac{\left(-a\right)^{\frac{1}{3}}}{a}} \log\left(\frac{2 \, b x^{3} - 3 \, \sqrt{\frac{1}{3}} {\left(2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} \left(-a\right)^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} a + \left(-a\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(-a\right)^{\frac{1}{3}}}{a}} - 3 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-a\right)^{\frac{2}{3}} + 3 \, a}{x^{3}}\right) + \left(-a\right)^{\frac{2}{3}} b x^{3} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-a\right)^{\frac{1}{3}} + \left(-a\right)^{\frac{2}{3}}\right) - 2 \, \left(-a\right)^{\frac{2}{3}} b x^{3} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} + \left(-a\right)^{\frac{1}{3}}\right) - 6 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} a}{18 \, a^{2} x^{3}}, -\frac{6 \, \sqrt{\frac{1}{3}} a b x^{3} \sqrt{-\frac{\left(-a\right)^{\frac{1}{3}}}{a}} \arctan\left(\sqrt{\frac{1}{3}} {\left(2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} - \left(-a\right)^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-a\right)^{\frac{1}{3}}}{a}}\right) - \left(-a\right)^{\frac{2}{3}} b x^{3} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-a\right)^{\frac{1}{3}} + \left(-a\right)^{\frac{2}{3}}\right) + 2 \, \left(-a\right)^{\frac{2}{3}} b x^{3} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} + \left(-a\right)^{\frac{1}{3}}\right) + 6 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} a}{18 \, a^{2} x^{3}}\right]"," ",0,"[1/18*(3*sqrt(1/3)*a*b*x^3*sqrt((-a)^(1/3)/a)*log((2*b*x^3 - 3*sqrt(1/3)*(2*(b*x^3 + a)^(2/3)*(-a)^(2/3) - (b*x^3 + a)^(1/3)*a + (-a)^(1/3)*a)*sqrt((-a)^(1/3)/a) - 3*(b*x^3 + a)^(1/3)*(-a)^(2/3) + 3*a)/x^3) + (-a)^(2/3)*b*x^3*log((b*x^3 + a)^(2/3) - (b*x^3 + a)^(1/3)*(-a)^(1/3) + (-a)^(2/3)) - 2*(-a)^(2/3)*b*x^3*log((b*x^3 + a)^(1/3) + (-a)^(1/3)) - 6*(b*x^3 + a)^(2/3)*a)/(a^2*x^3), -1/18*(6*sqrt(1/3)*a*b*x^3*sqrt(-(-a)^(1/3)/a)*arctan(sqrt(1/3)*(2*(b*x^3 + a)^(1/3) - (-a)^(1/3))*sqrt(-(-a)^(1/3)/a)) - (-a)^(2/3)*b*x^3*log((b*x^3 + a)^(2/3) - (b*x^3 + a)^(1/3)*(-a)^(1/3) + (-a)^(2/3)) + 2*(-a)^(2/3)*b*x^3*log((b*x^3 + a)^(1/3) + (-a)^(1/3)) + 6*(b*x^3 + a)^(2/3)*a)/(a^2*x^3)]","A",0
550,0,0,0,0.694314," ","integrate(x^7/(b*x^3+a)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{7}}{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}, x\right)"," ",0,"integral(x^7/(b*x^3 + a)^(1/3), x)","F",0
551,0,0,0,0.747829," ","integrate(x^4/(b*x^3+a)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{4}}{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}, x\right)"," ",0,"integral(x^4/(b*x^3 + a)^(1/3), x)","F",0
552,0,0,0,0.957781," ","integrate(x/(b*x^3+a)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}, x\right)"," ",0,"integral(x/(b*x^3 + a)^(1/3), x)","F",0
553,0,0,0,0.833670," ","integrate(1/x^2/(b*x^3+a)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}{b x^{5} + a x^{2}}, x\right)"," ",0,"integral((b*x^3 + a)^(2/3)/(b*x^5 + a*x^2), x)","F",0
554,0,0,0,0.712802," ","integrate(1/x^5/(b*x^3+a)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}{b x^{8} + a x^{5}}, x\right)"," ",0,"integral((b*x^3 + a)^(2/3)/(b*x^8 + a*x^5), x)","F",0
555,1,309,0,1.068772," ","integrate(x^3/(b*x^3+a)^(1/3),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{\frac{1}{3}} a b \sqrt{-\frac{1}{b^{\frac{2}{3}}}} \log\left(3 \, b x^{3} - 3 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{2}{3}} x^{2} - 3 \, \sqrt{\frac{1}{3}} {\left(b^{\frac{4}{3}} x^{3} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} b x^{2} - 2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} b^{\frac{2}{3}} x\right)} \sqrt{-\frac{1}{b^{\frac{2}{3}}}} + 2 \, a\right) + 6 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} b x + 2 \, a b^{\frac{2}{3}} \log\left(-\frac{b^{\frac{1}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) - a b^{\frac{2}{3}} \log\left(\frac{b^{\frac{2}{3}} x^{2} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{18 \, b^{2}}, \frac{6 \, \sqrt{\frac{1}{3}} a b^{\frac{2}{3}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(b^{\frac{1}{3}} x + 2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right)}}{b^{\frac{1}{3}} x}\right) + 6 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} b x + 2 \, a b^{\frac{2}{3}} \log\left(-\frac{b^{\frac{1}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) - a b^{\frac{2}{3}} \log\left(\frac{b^{\frac{2}{3}} x^{2} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{18 \, b^{2}}\right]"," ",0,"[1/18*(3*sqrt(1/3)*a*b*sqrt(-1/b^(2/3))*log(3*b*x^3 - 3*(b*x^3 + a)^(1/3)*b^(2/3)*x^2 - 3*sqrt(1/3)*(b^(4/3)*x^3 + (b*x^3 + a)^(1/3)*b*x^2 - 2*(b*x^3 + a)^(2/3)*b^(2/3)*x)*sqrt(-1/b^(2/3)) + 2*a) + 6*(b*x^3 + a)^(2/3)*b*x + 2*a*b^(2/3)*log(-(b^(1/3)*x - (b*x^3 + a)^(1/3))/x) - a*b^(2/3)*log((b^(2/3)*x^2 + (b*x^3 + a)^(1/3)*b^(1/3)*x + (b*x^3 + a)^(2/3))/x^2))/b^2, 1/18*(6*sqrt(1/3)*a*b^(2/3)*arctan(sqrt(1/3)*(b^(1/3)*x + 2*(b*x^3 + a)^(1/3))/(b^(1/3)*x)) + 6*(b*x^3 + a)^(2/3)*b*x + 2*a*b^(2/3)*log(-(b^(1/3)*x - (b*x^3 + a)^(1/3))/x) - a*b^(2/3)*log((b^(2/3)*x^2 + (b*x^3 + a)^(1/3)*b^(1/3)*x + (b*x^3 + a)^(2/3))/x^2))/b^2]","A",0
556,1,330,0,1.128320," ","integrate(1/(b*x^3+a)^(1/3),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{\frac{1}{3}} b \sqrt{\frac{\left(-b\right)^{\frac{1}{3}}}{b}} \log\left(3 \, b x^{3} - 3 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b\right)^{\frac{2}{3}} x^{2} - 3 \, \sqrt{\frac{1}{3}} {\left(\left(-b\right)^{\frac{1}{3}} b x^{3} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} b x^{2} + 2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} \left(-b\right)^{\frac{2}{3}} x\right)} \sqrt{\frac{\left(-b\right)^{\frac{1}{3}}}{b}} + 2 \, a\right) - 2 \, \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) + \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{2}{3}} x^{2} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{6 \, b}, -\frac{6 \, \sqrt{\frac{1}{3}} b \sqrt{-\frac{\left(-b\right)^{\frac{1}{3}}}{b}} \arctan\left(-\frac{\sqrt{\frac{1}{3}} {\left(\left(-b\right)^{\frac{1}{3}} x - 2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-b\right)^{\frac{1}{3}}}{b}}}{x}\right) + 2 \, \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) - \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{2}{3}} x^{2} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{6 \, b}\right]"," ",0,"[1/6*(3*sqrt(1/3)*b*sqrt((-b)^(1/3)/b)*log(3*b*x^3 - 3*(b*x^3 + a)^(1/3)*(-b)^(2/3)*x^2 - 3*sqrt(1/3)*((-b)^(1/3)*b*x^3 - (b*x^3 + a)^(1/3)*b*x^2 + 2*(b*x^3 + a)^(2/3)*(-b)^(2/3)*x)*sqrt((-b)^(1/3)/b) + 2*a) - 2*(-b)^(2/3)*log(((-b)^(1/3)*x + (b*x^3 + a)^(1/3))/x) + (-b)^(2/3)*log(((-b)^(2/3)*x^2 - (b*x^3 + a)^(1/3)*(-b)^(1/3)*x + (b*x^3 + a)^(2/3))/x^2))/b, -1/6*(6*sqrt(1/3)*b*sqrt(-(-b)^(1/3)/b)*arctan(-sqrt(1/3)*((-b)^(1/3)*x - 2*(b*x^3 + a)^(1/3))*sqrt(-(-b)^(1/3)/b)/x) + 2*(-b)^(2/3)*log(((-b)^(1/3)*x + (b*x^3 + a)^(1/3))/x) - (-b)^(2/3)*log(((-b)^(2/3)*x^2 - (b*x^3 + a)^(1/3)*(-b)^(1/3)*x + (b*x^3 + a)^(2/3))/x^2))/b]","B",0
557,1,17,0,0.886812," ","integrate(1/x^3/(b*x^3+a)^(1/3),x, algorithm=""fricas"")","-\frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}{2 \, a x^{2}}"," ",0,"-1/2*(b*x^3 + a)^(2/3)/(a*x^2)","A",0
558,1,27,0,1.239326," ","integrate(1/x^6/(b*x^3+a)^(1/3),x, algorithm=""fricas"")","\frac{{\left(3 \, b x^{3} - 2 \, a\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{10 \, a^{2} x^{5}}"," ",0,"1/10*(3*b*x^3 - 2*a)*(b*x^3 + a)^(2/3)/(a^2*x^5)","A",0
559,1,38,0,0.967948," ","integrate(1/x^9/(b*x^3+a)^(1/3),x, algorithm=""fricas"")","-\frac{{\left(9 \, b^{2} x^{6} - 6 \, a b x^{3} + 5 \, a^{2}\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{40 \, a^{3} x^{8}}"," ",0,"-1/40*(9*b^2*x^6 - 6*a*b*x^3 + 5*a^2)*(b*x^3 + a)^(2/3)/(a^3*x^8)","A",0
560,1,49,0,0.773331," ","integrate(1/x^12/(b*x^3+a)^(1/3),x, algorithm=""fricas"")","\frac{{\left(81 \, b^{3} x^{9} - 54 \, a b^{2} x^{6} + 45 \, a^{2} b x^{3} - 40 \, a^{3}\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{440 \, a^{4} x^{11}}"," ",0,"1/440*(81*b^3*x^9 - 54*a*b^2*x^6 + 45*a^2*b*x^3 - 40*a^3)*(b*x^3 + a)^(2/3)/(a^4*x^11)","A",0
561,1,46,0,0.875125," ","integrate(x^11/(b*x^3+a)^(2/3),x, algorithm=""fricas"")","\frac{{\left(14 \, b^{3} x^{9} - 18 \, a b^{2} x^{6} + 27 \, a^{2} b x^{3} - 81 \, a^{3}\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{140 \, b^{4}}"," ",0,"1/140*(14*b^3*x^9 - 18*a*b^2*x^6 + 27*a^2*b*x^3 - 81*a^3)*(b*x^3 + a)^(1/3)/b^4","A",0
562,1,35,0,1.040343," ","integrate(x^8/(b*x^3+a)^(2/3),x, algorithm=""fricas"")","\frac{{\left(2 \, b^{2} x^{6} - 3 \, a b x^{3} + 9 \, a^{2}\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{14 \, b^{3}}"," ",0,"1/14*(2*b^2*x^6 - 3*a*b*x^3 + 9*a^2)*(b*x^3 + a)^(1/3)/b^3","A",0
563,1,23,0,0.881407," ","integrate(x^5/(b*x^3+a)^(2/3),x, algorithm=""fricas"")","\frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b x^{3} - 3 \, a\right)}}{4 \, b^{2}}"," ",0,"1/4*(b*x^3 + a)^(1/3)*(b*x^3 - 3*a)/b^2","A",0
564,1,13,0,0.942375," ","integrate(x^2/(b*x^3+a)^(2/3),x, algorithm=""fricas"")","\frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{b}"," ",0,"(b*x^3 + a)^(1/3)/b","A",0
565,1,126,0,0.859661," ","integrate(1/x/(b*x^3+a)^(2/3),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} {\left(a^{2}\right)}^{\frac{1}{6}} a \arctan\left(\frac{{\left(a^{2}\right)}^{\frac{1}{6}} {\left(\sqrt{3} {\left(a^{2}\right)}^{\frac{1}{3}} a + 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(a^{2}\right)}^{\frac{2}{3}}\right)}}{3 \, a^{2}}\right) + {\left(a^{2}\right)}^{\frac{2}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} a + {\left(a^{2}\right)}^{\frac{1}{3}} a + {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(a^{2}\right)}^{\frac{2}{3}}\right) - 2 \, {\left(a^{2}\right)}^{\frac{2}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} a - {\left(a^{2}\right)}^{\frac{2}{3}}\right)}{6 \, a^{2}}"," ",0,"-1/6*(2*sqrt(3)*(a^2)^(1/6)*a*arctan(1/3*(a^2)^(1/6)*(sqrt(3)*(a^2)^(1/3)*a + 2*sqrt(3)*(b*x^3 + a)^(1/3)*(a^2)^(2/3))/a^2) + (a^2)^(2/3)*log((b*x^3 + a)^(2/3)*a + (a^2)^(1/3)*a + (b*x^3 + a)^(1/3)*(a^2)^(2/3)) - 2*(a^2)^(2/3)*log((b*x^3 + a)^(1/3)*a - (a^2)^(2/3)))/a^2","B",0
566,1,182,0,1.206148," ","integrate(1/x^4/(b*x^3+a)^(2/3),x, algorithm=""fricas"")","\frac{2 \, \sqrt{3} a b x^{3} \sqrt{-\left(-a^{2}\right)^{\frac{1}{3}}} \arctan\left(-\frac{{\left(\sqrt{3} \left(-a^{2}\right)^{\frac{1}{3}} a - 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-a^{2}\right)^{\frac{2}{3}}\right)} \sqrt{-\left(-a^{2}\right)^{\frac{1}{3}}}}{3 \, a^{2}}\right) + \left(-a^{2}\right)^{\frac{2}{3}} b x^{3} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} a - \left(-a^{2}\right)^{\frac{1}{3}} a + {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-a^{2}\right)^{\frac{2}{3}}\right) - 2 \, \left(-a^{2}\right)^{\frac{2}{3}} b x^{3} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} a - \left(-a^{2}\right)^{\frac{2}{3}}\right) - 3 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} a^{2}}{9 \, a^{3} x^{3}}"," ",0,"1/9*(2*sqrt(3)*a*b*x^3*sqrt(-(-a^2)^(1/3))*arctan(-1/3*(sqrt(3)*(-a^2)^(1/3)*a - 2*sqrt(3)*(b*x^3 + a)^(1/3)*(-a^2)^(2/3))*sqrt(-(-a^2)^(1/3))/a^2) + (-a^2)^(2/3)*b*x^3*log((b*x^3 + a)^(2/3)*a - (-a^2)^(1/3)*a + (b*x^3 + a)^(1/3)*(-a^2)^(2/3)) - 2*(-a^2)^(2/3)*b*x^3*log((b*x^3 + a)^(1/3)*a - (-a^2)^(2/3)) - 3*(b*x^3 + a)^(1/3)*a^2)/(a^3*x^3)","B",0
567,1,212,0,0.981963," ","integrate(x^7/(b*x^3+a)^(2/3),x, algorithm=""fricas"")","\frac{10 \, \sqrt{3} a^{2} b \sqrt{-\left(-b^{2}\right)^{\frac{1}{3}}} \arctan\left(-\frac{{\left(\sqrt{3} \left(-b^{2}\right)^{\frac{1}{3}} b x - 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b^{2}\right)^{\frac{2}{3}}\right)} \sqrt{-\left(-b^{2}\right)^{\frac{1}{3}}}}{3 \, b^{2} x}\right) - 10 \, \left(-b^{2}\right)^{\frac{2}{3}} a^{2} \log\left(-\frac{\left(-b^{2}\right)^{\frac{2}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}} b}{x}\right) + 5 \, \left(-b^{2}\right)^{\frac{2}{3}} a^{2} \log\left(-\frac{\left(-b^{2}\right)^{\frac{1}{3}} b x^{2} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b^{2}\right)^{\frac{2}{3}} x - {\left(b x^{3} + a\right)}^{\frac{2}{3}} b}{x^{2}}\right) + 3 \, {\left(3 \, b^{3} x^{5} - 5 \, a b^{2} x^{2}\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{54 \, b^{4}}"," ",0,"1/54*(10*sqrt(3)*a^2*b*sqrt(-(-b^2)^(1/3))*arctan(-1/3*(sqrt(3)*(-b^2)^(1/3)*b*x - 2*sqrt(3)*(b*x^3 + a)^(1/3)*(-b^2)^(2/3))*sqrt(-(-b^2)^(1/3))/(b^2*x)) - 10*(-b^2)^(2/3)*a^2*log(-((-b^2)^(2/3)*x - (b*x^3 + a)^(1/3)*b)/x) + 5*(-b^2)^(2/3)*a^2*log(-((-b^2)^(1/3)*b*x^2 - (b*x^3 + a)^(1/3)*(-b^2)^(2/3)*x - (b*x^3 + a)^(2/3)*b)/x^2) + 3*(3*b^3*x^5 - 5*a*b^2*x^2)*(b*x^3 + a)^(1/3))/b^4","B",0
568,1,165,0,0.747615," ","integrate(x^4/(b*x^3+a)^(2/3),x, algorithm=""fricas"")","\frac{3 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{2} x^{2} - 2 \, \sqrt{3} a {\left(b^{2}\right)}^{\frac{1}{6}} b \arctan\left(\frac{{\left(\sqrt{3} {\left(b^{2}\right)}^{\frac{1}{3}} b x + 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b^{2}\right)}^{\frac{2}{3}}\right)} {\left(b^{2}\right)}^{\frac{1}{6}}}{3 \, b^{2} x}\right) + 2 \, a {\left(b^{2}\right)}^{\frac{2}{3}} \log\left(-\frac{{\left(b^{2}\right)}^{\frac{2}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}} b}{x}\right) - a {\left(b^{2}\right)}^{\frac{2}{3}} \log\left(\frac{{\left(b^{2}\right)}^{\frac{1}{3}} b x^{2} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b^{2}\right)}^{\frac{2}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}} b}{x^{2}}\right)}{9 \, b^{3}}"," ",0,"1/9*(3*(b*x^3 + a)^(1/3)*b^2*x^2 - 2*sqrt(3)*a*(b^2)^(1/6)*b*arctan(1/3*(sqrt(3)*(b^2)^(1/3)*b*x + 2*sqrt(3)*(b*x^3 + a)^(1/3)*(b^2)^(2/3))*(b^2)^(1/6)/(b^2*x)) + 2*a*(b^2)^(2/3)*log(-((b^2)^(2/3)*x - (b*x^3 + a)^(1/3)*b)/x) - a*(b^2)^(2/3)*log(((b^2)^(1/3)*b*x^2 + (b*x^3 + a)^(1/3)*(b^2)^(2/3)*x + (b*x^3 + a)^(2/3)*b)/x^2))/b^3","B",0
569,1,173,0,0.861914," ","integrate(x/(b*x^3+a)^(2/3),x, algorithm=""fricas"")","\frac{2 \, \sqrt{3} b \sqrt{-\left(-b^{2}\right)^{\frac{1}{3}}} \arctan\left(-\frac{{\left(\sqrt{3} \left(-b^{2}\right)^{\frac{1}{3}} b x - 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b^{2}\right)^{\frac{2}{3}}\right)} \sqrt{-\left(-b^{2}\right)^{\frac{1}{3}}}}{3 \, b^{2} x}\right) - 2 \, \left(-b^{2}\right)^{\frac{2}{3}} \log\left(-\frac{\left(-b^{2}\right)^{\frac{2}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}} b}{x}\right) + \left(-b^{2}\right)^{\frac{2}{3}} \log\left(-\frac{\left(-b^{2}\right)^{\frac{1}{3}} b x^{2} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b^{2}\right)^{\frac{2}{3}} x - {\left(b x^{3} + a\right)}^{\frac{2}{3}} b}{x^{2}}\right)}{6 \, b^{2}}"," ",0,"1/6*(2*sqrt(3)*b*sqrt(-(-b^2)^(1/3))*arctan(-1/3*(sqrt(3)*(-b^2)^(1/3)*b*x - 2*sqrt(3)*(b*x^3 + a)^(1/3)*(-b^2)^(2/3))*sqrt(-(-b^2)^(1/3))/(b^2*x)) - 2*(-b^2)^(2/3)*log(-((-b^2)^(2/3)*x - (b*x^3 + a)^(1/3)*b)/x) + (-b^2)^(2/3)*log(-((-b^2)^(1/3)*b*x^2 - (b*x^3 + a)^(1/3)*(-b^2)^(2/3)*x - (b*x^3 + a)^(2/3)*b)/x^2))/b^2","B",0
570,1,17,0,1.090403," ","integrate(1/x^2/(b*x^3+a)^(2/3),x, algorithm=""fricas"")","-\frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{a x}"," ",0,"-(b*x^3 + a)^(1/3)/(a*x)","A",0
571,1,27,0,1.188766," ","integrate(1/x^5/(b*x^3+a)^(2/3),x, algorithm=""fricas"")","\frac{{\left(3 \, b x^{3} - a\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{4 \, a^{2} x^{4}}"," ",0,"1/4*(3*b*x^3 - a)*(b*x^3 + a)^(1/3)/(a^2*x^4)","A",0
572,1,38,0,0.969583," ","integrate(1/x^8/(b*x^3+a)^(2/3),x, algorithm=""fricas"")","-\frac{{\left(9 \, b^{2} x^{6} - 3 \, a b x^{3} + 2 \, a^{2}\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{14 \, a^{3} x^{7}}"," ",0,"-1/14*(9*b^2*x^6 - 3*a*b*x^3 + 2*a^2)*(b*x^3 + a)^(1/3)/(a^3*x^7)","A",0
573,1,49,0,1.061862," ","integrate(1/x^11/(b*x^3+a)^(2/3),x, algorithm=""fricas"")","\frac{{\left(81 \, b^{3} x^{9} - 27 \, a b^{2} x^{6} + 18 \, a^{2} b x^{3} - 14 \, a^{3}\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{140 \, a^{4} x^{10}}"," ",0,"1/140*(81*b^3*x^9 - 27*a*b^2*x^6 + 18*a^2*b*x^3 - 14*a^3)*(b*x^3 + a)^(1/3)/(a^4*x^10)","A",0
574,0,0,0,1.052089," ","integrate(x^6/(b*x^3+a)^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{6}}{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}, x\right)"," ",0,"integral(x^6/(b*x^3 + a)^(2/3), x)","F",0
575,0,0,0,1.010619," ","integrate(x^3/(b*x^3+a)^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3}}{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}, x\right)"," ",0,"integral(x^3/(b*x^3 + a)^(2/3), x)","F",0
576,0,0,0,1.014074," ","integrate(1/(b*x^3+a)^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}, x\right)"," ",0,"integral((b*x^3 + a)^(-2/3), x)","F",0
577,0,0,0,0.819585," ","integrate(1/x^3/(b*x^3+a)^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{b x^{6} + a x^{3}}, x\right)"," ",0,"integral((b*x^3 + a)^(1/3)/(b*x^6 + a*x^3), x)","F",0
578,0,0,0,0.798351," ","integrate(1/x^6/(b*x^3+a)^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{b x^{9} + a x^{6}}, x\right)"," ",0,"integral((b*x^3 + a)^(1/3)/(b*x^9 + a*x^6), x)","F",0
579,1,284,0,0.813203," ","integrate(1/(-b*x^3+a)^(1/3),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{\frac{1}{3}} b \sqrt{-\frac{1}{b^{\frac{2}{3}}}} \log\left(-3 \, b x^{3} - 3 \, {\left(-b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{2}{3}} x^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(b^{\frac{4}{3}} x^{3} - {\left(-b x^{3} + a\right)}^{\frac{1}{3}} b x^{2} - 2 \, {\left(-b x^{3} + a\right)}^{\frac{2}{3}} b^{\frac{2}{3}} x\right)} \sqrt{-\frac{1}{b^{\frac{2}{3}}}} + 2 \, a\right) + 2 \, b^{\frac{2}{3}} \log\left(\frac{b^{\frac{1}{3}} x + {\left(-b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) - b^{\frac{2}{3}} \log\left(\frac{b^{\frac{2}{3}} x^{2} - {\left(-b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}} x + {\left(-b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{6 \, b}, \frac{6 \, \sqrt{\frac{1}{3}} b^{\frac{2}{3}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(b^{\frac{1}{3}} x - 2 \, {\left(-b x^{3} + a\right)}^{\frac{1}{3}}\right)}}{b^{\frac{1}{3}} x}\right) + 2 \, b^{\frac{2}{3}} \log\left(\frac{b^{\frac{1}{3}} x + {\left(-b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) - b^{\frac{2}{3}} \log\left(\frac{b^{\frac{2}{3}} x^{2} - {\left(-b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}} x + {\left(-b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{6 \, b}\right]"," ",0,"[1/6*(3*sqrt(1/3)*b*sqrt(-1/b^(2/3))*log(-3*b*x^3 - 3*(-b*x^3 + a)^(1/3)*b^(2/3)*x^2 + 3*sqrt(1/3)*(b^(4/3)*x^3 - (-b*x^3 + a)^(1/3)*b*x^2 - 2*(-b*x^3 + a)^(2/3)*b^(2/3)*x)*sqrt(-1/b^(2/3)) + 2*a) + 2*b^(2/3)*log((b^(1/3)*x + (-b*x^3 + a)^(1/3))/x) - b^(2/3)*log((b^(2/3)*x^2 - (-b*x^3 + a)^(1/3)*b^(1/3)*x + (-b*x^3 + a)^(2/3))/x^2))/b, 1/6*(6*sqrt(1/3)*b^(2/3)*arctan(sqrt(1/3)*(b^(1/3)*x - 2*(-b*x^3 + a)^(1/3))/(b^(1/3)*x)) + 2*b^(2/3)*log((b^(1/3)*x + (-b*x^3 + a)^(1/3))/x) - b^(2/3)*log((b^(2/3)*x^2 - (-b*x^3 + a)^(1/3)*b^(1/3)*x + (-b*x^3 + a)^(2/3))/x^2))/b]","B",0
580,1,76,0,0.678553," ","integrate(1/(x^3+2)^(1/3),x, algorithm=""fricas"")","-\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{\sqrt{3} x + 2 \, \sqrt{3} {\left(x^{3} + 2\right)}^{\frac{1}{3}}}{3 \, x}\right) - \frac{1}{3} \, \log\left(-\frac{x - {\left(x^{3} + 2\right)}^{\frac{1}{3}}}{x}\right) + \frac{1}{6} \, \log\left(\frac{x^{2} + {\left(x^{3} + 2\right)}^{\frac{1}{3}} x + {\left(x^{3} + 2\right)}^{\frac{2}{3}}}{x^{2}}\right)"," ",0,"-1/3*sqrt(3)*arctan(1/3*(sqrt(3)*x + 2*sqrt(3)*(x^3 + 2)^(1/3))/x) - 1/3*log(-(x - (x^3 + 2)^(1/3))/x) + 1/6*log((x^2 + (x^3 + 2)^(1/3)*x + (x^3 + 2)^(2/3))/x^2)","A",0
581,1,82,0,0.880702," ","integrate(x/(-x^3+1)^(2/3),x, algorithm=""fricas"")","-\frac{1}{3} \, \sqrt{3} \arctan\left(-\frac{\sqrt{3} x - 2 \, \sqrt{3} {\left(-x^{3} + 1\right)}^{\frac{1}{3}}}{3 \, x}\right) - \frac{1}{3} \, \log\left(\frac{x + {\left(-x^{3} + 1\right)}^{\frac{1}{3}}}{x}\right) + \frac{1}{6} \, \log\left(\frac{x^{2} - {\left(-x^{3} + 1\right)}^{\frac{1}{3}} x + {\left(-x^{3} + 1\right)}^{\frac{2}{3}}}{x^{2}}\right)"," ",0,"-1/3*sqrt(3)*arctan(-1/3*(sqrt(3)*x - 2*sqrt(3)*(-x^3 + 1)^(1/3))/x) - 1/3*log((x + (-x^3 + 1)^(1/3))/x) + 1/6*log((x^2 - (-x^3 + 1)^(1/3)*x + (-x^3 + 1)^(2/3))/x^2)","A",0
582,1,9,0,0.728478," ","integrate(x^2/(x^3+2)^(1/4),x, algorithm=""fricas"")","\frac{4}{9} \, {\left(x^{3} + 2\right)}^{\frac{3}{4}}"," ",0,"4/9*(x^3 + 2)^(3/4)","A",0
583,1,847,0,0.661301," ","integrate(x^m*(b*x^3+a)^8,x, algorithm=""fricas"")","\frac{{\left({\left(b^{8} m^{8} + 92 \, b^{8} m^{7} + 3514 \, b^{8} m^{6} + 72128 \, b^{8} m^{5} + 859369 \, b^{8} m^{4} + 5974388 \, b^{8} m^{3} + 22963996 \, b^{8} m^{2} + 42124592 \, b^{8} m + 24344320 \, b^{8}\right)} x^{25} + 8 \, {\left(a b^{7} m^{8} + 95 \, a b^{7} m^{7} + 3724 \, a b^{7} m^{6} + 78050 \, a b^{7} m^{5} + 945469 \, a b^{7} m^{4} + 6658295 \, a b^{7} m^{3} + 25841206 \, a b^{7} m^{2} + 47717960 \, a b^{7} m + 27664000 \, a b^{7}\right)} x^{22} + 28 \, {\left(a^{2} b^{6} m^{8} + 98 \, a^{2} b^{6} m^{7} + 3952 \, a^{2} b^{6} m^{6} + 84890 \, a^{2} b^{6} m^{5} + 1049659 \, a^{2} b^{6} m^{4} + 7515092 \, a^{2} b^{6} m^{3} + 29536948 \, a^{2} b^{6} m^{2} + 55022480 \, a^{2} b^{6} m + 32032000 \, a^{2} b^{6}\right)} x^{19} + 56 \, {\left(a^{3} b^{5} m^{8} + 101 \, a^{3} b^{5} m^{7} + 4198 \, a^{3} b^{5} m^{6} + 92810 \, a^{3} b^{5} m^{5} + 1177609 \, a^{3} b^{5} m^{4} + 8616869 \, a^{3} b^{5} m^{3} + 34453792 \, a^{3} b^{5} m^{2} + 64963820 \, a^{3} b^{5} m + 38038000 \, a^{3} b^{5}\right)} x^{16} + 70 \, {\left(a^{4} b^{4} m^{8} + 104 \, a^{4} b^{4} m^{7} + 4462 \, a^{4} b^{4} m^{6} + 101972 \, a^{4} b^{4} m^{5} + 1336933 \, a^{4} b^{4} m^{4} + 10078484 \, a^{4} b^{4} m^{3} + 41303404 \, a^{4} b^{4} m^{2} + 79280240 \, a^{4} b^{4} m + 46816000 \, a^{4} b^{4}\right)} x^{13} + 56 \, {\left(a^{5} b^{3} m^{8} + 107 \, a^{5} b^{3} m^{7} + 4744 \, a^{5} b^{3} m^{6} + 112538 \, a^{5} b^{3} m^{5} + 1537189 \, a^{5} b^{3} m^{4} + 12086723 \, a^{5} b^{3} m^{3} + 51456466 \, a^{5} b^{3} m^{2} + 101659832 \, a^{5} b^{3} m + 60860800 \, a^{5} b^{3}\right)} x^{10} + 28 \, {\left(a^{6} b^{2} m^{8} + 110 \, a^{6} b^{2} m^{7} + 5044 \, a^{6} b^{2} m^{6} + 124670 \, a^{6} b^{2} m^{5} + 1789879 \, a^{6} b^{2} m^{4} + 14929460 \, a^{6} b^{2} m^{3} + 67817476 \, a^{6} b^{2} m^{2} + 141502160 \, a^{6} b^{2} m + 86944000 \, a^{6} b^{2}\right)} x^{7} + 8 \, {\left(a^{7} b m^{8} + 113 \, a^{7} b m^{7} + 5362 \, a^{7} b m^{6} + 138530 \, a^{7} b m^{5} + 2108449 \, a^{7} b m^{4} + 19024817 \, a^{7} b m^{3} + 96224428 \, a^{7} b m^{2} + 231326780 \, a^{7} b m + 152152000 \, a^{7} b\right)} x^{4} + {\left(a^{8} m^{8} + 116 \, a^{8} m^{7} + 5698 \, a^{8} m^{6} + 154280 \, a^{8} m^{5} + 2508289 \, a^{8} m^{4} + 24950324 \, a^{8} m^{3} + 147373372 \, a^{8} m^{2} + 468851120 \, a^{8} m + 608608000 \, a^{8}\right)} x\right)} x^{m}}{m^{9} + 117 \, m^{8} + 5814 \, m^{7} + 159978 \, m^{6} + 2662569 \, m^{5} + 27458613 \, m^{4} + 172323696 \, m^{3} + 616224492 \, m^{2} + 1077459120 \, m + 608608000}"," ",0,"((b^8*m^8 + 92*b^8*m^7 + 3514*b^8*m^6 + 72128*b^8*m^5 + 859369*b^8*m^4 + 5974388*b^8*m^3 + 22963996*b^8*m^2 + 42124592*b^8*m + 24344320*b^8)*x^25 + 8*(a*b^7*m^8 + 95*a*b^7*m^7 + 3724*a*b^7*m^6 + 78050*a*b^7*m^5 + 945469*a*b^7*m^4 + 6658295*a*b^7*m^3 + 25841206*a*b^7*m^2 + 47717960*a*b^7*m + 27664000*a*b^7)*x^22 + 28*(a^2*b^6*m^8 + 98*a^2*b^6*m^7 + 3952*a^2*b^6*m^6 + 84890*a^2*b^6*m^5 + 1049659*a^2*b^6*m^4 + 7515092*a^2*b^6*m^3 + 29536948*a^2*b^6*m^2 + 55022480*a^2*b^6*m + 32032000*a^2*b^6)*x^19 + 56*(a^3*b^5*m^8 + 101*a^3*b^5*m^7 + 4198*a^3*b^5*m^6 + 92810*a^3*b^5*m^5 + 1177609*a^3*b^5*m^4 + 8616869*a^3*b^5*m^3 + 34453792*a^3*b^5*m^2 + 64963820*a^3*b^5*m + 38038000*a^3*b^5)*x^16 + 70*(a^4*b^4*m^8 + 104*a^4*b^4*m^7 + 4462*a^4*b^4*m^6 + 101972*a^4*b^4*m^5 + 1336933*a^4*b^4*m^4 + 10078484*a^4*b^4*m^3 + 41303404*a^4*b^4*m^2 + 79280240*a^4*b^4*m + 46816000*a^4*b^4)*x^13 + 56*(a^5*b^3*m^8 + 107*a^5*b^3*m^7 + 4744*a^5*b^3*m^6 + 112538*a^5*b^3*m^5 + 1537189*a^5*b^3*m^4 + 12086723*a^5*b^3*m^3 + 51456466*a^5*b^3*m^2 + 101659832*a^5*b^3*m + 60860800*a^5*b^3)*x^10 + 28*(a^6*b^2*m^8 + 110*a^6*b^2*m^7 + 5044*a^6*b^2*m^6 + 124670*a^6*b^2*m^5 + 1789879*a^6*b^2*m^4 + 14929460*a^6*b^2*m^3 + 67817476*a^6*b^2*m^2 + 141502160*a^6*b^2*m + 86944000*a^6*b^2)*x^7 + 8*(a^7*b*m^8 + 113*a^7*b*m^7 + 5362*a^7*b*m^6 + 138530*a^7*b*m^5 + 2108449*a^7*b*m^4 + 19024817*a^7*b*m^3 + 96224428*a^7*b*m^2 + 231326780*a^7*b*m + 152152000*a^7*b)*x^4 + (a^8*m^8 + 116*a^8*m^7 + 5698*a^8*m^6 + 154280*a^8*m^5 + 2508289*a^8*m^4 + 24950324*a^8*m^3 + 147373372*a^8*m^2 + 468851120*a^8*m + 608608000*a^8)*x)*x^m/(m^9 + 117*m^8 + 5814*m^7 + 159978*m^6 + 2662569*m^5 + 27458613*m^4 + 172323696*m^3 + 616224492*m^2 + 1077459120*m + 608608000)","B",0
584,1,367,0,1.020264," ","integrate(x^m*(b*x^3+a)^5,x, algorithm=""fricas"")","\frac{{\left({\left(b^{5} m^{5} + 35 \, b^{5} m^{4} + 445 \, b^{5} m^{3} + 2485 \, b^{5} m^{2} + 5714 \, b^{5} m + 3640 \, b^{5}\right)} x^{16} + 5 \, {\left(a b^{4} m^{5} + 38 \, a b^{4} m^{4} + 511 \, a b^{4} m^{3} + 2962 \, a b^{4} m^{2} + 6968 \, a b^{4} m + 4480 \, a b^{4}\right)} x^{13} + 10 \, {\left(a^{2} b^{3} m^{5} + 41 \, a^{2} b^{3} m^{4} + 595 \, a^{2} b^{3} m^{3} + 3655 \, a^{2} b^{3} m^{2} + 8924 \, a^{2} b^{3} m + 5824 \, a^{2} b^{3}\right)} x^{10} + 10 \, {\left(a^{3} b^{2} m^{5} + 44 \, a^{3} b^{2} m^{4} + 697 \, a^{3} b^{2} m^{3} + 4726 \, a^{3} b^{2} m^{2} + 12392 \, a^{3} b^{2} m + 8320 \, a^{3} b^{2}\right)} x^{7} + 5 \, {\left(a^{4} b m^{5} + 47 \, a^{4} b m^{4} + 817 \, a^{4} b m^{3} + 6337 \, a^{4} b m^{2} + 20126 \, a^{4} b m + 14560 \, a^{4} b\right)} x^{4} + {\left(a^{5} m^{5} + 50 \, a^{5} m^{4} + 955 \, a^{5} m^{3} + 8650 \, a^{5} m^{2} + 36824 \, a^{5} m + 58240 \, a^{5}\right)} x\right)} x^{m}}{m^{6} + 51 \, m^{5} + 1005 \, m^{4} + 9605 \, m^{3} + 45474 \, m^{2} + 95064 \, m + 58240}"," ",0,"((b^5*m^5 + 35*b^5*m^4 + 445*b^5*m^3 + 2485*b^5*m^2 + 5714*b^5*m + 3640*b^5)*x^16 + 5*(a*b^4*m^5 + 38*a*b^4*m^4 + 511*a*b^4*m^3 + 2962*a*b^4*m^2 + 6968*a*b^4*m + 4480*a*b^4)*x^13 + 10*(a^2*b^3*m^5 + 41*a^2*b^3*m^4 + 595*a^2*b^3*m^3 + 3655*a^2*b^3*m^2 + 8924*a^2*b^3*m + 5824*a^2*b^3)*x^10 + 10*(a^3*b^2*m^5 + 44*a^3*b^2*m^4 + 697*a^3*b^2*m^3 + 4726*a^3*b^2*m^2 + 12392*a^3*b^2*m + 8320*a^3*b^2)*x^7 + 5*(a^4*b*m^5 + 47*a^4*b*m^4 + 817*a^4*b*m^3 + 6337*a^4*b*m^2 + 20126*a^4*b*m + 14560*a^4*b)*x^4 + (a^5*m^5 + 50*a^5*m^4 + 955*a^5*m^3 + 8650*a^5*m^2 + 36824*a^5*m + 58240*a^5)*x)*x^m/(m^6 + 51*m^5 + 1005*m^4 + 9605*m^3 + 45474*m^2 + 95064*m + 58240)","B",0
585,1,157,0,1.015690," ","integrate(x^m*(b*x^3+a)^3,x, algorithm=""fricas"")","\frac{{\left({\left(b^{3} m^{3} + 12 \, b^{3} m^{2} + 39 \, b^{3} m + 28 \, b^{3}\right)} x^{10} + 3 \, {\left(a b^{2} m^{3} + 15 \, a b^{2} m^{2} + 54 \, a b^{2} m + 40 \, a b^{2}\right)} x^{7} + 3 \, {\left(a^{2} b m^{3} + 18 \, a^{2} b m^{2} + 87 \, a^{2} b m + 70 \, a^{2} b\right)} x^{4} + {\left(a^{3} m^{3} + 21 \, a^{3} m^{2} + 138 \, a^{3} m + 280 \, a^{3}\right)} x\right)} x^{m}}{m^{4} + 22 \, m^{3} + 159 \, m^{2} + 418 \, m + 280}"," ",0,"((b^3*m^3 + 12*b^3*m^2 + 39*b^3*m + 28*b^3)*x^10 + 3*(a*b^2*m^3 + 15*a*b^2*m^2 + 54*a*b^2*m + 40*a*b^2)*x^7 + 3*(a^2*b*m^3 + 18*a^2*b*m^2 + 87*a^2*b*m + 70*a^2*b)*x^4 + (a^3*m^3 + 21*a^3*m^2 + 138*a^3*m + 280*a^3)*x)*x^m/(m^4 + 22*m^3 + 159*m^2 + 418*m + 280)","B",0
586,1,85,0,1.032382," ","integrate(x^m*(b*x^3+a)^2,x, algorithm=""fricas"")","\frac{{\left({\left(b^{2} m^{2} + 5 \, b^{2} m + 4 \, b^{2}\right)} x^{7} + 2 \, {\left(a b m^{2} + 8 \, a b m + 7 \, a b\right)} x^{4} + {\left(a^{2} m^{2} + 11 \, a^{2} m + 28 \, a^{2}\right)} x\right)} x^{m}}{m^{3} + 12 \, m^{2} + 39 \, m + 28}"," ",0,"((b^2*m^2 + 5*b^2*m + 4*b^2)*x^7 + 2*(a*b*m^2 + 8*a*b*m + 7*a*b)*x^4 + (a^2*m^2 + 11*a^2*m + 28*a^2)*x)*x^m/(m^3 + 12*m^2 + 39*m + 28)","A",0
587,1,33,0,0.938000," ","integrate(x^m*(b*x^3+a),x, algorithm=""fricas"")","\frac{{\left({\left(b m + b\right)} x^{4} + {\left(a m + 4 \, a\right)} x\right)} x^{m}}{m^{2} + 5 \, m + 4}"," ",0,"((b*m + b)*x^4 + (a*m + 4*a)*x)*x^m/(m^2 + 5*m + 4)","A",0
588,0,0,0,0.996018," ","integrate(x^m/(b*x^3+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{b x^{3} + a}, x\right)"," ",0,"integral(x^m/(b*x^3 + a), x)","F",0
589,0,0,0,1.107948," ","integrate(x^m/(b*x^3+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{b^{2} x^{6} + 2 \, a b x^{3} + a^{2}}, x\right)"," ",0,"integral(x^m/(b^2*x^6 + 2*a*b*x^3 + a^2), x)","F",0
590,0,0,0,0.853276," ","integrate(x^m/(b*x^3+a)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{b^{3} x^{9} + 3 \, a b^{2} x^{6} + 3 \, a^{2} b x^{3} + a^{3}}, x\right)"," ",0,"integral(x^m/(b^3*x^9 + 3*a*b^2*x^6 + 3*a^2*b*x^3 + a^3), x)","F",0
591,0,0,0,0.802885," ","integrate(x^m*(b*x^3+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{3} + a\right)}^{\frac{3}{2}} x^{m}, x\right)"," ",0,"integral((b*x^3 + a)^(3/2)*x^m, x)","F",0
592,0,0,0,0.865975," ","integrate(x^m*(b*x^3+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b x^{3} + a} x^{m}, x\right)"," ",0,"integral(sqrt(b*x^3 + a)*x^m, x)","F",0
593,0,0,0,0.677529," ","integrate(x^m/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{\sqrt{b x^{3} + a}}, x\right)"," ",0,"integral(x^m/sqrt(b*x^3 + a), x)","F",0
594,0,0,0,0.913510," ","integrate(x^m/(b*x^3+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{3} + a} x^{m}}{b^{2} x^{6} + 2 \, a b x^{3} + a^{2}}, x\right)"," ",0,"integral(sqrt(b*x^3 + a)*x^m/(b^2*x^6 + 2*a*b*x^3 + a^2), x)","F",0
595,0,0,0,0.944138," ","integrate((c*x)^m*(b*x^3+a)^(4/3),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{3} + a\right)}^{\frac{4}{3}} \left(c x\right)^{m}, x\right)"," ",0,"integral((b*x^3 + a)^(4/3)*(c*x)^m, x)","F",0
596,0,0,0,1.030348," ","integrate((c*x)^m*(b*x^3+a)^(2/3),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} \left(c x\right)^{m}, x\right)"," ",0,"integral((b*x^3 + a)^(2/3)*(c*x)^m, x)","F",0
597,0,0,0,1.109963," ","integrate((c*x)^m*(b*x^3+a)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(c x\right)^{m}, x\right)"," ",0,"integral((b*x^3 + a)^(1/3)*(c*x)^m, x)","F",0
598,0,0,0,0.778473," ","integrate((c*x)^m*(b*x^3+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{3} + a\right)}^{p} \left(c x\right)^{m}, x\right)"," ",0,"integral((b*x^3 + a)^p*(c*x)^m, x)","F",0
599,1,25,0,0.948199," ","integrate(x^2*(b*x^3+a)^p,x, algorithm=""fricas"")","\frac{{\left(b x^{3} + a\right)} {\left(b x^{3} + a\right)}^{p}}{3 \, {\left(b p + b\right)}}"," ",0,"1/3*(b*x^3 + a)*(b*x^3 + a)^p/(b*p + b)","A",0
600,1,58,0,0.847989," ","integrate(x^5*(b*x^3+a)^p,x, algorithm=""fricas"")","\frac{{\left({\left(b^{2} p + b^{2}\right)} x^{6} + a b p x^{3} - a^{2}\right)} {\left(b x^{3} + a\right)}^{p}}{3 \, {\left(b^{2} p^{2} + 3 \, b^{2} p + 2 \, b^{2}\right)}}"," ",0,"1/3*((b^2*p + b^2)*x^6 + a*b*p*x^3 - a^2)*(b*x^3 + a)^p/(b^2*p^2 + 3*b^2*p + 2*b^2)","A",0
601,1,98,0,0.820572," ","integrate(x^8*(b*x^3+a)^p,x, algorithm=""fricas"")","\frac{{\left({\left(b^{3} p^{2} + 3 \, b^{3} p + 2 \, b^{3}\right)} x^{9} - 2 \, a^{2} b p x^{3} + {\left(a b^{2} p^{2} + a b^{2} p\right)} x^{6} + 2 \, a^{3}\right)} {\left(b x^{3} + a\right)}^{p}}{3 \, {\left(b^{3} p^{3} + 6 \, b^{3} p^{2} + 11 \, b^{3} p + 6 \, b^{3}\right)}}"," ",0,"1/3*((b^3*p^2 + 3*b^3*p + 2*b^3)*x^9 - 2*a^2*b*p*x^3 + (a*b^2*p^2 + a*b^2*p)*x^6 + 2*a^3)*(b*x^3 + a)^p/(b^3*p^3 + 6*b^3*p^2 + 11*b^3*p + 6*b^3)","A",0
602,1,148,0,1.068662," ","integrate(x^11*(b*x^3+a)^p,x, algorithm=""fricas"")","\frac{{\left({\left(b^{4} p^{3} + 6 \, b^{4} p^{2} + 11 \, b^{4} p + 6 \, b^{4}\right)} x^{12} + {\left(a b^{3} p^{3} + 3 \, a b^{3} p^{2} + 2 \, a b^{3} p\right)} x^{9} + 6 \, a^{3} b p x^{3} - 3 \, {\left(a^{2} b^{2} p^{2} + a^{2} b^{2} p\right)} x^{6} - 6 \, a^{4}\right)} {\left(b x^{3} + a\right)}^{p}}{3 \, {\left(b^{4} p^{4} + 10 \, b^{4} p^{3} + 35 \, b^{4} p^{2} + 50 \, b^{4} p + 24 \, b^{4}\right)}}"," ",0,"1/3*((b^4*p^3 + 6*b^4*p^2 + 11*b^4*p + 6*b^4)*x^12 + (a*b^3*p^3 + 3*a*b^3*p^2 + 2*a*b^3*p)*x^9 + 6*a^3*b*p*x^3 - 3*(a^2*b^2*p^2 + a^2*b^2*p)*x^6 - 6*a^4)*(b*x^3 + a)^p/(b^4*p^4 + 10*b^4*p^3 + 35*b^4*p^2 + 50*b^4*p + 24*b^4)","A",0
603,1,33,0,0.796567," ","integrate(x^m*(b*x^4+a),x, algorithm=""fricas"")","\frac{{\left({\left(b m + b\right)} x^{5} + {\left(a m + 5 \, a\right)} x\right)} x^{m}}{m^{2} + 6 \, m + 5}"," ",0,"((b*m + b)*x^5 + (a*m + 5*a)*x)*x^m/(m^2 + 6*m + 5)","A",0
604,1,13,0,0.925410," ","integrate(x^5*(b*x^4+a),x, algorithm=""fricas"")","\frac{1}{10} x^{10} b + \frac{1}{6} x^{6} a"," ",0,"1/10*x^10*b + 1/6*x^6*a","A",0
605,1,13,0,0.808193," ","integrate(x^4*(b*x^4+a),x, algorithm=""fricas"")","\frac{1}{9} x^{9} b + \frac{1}{5} x^{5} a"," ",0,"1/9*x^9*b + 1/5*x^5*a","A",0
606,1,13,0,0.759851," ","integrate(x^3*(b*x^4+a),x, algorithm=""fricas"")","\frac{1}{8} x^{8} b + \frac{1}{4} x^{4} a"," ",0,"1/8*x^8*b + 1/4*x^4*a","A",0
607,1,13,0,0.971884," ","integrate(x^2*(b*x^4+a),x, algorithm=""fricas"")","\frac{1}{7} x^{7} b + \frac{1}{3} x^{3} a"," ",0,"1/7*x^7*b + 1/3*x^3*a","A",0
608,1,13,0,0.640374," ","integrate(x*(b*x^4+a),x, algorithm=""fricas"")","\frac{1}{6} x^{6} b + \frac{1}{2} x^{2} a"," ",0,"1/6*x^6*b + 1/2*x^2*a","A",0
609,1,10,0,0.566928," ","integrate(b*x^4+a,x, algorithm=""fricas"")","\frac{1}{5} x^{5} b + x a"," ",0,"1/5*x^5*b + x*a","A",0
610,1,11,0,0.887564," ","integrate((b*x^4+a)/x,x, algorithm=""fricas"")","\frac{1}{4} \, b x^{4} + a \log\left(x\right)"," ",0,"1/4*b*x^4 + a*log(x)","A",0
611,1,14,0,0.986068," ","integrate((b*x^4+a)/x^2,x, algorithm=""fricas"")","\frac{b x^{4} - 3 \, a}{3 \, x}"," ",0,"1/3*(b*x^4 - 3*a)/x","A",0
612,1,14,0,0.837505," ","integrate((b*x^4+a)/x^3,x, algorithm=""fricas"")","\frac{b x^{4} - a}{2 \, x^{2}}"," ",0,"1/2*(b*x^4 - a)/x^2","A",0
613,1,15,0,0.728749," ","integrate((b*x^4+a)/x^4,x, algorithm=""fricas"")","\frac{3 \, b x^{4} - a}{3 \, x^{3}}"," ",0,"1/3*(3*b*x^4 - a)/x^3","A",0
614,1,17,0,0.794444," ","integrate((b*x^4+a)/x^5,x, algorithm=""fricas"")","\frac{4 \, b x^{4} \log\left(x\right) - a}{4 \, x^{4}}"," ",0,"1/4*(4*b*x^4*log(x) - a)/x^4","A",0
615,1,13,0,0.870693," ","integrate((b*x^4+a)/x^6,x, algorithm=""fricas"")","-\frac{5 \, b x^{4} + a}{5 \, x^{5}}"," ",0,"-1/5*(5*b*x^4 + a)/x^5","A",0
616,1,13,0,0.750371," ","integrate((b*x^4+a)/x^7,x, algorithm=""fricas"")","-\frac{3 \, b x^{4} + a}{6 \, x^{6}}"," ",0,"-1/6*(3*b*x^4 + a)/x^6","A",0
617,1,15,0,0.775666," ","integrate((b*x^4+a)/x^8,x, algorithm=""fricas"")","-\frac{7 \, b x^{4} + 3 \, a}{21 \, x^{7}}"," ",0,"-1/21*(7*b*x^4 + 3*a)/x^7","A",0
618,1,13,0,0.813034," ","integrate((b*x^4+a)/x^9,x, algorithm=""fricas"")","-\frac{2 \, b x^{4} + a}{8 \, x^{8}}"," ",0,"-1/8*(2*b*x^4 + a)/x^8","A",0
619,1,15,0,0.710353," ","integrate((b*x^4+a)/x^10,x, algorithm=""fricas"")","-\frac{9 \, b x^{4} + 5 \, a}{45 \, x^{9}}"," ",0,"-1/45*(9*b*x^4 + 5*a)/x^9","A",0
620,1,85,0,0.612625," ","integrate(x^m*(b*x^4+a)^2,x, algorithm=""fricas"")","\frac{{\left({\left(b^{2} m^{2} + 6 \, b^{2} m + 5 \, b^{2}\right)} x^{9} + 2 \, {\left(a b m^{2} + 10 \, a b m + 9 \, a b\right)} x^{5} + {\left(a^{2} m^{2} + 14 \, a^{2} m + 45 \, a^{2}\right)} x\right)} x^{m}}{m^{3} + 15 \, m^{2} + 59 \, m + 45}"," ",0,"((b^2*m^2 + 6*b^2*m + 5*b^2)*x^9 + 2*(a*b*m^2 + 10*a*b*m + 9*a*b)*x^5 + (a^2*m^2 + 14*a^2*m + 45*a^2)*x)*x^m/(m^3 + 15*m^2 + 59*m + 45)","A",0
621,1,24,0,0.462818," ","integrate(x^5*(b*x^4+a)^2,x, algorithm=""fricas"")","\frac{1}{14} x^{14} b^{2} + \frac{1}{5} x^{10} b a + \frac{1}{6} x^{6} a^{2}"," ",0,"1/14*x^14*b^2 + 1/5*x^10*b*a + 1/6*x^6*a^2","A",0
622,1,24,0,0.420606," ","integrate(x^4*(b*x^4+a)^2,x, algorithm=""fricas"")","\frac{1}{13} x^{13} b^{2} + \frac{2}{9} x^{9} b a + \frac{1}{5} x^{5} a^{2}"," ",0,"1/13*x^13*b^2 + 2/9*x^9*b*a + 1/5*x^5*a^2","A",0
623,1,24,0,0.699489," ","integrate(x^3*(b*x^4+a)^2,x, algorithm=""fricas"")","\frac{1}{12} x^{12} b^{2} + \frac{1}{4} x^{8} b a + \frac{1}{4} x^{4} a^{2}"," ",0,"1/12*x^12*b^2 + 1/4*x^8*b*a + 1/4*x^4*a^2","A",0
624,1,24,0,0.613033," ","integrate(x^2*(b*x^4+a)^2,x, algorithm=""fricas"")","\frac{1}{11} x^{11} b^{2} + \frac{2}{7} x^{7} b a + \frac{1}{3} x^{3} a^{2}"," ",0,"1/11*x^11*b^2 + 2/7*x^7*b*a + 1/3*x^3*a^2","A",0
625,1,24,0,0.484366," ","integrate(x*(b*x^4+a)^2,x, algorithm=""fricas"")","\frac{1}{10} x^{10} b^{2} + \frac{1}{3} x^{6} b a + \frac{1}{2} x^{2} a^{2}"," ",0,"1/10*x^10*b^2 + 1/3*x^6*b*a + 1/2*x^2*a^2","A",0
626,1,21,0,0.751152," ","integrate((b*x^4+a)^2,x, algorithm=""fricas"")","\frac{1}{9} x^{9} b^{2} + \frac{2}{5} x^{5} b a + x a^{2}"," ",0,"1/9*x^9*b^2 + 2/5*x^5*b*a + x*a^2","A",0
627,1,22,0,0.831616," ","integrate((b*x^4+a)^2/x,x, algorithm=""fricas"")","\frac{1}{8} \, b^{2} x^{8} + \frac{1}{2} \, a b x^{4} + a^{2} \log\left(x\right)"," ",0,"1/8*b^2*x^8 + 1/2*a*b*x^4 + a^2*log(x)","A",0
628,1,26,0,0.735165," ","integrate((b*x^4+a)^2/x^2,x, algorithm=""fricas"")","\frac{3 \, b^{2} x^{8} + 14 \, a b x^{4} - 21 \, a^{2}}{21 \, x}"," ",0,"1/21*(3*b^2*x^8 + 14*a*b*x^4 - 21*a^2)/x","A",0
629,1,25,0,0.819650," ","integrate((b*x^4+a)^2/x^3,x, algorithm=""fricas"")","\frac{b^{2} x^{8} + 6 \, a b x^{4} - 3 \, a^{2}}{6 \, x^{2}}"," ",0,"1/6*(b^2*x^8 + 6*a*b*x^4 - 3*a^2)/x^2","A",0
630,1,26,0,0.779283," ","integrate((b*x^4+a)^2/x^4,x, algorithm=""fricas"")","\frac{3 \, b^{2} x^{8} + 30 \, a b x^{4} - 5 \, a^{2}}{15 \, x^{3}}"," ",0,"1/15*(3*b^2*x^8 + 30*a*b*x^4 - 5*a^2)/x^3","A",0
631,1,27,0,0.826387," ","integrate((b*x^4+a)^2/x^5,x, algorithm=""fricas"")","\frac{b^{2} x^{8} + 8 \, a b x^{4} \log\left(x\right) - a^{2}}{4 \, x^{4}}"," ",0,"1/4*(b^2*x^8 + 8*a*b*x^4*log(x) - a^2)/x^4","A",0
632,1,157,0,0.861116," ","integrate(x^m*(b*x^4+a)^3,x, algorithm=""fricas"")","\frac{{\left({\left(b^{3} m^{3} + 15 \, b^{3} m^{2} + 59 \, b^{3} m + 45 \, b^{3}\right)} x^{13} + 3 \, {\left(a b^{2} m^{3} + 19 \, a b^{2} m^{2} + 83 \, a b^{2} m + 65 \, a b^{2}\right)} x^{9} + 3 \, {\left(a^{2} b m^{3} + 23 \, a^{2} b m^{2} + 139 \, a^{2} b m + 117 \, a^{2} b\right)} x^{5} + {\left(a^{3} m^{3} + 27 \, a^{3} m^{2} + 227 \, a^{3} m + 585 \, a^{3}\right)} x\right)} x^{m}}{m^{4} + 28 \, m^{3} + 254 \, m^{2} + 812 \, m + 585}"," ",0,"((b^3*m^3 + 15*b^3*m^2 + 59*b^3*m + 45*b^3)*x^13 + 3*(a*b^2*m^3 + 19*a*b^2*m^2 + 83*a*b^2*m + 65*a*b^2)*x^9 + 3*(a^2*b*m^3 + 23*a^2*b*m^2 + 139*a^2*b*m + 117*a^2*b)*x^5 + (a^3*m^3 + 27*a^3*m^2 + 227*a^3*m + 585*a^3)*x)*x^m/(m^4 + 28*m^3 + 254*m^2 + 812*m + 585)","B",0
633,1,35,0,0.638048," ","integrate(x^5*(b*x^4+a)^3,x, algorithm=""fricas"")","\frac{1}{18} x^{18} b^{3} + \frac{3}{14} x^{14} b^{2} a + \frac{3}{10} x^{10} b a^{2} + \frac{1}{6} x^{6} a^{3}"," ",0,"1/18*x^18*b^3 + 3/14*x^14*b^2*a + 3/10*x^10*b*a^2 + 1/6*x^6*a^3","A",0
634,1,35,0,0.755376," ","integrate(x^4*(b*x^4+a)^3,x, algorithm=""fricas"")","\frac{1}{17} x^{17} b^{3} + \frac{3}{13} x^{13} b^{2} a + \frac{1}{3} x^{9} b a^{2} + \frac{1}{5} x^{5} a^{3}"," ",0,"1/17*x^17*b^3 + 3/13*x^13*b^2*a + 1/3*x^9*b*a^2 + 1/5*x^5*a^3","A",0
635,1,35,0,0.737926," ","integrate(x^3*(b*x^4+a)^3,x, algorithm=""fricas"")","\frac{1}{16} x^{16} b^{3} + \frac{1}{4} x^{12} b^{2} a + \frac{3}{8} x^{8} b a^{2} + \frac{1}{4} x^{4} a^{3}"," ",0,"1/16*x^16*b^3 + 1/4*x^12*b^2*a + 3/8*x^8*b*a^2 + 1/4*x^4*a^3","B",0
636,1,35,0,0.761156," ","integrate(x^2*(b*x^4+a)^3,x, algorithm=""fricas"")","\frac{1}{15} x^{15} b^{3} + \frac{3}{11} x^{11} b^{2} a + \frac{3}{7} x^{7} b a^{2} + \frac{1}{3} x^{3} a^{3}"," ",0,"1/15*x^15*b^3 + 3/11*x^11*b^2*a + 3/7*x^7*b*a^2 + 1/3*x^3*a^3","A",0
637,1,35,0,0.695487," ","integrate(x*(b*x^4+a)^3,x, algorithm=""fricas"")","\frac{1}{14} x^{14} b^{3} + \frac{3}{10} x^{10} b^{2} a + \frac{1}{2} x^{6} b a^{2} + \frac{1}{2} x^{2} a^{3}"," ",0,"1/14*x^14*b^3 + 3/10*x^10*b^2*a + 1/2*x^6*b*a^2 + 1/2*x^2*a^3","A",0
638,1,32,0,0.668275," ","integrate((b*x^4+a)^3,x, algorithm=""fricas"")","\frac{1}{13} x^{13} b^{3} + \frac{1}{3} x^{9} b^{2} a + \frac{3}{5} x^{5} b a^{2} + x a^{3}"," ",0,"1/13*x^13*b^3 + 1/3*x^9*b^2*a + 3/5*x^5*b*a^2 + x*a^3","A",0
639,1,33,0,0.827756," ","integrate((b*x^4+a)^3/x,x, algorithm=""fricas"")","\frac{1}{12} \, b^{3} x^{12} + \frac{3}{8} \, a b^{2} x^{8} + \frac{3}{4} \, a^{2} b x^{4} + a^{3} \log\left(x\right)"," ",0,"1/12*b^3*x^12 + 3/8*a*b^2*x^8 + 3/4*a^2*b*x^4 + a^3*log(x)","A",0
640,1,37,0,0.760811," ","integrate((b*x^4+a)^3/x^2,x, algorithm=""fricas"")","\frac{7 \, b^{3} x^{12} + 33 \, a b^{2} x^{8} + 77 \, a^{2} b x^{4} - 77 \, a^{3}}{77 \, x}"," ",0,"1/77*(7*b^3*x^12 + 33*a*b^2*x^8 + 77*a^2*b*x^4 - 77*a^3)/x","A",0
641,1,36,0,0.788624," ","integrate((b*x^4+a)^3/x^3,x, algorithm=""fricas"")","\frac{b^{3} x^{12} + 5 \, a b^{2} x^{8} + 15 \, a^{2} b x^{4} - 5 \, a^{3}}{10 \, x^{2}}"," ",0,"1/10*(b^3*x^12 + 5*a*b^2*x^8 + 15*a^2*b*x^4 - 5*a^3)/x^2","A",0
642,1,37,0,0.781320," ","integrate((b*x^4+a)^3/x^4,x, algorithm=""fricas"")","\frac{5 \, b^{3} x^{12} + 27 \, a b^{2} x^{8} + 135 \, a^{2} b x^{4} - 15 \, a^{3}}{45 \, x^{3}}"," ",0,"1/45*(5*b^3*x^12 + 27*a*b^2*x^8 + 135*a^2*b*x^4 - 15*a^3)/x^3","A",0
643,1,38,0,0.916242," ","integrate((b*x^4+a)^3/x^5,x, algorithm=""fricas"")","\frac{b^{3} x^{12} + 6 \, a b^{2} x^{8} + 24 \, a^{2} b x^{4} \log\left(x\right) - 2 \, a^{3}}{8 \, x^{4}}"," ",0,"1/8*(b^3*x^12 + 6*a*b^2*x^8 + 24*a^2*b*x^4*log(x) - 2*a^3)/x^4","A",0
644,1,107,0,0.518192," ","integrate(x^9/(c*x^4+a),x, algorithm=""fricas"")","\left[\frac{2 \, c x^{6} - 6 \, a x^{2} + 3 \, a \sqrt{-\frac{a}{c}} \log\left(\frac{c x^{4} + 2 \, c x^{2} \sqrt{-\frac{a}{c}} - a}{c x^{4} + a}\right)}{12 \, c^{2}}, \frac{c x^{6} - 3 \, a x^{2} + 3 \, a \sqrt{\frac{a}{c}} \arctan\left(\frac{c x^{2} \sqrt{\frac{a}{c}}}{a}\right)}{6 \, c^{2}}\right]"," ",0,"[1/12*(2*c*x^6 - 6*a*x^2 + 3*a*sqrt(-a/c)*log((c*x^4 + 2*c*x^2*sqrt(-a/c) - a)/(c*x^4 + a)))/c^2, 1/6*(c*x^6 - 3*a*x^2 + 3*a*sqrt(a/c)*arctan(c*x^2*sqrt(a/c)/a))/c^2]","A",0
645,1,22,0,0.758812," ","integrate(x^7/(c*x^4+a),x, algorithm=""fricas"")","\frac{c x^{4} - a \log\left(c x^{4} + a\right)}{4 \, c^{2}}"," ",0,"1/4*(c*x^4 - a*log(c*x^4 + a))/c^2","A",0
646,1,89,0,0.814264," ","integrate(x^5/(c*x^4+a),x, algorithm=""fricas"")","\left[\frac{2 \, x^{2} + \sqrt{-\frac{a}{c}} \log\left(\frac{c x^{4} - 2 \, c x^{2} \sqrt{-\frac{a}{c}} - a}{c x^{4} + a}\right)}{4 \, c}, \frac{x^{2} - \sqrt{\frac{a}{c}} \arctan\left(\frac{c x^{2} \sqrt{\frac{a}{c}}}{a}\right)}{2 \, c}\right]"," ",0,"[1/4*(2*x^2 + sqrt(-a/c)*log((c*x^4 - 2*c*x^2*sqrt(-a/c) - a)/(c*x^4 + a)))/c, 1/2*(x^2 - sqrt(a/c)*arctan(c*x^2*sqrt(a/c)/a))/c]","A",0
647,1,13,0,0.737964," ","integrate(x^3/(c*x^4+a),x, algorithm=""fricas"")","\frac{\log\left(c x^{4} + a\right)}{4 \, c}"," ",0,"1/4*log(c*x^4 + a)/c","A",0
648,1,72,0,0.823314," ","integrate(x/(c*x^4+a),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a c} \log\left(\frac{c x^{4} - 2 \, \sqrt{-a c} x^{2} - a}{c x^{4} + a}\right)}{4 \, a c}, -\frac{\sqrt{a c} \arctan\left(\frac{\sqrt{a c}}{c x^{2}}\right)}{2 \, a c}\right]"," ",0,"[-1/4*sqrt(-a*c)*log((c*x^4 - 2*sqrt(-a*c)*x^2 - a)/(c*x^4 + a))/(a*c), -1/2*sqrt(a*c)*arctan(sqrt(a*c)/(c*x^2))/(a*c)]","A",0
649,1,18,0,0.538428," ","integrate(1/x/(c*x^4+a),x, algorithm=""fricas"")","-\frac{\log\left(c x^{4} + a\right) - 4 \, \log\left(x\right)}{4 \, a}"," ",0,"-1/4*(log(c*x^4 + a) - 4*log(x))/a","A",0
650,1,94,0,1.058883," ","integrate(1/x^3/(c*x^4+a),x, algorithm=""fricas"")","\left[\frac{x^{2} \sqrt{-\frac{c}{a}} \log\left(\frac{c x^{4} - 2 \, a x^{2} \sqrt{-\frac{c}{a}} - a}{c x^{4} + a}\right) - 2}{4 \, a x^{2}}, \frac{x^{2} \sqrt{\frac{c}{a}} \arctan\left(\frac{a \sqrt{\frac{c}{a}}}{c x^{2}}\right) - 1}{2 \, a x^{2}}\right]"," ",0,"[1/4*(x^2*sqrt(-c/a)*log((c*x^4 - 2*a*x^2*sqrt(-c/a) - a)/(c*x^4 + a)) - 2)/(a*x^2), 1/2*(x^2*sqrt(c/a)*arctan(a*sqrt(c/a)/(c*x^2)) - 1)/(a*x^2)]","A",0
651,1,33,0,0.824633," ","integrate(1/x^5/(c*x^4+a),x, algorithm=""fricas"")","\frac{c x^{4} \log\left(c x^{4} + a\right) - 4 \, c x^{4} \log\left(x\right) - a}{4 \, a^{2} x^{4}}"," ",0,"1/4*(c*x^4*log(c*x^4 + a) - 4*c*x^4*log(x) - a)/(a^2*x^4)","A",0
652,1,112,0,0.844819," ","integrate(1/x^7/(c*x^4+a),x, algorithm=""fricas"")","\left[\frac{3 \, c x^{6} \sqrt{-\frac{c}{a}} \log\left(\frac{c x^{4} + 2 \, a x^{2} \sqrt{-\frac{c}{a}} - a}{c x^{4} + a}\right) + 6 \, c x^{4} - 2 \, a}{12 \, a^{2} x^{6}}, -\frac{3 \, c x^{6} \sqrt{\frac{c}{a}} \arctan\left(\frac{a \sqrt{\frac{c}{a}}}{c x^{2}}\right) - 3 \, c x^{4} + a}{6 \, a^{2} x^{6}}\right]"," ",0,"[1/12*(3*c*x^6*sqrt(-c/a)*log((c*x^4 + 2*a*x^2*sqrt(-c/a) - a)/(c*x^4 + a)) + 6*c*x^4 - 2*a)/(a^2*x^6), -1/6*(3*c*x^6*sqrt(c/a)*arctan(a*sqrt(c/a)/(c*x^2)) - 3*c*x^4 + a)/(a^2*x^6)]","A",0
653,1,119,0,0.908212," ","integrate(x^4/(c*x^4+a),x, algorithm=""fricas"")","-\frac{4 \, c \left(-\frac{a}{c^{5}}\right)^{\frac{1}{4}} \arctan\left(-\frac{c^{4} x \left(-\frac{a}{c^{5}}\right)^{\frac{3}{4}} - \sqrt{c^{2} \sqrt{-\frac{a}{c^{5}}} + x^{2}} c^{4} \left(-\frac{a}{c^{5}}\right)^{\frac{3}{4}}}{a}\right) + c \left(-\frac{a}{c^{5}}\right)^{\frac{1}{4}} \log\left(c \left(-\frac{a}{c^{5}}\right)^{\frac{1}{4}} + x\right) - c \left(-\frac{a}{c^{5}}\right)^{\frac{1}{4}} \log\left(-c \left(-\frac{a}{c^{5}}\right)^{\frac{1}{4}} + x\right) - 4 \, x}{4 \, c}"," ",0,"-1/4*(4*c*(-a/c^5)^(1/4)*arctan(-(c^4*x*(-a/c^5)^(3/4) - sqrt(c^2*sqrt(-a/c^5) + x^2)*c^4*(-a/c^5)^(3/4))/a) + c*(-a/c^5)^(1/4)*log(c*(-a/c^5)^(1/4) + x) - c*(-a/c^5)^(1/4)*log(-c*(-a/c^5)^(1/4) + x) - 4*x)/c","A",0
654,1,122,0,0.939046," ","integrate(x^2/(c*x^4+a),x, algorithm=""fricas"")","-\left(-\frac{1}{a c^{3}}\right)^{\frac{1}{4}} \arctan\left(-c x \left(-\frac{1}{a c^{3}}\right)^{\frac{1}{4}} + \sqrt{-a c \sqrt{-\frac{1}{a c^{3}}} + x^{2}} c \left(-\frac{1}{a c^{3}}\right)^{\frac{1}{4}}\right) + \frac{1}{4} \, \left(-\frac{1}{a c^{3}}\right)^{\frac{1}{4}} \log\left(a c^{2} \left(-\frac{1}{a c^{3}}\right)^{\frac{3}{4}} + x\right) - \frac{1}{4} \, \left(-\frac{1}{a c^{3}}\right)^{\frac{1}{4}} \log\left(-a c^{2} \left(-\frac{1}{a c^{3}}\right)^{\frac{3}{4}} + x\right)"," ",0,"-(-1/(a*c^3))^(1/4)*arctan(-c*x*(-1/(a*c^3))^(1/4) + sqrt(-a*c*sqrt(-1/(a*c^3)) + x^2)*c*(-1/(a*c^3))^(1/4)) + 1/4*(-1/(a*c^3))^(1/4)*log(a*c^2*(-1/(a*c^3))^(3/4) + x) - 1/4*(-1/(a*c^3))^(1/4)*log(-a*c^2*(-1/(a*c^3))^(3/4) + x)","A",0
655,1,121,0,0.907700," ","integrate(1/(c*x^4+a),x, algorithm=""fricas"")","\left(-\frac{1}{a^{3} c}\right)^{\frac{1}{4}} \arctan\left(-a^{2} c x \left(-\frac{1}{a^{3} c}\right)^{\frac{3}{4}} + \sqrt{a^{2} \sqrt{-\frac{1}{a^{3} c}} + x^{2}} a^{2} c \left(-\frac{1}{a^{3} c}\right)^{\frac{3}{4}}\right) + \frac{1}{4} \, \left(-\frac{1}{a^{3} c}\right)^{\frac{1}{4}} \log\left(a \left(-\frac{1}{a^{3} c}\right)^{\frac{1}{4}} + x\right) - \frac{1}{4} \, \left(-\frac{1}{a^{3} c}\right)^{\frac{1}{4}} \log\left(-a \left(-\frac{1}{a^{3} c}\right)^{\frac{1}{4}} + x\right)"," ",0,"(-1/(a^3*c))^(1/4)*arctan(-a^2*c*x*(-1/(a^3*c))^(3/4) + sqrt(a^2*sqrt(-1/(a^3*c)) + x^2)*a^2*c*(-1/(a^3*c))^(3/4)) + 1/4*(-1/(a^3*c))^(1/4)*log(a*(-1/(a^3*c))^(1/4) + x) - 1/4*(-1/(a^3*c))^(1/4)*log(-a*(-1/(a^3*c))^(1/4) + x)","A",0
656,1,130,0,0.868616," ","integrate(1/x^2/(c*x^4+a),x, algorithm=""fricas"")","\frac{4 \, a x \left(-\frac{c}{a^{5}}\right)^{\frac{1}{4}} \arctan\left(-a x \left(-\frac{c}{a^{5}}\right)^{\frac{1}{4}} + a \sqrt{-\frac{a^{3} \sqrt{-\frac{c}{a^{5}}} - c x^{2}}{c}} \left(-\frac{c}{a^{5}}\right)^{\frac{1}{4}}\right) - a x \left(-\frac{c}{a^{5}}\right)^{\frac{1}{4}} \log\left(a^{4} \left(-\frac{c}{a^{5}}\right)^{\frac{3}{4}} + c x\right) + a x \left(-\frac{c}{a^{5}}\right)^{\frac{1}{4}} \log\left(-a^{4} \left(-\frac{c}{a^{5}}\right)^{\frac{3}{4}} + c x\right) - 4}{4 \, a x}"," ",0,"1/4*(4*a*x*(-c/a^5)^(1/4)*arctan(-a*x*(-c/a^5)^(1/4) + a*sqrt(-(a^3*sqrt(-c/a^5) - c*x^2)/c)*(-c/a^5)^(1/4)) - a*x*(-c/a^5)^(1/4)*log(a^4*(-c/a^5)^(3/4) + c*x) + a*x*(-c/a^5)^(1/4)*log(-a^4*(-c/a^5)^(3/4) + c*x) - 4)/(a*x)","A",0
657,1,162,0,0.831948," ","integrate(1/x^4/(c*x^4+a),x, algorithm=""fricas"")","-\frac{12 \, a x^{3} \left(-\frac{c^{3}}{a^{7}}\right)^{\frac{1}{4}} \arctan\left(-\frac{a^{5} x \left(-\frac{c^{3}}{a^{7}}\right)^{\frac{3}{4}} - a^{5} \sqrt{\frac{a^{4} \sqrt{-\frac{c^{3}}{a^{7}}} + c^{2} x^{2}}{c^{2}}} \left(-\frac{c^{3}}{a^{7}}\right)^{\frac{3}{4}}}{c^{2}}\right) + 3 \, a x^{3} \left(-\frac{c^{3}}{a^{7}}\right)^{\frac{1}{4}} \log\left(a^{2} \left(-\frac{c^{3}}{a^{7}}\right)^{\frac{1}{4}} + c x\right) - 3 \, a x^{3} \left(-\frac{c^{3}}{a^{7}}\right)^{\frac{1}{4}} \log\left(-a^{2} \left(-\frac{c^{3}}{a^{7}}\right)^{\frac{1}{4}} + c x\right) + 4}{12 \, a x^{3}}"," ",0,"-1/12*(12*a*x^3*(-c^3/a^7)^(1/4)*arctan(-(a^5*x*(-c^3/a^7)^(3/4) - a^5*sqrt((a^4*sqrt(-c^3/a^7) + c^2*x^2)/c^2)*(-c^3/a^7)^(3/4))/c^2) + 3*a*x^3*(-c^3/a^7)^(1/4)*log(a^2*(-c^3/a^7)^(1/4) + c*x) - 3*a*x^3*(-c^3/a^7)^(1/4)*log(-a^2*(-c^3/a^7)^(1/4) + c*x) + 4)/(a*x^3)","A",0
658,1,56,0,0.785001," ","integrate(x^11/(c*x^4+a)^2,x, algorithm=""fricas"")","\frac{c^{2} x^{8} + a c x^{4} - a^{2} - 2 \, {\left(a c x^{4} + a^{2}\right)} \log\left(c x^{4} + a\right)}{4 \, {\left(c^{4} x^{4} + a c^{3}\right)}}"," ",0,"1/4*(c^2*x^8 + a*c*x^4 - a^2 - 2*(a*c*x^4 + a^2)*log(c*x^4 + a))/(c^4*x^4 + a*c^3)","A",0
659,1,144,0,0.834212," ","integrate(x^9/(c*x^4+a)^2,x, algorithm=""fricas"")","\left[\frac{4 \, c x^{6} + 6 \, a x^{2} + 3 \, {\left(c x^{4} + a\right)} \sqrt{-\frac{a}{c}} \log\left(\frac{c x^{4} - 2 \, c x^{2} \sqrt{-\frac{a}{c}} - a}{c x^{4} + a}\right)}{8 \, {\left(c^{3} x^{4} + a c^{2}\right)}}, \frac{2 \, c x^{6} + 3 \, a x^{2} - 3 \, {\left(c x^{4} + a\right)} \sqrt{\frac{a}{c}} \arctan\left(\frac{c x^{2} \sqrt{\frac{a}{c}}}{a}\right)}{4 \, {\left(c^{3} x^{4} + a c^{2}\right)}}\right]"," ",0,"[1/8*(4*c*x^6 + 6*a*x^2 + 3*(c*x^4 + a)*sqrt(-a/c)*log((c*x^4 - 2*c*x^2*sqrt(-a/c) - a)/(c*x^4 + a)))/(c^3*x^4 + a*c^2), 1/4*(2*c*x^6 + 3*a*x^2 - 3*(c*x^4 + a)*sqrt(a/c)*arctan(c*x^2*sqrt(a/c)/a))/(c^3*x^4 + a*c^2)]","A",0
660,1,35,0,0.753080," ","integrate(x^7/(c*x^4+a)^2,x, algorithm=""fricas"")","\frac{{\left(c x^{4} + a\right)} \log\left(c x^{4} + a\right) + a}{4 \, {\left(c^{3} x^{4} + a c^{2}\right)}}"," ",0,"1/4*((c*x^4 + a)*log(c*x^4 + a) + a)/(c^3*x^4 + a*c^2)","A",0
661,1,127,0,0.849852," ","integrate(x^5/(c*x^4+a)^2,x, algorithm=""fricas"")","\left[-\frac{2 \, a c x^{2} + {\left(c x^{4} + a\right)} \sqrt{-a c} \log\left(\frac{c x^{4} - 2 \, \sqrt{-a c} x^{2} - a}{c x^{4} + a}\right)}{8 \, {\left(a c^{3} x^{4} + a^{2} c^{2}\right)}}, -\frac{a c x^{2} + {\left(c x^{4} + a\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c}}{c x^{2}}\right)}{4 \, {\left(a c^{3} x^{4} + a^{2} c^{2}\right)}}\right]"," ",0,"[-1/8*(2*a*c*x^2 + (c*x^4 + a)*sqrt(-a*c)*log((c*x^4 - 2*sqrt(-a*c)*x^2 - a)/(c*x^4 + a)))/(a*c^3*x^4 + a^2*c^2), -1/4*(a*c*x^2 + (c*x^4 + a)*sqrt(a*c)*arctan(sqrt(a*c)/(c*x^2)))/(a*c^3*x^4 + a^2*c^2)]","A",0
662,1,15,0,0.844783," ","integrate(x^3/(c*x^4+a)^2,x, algorithm=""fricas"")","-\frac{1}{4 \, {\left(c^{2} x^{4} + a c\right)}}"," ",0,"-1/4/(c^2*x^4 + a*c)","A",0
663,1,129,0,0.830255," ","integrate(x/(c*x^4+a)^2,x, algorithm=""fricas"")","\left[\frac{2 \, a c x^{2} - {\left(c x^{4} + a\right)} \sqrt{-a c} \log\left(\frac{c x^{4} - 2 \, \sqrt{-a c} x^{2} - a}{c x^{4} + a}\right)}{8 \, {\left(a^{2} c^{2} x^{4} + a^{3} c\right)}}, \frac{a c x^{2} - {\left(c x^{4} + a\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c}}{c x^{2}}\right)}{4 \, {\left(a^{2} c^{2} x^{4} + a^{3} c\right)}}\right]"," ",0,"[1/8*(2*a*c*x^2 - (c*x^4 + a)*sqrt(-a*c)*log((c*x^4 - 2*sqrt(-a*c)*x^2 - a)/(c*x^4 + a)))/(a^2*c^2*x^4 + a^3*c), 1/4*(a*c*x^2 - (c*x^4 + a)*sqrt(a*c)*arctan(sqrt(a*c)/(c*x^2)))/(a^2*c^2*x^4 + a^3*c)]","A",0
664,1,47,0,0.860240," ","integrate(1/x/(c*x^4+a)^2,x, algorithm=""fricas"")","-\frac{{\left(c x^{4} + a\right)} \log\left(c x^{4} + a\right) - 4 \, {\left(c x^{4} + a\right)} \log\left(x\right) - a}{4 \, {\left(a^{2} c x^{4} + a^{3}\right)}}"," ",0,"-1/4*((c*x^4 + a)*log(c*x^4 + a) - 4*(c*x^4 + a)*log(x) - a)/(a^2*c*x^4 + a^3)","A",0
665,1,152,0,0.814600," ","integrate(1/x^3/(c*x^4+a)^2,x, algorithm=""fricas"")","\left[-\frac{6 \, c x^{4} - 3 \, {\left(c x^{6} + a x^{2}\right)} \sqrt{-\frac{c}{a}} \log\left(\frac{c x^{4} - 2 \, a x^{2} \sqrt{-\frac{c}{a}} - a}{c x^{4} + a}\right) + 4 \, a}{8 \, {\left(a^{2} c x^{6} + a^{3} x^{2}\right)}}, -\frac{3 \, c x^{4} - 3 \, {\left(c x^{6} + a x^{2}\right)} \sqrt{\frac{c}{a}} \arctan\left(\frac{a \sqrt{\frac{c}{a}}}{c x^{2}}\right) + 2 \, a}{4 \, {\left(a^{2} c x^{6} + a^{3} x^{2}\right)}}\right]"," ",0,"[-1/8*(6*c*x^4 - 3*(c*x^6 + a*x^2)*sqrt(-c/a)*log((c*x^4 - 2*a*x^2*sqrt(-c/a) - a)/(c*x^4 + a)) + 4*a)/(a^2*c*x^6 + a^3*x^2), -1/4*(3*c*x^4 - 3*(c*x^6 + a*x^2)*sqrt(c/a)*arctan(a*sqrt(c/a)/(c*x^2)) + 2*a)/(a^2*c*x^6 + a^3*x^2)]","A",0
666,1,181,0,0.806252," ","integrate(x^6/(c*x^4+a)^2,x, algorithm=""fricas"")","-\frac{4 \, x^{3} + 12 \, {\left(c^{2} x^{4} + a c\right)} \left(-\frac{1}{a c^{7}}\right)^{\frac{1}{4}} \arctan\left(-c^{2} x \left(-\frac{1}{a c^{7}}\right)^{\frac{1}{4}} + \sqrt{-a c^{3} \sqrt{-\frac{1}{a c^{7}}} + x^{2}} c^{2} \left(-\frac{1}{a c^{7}}\right)^{\frac{1}{4}}\right) - 3 \, {\left(c^{2} x^{4} + a c\right)} \left(-\frac{1}{a c^{7}}\right)^{\frac{1}{4}} \log\left(a c^{5} \left(-\frac{1}{a c^{7}}\right)^{\frac{3}{4}} + x\right) + 3 \, {\left(c^{2} x^{4} + a c\right)} \left(-\frac{1}{a c^{7}}\right)^{\frac{1}{4}} \log\left(-a c^{5} \left(-\frac{1}{a c^{7}}\right)^{\frac{3}{4}} + x\right)}{16 \, {\left(c^{2} x^{4} + a c\right)}}"," ",0,"-1/16*(4*x^3 + 12*(c^2*x^4 + a*c)*(-1/(a*c^7))^(1/4)*arctan(-c^2*x*(-1/(a*c^7))^(1/4) + sqrt(-a*c^3*sqrt(-1/(a*c^7)) + x^2)*c^2*(-1/(a*c^7))^(1/4)) - 3*(c^2*x^4 + a*c)*(-1/(a*c^7))^(1/4)*log(a*c^5*(-1/(a*c^7))^(3/4) + x) + 3*(c^2*x^4 + a*c)*(-1/(a*c^7))^(1/4)*log(-a*c^5*(-1/(a*c^7))^(3/4) + x))/(c^2*x^4 + a*c)","A",0
667,1,181,0,0.639932," ","integrate(x^4/(c*x^4+a)^2,x, algorithm=""fricas"")","\frac{4 \, {\left(c^{2} x^{4} + a c\right)} \left(-\frac{1}{a^{3} c^{5}}\right)^{\frac{1}{4}} \arctan\left(-a^{2} c^{4} x \left(-\frac{1}{a^{3} c^{5}}\right)^{\frac{3}{4}} + \sqrt{a^{2} c^{2} \sqrt{-\frac{1}{a^{3} c^{5}}} + x^{2}} a^{2} c^{4} \left(-\frac{1}{a^{3} c^{5}}\right)^{\frac{3}{4}}\right) + {\left(c^{2} x^{4} + a c\right)} \left(-\frac{1}{a^{3} c^{5}}\right)^{\frac{1}{4}} \log\left(a c \left(-\frac{1}{a^{3} c^{5}}\right)^{\frac{1}{4}} + x\right) - {\left(c^{2} x^{4} + a c\right)} \left(-\frac{1}{a^{3} c^{5}}\right)^{\frac{1}{4}} \log\left(-a c \left(-\frac{1}{a^{3} c^{5}}\right)^{\frac{1}{4}} + x\right) - 4 \, x}{16 \, {\left(c^{2} x^{4} + a c\right)}}"," ",0,"1/16*(4*(c^2*x^4 + a*c)*(-1/(a^3*c^5))^(1/4)*arctan(-a^2*c^4*x*(-1/(a^3*c^5))^(3/4) + sqrt(a^2*c^2*sqrt(-1/(a^3*c^5)) + x^2)*a^2*c^4*(-1/(a^3*c^5))^(3/4)) + (c^2*x^4 + a*c)*(-1/(a^3*c^5))^(1/4)*log(a*c*(-1/(a^3*c^5))^(1/4) + x) - (c^2*x^4 + a*c)*(-1/(a^3*c^5))^(1/4)*log(-a*c*(-1/(a^3*c^5))^(1/4) + x) - 4*x)/(c^2*x^4 + a*c)","A",0
668,1,178,0,1.241233," ","integrate(x^2/(c*x^4+a)^2,x, algorithm=""fricas"")","\frac{4 \, x^{3} - 4 \, {\left(a c x^{4} + a^{2}\right)} \left(-\frac{1}{a^{5} c^{3}}\right)^{\frac{1}{4}} \arctan\left(-a c x \left(-\frac{1}{a^{5} c^{3}}\right)^{\frac{1}{4}} + \sqrt{-a^{3} c \sqrt{-\frac{1}{a^{5} c^{3}}} + x^{2}} a c \left(-\frac{1}{a^{5} c^{3}}\right)^{\frac{1}{4}}\right) + {\left(a c x^{4} + a^{2}\right)} \left(-\frac{1}{a^{5} c^{3}}\right)^{\frac{1}{4}} \log\left(a^{4} c^{2} \left(-\frac{1}{a^{5} c^{3}}\right)^{\frac{3}{4}} + x\right) - {\left(a c x^{4} + a^{2}\right)} \left(-\frac{1}{a^{5} c^{3}}\right)^{\frac{1}{4}} \log\left(-a^{4} c^{2} \left(-\frac{1}{a^{5} c^{3}}\right)^{\frac{3}{4}} + x\right)}{16 \, {\left(a c x^{4} + a^{2}\right)}}"," ",0,"1/16*(4*x^3 - 4*(a*c*x^4 + a^2)*(-1/(a^5*c^3))^(1/4)*arctan(-a*c*x*(-1/(a^5*c^3))^(1/4) + sqrt(-a^3*c*sqrt(-1/(a^5*c^3)) + x^2)*a*c*(-1/(a^5*c^3))^(1/4)) + (a*c*x^4 + a^2)*(-1/(a^5*c^3))^(1/4)*log(a^4*c^2*(-1/(a^5*c^3))^(3/4) + x) - (a*c*x^4 + a^2)*(-1/(a^5*c^3))^(1/4)*log(-a^4*c^2*(-1/(a^5*c^3))^(3/4) + x))/(a*c*x^4 + a^2)","A",0
669,1,173,0,0.914556," ","integrate(1/(c*x^4+a)^2,x, algorithm=""fricas"")","\frac{12 \, {\left(a c x^{4} + a^{2}\right)} \left(-\frac{1}{a^{7} c}\right)^{\frac{1}{4}} \arctan\left(-a^{5} c x \left(-\frac{1}{a^{7} c}\right)^{\frac{3}{4}} + \sqrt{a^{4} \sqrt{-\frac{1}{a^{7} c}} + x^{2}} a^{5} c \left(-\frac{1}{a^{7} c}\right)^{\frac{3}{4}}\right) + 3 \, {\left(a c x^{4} + a^{2}\right)} \left(-\frac{1}{a^{7} c}\right)^{\frac{1}{4}} \log\left(a^{2} \left(-\frac{1}{a^{7} c}\right)^{\frac{1}{4}} + x\right) - 3 \, {\left(a c x^{4} + a^{2}\right)} \left(-\frac{1}{a^{7} c}\right)^{\frac{1}{4}} \log\left(-a^{2} \left(-\frac{1}{a^{7} c}\right)^{\frac{1}{4}} + x\right) + 4 \, x}{16 \, {\left(a c x^{4} + a^{2}\right)}}"," ",0,"1/16*(12*(a*c*x^4 + a^2)*(-1/(a^7*c))^(1/4)*arctan(-a^5*c*x*(-1/(a^7*c))^(3/4) + sqrt(a^4*sqrt(-1/(a^7*c)) + x^2)*a^5*c*(-1/(a^7*c))^(3/4)) + 3*(a*c*x^4 + a^2)*(-1/(a^7*c))^(1/4)*log(a^2*(-1/(a^7*c))^(1/4) + x) - 3*(a*c*x^4 + a^2)*(-1/(a^7*c))^(1/4)*log(-a^2*(-1/(a^7*c))^(1/4) + x) + 4*x)/(a*c*x^4 + a^2)","A",0
670,1,192,0,1.064513," ","integrate(1/x^2/(c*x^4+a)^2,x, algorithm=""fricas"")","-\frac{20 \, c x^{4} - 20 \, {\left(a^{2} c x^{5} + a^{3} x\right)} \left(-\frac{c}{a^{9}}\right)^{\frac{1}{4}} \arctan\left(-a^{2} x \left(-\frac{c}{a^{9}}\right)^{\frac{1}{4}} + a^{2} \sqrt{-\frac{a^{5} \sqrt{-\frac{c}{a^{9}}} - c x^{2}}{c}} \left(-\frac{c}{a^{9}}\right)^{\frac{1}{4}}\right) + 5 \, {\left(a^{2} c x^{5} + a^{3} x\right)} \left(-\frac{c}{a^{9}}\right)^{\frac{1}{4}} \log\left(125 \, a^{7} \left(-\frac{c}{a^{9}}\right)^{\frac{3}{4}} + 125 \, c x\right) - 5 \, {\left(a^{2} c x^{5} + a^{3} x\right)} \left(-\frac{c}{a^{9}}\right)^{\frac{1}{4}} \log\left(-125 \, a^{7} \left(-\frac{c}{a^{9}}\right)^{\frac{3}{4}} + 125 \, c x\right) + 16 \, a}{16 \, {\left(a^{2} c x^{5} + a^{3} x\right)}}"," ",0,"-1/16*(20*c*x^4 - 20*(a^2*c*x^5 + a^3*x)*(-c/a^9)^(1/4)*arctan(-a^2*x*(-c/a^9)^(1/4) + a^2*sqrt(-(a^5*sqrt(-c/a^9) - c*x^2)/c)*(-c/a^9)^(1/4)) + 5*(a^2*c*x^5 + a^3*x)*(-c/a^9)^(1/4)*log(125*a^7*(-c/a^9)^(3/4) + 125*c*x) - 5*(a^2*c*x^5 + a^3*x)*(-c/a^9)^(1/4)*log(-125*a^7*(-c/a^9)^(3/4) + 125*c*x) + 16*a)/(a^2*c*x^5 + a^3*x)","A",0
671,1,221,0,1.005544," ","integrate(1/x^4/(c*x^4+a)^2,x, algorithm=""fricas"")","-\frac{28 \, c x^{4} + 84 \, {\left(a^{2} c x^{7} + a^{3} x^{3}\right)} \left(-\frac{c^{3}}{a^{11}}\right)^{\frac{1}{4}} \arctan\left(-\frac{a^{8} x \left(-\frac{c^{3}}{a^{11}}\right)^{\frac{3}{4}} - a^{8} \sqrt{\frac{a^{6} \sqrt{-\frac{c^{3}}{a^{11}}} + c^{2} x^{2}}{c^{2}}} \left(-\frac{c^{3}}{a^{11}}\right)^{\frac{3}{4}}}{c^{2}}\right) + 21 \, {\left(a^{2} c x^{7} + a^{3} x^{3}\right)} \left(-\frac{c^{3}}{a^{11}}\right)^{\frac{1}{4}} \log\left(7 \, a^{3} \left(-\frac{c^{3}}{a^{11}}\right)^{\frac{1}{4}} + 7 \, c x\right) - 21 \, {\left(a^{2} c x^{7} + a^{3} x^{3}\right)} \left(-\frac{c^{3}}{a^{11}}\right)^{\frac{1}{4}} \log\left(-7 \, a^{3} \left(-\frac{c^{3}}{a^{11}}\right)^{\frac{1}{4}} + 7 \, c x\right) + 16 \, a}{48 \, {\left(a^{2} c x^{7} + a^{3} x^{3}\right)}}"," ",0,"-1/48*(28*c*x^4 + 84*(a^2*c*x^7 + a^3*x^3)*(-c^3/a^11)^(1/4)*arctan(-(a^8*x*(-c^3/a^11)^(3/4) - a^8*sqrt((a^6*sqrt(-c^3/a^11) + c^2*x^2)/c^2)*(-c^3/a^11)^(3/4))/c^2) + 21*(a^2*c*x^7 + a^3*x^3)*(-c^3/a^11)^(1/4)*log(7*a^3*(-c^3/a^11)^(1/4) + 7*c*x) - 21*(a^2*c*x^7 + a^3*x^3)*(-c^3/a^11)^(1/4)*log(-7*a^3*(-c^3/a^11)^(1/4) + 7*c*x) + 16*a)/(a^2*c*x^7 + a^3*x^3)","A",0
672,1,69,0,0.912974," ","integrate(x^11/(c*x^4+a)^3,x, algorithm=""fricas"")","\frac{4 \, a c x^{4} + 3 \, a^{2} + 2 \, {\left(c^{2} x^{8} + 2 \, a c x^{4} + a^{2}\right)} \log\left(c x^{4} + a\right)}{8 \, {\left(c^{5} x^{8} + 2 \, a c^{4} x^{4} + a^{2} c^{3}\right)}}"," ",0,"1/8*(4*a*c*x^4 + 3*a^2 + 2*(c^2*x^8 + 2*a*c*x^4 + a^2)*log(c*x^4 + a))/(c^5*x^8 + 2*a*c^4*x^4 + a^2*c^3)","A",0
673,1,196,0,1.057575," ","integrate(x^9/(c*x^4+a)^3,x, algorithm=""fricas"")","\left[-\frac{10 \, a c^{2} x^{6} + 6 \, a^{2} c x^{2} + 3 \, {\left(c^{2} x^{8} + 2 \, a c x^{4} + a^{2}\right)} \sqrt{-a c} \log\left(\frac{c x^{4} - 2 \, \sqrt{-a c} x^{2} - a}{c x^{4} + a}\right)}{32 \, {\left(a c^{5} x^{8} + 2 \, a^{2} c^{4} x^{4} + a^{3} c^{3}\right)}}, -\frac{5 \, a c^{2} x^{6} + 3 \, a^{2} c x^{2} + 3 \, {\left(c^{2} x^{8} + 2 \, a c x^{4} + a^{2}\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c}}{c x^{2}}\right)}{16 \, {\left(a c^{5} x^{8} + 2 \, a^{2} c^{4} x^{4} + a^{3} c^{3}\right)}}\right]"," ",0,"[-1/32*(10*a*c^2*x^6 + 6*a^2*c*x^2 + 3*(c^2*x^8 + 2*a*c*x^4 + a^2)*sqrt(-a*c)*log((c*x^4 - 2*sqrt(-a*c)*x^2 - a)/(c*x^4 + a)))/(a*c^5*x^8 + 2*a^2*c^4*x^4 + a^3*c^3), -1/16*(5*a*c^2*x^6 + 3*a^2*c*x^2 + 3*(c^2*x^8 + 2*a*c*x^4 + a^2)*sqrt(a*c)*arctan(sqrt(a*c)/(c*x^2)))/(a*c^5*x^8 + 2*a^2*c^4*x^4 + a^3*c^3)]","A",0
674,1,36,0,0.946625," ","integrate(x^7/(c*x^4+a)^3,x, algorithm=""fricas"")","-\frac{2 \, c x^{4} + a}{8 \, {\left(c^{4} x^{8} + 2 \, a c^{3} x^{4} + a^{2} c^{2}\right)}}"," ",0,"-1/8*(2*c*x^4 + a)/(c^4*x^8 + 2*a*c^3*x^4 + a^2*c^2)","B",0
675,1,199,0,0.811984," ","integrate(x^5/(c*x^4+a)^3,x, algorithm=""fricas"")","\left[\frac{2 \, a c^{2} x^{6} - 2 \, a^{2} c x^{2} - {\left(c^{2} x^{8} + 2 \, a c x^{4} + a^{2}\right)} \sqrt{-a c} \log\left(\frac{c x^{4} - 2 \, \sqrt{-a c} x^{2} - a}{c x^{4} + a}\right)}{32 \, {\left(a^{2} c^{4} x^{8} + 2 \, a^{3} c^{3} x^{4} + a^{4} c^{2}\right)}}, \frac{a c^{2} x^{6} - a^{2} c x^{2} - {\left(c^{2} x^{8} + 2 \, a c x^{4} + a^{2}\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c}}{c x^{2}}\right)}{16 \, {\left(a^{2} c^{4} x^{8} + 2 \, a^{3} c^{3} x^{4} + a^{4} c^{2}\right)}}\right]"," ",0,"[1/32*(2*a*c^2*x^6 - 2*a^2*c*x^2 - (c^2*x^8 + 2*a*c*x^4 + a^2)*sqrt(-a*c)*log((c*x^4 - 2*sqrt(-a*c)*x^2 - a)/(c*x^4 + a)))/(a^2*c^4*x^8 + 2*a^3*c^3*x^4 + a^4*c^2), 1/16*(a*c^2*x^6 - a^2*c*x^2 - (c^2*x^8 + 2*a*c*x^4 + a^2)*sqrt(a*c)*arctan(sqrt(a*c)/(c*x^2)))/(a^2*c^4*x^8 + 2*a^3*c^3*x^4 + a^4*c^2)]","A",0
676,1,26,0,0.882973," ","integrate(x^3/(c*x^4+a)^3,x, algorithm=""fricas"")","-\frac{1}{8 \, {\left(c^{3} x^{8} + 2 \, a c^{2} x^{4} + a^{2} c\right)}}"," ",0,"-1/8/(c^3*x^8 + 2*a*c^2*x^4 + a^2*c)","A",0
677,1,196,0,1.000201," ","integrate(x/(c*x^4+a)^3,x, algorithm=""fricas"")","\left[\frac{6 \, a c^{2} x^{6} + 10 \, a^{2} c x^{2} - 3 \, {\left(c^{2} x^{8} + 2 \, a c x^{4} + a^{2}\right)} \sqrt{-a c} \log\left(\frac{c x^{4} - 2 \, \sqrt{-a c} x^{2} - a}{c x^{4} + a}\right)}{32 \, {\left(a^{3} c^{3} x^{8} + 2 \, a^{4} c^{2} x^{4} + a^{5} c\right)}}, \frac{3 \, a c^{2} x^{6} + 5 \, a^{2} c x^{2} - 3 \, {\left(c^{2} x^{8} + 2 \, a c x^{4} + a^{2}\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c}}{c x^{2}}\right)}{16 \, {\left(a^{3} c^{3} x^{8} + 2 \, a^{4} c^{2} x^{4} + a^{5} c\right)}}\right]"," ",0,"[1/32*(6*a*c^2*x^6 + 10*a^2*c*x^2 - 3*(c^2*x^8 + 2*a*c*x^4 + a^2)*sqrt(-a*c)*log((c*x^4 - 2*sqrt(-a*c)*x^2 - a)/(c*x^4 + a)))/(a^3*c^3*x^8 + 2*a^4*c^2*x^4 + a^5*c), 1/16*(3*a*c^2*x^6 + 5*a^2*c*x^2 - 3*(c^2*x^8 + 2*a*c*x^4 + a^2)*sqrt(a*c)*arctan(sqrt(a*c)/(c*x^2)))/(a^3*c^3*x^8 + 2*a^4*c^2*x^4 + a^5*c)]","A",0
678,1,90,0,0.637178," ","integrate(1/x/(c*x^4+a)^3,x, algorithm=""fricas"")","\frac{2 \, a c x^{4} + 3 \, a^{2} - 2 \, {\left(c^{2} x^{8} + 2 \, a c x^{4} + a^{2}\right)} \log\left(c x^{4} + a\right) + 8 \, {\left(c^{2} x^{8} + 2 \, a c x^{4} + a^{2}\right)} \log\left(x\right)}{8 \, {\left(a^{3} c^{2} x^{8} + 2 \, a^{4} c x^{4} + a^{5}\right)}}"," ",0,"1/8*(2*a*c*x^4 + 3*a^2 - 2*(c^2*x^8 + 2*a*c*x^4 + a^2)*log(c*x^4 + a) + 8*(c^2*x^8 + 2*a*c*x^4 + a^2)*log(x))/(a^3*c^2*x^8 + 2*a^4*c*x^4 + a^5)","A",0
679,1,218,0,0.854288," ","integrate(1/x^3/(c*x^4+a)^3,x, algorithm=""fricas"")","\left[-\frac{30 \, c^{2} x^{8} + 50 \, a c x^{4} - 15 \, {\left(c^{2} x^{10} + 2 \, a c x^{6} + a^{2} x^{2}\right)} \sqrt{-\frac{c}{a}} \log\left(\frac{c x^{4} - 2 \, a x^{2} \sqrt{-\frac{c}{a}} - a}{c x^{4} + a}\right) + 16 \, a^{2}}{32 \, {\left(a^{3} c^{2} x^{10} + 2 \, a^{4} c x^{6} + a^{5} x^{2}\right)}}, -\frac{15 \, c^{2} x^{8} + 25 \, a c x^{4} - 15 \, {\left(c^{2} x^{10} + 2 \, a c x^{6} + a^{2} x^{2}\right)} \sqrt{\frac{c}{a}} \arctan\left(\frac{a \sqrt{\frac{c}{a}}}{c x^{2}}\right) + 8 \, a^{2}}{16 \, {\left(a^{3} c^{2} x^{10} + 2 \, a^{4} c x^{6} + a^{5} x^{2}\right)}}\right]"," ",0,"[-1/32*(30*c^2*x^8 + 50*a*c*x^4 - 15*(c^2*x^10 + 2*a*c*x^6 + a^2*x^2)*sqrt(-c/a)*log((c*x^4 - 2*a*x^2*sqrt(-c/a) - a)/(c*x^4 + a)) + 16*a^2)/(a^3*c^2*x^10 + 2*a^4*c*x^6 + a^5*x^2), -1/16*(15*c^2*x^8 + 25*a*c*x^4 - 15*(c^2*x^10 + 2*a*c*x^6 + a^2*x^2)*sqrt(c/a)*arctan(a*sqrt(c/a)/(c*x^2)) + 8*a^2)/(a^3*c^2*x^10 + 2*a^4*c*x^6 + a^5*x^2)]","A",0
680,1,240,0,0.997196," ","integrate(x^10/(c*x^4+a)^3,x, algorithm=""fricas"")","-\frac{44 \, c x^{7} + 28 \, a x^{3} + 84 \, {\left(c^{4} x^{8} + 2 \, a c^{3} x^{4} + a^{2} c^{2}\right)} \left(-\frac{1}{a c^{11}}\right)^{\frac{1}{4}} \arctan\left(-c^{3} x \left(-\frac{1}{a c^{11}}\right)^{\frac{1}{4}} + \sqrt{-a c^{5} \sqrt{-\frac{1}{a c^{11}}} + x^{2}} c^{3} \left(-\frac{1}{a c^{11}}\right)^{\frac{1}{4}}\right) - 21 \, {\left(c^{4} x^{8} + 2 \, a c^{3} x^{4} + a^{2} c^{2}\right)} \left(-\frac{1}{a c^{11}}\right)^{\frac{1}{4}} \log\left(a c^{8} \left(-\frac{1}{a c^{11}}\right)^{\frac{3}{4}} + x\right) + 21 \, {\left(c^{4} x^{8} + 2 \, a c^{3} x^{4} + a^{2} c^{2}\right)} \left(-\frac{1}{a c^{11}}\right)^{\frac{1}{4}} \log\left(-a c^{8} \left(-\frac{1}{a c^{11}}\right)^{\frac{3}{4}} + x\right)}{128 \, {\left(c^{4} x^{8} + 2 \, a c^{3} x^{4} + a^{2} c^{2}\right)}}"," ",0,"-1/128*(44*c*x^7 + 28*a*x^3 + 84*(c^4*x^8 + 2*a*c^3*x^4 + a^2*c^2)*(-1/(a*c^11))^(1/4)*arctan(-c^3*x*(-1/(a*c^11))^(1/4) + sqrt(-a*c^5*sqrt(-1/(a*c^11)) + x^2)*c^3*(-1/(a*c^11))^(1/4)) - 21*(c^4*x^8 + 2*a*c^3*x^4 + a^2*c^2)*(-1/(a*c^11))^(1/4)*log(a*c^8*(-1/(a*c^11))^(3/4) + x) + 21*(c^4*x^8 + 2*a*c^3*x^4 + a^2*c^2)*(-1/(a*c^11))^(1/4)*log(-a*c^8*(-1/(a*c^11))^(3/4) + x))/(c^4*x^8 + 2*a*c^3*x^4 + a^2*c^2)","A",0
681,1,245,0,0.999197," ","integrate(x^8/(c*x^4+a)^3,x, algorithm=""fricas"")","-\frac{36 \, c x^{5} - 20 \, {\left(c^{4} x^{8} + 2 \, a c^{3} x^{4} + a^{2} c^{2}\right)} \left(-\frac{1}{a^{3} c^{9}}\right)^{\frac{1}{4}} \arctan\left(-a^{2} c^{7} x \left(-\frac{1}{a^{3} c^{9}}\right)^{\frac{3}{4}} + \sqrt{a^{2} c^{4} \sqrt{-\frac{1}{a^{3} c^{9}}} + x^{2}} a^{2} c^{7} \left(-\frac{1}{a^{3} c^{9}}\right)^{\frac{3}{4}}\right) - 5 \, {\left(c^{4} x^{8} + 2 \, a c^{3} x^{4} + a^{2} c^{2}\right)} \left(-\frac{1}{a^{3} c^{9}}\right)^{\frac{1}{4}} \log\left(a c^{2} \left(-\frac{1}{a^{3} c^{9}}\right)^{\frac{1}{4}} + x\right) + 5 \, {\left(c^{4} x^{8} + 2 \, a c^{3} x^{4} + a^{2} c^{2}\right)} \left(-\frac{1}{a^{3} c^{9}}\right)^{\frac{1}{4}} \log\left(-a c^{2} \left(-\frac{1}{a^{3} c^{9}}\right)^{\frac{1}{4}} + x\right) + 20 \, a x}{128 \, {\left(c^{4} x^{8} + 2 \, a c^{3} x^{4} + a^{2} c^{2}\right)}}"," ",0,"-1/128*(36*c*x^5 - 20*(c^4*x^8 + 2*a*c^3*x^4 + a^2*c^2)*(-1/(a^3*c^9))^(1/4)*arctan(-a^2*c^7*x*(-1/(a^3*c^9))^(3/4) + sqrt(a^2*c^4*sqrt(-1/(a^3*c^9)) + x^2)*a^2*c^7*(-1/(a^3*c^9))^(3/4)) - 5*(c^4*x^8 + 2*a*c^3*x^4 + a^2*c^2)*(-1/(a^3*c^9))^(1/4)*log(a*c^2*(-1/(a^3*c^9))^(1/4) + x) + 5*(c^4*x^8 + 2*a*c^3*x^4 + a^2*c^2)*(-1/(a^3*c^9))^(1/4)*log(-a*c^2*(-1/(a^3*c^9))^(1/4) + x) + 20*a*x)/(c^4*x^8 + 2*a*c^3*x^4 + a^2*c^2)","A",0
682,1,252,0,0.979992," ","integrate(x^6/(c*x^4+a)^3,x, algorithm=""fricas"")","\frac{12 \, c x^{7} - 4 \, a x^{3} - 12 \, {\left(a c^{3} x^{8} + 2 \, a^{2} c^{2} x^{4} + a^{3} c\right)} \left(-\frac{1}{a^{5} c^{7}}\right)^{\frac{1}{4}} \arctan\left(-a c^{2} x \left(-\frac{1}{a^{5} c^{7}}\right)^{\frac{1}{4}} + \sqrt{-a^{3} c^{3} \sqrt{-\frac{1}{a^{5} c^{7}}} + x^{2}} a c^{2} \left(-\frac{1}{a^{5} c^{7}}\right)^{\frac{1}{4}}\right) + 3 \, {\left(a c^{3} x^{8} + 2 \, a^{2} c^{2} x^{4} + a^{3} c\right)} \left(-\frac{1}{a^{5} c^{7}}\right)^{\frac{1}{4}} \log\left(a^{4} c^{5} \left(-\frac{1}{a^{5} c^{7}}\right)^{\frac{3}{4}} + x\right) - 3 \, {\left(a c^{3} x^{8} + 2 \, a^{2} c^{2} x^{4} + a^{3} c\right)} \left(-\frac{1}{a^{5} c^{7}}\right)^{\frac{1}{4}} \log\left(-a^{4} c^{5} \left(-\frac{1}{a^{5} c^{7}}\right)^{\frac{3}{4}} + x\right)}{128 \, {\left(a c^{3} x^{8} + 2 \, a^{2} c^{2} x^{4} + a^{3} c\right)}}"," ",0,"1/128*(12*c*x^7 - 4*a*x^3 - 12*(a*c^3*x^8 + 2*a^2*c^2*x^4 + a^3*c)*(-1/(a^5*c^7))^(1/4)*arctan(-a*c^2*x*(-1/(a^5*c^7))^(1/4) + sqrt(-a^3*c^3*sqrt(-1/(a^5*c^7)) + x^2)*a*c^2*(-1/(a^5*c^7))^(1/4)) + 3*(a*c^3*x^8 + 2*a^2*c^2*x^4 + a^3*c)*(-1/(a^5*c^7))^(1/4)*log(a^4*c^5*(-1/(a^5*c^7))^(3/4) + x) - 3*(a*c^3*x^8 + 2*a^2*c^2*x^4 + a^3*c)*(-1/(a^5*c^7))^(1/4)*log(-a^4*c^5*(-1/(a^5*c^7))^(3/4) + x))/(a*c^3*x^8 + 2*a^2*c^2*x^4 + a^3*c)","A",0
683,1,249,0,1.057005," ","integrate(x^4/(c*x^4+a)^3,x, algorithm=""fricas"")","\frac{4 \, c x^{5} + 12 \, {\left(a c^{3} x^{8} + 2 \, a^{2} c^{2} x^{4} + a^{3} c\right)} \left(-\frac{1}{a^{7} c^{5}}\right)^{\frac{1}{4}} \arctan\left(-a^{5} c^{4} x \left(-\frac{1}{a^{7} c^{5}}\right)^{\frac{3}{4}} + \sqrt{a^{4} c^{2} \sqrt{-\frac{1}{a^{7} c^{5}}} + x^{2}} a^{5} c^{4} \left(-\frac{1}{a^{7} c^{5}}\right)^{\frac{3}{4}}\right) + 3 \, {\left(a c^{3} x^{8} + 2 \, a^{2} c^{2} x^{4} + a^{3} c\right)} \left(-\frac{1}{a^{7} c^{5}}\right)^{\frac{1}{4}} \log\left(a^{2} c \left(-\frac{1}{a^{7} c^{5}}\right)^{\frac{1}{4}} + x\right) - 3 \, {\left(a c^{3} x^{8} + 2 \, a^{2} c^{2} x^{4} + a^{3} c\right)} \left(-\frac{1}{a^{7} c^{5}}\right)^{\frac{1}{4}} \log\left(-a^{2} c \left(-\frac{1}{a^{7} c^{5}}\right)^{\frac{1}{4}} + x\right) - 12 \, a x}{128 \, {\left(a c^{3} x^{8} + 2 \, a^{2} c^{2} x^{4} + a^{3} c\right)}}"," ",0,"1/128*(4*c*x^5 + 12*(a*c^3*x^8 + 2*a^2*c^2*x^4 + a^3*c)*(-1/(a^7*c^5))^(1/4)*arctan(-a^5*c^4*x*(-1/(a^7*c^5))^(3/4) + sqrt(a^4*c^2*sqrt(-1/(a^7*c^5)) + x^2)*a^5*c^4*(-1/(a^7*c^5))^(3/4)) + 3*(a*c^3*x^8 + 2*a^2*c^2*x^4 + a^3*c)*(-1/(a^7*c^5))^(1/4)*log(a^2*c*(-1/(a^7*c^5))^(1/4) + x) - 3*(a*c^3*x^8 + 2*a^2*c^2*x^4 + a^3*c)*(-1/(a^7*c^5))^(1/4)*log(-a^2*c*(-1/(a^7*c^5))^(1/4) + x) - 12*a*x)/(a*c^3*x^8 + 2*a^2*c^2*x^4 + a^3*c)","A",0
684,1,242,0,0.657455," ","integrate(x^2/(c*x^4+a)^3,x, algorithm=""fricas"")","\frac{20 \, c x^{7} + 36 \, a x^{3} - 20 \, {\left(a^{2} c^{2} x^{8} + 2 \, a^{3} c x^{4} + a^{4}\right)} \left(-\frac{1}{a^{9} c^{3}}\right)^{\frac{1}{4}} \arctan\left(-a^{2} c x \left(-\frac{1}{a^{9} c^{3}}\right)^{\frac{1}{4}} + \sqrt{-a^{5} c \sqrt{-\frac{1}{a^{9} c^{3}}} + x^{2}} a^{2} c \left(-\frac{1}{a^{9} c^{3}}\right)^{\frac{1}{4}}\right) + 5 \, {\left(a^{2} c^{2} x^{8} + 2 \, a^{3} c x^{4} + a^{4}\right)} \left(-\frac{1}{a^{9} c^{3}}\right)^{\frac{1}{4}} \log\left(a^{7} c^{2} \left(-\frac{1}{a^{9} c^{3}}\right)^{\frac{3}{4}} + x\right) - 5 \, {\left(a^{2} c^{2} x^{8} + 2 \, a^{3} c x^{4} + a^{4}\right)} \left(-\frac{1}{a^{9} c^{3}}\right)^{\frac{1}{4}} \log\left(-a^{7} c^{2} \left(-\frac{1}{a^{9} c^{3}}\right)^{\frac{3}{4}} + x\right)}{128 \, {\left(a^{2} c^{2} x^{8} + 2 \, a^{3} c x^{4} + a^{4}\right)}}"," ",0,"1/128*(20*c*x^7 + 36*a*x^3 - 20*(a^2*c^2*x^8 + 2*a^3*c*x^4 + a^4)*(-1/(a^9*c^3))^(1/4)*arctan(-a^2*c*x*(-1/(a^9*c^3))^(1/4) + sqrt(-a^5*c*sqrt(-1/(a^9*c^3)) + x^2)*a^2*c*(-1/(a^9*c^3))^(1/4)) + 5*(a^2*c^2*x^8 + 2*a^3*c*x^4 + a^4)*(-1/(a^9*c^3))^(1/4)*log(a^7*c^2*(-1/(a^9*c^3))^(3/4) + x) - 5*(a^2*c^2*x^8 + 2*a^3*c*x^4 + a^4)*(-1/(a^9*c^3))^(1/4)*log(-a^7*c^2*(-1/(a^9*c^3))^(3/4) + x))/(a^2*c^2*x^8 + 2*a^3*c*x^4 + a^4)","A",0
685,1,232,0,0.938172," ","integrate(1/(c*x^4+a)^3,x, algorithm=""fricas"")","\frac{28 \, c x^{5} + 84 \, {\left(a^{2} c^{2} x^{8} + 2 \, a^{3} c x^{4} + a^{4}\right)} \left(-\frac{1}{a^{11} c}\right)^{\frac{1}{4}} \arctan\left(-a^{8} c x \left(-\frac{1}{a^{11} c}\right)^{\frac{3}{4}} + \sqrt{a^{6} \sqrt{-\frac{1}{a^{11} c}} + x^{2}} a^{8} c \left(-\frac{1}{a^{11} c}\right)^{\frac{3}{4}}\right) + 21 \, {\left(a^{2} c^{2} x^{8} + 2 \, a^{3} c x^{4} + a^{4}\right)} \left(-\frac{1}{a^{11} c}\right)^{\frac{1}{4}} \log\left(a^{3} \left(-\frac{1}{a^{11} c}\right)^{\frac{1}{4}} + x\right) - 21 \, {\left(a^{2} c^{2} x^{8} + 2 \, a^{3} c x^{4} + a^{4}\right)} \left(-\frac{1}{a^{11} c}\right)^{\frac{1}{4}} \log\left(-a^{3} \left(-\frac{1}{a^{11} c}\right)^{\frac{1}{4}} + x\right) + 44 \, a x}{128 \, {\left(a^{2} c^{2} x^{8} + 2 \, a^{3} c x^{4} + a^{4}\right)}}"," ",0,"1/128*(28*c*x^5 + 84*(a^2*c^2*x^8 + 2*a^3*c*x^4 + a^4)*(-1/(a^11*c))^(1/4)*arctan(-a^8*c*x*(-1/(a^11*c))^(3/4) + sqrt(a^6*sqrt(-1/(a^11*c)) + x^2)*a^8*c*(-1/(a^11*c))^(3/4)) + 21*(a^2*c^2*x^8 + 2*a^3*c*x^4 + a^4)*(-1/(a^11*c))^(1/4)*log(a^3*(-1/(a^11*c))^(1/4) + x) - 21*(a^2*c^2*x^8 + 2*a^3*c*x^4 + a^4)*(-1/(a^11*c))^(1/4)*log(-a^3*(-1/(a^11*c))^(1/4) + x) + 44*a*x)/(a^2*c^2*x^8 + 2*a^3*c*x^4 + a^4)","A",0
686,1,247,0,0.961256," ","integrate(1/x^2/(c*x^4+a)^3,x, algorithm=""fricas"")","-\frac{180 \, c^{2} x^{8} + 324 \, a c x^{4} - 180 \, {\left(a^{3} c^{2} x^{9} + 2 \, a^{4} c x^{5} + a^{5} x\right)} \left(-\frac{c}{a^{13}}\right)^{\frac{1}{4}} \arctan\left(-a^{3} x \left(-\frac{c}{a^{13}}\right)^{\frac{1}{4}} + a^{3} \sqrt{-\frac{a^{7} \sqrt{-\frac{c}{a^{13}}} - c x^{2}}{c}} \left(-\frac{c}{a^{13}}\right)^{\frac{1}{4}}\right) + 45 \, {\left(a^{3} c^{2} x^{9} + 2 \, a^{4} c x^{5} + a^{5} x\right)} \left(-\frac{c}{a^{13}}\right)^{\frac{1}{4}} \log\left(91125 \, a^{10} \left(-\frac{c}{a^{13}}\right)^{\frac{3}{4}} + 91125 \, c x\right) - 45 \, {\left(a^{3} c^{2} x^{9} + 2 \, a^{4} c x^{5} + a^{5} x\right)} \left(-\frac{c}{a^{13}}\right)^{\frac{1}{4}} \log\left(-91125 \, a^{10} \left(-\frac{c}{a^{13}}\right)^{\frac{3}{4}} + 91125 \, c x\right) + 128 \, a^{2}}{128 \, {\left(a^{3} c^{2} x^{9} + 2 \, a^{4} c x^{5} + a^{5} x\right)}}"," ",0,"-1/128*(180*c^2*x^8 + 324*a*c*x^4 - 180*(a^3*c^2*x^9 + 2*a^4*c*x^5 + a^5*x)*(-c/a^13)^(1/4)*arctan(-a^3*x*(-c/a^13)^(1/4) + a^3*sqrt(-(a^7*sqrt(-c/a^13) - c*x^2)/c)*(-c/a^13)^(1/4)) + 45*(a^3*c^2*x^9 + 2*a^4*c*x^5 + a^5*x)*(-c/a^13)^(1/4)*log(91125*a^10*(-c/a^13)^(3/4) + 91125*c*x) - 45*(a^3*c^2*x^9 + 2*a^4*c*x^5 + a^5*x)*(-c/a^13)^(1/4)*log(-91125*a^10*(-c/a^13)^(3/4) + 91125*c*x) + 128*a^2)/(a^3*c^2*x^9 + 2*a^4*c*x^5 + a^5*x)","A",0
687,1,31,0,0.761149," ","integrate(x^9/(3*x^4+2),x, algorithm=""fricas"")","\frac{1}{18} \, x^{6} - \frac{1}{9} \, x^{2} + \frac{1}{27} \, \sqrt{3} \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{3} \sqrt{2} x^{2}\right)"," ",0,"1/18*x^6 - 1/9*x^2 + 1/27*sqrt(3)*sqrt(2)*arctan(1/2*sqrt(3)*sqrt(2)*x^2)","A",0
688,1,16,0,0.955766," ","integrate(x^7/(3*x^4+2),x, algorithm=""fricas"")","\frac{1}{12} \, x^{4} - \frac{1}{18} \, \log\left(3 \, x^{4} + 2\right)"," ",0,"1/12*x^4 - 1/18*log(3*x^4 + 2)","A",0
689,1,20,0,0.900030," ","integrate(x^5/(3*x^4+2),x, algorithm=""fricas"")","\frac{1}{6} \, x^{2} - \frac{1}{18} \, \sqrt{6} \arctan\left(\frac{1}{2} \, \sqrt{6} x^{2}\right)"," ",0,"1/6*x^2 - 1/18*sqrt(6)*arctan(1/2*sqrt(6)*x^2)","A",0
690,1,10,0,0.925791," ","integrate(x^3/(3*x^4+2),x, algorithm=""fricas"")","\frac{1}{12} \, \log\left(3 \, x^{4} + 2\right)"," ",0,"1/12*log(3*x^4 + 2)","A",0
691,1,14,0,0.910899," ","integrate(x/(3*x^4+2),x, algorithm=""fricas"")","\frac{1}{12} \, \sqrt{6} \arctan\left(\frac{1}{2} \, \sqrt{6} x^{2}\right)"," ",0,"1/12*sqrt(6)*arctan(1/2*sqrt(6)*x^2)","A",0
692,1,15,0,0.954229," ","integrate(1/x/(3*x^4+2),x, algorithm=""fricas"")","-\frac{1}{8} \, \log\left(3 \, x^{4} + 2\right) + \frac{1}{2} \, \log\left(x\right)"," ",0,"-1/8*log(3*x^4 + 2) + 1/2*log(x)","A",0
693,1,29,0,1.177310," ","integrate(1/x^3/(3*x^4+2),x, algorithm=""fricas"")","-\frac{\sqrt{3} \sqrt{2} x^{2} \arctan\left(\frac{1}{2} \, \sqrt{3} \sqrt{2} x^{2}\right) + 2}{8 \, x^{2}}"," ",0,"-1/8*(sqrt(3)*sqrt(2)*x^2*arctan(1/2*sqrt(3)*sqrt(2)*x^2) + 2)/x^2","A",0
694,1,164,0,0.980261," ","integrate(x^6/(3*x^4+2),x, algorithm=""fricas"")","\frac{1}{9} \, x^{3} + \frac{1}{162} \cdot 54^{\frac{3}{4}} \sqrt{2} \arctan\left(-\frac{1}{18} \cdot 54^{\frac{3}{4}} \sqrt{2} x + \frac{1}{54} \cdot 54^{\frac{3}{4}} \sqrt{2} \sqrt{9 \, x^{2} + 3 \cdot 54^{\frac{1}{4}} \sqrt{2} x + 3 \, \sqrt{6}} - 1\right) + \frac{1}{162} \cdot 54^{\frac{3}{4}} \sqrt{2} \arctan\left(-\frac{1}{18} \cdot 54^{\frac{3}{4}} \sqrt{2} x + \frac{1}{54} \cdot 54^{\frac{3}{4}} \sqrt{2} \sqrt{9 \, x^{2} - 3 \cdot 54^{\frac{1}{4}} \sqrt{2} x + 3 \, \sqrt{6}} + 1\right) + \frac{1}{648} \cdot 54^{\frac{3}{4}} \sqrt{2} \log\left(9 \, x^{2} + 3 \cdot 54^{\frac{1}{4}} \sqrt{2} x + 3 \, \sqrt{6}\right) - \frac{1}{648} \cdot 54^{\frac{3}{4}} \sqrt{2} \log\left(9 \, x^{2} - 3 \cdot 54^{\frac{1}{4}} \sqrt{2} x + 3 \, \sqrt{6}\right)"," ",0,"1/9*x^3 + 1/162*54^(3/4)*sqrt(2)*arctan(-1/18*54^(3/4)*sqrt(2)*x + 1/54*54^(3/4)*sqrt(2)*sqrt(9*x^2 + 3*54^(1/4)*sqrt(2)*x + 3*sqrt(6)) - 1) + 1/162*54^(3/4)*sqrt(2)*arctan(-1/18*54^(3/4)*sqrt(2)*x + 1/54*54^(3/4)*sqrt(2)*sqrt(9*x^2 - 3*54^(1/4)*sqrt(2)*x + 3*sqrt(6)) + 1) + 1/648*54^(3/4)*sqrt(2)*log(9*x^2 + 3*54^(1/4)*sqrt(2)*x + 3*sqrt(6)) - 1/648*54^(3/4)*sqrt(2)*log(9*x^2 - 3*54^(1/4)*sqrt(2)*x + 3*sqrt(6))","B",0
695,1,166,0,0.977335," ","integrate(x^4/(3*x^4+2),x, algorithm=""fricas"")","\frac{1}{72} \cdot 24^{\frac{3}{4}} \sqrt{2} \arctan\left(\frac{1}{12} \cdot 24^{\frac{1}{4}} \sqrt{3} \sqrt{2} \sqrt{24^{\frac{3}{4}} \sqrt{2} x + 12 \, x^{2} + 4 \, \sqrt{6}} - \frac{1}{2} \cdot 24^{\frac{1}{4}} \sqrt{2} x - 1\right) + \frac{1}{72} \cdot 24^{\frac{3}{4}} \sqrt{2} \arctan\left(\frac{1}{12} \cdot 24^{\frac{1}{4}} \sqrt{3} \sqrt{2} \sqrt{-24^{\frac{3}{4}} \sqrt{2} x + 12 \, x^{2} + 4 \, \sqrt{6}} - \frac{1}{2} \cdot 24^{\frac{1}{4}} \sqrt{2} x + 1\right) - \frac{1}{288} \cdot 24^{\frac{3}{4}} \sqrt{2} \log\left(24^{\frac{3}{4}} \sqrt{2} x + 12 \, x^{2} + 4 \, \sqrt{6}\right) + \frac{1}{288} \cdot 24^{\frac{3}{4}} \sqrt{2} \log\left(-24^{\frac{3}{4}} \sqrt{2} x + 12 \, x^{2} + 4 \, \sqrt{6}\right) + \frac{1}{3} \, x"," ",0,"1/72*24^(3/4)*sqrt(2)*arctan(1/12*24^(1/4)*sqrt(3)*sqrt(2)*sqrt(24^(3/4)*sqrt(2)*x + 12*x^2 + 4*sqrt(6)) - 1/2*24^(1/4)*sqrt(2)*x - 1) + 1/72*24^(3/4)*sqrt(2)*arctan(1/12*24^(1/4)*sqrt(3)*sqrt(2)*sqrt(-24^(3/4)*sqrt(2)*x + 12*x^2 + 4*sqrt(6)) - 1/2*24^(1/4)*sqrt(2)*x + 1) - 1/288*24^(3/4)*sqrt(2)*log(24^(3/4)*sqrt(2)*x + 12*x^2 + 4*sqrt(6)) + 1/288*24^(3/4)*sqrt(2)*log(-24^(3/4)*sqrt(2)*x + 12*x^2 + 4*sqrt(6)) + 1/3*x","B",0
696,1,159,0,1.036941," ","integrate(x^2/(3*x^4+2),x, algorithm=""fricas"")","-\frac{1}{108} \cdot 54^{\frac{3}{4}} \sqrt{2} \arctan\left(-\frac{1}{18} \cdot 54^{\frac{3}{4}} \sqrt{2} x + \frac{1}{54} \cdot 54^{\frac{3}{4}} \sqrt{2} \sqrt{9 \, x^{2} + 3 \cdot 54^{\frac{1}{4}} \sqrt{2} x + 3 \, \sqrt{6}} - 1\right) - \frac{1}{108} \cdot 54^{\frac{3}{4}} \sqrt{2} \arctan\left(-\frac{1}{18} \cdot 54^{\frac{3}{4}} \sqrt{2} x + \frac{1}{54} \cdot 54^{\frac{3}{4}} \sqrt{2} \sqrt{9 \, x^{2} - 3 \cdot 54^{\frac{1}{4}} \sqrt{2} x + 3 \, \sqrt{6}} + 1\right) - \frac{1}{432} \cdot 54^{\frac{3}{4}} \sqrt{2} \log\left(9 \, x^{2} + 3 \cdot 54^{\frac{1}{4}} \sqrt{2} x + 3 \, \sqrt{6}\right) + \frac{1}{432} \cdot 54^{\frac{3}{4}} \sqrt{2} \log\left(9 \, x^{2} - 3 \cdot 54^{\frac{1}{4}} \sqrt{2} x + 3 \, \sqrt{6}\right)"," ",0,"-1/108*54^(3/4)*sqrt(2)*arctan(-1/18*54^(3/4)*sqrt(2)*x + 1/54*54^(3/4)*sqrt(2)*sqrt(9*x^2 + 3*54^(1/4)*sqrt(2)*x + 3*sqrt(6)) - 1) - 1/108*54^(3/4)*sqrt(2)*arctan(-1/18*54^(3/4)*sqrt(2)*x + 1/54*54^(3/4)*sqrt(2)*sqrt(9*x^2 - 3*54^(1/4)*sqrt(2)*x + 3*sqrt(6)) + 1) - 1/432*54^(3/4)*sqrt(2)*log(9*x^2 + 3*54^(1/4)*sqrt(2)*x + 3*sqrt(6)) + 1/432*54^(3/4)*sqrt(2)*log(9*x^2 - 3*54^(1/4)*sqrt(2)*x + 3*sqrt(6))","B",0
697,1,163,0,0.936193," ","integrate(1/(3*x^4+2),x, algorithm=""fricas"")","-\frac{1}{48} \cdot 24^{\frac{3}{4}} \sqrt{2} \arctan\left(\frac{1}{12} \cdot 24^{\frac{1}{4}} \sqrt{3} \sqrt{2} \sqrt{24^{\frac{3}{4}} \sqrt{2} x + 12 \, x^{2} + 4 \, \sqrt{6}} - \frac{1}{2} \cdot 24^{\frac{1}{4}} \sqrt{2} x - 1\right) - \frac{1}{48} \cdot 24^{\frac{3}{4}} \sqrt{2} \arctan\left(\frac{1}{12} \cdot 24^{\frac{1}{4}} \sqrt{3} \sqrt{2} \sqrt{-24^{\frac{3}{4}} \sqrt{2} x + 12 \, x^{2} + 4 \, \sqrt{6}} - \frac{1}{2} \cdot 24^{\frac{1}{4}} \sqrt{2} x + 1\right) + \frac{1}{192} \cdot 24^{\frac{3}{4}} \sqrt{2} \log\left(24^{\frac{3}{4}} \sqrt{2} x + 12 \, x^{2} + 4 \, \sqrt{6}\right) - \frac{1}{192} \cdot 24^{\frac{3}{4}} \sqrt{2} \log\left(-24^{\frac{3}{4}} \sqrt{2} x + 12 \, x^{2} + 4 \, \sqrt{6}\right)"," ",0,"-1/48*24^(3/4)*sqrt(2)*arctan(1/12*24^(1/4)*sqrt(3)*sqrt(2)*sqrt(24^(3/4)*sqrt(2)*x + 12*x^2 + 4*sqrt(6)) - 1/2*24^(1/4)*sqrt(2)*x - 1) - 1/48*24^(3/4)*sqrt(2)*arctan(1/12*24^(1/4)*sqrt(3)*sqrt(2)*sqrt(-24^(3/4)*sqrt(2)*x + 12*x^2 + 4*sqrt(6)) - 1/2*24^(1/4)*sqrt(2)*x + 1) + 1/192*24^(3/4)*sqrt(2)*log(24^(3/4)*sqrt(2)*x + 12*x^2 + 4*sqrt(6)) - 1/192*24^(3/4)*sqrt(2)*log(-24^(3/4)*sqrt(2)*x + 12*x^2 + 4*sqrt(6))","B",0
698,1,174,0,0.853890," ","integrate(1/x^2/(3*x^4+2),x, algorithm=""fricas"")","\frac{4 \cdot 3^{\frac{1}{4}} 2^{\frac{1}{4}} x \arctan\left(\frac{1}{3} \cdot 3^{\frac{3}{4}} 2^{\frac{1}{4}} \sqrt{3^{\frac{3}{4}} 2^{\frac{3}{4}} x + 3 \, x^{2} + \sqrt{3} \sqrt{2}} - 3^{\frac{1}{4}} 2^{\frac{1}{4}} x - 1\right) + 4 \cdot 3^{\frac{1}{4}} 2^{\frac{1}{4}} x \arctan\left(\frac{1}{3} \cdot 3^{\frac{3}{4}} 2^{\frac{1}{4}} \sqrt{-3^{\frac{3}{4}} 2^{\frac{3}{4}} x + 3 \, x^{2} + \sqrt{3} \sqrt{2}} - 3^{\frac{1}{4}} 2^{\frac{1}{4}} x + 1\right) + 3^{\frac{1}{4}} 2^{\frac{1}{4}} x \log\left(3^{\frac{3}{4}} 2^{\frac{3}{4}} x + 3 \, x^{2} + \sqrt{3} \sqrt{2}\right) - 3^{\frac{1}{4}} 2^{\frac{1}{4}} x \log\left(-3^{\frac{3}{4}} 2^{\frac{3}{4}} x + 3 \, x^{2} + \sqrt{3} \sqrt{2}\right) - 8}{16 \, x}"," ",0,"1/16*(4*3^(1/4)*2^(1/4)*x*arctan(1/3*3^(3/4)*2^(1/4)*sqrt(3^(3/4)*2^(3/4)*x + 3*x^2 + sqrt(3)*sqrt(2)) - 3^(1/4)*2^(1/4)*x - 1) + 4*3^(1/4)*2^(1/4)*x*arctan(1/3*3^(3/4)*2^(1/4)*sqrt(-3^(3/4)*2^(3/4)*x + 3*x^2 + sqrt(3)*sqrt(2)) - 3^(1/4)*2^(1/4)*x + 1) + 3^(1/4)*2^(1/4)*x*log(3^(3/4)*2^(3/4)*x + 3*x^2 + sqrt(3)*sqrt(2)) - 3^(1/4)*2^(1/4)*x*log(-3^(3/4)*2^(3/4)*x + 3*x^2 + sqrt(3)*sqrt(2)) - 8)/x","B",0
699,1,11,0,1.574923," ","integrate(x^3/(3*x^4+2)^2,x, algorithm=""fricas"")","-\frac{1}{12 \, {\left(3 \, x^{4} + 2\right)}}"," ",0,"-1/12/(3*x^4 + 2)","A",0
700,1,37,0,1.230240," ","integrate(x/(3*x^4+2)^2,x, algorithm=""fricas"")","\frac{\sqrt{6} {\left(3 \, x^{4} + 2\right)} \arctan\left(\frac{1}{2} \, \sqrt{6} x^{2}\right) + 6 \, x^{2}}{48 \, {\left(3 \, x^{4} + 2\right)}}"," ",0,"1/48*(sqrt(6)*(3*x^4 + 2)*arctan(1/2*sqrt(6)*x^2) + 6*x^2)/(3*x^4 + 2)","A",0
701,1,40,0,1.182020," ","integrate(1/x/(3*x^4+2)^2,x, algorithm=""fricas"")","-\frac{{\left(3 \, x^{4} + 2\right)} \log\left(3 \, x^{4} + 2\right) - 4 \, {\left(3 \, x^{4} + 2\right)} \log\left(x\right) - 2}{16 \, {\left(3 \, x^{4} + 2\right)}}"," ",0,"-1/16*((3*x^4 + 2)*log(3*x^4 + 2) - 4*(3*x^4 + 2)*log(x) - 2)/(3*x^4 + 2)","A",0
702,1,53,0,1.052784," ","integrate(1/x^3/(3*x^4+2)^2,x, algorithm=""fricas"")","-\frac{18 \, x^{4} + 3 \, \sqrt{3} \sqrt{2} {\left(3 \, x^{6} + 2 \, x^{2}\right)} \arctan\left(\frac{1}{2} \, \sqrt{3} \sqrt{2} x^{2}\right) + 8}{32 \, {\left(3 \, x^{6} + 2 \, x^{2}\right)}}"," ",0,"-1/32*(18*x^4 + 3*sqrt(3)*sqrt(2)*(3*x^6 + 2*x^2)*arctan(1/2*sqrt(3)*sqrt(2)*x^2) + 8)/(3*x^6 + 2*x^2)","A",0
703,1,204,0,1.157187," ","integrate(x^4/(3*x^4+2)^2,x, algorithm=""fricas"")","-\frac{4 \cdot 24^{\frac{3}{4}} \sqrt{2} {\left(3 \, x^{4} + 2\right)} \arctan\left(\frac{1}{12} \cdot 24^{\frac{1}{4}} \sqrt{3} \sqrt{2} \sqrt{24^{\frac{3}{4}} \sqrt{2} x + 12 \, x^{2} + 4 \, \sqrt{6}} - \frac{1}{2} \cdot 24^{\frac{1}{4}} \sqrt{2} x - 1\right) + 4 \cdot 24^{\frac{3}{4}} \sqrt{2} {\left(3 \, x^{4} + 2\right)} \arctan\left(\frac{1}{12} \cdot 24^{\frac{1}{4}} \sqrt{3} \sqrt{2} \sqrt{-24^{\frac{3}{4}} \sqrt{2} x + 12 \, x^{2} + 4 \, \sqrt{6}} - \frac{1}{2} \cdot 24^{\frac{1}{4}} \sqrt{2} x + 1\right) - 24^{\frac{3}{4}} \sqrt{2} {\left(3 \, x^{4} + 2\right)} \log\left(24^{\frac{3}{4}} \sqrt{2} x + 12 \, x^{2} + 4 \, \sqrt{6}\right) + 24^{\frac{3}{4}} \sqrt{2} {\left(3 \, x^{4} + 2\right)} \log\left(-24^{\frac{3}{4}} \sqrt{2} x + 12 \, x^{2} + 4 \, \sqrt{6}\right) + 192 \, x}{2304 \, {\left(3 \, x^{4} + 2\right)}}"," ",0,"-1/2304*(4*24^(3/4)*sqrt(2)*(3*x^4 + 2)*arctan(1/12*24^(1/4)*sqrt(3)*sqrt(2)*sqrt(24^(3/4)*sqrt(2)*x + 12*x^2 + 4*sqrt(6)) - 1/2*24^(1/4)*sqrt(2)*x - 1) + 4*24^(3/4)*sqrt(2)*(3*x^4 + 2)*arctan(1/12*24^(1/4)*sqrt(3)*sqrt(2)*sqrt(-24^(3/4)*sqrt(2)*x + 12*x^2 + 4*sqrt(6)) - 1/2*24^(1/4)*sqrt(2)*x + 1) - 24^(3/4)*sqrt(2)*(3*x^4 + 2)*log(24^(3/4)*sqrt(2)*x + 12*x^2 + 4*sqrt(6)) + 24^(3/4)*sqrt(2)*(3*x^4 + 2)*log(-24^(3/4)*sqrt(2)*x + 12*x^2 + 4*sqrt(6)) + 192*x)/(3*x^4 + 2)","B",0
704,1,202,0,1.033858," ","integrate(x^2/(3*x^4+2)^2,x, algorithm=""fricas"")","-\frac{4 \cdot 54^{\frac{3}{4}} \sqrt{2} {\left(3 \, x^{4} + 2\right)} \arctan\left(-\frac{1}{18} \cdot 54^{\frac{3}{4}} \sqrt{2} x + \frac{1}{54} \cdot 54^{\frac{3}{4}} \sqrt{2} \sqrt{9 \, x^{2} + 3 \cdot 54^{\frac{1}{4}} \sqrt{2} x + 3 \, \sqrt{6}} - 1\right) + 4 \cdot 54^{\frac{3}{4}} \sqrt{2} {\left(3 \, x^{4} + 2\right)} \arctan\left(-\frac{1}{18} \cdot 54^{\frac{3}{4}} \sqrt{2} x + \frac{1}{54} \cdot 54^{\frac{3}{4}} \sqrt{2} \sqrt{9 \, x^{2} - 3 \cdot 54^{\frac{1}{4}} \sqrt{2} x + 3 \, \sqrt{6}} + 1\right) + 54^{\frac{3}{4}} \sqrt{2} {\left(3 \, x^{4} + 2\right)} \log\left(9 \, x^{2} + 3 \cdot 54^{\frac{1}{4}} \sqrt{2} x + 3 \, \sqrt{6}\right) - 54^{\frac{3}{4}} \sqrt{2} {\left(3 \, x^{4} + 2\right)} \log\left(9 \, x^{2} - 3 \cdot 54^{\frac{1}{4}} \sqrt{2} x + 3 \, \sqrt{6}\right) - 432 \, x^{3}}{3456 \, {\left(3 \, x^{4} + 2\right)}}"," ",0,"-1/3456*(4*54^(3/4)*sqrt(2)*(3*x^4 + 2)*arctan(-1/18*54^(3/4)*sqrt(2)*x + 1/54*54^(3/4)*sqrt(2)*sqrt(9*x^2 + 3*54^(1/4)*sqrt(2)*x + 3*sqrt(6)) - 1) + 4*54^(3/4)*sqrt(2)*(3*x^4 + 2)*arctan(-1/18*54^(3/4)*sqrt(2)*x + 1/54*54^(3/4)*sqrt(2)*sqrt(9*x^2 - 3*54^(1/4)*sqrt(2)*x + 3*sqrt(6)) + 1) + 54^(3/4)*sqrt(2)*(3*x^4 + 2)*log(9*x^2 + 3*54^(1/4)*sqrt(2)*x + 3*sqrt(6)) - 54^(3/4)*sqrt(2)*(3*x^4 + 2)*log(9*x^2 - 3*54^(1/4)*sqrt(2)*x + 3*sqrt(6)) - 432*x^3)/(3*x^4 + 2)","B",0
705,1,248,0,1.047041," ","integrate(1/(3*x^4+2)^2,x, algorithm=""fricas"")","-\frac{4 \cdot 27^{\frac{1}{4}} 8^{\frac{3}{4}} \sqrt{2} {\left(3 \, x^{4} + 2\right)} \arctan\left(-\frac{1}{18} \cdot 27^{\frac{3}{4}} 8^{\frac{1}{4}} \sqrt{2} x + \frac{1}{108} \cdot 27^{\frac{3}{4}} 8^{\frac{1}{4}} \sqrt{2} \sqrt{3 \cdot 27^{\frac{1}{4}} 8^{\frac{3}{4}} \sqrt{2} x + 36 \, x^{2} + 12 \, \sqrt{3} \sqrt{2}} - 1\right) + 4 \cdot 27^{\frac{1}{4}} 8^{\frac{3}{4}} \sqrt{2} {\left(3 \, x^{4} + 2\right)} \arctan\left(-\frac{1}{18} \cdot 27^{\frac{3}{4}} 8^{\frac{1}{4}} \sqrt{2} x + \frac{1}{108} \cdot 27^{\frac{3}{4}} 8^{\frac{1}{4}} \sqrt{2} \sqrt{-3 \cdot 27^{\frac{1}{4}} 8^{\frac{3}{4}} \sqrt{2} x + 36 \, x^{2} + 12 \, \sqrt{3} \sqrt{2}} + 1\right) - 27^{\frac{1}{4}} 8^{\frac{3}{4}} \sqrt{2} {\left(3 \, x^{4} + 2\right)} \log\left(3 \cdot 27^{\frac{1}{4}} 8^{\frac{3}{4}} \sqrt{2} x + 36 \, x^{2} + 12 \, \sqrt{3} \sqrt{2}\right) + 27^{\frac{1}{4}} 8^{\frac{3}{4}} \sqrt{2} {\left(3 \, x^{4} + 2\right)} \log\left(-3 \cdot 27^{\frac{1}{4}} 8^{\frac{3}{4}} \sqrt{2} x + 36 \, x^{2} + 12 \, \sqrt{3} \sqrt{2}\right) - 64 \, x}{512 \, {\left(3 \, x^{4} + 2\right)}}"," ",0,"-1/512*(4*27^(1/4)*8^(3/4)*sqrt(2)*(3*x^4 + 2)*arctan(-1/18*27^(3/4)*8^(1/4)*sqrt(2)*x + 1/108*27^(3/4)*8^(1/4)*sqrt(2)*sqrt(3*27^(1/4)*8^(3/4)*sqrt(2)*x + 36*x^2 + 12*sqrt(3)*sqrt(2)) - 1) + 4*27^(1/4)*8^(3/4)*sqrt(2)*(3*x^4 + 2)*arctan(-1/18*27^(3/4)*8^(1/4)*sqrt(2)*x + 1/108*27^(3/4)*8^(1/4)*sqrt(2)*sqrt(-3*27^(1/4)*8^(3/4)*sqrt(2)*x + 36*x^2 + 12*sqrt(3)*sqrt(2)) + 1) - 27^(1/4)*8^(3/4)*sqrt(2)*(3*x^4 + 2)*log(3*27^(1/4)*8^(3/4)*sqrt(2)*x + 36*x^2 + 12*sqrt(3)*sqrt(2)) + 27^(1/4)*8^(3/4)*sqrt(2)*(3*x^4 + 2)*log(-3*27^(1/4)*8^(3/4)*sqrt(2)*x + 36*x^2 + 12*sqrt(3)*sqrt(2)) - 64*x)/(3*x^4 + 2)","B",0
706,1,220,0,0.978979," ","integrate(1/x^2/(3*x^4+2)^2,x, algorithm=""fricas"")","-\frac{120 \, x^{4} - 20 \cdot 3^{\frac{1}{4}} 2^{\frac{1}{4}} {\left(3 \, x^{5} + 2 \, x\right)} \arctan\left(\frac{1}{3} \cdot 3^{\frac{3}{4}} 2^{\frac{1}{4}} \sqrt{3^{\frac{3}{4}} 2^{\frac{3}{4}} x + 3 \, x^{2} + \sqrt{3} \sqrt{2}} - 3^{\frac{1}{4}} 2^{\frac{1}{4}} x - 1\right) - 20 \cdot 3^{\frac{1}{4}} 2^{\frac{1}{4}} {\left(3 \, x^{5} + 2 \, x\right)} \arctan\left(\frac{1}{3} \cdot 3^{\frac{3}{4}} 2^{\frac{1}{4}} \sqrt{-3^{\frac{3}{4}} 2^{\frac{3}{4}} x + 3 \, x^{2} + \sqrt{3} \sqrt{2}} - 3^{\frac{1}{4}} 2^{\frac{1}{4}} x + 1\right) - 5 \cdot 3^{\frac{1}{4}} 2^{\frac{1}{4}} {\left(3 \, x^{5} + 2 \, x\right)} \log\left(3^{\frac{3}{4}} 2^{\frac{3}{4}} x + 3 \, x^{2} + \sqrt{3} \sqrt{2}\right) + 5 \cdot 3^{\frac{1}{4}} 2^{\frac{1}{4}} {\left(3 \, x^{5} + 2 \, x\right)} \log\left(-3^{\frac{3}{4}} 2^{\frac{3}{4}} x + 3 \, x^{2} + \sqrt{3} \sqrt{2}\right) + 64}{128 \, {\left(3 \, x^{5} + 2 \, x\right)}}"," ",0,"-1/128*(120*x^4 - 20*3^(1/4)*2^(1/4)*(3*x^5 + 2*x)*arctan(1/3*3^(3/4)*2^(1/4)*sqrt(3^(3/4)*2^(3/4)*x + 3*x^2 + sqrt(3)*sqrt(2)) - 3^(1/4)*2^(1/4)*x - 1) - 20*3^(1/4)*2^(1/4)*(3*x^5 + 2*x)*arctan(1/3*3^(3/4)*2^(1/4)*sqrt(-3^(3/4)*2^(3/4)*x + 3*x^2 + sqrt(3)*sqrt(2)) - 3^(1/4)*2^(1/4)*x + 1) - 5*3^(1/4)*2^(1/4)*(3*x^5 + 2*x)*log(3^(3/4)*2^(3/4)*x + 3*x^2 + sqrt(3)*sqrt(2)) + 5*3^(1/4)*2^(1/4)*(3*x^5 + 2*x)*log(-3^(3/4)*2^(3/4)*x + 3*x^2 + sqrt(3)*sqrt(2)) + 64)/(3*x^5 + 2*x)","B",0
707,1,141,0,0.904621," ","integrate(x^2/(x^4+3),x, algorithm=""fricas"")","-\frac{1}{6} \cdot 3^{\frac{3}{4}} \sqrt{2} \arctan\left(-\frac{1}{3} \cdot 3^{\frac{3}{4}} \sqrt{2} x + \frac{1}{3} \cdot 3^{\frac{3}{4}} \sqrt{2} \sqrt{x^{2} + 3^{\frac{1}{4}} \sqrt{2} x + \sqrt{3}} - 1\right) - \frac{1}{6} \cdot 3^{\frac{3}{4}} \sqrt{2} \arctan\left(-\frac{1}{3} \cdot 3^{\frac{3}{4}} \sqrt{2} x + \frac{1}{3} \cdot 3^{\frac{3}{4}} \sqrt{2} \sqrt{x^{2} - 3^{\frac{1}{4}} \sqrt{2} x + \sqrt{3}} + 1\right) - \frac{1}{24} \cdot 3^{\frac{3}{4}} \sqrt{2} \log\left(x^{2} + 3^{\frac{1}{4}} \sqrt{2} x + \sqrt{3}\right) + \frac{1}{24} \cdot 3^{\frac{3}{4}} \sqrt{2} \log\left(x^{2} - 3^{\frac{1}{4}} \sqrt{2} x + \sqrt{3}\right)"," ",0,"-1/6*3^(3/4)*sqrt(2)*arctan(-1/3*3^(3/4)*sqrt(2)*x + 1/3*3^(3/4)*sqrt(2)*sqrt(x^2 + 3^(1/4)*sqrt(2)*x + sqrt(3)) - 1) - 1/6*3^(3/4)*sqrt(2)*arctan(-1/3*3^(3/4)*sqrt(2)*x + 1/3*3^(3/4)*sqrt(2)*sqrt(x^2 - 3^(1/4)*sqrt(2)*x + sqrt(3)) + 1) - 1/24*3^(3/4)*sqrt(2)*log(x^2 + 3^(1/4)*sqrt(2)*x + sqrt(3)) + 1/24*3^(3/4)*sqrt(2)*log(x^2 - 3^(1/4)*sqrt(2)*x + sqrt(3))","A",0
708,1,216,0,1.052176," ","integrate(1/(1+a+(-1+a)*x^4),x, algorithm=""fricas"")","\left(-\frac{1}{a^{4} + 2 \, a^{3} - 2 \, a - 1}\right)^{\frac{1}{4}} \arctan\left(-{\left(a^{3} + a^{2} - a - 1\right)} x \left(-\frac{1}{a^{4} + 2 \, a^{3} - 2 \, a - 1}\right)^{\frac{3}{4}} + {\left(a^{3} + a^{2} - a - 1\right)} \sqrt{x^{2} + {\left(a^{2} + 2 \, a + 1\right)} \sqrt{-\frac{1}{a^{4} + 2 \, a^{3} - 2 \, a - 1}}} \left(-\frac{1}{a^{4} + 2 \, a^{3} - 2 \, a - 1}\right)^{\frac{3}{4}}\right) + \frac{1}{4} \, \left(-\frac{1}{a^{4} + 2 \, a^{3} - 2 \, a - 1}\right)^{\frac{1}{4}} \log\left({\left(a + 1\right)} \left(-\frac{1}{a^{4} + 2 \, a^{3} - 2 \, a - 1}\right)^{\frac{1}{4}} + x\right) - \frac{1}{4} \, \left(-\frac{1}{a^{4} + 2 \, a^{3} - 2 \, a - 1}\right)^{\frac{1}{4}} \log\left(-{\left(a + 1\right)} \left(-\frac{1}{a^{4} + 2 \, a^{3} - 2 \, a - 1}\right)^{\frac{1}{4}} + x\right)"," ",0,"(-1/(a^4 + 2*a^3 - 2*a - 1))^(1/4)*arctan(-(a^3 + a^2 - a - 1)*x*(-1/(a^4 + 2*a^3 - 2*a - 1))^(3/4) + (a^3 + a^2 - a - 1)*sqrt(x^2 + (a^2 + 2*a + 1)*sqrt(-1/(a^4 + 2*a^3 - 2*a - 1)))*(-1/(a^4 + 2*a^3 - 2*a - 1))^(3/4)) + 1/4*(-1/(a^4 + 2*a^3 - 2*a - 1))^(1/4)*log((a + 1)*(-1/(a^4 + 2*a^3 - 2*a - 1))^(1/4) + x) - 1/4*(-1/(a^4 + 2*a^3 - 2*a - 1))^(1/4)*log(-(a + 1)*(-1/(a^4 + 2*a^3 - 2*a - 1))^(1/4) + x)","B",0
709,1,294,0,1.297443," ","integrate(1/(x^4+2*a+2*b),x, algorithm=""fricas"")","\left(\frac{1}{8}\right)^{\frac{1}{4}} \left(-\frac{1}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}}\right)^{\frac{1}{4}} \arctan\left(-4 \, \left(\frac{1}{8}\right)^{\frac{3}{4}} {\left(a^{2} + 2 \, a b + b^{2}\right)} x \left(-\frac{1}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}}\right)^{\frac{3}{4}} + 4 \, \left(\frac{1}{8}\right)^{\frac{3}{4}} {\left(a^{2} + 2 \, a b + b^{2}\right)} \sqrt{x^{2} + 2 \, \sqrt{\frac{1}{2}} {\left(a^{2} + 2 \, a b + b^{2}\right)} \sqrt{-\frac{1}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}}}} \left(-\frac{1}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}}\right)^{\frac{3}{4}}\right) + \frac{1}{4} \, \left(\frac{1}{8}\right)^{\frac{1}{4}} \left(-\frac{1}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}}\right)^{\frac{1}{4}} \log\left(2 \, \left(\frac{1}{8}\right)^{\frac{1}{4}} {\left(a + b\right)} \left(-\frac{1}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}}\right)^{\frac{1}{4}} + x\right) - \frac{1}{4} \, \left(\frac{1}{8}\right)^{\frac{1}{4}} \left(-\frac{1}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}}\right)^{\frac{1}{4}} \log\left(-2 \, \left(\frac{1}{8}\right)^{\frac{1}{4}} {\left(a + b\right)} \left(-\frac{1}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}}\right)^{\frac{1}{4}} + x\right)"," ",0,"(1/8)^(1/4)*(-1/(a^3 + 3*a^2*b + 3*a*b^2 + b^3))^(1/4)*arctan(-4*(1/8)^(3/4)*(a^2 + 2*a*b + b^2)*x*(-1/(a^3 + 3*a^2*b + 3*a*b^2 + b^3))^(3/4) + 4*(1/8)^(3/4)*(a^2 + 2*a*b + b^2)*sqrt(x^2 + 2*sqrt(1/2)*(a^2 + 2*a*b + b^2)*sqrt(-1/(a^3 + 3*a^2*b + 3*a*b^2 + b^3)))*(-1/(a^3 + 3*a^2*b + 3*a*b^2 + b^3))^(3/4)) + 1/4*(1/8)^(1/4)*(-1/(a^3 + 3*a^2*b + 3*a*b^2 + b^3))^(1/4)*log(2*(1/8)^(1/4)*(a + b)*(-1/(a^3 + 3*a^2*b + 3*a*b^2 + b^3))^(1/4) + x) - 1/4*(1/8)^(1/4)*(-1/(a^3 + 3*a^2*b + 3*a*b^2 + b^3))^(1/4)*log(-2*(1/8)^(1/4)*(a + b)*(-1/(a^3 + 3*a^2*b + 3*a*b^2 + b^3))^(1/4) + x)","B",0
710,1,294,0,1.327293," ","integrate(1/(x^4+2*a+2*b),x, algorithm=""fricas"")","\left(\frac{1}{8}\right)^{\frac{1}{4}} \left(-\frac{1}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}}\right)^{\frac{1}{4}} \arctan\left(-4 \, \left(\frac{1}{8}\right)^{\frac{3}{4}} {\left(a^{2} + 2 \, a b + b^{2}\right)} x \left(-\frac{1}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}}\right)^{\frac{3}{4}} + 4 \, \left(\frac{1}{8}\right)^{\frac{3}{4}} {\left(a^{2} + 2 \, a b + b^{2}\right)} \sqrt{x^{2} + 2 \, \sqrt{\frac{1}{2}} {\left(a^{2} + 2 \, a b + b^{2}\right)} \sqrt{-\frac{1}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}}}} \left(-\frac{1}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}}\right)^{\frac{3}{4}}\right) + \frac{1}{4} \, \left(\frac{1}{8}\right)^{\frac{1}{4}} \left(-\frac{1}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}}\right)^{\frac{1}{4}} \log\left(2 \, \left(\frac{1}{8}\right)^{\frac{1}{4}} {\left(a + b\right)} \left(-\frac{1}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}}\right)^{\frac{1}{4}} + x\right) - \frac{1}{4} \, \left(\frac{1}{8}\right)^{\frac{1}{4}} \left(-\frac{1}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}}\right)^{\frac{1}{4}} \log\left(-2 \, \left(\frac{1}{8}\right)^{\frac{1}{4}} {\left(a + b\right)} \left(-\frac{1}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}}\right)^{\frac{1}{4}} + x\right)"," ",0,"(1/8)^(1/4)*(-1/(a^3 + 3*a^2*b + 3*a*b^2 + b^3))^(1/4)*arctan(-4*(1/8)^(3/4)*(a^2 + 2*a*b + b^2)*x*(-1/(a^3 + 3*a^2*b + 3*a*b^2 + b^3))^(3/4) + 4*(1/8)^(3/4)*(a^2 + 2*a*b + b^2)*sqrt(x^2 + 2*sqrt(1/2)*(a^2 + 2*a*b + b^2)*sqrt(-1/(a^3 + 3*a^2*b + 3*a*b^2 + b^3)))*(-1/(a^3 + 3*a^2*b + 3*a*b^2 + b^3))^(3/4)) + 1/4*(1/8)^(1/4)*(-1/(a^3 + 3*a^2*b + 3*a*b^2 + b^3))^(1/4)*log(2*(1/8)^(1/4)*(a + b)*(-1/(a^3 + 3*a^2*b + 3*a*b^2 + b^3))^(1/4) + x) - 1/4*(1/8)^(1/4)*(-1/(a^3 + 3*a^2*b + 3*a*b^2 + b^3))^(1/4)*log(-2*(1/8)^(1/4)*(a + b)*(-1/(a^3 + 3*a^2*b + 3*a*b^2 + b^3))^(1/4) + x)","B",0
711,1,91,0,1.148026," ","integrate(x/(x^4+2*a+2*b),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-2 \, a - 2 \, b} \log\left(\frac{x^{4} - 2 \, \sqrt{-2 \, a - 2 \, b} x^{2} - 2 \, a - 2 \, b}{x^{4} + 2 \, a + 2 \, b}\right)}{8 \, {\left(a + b\right)}}, \frac{\sqrt{2 \, a + 2 \, b} \arctan\left(\frac{\sqrt{2 \, a + 2 \, b} x^{2}}{2 \, {\left(a + b\right)}}\right)}{4 \, {\left(a + b\right)}}\right]"," ",0,"[-1/8*sqrt(-2*a - 2*b)*log((x^4 - 2*sqrt(-2*a - 2*b)*x^2 - 2*a - 2*b)/(x^4 + 2*a + 2*b))/(a + b), 1/4*sqrt(2*a + 2*b)*arctan(1/2*sqrt(2*a + 2*b)*x^2/(a + b))/(a + b)]","A",0
712,1,91,0,1.024186," ","integrate(x/(x^4+2*a+2*b),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-2 \, a - 2 \, b} \log\left(\frac{x^{4} - 2 \, \sqrt{-2 \, a - 2 \, b} x^{2} - 2 \, a - 2 \, b}{x^{4} + 2 \, a + 2 \, b}\right)}{8 \, {\left(a + b\right)}}, \frac{\sqrt{2 \, a + 2 \, b} \arctan\left(\frac{\sqrt{2 \, a + 2 \, b} x^{2}}{2 \, {\left(a + b\right)}}\right)}{4 \, {\left(a + b\right)}}\right]"," ",0,"[-1/8*sqrt(-2*a - 2*b)*log((x^4 - 2*sqrt(-2*a - 2*b)*x^2 - 2*a - 2*b)/(x^4 + 2*a + 2*b))/(a + b), 1/4*sqrt(2*a + 2*b)*arctan(1/2*sqrt(2*a + 2*b)*x^2/(a + b))/(a + b)]","A",0
713,1,136,0,0.787002," ","integrate(x^2/(x^4+2*a+2*b),x, algorithm=""fricas"")","-\left(\frac{1}{2}\right)^{\frac{1}{4}} \left(-\frac{1}{a + b}\right)^{\frac{1}{4}} \arctan\left(-\left(\frac{1}{2}\right)^{\frac{1}{4}} x \left(-\frac{1}{a + b}\right)^{\frac{1}{4}} + \left(\frac{1}{2}\right)^{\frac{1}{4}} \sqrt{x^{2} - 2 \, \sqrt{\frac{1}{2}} {\left(a + b\right)} \sqrt{-\frac{1}{a + b}}} \left(-\frac{1}{a + b}\right)^{\frac{1}{4}}\right) + \frac{1}{4} \, \left(\frac{1}{2}\right)^{\frac{1}{4}} \left(-\frac{1}{a + b}\right)^{\frac{1}{4}} \log\left(2 \, \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(a + b\right)} \left(-\frac{1}{a + b}\right)^{\frac{3}{4}} + x\right) - \frac{1}{4} \, \left(\frac{1}{2}\right)^{\frac{1}{4}} \left(-\frac{1}{a + b}\right)^{\frac{1}{4}} \log\left(-2 \, \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(a + b\right)} \left(-\frac{1}{a + b}\right)^{\frac{3}{4}} + x\right)"," ",0,"-(1/2)^(1/4)*(-1/(a + b))^(1/4)*arctan(-(1/2)^(1/4)*x*(-1/(a + b))^(1/4) + (1/2)^(1/4)*sqrt(x^2 - 2*sqrt(1/2)*(a + b)*sqrt(-1/(a + b)))*(-1/(a + b))^(1/4)) + 1/4*(1/2)^(1/4)*(-1/(a + b))^(1/4)*log(2*(1/2)^(3/4)*(a + b)*(-1/(a + b))^(3/4) + x) - 1/4*(1/2)^(1/4)*(-1/(a + b))^(1/4)*log(-2*(1/2)^(3/4)*(a + b)*(-1/(a + b))^(3/4) + x)","B",0
714,1,136,0,1.031180," ","integrate(x^2/(x^4+2*a+2*b),x, algorithm=""fricas"")","-\left(\frac{1}{2}\right)^{\frac{1}{4}} \left(-\frac{1}{a + b}\right)^{\frac{1}{4}} \arctan\left(-\left(\frac{1}{2}\right)^{\frac{1}{4}} x \left(-\frac{1}{a + b}\right)^{\frac{1}{4}} + \left(\frac{1}{2}\right)^{\frac{1}{4}} \sqrt{x^{2} - 2 \, \sqrt{\frac{1}{2}} {\left(a + b\right)} \sqrt{-\frac{1}{a + b}}} \left(-\frac{1}{a + b}\right)^{\frac{1}{4}}\right) + \frac{1}{4} \, \left(\frac{1}{2}\right)^{\frac{1}{4}} \left(-\frac{1}{a + b}\right)^{\frac{1}{4}} \log\left(2 \, \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(a + b\right)} \left(-\frac{1}{a + b}\right)^{\frac{3}{4}} + x\right) - \frac{1}{4} \, \left(\frac{1}{2}\right)^{\frac{1}{4}} \left(-\frac{1}{a + b}\right)^{\frac{1}{4}} \log\left(-2 \, \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(a + b\right)} \left(-\frac{1}{a + b}\right)^{\frac{3}{4}} + x\right)"," ",0,"-(1/2)^(1/4)*(-1/(a + b))^(1/4)*arctan(-(1/2)^(1/4)*x*(-1/(a + b))^(1/4) + (1/2)^(1/4)*sqrt(x^2 - 2*sqrt(1/2)*(a + b)*sqrt(-1/(a + b)))*(-1/(a + b))^(1/4)) + 1/4*(1/2)^(1/4)*(-1/(a + b))^(1/4)*log(2*(1/2)^(3/4)*(a + b)*(-1/(a + b))^(3/4) + x) - 1/4*(1/2)^(1/4)*(-1/(a + b))^(1/4)*log(-2*(1/2)^(3/4)*(a + b)*(-1/(a + b))^(3/4) + x)","B",0
715,1,13,0,0.930467," ","integrate(x^3/(x^4+2*a+2*b),x, algorithm=""fricas"")","\frac{1}{4} \, \log\left(x^{4} + 2 \, a + 2 \, b\right)"," ",0,"1/4*log(x^4 + 2*a + 2*b)","A",0
716,1,13,0,0.801883," ","integrate(x^3/(x^4+2*a+2*b),x, algorithm=""fricas"")","\frac{1}{4} \, \log\left(x^{4} + 2 \, a + 2 \, b\right)"," ",0,"1/4*log(x^4 + 2*a + 2*b)","A",0
717,1,18,0,0.908857," ","integrate(x^(5/2)*(c*x^4+a),x, algorithm=""fricas"")","\frac{2}{105} \, {\left(7 \, c x^{7} + 15 \, a x^{3}\right)} \sqrt{x}"," ",0,"2/105*(7*c*x^7 + 15*a*x^3)*sqrt(x)","A",0
718,1,18,0,0.971409," ","integrate(x^(3/2)*(c*x^4+a),x, algorithm=""fricas"")","\frac{2}{65} \, {\left(5 \, c x^{6} + 13 \, a x^{2}\right)} \sqrt{x}"," ",0,"2/65*(5*c*x^6 + 13*a*x^2)*sqrt(x)","A",0
719,1,16,0,0.946056," ","integrate((c*x^4+a)*x^(1/2),x, algorithm=""fricas"")","\frac{2}{33} \, {\left(3 \, c x^{5} + 11 \, a x\right)} \sqrt{x}"," ",0,"2/33*(3*c*x^5 + 11*a*x)*sqrt(x)","A",0
720,1,14,0,0.954374," ","integrate((c*x^4+a)/x^(1/2),x, algorithm=""fricas"")","\frac{2}{9} \, {\left(c x^{4} + 9 \, a\right)} \sqrt{x}"," ",0,"2/9*(c*x^4 + 9*a)*sqrt(x)","A",0
721,1,14,0,0.911753," ","integrate((c*x^4+a)/x^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(c x^{4} - 7 \, a\right)}}{7 \, \sqrt{x}}"," ",0,"2/7*(c*x^4 - 7*a)/sqrt(x)","A",0
722,1,15,0,0.613203," ","integrate((c*x^4+a)/x^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, c x^{4} - 5 \, a\right)}}{15 \, x^{\frac{3}{2}}}"," ",0,"2/15*(3*c*x^4 - 5*a)/x^(3/2)","A",0
723,1,15,0,1.029930," ","integrate((c*x^4+a)/x^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, c x^{4} - 3 \, a\right)}}{15 \, x^{\frac{5}{2}}}"," ",0,"2/15*(5*c*x^4 - 3*a)/x^(5/2)","A",0
724,1,29,0,0.692259," ","integrate(x^(5/2)*(c*x^4+a)^2,x, algorithm=""fricas"")","\frac{2}{2415} \, {\left(105 \, c^{2} x^{11} + 322 \, a c x^{7} + 345 \, a^{2} x^{3}\right)} \sqrt{x}"," ",0,"2/2415*(105*c^2*x^11 + 322*a*c*x^7 + 345*a^2*x^3)*sqrt(x)","A",0
725,1,29,0,0.654288," ","integrate(x^(3/2)*(c*x^4+a)^2,x, algorithm=""fricas"")","\frac{2}{1365} \, {\left(65 \, c^{2} x^{10} + 210 \, a c x^{6} + 273 \, a^{2} x^{2}\right)} \sqrt{x}"," ",0,"2/1365*(65*c^2*x^10 + 210*a*c*x^6 + 273*a^2*x^2)*sqrt(x)","A",0
726,1,27,0,1.009614," ","integrate((c*x^4+a)^2*x^(1/2),x, algorithm=""fricas"")","\frac{2}{627} \, {\left(33 \, c^{2} x^{9} + 114 \, a c x^{5} + 209 \, a^{2} x\right)} \sqrt{x}"," ",0,"2/627*(33*c^2*x^9 + 114*a*c*x^5 + 209*a^2*x)*sqrt(x)","A",0
727,1,26,0,1.000990," ","integrate((c*x^4+a)^2/x^(1/2),x, algorithm=""fricas"")","\frac{2}{153} \, {\left(9 \, c^{2} x^{8} + 34 \, a c x^{4} + 153 \, a^{2}\right)} \sqrt{x}"," ",0,"2/153*(9*c^2*x^8 + 34*a*c*x^4 + 153*a^2)*sqrt(x)","A",0
728,1,26,0,1.153549," ","integrate((c*x^4+a)^2/x^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(7 \, c^{2} x^{8} + 30 \, a c x^{4} - 105 \, a^{2}\right)}}{105 \, \sqrt{x}}"," ",0,"2/105*(7*c^2*x^8 + 30*a*c*x^4 - 105*a^2)/sqrt(x)","A",0
729,1,26,0,1.003731," ","integrate((c*x^4+a)^2/x^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, c^{2} x^{8} + 78 \, a c x^{4} - 65 \, a^{2}\right)}}{195 \, x^{\frac{3}{2}}}"," ",0,"2/195*(15*c^2*x^8 + 78*a*c*x^4 - 65*a^2)/x^(3/2)","A",0
730,1,26,0,0.967121," ","integrate((c*x^4+a)^2/x^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, c^{2} x^{8} + 110 \, a c x^{4} - 33 \, a^{2}\right)}}{165 \, x^{\frac{5}{2}}}"," ",0,"2/165*(15*c^2*x^8 + 110*a*c*x^4 - 33*a^2)/x^(5/2)","A",0
731,1,40,0,0.855182," ","integrate(x^(5/2)*(c*x^4+a)^3,x, algorithm=""fricas"")","\frac{2}{24955} \, {\left(805 \, c^{3} x^{15} + 3255 \, a c^{2} x^{11} + 4991 \, a^{2} c x^{7} + 3565 \, a^{3} x^{3}\right)} \sqrt{x}"," ",0,"2/24955*(805*c^3*x^15 + 3255*a*c^2*x^11 + 4991*a^2*c*x^7 + 3565*a^3*x^3)*sqrt(x)","A",0
732,1,40,0,0.826874," ","integrate(x^(3/2)*(c*x^4+a)^3,x, algorithm=""fricas"")","\frac{2}{13195} \, {\left(455 \, c^{3} x^{14} + 1885 \, a c^{2} x^{10} + 3045 \, a^{2} c x^{6} + 2639 \, a^{3} x^{2}\right)} \sqrt{x}"," ",0,"2/13195*(455*c^3*x^14 + 1885*a*c^2*x^10 + 3045*a^2*c*x^6 + 2639*a^3*x^2)*sqrt(x)","A",0
733,1,38,0,0.976948," ","integrate((c*x^4+a)^3*x^(1/2),x, algorithm=""fricas"")","\frac{2}{5643} \, {\left(209 \, c^{3} x^{13} + 891 \, a c^{2} x^{9} + 1539 \, a^{2} c x^{5} + 1881 \, a^{3} x\right)} \sqrt{x}"," ",0,"2/5643*(209*c^3*x^13 + 891*a*c^2*x^9 + 1539*a^2*c*x^5 + 1881*a^3*x)*sqrt(x)","A",0
734,1,37,0,0.953166," ","integrate((c*x^4+a)^3/x^(1/2),x, algorithm=""fricas"")","\frac{2}{1275} \, {\left(51 \, c^{3} x^{12} + 225 \, a c^{2} x^{8} + 425 \, a^{2} c x^{4} + 1275 \, a^{3}\right)} \sqrt{x}"," ",0,"2/1275*(51*c^3*x^12 + 225*a*c^2*x^8 + 425*a^2*c*x^4 + 1275*a^3)*sqrt(x)","A",0
735,1,37,0,0.824041," ","integrate((c*x^4+a)^3/x^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, c^{3} x^{12} + 161 \, a c^{2} x^{8} + 345 \, a^{2} c x^{4} - 805 \, a^{3}\right)}}{805 \, \sqrt{x}}"," ",0,"2/805*(35*c^3*x^12 + 161*a*c^2*x^8 + 345*a^2*c*x^4 - 805*a^3)/sqrt(x)","A",0
736,1,37,0,0.738055," ","integrate((c*x^4+a)^3/x^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(65 \, c^{3} x^{12} + 315 \, a c^{2} x^{8} + 819 \, a^{2} c x^{4} - 455 \, a^{3}\right)}}{1365 \, x^{\frac{3}{2}}}"," ",0,"2/1365*(65*c^3*x^12 + 315*a*c^2*x^8 + 819*a^2*c*x^4 - 455*a^3)/x^(3/2)","A",0
737,1,37,0,0.993738," ","integrate((c*x^4+a)^3/x^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(55 \, c^{3} x^{12} + 285 \, a c^{2} x^{8} + 1045 \, a^{2} c x^{4} - 209 \, a^{3}\right)}}{1045 \, x^{\frac{5}{2}}}"," ",0,"2/1045*(55*c^3*x^12 + 285*a*c^2*x^8 + 1045*a^2*c*x^4 - 209*a^3)/x^(5/2)","A",0
738,1,491,0,1.181490," ","integrate(x^(9/2)/(c*x^4+a),x, algorithm=""fricas"")","\frac{12 \, \sqrt{2} c \left(-\frac{a^{3}}{c^{11}}\right)^{\frac{1}{8}} \arctan\left(-\frac{\sqrt{2} a c^{7} \sqrt{x} \left(-\frac{a^{3}}{c^{11}}\right)^{\frac{5}{8}} - \sqrt{2} \sqrt{c^{8} \left(-\frac{a^{3}}{c^{11}}\right)^{\frac{3}{4}} + \sqrt{2} a c^{4} \sqrt{x} \left(-\frac{a^{3}}{c^{11}}\right)^{\frac{3}{8}} + a^{2} x} c^{7} \left(-\frac{a^{3}}{c^{11}}\right)^{\frac{5}{8}} - a^{3}}{a^{3}}\right) + 12 \, \sqrt{2} c \left(-\frac{a^{3}}{c^{11}}\right)^{\frac{1}{8}} \arctan\left(-\frac{\sqrt{2} a c^{7} \sqrt{x} \left(-\frac{a^{3}}{c^{11}}\right)^{\frac{5}{8}} - \sqrt{2} \sqrt{c^{8} \left(-\frac{a^{3}}{c^{11}}\right)^{\frac{3}{4}} - \sqrt{2} a c^{4} \sqrt{x} \left(-\frac{a^{3}}{c^{11}}\right)^{\frac{3}{8}} + a^{2} x} c^{7} \left(-\frac{a^{3}}{c^{11}}\right)^{\frac{5}{8}} + a^{3}}{a^{3}}\right) - 3 \, \sqrt{2} c \left(-\frac{a^{3}}{c^{11}}\right)^{\frac{1}{8}} \log\left(c^{8} \left(-\frac{a^{3}}{c^{11}}\right)^{\frac{3}{4}} + \sqrt{2} a c^{4} \sqrt{x} \left(-\frac{a^{3}}{c^{11}}\right)^{\frac{3}{8}} + a^{2} x\right) + 3 \, \sqrt{2} c \left(-\frac{a^{3}}{c^{11}}\right)^{\frac{1}{8}} \log\left(c^{8} \left(-\frac{a^{3}}{c^{11}}\right)^{\frac{3}{4}} - \sqrt{2} a c^{4} \sqrt{x} \left(-\frac{a^{3}}{c^{11}}\right)^{\frac{3}{8}} + a^{2} x\right) - 24 \, c \left(-\frac{a^{3}}{c^{11}}\right)^{\frac{1}{8}} \arctan\left(-\frac{a c^{7} \sqrt{x} \left(-\frac{a^{3}}{c^{11}}\right)^{\frac{5}{8}} - \sqrt{c^{8} \left(-\frac{a^{3}}{c^{11}}\right)^{\frac{3}{4}} + a^{2} x} c^{7} \left(-\frac{a^{3}}{c^{11}}\right)^{\frac{5}{8}}}{a^{3}}\right) + 6 \, c \left(-\frac{a^{3}}{c^{11}}\right)^{\frac{1}{8}} \log\left(c^{4} \left(-\frac{a^{3}}{c^{11}}\right)^{\frac{3}{8}} + a \sqrt{x}\right) - 6 \, c \left(-\frac{a^{3}}{c^{11}}\right)^{\frac{1}{8}} \log\left(-c^{4} \left(-\frac{a^{3}}{c^{11}}\right)^{\frac{3}{8}} + a \sqrt{x}\right) + 16 \, x^{\frac{3}{2}}}{24 \, c}"," ",0,"1/24*(12*sqrt(2)*c*(-a^3/c^11)^(1/8)*arctan(-(sqrt(2)*a*c^7*sqrt(x)*(-a^3/c^11)^(5/8) - sqrt(2)*sqrt(c^8*(-a^3/c^11)^(3/4) + sqrt(2)*a*c^4*sqrt(x)*(-a^3/c^11)^(3/8) + a^2*x)*c^7*(-a^3/c^11)^(5/8) - a^3)/a^3) + 12*sqrt(2)*c*(-a^3/c^11)^(1/8)*arctan(-(sqrt(2)*a*c^7*sqrt(x)*(-a^3/c^11)^(5/8) - sqrt(2)*sqrt(c^8*(-a^3/c^11)^(3/4) - sqrt(2)*a*c^4*sqrt(x)*(-a^3/c^11)^(3/8) + a^2*x)*c^7*(-a^3/c^11)^(5/8) + a^3)/a^3) - 3*sqrt(2)*c*(-a^3/c^11)^(1/8)*log(c^8*(-a^3/c^11)^(3/4) + sqrt(2)*a*c^4*sqrt(x)*(-a^3/c^11)^(3/8) + a^2*x) + 3*sqrt(2)*c*(-a^3/c^11)^(1/8)*log(c^8*(-a^3/c^11)^(3/4) - sqrt(2)*a*c^4*sqrt(x)*(-a^3/c^11)^(3/8) + a^2*x) - 24*c*(-a^3/c^11)^(1/8)*arctan(-(a*c^7*sqrt(x)*(-a^3/c^11)^(5/8) - sqrt(c^8*(-a^3/c^11)^(3/4) + a^2*x)*c^7*(-a^3/c^11)^(5/8))/a^3) + 6*c*(-a^3/c^11)^(1/8)*log(c^4*(-a^3/c^11)^(3/8) + a*sqrt(x)) - 6*c*(-a^3/c^11)^(1/8)*log(-c^4*(-a^3/c^11)^(3/8) + a*sqrt(x)) + 16*x^(3/2))/c","B",0
739,1,392,0,1.098170," ","integrate(x^(7/2)/(c*x^4+a),x, algorithm=""fricas"")","-\frac{4 \, \sqrt{2} c \left(-\frac{a}{c^{9}}\right)^{\frac{1}{8}} \arctan\left(\frac{\sqrt{2} \sqrt{c^{2} \left(-\frac{a}{c^{9}}\right)^{\frac{1}{4}} + \sqrt{2} c \sqrt{x} \left(-\frac{a}{c^{9}}\right)^{\frac{1}{8}} + x} c^{8} \left(-\frac{a}{c^{9}}\right)^{\frac{7}{8}} - \sqrt{2} c^{8} \sqrt{x} \left(-\frac{a}{c^{9}}\right)^{\frac{7}{8}} + a}{a}\right) + 4 \, \sqrt{2} c \left(-\frac{a}{c^{9}}\right)^{\frac{1}{8}} \arctan\left(\frac{\sqrt{2} \sqrt{c^{2} \left(-\frac{a}{c^{9}}\right)^{\frac{1}{4}} - \sqrt{2} c \sqrt{x} \left(-\frac{a}{c^{9}}\right)^{\frac{1}{8}} + x} c^{8} \left(-\frac{a}{c^{9}}\right)^{\frac{7}{8}} - \sqrt{2} c^{8} \sqrt{x} \left(-\frac{a}{c^{9}}\right)^{\frac{7}{8}} - a}{a}\right) + \sqrt{2} c \left(-\frac{a}{c^{9}}\right)^{\frac{1}{8}} \log\left(c^{2} \left(-\frac{a}{c^{9}}\right)^{\frac{1}{4}} + \sqrt{2} c \sqrt{x} \left(-\frac{a}{c^{9}}\right)^{\frac{1}{8}} + x\right) - \sqrt{2} c \left(-\frac{a}{c^{9}}\right)^{\frac{1}{8}} \log\left(c^{2} \left(-\frac{a}{c^{9}}\right)^{\frac{1}{4}} - \sqrt{2} c \sqrt{x} \left(-\frac{a}{c^{9}}\right)^{\frac{1}{8}} + x\right) + 8 \, c \left(-\frac{a}{c^{9}}\right)^{\frac{1}{8}} \arctan\left(\frac{\sqrt{c^{2} \left(-\frac{a}{c^{9}}\right)^{\frac{1}{4}} + x} c^{8} \left(-\frac{a}{c^{9}}\right)^{\frac{7}{8}} - c^{8} \sqrt{x} \left(-\frac{a}{c^{9}}\right)^{\frac{7}{8}}}{a}\right) + 2 \, c \left(-\frac{a}{c^{9}}\right)^{\frac{1}{8}} \log\left(c \left(-\frac{a}{c^{9}}\right)^{\frac{1}{8}} + \sqrt{x}\right) - 2 \, c \left(-\frac{a}{c^{9}}\right)^{\frac{1}{8}} \log\left(-c \left(-\frac{a}{c^{9}}\right)^{\frac{1}{8}} + \sqrt{x}\right) - 16 \, \sqrt{x}}{8 \, c}"," ",0,"-1/8*(4*sqrt(2)*c*(-a/c^9)^(1/8)*arctan((sqrt(2)*sqrt(c^2*(-a/c^9)^(1/4) + sqrt(2)*c*sqrt(x)*(-a/c^9)^(1/8) + x)*c^8*(-a/c^9)^(7/8) - sqrt(2)*c^8*sqrt(x)*(-a/c^9)^(7/8) + a)/a) + 4*sqrt(2)*c*(-a/c^9)^(1/8)*arctan((sqrt(2)*sqrt(c^2*(-a/c^9)^(1/4) - sqrt(2)*c*sqrt(x)*(-a/c^9)^(1/8) + x)*c^8*(-a/c^9)^(7/8) - sqrt(2)*c^8*sqrt(x)*(-a/c^9)^(7/8) - a)/a) + sqrt(2)*c*(-a/c^9)^(1/8)*log(c^2*(-a/c^9)^(1/4) + sqrt(2)*c*sqrt(x)*(-a/c^9)^(1/8) + x) - sqrt(2)*c*(-a/c^9)^(1/8)*log(c^2*(-a/c^9)^(1/4) - sqrt(2)*c*sqrt(x)*(-a/c^9)^(1/8) + x) + 8*c*(-a/c^9)^(1/8)*arctan((sqrt(c^2*(-a/c^9)^(1/4) + x)*c^8*(-a/c^9)^(7/8) - c^8*sqrt(x)*(-a/c^9)^(7/8))/a) + 2*c*(-a/c^9)^(1/8)*log(c*(-a/c^9)^(1/8) + sqrt(x)) - 2*c*(-a/c^9)^(1/8)*log(-c*(-a/c^9)^(1/8) + sqrt(x)) - 16*sqrt(x))/c","A",0
740,1,426,0,0.895172," ","integrate(x^(5/2)/(c*x^4+a),x, algorithm=""fricas"")","-\frac{1}{2} \, \sqrt{2} \left(-\frac{1}{a c^{7}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{2} \sqrt{\sqrt{2} a c^{6} \sqrt{x} \left(-\frac{1}{a c^{7}}\right)^{\frac{7}{8}} - a c^{5} \left(-\frac{1}{a c^{7}}\right)^{\frac{3}{4}} + x} c \left(-\frac{1}{a c^{7}}\right)^{\frac{1}{8}} - \sqrt{2} c \sqrt{x} \left(-\frac{1}{a c^{7}}\right)^{\frac{1}{8}} + 1\right) - \frac{1}{2} \, \sqrt{2} \left(-\frac{1}{a c^{7}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{2} \sqrt{-\sqrt{2} a c^{6} \sqrt{x} \left(-\frac{1}{a c^{7}}\right)^{\frac{7}{8}} - a c^{5} \left(-\frac{1}{a c^{7}}\right)^{\frac{3}{4}} + x} c \left(-\frac{1}{a c^{7}}\right)^{\frac{1}{8}} - \sqrt{2} c \sqrt{x} \left(-\frac{1}{a c^{7}}\right)^{\frac{1}{8}} - 1\right) + \frac{1}{8} \, \sqrt{2} \left(-\frac{1}{a c^{7}}\right)^{\frac{1}{8}} \log\left(\sqrt{2} a c^{6} \sqrt{x} \left(-\frac{1}{a c^{7}}\right)^{\frac{7}{8}} - a c^{5} \left(-\frac{1}{a c^{7}}\right)^{\frac{3}{4}} + x\right) - \frac{1}{8} \, \sqrt{2} \left(-\frac{1}{a c^{7}}\right)^{\frac{1}{8}} \log\left(-\sqrt{2} a c^{6} \sqrt{x} \left(-\frac{1}{a c^{7}}\right)^{\frac{7}{8}} - a c^{5} \left(-\frac{1}{a c^{7}}\right)^{\frac{3}{4}} + x\right) - \left(-\frac{1}{a c^{7}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{-a c^{5} \left(-\frac{1}{a c^{7}}\right)^{\frac{3}{4}} + x} c \left(-\frac{1}{a c^{7}}\right)^{\frac{1}{8}} - c \sqrt{x} \left(-\frac{1}{a c^{7}}\right)^{\frac{1}{8}}\right) + \frac{1}{4} \, \left(-\frac{1}{a c^{7}}\right)^{\frac{1}{8}} \log\left(a c^{6} \left(-\frac{1}{a c^{7}}\right)^{\frac{7}{8}} + \sqrt{x}\right) - \frac{1}{4} \, \left(-\frac{1}{a c^{7}}\right)^{\frac{1}{8}} \log\left(-a c^{6} \left(-\frac{1}{a c^{7}}\right)^{\frac{7}{8}} + \sqrt{x}\right)"," ",0,"-1/2*sqrt(2)*(-1/(a*c^7))^(1/8)*arctan(sqrt(2)*sqrt(sqrt(2)*a*c^6*sqrt(x)*(-1/(a*c^7))^(7/8) - a*c^5*(-1/(a*c^7))^(3/4) + x)*c*(-1/(a*c^7))^(1/8) - sqrt(2)*c*sqrt(x)*(-1/(a*c^7))^(1/8) + 1) - 1/2*sqrt(2)*(-1/(a*c^7))^(1/8)*arctan(sqrt(2)*sqrt(-sqrt(2)*a*c^6*sqrt(x)*(-1/(a*c^7))^(7/8) - a*c^5*(-1/(a*c^7))^(3/4) + x)*c*(-1/(a*c^7))^(1/8) - sqrt(2)*c*sqrt(x)*(-1/(a*c^7))^(1/8) - 1) + 1/8*sqrt(2)*(-1/(a*c^7))^(1/8)*log(sqrt(2)*a*c^6*sqrt(x)*(-1/(a*c^7))^(7/8) - a*c^5*(-1/(a*c^7))^(3/4) + x) - 1/8*sqrt(2)*(-1/(a*c^7))^(1/8)*log(-sqrt(2)*a*c^6*sqrt(x)*(-1/(a*c^7))^(7/8) - a*c^5*(-1/(a*c^7))^(3/4) + x) - (-1/(a*c^7))^(1/8)*arctan(sqrt(-a*c^5*(-1/(a*c^7))^(3/4) + x)*c*(-1/(a*c^7))^(1/8) - c*sqrt(x)*(-1/(a*c^7))^(1/8)) + 1/4*(-1/(a*c^7))^(1/8)*log(a*c^6*(-1/(a*c^7))^(7/8) + sqrt(x)) - 1/4*(-1/(a*c^7))^(1/8)*log(-a*c^6*(-1/(a*c^7))^(7/8) + sqrt(x))","B",0
741,1,446,0,1.165352," ","integrate(x^(3/2)/(c*x^4+a),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{2} \left(-\frac{1}{a^{3} c^{5}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{2} \sqrt{\sqrt{2} a^{2} c^{3} \sqrt{x} \left(-\frac{1}{a^{3} c^{5}}\right)^{\frac{5}{8}} - a c \left(-\frac{1}{a^{3} c^{5}}\right)^{\frac{1}{4}} + x} a c^{2} \left(-\frac{1}{a^{3} c^{5}}\right)^{\frac{3}{8}} - \sqrt{2} a c^{2} \sqrt{x} \left(-\frac{1}{a^{3} c^{5}}\right)^{\frac{3}{8}} + 1\right) + \frac{1}{2} \, \sqrt{2} \left(-\frac{1}{a^{3} c^{5}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{2} \sqrt{-\sqrt{2} a^{2} c^{3} \sqrt{x} \left(-\frac{1}{a^{3} c^{5}}\right)^{\frac{5}{8}} - a c \left(-\frac{1}{a^{3} c^{5}}\right)^{\frac{1}{4}} + x} a c^{2} \left(-\frac{1}{a^{3} c^{5}}\right)^{\frac{3}{8}} - \sqrt{2} a c^{2} \sqrt{x} \left(-\frac{1}{a^{3} c^{5}}\right)^{\frac{3}{8}} - 1\right) + \frac{1}{8} \, \sqrt{2} \left(-\frac{1}{a^{3} c^{5}}\right)^{\frac{1}{8}} \log\left(\sqrt{2} a^{2} c^{3} \sqrt{x} \left(-\frac{1}{a^{3} c^{5}}\right)^{\frac{5}{8}} - a c \left(-\frac{1}{a^{3} c^{5}}\right)^{\frac{1}{4}} + x\right) - \frac{1}{8} \, \sqrt{2} \left(-\frac{1}{a^{3} c^{5}}\right)^{\frac{1}{8}} \log\left(-\sqrt{2} a^{2} c^{3} \sqrt{x} \left(-\frac{1}{a^{3} c^{5}}\right)^{\frac{5}{8}} - a c \left(-\frac{1}{a^{3} c^{5}}\right)^{\frac{1}{4}} + x\right) - \left(-\frac{1}{a^{3} c^{5}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{-a c \left(-\frac{1}{a^{3} c^{5}}\right)^{\frac{1}{4}} + x} a c^{2} \left(-\frac{1}{a^{3} c^{5}}\right)^{\frac{3}{8}} - a c^{2} \sqrt{x} \left(-\frac{1}{a^{3} c^{5}}\right)^{\frac{3}{8}}\right) - \frac{1}{4} \, \left(-\frac{1}{a^{3} c^{5}}\right)^{\frac{1}{8}} \log\left(a^{2} c^{3} \left(-\frac{1}{a^{3} c^{5}}\right)^{\frac{5}{8}} + \sqrt{x}\right) + \frac{1}{4} \, \left(-\frac{1}{a^{3} c^{5}}\right)^{\frac{1}{8}} \log\left(-a^{2} c^{3} \left(-\frac{1}{a^{3} c^{5}}\right)^{\frac{5}{8}} + \sqrt{x}\right)"," ",0,"1/2*sqrt(2)*(-1/(a^3*c^5))^(1/8)*arctan(sqrt(2)*sqrt(sqrt(2)*a^2*c^3*sqrt(x)*(-1/(a^3*c^5))^(5/8) - a*c*(-1/(a^3*c^5))^(1/4) + x)*a*c^2*(-1/(a^3*c^5))^(3/8) - sqrt(2)*a*c^2*sqrt(x)*(-1/(a^3*c^5))^(3/8) + 1) + 1/2*sqrt(2)*(-1/(a^3*c^5))^(1/8)*arctan(sqrt(2)*sqrt(-sqrt(2)*a^2*c^3*sqrt(x)*(-1/(a^3*c^5))^(5/8) - a*c*(-1/(a^3*c^5))^(1/4) + x)*a*c^2*(-1/(a^3*c^5))^(3/8) - sqrt(2)*a*c^2*sqrt(x)*(-1/(a^3*c^5))^(3/8) - 1) + 1/8*sqrt(2)*(-1/(a^3*c^5))^(1/8)*log(sqrt(2)*a^2*c^3*sqrt(x)*(-1/(a^3*c^5))^(5/8) - a*c*(-1/(a^3*c^5))^(1/4) + x) - 1/8*sqrt(2)*(-1/(a^3*c^5))^(1/8)*log(-sqrt(2)*a^2*c^3*sqrt(x)*(-1/(a^3*c^5))^(5/8) - a*c*(-1/(a^3*c^5))^(1/4) + x) - (-1/(a^3*c^5))^(1/8)*arctan(sqrt(-a*c*(-1/(a^3*c^5))^(1/4) + x)*a*c^2*(-1/(a^3*c^5))^(3/8) - a*c^2*sqrt(x)*(-1/(a^3*c^5))^(3/8)) - 1/4*(-1/(a^3*c^5))^(1/8)*log(a^2*c^3*(-1/(a^3*c^5))^(5/8) + sqrt(x)) + 1/4*(-1/(a^3*c^5))^(1/8)*log(-a^2*c^3*(-1/(a^3*c^5))^(5/8) + sqrt(x))","B",0
742,1,460,0,0.942411," ","integrate(x^(1/2)/(c*x^4+a),x, algorithm=""fricas"")","-\frac{1}{2} \, \sqrt{2} \left(-\frac{1}{a^{5} c^{3}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{2} \sqrt{a^{4} c^{2} \left(-\frac{1}{a^{5} c^{3}}\right)^{\frac{3}{4}} + \sqrt{2} a^{2} c \sqrt{x} \left(-\frac{1}{a^{5} c^{3}}\right)^{\frac{3}{8}} + x} a^{3} c^{2} \left(-\frac{1}{a^{5} c^{3}}\right)^{\frac{5}{8}} - \sqrt{2} a^{3} c^{2} \sqrt{x} \left(-\frac{1}{a^{5} c^{3}}\right)^{\frac{5}{8}} + 1\right) - \frac{1}{2} \, \sqrt{2} \left(-\frac{1}{a^{5} c^{3}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{2} \sqrt{a^{4} c^{2} \left(-\frac{1}{a^{5} c^{3}}\right)^{\frac{3}{4}} - \sqrt{2} a^{2} c \sqrt{x} \left(-\frac{1}{a^{5} c^{3}}\right)^{\frac{3}{8}} + x} a^{3} c^{2} \left(-\frac{1}{a^{5} c^{3}}\right)^{\frac{5}{8}} - \sqrt{2} a^{3} c^{2} \sqrt{x} \left(-\frac{1}{a^{5} c^{3}}\right)^{\frac{5}{8}} - 1\right) + \frac{1}{8} \, \sqrt{2} \left(-\frac{1}{a^{5} c^{3}}\right)^{\frac{1}{8}} \log\left(a^{4} c^{2} \left(-\frac{1}{a^{5} c^{3}}\right)^{\frac{3}{4}} + \sqrt{2} a^{2} c \sqrt{x} \left(-\frac{1}{a^{5} c^{3}}\right)^{\frac{3}{8}} + x\right) - \frac{1}{8} \, \sqrt{2} \left(-\frac{1}{a^{5} c^{3}}\right)^{\frac{1}{8}} \log\left(a^{4} c^{2} \left(-\frac{1}{a^{5} c^{3}}\right)^{\frac{3}{4}} - \sqrt{2} a^{2} c \sqrt{x} \left(-\frac{1}{a^{5} c^{3}}\right)^{\frac{3}{8}} + x\right) + \left(-\frac{1}{a^{5} c^{3}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{a^{4} c^{2} \left(-\frac{1}{a^{5} c^{3}}\right)^{\frac{3}{4}} + x} a^{3} c^{2} \left(-\frac{1}{a^{5} c^{3}}\right)^{\frac{5}{8}} - a^{3} c^{2} \sqrt{x} \left(-\frac{1}{a^{5} c^{3}}\right)^{\frac{5}{8}}\right) - \frac{1}{4} \, \left(-\frac{1}{a^{5} c^{3}}\right)^{\frac{1}{8}} \log\left(a^{2} c \left(-\frac{1}{a^{5} c^{3}}\right)^{\frac{3}{8}} + \sqrt{x}\right) + \frac{1}{4} \, \left(-\frac{1}{a^{5} c^{3}}\right)^{\frac{1}{8}} \log\left(-a^{2} c \left(-\frac{1}{a^{5} c^{3}}\right)^{\frac{3}{8}} + \sqrt{x}\right)"," ",0,"-1/2*sqrt(2)*(-1/(a^5*c^3))^(1/8)*arctan(sqrt(2)*sqrt(a^4*c^2*(-1/(a^5*c^3))^(3/4) + sqrt(2)*a^2*c*sqrt(x)*(-1/(a^5*c^3))^(3/8) + x)*a^3*c^2*(-1/(a^5*c^3))^(5/8) - sqrt(2)*a^3*c^2*sqrt(x)*(-1/(a^5*c^3))^(5/8) + 1) - 1/2*sqrt(2)*(-1/(a^5*c^3))^(1/8)*arctan(sqrt(2)*sqrt(a^4*c^2*(-1/(a^5*c^3))^(3/4) - sqrt(2)*a^2*c*sqrt(x)*(-1/(a^5*c^3))^(3/8) + x)*a^3*c^2*(-1/(a^5*c^3))^(5/8) - sqrt(2)*a^3*c^2*sqrt(x)*(-1/(a^5*c^3))^(5/8) - 1) + 1/8*sqrt(2)*(-1/(a^5*c^3))^(1/8)*log(a^4*c^2*(-1/(a^5*c^3))^(3/4) + sqrt(2)*a^2*c*sqrt(x)*(-1/(a^5*c^3))^(3/8) + x) - 1/8*sqrt(2)*(-1/(a^5*c^3))^(1/8)*log(a^4*c^2*(-1/(a^5*c^3))^(3/4) - sqrt(2)*a^2*c*sqrt(x)*(-1/(a^5*c^3))^(3/8) + x) + (-1/(a^5*c^3))^(1/8)*arctan(sqrt(a^4*c^2*(-1/(a^5*c^3))^(3/4) + x)*a^3*c^2*(-1/(a^5*c^3))^(5/8) - a^3*c^2*sqrt(x)*(-1/(a^5*c^3))^(5/8)) - 1/4*(-1/(a^5*c^3))^(1/8)*log(a^2*c*(-1/(a^5*c^3))^(3/8) + sqrt(x)) + 1/4*(-1/(a^5*c^3))^(1/8)*log(-a^2*c*(-1/(a^5*c^3))^(3/8) + sqrt(x))","B",0
743,1,415,0,0.871715," ","integrate(1/(c*x^4+a)/x^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{2} \left(-\frac{1}{a^{7} c}\right)^{\frac{1}{8}} \arctan\left(\sqrt{2} \sqrt{a^{2} \left(-\frac{1}{a^{7} c}\right)^{\frac{1}{4}} + \sqrt{2} a \sqrt{x} \left(-\frac{1}{a^{7} c}\right)^{\frac{1}{8}} + x} a^{6} c \left(-\frac{1}{a^{7} c}\right)^{\frac{7}{8}} - \sqrt{2} a^{6} c \sqrt{x} \left(-\frac{1}{a^{7} c}\right)^{\frac{7}{8}} + 1\right) + \frac{1}{2} \, \sqrt{2} \left(-\frac{1}{a^{7} c}\right)^{\frac{1}{8}} \arctan\left(\sqrt{2} \sqrt{a^{2} \left(-\frac{1}{a^{7} c}\right)^{\frac{1}{4}} - \sqrt{2} a \sqrt{x} \left(-\frac{1}{a^{7} c}\right)^{\frac{1}{8}} + x} a^{6} c \left(-\frac{1}{a^{7} c}\right)^{\frac{7}{8}} - \sqrt{2} a^{6} c \sqrt{x} \left(-\frac{1}{a^{7} c}\right)^{\frac{7}{8}} - 1\right) + \frac{1}{8} \, \sqrt{2} \left(-\frac{1}{a^{7} c}\right)^{\frac{1}{8}} \log\left(a^{2} \left(-\frac{1}{a^{7} c}\right)^{\frac{1}{4}} + \sqrt{2} a \sqrt{x} \left(-\frac{1}{a^{7} c}\right)^{\frac{1}{8}} + x\right) - \frac{1}{8} \, \sqrt{2} \left(-\frac{1}{a^{7} c}\right)^{\frac{1}{8}} \log\left(a^{2} \left(-\frac{1}{a^{7} c}\right)^{\frac{1}{4}} - \sqrt{2} a \sqrt{x} \left(-\frac{1}{a^{7} c}\right)^{\frac{1}{8}} + x\right) + \left(-\frac{1}{a^{7} c}\right)^{\frac{1}{8}} \arctan\left(\sqrt{a^{2} \left(-\frac{1}{a^{7} c}\right)^{\frac{1}{4}} + x} a^{6} c \left(-\frac{1}{a^{7} c}\right)^{\frac{7}{8}} - a^{6} c \sqrt{x} \left(-\frac{1}{a^{7} c}\right)^{\frac{7}{8}}\right) + \frac{1}{4} \, \left(-\frac{1}{a^{7} c}\right)^{\frac{1}{8}} \log\left(a \left(-\frac{1}{a^{7} c}\right)^{\frac{1}{8}} + \sqrt{x}\right) - \frac{1}{4} \, \left(-\frac{1}{a^{7} c}\right)^{\frac{1}{8}} \log\left(-a \left(-\frac{1}{a^{7} c}\right)^{\frac{1}{8}} + \sqrt{x}\right)"," ",0,"1/2*sqrt(2)*(-1/(a^7*c))^(1/8)*arctan(sqrt(2)*sqrt(a^2*(-1/(a^7*c))^(1/4) + sqrt(2)*a*sqrt(x)*(-1/(a^7*c))^(1/8) + x)*a^6*c*(-1/(a^7*c))^(7/8) - sqrt(2)*a^6*c*sqrt(x)*(-1/(a^7*c))^(7/8) + 1) + 1/2*sqrt(2)*(-1/(a^7*c))^(1/8)*arctan(sqrt(2)*sqrt(a^2*(-1/(a^7*c))^(1/4) - sqrt(2)*a*sqrt(x)*(-1/(a^7*c))^(1/8) + x)*a^6*c*(-1/(a^7*c))^(7/8) - sqrt(2)*a^6*c*sqrt(x)*(-1/(a^7*c))^(7/8) - 1) + 1/8*sqrt(2)*(-1/(a^7*c))^(1/8)*log(a^2*(-1/(a^7*c))^(1/4) + sqrt(2)*a*sqrt(x)*(-1/(a^7*c))^(1/8) + x) - 1/8*sqrt(2)*(-1/(a^7*c))^(1/8)*log(a^2*(-1/(a^7*c))^(1/4) - sqrt(2)*a*sqrt(x)*(-1/(a^7*c))^(1/8) + x) + (-1/(a^7*c))^(1/8)*arctan(sqrt(a^2*(-1/(a^7*c))^(1/4) + x)*a^6*c*(-1/(a^7*c))^(7/8) - a^6*c*sqrt(x)*(-1/(a^7*c))^(7/8)) + 1/4*(-1/(a^7*c))^(1/8)*log(a*(-1/(a^7*c))^(1/8) + sqrt(x)) - 1/4*(-1/(a^7*c))^(1/8)*log(-a*(-1/(a^7*c))^(1/8) + sqrt(x))","B",0
744,1,446,0,0.971957," ","integrate(1/x^(3/2)/(c*x^4+a),x, algorithm=""fricas"")","\frac{4 \, \sqrt{2} a x \left(-\frac{c}{a^{9}}\right)^{\frac{1}{8}} \arctan\left(-\frac{\sqrt{2} a c \sqrt{x} \left(-\frac{c}{a^{9}}\right)^{\frac{1}{8}} - \sqrt{2} \sqrt{\sqrt{2} a^{8} c \sqrt{x} \left(-\frac{c}{a^{9}}\right)^{\frac{7}{8}} - a^{7} c \left(-\frac{c}{a^{9}}\right)^{\frac{3}{4}} + c^{2} x} a \left(-\frac{c}{a^{9}}\right)^{\frac{1}{8}} - c}{c}\right) + 4 \, \sqrt{2} a x \left(-\frac{c}{a^{9}}\right)^{\frac{1}{8}} \arctan\left(-\frac{\sqrt{2} a c \sqrt{x} \left(-\frac{c}{a^{9}}\right)^{\frac{1}{8}} - \sqrt{2} \sqrt{-\sqrt{2} a^{8} c \sqrt{x} \left(-\frac{c}{a^{9}}\right)^{\frac{7}{8}} - a^{7} c \left(-\frac{c}{a^{9}}\right)^{\frac{3}{4}} + c^{2} x} a \left(-\frac{c}{a^{9}}\right)^{\frac{1}{8}} + c}{c}\right) - \sqrt{2} a x \left(-\frac{c}{a^{9}}\right)^{\frac{1}{8}} \log\left(\sqrt{2} a^{8} c \sqrt{x} \left(-\frac{c}{a^{9}}\right)^{\frac{7}{8}} - a^{7} c \left(-\frac{c}{a^{9}}\right)^{\frac{3}{4}} + c^{2} x\right) + \sqrt{2} a x \left(-\frac{c}{a^{9}}\right)^{\frac{1}{8}} \log\left(-\sqrt{2} a^{8} c \sqrt{x} \left(-\frac{c}{a^{9}}\right)^{\frac{7}{8}} - a^{7} c \left(-\frac{c}{a^{9}}\right)^{\frac{3}{4}} + c^{2} x\right) + 8 \, a x \left(-\frac{c}{a^{9}}\right)^{\frac{1}{8}} \arctan\left(-\frac{a c \sqrt{x} \left(-\frac{c}{a^{9}}\right)^{\frac{1}{8}} - \sqrt{-a^{7} c \left(-\frac{c}{a^{9}}\right)^{\frac{3}{4}} + c^{2} x} a \left(-\frac{c}{a^{9}}\right)^{\frac{1}{8}}}{c}\right) - 2 \, a x \left(-\frac{c}{a^{9}}\right)^{\frac{1}{8}} \log\left(a^{8} \left(-\frac{c}{a^{9}}\right)^{\frac{7}{8}} + c \sqrt{x}\right) + 2 \, a x \left(-\frac{c}{a^{9}}\right)^{\frac{1}{8}} \log\left(-a^{8} \left(-\frac{c}{a^{9}}\right)^{\frac{7}{8}} + c \sqrt{x}\right) - 16 \, \sqrt{x}}{8 \, a x}"," ",0,"1/8*(4*sqrt(2)*a*x*(-c/a^9)^(1/8)*arctan(-(sqrt(2)*a*c*sqrt(x)*(-c/a^9)^(1/8) - sqrt(2)*sqrt(sqrt(2)*a^8*c*sqrt(x)*(-c/a^9)^(7/8) - a^7*c*(-c/a^9)^(3/4) + c^2*x)*a*(-c/a^9)^(1/8) - c)/c) + 4*sqrt(2)*a*x*(-c/a^9)^(1/8)*arctan(-(sqrt(2)*a*c*sqrt(x)*(-c/a^9)^(1/8) - sqrt(2)*sqrt(-sqrt(2)*a^8*c*sqrt(x)*(-c/a^9)^(7/8) - a^7*c*(-c/a^9)^(3/4) + c^2*x)*a*(-c/a^9)^(1/8) + c)/c) - sqrt(2)*a*x*(-c/a^9)^(1/8)*log(sqrt(2)*a^8*c*sqrt(x)*(-c/a^9)^(7/8) - a^7*c*(-c/a^9)^(3/4) + c^2*x) + sqrt(2)*a*x*(-c/a^9)^(1/8)*log(-sqrt(2)*a^8*c*sqrt(x)*(-c/a^9)^(7/8) - a^7*c*(-c/a^9)^(3/4) + c^2*x) + 8*a*x*(-c/a^9)^(1/8)*arctan(-(a*c*sqrt(x)*(-c/a^9)^(1/8) - sqrt(-a^7*c*(-c/a^9)^(3/4) + c^2*x)*a*(-c/a^9)^(1/8))/c) - 2*a*x*(-c/a^9)^(1/8)*log(a^8*(-c/a^9)^(7/8) + c*sqrt(x)) + 2*a*x*(-c/a^9)^(1/8)*log(-a^8*(-c/a^9)^(7/8) + c*sqrt(x)) - 16*sqrt(x))/(a*x)","B",0
745,1,553,0,0.932189," ","integrate(1/x^(5/2)/(c*x^4+a),x, algorithm=""fricas"")","-\frac{12 \, \sqrt{2} a x^{2} \left(-\frac{c^{3}}{a^{11}}\right)^{\frac{1}{8}} \arctan\left(-\frac{\sqrt{2} a^{4} c^{2} \sqrt{x} \left(-\frac{c^{3}}{a^{11}}\right)^{\frac{3}{8}} - \sqrt{2} \sqrt{\sqrt{2} a^{7} c^{2} \sqrt{x} \left(-\frac{c^{3}}{a^{11}}\right)^{\frac{5}{8}} - a^{3} c^{3} \left(-\frac{c^{3}}{a^{11}}\right)^{\frac{1}{4}} + c^{4} x} a^{4} \left(-\frac{c^{3}}{a^{11}}\right)^{\frac{3}{8}} - c^{3}}{c^{3}}\right) + 12 \, \sqrt{2} a x^{2} \left(-\frac{c^{3}}{a^{11}}\right)^{\frac{1}{8}} \arctan\left(-\frac{\sqrt{2} a^{4} c^{2} \sqrt{x} \left(-\frac{c^{3}}{a^{11}}\right)^{\frac{3}{8}} - \sqrt{2} \sqrt{-\sqrt{2} a^{7} c^{2} \sqrt{x} \left(-\frac{c^{3}}{a^{11}}\right)^{\frac{5}{8}} - a^{3} c^{3} \left(-\frac{c^{3}}{a^{11}}\right)^{\frac{1}{4}} + c^{4} x} a^{4} \left(-\frac{c^{3}}{a^{11}}\right)^{\frac{3}{8}} + c^{3}}{c^{3}}\right) + 3 \, \sqrt{2} a x^{2} \left(-\frac{c^{3}}{a^{11}}\right)^{\frac{1}{8}} \log\left(\sqrt{2} a^{7} c^{2} \sqrt{x} \left(-\frac{c^{3}}{a^{11}}\right)^{\frac{5}{8}} - a^{3} c^{3} \left(-\frac{c^{3}}{a^{11}}\right)^{\frac{1}{4}} + c^{4} x\right) - 3 \, \sqrt{2} a x^{2} \left(-\frac{c^{3}}{a^{11}}\right)^{\frac{1}{8}} \log\left(-\sqrt{2} a^{7} c^{2} \sqrt{x} \left(-\frac{c^{3}}{a^{11}}\right)^{\frac{5}{8}} - a^{3} c^{3} \left(-\frac{c^{3}}{a^{11}}\right)^{\frac{1}{4}} + c^{4} x\right) - 24 \, a x^{2} \left(-\frac{c^{3}}{a^{11}}\right)^{\frac{1}{8}} \arctan\left(-\frac{a^{4} c^{2} \sqrt{x} \left(-\frac{c^{3}}{a^{11}}\right)^{\frac{3}{8}} - \sqrt{-a^{3} c^{3} \left(-\frac{c^{3}}{a^{11}}\right)^{\frac{1}{4}} + c^{4} x} a^{4} \left(-\frac{c^{3}}{a^{11}}\right)^{\frac{3}{8}}}{c^{3}}\right) - 6 \, a x^{2} \left(-\frac{c^{3}}{a^{11}}\right)^{\frac{1}{8}} \log\left(a^{7} \left(-\frac{c^{3}}{a^{11}}\right)^{\frac{5}{8}} + c^{2} \sqrt{x}\right) + 6 \, a x^{2} \left(-\frac{c^{3}}{a^{11}}\right)^{\frac{1}{8}} \log\left(-a^{7} \left(-\frac{c^{3}}{a^{11}}\right)^{\frac{5}{8}} + c^{2} \sqrt{x}\right) + 16 \, \sqrt{x}}{24 \, a x^{2}}"," ",0,"-1/24*(12*sqrt(2)*a*x^2*(-c^3/a^11)^(1/8)*arctan(-(sqrt(2)*a^4*c^2*sqrt(x)*(-c^3/a^11)^(3/8) - sqrt(2)*sqrt(sqrt(2)*a^7*c^2*sqrt(x)*(-c^3/a^11)^(5/8) - a^3*c^3*(-c^3/a^11)^(1/4) + c^4*x)*a^4*(-c^3/a^11)^(3/8) - c^3)/c^3) + 12*sqrt(2)*a*x^2*(-c^3/a^11)^(1/8)*arctan(-(sqrt(2)*a^4*c^2*sqrt(x)*(-c^3/a^11)^(3/8) - sqrt(2)*sqrt(-sqrt(2)*a^7*c^2*sqrt(x)*(-c^3/a^11)^(5/8) - a^3*c^3*(-c^3/a^11)^(1/4) + c^4*x)*a^4*(-c^3/a^11)^(3/8) + c^3)/c^3) + 3*sqrt(2)*a*x^2*(-c^3/a^11)^(1/8)*log(sqrt(2)*a^7*c^2*sqrt(x)*(-c^3/a^11)^(5/8) - a^3*c^3*(-c^3/a^11)^(1/4) + c^4*x) - 3*sqrt(2)*a*x^2*(-c^3/a^11)^(1/8)*log(-sqrt(2)*a^7*c^2*sqrt(x)*(-c^3/a^11)^(5/8) - a^3*c^3*(-c^3/a^11)^(1/4) + c^4*x) - 24*a*x^2*(-c^3/a^11)^(1/8)*arctan(-(a^4*c^2*sqrt(x)*(-c^3/a^11)^(3/8) - sqrt(-a^3*c^3*(-c^3/a^11)^(1/4) + c^4*x)*a^4*(-c^3/a^11)^(3/8))/c^3) - 6*a*x^2*(-c^3/a^11)^(1/8)*log(a^7*(-c^3/a^11)^(5/8) + c^2*sqrt(x)) + 6*a*x^2*(-c^3/a^11)^(1/8)*log(-a^7*(-c^3/a^11)^(5/8) + c^2*sqrt(x)) + 16*sqrt(x))/(a*x^2)","B",0
746,1,535,0,0.895566," ","integrate(x^(13/2)/(c*x^4+a)^2,x, algorithm=""fricas"")","-\frac{16 \, x^{\frac{7}{2}} + 28 \, \sqrt{2} {\left(c^{2} x^{4} + a c\right)} \left(-\frac{1}{a c^{15}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{2} \sqrt{\sqrt{2} a c^{13} \sqrt{x} \left(-\frac{1}{a c^{15}}\right)^{\frac{7}{8}} - a c^{11} \left(-\frac{1}{a c^{15}}\right)^{\frac{3}{4}} + x} c^{2} \left(-\frac{1}{a c^{15}}\right)^{\frac{1}{8}} - \sqrt{2} c^{2} \sqrt{x} \left(-\frac{1}{a c^{15}}\right)^{\frac{1}{8}} + 1\right) + 28 \, \sqrt{2} {\left(c^{2} x^{4} + a c\right)} \left(-\frac{1}{a c^{15}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{2} \sqrt{-\sqrt{2} a c^{13} \sqrt{x} \left(-\frac{1}{a c^{15}}\right)^{\frac{7}{8}} - a c^{11} \left(-\frac{1}{a c^{15}}\right)^{\frac{3}{4}} + x} c^{2} \left(-\frac{1}{a c^{15}}\right)^{\frac{1}{8}} - \sqrt{2} c^{2} \sqrt{x} \left(-\frac{1}{a c^{15}}\right)^{\frac{1}{8}} - 1\right) - 7 \, \sqrt{2} {\left(c^{2} x^{4} + a c\right)} \left(-\frac{1}{a c^{15}}\right)^{\frac{1}{8}} \log\left(\sqrt{2} a c^{13} \sqrt{x} \left(-\frac{1}{a c^{15}}\right)^{\frac{7}{8}} - a c^{11} \left(-\frac{1}{a c^{15}}\right)^{\frac{3}{4}} + x\right) + 7 \, \sqrt{2} {\left(c^{2} x^{4} + a c\right)} \left(-\frac{1}{a c^{15}}\right)^{\frac{1}{8}} \log\left(-\sqrt{2} a c^{13} \sqrt{x} \left(-\frac{1}{a c^{15}}\right)^{\frac{7}{8}} - a c^{11} \left(-\frac{1}{a c^{15}}\right)^{\frac{3}{4}} + x\right) + 56 \, {\left(c^{2} x^{4} + a c\right)} \left(-\frac{1}{a c^{15}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{-a c^{11} \left(-\frac{1}{a c^{15}}\right)^{\frac{3}{4}} + x} c^{2} \left(-\frac{1}{a c^{15}}\right)^{\frac{1}{8}} - c^{2} \sqrt{x} \left(-\frac{1}{a c^{15}}\right)^{\frac{1}{8}}\right) - 14 \, {\left(c^{2} x^{4} + a c\right)} \left(-\frac{1}{a c^{15}}\right)^{\frac{1}{8}} \log\left(a c^{13} \left(-\frac{1}{a c^{15}}\right)^{\frac{7}{8}} + \sqrt{x}\right) + 14 \, {\left(c^{2} x^{4} + a c\right)} \left(-\frac{1}{a c^{15}}\right)^{\frac{1}{8}} \log\left(-a c^{13} \left(-\frac{1}{a c^{15}}\right)^{\frac{7}{8}} + \sqrt{x}\right)}{64 \, {\left(c^{2} x^{4} + a c\right)}}"," ",0,"-1/64*(16*x^(7/2) + 28*sqrt(2)*(c^2*x^4 + a*c)*(-1/(a*c^15))^(1/8)*arctan(sqrt(2)*sqrt(sqrt(2)*a*c^13*sqrt(x)*(-1/(a*c^15))^(7/8) - a*c^11*(-1/(a*c^15))^(3/4) + x)*c^2*(-1/(a*c^15))^(1/8) - sqrt(2)*c^2*sqrt(x)*(-1/(a*c^15))^(1/8) + 1) + 28*sqrt(2)*(c^2*x^4 + a*c)*(-1/(a*c^15))^(1/8)*arctan(sqrt(2)*sqrt(-sqrt(2)*a*c^13*sqrt(x)*(-1/(a*c^15))^(7/8) - a*c^11*(-1/(a*c^15))^(3/4) + x)*c^2*(-1/(a*c^15))^(1/8) - sqrt(2)*c^2*sqrt(x)*(-1/(a*c^15))^(1/8) - 1) - 7*sqrt(2)*(c^2*x^4 + a*c)*(-1/(a*c^15))^(1/8)*log(sqrt(2)*a*c^13*sqrt(x)*(-1/(a*c^15))^(7/8) - a*c^11*(-1/(a*c^15))^(3/4) + x) + 7*sqrt(2)*(c^2*x^4 + a*c)*(-1/(a*c^15))^(1/8)*log(-sqrt(2)*a*c^13*sqrt(x)*(-1/(a*c^15))^(7/8) - a*c^11*(-1/(a*c^15))^(3/4) + x) + 56*(c^2*x^4 + a*c)*(-1/(a*c^15))^(1/8)*arctan(sqrt(-a*c^11*(-1/(a*c^15))^(3/4) + x)*c^2*(-1/(a*c^15))^(1/8) - c^2*sqrt(x)*(-1/(a*c^15))^(1/8)) - 14*(c^2*x^4 + a*c)*(-1/(a*c^15))^(1/8)*log(a*c^13*(-1/(a*c^15))^(7/8) + sqrt(x)) + 14*(c^2*x^4 + a*c)*(-1/(a*c^15))^(1/8)*log(-a*c^13*(-1/(a*c^15))^(7/8) + sqrt(x)))/(c^2*x^4 + a*c)","B",0
747,1,553,0,0.813365," ","integrate(x^(11/2)/(c*x^4+a)^2,x, algorithm=""fricas"")","\frac{20 \, \sqrt{2} {\left(c^{2} x^{4} + a c\right)} \left(-\frac{1}{a^{3} c^{13}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{2} \sqrt{\sqrt{2} a^{2} c^{8} \sqrt{x} \left(-\frac{1}{a^{3} c^{13}}\right)^{\frac{5}{8}} - a c^{3} \left(-\frac{1}{a^{3} c^{13}}\right)^{\frac{1}{4}} + x} a c^{5} \left(-\frac{1}{a^{3} c^{13}}\right)^{\frac{3}{8}} - \sqrt{2} a c^{5} \sqrt{x} \left(-\frac{1}{a^{3} c^{13}}\right)^{\frac{3}{8}} + 1\right) + 20 \, \sqrt{2} {\left(c^{2} x^{4} + a c\right)} \left(-\frac{1}{a^{3} c^{13}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{2} \sqrt{-\sqrt{2} a^{2} c^{8} \sqrt{x} \left(-\frac{1}{a^{3} c^{13}}\right)^{\frac{5}{8}} - a c^{3} \left(-\frac{1}{a^{3} c^{13}}\right)^{\frac{1}{4}} + x} a c^{5} \left(-\frac{1}{a^{3} c^{13}}\right)^{\frac{3}{8}} - \sqrt{2} a c^{5} \sqrt{x} \left(-\frac{1}{a^{3} c^{13}}\right)^{\frac{3}{8}} - 1\right) + 5 \, \sqrt{2} {\left(c^{2} x^{4} + a c\right)} \left(-\frac{1}{a^{3} c^{13}}\right)^{\frac{1}{8}} \log\left(\sqrt{2} a^{2} c^{8} \sqrt{x} \left(-\frac{1}{a^{3} c^{13}}\right)^{\frac{5}{8}} - a c^{3} \left(-\frac{1}{a^{3} c^{13}}\right)^{\frac{1}{4}} + x\right) - 5 \, \sqrt{2} {\left(c^{2} x^{4} + a c\right)} \left(-\frac{1}{a^{3} c^{13}}\right)^{\frac{1}{8}} \log\left(-\sqrt{2} a^{2} c^{8} \sqrt{x} \left(-\frac{1}{a^{3} c^{13}}\right)^{\frac{5}{8}} - a c^{3} \left(-\frac{1}{a^{3} c^{13}}\right)^{\frac{1}{4}} + x\right) - 16 \, x^{\frac{5}{2}} - 40 \, {\left(c^{2} x^{4} + a c\right)} \left(-\frac{1}{a^{3} c^{13}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{-a c^{3} \left(-\frac{1}{a^{3} c^{13}}\right)^{\frac{1}{4}} + x} a c^{5} \left(-\frac{1}{a^{3} c^{13}}\right)^{\frac{3}{8}} - a c^{5} \sqrt{x} \left(-\frac{1}{a^{3} c^{13}}\right)^{\frac{3}{8}}\right) - 10 \, {\left(c^{2} x^{4} + a c\right)} \left(-\frac{1}{a^{3} c^{13}}\right)^{\frac{1}{8}} \log\left(a^{2} c^{8} \left(-\frac{1}{a^{3} c^{13}}\right)^{\frac{5}{8}} + \sqrt{x}\right) + 10 \, {\left(c^{2} x^{4} + a c\right)} \left(-\frac{1}{a^{3} c^{13}}\right)^{\frac{1}{8}} \log\left(-a^{2} c^{8} \left(-\frac{1}{a^{3} c^{13}}\right)^{\frac{5}{8}} + \sqrt{x}\right)}{64 \, {\left(c^{2} x^{4} + a c\right)}}"," ",0,"1/64*(20*sqrt(2)*(c^2*x^4 + a*c)*(-1/(a^3*c^13))^(1/8)*arctan(sqrt(2)*sqrt(sqrt(2)*a^2*c^8*sqrt(x)*(-1/(a^3*c^13))^(5/8) - a*c^3*(-1/(a^3*c^13))^(1/4) + x)*a*c^5*(-1/(a^3*c^13))^(3/8) - sqrt(2)*a*c^5*sqrt(x)*(-1/(a^3*c^13))^(3/8) + 1) + 20*sqrt(2)*(c^2*x^4 + a*c)*(-1/(a^3*c^13))^(1/8)*arctan(sqrt(2)*sqrt(-sqrt(2)*a^2*c^8*sqrt(x)*(-1/(a^3*c^13))^(5/8) - a*c^3*(-1/(a^3*c^13))^(1/4) + x)*a*c^5*(-1/(a^3*c^13))^(3/8) - sqrt(2)*a*c^5*sqrt(x)*(-1/(a^3*c^13))^(3/8) - 1) + 5*sqrt(2)*(c^2*x^4 + a*c)*(-1/(a^3*c^13))^(1/8)*log(sqrt(2)*a^2*c^8*sqrt(x)*(-1/(a^3*c^13))^(5/8) - a*c^3*(-1/(a^3*c^13))^(1/4) + x) - 5*sqrt(2)*(c^2*x^4 + a*c)*(-1/(a^3*c^13))^(1/8)*log(-sqrt(2)*a^2*c^8*sqrt(x)*(-1/(a^3*c^13))^(5/8) - a*c^3*(-1/(a^3*c^13))^(1/4) + x) - 16*x^(5/2) - 40*(c^2*x^4 + a*c)*(-1/(a^3*c^13))^(1/8)*arctan(sqrt(-a*c^3*(-1/(a^3*c^13))^(1/4) + x)*a*c^5*(-1/(a^3*c^13))^(3/8) - a*c^5*sqrt(x)*(-1/(a^3*c^13))^(3/8)) - 10*(c^2*x^4 + a*c)*(-1/(a^3*c^13))^(1/8)*log(a^2*c^8*(-1/(a^3*c^13))^(5/8) + sqrt(x)) + 10*(c^2*x^4 + a*c)*(-1/(a^3*c^13))^(1/8)*log(-a^2*c^8*(-1/(a^3*c^13))^(5/8) + sqrt(x)))/(c^2*x^4 + a*c)","B",0
748,1,570,0,0.892359," ","integrate(x^(9/2)/(c*x^4+a)^2,x, algorithm=""fricas"")","-\frac{12 \, \sqrt{2} {\left(c^{2} x^{4} + a c\right)} \left(-\frac{1}{a^{5} c^{11}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{2} \sqrt{a^{4} c^{8} \left(-\frac{1}{a^{5} c^{11}}\right)^{\frac{3}{4}} + \sqrt{2} a^{2} c^{4} \sqrt{x} \left(-\frac{1}{a^{5} c^{11}}\right)^{\frac{3}{8}} + x} a^{3} c^{7} \left(-\frac{1}{a^{5} c^{11}}\right)^{\frac{5}{8}} - \sqrt{2} a^{3} c^{7} \sqrt{x} \left(-\frac{1}{a^{5} c^{11}}\right)^{\frac{5}{8}} + 1\right) + 12 \, \sqrt{2} {\left(c^{2} x^{4} + a c\right)} \left(-\frac{1}{a^{5} c^{11}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{2} \sqrt{a^{4} c^{8} \left(-\frac{1}{a^{5} c^{11}}\right)^{\frac{3}{4}} - \sqrt{2} a^{2} c^{4} \sqrt{x} \left(-\frac{1}{a^{5} c^{11}}\right)^{\frac{3}{8}} + x} a^{3} c^{7} \left(-\frac{1}{a^{5} c^{11}}\right)^{\frac{5}{8}} - \sqrt{2} a^{3} c^{7} \sqrt{x} \left(-\frac{1}{a^{5} c^{11}}\right)^{\frac{5}{8}} - 1\right) - 3 \, \sqrt{2} {\left(c^{2} x^{4} + a c\right)} \left(-\frac{1}{a^{5} c^{11}}\right)^{\frac{1}{8}} \log\left(a^{4} c^{8} \left(-\frac{1}{a^{5} c^{11}}\right)^{\frac{3}{4}} + \sqrt{2} a^{2} c^{4} \sqrt{x} \left(-\frac{1}{a^{5} c^{11}}\right)^{\frac{3}{8}} + x\right) + 3 \, \sqrt{2} {\left(c^{2} x^{4} + a c\right)} \left(-\frac{1}{a^{5} c^{11}}\right)^{\frac{1}{8}} \log\left(a^{4} c^{8} \left(-\frac{1}{a^{5} c^{11}}\right)^{\frac{3}{4}} - \sqrt{2} a^{2} c^{4} \sqrt{x} \left(-\frac{1}{a^{5} c^{11}}\right)^{\frac{3}{8}} + x\right) - 24 \, {\left(c^{2} x^{4} + a c\right)} \left(-\frac{1}{a^{5} c^{11}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{a^{4} c^{8} \left(-\frac{1}{a^{5} c^{11}}\right)^{\frac{3}{4}} + x} a^{3} c^{7} \left(-\frac{1}{a^{5} c^{11}}\right)^{\frac{5}{8}} - a^{3} c^{7} \sqrt{x} \left(-\frac{1}{a^{5} c^{11}}\right)^{\frac{5}{8}}\right) + 6 \, {\left(c^{2} x^{4} + a c\right)} \left(-\frac{1}{a^{5} c^{11}}\right)^{\frac{1}{8}} \log\left(a^{2} c^{4} \left(-\frac{1}{a^{5} c^{11}}\right)^{\frac{3}{8}} + \sqrt{x}\right) - 6 \, {\left(c^{2} x^{4} + a c\right)} \left(-\frac{1}{a^{5} c^{11}}\right)^{\frac{1}{8}} \log\left(-a^{2} c^{4} \left(-\frac{1}{a^{5} c^{11}}\right)^{\frac{3}{8}} + \sqrt{x}\right) + 16 \, x^{\frac{3}{2}}}{64 \, {\left(c^{2} x^{4} + a c\right)}}"," ",0,"-1/64*(12*sqrt(2)*(c^2*x^4 + a*c)*(-1/(a^5*c^11))^(1/8)*arctan(sqrt(2)*sqrt(a^4*c^8*(-1/(a^5*c^11))^(3/4) + sqrt(2)*a^2*c^4*sqrt(x)*(-1/(a^5*c^11))^(3/8) + x)*a^3*c^7*(-1/(a^5*c^11))^(5/8) - sqrt(2)*a^3*c^7*sqrt(x)*(-1/(a^5*c^11))^(5/8) + 1) + 12*sqrt(2)*(c^2*x^4 + a*c)*(-1/(a^5*c^11))^(1/8)*arctan(sqrt(2)*sqrt(a^4*c^8*(-1/(a^5*c^11))^(3/4) - sqrt(2)*a^2*c^4*sqrt(x)*(-1/(a^5*c^11))^(3/8) + x)*a^3*c^7*(-1/(a^5*c^11))^(5/8) - sqrt(2)*a^3*c^7*sqrt(x)*(-1/(a^5*c^11))^(5/8) - 1) - 3*sqrt(2)*(c^2*x^4 + a*c)*(-1/(a^5*c^11))^(1/8)*log(a^4*c^8*(-1/(a^5*c^11))^(3/4) + sqrt(2)*a^2*c^4*sqrt(x)*(-1/(a^5*c^11))^(3/8) + x) + 3*sqrt(2)*(c^2*x^4 + a*c)*(-1/(a^5*c^11))^(1/8)*log(a^4*c^8*(-1/(a^5*c^11))^(3/4) - sqrt(2)*a^2*c^4*sqrt(x)*(-1/(a^5*c^11))^(3/8) + x) - 24*(c^2*x^4 + a*c)*(-1/(a^5*c^11))^(1/8)*arctan(sqrt(a^4*c^8*(-1/(a^5*c^11))^(3/4) + x)*a^3*c^7*(-1/(a^5*c^11))^(5/8) - a^3*c^7*sqrt(x)*(-1/(a^5*c^11))^(5/8)) + 6*(c^2*x^4 + a*c)*(-1/(a^5*c^11))^(1/8)*log(a^2*c^4*(-1/(a^5*c^11))^(3/8) + sqrt(x)) - 6*(c^2*x^4 + a*c)*(-1/(a^5*c^11))^(1/8)*log(-a^2*c^4*(-1/(a^5*c^11))^(3/8) + sqrt(x)) + 16*x^(3/2))/(c^2*x^4 + a*c)","B",0
749,1,545,0,0.917701," ","integrate(x^(7/2)/(c*x^4+a)^2,x, algorithm=""fricas"")","\frac{4 \, \sqrt{2} {\left(c^{2} x^{4} + a c\right)} \left(-\frac{1}{a^{7} c^{9}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{2} \sqrt{a^{2} c^{2} \left(-\frac{1}{a^{7} c^{9}}\right)^{\frac{1}{4}} + \sqrt{2} a c \sqrt{x} \left(-\frac{1}{a^{7} c^{9}}\right)^{\frac{1}{8}} + x} a^{6} c^{8} \left(-\frac{1}{a^{7} c^{9}}\right)^{\frac{7}{8}} - \sqrt{2} a^{6} c^{8} \sqrt{x} \left(-\frac{1}{a^{7} c^{9}}\right)^{\frac{7}{8}} + 1\right) + 4 \, \sqrt{2} {\left(c^{2} x^{4} + a c\right)} \left(-\frac{1}{a^{7} c^{9}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{2} \sqrt{a^{2} c^{2} \left(-\frac{1}{a^{7} c^{9}}\right)^{\frac{1}{4}} - \sqrt{2} a c \sqrt{x} \left(-\frac{1}{a^{7} c^{9}}\right)^{\frac{1}{8}} + x} a^{6} c^{8} \left(-\frac{1}{a^{7} c^{9}}\right)^{\frac{7}{8}} - \sqrt{2} a^{6} c^{8} \sqrt{x} \left(-\frac{1}{a^{7} c^{9}}\right)^{\frac{7}{8}} - 1\right) + \sqrt{2} {\left(c^{2} x^{4} + a c\right)} \left(-\frac{1}{a^{7} c^{9}}\right)^{\frac{1}{8}} \log\left(a^{2} c^{2} \left(-\frac{1}{a^{7} c^{9}}\right)^{\frac{1}{4}} + \sqrt{2} a c \sqrt{x} \left(-\frac{1}{a^{7} c^{9}}\right)^{\frac{1}{8}} + x\right) - \sqrt{2} {\left(c^{2} x^{4} + a c\right)} \left(-\frac{1}{a^{7} c^{9}}\right)^{\frac{1}{8}} \log\left(a^{2} c^{2} \left(-\frac{1}{a^{7} c^{9}}\right)^{\frac{1}{4}} - \sqrt{2} a c \sqrt{x} \left(-\frac{1}{a^{7} c^{9}}\right)^{\frac{1}{8}} + x\right) + 8 \, {\left(c^{2} x^{4} + a c\right)} \left(-\frac{1}{a^{7} c^{9}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{a^{2} c^{2} \left(-\frac{1}{a^{7} c^{9}}\right)^{\frac{1}{4}} + x} a^{6} c^{8} \left(-\frac{1}{a^{7} c^{9}}\right)^{\frac{7}{8}} - a^{6} c^{8} \sqrt{x} \left(-\frac{1}{a^{7} c^{9}}\right)^{\frac{7}{8}}\right) + 2 \, {\left(c^{2} x^{4} + a c\right)} \left(-\frac{1}{a^{7} c^{9}}\right)^{\frac{1}{8}} \log\left(a c \left(-\frac{1}{a^{7} c^{9}}\right)^{\frac{1}{8}} + \sqrt{x}\right) - 2 \, {\left(c^{2} x^{4} + a c\right)} \left(-\frac{1}{a^{7} c^{9}}\right)^{\frac{1}{8}} \log\left(-a c \left(-\frac{1}{a^{7} c^{9}}\right)^{\frac{1}{8}} + \sqrt{x}\right) - 16 \, \sqrt{x}}{64 \, {\left(c^{2} x^{4} + a c\right)}}"," ",0,"1/64*(4*sqrt(2)*(c^2*x^4 + a*c)*(-1/(a^7*c^9))^(1/8)*arctan(sqrt(2)*sqrt(a^2*c^2*(-1/(a^7*c^9))^(1/4) + sqrt(2)*a*c*sqrt(x)*(-1/(a^7*c^9))^(1/8) + x)*a^6*c^8*(-1/(a^7*c^9))^(7/8) - sqrt(2)*a^6*c^8*sqrt(x)*(-1/(a^7*c^9))^(7/8) + 1) + 4*sqrt(2)*(c^2*x^4 + a*c)*(-1/(a^7*c^9))^(1/8)*arctan(sqrt(2)*sqrt(a^2*c^2*(-1/(a^7*c^9))^(1/4) - sqrt(2)*a*c*sqrt(x)*(-1/(a^7*c^9))^(1/8) + x)*a^6*c^8*(-1/(a^7*c^9))^(7/8) - sqrt(2)*a^6*c^8*sqrt(x)*(-1/(a^7*c^9))^(7/8) - 1) + sqrt(2)*(c^2*x^4 + a*c)*(-1/(a^7*c^9))^(1/8)*log(a^2*c^2*(-1/(a^7*c^9))^(1/4) + sqrt(2)*a*c*sqrt(x)*(-1/(a^7*c^9))^(1/8) + x) - sqrt(2)*(c^2*x^4 + a*c)*(-1/(a^7*c^9))^(1/8)*log(a^2*c^2*(-1/(a^7*c^9))^(1/4) - sqrt(2)*a*c*sqrt(x)*(-1/(a^7*c^9))^(1/8) + x) + 8*(c^2*x^4 + a*c)*(-1/(a^7*c^9))^(1/8)*arctan(sqrt(a^2*c^2*(-1/(a^7*c^9))^(1/4) + x)*a^6*c^8*(-1/(a^7*c^9))^(7/8) - a^6*c^8*sqrt(x)*(-1/(a^7*c^9))^(7/8)) + 2*(c^2*x^4 + a*c)*(-1/(a^7*c^9))^(1/8)*log(a*c*(-1/(a^7*c^9))^(1/8) + sqrt(x)) - 2*(c^2*x^4 + a*c)*(-1/(a^7*c^9))^(1/8)*log(-a*c*(-1/(a^7*c^9))^(1/8) + sqrt(x)) - 16*sqrt(x))/(c^2*x^4 + a*c)","B",0
750,1,542,0,0.797120," ","integrate(x^(5/2)/(c*x^4+a)^2,x, algorithm=""fricas"")","\frac{16 \, x^{\frac{7}{2}} - 4 \, \sqrt{2} {\left(a c x^{4} + a^{2}\right)} \left(-\frac{1}{a^{9} c^{7}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{2} \sqrt{\sqrt{2} a^{8} c^{6} \sqrt{x} \left(-\frac{1}{a^{9} c^{7}}\right)^{\frac{7}{8}} - a^{7} c^{5} \left(-\frac{1}{a^{9} c^{7}}\right)^{\frac{3}{4}} + x} a c \left(-\frac{1}{a^{9} c^{7}}\right)^{\frac{1}{8}} - \sqrt{2} a c \sqrt{x} \left(-\frac{1}{a^{9} c^{7}}\right)^{\frac{1}{8}} + 1\right) - 4 \, \sqrt{2} {\left(a c x^{4} + a^{2}\right)} \left(-\frac{1}{a^{9} c^{7}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{2} \sqrt{-\sqrt{2} a^{8} c^{6} \sqrt{x} \left(-\frac{1}{a^{9} c^{7}}\right)^{\frac{7}{8}} - a^{7} c^{5} \left(-\frac{1}{a^{9} c^{7}}\right)^{\frac{3}{4}} + x} a c \left(-\frac{1}{a^{9} c^{7}}\right)^{\frac{1}{8}} - \sqrt{2} a c \sqrt{x} \left(-\frac{1}{a^{9} c^{7}}\right)^{\frac{1}{8}} - 1\right) + \sqrt{2} {\left(a c x^{4} + a^{2}\right)} \left(-\frac{1}{a^{9} c^{7}}\right)^{\frac{1}{8}} \log\left(\sqrt{2} a^{8} c^{6} \sqrt{x} \left(-\frac{1}{a^{9} c^{7}}\right)^{\frac{7}{8}} - a^{7} c^{5} \left(-\frac{1}{a^{9} c^{7}}\right)^{\frac{3}{4}} + x\right) - \sqrt{2} {\left(a c x^{4} + a^{2}\right)} \left(-\frac{1}{a^{9} c^{7}}\right)^{\frac{1}{8}} \log\left(-\sqrt{2} a^{8} c^{6} \sqrt{x} \left(-\frac{1}{a^{9} c^{7}}\right)^{\frac{7}{8}} - a^{7} c^{5} \left(-\frac{1}{a^{9} c^{7}}\right)^{\frac{3}{4}} + x\right) - 8 \, {\left(a c x^{4} + a^{2}\right)} \left(-\frac{1}{a^{9} c^{7}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{-a^{7} c^{5} \left(-\frac{1}{a^{9} c^{7}}\right)^{\frac{3}{4}} + x} a c \left(-\frac{1}{a^{9} c^{7}}\right)^{\frac{1}{8}} - a c \sqrt{x} \left(-\frac{1}{a^{9} c^{7}}\right)^{\frac{1}{8}}\right) + 2 \, {\left(a c x^{4} + a^{2}\right)} \left(-\frac{1}{a^{9} c^{7}}\right)^{\frac{1}{8}} \log\left(a^{8} c^{6} \left(-\frac{1}{a^{9} c^{7}}\right)^{\frac{7}{8}} + \sqrt{x}\right) - 2 \, {\left(a c x^{4} + a^{2}\right)} \left(-\frac{1}{a^{9} c^{7}}\right)^{\frac{1}{8}} \log\left(-a^{8} c^{6} \left(-\frac{1}{a^{9} c^{7}}\right)^{\frac{7}{8}} + \sqrt{x}\right)}{64 \, {\left(a c x^{4} + a^{2}\right)}}"," ",0,"1/64*(16*x^(7/2) - 4*sqrt(2)*(a*c*x^4 + a^2)*(-1/(a^9*c^7))^(1/8)*arctan(sqrt(2)*sqrt(sqrt(2)*a^8*c^6*sqrt(x)*(-1/(a^9*c^7))^(7/8) - a^7*c^5*(-1/(a^9*c^7))^(3/4) + x)*a*c*(-1/(a^9*c^7))^(1/8) - sqrt(2)*a*c*sqrt(x)*(-1/(a^9*c^7))^(1/8) + 1) - 4*sqrt(2)*(a*c*x^4 + a^2)*(-1/(a^9*c^7))^(1/8)*arctan(sqrt(2)*sqrt(-sqrt(2)*a^8*c^6*sqrt(x)*(-1/(a^9*c^7))^(7/8) - a^7*c^5*(-1/(a^9*c^7))^(3/4) + x)*a*c*(-1/(a^9*c^7))^(1/8) - sqrt(2)*a*c*sqrt(x)*(-1/(a^9*c^7))^(1/8) - 1) + sqrt(2)*(a*c*x^4 + a^2)*(-1/(a^9*c^7))^(1/8)*log(sqrt(2)*a^8*c^6*sqrt(x)*(-1/(a^9*c^7))^(7/8) - a^7*c^5*(-1/(a^9*c^7))^(3/4) + x) - sqrt(2)*(a*c*x^4 + a^2)*(-1/(a^9*c^7))^(1/8)*log(-sqrt(2)*a^8*c^6*sqrt(x)*(-1/(a^9*c^7))^(7/8) - a^7*c^5*(-1/(a^9*c^7))^(3/4) + x) - 8*(a*c*x^4 + a^2)*(-1/(a^9*c^7))^(1/8)*arctan(sqrt(-a^7*c^5*(-1/(a^9*c^7))^(3/4) + x)*a*c*(-1/(a^9*c^7))^(1/8) - a*c*sqrt(x)*(-1/(a^9*c^7))^(1/8)) + 2*(a*c*x^4 + a^2)*(-1/(a^9*c^7))^(1/8)*log(a^8*c^6*(-1/(a^9*c^7))^(7/8) + sqrt(x)) - 2*(a*c*x^4 + a^2)*(-1/(a^9*c^7))^(1/8)*log(-a^8*c^6*(-1/(a^9*c^7))^(7/8) + sqrt(x)))/(a*c*x^4 + a^2)","B",0
751,1,557,0,0.830718," ","integrate(x^(3/2)/(c*x^4+a)^2,x, algorithm=""fricas"")","\frac{12 \, \sqrt{2} {\left(a c x^{4} + a^{2}\right)} \left(-\frac{1}{a^{11} c^{5}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{2} \sqrt{\sqrt{2} a^{7} c^{3} \sqrt{x} \left(-\frac{1}{a^{11} c^{5}}\right)^{\frac{5}{8}} - a^{3} c \left(-\frac{1}{a^{11} c^{5}}\right)^{\frac{1}{4}} + x} a^{4} c^{2} \left(-\frac{1}{a^{11} c^{5}}\right)^{\frac{3}{8}} - \sqrt{2} a^{4} c^{2} \sqrt{x} \left(-\frac{1}{a^{11} c^{5}}\right)^{\frac{3}{8}} + 1\right) + 12 \, \sqrt{2} {\left(a c x^{4} + a^{2}\right)} \left(-\frac{1}{a^{11} c^{5}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{2} \sqrt{-\sqrt{2} a^{7} c^{3} \sqrt{x} \left(-\frac{1}{a^{11} c^{5}}\right)^{\frac{5}{8}} - a^{3} c \left(-\frac{1}{a^{11} c^{5}}\right)^{\frac{1}{4}} + x} a^{4} c^{2} \left(-\frac{1}{a^{11} c^{5}}\right)^{\frac{3}{8}} - \sqrt{2} a^{4} c^{2} \sqrt{x} \left(-\frac{1}{a^{11} c^{5}}\right)^{\frac{3}{8}} - 1\right) + 3 \, \sqrt{2} {\left(a c x^{4} + a^{2}\right)} \left(-\frac{1}{a^{11} c^{5}}\right)^{\frac{1}{8}} \log\left(\sqrt{2} a^{7} c^{3} \sqrt{x} \left(-\frac{1}{a^{11} c^{5}}\right)^{\frac{5}{8}} - a^{3} c \left(-\frac{1}{a^{11} c^{5}}\right)^{\frac{1}{4}} + x\right) - 3 \, \sqrt{2} {\left(a c x^{4} + a^{2}\right)} \left(-\frac{1}{a^{11} c^{5}}\right)^{\frac{1}{8}} \log\left(-\sqrt{2} a^{7} c^{3} \sqrt{x} \left(-\frac{1}{a^{11} c^{5}}\right)^{\frac{5}{8}} - a^{3} c \left(-\frac{1}{a^{11} c^{5}}\right)^{\frac{1}{4}} + x\right) + 16 \, x^{\frac{5}{2}} - 24 \, {\left(a c x^{4} + a^{2}\right)} \left(-\frac{1}{a^{11} c^{5}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{-a^{3} c \left(-\frac{1}{a^{11} c^{5}}\right)^{\frac{1}{4}} + x} a^{4} c^{2} \left(-\frac{1}{a^{11} c^{5}}\right)^{\frac{3}{8}} - a^{4} c^{2} \sqrt{x} \left(-\frac{1}{a^{11} c^{5}}\right)^{\frac{3}{8}}\right) - 6 \, {\left(a c x^{4} + a^{2}\right)} \left(-\frac{1}{a^{11} c^{5}}\right)^{\frac{1}{8}} \log\left(a^{7} c^{3} \left(-\frac{1}{a^{11} c^{5}}\right)^{\frac{5}{8}} + \sqrt{x}\right) + 6 \, {\left(a c x^{4} + a^{2}\right)} \left(-\frac{1}{a^{11} c^{5}}\right)^{\frac{1}{8}} \log\left(-a^{7} c^{3} \left(-\frac{1}{a^{11} c^{5}}\right)^{\frac{5}{8}} + \sqrt{x}\right)}{64 \, {\left(a c x^{4} + a^{2}\right)}}"," ",0,"1/64*(12*sqrt(2)*(a*c*x^4 + a^2)*(-1/(a^11*c^5))^(1/8)*arctan(sqrt(2)*sqrt(sqrt(2)*a^7*c^3*sqrt(x)*(-1/(a^11*c^5))^(5/8) - a^3*c*(-1/(a^11*c^5))^(1/4) + x)*a^4*c^2*(-1/(a^11*c^5))^(3/8) - sqrt(2)*a^4*c^2*sqrt(x)*(-1/(a^11*c^5))^(3/8) + 1) + 12*sqrt(2)*(a*c*x^4 + a^2)*(-1/(a^11*c^5))^(1/8)*arctan(sqrt(2)*sqrt(-sqrt(2)*a^7*c^3*sqrt(x)*(-1/(a^11*c^5))^(5/8) - a^3*c*(-1/(a^11*c^5))^(1/4) + x)*a^4*c^2*(-1/(a^11*c^5))^(3/8) - sqrt(2)*a^4*c^2*sqrt(x)*(-1/(a^11*c^5))^(3/8) - 1) + 3*sqrt(2)*(a*c*x^4 + a^2)*(-1/(a^11*c^5))^(1/8)*log(sqrt(2)*a^7*c^3*sqrt(x)*(-1/(a^11*c^5))^(5/8) - a^3*c*(-1/(a^11*c^5))^(1/4) + x) - 3*sqrt(2)*(a*c*x^4 + a^2)*(-1/(a^11*c^5))^(1/8)*log(-sqrt(2)*a^7*c^3*sqrt(x)*(-1/(a^11*c^5))^(5/8) - a^3*c*(-1/(a^11*c^5))^(1/4) + x) + 16*x^(5/2) - 24*(a*c*x^4 + a^2)*(-1/(a^11*c^5))^(1/8)*arctan(sqrt(-a^3*c*(-1/(a^11*c^5))^(1/4) + x)*a^4*c^2*(-1/(a^11*c^5))^(3/8) - a^4*c^2*sqrt(x)*(-1/(a^11*c^5))^(3/8)) - 6*(a*c*x^4 + a^2)*(-1/(a^11*c^5))^(1/8)*log(a^7*c^3*(-1/(a^11*c^5))^(5/8) + sqrt(x)) + 6*(a*c*x^4 + a^2)*(-1/(a^11*c^5))^(1/8)*log(-a^7*c^3*(-1/(a^11*c^5))^(5/8) + sqrt(x)))/(a*c*x^4 + a^2)","B",0
752,1,550,0,0.892729," ","integrate(x^(1/2)/(c*x^4+a)^2,x, algorithm=""fricas"")","-\frac{20 \, \sqrt{2} {\left(a c x^{4} + a^{2}\right)} \left(-\frac{1}{a^{13} c^{3}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{2} \sqrt{a^{10} c^{2} \left(-\frac{1}{a^{13} c^{3}}\right)^{\frac{3}{4}} + \sqrt{2} a^{5} c \sqrt{x} \left(-\frac{1}{a^{13} c^{3}}\right)^{\frac{3}{8}} + x} a^{8} c^{2} \left(-\frac{1}{a^{13} c^{3}}\right)^{\frac{5}{8}} - \sqrt{2} a^{8} c^{2} \sqrt{x} \left(-\frac{1}{a^{13} c^{3}}\right)^{\frac{5}{8}} + 1\right) + 20 \, \sqrt{2} {\left(a c x^{4} + a^{2}\right)} \left(-\frac{1}{a^{13} c^{3}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{2} \sqrt{a^{10} c^{2} \left(-\frac{1}{a^{13} c^{3}}\right)^{\frac{3}{4}} - \sqrt{2} a^{5} c \sqrt{x} \left(-\frac{1}{a^{13} c^{3}}\right)^{\frac{3}{8}} + x} a^{8} c^{2} \left(-\frac{1}{a^{13} c^{3}}\right)^{\frac{5}{8}} - \sqrt{2} a^{8} c^{2} \sqrt{x} \left(-\frac{1}{a^{13} c^{3}}\right)^{\frac{5}{8}} - 1\right) - 5 \, \sqrt{2} {\left(a c x^{4} + a^{2}\right)} \left(-\frac{1}{a^{13} c^{3}}\right)^{\frac{1}{8}} \log\left(a^{10} c^{2} \left(-\frac{1}{a^{13} c^{3}}\right)^{\frac{3}{4}} + \sqrt{2} a^{5} c \sqrt{x} \left(-\frac{1}{a^{13} c^{3}}\right)^{\frac{3}{8}} + x\right) + 5 \, \sqrt{2} {\left(a c x^{4} + a^{2}\right)} \left(-\frac{1}{a^{13} c^{3}}\right)^{\frac{1}{8}} \log\left(a^{10} c^{2} \left(-\frac{1}{a^{13} c^{3}}\right)^{\frac{3}{4}} - \sqrt{2} a^{5} c \sqrt{x} \left(-\frac{1}{a^{13} c^{3}}\right)^{\frac{3}{8}} + x\right) - 40 \, {\left(a c x^{4} + a^{2}\right)} \left(-\frac{1}{a^{13} c^{3}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{a^{10} c^{2} \left(-\frac{1}{a^{13} c^{3}}\right)^{\frac{3}{4}} + x} a^{8} c^{2} \left(-\frac{1}{a^{13} c^{3}}\right)^{\frac{5}{8}} - a^{8} c^{2} \sqrt{x} \left(-\frac{1}{a^{13} c^{3}}\right)^{\frac{5}{8}}\right) + 10 \, {\left(a c x^{4} + a^{2}\right)} \left(-\frac{1}{a^{13} c^{3}}\right)^{\frac{1}{8}} \log\left(a^{5} c \left(-\frac{1}{a^{13} c^{3}}\right)^{\frac{3}{8}} + \sqrt{x}\right) - 10 \, {\left(a c x^{4} + a^{2}\right)} \left(-\frac{1}{a^{13} c^{3}}\right)^{\frac{1}{8}} \log\left(-a^{5} c \left(-\frac{1}{a^{13} c^{3}}\right)^{\frac{3}{8}} + \sqrt{x}\right) - 16 \, x^{\frac{3}{2}}}{64 \, {\left(a c x^{4} + a^{2}\right)}}"," ",0,"-1/64*(20*sqrt(2)*(a*c*x^4 + a^2)*(-1/(a^13*c^3))^(1/8)*arctan(sqrt(2)*sqrt(a^10*c^2*(-1/(a^13*c^3))^(3/4) + sqrt(2)*a^5*c*sqrt(x)*(-1/(a^13*c^3))^(3/8) + x)*a^8*c^2*(-1/(a^13*c^3))^(5/8) - sqrt(2)*a^8*c^2*sqrt(x)*(-1/(a^13*c^3))^(5/8) + 1) + 20*sqrt(2)*(a*c*x^4 + a^2)*(-1/(a^13*c^3))^(1/8)*arctan(sqrt(2)*sqrt(a^10*c^2*(-1/(a^13*c^3))^(3/4) - sqrt(2)*a^5*c*sqrt(x)*(-1/(a^13*c^3))^(3/8) + x)*a^8*c^2*(-1/(a^13*c^3))^(5/8) - sqrt(2)*a^8*c^2*sqrt(x)*(-1/(a^13*c^3))^(5/8) - 1) - 5*sqrt(2)*(a*c*x^4 + a^2)*(-1/(a^13*c^3))^(1/8)*log(a^10*c^2*(-1/(a^13*c^3))^(3/4) + sqrt(2)*a^5*c*sqrt(x)*(-1/(a^13*c^3))^(3/8) + x) + 5*sqrt(2)*(a*c*x^4 + a^2)*(-1/(a^13*c^3))^(1/8)*log(a^10*c^2*(-1/(a^13*c^3))^(3/4) - sqrt(2)*a^5*c*sqrt(x)*(-1/(a^13*c^3))^(3/8) + x) - 40*(a*c*x^4 + a^2)*(-1/(a^13*c^3))^(1/8)*arctan(sqrt(a^10*c^2*(-1/(a^13*c^3))^(3/4) + x)*a^8*c^2*(-1/(a^13*c^3))^(5/8) - a^8*c^2*sqrt(x)*(-1/(a^13*c^3))^(5/8)) + 10*(a*c*x^4 + a^2)*(-1/(a^13*c^3))^(1/8)*log(a^5*c*(-1/(a^13*c^3))^(3/8) + sqrt(x)) - 10*(a*c*x^4 + a^2)*(-1/(a^13*c^3))^(1/8)*log(-a^5*c*(-1/(a^13*c^3))^(3/8) + sqrt(x)) - 16*x^(3/2))/(a*c*x^4 + a^2)","B",0
753,1,517,0,0.876062," ","integrate(1/(c*x^4+a)^2/x^(1/2),x, algorithm=""fricas"")","\frac{28 \, \sqrt{2} {\left(a c x^{4} + a^{2}\right)} \left(-\frac{1}{a^{15} c}\right)^{\frac{1}{8}} \arctan\left(\sqrt{2} \sqrt{a^{4} \left(-\frac{1}{a^{15} c}\right)^{\frac{1}{4}} + \sqrt{2} a^{2} \sqrt{x} \left(-\frac{1}{a^{15} c}\right)^{\frac{1}{8}} + x} a^{13} c \left(-\frac{1}{a^{15} c}\right)^{\frac{7}{8}} - \sqrt{2} a^{13} c \sqrt{x} \left(-\frac{1}{a^{15} c}\right)^{\frac{7}{8}} + 1\right) + 28 \, \sqrt{2} {\left(a c x^{4} + a^{2}\right)} \left(-\frac{1}{a^{15} c}\right)^{\frac{1}{8}} \arctan\left(\sqrt{2} \sqrt{a^{4} \left(-\frac{1}{a^{15} c}\right)^{\frac{1}{4}} - \sqrt{2} a^{2} \sqrt{x} \left(-\frac{1}{a^{15} c}\right)^{\frac{1}{8}} + x} a^{13} c \left(-\frac{1}{a^{15} c}\right)^{\frac{7}{8}} - \sqrt{2} a^{13} c \sqrt{x} \left(-\frac{1}{a^{15} c}\right)^{\frac{7}{8}} - 1\right) + 7 \, \sqrt{2} {\left(a c x^{4} + a^{2}\right)} \left(-\frac{1}{a^{15} c}\right)^{\frac{1}{8}} \log\left(a^{4} \left(-\frac{1}{a^{15} c}\right)^{\frac{1}{4}} + \sqrt{2} a^{2} \sqrt{x} \left(-\frac{1}{a^{15} c}\right)^{\frac{1}{8}} + x\right) - 7 \, \sqrt{2} {\left(a c x^{4} + a^{2}\right)} \left(-\frac{1}{a^{15} c}\right)^{\frac{1}{8}} \log\left(a^{4} \left(-\frac{1}{a^{15} c}\right)^{\frac{1}{4}} - \sqrt{2} a^{2} \sqrt{x} \left(-\frac{1}{a^{15} c}\right)^{\frac{1}{8}} + x\right) + 56 \, {\left(a c x^{4} + a^{2}\right)} \left(-\frac{1}{a^{15} c}\right)^{\frac{1}{8}} \arctan\left(\sqrt{a^{4} \left(-\frac{1}{a^{15} c}\right)^{\frac{1}{4}} + x} a^{13} c \left(-\frac{1}{a^{15} c}\right)^{\frac{7}{8}} - a^{13} c \sqrt{x} \left(-\frac{1}{a^{15} c}\right)^{\frac{7}{8}}\right) + 14 \, {\left(a c x^{4} + a^{2}\right)} \left(-\frac{1}{a^{15} c}\right)^{\frac{1}{8}} \log\left(a^{2} \left(-\frac{1}{a^{15} c}\right)^{\frac{1}{8}} + \sqrt{x}\right) - 14 \, {\left(a c x^{4} + a^{2}\right)} \left(-\frac{1}{a^{15} c}\right)^{\frac{1}{8}} \log\left(-a^{2} \left(-\frac{1}{a^{15} c}\right)^{\frac{1}{8}} + \sqrt{x}\right) + 16 \, \sqrt{x}}{64 \, {\left(a c x^{4} + a^{2}\right)}}"," ",0,"1/64*(28*sqrt(2)*(a*c*x^4 + a^2)*(-1/(a^15*c))^(1/8)*arctan(sqrt(2)*sqrt(a^4*(-1/(a^15*c))^(1/4) + sqrt(2)*a^2*sqrt(x)*(-1/(a^15*c))^(1/8) + x)*a^13*c*(-1/(a^15*c))^(7/8) - sqrt(2)*a^13*c*sqrt(x)*(-1/(a^15*c))^(7/8) + 1) + 28*sqrt(2)*(a*c*x^4 + a^2)*(-1/(a^15*c))^(1/8)*arctan(sqrt(2)*sqrt(a^4*(-1/(a^15*c))^(1/4) - sqrt(2)*a^2*sqrt(x)*(-1/(a^15*c))^(1/8) + x)*a^13*c*(-1/(a^15*c))^(7/8) - sqrt(2)*a^13*c*sqrt(x)*(-1/(a^15*c))^(7/8) - 1) + 7*sqrt(2)*(a*c*x^4 + a^2)*(-1/(a^15*c))^(1/8)*log(a^4*(-1/(a^15*c))^(1/4) + sqrt(2)*a^2*sqrt(x)*(-1/(a^15*c))^(1/8) + x) - 7*sqrt(2)*(a*c*x^4 + a^2)*(-1/(a^15*c))^(1/8)*log(a^4*(-1/(a^15*c))^(1/4) - sqrt(2)*a^2*sqrt(x)*(-1/(a^15*c))^(1/8) + x) + 56*(a*c*x^4 + a^2)*(-1/(a^15*c))^(1/8)*arctan(sqrt(a^4*(-1/(a^15*c))^(1/4) + x)*a^13*c*(-1/(a^15*c))^(7/8) - a^13*c*sqrt(x)*(-1/(a^15*c))^(7/8)) + 14*(a*c*x^4 + a^2)*(-1/(a^15*c))^(1/8)*log(a^2*(-1/(a^15*c))^(1/8) + sqrt(x)) - 14*(a*c*x^4 + a^2)*(-1/(a^15*c))^(1/8)*log(-a^2*(-1/(a^15*c))^(1/8) + sqrt(x)) + 16*sqrt(x))/(a*c*x^4 + a^2)","B",0
754,1,575,0,0.935513," ","integrate(1/x^(3/2)/(c*x^4+a)^2,x, algorithm=""fricas"")","\frac{36 \, \sqrt{2} {\left(a^{2} c x^{5} + a^{3} x\right)} \left(-\frac{c}{a^{17}}\right)^{\frac{1}{8}} \arctan\left(-\frac{4782969 \, \sqrt{2} a^{2} c \sqrt{x} \left(-\frac{c}{a^{17}}\right)^{\frac{1}{8}} - \sqrt{2} \sqrt{-22876792454961 \, \sqrt{2} a^{15} c \sqrt{x} \left(-\frac{c}{a^{17}}\right)^{\frac{7}{8}} - 22876792454961 \, a^{13} c \left(-\frac{c}{a^{17}}\right)^{\frac{3}{4}} + 22876792454961 \, c^{2} x} a^{2} \left(-\frac{c}{a^{17}}\right)^{\frac{1}{8}} + 4782969 \, c}{4782969 \, c}\right) + 36 \, \sqrt{2} {\left(a^{2} c x^{5} + a^{3} x\right)} \left(-\frac{c}{a^{17}}\right)^{\frac{1}{8}} \arctan\left(-\frac{\sqrt{2} a^{2} c \sqrt{x} \left(-\frac{c}{a^{17}}\right)^{\frac{1}{8}} - \sqrt{2} \sqrt{\sqrt{2} a^{15} c \sqrt{x} \left(-\frac{c}{a^{17}}\right)^{\frac{7}{8}} - a^{13} c \left(-\frac{c}{a^{17}}\right)^{\frac{3}{4}} + c^{2} x} a^{2} \left(-\frac{c}{a^{17}}\right)^{\frac{1}{8}} - c}{c}\right) - 9 \, \sqrt{2} {\left(a^{2} c x^{5} + a^{3} x\right)} \left(-\frac{c}{a^{17}}\right)^{\frac{1}{8}} \log\left(22876792454961 \, \sqrt{2} a^{15} c \sqrt{x} \left(-\frac{c}{a^{17}}\right)^{\frac{7}{8}} - 22876792454961 \, a^{13} c \left(-\frac{c}{a^{17}}\right)^{\frac{3}{4}} + 22876792454961 \, c^{2} x\right) + 9 \, \sqrt{2} {\left(a^{2} c x^{5} + a^{3} x\right)} \left(-\frac{c}{a^{17}}\right)^{\frac{1}{8}} \log\left(-22876792454961 \, \sqrt{2} a^{15} c \sqrt{x} \left(-\frac{c}{a^{17}}\right)^{\frac{7}{8}} - 22876792454961 \, a^{13} c \left(-\frac{c}{a^{17}}\right)^{\frac{3}{4}} + 22876792454961 \, c^{2} x\right) + 72 \, {\left(a^{2} c x^{5} + a^{3} x\right)} \left(-\frac{c}{a^{17}}\right)^{\frac{1}{8}} \arctan\left(-\frac{4782969 \, a^{2} c \sqrt{x} \left(-\frac{c}{a^{17}}\right)^{\frac{1}{8}} - \sqrt{-22876792454961 \, a^{13} c \left(-\frac{c}{a^{17}}\right)^{\frac{3}{4}} + 22876792454961 \, c^{2} x} a^{2} \left(-\frac{c}{a^{17}}\right)^{\frac{1}{8}}}{4782969 \, c}\right) - 18 \, {\left(a^{2} c x^{5} + a^{3} x\right)} \left(-\frac{c}{a^{17}}\right)^{\frac{1}{8}} \log\left(4782969 \, a^{15} \left(-\frac{c}{a^{17}}\right)^{\frac{7}{8}} + 4782969 \, c \sqrt{x}\right) + 18 \, {\left(a^{2} c x^{5} + a^{3} x\right)} \left(-\frac{c}{a^{17}}\right)^{\frac{1}{8}} \log\left(-4782969 \, a^{15} \left(-\frac{c}{a^{17}}\right)^{\frac{7}{8}} + 4782969 \, c \sqrt{x}\right) - 16 \, {\left(9 \, c x^{4} + 8 \, a\right)} \sqrt{x}}{64 \, {\left(a^{2} c x^{5} + a^{3} x\right)}}"," ",0,"1/64*(36*sqrt(2)*(a^2*c*x^5 + a^3*x)*(-c/a^17)^(1/8)*arctan(-1/4782969*(4782969*sqrt(2)*a^2*c*sqrt(x)*(-c/a^17)^(1/8) - sqrt(2)*sqrt(-22876792454961*sqrt(2)*a^15*c*sqrt(x)*(-c/a^17)^(7/8) - 22876792454961*a^13*c*(-c/a^17)^(3/4) + 22876792454961*c^2*x)*a^2*(-c/a^17)^(1/8) + 4782969*c)/c) + 36*sqrt(2)*(a^2*c*x^5 + a^3*x)*(-c/a^17)^(1/8)*arctan(-(sqrt(2)*a^2*c*sqrt(x)*(-c/a^17)^(1/8) - sqrt(2)*sqrt(sqrt(2)*a^15*c*sqrt(x)*(-c/a^17)^(7/8) - a^13*c*(-c/a^17)^(3/4) + c^2*x)*a^2*(-c/a^17)^(1/8) - c)/c) - 9*sqrt(2)*(a^2*c*x^5 + a^3*x)*(-c/a^17)^(1/8)*log(22876792454961*sqrt(2)*a^15*c*sqrt(x)*(-c/a^17)^(7/8) - 22876792454961*a^13*c*(-c/a^17)^(3/4) + 22876792454961*c^2*x) + 9*sqrt(2)*(a^2*c*x^5 + a^3*x)*(-c/a^17)^(1/8)*log(-22876792454961*sqrt(2)*a^15*c*sqrt(x)*(-c/a^17)^(7/8) - 22876792454961*a^13*c*(-c/a^17)^(3/4) + 22876792454961*c^2*x) + 72*(a^2*c*x^5 + a^3*x)*(-c/a^17)^(1/8)*arctan(-1/4782969*(4782969*a^2*c*sqrt(x)*(-c/a^17)^(1/8) - sqrt(-22876792454961*a^13*c*(-c/a^17)^(3/4) + 22876792454961*c^2*x)*a^2*(-c/a^17)^(1/8))/c) - 18*(a^2*c*x^5 + a^3*x)*(-c/a^17)^(1/8)*log(4782969*a^15*(-c/a^17)^(7/8) + 4782969*c*sqrt(x)) + 18*(a^2*c*x^5 + a^3*x)*(-c/a^17)^(1/8)*log(-4782969*a^15*(-c/a^17)^(7/8) + 4782969*c*sqrt(x)) - 16*(9*c*x^4 + 8*a)*sqrt(x))/(a^2*c*x^5 + a^3*x)","B",0
755,1,672,0,0.923647," ","integrate(x^(15/2)/(c*x^4+a)^3,x, algorithm=""fricas"")","\frac{36 \, \sqrt{2} {\left(c^{4} x^{8} + 2 \, a c^{3} x^{4} + a^{2} c^{2}\right)} \left(-\frac{1}{a^{7} c^{17}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{2} \sqrt{a^{2} c^{4} \left(-\frac{1}{a^{7} c^{17}}\right)^{\frac{1}{4}} + \sqrt{2} a c^{2} \sqrt{x} \left(-\frac{1}{a^{7} c^{17}}\right)^{\frac{1}{8}} + x} a^{6} c^{15} \left(-\frac{1}{a^{7} c^{17}}\right)^{\frac{7}{8}} - \sqrt{2} a^{6} c^{15} \sqrt{x} \left(-\frac{1}{a^{7} c^{17}}\right)^{\frac{7}{8}} + 1\right) + 36 \, \sqrt{2} {\left(c^{4} x^{8} + 2 \, a c^{3} x^{4} + a^{2} c^{2}\right)} \left(-\frac{1}{a^{7} c^{17}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{2} \sqrt{a^{2} c^{4} \left(-\frac{1}{a^{7} c^{17}}\right)^{\frac{1}{4}} - \sqrt{2} a c^{2} \sqrt{x} \left(-\frac{1}{a^{7} c^{17}}\right)^{\frac{1}{8}} + x} a^{6} c^{15} \left(-\frac{1}{a^{7} c^{17}}\right)^{\frac{7}{8}} - \sqrt{2} a^{6} c^{15} \sqrt{x} \left(-\frac{1}{a^{7} c^{17}}\right)^{\frac{7}{8}} - 1\right) + 9 \, \sqrt{2} {\left(c^{4} x^{8} + 2 \, a c^{3} x^{4} + a^{2} c^{2}\right)} \left(-\frac{1}{a^{7} c^{17}}\right)^{\frac{1}{8}} \log\left(a^{2} c^{4} \left(-\frac{1}{a^{7} c^{17}}\right)^{\frac{1}{4}} + \sqrt{2} a c^{2} \sqrt{x} \left(-\frac{1}{a^{7} c^{17}}\right)^{\frac{1}{8}} + x\right) - 9 \, \sqrt{2} {\left(c^{4} x^{8} + 2 \, a c^{3} x^{4} + a^{2} c^{2}\right)} \left(-\frac{1}{a^{7} c^{17}}\right)^{\frac{1}{8}} \log\left(a^{2} c^{4} \left(-\frac{1}{a^{7} c^{17}}\right)^{\frac{1}{4}} - \sqrt{2} a c^{2} \sqrt{x} \left(-\frac{1}{a^{7} c^{17}}\right)^{\frac{1}{8}} + x\right) + 72 \, {\left(c^{4} x^{8} + 2 \, a c^{3} x^{4} + a^{2} c^{2}\right)} \left(-\frac{1}{a^{7} c^{17}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{a^{2} c^{4} \left(-\frac{1}{a^{7} c^{17}}\right)^{\frac{1}{4}} + x} a^{6} c^{15} \left(-\frac{1}{a^{7} c^{17}}\right)^{\frac{7}{8}} - a^{6} c^{15} \sqrt{x} \left(-\frac{1}{a^{7} c^{17}}\right)^{\frac{7}{8}}\right) + 18 \, {\left(c^{4} x^{8} + 2 \, a c^{3} x^{4} + a^{2} c^{2}\right)} \left(-\frac{1}{a^{7} c^{17}}\right)^{\frac{1}{8}} \log\left(a c^{2} \left(-\frac{1}{a^{7} c^{17}}\right)^{\frac{1}{8}} + \sqrt{x}\right) - 18 \, {\left(c^{4} x^{8} + 2 \, a c^{3} x^{4} + a^{2} c^{2}\right)} \left(-\frac{1}{a^{7} c^{17}}\right)^{\frac{1}{8}} \log\left(-a c^{2} \left(-\frac{1}{a^{7} c^{17}}\right)^{\frac{1}{8}} + \sqrt{x}\right) - 16 \, {\left(17 \, c x^{4} + 9 \, a\right)} \sqrt{x}}{1024 \, {\left(c^{4} x^{8} + 2 \, a c^{3} x^{4} + a^{2} c^{2}\right)}}"," ",0,"1/1024*(36*sqrt(2)*(c^4*x^8 + 2*a*c^3*x^4 + a^2*c^2)*(-1/(a^7*c^17))^(1/8)*arctan(sqrt(2)*sqrt(a^2*c^4*(-1/(a^7*c^17))^(1/4) + sqrt(2)*a*c^2*sqrt(x)*(-1/(a^7*c^17))^(1/8) + x)*a^6*c^15*(-1/(a^7*c^17))^(7/8) - sqrt(2)*a^6*c^15*sqrt(x)*(-1/(a^7*c^17))^(7/8) + 1) + 36*sqrt(2)*(c^4*x^8 + 2*a*c^3*x^4 + a^2*c^2)*(-1/(a^7*c^17))^(1/8)*arctan(sqrt(2)*sqrt(a^2*c^4*(-1/(a^7*c^17))^(1/4) - sqrt(2)*a*c^2*sqrt(x)*(-1/(a^7*c^17))^(1/8) + x)*a^6*c^15*(-1/(a^7*c^17))^(7/8) - sqrt(2)*a^6*c^15*sqrt(x)*(-1/(a^7*c^17))^(7/8) - 1) + 9*sqrt(2)*(c^4*x^8 + 2*a*c^3*x^4 + a^2*c^2)*(-1/(a^7*c^17))^(1/8)*log(a^2*c^4*(-1/(a^7*c^17))^(1/4) + sqrt(2)*a*c^2*sqrt(x)*(-1/(a^7*c^17))^(1/8) + x) - 9*sqrt(2)*(c^4*x^8 + 2*a*c^3*x^4 + a^2*c^2)*(-1/(a^7*c^17))^(1/8)*log(a^2*c^4*(-1/(a^7*c^17))^(1/4) - sqrt(2)*a*c^2*sqrt(x)*(-1/(a^7*c^17))^(1/8) + x) + 72*(c^4*x^8 + 2*a*c^3*x^4 + a^2*c^2)*(-1/(a^7*c^17))^(1/8)*arctan(sqrt(a^2*c^4*(-1/(a^7*c^17))^(1/4) + x)*a^6*c^15*(-1/(a^7*c^17))^(7/8) - a^6*c^15*sqrt(x)*(-1/(a^7*c^17))^(7/8)) + 18*(c^4*x^8 + 2*a*c^3*x^4 + a^2*c^2)*(-1/(a^7*c^17))^(1/8)*log(a*c^2*(-1/(a^7*c^17))^(1/8) + sqrt(x)) - 18*(c^4*x^8 + 2*a*c^3*x^4 + a^2*c^2)*(-1/(a^7*c^17))^(1/8)*log(-a*c^2*(-1/(a^7*c^17))^(1/8) + sqrt(x)) - 16*(17*c*x^4 + 9*a)*sqrt(x))/(c^4*x^8 + 2*a*c^3*x^4 + a^2*c^2)","B",0
756,1,688,0,0.878255," ","integrate(x^(13/2)/(c*x^4+a)^3,x, algorithm=""fricas"")","-\frac{28 \, \sqrt{2} {\left(a c^{3} x^{8} + 2 \, a^{2} c^{2} x^{4} + a^{3} c\right)} \left(-\frac{1}{a^{9} c^{15}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{2} \sqrt{\sqrt{2} a^{8} c^{13} \sqrt{x} \left(-\frac{1}{a^{9} c^{15}}\right)^{\frac{7}{8}} - a^{7} c^{11} \left(-\frac{1}{a^{9} c^{15}}\right)^{\frac{3}{4}} + x} a c^{2} \left(-\frac{1}{a^{9} c^{15}}\right)^{\frac{1}{8}} - \sqrt{2} a c^{2} \sqrt{x} \left(-\frac{1}{a^{9} c^{15}}\right)^{\frac{1}{8}} + 1\right) + 28 \, \sqrt{2} {\left(a c^{3} x^{8} + 2 \, a^{2} c^{2} x^{4} + a^{3} c\right)} \left(-\frac{1}{a^{9} c^{15}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{2} \sqrt{-\sqrt{2} a^{8} c^{13} \sqrt{x} \left(-\frac{1}{a^{9} c^{15}}\right)^{\frac{7}{8}} - a^{7} c^{11} \left(-\frac{1}{a^{9} c^{15}}\right)^{\frac{3}{4}} + x} a c^{2} \left(-\frac{1}{a^{9} c^{15}}\right)^{\frac{1}{8}} - \sqrt{2} a c^{2} \sqrt{x} \left(-\frac{1}{a^{9} c^{15}}\right)^{\frac{1}{8}} - 1\right) - 7 \, \sqrt{2} {\left(a c^{3} x^{8} + 2 \, a^{2} c^{2} x^{4} + a^{3} c\right)} \left(-\frac{1}{a^{9} c^{15}}\right)^{\frac{1}{8}} \log\left(\sqrt{2} a^{8} c^{13} \sqrt{x} \left(-\frac{1}{a^{9} c^{15}}\right)^{\frac{7}{8}} - a^{7} c^{11} \left(-\frac{1}{a^{9} c^{15}}\right)^{\frac{3}{4}} + x\right) + 7 \, \sqrt{2} {\left(a c^{3} x^{8} + 2 \, a^{2} c^{2} x^{4} + a^{3} c\right)} \left(-\frac{1}{a^{9} c^{15}}\right)^{\frac{1}{8}} \log\left(-\sqrt{2} a^{8} c^{13} \sqrt{x} \left(-\frac{1}{a^{9} c^{15}}\right)^{\frac{7}{8}} - a^{7} c^{11} \left(-\frac{1}{a^{9} c^{15}}\right)^{\frac{3}{4}} + x\right) + 56 \, {\left(a c^{3} x^{8} + 2 \, a^{2} c^{2} x^{4} + a^{3} c\right)} \left(-\frac{1}{a^{9} c^{15}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{-a^{7} c^{11} \left(-\frac{1}{a^{9} c^{15}}\right)^{\frac{3}{4}} + x} a c^{2} \left(-\frac{1}{a^{9} c^{15}}\right)^{\frac{1}{8}} - a c^{2} \sqrt{x} \left(-\frac{1}{a^{9} c^{15}}\right)^{\frac{1}{8}}\right) - 14 \, {\left(a c^{3} x^{8} + 2 \, a^{2} c^{2} x^{4} + a^{3} c\right)} \left(-\frac{1}{a^{9} c^{15}}\right)^{\frac{1}{8}} \log\left(a^{8} c^{13} \left(-\frac{1}{a^{9} c^{15}}\right)^{\frac{7}{8}} + \sqrt{x}\right) + 14 \, {\left(a c^{3} x^{8} + 2 \, a^{2} c^{2} x^{4} + a^{3} c\right)} \left(-\frac{1}{a^{9} c^{15}}\right)^{\frac{1}{8}} \log\left(-a^{8} c^{13} \left(-\frac{1}{a^{9} c^{15}}\right)^{\frac{7}{8}} + \sqrt{x}\right) - 16 \, {\left(7 \, c x^{7} - a x^{3}\right)} \sqrt{x}}{1024 \, {\left(a c^{3} x^{8} + 2 \, a^{2} c^{2} x^{4} + a^{3} c\right)}}"," ",0,"-1/1024*(28*sqrt(2)*(a*c^3*x^8 + 2*a^2*c^2*x^4 + a^3*c)*(-1/(a^9*c^15))^(1/8)*arctan(sqrt(2)*sqrt(sqrt(2)*a^8*c^13*sqrt(x)*(-1/(a^9*c^15))^(7/8) - a^7*c^11*(-1/(a^9*c^15))^(3/4) + x)*a*c^2*(-1/(a^9*c^15))^(1/8) - sqrt(2)*a*c^2*sqrt(x)*(-1/(a^9*c^15))^(1/8) + 1) + 28*sqrt(2)*(a*c^3*x^8 + 2*a^2*c^2*x^4 + a^3*c)*(-1/(a^9*c^15))^(1/8)*arctan(sqrt(2)*sqrt(-sqrt(2)*a^8*c^13*sqrt(x)*(-1/(a^9*c^15))^(7/8) - a^7*c^11*(-1/(a^9*c^15))^(3/4) + x)*a*c^2*(-1/(a^9*c^15))^(1/8) - sqrt(2)*a*c^2*sqrt(x)*(-1/(a^9*c^15))^(1/8) - 1) - 7*sqrt(2)*(a*c^3*x^8 + 2*a^2*c^2*x^4 + a^3*c)*(-1/(a^9*c^15))^(1/8)*log(sqrt(2)*a^8*c^13*sqrt(x)*(-1/(a^9*c^15))^(7/8) - a^7*c^11*(-1/(a^9*c^15))^(3/4) + x) + 7*sqrt(2)*(a*c^3*x^8 + 2*a^2*c^2*x^4 + a^3*c)*(-1/(a^9*c^15))^(1/8)*log(-sqrt(2)*a^8*c^13*sqrt(x)*(-1/(a^9*c^15))^(7/8) - a^7*c^11*(-1/(a^9*c^15))^(3/4) + x) + 56*(a*c^3*x^8 + 2*a^2*c^2*x^4 + a^3*c)*(-1/(a^9*c^15))^(1/8)*arctan(sqrt(-a^7*c^11*(-1/(a^9*c^15))^(3/4) + x)*a*c^2*(-1/(a^9*c^15))^(1/8) - a*c^2*sqrt(x)*(-1/(a^9*c^15))^(1/8)) - 14*(a*c^3*x^8 + 2*a^2*c^2*x^4 + a^3*c)*(-1/(a^9*c^15))^(1/8)*log(a^8*c^13*(-1/(a^9*c^15))^(7/8) + sqrt(x)) + 14*(a*c^3*x^8 + 2*a^2*c^2*x^4 + a^3*c)*(-1/(a^9*c^15))^(1/8)*log(-a^8*c^13*(-1/(a^9*c^15))^(7/8) + sqrt(x)) - 16*(7*c*x^7 - a*x^3)*sqrt(x))/(a*c^3*x^8 + 2*a^2*c^2*x^4 + a^3*c)","B",0
757,1,700,0,0.869510," ","integrate(x^(11/2)/(c*x^4+a)^3,x, algorithm=""fricas"")","\frac{60 \, \sqrt{2} {\left(a c^{3} x^{8} + 2 \, a^{2} c^{2} x^{4} + a^{3} c\right)} \left(-\frac{1}{a^{11} c^{13}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{2} \sqrt{\sqrt{2} a^{7} c^{8} \sqrt{x} \left(-\frac{1}{a^{11} c^{13}}\right)^{\frac{5}{8}} - a^{3} c^{3} \left(-\frac{1}{a^{11} c^{13}}\right)^{\frac{1}{4}} + x} a^{4} c^{5} \left(-\frac{1}{a^{11} c^{13}}\right)^{\frac{3}{8}} - \sqrt{2} a^{4} c^{5} \sqrt{x} \left(-\frac{1}{a^{11} c^{13}}\right)^{\frac{3}{8}} + 1\right) + 60 \, \sqrt{2} {\left(a c^{3} x^{8} + 2 \, a^{2} c^{2} x^{4} + a^{3} c\right)} \left(-\frac{1}{a^{11} c^{13}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{2} \sqrt{-\sqrt{2} a^{7} c^{8} \sqrt{x} \left(-\frac{1}{a^{11} c^{13}}\right)^{\frac{5}{8}} - a^{3} c^{3} \left(-\frac{1}{a^{11} c^{13}}\right)^{\frac{1}{4}} + x} a^{4} c^{5} \left(-\frac{1}{a^{11} c^{13}}\right)^{\frac{3}{8}} - \sqrt{2} a^{4} c^{5} \sqrt{x} \left(-\frac{1}{a^{11} c^{13}}\right)^{\frac{3}{8}} - 1\right) + 15 \, \sqrt{2} {\left(a c^{3} x^{8} + 2 \, a^{2} c^{2} x^{4} + a^{3} c\right)} \left(-\frac{1}{a^{11} c^{13}}\right)^{\frac{1}{8}} \log\left(\sqrt{2} a^{7} c^{8} \sqrt{x} \left(-\frac{1}{a^{11} c^{13}}\right)^{\frac{5}{8}} - a^{3} c^{3} \left(-\frac{1}{a^{11} c^{13}}\right)^{\frac{1}{4}} + x\right) - 15 \, \sqrt{2} {\left(a c^{3} x^{8} + 2 \, a^{2} c^{2} x^{4} + a^{3} c\right)} \left(-\frac{1}{a^{11} c^{13}}\right)^{\frac{1}{8}} \log\left(-\sqrt{2} a^{7} c^{8} \sqrt{x} \left(-\frac{1}{a^{11} c^{13}}\right)^{\frac{5}{8}} - a^{3} c^{3} \left(-\frac{1}{a^{11} c^{13}}\right)^{\frac{1}{4}} + x\right) - 120 \, {\left(a c^{3} x^{8} + 2 \, a^{2} c^{2} x^{4} + a^{3} c\right)} \left(-\frac{1}{a^{11} c^{13}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{-a^{3} c^{3} \left(-\frac{1}{a^{11} c^{13}}\right)^{\frac{1}{4}} + x} a^{4} c^{5} \left(-\frac{1}{a^{11} c^{13}}\right)^{\frac{3}{8}} - a^{4} c^{5} \sqrt{x} \left(-\frac{1}{a^{11} c^{13}}\right)^{\frac{3}{8}}\right) - 30 \, {\left(a c^{3} x^{8} + 2 \, a^{2} c^{2} x^{4} + a^{3} c\right)} \left(-\frac{1}{a^{11} c^{13}}\right)^{\frac{1}{8}} \log\left(a^{7} c^{8} \left(-\frac{1}{a^{11} c^{13}}\right)^{\frac{5}{8}} + \sqrt{x}\right) + 30 \, {\left(a c^{3} x^{8} + 2 \, a^{2} c^{2} x^{4} + a^{3} c\right)} \left(-\frac{1}{a^{11} c^{13}}\right)^{\frac{1}{8}} \log\left(-a^{7} c^{8} \left(-\frac{1}{a^{11} c^{13}}\right)^{\frac{5}{8}} + \sqrt{x}\right) + 16 \, {\left(5 \, c x^{6} - 3 \, a x^{2}\right)} \sqrt{x}}{1024 \, {\left(a c^{3} x^{8} + 2 \, a^{2} c^{2} x^{4} + a^{3} c\right)}}"," ",0,"1/1024*(60*sqrt(2)*(a*c^3*x^8 + 2*a^2*c^2*x^4 + a^3*c)*(-1/(a^11*c^13))^(1/8)*arctan(sqrt(2)*sqrt(sqrt(2)*a^7*c^8*sqrt(x)*(-1/(a^11*c^13))^(5/8) - a^3*c^3*(-1/(a^11*c^13))^(1/4) + x)*a^4*c^5*(-1/(a^11*c^13))^(3/8) - sqrt(2)*a^4*c^5*sqrt(x)*(-1/(a^11*c^13))^(3/8) + 1) + 60*sqrt(2)*(a*c^3*x^8 + 2*a^2*c^2*x^4 + a^3*c)*(-1/(a^11*c^13))^(1/8)*arctan(sqrt(2)*sqrt(-sqrt(2)*a^7*c^8*sqrt(x)*(-1/(a^11*c^13))^(5/8) - a^3*c^3*(-1/(a^11*c^13))^(1/4) + x)*a^4*c^5*(-1/(a^11*c^13))^(3/8) - sqrt(2)*a^4*c^5*sqrt(x)*(-1/(a^11*c^13))^(3/8) - 1) + 15*sqrt(2)*(a*c^3*x^8 + 2*a^2*c^2*x^4 + a^3*c)*(-1/(a^11*c^13))^(1/8)*log(sqrt(2)*a^7*c^8*sqrt(x)*(-1/(a^11*c^13))^(5/8) - a^3*c^3*(-1/(a^11*c^13))^(1/4) + x) - 15*sqrt(2)*(a*c^3*x^8 + 2*a^2*c^2*x^4 + a^3*c)*(-1/(a^11*c^13))^(1/8)*log(-sqrt(2)*a^7*c^8*sqrt(x)*(-1/(a^11*c^13))^(5/8) - a^3*c^3*(-1/(a^11*c^13))^(1/4) + x) - 120*(a*c^3*x^8 + 2*a^2*c^2*x^4 + a^3*c)*(-1/(a^11*c^13))^(1/8)*arctan(sqrt(-a^3*c^3*(-1/(a^11*c^13))^(1/4) + x)*a^4*c^5*(-1/(a^11*c^13))^(3/8) - a^4*c^5*sqrt(x)*(-1/(a^11*c^13))^(3/8)) - 30*(a*c^3*x^8 + 2*a^2*c^2*x^4 + a^3*c)*(-1/(a^11*c^13))^(1/8)*log(a^7*c^8*(-1/(a^11*c^13))^(5/8) + sqrt(x)) + 30*(a*c^3*x^8 + 2*a^2*c^2*x^4 + a^3*c)*(-1/(a^11*c^13))^(1/8)*log(-a^7*c^8*(-1/(a^11*c^13))^(5/8) + sqrt(x)) + 16*(5*c*x^6 - 3*a*x^2)*sqrt(x))/(a*c^3*x^8 + 2*a^2*c^2*x^4 + a^3*c)","B",0
758,1,693,0,0.927520," ","integrate(x^(9/2)/(c*x^4+a)^3,x, algorithm=""fricas"")","-\frac{60 \, \sqrt{2} {\left(a c^{3} x^{8} + 2 \, a^{2} c^{2} x^{4} + a^{3} c\right)} \left(-\frac{1}{a^{13} c^{11}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{2} \sqrt{a^{10} c^{8} \left(-\frac{1}{a^{13} c^{11}}\right)^{\frac{3}{4}} + \sqrt{2} a^{5} c^{4} \sqrt{x} \left(-\frac{1}{a^{13} c^{11}}\right)^{\frac{3}{8}} + x} a^{8} c^{7} \left(-\frac{1}{a^{13} c^{11}}\right)^{\frac{5}{8}} - \sqrt{2} a^{8} c^{7} \sqrt{x} \left(-\frac{1}{a^{13} c^{11}}\right)^{\frac{5}{8}} + 1\right) + 60 \, \sqrt{2} {\left(a c^{3} x^{8} + 2 \, a^{2} c^{2} x^{4} + a^{3} c\right)} \left(-\frac{1}{a^{13} c^{11}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{2} \sqrt{a^{10} c^{8} \left(-\frac{1}{a^{13} c^{11}}\right)^{\frac{3}{4}} - \sqrt{2} a^{5} c^{4} \sqrt{x} \left(-\frac{1}{a^{13} c^{11}}\right)^{\frac{3}{8}} + x} a^{8} c^{7} \left(-\frac{1}{a^{13} c^{11}}\right)^{\frac{5}{8}} - \sqrt{2} a^{8} c^{7} \sqrt{x} \left(-\frac{1}{a^{13} c^{11}}\right)^{\frac{5}{8}} - 1\right) - 15 \, \sqrt{2} {\left(a c^{3} x^{8} + 2 \, a^{2} c^{2} x^{4} + a^{3} c\right)} \left(-\frac{1}{a^{13} c^{11}}\right)^{\frac{1}{8}} \log\left(a^{10} c^{8} \left(-\frac{1}{a^{13} c^{11}}\right)^{\frac{3}{4}} + \sqrt{2} a^{5} c^{4} \sqrt{x} \left(-\frac{1}{a^{13} c^{11}}\right)^{\frac{3}{8}} + x\right) + 15 \, \sqrt{2} {\left(a c^{3} x^{8} + 2 \, a^{2} c^{2} x^{4} + a^{3} c\right)} \left(-\frac{1}{a^{13} c^{11}}\right)^{\frac{1}{8}} \log\left(a^{10} c^{8} \left(-\frac{1}{a^{13} c^{11}}\right)^{\frac{3}{4}} - \sqrt{2} a^{5} c^{4} \sqrt{x} \left(-\frac{1}{a^{13} c^{11}}\right)^{\frac{3}{8}} + x\right) - 120 \, {\left(a c^{3} x^{8} + 2 \, a^{2} c^{2} x^{4} + a^{3} c\right)} \left(-\frac{1}{a^{13} c^{11}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{a^{10} c^{8} \left(-\frac{1}{a^{13} c^{11}}\right)^{\frac{3}{4}} + x} a^{8} c^{7} \left(-\frac{1}{a^{13} c^{11}}\right)^{\frac{5}{8}} - a^{8} c^{7} \sqrt{x} \left(-\frac{1}{a^{13} c^{11}}\right)^{\frac{5}{8}}\right) + 30 \, {\left(a c^{3} x^{8} + 2 \, a^{2} c^{2} x^{4} + a^{3} c\right)} \left(-\frac{1}{a^{13} c^{11}}\right)^{\frac{1}{8}} \log\left(a^{5} c^{4} \left(-\frac{1}{a^{13} c^{11}}\right)^{\frac{3}{8}} + \sqrt{x}\right) - 30 \, {\left(a c^{3} x^{8} + 2 \, a^{2} c^{2} x^{4} + a^{3} c\right)} \left(-\frac{1}{a^{13} c^{11}}\right)^{\frac{1}{8}} \log\left(-a^{5} c^{4} \left(-\frac{1}{a^{13} c^{11}}\right)^{\frac{3}{8}} + \sqrt{x}\right) - 16 \, {\left(3 \, c x^{5} - 5 \, a x\right)} \sqrt{x}}{1024 \, {\left(a c^{3} x^{8} + 2 \, a^{2} c^{2} x^{4} + a^{3} c\right)}}"," ",0,"-1/1024*(60*sqrt(2)*(a*c^3*x^8 + 2*a^2*c^2*x^4 + a^3*c)*(-1/(a^13*c^11))^(1/8)*arctan(sqrt(2)*sqrt(a^10*c^8*(-1/(a^13*c^11))^(3/4) + sqrt(2)*a^5*c^4*sqrt(x)*(-1/(a^13*c^11))^(3/8) + x)*a^8*c^7*(-1/(a^13*c^11))^(5/8) - sqrt(2)*a^8*c^7*sqrt(x)*(-1/(a^13*c^11))^(5/8) + 1) + 60*sqrt(2)*(a*c^3*x^8 + 2*a^2*c^2*x^4 + a^3*c)*(-1/(a^13*c^11))^(1/8)*arctan(sqrt(2)*sqrt(a^10*c^8*(-1/(a^13*c^11))^(3/4) - sqrt(2)*a^5*c^4*sqrt(x)*(-1/(a^13*c^11))^(3/8) + x)*a^8*c^7*(-1/(a^13*c^11))^(5/8) - sqrt(2)*a^8*c^7*sqrt(x)*(-1/(a^13*c^11))^(5/8) - 1) - 15*sqrt(2)*(a*c^3*x^8 + 2*a^2*c^2*x^4 + a^3*c)*(-1/(a^13*c^11))^(1/8)*log(a^10*c^8*(-1/(a^13*c^11))^(3/4) + sqrt(2)*a^5*c^4*sqrt(x)*(-1/(a^13*c^11))^(3/8) + x) + 15*sqrt(2)*(a*c^3*x^8 + 2*a^2*c^2*x^4 + a^3*c)*(-1/(a^13*c^11))^(1/8)*log(a^10*c^8*(-1/(a^13*c^11))^(3/4) - sqrt(2)*a^5*c^4*sqrt(x)*(-1/(a^13*c^11))^(3/8) + x) - 120*(a*c^3*x^8 + 2*a^2*c^2*x^4 + a^3*c)*(-1/(a^13*c^11))^(1/8)*arctan(sqrt(a^10*c^8*(-1/(a^13*c^11))^(3/4) + x)*a^8*c^7*(-1/(a^13*c^11))^(5/8) - a^8*c^7*sqrt(x)*(-1/(a^13*c^11))^(5/8)) + 30*(a*c^3*x^8 + 2*a^2*c^2*x^4 + a^3*c)*(-1/(a^13*c^11))^(1/8)*log(a^5*c^4*(-1/(a^13*c^11))^(3/8) + sqrt(x)) - 30*(a*c^3*x^8 + 2*a^2*c^2*x^4 + a^3*c)*(-1/(a^13*c^11))^(1/8)*log(-a^5*c^4*(-1/(a^13*c^11))^(3/8) + sqrt(x)) - 16*(3*c*x^5 - 5*a*x)*sqrt(x))/(a*c^3*x^8 + 2*a^2*c^2*x^4 + a^3*c)","B",0
759,1,679,0,0.959462," ","integrate(x^(7/2)/(c*x^4+a)^3,x, algorithm=""fricas"")","\frac{28 \, \sqrt{2} {\left(a c^{3} x^{8} + 2 \, a^{2} c^{2} x^{4} + a^{3} c\right)} \left(-\frac{1}{a^{15} c^{9}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{2} \sqrt{a^{4} c^{2} \left(-\frac{1}{a^{15} c^{9}}\right)^{\frac{1}{4}} + \sqrt{2} a^{2} c \sqrt{x} \left(-\frac{1}{a^{15} c^{9}}\right)^{\frac{1}{8}} + x} a^{13} c^{8} \left(-\frac{1}{a^{15} c^{9}}\right)^{\frac{7}{8}} - \sqrt{2} a^{13} c^{8} \sqrt{x} \left(-\frac{1}{a^{15} c^{9}}\right)^{\frac{7}{8}} + 1\right) + 28 \, \sqrt{2} {\left(a c^{3} x^{8} + 2 \, a^{2} c^{2} x^{4} + a^{3} c\right)} \left(-\frac{1}{a^{15} c^{9}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{2} \sqrt{a^{4} c^{2} \left(-\frac{1}{a^{15} c^{9}}\right)^{\frac{1}{4}} - \sqrt{2} a^{2} c \sqrt{x} \left(-\frac{1}{a^{15} c^{9}}\right)^{\frac{1}{8}} + x} a^{13} c^{8} \left(-\frac{1}{a^{15} c^{9}}\right)^{\frac{7}{8}} - \sqrt{2} a^{13} c^{8} \sqrt{x} \left(-\frac{1}{a^{15} c^{9}}\right)^{\frac{7}{8}} - 1\right) + 7 \, \sqrt{2} {\left(a c^{3} x^{8} + 2 \, a^{2} c^{2} x^{4} + a^{3} c\right)} \left(-\frac{1}{a^{15} c^{9}}\right)^{\frac{1}{8}} \log\left(a^{4} c^{2} \left(-\frac{1}{a^{15} c^{9}}\right)^{\frac{1}{4}} + \sqrt{2} a^{2} c \sqrt{x} \left(-\frac{1}{a^{15} c^{9}}\right)^{\frac{1}{8}} + x\right) - 7 \, \sqrt{2} {\left(a c^{3} x^{8} + 2 \, a^{2} c^{2} x^{4} + a^{3} c\right)} \left(-\frac{1}{a^{15} c^{9}}\right)^{\frac{1}{8}} \log\left(a^{4} c^{2} \left(-\frac{1}{a^{15} c^{9}}\right)^{\frac{1}{4}} - \sqrt{2} a^{2} c \sqrt{x} \left(-\frac{1}{a^{15} c^{9}}\right)^{\frac{1}{8}} + x\right) + 56 \, {\left(a c^{3} x^{8} + 2 \, a^{2} c^{2} x^{4} + a^{3} c\right)} \left(-\frac{1}{a^{15} c^{9}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{a^{4} c^{2} \left(-\frac{1}{a^{15} c^{9}}\right)^{\frac{1}{4}} + x} a^{13} c^{8} \left(-\frac{1}{a^{15} c^{9}}\right)^{\frac{7}{8}} - a^{13} c^{8} \sqrt{x} \left(-\frac{1}{a^{15} c^{9}}\right)^{\frac{7}{8}}\right) + 14 \, {\left(a c^{3} x^{8} + 2 \, a^{2} c^{2} x^{4} + a^{3} c\right)} \left(-\frac{1}{a^{15} c^{9}}\right)^{\frac{1}{8}} \log\left(a^{2} c \left(-\frac{1}{a^{15} c^{9}}\right)^{\frac{1}{8}} + \sqrt{x}\right) - 14 \, {\left(a c^{3} x^{8} + 2 \, a^{2} c^{2} x^{4} + a^{3} c\right)} \left(-\frac{1}{a^{15} c^{9}}\right)^{\frac{1}{8}} \log\left(-a^{2} c \left(-\frac{1}{a^{15} c^{9}}\right)^{\frac{1}{8}} + \sqrt{x}\right) + 16 \, {\left(c x^{4} - 7 \, a\right)} \sqrt{x}}{1024 \, {\left(a c^{3} x^{8} + 2 \, a^{2} c^{2} x^{4} + a^{3} c\right)}}"," ",0,"1/1024*(28*sqrt(2)*(a*c^3*x^8 + 2*a^2*c^2*x^4 + a^3*c)*(-1/(a^15*c^9))^(1/8)*arctan(sqrt(2)*sqrt(a^4*c^2*(-1/(a^15*c^9))^(1/4) + sqrt(2)*a^2*c*sqrt(x)*(-1/(a^15*c^9))^(1/8) + x)*a^13*c^8*(-1/(a^15*c^9))^(7/8) - sqrt(2)*a^13*c^8*sqrt(x)*(-1/(a^15*c^9))^(7/8) + 1) + 28*sqrt(2)*(a*c^3*x^8 + 2*a^2*c^2*x^4 + a^3*c)*(-1/(a^15*c^9))^(1/8)*arctan(sqrt(2)*sqrt(a^4*c^2*(-1/(a^15*c^9))^(1/4) - sqrt(2)*a^2*c*sqrt(x)*(-1/(a^15*c^9))^(1/8) + x)*a^13*c^8*(-1/(a^15*c^9))^(7/8) - sqrt(2)*a^13*c^8*sqrt(x)*(-1/(a^15*c^9))^(7/8) - 1) + 7*sqrt(2)*(a*c^3*x^8 + 2*a^2*c^2*x^4 + a^3*c)*(-1/(a^15*c^9))^(1/8)*log(a^4*c^2*(-1/(a^15*c^9))^(1/4) + sqrt(2)*a^2*c*sqrt(x)*(-1/(a^15*c^9))^(1/8) + x) - 7*sqrt(2)*(a*c^3*x^8 + 2*a^2*c^2*x^4 + a^3*c)*(-1/(a^15*c^9))^(1/8)*log(a^4*c^2*(-1/(a^15*c^9))^(1/4) - sqrt(2)*a^2*c*sqrt(x)*(-1/(a^15*c^9))^(1/8) + x) + 56*(a*c^3*x^8 + 2*a^2*c^2*x^4 + a^3*c)*(-1/(a^15*c^9))^(1/8)*arctan(sqrt(a^4*c^2*(-1/(a^15*c^9))^(1/4) + x)*a^13*c^8*(-1/(a^15*c^9))^(7/8) - a^13*c^8*sqrt(x)*(-1/(a^15*c^9))^(7/8)) + 14*(a*c^3*x^8 + 2*a^2*c^2*x^4 + a^3*c)*(-1/(a^15*c^9))^(1/8)*log(a^2*c*(-1/(a^15*c^9))^(1/8) + sqrt(x)) - 14*(a*c^3*x^8 + 2*a^2*c^2*x^4 + a^3*c)*(-1/(a^15*c^9))^(1/8)*log(-a^2*c*(-1/(a^15*c^9))^(1/8) + sqrt(x)) + 16*(c*x^4 - 7*a)*sqrt(x))/(a*c^3*x^8 + 2*a^2*c^2*x^4 + a^3*c)","B",0
760,1,672,0,0.954998," ","integrate(x^(5/2)/(c*x^4+a)^3,x, algorithm=""fricas"")","-\frac{36 \, \sqrt{2} {\left(a^{2} c^{2} x^{8} + 2 \, a^{3} c x^{4} + a^{4}\right)} \left(-\frac{1}{a^{17} c^{7}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{2} \sqrt{\sqrt{2} a^{15} c^{6} \sqrt{x} \left(-\frac{1}{a^{17} c^{7}}\right)^{\frac{7}{8}} - a^{13} c^{5} \left(-\frac{1}{a^{17} c^{7}}\right)^{\frac{3}{4}} + x} a^{2} c \left(-\frac{1}{a^{17} c^{7}}\right)^{\frac{1}{8}} - \sqrt{2} a^{2} c \sqrt{x} \left(-\frac{1}{a^{17} c^{7}}\right)^{\frac{1}{8}} + 1\right) + 36 \, \sqrt{2} {\left(a^{2} c^{2} x^{8} + 2 \, a^{3} c x^{4} + a^{4}\right)} \left(-\frac{1}{a^{17} c^{7}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{2} \sqrt{-\sqrt{2} a^{15} c^{6} \sqrt{x} \left(-\frac{1}{a^{17} c^{7}}\right)^{\frac{7}{8}} - a^{13} c^{5} \left(-\frac{1}{a^{17} c^{7}}\right)^{\frac{3}{4}} + x} a^{2} c \left(-\frac{1}{a^{17} c^{7}}\right)^{\frac{1}{8}} - \sqrt{2} a^{2} c \sqrt{x} \left(-\frac{1}{a^{17} c^{7}}\right)^{\frac{1}{8}} - 1\right) - 9 \, \sqrt{2} {\left(a^{2} c^{2} x^{8} + 2 \, a^{3} c x^{4} + a^{4}\right)} \left(-\frac{1}{a^{17} c^{7}}\right)^{\frac{1}{8}} \log\left(\sqrt{2} a^{15} c^{6} \sqrt{x} \left(-\frac{1}{a^{17} c^{7}}\right)^{\frac{7}{8}} - a^{13} c^{5} \left(-\frac{1}{a^{17} c^{7}}\right)^{\frac{3}{4}} + x\right) + 9 \, \sqrt{2} {\left(a^{2} c^{2} x^{8} + 2 \, a^{3} c x^{4} + a^{4}\right)} \left(-\frac{1}{a^{17} c^{7}}\right)^{\frac{1}{8}} \log\left(-\sqrt{2} a^{15} c^{6} \sqrt{x} \left(-\frac{1}{a^{17} c^{7}}\right)^{\frac{7}{8}} - a^{13} c^{5} \left(-\frac{1}{a^{17} c^{7}}\right)^{\frac{3}{4}} + x\right) + 72 \, {\left(a^{2} c^{2} x^{8} + 2 \, a^{3} c x^{4} + a^{4}\right)} \left(-\frac{1}{a^{17} c^{7}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{-a^{13} c^{5} \left(-\frac{1}{a^{17} c^{7}}\right)^{\frac{3}{4}} + x} a^{2} c \left(-\frac{1}{a^{17} c^{7}}\right)^{\frac{1}{8}} - a^{2} c \sqrt{x} \left(-\frac{1}{a^{17} c^{7}}\right)^{\frac{1}{8}}\right) - 18 \, {\left(a^{2} c^{2} x^{8} + 2 \, a^{3} c x^{4} + a^{4}\right)} \left(-\frac{1}{a^{17} c^{7}}\right)^{\frac{1}{8}} \log\left(a^{15} c^{6} \left(-\frac{1}{a^{17} c^{7}}\right)^{\frac{7}{8}} + \sqrt{x}\right) + 18 \, {\left(a^{2} c^{2} x^{8} + 2 \, a^{3} c x^{4} + a^{4}\right)} \left(-\frac{1}{a^{17} c^{7}}\right)^{\frac{1}{8}} \log\left(-a^{15} c^{6} \left(-\frac{1}{a^{17} c^{7}}\right)^{\frac{7}{8}} + \sqrt{x}\right) - 16 \, {\left(9 \, c x^{7} + 17 \, a x^{3}\right)} \sqrt{x}}{1024 \, {\left(a^{2} c^{2} x^{8} + 2 \, a^{3} c x^{4} + a^{4}\right)}}"," ",0,"-1/1024*(36*sqrt(2)*(a^2*c^2*x^8 + 2*a^3*c*x^4 + a^4)*(-1/(a^17*c^7))^(1/8)*arctan(sqrt(2)*sqrt(sqrt(2)*a^15*c^6*sqrt(x)*(-1/(a^17*c^7))^(7/8) - a^13*c^5*(-1/(a^17*c^7))^(3/4) + x)*a^2*c*(-1/(a^17*c^7))^(1/8) - sqrt(2)*a^2*c*sqrt(x)*(-1/(a^17*c^7))^(1/8) + 1) + 36*sqrt(2)*(a^2*c^2*x^8 + 2*a^3*c*x^4 + a^4)*(-1/(a^17*c^7))^(1/8)*arctan(sqrt(2)*sqrt(-sqrt(2)*a^15*c^6*sqrt(x)*(-1/(a^17*c^7))^(7/8) - a^13*c^5*(-1/(a^17*c^7))^(3/4) + x)*a^2*c*(-1/(a^17*c^7))^(1/8) - sqrt(2)*a^2*c*sqrt(x)*(-1/(a^17*c^7))^(1/8) - 1) - 9*sqrt(2)*(a^2*c^2*x^8 + 2*a^3*c*x^4 + a^4)*(-1/(a^17*c^7))^(1/8)*log(sqrt(2)*a^15*c^6*sqrt(x)*(-1/(a^17*c^7))^(7/8) - a^13*c^5*(-1/(a^17*c^7))^(3/4) + x) + 9*sqrt(2)*(a^2*c^2*x^8 + 2*a^3*c*x^4 + a^4)*(-1/(a^17*c^7))^(1/8)*log(-sqrt(2)*a^15*c^6*sqrt(x)*(-1/(a^17*c^7))^(7/8) - a^13*c^5*(-1/(a^17*c^7))^(3/4) + x) + 72*(a^2*c^2*x^8 + 2*a^3*c*x^4 + a^4)*(-1/(a^17*c^7))^(1/8)*arctan(sqrt(-a^13*c^5*(-1/(a^17*c^7))^(3/4) + x)*a^2*c*(-1/(a^17*c^7))^(1/8) - a^2*c*sqrt(x)*(-1/(a^17*c^7))^(1/8)) - 18*(a^2*c^2*x^8 + 2*a^3*c*x^4 + a^4)*(-1/(a^17*c^7))^(1/8)*log(a^15*c^6*(-1/(a^17*c^7))^(7/8) + sqrt(x)) + 18*(a^2*c^2*x^8 + 2*a^3*c*x^4 + a^4)*(-1/(a^17*c^7))^(1/8)*log(-a^15*c^6*(-1/(a^17*c^7))^(7/8) + sqrt(x)) - 16*(9*c*x^7 + 17*a*x^3)*sqrt(x))/(a^2*c^2*x^8 + 2*a^3*c*x^4 + a^4)","B",0
761,1,674,0,1.005280," ","integrate(x^(3/2)/(c*x^4+a)^3,x, algorithm=""fricas"")","\frac{132 \, \sqrt{2} {\left(a^{2} c^{2} x^{8} + 2 \, a^{3} c x^{4} + a^{4}\right)} \left(-\frac{1}{a^{19} c^{5}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{2} \sqrt{\sqrt{2} a^{12} c^{3} \sqrt{x} \left(-\frac{1}{a^{19} c^{5}}\right)^{\frac{5}{8}} - a^{5} c \left(-\frac{1}{a^{19} c^{5}}\right)^{\frac{1}{4}} + x} a^{7} c^{2} \left(-\frac{1}{a^{19} c^{5}}\right)^{\frac{3}{8}} - \sqrt{2} a^{7} c^{2} \sqrt{x} \left(-\frac{1}{a^{19} c^{5}}\right)^{\frac{3}{8}} + 1\right) + 132 \, \sqrt{2} {\left(a^{2} c^{2} x^{8} + 2 \, a^{3} c x^{4} + a^{4}\right)} \left(-\frac{1}{a^{19} c^{5}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{2} \sqrt{-\sqrt{2} a^{12} c^{3} \sqrt{x} \left(-\frac{1}{a^{19} c^{5}}\right)^{\frac{5}{8}} - a^{5} c \left(-\frac{1}{a^{19} c^{5}}\right)^{\frac{1}{4}} + x} a^{7} c^{2} \left(-\frac{1}{a^{19} c^{5}}\right)^{\frac{3}{8}} - \sqrt{2} a^{7} c^{2} \sqrt{x} \left(-\frac{1}{a^{19} c^{5}}\right)^{\frac{3}{8}} - 1\right) + 33 \, \sqrt{2} {\left(a^{2} c^{2} x^{8} + 2 \, a^{3} c x^{4} + a^{4}\right)} \left(-\frac{1}{a^{19} c^{5}}\right)^{\frac{1}{8}} \log\left(\sqrt{2} a^{12} c^{3} \sqrt{x} \left(-\frac{1}{a^{19} c^{5}}\right)^{\frac{5}{8}} - a^{5} c \left(-\frac{1}{a^{19} c^{5}}\right)^{\frac{1}{4}} + x\right) - 33 \, \sqrt{2} {\left(a^{2} c^{2} x^{8} + 2 \, a^{3} c x^{4} + a^{4}\right)} \left(-\frac{1}{a^{19} c^{5}}\right)^{\frac{1}{8}} \log\left(-\sqrt{2} a^{12} c^{3} \sqrt{x} \left(-\frac{1}{a^{19} c^{5}}\right)^{\frac{5}{8}} - a^{5} c \left(-\frac{1}{a^{19} c^{5}}\right)^{\frac{1}{4}} + x\right) - 264 \, {\left(a^{2} c^{2} x^{8} + 2 \, a^{3} c x^{4} + a^{4}\right)} \left(-\frac{1}{a^{19} c^{5}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{-a^{5} c \left(-\frac{1}{a^{19} c^{5}}\right)^{\frac{1}{4}} + x} a^{7} c^{2} \left(-\frac{1}{a^{19} c^{5}}\right)^{\frac{3}{8}} - a^{7} c^{2} \sqrt{x} \left(-\frac{1}{a^{19} c^{5}}\right)^{\frac{3}{8}}\right) - 66 \, {\left(a^{2} c^{2} x^{8} + 2 \, a^{3} c x^{4} + a^{4}\right)} \left(-\frac{1}{a^{19} c^{5}}\right)^{\frac{1}{8}} \log\left(a^{12} c^{3} \left(-\frac{1}{a^{19} c^{5}}\right)^{\frac{5}{8}} + \sqrt{x}\right) + 66 \, {\left(a^{2} c^{2} x^{8} + 2 \, a^{3} c x^{4} + a^{4}\right)} \left(-\frac{1}{a^{19} c^{5}}\right)^{\frac{1}{8}} \log\left(-a^{12} c^{3} \left(-\frac{1}{a^{19} c^{5}}\right)^{\frac{5}{8}} + \sqrt{x}\right) + 16 \, {\left(11 \, c x^{6} + 19 \, a x^{2}\right)} \sqrt{x}}{1024 \, {\left(a^{2} c^{2} x^{8} + 2 \, a^{3} c x^{4} + a^{4}\right)}}"," ",0,"1/1024*(132*sqrt(2)*(a^2*c^2*x^8 + 2*a^3*c*x^4 + a^4)*(-1/(a^19*c^5))^(1/8)*arctan(sqrt(2)*sqrt(sqrt(2)*a^12*c^3*sqrt(x)*(-1/(a^19*c^5))^(5/8) - a^5*c*(-1/(a^19*c^5))^(1/4) + x)*a^7*c^2*(-1/(a^19*c^5))^(3/8) - sqrt(2)*a^7*c^2*sqrt(x)*(-1/(a^19*c^5))^(3/8) + 1) + 132*sqrt(2)*(a^2*c^2*x^8 + 2*a^3*c*x^4 + a^4)*(-1/(a^19*c^5))^(1/8)*arctan(sqrt(2)*sqrt(-sqrt(2)*a^12*c^3*sqrt(x)*(-1/(a^19*c^5))^(5/8) - a^5*c*(-1/(a^19*c^5))^(1/4) + x)*a^7*c^2*(-1/(a^19*c^5))^(3/8) - sqrt(2)*a^7*c^2*sqrt(x)*(-1/(a^19*c^5))^(3/8) - 1) + 33*sqrt(2)*(a^2*c^2*x^8 + 2*a^3*c*x^4 + a^4)*(-1/(a^19*c^5))^(1/8)*log(sqrt(2)*a^12*c^3*sqrt(x)*(-1/(a^19*c^5))^(5/8) - a^5*c*(-1/(a^19*c^5))^(1/4) + x) - 33*sqrt(2)*(a^2*c^2*x^8 + 2*a^3*c*x^4 + a^4)*(-1/(a^19*c^5))^(1/8)*log(-sqrt(2)*a^12*c^3*sqrt(x)*(-1/(a^19*c^5))^(5/8) - a^5*c*(-1/(a^19*c^5))^(1/4) + x) - 264*(a^2*c^2*x^8 + 2*a^3*c*x^4 + a^4)*(-1/(a^19*c^5))^(1/8)*arctan(sqrt(-a^5*c*(-1/(a^19*c^5))^(1/4) + x)*a^7*c^2*(-1/(a^19*c^5))^(3/8) - a^7*c^2*sqrt(x)*(-1/(a^19*c^5))^(3/8)) - 66*(a^2*c^2*x^8 + 2*a^3*c*x^4 + a^4)*(-1/(a^19*c^5))^(1/8)*log(a^12*c^3*(-1/(a^19*c^5))^(5/8) + sqrt(x)) + 66*(a^2*c^2*x^8 + 2*a^3*c*x^4 + a^4)*(-1/(a^19*c^5))^(1/8)*log(-a^12*c^3*(-1/(a^19*c^5))^(5/8) + sqrt(x)) + 16*(11*c*x^6 + 19*a*x^2)*sqrt(x))/(a^2*c^2*x^8 + 2*a^3*c*x^4 + a^4)","B",0
762,1,665,0,0.676883," ","integrate(x^(1/2)/(c*x^4+a)^3,x, algorithm=""fricas"")","-\frac{260 \, \sqrt{2} {\left(a^{2} c^{2} x^{8} + 2 \, a^{3} c x^{4} + a^{4}\right)} \left(-\frac{1}{a^{21} c^{3}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{2} \sqrt{a^{16} c^{2} \left(-\frac{1}{a^{21} c^{3}}\right)^{\frac{3}{4}} + \sqrt{2} a^{8} c \sqrt{x} \left(-\frac{1}{a^{21} c^{3}}\right)^{\frac{3}{8}} + x} a^{13} c^{2} \left(-\frac{1}{a^{21} c^{3}}\right)^{\frac{5}{8}} - \sqrt{2} a^{13} c^{2} \sqrt{x} \left(-\frac{1}{a^{21} c^{3}}\right)^{\frac{5}{8}} + 1\right) + 260 \, \sqrt{2} {\left(a^{2} c^{2} x^{8} + 2 \, a^{3} c x^{4} + a^{4}\right)} \left(-\frac{1}{a^{21} c^{3}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{2} \sqrt{a^{16} c^{2} \left(-\frac{1}{a^{21} c^{3}}\right)^{\frac{3}{4}} - \sqrt{2} a^{8} c \sqrt{x} \left(-\frac{1}{a^{21} c^{3}}\right)^{\frac{3}{8}} + x} a^{13} c^{2} \left(-\frac{1}{a^{21} c^{3}}\right)^{\frac{5}{8}} - \sqrt{2} a^{13} c^{2} \sqrt{x} \left(-\frac{1}{a^{21} c^{3}}\right)^{\frac{5}{8}} - 1\right) - 65 \, \sqrt{2} {\left(a^{2} c^{2} x^{8} + 2 \, a^{3} c x^{4} + a^{4}\right)} \left(-\frac{1}{a^{21} c^{3}}\right)^{\frac{1}{8}} \log\left(a^{16} c^{2} \left(-\frac{1}{a^{21} c^{3}}\right)^{\frac{3}{4}} + \sqrt{2} a^{8} c \sqrt{x} \left(-\frac{1}{a^{21} c^{3}}\right)^{\frac{3}{8}} + x\right) + 65 \, \sqrt{2} {\left(a^{2} c^{2} x^{8} + 2 \, a^{3} c x^{4} + a^{4}\right)} \left(-\frac{1}{a^{21} c^{3}}\right)^{\frac{1}{8}} \log\left(a^{16} c^{2} \left(-\frac{1}{a^{21} c^{3}}\right)^{\frac{3}{4}} - \sqrt{2} a^{8} c \sqrt{x} \left(-\frac{1}{a^{21} c^{3}}\right)^{\frac{3}{8}} + x\right) - 520 \, {\left(a^{2} c^{2} x^{8} + 2 \, a^{3} c x^{4} + a^{4}\right)} \left(-\frac{1}{a^{21} c^{3}}\right)^{\frac{1}{8}} \arctan\left(\sqrt{a^{16} c^{2} \left(-\frac{1}{a^{21} c^{3}}\right)^{\frac{3}{4}} + x} a^{13} c^{2} \left(-\frac{1}{a^{21} c^{3}}\right)^{\frac{5}{8}} - a^{13} c^{2} \sqrt{x} \left(-\frac{1}{a^{21} c^{3}}\right)^{\frac{5}{8}}\right) + 130 \, {\left(a^{2} c^{2} x^{8} + 2 \, a^{3} c x^{4} + a^{4}\right)} \left(-\frac{1}{a^{21} c^{3}}\right)^{\frac{1}{8}} \log\left(a^{8} c \left(-\frac{1}{a^{21} c^{3}}\right)^{\frac{3}{8}} + \sqrt{x}\right) - 130 \, {\left(a^{2} c^{2} x^{8} + 2 \, a^{3} c x^{4} + a^{4}\right)} \left(-\frac{1}{a^{21} c^{3}}\right)^{\frac{1}{8}} \log\left(-a^{8} c \left(-\frac{1}{a^{21} c^{3}}\right)^{\frac{3}{8}} + \sqrt{x}\right) - 16 \, {\left(13 \, c x^{5} + 21 \, a x\right)} \sqrt{x}}{1024 \, {\left(a^{2} c^{2} x^{8} + 2 \, a^{3} c x^{4} + a^{4}\right)}}"," ",0,"-1/1024*(260*sqrt(2)*(a^2*c^2*x^8 + 2*a^3*c*x^4 + a^4)*(-1/(a^21*c^3))^(1/8)*arctan(sqrt(2)*sqrt(a^16*c^2*(-1/(a^21*c^3))^(3/4) + sqrt(2)*a^8*c*sqrt(x)*(-1/(a^21*c^3))^(3/8) + x)*a^13*c^2*(-1/(a^21*c^3))^(5/8) - sqrt(2)*a^13*c^2*sqrt(x)*(-1/(a^21*c^3))^(5/8) + 1) + 260*sqrt(2)*(a^2*c^2*x^8 + 2*a^3*c*x^4 + a^4)*(-1/(a^21*c^3))^(1/8)*arctan(sqrt(2)*sqrt(a^16*c^2*(-1/(a^21*c^3))^(3/4) - sqrt(2)*a^8*c*sqrt(x)*(-1/(a^21*c^3))^(3/8) + x)*a^13*c^2*(-1/(a^21*c^3))^(5/8) - sqrt(2)*a^13*c^2*sqrt(x)*(-1/(a^21*c^3))^(5/8) - 1) - 65*sqrt(2)*(a^2*c^2*x^8 + 2*a^3*c*x^4 + a^4)*(-1/(a^21*c^3))^(1/8)*log(a^16*c^2*(-1/(a^21*c^3))^(3/4) + sqrt(2)*a^8*c*sqrt(x)*(-1/(a^21*c^3))^(3/8) + x) + 65*sqrt(2)*(a^2*c^2*x^8 + 2*a^3*c*x^4 + a^4)*(-1/(a^21*c^3))^(1/8)*log(a^16*c^2*(-1/(a^21*c^3))^(3/4) - sqrt(2)*a^8*c*sqrt(x)*(-1/(a^21*c^3))^(3/8) + x) - 520*(a^2*c^2*x^8 + 2*a^3*c*x^4 + a^4)*(-1/(a^21*c^3))^(1/8)*arctan(sqrt(a^16*c^2*(-1/(a^21*c^3))^(3/4) + x)*a^13*c^2*(-1/(a^21*c^3))^(5/8) - a^13*c^2*sqrt(x)*(-1/(a^21*c^3))^(5/8)) + 130*(a^2*c^2*x^8 + 2*a^3*c*x^4 + a^4)*(-1/(a^21*c^3))^(1/8)*log(a^8*c*(-1/(a^21*c^3))^(3/8) + sqrt(x)) - 130*(a^2*c^2*x^8 + 2*a^3*c*x^4 + a^4)*(-1/(a^21*c^3))^(1/8)*log(-a^8*c*(-1/(a^21*c^3))^(3/8) + sqrt(x)) - 16*(13*c*x^5 + 21*a*x)*sqrt(x))/(a^2*c^2*x^8 + 2*a^3*c*x^4 + a^4)","B",0
763,1,631,0,0.927092," ","integrate(1/(c*x^4+a)^3/x^(1/2),x, algorithm=""fricas"")","\frac{420 \, \sqrt{2} {\left(a^{2} c^{2} x^{8} + 2 \, a^{3} c x^{4} + a^{4}\right)} \left(-\frac{1}{a^{23} c}\right)^{\frac{1}{8}} \arctan\left(\sqrt{2} \sqrt{a^{6} \left(-\frac{1}{a^{23} c}\right)^{\frac{1}{4}} + \sqrt{2} a^{3} \sqrt{x} \left(-\frac{1}{a^{23} c}\right)^{\frac{1}{8}} + x} a^{20} c \left(-\frac{1}{a^{23} c}\right)^{\frac{7}{8}} - \sqrt{2} a^{20} c \sqrt{x} \left(-\frac{1}{a^{23} c}\right)^{\frac{7}{8}} + 1\right) + 420 \, \sqrt{2} {\left(a^{2} c^{2} x^{8} + 2 \, a^{3} c x^{4} + a^{4}\right)} \left(-\frac{1}{a^{23} c}\right)^{\frac{1}{8}} \arctan\left(\sqrt{2} \sqrt{a^{6} \left(-\frac{1}{a^{23} c}\right)^{\frac{1}{4}} - \sqrt{2} a^{3} \sqrt{x} \left(-\frac{1}{a^{23} c}\right)^{\frac{1}{8}} + x} a^{20} c \left(-\frac{1}{a^{23} c}\right)^{\frac{7}{8}} - \sqrt{2} a^{20} c \sqrt{x} \left(-\frac{1}{a^{23} c}\right)^{\frac{7}{8}} - 1\right) + 105 \, \sqrt{2} {\left(a^{2} c^{2} x^{8} + 2 \, a^{3} c x^{4} + a^{4}\right)} \left(-\frac{1}{a^{23} c}\right)^{\frac{1}{8}} \log\left(a^{6} \left(-\frac{1}{a^{23} c}\right)^{\frac{1}{4}} + \sqrt{2} a^{3} \sqrt{x} \left(-\frac{1}{a^{23} c}\right)^{\frac{1}{8}} + x\right) - 105 \, \sqrt{2} {\left(a^{2} c^{2} x^{8} + 2 \, a^{3} c x^{4} + a^{4}\right)} \left(-\frac{1}{a^{23} c}\right)^{\frac{1}{8}} \log\left(a^{6} \left(-\frac{1}{a^{23} c}\right)^{\frac{1}{4}} - \sqrt{2} a^{3} \sqrt{x} \left(-\frac{1}{a^{23} c}\right)^{\frac{1}{8}} + x\right) + 840 \, {\left(a^{2} c^{2} x^{8} + 2 \, a^{3} c x^{4} + a^{4}\right)} \left(-\frac{1}{a^{23} c}\right)^{\frac{1}{8}} \arctan\left(\sqrt{a^{6} \left(-\frac{1}{a^{23} c}\right)^{\frac{1}{4}} + x} a^{20} c \left(-\frac{1}{a^{23} c}\right)^{\frac{7}{8}} - a^{20} c \sqrt{x} \left(-\frac{1}{a^{23} c}\right)^{\frac{7}{8}}\right) + 210 \, {\left(a^{2} c^{2} x^{8} + 2 \, a^{3} c x^{4} + a^{4}\right)} \left(-\frac{1}{a^{23} c}\right)^{\frac{1}{8}} \log\left(a^{3} \left(-\frac{1}{a^{23} c}\right)^{\frac{1}{8}} + \sqrt{x}\right) - 210 \, {\left(a^{2} c^{2} x^{8} + 2 \, a^{3} c x^{4} + a^{4}\right)} \left(-\frac{1}{a^{23} c}\right)^{\frac{1}{8}} \log\left(-a^{3} \left(-\frac{1}{a^{23} c}\right)^{\frac{1}{8}} + \sqrt{x}\right) + 16 \, {\left(15 \, c x^{4} + 23 \, a\right)} \sqrt{x}}{1024 \, {\left(a^{2} c^{2} x^{8} + 2 \, a^{3} c x^{4} + a^{4}\right)}}"," ",0,"1/1024*(420*sqrt(2)*(a^2*c^2*x^8 + 2*a^3*c*x^4 + a^4)*(-1/(a^23*c))^(1/8)*arctan(sqrt(2)*sqrt(a^6*(-1/(a^23*c))^(1/4) + sqrt(2)*a^3*sqrt(x)*(-1/(a^23*c))^(1/8) + x)*a^20*c*(-1/(a^23*c))^(7/8) - sqrt(2)*a^20*c*sqrt(x)*(-1/(a^23*c))^(7/8) + 1) + 420*sqrt(2)*(a^2*c^2*x^8 + 2*a^3*c*x^4 + a^4)*(-1/(a^23*c))^(1/8)*arctan(sqrt(2)*sqrt(a^6*(-1/(a^23*c))^(1/4) - sqrt(2)*a^3*sqrt(x)*(-1/(a^23*c))^(1/8) + x)*a^20*c*(-1/(a^23*c))^(7/8) - sqrt(2)*a^20*c*sqrt(x)*(-1/(a^23*c))^(7/8) - 1) + 105*sqrt(2)*(a^2*c^2*x^8 + 2*a^3*c*x^4 + a^4)*(-1/(a^23*c))^(1/8)*log(a^6*(-1/(a^23*c))^(1/4) + sqrt(2)*a^3*sqrt(x)*(-1/(a^23*c))^(1/8) + x) - 105*sqrt(2)*(a^2*c^2*x^8 + 2*a^3*c*x^4 + a^4)*(-1/(a^23*c))^(1/8)*log(a^6*(-1/(a^23*c))^(1/4) - sqrt(2)*a^3*sqrt(x)*(-1/(a^23*c))^(1/8) + x) + 840*(a^2*c^2*x^8 + 2*a^3*c*x^4 + a^4)*(-1/(a^23*c))^(1/8)*arctan(sqrt(a^6*(-1/(a^23*c))^(1/4) + x)*a^20*c*(-1/(a^23*c))^(7/8) - a^20*c*sqrt(x)*(-1/(a^23*c))^(7/8)) + 210*(a^2*c^2*x^8 + 2*a^3*c*x^4 + a^4)*(-1/(a^23*c))^(1/8)*log(a^3*(-1/(a^23*c))^(1/8) + sqrt(x)) - 210*(a^2*c^2*x^8 + 2*a^3*c*x^4 + a^4)*(-1/(a^23*c))^(1/8)*log(-a^3*(-1/(a^23*c))^(1/8) + sqrt(x)) + 16*(15*c*x^4 + 23*a)*sqrt(x))/(a^2*c^2*x^8 + 2*a^3*c*x^4 + a^4)","B",0
764,1,46,0,0.911686," ","integrate(x^11*(c*x^4+a)^(1/2),x, algorithm=""fricas"")","\frac{{\left(15 \, c^{3} x^{12} + 3 \, a c^{2} x^{8} - 4 \, a^{2} c x^{4} + 8 \, a^{3}\right)} \sqrt{c x^{4} + a}}{210 \, c^{3}}"," ",0,"1/210*(15*c^3*x^12 + 3*a*c^2*x^8 - 4*a^2*c*x^4 + 8*a^3)*sqrt(c*x^4 + a)/c^3","A",0
765,1,34,0,0.744291," ","integrate(x^7*(c*x^4+a)^(1/2),x, algorithm=""fricas"")","\frac{{\left(3 \, c^{2} x^{8} + a c x^{4} - 2 \, a^{2}\right)} \sqrt{c x^{4} + a}}{30 \, c^{2}}"," ",0,"1/30*(3*c^2*x^8 + a*c*x^4 - 2*a^2)*sqrt(c*x^4 + a)/c^2","A",0
766,1,14,0,0.750862," ","integrate(x^3*(c*x^4+a)^(1/2),x, algorithm=""fricas"")","\frac{{\left(c x^{4} + a\right)}^{\frac{3}{2}}}{6 \, c}"," ",0,"1/6*(c*x^4 + a)^(3/2)/c","A",0
767,1,84,0,0.838623," ","integrate((c*x^4+a)^(1/2)/x,x, algorithm=""fricas"")","\left[\frac{1}{4} \, \sqrt{a} \log\left(\frac{c x^{4} - 2 \, \sqrt{c x^{4} + a} \sqrt{a} + 2 \, a}{x^{4}}\right) + \frac{1}{2} \, \sqrt{c x^{4} + a}, \frac{1}{2} \, \sqrt{-a} \arctan\left(\frac{\sqrt{c x^{4} + a} \sqrt{-a}}{a}\right) + \frac{1}{2} \, \sqrt{c x^{4} + a}\right]"," ",0,"[1/4*sqrt(a)*log((c*x^4 - 2*sqrt(c*x^4 + a)*sqrt(a) + 2*a)/x^4) + 1/2*sqrt(c*x^4 + a), 1/2*sqrt(-a)*arctan(sqrt(c*x^4 + a)*sqrt(-a)/a) + 1/2*sqrt(c*x^4 + a)]","A",0
768,1,108,0,0.894057," ","integrate((c*x^4+a)^(1/2)/x^5,x, algorithm=""fricas"")","\left[\frac{\sqrt{a} c x^{4} \log\left(\frac{c x^{4} - 2 \, \sqrt{c x^{4} + a} \sqrt{a} + 2 \, a}{x^{4}}\right) - 2 \, \sqrt{c x^{4} + a} a}{8 \, a x^{4}}, \frac{\sqrt{-a} c x^{4} \arctan\left(\frac{\sqrt{c x^{4} + a} \sqrt{-a}}{a}\right) - \sqrt{c x^{4} + a} a}{4 \, a x^{4}}\right]"," ",0,"[1/8*(sqrt(a)*c*x^4*log((c*x^4 - 2*sqrt(c*x^4 + a)*sqrt(a) + 2*a)/x^4) - 2*sqrt(c*x^4 + a)*a)/(a*x^4), 1/4*(sqrt(-a)*c*x^4*arctan(sqrt(c*x^4 + a)*sqrt(-a)/a) - sqrt(c*x^4 + a)*a)/(a*x^4)]","A",0
769,1,133,0,0.742748," ","integrate((c*x^4+a)^(1/2)/x^9,x, algorithm=""fricas"")","\left[\frac{\sqrt{a} c^{2} x^{8} \log\left(\frac{c x^{4} + 2 \, \sqrt{c x^{4} + a} \sqrt{a} + 2 \, a}{x^{4}}\right) - 2 \, {\left(a c x^{4} + 2 \, a^{2}\right)} \sqrt{c x^{4} + a}}{32 \, a^{2} x^{8}}, -\frac{\sqrt{-a} c^{2} x^{8} \arctan\left(\frac{\sqrt{c x^{4} + a} \sqrt{-a}}{a}\right) + {\left(a c x^{4} + 2 \, a^{2}\right)} \sqrt{c x^{4} + a}}{16 \, a^{2} x^{8}}\right]"," ",0,"[1/32*(sqrt(a)*c^2*x^8*log((c*x^4 + 2*sqrt(c*x^4 + a)*sqrt(a) + 2*a)/x^4) - 2*(a*c*x^4 + 2*a^2)*sqrt(c*x^4 + a))/(a^2*x^8), -1/16*(sqrt(-a)*c^2*x^8*arctan(sqrt(c*x^4 + a)*sqrt(-a)/a) + (a*c*x^4 + 2*a^2)*sqrt(c*x^4 + a))/(a^2*x^8)]","A",0
770,1,127,0,0.706488," ","integrate(x^5*(c*x^4+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{a^{2} \sqrt{c} \log\left(-2 \, c x^{4} + 2 \, \sqrt{c x^{4} + a} \sqrt{c} x^{2} - a\right) + 2 \, {\left(2 \, c^{2} x^{6} + a c x^{2}\right)} \sqrt{c x^{4} + a}}{32 \, c^{2}}, \frac{a^{2} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x^{2}}{\sqrt{c x^{4} + a}}\right) + {\left(2 \, c^{2} x^{6} + a c x^{2}\right)} \sqrt{c x^{4} + a}}{16 \, c^{2}}\right]"," ",0,"[1/32*(a^2*sqrt(c)*log(-2*c*x^4 + 2*sqrt(c*x^4 + a)*sqrt(c)*x^2 - a) + 2*(2*c^2*x^6 + a*c*x^2)*sqrt(c*x^4 + a))/c^2, 1/16*(a^2*sqrt(-c)*arctan(sqrt(-c)*x^2/sqrt(c*x^4 + a)) + (2*c^2*x^6 + a*c*x^2)*sqrt(c*x^4 + a))/c^2]","A",0
771,1,102,0,0.830817," ","integrate(x*(c*x^4+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{c x^{4} + a} c x^{2} + a \sqrt{c} \log\left(-2 \, c x^{4} - 2 \, \sqrt{c x^{4} + a} \sqrt{c} x^{2} - a\right)}{8 \, c}, \frac{\sqrt{c x^{4} + a} c x^{2} - a \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x^{2}}{\sqrt{c x^{4} + a}}\right)}{4 \, c}\right]"," ",0,"[1/8*(2*sqrt(c*x^4 + a)*c*x^2 + a*sqrt(c)*log(-2*c*x^4 - 2*sqrt(c*x^4 + a)*sqrt(c)*x^2 - a))/c, 1/4*(sqrt(c*x^4 + a)*c*x^2 - a*sqrt(-c)*arctan(sqrt(-c)*x^2/sqrt(c*x^4 + a)))/c]","A",0
772,1,96,0,0.883879," ","integrate((c*x^4+a)^(1/2)/x^3,x, algorithm=""fricas"")","\left[\frac{\sqrt{c} x^{2} \log\left(-2 \, c x^{4} - 2 \, \sqrt{c x^{4} + a} \sqrt{c} x^{2} - a\right) - 2 \, \sqrt{c x^{4} + a}}{4 \, x^{2}}, -\frac{\sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{-c} x^{2}}{\sqrt{c x^{4} + a}}\right) + \sqrt{c x^{4} + a}}{2 \, x^{2}}\right]"," ",0,"[1/4*(sqrt(c)*x^2*log(-2*c*x^4 - 2*sqrt(c*x^4 + a)*sqrt(c)*x^2 - a) - 2*sqrt(c*x^4 + a))/x^2, -1/2*(sqrt(-c)*x^2*arctan(sqrt(-c)*x^2/sqrt(c*x^4 + a)) + sqrt(c*x^4 + a))/x^2]","A",0
773,1,17,0,0.913333," ","integrate((c*x^4+a)^(1/2)/x^7,x, algorithm=""fricas"")","-\frac{{\left(c x^{4} + a\right)}^{\frac{3}{2}}}{6 \, a x^{6}}"," ",0,"-1/6*(c*x^4 + a)^(3/2)/(a*x^6)","A",0
774,1,38,0,0.668525," ","integrate((c*x^4+a)^(1/2)/x^11,x, algorithm=""fricas"")","\frac{{\left(2 \, c^{2} x^{8} - a c x^{4} - 3 \, a^{2}\right)} \sqrt{c x^{4} + a}}{30 \, a^{2} x^{10}}"," ",0,"1/30*(2*c^2*x^8 - a*c*x^4 - 3*a^2)*sqrt(c*x^4 + a)/(a^2*x^10)","A",0
775,1,49,0,0.631258," ","integrate((c*x^4+a)^(1/2)/x^15,x, algorithm=""fricas"")","-\frac{{\left(8 \, c^{3} x^{12} - 4 \, a c^{2} x^{8} + 3 \, a^{2} c x^{4} + 15 \, a^{3}\right)} \sqrt{c x^{4} + a}}{210 \, a^{3} x^{14}}"," ",0,"-1/210*(8*c^3*x^12 - 4*a*c^2*x^8 + 3*a^2*c*x^4 + 15*a^3)*sqrt(c*x^4 + a)/(a^3*x^14)","A",0
776,0,0,0,0.782512," ","integrate(x^4*(c*x^4+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{4} + a} x^{4}, x\right)"," ",0,"integral(sqrt(c*x^4 + a)*x^4, x)","F",0
777,0,0,0,0.813432," ","integrate((c*x^4+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{4} + a}, x\right)"," ",0,"integral(sqrt(c*x^4 + a), x)","F",0
778,0,0,0,0.802734," ","integrate((c*x^4+a)^(1/2)/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + a}}{x^{4}}, x\right)"," ",0,"integral(sqrt(c*x^4 + a)/x^4, x)","F",0
779,0,0,0,0.665273," ","integrate((c*x^4+a)^(1/2)/x^8,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + a}}{x^{8}}, x\right)"," ",0,"integral(sqrt(c*x^4 + a)/x^8, x)","F",0
780,0,0,0,0.656028," ","integrate(x^2*(c*x^4+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{4} + a} x^{2}, x\right)"," ",0,"integral(sqrt(c*x^4 + a)*x^2, x)","F",0
781,0,0,0,0.799710," ","integrate((c*x^4+a)^(1/2)/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + a}}{x^{2}}, x\right)"," ",0,"integral(sqrt(c*x^4 + a)/x^2, x)","F",0
782,0,0,0,0.852779," ","integrate((c*x^4+a)^(1/2)/x^6,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + a}}{x^{6}}, x\right)"," ",0,"integral(sqrt(c*x^4 + a)/x^6, x)","F",0
783,1,57,0,0.879786," ","integrate(x^11*(c*x^4+a)^(3/2),x, algorithm=""fricas"")","\frac{{\left(35 \, c^{4} x^{16} + 50 \, a c^{3} x^{12} + 3 \, a^{2} c^{2} x^{8} - 4 \, a^{3} c x^{4} + 8 \, a^{4}\right)} \sqrt{c x^{4} + a}}{630 \, c^{3}}"," ",0,"1/630*(35*c^4*x^16 + 50*a*c^3*x^12 + 3*a^2*c^2*x^8 - 4*a^3*c*x^4 + 8*a^4)*sqrt(c*x^4 + a)/c^3","A",0
784,1,45,0,0.795775," ","integrate(x^7*(c*x^4+a)^(3/2),x, algorithm=""fricas"")","\frac{{\left(5 \, c^{3} x^{12} + 8 \, a c^{2} x^{8} + a^{2} c x^{4} - 2 \, a^{3}\right)} \sqrt{c x^{4} + a}}{70 \, c^{2}}"," ",0,"1/70*(5*c^3*x^12 + 8*a*c^2*x^8 + a^2*c*x^4 - 2*a^3)*sqrt(c*x^4 + a)/c^2","A",0
785,1,32,0,0.765032," ","integrate(x^3*(c*x^4+a)^(3/2),x, algorithm=""fricas"")","\frac{{\left(c^{2} x^{8} + 2 \, a c x^{4} + a^{2}\right)} \sqrt{c x^{4} + a}}{10 \, c}"," ",0,"1/10*(c^2*x^8 + 2*a*c*x^4 + a^2)*sqrt(c*x^4 + a)/c","B",0
786,1,103,0,0.657256," ","integrate((c*x^4+a)^(3/2)/x,x, algorithm=""fricas"")","\left[\frac{1}{4} \, a^{\frac{3}{2}} \log\left(\frac{c x^{4} - 2 \, \sqrt{c x^{4} + a} \sqrt{a} + 2 \, a}{x^{4}}\right) + \frac{1}{6} \, {\left(c x^{4} + 4 \, a\right)} \sqrt{c x^{4} + a}, \frac{1}{2} \, \sqrt{-a} a \arctan\left(\frac{\sqrt{c x^{4} + a} \sqrt{-a}}{a}\right) + \frac{1}{6} \, {\left(c x^{4} + 4 \, a\right)} \sqrt{c x^{4} + a}\right]"," ",0,"[1/4*a^(3/2)*log((c*x^4 - 2*sqrt(c*x^4 + a)*sqrt(a) + 2*a)/x^4) + 1/6*(c*x^4 + 4*a)*sqrt(c*x^4 + a), 1/2*sqrt(-a)*a*arctan(sqrt(c*x^4 + a)*sqrt(-a)/a) + 1/6*(c*x^4 + 4*a)*sqrt(c*x^4 + a)]","A",0
787,1,121,0,0.821716," ","integrate((c*x^4+a)^(3/2)/x^5,x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{a} c x^{4} \log\left(\frac{c x^{4} - 2 \, \sqrt{c x^{4} + a} \sqrt{a} + 2 \, a}{x^{4}}\right) + 2 \, {\left(2 \, c x^{4} - a\right)} \sqrt{c x^{4} + a}}{8 \, x^{4}}, \frac{3 \, \sqrt{-a} c x^{4} \arctan\left(\frac{\sqrt{c x^{4} + a} \sqrt{-a}}{a}\right) + {\left(2 \, c x^{4} - a\right)} \sqrt{c x^{4} + a}}{4 \, x^{4}}\right]"," ",0,"[1/8*(3*sqrt(a)*c*x^4*log((c*x^4 - 2*sqrt(c*x^4 + a)*sqrt(a) + 2*a)/x^4) + 2*(2*c*x^4 - a)*sqrt(c*x^4 + a))/x^4, 1/4*(3*sqrt(-a)*c*x^4*arctan(sqrt(c*x^4 + a)*sqrt(-a)/a) + (2*c*x^4 - a)*sqrt(c*x^4 + a))/x^4]","A",0
788,1,138,0,0.879125," ","integrate((c*x^4+a)^(3/2)/x^9,x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{a} c^{2} x^{8} \log\left(\frac{c x^{4} - 2 \, \sqrt{c x^{4} + a} \sqrt{a} + 2 \, a}{x^{4}}\right) - 2 \, {\left(5 \, a c x^{4} + 2 \, a^{2}\right)} \sqrt{c x^{4} + a}}{32 \, a x^{8}}, \frac{3 \, \sqrt{-a} c^{2} x^{8} \arctan\left(\frac{\sqrt{c x^{4} + a} \sqrt{-a}}{a}\right) - {\left(5 \, a c x^{4} + 2 \, a^{2}\right)} \sqrt{c x^{4} + a}}{16 \, a x^{8}}\right]"," ",0,"[1/32*(3*sqrt(a)*c^2*x^8*log((c*x^4 - 2*sqrt(c*x^4 + a)*sqrt(a) + 2*a)/x^4) - 2*(5*a*c*x^4 + 2*a^2)*sqrt(c*x^4 + a))/(a*x^8), 1/16*(3*sqrt(-a)*c^2*x^8*arctan(sqrt(c*x^4 + a)*sqrt(-a)/a) - (5*a*c*x^4 + 2*a^2)*sqrt(c*x^4 + a))/(a*x^8)]","A",0
789,1,153,0,0.768961," ","integrate(x^5*(c*x^4+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, a^{3} \sqrt{c} \log\left(-2 \, c x^{4} + 2 \, \sqrt{c x^{4} + a} \sqrt{c} x^{2} - a\right) + 2 \, {\left(8 \, c^{3} x^{10} + 14 \, a c^{2} x^{6} + 3 \, a^{2} c x^{2}\right)} \sqrt{c x^{4} + a}}{192 \, c^{2}}, \frac{3 \, a^{3} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x^{2}}{\sqrt{c x^{4} + a}}\right) + {\left(8 \, c^{3} x^{10} + 14 \, a c^{2} x^{6} + 3 \, a^{2} c x^{2}\right)} \sqrt{c x^{4} + a}}{96 \, c^{2}}\right]"," ",0,"[1/192*(3*a^3*sqrt(c)*log(-2*c*x^4 + 2*sqrt(c*x^4 + a)*sqrt(c)*x^2 - a) + 2*(8*c^3*x^10 + 14*a*c^2*x^6 + 3*a^2*c*x^2)*sqrt(c*x^4 + a))/c^2, 1/96*(3*a^3*sqrt(-c)*arctan(sqrt(-c)*x^2/sqrt(c*x^4 + a)) + (8*c^3*x^10 + 14*a*c^2*x^6 + 3*a^2*c*x^2)*sqrt(c*x^4 + a))/c^2]","A",0
790,1,132,0,0.600036," ","integrate(x*(c*x^4+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, a^{2} \sqrt{c} \log\left(-2 \, c x^{4} - 2 \, \sqrt{c x^{4} + a} \sqrt{c} x^{2} - a\right) + 2 \, {\left(2 \, c^{2} x^{6} + 5 \, a c x^{2}\right)} \sqrt{c x^{4} + a}}{32 \, c}, -\frac{3 \, a^{2} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x^{2}}{\sqrt{c x^{4} + a}}\right) - {\left(2 \, c^{2} x^{6} + 5 \, a c x^{2}\right)} \sqrt{c x^{4} + a}}{16 \, c}\right]"," ",0,"[1/32*(3*a^2*sqrt(c)*log(-2*c*x^4 - 2*sqrt(c*x^4 + a)*sqrt(c)*x^2 - a) + 2*(2*c^2*x^6 + 5*a*c*x^2)*sqrt(c*x^4 + a))/c, -1/16*(3*a^2*sqrt(-c)*arctan(sqrt(-c)*x^2/sqrt(c*x^4 + a)) - (2*c^2*x^6 + 5*a*c*x^2)*sqrt(c*x^4 + a))/c]","A",0
791,1,120,0,0.672298," ","integrate((c*x^4+a)^(3/2)/x^3,x, algorithm=""fricas"")","\left[\frac{3 \, a \sqrt{c} x^{2} \log\left(-2 \, c x^{4} - 2 \, \sqrt{c x^{4} + a} \sqrt{c} x^{2} - a\right) + 2 \, \sqrt{c x^{4} + a} {\left(c x^{4} - 2 \, a\right)}}{8 \, x^{2}}, -\frac{3 \, a \sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{-c} x^{2}}{\sqrt{c x^{4} + a}}\right) - \sqrt{c x^{4} + a} {\left(c x^{4} - 2 \, a\right)}}{4 \, x^{2}}\right]"," ",0,"[1/8*(3*a*sqrt(c)*x^2*log(-2*c*x^4 - 2*sqrt(c*x^4 + a)*sqrt(c)*x^2 - a) + 2*sqrt(c*x^4 + a)*(c*x^4 - 2*a))/x^2, -1/4*(3*a*sqrt(-c)*x^2*arctan(sqrt(-c)*x^2/sqrt(c*x^4 + a)) - sqrt(c*x^4 + a)*(c*x^4 - 2*a))/x^2]","A",0
792,1,116,0,0.842531," ","integrate((c*x^4+a)^(3/2)/x^7,x, algorithm=""fricas"")","\left[\frac{3 \, c^{\frac{3}{2}} x^{6} \log\left(-2 \, c x^{4} - 2 \, \sqrt{c x^{4} + a} \sqrt{c} x^{2} - a\right) - 2 \, {\left(4 \, c x^{4} + a\right)} \sqrt{c x^{4} + a}}{12 \, x^{6}}, -\frac{3 \, \sqrt{-c} c x^{6} \arctan\left(\frac{\sqrt{-c} x^{2}}{\sqrt{c x^{4} + a}}\right) + {\left(4 \, c x^{4} + a\right)} \sqrt{c x^{4} + a}}{6 \, x^{6}}\right]"," ",0,"[1/12*(3*c^(3/2)*x^6*log(-2*c*x^4 - 2*sqrt(c*x^4 + a)*sqrt(c)*x^2 - a) - 2*(4*c*x^4 + a)*sqrt(c*x^4 + a))/x^6, -1/6*(3*sqrt(-c)*c*x^6*arctan(sqrt(-c)*x^2/sqrt(c*x^4 + a)) + (4*c*x^4 + a)*sqrt(c*x^4 + a))/x^6]","A",0
793,1,35,0,0.753653," ","integrate((c*x^4+a)^(3/2)/x^11,x, algorithm=""fricas"")","-\frac{{\left(c^{2} x^{8} + 2 \, a c x^{4} + a^{2}\right)} \sqrt{c x^{4} + a}}{10 \, a x^{10}}"," ",0,"-1/10*(c^2*x^8 + 2*a*c*x^4 + a^2)*sqrt(c*x^4 + a)/(a*x^10)","B",0
794,1,49,0,0.733298," ","integrate((c*x^4+a)^(3/2)/x^15,x, algorithm=""fricas"")","\frac{{\left(2 \, c^{3} x^{12} - a c^{2} x^{8} - 8 \, a^{2} c x^{4} - 5 \, a^{3}\right)} \sqrt{c x^{4} + a}}{70 \, a^{2} x^{14}}"," ",0,"1/70*(2*c^3*x^12 - a*c^2*x^8 - 8*a^2*c*x^4 - 5*a^3)*sqrt(c*x^4 + a)/(a^2*x^14)","A",0
795,1,60,0,0.916007," ","integrate((c*x^4+a)^(3/2)/x^19,x, algorithm=""fricas"")","-\frac{{\left(8 \, c^{4} x^{16} - 4 \, a c^{3} x^{12} + 3 \, a^{2} c^{2} x^{8} + 50 \, a^{3} c x^{4} + 35 \, a^{4}\right)} \sqrt{c x^{4} + a}}{630 \, a^{3} x^{18}}"," ",0,"-1/630*(8*c^4*x^16 - 4*a*c^3*x^12 + 3*a^2*c^2*x^8 + 50*a^3*c*x^4 + 35*a^4)*sqrt(c*x^4 + a)/(a^3*x^18)","A",0
796,0,0,0,0.766895," ","integrate(x^4*(c*x^4+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{8} + a x^{4}\right)} \sqrt{c x^{4} + a}, x\right)"," ",0,"integral((c*x^8 + a*x^4)*sqrt(c*x^4 + a), x)","F",0
797,0,0,0,0.581780," ","integrate((c*x^4+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{4} + a\right)}^{\frac{3}{2}}, x\right)"," ",0,"integral((c*x^4 + a)^(3/2), x)","F",0
798,0,0,0,0.836899," ","integrate((c*x^4+a)^(3/2)/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{4} + a\right)}^{\frac{3}{2}}}{x^{4}}, x\right)"," ",0,"integral((c*x^4 + a)^(3/2)/x^4, x)","F",0
799,0,0,0,0.858573," ","integrate((c*x^4+a)^(3/2)/x^8,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{4} + a\right)}^{\frac{3}{2}}}{x^{8}}, x\right)"," ",0,"integral((c*x^4 + a)^(3/2)/x^8, x)","F",0
800,0,0,0,0.840535," ","integrate(x^2*(c*x^4+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{6} + a x^{2}\right)} \sqrt{c x^{4} + a}, x\right)"," ",0,"integral((c*x^6 + a*x^2)*sqrt(c*x^4 + a), x)","F",0
801,0,0,0,0.788571," ","integrate((c*x^4+a)^(3/2)/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{4} + a\right)}^{\frac{3}{2}}}{x^{2}}, x\right)"," ",0,"integral((c*x^4 + a)^(3/2)/x^2, x)","F",0
802,0,0,0,0.678937," ","integrate((c*x^4+a)^(3/2)/x^6,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{4} + a\right)}^{\frac{3}{2}}}{x^{6}}, x\right)"," ",0,"integral((c*x^4 + a)^(3/2)/x^6, x)","F",0
803,0,0,0,0.755088," ","integrate((x^4+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(x^{4} + 1\right)}^{\frac{3}{2}}, x\right)"," ",0,"integral((x^4 + 1)^(3/2), x)","F",0
804,0,0,0,0.860235," ","integrate((-x^4+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(-x^{4} + 1\right)}^{\frac{3}{2}}, x\right)"," ",0,"integral((-x^4 + 1)^(3/2), x)","F",0
805,1,23,0,0.790729," ","integrate(x^7*(3*x^4+5)^(1/2),x, algorithm=""fricas"")","\frac{1}{270} \, {\left(27 \, x^{8} + 15 \, x^{4} - 50\right)} \sqrt{3 \, x^{4} + 5}"," ",0,"1/270*(27*x^8 + 15*x^4 - 50)*sqrt(3*x^4 + 5)","A",0
806,1,9,0,0.848632," ","integrate(x^3*(x^4+5)^(1/2),x, algorithm=""fricas"")","\frac{1}{6} \, {\left(x^{4} + 5\right)}^{\frac{3}{2}}"," ",0,"1/6*(x^4 + 5)^(3/2)","A",0
807,1,45,0,0.590188," ","integrate(x*(2*x^4+3)^(1/2),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{2 \, x^{4} + 3} x^{2} + \frac{3}{16} \, \sqrt{2} \log\left(-4 \, x^{4} - 2 \, \sqrt{2} \sqrt{2 \, x^{4} + 3} x^{2} - 3\right)"," ",0,"1/4*sqrt(2*x^4 + 3)*x^2 + 3/16*sqrt(2)*log(-4*x^4 - 2*sqrt(2)*sqrt(2*x^4 + 3)*x^2 - 3)","A",0
808,1,29,0,0.879272," ","integrate(x*(x^4-2)^(1/2),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{x^{4} - 2} x^{2} + \frac{1}{2} \, \log\left(-x^{2} + \sqrt{x^{4} - 2}\right)"," ",0,"1/4*sqrt(x^4 - 2)*x^2 + 1/2*log(-x^2 + sqrt(x^4 - 2))","A",0
809,0,0,0,0.896295," ","integrate((x^4+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{x^{4} + 1}, x\right)"," ",0,"integral(sqrt(x^4 + 1), x)","F",0
810,0,0,0,0.892395," ","integrate((-x^4+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{-x^{4} + 1}, x\right)"," ",0,"integral(sqrt(-x^4 + 1), x)","F",0
811,1,35,0,0.520947," ","integrate(x^11/(b*x^4+a)^(1/2),x, algorithm=""fricas"")","\frac{{\left(3 \, b^{2} x^{8} - 4 \, a b x^{4} + 8 \, a^{2}\right)} \sqrt{b x^{4} + a}}{30 \, b^{3}}"," ",0,"1/30*(3*b^2*x^8 - 4*a*b*x^4 + 8*a^2)*sqrt(b*x^4 + a)/b^3","A",0
812,1,23,0,0.718262," ","integrate(x^7/(b*x^4+a)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{b x^{4} + a} {\left(b x^{4} - 2 \, a\right)}}{6 \, b^{2}}"," ",0,"1/6*sqrt(b*x^4 + a)*(b*x^4 - 2*a)/b^2","A",0
813,1,14,0,0.821939," ","integrate(x^3/(b*x^4+a)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{b x^{4} + a}}{2 \, b}"," ",0,"1/2*sqrt(b*x^4 + a)/b","A",0
814,1,63,0,0.810448," ","integrate(1/x/(b*x^4+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{b x^{4} - 2 \, \sqrt{b x^{4} + a} \sqrt{a} + 2 \, a}{x^{4}}\right)}{4 \, \sqrt{a}}, \frac{\sqrt{-a} \arctan\left(\frac{\sqrt{b x^{4} + a} \sqrt{-a}}{a}\right)}{2 \, a}\right]"," ",0,"[1/4*log((b*x^4 - 2*sqrt(b*x^4 + a)*sqrt(a) + 2*a)/x^4)/sqrt(a), 1/2*sqrt(-a)*arctan(sqrt(b*x^4 + a)*sqrt(-a)/a)/a]","A",0
815,1,107,0,0.670330," ","integrate(1/x^5/(b*x^4+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a} b x^{4} \log\left(\frac{b x^{4} + 2 \, \sqrt{b x^{4} + a} \sqrt{a} + 2 \, a}{x^{4}}\right) - 2 \, \sqrt{b x^{4} + a} a}{8 \, a^{2} x^{4}}, -\frac{\sqrt{-a} b x^{4} \arctan\left(\frac{\sqrt{b x^{4} + a} \sqrt{-a}}{a}\right) + \sqrt{b x^{4} + a} a}{4 \, a^{2} x^{4}}\right]"," ",0,"[1/8*(sqrt(a)*b*x^4*log((b*x^4 + 2*sqrt(b*x^4 + a)*sqrt(a) + 2*a)/x^4) - 2*sqrt(b*x^4 + a)*a)/(a^2*x^4), -1/4*(sqrt(-a)*b*x^4*arctan(sqrt(b*x^4 + a)*sqrt(-a)/a) + sqrt(b*x^4 + a)*a)/(a^2*x^4)]","A",0
816,1,101,0,0.820594," ","integrate(x^5/(b*x^4+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{b x^{4} + a} b x^{2} + a \sqrt{b} \log\left(-2 \, b x^{4} + 2 \, \sqrt{b x^{4} + a} \sqrt{b} x^{2} - a\right)}{8 \, b^{2}}, \frac{\sqrt{b x^{4} + a} b x^{2} + a \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x^{2}}{\sqrt{b x^{4} + a}}\right)}{4 \, b^{2}}\right]"," ",0,"[1/8*(2*sqrt(b*x^4 + a)*b*x^2 + a*sqrt(b)*log(-2*b*x^4 + 2*sqrt(b*x^4 + a)*sqrt(b)*x^2 - a))/b^2, 1/4*(sqrt(b*x^4 + a)*b*x^2 + a*sqrt(-b)*arctan(sqrt(-b)*x^2/sqrt(b*x^4 + a)))/b^2]","A",0
817,1,63,0,0.598326," ","integrate(x/(b*x^4+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(-2 \, b x^{4} - 2 \, \sqrt{b x^{4} + a} \sqrt{b} x^{2} - a\right)}{4 \, \sqrt{b}}, -\frac{\sqrt{-b} \arctan\left(\frac{\sqrt{-b} x^{2}}{\sqrt{b x^{4} + a}}\right)}{2 \, b}\right]"," ",0,"[1/4*log(-2*b*x^4 - 2*sqrt(b*x^4 + a)*sqrt(b)*x^2 - a)/sqrt(b), -1/2*sqrt(-b)*arctan(sqrt(-b)*x^2/sqrt(b*x^4 + a))/b]","A",0
818,1,17,0,0.764828," ","integrate(1/x^3/(b*x^4+a)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{b x^{4} + a}}{2 \, a x^{2}}"," ",0,"-1/2*sqrt(b*x^4 + a)/(a*x^2)","A",0
819,1,27,0,0.713242," ","integrate(1/x^7/(b*x^4+a)^(1/2),x, algorithm=""fricas"")","\frac{{\left(2 \, b x^{4} - a\right)} \sqrt{b x^{4} + a}}{6 \, a^{2} x^{6}}"," ",0,"1/6*(2*b*x^4 - a)*sqrt(b*x^4 + a)/(a^2*x^6)","A",0
820,1,38,0,0.830930," ","integrate(1/x^11/(b*x^4+a)^(1/2),x, algorithm=""fricas"")","-\frac{{\left(8 \, b^{2} x^{8} - 4 \, a b x^{4} + 3 \, a^{2}\right)} \sqrt{b x^{4} + a}}{30 \, a^{3} x^{10}}"," ",0,"-1/30*(8*b^2*x^8 - 4*a*b*x^4 + 3*a^2)*sqrt(b*x^4 + a)/(a^3*x^10)","A",0
821,0,0,0,0.881992," ","integrate(x^8/(b*x^4+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{8}}{\sqrt{b x^{4} + a}}, x\right)"," ",0,"integral(x^8/sqrt(b*x^4 + a), x)","F",0
822,0,0,0,0.585050," ","integrate(x^4/(b*x^4+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{4}}{\sqrt{b x^{4} + a}}, x\right)"," ",0,"integral(x^4/sqrt(b*x^4 + a), x)","F",0
823,0,0,0,0.710315," ","integrate(1/(b*x^4+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{b x^{4} + a}}, x\right)"," ",0,"integral(1/sqrt(b*x^4 + a), x)","F",0
824,0,0,0,0.557036," ","integrate(1/x^4/(b*x^4+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{4} + a}}{b x^{8} + a x^{4}}, x\right)"," ",0,"integral(sqrt(b*x^4 + a)/(b*x^8 + a*x^4), x)","F",0
825,0,0,0,0.853309," ","integrate(1/x^8/(b*x^4+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{4} + a}}{b x^{12} + a x^{8}}, x\right)"," ",0,"integral(sqrt(b*x^4 + a)/(b*x^12 + a*x^8), x)","F",0
826,0,0,0,0.896318," ","integrate(x^10/(b*x^4+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{10}}{\sqrt{b x^{4} + a}}, x\right)"," ",0,"integral(x^10/sqrt(b*x^4 + a), x)","F",0
827,0,0,0,0.854967," ","integrate(x^6/(b*x^4+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{6}}{\sqrt{b x^{4} + a}}, x\right)"," ",0,"integral(x^6/sqrt(b*x^4 + a), x)","F",0
828,0,0,0,0.845324," ","integrate(x^2/(b*x^4+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2}}{\sqrt{b x^{4} + a}}, x\right)"," ",0,"integral(x^2/sqrt(b*x^4 + a), x)","F",0
829,0,0,0,0.657020," ","integrate(1/x^2/(b*x^4+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{4} + a}}{b x^{6} + a x^{2}}, x\right)"," ",0,"integral(sqrt(b*x^4 + a)/(b*x^6 + a*x^2), x)","F",0
830,0,0,0,0.820504," ","integrate(1/x^6/(b*x^4+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{4} + a}}{b x^{10} + a x^{6}}, x\right)"," ",0,"integral(sqrt(b*x^4 + a)/(b*x^10 + a*x^6), x)","F",0
831,1,36,0,0.627013," ","integrate(x^11/(-b*x^4+a)^(1/2),x, algorithm=""fricas"")","-\frac{{\left(3 \, b^{2} x^{8} + 4 \, a b x^{4} + 8 \, a^{2}\right)} \sqrt{-b x^{4} + a}}{30 \, b^{3}}"," ",0,"-1/30*(3*b^2*x^8 + 4*a*b*x^4 + 8*a^2)*sqrt(-b*x^4 + a)/b^3","A",0
832,1,24,0,0.996755," ","integrate(x^7/(-b*x^4+a)^(1/2),x, algorithm=""fricas"")","-\frac{{\left(b x^{4} + 2 \, a\right)} \sqrt{-b x^{4} + a}}{6 \, b^{2}}"," ",0,"-1/6*(b*x^4 + 2*a)*sqrt(-b*x^4 + a)/b^2","A",0
833,1,15,0,0.874982," ","integrate(x^3/(-b*x^4+a)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{-b x^{4} + a}}{2 \, b}"," ",0,"-1/2*sqrt(-b*x^4 + a)/b","A",0
834,1,65,0,1.326375," ","integrate(1/x/(-b*x^4+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{b x^{4} + 2 \, \sqrt{-b x^{4} + a} \sqrt{a} - 2 \, a}{x^{4}}\right)}{4 \, \sqrt{a}}, \frac{\sqrt{-a} \arctan\left(\frac{\sqrt{-b x^{4} + a} \sqrt{-a}}{a}\right)}{2 \, a}\right]"," ",0,"[1/4*log((b*x^4 + 2*sqrt(-b*x^4 + a)*sqrt(a) - 2*a)/x^4)/sqrt(a), 1/2*sqrt(-a)*arctan(sqrt(-b*x^4 + a)*sqrt(-a)/a)/a]","A",0
835,1,112,0,1.006968," ","integrate(1/x^5/(-b*x^4+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a} b x^{4} \log\left(\frac{b x^{4} + 2 \, \sqrt{-b x^{4} + a} \sqrt{a} - 2 \, a}{x^{4}}\right) - 2 \, \sqrt{-b x^{4} + a} a}{8 \, a^{2} x^{4}}, \frac{\sqrt{-a} b x^{4} \arctan\left(\frac{\sqrt{-b x^{4} + a} \sqrt{-a}}{a}\right) - \sqrt{-b x^{4} + a} a}{4 \, a^{2} x^{4}}\right]"," ",0,"[1/8*(sqrt(a)*b*x^4*log((b*x^4 + 2*sqrt(-b*x^4 + a)*sqrt(a) - 2*a)/x^4) - 2*sqrt(-b*x^4 + a)*a)/(a^2*x^4), 1/4*(sqrt(-a)*b*x^4*arctan(sqrt(-b*x^4 + a)*sqrt(-a)/a) - sqrt(-b*x^4 + a)*a)/(a^2*x^4)]","A",0
836,1,116,0,1.103674," ","integrate(x^5/(-b*x^4+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{2 \, \sqrt{-b x^{4} + a} b x^{2} + a \sqrt{-b} \log\left(2 \, b x^{4} - 2 \, \sqrt{-b x^{4} + a} \sqrt{-b} x^{2} - a\right)}{8 \, b^{2}}, -\frac{\sqrt{-b x^{4} + a} b x^{2} + a \sqrt{b} \arctan\left(\frac{\sqrt{-b x^{4} + a} \sqrt{b} x^{2}}{b x^{4} - a}\right)}{4 \, b^{2}}\right]"," ",0,"[-1/8*(2*sqrt(-b*x^4 + a)*b*x^2 + a*sqrt(-b)*log(2*b*x^4 - 2*sqrt(-b*x^4 + a)*sqrt(-b)*x^2 - a))/b^2, -1/4*(sqrt(-b*x^4 + a)*b*x^2 + a*sqrt(b)*arctan(sqrt(-b*x^4 + a)*sqrt(b)*x^2/(b*x^4 - a)))/b^2]","A",0
837,1,76,0,1.180632," ","integrate(x/(-b*x^4+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-b} \log\left(2 \, b x^{4} - 2 \, \sqrt{-b x^{4} + a} \sqrt{-b} x^{2} - a\right)}{4 \, b}, -\frac{\arctan\left(\frac{\sqrt{-b x^{4} + a} \sqrt{b} x^{2}}{b x^{4} - a}\right)}{2 \, \sqrt{b}}\right]"," ",0,"[-1/4*sqrt(-b)*log(2*b*x^4 - 2*sqrt(-b*x^4 + a)*sqrt(-b)*x^2 - a)/b, -1/2*arctan(sqrt(-b*x^4 + a)*sqrt(b)*x^2/(b*x^4 - a))/sqrt(b)]","A",0
838,1,18,0,1.210370," ","integrate(1/x^3/(-b*x^4+a)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{-b x^{4} + a}}{2 \, a x^{2}}"," ",0,"-1/2*sqrt(-b*x^4 + a)/(a*x^2)","A",0
839,1,26,0,0.888155," ","integrate(1/x^7/(-b*x^4+a)^(1/2),x, algorithm=""fricas"")","-\frac{{\left(2 \, b x^{4} + a\right)} \sqrt{-b x^{4} + a}}{6 \, a^{2} x^{6}}"," ",0,"-1/6*(2*b*x^4 + a)*sqrt(-b*x^4 + a)/(a^2*x^6)","A",0
840,1,39,0,1.157589," ","integrate(1/x^11/(-b*x^4+a)^(1/2),x, algorithm=""fricas"")","-\frac{{\left(8 \, b^{2} x^{8} + 4 \, a b x^{4} + 3 \, a^{2}\right)} \sqrt{-b x^{4} + a}}{30 \, a^{3} x^{10}}"," ",0,"-1/30*(8*b^2*x^8 + 4*a*b*x^4 + 3*a^2)*sqrt(-b*x^4 + a)/(a^3*x^10)","A",0
841,0,0,0,0.774338," ","integrate(x^8/(-b*x^4+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-b x^{4} + a} x^{8}}{b x^{4} - a}, x\right)"," ",0,"integral(-sqrt(-b*x^4 + a)*x^8/(b*x^4 - a), x)","F",0
842,0,0,0,0.904759," ","integrate(x^4/(-b*x^4+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-b x^{4} + a} x^{4}}{b x^{4} - a}, x\right)"," ",0,"integral(-sqrt(-b*x^4 + a)*x^4/(b*x^4 - a), x)","F",0
843,0,0,0,0.987043," ","integrate(1/(-b*x^4+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-b x^{4} + a}}{b x^{4} - a}, x\right)"," ",0,"integral(-sqrt(-b*x^4 + a)/(b*x^4 - a), x)","F",0
844,0,0,0,0.783303," ","integrate(1/x^4/(-b*x^4+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-b x^{4} + a}}{b x^{8} - a x^{4}}, x\right)"," ",0,"integral(-sqrt(-b*x^4 + a)/(b*x^8 - a*x^4), x)","F",0
845,0,0,0,1.048089," ","integrate(1/x^8/(-b*x^4+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-b x^{4} + a}}{b x^{12} - a x^{8}}, x\right)"," ",0,"integral(-sqrt(-b*x^4 + a)/(b*x^12 - a*x^8), x)","F",0
846,0,0,0,1.086152," ","integrate(x^10/(-b*x^4+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-b x^{4} + a} x^{10}}{b x^{4} - a}, x\right)"," ",0,"integral(-sqrt(-b*x^4 + a)*x^10/(b*x^4 - a), x)","F",0
847,0,0,0,0.829146," ","integrate(x^6/(-b*x^4+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-b x^{4} + a} x^{6}}{b x^{4} - a}, x\right)"," ",0,"integral(-sqrt(-b*x^4 + a)*x^6/(b*x^4 - a), x)","F",0
848,0,0,0,0.621030," ","integrate(x^2/(-b*x^4+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-b x^{4} + a} x^{2}}{b x^{4} - a}, x\right)"," ",0,"integral(-sqrt(-b*x^4 + a)*x^2/(b*x^4 - a), x)","F",0
849,0,0,0,1.040558," ","integrate(1/x^2/(-b*x^4+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-b x^{4} + a}}{b x^{6} - a x^{2}}, x\right)"," ",0,"integral(-sqrt(-b*x^4 + a)/(b*x^6 - a*x^2), x)","F",0
850,0,0,0,0.957305," ","integrate(1/x^6/(-b*x^4+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-b x^{4} + a}}{b x^{10} - a x^{6}}, x\right)"," ",0,"integral(-sqrt(-b*x^4 + a)/(b*x^10 - a*x^6), x)","F",0
851,1,46,0,1.052508," ","integrate(x^11/(b*x^4+a)^(3/2),x, algorithm=""fricas"")","\frac{{\left(b^{2} x^{8} - 4 \, a b x^{4} - 8 \, a^{2}\right)} \sqrt{b x^{4} + a}}{6 \, {\left(b^{4} x^{4} + a b^{3}\right)}}"," ",0,"1/6*(b^2*x^8 - 4*a*b*x^4 - 8*a^2)*sqrt(b*x^4 + a)/(b^4*x^4 + a*b^3)","A",0
852,1,35,0,1.040893," ","integrate(x^7/(b*x^4+a)^(3/2),x, algorithm=""fricas"")","\frac{{\left(b x^{4} + 2 \, a\right)} \sqrt{b x^{4} + a}}{2 \, {\left(b^{3} x^{4} + a b^{2}\right)}}"," ",0,"1/2*(b*x^4 + 2*a)*sqrt(b*x^4 + a)/(b^3*x^4 + a*b^2)","A",0
853,1,24,0,0.876262," ","integrate(x^3/(b*x^4+a)^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{b x^{4} + a}}{2 \, {\left(b^{2} x^{4} + a b\right)}}"," ",0,"-1/2*sqrt(b*x^4 + a)/(b^2*x^4 + a*b)","A",0
854,1,129,0,0.758017," ","integrate(1/x/(b*x^4+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(b x^{4} + a\right)} \sqrt{a} \log\left(\frac{b x^{4} - 2 \, \sqrt{b x^{4} + a} \sqrt{a} + 2 \, a}{x^{4}}\right) + 2 \, \sqrt{b x^{4} + a} a}{4 \, {\left(a^{2} b x^{4} + a^{3}\right)}}, \frac{{\left(b x^{4} + a\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{b x^{4} + a} \sqrt{-a}}{a}\right) + \sqrt{b x^{4} + a} a}{2 \, {\left(a^{2} b x^{4} + a^{3}\right)}}\right]"," ",0,"[1/4*((b*x^4 + a)*sqrt(a)*log((b*x^4 - 2*sqrt(b*x^4 + a)*sqrt(a) + 2*a)/x^4) + 2*sqrt(b*x^4 + a)*a)/(a^2*b*x^4 + a^3), 1/2*((b*x^4 + a)*sqrt(-a)*arctan(sqrt(b*x^4 + a)*sqrt(-a)/a) + sqrt(b*x^4 + a)*a)/(a^2*b*x^4 + a^3)]","A",0
855,1,173,0,1.078177," ","integrate(1/x^5/(b*x^4+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{2} x^{8} + a b x^{4}\right)} \sqrt{a} \log\left(\frac{b x^{4} + 2 \, \sqrt{b x^{4} + a} \sqrt{a} + 2 \, a}{x^{4}}\right) - 2 \, {\left(3 \, a b x^{4} + a^{2}\right)} \sqrt{b x^{4} + a}}{8 \, {\left(a^{3} b x^{8} + a^{4} x^{4}\right)}}, -\frac{3 \, {\left(b^{2} x^{8} + a b x^{4}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{b x^{4} + a} \sqrt{-a}}{a}\right) + {\left(3 \, a b x^{4} + a^{2}\right)} \sqrt{b x^{4} + a}}{4 \, {\left(a^{3} b x^{8} + a^{4} x^{4}\right)}}\right]"," ",0,"[1/8*(3*(b^2*x^8 + a*b*x^4)*sqrt(a)*log((b*x^4 + 2*sqrt(b*x^4 + a)*sqrt(a) + 2*a)/x^4) - 2*(3*a*b*x^4 + a^2)*sqrt(b*x^4 + a))/(a^3*b*x^8 + a^4*x^4), -1/4*(3*(b^2*x^8 + a*b*x^4)*sqrt(-a)*arctan(sqrt(b*x^4 + a)*sqrt(-a)/a) + (3*a*b*x^4 + a^2)*sqrt(b*x^4 + a))/(a^3*b*x^8 + a^4*x^4)]","A",0
856,1,167,0,0.929710," ","integrate(x^9/(b*x^4+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a b x^{4} + a^{2}\right)} \sqrt{b} \log\left(-2 \, b x^{4} + 2 \, \sqrt{b x^{4} + a} \sqrt{b} x^{2} - a\right) + 2 \, {\left(b^{2} x^{6} + 3 \, a b x^{2}\right)} \sqrt{b x^{4} + a}}{8 \, {\left(b^{4} x^{4} + a b^{3}\right)}}, \frac{3 \, {\left(a b x^{4} + a^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x^{2}}{\sqrt{b x^{4} + a}}\right) + {\left(b^{2} x^{6} + 3 \, a b x^{2}\right)} \sqrt{b x^{4} + a}}{4 \, {\left(b^{4} x^{4} + a b^{3}\right)}}\right]"," ",0,"[1/8*(3*(a*b*x^4 + a^2)*sqrt(b)*log(-2*b*x^4 + 2*sqrt(b*x^4 + a)*sqrt(b)*x^2 - a) + 2*(b^2*x^6 + 3*a*b*x^2)*sqrt(b*x^4 + a))/(b^4*x^4 + a*b^3), 1/4*(3*(a*b*x^4 + a^2)*sqrt(-b)*arctan(sqrt(-b)*x^2/sqrt(b*x^4 + a)) + (b^2*x^6 + 3*a*b*x^2)*sqrt(b*x^4 + a))/(b^4*x^4 + a*b^3)]","A",0
857,1,138,0,1.047819," ","integrate(x^5/(b*x^4+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{2 \, \sqrt{b x^{4} + a} b x^{2} - {\left(b x^{4} + a\right)} \sqrt{b} \log\left(-2 \, b x^{4} - 2 \, \sqrt{b x^{4} + a} \sqrt{b} x^{2} - a\right)}{4 \, {\left(b^{3} x^{4} + a b^{2}\right)}}, -\frac{\sqrt{b x^{4} + a} b x^{2} + {\left(b x^{4} + a\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x^{2}}{\sqrt{b x^{4} + a}}\right)}{2 \, {\left(b^{3} x^{4} + a b^{2}\right)}}\right]"," ",0,"[-1/4*(2*sqrt(b*x^4 + a)*b*x^2 - (b*x^4 + a)*sqrt(b)*log(-2*b*x^4 - 2*sqrt(b*x^4 + a)*sqrt(b)*x^2 - a))/(b^3*x^4 + a*b^2), -1/2*(sqrt(b*x^4 + a)*b*x^2 + (b*x^4 + a)*sqrt(-b)*arctan(sqrt(-b)*x^2/sqrt(b*x^4 + a)))/(b^3*x^4 + a*b^2)]","A",0
858,1,26,0,1.115456," ","integrate(x/(b*x^4+a)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{b x^{4} + a} x^{2}}{2 \, {\left(a b x^{4} + a^{2}\right)}}"," ",0,"1/2*sqrt(b*x^4 + a)*x^2/(a*b*x^4 + a^2)","A",0
859,1,37,0,1.292307," ","integrate(1/x^3/(b*x^4+a)^(3/2),x, algorithm=""fricas"")","-\frac{{\left(2 \, b x^{4} + a\right)} \sqrt{b x^{4} + a}}{2 \, {\left(a^{2} b x^{6} + a^{3} x^{2}\right)}}"," ",0,"-1/2*(2*b*x^4 + a)*sqrt(b*x^4 + a)/(a^2*b*x^6 + a^3*x^2)","A",0
860,1,50,0,1.302057," ","integrate(1/x^7/(b*x^4+a)^(3/2),x, algorithm=""fricas"")","\frac{{\left(8 \, b^{2} x^{8} + 4 \, a b x^{4} - a^{2}\right)} \sqrt{b x^{4} + a}}{6 \, {\left(a^{3} b x^{10} + a^{4} x^{6}\right)}}"," ",0,"1/6*(8*b^2*x^8 + 4*a*b*x^4 - a^2)*sqrt(b*x^4 + a)/(a^3*b*x^10 + a^4*x^6)","A",0
861,0,0,0,1.198040," ","integrate(x^12/(b*x^4+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{4} + a} x^{12}}{b^{2} x^{8} + 2 \, a b x^{4} + a^{2}}, x\right)"," ",0,"integral(sqrt(b*x^4 + a)*x^12/(b^2*x^8 + 2*a*b*x^4 + a^2), x)","F",0
862,0,0,0,1.333271," ","integrate(x^8/(b*x^4+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{4} + a} x^{8}}{b^{2} x^{8} + 2 \, a b x^{4} + a^{2}}, x\right)"," ",0,"integral(sqrt(b*x^4 + a)*x^8/(b^2*x^8 + 2*a*b*x^4 + a^2), x)","F",0
863,0,0,0,1.226139," ","integrate(x^4/(b*x^4+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{4} + a} x^{4}}{b^{2} x^{8} + 2 \, a b x^{4} + a^{2}}, x\right)"," ",0,"integral(sqrt(b*x^4 + a)*x^4/(b^2*x^8 + 2*a*b*x^4 + a^2), x)","F",0
864,0,0,0,1.236095," ","integrate(1/(b*x^4+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{4} + a}}{b^{2} x^{8} + 2 \, a b x^{4} + a^{2}}, x\right)"," ",0,"integral(sqrt(b*x^4 + a)/(b^2*x^8 + 2*a*b*x^4 + a^2), x)","F",0
865,0,0,0,0.992394," ","integrate(1/x^4/(b*x^4+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{4} + a}}{b^{2} x^{12} + 2 \, a b x^{8} + a^{2} x^{4}}, x\right)"," ",0,"integral(sqrt(b*x^4 + a)/(b^2*x^12 + 2*a*b*x^8 + a^2*x^4), x)","F",0
866,0,0,0,1.149344," ","integrate(1/x^8/(b*x^4+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{4} + a}}{b^{2} x^{16} + 2 \, a b x^{12} + a^{2} x^{8}}, x\right)"," ",0,"integral(sqrt(b*x^4 + a)/(b^2*x^16 + 2*a*b*x^12 + a^2*x^8), x)","F",0
867,0,0,0,1.171928," ","integrate(x^14/(b*x^4+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{4} + a} x^{14}}{b^{2} x^{8} + 2 \, a b x^{4} + a^{2}}, x\right)"," ",0,"integral(sqrt(b*x^4 + a)*x^14/(b^2*x^8 + 2*a*b*x^4 + a^2), x)","F",0
868,0,0,0,0.932920," ","integrate(x^10/(b*x^4+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{4} + a} x^{10}}{b^{2} x^{8} + 2 \, a b x^{4} + a^{2}}, x\right)"," ",0,"integral(sqrt(b*x^4 + a)*x^10/(b^2*x^8 + 2*a*b*x^4 + a^2), x)","F",0
869,0,0,0,1.512435," ","integrate(x^6/(b*x^4+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{4} + a} x^{6}}{b^{2} x^{8} + 2 \, a b x^{4} + a^{2}}, x\right)"," ",0,"integral(sqrt(b*x^4 + a)*x^6/(b^2*x^8 + 2*a*b*x^4 + a^2), x)","F",0
870,0,0,0,1.372538," ","integrate(x^2/(b*x^4+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{4} + a} x^{2}}{b^{2} x^{8} + 2 \, a b x^{4} + a^{2}}, x\right)"," ",0,"integral(sqrt(b*x^4 + a)*x^2/(b^2*x^8 + 2*a*b*x^4 + a^2), x)","F",0
871,0,0,0,1.511586," ","integrate(1/x^2/(b*x^4+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{4} + a}}{b^{2} x^{10} + 2 \, a b x^{6} + a^{2} x^{2}}, x\right)"," ",0,"integral(sqrt(b*x^4 + a)/(b^2*x^10 + 2*a*b*x^6 + a^2*x^2), x)","F",0
872,0,0,0,1.074823," ","integrate(1/x^6/(b*x^4+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{4} + a}}{b^{2} x^{14} + 2 \, a b x^{10} + a^{2} x^{6}}, x\right)"," ",0,"integral(sqrt(b*x^4 + a)/(b^2*x^14 + 2*a*b*x^10 + a^2*x^6), x)","F",0
873,0,0,0,0.654965," ","integrate(1/(b*x^4+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{4} + a}}{b^{3} x^{12} + 3 \, a b^{2} x^{8} + 3 \, a^{2} b x^{4} + a^{3}}, x\right)"," ",0,"integral(sqrt(b*x^4 + a)/(b^3*x^12 + 3*a*b^2*x^8 + 3*a^2*b*x^4 + a^3), x)","F",0
874,1,23,0,0.967044," ","integrate(x^11/(-x^4+1)^(1/2),x, algorithm=""fricas"")","-\frac{1}{30} \, {\left(3 \, x^{8} + 4 \, x^{4} + 8\right)} \sqrt{-x^{4} + 1}"," ",0,"-1/30*(3*x^8 + 4*x^4 + 8)*sqrt(-x^4 + 1)","A",0
875,1,16,0,1.049939," ","integrate(x^7/(-x^4+1)^(1/2),x, algorithm=""fricas"")","-\frac{1}{6} \, {\left(x^{4} + 2\right)} \sqrt{-x^{4} + 1}"," ",0,"-1/6*(x^4 + 2)*sqrt(-x^4 + 1)","A",0
876,1,11,0,1.211130," ","integrate(x^3/(-x^4+1)^(1/2),x, algorithm=""fricas"")","-\frac{1}{2} \, \sqrt{-x^{4} + 1}"," ",0,"-1/2*sqrt(-x^4 + 1)","A",0
877,1,29,0,0.978486," ","integrate(1/x/(-x^4+1)^(1/2),x, algorithm=""fricas"")","-\frac{1}{4} \, \log\left(\sqrt{-x^{4} + 1} + 1\right) + \frac{1}{4} \, \log\left(\sqrt{-x^{4} + 1} - 1\right)"," ",0,"-1/4*log(sqrt(-x^4 + 1) + 1) + 1/4*log(sqrt(-x^4 + 1) - 1)","B",0
878,1,50,0,1.036638," ","integrate(1/x^5/(-x^4+1)^(1/2),x, algorithm=""fricas"")","-\frac{x^{4} \log\left(\sqrt{-x^{4} + 1} + 1\right) - x^{4} \log\left(\sqrt{-x^{4} + 1} - 1\right) + 2 \, \sqrt{-x^{4} + 1}}{8 \, x^{4}}"," ",0,"-1/8*(x^4*log(sqrt(-x^4 + 1) + 1) - x^4*log(sqrt(-x^4 + 1) - 1) + 2*sqrt(-x^4 + 1))/x^4","A",0
879,1,33,0,1.069183," ","integrate(x^5/(-x^4+1)^(1/2),x, algorithm=""fricas"")","-\frac{1}{4} \, \sqrt{-x^{4} + 1} x^{2} - \frac{1}{2} \, \arctan\left(\frac{\sqrt{-x^{4} + 1} - 1}{x^{2}}\right)"," ",0,"-1/4*sqrt(-x^4 + 1)*x^2 - 1/2*arctan((sqrt(-x^4 + 1) - 1)/x^2)","A",0
880,1,18,0,1.264827," ","integrate(x/(-x^4+1)^(1/2),x, algorithm=""fricas"")","-\arctan\left(\frac{\sqrt{-x^{4} + 1} - 1}{x^{2}}\right)"," ",0,"-arctan((sqrt(-x^4 + 1) - 1)/x^2)","B",0
881,1,14,0,1.238500," ","integrate(1/x^3/(-x^4+1)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{-x^{4} + 1}}{2 \, x^{2}}"," ",0,"-1/2*sqrt(-x^4 + 1)/x^2","A",0
882,1,21,0,1.183053," ","integrate(1/x^7/(-x^4+1)^(1/2),x, algorithm=""fricas"")","-\frac{{\left(2 \, x^{4} + 1\right)} \sqrt{-x^{4} + 1}}{6 \, x^{6}}"," ",0,"-1/6*(2*x^4 + 1)*sqrt(-x^4 + 1)/x^6","A",0
883,1,26,0,1.205077," ","integrate(1/x^11/(-x^4+1)^(1/2),x, algorithm=""fricas"")","-\frac{{\left(8 \, x^{8} + 4 \, x^{4} + 3\right)} \sqrt{-x^{4} + 1}}{30 \, x^{10}}"," ",0,"-1/30*(8*x^8 + 4*x^4 + 3)*sqrt(-x^4 + 1)/x^10","A",0
884,0,0,0,1.202860," ","integrate(x^8/(-x^4+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{4} + 1} x^{8}}{x^{4} - 1}, x\right)"," ",0,"integral(-sqrt(-x^4 + 1)*x^8/(x^4 - 1), x)","F",0
885,0,0,0,1.312812," ","integrate(x^4/(-x^4+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{4} + 1} x^{4}}{x^{4} - 1}, x\right)"," ",0,"integral(-sqrt(-x^4 + 1)*x^4/(x^4 - 1), x)","F",0
886,0,0,0,1.257930," ","integrate(1/(-x^4+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{4} + 1}}{x^{4} - 1}, x\right)"," ",0,"integral(-sqrt(-x^4 + 1)/(x^4 - 1), x)","F",0
887,0,0,0,1.190796," ","integrate(1/x^4/(-x^4+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{4} + 1}}{x^{8} - x^{4}}, x\right)"," ",0,"integral(-sqrt(-x^4 + 1)/(x^8 - x^4), x)","F",0
888,0,0,0,1.045187," ","integrate(1/x^8/(-x^4+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{4} + 1}}{x^{12} - x^{8}}, x\right)"," ",0,"integral(-sqrt(-x^4 + 1)/(x^12 - x^8), x)","F",0
889,0,0,0,1.007691," ","integrate(x^10/(-x^4+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{4} + 1} x^{10}}{x^{4} - 1}, x\right)"," ",0,"integral(-sqrt(-x^4 + 1)*x^10/(x^4 - 1), x)","F",0
890,0,0,0,1.232935," ","integrate(x^6/(-x^4+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{4} + 1} x^{6}}{x^{4} - 1}, x\right)"," ",0,"integral(-sqrt(-x^4 + 1)*x^6/(x^4 - 1), x)","F",0
891,0,0,0,1.275014," ","integrate(x^2/(-x^4+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{4} + 1} x^{2}}{x^{4} - 1}, x\right)"," ",0,"integral(-sqrt(-x^4 + 1)*x^2/(x^4 - 1), x)","F",0
892,0,0,0,1.254183," ","integrate(1/x^2/(-x^4+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{4} + 1}}{x^{6} - x^{2}}, x\right)"," ",0,"integral(-sqrt(-x^4 + 1)/(x^6 - x^2), x)","F",0
893,0,0,0,1.243874," ","integrate(1/x^6/(-x^4+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{4} + 1}}{x^{10} - x^{6}}, x\right)"," ",0,"integral(-sqrt(-x^4 + 1)/(x^10 - x^6), x)","F",0
894,1,28,0,1.117271," ","integrate(x^11/(-x^4+1)^(3/2),x, algorithm=""fricas"")","\frac{{\left(x^{8} + 4 \, x^{4} - 8\right)} \sqrt{-x^{4} + 1}}{6 \, {\left(x^{4} - 1\right)}}"," ",0,"1/6*(x^8 + 4*x^4 - 8)*sqrt(-x^4 + 1)/(x^4 - 1)","A",0
895,1,23,0,1.068675," ","integrate(x^7/(-x^4+1)^(3/2),x, algorithm=""fricas"")","\frac{{\left(x^{4} - 2\right)} \sqrt{-x^{4} + 1}}{2 \, {\left(x^{4} - 1\right)}}"," ",0,"1/2*(x^4 - 2)*sqrt(-x^4 + 1)/(x^4 - 1)","A",0
896,1,18,0,1.108208," ","integrate(x^3/(-x^4+1)^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{-x^{4} + 1}}{2 \, {\left(x^{4} - 1\right)}}"," ",0,"-1/2*sqrt(-x^4 + 1)/(x^4 - 1)","A",0
897,1,58,0,0.854048," ","integrate(1/x/(-x^4+1)^(3/2),x, algorithm=""fricas"")","-\frac{{\left(x^{4} - 1\right)} \log\left(\sqrt{-x^{4} + 1} + 1\right) - {\left(x^{4} - 1\right)} \log\left(\sqrt{-x^{4} + 1} - 1\right) + 2 \, \sqrt{-x^{4} + 1}}{4 \, {\left(x^{4} - 1\right)}}"," ",0,"-1/4*((x^4 - 1)*log(sqrt(-x^4 + 1) + 1) - (x^4 - 1)*log(sqrt(-x^4 + 1) - 1) + 2*sqrt(-x^4 + 1))/(x^4 - 1)","B",0
898,1,78,0,1.093613," ","integrate(1/x^5/(-x^4+1)^(3/2),x, algorithm=""fricas"")","-\frac{3 \, {\left(x^{8} - x^{4}\right)} \log\left(\sqrt{-x^{4} + 1} + 1\right) - 3 \, {\left(x^{8} - x^{4}\right)} \log\left(\sqrt{-x^{4} + 1} - 1\right) + 2 \, {\left(3 \, x^{4} - 1\right)} \sqrt{-x^{4} + 1}}{8 \, {\left(x^{8} - x^{4}\right)}}"," ",0,"-1/8*(3*(x^8 - x^4)*log(sqrt(-x^4 + 1) + 1) - 3*(x^8 - x^4)*log(sqrt(-x^4 + 1) - 1) + 2*(3*x^4 - 1)*sqrt(-x^4 + 1))/(x^8 - x^4)","B",0
899,1,52,0,0.763895," ","integrate(x^9/(-x^4+1)^(3/2),x, algorithm=""fricas"")","\frac{6 \, {\left(x^{4} - 1\right)} \arctan\left(\frac{\sqrt{-x^{4} + 1} - 1}{x^{2}}\right) + {\left(x^{6} - 3 \, x^{2}\right)} \sqrt{-x^{4} + 1}}{4 \, {\left(x^{4} - 1\right)}}"," ",0,"1/4*(6*(x^4 - 1)*arctan((sqrt(-x^4 + 1) - 1)/x^2) + (x^6 - 3*x^2)*sqrt(-x^4 + 1))/(x^4 - 1)","A",0
900,1,46,0,1.050145," ","integrate(x^5/(-x^4+1)^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{-x^{4} + 1} x^{2} - 2 \, {\left(x^{4} - 1\right)} \arctan\left(\frac{\sqrt{-x^{4} + 1} - 1}{x^{2}}\right)}{2 \, {\left(x^{4} - 1\right)}}"," ",0,"-1/2*(sqrt(-x^4 + 1)*x^2 - 2*(x^4 - 1)*arctan((sqrt(-x^4 + 1) - 1)/x^2))/(x^4 - 1)","B",0
901,1,21,0,1.211301," ","integrate(x/(-x^4+1)^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{-x^{4} + 1} x^{2}}{2 \, {\left(x^{4} - 1\right)}}"," ",0,"-1/2*sqrt(-x^4 + 1)*x^2/(x^4 - 1)","A",0
902,1,29,0,0.906571," ","integrate(1/x^3/(-x^4+1)^(3/2),x, algorithm=""fricas"")","-\frac{{\left(2 \, x^{4} - 1\right)} \sqrt{-x^{4} + 1}}{2 \, {\left(x^{6} - x^{2}\right)}}"," ",0,"-1/2*(2*x^4 - 1)*sqrt(-x^4 + 1)/(x^6 - x^2)","A",0
903,1,34,0,1.654402," ","integrate(1/x^7/(-x^4+1)^(3/2),x, algorithm=""fricas"")","-\frac{{\left(8 \, x^{8} - 4 \, x^{4} - 1\right)} \sqrt{-x^{4} + 1}}{6 \, {\left(x^{10} - x^{6}\right)}}"," ",0,"-1/6*(8*x^8 - 4*x^4 - 1)*sqrt(-x^4 + 1)/(x^10 - x^6)","A",0
904,0,0,0,0.972569," ","integrate(x^12/(-x^4+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{4} + 1} x^{12}}{x^{8} - 2 \, x^{4} + 1}, x\right)"," ",0,"integral(sqrt(-x^4 + 1)*x^12/(x^8 - 2*x^4 + 1), x)","F",0
905,0,0,0,1.381455," ","integrate(x^8/(-x^4+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{4} + 1} x^{8}}{x^{8} - 2 \, x^{4} + 1}, x\right)"," ",0,"integral(sqrt(-x^4 + 1)*x^8/(x^8 - 2*x^4 + 1), x)","F",0
906,0,0,0,1.441972," ","integrate(x^4/(-x^4+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{4} + 1} x^{4}}{x^{8} - 2 \, x^{4} + 1}, x\right)"," ",0,"integral(sqrt(-x^4 + 1)*x^4/(x^8 - 2*x^4 + 1), x)","F",0
907,0,0,0,0.743410," ","integrate(1/(-x^4+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{4} + 1}}{x^{8} - 2 \, x^{4} + 1}, x\right)"," ",0,"integral(sqrt(-x^4 + 1)/(x^8 - 2*x^4 + 1), x)","F",0
908,0,0,0,1.268145," ","integrate(1/x^4/(-x^4+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{4} + 1}}{x^{12} - 2 \, x^{8} + x^{4}}, x\right)"," ",0,"integral(sqrt(-x^4 + 1)/(x^12 - 2*x^8 + x^4), x)","F",0
909,0,0,0,1.192379," ","integrate(1/x^8/(-x^4+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{4} + 1}}{x^{16} - 2 \, x^{12} + x^{8}}, x\right)"," ",0,"integral(sqrt(-x^4 + 1)/(x^16 - 2*x^12 + x^8), x)","F",0
910,0,0,0,1.253630," ","integrate(x^14/(-x^4+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{4} + 1} x^{14}}{x^{8} - 2 \, x^{4} + 1}, x\right)"," ",0,"integral(sqrt(-x^4 + 1)*x^14/(x^8 - 2*x^4 + 1), x)","F",0
911,0,0,0,0.932947," ","integrate(x^10/(-x^4+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{4} + 1} x^{10}}{x^{8} - 2 \, x^{4} + 1}, x\right)"," ",0,"integral(sqrt(-x^4 + 1)*x^10/(x^8 - 2*x^4 + 1), x)","F",0
912,0,0,0,1.218871," ","integrate(x^6/(-x^4+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{4} + 1} x^{6}}{x^{8} - 2 \, x^{4} + 1}, x\right)"," ",0,"integral(sqrt(-x^4 + 1)*x^6/(x^8 - 2*x^4 + 1), x)","F",0
913,0,0,0,1.124025," ","integrate(x^2/(-x^4+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{4} + 1} x^{2}}{x^{8} - 2 \, x^{4} + 1}, x\right)"," ",0,"integral(sqrt(-x^4 + 1)*x^2/(x^8 - 2*x^4 + 1), x)","F",0
914,0,0,0,0.980184," ","integrate(1/x^2/(-x^4+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{4} + 1}}{x^{10} - 2 \, x^{6} + x^{2}}, x\right)"," ",0,"integral(sqrt(-x^4 + 1)/(x^10 - 2*x^6 + x^2), x)","F",0
915,0,0,0,1.003493," ","integrate(1/x^6/(-x^4+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{4} + 1}}{x^{14} - 2 \, x^{10} + x^{6}}, x\right)"," ",0,"integral(sqrt(-x^4 + 1)/(x^14 - 2*x^10 + x^6), x)","F",0
916,0,0,0,1.050235," ","integrate(1/(-x^4+1)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{4} + 1}}{x^{12} - 3 \, x^{8} + 3 \, x^{4} - 1}, x\right)"," ",0,"integral(-sqrt(-x^4 + 1)/(x^12 - 3*x^8 + 3*x^4 - 1), x)","F",0
917,1,21,0,1.309372," ","integrate(x^11/(x^4+1)^(1/2),x, algorithm=""fricas"")","\frac{1}{30} \, {\left(3 \, x^{8} - 4 \, x^{4} + 8\right)} \sqrt{x^{4} + 1}"," ",0,"1/30*(3*x^8 - 4*x^4 + 8)*sqrt(x^4 + 1)","A",0
918,1,14,0,1.169600," ","integrate(x^7/(x^4+1)^(1/2),x, algorithm=""fricas"")","\frac{1}{6} \, \sqrt{x^{4} + 1} {\left(x^{4} - 2\right)}"," ",0,"1/6*sqrt(x^4 + 1)*(x^4 - 2)","A",0
919,1,9,0,1.294062," ","integrate(x^3/(x^4+1)^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{x^{4} + 1}"," ",0,"1/2*sqrt(x^4 + 1)","A",0
920,1,25,0,1.019948," ","integrate(1/x/(x^4+1)^(1/2),x, algorithm=""fricas"")","-\frac{1}{4} \, \log\left(\sqrt{x^{4} + 1} + 1\right) + \frac{1}{4} \, \log\left(\sqrt{x^{4} + 1} - 1\right)"," ",0,"-1/4*log(sqrt(x^4 + 1) + 1) + 1/4*log(sqrt(x^4 + 1) - 1)","B",0
921,1,44,0,1.018776," ","integrate(1/x^5/(x^4+1)^(1/2),x, algorithm=""fricas"")","\frac{x^{4} \log\left(\sqrt{x^{4} + 1} + 1\right) - x^{4} \log\left(\sqrt{x^{4} + 1} - 1\right) - 2 \, \sqrt{x^{4} + 1}}{8 \, x^{4}}"," ",0,"1/8*(x^4*log(sqrt(x^4 + 1) + 1) - x^4*log(sqrt(x^4 + 1) - 1) - 2*sqrt(x^4 + 1))/x^4","A",0
922,1,29,0,1.142848," ","integrate(x^5/(x^4+1)^(1/2),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{x^{4} + 1} x^{2} + \frac{1}{4} \, \log\left(-x^{2} + \sqrt{x^{4} + 1}\right)"," ",0,"1/4*sqrt(x^4 + 1)*x^2 + 1/4*log(-x^2 + sqrt(x^4 + 1))","A",0
923,1,16,0,1.238674," ","integrate(x/(x^4+1)^(1/2),x, algorithm=""fricas"")","-\frac{1}{2} \, \log\left(-x^{2} + \sqrt{x^{4} + 1}\right)"," ",0,"-1/2*log(-x^2 + sqrt(x^4 + 1))","B",0
924,1,16,0,1.130448," ","integrate(1/x^3/(x^4+1)^(1/2),x, algorithm=""fricas"")","-\frac{x^{2} + \sqrt{x^{4} + 1}}{2 \, x^{2}}"," ",0,"-1/2*(x^2 + sqrt(x^4 + 1))/x^2","A",0
925,1,26,0,1.144918," ","integrate(1/x^7/(x^4+1)^(1/2),x, algorithm=""fricas"")","\frac{2 \, x^{6} + {\left(2 \, x^{4} - 1\right)} \sqrt{x^{4} + 1}}{6 \, x^{6}}"," ",0,"1/6*(2*x^6 + (2*x^4 - 1)*sqrt(x^4 + 1))/x^6","A",0
926,1,31,0,1.194273," ","integrate(1/x^11/(x^4+1)^(1/2),x, algorithm=""fricas"")","-\frac{8 \, x^{10} + {\left(8 \, x^{8} - 4 \, x^{4} + 3\right)} \sqrt{x^{4} + 1}}{30 \, x^{10}}"," ",0,"-1/30*(8*x^10 + (8*x^8 - 4*x^4 + 3)*sqrt(x^4 + 1))/x^10","A",0
927,0,0,0,1.202406," ","integrate(x^8/(x^4+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{8}}{\sqrt{x^{4} + 1}}, x\right)"," ",0,"integral(x^8/sqrt(x^4 + 1), x)","F",0
928,0,0,0,1.236397," ","integrate(x^4/(x^4+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{4}}{\sqrt{x^{4} + 1}}, x\right)"," ",0,"integral(x^4/sqrt(x^4 + 1), x)","F",0
929,0,0,0,1.251858," ","integrate(1/(x^4+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{x^{4} + 1}}, x\right)"," ",0,"integral(1/sqrt(x^4 + 1), x)","F",0
930,0,0,0,1.197650," ","integrate(1/x^4/(x^4+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 1}}{x^{8} + x^{4}}, x\right)"," ",0,"integral(sqrt(x^4 + 1)/(x^8 + x^4), x)","F",0
931,0,0,0,1.160772," ","integrate(1/x^8/(x^4+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 1}}{x^{12} + x^{8}}, x\right)"," ",0,"integral(sqrt(x^4 + 1)/(x^12 + x^8), x)","F",0
932,0,0,0,1.342507," ","integrate(x^10/(x^4+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{10}}{\sqrt{x^{4} + 1}}, x\right)"," ",0,"integral(x^10/sqrt(x^4 + 1), x)","F",0
933,0,0,0,1.221054," ","integrate(x^6/(x^4+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{6}}{\sqrt{x^{4} + 1}}, x\right)"," ",0,"integral(x^6/sqrt(x^4 + 1), x)","F",0
934,0,0,0,0.675239," ","integrate(x^2/(x^4+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2}}{\sqrt{x^{4} + 1}}, x\right)"," ",0,"integral(x^2/sqrt(x^4 + 1), x)","F",0
935,0,0,0,1.211874," ","integrate(1/x^2/(x^4+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 1}}{x^{6} + x^{2}}, x\right)"," ",0,"integral(sqrt(x^4 + 1)/(x^6 + x^2), x)","F",0
936,0,0,0,0.721644," ","integrate(1/x^6/(x^4+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 1}}{x^{10} + x^{6}}, x\right)"," ",0,"integral(sqrt(x^4 + 1)/(x^10 + x^6), x)","F",0
937,1,19,0,1.060859," ","integrate(x^11/(x^4+1)^(3/2),x, algorithm=""fricas"")","\frac{x^{8} - 4 \, x^{4} - 8}{6 \, \sqrt{x^{4} + 1}}"," ",0,"1/6*(x^8 - 4*x^4 - 8)/sqrt(x^4 + 1)","A",0
938,1,14,0,0.704793," ","integrate(x^7/(x^4+1)^(3/2),x, algorithm=""fricas"")","\frac{x^{4} + 2}{2 \, \sqrt{x^{4} + 1}}"," ",0,"1/2*(x^4 + 2)/sqrt(x^4 + 1)","A",0
939,1,9,0,0.948789," ","integrate(x^3/(x^4+1)^(3/2),x, algorithm=""fricas"")","-\frac{1}{2 \, \sqrt{x^{4} + 1}}"," ",0,"-1/2/sqrt(x^4 + 1)","A",0
940,1,52,0,1.206563," ","integrate(1/x/(x^4+1)^(3/2),x, algorithm=""fricas"")","-\frac{{\left(x^{4} + 1\right)} \log\left(\sqrt{x^{4} + 1} + 1\right) - {\left(x^{4} + 1\right)} \log\left(\sqrt{x^{4} + 1} - 1\right) - 2 \, \sqrt{x^{4} + 1}}{4 \, {\left(x^{4} + 1\right)}}"," ",0,"-1/4*((x^4 + 1)*log(sqrt(x^4 + 1) + 1) - (x^4 + 1)*log(sqrt(x^4 + 1) - 1) - 2*sqrt(x^4 + 1))/(x^4 + 1)","B",0
941,1,66,0,1.302371," ","integrate(1/x^5/(x^4+1)^(3/2),x, algorithm=""fricas"")","\frac{3 \, {\left(x^{8} + x^{4}\right)} \log\left(\sqrt{x^{4} + 1} + 1\right) - 3 \, {\left(x^{8} + x^{4}\right)} \log\left(\sqrt{x^{4} + 1} - 1\right) - 2 \, {\left(3 \, x^{4} + 1\right)} \sqrt{x^{4} + 1}}{8 \, {\left(x^{8} + x^{4}\right)}}"," ",0,"1/8*(3*(x^8 + x^4)*log(sqrt(x^4 + 1) + 1) - 3*(x^8 + x^4)*log(sqrt(x^4 + 1) - 1) - 2*(3*x^4 + 1)*sqrt(x^4 + 1))/(x^8 + x^4)","B",0
942,1,54,0,0.694447," ","integrate(x^9/(x^4+1)^(3/2),x, algorithm=""fricas"")","\frac{2 \, x^{4} + 3 \, {\left(x^{4} + 1\right)} \log\left(-x^{2} + \sqrt{x^{4} + 1}\right) + {\left(x^{6} + 3 \, x^{2}\right)} \sqrt{x^{4} + 1} + 2}{4 \, {\left(x^{4} + 1\right)}}"," ",0,"1/4*(2*x^4 + 3*(x^4 + 1)*log(-x^2 + sqrt(x^4 + 1)) + (x^6 + 3*x^2)*sqrt(x^4 + 1) + 2)/(x^4 + 1)","A",0
943,1,45,0,1.285457," ","integrate(x^5/(x^4+1)^(3/2),x, algorithm=""fricas"")","-\frac{x^{4} + \sqrt{x^{4} + 1} x^{2} + {\left(x^{4} + 1\right)} \log\left(-x^{2} + \sqrt{x^{4} + 1}\right) + 1}{2 \, {\left(x^{4} + 1\right)}}"," ",0,"-1/2*(x^4 + sqrt(x^4 + 1)*x^2 + (x^4 + 1)*log(-x^2 + sqrt(x^4 + 1)) + 1)/(x^4 + 1)","B",0
944,1,25,0,1.266903," ","integrate(x/(x^4+1)^(3/2),x, algorithm=""fricas"")","\frac{x^{4} + \sqrt{x^{4} + 1} x^{2} + 1}{2 \, {\left(x^{4} + 1\right)}}"," ",0,"1/2*(x^4 + sqrt(x^4 + 1)*x^2 + 1)/(x^4 + 1)","B",0
945,1,37,0,1.273858," ","integrate(1/x^3/(x^4+1)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, x^{6} + 2 \, x^{2} + {\left(2 \, x^{4} + 1\right)} \sqrt{x^{4} + 1}}{2 \, {\left(x^{6} + x^{2}\right)}}"," ",0,"-1/2*(2*x^6 + 2*x^2 + (2*x^4 + 1)*sqrt(x^4 + 1))/(x^6 + x^2)","A",0
946,1,42,0,1.105014," ","integrate(1/x^7/(x^4+1)^(3/2),x, algorithm=""fricas"")","\frac{8 \, x^{10} + 8 \, x^{6} + {\left(8 \, x^{8} + 4 \, x^{4} - 1\right)} \sqrt{x^{4} + 1}}{6 \, {\left(x^{10} + x^{6}\right)}}"," ",0,"1/6*(8*x^10 + 8*x^6 + (8*x^8 + 4*x^4 - 1)*sqrt(x^4 + 1))/(x^10 + x^6)","A",0
947,0,0,0,0.986787," ","integrate(x^12/(x^4+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 1} x^{12}}{x^{8} + 2 \, x^{4} + 1}, x\right)"," ",0,"integral(sqrt(x^4 + 1)*x^12/(x^8 + 2*x^4 + 1), x)","F",0
948,0,0,0,0.986316," ","integrate(x^8/(x^4+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 1} x^{8}}{x^{8} + 2 \, x^{4} + 1}, x\right)"," ",0,"integral(sqrt(x^4 + 1)*x^8/(x^8 + 2*x^4 + 1), x)","F",0
949,0,0,0,1.086848," ","integrate(x^4/(x^4+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 1} x^{4}}{x^{8} + 2 \, x^{4} + 1}, x\right)"," ",0,"integral(sqrt(x^4 + 1)*x^4/(x^8 + 2*x^4 + 1), x)","F",0
950,0,0,0,1.021201," ","integrate(1/(x^4+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 1}}{x^{8} + 2 \, x^{4} + 1}, x\right)"," ",0,"integral(sqrt(x^4 + 1)/(x^8 + 2*x^4 + 1), x)","F",0
951,0,0,0,1.209230," ","integrate(1/x^4/(x^4+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 1}}{x^{12} + 2 \, x^{8} + x^{4}}, x\right)"," ",0,"integral(sqrt(x^4 + 1)/(x^12 + 2*x^8 + x^4), x)","F",0
952,0,0,0,1.405297," ","integrate(1/x^8/(x^4+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 1}}{x^{16} + 2 \, x^{12} + x^{8}}, x\right)"," ",0,"integral(sqrt(x^4 + 1)/(x^16 + 2*x^12 + x^8), x)","F",0
953,0,0,0,1.339010," ","integrate(x^14/(x^4+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 1} x^{14}}{x^{8} + 2 \, x^{4} + 1}, x\right)"," ",0,"integral(sqrt(x^4 + 1)*x^14/(x^8 + 2*x^4 + 1), x)","F",0
954,0,0,0,1.256939," ","integrate(x^10/(x^4+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 1} x^{10}}{x^{8} + 2 \, x^{4} + 1}, x\right)"," ",0,"integral(sqrt(x^4 + 1)*x^10/(x^8 + 2*x^4 + 1), x)","F",0
955,0,0,0,1.705544," ","integrate(x^6/(x^4+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 1} x^{6}}{x^{8} + 2 \, x^{4} + 1}, x\right)"," ",0,"integral(sqrt(x^4 + 1)*x^6/(x^8 + 2*x^4 + 1), x)","F",0
956,0,0,0,1.070412," ","integrate(x^2/(x^4+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 1} x^{2}}{x^{8} + 2 \, x^{4} + 1}, x\right)"," ",0,"integral(sqrt(x^4 + 1)*x^2/(x^8 + 2*x^4 + 1), x)","F",0
957,0,0,0,0.997682," ","integrate(1/x^2/(x^4+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 1}}{x^{10} + 2 \, x^{6} + x^{2}}, x\right)"," ",0,"integral(sqrt(x^4 + 1)/(x^10 + 2*x^6 + x^2), x)","F",0
958,0,0,0,1.179378," ","integrate(1/x^6/(x^4+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 1}}{x^{14} + 2 \, x^{10} + x^{6}}, x\right)"," ",0,"integral(sqrt(x^4 + 1)/(x^14 + 2*x^10 + x^6), x)","F",0
959,0,0,0,1.212085," ","integrate(1/(x^4+1)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 1}}{x^{12} + 3 \, x^{8} + 3 \, x^{4} + 1}, x\right)"," ",0,"integral(sqrt(x^4 + 1)/(x^12 + 3*x^8 + 3*x^4 + 1), x)","F",0
960,1,16,0,0.675577," ","integrate(x^7/(-x^4+16)^(1/2),x, algorithm=""fricas"")","-\frac{1}{6} \, {\left(x^{4} + 32\right)} \sqrt{-x^{4} + 16}"," ",0,"-1/6*(x^4 + 32)*sqrt(-x^4 + 16)","A",0
961,1,33,0,1.022473," ","integrate(x^5/(-x^4+16)^(1/2),x, algorithm=""fricas"")","-\frac{1}{4} \, \sqrt{-x^{4} + 16} x^{2} - 8 \, \arctan\left(\frac{\sqrt{-x^{4} + 16} - 4}{x^{2}}\right)"," ",0,"-1/4*sqrt(-x^4 + 16)*x^2 - 8*arctan((sqrt(-x^4 + 16) - 4)/x^2)","A",0
962,1,11,0,1.163482," ","integrate(x^3/(-x^4+16)^(1/2),x, algorithm=""fricas"")","-\frac{1}{2} \, \sqrt{-x^{4} + 16}"," ",0,"-1/2*sqrt(-x^4 + 16)","A",0
963,1,18,0,0.994005," ","integrate(x/(-x^4+16)^(1/2),x, algorithm=""fricas"")","-\arctan\left(\frac{\sqrt{-x^{4} + 16} - 4}{x^{2}}\right)"," ",0,"-arctan((sqrt(-x^4 + 16) - 4)/x^2)","B",0
964,1,29,0,1.163821," ","integrate(1/x/(-x^4+16)^(1/2),x, algorithm=""fricas"")","-\frac{1}{16} \, \log\left(\sqrt{-x^{4} + 16} + 4\right) + \frac{1}{16} \, \log\left(\sqrt{-x^{4} + 16} - 4\right)"," ",0,"-1/16*log(sqrt(-x^4 + 16) + 4) + 1/16*log(sqrt(-x^4 + 16) - 4)","B",0
965,1,14,0,1.116447," ","integrate(1/x^3/(-x^4+16)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{-x^{4} + 16}}{32 \, x^{2}}"," ",0,"-1/32*sqrt(-x^4 + 16)/x^2","A",0
966,1,50,0,1.283781," ","integrate(1/x^5/(-x^4+16)^(1/2),x, algorithm=""fricas"")","-\frac{x^{4} \log\left(\sqrt{-x^{4} + 16} + 4\right) - x^{4} \log\left(\sqrt{-x^{4} + 16} - 4\right) + 8 \, \sqrt{-x^{4} + 16}}{512 \, x^{4}}"," ",0,"-1/512*(x^4*log(sqrt(-x^4 + 16) + 4) - x^4*log(sqrt(-x^4 + 16) - 4) + 8*sqrt(-x^4 + 16))/x^4","A",0
967,1,19,0,1.095229," ","integrate(1/x^7/(-x^4+16)^(1/2),x, algorithm=""fricas"")","-\frac{{\left(x^{4} + 8\right)} \sqrt{-x^{4} + 16}}{768 \, x^{6}}"," ",0,"-1/768*(x^4 + 8)*sqrt(-x^4 + 16)/x^6","A",0
968,0,0,0,1.114296," ","integrate(x^6/(-x^4+16)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{4} + 16} x^{6}}{x^{4} - 16}, x\right)"," ",0,"integral(-sqrt(-x^4 + 16)*x^6/(x^4 - 16), x)","F",0
969,0,0,0,1.276283," ","integrate(x^4/(-x^4+16)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{4} + 16} x^{4}}{x^{4} - 16}, x\right)"," ",0,"integral(-sqrt(-x^4 + 16)*x^4/(x^4 - 16), x)","F",0
970,0,0,0,1.313657," ","integrate(x^2/(-x^4+16)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{4} + 16} x^{2}}{x^{4} - 16}, x\right)"," ",0,"integral(-sqrt(-x^4 + 16)*x^2/(x^4 - 16), x)","F",0
971,0,0,0,1.262491," ","integrate(1/(-x^4+16)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{4} + 16}}{x^{4} - 16}, x\right)"," ",0,"integral(-sqrt(-x^4 + 16)/(x^4 - 16), x)","F",0
972,0,0,0,1.124302," ","integrate(1/x^2/(-x^4+16)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{4} + 16}}{x^{6} - 16 \, x^{2}}, x\right)"," ",0,"integral(-sqrt(-x^4 + 16)/(x^6 - 16*x^2), x)","F",0
973,0,0,0,0.961973," ","integrate(1/x^4/(-x^4+16)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{4} + 16}}{x^{8} - 16 \, x^{4}}, x\right)"," ",0,"integral(-sqrt(-x^4 + 16)/(x^8 - 16*x^4), x)","F",0
974,1,16,0,1.254879," ","integrate(x/(x^4-4)^(1/2),x, algorithm=""fricas"")","-\frac{1}{2} \, \log\left(-x^{2} + \sqrt{x^{4} - 4}\right)"," ",0,"-1/2*log(-x^2 + sqrt(x^4 - 4))","A",0
975,1,16,0,1.274010," ","integrate(x/(x^4+4)^(1/2),x, algorithm=""fricas"")","-\frac{1}{2} \, \log\left(-x^{2} + \sqrt{x^{4} + 4}\right)"," ",0,"-1/2*log(-x^2 + sqrt(x^4 + 4))","A",0
976,1,10,0,0.783831," ","integrate(1/x/(x^4-1)^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \arctan\left(\sqrt{x^{4} - 1}\right)"," ",0,"1/2*arctan(sqrt(x^4 - 1))","A",0
977,0,0,0,1.152750," ","integrate(x^4/(x^4-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{4}}{\sqrt{x^{4} - 1}}, x\right)"," ",0,"integral(x^4/sqrt(x^4 - 1), x)","F",0
978,0,0,0,0.913076," ","integrate(1/(x^4-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{x^{4} - 1}}, x\right)"," ",0,"integral(1/sqrt(x^4 - 1), x)","F",0
979,0,0,0,0.917405," ","integrate(1/x^4/(x^4-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} - 1}}{x^{8} - x^{4}}, x\right)"," ",0,"integral(sqrt(x^4 - 1)/(x^8 - x^4), x)","F",0
980,0,0,0,0.941751," ","integrate(x^6/(x^4-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{6}}{\sqrt{x^{4} - 1}}, x\right)"," ",0,"integral(x^6/sqrt(x^4 - 1), x)","F",0
981,0,0,0,1.138450," ","integrate(x^2/(x^4-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2}}{\sqrt{x^{4} - 1}}, x\right)"," ",0,"integral(x^2/sqrt(x^4 - 1), x)","F",0
982,0,0,0,1.009434," ","integrate(1/x^2/(x^4-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} - 1}}{x^{6} - x^{2}}, x\right)"," ",0,"integral(sqrt(x^4 - 1)/(x^6 - x^2), x)","F",0
983,0,0,0,1.095844," ","integrate(x^2/(-2*x^4+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-2 \, x^{4} + 3} x^{2}}{2 \, x^{4} - 3}, x\right)"," ",0,"integral(-sqrt(-2*x^4 + 3)*x^2/(2*x^4 - 3), x)","F",0
984,0,0,0,1.138462," ","integrate(x^2/(-b*x^4+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-b x^{4} + 3} x^{2}}{b x^{4} - 3}, x\right)"," ",0,"integral(-sqrt(-b*x^4 + 3)*x^2/(b*x^4 - 3), x)","F",0
985,1,19,0,1.142689," ","integrate(x^7*(x^4+1)^(1/3),x, algorithm=""fricas"")","\frac{3}{112} \, {\left(4 \, x^{8} + x^{4} - 3\right)} {\left(x^{4} + 1\right)}^{\frac{1}{3}}"," ",0,"3/112*(4*x^8 + x^4 - 3)*(x^4 + 1)^(1/3)","A",0
986,1,9,0,0.921029," ","integrate(x^3/(x^4+1)^(4/3),x, algorithm=""fricas"")","-\frac{3}{4 \, {\left(x^{4} + 1\right)}^{\frac{1}{3}}}"," ",0,"-3/4/(x^4 + 1)^(1/3)","A",0
987,1,9,0,0.759998," ","integrate(x^3/(x^4+1)^(1/3),x, algorithm=""fricas"")","\frac{3}{8} \, {\left(x^{4} + 1\right)}^{\frac{2}{3}}"," ",0,"3/8*(x^4 + 1)^(2/3)","A",0
988,1,68,0,1.031027," ","integrate(x^19*(b*x^4+a)^(1/4),x, algorithm=""fricas"")","\frac{{\left(3315 \, b^{5} x^{20} + 195 \, a b^{4} x^{16} - 240 \, a^{2} b^{3} x^{12} + 320 \, a^{3} b^{2} x^{8} - 512 \, a^{4} b x^{4} + 2048 \, a^{5}\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}}}{69615 \, b^{5}}"," ",0,"1/69615*(3315*b^5*x^20 + 195*a*b^4*x^16 - 240*a^2*b^3*x^12 + 320*a^3*b^2*x^8 - 512*a^4*b*x^4 + 2048*a^5)*(b*x^4 + a)^(1/4)/b^5","A",0
989,1,57,0,0.835554," ","integrate(x^15*(b*x^4+a)^(1/4),x, algorithm=""fricas"")","\frac{{\left(195 \, b^{4} x^{16} + 15 \, a b^{3} x^{12} - 20 \, a^{2} b^{2} x^{8} + 32 \, a^{3} b x^{4} - 128 \, a^{4}\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}}}{3315 \, b^{4}}"," ",0,"1/3315*(195*b^4*x^16 + 15*a*b^3*x^12 - 20*a^2*b^2*x^8 + 32*a^3*b*x^4 - 128*a^4)*(b*x^4 + a)^(1/4)/b^4","A",0
990,1,46,0,0.989432," ","integrate(x^11*(b*x^4+a)^(1/4),x, algorithm=""fricas"")","\frac{{\left(45 \, b^{3} x^{12} + 5 \, a b^{2} x^{8} - 8 \, a^{2} b x^{4} + 32 \, a^{3}\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}}}{585 \, b^{3}}"," ",0,"1/585*(45*b^3*x^12 + 5*a*b^2*x^8 - 8*a^2*b*x^4 + 32*a^3)*(b*x^4 + a)^(1/4)/b^3","A",0
991,1,34,0,1.254092," ","integrate(x^7*(b*x^4+a)^(1/4),x, algorithm=""fricas"")","\frac{{\left(5 \, b^{2} x^{8} + a b x^{4} - 4 \, a^{2}\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}}}{45 \, b^{2}}"," ",0,"1/45*(5*b^2*x^8 + a*b*x^4 - 4*a^2)*(b*x^4 + a)^(1/4)/b^2","A",0
992,1,14,0,0.517853," ","integrate(x^3*(b*x^4+a)^(1/4),x, algorithm=""fricas"")","\frac{{\left(b x^{4} + a\right)}^{\frac{5}{4}}}{5 \, b}"," ",0,"1/5*(b*x^4 + a)^(5/4)/b","A",0
993,1,93,0,1.081035," ","integrate((b*x^4+a)^(1/4)/x,x, algorithm=""fricas"")","a^{\frac{1}{4}} \arctan\left(\frac{a^{\frac{3}{4}} \sqrt{\sqrt{b x^{4} + a} + \sqrt{a}} - {\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{\frac{3}{4}}}{a}\right) - \frac{1}{4} \, a^{\frac{1}{4}} \log\left({\left(b x^{4} + a\right)}^{\frac{1}{4}} + a^{\frac{1}{4}}\right) + \frac{1}{4} \, a^{\frac{1}{4}} \log\left({\left(b x^{4} + a\right)}^{\frac{1}{4}} - a^{\frac{1}{4}}\right) + {\left(b x^{4} + a\right)}^{\frac{1}{4}}"," ",0,"a^(1/4)*arctan((a^(3/4)*sqrt(sqrt(b*x^4 + a) + sqrt(a)) - (b*x^4 + a)^(1/4)*a^(3/4))/a) - 1/4*a^(1/4)*log((b*x^4 + a)^(1/4) + a^(1/4)) + 1/4*a^(1/4)*log((b*x^4 + a)^(1/4) - a^(1/4)) + (b*x^4 + a)^(1/4)","A",0
994,1,180,0,0.861320," ","integrate((b*x^4+a)^(1/4)/x^5,x, algorithm=""fricas"")","\frac{4 \, \left(\frac{b^{4}}{a^{3}}\right)^{\frac{1}{4}} x^{4} \arctan\left(-\frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{2} b \left(\frac{b^{4}}{a^{3}}\right)^{\frac{3}{4}} - \sqrt{\sqrt{b x^{4} + a} b^{2} + a^{2} \sqrt{\frac{b^{4}}{a^{3}}}} a^{2} \left(\frac{b^{4}}{a^{3}}\right)^{\frac{3}{4}}}{b^{4}}\right) - \left(\frac{b^{4}}{a^{3}}\right)^{\frac{1}{4}} x^{4} \log\left({\left(b x^{4} + a\right)}^{\frac{1}{4}} b + a \left(\frac{b^{4}}{a^{3}}\right)^{\frac{1}{4}}\right) + \left(\frac{b^{4}}{a^{3}}\right)^{\frac{1}{4}} x^{4} \log\left({\left(b x^{4} + a\right)}^{\frac{1}{4}} b - a \left(\frac{b^{4}}{a^{3}}\right)^{\frac{1}{4}}\right) - 4 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}}}{16 \, x^{4}}"," ",0,"1/16*(4*(b^4/a^3)^(1/4)*x^4*arctan(-((b*x^4 + a)^(1/4)*a^2*b*(b^4/a^3)^(3/4) - sqrt(sqrt(b*x^4 + a)*b^2 + a^2*sqrt(b^4/a^3))*a^2*(b^4/a^3)^(3/4))/b^4) - (b^4/a^3)^(1/4)*x^4*log((b*x^4 + a)^(1/4)*b + a*(b^4/a^3)^(1/4)) + (b^4/a^3)^(1/4)*x^4*log((b*x^4 + a)^(1/4)*b - a*(b^4/a^3)^(1/4)) - 4*(b*x^4 + a)^(1/4))/x^4","B",0
995,1,209,0,1.075394," ","integrate((b*x^4+a)^(1/4)/x^9,x, algorithm=""fricas"")","-\frac{12 \, a \left(\frac{b^{8}}{a^{7}}\right)^{\frac{1}{4}} x^{8} \arctan\left(-\frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{5} b^{2} \left(\frac{b^{8}}{a^{7}}\right)^{\frac{3}{4}} - \sqrt{\sqrt{b x^{4} + a} b^{4} + a^{4} \sqrt{\frac{b^{8}}{a^{7}}}} a^{5} \left(\frac{b^{8}}{a^{7}}\right)^{\frac{3}{4}}}{b^{8}}\right) - 3 \, a \left(\frac{b^{8}}{a^{7}}\right)^{\frac{1}{4}} x^{8} \log\left(3 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}} b^{2} + 3 \, a^{2} \left(\frac{b^{8}}{a^{7}}\right)^{\frac{1}{4}}\right) + 3 \, a \left(\frac{b^{8}}{a^{7}}\right)^{\frac{1}{4}} x^{8} \log\left(3 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}} b^{2} - 3 \, a^{2} \left(\frac{b^{8}}{a^{7}}\right)^{\frac{1}{4}}\right) + 4 \, {\left(b x^{4} + 4 \, a\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}}}{128 \, a x^{8}}"," ",0,"-1/128*(12*a*(b^8/a^7)^(1/4)*x^8*arctan(-((b*x^4 + a)^(1/4)*a^5*b^2*(b^8/a^7)^(3/4) - sqrt(sqrt(b*x^4 + a)*b^4 + a^4*sqrt(b^8/a^7))*a^5*(b^8/a^7)^(3/4))/b^8) - 3*a*(b^8/a^7)^(1/4)*x^8*log(3*(b*x^4 + a)^(1/4)*b^2 + 3*a^2*(b^8/a^7)^(1/4)) + 3*a*(b^8/a^7)^(1/4)*x^8*log(3*(b*x^4 + a)^(1/4)*b^2 - 3*a^2*(b^8/a^7)^(1/4)) + 4*(b*x^4 + 4*a)*(b*x^4 + a)^(1/4))/(a*x^8)","B",0
996,0,0,0,1.037507," ","integrate(x^9*(b*x^4+a)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{4} + a\right)}^{\frac{1}{4}} x^{9}, x\right)"," ",0,"integral((b*x^4 + a)^(1/4)*x^9, x)","F",0
997,0,0,0,0.963760," ","integrate(x^5*(b*x^4+a)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{4} + a\right)}^{\frac{1}{4}} x^{5}, x\right)"," ",0,"integral((b*x^4 + a)^(1/4)*x^5, x)","F",0
998,0,0,0,0.952630," ","integrate(x*(b*x^4+a)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{4} + a\right)}^{\frac{1}{4}} x, x\right)"," ",0,"integral((b*x^4 + a)^(1/4)*x, x)","F",0
999,0,0,0,0.848908," ","integrate((b*x^4+a)^(1/4)/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}{x^{3}}, x\right)"," ",0,"integral((b*x^4 + a)^(1/4)/x^3, x)","F",0
1000,0,0,0,1.355682," ","integrate((b*x^4+a)^(1/4)/x^7,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}{x^{7}}, x\right)"," ",0,"integral((b*x^4 + a)^(1/4)/x^7, x)","F",0
1001,0,0,0,0.735620," ","integrate((b*x^4+a)^(1/4)/x^11,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}{x^{11}}, x\right)"," ",0,"integral((b*x^4 + a)^(1/4)/x^11, x)","F",0
1002,1,220,0,1.396565," ","integrate(x^6*(b*x^4+a)^(1/4),x, algorithm=""fricas"")","\frac{12 \, \left(\frac{a^{8}}{b^{7}}\right)^{\frac{1}{4}} b \arctan\left(-\frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{2} \left(\frac{a^{8}}{b^{7}}\right)^{\frac{3}{4}} b^{5} - \left(\frac{a^{8}}{b^{7}}\right)^{\frac{3}{4}} b^{5} x \sqrt{\frac{\sqrt{\frac{a^{8}}{b^{7}}} b^{4} x^{2} + \sqrt{b x^{4} + a} a^{4}}{x^{2}}}}{a^{8} x}\right) - 3 \, \left(\frac{a^{8}}{b^{7}}\right)^{\frac{1}{4}} b \log\left(\frac{3 \, {\left(\left(\frac{a^{8}}{b^{7}}\right)^{\frac{1}{4}} b^{2} x + {\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{2}\right)}}{x}\right) + 3 \, \left(\frac{a^{8}}{b^{7}}\right)^{\frac{1}{4}} b \log\left(-\frac{3 \, {\left(\left(\frac{a^{8}}{b^{7}}\right)^{\frac{1}{4}} b^{2} x - {\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{2}\right)}}{x}\right) + 4 \, {\left(4 \, b x^{7} + a x^{3}\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}}}{128 \, b}"," ",0,"1/128*(12*(a^8/b^7)^(1/4)*b*arctan(-((b*x^4 + a)^(1/4)*a^2*(a^8/b^7)^(3/4)*b^5 - (a^8/b^7)^(3/4)*b^5*x*sqrt((sqrt(a^8/b^7)*b^4*x^2 + sqrt(b*x^4 + a)*a^4)/x^2))/(a^8*x)) - 3*(a^8/b^7)^(1/4)*b*log(3*((a^8/b^7)^(1/4)*b^2*x + (b*x^4 + a)^(1/4)*a^2)/x) + 3*(a^8/b^7)^(1/4)*b*log(-3*((a^8/b^7)^(1/4)*b^2*x - (b*x^4 + a)^(1/4)*a^2)/x) + 4*(4*b*x^7 + a*x^3)*(b*x^4 + a)^(1/4))/b","B",0
1003,1,191,0,1.154945," ","integrate(x^2*(b*x^4+a)^(1/4),x, algorithm=""fricas"")","\frac{1}{4} \, {\left(b x^{4} + a\right)}^{\frac{1}{4}} x^{3} - \frac{1}{4} \, \left(\frac{a^{4}}{b^{3}}\right)^{\frac{1}{4}} \arctan\left(\frac{\left(\frac{a^{4}}{b^{3}}\right)^{\frac{3}{4}} b^{2} x \sqrt{\frac{\sqrt{\frac{a^{4}}{b^{3}}} b^{2} x^{2} + \sqrt{b x^{4} + a} a^{2}}{x^{2}}} - {\left(b x^{4} + a\right)}^{\frac{1}{4}} a \left(\frac{a^{4}}{b^{3}}\right)^{\frac{3}{4}} b^{2}}{a^{4} x}\right) + \frac{1}{16} \, \left(\frac{a^{4}}{b^{3}}\right)^{\frac{1}{4}} \log\left(\frac{\left(\frac{a^{4}}{b^{3}}\right)^{\frac{1}{4}} b x + {\left(b x^{4} + a\right)}^{\frac{1}{4}} a}{x}\right) - \frac{1}{16} \, \left(\frac{a^{4}}{b^{3}}\right)^{\frac{1}{4}} \log\left(-\frac{\left(\frac{a^{4}}{b^{3}}\right)^{\frac{1}{4}} b x - {\left(b x^{4} + a\right)}^{\frac{1}{4}} a}{x}\right)"," ",0,"1/4*(b*x^4 + a)^(1/4)*x^3 - 1/4*(a^4/b^3)^(1/4)*arctan(((a^4/b^3)^(3/4)*b^2*x*sqrt((sqrt(a^4/b^3)*b^2*x^2 + sqrt(b*x^4 + a)*a^2)/x^2) - (b*x^4 + a)^(1/4)*a*(a^4/b^3)^(3/4)*b^2)/(a^4*x)) + 1/16*(a^4/b^3)^(1/4)*log(((a^4/b^3)^(1/4)*b*x + (b*x^4 + a)^(1/4)*a)/x) - 1/16*(a^4/b^3)^(1/4)*log(-((a^4/b^3)^(1/4)*b*x - (b*x^4 + a)^(1/4)*a)/x)","B",0
1004,-1,0,0,0.000000," ","integrate((b*x^4+a)^(1/4)/x^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1005,1,17,0,1.537888," ","integrate((b*x^4+a)^(1/4)/x^6,x, algorithm=""fricas"")","-\frac{{\left(b x^{4} + a\right)}^{\frac{5}{4}}}{5 \, a x^{5}}"," ",0,"-1/5*(b*x^4 + a)^(5/4)/(a*x^5)","A",0
1006,1,38,0,1.535607," ","integrate((b*x^4+a)^(1/4)/x^10,x, algorithm=""fricas"")","\frac{{\left(4 \, b^{2} x^{8} - a b x^{4} - 5 \, a^{2}\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}}}{45 \, a^{2} x^{9}}"," ",0,"1/45*(4*b^2*x^8 - a*b*x^4 - 5*a^2)*(b*x^4 + a)^(1/4)/(a^2*x^9)","A",0
1007,1,49,0,1.629554," ","integrate((b*x^4+a)^(1/4)/x^14,x, algorithm=""fricas"")","-\frac{{\left(32 \, b^{3} x^{12} - 8 \, a b^{2} x^{8} + 5 \, a^{2} b x^{4} + 45 \, a^{3}\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}}}{585 \, a^{3} x^{13}}"," ",0,"-1/585*(32*b^3*x^12 - 8*a*b^2*x^8 + 5*a^2*b*x^4 + 45*a^3)*(b*x^4 + a)^(1/4)/(a^3*x^13)","A",0
1008,1,60,0,1.595160," ","integrate((b*x^4+a)^(1/4)/x^18,x, algorithm=""fricas"")","\frac{{\left(128 \, b^{4} x^{16} - 32 \, a b^{3} x^{12} + 20 \, a^{2} b^{2} x^{8} - 15 \, a^{3} b x^{4} - 195 \, a^{4}\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}}}{3315 \, a^{4} x^{17}}"," ",0,"1/3315*(128*b^4*x^16 - 32*a*b^3*x^12 + 20*a^2*b^2*x^8 - 15*a^3*b*x^4 - 195*a^4)*(b*x^4 + a)^(1/4)/(a^4*x^17)","A",0
1009,0,0,0,1.309830," ","integrate(x^12*(b*x^4+a)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{4} + a\right)}^{\frac{1}{4}} x^{12}, x\right)"," ",0,"integral((b*x^4 + a)^(1/4)*x^12, x)","F",0
1010,0,0,0,1.500505," ","integrate(x^8*(b*x^4+a)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{4} + a\right)}^{\frac{1}{4}} x^{8}, x\right)"," ",0,"integral((b*x^4 + a)^(1/4)*x^8, x)","F",0
1011,0,0,0,1.620703," ","integrate(x^4*(b*x^4+a)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{4} + a\right)}^{\frac{1}{4}} x^{4}, x\right)"," ",0,"integral((b*x^4 + a)^(1/4)*x^4, x)","F",0
1012,0,0,0,1.466705," ","integrate((b*x^4+a)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{4} + a\right)}^{\frac{1}{4}}, x\right)"," ",0,"integral((b*x^4 + a)^(1/4), x)","F",0
1013,0,0,0,1.463405," ","integrate((b*x^4+a)^(1/4)/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}{x^{4}}, x\right)"," ",0,"integral((b*x^4 + a)^(1/4)/x^4, x)","F",0
1014,0,0,0,1.115290," ","integrate((b*x^4+a)^(1/4)/x^8,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}{x^{8}}, x\right)"," ",0,"integral((b*x^4 + a)^(1/4)/x^8, x)","F",0
1015,0,0,0,1.300678," ","integrate((b*x^4+a)^(1/4)/x^12,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}{x^{12}}, x\right)"," ",0,"integral((b*x^4 + a)^(1/4)/x^12, x)","F",0
1016,0,0,0,1.227413," ","integrate((b*x^4+a)^(1/4)/x^16,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}{x^{16}}, x\right)"," ",0,"integral((b*x^4 + a)^(1/4)/x^16, x)","F",0
1017,1,68,0,1.300111," ","integrate(x^19*(b*x^4+a)^(3/4),x, algorithm=""fricas"")","\frac{{\left(7315 \, b^{5} x^{20} + 1155 \, a b^{4} x^{16} - 1232 \, a^{2} b^{3} x^{12} + 1344 \, a^{3} b^{2} x^{8} - 1536 \, a^{4} b x^{4} + 2048 \, a^{5}\right)} {\left(b x^{4} + a\right)}^{\frac{3}{4}}}{168245 \, b^{5}}"," ",0,"1/168245*(7315*b^5*x^20 + 1155*a*b^4*x^16 - 1232*a^2*b^3*x^12 + 1344*a^3*b^2*x^8 - 1536*a^4*b*x^4 + 2048*a^5)*(b*x^4 + a)^(3/4)/b^5","A",0
1018,1,57,0,0.809094," ","integrate(x^15*(b*x^4+a)^(3/4),x, algorithm=""fricas"")","\frac{{\left(385 \, b^{4} x^{16} + 77 \, a b^{3} x^{12} - 84 \, a^{2} b^{2} x^{8} + 96 \, a^{3} b x^{4} - 128 \, a^{4}\right)} {\left(b x^{4} + a\right)}^{\frac{3}{4}}}{7315 \, b^{4}}"," ",0,"1/7315*(385*b^4*x^16 + 77*a*b^3*x^12 - 84*a^2*b^2*x^8 + 96*a^3*b*x^4 - 128*a^4)*(b*x^4 + a)^(3/4)/b^4","A",0
1019,1,46,0,1.213458," ","integrate(x^11*(b*x^4+a)^(3/4),x, algorithm=""fricas"")","\frac{{\left(77 \, b^{3} x^{12} + 21 \, a b^{2} x^{8} - 24 \, a^{2} b x^{4} + 32 \, a^{3}\right)} {\left(b x^{4} + a\right)}^{\frac{3}{4}}}{1155 \, b^{3}}"," ",0,"1/1155*(77*b^3*x^12 + 21*a*b^2*x^8 - 24*a^2*b*x^4 + 32*a^3)*(b*x^4 + a)^(3/4)/b^3","A",0
1020,1,35,0,1.403072," ","integrate(x^7*(b*x^4+a)^(3/4),x, algorithm=""fricas"")","\frac{{\left(7 \, b^{2} x^{8} + 3 \, a b x^{4} - 4 \, a^{2}\right)} {\left(b x^{4} + a\right)}^{\frac{3}{4}}}{77 \, b^{2}}"," ",0,"1/77*(7*b^2*x^8 + 3*a*b*x^4 - 4*a^2)*(b*x^4 + a)^(3/4)/b^2","A",0
1021,1,14,0,1.300769," ","integrate(x^3*(b*x^4+a)^(3/4),x, algorithm=""fricas"")","\frac{{\left(b x^{4} + a\right)}^{\frac{7}{4}}}{7 \, b}"," ",0,"1/7*(b*x^4 + a)^(7/4)/b","A",0
1022,1,132,0,0.742054," ","integrate((b*x^4+a)^(3/4)/x,x, algorithm=""fricas"")","-{\left(a^{3}\right)}^{\frac{1}{4}} \arctan\left(-\frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}} {\left(a^{3}\right)}^{\frac{1}{4}} a^{2} - \sqrt{\sqrt{b x^{4} + a} a^{4} + \sqrt{a^{3}} a^{3}} {\left(a^{3}\right)}^{\frac{1}{4}}}{a^{3}}\right) - \frac{1}{4} \, {\left(a^{3}\right)}^{\frac{1}{4}} \log\left({\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{2} + {\left(a^{3}\right)}^{\frac{3}{4}}\right) + \frac{1}{4} \, {\left(a^{3}\right)}^{\frac{1}{4}} \log\left({\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{2} - {\left(a^{3}\right)}^{\frac{3}{4}}\right) + \frac{1}{3} \, {\left(b x^{4} + a\right)}^{\frac{3}{4}}"," ",0,"-(a^3)^(1/4)*arctan(-((b*x^4 + a)^(1/4)*(a^3)^(1/4)*a^2 - sqrt(sqrt(b*x^4 + a)*a^4 + sqrt(a^3)*a^3)*(a^3)^(1/4))/a^3) - 1/4*(a^3)^(1/4)*log((b*x^4 + a)^(1/4)*a^2 + (a^3)^(3/4)) + 1/4*(a^3)^(1/4)*log((b*x^4 + a)^(1/4)*a^2 - (a^3)^(3/4)) + 1/3*(b*x^4 + a)^(3/4)","B",0
1023,1,185,0,1.663622," ","integrate((b*x^4+a)^(3/4)/x^5,x, algorithm=""fricas"")","-\frac{12 \, \left(\frac{b^{4}}{a}\right)^{\frac{1}{4}} x^{4} \arctan\left(-\frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}} \left(\frac{b^{4}}{a}\right)^{\frac{1}{4}} b^{3} - \sqrt{\sqrt{b x^{4} + a} b^{6} + \sqrt{\frac{b^{4}}{a}} a b^{4}} \left(\frac{b^{4}}{a}\right)^{\frac{1}{4}}}{b^{4}}\right) + 3 \, \left(\frac{b^{4}}{a}\right)^{\frac{1}{4}} x^{4} \log\left(27 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}} b^{3} + 27 \, \left(\frac{b^{4}}{a}\right)^{\frac{3}{4}} a\right) - 3 \, \left(\frac{b^{4}}{a}\right)^{\frac{1}{4}} x^{4} \log\left(27 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}} b^{3} - 27 \, \left(\frac{b^{4}}{a}\right)^{\frac{3}{4}} a\right) + 4 \, {\left(b x^{4} + a\right)}^{\frac{3}{4}}}{16 \, x^{4}}"," ",0,"-1/16*(12*(b^4/a)^(1/4)*x^4*arctan(-((b*x^4 + a)^(1/4)*(b^4/a)^(1/4)*b^3 - sqrt(sqrt(b*x^4 + a)*b^6 + sqrt(b^4/a)*a*b^4)*(b^4/a)^(1/4))/b^4) + 3*(b^4/a)^(1/4)*x^4*log(27*(b*x^4 + a)^(1/4)*b^3 + 27*(b^4/a)^(3/4)*a) - 3*(b^4/a)^(1/4)*x^4*log(27*(b*x^4 + a)^(1/4)*b^3 - 27*(b^4/a)^(3/4)*a) + 4*(b*x^4 + a)^(3/4))/x^4","B",0
1024,1,209,0,1.214698," ","integrate((b*x^4+a)^(3/4)/x^9,x, algorithm=""fricas"")","\frac{12 \, \left(\frac{b^{8}}{a^{5}}\right)^{\frac{1}{4}} a x^{8} \arctan\left(-\frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}} \left(\frac{b^{8}}{a^{5}}\right)^{\frac{1}{4}} a b^{6} - \sqrt{\sqrt{b x^{4} + a} b^{12} + \sqrt{\frac{b^{8}}{a^{5}}} a^{3} b^{8}} \left(\frac{b^{8}}{a^{5}}\right)^{\frac{1}{4}} a}{b^{8}}\right) + 3 \, \left(\frac{b^{8}}{a^{5}}\right)^{\frac{1}{4}} a x^{8} \log\left(27 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}} b^{6} + 27 \, \left(\frac{b^{8}}{a^{5}}\right)^{\frac{3}{4}} a^{4}\right) - 3 \, \left(\frac{b^{8}}{a^{5}}\right)^{\frac{1}{4}} a x^{8} \log\left(27 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}} b^{6} - 27 \, \left(\frac{b^{8}}{a^{5}}\right)^{\frac{3}{4}} a^{4}\right) - 4 \, {\left(3 \, b x^{4} + 4 \, a\right)} {\left(b x^{4} + a\right)}^{\frac{3}{4}}}{128 \, a x^{8}}"," ",0,"1/128*(12*(b^8/a^5)^(1/4)*a*x^8*arctan(-((b*x^4 + a)^(1/4)*(b^8/a^5)^(1/4)*a*b^6 - sqrt(sqrt(b*x^4 + a)*b^12 + sqrt(b^8/a^5)*a^3*b^8)*(b^8/a^5)^(1/4)*a)/b^8) + 3*(b^8/a^5)^(1/4)*a*x^8*log(27*(b*x^4 + a)^(1/4)*b^6 + 27*(b^8/a^5)^(3/4)*a^4) - 3*(b^8/a^5)^(1/4)*a*x^8*log(27*(b*x^4 + a)^(1/4)*b^6 - 27*(b^8/a^5)^(3/4)*a^4) - 4*(3*b*x^4 + 4*a)*(b*x^4 + a)^(3/4))/(a*x^8)","B",0
1025,0,0,0,1.063467," ","integrate(x^9*(b*x^4+a)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{4} + a\right)}^{\frac{3}{4}} x^{9}, x\right)"," ",0,"integral((b*x^4 + a)^(3/4)*x^9, x)","F",0
1026,0,0,0,1.534491," ","integrate(x^5*(b*x^4+a)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{4} + a\right)}^{\frac{3}{4}} x^{5}, x\right)"," ",0,"integral((b*x^4 + a)^(3/4)*x^5, x)","F",0
1027,0,0,0,1.478527," ","integrate(x*(b*x^4+a)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{4} + a\right)}^{\frac{3}{4}} x, x\right)"," ",0,"integral((b*x^4 + a)^(3/4)*x, x)","F",0
1028,0,0,0,1.575013," ","integrate((b*x^4+a)^(3/4)/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}{x^{3}}, x\right)"," ",0,"integral((b*x^4 + a)^(3/4)/x^3, x)","F",0
1029,0,0,0,0.858321," ","integrate((b*x^4+a)^(3/4)/x^7,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}{x^{7}}, x\right)"," ",0,"integral((b*x^4 + a)^(3/4)/x^7, x)","F",0
1030,0,0,0,1.403751," ","integrate((b*x^4+a)^(3/4)/x^11,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}{x^{11}}, x\right)"," ",0,"integral((b*x^4 + a)^(3/4)/x^11, x)","F",0
1031,1,250,0,1.229263," ","integrate(x^12*(b*x^4+a)^(3/4),x, algorithm=""fricas"")","-\frac{180 \, \left(\frac{a^{16}}{b^{13}}\right)^{\frac{1}{4}} b^{3} \arctan\left(-\frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}} \left(\frac{a^{16}}{b^{13}}\right)^{\frac{1}{4}} a^{12} b^{3} - \left(\frac{a^{16}}{b^{13}}\right)^{\frac{1}{4}} b^{3} x \sqrt{\frac{\sqrt{\frac{a^{16}}{b^{13}}} a^{16} b^{7} x^{2} + \sqrt{b x^{4} + a} a^{24}}{x^{2}}}}{a^{16} x}\right) + 45 \, \left(\frac{a^{16}}{b^{13}}\right)^{\frac{1}{4}} b^{3} \log\left(\frac{91125 \, {\left({\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{12} + \left(\frac{a^{16}}{b^{13}}\right)^{\frac{3}{4}} b^{10} x\right)}}{x}\right) - 45 \, \left(\frac{a^{16}}{b^{13}}\right)^{\frac{1}{4}} b^{3} \log\left(\frac{91125 \, {\left({\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{12} - \left(\frac{a^{16}}{b^{13}}\right)^{\frac{3}{4}} b^{10} x\right)}}{x}\right) - 4 \, {\left(128 \, b^{3} x^{13} + 32 \, a b^{2} x^{9} - 36 \, a^{2} b x^{5} + 45 \, a^{3} x\right)} {\left(b x^{4} + a\right)}^{\frac{3}{4}}}{8192 \, b^{3}}"," ",0,"-1/8192*(180*(a^16/b^13)^(1/4)*b^3*arctan(-((b*x^4 + a)^(1/4)*(a^16/b^13)^(1/4)*a^12*b^3 - (a^16/b^13)^(1/4)*b^3*x*sqrt((sqrt(a^16/b^13)*a^16*b^7*x^2 + sqrt(b*x^4 + a)*a^24)/x^2))/(a^16*x)) + 45*(a^16/b^13)^(1/4)*b^3*log(91125*((b*x^4 + a)^(1/4)*a^12 + (a^16/b^13)^(3/4)*b^10*x)/x) - 45*(a^16/b^13)^(1/4)*b^3*log(91125*((b*x^4 + a)^(1/4)*a^12 - (a^16/b^13)^(3/4)*b^10*x)/x) - 4*(128*b^3*x^13 + 32*a*b^2*x^9 - 36*a^2*b*x^5 + 45*a^3*x)*(b*x^4 + a)^(3/4))/b^3","B",0
1032,1,239,0,1.599618," ","integrate(x^8*(b*x^4+a)^(3/4),x, algorithm=""fricas"")","\frac{60 \, \left(\frac{a^{12}}{b^{9}}\right)^{\frac{1}{4}} b^{2} \arctan\left(-\frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}} \left(\frac{a^{12}}{b^{9}}\right)^{\frac{1}{4}} a^{9} b^{2} - \left(\frac{a^{12}}{b^{9}}\right)^{\frac{1}{4}} b^{2} x \sqrt{\frac{\sqrt{\frac{a^{12}}{b^{9}}} a^{12} b^{5} x^{2} + \sqrt{b x^{4} + a} a^{18}}{x^{2}}}}{a^{12} x}\right) + 15 \, \left(\frac{a^{12}}{b^{9}}\right)^{\frac{1}{4}} b^{2} \log\left(\frac{125 \, {\left({\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{9} + \left(\frac{a^{12}}{b^{9}}\right)^{\frac{3}{4}} b^{7} x\right)}}{x}\right) - 15 \, \left(\frac{a^{12}}{b^{9}}\right)^{\frac{1}{4}} b^{2} \log\left(\frac{125 \, {\left({\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{9} - \left(\frac{a^{12}}{b^{9}}\right)^{\frac{3}{4}} b^{7} x\right)}}{x}\right) + 4 \, {\left(32 \, b^{2} x^{9} + 12 \, a b x^{5} - 15 \, a^{2} x\right)} {\left(b x^{4} + a\right)}^{\frac{3}{4}}}{1536 \, b^{2}}"," ",0,"1/1536*(60*(a^12/b^9)^(1/4)*b^2*arctan(-((b*x^4 + a)^(1/4)*(a^12/b^9)^(1/4)*a^9*b^2 - (a^12/b^9)^(1/4)*b^2*x*sqrt((sqrt(a^12/b^9)*a^12*b^5*x^2 + sqrt(b*x^4 + a)*a^18)/x^2))/(a^12*x)) + 15*(a^12/b^9)^(1/4)*b^2*log(125*((b*x^4 + a)^(1/4)*a^9 + (a^12/b^9)^(3/4)*b^7*x)/x) - 15*(a^12/b^9)^(1/4)*b^2*log(125*((b*x^4 + a)^(1/4)*a^9 - (a^12/b^9)^(3/4)*b^7*x)/x) + 4*(32*b^2*x^9 + 12*a*b*x^5 - 15*a^2*x)*(b*x^4 + a)^(3/4))/b^2","B",0
1033,1,218,0,1.458235," ","integrate(x^4*(b*x^4+a)^(3/4),x, algorithm=""fricas"")","-\frac{12 \, \left(\frac{a^{8}}{b^{5}}\right)^{\frac{1}{4}} b \arctan\left(-\frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}} \left(\frac{a^{8}}{b^{5}}\right)^{\frac{1}{4}} a^{6} b - \left(\frac{a^{8}}{b^{5}}\right)^{\frac{1}{4}} b x \sqrt{\frac{\sqrt{\frac{a^{8}}{b^{5}}} a^{8} b^{3} x^{2} + \sqrt{b x^{4} + a} a^{12}}{x^{2}}}}{a^{8} x}\right) + 3 \, \left(\frac{a^{8}}{b^{5}}\right)^{\frac{1}{4}} b \log\left(\frac{27 \, {\left({\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{6} + \left(\frac{a^{8}}{b^{5}}\right)^{\frac{3}{4}} b^{4} x\right)}}{x}\right) - 3 \, \left(\frac{a^{8}}{b^{5}}\right)^{\frac{1}{4}} b \log\left(\frac{27 \, {\left({\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{6} - \left(\frac{a^{8}}{b^{5}}\right)^{\frac{3}{4}} b^{4} x\right)}}{x}\right) - 4 \, {\left(4 \, b x^{5} + 3 \, a x\right)} {\left(b x^{4} + a\right)}^{\frac{3}{4}}}{128 \, b}"," ",0,"-1/128*(12*(a^8/b^5)^(1/4)*b*arctan(-((b*x^4 + a)^(1/4)*(a^8/b^5)^(1/4)*a^6*b - (a^8/b^5)^(1/4)*b*x*sqrt((sqrt(a^8/b^5)*a^8*b^3*x^2 + sqrt(b*x^4 + a)*a^12)/x^2))/(a^8*x)) + 3*(a^8/b^5)^(1/4)*b*log(27*((b*x^4 + a)^(1/4)*a^6 + (a^8/b^5)^(3/4)*b^4*x)/x) - 3*(a^8/b^5)^(1/4)*b*log(27*((b*x^4 + a)^(1/4)*a^6 - (a^8/b^5)^(3/4)*b^4*x)/x) - 4*(4*b*x^5 + 3*a*x)*(b*x^4 + a)^(3/4))/b","B",0
1034,1,192,0,1.450722," ","integrate((b*x^4+a)^(3/4),x, algorithm=""fricas"")","\frac{1}{4} \, {\left(b x^{4} + a\right)}^{\frac{3}{4}} x + \frac{3}{4} \, \left(\frac{a^{4}}{b}\right)^{\frac{1}{4}} \arctan\left(-\frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}} \left(\frac{a^{4}}{b}\right)^{\frac{1}{4}} a^{3} - \left(\frac{a^{4}}{b}\right)^{\frac{1}{4}} x \sqrt{\frac{\sqrt{\frac{a^{4}}{b}} a^{4} b x^{2} + \sqrt{b x^{4} + a} a^{6}}{x^{2}}}}{a^{4} x}\right) + \frac{3}{16} \, \left(\frac{a^{4}}{b}\right)^{\frac{1}{4}} \log\left(\frac{27 \, {\left({\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{3} + \left(\frac{a^{4}}{b}\right)^{\frac{3}{4}} b x\right)}}{x}\right) - \frac{3}{16} \, \left(\frac{a^{4}}{b}\right)^{\frac{1}{4}} \log\left(\frac{27 \, {\left({\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{3} - \left(\frac{a^{4}}{b}\right)^{\frac{3}{4}} b x\right)}}{x}\right)"," ",0,"1/4*(b*x^4 + a)^(3/4)*x + 3/4*(a^4/b)^(1/4)*arctan(-((b*x^4 + a)^(1/4)*(a^4/b)^(1/4)*a^3 - (a^4/b)^(1/4)*x*sqrt((sqrt(a^4/b)*a^4*b*x^2 + sqrt(b*x^4 + a)*a^6)/x^2))/(a^4*x)) + 3/16*(a^4/b)^(1/4)*log(27*((b*x^4 + a)^(1/4)*a^3 + (a^4/b)^(3/4)*b*x)/x) - 3/16*(a^4/b)^(1/4)*log(27*((b*x^4 + a)^(1/4)*a^3 - (a^4/b)^(3/4)*b*x)/x)","B",0
1035,-1,0,0,0.000000," ","integrate((b*x^4+a)^(3/4)/x^4,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1036,1,17,0,0.986747," ","integrate((b*x^4+a)^(3/4)/x^8,x, algorithm=""fricas"")","-\frac{{\left(b x^{4} + a\right)}^{\frac{7}{4}}}{7 \, a x^{7}}"," ",0,"-1/7*(b*x^4 + a)^(7/4)/(a*x^7)","A",0
1037,1,38,0,1.221413," ","integrate((b*x^4+a)^(3/4)/x^12,x, algorithm=""fricas"")","\frac{{\left(4 \, b^{2} x^{8} - 3 \, a b x^{4} - 7 \, a^{2}\right)} {\left(b x^{4} + a\right)}^{\frac{3}{4}}}{77 \, a^{2} x^{11}}"," ",0,"1/77*(4*b^2*x^8 - 3*a*b*x^4 - 7*a^2)*(b*x^4 + a)^(3/4)/(a^2*x^11)","A",0
1038,1,49,0,1.222267," ","integrate((b*x^4+a)^(3/4)/x^16,x, algorithm=""fricas"")","-\frac{{\left(32 \, b^{3} x^{12} - 24 \, a b^{2} x^{8} + 21 \, a^{2} b x^{4} + 77 \, a^{3}\right)} {\left(b x^{4} + a\right)}^{\frac{3}{4}}}{1155 \, a^{3} x^{15}}"," ",0,"-1/1155*(32*b^3*x^12 - 24*a*b^2*x^8 + 21*a^2*b*x^4 + 77*a^3)*(b*x^4 + a)^(3/4)/(a^3*x^15)","A",0
1039,1,60,0,1.464571," ","integrate((b*x^4+a)^(3/4)/x^20,x, algorithm=""fricas"")","\frac{{\left(128 \, b^{4} x^{16} - 96 \, a b^{3} x^{12} + 84 \, a^{2} b^{2} x^{8} - 77 \, a^{3} b x^{4} - 385 \, a^{4}\right)} {\left(b x^{4} + a\right)}^{\frac{3}{4}}}{7315 \, a^{4} x^{19}}"," ",0,"1/7315*(128*b^4*x^16 - 96*a*b^3*x^12 + 84*a^2*b^2*x^8 - 77*a^3*b*x^4 - 385*a^4)*(b*x^4 + a)^(3/4)/(a^4*x^19)","A",0
1040,0,0,0,1.129611," ","integrate(x^10*(b*x^4+a)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{4} + a\right)}^{\frac{3}{4}} x^{10}, x\right)"," ",0,"integral((b*x^4 + a)^(3/4)*x^10, x)","F",0
1041,0,0,0,0.988343," ","integrate(x^6*(b*x^4+a)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{4} + a\right)}^{\frac{3}{4}} x^{6}, x\right)"," ",0,"integral((b*x^4 + a)^(3/4)*x^6, x)","F",0
1042,0,0,0,1.640783," ","integrate(x^2*(b*x^4+a)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{4} + a\right)}^{\frac{3}{4}} x^{2}, x\right)"," ",0,"integral((b*x^4 + a)^(3/4)*x^2, x)","F",0
1043,0,0,0,1.178875," ","integrate((b*x^4+a)^(3/4)/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}{x^{2}}, x\right)"," ",0,"integral((b*x^4 + a)^(3/4)/x^2, x)","F",0
1044,0,0,0,1.198748," ","integrate((b*x^4+a)^(3/4)/x^6,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}{x^{6}}, x\right)"," ",0,"integral((b*x^4 + a)^(3/4)/x^6, x)","F",0
1045,0,0,0,1.185584," ","integrate((b*x^4+a)^(3/4)/x^10,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}{x^{10}}, x\right)"," ",0,"integral((b*x^4 + a)^(3/4)/x^10, x)","F",0
1046,0,0,0,1.095153," ","integrate((b*x^4+a)^(3/4)/x^14,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}{x^{14}}, x\right)"," ",0,"integral((b*x^4 + a)^(3/4)/x^14, x)","F",0
1047,1,79,0,1.168795," ","integrate(x^19*(b*x^4+a)^(5/4),x, algorithm=""fricas"")","\frac{{\left(13923 \, b^{6} x^{24} + 17238 \, a b^{5} x^{20} + 195 \, a^{2} b^{4} x^{16} - 240 \, a^{3} b^{3} x^{12} + 320 \, a^{4} b^{2} x^{8} - 512 \, a^{5} b x^{4} + 2048 \, a^{6}\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}}}{348075 \, b^{5}}"," ",0,"1/348075*(13923*b^6*x^24 + 17238*a*b^5*x^20 + 195*a^2*b^4*x^16 - 240*a^3*b^3*x^12 + 320*a^4*b^2*x^8 - 512*a^5*b*x^4 + 2048*a^6)*(b*x^4 + a)^(1/4)/b^5","A",0
1048,1,68,0,1.104181," ","integrate(x^15*(b*x^4+a)^(5/4),x, algorithm=""fricas"")","\frac{{\left(663 \, b^{5} x^{20} + 858 \, a b^{4} x^{16} + 15 \, a^{2} b^{3} x^{12} - 20 \, a^{3} b^{2} x^{8} + 32 \, a^{4} b x^{4} - 128 \, a^{5}\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}}}{13923 \, b^{4}}"," ",0,"1/13923*(663*b^5*x^20 + 858*a*b^4*x^16 + 15*a^2*b^3*x^12 - 20*a^3*b^2*x^8 + 32*a^4*b*x^4 - 128*a^5)*(b*x^4 + a)^(1/4)/b^4","A",0
1049,1,57,0,1.248605," ","integrate(x^11*(b*x^4+a)^(5/4),x, algorithm=""fricas"")","\frac{{\left(117 \, b^{4} x^{16} + 162 \, a b^{3} x^{12} + 5 \, a^{2} b^{2} x^{8} - 8 \, a^{3} b x^{4} + 32 \, a^{4}\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}}}{1989 \, b^{3}}"," ",0,"1/1989*(117*b^4*x^16 + 162*a*b^3*x^12 + 5*a^2*b^2*x^8 - 8*a^3*b*x^4 + 32*a^4)*(b*x^4 + a)^(1/4)/b^3","A",0
1050,1,45,0,1.091365," ","integrate(x^7*(b*x^4+a)^(5/4),x, algorithm=""fricas"")","\frac{{\left(9 \, b^{3} x^{12} + 14 \, a b^{2} x^{8} + a^{2} b x^{4} - 4 \, a^{3}\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}}}{117 \, b^{2}}"," ",0,"1/117*(9*b^3*x^12 + 14*a*b^2*x^8 + a^2*b*x^4 - 4*a^3)*(b*x^4 + a)^(1/4)/b^2","A",0
1051,1,32,0,1.148133," ","integrate(x^3*(b*x^4+a)^(5/4),x, algorithm=""fricas"")","\frac{{\left(b^{2} x^{8} + 2 \, a b x^{4} + a^{2}\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}}}{9 \, b}"," ",0,"1/9*(b^2*x^8 + 2*a*b*x^4 + a^2)*(b*x^4 + a)^(1/4)/b","B",0
1052,1,130,0,1.318665," ","integrate((b*x^4+a)^(5/4)/x,x, algorithm=""fricas"")","\frac{1}{5} \, {\left(b x^{4} + 6 \, a\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}} + {\left(a^{5}\right)}^{\frac{1}{4}} \arctan\left(-\frac{{\left(a^{5}\right)}^{\frac{3}{4}} {\left(b x^{4} + a\right)}^{\frac{1}{4}} a - {\left(a^{5}\right)}^{\frac{3}{4}} \sqrt{\sqrt{b x^{4} + a} a^{2} + \sqrt{a^{5}}}}{a^{5}}\right) - \frac{1}{4} \, {\left(a^{5}\right)}^{\frac{1}{4}} \log\left({\left(b x^{4} + a\right)}^{\frac{1}{4}} a + {\left(a^{5}\right)}^{\frac{1}{4}}\right) + \frac{1}{4} \, {\left(a^{5}\right)}^{\frac{1}{4}} \log\left({\left(b x^{4} + a\right)}^{\frac{1}{4}} a - {\left(a^{5}\right)}^{\frac{1}{4}}\right)"," ",0,"1/5*(b*x^4 + 6*a)*(b*x^4 + a)^(1/4) + (a^5)^(1/4)*arctan(-((a^5)^(3/4)*(b*x^4 + a)^(1/4)*a - (a^5)^(3/4)*sqrt(sqrt(b*x^4 + a)*a^2 + sqrt(a^5)))/a^5) - 1/4*(a^5)^(1/4)*log((b*x^4 + a)^(1/4)*a + (a^5)^(1/4)) + 1/4*(a^5)^(1/4)*log((b*x^4 + a)^(1/4)*a - (a^5)^(1/4))","B",0
1053,1,169,0,1.246624," ","integrate((b*x^4+a)^(5/4)/x^5,x, algorithm=""fricas"")","\frac{20 \, \left(a b^{4}\right)^{\frac{1}{4}} x^{4} \arctan\left(-\frac{\left(a b^{4}\right)^{\frac{3}{4}} {\left(b x^{4} + a\right)}^{\frac{1}{4}} b - \left(a b^{4}\right)^{\frac{3}{4}} \sqrt{\sqrt{b x^{4} + a} b^{2} + \sqrt{a b^{4}}}}{a b^{4}}\right) - 5 \, \left(a b^{4}\right)^{\frac{1}{4}} x^{4} \log\left(5 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}} b + 5 \, \left(a b^{4}\right)^{\frac{1}{4}}\right) + 5 \, \left(a b^{4}\right)^{\frac{1}{4}} x^{4} \log\left(5 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}} b - 5 \, \left(a b^{4}\right)^{\frac{1}{4}}\right) + 4 \, {\left(4 \, b x^{4} - a\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}}}{16 \, x^{4}}"," ",0,"1/16*(20*(a*b^4)^(1/4)*x^4*arctan(-((a*b^4)^(3/4)*(b*x^4 + a)^(1/4)*b - (a*b^4)^(3/4)*sqrt(sqrt(b*x^4 + a)*b^2 + sqrt(a*b^4)))/(a*b^4)) - 5*(a*b^4)^(1/4)*x^4*log(5*(b*x^4 + a)^(1/4)*b + 5*(a*b^4)^(1/4)) + 5*(a*b^4)^(1/4)*x^4*log(5*(b*x^4 + a)^(1/4)*b - 5*(a*b^4)^(1/4)) + 4*(4*b*x^4 - a)*(b*x^4 + a)^(1/4))/x^4","B",0
1054,1,200,0,1.402566," ","integrate((b*x^4+a)^(5/4)/x^9,x, algorithm=""fricas"")","\frac{20 \, \left(\frac{b^{8}}{a^{3}}\right)^{\frac{1}{4}} x^{8} \arctan\left(-\frac{\left(\frac{b^{8}}{a^{3}}\right)^{\frac{3}{4}} {\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{2} b^{2} - \left(\frac{b^{8}}{a^{3}}\right)^{\frac{3}{4}} \sqrt{\sqrt{b x^{4} + a} b^{4} + \sqrt{\frac{b^{8}}{a^{3}}} a^{2}} a^{2}}{b^{8}}\right) - 5 \, \left(\frac{b^{8}}{a^{3}}\right)^{\frac{1}{4}} x^{8} \log\left(5 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}} b^{2} + 5 \, \left(\frac{b^{8}}{a^{3}}\right)^{\frac{1}{4}} a\right) + 5 \, \left(\frac{b^{8}}{a^{3}}\right)^{\frac{1}{4}} x^{8} \log\left(5 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}} b^{2} - 5 \, \left(\frac{b^{8}}{a^{3}}\right)^{\frac{1}{4}} a\right) - 4 \, {\left(9 \, b x^{4} + 4 \, a\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}}}{128 \, x^{8}}"," ",0,"1/128*(20*(b^8/a^3)^(1/4)*x^8*arctan(-((b^8/a^3)^(3/4)*(b*x^4 + a)^(1/4)*a^2*b^2 - (b^8/a^3)^(3/4)*sqrt(sqrt(b*x^4 + a)*b^4 + sqrt(b^8/a^3)*a^2)*a^2)/b^8) - 5*(b^8/a^3)^(1/4)*x^8*log(5*(b*x^4 + a)^(1/4)*b^2 + 5*(b^8/a^3)^(1/4)*a) + 5*(b^8/a^3)^(1/4)*x^8*log(5*(b*x^4 + a)^(1/4)*b^2 - 5*(b^8/a^3)^(1/4)*a) - 4*(9*b*x^4 + 4*a)*(b*x^4 + a)^(1/4))/x^8","B",0
1055,0,0,0,1.284814," ","integrate(x^9*(b*x^4+a)^(5/4),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{13} + a x^{9}\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}}, x\right)"," ",0,"integral((b*x^13 + a*x^9)*(b*x^4 + a)^(1/4), x)","F",0
1056,0,0,0,1.281477," ","integrate(x^5*(b*x^4+a)^(5/4),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{9} + a x^{5}\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}}, x\right)"," ",0,"integral((b*x^9 + a*x^5)*(b*x^4 + a)^(1/4), x)","F",0
1057,0,0,0,1.152310," ","integrate(x*(b*x^4+a)^(5/4),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{5} + a x\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}}, x\right)"," ",0,"integral((b*x^5 + a*x)*(b*x^4 + a)^(1/4), x)","F",0
1058,0,0,0,1.296607," ","integrate((b*x^4+a)^(5/4)/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{\frac{5}{4}}}{x^{3}}, x\right)"," ",0,"integral((b*x^4 + a)^(5/4)/x^3, x)","F",0
1059,0,0,0,1.344426," ","integrate((b*x^4+a)^(5/4)/x^7,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{\frac{5}{4}}}{x^{7}}, x\right)"," ",0,"integral((b*x^4 + a)^(5/4)/x^7, x)","F",0
1060,0,0,0,1.176442," ","integrate((b*x^4+a)^(5/4)/x^11,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{\frac{5}{4}}}{x^{11}}, x\right)"," ",0,"integral((b*x^4 + a)^(5/4)/x^11, x)","F",0
1061,0,0,0,1.119519," ","integrate((b*x^4+a)^(5/4)/x^15,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{\frac{5}{4}}}{x^{15}}, x\right)"," ",0,"integral((b*x^4 + a)^(5/4)/x^15, x)","F",0
1062,1,249,0,0.894286," ","integrate(x^10*(b*x^4+a)^(5/4),x, algorithm=""fricas"")","-\frac{420 \, \left(\frac{a^{16}}{b^{11}}\right)^{\frac{1}{4}} b^{2} \arctan\left(-\frac{\left(\frac{a^{16}}{b^{11}}\right)^{\frac{3}{4}} {\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{4} b^{8} - \left(\frac{a^{16}}{b^{11}}\right)^{\frac{3}{4}} b^{8} x \sqrt{\frac{\sqrt{b x^{4} + a} a^{8} + \sqrt{\frac{a^{16}}{b^{11}}} b^{6} x^{2}}{x^{2}}}}{a^{16} x}\right) - 105 \, \left(\frac{a^{16}}{b^{11}}\right)^{\frac{1}{4}} b^{2} \log\left(\frac{35 \, {\left({\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{4} + \left(\frac{a^{16}}{b^{11}}\right)^{\frac{1}{4}} b^{3} x\right)}}{x}\right) + 105 \, \left(\frac{a^{16}}{b^{11}}\right)^{\frac{1}{4}} b^{2} \log\left(\frac{35 \, {\left({\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{4} - \left(\frac{a^{16}}{b^{11}}\right)^{\frac{1}{4}} b^{3} x\right)}}{x}\right) - 4 \, {\left(384 \, b^{3} x^{15} + 544 \, a b^{2} x^{11} + 20 \, a^{2} b x^{7} - 35 \, a^{3} x^{3}\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}}}{24576 \, b^{2}}"," ",0,"-1/24576*(420*(a^16/b^11)^(1/4)*b^2*arctan(-((a^16/b^11)^(3/4)*(b*x^4 + a)^(1/4)*a^4*b^8 - (a^16/b^11)^(3/4)*b^8*x*sqrt((sqrt(b*x^4 + a)*a^8 + sqrt(a^16/b^11)*b^6*x^2)/x^2))/(a^16*x)) - 105*(a^16/b^11)^(1/4)*b^2*log(35*((b*x^4 + a)^(1/4)*a^4 + (a^16/b^11)^(1/4)*b^3*x)/x) + 105*(a^16/b^11)^(1/4)*b^2*log(35*((b*x^4 + a)^(1/4)*a^4 - (a^16/b^11)^(1/4)*b^3*x)/x) - 4*(384*b^3*x^15 + 544*a*b^2*x^11 + 20*a^2*b*x^7 - 35*a^3*x^3)*(b*x^4 + a)^(1/4))/b^2","B",0
1063,1,232,0,0.786351," ","integrate(x^6*(b*x^4+a)^(5/4),x, algorithm=""fricas"")","\frac{60 \, \left(\frac{a^{12}}{b^{7}}\right)^{\frac{1}{4}} b \arctan\left(-\frac{\left(\frac{a^{12}}{b^{7}}\right)^{\frac{3}{4}} {\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{3} b^{5} - \left(\frac{a^{12}}{b^{7}}\right)^{\frac{3}{4}} b^{5} x \sqrt{\frac{\sqrt{b x^{4} + a} a^{6} + \sqrt{\frac{a^{12}}{b^{7}}} b^{4} x^{2}}{x^{2}}}}{a^{12} x}\right) - 15 \, \left(\frac{a^{12}}{b^{7}}\right)^{\frac{1}{4}} b \log\left(\frac{5 \, {\left({\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{3} + \left(\frac{a^{12}}{b^{7}}\right)^{\frac{1}{4}} b^{2} x\right)}}{x}\right) + 15 \, \left(\frac{a^{12}}{b^{7}}\right)^{\frac{1}{4}} b \log\left(\frac{5 \, {\left({\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{3} - \left(\frac{a^{12}}{b^{7}}\right)^{\frac{1}{4}} b^{2} x\right)}}{x}\right) + 4 \, {\left(32 \, b^{2} x^{11} + 52 \, a b x^{7} + 5 \, a^{2} x^{3}\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}}}{1536 \, b}"," ",0,"1/1536*(60*(a^12/b^7)^(1/4)*b*arctan(-((a^12/b^7)^(3/4)*(b*x^4 + a)^(1/4)*a^3*b^5 - (a^12/b^7)^(3/4)*b^5*x*sqrt((sqrt(b*x^4 + a)*a^6 + sqrt(a^12/b^7)*b^4*x^2)/x^2))/(a^12*x)) - 15*(a^12/b^7)^(1/4)*b*log(5*((b*x^4 + a)^(1/4)*a^3 + (a^12/b^7)^(1/4)*b^2*x)/x) + 15*(a^12/b^7)^(1/4)*b*log(5*((b*x^4 + a)^(1/4)*a^3 - (a^12/b^7)^(1/4)*b^2*x)/x) + 4*(32*b^2*x^11 + 52*a*b*x^7 + 5*a^2*x^3)*(b*x^4 + a)^(1/4))/b","B",0
1064,1,209,0,1.284085," ","integrate(x^2*(b*x^4+a)^(5/4),x, algorithm=""fricas"")","\frac{1}{32} \, {\left(4 \, b x^{7} + 9 \, a x^{3}\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}} - \frac{5}{32} \, \left(\frac{a^{8}}{b^{3}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\left(\frac{a^{8}}{b^{3}}\right)^{\frac{3}{4}} {\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{2} b^{2} - \left(\frac{a^{8}}{b^{3}}\right)^{\frac{3}{4}} b^{2} x \sqrt{\frac{\sqrt{b x^{4} + a} a^{4} + \sqrt{\frac{a^{8}}{b^{3}}} b^{2} x^{2}}{x^{2}}}}{a^{8} x}\right) + \frac{5}{128} \, \left(\frac{a^{8}}{b^{3}}\right)^{\frac{1}{4}} \log\left(\frac{5 \, {\left({\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{2} + \left(\frac{a^{8}}{b^{3}}\right)^{\frac{1}{4}} b x\right)}}{x}\right) - \frac{5}{128} \, \left(\frac{a^{8}}{b^{3}}\right)^{\frac{1}{4}} \log\left(\frac{5 \, {\left({\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{2} - \left(\frac{a^{8}}{b^{3}}\right)^{\frac{1}{4}} b x\right)}}{x}\right)"," ",0,"1/32*(4*b*x^7 + 9*a*x^3)*(b*x^4 + a)^(1/4) - 5/32*(a^8/b^3)^(1/4)*arctan(-((a^8/b^3)^(3/4)*(b*x^4 + a)^(1/4)*a^2*b^2 - (a^8/b^3)^(3/4)*b^2*x*sqrt((sqrt(b*x^4 + a)*a^4 + sqrt(a^8/b^3)*b^2*x^2)/x^2))/(a^8*x)) + 5/128*(a^8/b^3)^(1/4)*log(5*((b*x^4 + a)^(1/4)*a^2 + (a^8/b^3)^(1/4)*b*x)/x) - 5/128*(a^8/b^3)^(1/4)*log(5*((b*x^4 + a)^(1/4)*a^2 - (a^8/b^3)^(1/4)*b*x)/x)","B",0
1065,-1,0,0,0.000000," ","integrate((b*x^4+a)^(5/4)/x^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1066,-1,0,0,0.000000," ","integrate((b*x^4+a)^(5/4)/x^6,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1067,1,35,0,1.618967," ","integrate((b*x^4+a)^(5/4)/x^10,x, algorithm=""fricas"")","-\frac{{\left(b^{2} x^{8} + 2 \, a b x^{4} + a^{2}\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}}}{9 \, a x^{9}}"," ",0,"-1/9*(b^2*x^8 + 2*a*b*x^4 + a^2)*(b*x^4 + a)^(1/4)/(a*x^9)","B",0
1068,1,49,0,1.734472," ","integrate((b*x^4+a)^(5/4)/x^14,x, algorithm=""fricas"")","\frac{{\left(4 \, b^{3} x^{12} - a b^{2} x^{8} - 14 \, a^{2} b x^{4} - 9 \, a^{3}\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}}}{117 \, a^{2} x^{13}}"," ",0,"1/117*(4*b^3*x^12 - a*b^2*x^8 - 14*a^2*b*x^4 - 9*a^3)*(b*x^4 + a)^(1/4)/(a^2*x^13)","A",0
1069,1,60,0,1.458545," ","integrate((b*x^4+a)^(5/4)/x^18,x, algorithm=""fricas"")","-\frac{{\left(32 \, b^{4} x^{16} - 8 \, a b^{3} x^{12} + 5 \, a^{2} b^{2} x^{8} + 162 \, a^{3} b x^{4} + 117 \, a^{4}\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}}}{1989 \, a^{3} x^{17}}"," ",0,"-1/1989*(32*b^4*x^16 - 8*a*b^3*x^12 + 5*a^2*b^2*x^8 + 162*a^3*b*x^4 + 117*a^4)*(b*x^4 + a)^(1/4)/(a^3*x^17)","A",0
1070,1,71,0,1.639506," ","integrate((b*x^4+a)^(5/4)/x^22,x, algorithm=""fricas"")","\frac{{\left(128 \, b^{5} x^{20} - 32 \, a b^{4} x^{16} + 20 \, a^{2} b^{3} x^{12} - 15 \, a^{3} b^{2} x^{8} - 858 \, a^{4} b x^{4} - 663 \, a^{5}\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}}}{13923 \, a^{4} x^{21}}"," ",0,"1/13923*(128*b^5*x^20 - 32*a*b^4*x^16 + 20*a^2*b^3*x^12 - 15*a^3*b^2*x^8 - 858*a^4*b*x^4 - 663*a^5)*(b*x^4 + a)^(1/4)/(a^4*x^21)","A",0
1071,0,0,0,1.096258," ","integrate(x^12*(b*x^4+a)^(5/4),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{16} + a x^{12}\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}}, x\right)"," ",0,"integral((b*x^16 + a*x^12)*(b*x^4 + a)^(1/4), x)","F",0
1072,0,0,0,1.512435," ","integrate(x^8*(b*x^4+a)^(5/4),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{12} + a x^{8}\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}}, x\right)"," ",0,"integral((b*x^12 + a*x^8)*(b*x^4 + a)^(1/4), x)","F",0
1073,0,0,0,1.157732," ","integrate(x^4*(b*x^4+a)^(5/4),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{8} + a x^{4}\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}}, x\right)"," ",0,"integral((b*x^8 + a*x^4)*(b*x^4 + a)^(1/4), x)","F",0
1074,0,0,0,1.418353," ","integrate((b*x^4+a)^(5/4),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{4} + a\right)}^{\frac{5}{4}}, x\right)"," ",0,"integral((b*x^4 + a)^(5/4), x)","F",0
1075,0,0,0,0.899547," ","integrate((b*x^4+a)^(5/4)/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{\frac{5}{4}}}{x^{4}}, x\right)"," ",0,"integral((b*x^4 + a)^(5/4)/x^4, x)","F",0
1076,0,0,0,0.948551," ","integrate((b*x^4+a)^(5/4)/x^8,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{\frac{5}{4}}}{x^{8}}, x\right)"," ",0,"integral((b*x^4 + a)^(5/4)/x^8, x)","F",0
1077,0,0,0,1.012602," ","integrate((b*x^4+a)^(5/4)/x^12,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{\frac{5}{4}}}{x^{12}}, x\right)"," ",0,"integral((b*x^4 + a)^(5/4)/x^12, x)","F",0
1078,0,0,0,1.294731," ","integrate((b*x^4+a)^(5/4)/x^16,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{\frac{5}{4}}}{x^{16}}, x\right)"," ",0,"integral((b*x^4 + a)^(5/4)/x^16, x)","F",0
1079,1,202,0,1.299660," ","integrate((b*x^4+a)^(7/4),x, algorithm=""fricas"")","\frac{1}{32} \, {\left(4 \, b x^{5} + 11 \, a x\right)} {\left(b x^{4} + a\right)}^{\frac{3}{4}} + \frac{21}{32} \, \left(\frac{a^{8}}{b}\right)^{\frac{1}{4}} \arctan\left(-\frac{\left(\frac{a^{8}}{b}\right)^{\frac{1}{4}} {\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{6} - \left(\frac{a^{8}}{b}\right)^{\frac{1}{4}} x \sqrt{\frac{\sqrt{b x^{4} + a} a^{12} + \sqrt{\frac{a^{8}}{b}} a^{8} b x^{2}}{x^{2}}}}{a^{8} x}\right) + \frac{21}{128} \, \left(\frac{a^{8}}{b}\right)^{\frac{1}{4}} \log\left(\frac{9261 \, {\left({\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{6} + \left(\frac{a^{8}}{b}\right)^{\frac{3}{4}} b x\right)}}{x}\right) - \frac{21}{128} \, \left(\frac{a^{8}}{b}\right)^{\frac{1}{4}} \log\left(\frac{9261 \, {\left({\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{6} - \left(\frac{a^{8}}{b}\right)^{\frac{3}{4}} b x\right)}}{x}\right)"," ",0,"1/32*(4*b*x^5 + 11*a*x)*(b*x^4 + a)^(3/4) + 21/32*(a^8/b)^(1/4)*arctan(-((a^8/b)^(1/4)*(b*x^4 + a)^(1/4)*a^6 - (a^8/b)^(1/4)*x*sqrt((sqrt(b*x^4 + a)*a^12 + sqrt(a^8/b)*a^8*b*x^2)/x^2))/(a^8*x)) + 21/128*(a^8/b)^(1/4)*log(9261*((b*x^4 + a)^(1/4)*a^6 + (a^8/b)^(3/4)*b*x)/x) - 21/128*(a^8/b)^(1/4)*log(9261*((b*x^4 + a)^(1/4)*a^6 - (a^8/b)^(3/4)*b*x)/x)","B",0
1080,1,57,0,0.956135," ","integrate(x^19/(b*x^4+a)^(1/4),x, algorithm=""fricas"")","\frac{{\left(1155 \, b^{4} x^{16} - 1232 \, a b^{3} x^{12} + 1344 \, a^{2} b^{2} x^{8} - 1536 \, a^{3} b x^{4} + 2048 \, a^{4}\right)} {\left(b x^{4} + a\right)}^{\frac{3}{4}}}{21945 \, b^{5}}"," ",0,"1/21945*(1155*b^4*x^16 - 1232*a*b^3*x^12 + 1344*a^2*b^2*x^8 - 1536*a^3*b*x^4 + 2048*a^4)*(b*x^4 + a)^(3/4)/b^5","A",0
1081,1,46,0,1.310463," ","integrate(x^15/(b*x^4+a)^(1/4),x, algorithm=""fricas"")","\frac{{\left(77 \, b^{3} x^{12} - 84 \, a b^{2} x^{8} + 96 \, a^{2} b x^{4} - 128 \, a^{3}\right)} {\left(b x^{4} + a\right)}^{\frac{3}{4}}}{1155 \, b^{4}}"," ",0,"1/1155*(77*b^3*x^12 - 84*a*b^2*x^8 + 96*a^2*b*x^4 - 128*a^3)*(b*x^4 + a)^(3/4)/b^4","A",0
1082,1,35,0,1.061569," ","integrate(x^11/(b*x^4+a)^(1/4),x, algorithm=""fricas"")","\frac{{\left(21 \, b^{2} x^{8} - 24 \, a b x^{4} + 32 \, a^{2}\right)} {\left(b x^{4} + a\right)}^{\frac{3}{4}}}{231 \, b^{3}}"," ",0,"1/231*(21*b^2*x^8 - 24*a*b*x^4 + 32*a^2)*(b*x^4 + a)^(3/4)/b^3","A",0
1083,1,24,0,0.639372," ","integrate(x^7/(b*x^4+a)^(1/4),x, algorithm=""fricas"")","\frac{{\left(3 \, b x^{4} - 4 \, a\right)} {\left(b x^{4} + a\right)}^{\frac{3}{4}}}{21 \, b^{2}}"," ",0,"1/21*(3*b*x^4 - 4*a)*(b*x^4 + a)^(3/4)/b^2","A",0
1084,1,14,0,1.061083," ","integrate(x^3/(b*x^4+a)^(1/4),x, algorithm=""fricas"")","\frac{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}{3 \, b}"," ",0,"1/3*(b*x^4 + a)^(3/4)/b","A",0
1085,1,81,0,0.695786," ","integrate(1/x/(b*x^4+a)^(1/4),x, algorithm=""fricas"")","-\frac{\arctan\left(\frac{\sqrt{\sqrt{b x^{4} + a} + \sqrt{a}}}{a^{\frac{1}{4}}} - \frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}{a^{\frac{1}{4}}}\right)}{a^{\frac{1}{4}}} - \frac{\log\left({\left(b x^{4} + a\right)}^{\frac{1}{4}} + a^{\frac{1}{4}}\right)}{4 \, a^{\frac{1}{4}}} + \frac{\log\left({\left(b x^{4} + a\right)}^{\frac{1}{4}} - a^{\frac{1}{4}}\right)}{4 \, a^{\frac{1}{4}}}"," ",0,"-arctan(sqrt(sqrt(b*x^4 + a) + sqrt(a))/a^(1/4) - (b*x^4 + a)^(1/4)/a^(1/4))/a^(1/4) - 1/4*log((b*x^4 + a)^(1/4) + a^(1/4))/a^(1/4) + 1/4*log((b*x^4 + a)^(1/4) - a^(1/4))/a^(1/4)","B",0
1086,1,195,0,1.281322," ","integrate(1/x^5/(b*x^4+a)^(1/4),x, algorithm=""fricas"")","\frac{4 \, a x^{4} \left(\frac{b^{4}}{a^{5}}\right)^{\frac{1}{4}} \arctan\left(-\frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}} a b^{3} \left(\frac{b^{4}}{a^{5}}\right)^{\frac{1}{4}} - \sqrt{a^{3} b^{4} \sqrt{\frac{b^{4}}{a^{5}}} + \sqrt{b x^{4} + a} b^{6}} a \left(\frac{b^{4}}{a^{5}}\right)^{\frac{1}{4}}}{b^{4}}\right) + a x^{4} \left(\frac{b^{4}}{a^{5}}\right)^{\frac{1}{4}} \log\left(a^{4} \left(\frac{b^{4}}{a^{5}}\right)^{\frac{3}{4}} + {\left(b x^{4} + a\right)}^{\frac{1}{4}} b^{3}\right) - a x^{4} \left(\frac{b^{4}}{a^{5}}\right)^{\frac{1}{4}} \log\left(-a^{4} \left(\frac{b^{4}}{a^{5}}\right)^{\frac{3}{4}} + {\left(b x^{4} + a\right)}^{\frac{1}{4}} b^{3}\right) - 4 \, {\left(b x^{4} + a\right)}^{\frac{3}{4}}}{16 \, a x^{4}}"," ",0,"1/16*(4*a*x^4*(b^4/a^5)^(1/4)*arctan(-((b*x^4 + a)^(1/4)*a*b^3*(b^4/a^5)^(1/4) - sqrt(a^3*b^4*sqrt(b^4/a^5) + sqrt(b*x^4 + a)*b^6)*a*(b^4/a^5)^(1/4))/b^4) + a*x^4*(b^4/a^5)^(1/4)*log(a^4*(b^4/a^5)^(3/4) + (b*x^4 + a)^(1/4)*b^3) - a*x^4*(b^4/a^5)^(1/4)*log(-a^4*(b^4/a^5)^(3/4) + (b*x^4 + a)^(1/4)*b^3) - 4*(b*x^4 + a)^(3/4))/(a*x^4)","B",0
1087,1,219,0,1.115172," ","integrate(1/x^9/(b*x^4+a)^(1/4),x, algorithm=""fricas"")","-\frac{20 \, a^{2} x^{8} \left(\frac{b^{8}}{a^{9}}\right)^{\frac{1}{4}} \arctan\left(-\frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{2} b^{6} \left(\frac{b^{8}}{a^{9}}\right)^{\frac{1}{4}} - \sqrt{a^{5} b^{8} \sqrt{\frac{b^{8}}{a^{9}}} + \sqrt{b x^{4} + a} b^{12}} a^{2} \left(\frac{b^{8}}{a^{9}}\right)^{\frac{1}{4}}}{b^{8}}\right) + 5 \, a^{2} x^{8} \left(\frac{b^{8}}{a^{9}}\right)^{\frac{1}{4}} \log\left(125 \, a^{7} \left(\frac{b^{8}}{a^{9}}\right)^{\frac{3}{4}} + 125 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}} b^{6}\right) - 5 \, a^{2} x^{8} \left(\frac{b^{8}}{a^{9}}\right)^{\frac{1}{4}} \log\left(-125 \, a^{7} \left(\frac{b^{8}}{a^{9}}\right)^{\frac{3}{4}} + 125 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}} b^{6}\right) - 4 \, {\left(5 \, b x^{4} - 4 \, a\right)} {\left(b x^{4} + a\right)}^{\frac{3}{4}}}{128 \, a^{2} x^{8}}"," ",0,"-1/128*(20*a^2*x^8*(b^8/a^9)^(1/4)*arctan(-((b*x^4 + a)^(1/4)*a^2*b^6*(b^8/a^9)^(1/4) - sqrt(a^5*b^8*sqrt(b^8/a^9) + sqrt(b*x^4 + a)*b^12)*a^2*(b^8/a^9)^(1/4))/b^8) + 5*a^2*x^8*(b^8/a^9)^(1/4)*log(125*a^7*(b^8/a^9)^(3/4) + 125*(b*x^4 + a)^(1/4)*b^6) - 5*a^2*x^8*(b^8/a^9)^(1/4)*log(-125*a^7*(b^8/a^9)^(3/4) + 125*(b*x^4 + a)^(1/4)*b^6) - 4*(5*b*x^4 - 4*a)*(b*x^4 + a)^(3/4))/(a^2*x^8)","B",0
1088,0,0,0,1.125701," ","integrate(x^13/(b*x^4+a)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{13}}{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}, x\right)"," ",0,"integral(x^13/(b*x^4 + a)^(1/4), x)","F",0
1089,0,0,0,0.641252," ","integrate(x^9/(b*x^4+a)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{9}}{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}, x\right)"," ",0,"integral(x^9/(b*x^4 + a)^(1/4), x)","F",0
1090,0,0,0,1.084012," ","integrate(x^5/(b*x^4+a)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{5}}{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}, x\right)"," ",0,"integral(x^5/(b*x^4 + a)^(1/4), x)","F",0
1091,0,0,0,1.231414," ","integrate(x/(b*x^4+a)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}, x\right)"," ",0,"integral(x/(b*x^4 + a)^(1/4), x)","F",0
1092,0,0,0,0.925756," ","integrate(1/x^3/(b*x^4+a)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}{b x^{7} + a x^{3}}, x\right)"," ",0,"integral((b*x^4 + a)^(3/4)/(b*x^7 + a*x^3), x)","F",0
1093,0,0,0,1.136787," ","integrate(1/x^7/(b*x^4+a)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}{b x^{11} + a x^{7}}, x\right)"," ",0,"integral((b*x^4 + a)^(3/4)/(b*x^11 + a*x^7), x)","F",0
1094,0,0,0,1.088958," ","integrate(1/x^11/(b*x^4+a)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}{b x^{15} + a x^{11}}, x\right)"," ",0,"integral((b*x^4 + a)^(3/4)/(b*x^15 + a*x^11), x)","F",0
1095,1,228,0,0.699576," ","integrate(x^8/(b*x^4+a)^(1/4),x, algorithm=""fricas"")","\frac{20 \, b^{2} \left(\frac{a^{8}}{b^{9}}\right)^{\frac{1}{4}} \arctan\left(-\frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{6} b^{2} \left(\frac{a^{8}}{b^{9}}\right)^{\frac{1}{4}} - b^{2} x \left(\frac{a^{8}}{b^{9}}\right)^{\frac{1}{4}} \sqrt{\frac{a^{8} b^{5} x^{2} \sqrt{\frac{a^{8}}{b^{9}}} + \sqrt{b x^{4} + a} a^{12}}{x^{2}}}}{a^{8} x}\right) + 5 \, b^{2} \left(\frac{a^{8}}{b^{9}}\right)^{\frac{1}{4}} \log\left(\frac{125 \, {\left(b^{7} x \left(\frac{a^{8}}{b^{9}}\right)^{\frac{3}{4}} + {\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{6}\right)}}{x}\right) - 5 \, b^{2} \left(\frac{a^{8}}{b^{9}}\right)^{\frac{1}{4}} \log\left(-\frac{125 \, {\left(b^{7} x \left(\frac{a^{8}}{b^{9}}\right)^{\frac{3}{4}} - {\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{6}\right)}}{x}\right) + 4 \, {\left(4 \, b x^{5} - 5 \, a x\right)} {\left(b x^{4} + a\right)}^{\frac{3}{4}}}{128 \, b^{2}}"," ",0,"1/128*(20*b^2*(a^8/b^9)^(1/4)*arctan(-((b*x^4 + a)^(1/4)*a^6*b^2*(a^8/b^9)^(1/4) - b^2*x*(a^8/b^9)^(1/4)*sqrt((a^8*b^5*x^2*sqrt(a^8/b^9) + sqrt(b*x^4 + a)*a^12)/x^2))/(a^8*x)) + 5*b^2*(a^8/b^9)^(1/4)*log(125*(b^7*x*(a^8/b^9)^(3/4) + (b*x^4 + a)^(1/4)*a^6)/x) - 5*b^2*(a^8/b^9)^(1/4)*log(-125*(b^7*x*(a^8/b^9)^(3/4) - (b*x^4 + a)^(1/4)*a^6)/x) + 4*(4*b*x^5 - 5*a*x)*(b*x^4 + a)^(3/4))/b^2","B",0
1096,1,206,0,1.163848," ","integrate(x^4/(b*x^4+a)^(1/4),x, algorithm=""fricas"")","-\frac{4 \, b \left(\frac{a^{4}}{b^{5}}\right)^{\frac{1}{4}} \arctan\left(-\frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{3} b \left(\frac{a^{4}}{b^{5}}\right)^{\frac{1}{4}} - b x \left(\frac{a^{4}}{b^{5}}\right)^{\frac{1}{4}} \sqrt{\frac{a^{4} b^{3} x^{2} \sqrt{\frac{a^{4}}{b^{5}}} + \sqrt{b x^{4} + a} a^{6}}{x^{2}}}}{a^{4} x}\right) + b \left(\frac{a^{4}}{b^{5}}\right)^{\frac{1}{4}} \log\left(\frac{b^{4} x \left(\frac{a^{4}}{b^{5}}\right)^{\frac{3}{4}} + {\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{3}}{x}\right) - b \left(\frac{a^{4}}{b^{5}}\right)^{\frac{1}{4}} \log\left(-\frac{b^{4} x \left(\frac{a^{4}}{b^{5}}\right)^{\frac{3}{4}} - {\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{3}}{x}\right) - 4 \, {\left(b x^{4} + a\right)}^{\frac{3}{4}} x}{16 \, b}"," ",0,"-1/16*(4*b*(a^4/b^5)^(1/4)*arctan(-((b*x^4 + a)^(1/4)*a^3*b*(a^4/b^5)^(1/4) - b*x*(a^4/b^5)^(1/4)*sqrt((a^4*b^3*x^2*sqrt(a^4/b^5) + sqrt(b*x^4 + a)*a^6)/x^2))/(a^4*x)) + b*(a^4/b^5)^(1/4)*log((b^4*x*(a^4/b^5)^(3/4) + (b*x^4 + a)^(1/4)*a^3)/x) - b*(a^4/b^5)^(1/4)*log(-(b^4*x*(a^4/b^5)^(3/4) - (b*x^4 + a)^(1/4)*a^3)/x) - 4*(b*x^4 + a)^(3/4)*x)/b","B",0
1097,1,106,0,0.808318," ","integrate(1/(b*x^4+a)^(1/4),x, algorithm=""fricas"")","\frac{\arctan\left(\frac{\frac{x \sqrt{\frac{\sqrt{b} x^{2} + \sqrt{b x^{4} + a}}{x^{2}}}}{b^{\frac{1}{4}}} - \frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}{b^{\frac{1}{4}}}}{x}\right)}{b^{\frac{1}{4}}} + \frac{\log\left(\frac{b^{\frac{1}{4}} x + {\left(b x^{4} + a\right)}^{\frac{1}{4}}}{x}\right)}{4 \, b^{\frac{1}{4}}} - \frac{\log\left(-\frac{b^{\frac{1}{4}} x - {\left(b x^{4} + a\right)}^{\frac{1}{4}}}{x}\right)}{4 \, b^{\frac{1}{4}}}"," ",0,"arctan((x*sqrt((sqrt(b)*x^2 + sqrt(b*x^4 + a))/x^2)/b^(1/4) - (b*x^4 + a)^(1/4)/b^(1/4))/x)/b^(1/4) + 1/4*log((b^(1/4)*x + (b*x^4 + a)^(1/4))/x)/b^(1/4) - 1/4*log(-(b^(1/4)*x - (b*x^4 + a)^(1/4))/x)/b^(1/4)","B",0
1098,1,17,0,1.102443," ","integrate(1/x^4/(b*x^4+a)^(1/4),x, algorithm=""fricas"")","-\frac{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}{3 \, a x^{3}}"," ",0,"-1/3*(b*x^4 + a)^(3/4)/(a*x^3)","A",0
1099,1,27,0,1.286332," ","integrate(1/x^8/(b*x^4+a)^(1/4),x, algorithm=""fricas"")","\frac{{\left(4 \, b x^{4} - 3 \, a\right)} {\left(b x^{4} + a\right)}^{\frac{3}{4}}}{21 \, a^{2} x^{7}}"," ",0,"1/21*(4*b*x^4 - 3*a)*(b*x^4 + a)^(3/4)/(a^2*x^7)","A",0
1100,1,38,0,0.825156," ","integrate(1/x^12/(b*x^4+a)^(1/4),x, algorithm=""fricas"")","-\frac{{\left(32 \, b^{2} x^{8} - 24 \, a b x^{4} + 21 \, a^{2}\right)} {\left(b x^{4} + a\right)}^{\frac{3}{4}}}{231 \, a^{3} x^{11}}"," ",0,"-1/231*(32*b^2*x^8 - 24*a*b*x^4 + 21*a^2)*(b*x^4 + a)^(3/4)/(a^3*x^11)","A",0
1101,1,49,0,1.126612," ","integrate(1/x^16/(b*x^4+a)^(1/4),x, algorithm=""fricas"")","\frac{{\left(128 \, b^{3} x^{12} - 96 \, a b^{2} x^{8} + 84 \, a^{2} b x^{4} - 77 \, a^{3}\right)} {\left(b x^{4} + a\right)}^{\frac{3}{4}}}{1155 \, a^{4} x^{15}}"," ",0,"1/1155*(128*b^3*x^12 - 96*a*b^2*x^8 + 84*a^2*b*x^4 - 77*a^3)*(b*x^4 + a)^(3/4)/(a^4*x^15)","A",0
1102,1,60,0,1.257333," ","integrate(1/x^20/(b*x^4+a)^(1/4),x, algorithm=""fricas"")","-\frac{{\left(2048 \, b^{4} x^{16} - 1536 \, a b^{3} x^{12} + 1344 \, a^{2} b^{2} x^{8} - 1232 \, a^{3} b x^{4} + 1155 \, a^{4}\right)} {\left(b x^{4} + a\right)}^{\frac{3}{4}}}{21945 \, a^{5} x^{19}}"," ",0,"-1/21945*(2048*b^4*x^16 - 1536*a*b^3*x^12 + 1344*a^2*b^2*x^8 - 1232*a^3*b*x^4 + 1155*a^4)*(b*x^4 + a)^(3/4)/(a^5*x^19)","A",0
1103,0,0,0,1.041637," ","integrate(x^10/(b*x^4+a)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{10}}{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}, x\right)"," ",0,"integral(x^10/(b*x^4 + a)^(1/4), x)","F",0
1104,0,0,0,1.178025," ","integrate(x^6/(b*x^4+a)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{6}}{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}, x\right)"," ",0,"integral(x^6/(b*x^4 + a)^(1/4), x)","F",0
1105,0,0,0,1.164213," ","integrate(x^2/(b*x^4+a)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2}}{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}, x\right)"," ",0,"integral(x^2/(b*x^4 + a)^(1/4), x)","F",0
1106,0,0,0,1.211511," ","integrate(1/x^2/(b*x^4+a)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}{b x^{6} + a x^{2}}, x\right)"," ",0,"integral((b*x^4 + a)^(3/4)/(b*x^6 + a*x^2), x)","F",0
1107,0,0,0,1.277139," ","integrate(1/x^6/(b*x^4+a)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}{b x^{10} + a x^{6}}, x\right)"," ",0,"integral((b*x^4 + a)^(3/4)/(b*x^10 + a*x^6), x)","F",0
1108,0,0,0,1.200771," ","integrate(1/x^10/(b*x^4+a)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}{b x^{14} + a x^{10}}, x\right)"," ",0,"integral((b*x^4 + a)^(3/4)/(b*x^14 + a*x^10), x)","F",0
1109,0,0,0,1.222352," ","integrate(1/x^14/(b*x^4+a)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}{b x^{18} + a x^{14}}, x\right)"," ",0,"integral((b*x^4 + a)^(3/4)/(b*x^18 + a*x^14), x)","F",0
1110,1,57,0,1.130892," ","integrate(x^19/(b*x^4+a)^(3/4),x, algorithm=""fricas"")","\frac{{\left(195 \, b^{4} x^{16} - 240 \, a b^{3} x^{12} + 320 \, a^{2} b^{2} x^{8} - 512 \, a^{3} b x^{4} + 2048 \, a^{4}\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}}}{3315 \, b^{5}}"," ",0,"1/3315*(195*b^4*x^16 - 240*a*b^3*x^12 + 320*a^2*b^2*x^8 - 512*a^3*b*x^4 + 2048*a^4)*(b*x^4 + a)^(1/4)/b^5","A",0
1111,1,46,0,1.189986," ","integrate(x^15/(b*x^4+a)^(3/4),x, algorithm=""fricas"")","\frac{{\left(15 \, b^{3} x^{12} - 20 \, a b^{2} x^{8} + 32 \, a^{2} b x^{4} - 128 \, a^{3}\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}}}{195 \, b^{4}}"," ",0,"1/195*(15*b^3*x^12 - 20*a*b^2*x^8 + 32*a^2*b*x^4 - 128*a^3)*(b*x^4 + a)^(1/4)/b^4","A",0
1112,1,35,0,1.103680," ","integrate(x^11/(b*x^4+a)^(3/4),x, algorithm=""fricas"")","\frac{{\left(5 \, b^{2} x^{8} - 8 \, a b x^{4} + 32 \, a^{2}\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}}}{45 \, b^{3}}"," ",0,"1/45*(5*b^2*x^8 - 8*a*b*x^4 + 32*a^2)*(b*x^4 + a)^(1/4)/b^3","A",0
1113,1,23,0,1.265130," ","integrate(x^7/(b*x^4+a)^(3/4),x, algorithm=""fricas"")","\frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}} {\left(b x^{4} - 4 \, a\right)}}{5 \, b^{2}}"," ",0,"1/5*(b*x^4 + a)^(1/4)*(b*x^4 - 4*a)/b^2","A",0
1114,1,13,0,1.074934," ","integrate(x^3/(b*x^4+a)^(3/4),x, algorithm=""fricas"")","\frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}{b}"," ",0,"(b*x^4 + a)^(1/4)/b","A",0
1115,1,109,0,1.133589," ","integrate(1/x/(b*x^4+a)^(3/4),x, algorithm=""fricas"")","\frac{1}{a^{3}}^{\frac{1}{4}} \arctan\left(\sqrt{a^{2} \sqrt{\frac{1}{a^{3}}} + \sqrt{b x^{4} + a}} a^{2} \frac{1}{a^{3}}^{\frac{3}{4}} - {\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{2} \frac{1}{a^{3}}^{\frac{3}{4}}\right) - \frac{1}{4} \, \frac{1}{a^{3}}^{\frac{1}{4}} \log\left(a \frac{1}{a^{3}}^{\frac{1}{4}} + {\left(b x^{4} + a\right)}^{\frac{1}{4}}\right) + \frac{1}{4} \, \frac{1}{a^{3}}^{\frac{1}{4}} \log\left(-a \frac{1}{a^{3}}^{\frac{1}{4}} + {\left(b x^{4} + a\right)}^{\frac{1}{4}}\right)"," ",0,"(a^(-3))^(1/4)*arctan(sqrt(a^2*sqrt(a^(-3)) + sqrt(b*x^4 + a))*a^2*(a^(-3))^(3/4) - (b*x^4 + a)^(1/4)*a^2*(a^(-3))^(3/4)) - 1/4*(a^(-3))^(1/4)*log(a*(a^(-3))^(1/4) + (b*x^4 + a)^(1/4)) + 1/4*(a^(-3))^(1/4)*log(-a*(a^(-3))^(1/4) + (b*x^4 + a)^(1/4))","B",0
1116,1,194,0,1.217940," ","integrate(1/x^5/(b*x^4+a)^(3/4),x, algorithm=""fricas"")","-\frac{12 \, a x^{4} \left(\frac{b^{4}}{a^{7}}\right)^{\frac{1}{4}} \arctan\left(-\frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{5} b \left(\frac{b^{4}}{a^{7}}\right)^{\frac{3}{4}} - \sqrt{a^{4} \sqrt{\frac{b^{4}}{a^{7}}} + \sqrt{b x^{4} + a} b^{2}} a^{5} \left(\frac{b^{4}}{a^{7}}\right)^{\frac{3}{4}}}{b^{4}}\right) - 3 \, a x^{4} \left(\frac{b^{4}}{a^{7}}\right)^{\frac{1}{4}} \log\left(3 \, a^{2} \left(\frac{b^{4}}{a^{7}}\right)^{\frac{1}{4}} + 3 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}} b\right) + 3 \, a x^{4} \left(\frac{b^{4}}{a^{7}}\right)^{\frac{1}{4}} \log\left(-3 \, a^{2} \left(\frac{b^{4}}{a^{7}}\right)^{\frac{1}{4}} + 3 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}} b\right) + 4 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}}}{16 \, a x^{4}}"," ",0,"-1/16*(12*a*x^4*(b^4/a^7)^(1/4)*arctan(-((b*x^4 + a)^(1/4)*a^5*b*(b^4/a^7)^(3/4) - sqrt(a^4*sqrt(b^4/a^7) + sqrt(b*x^4 + a)*b^2)*a^5*(b^4/a^7)^(3/4))/b^4) - 3*a*x^4*(b^4/a^7)^(1/4)*log(3*a^2*(b^4/a^7)^(1/4) + 3*(b*x^4 + a)^(1/4)*b) + 3*a*x^4*(b^4/a^7)^(1/4)*log(-3*a^2*(b^4/a^7)^(1/4) + 3*(b*x^4 + a)^(1/4)*b) + 4*(b*x^4 + a)^(1/4))/(a*x^4)","B",0
1117,1,216,0,1.373942," ","integrate(1/x^9/(b*x^4+a)^(3/4),x, algorithm=""fricas"")","\frac{84 \, a^{2} x^{8} \left(\frac{b^{8}}{a^{11}}\right)^{\frac{1}{4}} \arctan\left(-\frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{8} b^{2} \left(\frac{b^{8}}{a^{11}}\right)^{\frac{3}{4}} - \sqrt{a^{6} \sqrt{\frac{b^{8}}{a^{11}}} + \sqrt{b x^{4} + a} b^{4}} a^{8} \left(\frac{b^{8}}{a^{11}}\right)^{\frac{3}{4}}}{b^{8}}\right) - 21 \, a^{2} x^{8} \left(\frac{b^{8}}{a^{11}}\right)^{\frac{1}{4}} \log\left(21 \, a^{3} \left(\frac{b^{8}}{a^{11}}\right)^{\frac{1}{4}} + 21 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}} b^{2}\right) + 21 \, a^{2} x^{8} \left(\frac{b^{8}}{a^{11}}\right)^{\frac{1}{4}} \log\left(-21 \, a^{3} \left(\frac{b^{8}}{a^{11}}\right)^{\frac{1}{4}} + 21 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}} b^{2}\right) + 4 \, {\left(7 \, b x^{4} - 4 \, a\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}}}{128 \, a^{2} x^{8}}"," ",0,"1/128*(84*a^2*x^8*(b^8/a^11)^(1/4)*arctan(-((b*x^4 + a)^(1/4)*a^8*b^2*(b^8/a^11)^(3/4) - sqrt(a^6*sqrt(b^8/a^11) + sqrt(b*x^4 + a)*b^4)*a^8*(b^8/a^11)^(3/4))/b^8) - 21*a^2*x^8*(b^8/a^11)^(1/4)*log(21*a^3*(b^8/a^11)^(1/4) + 21*(b*x^4 + a)^(1/4)*b^2) + 21*a^2*x^8*(b^8/a^11)^(1/4)*log(-21*a^3*(b^8/a^11)^(1/4) + 21*(b*x^4 + a)^(1/4)*b^2) + 4*(7*b*x^4 - 4*a)*(b*x^4 + a)^(1/4))/(a^2*x^8)","B",0
1118,0,0,0,1.384231," ","integrate(x^13/(b*x^4+a)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{13}}{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}, x\right)"," ",0,"integral(x^13/(b*x^4 + a)^(3/4), x)","F",0
1119,0,0,0,1.201241," ","integrate(x^9/(b*x^4+a)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{9}}{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}, x\right)"," ",0,"integral(x^9/(b*x^4 + a)^(3/4), x)","F",0
1120,0,0,0,1.288021," ","integrate(x^5/(b*x^4+a)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{5}}{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}, x\right)"," ",0,"integral(x^5/(b*x^4 + a)^(3/4), x)","F",0
1121,0,0,0,1.277943," ","integrate(x/(b*x^4+a)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}, x\right)"," ",0,"integral(x/(b*x^4 + a)^(3/4), x)","F",0
1122,0,0,0,1.361835," ","integrate(1/x^3/(b*x^4+a)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}{b x^{7} + a x^{3}}, x\right)"," ",0,"integral((b*x^4 + a)^(1/4)/(b*x^7 + a*x^3), x)","F",0
1123,0,0,0,1.534798," ","integrate(1/x^7/(b*x^4+a)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}{b x^{11} + a x^{7}}, x\right)"," ",0,"integral((b*x^4 + a)^(1/4)/(b*x^11 + a*x^7), x)","F",0
1124,0,0,0,1.452069," ","integrate(1/x^11/(b*x^4+a)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}{b x^{15} + a x^{11}}, x\right)"," ",0,"integral((b*x^4 + a)^(1/4)/(b*x^15 + a*x^11), x)","F",0
1125,1,227,0,1.590868," ","integrate(x^10/(b*x^4+a)^(3/4),x, algorithm=""fricas"")","-\frac{84 \, b^{2} \left(\frac{a^{8}}{b^{11}}\right)^{\frac{1}{4}} \arctan\left(-\frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{2} b^{8} \left(\frac{a^{8}}{b^{11}}\right)^{\frac{3}{4}} - b^{8} x \sqrt{\frac{b^{6} x^{2} \sqrt{\frac{a^{8}}{b^{11}}} + \sqrt{b x^{4} + a} a^{4}}{x^{2}}} \left(\frac{a^{8}}{b^{11}}\right)^{\frac{3}{4}}}{a^{8} x}\right) - 21 \, b^{2} \left(\frac{a^{8}}{b^{11}}\right)^{\frac{1}{4}} \log\left(\frac{21 \, {\left(b^{3} x \left(\frac{a^{8}}{b^{11}}\right)^{\frac{1}{4}} + {\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{2}\right)}}{x}\right) + 21 \, b^{2} \left(\frac{a^{8}}{b^{11}}\right)^{\frac{1}{4}} \log\left(-\frac{21 \, {\left(b^{3} x \left(\frac{a^{8}}{b^{11}}\right)^{\frac{1}{4}} - {\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{2}\right)}}{x}\right) - 4 \, {\left(4 \, b x^{7} - 7 \, a x^{3}\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}}}{128 \, b^{2}}"," ",0,"-1/128*(84*b^2*(a^8/b^11)^(1/4)*arctan(-((b*x^4 + a)^(1/4)*a^2*b^8*(a^8/b^11)^(3/4) - b^8*x*sqrt((b^6*x^2*sqrt(a^8/b^11) + sqrt(b*x^4 + a)*a^4)/x^2)*(a^8/b^11)^(3/4))/(a^8*x)) - 21*b^2*(a^8/b^11)^(1/4)*log(21*(b^3*x*(a^8/b^11)^(1/4) + (b*x^4 + a)^(1/4)*a^2)/x) + 21*b^2*(a^8/b^11)^(1/4)*log(-21*(b^3*x*(a^8/b^11)^(1/4) - (b*x^4 + a)^(1/4)*a^2)/x) - 4*(4*b*x^7 - 7*a*x^3)*(b*x^4 + a)^(1/4))/b^2","B",0
1126,1,204,0,1.351544," ","integrate(x^6/(b*x^4+a)^(3/4),x, algorithm=""fricas"")","\frac{4 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}} x^{3} + 12 \, b \left(\frac{a^{4}}{b^{7}}\right)^{\frac{1}{4}} \arctan\left(\frac{b^{5} x \sqrt{\frac{b^{4} x^{2} \sqrt{\frac{a^{4}}{b^{7}}} + \sqrt{b x^{4} + a} a^{2}}{x^{2}}} \left(\frac{a^{4}}{b^{7}}\right)^{\frac{3}{4}} - {\left(b x^{4} + a\right)}^{\frac{1}{4}} a b^{5} \left(\frac{a^{4}}{b^{7}}\right)^{\frac{3}{4}}}{a^{4} x}\right) - 3 \, b \left(\frac{a^{4}}{b^{7}}\right)^{\frac{1}{4}} \log\left(\frac{3 \, {\left(b^{2} x \left(\frac{a^{4}}{b^{7}}\right)^{\frac{1}{4}} + {\left(b x^{4} + a\right)}^{\frac{1}{4}} a\right)}}{x}\right) + 3 \, b \left(\frac{a^{4}}{b^{7}}\right)^{\frac{1}{4}} \log\left(-\frac{3 \, {\left(b^{2} x \left(\frac{a^{4}}{b^{7}}\right)^{\frac{1}{4}} - {\left(b x^{4} + a\right)}^{\frac{1}{4}} a\right)}}{x}\right)}{16 \, b}"," ",0,"1/16*(4*(b*x^4 + a)^(1/4)*x^3 + 12*b*(a^4/b^7)^(1/4)*arctan((b^5*x*sqrt((b^4*x^2*sqrt(a^4/b^7) + sqrt(b*x^4 + a)*a^2)/x^2)*(a^4/b^7)^(3/4) - (b*x^4 + a)^(1/4)*a*b^5*(a^4/b^7)^(3/4))/(a^4*x)) - 3*b*(a^4/b^7)^(1/4)*log(3*(b^2*x*(a^4/b^7)^(1/4) + (b*x^4 + a)^(1/4)*a)/x) + 3*b*(a^4/b^7)^(1/4)*log(-3*(b^2*x*(a^4/b^7)^(1/4) - (b*x^4 + a)^(1/4)*a)/x))/b","B",0
1127,1,134,0,1.309094," ","integrate(x^2/(b*x^4+a)^(3/4),x, algorithm=""fricas"")","-\frac{1}{b^{3}}^{\frac{1}{4}} \arctan\left(\frac{b^{2} \sqrt{\frac{b^{2} \sqrt{\frac{1}{b^{3}}} x^{2} + \sqrt{b x^{4} + a}}{x^{2}}} \frac{1}{b^{3}}^{\frac{3}{4}} x - {\left(b x^{4} + a\right)}^{\frac{1}{4}} b^{2} \frac{1}{b^{3}}^{\frac{3}{4}}}{x}\right) + \frac{1}{4} \, \frac{1}{b^{3}}^{\frac{1}{4}} \log\left(\frac{b \frac{1}{b^{3}}^{\frac{1}{4}} x + {\left(b x^{4} + a\right)}^{\frac{1}{4}}}{x}\right) - \frac{1}{4} \, \frac{1}{b^{3}}^{\frac{1}{4}} \log\left(-\frac{b \frac{1}{b^{3}}^{\frac{1}{4}} x - {\left(b x^{4} + a\right)}^{\frac{1}{4}}}{x}\right)"," ",0,"-(b^(-3))^(1/4)*arctan((b^2*sqrt((b^2*sqrt(b^(-3))*x^2 + sqrt(b*x^4 + a))/x^2)*(b^(-3))^(3/4)*x - (b*x^4 + a)^(1/4)*b^2*(b^(-3))^(3/4))/x) + 1/4*(b^(-3))^(1/4)*log((b*(b^(-3))^(1/4)*x + (b*x^4 + a)^(1/4))/x) - 1/4*(b^(-3))^(1/4)*log(-(b*(b^(-3))^(1/4)*x - (b*x^4 + a)^(1/4))/x)","B",0
1128,1,17,0,1.169567," ","integrate(1/x^2/(b*x^4+a)^(3/4),x, algorithm=""fricas"")","-\frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}{a x}"," ",0,"-(b*x^4 + a)^(1/4)/(a*x)","A",0
1129,1,27,0,0.772806," ","integrate(1/x^6/(b*x^4+a)^(3/4),x, algorithm=""fricas"")","\frac{{\left(4 \, b x^{4} - a\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}}}{5 \, a^{2} x^{5}}"," ",0,"1/5*(4*b*x^4 - a)*(b*x^4 + a)^(1/4)/(a^2*x^5)","A",0
1130,1,38,0,1.335353," ","integrate(1/x^10/(b*x^4+a)^(3/4),x, algorithm=""fricas"")","-\frac{{\left(32 \, b^{2} x^{8} - 8 \, a b x^{4} + 5 \, a^{2}\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}}}{45 \, a^{3} x^{9}}"," ",0,"-1/45*(32*b^2*x^8 - 8*a*b*x^4 + 5*a^2)*(b*x^4 + a)^(1/4)/(a^3*x^9)","A",0
1131,1,49,0,1.243319," ","integrate(1/x^14/(b*x^4+a)^(3/4),x, algorithm=""fricas"")","\frac{{\left(128 \, b^{3} x^{12} - 32 \, a b^{2} x^{8} + 20 \, a^{2} b x^{4} - 15 \, a^{3}\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}}}{195 \, a^{4} x^{13}}"," ",0,"1/195*(128*b^3*x^12 - 32*a*b^2*x^8 + 20*a^2*b*x^4 - 15*a^3)*(b*x^4 + a)^(1/4)/(a^4*x^13)","A",0
1132,0,0,0,1.105058," ","integrate(x^12/(b*x^4+a)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{12}}{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}, x\right)"," ",0,"integral(x^12/(b*x^4 + a)^(3/4), x)","F",0
1133,0,0,0,1.317251," ","integrate(x^8/(b*x^4+a)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{8}}{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}, x\right)"," ",0,"integral(x^8/(b*x^4 + a)^(3/4), x)","F",0
1134,0,0,0,1.174379," ","integrate(x^4/(b*x^4+a)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{4}}{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}, x\right)"," ",0,"integral(x^4/(b*x^4 + a)^(3/4), x)","F",0
1135,0,0,0,1.329942," ","integrate(1/(b*x^4+a)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}, x\right)"," ",0,"integral((b*x^4 + a)^(-3/4), x)","F",0
1136,0,0,0,0.790677," ","integrate(1/x^4/(b*x^4+a)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}{b x^{8} + a x^{4}}, x\right)"," ",0,"integral((b*x^4 + a)^(1/4)/(b*x^8 + a*x^4), x)","F",0
1137,0,0,0,1.102587," ","integrate(1/x^8/(b*x^4+a)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}{b x^{12} + a x^{8}}, x\right)"," ",0,"integral((b*x^4 + a)^(1/4)/(b*x^12 + a*x^8), x)","F",0
1138,0,0,0,1.266589," ","integrate(1/x^12/(b*x^4+a)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}{b x^{16} + a x^{12}}, x\right)"," ",0,"integral((b*x^4 + a)^(1/4)/(b*x^16 + a*x^12), x)","F",0
1139,1,69,0,1.074255," ","integrate(x^19/(b*x^4+a)^(5/4),x, algorithm=""fricas"")","\frac{{\left(77 \, b^{4} x^{16} - 112 \, a b^{3} x^{12} + 192 \, a^{2} b^{2} x^{8} - 512 \, a^{3} b x^{4} - 2048 \, a^{4}\right)} {\left(b x^{4} + a\right)}^{\frac{3}{4}}}{1155 \, {\left(b^{6} x^{4} + a b^{5}\right)}}"," ",0,"1/1155*(77*b^4*x^16 - 112*a*b^3*x^12 + 192*a^2*b^2*x^8 - 512*a^3*b*x^4 - 2048*a^4)*(b*x^4 + a)^(3/4)/(b^6*x^4 + a*b^5)","A",0
1140,1,58,0,1.350904," ","integrate(x^15/(b*x^4+a)^(5/4),x, algorithm=""fricas"")","\frac{{\left(7 \, b^{3} x^{12} - 12 \, a b^{2} x^{8} + 32 \, a^{2} b x^{4} + 128 \, a^{3}\right)} {\left(b x^{4} + a\right)}^{\frac{3}{4}}}{77 \, {\left(b^{5} x^{4} + a b^{4}\right)}}"," ",0,"1/77*(7*b^3*x^12 - 12*a*b^2*x^8 + 32*a^2*b*x^4 + 128*a^3)*(b*x^4 + a)^(3/4)/(b^5*x^4 + a*b^4)","A",0
1141,1,47,0,0.623661," ","integrate(x^11/(b*x^4+a)^(5/4),x, algorithm=""fricas"")","\frac{{\left(3 \, b^{2} x^{8} - 8 \, a b x^{4} - 32 \, a^{2}\right)} {\left(b x^{4} + a\right)}^{\frac{3}{4}}}{21 \, {\left(b^{4} x^{4} + a b^{3}\right)}}"," ",0,"1/21*(3*b^2*x^8 - 8*a*b*x^4 - 32*a^2)*(b*x^4 + a)^(3/4)/(b^4*x^4 + a*b^3)","A",0
1142,1,35,0,1.158711," ","integrate(x^7/(b*x^4+a)^(5/4),x, algorithm=""fricas"")","\frac{{\left(b x^{4} + 4 \, a\right)} {\left(b x^{4} + a\right)}^{\frac{3}{4}}}{3 \, {\left(b^{3} x^{4} + a b^{2}\right)}}"," ",0,"1/3*(b*x^4 + 4*a)*(b*x^4 + a)^(3/4)/(b^3*x^4 + a*b^2)","A",0
1143,1,24,0,1.263941," ","integrate(x^3/(b*x^4+a)^(5/4),x, algorithm=""fricas"")","-\frac{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}{b^{2} x^{4} + a b}"," ",0,"-(b*x^4 + a)^(3/4)/(b^2*x^4 + a*b)","A",0
1144,1,164,0,1.261518," ","integrate(1/x/(b*x^4+a)^(5/4),x, algorithm=""fricas"")","-\frac{4 \, {\left(a b x^{4} + a^{2}\right)} \frac{1}{a^{5}}^{\frac{1}{4}} \arctan\left(\sqrt{a^{3} \sqrt{\frac{1}{a^{5}}} + \sqrt{b x^{4} + a}} a \frac{1}{a^{5}}^{\frac{1}{4}} - {\left(b x^{4} + a\right)}^{\frac{1}{4}} a \frac{1}{a^{5}}^{\frac{1}{4}}\right) + {\left(a b x^{4} + a^{2}\right)} \frac{1}{a^{5}}^{\frac{1}{4}} \log\left(a^{4} \frac{1}{a^{5}}^{\frac{3}{4}} + {\left(b x^{4} + a\right)}^{\frac{1}{4}}\right) - {\left(a b x^{4} + a^{2}\right)} \frac{1}{a^{5}}^{\frac{1}{4}} \log\left(-a^{4} \frac{1}{a^{5}}^{\frac{3}{4}} + {\left(b x^{4} + a\right)}^{\frac{1}{4}}\right) - 4 \, {\left(b x^{4} + a\right)}^{\frac{3}{4}}}{4 \, {\left(a b x^{4} + a^{2}\right)}}"," ",0,"-1/4*(4*(a*b*x^4 + a^2)*(a^(-5))^(1/4)*arctan(sqrt(a^3*sqrt(a^(-5)) + sqrt(b*x^4 + a))*a*(a^(-5))^(1/4) - (b*x^4 + a)^(1/4)*a*(a^(-5))^(1/4)) + (a*b*x^4 + a^2)*(a^(-5))^(1/4)*log(a^4*(a^(-5))^(3/4) + (b*x^4 + a)^(1/4)) - (a*b*x^4 + a^2)*(a^(-5))^(1/4)*log(-a^4*(a^(-5))^(3/4) + (b*x^4 + a)^(1/4)) - 4*(b*x^4 + a)^(3/4))/(a*b*x^4 + a^2)","B",0
1145,1,259,0,1.154105," ","integrate(1/x^5/(b*x^4+a)^(5/4),x, algorithm=""fricas"")","\frac{20 \, {\left(a^{2} b x^{8} + a^{3} x^{4}\right)} \left(\frac{b^{4}}{a^{9}}\right)^{\frac{1}{4}} \arctan\left(-\frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{2} b^{3} \left(\frac{b^{4}}{a^{9}}\right)^{\frac{1}{4}} - \sqrt{a^{5} b^{4} \sqrt{\frac{b^{4}}{a^{9}}} + \sqrt{b x^{4} + a} b^{6}} a^{2} \left(\frac{b^{4}}{a^{9}}\right)^{\frac{1}{4}}}{b^{4}}\right) + 5 \, {\left(a^{2} b x^{8} + a^{3} x^{4}\right)} \left(\frac{b^{4}}{a^{9}}\right)^{\frac{1}{4}} \log\left(125 \, a^{7} \left(\frac{b^{4}}{a^{9}}\right)^{\frac{3}{4}} + 125 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}} b^{3}\right) - 5 \, {\left(a^{2} b x^{8} + a^{3} x^{4}\right)} \left(\frac{b^{4}}{a^{9}}\right)^{\frac{1}{4}} \log\left(-125 \, a^{7} \left(\frac{b^{4}}{a^{9}}\right)^{\frac{3}{4}} + 125 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}} b^{3}\right) - 4 \, {\left(5 \, b x^{4} + a\right)} {\left(b x^{4} + a\right)}^{\frac{3}{4}}}{16 \, {\left(a^{2} b x^{8} + a^{3} x^{4}\right)}}"," ",0,"1/16*(20*(a^2*b*x^8 + a^3*x^4)*(b^4/a^9)^(1/4)*arctan(-((b*x^4 + a)^(1/4)*a^2*b^3*(b^4/a^9)^(1/4) - sqrt(a^5*b^4*sqrt(b^4/a^9) + sqrt(b*x^4 + a)*b^6)*a^2*(b^4/a^9)^(1/4))/b^4) + 5*(a^2*b*x^8 + a^3*x^4)*(b^4/a^9)^(1/4)*log(125*a^7*(b^4/a^9)^(3/4) + 125*(b*x^4 + a)^(1/4)*b^3) - 5*(a^2*b*x^8 + a^3*x^4)*(b^4/a^9)^(1/4)*log(-125*a^7*(b^4/a^9)^(3/4) + 125*(b*x^4 + a)^(1/4)*b^3) - 4*(5*b*x^4 + a)*(b*x^4 + a)^(3/4))/(a^2*b*x^8 + a^3*x^4)","B",0
1146,1,272,0,1.213562," ","integrate(1/x^9/(b*x^4+a)^(5/4),x, algorithm=""fricas"")","-\frac{180 \, {\left(a^{3} b x^{12} + a^{4} x^{8}\right)} \left(\frac{b^{8}}{a^{13}}\right)^{\frac{1}{4}} \arctan\left(-\frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{3} b^{6} \left(\frac{b^{8}}{a^{13}}\right)^{\frac{1}{4}} - \sqrt{a^{7} b^{8} \sqrt{\frac{b^{8}}{a^{13}}} + \sqrt{b x^{4} + a} b^{12}} a^{3} \left(\frac{b^{8}}{a^{13}}\right)^{\frac{1}{4}}}{b^{8}}\right) + 45 \, {\left(a^{3} b x^{12} + a^{4} x^{8}\right)} \left(\frac{b^{8}}{a^{13}}\right)^{\frac{1}{4}} \log\left(91125 \, a^{10} \left(\frac{b^{8}}{a^{13}}\right)^{\frac{3}{4}} + 91125 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}} b^{6}\right) - 45 \, {\left(a^{3} b x^{12} + a^{4} x^{8}\right)} \left(\frac{b^{8}}{a^{13}}\right)^{\frac{1}{4}} \log\left(-91125 \, a^{10} \left(\frac{b^{8}}{a^{13}}\right)^{\frac{3}{4}} + 91125 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}} b^{6}\right) - 4 \, {\left(45 \, b^{2} x^{8} + 9 \, a b x^{4} - 4 \, a^{2}\right)} {\left(b x^{4} + a\right)}^{\frac{3}{4}}}{128 \, {\left(a^{3} b x^{12} + a^{4} x^{8}\right)}}"," ",0,"-1/128*(180*(a^3*b*x^12 + a^4*x^8)*(b^8/a^13)^(1/4)*arctan(-((b*x^4 + a)^(1/4)*a^3*b^6*(b^8/a^13)^(1/4) - sqrt(a^7*b^8*sqrt(b^8/a^13) + sqrt(b*x^4 + a)*b^12)*a^3*(b^8/a^13)^(1/4))/b^8) + 45*(a^3*b*x^12 + a^4*x^8)*(b^8/a^13)^(1/4)*log(91125*a^10*(b^8/a^13)^(3/4) + 91125*(b*x^4 + a)^(1/4)*b^6) - 45*(a^3*b*x^12 + a^4*x^8)*(b^8/a^13)^(1/4)*log(-91125*a^10*(b^8/a^13)^(3/4) + 91125*(b*x^4 + a)^(1/4)*b^6) - 4*(45*b^2*x^8 + 9*a*b*x^4 - 4*a^2)*(b*x^4 + a)^(3/4))/(a^3*b*x^12 + a^4*x^8)","B",0
1147,0,0,0,0.870997," ","integrate(x^13/(b*x^4+a)^(5/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{\frac{3}{4}} x^{13}}{b^{2} x^{8} + 2 \, a b x^{4} + a^{2}}, x\right)"," ",0,"integral((b*x^4 + a)^(3/4)*x^13/(b^2*x^8 + 2*a*b*x^4 + a^2), x)","F",0
1148,0,0,0,1.376543," ","integrate(x^9/(b*x^4+a)^(5/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{\frac{3}{4}} x^{9}}{b^{2} x^{8} + 2 \, a b x^{4} + a^{2}}, x\right)"," ",0,"integral((b*x^4 + a)^(3/4)*x^9/(b^2*x^8 + 2*a*b*x^4 + a^2), x)","F",0
1149,0,0,0,1.169953," ","integrate(x^5/(b*x^4+a)^(5/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{\frac{3}{4}} x^{5}}{b^{2} x^{8} + 2 \, a b x^{4} + a^{2}}, x\right)"," ",0,"integral((b*x^4 + a)^(3/4)*x^5/(b^2*x^8 + 2*a*b*x^4 + a^2), x)","F",0
1150,0,0,0,1.149704," ","integrate(x/(b*x^4+a)^(5/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{\frac{3}{4}} x}{b^{2} x^{8} + 2 \, a b x^{4} + a^{2}}, x\right)"," ",0,"integral((b*x^4 + a)^(3/4)*x/(b^2*x^8 + 2*a*b*x^4 + a^2), x)","F",0
1151,0,0,0,1.225560," ","integrate(1/x^3/(b*x^4+a)^(5/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}{b^{2} x^{11} + 2 \, a b x^{7} + a^{2} x^{3}}, x\right)"," ",0,"integral((b*x^4 + a)^(3/4)/(b^2*x^11 + 2*a*b*x^7 + a^2*x^3), x)","F",0
1152,0,0,0,0.915253," ","integrate(1/x^7/(b*x^4+a)^(5/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}{b^{2} x^{15} + 2 \, a b x^{11} + a^{2} x^{7}}, x\right)"," ",0,"integral((b*x^4 + a)^(3/4)/(b^2*x^15 + 2*a*b*x^11 + a^2*x^7), x)","F",0
1153,0,0,0,1.351351," ","integrate(1/x^11/(b*x^4+a)^(5/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}{b^{2} x^{19} + 2 \, a b x^{15} + a^{2} x^{11}}, x\right)"," ",0,"integral((b*x^4 + a)^(3/4)/(b^2*x^19 + 2*a*b*x^15 + a^2*x^11), x)","F",0
1154,1,281,0,1.289562," ","integrate(x^12/(b*x^4+a)^(5/4),x, algorithm=""fricas"")","\frac{180 \, {\left(b^{4} x^{4} + a b^{3}\right)} \left(\frac{a^{8}}{b^{13}}\right)^{\frac{1}{4}} \arctan\left(-\frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{6} b^{3} \left(\frac{a^{8}}{b^{13}}\right)^{\frac{1}{4}} - b^{3} x \sqrt{\frac{a^{8} b^{7} x^{2} \sqrt{\frac{a^{8}}{b^{13}}} + \sqrt{b x^{4} + a} a^{12}}{x^{2}}} \left(\frac{a^{8}}{b^{13}}\right)^{\frac{1}{4}}}{a^{8} x}\right) + 45 \, {\left(b^{4} x^{4} + a b^{3}\right)} \left(\frac{a^{8}}{b^{13}}\right)^{\frac{1}{4}} \log\left(\frac{91125 \, {\left(b^{10} x \left(\frac{a^{8}}{b^{13}}\right)^{\frac{3}{4}} + {\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{6}\right)}}{x}\right) - 45 \, {\left(b^{4} x^{4} + a b^{3}\right)} \left(\frac{a^{8}}{b^{13}}\right)^{\frac{1}{4}} \log\left(-\frac{91125 \, {\left(b^{10} x \left(\frac{a^{8}}{b^{13}}\right)^{\frac{3}{4}} - {\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{6}\right)}}{x}\right) + 4 \, {\left(4 \, b^{2} x^{9} - 9 \, a b x^{5} - 45 \, a^{2} x\right)} {\left(b x^{4} + a\right)}^{\frac{3}{4}}}{128 \, {\left(b^{4} x^{4} + a b^{3}\right)}}"," ",0,"1/128*(180*(b^4*x^4 + a*b^3)*(a^8/b^13)^(1/4)*arctan(-((b*x^4 + a)^(1/4)*a^6*b^3*(a^8/b^13)^(1/4) - b^3*x*sqrt((a^8*b^7*x^2*sqrt(a^8/b^13) + sqrt(b*x^4 + a)*a^12)/x^2)*(a^8/b^13)^(1/4))/(a^8*x)) + 45*(b^4*x^4 + a*b^3)*(a^8/b^13)^(1/4)*log(91125*(b^10*x*(a^8/b^13)^(3/4) + (b*x^4 + a)^(1/4)*a^6)/x) - 45*(b^4*x^4 + a*b^3)*(a^8/b^13)^(1/4)*log(-91125*(b^10*x*(a^8/b^13)^(3/4) - (b*x^4 + a)^(1/4)*a^6)/x) + 4*(4*b^2*x^9 - 9*a*b*x^5 - 45*a^2*x)*(b*x^4 + a)^(3/4))/(b^4*x^4 + a*b^3)","B",0
1155,1,269,0,1.040796," ","integrate(x^8/(b*x^4+a)^(5/4),x, algorithm=""fricas"")","-\frac{20 \, {\left(b^{3} x^{4} + a b^{2}\right)} \left(\frac{a^{4}}{b^{9}}\right)^{\frac{1}{4}} \arctan\left(-\frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{3} b^{2} \left(\frac{a^{4}}{b^{9}}\right)^{\frac{1}{4}} - b^{2} x \sqrt{\frac{a^{4} b^{5} x^{2} \sqrt{\frac{a^{4}}{b^{9}}} + \sqrt{b x^{4} + a} a^{6}}{x^{2}}} \left(\frac{a^{4}}{b^{9}}\right)^{\frac{1}{4}}}{a^{4} x}\right) + 5 \, {\left(b^{3} x^{4} + a b^{2}\right)} \left(\frac{a^{4}}{b^{9}}\right)^{\frac{1}{4}} \log\left(\frac{125 \, {\left(b^{7} x \left(\frac{a^{4}}{b^{9}}\right)^{\frac{3}{4}} + {\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{3}\right)}}{x}\right) - 5 \, {\left(b^{3} x^{4} + a b^{2}\right)} \left(\frac{a^{4}}{b^{9}}\right)^{\frac{1}{4}} \log\left(-\frac{125 \, {\left(b^{7} x \left(\frac{a^{4}}{b^{9}}\right)^{\frac{3}{4}} - {\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{3}\right)}}{x}\right) - 4 \, {\left(b x^{5} + 5 \, a x\right)} {\left(b x^{4} + a\right)}^{\frac{3}{4}}}{16 \, {\left(b^{3} x^{4} + a b^{2}\right)}}"," ",0,"-1/16*(20*(b^3*x^4 + a*b^2)*(a^4/b^9)^(1/4)*arctan(-((b*x^4 + a)^(1/4)*a^3*b^2*(a^4/b^9)^(1/4) - b^2*x*sqrt((a^4*b^5*x^2*sqrt(a^4/b^9) + sqrt(b*x^4 + a)*a^6)/x^2)*(a^4/b^9)^(1/4))/(a^4*x)) + 5*(b^3*x^4 + a*b^2)*(a^4/b^9)^(1/4)*log(125*(b^7*x*(a^4/b^9)^(3/4) + (b*x^4 + a)^(1/4)*a^3)/x) - 5*(b^3*x^4 + a*b^2)*(a^4/b^9)^(1/4)*log(-125*(b^7*x*(a^4/b^9)^(3/4) - (b*x^4 + a)^(1/4)*a^3)/x) - 4*(b*x^5 + 5*a*x)*(b*x^4 + a)^(3/4))/(b^3*x^4 + a*b^2)","B",0
1156,1,193,0,1.246677," ","integrate(x^4/(b*x^4+a)^(5/4),x, algorithm=""fricas"")","\frac{4 \, {\left(b^{2} x^{4} + a b\right)} \frac{1}{b^{5}}^{\frac{1}{4}} \arctan\left(\frac{b \sqrt{\frac{b^{3} \sqrt{\frac{1}{b^{5}}} x^{2} + \sqrt{b x^{4} + a}}{x^{2}}} \frac{1}{b^{5}}^{\frac{1}{4}} x - {\left(b x^{4} + a\right)}^{\frac{1}{4}} b \frac{1}{b^{5}}^{\frac{1}{4}}}{x}\right) + {\left(b^{2} x^{4} + a b\right)} \frac{1}{b^{5}}^{\frac{1}{4}} \log\left(\frac{b^{4} \frac{1}{b^{5}}^{\frac{3}{4}} x + {\left(b x^{4} + a\right)}^{\frac{1}{4}}}{x}\right) - {\left(b^{2} x^{4} + a b\right)} \frac{1}{b^{5}}^{\frac{1}{4}} \log\left(-\frac{b^{4} \frac{1}{b^{5}}^{\frac{3}{4}} x - {\left(b x^{4} + a\right)}^{\frac{1}{4}}}{x}\right) - 4 \, {\left(b x^{4} + a\right)}^{\frac{3}{4}} x}{4 \, {\left(b^{2} x^{4} + a b\right)}}"," ",0,"1/4*(4*(b^2*x^4 + a*b)*(b^(-5))^(1/4)*arctan((b*sqrt((b^3*sqrt(b^(-5))*x^2 + sqrt(b*x^4 + a))/x^2)*(b^(-5))^(1/4)*x - (b*x^4 + a)^(1/4)*b*(b^(-5))^(1/4))/x) + (b^2*x^4 + a*b)*(b^(-5))^(1/4)*log((b^4*(b^(-5))^(3/4)*x + (b*x^4 + a)^(1/4))/x) - (b^2*x^4 + a*b)*(b^(-5))^(1/4)*log(-(b^4*(b^(-5))^(3/4)*x - (b*x^4 + a)^(1/4))/x) - 4*(b*x^4 + a)^(3/4)*x)/(b^2*x^4 + a*b)","B",0
1157,1,23,0,0.580450," ","integrate(1/(b*x^4+a)^(5/4),x, algorithm=""fricas"")","\frac{{\left(b x^{4} + a\right)}^{\frac{3}{4}} x}{a b x^{4} + a^{2}}"," ",0,"(b*x^4 + a)^(3/4)*x/(a*b*x^4 + a^2)","A",0
1158,1,37,0,1.203941," ","integrate(1/x^4/(b*x^4+a)^(5/4),x, algorithm=""fricas"")","-\frac{{\left(4 \, b x^{4} + a\right)} {\left(b x^{4} + a\right)}^{\frac{3}{4}}}{3 \, {\left(a^{2} b x^{7} + a^{3} x^{3}\right)}}"," ",0,"-1/3*(4*b*x^4 + a)*(b*x^4 + a)^(3/4)/(a^2*b*x^7 + a^3*x^3)","A",0
1159,1,50,0,1.050420," ","integrate(1/x^8/(b*x^4+a)^(5/4),x, algorithm=""fricas"")","\frac{{\left(32 \, b^{2} x^{8} + 8 \, a b x^{4} - 3 \, a^{2}\right)} {\left(b x^{4} + a\right)}^{\frac{3}{4}}}{21 \, {\left(a^{3} b x^{11} + a^{4} x^{7}\right)}}"," ",0,"1/21*(32*b^2*x^8 + 8*a*b*x^4 - 3*a^2)*(b*x^4 + a)^(3/4)/(a^3*b*x^11 + a^4*x^7)","A",0
1160,1,61,0,1.050397," ","integrate(1/x^12/(b*x^4+a)^(5/4),x, algorithm=""fricas"")","-\frac{{\left(128 \, b^{3} x^{12} + 32 \, a b^{2} x^{8} - 12 \, a^{2} b x^{4} + 7 \, a^{3}\right)} {\left(b x^{4} + a\right)}^{\frac{3}{4}}}{77 \, {\left(a^{4} b x^{15} + a^{5} x^{11}\right)}}"," ",0,"-1/77*(128*b^3*x^12 + 32*a*b^2*x^8 - 12*a^2*b*x^4 + 7*a^3)*(b*x^4 + a)^(3/4)/(a^4*b*x^15 + a^5*x^11)","A",0
1161,1,72,0,1.362290," ","integrate(1/x^16/(b*x^4+a)^(5/4),x, algorithm=""fricas"")","\frac{{\left(2048 \, b^{4} x^{16} + 512 \, a b^{3} x^{12} - 192 \, a^{2} b^{2} x^{8} + 112 \, a^{3} b x^{4} - 77 \, a^{4}\right)} {\left(b x^{4} + a\right)}^{\frac{3}{4}}}{1155 \, {\left(a^{5} b x^{19} + a^{6} x^{15}\right)}}"," ",0,"1/1155*(2048*b^4*x^16 + 512*a*b^3*x^12 - 192*a^2*b^2*x^8 + 112*a^3*b*x^4 - 77*a^4)*(b*x^4 + a)^(3/4)/(a^5*b*x^19 + a^6*x^15)","A",0
1162,0,0,0,1.130562," ","integrate(x^14/(b*x^4+a)^(5/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{\frac{3}{4}} x^{14}}{b^{2} x^{8} + 2 \, a b x^{4} + a^{2}}, x\right)"," ",0,"integral((b*x^4 + a)^(3/4)*x^14/(b^2*x^8 + 2*a*b*x^4 + a^2), x)","F",0
1163,0,0,0,1.263749," ","integrate(x^10/(b*x^4+a)^(5/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{\frac{3}{4}} x^{10}}{b^{2} x^{8} + 2 \, a b x^{4} + a^{2}}, x\right)"," ",0,"integral((b*x^4 + a)^(3/4)*x^10/(b^2*x^8 + 2*a*b*x^4 + a^2), x)","F",0
1164,0,0,0,1.259699," ","integrate(x^6/(b*x^4+a)^(5/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{\frac{3}{4}} x^{6}}{b^{2} x^{8} + 2 \, a b x^{4} + a^{2}}, x\right)"," ",0,"integral((b*x^4 + a)^(3/4)*x^6/(b^2*x^8 + 2*a*b*x^4 + a^2), x)","F",0
1165,0,0,0,1.048813," ","integrate(x^2/(b*x^4+a)^(5/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{\frac{3}{4}} x^{2}}{b^{2} x^{8} + 2 \, a b x^{4} + a^{2}}, x\right)"," ",0,"integral((b*x^4 + a)^(3/4)*x^2/(b^2*x^8 + 2*a*b*x^4 + a^2), x)","F",0
1166,0,0,0,1.313219," ","integrate(1/x^2/(b*x^4+a)^(5/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}{b^{2} x^{10} + 2 \, a b x^{6} + a^{2} x^{2}}, x\right)"," ",0,"integral((b*x^4 + a)^(3/4)/(b^2*x^10 + 2*a*b*x^6 + a^2*x^2), x)","F",0
1167,0,0,0,0.753728," ","integrate(1/x^6/(b*x^4+a)^(5/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}{b^{2} x^{14} + 2 \, a b x^{10} + a^{2} x^{6}}, x\right)"," ",0,"integral((b*x^4 + a)^(3/4)/(b^2*x^14 + 2*a*b*x^10 + a^2*x^6), x)","F",0
1168,0,0,0,0.660383," ","integrate(1/x^10/(b*x^4+a)^(5/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}{b^{2} x^{18} + 2 \, a b x^{14} + a^{2} x^{10}}, x\right)"," ",0,"integral((b*x^4 + a)^(3/4)/(b^2*x^18 + 2*a*b*x^14 + a^2*x^10), x)","F",0
1169,0,0,0,0.890455," ","integrate(1/x^14/(b*x^4+a)^(5/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}{b^{2} x^{22} + 2 \, a b x^{18} + a^{2} x^{14}}, x\right)"," ",0,"integral((b*x^4 + a)^(3/4)/(b^2*x^22 + 2*a*b*x^18 + a^2*x^14), x)","F",0
1170,0,0,0,1.137812," ","integrate(1/(b*x^4+a)^(7/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}{b^{2} x^{8} + 2 \, a b x^{4} + a^{2}}, x\right)"," ",0,"integral((b*x^4 + a)^(1/4)/(b^2*x^8 + 2*a*b*x^4 + a^2), x)","F",0
1171,1,47,0,1.405601," ","integrate(1/(b*x^4+a)^(9/4),x, algorithm=""fricas"")","\frac{{\left(4 \, b x^{5} + 5 \, a x\right)} {\left(b x^{4} + a\right)}^{\frac{3}{4}}}{5 \, {\left(a^{2} b^{2} x^{8} + 2 \, a^{3} b x^{4} + a^{4}\right)}}"," ",0,"1/5*(4*b*x^5 + 5*a*x)*(b*x^4 + a)^(3/4)/(a^2*b^2*x^8 + 2*a^3*b*x^4 + a^4)","A",0
1172,0,0,0,1.138157," ","integrate(1/(b*x^4+a)^(11/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}{b^{3} x^{12} + 3 \, a b^{2} x^{8} + 3 \, a^{2} b x^{4} + a^{3}}, x\right)"," ",0,"integral((b*x^4 + a)^(1/4)/(b^3*x^12 + 3*a*b^2*x^8 + 3*a^2*b*x^4 + a^3), x)","F",0
1173,1,69,0,0.784549," ","integrate(1/(b*x^4+a)^(13/4),x, algorithm=""fricas"")","\frac{{\left(32 \, b^{2} x^{9} + 72 \, a b x^{5} + 45 \, a^{2} x\right)} {\left(b x^{4} + a\right)}^{\frac{3}{4}}}{45 \, {\left(a^{3} b^{3} x^{12} + 3 \, a^{4} b^{2} x^{8} + 3 \, a^{5} b x^{4} + a^{6}\right)}}"," ",0,"1/45*(32*b^2*x^9 + 72*a*b*x^5 + 45*a^2*x)*(b*x^4 + a)^(3/4)/(a^3*b^3*x^12 + 3*a^4*b^2*x^8 + 3*a^5*b*x^4 + a^6)","A",0
1174,1,91,0,1.220082," ","integrate(1/(b*x^4+a)^(17/4),x, algorithm=""fricas"")","\frac{{\left(128 \, b^{3} x^{13} + 416 \, a b^{2} x^{9} + 468 \, a^{2} b x^{5} + 195 \, a^{3} x\right)} {\left(b x^{4} + a\right)}^{\frac{3}{4}}}{195 \, {\left(a^{4} b^{4} x^{16} + 4 \, a^{5} b^{3} x^{12} + 6 \, a^{6} b^{2} x^{8} + 4 \, a^{7} b x^{4} + a^{8}\right)}}"," ",0,"1/195*(128*b^3*x^13 + 416*a*b^2*x^9 + 468*a^2*b*x^5 + 195*a^3*x)*(b*x^4 + a)^(3/4)/(a^4*b^4*x^16 + 4*a^5*b^3*x^12 + 6*a^6*b^2*x^8 + 4*a^7*b*x^4 + a^8)","A",0
1175,1,69,0,1.124005," ","integrate(x^19*(-b*x^4+a)^(1/4),x, algorithm=""fricas"")","\frac{{\left(3315 \, b^{5} x^{20} - 195 \, a b^{4} x^{16} - 240 \, a^{2} b^{3} x^{12} - 320 \, a^{3} b^{2} x^{8} - 512 \, a^{4} b x^{4} - 2048 \, a^{5}\right)} {\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{69615 \, b^{5}}"," ",0,"1/69615*(3315*b^5*x^20 - 195*a*b^4*x^16 - 240*a^2*b^3*x^12 - 320*a^3*b^2*x^8 - 512*a^4*b*x^4 - 2048*a^5)*(-b*x^4 + a)^(1/4)/b^5","A",0
1176,1,58,0,1.077258," ","integrate(x^15*(-b*x^4+a)^(1/4),x, algorithm=""fricas"")","\frac{{\left(195 \, b^{4} x^{16} - 15 \, a b^{3} x^{12} - 20 \, a^{2} b^{2} x^{8} - 32 \, a^{3} b x^{4} - 128 \, a^{4}\right)} {\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{3315 \, b^{4}}"," ",0,"1/3315*(195*b^4*x^16 - 15*a*b^3*x^12 - 20*a^2*b^2*x^8 - 32*a^3*b*x^4 - 128*a^4)*(-b*x^4 + a)^(1/4)/b^4","A",0
1177,1,47,0,0.947504," ","integrate(x^11*(-b*x^4+a)^(1/4),x, algorithm=""fricas"")","\frac{{\left(45 \, b^{3} x^{12} - 5 \, a b^{2} x^{8} - 8 \, a^{2} b x^{4} - 32 \, a^{3}\right)} {\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{585 \, b^{3}}"," ",0,"1/585*(45*b^3*x^12 - 5*a*b^2*x^8 - 8*a^2*b*x^4 - 32*a^3)*(-b*x^4 + a)^(1/4)/b^3","A",0
1178,1,36,0,1.208815," ","integrate(x^7*(-b*x^4+a)^(1/4),x, algorithm=""fricas"")","\frac{{\left(5 \, b^{2} x^{8} - a b x^{4} - 4 \, a^{2}\right)} {\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{45 \, b^{2}}"," ",0,"1/45*(5*b^2*x^8 - a*b*x^4 - 4*a^2)*(-b*x^4 + a)^(1/4)/b^2","A",0
1179,1,24,0,0.812081," ","integrate(x^3*(-b*x^4+a)^(1/4),x, algorithm=""fricas"")","\frac{{\left(b x^{4} - a\right)} {\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{5 \, b}"," ",0,"1/5*(b*x^4 - a)*(-b*x^4 + a)^(1/4)/b","A",0
1180,1,98,0,1.365926," ","integrate((-b*x^4+a)^(1/4)/x,x, algorithm=""fricas"")","a^{\frac{1}{4}} \arctan\left(\frac{a^{\frac{3}{4}} \sqrt{\sqrt{-b x^{4} + a} + \sqrt{a}} - {\left(-b x^{4} + a\right)}^{\frac{1}{4}} a^{\frac{3}{4}}}{a}\right) - \frac{1}{4} \, a^{\frac{1}{4}} \log\left({\left(-b x^{4} + a\right)}^{\frac{1}{4}} + a^{\frac{1}{4}}\right) + \frac{1}{4} \, a^{\frac{1}{4}} \log\left({\left(-b x^{4} + a\right)}^{\frac{1}{4}} - a^{\frac{1}{4}}\right) + {\left(-b x^{4} + a\right)}^{\frac{1}{4}}"," ",0,"a^(1/4)*arctan((a^(3/4)*sqrt(sqrt(-b*x^4 + a) + sqrt(a)) - (-b*x^4 + a)^(1/4)*a^(3/4))/a) - 1/4*a^(1/4)*log((-b*x^4 + a)^(1/4) + a^(1/4)) + 1/4*a^(1/4)*log((-b*x^4 + a)^(1/4) - a^(1/4)) + (-b*x^4 + a)^(1/4)","A",0
1181,1,185,0,1.115648," ","integrate((-b*x^4+a)^(1/4)/x^5,x, algorithm=""fricas"")","-\frac{4 \, \left(\frac{b^{4}}{a^{3}}\right)^{\frac{1}{4}} x^{4} \arctan\left(-\frac{{\left(-b x^{4} + a\right)}^{\frac{1}{4}} a^{2} b \left(\frac{b^{4}}{a^{3}}\right)^{\frac{3}{4}} - \sqrt{\sqrt{-b x^{4} + a} b^{2} + a^{2} \sqrt{\frac{b^{4}}{a^{3}}}} a^{2} \left(\frac{b^{4}}{a^{3}}\right)^{\frac{3}{4}}}{b^{4}}\right) - \left(\frac{b^{4}}{a^{3}}\right)^{\frac{1}{4}} x^{4} \log\left({\left(-b x^{4} + a\right)}^{\frac{1}{4}} b + a \left(\frac{b^{4}}{a^{3}}\right)^{\frac{1}{4}}\right) + \left(\frac{b^{4}}{a^{3}}\right)^{\frac{1}{4}} x^{4} \log\left({\left(-b x^{4} + a\right)}^{\frac{1}{4}} b - a \left(\frac{b^{4}}{a^{3}}\right)^{\frac{1}{4}}\right) + 4 \, {\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{16 \, x^{4}}"," ",0,"-1/16*(4*(b^4/a^3)^(1/4)*x^4*arctan(-((-b*x^4 + a)^(1/4)*a^2*b*(b^4/a^3)^(3/4) - sqrt(sqrt(-b*x^4 + a)*b^2 + a^2*sqrt(b^4/a^3))*a^2*(b^4/a^3)^(3/4))/b^4) - (b^4/a^3)^(1/4)*x^4*log((-b*x^4 + a)^(1/4)*b + a*(b^4/a^3)^(1/4)) + (b^4/a^3)^(1/4)*x^4*log((-b*x^4 + a)^(1/4)*b - a*(b^4/a^3)^(1/4)) + 4*(-b*x^4 + a)^(1/4))/x^4","B",0
1182,1,214,0,1.524027," ","integrate((-b*x^4+a)^(1/4)/x^9,x, algorithm=""fricas"")","-\frac{12 \, a \left(\frac{b^{8}}{a^{7}}\right)^{\frac{1}{4}} x^{8} \arctan\left(-\frac{{\left(-b x^{4} + a\right)}^{\frac{1}{4}} a^{5} b^{2} \left(\frac{b^{8}}{a^{7}}\right)^{\frac{3}{4}} - \sqrt{\sqrt{-b x^{4} + a} b^{4} + a^{4} \sqrt{\frac{b^{8}}{a^{7}}}} a^{5} \left(\frac{b^{8}}{a^{7}}\right)^{\frac{3}{4}}}{b^{8}}\right) - 3 \, a \left(\frac{b^{8}}{a^{7}}\right)^{\frac{1}{4}} x^{8} \log\left(3 \, {\left(-b x^{4} + a\right)}^{\frac{1}{4}} b^{2} + 3 \, a^{2} \left(\frac{b^{8}}{a^{7}}\right)^{\frac{1}{4}}\right) + 3 \, a \left(\frac{b^{8}}{a^{7}}\right)^{\frac{1}{4}} x^{8} \log\left(3 \, {\left(-b x^{4} + a\right)}^{\frac{1}{4}} b^{2} - 3 \, a^{2} \left(\frac{b^{8}}{a^{7}}\right)^{\frac{1}{4}}\right) - 4 \, {\left(b x^{4} - 4 \, a\right)} {\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{128 \, a x^{8}}"," ",0,"-1/128*(12*a*(b^8/a^7)^(1/4)*x^8*arctan(-((-b*x^4 + a)^(1/4)*a^5*b^2*(b^8/a^7)^(3/4) - sqrt(sqrt(-b*x^4 + a)*b^4 + a^4*sqrt(b^8/a^7))*a^5*(b^8/a^7)^(3/4))/b^8) - 3*a*(b^8/a^7)^(1/4)*x^8*log(3*(-b*x^4 + a)^(1/4)*b^2 + 3*a^2*(b^8/a^7)^(1/4)) + 3*a*(b^8/a^7)^(1/4)*x^8*log(3*(-b*x^4 + a)^(1/4)*b^2 - 3*a^2*(b^8/a^7)^(1/4)) - 4*(b*x^4 - 4*a)*(-b*x^4 + a)^(1/4))/(a*x^8)","B",0
1183,0,0,0,1.174959," ","integrate(x^9*(-b*x^4+a)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left({\left(-b x^{4} + a\right)}^{\frac{1}{4}} x^{9}, x\right)"," ",0,"integral((-b*x^4 + a)^(1/4)*x^9, x)","F",0
1184,0,0,0,1.157389," ","integrate(x^5*(-b*x^4+a)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left({\left(-b x^{4} + a\right)}^{\frac{1}{4}} x^{5}, x\right)"," ",0,"integral((-b*x^4 + a)^(1/4)*x^5, x)","F",0
1185,0,0,0,1.221211," ","integrate(x*(-b*x^4+a)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left({\left(-b x^{4} + a\right)}^{\frac{1}{4}} x, x\right)"," ",0,"integral((-b*x^4 + a)^(1/4)*x, x)","F",0
1186,0,0,0,0.871387," ","integrate((-b*x^4+a)^(1/4)/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{x^{3}}, x\right)"," ",0,"integral((-b*x^4 + a)^(1/4)/x^3, x)","F",0
1187,0,0,0,1.331258," ","integrate((-b*x^4+a)^(1/4)/x^7,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{x^{7}}, x\right)"," ",0,"integral((-b*x^4 + a)^(1/4)/x^7, x)","F",0
1188,0,0,0,1.252525," ","integrate((-b*x^4+a)^(1/4)/x^11,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{x^{11}}, x\right)"," ",0,"integral((-b*x^4 + a)^(1/4)/x^11, x)","F",0
1189,1,234,0,1.230502," ","integrate(x^6*(-b*x^4+a)^(1/4),x, algorithm=""fricas"")","-\frac{12 \, \left(-\frac{a^{8}}{b^{7}}\right)^{\frac{1}{4}} b \arctan\left(-\frac{{\left(-b x^{4} + a\right)}^{\frac{1}{4}} a^{2} \left(-\frac{a^{8}}{b^{7}}\right)^{\frac{3}{4}} b^{5} - \left(-\frac{a^{8}}{b^{7}}\right)^{\frac{3}{4}} b^{5} x \sqrt{\frac{\sqrt{-\frac{a^{8}}{b^{7}}} b^{4} x^{2} + \sqrt{-b x^{4} + a} a^{4}}{x^{2}}}}{a^{8} x}\right) + 3 \, \left(-\frac{a^{8}}{b^{7}}\right)^{\frac{1}{4}} b \log\left(\frac{3 \, {\left(\left(-\frac{a^{8}}{b^{7}}\right)^{\frac{1}{4}} b^{2} x + {\left(-b x^{4} + a\right)}^{\frac{1}{4}} a^{2}\right)}}{x}\right) - 3 \, \left(-\frac{a^{8}}{b^{7}}\right)^{\frac{1}{4}} b \log\left(-\frac{3 \, {\left(\left(-\frac{a^{8}}{b^{7}}\right)^{\frac{1}{4}} b^{2} x - {\left(-b x^{4} + a\right)}^{\frac{1}{4}} a^{2}\right)}}{x}\right) - 4 \, {\left(4 \, b x^{7} - a x^{3}\right)} {\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{128 \, b}"," ",0,"-1/128*(12*(-a^8/b^7)^(1/4)*b*arctan(-((-b*x^4 + a)^(1/4)*a^2*(-a^8/b^7)^(3/4)*b^5 - (-a^8/b^7)^(3/4)*b^5*x*sqrt((sqrt(-a^8/b^7)*b^4*x^2 + sqrt(-b*x^4 + a)*a^4)/x^2))/(a^8*x)) + 3*(-a^8/b^7)^(1/4)*b*log(3*((-a^8/b^7)^(1/4)*b^2*x + (-b*x^4 + a)^(1/4)*a^2)/x) - 3*(-a^8/b^7)^(1/4)*b*log(-3*((-a^8/b^7)^(1/4)*b^2*x - (-b*x^4 + a)^(1/4)*a^2)/x) - 4*(4*b*x^7 - a*x^3)*(-b*x^4 + a)^(1/4))/b","A",0
1190,1,204,0,1.374077," ","integrate(x^2*(-b*x^4+a)^(1/4),x, algorithm=""fricas"")","\frac{1}{4} \, {\left(-b x^{4} + a\right)}^{\frac{1}{4}} x^{3} - \frac{1}{4} \, \left(-\frac{a^{4}}{b^{3}}\right)^{\frac{1}{4}} \arctan\left(\frac{\left(-\frac{a^{4}}{b^{3}}\right)^{\frac{3}{4}} b^{2} x \sqrt{\frac{\sqrt{-\frac{a^{4}}{b^{3}}} b^{2} x^{2} + \sqrt{-b x^{4} + a} a^{2}}{x^{2}}} - {\left(-b x^{4} + a\right)}^{\frac{1}{4}} a \left(-\frac{a^{4}}{b^{3}}\right)^{\frac{3}{4}} b^{2}}{a^{4} x}\right) - \frac{1}{16} \, \left(-\frac{a^{4}}{b^{3}}\right)^{\frac{1}{4}} \log\left(\frac{\left(-\frac{a^{4}}{b^{3}}\right)^{\frac{1}{4}} b x + {\left(-b x^{4} + a\right)}^{\frac{1}{4}} a}{x}\right) + \frac{1}{16} \, \left(-\frac{a^{4}}{b^{3}}\right)^{\frac{1}{4}} \log\left(-\frac{\left(-\frac{a^{4}}{b^{3}}\right)^{\frac{1}{4}} b x - {\left(-b x^{4} + a\right)}^{\frac{1}{4}} a}{x}\right)"," ",0,"1/4*(-b*x^4 + a)^(1/4)*x^3 - 1/4*(-a^4/b^3)^(1/4)*arctan(((-a^4/b^3)^(3/4)*b^2*x*sqrt((sqrt(-a^4/b^3)*b^2*x^2 + sqrt(-b*x^4 + a)*a^2)/x^2) - (-b*x^4 + a)^(1/4)*a*(-a^4/b^3)^(3/4)*b^2)/(a^4*x)) - 1/16*(-a^4/b^3)^(1/4)*log(((-a^4/b^3)^(1/4)*b*x + (-b*x^4 + a)^(1/4)*a)/x) + 1/16*(-a^4/b^3)^(1/4)*log(-((-a^4/b^3)^(1/4)*b*x - (-b*x^4 + a)^(1/4)*a)/x)","A",0
1191,-1,0,0,0.000000," ","integrate((-b*x^4+a)^(1/4)/x^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1192,1,27,0,1.012113," ","integrate((-b*x^4+a)^(1/4)/x^6,x, algorithm=""fricas"")","\frac{{\left(b x^{4} - a\right)} {\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{5 \, a x^{5}}"," ",0,"1/5*(b*x^4 - a)*(-b*x^4 + a)^(1/4)/(a*x^5)","A",0
1193,1,38,0,1.019472," ","integrate((-b*x^4+a)^(1/4)/x^10,x, algorithm=""fricas"")","\frac{{\left(4 \, b^{2} x^{8} + a b x^{4} - 5 \, a^{2}\right)} {\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{45 \, a^{2} x^{9}}"," ",0,"1/45*(4*b^2*x^8 + a*b*x^4 - 5*a^2)*(-b*x^4 + a)^(1/4)/(a^2*x^9)","A",0
1194,1,50,0,1.260884," ","integrate((-b*x^4+a)^(1/4)/x^14,x, algorithm=""fricas"")","\frac{{\left(32 \, b^{3} x^{12} + 8 \, a b^{2} x^{8} + 5 \, a^{2} b x^{4} - 45 \, a^{3}\right)} {\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{585 \, a^{3} x^{13}}"," ",0,"1/585*(32*b^3*x^12 + 8*a*b^2*x^8 + 5*a^2*b*x^4 - 45*a^3)*(-b*x^4 + a)^(1/4)/(a^3*x^13)","A",0
1195,1,61,0,0.941690," ","integrate((-b*x^4+a)^(1/4)/x^18,x, algorithm=""fricas"")","\frac{{\left(128 \, b^{4} x^{16} + 32 \, a b^{3} x^{12} + 20 \, a^{2} b^{2} x^{8} + 15 \, a^{3} b x^{4} - 195 \, a^{4}\right)} {\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{3315 \, a^{4} x^{17}}"," ",0,"1/3315*(128*b^4*x^16 + 32*a*b^3*x^12 + 20*a^2*b^2*x^8 + 15*a^3*b*x^4 - 195*a^4)*(-b*x^4 + a)^(1/4)/(a^4*x^17)","A",0
1196,0,0,0,1.500749," ","integrate(x^12*(-b*x^4+a)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left({\left(-b x^{4} + a\right)}^{\frac{1}{4}} x^{12}, x\right)"," ",0,"integral((-b*x^4 + a)^(1/4)*x^12, x)","F",0
1197,0,0,0,1.577149," ","integrate(x^8*(-b*x^4+a)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left({\left(-b x^{4} + a\right)}^{\frac{1}{4}} x^{8}, x\right)"," ",0,"integral((-b*x^4 + a)^(1/4)*x^8, x)","F",0
1198,0,0,0,1.154483," ","integrate(x^4*(-b*x^4+a)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left({\left(-b x^{4} + a\right)}^{\frac{1}{4}} x^{4}, x\right)"," ",0,"integral((-b*x^4 + a)^(1/4)*x^4, x)","F",0
1199,0,0,0,1.121114," ","integrate((-b*x^4+a)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left({\left(-b x^{4} + a\right)}^{\frac{1}{4}}, x\right)"," ",0,"integral((-b*x^4 + a)^(1/4), x)","F",0
1200,0,0,0,1.243072," ","integrate((-b*x^4+a)^(1/4)/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{x^{4}}, x\right)"," ",0,"integral((-b*x^4 + a)^(1/4)/x^4, x)","F",0
1201,0,0,0,1.136474," ","integrate((-b*x^4+a)^(1/4)/x^8,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{x^{8}}, x\right)"," ",0,"integral((-b*x^4 + a)^(1/4)/x^8, x)","F",0
1202,0,0,0,1.358376," ","integrate((-b*x^4+a)^(1/4)/x^12,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{x^{12}}, x\right)"," ",0,"integral((-b*x^4 + a)^(1/4)/x^12, x)","F",0
1203,0,0,0,0.923454," ","integrate((-b*x^4+a)^(1/4)/x^16,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{x^{16}}, x\right)"," ",0,"integral((-b*x^4 + a)^(1/4)/x^16, x)","F",0
1204,1,58,0,1.223548," ","integrate(x^19/(-b*x^4+a)^(1/4),x, algorithm=""fricas"")","-\frac{{\left(1155 \, b^{4} x^{16} + 1232 \, a b^{3} x^{12} + 1344 \, a^{2} b^{2} x^{8} + 1536 \, a^{3} b x^{4} + 2048 \, a^{4}\right)} {\left(-b x^{4} + a\right)}^{\frac{3}{4}}}{21945 \, b^{5}}"," ",0,"-1/21945*(1155*b^4*x^16 + 1232*a*b^3*x^12 + 1344*a^2*b^2*x^8 + 1536*a^3*b*x^4 + 2048*a^4)*(-b*x^4 + a)^(3/4)/b^5","A",0
1205,1,47,0,0.716886," ","integrate(x^15/(-b*x^4+a)^(1/4),x, algorithm=""fricas"")","-\frac{{\left(77 \, b^{3} x^{12} + 84 \, a b^{2} x^{8} + 96 \, a^{2} b x^{4} + 128 \, a^{3}\right)} {\left(-b x^{4} + a\right)}^{\frac{3}{4}}}{1155 \, b^{4}}"," ",0,"-1/1155*(77*b^3*x^12 + 84*a*b^2*x^8 + 96*a^2*b*x^4 + 128*a^3)*(-b*x^4 + a)^(3/4)/b^4","A",0
1206,1,36,0,1.187538," ","integrate(x^11/(-b*x^4+a)^(1/4),x, algorithm=""fricas"")","-\frac{{\left(21 \, b^{2} x^{8} + 24 \, a b x^{4} + 32 \, a^{2}\right)} {\left(-b x^{4} + a\right)}^{\frac{3}{4}}}{231 \, b^{3}}"," ",0,"-1/231*(21*b^2*x^8 + 24*a*b*x^4 + 32*a^2)*(-b*x^4 + a)^(3/4)/b^3","A",0
1207,1,25,0,1.258124," ","integrate(x^7/(-b*x^4+a)^(1/4),x, algorithm=""fricas"")","-\frac{{\left(3 \, b x^{4} + 4 \, a\right)} {\left(-b x^{4} + a\right)}^{\frac{3}{4}}}{21 \, b^{2}}"," ",0,"-1/21*(3*b*x^4 + 4*a)*(-b*x^4 + a)^(3/4)/b^2","A",0
1208,1,15,0,0.977482," ","integrate(x^3/(-b*x^4+a)^(1/4),x, algorithm=""fricas"")","-\frac{{\left(-b x^{4} + a\right)}^{\frac{3}{4}}}{3 \, b}"," ",0,"-1/3*(-b*x^4 + a)^(3/4)/b","A",0
1209,1,85,0,1.091174," ","integrate(1/x/(-b*x^4+a)^(1/4),x, algorithm=""fricas"")","-\frac{\arctan\left(\frac{\sqrt{\sqrt{-b x^{4} + a} + \sqrt{a}}}{a^{\frac{1}{4}}} - \frac{{\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{a^{\frac{1}{4}}}\right)}{a^{\frac{1}{4}}} - \frac{\log\left({\left(-b x^{4} + a\right)}^{\frac{1}{4}} + a^{\frac{1}{4}}\right)}{4 \, a^{\frac{1}{4}}} + \frac{\log\left({\left(-b x^{4} + a\right)}^{\frac{1}{4}} - a^{\frac{1}{4}}\right)}{4 \, a^{\frac{1}{4}}}"," ",0,"-arctan(sqrt(sqrt(-b*x^4 + a) + sqrt(a))/a^(1/4) - (-b*x^4 + a)^(1/4)/a^(1/4))/a^(1/4) - 1/4*log((-b*x^4 + a)^(1/4) + a^(1/4))/a^(1/4) + 1/4*log((-b*x^4 + a)^(1/4) - a^(1/4))/a^(1/4)","B",0
1210,1,200,0,1.131131," ","integrate(1/x^5/(-b*x^4+a)^(1/4),x, algorithm=""fricas"")","-\frac{4 \, a x^{4} \left(\frac{b^{4}}{a^{5}}\right)^{\frac{1}{4}} \arctan\left(-\frac{{\left(-b x^{4} + a\right)}^{\frac{1}{4}} a b^{3} \left(\frac{b^{4}}{a^{5}}\right)^{\frac{1}{4}} - \sqrt{a^{3} b^{4} \sqrt{\frac{b^{4}}{a^{5}}} + \sqrt{-b x^{4} + a} b^{6}} a \left(\frac{b^{4}}{a^{5}}\right)^{\frac{1}{4}}}{b^{4}}\right) + a x^{4} \left(\frac{b^{4}}{a^{5}}\right)^{\frac{1}{4}} \log\left(a^{4} \left(\frac{b^{4}}{a^{5}}\right)^{\frac{3}{4}} + {\left(-b x^{4} + a\right)}^{\frac{1}{4}} b^{3}\right) - a x^{4} \left(\frac{b^{4}}{a^{5}}\right)^{\frac{1}{4}} \log\left(-a^{4} \left(\frac{b^{4}}{a^{5}}\right)^{\frac{3}{4}} + {\left(-b x^{4} + a\right)}^{\frac{1}{4}} b^{3}\right) + 4 \, {\left(-b x^{4} + a\right)}^{\frac{3}{4}}}{16 \, a x^{4}}"," ",0,"-1/16*(4*a*x^4*(b^4/a^5)^(1/4)*arctan(-((-b*x^4 + a)^(1/4)*a*b^3*(b^4/a^5)^(1/4) - sqrt(a^3*b^4*sqrt(b^4/a^5) + sqrt(-b*x^4 + a)*b^6)*a*(b^4/a^5)^(1/4))/b^4) + a*x^4*(b^4/a^5)^(1/4)*log(a^4*(b^4/a^5)^(3/4) + (-b*x^4 + a)^(1/4)*b^3) - a*x^4*(b^4/a^5)^(1/4)*log(-a^4*(b^4/a^5)^(3/4) + (-b*x^4 + a)^(1/4)*b^3) + 4*(-b*x^4 + a)^(3/4))/(a*x^4)","B",0
1211,1,224,0,1.297937," ","integrate(1/x^9/(-b*x^4+a)^(1/4),x, algorithm=""fricas"")","-\frac{20 \, a^{2} x^{8} \left(\frac{b^{8}}{a^{9}}\right)^{\frac{1}{4}} \arctan\left(-\frac{{\left(-b x^{4} + a\right)}^{\frac{1}{4}} a^{2} b^{6} \left(\frac{b^{8}}{a^{9}}\right)^{\frac{1}{4}} - \sqrt{a^{5} b^{8} \sqrt{\frac{b^{8}}{a^{9}}} + \sqrt{-b x^{4} + a} b^{12}} a^{2} \left(\frac{b^{8}}{a^{9}}\right)^{\frac{1}{4}}}{b^{8}}\right) + 5 \, a^{2} x^{8} \left(\frac{b^{8}}{a^{9}}\right)^{\frac{1}{4}} \log\left(125 \, a^{7} \left(\frac{b^{8}}{a^{9}}\right)^{\frac{3}{4}} + 125 \, {\left(-b x^{4} + a\right)}^{\frac{1}{4}} b^{6}\right) - 5 \, a^{2} x^{8} \left(\frac{b^{8}}{a^{9}}\right)^{\frac{1}{4}} \log\left(-125 \, a^{7} \left(\frac{b^{8}}{a^{9}}\right)^{\frac{3}{4}} + 125 \, {\left(-b x^{4} + a\right)}^{\frac{1}{4}} b^{6}\right) + 4 \, {\left(5 \, b x^{4} + 4 \, a\right)} {\left(-b x^{4} + a\right)}^{\frac{3}{4}}}{128 \, a^{2} x^{8}}"," ",0,"-1/128*(20*a^2*x^8*(b^8/a^9)^(1/4)*arctan(-((-b*x^4 + a)^(1/4)*a^2*b^6*(b^8/a^9)^(1/4) - sqrt(a^5*b^8*sqrt(b^8/a^9) + sqrt(-b*x^4 + a)*b^12)*a^2*(b^8/a^9)^(1/4))/b^8) + 5*a^2*x^8*(b^8/a^9)^(1/4)*log(125*a^7*(b^8/a^9)^(3/4) + 125*(-b*x^4 + a)^(1/4)*b^6) - 5*a^2*x^8*(b^8/a^9)^(1/4)*log(-125*a^7*(b^8/a^9)^(3/4) + 125*(-b*x^4 + a)^(1/4)*b^6) + 4*(5*b*x^4 + 4*a)*(-b*x^4 + a)^(3/4))/(a^2*x^8)","B",0
1212,0,0,0,1.246758," ","integrate(x^13/(-b*x^4+a)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(-b x^{4} + a\right)}^{\frac{3}{4}} x^{13}}{b x^{4} - a}, x\right)"," ",0,"integral(-(-b*x^4 + a)^(3/4)*x^13/(b*x^4 - a), x)","F",0
1213,0,0,0,1.238928," ","integrate(x^9/(-b*x^4+a)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(-b x^{4} + a\right)}^{\frac{3}{4}} x^{9}}{b x^{4} - a}, x\right)"," ",0,"integral(-(-b*x^4 + a)^(3/4)*x^9/(b*x^4 - a), x)","F",0
1214,0,0,0,1.309202," ","integrate(x^5/(-b*x^4+a)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(-b x^{4} + a\right)}^{\frac{3}{4}} x^{5}}{b x^{4} - a}, x\right)"," ",0,"integral(-(-b*x^4 + a)^(3/4)*x^5/(b*x^4 - a), x)","F",0
1215,0,0,0,0.744830," ","integrate(x/(-b*x^4+a)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(-b x^{4} + a\right)}^{\frac{3}{4}} x}{b x^{4} - a}, x\right)"," ",0,"integral(-(-b*x^4 + a)^(3/4)*x/(b*x^4 - a), x)","F",0
1216,0,0,0,1.105398," ","integrate(1/x^3/(-b*x^4+a)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(-b x^{4} + a\right)}^{\frac{3}{4}}}{b x^{7} - a x^{3}}, x\right)"," ",0,"integral(-(-b*x^4 + a)^(3/4)/(b*x^7 - a*x^3), x)","F",0
1217,0,0,0,1.243188," ","integrate(1/x^7/(-b*x^4+a)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(-b x^{4} + a\right)}^{\frac{3}{4}}}{b x^{11} - a x^{7}}, x\right)"," ",0,"integral(-(-b*x^4 + a)^(3/4)/(b*x^11 - a*x^7), x)","F",0
1218,0,0,0,0.681088," ","integrate(1/x^11/(-b*x^4+a)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(-b x^{4} + a\right)}^{\frac{3}{4}}}{b x^{15} - a x^{11}}, x\right)"," ",0,"integral(-(-b*x^4 + a)^(3/4)/(b*x^15 - a*x^11), x)","F",0
1219,1,243,0,1.343019," ","integrate(x^8/(-b*x^4+a)^(1/4),x, algorithm=""fricas"")","\frac{20 \, b^{2} \left(-\frac{a^{8}}{b^{9}}\right)^{\frac{1}{4}} \arctan\left(-\frac{{\left(-b x^{4} + a\right)}^{\frac{1}{4}} a^{6} b^{2} \left(-\frac{a^{8}}{b^{9}}\right)^{\frac{1}{4}} - b^{2} x \left(-\frac{a^{8}}{b^{9}}\right)^{\frac{1}{4}} \sqrt{-\frac{a^{8} b^{5} x^{2} \sqrt{-\frac{a^{8}}{b^{9}}} - \sqrt{-b x^{4} + a} a^{12}}{x^{2}}}}{a^{8} x}\right) - 5 \, b^{2} \left(-\frac{a^{8}}{b^{9}}\right)^{\frac{1}{4}} \log\left(\frac{125 \, {\left(b^{7} x \left(-\frac{a^{8}}{b^{9}}\right)^{\frac{3}{4}} + {\left(-b x^{4} + a\right)}^{\frac{1}{4}} a^{6}\right)}}{x}\right) + 5 \, b^{2} \left(-\frac{a^{8}}{b^{9}}\right)^{\frac{1}{4}} \log\left(-\frac{125 \, {\left(b^{7} x \left(-\frac{a^{8}}{b^{9}}\right)^{\frac{3}{4}} - {\left(-b x^{4} + a\right)}^{\frac{1}{4}} a^{6}\right)}}{x}\right) - 4 \, {\left(4 \, b x^{5} + 5 \, a x\right)} {\left(-b x^{4} + a\right)}^{\frac{3}{4}}}{128 \, b^{2}}"," ",0,"1/128*(20*b^2*(-a^8/b^9)^(1/4)*arctan(-((-b*x^4 + a)^(1/4)*a^6*b^2*(-a^8/b^9)^(1/4) - b^2*x*(-a^8/b^9)^(1/4)*sqrt(-(a^8*b^5*x^2*sqrt(-a^8/b^9) - sqrt(-b*x^4 + a)*a^12)/x^2))/(a^8*x)) - 5*b^2*(-a^8/b^9)^(1/4)*log(125*(b^7*x*(-a^8/b^9)^(3/4) + (-b*x^4 + a)^(1/4)*a^6)/x) + 5*b^2*(-a^8/b^9)^(1/4)*log(-125*(b^7*x*(-a^8/b^9)^(3/4) - (-b*x^4 + a)^(1/4)*a^6)/x) - 4*(4*b*x^5 + 5*a*x)*(-b*x^4 + a)^(3/4))/b^2","A",0
1220,1,221,0,1.345045," ","integrate(x^4/(-b*x^4+a)^(1/4),x, algorithm=""fricas"")","\frac{4 \, b \left(-\frac{a^{4}}{b^{5}}\right)^{\frac{1}{4}} \arctan\left(-\frac{{\left(-b x^{4} + a\right)}^{\frac{1}{4}} a^{3} b \left(-\frac{a^{4}}{b^{5}}\right)^{\frac{1}{4}} - b x \left(-\frac{a^{4}}{b^{5}}\right)^{\frac{1}{4}} \sqrt{-\frac{a^{4} b^{3} x^{2} \sqrt{-\frac{a^{4}}{b^{5}}} - \sqrt{-b x^{4} + a} a^{6}}{x^{2}}}}{a^{4} x}\right) - b \left(-\frac{a^{4}}{b^{5}}\right)^{\frac{1}{4}} \log\left(\frac{b^{4} x \left(-\frac{a^{4}}{b^{5}}\right)^{\frac{3}{4}} + {\left(-b x^{4} + a\right)}^{\frac{1}{4}} a^{3}}{x}\right) + b \left(-\frac{a^{4}}{b^{5}}\right)^{\frac{1}{4}} \log\left(-\frac{b^{4} x \left(-\frac{a^{4}}{b^{5}}\right)^{\frac{3}{4}} - {\left(-b x^{4} + a\right)}^{\frac{1}{4}} a^{3}}{x}\right) - 4 \, {\left(-b x^{4} + a\right)}^{\frac{3}{4}} x}{16 \, b}"," ",0,"1/16*(4*b*(-a^4/b^5)^(1/4)*arctan(-((-b*x^4 + a)^(1/4)*a^3*b*(-a^4/b^5)^(1/4) - b*x*(-a^4/b^5)^(1/4)*sqrt(-(a^4*b^3*x^2*sqrt(-a^4/b^5) - sqrt(-b*x^4 + a)*a^6)/x^2))/(a^4*x)) - b*(-a^4/b^5)^(1/4)*log((b^4*x*(-a^4/b^5)^(3/4) + (-b*x^4 + a)^(1/4)*a^3)/x) + b*(-a^4/b^5)^(1/4)*log(-(b^4*x*(-a^4/b^5)^(3/4) - (-b*x^4 + a)^(1/4)*a^3)/x) - 4*(-b*x^4 + a)^(3/4)*x)/b","A",0
1221,1,148,0,1.261667," ","integrate(1/(-b*x^4+a)^(1/4),x, algorithm=""fricas"")","\left(-\frac{1}{b}\right)^{\frac{1}{4}} \arctan\left(\frac{x \left(-\frac{1}{b}\right)^{\frac{1}{4}} \sqrt{-\frac{b x^{2} \sqrt{-\frac{1}{b}} - \sqrt{-b x^{4} + a}}{x^{2}}} - {\left(-b x^{4} + a\right)}^{\frac{1}{4}} \left(-\frac{1}{b}\right)^{\frac{1}{4}}}{x}\right) - \frac{1}{4} \, \left(-\frac{1}{b}\right)^{\frac{1}{4}} \log\left(\frac{b x \left(-\frac{1}{b}\right)^{\frac{3}{4}} + {\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{x}\right) + \frac{1}{4} \, \left(-\frac{1}{b}\right)^{\frac{1}{4}} \log\left(-\frac{b x \left(-\frac{1}{b}\right)^{\frac{3}{4}} - {\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{x}\right)"," ",0,"(-1/b)^(1/4)*arctan((x*(-1/b)^(1/4)*sqrt(-(b*x^2*sqrt(-1/b) - sqrt(-b*x^4 + a))/x^2) - (-b*x^4 + a)^(1/4)*(-1/b)^(1/4))/x) - 1/4*(-1/b)^(1/4)*log((b*x*(-1/b)^(3/4) + (-b*x^4 + a)^(1/4))/x) + 1/4*(-1/b)^(1/4)*log(-(b*x*(-1/b)^(3/4) - (-b*x^4 + a)^(1/4))/x)","A",0
1222,1,18,0,0.838075," ","integrate(1/x^4/(-b*x^4+a)^(1/4),x, algorithm=""fricas"")","-\frac{{\left(-b x^{4} + a\right)}^{\frac{3}{4}}}{3 \, a x^{3}}"," ",0,"-1/3*(-b*x^4 + a)^(3/4)/(a*x^3)","A",0
1223,1,28,0,1.258065," ","integrate(1/x^8/(-b*x^4+a)^(1/4),x, algorithm=""fricas"")","-\frac{{\left(4 \, b x^{4} + 3 \, a\right)} {\left(-b x^{4} + a\right)}^{\frac{3}{4}}}{21 \, a^{2} x^{7}}"," ",0,"-1/21*(4*b*x^4 + 3*a)*(-b*x^4 + a)^(3/4)/(a^2*x^7)","A",0
1224,1,39,0,1.149930," ","integrate(1/x^12/(-b*x^4+a)^(1/4),x, algorithm=""fricas"")","-\frac{{\left(32 \, b^{2} x^{8} + 24 \, a b x^{4} + 21 \, a^{2}\right)} {\left(-b x^{4} + a\right)}^{\frac{3}{4}}}{231 \, a^{3} x^{11}}"," ",0,"-1/231*(32*b^2*x^8 + 24*a*b*x^4 + 21*a^2)*(-b*x^4 + a)^(3/4)/(a^3*x^11)","A",0
1225,1,50,0,0.686050," ","integrate(1/x^16/(-b*x^4+a)^(1/4),x, algorithm=""fricas"")","-\frac{{\left(128 \, b^{3} x^{12} + 96 \, a b^{2} x^{8} + 84 \, a^{2} b x^{4} + 77 \, a^{3}\right)} {\left(-b x^{4} + a\right)}^{\frac{3}{4}}}{1155 \, a^{4} x^{15}}"," ",0,"-1/1155*(128*b^3*x^12 + 96*a*b^2*x^8 + 84*a^2*b*x^4 + 77*a^3)*(-b*x^4 + a)^(3/4)/(a^4*x^15)","A",0
1226,1,61,0,1.221781," ","integrate(1/x^20/(-b*x^4+a)^(1/4),x, algorithm=""fricas"")","-\frac{{\left(2048 \, b^{4} x^{16} + 1536 \, a b^{3} x^{12} + 1344 \, a^{2} b^{2} x^{8} + 1232 \, a^{3} b x^{4} + 1155 \, a^{4}\right)} {\left(-b x^{4} + a\right)}^{\frac{3}{4}}}{21945 \, a^{5} x^{19}}"," ",0,"-1/21945*(2048*b^4*x^16 + 1536*a*b^3*x^12 + 1344*a^2*b^2*x^8 + 1232*a^3*b*x^4 + 1155*a^4)*(-b*x^4 + a)^(3/4)/(a^5*x^19)","A",0
1227,0,0,0,0.804992," ","integrate(x^10/(-b*x^4+a)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(-b x^{4} + a\right)}^{\frac{3}{4}} x^{10}}{b x^{4} - a}, x\right)"," ",0,"integral(-(-b*x^4 + a)^(3/4)*x^10/(b*x^4 - a), x)","F",0
1228,0,0,0,1.510453," ","integrate(x^6/(-b*x^4+a)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(-b x^{4} + a\right)}^{\frac{3}{4}} x^{6}}{b x^{4} - a}, x\right)"," ",0,"integral(-(-b*x^4 + a)^(3/4)*x^6/(b*x^4 - a), x)","F",0
1229,0,0,0,0.826794," ","integrate(x^2/(-b*x^4+a)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(-b x^{4} + a\right)}^{\frac{3}{4}} x^{2}}{b x^{4} - a}, x\right)"," ",0,"integral(-(-b*x^4 + a)^(3/4)*x^2/(b*x^4 - a), x)","F",0
1230,0,0,0,1.247889," ","integrate(1/x^2/(-b*x^4+a)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(-b x^{4} + a\right)}^{\frac{3}{4}}}{b x^{6} - a x^{2}}, x\right)"," ",0,"integral(-(-b*x^4 + a)^(3/4)/(b*x^6 - a*x^2), x)","F",0
1231,0,0,0,1.267865," ","integrate(1/x^6/(-b*x^4+a)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(-b x^{4} + a\right)}^{\frac{3}{4}}}{b x^{10} - a x^{6}}, x\right)"," ",0,"integral(-(-b*x^4 + a)^(3/4)/(b*x^10 - a*x^6), x)","F",0
1232,0,0,0,1.147433," ","integrate(1/x^10/(-b*x^4+a)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(-b x^{4} + a\right)}^{\frac{3}{4}}}{b x^{14} - a x^{10}}, x\right)"," ",0,"integral(-(-b*x^4 + a)^(3/4)/(b*x^14 - a*x^10), x)","F",0
1233,0,0,0,1.187121," ","integrate(1/x^14/(-b*x^4+a)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(-b x^{4} + a\right)}^{\frac{3}{4}}}{b x^{18} - a x^{14}}, x\right)"," ",0,"integral(-(-b*x^4 + a)^(3/4)/(b*x^18 - a*x^14), x)","F",0
1234,1,58,0,0.775074," ","integrate(x^19/(-b*x^4+a)^(3/4),x, algorithm=""fricas"")","-\frac{{\left(195 \, b^{4} x^{16} + 240 \, a b^{3} x^{12} + 320 \, a^{2} b^{2} x^{8} + 512 \, a^{3} b x^{4} + 2048 \, a^{4}\right)} {\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{3315 \, b^{5}}"," ",0,"-1/3315*(195*b^4*x^16 + 240*a*b^3*x^12 + 320*a^2*b^2*x^8 + 512*a^3*b*x^4 + 2048*a^4)*(-b*x^4 + a)^(1/4)/b^5","A",0
1235,1,47,0,0.872015," ","integrate(x^15/(-b*x^4+a)^(3/4),x, algorithm=""fricas"")","-\frac{{\left(15 \, b^{3} x^{12} + 20 \, a b^{2} x^{8} + 32 \, a^{2} b x^{4} + 128 \, a^{3}\right)} {\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{195 \, b^{4}}"," ",0,"-1/195*(15*b^3*x^12 + 20*a*b^2*x^8 + 32*a^2*b*x^4 + 128*a^3)*(-b*x^4 + a)^(1/4)/b^4","A",0
1236,1,36,0,1.104287," ","integrate(x^11/(-b*x^4+a)^(3/4),x, algorithm=""fricas"")","-\frac{{\left(5 \, b^{2} x^{8} + 8 \, a b x^{4} + 32 \, a^{2}\right)} {\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{45 \, b^{3}}"," ",0,"-1/45*(5*b^2*x^8 + 8*a*b*x^4 + 32*a^2)*(-b*x^4 + a)^(1/4)/b^3","A",0
1237,1,24,0,1.246305," ","integrate(x^7/(-b*x^4+a)^(3/4),x, algorithm=""fricas"")","-\frac{{\left(b x^{4} + 4 \, a\right)} {\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{5 \, b^{2}}"," ",0,"-1/5*(b*x^4 + 4*a)*(-b*x^4 + a)^(1/4)/b^2","A",0
1238,1,15,0,1.162484," ","integrate(x^3/(-b*x^4+a)^(3/4),x, algorithm=""fricas"")","-\frac{{\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{b}"," ",0,"-(-b*x^4 + a)^(1/4)/b","A",0
1239,1,113,0,0.806840," ","integrate(1/x/(-b*x^4+a)^(3/4),x, algorithm=""fricas"")","\frac{1}{a^{3}}^{\frac{1}{4}} \arctan\left(\sqrt{a^{2} \sqrt{\frac{1}{a^{3}}} + \sqrt{-b x^{4} + a}} a^{2} \frac{1}{a^{3}}^{\frac{3}{4}} - {\left(-b x^{4} + a\right)}^{\frac{1}{4}} a^{2} \frac{1}{a^{3}}^{\frac{3}{4}}\right) - \frac{1}{4} \, \frac{1}{a^{3}}^{\frac{1}{4}} \log\left(a \frac{1}{a^{3}}^{\frac{1}{4}} + {\left(-b x^{4} + a\right)}^{\frac{1}{4}}\right) + \frac{1}{4} \, \frac{1}{a^{3}}^{\frac{1}{4}} \log\left(-a \frac{1}{a^{3}}^{\frac{1}{4}} + {\left(-b x^{4} + a\right)}^{\frac{1}{4}}\right)"," ",0,"(a^(-3))^(1/4)*arctan(sqrt(a^2*sqrt(a^(-3)) + sqrt(-b*x^4 + a))*a^2*(a^(-3))^(3/4) - (-b*x^4 + a)^(1/4)*a^2*(a^(-3))^(3/4)) - 1/4*(a^(-3))^(1/4)*log(a*(a^(-3))^(1/4) + (-b*x^4 + a)^(1/4)) + 1/4*(a^(-3))^(1/4)*log(-a*(a^(-3))^(1/4) + (-b*x^4 + a)^(1/4))","B",0
1240,1,199,0,1.012681," ","integrate(1/x^5/(-b*x^4+a)^(3/4),x, algorithm=""fricas"")","\frac{12 \, a x^{4} \left(\frac{b^{4}}{a^{7}}\right)^{\frac{1}{4}} \arctan\left(-\frac{{\left(-b x^{4} + a\right)}^{\frac{1}{4}} a^{5} b \left(\frac{b^{4}}{a^{7}}\right)^{\frac{3}{4}} - \sqrt{a^{4} \sqrt{\frac{b^{4}}{a^{7}}} + \sqrt{-b x^{4} + a} b^{2}} a^{5} \left(\frac{b^{4}}{a^{7}}\right)^{\frac{3}{4}}}{b^{4}}\right) - 3 \, a x^{4} \left(\frac{b^{4}}{a^{7}}\right)^{\frac{1}{4}} \log\left(3 \, a^{2} \left(\frac{b^{4}}{a^{7}}\right)^{\frac{1}{4}} + 3 \, {\left(-b x^{4} + a\right)}^{\frac{1}{4}} b\right) + 3 \, a x^{4} \left(\frac{b^{4}}{a^{7}}\right)^{\frac{1}{4}} \log\left(-3 \, a^{2} \left(\frac{b^{4}}{a^{7}}\right)^{\frac{1}{4}} + 3 \, {\left(-b x^{4} + a\right)}^{\frac{1}{4}} b\right) - 4 \, {\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{16 \, a x^{4}}"," ",0,"1/16*(12*a*x^4*(b^4/a^7)^(1/4)*arctan(-((-b*x^4 + a)^(1/4)*a^5*b*(b^4/a^7)^(3/4) - sqrt(a^4*sqrt(b^4/a^7) + sqrt(-b*x^4 + a)*b^2)*a^5*(b^4/a^7)^(3/4))/b^4) - 3*a*x^4*(b^4/a^7)^(1/4)*log(3*a^2*(b^4/a^7)^(1/4) + 3*(-b*x^4 + a)^(1/4)*b) + 3*a*x^4*(b^4/a^7)^(1/4)*log(-3*a^2*(b^4/a^7)^(1/4) + 3*(-b*x^4 + a)^(1/4)*b) - 4*(-b*x^4 + a)^(1/4))/(a*x^4)","B",0
1241,1,221,0,1.250175," ","integrate(1/x^9/(-b*x^4+a)^(3/4),x, algorithm=""fricas"")","\frac{84 \, a^{2} x^{8} \left(\frac{b^{8}}{a^{11}}\right)^{\frac{1}{4}} \arctan\left(-\frac{{\left(-b x^{4} + a\right)}^{\frac{1}{4}} a^{8} b^{2} \left(\frac{b^{8}}{a^{11}}\right)^{\frac{3}{4}} - \sqrt{a^{6} \sqrt{\frac{b^{8}}{a^{11}}} + \sqrt{-b x^{4} + a} b^{4}} a^{8} \left(\frac{b^{8}}{a^{11}}\right)^{\frac{3}{4}}}{b^{8}}\right) - 21 \, a^{2} x^{8} \left(\frac{b^{8}}{a^{11}}\right)^{\frac{1}{4}} \log\left(21 \, a^{3} \left(\frac{b^{8}}{a^{11}}\right)^{\frac{1}{4}} + 21 \, {\left(-b x^{4} + a\right)}^{\frac{1}{4}} b^{2}\right) + 21 \, a^{2} x^{8} \left(\frac{b^{8}}{a^{11}}\right)^{\frac{1}{4}} \log\left(-21 \, a^{3} \left(\frac{b^{8}}{a^{11}}\right)^{\frac{1}{4}} + 21 \, {\left(-b x^{4} + a\right)}^{\frac{1}{4}} b^{2}\right) - 4 \, {\left(7 \, b x^{4} + 4 \, a\right)} {\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{128 \, a^{2} x^{8}}"," ",0,"1/128*(84*a^2*x^8*(b^8/a^11)^(1/4)*arctan(-((-b*x^4 + a)^(1/4)*a^8*b^2*(b^8/a^11)^(3/4) - sqrt(a^6*sqrt(b^8/a^11) + sqrt(-b*x^4 + a)*b^4)*a^8*(b^8/a^11)^(3/4))/b^8) - 21*a^2*x^8*(b^8/a^11)^(1/4)*log(21*a^3*(b^8/a^11)^(1/4) + 21*(-b*x^4 + a)^(1/4)*b^2) + 21*a^2*x^8*(b^8/a^11)^(1/4)*log(-21*a^3*(b^8/a^11)^(1/4) + 21*(-b*x^4 + a)^(1/4)*b^2) - 4*(7*b*x^4 + 4*a)*(-b*x^4 + a)^(1/4))/(a^2*x^8)","B",0
1242,0,0,0,1.228775," ","integrate(x^13/(-b*x^4+a)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(-b x^{4} + a\right)}^{\frac{1}{4}} x^{13}}{b x^{4} - a}, x\right)"," ",0,"integral(-(-b*x^4 + a)^(1/4)*x^13/(b*x^4 - a), x)","F",0
1243,0,0,0,0.944313," ","integrate(x^9/(-b*x^4+a)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(-b x^{4} + a\right)}^{\frac{1}{4}} x^{9}}{b x^{4} - a}, x\right)"," ",0,"integral(-(-b*x^4 + a)^(1/4)*x^9/(b*x^4 - a), x)","F",0
1244,0,0,0,1.132262," ","integrate(x^5/(-b*x^4+a)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(-b x^{4} + a\right)}^{\frac{1}{4}} x^{5}}{b x^{4} - a}, x\right)"," ",0,"integral(-(-b*x^4 + a)^(1/4)*x^5/(b*x^4 - a), x)","F",0
1245,0,0,0,1.316020," ","integrate(x/(-b*x^4+a)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(-b x^{4} + a\right)}^{\frac{1}{4}} x}{b x^{4} - a}, x\right)"," ",0,"integral(-(-b*x^4 + a)^(1/4)*x/(b*x^4 - a), x)","F",0
1246,0,0,0,1.299705," ","integrate(1/x^3/(-b*x^4+a)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{b x^{7} - a x^{3}}, x\right)"," ",0,"integral(-(-b*x^4 + a)^(1/4)/(b*x^7 - a*x^3), x)","F",0
1247,0,0,0,0.742294," ","integrate(1/x^7/(-b*x^4+a)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{b x^{11} - a x^{7}}, x\right)"," ",0,"integral(-(-b*x^4 + a)^(1/4)/(b*x^11 - a*x^7), x)","F",0
1248,0,0,0,1.386618," ","integrate(1/x^11/(-b*x^4+a)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{b x^{15} - a x^{11}}, x\right)"," ",0,"integral(-(-b*x^4 + a)^(1/4)/(b*x^15 - a*x^11), x)","F",0
1249,1,240,0,1.537117," ","integrate(x^10/(-b*x^4+a)^(3/4),x, algorithm=""fricas"")","-\frac{84 \, b^{2} \left(-\frac{a^{8}}{b^{11}}\right)^{\frac{1}{4}} \arctan\left(-\frac{{\left(-b x^{4} + a\right)}^{\frac{1}{4}} a^{2} b^{8} \left(-\frac{a^{8}}{b^{11}}\right)^{\frac{3}{4}} - b^{8} x \sqrt{\frac{b^{6} x^{2} \sqrt{-\frac{a^{8}}{b^{11}}} + \sqrt{-b x^{4} + a} a^{4}}{x^{2}}} \left(-\frac{a^{8}}{b^{11}}\right)^{\frac{3}{4}}}{a^{8} x}\right) + 21 \, b^{2} \left(-\frac{a^{8}}{b^{11}}\right)^{\frac{1}{4}} \log\left(\frac{21 \, {\left(b^{3} x \left(-\frac{a^{8}}{b^{11}}\right)^{\frac{1}{4}} + {\left(-b x^{4} + a\right)}^{\frac{1}{4}} a^{2}\right)}}{x}\right) - 21 \, b^{2} \left(-\frac{a^{8}}{b^{11}}\right)^{\frac{1}{4}} \log\left(-\frac{21 \, {\left(b^{3} x \left(-\frac{a^{8}}{b^{11}}\right)^{\frac{1}{4}} - {\left(-b x^{4} + a\right)}^{\frac{1}{4}} a^{2}\right)}}{x}\right) + 4 \, {\left(4 \, b x^{7} + 7 \, a x^{3}\right)} {\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{128 \, b^{2}}"," ",0,"-1/128*(84*b^2*(-a^8/b^11)^(1/4)*arctan(-((-b*x^4 + a)^(1/4)*a^2*b^8*(-a^8/b^11)^(3/4) - b^8*x*sqrt((b^6*x^2*sqrt(-a^8/b^11) + sqrt(-b*x^4 + a)*a^4)/x^2)*(-a^8/b^11)^(3/4))/(a^8*x)) + 21*b^2*(-a^8/b^11)^(1/4)*log(21*(b^3*x*(-a^8/b^11)^(1/4) + (-b*x^4 + a)^(1/4)*a^2)/x) - 21*b^2*(-a^8/b^11)^(1/4)*log(-21*(b^3*x*(-a^8/b^11)^(1/4) - (-b*x^4 + a)^(1/4)*a^2)/x) + 4*(4*b*x^7 + 7*a*x^3)*(-b*x^4 + a)^(1/4))/b^2","A",0
1250,1,217,0,1.597028," ","integrate(x^6/(-b*x^4+a)^(3/4),x, algorithm=""fricas"")","-\frac{4 \, {\left(-b x^{4} + a\right)}^{\frac{1}{4}} x^{3} + 12 \, b \left(-\frac{a^{4}}{b^{7}}\right)^{\frac{1}{4}} \arctan\left(\frac{b^{5} x \sqrt{\frac{b^{4} x^{2} \sqrt{-\frac{a^{4}}{b^{7}}} + \sqrt{-b x^{4} + a} a^{2}}{x^{2}}} \left(-\frac{a^{4}}{b^{7}}\right)^{\frac{3}{4}} - {\left(-b x^{4} + a\right)}^{\frac{1}{4}} a b^{5} \left(-\frac{a^{4}}{b^{7}}\right)^{\frac{3}{4}}}{a^{4} x}\right) + 3 \, b \left(-\frac{a^{4}}{b^{7}}\right)^{\frac{1}{4}} \log\left(\frac{3 \, {\left(b^{2} x \left(-\frac{a^{4}}{b^{7}}\right)^{\frac{1}{4}} + {\left(-b x^{4} + a\right)}^{\frac{1}{4}} a\right)}}{x}\right) - 3 \, b \left(-\frac{a^{4}}{b^{7}}\right)^{\frac{1}{4}} \log\left(-\frac{3 \, {\left(b^{2} x \left(-\frac{a^{4}}{b^{7}}\right)^{\frac{1}{4}} - {\left(-b x^{4} + a\right)}^{\frac{1}{4}} a\right)}}{x}\right)}{16 \, b}"," ",0,"-1/16*(4*(-b*x^4 + a)^(1/4)*x^3 + 12*b*(-a^4/b^7)^(1/4)*arctan((b^5*x*sqrt((b^4*x^2*sqrt(-a^4/b^7) + sqrt(-b*x^4 + a)*a^2)/x^2)*(-a^4/b^7)^(3/4) - (-b*x^4 + a)^(1/4)*a*b^5*(-a^4/b^7)^(3/4))/(a^4*x)) + 3*b*(-a^4/b^7)^(1/4)*log(3*(b^2*x*(-a^4/b^7)^(1/4) + (-b*x^4 + a)^(1/4)*a)/x) - 3*b*(-a^4/b^7)^(1/4)*log(-3*(b^2*x*(-a^4/b^7)^(1/4) - (-b*x^4 + a)^(1/4)*a)/x))/b","A",0
1251,1,154,0,0.874759," ","integrate(x^2/(-b*x^4+a)^(3/4),x, algorithm=""fricas"")","-\left(-\frac{1}{b^{3}}\right)^{\frac{1}{4}} \arctan\left(\frac{b^{2} x \sqrt{\frac{b^{2} x^{2} \sqrt{-\frac{1}{b^{3}}} + \sqrt{-b x^{4} + a}}{x^{2}}} \left(-\frac{1}{b^{3}}\right)^{\frac{3}{4}} - {\left(-b x^{4} + a\right)}^{\frac{1}{4}} b^{2} \left(-\frac{1}{b^{3}}\right)^{\frac{3}{4}}}{x}\right) - \frac{1}{4} \, \left(-\frac{1}{b^{3}}\right)^{\frac{1}{4}} \log\left(\frac{b x \left(-\frac{1}{b^{3}}\right)^{\frac{1}{4}} + {\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{x}\right) + \frac{1}{4} \, \left(-\frac{1}{b^{3}}\right)^{\frac{1}{4}} \log\left(-\frac{b x \left(-\frac{1}{b^{3}}\right)^{\frac{1}{4}} - {\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{x}\right)"," ",0,"-(-1/b^3)^(1/4)*arctan((b^2*x*sqrt((b^2*x^2*sqrt(-1/b^3) + sqrt(-b*x^4 + a))/x^2)*(-1/b^3)^(3/4) - (-b*x^4 + a)^(1/4)*b^2*(-1/b^3)^(3/4))/x) - 1/4*(-1/b^3)^(1/4)*log((b*x*(-1/b^3)^(1/4) + (-b*x^4 + a)^(1/4))/x) + 1/4*(-1/b^3)^(1/4)*log(-(b*x*(-1/b^3)^(1/4) - (-b*x^4 + a)^(1/4))/x)","A",0
1252,1,18,0,1.107370," ","integrate(1/x^2/(-b*x^4+a)^(3/4),x, algorithm=""fricas"")","-\frac{{\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{a x}"," ",0,"-(-b*x^4 + a)^(1/4)/(a*x)","A",0
1253,1,26,0,1.384511," ","integrate(1/x^6/(-b*x^4+a)^(3/4),x, algorithm=""fricas"")","-\frac{{\left(4 \, b x^{4} + a\right)} {\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{5 \, a^{2} x^{5}}"," ",0,"-1/5*(4*b*x^4 + a)*(-b*x^4 + a)^(1/4)/(a^2*x^5)","A",0
1254,1,39,0,1.671468," ","integrate(1/x^10/(-b*x^4+a)^(3/4),x, algorithm=""fricas"")","-\frac{{\left(32 \, b^{2} x^{8} + 8 \, a b x^{4} + 5 \, a^{2}\right)} {\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{45 \, a^{3} x^{9}}"," ",0,"-1/45*(32*b^2*x^8 + 8*a*b*x^4 + 5*a^2)*(-b*x^4 + a)^(1/4)/(a^3*x^9)","A",0
1255,1,50,0,1.148637," ","integrate(1/x^14/(-b*x^4+a)^(3/4),x, algorithm=""fricas"")","-\frac{{\left(128 \, b^{3} x^{12} + 32 \, a b^{2} x^{8} + 20 \, a^{2} b x^{4} + 15 \, a^{3}\right)} {\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{195 \, a^{4} x^{13}}"," ",0,"-1/195*(128*b^3*x^12 + 32*a*b^2*x^8 + 20*a^2*b*x^4 + 15*a^3)*(-b*x^4 + a)^(1/4)/(a^4*x^13)","A",0
1256,0,0,0,1.213775," ","integrate(x^12/(-b*x^4+a)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(-b x^{4} + a\right)}^{\frac{1}{4}} x^{12}}{b x^{4} - a}, x\right)"," ",0,"integral(-(-b*x^4 + a)^(1/4)*x^12/(b*x^4 - a), x)","F",0
1257,0,0,0,1.229878," ","integrate(x^8/(-b*x^4+a)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(-b x^{4} + a\right)}^{\frac{1}{4}} x^{8}}{b x^{4} - a}, x\right)"," ",0,"integral(-(-b*x^4 + a)^(1/4)*x^8/(b*x^4 - a), x)","F",0
1258,0,0,0,0.954487," ","integrate(x^4/(-b*x^4+a)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(-b x^{4} + a\right)}^{\frac{1}{4}} x^{4}}{b x^{4} - a}, x\right)"," ",0,"integral(-(-b*x^4 + a)^(1/4)*x^4/(b*x^4 - a), x)","F",0
1259,0,0,0,1.223581," ","integrate(1/(-b*x^4+a)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{b x^{4} - a}, x\right)"," ",0,"integral(-(-b*x^4 + a)^(1/4)/(b*x^4 - a), x)","F",0
1260,0,0,0,1.240299," ","integrate(1/x^4/(-b*x^4+a)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{b x^{8} - a x^{4}}, x\right)"," ",0,"integral(-(-b*x^4 + a)^(1/4)/(b*x^8 - a*x^4), x)","F",0
1261,0,0,0,1.268885," ","integrate(1/x^8/(-b*x^4+a)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{b x^{12} - a x^{8}}, x\right)"," ",0,"integral(-(-b*x^4 + a)^(1/4)/(b*x^12 - a*x^8), x)","F",0
1262,0,0,0,0.784199," ","integrate(1/x^12/(-b*x^4+a)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{b x^{16} - a x^{12}}, x\right)"," ",0,"integral(-(-b*x^4 + a)^(1/4)/(b*x^16 - a*x^12), x)","F",0
1263,0,0,0,1.066950," ","integrate(x^2/(-b*x^4+a)^(5/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-b x^{4} + a\right)}^{\frac{3}{4}} x^{2}}{b^{2} x^{8} - 2 \, a b x^{4} + a^{2}}, x\right)"," ",0,"integral((-b*x^4 + a)^(3/4)*x^2/(b^2*x^8 - 2*a*b*x^4 + a^2), x)","F",0
1264,1,58,0,1.070141," ","integrate(x^7*(b*x^4+a)^p,x, algorithm=""fricas"")","\frac{{\left({\left(b^{2} p + b^{2}\right)} x^{8} + a b p x^{4} - a^{2}\right)} {\left(b x^{4} + a\right)}^{p}}{4 \, {\left(b^{2} p^{2} + 3 \, b^{2} p + 2 \, b^{2}\right)}}"," ",0,"1/4*((b^2*p + b^2)*x^8 + a*b*p*x^4 - a^2)*(b*x^4 + a)^p/(b^2*p^2 + 3*b^2*p + 2*b^2)","A",0
1265,1,25,0,1.508003," ","integrate(x^3*(b*x^4+a)^p,x, algorithm=""fricas"")","\frac{{\left(b x^{4} + a\right)} {\left(b x^{4} + a\right)}^{p}}{4 \, {\left(b p + b\right)}}"," ",0,"1/4*(b*x^4 + a)*(b*x^4 + a)^p/(b*p + b)","A",0
1266,0,0,0,1.318118," ","integrate((b*x^4+a)^p/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{p}}{x}, x\right)"," ",0,"integral((b*x^4 + a)^p/x, x)","F",0
1267,1,56,0,1.225026," ","integrate(x^24/(b*x^5+a),x, algorithm=""fricas"")","\frac{3 \, b^{4} x^{20} - 4 \, a b^{3} x^{15} + 6 \, a^{2} b^{2} x^{10} - 12 \, a^{3} b x^{5} + 12 \, a^{4} \log\left(b x^{5} + a\right)}{60 \, b^{5}}"," ",0,"1/60*(3*b^4*x^20 - 4*a*b^3*x^15 + 6*a^2*b^2*x^10 - 12*a^3*b*x^5 + 12*a^4*log(b*x^5 + a))/b^5","A",0
1268,1,45,0,1.190103," ","integrate(x^19/(b*x^5+a),x, algorithm=""fricas"")","\frac{2 \, b^{3} x^{15} - 3 \, a b^{2} x^{10} + 6 \, a^{2} b x^{5} - 6 \, a^{3} \log\left(b x^{5} + a\right)}{30 \, b^{4}}"," ",0,"1/30*(2*b^3*x^15 - 3*a*b^2*x^10 + 6*a^2*b*x^5 - 6*a^3*log(b*x^5 + a))/b^4","A",0
1269,1,33,0,1.112348," ","integrate(x^14/(b*x^5+a),x, algorithm=""fricas"")","\frac{b^{2} x^{10} - 2 \, a b x^{5} + 2 \, a^{2} \log\left(b x^{5} + a\right)}{10 \, b^{3}}"," ",0,"1/10*(b^2*x^10 - 2*a*b*x^5 + 2*a^2*log(b*x^5 + a))/b^3","A",0
1270,1,22,0,1.146266," ","integrate(x^9/(b*x^5+a),x, algorithm=""fricas"")","\frac{b x^{5} - a \log\left(b x^{5} + a\right)}{5 \, b^{2}}"," ",0,"1/5*(b*x^5 - a*log(b*x^5 + a))/b^2","A",0
1271,1,13,0,1.199217," ","integrate(x^4/(b*x^5+a),x, algorithm=""fricas"")","\frac{\log\left(b x^{5} + a\right)}{5 \, b}"," ",0,"1/5*log(b*x^5 + a)/b","A",0
1272,1,18,0,1.176678," ","integrate(1/x/(b*x^5+a),x, algorithm=""fricas"")","-\frac{\log\left(b x^{5} + a\right) - 5 \, \log\left(x\right)}{5 \, a}"," ",0,"-1/5*(log(b*x^5 + a) - 5*log(x))/a","A",0
1273,1,33,0,1.170391," ","integrate(1/x^6/(b*x^5+a),x, algorithm=""fricas"")","\frac{b x^{5} \log\left(b x^{5} + a\right) - 5 \, b x^{5} \log\left(x\right) - a}{5 \, a^{2} x^{5}}"," ",0,"1/5*(b*x^5*log(b*x^5 + a) - 5*b*x^5*log(x) - a)/(a^2*x^5)","A",0
1274,1,45,0,1.214235," ","integrate(1/x^11/(b*x^5+a),x, algorithm=""fricas"")","-\frac{2 \, b^{2} x^{10} \log\left(b x^{5} + a\right) - 10 \, b^{2} x^{10} \log\left(x\right) - 2 \, a b x^{5} + a^{2}}{10 \, a^{3} x^{10}}"," ",0,"-1/10*(2*b^2*x^10*log(b*x^5 + a) - 10*b^2*x^10*log(x) - 2*a*b*x^5 + a^2)/(a^3*x^10)","A",0
1275,1,58,0,1.357294," ","integrate(1/x^16/(b*x^5+a),x, algorithm=""fricas"")","\frac{6 \, b^{3} x^{15} \log\left(b x^{5} + a\right) - 30 \, b^{3} x^{15} \log\left(x\right) - 6 \, a b^{2} x^{10} + 3 \, a^{2} b x^{5} - 2 \, a^{3}}{30 \, a^{4} x^{15}}"," ",0,"1/30*(6*b^3*x^15*log(b*x^5 + a) - 30*b^3*x^15*log(x) - 6*a*b^2*x^10 + 3*a^2*b*x^5 - 2*a^3)/(a^4*x^15)","A",0
1276,-1,0,0,0.000000," ","integrate(1/(b*x^5+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1277,1,81,0,1.469900," ","integrate(x^24/(b*x^5+a)^2,x, algorithm=""fricas"")","\frac{b^{4} x^{20} - 2 \, a b^{3} x^{15} + 6 \, a^{2} b^{2} x^{10} + 9 \, a^{3} b x^{5} - 3 \, a^{4} - 12 \, {\left(a^{3} b x^{5} + a^{4}\right)} \log\left(b x^{5} + a\right)}{15 \, {\left(b^{6} x^{5} + a b^{5}\right)}}"," ",0,"1/15*(b^4*x^20 - 2*a*b^3*x^15 + 6*a^2*b^2*x^10 + 9*a^3*b*x^5 - 3*a^4 - 12*(a^3*b*x^5 + a^4)*log(b*x^5 + a))/(b^6*x^5 + a*b^5)","A",0
1278,1,70,0,1.402765," ","integrate(x^19/(b*x^5+a)^2,x, algorithm=""fricas"")","\frac{b^{3} x^{15} - 3 \, a b^{2} x^{10} - 4 \, a^{2} b x^{5} + 2 \, a^{3} + 6 \, {\left(a^{2} b x^{5} + a^{3}\right)} \log\left(b x^{5} + a\right)}{10 \, {\left(b^{5} x^{5} + a b^{4}\right)}}"," ",0,"1/10*(b^3*x^15 - 3*a*b^2*x^10 - 4*a^2*b*x^5 + 2*a^3 + 6*(a^2*b*x^5 + a^3)*log(b*x^5 + a))/(b^5*x^5 + a*b^4)","A",0
1279,1,56,0,1.260739," ","integrate(x^14/(b*x^5+a)^2,x, algorithm=""fricas"")","\frac{b^{2} x^{10} + a b x^{5} - a^{2} - 2 \, {\left(a b x^{5} + a^{2}\right)} \log\left(b x^{5} + a\right)}{5 \, {\left(b^{4} x^{5} + a b^{3}\right)}}"," ",0,"1/5*(b^2*x^10 + a*b*x^5 - a^2 - 2*(a*b*x^5 + a^2)*log(b*x^5 + a))/(b^4*x^5 + a*b^3)","A",0
1280,1,35,0,1.112067," ","integrate(x^9/(b*x^5+a)^2,x, algorithm=""fricas"")","\frac{{\left(b x^{5} + a\right)} \log\left(b x^{5} + a\right) + a}{5 \, {\left(b^{3} x^{5} + a b^{2}\right)}}"," ",0,"1/5*((b*x^5 + a)*log(b*x^5 + a) + a)/(b^3*x^5 + a*b^2)","A",0
1281,1,15,0,1.039507," ","integrate(x^4/(b*x^5+a)^2,x, algorithm=""fricas"")","-\frac{1}{5 \, {\left(b^{2} x^{5} + a b\right)}}"," ",0,"-1/5/(b^2*x^5 + a*b)","A",0
1282,1,47,0,1.194506," ","integrate(1/x/(b*x^5+a)^2,x, algorithm=""fricas"")","-\frac{{\left(b x^{5} + a\right)} \log\left(b x^{5} + a\right) - 5 \, {\left(b x^{5} + a\right)} \log\left(x\right) - a}{5 \, {\left(a^{2} b x^{5} + a^{3}\right)}}"," ",0,"-1/5*((b*x^5 + a)*log(b*x^5 + a) - 5*(b*x^5 + a)*log(x) - a)/(a^2*b*x^5 + a^3)","A",0
1283,1,73,0,1.211080," ","integrate(1/x^6/(b*x^5+a)^2,x, algorithm=""fricas"")","-\frac{2 \, a b x^{5} + a^{2} - 2 \, {\left(b^{2} x^{10} + a b x^{5}\right)} \log\left(b x^{5} + a\right) + 10 \, {\left(b^{2} x^{10} + a b x^{5}\right)} \log\left(x\right)}{5 \, {\left(a^{3} b x^{10} + a^{4} x^{5}\right)}}"," ",0,"-1/5*(2*a*b*x^5 + a^2 - 2*(b^2*x^10 + a*b*x^5)*log(b*x^5 + a) + 10*(b^2*x^10 + a*b*x^5)*log(x))/(a^3*b*x^10 + a^4*x^5)","A",0
1284,1,90,0,1.261256," ","integrate(1/x^11/(b*x^5+a)^2,x, algorithm=""fricas"")","\frac{6 \, a b^{2} x^{10} + 3 \, a^{2} b x^{5} - a^{3} - 6 \, {\left(b^{3} x^{15} + a b^{2} x^{10}\right)} \log\left(b x^{5} + a\right) + 30 \, {\left(b^{3} x^{15} + a b^{2} x^{10}\right)} \log\left(x\right)}{10 \, {\left(a^{4} b x^{15} + a^{5} x^{10}\right)}}"," ",0,"1/10*(6*a*b^2*x^10 + 3*a^2*b*x^5 - a^3 - 6*(b^3*x^15 + a*b^2*x^10)*log(b*x^5 + a) + 30*(b^3*x^15 + a*b^2*x^10)*log(x))/(a^4*b*x^15 + a^5*x^10)","A",0
1285,1,22,0,1.044917," ","integrate(x^14/(b*x^5+2*b),x, algorithm=""fricas"")","\frac{x^{10} - 4 \, x^{5} + 8 \, \log\left(x^{5} + 2\right)}{10 \, b}"," ",0,"1/10*(x^10 - 4*x^5 + 8*log(x^5 + 2))/b","A",0
1286,1,17,0,1.125413," ","integrate(x^9/(b*x^5+2*b),x, algorithm=""fricas"")","\frac{x^{5} - 2 \, \log\left(x^{5} + 2\right)}{5 \, b}"," ",0,"1/5*(x^5 - 2*log(x^5 + 2))/b","A",0
1287,1,11,0,1.173958," ","integrate(x^4/(b*x^5+2*b),x, algorithm=""fricas"")","\frac{\log\left(x^{5} + 2\right)}{5 \, b}"," ",0,"1/5*log(x^5 + 2)/b","A",0
1288,1,16,0,1.101676," ","integrate(1/x/(b*x^5+2*b),x, algorithm=""fricas"")","-\frac{\log\left(x^{5} + 2\right) - 5 \, \log\left(x\right)}{10 \, b}"," ",0,"-1/10*(log(x^5 + 2) - 5*log(x))/b","A",0
1289,1,27,0,1.220849," ","integrate(1/x^6/(b*x^5+2*b),x, algorithm=""fricas"")","\frac{x^{5} \log\left(x^{5} + 2\right) - 5 \, x^{5} \log\left(x\right) - 2}{20 \, b x^{5}}"," ",0,"1/20*(x^5*log(x^5 + 2) - 5*x^5*log(x) - 2)/(b*x^5)","A",0
1290,1,29,0,1.268967," ","integrate(x^14/(b*x^5+3),x, algorithm=""fricas"")","\frac{b^{2} x^{10} - 6 \, b x^{5} + 18 \, \log\left(b x^{5} + 3\right)}{10 \, b^{3}}"," ",0,"1/10*(b^2*x^10 - 6*b*x^5 + 18*log(b*x^5 + 3))/b^3","A",0
1291,1,21,0,1.198861," ","integrate(x^9/(b*x^5+3),x, algorithm=""fricas"")","\frac{b x^{5} - 3 \, \log\left(b x^{5} + 3\right)}{5 \, b^{2}}"," ",0,"1/5*(b*x^5 - 3*log(b*x^5 + 3))/b^2","A",0
1292,1,13,0,0.881314," ","integrate(x^4/(b*x^5+3),x, algorithm=""fricas"")","\frac{\log\left(b x^{5} + 3\right)}{5 \, b}"," ",0,"1/5*log(b*x^5 + 3)/b","A",0
1293,1,15,0,1.785235," ","integrate(1/x/(b*x^5+3),x, algorithm=""fricas"")","-\frac{1}{15} \, \log\left(b x^{5} + 3\right) + \frac{1}{3} \, \log\left(x\right)"," ",0,"-1/15*log(b*x^5 + 3) + 1/3*log(x)","A",0
1294,1,28,0,0.670938," ","integrate(1/x^6/(b*x^5+3),x, algorithm=""fricas"")","\frac{b x^{5} \log\left(b x^{5} + 3\right) - 5 \, b x^{5} \log\left(x\right) - 3}{45 \, x^{5}}"," ",0,"1/45*(b*x^5*log(b*x^5 + 3) - 5*b*x^5*log(x) - 3)/x^5","A",0
1295,1,19,0,1.131717," ","integrate(x^14/(x^5+1),x, algorithm=""fricas"")","\frac{1}{10} \, x^{10} - \frac{1}{5} \, x^{5} + \frac{1}{5} \, \log\left(x^{5} + 1\right)"," ",0,"1/10*x^10 - 1/5*x^5 + 1/5*log(x^5 + 1)","A",0
1296,1,14,0,1.138280," ","integrate(x^9/(x^5+1),x, algorithm=""fricas"")","\frac{1}{5} \, x^{5} - \frac{1}{5} \, \log\left(x^{5} + 1\right)"," ",0,"1/5*x^5 - 1/5*log(x^5 + 1)","A",0
1297,1,8,0,1.209828," ","integrate(x^4/(x^5+1),x, algorithm=""fricas"")","\frac{1}{5} \, \log\left(x^{5} + 1\right)"," ",0,"1/5*log(x^5 + 1)","A",0
1298,1,11,0,1.253512," ","integrate(1/x/(x^5+1),x, algorithm=""fricas"")","-\frac{1}{5} \, \log\left(x^{5} + 1\right) + \log\left(x\right)"," ",0,"-1/5*log(x^5 + 1) + log(x)","A",0
1299,1,24,0,1.201563," ","integrate(1/x^6/(x^5+1),x, algorithm=""fricas"")","\frac{x^{5} \log\left(x^{5} + 1\right) - 5 \, x^{5} \log\left(x\right) - 1}{5 \, x^{5}}"," ",0,"1/5*(x^5*log(x^5 + 1) - 5*x^5*log(x) - 1)/x^5","A",0
1300,1,502,0,4.119426," ","integrate(x^5/(x^5+1),x, algorithm=""fricas"")","\frac{1}{20} \, {\left(\sqrt{5} - 2 \, \sqrt{-\frac{3}{16} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} - \frac{1}{8} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} + 3\right)} {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)} - \frac{3}{16} \, {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} - \frac{1}{2} \, \sqrt{5} - 5 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - \frac{5}{2}} + 1\right)} \log\left(2 \, x - \frac{1}{2} \, \sqrt{5} + \sqrt{-\frac{3}{16} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} - \frac{1}{8} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} + 3\right)} {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)} - \frac{3}{16} \, {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} - \frac{1}{2} \, \sqrt{5} - 5 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - \frac{5}{2}} - \frac{1}{2}\right) + \frac{1}{20} \, {\left(\sqrt{5} + 2 \, \sqrt{-\frac{3}{16} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} - \frac{1}{8} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} + 3\right)} {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)} - \frac{3}{16} \, {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} - \frac{1}{2} \, \sqrt{5} - 5 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - \frac{5}{2}} + 1\right)} \log\left(2 \, x - \frac{1}{2} \, \sqrt{5} - \sqrt{-\frac{3}{16} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} - \frac{1}{8} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} + 3\right)} {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)} - \frac{3}{16} \, {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} - \frac{1}{2} \, \sqrt{5} - 5 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - \frac{5}{2}} - \frac{1}{2}\right) - \frac{1}{20} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)} \log\left(x + \frac{1}{4} \, \sqrt{5} + \frac{5}{2} \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - \frac{1}{4}\right) - \frac{1}{20} \, {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)} \log\left(x + \frac{1}{4} \, \sqrt{5} - \frac{5}{2} \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - \frac{1}{4}\right) + x - \frac{1}{5} \, \log\left(x + 1\right)"," ",0,"1/20*(sqrt(5) - 2*sqrt(-3/16*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 - 1/8*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) + 3)*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1) - 3/16*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 - 1/2*sqrt(5) - 5*sqrt(-1/50*sqrt(5) - 1/10) - 5/2) + 1)*log(2*x - 1/2*sqrt(5) + sqrt(-3/16*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 - 1/8*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) + 3)*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1) - 3/16*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 - 1/2*sqrt(5) - 5*sqrt(-1/50*sqrt(5) - 1/10) - 5/2) - 1/2) + 1/20*(sqrt(5) + 2*sqrt(-3/16*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 - 1/8*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) + 3)*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1) - 3/16*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 - 1/2*sqrt(5) - 5*sqrt(-1/50*sqrt(5) - 1/10) - 5/2) + 1)*log(2*x - 1/2*sqrt(5) - sqrt(-3/16*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 - 1/8*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) + 3)*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1) - 3/16*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 - 1/2*sqrt(5) - 5*sqrt(-1/50*sqrt(5) - 1/10) - 5/2) - 1/2) - 1/20*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)*log(x + 1/4*sqrt(5) + 5/2*sqrt(-1/50*sqrt(5) - 1/10) - 1/4) - 1/20*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)*log(x + 1/4*sqrt(5) - 5/2*sqrt(-1/50*sqrt(5) - 1/10) - 1/4) + x - 1/5*log(x + 1)","B",0
1301,1,905,0,4.310300," ","integrate(x^3/(x^5+1),x, algorithm=""fricas"")","-\frac{1}{20} \, {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)} \log\left(\frac{1}{64} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{3} + \frac{1}{64} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)} {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} + \frac{1}{16} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} + \frac{1}{64} \, {\left({\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} + 4 \, \sqrt{5} + 40 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 4\right)} {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)} + x + \frac{1}{4} \, \sqrt{5} + \frac{5}{2} \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - \frac{1}{4}\right) - \frac{1}{20} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)} \log\left(-\frac{1}{64} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{3} - \frac{1}{16} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} + x - \frac{1}{4} \, \sqrt{5} - \frac{5}{2} \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - \frac{3}{4}\right) + \frac{1}{20} \, {\left(\sqrt{5} + 2 \, \sqrt{-\frac{3}{16} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} - \frac{1}{8} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} + 3\right)} {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)} - \frac{3}{16} \, {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} - \frac{1}{2} \, \sqrt{5} - 5 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - \frac{5}{2}} + 1\right)} \log\left(-\frac{1}{64} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)} {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} + \frac{1}{16} \, \sqrt{-\frac{3}{16} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} - \frac{1}{8} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} + 3\right)} {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)} - \frac{3}{16} \, {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} - \frac{1}{2} \, \sqrt{5} - 5 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - \frac{5}{2}} {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)} {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)} - \frac{1}{64} \, {\left({\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} + 4 \, \sqrt{5} + 40 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 4\right)} {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)} + 2 \, x\right) + \frac{1}{20} \, {\left(\sqrt{5} - 2 \, \sqrt{-\frac{3}{16} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} - \frac{1}{8} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} + 3\right)} {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)} - \frac{3}{16} \, {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} - \frac{1}{2} \, \sqrt{5} - 5 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - \frac{5}{2}} + 1\right)} \log\left(-\frac{1}{64} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)} {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} - \frac{1}{16} \, \sqrt{-\frac{3}{16} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} - \frac{1}{8} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} + 3\right)} {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)} - \frac{3}{16} \, {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} - \frac{1}{2} \, \sqrt{5} - 5 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - \frac{5}{2}} {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)} {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)} - \frac{1}{64} \, {\left({\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} + 4 \, \sqrt{5} + 40 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 4\right)} {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)} + 2 \, x\right) - \frac{1}{5} \, \log\left(x + 1\right)"," ",0,"-1/20*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)*log(1/64*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^3 + 1/64*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 + 1/16*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 + 1/64*((sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 + 4*sqrt(5) + 40*sqrt(-1/50*sqrt(5) - 1/10) - 4)*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1) + x + 1/4*sqrt(5) + 5/2*sqrt(-1/50*sqrt(5) - 1/10) - 1/4) - 1/20*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)*log(-1/64*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^3 - 1/16*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 + x - 1/4*sqrt(5) - 5/2*sqrt(-1/50*sqrt(5) - 1/10) - 3/4) + 1/20*(sqrt(5) + 2*sqrt(-3/16*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 - 1/8*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) + 3)*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1) - 3/16*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 - 1/2*sqrt(5) - 5*sqrt(-1/50*sqrt(5) - 1/10) - 5/2) + 1)*log(-1/64*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 + 1/16*sqrt(-3/16*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 - 1/8*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) + 3)*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1) - 3/16*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 - 1/2*sqrt(5) - 5*sqrt(-1/50*sqrt(5) - 1/10) - 5/2)*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1) - 1/64*((sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 + 4*sqrt(5) + 40*sqrt(-1/50*sqrt(5) - 1/10) - 4)*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1) + 2*x) + 1/20*(sqrt(5) - 2*sqrt(-3/16*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 - 1/8*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) + 3)*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1) - 3/16*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 - 1/2*sqrt(5) - 5*sqrt(-1/50*sqrt(5) - 1/10) - 5/2) + 1)*log(-1/64*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 - 1/16*sqrt(-3/16*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 - 1/8*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) + 3)*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1) - 3/16*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 - 1/2*sqrt(5) - 5*sqrt(-1/50*sqrt(5) - 1/10) - 5/2)*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1) - 1/64*((sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 + 4*sqrt(5) + 40*sqrt(-1/50*sqrt(5) - 1/10) - 4)*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1) + 2*x) - 1/5*log(x + 1)","B",0
1302,1,637,0,4.286757," ","integrate(x^2/(x^5+1),x, algorithm=""fricas"")","-\frac{1}{20} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)} \log\left(\frac{1}{16} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{2} + x\right) + \frac{1}{20} \, {\left(\sqrt{5} + 2 \, \sqrt{-\frac{3}{16} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{2} + \frac{1}{8} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} - 3\right)} {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} - \frac{3}{16} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)}^{2} + \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \frac{1}{2} \, \sqrt{5} - \frac{5}{2}} - 1\right)} \log\left(-\frac{1}{16} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{2} - \frac{1}{16} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)}^{2} + \frac{1}{2} \, \sqrt{-\frac{3}{16} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{2} + \frac{1}{8} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} - 3\right)} {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} - \frac{3}{16} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)}^{2} + \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \frac{1}{2} \, \sqrt{5} - \frac{5}{2}} {\left(\sqrt{5} - 1\right)} + 2 \, x - 1\right) + \frac{1}{20} \, {\left(\sqrt{5} - 2 \, \sqrt{-\frac{3}{16} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{2} + \frac{1}{8} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} - 3\right)} {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} - \frac{3}{16} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)}^{2} + \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \frac{1}{2} \, \sqrt{5} - \frac{5}{2}} - 1\right)} \log\left(-\frac{1}{16} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{2} - \frac{1}{16} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)}^{2} - \frac{1}{2} \, \sqrt{-\frac{3}{16} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{2} + \frac{1}{8} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} - 3\right)} {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} - \frac{3}{16} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)}^{2} + \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \frac{1}{2} \, \sqrt{5} - \frac{5}{2}} {\left(\sqrt{5} - 1\right)} + 2 \, x - 1\right) + \frac{1}{20} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} \log\left(\frac{1}{16} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)}^{2} + x\right) + \frac{1}{5} \, \log\left(x + 1\right)"," ",0,"-1/20*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)*log(1/16*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^2 + x) + 1/20*(sqrt(5) + 2*sqrt(-3/16*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^2 + 1/8*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) - 3)*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1) - 3/16*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)^2 + sqrt(1/2)*sqrt(sqrt(5) - 5) + 1/2*sqrt(5) - 5/2) - 1)*log(-1/16*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^2 - 1/16*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)^2 + 1/2*sqrt(-3/16*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^2 + 1/8*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) - 3)*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1) - 3/16*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)^2 + sqrt(1/2)*sqrt(sqrt(5) - 5) + 1/2*sqrt(5) - 5/2)*(sqrt(5) - 1) + 2*x - 1) + 1/20*(sqrt(5) - 2*sqrt(-3/16*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^2 + 1/8*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) - 3)*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1) - 3/16*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)^2 + sqrt(1/2)*sqrt(sqrt(5) - 5) + 1/2*sqrt(5) - 5/2) - 1)*log(-1/16*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^2 - 1/16*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)^2 - 1/2*sqrt(-3/16*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^2 + 1/8*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) - 3)*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1) - 3/16*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)^2 + sqrt(1/2)*sqrt(sqrt(5) - 5) + 1/2*sqrt(5) - 5/2)*(sqrt(5) - 1) + 2*x - 1) + 1/20*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)*log(1/16*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)^2 + x) + 1/5*log(x + 1)","B",0
1303,1,980,0,3.854089," ","integrate(x/(x^5+1),x, algorithm=""fricas"")","-\frac{1}{20} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)} \log\left(\frac{1}{64} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{3} + x\right) - \frac{1}{20} \, {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)} \log\left(-\frac{1}{64} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{3} - \frac{1}{64} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} + 3\right)} {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} - \frac{1}{16} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} - \frac{1}{64} \, {\left({\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} + 4 \, \sqrt{5} + 40 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} + 12\right)} {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)} + x - \frac{1}{4} \, \sqrt{5} - \frac{5}{2} \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - \frac{3}{4}\right) + \frac{1}{20} \, {\left(\sqrt{5} - 2 \, \sqrt{-\frac{3}{16} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} - \frac{1}{8} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} + 3\right)} {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)} - \frac{3}{16} \, {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} - \frac{1}{2} \, \sqrt{5} - 5 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - \frac{5}{2}} + 1\right)} \log\left(\frac{1}{64} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} + 3\right)} {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} + \frac{1}{16} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} + \frac{1}{64} \, {\left({\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} + 4 \, \sqrt{5} + 40 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} + 12\right)} {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)} + \frac{1}{16} \, \sqrt{-\frac{3}{16} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} - \frac{1}{8} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} + 3\right)} {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)} - \frac{3}{16} \, {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} - \frac{1}{2} \, \sqrt{5} - 5 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - \frac{5}{2}} {\left({\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} + 3\right)} {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)} + 4 \, \sqrt{5} + 40 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 4\right)} + 2 \, x + \frac{1}{4} \, \sqrt{5} + \frac{5}{2} \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - \frac{1}{4}\right) + \frac{1}{20} \, {\left(\sqrt{5} + 2 \, \sqrt{-\frac{3}{16} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} - \frac{1}{8} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} + 3\right)} {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)} - \frac{3}{16} \, {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} - \frac{1}{2} \, \sqrt{5} - 5 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - \frac{5}{2}} + 1\right)} \log\left(\frac{1}{64} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} + 3\right)} {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} + \frac{1}{16} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} + \frac{1}{64} \, {\left({\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} + 4 \, \sqrt{5} + 40 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} + 12\right)} {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)} - \frac{1}{16} \, \sqrt{-\frac{3}{16} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} - \frac{1}{8} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} + 3\right)} {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)} - \frac{3}{16} \, {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} - \frac{1}{2} \, \sqrt{5} - 5 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - \frac{5}{2}} {\left({\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} + 3\right)} {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)} + 4 \, \sqrt{5} + 40 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 4\right)} + 2 \, x + \frac{1}{4} \, \sqrt{5} + \frac{5}{2} \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - \frac{1}{4}\right) - \frac{1}{5} \, \log\left(x + 1\right)"," ",0,"-1/20*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)*log(1/64*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^3 + x) - 1/20*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)*log(-1/64*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^3 - 1/64*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) + 3)*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 - 1/16*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 - 1/64*((sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 + 4*sqrt(5) + 40*sqrt(-1/50*sqrt(5) - 1/10) + 12)*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1) + x - 1/4*sqrt(5) - 5/2*sqrt(-1/50*sqrt(5) - 1/10) - 3/4) + 1/20*(sqrt(5) - 2*sqrt(-3/16*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 - 1/8*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) + 3)*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1) - 3/16*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 - 1/2*sqrt(5) - 5*sqrt(-1/50*sqrt(5) - 1/10) - 5/2) + 1)*log(1/64*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) + 3)*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 + 1/16*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 + 1/64*((sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 + 4*sqrt(5) + 40*sqrt(-1/50*sqrt(5) - 1/10) + 12)*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1) + 1/16*sqrt(-3/16*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 - 1/8*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) + 3)*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1) - 3/16*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 - 1/2*sqrt(5) - 5*sqrt(-1/50*sqrt(5) - 1/10) - 5/2)*((sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) + 3)*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1) + 4*sqrt(5) + 40*sqrt(-1/50*sqrt(5) - 1/10) - 4) + 2*x + 1/4*sqrt(5) + 5/2*sqrt(-1/50*sqrt(5) - 1/10) - 1/4) + 1/20*(sqrt(5) + 2*sqrt(-3/16*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 - 1/8*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) + 3)*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1) - 3/16*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 - 1/2*sqrt(5) - 5*sqrt(-1/50*sqrt(5) - 1/10) - 5/2) + 1)*log(1/64*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) + 3)*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 + 1/16*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 + 1/64*((sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 + 4*sqrt(5) + 40*sqrt(-1/50*sqrt(5) - 1/10) + 12)*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1) - 1/16*sqrt(-3/16*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 - 1/8*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) + 3)*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1) - 3/16*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 - 1/2*sqrt(5) - 5*sqrt(-1/50*sqrt(5) - 1/10) - 5/2)*((sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) + 3)*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1) + 4*sqrt(5) + 40*sqrt(-1/50*sqrt(5) - 1/10) - 4) + 2*x + 1/4*sqrt(5) + 5/2*sqrt(-1/50*sqrt(5) - 1/10) - 1/4) - 1/5*log(x + 1)","B",0
1304,1,539,0,3.866711," ","integrate(1/(x^5+1),x, algorithm=""fricas"")","\frac{1}{20} \, {\left(\sqrt{5} + 2 \, \sqrt{-\frac{3}{16} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{2} + \frac{1}{8} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} - 3\right)} {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} - \frac{3}{16} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)}^{2} + \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \frac{1}{2} \, \sqrt{5} - \frac{5}{2}} - 1\right)} \log\left(2 \, x + \frac{1}{2} \, \sqrt{5} + \sqrt{-\frac{3}{16} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{2} + \frac{1}{8} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} - 3\right)} {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} - \frac{3}{16} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)}^{2} + \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \frac{1}{2} \, \sqrt{5} - \frac{5}{2}} - \frac{1}{2}\right) + \frac{1}{20} \, {\left(\sqrt{5} - 2 \, \sqrt{-\frac{3}{16} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{2} + \frac{1}{8} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} - 3\right)} {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} - \frac{3}{16} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)}^{2} + \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \frac{1}{2} \, \sqrt{5} - \frac{5}{2}} - 1\right)} \log\left(2 \, x + \frac{1}{2} \, \sqrt{5} - \sqrt{-\frac{3}{16} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{2} + \frac{1}{8} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} - 3\right)} {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} - \frac{3}{16} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)}^{2} + \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \frac{1}{2} \, \sqrt{5} - \frac{5}{2}} - \frac{1}{2}\right) + \frac{1}{20} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} \log\left(x + \frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \frac{1}{4} \, \sqrt{5} - \frac{1}{4}\right) - \frac{1}{20} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)} \log\left(x - \frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \frac{1}{4} \, \sqrt{5} - \frac{1}{4}\right) + \frac{1}{5} \, \log\left(x + 1\right)"," ",0,"1/20*(sqrt(5) + 2*sqrt(-3/16*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^2 + 1/8*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) - 3)*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1) - 3/16*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)^2 + sqrt(1/2)*sqrt(sqrt(5) - 5) + 1/2*sqrt(5) - 5/2) - 1)*log(2*x + 1/2*sqrt(5) + sqrt(-3/16*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^2 + 1/8*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) - 3)*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1) - 3/16*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)^2 + sqrt(1/2)*sqrt(sqrt(5) - 5) + 1/2*sqrt(5) - 5/2) - 1/2) + 1/20*(sqrt(5) - 2*sqrt(-3/16*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^2 + 1/8*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) - 3)*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1) - 3/16*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)^2 + sqrt(1/2)*sqrt(sqrt(5) - 5) + 1/2*sqrt(5) - 5/2) - 1)*log(2*x + 1/2*sqrt(5) - sqrt(-3/16*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^2 + 1/8*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) - 3)*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1) - 3/16*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)^2 + sqrt(1/2)*sqrt(sqrt(5) - 5) + 1/2*sqrt(5) - 5/2) - 1/2) + 1/20*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)*log(x + 1/2*sqrt(1/2)*sqrt(sqrt(5) - 5) - 1/4*sqrt(5) - 1/4) - 1/20*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)*log(x - 1/2*sqrt(1/2)*sqrt(sqrt(5) - 5) - 1/4*sqrt(5) - 1/4) + 1/5*log(x + 1)","B",0
1305,1,1073,0,3.804018," ","integrate(1/x^2/(x^5+1),x, algorithm=""fricas"")","-\frac{2 \, x {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)} \log\left(\frac{1}{64} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{3} - \frac{1}{16} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{2} + x + \frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \frac{1}{4} \, \sqrt{5} - \frac{3}{4}\right) - 2 \, x {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} \log\left(-\frac{1}{64} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{3} - \frac{1}{64} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)} {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)}^{2} + \frac{1}{16} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{2} + \frac{1}{64} \, {\left({\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{2} - 8 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - 4 \, \sqrt{5} - 4\right)} {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} + x - \frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \frac{1}{4} \, \sqrt{5} - \frac{1}{4}\right) - {\left(x {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)} - x {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} + 4 \, \sqrt{-\frac{3}{16} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{2} + \frac{1}{8} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} - 3\right)} {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} - \frac{3}{16} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)}^{2} + \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \frac{1}{2} \, \sqrt{5} - \frac{5}{2}} x - 4 \, x\right)} \log\left(\frac{1}{64} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)} {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)}^{2} + \frac{1}{16} \, \sqrt{-\frac{3}{16} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{2} + \frac{1}{8} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} - 3\right)} {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} - \frac{3}{16} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)}^{2} + \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \frac{1}{2} \, \sqrt{5} - \frac{5}{2}} {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)} {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} - \frac{1}{64} \, {\left({\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{2} - 8 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - 4 \, \sqrt{5} - 4\right)} {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} + 2 \, x\right) - {\left(x {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)} - x {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} - 4 \, \sqrt{-\frac{3}{16} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{2} + \frac{1}{8} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} - 3\right)} {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} - \frac{3}{16} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)}^{2} + \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \frac{1}{2} \, \sqrt{5} - \frac{5}{2}} x - 4 \, x\right)} \log\left(\frac{1}{64} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)} {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)}^{2} - \frac{1}{16} \, \sqrt{-\frac{3}{16} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{2} + \frac{1}{8} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} - 3\right)} {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} - \frac{3}{16} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)}^{2} + \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \frac{1}{2} \, \sqrt{5} - \frac{5}{2}} {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)} {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} - \frac{1}{64} \, {\left({\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{2} - 8 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - 4 \, \sqrt{5} - 4\right)} {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} + 2 \, x\right) - 8 \, x \log\left(x + 1\right) + 40}{40 \, x}"," ",0,"-1/40*(2*x*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)*log(1/64*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^3 - 1/16*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^2 + x + 1/2*sqrt(1/2)*sqrt(sqrt(5) - 5) + 1/4*sqrt(5) - 3/4) - 2*x*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)*log(-1/64*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^3 - 1/64*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)^2 + 1/16*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^2 + 1/64*((2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^2 - 8*sqrt(1/2)*sqrt(sqrt(5) - 5) - 4*sqrt(5) - 4)*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1) + x - 1/2*sqrt(1/2)*sqrt(sqrt(5) - 5) - 1/4*sqrt(5) - 1/4) - (x*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1) - x*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1) + 4*sqrt(-3/16*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^2 + 1/8*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) - 3)*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1) - 3/16*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)^2 + sqrt(1/2)*sqrt(sqrt(5) - 5) + 1/2*sqrt(5) - 5/2)*x - 4*x)*log(1/64*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)^2 + 1/16*sqrt(-3/16*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^2 + 1/8*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) - 3)*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1) - 3/16*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)^2 + sqrt(1/2)*sqrt(sqrt(5) - 5) + 1/2*sqrt(5) - 5/2)*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1) - 1/64*((2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^2 - 8*sqrt(1/2)*sqrt(sqrt(5) - 5) - 4*sqrt(5) - 4)*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1) + 2*x) - (x*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1) - x*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1) - 4*sqrt(-3/16*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^2 + 1/8*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) - 3)*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1) - 3/16*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)^2 + sqrt(1/2)*sqrt(sqrt(5) - 5) + 1/2*sqrt(5) - 5/2)*x - 4*x)*log(1/64*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)^2 - 1/16*sqrt(-3/16*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^2 + 1/8*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) - 3)*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1) - 3/16*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)^2 + sqrt(1/2)*sqrt(sqrt(5) - 5) + 1/2*sqrt(5) - 5/2)*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1) - 1/64*((2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^2 - 8*sqrt(1/2)*sqrt(sqrt(5) - 5) - 4*sqrt(5) - 4)*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1) + 2*x) - 8*x*log(x + 1) + 40)/x","B",0
1306,1,692,0,3.701927," ","integrate(1/x^3/(x^5+1),x, algorithm=""fricas"")","-\frac{2 \, x^{2} {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)} \log\left(\frac{1}{16} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} + x\right) + 2 \, x^{2} {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)} \log\left(\frac{1}{16} \, {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} + x\right) + 8 \, x^{2} \log\left(x + 1\right) - {\left(x^{2} {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)} + x^{2} {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)} + 4 \, \sqrt{-\frac{3}{16} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} - \frac{1}{8} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} + 3\right)} {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)} - \frac{3}{16} \, {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} - \frac{1}{2} \, \sqrt{5} - 5 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - \frac{5}{2}} x^{2} + 4 \, x^{2}\right)} \log\left(-\frac{1}{16} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} - \frac{1}{16} \, {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} + \frac{1}{2} \, \sqrt{-\frac{3}{16} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} - \frac{1}{8} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} + 3\right)} {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)} - \frac{3}{16} \, {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} - \frac{1}{2} \, \sqrt{5} - 5 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - \frac{5}{2}} {\left(\sqrt{5} + 1\right)} + 2 \, x - 1\right) - {\left(x^{2} {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)} + x^{2} {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)} - 4 \, \sqrt{-\frac{3}{16} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} - \frac{1}{8} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} + 3\right)} {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)} - \frac{3}{16} \, {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} - \frac{1}{2} \, \sqrt{5} - 5 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - \frac{5}{2}} x^{2} + 4 \, x^{2}\right)} \log\left(-\frac{1}{16} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} - \frac{1}{16} \, {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} - \frac{1}{2} \, \sqrt{-\frac{3}{16} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} - \frac{1}{8} \, {\left(\sqrt{5} + 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} + 3\right)} {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)} - \frac{3}{16} \, {\left(\sqrt{5} - 10 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - 1\right)}^{2} - \frac{1}{2} \, \sqrt{5} - 5 \, \sqrt{-\frac{1}{50} \, \sqrt{5} - \frac{1}{10}} - \frac{5}{2}} {\left(\sqrt{5} + 1\right)} + 2 \, x - 1\right) + 20}{40 \, x^{2}}"," ",0,"-1/40*(2*x^2*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)*log(1/16*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 + x) + 2*x^2*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)*log(1/16*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 + x) + 8*x^2*log(x + 1) - (x^2*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) - 1) + x^2*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1) + 4*sqrt(-3/16*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 - 1/8*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) + 3)*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1) - 3/16*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 - 1/2*sqrt(5) - 5*sqrt(-1/50*sqrt(5) - 1/10) - 5/2)*x^2 + 4*x^2)*log(-1/16*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 - 1/16*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 + 1/2*sqrt(-3/16*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 - 1/8*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) + 3)*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1) - 3/16*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 - 1/2*sqrt(5) - 5*sqrt(-1/50*sqrt(5) - 1/10) - 5/2)*(sqrt(5) + 1) + 2*x - 1) - (x^2*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) - 1) + x^2*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1) - 4*sqrt(-3/16*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 - 1/8*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) + 3)*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1) - 3/16*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 - 1/2*sqrt(5) - 5*sqrt(-1/50*sqrt(5) - 1/10) - 5/2)*x^2 + 4*x^2)*log(-1/16*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 - 1/16*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 - 1/2*sqrt(-3/16*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 - 1/8*(sqrt(5) + 10*sqrt(-1/50*sqrt(5) - 1/10) + 3)*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1) - 3/16*(sqrt(5) - 10*sqrt(-1/50*sqrt(5) - 1/10) - 1)^2 - 1/2*sqrt(5) - 5*sqrt(-1/50*sqrt(5) - 1/10) - 5/2)*(sqrt(5) + 1) + 2*x - 1) + 20)/x^2","B",0
1307,1,1174,0,4.595686," ","integrate(1/x^4/(x^5+1),x, algorithm=""fricas"")","\frac{6 \, x^{3} {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} \log\left(\frac{1}{64} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{3} + \frac{1}{64} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} - 3\right)} {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)}^{2} - \frac{1}{16} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{2} - \frac{1}{64} \, {\left({\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{2} - 8 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - 4 \, \sqrt{5} + 12\right)} {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} + x + \frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \frac{1}{4} \, \sqrt{5} - \frac{3}{4}\right) - 6 \, x^{3} {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)} \log\left(-\frac{1}{64} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{3} + x\right) + 24 \, x^{3} \log\left(x + 1\right) + 3 \, {\left(x^{3} {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)} - x^{3} {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} - 4 \, \sqrt{-\frac{3}{16} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{2} + \frac{1}{8} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} - 3\right)} {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} - \frac{3}{16} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)}^{2} + \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \frac{1}{2} \, \sqrt{5} - \frac{5}{2}} x^{3} - 4 \, x^{3}\right)} \log\left(-\frac{1}{64} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} - 3\right)} {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)}^{2} + \frac{1}{16} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{2} + \frac{1}{64} \, {\left({\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{2} - 8 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - 4 \, \sqrt{5} + 12\right)} {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} + \frac{1}{16} \, \sqrt{-\frac{3}{16} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{2} + \frac{1}{8} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} - 3\right)} {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} - \frac{3}{16} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)}^{2} + \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \frac{1}{2} \, \sqrt{5} - \frac{5}{2}} {\left({\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} - 3\right)} {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} + 8 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + 4 \, \sqrt{5} + 4\right)} + 2 \, x - \frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \frac{1}{4} \, \sqrt{5} - \frac{1}{4}\right) + 3 \, {\left(x^{3} {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)} - x^{3} {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} + 4 \, \sqrt{-\frac{3}{16} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{2} + \frac{1}{8} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} - 3\right)} {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} - \frac{3}{16} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)}^{2} + \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \frac{1}{2} \, \sqrt{5} - \frac{5}{2}} x^{3} - 4 \, x^{3}\right)} \log\left(-\frac{1}{64} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} - 3\right)} {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)}^{2} + \frac{1}{16} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{2} + \frac{1}{64} \, {\left({\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{2} - 8 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - 4 \, \sqrt{5} + 12\right)} {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} - \frac{1}{16} \, \sqrt{-\frac{3}{16} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{2} + \frac{1}{8} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} - 3\right)} {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} - \frac{3}{16} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)}^{2} + \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \frac{1}{2} \, \sqrt{5} - \frac{5}{2}} {\left({\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} - 3\right)} {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} + 8 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + 4 \, \sqrt{5} + 4\right)} + 2 \, x - \frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \frac{1}{4} \, \sqrt{5} - \frac{1}{4}\right) - 40}{120 \, x^{3}}"," ",0,"1/120*(6*x^3*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)*log(1/64*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^3 + 1/64*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) - 3)*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)^2 - 1/16*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^2 - 1/64*((2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^2 - 8*sqrt(1/2)*sqrt(sqrt(5) - 5) - 4*sqrt(5) + 12)*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1) + x + 1/2*sqrt(1/2)*sqrt(sqrt(5) - 5) + 1/4*sqrt(5) - 3/4) - 6*x^3*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)*log(-1/64*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^3 + x) + 24*x^3*log(x + 1) + 3*(x^3*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1) - x^3*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1) - 4*sqrt(-3/16*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^2 + 1/8*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) - 3)*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1) - 3/16*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)^2 + sqrt(1/2)*sqrt(sqrt(5) - 5) + 1/2*sqrt(5) - 5/2)*x^3 - 4*x^3)*log(-1/64*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) - 3)*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)^2 + 1/16*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^2 + 1/64*((2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^2 - 8*sqrt(1/2)*sqrt(sqrt(5) - 5) - 4*sqrt(5) + 12)*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1) + 1/16*sqrt(-3/16*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^2 + 1/8*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) - 3)*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1) - 3/16*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)^2 + sqrt(1/2)*sqrt(sqrt(5) - 5) + 1/2*sqrt(5) - 5/2)*((2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) - 3)*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1) + 8*sqrt(1/2)*sqrt(sqrt(5) - 5) + 4*sqrt(5) + 4) + 2*x - 1/2*sqrt(1/2)*sqrt(sqrt(5) - 5) - 1/4*sqrt(5) - 1/4) + 3*(x^3*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1) - x^3*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1) + 4*sqrt(-3/16*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^2 + 1/8*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) - 3)*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1) - 3/16*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)^2 + sqrt(1/2)*sqrt(sqrt(5) - 5) + 1/2*sqrt(5) - 5/2)*x^3 - 4*x^3)*log(-1/64*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) - 3)*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)^2 + 1/16*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^2 + 1/64*((2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^2 - 8*sqrt(1/2)*sqrt(sqrt(5) - 5) - 4*sqrt(5) + 12)*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1) - 1/16*sqrt(-3/16*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^2 + 1/8*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) - 3)*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1) - 3/16*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)^2 + sqrt(1/2)*sqrt(sqrt(5) - 5) + 1/2*sqrt(5) - 5/2)*((2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) - 3)*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1) + 8*sqrt(1/2)*sqrt(sqrt(5) - 5) + 4*sqrt(5) + 4) + 2*x - 1/2*sqrt(1/2)*sqrt(sqrt(5) - 5) - 1/4*sqrt(5) - 1/4) - 40)/x^3","B",0
1308,1,172,0,2.770491," ","integrate(x^(23/2)/(b*x^5+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, a^{2} \sqrt{b} \log\left(-8 \, b^{2} x^{10} - 8 \, a b x^{5} - 4 \, {\left(2 \, b x^{7} + a x^{2}\right)} \sqrt{b x^{5} + a} \sqrt{b} \sqrt{x} - a^{2}\right) + 4 \, {\left(2 \, b^{2} x^{7} - 3 \, a b x^{2}\right)} \sqrt{b x^{5} + a} \sqrt{x}}{80 \, b^{3}}, -\frac{3 \, a^{2} \sqrt{-b} \arctan\left(\frac{2 \, \sqrt{b x^{5} + a} \sqrt{-b} x^{\frac{5}{2}}}{2 \, b x^{5} + a}\right) - 2 \, {\left(2 \, b^{2} x^{7} - 3 \, a b x^{2}\right)} \sqrt{b x^{5} + a} \sqrt{x}}{40 \, b^{3}}\right]"," ",0,"[1/80*(3*a^2*sqrt(b)*log(-8*b^2*x^10 - 8*a*b*x^5 - 4*(2*b*x^7 + a*x^2)*sqrt(b*x^5 + a)*sqrt(b)*sqrt(x) - a^2) + 4*(2*b^2*x^7 - 3*a*b*x^2)*sqrt(b*x^5 + a)*sqrt(x))/b^3, -1/40*(3*a^2*sqrt(-b)*arctan(2*sqrt(b*x^5 + a)*sqrt(-b)*x^(5/2)/(2*b*x^5 + a)) - 2*(2*b^2*x^7 - 3*a*b*x^2)*sqrt(b*x^5 + a)*sqrt(x))/b^3]","A",0
1309,1,136,0,2.480054," ","integrate(x^(13/2)/(b*x^5+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{b x^{5} + a} b x^{\frac{5}{2}} + a \sqrt{b} \log\left(-8 \, b^{2} x^{10} - 8 \, a b x^{5} + 4 \, {\left(2 \, b x^{7} + a x^{2}\right)} \sqrt{b x^{5} + a} \sqrt{b} \sqrt{x} - a^{2}\right)}{20 \, b^{2}}, \frac{2 \, \sqrt{b x^{5} + a} b x^{\frac{5}{2}} + a \sqrt{-b} \arctan\left(\frac{2 \, \sqrt{b x^{5} + a} \sqrt{-b} x^{\frac{5}{2}}}{2 \, b x^{5} + a}\right)}{10 \, b^{2}}\right]"," ",0,"[1/20*(4*sqrt(b*x^5 + a)*b*x^(5/2) + a*sqrt(b)*log(-8*b^2*x^10 - 8*a*b*x^5 + 4*(2*b*x^7 + a*x^2)*sqrt(b*x^5 + a)*sqrt(b)*sqrt(x) - a^2))/b^2, 1/10*(2*sqrt(b*x^5 + a)*b*x^(5/2) + a*sqrt(-b)*arctan(2*sqrt(b*x^5 + a)*sqrt(-b)*x^(5/2)/(2*b*x^5 + a)))/b^2]","A",0
1310,1,97,0,2.752597," ","integrate(x^(3/2)/(b*x^5+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(-8 \, b^{2} x^{10} - 8 \, a b x^{5} - 4 \, {\left(2 \, b x^{7} + a x^{2}\right)} \sqrt{b x^{5} + a} \sqrt{b} \sqrt{x} - a^{2}\right)}{10 \, \sqrt{b}}, -\frac{\sqrt{-b} \arctan\left(\frac{2 \, \sqrt{b x^{5} + a} \sqrt{-b} x^{\frac{5}{2}}}{2 \, b x^{5} + a}\right)}{5 \, b}\right]"," ",0,"[1/10*log(-8*b^2*x^10 - 8*a*b*x^5 - 4*(2*b*x^7 + a*x^2)*sqrt(b*x^5 + a)*sqrt(b)*sqrt(x) - a^2)/sqrt(b), -1/5*sqrt(-b)*arctan(2*sqrt(b*x^5 + a)*sqrt(-b)*x^(5/2)/(2*b*x^5 + a))/b]","A",0
1311,1,17,0,1.296948," ","integrate(1/x^(7/2)/(b*x^5+a)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{b x^{5} + a}}{5 \, a x^{\frac{5}{2}}}"," ",0,"-2/5*sqrt(b*x^5 + a)/(a*x^(5/2))","A",0
1312,1,27,0,1.102797," ","integrate(1/x^(17/2)/(b*x^5+a)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, b x^{5} - a\right)} \sqrt{b x^{5} + a}}{15 \, a^{2} x^{\frac{15}{2}}}"," ",0,"2/15*(2*b*x^5 - a)*sqrt(b*x^5 + a)/(a^2*x^(15/2))","A",0
1313,1,46,0,1.276418," ","integrate(x^(23/2)/(x^5+1)^(1/2),x, algorithm=""fricas"")","\frac{1}{20} \, {\left(2 \, x^{7} - 3 \, x^{2}\right)} \sqrt{x^{5} + 1} \sqrt{x} + \frac{3}{40} \, \log\left(2 \, x^{5} + 2 \, \sqrt{x^{5} + 1} x^{\frac{5}{2}} + 1\right)"," ",0,"1/20*(2*x^7 - 3*x^2)*sqrt(x^5 + 1)*sqrt(x) + 3/40*log(2*x^5 + 2*sqrt(x^5 + 1)*x^(5/2) + 1)","A",0
1314,1,35,0,1.306665," ","integrate(x^(13/2)/(x^5+1)^(1/2),x, algorithm=""fricas"")","\frac{1}{5} \, \sqrt{x^{5} + 1} x^{\frac{5}{2}} + \frac{1}{10} \, \log\left(-2 \, x^{5} + 2 \, \sqrt{x^{5} + 1} x^{\frac{5}{2}} - 1\right)"," ",0,"1/5*sqrt(x^5 + 1)*x^(5/2) + 1/10*log(-2*x^5 + 2*sqrt(x^5 + 1)*x^(5/2) - 1)","A",0
1315,1,22,0,1.213254," ","integrate(x^(3/2)/(x^5+1)^(1/2),x, algorithm=""fricas"")","\frac{1}{5} \, \log\left(2 \, x^{5} + 2 \, \sqrt{x^{5} + 1} x^{\frac{5}{2}} + 1\right)"," ",0,"1/5*log(2*x^5 + 2*sqrt(x^5 + 1)*x^(5/2) + 1)","B",0
1316,1,12,0,1.071726," ","integrate(1/x^(7/2)/(x^5+1)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{x^{5} + 1}}{5 \, x^{\frac{5}{2}}}"," ",0,"-2/5*sqrt(x^5 + 1)/x^(5/2)","A",0
1317,1,19,0,0.821281," ","integrate(1/x^(17/2)/(x^5+1)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, x^{5} - 1\right)} \sqrt{x^{5} + 1}}{15 \, x^{\frac{15}{2}}}"," ",0,"2/15*(2*x^5 - 1)*sqrt(x^5 + 1)/x^(15/2)","A",0
1318,1,89,0,1.183732," ","integrate(x^8/(b*x^6+a),x, algorithm=""fricas"")","\left[\frac{2 \, x^{3} + \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{6} - 2 \, b x^{3} \sqrt{-\frac{a}{b}} - a}{b x^{6} + a}\right)}{6 \, b}, \frac{x^{3} - \sqrt{\frac{a}{b}} \arctan\left(\frac{b x^{3} \sqrt{\frac{a}{b}}}{a}\right)}{3 \, b}\right]"," ",0,"[1/6*(2*x^3 + sqrt(-a/b)*log((b*x^6 - 2*b*x^3*sqrt(-a/b) - a)/(b*x^6 + a)))/b, 1/3*(x^3 - sqrt(a/b)*arctan(b*x^3*sqrt(a/b)/a))/b]","A",0
1319,1,114,0,1.247454," ","integrate(x^7/(b*x^6+a),x, algorithm=""fricas"")","\frac{6 \, x^{2} + 2 \, \sqrt{3} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} b x^{2} \left(-\frac{a}{b}\right)^{\frac{2}{3}} - \sqrt{3} a}{3 \, a}\right) - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left(x^{4} + x^{2} \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right) + 2 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left(x^{2} - \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}{12 \, b}"," ",0,"1/12*(6*x^2 + 2*sqrt(3)*(-a/b)^(1/3)*arctan(1/3*(2*sqrt(3)*b*x^2*(-a/b)^(2/3) - sqrt(3)*a)/a) - (-a/b)^(1/3)*log(x^4 + x^2*(-a/b)^(1/3) + (-a/b)^(2/3)) + 2*(-a/b)^(1/3)*log(x^2 - (-a/b)^(1/3)))/b","A",0
1320,1,314,0,1.247838," ","integrate(x^6/(b*x^6+a),x, algorithm=""fricas"")","-\frac{4 \, \sqrt{3} b \left(-\frac{a}{b^{7}}\right)^{\frac{1}{6}} \arctan\left(-\frac{2 \, \sqrt{3} b^{6} x \left(-\frac{a}{b^{7}}\right)^{\frac{5}{6}} - 2 \, \sqrt{3} \sqrt{b^{2} \left(-\frac{a}{b^{7}}\right)^{\frac{1}{3}} + b x \left(-\frac{a}{b^{7}}\right)^{\frac{1}{6}} + x^{2}} b^{6} \left(-\frac{a}{b^{7}}\right)^{\frac{5}{6}} - \sqrt{3} a}{3 \, a}\right) + 4 \, \sqrt{3} b \left(-\frac{a}{b^{7}}\right)^{\frac{1}{6}} \arctan\left(-\frac{2 \, \sqrt{3} b^{6} x \left(-\frac{a}{b^{7}}\right)^{\frac{5}{6}} - 2 \, \sqrt{3} \sqrt{b^{2} \left(-\frac{a}{b^{7}}\right)^{\frac{1}{3}} - b x \left(-\frac{a}{b^{7}}\right)^{\frac{1}{6}} + x^{2}} b^{6} \left(-\frac{a}{b^{7}}\right)^{\frac{5}{6}} + \sqrt{3} a}{3 \, a}\right) + b \left(-\frac{a}{b^{7}}\right)^{\frac{1}{6}} \log\left(b^{2} \left(-\frac{a}{b^{7}}\right)^{\frac{1}{3}} + b x \left(-\frac{a}{b^{7}}\right)^{\frac{1}{6}} + x^{2}\right) - b \left(-\frac{a}{b^{7}}\right)^{\frac{1}{6}} \log\left(b^{2} \left(-\frac{a}{b^{7}}\right)^{\frac{1}{3}} - b x \left(-\frac{a}{b^{7}}\right)^{\frac{1}{6}} + x^{2}\right) + 2 \, b \left(-\frac{a}{b^{7}}\right)^{\frac{1}{6}} \log\left(b \left(-\frac{a}{b^{7}}\right)^{\frac{1}{6}} + x\right) - 2 \, b \left(-\frac{a}{b^{7}}\right)^{\frac{1}{6}} \log\left(-b \left(-\frac{a}{b^{7}}\right)^{\frac{1}{6}} + x\right) - 12 \, x}{12 \, b}"," ",0,"-1/12*(4*sqrt(3)*b*(-a/b^7)^(1/6)*arctan(-1/3*(2*sqrt(3)*b^6*x*(-a/b^7)^(5/6) - 2*sqrt(3)*sqrt(b^2*(-a/b^7)^(1/3) + b*x*(-a/b^7)^(1/6) + x^2)*b^6*(-a/b^7)^(5/6) - sqrt(3)*a)/a) + 4*sqrt(3)*b*(-a/b^7)^(1/6)*arctan(-1/3*(2*sqrt(3)*b^6*x*(-a/b^7)^(5/6) - 2*sqrt(3)*sqrt(b^2*(-a/b^7)^(1/3) - b*x*(-a/b^7)^(1/6) + x^2)*b^6*(-a/b^7)^(5/6) + sqrt(3)*a)/a) + b*(-a/b^7)^(1/6)*log(b^2*(-a/b^7)^(1/3) + b*x*(-a/b^7)^(1/6) + x^2) - b*(-a/b^7)^(1/6)*log(b^2*(-a/b^7)^(1/3) - b*x*(-a/b^7)^(1/6) + x^2) + 2*b*(-a/b^7)^(1/6)*log(b*(-a/b^7)^(1/6) + x) - 2*b*(-a/b^7)^(1/6)*log(-b*(-a/b^7)^(1/6) + x) - 12*x)/b","B",0
1321,1,13,0,1.128862," ","integrate(x^5/(b*x^6+a),x, algorithm=""fricas"")","\frac{\log\left(b x^{6} + a\right)}{6 \, b}"," ",0,"1/6*log(b*x^6 + a)/b","A",0
1322,1,348,0,1.271113," ","integrate(x^4/(b*x^6+a),x, algorithm=""fricas"")","-\frac{1}{3} \, \sqrt{3} \left(-\frac{1}{a b^{5}}\right)^{\frac{1}{6}} \arctan\left(-\frac{2}{3} \, \sqrt{3} b x \left(-\frac{1}{a b^{5}}\right)^{\frac{1}{6}} + \frac{2}{3} \, \sqrt{3} \sqrt{a b^{4} x \left(-\frac{1}{a b^{5}}\right)^{\frac{5}{6}} - a b^{3} \left(-\frac{1}{a b^{5}}\right)^{\frac{2}{3}} + x^{2}} b \left(-\frac{1}{a b^{5}}\right)^{\frac{1}{6}} + \frac{1}{3} \, \sqrt{3}\right) - \frac{1}{3} \, \sqrt{3} \left(-\frac{1}{a b^{5}}\right)^{\frac{1}{6}} \arctan\left(-\frac{2}{3} \, \sqrt{3} b x \left(-\frac{1}{a b^{5}}\right)^{\frac{1}{6}} + \frac{2}{3} \, \sqrt{3} \sqrt{-a b^{4} x \left(-\frac{1}{a b^{5}}\right)^{\frac{5}{6}} - a b^{3} \left(-\frac{1}{a b^{5}}\right)^{\frac{2}{3}} + x^{2}} b \left(-\frac{1}{a b^{5}}\right)^{\frac{1}{6}} - \frac{1}{3} \, \sqrt{3}\right) + \frac{1}{12} \, \left(-\frac{1}{a b^{5}}\right)^{\frac{1}{6}} \log\left(a b^{4} x \left(-\frac{1}{a b^{5}}\right)^{\frac{5}{6}} - a b^{3} \left(-\frac{1}{a b^{5}}\right)^{\frac{2}{3}} + x^{2}\right) - \frac{1}{12} \, \left(-\frac{1}{a b^{5}}\right)^{\frac{1}{6}} \log\left(-a b^{4} x \left(-\frac{1}{a b^{5}}\right)^{\frac{5}{6}} - a b^{3} \left(-\frac{1}{a b^{5}}\right)^{\frac{2}{3}} + x^{2}\right) + \frac{1}{6} \, \left(-\frac{1}{a b^{5}}\right)^{\frac{1}{6}} \log\left(a b^{4} \left(-\frac{1}{a b^{5}}\right)^{\frac{5}{6}} + x\right) - \frac{1}{6} \, \left(-\frac{1}{a b^{5}}\right)^{\frac{1}{6}} \log\left(-a b^{4} \left(-\frac{1}{a b^{5}}\right)^{\frac{5}{6}} + x\right)"," ",0,"-1/3*sqrt(3)*(-1/(a*b^5))^(1/6)*arctan(-2/3*sqrt(3)*b*x*(-1/(a*b^5))^(1/6) + 2/3*sqrt(3)*sqrt(a*b^4*x*(-1/(a*b^5))^(5/6) - a*b^3*(-1/(a*b^5))^(2/3) + x^2)*b*(-1/(a*b^5))^(1/6) + 1/3*sqrt(3)) - 1/3*sqrt(3)*(-1/(a*b^5))^(1/6)*arctan(-2/3*sqrt(3)*b*x*(-1/(a*b^5))^(1/6) + 2/3*sqrt(3)*sqrt(-a*b^4*x*(-1/(a*b^5))^(5/6) - a*b^3*(-1/(a*b^5))^(2/3) + x^2)*b*(-1/(a*b^5))^(1/6) - 1/3*sqrt(3)) + 1/12*(-1/(a*b^5))^(1/6)*log(a*b^4*x*(-1/(a*b^5))^(5/6) - a*b^3*(-1/(a*b^5))^(2/3) + x^2) - 1/12*(-1/(a*b^5))^(1/6)*log(-a*b^4*x*(-1/(a*b^5))^(5/6) - a*b^3*(-1/(a*b^5))^(2/3) + x^2) + 1/6*(-1/(a*b^5))^(1/6)*log(a*b^4*(-1/(a*b^5))^(5/6) + x) - 1/6*(-1/(a*b^5))^(1/6)*log(-a*b^4*(-1/(a*b^5))^(5/6) + x)","B",0
1323,1,318,0,1.144081," ","integrate(x^3/(b*x^6+a),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{\frac{1}{3}} a b \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \log\left(\frac{2 \, b^{2} x^{6} - 3 \, \left(-a b^{2}\right)^{\frac{2}{3}} x^{2} - a b + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, \left(-a b^{2}\right)^{\frac{2}{3}} x^{4} + a b x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}}}{b x^{6} + a}\right) + \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} x^{4} + \left(-a b^{2}\right)^{\frac{1}{3}} b x^{2} + \left(-a b^{2}\right)^{\frac{2}{3}}\right) - 2 \, \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b x^{2} - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{12 \, a b^{2}}, \frac{6 \, \sqrt{\frac{1}{3}} a b \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, b x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}}}{b}\right) + \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} x^{4} + \left(-a b^{2}\right)^{\frac{1}{3}} b x^{2} + \left(-a b^{2}\right)^{\frac{2}{3}}\right) - 2 \, \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b x^{2} - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{12 \, a b^{2}}\right]"," ",0,"[1/12*(3*sqrt(1/3)*a*b*sqrt((-a*b^2)^(1/3)/a)*log((2*b^2*x^6 - 3*(-a*b^2)^(2/3)*x^2 - a*b + 3*sqrt(1/3)*(2*(-a*b^2)^(2/3)*x^4 + a*b*x^2 + (-a*b^2)^(1/3)*a)*sqrt((-a*b^2)^(1/3)/a))/(b*x^6 + a)) + (-a*b^2)^(2/3)*log(b^2*x^4 + (-a*b^2)^(1/3)*b*x^2 + (-a*b^2)^(2/3)) - 2*(-a*b^2)^(2/3)*log(b*x^2 - (-a*b^2)^(1/3)))/(a*b^2), 1/12*(6*sqrt(1/3)*a*b*sqrt(-(-a*b^2)^(1/3)/a)*arctan(sqrt(1/3)*(2*b*x^2 + (-a*b^2)^(1/3))*sqrt(-(-a*b^2)^(1/3)/a)/b) + (-a*b^2)^(2/3)*log(b^2*x^4 + (-a*b^2)^(1/3)*b*x^2 + (-a*b^2)^(2/3)) - 2*(-a*b^2)^(2/3)*log(b*x^2 - (-a*b^2)^(1/3)))/(a*b^2)]","A",0
1324,1,72,0,1.168557," ","integrate(x^2/(b*x^6+a),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a b} \log\left(\frac{b x^{6} - 2 \, \sqrt{-a b} x^{3} - a}{b x^{6} + a}\right)}{6 \, a b}, \frac{\sqrt{a b} \arctan\left(\frac{\sqrt{a b} x^{3}}{a}\right)}{3 \, a b}\right]"," ",0,"[-1/6*sqrt(-a*b)*log((b*x^6 - 2*sqrt(-a*b)*x^3 - a)/(b*x^6 + a))/(a*b), 1/3*sqrt(a*b)*arctan(sqrt(a*b)*x^3/a)/(a*b)]","A",0
1325,1,313,0,1.051341," ","integrate(x/(b*x^6+a),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{\frac{1}{3}} a b \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \log\left(\frac{2 \, a b x^{6} - 3 \, \left(a^{2} b\right)^{\frac{1}{3}} a x^{2} - a^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, a b x^{4} + \left(a^{2} b\right)^{\frac{2}{3}} x^{2} - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{b x^{6} + a}\right) - \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{4} - \left(a^{2} b\right)^{\frac{2}{3}} x^{2} + \left(a^{2} b\right)^{\frac{1}{3}} a\right) + 2 \, \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} + \left(a^{2} b\right)^{\frac{2}{3}}\right)}{12 \, a^{2} b}, \frac{6 \, \sqrt{\frac{1}{3}} a b \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(a^{2} b\right)^{\frac{2}{3}} x^{2} - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{a^{2}}\right) - \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{4} - \left(a^{2} b\right)^{\frac{2}{3}} x^{2} + \left(a^{2} b\right)^{\frac{1}{3}} a\right) + 2 \, \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} + \left(a^{2} b\right)^{\frac{2}{3}}\right)}{12 \, a^{2} b}\right]"," ",0,"[1/12*(3*sqrt(1/3)*a*b*sqrt(-(a^2*b)^(1/3)/b)*log((2*a*b*x^6 - 3*(a^2*b)^(1/3)*a*x^2 - a^2 + 3*sqrt(1/3)*(2*a*b*x^4 + (a^2*b)^(2/3)*x^2 - (a^2*b)^(1/3)*a)*sqrt(-(a^2*b)^(1/3)/b))/(b*x^6 + a)) - (a^2*b)^(2/3)*log(a*b*x^4 - (a^2*b)^(2/3)*x^2 + (a^2*b)^(1/3)*a) + 2*(a^2*b)^(2/3)*log(a*b*x^2 + (a^2*b)^(2/3)))/(a^2*b), 1/12*(6*sqrt(1/3)*a*b*sqrt((a^2*b)^(1/3)/b)*arctan(sqrt(1/3)*(2*(a^2*b)^(2/3)*x^2 - (a^2*b)^(1/3)*a)*sqrt((a^2*b)^(1/3)/b)/a^2) - (a^2*b)^(2/3)*log(a*b*x^4 - (a^2*b)^(2/3)*x^2 + (a^2*b)^(1/3)*a) + 2*(a^2*b)^(2/3)*log(a*b*x^2 + (a^2*b)^(2/3)))/(a^2*b)]","A",0
1326,1,334,0,1.206309," ","integrate(1/(b*x^6+a),x, algorithm=""fricas"")","\frac{1}{3} \, \sqrt{3} \left(-\frac{1}{a^{5} b}\right)^{\frac{1}{6}} \arctan\left(-\frac{2}{3} \, \sqrt{3} a^{4} b x \left(-\frac{1}{a^{5} b}\right)^{\frac{5}{6}} + \frac{2}{3} \, \sqrt{3} \sqrt{a^{2} \left(-\frac{1}{a^{5} b}\right)^{\frac{1}{3}} + a x \left(-\frac{1}{a^{5} b}\right)^{\frac{1}{6}} + x^{2}} a^{4} b \left(-\frac{1}{a^{5} b}\right)^{\frac{5}{6}} + \frac{1}{3} \, \sqrt{3}\right) + \frac{1}{3} \, \sqrt{3} \left(-\frac{1}{a^{5} b}\right)^{\frac{1}{6}} \arctan\left(-\frac{2}{3} \, \sqrt{3} a^{4} b x \left(-\frac{1}{a^{5} b}\right)^{\frac{5}{6}} + \frac{2}{3} \, \sqrt{3} \sqrt{a^{2} \left(-\frac{1}{a^{5} b}\right)^{\frac{1}{3}} - a x \left(-\frac{1}{a^{5} b}\right)^{\frac{1}{6}} + x^{2}} a^{4} b \left(-\frac{1}{a^{5} b}\right)^{\frac{5}{6}} - \frac{1}{3} \, \sqrt{3}\right) + \frac{1}{12} \, \left(-\frac{1}{a^{5} b}\right)^{\frac{1}{6}} \log\left(a^{2} \left(-\frac{1}{a^{5} b}\right)^{\frac{1}{3}} + a x \left(-\frac{1}{a^{5} b}\right)^{\frac{1}{6}} + x^{2}\right) - \frac{1}{12} \, \left(-\frac{1}{a^{5} b}\right)^{\frac{1}{6}} \log\left(a^{2} \left(-\frac{1}{a^{5} b}\right)^{\frac{1}{3}} - a x \left(-\frac{1}{a^{5} b}\right)^{\frac{1}{6}} + x^{2}\right) + \frac{1}{6} \, \left(-\frac{1}{a^{5} b}\right)^{\frac{1}{6}} \log\left(a \left(-\frac{1}{a^{5} b}\right)^{\frac{1}{6}} + x\right) - \frac{1}{6} \, \left(-\frac{1}{a^{5} b}\right)^{\frac{1}{6}} \log\left(-a \left(-\frac{1}{a^{5} b}\right)^{\frac{1}{6}} + x\right)"," ",0,"1/3*sqrt(3)*(-1/(a^5*b))^(1/6)*arctan(-2/3*sqrt(3)*a^4*b*x*(-1/(a^5*b))^(5/6) + 2/3*sqrt(3)*sqrt(a^2*(-1/(a^5*b))^(1/3) + a*x*(-1/(a^5*b))^(1/6) + x^2)*a^4*b*(-1/(a^5*b))^(5/6) + 1/3*sqrt(3)) + 1/3*sqrt(3)*(-1/(a^5*b))^(1/6)*arctan(-2/3*sqrt(3)*a^4*b*x*(-1/(a^5*b))^(5/6) + 2/3*sqrt(3)*sqrt(a^2*(-1/(a^5*b))^(1/3) - a*x*(-1/(a^5*b))^(1/6) + x^2)*a^4*b*(-1/(a^5*b))^(5/6) - 1/3*sqrt(3)) + 1/12*(-1/(a^5*b))^(1/6)*log(a^2*(-1/(a^5*b))^(1/3) + a*x*(-1/(a^5*b))^(1/6) + x^2) - 1/12*(-1/(a^5*b))^(1/6)*log(a^2*(-1/(a^5*b))^(1/3) - a*x*(-1/(a^5*b))^(1/6) + x^2) + 1/6*(-1/(a^5*b))^(1/6)*log(a*(-1/(a^5*b))^(1/6) + x) - 1/6*(-1/(a^5*b))^(1/6)*log(-a*(-1/(a^5*b))^(1/6) + x)","B",0
1327,1,18,0,1.115476," ","integrate(1/x/(b*x^6+a),x, algorithm=""fricas"")","-\frac{\log\left(b x^{6} + a\right) - 6 \, \log\left(x\right)}{6 \, a}"," ",0,"-1/6*(log(b*x^6 + a) - 6*log(x))/a","A",0
1328,1,338,0,1.225065," ","integrate(1/x^2/(b*x^6+a),x, algorithm=""fricas"")","\frac{4 \, \sqrt{3} a x \left(-\frac{b}{a^{7}}\right)^{\frac{1}{6}} \arctan\left(-\frac{2}{3} \, \sqrt{3} a x \left(-\frac{b}{a^{7}}\right)^{\frac{1}{6}} + \frac{2}{3} \, \sqrt{3} a \sqrt{-\frac{a^{6} x \left(-\frac{b}{a^{7}}\right)^{\frac{5}{6}} + a^{5} \left(-\frac{b}{a^{7}}\right)^{\frac{2}{3}} - b x^{2}}{b}} \left(-\frac{b}{a^{7}}\right)^{\frac{1}{6}} - \frac{1}{3} \, \sqrt{3}\right) + 4 \, \sqrt{3} a x \left(-\frac{b}{a^{7}}\right)^{\frac{1}{6}} \arctan\left(-\frac{2}{3} \, \sqrt{3} a x \left(-\frac{b}{a^{7}}\right)^{\frac{1}{6}} + \frac{2}{3} \, \sqrt{3} a \sqrt{\frac{a^{6} x \left(-\frac{b}{a^{7}}\right)^{\frac{5}{6}} - a^{5} \left(-\frac{b}{a^{7}}\right)^{\frac{2}{3}} + b x^{2}}{b}} \left(-\frac{b}{a^{7}}\right)^{\frac{1}{6}} + \frac{1}{3} \, \sqrt{3}\right) - a x \left(-\frac{b}{a^{7}}\right)^{\frac{1}{6}} \log\left(a^{6} x \left(-\frac{b}{a^{7}}\right)^{\frac{5}{6}} - a^{5} \left(-\frac{b}{a^{7}}\right)^{\frac{2}{3}} + b x^{2}\right) + a x \left(-\frac{b}{a^{7}}\right)^{\frac{1}{6}} \log\left(-a^{6} x \left(-\frac{b}{a^{7}}\right)^{\frac{5}{6}} - a^{5} \left(-\frac{b}{a^{7}}\right)^{\frac{2}{3}} + b x^{2}\right) - 2 \, a x \left(-\frac{b}{a^{7}}\right)^{\frac{1}{6}} \log\left(a^{6} \left(-\frac{b}{a^{7}}\right)^{\frac{5}{6}} + b x\right) + 2 \, a x \left(-\frac{b}{a^{7}}\right)^{\frac{1}{6}} \log\left(-a^{6} \left(-\frac{b}{a^{7}}\right)^{\frac{5}{6}} + b x\right) - 12}{12 \, a x}"," ",0,"1/12*(4*sqrt(3)*a*x*(-b/a^7)^(1/6)*arctan(-2/3*sqrt(3)*a*x*(-b/a^7)^(1/6) + 2/3*sqrt(3)*a*sqrt(-(a^6*x*(-b/a^7)^(5/6) + a^5*(-b/a^7)^(2/3) - b*x^2)/b)*(-b/a^7)^(1/6) - 1/3*sqrt(3)) + 4*sqrt(3)*a*x*(-b/a^7)^(1/6)*arctan(-2/3*sqrt(3)*a*x*(-b/a^7)^(1/6) + 2/3*sqrt(3)*a*sqrt((a^6*x*(-b/a^7)^(5/6) - a^5*(-b/a^7)^(2/3) + b*x^2)/b)*(-b/a^7)^(1/6) + 1/3*sqrt(3)) - a*x*(-b/a^7)^(1/6)*log(a^6*x*(-b/a^7)^(5/6) - a^5*(-b/a^7)^(2/3) + b*x^2) + a*x*(-b/a^7)^(1/6)*log(-a^6*x*(-b/a^7)^(5/6) - a^5*(-b/a^7)^(2/3) + b*x^2) - 2*a*x*(-b/a^7)^(1/6)*log(a^6*(-b/a^7)^(5/6) + b*x) + 2*a*x*(-b/a^7)^(1/6)*log(-a^6*(-b/a^7)^(5/6) + b*x) - 12)/(a*x)","B",0
1329,1,115,0,1.621561," ","integrate(1/x^3/(b*x^6+a),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} x^{2} \left(\frac{b}{a}\right)^{\frac{1}{3}} \arctan\left(\frac{2}{3} \, \sqrt{3} x^{2} \left(\frac{b}{a}\right)^{\frac{1}{3}} - \frac{1}{3} \, \sqrt{3}\right) + x^{2} \left(\frac{b}{a}\right)^{\frac{1}{3}} \log\left(b x^{4} - a x^{2} \left(\frac{b}{a}\right)^{\frac{2}{3}} + a \left(\frac{b}{a}\right)^{\frac{1}{3}}\right) - 2 \, x^{2} \left(\frac{b}{a}\right)^{\frac{1}{3}} \log\left(b x^{2} + a \left(\frac{b}{a}\right)^{\frac{2}{3}}\right) + 6}{12 \, a x^{2}}"," ",0,"-1/12*(2*sqrt(3)*x^2*(b/a)^(1/3)*arctan(2/3*sqrt(3)*x^2*(b/a)^(1/3) - 1/3*sqrt(3)) + x^2*(b/a)^(1/3)*log(b*x^4 - a*x^2*(b/a)^(2/3) + a*(b/a)^(1/3)) - 2*x^2*(b/a)^(1/3)*log(b*x^2 + a*(b/a)^(2/3)) + 6)/(a*x^2)","A",0
1330,1,90,0,1.149523," ","integrate(1/x^4/(b*x^6+a),x, algorithm=""fricas"")","\left[\frac{x^{3} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{6} - 2 \, a x^{3} \sqrt{-\frac{b}{a}} - a}{b x^{6} + a}\right) - 2}{6 \, a x^{3}}, -\frac{x^{3} \sqrt{\frac{b}{a}} \arctan\left(x^{3} \sqrt{\frac{b}{a}}\right) + 1}{3 \, a x^{3}}\right]"," ",0,"[1/6*(x^3*sqrt(-b/a)*log((b*x^6 - 2*a*x^3*sqrt(-b/a) - a)/(b*x^6 + a)) - 2)/(a*x^3), -1/3*(x^3*sqrt(b/a)*arctan(x^3*sqrt(b/a)) + 1)/(a*x^3)]","A",0
1331,1,128,0,0.921988," ","integrate(x^8/(b*x^6+a)^2,x, algorithm=""fricas"")","\left[-\frac{2 \, a b x^{3} + {\left(b x^{6} + a\right)} \sqrt{-a b} \log\left(\frac{b x^{6} - 2 \, \sqrt{-a b} x^{3} - a}{b x^{6} + a}\right)}{12 \, {\left(a b^{3} x^{6} + a^{2} b^{2}\right)}}, -\frac{a b x^{3} - {\left(b x^{6} + a\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x^{3}}{a}\right)}{6 \, {\left(a b^{3} x^{6} + a^{2} b^{2}\right)}}\right]"," ",0,"[-1/12*(2*a*b*x^3 + (b*x^6 + a)*sqrt(-a*b)*log((b*x^6 - 2*sqrt(-a*b)*x^3 - a)/(b*x^6 + a)))/(a*b^3*x^6 + a^2*b^2), -1/6*(a*b*x^3 - (b*x^6 + a)*sqrt(a*b)*arctan(sqrt(a*b)*x^3/a))/(a*b^3*x^6 + a^2*b^2)]","A",0
1332,1,409,0,1.061096," ","integrate(x^7/(b*x^6+a)^2,x, algorithm=""fricas"")","\left[-\frac{6 \, a^{2} b x^{2} - 3 \, \sqrt{\frac{1}{3}} {\left(a b^{2} x^{6} + a^{2} b\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \log\left(\frac{2 \, a b x^{6} - 3 \, \left(a^{2} b\right)^{\frac{1}{3}} a x^{2} - a^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, a b x^{4} + \left(a^{2} b\right)^{\frac{2}{3}} x^{2} - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{b x^{6} + a}\right) + {\left(b x^{6} + a\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{4} - \left(a^{2} b\right)^{\frac{2}{3}} x^{2} + \left(a^{2} b\right)^{\frac{1}{3}} a\right) - 2 \, {\left(b x^{6} + a\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} + \left(a^{2} b\right)^{\frac{2}{3}}\right)}{36 \, {\left(a^{2} b^{3} x^{6} + a^{3} b^{2}\right)}}, -\frac{6 \, a^{2} b x^{2} - 6 \, \sqrt{\frac{1}{3}} {\left(a b^{2} x^{6} + a^{2} b\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(a^{2} b\right)^{\frac{2}{3}} x^{2} - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{a^{2}}\right) + {\left(b x^{6} + a\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{4} - \left(a^{2} b\right)^{\frac{2}{3}} x^{2} + \left(a^{2} b\right)^{\frac{1}{3}} a\right) - 2 \, {\left(b x^{6} + a\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} + \left(a^{2} b\right)^{\frac{2}{3}}\right)}{36 \, {\left(a^{2} b^{3} x^{6} + a^{3} b^{2}\right)}}\right]"," ",0,"[-1/36*(6*a^2*b*x^2 - 3*sqrt(1/3)*(a*b^2*x^6 + a^2*b)*sqrt(-(a^2*b)^(1/3)/b)*log((2*a*b*x^6 - 3*(a^2*b)^(1/3)*a*x^2 - a^2 + 3*sqrt(1/3)*(2*a*b*x^4 + (a^2*b)^(2/3)*x^2 - (a^2*b)^(1/3)*a)*sqrt(-(a^2*b)^(1/3)/b))/(b*x^6 + a)) + (b*x^6 + a)*(a^2*b)^(2/3)*log(a*b*x^4 - (a^2*b)^(2/3)*x^2 + (a^2*b)^(1/3)*a) - 2*(b*x^6 + a)*(a^2*b)^(2/3)*log(a*b*x^2 + (a^2*b)^(2/3)))/(a^2*b^3*x^6 + a^3*b^2), -1/36*(6*a^2*b*x^2 - 6*sqrt(1/3)*(a*b^2*x^6 + a^2*b)*sqrt((a^2*b)^(1/3)/b)*arctan(sqrt(1/3)*(2*(a^2*b)^(2/3)*x^2 - (a^2*b)^(1/3)*a)*sqrt((a^2*b)^(1/3)/b)/a^2) + (b*x^6 + a)*(a^2*b)^(2/3)*log(a*b*x^4 - (a^2*b)^(2/3)*x^2 + (a^2*b)^(1/3)*a) - 2*(b*x^6 + a)*(a^2*b)^(2/3)*log(a*b*x^2 + (a^2*b)^(2/3)))/(a^2*b^3*x^6 + a^3*b^2)]","A",0
1333,1,443,0,1.203512," ","integrate(x^6/(b*x^6+a)^2,x, algorithm=""fricas"")","\frac{4 \, \sqrt{3} {\left(b^{2} x^{6} + a b\right)} \left(-\frac{1}{a^{5} b^{7}}\right)^{\frac{1}{6}} \arctan\left(-\frac{2}{3} \, \sqrt{3} a^{4} b^{6} x \left(-\frac{1}{a^{5} b^{7}}\right)^{\frac{5}{6}} + \frac{2}{3} \, \sqrt{3} \sqrt{a^{2} b^{2} \left(-\frac{1}{a^{5} b^{7}}\right)^{\frac{1}{3}} + a b x \left(-\frac{1}{a^{5} b^{7}}\right)^{\frac{1}{6}} + x^{2}} a^{4} b^{6} \left(-\frac{1}{a^{5} b^{7}}\right)^{\frac{5}{6}} + \frac{1}{3} \, \sqrt{3}\right) + 4 \, \sqrt{3} {\left(b^{2} x^{6} + a b\right)} \left(-\frac{1}{a^{5} b^{7}}\right)^{\frac{1}{6}} \arctan\left(-\frac{2}{3} \, \sqrt{3} a^{4} b^{6} x \left(-\frac{1}{a^{5} b^{7}}\right)^{\frac{5}{6}} + \frac{2}{3} \, \sqrt{3} \sqrt{a^{2} b^{2} \left(-\frac{1}{a^{5} b^{7}}\right)^{\frac{1}{3}} - a b x \left(-\frac{1}{a^{5} b^{7}}\right)^{\frac{1}{6}} + x^{2}} a^{4} b^{6} \left(-\frac{1}{a^{5} b^{7}}\right)^{\frac{5}{6}} - \frac{1}{3} \, \sqrt{3}\right) + {\left(b^{2} x^{6} + a b\right)} \left(-\frac{1}{a^{5} b^{7}}\right)^{\frac{1}{6}} \log\left(a^{2} b^{2} \left(-\frac{1}{a^{5} b^{7}}\right)^{\frac{1}{3}} + a b x \left(-\frac{1}{a^{5} b^{7}}\right)^{\frac{1}{6}} + x^{2}\right) - {\left(b^{2} x^{6} + a b\right)} \left(-\frac{1}{a^{5} b^{7}}\right)^{\frac{1}{6}} \log\left(a^{2} b^{2} \left(-\frac{1}{a^{5} b^{7}}\right)^{\frac{1}{3}} - a b x \left(-\frac{1}{a^{5} b^{7}}\right)^{\frac{1}{6}} + x^{2}\right) + 2 \, {\left(b^{2} x^{6} + a b\right)} \left(-\frac{1}{a^{5} b^{7}}\right)^{\frac{1}{6}} \log\left(a b \left(-\frac{1}{a^{5} b^{7}}\right)^{\frac{1}{6}} + x\right) - 2 \, {\left(b^{2} x^{6} + a b\right)} \left(-\frac{1}{a^{5} b^{7}}\right)^{\frac{1}{6}} \log\left(-a b \left(-\frac{1}{a^{5} b^{7}}\right)^{\frac{1}{6}} + x\right) - 12 \, x}{72 \, {\left(b^{2} x^{6} + a b\right)}}"," ",0,"1/72*(4*sqrt(3)*(b^2*x^6 + a*b)*(-1/(a^5*b^7))^(1/6)*arctan(-2/3*sqrt(3)*a^4*b^6*x*(-1/(a^5*b^7))^(5/6) + 2/3*sqrt(3)*sqrt(a^2*b^2*(-1/(a^5*b^7))^(1/3) + a*b*x*(-1/(a^5*b^7))^(1/6) + x^2)*a^4*b^6*(-1/(a^5*b^7))^(5/6) + 1/3*sqrt(3)) + 4*sqrt(3)*(b^2*x^6 + a*b)*(-1/(a^5*b^7))^(1/6)*arctan(-2/3*sqrt(3)*a^4*b^6*x*(-1/(a^5*b^7))^(5/6) + 2/3*sqrt(3)*sqrt(a^2*b^2*(-1/(a^5*b^7))^(1/3) - a*b*x*(-1/(a^5*b^7))^(1/6) + x^2)*a^4*b^6*(-1/(a^5*b^7))^(5/6) - 1/3*sqrt(3)) + (b^2*x^6 + a*b)*(-1/(a^5*b^7))^(1/6)*log(a^2*b^2*(-1/(a^5*b^7))^(1/3) + a*b*x*(-1/(a^5*b^7))^(1/6) + x^2) - (b^2*x^6 + a*b)*(-1/(a^5*b^7))^(1/6)*log(a^2*b^2*(-1/(a^5*b^7))^(1/3) - a*b*x*(-1/(a^5*b^7))^(1/6) + x^2) + 2*(b^2*x^6 + a*b)*(-1/(a^5*b^7))^(1/6)*log(a*b*(-1/(a^5*b^7))^(1/6) + x) - 2*(b^2*x^6 + a*b)*(-1/(a^5*b^7))^(1/6)*log(-a*b*(-1/(a^5*b^7))^(1/6) + x) - 12*x)/(b^2*x^6 + a*b)","B",0
1334,1,15,0,1.080609," ","integrate(x^5/(b*x^6+a)^2,x, algorithm=""fricas"")","-\frac{1}{6 \, {\left(b^{2} x^{6} + a b\right)}}"," ",0,"-1/6/(b^2*x^6 + a*b)","A",0
1335,1,450,0,1.302050," ","integrate(x^4/(b*x^6+a)^2,x, algorithm=""fricas"")","\frac{12 \, x^{5} - 4 \, \sqrt{3} {\left(a b x^{6} + a^{2}\right)} \left(-\frac{1}{a^{7} b^{5}}\right)^{\frac{1}{6}} \arctan\left(-\frac{2}{3} \, \sqrt{3} a b x \left(-\frac{1}{a^{7} b^{5}}\right)^{\frac{1}{6}} + \frac{2}{3} \, \sqrt{3} \sqrt{a^{6} b^{4} x \left(-\frac{1}{a^{7} b^{5}}\right)^{\frac{5}{6}} - a^{5} b^{3} \left(-\frac{1}{a^{7} b^{5}}\right)^{\frac{2}{3}} + x^{2}} a b \left(-\frac{1}{a^{7} b^{5}}\right)^{\frac{1}{6}} + \frac{1}{3} \, \sqrt{3}\right) - 4 \, \sqrt{3} {\left(a b x^{6} + a^{2}\right)} \left(-\frac{1}{a^{7} b^{5}}\right)^{\frac{1}{6}} \arctan\left(-\frac{2}{3} \, \sqrt{3} a b x \left(-\frac{1}{a^{7} b^{5}}\right)^{\frac{1}{6}} + \frac{2}{3} \, \sqrt{3} \sqrt{-a^{6} b^{4} x \left(-\frac{1}{a^{7} b^{5}}\right)^{\frac{5}{6}} - a^{5} b^{3} \left(-\frac{1}{a^{7} b^{5}}\right)^{\frac{2}{3}} + x^{2}} a b \left(-\frac{1}{a^{7} b^{5}}\right)^{\frac{1}{6}} - \frac{1}{3} \, \sqrt{3}\right) + {\left(a b x^{6} + a^{2}\right)} \left(-\frac{1}{a^{7} b^{5}}\right)^{\frac{1}{6}} \log\left(a^{6} b^{4} x \left(-\frac{1}{a^{7} b^{5}}\right)^{\frac{5}{6}} - a^{5} b^{3} \left(-\frac{1}{a^{7} b^{5}}\right)^{\frac{2}{3}} + x^{2}\right) - {\left(a b x^{6} + a^{2}\right)} \left(-\frac{1}{a^{7} b^{5}}\right)^{\frac{1}{6}} \log\left(-a^{6} b^{4} x \left(-\frac{1}{a^{7} b^{5}}\right)^{\frac{5}{6}} - a^{5} b^{3} \left(-\frac{1}{a^{7} b^{5}}\right)^{\frac{2}{3}} + x^{2}\right) + 2 \, {\left(a b x^{6} + a^{2}\right)} \left(-\frac{1}{a^{7} b^{5}}\right)^{\frac{1}{6}} \log\left(a^{6} b^{4} \left(-\frac{1}{a^{7} b^{5}}\right)^{\frac{5}{6}} + x\right) - 2 \, {\left(a b x^{6} + a^{2}\right)} \left(-\frac{1}{a^{7} b^{5}}\right)^{\frac{1}{6}} \log\left(-a^{6} b^{4} \left(-\frac{1}{a^{7} b^{5}}\right)^{\frac{5}{6}} + x\right)}{72 \, {\left(a b x^{6} + a^{2}\right)}}"," ",0,"1/72*(12*x^5 - 4*sqrt(3)*(a*b*x^6 + a^2)*(-1/(a^7*b^5))^(1/6)*arctan(-2/3*sqrt(3)*a*b*x*(-1/(a^7*b^5))^(1/6) + 2/3*sqrt(3)*sqrt(a^6*b^4*x*(-1/(a^7*b^5))^(5/6) - a^5*b^3*(-1/(a^7*b^5))^(2/3) + x^2)*a*b*(-1/(a^7*b^5))^(1/6) + 1/3*sqrt(3)) - 4*sqrt(3)*(a*b*x^6 + a^2)*(-1/(a^7*b^5))^(1/6)*arctan(-2/3*sqrt(3)*a*b*x*(-1/(a^7*b^5))^(1/6) + 2/3*sqrt(3)*sqrt(-a^6*b^4*x*(-1/(a^7*b^5))^(5/6) - a^5*b^3*(-1/(a^7*b^5))^(2/3) + x^2)*a*b*(-1/(a^7*b^5))^(1/6) - 1/3*sqrt(3)) + (a*b*x^6 + a^2)*(-1/(a^7*b^5))^(1/6)*log(a^6*b^4*x*(-1/(a^7*b^5))^(5/6) - a^5*b^3*(-1/(a^7*b^5))^(2/3) + x^2) - (a*b*x^6 + a^2)*(-1/(a^7*b^5))^(1/6)*log(-a^6*b^4*x*(-1/(a^7*b^5))^(5/6) - a^5*b^3*(-1/(a^7*b^5))^(2/3) + x^2) + 2*(a*b*x^6 + a^2)*(-1/(a^7*b^5))^(1/6)*log(a^6*b^4*(-1/(a^7*b^5))^(5/6) + x) - 2*(a*b*x^6 + a^2)*(-1/(a^7*b^5))^(1/6)*log(-a^6*b^4*(-1/(a^7*b^5))^(5/6) + x))/(a*b*x^6 + a^2)","B",0
1336,1,416,0,0.793941," ","integrate(x^3/(b*x^6+a)^2,x, algorithm=""fricas"")","\left[\frac{6 \, a b^{2} x^{4} + 3 \, \sqrt{\frac{1}{3}} {\left(a b^{2} x^{6} + a^{2} b\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \log\left(\frac{2 \, b^{2} x^{6} - 3 \, \left(-a b^{2}\right)^{\frac{2}{3}} x^{2} - a b + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, \left(-a b^{2}\right)^{\frac{2}{3}} x^{4} + a b x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}}}{b x^{6} + a}\right) + {\left(b x^{6} + a\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} x^{4} + \left(-a b^{2}\right)^{\frac{1}{3}} b x^{2} + \left(-a b^{2}\right)^{\frac{2}{3}}\right) - 2 \, {\left(b x^{6} + a\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b x^{2} - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{36 \, {\left(a^{2} b^{3} x^{6} + a^{3} b^{2}\right)}}, \frac{6 \, a b^{2} x^{4} + 6 \, \sqrt{\frac{1}{3}} {\left(a b^{2} x^{6} + a^{2} b\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, b x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}}}{b}\right) + {\left(b x^{6} + a\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} x^{4} + \left(-a b^{2}\right)^{\frac{1}{3}} b x^{2} + \left(-a b^{2}\right)^{\frac{2}{3}}\right) - 2 \, {\left(b x^{6} + a\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b x^{2} - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{36 \, {\left(a^{2} b^{3} x^{6} + a^{3} b^{2}\right)}}\right]"," ",0,"[1/36*(6*a*b^2*x^4 + 3*sqrt(1/3)*(a*b^2*x^6 + a^2*b)*sqrt((-a*b^2)^(1/3)/a)*log((2*b^2*x^6 - 3*(-a*b^2)^(2/3)*x^2 - a*b + 3*sqrt(1/3)*(2*(-a*b^2)^(2/3)*x^4 + a*b*x^2 + (-a*b^2)^(1/3)*a)*sqrt((-a*b^2)^(1/3)/a))/(b*x^6 + a)) + (b*x^6 + a)*(-a*b^2)^(2/3)*log(b^2*x^4 + (-a*b^2)^(1/3)*b*x^2 + (-a*b^2)^(2/3)) - 2*(b*x^6 + a)*(-a*b^2)^(2/3)*log(b*x^2 - (-a*b^2)^(1/3)))/(a^2*b^3*x^6 + a^3*b^2), 1/36*(6*a*b^2*x^4 + 6*sqrt(1/3)*(a*b^2*x^6 + a^2*b)*sqrt(-(-a*b^2)^(1/3)/a)*arctan(sqrt(1/3)*(2*b*x^2 + (-a*b^2)^(1/3))*sqrt(-(-a*b^2)^(1/3)/a)/b) + (b*x^6 + a)*(-a*b^2)^(2/3)*log(b^2*x^4 + (-a*b^2)^(1/3)*b*x^2 + (-a*b^2)^(2/3)) - 2*(b*x^6 + a)*(-a*b^2)^(2/3)*log(b*x^2 - (-a*b^2)^(1/3)))/(a^2*b^3*x^6 + a^3*b^2)]","A",0
1337,1,128,0,1.275700," ","integrate(x^2/(b*x^6+a)^2,x, algorithm=""fricas"")","\left[\frac{2 \, a b x^{3} - {\left(b x^{6} + a\right)} \sqrt{-a b} \log\left(\frac{b x^{6} - 2 \, \sqrt{-a b} x^{3} - a}{b x^{6} + a}\right)}{12 \, {\left(a^{2} b^{2} x^{6} + a^{3} b\right)}}, \frac{a b x^{3} + {\left(b x^{6} + a\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x^{3}}{a}\right)}{6 \, {\left(a^{2} b^{2} x^{6} + a^{3} b\right)}}\right]"," ",0,"[1/12*(2*a*b*x^3 - (b*x^6 + a)*sqrt(-a*b)*log((b*x^6 - 2*sqrt(-a*b)*x^3 - a)/(b*x^6 + a)))/(a^2*b^2*x^6 + a^3*b), 1/6*(a*b*x^3 + (b*x^6 + a)*sqrt(a*b)*arctan(sqrt(a*b)*x^3/a))/(a^2*b^2*x^6 + a^3*b)]","A",0
1338,1,407,0,1.193496," ","integrate(x/(b*x^6+a)^2,x, algorithm=""fricas"")","\left[\frac{3 \, a^{2} b x^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(a b^{2} x^{6} + a^{2} b\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \log\left(\frac{2 \, a b x^{6} - 3 \, \left(a^{2} b\right)^{\frac{1}{3}} a x^{2} - a^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, a b x^{4} + \left(a^{2} b\right)^{\frac{2}{3}} x^{2} - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{b x^{6} + a}\right) - {\left(b x^{6} + a\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{4} - \left(a^{2} b\right)^{\frac{2}{3}} x^{2} + \left(a^{2} b\right)^{\frac{1}{3}} a\right) + 2 \, {\left(b x^{6} + a\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} + \left(a^{2} b\right)^{\frac{2}{3}}\right)}{18 \, {\left(a^{3} b^{2} x^{6} + a^{4} b\right)}}, \frac{3 \, a^{2} b x^{2} + 6 \, \sqrt{\frac{1}{3}} {\left(a b^{2} x^{6} + a^{2} b\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(a^{2} b\right)^{\frac{2}{3}} x^{2} - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{a^{2}}\right) - {\left(b x^{6} + a\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{4} - \left(a^{2} b\right)^{\frac{2}{3}} x^{2} + \left(a^{2} b\right)^{\frac{1}{3}} a\right) + 2 \, {\left(b x^{6} + a\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} + \left(a^{2} b\right)^{\frac{2}{3}}\right)}{18 \, {\left(a^{3} b^{2} x^{6} + a^{4} b\right)}}\right]"," ",0,"[1/18*(3*a^2*b*x^2 + 3*sqrt(1/3)*(a*b^2*x^6 + a^2*b)*sqrt(-(a^2*b)^(1/3)/b)*log((2*a*b*x^6 - 3*(a^2*b)^(1/3)*a*x^2 - a^2 + 3*sqrt(1/3)*(2*a*b*x^4 + (a^2*b)^(2/3)*x^2 - (a^2*b)^(1/3)*a)*sqrt(-(a^2*b)^(1/3)/b))/(b*x^6 + a)) - (b*x^6 + a)*(a^2*b)^(2/3)*log(a*b*x^4 - (a^2*b)^(2/3)*x^2 + (a^2*b)^(1/3)*a) + 2*(b*x^6 + a)*(a^2*b)^(2/3)*log(a*b*x^2 + (a^2*b)^(2/3)))/(a^3*b^2*x^6 + a^4*b), 1/18*(3*a^2*b*x^2 + 6*sqrt(1/3)*(a*b^2*x^6 + a^2*b)*sqrt((a^2*b)^(1/3)/b)*arctan(sqrt(1/3)*(2*(a^2*b)^(2/3)*x^2 - (a^2*b)^(1/3)*a)*sqrt((a^2*b)^(1/3)/b)/a^2) - (b*x^6 + a)*(a^2*b)^(2/3)*log(a*b*x^4 - (a^2*b)^(2/3)*x^2 + (a^2*b)^(1/3)*a) + 2*(b*x^6 + a)*(a^2*b)^(2/3)*log(a*b*x^2 + (a^2*b)^(2/3)))/(a^3*b^2*x^6 + a^4*b)]","A",0
1339,1,423,0,1.161934," ","integrate(1/(b*x^6+a)^2,x, algorithm=""fricas"")","\frac{20 \, \sqrt{3} {\left(a b x^{6} + a^{2}\right)} \left(-\frac{1}{a^{11} b}\right)^{\frac{1}{6}} \arctan\left(-\frac{2}{3} \, \sqrt{3} a^{9} b x \left(-\frac{1}{a^{11} b}\right)^{\frac{5}{6}} + \frac{2}{3} \, \sqrt{3} \sqrt{a^{4} \left(-\frac{1}{a^{11} b}\right)^{\frac{1}{3}} + a^{2} x \left(-\frac{1}{a^{11} b}\right)^{\frac{1}{6}} + x^{2}} a^{9} b \left(-\frac{1}{a^{11} b}\right)^{\frac{5}{6}} + \frac{1}{3} \, \sqrt{3}\right) + 20 \, \sqrt{3} {\left(a b x^{6} + a^{2}\right)} \left(-\frac{1}{a^{11} b}\right)^{\frac{1}{6}} \arctan\left(-\frac{2}{3} \, \sqrt{3} a^{9} b x \left(-\frac{1}{a^{11} b}\right)^{\frac{5}{6}} + \frac{2}{3} \, \sqrt{3} \sqrt{a^{4} \left(-\frac{1}{a^{11} b}\right)^{\frac{1}{3}} - a^{2} x \left(-\frac{1}{a^{11} b}\right)^{\frac{1}{6}} + x^{2}} a^{9} b \left(-\frac{1}{a^{11} b}\right)^{\frac{5}{6}} - \frac{1}{3} \, \sqrt{3}\right) + 5 \, {\left(a b x^{6} + a^{2}\right)} \left(-\frac{1}{a^{11} b}\right)^{\frac{1}{6}} \log\left(a^{4} \left(-\frac{1}{a^{11} b}\right)^{\frac{1}{3}} + a^{2} x \left(-\frac{1}{a^{11} b}\right)^{\frac{1}{6}} + x^{2}\right) - 5 \, {\left(a b x^{6} + a^{2}\right)} \left(-\frac{1}{a^{11} b}\right)^{\frac{1}{6}} \log\left(a^{4} \left(-\frac{1}{a^{11} b}\right)^{\frac{1}{3}} - a^{2} x \left(-\frac{1}{a^{11} b}\right)^{\frac{1}{6}} + x^{2}\right) + 10 \, {\left(a b x^{6} + a^{2}\right)} \left(-\frac{1}{a^{11} b}\right)^{\frac{1}{6}} \log\left(a^{2} \left(-\frac{1}{a^{11} b}\right)^{\frac{1}{6}} + x\right) - 10 \, {\left(a b x^{6} + a^{2}\right)} \left(-\frac{1}{a^{11} b}\right)^{\frac{1}{6}} \log\left(-a^{2} \left(-\frac{1}{a^{11} b}\right)^{\frac{1}{6}} + x\right) + 12 \, x}{72 \, {\left(a b x^{6} + a^{2}\right)}}"," ",0,"1/72*(20*sqrt(3)*(a*b*x^6 + a^2)*(-1/(a^11*b))^(1/6)*arctan(-2/3*sqrt(3)*a^9*b*x*(-1/(a^11*b))^(5/6) + 2/3*sqrt(3)*sqrt(a^4*(-1/(a^11*b))^(1/3) + a^2*x*(-1/(a^11*b))^(1/6) + x^2)*a^9*b*(-1/(a^11*b))^(5/6) + 1/3*sqrt(3)) + 20*sqrt(3)*(a*b*x^6 + a^2)*(-1/(a^11*b))^(1/6)*arctan(-2/3*sqrt(3)*a^9*b*x*(-1/(a^11*b))^(5/6) + 2/3*sqrt(3)*sqrt(a^4*(-1/(a^11*b))^(1/3) - a^2*x*(-1/(a^11*b))^(1/6) + x^2)*a^9*b*(-1/(a^11*b))^(5/6) - 1/3*sqrt(3)) + 5*(a*b*x^6 + a^2)*(-1/(a^11*b))^(1/6)*log(a^4*(-1/(a^11*b))^(1/3) + a^2*x*(-1/(a^11*b))^(1/6) + x^2) - 5*(a*b*x^6 + a^2)*(-1/(a^11*b))^(1/6)*log(a^4*(-1/(a^11*b))^(1/3) - a^2*x*(-1/(a^11*b))^(1/6) + x^2) + 10*(a*b*x^6 + a^2)*(-1/(a^11*b))^(1/6)*log(a^2*(-1/(a^11*b))^(1/6) + x) - 10*(a*b*x^6 + a^2)*(-1/(a^11*b))^(1/6)*log(-a^2*(-1/(a^11*b))^(1/6) + x) + 12*x)/(a*b*x^6 + a^2)","B",0
1340,1,47,0,1.115905," ","integrate(1/x/(b*x^6+a)^2,x, algorithm=""fricas"")","-\frac{{\left(b x^{6} + a\right)} \log\left(b x^{6} + a\right) - 6 \, {\left(b x^{6} + a\right)} \log\left(x\right) - a}{6 \, {\left(a^{2} b x^{6} + a^{3}\right)}}"," ",0,"-1/6*((b*x^6 + a)*log(b*x^6 + a) - 6*(b*x^6 + a)*log(x) - a)/(a^2*b*x^6 + a^3)","A",0
1341,1,443,0,1.299378," ","integrate(1/x^2/(b*x^6+a)^2,x, algorithm=""fricas"")","-\frac{84 \, b x^{6} - 28 \, \sqrt{3} {\left(a^{2} b x^{7} + a^{3} x\right)} \left(-\frac{b}{a^{13}}\right)^{\frac{1}{6}} \arctan\left(-\frac{2}{3} \, \sqrt{3} a^{2} x \left(-\frac{b}{a^{13}}\right)^{\frac{1}{6}} + \frac{2}{3} \, \sqrt{3} a^{2} \sqrt{-\frac{a^{11} x \left(-\frac{b}{a^{13}}\right)^{\frac{5}{6}} + a^{9} \left(-\frac{b}{a^{13}}\right)^{\frac{2}{3}} - b x^{2}}{b}} \left(-\frac{b}{a^{13}}\right)^{\frac{1}{6}} - \frac{1}{3} \, \sqrt{3}\right) - 28 \, \sqrt{3} {\left(a^{2} b x^{7} + a^{3} x\right)} \left(-\frac{b}{a^{13}}\right)^{\frac{1}{6}} \arctan\left(-\frac{2}{3} \, \sqrt{3} a^{2} x \left(-\frac{b}{a^{13}}\right)^{\frac{1}{6}} + \frac{2}{3} \, \sqrt{3} a^{2} \sqrt{\frac{a^{11} x \left(-\frac{b}{a^{13}}\right)^{\frac{5}{6}} - a^{9} \left(-\frac{b}{a^{13}}\right)^{\frac{2}{3}} + b x^{2}}{b}} \left(-\frac{b}{a^{13}}\right)^{\frac{1}{6}} + \frac{1}{3} \, \sqrt{3}\right) + 7 \, {\left(a^{2} b x^{7} + a^{3} x\right)} \left(-\frac{b}{a^{13}}\right)^{\frac{1}{6}} \log\left(16807 \, a^{11} x \left(-\frac{b}{a^{13}}\right)^{\frac{5}{6}} - 16807 \, a^{9} \left(-\frac{b}{a^{13}}\right)^{\frac{2}{3}} + 16807 \, b x^{2}\right) - 7 \, {\left(a^{2} b x^{7} + a^{3} x\right)} \left(-\frac{b}{a^{13}}\right)^{\frac{1}{6}} \log\left(-16807 \, a^{11} x \left(-\frac{b}{a^{13}}\right)^{\frac{5}{6}} - 16807 \, a^{9} \left(-\frac{b}{a^{13}}\right)^{\frac{2}{3}} + 16807 \, b x^{2}\right) + 14 \, {\left(a^{2} b x^{7} + a^{3} x\right)} \left(-\frac{b}{a^{13}}\right)^{\frac{1}{6}} \log\left(16807 \, a^{11} \left(-\frac{b}{a^{13}}\right)^{\frac{5}{6}} + 16807 \, b x\right) - 14 \, {\left(a^{2} b x^{7} + a^{3} x\right)} \left(-\frac{b}{a^{13}}\right)^{\frac{1}{6}} \log\left(-16807 \, a^{11} \left(-\frac{b}{a^{13}}\right)^{\frac{5}{6}} + 16807 \, b x\right) + 72 \, a}{72 \, {\left(a^{2} b x^{7} + a^{3} x\right)}}"," ",0,"-1/72*(84*b*x^6 - 28*sqrt(3)*(a^2*b*x^7 + a^3*x)*(-b/a^13)^(1/6)*arctan(-2/3*sqrt(3)*a^2*x*(-b/a^13)^(1/6) + 2/3*sqrt(3)*a^2*sqrt(-(a^11*x*(-b/a^13)^(5/6) + a^9*(-b/a^13)^(2/3) - b*x^2)/b)*(-b/a^13)^(1/6) - 1/3*sqrt(3)) - 28*sqrt(3)*(a^2*b*x^7 + a^3*x)*(-b/a^13)^(1/6)*arctan(-2/3*sqrt(3)*a^2*x*(-b/a^13)^(1/6) + 2/3*sqrt(3)*a^2*sqrt((a^11*x*(-b/a^13)^(5/6) - a^9*(-b/a^13)^(2/3) + b*x^2)/b)*(-b/a^13)^(1/6) + 1/3*sqrt(3)) + 7*(a^2*b*x^7 + a^3*x)*(-b/a^13)^(1/6)*log(16807*a^11*x*(-b/a^13)^(5/6) - 16807*a^9*(-b/a^13)^(2/3) + 16807*b*x^2) - 7*(a^2*b*x^7 + a^3*x)*(-b/a^13)^(1/6)*log(-16807*a^11*x*(-b/a^13)^(5/6) - 16807*a^9*(-b/a^13)^(2/3) + 16807*b*x^2) + 14*(a^2*b*x^7 + a^3*x)*(-b/a^13)^(1/6)*log(16807*a^11*(-b/a^13)^(5/6) + 16807*b*x) - 14*(a^2*b*x^7 + a^3*x)*(-b/a^13)^(1/6)*log(-16807*a^11*(-b/a^13)^(5/6) + 16807*b*x) + 72*a)/(a^2*b*x^7 + a^3*x)","B",0
1342,1,160,0,1.164792," ","integrate(1/x^3/(b*x^6+a)^2,x, algorithm=""fricas"")","-\frac{12 \, b x^{6} + 4 \, \sqrt{3} {\left(b x^{8} + a x^{2}\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}} \arctan\left(\frac{2}{3} \, \sqrt{3} x^{2} \left(\frac{b}{a}\right)^{\frac{1}{3}} - \frac{1}{3} \, \sqrt{3}\right) + 2 \, {\left(b x^{8} + a x^{2}\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}} \log\left(b x^{4} - a x^{2} \left(\frac{b}{a}\right)^{\frac{2}{3}} + a \left(\frac{b}{a}\right)^{\frac{1}{3}}\right) - 4 \, {\left(b x^{8} + a x^{2}\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}} \log\left(b x^{2} + a \left(\frac{b}{a}\right)^{\frac{2}{3}}\right) + 9 \, a}{18 \, {\left(a^{2} b x^{8} + a^{3} x^{2}\right)}}"," ",0,"-1/18*(12*b*x^6 + 4*sqrt(3)*(b*x^8 + a*x^2)*(b/a)^(1/3)*arctan(2/3*sqrt(3)*x^2*(b/a)^(1/3) - 1/3*sqrt(3)) + 2*(b*x^8 + a*x^2)*(b/a)^(1/3)*log(b*x^4 - a*x^2*(b/a)^(2/3) + a*(b/a)^(1/3)) - 4*(b*x^8 + a*x^2)*(b/a)^(1/3)*log(b*x^2 + a*(b/a)^(2/3)) + 9*a)/(a^2*b*x^8 + a^3*x^2)","A",0
1343,1,148,0,1.148691," ","integrate(1/x^4/(b*x^6+a)^2,x, algorithm=""fricas"")","\left[-\frac{6 \, b x^{6} - 3 \, {\left(b x^{9} + a x^{3}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{6} - 2 \, a x^{3} \sqrt{-\frac{b}{a}} - a}{b x^{6} + a}\right) + 4 \, a}{12 \, {\left(a^{2} b x^{9} + a^{3} x^{3}\right)}}, -\frac{3 \, b x^{6} + 3 \, {\left(b x^{9} + a x^{3}\right)} \sqrt{\frac{b}{a}} \arctan\left(x^{3} \sqrt{\frac{b}{a}}\right) + 2 \, a}{6 \, {\left(a^{2} b x^{9} + a^{3} x^{3}\right)}}\right]"," ",0,"[-1/12*(6*b*x^6 - 3*(b*x^9 + a*x^3)*sqrt(-b/a)*log((b*x^6 - 2*a*x^3*sqrt(-b/a) - a)/(b*x^6 + a)) + 4*a)/(a^2*b*x^9 + a^3*x^3), -1/6*(3*b*x^6 + 3*(b*x^9 + a*x^3)*sqrt(b/a)*arctan(x^3*sqrt(b/a)) + 2*a)/(a^2*b*x^9 + a^3*x^3)]","A",0
1344,1,22,0,1.237278," ","integrate(x^8/(-x^6+1),x, algorithm=""fricas"")","-\frac{1}{3} \, x^{3} + \frac{1}{6} \, \log\left(x^{3} + 1\right) - \frac{1}{6} \, \log\left(x^{3} - 1\right)"," ",0,"-1/3*x^3 + 1/6*log(x^3 + 1) - 1/6*log(x^3 - 1)","A",0
1345,1,43,0,1.313803," ","integrate(x^7/(-x^6+1),x, algorithm=""fricas"")","-\frac{1}{2} \, x^{2} + \frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{2} + 1\right)}\right) + \frac{1}{12} \, \log\left(x^{4} + x^{2} + 1\right) - \frac{1}{6} \, \log\left(x^{2} - 1\right)"," ",0,"-1/2*x^2 + 1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^2 + 1)) + 1/12*log(x^4 + x^2 + 1) - 1/6*log(x^2 - 1)","A",0
1346,1,68,0,1.173120," ","integrate(x^6/(-x^6+1),x, algorithm=""fricas"")","\frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + \frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) - x + \frac{1}{12} \, \log\left(x^{2} + x + 1\right) - \frac{1}{12} \, \log\left(x^{2} - x + 1\right) + \frac{1}{6} \, \log\left(x + 1\right) - \frac{1}{6} \, \log\left(x - 1\right)"," ",0,"1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) + 1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) - x + 1/12*log(x^2 + x + 1) - 1/12*log(x^2 - x + 1) + 1/6*log(x + 1) - 1/6*log(x - 1)","A",0
1347,1,8,0,1.110904," ","integrate(x^5/(-x^6+1),x, algorithm=""fricas"")","-\frac{1}{6} \, \log\left(x^{6} - 1\right)"," ",0,"-1/6*log(x^6 - 1)","A",0
1348,1,65,0,1.075065," ","integrate(x^4/(-x^6+1),x, algorithm=""fricas"")","-\frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) - \frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + \frac{1}{12} \, \log\left(x^{2} + x + 1\right) - \frac{1}{12} \, \log\left(x^{2} - x + 1\right) + \frac{1}{6} \, \log\left(x + 1\right) - \frac{1}{6} \, \log\left(x - 1\right)"," ",0,"-1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) - 1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) + 1/12*log(x^2 + x + 1) - 1/12*log(x^2 - x + 1) + 1/6*log(x + 1) - 1/6*log(x - 1)","A",0
1349,1,38,0,1.283080," ","integrate(x^3/(-x^6+1),x, algorithm=""fricas"")","-\frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{2} + 1\right)}\right) + \frac{1}{12} \, \log\left(x^{4} + x^{2} + 1\right) - \frac{1}{6} \, \log\left(x^{2} - 1\right)"," ",0,"-1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^2 + 1)) + 1/12*log(x^4 + x^2 + 1) - 1/6*log(x^2 - 1)","A",0
1350,1,17,0,1.249709," ","integrate(x^2/(-x^6+1),x, algorithm=""fricas"")","\frac{1}{6} \, \log\left(x^{3} + 1\right) - \frac{1}{6} \, \log\left(x^{3} - 1\right)"," ",0,"1/6*log(x^3 + 1) - 1/6*log(x^3 - 1)","B",0
1351,1,38,0,1.213063," ","integrate(x/(-x^6+1),x, algorithm=""fricas"")","\frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{2} + 1\right)}\right) + \frac{1}{12} \, \log\left(x^{4} + x^{2} + 1\right) - \frac{1}{6} \, \log\left(x^{2} - 1\right)"," ",0,"1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^2 + 1)) + 1/12*log(x^4 + x^2 + 1) - 1/6*log(x^2 - 1)","A",0
1352,1,65,0,1.292412," ","integrate(1/(-x^6+1),x, algorithm=""fricas"")","\frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + \frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + \frac{1}{12} \, \log\left(x^{2} + x + 1\right) - \frac{1}{12} \, \log\left(x^{2} - x + 1\right) + \frac{1}{6} \, \log\left(x + 1\right) - \frac{1}{6} \, \log\left(x - 1\right)"," ",0,"1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) + 1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) + 1/12*log(x^2 + x + 1) - 1/12*log(x^2 - x + 1) + 1/6*log(x + 1) - 1/6*log(x - 1)","A",0
1353,1,11,0,1.091433," ","integrate(1/x/(-x^6+1),x, algorithm=""fricas"")","-\frac{1}{6} \, \log\left(x^{6} - 1\right) + \log\left(x\right)"," ",0,"-1/6*log(x^6 - 1) + log(x)","A",0
1354,1,76,0,1.196033," ","integrate(1/x^2/(-x^6+1),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} x \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + 2 \, \sqrt{3} x \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) - x \log\left(x^{2} + x + 1\right) + x \log\left(x^{2} - x + 1\right) - 2 \, x \log\left(x + 1\right) + 2 \, x \log\left(x - 1\right) + 12}{12 \, x}"," ",0,"-1/12*(2*sqrt(3)*x*arctan(1/3*sqrt(3)*(2*x + 1)) + 2*sqrt(3)*x*arctan(1/3*sqrt(3)*(2*x - 1)) - x*log(x^2 + x + 1) + x*log(x^2 - x + 1) - 2*x*log(x + 1) + 2*x*log(x - 1) + 12)/x","A",0
1355,1,53,0,1.691813," ","integrate(1/x^3/(-x^6+1),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} x^{2} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{2} + 1\right)}\right) - x^{2} \log\left(x^{4} + x^{2} + 1\right) + 2 \, x^{2} \log\left(x^{2} - 1\right) + 6}{12 \, x^{2}}"," ",0,"-1/12*(2*sqrt(3)*x^2*arctan(1/3*sqrt(3)*(2*x^2 + 1)) - x^2*log(x^4 + x^2 + 1) + 2*x^2*log(x^2 - 1) + 6)/x^2","A",0
1356,1,28,0,1.159121," ","integrate(1/x^4/(-x^6+1),x, algorithm=""fricas"")","\frac{x^{3} \log\left(x^{3} + 1\right) - x^{3} \log\left(x^{3} - 1\right) - 2}{6 \, x^{3}}"," ",0,"1/6*(x^3*log(x^3 + 1) - x^3*log(x^3 - 1) - 2)/x^3","B",0
1357,1,52,0,1.189032," ","integrate(1/x^5/(-x^6+1),x, algorithm=""fricas"")","\frac{2 \, \sqrt{3} x^{4} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{2} + 1\right)}\right) + x^{4} \log\left(x^{4} + x^{2} + 1\right) - 2 \, x^{4} \log\left(x^{2} - 1\right) - 3}{12 \, x^{4}}"," ",0,"1/12*(2*sqrt(3)*x^4*arctan(1/3*sqrt(3)*(2*x^2 + 1)) + x^4*log(x^4 + x^2 + 1) - 2*x^4*log(x^2 - 1) - 3)/x^4","A",0
1358,1,89,0,1.148121," ","integrate(1/x^6/(-x^6+1),x, algorithm=""fricas"")","\frac{10 \, \sqrt{3} x^{5} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + 10 \, \sqrt{3} x^{5} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + 5 \, x^{5} \log\left(x^{2} + x + 1\right) - 5 \, x^{5} \log\left(x^{2} - x + 1\right) + 10 \, x^{5} \log\left(x + 1\right) - 10 \, x^{5} \log\left(x - 1\right) - 12}{60 \, x^{5}}"," ",0,"1/60*(10*sqrt(3)*x^5*arctan(1/3*sqrt(3)*(2*x + 1)) + 10*sqrt(3)*x^5*arctan(1/3*sqrt(3)*(2*x - 1)) + 5*x^5*log(x^2 + x + 1) - 5*x^5*log(x^2 - x + 1) + 10*x^5*log(x + 1) - 10*x^5*log(x - 1) - 12)/x^5","A",0
1359,1,24,0,1.107909," ","integrate(1/x^7/(-x^6+1),x, algorithm=""fricas"")","-\frac{x^{6} \log\left(x^{6} - 1\right) - 6 \, x^{6} \log\left(x\right) + 1}{6 \, x^{6}}"," ",0,"-1/6*(x^6*log(x^6 - 1) - 6*x^6*log(x) + 1)/x^6","A",0
1360,1,94,0,1.226831," ","integrate(1/x^8/(-x^6+1),x, algorithm=""fricas"")","-\frac{14 \, \sqrt{3} x^{7} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + 14 \, \sqrt{3} x^{7} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) - 7 \, x^{7} \log\left(x^{2} + x + 1\right) + 7 \, x^{7} \log\left(x^{2} - x + 1\right) - 14 \, x^{7} \log\left(x + 1\right) + 14 \, x^{7} \log\left(x - 1\right) + 84 \, x^{6} + 12}{84 \, x^{7}}"," ",0,"-1/84*(14*sqrt(3)*x^7*arctan(1/3*sqrt(3)*(2*x + 1)) + 14*sqrt(3)*x^7*arctan(1/3*sqrt(3)*(2*x - 1)) - 7*x^7*log(x^2 + x + 1) + 7*x^7*log(x^2 - x + 1) - 14*x^7*log(x + 1) + 14*x^7*log(x - 1) + 84*x^6 + 12)/x^7","A",0
1361,1,12,0,1.050309," ","integrate(x^8/(x^6+1),x, algorithm=""fricas"")","\frac{1}{3} \, x^{3} - \frac{1}{3} \, \arctan\left(x^{3}\right)"," ",0,"1/3*x^3 - 1/3*arctan(x^3)","A",0
1362,1,45,0,1.157840," ","integrate(x^7/(x^6+1),x, algorithm=""fricas"")","\frac{1}{2} \, x^{2} - \frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{2} - 1\right)}\right) + \frac{1}{12} \, \log\left(x^{4} - x^{2} + 1\right) - \frac{1}{6} \, \log\left(x^{2} + 1\right)"," ",0,"1/2*x^2 - 1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^2 - 1)) + 1/12*log(x^4 - x^2 + 1) - 1/6*log(x^2 + 1)","A",0
1363,1,90,0,1.217741," ","integrate(x^6/(x^6+1),x, algorithm=""fricas"")","-\frac{1}{12} \, \sqrt{3} \log\left(x^{2} + \sqrt{3} x + 1\right) + \frac{1}{12} \, \sqrt{3} \log\left(x^{2} - \sqrt{3} x + 1\right) + x - \frac{1}{3} \, \arctan\left(x\right) + \frac{1}{3} \, \arctan\left(-2 \, x + \sqrt{3} + 2 \, \sqrt{x^{2} - \sqrt{3} x + 1}\right) + \frac{1}{3} \, \arctan\left(-2 \, x - \sqrt{3} + 2 \, \sqrt{x^{2} + \sqrt{3} x + 1}\right)"," ",0,"-1/12*sqrt(3)*log(x^2 + sqrt(3)*x + 1) + 1/12*sqrt(3)*log(x^2 - sqrt(3)*x + 1) + x - 1/3*arctan(x) + 1/3*arctan(-2*x + sqrt(3) + 2*sqrt(x^2 - sqrt(3)*x + 1)) + 1/3*arctan(-2*x - sqrt(3) + 2*sqrt(x^2 + sqrt(3)*x + 1))","A",0
1364,1,8,0,1.039912," ","integrate(x^5/(x^6+1),x, algorithm=""fricas"")","\frac{1}{6} \, \log\left(x^{6} + 1\right)"," ",0,"1/6*log(x^6 + 1)","A",0
1365,1,89,0,1.332266," ","integrate(x^4/(x^6+1),x, algorithm=""fricas"")","-\frac{1}{12} \, \sqrt{3} \log\left(x^{2} + \sqrt{3} x + 1\right) + \frac{1}{12} \, \sqrt{3} \log\left(x^{2} - \sqrt{3} x + 1\right) + \frac{1}{3} \, \arctan\left(x\right) - \frac{1}{3} \, \arctan\left(-2 \, x + \sqrt{3} + 2 \, \sqrt{x^{2} - \sqrt{3} x + 1}\right) - \frac{1}{3} \, \arctan\left(-2 \, x - \sqrt{3} + 2 \, \sqrt{x^{2} + \sqrt{3} x + 1}\right)"," ",0,"-1/12*sqrt(3)*log(x^2 + sqrt(3)*x + 1) + 1/12*sqrt(3)*log(x^2 - sqrt(3)*x + 1) + 1/3*arctan(x) - 1/3*arctan(-2*x + sqrt(3) + 2*sqrt(x^2 - sqrt(3)*x + 1)) - 1/3*arctan(-2*x - sqrt(3) + 2*sqrt(x^2 + sqrt(3)*x + 1))","A",0
1366,1,40,0,1.245868," ","integrate(x^3/(x^6+1),x, algorithm=""fricas"")","\frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{2} - 1\right)}\right) + \frac{1}{12} \, \log\left(x^{4} - x^{2} + 1\right) - \frac{1}{6} \, \log\left(x^{2} + 1\right)"," ",0,"1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^2 - 1)) + 1/12*log(x^4 - x^2 + 1) - 1/6*log(x^2 + 1)","A",0
1367,1,6,0,1.114192," ","integrate(x^2/(x^6+1),x, algorithm=""fricas"")","\frac{1}{3} \, \arctan\left(x^{3}\right)"," ",0,"1/3*arctan(x^3)","A",0
1368,1,40,0,1.027886," ","integrate(x/(x^6+1),x, algorithm=""fricas"")","\frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{2} - 1\right)}\right) - \frac{1}{12} \, \log\left(x^{4} - x^{2} + 1\right) + \frac{1}{6} \, \log\left(x^{2} + 1\right)"," ",0,"1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^2 - 1)) - 1/12*log(x^4 - x^2 + 1) + 1/6*log(x^2 + 1)","A",0
1369,1,89,0,1.330185," ","integrate(1/(x^6+1),x, algorithm=""fricas"")","\frac{1}{12} \, \sqrt{3} \log\left(x^{2} + \sqrt{3} x + 1\right) - \frac{1}{12} \, \sqrt{3} \log\left(x^{2} - \sqrt{3} x + 1\right) + \frac{1}{3} \, \arctan\left(x\right) - \frac{1}{3} \, \arctan\left(-2 \, x + \sqrt{3} + 2 \, \sqrt{x^{2} - \sqrt{3} x + 1}\right) - \frac{1}{3} \, \arctan\left(-2 \, x - \sqrt{3} + 2 \, \sqrt{x^{2} + \sqrt{3} x + 1}\right)"," ",0,"1/12*sqrt(3)*log(x^2 + sqrt(3)*x + 1) - 1/12*sqrt(3)*log(x^2 - sqrt(3)*x + 1) + 1/3*arctan(x) - 1/3*arctan(-2*x + sqrt(3) + 2*sqrt(x^2 - sqrt(3)*x + 1)) - 1/3*arctan(-2*x - sqrt(3) + 2*sqrt(x^2 + sqrt(3)*x + 1))","A",0
1370,1,11,0,1.119964," ","integrate(1/x/(x^6+1),x, algorithm=""fricas"")","-\frac{1}{6} \, \log\left(x^{6} + 1\right) + \log\left(x\right)"," ",0,"-1/6*log(x^6 + 1) + log(x)","A",0
1371,1,99,0,1.265028," ","integrate(1/x^2/(x^6+1),x, algorithm=""fricas"")","\frac{\sqrt{3} x \log\left(x^{2} + \sqrt{3} x + 1\right) - \sqrt{3} x \log\left(x^{2} - \sqrt{3} x + 1\right) - 4 \, x \arctan\left(x\right) + 4 \, x \arctan\left(-2 \, x + \sqrt{3} + 2 \, \sqrt{x^{2} - \sqrt{3} x + 1}\right) + 4 \, x \arctan\left(-2 \, x - \sqrt{3} + 2 \, \sqrt{x^{2} + \sqrt{3} x + 1}\right) - 12}{12 \, x}"," ",0,"1/12*(sqrt(3)*x*log(x^2 + sqrt(3)*x + 1) - sqrt(3)*x*log(x^2 - sqrt(3)*x + 1) - 4*x*arctan(x) + 4*x*arctan(-2*x + sqrt(3) + 2*sqrt(x^2 - sqrt(3)*x + 1)) + 4*x*arctan(-2*x - sqrt(3) + 2*sqrt(x^2 + sqrt(3)*x + 1)) - 12)/x","A",0
1372,1,54,0,1.092816," ","integrate(1/x^3/(x^6+1),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} x^{2} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{2} - 1\right)}\right) + x^{2} \log\left(x^{4} - x^{2} + 1\right) - 2 \, x^{2} \log\left(x^{2} + 1\right) + 6}{12 \, x^{2}}"," ",0,"-1/12*(2*sqrt(3)*x^2*arctan(1/3*sqrt(3)*(2*x^2 - 1)) + x^2*log(x^4 - x^2 + 1) - 2*x^2*log(x^2 + 1) + 6)/x^2","A",0
1373,1,15,0,0.783684," ","integrate(1/x^4/(x^6+1),x, algorithm=""fricas"")","-\frac{x^{3} \arctan\left(x^{3}\right) + 1}{3 \, x^{3}}"," ",0,"-1/3*(x^3*arctan(x^3) + 1)/x^3","A",0
1374,1,55,0,1.212512," ","integrate(1/x^5/(x^6+1),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} x^{4} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{2} - 1\right)}\right) - x^{4} \log\left(x^{4} - x^{2} + 1\right) + 2 \, x^{4} \log\left(x^{2} + 1\right) + 3}{12 \, x^{4}}"," ",0,"-1/12*(2*sqrt(3)*x^4*arctan(1/3*sqrt(3)*(2*x^2 - 1)) - x^4*log(x^4 - x^2 + 1) + 2*x^4*log(x^2 + 1) + 3)/x^4","A",0
1375,1,110,0,1.213440," ","integrate(1/x^6/(x^6+1),x, algorithm=""fricas"")","-\frac{5 \, \sqrt{3} x^{5} \log\left(x^{2} + \sqrt{3} x + 1\right) - 5 \, \sqrt{3} x^{5} \log\left(x^{2} - \sqrt{3} x + 1\right) + 20 \, x^{5} \arctan\left(x\right) - 20 \, x^{5} \arctan\left(-2 \, x + \sqrt{3} + 2 \, \sqrt{x^{2} - \sqrt{3} x + 1}\right) - 20 \, x^{5} \arctan\left(-2 \, x - \sqrt{3} + 2 \, \sqrt{x^{2} + \sqrt{3} x + 1}\right) + 12}{60 \, x^{5}}"," ",0,"-1/60*(5*sqrt(3)*x^5*log(x^2 + sqrt(3)*x + 1) - 5*sqrt(3)*x^5*log(x^2 - sqrt(3)*x + 1) + 20*x^5*arctan(x) - 20*x^5*arctan(-2*x + sqrt(3) + 2*sqrt(x^2 - sqrt(3)*x + 1)) - 20*x^5*arctan(-2*x - sqrt(3) + 2*sqrt(x^2 + sqrt(3)*x + 1)) + 12)/x^5","A",0
1376,1,24,0,1.091894," ","integrate(1/x^7/(x^6+1),x, algorithm=""fricas"")","\frac{x^{6} \log\left(x^{6} + 1\right) - 6 \, x^{6} \log\left(x\right) - 1}{6 \, x^{6}}"," ",0,"1/6*(x^6*log(x^6 + 1) - 6*x^6*log(x) - 1)/x^6","A",0
1377,1,115,0,1.062143," ","integrate(1/x^8/(x^6+1),x, algorithm=""fricas"")","-\frac{7 \, \sqrt{3} x^{7} \log\left(x^{2} + \sqrt{3} x + 1\right) - 7 \, \sqrt{3} x^{7} \log\left(x^{2} - \sqrt{3} x + 1\right) - 28 \, x^{7} \arctan\left(x\right) + 28 \, x^{7} \arctan\left(-2 \, x + \sqrt{3} + 2 \, \sqrt{x^{2} - \sqrt{3} x + 1}\right) + 28 \, x^{7} \arctan\left(-2 \, x - \sqrt{3} + 2 \, \sqrt{x^{2} + \sqrt{3} x + 1}\right) - 84 \, x^{6} + 12}{84 \, x^{7}}"," ",0,"-1/84*(7*sqrt(3)*x^7*log(x^2 + sqrt(3)*x + 1) - 7*sqrt(3)*x^7*log(x^2 - sqrt(3)*x + 1) - 28*x^7*arctan(x) + 28*x^7*arctan(-2*x + sqrt(3) + 2*sqrt(x^2 - sqrt(3)*x + 1)) + 28*x^7*arctan(-2*x - sqrt(3) + 2*sqrt(x^2 + sqrt(3)*x + 1)) - 84*x^6 + 12)/x^7","A",0
1378,1,169,0,1.141238," ","integrate(1/(-3*x^6+2),x, algorithm=""fricas"")","-\frac{1}{288} \cdot 96^{\frac{5}{6}} \sqrt{3} \arctan\left(-\frac{1}{3} \cdot 96^{\frac{1}{6}} \sqrt{3} x + \frac{1}{12} \cdot 96^{\frac{1}{6}} \sqrt{48 \, x^{2} + 96^{\frac{5}{6}} x + 8 \cdot 12^{\frac{2}{3}}} - \frac{1}{3} \, \sqrt{3}\right) - \frac{1}{288} \cdot 96^{\frac{5}{6}} \sqrt{3} \arctan\left(-\frac{1}{3} \cdot 96^{\frac{1}{6}} \sqrt{3} x + \frac{1}{12} \cdot 96^{\frac{1}{6}} \sqrt{48 \, x^{2} - 96^{\frac{5}{6}} x + 8 \cdot 12^{\frac{2}{3}}} + \frac{1}{3} \, \sqrt{3}\right) + \frac{1}{1152} \cdot 96^{\frac{5}{6}} \log\left(48 \, x^{2} + 96^{\frac{5}{6}} x + 8 \cdot 12^{\frac{2}{3}}\right) - \frac{1}{1152} \cdot 96^{\frac{5}{6}} \log\left(48 \, x^{2} - 96^{\frac{5}{6}} x + 8 \cdot 12^{\frac{2}{3}}\right) + \frac{1}{576} \cdot 96^{\frac{5}{6}} \log\left(48 \, x + 96^{\frac{5}{6}}\right) - \frac{1}{576} \cdot 96^{\frac{5}{6}} \log\left(48 \, x - 96^{\frac{5}{6}}\right)"," ",0,"-1/288*96^(5/6)*sqrt(3)*arctan(-1/3*96^(1/6)*sqrt(3)*x + 1/12*96^(1/6)*sqrt(48*x^2 + 96^(5/6)*x + 8*12^(2/3)) - 1/3*sqrt(3)) - 1/288*96^(5/6)*sqrt(3)*arctan(-1/3*96^(1/6)*sqrt(3)*x + 1/12*96^(1/6)*sqrt(48*x^2 - 96^(5/6)*x + 8*12^(2/3)) + 1/3*sqrt(3)) + 1/1152*96^(5/6)*log(48*x^2 + 96^(5/6)*x + 8*12^(2/3)) - 1/1152*96^(5/6)*log(48*x^2 - 96^(5/6)*x + 8*12^(2/3)) + 1/576*96^(5/6)*log(48*x + 96^(5/6)) - 1/576*96^(5/6)*log(48*x - 96^(5/6))","A",0
1379,1,555,0,1.254393," ","integrate(x^(1/3)/(-x^6+1),x, algorithm=""fricas"")","\frac{1}{3} \, {\left(\sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) - \sin\left(\frac{1}{9} \, \pi\right)\right)} \arctan\left(-\frac{8 \, {\left(2 \, \cos\left(\frac{1}{9} \, \pi\right)^{3} - \cos\left(\frac{1}{9} \, \pi\right)\right)} \sin\left(\frac{1}{9} \, \pi\right) + 2 \, {\left(2 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{2} + 2 \, \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right) - \sqrt{3}\right)} x^{\frac{2}{3}} - 2 \, {\left(2 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{2} + 2 \, \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right) - \sqrt{3}\right)} \sqrt{{\left(2 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right) + 2 \, \cos\left(\frac{1}{9} \, \pi\right)^{2} - 1\right)} x^{\frac{2}{3}} + x^{\frac{4}{3}} + 1} + \sqrt{3}}{16 \, \cos\left(\frac{1}{9} \, \pi\right)^{4} - 16 \, \cos\left(\frac{1}{9} \, \pi\right)^{2} + 3}\right) - \frac{1}{3} \, {\left(\sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) + \sin\left(\frac{1}{9} \, \pi\right)\right)} \arctan\left(\frac{16 \, \cos\left(\frac{1}{9} \, \pi\right)^{2} - 8 \, x^{\frac{2}{3}} + \sqrt{-128 \, {\left(2 \, \cos\left(\frac{1}{9} \, \pi\right)^{2} - 1\right)} x^{\frac{2}{3}} + 64 \, x^{\frac{4}{3}} + 64} - 8}{16 \, \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)}\right) - \frac{1}{12} \, {\left(\sqrt{3} \sin\left(\frac{1}{9} \, \pi\right) + \cos\left(\frac{1}{9} \, \pi\right)\right)} \log\left(64 \, {\left(2 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right) + 2 \, \cos\left(\frac{1}{9} \, \pi\right)^{2} - 1\right)} x^{\frac{2}{3}} + 64 \, x^{\frac{4}{3}} + 64\right) + \frac{1}{6} \, \cos\left(\frac{1}{9} \, \pi\right) \log\left(-16 \, {\left(2 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right) - 2 \, \cos\left(\frac{1}{9} \, \pi\right)^{2} + 1\right)} x^{\frac{2}{3}} + 16 \, x^{\frac{4}{3}} + 16\right) + \frac{1}{12} \, {\left(\sqrt{3} \sin\left(\frac{1}{9} \, \pi\right) - \cos\left(\frac{1}{9} \, \pi\right)\right)} \log\left(-128 \, {\left(2 \, \cos\left(\frac{1}{9} \, \pi\right)^{2} - 1\right)} x^{\frac{2}{3}} + 64 \, x^{\frac{4}{3}} + 64\right) + \frac{2}{3} \, \arctan\left(-\frac{16 \, {\left(2 \, \cos\left(\frac{1}{9} \, \pi\right)^{3} - \cos\left(\frac{1}{9} \, \pi\right)\right)} \sin\left(\frac{1}{9} \, \pi\right) - 4 \, {\left(2 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{2} - 2 \, \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right) - \sqrt{3}\right)} x^{\frac{2}{3}} + {\left(2 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{2} - 2 \, \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right) - \sqrt{3}\right)} \sqrt{-16 \, {\left(2 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right) - 2 \, \cos\left(\frac{1}{9} \, \pi\right)^{2} + 1\right)} x^{\frac{2}{3}} + 16 \, x^{\frac{4}{3}} + 16} - 2 \, \sqrt{3}}{2 \, {\left(16 \, \cos\left(\frac{1}{9} \, \pi\right)^{4} - 16 \, \cos\left(\frac{1}{9} \, \pi\right)^{2} + 3\right)}}\right) \sin\left(\frac{1}{9} \, \pi\right) - \frac{1}{6} \, \sqrt{3} \arctan\left(\frac{2}{3} \, \sqrt{3} x^{\frac{2}{3}} + \frac{1}{3} \, \sqrt{3}\right) + \frac{1}{12} \, \log\left(x^{\frac{4}{3}} + x^{\frac{2}{3}} + 1\right) - \frac{1}{6} \, \log\left(x^{\frac{2}{3}} - 1\right)"," ",0,"1/3*(sqrt(3)*cos(1/9*pi) - sin(1/9*pi))*arctan(-(8*(2*cos(1/9*pi)^3 - cos(1/9*pi))*sin(1/9*pi) + 2*(2*sqrt(3)*cos(1/9*pi)^2 + 2*cos(1/9*pi)*sin(1/9*pi) - sqrt(3))*x^(2/3) - 2*(2*sqrt(3)*cos(1/9*pi)^2 + 2*cos(1/9*pi)*sin(1/9*pi) - sqrt(3))*sqrt((2*sqrt(3)*cos(1/9*pi)*sin(1/9*pi) + 2*cos(1/9*pi)^2 - 1)*x^(2/3) + x^(4/3) + 1) + sqrt(3))/(16*cos(1/9*pi)^4 - 16*cos(1/9*pi)^2 + 3)) - 1/3*(sqrt(3)*cos(1/9*pi) + sin(1/9*pi))*arctan(1/16*(16*cos(1/9*pi)^2 - 8*x^(2/3) + sqrt(-128*(2*cos(1/9*pi)^2 - 1)*x^(2/3) + 64*x^(4/3) + 64) - 8)/(cos(1/9*pi)*sin(1/9*pi))) - 1/12*(sqrt(3)*sin(1/9*pi) + cos(1/9*pi))*log(64*(2*sqrt(3)*cos(1/9*pi)*sin(1/9*pi) + 2*cos(1/9*pi)^2 - 1)*x^(2/3) + 64*x^(4/3) + 64) + 1/6*cos(1/9*pi)*log(-16*(2*sqrt(3)*cos(1/9*pi)*sin(1/9*pi) - 2*cos(1/9*pi)^2 + 1)*x^(2/3) + 16*x^(4/3) + 16) + 1/12*(sqrt(3)*sin(1/9*pi) - cos(1/9*pi))*log(-128*(2*cos(1/9*pi)^2 - 1)*x^(2/3) + 64*x^(4/3) + 64) + 2/3*arctan(-1/2*(16*(2*cos(1/9*pi)^3 - cos(1/9*pi))*sin(1/9*pi) - 4*(2*sqrt(3)*cos(1/9*pi)^2 - 2*cos(1/9*pi)*sin(1/9*pi) - sqrt(3))*x^(2/3) + (2*sqrt(3)*cos(1/9*pi)^2 - 2*cos(1/9*pi)*sin(1/9*pi) - sqrt(3))*sqrt(-16*(2*sqrt(3)*cos(1/9*pi)*sin(1/9*pi) - 2*cos(1/9*pi)^2 + 1)*x^(2/3) + 16*x^(4/3) + 16) - 2*sqrt(3))/(16*cos(1/9*pi)^4 - 16*cos(1/9*pi)^2 + 3))*sin(1/9*pi) - 1/6*sqrt(3)*arctan(2/3*sqrt(3)*x^(2/3) + 1/3*sqrt(3)) + 1/12*log(x^(4/3) + x^(2/3) + 1) - 1/6*log(x^(2/3) - 1)","B",0
1380,1,41,0,1.112564," ","integrate(x^8*(4*x^6-1)^(1/2),x, algorithm=""fricas"")","\frac{1}{96} \, {\left(8 \, x^{9} - x^{3}\right)} \sqrt{4 \, x^{6} - 1} + \frac{1}{192} \, \log\left(-2 \, x^{3} + \sqrt{4 \, x^{6} - 1}\right)"," ",0,"1/96*(8*x^9 - x^3)*sqrt(4*x^6 - 1) + 1/192*log(-2*x^3 + sqrt(4*x^6 - 1))","A",0
1381,1,13,0,0.966811," ","integrate(x^5*(a^6-x^6)^(1/2),x, algorithm=""fricas"")","-\frac{1}{9} \, {\left(a^{6} - x^{6}\right)}^{\frac{3}{2}}"," ",0,"-1/9*(a^6 - x^6)^(3/2)","A",0
1382,1,29,0,1.132121," ","integrate(x^2*(x^6-2)^(1/2),x, algorithm=""fricas"")","\frac{1}{6} \, \sqrt{x^{6} - 2} x^{3} + \frac{1}{3} \, \log\left(-x^{3} + \sqrt{x^{6} - 2}\right)"," ",0,"1/6*sqrt(x^6 - 2)*x^3 + 1/3*log(-x^3 + sqrt(x^6 - 2))","A",0
1383,1,26,0,1.117910," ","integrate(x^23/(x^6+2)^(1/2),x, algorithm=""fricas"")","\frac{1}{105} \, {\left(5 \, x^{18} - 12 \, x^{12} + 32 \, x^{6} - 128\right)} \sqrt{x^{6} + 2}"," ",0,"1/105*(5*x^18 - 12*x^12 + 32*x^6 - 128)*sqrt(x^6 + 2)","A",0
1384,1,21,0,0.772638," ","integrate(x^17/(x^6+2)^(1/2),x, algorithm=""fricas"")","\frac{1}{45} \, {\left(3 \, x^{12} - 8 \, x^{6} + 32\right)} \sqrt{x^{6} + 2}"," ",0,"1/45*(3*x^12 - 8*x^6 + 32)*sqrt(x^6 + 2)","A",0
1385,1,14,0,1.220694," ","integrate(x^11/(x^6+2)^(1/2),x, algorithm=""fricas"")","\frac{1}{9} \, \sqrt{x^{6} + 2} {\left(x^{6} - 4\right)}"," ",0,"1/9*sqrt(x^6 + 2)*(x^6 - 4)","A",0
1386,1,9,0,0.840552," ","integrate(x^5/(x^6+2)^(1/2),x, algorithm=""fricas"")","\frac{1}{3} \, \sqrt{x^{6} + 2}"," ",0,"1/3*sqrt(x^6 + 2)","A",0
1387,1,27,0,1.277410," ","integrate(1/x/(x^6+2)^(1/2),x, algorithm=""fricas"")","\frac{1}{12} \, \sqrt{2} \log\left(\frac{x^{6} - 2 \, \sqrt{2} \sqrt{x^{6} + 2} + 4}{x^{6}}\right)"," ",0,"1/12*sqrt(2)*log((x^6 - 2*sqrt(2)*sqrt(x^6 + 2) + 4)/x^6)","A",0
1388,1,44,0,1.168566," ","integrate(1/x^7/(x^6+2)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} x^{6} \log\left(\frac{x^{6} + 2 \, \sqrt{2} \sqrt{x^{6} + 2} + 4}{x^{6}}\right) - 4 \, \sqrt{x^{6} + 2}}{48 \, x^{6}}"," ",0,"1/48*(sqrt(2)*x^6*log((x^6 + 2*sqrt(2)*sqrt(x^6 + 2) + 4)/x^6) - 4*sqrt(x^6 + 2))/x^6","A",0
1389,1,52,0,1.238200," ","integrate(1/x^13/(x^6+2)^(1/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{2} x^{12} \log\left(\frac{x^{6} - 2 \, \sqrt{2} \sqrt{x^{6} + 2} + 4}{x^{6}}\right) + 4 \, {\left(3 \, x^{6} - 4\right)} \sqrt{x^{6} + 2}}{384 \, x^{12}}"," ",0,"1/384*(3*sqrt(2)*x^12*log((x^6 - 2*sqrt(2)*sqrt(x^6 + 2) + 4)/x^6) + 4*(3*x^6 - 4)*sqrt(x^6 + 2))/x^12","A",0
1390,1,35,0,1.151285," ","integrate(x^14/(x^6+2)^(1/2),x, algorithm=""fricas"")","\frac{1}{12} \, {\left(x^{9} - 3 \, x^{3}\right)} \sqrt{x^{6} + 2} - \frac{1}{2} \, \log\left(-x^{3} + \sqrt{x^{6} + 2}\right)"," ",0,"1/12*(x^9 - 3*x^3)*sqrt(x^6 + 2) - 1/2*log(-x^3 + sqrt(x^6 + 2))","A",0
1391,1,29,0,0.727410," ","integrate(x^8/(x^6+2)^(1/2),x, algorithm=""fricas"")","\frac{1}{6} \, \sqrt{x^{6} + 2} x^{3} + \frac{1}{3} \, \log\left(-x^{3} + \sqrt{x^{6} + 2}\right)"," ",0,"1/6*sqrt(x^6 + 2)*x^3 + 1/3*log(-x^3 + sqrt(x^6 + 2))","A",0
1392,1,16,0,1.144561," ","integrate(x^2/(x^6+2)^(1/2),x, algorithm=""fricas"")","-\frac{1}{3} \, \log\left(-x^{3} + \sqrt{x^{6} + 2}\right)"," ",0,"-1/3*log(-x^3 + sqrt(x^6 + 2))","A",0
1393,1,16,0,1.201907," ","integrate(1/x^4/(x^6+2)^(1/2),x, algorithm=""fricas"")","-\frac{x^{3} + \sqrt{x^{6} + 2}}{6 \, x^{3}}"," ",0,"-1/6*(x^3 + sqrt(x^6 + 2))/x^3","A",0
1394,1,22,0,0.968263," ","integrate(1/x^10/(x^6+2)^(1/2),x, algorithm=""fricas"")","\frac{x^{9} + \sqrt{x^{6} + 2} {\left(x^{6} - 1\right)}}{18 \, x^{9}}"," ",0,"1/18*(x^9 + sqrt(x^6 + 2)*(x^6 - 1))/x^9","A",0
1395,1,31,0,0.706744," ","integrate(1/x^16/(x^6+2)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, x^{15} + {\left(2 \, x^{12} - 2 \, x^{6} + 3\right)} \sqrt{x^{6} + 2}}{90 \, x^{15}}"," ",0,"-1/90*(2*x^15 + (2*x^12 - 2*x^6 + 3)*sqrt(x^6 + 2))/x^15","A",0
1396,0,0,0,1.370584," ","integrate(x^7/(x^6+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{7}}{\sqrt{x^{6} + 2}}, x\right)"," ",0,"integral(x^7/sqrt(x^6 + 2), x)","F",0
1397,0,0,0,0.750362," ","integrate(x/(x^6+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{\sqrt{x^{6} + 2}}, x\right)"," ",0,"integral(x/sqrt(x^6 + 2), x)","F",0
1398,0,0,0,1.115038," ","integrate(1/x^5/(x^6+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{6} + 2}}{x^{11} + 2 \, x^{5}}, x\right)"," ",0,"integral(sqrt(x^6 + 2)/(x^11 + 2*x^5), x)","F",0
1399,0,0,0,1.144195," ","integrate(x^6/(x^6+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{6}}{\sqrt{x^{6} + 2}}, x\right)"," ",0,"integral(x^6/sqrt(x^6 + 2), x)","F",0
1400,0,0,0,1.179421," ","integrate(1/(x^6+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{x^{6} + 2}}, x\right)"," ",0,"integral(1/sqrt(x^6 + 2), x)","F",0
1401,0,0,0,1.215678," ","integrate(1/x^6/(x^6+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{6} + 2}}{x^{12} + 2 \, x^{6}}, x\right)"," ",0,"integral(sqrt(x^6 + 2)/(x^12 + 2*x^6), x)","F",0
1402,0,0,0,1.297554," ","integrate(x^9/(x^6+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{9}}{\sqrt{x^{6} + 2}}, x\right)"," ",0,"integral(x^9/sqrt(x^6 + 2), x)","F",0
1403,0,0,0,1.075011," ","integrate(x^3/(x^6+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3}}{\sqrt{x^{6} + 2}}, x\right)"," ",0,"integral(x^3/sqrt(x^6 + 2), x)","F",0
1404,0,0,0,1.095356," ","integrate(1/x^3/(x^6+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{6} + 2}}{x^{9} + 2 \, x^{3}}, x\right)"," ",0,"integral(sqrt(x^6 + 2)/(x^9 + 2*x^3), x)","F",0
1405,0,0,0,0.659460," ","integrate(x^10/(x^6+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{10}}{\sqrt{x^{6} + 2}}, x\right)"," ",0,"integral(x^10/sqrt(x^6 + 2), x)","F",0
1406,0,0,0,1.179360," ","integrate(x^4/(x^6+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{4}}{\sqrt{x^{6} + 2}}, x\right)"," ",0,"integral(x^4/sqrt(x^6 + 2), x)","F",0
1407,0,0,0,0.969009," ","integrate(1/x^2/(x^6+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{6} + 2}}{x^{8} + 2 \, x^{2}}, x\right)"," ",0,"integral(sqrt(x^6 + 2)/(x^8 + 2*x^2), x)","F",0
1408,1,24,0,1.276215," ","integrate(x^23/(x^6+2)^(3/2),x, algorithm=""fricas"")","\frac{x^{18} - 4 \, x^{12} + 32 \, x^{6} + 128}{15 \, \sqrt{x^{6} + 2}}"," ",0,"1/15*(x^18 - 4*x^12 + 32*x^6 + 128)/sqrt(x^6 + 2)","A",0
1409,1,19,0,0.572302," ","integrate(x^17/(x^6+2)^(3/2),x, algorithm=""fricas"")","\frac{x^{12} - 8 \, x^{6} - 32}{9 \, \sqrt{x^{6} + 2}}"," ",0,"1/9*(x^12 - 8*x^6 - 32)/sqrt(x^6 + 2)","A",0
1410,1,14,0,1.040904," ","integrate(x^11/(x^6+2)^(3/2),x, algorithm=""fricas"")","\frac{x^{6} + 4}{3 \, \sqrt{x^{6} + 2}}"," ",0,"1/3*(x^6 + 4)/sqrt(x^6 + 2)","A",0
1411,1,9,0,0.894229," ","integrate(x^5/(x^6+2)^(3/2),x, algorithm=""fricas"")","-\frac{1}{3 \, \sqrt{x^{6} + 2}}"," ",0,"-1/3/sqrt(x^6 + 2)","A",0
1412,1,50,0,1.248368," ","integrate(1/x/(x^6+2)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(x^{6} + 2\right)} \log\left(\frac{x^{6} - 2 \, \sqrt{2} \sqrt{x^{6} + 2} + 4}{x^{6}}\right) + 4 \, \sqrt{x^{6} + 2}}{24 \, {\left(x^{6} + 2\right)}}"," ",0,"1/24*(sqrt(2)*(x^6 + 2)*log((x^6 - 2*sqrt(2)*sqrt(x^6 + 2) + 4)/x^6) + 4*sqrt(x^6 + 2))/(x^6 + 2)","A",0
1413,1,66,0,0.615803," ","integrate(1/x^7/(x^6+2)^(3/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{2} {\left(x^{12} + 2 \, x^{6}\right)} \log\left(\frac{x^{6} + 2 \, \sqrt{2} \sqrt{x^{6} + 2} + 4}{x^{6}}\right) - 4 \, {\left(3 \, x^{6} + 2\right)} \sqrt{x^{6} + 2}}{96 \, {\left(x^{12} + 2 \, x^{6}\right)}}"," ",0,"1/96*(3*sqrt(2)*(x^12 + 2*x^6)*log((x^6 + 2*sqrt(2)*sqrt(x^6 + 2) + 4)/x^6) - 4*(3*x^6 + 2)*sqrt(x^6 + 2))/(x^12 + 2*x^6)","A",0
1414,1,71,0,1.147416," ","integrate(1/x^13/(x^6+2)^(3/2),x, algorithm=""fricas"")","\frac{15 \, \sqrt{2} {\left(x^{18} + 2 \, x^{12}\right)} \log\left(\frac{x^{6} - 2 \, \sqrt{2} \sqrt{x^{6} + 2} + 4}{x^{6}}\right) + 4 \, {\left(15 \, x^{12} + 10 \, x^{6} - 8\right)} \sqrt{x^{6} + 2}}{768 \, {\left(x^{18} + 2 \, x^{12}\right)}}"," ",0,"1/768*(15*sqrt(2)*(x^18 + 2*x^12)*log((x^6 - 2*sqrt(2)*sqrt(x^6 + 2) + 4)/x^6) + 4*(15*x^12 + 10*x^6 - 8)*sqrt(x^6 + 2))/(x^18 + 2*x^12)","A",0
1415,1,54,0,0.758795," ","integrate(x^14/(x^6+2)^(3/2),x, algorithm=""fricas"")","\frac{4 \, x^{6} + 6 \, {\left(x^{6} + 2\right)} \log\left(-x^{3} + \sqrt{x^{6} + 2}\right) + {\left(x^{9} + 6 \, x^{3}\right)} \sqrt{x^{6} + 2} + 8}{6 \, {\left(x^{6} + 2\right)}}"," ",0,"1/6*(4*x^6 + 6*(x^6 + 2)*log(-x^3 + sqrt(x^6 + 2)) + (x^9 + 6*x^3)*sqrt(x^6 + 2) + 8)/(x^6 + 2)","A",0
1416,1,45,0,1.105525," ","integrate(x^8/(x^6+2)^(3/2),x, algorithm=""fricas"")","-\frac{x^{6} + \sqrt{x^{6} + 2} x^{3} + {\left(x^{6} + 2\right)} \log\left(-x^{3} + \sqrt{x^{6} + 2}\right) + 2}{3 \, {\left(x^{6} + 2\right)}}"," ",0,"-1/3*(x^6 + sqrt(x^6 + 2)*x^3 + (x^6 + 2)*log(-x^3 + sqrt(x^6 + 2)) + 2)/(x^6 + 2)","A",0
1417,1,25,0,1.218151," ","integrate(x^2/(x^6+2)^(3/2),x, algorithm=""fricas"")","\frac{x^{6} + \sqrt{x^{6} + 2} x^{3} + 2}{6 \, {\left(x^{6} + 2\right)}}"," ",0,"1/6*(x^6 + sqrt(x^6 + 2)*x^3 + 2)/(x^6 + 2)","B",0
1418,1,35,0,1.090498," ","integrate(1/x^4/(x^6+2)^(3/2),x, algorithm=""fricas"")","-\frac{x^{9} + 2 \, x^{3} + \sqrt{x^{6} + 2} {\left(x^{6} + 1\right)}}{6 \, {\left(x^{9} + 2 \, x^{3}\right)}}"," ",0,"-1/6*(x^9 + 2*x^3 + sqrt(x^6 + 2)*(x^6 + 1))/(x^9 + 2*x^3)","A",0
1419,1,44,0,0.986254," ","integrate(1/x^10/(x^6+2)^(3/2),x, algorithm=""fricas"")","\frac{2 \, x^{15} + 4 \, x^{9} + {\left(2 \, x^{12} + 2 \, x^{6} - 1\right)} \sqrt{x^{6} + 2}}{18 \, {\left(x^{15} + 2 \, x^{9}\right)}}"," ",0,"1/18*(2*x^15 + 4*x^9 + (2*x^12 + 2*x^6 - 1)*sqrt(x^6 + 2))/(x^15 + 2*x^9)","A",0
1420,0,0,0,1.269835," ","integrate(x^13/(x^6+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{6} + 2} x^{13}}{x^{12} + 4 \, x^{6} + 4}, x\right)"," ",0,"integral(sqrt(x^6 + 2)*x^13/(x^12 + 4*x^6 + 4), x)","F",0
1421,0,0,0,1.353152," ","integrate(x^7/(x^6+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{6} + 2} x^{7}}{x^{12} + 4 \, x^{6} + 4}, x\right)"," ",0,"integral(sqrt(x^6 + 2)*x^7/(x^12 + 4*x^6 + 4), x)","F",0
1422,0,0,0,1.264980," ","integrate(x/(x^6+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{6} + 2} x}{x^{12} + 4 \, x^{6} + 4}, x\right)"," ",0,"integral(sqrt(x^6 + 2)*x/(x^12 + 4*x^6 + 4), x)","F",0
1423,0,0,0,0.976621," ","integrate(1/x^5/(x^6+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{6} + 2}}{x^{17} + 4 \, x^{11} + 4 \, x^{5}}, x\right)"," ",0,"integral(sqrt(x^6 + 2)/(x^17 + 4*x^11 + 4*x^5), x)","F",0
1424,0,0,0,1.196690," ","integrate(x^12/(x^6+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{6} + 2} x^{12}}{x^{12} + 4 \, x^{6} + 4}, x\right)"," ",0,"integral(sqrt(x^6 + 2)*x^12/(x^12 + 4*x^6 + 4), x)","F",0
1425,0,0,0,0.773801," ","integrate(x^6/(x^6+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{6} + 2} x^{6}}{x^{12} + 4 \, x^{6} + 4}, x\right)"," ",0,"integral(sqrt(x^6 + 2)*x^6/(x^12 + 4*x^6 + 4), x)","F",0
1426,0,0,0,0.793287," ","integrate(1/(x^6+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{6} + 2}}{x^{12} + 4 \, x^{6} + 4}, x\right)"," ",0,"integral(sqrt(x^6 + 2)/(x^12 + 4*x^6 + 4), x)","F",0
1427,0,0,0,1.391067," ","integrate(1/x^6/(x^6+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{6} + 2}}{x^{18} + 4 \, x^{12} + 4 \, x^{6}}, x\right)"," ",0,"integral(sqrt(x^6 + 2)/(x^18 + 4*x^12 + 4*x^6), x)","F",0
1428,0,0,0,1.160905," ","integrate(x^15/(x^6+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{6} + 2} x^{15}}{x^{12} + 4 \, x^{6} + 4}, x\right)"," ",0,"integral(sqrt(x^6 + 2)*x^15/(x^12 + 4*x^6 + 4), x)","F",0
1429,0,0,0,0.959677," ","integrate(x^9/(x^6+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{6} + 2} x^{9}}{x^{12} + 4 \, x^{6} + 4}, x\right)"," ",0,"integral(sqrt(x^6 + 2)*x^9/(x^12 + 4*x^6 + 4), x)","F",0
1430,0,0,0,0.956541," ","integrate(x^3/(x^6+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{6} + 2} x^{3}}{x^{12} + 4 \, x^{6} + 4}, x\right)"," ",0,"integral(sqrt(x^6 + 2)*x^3/(x^12 + 4*x^6 + 4), x)","F",0
1431,0,0,0,1.106219," ","integrate(1/x^3/(x^6+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{6} + 2}}{x^{15} + 4 \, x^{9} + 4 \, x^{3}}, x\right)"," ",0,"integral(sqrt(x^6 + 2)/(x^15 + 4*x^9 + 4*x^3), x)","F",0
1432,0,0,0,0.870054," ","integrate(x^10/(x^6+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{6} + 2} x^{10}}{x^{12} + 4 \, x^{6} + 4}, x\right)"," ",0,"integral(sqrt(x^6 + 2)*x^10/(x^12 + 4*x^6 + 4), x)","F",0
1433,0,0,0,0.853606," ","integrate(x^4/(x^6+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{6} + 2} x^{4}}{x^{12} + 4 \, x^{6} + 4}, x\right)"," ",0,"integral(sqrt(x^6 + 2)*x^4/(x^12 + 4*x^6 + 4), x)","F",0
1434,0,0,0,0.847542," ","integrate(1/x^2/(x^6+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{6} + 2}}{x^{14} + 4 \, x^{8} + 4 \, x^{2}}, x\right)"," ",0,"integral(sqrt(x^6 + 2)/(x^14 + 4*x^8 + 4*x^2), x)","F",0
1435,1,33,0,0.685520," ","integrate(x^m*(b*x^7+a),x, algorithm=""fricas"")","\frac{{\left({\left(b m + b\right)} x^{8} + {\left(a m + 8 \, a\right)} x\right)} x^{m}}{m^{2} + 9 \, m + 8}"," ",0,"((b*m + b)*x^8 + (a*m + 8*a)*x)*x^m/(m^2 + 9*m + 8)","A",0
1436,1,13,0,0.810076," ","integrate(x^8*(b*x^7+a),x, algorithm=""fricas"")","\frac{1}{16} x^{16} b + \frac{1}{9} x^{9} a"," ",0,"1/16*x^16*b + 1/9*x^9*a","A",0
1437,1,17,0,0.834287," ","integrate((b*x^7+a)/x^8,x, algorithm=""fricas"")","\frac{7 \, b x^{7} \log\left(x\right) - a}{7 \, x^{7}}"," ",0,"1/7*(7*b*x^7*log(x) - a)/x^7","A",0
1438,1,85,0,0.829634," ","integrate(x^m*(b*x^7+a)^2,x, algorithm=""fricas"")","\frac{{\left({\left(b^{2} m^{2} + 9 \, b^{2} m + 8 \, b^{2}\right)} x^{15} + 2 \, {\left(a b m^{2} + 16 \, a b m + 15 \, a b\right)} x^{8} + {\left(a^{2} m^{2} + 23 \, a^{2} m + 120 \, a^{2}\right)} x\right)} x^{m}}{m^{3} + 24 \, m^{2} + 143 \, m + 120}"," ",0,"((b^2*m^2 + 9*b^2*m + 8*b^2)*x^15 + 2*(a*b*m^2 + 16*a*b*m + 15*a*b)*x^8 + (a^2*m^2 + 23*a^2*m + 120*a^2)*x)*x^m/(m^3 + 24*m^2 + 143*m + 120)","A",0
1439,1,24,0,0.852760," ","integrate(x^8*(b*x^7+a)^2,x, algorithm=""fricas"")","\frac{1}{23} x^{23} b^{2} + \frac{1}{8} x^{16} b a + \frac{1}{9} x^{9} a^{2}"," ",0,"1/23*x^23*b^2 + 1/8*x^16*b*a + 1/9*x^9*a^2","A",0
1440,1,27,0,0.889459," ","integrate((b*x^7+a)^2/x^8,x, algorithm=""fricas"")","\frac{b^{2} x^{14} + 14 \, a b x^{7} \log\left(x\right) - a^{2}}{7 \, x^{7}}"," ",0,"1/7*(b^2*x^14 + 14*a*b*x^7*log(x) - a^2)/x^7","A",0
1441,0,0,0,0.956793," ","integrate(x^m/(b*x^7+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{b x^{7} + a}, x\right)"," ",0,"integral(x^m/(b*x^7 + a), x)","F",0
1442,1,13,0,1.160094," ","integrate(x^6/(b*x^7+a),x, algorithm=""fricas"")","\frac{\log\left(b x^{7} + a\right)}{7 \, b}"," ",0,"1/7*log(b*x^7 + a)/b","A",0
1443,-2,0,0,0.000000," ","integrate(1/(b*x^7+a),x, algorithm=""fricas"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> no explicit roots found","F(-2)",0
1444,1,18,0,0.655511," ","integrate(1/x/(b*x^7+a),x, algorithm=""fricas"")","-\frac{\log\left(b x^{7} + a\right) - 7 \, \log\left(x\right)}{7 \, a}"," ",0,"-1/7*(log(b*x^7 + a) - 7*log(x))/a","A",0
1445,0,0,0,0.833235," ","integrate(x^m/(-b*x^7+a),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{x^{m}}{b x^{7} - a}, x\right)"," ",0,"integral(-x^m/(b*x^7 - a), x)","F",0
1446,1,15,0,1.166763," ","integrate(x^6/(-b*x^7+a),x, algorithm=""fricas"")","-\frac{\log\left(b x^{7} - a\right)}{7 \, b}"," ",0,"-1/7*log(b*x^7 - a)/b","A",0
1447,-2,0,0,0.000000," ","integrate(1/(-b*x^7+a),x, algorithm=""fricas"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> no explicit roots found","F(-2)",0
1448,1,20,0,0.930687," ","integrate(1/x/(-b*x^7+a),x, algorithm=""fricas"")","-\frac{\log\left(b x^{7} - a\right) - 7 \, \log\left(x\right)}{7 \, a}"," ",0,"-1/7*(log(b*x^7 - a) - 7*log(x))/a","A",0
1449,1,65,0,16.372718," ","integrate(1/(-x^7+1),x, algorithm=""fricas"")","\frac{1}{14} \, {\left(\sqrt{-0.7530203962825330? + 0.?e-36 \sqrt{-1}} + 1.801937735804839? + 0.?e-36 \sqrt{-1}\right)} \log\left(2 \, x + \sqrt{-0.7530203962825330? + 0.?e-36 \sqrt{-1}} + 1.801937735804839? + 0.?e-36 \sqrt{-1}\right) - \frac{1}{14} \, {\left(\sqrt{-0.7530203962825330? + 0.?e-36 \sqrt{-1}} - 1.801937735804839? + 0.?e-36 \sqrt{-1}\right)} \log\left(2 \, x - \sqrt{-0.7530203962825330? + 0.?e-36 \sqrt{-1}} + 1.801937735804839? + 0.?e-36 \sqrt{-1}\right) + \left(0.03178870485090206? + 0.1392754160259748? \sqrt{-1}\right) \, \log\left(x + 0.2225209339563144? + 0.9749279121818236? \sqrt{-1}\right) + \left(0.03178870485090206? - 0.1392754160259748? \sqrt{-1}\right) \, \log\left(x + 0.2225209339563144? - 0.9749279121818236? \sqrt{-1}\right) - \left(0.08906997169410479? - 0.11169021178114711? \sqrt{-1}\right) \, \log\left(x - 0.6234898018587335? + 0.7818314824680299? \sqrt{-1}\right) - \left(0.08906997169410479? + 0.11169021178114711? \sqrt{-1}\right) \, \log\left(x - 0.6234898018587335? - 0.7818314824680299? \sqrt{-1}\right) - \frac{1}{7} \, \log\left(x - 1\right)"," ",0,"1/14*(sqrt(-0.7530203962825330? + 0.?e-36*I) + 1.801937735804839? + 0.?e-36*I)*log(2*x + sqrt(-0.7530203962825330? + 0.?e-36*I) + 1.801937735804839? + 0.?e-36*I) - 1/14*(sqrt(-0.7530203962825330? + 0.?e-36*I) - 1.801937735804839? + 0.?e-36*I)*log(2*x - sqrt(-0.7530203962825330? + 0.?e-36*I) + 1.801937735804839? + 0.?e-36*I) + (0.03178870485090206? + 0.1392754160259748?*I)*log(x + 0.2225209339563144? + 0.9749279121818236?*I) + (0.03178870485090206? - 0.1392754160259748?*I)*log(x + 0.2225209339563144? - 0.9749279121818236?*I) - (0.08906997169410479? - 0.11169021178114711?*I)*log(x - 0.6234898018587335? + 0.7818314824680299?*I) - (0.08906997169410479? + 0.11169021178114711?*I)*log(x - 0.6234898018587335? - 0.7818314824680299?*I) - 1/7*log(x - 1)","C",0
1450,1,65,0,16.324874," ","integrate(1/(x^7+1),x, algorithm=""fricas"")","\frac{1}{14} \, {\left(\sqrt{-2.445041867912629? + 0.?e-37 \sqrt{-1}} + 1.246979603717467? + 0.?e-36 \sqrt{-1}\right)} \log\left(2 \, x + \sqrt{-2.445041867912629? + 0.?e-37 \sqrt{-1}} + 1.246979603717467? + 0.?e-36 \sqrt{-1}\right) - \frac{1}{14} \, {\left(\sqrt{-2.445041867912629? + 0.?e-37 \sqrt{-1}} - 1.246979603717467? + 0.?e-36 \sqrt{-1}\right)} \log\left(2 \, x - \sqrt{-2.445041867912629? + 0.?e-37 \sqrt{-1}} + 1.246979603717467? + 0.?e-36 \sqrt{-1}\right) + \frac{1}{7} \, \log\left(x + 1\right) - \left(0.03178870485090206? - 0.1392754160259748? \sqrt{-1}\right) \, \log\left(x - 0.2225209339563144? + 0.9749279121818236? \sqrt{-1}\right) - \left(0.03178870485090206? + 0.1392754160259748? \sqrt{-1}\right) \, \log\left(x - 0.2225209339563144? - 0.9749279121818236? \sqrt{-1}\right) - \left(0.1287098382717742? - 0.06198339130250831? \sqrt{-1}\right) \, \log\left(x - 0.9009688679024191? + 0.4338837391175581? \sqrt{-1}\right) - \left(0.1287098382717742? + 0.06198339130250831? \sqrt{-1}\right) \, \log\left(x - 0.9009688679024191? - 0.4338837391175582? \sqrt{-1}\right)"," ",0,"1/14*(sqrt(-2.445041867912629? + 0.?e-37*I) + 1.246979603717467? + 0.?e-36*I)*log(2*x + sqrt(-2.445041867912629? + 0.?e-37*I) + 1.246979603717467? + 0.?e-36*I) - 1/14*(sqrt(-2.445041867912629? + 0.?e-37*I) - 1.246979603717467? + 0.?e-36*I)*log(2*x - sqrt(-2.445041867912629? + 0.?e-37*I) + 1.246979603717467? + 0.?e-36*I) + 1/7*log(x + 1) - (0.03178870485090206? - 0.1392754160259748?*I)*log(x - 0.2225209339563144? + 0.9749279121818236?*I) - (0.03178870485090206? + 0.1392754160259748?*I)*log(x - 0.2225209339563144? - 0.9749279121818236?*I) - (0.1287098382717742? - 0.06198339130250831?*I)*log(x - 0.9009688679024191? + 0.4338837391175581?*I) - (0.1287098382717742? + 0.06198339130250831?*I)*log(x - 0.9009688679024191? - 0.4338837391175582?*I)","C",0
1451,1,127,0,0.917634," ","integrate(x^9/(b*x^8+a),x, algorithm=""fricas"")","-\frac{4 \, b \left(-\frac{a}{b^{5}}\right)^{\frac{1}{4}} \arctan\left(-\frac{b^{4} x^{2} \left(-\frac{a}{b^{5}}\right)^{\frac{3}{4}} - \sqrt{x^{4} + b^{2} \sqrt{-\frac{a}{b^{5}}}} b^{4} \left(-\frac{a}{b^{5}}\right)^{\frac{3}{4}}}{a}\right) + b \left(-\frac{a}{b^{5}}\right)^{\frac{1}{4}} \log\left(x^{2} + b \left(-\frac{a}{b^{5}}\right)^{\frac{1}{4}}\right) - b \left(-\frac{a}{b^{5}}\right)^{\frac{1}{4}} \log\left(x^{2} - b \left(-\frac{a}{b^{5}}\right)^{\frac{1}{4}}\right) - 4 \, x^{2}}{8 \, b}"," ",0,"-1/8*(4*b*(-a/b^5)^(1/4)*arctan(-(b^4*x^2*(-a/b^5)^(3/4) - sqrt(x^4 + b^2*sqrt(-a/b^5))*b^4*(-a/b^5)^(3/4))/a) + b*(-a/b^5)^(1/4)*log(x^2 + b*(-a/b^5)^(1/4)) - b*(-a/b^5)^(1/4)*log(x^2 - b*(-a/b^5)^(1/4)) - 4*x^2)/b","A",0
1452,1,13,0,0.807106," ","integrate(x^7/(b*x^8+a),x, algorithm=""fricas"")","\frac{\log\left(b x^{8} + a\right)}{8 \, b}"," ",0,"1/8*log(b*x^8 + a)/b","A",0
1453,1,128,0,0.957045," ","integrate(x^5/(b*x^8+a),x, algorithm=""fricas"")","-\frac{1}{2} \, \left(-\frac{1}{a b^{3}}\right)^{\frac{1}{4}} \arctan\left(-b x^{2} \left(-\frac{1}{a b^{3}}\right)^{\frac{1}{4}} + \sqrt{x^{4} - a b \sqrt{-\frac{1}{a b^{3}}}} b \left(-\frac{1}{a b^{3}}\right)^{\frac{1}{4}}\right) + \frac{1}{8} \, \left(-\frac{1}{a b^{3}}\right)^{\frac{1}{4}} \log\left(a b^{2} \left(-\frac{1}{a b^{3}}\right)^{\frac{3}{4}} + x^{2}\right) - \frac{1}{8} \, \left(-\frac{1}{a b^{3}}\right)^{\frac{1}{4}} \log\left(-a b^{2} \left(-\frac{1}{a b^{3}}\right)^{\frac{3}{4}} + x^{2}\right)"," ",0,"-1/2*(-1/(a*b^3))^(1/4)*arctan(-b*x^2*(-1/(a*b^3))^(1/4) + sqrt(x^4 - a*b*sqrt(-1/(a*b^3)))*b*(-1/(a*b^3))^(1/4)) + 1/8*(-1/(a*b^3))^(1/4)*log(a*b^2*(-1/(a*b^3))^(3/4) + x^2) - 1/8*(-1/(a*b^3))^(1/4)*log(-a*b^2*(-1/(a*b^3))^(3/4) + x^2)","A",0
1454,1,72,0,1.110396," ","integrate(x^3/(b*x^8+a),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a b} \log\left(\frac{b x^{8} - 2 \, \sqrt{-a b} x^{4} - a}{b x^{8} + a}\right)}{8 \, a b}, -\frac{\sqrt{a b} \arctan\left(\frac{\sqrt{a b}}{b x^{4}}\right)}{4 \, a b}\right]"," ",0,"[-1/8*sqrt(-a*b)*log((b*x^8 - 2*sqrt(-a*b)*x^4 - a)/(b*x^8 + a))/(a*b), -1/4*sqrt(a*b)*arctan(sqrt(a*b)/(b*x^4))/(a*b)]","A",0
1455,1,128,0,0.885605," ","integrate(x/(b*x^8+a),x, algorithm=""fricas"")","\frac{1}{2} \, \left(-\frac{1}{a^{3} b}\right)^{\frac{1}{4}} \arctan\left(-a^{2} b x^{2} \left(-\frac{1}{a^{3} b}\right)^{\frac{3}{4}} + \sqrt{x^{4} + a^{2} \sqrt{-\frac{1}{a^{3} b}}} a^{2} b \left(-\frac{1}{a^{3} b}\right)^{\frac{3}{4}}\right) + \frac{1}{8} \, \left(-\frac{1}{a^{3} b}\right)^{\frac{1}{4}} \log\left(x^{2} + a \left(-\frac{1}{a^{3} b}\right)^{\frac{1}{4}}\right) - \frac{1}{8} \, \left(-\frac{1}{a^{3} b}\right)^{\frac{1}{4}} \log\left(x^{2} - a \left(-\frac{1}{a^{3} b}\right)^{\frac{1}{4}}\right)"," ",0,"1/2*(-1/(a^3*b))^(1/4)*arctan(-a^2*b*x^2*(-1/(a^3*b))^(3/4) + sqrt(x^4 + a^2*sqrt(-1/(a^3*b)))*a^2*b*(-1/(a^3*b))^(3/4)) + 1/8*(-1/(a^3*b))^(1/4)*log(x^2 + a*(-1/(a^3*b))^(1/4)) - 1/8*(-1/(a^3*b))^(1/4)*log(x^2 - a*(-1/(a^3*b))^(1/4))","A",0
1456,1,18,0,1.076681," ","integrate(1/x/(b*x^8+a),x, algorithm=""fricas"")","-\frac{\log\left(b x^{8} + a\right) - 8 \, \log\left(x\right)}{8 \, a}"," ",0,"-1/8*(log(b*x^8 + a) - 8*log(x))/a","A",0
1457,1,141,0,0.880474," ","integrate(1/x^3/(b*x^8+a),x, algorithm=""fricas"")","\frac{4 \, a x^{2} \left(-\frac{b}{a^{5}}\right)^{\frac{1}{4}} \arctan\left(-a x^{2} \left(-\frac{b}{a^{5}}\right)^{\frac{1}{4}} + a \sqrt{\frac{b x^{4} - a^{3} \sqrt{-\frac{b}{a^{5}}}}{b}} \left(-\frac{b}{a^{5}}\right)^{\frac{1}{4}}\right) - a x^{2} \left(-\frac{b}{a^{5}}\right)^{\frac{1}{4}} \log\left(a^{4} \left(-\frac{b}{a^{5}}\right)^{\frac{3}{4}} + b x^{2}\right) + a x^{2} \left(-\frac{b}{a^{5}}\right)^{\frac{1}{4}} \log\left(-a^{4} \left(-\frac{b}{a^{5}}\right)^{\frac{3}{4}} + b x^{2}\right) - 4}{8 \, a x^{2}}"," ",0,"1/8*(4*a*x^2*(-b/a^5)^(1/4)*arctan(-a*x^2*(-b/a^5)^(1/4) + a*sqrt((b*x^4 - a^3*sqrt(-b/a^5))/b)*(-b/a^5)^(1/4)) - a*x^2*(-b/a^5)^(1/4)*log(a^4*(-b/a^5)^(3/4) + b*x^2) + a*x^2*(-b/a^5)^(1/4)*log(-a^4*(-b/a^5)^(3/4) + b*x^2) - 4)/(a*x^2)","A",0
1458,1,94,0,0.970057," ","integrate(1/x^5/(b*x^8+a),x, algorithm=""fricas"")","\left[\frac{x^{4} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{8} - 2 \, a x^{4} \sqrt{-\frac{b}{a}} - a}{b x^{8} + a}\right) - 2}{8 \, a x^{4}}, \frac{x^{4} \sqrt{\frac{b}{a}} \arctan\left(\frac{a \sqrt{\frac{b}{a}}}{b x^{4}}\right) - 1}{4 \, a x^{4}}\right]"," ",0,"[1/8*(x^4*sqrt(-b/a)*log((b*x^8 - 2*a*x^4*sqrt(-b/a) - a)/(b*x^8 + a)) - 2)/(a*x^4), 1/4*(x^4*sqrt(b/a)*arctan(a*sqrt(b/a)/(b*x^4)) - 1)/(a*x^4)]","A",0
1459,1,168,0,0.747509," ","integrate(1/x^7/(b*x^8+a),x, algorithm=""fricas"")","-\frac{12 \, a x^{6} \left(-\frac{b^{3}}{a^{7}}\right)^{\frac{1}{4}} \arctan\left(-\frac{a^{5} x^{2} \left(-\frac{b^{3}}{a^{7}}\right)^{\frac{3}{4}} - a^{5} \sqrt{\frac{b^{2} x^{4} + a^{4} \sqrt{-\frac{b^{3}}{a^{7}}}}{b^{2}}} \left(-\frac{b^{3}}{a^{7}}\right)^{\frac{3}{4}}}{b^{2}}\right) + 3 \, a x^{6} \left(-\frac{b^{3}}{a^{7}}\right)^{\frac{1}{4}} \log\left(b x^{2} + a^{2} \left(-\frac{b^{3}}{a^{7}}\right)^{\frac{1}{4}}\right) - 3 \, a x^{6} \left(-\frac{b^{3}}{a^{7}}\right)^{\frac{1}{4}} \log\left(b x^{2} - a^{2} \left(-\frac{b^{3}}{a^{7}}\right)^{\frac{1}{4}}\right) + 4}{24 \, a x^{6}}"," ",0,"-1/24*(12*a*x^6*(-b^3/a^7)^(1/4)*arctan(-(a^5*x^2*(-b^3/a^7)^(3/4) - a^5*sqrt((b^2*x^4 + a^4*sqrt(-b^3/a^7))/b^2)*(-b^3/a^7)^(3/4))/b^2) + 3*a*x^6*(-b^3/a^7)^(1/4)*log(b*x^2 + a^2*(-b^3/a^7)^(1/4)) - 3*a*x^6*(-b^3/a^7)^(1/4)*log(b*x^2 - a^2*(-b^3/a^7)^(1/4)) + 4)/(a*x^6)","A",0
1460,1,33,0,0.879198," ","integrate(1/x^9/(b*x^8+a),x, algorithm=""fricas"")","\frac{b x^{8} \log\left(b x^{8} + a\right) - 8 \, b x^{8} \log\left(x\right) - a}{8 \, a^{2} x^{8}}"," ",0,"1/8*(b*x^8*log(b*x^8 + a) - 8*b*x^8*log(x) - a)/(a^2*x^8)","A",0
1461,1,385,0,0.996938," ","integrate(x^8/(b*x^8+a),x, algorithm=""fricas"")","-\frac{4 \, \sqrt{2} b \left(-\frac{a}{b^{9}}\right)^{\frac{1}{8}} \arctan\left(-\frac{\sqrt{2} b^{8} x \left(-\frac{a}{b^{9}}\right)^{\frac{7}{8}} - \sqrt{2} \sqrt{\sqrt{2} b x \left(-\frac{a}{b^{9}}\right)^{\frac{1}{8}} + b^{2} \left(-\frac{a}{b^{9}}\right)^{\frac{1}{4}} + x^{2}} b^{8} \left(-\frac{a}{b^{9}}\right)^{\frac{7}{8}} - a}{a}\right) + 4 \, \sqrt{2} b \left(-\frac{a}{b^{9}}\right)^{\frac{1}{8}} \arctan\left(-\frac{\sqrt{2} b^{8} x \left(-\frac{a}{b^{9}}\right)^{\frac{7}{8}} - \sqrt{2} \sqrt{-\sqrt{2} b x \left(-\frac{a}{b^{9}}\right)^{\frac{1}{8}} + b^{2} \left(-\frac{a}{b^{9}}\right)^{\frac{1}{4}} + x^{2}} b^{8} \left(-\frac{a}{b^{9}}\right)^{\frac{7}{8}} + a}{a}\right) + \sqrt{2} b \left(-\frac{a}{b^{9}}\right)^{\frac{1}{8}} \log\left(\sqrt{2} b x \left(-\frac{a}{b^{9}}\right)^{\frac{1}{8}} + b^{2} \left(-\frac{a}{b^{9}}\right)^{\frac{1}{4}} + x^{2}\right) - \sqrt{2} b \left(-\frac{a}{b^{9}}\right)^{\frac{1}{8}} \log\left(-\sqrt{2} b x \left(-\frac{a}{b^{9}}\right)^{\frac{1}{8}} + b^{2} \left(-\frac{a}{b^{9}}\right)^{\frac{1}{4}} + x^{2}\right) + 8 \, b \left(-\frac{a}{b^{9}}\right)^{\frac{1}{8}} \arctan\left(-\frac{b^{8} x \left(-\frac{a}{b^{9}}\right)^{\frac{7}{8}} - \sqrt{b^{2} \left(-\frac{a}{b^{9}}\right)^{\frac{1}{4}} + x^{2}} b^{8} \left(-\frac{a}{b^{9}}\right)^{\frac{7}{8}}}{a}\right) + 2 \, b \left(-\frac{a}{b^{9}}\right)^{\frac{1}{8}} \log\left(b \left(-\frac{a}{b^{9}}\right)^{\frac{1}{8}} + x\right) - 2 \, b \left(-\frac{a}{b^{9}}\right)^{\frac{1}{8}} \log\left(-b \left(-\frac{a}{b^{9}}\right)^{\frac{1}{8}} + x\right) - 16 \, x}{16 \, b}"," ",0,"-1/16*(4*sqrt(2)*b*(-a/b^9)^(1/8)*arctan(-(sqrt(2)*b^8*x*(-a/b^9)^(7/8) - sqrt(2)*sqrt(sqrt(2)*b*x*(-a/b^9)^(1/8) + b^2*(-a/b^9)^(1/4) + x^2)*b^8*(-a/b^9)^(7/8) - a)/a) + 4*sqrt(2)*b*(-a/b^9)^(1/8)*arctan(-(sqrt(2)*b^8*x*(-a/b^9)^(7/8) - sqrt(2)*sqrt(-sqrt(2)*b*x*(-a/b^9)^(1/8) + b^2*(-a/b^9)^(1/4) + x^2)*b^8*(-a/b^9)^(7/8) + a)/a) + sqrt(2)*b*(-a/b^9)^(1/8)*log(sqrt(2)*b*x*(-a/b^9)^(1/8) + b^2*(-a/b^9)^(1/4) + x^2) - sqrt(2)*b*(-a/b^9)^(1/8)*log(-sqrt(2)*b*x*(-a/b^9)^(1/8) + b^2*(-a/b^9)^(1/4) + x^2) + 8*b*(-a/b^9)^(1/8)*arctan(-(b^8*x*(-a/b^9)^(7/8) - sqrt(b^2*(-a/b^9)^(1/4) + x^2)*b^8*(-a/b^9)^(7/8))/a) + 2*b*(-a/b^9)^(1/8)*log(b*(-a/b^9)^(1/8) + x) - 2*b*(-a/b^9)^(1/8)*log(-b*(-a/b^9)^(1/8) + x) - 16*x)/b","B",0
1462,1,418,0,1.002949," ","integrate(x^6/(b*x^8+a),x, algorithm=""fricas"")","-\frac{1}{4} \, \sqrt{2} \left(-\frac{1}{a b^{7}}\right)^{\frac{1}{8}} \arctan\left(-\sqrt{2} b x \left(-\frac{1}{a b^{7}}\right)^{\frac{1}{8}} + \sqrt{2} \sqrt{\sqrt{2} a b^{6} x \left(-\frac{1}{a b^{7}}\right)^{\frac{7}{8}} - a b^{5} \left(-\frac{1}{a b^{7}}\right)^{\frac{3}{4}} + x^{2}} b \left(-\frac{1}{a b^{7}}\right)^{\frac{1}{8}} + 1\right) - \frac{1}{4} \, \sqrt{2} \left(-\frac{1}{a b^{7}}\right)^{\frac{1}{8}} \arctan\left(-\sqrt{2} b x \left(-\frac{1}{a b^{7}}\right)^{\frac{1}{8}} + \sqrt{2} \sqrt{-\sqrt{2} a b^{6} x \left(-\frac{1}{a b^{7}}\right)^{\frac{7}{8}} - a b^{5} \left(-\frac{1}{a b^{7}}\right)^{\frac{3}{4}} + x^{2}} b \left(-\frac{1}{a b^{7}}\right)^{\frac{1}{8}} - 1\right) + \frac{1}{16} \, \sqrt{2} \left(-\frac{1}{a b^{7}}\right)^{\frac{1}{8}} \log\left(\sqrt{2} a b^{6} x \left(-\frac{1}{a b^{7}}\right)^{\frac{7}{8}} - a b^{5} \left(-\frac{1}{a b^{7}}\right)^{\frac{3}{4}} + x^{2}\right) - \frac{1}{16} \, \sqrt{2} \left(-\frac{1}{a b^{7}}\right)^{\frac{1}{8}} \log\left(-\sqrt{2} a b^{6} x \left(-\frac{1}{a b^{7}}\right)^{\frac{7}{8}} - a b^{5} \left(-\frac{1}{a b^{7}}\right)^{\frac{3}{4}} + x^{2}\right) - \frac{1}{2} \, \left(-\frac{1}{a b^{7}}\right)^{\frac{1}{8}} \arctan\left(-b x \left(-\frac{1}{a b^{7}}\right)^{\frac{1}{8}} + \sqrt{-a b^{5} \left(-\frac{1}{a b^{7}}\right)^{\frac{3}{4}} + x^{2}} b \left(-\frac{1}{a b^{7}}\right)^{\frac{1}{8}}\right) + \frac{1}{8} \, \left(-\frac{1}{a b^{7}}\right)^{\frac{1}{8}} \log\left(a b^{6} \left(-\frac{1}{a b^{7}}\right)^{\frac{7}{8}} + x\right) - \frac{1}{8} \, \left(-\frac{1}{a b^{7}}\right)^{\frac{1}{8}} \log\left(-a b^{6} \left(-\frac{1}{a b^{7}}\right)^{\frac{7}{8}} + x\right)"," ",0,"-1/4*sqrt(2)*(-1/(a*b^7))^(1/8)*arctan(-sqrt(2)*b*x*(-1/(a*b^7))^(1/8) + sqrt(2)*sqrt(sqrt(2)*a*b^6*x*(-1/(a*b^7))^(7/8) - a*b^5*(-1/(a*b^7))^(3/4) + x^2)*b*(-1/(a*b^7))^(1/8) + 1) - 1/4*sqrt(2)*(-1/(a*b^7))^(1/8)*arctan(-sqrt(2)*b*x*(-1/(a*b^7))^(1/8) + sqrt(2)*sqrt(-sqrt(2)*a*b^6*x*(-1/(a*b^7))^(7/8) - a*b^5*(-1/(a*b^7))^(3/4) + x^2)*b*(-1/(a*b^7))^(1/8) - 1) + 1/16*sqrt(2)*(-1/(a*b^7))^(1/8)*log(sqrt(2)*a*b^6*x*(-1/(a*b^7))^(7/8) - a*b^5*(-1/(a*b^7))^(3/4) + x^2) - 1/16*sqrt(2)*(-1/(a*b^7))^(1/8)*log(-sqrt(2)*a*b^6*x*(-1/(a*b^7))^(7/8) - a*b^5*(-1/(a*b^7))^(3/4) + x^2) - 1/2*(-1/(a*b^7))^(1/8)*arctan(-b*x*(-1/(a*b^7))^(1/8) + sqrt(-a*b^5*(-1/(a*b^7))^(3/4) + x^2)*b*(-1/(a*b^7))^(1/8)) + 1/8*(-1/(a*b^7))^(1/8)*log(a*b^6*(-1/(a*b^7))^(7/8) + x) - 1/8*(-1/(a*b^7))^(1/8)*log(-a*b^6*(-1/(a*b^7))^(7/8) + x)","B",0
1463,1,438,0,1.185378," ","integrate(x^4/(b*x^8+a),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{2} \left(-\frac{1}{a^{3} b^{5}}\right)^{\frac{1}{8}} \arctan\left(-\sqrt{2} a b^{2} x \left(-\frac{1}{a^{3} b^{5}}\right)^{\frac{3}{8}} + \sqrt{2} \sqrt{\sqrt{2} a^{2} b^{3} x \left(-\frac{1}{a^{3} b^{5}}\right)^{\frac{5}{8}} - a b \left(-\frac{1}{a^{3} b^{5}}\right)^{\frac{1}{4}} + x^{2}} a b^{2} \left(-\frac{1}{a^{3} b^{5}}\right)^{\frac{3}{8}} + 1\right) + \frac{1}{4} \, \sqrt{2} \left(-\frac{1}{a^{3} b^{5}}\right)^{\frac{1}{8}} \arctan\left(-\sqrt{2} a b^{2} x \left(-\frac{1}{a^{3} b^{5}}\right)^{\frac{3}{8}} + \sqrt{2} \sqrt{-\sqrt{2} a^{2} b^{3} x \left(-\frac{1}{a^{3} b^{5}}\right)^{\frac{5}{8}} - a b \left(-\frac{1}{a^{3} b^{5}}\right)^{\frac{1}{4}} + x^{2}} a b^{2} \left(-\frac{1}{a^{3} b^{5}}\right)^{\frac{3}{8}} - 1\right) + \frac{1}{16} \, \sqrt{2} \left(-\frac{1}{a^{3} b^{5}}\right)^{\frac{1}{8}} \log\left(\sqrt{2} a^{2} b^{3} x \left(-\frac{1}{a^{3} b^{5}}\right)^{\frac{5}{8}} - a b \left(-\frac{1}{a^{3} b^{5}}\right)^{\frac{1}{4}} + x^{2}\right) - \frac{1}{16} \, \sqrt{2} \left(-\frac{1}{a^{3} b^{5}}\right)^{\frac{1}{8}} \log\left(-\sqrt{2} a^{2} b^{3} x \left(-\frac{1}{a^{3} b^{5}}\right)^{\frac{5}{8}} - a b \left(-\frac{1}{a^{3} b^{5}}\right)^{\frac{1}{4}} + x^{2}\right) - \frac{1}{2} \, \left(-\frac{1}{a^{3} b^{5}}\right)^{\frac{1}{8}} \arctan\left(-a b^{2} x \left(-\frac{1}{a^{3} b^{5}}\right)^{\frac{3}{8}} + \sqrt{-a b \left(-\frac{1}{a^{3} b^{5}}\right)^{\frac{1}{4}} + x^{2}} a b^{2} \left(-\frac{1}{a^{3} b^{5}}\right)^{\frac{3}{8}}\right) - \frac{1}{8} \, \left(-\frac{1}{a^{3} b^{5}}\right)^{\frac{1}{8}} \log\left(a^{2} b^{3} \left(-\frac{1}{a^{3} b^{5}}\right)^{\frac{5}{8}} + x\right) + \frac{1}{8} \, \left(-\frac{1}{a^{3} b^{5}}\right)^{\frac{1}{8}} \log\left(-a^{2} b^{3} \left(-\frac{1}{a^{3} b^{5}}\right)^{\frac{5}{8}} + x\right)"," ",0,"1/4*sqrt(2)*(-1/(a^3*b^5))^(1/8)*arctan(-sqrt(2)*a*b^2*x*(-1/(a^3*b^5))^(3/8) + sqrt(2)*sqrt(sqrt(2)*a^2*b^3*x*(-1/(a^3*b^5))^(5/8) - a*b*(-1/(a^3*b^5))^(1/4) + x^2)*a*b^2*(-1/(a^3*b^5))^(3/8) + 1) + 1/4*sqrt(2)*(-1/(a^3*b^5))^(1/8)*arctan(-sqrt(2)*a*b^2*x*(-1/(a^3*b^5))^(3/8) + sqrt(2)*sqrt(-sqrt(2)*a^2*b^3*x*(-1/(a^3*b^5))^(5/8) - a*b*(-1/(a^3*b^5))^(1/4) + x^2)*a*b^2*(-1/(a^3*b^5))^(3/8) - 1) + 1/16*sqrt(2)*(-1/(a^3*b^5))^(1/8)*log(sqrt(2)*a^2*b^3*x*(-1/(a^3*b^5))^(5/8) - a*b*(-1/(a^3*b^5))^(1/4) + x^2) - 1/16*sqrt(2)*(-1/(a^3*b^5))^(1/8)*log(-sqrt(2)*a^2*b^3*x*(-1/(a^3*b^5))^(5/8) - a*b*(-1/(a^3*b^5))^(1/4) + x^2) - 1/2*(-1/(a^3*b^5))^(1/8)*arctan(-a*b^2*x*(-1/(a^3*b^5))^(3/8) + sqrt(-a*b*(-1/(a^3*b^5))^(1/4) + x^2)*a*b^2*(-1/(a^3*b^5))^(3/8)) - 1/8*(-1/(a^3*b^5))^(1/8)*log(a^2*b^3*(-1/(a^3*b^5))^(5/8) + x) + 1/8*(-1/(a^3*b^5))^(1/8)*log(-a^2*b^3*(-1/(a^3*b^5))^(5/8) + x)","B",0
1464,1,453,0,1.017726," ","integrate(x^2/(b*x^8+a),x, algorithm=""fricas"")","-\frac{1}{4} \, \sqrt{2} \left(-\frac{1}{a^{5} b^{3}}\right)^{\frac{1}{8}} \arctan\left(-\sqrt{2} a^{3} b^{2} x \left(-\frac{1}{a^{5} b^{3}}\right)^{\frac{5}{8}} + \sqrt{2} \sqrt{a^{4} b^{2} \left(-\frac{1}{a^{5} b^{3}}\right)^{\frac{3}{4}} + \sqrt{2} a^{2} b x \left(-\frac{1}{a^{5} b^{3}}\right)^{\frac{3}{8}} + x^{2}} a^{3} b^{2} \left(-\frac{1}{a^{5} b^{3}}\right)^{\frac{5}{8}} + 1\right) - \frac{1}{4} \, \sqrt{2} \left(-\frac{1}{a^{5} b^{3}}\right)^{\frac{1}{8}} \arctan\left(-\sqrt{2} a^{3} b^{2} x \left(-\frac{1}{a^{5} b^{3}}\right)^{\frac{5}{8}} + \sqrt{2} \sqrt{a^{4} b^{2} \left(-\frac{1}{a^{5} b^{3}}\right)^{\frac{3}{4}} - \sqrt{2} a^{2} b x \left(-\frac{1}{a^{5} b^{3}}\right)^{\frac{3}{8}} + x^{2}} a^{3} b^{2} \left(-\frac{1}{a^{5} b^{3}}\right)^{\frac{5}{8}} - 1\right) + \frac{1}{16} \, \sqrt{2} \left(-\frac{1}{a^{5} b^{3}}\right)^{\frac{1}{8}} \log\left(a^{4} b^{2} \left(-\frac{1}{a^{5} b^{3}}\right)^{\frac{3}{4}} + \sqrt{2} a^{2} b x \left(-\frac{1}{a^{5} b^{3}}\right)^{\frac{3}{8}} + x^{2}\right) - \frac{1}{16} \, \sqrt{2} \left(-\frac{1}{a^{5} b^{3}}\right)^{\frac{1}{8}} \log\left(a^{4} b^{2} \left(-\frac{1}{a^{5} b^{3}}\right)^{\frac{3}{4}} - \sqrt{2} a^{2} b x \left(-\frac{1}{a^{5} b^{3}}\right)^{\frac{3}{8}} + x^{2}\right) + \frac{1}{2} \, \left(-\frac{1}{a^{5} b^{3}}\right)^{\frac{1}{8}} \arctan\left(-a^{3} b^{2} x \left(-\frac{1}{a^{5} b^{3}}\right)^{\frac{5}{8}} + \sqrt{a^{4} b^{2} \left(-\frac{1}{a^{5} b^{3}}\right)^{\frac{3}{4}} + x^{2}} a^{3} b^{2} \left(-\frac{1}{a^{5} b^{3}}\right)^{\frac{5}{8}}\right) - \frac{1}{8} \, \left(-\frac{1}{a^{5} b^{3}}\right)^{\frac{1}{8}} \log\left(a^{2} b \left(-\frac{1}{a^{5} b^{3}}\right)^{\frac{3}{8}} + x\right) + \frac{1}{8} \, \left(-\frac{1}{a^{5} b^{3}}\right)^{\frac{1}{8}} \log\left(-a^{2} b \left(-\frac{1}{a^{5} b^{3}}\right)^{\frac{3}{8}} + x\right)"," ",0,"-1/4*sqrt(2)*(-1/(a^5*b^3))^(1/8)*arctan(-sqrt(2)*a^3*b^2*x*(-1/(a^5*b^3))^(5/8) + sqrt(2)*sqrt(a^4*b^2*(-1/(a^5*b^3))^(3/4) + sqrt(2)*a^2*b*x*(-1/(a^5*b^3))^(3/8) + x^2)*a^3*b^2*(-1/(a^5*b^3))^(5/8) + 1) - 1/4*sqrt(2)*(-1/(a^5*b^3))^(1/8)*arctan(-sqrt(2)*a^3*b^2*x*(-1/(a^5*b^3))^(5/8) + sqrt(2)*sqrt(a^4*b^2*(-1/(a^5*b^3))^(3/4) - sqrt(2)*a^2*b*x*(-1/(a^5*b^3))^(3/8) + x^2)*a^3*b^2*(-1/(a^5*b^3))^(5/8) - 1) + 1/16*sqrt(2)*(-1/(a^5*b^3))^(1/8)*log(a^4*b^2*(-1/(a^5*b^3))^(3/4) + sqrt(2)*a^2*b*x*(-1/(a^5*b^3))^(3/8) + x^2) - 1/16*sqrt(2)*(-1/(a^5*b^3))^(1/8)*log(a^4*b^2*(-1/(a^5*b^3))^(3/4) - sqrt(2)*a^2*b*x*(-1/(a^5*b^3))^(3/8) + x^2) + 1/2*(-1/(a^5*b^3))^(1/8)*arctan(-a^3*b^2*x*(-1/(a^5*b^3))^(5/8) + sqrt(a^4*b^2*(-1/(a^5*b^3))^(3/4) + x^2)*a^3*b^2*(-1/(a^5*b^3))^(5/8)) - 1/8*(-1/(a^5*b^3))^(1/8)*log(a^2*b*(-1/(a^5*b^3))^(3/8) + x) + 1/8*(-1/(a^5*b^3))^(1/8)*log(-a^2*b*(-1/(a^5*b^3))^(3/8) + x)","B",0
1465,1,408,0,1.093171," ","integrate(1/(b*x^8+a),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{2} \left(-\frac{1}{a^{7} b}\right)^{\frac{1}{8}} \arctan\left(-\sqrt{2} a^{6} b x \left(-\frac{1}{a^{7} b}\right)^{\frac{7}{8}} + \sqrt{2} \sqrt{\sqrt{2} a x \left(-\frac{1}{a^{7} b}\right)^{\frac{1}{8}} + a^{2} \left(-\frac{1}{a^{7} b}\right)^{\frac{1}{4}} + x^{2}} a^{6} b \left(-\frac{1}{a^{7} b}\right)^{\frac{7}{8}} + 1\right) + \frac{1}{4} \, \sqrt{2} \left(-\frac{1}{a^{7} b}\right)^{\frac{1}{8}} \arctan\left(-\sqrt{2} a^{6} b x \left(-\frac{1}{a^{7} b}\right)^{\frac{7}{8}} + \sqrt{2} \sqrt{-\sqrt{2} a x \left(-\frac{1}{a^{7} b}\right)^{\frac{1}{8}} + a^{2} \left(-\frac{1}{a^{7} b}\right)^{\frac{1}{4}} + x^{2}} a^{6} b \left(-\frac{1}{a^{7} b}\right)^{\frac{7}{8}} - 1\right) + \frac{1}{16} \, \sqrt{2} \left(-\frac{1}{a^{7} b}\right)^{\frac{1}{8}} \log\left(\sqrt{2} a x \left(-\frac{1}{a^{7} b}\right)^{\frac{1}{8}} + a^{2} \left(-\frac{1}{a^{7} b}\right)^{\frac{1}{4}} + x^{2}\right) - \frac{1}{16} \, \sqrt{2} \left(-\frac{1}{a^{7} b}\right)^{\frac{1}{8}} \log\left(-\sqrt{2} a x \left(-\frac{1}{a^{7} b}\right)^{\frac{1}{8}} + a^{2} \left(-\frac{1}{a^{7} b}\right)^{\frac{1}{4}} + x^{2}\right) + \frac{1}{2} \, \left(-\frac{1}{a^{7} b}\right)^{\frac{1}{8}} \arctan\left(-a^{6} b x \left(-\frac{1}{a^{7} b}\right)^{\frac{7}{8}} + \sqrt{a^{2} \left(-\frac{1}{a^{7} b}\right)^{\frac{1}{4}} + x^{2}} a^{6} b \left(-\frac{1}{a^{7} b}\right)^{\frac{7}{8}}\right) + \frac{1}{8} \, \left(-\frac{1}{a^{7} b}\right)^{\frac{1}{8}} \log\left(a \left(-\frac{1}{a^{7} b}\right)^{\frac{1}{8}} + x\right) - \frac{1}{8} \, \left(-\frac{1}{a^{7} b}\right)^{\frac{1}{8}} \log\left(-a \left(-\frac{1}{a^{7} b}\right)^{\frac{1}{8}} + x\right)"," ",0,"1/4*sqrt(2)*(-1/(a^7*b))^(1/8)*arctan(-sqrt(2)*a^6*b*x*(-1/(a^7*b))^(7/8) + sqrt(2)*sqrt(sqrt(2)*a*x*(-1/(a^7*b))^(1/8) + a^2*(-1/(a^7*b))^(1/4) + x^2)*a^6*b*(-1/(a^7*b))^(7/8) + 1) + 1/4*sqrt(2)*(-1/(a^7*b))^(1/8)*arctan(-sqrt(2)*a^6*b*x*(-1/(a^7*b))^(7/8) + sqrt(2)*sqrt(-sqrt(2)*a*x*(-1/(a^7*b))^(1/8) + a^2*(-1/(a^7*b))^(1/4) + x^2)*a^6*b*(-1/(a^7*b))^(7/8) - 1) + 1/16*sqrt(2)*(-1/(a^7*b))^(1/8)*log(sqrt(2)*a*x*(-1/(a^7*b))^(1/8) + a^2*(-1/(a^7*b))^(1/4) + x^2) - 1/16*sqrt(2)*(-1/(a^7*b))^(1/8)*log(-sqrt(2)*a*x*(-1/(a^7*b))^(1/8) + a^2*(-1/(a^7*b))^(1/4) + x^2) + 1/2*(-1/(a^7*b))^(1/8)*arctan(-a^6*b*x*(-1/(a^7*b))^(7/8) + sqrt(a^2*(-1/(a^7*b))^(1/4) + x^2)*a^6*b*(-1/(a^7*b))^(7/8)) + 1/8*(-1/(a^7*b))^(1/8)*log(a*(-1/(a^7*b))^(1/8) + x) - 1/8*(-1/(a^7*b))^(1/8)*log(-a*(-1/(a^7*b))^(1/8) + x)","B",0
1466,1,408,0,0.638485," ","integrate(1/x^2/(b*x^8+a),x, algorithm=""fricas"")","\frac{4 \, \sqrt{2} a x \left(-\frac{b}{a^{9}}\right)^{\frac{1}{8}} \arctan\left(-\sqrt{2} a x \left(-\frac{b}{a^{9}}\right)^{\frac{1}{8}} + \sqrt{2} a \sqrt{-\frac{\sqrt{2} a^{8} x \left(-\frac{b}{a^{9}}\right)^{\frac{7}{8}} + a^{7} \left(-\frac{b}{a^{9}}\right)^{\frac{3}{4}} - b x^{2}}{b}} \left(-\frac{b}{a^{9}}\right)^{\frac{1}{8}} - 1\right) + 4 \, \sqrt{2} a x \left(-\frac{b}{a^{9}}\right)^{\frac{1}{8}} \arctan\left(-\sqrt{2} a x \left(-\frac{b}{a^{9}}\right)^{\frac{1}{8}} + \sqrt{2} a \sqrt{\frac{\sqrt{2} a^{8} x \left(-\frac{b}{a^{9}}\right)^{\frac{7}{8}} - a^{7} \left(-\frac{b}{a^{9}}\right)^{\frac{3}{4}} + b x^{2}}{b}} \left(-\frac{b}{a^{9}}\right)^{\frac{1}{8}} + 1\right) - \sqrt{2} a x \left(-\frac{b}{a^{9}}\right)^{\frac{1}{8}} \log\left(\sqrt{2} a^{8} x \left(-\frac{b}{a^{9}}\right)^{\frac{7}{8}} - a^{7} \left(-\frac{b}{a^{9}}\right)^{\frac{3}{4}} + b x^{2}\right) + \sqrt{2} a x \left(-\frac{b}{a^{9}}\right)^{\frac{1}{8}} \log\left(-\sqrt{2} a^{8} x \left(-\frac{b}{a^{9}}\right)^{\frac{7}{8}} - a^{7} \left(-\frac{b}{a^{9}}\right)^{\frac{3}{4}} + b x^{2}\right) + 8 \, a x \left(-\frac{b}{a^{9}}\right)^{\frac{1}{8}} \arctan\left(-a x \left(-\frac{b}{a^{9}}\right)^{\frac{1}{8}} + a \sqrt{-\frac{a^{7} \left(-\frac{b}{a^{9}}\right)^{\frac{3}{4}} - b x^{2}}{b}} \left(-\frac{b}{a^{9}}\right)^{\frac{1}{8}}\right) - 2 \, a x \left(-\frac{b}{a^{9}}\right)^{\frac{1}{8}} \log\left(a^{8} \left(-\frac{b}{a^{9}}\right)^{\frac{7}{8}} + b x\right) + 2 \, a x \left(-\frac{b}{a^{9}}\right)^{\frac{1}{8}} \log\left(-a^{8} \left(-\frac{b}{a^{9}}\right)^{\frac{7}{8}} + b x\right) - 16}{16 \, a x}"," ",0,"1/16*(4*sqrt(2)*a*x*(-b/a^9)^(1/8)*arctan(-sqrt(2)*a*x*(-b/a^9)^(1/8) + sqrt(2)*a*sqrt(-(sqrt(2)*a^8*x*(-b/a^9)^(7/8) + a^7*(-b/a^9)^(3/4) - b*x^2)/b)*(-b/a^9)^(1/8) - 1) + 4*sqrt(2)*a*x*(-b/a^9)^(1/8)*arctan(-sqrt(2)*a*x*(-b/a^9)^(1/8) + sqrt(2)*a*sqrt((sqrt(2)*a^8*x*(-b/a^9)^(7/8) - a^7*(-b/a^9)^(3/4) + b*x^2)/b)*(-b/a^9)^(1/8) + 1) - sqrt(2)*a*x*(-b/a^9)^(1/8)*log(sqrt(2)*a^8*x*(-b/a^9)^(7/8) - a^7*(-b/a^9)^(3/4) + b*x^2) + sqrt(2)*a*x*(-b/a^9)^(1/8)*log(-sqrt(2)*a^8*x*(-b/a^9)^(7/8) - a^7*(-b/a^9)^(3/4) + b*x^2) + 8*a*x*(-b/a^9)^(1/8)*arctan(-a*x*(-b/a^9)^(1/8) + a*sqrt(-(a^7*(-b/a^9)^(3/4) - b*x^2)/b)*(-b/a^9)^(1/8)) - 2*a*x*(-b/a^9)^(1/8)*log(a^8*(-b/a^9)^(7/8) + b*x) + 2*a*x*(-b/a^9)^(1/8)*log(-a^8*(-b/a^9)^(7/8) + b*x) - 16)/(a*x)","B",0
1467,1,516,0,1.404702," ","integrate(1/x^4/(b*x^8+a),x, algorithm=""fricas"")","-\frac{12 \, \sqrt{2} a x^{3} \left(-\frac{b^{3}}{a^{11}}\right)^{\frac{1}{8}} \arctan\left(-\frac{\sqrt{2} a^{4} x \left(-\frac{b^{3}}{a^{11}}\right)^{\frac{3}{8}} - \sqrt{2} a^{4} \sqrt{-\frac{\sqrt{2} a^{7} x \left(-\frac{b^{3}}{a^{11}}\right)^{\frac{5}{8}} + a^{3} b \left(-\frac{b^{3}}{a^{11}}\right)^{\frac{1}{4}} - b^{2} x^{2}}{b^{2}}} \left(-\frac{b^{3}}{a^{11}}\right)^{\frac{3}{8}} + b}{b}\right) + 12 \, \sqrt{2} a x^{3} \left(-\frac{b^{3}}{a^{11}}\right)^{\frac{1}{8}} \arctan\left(-\frac{\sqrt{2} a^{4} x \left(-\frac{b^{3}}{a^{11}}\right)^{\frac{3}{8}} - \sqrt{2} a^{4} \sqrt{\frac{\sqrt{2} a^{7} x \left(-\frac{b^{3}}{a^{11}}\right)^{\frac{5}{8}} - a^{3} b \left(-\frac{b^{3}}{a^{11}}\right)^{\frac{1}{4}} + b^{2} x^{2}}{b^{2}}} \left(-\frac{b^{3}}{a^{11}}\right)^{\frac{3}{8}} - b}{b}\right) + 3 \, \sqrt{2} a x^{3} \left(-\frac{b^{3}}{a^{11}}\right)^{\frac{1}{8}} \log\left(\sqrt{2} a^{7} x \left(-\frac{b^{3}}{a^{11}}\right)^{\frac{5}{8}} - a^{3} b \left(-\frac{b^{3}}{a^{11}}\right)^{\frac{1}{4}} + b^{2} x^{2}\right) - 3 \, \sqrt{2} a x^{3} \left(-\frac{b^{3}}{a^{11}}\right)^{\frac{1}{8}} \log\left(-\sqrt{2} a^{7} x \left(-\frac{b^{3}}{a^{11}}\right)^{\frac{5}{8}} - a^{3} b \left(-\frac{b^{3}}{a^{11}}\right)^{\frac{1}{4}} + b^{2} x^{2}\right) - 24 \, a x^{3} \left(-\frac{b^{3}}{a^{11}}\right)^{\frac{1}{8}} \arctan\left(-\frac{a^{4} x \left(-\frac{b^{3}}{a^{11}}\right)^{\frac{3}{8}} - a^{4} \sqrt{-\frac{a^{3} \left(-\frac{b^{3}}{a^{11}}\right)^{\frac{1}{4}} - b x^{2}}{b}} \left(-\frac{b^{3}}{a^{11}}\right)^{\frac{3}{8}}}{b}\right) - 6 \, a x^{3} \left(-\frac{b^{3}}{a^{11}}\right)^{\frac{1}{8}} \log\left(a^{7} \left(-\frac{b^{3}}{a^{11}}\right)^{\frac{5}{8}} + b^{2} x\right) + 6 \, a x^{3} \left(-\frac{b^{3}}{a^{11}}\right)^{\frac{1}{8}} \log\left(-a^{7} \left(-\frac{b^{3}}{a^{11}}\right)^{\frac{5}{8}} + b^{2} x\right) + 16}{48 \, a x^{3}}"," ",0,"-1/48*(12*sqrt(2)*a*x^3*(-b^3/a^11)^(1/8)*arctan(-(sqrt(2)*a^4*x*(-b^3/a^11)^(3/8) - sqrt(2)*a^4*sqrt(-(sqrt(2)*a^7*x*(-b^3/a^11)^(5/8) + a^3*b*(-b^3/a^11)^(1/4) - b^2*x^2)/b^2)*(-b^3/a^11)^(3/8) + b)/b) + 12*sqrt(2)*a*x^3*(-b^3/a^11)^(1/8)*arctan(-(sqrt(2)*a^4*x*(-b^3/a^11)^(3/8) - sqrt(2)*a^4*sqrt((sqrt(2)*a^7*x*(-b^3/a^11)^(5/8) - a^3*b*(-b^3/a^11)^(1/4) + b^2*x^2)/b^2)*(-b^3/a^11)^(3/8) - b)/b) + 3*sqrt(2)*a*x^3*(-b^3/a^11)^(1/8)*log(sqrt(2)*a^7*x*(-b^3/a^11)^(5/8) - a^3*b*(-b^3/a^11)^(1/4) + b^2*x^2) - 3*sqrt(2)*a*x^3*(-b^3/a^11)^(1/8)*log(-sqrt(2)*a^7*x*(-b^3/a^11)^(5/8) - a^3*b*(-b^3/a^11)^(1/4) + b^2*x^2) - 24*a*x^3*(-b^3/a^11)^(1/8)*arctan(-(a^4*x*(-b^3/a^11)^(3/8) - a^4*sqrt(-(a^3*(-b^3/a^11)^(1/4) - b*x^2)/b)*(-b^3/a^11)^(3/8))/b) - 6*a*x^3*(-b^3/a^11)^(1/8)*log(a^7*(-b^3/a^11)^(5/8) + b^2*x) + 6*a*x^3*(-b^3/a^11)^(1/8)*log(-a^7*(-b^3/a^11)^(5/8) + b^2*x) + 16)/(a*x^3)","B",0
1468,1,524,0,1.193187," ","integrate(1/x^6/(b*x^8+a),x, algorithm=""fricas"")","\frac{20 \, \sqrt{2} a x^{5} \left(-\frac{b^{5}}{a^{13}}\right)^{\frac{1}{8}} \arctan\left(-\frac{\sqrt{2} a^{8} x \left(-\frac{b^{5}}{a^{13}}\right)^{\frac{5}{8}} - \sqrt{2} a^{8} \sqrt{\frac{a^{10} \left(-\frac{b^{5}}{a^{13}}\right)^{\frac{3}{4}} + \sqrt{2} a^{5} b^{2} x \left(-\frac{b^{5}}{a^{13}}\right)^{\frac{3}{8}} + b^{4} x^{2}}{b^{4}}} \left(-\frac{b^{5}}{a^{13}}\right)^{\frac{5}{8}} - b^{3}}{b^{3}}\right) + 20 \, \sqrt{2} a x^{5} \left(-\frac{b^{5}}{a^{13}}\right)^{\frac{1}{8}} \arctan\left(-\frac{\sqrt{2} a^{8} x \left(-\frac{b^{5}}{a^{13}}\right)^{\frac{5}{8}} - \sqrt{2} a^{8} \sqrt{\frac{a^{10} \left(-\frac{b^{5}}{a^{13}}\right)^{\frac{3}{4}} - \sqrt{2} a^{5} b^{2} x \left(-\frac{b^{5}}{a^{13}}\right)^{\frac{3}{8}} + b^{4} x^{2}}{b^{4}}} \left(-\frac{b^{5}}{a^{13}}\right)^{\frac{5}{8}} + b^{3}}{b^{3}}\right) - 5 \, \sqrt{2} a x^{5} \left(-\frac{b^{5}}{a^{13}}\right)^{\frac{1}{8}} \log\left(a^{10} \left(-\frac{b^{5}}{a^{13}}\right)^{\frac{3}{4}} + \sqrt{2} a^{5} b^{2} x \left(-\frac{b^{5}}{a^{13}}\right)^{\frac{3}{8}} + b^{4} x^{2}\right) + 5 \, \sqrt{2} a x^{5} \left(-\frac{b^{5}}{a^{13}}\right)^{\frac{1}{8}} \log\left(a^{10} \left(-\frac{b^{5}}{a^{13}}\right)^{\frac{3}{4}} - \sqrt{2} a^{5} b^{2} x \left(-\frac{b^{5}}{a^{13}}\right)^{\frac{3}{8}} + b^{4} x^{2}\right) - 40 \, a x^{5} \left(-\frac{b^{5}}{a^{13}}\right)^{\frac{1}{8}} \arctan\left(-\frac{a^{8} x \left(-\frac{b^{5}}{a^{13}}\right)^{\frac{5}{8}} - a^{8} \sqrt{\frac{a^{10} \left(-\frac{b^{5}}{a^{13}}\right)^{\frac{3}{4}} + b^{4} x^{2}}{b^{4}}} \left(-\frac{b^{5}}{a^{13}}\right)^{\frac{5}{8}}}{b^{3}}\right) + 10 \, a x^{5} \left(-\frac{b^{5}}{a^{13}}\right)^{\frac{1}{8}} \log\left(a^{5} \left(-\frac{b^{5}}{a^{13}}\right)^{\frac{3}{8}} + b^{2} x\right) - 10 \, a x^{5} \left(-\frac{b^{5}}{a^{13}}\right)^{\frac{1}{8}} \log\left(-a^{5} \left(-\frac{b^{5}}{a^{13}}\right)^{\frac{3}{8}} + b^{2} x\right) - 16}{80 \, a x^{5}}"," ",0,"1/80*(20*sqrt(2)*a*x^5*(-b^5/a^13)^(1/8)*arctan(-(sqrt(2)*a^8*x*(-b^5/a^13)^(5/8) - sqrt(2)*a^8*sqrt((a^10*(-b^5/a^13)^(3/4) + sqrt(2)*a^5*b^2*x*(-b^5/a^13)^(3/8) + b^4*x^2)/b^4)*(-b^5/a^13)^(5/8) - b^3)/b^3) + 20*sqrt(2)*a*x^5*(-b^5/a^13)^(1/8)*arctan(-(sqrt(2)*a^8*x*(-b^5/a^13)^(5/8) - sqrt(2)*a^8*sqrt((a^10*(-b^5/a^13)^(3/4) - sqrt(2)*a^5*b^2*x*(-b^5/a^13)^(3/8) + b^4*x^2)/b^4)*(-b^5/a^13)^(5/8) + b^3)/b^3) - 5*sqrt(2)*a*x^5*(-b^5/a^13)^(1/8)*log(a^10*(-b^5/a^13)^(3/4) + sqrt(2)*a^5*b^2*x*(-b^5/a^13)^(3/8) + b^4*x^2) + 5*sqrt(2)*a*x^5*(-b^5/a^13)^(1/8)*log(a^10*(-b^5/a^13)^(3/4) - sqrt(2)*a^5*b^2*x*(-b^5/a^13)^(3/8) + b^4*x^2) - 40*a*x^5*(-b^5/a^13)^(1/8)*arctan(-(a^8*x*(-b^5/a^13)^(5/8) - a^8*sqrt((a^10*(-b^5/a^13)^(3/4) + b^4*x^2)/b^4)*(-b^5/a^13)^(5/8))/b^3) + 10*a*x^5*(-b^5/a^13)^(1/8)*log(a^5*(-b^5/a^13)^(3/8) + b^2*x) - 10*a*x^5*(-b^5/a^13)^(1/8)*log(-a^5*(-b^5/a^13)^(3/8) + b^2*x) - 16)/(a*x^5)","B",0
1469,1,514,0,0.886655," ","integrate(1/x^8/(b*x^8+a),x, algorithm=""fricas"")","-\frac{28 \, \sqrt{2} a x^{7} \left(-\frac{b^{7}}{a^{15}}\right)^{\frac{1}{8}} \arctan\left(-\frac{\sqrt{2} a^{13} x \left(-\frac{b^{7}}{a^{15}}\right)^{\frac{7}{8}} - \sqrt{2} a^{13} \sqrt{\frac{\sqrt{2} a^{2} b x \left(-\frac{b^{7}}{a^{15}}\right)^{\frac{1}{8}} + a^{4} \left(-\frac{b^{7}}{a^{15}}\right)^{\frac{1}{4}} + b^{2} x^{2}}{b^{2}}} \left(-\frac{b^{7}}{a^{15}}\right)^{\frac{7}{8}} - b^{6}}{b^{6}}\right) + 28 \, \sqrt{2} a x^{7} \left(-\frac{b^{7}}{a^{15}}\right)^{\frac{1}{8}} \arctan\left(-\frac{\sqrt{2} a^{13} x \left(-\frac{b^{7}}{a^{15}}\right)^{\frac{7}{8}} - \sqrt{2} a^{13} \sqrt{-\frac{\sqrt{2} a^{2} b x \left(-\frac{b^{7}}{a^{15}}\right)^{\frac{1}{8}} - a^{4} \left(-\frac{b^{7}}{a^{15}}\right)^{\frac{1}{4}} - b^{2} x^{2}}{b^{2}}} \left(-\frac{b^{7}}{a^{15}}\right)^{\frac{7}{8}} + b^{6}}{b^{6}}\right) + 7 \, \sqrt{2} a x^{7} \left(-\frac{b^{7}}{a^{15}}\right)^{\frac{1}{8}} \log\left(\sqrt{2} a^{2} b x \left(-\frac{b^{7}}{a^{15}}\right)^{\frac{1}{8}} + a^{4} \left(-\frac{b^{7}}{a^{15}}\right)^{\frac{1}{4}} + b^{2} x^{2}\right) - 7 \, \sqrt{2} a x^{7} \left(-\frac{b^{7}}{a^{15}}\right)^{\frac{1}{8}} \log\left(-\sqrt{2} a^{2} b x \left(-\frac{b^{7}}{a^{15}}\right)^{\frac{1}{8}} + a^{4} \left(-\frac{b^{7}}{a^{15}}\right)^{\frac{1}{4}} + b^{2} x^{2}\right) + 56 \, a x^{7} \left(-\frac{b^{7}}{a^{15}}\right)^{\frac{1}{8}} \arctan\left(-\frac{a^{13} x \left(-\frac{b^{7}}{a^{15}}\right)^{\frac{7}{8}} - a^{13} \sqrt{\frac{a^{4} \left(-\frac{b^{7}}{a^{15}}\right)^{\frac{1}{4}} + b^{2} x^{2}}{b^{2}}} \left(-\frac{b^{7}}{a^{15}}\right)^{\frac{7}{8}}}{b^{6}}\right) + 14 \, a x^{7} \left(-\frac{b^{7}}{a^{15}}\right)^{\frac{1}{8}} \log\left(a^{2} \left(-\frac{b^{7}}{a^{15}}\right)^{\frac{1}{8}} + b x\right) - 14 \, a x^{7} \left(-\frac{b^{7}}{a^{15}}\right)^{\frac{1}{8}} \log\left(-a^{2} \left(-\frac{b^{7}}{a^{15}}\right)^{\frac{1}{8}} + b x\right) + 16}{112 \, a x^{7}}"," ",0,"-1/112*(28*sqrt(2)*a*x^7*(-b^7/a^15)^(1/8)*arctan(-(sqrt(2)*a^13*x*(-b^7/a^15)^(7/8) - sqrt(2)*a^13*sqrt((sqrt(2)*a^2*b*x*(-b^7/a^15)^(1/8) + a^4*(-b^7/a^15)^(1/4) + b^2*x^2)/b^2)*(-b^7/a^15)^(7/8) - b^6)/b^6) + 28*sqrt(2)*a*x^7*(-b^7/a^15)^(1/8)*arctan(-(sqrt(2)*a^13*x*(-b^7/a^15)^(7/8) - sqrt(2)*a^13*sqrt(-(sqrt(2)*a^2*b*x*(-b^7/a^15)^(1/8) - a^4*(-b^7/a^15)^(1/4) - b^2*x^2)/b^2)*(-b^7/a^15)^(7/8) + b^6)/b^6) + 7*sqrt(2)*a*x^7*(-b^7/a^15)^(1/8)*log(sqrt(2)*a^2*b*x*(-b^7/a^15)^(1/8) + a^4*(-b^7/a^15)^(1/4) + b^2*x^2) - 7*sqrt(2)*a*x^7*(-b^7/a^15)^(1/8)*log(-sqrt(2)*a^2*b*x*(-b^7/a^15)^(1/8) + a^4*(-b^7/a^15)^(1/4) + b^2*x^2) + 56*a*x^7*(-b^7/a^15)^(1/8)*arctan(-(a^13*x*(-b^7/a^15)^(7/8) - a^13*sqrt((a^4*(-b^7/a^15)^(1/4) + b^2*x^2)/b^2)*(-b^7/a^15)^(7/8))/b^6) + 14*a*x^7*(-b^7/a^15)^(1/8)*log(a^2*(-b^7/a^15)^(1/8) + b*x) - 14*a*x^7*(-b^7/a^15)^(1/8)*log(-a^2*(-b^7/a^15)^(1/8) + b*x) + 16)/(a*x^7)","B",0
1470,1,384,0,0.996485," ","integrate(1/(-b*x^8+a),x, algorithm=""fricas"")","-\frac{1}{4} \, \sqrt{2} \left(\frac{1}{a^{7} b}\right)^{\frac{1}{8}} \arctan\left(-\sqrt{2} a^{6} b x \left(\frac{1}{a^{7} b}\right)^{\frac{7}{8}} + \sqrt{2} \sqrt{\sqrt{2} a x \left(\frac{1}{a^{7} b}\right)^{\frac{1}{8}} + a^{2} \left(\frac{1}{a^{7} b}\right)^{\frac{1}{4}} + x^{2}} a^{6} b \left(\frac{1}{a^{7} b}\right)^{\frac{7}{8}} - 1\right) - \frac{1}{4} \, \sqrt{2} \left(\frac{1}{a^{7} b}\right)^{\frac{1}{8}} \arctan\left(-\sqrt{2} a^{6} b x \left(\frac{1}{a^{7} b}\right)^{\frac{7}{8}} + \sqrt{2} \sqrt{-\sqrt{2} a x \left(\frac{1}{a^{7} b}\right)^{\frac{1}{8}} + a^{2} \left(\frac{1}{a^{7} b}\right)^{\frac{1}{4}} + x^{2}} a^{6} b \left(\frac{1}{a^{7} b}\right)^{\frac{7}{8}} + 1\right) + \frac{1}{16} \, \sqrt{2} \left(\frac{1}{a^{7} b}\right)^{\frac{1}{8}} \log\left(\sqrt{2} a x \left(\frac{1}{a^{7} b}\right)^{\frac{1}{8}} + a^{2} \left(\frac{1}{a^{7} b}\right)^{\frac{1}{4}} + x^{2}\right) - \frac{1}{16} \, \sqrt{2} \left(\frac{1}{a^{7} b}\right)^{\frac{1}{8}} \log\left(-\sqrt{2} a x \left(\frac{1}{a^{7} b}\right)^{\frac{1}{8}} + a^{2} \left(\frac{1}{a^{7} b}\right)^{\frac{1}{4}} + x^{2}\right) - \frac{1}{2} \, \left(\frac{1}{a^{7} b}\right)^{\frac{1}{8}} \arctan\left(-a^{6} b x \left(\frac{1}{a^{7} b}\right)^{\frac{7}{8}} + \sqrt{a^{2} \left(\frac{1}{a^{7} b}\right)^{\frac{1}{4}} + x^{2}} a^{6} b \left(\frac{1}{a^{7} b}\right)^{\frac{7}{8}}\right) + \frac{1}{8} \, \left(\frac{1}{a^{7} b}\right)^{\frac{1}{8}} \log\left(a \left(\frac{1}{a^{7} b}\right)^{\frac{1}{8}} + x\right) - \frac{1}{8} \, \left(\frac{1}{a^{7} b}\right)^{\frac{1}{8}} \log\left(-a \left(\frac{1}{a^{7} b}\right)^{\frac{1}{8}} + x\right)"," ",0,"-1/4*sqrt(2)*(1/(a^7*b))^(1/8)*arctan(-sqrt(2)*a^6*b*x*(1/(a^7*b))^(7/8) + sqrt(2)*sqrt(sqrt(2)*a*x*(1/(a^7*b))^(1/8) + a^2*(1/(a^7*b))^(1/4) + x^2)*a^6*b*(1/(a^7*b))^(7/8) - 1) - 1/4*sqrt(2)*(1/(a^7*b))^(1/8)*arctan(-sqrt(2)*a^6*b*x*(1/(a^7*b))^(7/8) + sqrt(2)*sqrt(-sqrt(2)*a*x*(1/(a^7*b))^(1/8) + a^2*(1/(a^7*b))^(1/4) + x^2)*a^6*b*(1/(a^7*b))^(7/8) + 1) + 1/16*sqrt(2)*(1/(a^7*b))^(1/8)*log(sqrt(2)*a*x*(1/(a^7*b))^(1/8) + a^2*(1/(a^7*b))^(1/4) + x^2) - 1/16*sqrt(2)*(1/(a^7*b))^(1/8)*log(-sqrt(2)*a*x*(1/(a^7*b))^(1/8) + a^2*(1/(a^7*b))^(1/4) + x^2) - 1/2*(1/(a^7*b))^(1/8)*arctan(-a^6*b*x*(1/(a^7*b))^(7/8) + sqrt(a^2*(1/(a^7*b))^(1/4) + x^2)*a^6*b*(1/(a^7*b))^(7/8)) + 1/8*(1/(a^7*b))^(1/8)*log(a*(1/(a^7*b))^(1/8) + x) - 1/8*(1/(a^7*b))^(1/8)*log(-a*(1/(a^7*b))^(1/8) + x)","B",0
1471,1,28,0,0.864824," ","integrate(x^9/(-x^8+1),x, algorithm=""fricas"")","-\frac{1}{2} \, x^{2} + \frac{1}{4} \, \arctan\left(x^{2}\right) + \frac{1}{8} \, \log\left(x^{2} + 1\right) - \frac{1}{8} \, \log\left(x^{2} - 1\right)"," ",0,"-1/2*x^2 + 1/4*arctan(x^2) + 1/8*log(x^2 + 1) - 1/8*log(x^2 - 1)","A",0
1472,1,8,0,0.955761," ","integrate(x^7/(-x^8+1),x, algorithm=""fricas"")","-\frac{1}{8} \, \log\left(x^{8} - 1\right)"," ",0,"-1/8*log(x^8 - 1)","A",0
1473,1,23,0,0.955038," ","integrate(x^5/(-x^8+1),x, algorithm=""fricas"")","-\frac{1}{4} \, \arctan\left(x^{2}\right) + \frac{1}{8} \, \log\left(x^{2} + 1\right) - \frac{1}{8} \, \log\left(x^{2} - 1\right)"," ",0,"-1/4*arctan(x^2) + 1/8*log(x^2 + 1) - 1/8*log(x^2 - 1)","A",0
1474,1,17,0,0.826324," ","integrate(x^3/(-x^8+1),x, algorithm=""fricas"")","\frac{1}{8} \, \log\left(x^{4} + 1\right) - \frac{1}{8} \, \log\left(x^{4} - 1\right)"," ",0,"1/8*log(x^4 + 1) - 1/8*log(x^4 - 1)","B",0
1475,1,23,0,0.576240," ","integrate(x/(-x^8+1),x, algorithm=""fricas"")","\frac{1}{4} \, \arctan\left(x^{2}\right) + \frac{1}{8} \, \log\left(x^{2} + 1\right) - \frac{1}{8} \, \log\left(x^{2} - 1\right)"," ",0,"1/4*arctan(x^2) + 1/8*log(x^2 + 1) - 1/8*log(x^2 - 1)","A",0
1476,1,11,0,1.149156," ","integrate(1/x/(-x^8+1),x, algorithm=""fricas"")","-\frac{1}{8} \, \log\left(x^{8} - 1\right) + \log\left(x\right)"," ",0,"-1/8*log(x^8 - 1) + log(x)","A",0
1477,1,37,0,0.849128," ","integrate(1/x^3/(-x^8+1),x, algorithm=""fricas"")","-\frac{2 \, x^{2} \arctan\left(x^{2}\right) - x^{2} \log\left(x^{2} + 1\right) + x^{2} \log\left(x^{2} - 1\right) + 4}{8 \, x^{2}}"," ",0,"-1/8*(2*x^2*arctan(x^2) - x^2*log(x^2 + 1) + x^2*log(x^2 - 1) + 4)/x^2","B",0
1478,1,28,0,0.998146," ","integrate(1/x^5/(-x^8+1),x, algorithm=""fricas"")","\frac{x^{4} \log\left(x^{4} + 1\right) - x^{4} \log\left(x^{4} - 1\right) - 2}{8 \, x^{4}}"," ",0,"1/8*(x^4*log(x^4 + 1) - x^4*log(x^4 - 1) - 2)/x^4","B",0
1479,1,38,0,0.953241," ","integrate(1/x^7/(-x^8+1),x, algorithm=""fricas"")","\frac{6 \, x^{6} \arctan\left(x^{2}\right) + 3 \, x^{6} \log\left(x^{2} + 1\right) - 3 \, x^{6} \log\left(x^{2} - 1\right) - 4}{24 \, x^{6}}"," ",0,"1/24*(6*x^6*arctan(x^2) + 3*x^6*log(x^2 + 1) - 3*x^6*log(x^2 - 1) - 4)/x^6","B",0
1480,1,24,0,1.039085," ","integrate(1/x^9/(-x^8+1),x, algorithm=""fricas"")","-\frac{x^{8} \log\left(x^{8} - 1\right) - 8 \, x^{8} \log\left(x\right) + 1}{8 \, x^{8}}"," ",0,"-1/8*(x^8*log(x^8 - 1) - 8*x^8*log(x) + 1)/x^8","A",0
1481,1,114,0,0.749660," ","integrate(x^8/(-x^8+1),x, algorithm=""fricas"")","-\frac{1}{4} \, \sqrt{2} \arctan\left(-\sqrt{2} x + \sqrt{2} \sqrt{x^{2} + \sqrt{2} x + 1} - 1\right) - \frac{1}{4} \, \sqrt{2} \arctan\left(-\sqrt{2} x + \sqrt{2} \sqrt{x^{2} - \sqrt{2} x + 1} + 1\right) + \frac{1}{16} \, \sqrt{2} \log\left(x^{2} + \sqrt{2} x + 1\right) - \frac{1}{16} \, \sqrt{2} \log\left(x^{2} - \sqrt{2} x + 1\right) - x + \frac{1}{4} \, \arctan\left(x\right) + \frac{1}{8} \, \log\left(x + 1\right) - \frac{1}{8} \, \log\left(x - 1\right)"," ",0,"-1/4*sqrt(2)*arctan(-sqrt(2)*x + sqrt(2)*sqrt(x^2 + sqrt(2)*x + 1) - 1) - 1/4*sqrt(2)*arctan(-sqrt(2)*x + sqrt(2)*sqrt(x^2 - sqrt(2)*x + 1) + 1) + 1/16*sqrt(2)*log(x^2 + sqrt(2)*x + 1) - 1/16*sqrt(2)*log(x^2 - sqrt(2)*x + 1) - x + 1/4*arctan(x) + 1/8*log(x + 1) - 1/8*log(x - 1)","A",0
1482,1,111,0,1.033366," ","integrate(x^6/(-x^8+1),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{2} \arctan\left(-\sqrt{2} x + \sqrt{2} \sqrt{x^{2} + \sqrt{2} x + 1} - 1\right) + \frac{1}{4} \, \sqrt{2} \arctan\left(-\sqrt{2} x + \sqrt{2} \sqrt{x^{2} - \sqrt{2} x + 1} + 1\right) + \frac{1}{16} \, \sqrt{2} \log\left(x^{2} + \sqrt{2} x + 1\right) - \frac{1}{16} \, \sqrt{2} \log\left(x^{2} - \sqrt{2} x + 1\right) - \frac{1}{4} \, \arctan\left(x\right) + \frac{1}{8} \, \log\left(x + 1\right) - \frac{1}{8} \, \log\left(x - 1\right)"," ",0,"1/4*sqrt(2)*arctan(-sqrt(2)*x + sqrt(2)*sqrt(x^2 + sqrt(2)*x + 1) - 1) + 1/4*sqrt(2)*arctan(-sqrt(2)*x + sqrt(2)*sqrt(x^2 - sqrt(2)*x + 1) + 1) + 1/16*sqrt(2)*log(x^2 + sqrt(2)*x + 1) - 1/16*sqrt(2)*log(x^2 - sqrt(2)*x + 1) - 1/4*arctan(x) + 1/8*log(x + 1) - 1/8*log(x - 1)","A",0
1483,1,111,0,0.938807," ","integrate(x^4/(-x^8+1),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{2} \arctan\left(-\sqrt{2} x + \sqrt{2} \sqrt{x^{2} + \sqrt{2} x + 1} - 1\right) + \frac{1}{4} \, \sqrt{2} \arctan\left(-\sqrt{2} x + \sqrt{2} \sqrt{x^{2} - \sqrt{2} x + 1} + 1\right) - \frac{1}{16} \, \sqrt{2} \log\left(x^{2} + \sqrt{2} x + 1\right) + \frac{1}{16} \, \sqrt{2} \log\left(x^{2} - \sqrt{2} x + 1\right) + \frac{1}{4} \, \arctan\left(x\right) + \frac{1}{8} \, \log\left(x + 1\right) - \frac{1}{8} \, \log\left(x - 1\right)"," ",0,"1/4*sqrt(2)*arctan(-sqrt(2)*x + sqrt(2)*sqrt(x^2 + sqrt(2)*x + 1) - 1) + 1/4*sqrt(2)*arctan(-sqrt(2)*x + sqrt(2)*sqrt(x^2 - sqrt(2)*x + 1) + 1) - 1/16*sqrt(2)*log(x^2 + sqrt(2)*x + 1) + 1/16*sqrt(2)*log(x^2 - sqrt(2)*x + 1) + 1/4*arctan(x) + 1/8*log(x + 1) - 1/8*log(x - 1)","A",0
1484,1,111,0,0.851169," ","integrate(x^2/(-x^8+1),x, algorithm=""fricas"")","-\frac{1}{4} \, \sqrt{2} \arctan\left(-\sqrt{2} x + \sqrt{2} \sqrt{x^{2} + \sqrt{2} x + 1} - 1\right) - \frac{1}{4} \, \sqrt{2} \arctan\left(-\sqrt{2} x + \sqrt{2} \sqrt{x^{2} - \sqrt{2} x + 1} + 1\right) - \frac{1}{16} \, \sqrt{2} \log\left(x^{2} + \sqrt{2} x + 1\right) + \frac{1}{16} \, \sqrt{2} \log\left(x^{2} - \sqrt{2} x + 1\right) - \frac{1}{4} \, \arctan\left(x\right) + \frac{1}{8} \, \log\left(x + 1\right) - \frac{1}{8} \, \log\left(x - 1\right)"," ",0,"-1/4*sqrt(2)*arctan(-sqrt(2)*x + sqrt(2)*sqrt(x^2 + sqrt(2)*x + 1) - 1) - 1/4*sqrt(2)*arctan(-sqrt(2)*x + sqrt(2)*sqrt(x^2 - sqrt(2)*x + 1) + 1) - 1/16*sqrt(2)*log(x^2 + sqrt(2)*x + 1) + 1/16*sqrt(2)*log(x^2 - sqrt(2)*x + 1) - 1/4*arctan(x) + 1/8*log(x + 1) - 1/8*log(x - 1)","A",0
1485,1,111,0,0.721165," ","integrate(1/(-x^8+1),x, algorithm=""fricas"")","-\frac{1}{4} \, \sqrt{2} \arctan\left(-\sqrt{2} x + \sqrt{2} \sqrt{x^{2} + \sqrt{2} x + 1} - 1\right) - \frac{1}{4} \, \sqrt{2} \arctan\left(-\sqrt{2} x + \sqrt{2} \sqrt{x^{2} - \sqrt{2} x + 1} + 1\right) + \frac{1}{16} \, \sqrt{2} \log\left(x^{2} + \sqrt{2} x + 1\right) - \frac{1}{16} \, \sqrt{2} \log\left(x^{2} - \sqrt{2} x + 1\right) + \frac{1}{4} \, \arctan\left(x\right) + \frac{1}{8} \, \log\left(x + 1\right) - \frac{1}{8} \, \log\left(x - 1\right)"," ",0,"-1/4*sqrt(2)*arctan(-sqrt(2)*x + sqrt(2)*sqrt(x^2 + sqrt(2)*x + 1) - 1) - 1/4*sqrt(2)*arctan(-sqrt(2)*x + sqrt(2)*sqrt(x^2 - sqrt(2)*x + 1) + 1) + 1/16*sqrt(2)*log(x^2 + sqrt(2)*x + 1) - 1/16*sqrt(2)*log(x^2 - sqrt(2)*x + 1) + 1/4*arctan(x) + 1/8*log(x + 1) - 1/8*log(x - 1)","A",0
1486,1,123,0,1.378476," ","integrate(1/x^2/(-x^8+1),x, algorithm=""fricas"")","\frac{4 \, \sqrt{2} x \arctan\left(-\sqrt{2} x + \sqrt{2} \sqrt{x^{2} + \sqrt{2} x + 1} - 1\right) + 4 \, \sqrt{2} x \arctan\left(-\sqrt{2} x + \sqrt{2} \sqrt{x^{2} - \sqrt{2} x + 1} + 1\right) + \sqrt{2} x \log\left(x^{2} + \sqrt{2} x + 1\right) - \sqrt{2} x \log\left(x^{2} - \sqrt{2} x + 1\right) - 4 \, x \arctan\left(x\right) + 2 \, x \log\left(x + 1\right) - 2 \, x \log\left(x - 1\right) - 16}{16 \, x}"," ",0,"1/16*(4*sqrt(2)*x*arctan(-sqrt(2)*x + sqrt(2)*sqrt(x^2 + sqrt(2)*x + 1) - 1) + 4*sqrt(2)*x*arctan(-sqrt(2)*x + sqrt(2)*sqrt(x^2 - sqrt(2)*x + 1) + 1) + sqrt(2)*x*log(x^2 + sqrt(2)*x + 1) - sqrt(2)*x*log(x^2 - sqrt(2)*x + 1) - 4*x*arctan(x) + 2*x*log(x + 1) - 2*x*log(x - 1) - 16)/x","A",0
1487,1,138,0,0.960471," ","integrate(1/x^4/(-x^8+1),x, algorithm=""fricas"")","\frac{12 \, \sqrt{2} x^{3} \arctan\left(-\sqrt{2} x + \sqrt{2} \sqrt{x^{2} + \sqrt{2} x + 1} - 1\right) + 12 \, \sqrt{2} x^{3} \arctan\left(-\sqrt{2} x + \sqrt{2} \sqrt{x^{2} - \sqrt{2} x + 1} + 1\right) - 3 \, \sqrt{2} x^{3} \log\left(x^{2} + \sqrt{2} x + 1\right) + 3 \, \sqrt{2} x^{3} \log\left(x^{2} - \sqrt{2} x + 1\right) + 12 \, x^{3} \arctan\left(x\right) + 6 \, x^{3} \log\left(x + 1\right) - 6 \, x^{3} \log\left(x - 1\right) - 16}{48 \, x^{3}}"," ",0,"1/48*(12*sqrt(2)*x^3*arctan(-sqrt(2)*x + sqrt(2)*sqrt(x^2 + sqrt(2)*x + 1) - 1) + 12*sqrt(2)*x^3*arctan(-sqrt(2)*x + sqrt(2)*sqrt(x^2 - sqrt(2)*x + 1) + 1) - 3*sqrt(2)*x^3*log(x^2 + sqrt(2)*x + 1) + 3*sqrt(2)*x^3*log(x^2 - sqrt(2)*x + 1) + 12*x^3*arctan(x) + 6*x^3*log(x + 1) - 6*x^3*log(x - 1) - 16)/x^3","A",0
1488,1,138,0,0.839506," ","integrate(1/x^6/(-x^8+1),x, algorithm=""fricas"")","-\frac{20 \, \sqrt{2} x^{5} \arctan\left(-\sqrt{2} x + \sqrt{2} \sqrt{x^{2} + \sqrt{2} x + 1} - 1\right) + 20 \, \sqrt{2} x^{5} \arctan\left(-\sqrt{2} x + \sqrt{2} \sqrt{x^{2} - \sqrt{2} x + 1} + 1\right) + 5 \, \sqrt{2} x^{5} \log\left(x^{2} + \sqrt{2} x + 1\right) - 5 \, \sqrt{2} x^{5} \log\left(x^{2} - \sqrt{2} x + 1\right) + 20 \, x^{5} \arctan\left(x\right) - 10 \, x^{5} \log\left(x + 1\right) + 10 \, x^{5} \log\left(x - 1\right) + 16}{80 \, x^{5}}"," ",0,"-1/80*(20*sqrt(2)*x^5*arctan(-sqrt(2)*x + sqrt(2)*sqrt(x^2 + sqrt(2)*x + 1) - 1) + 20*sqrt(2)*x^5*arctan(-sqrt(2)*x + sqrt(2)*sqrt(x^2 - sqrt(2)*x + 1) + 1) + 5*sqrt(2)*x^5*log(x^2 + sqrt(2)*x + 1) - 5*sqrt(2)*x^5*log(x^2 - sqrt(2)*x + 1) + 20*x^5*arctan(x) - 10*x^5*log(x + 1) + 10*x^5*log(x - 1) + 16)/x^5","A",0
1489,1,138,0,1.098593," ","integrate(1/x^8/(-x^8+1),x, algorithm=""fricas"")","-\frac{28 \, \sqrt{2} x^{7} \arctan\left(-\sqrt{2} x + \sqrt{2} \sqrt{x^{2} + \sqrt{2} x + 1} - 1\right) + 28 \, \sqrt{2} x^{7} \arctan\left(-\sqrt{2} x + \sqrt{2} \sqrt{x^{2} - \sqrt{2} x + 1} + 1\right) - 7 \, \sqrt{2} x^{7} \log\left(x^{2} + \sqrt{2} x + 1\right) + 7 \, \sqrt{2} x^{7} \log\left(x^{2} - \sqrt{2} x + 1\right) - 28 \, x^{7} \arctan\left(x\right) - 14 \, x^{7} \log\left(x + 1\right) + 14 \, x^{7} \log\left(x - 1\right) + 16}{112 \, x^{7}}"," ",0,"-1/112*(28*sqrt(2)*x^7*arctan(-sqrt(2)*x + sqrt(2)*sqrt(x^2 + sqrt(2)*x + 1) - 1) + 28*sqrt(2)*x^7*arctan(-sqrt(2)*x + sqrt(2)*sqrt(x^2 - sqrt(2)*x + 1) + 1) - 7*sqrt(2)*x^7*log(x^2 + sqrt(2)*x + 1) + 7*sqrt(2)*x^7*log(x^2 - sqrt(2)*x + 1) - 28*x^7*arctan(x) - 14*x^7*log(x + 1) + 14*x^7*log(x - 1) + 16)/x^7","A",0
1490,1,112,0,1.293595," ","integrate(x^9/(x^8+1),x, algorithm=""fricas"")","\frac{1}{2} \, x^{2} + \frac{1}{4} \, \sqrt{2} \arctan\left(-\sqrt{2} x^{2} + \sqrt{2} \sqrt{x^{4} + \sqrt{2} x^{2} + 1} - 1\right) + \frac{1}{4} \, \sqrt{2} \arctan\left(-\sqrt{2} x^{2} + \sqrt{2} \sqrt{x^{4} - \sqrt{2} x^{2} + 1} + 1\right) - \frac{1}{16} \, \sqrt{2} \log\left(x^{4} + \sqrt{2} x^{2} + 1\right) + \frac{1}{16} \, \sqrt{2} \log\left(x^{4} - \sqrt{2} x^{2} + 1\right)"," ",0,"1/2*x^2 + 1/4*sqrt(2)*arctan(-sqrt(2)*x^2 + sqrt(2)*sqrt(x^4 + sqrt(2)*x^2 + 1) - 1) + 1/4*sqrt(2)*arctan(-sqrt(2)*x^2 + sqrt(2)*sqrt(x^4 - sqrt(2)*x^2 + 1) + 1) - 1/16*sqrt(2)*log(x^4 + sqrt(2)*x^2 + 1) + 1/16*sqrt(2)*log(x^4 - sqrt(2)*x^2 + 1)","A",0
1491,1,8,0,1.078152," ","integrate(x^7/(x^8+1),x, algorithm=""fricas"")","\frac{1}{8} \, \log\left(x^{8} + 1\right)"," ",0,"1/8*log(x^8 + 1)","A",0
1492,1,107,0,1.353606," ","integrate(x^5/(x^8+1),x, algorithm=""fricas"")","-\frac{1}{4} \, \sqrt{2} \arctan\left(-\sqrt{2} x^{2} + \sqrt{2} \sqrt{x^{4} + \sqrt{2} x^{2} + 1} - 1\right) - \frac{1}{4} \, \sqrt{2} \arctan\left(-\sqrt{2} x^{2} + \sqrt{2} \sqrt{x^{4} - \sqrt{2} x^{2} + 1} + 1\right) - \frac{1}{16} \, \sqrt{2} \log\left(x^{4} + \sqrt{2} x^{2} + 1\right) + \frac{1}{16} \, \sqrt{2} \log\left(x^{4} - \sqrt{2} x^{2} + 1\right)"," ",0,"-1/4*sqrt(2)*arctan(-sqrt(2)*x^2 + sqrt(2)*sqrt(x^4 + sqrt(2)*x^2 + 1) - 1) - 1/4*sqrt(2)*arctan(-sqrt(2)*x^2 + sqrt(2)*sqrt(x^4 - sqrt(2)*x^2 + 1) + 1) - 1/16*sqrt(2)*log(x^4 + sqrt(2)*x^2 + 1) + 1/16*sqrt(2)*log(x^4 - sqrt(2)*x^2 + 1)","A",0
1493,1,6,0,1.102231," ","integrate(x^3/(x^8+1),x, algorithm=""fricas"")","\frac{1}{4} \, \arctan\left(x^{4}\right)"," ",0,"1/4*arctan(x^4)","A",0
1494,1,107,0,0.770613," ","integrate(x/(x^8+1),x, algorithm=""fricas"")","-\frac{1}{4} \, \sqrt{2} \arctan\left(-\sqrt{2} x^{2} + \sqrt{2} \sqrt{x^{4} + \sqrt{2} x^{2} + 1} - 1\right) - \frac{1}{4} \, \sqrt{2} \arctan\left(-\sqrt{2} x^{2} + \sqrt{2} \sqrt{x^{4} - \sqrt{2} x^{2} + 1} + 1\right) + \frac{1}{16} \, \sqrt{2} \log\left(x^{4} + \sqrt{2} x^{2} + 1\right) - \frac{1}{16} \, \sqrt{2} \log\left(x^{4} - \sqrt{2} x^{2} + 1\right)"," ",0,"-1/4*sqrt(2)*arctan(-sqrt(2)*x^2 + sqrt(2)*sqrt(x^4 + sqrt(2)*x^2 + 1) - 1) - 1/4*sqrt(2)*arctan(-sqrt(2)*x^2 + sqrt(2)*sqrt(x^4 - sqrt(2)*x^2 + 1) + 1) + 1/16*sqrt(2)*log(x^4 + sqrt(2)*x^2 + 1) - 1/16*sqrt(2)*log(x^4 - sqrt(2)*x^2 + 1)","A",0
1495,1,11,0,1.138391," ","integrate(1/x/(x^8+1),x, algorithm=""fricas"")","-\frac{1}{8} \, \log\left(x^{8} + 1\right) + \log\left(x\right)"," ",0,"-1/8*log(x^8 + 1) + log(x)","A",0
1496,1,124,0,1.405644," ","integrate(1/x^3/(x^8+1),x, algorithm=""fricas"")","\frac{4 \, \sqrt{2} x^{2} \arctan\left(-\sqrt{2} x^{2} + \sqrt{2} \sqrt{x^{4} + \sqrt{2} x^{2} + 1} - 1\right) + 4 \, \sqrt{2} x^{2} \arctan\left(-\sqrt{2} x^{2} + \sqrt{2} \sqrt{x^{4} - \sqrt{2} x^{2} + 1} + 1\right) + \sqrt{2} x^{2} \log\left(x^{4} + \sqrt{2} x^{2} + 1\right) - \sqrt{2} x^{2} \log\left(x^{4} - \sqrt{2} x^{2} + 1\right) - 8}{16 \, x^{2}}"," ",0,"1/16*(4*sqrt(2)*x^2*arctan(-sqrt(2)*x^2 + sqrt(2)*sqrt(x^4 + sqrt(2)*x^2 + 1) - 1) + 4*sqrt(2)*x^2*arctan(-sqrt(2)*x^2 + sqrt(2)*sqrt(x^4 - sqrt(2)*x^2 + 1) + 1) + sqrt(2)*x^2*log(x^4 + sqrt(2)*x^2 + 1) - sqrt(2)*x^2*log(x^4 - sqrt(2)*x^2 + 1) - 8)/x^2","A",0
1497,1,15,0,1.244225," ","integrate(1/x^5/(x^8+1),x, algorithm=""fricas"")","-\frac{x^{4} \arctan\left(x^{4}\right) + 1}{4 \, x^{4}}"," ",0,"-1/4*(x^4*arctan(x^4) + 1)/x^4","A",0
1498,1,125,0,0.962456," ","integrate(1/x^7/(x^8+1),x, algorithm=""fricas"")","\frac{12 \, \sqrt{2} x^{6} \arctan\left(-\sqrt{2} x^{2} + \sqrt{2} \sqrt{x^{4} + \sqrt{2} x^{2} + 1} - 1\right) + 12 \, \sqrt{2} x^{6} \arctan\left(-\sqrt{2} x^{2} + \sqrt{2} \sqrt{x^{4} - \sqrt{2} x^{2} + 1} + 1\right) - 3 \, \sqrt{2} x^{6} \log\left(x^{4} + \sqrt{2} x^{2} + 1\right) + 3 \, \sqrt{2} x^{6} \log\left(x^{4} - \sqrt{2} x^{2} + 1\right) - 8}{48 \, x^{6}}"," ",0,"1/48*(12*sqrt(2)*x^6*arctan(-sqrt(2)*x^2 + sqrt(2)*sqrt(x^4 + sqrt(2)*x^2 + 1) - 1) + 12*sqrt(2)*x^6*arctan(-sqrt(2)*x^2 + sqrt(2)*sqrt(x^4 - sqrt(2)*x^2 + 1) + 1) - 3*sqrt(2)*x^6*log(x^4 + sqrt(2)*x^2 + 1) + 3*sqrt(2)*x^6*log(x^4 - sqrt(2)*x^2 + 1) - 8)/x^6","A",0
1499,1,24,0,1.024145," ","integrate(1/x^9/(x^8+1),x, algorithm=""fricas"")","\frac{x^{8} \log\left(x^{8} + 1\right) - 8 \, x^{8} \log\left(x\right) - 1}{8 \, x^{8}}"," ",0,"1/8*(x^8*log(x^8 + 1) - 8*x^8*log(x) - 1)/x^8","A",0
1500,1,1028,0,0.924065," ","integrate(x^8/(x^8+1),x, algorithm=""fricas"")","\frac{1}{16} \, {\left(\sqrt{2} \sqrt{\sqrt{2} + 2} + \sqrt{2} \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(-\frac{2 \, \sqrt{2} x - 2 \, \sqrt{2} \sqrt{x^{2} + \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} - \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1} + \sqrt{\sqrt{2} + 2} - \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2} + \sqrt{-\sqrt{2} + 2}}\right) + \frac{1}{16} \, {\left(\sqrt{2} \sqrt{\sqrt{2} + 2} + \sqrt{2} \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(-\frac{2 \, \sqrt{2} x - 2 \, \sqrt{2} \sqrt{x^{2} - \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} + \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1} - \sqrt{\sqrt{2} + 2} + \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2} + \sqrt{-\sqrt{2} + 2}}\right) - \frac{1}{16} \, {\left(\sqrt{2} \sqrt{\sqrt{2} + 2} - \sqrt{2} \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(\frac{2 \, \sqrt{2} x - 2 \, \sqrt{2} \sqrt{x^{2} + \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} + \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1} + \sqrt{\sqrt{2} + 2} + \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2} - \sqrt{-\sqrt{2} + 2}}\right) - \frac{1}{16} \, {\left(\sqrt{2} \sqrt{\sqrt{2} + 2} - \sqrt{2} \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(\frac{2 \, \sqrt{2} x - 2 \, \sqrt{2} \sqrt{x^{2} - \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} - \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1} - \sqrt{\sqrt{2} + 2} - \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2} - \sqrt{-\sqrt{2} + 2}}\right) - \frac{1}{64} \, {\left(\sqrt{2} \sqrt{\sqrt{2} + 2} + \sqrt{2} \sqrt{-\sqrt{2} + 2}\right)} \log\left(x^{2} + \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} + \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1\right) - \frac{1}{64} \, {\left(\sqrt{2} \sqrt{\sqrt{2} + 2} - \sqrt{2} \sqrt{-\sqrt{2} + 2}\right)} \log\left(x^{2} + \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} - \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1\right) + \frac{1}{64} \, {\left(\sqrt{2} \sqrt{\sqrt{2} + 2} - \sqrt{2} \sqrt{-\sqrt{2} + 2}\right)} \log\left(x^{2} - \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} + \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1\right) + \frac{1}{64} \, {\left(\sqrt{2} \sqrt{\sqrt{2} + 2} + \sqrt{2} \sqrt{-\sqrt{2} + 2}\right)} \log\left(x^{2} - \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} - \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1\right) + \frac{1}{8} \, \sqrt{\sqrt{2} + 2} \arctan\left(-\frac{2 \, x - 2 \, \sqrt{x^{2} + x \sqrt{-\sqrt{2} + 2} + 1} + \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2}}\right) + \frac{1}{8} \, \sqrt{\sqrt{2} + 2} \arctan\left(-\frac{2 \, x - 2 \, \sqrt{x^{2} - x \sqrt{-\sqrt{2} + 2} + 1} - \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2}}\right) + \frac{1}{8} \, \sqrt{-\sqrt{2} + 2} \arctan\left(-\frac{2 \, x - 2 \, \sqrt{x^{2} + x \sqrt{\sqrt{2} + 2} + 1} + \sqrt{\sqrt{2} + 2}}{\sqrt{-\sqrt{2} + 2}}\right) + \frac{1}{8} \, \sqrt{-\sqrt{2} + 2} \arctan\left(-\frac{2 \, x - 2 \, \sqrt{x^{2} - x \sqrt{\sqrt{2} + 2} + 1} - \sqrt{\sqrt{2} + 2}}{\sqrt{-\sqrt{2} + 2}}\right) - \frac{1}{32} \, \sqrt{\sqrt{2} + 2} \log\left(x^{2} + x \sqrt{\sqrt{2} + 2} + 1\right) + \frac{1}{32} \, \sqrt{\sqrt{2} + 2} \log\left(x^{2} - x \sqrt{\sqrt{2} + 2} + 1\right) - \frac{1}{32} \, \sqrt{-\sqrt{2} + 2} \log\left(x^{2} + x \sqrt{-\sqrt{2} + 2} + 1\right) + \frac{1}{32} \, \sqrt{-\sqrt{2} + 2} \log\left(x^{2} - x \sqrt{-\sqrt{2} + 2} + 1\right) + x"," ",0,"1/16*(sqrt(2)*sqrt(sqrt(2) + 2) + sqrt(2)*sqrt(-sqrt(2) + 2))*arctan(-(2*sqrt(2)*x - 2*sqrt(2)*sqrt(x^2 + 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) - 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) + sqrt(sqrt(2) + 2) - sqrt(-sqrt(2) + 2))/(sqrt(sqrt(2) + 2) + sqrt(-sqrt(2) + 2))) + 1/16*(sqrt(2)*sqrt(sqrt(2) + 2) + sqrt(2)*sqrt(-sqrt(2) + 2))*arctan(-(2*sqrt(2)*x - 2*sqrt(2)*sqrt(x^2 - 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) + 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) - sqrt(sqrt(2) + 2) + sqrt(-sqrt(2) + 2))/(sqrt(sqrt(2) + 2) + sqrt(-sqrt(2) + 2))) - 1/16*(sqrt(2)*sqrt(sqrt(2) + 2) - sqrt(2)*sqrt(-sqrt(2) + 2))*arctan((2*sqrt(2)*x - 2*sqrt(2)*sqrt(x^2 + 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) + 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) + sqrt(sqrt(2) + 2) + sqrt(-sqrt(2) + 2))/(sqrt(sqrt(2) + 2) - sqrt(-sqrt(2) + 2))) - 1/16*(sqrt(2)*sqrt(sqrt(2) + 2) - sqrt(2)*sqrt(-sqrt(2) + 2))*arctan((2*sqrt(2)*x - 2*sqrt(2)*sqrt(x^2 - 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) - 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) - sqrt(sqrt(2) + 2) - sqrt(-sqrt(2) + 2))/(sqrt(sqrt(2) + 2) - sqrt(-sqrt(2) + 2))) - 1/64*(sqrt(2)*sqrt(sqrt(2) + 2) + sqrt(2)*sqrt(-sqrt(2) + 2))*log(x^2 + 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) + 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) - 1/64*(sqrt(2)*sqrt(sqrt(2) + 2) - sqrt(2)*sqrt(-sqrt(2) + 2))*log(x^2 + 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) - 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) + 1/64*(sqrt(2)*sqrt(sqrt(2) + 2) - sqrt(2)*sqrt(-sqrt(2) + 2))*log(x^2 - 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) + 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) + 1/64*(sqrt(2)*sqrt(sqrt(2) + 2) + sqrt(2)*sqrt(-sqrt(2) + 2))*log(x^2 - 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) - 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) + 1/8*sqrt(sqrt(2) + 2)*arctan(-(2*x - 2*sqrt(x^2 + x*sqrt(-sqrt(2) + 2) + 1) + sqrt(-sqrt(2) + 2))/sqrt(sqrt(2) + 2)) + 1/8*sqrt(sqrt(2) + 2)*arctan(-(2*x - 2*sqrt(x^2 - x*sqrt(-sqrt(2) + 2) + 1) - sqrt(-sqrt(2) + 2))/sqrt(sqrt(2) + 2)) + 1/8*sqrt(-sqrt(2) + 2)*arctan(-(2*x - 2*sqrt(x^2 + x*sqrt(sqrt(2) + 2) + 1) + sqrt(sqrt(2) + 2))/sqrt(-sqrt(2) + 2)) + 1/8*sqrt(-sqrt(2) + 2)*arctan(-(2*x - 2*sqrt(x^2 - x*sqrt(sqrt(2) + 2) + 1) - sqrt(sqrt(2) + 2))/sqrt(-sqrt(2) + 2)) - 1/32*sqrt(sqrt(2) + 2)*log(x^2 + x*sqrt(sqrt(2) + 2) + 1) + 1/32*sqrt(sqrt(2) + 2)*log(x^2 - x*sqrt(sqrt(2) + 2) + 1) - 1/32*sqrt(-sqrt(2) + 2)*log(x^2 + x*sqrt(-sqrt(2) + 2) + 1) + 1/32*sqrt(-sqrt(2) + 2)*log(x^2 - x*sqrt(-sqrt(2) + 2) + 1) + x","B",0
1501,1,2513,0,1.147287," ","integrate(x^6/(x^8+1),x, algorithm=""fricas"")","\frac{1}{16} \, {\left(\sqrt{2} \sqrt{\sqrt{2} + 2} + \sqrt{2} \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(\frac{8 \, \sqrt{2} x + {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + 3 \, \sqrt{\sqrt{2} + 2} {\left(\sqrt{2} - 2\right)} - 3 \, {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} + {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} - \sqrt{2} \sqrt{8 \, \sqrt{2} x {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + {\left(\sqrt{2} + 2\right)}^{3} + 3 \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - {\left(\sqrt{2} - 2\right)}^{3} - 24 \, \sqrt{2} x {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} + 8 \, \sqrt{2} x {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} + 64 \, x^{2} + 3 \, {\left(8 \, \sqrt{2} x \sqrt{\sqrt{2} + 2} - {\left(\sqrt{2} + 2\right)}^{2}\right)} {\left(\sqrt{2} - 2\right)}}}{{\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + 3 \, \sqrt{\sqrt{2} + 2} {\left(\sqrt{2} - 2\right)} + 3 \, {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}}}\right) + \frac{1}{16} \, {\left(\sqrt{2} \sqrt{\sqrt{2} + 2} + \sqrt{2} \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(\frac{8 \, \sqrt{2} x - {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, \sqrt{\sqrt{2} + 2} {\left(\sqrt{2} - 2\right)} + 3 \, {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} - 8 \, \sqrt{2} \sqrt{-\frac{1}{8} \, \sqrt{2} x {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + \frac{1}{64} \, {\left(\sqrt{2} + 2\right)}^{3} + \frac{3}{64} \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - \frac{1}{64} \, {\left(\sqrt{2} - 2\right)}^{3} + \frac{3}{8} \, \sqrt{2} x {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - \frac{1}{8} \, \sqrt{2} x {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} + x^{2} - \frac{3}{64} \, {\left(8 \, \sqrt{2} x \sqrt{\sqrt{2} + 2} + {\left(\sqrt{2} + 2\right)}^{2}\right)} {\left(\sqrt{2} - 2\right)}}}{{\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + 3 \, \sqrt{\sqrt{2} + 2} {\left(\sqrt{2} - 2\right)} + 3 \, {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}}}\right) + \frac{1}{16} \, {\left(\sqrt{2} \sqrt{\sqrt{2} + 2} - \sqrt{2} \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(-\frac{8 \, \sqrt{2} x + {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + 3 \, \sqrt{\sqrt{2} + 2} {\left(\sqrt{2} - 2\right)} + 3 \, {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} - \sqrt{2} \sqrt{8 \, \sqrt{2} x {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + {\left(\sqrt{2} + 2\right)}^{3} + 3 \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - {\left(\sqrt{2} - 2\right)}^{3} + 24 \, \sqrt{2} x {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - 8 \, \sqrt{2} x {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} + 64 \, x^{2} + 3 \, {\left(8 \, \sqrt{2} x \sqrt{\sqrt{2} + 2} - {\left(\sqrt{2} + 2\right)}^{2}\right)} {\left(\sqrt{2} - 2\right)}}}{{\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + 3 \, \sqrt{\sqrt{2} + 2} {\left(\sqrt{2} - 2\right)} - 3 \, {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} + {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}}}\right) + \frac{1}{16} \, {\left(\sqrt{2} \sqrt{\sqrt{2} + 2} - \sqrt{2} \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(-\frac{8 \, \sqrt{2} x - {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, \sqrt{\sqrt{2} + 2} {\left(\sqrt{2} - 2\right)} - 3 \, {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} + {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} - 8 \, \sqrt{2} \sqrt{-\frac{1}{8} \, \sqrt{2} x {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + \frac{1}{64} \, {\left(\sqrt{2} + 2\right)}^{3} + \frac{3}{64} \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - \frac{1}{64} \, {\left(\sqrt{2} - 2\right)}^{3} - \frac{3}{8} \, \sqrt{2} x {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} + \frac{1}{8} \, \sqrt{2} x {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} + x^{2} - \frac{3}{64} \, {\left(8 \, \sqrt{2} x \sqrt{\sqrt{2} + 2} + {\left(\sqrt{2} + 2\right)}^{2}\right)} {\left(\sqrt{2} - 2\right)}}}{{\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + 3 \, \sqrt{\sqrt{2} + 2} {\left(\sqrt{2} - 2\right)} - 3 \, {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} + {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}}}\right) - \frac{1}{64} \, {\left(\sqrt{2} \sqrt{\sqrt{2} + 2} + \sqrt{2} \sqrt{-\sqrt{2} + 2}\right)} \log\left(\frac{1}{8} \, \sqrt{2} x {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + \frac{1}{64} \, {\left(\sqrt{2} + 2\right)}^{3} + \frac{3}{64} \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - \frac{1}{64} \, {\left(\sqrt{2} - 2\right)}^{3} + \frac{3}{8} \, \sqrt{2} x {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - \frac{1}{8} \, \sqrt{2} x {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} + x^{2} + \frac{3}{64} \, {\left(8 \, \sqrt{2} x \sqrt{\sqrt{2} + 2} - {\left(\sqrt{2} + 2\right)}^{2}\right)} {\left(\sqrt{2} - 2\right)}\right) + \frac{1}{64} \, {\left(\sqrt{2} \sqrt{\sqrt{2} + 2} - \sqrt{2} \sqrt{-\sqrt{2} + 2}\right)} \log\left(\frac{1}{8} \, \sqrt{2} x {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + \frac{1}{64} \, {\left(\sqrt{2} + 2\right)}^{3} + \frac{3}{64} \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - \frac{1}{64} \, {\left(\sqrt{2} - 2\right)}^{3} - \frac{3}{8} \, \sqrt{2} x {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} + \frac{1}{8} \, \sqrt{2} x {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} + x^{2} + \frac{3}{64} \, {\left(8 \, \sqrt{2} x \sqrt{\sqrt{2} + 2} - {\left(\sqrt{2} + 2\right)}^{2}\right)} {\left(\sqrt{2} - 2\right)}\right) - \frac{1}{64} \, {\left(\sqrt{2} \sqrt{\sqrt{2} + 2} - \sqrt{2} \sqrt{-\sqrt{2} + 2}\right)} \log\left(-\frac{1}{8} \, \sqrt{2} x {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + \frac{1}{64} \, {\left(\sqrt{2} + 2\right)}^{3} + \frac{3}{64} \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - \frac{1}{64} \, {\left(\sqrt{2} - 2\right)}^{3} + \frac{3}{8} \, \sqrt{2} x {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - \frac{1}{8} \, \sqrt{2} x {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} + x^{2} - \frac{3}{64} \, {\left(8 \, \sqrt{2} x \sqrt{\sqrt{2} + 2} + {\left(\sqrt{2} + 2\right)}^{2}\right)} {\left(\sqrt{2} - 2\right)}\right) + \frac{1}{64} \, {\left(\sqrt{2} \sqrt{\sqrt{2} + 2} + \sqrt{2} \sqrt{-\sqrt{2} + 2}\right)} \log\left(-\frac{1}{8} \, \sqrt{2} x {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + \frac{1}{64} \, {\left(\sqrt{2} + 2\right)}^{3} + \frac{3}{64} \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - \frac{1}{64} \, {\left(\sqrt{2} - 2\right)}^{3} - \frac{3}{8} \, \sqrt{2} x {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} + \frac{1}{8} \, \sqrt{2} x {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} + x^{2} - \frac{3}{64} \, {\left(8 \, \sqrt{2} x \sqrt{\sqrt{2} + 2} + {\left(\sqrt{2} + 2\right)}^{2}\right)} {\left(\sqrt{2} - 2\right)}\right) + \frac{1}{8} \, \sqrt{-\sqrt{2} + 2} \arctan\left(\frac{3 \, {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} + 8 \, x - \sqrt{{\left(\sqrt{2} + 2\right)}^{3} - 3 \, {\left(\sqrt{2} + 2\right)}^{2} {\left(\sqrt{2} - 2\right)} + 3 \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - {\left(\sqrt{2} - 2\right)}^{3} + 48 \, x {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - 16 \, x {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} + 64 \, x^{2}}}{{\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + 3 \, \sqrt{\sqrt{2} + 2} {\left(\sqrt{2} - 2\right)}}\right) + \frac{1}{8} \, \sqrt{-\sqrt{2} + 2} \arctan\left(-\frac{3 \, {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} - 8 \, x + \sqrt{{\left(\sqrt{2} + 2\right)}^{3} - 3 \, {\left(\sqrt{2} + 2\right)}^{2} {\left(\sqrt{2} - 2\right)} + 3 \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - {\left(\sqrt{2} - 2\right)}^{3} - 48 \, x {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} + 16 \, x {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} + 64 \, x^{2}}}{{\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + 3 \, \sqrt{\sqrt{2} + 2} {\left(\sqrt{2} - 2\right)}}\right) + \frac{1}{8} \, \sqrt{\sqrt{2} + 2} \arctan\left(\frac{{\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + 3 \, \sqrt{\sqrt{2} + 2} {\left(\sqrt{2} - 2\right)} + 8 \, x - \sqrt{{\left(\sqrt{2} + 2\right)}^{3} + 3 \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - {\left(\sqrt{2} - 2\right)}^{3} + 16 \, x {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + 64 \, x^{2} - 3 \, {\left({\left(\sqrt{2} + 2\right)}^{2} - 16 \, x \sqrt{\sqrt{2} + 2}\right)} {\left(\sqrt{2} - 2\right)}}}{3 \, {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}}}\right) + \frac{1}{8} \, \sqrt{\sqrt{2} + 2} \arctan\left(-\frac{{\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + 3 \, \sqrt{\sqrt{2} + 2} {\left(\sqrt{2} - 2\right)} - 8 \, x + \sqrt{{\left(\sqrt{2} + 2\right)}^{3} + 3 \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - {\left(\sqrt{2} - 2\right)}^{3} - 16 \, x {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + 64 \, x^{2} - 3 \, {\left({\left(\sqrt{2} + 2\right)}^{2} + 16 \, x \sqrt{\sqrt{2} + 2}\right)} {\left(\sqrt{2} - 2\right)}}}{3 \, {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}}}\right) - \frac{1}{32} \, \sqrt{\sqrt{2} + 2} \log\left(\frac{1}{64} \, {\left(\sqrt{2} + 2\right)}^{3} - \frac{3}{64} \, {\left(\sqrt{2} + 2\right)}^{2} {\left(\sqrt{2} - 2\right)} + \frac{3}{64} \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - \frac{1}{64} \, {\left(\sqrt{2} - 2\right)}^{3} + \frac{3}{4} \, x {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - \frac{1}{4} \, x {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} + x^{2}\right) + \frac{1}{32} \, \sqrt{\sqrt{2} + 2} \log\left(\frac{1}{64} \, {\left(\sqrt{2} + 2\right)}^{3} - \frac{3}{64} \, {\left(\sqrt{2} + 2\right)}^{2} {\left(\sqrt{2} - 2\right)} + \frac{3}{64} \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - \frac{1}{64} \, {\left(\sqrt{2} - 2\right)}^{3} - \frac{3}{4} \, x {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} + \frac{1}{4} \, x {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} + x^{2}\right) - \frac{1}{32} \, \sqrt{-\sqrt{2} + 2} \log\left(\frac{1}{64} \, {\left(\sqrt{2} + 2\right)}^{3} + \frac{3}{64} \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - \frac{1}{64} \, {\left(\sqrt{2} - 2\right)}^{3} + \frac{1}{4} \, x {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + x^{2} - \frac{3}{64} \, {\left({\left(\sqrt{2} + 2\right)}^{2} - 16 \, x \sqrt{\sqrt{2} + 2}\right)} {\left(\sqrt{2} - 2\right)}\right) + \frac{1}{32} \, \sqrt{-\sqrt{2} + 2} \log\left(\frac{1}{64} \, {\left(\sqrt{2} + 2\right)}^{3} + \frac{3}{64} \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - \frac{1}{64} \, {\left(\sqrt{2} - 2\right)}^{3} - \frac{1}{4} \, x {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + x^{2} - \frac{3}{64} \, {\left({\left(\sqrt{2} + 2\right)}^{2} + 16 \, x \sqrt{\sqrt{2} + 2}\right)} {\left(\sqrt{2} - 2\right)}\right)"," ",0,"1/16*(sqrt(2)*sqrt(sqrt(2) + 2) + sqrt(2)*sqrt(-sqrt(2) + 2))*arctan((8*sqrt(2)*x + (sqrt(2) + 2)^(3/2) + 3*sqrt(sqrt(2) + 2)*(sqrt(2) - 2) - 3*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) + (-sqrt(2) + 2)^(3/2) - sqrt(2)*sqrt(8*sqrt(2)*x*(sqrt(2) + 2)^(3/2) + (sqrt(2) + 2)^3 + 3*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - (sqrt(2) - 2)^3 - 24*sqrt(2)*x*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) + 8*sqrt(2)*x*(-sqrt(2) + 2)^(3/2) + 64*x^2 + 3*(8*sqrt(2)*x*sqrt(sqrt(2) + 2) - (sqrt(2) + 2)^2)*(sqrt(2) - 2)))/((sqrt(2) + 2)^(3/2) + 3*sqrt(sqrt(2) + 2)*(sqrt(2) - 2) + 3*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - (-sqrt(2) + 2)^(3/2))) + 1/16*(sqrt(2)*sqrt(sqrt(2) + 2) + sqrt(2)*sqrt(-sqrt(2) + 2))*arctan((8*sqrt(2)*x - (sqrt(2) + 2)^(3/2) - 3*sqrt(sqrt(2) + 2)*(sqrt(2) - 2) + 3*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - (-sqrt(2) + 2)^(3/2) - 8*sqrt(2)*sqrt(-1/8*sqrt(2)*x*(sqrt(2) + 2)^(3/2) + 1/64*(sqrt(2) + 2)^3 + 3/64*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - 1/64*(sqrt(2) - 2)^3 + 3/8*sqrt(2)*x*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - 1/8*sqrt(2)*x*(-sqrt(2) + 2)^(3/2) + x^2 - 3/64*(8*sqrt(2)*x*sqrt(sqrt(2) + 2) + (sqrt(2) + 2)^2)*(sqrt(2) - 2)))/((sqrt(2) + 2)^(3/2) + 3*sqrt(sqrt(2) + 2)*(sqrt(2) - 2) + 3*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - (-sqrt(2) + 2)^(3/2))) + 1/16*(sqrt(2)*sqrt(sqrt(2) + 2) - sqrt(2)*sqrt(-sqrt(2) + 2))*arctan(-(8*sqrt(2)*x + (sqrt(2) + 2)^(3/2) + 3*sqrt(sqrt(2) + 2)*(sqrt(2) - 2) + 3*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - (-sqrt(2) + 2)^(3/2) - sqrt(2)*sqrt(8*sqrt(2)*x*(sqrt(2) + 2)^(3/2) + (sqrt(2) + 2)^3 + 3*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - (sqrt(2) - 2)^3 + 24*sqrt(2)*x*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - 8*sqrt(2)*x*(-sqrt(2) + 2)^(3/2) + 64*x^2 + 3*(8*sqrt(2)*x*sqrt(sqrt(2) + 2) - (sqrt(2) + 2)^2)*(sqrt(2) - 2)))/((sqrt(2) + 2)^(3/2) + 3*sqrt(sqrt(2) + 2)*(sqrt(2) - 2) - 3*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) + (-sqrt(2) + 2)^(3/2))) + 1/16*(sqrt(2)*sqrt(sqrt(2) + 2) - sqrt(2)*sqrt(-sqrt(2) + 2))*arctan(-(8*sqrt(2)*x - (sqrt(2) + 2)^(3/2) - 3*sqrt(sqrt(2) + 2)*(sqrt(2) - 2) - 3*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) + (-sqrt(2) + 2)^(3/2) - 8*sqrt(2)*sqrt(-1/8*sqrt(2)*x*(sqrt(2) + 2)^(3/2) + 1/64*(sqrt(2) + 2)^3 + 3/64*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - 1/64*(sqrt(2) - 2)^3 - 3/8*sqrt(2)*x*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) + 1/8*sqrt(2)*x*(-sqrt(2) + 2)^(3/2) + x^2 - 3/64*(8*sqrt(2)*x*sqrt(sqrt(2) + 2) + (sqrt(2) + 2)^2)*(sqrt(2) - 2)))/((sqrt(2) + 2)^(3/2) + 3*sqrt(sqrt(2) + 2)*(sqrt(2) - 2) - 3*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) + (-sqrt(2) + 2)^(3/2))) - 1/64*(sqrt(2)*sqrt(sqrt(2) + 2) + sqrt(2)*sqrt(-sqrt(2) + 2))*log(1/8*sqrt(2)*x*(sqrt(2) + 2)^(3/2) + 1/64*(sqrt(2) + 2)^3 + 3/64*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - 1/64*(sqrt(2) - 2)^3 + 3/8*sqrt(2)*x*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - 1/8*sqrt(2)*x*(-sqrt(2) + 2)^(3/2) + x^2 + 3/64*(8*sqrt(2)*x*sqrt(sqrt(2) + 2) - (sqrt(2) + 2)^2)*(sqrt(2) - 2)) + 1/64*(sqrt(2)*sqrt(sqrt(2) + 2) - sqrt(2)*sqrt(-sqrt(2) + 2))*log(1/8*sqrt(2)*x*(sqrt(2) + 2)^(3/2) + 1/64*(sqrt(2) + 2)^3 + 3/64*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - 1/64*(sqrt(2) - 2)^3 - 3/8*sqrt(2)*x*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) + 1/8*sqrt(2)*x*(-sqrt(2) + 2)^(3/2) + x^2 + 3/64*(8*sqrt(2)*x*sqrt(sqrt(2) + 2) - (sqrt(2) + 2)^2)*(sqrt(2) - 2)) - 1/64*(sqrt(2)*sqrt(sqrt(2) + 2) - sqrt(2)*sqrt(-sqrt(2) + 2))*log(-1/8*sqrt(2)*x*(sqrt(2) + 2)^(3/2) + 1/64*(sqrt(2) + 2)^3 + 3/64*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - 1/64*(sqrt(2) - 2)^3 + 3/8*sqrt(2)*x*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - 1/8*sqrt(2)*x*(-sqrt(2) + 2)^(3/2) + x^2 - 3/64*(8*sqrt(2)*x*sqrt(sqrt(2) + 2) + (sqrt(2) + 2)^2)*(sqrt(2) - 2)) + 1/64*(sqrt(2)*sqrt(sqrt(2) + 2) + sqrt(2)*sqrt(-sqrt(2) + 2))*log(-1/8*sqrt(2)*x*(sqrt(2) + 2)^(3/2) + 1/64*(sqrt(2) + 2)^3 + 3/64*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - 1/64*(sqrt(2) - 2)^3 - 3/8*sqrt(2)*x*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) + 1/8*sqrt(2)*x*(-sqrt(2) + 2)^(3/2) + x^2 - 3/64*(8*sqrt(2)*x*sqrt(sqrt(2) + 2) + (sqrt(2) + 2)^2)*(sqrt(2) - 2)) + 1/8*sqrt(-sqrt(2) + 2)*arctan((3*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - (-sqrt(2) + 2)^(3/2) + 8*x - sqrt((sqrt(2) + 2)^3 - 3*(sqrt(2) + 2)^2*(sqrt(2) - 2) + 3*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - (sqrt(2) - 2)^3 + 48*x*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - 16*x*(-sqrt(2) + 2)^(3/2) + 64*x^2))/((sqrt(2) + 2)^(3/2) + 3*sqrt(sqrt(2) + 2)*(sqrt(2) - 2))) + 1/8*sqrt(-sqrt(2) + 2)*arctan(-(3*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - (-sqrt(2) + 2)^(3/2) - 8*x + sqrt((sqrt(2) + 2)^3 - 3*(sqrt(2) + 2)^2*(sqrt(2) - 2) + 3*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - (sqrt(2) - 2)^3 - 48*x*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) + 16*x*(-sqrt(2) + 2)^(3/2) + 64*x^2))/((sqrt(2) + 2)^(3/2) + 3*sqrt(sqrt(2) + 2)*(sqrt(2) - 2))) + 1/8*sqrt(sqrt(2) + 2)*arctan(((sqrt(2) + 2)^(3/2) + 3*sqrt(sqrt(2) + 2)*(sqrt(2) - 2) + 8*x - sqrt((sqrt(2) + 2)^3 + 3*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - (sqrt(2) - 2)^3 + 16*x*(sqrt(2) + 2)^(3/2) + 64*x^2 - 3*((sqrt(2) + 2)^2 - 16*x*sqrt(sqrt(2) + 2))*(sqrt(2) - 2)))/(3*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - (-sqrt(2) + 2)^(3/2))) + 1/8*sqrt(sqrt(2) + 2)*arctan(-((sqrt(2) + 2)^(3/2) + 3*sqrt(sqrt(2) + 2)*(sqrt(2) - 2) - 8*x + sqrt((sqrt(2) + 2)^3 + 3*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - (sqrt(2) - 2)^3 - 16*x*(sqrt(2) + 2)^(3/2) + 64*x^2 - 3*((sqrt(2) + 2)^2 + 16*x*sqrt(sqrt(2) + 2))*(sqrt(2) - 2)))/(3*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - (-sqrt(2) + 2)^(3/2))) - 1/32*sqrt(sqrt(2) + 2)*log(1/64*(sqrt(2) + 2)^3 - 3/64*(sqrt(2) + 2)^2*(sqrt(2) - 2) + 3/64*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - 1/64*(sqrt(2) - 2)^3 + 3/4*x*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - 1/4*x*(-sqrt(2) + 2)^(3/2) + x^2) + 1/32*sqrt(sqrt(2) + 2)*log(1/64*(sqrt(2) + 2)^3 - 3/64*(sqrt(2) + 2)^2*(sqrt(2) - 2) + 3/64*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - 1/64*(sqrt(2) - 2)^3 - 3/4*x*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) + 1/4*x*(-sqrt(2) + 2)^(3/2) + x^2) - 1/32*sqrt(-sqrt(2) + 2)*log(1/64*(sqrt(2) + 2)^3 + 3/64*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - 1/64*(sqrt(2) - 2)^3 + 1/4*x*(sqrt(2) + 2)^(3/2) + x^2 - 3/64*((sqrt(2) + 2)^2 - 16*x*sqrt(sqrt(2) + 2))*(sqrt(2) - 2)) + 1/32*sqrt(-sqrt(2) + 2)*log(1/64*(sqrt(2) + 2)^3 + 3/64*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - 1/64*(sqrt(2) - 2)^3 - 1/4*x*(sqrt(2) + 2)^(3/2) + x^2 - 3/64*((sqrt(2) + 2)^2 + 16*x*sqrt(sqrt(2) + 2))*(sqrt(2) - 2))","B",0
1502,1,1027,0,0.869096," ","integrate(x^4/(x^8+1),x, algorithm=""fricas"")","\frac{1}{16} \, {\left(\sqrt{2} \sqrt{\sqrt{2} + 2} - \sqrt{2} \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(-\frac{2 \, \sqrt{2} x - 2 \, \sqrt{2} \sqrt{x^{2} + \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} - \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1} + \sqrt{\sqrt{2} + 2} - \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2} + \sqrt{-\sqrt{2} + 2}}\right) + \frac{1}{16} \, {\left(\sqrt{2} \sqrt{\sqrt{2} + 2} - \sqrt{2} \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(-\frac{2 \, \sqrt{2} x - 2 \, \sqrt{2} \sqrt{x^{2} - \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} + \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1} - \sqrt{\sqrt{2} + 2} + \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2} + \sqrt{-\sqrt{2} + 2}}\right) + \frac{1}{16} \, {\left(\sqrt{2} \sqrt{\sqrt{2} + 2} + \sqrt{2} \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(\frac{2 \, \sqrt{2} x - 2 \, \sqrt{2} \sqrt{x^{2} + \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} + \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1} + \sqrt{\sqrt{2} + 2} + \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2} - \sqrt{-\sqrt{2} + 2}}\right) + \frac{1}{16} \, {\left(\sqrt{2} \sqrt{\sqrt{2} + 2} + \sqrt{2} \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(\frac{2 \, \sqrt{2} x - 2 \, \sqrt{2} \sqrt{x^{2} - \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} - \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1} - \sqrt{\sqrt{2} + 2} - \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2} - \sqrt{-\sqrt{2} + 2}}\right) - \frac{1}{64} \, {\left(\sqrt{2} \sqrt{\sqrt{2} + 2} - \sqrt{2} \sqrt{-\sqrt{2} + 2}\right)} \log\left(x^{2} + \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} + \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1\right) + \frac{1}{64} \, {\left(\sqrt{2} \sqrt{\sqrt{2} + 2} + \sqrt{2} \sqrt{-\sqrt{2} + 2}\right)} \log\left(x^{2} + \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} - \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1\right) - \frac{1}{64} \, {\left(\sqrt{2} \sqrt{\sqrt{2} + 2} + \sqrt{2} \sqrt{-\sqrt{2} + 2}\right)} \log\left(x^{2} - \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} + \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1\right) + \frac{1}{64} \, {\left(\sqrt{2} \sqrt{\sqrt{2} + 2} - \sqrt{2} \sqrt{-\sqrt{2} + 2}\right)} \log\left(x^{2} - \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} - \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1\right) + \frac{1}{8} \, \sqrt{-\sqrt{2} + 2} \arctan\left(-\frac{2 \, x - 2 \, \sqrt{x^{2} + x \sqrt{-\sqrt{2} + 2} + 1} + \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2}}\right) + \frac{1}{8} \, \sqrt{-\sqrt{2} + 2} \arctan\left(-\frac{2 \, x - 2 \, \sqrt{x^{2} - x \sqrt{-\sqrt{2} + 2} + 1} - \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2}}\right) - \frac{1}{8} \, \sqrt{\sqrt{2} + 2} \arctan\left(-\frac{2 \, x - 2 \, \sqrt{x^{2} + x \sqrt{\sqrt{2} + 2} + 1} + \sqrt{\sqrt{2} + 2}}{\sqrt{-\sqrt{2} + 2}}\right) - \frac{1}{8} \, \sqrt{\sqrt{2} + 2} \arctan\left(-\frac{2 \, x - 2 \, \sqrt{x^{2} - x \sqrt{\sqrt{2} + 2} + 1} - \sqrt{\sqrt{2} + 2}}{\sqrt{-\sqrt{2} + 2}}\right) - \frac{1}{32} \, \sqrt{-\sqrt{2} + 2} \log\left(x^{2} + x \sqrt{\sqrt{2} + 2} + 1\right) + \frac{1}{32} \, \sqrt{-\sqrt{2} + 2} \log\left(x^{2} - x \sqrt{\sqrt{2} + 2} + 1\right) + \frac{1}{32} \, \sqrt{\sqrt{2} + 2} \log\left(x^{2} + x \sqrt{-\sqrt{2} + 2} + 1\right) - \frac{1}{32} \, \sqrt{\sqrt{2} + 2} \log\left(x^{2} - x \sqrt{-\sqrt{2} + 2} + 1\right)"," ",0,"1/16*(sqrt(2)*sqrt(sqrt(2) + 2) - sqrt(2)*sqrt(-sqrt(2) + 2))*arctan(-(2*sqrt(2)*x - 2*sqrt(2)*sqrt(x^2 + 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) - 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) + sqrt(sqrt(2) + 2) - sqrt(-sqrt(2) + 2))/(sqrt(sqrt(2) + 2) + sqrt(-sqrt(2) + 2))) + 1/16*(sqrt(2)*sqrt(sqrt(2) + 2) - sqrt(2)*sqrt(-sqrt(2) + 2))*arctan(-(2*sqrt(2)*x - 2*sqrt(2)*sqrt(x^2 - 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) + 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) - sqrt(sqrt(2) + 2) + sqrt(-sqrt(2) + 2))/(sqrt(sqrt(2) + 2) + sqrt(-sqrt(2) + 2))) + 1/16*(sqrt(2)*sqrt(sqrt(2) + 2) + sqrt(2)*sqrt(-sqrt(2) + 2))*arctan((2*sqrt(2)*x - 2*sqrt(2)*sqrt(x^2 + 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) + 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) + sqrt(sqrt(2) + 2) + sqrt(-sqrt(2) + 2))/(sqrt(sqrt(2) + 2) - sqrt(-sqrt(2) + 2))) + 1/16*(sqrt(2)*sqrt(sqrt(2) + 2) + sqrt(2)*sqrt(-sqrt(2) + 2))*arctan((2*sqrt(2)*x - 2*sqrt(2)*sqrt(x^2 - 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) - 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) - sqrt(sqrt(2) + 2) - sqrt(-sqrt(2) + 2))/(sqrt(sqrt(2) + 2) - sqrt(-sqrt(2) + 2))) - 1/64*(sqrt(2)*sqrt(sqrt(2) + 2) - sqrt(2)*sqrt(-sqrt(2) + 2))*log(x^2 + 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) + 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) + 1/64*(sqrt(2)*sqrt(sqrt(2) + 2) + sqrt(2)*sqrt(-sqrt(2) + 2))*log(x^2 + 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) - 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) - 1/64*(sqrt(2)*sqrt(sqrt(2) + 2) + sqrt(2)*sqrt(-sqrt(2) + 2))*log(x^2 - 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) + 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) + 1/64*(sqrt(2)*sqrt(sqrt(2) + 2) - sqrt(2)*sqrt(-sqrt(2) + 2))*log(x^2 - 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) - 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) + 1/8*sqrt(-sqrt(2) + 2)*arctan(-(2*x - 2*sqrt(x^2 + x*sqrt(-sqrt(2) + 2) + 1) + sqrt(-sqrt(2) + 2))/sqrt(sqrt(2) + 2)) + 1/8*sqrt(-sqrt(2) + 2)*arctan(-(2*x - 2*sqrt(x^2 - x*sqrt(-sqrt(2) + 2) + 1) - sqrt(-sqrt(2) + 2))/sqrt(sqrt(2) + 2)) - 1/8*sqrt(sqrt(2) + 2)*arctan(-(2*x - 2*sqrt(x^2 + x*sqrt(sqrt(2) + 2) + 1) + sqrt(sqrt(2) + 2))/sqrt(-sqrt(2) + 2)) - 1/8*sqrt(sqrt(2) + 2)*arctan(-(2*x - 2*sqrt(x^2 - x*sqrt(sqrt(2) + 2) + 1) - sqrt(sqrt(2) + 2))/sqrt(-sqrt(2) + 2)) - 1/32*sqrt(-sqrt(2) + 2)*log(x^2 + x*sqrt(sqrt(2) + 2) + 1) + 1/32*sqrt(-sqrt(2) + 2)*log(x^2 - x*sqrt(sqrt(2) + 2) + 1) + 1/32*sqrt(sqrt(2) + 2)*log(x^2 + x*sqrt(-sqrt(2) + 2) + 1) - 1/32*sqrt(sqrt(2) + 2)*log(x^2 - x*sqrt(-sqrt(2) + 2) + 1)","B",0
1503,1,2513,0,0.797921," ","integrate(x^2/(x^8+1),x, algorithm=""fricas"")","-\frac{1}{16} \, {\left(\sqrt{2} \sqrt{\sqrt{2} + 2} - \sqrt{2} \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(\frac{8 \, \sqrt{2} x + {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + 3 \, \sqrt{\sqrt{2} + 2} {\left(\sqrt{2} - 2\right)} - 3 \, {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} + {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} - \sqrt{2} \sqrt{8 \, \sqrt{2} x {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + {\left(\sqrt{2} + 2\right)}^{3} + 3 \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - {\left(\sqrt{2} - 2\right)}^{3} - 24 \, \sqrt{2} x {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} + 8 \, \sqrt{2} x {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} + 64 \, x^{2} + 3 \, {\left(8 \, \sqrt{2} x \sqrt{\sqrt{2} + 2} - {\left(\sqrt{2} + 2\right)}^{2}\right)} {\left(\sqrt{2} - 2\right)}}}{{\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + 3 \, \sqrt{\sqrt{2} + 2} {\left(\sqrt{2} - 2\right)} + 3 \, {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}}}\right) - \frac{1}{16} \, {\left(\sqrt{2} \sqrt{\sqrt{2} + 2} - \sqrt{2} \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(\frac{8 \, \sqrt{2} x - {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, \sqrt{\sqrt{2} + 2} {\left(\sqrt{2} - 2\right)} + 3 \, {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} - 8 \, \sqrt{2} \sqrt{-\frac{1}{8} \, \sqrt{2} x {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + \frac{1}{64} \, {\left(\sqrt{2} + 2\right)}^{3} + \frac{3}{64} \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - \frac{1}{64} \, {\left(\sqrt{2} - 2\right)}^{3} + \frac{3}{8} \, \sqrt{2} x {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - \frac{1}{8} \, \sqrt{2} x {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} + x^{2} - \frac{3}{64} \, {\left(8 \, \sqrt{2} x \sqrt{\sqrt{2} + 2} + {\left(\sqrt{2} + 2\right)}^{2}\right)} {\left(\sqrt{2} - 2\right)}}}{{\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + 3 \, \sqrt{\sqrt{2} + 2} {\left(\sqrt{2} - 2\right)} + 3 \, {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}}}\right) + \frac{1}{16} \, {\left(\sqrt{2} \sqrt{\sqrt{2} + 2} + \sqrt{2} \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(-\frac{8 \, \sqrt{2} x + {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + 3 \, \sqrt{\sqrt{2} + 2} {\left(\sqrt{2} - 2\right)} + 3 \, {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} - \sqrt{2} \sqrt{8 \, \sqrt{2} x {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + {\left(\sqrt{2} + 2\right)}^{3} + 3 \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - {\left(\sqrt{2} - 2\right)}^{3} + 24 \, \sqrt{2} x {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - 8 \, \sqrt{2} x {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} + 64 \, x^{2} + 3 \, {\left(8 \, \sqrt{2} x \sqrt{\sqrt{2} + 2} - {\left(\sqrt{2} + 2\right)}^{2}\right)} {\left(\sqrt{2} - 2\right)}}}{{\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + 3 \, \sqrt{\sqrt{2} + 2} {\left(\sqrt{2} - 2\right)} - 3 \, {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} + {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}}}\right) + \frac{1}{16} \, {\left(\sqrt{2} \sqrt{\sqrt{2} + 2} + \sqrt{2} \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(-\frac{8 \, \sqrt{2} x - {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, \sqrt{\sqrt{2} + 2} {\left(\sqrt{2} - 2\right)} - 3 \, {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} + {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} - 8 \, \sqrt{2} \sqrt{-\frac{1}{8} \, \sqrt{2} x {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + \frac{1}{64} \, {\left(\sqrt{2} + 2\right)}^{3} + \frac{3}{64} \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - \frac{1}{64} \, {\left(\sqrt{2} - 2\right)}^{3} - \frac{3}{8} \, \sqrt{2} x {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} + \frac{1}{8} \, \sqrt{2} x {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} + x^{2} - \frac{3}{64} \, {\left(8 \, \sqrt{2} x \sqrt{\sqrt{2} + 2} + {\left(\sqrt{2} + 2\right)}^{2}\right)} {\left(\sqrt{2} - 2\right)}}}{{\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + 3 \, \sqrt{\sqrt{2} + 2} {\left(\sqrt{2} - 2\right)} - 3 \, {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} + {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}}}\right) + \frac{1}{64} \, {\left(\sqrt{2} \sqrt{\sqrt{2} + 2} - \sqrt{2} \sqrt{-\sqrt{2} + 2}\right)} \log\left(\frac{1}{8} \, \sqrt{2} x {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + \frac{1}{64} \, {\left(\sqrt{2} + 2\right)}^{3} + \frac{3}{64} \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - \frac{1}{64} \, {\left(\sqrt{2} - 2\right)}^{3} + \frac{3}{8} \, \sqrt{2} x {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - \frac{1}{8} \, \sqrt{2} x {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} + x^{2} + \frac{3}{64} \, {\left(8 \, \sqrt{2} x \sqrt{\sqrt{2} + 2} - {\left(\sqrt{2} + 2\right)}^{2}\right)} {\left(\sqrt{2} - 2\right)}\right) + \frac{1}{64} \, {\left(\sqrt{2} \sqrt{\sqrt{2} + 2} + \sqrt{2} \sqrt{-\sqrt{2} + 2}\right)} \log\left(\frac{1}{8} \, \sqrt{2} x {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + \frac{1}{64} \, {\left(\sqrt{2} + 2\right)}^{3} + \frac{3}{64} \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - \frac{1}{64} \, {\left(\sqrt{2} - 2\right)}^{3} - \frac{3}{8} \, \sqrt{2} x {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} + \frac{1}{8} \, \sqrt{2} x {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} + x^{2} + \frac{3}{64} \, {\left(8 \, \sqrt{2} x \sqrt{\sqrt{2} + 2} - {\left(\sqrt{2} + 2\right)}^{2}\right)} {\left(\sqrt{2} - 2\right)}\right) - \frac{1}{64} \, {\left(\sqrt{2} \sqrt{\sqrt{2} + 2} + \sqrt{2} \sqrt{-\sqrt{2} + 2}\right)} \log\left(-\frac{1}{8} \, \sqrt{2} x {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + \frac{1}{64} \, {\left(\sqrt{2} + 2\right)}^{3} + \frac{3}{64} \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - \frac{1}{64} \, {\left(\sqrt{2} - 2\right)}^{3} + \frac{3}{8} \, \sqrt{2} x {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - \frac{1}{8} \, \sqrt{2} x {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} + x^{2} - \frac{3}{64} \, {\left(8 \, \sqrt{2} x \sqrt{\sqrt{2} + 2} + {\left(\sqrt{2} + 2\right)}^{2}\right)} {\left(\sqrt{2} - 2\right)}\right) - \frac{1}{64} \, {\left(\sqrt{2} \sqrt{\sqrt{2} + 2} - \sqrt{2} \sqrt{-\sqrt{2} + 2}\right)} \log\left(-\frac{1}{8} \, \sqrt{2} x {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + \frac{1}{64} \, {\left(\sqrt{2} + 2\right)}^{3} + \frac{3}{64} \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - \frac{1}{64} \, {\left(\sqrt{2} - 2\right)}^{3} - \frac{3}{8} \, \sqrt{2} x {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} + \frac{1}{8} \, \sqrt{2} x {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} + x^{2} - \frac{3}{64} \, {\left(8 \, \sqrt{2} x \sqrt{\sqrt{2} + 2} + {\left(\sqrt{2} + 2\right)}^{2}\right)} {\left(\sqrt{2} - 2\right)}\right) + \frac{1}{8} \, \sqrt{\sqrt{2} + 2} \arctan\left(\frac{3 \, {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} + 8 \, x - \sqrt{{\left(\sqrt{2} + 2\right)}^{3} - 3 \, {\left(\sqrt{2} + 2\right)}^{2} {\left(\sqrt{2} - 2\right)} + 3 \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - {\left(\sqrt{2} - 2\right)}^{3} + 48 \, x {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - 16 \, x {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} + 64 \, x^{2}}}{{\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + 3 \, \sqrt{\sqrt{2} + 2} {\left(\sqrt{2} - 2\right)}}\right) + \frac{1}{8} \, \sqrt{\sqrt{2} + 2} \arctan\left(-\frac{3 \, {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} - 8 \, x + \sqrt{{\left(\sqrt{2} + 2\right)}^{3} - 3 \, {\left(\sqrt{2} + 2\right)}^{2} {\left(\sqrt{2} - 2\right)} + 3 \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - {\left(\sqrt{2} - 2\right)}^{3} - 48 \, x {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} + 16 \, x {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} + 64 \, x^{2}}}{{\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + 3 \, \sqrt{\sqrt{2} + 2} {\left(\sqrt{2} - 2\right)}}\right) - \frac{1}{8} \, \sqrt{-\sqrt{2} + 2} \arctan\left(\frac{{\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + 3 \, \sqrt{\sqrt{2} + 2} {\left(\sqrt{2} - 2\right)} + 8 \, x - \sqrt{{\left(\sqrt{2} + 2\right)}^{3} + 3 \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - {\left(\sqrt{2} - 2\right)}^{3} + 16 \, x {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + 64 \, x^{2} - 3 \, {\left({\left(\sqrt{2} + 2\right)}^{2} - 16 \, x \sqrt{\sqrt{2} + 2}\right)} {\left(\sqrt{2} - 2\right)}}}{3 \, {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}}}\right) - \frac{1}{8} \, \sqrt{-\sqrt{2} + 2} \arctan\left(-\frac{{\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + 3 \, \sqrt{\sqrt{2} + 2} {\left(\sqrt{2} - 2\right)} - 8 \, x + \sqrt{{\left(\sqrt{2} + 2\right)}^{3} + 3 \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - {\left(\sqrt{2} - 2\right)}^{3} - 16 \, x {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + 64 \, x^{2} - 3 \, {\left({\left(\sqrt{2} + 2\right)}^{2} + 16 \, x \sqrt{\sqrt{2} + 2}\right)} {\left(\sqrt{2} - 2\right)}}}{3 \, {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}}}\right) + \frac{1}{32} \, \sqrt{-\sqrt{2} + 2} \log\left(\frac{1}{64} \, {\left(\sqrt{2} + 2\right)}^{3} - \frac{3}{64} \, {\left(\sqrt{2} + 2\right)}^{2} {\left(\sqrt{2} - 2\right)} + \frac{3}{64} \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - \frac{1}{64} \, {\left(\sqrt{2} - 2\right)}^{3} + \frac{3}{4} \, x {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - \frac{1}{4} \, x {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} + x^{2}\right) - \frac{1}{32} \, \sqrt{-\sqrt{2} + 2} \log\left(\frac{1}{64} \, {\left(\sqrt{2} + 2\right)}^{3} - \frac{3}{64} \, {\left(\sqrt{2} + 2\right)}^{2} {\left(\sqrt{2} - 2\right)} + \frac{3}{64} \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - \frac{1}{64} \, {\left(\sqrt{2} - 2\right)}^{3} - \frac{3}{4} \, x {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} + \frac{1}{4} \, x {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} + x^{2}\right) - \frac{1}{32} \, \sqrt{\sqrt{2} + 2} \log\left(\frac{1}{64} \, {\left(\sqrt{2} + 2\right)}^{3} + \frac{3}{64} \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - \frac{1}{64} \, {\left(\sqrt{2} - 2\right)}^{3} + \frac{1}{4} \, x {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + x^{2} - \frac{3}{64} \, {\left({\left(\sqrt{2} + 2\right)}^{2} - 16 \, x \sqrt{\sqrt{2} + 2}\right)} {\left(\sqrt{2} - 2\right)}\right) + \frac{1}{32} \, \sqrt{\sqrt{2} + 2} \log\left(\frac{1}{64} \, {\left(\sqrt{2} + 2\right)}^{3} + \frac{3}{64} \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - \frac{1}{64} \, {\left(\sqrt{2} - 2\right)}^{3} - \frac{1}{4} \, x {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + x^{2} - \frac{3}{64} \, {\left({\left(\sqrt{2} + 2\right)}^{2} + 16 \, x \sqrt{\sqrt{2} + 2}\right)} {\left(\sqrt{2} - 2\right)}\right)"," ",0,"-1/16*(sqrt(2)*sqrt(sqrt(2) + 2) - sqrt(2)*sqrt(-sqrt(2) + 2))*arctan((8*sqrt(2)*x + (sqrt(2) + 2)^(3/2) + 3*sqrt(sqrt(2) + 2)*(sqrt(2) - 2) - 3*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) + (-sqrt(2) + 2)^(3/2) - sqrt(2)*sqrt(8*sqrt(2)*x*(sqrt(2) + 2)^(3/2) + (sqrt(2) + 2)^3 + 3*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - (sqrt(2) - 2)^3 - 24*sqrt(2)*x*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) + 8*sqrt(2)*x*(-sqrt(2) + 2)^(3/2) + 64*x^2 + 3*(8*sqrt(2)*x*sqrt(sqrt(2) + 2) - (sqrt(2) + 2)^2)*(sqrt(2) - 2)))/((sqrt(2) + 2)^(3/2) + 3*sqrt(sqrt(2) + 2)*(sqrt(2) - 2) + 3*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - (-sqrt(2) + 2)^(3/2))) - 1/16*(sqrt(2)*sqrt(sqrt(2) + 2) - sqrt(2)*sqrt(-sqrt(2) + 2))*arctan((8*sqrt(2)*x - (sqrt(2) + 2)^(3/2) - 3*sqrt(sqrt(2) + 2)*(sqrt(2) - 2) + 3*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - (-sqrt(2) + 2)^(3/2) - 8*sqrt(2)*sqrt(-1/8*sqrt(2)*x*(sqrt(2) + 2)^(3/2) + 1/64*(sqrt(2) + 2)^3 + 3/64*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - 1/64*(sqrt(2) - 2)^3 + 3/8*sqrt(2)*x*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - 1/8*sqrt(2)*x*(-sqrt(2) + 2)^(3/2) + x^2 - 3/64*(8*sqrt(2)*x*sqrt(sqrt(2) + 2) + (sqrt(2) + 2)^2)*(sqrt(2) - 2)))/((sqrt(2) + 2)^(3/2) + 3*sqrt(sqrt(2) + 2)*(sqrt(2) - 2) + 3*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - (-sqrt(2) + 2)^(3/2))) + 1/16*(sqrt(2)*sqrt(sqrt(2) + 2) + sqrt(2)*sqrt(-sqrt(2) + 2))*arctan(-(8*sqrt(2)*x + (sqrt(2) + 2)^(3/2) + 3*sqrt(sqrt(2) + 2)*(sqrt(2) - 2) + 3*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - (-sqrt(2) + 2)^(3/2) - sqrt(2)*sqrt(8*sqrt(2)*x*(sqrt(2) + 2)^(3/2) + (sqrt(2) + 2)^3 + 3*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - (sqrt(2) - 2)^3 + 24*sqrt(2)*x*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - 8*sqrt(2)*x*(-sqrt(2) + 2)^(3/2) + 64*x^2 + 3*(8*sqrt(2)*x*sqrt(sqrt(2) + 2) - (sqrt(2) + 2)^2)*(sqrt(2) - 2)))/((sqrt(2) + 2)^(3/2) + 3*sqrt(sqrt(2) + 2)*(sqrt(2) - 2) - 3*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) + (-sqrt(2) + 2)^(3/2))) + 1/16*(sqrt(2)*sqrt(sqrt(2) + 2) + sqrt(2)*sqrt(-sqrt(2) + 2))*arctan(-(8*sqrt(2)*x - (sqrt(2) + 2)^(3/2) - 3*sqrt(sqrt(2) + 2)*(sqrt(2) - 2) - 3*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) + (-sqrt(2) + 2)^(3/2) - 8*sqrt(2)*sqrt(-1/8*sqrt(2)*x*(sqrt(2) + 2)^(3/2) + 1/64*(sqrt(2) + 2)^3 + 3/64*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - 1/64*(sqrt(2) - 2)^3 - 3/8*sqrt(2)*x*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) + 1/8*sqrt(2)*x*(-sqrt(2) + 2)^(3/2) + x^2 - 3/64*(8*sqrt(2)*x*sqrt(sqrt(2) + 2) + (sqrt(2) + 2)^2)*(sqrt(2) - 2)))/((sqrt(2) + 2)^(3/2) + 3*sqrt(sqrt(2) + 2)*(sqrt(2) - 2) - 3*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) + (-sqrt(2) + 2)^(3/2))) + 1/64*(sqrt(2)*sqrt(sqrt(2) + 2) - sqrt(2)*sqrt(-sqrt(2) + 2))*log(1/8*sqrt(2)*x*(sqrt(2) + 2)^(3/2) + 1/64*(sqrt(2) + 2)^3 + 3/64*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - 1/64*(sqrt(2) - 2)^3 + 3/8*sqrt(2)*x*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - 1/8*sqrt(2)*x*(-sqrt(2) + 2)^(3/2) + x^2 + 3/64*(8*sqrt(2)*x*sqrt(sqrt(2) + 2) - (sqrt(2) + 2)^2)*(sqrt(2) - 2)) + 1/64*(sqrt(2)*sqrt(sqrt(2) + 2) + sqrt(2)*sqrt(-sqrt(2) + 2))*log(1/8*sqrt(2)*x*(sqrt(2) + 2)^(3/2) + 1/64*(sqrt(2) + 2)^3 + 3/64*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - 1/64*(sqrt(2) - 2)^3 - 3/8*sqrt(2)*x*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) + 1/8*sqrt(2)*x*(-sqrt(2) + 2)^(3/2) + x^2 + 3/64*(8*sqrt(2)*x*sqrt(sqrt(2) + 2) - (sqrt(2) + 2)^2)*(sqrt(2) - 2)) - 1/64*(sqrt(2)*sqrt(sqrt(2) + 2) + sqrt(2)*sqrt(-sqrt(2) + 2))*log(-1/8*sqrt(2)*x*(sqrt(2) + 2)^(3/2) + 1/64*(sqrt(2) + 2)^3 + 3/64*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - 1/64*(sqrt(2) - 2)^3 + 3/8*sqrt(2)*x*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - 1/8*sqrt(2)*x*(-sqrt(2) + 2)^(3/2) + x^2 - 3/64*(8*sqrt(2)*x*sqrt(sqrt(2) + 2) + (sqrt(2) + 2)^2)*(sqrt(2) - 2)) - 1/64*(sqrt(2)*sqrt(sqrt(2) + 2) - sqrt(2)*sqrt(-sqrt(2) + 2))*log(-1/8*sqrt(2)*x*(sqrt(2) + 2)^(3/2) + 1/64*(sqrt(2) + 2)^3 + 3/64*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - 1/64*(sqrt(2) - 2)^3 - 3/8*sqrt(2)*x*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) + 1/8*sqrt(2)*x*(-sqrt(2) + 2)^(3/2) + x^2 - 3/64*(8*sqrt(2)*x*sqrt(sqrt(2) + 2) + (sqrt(2) + 2)^2)*(sqrt(2) - 2)) + 1/8*sqrt(sqrt(2) + 2)*arctan((3*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - (-sqrt(2) + 2)^(3/2) + 8*x - sqrt((sqrt(2) + 2)^3 - 3*(sqrt(2) + 2)^2*(sqrt(2) - 2) + 3*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - (sqrt(2) - 2)^3 + 48*x*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - 16*x*(-sqrt(2) + 2)^(3/2) + 64*x^2))/((sqrt(2) + 2)^(3/2) + 3*sqrt(sqrt(2) + 2)*(sqrt(2) - 2))) + 1/8*sqrt(sqrt(2) + 2)*arctan(-(3*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - (-sqrt(2) + 2)^(3/2) - 8*x + sqrt((sqrt(2) + 2)^3 - 3*(sqrt(2) + 2)^2*(sqrt(2) - 2) + 3*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - (sqrt(2) - 2)^3 - 48*x*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) + 16*x*(-sqrt(2) + 2)^(3/2) + 64*x^2))/((sqrt(2) + 2)^(3/2) + 3*sqrt(sqrt(2) + 2)*(sqrt(2) - 2))) - 1/8*sqrt(-sqrt(2) + 2)*arctan(((sqrt(2) + 2)^(3/2) + 3*sqrt(sqrt(2) + 2)*(sqrt(2) - 2) + 8*x - sqrt((sqrt(2) + 2)^3 + 3*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - (sqrt(2) - 2)^3 + 16*x*(sqrt(2) + 2)^(3/2) + 64*x^2 - 3*((sqrt(2) + 2)^2 - 16*x*sqrt(sqrt(2) + 2))*(sqrt(2) - 2)))/(3*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - (-sqrt(2) + 2)^(3/2))) - 1/8*sqrt(-sqrt(2) + 2)*arctan(-((sqrt(2) + 2)^(3/2) + 3*sqrt(sqrt(2) + 2)*(sqrt(2) - 2) - 8*x + sqrt((sqrt(2) + 2)^3 + 3*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - (sqrt(2) - 2)^3 - 16*x*(sqrt(2) + 2)^(3/2) + 64*x^2 - 3*((sqrt(2) + 2)^2 + 16*x*sqrt(sqrt(2) + 2))*(sqrt(2) - 2)))/(3*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - (-sqrt(2) + 2)^(3/2))) + 1/32*sqrt(-sqrt(2) + 2)*log(1/64*(sqrt(2) + 2)^3 - 3/64*(sqrt(2) + 2)^2*(sqrt(2) - 2) + 3/64*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - 1/64*(sqrt(2) - 2)^3 + 3/4*x*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - 1/4*x*(-sqrt(2) + 2)^(3/2) + x^2) - 1/32*sqrt(-sqrt(2) + 2)*log(1/64*(sqrt(2) + 2)^3 - 3/64*(sqrt(2) + 2)^2*(sqrt(2) - 2) + 3/64*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - 1/64*(sqrt(2) - 2)^3 - 3/4*x*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) + 1/4*x*(-sqrt(2) + 2)^(3/2) + x^2) - 1/32*sqrt(sqrt(2) + 2)*log(1/64*(sqrt(2) + 2)^3 + 3/64*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - 1/64*(sqrt(2) - 2)^3 + 1/4*x*(sqrt(2) + 2)^(3/2) + x^2 - 3/64*((sqrt(2) + 2)^2 - 16*x*sqrt(sqrt(2) + 2))*(sqrt(2) - 2)) + 1/32*sqrt(sqrt(2) + 2)*log(1/64*(sqrt(2) + 2)^3 + 3/64*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - 1/64*(sqrt(2) - 2)^3 - 1/4*x*(sqrt(2) + 2)^(3/2) + x^2 - 3/64*((sqrt(2) + 2)^2 + 16*x*sqrt(sqrt(2) + 2))*(sqrt(2) - 2))","B",0
1504,1,1027,0,0.994520," ","integrate(1/(x^8+1),x, algorithm=""fricas"")","-\frac{1}{16} \, {\left(\sqrt{2} \sqrt{\sqrt{2} + 2} + \sqrt{2} \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(-\frac{2 \, \sqrt{2} x - 2 \, \sqrt{2} \sqrt{x^{2} + \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} - \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1} + \sqrt{\sqrt{2} + 2} - \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2} + \sqrt{-\sqrt{2} + 2}}\right) - \frac{1}{16} \, {\left(\sqrt{2} \sqrt{\sqrt{2} + 2} + \sqrt{2} \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(-\frac{2 \, \sqrt{2} x - 2 \, \sqrt{2} \sqrt{x^{2} - \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} + \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1} - \sqrt{\sqrt{2} + 2} + \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2} + \sqrt{-\sqrt{2} + 2}}\right) + \frac{1}{16} \, {\left(\sqrt{2} \sqrt{\sqrt{2} + 2} - \sqrt{2} \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(\frac{2 \, \sqrt{2} x - 2 \, \sqrt{2} \sqrt{x^{2} + \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} + \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1} + \sqrt{\sqrt{2} + 2} + \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2} - \sqrt{-\sqrt{2} + 2}}\right) + \frac{1}{16} \, {\left(\sqrt{2} \sqrt{\sqrt{2} + 2} - \sqrt{2} \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(\frac{2 \, \sqrt{2} x - 2 \, \sqrt{2} \sqrt{x^{2} - \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} - \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1} - \sqrt{\sqrt{2} + 2} - \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2} - \sqrt{-\sqrt{2} + 2}}\right) + \frac{1}{64} \, {\left(\sqrt{2} \sqrt{\sqrt{2} + 2} + \sqrt{2} \sqrt{-\sqrt{2} + 2}\right)} \log\left(x^{2} + \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} + \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1\right) + \frac{1}{64} \, {\left(\sqrt{2} \sqrt{\sqrt{2} + 2} - \sqrt{2} \sqrt{-\sqrt{2} + 2}\right)} \log\left(x^{2} + \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} - \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1\right) - \frac{1}{64} \, {\left(\sqrt{2} \sqrt{\sqrt{2} + 2} - \sqrt{2} \sqrt{-\sqrt{2} + 2}\right)} \log\left(x^{2} - \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} + \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1\right) - \frac{1}{64} \, {\left(\sqrt{2} \sqrt{\sqrt{2} + 2} + \sqrt{2} \sqrt{-\sqrt{2} + 2}\right)} \log\left(x^{2} - \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} - \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1\right) - \frac{1}{8} \, \sqrt{\sqrt{2} + 2} \arctan\left(-\frac{2 \, x - 2 \, \sqrt{x^{2} + x \sqrt{-\sqrt{2} + 2} + 1} + \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2}}\right) - \frac{1}{8} \, \sqrt{\sqrt{2} + 2} \arctan\left(-\frac{2 \, x - 2 \, \sqrt{x^{2} - x \sqrt{-\sqrt{2} + 2} + 1} - \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2}}\right) - \frac{1}{8} \, \sqrt{-\sqrt{2} + 2} \arctan\left(-\frac{2 \, x - 2 \, \sqrt{x^{2} + x \sqrt{\sqrt{2} + 2} + 1} + \sqrt{\sqrt{2} + 2}}{\sqrt{-\sqrt{2} + 2}}\right) - \frac{1}{8} \, \sqrt{-\sqrt{2} + 2} \arctan\left(-\frac{2 \, x - 2 \, \sqrt{x^{2} - x \sqrt{\sqrt{2} + 2} + 1} - \sqrt{\sqrt{2} + 2}}{\sqrt{-\sqrt{2} + 2}}\right) + \frac{1}{32} \, \sqrt{\sqrt{2} + 2} \log\left(x^{2} + x \sqrt{\sqrt{2} + 2} + 1\right) - \frac{1}{32} \, \sqrt{\sqrt{2} + 2} \log\left(x^{2} - x \sqrt{\sqrt{2} + 2} + 1\right) + \frac{1}{32} \, \sqrt{-\sqrt{2} + 2} \log\left(x^{2} + x \sqrt{-\sqrt{2} + 2} + 1\right) - \frac{1}{32} \, \sqrt{-\sqrt{2} + 2} \log\left(x^{2} - x \sqrt{-\sqrt{2} + 2} + 1\right)"," ",0,"-1/16*(sqrt(2)*sqrt(sqrt(2) + 2) + sqrt(2)*sqrt(-sqrt(2) + 2))*arctan(-(2*sqrt(2)*x - 2*sqrt(2)*sqrt(x^2 + 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) - 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) + sqrt(sqrt(2) + 2) - sqrt(-sqrt(2) + 2))/(sqrt(sqrt(2) + 2) + sqrt(-sqrt(2) + 2))) - 1/16*(sqrt(2)*sqrt(sqrt(2) + 2) + sqrt(2)*sqrt(-sqrt(2) + 2))*arctan(-(2*sqrt(2)*x - 2*sqrt(2)*sqrt(x^2 - 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) + 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) - sqrt(sqrt(2) + 2) + sqrt(-sqrt(2) + 2))/(sqrt(sqrt(2) + 2) + sqrt(-sqrt(2) + 2))) + 1/16*(sqrt(2)*sqrt(sqrt(2) + 2) - sqrt(2)*sqrt(-sqrt(2) + 2))*arctan((2*sqrt(2)*x - 2*sqrt(2)*sqrt(x^2 + 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) + 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) + sqrt(sqrt(2) + 2) + sqrt(-sqrt(2) + 2))/(sqrt(sqrt(2) + 2) - sqrt(-sqrt(2) + 2))) + 1/16*(sqrt(2)*sqrt(sqrt(2) + 2) - sqrt(2)*sqrt(-sqrt(2) + 2))*arctan((2*sqrt(2)*x - 2*sqrt(2)*sqrt(x^2 - 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) - 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) - sqrt(sqrt(2) + 2) - sqrt(-sqrt(2) + 2))/(sqrt(sqrt(2) + 2) - sqrt(-sqrt(2) + 2))) + 1/64*(sqrt(2)*sqrt(sqrt(2) + 2) + sqrt(2)*sqrt(-sqrt(2) + 2))*log(x^2 + 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) + 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) + 1/64*(sqrt(2)*sqrt(sqrt(2) + 2) - sqrt(2)*sqrt(-sqrt(2) + 2))*log(x^2 + 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) - 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) - 1/64*(sqrt(2)*sqrt(sqrt(2) + 2) - sqrt(2)*sqrt(-sqrt(2) + 2))*log(x^2 - 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) + 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) - 1/64*(sqrt(2)*sqrt(sqrt(2) + 2) + sqrt(2)*sqrt(-sqrt(2) + 2))*log(x^2 - 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) - 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) - 1/8*sqrt(sqrt(2) + 2)*arctan(-(2*x - 2*sqrt(x^2 + x*sqrt(-sqrt(2) + 2) + 1) + sqrt(-sqrt(2) + 2))/sqrt(sqrt(2) + 2)) - 1/8*sqrt(sqrt(2) + 2)*arctan(-(2*x - 2*sqrt(x^2 - x*sqrt(-sqrt(2) + 2) + 1) - sqrt(-sqrt(2) + 2))/sqrt(sqrt(2) + 2)) - 1/8*sqrt(-sqrt(2) + 2)*arctan(-(2*x - 2*sqrt(x^2 + x*sqrt(sqrt(2) + 2) + 1) + sqrt(sqrt(2) + 2))/sqrt(-sqrt(2) + 2)) - 1/8*sqrt(-sqrt(2) + 2)*arctan(-(2*x - 2*sqrt(x^2 - x*sqrt(sqrt(2) + 2) + 1) - sqrt(sqrt(2) + 2))/sqrt(-sqrt(2) + 2)) + 1/32*sqrt(sqrt(2) + 2)*log(x^2 + x*sqrt(sqrt(2) + 2) + 1) - 1/32*sqrt(sqrt(2) + 2)*log(x^2 - x*sqrt(sqrt(2) + 2) + 1) + 1/32*sqrt(-sqrt(2) + 2)*log(x^2 + x*sqrt(-sqrt(2) + 2) + 1) - 1/32*sqrt(-sqrt(2) + 2)*log(x^2 - x*sqrt(-sqrt(2) + 2) + 1)","B",0
1505,1,2541,0,1.033149," ","integrate(1/x^2/(x^8+1),x, algorithm=""fricas"")","-\frac{8 \, x \sqrt{-\sqrt{2} + 2} \arctan\left(\frac{3 \, {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} + 8 \, x - \sqrt{{\left(\sqrt{2} + 2\right)}^{3} - 3 \, {\left(\sqrt{2} + 2\right)}^{2} {\left(\sqrt{2} - 2\right)} + 3 \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - {\left(\sqrt{2} - 2\right)}^{3} + 48 \, x {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - 16 \, x {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} + 64 \, x^{2}}}{{\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + 3 \, \sqrt{\sqrt{2} + 2} {\left(\sqrt{2} - 2\right)}}\right) + 8 \, x \sqrt{-\sqrt{2} + 2} \arctan\left(-\frac{3 \, {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} - 8 \, x + \sqrt{{\left(\sqrt{2} + 2\right)}^{3} - 3 \, {\left(\sqrt{2} + 2\right)}^{2} {\left(\sqrt{2} - 2\right)} + 3 \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - {\left(\sqrt{2} - 2\right)}^{3} - 48 \, x {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} + 16 \, x {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} + 64 \, x^{2}}}{{\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + 3 \, \sqrt{\sqrt{2} + 2} {\left(\sqrt{2} - 2\right)}}\right) + 8 \, x \sqrt{\sqrt{2} + 2} \arctan\left(\frac{{\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + 3 \, \sqrt{\sqrt{2} + 2} {\left(\sqrt{2} - 2\right)} + 8 \, x - \sqrt{{\left(\sqrt{2} + 2\right)}^{3} + 3 \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - {\left(\sqrt{2} - 2\right)}^{3} + 16 \, x {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + 64 \, x^{2} - 3 \, {\left({\left(\sqrt{2} + 2\right)}^{2} - 16 \, x \sqrt{\sqrt{2} + 2}\right)} {\left(\sqrt{2} - 2\right)}}}{3 \, {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}}}\right) + 8 \, x \sqrt{\sqrt{2} + 2} \arctan\left(-\frac{{\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + 3 \, \sqrt{\sqrt{2} + 2} {\left(\sqrt{2} - 2\right)} - 8 \, x + \sqrt{{\left(\sqrt{2} + 2\right)}^{3} + 3 \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - {\left(\sqrt{2} - 2\right)}^{3} - 16 \, x {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + 64 \, x^{2} - 3 \, {\left({\left(\sqrt{2} + 2\right)}^{2} + 16 \, x \sqrt{\sqrt{2} + 2}\right)} {\left(\sqrt{2} - 2\right)}}}{3 \, {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}}}\right) - 2 \, x \sqrt{\sqrt{2} + 2} \log\left(\frac{1}{64} \, {\left(\sqrt{2} + 2\right)}^{3} - \frac{3}{64} \, {\left(\sqrt{2} + 2\right)}^{2} {\left(\sqrt{2} - 2\right)} + \frac{3}{64} \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - \frac{1}{64} \, {\left(\sqrt{2} - 2\right)}^{3} + \frac{3}{4} \, x {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - \frac{1}{4} \, x {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} + x^{2}\right) + 2 \, x \sqrt{\sqrt{2} + 2} \log\left(\frac{1}{64} \, {\left(\sqrt{2} + 2\right)}^{3} - \frac{3}{64} \, {\left(\sqrt{2} + 2\right)}^{2} {\left(\sqrt{2} - 2\right)} + \frac{3}{64} \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - \frac{1}{64} \, {\left(\sqrt{2} - 2\right)}^{3} - \frac{3}{4} \, x {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} + \frac{1}{4} \, x {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} + x^{2}\right) - 2 \, x \sqrt{-\sqrt{2} + 2} \log\left(\frac{1}{64} \, {\left(\sqrt{2} + 2\right)}^{3} + \frac{3}{64} \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - \frac{1}{64} \, {\left(\sqrt{2} - 2\right)}^{3} + \frac{1}{4} \, x {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + x^{2} - \frac{3}{64} \, {\left({\left(\sqrt{2} + 2\right)}^{2} - 16 \, x \sqrt{\sqrt{2} + 2}\right)} {\left(\sqrt{2} - 2\right)}\right) + 2 \, x \sqrt{-\sqrt{2} + 2} \log\left(\frac{1}{64} \, {\left(\sqrt{2} + 2\right)}^{3} + \frac{3}{64} \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - \frac{1}{64} \, {\left(\sqrt{2} - 2\right)}^{3} - \frac{1}{4} \, x {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + x^{2} - \frac{3}{64} \, {\left({\left(\sqrt{2} + 2\right)}^{2} + 16 \, x \sqrt{\sqrt{2} + 2}\right)} {\left(\sqrt{2} - 2\right)}\right) + 4 \, {\left(\sqrt{2} x \sqrt{\sqrt{2} + 2} + \sqrt{2} x \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(\frac{8 \, \sqrt{2} x + {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + 3 \, \sqrt{\sqrt{2} + 2} {\left(\sqrt{2} - 2\right)} - 3 \, {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} + {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} - \sqrt{2} \sqrt{8 \, \sqrt{2} x {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + {\left(\sqrt{2} + 2\right)}^{3} + 3 \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - {\left(\sqrt{2} - 2\right)}^{3} - 24 \, \sqrt{2} x {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} + 8 \, \sqrt{2} x {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} + 64 \, x^{2} + 3 \, {\left(8 \, \sqrt{2} x \sqrt{\sqrt{2} + 2} - {\left(\sqrt{2} + 2\right)}^{2}\right)} {\left(\sqrt{2} - 2\right)}}}{{\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + 3 \, \sqrt{\sqrt{2} + 2} {\left(\sqrt{2} - 2\right)} + 3 \, {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}}}\right) + 4 \, {\left(\sqrt{2} x \sqrt{\sqrt{2} + 2} + \sqrt{2} x \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(\frac{8 \, \sqrt{2} x - {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, \sqrt{\sqrt{2} + 2} {\left(\sqrt{2} - 2\right)} + 3 \, {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} - 8 \, \sqrt{2} \sqrt{-\frac{1}{8} \, \sqrt{2} x {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + \frac{1}{64} \, {\left(\sqrt{2} + 2\right)}^{3} + \frac{3}{64} \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - \frac{1}{64} \, {\left(\sqrt{2} - 2\right)}^{3} + \frac{3}{8} \, \sqrt{2} x {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - \frac{1}{8} \, \sqrt{2} x {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} + x^{2} - \frac{3}{64} \, {\left(8 \, \sqrt{2} x \sqrt{\sqrt{2} + 2} + {\left(\sqrt{2} + 2\right)}^{2}\right)} {\left(\sqrt{2} - 2\right)}}}{{\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + 3 \, \sqrt{\sqrt{2} + 2} {\left(\sqrt{2} - 2\right)} + 3 \, {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}}}\right) + 4 \, {\left(\sqrt{2} x \sqrt{\sqrt{2} + 2} - \sqrt{2} x \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(-\frac{8 \, \sqrt{2} x + {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + 3 \, \sqrt{\sqrt{2} + 2} {\left(\sqrt{2} - 2\right)} + 3 \, {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} - \sqrt{2} \sqrt{8 \, \sqrt{2} x {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + {\left(\sqrt{2} + 2\right)}^{3} + 3 \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - {\left(\sqrt{2} - 2\right)}^{3} + 24 \, \sqrt{2} x {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - 8 \, \sqrt{2} x {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} + 64 \, x^{2} + 3 \, {\left(8 \, \sqrt{2} x \sqrt{\sqrt{2} + 2} - {\left(\sqrt{2} + 2\right)}^{2}\right)} {\left(\sqrt{2} - 2\right)}}}{{\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + 3 \, \sqrt{\sqrt{2} + 2} {\left(\sqrt{2} - 2\right)} - 3 \, {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} + {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}}}\right) + 4 \, {\left(\sqrt{2} x \sqrt{\sqrt{2} + 2} - \sqrt{2} x \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(-\frac{8 \, \sqrt{2} x - {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, \sqrt{\sqrt{2} + 2} {\left(\sqrt{2} - 2\right)} - 3 \, {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} + {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} - 8 \, \sqrt{2} \sqrt{-\frac{1}{8} \, \sqrt{2} x {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + \frac{1}{64} \, {\left(\sqrt{2} + 2\right)}^{3} + \frac{3}{64} \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - \frac{1}{64} \, {\left(\sqrt{2} - 2\right)}^{3} - \frac{3}{8} \, \sqrt{2} x {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} + \frac{1}{8} \, \sqrt{2} x {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} + x^{2} - \frac{3}{64} \, {\left(8 \, \sqrt{2} x \sqrt{\sqrt{2} + 2} + {\left(\sqrt{2} + 2\right)}^{2}\right)} {\left(\sqrt{2} - 2\right)}}}{{\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + 3 \, \sqrt{\sqrt{2} + 2} {\left(\sqrt{2} - 2\right)} - 3 \, {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} + {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}}}\right) - {\left(\sqrt{2} x \sqrt{\sqrt{2} + 2} + \sqrt{2} x \sqrt{-\sqrt{2} + 2}\right)} \log\left(\frac{1}{8} \, \sqrt{2} x {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + \frac{1}{64} \, {\left(\sqrt{2} + 2\right)}^{3} + \frac{3}{64} \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - \frac{1}{64} \, {\left(\sqrt{2} - 2\right)}^{3} + \frac{3}{8} \, \sqrt{2} x {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - \frac{1}{8} \, \sqrt{2} x {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} + x^{2} + \frac{3}{64} \, {\left(8 \, \sqrt{2} x \sqrt{\sqrt{2} + 2} - {\left(\sqrt{2} + 2\right)}^{2}\right)} {\left(\sqrt{2} - 2\right)}\right) + {\left(\sqrt{2} x \sqrt{\sqrt{2} + 2} - \sqrt{2} x \sqrt{-\sqrt{2} + 2}\right)} \log\left(\frac{1}{8} \, \sqrt{2} x {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + \frac{1}{64} \, {\left(\sqrt{2} + 2\right)}^{3} + \frac{3}{64} \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - \frac{1}{64} \, {\left(\sqrt{2} - 2\right)}^{3} - \frac{3}{8} \, \sqrt{2} x {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} + \frac{1}{8} \, \sqrt{2} x {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} + x^{2} + \frac{3}{64} \, {\left(8 \, \sqrt{2} x \sqrt{\sqrt{2} + 2} - {\left(\sqrt{2} + 2\right)}^{2}\right)} {\left(\sqrt{2} - 2\right)}\right) - {\left(\sqrt{2} x \sqrt{\sqrt{2} + 2} - \sqrt{2} x \sqrt{-\sqrt{2} + 2}\right)} \log\left(-\frac{1}{8} \, \sqrt{2} x {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + \frac{1}{64} \, {\left(\sqrt{2} + 2\right)}^{3} + \frac{3}{64} \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - \frac{1}{64} \, {\left(\sqrt{2} - 2\right)}^{3} + \frac{3}{8} \, \sqrt{2} x {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - \frac{1}{8} \, \sqrt{2} x {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} + x^{2} - \frac{3}{64} \, {\left(8 \, \sqrt{2} x \sqrt{\sqrt{2} + 2} + {\left(\sqrt{2} + 2\right)}^{2}\right)} {\left(\sqrt{2} - 2\right)}\right) + {\left(\sqrt{2} x \sqrt{\sqrt{2} + 2} + \sqrt{2} x \sqrt{-\sqrt{2} + 2}\right)} \log\left(-\frac{1}{8} \, \sqrt{2} x {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + \frac{1}{64} \, {\left(\sqrt{2} + 2\right)}^{3} + \frac{3}{64} \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - \frac{1}{64} \, {\left(\sqrt{2} - 2\right)}^{3} - \frac{3}{8} \, \sqrt{2} x {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} + \frac{1}{8} \, \sqrt{2} x {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} + x^{2} - \frac{3}{64} \, {\left(8 \, \sqrt{2} x \sqrt{\sqrt{2} + 2} + {\left(\sqrt{2} + 2\right)}^{2}\right)} {\left(\sqrt{2} - 2\right)}\right) + 64}{64 \, x}"," ",0,"-1/64*(8*x*sqrt(-sqrt(2) + 2)*arctan((3*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - (-sqrt(2) + 2)^(3/2) + 8*x - sqrt((sqrt(2) + 2)^3 - 3*(sqrt(2) + 2)^2*(sqrt(2) - 2) + 3*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - (sqrt(2) - 2)^3 + 48*x*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - 16*x*(-sqrt(2) + 2)^(3/2) + 64*x^2))/((sqrt(2) + 2)^(3/2) + 3*sqrt(sqrt(2) + 2)*(sqrt(2) - 2))) + 8*x*sqrt(-sqrt(2) + 2)*arctan(-(3*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - (-sqrt(2) + 2)^(3/2) - 8*x + sqrt((sqrt(2) + 2)^3 - 3*(sqrt(2) + 2)^2*(sqrt(2) - 2) + 3*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - (sqrt(2) - 2)^3 - 48*x*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) + 16*x*(-sqrt(2) + 2)^(3/2) + 64*x^2))/((sqrt(2) + 2)^(3/2) + 3*sqrt(sqrt(2) + 2)*(sqrt(2) - 2))) + 8*x*sqrt(sqrt(2) + 2)*arctan(((sqrt(2) + 2)^(3/2) + 3*sqrt(sqrt(2) + 2)*(sqrt(2) - 2) + 8*x - sqrt((sqrt(2) + 2)^3 + 3*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - (sqrt(2) - 2)^3 + 16*x*(sqrt(2) + 2)^(3/2) + 64*x^2 - 3*((sqrt(2) + 2)^2 - 16*x*sqrt(sqrt(2) + 2))*(sqrt(2) - 2)))/(3*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - (-sqrt(2) + 2)^(3/2))) + 8*x*sqrt(sqrt(2) + 2)*arctan(-((sqrt(2) + 2)^(3/2) + 3*sqrt(sqrt(2) + 2)*(sqrt(2) - 2) - 8*x + sqrt((sqrt(2) + 2)^3 + 3*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - (sqrt(2) - 2)^3 - 16*x*(sqrt(2) + 2)^(3/2) + 64*x^2 - 3*((sqrt(2) + 2)^2 + 16*x*sqrt(sqrt(2) + 2))*(sqrt(2) - 2)))/(3*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - (-sqrt(2) + 2)^(3/2))) - 2*x*sqrt(sqrt(2) + 2)*log(1/64*(sqrt(2) + 2)^3 - 3/64*(sqrt(2) + 2)^2*(sqrt(2) - 2) + 3/64*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - 1/64*(sqrt(2) - 2)^3 + 3/4*x*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - 1/4*x*(-sqrt(2) + 2)^(3/2) + x^2) + 2*x*sqrt(sqrt(2) + 2)*log(1/64*(sqrt(2) + 2)^3 - 3/64*(sqrt(2) + 2)^2*(sqrt(2) - 2) + 3/64*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - 1/64*(sqrt(2) - 2)^3 - 3/4*x*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) + 1/4*x*(-sqrt(2) + 2)^(3/2) + x^2) - 2*x*sqrt(-sqrt(2) + 2)*log(1/64*(sqrt(2) + 2)^3 + 3/64*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - 1/64*(sqrt(2) - 2)^3 + 1/4*x*(sqrt(2) + 2)^(3/2) + x^2 - 3/64*((sqrt(2) + 2)^2 - 16*x*sqrt(sqrt(2) + 2))*(sqrt(2) - 2)) + 2*x*sqrt(-sqrt(2) + 2)*log(1/64*(sqrt(2) + 2)^3 + 3/64*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - 1/64*(sqrt(2) - 2)^3 - 1/4*x*(sqrt(2) + 2)^(3/2) + x^2 - 3/64*((sqrt(2) + 2)^2 + 16*x*sqrt(sqrt(2) + 2))*(sqrt(2) - 2)) + 4*(sqrt(2)*x*sqrt(sqrt(2) + 2) + sqrt(2)*x*sqrt(-sqrt(2) + 2))*arctan((8*sqrt(2)*x + (sqrt(2) + 2)^(3/2) + 3*sqrt(sqrt(2) + 2)*(sqrt(2) - 2) - 3*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) + (-sqrt(2) + 2)^(3/2) - sqrt(2)*sqrt(8*sqrt(2)*x*(sqrt(2) + 2)^(3/2) + (sqrt(2) + 2)^3 + 3*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - (sqrt(2) - 2)^3 - 24*sqrt(2)*x*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) + 8*sqrt(2)*x*(-sqrt(2) + 2)^(3/2) + 64*x^2 + 3*(8*sqrt(2)*x*sqrt(sqrt(2) + 2) - (sqrt(2) + 2)^2)*(sqrt(2) - 2)))/((sqrt(2) + 2)^(3/2) + 3*sqrt(sqrt(2) + 2)*(sqrt(2) - 2) + 3*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - (-sqrt(2) + 2)^(3/2))) + 4*(sqrt(2)*x*sqrt(sqrt(2) + 2) + sqrt(2)*x*sqrt(-sqrt(2) + 2))*arctan((8*sqrt(2)*x - (sqrt(2) + 2)^(3/2) - 3*sqrt(sqrt(2) + 2)*(sqrt(2) - 2) + 3*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - (-sqrt(2) + 2)^(3/2) - 8*sqrt(2)*sqrt(-1/8*sqrt(2)*x*(sqrt(2) + 2)^(3/2) + 1/64*(sqrt(2) + 2)^3 + 3/64*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - 1/64*(sqrt(2) - 2)^3 + 3/8*sqrt(2)*x*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - 1/8*sqrt(2)*x*(-sqrt(2) + 2)^(3/2) + x^2 - 3/64*(8*sqrt(2)*x*sqrt(sqrt(2) + 2) + (sqrt(2) + 2)^2)*(sqrt(2) - 2)))/((sqrt(2) + 2)^(3/2) + 3*sqrt(sqrt(2) + 2)*(sqrt(2) - 2) + 3*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - (-sqrt(2) + 2)^(3/2))) + 4*(sqrt(2)*x*sqrt(sqrt(2) + 2) - sqrt(2)*x*sqrt(-sqrt(2) + 2))*arctan(-(8*sqrt(2)*x + (sqrt(2) + 2)^(3/2) + 3*sqrt(sqrt(2) + 2)*(sqrt(2) - 2) + 3*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - (-sqrt(2) + 2)^(3/2) - sqrt(2)*sqrt(8*sqrt(2)*x*(sqrt(2) + 2)^(3/2) + (sqrt(2) + 2)^3 + 3*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - (sqrt(2) - 2)^3 + 24*sqrt(2)*x*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - 8*sqrt(2)*x*(-sqrt(2) + 2)^(3/2) + 64*x^2 + 3*(8*sqrt(2)*x*sqrt(sqrt(2) + 2) - (sqrt(2) + 2)^2)*(sqrt(2) - 2)))/((sqrt(2) + 2)^(3/2) + 3*sqrt(sqrt(2) + 2)*(sqrt(2) - 2) - 3*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) + (-sqrt(2) + 2)^(3/2))) + 4*(sqrt(2)*x*sqrt(sqrt(2) + 2) - sqrt(2)*x*sqrt(-sqrt(2) + 2))*arctan(-(8*sqrt(2)*x - (sqrt(2) + 2)^(3/2) - 3*sqrt(sqrt(2) + 2)*(sqrt(2) - 2) - 3*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) + (-sqrt(2) + 2)^(3/2) - 8*sqrt(2)*sqrt(-1/8*sqrt(2)*x*(sqrt(2) + 2)^(3/2) + 1/64*(sqrt(2) + 2)^3 + 3/64*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - 1/64*(sqrt(2) - 2)^3 - 3/8*sqrt(2)*x*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) + 1/8*sqrt(2)*x*(-sqrt(2) + 2)^(3/2) + x^2 - 3/64*(8*sqrt(2)*x*sqrt(sqrt(2) + 2) + (sqrt(2) + 2)^2)*(sqrt(2) - 2)))/((sqrt(2) + 2)^(3/2) + 3*sqrt(sqrt(2) + 2)*(sqrt(2) - 2) - 3*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) + (-sqrt(2) + 2)^(3/2))) - (sqrt(2)*x*sqrt(sqrt(2) + 2) + sqrt(2)*x*sqrt(-sqrt(2) + 2))*log(1/8*sqrt(2)*x*(sqrt(2) + 2)^(3/2) + 1/64*(sqrt(2) + 2)^3 + 3/64*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - 1/64*(sqrt(2) - 2)^3 + 3/8*sqrt(2)*x*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - 1/8*sqrt(2)*x*(-sqrt(2) + 2)^(3/2) + x^2 + 3/64*(8*sqrt(2)*x*sqrt(sqrt(2) + 2) - (sqrt(2) + 2)^2)*(sqrt(2) - 2)) + (sqrt(2)*x*sqrt(sqrt(2) + 2) - sqrt(2)*x*sqrt(-sqrt(2) + 2))*log(1/8*sqrt(2)*x*(sqrt(2) + 2)^(3/2) + 1/64*(sqrt(2) + 2)^3 + 3/64*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - 1/64*(sqrt(2) - 2)^3 - 3/8*sqrt(2)*x*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) + 1/8*sqrt(2)*x*(-sqrt(2) + 2)^(3/2) + x^2 + 3/64*(8*sqrt(2)*x*sqrt(sqrt(2) + 2) - (sqrt(2) + 2)^2)*(sqrt(2) - 2)) - (sqrt(2)*x*sqrt(sqrt(2) + 2) - sqrt(2)*x*sqrt(-sqrt(2) + 2))*log(-1/8*sqrt(2)*x*(sqrt(2) + 2)^(3/2) + 1/64*(sqrt(2) + 2)^3 + 3/64*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - 1/64*(sqrt(2) - 2)^3 + 3/8*sqrt(2)*x*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - 1/8*sqrt(2)*x*(-sqrt(2) + 2)^(3/2) + x^2 - 3/64*(8*sqrt(2)*x*sqrt(sqrt(2) + 2) + (sqrt(2) + 2)^2)*(sqrt(2) - 2)) + (sqrt(2)*x*sqrt(sqrt(2) + 2) + sqrt(2)*x*sqrt(-sqrt(2) + 2))*log(-1/8*sqrt(2)*x*(sqrt(2) + 2)^(3/2) + 1/64*(sqrt(2) + 2)^3 + 3/64*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - 1/64*(sqrt(2) - 2)^3 - 3/8*sqrt(2)*x*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) + 1/8*sqrt(2)*x*(-sqrt(2) + 2)^(3/2) + x^2 - 3/64*(8*sqrt(2)*x*sqrt(sqrt(2) + 2) + (sqrt(2) + 2)^2)*(sqrt(2) - 2)) + 64)/x","B",0
1506,1,1105,0,0.884573," ","integrate(1/x^4/(x^8+1),x, algorithm=""fricas"")","-\frac{24 \, x^{3} \sqrt{-\sqrt{2} + 2} \arctan\left(-\frac{2 \, x - 2 \, \sqrt{x^{2} + x \sqrt{-\sqrt{2} + 2} + 1} + \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2}}\right) + 24 \, x^{3} \sqrt{-\sqrt{2} + 2} \arctan\left(-\frac{2 \, x - 2 \, \sqrt{x^{2} - x \sqrt{-\sqrt{2} + 2} + 1} - \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2}}\right) - 24 \, x^{3} \sqrt{\sqrt{2} + 2} \arctan\left(-\frac{2 \, x - 2 \, \sqrt{x^{2} + x \sqrt{\sqrt{2} + 2} + 1} + \sqrt{\sqrt{2} + 2}}{\sqrt{-\sqrt{2} + 2}}\right) - 24 \, x^{3} \sqrt{\sqrt{2} + 2} \arctan\left(-\frac{2 \, x - 2 \, \sqrt{x^{2} - x \sqrt{\sqrt{2} + 2} + 1} - \sqrt{\sqrt{2} + 2}}{\sqrt{-\sqrt{2} + 2}}\right) - 6 \, x^{3} \sqrt{-\sqrt{2} + 2} \log\left(x^{2} + x \sqrt{\sqrt{2} + 2} + 1\right) + 6 \, x^{3} \sqrt{-\sqrt{2} + 2} \log\left(x^{2} - x \sqrt{\sqrt{2} + 2} + 1\right) + 6 \, x^{3} \sqrt{\sqrt{2} + 2} \log\left(x^{2} + x \sqrt{-\sqrt{2} + 2} + 1\right) - 6 \, x^{3} \sqrt{\sqrt{2} + 2} \log\left(x^{2} - x \sqrt{-\sqrt{2} + 2} + 1\right) + 12 \, {\left(\sqrt{2} x^{3} \sqrt{\sqrt{2} + 2} - \sqrt{2} x^{3} \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(-\frac{2 \, \sqrt{2} x - 2 \, \sqrt{2} \sqrt{x^{2} + \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} - \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1} + \sqrt{\sqrt{2} + 2} - \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2} + \sqrt{-\sqrt{2} + 2}}\right) + 12 \, {\left(\sqrt{2} x^{3} \sqrt{\sqrt{2} + 2} - \sqrt{2} x^{3} \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(-\frac{2 \, \sqrt{2} x - 2 \, \sqrt{2} \sqrt{x^{2} - \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} + \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1} - \sqrt{\sqrt{2} + 2} + \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2} + \sqrt{-\sqrt{2} + 2}}\right) + 12 \, {\left(\sqrt{2} x^{3} \sqrt{\sqrt{2} + 2} + \sqrt{2} x^{3} \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(\frac{2 \, \sqrt{2} x - 2 \, \sqrt{2} \sqrt{x^{2} + \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} + \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1} + \sqrt{\sqrt{2} + 2} + \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2} - \sqrt{-\sqrt{2} + 2}}\right) + 12 \, {\left(\sqrt{2} x^{3} \sqrt{\sqrt{2} + 2} + \sqrt{2} x^{3} \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(\frac{2 \, \sqrt{2} x - 2 \, \sqrt{2} \sqrt{x^{2} - \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} - \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1} - \sqrt{\sqrt{2} + 2} - \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2} - \sqrt{-\sqrt{2} + 2}}\right) - 3 \, {\left(\sqrt{2} x^{3} \sqrt{\sqrt{2} + 2} - \sqrt{2} x^{3} \sqrt{-\sqrt{2} + 2}\right)} \log\left(x^{2} + \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} + \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1\right) + 3 \, {\left(\sqrt{2} x^{3} \sqrt{\sqrt{2} + 2} + \sqrt{2} x^{3} \sqrt{-\sqrt{2} + 2}\right)} \log\left(x^{2} + \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} - \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1\right) - 3 \, {\left(\sqrt{2} x^{3} \sqrt{\sqrt{2} + 2} + \sqrt{2} x^{3} \sqrt{-\sqrt{2} + 2}\right)} \log\left(x^{2} - \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} + \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1\right) + 3 \, {\left(\sqrt{2} x^{3} \sqrt{\sqrt{2} + 2} - \sqrt{2} x^{3} \sqrt{-\sqrt{2} + 2}\right)} \log\left(x^{2} - \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} - \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1\right) + 64}{192 \, x^{3}}"," ",0,"-1/192*(24*x^3*sqrt(-sqrt(2) + 2)*arctan(-(2*x - 2*sqrt(x^2 + x*sqrt(-sqrt(2) + 2) + 1) + sqrt(-sqrt(2) + 2))/sqrt(sqrt(2) + 2)) + 24*x^3*sqrt(-sqrt(2) + 2)*arctan(-(2*x - 2*sqrt(x^2 - x*sqrt(-sqrt(2) + 2) + 1) - sqrt(-sqrt(2) + 2))/sqrt(sqrt(2) + 2)) - 24*x^3*sqrt(sqrt(2) + 2)*arctan(-(2*x - 2*sqrt(x^2 + x*sqrt(sqrt(2) + 2) + 1) + sqrt(sqrt(2) + 2))/sqrt(-sqrt(2) + 2)) - 24*x^3*sqrt(sqrt(2) + 2)*arctan(-(2*x - 2*sqrt(x^2 - x*sqrt(sqrt(2) + 2) + 1) - sqrt(sqrt(2) + 2))/sqrt(-sqrt(2) + 2)) - 6*x^3*sqrt(-sqrt(2) + 2)*log(x^2 + x*sqrt(sqrt(2) + 2) + 1) + 6*x^3*sqrt(-sqrt(2) + 2)*log(x^2 - x*sqrt(sqrt(2) + 2) + 1) + 6*x^3*sqrt(sqrt(2) + 2)*log(x^2 + x*sqrt(-sqrt(2) + 2) + 1) - 6*x^3*sqrt(sqrt(2) + 2)*log(x^2 - x*sqrt(-sqrt(2) + 2) + 1) + 12*(sqrt(2)*x^3*sqrt(sqrt(2) + 2) - sqrt(2)*x^3*sqrt(-sqrt(2) + 2))*arctan(-(2*sqrt(2)*x - 2*sqrt(2)*sqrt(x^2 + 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) - 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) + sqrt(sqrt(2) + 2) - sqrt(-sqrt(2) + 2))/(sqrt(sqrt(2) + 2) + sqrt(-sqrt(2) + 2))) + 12*(sqrt(2)*x^3*sqrt(sqrt(2) + 2) - sqrt(2)*x^3*sqrt(-sqrt(2) + 2))*arctan(-(2*sqrt(2)*x - 2*sqrt(2)*sqrt(x^2 - 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) + 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) - sqrt(sqrt(2) + 2) + sqrt(-sqrt(2) + 2))/(sqrt(sqrt(2) + 2) + sqrt(-sqrt(2) + 2))) + 12*(sqrt(2)*x^3*sqrt(sqrt(2) + 2) + sqrt(2)*x^3*sqrt(-sqrt(2) + 2))*arctan((2*sqrt(2)*x - 2*sqrt(2)*sqrt(x^2 + 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) + 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) + sqrt(sqrt(2) + 2) + sqrt(-sqrt(2) + 2))/(sqrt(sqrt(2) + 2) - sqrt(-sqrt(2) + 2))) + 12*(sqrt(2)*x^3*sqrt(sqrt(2) + 2) + sqrt(2)*x^3*sqrt(-sqrt(2) + 2))*arctan((2*sqrt(2)*x - 2*sqrt(2)*sqrt(x^2 - 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) - 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) - sqrt(sqrt(2) + 2) - sqrt(-sqrt(2) + 2))/(sqrt(sqrt(2) + 2) - sqrt(-sqrt(2) + 2))) - 3*(sqrt(2)*x^3*sqrt(sqrt(2) + 2) - sqrt(2)*x^3*sqrt(-sqrt(2) + 2))*log(x^2 + 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) + 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) + 3*(sqrt(2)*x^3*sqrt(sqrt(2) + 2) + sqrt(2)*x^3*sqrt(-sqrt(2) + 2))*log(x^2 + 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) - 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) - 3*(sqrt(2)*x^3*sqrt(sqrt(2) + 2) + sqrt(2)*x^3*sqrt(-sqrt(2) + 2))*log(x^2 - 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) + 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) + 3*(sqrt(2)*x^3*sqrt(sqrt(2) + 2) - sqrt(2)*x^3*sqrt(-sqrt(2) + 2))*log(x^2 - 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) - 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) + 64)/x^3","B",0
1507,1,2591,0,0.875437," ","integrate(1/x^6/(x^8+1),x, algorithm=""fricas"")","-\frac{40 \, x^{5} \sqrt{\sqrt{2} + 2} \arctan\left(\frac{3 \, {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} + 8 \, x - \sqrt{{\left(\sqrt{2} + 2\right)}^{3} - 3 \, {\left(\sqrt{2} + 2\right)}^{2} {\left(\sqrt{2} - 2\right)} + 3 \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - {\left(\sqrt{2} - 2\right)}^{3} + 48 \, x {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - 16 \, x {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} + 64 \, x^{2}}}{{\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + 3 \, \sqrt{\sqrt{2} + 2} {\left(\sqrt{2} - 2\right)}}\right) + 40 \, x^{5} \sqrt{\sqrt{2} + 2} \arctan\left(-\frac{3 \, {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} - 8 \, x + \sqrt{{\left(\sqrt{2} + 2\right)}^{3} - 3 \, {\left(\sqrt{2} + 2\right)}^{2} {\left(\sqrt{2} - 2\right)} + 3 \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - {\left(\sqrt{2} - 2\right)}^{3} - 48 \, x {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} + 16 \, x {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} + 64 \, x^{2}}}{{\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + 3 \, \sqrt{\sqrt{2} + 2} {\left(\sqrt{2} - 2\right)}}\right) - 40 \, x^{5} \sqrt{-\sqrt{2} + 2} \arctan\left(\frac{{\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + 3 \, \sqrt{\sqrt{2} + 2} {\left(\sqrt{2} - 2\right)} + 8 \, x - \sqrt{{\left(\sqrt{2} + 2\right)}^{3} + 3 \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - {\left(\sqrt{2} - 2\right)}^{3} + 16 \, x {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + 64 \, x^{2} - 3 \, {\left({\left(\sqrt{2} + 2\right)}^{2} - 16 \, x \sqrt{\sqrt{2} + 2}\right)} {\left(\sqrt{2} - 2\right)}}}{3 \, {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}}}\right) - 40 \, x^{5} \sqrt{-\sqrt{2} + 2} \arctan\left(-\frac{{\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + 3 \, \sqrt{\sqrt{2} + 2} {\left(\sqrt{2} - 2\right)} - 8 \, x + \sqrt{{\left(\sqrt{2} + 2\right)}^{3} + 3 \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - {\left(\sqrt{2} - 2\right)}^{3} - 16 \, x {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + 64 \, x^{2} - 3 \, {\left({\left(\sqrt{2} + 2\right)}^{2} + 16 \, x \sqrt{\sqrt{2} + 2}\right)} {\left(\sqrt{2} - 2\right)}}}{3 \, {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}}}\right) + 10 \, x^{5} \sqrt{-\sqrt{2} + 2} \log\left(\frac{1}{64} \, {\left(\sqrt{2} + 2\right)}^{3} - \frac{3}{64} \, {\left(\sqrt{2} + 2\right)}^{2} {\left(\sqrt{2} - 2\right)} + \frac{3}{64} \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - \frac{1}{64} \, {\left(\sqrt{2} - 2\right)}^{3} + \frac{3}{4} \, x {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - \frac{1}{4} \, x {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} + x^{2}\right) - 10 \, x^{5} \sqrt{-\sqrt{2} + 2} \log\left(\frac{1}{64} \, {\left(\sqrt{2} + 2\right)}^{3} - \frac{3}{64} \, {\left(\sqrt{2} + 2\right)}^{2} {\left(\sqrt{2} - 2\right)} + \frac{3}{64} \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - \frac{1}{64} \, {\left(\sqrt{2} - 2\right)}^{3} - \frac{3}{4} \, x {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} + \frac{1}{4} \, x {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} + x^{2}\right) - 10 \, x^{5} \sqrt{\sqrt{2} + 2} \log\left(\frac{1}{64} \, {\left(\sqrt{2} + 2\right)}^{3} + \frac{3}{64} \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - \frac{1}{64} \, {\left(\sqrt{2} - 2\right)}^{3} + \frac{1}{4} \, x {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + x^{2} - \frac{3}{64} \, {\left({\left(\sqrt{2} + 2\right)}^{2} - 16 \, x \sqrt{\sqrt{2} + 2}\right)} {\left(\sqrt{2} - 2\right)}\right) + 10 \, x^{5} \sqrt{\sqrt{2} + 2} \log\left(\frac{1}{64} \, {\left(\sqrt{2} + 2\right)}^{3} + \frac{3}{64} \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - \frac{1}{64} \, {\left(\sqrt{2} - 2\right)}^{3} - \frac{1}{4} \, x {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + x^{2} - \frac{3}{64} \, {\left({\left(\sqrt{2} + 2\right)}^{2} + 16 \, x \sqrt{\sqrt{2} + 2}\right)} {\left(\sqrt{2} - 2\right)}\right) - 20 \, {\left(\sqrt{2} x^{5} \sqrt{\sqrt{2} + 2} - \sqrt{2} x^{5} \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(\frac{8 \, \sqrt{2} x + {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + 3 \, \sqrt{\sqrt{2} + 2} {\left(\sqrt{2} - 2\right)} - 3 \, {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} + {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} - \sqrt{2} \sqrt{8 \, \sqrt{2} x {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + {\left(\sqrt{2} + 2\right)}^{3} + 3 \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - {\left(\sqrt{2} - 2\right)}^{3} - 24 \, \sqrt{2} x {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} + 8 \, \sqrt{2} x {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} + 64 \, x^{2} + 3 \, {\left(8 \, \sqrt{2} x \sqrt{\sqrt{2} + 2} - {\left(\sqrt{2} + 2\right)}^{2}\right)} {\left(\sqrt{2} - 2\right)}}}{{\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + 3 \, \sqrt{\sqrt{2} + 2} {\left(\sqrt{2} - 2\right)} + 3 \, {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}}}\right) - 20 \, {\left(\sqrt{2} x^{5} \sqrt{\sqrt{2} + 2} - \sqrt{2} x^{5} \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(\frac{8 \, \sqrt{2} x - {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, \sqrt{\sqrt{2} + 2} {\left(\sqrt{2} - 2\right)} + 3 \, {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} - 8 \, \sqrt{2} \sqrt{-\frac{1}{8} \, \sqrt{2} x {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + \frac{1}{64} \, {\left(\sqrt{2} + 2\right)}^{3} + \frac{3}{64} \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - \frac{1}{64} \, {\left(\sqrt{2} - 2\right)}^{3} + \frac{3}{8} \, \sqrt{2} x {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - \frac{1}{8} \, \sqrt{2} x {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} + x^{2} - \frac{3}{64} \, {\left(8 \, \sqrt{2} x \sqrt{\sqrt{2} + 2} + {\left(\sqrt{2} + 2\right)}^{2}\right)} {\left(\sqrt{2} - 2\right)}}}{{\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + 3 \, \sqrt{\sqrt{2} + 2} {\left(\sqrt{2} - 2\right)} + 3 \, {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}}}\right) + 20 \, {\left(\sqrt{2} x^{5} \sqrt{\sqrt{2} + 2} + \sqrt{2} x^{5} \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(-\frac{8 \, \sqrt{2} x + {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + 3 \, \sqrt{\sqrt{2} + 2} {\left(\sqrt{2} - 2\right)} + 3 \, {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} - \sqrt{2} \sqrt{8 \, \sqrt{2} x {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + {\left(\sqrt{2} + 2\right)}^{3} + 3 \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - {\left(\sqrt{2} - 2\right)}^{3} + 24 \, \sqrt{2} x {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - 8 \, \sqrt{2} x {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} + 64 \, x^{2} + 3 \, {\left(8 \, \sqrt{2} x \sqrt{\sqrt{2} + 2} - {\left(\sqrt{2} + 2\right)}^{2}\right)} {\left(\sqrt{2} - 2\right)}}}{{\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + 3 \, \sqrt{\sqrt{2} + 2} {\left(\sqrt{2} - 2\right)} - 3 \, {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} + {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}}}\right) + 20 \, {\left(\sqrt{2} x^{5} \sqrt{\sqrt{2} + 2} + \sqrt{2} x^{5} \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(-\frac{8 \, \sqrt{2} x - {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, \sqrt{\sqrt{2} + 2} {\left(\sqrt{2} - 2\right)} - 3 \, {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} + {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} - 8 \, \sqrt{2} \sqrt{-\frac{1}{8} \, \sqrt{2} x {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + \frac{1}{64} \, {\left(\sqrt{2} + 2\right)}^{3} + \frac{3}{64} \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - \frac{1}{64} \, {\left(\sqrt{2} - 2\right)}^{3} - \frac{3}{8} \, \sqrt{2} x {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} + \frac{1}{8} \, \sqrt{2} x {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} + x^{2} - \frac{3}{64} \, {\left(8 \, \sqrt{2} x \sqrt{\sqrt{2} + 2} + {\left(\sqrt{2} + 2\right)}^{2}\right)} {\left(\sqrt{2} - 2\right)}}}{{\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + 3 \, \sqrt{\sqrt{2} + 2} {\left(\sqrt{2} - 2\right)} - 3 \, {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} + {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}}}\right) + 5 \, {\left(\sqrt{2} x^{5} \sqrt{\sqrt{2} + 2} - \sqrt{2} x^{5} \sqrt{-\sqrt{2} + 2}\right)} \log\left(\frac{1}{8} \, \sqrt{2} x {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + \frac{1}{64} \, {\left(\sqrt{2} + 2\right)}^{3} + \frac{3}{64} \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - \frac{1}{64} \, {\left(\sqrt{2} - 2\right)}^{3} + \frac{3}{8} \, \sqrt{2} x {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - \frac{1}{8} \, \sqrt{2} x {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} + x^{2} + \frac{3}{64} \, {\left(8 \, \sqrt{2} x \sqrt{\sqrt{2} + 2} - {\left(\sqrt{2} + 2\right)}^{2}\right)} {\left(\sqrt{2} - 2\right)}\right) + 5 \, {\left(\sqrt{2} x^{5} \sqrt{\sqrt{2} + 2} + \sqrt{2} x^{5} \sqrt{-\sqrt{2} + 2}\right)} \log\left(\frac{1}{8} \, \sqrt{2} x {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + \frac{1}{64} \, {\left(\sqrt{2} + 2\right)}^{3} + \frac{3}{64} \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - \frac{1}{64} \, {\left(\sqrt{2} - 2\right)}^{3} - \frac{3}{8} \, \sqrt{2} x {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} + \frac{1}{8} \, \sqrt{2} x {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} + x^{2} + \frac{3}{64} \, {\left(8 \, \sqrt{2} x \sqrt{\sqrt{2} + 2} - {\left(\sqrt{2} + 2\right)}^{2}\right)} {\left(\sqrt{2} - 2\right)}\right) - 5 \, {\left(\sqrt{2} x^{5} \sqrt{\sqrt{2} + 2} + \sqrt{2} x^{5} \sqrt{-\sqrt{2} + 2}\right)} \log\left(-\frac{1}{8} \, \sqrt{2} x {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + \frac{1}{64} \, {\left(\sqrt{2} + 2\right)}^{3} + \frac{3}{64} \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - \frac{1}{64} \, {\left(\sqrt{2} - 2\right)}^{3} + \frac{3}{8} \, \sqrt{2} x {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} - \frac{1}{8} \, \sqrt{2} x {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} + x^{2} - \frac{3}{64} \, {\left(8 \, \sqrt{2} x \sqrt{\sqrt{2} + 2} + {\left(\sqrt{2} + 2\right)}^{2}\right)} {\left(\sqrt{2} - 2\right)}\right) - 5 \, {\left(\sqrt{2} x^{5} \sqrt{\sqrt{2} + 2} - \sqrt{2} x^{5} \sqrt{-\sqrt{2} + 2}\right)} \log\left(-\frac{1}{8} \, \sqrt{2} x {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + \frac{1}{64} \, {\left(\sqrt{2} + 2\right)}^{3} + \frac{3}{64} \, {\left(\sqrt{2} + 2\right)} {\left(\sqrt{2} - 2\right)}^{2} - \frac{1}{64} \, {\left(\sqrt{2} - 2\right)}^{3} - \frac{3}{8} \, \sqrt{2} x {\left(\sqrt{2} + 2\right)} \sqrt{-\sqrt{2} + 2} + \frac{1}{8} \, \sqrt{2} x {\left(-\sqrt{2} + 2\right)}^{\frac{3}{2}} + x^{2} - \frac{3}{64} \, {\left(8 \, \sqrt{2} x \sqrt{\sqrt{2} + 2} + {\left(\sqrt{2} + 2\right)}^{2}\right)} {\left(\sqrt{2} - 2\right)}\right) + 64}{320 \, x^{5}}"," ",0,"-1/320*(40*x^5*sqrt(sqrt(2) + 2)*arctan((3*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - (-sqrt(2) + 2)^(3/2) + 8*x - sqrt((sqrt(2) + 2)^3 - 3*(sqrt(2) + 2)^2*(sqrt(2) - 2) + 3*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - (sqrt(2) - 2)^3 + 48*x*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - 16*x*(-sqrt(2) + 2)^(3/2) + 64*x^2))/((sqrt(2) + 2)^(3/2) + 3*sqrt(sqrt(2) + 2)*(sqrt(2) - 2))) + 40*x^5*sqrt(sqrt(2) + 2)*arctan(-(3*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - (-sqrt(2) + 2)^(3/2) - 8*x + sqrt((sqrt(2) + 2)^3 - 3*(sqrt(2) + 2)^2*(sqrt(2) - 2) + 3*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - (sqrt(2) - 2)^3 - 48*x*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) + 16*x*(-sqrt(2) + 2)^(3/2) + 64*x^2))/((sqrt(2) + 2)^(3/2) + 3*sqrt(sqrt(2) + 2)*(sqrt(2) - 2))) - 40*x^5*sqrt(-sqrt(2) + 2)*arctan(((sqrt(2) + 2)^(3/2) + 3*sqrt(sqrt(2) + 2)*(sqrt(2) - 2) + 8*x - sqrt((sqrt(2) + 2)^3 + 3*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - (sqrt(2) - 2)^3 + 16*x*(sqrt(2) + 2)^(3/2) + 64*x^2 - 3*((sqrt(2) + 2)^2 - 16*x*sqrt(sqrt(2) + 2))*(sqrt(2) - 2)))/(3*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - (-sqrt(2) + 2)^(3/2))) - 40*x^5*sqrt(-sqrt(2) + 2)*arctan(-((sqrt(2) + 2)^(3/2) + 3*sqrt(sqrt(2) + 2)*(sqrt(2) - 2) - 8*x + sqrt((sqrt(2) + 2)^3 + 3*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - (sqrt(2) - 2)^3 - 16*x*(sqrt(2) + 2)^(3/2) + 64*x^2 - 3*((sqrt(2) + 2)^2 + 16*x*sqrt(sqrt(2) + 2))*(sqrt(2) - 2)))/(3*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - (-sqrt(2) + 2)^(3/2))) + 10*x^5*sqrt(-sqrt(2) + 2)*log(1/64*(sqrt(2) + 2)^3 - 3/64*(sqrt(2) + 2)^2*(sqrt(2) - 2) + 3/64*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - 1/64*(sqrt(2) - 2)^3 + 3/4*x*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - 1/4*x*(-sqrt(2) + 2)^(3/2) + x^2) - 10*x^5*sqrt(-sqrt(2) + 2)*log(1/64*(sqrt(2) + 2)^3 - 3/64*(sqrt(2) + 2)^2*(sqrt(2) - 2) + 3/64*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - 1/64*(sqrt(2) - 2)^3 - 3/4*x*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) + 1/4*x*(-sqrt(2) + 2)^(3/2) + x^2) - 10*x^5*sqrt(sqrt(2) + 2)*log(1/64*(sqrt(2) + 2)^3 + 3/64*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - 1/64*(sqrt(2) - 2)^3 + 1/4*x*(sqrt(2) + 2)^(3/2) + x^2 - 3/64*((sqrt(2) + 2)^2 - 16*x*sqrt(sqrt(2) + 2))*(sqrt(2) - 2)) + 10*x^5*sqrt(sqrt(2) + 2)*log(1/64*(sqrt(2) + 2)^3 + 3/64*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - 1/64*(sqrt(2) - 2)^3 - 1/4*x*(sqrt(2) + 2)^(3/2) + x^2 - 3/64*((sqrt(2) + 2)^2 + 16*x*sqrt(sqrt(2) + 2))*(sqrt(2) - 2)) - 20*(sqrt(2)*x^5*sqrt(sqrt(2) + 2) - sqrt(2)*x^5*sqrt(-sqrt(2) + 2))*arctan((8*sqrt(2)*x + (sqrt(2) + 2)^(3/2) + 3*sqrt(sqrt(2) + 2)*(sqrt(2) - 2) - 3*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) + (-sqrt(2) + 2)^(3/2) - sqrt(2)*sqrt(8*sqrt(2)*x*(sqrt(2) + 2)^(3/2) + (sqrt(2) + 2)^3 + 3*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - (sqrt(2) - 2)^3 - 24*sqrt(2)*x*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) + 8*sqrt(2)*x*(-sqrt(2) + 2)^(3/2) + 64*x^2 + 3*(8*sqrt(2)*x*sqrt(sqrt(2) + 2) - (sqrt(2) + 2)^2)*(sqrt(2) - 2)))/((sqrt(2) + 2)^(3/2) + 3*sqrt(sqrt(2) + 2)*(sqrt(2) - 2) + 3*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - (-sqrt(2) + 2)^(3/2))) - 20*(sqrt(2)*x^5*sqrt(sqrt(2) + 2) - sqrt(2)*x^5*sqrt(-sqrt(2) + 2))*arctan((8*sqrt(2)*x - (sqrt(2) + 2)^(3/2) - 3*sqrt(sqrt(2) + 2)*(sqrt(2) - 2) + 3*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - (-sqrt(2) + 2)^(3/2) - 8*sqrt(2)*sqrt(-1/8*sqrt(2)*x*(sqrt(2) + 2)^(3/2) + 1/64*(sqrt(2) + 2)^3 + 3/64*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - 1/64*(sqrt(2) - 2)^3 + 3/8*sqrt(2)*x*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - 1/8*sqrt(2)*x*(-sqrt(2) + 2)^(3/2) + x^2 - 3/64*(8*sqrt(2)*x*sqrt(sqrt(2) + 2) + (sqrt(2) + 2)^2)*(sqrt(2) - 2)))/((sqrt(2) + 2)^(3/2) + 3*sqrt(sqrt(2) + 2)*(sqrt(2) - 2) + 3*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - (-sqrt(2) + 2)^(3/2))) + 20*(sqrt(2)*x^5*sqrt(sqrt(2) + 2) + sqrt(2)*x^5*sqrt(-sqrt(2) + 2))*arctan(-(8*sqrt(2)*x + (sqrt(2) + 2)^(3/2) + 3*sqrt(sqrt(2) + 2)*(sqrt(2) - 2) + 3*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - (-sqrt(2) + 2)^(3/2) - sqrt(2)*sqrt(8*sqrt(2)*x*(sqrt(2) + 2)^(3/2) + (sqrt(2) + 2)^3 + 3*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - (sqrt(2) - 2)^3 + 24*sqrt(2)*x*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - 8*sqrt(2)*x*(-sqrt(2) + 2)^(3/2) + 64*x^2 + 3*(8*sqrt(2)*x*sqrt(sqrt(2) + 2) - (sqrt(2) + 2)^2)*(sqrt(2) - 2)))/((sqrt(2) + 2)^(3/2) + 3*sqrt(sqrt(2) + 2)*(sqrt(2) - 2) - 3*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) + (-sqrt(2) + 2)^(3/2))) + 20*(sqrt(2)*x^5*sqrt(sqrt(2) + 2) + sqrt(2)*x^5*sqrt(-sqrt(2) + 2))*arctan(-(8*sqrt(2)*x - (sqrt(2) + 2)^(3/2) - 3*sqrt(sqrt(2) + 2)*(sqrt(2) - 2) - 3*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) + (-sqrt(2) + 2)^(3/2) - 8*sqrt(2)*sqrt(-1/8*sqrt(2)*x*(sqrt(2) + 2)^(3/2) + 1/64*(sqrt(2) + 2)^3 + 3/64*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - 1/64*(sqrt(2) - 2)^3 - 3/8*sqrt(2)*x*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) + 1/8*sqrt(2)*x*(-sqrt(2) + 2)^(3/2) + x^2 - 3/64*(8*sqrt(2)*x*sqrt(sqrt(2) + 2) + (sqrt(2) + 2)^2)*(sqrt(2) - 2)))/((sqrt(2) + 2)^(3/2) + 3*sqrt(sqrt(2) + 2)*(sqrt(2) - 2) - 3*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) + (-sqrt(2) + 2)^(3/2))) + 5*(sqrt(2)*x^5*sqrt(sqrt(2) + 2) - sqrt(2)*x^5*sqrt(-sqrt(2) + 2))*log(1/8*sqrt(2)*x*(sqrt(2) + 2)^(3/2) + 1/64*(sqrt(2) + 2)^3 + 3/64*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - 1/64*(sqrt(2) - 2)^3 + 3/8*sqrt(2)*x*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - 1/8*sqrt(2)*x*(-sqrt(2) + 2)^(3/2) + x^2 + 3/64*(8*sqrt(2)*x*sqrt(sqrt(2) + 2) - (sqrt(2) + 2)^2)*(sqrt(2) - 2)) + 5*(sqrt(2)*x^5*sqrt(sqrt(2) + 2) + sqrt(2)*x^5*sqrt(-sqrt(2) + 2))*log(1/8*sqrt(2)*x*(sqrt(2) + 2)^(3/2) + 1/64*(sqrt(2) + 2)^3 + 3/64*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - 1/64*(sqrt(2) - 2)^3 - 3/8*sqrt(2)*x*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) + 1/8*sqrt(2)*x*(-sqrt(2) + 2)^(3/2) + x^2 + 3/64*(8*sqrt(2)*x*sqrt(sqrt(2) + 2) - (sqrt(2) + 2)^2)*(sqrt(2) - 2)) - 5*(sqrt(2)*x^5*sqrt(sqrt(2) + 2) + sqrt(2)*x^5*sqrt(-sqrt(2) + 2))*log(-1/8*sqrt(2)*x*(sqrt(2) + 2)^(3/2) + 1/64*(sqrt(2) + 2)^3 + 3/64*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - 1/64*(sqrt(2) - 2)^3 + 3/8*sqrt(2)*x*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) - 1/8*sqrt(2)*x*(-sqrt(2) + 2)^(3/2) + x^2 - 3/64*(8*sqrt(2)*x*sqrt(sqrt(2) + 2) + (sqrt(2) + 2)^2)*(sqrt(2) - 2)) - 5*(sqrt(2)*x^5*sqrt(sqrt(2) + 2) - sqrt(2)*x^5*sqrt(-sqrt(2) + 2))*log(-1/8*sqrt(2)*x*(sqrt(2) + 2)^(3/2) + 1/64*(sqrt(2) + 2)^3 + 3/64*(sqrt(2) + 2)*(sqrt(2) - 2)^2 - 1/64*(sqrt(2) - 2)^3 - 3/8*sqrt(2)*x*(sqrt(2) + 2)*sqrt(-sqrt(2) + 2) + 1/8*sqrt(2)*x*(-sqrt(2) + 2)^(3/2) + x^2 - 3/64*(8*sqrt(2)*x*sqrt(sqrt(2) + 2) + (sqrt(2) + 2)^2)*(sqrt(2) - 2)) + 64)/x^5","B",0
1508,1,1105,0,0.987420," ","integrate(1/x^8/(x^8+1),x, algorithm=""fricas"")","\frac{56 \, x^{7} \sqrt{\sqrt{2} + 2} \arctan\left(-\frac{2 \, x - 2 \, \sqrt{x^{2} + x \sqrt{-\sqrt{2} + 2} + 1} + \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2}}\right) + 56 \, x^{7} \sqrt{\sqrt{2} + 2} \arctan\left(-\frac{2 \, x - 2 \, \sqrt{x^{2} - x \sqrt{-\sqrt{2} + 2} + 1} - \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2}}\right) + 56 \, x^{7} \sqrt{-\sqrt{2} + 2} \arctan\left(-\frac{2 \, x - 2 \, \sqrt{x^{2} + x \sqrt{\sqrt{2} + 2} + 1} + \sqrt{\sqrt{2} + 2}}{\sqrt{-\sqrt{2} + 2}}\right) + 56 \, x^{7} \sqrt{-\sqrt{2} + 2} \arctan\left(-\frac{2 \, x - 2 \, \sqrt{x^{2} - x \sqrt{\sqrt{2} + 2} + 1} - \sqrt{\sqrt{2} + 2}}{\sqrt{-\sqrt{2} + 2}}\right) - 14 \, x^{7} \sqrt{\sqrt{2} + 2} \log\left(x^{2} + x \sqrt{\sqrt{2} + 2} + 1\right) + 14 \, x^{7} \sqrt{\sqrt{2} + 2} \log\left(x^{2} - x \sqrt{\sqrt{2} + 2} + 1\right) - 14 \, x^{7} \sqrt{-\sqrt{2} + 2} \log\left(x^{2} + x \sqrt{-\sqrt{2} + 2} + 1\right) + 14 \, x^{7} \sqrt{-\sqrt{2} + 2} \log\left(x^{2} - x \sqrt{-\sqrt{2} + 2} + 1\right) + 28 \, {\left(\sqrt{2} x^{7} \sqrt{\sqrt{2} + 2} + \sqrt{2} x^{7} \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(-\frac{2 \, \sqrt{2} x - 2 \, \sqrt{2} \sqrt{x^{2} + \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} - \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1} + \sqrt{\sqrt{2} + 2} - \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2} + \sqrt{-\sqrt{2} + 2}}\right) + 28 \, {\left(\sqrt{2} x^{7} \sqrt{\sqrt{2} + 2} + \sqrt{2} x^{7} \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(-\frac{2 \, \sqrt{2} x - 2 \, \sqrt{2} \sqrt{x^{2} - \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} + \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1} - \sqrt{\sqrt{2} + 2} + \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2} + \sqrt{-\sqrt{2} + 2}}\right) - 28 \, {\left(\sqrt{2} x^{7} \sqrt{\sqrt{2} + 2} - \sqrt{2} x^{7} \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(\frac{2 \, \sqrt{2} x - 2 \, \sqrt{2} \sqrt{x^{2} + \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} + \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1} + \sqrt{\sqrt{2} + 2} + \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2} - \sqrt{-\sqrt{2} + 2}}\right) - 28 \, {\left(\sqrt{2} x^{7} \sqrt{\sqrt{2} + 2} - \sqrt{2} x^{7} \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(\frac{2 \, \sqrt{2} x - 2 \, \sqrt{2} \sqrt{x^{2} - \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} - \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1} - \sqrt{\sqrt{2} + 2} - \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2} - \sqrt{-\sqrt{2} + 2}}\right) - 7 \, {\left(\sqrt{2} x^{7} \sqrt{\sqrt{2} + 2} + \sqrt{2} x^{7} \sqrt{-\sqrt{2} + 2}\right)} \log\left(x^{2} + \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} + \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1\right) - 7 \, {\left(\sqrt{2} x^{7} \sqrt{\sqrt{2} + 2} - \sqrt{2} x^{7} \sqrt{-\sqrt{2} + 2}\right)} \log\left(x^{2} + \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} - \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1\right) + 7 \, {\left(\sqrt{2} x^{7} \sqrt{\sqrt{2} + 2} - \sqrt{2} x^{7} \sqrt{-\sqrt{2} + 2}\right)} \log\left(x^{2} - \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} + \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1\right) + 7 \, {\left(\sqrt{2} x^{7} \sqrt{\sqrt{2} + 2} + \sqrt{2} x^{7} \sqrt{-\sqrt{2} + 2}\right)} \log\left(x^{2} - \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} - \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1\right) - 64}{448 \, x^{7}}"," ",0,"1/448*(56*x^7*sqrt(sqrt(2) + 2)*arctan(-(2*x - 2*sqrt(x^2 + x*sqrt(-sqrt(2) + 2) + 1) + sqrt(-sqrt(2) + 2))/sqrt(sqrt(2) + 2)) + 56*x^7*sqrt(sqrt(2) + 2)*arctan(-(2*x - 2*sqrt(x^2 - x*sqrt(-sqrt(2) + 2) + 1) - sqrt(-sqrt(2) + 2))/sqrt(sqrt(2) + 2)) + 56*x^7*sqrt(-sqrt(2) + 2)*arctan(-(2*x - 2*sqrt(x^2 + x*sqrt(sqrt(2) + 2) + 1) + sqrt(sqrt(2) + 2))/sqrt(-sqrt(2) + 2)) + 56*x^7*sqrt(-sqrt(2) + 2)*arctan(-(2*x - 2*sqrt(x^2 - x*sqrt(sqrt(2) + 2) + 1) - sqrt(sqrt(2) + 2))/sqrt(-sqrt(2) + 2)) - 14*x^7*sqrt(sqrt(2) + 2)*log(x^2 + x*sqrt(sqrt(2) + 2) + 1) + 14*x^7*sqrt(sqrt(2) + 2)*log(x^2 - x*sqrt(sqrt(2) + 2) + 1) - 14*x^7*sqrt(-sqrt(2) + 2)*log(x^2 + x*sqrt(-sqrt(2) + 2) + 1) + 14*x^7*sqrt(-sqrt(2) + 2)*log(x^2 - x*sqrt(-sqrt(2) + 2) + 1) + 28*(sqrt(2)*x^7*sqrt(sqrt(2) + 2) + sqrt(2)*x^7*sqrt(-sqrt(2) + 2))*arctan(-(2*sqrt(2)*x - 2*sqrt(2)*sqrt(x^2 + 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) - 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) + sqrt(sqrt(2) + 2) - sqrt(-sqrt(2) + 2))/(sqrt(sqrt(2) + 2) + sqrt(-sqrt(2) + 2))) + 28*(sqrt(2)*x^7*sqrt(sqrt(2) + 2) + sqrt(2)*x^7*sqrt(-sqrt(2) + 2))*arctan(-(2*sqrt(2)*x - 2*sqrt(2)*sqrt(x^2 - 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) + 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) - sqrt(sqrt(2) + 2) + sqrt(-sqrt(2) + 2))/(sqrt(sqrt(2) + 2) + sqrt(-sqrt(2) + 2))) - 28*(sqrt(2)*x^7*sqrt(sqrt(2) + 2) - sqrt(2)*x^7*sqrt(-sqrt(2) + 2))*arctan((2*sqrt(2)*x - 2*sqrt(2)*sqrt(x^2 + 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) + 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) + sqrt(sqrt(2) + 2) + sqrt(-sqrt(2) + 2))/(sqrt(sqrt(2) + 2) - sqrt(-sqrt(2) + 2))) - 28*(sqrt(2)*x^7*sqrt(sqrt(2) + 2) - sqrt(2)*x^7*sqrt(-sqrt(2) + 2))*arctan((2*sqrt(2)*x - 2*sqrt(2)*sqrt(x^2 - 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) - 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) - sqrt(sqrt(2) + 2) - sqrt(-sqrt(2) + 2))/(sqrt(sqrt(2) + 2) - sqrt(-sqrt(2) + 2))) - 7*(sqrt(2)*x^7*sqrt(sqrt(2) + 2) + sqrt(2)*x^7*sqrt(-sqrt(2) + 2))*log(x^2 + 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) + 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) - 7*(sqrt(2)*x^7*sqrt(sqrt(2) + 2) - sqrt(2)*x^7*sqrt(-sqrt(2) + 2))*log(x^2 + 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) - 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) + 7*(sqrt(2)*x^7*sqrt(sqrt(2) + 2) - sqrt(2)*x^7*sqrt(-sqrt(2) + 2))*log(x^2 - 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) + 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) + 7*(sqrt(2)*x^7*sqrt(sqrt(2) + 2) + sqrt(2)*x^7*sqrt(-sqrt(2) + 2))*log(x^2 - 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) - 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) - 64)/x^7","B",0
1509,1,29,0,0.675760," ","integrate(x^3*(x^8+1)^(1/2),x, algorithm=""fricas"")","\frac{1}{8} \, \sqrt{x^{8} + 1} x^{4} - \frac{1}{8} \, \log\left(-x^{4} + \sqrt{x^{8} + 1}\right)"," ",0,"1/8*sqrt(x^8 + 1)*x^4 - 1/8*log(-x^4 + sqrt(x^8 + 1))","A",0
1510,0,0,0,0.764685," ","integrate(x*(x^8+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{x^{8} + 1} x, x\right)"," ",0,"integral(sqrt(x^8 + 1)*x, x)","F",0
1511,1,34,0,0.822069," ","integrate((x^8+1)^(1/2)/x,x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{x^{8} + 1} - \frac{1}{8} \, \log\left(\sqrt{x^{8} + 1} + 1\right) + \frac{1}{8} \, \log\left(\sqrt{x^{8} + 1} - 1\right)"," ",0,"1/4*sqrt(x^8 + 1) - 1/8*log(sqrt(x^8 + 1) + 1) + 1/8*log(sqrt(x^8 + 1) - 1)","A",0
1512,0,0,0,0.994897," ","integrate((x^8+1)^(1/2)/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{8} + 1}}{x^{3}}, x\right)"," ",0,"integral(sqrt(x^8 + 1)/x^3, x)","F",0
1513,1,29,0,0.672406," ","integrate(x^3*(x^8-2)^(1/2),x, algorithm=""fricas"")","\frac{1}{8} \, \sqrt{x^{8} - 2} x^{4} + \frac{1}{4} \, \log\left(-x^{4} + \sqrt{x^{8} - 2}\right)"," ",0,"1/8*sqrt(x^8 - 2)*x^4 + 1/4*log(-x^4 + sqrt(x^8 - 2))","A",0
1514,1,37,0,1.147998," ","integrate(x^19/(x^8+1)^(1/2),x, algorithm=""fricas"")","\frac{1}{32} \, {\left(2 \, x^{12} - 3 \, x^{4}\right)} \sqrt{x^{8} + 1} - \frac{3}{32} \, \log\left(-x^{4} + \sqrt{x^{8} + 1}\right)"," ",0,"1/32*(2*x^12 - 3*x^4)*sqrt(x^8 + 1) - 3/32*log(-x^4 + sqrt(x^8 + 1))","A",0
1515,1,14,0,0.767656," ","integrate(x^15/(x^8+1)^(1/2),x, algorithm=""fricas"")","\frac{1}{12} \, \sqrt{x^{8} + 1} {\left(x^{8} - 2\right)}"," ",0,"1/12*sqrt(x^8 + 1)*(x^8 - 2)","A",0
1516,1,29,0,0.920961," ","integrate(x^11/(x^8+1)^(1/2),x, algorithm=""fricas"")","\frac{1}{8} \, \sqrt{x^{8} + 1} x^{4} + \frac{1}{8} \, \log\left(-x^{4} + \sqrt{x^{8} + 1}\right)"," ",0,"1/8*sqrt(x^8 + 1)*x^4 + 1/8*log(-x^4 + sqrt(x^8 + 1))","A",0
1517,1,9,0,0.804528," ","integrate(x^7/(x^8+1)^(1/2),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{x^{8} + 1}"," ",0,"1/4*sqrt(x^8 + 1)","A",0
1518,1,16,0,0.740587," ","integrate(x^3/(x^8+1)^(1/2),x, algorithm=""fricas"")","-\frac{1}{4} \, \log\left(-x^{4} + \sqrt{x^{8} + 1}\right)"," ",0,"-1/4*log(-x^4 + sqrt(x^8 + 1))","B",0
1519,1,25,0,0.839835," ","integrate(1/x/(x^8+1)^(1/2),x, algorithm=""fricas"")","-\frac{1}{8} \, \log\left(\sqrt{x^{8} + 1} + 1\right) + \frac{1}{8} \, \log\left(\sqrt{x^{8} + 1} - 1\right)"," ",0,"-1/8*log(sqrt(x^8 + 1) + 1) + 1/8*log(sqrt(x^8 + 1) - 1)","B",0
1520,1,16,0,0.654791," ","integrate(1/x^5/(x^8+1)^(1/2),x, algorithm=""fricas"")","-\frac{x^{4} + \sqrt{x^{8} + 1}}{4 \, x^{4}}"," ",0,"-1/4*(x^4 + sqrt(x^8 + 1))/x^4","A",0
1521,1,44,0,0.578443," ","integrate(1/x^9/(x^8+1)^(1/2),x, algorithm=""fricas"")","\frac{x^{8} \log\left(\sqrt{x^{8} + 1} + 1\right) - x^{8} \log\left(\sqrt{x^{8} + 1} - 1\right) - 2 \, \sqrt{x^{8} + 1}}{16 \, x^{8}}"," ",0,"1/16*(x^8*log(sqrt(x^8 + 1) + 1) - x^8*log(sqrt(x^8 + 1) - 1) - 2*sqrt(x^8 + 1))/x^8","A",0
1522,1,26,0,0.948128," ","integrate(1/x^13/(x^8+1)^(1/2),x, algorithm=""fricas"")","\frac{2 \, x^{12} + {\left(2 \, x^{8} - 1\right)} \sqrt{x^{8} + 1}}{12 \, x^{12}}"," ",0,"1/12*(2*x^12 + (2*x^8 - 1)*sqrt(x^8 + 1))/x^12","A",0
1523,1,52,0,1.002979," ","integrate(1/x^17/(x^8+1)^(1/2),x, algorithm=""fricas"")","-\frac{3 \, x^{16} \log\left(\sqrt{x^{8} + 1} + 1\right) - 3 \, x^{16} \log\left(\sqrt{x^{8} + 1} - 1\right) - 2 \, {\left(3 \, x^{8} - 2\right)} \sqrt{x^{8} + 1}}{64 \, x^{16}}"," ",0,"-1/64*(3*x^16*log(sqrt(x^8 + 1) + 1) - 3*x^16*log(sqrt(x^8 + 1) - 1) - 2*(3*x^8 - 2)*sqrt(x^8 + 1))/x^16","A",0
1524,0,0,0,1.164518," ","integrate(x^13/(x^8+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{13}}{\sqrt{x^{8} + 1}}, x\right)"," ",0,"integral(x^13/sqrt(x^8 + 1), x)","F",0
1525,0,0,0,0.828744," ","integrate(x^9/(x^8+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{9}}{\sqrt{x^{8} + 1}}, x\right)"," ",0,"integral(x^9/sqrt(x^8 + 1), x)","F",0
1526,0,0,0,1.045644," ","integrate(x^5/(x^8+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{5}}{\sqrt{x^{8} + 1}}, x\right)"," ",0,"integral(x^5/sqrt(x^8 + 1), x)","F",0
1527,0,0,0,0.882028," ","integrate(x/(x^8+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{\sqrt{x^{8} + 1}}, x\right)"," ",0,"integral(x/sqrt(x^8 + 1), x)","F",0
1528,0,0,0,0.922881," ","integrate(1/x^3/(x^8+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{8} + 1}}{x^{11} + x^{3}}, x\right)"," ",0,"integral(sqrt(x^8 + 1)/(x^11 + x^3), x)","F",0
1529,0,0,0,0.982418," ","integrate(1/x^7/(x^8+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{8} + 1}}{x^{15} + x^{7}}, x\right)"," ",0,"integral(sqrt(x^8 + 1)/(x^15 + x^7), x)","F",0
1530,0,0,0,1.005526," ","integrate(x^10/(x^8+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{10}}{\sqrt{x^{8} + 1}}, x\right)"," ",0,"integral(x^10/sqrt(x^8 + 1), x)","F",0
1531,0,0,0,0.997991," ","integrate(x^8/(x^8+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{8}}{\sqrt{x^{8} + 1}}, x\right)"," ",0,"integral(x^8/sqrt(x^8 + 1), x)","F",0
1532,0,0,0,0.940780," ","integrate(x^6/(x^8+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{6}}{\sqrt{x^{8} + 1}}, x\right)"," ",0,"integral(x^6/sqrt(x^8 + 1), x)","F",0
1533,0,0,0,0.864082," ","integrate(x^4/(x^8+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{4}}{\sqrt{x^{8} + 1}}, x\right)"," ",0,"integral(x^4/sqrt(x^8 + 1), x)","F",0
1534,0,0,0,0.957915," ","integrate(x^2/(x^8+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2}}{\sqrt{x^{8} + 1}}, x\right)"," ",0,"integral(x^2/sqrt(x^8 + 1), x)","F",0
1535,0,0,0,1.000614," ","integrate(1/(x^8+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{x^{8} + 1}}, x\right)"," ",0,"integral(1/sqrt(x^8 + 1), x)","F",0
1536,0,0,0,1.117500," ","integrate(1/x^2/(x^8+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{8} + 1}}{x^{10} + x^{2}}, x\right)"," ",0,"integral(sqrt(x^8 + 1)/(x^10 + x^2), x)","F",0
1537,0,0,0,0.786692," ","integrate(1/x^4/(x^8+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{8} + 1}}{x^{12} + x^{4}}, x\right)"," ",0,"integral(sqrt(x^8 + 1)/(x^12 + x^4), x)","F",0
1538,0,0,0,0.997389," ","integrate(1/x^6/(x^8+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{8} + 1}}{x^{14} + x^{6}}, x\right)"," ",0,"integral(sqrt(x^8 + 1)/(x^14 + x^6), x)","F",0
1539,0,0,0,0.743339," ","integrate(1/x^8/(x^8+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{8} + 1}}{x^{16} + x^{8}}, x\right)"," ",0,"integral(sqrt(x^8 + 1)/(x^16 + x^8), x)","F",0
1540,1,1039,0,3.272265," ","integrate(1/(-x^10+1),x, algorithm=""fricas"")","\frac{1}{40} \, {\left(\sqrt{5} + 2 \, \sqrt{-\frac{3}{16} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{2} + \frac{1}{8} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} - 3\right)} {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} - \frac{3}{16} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)}^{2} + \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \frac{1}{2} \, \sqrt{5} - \frac{5}{2}} - 1\right)} \log\left(2 \, x + \frac{1}{2} \, \sqrt{5} + \sqrt{-\frac{3}{16} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{2} + \frac{1}{8} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} - 3\right)} {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} - \frac{3}{16} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)}^{2} + \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \frac{1}{2} \, \sqrt{5} - \frac{5}{2}} - \frac{1}{2}\right) + \frac{1}{40} \, {\left(\sqrt{5} - 2 \, \sqrt{-\frac{3}{16} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{2} + \frac{1}{8} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} - 3\right)} {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} - \frac{3}{16} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)}^{2} + \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \frac{1}{2} \, \sqrt{5} - \frac{5}{2}} - 1\right)} \log\left(2 \, x + \frac{1}{2} \, \sqrt{5} - \sqrt{-\frac{3}{16} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{2} + \frac{1}{8} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} - 3\right)} {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} - \frac{3}{16} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)}^{2} + \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \frac{1}{2} \, \sqrt{5} - \frac{5}{2}} - \frac{1}{2}\right) + \frac{1}{40} \, {\left(\sqrt{5} + 2 \, \sqrt{-\frac{3}{16} \, {\left(\sqrt{5} + 20 \, \sqrt{-\frac{1}{200} \, \sqrt{5} - \frac{1}{40}} - 1\right)}^{2} - \frac{1}{8} \, {\left(\sqrt{5} + 20 \, \sqrt{-\frac{1}{200} \, \sqrt{5} - \frac{1}{40}} + 3\right)} {\left(\sqrt{5} - 20 \, \sqrt{-\frac{1}{200} \, \sqrt{5} - \frac{1}{40}} - 1\right)} - \frac{3}{16} \, {\left(\sqrt{5} - 20 \, \sqrt{-\frac{1}{200} \, \sqrt{5} - \frac{1}{40}} - 1\right)}^{2} - \frac{1}{2} \, \sqrt{5} - 10 \, \sqrt{-\frac{1}{200} \, \sqrt{5} - \frac{1}{40}} - \frac{5}{2}} + 1\right)} \log\left(2 \, x + \frac{1}{2} \, \sqrt{5} + \sqrt{-\frac{3}{16} \, {\left(\sqrt{5} + 20 \, \sqrt{-\frac{1}{200} \, \sqrt{5} - \frac{1}{40}} - 1\right)}^{2} - \frac{1}{8} \, {\left(\sqrt{5} + 20 \, \sqrt{-\frac{1}{200} \, \sqrt{5} - \frac{1}{40}} + 3\right)} {\left(\sqrt{5} - 20 \, \sqrt{-\frac{1}{200} \, \sqrt{5} - \frac{1}{40}} - 1\right)} - \frac{3}{16} \, {\left(\sqrt{5} - 20 \, \sqrt{-\frac{1}{200} \, \sqrt{5} - \frac{1}{40}} - 1\right)}^{2} - \frac{1}{2} \, \sqrt{5} - 10 \, \sqrt{-\frac{1}{200} \, \sqrt{5} - \frac{1}{40}} - \frac{5}{2}} + \frac{1}{2}\right) + \frac{1}{40} \, {\left(\sqrt{5} - 2 \, \sqrt{-\frac{3}{16} \, {\left(\sqrt{5} + 20 \, \sqrt{-\frac{1}{200} \, \sqrt{5} - \frac{1}{40}} - 1\right)}^{2} - \frac{1}{8} \, {\left(\sqrt{5} + 20 \, \sqrt{-\frac{1}{200} \, \sqrt{5} - \frac{1}{40}} + 3\right)} {\left(\sqrt{5} - 20 \, \sqrt{-\frac{1}{200} \, \sqrt{5} - \frac{1}{40}} - 1\right)} - \frac{3}{16} \, {\left(\sqrt{5} - 20 \, \sqrt{-\frac{1}{200} \, \sqrt{5} - \frac{1}{40}} - 1\right)}^{2} - \frac{1}{2} \, \sqrt{5} - 10 \, \sqrt{-\frac{1}{200} \, \sqrt{5} - \frac{1}{40}} - \frac{5}{2}} + 1\right)} \log\left(2 \, x + \frac{1}{2} \, \sqrt{5} - \sqrt{-\frac{3}{16} \, {\left(\sqrt{5} + 20 \, \sqrt{-\frac{1}{200} \, \sqrt{5} - \frac{1}{40}} - 1\right)}^{2} - \frac{1}{8} \, {\left(\sqrt{5} + 20 \, \sqrt{-\frac{1}{200} \, \sqrt{5} - \frac{1}{40}} + 3\right)} {\left(\sqrt{5} - 20 \, \sqrt{-\frac{1}{200} \, \sqrt{5} - \frac{1}{40}} - 1\right)} - \frac{3}{16} \, {\left(\sqrt{5} - 20 \, \sqrt{-\frac{1}{200} \, \sqrt{5} - \frac{1}{40}} - 1\right)}^{2} - \frac{1}{2} \, \sqrt{5} - 10 \, \sqrt{-\frac{1}{200} \, \sqrt{5} - \frac{1}{40}} - \frac{5}{2}} + \frac{1}{2}\right) + \frac{1}{40} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} \log\left(x + \frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \frac{1}{4} \, \sqrt{5} - \frac{1}{4}\right) - \frac{1}{40} \, {\left(2 \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)} \log\left(x - \frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} - 5} - \frac{1}{4} \, \sqrt{5} - \frac{1}{4}\right) - \frac{1}{40} \, {\left(\sqrt{5} - 20 \, \sqrt{-\frac{1}{200} \, \sqrt{5} - \frac{1}{40}} - 1\right)} \log\left(x - \frac{1}{4} \, \sqrt{5} + 5 \, \sqrt{-\frac{1}{200} \, \sqrt{5} - \frac{1}{40}} + \frac{1}{4}\right) - \frac{1}{40} \, {\left(\sqrt{5} + 20 \, \sqrt{-\frac{1}{200} \, \sqrt{5} - \frac{1}{40}} - 1\right)} \log\left(x - \frac{1}{4} \, \sqrt{5} - 5 \, \sqrt{-\frac{1}{200} \, \sqrt{5} - \frac{1}{40}} + \frac{1}{4}\right) + \frac{1}{10} \, \log\left(x + 1\right) - \frac{1}{10} \, \log\left(x - 1\right)"," ",0,"1/40*(sqrt(5) + 2*sqrt(-3/16*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^2 + 1/8*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) - 3)*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1) - 3/16*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)^2 + sqrt(1/2)*sqrt(sqrt(5) - 5) + 1/2*sqrt(5) - 5/2) - 1)*log(2*x + 1/2*sqrt(5) + sqrt(-3/16*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^2 + 1/8*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) - 3)*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1) - 3/16*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)^2 + sqrt(1/2)*sqrt(sqrt(5) - 5) + 1/2*sqrt(5) - 5/2) - 1/2) + 1/40*(sqrt(5) - 2*sqrt(-3/16*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^2 + 1/8*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) - 3)*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1) - 3/16*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)^2 + sqrt(1/2)*sqrt(sqrt(5) - 5) + 1/2*sqrt(5) - 5/2) - 1)*log(2*x + 1/2*sqrt(5) - sqrt(-3/16*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^2 + 1/8*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) - 3)*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1) - 3/16*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)^2 + sqrt(1/2)*sqrt(sqrt(5) - 5) + 1/2*sqrt(5) - 5/2) - 1/2) + 1/40*(sqrt(5) + 2*sqrt(-3/16*(sqrt(5) + 20*sqrt(-1/200*sqrt(5) - 1/40) - 1)^2 - 1/8*(sqrt(5) + 20*sqrt(-1/200*sqrt(5) - 1/40) + 3)*(sqrt(5) - 20*sqrt(-1/200*sqrt(5) - 1/40) - 1) - 3/16*(sqrt(5) - 20*sqrt(-1/200*sqrt(5) - 1/40) - 1)^2 - 1/2*sqrt(5) - 10*sqrt(-1/200*sqrt(5) - 1/40) - 5/2) + 1)*log(2*x + 1/2*sqrt(5) + sqrt(-3/16*(sqrt(5) + 20*sqrt(-1/200*sqrt(5) - 1/40) - 1)^2 - 1/8*(sqrt(5) + 20*sqrt(-1/200*sqrt(5) - 1/40) + 3)*(sqrt(5) - 20*sqrt(-1/200*sqrt(5) - 1/40) - 1) - 3/16*(sqrt(5) - 20*sqrt(-1/200*sqrt(5) - 1/40) - 1)^2 - 1/2*sqrt(5) - 10*sqrt(-1/200*sqrt(5) - 1/40) - 5/2) + 1/2) + 1/40*(sqrt(5) - 2*sqrt(-3/16*(sqrt(5) + 20*sqrt(-1/200*sqrt(5) - 1/40) - 1)^2 - 1/8*(sqrt(5) + 20*sqrt(-1/200*sqrt(5) - 1/40) + 3)*(sqrt(5) - 20*sqrt(-1/200*sqrt(5) - 1/40) - 1) - 3/16*(sqrt(5) - 20*sqrt(-1/200*sqrt(5) - 1/40) - 1)^2 - 1/2*sqrt(5) - 10*sqrt(-1/200*sqrt(5) - 1/40) - 5/2) + 1)*log(2*x + 1/2*sqrt(5) - sqrt(-3/16*(sqrt(5) + 20*sqrt(-1/200*sqrt(5) - 1/40) - 1)^2 - 1/8*(sqrt(5) + 20*sqrt(-1/200*sqrt(5) - 1/40) + 3)*(sqrt(5) - 20*sqrt(-1/200*sqrt(5) - 1/40) - 1) - 3/16*(sqrt(5) - 20*sqrt(-1/200*sqrt(5) - 1/40) - 1)^2 - 1/2*sqrt(5) - 10*sqrt(-1/200*sqrt(5) - 1/40) - 5/2) + 1/2) + 1/40*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)*log(x + 1/2*sqrt(1/2)*sqrt(sqrt(5) - 5) - 1/4*sqrt(5) - 1/4) - 1/40*(2*sqrt(1/2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)*log(x - 1/2*sqrt(1/2)*sqrt(sqrt(5) - 5) - 1/4*sqrt(5) - 1/4) - 1/40*(sqrt(5) - 20*sqrt(-1/200*sqrt(5) - 1/40) - 1)*log(x - 1/4*sqrt(5) + 5*sqrt(-1/200*sqrt(5) - 1/40) + 1/4) - 1/40*(sqrt(5) + 20*sqrt(-1/200*sqrt(5) - 1/40) - 1)*log(x - 1/4*sqrt(5) - 5*sqrt(-1/200*sqrt(5) - 1/40) + 1/4) + 1/10*log(x + 1) - 1/10*log(x - 1)","B",0
1541,1,18,0,0.908453," ","integrate(x^4/(-x^10+1)^(1/2),x, algorithm=""fricas"")","-\frac{2}{5} \, \arctan\left(\frac{\sqrt{-x^{10} + 1} - 1}{x^{5}}\right)"," ",0,"-2/5*arctan((sqrt(-x^10 + 1) - 1)/x^5)","B",0
1542,1,16,0,0.611607," ","integrate(x^4/(x^10-2)^(1/2),x, algorithm=""fricas"")","-\frac{1}{5} \, \log\left(-x^{5} + \sqrt{x^{10} - 2}\right)"," ",0,"-1/5*log(-x^5 + sqrt(x^10 - 2))","A",0
1543,1,8,0,0.603494," ","integrate(x^5/(x^12+9),x, algorithm=""fricas"")","\frac{1}{18} \, \arctan\left(\frac{1}{3} \, x^{6}\right)"," ",0,"1/18*arctan(1/3*x^6)","A",0
1544,1,17,0,0.874304," ","integrate(x^5/(-x^12+9),x, algorithm=""fricas"")","\frac{1}{36} \, \log\left(x^{6} + 3\right) - \frac{1}{36} \, \log\left(x^{6} - 3\right)"," ",0,"1/36*log(x^6 + 3) - 1/36*log(x^6 - 3)","B",0
1545,1,29,0,0.614321," ","integrate(x^5*(x^12+9)^(1/2),x, algorithm=""fricas"")","\frac{1}{12} \, \sqrt{x^{12} + 9} x^{6} - \frac{3}{4} \, \log\left(-x^{6} + \sqrt{x^{12} + 9}\right)"," ",0,"1/12*sqrt(x^12 + 9)*x^6 - 3/4*log(-x^6 + sqrt(x^12 + 9))","A",0
1546,1,13,0,0.793136," ","integrate((a+b/x)*x^6,x, algorithm=""fricas"")","\frac{1}{7} \, a x^{7} + \frac{1}{6} \, b x^{6}"," ",0,"1/7*a*x^7 + 1/6*b*x^6","A",0
1547,1,13,0,0.652299," ","integrate((a+b/x)*x^5,x, algorithm=""fricas"")","\frac{1}{6} \, a x^{6} + \frac{1}{5} \, b x^{5}"," ",0,"1/6*a*x^6 + 1/5*b*x^5","A",0
1548,1,13,0,0.809204," ","integrate((a+b/x)*x^4,x, algorithm=""fricas"")","\frac{1}{5} \, a x^{5} + \frac{1}{4} \, b x^{4}"," ",0,"1/5*a*x^5 + 1/4*b*x^4","A",0
1549,1,13,0,0.718935," ","integrate((a+b/x)*x^3,x, algorithm=""fricas"")","\frac{1}{4} \, a x^{4} + \frac{1}{3} \, b x^{3}"," ",0,"1/4*a*x^4 + 1/3*b*x^3","A",0
1550,1,13,0,0.813385," ","integrate((a+b/x)*x^2,x, algorithm=""fricas"")","\frac{1}{3} \, a x^{3} + \frac{1}{2} \, b x^{2}"," ",0,"1/3*a*x^3 + 1/2*b*x^2","A",0
1551,1,10,0,0.777213," ","integrate((a+b/x)*x,x, algorithm=""fricas"")","\frac{1}{2} \, a x^{2} + b x"," ",0,"1/2*a*x^2 + b*x","A",0
1552,1,8,0,0.981203," ","integrate(a+b/x,x, algorithm=""fricas"")","a x + b \log\left(x\right)"," ",0,"a*x + b*log(x)","A",0
1553,1,13,0,0.577347," ","integrate((a+b/x)/x,x, algorithm=""fricas"")","\frac{a x \log\left(x\right) - b}{x}"," ",0,"(a*x*log(x) - b)/x","A",0
1554,1,11,0,0.819669," ","integrate((a+b/x)/x^2,x, algorithm=""fricas"")","-\frac{2 \, a x + b}{2 \, x^{2}}"," ",0,"-1/2*(2*a*x + b)/x^2","A",0
1555,1,13,0,0.687455," ","integrate((a+b/x)/x^3,x, algorithm=""fricas"")","-\frac{3 \, a x + 2 \, b}{6 \, x^{3}}"," ",0,"-1/6*(3*a*x + 2*b)/x^3","A",0
1556,1,13,0,0.799096," ","integrate((a+b/x)/x^4,x, algorithm=""fricas"")","-\frac{4 \, a x + 3 \, b}{12 \, x^{4}}"," ",0,"-1/12*(4*a*x + 3*b)/x^4","A",0
1557,1,13,0,0.709071," ","integrate((a+b/x)/x^5,x, algorithm=""fricas"")","-\frac{5 \, a x + 4 \, b}{20 \, x^{5}}"," ",0,"-1/20*(5*a*x + 4*b)/x^5","A",0
1558,1,13,0,0.804786," ","integrate((a+b/x)/x^6,x, algorithm=""fricas"")","-\frac{6 \, a x + 5 \, b}{30 \, x^{6}}"," ",0,"-1/30*(6*a*x + 5*b)/x^6","A",0
1559,1,24,0,0.748232," ","integrate((a+b/x)^2*x^5,x, algorithm=""fricas"")","\frac{1}{6} \, a^{2} x^{6} + \frac{2}{5} \, a b x^{5} + \frac{1}{4} \, b^{2} x^{4}"," ",0,"1/6*a^2*x^6 + 2/5*a*b*x^5 + 1/4*b^2*x^4","A",0
1560,1,24,0,0.728919," ","integrate((a+b/x)^2*x^4,x, algorithm=""fricas"")","\frac{1}{5} \, a^{2} x^{5} + \frac{1}{2} \, a b x^{4} + \frac{1}{3} \, b^{2} x^{3}"," ",0,"1/5*a^2*x^5 + 1/2*a*b*x^4 + 1/3*b^2*x^3","A",0
1561,1,24,0,0.808951," ","integrate((a+b/x)^2*x^3,x, algorithm=""fricas"")","\frac{1}{4} \, a^{2} x^{4} + \frac{2}{3} \, a b x^{3} + \frac{1}{2} \, b^{2} x^{2}"," ",0,"1/4*a^2*x^4 + 2/3*a*b*x^3 + 1/2*b^2*x^2","A",0
1562,1,20,0,0.772125," ","integrate((a+b/x)^2*x^2,x, algorithm=""fricas"")","\frac{1}{3} \, a^{2} x^{3} + a b x^{2} + b^{2} x"," ",0,"1/3*a^2*x^3 + a*b*x^2 + b^2*x","A",0
1563,1,20,0,0.911693," ","integrate((a+b/x)^2*x,x, algorithm=""fricas"")","\frac{1}{2} \, a^{2} x^{2} + 2 \, a b x + b^{2} \log\left(x\right)"," ",0,"1/2*a^2*x^2 + 2*a*b*x + b^2*log(x)","A",0
1564,1,24,0,0.808195," ","integrate((a+b/x)^2,x, algorithm=""fricas"")","\frac{a^{2} x^{2} + 2 \, a b x \log\left(x\right) - b^{2}}{x}"," ",0,"(a^2*x^2 + 2*a*b*x*log(x) - b^2)/x","A",0
1565,1,26,0,0.711978," ","integrate((a+b/x)^2/x,x, algorithm=""fricas"")","\frac{2 \, a^{2} x^{2} \log\left(x\right) - 4 \, a b x - b^{2}}{2 \, x^{2}}"," ",0,"1/2*(2*a^2*x^2*log(x) - 4*a*b*x - b^2)/x^2","A",0
1566,1,22,0,0.881105," ","integrate((a+b/x)^2/x^2,x, algorithm=""fricas"")","-\frac{3 \, a^{2} x^{2} + 3 \, a b x + b^{2}}{3 \, x^{3}}"," ",0,"-1/3*(3*a^2*x^2 + 3*a*b*x + b^2)/x^3","A",0
1567,1,24,0,0.542629," ","integrate((a+b/x)^2/x^3,x, algorithm=""fricas"")","-\frac{6 \, a^{2} x^{2} + 8 \, a b x + 3 \, b^{2}}{12 \, x^{4}}"," ",0,"-1/12*(6*a^2*x^2 + 8*a*b*x + 3*b^2)/x^4","A",0
1568,1,24,0,0.519316," ","integrate((a+b/x)^2/x^4,x, algorithm=""fricas"")","-\frac{10 \, a^{2} x^{2} + 15 \, a b x + 6 \, b^{2}}{30 \, x^{5}}"," ",0,"-1/30*(10*a^2*x^2 + 15*a*b*x + 6*b^2)/x^5","A",0
1569,1,24,0,0.761467," ","integrate((a+b/x)^2/x^5,x, algorithm=""fricas"")","-\frac{15 \, a^{2} x^{2} + 24 \, a b x + 10 \, b^{2}}{60 \, x^{6}}"," ",0,"-1/60*(15*a^2*x^2 + 24*a*b*x + 10*b^2)/x^6","A",0
1570,1,35,0,0.751764," ","integrate((a+b/x)^3*x^6,x, algorithm=""fricas"")","\frac{1}{7} \, a^{3} x^{7} + \frac{1}{2} \, a^{2} b x^{6} + \frac{3}{5} \, a b^{2} x^{5} + \frac{1}{4} \, b^{3} x^{4}"," ",0,"1/7*a^3*x^7 + 1/2*a^2*b*x^6 + 3/5*a*b^2*x^5 + 1/4*b^3*x^4","A",0
1571,1,35,0,0.821874," ","integrate((a+b/x)^3*x^5,x, algorithm=""fricas"")","\frac{1}{6} \, a^{3} x^{6} + \frac{3}{5} \, a^{2} b x^{5} + \frac{3}{4} \, a b^{2} x^{4} + \frac{1}{3} \, b^{3} x^{3}"," ",0,"1/6*a^3*x^6 + 3/5*a^2*b*x^5 + 3/4*a*b^2*x^4 + 1/3*b^3*x^3","A",0
1572,1,34,0,0.863310," ","integrate((a+b/x)^3*x^4,x, algorithm=""fricas"")","\frac{1}{5} \, a^{3} x^{5} + \frac{3}{4} \, a^{2} b x^{4} + a b^{2} x^{3} + \frac{1}{2} \, b^{3} x^{2}"," ",0,"1/5*a^3*x^5 + 3/4*a^2*b*x^4 + a*b^2*x^3 + 1/2*b^3*x^2","A",0
1573,1,31,0,0.624287," ","integrate((a+b/x)^3*x^3,x, algorithm=""fricas"")","\frac{1}{4} \, a^{3} x^{4} + a^{2} b x^{3} + \frac{3}{2} \, a b^{2} x^{2} + b^{3} x"," ",0,"1/4*a^3*x^4 + a^2*b*x^3 + 3/2*a*b^2*x^2 + b^3*x","B",0
1574,1,31,0,0.707365," ","integrate((a+b/x)^3*x^2,x, algorithm=""fricas"")","\frac{1}{3} \, a^{3} x^{3} + \frac{3}{2} \, a^{2} b x^{2} + 3 \, a b^{2} x + b^{3} \log\left(x\right)"," ",0,"1/3*a^3*x^3 + 3/2*a^2*b*x^2 + 3*a*b^2*x + b^3*log(x)","A",0
1575,1,36,0,0.717506," ","integrate((a+b/x)^3*x,x, algorithm=""fricas"")","\frac{a^{3} x^{3} + 6 \, a^{2} b x^{2} + 6 \, a b^{2} x \log\left(x\right) - 2 \, b^{3}}{2 \, x}"," ",0,"1/2*(a^3*x^3 + 6*a^2*b*x^2 + 6*a*b^2*x*log(x) - 2*b^3)/x","A",0
1576,1,37,0,0.590155," ","integrate((a+b/x)^3,x, algorithm=""fricas"")","\frac{2 \, a^{3} x^{3} + 6 \, a^{2} b x^{2} \log\left(x\right) - 6 \, a b^{2} x - b^{3}}{2 \, x^{2}}"," ",0,"1/2*(2*a^3*x^3 + 6*a^2*b*x^2*log(x) - 6*a*b^2*x - b^3)/x^2","A",0
1577,1,37,0,0.533605," ","integrate((a+b/x)^3/x,x, algorithm=""fricas"")","\frac{6 \, a^{3} x^{3} \log\left(x\right) - 18 \, a^{2} b x^{2} - 9 \, a b^{2} x - 2 \, b^{3}}{6 \, x^{3}}"," ",0,"1/6*(6*a^3*x^3*log(x) - 18*a^2*b*x^2 - 9*a*b^2*x - 2*b^3)/x^3","A",0
1578,1,33,0,0.664779," ","integrate((a+b/x)^3/x^2,x, algorithm=""fricas"")","-\frac{4 \, a^{3} x^{3} + 6 \, a^{2} b x^{2} + 4 \, a b^{2} x + b^{3}}{4 \, x^{4}}"," ",0,"-1/4*(4*a^3*x^3 + 6*a^2*b*x^2 + 4*a*b^2*x + b^3)/x^4","B",0
1579,1,35,0,0.756349," ","integrate((a+b/x)^3/x^3,x, algorithm=""fricas"")","-\frac{10 \, a^{3} x^{3} + 20 \, a^{2} b x^{2} + 15 \, a b^{2} x + 4 \, b^{3}}{20 \, x^{5}}"," ",0,"-1/20*(10*a^3*x^3 + 20*a^2*b*x^2 + 15*a*b^2*x + 4*b^3)/x^5","A",0
1580,1,35,0,0.804919," ","integrate((a+b/x)^3/x^4,x, algorithm=""fricas"")","-\frac{20 \, a^{3} x^{3} + 45 \, a^{2} b x^{2} + 36 \, a b^{2} x + 10 \, b^{3}}{60 \, x^{6}}"," ",0,"-1/60*(20*a^3*x^3 + 45*a^2*b*x^2 + 36*a*b^2*x + 10*b^3)/x^6","A",0
1581,1,35,0,0.848464," ","integrate((a+b/x)^3/x^5,x, algorithm=""fricas"")","-\frac{35 \, a^{3} x^{3} + 84 \, a^{2} b x^{2} + 70 \, a b^{2} x + 20 \, b^{3}}{140 \, x^{7}}"," ",0,"-1/140*(35*a^3*x^3 + 84*a^2*b*x^2 + 70*a*b^2*x + 20*b^3)/x^7","A",0
1582,1,35,0,0.611892," ","integrate((a+b/x)^3/x^6,x, algorithm=""fricas"")","-\frac{56 \, a^{3} x^{3} + 140 \, a^{2} b x^{2} + 120 \, a b^{2} x + 35 \, b^{3}}{280 \, x^{8}}"," ",0,"-1/280*(56*a^3*x^3 + 140*a^2*b*x^2 + 120*a*b^2*x + 35*b^3)/x^8","A",0
1583,1,90,0,0.748329," ","integrate((a+b/x)^8*x^16,x, algorithm=""fricas"")","\frac{1}{17} \, a^{8} x^{17} + \frac{1}{2} \, a^{7} b x^{16} + \frac{28}{15} \, a^{6} b^{2} x^{15} + 4 \, a^{5} b^{3} x^{14} + \frac{70}{13} \, a^{4} b^{4} x^{13} + \frac{14}{3} \, a^{3} b^{5} x^{12} + \frac{28}{11} \, a^{2} b^{6} x^{11} + \frac{4}{5} \, a b^{7} x^{10} + \frac{1}{9} \, b^{8} x^{9}"," ",0,"1/17*a^8*x^17 + 1/2*a^7*b*x^16 + 28/15*a^6*b^2*x^15 + 4*a^5*b^3*x^14 + 70/13*a^4*b^4*x^13 + 14/3*a^3*b^5*x^12 + 28/11*a^2*b^6*x^11 + 4/5*a*b^7*x^10 + 1/9*b^8*x^9","A",0
1584,1,90,0,0.510413," ","integrate((a+b/x)^8*x^15,x, algorithm=""fricas"")","\frac{1}{16} \, a^{8} x^{16} + \frac{8}{15} \, a^{7} b x^{15} + 2 \, a^{6} b^{2} x^{14} + \frac{56}{13} \, a^{5} b^{3} x^{13} + \frac{35}{6} \, a^{4} b^{4} x^{12} + \frac{56}{11} \, a^{3} b^{5} x^{11} + \frac{14}{5} \, a^{2} b^{6} x^{10} + \frac{8}{9} \, a b^{7} x^{9} + \frac{1}{8} \, b^{8} x^{8}"," ",0,"1/16*a^8*x^16 + 8/15*a^7*b*x^15 + 2*a^6*b^2*x^14 + 56/13*a^5*b^3*x^13 + 35/6*a^4*b^4*x^12 + 56/11*a^3*b^5*x^11 + 14/5*a^2*b^6*x^10 + 8/9*a*b^7*x^9 + 1/8*b^8*x^8","A",0
1585,1,90,0,0.878489," ","integrate((a+b/x)^8*x^13,x, algorithm=""fricas"")","\frac{1}{14} \, a^{8} x^{14} + \frac{8}{13} \, a^{7} b x^{13} + \frac{7}{3} \, a^{6} b^{2} x^{12} + \frac{56}{11} \, a^{5} b^{3} x^{11} + 7 \, a^{4} b^{4} x^{10} + \frac{56}{9} \, a^{3} b^{5} x^{9} + \frac{7}{2} \, a^{2} b^{6} x^{8} + \frac{8}{7} \, a b^{7} x^{7} + \frac{1}{6} \, b^{8} x^{6}"," ",0,"1/14*a^8*x^14 + 8/13*a^7*b*x^13 + 7/3*a^6*b^2*x^12 + 56/11*a^5*b^3*x^11 + 7*a^4*b^4*x^10 + 56/9*a^3*b^5*x^9 + 7/2*a^2*b^6*x^8 + 8/7*a*b^7*x^7 + 1/6*b^8*x^6","A",0
1586,1,90,0,0.616112," ","integrate((a+b/x)^8*x^12,x, algorithm=""fricas"")","\frac{1}{13} \, a^{8} x^{13} + \frac{2}{3} \, a^{7} b x^{12} + \frac{28}{11} \, a^{6} b^{2} x^{11} + \frac{28}{5} \, a^{5} b^{3} x^{10} + \frac{70}{9} \, a^{4} b^{4} x^{9} + 7 \, a^{3} b^{5} x^{8} + 4 \, a^{2} b^{6} x^{7} + \frac{4}{3} \, a b^{7} x^{6} + \frac{1}{5} \, b^{8} x^{5}"," ",0,"1/13*a^8*x^13 + 2/3*a^7*b*x^12 + 28/11*a^6*b^2*x^11 + 28/5*a^5*b^3*x^10 + 70/9*a^4*b^4*x^9 + 7*a^3*b^5*x^8 + 4*a^2*b^6*x^7 + 4/3*a*b^7*x^6 + 1/5*b^8*x^5","A",0
1587,1,90,0,0.731044," ","integrate((a+b/x)^8*x^11,x, algorithm=""fricas"")","\frac{1}{12} \, a^{8} x^{12} + \frac{8}{11} \, a^{7} b x^{11} + \frac{14}{5} \, a^{6} b^{2} x^{10} + \frac{56}{9} \, a^{5} b^{3} x^{9} + \frac{35}{4} \, a^{4} b^{4} x^{8} + 8 \, a^{3} b^{5} x^{7} + \frac{14}{3} \, a^{2} b^{6} x^{6} + \frac{8}{5} \, a b^{7} x^{5} + \frac{1}{4} \, b^{8} x^{4}"," ",0,"1/12*a^8*x^12 + 8/11*a^7*b*x^11 + 14/5*a^6*b^2*x^10 + 56/9*a^5*b^3*x^9 + 35/4*a^4*b^4*x^8 + 8*a^3*b^5*x^7 + 14/3*a^2*b^6*x^6 + 8/5*a*b^7*x^5 + 1/4*b^8*x^4","A",0
1588,1,90,0,0.577032," ","integrate((a+b/x)^8*x^10,x, algorithm=""fricas"")","\frac{1}{11} \, a^{8} x^{11} + \frac{4}{5} \, a^{7} b x^{10} + \frac{28}{9} \, a^{6} b^{2} x^{9} + 7 \, a^{5} b^{3} x^{8} + 10 \, a^{4} b^{4} x^{7} + \frac{28}{3} \, a^{3} b^{5} x^{6} + \frac{28}{5} \, a^{2} b^{6} x^{5} + 2 \, a b^{7} x^{4} + \frac{1}{3} \, b^{8} x^{3}"," ",0,"1/11*a^8*x^11 + 4/5*a^7*b*x^10 + 28/9*a^6*b^2*x^9 + 7*a^5*b^3*x^8 + 10*a^4*b^4*x^7 + 28/3*a^3*b^5*x^6 + 28/5*a^2*b^6*x^5 + 2*a*b^7*x^4 + 1/3*b^8*x^3","B",0
1589,1,90,0,0.678067," ","integrate((a+b/x)^8*x^9,x, algorithm=""fricas"")","\frac{1}{10} \, a^{8} x^{10} + \frac{8}{9} \, a^{7} b x^{9} + \frac{7}{2} \, a^{6} b^{2} x^{8} + 8 \, a^{5} b^{3} x^{7} + \frac{35}{3} \, a^{4} b^{4} x^{6} + \frac{56}{5} \, a^{3} b^{5} x^{5} + 7 \, a^{2} b^{6} x^{4} + \frac{8}{3} \, a b^{7} x^{3} + \frac{1}{2} \, b^{8} x^{2}"," ",0,"1/10*a^8*x^10 + 8/9*a^7*b*x^9 + 7/2*a^6*b^2*x^8 + 8*a^5*b^3*x^7 + 35/3*a^4*b^4*x^6 + 56/5*a^3*b^5*x^5 + 7*a^2*b^6*x^4 + 8/3*a*b^7*x^3 + 1/2*b^8*x^2","B",0
1590,1,86,0,0.785077," ","integrate((a+b/x)^8*x^8,x, algorithm=""fricas"")","\frac{1}{9} \, a^{8} x^{9} + a^{7} b x^{8} + 4 \, a^{6} b^{2} x^{7} + \frac{28}{3} \, a^{5} b^{3} x^{6} + 14 \, a^{4} b^{4} x^{5} + 14 \, a^{3} b^{5} x^{4} + \frac{28}{3} \, a^{2} b^{6} x^{3} + 4 \, a b^{7} x^{2} + b^{8} x"," ",0,"1/9*a^8*x^9 + a^7*b*x^8 + 4*a^6*b^2*x^7 + 28/3*a^5*b^3*x^6 + 14*a^4*b^4*x^5 + 14*a^3*b^5*x^4 + 28/3*a^2*b^6*x^3 + 4*a*b^7*x^2 + b^8*x","B",0
1591,1,86,0,0.530028," ","integrate((a+b/x)^8*x^7,x, algorithm=""fricas"")","\frac{1}{8} \, a^{8} x^{8} + \frac{8}{7} \, a^{7} b x^{7} + \frac{14}{3} \, a^{6} b^{2} x^{6} + \frac{56}{5} \, a^{5} b^{3} x^{5} + \frac{35}{2} \, a^{4} b^{4} x^{4} + \frac{56}{3} \, a^{3} b^{5} x^{3} + 14 \, a^{2} b^{6} x^{2} + 8 \, a b^{7} x + b^{8} \log\left(x\right)"," ",0,"1/8*a^8*x^8 + 8/7*a^7*b*x^7 + 14/3*a^6*b^2*x^6 + 56/5*a^5*b^3*x^5 + 35/2*a^4*b^4*x^4 + 56/3*a^3*b^5*x^3 + 14*a^2*b^6*x^2 + 8*a*b^7*x + b^8*log(x)","A",0
1592,1,92,0,0.756471," ","integrate((a+b/x)^8*x^6,x, algorithm=""fricas"")","\frac{15 \, a^{8} x^{8} + 140 \, a^{7} b x^{7} + 588 \, a^{6} b^{2} x^{6} + 1470 \, a^{5} b^{3} x^{5} + 2450 \, a^{4} b^{4} x^{4} + 2940 \, a^{3} b^{5} x^{3} + 2940 \, a^{2} b^{6} x^{2} + 840 \, a b^{7} x \log\left(x\right) - 105 \, b^{8}}{105 \, x}"," ",0,"1/105*(15*a^8*x^8 + 140*a^7*b*x^7 + 588*a^6*b^2*x^6 + 1470*a^5*b^3*x^5 + 2450*a^4*b^4*x^4 + 2940*a^3*b^5*x^3 + 2940*a^2*b^6*x^2 + 840*a*b^7*x*log(x) - 105*b^8)/x","A",0
1593,1,92,0,0.843181," ","integrate((a+b/x)^8*x^5,x, algorithm=""fricas"")","\frac{5 \, a^{8} x^{8} + 48 \, a^{7} b x^{7} + 210 \, a^{6} b^{2} x^{6} + 560 \, a^{5} b^{3} x^{5} + 1050 \, a^{4} b^{4} x^{4} + 1680 \, a^{3} b^{5} x^{3} + 840 \, a^{2} b^{6} x^{2} \log\left(x\right) - 240 \, a b^{7} x - 15 \, b^{8}}{30 \, x^{2}}"," ",0,"1/30*(5*a^8*x^8 + 48*a^7*b*x^7 + 210*a^6*b^2*x^6 + 560*a^5*b^3*x^5 + 1050*a^4*b^4*x^4 + 1680*a^3*b^5*x^3 + 840*a^2*b^6*x^2*log(x) - 240*a*b^7*x - 15*b^8)/x^2","A",0
1594,1,92,0,0.650906," ","integrate((a+b/x)^8*x^4,x, algorithm=""fricas"")","\frac{3 \, a^{8} x^{8} + 30 \, a^{7} b x^{7} + 140 \, a^{6} b^{2} x^{6} + 420 \, a^{5} b^{3} x^{5} + 1050 \, a^{4} b^{4} x^{4} + 840 \, a^{3} b^{5} x^{3} \log\left(x\right) - 420 \, a^{2} b^{6} x^{2} - 60 \, a b^{7} x - 5 \, b^{8}}{15 \, x^{3}}"," ",0,"1/15*(3*a^8*x^8 + 30*a^7*b*x^7 + 140*a^6*b^2*x^6 + 420*a^5*b^3*x^5 + 1050*a^4*b^4*x^4 + 840*a^3*b^5*x^3*log(x) - 420*a^2*b^6*x^2 - 60*a*b^7*x - 5*b^8)/x^3","A",0
1595,1,92,0,0.931710," ","integrate((a+b/x)^8*x^3,x, algorithm=""fricas"")","\frac{3 \, a^{8} x^{8} + 32 \, a^{7} b x^{7} + 168 \, a^{6} b^{2} x^{6} + 672 \, a^{5} b^{3} x^{5} + 840 \, a^{4} b^{4} x^{4} \log\left(x\right) - 672 \, a^{3} b^{5} x^{3} - 168 \, a^{2} b^{6} x^{2} - 32 \, a b^{7} x - 3 \, b^{8}}{12 \, x^{4}}"," ",0,"1/12*(3*a^8*x^8 + 32*a^7*b*x^7 + 168*a^6*b^2*x^6 + 672*a^5*b^3*x^5 + 840*a^4*b^4*x^4*log(x) - 672*a^3*b^5*x^3 - 168*a^2*b^6*x^2 - 32*a*b^7*x - 3*b^8)/x^4","A",0
1596,1,92,0,0.791608," ","integrate((a+b/x)^8*x^2,x, algorithm=""fricas"")","\frac{5 \, a^{8} x^{8} + 60 \, a^{7} b x^{7} + 420 \, a^{6} b^{2} x^{6} + 840 \, a^{5} b^{3} x^{5} \log\left(x\right) - 1050 \, a^{4} b^{4} x^{4} - 420 \, a^{3} b^{5} x^{3} - 140 \, a^{2} b^{6} x^{2} - 30 \, a b^{7} x - 3 \, b^{8}}{15 \, x^{5}}"," ",0,"1/15*(5*a^8*x^8 + 60*a^7*b*x^7 + 420*a^6*b^2*x^6 + 840*a^5*b^3*x^5*log(x) - 1050*a^4*b^4*x^4 - 420*a^3*b^5*x^3 - 140*a^2*b^6*x^2 - 30*a*b^7*x - 3*b^8)/x^5","A",0
1597,1,92,0,0.902873," ","integrate((a+b/x)^8*x,x, algorithm=""fricas"")","\frac{15 \, a^{8} x^{8} + 240 \, a^{7} b x^{7} + 840 \, a^{6} b^{2} x^{6} \log\left(x\right) - 1680 \, a^{5} b^{3} x^{5} - 1050 \, a^{4} b^{4} x^{4} - 560 \, a^{3} b^{5} x^{3} - 210 \, a^{2} b^{6} x^{2} - 48 \, a b^{7} x - 5 \, b^{8}}{30 \, x^{6}}"," ",0,"1/30*(15*a^8*x^8 + 240*a^7*b*x^7 + 840*a^6*b^2*x^6*log(x) - 1680*a^5*b^3*x^5 - 1050*a^4*b^4*x^4 - 560*a^3*b^5*x^3 - 210*a^2*b^6*x^2 - 48*a*b^7*x - 5*b^8)/x^6","A",0
1598,1,92,0,0.668895," ","integrate((a+b/x)^8,x, algorithm=""fricas"")","\frac{105 \, a^{8} x^{8} + 840 \, a^{7} b x^{7} \log\left(x\right) - 2940 \, a^{6} b^{2} x^{6} - 2940 \, a^{5} b^{3} x^{5} - 2450 \, a^{4} b^{4} x^{4} - 1470 \, a^{3} b^{5} x^{3} - 588 \, a^{2} b^{6} x^{2} - 140 \, a b^{7} x - 15 \, b^{8}}{105 \, x^{7}}"," ",0,"1/105*(105*a^8*x^8 + 840*a^7*b*x^7*log(x) - 2940*a^6*b^2*x^6 - 2940*a^5*b^3*x^5 - 2450*a^4*b^4*x^4 - 1470*a^3*b^5*x^3 - 588*a^2*b^6*x^2 - 140*a*b^7*x - 15*b^8)/x^7","A",0
1599,1,92,0,1.140347," ","integrate((a+b/x)^8/x,x, algorithm=""fricas"")","\frac{840 \, a^{8} x^{8} \log\left(x\right) - 6720 \, a^{7} b x^{7} - 11760 \, a^{6} b^{2} x^{6} - 15680 \, a^{5} b^{3} x^{5} - 14700 \, a^{4} b^{4} x^{4} - 9408 \, a^{3} b^{5} x^{3} - 3920 \, a^{2} b^{6} x^{2} - 960 \, a b^{7} x - 105 \, b^{8}}{840 \, x^{8}}"," ",0,"1/840*(840*a^8*x^8*log(x) - 6720*a^7*b*x^7 - 11760*a^6*b^2*x^6 - 15680*a^5*b^3*x^5 - 14700*a^4*b^4*x^4 - 9408*a^3*b^5*x^3 - 3920*a^2*b^6*x^2 - 960*a*b^7*x - 105*b^8)/x^8","A",0
1600,1,88,0,0.779993," ","integrate((a+b/x)^8/x^2,x, algorithm=""fricas"")","-\frac{9 \, a^{8} x^{8} + 36 \, a^{7} b x^{7} + 84 \, a^{6} b^{2} x^{6} + 126 \, a^{5} b^{3} x^{5} + 126 \, a^{4} b^{4} x^{4} + 84 \, a^{3} b^{5} x^{3} + 36 \, a^{2} b^{6} x^{2} + 9 \, a b^{7} x + b^{8}}{9 \, x^{9}}"," ",0,"-1/9*(9*a^8*x^8 + 36*a^7*b*x^7 + 84*a^6*b^2*x^6 + 126*a^5*b^3*x^5 + 126*a^4*b^4*x^4 + 84*a^3*b^5*x^3 + 36*a^2*b^6*x^2 + 9*a*b^7*x + b^8)/x^9","B",0
1601,1,90,0,1.066307," ","integrate((a+b/x)^8/x^3,x, algorithm=""fricas"")","-\frac{45 \, a^{8} x^{8} + 240 \, a^{7} b x^{7} + 630 \, a^{6} b^{2} x^{6} + 1008 \, a^{5} b^{3} x^{5} + 1050 \, a^{4} b^{4} x^{4} + 720 \, a^{3} b^{5} x^{3} + 315 \, a^{2} b^{6} x^{2} + 80 \, a b^{7} x + 9 \, b^{8}}{90 \, x^{10}}"," ",0,"-1/90*(45*a^8*x^8 + 240*a^7*b*x^7 + 630*a^6*b^2*x^6 + 1008*a^5*b^3*x^5 + 1050*a^4*b^4*x^4 + 720*a^3*b^5*x^3 + 315*a^2*b^6*x^2 + 80*a*b^7*x + 9*b^8)/x^10","B",0
1602,1,90,0,0.921838," ","integrate((a+b/x)^8/x^4,x, algorithm=""fricas"")","-\frac{165 \, a^{8} x^{8} + 990 \, a^{7} b x^{7} + 2772 \, a^{6} b^{2} x^{6} + 4620 \, a^{5} b^{3} x^{5} + 4950 \, a^{4} b^{4} x^{4} + 3465 \, a^{3} b^{5} x^{3} + 1540 \, a^{2} b^{6} x^{2} + 396 \, a b^{7} x + 45 \, b^{8}}{495 \, x^{11}}"," ",0,"-1/495*(165*a^8*x^8 + 990*a^7*b*x^7 + 2772*a^6*b^2*x^6 + 4620*a^5*b^3*x^5 + 4950*a^4*b^4*x^4 + 3465*a^3*b^5*x^3 + 1540*a^2*b^6*x^2 + 396*a*b^7*x + 45*b^8)/x^11","A",0
1603,1,90,0,0.789713," ","integrate((a+b/x)^8/x^5,x, algorithm=""fricas"")","-\frac{495 \, a^{8} x^{8} + 3168 \, a^{7} b x^{7} + 9240 \, a^{6} b^{2} x^{6} + 15840 \, a^{5} b^{3} x^{5} + 17325 \, a^{4} b^{4} x^{4} + 12320 \, a^{3} b^{5} x^{3} + 5544 \, a^{2} b^{6} x^{2} + 1440 \, a b^{7} x + 165 \, b^{8}}{1980 \, x^{12}}"," ",0,"-1/1980*(495*a^8*x^8 + 3168*a^7*b*x^7 + 9240*a^6*b^2*x^6 + 15840*a^5*b^3*x^5 + 17325*a^4*b^4*x^4 + 12320*a^3*b^5*x^3 + 5544*a^2*b^6*x^2 + 1440*a*b^7*x + 165*b^8)/x^12","A",0
1604,1,90,0,0.783478," ","integrate((a+b/x)^8/x^6,x, algorithm=""fricas"")","-\frac{1287 \, a^{8} x^{8} + 8580 \, a^{7} b x^{7} + 25740 \, a^{6} b^{2} x^{6} + 45045 \, a^{5} b^{3} x^{5} + 50050 \, a^{4} b^{4} x^{4} + 36036 \, a^{3} b^{5} x^{3} + 16380 \, a^{2} b^{6} x^{2} + 4290 \, a b^{7} x + 495 \, b^{8}}{6435 \, x^{13}}"," ",0,"-1/6435*(1287*a^8*x^8 + 8580*a^7*b*x^7 + 25740*a^6*b^2*x^6 + 45045*a^5*b^3*x^5 + 50050*a^4*b^4*x^4 + 36036*a^3*b^5*x^3 + 16380*a^2*b^6*x^2 + 4290*a*b^7*x + 495*b^8)/x^13","A",0
1605,1,90,0,0.634657," ","integrate((a+b/x)^8/x^7,x, algorithm=""fricas"")","-\frac{3003 \, a^{8} x^{8} + 20592 \, a^{7} b x^{7} + 63063 \, a^{6} b^{2} x^{6} + 112112 \, a^{5} b^{3} x^{5} + 126126 \, a^{4} b^{4} x^{4} + 91728 \, a^{3} b^{5} x^{3} + 42042 \, a^{2} b^{6} x^{2} + 11088 \, a b^{7} x + 1287 \, b^{8}}{18018 \, x^{14}}"," ",0,"-1/18018*(3003*a^8*x^8 + 20592*a^7*b*x^7 + 63063*a^6*b^2*x^6 + 112112*a^5*b^3*x^5 + 126126*a^4*b^4*x^4 + 91728*a^3*b^5*x^3 + 42042*a^2*b^6*x^2 + 11088*a*b^7*x + 1287*b^8)/x^14","A",0
1606,1,90,0,0.787259," ","integrate((a+b/x)^8/x^8,x, algorithm=""fricas"")","-\frac{6435 \, a^{8} x^{8} + 45045 \, a^{7} b x^{7} + 140140 \, a^{6} b^{2} x^{6} + 252252 \, a^{5} b^{3} x^{5} + 286650 \, a^{4} b^{4} x^{4} + 210210 \, a^{3} b^{5} x^{3} + 97020 \, a^{2} b^{6} x^{2} + 25740 \, a b^{7} x + 3003 \, b^{8}}{45045 \, x^{15}}"," ",0,"-1/45045*(6435*a^8*x^8 + 45045*a^7*b*x^7 + 140140*a^6*b^2*x^6 + 252252*a^5*b^3*x^5 + 286650*a^4*b^4*x^4 + 210210*a^3*b^5*x^3 + 97020*a^2*b^6*x^2 + 25740*a*b^7*x + 3003*b^8)/x^15","A",0
1607,1,63,0,0.753347," ","integrate(x^4/(a+b/x),x, algorithm=""fricas"")","\frac{12 \, a^{5} x^{5} - 15 \, a^{4} b x^{4} + 20 \, a^{3} b^{2} x^{3} - 30 \, a^{2} b^{3} x^{2} + 60 \, a b^{4} x - 60 \, b^{5} \log\left(a x + b\right)}{60 \, a^{6}}"," ",0,"1/60*(12*a^5*x^5 - 15*a^4*b*x^4 + 20*a^3*b^2*x^3 - 30*a^2*b^3*x^2 + 60*a*b^4*x - 60*b^5*log(a*x + b))/a^6","A",0
1608,1,52,0,0.838145," ","integrate(x^3/(a+b/x),x, algorithm=""fricas"")","\frac{3 \, a^{4} x^{4} - 4 \, a^{3} b x^{3} + 6 \, a^{2} b^{2} x^{2} - 12 \, a b^{3} x + 12 \, b^{4} \log\left(a x + b\right)}{12 \, a^{5}}"," ",0,"1/12*(3*a^4*x^4 - 4*a^3*b*x^3 + 6*a^2*b^2*x^2 - 12*a*b^3*x + 12*b^4*log(a*x + b))/a^5","A",0
1609,1,41,0,0.911967," ","integrate(x^2/(a+b/x),x, algorithm=""fricas"")","\frac{2 \, a^{3} x^{3} - 3 \, a^{2} b x^{2} + 6 \, a b^{2} x - 6 \, b^{3} \log\left(a x + b\right)}{6 \, a^{4}}"," ",0,"1/6*(2*a^3*x^3 - 3*a^2*b*x^2 + 6*a*b^2*x - 6*b^3*log(a*x + b))/a^4","A",0
1610,1,29,0,0.805502," ","integrate(x/(a+b/x),x, algorithm=""fricas"")","\frac{a^{2} x^{2} - 2 \, a b x + 2 \, b^{2} \log\left(a x + b\right)}{2 \, a^{3}}"," ",0,"1/2*(a^2*x^2 - 2*a*b*x + 2*b^2*log(a*x + b))/a^3","A",0
1611,1,17,0,0.978377," ","integrate(1/(a+b/x),x, algorithm=""fricas"")","\frac{a x - b \log\left(a x + b\right)}{a^{2}}"," ",0,"(a*x - b*log(a*x + b))/a^2","A",0
1612,1,10,0,0.729603," ","integrate(1/(a+b/x)/x,x, algorithm=""fricas"")","\frac{\log\left(a x + b\right)}{a}"," ",0,"log(a*x + b)/a","A",0
1613,1,16,0,0.826421," ","integrate(1/(a+b/x)/x^2,x, algorithm=""fricas"")","-\frac{\log\left(a x + b\right) - \log\left(x\right)}{b}"," ",0,"-(log(a*x + b) - log(x))/b","A",0
1614,1,26,0,0.808445," ","integrate(1/(a+b/x)/x^3,x, algorithm=""fricas"")","\frac{a x \log\left(a x + b\right) - a x \log\left(x\right) - b}{b^{2} x}"," ",0,"(a*x*log(a*x + b) - a*x*log(x) - b)/(b^2*x)","A",0
1615,1,41,0,0.671269," ","integrate(1/(a+b/x)/x^4,x, algorithm=""fricas"")","-\frac{2 \, a^{2} x^{2} \log\left(a x + b\right) - 2 \, a^{2} x^{2} \log\left(x\right) - 2 \, a b x + b^{2}}{2 \, b^{3} x^{2}}"," ",0,"-1/2*(2*a^2*x^2*log(a*x + b) - 2*a^2*x^2*log(x) - 2*a*b*x + b^2)/(b^3*x^2)","A",0
1616,1,54,0,0.794781," ","integrate(1/(a+b/x)/x^5,x, algorithm=""fricas"")","\frac{6 \, a^{3} x^{3} \log\left(a x + b\right) - 6 \, a^{3} x^{3} \log\left(x\right) - 6 \, a^{2} b x^{2} + 3 \, a b^{2} x - 2 \, b^{3}}{6 \, b^{4} x^{3}}"," ",0,"1/6*(6*a^3*x^3*log(a*x + b) - 6*a^3*x^3*log(x) - 6*a^2*b*x^2 + 3*a*b^2*x - 2*b^3)/(b^4*x^3)","A",0
1617,1,65,0,0.794473," ","integrate(1/(a+b/x)/x^6,x, algorithm=""fricas"")","-\frac{12 \, a^{4} x^{4} \log\left(a x + b\right) - 12 \, a^{4} x^{4} \log\left(x\right) - 12 \, a^{3} b x^{3} + 6 \, a^{2} b^{2} x^{2} - 4 \, a b^{3} x + 3 \, b^{4}}{12 \, b^{5} x^{4}}"," ",0,"-1/12*(12*a^4*x^4*log(a*x + b) - 12*a^4*x^4*log(x) - 12*a^3*b*x^3 + 6*a^2*b^2*x^2 - 4*a*b^3*x + 3*b^4)/(b^5*x^4)","A",0
1618,1,76,0,0.729357," ","integrate(1/(a+b/x)/x^7,x, algorithm=""fricas"")","\frac{60 \, a^{5} x^{5} \log\left(a x + b\right) - 60 \, a^{5} x^{5} \log\left(x\right) - 60 \, a^{4} b x^{4} + 30 \, a^{3} b^{2} x^{3} - 20 \, a^{2} b^{3} x^{2} + 15 \, a b^{4} x - 12 \, b^{5}}{60 \, b^{6} x^{5}}"," ",0,"1/60*(60*a^5*x^5*log(a*x + b) - 60*a^5*x^5*log(x) - 60*a^4*b*x^4 + 30*a^3*b^2*x^3 - 20*a^2*b^3*x^2 + 15*a*b^4*x - 12*b^5)/(b^6*x^5)","A",0
1619,1,107,0,0.880760," ","integrate(x^5/(a+b/x)^2,x, algorithm=""fricas"")","\frac{10 \, a^{7} x^{7} - 14 \, a^{6} b x^{6} + 21 \, a^{5} b^{2} x^{5} - 35 \, a^{4} b^{3} x^{4} + 70 \, a^{3} b^{4} x^{3} - 210 \, a^{2} b^{5} x^{2} - 360 \, a b^{6} x + 60 \, b^{7} + 420 \, {\left(a b^{6} x + b^{7}\right)} \log\left(a x + b\right)}{60 \, {\left(a^{9} x + a^{8} b\right)}}"," ",0,"1/60*(10*a^7*x^7 - 14*a^6*b*x^6 + 21*a^5*b^2*x^5 - 35*a^4*b^3*x^4 + 70*a^3*b^4*x^3 - 210*a^2*b^5*x^2 - 360*a*b^6*x + 60*b^7 + 420*(a*b^6*x + b^7)*log(a*x + b))/(a^9*x + a^8*b)","A",0
1620,1,96,0,0.621134," ","integrate(x^4/(a+b/x)^2,x, algorithm=""fricas"")","\frac{2 \, a^{6} x^{6} - 3 \, a^{5} b x^{5} + 5 \, a^{4} b^{2} x^{4} - 10 \, a^{3} b^{3} x^{3} + 30 \, a^{2} b^{4} x^{2} + 50 \, a b^{5} x - 10 \, b^{6} - 60 \, {\left(a b^{5} x + b^{6}\right)} \log\left(a x + b\right)}{10 \, {\left(a^{8} x + a^{7} b\right)}}"," ",0,"1/10*(2*a^6*x^6 - 3*a^5*b*x^5 + 5*a^4*b^2*x^4 - 10*a^3*b^3*x^3 + 30*a^2*b^4*x^2 + 50*a*b^5*x - 10*b^6 - 60*(a*b^5*x + b^6)*log(a*x + b))/(a^8*x + a^7*b)","A",0
1621,1,85,0,0.780528," ","integrate(x^3/(a+b/x)^2,x, algorithm=""fricas"")","\frac{3 \, a^{5} x^{5} - 5 \, a^{4} b x^{4} + 10 \, a^{3} b^{2} x^{3} - 30 \, a^{2} b^{3} x^{2} - 48 \, a b^{4} x + 12 \, b^{5} + 60 \, {\left(a b^{4} x + b^{5}\right)} \log\left(a x + b\right)}{12 \, {\left(a^{7} x + a^{6} b\right)}}"," ",0,"1/12*(3*a^5*x^5 - 5*a^4*b*x^4 + 10*a^3*b^2*x^3 - 30*a^2*b^3*x^2 - 48*a*b^4*x + 12*b^5 + 60*(a*b^4*x + b^5)*log(a*x + b))/(a^7*x + a^6*b)","A",0
1622,1,73,0,0.782401," ","integrate(x^2/(a+b/x)^2,x, algorithm=""fricas"")","\frac{a^{4} x^{4} - 2 \, a^{3} b x^{3} + 6 \, a^{2} b^{2} x^{2} + 9 \, a b^{3} x - 3 \, b^{4} - 12 \, {\left(a b^{3} x + b^{4}\right)} \log\left(a x + b\right)}{3 \, {\left(a^{6} x + a^{5} b\right)}}"," ",0,"1/3*(a^4*x^4 - 2*a^3*b*x^3 + 6*a^2*b^2*x^2 + 9*a*b^3*x - 3*b^4 - 12*(a*b^3*x + b^4)*log(a*x + b))/(a^6*x + a^5*b)","A",0
1623,1,62,0,0.739103," ","integrate(x/(a+b/x)^2,x, algorithm=""fricas"")","\frac{a^{3} x^{3} - 3 \, a^{2} b x^{2} - 4 \, a b^{2} x + 2 \, b^{3} + 6 \, {\left(a b^{2} x + b^{3}\right)} \log\left(a x + b\right)}{2 \, {\left(a^{5} x + a^{4} b\right)}}"," ",0,"1/2*(a^3*x^3 - 3*a^2*b*x^2 - 4*a*b^2*x + 2*b^3 + 6*(a*b^2*x + b^3)*log(a*x + b))/(a^5*x + a^4*b)","A",0
1624,1,47,0,0.822254," ","integrate(1/(a+b/x)^2,x, algorithm=""fricas"")","\frac{a^{2} x^{2} + a b x - b^{2} - 2 \, {\left(a b x + b^{2}\right)} \log\left(a x + b\right)}{a^{4} x + a^{3} b}"," ",0,"(a^2*x^2 + a*b*x - b^2 - 2*(a*b*x + b^2)*log(a*x + b))/(a^4*x + a^3*b)","A",0
1625,1,28,0,0.746135," ","integrate(1/(a+b/x)^2/x,x, algorithm=""fricas"")","\frac{{\left(a x + b\right)} \log\left(a x + b\right) + b}{a^{3} x + a^{2} b}"," ",0,"((a*x + b)*log(a*x + b) + b)/(a^3*x + a^2*b)","A",0
1626,1,13,0,0.713911," ","integrate(1/(a+b/x)^2/x^2,x, algorithm=""fricas"")","-\frac{1}{a^{2} x + a b}"," ",0,"-1/(a^2*x + a*b)","A",0
1627,1,39,0,0.780945," ","integrate(1/(a+b/x)^2/x^3,x, algorithm=""fricas"")","-\frac{{\left(a x + b\right)} \log\left(a x + b\right) - {\left(a x + b\right)} \log\left(x\right) - b}{a b^{2} x + b^{3}}"," ",0,"-((a*x + b)*log(a*x + b) - (a*x + b)*log(x) - b)/(a*b^2*x + b^3)","A",0
1628,1,63,0,0.799822," ","integrate(1/(a+b/x)^2/x^4,x, algorithm=""fricas"")","-\frac{2 \, a b x + b^{2} - 2 \, {\left(a^{2} x^{2} + a b x\right)} \log\left(a x + b\right) + 2 \, {\left(a^{2} x^{2} + a b x\right)} \log\left(x\right)}{a b^{3} x^{2} + b^{4} x}"," ",0,"-(2*a*b*x + b^2 - 2*(a^2*x^2 + a*b*x)*log(a*x + b) + 2*(a^2*x^2 + a*b*x)*log(x))/(a*b^3*x^2 + b^4*x)","A",0
1629,1,86,0,0.784414," ","integrate(1/(a+b/x)^2/x^5,x, algorithm=""fricas"")","\frac{6 \, a^{2} b x^{2} + 3 \, a b^{2} x - b^{3} - 6 \, {\left(a^{3} x^{3} + a^{2} b x^{2}\right)} \log\left(a x + b\right) + 6 \, {\left(a^{3} x^{3} + a^{2} b x^{2}\right)} \log\left(x\right)}{2 \, {\left(a b^{4} x^{3} + b^{5} x^{2}\right)}}"," ",0,"1/2*(6*a^2*b*x^2 + 3*a*b^2*x - b^3 - 6*(a^3*x^3 + a^2*b*x^2)*log(a*x + b) + 6*(a^3*x^3 + a^2*b*x^2)*log(x))/(a*b^4*x^3 + b^5*x^2)","A",0
1630,1,95,0,0.789291," ","integrate(1/(a+b/x)^2/x^6,x, algorithm=""fricas"")","-\frac{12 \, a^{3} b x^{3} + 6 \, a^{2} b^{2} x^{2} - 2 \, a b^{3} x + b^{4} - 12 \, {\left(a^{4} x^{4} + a^{3} b x^{3}\right)} \log\left(a x + b\right) + 12 \, {\left(a^{4} x^{4} + a^{3} b x^{3}\right)} \log\left(x\right)}{3 \, {\left(a b^{5} x^{4} + b^{6} x^{3}\right)}}"," ",0,"-1/3*(12*a^3*b*x^3 + 6*a^2*b^2*x^2 - 2*a*b^3*x + b^4 - 12*(a^4*x^4 + a^3*b*x^3)*log(a*x + b) + 12*(a^4*x^4 + a^3*b*x^3)*log(x))/(a*b^5*x^4 + b^6*x^3)","A",0
1631,1,108,0,0.747152," ","integrate(1/(a+b/x)^2/x^7,x, algorithm=""fricas"")","\frac{60 \, a^{4} b x^{4} + 30 \, a^{3} b^{2} x^{3} - 10 \, a^{2} b^{3} x^{2} + 5 \, a b^{4} x - 3 \, b^{5} - 60 \, {\left(a^{5} x^{5} + a^{4} b x^{4}\right)} \log\left(a x + b\right) + 60 \, {\left(a^{5} x^{5} + a^{4} b x^{4}\right)} \log\left(x\right)}{12 \, {\left(a b^{6} x^{5} + b^{7} x^{4}\right)}}"," ",0,"1/12*(60*a^4*b*x^4 + 30*a^3*b^2*x^3 - 10*a^2*b^3*x^2 + 5*a*b^4*x - 3*b^5 - 60*(a^5*x^5 + a^4*b*x^4)*log(a*x + b) + 60*(a^5*x^5 + a^4*b*x^4)*log(x))/(a*b^6*x^5 + b^7*x^4)","A",0
1632,1,119,0,0.647802," ","integrate(1/(a+b/x)^2/x^8,x, algorithm=""fricas"")","-\frac{60 \, a^{5} b x^{5} + 30 \, a^{4} b^{2} x^{4} - 10 \, a^{3} b^{3} x^{3} + 5 \, a^{2} b^{4} x^{2} - 3 \, a b^{5} x + 2 \, b^{6} - 60 \, {\left(a^{6} x^{6} + a^{5} b x^{5}\right)} \log\left(a x + b\right) + 60 \, {\left(a^{6} x^{6} + a^{5} b x^{5}\right)} \log\left(x\right)}{10 \, {\left(a b^{7} x^{6} + b^{8} x^{5}\right)}}"," ",0,"-1/10*(60*a^5*b*x^5 + 30*a^4*b^2*x^4 - 10*a^3*b^3*x^3 + 5*a^2*b^4*x^2 - 3*a*b^5*x + 2*b^6 - 60*(a^6*x^6 + a^5*b*x^5)*log(a*x + b) + 60*(a^6*x^6 + a^5*b*x^5)*log(x))/(a*b^7*x^6 + b^8*x^5)","A",0
1633,1,129,0,0.777691," ","integrate(x^4/(a+b/x)^3,x, algorithm=""fricas"")","\frac{4 \, a^{7} x^{7} - 7 \, a^{6} b x^{6} + 14 \, a^{5} b^{2} x^{5} - 35 \, a^{4} b^{3} x^{4} + 140 \, a^{3} b^{4} x^{3} + 500 \, a^{2} b^{5} x^{2} + 160 \, a b^{6} x - 130 \, b^{7} - 420 \, {\left(a^{2} b^{5} x^{2} + 2 \, a b^{6} x + b^{7}\right)} \log\left(a x + b\right)}{20 \, {\left(a^{10} x^{2} + 2 \, a^{9} b x + a^{8} b^{2}\right)}}"," ",0,"1/20*(4*a^7*x^7 - 7*a^6*b*x^6 + 14*a^5*b^2*x^5 - 35*a^4*b^3*x^4 + 140*a^3*b^4*x^3 + 500*a^2*b^5*x^2 + 160*a*b^6*x - 130*b^7 - 420*(a^2*b^5*x^2 + 2*a*b^6*x + b^7)*log(a*x + b))/(a^10*x^2 + 2*a^9*b*x + a^8*b^2)","A",0
1634,1,117,0,0.848697," ","integrate(x^3/(a+b/x)^3,x, algorithm=""fricas"")","\frac{a^{6} x^{6} - 2 \, a^{5} b x^{5} + 5 \, a^{4} b^{2} x^{4} - 20 \, a^{3} b^{3} x^{3} - 68 \, a^{2} b^{4} x^{2} - 16 \, a b^{5} x + 22 \, b^{6} + 60 \, {\left(a^{2} b^{4} x^{2} + 2 \, a b^{5} x + b^{6}\right)} \log\left(a x + b\right)}{4 \, {\left(a^{9} x^{2} + 2 \, a^{8} b x + a^{7} b^{2}\right)}}"," ",0,"1/4*(a^6*x^6 - 2*a^5*b*x^5 + 5*a^4*b^2*x^4 - 20*a^3*b^3*x^3 - 68*a^2*b^4*x^2 - 16*a*b^5*x + 22*b^6 + 60*(a^2*b^4*x^2 + 2*a*b^5*x + b^6)*log(a*x + b))/(a^9*x^2 + 2*a^8*b*x + a^7*b^2)","A",0
1635,1,107,0,0.612807," ","integrate(x^2/(a+b/x)^3,x, algorithm=""fricas"")","\frac{2 \, a^{5} x^{5} - 5 \, a^{4} b x^{4} + 20 \, a^{3} b^{2} x^{3} + 63 \, a^{2} b^{3} x^{2} + 6 \, a b^{4} x - 27 \, b^{5} - 60 \, {\left(a^{2} b^{3} x^{2} + 2 \, a b^{4} x + b^{5}\right)} \log\left(a x + b\right)}{6 \, {\left(a^{8} x^{2} + 2 \, a^{7} b x + a^{6} b^{2}\right)}}"," ",0,"1/6*(2*a^5*x^5 - 5*a^4*b*x^4 + 20*a^3*b^2*x^3 + 63*a^2*b^3*x^2 + 6*a*b^4*x - 27*b^5 - 60*(a^2*b^3*x^2 + 2*a*b^4*x + b^5)*log(a*x + b))/(a^8*x^2 + 2*a^7*b*x + a^6*b^2)","A",0
1636,1,95,0,0.819118," ","integrate(x/(a+b/x)^3,x, algorithm=""fricas"")","\frac{a^{4} x^{4} - 4 \, a^{3} b x^{3} - 11 \, a^{2} b^{2} x^{2} + 2 \, a b^{3} x + 7 \, b^{4} + 12 \, {\left(a^{2} b^{2} x^{2} + 2 \, a b^{3} x + b^{4}\right)} \log\left(a x + b\right)}{2 \, {\left(a^{7} x^{2} + 2 \, a^{6} b x + a^{5} b^{2}\right)}}"," ",0,"1/2*(a^4*x^4 - 4*a^3*b*x^3 - 11*a^2*b^2*x^2 + 2*a*b^3*x + 7*b^4 + 12*(a^2*b^2*x^2 + 2*a*b^3*x + b^4)*log(a*x + b))/(a^7*x^2 + 2*a^6*b*x + a^5*b^2)","A",0
1637,1,83,0,0.854841," ","integrate(1/(a+b/x)^3,x, algorithm=""fricas"")","\frac{2 \, a^{3} x^{3} + 4 \, a^{2} b x^{2} - 4 \, a b^{2} x - 5 \, b^{3} - 6 \, {\left(a^{2} b x^{2} + 2 \, a b^{2} x + b^{3}\right)} \log\left(a x + b\right)}{2 \, {\left(a^{6} x^{2} + 2 \, a^{5} b x + a^{4} b^{2}\right)}}"," ",0,"1/2*(2*a^3*x^3 + 4*a^2*b*x^2 - 4*a*b^2*x - 5*b^3 - 6*(a^2*b*x^2 + 2*a*b^2*x + b^3)*log(a*x + b))/(a^6*x^2 + 2*a^5*b*x + a^4*b^2)","A",0
1638,1,61,0,0.750568," ","integrate(1/(a+b/x)^3/x,x, algorithm=""fricas"")","\frac{4 \, a b x + 3 \, b^{2} + 2 \, {\left(a^{2} x^{2} + 2 \, a b x + b^{2}\right)} \log\left(a x + b\right)}{2 \, {\left(a^{5} x^{2} + 2 \, a^{4} b x + a^{3} b^{2}\right)}}"," ",0,"1/2*(4*a*b*x + 3*b^2 + 2*(a^2*x^2 + 2*a*b*x + b^2)*log(a*x + b))/(a^5*x^2 + 2*a^4*b*x + a^3*b^2)","A",0
1639,1,32,0,0.772496," ","integrate(1/(a+b/x)^3/x^2,x, algorithm=""fricas"")","-\frac{2 \, a x + b}{2 \, {\left(a^{4} x^{2} + 2 \, a^{3} b x + a^{2} b^{2}\right)}}"," ",0,"-1/2*(2*a*x + b)/(a^4*x^2 + 2*a^3*b*x + a^2*b^2)","B",0
1640,1,24,0,0.789277," ","integrate(1/(a+b/x)^3/x^3,x, algorithm=""fricas"")","-\frac{1}{2 \, {\left(a^{3} x^{2} + 2 \, a^{2} b x + a b^{2}\right)}}"," ",0,"-1/2/(a^3*x^2 + 2*a^2*b*x + a*b^2)","A",0
1641,1,80,0,0.787704," ","integrate(1/(a+b/x)^3/x^4,x, algorithm=""fricas"")","\frac{2 \, a b x + 3 \, b^{2} - 2 \, {\left(a^{2} x^{2} + 2 \, a b x + b^{2}\right)} \log\left(a x + b\right) + 2 \, {\left(a^{2} x^{2} + 2 \, a b x + b^{2}\right)} \log\left(x\right)}{2 \, {\left(a^{2} b^{3} x^{2} + 2 \, a b^{4} x + b^{5}\right)}}"," ",0,"1/2*(2*a*b*x + 3*b^2 - 2*(a^2*x^2 + 2*a*b*x + b^2)*log(a*x + b) + 2*(a^2*x^2 + 2*a*b*x + b^2)*log(x))/(a^2*b^3*x^2 + 2*a*b^4*x + b^5)","A",0
1642,1,109,0,0.820856," ","integrate(1/(a+b/x)^3/x^5,x, algorithm=""fricas"")","-\frac{6 \, a^{2} b x^{2} + 9 \, a b^{2} x + 2 \, b^{3} - 6 \, {\left(a^{3} x^{3} + 2 \, a^{2} b x^{2} + a b^{2} x\right)} \log\left(a x + b\right) + 6 \, {\left(a^{3} x^{3} + 2 \, a^{2} b x^{2} + a b^{2} x\right)} \log\left(x\right)}{2 \, {\left(a^{2} b^{4} x^{3} + 2 \, a b^{5} x^{2} + b^{6} x\right)}}"," ",0,"-1/2*(6*a^2*b*x^2 + 9*a*b^2*x + 2*b^3 - 6*(a^3*x^3 + 2*a^2*b*x^2 + a*b^2*x)*log(a*x + b) + 6*(a^3*x^3 + 2*a^2*b*x^2 + a*b^2*x)*log(x))/(a^2*b^4*x^3 + 2*a*b^5*x^2 + b^6*x)","A",0
1643,1,130,0,0.879715," ","integrate(1/(a+b/x)^3/x^6,x, algorithm=""fricas"")","\frac{12 \, a^{3} b x^{3} + 18 \, a^{2} b^{2} x^{2} + 4 \, a b^{3} x - b^{4} - 12 \, {\left(a^{4} x^{4} + 2 \, a^{3} b x^{3} + a^{2} b^{2} x^{2}\right)} \log\left(a x + b\right) + 12 \, {\left(a^{4} x^{4} + 2 \, a^{3} b x^{3} + a^{2} b^{2} x^{2}\right)} \log\left(x\right)}{2 \, {\left(a^{2} b^{5} x^{4} + 2 \, a b^{6} x^{3} + b^{7} x^{2}\right)}}"," ",0,"1/2*(12*a^3*b*x^3 + 18*a^2*b^2*x^2 + 4*a*b^3*x - b^4 - 12*(a^4*x^4 + 2*a^3*b*x^3 + a^2*b^2*x^2)*log(a*x + b) + 12*(a^4*x^4 + 2*a^3*b*x^3 + a^2*b^2*x^2)*log(x))/(a^2*b^5*x^4 + 2*a*b^6*x^3 + b^7*x^2)","A",0
1644,1,141,0,0.762867," ","integrate(1/(a+b/x)^3/x^7,x, algorithm=""fricas"")","-\frac{60 \, a^{4} b x^{4} + 90 \, a^{3} b^{2} x^{3} + 20 \, a^{2} b^{3} x^{2} - 5 \, a b^{4} x + 2 \, b^{5} - 60 \, {\left(a^{5} x^{5} + 2 \, a^{4} b x^{4} + a^{3} b^{2} x^{3}\right)} \log\left(a x + b\right) + 60 \, {\left(a^{5} x^{5} + 2 \, a^{4} b x^{4} + a^{3} b^{2} x^{3}\right)} \log\left(x\right)}{6 \, {\left(a^{2} b^{6} x^{5} + 2 \, a b^{7} x^{4} + b^{8} x^{3}\right)}}"," ",0,"-1/6*(60*a^4*b*x^4 + 90*a^3*b^2*x^3 + 20*a^2*b^3*x^2 - 5*a*b^4*x + 2*b^5 - 60*(a^5*x^5 + 2*a^4*b*x^4 + a^3*b^2*x^3)*log(a*x + b) + 60*(a^5*x^5 + 2*a^4*b*x^4 + a^3*b^2*x^3)*log(x))/(a^2*b^6*x^5 + 2*a*b^7*x^4 + b^8*x^3)","A",0
1645,1,152,0,0.848257," ","integrate(1/(a+b/x)^3/x^8,x, algorithm=""fricas"")","\frac{60 \, a^{5} b x^{5} + 90 \, a^{4} b^{2} x^{4} + 20 \, a^{3} b^{3} x^{3} - 5 \, a^{2} b^{4} x^{2} + 2 \, a b^{5} x - b^{6} - 60 \, {\left(a^{6} x^{6} + 2 \, a^{5} b x^{5} + a^{4} b^{2} x^{4}\right)} \log\left(a x + b\right) + 60 \, {\left(a^{6} x^{6} + 2 \, a^{5} b x^{5} + a^{4} b^{2} x^{4}\right)} \log\left(x\right)}{4 \, {\left(a^{2} b^{7} x^{6} + 2 \, a b^{8} x^{5} + b^{9} x^{4}\right)}}"," ",0,"1/4*(60*a^5*b*x^5 + 90*a^4*b^2*x^4 + 20*a^3*b^3*x^3 - 5*a^2*b^4*x^2 + 2*a*b^5*x - b^6 - 60*(a^6*x^6 + 2*a^5*b*x^5 + a^4*b^2*x^4)*log(a*x + b) + 60*(a^6*x^6 + 2*a^5*b*x^5 + a^4*b^2*x^4)*log(x))/(a^2*b^7*x^6 + 2*a*b^8*x^5 + b^9*x^4)","A",0
1646,1,163,0,0.830738," ","integrate(1/(a+b/x)^3/x^9,x, algorithm=""fricas"")","-\frac{420 \, a^{6} b x^{6} + 630 \, a^{5} b^{2} x^{5} + 140 \, a^{4} b^{3} x^{4} - 35 \, a^{3} b^{4} x^{3} + 14 \, a^{2} b^{5} x^{2} - 7 \, a b^{6} x + 4 \, b^{7} - 420 \, {\left(a^{7} x^{7} + 2 \, a^{6} b x^{6} + a^{5} b^{2} x^{5}\right)} \log\left(a x + b\right) + 420 \, {\left(a^{7} x^{7} + 2 \, a^{6} b x^{6} + a^{5} b^{2} x^{5}\right)} \log\left(x\right)}{20 \, {\left(a^{2} b^{8} x^{7} + 2 \, a b^{9} x^{6} + b^{10} x^{5}\right)}}"," ",0,"-1/20*(420*a^6*b*x^6 + 630*a^5*b^2*x^5 + 140*a^4*b^3*x^4 - 35*a^3*b^4*x^3 + 14*a^2*b^5*x^2 - 7*a*b^6*x + 4*b^7 - 420*(a^7*x^7 + 2*a^6*b*x^6 + a^5*b^2*x^5)*log(a*x + b) + 420*(a^7*x^7 + 2*a^6*b*x^6 + a^5*b^2*x^5)*log(x))/(a^2*b^8*x^7 + 2*a*b^9*x^6 + b^10*x^5)","A",0
1647,1,18,0,0.672334," ","integrate((a+b/x)*x^(5/2),x, algorithm=""fricas"")","\frac{2}{35} \, {\left(5 \, a x^{3} + 7 \, b x^{2}\right)} \sqrt{x}"," ",0,"2/35*(5*a*x^3 + 7*b*x^2)*sqrt(x)","A",0
1648,1,16,0,0.808289," ","integrate((a+b/x)*x^(3/2),x, algorithm=""fricas"")","\frac{2}{15} \, {\left(3 \, a x^{2} + 5 \, b x\right)} \sqrt{x}"," ",0,"2/15*(3*a*x^2 + 5*b*x)*sqrt(x)","A",0
1649,1,12,0,0.841769," ","integrate((a+b/x)*x^(1/2),x, algorithm=""fricas"")","\frac{2}{3} \, {\left(a x + 3 \, b\right)} \sqrt{x}"," ",0,"2/3*(a*x + 3*b)*sqrt(x)","A",0
1650,1,12,0,0.732893," ","integrate((a+b/x)/x^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(a x - b\right)}}{\sqrt{x}}"," ",0,"2*(a*x - b)/sqrt(x)","A",0
1651,1,11,0,0.572131," ","integrate((a+b/x)/x^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, a x + b\right)}}{3 \, x^{\frac{3}{2}}}"," ",0,"-2/3*(3*a*x + b)/x^(3/2)","A",0
1652,1,13,0,0.897457," ","integrate((a+b/x)/x^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(5 \, a x + 3 \, b\right)}}{15 \, x^{\frac{5}{2}}}"," ",0,"-2/15*(5*a*x + 3*b)/x^(5/2)","A",0
1653,1,27,0,0.810797," ","integrate((a+b/x)^2*x^(5/2),x, algorithm=""fricas"")","\frac{2}{105} \, {\left(15 \, a^{2} x^{3} + 42 \, a b x^{2} + 35 \, b^{2} x\right)} \sqrt{x}"," ",0,"2/105*(15*a^2*x^3 + 42*a*b*x^2 + 35*b^2*x)*sqrt(x)","A",0
1654,1,24,0,0.825541," ","integrate((a+b/x)^2*x^(3/2),x, algorithm=""fricas"")","\frac{2}{15} \, {\left(3 \, a^{2} x^{2} + 10 \, a b x + 15 \, b^{2}\right)} \sqrt{x}"," ",0,"2/15*(3*a^2*x^2 + 10*a*b*x + 15*b^2)*sqrt(x)","A",0
1655,1,23,0,0.762209," ","integrate((a+b/x)^2*x^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(a^{2} x^{2} + 6 \, a b x - 3 \, b^{2}\right)}}{3 \, \sqrt{x}}"," ",0,"2/3*(a^2*x^2 + 6*a*b*x - 3*b^2)/sqrt(x)","A",0
1656,1,24,0,0.786117," ","integrate((a+b/x)^2/x^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, a^{2} x^{2} - 6 \, a b x - b^{2}\right)}}{3 \, x^{\frac{3}{2}}}"," ",0,"2/3*(3*a^2*x^2 - 6*a*b*x - b^2)/x^(3/2)","A",0
1657,1,24,0,0.876443," ","integrate((a+b/x)^2/x^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(15 \, a^{2} x^{2} + 10 \, a b x + 3 \, b^{2}\right)}}{15 \, x^{\frac{5}{2}}}"," ",0,"-2/15*(15*a^2*x^2 + 10*a*b*x + 3*b^2)/x^(5/2)","A",0
1658,1,24,0,0.810549," ","integrate((a+b/x)^2/x^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(35 \, a^{2} x^{2} + 42 \, a b x + 15 \, b^{2}\right)}}{105 \, x^{\frac{7}{2}}}"," ",0,"-2/105*(35*a^2*x^2 + 42*a*b*x + 15*b^2)/x^(7/2)","A",0
1659,1,35,0,0.742749," ","integrate((a+b/x)^3*x^(5/2),x, algorithm=""fricas"")","\frac{2}{35} \, {\left(5 \, a^{3} x^{3} + 21 \, a^{2} b x^{2} + 35 \, a b^{2} x + 35 \, b^{3}\right)} \sqrt{x}"," ",0,"2/35*(5*a^3*x^3 + 21*a^2*b*x^2 + 35*a*b^2*x + 35*b^3)*sqrt(x)","A",0
1660,1,34,0,0.855767," ","integrate((a+b/x)^3*x^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(a^{3} x^{3} + 5 \, a^{2} b x^{2} + 15 \, a b^{2} x - 5 \, b^{3}\right)}}{5 \, \sqrt{x}}"," ",0,"2/5*(a^3*x^3 + 5*a^2*b*x^2 + 15*a*b^2*x - 5*b^3)/sqrt(x)","A",0
1661,1,34,0,0.706274," ","integrate((a+b/x)^3*x^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(a^{3} x^{3} + 9 \, a^{2} b x^{2} - 9 \, a b^{2} x - b^{3}\right)}}{3 \, x^{\frac{3}{2}}}"," ",0,"2/3*(a^3*x^3 + 9*a^2*b*x^2 - 9*a*b^2*x - b^3)/x^(3/2)","A",0
1662,1,35,0,0.643436," ","integrate((a+b/x)^3/x^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, a^{3} x^{3} - 15 \, a^{2} b x^{2} - 5 \, a b^{2} x - b^{3}\right)}}{5 \, x^{\frac{5}{2}}}"," ",0,"2/5*(5*a^3*x^3 - 15*a^2*b*x^2 - 5*a*b^2*x - b^3)/x^(5/2)","A",0
1663,1,35,0,0.808294," ","integrate((a+b/x)^3/x^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(35 \, a^{3} x^{3} + 35 \, a^{2} b x^{2} + 21 \, a b^{2} x + 5 \, b^{3}\right)}}{35 \, x^{\frac{7}{2}}}"," ",0,"-2/35*(35*a^3*x^3 + 35*a^2*b*x^2 + 21*a*b^2*x + 5*b^3)/x^(7/2)","A",0
1664,1,35,0,0.892494," ","integrate((a+b/x)^3/x^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(105 \, a^{3} x^{3} + 189 \, a^{2} b x^{2} + 135 \, a b^{2} x + 35 \, b^{3}\right)}}{315 \, x^{\frac{9}{2}}}"," ",0,"-2/315*(105*a^3*x^3 + 189*a^2*b*x^2 + 135*a*b^2*x + 35*b^3)/x^(9/2)","A",0
1665,1,153,0,0.822179," ","integrate(x^(5/2)/(a+b/x),x, algorithm=""fricas"")","\left[\frac{105 \, b^{3} \sqrt{-\frac{b}{a}} \log\left(\frac{a x + 2 \, a \sqrt{x} \sqrt{-\frac{b}{a}} - b}{a x + b}\right) + 2 \, {\left(15 \, a^{3} x^{3} - 21 \, a^{2} b x^{2} + 35 \, a b^{2} x - 105 \, b^{3}\right)} \sqrt{x}}{105 \, a^{4}}, \frac{2 \, {\left(105 \, b^{3} \sqrt{\frac{b}{a}} \arctan\left(\frac{a \sqrt{x} \sqrt{\frac{b}{a}}}{b}\right) + {\left(15 \, a^{3} x^{3} - 21 \, a^{2} b x^{2} + 35 \, a b^{2} x - 105 \, b^{3}\right)} \sqrt{x}\right)}}{105 \, a^{4}}\right]"," ",0,"[1/105*(105*b^3*sqrt(-b/a)*log((a*x + 2*a*sqrt(x)*sqrt(-b/a) - b)/(a*x + b)) + 2*(15*a^3*x^3 - 21*a^2*b*x^2 + 35*a*b^2*x - 105*b^3)*sqrt(x))/a^4, 2/105*(105*b^3*sqrt(b/a)*arctan(a*sqrt(x)*sqrt(b/a)/b) + (15*a^3*x^3 - 21*a^2*b*x^2 + 35*a*b^2*x - 105*b^3)*sqrt(x))/a^4]","A",0
1666,1,132,0,0.842437," ","integrate(x^(3/2)/(a+b/x),x, algorithm=""fricas"")","\left[\frac{15 \, b^{2} \sqrt{-\frac{b}{a}} \log\left(\frac{a x - 2 \, a \sqrt{x} \sqrt{-\frac{b}{a}} - b}{a x + b}\right) + 2 \, {\left(3 \, a^{2} x^{2} - 5 \, a b x + 15 \, b^{2}\right)} \sqrt{x}}{15 \, a^{3}}, -\frac{2 \, {\left(15 \, b^{2} \sqrt{\frac{b}{a}} \arctan\left(\frac{a \sqrt{x} \sqrt{\frac{b}{a}}}{b}\right) - {\left(3 \, a^{2} x^{2} - 5 \, a b x + 15 \, b^{2}\right)} \sqrt{x}\right)}}{15 \, a^{3}}\right]"," ",0,"[1/15*(15*b^2*sqrt(-b/a)*log((a*x - 2*a*sqrt(x)*sqrt(-b/a) - b)/(a*x + b)) + 2*(3*a^2*x^2 - 5*a*b*x + 15*b^2)*sqrt(x))/a^3, -2/15*(15*b^2*sqrt(b/a)*arctan(a*sqrt(x)*sqrt(b/a)/b) - (3*a^2*x^2 - 5*a*b*x + 15*b^2)*sqrt(x))/a^3]","A",0
1667,1,103,0,0.745933," ","integrate(x^(1/2)/(a+b/x),x, algorithm=""fricas"")","\left[\frac{3 \, b \sqrt{-\frac{b}{a}} \log\left(\frac{a x + 2 \, a \sqrt{x} \sqrt{-\frac{b}{a}} - b}{a x + b}\right) + 2 \, {\left(a x - 3 \, b\right)} \sqrt{x}}{3 \, a^{2}}, \frac{2 \, {\left(3 \, b \sqrt{\frac{b}{a}} \arctan\left(\frac{a \sqrt{x} \sqrt{\frac{b}{a}}}{b}\right) + {\left(a x - 3 \, b\right)} \sqrt{x}\right)}}{3 \, a^{2}}\right]"," ",0,"[1/3*(3*b*sqrt(-b/a)*log((a*x + 2*a*sqrt(x)*sqrt(-b/a) - b)/(a*x + b)) + 2*(a*x - 3*b)*sqrt(x))/a^2, 2/3*(3*b*sqrt(b/a)*arctan(a*sqrt(x)*sqrt(b/a)/b) + (a*x - 3*b)*sqrt(x))/a^2]","A",0
1668,1,85,0,0.677163," ","integrate(1/(a+b/x)/x^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{-\frac{b}{a}} \log\left(\frac{a x - 2 \, a \sqrt{x} \sqrt{-\frac{b}{a}} - b}{a x + b}\right) + 2 \, \sqrt{x}}{a}, -\frac{2 \, {\left(\sqrt{\frac{b}{a}} \arctan\left(\frac{a \sqrt{x} \sqrt{\frac{b}{a}}}{b}\right) - \sqrt{x}\right)}}{a}\right]"," ",0,"[(sqrt(-b/a)*log((a*x - 2*a*sqrt(x)*sqrt(-b/a) - b)/(a*x + b)) + 2*sqrt(x))/a, -2*(sqrt(b/a)*arctan(a*sqrt(x)*sqrt(b/a)/b) - sqrt(x))/a]","A",0
1669,1,68,0,0.809559," ","integrate(1/(a+b/x)/x^(3/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a b} \log\left(\frac{a x - b - 2 \, \sqrt{-a b} \sqrt{x}}{a x + b}\right)}{a b}, -\frac{2 \, \sqrt{a b} \arctan\left(\frac{\sqrt{a b}}{a \sqrt{x}}\right)}{a b}\right]"," ",0,"[-sqrt(-a*b)*log((a*x - b - 2*sqrt(-a*b)*sqrt(x))/(a*x + b))/(a*b), -2*sqrt(a*b)*arctan(sqrt(a*b)/(a*sqrt(x)))/(a*b)]","A",0
1670,1,93,0,0.844383," ","integrate(1/(a+b/x)/x^(5/2),x, algorithm=""fricas"")","\left[\frac{x \sqrt{-\frac{a}{b}} \log\left(\frac{a x - 2 \, b \sqrt{x} \sqrt{-\frac{a}{b}} - b}{a x + b}\right) - 2 \, \sqrt{x}}{b x}, \frac{2 \, {\left(x \sqrt{\frac{a}{b}} \arctan\left(\frac{b \sqrt{\frac{a}{b}}}{a \sqrt{x}}\right) - \sqrt{x}\right)}}{b x}\right]"," ",0,"[(x*sqrt(-a/b)*log((a*x - 2*b*sqrt(x)*sqrt(-a/b) - b)/(a*x + b)) - 2*sqrt(x))/(b*x), 2*(x*sqrt(a/b)*arctan(b*sqrt(a/b)/(a*sqrt(x))) - sqrt(x))/(b*x)]","A",0
1671,1,118,0,0.778373," ","integrate(1/(a+b/x)/x^(7/2),x, algorithm=""fricas"")","\left[\frac{3 \, a x^{2} \sqrt{-\frac{a}{b}} \log\left(\frac{a x + 2 \, b \sqrt{x} \sqrt{-\frac{a}{b}} - b}{a x + b}\right) + 2 \, {\left(3 \, a x - b\right)} \sqrt{x}}{3 \, b^{2} x^{2}}, -\frac{2 \, {\left(3 \, a x^{2} \sqrt{\frac{a}{b}} \arctan\left(\frac{b \sqrt{\frac{a}{b}}}{a \sqrt{x}}\right) - {\left(3 \, a x - b\right)} \sqrt{x}\right)}}{3 \, b^{2} x^{2}}\right]"," ",0,"[1/3*(3*a*x^2*sqrt(-a/b)*log((a*x + 2*b*sqrt(x)*sqrt(-a/b) - b)/(a*x + b)) + 2*(3*a*x - b)*sqrt(x))/(b^2*x^2), -2/3*(3*a*x^2*sqrt(a/b)*arctan(b*sqrt(a/b)/(a*sqrt(x))) - (3*a*x - b)*sqrt(x))/(b^2*x^2)]","A",0
1672,1,144,0,0.846730," ","integrate(1/(a+b/x)/x^(9/2),x, algorithm=""fricas"")","\left[\frac{15 \, a^{2} x^{3} \sqrt{-\frac{a}{b}} \log\left(\frac{a x - 2 \, b \sqrt{x} \sqrt{-\frac{a}{b}} - b}{a x + b}\right) - 2 \, {\left(15 \, a^{2} x^{2} - 5 \, a b x + 3 \, b^{2}\right)} \sqrt{x}}{15 \, b^{3} x^{3}}, \frac{2 \, {\left(15 \, a^{2} x^{3} \sqrt{\frac{a}{b}} \arctan\left(\frac{b \sqrt{\frac{a}{b}}}{a \sqrt{x}}\right) - {\left(15 \, a^{2} x^{2} - 5 \, a b x + 3 \, b^{2}\right)} \sqrt{x}\right)}}{15 \, b^{3} x^{3}}\right]"," ",0,"[1/15*(15*a^2*x^3*sqrt(-a/b)*log((a*x - 2*b*sqrt(x)*sqrt(-a/b) - b)/(a*x + b)) - 2*(15*a^2*x^2 - 5*a*b*x + 3*b^2)*sqrt(x))/(b^3*x^3), 2/15*(15*a^2*x^3*sqrt(a/b)*arctan(b*sqrt(a/b)/(a*sqrt(x))) - (15*a^2*x^2 - 5*a*b*x + 3*b^2)*sqrt(x))/(b^3*x^3)]","A",0
1673,1,209,0,0.926413," ","integrate(x^(5/2)/(a+b/x)^2,x, algorithm=""fricas"")","\left[\frac{315 \, {\left(a b^{3} x + b^{4}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{a x + 2 \, a \sqrt{x} \sqrt{-\frac{b}{a}} - b}{a x + b}\right) + 2 \, {\left(10 \, a^{4} x^{4} - 18 \, a^{3} b x^{3} + 42 \, a^{2} b^{2} x^{2} - 210 \, a b^{3} x - 315 \, b^{4}\right)} \sqrt{x}}{70 \, {\left(a^{6} x + a^{5} b\right)}}, \frac{315 \, {\left(a b^{3} x + b^{4}\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{a \sqrt{x} \sqrt{\frac{b}{a}}}{b}\right) + {\left(10 \, a^{4} x^{4} - 18 \, a^{3} b x^{3} + 42 \, a^{2} b^{2} x^{2} - 210 \, a b^{3} x - 315 \, b^{4}\right)} \sqrt{x}}{35 \, {\left(a^{6} x + a^{5} b\right)}}\right]"," ",0,"[1/70*(315*(a*b^3*x + b^4)*sqrt(-b/a)*log((a*x + 2*a*sqrt(x)*sqrt(-b/a) - b)/(a*x + b)) + 2*(10*a^4*x^4 - 18*a^3*b*x^3 + 42*a^2*b^2*x^2 - 210*a*b^3*x - 315*b^4)*sqrt(x))/(a^6*x + a^5*b), 1/35*(315*(a*b^3*x + b^4)*sqrt(b/a)*arctan(a*sqrt(x)*sqrt(b/a)/b) + (10*a^4*x^4 - 18*a^3*b*x^3 + 42*a^2*b^2*x^2 - 210*a*b^3*x - 315*b^4)*sqrt(x))/(a^6*x + a^5*b)]","A",0
1674,1,188,0,0.750712," ","integrate(x^(3/2)/(a+b/x)^2,x, algorithm=""fricas"")","\left[\frac{105 \, {\left(a b^{2} x + b^{3}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{a x - 2 \, a \sqrt{x} \sqrt{-\frac{b}{a}} - b}{a x + b}\right) + 2 \, {\left(6 \, a^{3} x^{3} - 14 \, a^{2} b x^{2} + 70 \, a b^{2} x + 105 \, b^{3}\right)} \sqrt{x}}{30 \, {\left(a^{5} x + a^{4} b\right)}}, -\frac{105 \, {\left(a b^{2} x + b^{3}\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{a \sqrt{x} \sqrt{\frac{b}{a}}}{b}\right) - {\left(6 \, a^{3} x^{3} - 14 \, a^{2} b x^{2} + 70 \, a b^{2} x + 105 \, b^{3}\right)} \sqrt{x}}{15 \, {\left(a^{5} x + a^{4} b\right)}}\right]"," ",0,"[1/30*(105*(a*b^2*x + b^3)*sqrt(-b/a)*log((a*x - 2*a*sqrt(x)*sqrt(-b/a) - b)/(a*x + b)) + 2*(6*a^3*x^3 - 14*a^2*b*x^2 + 70*a*b^2*x + 105*b^3)*sqrt(x))/(a^5*x + a^4*b), -1/15*(105*(a*b^2*x + b^3)*sqrt(b/a)*arctan(a*sqrt(x)*sqrt(b/a)/b) - (6*a^3*x^3 - 14*a^2*b*x^2 + 70*a*b^2*x + 105*b^3)*sqrt(x))/(a^5*x + a^4*b)]","A",0
1675,1,161,0,0.843893," ","integrate(x^(1/2)/(a+b/x)^2,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(a b x + b^{2}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{a x + 2 \, a \sqrt{x} \sqrt{-\frac{b}{a}} - b}{a x + b}\right) + 2 \, {\left(2 \, a^{2} x^{2} - 10 \, a b x - 15 \, b^{2}\right)} \sqrt{x}}{6 \, {\left(a^{4} x + a^{3} b\right)}}, \frac{15 \, {\left(a b x + b^{2}\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{a \sqrt{x} \sqrt{\frac{b}{a}}}{b}\right) + {\left(2 \, a^{2} x^{2} - 10 \, a b x - 15 \, b^{2}\right)} \sqrt{x}}{3 \, {\left(a^{4} x + a^{3} b\right)}}\right]"," ",0,"[1/6*(15*(a*b*x + b^2)*sqrt(-b/a)*log((a*x + 2*a*sqrt(x)*sqrt(-b/a) - b)/(a*x + b)) + 2*(2*a^2*x^2 - 10*a*b*x - 15*b^2)*sqrt(x))/(a^4*x + a^3*b), 1/3*(15*(a*b*x + b^2)*sqrt(b/a)*arctan(a*sqrt(x)*sqrt(b/a)/b) + (2*a^2*x^2 - 10*a*b*x - 15*b^2)*sqrt(x))/(a^4*x + a^3*b)]","A",0
1676,1,134,0,0.688194," ","integrate(1/(a+b/x)^2/x^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a x + b\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{a x - 2 \, a \sqrt{x} \sqrt{-\frac{b}{a}} - b}{a x + b}\right) + 2 \, {\left(2 \, a x + 3 \, b\right)} \sqrt{x}}{2 \, {\left(a^{3} x + a^{2} b\right)}}, -\frac{3 \, {\left(a x + b\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{a \sqrt{x} \sqrt{\frac{b}{a}}}{b}\right) - {\left(2 \, a x + 3 \, b\right)} \sqrt{x}}{a^{3} x + a^{2} b}\right]"," ",0,"[1/2*(3*(a*x + b)*sqrt(-b/a)*log((a*x - 2*a*sqrt(x)*sqrt(-b/a) - b)/(a*x + b)) + 2*(2*a*x + 3*b)*sqrt(x))/(a^3*x + a^2*b), -(3*(a*x + b)*sqrt(b/a)*arctan(a*sqrt(x)*sqrt(b/a)/b) - (2*a*x + 3*b)*sqrt(x))/(a^3*x + a^2*b)]","A",0
1677,1,115,0,0.540626," ","integrate(1/(a+b/x)^2/x^(3/2),x, algorithm=""fricas"")","\left[-\frac{2 \, a b \sqrt{x} + \sqrt{-a b} {\left(a x + b\right)} \log\left(\frac{a x - b - 2 \, \sqrt{-a b} \sqrt{x}}{a x + b}\right)}{2 \, {\left(a^{3} b x + a^{2} b^{2}\right)}}, -\frac{a b \sqrt{x} + \sqrt{a b} {\left(a x + b\right)} \arctan\left(\frac{\sqrt{a b}}{a \sqrt{x}}\right)}{a^{3} b x + a^{2} b^{2}}\right]"," ",0,"[-1/2*(2*a*b*sqrt(x) + sqrt(-a*b)*(a*x + b)*log((a*x - b - 2*sqrt(-a*b)*sqrt(x))/(a*x + b)))/(a^3*b*x + a^2*b^2), -(a*b*sqrt(x) + sqrt(a*b)*(a*x + b)*arctan(sqrt(a*b)/(a*sqrt(x))))/(a^3*b*x + a^2*b^2)]","A",0
1678,1,116,0,0.760024," ","integrate(1/(a+b/x)^2/x^(5/2),x, algorithm=""fricas"")","\left[\frac{2 \, a b \sqrt{x} - \sqrt{-a b} {\left(a x + b\right)} \log\left(\frac{a x - b - 2 \, \sqrt{-a b} \sqrt{x}}{a x + b}\right)}{2 \, {\left(a^{2} b^{2} x + a b^{3}\right)}}, \frac{a b \sqrt{x} - \sqrt{a b} {\left(a x + b\right)} \arctan\left(\frac{\sqrt{a b}}{a \sqrt{x}}\right)}{a^{2} b^{2} x + a b^{3}}\right]"," ",0,"[1/2*(2*a*b*sqrt(x) - sqrt(-a*b)*(a*x + b)*log((a*x - b - 2*sqrt(-a*b)*sqrt(x))/(a*x + b)))/(a^2*b^2*x + a*b^3), (a*b*sqrt(x) - sqrt(a*b)*(a*x + b)*arctan(sqrt(a*b)/(a*sqrt(x))))/(a^2*b^2*x + a*b^3)]","A",0
1679,1,147,0,0.788550," ","integrate(1/(a+b/x)^2/x^(7/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a x^{2} + b x\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{a x - 2 \, b \sqrt{x} \sqrt{-\frac{a}{b}} - b}{a x + b}\right) - 2 \, {\left(3 \, a x + 2 \, b\right)} \sqrt{x}}{2 \, {\left(a b^{2} x^{2} + b^{3} x\right)}}, \frac{3 \, {\left(a x^{2} + b x\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b \sqrt{\frac{a}{b}}}{a \sqrt{x}}\right) - {\left(3 \, a x + 2 \, b\right)} \sqrt{x}}{a b^{2} x^{2} + b^{3} x}\right]"," ",0,"[1/2*(3*(a*x^2 + b*x)*sqrt(-a/b)*log((a*x - 2*b*sqrt(x)*sqrt(-a/b) - b)/(a*x + b)) - 2*(3*a*x + 2*b)*sqrt(x))/(a*b^2*x^2 + b^3*x), (3*(a*x^2 + b*x)*sqrt(a/b)*arctan(b*sqrt(a/b)/(a*sqrt(x))) - (3*a*x + 2*b)*sqrt(x))/(a*b^2*x^2 + b^3*x)]","A",0
1680,1,184,0,0.831774," ","integrate(1/(a+b/x)^2/x^(9/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(a^{2} x^{3} + a b x^{2}\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{a x + 2 \, b \sqrt{x} \sqrt{-\frac{a}{b}} - b}{a x + b}\right) + 2 \, {\left(15 \, a^{2} x^{2} + 10 \, a b x - 2 \, b^{2}\right)} \sqrt{x}}{6 \, {\left(a b^{3} x^{3} + b^{4} x^{2}\right)}}, -\frac{15 \, {\left(a^{2} x^{3} + a b x^{2}\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b \sqrt{\frac{a}{b}}}{a \sqrt{x}}\right) - {\left(15 \, a^{2} x^{2} + 10 \, a b x - 2 \, b^{2}\right)} \sqrt{x}}{3 \, {\left(a b^{3} x^{3} + b^{4} x^{2}\right)}}\right]"," ",0,"[1/6*(15*(a^2*x^3 + a*b*x^2)*sqrt(-a/b)*log((a*x + 2*b*sqrt(x)*sqrt(-a/b) - b)/(a*x + b)) + 2*(15*a^2*x^2 + 10*a*b*x - 2*b^2)*sqrt(x))/(a*b^3*x^3 + b^4*x^2), -1/3*(15*(a^2*x^3 + a*b*x^2)*sqrt(a/b)*arctan(b*sqrt(a/b)/(a*sqrt(x))) - (15*a^2*x^2 + 10*a*b*x - 2*b^2)*sqrt(x))/(a*b^3*x^3 + b^4*x^2)]","A",0
1681,1,210,0,0.768461," ","integrate(1/(a+b/x)^2/x^(11/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(a^{3} x^{4} + a^{2} b x^{3}\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{a x - 2 \, b \sqrt{x} \sqrt{-\frac{a}{b}} - b}{a x + b}\right) - 2 \, {\left(105 \, a^{3} x^{3} + 70 \, a^{2} b x^{2} - 14 \, a b^{2} x + 6 \, b^{3}\right)} \sqrt{x}}{30 \, {\left(a b^{4} x^{4} + b^{5} x^{3}\right)}}, \frac{105 \, {\left(a^{3} x^{4} + a^{2} b x^{3}\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b \sqrt{\frac{a}{b}}}{a \sqrt{x}}\right) - {\left(105 \, a^{3} x^{3} + 70 \, a^{2} b x^{2} - 14 \, a b^{2} x + 6 \, b^{3}\right)} \sqrt{x}}{15 \, {\left(a b^{4} x^{4} + b^{5} x^{3}\right)}}\right]"," ",0,"[1/30*(105*(a^3*x^4 + a^2*b*x^3)*sqrt(-a/b)*log((a*x - 2*b*sqrt(x)*sqrt(-a/b) - b)/(a*x + b)) - 2*(105*a^3*x^3 + 70*a^2*b*x^2 - 14*a*b^2*x + 6*b^3)*sqrt(x))/(a*b^4*x^4 + b^5*x^3), 1/15*(105*(a^3*x^4 + a^2*b*x^3)*sqrt(a/b)*arctan(b*sqrt(a/b)/(a*sqrt(x))) - (105*a^3*x^3 + 70*a^2*b*x^2 - 14*a*b^2*x + 6*b^3)*sqrt(x))/(a*b^4*x^4 + b^5*x^3)]","A",0
1682,1,254,0,0.781742," ","integrate(x^(3/2)/(a+b/x)^3,x, algorithm=""fricas"")","\left[\frac{315 \, {\left(a^{2} b^{2} x^{2} + 2 \, a b^{3} x + b^{4}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{a x - 2 \, a \sqrt{x} \sqrt{-\frac{b}{a}} - b}{a x + b}\right) + 2 \, {\left(8 \, a^{4} x^{4} - 24 \, a^{3} b x^{3} + 168 \, a^{2} b^{2} x^{2} + 525 \, a b^{3} x + 315 \, b^{4}\right)} \sqrt{x}}{40 \, {\left(a^{7} x^{2} + 2 \, a^{6} b x + a^{5} b^{2}\right)}}, -\frac{315 \, {\left(a^{2} b^{2} x^{2} + 2 \, a b^{3} x + b^{4}\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{a \sqrt{x} \sqrt{\frac{b}{a}}}{b}\right) - {\left(8 \, a^{4} x^{4} - 24 \, a^{3} b x^{3} + 168 \, a^{2} b^{2} x^{2} + 525 \, a b^{3} x + 315 \, b^{4}\right)} \sqrt{x}}{20 \, {\left(a^{7} x^{2} + 2 \, a^{6} b x + a^{5} b^{2}\right)}}\right]"," ",0,"[1/40*(315*(a^2*b^2*x^2 + 2*a*b^3*x + b^4)*sqrt(-b/a)*log((a*x - 2*a*sqrt(x)*sqrt(-b/a) - b)/(a*x + b)) + 2*(8*a^4*x^4 - 24*a^3*b*x^3 + 168*a^2*b^2*x^2 + 525*a*b^3*x + 315*b^4)*sqrt(x))/(a^7*x^2 + 2*a^6*b*x + a^5*b^2), -1/20*(315*(a^2*b^2*x^2 + 2*a*b^3*x + b^4)*sqrt(b/a)*arctan(a*sqrt(x)*sqrt(b/a)/b) - (8*a^4*x^4 - 24*a^3*b*x^3 + 168*a^2*b^2*x^2 + 525*a*b^3*x + 315*b^4)*sqrt(x))/(a^7*x^2 + 2*a^6*b*x + a^5*b^2)]","A",0
1683,1,227,0,0.869103," ","integrate(x^(1/2)/(a+b/x)^3,x, algorithm=""fricas"")","\left[\frac{105 \, {\left(a^{2} b x^{2} + 2 \, a b^{2} x + b^{3}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{a x + 2 \, a \sqrt{x} \sqrt{-\frac{b}{a}} - b}{a x + b}\right) + 2 \, {\left(8 \, a^{3} x^{3} - 56 \, a^{2} b x^{2} - 175 \, a b^{2} x - 105 \, b^{3}\right)} \sqrt{x}}{24 \, {\left(a^{6} x^{2} + 2 \, a^{5} b x + a^{4} b^{2}\right)}}, \frac{105 \, {\left(a^{2} b x^{2} + 2 \, a b^{2} x + b^{3}\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{a \sqrt{x} \sqrt{\frac{b}{a}}}{b}\right) + {\left(8 \, a^{3} x^{3} - 56 \, a^{2} b x^{2} - 175 \, a b^{2} x - 105 \, b^{3}\right)} \sqrt{x}}{12 \, {\left(a^{6} x^{2} + 2 \, a^{5} b x + a^{4} b^{2}\right)}}\right]"," ",0,"[1/24*(105*(a^2*b*x^2 + 2*a*b^2*x + b^3)*sqrt(-b/a)*log((a*x + 2*a*sqrt(x)*sqrt(-b/a) - b)/(a*x + b)) + 2*(8*a^3*x^3 - 56*a^2*b*x^2 - 175*a*b^2*x - 105*b^3)*sqrt(x))/(a^6*x^2 + 2*a^5*b*x + a^4*b^2), 1/12*(105*(a^2*b*x^2 + 2*a*b^2*x + b^3)*sqrt(b/a)*arctan(a*sqrt(x)*sqrt(b/a)/b) + (8*a^3*x^3 - 56*a^2*b*x^2 - 175*a*b^2*x - 105*b^3)*sqrt(x))/(a^6*x^2 + 2*a^5*b*x + a^4*b^2)]","A",0
1684,1,200,0,0.827024," ","integrate(1/(a+b/x)^3/x^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(a^{2} x^{2} + 2 \, a b x + b^{2}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{a x - 2 \, a \sqrt{x} \sqrt{-\frac{b}{a}} - b}{a x + b}\right) + 2 \, {\left(8 \, a^{2} x^{2} + 25 \, a b x + 15 \, b^{2}\right)} \sqrt{x}}{8 \, {\left(a^{5} x^{2} + 2 \, a^{4} b x + a^{3} b^{2}\right)}}, -\frac{15 \, {\left(a^{2} x^{2} + 2 \, a b x + b^{2}\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{a \sqrt{x} \sqrt{\frac{b}{a}}}{b}\right) - {\left(8 \, a^{2} x^{2} + 25 \, a b x + 15 \, b^{2}\right)} \sqrt{x}}{4 \, {\left(a^{5} x^{2} + 2 \, a^{4} b x + a^{3} b^{2}\right)}}\right]"," ",0,"[1/8*(15*(a^2*x^2 + 2*a*b*x + b^2)*sqrt(-b/a)*log((a*x - 2*a*sqrt(x)*sqrt(-b/a) - b)/(a*x + b)) + 2*(8*a^2*x^2 + 25*a*b*x + 15*b^2)*sqrt(x))/(a^5*x^2 + 2*a^4*b*x + a^3*b^2), -1/4*(15*(a^2*x^2 + 2*a*b*x + b^2)*sqrt(b/a)*arctan(a*sqrt(x)*sqrt(b/a)/b) - (8*a^2*x^2 + 25*a*b*x + 15*b^2)*sqrt(x))/(a^5*x^2 + 2*a^4*b*x + a^3*b^2)]","A",0
1685,1,185,0,0.699469," ","integrate(1/(a+b/x)^3/x^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(a^{2} x^{2} + 2 \, a b x + b^{2}\right)} \sqrt{-a b} \log\left(\frac{a x - b - 2 \, \sqrt{-a b} \sqrt{x}}{a x + b}\right) + 2 \, {\left(5 \, a^{2} b x + 3 \, a b^{2}\right)} \sqrt{x}}{8 \, {\left(a^{5} b x^{2} + 2 \, a^{4} b^{2} x + a^{3} b^{3}\right)}}, -\frac{3 \, {\left(a^{2} x^{2} + 2 \, a b x + b^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b}}{a \sqrt{x}}\right) + {\left(5 \, a^{2} b x + 3 \, a b^{2}\right)} \sqrt{x}}{4 \, {\left(a^{5} b x^{2} + 2 \, a^{4} b^{2} x + a^{3} b^{3}\right)}}\right]"," ",0,"[-1/8*(3*(a^2*x^2 + 2*a*b*x + b^2)*sqrt(-a*b)*log((a*x - b - 2*sqrt(-a*b)*sqrt(x))/(a*x + b)) + 2*(5*a^2*b*x + 3*a*b^2)*sqrt(x))/(a^5*b*x^2 + 2*a^4*b^2*x + a^3*b^3), -1/4*(3*(a^2*x^2 + 2*a*b*x + b^2)*sqrt(a*b)*arctan(sqrt(a*b)/(a*sqrt(x))) + (5*a^2*b*x + 3*a*b^2)*sqrt(x))/(a^5*b*x^2 + 2*a^4*b^2*x + a^3*b^3)]","A",0
1686,1,186,0,0.805448," ","integrate(1/(a+b/x)^3/x^(5/2),x, algorithm=""fricas"")","\left[-\frac{{\left(a^{2} x^{2} + 2 \, a b x + b^{2}\right)} \sqrt{-a b} \log\left(\frac{a x - b - 2 \, \sqrt{-a b} \sqrt{x}}{a x + b}\right) - 2 \, {\left(a^{2} b x - a b^{2}\right)} \sqrt{x}}{8 \, {\left(a^{4} b^{2} x^{2} + 2 \, a^{3} b^{3} x + a^{2} b^{4}\right)}}, -\frac{{\left(a^{2} x^{2} + 2 \, a b x + b^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b}}{a \sqrt{x}}\right) - {\left(a^{2} b x - a b^{2}\right)} \sqrt{x}}{4 \, {\left(a^{4} b^{2} x^{2} + 2 \, a^{3} b^{3} x + a^{2} b^{4}\right)}}\right]"," ",0,"[-1/8*((a^2*x^2 + 2*a*b*x + b^2)*sqrt(-a*b)*log((a*x - b - 2*sqrt(-a*b)*sqrt(x))/(a*x + b)) - 2*(a^2*b*x - a*b^2)*sqrt(x))/(a^4*b^2*x^2 + 2*a^3*b^3*x + a^2*b^4), -1/4*((a^2*x^2 + 2*a*b*x + b^2)*sqrt(a*b)*arctan(sqrt(a*b)/(a*sqrt(x))) - (a^2*b*x - a*b^2)*sqrt(x))/(a^4*b^2*x^2 + 2*a^3*b^3*x + a^2*b^4)]","A",0
1687,1,186,0,0.776356," ","integrate(1/(a+b/x)^3/x^(7/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(a^{2} x^{2} + 2 \, a b x + b^{2}\right)} \sqrt{-a b} \log\left(\frac{a x - b - 2 \, \sqrt{-a b} \sqrt{x}}{a x + b}\right) - 2 \, {\left(3 \, a^{2} b x + 5 \, a b^{2}\right)} \sqrt{x}}{8 \, {\left(a^{3} b^{3} x^{2} + 2 \, a^{2} b^{4} x + a b^{5}\right)}}, -\frac{3 \, {\left(a^{2} x^{2} + 2 \, a b x + b^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b}}{a \sqrt{x}}\right) - {\left(3 \, a^{2} b x + 5 \, a b^{2}\right)} \sqrt{x}}{4 \, {\left(a^{3} b^{3} x^{2} + 2 \, a^{2} b^{4} x + a b^{5}\right)}}\right]"," ",0,"[-1/8*(3*(a^2*x^2 + 2*a*b*x + b^2)*sqrt(-a*b)*log((a*x - b - 2*sqrt(-a*b)*sqrt(x))/(a*x + b)) - 2*(3*a^2*b*x + 5*a*b^2)*sqrt(x))/(a^3*b^3*x^2 + 2*a^2*b^4*x + a*b^5), -1/4*(3*(a^2*x^2 + 2*a*b*x + b^2)*sqrt(a*b)*arctan(sqrt(a*b)/(a*sqrt(x))) - (3*a^2*b*x + 5*a*b^2)*sqrt(x))/(a^3*b^3*x^2 + 2*a^2*b^4*x + a*b^5)]","A",0
1688,1,214,0,0.679913," ","integrate(1/(a+b/x)^3/x^(9/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(a^{2} x^{3} + 2 \, a b x^{2} + b^{2} x\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{a x - 2 \, b \sqrt{x} \sqrt{-\frac{a}{b}} - b}{a x + b}\right) - 2 \, {\left(15 \, a^{2} x^{2} + 25 \, a b x + 8 \, b^{2}\right)} \sqrt{x}}{8 \, {\left(a^{2} b^{3} x^{3} + 2 \, a b^{4} x^{2} + b^{5} x\right)}}, \frac{15 \, {\left(a^{2} x^{3} + 2 \, a b x^{2} + b^{2} x\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b \sqrt{\frac{a}{b}}}{a \sqrt{x}}\right) - {\left(15 \, a^{2} x^{2} + 25 \, a b x + 8 \, b^{2}\right)} \sqrt{x}}{4 \, {\left(a^{2} b^{3} x^{3} + 2 \, a b^{4} x^{2} + b^{5} x\right)}}\right]"," ",0,"[1/8*(15*(a^2*x^3 + 2*a*b*x^2 + b^2*x)*sqrt(-a/b)*log((a*x - 2*b*sqrt(x)*sqrt(-a/b) - b)/(a*x + b)) - 2*(15*a^2*x^2 + 25*a*b*x + 8*b^2)*sqrt(x))/(a^2*b^3*x^3 + 2*a*b^4*x^2 + b^5*x), 1/4*(15*(a^2*x^3 + 2*a*b*x^2 + b^2*x)*sqrt(a/b)*arctan(b*sqrt(a/b)/(a*sqrt(x))) - (15*a^2*x^2 + 25*a*b*x + 8*b^2)*sqrt(x))/(a^2*b^3*x^3 + 2*a*b^4*x^2 + b^5*x)]","A",0
1689,1,250,0,0.800919," ","integrate(1/(a+b/x)^3/x^(11/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(a^{3} x^{4} + 2 \, a^{2} b x^{3} + a b^{2} x^{2}\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{a x + 2 \, b \sqrt{x} \sqrt{-\frac{a}{b}} - b}{a x + b}\right) + 2 \, {\left(105 \, a^{3} x^{3} + 175 \, a^{2} b x^{2} + 56 \, a b^{2} x - 8 \, b^{3}\right)} \sqrt{x}}{24 \, {\left(a^{2} b^{4} x^{4} + 2 \, a b^{5} x^{3} + b^{6} x^{2}\right)}}, -\frac{105 \, {\left(a^{3} x^{4} + 2 \, a^{2} b x^{3} + a b^{2} x^{2}\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b \sqrt{\frac{a}{b}}}{a \sqrt{x}}\right) - {\left(105 \, a^{3} x^{3} + 175 \, a^{2} b x^{2} + 56 \, a b^{2} x - 8 \, b^{3}\right)} \sqrt{x}}{12 \, {\left(a^{2} b^{4} x^{4} + 2 \, a b^{5} x^{3} + b^{6} x^{2}\right)}}\right]"," ",0,"[1/24*(105*(a^3*x^4 + 2*a^2*b*x^3 + a*b^2*x^2)*sqrt(-a/b)*log((a*x + 2*b*sqrt(x)*sqrt(-a/b) - b)/(a*x + b)) + 2*(105*a^3*x^3 + 175*a^2*b*x^2 + 56*a*b^2*x - 8*b^3)*sqrt(x))/(a^2*b^4*x^4 + 2*a*b^5*x^3 + b^6*x^2), -1/12*(105*(a^3*x^4 + 2*a^2*b*x^3 + a*b^2*x^2)*sqrt(a/b)*arctan(b*sqrt(a/b)/(a*sqrt(x))) - (105*a^3*x^3 + 175*a^2*b*x^2 + 56*a*b^2*x - 8*b^3)*sqrt(x))/(a^2*b^4*x^4 + 2*a*b^5*x^3 + b^6*x^2)]","A",0
1690,1,276,0,1.118824," ","integrate(1/(a+b/x)^3/x^(13/2),x, algorithm=""fricas"")","\left[\frac{315 \, {\left(a^{4} x^{5} + 2 \, a^{3} b x^{4} + a^{2} b^{2} x^{3}\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{a x - 2 \, b \sqrt{x} \sqrt{-\frac{a}{b}} - b}{a x + b}\right) - 2 \, {\left(315 \, a^{4} x^{4} + 525 \, a^{3} b x^{3} + 168 \, a^{2} b^{2} x^{2} - 24 \, a b^{3} x + 8 \, b^{4}\right)} \sqrt{x}}{40 \, {\left(a^{2} b^{5} x^{5} + 2 \, a b^{6} x^{4} + b^{7} x^{3}\right)}}, \frac{315 \, {\left(a^{4} x^{5} + 2 \, a^{3} b x^{4} + a^{2} b^{2} x^{3}\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b \sqrt{\frac{a}{b}}}{a \sqrt{x}}\right) - {\left(315 \, a^{4} x^{4} + 525 \, a^{3} b x^{3} + 168 \, a^{2} b^{2} x^{2} - 24 \, a b^{3} x + 8 \, b^{4}\right)} \sqrt{x}}{20 \, {\left(a^{2} b^{5} x^{5} + 2 \, a b^{6} x^{4} + b^{7} x^{3}\right)}}\right]"," ",0,"[1/40*(315*(a^4*x^5 + 2*a^3*b*x^4 + a^2*b^2*x^3)*sqrt(-a/b)*log((a*x - 2*b*sqrt(x)*sqrt(-a/b) - b)/(a*x + b)) - 2*(315*a^4*x^4 + 525*a^3*b*x^3 + 168*a^2*b^2*x^2 - 24*a*b^3*x + 8*b^4)*sqrt(x))/(a^2*b^5*x^5 + 2*a*b^6*x^4 + b^7*x^3), 1/20*(315*(a^4*x^5 + 2*a^3*b*x^4 + a^2*b^2*x^3)*sqrt(a/b)*arctan(b*sqrt(a/b)/(a*sqrt(x))) - (315*a^4*x^4 + 525*a^3*b*x^3 + 168*a^2*b^2*x^2 - 24*a*b^3*x + 8*b^4)*sqrt(x))/(a^2*b^5*x^5 + 2*a*b^6*x^4 + b^7*x^3)]","A",0
1691,1,173,0,0.856162," ","integrate(x^3*(a+b/x)^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, \sqrt{a} b^{4} \log\left(2 \, a x - 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + 2 \, {\left(48 \, a^{4} x^{4} + 8 \, a^{3} b x^{3} - 10 \, a^{2} b^{2} x^{2} + 15 \, a b^{3} x\right)} \sqrt{\frac{a x + b}{x}}}{384 \, a^{4}}, \frac{15 \, \sqrt{-a} b^{4} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) + {\left(48 \, a^{4} x^{4} + 8 \, a^{3} b x^{3} - 10 \, a^{2} b^{2} x^{2} + 15 \, a b^{3} x\right)} \sqrt{\frac{a x + b}{x}}}{192 \, a^{4}}\right]"," ",0,"[1/384*(15*sqrt(a)*b^4*log(2*a*x - 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + 2*(48*a^4*x^4 + 8*a^3*b*x^3 - 10*a^2*b^2*x^2 + 15*a*b^3*x)*sqrt((a*x + b)/x))/a^4, 1/192*(15*sqrt(-a)*b^4*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) + (48*a^4*x^4 + 8*a^3*b*x^3 - 10*a^2*b^2*x^2 + 15*a*b^3*x)*sqrt((a*x + b)/x))/a^4]","A",0
1692,1,152,0,1.071125," ","integrate(x^2*(a+b/x)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{a} b^{3} \log\left(2 \, a x + 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + 2 \, {\left(8 \, a^{3} x^{3} + 2 \, a^{2} b x^{2} - 3 \, a b^{2} x\right)} \sqrt{\frac{a x + b}{x}}}{48 \, a^{3}}, -\frac{3 \, \sqrt{-a} b^{3} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) - {\left(8 \, a^{3} x^{3} + 2 \, a^{2} b x^{2} - 3 \, a b^{2} x\right)} \sqrt{\frac{a x + b}{x}}}{24 \, a^{3}}\right]"," ",0,"[1/48*(3*sqrt(a)*b^3*log(2*a*x + 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + 2*(8*a^3*x^3 + 2*a^2*b*x^2 - 3*a*b^2*x)*sqrt((a*x + b)/x))/a^3, -1/24*(3*sqrt(-a)*b^3*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) - (8*a^3*x^3 + 2*a^2*b*x^2 - 3*a*b^2*x)*sqrt((a*x + b)/x))/a^3]","A",0
1693,1,125,0,0.580933," ","integrate(x*(a+b/x)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a} b^{2} \log\left(2 \, a x - 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + 2 \, {\left(2 \, a^{2} x^{2} + a b x\right)} \sqrt{\frac{a x + b}{x}}}{8 \, a^{2}}, \frac{\sqrt{-a} b^{2} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) + {\left(2 \, a^{2} x^{2} + a b x\right)} \sqrt{\frac{a x + b}{x}}}{4 \, a^{2}}\right]"," ",0,"[1/8*(sqrt(a)*b^2*log(2*a*x - 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + 2*(2*a^2*x^2 + a*b*x)*sqrt((a*x + b)/x))/a^2, 1/4*(sqrt(-a)*b^2*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) + (2*a^2*x^2 + a*b*x)*sqrt((a*x + b)/x))/a^2]","A",0
1694,1,99,0,0.837650," ","integrate((a+b/x)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, a x \sqrt{\frac{a x + b}{x}} + \sqrt{a} b \log\left(2 \, a x + 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right)}{2 \, a}, \frac{a x \sqrt{\frac{a x + b}{x}} - \sqrt{-a} b \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right)}{a}\right]"," ",0,"[1/2*(2*a*x*sqrt((a*x + b)/x) + sqrt(a)*b*log(2*a*x + 2*sqrt(a)*x*sqrt((a*x + b)/x) + b))/a, (a*x*sqrt((a*x + b)/x) - sqrt(-a)*b*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a))/a]","A",0
1695,1,85,0,0.755536," ","integrate((a+b/x)^(1/2)/x,x, algorithm=""fricas"")","\left[\sqrt{a} \log\left(2 \, a x + 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) - 2 \, \sqrt{\frac{a x + b}{x}}, -2 \, \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) - 2 \, \sqrt{\frac{a x + b}{x}}\right]"," ",0,"[sqrt(a)*log(2*a*x + 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) - 2*sqrt((a*x + b)/x), -2*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) - 2*sqrt((a*x + b)/x)]","A",0
1696,1,24,0,0.743363," ","integrate((a+b/x)^(1/2)/x^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(a x + b\right)} \sqrt{\frac{a x + b}{x}}}{3 \, b x}"," ",0,"-2/3*(a*x + b)*sqrt((a*x + b)/x)/(b*x)","A",0
1697,1,38,0,0.844181," ","integrate((a+b/x)^(1/2)/x^3,x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, a^{2} x^{2} - a b x - 3 \, b^{2}\right)} \sqrt{\frac{a x + b}{x}}}{15 \, b^{2} x^{2}}"," ",0,"2/15*(2*a^2*x^2 - a*b*x - 3*b^2)*sqrt((a*x + b)/x)/(b^2*x^2)","A",0
1698,1,49,0,0.805621," ","integrate((a+b/x)^(1/2)/x^4,x, algorithm=""fricas"")","-\frac{2 \, {\left(8 \, a^{3} x^{3} - 4 \, a^{2} b x^{2} + 3 \, a b^{2} x + 15 \, b^{3}\right)} \sqrt{\frac{a x + b}{x}}}{105 \, b^{3} x^{3}}"," ",0,"-2/105*(8*a^3*x^3 - 4*a^2*b*x^2 + 3*a*b^2*x + 15*b^3)*sqrt((a*x + b)/x)/(b^3*x^3)","A",0
1699,1,60,0,0.762997," ","integrate((a+b/x)^(1/2)/x^5,x, algorithm=""fricas"")","\frac{2 \, {\left(16 \, a^{4} x^{4} - 8 \, a^{3} b x^{3} + 6 \, a^{2} b^{2} x^{2} - 5 \, a b^{3} x - 35 \, b^{4}\right)} \sqrt{\frac{a x + b}{x}}}{315 \, b^{4} x^{4}}"," ",0,"2/315*(16*a^4*x^4 - 8*a^3*b*x^3 + 6*a^2*b^2*x^2 - 5*a*b^3*x - 35*b^4)*sqrt((a*x + b)/x)/(b^4*x^4)","A",0
1700,1,71,0,0.742114," ","integrate((a+b/x)^(1/2)/x^6,x, algorithm=""fricas"")","-\frac{2 \, {\left(128 \, a^{5} x^{5} - 64 \, a^{4} b x^{4} + 48 \, a^{3} b^{2} x^{3} - 40 \, a^{2} b^{3} x^{2} + 35 \, a b^{4} x + 315 \, b^{5}\right)} \sqrt{\frac{a x + b}{x}}}{3465 \, b^{5} x^{5}}"," ",0,"-2/3465*(128*a^5*x^5 - 64*a^4*b*x^4 + 48*a^3*b^2*x^3 - 40*a^2*b^3*x^2 + 35*a*b^4*x + 315*b^5)*sqrt((a*x + b)/x)/(b^5*x^5)","A",0
1701,1,174,0,0.651837," ","integrate((a+b/x)^(3/2)*x^3,x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{a} b^{4} \log\left(2 \, a x + 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + 2 \, {\left(16 \, a^{4} x^{4} + 24 \, a^{3} b x^{3} + 2 \, a^{2} b^{2} x^{2} - 3 \, a b^{3} x\right)} \sqrt{\frac{a x + b}{x}}}{128 \, a^{3}}, -\frac{3 \, \sqrt{-a} b^{4} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) - {\left(16 \, a^{4} x^{4} + 24 \, a^{3} b x^{3} + 2 \, a^{2} b^{2} x^{2} - 3 \, a b^{3} x\right)} \sqrt{\frac{a x + b}{x}}}{64 \, a^{3}}\right]"," ",0,"[1/128*(3*sqrt(a)*b^4*log(2*a*x + 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + 2*(16*a^4*x^4 + 24*a^3*b*x^3 + 2*a^2*b^2*x^2 - 3*a*b^3*x)*sqrt((a*x + b)/x))/a^3, -1/64*(3*sqrt(-a)*b^4*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) - (16*a^4*x^4 + 24*a^3*b*x^3 + 2*a^2*b^2*x^2 - 3*a*b^3*x)*sqrt((a*x + b)/x))/a^3]","A",0
1702,1,151,0,0.829694," ","integrate((a+b/x)^(3/2)*x^2,x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{a} b^{3} \log\left(2 \, a x - 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + 2 \, {\left(8 \, a^{3} x^{3} + 14 \, a^{2} b x^{2} + 3 \, a b^{2} x\right)} \sqrt{\frac{a x + b}{x}}}{48 \, a^{2}}, \frac{3 \, \sqrt{-a} b^{3} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) + {\left(8 \, a^{3} x^{3} + 14 \, a^{2} b x^{2} + 3 \, a b^{2} x\right)} \sqrt{\frac{a x + b}{x}}}{24 \, a^{2}}\right]"," ",0,"[1/48*(3*sqrt(a)*b^3*log(2*a*x - 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + 2*(8*a^3*x^3 + 14*a^2*b*x^2 + 3*a*b^2*x)*sqrt((a*x + b)/x))/a^2, 1/24*(3*sqrt(-a)*b^3*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) + (8*a^3*x^3 + 14*a^2*b*x^2 + 3*a*b^2*x)*sqrt((a*x + b)/x))/a^2]","A",0
1703,1,130,0,0.552974," ","integrate((a+b/x)^(3/2)*x,x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{a} b^{2} \log\left(2 \, a x + 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + 2 \, {\left(2 \, a^{2} x^{2} + 5 \, a b x\right)} \sqrt{\frac{a x + b}{x}}}{8 \, a}, -\frac{3 \, \sqrt{-a} b^{2} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) - {\left(2 \, a^{2} x^{2} + 5 \, a b x\right)} \sqrt{\frac{a x + b}{x}}}{4 \, a}\right]"," ",0,"[1/8*(3*sqrt(a)*b^2*log(2*a*x + 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + 2*(2*a^2*x^2 + 5*a*b*x)*sqrt((a*x + b)/x))/a, -1/4*(3*sqrt(-a)*b^2*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) - (2*a^2*x^2 + 5*a*b*x)*sqrt((a*x + b)/x))/a]","A",0
1704,1,100,0,0.853885," ","integrate((a+b/x)^(3/2),x, algorithm=""fricas"")","\left[\frac{3}{2} \, \sqrt{a} b \log\left(2 \, a x + 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + {\left(a x - 2 \, b\right)} \sqrt{\frac{a x + b}{x}}, -3 \, \sqrt{-a} b \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) + {\left(a x - 2 \, b\right)} \sqrt{\frac{a x + b}{x}}\right]"," ",0,"[3/2*sqrt(a)*b*log(2*a*x + 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + (a*x - 2*b)*sqrt((a*x + b)/x), -3*sqrt(-a)*b*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) + (a*x - 2*b)*sqrt((a*x + b)/x)]","A",0
1705,1,110,0,0.674565," ","integrate((a+b/x)^(3/2)/x,x, algorithm=""fricas"")","\left[\frac{3 \, a^{\frac{3}{2}} x \log\left(2 \, a x + 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) - 2 \, {\left(4 \, a x + b\right)} \sqrt{\frac{a x + b}{x}}}{3 \, x}, -\frac{2 \, {\left(3 \, \sqrt{-a} a x \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) + {\left(4 \, a x + b\right)} \sqrt{\frac{a x + b}{x}}\right)}}{3 \, x}\right]"," ",0,"[1/3*(3*a^(3/2)*x*log(2*a*x + 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) - 2*(4*a*x + b)*sqrt((a*x + b)/x))/x, -2/3*(3*sqrt(-a)*a*x*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) + (4*a*x + b)*sqrt((a*x + b)/x))/x]","A",0
1706,1,35,0,0.817491," ","integrate((a+b/x)^(3/2)/x^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(a^{2} x^{2} + 2 \, a b x + b^{2}\right)} \sqrt{\frac{a x + b}{x}}}{5 \, b x^{2}}"," ",0,"-2/5*(a^2*x^2 + 2*a*b*x + b^2)*sqrt((a*x + b)/x)/(b*x^2)","B",0
1707,1,49,0,0.808631," ","integrate((a+b/x)^(3/2)/x^3,x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, a^{3} x^{3} - a^{2} b x^{2} - 8 \, a b^{2} x - 5 \, b^{3}\right)} \sqrt{\frac{a x + b}{x}}}{35 \, b^{2} x^{3}}"," ",0,"2/35*(2*a^3*x^3 - a^2*b*x^2 - 8*a*b^2*x - 5*b^3)*sqrt((a*x + b)/x)/(b^2*x^3)","A",0
1708,1,60,0,0.688752," ","integrate((a+b/x)^(3/2)/x^4,x, algorithm=""fricas"")","-\frac{2 \, {\left(8 \, a^{4} x^{4} - 4 \, a^{3} b x^{3} + 3 \, a^{2} b^{2} x^{2} + 50 \, a b^{3} x + 35 \, b^{4}\right)} \sqrt{\frac{a x + b}{x}}}{315 \, b^{3} x^{4}}"," ",0,"-2/315*(8*a^4*x^4 - 4*a^3*b*x^3 + 3*a^2*b^2*x^2 + 50*a*b^3*x + 35*b^4)*sqrt((a*x + b)/x)/(b^3*x^4)","A",0
1709,1,71,0,0.724595," ","integrate((a+b/x)^(3/2)/x^5,x, algorithm=""fricas"")","\frac{2 \, {\left(16 \, a^{5} x^{5} - 8 \, a^{4} b x^{4} + 6 \, a^{3} b^{2} x^{3} - 5 \, a^{2} b^{3} x^{2} - 140 \, a b^{4} x - 105 \, b^{5}\right)} \sqrt{\frac{a x + b}{x}}}{1155 \, b^{4} x^{5}}"," ",0,"2/1155*(16*a^5*x^5 - 8*a^4*b*x^4 + 6*a^3*b^2*x^3 - 5*a^2*b^3*x^2 - 140*a*b^4*x - 105*b^5)*sqrt((a*x + b)/x)/(b^4*x^5)","A",0
1710,1,82,0,0.602141," ","integrate((a+b/x)^(3/2)/x^6,x, algorithm=""fricas"")","-\frac{2 \, {\left(128 \, a^{6} x^{6} - 64 \, a^{5} b x^{5} + 48 \, a^{4} b^{2} x^{4} - 40 \, a^{3} b^{3} x^{3} + 35 \, a^{2} b^{4} x^{2} + 1470 \, a b^{5} x + 1155 \, b^{6}\right)} \sqrt{\frac{a x + b}{x}}}{15015 \, b^{5} x^{6}}"," ",0,"-2/15015*(128*a^6*x^6 - 64*a^5*b*x^5 + 48*a^4*b^2*x^4 - 40*a^3*b^3*x^3 + 35*a^2*b^4*x^2 + 1470*a*b^5*x + 1155*b^6)*sqrt((a*x + b)/x)/(b^5*x^6)","A",0
1711,1,93,0,0.788498," ","integrate((a+b/x)^(3/2)/x^7,x, algorithm=""fricas"")","\frac{2 \, {\left(256 \, a^{7} x^{7} - 128 \, a^{6} b x^{6} + 96 \, a^{5} b^{2} x^{5} - 80 \, a^{4} b^{3} x^{4} + 70 \, a^{3} b^{4} x^{3} - 63 \, a^{2} b^{5} x^{2} - 3696 \, a b^{6} x - 3003 \, b^{7}\right)} \sqrt{\frac{a x + b}{x}}}{45045 \, b^{6} x^{7}}"," ",0,"2/45045*(256*a^7*x^7 - 128*a^6*b*x^6 + 96*a^5*b^2*x^5 - 80*a^4*b^3*x^4 + 70*a^3*b^4*x^3 - 63*a^2*b^5*x^2 - 3696*a*b^6*x - 3003*b^7)*sqrt((a*x + b)/x)/(b^6*x^7)","A",0
1712,1,173,0,0.917346," ","integrate((a+b/x)^(5/2)*x^3,x, algorithm=""fricas"")","\left[\frac{15 \, \sqrt{a} b^{4} \log\left(2 \, a x - 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + 2 \, {\left(48 \, a^{4} x^{4} + 136 \, a^{3} b x^{3} + 118 \, a^{2} b^{2} x^{2} + 15 \, a b^{3} x\right)} \sqrt{\frac{a x + b}{x}}}{384 \, a^{2}}, \frac{15 \, \sqrt{-a} b^{4} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) + {\left(48 \, a^{4} x^{4} + 136 \, a^{3} b x^{3} + 118 \, a^{2} b^{2} x^{2} + 15 \, a b^{3} x\right)} \sqrt{\frac{a x + b}{x}}}{192 \, a^{2}}\right]"," ",0,"[1/384*(15*sqrt(a)*b^4*log(2*a*x - 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + 2*(48*a^4*x^4 + 136*a^3*b*x^3 + 118*a^2*b^2*x^2 + 15*a*b^3*x)*sqrt((a*x + b)/x))/a^2, 1/192*(15*sqrt(-a)*b^4*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) + (48*a^4*x^4 + 136*a^3*b*x^3 + 118*a^2*b^2*x^2 + 15*a*b^3*x)*sqrt((a*x + b)/x))/a^2]","A",0
1713,1,152,0,0.842409," ","integrate((a+b/x)^(5/2)*x^2,x, algorithm=""fricas"")","\left[\frac{15 \, \sqrt{a} b^{3} \log\left(2 \, a x + 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + 2 \, {\left(8 \, a^{3} x^{3} + 26 \, a^{2} b x^{2} + 33 \, a b^{2} x\right)} \sqrt{\frac{a x + b}{x}}}{48 \, a}, -\frac{15 \, \sqrt{-a} b^{3} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) - {\left(8 \, a^{3} x^{3} + 26 \, a^{2} b x^{2} + 33 \, a b^{2} x\right)} \sqrt{\frac{a x + b}{x}}}{24 \, a}\right]"," ",0,"[1/48*(15*sqrt(a)*b^3*log(2*a*x + 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + 2*(8*a^3*x^3 + 26*a^2*b*x^2 + 33*a*b^2*x)*sqrt((a*x + b)/x))/a, -1/24*(15*sqrt(-a)*b^3*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) - (8*a^3*x^3 + 26*a^2*b*x^2 + 33*a*b^2*x)*sqrt((a*x + b)/x))/a]","A",0
1714,1,130,0,0.615662," ","integrate((a+b/x)^(5/2)*x,x, algorithm=""fricas"")","\left[\frac{15}{8} \, \sqrt{a} b^{2} \log\left(2 \, a x + 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + \frac{1}{4} \, {\left(2 \, a^{2} x^{2} + 9 \, a b x - 8 \, b^{2}\right)} \sqrt{\frac{a x + b}{x}}, -\frac{15}{4} \, \sqrt{-a} b^{2} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) + \frac{1}{4} \, {\left(2 \, a^{2} x^{2} + 9 \, a b x - 8 \, b^{2}\right)} \sqrt{\frac{a x + b}{x}}\right]"," ",0,"[15/8*sqrt(a)*b^2*log(2*a*x + 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + 1/4*(2*a^2*x^2 + 9*a*b*x - 8*b^2)*sqrt((a*x + b)/x), -15/4*sqrt(-a)*b^2*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) + 1/4*(2*a^2*x^2 + 9*a*b*x - 8*b^2)*sqrt((a*x + b)/x)]","A",0
1715,1,139,0,0.596905," ","integrate((a+b/x)^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, a^{\frac{3}{2}} b x \log\left(2 \, a x + 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + 2 \, {\left(3 \, a^{2} x^{2} - 14 \, a b x - 2 \, b^{2}\right)} \sqrt{\frac{a x + b}{x}}}{6 \, x}, -\frac{15 \, \sqrt{-a} a b x \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) - {\left(3 \, a^{2} x^{2} - 14 \, a b x - 2 \, b^{2}\right)} \sqrt{\frac{a x + b}{x}}}{3 \, x}\right]"," ",0,"[1/6*(15*a^(3/2)*b*x*log(2*a*x + 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + 2*(3*a^2*x^2 - 14*a*b*x - 2*b^2)*sqrt((a*x + b)/x))/x, -1/3*(15*sqrt(-a)*a*b*x*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) - (3*a^2*x^2 - 14*a*b*x - 2*b^2)*sqrt((a*x + b)/x))/x]","A",0
1716,1,142,0,0.769813," ","integrate((a+b/x)^(5/2)/x,x, algorithm=""fricas"")","\left[\frac{15 \, a^{\frac{5}{2}} x^{2} \log\left(2 \, a x + 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) - 2 \, {\left(23 \, a^{2} x^{2} + 11 \, a b x + 3 \, b^{2}\right)} \sqrt{\frac{a x + b}{x}}}{15 \, x^{2}}, -\frac{2 \, {\left(15 \, \sqrt{-a} a^{2} x^{2} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) + {\left(23 \, a^{2} x^{2} + 11 \, a b x + 3 \, b^{2}\right)} \sqrt{\frac{a x + b}{x}}\right)}}{15 \, x^{2}}\right]"," ",0,"[1/15*(15*a^(5/2)*x^2*log(2*a*x + 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) - 2*(23*a^2*x^2 + 11*a*b*x + 3*b^2)*sqrt((a*x + b)/x))/x^2, -2/15*(15*sqrt(-a)*a^2*x^2*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) + (23*a^2*x^2 + 11*a*b*x + 3*b^2)*sqrt((a*x + b)/x))/x^2]","A",0
1717,1,46,0,0.827596," ","integrate((a+b/x)^(5/2)/x^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(a^{3} x^{3} + 3 \, a^{2} b x^{2} + 3 \, a b^{2} x + b^{3}\right)} \sqrt{\frac{a x + b}{x}}}{7 \, b x^{3}}"," ",0,"-2/7*(a^3*x^3 + 3*a^2*b*x^2 + 3*a*b^2*x + b^3)*sqrt((a*x + b)/x)/(b*x^3)","B",0
1718,1,60,0,0.762757," ","integrate((a+b/x)^(5/2)/x^3,x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, a^{4} x^{4} - a^{3} b x^{3} - 15 \, a^{2} b^{2} x^{2} - 19 \, a b^{3} x - 7 \, b^{4}\right)} \sqrt{\frac{a x + b}{x}}}{63 \, b^{2} x^{4}}"," ",0,"2/63*(2*a^4*x^4 - a^3*b*x^3 - 15*a^2*b^2*x^2 - 19*a*b^3*x - 7*b^4)*sqrt((a*x + b)/x)/(b^2*x^4)","A",0
1719,1,71,0,0.712853," ","integrate((a+b/x)^(5/2)/x^4,x, algorithm=""fricas"")","-\frac{2 \, {\left(8 \, a^{5} x^{5} - 4 \, a^{4} b x^{4} + 3 \, a^{3} b^{2} x^{3} + 113 \, a^{2} b^{3} x^{2} + 161 \, a b^{4} x + 63 \, b^{5}\right)} \sqrt{\frac{a x + b}{x}}}{693 \, b^{3} x^{5}}"," ",0,"-2/693*(8*a^5*x^5 - 4*a^4*b*x^4 + 3*a^3*b^2*x^3 + 113*a^2*b^3*x^2 + 161*a*b^4*x + 63*b^5)*sqrt((a*x + b)/x)/(b^3*x^5)","A",0
1720,1,82,0,0.589817," ","integrate((a+b/x)^(5/2)/x^5,x, algorithm=""fricas"")","\frac{2 \, {\left(16 \, a^{6} x^{6} - 8 \, a^{5} b x^{5} + 6 \, a^{4} b^{2} x^{4} - 5 \, a^{3} b^{3} x^{3} - 371 \, a^{2} b^{4} x^{2} - 567 \, a b^{5} x - 231 \, b^{6}\right)} \sqrt{\frac{a x + b}{x}}}{3003 \, b^{4} x^{6}}"," ",0,"2/3003*(16*a^6*x^6 - 8*a^5*b*x^5 + 6*a^4*b^2*x^4 - 5*a^3*b^3*x^3 - 371*a^2*b^4*x^2 - 567*a*b^5*x - 231*b^6)*sqrt((a*x + b)/x)/(b^4*x^6)","A",0
1721,1,93,0,0.894990," ","integrate((a+b/x)^(5/2)/x^6,x, algorithm=""fricas"")","-\frac{2 \, {\left(128 \, a^{7} x^{7} - 64 \, a^{6} b x^{6} + 48 \, a^{5} b^{2} x^{5} - 40 \, a^{4} b^{3} x^{4} + 35 \, a^{3} b^{4} x^{3} + 4473 \, a^{2} b^{5} x^{2} + 7161 \, a b^{6} x + 3003 \, b^{7}\right)} \sqrt{\frac{a x + b}{x}}}{45045 \, b^{5} x^{7}}"," ",0,"-2/45045*(128*a^7*x^7 - 64*a^6*b*x^6 + 48*a^5*b^2*x^5 - 40*a^4*b^3*x^4 + 35*a^3*b^4*x^3 + 4473*a^2*b^5*x^2 + 7161*a*b^6*x + 3003*b^7)*sqrt((a*x + b)/x)/(b^5*x^7)","A",0
1722,1,174,0,1.176036," ","integrate(x^3/(a+b/x)^(1/2),x, algorithm=""fricas"")","\left[\frac{105 \, \sqrt{a} b^{4} \log\left(2 \, a x + 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + 2 \, {\left(48 \, a^{4} x^{4} - 56 \, a^{3} b x^{3} + 70 \, a^{2} b^{2} x^{2} - 105 \, a b^{3} x\right)} \sqrt{\frac{a x + b}{x}}}{384 \, a^{5}}, -\frac{105 \, \sqrt{-a} b^{4} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) - {\left(48 \, a^{4} x^{4} - 56 \, a^{3} b x^{3} + 70 \, a^{2} b^{2} x^{2} - 105 \, a b^{3} x\right)} \sqrt{\frac{a x + b}{x}}}{192 \, a^{5}}\right]"," ",0,"[1/384*(105*sqrt(a)*b^4*log(2*a*x + 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + 2*(48*a^4*x^4 - 56*a^3*b*x^3 + 70*a^2*b^2*x^2 - 105*a*b^3*x)*sqrt((a*x + b)/x))/a^5, -1/192*(105*sqrt(-a)*b^4*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) - (48*a^4*x^4 - 56*a^3*b*x^3 + 70*a^2*b^2*x^2 - 105*a*b^3*x)*sqrt((a*x + b)/x))/a^5]","A",0
1723,1,151,0,0.806068," ","integrate(x^2/(a+b/x)^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, \sqrt{a} b^{3} \log\left(2 \, a x - 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + 2 \, {\left(8 \, a^{3} x^{3} - 10 \, a^{2} b x^{2} + 15 \, a b^{2} x\right)} \sqrt{\frac{a x + b}{x}}}{48 \, a^{4}}, \frac{15 \, \sqrt{-a} b^{3} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) + {\left(8 \, a^{3} x^{3} - 10 \, a^{2} b x^{2} + 15 \, a b^{2} x\right)} \sqrt{\frac{a x + b}{x}}}{24 \, a^{4}}\right]"," ",0,"[1/48*(15*sqrt(a)*b^3*log(2*a*x - 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + 2*(8*a^3*x^3 - 10*a^2*b*x^2 + 15*a*b^2*x)*sqrt((a*x + b)/x))/a^4, 1/24*(15*sqrt(-a)*b^3*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) + (8*a^3*x^3 - 10*a^2*b*x^2 + 15*a*b^2*x)*sqrt((a*x + b)/x))/a^4]","A",0
1724,1,130,0,0.790225," ","integrate(x/(a+b/x)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{a} b^{2} \log\left(2 \, a x + 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + 2 \, {\left(2 \, a^{2} x^{2} - 3 \, a b x\right)} \sqrt{\frac{a x + b}{x}}}{8 \, a^{3}}, -\frac{3 \, \sqrt{-a} b^{2} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) - {\left(2 \, a^{2} x^{2} - 3 \, a b x\right)} \sqrt{\frac{a x + b}{x}}}{4 \, a^{3}}\right]"," ",0,"[1/8*(3*sqrt(a)*b^2*log(2*a*x + 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + 2*(2*a^2*x^2 - 3*a*b*x)*sqrt((a*x + b)/x))/a^3, -1/4*(3*sqrt(-a)*b^2*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) - (2*a^2*x^2 - 3*a*b*x)*sqrt((a*x + b)/x))/a^3]","A",0
1725,1,98,0,0.875809," ","integrate(1/(a+b/x)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, a x \sqrt{\frac{a x + b}{x}} + \sqrt{a} b \log\left(2 \, a x - 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right)}{2 \, a^{2}}, \frac{a x \sqrt{\frac{a x + b}{x}} + \sqrt{-a} b \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right)}{a^{2}}\right]"," ",0,"[1/2*(2*a*x*sqrt((a*x + b)/x) + sqrt(a)*b*log(2*a*x - 2*sqrt(a)*x*sqrt((a*x + b)/x) + b))/a^2, (a*x*sqrt((a*x + b)/x) + sqrt(-a)*b*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a))/a^2]","A",0
1726,1,60,0,0.611734," ","integrate(1/x/(a+b/x)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(2 \, a x + 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right)}{\sqrt{a}}, -\frac{2 \, \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right)}{a}\right]"," ",0,"[log(2*a*x + 2*sqrt(a)*x*sqrt((a*x + b)/x) + b)/sqrt(a), -2*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a)/a]","A",0
1727,1,16,0,0.847306," ","integrate(1/x^2/(a+b/x)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{\frac{a x + b}{x}}}{b}"," ",0,"-2*sqrt((a*x + b)/x)/b","A",0
1728,1,27,0,0.633494," ","integrate(1/x^3/(a+b/x)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, a x - b\right)} \sqrt{\frac{a x + b}{x}}}{3 \, b^{2} x}"," ",0,"2/3*(2*a*x - b)*sqrt((a*x + b)/x)/(b^2*x)","A",0
1729,1,38,0,0.886179," ","integrate(1/x^4/(a+b/x)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(8 \, a^{2} x^{2} - 4 \, a b x + 3 \, b^{2}\right)} \sqrt{\frac{a x + b}{x}}}{15 \, b^{3} x^{2}}"," ",0,"-2/15*(8*a^2*x^2 - 4*a*b*x + 3*b^2)*sqrt((a*x + b)/x)/(b^3*x^2)","A",0
1730,1,49,0,0.802967," ","integrate(1/x^5/(a+b/x)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(16 \, a^{3} x^{3} - 8 \, a^{2} b x^{2} + 6 \, a b^{2} x - 5 \, b^{3}\right)} \sqrt{\frac{a x + b}{x}}}{35 \, b^{4} x^{3}}"," ",0,"2/35*(16*a^3*x^3 - 8*a^2*b*x^2 + 6*a*b^2*x - 5*b^3)*sqrt((a*x + b)/x)/(b^4*x^3)","A",0
1731,1,60,0,0.808678," ","integrate(1/x^6/(a+b/x)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(128 \, a^{4} x^{4} - 64 \, a^{3} b x^{3} + 48 \, a^{2} b^{2} x^{2} - 40 \, a b^{3} x + 35 \, b^{4}\right)} \sqrt{\frac{a x + b}{x}}}{315 \, b^{5} x^{4}}"," ",0,"-2/315*(128*a^4*x^4 - 64*a^3*b*x^3 + 48*a^2*b^2*x^2 - 40*a*b^3*x + 35*b^4)*sqrt((a*x + b)/x)/(b^5*x^4)","A",0
1732,1,207,0,0.872087," ","integrate(x^2/(a+b/x)^(3/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(a b^{3} x + b^{4}\right)} \sqrt{a} \log\left(2 \, a x - 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + 2 \, {\left(8 \, a^{4} x^{4} - 14 \, a^{3} b x^{3} + 35 \, a^{2} b^{2} x^{2} + 105 \, a b^{3} x\right)} \sqrt{\frac{a x + b}{x}}}{48 \, {\left(a^{6} x + a^{5} b\right)}}, \frac{105 \, {\left(a b^{3} x + b^{4}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) + {\left(8 \, a^{4} x^{4} - 14 \, a^{3} b x^{3} + 35 \, a^{2} b^{2} x^{2} + 105 \, a b^{3} x\right)} \sqrt{\frac{a x + b}{x}}}{24 \, {\left(a^{6} x + a^{5} b\right)}}\right]"," ",0,"[1/48*(105*(a*b^3*x + b^4)*sqrt(a)*log(2*a*x - 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + 2*(8*a^4*x^4 - 14*a^3*b*x^3 + 35*a^2*b^2*x^2 + 105*a*b^3*x)*sqrt((a*x + b)/x))/(a^6*x + a^5*b), 1/24*(105*(a*b^3*x + b^4)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) + (8*a^4*x^4 - 14*a^3*b*x^3 + 35*a^2*b^2*x^2 + 105*a*b^3*x)*sqrt((a*x + b)/x))/(a^6*x + a^5*b)]","A",0
1733,1,186,0,0.805350," ","integrate(x/(a+b/x)^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(a b^{2} x + b^{3}\right)} \sqrt{a} \log\left(2 \, a x + 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + 2 \, {\left(2 \, a^{3} x^{3} - 5 \, a^{2} b x^{2} - 15 \, a b^{2} x\right)} \sqrt{\frac{a x + b}{x}}}{8 \, {\left(a^{5} x + a^{4} b\right)}}, -\frac{15 \, {\left(a b^{2} x + b^{3}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) - {\left(2 \, a^{3} x^{3} - 5 \, a^{2} b x^{2} - 15 \, a b^{2} x\right)} \sqrt{\frac{a x + b}{x}}}{4 \, {\left(a^{5} x + a^{4} b\right)}}\right]"," ",0,"[1/8*(15*(a*b^2*x + b^3)*sqrt(a)*log(2*a*x + 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + 2*(2*a^3*x^3 - 5*a^2*b*x^2 - 15*a*b^2*x)*sqrt((a*x + b)/x))/(a^5*x + a^4*b), -1/4*(15*(a*b^2*x + b^3)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) - (2*a^3*x^3 - 5*a^2*b*x^2 - 15*a*b^2*x)*sqrt((a*x + b)/x))/(a^5*x + a^4*b)]","A",0
1734,1,156,0,0.609163," ","integrate(1/(a+b/x)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a b x + b^{2}\right)} \sqrt{a} \log\left(2 \, a x - 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + 2 \, {\left(a^{2} x^{2} + 3 \, a b x\right)} \sqrt{\frac{a x + b}{x}}}{2 \, {\left(a^{4} x + a^{3} b\right)}}, \frac{3 \, {\left(a b x + b^{2}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) + {\left(a^{2} x^{2} + 3 \, a b x\right)} \sqrt{\frac{a x + b}{x}}}{a^{4} x + a^{3} b}\right]"," ",0,"[1/2*(3*(a*b*x + b^2)*sqrt(a)*log(2*a*x - 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + 2*(a^2*x^2 + 3*a*b*x)*sqrt((a*x + b)/x))/(a^4*x + a^3*b), (3*(a*b*x + b^2)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) + (a^2*x^2 + 3*a*b*x)*sqrt((a*x + b)/x))/(a^4*x + a^3*b)]","A",0
1735,1,128,0,0.840833," ","integrate(1/(a+b/x)^(3/2)/x,x, algorithm=""fricas"")","\left[-\frac{2 \, a x \sqrt{\frac{a x + b}{x}} - {\left(a x + b\right)} \sqrt{a} \log\left(2 \, a x + 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right)}{a^{3} x + a^{2} b}, -\frac{2 \, {\left(a x \sqrt{\frac{a x + b}{x}} + {\left(a x + b\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right)\right)}}{a^{3} x + a^{2} b}\right]"," ",0,"[-(2*a*x*sqrt((a*x + b)/x) - (a*x + b)*sqrt(a)*log(2*a*x + 2*sqrt(a)*x*sqrt((a*x + b)/x) + b))/(a^3*x + a^2*b), -2*(a*x*sqrt((a*x + b)/x) + (a*x + b)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a))/(a^3*x + a^2*b)]","A",0
1736,1,24,0,0.750521," ","integrate(1/(a+b/x)^(3/2)/x^2,x, algorithm=""fricas"")","\frac{2 \, x \sqrt{\frac{a x + b}{x}}}{a b x + b^{2}}"," ",0,"2*x*sqrt((a*x + b)/x)/(a*b*x + b^2)","A",0
1737,1,31,0,0.748449," ","integrate(1/(a+b/x)^(3/2)/x^3,x, algorithm=""fricas"")","-\frac{2 \, {\left(2 \, a x + b\right)} \sqrt{\frac{a x + b}{x}}}{a b^{2} x + b^{3}}"," ",0,"-2*(2*a*x + b)*sqrt((a*x + b)/x)/(a*b^2*x + b^3)","A",0
1738,1,48,0,0.820978," ","integrate(1/(a+b/x)^(3/2)/x^4,x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, a^{2} x^{2} + 4 \, a b x - b^{2}\right)} \sqrt{\frac{a x + b}{x}}}{3 \, {\left(a b^{3} x^{2} + b^{4} x\right)}}"," ",0,"2/3*(8*a^2*x^2 + 4*a*b*x - b^2)*sqrt((a*x + b)/x)/(a*b^3*x^2 + b^4*x)","A",0
1739,1,59,0,0.815319," ","integrate(1/(a+b/x)^(3/2)/x^5,x, algorithm=""fricas"")","-\frac{2 \, {\left(16 \, a^{3} x^{3} + 8 \, a^{2} b x^{2} - 2 \, a b^{2} x + b^{3}\right)} \sqrt{\frac{a x + b}{x}}}{5 \, {\left(a b^{4} x^{3} + b^{5} x^{2}\right)}}"," ",0,"-2/5*(16*a^3*x^3 + 8*a^2*b*x^2 - 2*a*b^2*x + b^3)*sqrt((a*x + b)/x)/(a*b^4*x^3 + b^5*x^2)","A",0
1740,1,72,0,0.616984," ","integrate(1/(a+b/x)^(3/2)/x^6,x, algorithm=""fricas"")","\frac{2 \, {\left(128 \, a^{4} x^{4} + 64 \, a^{3} b x^{3} - 16 \, a^{2} b^{2} x^{2} + 8 \, a b^{3} x - 5 \, b^{4}\right)} \sqrt{\frac{a x + b}{x}}}{35 \, {\left(a b^{5} x^{4} + b^{6} x^{3}\right)}}"," ",0,"2/35*(128*a^4*x^4 + 64*a^3*b*x^3 - 16*a^2*b^2*x^2 + 8*a*b^3*x - 5*b^4)*sqrt((a*x + b)/x)/(a*b^5*x^4 + b^6*x^3)","A",0
1741,1,83,0,0.669325," ","integrate(1/(a+b/x)^(3/2)/x^7,x, algorithm=""fricas"")","-\frac{2 \, {\left(256 \, a^{5} x^{5} + 128 \, a^{4} b x^{4} - 32 \, a^{3} b^{2} x^{3} + 16 \, a^{2} b^{3} x^{2} - 10 \, a b^{4} x + 7 \, b^{5}\right)} \sqrt{\frac{a x + b}{x}}}{63 \, {\left(a b^{6} x^{5} + b^{7} x^{4}\right)}}"," ",0,"-2/63*(256*a^5*x^5 + 128*a^4*b*x^4 - 32*a^3*b^2*x^3 + 16*a^2*b^3*x^2 - 10*a*b^4*x + 7*b^5)*sqrt((a*x + b)/x)/(a*b^6*x^5 + b^7*x^4)","A",0
1742,1,273,0,0.843830," ","integrate(x^2/(a+b/x)^(5/2),x, algorithm=""fricas"")","\left[\frac{315 \, {\left(a^{2} b^{3} x^{2} + 2 \, a b^{4} x + b^{5}\right)} \sqrt{a} \log\left(2 \, a x - 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + 2 \, {\left(8 \, a^{5} x^{5} - 18 \, a^{4} b x^{4} + 63 \, a^{3} b^{2} x^{3} + 420 \, a^{2} b^{3} x^{2} + 315 \, a b^{4} x\right)} \sqrt{\frac{a x + b}{x}}}{48 \, {\left(a^{8} x^{2} + 2 \, a^{7} b x + a^{6} b^{2}\right)}}, \frac{315 \, {\left(a^{2} b^{3} x^{2} + 2 \, a b^{4} x + b^{5}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) + {\left(8 \, a^{5} x^{5} - 18 \, a^{4} b x^{4} + 63 \, a^{3} b^{2} x^{3} + 420 \, a^{2} b^{3} x^{2} + 315 \, a b^{4} x\right)} \sqrt{\frac{a x + b}{x}}}{24 \, {\left(a^{8} x^{2} + 2 \, a^{7} b x + a^{6} b^{2}\right)}}\right]"," ",0,"[1/48*(315*(a^2*b^3*x^2 + 2*a*b^4*x + b^5)*sqrt(a)*log(2*a*x - 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + 2*(8*a^5*x^5 - 18*a^4*b*x^4 + 63*a^3*b^2*x^3 + 420*a^2*b^3*x^2 + 315*a*b^4*x)*sqrt((a*x + b)/x))/(a^8*x^2 + 2*a^7*b*x + a^6*b^2), 1/24*(315*(a^2*b^3*x^2 + 2*a*b^4*x + b^5)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) + (8*a^5*x^5 - 18*a^4*b*x^4 + 63*a^3*b^2*x^3 + 420*a^2*b^3*x^2 + 315*a*b^4*x)*sqrt((a*x + b)/x))/(a^8*x^2 + 2*a^7*b*x + a^6*b^2)]","A",0
1743,1,252,0,0.884431," ","integrate(x/(a+b/x)^(5/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(a^{2} b^{2} x^{2} + 2 \, a b^{3} x + b^{4}\right)} \sqrt{a} \log\left(2 \, a x + 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + 2 \, {\left(6 \, a^{4} x^{4} - 21 \, a^{3} b x^{3} - 140 \, a^{2} b^{2} x^{2} - 105 \, a b^{3} x\right)} \sqrt{\frac{a x + b}{x}}}{24 \, {\left(a^{7} x^{2} + 2 \, a^{6} b x + a^{5} b^{2}\right)}}, -\frac{105 \, {\left(a^{2} b^{2} x^{2} + 2 \, a b^{3} x + b^{4}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) - {\left(6 \, a^{4} x^{4} - 21 \, a^{3} b x^{3} - 140 \, a^{2} b^{2} x^{2} - 105 \, a b^{3} x\right)} \sqrt{\frac{a x + b}{x}}}{12 \, {\left(a^{7} x^{2} + 2 \, a^{6} b x + a^{5} b^{2}\right)}}\right]"," ",0,"[1/24*(105*(a^2*b^2*x^2 + 2*a*b^3*x + b^4)*sqrt(a)*log(2*a*x + 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + 2*(6*a^4*x^4 - 21*a^3*b*x^3 - 140*a^2*b^2*x^2 - 105*a*b^3*x)*sqrt((a*x + b)/x))/(a^7*x^2 + 2*a^6*b*x + a^5*b^2), -1/12*(105*(a^2*b^2*x^2 + 2*a*b^3*x + b^4)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) - (6*a^4*x^4 - 21*a^3*b*x^3 - 140*a^2*b^2*x^2 - 105*a*b^3*x)*sqrt((a*x + b)/x))/(a^7*x^2 + 2*a^6*b*x + a^5*b^2)]","A",0
1744,1,225,0,0.703702," ","integrate(1/(a+b/x)^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(a^{2} b x^{2} + 2 \, a b^{2} x + b^{3}\right)} \sqrt{a} \log\left(2 \, a x - 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) + 2 \, {\left(3 \, a^{3} x^{3} + 20 \, a^{2} b x^{2} + 15 \, a b^{2} x\right)} \sqrt{\frac{a x + b}{x}}}{6 \, {\left(a^{6} x^{2} + 2 \, a^{5} b x + a^{4} b^{2}\right)}}, \frac{15 \, {\left(a^{2} b x^{2} + 2 \, a b^{2} x + b^{3}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) + {\left(3 \, a^{3} x^{3} + 20 \, a^{2} b x^{2} + 15 \, a b^{2} x\right)} \sqrt{\frac{a x + b}{x}}}{3 \, {\left(a^{6} x^{2} + 2 \, a^{5} b x + a^{4} b^{2}\right)}}\right]"," ",0,"[1/6*(15*(a^2*b*x^2 + 2*a*b^2*x + b^3)*sqrt(a)*log(2*a*x - 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) + 2*(3*a^3*x^3 + 20*a^2*b*x^2 + 15*a*b^2*x)*sqrt((a*x + b)/x))/(a^6*x^2 + 2*a^5*b*x + a^4*b^2), 1/3*(15*(a^2*b*x^2 + 2*a*b^2*x + b^3)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) + (3*a^3*x^3 + 20*a^2*b*x^2 + 15*a*b^2*x)*sqrt((a*x + b)/x))/(a^6*x^2 + 2*a^5*b*x + a^4*b^2)]","A",0
1745,1,197,0,0.952649," ","integrate(1/(a+b/x)^(5/2)/x,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a^{2} x^{2} + 2 \, a b x + b^{2}\right)} \sqrt{a} \log\left(2 \, a x + 2 \, \sqrt{a} x \sqrt{\frac{a x + b}{x}} + b\right) - 2 \, {\left(4 \, a^{2} x^{2} + 3 \, a b x\right)} \sqrt{\frac{a x + b}{x}}}{3 \, {\left(a^{5} x^{2} + 2 \, a^{4} b x + a^{3} b^{2}\right)}}, -\frac{2 \, {\left(3 \, {\left(a^{2} x^{2} + 2 \, a b x + b^{2}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{\frac{a x + b}{x}}}{a}\right) + {\left(4 \, a^{2} x^{2} + 3 \, a b x\right)} \sqrt{\frac{a x + b}{x}}\right)}}{3 \, {\left(a^{5} x^{2} + 2 \, a^{4} b x + a^{3} b^{2}\right)}}\right]"," ",0,"[1/3*(3*(a^2*x^2 + 2*a*b*x + b^2)*sqrt(a)*log(2*a*x + 2*sqrt(a)*x*sqrt((a*x + b)/x) + b) - 2*(4*a^2*x^2 + 3*a*b*x)*sqrt((a*x + b)/x))/(a^5*x^2 + 2*a^4*b*x + a^3*b^2), -2/3*(3*(a^2*x^2 + 2*a*b*x + b^2)*sqrt(-a)*arctan(sqrt(-a)*sqrt((a*x + b)/x)/a) + (4*a^2*x^2 + 3*a*b*x)*sqrt((a*x + b)/x))/(a^5*x^2 + 2*a^4*b*x + a^3*b^2)]","B",0
1746,1,37,0,0.818902," ","integrate(1/(a+b/x)^(5/2)/x^2,x, algorithm=""fricas"")","\frac{2 \, x^{2} \sqrt{\frac{a x + b}{x}}}{3 \, {\left(a^{2} b x^{2} + 2 \, a b^{2} x + b^{3}\right)}}"," ",0,"2/3*x^2*sqrt((a*x + b)/x)/(a^2*b*x^2 + 2*a*b^2*x + b^3)","B",0
1747,1,47,0,0.884317," ","integrate(1/(a+b/x)^(5/2)/x^3,x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, a x^{2} + 3 \, b x\right)} \sqrt{\frac{a x + b}{x}}}{3 \, {\left(a^{2} b^{2} x^{2} + 2 \, a b^{3} x + b^{4}\right)}}"," ",0,"2/3*(2*a*x^2 + 3*b*x)*sqrt((a*x + b)/x)/(a^2*b^2*x^2 + 2*a*b^3*x + b^4)","A",0
1748,1,55,0,0.611793," ","integrate(1/(a+b/x)^(5/2)/x^4,x, algorithm=""fricas"")","-\frac{2 \, {\left(8 \, a^{2} x^{2} + 12 \, a b x + 3 \, b^{2}\right)} \sqrt{\frac{a x + b}{x}}}{3 \, {\left(a^{2} b^{3} x^{2} + 2 \, a b^{4} x + b^{5}\right)}}"," ",0,"-2/3*(8*a^2*x^2 + 12*a*b*x + 3*b^2)*sqrt((a*x + b)/x)/(a^2*b^3*x^2 + 2*a*b^4*x + b^5)","A",0
1749,1,70,0,0.787305," ","integrate(1/(a+b/x)^(5/2)/x^5,x, algorithm=""fricas"")","\frac{2 \, {\left(16 \, a^{3} x^{3} + 24 \, a^{2} b x^{2} + 6 \, a b^{2} x - b^{3}\right)} \sqrt{\frac{a x + b}{x}}}{3 \, {\left(a^{2} b^{4} x^{3} + 2 \, a b^{5} x^{2} + b^{6} x\right)}}"," ",0,"2/3*(16*a^3*x^3 + 24*a^2*b*x^2 + 6*a*b^2*x - b^3)*sqrt((a*x + b)/x)/(a^2*b^4*x^3 + 2*a*b^5*x^2 + b^6*x)","A",0
1750,1,83,0,0.615376," ","integrate(1/(a+b/x)^(5/2)/x^6,x, algorithm=""fricas"")","-\frac{2 \, {\left(128 \, a^{4} x^{4} + 192 \, a^{3} b x^{3} + 48 \, a^{2} b^{2} x^{2} - 8 \, a b^{3} x + 3 \, b^{4}\right)} \sqrt{\frac{a x + b}{x}}}{15 \, {\left(a^{2} b^{5} x^{4} + 2 \, a b^{6} x^{3} + b^{7} x^{2}\right)}}"," ",0,"-2/15*(128*a^4*x^4 + 192*a^3*b*x^3 + 48*a^2*b^2*x^2 - 8*a*b^3*x + 3*b^4)*sqrt((a*x + b)/x)/(a^2*b^5*x^4 + 2*a*b^6*x^3 + b^7*x^2)","A",0
1751,1,94,0,0.691513," ","integrate(1/(a+b/x)^(5/2)/x^7,x, algorithm=""fricas"")","\frac{2 \, {\left(256 \, a^{5} x^{5} + 384 \, a^{4} b x^{4} + 96 \, a^{3} b^{2} x^{3} - 16 \, a^{2} b^{3} x^{2} + 6 \, a b^{4} x - 3 \, b^{5}\right)} \sqrt{\frac{a x + b}{x}}}{21 \, {\left(a^{2} b^{6} x^{5} + 2 \, a b^{7} x^{4} + b^{8} x^{3}\right)}}"," ",0,"2/21*(256*a^5*x^5 + 384*a^4*b*x^4 + 96*a^3*b^2*x^3 - 16*a^2*b^3*x^2 + 6*a*b^4*x - 3*b^5)*sqrt((a*x + b)/x)/(a^2*b^6*x^5 + 2*a*b^7*x^4 + b^8*x^3)","A",0
1752,1,60,0,0.763830," ","integrate((a+b/x)^(1/2)*x^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, a^{4} x^{4} + 5 \, a^{3} b x^{3} - 6 \, a^{2} b^{2} x^{2} + 8 \, a b^{3} x - 16 \, b^{4}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{315 \, a^{4}}"," ",0,"2/315*(35*a^4*x^4 + 5*a^3*b*x^3 - 6*a^2*b^2*x^2 + 8*a*b^3*x - 16*b^4)*sqrt(x)*sqrt((a*x + b)/x)/a^4","A",0
1753,1,49,0,0.803584," ","integrate((a+b/x)^(1/2)*x^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, a^{3} x^{3} + 3 \, a^{2} b x^{2} - 4 \, a b^{2} x + 8 \, b^{3}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{105 \, a^{3}}"," ",0,"2/105*(15*a^3*x^3 + 3*a^2*b*x^2 - 4*a*b^2*x + 8*b^3)*sqrt(x)*sqrt((a*x + b)/x)/a^3","A",0
1754,1,37,0,0.757207," ","integrate((a+b/x)^(1/2)*x^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, a^{2} x^{2} + a b x - 2 \, b^{2}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{15 \, a^{2}}"," ",0,"2/15*(3*a^2*x^2 + a*b*x - 2*b^2)*sqrt(x)*sqrt((a*x + b)/x)/a^2","A",0
1755,1,24,0,0.764730," ","integrate((a+b/x)^(1/2)*x^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(a x + b\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{3 \, a}"," ",0,"2/3*(a*x + b)*sqrt(x)*sqrt((a*x + b)/x)/a","A",0
1756,1,101,0,0.905540," ","integrate((a+b/x)^(1/2)/x^(1/2),x, algorithm=""fricas"")","\left[\sqrt{b} \log\left(\frac{a x - 2 \, \sqrt{b} \sqrt{x} \sqrt{\frac{a x + b}{x}} + 2 \, b}{x}\right) + 2 \, \sqrt{x} \sqrt{\frac{a x + b}{x}}, 2 \, \sqrt{-b} \arctan\left(\frac{\sqrt{-b} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{b}\right) + 2 \, \sqrt{x} \sqrt{\frac{a x + b}{x}}\right]"," ",0,"[sqrt(b)*log((a*x - 2*sqrt(b)*sqrt(x)*sqrt((a*x + b)/x) + 2*b)/x) + 2*sqrt(x)*sqrt((a*x + b)/x), 2*sqrt(-b)*arctan(sqrt(-b)*sqrt(x)*sqrt((a*x + b)/x)/b) + 2*sqrt(x)*sqrt((a*x + b)/x)]","A",0
1757,1,121,0,0.840717," ","integrate((a+b/x)^(1/2)/x^(3/2),x, algorithm=""fricas"")","\left[\frac{a \sqrt{b} x \log\left(\frac{a x - 2 \, \sqrt{b} \sqrt{x} \sqrt{\frac{a x + b}{x}} + 2 \, b}{x}\right) - 2 \, b \sqrt{x} \sqrt{\frac{a x + b}{x}}}{2 \, b x}, \frac{a \sqrt{-b} x \arctan\left(\frac{\sqrt{-b} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{b}\right) - b \sqrt{x} \sqrt{\frac{a x + b}{x}}}{b x}\right]"," ",0,"[1/2*(a*sqrt(b)*x*log((a*x - 2*sqrt(b)*sqrt(x)*sqrt((a*x + b)/x) + 2*b)/x) - 2*b*sqrt(x)*sqrt((a*x + b)/x))/(b*x), (a*sqrt(-b)*x*arctan(sqrt(-b)*sqrt(x)*sqrt((a*x + b)/x)/b) - b*sqrt(x)*sqrt((a*x + b)/x))/(b*x)]","A",0
1758,1,147,0,0.857398," ","integrate((a+b/x)^(1/2)/x^(5/2),x, algorithm=""fricas"")","\left[\frac{a^{2} \sqrt{b} x^{2} \log\left(\frac{a x + 2 \, \sqrt{b} \sqrt{x} \sqrt{\frac{a x + b}{x}} + 2 \, b}{x}\right) - 2 \, {\left(a b x + 2 \, b^{2}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{8 \, b^{2} x^{2}}, -\frac{a^{2} \sqrt{-b} x^{2} \arctan\left(\frac{\sqrt{-b} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{b}\right) + {\left(a b x + 2 \, b^{2}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{4 \, b^{2} x^{2}}\right]"," ",0,"[1/8*(a^2*sqrt(b)*x^2*log((a*x + 2*sqrt(b)*sqrt(x)*sqrt((a*x + b)/x) + 2*b)/x) - 2*(a*b*x + 2*b^2)*sqrt(x)*sqrt((a*x + b)/x))/(b^2*x^2), -1/4*(a^2*sqrt(-b)*x^2*arctan(sqrt(-b)*sqrt(x)*sqrt((a*x + b)/x)/b) + (a*b*x + 2*b^2)*sqrt(x)*sqrt((a*x + b)/x))/(b^2*x^2)]","A",0
1759,1,173,0,0.777900," ","integrate((a+b/x)^(1/2)/x^(7/2),x, algorithm=""fricas"")","\left[\frac{3 \, a^{3} \sqrt{b} x^{3} \log\left(\frac{a x - 2 \, \sqrt{b} \sqrt{x} \sqrt{\frac{a x + b}{x}} + 2 \, b}{x}\right) + 2 \, {\left(3 \, a^{2} b x^{2} - 2 \, a b^{2} x - 8 \, b^{3}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{48 \, b^{3} x^{3}}, \frac{3 \, a^{3} \sqrt{-b} x^{3} \arctan\left(\frac{\sqrt{-b} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{b}\right) + {\left(3 \, a^{2} b x^{2} - 2 \, a b^{2} x - 8 \, b^{3}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{24 \, b^{3} x^{3}}\right]"," ",0,"[1/48*(3*a^3*sqrt(b)*x^3*log((a*x - 2*sqrt(b)*sqrt(x)*sqrt((a*x + b)/x) + 2*b)/x) + 2*(3*a^2*b*x^2 - 2*a*b^2*x - 8*b^3)*sqrt(x)*sqrt((a*x + b)/x))/(b^3*x^3), 1/24*(3*a^3*sqrt(-b)*x^3*arctan(sqrt(-b)*sqrt(x)*sqrt((a*x + b)/x)/b) + (3*a^2*b*x^2 - 2*a*b^2*x - 8*b^3)*sqrt(x)*sqrt((a*x + b)/x))/(b^3*x^3)]","A",0
1760,1,71,0,0.730209," ","integrate((a+b/x)^(3/2)*x^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left(105 \, a^{5} x^{5} + 140 \, a^{4} b x^{4} + 5 \, a^{3} b^{2} x^{3} - 6 \, a^{2} b^{3} x^{2} + 8 \, a b^{4} x - 16 \, b^{5}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{1155 \, a^{4}}"," ",0,"2/1155*(105*a^5*x^5 + 140*a^4*b*x^4 + 5*a^3*b^2*x^3 - 6*a^2*b^3*x^2 + 8*a*b^4*x - 16*b^5)*sqrt(x)*sqrt((a*x + b)/x)/a^4","A",0
1761,1,60,0,0.645022," ","integrate((a+b/x)^(3/2)*x^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, a^{4} x^{4} + 50 \, a^{3} b x^{3} + 3 \, a^{2} b^{2} x^{2} - 4 \, a b^{3} x + 8 \, b^{4}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{315 \, a^{3}}"," ",0,"2/315*(35*a^4*x^4 + 50*a^3*b*x^3 + 3*a^2*b^2*x^2 - 4*a*b^3*x + 8*b^4)*sqrt(x)*sqrt((a*x + b)/x)/a^3","A",0
1762,1,48,0,0.825697," ","integrate((a+b/x)^(3/2)*x^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, a^{3} x^{3} + 8 \, a^{2} b x^{2} + a b^{2} x - 2 \, b^{3}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{35 \, a^{2}}"," ",0,"2/35*(5*a^3*x^3 + 8*a^2*b*x^2 + a*b^2*x - 2*b^3)*sqrt(x)*sqrt((a*x + b)/x)/a^2","A",0
1763,1,35,0,0.835049," ","integrate((a+b/x)^(3/2)*x^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(a^{2} x^{2} + 2 \, a b x + b^{2}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{5 \, a}"," ",0,"2/5*(a^2*x^2 + 2*a*b*x + b^2)*sqrt(x)*sqrt((a*x + b)/x)/a","B",0
1764,1,116,0,0.841200," ","integrate((a+b/x)^(3/2)*x^(1/2),x, algorithm=""fricas"")","\left[b^{\frac{3}{2}} \log\left(\frac{a x - 2 \, \sqrt{b} \sqrt{x} \sqrt{\frac{a x + b}{x}} + 2 \, b}{x}\right) + \frac{2}{3} \, {\left(a x + 4 \, b\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}, 2 \, \sqrt{-b} b \arctan\left(\frac{\sqrt{-b} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{b}\right) + \frac{2}{3} \, {\left(a x + 4 \, b\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}\right]"," ",0,"[b^(3/2)*log((a*x - 2*sqrt(b)*sqrt(x)*sqrt((a*x + b)/x) + 2*b)/x) + 2/3*(a*x + 4*b)*sqrt(x)*sqrt((a*x + b)/x), 2*sqrt(-b)*b*arctan(sqrt(-b)*sqrt(x)*sqrt((a*x + b)/x)/b) + 2/3*(a*x + 4*b)*sqrt(x)*sqrt((a*x + b)/x)]","A",0
1765,1,130,0,0.802779," ","integrate((a+b/x)^(3/2)/x^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, a \sqrt{b} x \log\left(\frac{a x - 2 \, \sqrt{b} \sqrt{x} \sqrt{\frac{a x + b}{x}} + 2 \, b}{x}\right) + 2 \, {\left(2 \, a x - b\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{2 \, x}, \frac{3 \, a \sqrt{-b} x \arctan\left(\frac{\sqrt{-b} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{b}\right) + {\left(2 \, a x - b\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{x}\right]"," ",0,"[1/2*(3*a*sqrt(b)*x*log((a*x - 2*sqrt(b)*sqrt(x)*sqrt((a*x + b)/x) + 2*b)/x) + 2*(2*a*x - b)*sqrt(x)*sqrt((a*x + b)/x))/x, (3*a*sqrt(-b)*x*arctan(sqrt(-b)*sqrt(x)*sqrt((a*x + b)/x)/b) + (2*a*x - b)*sqrt(x)*sqrt((a*x + b)/x))/x]","A",0
1766,1,152,0,0.898049," ","integrate((a+b/x)^(3/2)/x^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, a^{2} \sqrt{b} x^{2} \log\left(\frac{a x - 2 \, \sqrt{b} \sqrt{x} \sqrt{\frac{a x + b}{x}} + 2 \, b}{x}\right) - 2 \, {\left(5 \, a b x + 2 \, b^{2}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{8 \, b x^{2}}, \frac{3 \, a^{2} \sqrt{-b} x^{2} \arctan\left(\frac{\sqrt{-b} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{b}\right) - {\left(5 \, a b x + 2 \, b^{2}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{4 \, b x^{2}}\right]"," ",0,"[1/8*(3*a^2*sqrt(b)*x^2*log((a*x - 2*sqrt(b)*sqrt(x)*sqrt((a*x + b)/x) + 2*b)/x) - 2*(5*a*b*x + 2*b^2)*sqrt(x)*sqrt((a*x + b)/x))/(b*x^2), 1/4*(3*a^2*sqrt(-b)*x^2*arctan(sqrt(-b)*sqrt(x)*sqrt((a*x + b)/x)/b) - (5*a*b*x + 2*b^2)*sqrt(x)*sqrt((a*x + b)/x))/(b*x^2)]","A",0
1767,1,173,0,0.733245," ","integrate((a+b/x)^(3/2)/x^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, a^{3} \sqrt{b} x^{3} \log\left(\frac{a x + 2 \, \sqrt{b} \sqrt{x} \sqrt{\frac{a x + b}{x}} + 2 \, b}{x}\right) - 2 \, {\left(3 \, a^{2} b x^{2} + 14 \, a b^{2} x + 8 \, b^{3}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{48 \, b^{2} x^{3}}, -\frac{3 \, a^{3} \sqrt{-b} x^{3} \arctan\left(\frac{\sqrt{-b} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{b}\right) + {\left(3 \, a^{2} b x^{2} + 14 \, a b^{2} x + 8 \, b^{3}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{24 \, b^{2} x^{3}}\right]"," ",0,"[1/48*(3*a^3*sqrt(b)*x^3*log((a*x + 2*sqrt(b)*sqrt(x)*sqrt((a*x + b)/x) + 2*b)/x) - 2*(3*a^2*b*x^2 + 14*a*b^2*x + 8*b^3)*sqrt(x)*sqrt((a*x + b)/x))/(b^2*x^3), -1/24*(3*a^3*sqrt(-b)*x^3*arctan(sqrt(-b)*sqrt(x)*sqrt((a*x + b)/x)/b) + (3*a^2*b*x^2 + 14*a*b^2*x + 8*b^3)*sqrt(x)*sqrt((a*x + b)/x))/(b^2*x^3)]","A",0
1768,1,82,0,0.818947," ","integrate((a+b/x)^(5/2)*x^(11/2),x, algorithm=""fricas"")","\frac{2 \, {\left(231 \, a^{6} x^{6} + 567 \, a^{5} b x^{5} + 371 \, a^{4} b^{2} x^{4} + 5 \, a^{3} b^{3} x^{3} - 6 \, a^{2} b^{4} x^{2} + 8 \, a b^{5} x - 16 \, b^{6}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{3003 \, a^{4}}"," ",0,"2/3003*(231*a^6*x^6 + 567*a^5*b*x^5 + 371*a^4*b^2*x^4 + 5*a^3*b^3*x^3 - 6*a^2*b^4*x^2 + 8*a*b^5*x - 16*b^6)*sqrt(x)*sqrt((a*x + b)/x)/a^4","A",0
1769,1,71,0,0.750842," ","integrate((a+b/x)^(5/2)*x^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left(63 \, a^{5} x^{5} + 161 \, a^{4} b x^{4} + 113 \, a^{3} b^{2} x^{3} + 3 \, a^{2} b^{3} x^{2} - 4 \, a b^{4} x + 8 \, b^{5}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{693 \, a^{3}}"," ",0,"2/693*(63*a^5*x^5 + 161*a^4*b*x^4 + 113*a^3*b^2*x^3 + 3*a^2*b^3*x^2 - 4*a*b^4*x + 8*b^5)*sqrt(x)*sqrt((a*x + b)/x)/a^3","A",0
1770,1,59,0,0.568767," ","integrate((a+b/x)^(5/2)*x^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(7 \, a^{4} x^{4} + 19 \, a^{3} b x^{3} + 15 \, a^{2} b^{2} x^{2} + a b^{3} x - 2 \, b^{4}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{63 \, a^{2}}"," ",0,"2/63*(7*a^4*x^4 + 19*a^3*b*x^3 + 15*a^2*b^2*x^2 + a*b^3*x - 2*b^4)*sqrt(x)*sqrt((a*x + b)/x)/a^2","A",0
1771,1,46,0,0.612713," ","integrate((a+b/x)^(5/2)*x^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(a^{3} x^{3} + 3 \, a^{2} b x^{2} + 3 \, a b^{2} x + b^{3}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{7 \, a}"," ",0,"2/7*(a^3*x^3 + 3*a^2*b*x^2 + 3*a*b^2*x + b^3)*sqrt(x)*sqrt((a*x + b)/x)/a","B",0
1772,1,142,0,0.862353," ","integrate((a+b/x)^(5/2)*x^(3/2),x, algorithm=""fricas"")","\left[b^{\frac{5}{2}} \log\left(\frac{a x - 2 \, \sqrt{b} \sqrt{x} \sqrt{\frac{a x + b}{x}} + 2 \, b}{x}\right) + \frac{2}{15} \, {\left(3 \, a^{2} x^{2} + 11 \, a b x + 23 \, b^{2}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}, 2 \, \sqrt{-b} b^{2} \arctan\left(\frac{\sqrt{-b} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{b}\right) + \frac{2}{15} \, {\left(3 \, a^{2} x^{2} + 11 \, a b x + 23 \, b^{2}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}\right]"," ",0,"[b^(5/2)*log((a*x - 2*sqrt(b)*sqrt(x)*sqrt((a*x + b)/x) + 2*b)/x) + 2/15*(3*a^2*x^2 + 11*a*b*x + 23*b^2)*sqrt(x)*sqrt((a*x + b)/x), 2*sqrt(-b)*b^2*arctan(sqrt(-b)*sqrt(x)*sqrt((a*x + b)/x)/b) + 2/15*(3*a^2*x^2 + 11*a*b*x + 23*b^2)*sqrt(x)*sqrt((a*x + b)/x)]","A",0
1773,1,154,0,0.832197," ","integrate((a+b/x)^(5/2)*x^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, a b^{\frac{3}{2}} x \log\left(\frac{a x - 2 \, \sqrt{b} \sqrt{x} \sqrt{\frac{a x + b}{x}} + 2 \, b}{x}\right) + 2 \, {\left(2 \, a^{2} x^{2} + 14 \, a b x - 3 \, b^{2}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{6 \, x}, \frac{15 \, a \sqrt{-b} b x \arctan\left(\frac{\sqrt{-b} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{b}\right) + {\left(2 \, a^{2} x^{2} + 14 \, a b x - 3 \, b^{2}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{3 \, x}\right]"," ",0,"[1/6*(15*a*b^(3/2)*x*log((a*x - 2*sqrt(b)*sqrt(x)*sqrt((a*x + b)/x) + 2*b)/x) + 2*(2*a^2*x^2 + 14*a*b*x - 3*b^2)*sqrt(x)*sqrt((a*x + b)/x))/x, 1/3*(15*a*sqrt(-b)*b*x*arctan(sqrt(-b)*sqrt(x)*sqrt((a*x + b)/x)/b) + (2*a^2*x^2 + 14*a*b*x - 3*b^2)*sqrt(x)*sqrt((a*x + b)/x))/x]","A",0
1774,1,161,0,0.862943," ","integrate((a+b/x)^(5/2)/x^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, a^{2} \sqrt{b} x^{2} \log\left(\frac{a x - 2 \, \sqrt{b} \sqrt{x} \sqrt{\frac{a x + b}{x}} + 2 \, b}{x}\right) + 2 \, {\left(8 \, a^{2} x^{2} - 9 \, a b x - 2 \, b^{2}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{8 \, x^{2}}, \frac{15 \, a^{2} \sqrt{-b} x^{2} \arctan\left(\frac{\sqrt{-b} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{b}\right) + {\left(8 \, a^{2} x^{2} - 9 \, a b x - 2 \, b^{2}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{4 \, x^{2}}\right]"," ",0,"[1/8*(15*a^2*sqrt(b)*x^2*log((a*x - 2*sqrt(b)*sqrt(x)*sqrt((a*x + b)/x) + 2*b)/x) + 2*(8*a^2*x^2 - 9*a*b*x - 2*b^2)*sqrt(x)*sqrt((a*x + b)/x))/x^2, 1/4*(15*a^2*sqrt(-b)*x^2*arctan(sqrt(-b)*sqrt(x)*sqrt((a*x + b)/x)/b) + (8*a^2*x^2 - 9*a*b*x - 2*b^2)*sqrt(x)*sqrt((a*x + b)/x))/x^2]","A",0
1775,1,174,0,0.837382," ","integrate((a+b/x)^(5/2)/x^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, a^{3} \sqrt{b} x^{3} \log\left(\frac{a x - 2 \, \sqrt{b} \sqrt{x} \sqrt{\frac{a x + b}{x}} + 2 \, b}{x}\right) - 2 \, {\left(33 \, a^{2} b x^{2} + 26 \, a b^{2} x + 8 \, b^{3}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{48 \, b x^{3}}, \frac{15 \, a^{3} \sqrt{-b} x^{3} \arctan\left(\frac{\sqrt{-b} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{b}\right) - {\left(33 \, a^{2} b x^{2} + 26 \, a b^{2} x + 8 \, b^{3}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{24 \, b x^{3}}\right]"," ",0,"[1/48*(15*a^3*sqrt(b)*x^3*log((a*x - 2*sqrt(b)*sqrt(x)*sqrt((a*x + b)/x) + 2*b)/x) - 2*(33*a^2*b*x^2 + 26*a*b^2*x + 8*b^3)*sqrt(x)*sqrt((a*x + b)/x))/(b*x^3), 1/24*(15*a^3*sqrt(-b)*x^3*arctan(sqrt(-b)*sqrt(x)*sqrt((a*x + b)/x)/b) - (33*a^2*b*x^2 + 26*a*b^2*x + 8*b^3)*sqrt(x)*sqrt((a*x + b)/x))/(b*x^3)]","A",0
1776,1,195,0,0.883233," ","integrate((a+b/x)^(5/2)/x^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, a^{4} \sqrt{b} x^{4} \log\left(\frac{a x + 2 \, \sqrt{b} \sqrt{x} \sqrt{\frac{a x + b}{x}} + 2 \, b}{x}\right) - 2 \, {\left(15 \, a^{3} b x^{3} + 118 \, a^{2} b^{2} x^{2} + 136 \, a b^{3} x + 48 \, b^{4}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{384 \, b^{2} x^{4}}, -\frac{15 \, a^{4} \sqrt{-b} x^{4} \arctan\left(\frac{\sqrt{-b} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{b}\right) + {\left(15 \, a^{3} b x^{3} + 118 \, a^{2} b^{2} x^{2} + 136 \, a b^{3} x + 48 \, b^{4}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{192 \, b^{2} x^{4}}\right]"," ",0,"[1/384*(15*a^4*sqrt(b)*x^4*log((a*x + 2*sqrt(b)*sqrt(x)*sqrt((a*x + b)/x) + 2*b)/x) - 2*(15*a^3*b*x^3 + 118*a^2*b^2*x^2 + 136*a*b^3*x + 48*b^4)*sqrt(x)*sqrt((a*x + b)/x))/(b^2*x^4), -1/192*(15*a^4*sqrt(-b)*x^4*arctan(sqrt(-b)*sqrt(x)*sqrt((a*x + b)/x)/b) + (15*a^3*b*x^3 + 118*a^2*b^2*x^2 + 136*a*b^3*x + 48*b^4)*sqrt(x)*sqrt((a*x + b)/x))/(b^2*x^4)]","A",0
1777,1,60,0,0.824544," ","integrate(x^(7/2)/(a+b/x)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, a^{4} x^{4} - 40 \, a^{3} b x^{3} + 48 \, a^{2} b^{2} x^{2} - 64 \, a b^{3} x + 128 \, b^{4}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{315 \, a^{5}}"," ",0,"2/315*(35*a^4*x^4 - 40*a^3*b*x^3 + 48*a^2*b^2*x^2 - 64*a*b^3*x + 128*b^4)*sqrt(x)*sqrt((a*x + b)/x)/a^5","A",0
1778,1,49,0,0.945456," ","integrate(x^(5/2)/(a+b/x)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, a^{3} x^{3} - 6 \, a^{2} b x^{2} + 8 \, a b^{2} x - 16 \, b^{3}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{35 \, a^{4}}"," ",0,"2/35*(5*a^3*x^3 - 6*a^2*b*x^2 + 8*a*b^2*x - 16*b^3)*sqrt(x)*sqrt((a*x + b)/x)/a^4","A",0
1779,1,38,0,0.992007," ","integrate(x^(3/2)/(a+b/x)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, a^{2} x^{2} - 4 \, a b x + 8 \, b^{2}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{15 \, a^{3}}"," ",0,"2/15*(3*a^2*x^2 - 4*a*b*x + 8*b^2)*sqrt(x)*sqrt((a*x + b)/x)/a^3","A",0
1780,1,26,0,0.978765," ","integrate(x^(1/2)/(a+b/x)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(a x - 2 \, b\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{3 \, a^{2}}"," ",0,"2/3*(a*x - 2*b)*sqrt(x)*sqrt((a*x + b)/x)/a^2","A",0
1781,1,19,0,0.882230," ","integrate(1/(a+b/x)^(1/2)/x^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{x} \sqrt{\frac{a x + b}{x}}}{a}"," ",0,"2*sqrt(x)*sqrt((a*x + b)/x)/a","A",0
1782,1,70,0,0.946399," ","integrate(1/(a+b/x)^(1/2)/x^(3/2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{a x - 2 \, \sqrt{b} \sqrt{x} \sqrt{\frac{a x + b}{x}} + 2 \, b}{x}\right)}{\sqrt{b}}, \frac{2 \, \sqrt{-b} \arctan\left(\frac{\sqrt{-b} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{b}\right)}{b}\right]"," ",0,"[log((a*x - 2*sqrt(b)*sqrt(x)*sqrt((a*x + b)/x) + 2*b)/x)/sqrt(b), 2*sqrt(-b)*arctan(sqrt(-b)*sqrt(x)*sqrt((a*x + b)/x)/b)/b]","A",0
1783,1,121,0,0.852435," ","integrate(1/(a+b/x)^(1/2)/x^(5/2),x, algorithm=""fricas"")","\left[\frac{a \sqrt{b} x \log\left(\frac{a x + 2 \, \sqrt{b} \sqrt{x} \sqrt{\frac{a x + b}{x}} + 2 \, b}{x}\right) - 2 \, b \sqrt{x} \sqrt{\frac{a x + b}{x}}}{2 \, b^{2} x}, -\frac{a \sqrt{-b} x \arctan\left(\frac{\sqrt{-b} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{b}\right) + b \sqrt{x} \sqrt{\frac{a x + b}{x}}}{b^{2} x}\right]"," ",0,"[1/2*(a*sqrt(b)*x*log((a*x + 2*sqrt(b)*sqrt(x)*sqrt((a*x + b)/x) + 2*b)/x) - 2*b*sqrt(x)*sqrt((a*x + b)/x))/(b^2*x), -(a*sqrt(-b)*x*arctan(sqrt(-b)*sqrt(x)*sqrt((a*x + b)/x)/b) + b*sqrt(x)*sqrt((a*x + b)/x))/(b^2*x)]","A",0
1784,1,151,0,0.946137," ","integrate(1/(a+b/x)^(1/2)/x^(7/2),x, algorithm=""fricas"")","\left[\frac{3 \, a^{2} \sqrt{b} x^{2} \log\left(\frac{a x - 2 \, \sqrt{b} \sqrt{x} \sqrt{\frac{a x + b}{x}} + 2 \, b}{x}\right) + 2 \, {\left(3 \, a b x - 2 \, b^{2}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{8 \, b^{3} x^{2}}, \frac{3 \, a^{2} \sqrt{-b} x^{2} \arctan\left(\frac{\sqrt{-b} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{b}\right) + {\left(3 \, a b x - 2 \, b^{2}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{4 \, b^{3} x^{2}}\right]"," ",0,"[1/8*(3*a^2*sqrt(b)*x^2*log((a*x - 2*sqrt(b)*sqrt(x)*sqrt((a*x + b)/x) + 2*b)/x) + 2*(3*a*b*x - 2*b^2)*sqrt(x)*sqrt((a*x + b)/x))/(b^3*x^2), 1/4*(3*a^2*sqrt(-b)*x^2*arctan(sqrt(-b)*sqrt(x)*sqrt((a*x + b)/x)/b) + (3*a*b*x - 2*b^2)*sqrt(x)*sqrt((a*x + b)/x))/(b^3*x^2)]","A",0
1785,1,173,0,0.791989," ","integrate(1/(a+b/x)^(1/2)/x^(9/2),x, algorithm=""fricas"")","\left[\frac{15 \, a^{3} \sqrt{b} x^{3} \log\left(\frac{a x + 2 \, \sqrt{b} \sqrt{x} \sqrt{\frac{a x + b}{x}} + 2 \, b}{x}\right) - 2 \, {\left(15 \, a^{2} b x^{2} - 10 \, a b^{2} x + 8 \, b^{3}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{48 \, b^{4} x^{3}}, -\frac{15 \, a^{3} \sqrt{-b} x^{3} \arctan\left(\frac{\sqrt{-b} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{b}\right) + {\left(15 \, a^{2} b x^{2} - 10 \, a b^{2} x + 8 \, b^{3}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{24 \, b^{4} x^{3}}\right]"," ",0,"[1/48*(15*a^3*sqrt(b)*x^3*log((a*x + 2*sqrt(b)*sqrt(x)*sqrt((a*x + b)/x) + 2*b)/x) - 2*(15*a^2*b*x^2 - 10*a*b^2*x + 8*b^3)*sqrt(x)*sqrt((a*x + b)/x))/(b^4*x^3), -1/24*(15*a^3*sqrt(-b)*x^3*arctan(sqrt(-b)*sqrt(x)*sqrt((a*x + b)/x)/b) + (15*a^2*b*x^2 - 10*a*b^2*x + 8*b^3)*sqrt(x)*sqrt((a*x + b)/x))/(b^4*x^3)]","A",0
1786,1,70,0,0.998404," ","integrate(x^(5/2)/(a+b/x)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, a^{4} x^{4} - 8 \, a^{3} b x^{3} + 16 \, a^{2} b^{2} x^{2} - 64 \, a b^{3} x - 128 \, b^{4}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{35 \, {\left(a^{6} x + a^{5} b\right)}}"," ",0,"2/35*(5*a^4*x^4 - 8*a^3*b*x^3 + 16*a^2*b^2*x^2 - 64*a*b^3*x - 128*b^4)*sqrt(x)*sqrt((a*x + b)/x)/(a^6*x + a^5*b)","A",0
1787,1,58,0,0.815443," ","integrate(x^(3/2)/(a+b/x)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(a^{3} x^{3} - 2 \, a^{2} b x^{2} + 8 \, a b^{2} x + 16 \, b^{3}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{5 \, {\left(a^{5} x + a^{4} b\right)}}"," ",0,"2/5*(a^3*x^3 - 2*a^2*b*x^2 + 8*a*b^2*x + 16*b^3)*sqrt(x)*sqrt((a*x + b)/x)/(a^5*x + a^4*b)","A",0
1788,1,47,0,1.043201," ","integrate(x^(1/2)/(a+b/x)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(a^{2} x^{2} - 4 \, a b x - 8 \, b^{2}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{3 \, {\left(a^{4} x + a^{3} b\right)}}"," ",0,"2/3*(a^2*x^2 - 4*a*b*x - 8*b^2)*sqrt(x)*sqrt((a*x + b)/x)/(a^4*x + a^3*b)","A",0
1789,1,36,0,1.213886," ","integrate(1/(a+b/x)^(3/2)/x^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(a x + 2 \, b\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{a^{3} x + a^{2} b}"," ",0,"2*(a*x + 2*b)*sqrt(x)*sqrt((a*x + b)/x)/(a^3*x + a^2*b)","A",0
1790,1,27,0,1.245856," ","integrate(1/(a+b/x)^(3/2)/x^(3/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{x} \sqrt{\frac{a x + b}{x}}}{a^{2} x + a b}"," ",0,"-2*sqrt(x)*sqrt((a*x + b)/x)/(a^2*x + a*b)","A",0
1791,1,138,0,1.102842," ","integrate(1/(a+b/x)^(3/2)/x^(5/2),x, algorithm=""fricas"")","\left[\frac{{\left(a x + b\right)} \sqrt{b} \log\left(\frac{a x - 2 \, \sqrt{b} \sqrt{x} \sqrt{\frac{a x + b}{x}} + 2 \, b}{x}\right) + 2 \, b \sqrt{x} \sqrt{\frac{a x + b}{x}}}{a b^{2} x + b^{3}}, \frac{2 \, {\left({\left(a x + b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{b}\right) + b \sqrt{x} \sqrt{\frac{a x + b}{x}}\right)}}{a b^{2} x + b^{3}}\right]"," ",0,"[((a*x + b)*sqrt(b)*log((a*x - 2*sqrt(b)*sqrt(x)*sqrt((a*x + b)/x) + 2*b)/x) + 2*b*sqrt(x)*sqrt((a*x + b)/x))/(a*b^2*x + b^3), 2*((a*x + b)*sqrt(-b)*arctan(sqrt(-b)*sqrt(x)*sqrt((a*x + b)/x)/b) + b*sqrt(x)*sqrt((a*x + b)/x))/(a*b^2*x + b^3)]","A",0
1792,1,179,0,0.722069," ","integrate(1/(a+b/x)^(3/2)/x^(7/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a^{2} x^{2} + a b x\right)} \sqrt{b} \log\left(\frac{a x + 2 \, \sqrt{b} \sqrt{x} \sqrt{\frac{a x + b}{x}} + 2 \, b}{x}\right) - 2 \, {\left(3 \, a b x + b^{2}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{2 \, {\left(a b^{3} x^{2} + b^{4} x\right)}}, -\frac{3 \, {\left(a^{2} x^{2} + a b x\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{b}\right) + {\left(3 \, a b x + b^{2}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{a b^{3} x^{2} + b^{4} x}\right]"," ",0,"[1/2*(3*(a^2*x^2 + a*b*x)*sqrt(b)*log((a*x + 2*sqrt(b)*sqrt(x)*sqrt((a*x + b)/x) + 2*b)/x) - 2*(3*a*b*x + b^2)*sqrt(x)*sqrt((a*x + b)/x))/(a*b^3*x^2 + b^4*x), -(3*(a^2*x^2 + a*b*x)*sqrt(-b)*arctan(sqrt(-b)*sqrt(x)*sqrt((a*x + b)/x)/b) + (3*a*b*x + b^2)*sqrt(x)*sqrt((a*x + b)/x))/(a*b^3*x^2 + b^4*x)]","A",0
1793,1,217,0,0.658840," ","integrate(1/(a+b/x)^(3/2)/x^(9/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(a^{3} x^{3} + a^{2} b x^{2}\right)} \sqrt{b} \log\left(\frac{a x - 2 \, \sqrt{b} \sqrt{x} \sqrt{\frac{a x + b}{x}} + 2 \, b}{x}\right) + 2 \, {\left(15 \, a^{2} b x^{2} + 5 \, a b^{2} x - 2 \, b^{3}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{8 \, {\left(a b^{4} x^{3} + b^{5} x^{2}\right)}}, \frac{15 \, {\left(a^{3} x^{3} + a^{2} b x^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{b}\right) + {\left(15 \, a^{2} b x^{2} + 5 \, a b^{2} x - 2 \, b^{3}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{4 \, {\left(a b^{4} x^{3} + b^{5} x^{2}\right)}}\right]"," ",0,"[1/8*(15*(a^3*x^3 + a^2*b*x^2)*sqrt(b)*log((a*x - 2*sqrt(b)*sqrt(x)*sqrt((a*x + b)/x) + 2*b)/x) + 2*(15*a^2*b*x^2 + 5*a*b^2*x - 2*b^3)*sqrt(x)*sqrt((a*x + b)/x))/(a*b^4*x^3 + b^5*x^2), 1/4*(15*(a^3*x^3 + a^2*b*x^2)*sqrt(-b)*arctan(sqrt(-b)*sqrt(x)*sqrt((a*x + b)/x)/b) + (15*a^2*b*x^2 + 5*a*b^2*x - 2*b^3)*sqrt(x)*sqrt((a*x + b)/x))/(a*b^4*x^3 + b^5*x^2)]","A",0
1794,1,239,0,0.937532," ","integrate(1/(a+b/x)^(3/2)/x^(11/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(a^{4} x^{4} + a^{3} b x^{3}\right)} \sqrt{b} \log\left(\frac{a x + 2 \, \sqrt{b} \sqrt{x} \sqrt{\frac{a x + b}{x}} + 2 \, b}{x}\right) - 2 \, {\left(105 \, a^{3} b x^{3} + 35 \, a^{2} b^{2} x^{2} - 14 \, a b^{3} x + 8 \, b^{4}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{48 \, {\left(a b^{5} x^{4} + b^{6} x^{3}\right)}}, -\frac{105 \, {\left(a^{4} x^{4} + a^{3} b x^{3}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{b}\right) + {\left(105 \, a^{3} b x^{3} + 35 \, a^{2} b^{2} x^{2} - 14 \, a b^{3} x + 8 \, b^{4}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{24 \, {\left(a b^{5} x^{4} + b^{6} x^{3}\right)}}\right]"," ",0,"[1/48*(105*(a^4*x^4 + a^3*b*x^3)*sqrt(b)*log((a*x + 2*sqrt(b)*sqrt(x)*sqrt((a*x + b)/x) + 2*b)/x) - 2*(105*a^3*b*x^3 + 35*a^2*b^2*x^2 - 14*a*b^3*x + 8*b^4)*sqrt(x)*sqrt((a*x + b)/x))/(a*b^5*x^4 + b^6*x^3), -1/24*(105*(a^4*x^4 + a^3*b*x^3)*sqrt(-b)*arctan(sqrt(-b)*sqrt(x)*sqrt((a*x + b)/x)/b) + (105*a^3*b*x^3 + 35*a^2*b^2*x^2 - 14*a*b^3*x + 8*b^4)*sqrt(x)*sqrt((a*x + b)/x))/(a*b^5*x^4 + b^6*x^3)]","A",0
1795,1,92,0,0.899843," ","integrate(x^(5/2)/(a+b/x)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, a^{5} x^{5} - 6 \, a^{4} b x^{4} + 16 \, a^{3} b^{2} x^{3} - 96 \, a^{2} b^{3} x^{2} - 384 \, a b^{4} x - 256 \, b^{5}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{21 \, {\left(a^{8} x^{2} + 2 \, a^{7} b x + a^{6} b^{2}\right)}}"," ",0,"2/21*(3*a^5*x^5 - 6*a^4*b*x^4 + 16*a^3*b^2*x^3 - 96*a^2*b^3*x^2 - 384*a*b^4*x - 256*b^5)*sqrt(x)*sqrt((a*x + b)/x)/(a^8*x^2 + 2*a^7*b*x + a^6*b^2)","A",0
1796,1,81,0,0.966399," ","integrate(x^(3/2)/(a+b/x)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, a^{4} x^{4} - 8 \, a^{3} b x^{3} + 48 \, a^{2} b^{2} x^{2} + 192 \, a b^{3} x + 128 \, b^{4}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{15 \, {\left(a^{7} x^{2} + 2 \, a^{6} b x + a^{5} b^{2}\right)}}"," ",0,"2/15*(3*a^4*x^4 - 8*a^3*b*x^3 + 48*a^2*b^2*x^2 + 192*a*b^3*x + 128*b^4)*sqrt(x)*sqrt((a*x + b)/x)/(a^7*x^2 + 2*a^6*b*x + a^5*b^2)","A",0
1797,1,69,0,1.031034," ","integrate(x^(1/2)/(a+b/x)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(a^{3} x^{3} - 6 \, a^{2} b x^{2} - 24 \, a b^{2} x - 16 \, b^{3}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{3 \, {\left(a^{6} x^{2} + 2 \, a^{5} b x + a^{4} b^{2}\right)}}"," ",0,"2/3*(a^3*x^3 - 6*a^2*b*x^2 - 24*a*b^2*x - 16*b^3)*sqrt(x)*sqrt((a*x + b)/x)/(a^6*x^2 + 2*a^5*b*x + a^4*b^2)","A",0
1798,1,59,0,0.971674," ","integrate(1/(a+b/x)^(5/2)/x^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, a^{2} x^{2} + 12 \, a b x + 8 \, b^{2}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{3 \, {\left(a^{5} x^{2} + 2 \, a^{4} b x + a^{3} b^{2}\right)}}"," ",0,"2/3*(3*a^2*x^2 + 12*a*b*x + 8*b^2)*sqrt(x)*sqrt((a*x + b)/x)/(a^5*x^2 + 2*a^4*b*x + a^3*b^2)","A",0
1799,1,48,0,1.004174," ","integrate(1/(a+b/x)^(5/2)/x^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, a x + 2 \, b\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{3 \, {\left(a^{4} x^{2} + 2 \, a^{3} b x + a^{2} b^{2}\right)}}"," ",0,"-2/3*(3*a*x + 2*b)*sqrt(x)*sqrt((a*x + b)/x)/(a^4*x^2 + 2*a^3*b*x + a^2*b^2)","A",0
1800,1,38,0,1.087854," ","integrate(1/(a+b/x)^(5/2)/x^(5/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{x} \sqrt{\frac{a x + b}{x}}}{3 \, {\left(a^{3} x^{2} + 2 \, a^{2} b x + a b^{2}\right)}}"," ",0,"-2/3*sqrt(x)*sqrt((a*x + b)/x)/(a^3*x^2 + 2*a^2*b*x + a*b^2)","B",0
1801,1,205,0,1.133986," ","integrate(1/(a+b/x)^(5/2)/x^(7/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a^{2} x^{2} + 2 \, a b x + b^{2}\right)} \sqrt{b} \log\left(\frac{a x - 2 \, \sqrt{b} \sqrt{x} \sqrt{\frac{a x + b}{x}} + 2 \, b}{x}\right) + 2 \, {\left(3 \, a b x + 4 \, b^{2}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{3 \, {\left(a^{2} b^{3} x^{2} + 2 \, a b^{4} x + b^{5}\right)}}, \frac{2 \, {\left(3 \, {\left(a^{2} x^{2} + 2 \, a b x + b^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{b}\right) + {\left(3 \, a b x + 4 \, b^{2}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}\right)}}{3 \, {\left(a^{2} b^{3} x^{2} + 2 \, a b^{4} x + b^{5}\right)}}\right]"," ",0,"[1/3*(3*(a^2*x^2 + 2*a*b*x + b^2)*sqrt(b)*log((a*x - 2*sqrt(b)*sqrt(x)*sqrt((a*x + b)/x) + 2*b)/x) + 2*(3*a*b*x + 4*b^2)*sqrt(x)*sqrt((a*x + b)/x))/(a^2*b^3*x^2 + 2*a*b^4*x + b^5), 2/3*(3*(a^2*x^2 + 2*a*b*x + b^2)*sqrt(-b)*arctan(sqrt(-b)*sqrt(x)*sqrt((a*x + b)/x)/b) + (3*a*b*x + 4*b^2)*sqrt(x)*sqrt((a*x + b)/x))/(a^2*b^3*x^2 + 2*a*b^4*x + b^5)]","A",0
1802,1,249,0,0.927689," ","integrate(1/(a+b/x)^(5/2)/x^(9/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(a^{3} x^{3} + 2 \, a^{2} b x^{2} + a b^{2} x\right)} \sqrt{b} \log\left(\frac{a x + 2 \, \sqrt{b} \sqrt{x} \sqrt{\frac{a x + b}{x}} + 2 \, b}{x}\right) - 2 \, {\left(15 \, a^{2} b x^{2} + 20 \, a b^{2} x + 3 \, b^{3}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{6 \, {\left(a^{2} b^{4} x^{3} + 2 \, a b^{5} x^{2} + b^{6} x\right)}}, -\frac{15 \, {\left(a^{3} x^{3} + 2 \, a^{2} b x^{2} + a b^{2} x\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{b}\right) + {\left(15 \, a^{2} b x^{2} + 20 \, a b^{2} x + 3 \, b^{3}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{3 \, {\left(a^{2} b^{4} x^{3} + 2 \, a b^{5} x^{2} + b^{6} x\right)}}\right]"," ",0,"[1/6*(15*(a^3*x^3 + 2*a^2*b*x^2 + a*b^2*x)*sqrt(b)*log((a*x + 2*sqrt(b)*sqrt(x)*sqrt((a*x + b)/x) + 2*b)/x) - 2*(15*a^2*b*x^2 + 20*a*b^2*x + 3*b^3)*sqrt(x)*sqrt((a*x + b)/x))/(a^2*b^4*x^3 + 2*a*b^5*x^2 + b^6*x), -1/3*(15*(a^3*x^3 + 2*a^2*b*x^2 + a*b^2*x)*sqrt(-b)*arctan(sqrt(-b)*sqrt(x)*sqrt((a*x + b)/x)/b) + (15*a^2*b*x^2 + 20*a*b^2*x + 3*b^3)*sqrt(x)*sqrt((a*x + b)/x))/(a^2*b^4*x^3 + 2*a*b^5*x^2 + b^6*x)]","A",0
1803,1,283,0,0.986645," ","integrate(1/(a+b/x)^(5/2)/x^(11/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(a^{4} x^{4} + 2 \, a^{3} b x^{3} + a^{2} b^{2} x^{2}\right)} \sqrt{b} \log\left(\frac{a x - 2 \, \sqrt{b} \sqrt{x} \sqrt{\frac{a x + b}{x}} + 2 \, b}{x}\right) + 2 \, {\left(105 \, a^{3} b x^{3} + 140 \, a^{2} b^{2} x^{2} + 21 \, a b^{3} x - 6 \, b^{4}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{24 \, {\left(a^{2} b^{5} x^{4} + 2 \, a b^{6} x^{3} + b^{7} x^{2}\right)}}, \frac{105 \, {\left(a^{4} x^{4} + 2 \, a^{3} b x^{3} + a^{2} b^{2} x^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{b}\right) + {\left(105 \, a^{3} b x^{3} + 140 \, a^{2} b^{2} x^{2} + 21 \, a b^{3} x - 6 \, b^{4}\right)} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{12 \, {\left(a^{2} b^{5} x^{4} + 2 \, a b^{6} x^{3} + b^{7} x^{2}\right)}}\right]"," ",0,"[1/24*(105*(a^4*x^4 + 2*a^3*b*x^3 + a^2*b^2*x^2)*sqrt(b)*log((a*x - 2*sqrt(b)*sqrt(x)*sqrt((a*x + b)/x) + 2*b)/x) + 2*(105*a^3*b*x^3 + 140*a^2*b^2*x^2 + 21*a*b^3*x - 6*b^4)*sqrt(x)*sqrt((a*x + b)/x))/(a^2*b^5*x^4 + 2*a*b^6*x^3 + b^7*x^2), 1/12*(105*(a^4*x^4 + 2*a^3*b*x^3 + a^2*b^2*x^2)*sqrt(-b)*arctan(sqrt(-b)*sqrt(x)*sqrt((a*x + b)/x)/b) + (105*a^3*b*x^3 + 140*a^2*b^2*x^2 + 21*a*b^3*x - 6*b^4)*sqrt(x)*sqrt((a*x + b)/x))/(a^2*b^5*x^4 + 2*a*b^6*x^3 + b^7*x^2)]","A",0
1804,1,13,0,0.908908," ","integrate((a+b/x^2)*x^6,x, algorithm=""fricas"")","\frac{1}{7} \, a x^{7} + \frac{1}{5} \, b x^{5}"," ",0,"1/7*a*x^7 + 1/5*b*x^5","A",0
1805,1,13,0,0.956535," ","integrate((a+b/x^2)*x^5,x, algorithm=""fricas"")","\frac{1}{6} \, a x^{6} + \frac{1}{4} \, b x^{4}"," ",0,"1/6*a*x^6 + 1/4*b*x^4","A",0
1806,1,13,0,0.742437," ","integrate((a+b/x^2)*x^4,x, algorithm=""fricas"")","\frac{1}{5} \, a x^{5} + \frac{1}{3} \, b x^{3}"," ",0,"1/5*a*x^5 + 1/3*b*x^3","A",0
1807,1,13,0,0.814798," ","integrate((a+b/x^2)*x^3,x, algorithm=""fricas"")","\frac{1}{4} \, a x^{4} + \frac{1}{2} \, b x^{2}"," ",0,"1/4*a*x^4 + 1/2*b*x^2","A",0
1808,1,10,0,0.932943," ","integrate((a+b/x^2)*x^2,x, algorithm=""fricas"")","\frac{1}{3} \, a x^{3} + b x"," ",0,"1/3*a*x^3 + b*x","A",0
1809,1,11,0,0.840776," ","integrate((a+b/x^2)*x,x, algorithm=""fricas"")","\frac{1}{2} \, a x^{2} + b \log\left(x\right)"," ",0,"1/2*a*x^2 + b*log(x)","A",0
1810,1,13,0,0.862850," ","integrate(a+b/x^2,x, algorithm=""fricas"")","\frac{a x^{2} - b}{x}"," ",0,"(a*x^2 - b)/x","A",0
1811,1,17,0,0.857618," ","integrate((a+b/x^2)/x,x, algorithm=""fricas"")","\frac{2 \, a x^{2} \log\left(x\right) - b}{2 \, x^{2}}"," ",0,"1/2*(2*a*x^2*log(x) - b)/x^2","A",0
1812,1,13,0,0.822576," ","integrate((a+b/x^2)/x^2,x, algorithm=""fricas"")","-\frac{3 \, a x^{2} + b}{3 \, x^{3}}"," ",0,"-1/3*(3*a*x^2 + b)/x^3","A",0
1813,1,13,0,1.004412," ","integrate((a+b/x^2)/x^3,x, algorithm=""fricas"")","-\frac{2 \, a x^{2} + b}{4 \, x^{4}}"," ",0,"-1/4*(2*a*x^2 + b)/x^4","A",0
1814,1,15,0,0.918499," ","integrate((a+b/x^2)/x^4,x, algorithm=""fricas"")","-\frac{5 \, a x^{2} + 3 \, b}{15 \, x^{5}}"," ",0,"-1/15*(5*a*x^2 + 3*b)/x^5","A",0
1815,1,15,0,0.816552," ","integrate((a+b/x^2)/x^5,x, algorithm=""fricas"")","-\frac{3 \, a x^{2} + 2 \, b}{12 \, x^{6}}"," ",0,"-1/12*(3*a*x^2 + 2*b)/x^6","A",0
1816,1,15,0,0.971378," ","integrate((a+b/x^2)/x^6,x, algorithm=""fricas"")","-\frac{7 \, a x^{2} + 5 \, b}{35 \, x^{7}}"," ",0,"-1/35*(7*a*x^2 + 5*b)/x^7","A",0
1817,1,24,0,0.865712," ","integrate((a+b/x^2)^2*x^6,x, algorithm=""fricas"")","\frac{1}{7} \, a^{2} x^{7} + \frac{2}{5} \, a b x^{5} + \frac{1}{3} \, b^{2} x^{3}"," ",0,"1/7*a^2*x^7 + 2/5*a*b*x^5 + 1/3*b^2*x^3","A",0
1818,1,24,0,0.906907," ","integrate((a+b/x^2)^2*x^5,x, algorithm=""fricas"")","\frac{1}{6} \, a^{2} x^{6} + \frac{1}{2} \, a b x^{4} + \frac{1}{2} \, b^{2} x^{2}"," ",0,"1/6*a^2*x^6 + 1/2*a*b*x^4 + 1/2*b^2*x^2","A",0
1819,1,21,0,0.888795," ","integrate((a+b/x^2)^2*x^4,x, algorithm=""fricas"")","\frac{1}{5} \, a^{2} x^{5} + \frac{2}{3} \, a b x^{3} + b^{2} x"," ",0,"1/5*a^2*x^5 + 2/3*a*b*x^3 + b^2*x","A",0
1820,1,21,0,0.596910," ","integrate((a+b/x^2)^2*x^3,x, algorithm=""fricas"")","\frac{1}{4} \, a^{2} x^{4} + a b x^{2} + b^{2} \log\left(x\right)"," ",0,"1/4*a^2*x^4 + a*b*x^2 + b^2*log(x)","A",0
1821,1,25,0,1.036128," ","integrate((a+b/x^2)^2*x^2,x, algorithm=""fricas"")","\frac{a^{2} x^{4} + 6 \, a b x^{2} - 3 \, b^{2}}{3 \, x}"," ",0,"1/3*(a^2*x^4 + 6*a*b*x^2 - 3*b^2)/x","A",0
1822,1,27,0,1.024504," ","integrate((a+b/x^2)^2*x,x, algorithm=""fricas"")","\frac{a^{2} x^{4} + 4 \, a b x^{2} \log\left(x\right) - b^{2}}{2 \, x^{2}}"," ",0,"1/2*(a^2*x^4 + 4*a*b*x^2*log(x) - b^2)/x^2","A",0
1823,1,26,0,0.934049," ","integrate((a+b/x^2)^2,x, algorithm=""fricas"")","\frac{3 \, a^{2} x^{4} - 6 \, a b x^{2} - b^{2}}{3 \, x^{3}}"," ",0,"1/3*(3*a^2*x^4 - 6*a*b*x^2 - b^2)/x^3","A",0
1824,1,28,0,0.600327," ","integrate((a+b/x^2)^2/x,x, algorithm=""fricas"")","\frac{4 \, a^{2} x^{4} \log\left(x\right) - 4 \, a b x^{2} - b^{2}}{4 \, x^{4}}"," ",0,"1/4*(4*a^2*x^4*log(x) - 4*a*b*x^2 - b^2)/x^4","A",0
1825,1,26,0,1.012059," ","integrate((a+b/x^2)^2/x^2,x, algorithm=""fricas"")","-\frac{15 \, a^{2} x^{4} + 10 \, a b x^{2} + 3 \, b^{2}}{15 \, x^{5}}"," ",0,"-1/15*(15*a^2*x^4 + 10*a*b*x^2 + 3*b^2)/x^5","A",0
1826,1,24,0,0.935084," ","integrate((a+b/x^2)^2/x^3,x, algorithm=""fricas"")","-\frac{3 \, a^{2} x^{4} + 3 \, a b x^{2} + b^{2}}{6 \, x^{6}}"," ",0,"-1/6*(3*a^2*x^4 + 3*a*b*x^2 + b^2)/x^6","A",0
1827,1,26,0,0.967446," ","integrate((a+b/x^2)^2/x^4,x, algorithm=""fricas"")","-\frac{35 \, a^{2} x^{4} + 42 \, a b x^{2} + 15 \, b^{2}}{105 \, x^{7}}"," ",0,"-1/105*(35*a^2*x^4 + 42*a*b*x^2 + 15*b^2)/x^7","A",0
1828,1,26,0,1.057375," ","integrate((a+b/x^2)^2/x^5,x, algorithm=""fricas"")","-\frac{6 \, a^{2} x^{4} + 8 \, a b x^{2} + 3 \, b^{2}}{24 \, x^{8}}"," ",0,"-1/24*(6*a^2*x^4 + 8*a*b*x^2 + 3*b^2)/x^8","A",0
1829,1,26,0,1.087210," ","integrate((a+b/x^2)^2/x^6,x, algorithm=""fricas"")","-\frac{63 \, a^{2} x^{4} + 90 \, a b x^{2} + 35 \, b^{2}}{315 \, x^{9}}"," ",0,"-1/315*(63*a^2*x^4 + 90*a*b*x^2 + 35*b^2)/x^9","A",0
1830,1,31,0,0.720560," ","integrate((a+b/x^2)^3*x^6,x, algorithm=""fricas"")","\frac{1}{7} \, a^{3} x^{7} + \frac{3}{5} \, a^{2} b x^{5} + a b^{2} x^{3} + b^{3} x"," ",0,"1/7*a^3*x^7 + 3/5*a^2*b*x^5 + a*b^2*x^3 + b^3*x","A",0
1831,1,33,0,0.961530," ","integrate((a+b/x^2)^3*x^5,x, algorithm=""fricas"")","\frac{1}{6} \, a^{3} x^{6} + \frac{3}{4} \, a^{2} b x^{4} + \frac{3}{2} \, a b^{2} x^{2} + b^{3} \log\left(x\right)"," ",0,"1/6*a^3*x^6 + 3/4*a^2*b*x^4 + 3/2*a*b^2*x^2 + b^3*log(x)","A",0
1832,1,36,0,1.062485," ","integrate((a+b/x^2)^3*x^4,x, algorithm=""fricas"")","\frac{a^{3} x^{6} + 5 \, a^{2} b x^{4} + 15 \, a b^{2} x^{2} - 5 \, b^{3}}{5 \, x}"," ",0,"1/5*(a^3*x^6 + 5*a^2*b*x^4 + 15*a*b^2*x^2 - 5*b^3)/x","A",0
1833,1,38,0,0.976435," ","integrate((a+b/x^2)^3*x^3,x, algorithm=""fricas"")","\frac{a^{3} x^{6} + 6 \, a^{2} b x^{4} + 12 \, a b^{2} x^{2} \log\left(x\right) - 2 \, b^{3}}{4 \, x^{2}}"," ",0,"1/4*(a^3*x^6 + 6*a^2*b*x^4 + 12*a*b^2*x^2*log(x) - 2*b^3)/x^2","A",0
1834,1,36,0,0.761523," ","integrate((a+b/x^2)^3*x^2,x, algorithm=""fricas"")","\frac{a^{3} x^{6} + 9 \, a^{2} b x^{4} - 9 \, a b^{2} x^{2} - b^{3}}{3 \, x^{3}}"," ",0,"1/3*(a^3*x^6 + 9*a^2*b*x^4 - 9*a*b^2*x^2 - b^3)/x^3","A",0
1835,1,39,0,1.038923," ","integrate((a+b/x^2)^3*x,x, algorithm=""fricas"")","\frac{2 \, a^{3} x^{6} + 12 \, a^{2} b x^{4} \log\left(x\right) - 6 \, a b^{2} x^{2} - b^{3}}{4 \, x^{4}}"," ",0,"1/4*(2*a^3*x^6 + 12*a^2*b*x^4*log(x) - 6*a*b^2*x^2 - b^3)/x^4","A",0
1836,1,37,0,0.895718," ","integrate((a+b/x^2)^3,x, algorithm=""fricas"")","\frac{5 \, a^{3} x^{6} - 15 \, a^{2} b x^{4} - 5 \, a b^{2} x^{2} - b^{3}}{5 \, x^{5}}"," ",0,"1/5*(5*a^3*x^6 - 15*a^2*b*x^4 - 5*a*b^2*x^2 - b^3)/x^5","A",0
1837,1,39,0,1.028760," ","integrate((a+b/x^2)^3/x,x, algorithm=""fricas"")","\frac{12 \, a^{3} x^{6} \log\left(x\right) - 18 \, a^{2} b x^{4} - 9 \, a b^{2} x^{2} - 2 \, b^{3}}{12 \, x^{6}}"," ",0,"1/12*(12*a^3*x^6*log(x) - 18*a^2*b*x^4 - 9*a*b^2*x^2 - 2*b^3)/x^6","A",0
1838,1,37,0,1.093385," ","integrate((a+b/x^2)^3/x^2,x, algorithm=""fricas"")","-\frac{35 \, a^{3} x^{6} + 35 \, a^{2} b x^{4} + 21 \, a b^{2} x^{2} + 5 \, b^{3}}{35 \, x^{7}}"," ",0,"-1/35*(35*a^3*x^6 + 35*a^2*b*x^4 + 21*a*b^2*x^2 + 5*b^3)/x^7","A",0
1839,1,35,0,0.965519," ","integrate((a+b/x^2)^3/x^3,x, algorithm=""fricas"")","-\frac{4 \, a^{3} x^{6} + 6 \, a^{2} b x^{4} + 4 \, a b^{2} x^{2} + b^{3}}{8 \, x^{8}}"," ",0,"-1/8*(4*a^3*x^6 + 6*a^2*b*x^4 + 4*a*b^2*x^2 + b^3)/x^8","B",0
1840,1,37,0,1.086038," ","integrate((a+b/x^2)^3/x^4,x, algorithm=""fricas"")","-\frac{105 \, a^{3} x^{6} + 189 \, a^{2} b x^{4} + 135 \, a b^{2} x^{2} + 35 \, b^{3}}{315 \, x^{9}}"," ",0,"-1/315*(105*a^3*x^6 + 189*a^2*b*x^4 + 135*a*b^2*x^2 + 35*b^3)/x^9","A",0
1841,1,37,0,0.718442," ","integrate((a+b/x^2)^3/x^5,x, algorithm=""fricas"")","-\frac{10 \, a^{3} x^{6} + 20 \, a^{2} b x^{4} + 15 \, a b^{2} x^{2} + 4 \, b^{3}}{40 \, x^{10}}"," ",0,"-1/40*(10*a^3*x^6 + 20*a^2*b*x^4 + 15*a*b^2*x^2 + 4*b^3)/x^10","A",0
1842,1,37,0,0.814376," ","integrate((a+b/x^2)^3/x^6,x, algorithm=""fricas"")","-\frac{231 \, a^{3} x^{6} + 495 \, a^{2} b x^{4} + 385 \, a b^{2} x^{2} + 105 \, b^{3}}{1155 \, x^{11}}"," ",0,"-1/1155*(231*a^3*x^6 + 495*a^2*b*x^4 + 385*a*b^2*x^2 + 105*b^3)/x^11","A",0
1843,1,148,0,0.952914," ","integrate(x^6/(a+b/x^2),x, algorithm=""fricas"")","\left[\frac{30 \, a^{3} x^{7} - 42 \, a^{2} b x^{5} + 70 \, a b^{2} x^{3} + 105 \, b^{3} \sqrt{-\frac{b}{a}} \log\left(\frac{a x^{2} + 2 \, a x \sqrt{-\frac{b}{a}} - b}{a x^{2} + b}\right) - 210 \, b^{3} x}{210 \, a^{4}}, \frac{15 \, a^{3} x^{7} - 21 \, a^{2} b x^{5} + 35 \, a b^{2} x^{3} + 105 \, b^{3} \sqrt{\frac{b}{a}} \arctan\left(\frac{a x \sqrt{\frac{b}{a}}}{b}\right) - 105 \, b^{3} x}{105 \, a^{4}}\right]"," ",0,"[1/210*(30*a^3*x^7 - 42*a^2*b*x^5 + 70*a*b^2*x^3 + 105*b^3*sqrt(-b/a)*log((a*x^2 + 2*a*x*sqrt(-b/a) - b)/(a*x^2 + b)) - 210*b^3*x)/a^4, 1/105*(15*a^3*x^7 - 21*a^2*b*x^5 + 35*a*b^2*x^3 + 105*b^3*sqrt(b/a)*arctan(a*x*sqrt(b/a)/b) - 105*b^3*x)/a^4]","A",0
1844,1,45,0,1.063721," ","integrate(x^5/(a+b/x^2),x, algorithm=""fricas"")","\frac{2 \, a^{3} x^{6} - 3 \, a^{2} b x^{4} + 6 \, a b^{2} x^{2} - 6 \, b^{3} \log\left(a x^{2} + b\right)}{12 \, a^{4}}"," ",0,"1/12*(2*a^3*x^6 - 3*a^2*b*x^4 + 6*a*b^2*x^2 - 6*b^3*log(a*x^2 + b))/a^4","A",0
1845,1,126,0,1.039590," ","integrate(x^4/(a+b/x^2),x, algorithm=""fricas"")","\left[\frac{6 \, a^{2} x^{5} - 10 \, a b x^{3} + 15 \, b^{2} \sqrt{-\frac{b}{a}} \log\left(\frac{a x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - b}{a x^{2} + b}\right) + 30 \, b^{2} x}{30 \, a^{3}}, \frac{3 \, a^{2} x^{5} - 5 \, a b x^{3} - 15 \, b^{2} \sqrt{\frac{b}{a}} \arctan\left(\frac{a x \sqrt{\frac{b}{a}}}{b}\right) + 15 \, b^{2} x}{15 \, a^{3}}\right]"," ",0,"[1/30*(6*a^2*x^5 - 10*a*b*x^3 + 15*b^2*sqrt(-b/a)*log((a*x^2 - 2*a*x*sqrt(-b/a) - b)/(a*x^2 + b)) + 30*b^2*x)/a^3, 1/15*(3*a^2*x^5 - 5*a*b*x^3 - 15*b^2*sqrt(b/a)*arctan(a*x*sqrt(b/a)/b) + 15*b^2*x)/a^3]","A",0
1846,1,33,0,0.944865," ","integrate(x^3/(a+b/x^2),x, algorithm=""fricas"")","\frac{a^{2} x^{4} - 2 \, a b x^{2} + 2 \, b^{2} \log\left(a x^{2} + b\right)}{4 \, a^{3}}"," ",0,"1/4*(a^2*x^4 - 2*a*b*x^2 + 2*b^2*log(a*x^2 + b))/a^3","A",0
1847,1,99,0,0.848193," ","integrate(x^2/(a+b/x^2),x, algorithm=""fricas"")","\left[\frac{2 \, a x^{3} + 3 \, b \sqrt{-\frac{b}{a}} \log\left(\frac{a x^{2} + 2 \, a x \sqrt{-\frac{b}{a}} - b}{a x^{2} + b}\right) - 6 \, b x}{6 \, a^{2}}, \frac{a x^{3} + 3 \, b \sqrt{\frac{b}{a}} \arctan\left(\frac{a x \sqrt{\frac{b}{a}}}{b}\right) - 3 \, b x}{3 \, a^{2}}\right]"," ",0,"[1/6*(2*a*x^3 + 3*b*sqrt(-b/a)*log((a*x^2 + 2*a*x*sqrt(-b/a) - b)/(a*x^2 + b)) - 6*b*x)/a^2, 1/3*(a*x^3 + 3*b*sqrt(b/a)*arctan(a*x*sqrt(b/a)/b) - 3*b*x)/a^2]","A",0
1848,1,22,0,0.977008," ","integrate(x/(a+b/x^2),x, algorithm=""fricas"")","\frac{a x^{2} - b \log\left(a x^{2} + b\right)}{2 \, a^{2}}"," ",0,"1/2*(a*x^2 - b*log(a*x^2 + b))/a^2","A",0
1849,1,82,0,0.985137," ","integrate(1/(a+b/x^2),x, algorithm=""fricas"")","\left[\frac{\sqrt{-\frac{b}{a}} \log\left(\frac{a x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - b}{a x^{2} + b}\right) + 2 \, x}{2 \, a}, -\frac{\sqrt{\frac{b}{a}} \arctan\left(\frac{a x \sqrt{\frac{b}{a}}}{b}\right) - x}{a}\right]"," ",0,"[1/2*(sqrt(-b/a)*log((a*x^2 - 2*a*x*sqrt(-b/a) - b)/(a*x^2 + b)) + 2*x)/a, -(sqrt(b/a)*arctan(a*x*sqrt(b/a)/b) - x)/a]","A",0
1850,1,13,0,0.839286," ","integrate(1/(a+b/x^2)/x,x, algorithm=""fricas"")","\frac{\log\left(a x^{2} + b\right)}{2 \, a}"," ",0,"1/2*log(a*x^2 + b)/a","A",0
1851,1,67,0,0.779217," ","integrate(1/(a+b/x^2)/x^2,x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a b} \log\left(\frac{a x^{2} - 2 \, \sqrt{-a b} x - b}{a x^{2} + b}\right)}{2 \, a b}, \frac{\sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{b}\right)}{a b}\right]"," ",0,"[-1/2*sqrt(-a*b)*log((a*x^2 - 2*sqrt(-a*b)*x - b)/(a*x^2 + b))/(a*b), sqrt(a*b)*arctan(sqrt(a*b)*x/b)/(a*b)]","A",0
1852,1,18,0,1.011798," ","integrate(1/(a+b/x^2)/x^3,x, algorithm=""fricas"")","-\frac{\log\left(a x^{2} + b\right) - 2 \, \log\left(x\right)}{2 \, b}"," ",0,"-1/2*(log(a*x^2 + b) - 2*log(x))/b","A",0
1853,1,82,0,1.111157," ","integrate(1/(a+b/x^2)/x^4,x, algorithm=""fricas"")","\left[\frac{x \sqrt{-\frac{a}{b}} \log\left(\frac{a x^{2} - 2 \, b x \sqrt{-\frac{a}{b}} - b}{a x^{2} + b}\right) - 2}{2 \, b x}, -\frac{x \sqrt{\frac{a}{b}} \arctan\left(x \sqrt{\frac{a}{b}}\right) + 1}{b x}\right]"," ",0,"[1/2*(x*sqrt(-a/b)*log((a*x^2 - 2*b*x*sqrt(-a/b) - b)/(a*x^2 + b)) - 2)/(b*x), -(x*sqrt(a/b)*arctan(x*sqrt(a/b)) + 1)/(b*x)]","A",0
1854,1,33,0,1.126845," ","integrate(1/(a+b/x^2)/x^5,x, algorithm=""fricas"")","\frac{a x^{2} \log\left(a x^{2} + b\right) - 2 \, a x^{2} \log\left(x\right) - b}{2 \, b^{2} x^{2}}"," ",0,"1/2*(a*x^2*log(a*x^2 + b) - 2*a*x^2*log(x) - b)/(b^2*x^2)","A",0
1855,1,106,0,1.541850," ","integrate(1/(a+b/x^2)/x^6,x, algorithm=""fricas"")","\left[\frac{3 \, a x^{3} \sqrt{-\frac{a}{b}} \log\left(\frac{a x^{2} + 2 \, b x \sqrt{-\frac{a}{b}} - b}{a x^{2} + b}\right) + 6 \, a x^{2} - 2 \, b}{6 \, b^{2} x^{3}}, \frac{3 \, a x^{3} \sqrt{\frac{a}{b}} \arctan\left(x \sqrt{\frac{a}{b}}\right) + 3 \, a x^{2} - b}{3 \, b^{2} x^{3}}\right]"," ",0,"[1/6*(3*a*x^3*sqrt(-a/b)*log((a*x^2 + 2*b*x*sqrt(-a/b) - b)/(a*x^2 + b)) + 6*a*x^2 - 2*b)/(b^2*x^3), 1/3*(3*a*x^3*sqrt(a/b)*arctan(x*sqrt(a/b)) + 3*a*x^2 - b)/(b^2*x^3)]","A",0
1856,1,45,0,1.131441," ","integrate(1/(a+b/x^2)/x^7,x, algorithm=""fricas"")","-\frac{2 \, a^{2} x^{4} \log\left(a x^{2} + b\right) - 4 \, a^{2} x^{4} \log\left(x\right) - 2 \, a b x^{2} + b^{2}}{4 \, b^{3} x^{4}}"," ",0,"-1/4*(2*a^2*x^4*log(a*x^2 + b) - 4*a^2*x^4*log(x) - 2*a*b*x^2 + b^2)/(b^3*x^4)","A",0
1857,1,132,0,1.327339," ","integrate(1/(a+b/x^2)/x^8,x, algorithm=""fricas"")","\left[\frac{15 \, a^{2} x^{5} \sqrt{-\frac{a}{b}} \log\left(\frac{a x^{2} - 2 \, b x \sqrt{-\frac{a}{b}} - b}{a x^{2} + b}\right) - 30 \, a^{2} x^{4} + 10 \, a b x^{2} - 6 \, b^{2}}{30 \, b^{3} x^{5}}, -\frac{15 \, a^{2} x^{5} \sqrt{\frac{a}{b}} \arctan\left(x \sqrt{\frac{a}{b}}\right) + 15 \, a^{2} x^{4} - 5 \, a b x^{2} + 3 \, b^{2}}{15 \, b^{3} x^{5}}\right]"," ",0,"[1/30*(15*a^2*x^5*sqrt(-a/b)*log((a*x^2 - 2*b*x*sqrt(-a/b) - b)/(a*x^2 + b)) - 30*a^2*x^4 + 10*a*b*x^2 - 6*b^2)/(b^3*x^5), -1/15*(15*a^2*x^5*sqrt(a/b)*arctan(x*sqrt(a/b)) + 15*a^2*x^4 - 5*a*b*x^2 + 3*b^2)/(b^3*x^5)]","A",0
1858,1,212,0,1.323533," ","integrate(x^6/(a+b/x^2)^2,x, algorithm=""fricas"")","\left[\frac{20 \, a^{4} x^{9} - 36 \, a^{3} b x^{7} + 84 \, a^{2} b^{2} x^{5} - 420 \, a b^{3} x^{3} - 630 \, b^{4} x + 315 \, {\left(a b^{3} x^{2} + b^{4}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{a x^{2} + 2 \, a x \sqrt{-\frac{b}{a}} - b}{a x^{2} + b}\right)}{140 \, {\left(a^{6} x^{2} + a^{5} b\right)}}, \frac{10 \, a^{4} x^{9} - 18 \, a^{3} b x^{7} + 42 \, a^{2} b^{2} x^{5} - 210 \, a b^{3} x^{3} - 315 \, b^{4} x + 315 \, {\left(a b^{3} x^{2} + b^{4}\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{a x \sqrt{\frac{b}{a}}}{b}\right)}{70 \, {\left(a^{6} x^{2} + a^{5} b\right)}}\right]"," ",0,"[1/140*(20*a^4*x^9 - 36*a^3*b*x^7 + 84*a^2*b^2*x^5 - 420*a*b^3*x^3 - 630*b^4*x + 315*(a*b^3*x^2 + b^4)*sqrt(-b/a)*log((a*x^2 + 2*a*x*sqrt(-b/a) - b)/(a*x^2 + b)))/(a^6*x^2 + a^5*b), 1/70*(10*a^4*x^9 - 18*a^3*b*x^7 + 42*a^2*b^2*x^5 - 210*a*b^3*x^3 - 315*b^4*x + 315*(a*b^3*x^2 + b^4)*sqrt(b/a)*arctan(a*x*sqrt(b/a)/b))/(a^6*x^2 + a^5*b)]","A",0
1859,1,81,0,1.293988," ","integrate(x^5/(a+b/x^2)^2,x, algorithm=""fricas"")","\frac{a^{4} x^{8} - 2 \, a^{3} b x^{6} + 6 \, a^{2} b^{2} x^{4} + 9 \, a b^{3} x^{2} - 3 \, b^{4} - 12 \, {\left(a b^{3} x^{2} + b^{4}\right)} \log\left(a x^{2} + b\right)}{6 \, {\left(a^{6} x^{2} + a^{5} b\right)}}"," ",0,"1/6*(a^4*x^8 - 2*a^3*b*x^6 + 6*a^2*b^2*x^4 + 9*a*b^3*x^2 - 3*b^4 - 12*(a*b^3*x^2 + b^4)*log(a*x^2 + b))/(a^6*x^2 + a^5*b)","A",0
1860,1,190,0,1.100785," ","integrate(x^4/(a+b/x^2)^2,x, algorithm=""fricas"")","\left[\frac{12 \, a^{3} x^{7} - 28 \, a^{2} b x^{5} + 140 \, a b^{2} x^{3} + 210 \, b^{3} x + 105 \, {\left(a b^{2} x^{2} + b^{3}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{a x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - b}{a x^{2} + b}\right)}{60 \, {\left(a^{5} x^{2} + a^{4} b\right)}}, \frac{6 \, a^{3} x^{7} - 14 \, a^{2} b x^{5} + 70 \, a b^{2} x^{3} + 105 \, b^{3} x - 105 \, {\left(a b^{2} x^{2} + b^{3}\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{a x \sqrt{\frac{b}{a}}}{b}\right)}{30 \, {\left(a^{5} x^{2} + a^{4} b\right)}}\right]"," ",0,"[1/60*(12*a^3*x^7 - 28*a^2*b*x^5 + 140*a*b^2*x^3 + 210*b^3*x + 105*(a*b^2*x^2 + b^3)*sqrt(-b/a)*log((a*x^2 - 2*a*x*sqrt(-b/a) - b)/(a*x^2 + b)))/(a^5*x^2 + a^4*b), 1/30*(6*a^3*x^7 - 14*a^2*b*x^5 + 70*a*b^2*x^3 + 105*b^3*x - 105*(a*b^2*x^2 + b^3)*sqrt(b/a)*arctan(a*x*sqrt(b/a)/b))/(a^5*x^2 + a^4*b)]","A",0
1861,1,70,0,0.712551," ","integrate(x^3/(a+b/x^2)^2,x, algorithm=""fricas"")","\frac{a^{3} x^{6} - 3 \, a^{2} b x^{4} - 4 \, a b^{2} x^{2} + 2 \, b^{3} + 6 \, {\left(a b^{2} x^{2} + b^{3}\right)} \log\left(a x^{2} + b\right)}{4 \, {\left(a^{5} x^{2} + a^{4} b\right)}}"," ",0,"1/4*(a^3*x^6 - 3*a^2*b*x^4 - 4*a*b^2*x^2 + 2*b^3 + 6*(a*b^2*x^2 + b^3)*log(a*x^2 + b))/(a^5*x^2 + a^4*b)","A",0
1862,1,164,0,1.388733," ","integrate(x^2/(a+b/x^2)^2,x, algorithm=""fricas"")","\left[\frac{4 \, a^{2} x^{5} - 20 \, a b x^{3} - 30 \, b^{2} x + 15 \, {\left(a b x^{2} + b^{2}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{a x^{2} + 2 \, a x \sqrt{-\frac{b}{a}} - b}{a x^{2} + b}\right)}{12 \, {\left(a^{4} x^{2} + a^{3} b\right)}}, \frac{2 \, a^{2} x^{5} - 10 \, a b x^{3} - 15 \, b^{2} x + 15 \, {\left(a b x^{2} + b^{2}\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{a x \sqrt{\frac{b}{a}}}{b}\right)}{6 \, {\left(a^{4} x^{2} + a^{3} b\right)}}\right]"," ",0,"[1/12*(4*a^2*x^5 - 20*a*b*x^3 - 30*b^2*x + 15*(a*b*x^2 + b^2)*sqrt(-b/a)*log((a*x^2 + 2*a*x*sqrt(-b/a) - b)/(a*x^2 + b)))/(a^4*x^2 + a^3*b), 1/6*(2*a^2*x^5 - 10*a*b*x^3 - 15*b^2*x + 15*(a*b*x^2 + b^2)*sqrt(b/a)*arctan(a*x*sqrt(b/a)/b))/(a^4*x^2 + a^3*b)]","A",0
1863,1,56,0,1.124502," ","integrate(x/(a+b/x^2)^2,x, algorithm=""fricas"")","\frac{a^{2} x^{4} + a b x^{2} - b^{2} - 2 \, {\left(a b x^{2} + b^{2}\right)} \log\left(a x^{2} + b\right)}{2 \, {\left(a^{4} x^{2} + a^{3} b\right)}}"," ",0,"1/2*(a^2*x^4 + a*b*x^2 - b^2 - 2*(a*b*x^2 + b^2)*log(a*x^2 + b))/(a^4*x^2 + a^3*b)","A",0
1864,1,136,0,1.135098," ","integrate(1/(a+b/x^2)^2,x, algorithm=""fricas"")","\left[\frac{4 \, a x^{3} + 3 \, {\left(a x^{2} + b\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{a x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - b}{a x^{2} + b}\right) + 6 \, b x}{4 \, {\left(a^{3} x^{2} + a^{2} b\right)}}, \frac{2 \, a x^{3} - 3 \, {\left(a x^{2} + b\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{a x \sqrt{\frac{b}{a}}}{b}\right) + 3 \, b x}{2 \, {\left(a^{3} x^{2} + a^{2} b\right)}}\right]"," ",0,"[1/4*(4*a*x^3 + 3*(a*x^2 + b)*sqrt(-b/a)*log((a*x^2 - 2*a*x*sqrt(-b/a) - b)/(a*x^2 + b)) + 6*b*x)/(a^3*x^2 + a^2*b), 1/2*(2*a*x^3 - 3*(a*x^2 + b)*sqrt(b/a)*arctan(a*x*sqrt(b/a)/b) + 3*b*x)/(a^3*x^2 + a^2*b)]","A",0
1865,1,35,0,0.691946," ","integrate(1/(a+b/x^2)^2/x,x, algorithm=""fricas"")","\frac{{\left(a x^{2} + b\right)} \log\left(a x^{2} + b\right) + b}{2 \, {\left(a^{3} x^{2} + a^{2} b\right)}}"," ",0,"1/2*((a*x^2 + b)*log(a*x^2 + b) + b)/(a^3*x^2 + a^2*b)","A",0
1866,1,120,0,1.292550," ","integrate(1/(a+b/x^2)^2/x^2,x, algorithm=""fricas"")","\left[-\frac{2 \, a b x + {\left(a x^{2} + b\right)} \sqrt{-a b} \log\left(\frac{a x^{2} - 2 \, \sqrt{-a b} x - b}{a x^{2} + b}\right)}{4 \, {\left(a^{3} b x^{2} + a^{2} b^{2}\right)}}, -\frac{a b x - {\left(a x^{2} + b\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{b}\right)}{2 \, {\left(a^{3} b x^{2} + a^{2} b^{2}\right)}}\right]"," ",0,"[-1/4*(2*a*b*x + (a*x^2 + b)*sqrt(-a*b)*log((a*x^2 - 2*sqrt(-a*b)*x - b)/(a*x^2 + b)))/(a^3*b*x^2 + a^2*b^2), -1/2*(a*b*x - (a*x^2 + b)*sqrt(a*b)*arctan(sqrt(a*b)*x/b))/(a^3*b*x^2 + a^2*b^2)]","A",0
1867,1,15,0,1.192315," ","integrate(1/(a+b/x^2)^2/x^3,x, algorithm=""fricas"")","-\frac{1}{2 \, {\left(a^{2} x^{2} + a b\right)}}"," ",0,"-1/2/(a^2*x^2 + a*b)","A",0
1868,1,120,0,1.208333," ","integrate(1/(a+b/x^2)^2/x^4,x, algorithm=""fricas"")","\left[\frac{2 \, a b x - {\left(a x^{2} + b\right)} \sqrt{-a b} \log\left(\frac{a x^{2} - 2 \, \sqrt{-a b} x - b}{a x^{2} + b}\right)}{4 \, {\left(a^{2} b^{2} x^{2} + a b^{3}\right)}}, \frac{a b x + {\left(a x^{2} + b\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{b}\right)}{2 \, {\left(a^{2} b^{2} x^{2} + a b^{3}\right)}}\right]"," ",0,"[1/4*(2*a*b*x - (a*x^2 + b)*sqrt(-a*b)*log((a*x^2 - 2*sqrt(-a*b)*x - b)/(a*x^2 + b)))/(a^2*b^2*x^2 + a*b^3), 1/2*(a*b*x + (a*x^2 + b)*sqrt(a*b)*arctan(sqrt(a*b)*x/b))/(a^2*b^2*x^2 + a*b^3)]","A",0
1869,1,47,0,1.168192," ","integrate(1/(a+b/x^2)^2/x^5,x, algorithm=""fricas"")","-\frac{{\left(a x^{2} + b\right)} \log\left(a x^{2} + b\right) - 2 \, {\left(a x^{2} + b\right)} \log\left(x\right) - b}{2 \, {\left(a b^{2} x^{2} + b^{3}\right)}}"," ",0,"-1/2*((a*x^2 + b)*log(a*x^2 + b) - 2*(a*x^2 + b)*log(x) - b)/(a*b^2*x^2 + b^3)","A",0
1870,1,136,0,1.058438," ","integrate(1/(a+b/x^2)^2/x^6,x, algorithm=""fricas"")","\left[-\frac{6 \, a x^{2} - 3 \, {\left(a x^{3} + b x\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{a x^{2} - 2 \, b x \sqrt{-\frac{a}{b}} - b}{a x^{2} + b}\right) + 4 \, b}{4 \, {\left(a b^{2} x^{3} + b^{3} x\right)}}, -\frac{3 \, a x^{2} + 3 \, {\left(a x^{3} + b x\right)} \sqrt{\frac{a}{b}} \arctan\left(x \sqrt{\frac{a}{b}}\right) + 2 \, b}{2 \, {\left(a b^{2} x^{3} + b^{3} x\right)}}\right]"," ",0,"[-1/4*(6*a*x^2 - 3*(a*x^3 + b*x)*sqrt(-a/b)*log((a*x^2 - 2*b*x*sqrt(-a/b) - b)/(a*x^2 + b)) + 4*b)/(a*b^2*x^3 + b^3*x), -1/2*(3*a*x^2 + 3*(a*x^3 + b*x)*sqrt(a/b)*arctan(x*sqrt(a/b)) + 2*b)/(a*b^2*x^3 + b^3*x)]","A",0
1871,1,73,0,1.295039," ","integrate(1/(a+b/x^2)^2/x^7,x, algorithm=""fricas"")","-\frac{2 \, a b x^{2} + b^{2} - 2 \, {\left(a^{2} x^{4} + a b x^{2}\right)} \log\left(a x^{2} + b\right) + 4 \, {\left(a^{2} x^{4} + a b x^{2}\right)} \log\left(x\right)}{2 \, {\left(a b^{3} x^{4} + b^{4} x^{2}\right)}}"," ",0,"-1/2*(2*a*b*x^2 + b^2 - 2*(a^2*x^4 + a*b*x^2)*log(a*x^2 + b) + 4*(a^2*x^4 + a*b*x^2)*log(x))/(a*b^3*x^4 + b^4*x^2)","A",0
1872,1,172,0,1.243245," ","integrate(1/(a+b/x^2)^2/x^8,x, algorithm=""fricas"")","\left[\frac{30 \, a^{2} x^{4} + 20 \, a b x^{2} + 15 \, {\left(a^{2} x^{5} + a b x^{3}\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{a x^{2} + 2 \, b x \sqrt{-\frac{a}{b}} - b}{a x^{2} + b}\right) - 4 \, b^{2}}{12 \, {\left(a b^{3} x^{5} + b^{4} x^{3}\right)}}, \frac{15 \, a^{2} x^{4} + 10 \, a b x^{2} + 15 \, {\left(a^{2} x^{5} + a b x^{3}\right)} \sqrt{\frac{a}{b}} \arctan\left(x \sqrt{\frac{a}{b}}\right) - 2 \, b^{2}}{6 \, {\left(a b^{3} x^{5} + b^{4} x^{3}\right)}}\right]"," ",0,"[1/12*(30*a^2*x^4 + 20*a*b*x^2 + 15*(a^2*x^5 + a*b*x^3)*sqrt(-a/b)*log((a*x^2 + 2*b*x*sqrt(-a/b) - b)/(a*x^2 + b)) - 4*b^2)/(a*b^3*x^5 + b^4*x^3), 1/6*(15*a^2*x^4 + 10*a*b*x^2 + 15*(a^2*x^5 + a*b*x^3)*sqrt(a/b)*arctan(x*sqrt(a/b)) - 2*b^2)/(a*b^3*x^5 + b^4*x^3)]","A",0
1873,1,90,0,1.160237," ","integrate(1/(a+b/x^2)^2/x^9,x, algorithm=""fricas"")","\frac{6 \, a^{2} b x^{4} + 3 \, a b^{2} x^{2} - b^{3} - 6 \, {\left(a^{3} x^{6} + a^{2} b x^{4}\right)} \log\left(a x^{2} + b\right) + 12 \, {\left(a^{3} x^{6} + a^{2} b x^{4}\right)} \log\left(x\right)}{4 \, {\left(a b^{4} x^{6} + b^{5} x^{4}\right)}}"," ",0,"1/4*(6*a^2*b*x^4 + 3*a*b^2*x^2 - b^3 - 6*(a^3*x^6 + a^2*b*x^4)*log(a*x^2 + b) + 12*(a^3*x^6 + a^2*b*x^4)*log(x))/(a*b^4*x^6 + b^5*x^4)","A",0
1874,1,115,0,0.761007," ","integrate(x^5/(a+b/x^2)^3,x, algorithm=""fricas"")","\frac{2 \, a^{5} x^{10} - 5 \, a^{4} b x^{8} + 20 \, a^{3} b^{2} x^{6} + 63 \, a^{2} b^{3} x^{4} + 6 \, a b^{4} x^{2} - 27 \, b^{5} - 60 \, {\left(a^{2} b^{3} x^{4} + 2 \, a b^{4} x^{2} + b^{5}\right)} \log\left(a x^{2} + b\right)}{12 \, {\left(a^{8} x^{4} + 2 \, a^{7} b x^{2} + a^{6} b^{2}\right)}}"," ",0,"1/12*(2*a^5*x^10 - 5*a^4*b*x^8 + 20*a^3*b^2*x^6 + 63*a^2*b^3*x^4 + 6*a*b^4*x^2 - 27*b^5 - 60*(a^2*b^3*x^4 + 2*a*b^4*x^2 + b^5)*log(a*x^2 + b))/(a^8*x^4 + 2*a^7*b*x^2 + a^6*b^2)","A",0
1875,1,256,0,1.263539," ","integrate(x^4/(a+b/x^2)^3,x, algorithm=""fricas"")","\left[\frac{16 \, a^{4} x^{9} - 48 \, a^{3} b x^{7} + 336 \, a^{2} b^{2} x^{5} + 1050 \, a b^{3} x^{3} + 630 \, b^{4} x + 315 \, {\left(a^{2} b^{2} x^{4} + 2 \, a b^{3} x^{2} + b^{4}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{a x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - b}{a x^{2} + b}\right)}{80 \, {\left(a^{7} x^{4} + 2 \, a^{6} b x^{2} + a^{5} b^{2}\right)}}, \frac{8 \, a^{4} x^{9} - 24 \, a^{3} b x^{7} + 168 \, a^{2} b^{2} x^{5} + 525 \, a b^{3} x^{3} + 315 \, b^{4} x - 315 \, {\left(a^{2} b^{2} x^{4} + 2 \, a b^{3} x^{2} + b^{4}\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{a x \sqrt{\frac{b}{a}}}{b}\right)}{40 \, {\left(a^{7} x^{4} + 2 \, a^{6} b x^{2} + a^{5} b^{2}\right)}}\right]"," ",0,"[1/80*(16*a^4*x^9 - 48*a^3*b*x^7 + 336*a^2*b^2*x^5 + 1050*a*b^3*x^3 + 630*b^4*x + 315*(a^2*b^2*x^4 + 2*a*b^3*x^2 + b^4)*sqrt(-b/a)*log((a*x^2 - 2*a*x*sqrt(-b/a) - b)/(a*x^2 + b)))/(a^7*x^4 + 2*a^6*b*x^2 + a^5*b^2), 1/40*(8*a^4*x^9 - 24*a^3*b*x^7 + 168*a^2*b^2*x^5 + 525*a*b^3*x^3 + 315*b^4*x - 315*(a^2*b^2*x^4 + 2*a*b^3*x^2 + b^4)*sqrt(b/a)*arctan(a*x*sqrt(b/a)/b))/(a^7*x^4 + 2*a^6*b*x^2 + a^5*b^2)]","A",0
1876,1,103,0,1.163818," ","integrate(x^3/(a+b/x^2)^3,x, algorithm=""fricas"")","\frac{a^{4} x^{8} - 4 \, a^{3} b x^{6} - 11 \, a^{2} b^{2} x^{4} + 2 \, a b^{3} x^{2} + 7 \, b^{4} + 12 \, {\left(a^{2} b^{2} x^{4} + 2 \, a b^{3} x^{2} + b^{4}\right)} \log\left(a x^{2} + b\right)}{4 \, {\left(a^{7} x^{4} + 2 \, a^{6} b x^{2} + a^{5} b^{2}\right)}}"," ",0,"1/4*(a^4*x^8 - 4*a^3*b*x^6 - 11*a^2*b^2*x^4 + 2*a*b^3*x^2 + 7*b^4 + 12*(a^2*b^2*x^4 + 2*a*b^3*x^2 + b^4)*log(a*x^2 + b))/(a^7*x^4 + 2*a^6*b*x^2 + a^5*b^2)","A",0
1877,1,230,0,1.317520," ","integrate(x^2/(a+b/x^2)^3,x, algorithm=""fricas"")","\left[\frac{16 \, a^{3} x^{7} - 112 \, a^{2} b x^{5} - 350 \, a b^{2} x^{3} - 210 \, b^{3} x + 105 \, {\left(a^{2} b x^{4} + 2 \, a b^{2} x^{2} + b^{3}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{a x^{2} + 2 \, a x \sqrt{-\frac{b}{a}} - b}{a x^{2} + b}\right)}{48 \, {\left(a^{6} x^{4} + 2 \, a^{5} b x^{2} + a^{4} b^{2}\right)}}, \frac{8 \, a^{3} x^{7} - 56 \, a^{2} b x^{5} - 175 \, a b^{2} x^{3} - 105 \, b^{3} x + 105 \, {\left(a^{2} b x^{4} + 2 \, a b^{2} x^{2} + b^{3}\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{a x \sqrt{\frac{b}{a}}}{b}\right)}{24 \, {\left(a^{6} x^{4} + 2 \, a^{5} b x^{2} + a^{4} b^{2}\right)}}\right]"," ",0,"[1/48*(16*a^3*x^7 - 112*a^2*b*x^5 - 350*a*b^2*x^3 - 210*b^3*x + 105*(a^2*b*x^4 + 2*a*b^2*x^2 + b^3)*sqrt(-b/a)*log((a*x^2 + 2*a*x*sqrt(-b/a) - b)/(a*x^2 + b)))/(a^6*x^4 + 2*a^5*b*x^2 + a^4*b^2), 1/24*(8*a^3*x^7 - 56*a^2*b*x^5 - 175*a*b^2*x^3 - 105*b^3*x + 105*(a^2*b*x^4 + 2*a*b^2*x^2 + b^3)*sqrt(b/a)*arctan(a*x*sqrt(b/a)/b))/(a^6*x^4 + 2*a^5*b*x^2 + a^4*b^2)]","A",0
1878,1,91,0,1.195333," ","integrate(x/(a+b/x^2)^3,x, algorithm=""fricas"")","\frac{2 \, a^{3} x^{6} + 4 \, a^{2} b x^{4} - 4 \, a b^{2} x^{2} - 5 \, b^{3} - 6 \, {\left(a^{2} b x^{4} + 2 \, a b^{2} x^{2} + b^{3}\right)} \log\left(a x^{2} + b\right)}{4 \, {\left(a^{6} x^{4} + 2 \, a^{5} b x^{2} + a^{4} b^{2}\right)}}"," ",0,"1/4*(2*a^3*x^6 + 4*a^2*b*x^4 - 4*a*b^2*x^2 - 5*b^3 - 6*(a^2*b*x^4 + 2*a*b^2*x^2 + b^3)*log(a*x^2 + b))/(a^6*x^4 + 2*a^5*b*x^2 + a^4*b^2)","A",0
1879,1,202,0,1.242298," ","integrate(1/(a+b/x^2)^3,x, algorithm=""fricas"")","\left[\frac{16 \, a^{2} x^{5} + 50 \, a b x^{3} + 30 \, b^{2} x + 15 \, {\left(a^{2} x^{4} + 2 \, a b x^{2} + b^{2}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{a x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - b}{a x^{2} + b}\right)}{16 \, {\left(a^{5} x^{4} + 2 \, a^{4} b x^{2} + a^{3} b^{2}\right)}}, \frac{8 \, a^{2} x^{5} + 25 \, a b x^{3} + 15 \, b^{2} x - 15 \, {\left(a^{2} x^{4} + 2 \, a b x^{2} + b^{2}\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{a x \sqrt{\frac{b}{a}}}{b}\right)}{8 \, {\left(a^{5} x^{4} + 2 \, a^{4} b x^{2} + a^{3} b^{2}\right)}}\right]"," ",0,"[1/16*(16*a^2*x^5 + 50*a*b*x^3 + 30*b^2*x + 15*(a^2*x^4 + 2*a*b*x^2 + b^2)*sqrt(-b/a)*log((a*x^2 - 2*a*x*sqrt(-b/a) - b)/(a*x^2 + b)))/(a^5*x^4 + 2*a^4*b*x^2 + a^3*b^2), 1/8*(8*a^2*x^5 + 25*a*b*x^3 + 15*b^2*x - 15*(a^2*x^4 + 2*a*b*x^2 + b^2)*sqrt(b/a)*arctan(a*x*sqrt(b/a)/b))/(a^5*x^4 + 2*a^4*b*x^2 + a^3*b^2)]","A",0
1880,1,69,0,1.030872," ","integrate(1/(a+b/x^2)^3/x,x, algorithm=""fricas"")","\frac{4 \, a b x^{2} + 3 \, b^{2} + 2 \, {\left(a^{2} x^{4} + 2 \, a b x^{2} + b^{2}\right)} \log\left(a x^{2} + b\right)}{4 \, {\left(a^{5} x^{4} + 2 \, a^{4} b x^{2} + a^{3} b^{2}\right)}}"," ",0,"1/4*(4*a*b*x^2 + 3*b^2 + 2*(a^2*x^4 + 2*a*b*x^2 + b^2)*log(a*x^2 + b))/(a^5*x^4 + 2*a^4*b*x^2 + a^3*b^2)","A",0
1881,1,188,0,1.126432," ","integrate(1/(a+b/x^2)^3/x^2,x, algorithm=""fricas"")","\left[-\frac{10 \, a^{2} b x^{3} + 6 \, a b^{2} x + 3 \, {\left(a^{2} x^{4} + 2 \, a b x^{2} + b^{2}\right)} \sqrt{-a b} \log\left(\frac{a x^{2} - 2 \, \sqrt{-a b} x - b}{a x^{2} + b}\right)}{16 \, {\left(a^{5} b x^{4} + 2 \, a^{4} b^{2} x^{2} + a^{3} b^{3}\right)}}, -\frac{5 \, a^{2} b x^{3} + 3 \, a b^{2} x - 3 \, {\left(a^{2} x^{4} + 2 \, a b x^{2} + b^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{b}\right)}{8 \, {\left(a^{5} b x^{4} + 2 \, a^{4} b^{2} x^{2} + a^{3} b^{3}\right)}}\right]"," ",0,"[-1/16*(10*a^2*b*x^3 + 6*a*b^2*x + 3*(a^2*x^4 + 2*a*b*x^2 + b^2)*sqrt(-a*b)*log((a*x^2 - 2*sqrt(-a*b)*x - b)/(a*x^2 + b)))/(a^5*b*x^4 + 2*a^4*b^2*x^2 + a^3*b^3), -1/8*(5*a^2*b*x^3 + 3*a*b^2*x - 3*(a^2*x^4 + 2*a*b*x^2 + b^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/b))/(a^5*b*x^4 + 2*a^4*b^2*x^2 + a^3*b^3)]","A",0
1882,1,36,0,1.185315," ","integrate(1/(a+b/x^2)^3/x^3,x, algorithm=""fricas"")","-\frac{2 \, a x^{2} + b}{4 \, {\left(a^{4} x^{4} + 2 \, a^{3} b x^{2} + a^{2} b^{2}\right)}}"," ",0,"-1/4*(2*a*x^2 + b)/(a^4*x^4 + 2*a^3*b*x^2 + a^2*b^2)","B",0
1883,1,190,0,1.324888," ","integrate(1/(a+b/x^2)^3/x^4,x, algorithm=""fricas"")","\left[\frac{2 \, a^{2} b x^{3} - 2 \, a b^{2} x - {\left(a^{2} x^{4} + 2 \, a b x^{2} + b^{2}\right)} \sqrt{-a b} \log\left(\frac{a x^{2} - 2 \, \sqrt{-a b} x - b}{a x^{2} + b}\right)}{16 \, {\left(a^{4} b^{2} x^{4} + 2 \, a^{3} b^{3} x^{2} + a^{2} b^{4}\right)}}, \frac{a^{2} b x^{3} - a b^{2} x + {\left(a^{2} x^{4} + 2 \, a b x^{2} + b^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{b}\right)}{8 \, {\left(a^{4} b^{2} x^{4} + 2 \, a^{3} b^{3} x^{2} + a^{2} b^{4}\right)}}\right]"," ",0,"[1/16*(2*a^2*b*x^3 - 2*a*b^2*x - (a^2*x^4 + 2*a*b*x^2 + b^2)*sqrt(-a*b)*log((a*x^2 - 2*sqrt(-a*b)*x - b)/(a*x^2 + b)))/(a^4*b^2*x^4 + 2*a^3*b^3*x^2 + a^2*b^4), 1/8*(a^2*b*x^3 - a*b^2*x + (a^2*x^4 + 2*a*b*x^2 + b^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/b))/(a^4*b^2*x^4 + 2*a^3*b^3*x^2 + a^2*b^4)]","A",0
1884,1,26,0,1.080612," ","integrate(1/(a+b/x^2)^3/x^5,x, algorithm=""fricas"")","-\frac{1}{4 \, {\left(a^{3} x^{4} + 2 \, a^{2} b x^{2} + a b^{2}\right)}}"," ",0,"-1/4/(a^3*x^4 + 2*a^2*b*x^2 + a*b^2)","A",0
1885,1,188,0,1.236965," ","integrate(1/(a+b/x^2)^3/x^6,x, algorithm=""fricas"")","\left[\frac{6 \, a^{2} b x^{3} + 10 \, a b^{2} x - 3 \, {\left(a^{2} x^{4} + 2 \, a b x^{2} + b^{2}\right)} \sqrt{-a b} \log\left(\frac{a x^{2} - 2 \, \sqrt{-a b} x - b}{a x^{2} + b}\right)}{16 \, {\left(a^{3} b^{3} x^{4} + 2 \, a^{2} b^{4} x^{2} + a b^{5}\right)}}, \frac{3 \, a^{2} b x^{3} + 5 \, a b^{2} x + 3 \, {\left(a^{2} x^{4} + 2 \, a b x^{2} + b^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{b}\right)}{8 \, {\left(a^{3} b^{3} x^{4} + 2 \, a^{2} b^{4} x^{2} + a b^{5}\right)}}\right]"," ",0,"[1/16*(6*a^2*b*x^3 + 10*a*b^2*x - 3*(a^2*x^4 + 2*a*b*x^2 + b^2)*sqrt(-a*b)*log((a*x^2 - 2*sqrt(-a*b)*x - b)/(a*x^2 + b)))/(a^3*b^3*x^4 + 2*a^2*b^4*x^2 + a*b^5), 1/8*(3*a^2*b*x^3 + 5*a*b^2*x + 3*(a^2*x^4 + 2*a*b*x^2 + b^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/b))/(a^3*b^3*x^4 + 2*a^2*b^4*x^2 + a*b^5)]","A",0
1886,1,90,0,1.189522," ","integrate(1/(a+b/x^2)^3/x^7,x, algorithm=""fricas"")","\frac{2 \, a b x^{2} + 3 \, b^{2} - 2 \, {\left(a^{2} x^{4} + 2 \, a b x^{2} + b^{2}\right)} \log\left(a x^{2} + b\right) + 4 \, {\left(a^{2} x^{4} + 2 \, a b x^{2} + b^{2}\right)} \log\left(x\right)}{4 \, {\left(a^{2} b^{3} x^{4} + 2 \, a b^{4} x^{2} + b^{5}\right)}}"," ",0,"1/4*(2*a*b*x^2 + 3*b^2 - 2*(a^2*x^4 + 2*a*b*x^2 + b^2)*log(a*x^2 + b) + 4*(a^2*x^4 + 2*a*b*x^2 + b^2)*log(x))/(a^2*b^3*x^4 + 2*a*b^4*x^2 + b^5)","A",0
1887,1,202,0,1.258056," ","integrate(1/(a+b/x^2)^3/x^8,x, algorithm=""fricas"")","\left[-\frac{30 \, a^{2} x^{4} + 50 \, a b x^{2} - 15 \, {\left(a^{2} x^{5} + 2 \, a b x^{3} + b^{2} x\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{a x^{2} - 2 \, b x \sqrt{-\frac{a}{b}} - b}{a x^{2} + b}\right) + 16 \, b^{2}}{16 \, {\left(a^{2} b^{3} x^{5} + 2 \, a b^{4} x^{3} + b^{5} x\right)}}, -\frac{15 \, a^{2} x^{4} + 25 \, a b x^{2} + 15 \, {\left(a^{2} x^{5} + 2 \, a b x^{3} + b^{2} x\right)} \sqrt{\frac{a}{b}} \arctan\left(x \sqrt{\frac{a}{b}}\right) + 8 \, b^{2}}{8 \, {\left(a^{2} b^{3} x^{5} + 2 \, a b^{4} x^{3} + b^{5} x\right)}}\right]"," ",0,"[-1/16*(30*a^2*x^4 + 50*a*b*x^2 - 15*(a^2*x^5 + 2*a*b*x^3 + b^2*x)*sqrt(-a/b)*log((a*x^2 - 2*b*x*sqrt(-a/b) - b)/(a*x^2 + b)) + 16*b^2)/(a^2*b^3*x^5 + 2*a*b^4*x^3 + b^5*x), -1/8*(15*a^2*x^4 + 25*a*b*x^2 + 15*(a^2*x^5 + 2*a*b*x^3 + b^2*x)*sqrt(a/b)*arctan(x*sqrt(a/b)) + 8*b^2)/(a^2*b^3*x^5 + 2*a*b^4*x^3 + b^5*x)]","A",0
1888,1,119,0,1.203655," ","integrate(1/(a+b/x^2)^3/x^9,x, algorithm=""fricas"")","-\frac{6 \, a^{2} b x^{4} + 9 \, a b^{2} x^{2} + 2 \, b^{3} - 6 \, {\left(a^{3} x^{6} + 2 \, a^{2} b x^{4} + a b^{2} x^{2}\right)} \log\left(a x^{2} + b\right) + 12 \, {\left(a^{3} x^{6} + 2 \, a^{2} b x^{4} + a b^{2} x^{2}\right)} \log\left(x\right)}{4 \, {\left(a^{2} b^{4} x^{6} + 2 \, a b^{5} x^{4} + b^{6} x^{2}\right)}}"," ",0,"-1/4*(6*a^2*b*x^4 + 9*a*b^2*x^2 + 2*b^3 - 6*(a^3*x^6 + 2*a^2*b*x^4 + a*b^2*x^2)*log(a*x^2 + b) + 12*(a^3*x^6 + 2*a^2*b*x^4 + a*b^2*x^2)*log(x))/(a^2*b^4*x^6 + 2*a*b^5*x^4 + b^6*x^2)","A",0
1889,1,238,0,1.189267," ","integrate(1/(a+b/x^2)^3/x^10,x, algorithm=""fricas"")","\left[\frac{210 \, a^{3} x^{6} + 350 \, a^{2} b x^{4} + 112 \, a b^{2} x^{2} - 16 \, b^{3} + 105 \, {\left(a^{3} x^{7} + 2 \, a^{2} b x^{5} + a b^{2} x^{3}\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{a x^{2} + 2 \, b x \sqrt{-\frac{a}{b}} - b}{a x^{2} + b}\right)}{48 \, {\left(a^{2} b^{4} x^{7} + 2 \, a b^{5} x^{5} + b^{6} x^{3}\right)}}, \frac{105 \, a^{3} x^{6} + 175 \, a^{2} b x^{4} + 56 \, a b^{2} x^{2} - 8 \, b^{3} + 105 \, {\left(a^{3} x^{7} + 2 \, a^{2} b x^{5} + a b^{2} x^{3}\right)} \sqrt{\frac{a}{b}} \arctan\left(x \sqrt{\frac{a}{b}}\right)}{24 \, {\left(a^{2} b^{4} x^{7} + 2 \, a b^{5} x^{5} + b^{6} x^{3}\right)}}\right]"," ",0,"[1/48*(210*a^3*x^6 + 350*a^2*b*x^4 + 112*a*b^2*x^2 - 16*b^3 + 105*(a^3*x^7 + 2*a^2*b*x^5 + a*b^2*x^3)*sqrt(-a/b)*log((a*x^2 + 2*b*x*sqrt(-a/b) - b)/(a*x^2 + b)))/(a^2*b^4*x^7 + 2*a*b^5*x^5 + b^6*x^3), 1/24*(105*a^3*x^6 + 175*a^2*b*x^4 + 56*a*b^2*x^2 - 8*b^3 + 105*(a^3*x^7 + 2*a^2*b*x^5 + a*b^2*x^3)*sqrt(a/b)*arctan(x*sqrt(a/b)))/(a^2*b^4*x^7 + 2*a*b^5*x^5 + b^6*x^3)]","A",0
1890,1,134,0,1.075861," ","integrate(1/(a+b/x^2)^3/x^11,x, algorithm=""fricas"")","\frac{12 \, a^{3} b x^{6} + 18 \, a^{2} b^{2} x^{4} + 4 \, a b^{3} x^{2} - b^{4} - 12 \, {\left(a^{4} x^{8} + 2 \, a^{3} b x^{6} + a^{2} b^{2} x^{4}\right)} \log\left(a x^{2} + b\right) + 24 \, {\left(a^{4} x^{8} + 2 \, a^{3} b x^{6} + a^{2} b^{2} x^{4}\right)} \log\left(x\right)}{4 \, {\left(a^{2} b^{5} x^{8} + 2 \, a b^{6} x^{6} + b^{7} x^{4}\right)}}"," ",0,"1/4*(12*a^3*b*x^6 + 18*a^2*b^2*x^4 + 4*a*b^3*x^2 - b^4 - 12*(a^4*x^8 + 2*a^3*b*x^6 + a^2*b^2*x^4)*log(a*x^2 + b) + 24*(a^4*x^8 + 2*a^3*b*x^6 + a^2*b^2*x^4)*log(x))/(a^2*b^5*x^8 + 2*a*b^6*x^6 + b^7*x^4)","A",0
1891,1,152,0,1.110464," ","integrate((a+b/x^2)^(1/2)*x^3,x, algorithm=""fricas"")","\left[\frac{\sqrt{a} b^{2} \log\left(-2 \, a x^{2} + 2 \, \sqrt{a} x^{2} \sqrt{\frac{a x^{2} + b}{x^{2}}} - b\right) + 2 \, {\left(2 \, a^{2} x^{4} + a b x^{2}\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{16 \, a^{2}}, \frac{\sqrt{-a} b^{2} \arctan\left(\frac{\sqrt{-a} x^{2} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{a x^{2} + b}\right) + {\left(2 \, a^{2} x^{4} + a b x^{2}\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{8 \, a^{2}}\right]"," ",0,"[1/16*(sqrt(a)*b^2*log(-2*a*x^2 + 2*sqrt(a)*x^2*sqrt((a*x^2 + b)/x^2) - b) + 2*(2*a^2*x^4 + a*b*x^2)*sqrt((a*x^2 + b)/x^2))/a^2, 1/8*(sqrt(-a)*b^2*arctan(sqrt(-a)*x^2*sqrt((a*x^2 + b)/x^2)/(a*x^2 + b)) + (2*a^2*x^4 + a*b*x^2)*sqrt((a*x^2 + b)/x^2))/a^2]","A",0
1892,1,27,0,1.056715," ","integrate((a+b/x^2)^(1/2)*x^2,x, algorithm=""fricas"")","\frac{{\left(a x^{3} + b x\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{3 \, a}"," ",0,"1/3*(a*x^3 + b*x)*sqrt((a*x^2 + b)/x^2)/a","A",0
1893,1,127,0,1.340515," ","integrate((a+b/x^2)^(1/2)*x,x, algorithm=""fricas"")","\left[\frac{2 \, a x^{2} \sqrt{\frac{a x^{2} + b}{x^{2}}} + \sqrt{a} b \log\left(-2 \, a x^{2} - 2 \, \sqrt{a} x^{2} \sqrt{\frac{a x^{2} + b}{x^{2}}} - b\right)}{4 \, a}, \frac{a x^{2} \sqrt{\frac{a x^{2} + b}{x^{2}}} - \sqrt{-a} b \arctan\left(\frac{\sqrt{-a} x^{2} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{a x^{2} + b}\right)}{2 \, a}\right]"," ",0,"[1/4*(2*a*x^2*sqrt((a*x^2 + b)/x^2) + sqrt(a)*b*log(-2*a*x^2 - 2*sqrt(a)*x^2*sqrt((a*x^2 + b)/x^2) - b))/a, 1/2*(a*x^2*sqrt((a*x^2 + b)/x^2) - sqrt(-a)*b*arctan(sqrt(-a)*x^2*sqrt((a*x^2 + b)/x^2)/(a*x^2 + b)))/a]","A",0
1894,1,108,0,1.268589," ","integrate((a+b/x^2)^(1/2),x, algorithm=""fricas"")","\left[x \sqrt{\frac{a x^{2} + b}{x^{2}}} + \frac{1}{2} \, \sqrt{b} \log\left(-\frac{a x^{2} - 2 \, \sqrt{b} x \sqrt{\frac{a x^{2} + b}{x^{2}}} + 2 \, b}{x^{2}}\right), x \sqrt{\frac{a x^{2} + b}{x^{2}}} + \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x \sqrt{\frac{a x^{2} + b}{x^{2}}}}{a x^{2} + b}\right)\right]"," ",0,"[x*sqrt((a*x^2 + b)/x^2) + 1/2*sqrt(b)*log(-(a*x^2 - 2*sqrt(b)*x*sqrt((a*x^2 + b)/x^2) + 2*b)/x^2), x*sqrt((a*x^2 + b)/x^2) + sqrt(-b)*arctan(sqrt(-b)*x*sqrt((a*x^2 + b)/x^2)/(a*x^2 + b))]","A",0
1895,1,109,0,1.256003," ","integrate((a+b/x^2)^(1/2)/x,x, algorithm=""fricas"")","\left[\frac{1}{2} \, \sqrt{a} \log\left(-2 \, a x^{2} - 2 \, \sqrt{a} x^{2} \sqrt{\frac{a x^{2} + b}{x^{2}}} - b\right) - \sqrt{\frac{a x^{2} + b}{x^{2}}}, -\sqrt{-a} \arctan\left(\frac{\sqrt{-a} x^{2} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{a x^{2} + b}\right) - \sqrt{\frac{a x^{2} + b}{x^{2}}}\right]"," ",0,"[1/2*sqrt(a)*log(-2*a*x^2 - 2*sqrt(a)*x^2*sqrt((a*x^2 + b)/x^2) - b) - sqrt((a*x^2 + b)/x^2), -sqrt(-a)*arctan(sqrt(-a)*x^2*sqrt((a*x^2 + b)/x^2)/(a*x^2 + b)) - sqrt((a*x^2 + b)/x^2)]","A",0
1896,1,129,0,1.284650," ","integrate((a+b/x^2)^(1/2)/x^2,x, algorithm=""fricas"")","\left[\frac{a \sqrt{b} x \log\left(-\frac{a x^{2} - 2 \, \sqrt{b} x \sqrt{\frac{a x^{2} + b}{x^{2}}} + 2 \, b}{x^{2}}\right) - 2 \, b \sqrt{\frac{a x^{2} + b}{x^{2}}}}{4 \, b x}, \frac{a \sqrt{-b} x \arctan\left(\frac{\sqrt{-b} x \sqrt{\frac{a x^{2} + b}{x^{2}}}}{a x^{2} + b}\right) - b \sqrt{\frac{a x^{2} + b}{x^{2}}}}{2 \, b x}\right]"," ",0,"[1/4*(a*sqrt(b)*x*log(-(a*x^2 - 2*sqrt(b)*x*sqrt((a*x^2 + b)/x^2) + 2*b)/x^2) - 2*b*sqrt((a*x^2 + b)/x^2))/(b*x), 1/2*(a*sqrt(-b)*x*arctan(sqrt(-b)*x*sqrt((a*x^2 + b)/x^2)/(a*x^2 + b)) - b*sqrt((a*x^2 + b)/x^2))/(b*x)]","A",0
1897,1,28,0,1.293013," ","integrate((a+b/x^2)^(1/2)/x^3,x, algorithm=""fricas"")","-\frac{{\left(a x^{2} + b\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{3 \, b x^{2}}"," ",0,"-1/3*(a*x^2 + b)*sqrt((a*x^2 + b)/x^2)/(b*x^2)","A",0
1898,1,158,0,1.285849," ","integrate((a+b/x^2)^(1/2)/x^4,x, algorithm=""fricas"")","\left[\frac{a^{2} \sqrt{b} x^{3} \log\left(-\frac{a x^{2} + 2 \, \sqrt{b} x \sqrt{\frac{a x^{2} + b}{x^{2}}} + 2 \, b}{x^{2}}\right) - 2 \, {\left(a b x^{2} + 2 \, b^{2}\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{16 \, b^{2} x^{3}}, -\frac{a^{2} \sqrt{-b} x^{3} \arctan\left(\frac{\sqrt{-b} x \sqrt{\frac{a x^{2} + b}{x^{2}}}}{a x^{2} + b}\right) + {\left(a b x^{2} + 2 \, b^{2}\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{8 \, b^{2} x^{3}}\right]"," ",0,"[1/16*(a^2*sqrt(b)*x^3*log(-(a*x^2 + 2*sqrt(b)*x*sqrt((a*x^2 + b)/x^2) + 2*b)/x^2) - 2*(a*b*x^2 + 2*b^2)*sqrt((a*x^2 + b)/x^2))/(b^2*x^3), -1/8*(a^2*sqrt(-b)*x^3*arctan(sqrt(-b)*x*sqrt((a*x^2 + b)/x^2)/(a*x^2 + b)) + (a*b*x^2 + 2*b^2)*sqrt((a*x^2 + b)/x^2))/(b^2*x^3)]","A",0
1899,1,157,0,1.369347," ","integrate((a+b/x^2)^(3/2)*x^3,x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{a} b^{2} \log\left(-2 \, a x^{2} - 2 \, \sqrt{a} x^{2} \sqrt{\frac{a x^{2} + b}{x^{2}}} - b\right) + 2 \, {\left(2 \, a^{2} x^{4} + 5 \, a b x^{2}\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{16 \, a}, -\frac{3 \, \sqrt{-a} b^{2} \arctan\left(\frac{\sqrt{-a} x^{2} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{a x^{2} + b}\right) - {\left(2 \, a^{2} x^{4} + 5 \, a b x^{2}\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{8 \, a}\right]"," ",0,"[1/16*(3*sqrt(a)*b^2*log(-2*a*x^2 - 2*sqrt(a)*x^2*sqrt((a*x^2 + b)/x^2) - b) + 2*(2*a^2*x^4 + 5*a*b*x^2)*sqrt((a*x^2 + b)/x^2))/a, -1/8*(3*sqrt(-a)*b^2*arctan(sqrt(-a)*x^2*sqrt((a*x^2 + b)/x^2)/(a*x^2 + b)) - (2*a^2*x^4 + 5*a*b*x^2)*sqrt((a*x^2 + b)/x^2))/a]","A",0
1900,1,129,0,0.920135," ","integrate((a+b/x^2)^(3/2)*x^2,x, algorithm=""fricas"")","\left[\frac{1}{2} \, b^{\frac{3}{2}} \log\left(-\frac{a x^{2} - 2 \, \sqrt{b} x \sqrt{\frac{a x^{2} + b}{x^{2}}} + 2 \, b}{x^{2}}\right) + \frac{1}{3} \, {\left(a x^{3} + 4 \, b x\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}, \sqrt{-b} b \arctan\left(\frac{\sqrt{-b} x \sqrt{\frac{a x^{2} + b}{x^{2}}}}{a x^{2} + b}\right) + \frac{1}{3} \, {\left(a x^{3} + 4 \, b x\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}\right]"," ",0,"[1/2*b^(3/2)*log(-(a*x^2 - 2*sqrt(b)*x*sqrt((a*x^2 + b)/x^2) + 2*b)/x^2) + 1/3*(a*x^3 + 4*b*x)*sqrt((a*x^2 + b)/x^2), sqrt(-b)*b*arctan(sqrt(-b)*x*sqrt((a*x^2 + b)/x^2)/(a*x^2 + b)) + 1/3*(a*x^3 + 4*b*x)*sqrt((a*x^2 + b)/x^2)]","A",0
1901,1,129,0,1.265632," ","integrate((a+b/x^2)^(3/2)*x,x, algorithm=""fricas"")","\left[\frac{3}{4} \, \sqrt{a} b \log\left(-2 \, a x^{2} - 2 \, \sqrt{a} x^{2} \sqrt{\frac{a x^{2} + b}{x^{2}}} - b\right) + \frac{1}{2} \, {\left(a x^{2} - 2 \, b\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}, -\frac{3}{2} \, \sqrt{-a} b \arctan\left(\frac{\sqrt{-a} x^{2} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{a x^{2} + b}\right) + \frac{1}{2} \, {\left(a x^{2} - 2 \, b\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}\right]"," ",0,"[3/4*sqrt(a)*b*log(-2*a*x^2 - 2*sqrt(a)*x^2*sqrt((a*x^2 + b)/x^2) - b) + 1/2*(a*x^2 - 2*b)*sqrt((a*x^2 + b)/x^2), -3/2*sqrt(-a)*b*arctan(sqrt(-a)*x^2*sqrt((a*x^2 + b)/x^2)/(a*x^2 + b)) + 1/2*(a*x^2 - 2*b)*sqrt((a*x^2 + b)/x^2)]","A",0
1902,1,142,0,1.188368," ","integrate((a+b/x^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, a \sqrt{b} x \log\left(-\frac{a x^{2} - 2 \, \sqrt{b} x \sqrt{\frac{a x^{2} + b}{x^{2}}} + 2 \, b}{x^{2}}\right) + 2 \, {\left(2 \, a x^{2} - b\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{4 \, x}, \frac{3 \, a \sqrt{-b} x \arctan\left(\frac{\sqrt{-b} x \sqrt{\frac{a x^{2} + b}{x^{2}}}}{a x^{2} + b}\right) + {\left(2 \, a x^{2} - b\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{2 \, x}\right]"," ",0,"[1/4*(3*a*sqrt(b)*x*log(-(a*x^2 - 2*sqrt(b)*x*sqrt((a*x^2 + b)/x^2) + 2*b)/x^2) + 2*(2*a*x^2 - b)*sqrt((a*x^2 + b)/x^2))/x, 1/2*(3*a*sqrt(-b)*x*arctan(sqrt(-b)*x*sqrt((a*x^2 + b)/x^2)/(a*x^2 + b)) + (2*a*x^2 - b)*sqrt((a*x^2 + b)/x^2))/x]","A",0
1903,1,141,0,1.352798," ","integrate((a+b/x^2)^(3/2)/x,x, algorithm=""fricas"")","\left[\frac{3 \, a^{\frac{3}{2}} x^{2} \log\left(-2 \, a x^{2} - 2 \, \sqrt{a} x^{2} \sqrt{\frac{a x^{2} + b}{x^{2}}} - b\right) - 2 \, {\left(4 \, a x^{2} + b\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{6 \, x^{2}}, -\frac{3 \, \sqrt{-a} a x^{2} \arctan\left(\frac{\sqrt{-a} x^{2} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{a x^{2} + b}\right) + {\left(4 \, a x^{2} + b\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{3 \, x^{2}}\right]"," ",0,"[1/6*(3*a^(3/2)*x^2*log(-2*a*x^2 - 2*sqrt(a)*x^2*sqrt((a*x^2 + b)/x^2) - b) - 2*(4*a*x^2 + b)*sqrt((a*x^2 + b)/x^2))/x^2, -1/3*(3*sqrt(-a)*a*x^2*arctan(sqrt(-a)*x^2*sqrt((a*x^2 + b)/x^2)/(a*x^2 + b)) + (4*a*x^2 + b)*sqrt((a*x^2 + b)/x^2))/x^2]","A",0
1904,1,163,0,1.233853," ","integrate((a+b/x^2)^(3/2)/x^2,x, algorithm=""fricas"")","\left[\frac{3 \, a^{2} \sqrt{b} x^{3} \log\left(-\frac{a x^{2} - 2 \, \sqrt{b} x \sqrt{\frac{a x^{2} + b}{x^{2}}} + 2 \, b}{x^{2}}\right) - 2 \, {\left(5 \, a b x^{2} + 2 \, b^{2}\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{16 \, b x^{3}}, \frac{3 \, a^{2} \sqrt{-b} x^{3} \arctan\left(\frac{\sqrt{-b} x \sqrt{\frac{a x^{2} + b}{x^{2}}}}{a x^{2} + b}\right) - {\left(5 \, a b x^{2} + 2 \, b^{2}\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{8 \, b x^{3}}\right]"," ",0,"[1/16*(3*a^2*sqrt(b)*x^3*log(-(a*x^2 - 2*sqrt(b)*x*sqrt((a*x^2 + b)/x^2) + 2*b)/x^2) - 2*(5*a*b*x^2 + 2*b^2)*sqrt((a*x^2 + b)/x^2))/(b*x^3), 1/8*(3*a^2*sqrt(-b)*x^3*arctan(sqrt(-b)*x*sqrt((a*x^2 + b)/x^2)/(a*x^2 + b)) - (5*a*b*x^2 + 2*b^2)*sqrt((a*x^2 + b)/x^2))/(b*x^3)]","A",0
1905,1,39,0,0.763497," ","integrate((a+b/x^2)^(3/2)/x^3,x, algorithm=""fricas"")","-\frac{{\left(a^{2} x^{4} + 2 \, a b x^{2} + b^{2}\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{5 \, b x^{4}}"," ",0,"-1/5*(a^2*x^4 + 2*a*b*x^2 + b^2)*sqrt((a*x^2 + b)/x^2)/(b*x^4)","B",0
1906,1,184,0,1.177487," ","integrate((a+b/x^2)^(3/2)/x^4,x, algorithm=""fricas"")","\left[\frac{3 \, a^{3} \sqrt{b} x^{5} \log\left(-\frac{a x^{2} + 2 \, \sqrt{b} x \sqrt{\frac{a x^{2} + b}{x^{2}}} + 2 \, b}{x^{2}}\right) - 2 \, {\left(3 \, a^{2} b x^{4} + 14 \, a b^{2} x^{2} + 8 \, b^{3}\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{96 \, b^{2} x^{5}}, -\frac{3 \, a^{3} \sqrt{-b} x^{5} \arctan\left(\frac{\sqrt{-b} x \sqrt{\frac{a x^{2} + b}{x^{2}}}}{a x^{2} + b}\right) + {\left(3 \, a^{2} b x^{4} + 14 \, a b^{2} x^{2} + 8 \, b^{3}\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{48 \, b^{2} x^{5}}\right]"," ",0,"[1/96*(3*a^3*sqrt(b)*x^5*log(-(a*x^2 + 2*sqrt(b)*x*sqrt((a*x^2 + b)/x^2) + 2*b)/x^2) - 2*(3*a^2*b*x^4 + 14*a*b^2*x^2 + 8*b^3)*sqrt((a*x^2 + b)/x^2))/(b^2*x^5), -1/48*(3*a^3*sqrt(-b)*x^5*arctan(sqrt(-b)*x*sqrt((a*x^2 + b)/x^2)/(a*x^2 + b)) + (3*a^2*b*x^4 + 14*a*b^2*x^2 + 8*b^3)*sqrt((a*x^2 + b)/x^2))/(b^2*x^5)]","A",0
1907,1,157,0,1.287404," ","integrate((a+b/x^2)^(5/2)*x^3,x, algorithm=""fricas"")","\left[\frac{15}{16} \, \sqrt{a} b^{2} \log\left(-2 \, a x^{2} - 2 \, \sqrt{a} x^{2} \sqrt{\frac{a x^{2} + b}{x^{2}}} - b\right) + \frac{1}{8} \, {\left(2 \, a^{2} x^{4} + 9 \, a b x^{2} - 8 \, b^{2}\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}, -\frac{15}{8} \, \sqrt{-a} b^{2} \arctan\left(\frac{\sqrt{-a} x^{2} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{a x^{2} + b}\right) + \frac{1}{8} \, {\left(2 \, a^{2} x^{4} + 9 \, a b x^{2} - 8 \, b^{2}\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}\right]"," ",0,"[15/16*sqrt(a)*b^2*log(-2*a*x^2 - 2*sqrt(a)*x^2*sqrt((a*x^2 + b)/x^2) - b) + 1/8*(2*a^2*x^4 + 9*a*b*x^2 - 8*b^2)*sqrt((a*x^2 + b)/x^2), -15/8*sqrt(-a)*b^2*arctan(sqrt(-a)*x^2*sqrt((a*x^2 + b)/x^2)/(a*x^2 + b)) + 1/8*(2*a^2*x^4 + 9*a*b*x^2 - 8*b^2)*sqrt((a*x^2 + b)/x^2)]","A",0
1908,1,165,0,1.262011," ","integrate((a+b/x^2)^(5/2)*x^2,x, algorithm=""fricas"")","\left[\frac{15 \, a b^{\frac{3}{2}} x \log\left(-\frac{a x^{2} - 2 \, \sqrt{b} x \sqrt{\frac{a x^{2} + b}{x^{2}}} + 2 \, b}{x^{2}}\right) + 2 \, {\left(2 \, a^{2} x^{4} + 14 \, a b x^{2} - 3 \, b^{2}\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{12 \, x}, \frac{15 \, a \sqrt{-b} b x \arctan\left(\frac{\sqrt{-b} x \sqrt{\frac{a x^{2} + b}{x^{2}}}}{a x^{2} + b}\right) + {\left(2 \, a^{2} x^{4} + 14 \, a b x^{2} - 3 \, b^{2}\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{6 \, x}\right]"," ",0,"[1/12*(15*a*b^(3/2)*x*log(-(a*x^2 - 2*sqrt(b)*x*sqrt((a*x^2 + b)/x^2) + 2*b)/x^2) + 2*(2*a^2*x^4 + 14*a*b*x^2 - 3*b^2)*sqrt((a*x^2 + b)/x^2))/x, 1/6*(15*a*sqrt(-b)*b*x*arctan(sqrt(-b)*x*sqrt((a*x^2 + b)/x^2)/(a*x^2 + b)) + (2*a^2*x^4 + 14*a*b*x^2 - 3*b^2)*sqrt((a*x^2 + b)/x^2))/x]","A",0
1909,1,170,0,1.268266," ","integrate((a+b/x^2)^(5/2)*x,x, algorithm=""fricas"")","\left[\frac{15 \, a^{\frac{3}{2}} b x^{2} \log\left(-2 \, a x^{2} - 2 \, \sqrt{a} x^{2} \sqrt{\frac{a x^{2} + b}{x^{2}}} - b\right) + 2 \, {\left(3 \, a^{2} x^{4} - 14 \, a b x^{2} - 2 \, b^{2}\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{12 \, x^{2}}, -\frac{15 \, \sqrt{-a} a b x^{2} \arctan\left(\frac{\sqrt{-a} x^{2} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{a x^{2} + b}\right) - {\left(3 \, a^{2} x^{4} - 14 \, a b x^{2} - 2 \, b^{2}\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{6 \, x^{2}}\right]"," ",0,"[1/12*(15*a^(3/2)*b*x^2*log(-2*a*x^2 - 2*sqrt(a)*x^2*sqrt((a*x^2 + b)/x^2) - b) + 2*(3*a^2*x^4 - 14*a*b*x^2 - 2*b^2)*sqrt((a*x^2 + b)/x^2))/x^2, -1/6*(15*sqrt(-a)*a*b*x^2*arctan(sqrt(-a)*x^2*sqrt((a*x^2 + b)/x^2)/(a*x^2 + b)) - (3*a^2*x^4 - 14*a*b*x^2 - 2*b^2)*sqrt((a*x^2 + b)/x^2))/x^2]","A",0
1910,1,172,0,1.280775," ","integrate((a+b/x^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, a^{2} \sqrt{b} x^{3} \log\left(-\frac{a x^{2} - 2 \, \sqrt{b} x \sqrt{\frac{a x^{2} + b}{x^{2}}} + 2 \, b}{x^{2}}\right) + 2 \, {\left(8 \, a^{2} x^{4} - 9 \, a b x^{2} - 2 \, b^{2}\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{16 \, x^{3}}, \frac{15 \, a^{2} \sqrt{-b} x^{3} \arctan\left(\frac{\sqrt{-b} x \sqrt{\frac{a x^{2} + b}{x^{2}}}}{a x^{2} + b}\right) + {\left(8 \, a^{2} x^{4} - 9 \, a b x^{2} - 2 \, b^{2}\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{8 \, x^{3}}\right]"," ",0,"[1/16*(15*a^2*sqrt(b)*x^3*log(-(a*x^2 - 2*sqrt(b)*x*sqrt((a*x^2 + b)/x^2) + 2*b)/x^2) + 2*(8*a^2*x^4 - 9*a*b*x^2 - 2*b^2)*sqrt((a*x^2 + b)/x^2))/x^3, 1/8*(15*a^2*sqrt(-b)*x^3*arctan(sqrt(-b)*x*sqrt((a*x^2 + b)/x^2)/(a*x^2 + b)) + (8*a^2*x^4 - 9*a*b*x^2 - 2*b^2)*sqrt((a*x^2 + b)/x^2))/x^3]","A",0
1911,1,169,0,1.096008," ","integrate((a+b/x^2)^(5/2)/x,x, algorithm=""fricas"")","\left[\frac{15 \, a^{\frac{5}{2}} x^{4} \log\left(-2 \, a x^{2} - 2 \, \sqrt{a} x^{2} \sqrt{\frac{a x^{2} + b}{x^{2}}} - b\right) - 2 \, {\left(23 \, a^{2} x^{4} + 11 \, a b x^{2} + 3 \, b^{2}\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{30 \, x^{4}}, -\frac{15 \, \sqrt{-a} a^{2} x^{4} \arctan\left(\frac{\sqrt{-a} x^{2} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{a x^{2} + b}\right) + {\left(23 \, a^{2} x^{4} + 11 \, a b x^{2} + 3 \, b^{2}\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{15 \, x^{4}}\right]"," ",0,"[1/30*(15*a^(5/2)*x^4*log(-2*a*x^2 - 2*sqrt(a)*x^2*sqrt((a*x^2 + b)/x^2) - b) - 2*(23*a^2*x^4 + 11*a*b*x^2 + 3*b^2)*sqrt((a*x^2 + b)/x^2))/x^4, -1/15*(15*sqrt(-a)*a^2*x^4*arctan(sqrt(-a)*x^2*sqrt((a*x^2 + b)/x^2)/(a*x^2 + b)) + (23*a^2*x^4 + 11*a*b*x^2 + 3*b^2)*sqrt((a*x^2 + b)/x^2))/x^4]","A",0
1912,1,185,0,1.483396," ","integrate((a+b/x^2)^(5/2)/x^2,x, algorithm=""fricas"")","\left[\frac{15 \, a^{3} \sqrt{b} x^{5} \log\left(-\frac{a x^{2} - 2 \, \sqrt{b} x \sqrt{\frac{a x^{2} + b}{x^{2}}} + 2 \, b}{x^{2}}\right) - 2 \, {\left(33 \, a^{2} b x^{4} + 26 \, a b^{2} x^{2} + 8 \, b^{3}\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{96 \, b x^{5}}, \frac{15 \, a^{3} \sqrt{-b} x^{5} \arctan\left(\frac{\sqrt{-b} x \sqrt{\frac{a x^{2} + b}{x^{2}}}}{a x^{2} + b}\right) - {\left(33 \, a^{2} b x^{4} + 26 \, a b^{2} x^{2} + 8 \, b^{3}\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{48 \, b x^{5}}\right]"," ",0,"[1/96*(15*a^3*sqrt(b)*x^5*log(-(a*x^2 - 2*sqrt(b)*x*sqrt((a*x^2 + b)/x^2) + 2*b)/x^2) - 2*(33*a^2*b*x^4 + 26*a*b^2*x^2 + 8*b^3)*sqrt((a*x^2 + b)/x^2))/(b*x^5), 1/48*(15*a^3*sqrt(-b)*x^5*arctan(sqrt(-b)*x*sqrt((a*x^2 + b)/x^2)/(a*x^2 + b)) - (33*a^2*b*x^4 + 26*a*b^2*x^2 + 8*b^3)*sqrt((a*x^2 + b)/x^2))/(b*x^5)]","A",0
1913,1,50,0,1.450197," ","integrate((a+b/x^2)^(5/2)/x^3,x, algorithm=""fricas"")","-\frac{{\left(a^{3} x^{6} + 3 \, a^{2} b x^{4} + 3 \, a b^{2} x^{2} + b^{3}\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{7 \, b x^{6}}"," ",0,"-1/7*(a^3*x^6 + 3*a^2*b*x^4 + 3*a*b^2*x^2 + b^3)*sqrt((a*x^2 + b)/x^2)/(b*x^6)","B",0
1914,1,206,0,1.644943," ","integrate((a+b/x^2)^(5/2)/x^4,x, algorithm=""fricas"")","\left[\frac{15 \, a^{4} \sqrt{b} x^{7} \log\left(-\frac{a x^{2} + 2 \, \sqrt{b} x \sqrt{\frac{a x^{2} + b}{x^{2}}} + 2 \, b}{x^{2}}\right) - 2 \, {\left(15 \, a^{3} b x^{6} + 118 \, a^{2} b^{2} x^{4} + 136 \, a b^{3} x^{2} + 48 \, b^{4}\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{768 \, b^{2} x^{7}}, -\frac{15 \, a^{4} \sqrt{-b} x^{7} \arctan\left(\frac{\sqrt{-b} x \sqrt{\frac{a x^{2} + b}{x^{2}}}}{a x^{2} + b}\right) + {\left(15 \, a^{3} b x^{6} + 118 \, a^{2} b^{2} x^{4} + 136 \, a b^{3} x^{2} + 48 \, b^{4}\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{384 \, b^{2} x^{7}}\right]"," ",0,"[1/768*(15*a^4*sqrt(b)*x^7*log(-(a*x^2 + 2*sqrt(b)*x*sqrt((a*x^2 + b)/x^2) + 2*b)/x^2) - 2*(15*a^3*b*x^6 + 118*a^2*b^2*x^4 + 136*a*b^3*x^2 + 48*b^4)*sqrt((a*x^2 + b)/x^2))/(b^2*x^7), -1/384*(15*a^4*sqrt(-b)*x^7*arctan(sqrt(-b)*x*sqrt((a*x^2 + b)/x^2)/(a*x^2 + b)) + (15*a^3*b*x^6 + 118*a^2*b^2*x^4 + 136*a*b^3*x^2 + 48*b^4)*sqrt((a*x^2 + b)/x^2))/(b^2*x^7)]","A",0
1915,1,157,0,1.498819," ","integrate(x^3/(a+b/x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{a} b^{2} \log\left(-2 \, a x^{2} - 2 \, \sqrt{a} x^{2} \sqrt{\frac{a x^{2} + b}{x^{2}}} - b\right) + 2 \, {\left(2 \, a^{2} x^{4} - 3 \, a b x^{2}\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{16 \, a^{3}}, -\frac{3 \, \sqrt{-a} b^{2} \arctan\left(\frac{\sqrt{-a} x^{2} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{a x^{2} + b}\right) - {\left(2 \, a^{2} x^{4} - 3 \, a b x^{2}\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{8 \, a^{3}}\right]"," ",0,"[1/16*(3*sqrt(a)*b^2*log(-2*a*x^2 - 2*sqrt(a)*x^2*sqrt((a*x^2 + b)/x^2) - b) + 2*(2*a^2*x^4 - 3*a*b*x^2)*sqrt((a*x^2 + b)/x^2))/a^3, -1/8*(3*sqrt(-a)*b^2*arctan(sqrt(-a)*x^2*sqrt((a*x^2 + b)/x^2)/(a*x^2 + b)) - (2*a^2*x^4 - 3*a*b*x^2)*sqrt((a*x^2 + b)/x^2))/a^3]","A",0
1916,1,126,0,1.591498," ","integrate(x/(a+b/x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, a x^{2} \sqrt{\frac{a x^{2} + b}{x^{2}}} + \sqrt{a} b \log\left(-2 \, a x^{2} + 2 \, \sqrt{a} x^{2} \sqrt{\frac{a x^{2} + b}{x^{2}}} - b\right)}{4 \, a^{2}}, \frac{a x^{2} \sqrt{\frac{a x^{2} + b}{x^{2}}} + \sqrt{-a} b \arctan\left(\frac{\sqrt{-a} x^{2} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{a x^{2} + b}\right)}{2 \, a^{2}}\right]"," ",0,"[1/4*(2*a*x^2*sqrt((a*x^2 + b)/x^2) + sqrt(a)*b*log(-2*a*x^2 + 2*sqrt(a)*x^2*sqrt((a*x^2 + b)/x^2) - b))/a^2, 1/2*(a*x^2*sqrt((a*x^2 + b)/x^2) + sqrt(-a)*b*arctan(sqrt(-a)*x^2*sqrt((a*x^2 + b)/x^2)/(a*x^2 + b)))/a^2]","A",0
1917,1,80,0,1.258254," ","integrate(1/(a+b/x^2)^(1/2)/x,x, algorithm=""fricas"")","\left[\frac{\log\left(-2 \, a x^{2} - 2 \, \sqrt{a} x^{2} \sqrt{\frac{a x^{2} + b}{x^{2}}} - b\right)}{2 \, \sqrt{a}}, -\frac{\sqrt{-a} \arctan\left(\frac{\sqrt{-a} x^{2} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{a x^{2} + b}\right)}{a}\right]"," ",0,"[1/2*log(-2*a*x^2 - 2*sqrt(a)*x^2*sqrt((a*x^2 + b)/x^2) - b)/sqrt(a), -sqrt(-a)*arctan(sqrt(-a)*x^2*sqrt((a*x^2 + b)/x^2)/(a*x^2 + b))/a]","B",0
1918,1,18,0,1.190219," ","integrate(1/(a+b/x^2)^(1/2)/x^3,x, algorithm=""fricas"")","-\frac{\sqrt{\frac{a x^{2} + b}{x^{2}}}}{b}"," ",0,"-sqrt((a*x^2 + b)/x^2)/b","A",0
1919,1,31,0,1.295001," ","integrate(1/(a+b/x^2)^(1/2)/x^5,x, algorithm=""fricas"")","\frac{{\left(2 \, a x^{2} - b\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{3 \, b^{2} x^{2}}"," ",0,"1/3*(2*a*x^2 - b)*sqrt((a*x^2 + b)/x^2)/(b^2*x^2)","A",0
1920,1,42,0,0.774433," ","integrate(1/(a+b/x^2)^(1/2)/x^7,x, algorithm=""fricas"")","-\frac{{\left(8 \, a^{2} x^{4} - 4 \, a b x^{2} + 3 \, b^{2}\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{15 \, b^{3} x^{4}}"," ",0,"-1/15*(8*a^2*x^4 - 4*a*b*x^2 + 3*b^2)*sqrt((a*x^2 + b)/x^2)/(b^3*x^4)","A",0
1921,1,53,0,1.345801," ","integrate(1/(a+b/x^2)^(1/2)/x^9,x, algorithm=""fricas"")","\frac{{\left(16 \, a^{3} x^{6} - 8 \, a^{2} b x^{4} + 6 \, a b^{2} x^{2} - 5 \, b^{3}\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{35 \, b^{4} x^{6}}"," ",0,"1/35*(16*a^3*x^6 - 8*a^2*b*x^4 + 6*a*b^2*x^2 - 5*b^3)*sqrt((a*x^2 + b)/x^2)/(b^4*x^6)","A",0
1922,1,40,0,1.234756," ","integrate(x^4/(a+b/x^2)^(1/2),x, algorithm=""fricas"")","\frac{{\left(3 \, a^{2} x^{5} - 4 \, a b x^{3} + 8 \, b^{2} x\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{15 \, a^{3}}"," ",0,"1/15*(3*a^2*x^5 - 4*a*b*x^3 + 8*b^2*x)*sqrt((a*x^2 + b)/x^2)/a^3","A",0
1923,1,28,0,1.295278," ","integrate(x^2/(a+b/x^2)^(1/2),x, algorithm=""fricas"")","\frac{{\left(a x^{3} - 2 \, b x\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{3 \, a^{2}}"," ",0,"1/3*(a*x^3 - 2*b*x)*sqrt((a*x^2 + b)/x^2)/a^2","A",0
1924,1,18,0,1.274488," ","integrate(1/(a+b/x^2)^(1/2),x, algorithm=""fricas"")","\frac{x \sqrt{\frac{a x^{2} + b}{x^{2}}}}{a}"," ",0,"x*sqrt((a*x^2 + b)/x^2)/a","A",0
1925,1,79,0,1.296833," ","integrate(1/(a+b/x^2)^(1/2)/x^2,x, algorithm=""fricas"")","\left[\frac{\log\left(-\frac{a x^{2} - 2 \, \sqrt{b} x \sqrt{\frac{a x^{2} + b}{x^{2}}} + 2 \, b}{x^{2}}\right)}{2 \, \sqrt{b}}, \frac{\sqrt{-b} \arctan\left(\frac{\sqrt{-b} x \sqrt{\frac{a x^{2} + b}{x^{2}}}}{a x^{2} + b}\right)}{b}\right]"," ",0,"[1/2*log(-(a*x^2 - 2*sqrt(b)*x*sqrt((a*x^2 + b)/x^2) + 2*b)/x^2)/sqrt(b), sqrt(-b)*arctan(sqrt(-b)*x*sqrt((a*x^2 + b)/x^2)/(a*x^2 + b))/b]","A",0
1926,1,128,0,1.186200," ","integrate(1/(a+b/x^2)^(1/2)/x^4,x, algorithm=""fricas"")","\left[\frac{a \sqrt{b} x \log\left(-\frac{a x^{2} + 2 \, \sqrt{b} x \sqrt{\frac{a x^{2} + b}{x^{2}}} + 2 \, b}{x^{2}}\right) - 2 \, b \sqrt{\frac{a x^{2} + b}{x^{2}}}}{4 \, b^{2} x}, -\frac{a \sqrt{-b} x \arctan\left(\frac{\sqrt{-b} x \sqrt{\frac{a x^{2} + b}{x^{2}}}}{a x^{2} + b}\right) + b \sqrt{\frac{a x^{2} + b}{x^{2}}}}{2 \, b^{2} x}\right]"," ",0,"[1/4*(a*sqrt(b)*x*log(-(a*x^2 + 2*sqrt(b)*x*sqrt((a*x^2 + b)/x^2) + 2*b)/x^2) - 2*b*sqrt((a*x^2 + b)/x^2))/(b^2*x), -1/2*(a*sqrt(-b)*x*arctan(sqrt(-b)*x*sqrt((a*x^2 + b)/x^2)/(a*x^2 + b)) + b*sqrt((a*x^2 + b)/x^2))/(b^2*x)]","A",0
1927,1,88,0,1.366757," ","integrate(1/x/(-a+b/x^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a} \log\left(2 \, a x^{2} - 2 \, \sqrt{-a} x^{2} \sqrt{-\frac{a x^{2} - b}{x^{2}}} - b\right)}{2 \, a}, -\frac{\arctan\left(\frac{\sqrt{a} x^{2} \sqrt{-\frac{a x^{2} - b}{x^{2}}}}{a x^{2} - b}\right)}{\sqrt{a}}\right]"," ",0,"[-1/2*sqrt(-a)*log(2*a*x^2 - 2*sqrt(-a)*x^2*sqrt(-(a*x^2 - b)/x^2) - b)/a, -arctan(sqrt(a)*x^2*sqrt(-(a*x^2 - b)/x^2)/(a*x^2 - b))/sqrt(a)]","A",0
1928,1,75,0,1.233808," ","integrate(1/x^2/(2+b/x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(-\frac{x^{2} - \sqrt{b} x \sqrt{\frac{2 \, x^{2} + b}{x^{2}}} + b}{x^{2}}\right)}{2 \, \sqrt{b}}, \frac{\sqrt{-b} \arctan\left(\frac{\sqrt{-b} x \sqrt{\frac{2 \, x^{2} + b}{x^{2}}}}{2 \, x^{2} + b}\right)}{b}\right]"," ",0,"[1/2*log(-(x^2 - sqrt(b)*x*sqrt((2*x^2 + b)/x^2) + b)/x^2)/sqrt(b), sqrt(-b)*arctan(sqrt(-b)*x*sqrt((2*x^2 + b)/x^2)/(2*x^2 + b))/b]","B",0
1929,1,84,0,1.249921," ","integrate(1/x^2/(2-b/x^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-b} \log\left(-\frac{x^{2} - \sqrt{-b} x \sqrt{\frac{2 \, x^{2} - b}{x^{2}}} - b}{x^{2}}\right)}{2 \, b}, -\frac{\arctan\left(\frac{\sqrt{b} x \sqrt{\frac{2 \, x^{2} - b}{x^{2}}}}{2 \, x^{2} - b}\right)}{\sqrt{b}}\right]"," ",0,"[-1/2*sqrt(-b)*log(-(x^2 - sqrt(-b)*x*sqrt((2*x^2 - b)/x^2) - b)/x^2)/b, -arctan(sqrt(b)*x*sqrt((2*x^2 - b)/x^2)/(2*x^2 - b))/sqrt(b)]","B",0
1930,1,221,0,1.167999," ","integrate(x^3/(a+b/x^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(a b^{2} x^{2} + b^{3}\right)} \sqrt{a} \log\left(-2 \, a x^{2} - 2 \, \sqrt{a} x^{2} \sqrt{\frac{a x^{2} + b}{x^{2}}} - b\right) + 2 \, {\left(2 \, a^{3} x^{6} - 5 \, a^{2} b x^{4} - 15 \, a b^{2} x^{2}\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{16 \, {\left(a^{5} x^{2} + a^{4} b\right)}}, -\frac{15 \, {\left(a b^{2} x^{2} + b^{3}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} x^{2} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{a x^{2} + b}\right) - {\left(2 \, a^{3} x^{6} - 5 \, a^{2} b x^{4} - 15 \, a b^{2} x^{2}\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{8 \, {\left(a^{5} x^{2} + a^{4} b\right)}}\right]"," ",0,"[1/16*(15*(a*b^2*x^2 + b^3)*sqrt(a)*log(-2*a*x^2 - 2*sqrt(a)*x^2*sqrt((a*x^2 + b)/x^2) - b) + 2*(2*a^3*x^6 - 5*a^2*b*x^4 - 15*a*b^2*x^2)*sqrt((a*x^2 + b)/x^2))/(a^5*x^2 + a^4*b), -1/8*(15*(a*b^2*x^2 + b^3)*sqrt(-a)*arctan(sqrt(-a)*x^2*sqrt((a*x^2 + b)/x^2)/(a*x^2 + b)) - (2*a^3*x^6 - 5*a^2*b*x^4 - 15*a*b^2*x^2)*sqrt((a*x^2 + b)/x^2))/(a^5*x^2 + a^4*b)]","A",0
1931,1,192,0,0.868724," ","integrate(x/(a+b/x^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a b x^{2} + b^{2}\right)} \sqrt{a} \log\left(-2 \, a x^{2} + 2 \, \sqrt{a} x^{2} \sqrt{\frac{a x^{2} + b}{x^{2}}} - b\right) + 2 \, {\left(a^{2} x^{4} + 3 \, a b x^{2}\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{4 \, {\left(a^{4} x^{2} + a^{3} b\right)}}, \frac{3 \, {\left(a b x^{2} + b^{2}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} x^{2} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{a x^{2} + b}\right) + {\left(a^{2} x^{4} + 3 \, a b x^{2}\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{2 \, {\left(a^{4} x^{2} + a^{3} b\right)}}\right]"," ",0,"[1/4*(3*(a*b*x^2 + b^2)*sqrt(a)*log(-2*a*x^2 + 2*sqrt(a)*x^2*sqrt((a*x^2 + b)/x^2) - b) + 2*(a^2*x^4 + 3*a*b*x^2)*sqrt((a*x^2 + b)/x^2))/(a^4*x^2 + a^3*b), 1/2*(3*(a*b*x^2 + b^2)*sqrt(-a)*arctan(sqrt(-a)*x^2*sqrt((a*x^2 + b)/x^2)/(a*x^2 + b)) + (a^2*x^4 + 3*a*b*x^2)*sqrt((a*x^2 + b)/x^2))/(a^4*x^2 + a^3*b)]","A",0
1932,1,163,0,0.841992," ","integrate(1/(a+b/x^2)^(3/2)/x,x, algorithm=""fricas"")","\left[-\frac{2 \, a x^{2} \sqrt{\frac{a x^{2} + b}{x^{2}}} - {\left(a x^{2} + b\right)} \sqrt{a} \log\left(-2 \, a x^{2} - 2 \, \sqrt{a} x^{2} \sqrt{\frac{a x^{2} + b}{x^{2}}} - b\right)}{2 \, {\left(a^{3} x^{2} + a^{2} b\right)}}, -\frac{a x^{2} \sqrt{\frac{a x^{2} + b}{x^{2}}} + {\left(a x^{2} + b\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} x^{2} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{a x^{2} + b}\right)}{a^{3} x^{2} + a^{2} b}\right]"," ",0,"[-1/2*(2*a*x^2*sqrt((a*x^2 + b)/x^2) - (a*x^2 + b)*sqrt(a)*log(-2*a*x^2 - 2*sqrt(a)*x^2*sqrt((a*x^2 + b)/x^2) - b))/(a^3*x^2 + a^2*b), -(a*x^2*sqrt((a*x^2 + b)/x^2) + (a*x^2 + b)*sqrt(-a)*arctan(sqrt(-a)*x^2*sqrt((a*x^2 + b)/x^2)/(a*x^2 + b)))/(a^3*x^2 + a^2*b)]","B",0
1933,1,29,0,0.816525," ","integrate(1/(a+b/x^2)^(3/2)/x^3,x, algorithm=""fricas"")","\frac{x^{2} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{a b x^{2} + b^{2}}"," ",0,"x^2*sqrt((a*x^2 + b)/x^2)/(a*b*x^2 + b^2)","B",0
1934,1,37,0,1.362595," ","integrate(1/(a+b/x^2)^(3/2)/x^5,x, algorithm=""fricas"")","-\frac{{\left(2 \, a x^{2} + b\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{a b^{2} x^{2} + b^{3}}"," ",0,"-(2*a*x^2 + b)*sqrt((a*x^2 + b)/x^2)/(a*b^2*x^2 + b^3)","A",0
1935,1,54,0,1.083894," ","integrate(1/(a+b/x^2)^(3/2)/x^7,x, algorithm=""fricas"")","\frac{{\left(8 \, a^{2} x^{4} + 4 \, a b x^{2} - b^{2}\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{3 \, {\left(a b^{3} x^{4} + b^{4} x^{2}\right)}}"," ",0,"1/3*(8*a^2*x^4 + 4*a*b*x^2 - b^2)*sqrt((a*x^2 + b)/x^2)/(a*b^3*x^4 + b^4*x^2)","A",0
1936,1,63,0,1.612897," ","integrate(1/(a+b/x^2)^(3/2)/x^9,x, algorithm=""fricas"")","-\frac{{\left(16 \, a^{3} x^{6} + 8 \, a^{2} b x^{4} - 2 \, a b^{2} x^{2} + b^{3}\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{5 \, {\left(a b^{4} x^{6} + b^{5} x^{4}\right)}}"," ",0,"-1/5*(16*a^3*x^6 + 8*a^2*b*x^4 - 2*a*b^2*x^2 + b^3)*sqrt((a*x^2 + b)/x^2)/(a*b^4*x^6 + b^5*x^4)","A",0
1937,1,62,0,1.160170," ","integrate(x^4/(a+b/x^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left(a^{3} x^{7} - 2 \, a^{2} b x^{5} + 8 \, a b^{2} x^{3} + 16 \, b^{3} x\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{5 \, {\left(a^{5} x^{2} + a^{4} b\right)}}"," ",0,"1/5*(a^3*x^7 - 2*a^2*b*x^5 + 8*a*b^2*x^3 + 16*b^3*x)*sqrt((a*x^2 + b)/x^2)/(a^5*x^2 + a^4*b)","A",0
1938,1,51,0,1.316968," ","integrate(x^2/(a+b/x^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left(a^{2} x^{5} - 4 \, a b x^{3} - 8 \, b^{2} x\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{3 \, {\left(a^{4} x^{2} + a^{3} b\right)}}"," ",0,"1/3*(a^2*x^5 - 4*a*b*x^3 - 8*b^2*x)*sqrt((a*x^2 + b)/x^2)/(a^4*x^2 + a^3*b)","A",0
1939,1,39,0,1.003196," ","integrate(1/(a+b/x^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left(a x^{3} + 2 \, b x\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{a^{3} x^{2} + a^{2} b}"," ",0,"(a*x^3 + 2*b*x)*sqrt((a*x^2 + b)/x^2)/(a^3*x^2 + a^2*b)","A",0
1940,1,29,0,1.231757," ","integrate(1/(a+b/x^2)^(3/2)/x^2,x, algorithm=""fricas"")","-\frac{x \sqrt{\frac{a x^{2} + b}{x^{2}}}}{a^{2} x^{2} + a b}"," ",0,"-x*sqrt((a*x^2 + b)/x^2)/(a^2*x^2 + a*b)","A",0
1941,1,155,0,1.220964," ","integrate(1/(a+b/x^2)^(3/2)/x^4,x, algorithm=""fricas"")","\left[\frac{2 \, b x \sqrt{\frac{a x^{2} + b}{x^{2}}} + {\left(a x^{2} + b\right)} \sqrt{b} \log\left(-\frac{a x^{2} - 2 \, \sqrt{b} x \sqrt{\frac{a x^{2} + b}{x^{2}}} + 2 \, b}{x^{2}}\right)}{2 \, {\left(a b^{2} x^{2} + b^{3}\right)}}, \frac{b x \sqrt{\frac{a x^{2} + b}{x^{2}}} + {\left(a x^{2} + b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x \sqrt{\frac{a x^{2} + b}{x^{2}}}}{a x^{2} + b}\right)}{a b^{2} x^{2} + b^{3}}\right]"," ",0,"[1/2*(2*b*x*sqrt((a*x^2 + b)/x^2) + (a*x^2 + b)*sqrt(b)*log(-(a*x^2 - 2*sqrt(b)*x*sqrt((a*x^2 + b)/x^2) + 2*b)/x^2))/(a*b^2*x^2 + b^3), (b*x*sqrt((a*x^2 + b)/x^2) + (a*x^2 + b)*sqrt(-b)*arctan(sqrt(-b)*x*sqrt((a*x^2 + b)/x^2)/(a*x^2 + b)))/(a*b^2*x^2 + b^3)]","A",0
1942,1,190,0,1.324714," ","integrate(1/(a+b/x^2)^(3/2)/x^6,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a^{2} x^{3} + a b x\right)} \sqrt{b} \log\left(-\frac{a x^{2} + 2 \, \sqrt{b} x \sqrt{\frac{a x^{2} + b}{x^{2}}} + 2 \, b}{x^{2}}\right) - 2 \, {\left(3 \, a b x^{2} + b^{2}\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{4 \, {\left(a b^{3} x^{3} + b^{4} x\right)}}, -\frac{3 \, {\left(a^{2} x^{3} + a b x\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x \sqrt{\frac{a x^{2} + b}{x^{2}}}}{a x^{2} + b}\right) + {\left(3 \, a b x^{2} + b^{2}\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{2 \, {\left(a b^{3} x^{3} + b^{4} x\right)}}\right]"," ",0,"[1/4*(3*(a^2*x^3 + a*b*x)*sqrt(b)*log(-(a*x^2 + 2*sqrt(b)*x*sqrt((a*x^2 + b)/x^2) + 2*b)/x^2) - 2*(3*a*b*x^2 + b^2)*sqrt((a*x^2 + b)/x^2))/(a*b^3*x^3 + b^4*x), -1/2*(3*(a^2*x^3 + a*b*x)*sqrt(-b)*arctan(sqrt(-b)*x*sqrt((a*x^2 + b)/x^2)/(a*x^2 + b)) + (3*a*b*x^2 + b^2)*sqrt((a*x^2 + b)/x^2))/(a*b^3*x^3 + b^4*x)]","A",0
1943,1,228,0,1.414726," ","integrate(1/(a+b/x^2)^(3/2)/x^8,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(a^{3} x^{5} + a^{2} b x^{3}\right)} \sqrt{b} \log\left(-\frac{a x^{2} - 2 \, \sqrt{b} x \sqrt{\frac{a x^{2} + b}{x^{2}}} + 2 \, b}{x^{2}}\right) + 2 \, {\left(15 \, a^{2} b x^{4} + 5 \, a b^{2} x^{2} - 2 \, b^{3}\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{16 \, {\left(a b^{4} x^{5} + b^{5} x^{3}\right)}}, \frac{15 \, {\left(a^{3} x^{5} + a^{2} b x^{3}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x \sqrt{\frac{a x^{2} + b}{x^{2}}}}{a x^{2} + b}\right) + {\left(15 \, a^{2} b x^{4} + 5 \, a b^{2} x^{2} - 2 \, b^{3}\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{8 \, {\left(a b^{4} x^{5} + b^{5} x^{3}\right)}}\right]"," ",0,"[1/16*(15*(a^3*x^5 + a^2*b*x^3)*sqrt(b)*log(-(a*x^2 - 2*sqrt(b)*x*sqrt((a*x^2 + b)/x^2) + 2*b)/x^2) + 2*(15*a^2*b*x^4 + 5*a*b^2*x^2 - 2*b^3)*sqrt((a*x^2 + b)/x^2))/(a*b^4*x^5 + b^5*x^3), 1/8*(15*(a^3*x^5 + a^2*b*x^3)*sqrt(-b)*arctan(sqrt(-b)*x*sqrt((a*x^2 + b)/x^2)/(a*x^2 + b)) + (15*a^2*b*x^4 + 5*a*b^2*x^2 - 2*b^3)*sqrt((a*x^2 + b)/x^2))/(a*b^4*x^5 + b^5*x^3)]","A",0
1944,1,287,0,1.195920," ","integrate(x^3/(a+b/x^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(a^{2} b^{2} x^{4} + 2 \, a b^{3} x^{2} + b^{4}\right)} \sqrt{a} \log\left(-2 \, a x^{2} - 2 \, \sqrt{a} x^{2} \sqrt{\frac{a x^{2} + b}{x^{2}}} - b\right) + 2 \, {\left(6 \, a^{4} x^{8} - 21 \, a^{3} b x^{6} - 140 \, a^{2} b^{2} x^{4} - 105 \, a b^{3} x^{2}\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{48 \, {\left(a^{7} x^{4} + 2 \, a^{6} b x^{2} + a^{5} b^{2}\right)}}, -\frac{105 \, {\left(a^{2} b^{2} x^{4} + 2 \, a b^{3} x^{2} + b^{4}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} x^{2} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{a x^{2} + b}\right) - {\left(6 \, a^{4} x^{8} - 21 \, a^{3} b x^{6} - 140 \, a^{2} b^{2} x^{4} - 105 \, a b^{3} x^{2}\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{24 \, {\left(a^{7} x^{4} + 2 \, a^{6} b x^{2} + a^{5} b^{2}\right)}}\right]"," ",0,"[1/48*(105*(a^2*b^2*x^4 + 2*a*b^3*x^2 + b^4)*sqrt(a)*log(-2*a*x^2 - 2*sqrt(a)*x^2*sqrt((a*x^2 + b)/x^2) - b) + 2*(6*a^4*x^8 - 21*a^3*b*x^6 - 140*a^2*b^2*x^4 - 105*a*b^3*x^2)*sqrt((a*x^2 + b)/x^2))/(a^7*x^4 + 2*a^6*b*x^2 + a^5*b^2), -1/24*(105*(a^2*b^2*x^4 + 2*a*b^3*x^2 + b^4)*sqrt(-a)*arctan(sqrt(-a)*x^2*sqrt((a*x^2 + b)/x^2)/(a*x^2 + b)) - (6*a^4*x^8 - 21*a^3*b*x^6 - 140*a^2*b^2*x^4 - 105*a*b^3*x^2)*sqrt((a*x^2 + b)/x^2))/(a^7*x^4 + 2*a^6*b*x^2 + a^5*b^2)]","A",0
1945,1,260,0,1.178097," ","integrate(x/(a+b/x^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(a^{2} b x^{4} + 2 \, a b^{2} x^{2} + b^{3}\right)} \sqrt{a} \log\left(-2 \, a x^{2} + 2 \, \sqrt{a} x^{2} \sqrt{\frac{a x^{2} + b}{x^{2}}} - b\right) + 2 \, {\left(3 \, a^{3} x^{6} + 20 \, a^{2} b x^{4} + 15 \, a b^{2} x^{2}\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{12 \, {\left(a^{6} x^{4} + 2 \, a^{5} b x^{2} + a^{4} b^{2}\right)}}, \frac{15 \, {\left(a^{2} b x^{4} + 2 \, a b^{2} x^{2} + b^{3}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} x^{2} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{a x^{2} + b}\right) + {\left(3 \, a^{3} x^{6} + 20 \, a^{2} b x^{4} + 15 \, a b^{2} x^{2}\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{6 \, {\left(a^{6} x^{4} + 2 \, a^{5} b x^{2} + a^{4} b^{2}\right)}}\right]"," ",0,"[1/12*(15*(a^2*b*x^4 + 2*a*b^2*x^2 + b^3)*sqrt(a)*log(-2*a*x^2 + 2*sqrt(a)*x^2*sqrt((a*x^2 + b)/x^2) - b) + 2*(3*a^3*x^6 + 20*a^2*b*x^4 + 15*a*b^2*x^2)*sqrt((a*x^2 + b)/x^2))/(a^6*x^4 + 2*a^5*b*x^2 + a^4*b^2), 1/6*(15*(a^2*b*x^4 + 2*a*b^2*x^2 + b^3)*sqrt(-a)*arctan(sqrt(-a)*x^2*sqrt((a*x^2 + b)/x^2)/(a*x^2 + b)) + (3*a^3*x^6 + 20*a^2*b*x^4 + 15*a*b^2*x^2)*sqrt((a*x^2 + b)/x^2))/(a^6*x^4 + 2*a^5*b*x^2 + a^4*b^2)]","A",0
1946,1,232,0,0.985281," ","integrate(1/(a+b/x^2)^(5/2)/x,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a^{2} x^{4} + 2 \, a b x^{2} + b^{2}\right)} \sqrt{a} \log\left(-2 \, a x^{2} - 2 \, \sqrt{a} x^{2} \sqrt{\frac{a x^{2} + b}{x^{2}}} - b\right) - 2 \, {\left(4 \, a^{2} x^{4} + 3 \, a b x^{2}\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{6 \, {\left(a^{5} x^{4} + 2 \, a^{4} b x^{2} + a^{3} b^{2}\right)}}, -\frac{3 \, {\left(a^{2} x^{4} + 2 \, a b x^{2} + b^{2}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} x^{2} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{a x^{2} + b}\right) + {\left(4 \, a^{2} x^{4} + 3 \, a b x^{2}\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{3 \, {\left(a^{5} x^{4} + 2 \, a^{4} b x^{2} + a^{3} b^{2}\right)}}\right]"," ",0,"[1/6*(3*(a^2*x^4 + 2*a*b*x^2 + b^2)*sqrt(a)*log(-2*a*x^2 - 2*sqrt(a)*x^2*sqrt((a*x^2 + b)/x^2) - b) - 2*(4*a^2*x^4 + 3*a*b*x^2)*sqrt((a*x^2 + b)/x^2))/(a^5*x^4 + 2*a^4*b*x^2 + a^3*b^2), -1/3*(3*(a^2*x^4 + 2*a*b*x^2 + b^2)*sqrt(-a)*arctan(sqrt(-a)*x^2*sqrt((a*x^2 + b)/x^2)/(a*x^2 + b)) + (4*a^2*x^4 + 3*a*b*x^2)*sqrt((a*x^2 + b)/x^2))/(a^5*x^4 + 2*a^4*b*x^2 + a^3*b^2)]","B",0
1947,1,41,0,1.337193," ","integrate(1/(a+b/x^2)^(5/2)/x^3,x, algorithm=""fricas"")","\frac{x^{4} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{3 \, {\left(a^{2} b x^{4} + 2 \, a b^{2} x^{2} + b^{3}\right)}}"," ",0,"1/3*x^4*sqrt((a*x^2 + b)/x^2)/(a^2*b*x^4 + 2*a*b^2*x^2 + b^3)","B",0
1948,1,53,0,0.995019," ","integrate(1/(a+b/x^2)^(5/2)/x^5,x, algorithm=""fricas"")","\frac{{\left(2 \, a x^{4} + 3 \, b x^{2}\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{3 \, {\left(a^{2} b^{2} x^{4} + 2 \, a b^{3} x^{2} + b^{4}\right)}}"," ",0,"1/3*(2*a*x^4 + 3*b*x^2)*sqrt((a*x^2 + b)/x^2)/(a^2*b^2*x^4 + 2*a*b^3*x^2 + b^4)","A",0
1949,1,61,0,1.150947," ","integrate(1/(a+b/x^2)^(5/2)/x^7,x, algorithm=""fricas"")","-\frac{{\left(8 \, a^{2} x^{4} + 12 \, a b x^{2} + 3 \, b^{2}\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{3 \, {\left(a^{2} b^{3} x^{4} + 2 \, a b^{4} x^{2} + b^{5}\right)}}"," ",0,"-1/3*(8*a^2*x^4 + 12*a*b*x^2 + 3*b^2)*sqrt((a*x^2 + b)/x^2)/(a^2*b^3*x^4 + 2*a*b^4*x^2 + b^5)","A",0
1950,1,76,0,1.001910," ","integrate(1/(a+b/x^2)^(5/2)/x^9,x, algorithm=""fricas"")","\frac{{\left(16 \, a^{3} x^{6} + 24 \, a^{2} b x^{4} + 6 \, a b^{2} x^{2} - b^{3}\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{3 \, {\left(a^{2} b^{4} x^{6} + 2 \, a b^{5} x^{4} + b^{6} x^{2}\right)}}"," ",0,"1/3*(16*a^3*x^6 + 24*a^2*b*x^4 + 6*a*b^2*x^2 - b^3)*sqrt((a*x^2 + b)/x^2)/(a^2*b^4*x^6 + 2*a*b^5*x^4 + b^6*x^2)","A",0
1951,1,73,0,1.062594," ","integrate(x^2/(a+b/x^2)^(5/2),x, algorithm=""fricas"")","\frac{{\left(a^{3} x^{7} - 6 \, a^{2} b x^{5} - 24 \, a b^{2} x^{3} - 16 \, b^{3} x\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{3 \, {\left(a^{6} x^{4} + 2 \, a^{5} b x^{2} + a^{4} b^{2}\right)}}"," ",0,"1/3*(a^3*x^7 - 6*a^2*b*x^5 - 24*a*b^2*x^3 - 16*b^3*x)*sqrt((a*x^2 + b)/x^2)/(a^6*x^4 + 2*a^5*b*x^2 + a^4*b^2)","A",0
1952,1,63,0,1.105983," ","integrate(1/(a+b/x^2)^(5/2),x, algorithm=""fricas"")","\frac{{\left(3 \, a^{2} x^{5} + 12 \, a b x^{3} + 8 \, b^{2} x\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{3 \, {\left(a^{5} x^{4} + 2 \, a^{4} b x^{2} + a^{3} b^{2}\right)}}"," ",0,"1/3*(3*a^2*x^5 + 12*a*b*x^3 + 8*b^2*x)*sqrt((a*x^2 + b)/x^2)/(a^5*x^4 + 2*a^4*b*x^2 + a^3*b^2)","A",0
1953,1,52,0,0.778023," ","integrate(1/(a+b/x^2)^(5/2)/x^2,x, algorithm=""fricas"")","-\frac{{\left(3 \, a x^{3} + 2 \, b x\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{3 \, {\left(a^{4} x^{4} + 2 \, a^{3} b x^{2} + a^{2} b^{2}\right)}}"," ",0,"-1/3*(3*a*x^3 + 2*b*x)*sqrt((a*x^2 + b)/x^2)/(a^4*x^4 + 2*a^3*b*x^2 + a^2*b^2)","A",0
1954,1,40,0,0.923581," ","integrate(1/(a+b/x^2)^(5/2)/x^4,x, algorithm=""fricas"")","-\frac{x \sqrt{\frac{a x^{2} + b}{x^{2}}}}{3 \, {\left(a^{3} x^{4} + 2 \, a^{2} b x^{2} + a b^{2}\right)}}"," ",0,"-1/3*x*sqrt((a*x^2 + b)/x^2)/(a^3*x^4 + 2*a^2*b*x^2 + a*b^2)","B",0
1955,1,226,0,1.235708," ","integrate(1/(a+b/x^2)^(5/2)/x^6,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a^{2} x^{4} + 2 \, a b x^{2} + b^{2}\right)} \sqrt{b} \log\left(-\frac{a x^{2} - 2 \, \sqrt{b} x \sqrt{\frac{a x^{2} + b}{x^{2}}} + 2 \, b}{x^{2}}\right) + 2 \, {\left(3 \, a b x^{3} + 4 \, b^{2} x\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{6 \, {\left(a^{2} b^{3} x^{4} + 2 \, a b^{4} x^{2} + b^{5}\right)}}, \frac{3 \, {\left(a^{2} x^{4} + 2 \, a b x^{2} + b^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x \sqrt{\frac{a x^{2} + b}{x^{2}}}}{a x^{2} + b}\right) + {\left(3 \, a b x^{3} + 4 \, b^{2} x\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{3 \, {\left(a^{2} b^{3} x^{4} + 2 \, a b^{4} x^{2} + b^{5}\right)}}\right]"," ",0,"[1/6*(3*(a^2*x^4 + 2*a*b*x^2 + b^2)*sqrt(b)*log(-(a*x^2 - 2*sqrt(b)*x*sqrt((a*x^2 + b)/x^2) + 2*b)/x^2) + 2*(3*a*b*x^3 + 4*b^2*x)*sqrt((a*x^2 + b)/x^2))/(a^2*b^3*x^4 + 2*a*b^4*x^2 + b^5), 1/3*(3*(a^2*x^4 + 2*a*b*x^2 + b^2)*sqrt(-b)*arctan(sqrt(-b)*x*sqrt((a*x^2 + b)/x^2)/(a*x^2 + b)) + (3*a*b*x^3 + 4*b^2*x)*sqrt((a*x^2 + b)/x^2))/(a^2*b^3*x^4 + 2*a*b^4*x^2 + b^5)]","A",0
1956,1,260,0,0.929920," ","integrate(1/(a+b/x^2)^(5/2)/x^8,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(a^{3} x^{5} + 2 \, a^{2} b x^{3} + a b^{2} x\right)} \sqrt{b} \log\left(-\frac{a x^{2} + 2 \, \sqrt{b} x \sqrt{\frac{a x^{2} + b}{x^{2}}} + 2 \, b}{x^{2}}\right) - 2 \, {\left(15 \, a^{2} b x^{4} + 20 \, a b^{2} x^{2} + 3 \, b^{3}\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{12 \, {\left(a^{2} b^{4} x^{5} + 2 \, a b^{5} x^{3} + b^{6} x\right)}}, -\frac{15 \, {\left(a^{3} x^{5} + 2 \, a^{2} b x^{3} + a b^{2} x\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x \sqrt{\frac{a x^{2} + b}{x^{2}}}}{a x^{2} + b}\right) + {\left(15 \, a^{2} b x^{4} + 20 \, a b^{2} x^{2} + 3 \, b^{3}\right)} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{6 \, {\left(a^{2} b^{4} x^{5} + 2 \, a b^{5} x^{3} + b^{6} x\right)}}\right]"," ",0,"[1/12*(15*(a^3*x^5 + 2*a^2*b*x^3 + a*b^2*x)*sqrt(b)*log(-(a*x^2 + 2*sqrt(b)*x*sqrt((a*x^2 + b)/x^2) + 2*b)/x^2) - 2*(15*a^2*b*x^4 + 20*a*b^2*x^2 + 3*b^3)*sqrt((a*x^2 + b)/x^2))/(a^2*b^4*x^5 + 2*a*b^5*x^3 + b^6*x), -1/6*(15*(a^3*x^5 + 2*a^2*b*x^3 + a*b^2*x)*sqrt(-b)*arctan(sqrt(-b)*x*sqrt((a*x^2 + b)/x^2)/(a*x^2 + b)) + (15*a^2*b*x^4 + 20*a*b^2*x^2 + 3*b^3)*sqrt((a*x^2 + b)/x^2))/(a^2*b^4*x^5 + 2*a*b^5*x^3 + b^6*x)]","A",0
1957,1,21,0,0.627007," ","integrate((1+1/x^2)^(1/3)/x^3,x, algorithm=""fricas"")","-\frac{3 \, {\left(x^{2} + 1\right)} \left(\frac{x^{2} + 1}{x^{2}}\right)^{\frac{1}{3}}}{8 \, x^{2}}"," ",0,"-3/8*(x^2 + 1)*((x^2 + 1)/x^2)^(1/3)/x^2","B",0
1958,1,26,0,1.024997," ","integrate((1+1/x^2)^(5/3)/x^3,x, algorithm=""fricas"")","-\frac{3 \, {\left(x^{4} + 2 \, x^{2} + 1\right)} \left(\frac{x^{2} + 1}{x^{2}}\right)^{\frac{2}{3}}}{16 \, x^{4}}"," ",0,"-3/16*(x^4 + 2*x^2 + 1)*((x^2 + 1)/x^2)^(2/3)/x^4","B",0
1959,0,0,0,1.032275," ","integrate((1+b/x^2)^(3/2)*(c*x)^m,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(x^{2} + b\right)} \left(c x\right)^{m} \sqrt{\frac{x^{2} + b}{x^{2}}}}{x^{2}}, x\right)"," ",0,"integral((x^2 + b)*(c*x)^m*sqrt((x^2 + b)/x^2)/x^2, x)","F",0
1960,0,0,0,0.996305," ","integrate((1+b/x^2)^(1/2)*(c*x)^m,x, algorithm=""fricas"")","{\rm integral}\left(\left(c x\right)^{m} \sqrt{\frac{x^{2} + b}{x^{2}}}, x\right)"," ",0,"integral((c*x)^m*sqrt((x^2 + b)/x^2), x)","F",0
1961,0,0,0,0.910365," ","integrate((c*x)^m/(1+b/x^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(c x\right)^{m} x^{2} \sqrt{\frac{x^{2} + b}{x^{2}}}}{x^{2} + b}, x\right)"," ",0,"integral((c*x)^m*x^2*sqrt((x^2 + b)/x^2)/(x^2 + b), x)","F",0
1962,0,0,0,1.103074," ","integrate((c*x)^m/(1+b/x^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(c x\right)^{m} x^{4} \sqrt{\frac{x^{2} + b}{x^{2}}}}{x^{4} + 2 \, b x^{2} + b^{2}}, x\right)"," ",0,"integral((c*x)^m*x^4*sqrt((x^2 + b)/x^2)/(x^4 + 2*b*x^2 + b^2), x)","F",0
1963,0,0,0,0.953186," ","integrate((1+b/x^2)^p*(c*x)^m,x, algorithm=""fricas"")","{\rm integral}\left(\left(c x\right)^{m} \left(\frac{x^{2} + b}{x^{2}}\right)^{p}, x\right)"," ",0,"integral((c*x)^m*((x^2 + b)/x^2)^p, x)","F",0
1964,0,0,0,0.975800," ","integrate((a+b/x^2)^p*(c*x)^m,x, algorithm=""fricas"")","{\rm integral}\left(\left(c x\right)^{m} \left(\frac{a x^{2} + b}{x^{2}}\right)^{p}, x\right)"," ",0,"integral((c*x)^m*((a*x^2 + b)/x^2)^p, x)","F",0
1965,1,33,0,0.885390," ","integrate(x^5/(a+b/x^3),x, algorithm=""fricas"")","\frac{a^{2} x^{6} - 2 \, a b x^{3} + 2 \, b^{2} \log\left(a x^{3} + b\right)}{6 \, a^{3}}"," ",0,"1/6*(a^2*x^6 - 2*a*b*x^3 + 2*b^2*log(a*x^3 + b))/a^3","A",0
1966,1,140,0,0.897433," ","integrate(x^4/(a+b/x^3),x, algorithm=""fricas"")","\frac{6 \, a x^{5} - 15 \, b x^{2} + 10 \, \sqrt{3} b \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} a x \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} + \sqrt{3} b}{3 \, b}\right) - 5 \, b \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b x^{2} - a x \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}} - b \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}}\right) + 10 \, b \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b x + a \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}}\right)}{30 \, a^{2}}"," ",0,"1/30*(6*a*x^5 - 15*b*x^2 + 10*sqrt(3)*b*(-b^2/a^2)^(1/3)*arctan(1/3*(2*sqrt(3)*a*x*(-b^2/a^2)^(1/3) + sqrt(3)*b)/b) - 5*b*(-b^2/a^2)^(1/3)*log(b*x^2 - a*x*(-b^2/a^2)^(2/3) - b*(-b^2/a^2)^(1/3)) + 10*b*(-b^2/a^2)^(1/3)*log(b*x + a*(-b^2/a^2)^(2/3)))/a^2","A",0
1967,1,108,0,0.843579," ","integrate(x^3/(a+b/x^3),x, algorithm=""fricas"")","\frac{3 \, a x^{4} + 4 \, \sqrt{3} b \left(\frac{b}{a}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} a x \left(\frac{b}{a}\right)^{\frac{2}{3}} - \sqrt{3} b}{3 \, b}\right) - 2 \, b \left(\frac{b}{a}\right)^{\frac{1}{3}} \log\left(x^{2} - x \left(\frac{b}{a}\right)^{\frac{1}{3}} + \left(\frac{b}{a}\right)^{\frac{2}{3}}\right) + 4 \, b \left(\frac{b}{a}\right)^{\frac{1}{3}} \log\left(x + \left(\frac{b}{a}\right)^{\frac{1}{3}}\right) - 12 \, b x}{12 \, a^{2}}"," ",0,"1/12*(3*a*x^4 + 4*sqrt(3)*b*(b/a)^(1/3)*arctan(1/3*(2*sqrt(3)*a*x*(b/a)^(2/3) - sqrt(3)*b)/b) - 2*b*(b/a)^(1/3)*log(x^2 - x*(b/a)^(1/3) + (b/a)^(2/3)) + 4*b*(b/a)^(1/3)*log(x + (b/a)^(1/3)) - 12*b*x)/a^2","A",0
1968,1,22,0,1.412270," ","integrate(x^2/(a+b/x^3),x, algorithm=""fricas"")","\frac{a x^{3} - b \log\left(a x^{3} + b\right)}{3 \, a^{2}}"," ",0,"1/3*(a*x^3 - b*log(a*x^3 + b))/a^2","A",0
1969,1,123,0,0.521793," ","integrate(x/(a+b/x^3),x, algorithm=""fricas"")","\frac{3 \, x^{2} - 2 \, \sqrt{3} \left(\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} a x \left(\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} - \sqrt{3} b}{3 \, b}\right) - \left(\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b x^{2} - a x \left(\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}} + b \left(\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}}\right) + 2 \, \left(\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b x + a \left(\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}}\right)}{6 \, a}"," ",0,"1/6*(3*x^2 - 2*sqrt(3)*(b^2/a^2)^(1/3)*arctan(1/3*(2*sqrt(3)*a*x*(b^2/a^2)^(1/3) - sqrt(3)*b)/b) - (b^2/a^2)^(1/3)*log(b*x^2 - a*x*(b^2/a^2)^(2/3) + b*(b^2/a^2)^(1/3)) + 2*(b^2/a^2)^(1/3)*log(b*x + a*(b^2/a^2)^(2/3)))/a","A",0
1970,1,106,0,1.005352," ","integrate(1/(a+b/x^3),x, algorithm=""fricas"")","\frac{2 \, \sqrt{3} \left(-\frac{b}{a}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} a x \left(-\frac{b}{a}\right)^{\frac{2}{3}} - \sqrt{3} b}{3 \, b}\right) - \left(-\frac{b}{a}\right)^{\frac{1}{3}} \log\left(x^{2} + x \left(-\frac{b}{a}\right)^{\frac{1}{3}} + \left(-\frac{b}{a}\right)^{\frac{2}{3}}\right) + 2 \, \left(-\frac{b}{a}\right)^{\frac{1}{3}} \log\left(x - \left(-\frac{b}{a}\right)^{\frac{1}{3}}\right) + 6 \, x}{6 \, a}"," ",0,"1/6*(2*sqrt(3)*(-b/a)^(1/3)*arctan(1/3*(2*sqrt(3)*a*x*(-b/a)^(2/3) - sqrt(3)*b)/b) - (-b/a)^(1/3)*log(x^2 + x*(-b/a)^(1/3) + (-b/a)^(2/3)) + 2*(-b/a)^(1/3)*log(x - (-b/a)^(1/3)) + 6*x)/a","A",0
1971,1,13,0,0.817948," ","integrate(1/(a+b/x^3)/x,x, algorithm=""fricas"")","\frac{\log\left(a x^{3} + b\right)}{3 \, a}"," ",0,"1/3*log(a*x^3 + b)/a","A",0
1972,1,304,0,0.924973," ","integrate(1/(a+b/x^3)/x^2,x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{\frac{1}{3}} a b \sqrt{\frac{\left(-a^{2} b\right)^{\frac{1}{3}}}{b}} \log\left(\frac{2 \, a^{2} x^{3} - a b + 3 \, \sqrt{\frac{1}{3}} {\left(a b x + 2 \, \left(-a^{2} b\right)^{\frac{2}{3}} x^{2} + \left(-a^{2} b\right)^{\frac{1}{3}} b\right)} \sqrt{\frac{\left(-a^{2} b\right)^{\frac{1}{3}}}{b}} - 3 \, \left(-a^{2} b\right)^{\frac{2}{3}} x}{a x^{3} + b}\right) + \left(-a^{2} b\right)^{\frac{2}{3}} \log\left(a^{2} x^{2} + \left(-a^{2} b\right)^{\frac{1}{3}} a x + \left(-a^{2} b\right)^{\frac{2}{3}}\right) - 2 \, \left(-a^{2} b\right)^{\frac{2}{3}} \log\left(a x - \left(-a^{2} b\right)^{\frac{1}{3}}\right)}{6 \, a^{2} b}, \frac{6 \, \sqrt{\frac{1}{3}} a b \sqrt{-\frac{\left(-a^{2} b\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, a x + \left(-a^{2} b\right)^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-a^{2} b\right)^{\frac{1}{3}}}{b}}}{a}\right) + \left(-a^{2} b\right)^{\frac{2}{3}} \log\left(a^{2} x^{2} + \left(-a^{2} b\right)^{\frac{1}{3}} a x + \left(-a^{2} b\right)^{\frac{2}{3}}\right) - 2 \, \left(-a^{2} b\right)^{\frac{2}{3}} \log\left(a x - \left(-a^{2} b\right)^{\frac{1}{3}}\right)}{6 \, a^{2} b}\right]"," ",0,"[1/6*(3*sqrt(1/3)*a*b*sqrt((-a^2*b)^(1/3)/b)*log((2*a^2*x^3 - a*b + 3*sqrt(1/3)*(a*b*x + 2*(-a^2*b)^(2/3)*x^2 + (-a^2*b)^(1/3)*b)*sqrt((-a^2*b)^(1/3)/b) - 3*(-a^2*b)^(2/3)*x)/(a*x^3 + b)) + (-a^2*b)^(2/3)*log(a^2*x^2 + (-a^2*b)^(1/3)*a*x + (-a^2*b)^(2/3)) - 2*(-a^2*b)^(2/3)*log(a*x - (-a^2*b)^(1/3)))/(a^2*b), 1/6*(6*sqrt(1/3)*a*b*sqrt(-(-a^2*b)^(1/3)/b)*arctan(sqrt(1/3)*(2*a*x + (-a^2*b)^(1/3))*sqrt(-(-a^2*b)^(1/3)/b)/a) + (-a^2*b)^(2/3)*log(a^2*x^2 + (-a^2*b)^(1/3)*a*x + (-a^2*b)^(2/3)) - 2*(-a^2*b)^(2/3)*log(a*x - (-a^2*b)^(1/3)))/(a^2*b)]","A",0
1973,1,299,0,0.997935," ","integrate(1/(a+b/x^3)/x^3,x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{\frac{1}{3}} a b \sqrt{-\frac{\left(a b^{2}\right)^{\frac{1}{3}}}{a}} \log\left(\frac{2 \, a b x^{3} - 3 \, \left(a b^{2}\right)^{\frac{1}{3}} b x - b^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, a b x^{2} + \left(a b^{2}\right)^{\frac{2}{3}} x - \left(a b^{2}\right)^{\frac{1}{3}} b\right)} \sqrt{-\frac{\left(a b^{2}\right)^{\frac{1}{3}}}{a}}}{a x^{3} + b}\right) - \left(a b^{2}\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(a b^{2}\right)^{\frac{2}{3}} x + \left(a b^{2}\right)^{\frac{1}{3}} b\right) + 2 \, \left(a b^{2}\right)^{\frac{2}{3}} \log\left(a b x + \left(a b^{2}\right)^{\frac{2}{3}}\right)}{6 \, a b^{2}}, \frac{6 \, \sqrt{\frac{1}{3}} a b \sqrt{\frac{\left(a b^{2}\right)^{\frac{1}{3}}}{a}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(a b^{2}\right)^{\frac{2}{3}} x - \left(a b^{2}\right)^{\frac{1}{3}} b\right)} \sqrt{\frac{\left(a b^{2}\right)^{\frac{1}{3}}}{a}}}{b^{2}}\right) - \left(a b^{2}\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(a b^{2}\right)^{\frac{2}{3}} x + \left(a b^{2}\right)^{\frac{1}{3}} b\right) + 2 \, \left(a b^{2}\right)^{\frac{2}{3}} \log\left(a b x + \left(a b^{2}\right)^{\frac{2}{3}}\right)}{6 \, a b^{2}}\right]"," ",0,"[1/6*(3*sqrt(1/3)*a*b*sqrt(-(a*b^2)^(1/3)/a)*log((2*a*b*x^3 - 3*(a*b^2)^(1/3)*b*x - b^2 + 3*sqrt(1/3)*(2*a*b*x^2 + (a*b^2)^(2/3)*x - (a*b^2)^(1/3)*b)*sqrt(-(a*b^2)^(1/3)/a))/(a*x^3 + b)) - (a*b^2)^(2/3)*log(a*b*x^2 - (a*b^2)^(2/3)*x + (a*b^2)^(1/3)*b) + 2*(a*b^2)^(2/3)*log(a*b*x + (a*b^2)^(2/3)))/(a*b^2), 1/6*(6*sqrt(1/3)*a*b*sqrt((a*b^2)^(1/3)/a)*arctan(sqrt(1/3)*(2*(a*b^2)^(2/3)*x - (a*b^2)^(1/3)*b)*sqrt((a*b^2)^(1/3)/a)/b^2) - (a*b^2)^(2/3)*log(a*b*x^2 - (a*b^2)^(2/3)*x + (a*b^2)^(1/3)*b) + 2*(a*b^2)^(2/3)*log(a*b*x + (a*b^2)^(2/3)))/(a*b^2)]","A",0
1974,1,18,0,0.933074," ","integrate(1/(a+b/x^3)/x^4,x, algorithm=""fricas"")","-\frac{\log\left(a x^{3} + b\right) - 3 \, \log\left(x\right)}{3 \, b}"," ",0,"-1/3*(log(a*x^3 + b) - 3*log(x))/b","A",0
1975,1,103,0,0.775014," ","integrate(1/(a+b/x^3)/x^5,x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} x \left(\frac{a}{b}\right)^{\frac{1}{3}} \arctan\left(\frac{2}{3} \, \sqrt{3} x \left(\frac{a}{b}\right)^{\frac{1}{3}} - \frac{1}{3} \, \sqrt{3}\right) + x \left(\frac{a}{b}\right)^{\frac{1}{3}} \log\left(a x^{2} - b x \left(\frac{a}{b}\right)^{\frac{2}{3}} + b \left(\frac{a}{b}\right)^{\frac{1}{3}}\right) - 2 \, x \left(\frac{a}{b}\right)^{\frac{1}{3}} \log\left(a x + b \left(\frac{a}{b}\right)^{\frac{2}{3}}\right) + 6}{6 \, b x}"," ",0,"-1/6*(2*sqrt(3)*x*(a/b)^(1/3)*arctan(2/3*sqrt(3)*x*(a/b)^(1/3) - 1/3*sqrt(3)) + x*(a/b)^(1/3)*log(a*x^2 - b*x*(a/b)^(2/3) + b*(a/b)^(1/3)) - 2*x*(a/b)^(1/3)*log(a*x + b*(a/b)^(2/3)) + 6)/(b*x)","A",0
1976,1,143,0,1.006797," ","integrate(1/(a+b/x^3)/x^6,x, algorithm=""fricas"")","\frac{2 \, \sqrt{3} x^{2} \left(-\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} b x \left(-\frac{a^{2}}{b^{2}}\right)^{\frac{2}{3}} - \sqrt{3} a}{3 \, a}\right) - x^{2} \left(-\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}} \log\left(a^{2} x^{2} + a b x \left(-\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}} + b^{2} \left(-\frac{a^{2}}{b^{2}}\right)^{\frac{2}{3}}\right) + 2 \, x^{2} \left(-\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}} \log\left(a x - b \left(-\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}}\right) - 3}{6 \, b x^{2}}"," ",0,"1/6*(2*sqrt(3)*x^2*(-a^2/b^2)^(1/3)*arctan(1/3*(2*sqrt(3)*b*x*(-a^2/b^2)^(2/3) - sqrt(3)*a)/a) - x^2*(-a^2/b^2)^(1/3)*log(a^2*x^2 + a*b*x*(-a^2/b^2)^(1/3) + b^2*(-a^2/b^2)^(2/3)) + 2*x^2*(-a^2/b^2)^(1/3)*log(a*x - b*(-a^2/b^2)^(1/3)) - 3)/(b*x^2)","A",0
1977,1,33,0,1.061555," ","integrate(1/(a+b/x^3)/x^7,x, algorithm=""fricas"")","\frac{a x^{3} \log\left(a x^{3} + b\right) - 3 \, a x^{3} \log\left(x\right) - b}{3 \, b^{2} x^{3}}"," ",0,"1/3*(a*x^3*log(a*x^3 + b) - 3*a*x^3*log(x) - b)/(b^2*x^3)","A",0
1978,1,70,0,0.975589," ","integrate(x^5/(a+b/x^3)^2,x, algorithm=""fricas"")","\frac{a^{3} x^{9} - 3 \, a^{2} b x^{6} - 4 \, a b^{2} x^{3} + 2 \, b^{3} + 6 \, {\left(a b^{2} x^{3} + b^{3}\right)} \log\left(a x^{3} + b\right)}{6 \, {\left(a^{5} x^{3} + a^{4} b\right)}}"," ",0,"1/6*(a^3*x^9 - 3*a^2*b*x^6 - 4*a*b^2*x^3 + 2*b^3 + 6*(a*b^2*x^3 + b^3)*log(a*x^3 + b))/(a^5*x^3 + a^4*b)","A",0
1979,1,190,0,1.180686," ","integrate(x^4/(a+b/x^3)^2,x, algorithm=""fricas"")","\frac{9 \, a^{2} x^{8} - 36 \, a b x^{5} - 60 \, b^{2} x^{2} + 40 \, \sqrt{3} {\left(a b x^{3} + b^{2}\right)} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} a x \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} + \sqrt{3} b}{3 \, b}\right) - 20 \, {\left(a b x^{3} + b^{2}\right)} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b x^{2} - a x \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}} - b \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}}\right) + 40 \, {\left(a b x^{3} + b^{2}\right)} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b x + a \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}}\right)}{45 \, {\left(a^{4} x^{3} + a^{3} b\right)}}"," ",0,"1/45*(9*a^2*x^8 - 36*a*b*x^5 - 60*b^2*x^2 + 40*sqrt(3)*(a*b*x^3 + b^2)*(-b^2/a^2)^(1/3)*arctan(1/3*(2*sqrt(3)*a*x*(-b^2/a^2)^(1/3) + sqrt(3)*b)/b) - 20*(a*b*x^3 + b^2)*(-b^2/a^2)^(1/3)*log(b*x^2 - a*x*(-b^2/a^2)^(2/3) - b*(-b^2/a^2)^(1/3)) + 40*(a*b*x^3 + b^2)*(-b^2/a^2)^(1/3)*log(b*x + a*(-b^2/a^2)^(2/3)))/(a^4*x^3 + a^3*b)","A",0
1980,1,158,0,1.197993," ","integrate(x^3/(a+b/x^3)^2,x, algorithm=""fricas"")","\frac{9 \, a^{2} x^{7} - 63 \, a b x^{4} - 84 \, b^{2} x + 28 \, \sqrt{3} {\left(a b x^{3} + b^{2}\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} a x \left(\frac{b}{a}\right)^{\frac{2}{3}} - \sqrt{3} b}{3 \, b}\right) - 14 \, {\left(a b x^{3} + b^{2}\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}} \log\left(x^{2} - x \left(\frac{b}{a}\right)^{\frac{1}{3}} + \left(\frac{b}{a}\right)^{\frac{2}{3}}\right) + 28 \, {\left(a b x^{3} + b^{2}\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}} \log\left(x + \left(\frac{b}{a}\right)^{\frac{1}{3}}\right)}{36 \, {\left(a^{4} x^{3} + a^{3} b\right)}}"," ",0,"1/36*(9*a^2*x^7 - 63*a*b*x^4 - 84*b^2*x + 28*sqrt(3)*(a*b*x^3 + b^2)*(b/a)^(1/3)*arctan(1/3*(2*sqrt(3)*a*x*(b/a)^(2/3) - sqrt(3)*b)/b) - 14*(a*b*x^3 + b^2)*(b/a)^(1/3)*log(x^2 - x*(b/a)^(1/3) + (b/a)^(2/3)) + 28*(a*b*x^3 + b^2)*(b/a)^(1/3)*log(x + (b/a)^(1/3)))/(a^4*x^3 + a^3*b)","A",0
1981,1,56,0,1.158608," ","integrate(x^2/(a+b/x^3)^2,x, algorithm=""fricas"")","\frac{a^{2} x^{6} + a b x^{3} - b^{2} - 2 \, {\left(a b x^{3} + b^{2}\right)} \log\left(a x^{3} + b\right)}{3 \, {\left(a^{4} x^{3} + a^{3} b\right)}}"," ",0,"1/3*(a^2*x^6 + a*b*x^3 - b^2 - 2*(a*b*x^3 + b^2)*log(a*x^3 + b))/(a^4*x^3 + a^3*b)","A",0
1982,1,163,0,1.259333," ","integrate(x/(a+b/x^3)^2,x, algorithm=""fricas"")","\frac{9 \, a x^{5} + 15 \, b x^{2} - 10 \, \sqrt{3} {\left(a x^{3} + b\right)} \left(\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} a x \left(\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} - \sqrt{3} b}{3 \, b}\right) - 5 \, {\left(a x^{3} + b\right)} \left(\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b x^{2} - a x \left(\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}} + b \left(\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}}\right) + 10 \, {\left(a x^{3} + b\right)} \left(\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b x + a \left(\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}}\right)}{18 \, {\left(a^{3} x^{3} + a^{2} b\right)}}"," ",0,"1/18*(9*a*x^5 + 15*b*x^2 - 10*sqrt(3)*(a*x^3 + b)*(b^2/a^2)^(1/3)*arctan(1/3*(2*sqrt(3)*a*x*(b^2/a^2)^(1/3) - sqrt(3)*b)/b) - 5*(a*x^3 + b)*(b^2/a^2)^(1/3)*log(b*x^2 - a*x*(b^2/a^2)^(2/3) + b*(b^2/a^2)^(1/3)) + 10*(a*x^3 + b)*(b^2/a^2)^(1/3)*log(b*x + a*(b^2/a^2)^(2/3)))/(a^3*x^3 + a^2*b)","A",0
1983,1,146,0,1.159459," ","integrate(1/(a+b/x^3)^2,x, algorithm=""fricas"")","\frac{9 \, a x^{4} + 4 \, \sqrt{3} {\left(a x^{3} + b\right)} \left(-\frac{b}{a}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} a x \left(-\frac{b}{a}\right)^{\frac{2}{3}} - \sqrt{3} b}{3 \, b}\right) - 2 \, {\left(a x^{3} + b\right)} \left(-\frac{b}{a}\right)^{\frac{1}{3}} \log\left(x^{2} + x \left(-\frac{b}{a}\right)^{\frac{1}{3}} + \left(-\frac{b}{a}\right)^{\frac{2}{3}}\right) + 4 \, {\left(a x^{3} + b\right)} \left(-\frac{b}{a}\right)^{\frac{1}{3}} \log\left(x - \left(-\frac{b}{a}\right)^{\frac{1}{3}}\right) + 12 \, b x}{9 \, {\left(a^{3} x^{3} + a^{2} b\right)}}"," ",0,"1/9*(9*a*x^4 + 4*sqrt(3)*(a*x^3 + b)*(-b/a)^(1/3)*arctan(1/3*(2*sqrt(3)*a*x*(-b/a)^(2/3) - sqrt(3)*b)/b) - 2*(a*x^3 + b)*(-b/a)^(1/3)*log(x^2 + x*(-b/a)^(1/3) + (-b/a)^(2/3)) + 4*(a*x^3 + b)*(-b/a)^(1/3)*log(x - (-b/a)^(1/3)) + 12*b*x)/(a^3*x^3 + a^2*b)","A",0
1984,1,35,0,0.941883," ","integrate(1/(a+b/x^3)^2/x,x, algorithm=""fricas"")","\frac{{\left(a x^{3} + b\right)} \log\left(a x^{3} + b\right) + b}{3 \, {\left(a^{3} x^{3} + a^{2} b\right)}}"," ",0,"1/3*((a*x^3 + b)*log(a*x^3 + b) + b)/(a^3*x^3 + a^2*b)","A",0
1985,1,400,0,0.727289," ","integrate(1/(a+b/x^3)^2/x^2,x, algorithm=""fricas"")","\left[-\frac{3 \, a^{2} b x^{2} - 3 \, \sqrt{\frac{1}{3}} {\left(a^{2} b x^{3} + a b^{2}\right)} \sqrt{\frac{\left(-a^{2} b\right)^{\frac{1}{3}}}{b}} \log\left(\frac{2 \, a^{2} x^{3} - a b + 3 \, \sqrt{\frac{1}{3}} {\left(a b x + 2 \, \left(-a^{2} b\right)^{\frac{2}{3}} x^{2} + \left(-a^{2} b\right)^{\frac{1}{3}} b\right)} \sqrt{\frac{\left(-a^{2} b\right)^{\frac{1}{3}}}{b}} - 3 \, \left(-a^{2} b\right)^{\frac{2}{3}} x}{a x^{3} + b}\right) - {\left(a x^{3} + b\right)} \left(-a^{2} b\right)^{\frac{2}{3}} \log\left(a^{2} x^{2} + \left(-a^{2} b\right)^{\frac{1}{3}} a x + \left(-a^{2} b\right)^{\frac{2}{3}}\right) + 2 \, {\left(a x^{3} + b\right)} \left(-a^{2} b\right)^{\frac{2}{3}} \log\left(a x - \left(-a^{2} b\right)^{\frac{1}{3}}\right)}{9 \, {\left(a^{4} b x^{3} + a^{3} b^{2}\right)}}, -\frac{3 \, a^{2} b x^{2} - 6 \, \sqrt{\frac{1}{3}} {\left(a^{2} b x^{3} + a b^{2}\right)} \sqrt{-\frac{\left(-a^{2} b\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, a x + \left(-a^{2} b\right)^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-a^{2} b\right)^{\frac{1}{3}}}{b}}}{a}\right) - {\left(a x^{3} + b\right)} \left(-a^{2} b\right)^{\frac{2}{3}} \log\left(a^{2} x^{2} + \left(-a^{2} b\right)^{\frac{1}{3}} a x + \left(-a^{2} b\right)^{\frac{2}{3}}\right) + 2 \, {\left(a x^{3} + b\right)} \left(-a^{2} b\right)^{\frac{2}{3}} \log\left(a x - \left(-a^{2} b\right)^{\frac{1}{3}}\right)}{9 \, {\left(a^{4} b x^{3} + a^{3} b^{2}\right)}}\right]"," ",0,"[-1/9*(3*a^2*b*x^2 - 3*sqrt(1/3)*(a^2*b*x^3 + a*b^2)*sqrt((-a^2*b)^(1/3)/b)*log((2*a^2*x^3 - a*b + 3*sqrt(1/3)*(a*b*x + 2*(-a^2*b)^(2/3)*x^2 + (-a^2*b)^(1/3)*b)*sqrt((-a^2*b)^(1/3)/b) - 3*(-a^2*b)^(2/3)*x)/(a*x^3 + b)) - (a*x^3 + b)*(-a^2*b)^(2/3)*log(a^2*x^2 + (-a^2*b)^(1/3)*a*x + (-a^2*b)^(2/3)) + 2*(a*x^3 + b)*(-a^2*b)^(2/3)*log(a*x - (-a^2*b)^(1/3)))/(a^4*b*x^3 + a^3*b^2), -1/9*(3*a^2*b*x^2 - 6*sqrt(1/3)*(a^2*b*x^3 + a*b^2)*sqrt(-(-a^2*b)^(1/3)/b)*arctan(sqrt(1/3)*(2*a*x + (-a^2*b)^(1/3))*sqrt(-(-a^2*b)^(1/3)/b)/a) - (a*x^3 + b)*(-a^2*b)^(2/3)*log(a^2*x^2 + (-a^2*b)^(1/3)*a*x + (-a^2*b)^(2/3)) + 2*(a*x^3 + b)*(-a^2*b)^(2/3)*log(a*x - (-a^2*b)^(1/3)))/(a^4*b*x^3 + a^3*b^2)]","A",0
1986,1,391,0,1.142028," ","integrate(1/(a+b/x^3)^2/x^3,x, algorithm=""fricas"")","\left[-\frac{6 \, a b^{2} x - 3 \, \sqrt{\frac{1}{3}} {\left(a^{2} b x^{3} + a b^{2}\right)} \sqrt{-\frac{\left(a b^{2}\right)^{\frac{1}{3}}}{a}} \log\left(\frac{2 \, a b x^{3} - 3 \, \left(a b^{2}\right)^{\frac{1}{3}} b x - b^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, a b x^{2} + \left(a b^{2}\right)^{\frac{2}{3}} x - \left(a b^{2}\right)^{\frac{1}{3}} b\right)} \sqrt{-\frac{\left(a b^{2}\right)^{\frac{1}{3}}}{a}}}{a x^{3} + b}\right) + {\left(a x^{3} + b\right)} \left(a b^{2}\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(a b^{2}\right)^{\frac{2}{3}} x + \left(a b^{2}\right)^{\frac{1}{3}} b\right) - 2 \, {\left(a x^{3} + b\right)} \left(a b^{2}\right)^{\frac{2}{3}} \log\left(a b x + \left(a b^{2}\right)^{\frac{2}{3}}\right)}{18 \, {\left(a^{3} b^{2} x^{3} + a^{2} b^{3}\right)}}, -\frac{6 \, a b^{2} x - 6 \, \sqrt{\frac{1}{3}} {\left(a^{2} b x^{3} + a b^{2}\right)} \sqrt{\frac{\left(a b^{2}\right)^{\frac{1}{3}}}{a}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(a b^{2}\right)^{\frac{2}{3}} x - \left(a b^{2}\right)^{\frac{1}{3}} b\right)} \sqrt{\frac{\left(a b^{2}\right)^{\frac{1}{3}}}{a}}}{b^{2}}\right) + {\left(a x^{3} + b\right)} \left(a b^{2}\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(a b^{2}\right)^{\frac{2}{3}} x + \left(a b^{2}\right)^{\frac{1}{3}} b\right) - 2 \, {\left(a x^{3} + b\right)} \left(a b^{2}\right)^{\frac{2}{3}} \log\left(a b x + \left(a b^{2}\right)^{\frac{2}{3}}\right)}{18 \, {\left(a^{3} b^{2} x^{3} + a^{2} b^{3}\right)}}\right]"," ",0,"[-1/18*(6*a*b^2*x - 3*sqrt(1/3)*(a^2*b*x^3 + a*b^2)*sqrt(-(a*b^2)^(1/3)/a)*log((2*a*b*x^3 - 3*(a*b^2)^(1/3)*b*x - b^2 + 3*sqrt(1/3)*(2*a*b*x^2 + (a*b^2)^(2/3)*x - (a*b^2)^(1/3)*b)*sqrt(-(a*b^2)^(1/3)/a))/(a*x^3 + b)) + (a*x^3 + b)*(a*b^2)^(2/3)*log(a*b*x^2 - (a*b^2)^(2/3)*x + (a*b^2)^(1/3)*b) - 2*(a*x^3 + b)*(a*b^2)^(2/3)*log(a*b*x + (a*b^2)^(2/3)))/(a^3*b^2*x^3 + a^2*b^3), -1/18*(6*a*b^2*x - 6*sqrt(1/3)*(a^2*b*x^3 + a*b^2)*sqrt((a*b^2)^(1/3)/a)*arctan(sqrt(1/3)*(2*(a*b^2)^(2/3)*x - (a*b^2)^(1/3)*b)*sqrt((a*b^2)^(1/3)/a)/b^2) + (a*x^3 + b)*(a*b^2)^(2/3)*log(a*b*x^2 - (a*b^2)^(2/3)*x + (a*b^2)^(1/3)*b) - 2*(a*x^3 + b)*(a*b^2)^(2/3)*log(a*b*x + (a*b^2)^(2/3)))/(a^3*b^2*x^3 + a^2*b^3)]","A",0
1987,1,15,0,0.893157," ","integrate(1/(a+b/x^3)^2/x^4,x, algorithm=""fricas"")","-\frac{1}{3 \, {\left(a^{2} x^{3} + a b\right)}}"," ",0,"-1/3/(a^2*x^3 + a*b)","A",0
1988,1,402,0,1.014113," ","integrate(1/(a+b/x^3)^2/x^5,x, algorithm=""fricas"")","\left[\frac{6 \, a^{2} b x^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(a^{2} b x^{3} + a b^{2}\right)} \sqrt{\frac{\left(-a^{2} b\right)^{\frac{1}{3}}}{b}} \log\left(\frac{2 \, a^{2} x^{3} - a b + 3 \, \sqrt{\frac{1}{3}} {\left(a b x + 2 \, \left(-a^{2} b\right)^{\frac{2}{3}} x^{2} + \left(-a^{2} b\right)^{\frac{1}{3}} b\right)} \sqrt{\frac{\left(-a^{2} b\right)^{\frac{1}{3}}}{b}} - 3 \, \left(-a^{2} b\right)^{\frac{2}{3}} x}{a x^{3} + b}\right) + {\left(a x^{3} + b\right)} \left(-a^{2} b\right)^{\frac{2}{3}} \log\left(a^{2} x^{2} + \left(-a^{2} b\right)^{\frac{1}{3}} a x + \left(-a^{2} b\right)^{\frac{2}{3}}\right) - 2 \, {\left(a x^{3} + b\right)} \left(-a^{2} b\right)^{\frac{2}{3}} \log\left(a x - \left(-a^{2} b\right)^{\frac{1}{3}}\right)}{18 \, {\left(a^{3} b^{2} x^{3} + a^{2} b^{3}\right)}}, \frac{6 \, a^{2} b x^{2} + 6 \, \sqrt{\frac{1}{3}} {\left(a^{2} b x^{3} + a b^{2}\right)} \sqrt{-\frac{\left(-a^{2} b\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, a x + \left(-a^{2} b\right)^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-a^{2} b\right)^{\frac{1}{3}}}{b}}}{a}\right) + {\left(a x^{3} + b\right)} \left(-a^{2} b\right)^{\frac{2}{3}} \log\left(a^{2} x^{2} + \left(-a^{2} b\right)^{\frac{1}{3}} a x + \left(-a^{2} b\right)^{\frac{2}{3}}\right) - 2 \, {\left(a x^{3} + b\right)} \left(-a^{2} b\right)^{\frac{2}{3}} \log\left(a x - \left(-a^{2} b\right)^{\frac{1}{3}}\right)}{18 \, {\left(a^{3} b^{2} x^{3} + a^{2} b^{3}\right)}}\right]"," ",0,"[1/18*(6*a^2*b*x^2 + 3*sqrt(1/3)*(a^2*b*x^3 + a*b^2)*sqrt((-a^2*b)^(1/3)/b)*log((2*a^2*x^3 - a*b + 3*sqrt(1/3)*(a*b*x + 2*(-a^2*b)^(2/3)*x^2 + (-a^2*b)^(1/3)*b)*sqrt((-a^2*b)^(1/3)/b) - 3*(-a^2*b)^(2/3)*x)/(a*x^3 + b)) + (a*x^3 + b)*(-a^2*b)^(2/3)*log(a^2*x^2 + (-a^2*b)^(1/3)*a*x + (-a^2*b)^(2/3)) - 2*(a*x^3 + b)*(-a^2*b)^(2/3)*log(a*x - (-a^2*b)^(1/3)))/(a^3*b^2*x^3 + a^2*b^3), 1/18*(6*a^2*b*x^2 + 6*sqrt(1/3)*(a^2*b*x^3 + a*b^2)*sqrt(-(-a^2*b)^(1/3)/b)*arctan(sqrt(1/3)*(2*a*x + (-a^2*b)^(1/3))*sqrt(-(-a^2*b)^(1/3)/b)/a) + (a*x^3 + b)*(-a^2*b)^(2/3)*log(a^2*x^2 + (-a^2*b)^(1/3)*a*x + (-a^2*b)^(2/3)) - 2*(a*x^3 + b)*(-a^2*b)^(2/3)*log(a*x - (-a^2*b)^(1/3)))/(a^3*b^2*x^3 + a^2*b^3)]","A",0
1989,1,389,0,1.177923," ","integrate(1/(a+b/x^3)^2/x^6,x, algorithm=""fricas"")","\left[\frac{3 \, a b^{2} x + 3 \, \sqrt{\frac{1}{3}} {\left(a^{2} b x^{3} + a b^{2}\right)} \sqrt{-\frac{\left(a b^{2}\right)^{\frac{1}{3}}}{a}} \log\left(\frac{2 \, a b x^{3} - 3 \, \left(a b^{2}\right)^{\frac{1}{3}} b x - b^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, a b x^{2} + \left(a b^{2}\right)^{\frac{2}{3}} x - \left(a b^{2}\right)^{\frac{1}{3}} b\right)} \sqrt{-\frac{\left(a b^{2}\right)^{\frac{1}{3}}}{a}}}{a x^{3} + b}\right) - {\left(a x^{3} + b\right)} \left(a b^{2}\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(a b^{2}\right)^{\frac{2}{3}} x + \left(a b^{2}\right)^{\frac{1}{3}} b\right) + 2 \, {\left(a x^{3} + b\right)} \left(a b^{2}\right)^{\frac{2}{3}} \log\left(a b x + \left(a b^{2}\right)^{\frac{2}{3}}\right)}{9 \, {\left(a^{2} b^{3} x^{3} + a b^{4}\right)}}, \frac{3 \, a b^{2} x + 6 \, \sqrt{\frac{1}{3}} {\left(a^{2} b x^{3} + a b^{2}\right)} \sqrt{\frac{\left(a b^{2}\right)^{\frac{1}{3}}}{a}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(a b^{2}\right)^{\frac{2}{3}} x - \left(a b^{2}\right)^{\frac{1}{3}} b\right)} \sqrt{\frac{\left(a b^{2}\right)^{\frac{1}{3}}}{a}}}{b^{2}}\right) - {\left(a x^{3} + b\right)} \left(a b^{2}\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(a b^{2}\right)^{\frac{2}{3}} x + \left(a b^{2}\right)^{\frac{1}{3}} b\right) + 2 \, {\left(a x^{3} + b\right)} \left(a b^{2}\right)^{\frac{2}{3}} \log\left(a b x + \left(a b^{2}\right)^{\frac{2}{3}}\right)}{9 \, {\left(a^{2} b^{3} x^{3} + a b^{4}\right)}}\right]"," ",0,"[1/9*(3*a*b^2*x + 3*sqrt(1/3)*(a^2*b*x^3 + a*b^2)*sqrt(-(a*b^2)^(1/3)/a)*log((2*a*b*x^3 - 3*(a*b^2)^(1/3)*b*x - b^2 + 3*sqrt(1/3)*(2*a*b*x^2 + (a*b^2)^(2/3)*x - (a*b^2)^(1/3)*b)*sqrt(-(a*b^2)^(1/3)/a))/(a*x^3 + b)) - (a*x^3 + b)*(a*b^2)^(2/3)*log(a*b*x^2 - (a*b^2)^(2/3)*x + (a*b^2)^(1/3)*b) + 2*(a*x^3 + b)*(a*b^2)^(2/3)*log(a*b*x + (a*b^2)^(2/3)))/(a^2*b^3*x^3 + a*b^4), 1/9*(3*a*b^2*x + 6*sqrt(1/3)*(a^2*b*x^3 + a*b^2)*sqrt((a*b^2)^(1/3)/a)*arctan(sqrt(1/3)*(2*(a*b^2)^(2/3)*x - (a*b^2)^(1/3)*b)*sqrt((a*b^2)^(1/3)/a)/b^2) - (a*x^3 + b)*(a*b^2)^(2/3)*log(a*b*x^2 - (a*b^2)^(2/3)*x + (a*b^2)^(1/3)*b) + 2*(a*x^3 + b)*(a*b^2)^(2/3)*log(a*b*x + (a*b^2)^(2/3)))/(a^2*b^3*x^3 + a*b^4)]","A",0
1990,1,47,0,0.550950," ","integrate(1/(a+b/x^3)^2/x^7,x, algorithm=""fricas"")","-\frac{{\left(a x^{3} + b\right)} \log\left(a x^{3} + b\right) - 3 \, {\left(a x^{3} + b\right)} \log\left(x\right) - b}{3 \, {\left(a b^{2} x^{3} + b^{3}\right)}}"," ",0,"-1/3*((a*x^3 + b)*log(a*x^3 + b) - 3*(a*x^3 + b)*log(x) - b)/(a*b^2*x^3 + b^3)","A",0
1991,1,175,0,1.643084," ","integrate(x^5*(a+b/x^3)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a} b^{2} \log\left(-8 \, a^{2} x^{6} - 8 \, a b x^{3} - b^{2} + 4 \, {\left(2 \, a x^{6} + b x^{3}\right)} \sqrt{a} \sqrt{\frac{a x^{3} + b}{x^{3}}}\right) + 4 \, {\left(2 \, a^{2} x^{6} + a b x^{3}\right)} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{48 \, a^{2}}, \frac{\sqrt{-a} b^{2} \arctan\left(\frac{2 \, \sqrt{-a} x^{3} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{2 \, a x^{3} + b}\right) + 2 \, {\left(2 \, a^{2} x^{6} + a b x^{3}\right)} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{24 \, a^{2}}\right]"," ",0,"[1/48*(sqrt(a)*b^2*log(-8*a^2*x^6 - 8*a*b*x^3 - b^2 + 4*(2*a*x^6 + b*x^3)*sqrt(a)*sqrt((a*x^3 + b)/x^3)) + 4*(2*a^2*x^6 + a*b*x^3)*sqrt((a*x^3 + b)/x^3))/a^2, 1/24*(sqrt(-a)*b^2*arctan(2*sqrt(-a)*x^3*sqrt((a*x^3 + b)/x^3)/(2*a*x^3 + b)) + 2*(2*a^2*x^6 + a*b*x^3)*sqrt((a*x^3 + b)/x^3))/a^2]","A",0
1992,1,150,0,1.091616," ","integrate(x^2*(a+b/x^3)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, a x^{3} \sqrt{\frac{a x^{3} + b}{x^{3}}} + \sqrt{a} b \log\left(-8 \, a^{2} x^{6} - 8 \, a b x^{3} - b^{2} - 4 \, {\left(2 \, a x^{6} + b x^{3}\right)} \sqrt{a} \sqrt{\frac{a x^{3} + b}{x^{3}}}\right)}{12 \, a}, \frac{2 \, a x^{3} \sqrt{\frac{a x^{3} + b}{x^{3}}} - \sqrt{-a} b \arctan\left(\frac{2 \, \sqrt{-a} x^{3} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{2 \, a x^{3} + b}\right)}{6 \, a}\right]"," ",0,"[1/12*(4*a*x^3*sqrt((a*x^3 + b)/x^3) + sqrt(a)*b*log(-8*a^2*x^6 - 8*a*b*x^3 - b^2 - 4*(2*a*x^6 + b*x^3)*sqrt(a)*sqrt((a*x^3 + b)/x^3)))/a, 1/6*(2*a*x^3*sqrt((a*x^3 + b)/x^3) - sqrt(-a)*b*arctan(2*sqrt(-a)*x^3*sqrt((a*x^3 + b)/x^3)/(2*a*x^3 + b)))/a]","A",0
1993,1,131,0,1.037180," ","integrate((a+b/x^3)^(1/2)/x,x, algorithm=""fricas"")","\left[\frac{1}{6} \, \sqrt{a} \log\left(-8 \, a^{2} x^{6} - 8 \, a b x^{3} - b^{2} - 4 \, {\left(2 \, a x^{6} + b x^{3}\right)} \sqrt{a} \sqrt{\frac{a x^{3} + b}{x^{3}}}\right) - \frac{2}{3} \, \sqrt{\frac{a x^{3} + b}{x^{3}}}, -\frac{1}{3} \, \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} x^{3} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{2 \, a x^{3} + b}\right) - \frac{2}{3} \, \sqrt{\frac{a x^{3} + b}{x^{3}}}\right]"," ",0,"[1/6*sqrt(a)*log(-8*a^2*x^6 - 8*a*b*x^3 - b^2 - 4*(2*a*x^6 + b*x^3)*sqrt(a)*sqrt((a*x^3 + b)/x^3)) - 2/3*sqrt((a*x^3 + b)/x^3), -1/3*sqrt(-a)*arctan(2*sqrt(-a)*x^3*sqrt((a*x^3 + b)/x^3)/(2*a*x^3 + b)) - 2/3*sqrt((a*x^3 + b)/x^3)]","A",0
1994,1,28,0,0.823088," ","integrate((a+b/x^3)^(1/2)/x^4,x, algorithm=""fricas"")","-\frac{2 \, {\left(a x^{3} + b\right)} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{9 \, b x^{3}}"," ",0,"-2/9*(a*x^3 + b)*sqrt((a*x^3 + b)/x^3)/(b*x^3)","A",0
1995,1,42,0,0.987403," ","integrate((a+b/x^3)^(1/2)/x^7,x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, a^{2} x^{6} - a b x^{3} - 3 \, b^{2}\right)} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{45 \, b^{2} x^{6}}"," ",0,"2/45*(2*a^2*x^6 - a*b*x^3 - 3*b^2)*sqrt((a*x^3 + b)/x^3)/(b^2*x^6)","A",0
1996,1,53,0,0.909537," ","integrate((a+b/x^3)^(1/2)/x^10,x, algorithm=""fricas"")","-\frac{2 \, {\left(8 \, a^{3} x^{9} - 4 \, a^{2} b x^{6} + 3 \, a b^{2} x^{3} + 15 \, b^{3}\right)} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{315 \, b^{3} x^{9}}"," ",0,"-2/315*(8*a^3*x^9 - 4*a^2*b*x^6 + 3*a*b^2*x^3 + 15*b^3)*sqrt((a*x^3 + b)/x^3)/(b^3*x^9)","A",0
1997,1,64,0,1.127104," ","integrate((a+b/x^3)^(1/2)/x^13,x, algorithm=""fricas"")","\frac{2 \, {\left(16 \, a^{4} x^{12} - 8 \, a^{3} b x^{9} + 6 \, a^{2} b^{2} x^{6} - 5 \, a b^{3} x^{3} - 35 \, b^{4}\right)} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{945 \, b^{4} x^{12}}"," ",0,"2/945*(16*a^4*x^12 - 8*a^3*b*x^9 + 6*a^2*b^2*x^6 - 5*a*b^3*x^3 - 35*b^4)*sqrt((a*x^3 + b)/x^3)/(b^4*x^12)","A",0
1998,0,0,0,1.047976," ","integrate(x^7*(a+b/x^3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(x^{7} \sqrt{\frac{a x^{3} + b}{x^{3}}}, x\right)"," ",0,"integral(x^7*sqrt((a*x^3 + b)/x^3), x)","F",0
1999,0,0,0,1.063580," ","integrate(x^4*(a+b/x^3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(x^{4} \sqrt{\frac{a x^{3} + b}{x^{3}}}, x\right)"," ",0,"integral(x^4*sqrt((a*x^3 + b)/x^3), x)","F",0
2000,0,0,0,1.092716," ","integrate(x*(a+b/x^3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(x \sqrt{\frac{a x^{3} + b}{x^{3}}}, x\right)"," ",0,"integral(x*sqrt((a*x^3 + b)/x^3), x)","F",0
2001,0,0,0,0.917104," ","integrate((a+b/x^3)^(1/2)/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\frac{a x^{3} + b}{x^{3}}}}{x^{2}}, x\right)"," ",0,"integral(sqrt((a*x^3 + b)/x^3)/x^2, x)","F",0
2002,0,0,0,0.879748," ","integrate((a+b/x^3)^(1/2)/x^5,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\frac{a x^{3} + b}{x^{3}}}}{x^{5}}, x\right)"," ",0,"integral(sqrt((a*x^3 + b)/x^3)/x^5, x)","F",0
2003,0,0,0,1.123720," ","integrate((a+b/x^3)^(1/2)/x^8,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\frac{a x^{3} + b}{x^{3}}}}{x^{8}}, x\right)"," ",0,"integral(sqrt((a*x^3 + b)/x^3)/x^8, x)","F",0
2004,0,0,0,1.008094," ","integrate(x^6*(a+b/x^3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(x^{6} \sqrt{\frac{a x^{3} + b}{x^{3}}}, x\right)"," ",0,"integral(x^6*sqrt((a*x^3 + b)/x^3), x)","F",0
2005,0,0,0,1.078352," ","integrate(x^3*(a+b/x^3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(x^{3} \sqrt{\frac{a x^{3} + b}{x^{3}}}, x\right)"," ",0,"integral(x^3*sqrt((a*x^3 + b)/x^3), x)","F",0
2006,0,0,0,1.091683," ","integrate((a+b/x^3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{\frac{a x^{3} + b}{x^{3}}}, x\right)"," ",0,"integral(sqrt((a*x^3 + b)/x^3), x)","F",0
2007,0,0,0,0.892981," ","integrate((a+b/x^3)^(1/2)/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\frac{a x^{3} + b}{x^{3}}}}{x^{3}}, x\right)"," ",0,"integral(sqrt((a*x^3 + b)/x^3)/x^3, x)","F",0
2008,0,0,0,0.953282," ","integrate((a+b/x^3)^(1/2)/x^6,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\frac{a x^{3} + b}{x^{3}}}}{x^{6}}, x\right)"," ",0,"integral(sqrt((a*x^3 + b)/x^3)/x^6, x)","F",0
2009,0,0,0,0.952886," ","integrate((a+b/x^3)^(1/2)/x^9,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\frac{a x^{3} + b}{x^{3}}}}{x^{9}}, x\right)"," ",0,"integral(sqrt((a*x^3 + b)/x^3)/x^9, x)","F",0
2010,1,179,0,1.465452," ","integrate((a+b/x^3)^(3/2)*x^5,x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{a} b^{2} \log\left(-8 \, a^{2} x^{6} - 8 \, a b x^{3} - b^{2} - 4 \, {\left(2 \, a x^{6} + b x^{3}\right)} \sqrt{a} \sqrt{\frac{a x^{3} + b}{x^{3}}}\right) + 4 \, {\left(2 \, a^{2} x^{6} + 5 \, a b x^{3}\right)} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{48 \, a}, -\frac{3 \, \sqrt{-a} b^{2} \arctan\left(\frac{2 \, \sqrt{-a} x^{3} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{2 \, a x^{3} + b}\right) - 2 \, {\left(2 \, a^{2} x^{6} + 5 \, a b x^{3}\right)} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{24 \, a}\right]"," ",0,"[1/48*(3*sqrt(a)*b^2*log(-8*a^2*x^6 - 8*a*b*x^3 - b^2 - 4*(2*a*x^6 + b*x^3)*sqrt(a)*sqrt((a*x^3 + b)/x^3)) + 4*(2*a^2*x^6 + 5*a*b*x^3)*sqrt((a*x^3 + b)/x^3))/a, -1/24*(3*sqrt(-a)*b^2*arctan(2*sqrt(-a)*x^3*sqrt((a*x^3 + b)/x^3)/(2*a*x^3 + b)) - 2*(2*a^2*x^6 + 5*a*b*x^3)*sqrt((a*x^3 + b)/x^3))/a]","A",0
2011,1,151,0,1.110645," ","integrate((a+b/x^3)^(3/2)*x^2,x, algorithm=""fricas"")","\left[\frac{1}{4} \, \sqrt{a} b \log\left(-8 \, a^{2} x^{6} - 8 \, a b x^{3} - b^{2} - 4 \, {\left(2 \, a x^{6} + b x^{3}\right)} \sqrt{a} \sqrt{\frac{a x^{3} + b}{x^{3}}}\right) + \frac{1}{3} \, {\left(a x^{3} - 2 \, b\right)} \sqrt{\frac{a x^{3} + b}{x^{3}}}, -\frac{1}{2} \, \sqrt{-a} b \arctan\left(\frac{2 \, \sqrt{-a} x^{3} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{2 \, a x^{3} + b}\right) + \frac{1}{3} \, {\left(a x^{3} - 2 \, b\right)} \sqrt{\frac{a x^{3} + b}{x^{3}}}\right]"," ",0,"[1/4*sqrt(a)*b*log(-8*a^2*x^6 - 8*a*b*x^3 - b^2 - 4*(2*a*x^6 + b*x^3)*sqrt(a)*sqrt((a*x^3 + b)/x^3)) + 1/3*(a*x^3 - 2*b)*sqrt((a*x^3 + b)/x^3), -1/2*sqrt(-a)*b*arctan(2*sqrt(-a)*x^3*sqrt((a*x^3 + b)/x^3)/(2*a*x^3 + b)) + 1/3*(a*x^3 - 2*b)*sqrt((a*x^3 + b)/x^3)]","A",0
2012,1,164,0,1.479629," ","integrate((a+b/x^3)^(3/2)/x,x, algorithm=""fricas"")","\left[\frac{3 \, a^{\frac{3}{2}} x^{3} \log\left(-8 \, a^{2} x^{6} - 8 \, a b x^{3} - b^{2} - 4 \, {\left(2 \, a x^{6} + b x^{3}\right)} \sqrt{a} \sqrt{\frac{a x^{3} + b}{x^{3}}}\right) - 4 \, {\left(4 \, a x^{3} + b\right)} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{18 \, x^{3}}, -\frac{3 \, \sqrt{-a} a x^{3} \arctan\left(\frac{2 \, \sqrt{-a} x^{3} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{2 \, a x^{3} + b}\right) + 2 \, {\left(4 \, a x^{3} + b\right)} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{9 \, x^{3}}\right]"," ",0,"[1/18*(3*a^(3/2)*x^3*log(-8*a^2*x^6 - 8*a*b*x^3 - b^2 - 4*(2*a*x^6 + b*x^3)*sqrt(a)*sqrt((a*x^3 + b)/x^3)) - 4*(4*a*x^3 + b)*sqrt((a*x^3 + b)/x^3))/x^3, -1/9*(3*sqrt(-a)*a*x^3*arctan(2*sqrt(-a)*x^3*sqrt((a*x^3 + b)/x^3)/(2*a*x^3 + b)) + 2*(4*a*x^3 + b)*sqrt((a*x^3 + b)/x^3))/x^3]","A",0
2013,1,39,0,0.794567," ","integrate((a+b/x^3)^(3/2)/x^4,x, algorithm=""fricas"")","-\frac{2 \, {\left(a^{2} x^{6} + 2 \, a b x^{3} + b^{2}\right)} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{15 \, b x^{6}}"," ",0,"-2/15*(a^2*x^6 + 2*a*b*x^3 + b^2)*sqrt((a*x^3 + b)/x^3)/(b*x^6)","B",0
2014,1,53,0,1.027373," ","integrate((a+b/x^3)^(3/2)/x^7,x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, a^{3} x^{9} - a^{2} b x^{6} - 8 \, a b^{2} x^{3} - 5 \, b^{3}\right)} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{105 \, b^{2} x^{9}}"," ",0,"2/105*(2*a^3*x^9 - a^2*b*x^6 - 8*a*b^2*x^3 - 5*b^3)*sqrt((a*x^3 + b)/x^3)/(b^2*x^9)","A",0
2015,1,64,0,0.862046," ","integrate((a+b/x^3)^(3/2)/x^10,x, algorithm=""fricas"")","-\frac{2 \, {\left(8 \, a^{4} x^{12} - 4 \, a^{3} b x^{9} + 3 \, a^{2} b^{2} x^{6} + 50 \, a b^{3} x^{3} + 35 \, b^{4}\right)} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{945 \, b^{3} x^{12}}"," ",0,"-2/945*(8*a^4*x^12 - 4*a^3*b*x^9 + 3*a^2*b^2*x^6 + 50*a*b^3*x^3 + 35*b^4)*sqrt((a*x^3 + b)/x^3)/(b^3*x^12)","A",0
2016,1,75,0,0.748696," ","integrate((a+b/x^3)^(3/2)/x^13,x, algorithm=""fricas"")","\frac{2 \, {\left(16 \, a^{5} x^{15} - 8 \, a^{4} b x^{12} + 6 \, a^{3} b^{2} x^{9} - 5 \, a^{2} b^{3} x^{6} - 140 \, a b^{4} x^{3} - 105 \, b^{5}\right)} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{3465 \, b^{4} x^{15}}"," ",0,"2/3465*(16*a^5*x^15 - 8*a^4*b*x^12 + 6*a^3*b^2*x^9 - 5*a^2*b^3*x^6 - 140*a*b^4*x^3 - 105*b^5)*sqrt((a*x^3 + b)/x^3)/(b^4*x^15)","A",0
2017,1,179,0,1.400110," ","integrate(x^5/(a+b/x^3)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{a} b^{2} \log\left(-8 \, a^{2} x^{6} - 8 \, a b x^{3} - b^{2} - 4 \, {\left(2 \, a x^{6} + b x^{3}\right)} \sqrt{a} \sqrt{\frac{a x^{3} + b}{x^{3}}}\right) + 4 \, {\left(2 \, a^{2} x^{6} - 3 \, a b x^{3}\right)} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{48 \, a^{3}}, -\frac{3 \, \sqrt{-a} b^{2} \arctan\left(\frac{2 \, \sqrt{-a} x^{3} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{2 \, a x^{3} + b}\right) - 2 \, {\left(2 \, a^{2} x^{6} - 3 \, a b x^{3}\right)} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{24 \, a^{3}}\right]"," ",0,"[1/48*(3*sqrt(a)*b^2*log(-8*a^2*x^6 - 8*a*b*x^3 - b^2 - 4*(2*a*x^6 + b*x^3)*sqrt(a)*sqrt((a*x^3 + b)/x^3)) + 4*(2*a^2*x^6 - 3*a*b*x^3)*sqrt((a*x^3 + b)/x^3))/a^3, -1/24*(3*sqrt(-a)*b^2*arctan(2*sqrt(-a)*x^3*sqrt((a*x^3 + b)/x^3)/(2*a*x^3 + b)) - 2*(2*a^2*x^6 - 3*a*b*x^3)*sqrt((a*x^3 + b)/x^3))/a^3]","A",0
2018,1,149,0,1.354939," ","integrate(x^2/(a+b/x^3)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, a x^{3} \sqrt{\frac{a x^{3} + b}{x^{3}}} + \sqrt{a} b \log\left(-8 \, a^{2} x^{6} - 8 \, a b x^{3} - b^{2} + 4 \, {\left(2 \, a x^{6} + b x^{3}\right)} \sqrt{a} \sqrt{\frac{a x^{3} + b}{x^{3}}}\right)}{12 \, a^{2}}, \frac{2 \, a x^{3} \sqrt{\frac{a x^{3} + b}{x^{3}}} + \sqrt{-a} b \arctan\left(\frac{2 \, \sqrt{-a} x^{3} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{2 \, a x^{3} + b}\right)}{6 \, a^{2}}\right]"," ",0,"[1/12*(4*a*x^3*sqrt((a*x^3 + b)/x^3) + sqrt(a)*b*log(-8*a^2*x^6 - 8*a*b*x^3 - b^2 + 4*(2*a*x^6 + b*x^3)*sqrt(a)*sqrt((a*x^3 + b)/x^3)))/a^2, 1/6*(2*a*x^3*sqrt((a*x^3 + b)/x^3) + sqrt(-a)*b*arctan(2*sqrt(-a)*x^3*sqrt((a*x^3 + b)/x^3)/(2*a*x^3 + b)))/a^2]","A",0
2019,1,102,0,1.045880," ","integrate(1/x/(a+b/x^3)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(-8 \, a^{2} x^{6} - 8 \, a b x^{3} - b^{2} - 4 \, {\left(2 \, a x^{6} + b x^{3}\right)} \sqrt{a} \sqrt{\frac{a x^{3} + b}{x^{3}}}\right)}{6 \, \sqrt{a}}, -\frac{\sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} x^{3} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{2 \, a x^{3} + b}\right)}{3 \, a}\right]"," ",0,"[1/6*log(-8*a^2*x^6 - 8*a*b*x^3 - b^2 - 4*(2*a*x^6 + b*x^3)*sqrt(a)*sqrt((a*x^3 + b)/x^3))/sqrt(a), -1/3*sqrt(-a)*arctan(2*sqrt(-a)*x^3*sqrt((a*x^3 + b)/x^3)/(2*a*x^3 + b))/a]","B",0
2020,1,18,0,1.119928," ","integrate(1/x^4/(a+b/x^3)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{\frac{a x^{3} + b}{x^{3}}}}{3 \, b}"," ",0,"-2/3*sqrt((a*x^3 + b)/x^3)/b","A",0
2021,1,31,0,0.695220," ","integrate(1/x^7/(a+b/x^3)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, a x^{3} - b\right)} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{9 \, b^{2} x^{3}}"," ",0,"2/9*(2*a*x^3 - b)*sqrt((a*x^3 + b)/x^3)/(b^2*x^3)","A",0
2022,1,42,0,0.828197," ","integrate(1/x^10/(a+b/x^3)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(8 \, a^{2} x^{6} - 4 \, a b x^{3} + 3 \, b^{2}\right)} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{45 \, b^{3} x^{6}}"," ",0,"-2/45*(8*a^2*x^6 - 4*a*b*x^3 + 3*b^2)*sqrt((a*x^3 + b)/x^3)/(b^3*x^6)","A",0
2023,1,53,0,1.046001," ","integrate(1/x^13/(a+b/x^3)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(16 \, a^{3} x^{9} - 8 \, a^{2} b x^{6} + 6 \, a b^{2} x^{3} - 5 \, b^{3}\right)} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{105 \, b^{4} x^{9}}"," ",0,"2/105*(16*a^3*x^9 - 8*a^2*b*x^6 + 6*a*b^2*x^3 - 5*b^3)*sqrt((a*x^3 + b)/x^3)/(b^4*x^9)","A",0
2024,0,0,0,1.140958," ","integrate(x^7/(a+b/x^3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{10} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{a x^{3} + b}, x\right)"," ",0,"integral(x^10*sqrt((a*x^3 + b)/x^3)/(a*x^3 + b), x)","F",0
2025,0,0,0,1.078838," ","integrate(x^4/(a+b/x^3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{7} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{a x^{3} + b}, x\right)"," ",0,"integral(x^7*sqrt((a*x^3 + b)/x^3)/(a*x^3 + b), x)","F",0
2026,0,0,0,1.103494," ","integrate(x/(a+b/x^3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{4} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{a x^{3} + b}, x\right)"," ",0,"integral(x^4*sqrt((a*x^3 + b)/x^3)/(a*x^3 + b), x)","F",0
2027,0,0,0,1.069106," ","integrate(1/x^2/(a+b/x^3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x \sqrt{\frac{a x^{3} + b}{x^{3}}}}{a x^{3} + b}, x\right)"," ",0,"integral(x*sqrt((a*x^3 + b)/x^3)/(a*x^3 + b), x)","F",0
2028,0,0,0,0.879577," ","integrate(1/x^5/(a+b/x^3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\frac{a x^{3} + b}{x^{3}}}}{a x^{5} + b x^{2}}, x\right)"," ",0,"integral(sqrt((a*x^3 + b)/x^3)/(a*x^5 + b*x^2), x)","F",0
2029,0,0,0,1.059863," ","integrate(1/x^8/(a+b/x^3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\frac{a x^{3} + b}{x^{3}}}}{a x^{8} + b x^{5}}, x\right)"," ",0,"integral(sqrt((a*x^3 + b)/x^3)/(a*x^8 + b*x^5), x)","F",0
2030,0,0,0,1.018065," ","integrate(x^6/(a+b/x^3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{9} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{a x^{3} + b}, x\right)"," ",0,"integral(x^9*sqrt((a*x^3 + b)/x^3)/(a*x^3 + b), x)","F",0
2031,0,0,0,1.044163," ","integrate(x^3/(a+b/x^3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{6} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{a x^{3} + b}, x\right)"," ",0,"integral(x^6*sqrt((a*x^3 + b)/x^3)/(a*x^3 + b), x)","F",0
2032,0,0,0,1.113215," ","integrate(1/(a+b/x^3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{a x^{3} + b}, x\right)"," ",0,"integral(x^3*sqrt((a*x^3 + b)/x^3)/(a*x^3 + b), x)","F",0
2033,0,0,0,1.086616," ","integrate(1/x^3/(a+b/x^3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\frac{a x^{3} + b}{x^{3}}}}{a x^{3} + b}, x\right)"," ",0,"integral(sqrt((a*x^3 + b)/x^3)/(a*x^3 + b), x)","F",0
2034,0,0,0,0.823592," ","integrate(1/x^6/(a+b/x^3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\frac{a x^{3} + b}{x^{3}}}}{a x^{6} + b x^{3}}, x\right)"," ",0,"integral(sqrt((a*x^3 + b)/x^3)/(a*x^6 + b*x^3), x)","F",0
2035,0,0,0,1.104766," ","integrate(1/x^9/(a+b/x^3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\frac{a x^{3} + b}{x^{3}}}}{a x^{9} + b x^{6}}, x\right)"," ",0,"integral(sqrt((a*x^3 + b)/x^3)/(a*x^9 + b*x^6), x)","F",0
2036,0,0,0,1.008684," ","integrate(1/x^12/(a+b/x^3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\frac{a x^{3} + b}{x^{3}}}}{a x^{12} + b x^{9}}, x\right)"," ",0,"integral(sqrt((a*x^3 + b)/x^3)/(a*x^12 + b*x^9), x)","F",0
2037,1,243,0,1.480327," ","integrate(x^5/(a+b/x^3)^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(a b^{2} x^{3} + b^{3}\right)} \sqrt{a} \log\left(-8 \, a^{2} x^{6} - 8 \, a b x^{3} - b^{2} - 4 \, {\left(2 \, a x^{6} + b x^{3}\right)} \sqrt{a} \sqrt{\frac{a x^{3} + b}{x^{3}}}\right) + 4 \, {\left(2 \, a^{3} x^{9} - 5 \, a^{2} b x^{6} - 15 \, a b^{2} x^{3}\right)} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{48 \, {\left(a^{5} x^{3} + a^{4} b\right)}}, -\frac{15 \, {\left(a b^{2} x^{3} + b^{3}\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} x^{3} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{2 \, a x^{3} + b}\right) - 2 \, {\left(2 \, a^{3} x^{9} - 5 \, a^{2} b x^{6} - 15 \, a b^{2} x^{3}\right)} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{24 \, {\left(a^{5} x^{3} + a^{4} b\right)}}\right]"," ",0,"[1/48*(15*(a*b^2*x^3 + b^3)*sqrt(a)*log(-8*a^2*x^6 - 8*a*b*x^3 - b^2 - 4*(2*a*x^6 + b*x^3)*sqrt(a)*sqrt((a*x^3 + b)/x^3)) + 4*(2*a^3*x^9 - 5*a^2*b*x^6 - 15*a*b^2*x^3)*sqrt((a*x^3 + b)/x^3))/(a^5*x^3 + a^4*b), -1/24*(15*(a*b^2*x^3 + b^3)*sqrt(-a)*arctan(2*sqrt(-a)*x^3*sqrt((a*x^3 + b)/x^3)/(2*a*x^3 + b)) - 2*(2*a^3*x^9 - 5*a^2*b*x^6 - 15*a*b^2*x^3)*sqrt((a*x^3 + b)/x^3))/(a^5*x^3 + a^4*b)]","A",0
2038,1,215,0,1.567055," ","integrate(x^2/(a+b/x^3)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a b x^{3} + b^{2}\right)} \sqrt{a} \log\left(-8 \, a^{2} x^{6} - 8 \, a b x^{3} - b^{2} + 4 \, {\left(2 \, a x^{6} + b x^{3}\right)} \sqrt{a} \sqrt{\frac{a x^{3} + b}{x^{3}}}\right) + 4 \, {\left(a^{2} x^{6} + 3 \, a b x^{3}\right)} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{12 \, {\left(a^{4} x^{3} + a^{3} b\right)}}, \frac{3 \, {\left(a b x^{3} + b^{2}\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} x^{3} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{2 \, a x^{3} + b}\right) + 2 \, {\left(a^{2} x^{6} + 3 \, a b x^{3}\right)} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{6 \, {\left(a^{4} x^{3} + a^{3} b\right)}}\right]"," ",0,"[1/12*(3*(a*b*x^3 + b^2)*sqrt(a)*log(-8*a^2*x^6 - 8*a*b*x^3 - b^2 + 4*(2*a*x^6 + b*x^3)*sqrt(a)*sqrt((a*x^3 + b)/x^3)) + 4*(a^2*x^6 + 3*a*b*x^3)*sqrt((a*x^3 + b)/x^3))/(a^4*x^3 + a^3*b), 1/6*(3*(a*b*x^3 + b^2)*sqrt(-a)*arctan(2*sqrt(-a)*x^3*sqrt((a*x^3 + b)/x^3)/(2*a*x^3 + b)) + 2*(a^2*x^6 + 3*a*b*x^3)*sqrt((a*x^3 + b)/x^3))/(a^4*x^3 + a^3*b)]","A",0
2039,1,186,0,1.530719," ","integrate(1/(a+b/x^3)^(3/2)/x,x, algorithm=""fricas"")","\left[-\frac{4 \, a x^{3} \sqrt{\frac{a x^{3} + b}{x^{3}}} - {\left(a x^{3} + b\right)} \sqrt{a} \log\left(-8 \, a^{2} x^{6} - 8 \, a b x^{3} - b^{2} - 4 \, {\left(2 \, a x^{6} + b x^{3}\right)} \sqrt{a} \sqrt{\frac{a x^{3} + b}{x^{3}}}\right)}{6 \, {\left(a^{3} x^{3} + a^{2} b\right)}}, -\frac{2 \, a x^{3} \sqrt{\frac{a x^{3} + b}{x^{3}}} + {\left(a x^{3} + b\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} x^{3} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{2 \, a x^{3} + b}\right)}{3 \, {\left(a^{3} x^{3} + a^{2} b\right)}}\right]"," ",0,"[-1/6*(4*a*x^3*sqrt((a*x^3 + b)/x^3) - (a*x^3 + b)*sqrt(a)*log(-8*a^2*x^6 - 8*a*b*x^3 - b^2 - 4*(2*a*x^6 + b*x^3)*sqrt(a)*sqrt((a*x^3 + b)/x^3)))/(a^3*x^3 + a^2*b), -1/3*(2*a*x^3*sqrt((a*x^3 + b)/x^3) + (a*x^3 + b)*sqrt(-a)*arctan(2*sqrt(-a)*x^3*sqrt((a*x^3 + b)/x^3)/(2*a*x^3 + b)))/(a^3*x^3 + a^2*b)]","B",0
2040,1,30,0,0.959517," ","integrate(1/(a+b/x^3)^(3/2)/x^4,x, algorithm=""fricas"")","\frac{2 \, x^{3} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{3 \, {\left(a b x^{3} + b^{2}\right)}}"," ",0,"2/3*x^3*sqrt((a*x^3 + b)/x^3)/(a*b*x^3 + b^2)","B",0
2041,1,37,0,0.922875," ","integrate(1/(a+b/x^3)^(3/2)/x^7,x, algorithm=""fricas"")","-\frac{2 \, {\left(2 \, a x^{3} + b\right)} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{3 \, {\left(a b^{2} x^{3} + b^{3}\right)}}"," ",0,"-2/3*(2*a*x^3 + b)*sqrt((a*x^3 + b)/x^3)/(a*b^2*x^3 + b^3)","A",0
2042,1,54,0,0.879422," ","integrate(1/(a+b/x^3)^(3/2)/x^10,x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, a^{2} x^{6} + 4 \, a b x^{3} - b^{2}\right)} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{9 \, {\left(a b^{3} x^{6} + b^{4} x^{3}\right)}}"," ",0,"2/9*(8*a^2*x^6 + 4*a*b*x^3 - b^2)*sqrt((a*x^3 + b)/x^3)/(a*b^3*x^6 + b^4*x^3)","A",0
2043,1,63,0,0.955152," ","integrate(1/(a+b/x^3)^(3/2)/x^13,x, algorithm=""fricas"")","-\frac{2 \, {\left(16 \, a^{3} x^{9} + 8 \, a^{2} b x^{6} - 2 \, a b^{2} x^{3} + b^{3}\right)} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{15 \, {\left(a b^{4} x^{9} + b^{5} x^{6}\right)}}"," ",0,"-2/15*(16*a^3*x^9 + 8*a^2*b*x^6 - 2*a*b^2*x^3 + b^3)*sqrt((a*x^3 + b)/x^3)/(a*b^4*x^9 + b^5*x^6)","A",0
2044,0,0,0,1.122385," ","integrate(x^7/(a+b/x^3)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{13} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{a^{2} x^{6} + 2 \, a b x^{3} + b^{2}}, x\right)"," ",0,"integral(x^13*sqrt((a*x^3 + b)/x^3)/(a^2*x^6 + 2*a*b*x^3 + b^2), x)","F",0
2045,0,0,0,1.155519," ","integrate(x^4/(a+b/x^3)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{10} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{a^{2} x^{6} + 2 \, a b x^{3} + b^{2}}, x\right)"," ",0,"integral(x^10*sqrt((a*x^3 + b)/x^3)/(a^2*x^6 + 2*a*b*x^3 + b^2), x)","F",0
2046,0,0,0,0.937510," ","integrate(x/(a+b/x^3)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{7} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{a^{2} x^{6} + 2 \, a b x^{3} + b^{2}}, x\right)"," ",0,"integral(x^7*sqrt((a*x^3 + b)/x^3)/(a^2*x^6 + 2*a*b*x^3 + b^2), x)","F",0
2047,0,0,0,1.106831," ","integrate(1/(a+b/x^3)^(3/2)/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{4} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{a^{2} x^{6} + 2 \, a b x^{3} + b^{2}}, x\right)"," ",0,"integral(x^4*sqrt((a*x^3 + b)/x^3)/(a^2*x^6 + 2*a*b*x^3 + b^2), x)","F",0
2048,0,0,0,1.105598," ","integrate(1/(a+b/x^3)^(3/2)/x^5,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x \sqrt{\frac{a x^{3} + b}{x^{3}}}}{a^{2} x^{6} + 2 \, a b x^{3} + b^{2}}, x\right)"," ",0,"integral(x*sqrt((a*x^3 + b)/x^3)/(a^2*x^6 + 2*a*b*x^3 + b^2), x)","F",0
2049,0,0,0,1.140660," ","integrate(1/(a+b/x^3)^(3/2)/x^8,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\frac{a x^{3} + b}{x^{3}}}}{a^{2} x^{8} + 2 \, a b x^{5} + b^{2} x^{2}}, x\right)"," ",0,"integral(sqrt((a*x^3 + b)/x^3)/(a^2*x^8 + 2*a*b*x^5 + b^2*x^2), x)","F",0
2050,0,0,0,0.880789," ","integrate(x^6/(a+b/x^3)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{12} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{a^{2} x^{6} + 2 \, a b x^{3} + b^{2}}, x\right)"," ",0,"integral(x^12*sqrt((a*x^3 + b)/x^3)/(a^2*x^6 + 2*a*b*x^3 + b^2), x)","F",0
2051,0,0,0,1.224558," ","integrate(x^3/(a+b/x^3)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{9} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{a^{2} x^{6} + 2 \, a b x^{3} + b^{2}}, x\right)"," ",0,"integral(x^9*sqrt((a*x^3 + b)/x^3)/(a^2*x^6 + 2*a*b*x^3 + b^2), x)","F",0
2052,0,0,0,0.931825," ","integrate(1/(a+b/x^3)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{6} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{a^{2} x^{6} + 2 \, a b x^{3} + b^{2}}, x\right)"," ",0,"integral(x^6*sqrt((a*x^3 + b)/x^3)/(a^2*x^6 + 2*a*b*x^3 + b^2), x)","F",0
2053,0,0,0,1.020792," ","integrate(1/(a+b/x^3)^(3/2)/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{a^{2} x^{6} + 2 \, a b x^{3} + b^{2}}, x\right)"," ",0,"integral(x^3*sqrt((a*x^3 + b)/x^3)/(a^2*x^6 + 2*a*b*x^3 + b^2), x)","F",0
2054,0,0,0,1.174949," ","integrate(1/(a+b/x^3)^(3/2)/x^6,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\frac{a x^{3} + b}{x^{3}}}}{a^{2} x^{6} + 2 \, a b x^{3} + b^{2}}, x\right)"," ",0,"integral(sqrt((a*x^3 + b)/x^3)/(a^2*x^6 + 2*a*b*x^3 + b^2), x)","F",0
2055,0,0,0,0.905089," ","integrate(1/(a+b/x^3)^(3/2)/x^9,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\frac{a x^{3} + b}{x^{3}}}}{a^{2} x^{9} + 2 \, a b x^{6} + b^{2} x^{3}}, x\right)"," ",0,"integral(sqrt((a*x^3 + b)/x^3)/(a^2*x^9 + 2*a*b*x^6 + b^2*x^3), x)","F",0
2056,0,0,0,1.157089," ","integrate(1/(a+b/x^3)^(3/2)/x^12,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\frac{a x^{3} + b}{x^{3}}}}{a^{2} x^{12} + 2 \, a b x^{9} + b^{2} x^{6}}, x\right)"," ",0,"integral(sqrt((a*x^3 + b)/x^3)/(a^2*x^12 + 2*a*b*x^9 + b^2*x^6), x)","F",0
2057,1,119,0,0.966550," ","integrate(1/(a+b/x^4),x, algorithm=""fricas"")","-\frac{4 \, a \left(-\frac{b}{a^{5}}\right)^{\frac{1}{4}} \arctan\left(-\frac{a^{4} x \left(-\frac{b}{a^{5}}\right)^{\frac{3}{4}} - \sqrt{a^{2} \sqrt{-\frac{b}{a^{5}}} + x^{2}} a^{4} \left(-\frac{b}{a^{5}}\right)^{\frac{3}{4}}}{b}\right) + a \left(-\frac{b}{a^{5}}\right)^{\frac{1}{4}} \log\left(a \left(-\frac{b}{a^{5}}\right)^{\frac{1}{4}} + x\right) - a \left(-\frac{b}{a^{5}}\right)^{\frac{1}{4}} \log\left(-a \left(-\frac{b}{a^{5}}\right)^{\frac{1}{4}} + x\right) - 4 \, x}{4 \, a}"," ",0,"-1/4*(4*a*(-b/a^5)^(1/4)*arctan(-(a^4*x*(-b/a^5)^(3/4) - sqrt(a^2*sqrt(-b/a^5) + x^2)*a^4*(-b/a^5)^(3/4))/b) + a*(-b/a^5)^(1/4)*log(a*(-b/a^5)^(1/4) + x) - a*(-b/a^5)^(1/4)*log(-a*(-b/a^5)^(1/4) + x) - 4*x)/a","A",0
2058,1,127,0,1.143831," ","integrate(x^3*(a+b/x^4)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, a x^{4} \sqrt{\frac{a x^{4} + b}{x^{4}}} + \sqrt{a} b \log\left(-2 \, a x^{4} - 2 \, \sqrt{a} x^{4} \sqrt{\frac{a x^{4} + b}{x^{4}}} - b\right)}{8 \, a}, \frac{a x^{4} \sqrt{\frac{a x^{4} + b}{x^{4}}} - \sqrt{-a} b \arctan\left(\frac{\sqrt{-a} x^{4} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{a x^{4} + b}\right)}{4 \, a}\right]"," ",0,"[1/8*(2*a*x^4*sqrt((a*x^4 + b)/x^4) + sqrt(a)*b*log(-2*a*x^4 - 2*sqrt(a)*x^4*sqrt((a*x^4 + b)/x^4) - b))/a, 1/4*(a*x^4*sqrt((a*x^4 + b)/x^4) - sqrt(-a)*b*arctan(sqrt(-a)*x^4*sqrt((a*x^4 + b)/x^4)/(a*x^4 + b)))/a]","A",0
2059,1,112,0,1.045428," ","integrate(x*(a+b/x^4)^(1/2),x, algorithm=""fricas"")","\left[\frac{1}{2} \, x^{2} \sqrt{\frac{a x^{4} + b}{x^{4}}} + \frac{1}{4} \, \sqrt{b} \log\left(\frac{a x^{4} - 2 \, \sqrt{b} x^{2} \sqrt{\frac{a x^{4} + b}{x^{4}}} + 2 \, b}{x^{4}}\right), \frac{1}{2} \, x^{2} \sqrt{\frac{a x^{4} + b}{x^{4}}} + \frac{1}{2} \, \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x^{2} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{b}\right)\right]"," ",0,"[1/2*x^2*sqrt((a*x^4 + b)/x^4) + 1/4*sqrt(b)*log((a*x^4 - 2*sqrt(b)*x^2*sqrt((a*x^4 + b)/x^4) + 2*b)/x^4), 1/2*x^2*sqrt((a*x^4 + b)/x^4) + 1/2*sqrt(-b)*arctan(sqrt(-b)*x^2*sqrt((a*x^4 + b)/x^4)/b)]","A",0
2060,1,109,0,0.931199," ","integrate((a+b/x^4)^(1/2)/x,x, algorithm=""fricas"")","\left[\frac{1}{4} \, \sqrt{a} \log\left(-2 \, a x^{4} - 2 \, \sqrt{a} x^{4} \sqrt{\frac{a x^{4} + b}{x^{4}}} - b\right) - \frac{1}{2} \, \sqrt{\frac{a x^{4} + b}{x^{4}}}, -\frac{1}{2} \, \sqrt{-a} \arctan\left(\frac{\sqrt{-a} x^{4} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{a x^{4} + b}\right) - \frac{1}{2} \, \sqrt{\frac{a x^{4} + b}{x^{4}}}\right]"," ",0,"[1/4*sqrt(a)*log(-2*a*x^4 - 2*sqrt(a)*x^4*sqrt((a*x^4 + b)/x^4) - b) - 1/2*sqrt((a*x^4 + b)/x^4), -1/2*sqrt(-a)*arctan(sqrt(-a)*x^4*sqrt((a*x^4 + b)/x^4)/(a*x^4 + b)) - 1/2*sqrt((a*x^4 + b)/x^4)]","A",0
2061,1,130,0,1.103688," ","integrate((a+b/x^4)^(1/2)/x^3,x, algorithm=""fricas"")","\left[\frac{a \sqrt{b} x^{2} \log\left(\frac{a x^{4} - 2 \, \sqrt{b} x^{2} \sqrt{\frac{a x^{4} + b}{x^{4}}} + 2 \, b}{x^{4}}\right) - 2 \, b \sqrt{\frac{a x^{4} + b}{x^{4}}}}{8 \, b x^{2}}, \frac{a \sqrt{-b} x^{2} \arctan\left(\frac{\sqrt{-b} x^{2} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{b}\right) - b \sqrt{\frac{a x^{4} + b}{x^{4}}}}{4 \, b x^{2}}\right]"," ",0,"[1/8*(a*sqrt(b)*x^2*log((a*x^4 - 2*sqrt(b)*x^2*sqrt((a*x^4 + b)/x^4) + 2*b)/x^4) - 2*b*sqrt((a*x^4 + b)/x^4))/(b*x^2), 1/4*(a*sqrt(-b)*x^2*arctan(sqrt(-b)*x^2*sqrt((a*x^4 + b)/x^4)/b) - b*sqrt((a*x^4 + b)/x^4))/(b*x^2)]","A",0
2062,0,0,0,0.981098," ","integrate(x^2*(a+b/x^4)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(x^{2} \sqrt{\frac{a x^{4} + b}{x^{4}}}, x\right)"," ",0,"integral(x^2*sqrt((a*x^4 + b)/x^4), x)","F",0
2063,0,0,0,0.955686," ","integrate((a+b/x^4)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{\frac{a x^{4} + b}{x^{4}}}, x\right)"," ",0,"integral(sqrt((a*x^4 + b)/x^4), x)","F",0
2064,0,0,0,0.718830," ","integrate((a+b/x^4)^(1/2)/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\frac{a x^{4} + b}{x^{4}}}}{x^{2}}, x\right)"," ",0,"integral(sqrt((a*x^4 + b)/x^4)/x^2, x)","F",0
2065,0,0,0,0.976967," ","integrate((a+b/x^4)^(1/2)/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\frac{a x^{4} + b}{x^{4}}}}{x^{4}}, x\right)"," ",0,"integral(sqrt((a*x^4 + b)/x^4)/x^4, x)","F",0
2066,1,129,0,1.021192," ","integrate((a+b/x^4)^(3/2)*x^3,x, algorithm=""fricas"")","\left[\frac{3}{8} \, \sqrt{a} b \log\left(-2 \, a x^{4} - 2 \, \sqrt{a} x^{4} \sqrt{\frac{a x^{4} + b}{x^{4}}} - b\right) + \frac{1}{4} \, {\left(a x^{4} - 2 \, b\right)} \sqrt{\frac{a x^{4} + b}{x^{4}}}, -\frac{3}{4} \, \sqrt{-a} b \arctan\left(\frac{\sqrt{-a} x^{4} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{a x^{4} + b}\right) + \frac{1}{4} \, {\left(a x^{4} - 2 \, b\right)} \sqrt{\frac{a x^{4} + b}{x^{4}}}\right]"," ",0,"[3/8*sqrt(a)*b*log(-2*a*x^4 - 2*sqrt(a)*x^4*sqrt((a*x^4 + b)/x^4) - b) + 1/4*(a*x^4 - 2*b)*sqrt((a*x^4 + b)/x^4), -3/4*sqrt(-a)*b*arctan(sqrt(-a)*x^4*sqrt((a*x^4 + b)/x^4)/(a*x^4 + b)) + 1/4*(a*x^4 - 2*b)*sqrt((a*x^4 + b)/x^4)]","A",0
2067,1,143,0,1.138559," ","integrate((a+b/x^4)^(3/2)*x,x, algorithm=""fricas"")","\left[\frac{3 \, a \sqrt{b} x^{2} \log\left(\frac{a x^{4} - 2 \, \sqrt{b} x^{2} \sqrt{\frac{a x^{4} + b}{x^{4}}} + 2 \, b}{x^{4}}\right) + 2 \, {\left(2 \, a x^{4} - b\right)} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{8 \, x^{2}}, \frac{3 \, a \sqrt{-b} x^{2} \arctan\left(\frac{\sqrt{-b} x^{2} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{b}\right) + {\left(2 \, a x^{4} - b\right)} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{4 \, x^{2}}\right]"," ",0,"[1/8*(3*a*sqrt(b)*x^2*log((a*x^4 - 2*sqrt(b)*x^2*sqrt((a*x^4 + b)/x^4) + 2*b)/x^4) + 2*(2*a*x^4 - b)*sqrt((a*x^4 + b)/x^4))/x^2, 1/4*(3*a*sqrt(-b)*x^2*arctan(sqrt(-b)*x^2*sqrt((a*x^4 + b)/x^4)/b) + (2*a*x^4 - b)*sqrt((a*x^4 + b)/x^4))/x^2]","A",0
2068,1,141,0,1.049969," ","integrate((a+b/x^4)^(3/2)/x,x, algorithm=""fricas"")","\left[\frac{3 \, a^{\frac{3}{2}} x^{4} \log\left(-2 \, a x^{4} - 2 \, \sqrt{a} x^{4} \sqrt{\frac{a x^{4} + b}{x^{4}}} - b\right) - 2 \, {\left(4 \, a x^{4} + b\right)} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{12 \, x^{4}}, -\frac{3 \, \sqrt{-a} a x^{4} \arctan\left(\frac{\sqrt{-a} x^{4} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{a x^{4} + b}\right) + {\left(4 \, a x^{4} + b\right)} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{6 \, x^{4}}\right]"," ",0,"[1/12*(3*a^(3/2)*x^4*log(-2*a*x^4 - 2*sqrt(a)*x^4*sqrt((a*x^4 + b)/x^4) - b) - 2*(4*a*x^4 + b)*sqrt((a*x^4 + b)/x^4))/x^4, -1/6*(3*sqrt(-a)*a*x^4*arctan(sqrt(-a)*x^4*sqrt((a*x^4 + b)/x^4)/(a*x^4 + b)) + (4*a*x^4 + b)*sqrt((a*x^4 + b)/x^4))/x^4]","A",0
2069,1,160,0,1.043789," ","integrate((a+b/x^4)^(3/2)/x^3,x, algorithm=""fricas"")","\left[\frac{3 \, a^{2} \sqrt{b} x^{6} \log\left(\frac{a x^{4} - 2 \, \sqrt{b} x^{2} \sqrt{\frac{a x^{4} + b}{x^{4}}} + 2 \, b}{x^{4}}\right) - 2 \, {\left(5 \, a b x^{4} + 2 \, b^{2}\right)} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{32 \, b x^{6}}, \frac{3 \, a^{2} \sqrt{-b} x^{6} \arctan\left(\frac{\sqrt{-b} x^{2} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{b}\right) - {\left(5 \, a b x^{4} + 2 \, b^{2}\right)} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{16 \, b x^{6}}\right]"," ",0,"[1/32*(3*a^2*sqrt(b)*x^6*log((a*x^4 - 2*sqrt(b)*x^2*sqrt((a*x^4 + b)/x^4) + 2*b)/x^4) - 2*(5*a*b*x^4 + 2*b^2)*sqrt((a*x^4 + b)/x^4))/(b*x^6), 1/16*(3*a^2*sqrt(-b)*x^6*arctan(sqrt(-b)*x^2*sqrt((a*x^4 + b)/x^4)/b) - (5*a*b*x^4 + 2*b^2)*sqrt((a*x^4 + b)/x^4))/(b*x^6)]","A",0
2070,0,0,0,1.185961," ","integrate((a+b/x^4)^(3/2)*x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a x^{4} + b\right)} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{x^{2}}, x\right)"," ",0,"integral((a*x^4 + b)*sqrt((a*x^4 + b)/x^4)/x^2, x)","F",0
2071,0,0,0,0.959103," ","integrate((a+b/x^4)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a x^{4} + b\right)} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{x^{4}}, x\right)"," ",0,"integral((a*x^4 + b)*sqrt((a*x^4 + b)/x^4)/x^4, x)","F",0
2072,0,0,0,0.987921," ","integrate((a+b/x^4)^(3/2)/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a x^{4} + b\right)} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{x^{6}}, x\right)"," ",0,"integral((a*x^4 + b)*sqrt((a*x^4 + b)/x^4)/x^6, x)","F",0
2073,0,0,0,0.840493," ","integrate((a+b/x^4)^(3/2)/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a x^{4} + b\right)} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{x^{8}}, x\right)"," ",0,"integral((a*x^4 + b)*sqrt((a*x^4 + b)/x^4)/x^8, x)","F",0
2074,1,170,0,1.070108," ","integrate((a+b/x^4)^(5/2)*x^3,x, algorithm=""fricas"")","\left[\frac{15 \, a^{\frac{3}{2}} b x^{4} \log\left(-2 \, a x^{4} - 2 \, \sqrt{a} x^{4} \sqrt{\frac{a x^{4} + b}{x^{4}}} - b\right) + 2 \, {\left(3 \, a^{2} x^{8} - 14 \, a b x^{4} - 2 \, b^{2}\right)} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{24 \, x^{4}}, -\frac{15 \, \sqrt{-a} a b x^{4} \arctan\left(\frac{\sqrt{-a} x^{4} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{a x^{4} + b}\right) - {\left(3 \, a^{2} x^{8} - 14 \, a b x^{4} - 2 \, b^{2}\right)} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{12 \, x^{4}}\right]"," ",0,"[1/24*(15*a^(3/2)*b*x^4*log(-2*a*x^4 - 2*sqrt(a)*x^4*sqrt((a*x^4 + b)/x^4) - b) + 2*(3*a^2*x^8 - 14*a*b*x^4 - 2*b^2)*sqrt((a*x^4 + b)/x^4))/x^4, -1/12*(15*sqrt(-a)*a*b*x^4*arctan(sqrt(-a)*x^4*sqrt((a*x^4 + b)/x^4)/(a*x^4 + b)) - (3*a^2*x^8 - 14*a*b*x^4 - 2*b^2)*sqrt((a*x^4 + b)/x^4))/x^4]","A",0
2075,1,169,0,0.631445," ","integrate((a+b/x^4)^(5/2)*x,x, algorithm=""fricas"")","\left[\frac{15 \, a^{2} \sqrt{b} x^{6} \log\left(\frac{a x^{4} - 2 \, \sqrt{b} x^{2} \sqrt{\frac{a x^{4} + b}{x^{4}}} + 2 \, b}{x^{4}}\right) + 2 \, {\left(8 \, a^{2} x^{8} - 9 \, a b x^{4} - 2 \, b^{2}\right)} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{32 \, x^{6}}, \frac{15 \, a^{2} \sqrt{-b} x^{6} \arctan\left(\frac{\sqrt{-b} x^{2} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{b}\right) + {\left(8 \, a^{2} x^{8} - 9 \, a b x^{4} - 2 \, b^{2}\right)} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{16 \, x^{6}}\right]"," ",0,"[1/32*(15*a^2*sqrt(b)*x^6*log((a*x^4 - 2*sqrt(b)*x^2*sqrt((a*x^4 + b)/x^4) + 2*b)/x^4) + 2*(8*a^2*x^8 - 9*a*b*x^4 - 2*b^2)*sqrt((a*x^4 + b)/x^4))/x^6, 1/16*(15*a^2*sqrt(-b)*x^6*arctan(sqrt(-b)*x^2*sqrt((a*x^4 + b)/x^4)/b) + (8*a^2*x^8 - 9*a*b*x^4 - 2*b^2)*sqrt((a*x^4 + b)/x^4))/x^6]","A",0
2076,1,169,0,1.030469," ","integrate((a+b/x^4)^(5/2)/x,x, algorithm=""fricas"")","\left[\frac{15 \, a^{\frac{5}{2}} x^{8} \log\left(-2 \, a x^{4} - 2 \, \sqrt{a} x^{4} \sqrt{\frac{a x^{4} + b}{x^{4}}} - b\right) - 2 \, {\left(23 \, a^{2} x^{8} + 11 \, a b x^{4} + 3 \, b^{2}\right)} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{60 \, x^{8}}, -\frac{15 \, \sqrt{-a} a^{2} x^{8} \arctan\left(\frac{\sqrt{-a} x^{4} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{a x^{4} + b}\right) + {\left(23 \, a^{2} x^{8} + 11 \, a b x^{4} + 3 \, b^{2}\right)} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{30 \, x^{8}}\right]"," ",0,"[1/60*(15*a^(5/2)*x^8*log(-2*a*x^4 - 2*sqrt(a)*x^4*sqrt((a*x^4 + b)/x^4) - b) - 2*(23*a^2*x^8 + 11*a*b*x^4 + 3*b^2)*sqrt((a*x^4 + b)/x^4))/x^8, -1/30*(15*sqrt(-a)*a^2*x^8*arctan(sqrt(-a)*x^4*sqrt((a*x^4 + b)/x^4)/(a*x^4 + b)) + (23*a^2*x^8 + 11*a*b*x^4 + 3*b^2)*sqrt((a*x^4 + b)/x^4))/x^8]","A",0
2077,1,182,0,1.079475," ","integrate((a+b/x^4)^(5/2)/x^3,x, algorithm=""fricas"")","\left[\frac{15 \, a^{3} \sqrt{b} x^{10} \log\left(\frac{a x^{4} - 2 \, \sqrt{b} x^{2} \sqrt{\frac{a x^{4} + b}{x^{4}}} + 2 \, b}{x^{4}}\right) - 2 \, {\left(33 \, a^{2} b x^{8} + 26 \, a b^{2} x^{4} + 8 \, b^{3}\right)} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{192 \, b x^{10}}, \frac{15 \, a^{3} \sqrt{-b} x^{10} \arctan\left(\frac{\sqrt{-b} x^{2} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{b}\right) - {\left(33 \, a^{2} b x^{8} + 26 \, a b^{2} x^{4} + 8 \, b^{3}\right)} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{96 \, b x^{10}}\right]"," ",0,"[1/192*(15*a^3*sqrt(b)*x^10*log((a*x^4 - 2*sqrt(b)*x^2*sqrt((a*x^4 + b)/x^4) + 2*b)/x^4) - 2*(33*a^2*b*x^8 + 26*a*b^2*x^4 + 8*b^3)*sqrt((a*x^4 + b)/x^4))/(b*x^10), 1/96*(15*a^3*sqrt(-b)*x^10*arctan(sqrt(-b)*x^2*sqrt((a*x^4 + b)/x^4)/b) - (33*a^2*b*x^8 + 26*a*b^2*x^4 + 8*b^3)*sqrt((a*x^4 + b)/x^4))/(b*x^10)]","A",0
2078,0,0,0,1.099204," ","integrate((a+b/x^4)^(5/2)*x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} x^{8} + 2 \, a b x^{4} + b^{2}\right)} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{x^{6}}, x\right)"," ",0,"integral((a^2*x^8 + 2*a*b*x^4 + b^2)*sqrt((a*x^4 + b)/x^4)/x^6, x)","F",0
2079,0,0,0,1.128168," ","integrate((a+b/x^4)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} x^{8} + 2 \, a b x^{4} + b^{2}\right)} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{x^{8}}, x\right)"," ",0,"integral((a^2*x^8 + 2*a*b*x^4 + b^2)*sqrt((a*x^4 + b)/x^4)/x^8, x)","F",0
2080,0,0,0,1.118712," ","integrate((a+b/x^4)^(5/2)/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} x^{8} + 2 \, a b x^{4} + b^{2}\right)} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{x^{10}}, x\right)"," ",0,"integral((a^2*x^8 + 2*a*b*x^4 + b^2)*sqrt((a*x^4 + b)/x^4)/x^10, x)","F",0
2081,0,0,0,0.944903," ","integrate((a+b/x^4)^(5/2)/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} x^{8} + 2 \, a b x^{4} + b^{2}\right)} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{x^{12}}, x\right)"," ",0,"integral((a^2*x^8 + 2*a*b*x^4 + b^2)*sqrt((a*x^4 + b)/x^4)/x^12, x)","F",0
2082,1,126,0,1.118029," ","integrate(x^3/(a+b/x^4)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, a x^{4} \sqrt{\frac{a x^{4} + b}{x^{4}}} + \sqrt{a} b \log\left(-2 \, a x^{4} + 2 \, \sqrt{a} x^{4} \sqrt{\frac{a x^{4} + b}{x^{4}}} - b\right)}{8 \, a^{2}}, \frac{a x^{4} \sqrt{\frac{a x^{4} + b}{x^{4}}} + \sqrt{-a} b \arctan\left(\frac{\sqrt{-a} x^{4} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{a x^{4} + b}\right)}{4 \, a^{2}}\right]"," ",0,"[1/8*(2*a*x^4*sqrt((a*x^4 + b)/x^4) + sqrt(a)*b*log(-2*a*x^4 + 2*sqrt(a)*x^4*sqrt((a*x^4 + b)/x^4) - b))/a^2, 1/4*(a*x^4*sqrt((a*x^4 + b)/x^4) + sqrt(-a)*b*arctan(sqrt(-a)*x^4*sqrt((a*x^4 + b)/x^4)/(a*x^4 + b)))/a^2]","A",0
2083,1,21,0,0.847692," ","integrate(x/(a+b/x^4)^(1/2),x, algorithm=""fricas"")","\frac{x^{2} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{2 \, a}"," ",0,"1/2*x^2*sqrt((a*x^4 + b)/x^4)/a","A",0
2084,1,80,0,0.813273," ","integrate(1/x/(a+b/x^4)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(-2 \, a x^{4} - 2 \, \sqrt{a} x^{4} \sqrt{\frac{a x^{4} + b}{x^{4}}} - b\right)}{4 \, \sqrt{a}}, -\frac{\sqrt{-a} \arctan\left(\frac{\sqrt{-a} x^{4} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{a x^{4} + b}\right)}{2 \, a}\right]"," ",0,"[1/4*log(-2*a*x^4 - 2*sqrt(a)*x^4*sqrt((a*x^4 + b)/x^4) - b)/sqrt(a), -1/2*sqrt(-a)*arctan(sqrt(-a)*x^4*sqrt((a*x^4 + b)/x^4)/(a*x^4 + b))/a]","A",0
2085,1,77,0,0.982816," ","integrate(1/x^3/(a+b/x^4)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{a x^{4} - 2 \, \sqrt{b} x^{2} \sqrt{\frac{a x^{4} + b}{x^{4}}} + 2 \, b}{x^{4}}\right)}{4 \, \sqrt{b}}, \frac{\sqrt{-b} \arctan\left(\frac{\sqrt{-b} x^{2} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{b}\right)}{2 \, b}\right]"," ",0,"[1/4*log((a*x^4 - 2*sqrt(b)*x^2*sqrt((a*x^4 + b)/x^4) + 2*b)/x^4)/sqrt(b), 1/2*sqrt(-b)*arctan(sqrt(-b)*x^2*sqrt((a*x^4 + b)/x^4)/b)/b]","A",0
2086,0,0,0,0.721988," ","integrate(x^2/(a+b/x^4)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{6} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{a x^{4} + b}, x\right)"," ",0,"integral(x^6*sqrt((a*x^4 + b)/x^4)/(a*x^4 + b), x)","F",0
2087,0,0,0,0.774302," ","integrate(1/(a+b/x^4)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{4} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{a x^{4} + b}, x\right)"," ",0,"integral(x^4*sqrt((a*x^4 + b)/x^4)/(a*x^4 + b), x)","F",0
2088,0,0,0,1.084959," ","integrate(1/x^2/(a+b/x^4)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{a x^{4} + b}, x\right)"," ",0,"integral(x^2*sqrt((a*x^4 + b)/x^4)/(a*x^4 + b), x)","F",0
2089,0,0,0,1.083050," ","integrate(1/x^4/(a+b/x^4)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\frac{a x^{4} + b}{x^{4}}}}{a x^{4} + b}, x\right)"," ",0,"integral(sqrt((a*x^4 + b)/x^4)/(a*x^4 + b), x)","F",0
2090,1,192,0,0.814097," ","integrate(x^3/(a+b/x^4)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a b x^{4} + b^{2}\right)} \sqrt{a} \log\left(-2 \, a x^{4} + 2 \, \sqrt{a} x^{4} \sqrt{\frac{a x^{4} + b}{x^{4}}} - b\right) + 2 \, {\left(a^{2} x^{8} + 3 \, a b x^{4}\right)} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{8 \, {\left(a^{4} x^{4} + a^{3} b\right)}}, \frac{3 \, {\left(a b x^{4} + b^{2}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} x^{4} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{a x^{4} + b}\right) + {\left(a^{2} x^{8} + 3 \, a b x^{4}\right)} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{4 \, {\left(a^{4} x^{4} + a^{3} b\right)}}\right]"," ",0,"[1/8*(3*(a*b*x^4 + b^2)*sqrt(a)*log(-2*a*x^4 + 2*sqrt(a)*x^4*sqrt((a*x^4 + b)/x^4) - b) + 2*(a^2*x^8 + 3*a*b*x^4)*sqrt((a*x^4 + b)/x^4))/(a^4*x^4 + a^3*b), 1/4*(3*(a*b*x^4 + b^2)*sqrt(-a)*arctan(sqrt(-a)*x^4*sqrt((a*x^4 + b)/x^4)/(a*x^4 + b)) + (a^2*x^8 + 3*a*b*x^4)*sqrt((a*x^4 + b)/x^4))/(a^4*x^4 + a^3*b)]","A",0
2091,1,42,0,0.752971," ","integrate(x/(a+b/x^4)^(3/2),x, algorithm=""fricas"")","\frac{{\left(a x^{6} + 2 \, b x^{2}\right)} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{2 \, {\left(a^{3} x^{4} + a^{2} b\right)}}"," ",0,"1/2*(a*x^6 + 2*b*x^2)*sqrt((a*x^4 + b)/x^4)/(a^3*x^4 + a^2*b)","A",0
2092,1,163,0,1.037677," ","integrate(1/(a+b/x^4)^(3/2)/x,x, algorithm=""fricas"")","\left[-\frac{2 \, a x^{4} \sqrt{\frac{a x^{4} + b}{x^{4}}} - {\left(a x^{4} + b\right)} \sqrt{a} \log\left(-2 \, a x^{4} - 2 \, \sqrt{a} x^{4} \sqrt{\frac{a x^{4} + b}{x^{4}}} - b\right)}{4 \, {\left(a^{3} x^{4} + a^{2} b\right)}}, -\frac{a x^{4} \sqrt{\frac{a x^{4} + b}{x^{4}}} + {\left(a x^{4} + b\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} x^{4} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{a x^{4} + b}\right)}{2 \, {\left(a^{3} x^{4} + a^{2} b\right)}}\right]"," ",0,"[-1/4*(2*a*x^4*sqrt((a*x^4 + b)/x^4) - (a*x^4 + b)*sqrt(a)*log(-2*a*x^4 - 2*sqrt(a)*x^4*sqrt((a*x^4 + b)/x^4) - b))/(a^3*x^4 + a^2*b), -1/2*(a*x^4*sqrt((a*x^4 + b)/x^4) + (a*x^4 + b)*sqrt(-a)*arctan(sqrt(-a)*x^4*sqrt((a*x^4 + b)/x^4)/(a*x^4 + b)))/(a^3*x^4 + a^2*b)]","B",0
2093,1,31,0,1.129173," ","integrate(1/(a+b/x^4)^(3/2)/x^3,x, algorithm=""fricas"")","-\frac{x^{2} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{2 \, {\left(a^{2} x^{4} + a b\right)}}"," ",0,"-1/2*x^2*sqrt((a*x^4 + b)/x^4)/(a^2*x^4 + a*b)","A",0
2094,0,0,0,0.989633," ","integrate(x^2/(a+b/x^4)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{10} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{a^{2} x^{8} + 2 \, a b x^{4} + b^{2}}, x\right)"," ",0,"integral(x^10*sqrt((a*x^4 + b)/x^4)/(a^2*x^8 + 2*a*b*x^4 + b^2), x)","F",0
2095,0,0,0,0.641892," ","integrate(1/(a+b/x^4)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{8} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{a^{2} x^{8} + 2 \, a b x^{4} + b^{2}}, x\right)"," ",0,"integral(x^8*sqrt((a*x^4 + b)/x^4)/(a^2*x^8 + 2*a*b*x^4 + b^2), x)","F",0
2096,0,0,0,1.070616," ","integrate(1/(a+b/x^4)^(3/2)/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{6} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{a^{2} x^{8} + 2 \, a b x^{4} + b^{2}}, x\right)"," ",0,"integral(x^6*sqrt((a*x^4 + b)/x^4)/(a^2*x^8 + 2*a*b*x^4 + b^2), x)","F",0
2097,0,0,0,0.967775," ","integrate(1/(a+b/x^4)^(3/2)/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{4} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{a^{2} x^{8} + 2 \, a b x^{4} + b^{2}}, x\right)"," ",0,"integral(x^4*sqrt((a*x^4 + b)/x^4)/(a^2*x^8 + 2*a*b*x^4 + b^2), x)","F",0
2098,1,260,0,0.931028," ","integrate(x^3/(a+b/x^4)^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(a^{2} b x^{8} + 2 \, a b^{2} x^{4} + b^{3}\right)} \sqrt{a} \log\left(-2 \, a x^{4} + 2 \, \sqrt{a} x^{4} \sqrt{\frac{a x^{4} + b}{x^{4}}} - b\right) + 2 \, {\left(3 \, a^{3} x^{12} + 20 \, a^{2} b x^{8} + 15 \, a b^{2} x^{4}\right)} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{24 \, {\left(a^{6} x^{8} + 2 \, a^{5} b x^{4} + a^{4} b^{2}\right)}}, \frac{15 \, {\left(a^{2} b x^{8} + 2 \, a b^{2} x^{4} + b^{3}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} x^{4} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{a x^{4} + b}\right) + {\left(3 \, a^{3} x^{12} + 20 \, a^{2} b x^{8} + 15 \, a b^{2} x^{4}\right)} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{12 \, {\left(a^{6} x^{8} + 2 \, a^{5} b x^{4} + a^{4} b^{2}\right)}}\right]"," ",0,"[1/24*(15*(a^2*b*x^8 + 2*a*b^2*x^4 + b^3)*sqrt(a)*log(-2*a*x^4 + 2*sqrt(a)*x^4*sqrt((a*x^4 + b)/x^4) - b) + 2*(3*a^3*x^12 + 20*a^2*b*x^8 + 15*a*b^2*x^4)*sqrt((a*x^4 + b)/x^4))/(a^6*x^8 + 2*a^5*b*x^4 + a^4*b^2), 1/12*(15*(a^2*b*x^8 + 2*a*b^2*x^4 + b^3)*sqrt(-a)*arctan(sqrt(-a)*x^4*sqrt((a*x^4 + b)/x^4)/(a*x^4 + b)) + (3*a^3*x^12 + 20*a^2*b*x^8 + 15*a*b^2*x^4)*sqrt((a*x^4 + b)/x^4))/(a^6*x^8 + 2*a^5*b*x^4 + a^4*b^2)]","A",0
2099,1,65,0,0.860144," ","integrate(x/(a+b/x^4)^(5/2),x, algorithm=""fricas"")","\frac{{\left(3 \, a^{2} x^{10} + 12 \, a b x^{6} + 8 \, b^{2} x^{2}\right)} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{6 \, {\left(a^{5} x^{8} + 2 \, a^{4} b x^{4} + a^{3} b^{2}\right)}}"," ",0,"1/6*(3*a^2*x^10 + 12*a*b*x^6 + 8*b^2*x^2)*sqrt((a*x^4 + b)/x^4)/(a^5*x^8 + 2*a^4*b*x^4 + a^3*b^2)","A",0
2100,1,232,0,1.015131," ","integrate(1/(a+b/x^4)^(5/2)/x,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a^{2} x^{8} + 2 \, a b x^{4} + b^{2}\right)} \sqrt{a} \log\left(-2 \, a x^{4} - 2 \, \sqrt{a} x^{4} \sqrt{\frac{a x^{4} + b}{x^{4}}} - b\right) - 2 \, {\left(4 \, a^{2} x^{8} + 3 \, a b x^{4}\right)} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{12 \, {\left(a^{5} x^{8} + 2 \, a^{4} b x^{4} + a^{3} b^{2}\right)}}, -\frac{3 \, {\left(a^{2} x^{8} + 2 \, a b x^{4} + b^{2}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a} x^{4} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{a x^{4} + b}\right) + {\left(4 \, a^{2} x^{8} + 3 \, a b x^{4}\right)} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{6 \, {\left(a^{5} x^{8} + 2 \, a^{4} b x^{4} + a^{3} b^{2}\right)}}\right]"," ",0,"[1/12*(3*(a^2*x^8 + 2*a*b*x^4 + b^2)*sqrt(a)*log(-2*a*x^4 - 2*sqrt(a)*x^4*sqrt((a*x^4 + b)/x^4) - b) - 2*(4*a^2*x^8 + 3*a*b*x^4)*sqrt((a*x^4 + b)/x^4))/(a^5*x^8 + 2*a^4*b*x^4 + a^3*b^2), -1/6*(3*(a^2*x^8 + 2*a*b*x^4 + b^2)*sqrt(-a)*arctan(sqrt(-a)*x^4*sqrt((a*x^4 + b)/x^4)/(a*x^4 + b)) + (4*a^2*x^8 + 3*a*b*x^4)*sqrt((a*x^4 + b)/x^4))/(a^5*x^8 + 2*a^4*b*x^4 + a^3*b^2)]","B",0
2101,1,54,0,0.894576," ","integrate(1/(a+b/x^4)^(5/2)/x^3,x, algorithm=""fricas"")","-\frac{{\left(3 \, a x^{6} + 2 \, b x^{2}\right)} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{6 \, {\left(a^{4} x^{8} + 2 \, a^{3} b x^{4} + a^{2} b^{2}\right)}}"," ",0,"-1/6*(3*a*x^6 + 2*b*x^2)*sqrt((a*x^4 + b)/x^4)/(a^4*x^8 + 2*a^3*b*x^4 + a^2*b^2)","A",0
2102,0,0,0,0.993468," ","integrate(x^2/(a+b/x^4)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{14} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{a^{3} x^{12} + 3 \, a^{2} b x^{8} + 3 \, a b^{2} x^{4} + b^{3}}, x\right)"," ",0,"integral(x^14*sqrt((a*x^4 + b)/x^4)/(a^3*x^12 + 3*a^2*b*x^8 + 3*a*b^2*x^4 + b^3), x)","F",0
2103,0,0,0,0.659729," ","integrate(1/(a+b/x^4)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{12} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{a^{3} x^{12} + 3 \, a^{2} b x^{8} + 3 \, a b^{2} x^{4} + b^{3}}, x\right)"," ",0,"integral(x^12*sqrt((a*x^4 + b)/x^4)/(a^3*x^12 + 3*a^2*b*x^8 + 3*a*b^2*x^4 + b^3), x)","F",0
2104,0,0,0,1.007694," ","integrate(1/(a+b/x^4)^(5/2)/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{10} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{a^{3} x^{12} + 3 \, a^{2} b x^{8} + 3 \, a b^{2} x^{4} + b^{3}}, x\right)"," ",0,"integral(x^10*sqrt((a*x^4 + b)/x^4)/(a^3*x^12 + 3*a^2*b*x^8 + 3*a*b^2*x^4 + b^3), x)","F",0
2105,0,0,0,1.146144," ","integrate(1/(a+b/x^4)^(5/2)/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{8} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{a^{3} x^{12} + 3 \, a^{2} b x^{8} + 3 \, a b^{2} x^{4} + b^{3}}, x\right)"," ",0,"integral(x^8*sqrt((a*x^4 + b)/x^4)/(a^3*x^12 + 3*a^2*b*x^8 + 3*a*b^2*x^4 + b^3), x)","F",0
2106,-1,0,0,0.000000," ","integrate(1/(a+b/x^5),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2107,1,102,0,2.594229," ","integrate(1/x/(a+b/x^5)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(-8 \, a^{2} x^{10} - 8 \, a b x^{5} - b^{2} - 4 \, {\left(2 \, a x^{10} + b x^{5}\right)} \sqrt{a} \sqrt{\frac{a x^{5} + b}{x^{5}}}\right)}{10 \, \sqrt{a}}, -\frac{\sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} x^{5} \sqrt{\frac{a x^{5} + b}{x^{5}}}}{2 \, a x^{5} + b}\right)}{5 \, a}\right]"," ",0,"[1/10*log(-8*a^2*x^10 - 8*a*b*x^5 - b^2 - 4*(2*a*x^10 + b*x^5)*sqrt(a)*sqrt((a*x^5 + b)/x^5))/sqrt(a), -1/5*sqrt(-a)*arctan(2*sqrt(-a)*x^5*sqrt((a*x^5 + b)/x^5)/(2*a*x^5 + b))/a]","B",0
2108,1,111,0,2.588108," ","integrate(1/x/(-a+b/x^5)^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a} \log\left(-8 \, a^{2} x^{10} + 8 \, a b x^{5} - b^{2} + 4 \, {\left(2 \, a x^{10} - b x^{5}\right)} \sqrt{-a} \sqrt{-\frac{a x^{5} - b}{x^{5}}}\right)}{10 \, a}, -\frac{\arctan\left(\frac{2 \, \sqrt{a} x^{5} \sqrt{-\frac{a x^{5} - b}{x^{5}}}}{2 \, a x^{5} - b}\right)}{5 \, \sqrt{a}}\right]"," ",0,"[-1/10*sqrt(-a)*log(-8*a^2*x^10 + 8*a*b*x^5 - b^2 + 4*(2*a*x^10 - b*x^5)*sqrt(-a)*sqrt(-(a*x^5 - b)/x^5))/a, -1/5*arctan(2*sqrt(a)*x^5*sqrt(-(a*x^5 - b)/x^5)/(2*a*x^5 - b))/sqrt(a)]","A",0
2109,1,314,0,1.174098," ","integrate(1/(a+b/x^6),x, algorithm=""fricas"")","-\frac{4 \, \sqrt{3} a \left(-\frac{b}{a^{7}}\right)^{\frac{1}{6}} \arctan\left(-\frac{2 \, \sqrt{3} a^{6} x \left(-\frac{b}{a^{7}}\right)^{\frac{5}{6}} - 2 \, \sqrt{3} \sqrt{a^{2} \left(-\frac{b}{a^{7}}\right)^{\frac{1}{3}} + a x \left(-\frac{b}{a^{7}}\right)^{\frac{1}{6}} + x^{2}} a^{6} \left(-\frac{b}{a^{7}}\right)^{\frac{5}{6}} - \sqrt{3} b}{3 \, b}\right) + 4 \, \sqrt{3} a \left(-\frac{b}{a^{7}}\right)^{\frac{1}{6}} \arctan\left(-\frac{2 \, \sqrt{3} a^{6} x \left(-\frac{b}{a^{7}}\right)^{\frac{5}{6}} - 2 \, \sqrt{3} \sqrt{a^{2} \left(-\frac{b}{a^{7}}\right)^{\frac{1}{3}} - a x \left(-\frac{b}{a^{7}}\right)^{\frac{1}{6}} + x^{2}} a^{6} \left(-\frac{b}{a^{7}}\right)^{\frac{5}{6}} + \sqrt{3} b}{3 \, b}\right) + a \left(-\frac{b}{a^{7}}\right)^{\frac{1}{6}} \log\left(a^{2} \left(-\frac{b}{a^{7}}\right)^{\frac{1}{3}} + a x \left(-\frac{b}{a^{7}}\right)^{\frac{1}{6}} + x^{2}\right) - a \left(-\frac{b}{a^{7}}\right)^{\frac{1}{6}} \log\left(a^{2} \left(-\frac{b}{a^{7}}\right)^{\frac{1}{3}} - a x \left(-\frac{b}{a^{7}}\right)^{\frac{1}{6}} + x^{2}\right) + 2 \, a \left(-\frac{b}{a^{7}}\right)^{\frac{1}{6}} \log\left(a \left(-\frac{b}{a^{7}}\right)^{\frac{1}{6}} + x\right) - 2 \, a \left(-\frac{b}{a^{7}}\right)^{\frac{1}{6}} \log\left(-a \left(-\frac{b}{a^{7}}\right)^{\frac{1}{6}} + x\right) - 12 \, x}{12 \, a}"," ",0,"-1/12*(4*sqrt(3)*a*(-b/a^7)^(1/6)*arctan(-1/3*(2*sqrt(3)*a^6*x*(-b/a^7)^(5/6) - 2*sqrt(3)*sqrt(a^2*(-b/a^7)^(1/3) + a*x*(-b/a^7)^(1/6) + x^2)*a^6*(-b/a^7)^(5/6) - sqrt(3)*b)/b) + 4*sqrt(3)*a*(-b/a^7)^(1/6)*arctan(-1/3*(2*sqrt(3)*a^6*x*(-b/a^7)^(5/6) - 2*sqrt(3)*sqrt(a^2*(-b/a^7)^(1/3) - a*x*(-b/a^7)^(1/6) + x^2)*a^6*(-b/a^7)^(5/6) + sqrt(3)*b)/b) + a*(-b/a^7)^(1/6)*log(a^2*(-b/a^7)^(1/3) + a*x*(-b/a^7)^(1/6) + x^2) - a*(-b/a^7)^(1/6)*log(a^2*(-b/a^7)^(1/3) - a*x*(-b/a^7)^(1/6) + x^2) + 2*a*(-b/a^7)^(1/6)*log(a*(-b/a^7)^(1/6) + x) - 2*a*(-b/a^7)^(1/6)*log(-a*(-b/a^7)^(1/6) + x) - 12*x)/a","B",0
2110,1,385,0,1.199101," ","integrate(1/(a+b/x^8),x, algorithm=""fricas"")","-\frac{4 \, \sqrt{2} a \left(-\frac{b}{a^{9}}\right)^{\frac{1}{8}} \arctan\left(-\frac{\sqrt{2} a^{8} x \left(-\frac{b}{a^{9}}\right)^{\frac{7}{8}} - \sqrt{2} \sqrt{\sqrt{2} a x \left(-\frac{b}{a^{9}}\right)^{\frac{1}{8}} + a^{2} \left(-\frac{b}{a^{9}}\right)^{\frac{1}{4}} + x^{2}} a^{8} \left(-\frac{b}{a^{9}}\right)^{\frac{7}{8}} - b}{b}\right) + 4 \, \sqrt{2} a \left(-\frac{b}{a^{9}}\right)^{\frac{1}{8}} \arctan\left(-\frac{\sqrt{2} a^{8} x \left(-\frac{b}{a^{9}}\right)^{\frac{7}{8}} - \sqrt{2} \sqrt{-\sqrt{2} a x \left(-\frac{b}{a^{9}}\right)^{\frac{1}{8}} + a^{2} \left(-\frac{b}{a^{9}}\right)^{\frac{1}{4}} + x^{2}} a^{8} \left(-\frac{b}{a^{9}}\right)^{\frac{7}{8}} + b}{b}\right) + \sqrt{2} a \left(-\frac{b}{a^{9}}\right)^{\frac{1}{8}} \log\left(\sqrt{2} a x \left(-\frac{b}{a^{9}}\right)^{\frac{1}{8}} + a^{2} \left(-\frac{b}{a^{9}}\right)^{\frac{1}{4}} + x^{2}\right) - \sqrt{2} a \left(-\frac{b}{a^{9}}\right)^{\frac{1}{8}} \log\left(-\sqrt{2} a x \left(-\frac{b}{a^{9}}\right)^{\frac{1}{8}} + a^{2} \left(-\frac{b}{a^{9}}\right)^{\frac{1}{4}} + x^{2}\right) + 8 \, a \left(-\frac{b}{a^{9}}\right)^{\frac{1}{8}} \arctan\left(-\frac{a^{8} x \left(-\frac{b}{a^{9}}\right)^{\frac{7}{8}} - \sqrt{a^{2} \left(-\frac{b}{a^{9}}\right)^{\frac{1}{4}} + x^{2}} a^{8} \left(-\frac{b}{a^{9}}\right)^{\frac{7}{8}}}{b}\right) + 2 \, a \left(-\frac{b}{a^{9}}\right)^{\frac{1}{8}} \log\left(a \left(-\frac{b}{a^{9}}\right)^{\frac{1}{8}} + x\right) - 2 \, a \left(-\frac{b}{a^{9}}\right)^{\frac{1}{8}} \log\left(-a \left(-\frac{b}{a^{9}}\right)^{\frac{1}{8}} + x\right) - 16 \, x}{16 \, a}"," ",0,"-1/16*(4*sqrt(2)*a*(-b/a^9)^(1/8)*arctan(-(sqrt(2)*a^8*x*(-b/a^9)^(7/8) - sqrt(2)*sqrt(sqrt(2)*a*x*(-b/a^9)^(1/8) + a^2*(-b/a^9)^(1/4) + x^2)*a^8*(-b/a^9)^(7/8) - b)/b) + 4*sqrt(2)*a*(-b/a^9)^(1/8)*arctan(-(sqrt(2)*a^8*x*(-b/a^9)^(7/8) - sqrt(2)*sqrt(-sqrt(2)*a*x*(-b/a^9)^(1/8) + a^2*(-b/a^9)^(1/4) + x^2)*a^8*(-b/a^9)^(7/8) + b)/b) + sqrt(2)*a*(-b/a^9)^(1/8)*log(sqrt(2)*a*x*(-b/a^9)^(1/8) + a^2*(-b/a^9)^(1/4) + x^2) - sqrt(2)*a*(-b/a^9)^(1/8)*log(-sqrt(2)*a*x*(-b/a^9)^(1/8) + a^2*(-b/a^9)^(1/4) + x^2) + 8*a*(-b/a^9)^(1/8)*arctan(-(a^8*x*(-b/a^9)^(7/8) - sqrt(a^2*(-b/a^9)^(1/4) + x^2)*a^8*(-b/a^9)^(7/8))/b) + 2*a*(-b/a^9)^(1/8)*log(a*(-b/a^9)^(1/8) + x) - 2*a*(-b/a^9)^(1/8)*log(-a*(-b/a^9)^(1/8) + x) - 16*x)/a","B",0
2111,1,13,0,1.091367," ","integrate(x^4*(a+b*x^(1/2)),x, algorithm=""fricas"")","\frac{2}{11} \, b x^{\frac{11}{2}} + \frac{1}{5} \, a x^{5}"," ",0,"2/11*b*x^(11/2) + 1/5*a*x^5","A",0
2112,1,13,0,0.617724," ","integrate(x^3*(a+b*x^(1/2)),x, algorithm=""fricas"")","\frac{2}{9} \, b x^{\frac{9}{2}} + \frac{1}{4} \, a x^{4}"," ",0,"2/9*b*x^(9/2) + 1/4*a*x^4","A",0
2113,1,13,0,1.181146," ","integrate(x^2*(a+b*x^(1/2)),x, algorithm=""fricas"")","\frac{2}{7} \, b x^{\frac{7}{2}} + \frac{1}{3} \, a x^{3}"," ",0,"2/7*b*x^(7/2) + 1/3*a*x^3","A",0
2114,1,13,0,1.033169," ","integrate(x*(a+b*x^(1/2)),x, algorithm=""fricas"")","\frac{2}{5} \, b x^{\frac{5}{2}} + \frac{1}{2} \, a x^{2}"," ",0,"2/5*b*x^(5/2) + 1/2*a*x^2","A",0
2115,1,10,0,1.014883," ","integrate(a+b*x^(1/2),x, algorithm=""fricas"")","\frac{2}{3} \, b x^{\frac{3}{2}} + a x"," ",0,"2/3*b*x^(3/2) + a*x","A",0
2116,1,14,0,1.407291," ","integrate((a+b*x^(1/2))/x,x, algorithm=""fricas"")","2 \, a \log\left(\sqrt{x}\right) + 2 \, b \sqrt{x}"," ",0,"2*a*log(sqrt(x)) + 2*b*sqrt(x)","A",0
2117,1,13,0,1.300991," ","integrate((a+b*x^(1/2))/x^2,x, algorithm=""fricas"")","-\frac{2 \, b \sqrt{x} + a}{x}"," ",0,"-(2*b*sqrt(x) + a)/x","A",0
2118,1,15,0,1.253916," ","integrate((a+b*x^(1/2))/x^3,x, algorithm=""fricas"")","-\frac{4 \, b \sqrt{x} + 3 \, a}{6 \, x^{2}}"," ",0,"-1/6*(4*b*sqrt(x) + 3*a)/x^2","A",0
2119,1,15,0,1.422090," ","integrate((a+b*x^(1/2))/x^4,x, algorithm=""fricas"")","-\frac{6 \, b \sqrt{x} + 5 \, a}{15 \, x^{3}}"," ",0,"-1/15*(6*b*sqrt(x) + 5*a)/x^3","A",0
2120,1,24,0,1.424739," ","integrate(x^4*(a+b*x^(1/2))^2,x, algorithm=""fricas"")","\frac{1}{6} \, b^{2} x^{6} + \frac{4}{11} \, a b x^{\frac{11}{2}} + \frac{1}{5} \, a^{2} x^{5}"," ",0,"1/6*b^2*x^6 + 4/11*a*b*x^(11/2) + 1/5*a^2*x^5","A",0
2121,1,24,0,1.460315," ","integrate(x^3*(a+b*x^(1/2))^2,x, algorithm=""fricas"")","\frac{1}{5} \, b^{2} x^{5} + \frac{4}{9} \, a b x^{\frac{9}{2}} + \frac{1}{4} \, a^{2} x^{4}"," ",0,"1/5*b^2*x^5 + 4/9*a*b*x^(9/2) + 1/4*a^2*x^4","A",0
2122,1,24,0,1.023595," ","integrate(x^2*(a+b*x^(1/2))^2,x, algorithm=""fricas"")","\frac{1}{4} \, b^{2} x^{4} + \frac{4}{7} \, a b x^{\frac{7}{2}} + \frac{1}{3} \, a^{2} x^{3}"," ",0,"1/4*b^2*x^4 + 4/7*a*b*x^(7/2) + 1/3*a^2*x^3","A",0
2123,1,24,0,0.866940," ","integrate(x*(a+b*x^(1/2))^2,x, algorithm=""fricas"")","\frac{1}{3} \, b^{2} x^{3} + \frac{4}{5} \, a b x^{\frac{5}{2}} + \frac{1}{2} \, a^{2} x^{2}"," ",0,"1/3*b^2*x^3 + 4/5*a*b*x^(5/2) + 1/2*a^2*x^2","A",0
2124,1,21,0,0.738472," ","integrate((a+b*x^(1/2))^2,x, algorithm=""fricas"")","\frac{1}{2} \, b^{2} x^{2} + \frac{4}{3} \, a b x^{\frac{3}{2}} + a^{2} x"," ",0,"1/2*b^2*x^2 + 4/3*a*b*x^(3/2) + a^2*x","A",0
2125,1,22,0,1.333733," ","integrate((a+b*x^(1/2))^2/x,x, algorithm=""fricas"")","b^{2} x + 2 \, a^{2} \log\left(\sqrt{x}\right) + 4 \, a b \sqrt{x}"," ",0,"b^2*x + 2*a^2*log(sqrt(x)) + 4*a*b*sqrt(x)","A",0
2126,1,27,0,1.017037," ","integrate((a+b*x^(1/2))^2/x^2,x, algorithm=""fricas"")","\frac{2 \, b^{2} x \log\left(\sqrt{x}\right) - 4 \, a b \sqrt{x} - a^{2}}{x}"," ",0,"(2*b^2*x*log(sqrt(x)) - 4*a*b*sqrt(x) - a^2)/x","A",0
2127,1,24,0,0.667059," ","integrate((a+b*x^(1/2))^2/x^3,x, algorithm=""fricas"")","-\frac{6 \, b^{2} x + 8 \, a b \sqrt{x} + 3 \, a^{2}}{6 \, x^{2}}"," ",0,"-1/6*(6*b^2*x + 8*a*b*sqrt(x) + 3*a^2)/x^2","A",0
2128,1,24,0,0.849950," ","integrate((a+b*x^(1/2))^2/x^4,x, algorithm=""fricas"")","-\frac{15 \, b^{2} x + 24 \, a b \sqrt{x} + 10 \, a^{2}}{30 \, x^{3}}"," ",0,"-1/30*(15*b^2*x + 24*a*b*sqrt(x) + 10*a^2)/x^3","A",0
2129,1,24,0,0.998188," ","integrate((a+b*x^(1/2))^2/x^5,x, algorithm=""fricas"")","-\frac{28 \, b^{2} x + 48 \, a b \sqrt{x} + 21 \, a^{2}}{84 \, x^{4}}"," ",0,"-1/84*(28*b^2*x + 48*a*b*sqrt(x) + 21*a^2)/x^4","A",0
2130,1,41,0,1.074979," ","integrate(x^4*(a+b*x^(1/2))^3,x, algorithm=""fricas"")","\frac{1}{2} \, a b^{2} x^{6} + \frac{1}{5} \, a^{3} x^{5} + \frac{2}{143} \, {\left(11 \, b^{3} x^{6} + 39 \, a^{2} b x^{5}\right)} \sqrt{x}"," ",0,"1/2*a*b^2*x^6 + 1/5*a^3*x^5 + 2/143*(11*b^3*x^6 + 39*a^2*b*x^5)*sqrt(x)","A",0
2131,1,41,0,1.018451," ","integrate(x^3*(a+b*x^(1/2))^3,x, algorithm=""fricas"")","\frac{3}{5} \, a b^{2} x^{5} + \frac{1}{4} \, a^{3} x^{4} + \frac{2}{33} \, {\left(3 \, b^{3} x^{5} + 11 \, a^{2} b x^{4}\right)} \sqrt{x}"," ",0,"3/5*a*b^2*x^5 + 1/4*a^3*x^4 + 2/33*(3*b^3*x^5 + 11*a^2*b*x^4)*sqrt(x)","A",0
2132,1,41,0,0.923946," ","integrate(x^2*(a+b*x^(1/2))^3,x, algorithm=""fricas"")","\frac{3}{4} \, a b^{2} x^{4} + \frac{1}{3} \, a^{3} x^{3} + \frac{2}{63} \, {\left(7 \, b^{3} x^{4} + 27 \, a^{2} b x^{3}\right)} \sqrt{x}"," ",0,"3/4*a*b^2*x^4 + 1/3*a^3*x^3 + 2/63*(7*b^3*x^4 + 27*a^2*b*x^3)*sqrt(x)","A",0
2133,1,40,0,1.082750," ","integrate(x*(a+b*x^(1/2))^3,x, algorithm=""fricas"")","a b^{2} x^{3} + \frac{1}{2} \, a^{3} x^{2} + \frac{2}{35} \, {\left(5 \, b^{3} x^{3} + 21 \, a^{2} b x^{2}\right)} \sqrt{x}"," ",0,"a*b^2*x^3 + 1/2*a^3*x^2 + 2/35*(5*b^3*x^3 + 21*a^2*b*x^2)*sqrt(x)","A",0
2134,1,35,0,0.846921," ","integrate((a+b*x^(1/2))^3,x, algorithm=""fricas"")","\frac{3}{2} \, a b^{2} x^{2} + a^{3} x + \frac{2}{5} \, {\left(b^{3} x^{2} + 5 \, a^{2} b x\right)} \sqrt{x}"," ",0,"3/2*a*b^2*x^2 + a^3*x + 2/5*(b^3*x^2 + 5*a^2*b*x)*sqrt(x)","A",0
2135,1,34,0,1.222373," ","integrate((a+b*x^(1/2))^3/x,x, algorithm=""fricas"")","3 \, a b^{2} x + 2 \, a^{3} \log\left(\sqrt{x}\right) + \frac{2}{3} \, {\left(b^{3} x + 9 \, a^{2} b\right)} \sqrt{x}"," ",0,"3*a*b^2*x + 2*a^3*log(sqrt(x)) + 2/3*(b^3*x + 9*a^2*b)*sqrt(x)","A",0
2136,1,38,0,1.134186," ","integrate((a+b*x^(1/2))^3/x^2,x, algorithm=""fricas"")","\frac{6 \, a b^{2} x \log\left(\sqrt{x}\right) - a^{3} + 2 \, {\left(b^{3} x - 3 \, a^{2} b\right)} \sqrt{x}}{x}"," ",0,"(6*a*b^2*x*log(sqrt(x)) - a^3 + 2*(b^3*x - 3*a^2*b)*sqrt(x))/x","A",0
2137,1,32,0,0.869055," ","integrate((a+b*x^(1/2))^3/x^3,x, algorithm=""fricas"")","-\frac{6 \, a b^{2} x + a^{3} + 4 \, {\left(b^{3} x + a^{2} b\right)} \sqrt{x}}{2 \, x^{2}}"," ",0,"-1/2*(6*a*b^2*x + a^3 + 4*(b^3*x + a^2*b)*sqrt(x))/x^2","A",0
2138,1,36,0,0.998604," ","integrate((a+b*x^(1/2))^3/x^4,x, algorithm=""fricas"")","-\frac{45 \, a b^{2} x + 10 \, a^{3} + 4 \, {\left(5 \, b^{3} x + 9 \, a^{2} b\right)} \sqrt{x}}{30 \, x^{3}}"," ",0,"-1/30*(45*a*b^2*x + 10*a^3 + 4*(5*b^3*x + 9*a^2*b)*sqrt(x))/x^3","A",0
2139,1,36,0,1.065079," ","integrate((a+b*x^(1/2))^3/x^5,x, algorithm=""fricas"")","-\frac{140 \, a b^{2} x + 35 \, a^{3} + 8 \, {\left(7 \, b^{3} x + 15 \, a^{2} b\right)} \sqrt{x}}{140 \, x^{4}}"," ",0,"-1/140*(140*a*b^2*x + 35*a^3 + 8*(7*b^3*x + 15*a^2*b)*sqrt(x))/x^4","A",0
2140,1,36,0,1.020989," ","integrate((a+b*x^(1/2))^3/x^6,x, algorithm=""fricas"")","-\frac{315 \, a b^{2} x + 84 \, a^{3} + 40 \, {\left(3 \, b^{3} x + 7 \, a^{2} b\right)} \sqrt{x}}{420 \, x^{5}}"," ",0,"-1/420*(315*a*b^2*x + 84*a^3 + 40*(3*b^3*x + 7*a^2*b)*sqrt(x))/x^5","A",0
2141,1,63,0,0.998157," ","integrate(x^4*(a+b*x^(1/2))^5,x, algorithm=""fricas"")","\frac{5}{7} \, a b^{4} x^{7} + \frac{5}{3} \, a^{3} b^{2} x^{6} + \frac{1}{5} \, a^{5} x^{5} + \frac{2}{2145} \, {\left(143 \, b^{5} x^{7} + 1650 \, a^{2} b^{3} x^{6} + 975 \, a^{4} b x^{5}\right)} \sqrt{x}"," ",0,"5/7*a*b^4*x^7 + 5/3*a^3*b^2*x^6 + 1/5*a^5*x^5 + 2/2145*(143*b^5*x^7 + 1650*a^2*b^3*x^6 + 975*a^4*b*x^5)*sqrt(x)","A",0
2142,1,63,0,0.880967," ","integrate(x^3*(a+b*x^(1/2))^5,x, algorithm=""fricas"")","\frac{5}{6} \, a b^{4} x^{6} + 2 \, a^{3} b^{2} x^{5} + \frac{1}{4} \, a^{5} x^{4} + \frac{2}{1287} \, {\left(99 \, b^{5} x^{6} + 1170 \, a^{2} b^{3} x^{5} + 715 \, a^{4} b x^{4}\right)} \sqrt{x}"," ",0,"5/6*a*b^4*x^6 + 2*a^3*b^2*x^5 + 1/4*a^5*x^4 + 2/1287*(99*b^5*x^6 + 1170*a^2*b^3*x^5 + 715*a^4*b*x^4)*sqrt(x)","A",0
2143,1,62,0,0.954201," ","integrate(x^2*(a+b*x^(1/2))^5,x, algorithm=""fricas"")","a b^{4} x^{5} + \frac{5}{2} \, a^{3} b^{2} x^{4} + \frac{1}{3} \, a^{5} x^{3} + \frac{2}{693} \, {\left(63 \, b^{5} x^{5} + 770 \, a^{2} b^{3} x^{4} + 495 \, a^{4} b x^{3}\right)} \sqrt{x}"," ",0,"a*b^4*x^5 + 5/2*a^3*b^2*x^4 + 1/3*a^5*x^3 + 2/693*(63*b^5*x^5 + 770*a^2*b^3*x^4 + 495*a^4*b*x^3)*sqrt(x)","A",0
2144,1,63,0,0.824524," ","integrate(x*(a+b*x^(1/2))^5,x, algorithm=""fricas"")","\frac{5}{4} \, a b^{4} x^{4} + \frac{10}{3} \, a^{3} b^{2} x^{3} + \frac{1}{2} \, a^{5} x^{2} + \frac{2}{63} \, {\left(7 \, b^{5} x^{4} + 90 \, a^{2} b^{3} x^{3} + 63 \, a^{4} b x^{2}\right)} \sqrt{x}"," ",0,"5/4*a*b^4*x^4 + 10/3*a^3*b^2*x^3 + 1/2*a^5*x^2 + 2/63*(7*b^5*x^4 + 90*a^2*b^3*x^3 + 63*a^4*b*x^2)*sqrt(x)","A",0
2145,1,58,0,1.198820," ","integrate((a+b*x^(1/2))^5,x, algorithm=""fricas"")","\frac{5}{3} \, a b^{4} x^{3} + 5 \, a^{3} b^{2} x^{2} + a^{5} x + \frac{2}{21} \, {\left(3 \, b^{5} x^{3} + 42 \, a^{2} b^{3} x^{2} + 35 \, a^{4} b x\right)} \sqrt{x}"," ",0,"5/3*a*b^4*x^3 + 5*a^3*b^2*x^2 + a^5*x + 2/21*(3*b^5*x^3 + 42*a^2*b^3*x^2 + 35*a^4*b*x)*sqrt(x)","A",0
2146,1,57,0,0.804010," ","integrate((a+b*x^(1/2))^5/x,x, algorithm=""fricas"")","\frac{5}{2} \, a b^{4} x^{2} + 10 \, a^{3} b^{2} x + 2 \, a^{5} \log\left(\sqrt{x}\right) + \frac{2}{15} \, {\left(3 \, b^{5} x^{2} + 50 \, a^{2} b^{3} x + 75 \, a^{4} b\right)} \sqrt{x}"," ",0,"5/2*a*b^4*x^2 + 10*a^3*b^2*x + 2*a^5*log(sqrt(x)) + 2/15*(3*b^5*x^2 + 50*a^2*b^3*x + 75*a^4*b)*sqrt(x)","A",0
2147,1,61,0,0.893829," ","integrate((a+b*x^(1/2))^5/x^2,x, algorithm=""fricas"")","\frac{15 \, a b^{4} x^{2} + 60 \, a^{3} b^{2} x \log\left(\sqrt{x}\right) - 3 \, a^{5} + 2 \, {\left(b^{5} x^{2} + 30 \, a^{2} b^{3} x - 15 \, a^{4} b\right)} \sqrt{x}}{3 \, x}"," ",0,"1/3*(15*a*b^4*x^2 + 60*a^3*b^2*x*log(sqrt(x)) - 3*a^5 + 2*(b^5*x^2 + 30*a^2*b^3*x - 15*a^4*b)*sqrt(x))/x","A",0
2148,1,62,0,0.726771," ","integrate((a+b*x^(1/2))^5/x^3,x, algorithm=""fricas"")","\frac{60 \, a b^{4} x^{2} \log\left(\sqrt{x}\right) - 60 \, a^{3} b^{2} x - 3 \, a^{5} + 4 \, {\left(3 \, b^{5} x^{2} - 30 \, a^{2} b^{3} x - 5 \, a^{4} b\right)} \sqrt{x}}{6 \, x^{2}}"," ",0,"1/6*(60*a*b^4*x^2*log(sqrt(x)) - 60*a^3*b^2*x - 3*a^5 + 4*(3*b^5*x^2 - 30*a^2*b^3*x - 5*a^4*b)*sqrt(x))/x^2","A",0
2149,1,56,0,0.839250," ","integrate((a+b*x^(1/2))^5/x^4,x, algorithm=""fricas"")","-\frac{15 \, a b^{4} x^{2} + 15 \, a^{3} b^{2} x + a^{5} + 2 \, {\left(3 \, b^{5} x^{2} + 10 \, a^{2} b^{3} x + 3 \, a^{4} b\right)} \sqrt{x}}{3 \, x^{3}}"," ",0,"-1/3*(15*a*b^4*x^2 + 15*a^3*b^2*x + a^5 + 2*(3*b^5*x^2 + 10*a^2*b^3*x + 3*a^4*b)*sqrt(x))/x^3","B",0
2150,1,58,0,0.644039," ","integrate((a+b*x^(1/2))^5/x^5,x, algorithm=""fricas"")","-\frac{210 \, a b^{4} x^{2} + 280 \, a^{3} b^{2} x + 21 \, a^{5} + 8 \, {\left(7 \, b^{5} x^{2} + 42 \, a^{2} b^{3} x + 15 \, a^{4} b\right)} \sqrt{x}}{84 \, x^{4}}"," ",0,"-1/84*(210*a*b^4*x^2 + 280*a^3*b^2*x + 21*a^5 + 8*(7*b^5*x^2 + 42*a^2*b^3*x + 15*a^4*b)*sqrt(x))/x^4","A",0
2151,1,58,0,1.064303," ","integrate((a+b*x^(1/2))^5/x^6,x, algorithm=""fricas"")","-\frac{1050 \, a b^{4} x^{2} + 1575 \, a^{3} b^{2} x + 126 \, a^{5} + 4 \, {\left(63 \, b^{5} x^{2} + 450 \, a^{2} b^{3} x + 175 \, a^{4} b\right)} \sqrt{x}}{630 \, x^{5}}"," ",0,"-1/630*(1050*a*b^4*x^2 + 1575*a^3*b^2*x + 126*a^5 + 4*(63*b^5*x^2 + 450*a^2*b^3*x + 175*a^4*b)*sqrt(x))/x^5","A",0
2152,1,58,0,0.983991," ","integrate((a+b*x^(1/2))^5/x^7,x, algorithm=""fricas"")","-\frac{3465 \, a b^{4} x^{2} + 5544 \, a^{3} b^{2} x + 462 \, a^{5} + 8 \, {\left(99 \, b^{5} x^{2} + 770 \, a^{2} b^{3} x + 315 \, a^{4} b\right)} \sqrt{x}}{2772 \, x^{6}}"," ",0,"-1/2772*(3465*a*b^4*x^2 + 5544*a^3*b^2*x + 462*a^5 + 8*(99*b^5*x^2 + 770*a^2*b^3*x + 315*a^4*b)*sqrt(x))/x^6","A",0
2153,1,118,0,0.881598," ","integrate(x^4*(a+b*x^(1/2))^10,x, algorithm=""fricas"")","\frac{1}{10} \, b^{10} x^{10} + 5 \, a^{2} b^{8} x^{9} + \frac{105}{4} \, a^{4} b^{6} x^{8} + 30 \, a^{6} b^{4} x^{7} + \frac{15}{2} \, a^{8} b^{2} x^{6} + \frac{1}{5} \, a^{10} x^{5} + \frac{4}{230945} \, {\left(60775 \, a b^{9} x^{9} + 815100 \, a^{3} b^{7} x^{8} + 1939938 \, a^{5} b^{5} x^{7} + 1065900 \, a^{7} b^{3} x^{6} + 104975 \, a^{9} b x^{5}\right)} \sqrt{x}"," ",0,"1/10*b^10*x^10 + 5*a^2*b^8*x^9 + 105/4*a^4*b^6*x^8 + 30*a^6*b^4*x^7 + 15/2*a^8*b^2*x^6 + 1/5*a^10*x^5 + 4/230945*(60775*a*b^9*x^9 + 815100*a^3*b^7*x^8 + 1939938*a^5*b^5*x^7 + 1065900*a^7*b^3*x^6 + 104975*a^9*b*x^5)*sqrt(x)","A",0
2154,1,118,0,1.180959," ","integrate(x^3*(a+b*x^(1/2))^10,x, algorithm=""fricas"")","\frac{1}{9} \, b^{10} x^{9} + \frac{45}{8} \, a^{2} b^{8} x^{8} + 30 \, a^{4} b^{6} x^{7} + 35 \, a^{6} b^{4} x^{6} + 9 \, a^{8} b^{2} x^{5} + \frac{1}{4} \, a^{10} x^{4} + \frac{4}{21879} \, {\left(6435 \, a b^{9} x^{8} + 87516 \, a^{3} b^{7} x^{7} + 212058 \, a^{5} b^{5} x^{6} + 119340 \, a^{7} b^{3} x^{5} + 12155 \, a^{9} b x^{4}\right)} \sqrt{x}"," ",0,"1/9*b^10*x^9 + 45/8*a^2*b^8*x^8 + 30*a^4*b^6*x^7 + 35*a^6*b^4*x^6 + 9*a^8*b^2*x^5 + 1/4*a^10*x^4 + 4/21879*(6435*a*b^9*x^8 + 87516*a^3*b^7*x^7 + 212058*a^5*b^5*x^6 + 119340*a^7*b^3*x^5 + 12155*a^9*b*x^4)*sqrt(x)","A",0
2155,1,118,0,0.972010," ","integrate(x^2*(a+b*x^(1/2))^10,x, algorithm=""fricas"")","\frac{1}{8} \, b^{10} x^{8} + \frac{45}{7} \, a^{2} b^{8} x^{7} + 35 \, a^{4} b^{6} x^{6} + 42 \, a^{6} b^{4} x^{5} + \frac{45}{4} \, a^{8} b^{2} x^{4} + \frac{1}{3} \, a^{10} x^{3} + \frac{4}{3003} \, {\left(1001 \, a b^{9} x^{7} + 13860 \, a^{3} b^{7} x^{6} + 34398 \, a^{5} b^{5} x^{5} + 20020 \, a^{7} b^{3} x^{4} + 2145 \, a^{9} b x^{3}\right)} \sqrt{x}"," ",0,"1/8*b^10*x^8 + 45/7*a^2*b^8*x^7 + 35*a^4*b^6*x^6 + 42*a^6*b^4*x^5 + 45/4*a^8*b^2*x^4 + 1/3*a^10*x^3 + 4/3003*(1001*a*b^9*x^7 + 13860*a^3*b^7*x^6 + 34398*a^5*b^5*x^5 + 20020*a^7*b^3*x^4 + 2145*a^9*b*x^3)*sqrt(x)","A",0
2156,1,118,0,1.148441," ","integrate(x*(a+b*x^(1/2))^10,x, algorithm=""fricas"")","\frac{1}{7} \, b^{10} x^{7} + \frac{15}{2} \, a^{2} b^{8} x^{6} + 42 \, a^{4} b^{6} x^{5} + \frac{105}{2} \, a^{6} b^{4} x^{4} + 15 \, a^{8} b^{2} x^{3} + \frac{1}{2} \, a^{10} x^{2} + \frac{4}{1001} \, {\left(385 \, a b^{9} x^{6} + 5460 \, a^{3} b^{7} x^{5} + 14014 \, a^{5} b^{5} x^{4} + 8580 \, a^{7} b^{3} x^{3} + 1001 \, a^{9} b x^{2}\right)} \sqrt{x}"," ",0,"1/7*b^10*x^7 + 15/2*a^2*b^8*x^6 + 42*a^4*b^6*x^5 + 105/2*a^6*b^4*x^4 + 15*a^8*b^2*x^3 + 1/2*a^10*x^2 + 4/1001*(385*a*b^9*x^6 + 5460*a^3*b^7*x^5 + 14014*a^5*b^5*x^4 + 8580*a^7*b^3*x^3 + 1001*a^9*b*x^2)*sqrt(x)","A",0
2157,1,113,0,0.805227," ","integrate((a+b*x^(1/2))^10,x, algorithm=""fricas"")","\frac{1}{6} \, b^{10} x^{6} + 9 \, a^{2} b^{8} x^{5} + \frac{105}{2} \, a^{4} b^{6} x^{4} + 70 \, a^{6} b^{4} x^{3} + \frac{45}{2} \, a^{8} b^{2} x^{2} + a^{10} x + \frac{4}{33} \, {\left(15 \, a b^{9} x^{5} + 220 \, a^{3} b^{7} x^{4} + 594 \, a^{5} b^{5} x^{3} + 396 \, a^{7} b^{3} x^{2} + 55 \, a^{9} b x\right)} \sqrt{x}"," ",0,"1/6*b^10*x^6 + 9*a^2*b^8*x^5 + 105/2*a^4*b^6*x^4 + 70*a^6*b^4*x^3 + 45/2*a^8*b^2*x^2 + a^10*x + 4/33*(15*a*b^9*x^5 + 220*a^3*b^7*x^4 + 594*a^5*b^5*x^3 + 396*a^7*b^3*x^2 + 55*a^9*b*x)*sqrt(x)","B",0
2158,1,112,0,0.820550," ","integrate((a+b*x^(1/2))^10/x,x, algorithm=""fricas"")","\frac{1}{5} \, b^{10} x^{5} + \frac{45}{4} \, a^{2} b^{8} x^{4} + 70 \, a^{4} b^{6} x^{3} + 105 \, a^{6} b^{4} x^{2} + 45 \, a^{8} b^{2} x + 2 \, a^{10} \log\left(\sqrt{x}\right) + \frac{4}{315} \, {\left(175 \, a b^{9} x^{4} + 2700 \, a^{3} b^{7} x^{3} + 7938 \, a^{5} b^{5} x^{2} + 6300 \, a^{7} b^{3} x + 1575 \, a^{9} b\right)} \sqrt{x}"," ",0,"1/5*b^10*x^5 + 45/4*a^2*b^8*x^4 + 70*a^4*b^6*x^3 + 105*a^6*b^4*x^2 + 45*a^8*b^2*x + 2*a^10*log(sqrt(x)) + 4/315*(175*a*b^9*x^4 + 2700*a^3*b^7*x^3 + 7938*a^5*b^5*x^2 + 6300*a^7*b^3*x + 1575*a^9*b)*sqrt(x)","A",0
2159,1,117,0,0.581202," ","integrate((a+b*x^(1/2))^10/x^2,x, algorithm=""fricas"")","\frac{7 \, b^{10} x^{5} + 420 \, a^{2} b^{8} x^{4} + 2940 \, a^{4} b^{6} x^{3} + 5880 \, a^{6} b^{4} x^{2} + 2520 \, a^{8} b^{2} x \log\left(\sqrt{x}\right) - 28 \, a^{10} + 16 \, {\left(5 \, a b^{9} x^{4} + 84 \, a^{3} b^{7} x^{3} + 294 \, a^{5} b^{5} x^{2} + 420 \, a^{7} b^{3} x - 35 \, a^{9} b\right)} \sqrt{x}}{28 \, x}"," ",0,"1/28*(7*b^10*x^5 + 420*a^2*b^8*x^4 + 2940*a^4*b^6*x^3 + 5880*a^6*b^4*x^2 + 2520*a^8*b^2*x*log(sqrt(x)) - 28*a^10 + 16*(5*a*b^9*x^4 + 84*a^3*b^7*x^3 + 294*a^5*b^5*x^2 + 420*a^7*b^3*x - 35*a^9*b)*sqrt(x))/x","A",0
2160,1,117,0,0.781116," ","integrate((a+b*x^(1/2))^10/x^3,x, algorithm=""fricas"")","\frac{2 \, b^{10} x^{5} + 135 \, a^{2} b^{8} x^{4} + 1260 \, a^{4} b^{6} x^{3} + 2520 \, a^{6} b^{4} x^{2} \log\left(\sqrt{x}\right) - 270 \, a^{8} b^{2} x - 3 \, a^{10} + 8 \, {\left(3 \, a b^{9} x^{4} + 60 \, a^{3} b^{7} x^{3} + 378 \, a^{5} b^{5} x^{2} - 180 \, a^{7} b^{3} x - 5 \, a^{9} b\right)} \sqrt{x}}{6 \, x^{2}}"," ",0,"1/6*(2*b^10*x^5 + 135*a^2*b^8*x^4 + 1260*a^4*b^6*x^3 + 2520*a^6*b^4*x^2*log(sqrt(x)) - 270*a^8*b^2*x - 3*a^10 + 8*(3*a*b^9*x^4 + 60*a^3*b^7*x^3 + 378*a^5*b^5*x^2 - 180*a^7*b^3*x - 5*a^9*b)*sqrt(x))/x^2","A",0
2161,1,117,0,0.580888," ","integrate((a+b*x^(1/2))^10/x^4,x, algorithm=""fricas"")","\frac{3 \, b^{10} x^{5} + 270 \, a^{2} b^{8} x^{4} + 2520 \, a^{4} b^{6} x^{3} \log\left(\sqrt{x}\right) - 1260 \, a^{6} b^{4} x^{2} - 135 \, a^{8} b^{2} x - 2 \, a^{10} + 8 \, {\left(5 \, a b^{9} x^{4} + 180 \, a^{3} b^{7} x^{3} - 378 \, a^{5} b^{5} x^{2} - 60 \, a^{7} b^{3} x - 3 \, a^{9} b\right)} \sqrt{x}}{6 \, x^{3}}"," ",0,"1/6*(3*b^10*x^5 + 270*a^2*b^8*x^4 + 2520*a^4*b^6*x^3*log(sqrt(x)) - 1260*a^6*b^4*x^2 - 135*a^8*b^2*x - 2*a^10 + 8*(5*a*b^9*x^4 + 180*a^3*b^7*x^3 - 378*a^5*b^5*x^2 - 60*a^7*b^3*x - 3*a^9*b)*sqrt(x))/x^3","A",0
2162,1,117,0,0.807513," ","integrate((a+b*x^(1/2))^10/x^5,x, algorithm=""fricas"")","\frac{28 \, b^{10} x^{5} + 2520 \, a^{2} b^{8} x^{4} \log\left(\sqrt{x}\right) - 5880 \, a^{4} b^{6} x^{3} - 2940 \, a^{6} b^{4} x^{2} - 420 \, a^{8} b^{2} x - 7 \, a^{10} + 16 \, {\left(35 \, a b^{9} x^{4} - 420 \, a^{3} b^{7} x^{3} - 294 \, a^{5} b^{5} x^{2} - 84 \, a^{7} b^{3} x - 5 \, a^{9} b\right)} \sqrt{x}}{28 \, x^{4}}"," ",0,"1/28*(28*b^10*x^5 + 2520*a^2*b^8*x^4*log(sqrt(x)) - 5880*a^4*b^6*x^3 - 2940*a^6*b^4*x^2 - 420*a^8*b^2*x - 7*a^10 + 16*(35*a*b^9*x^4 - 420*a^3*b^7*x^3 - 294*a^5*b^5*x^2 - 84*a^7*b^3*x - 5*a^9*b)*sqrt(x))/x^4","A",0
2163,1,117,0,0.642815," ","integrate((a+b*x^(1/2))^10/x^6,x, algorithm=""fricas"")","\frac{2520 \, b^{10} x^{5} \log\left(\sqrt{x}\right) - 56700 \, a^{2} b^{8} x^{4} - 132300 \, a^{4} b^{6} x^{3} - 88200 \, a^{6} b^{4} x^{2} - 14175 \, a^{8} b^{2} x - 252 \, a^{10} - 16 \, {\left(1575 \, a b^{9} x^{4} + 6300 \, a^{3} b^{7} x^{3} + 7938 \, a^{5} b^{5} x^{2} + 2700 \, a^{7} b^{3} x + 175 \, a^{9} b\right)} \sqrt{x}}{1260 \, x^{5}}"," ",0,"1/1260*(2520*b^10*x^5*log(sqrt(x)) - 56700*a^2*b^8*x^4 - 132300*a^4*b^6*x^3 - 88200*a^6*b^4*x^2 - 14175*a^8*b^2*x - 252*a^10 - 16*(1575*a*b^9*x^4 + 6300*a^3*b^7*x^3 + 7938*a^5*b^5*x^2 + 2700*a^7*b^3*x + 175*a^9*b)*sqrt(x))/x^5","A",0
2164,1,113,0,0.785205," ","integrate((a+b*x^(1/2))^10/x^7,x, algorithm=""fricas"")","-\frac{66 \, b^{10} x^{5} + 1485 \, a^{2} b^{8} x^{4} + 4620 \, a^{4} b^{6} x^{3} + 3465 \, a^{6} b^{4} x^{2} + 594 \, a^{8} b^{2} x + 11 \, a^{10} + 8 \, {\left(55 \, a b^{9} x^{4} + 396 \, a^{3} b^{7} x^{3} + 594 \, a^{5} b^{5} x^{2} + 220 \, a^{7} b^{3} x + 15 \, a^{9} b\right)} \sqrt{x}}{66 \, x^{6}}"," ",0,"-1/66*(66*b^10*x^5 + 1485*a^2*b^8*x^4 + 4620*a^4*b^6*x^3 + 3465*a^6*b^4*x^2 + 594*a^8*b^2*x + 11*a^10 + 8*(55*a*b^9*x^4 + 396*a^3*b^7*x^3 + 594*a^5*b^5*x^2 + 220*a^7*b^3*x + 15*a^9*b)*sqrt(x))/x^6","B",0
2165,1,113,0,0.888694," ","integrate((a+b*x^(1/2))^10/x^8,x, algorithm=""fricas"")","-\frac{1001 \, b^{10} x^{5} + 30030 \, a^{2} b^{8} x^{4} + 105105 \, a^{4} b^{6} x^{3} + 84084 \, a^{6} b^{4} x^{2} + 15015 \, a^{8} b^{2} x + 286 \, a^{10} + 8 \, {\left(1001 \, a b^{9} x^{4} + 8580 \, a^{3} b^{7} x^{3} + 14014 \, a^{5} b^{5} x^{2} + 5460 \, a^{7} b^{3} x + 385 \, a^{9} b\right)} \sqrt{x}}{2002 \, x^{7}}"," ",0,"-1/2002*(1001*b^10*x^5 + 30030*a^2*b^8*x^4 + 105105*a^4*b^6*x^3 + 84084*a^6*b^4*x^2 + 15015*a^8*b^2*x + 286*a^10 + 8*(1001*a*b^9*x^4 + 8580*a^3*b^7*x^3 + 14014*a^5*b^5*x^2 + 5460*a^7*b^3*x + 385*a^9*b)*sqrt(x))/x^7","A",0
2166,1,113,0,0.881837," ","integrate((a+b*x^(1/2))^10/x^9,x, algorithm=""fricas"")","-\frac{8008 \, b^{10} x^{5} + 270270 \, a^{2} b^{8} x^{4} + 1009008 \, a^{4} b^{6} x^{3} + 840840 \, a^{6} b^{4} x^{2} + 154440 \, a^{8} b^{2} x + 3003 \, a^{10} + 32 \, {\left(2145 \, a b^{9} x^{4} + 20020 \, a^{3} b^{7} x^{3} + 34398 \, a^{5} b^{5} x^{2} + 13860 \, a^{7} b^{3} x + 1001 \, a^{9} b\right)} \sqrt{x}}{24024 \, x^{8}}"," ",0,"-1/24024*(8008*b^10*x^5 + 270270*a^2*b^8*x^4 + 1009008*a^4*b^6*x^3 + 840840*a^6*b^4*x^2 + 154440*a^8*b^2*x + 3003*a^10 + 32*(2145*a*b^9*x^4 + 20020*a^3*b^7*x^3 + 34398*a^5*b^5*x^2 + 13860*a^7*b^3*x + 1001*a^9*b)*sqrt(x))/x^8","A",0
2167,1,113,0,0.846578," ","integrate((a+b*x^(1/2))^10/x^10,x, algorithm=""fricas"")","-\frac{43758 \, b^{10} x^{5} + 1575288 \, a^{2} b^{8} x^{4} + 6126120 \, a^{4} b^{6} x^{3} + 5250960 \, a^{6} b^{4} x^{2} + 984555 \, a^{8} b^{2} x + 19448 \, a^{10} + 32 \, {\left(12155 \, a b^{9} x^{4} + 119340 \, a^{3} b^{7} x^{3} + 212058 \, a^{5} b^{5} x^{2} + 87516 \, a^{7} b^{3} x + 6435 \, a^{9} b\right)} \sqrt{x}}{175032 \, x^{9}}"," ",0,"-1/175032*(43758*b^10*x^5 + 1575288*a^2*b^8*x^4 + 6126120*a^4*b^6*x^3 + 5250960*a^6*b^4*x^2 + 984555*a^8*b^2*x + 19448*a^10 + 32*(12155*a*b^9*x^4 + 119340*a^3*b^7*x^3 + 212058*a^5*b^5*x^2 + 87516*a^7*b^3*x + 6435*a^9*b)*sqrt(x))/x^9","A",0
2168,1,113,0,0.814852," ","integrate((a+b*x^(1/2))^10/x^11,x, algorithm=""fricas"")","-\frac{184756 \, b^{10} x^{5} + 6928350 \, a^{2} b^{8} x^{4} + 27713400 \, a^{4} b^{6} x^{3} + 24249225 \, a^{6} b^{4} x^{2} + 4618900 \, a^{8} b^{2} x + 92378 \, a^{10} + 16 \, {\left(104975 \, a b^{9} x^{4} + 1065900 \, a^{3} b^{7} x^{3} + 1939938 \, a^{5} b^{5} x^{2} + 815100 \, a^{7} b^{3} x + 60775 \, a^{9} b\right)} \sqrt{x}}{923780 \, x^{10}}"," ",0,"-1/923780*(184756*b^10*x^5 + 6928350*a^2*b^8*x^4 + 27713400*a^4*b^6*x^3 + 24249225*a^6*b^4*x^2 + 4618900*a^8*b^2*x + 92378*a^10 + 16*(104975*a*b^9*x^4 + 1065900*a^3*b^7*x^3 + 1939938*a^5*b^5*x^2 + 815100*a^7*b^3*x + 60775*a^9*b)*sqrt(x))/x^10","A",0
2169,1,173,0,0.930971," ","integrate(x^5*(a+b*x^(1/2))^15,x, algorithm=""fricas"")","\frac{15}{13} \, a b^{14} x^{13} + \frac{455}{12} \, a^{3} b^{12} x^{12} + 273 \, a^{5} b^{10} x^{11} + \frac{1287}{2} \, a^{7} b^{8} x^{10} + \frac{5005}{9} \, a^{9} b^{6} x^{9} + \frac{1365}{8} \, a^{11} b^{4} x^{8} + 15 \, a^{13} b^{2} x^{7} + \frac{1}{6} \, a^{15} x^{6} + \frac{2}{13037895} \, {\left(482885 \, b^{15} x^{13} + 54759159 \, a^{2} b^{13} x^{12} + 773770725 \, a^{4} b^{11} x^{11} + 3107364975 \, a^{6} b^{9} x^{10} + 4415729175 \, a^{8} b^{7} x^{9} + 2303105805 \, a^{10} b^{5} x^{8} + 395482815 \, a^{12} b^{3} x^{7} + 15043725 \, a^{14} b x^{6}\right)} \sqrt{x}"," ",0,"15/13*a*b^14*x^13 + 455/12*a^3*b^12*x^12 + 273*a^5*b^10*x^11 + 1287/2*a^7*b^8*x^10 + 5005/9*a^9*b^6*x^9 + 1365/8*a^11*b^4*x^8 + 15*a^13*b^2*x^7 + 1/6*a^15*x^6 + 2/13037895*(482885*b^15*x^13 + 54759159*a^2*b^13*x^12 + 773770725*a^4*b^11*x^11 + 3107364975*a^6*b^9*x^10 + 4415729175*a^8*b^7*x^9 + 2303105805*a^10*b^5*x^8 + 395482815*a^12*b^3*x^7 + 15043725*a^14*b*x^6)*sqrt(x)","A",0
2170,1,173,0,0.519859," ","integrate(x^4*(a+b*x^(1/2))^15,x, algorithm=""fricas"")","\frac{5}{4} \, a b^{14} x^{12} + \frac{455}{11} \, a^{3} b^{12} x^{11} + \frac{3003}{10} \, a^{5} b^{10} x^{10} + 715 \, a^{7} b^{8} x^{9} + \frac{5005}{8} \, a^{9} b^{6} x^{8} + 195 \, a^{11} b^{4} x^{7} + \frac{35}{2} \, a^{13} b^{2} x^{6} + \frac{1}{5} \, a^{15} x^{5} + \frac{2}{2042975} \, {\left(81719 \, b^{15} x^{12} + 9326625 \, a^{2} b^{13} x^{11} + 132793375 \, a^{4} b^{11} x^{10} + 538162625 \, a^{6} b^{9} x^{9} + 773326125 \, a^{8} b^{7} x^{8} + 409003595 \, a^{10} b^{5} x^{7} + 71504125 \, a^{12} b^{3} x^{6} + 2785875 \, a^{14} b x^{5}\right)} \sqrt{x}"," ",0,"5/4*a*b^14*x^12 + 455/11*a^3*b^12*x^11 + 3003/10*a^5*b^10*x^10 + 715*a^7*b^8*x^9 + 5005/8*a^9*b^6*x^8 + 195*a^11*b^4*x^7 + 35/2*a^13*b^2*x^6 + 1/5*a^15*x^5 + 2/2042975*(81719*b^15*x^12 + 9326625*a^2*b^13*x^11 + 132793375*a^4*b^11*x^10 + 538162625*a^6*b^9*x^9 + 773326125*a^8*b^7*x^8 + 409003595*a^10*b^5*x^7 + 71504125*a^12*b^3*x^6 + 2785875*a^14*b*x^5)*sqrt(x)","A",0
2171,1,173,0,0.755755," ","integrate(x^3*(a+b*x^(1/2))^15,x, algorithm=""fricas"")","\frac{15}{11} \, a b^{14} x^{11} + \frac{91}{2} \, a^{3} b^{12} x^{10} + \frac{1001}{3} \, a^{5} b^{10} x^{9} + \frac{6435}{8} \, a^{7} b^{8} x^{8} + 715 \, a^{9} b^{6} x^{7} + \frac{455}{2} \, a^{11} b^{4} x^{6} + 21 \, a^{13} b^{2} x^{5} + \frac{1}{4} \, a^{15} x^{4} + \frac{2}{245157} \, {\left(10659 \, b^{15} x^{11} + 1225785 \, a^{2} b^{13} x^{10} + 17612595 \, a^{4} b^{11} x^{9} + 72177105 \, a^{6} b^{9} x^{8} + 105172353 \, a^{8} b^{7} x^{7} + 56631267 \, a^{10} b^{5} x^{6} + 10140585 \, a^{12} b^{3} x^{5} + 408595 \, a^{14} b x^{4}\right)} \sqrt{x}"," ",0,"15/11*a*b^14*x^11 + 91/2*a^3*b^12*x^10 + 1001/3*a^5*b^10*x^9 + 6435/8*a^7*b^8*x^8 + 715*a^9*b^6*x^7 + 455/2*a^11*b^4*x^6 + 21*a^13*b^2*x^5 + 1/4*a^15*x^4 + 2/245157*(10659*b^15*x^11 + 1225785*a^2*b^13*x^10 + 17612595*a^4*b^11*x^9 + 72177105*a^6*b^9*x^8 + 105172353*a^8*b^7*x^7 + 56631267*a^10*b^5*x^6 + 10140585*a^12*b^3*x^5 + 408595*a^14*b*x^4)*sqrt(x)","A",0
2172,1,173,0,0.881399," ","integrate(x^2*(a+b*x^(1/2))^15,x, algorithm=""fricas"")","\frac{3}{2} \, a b^{14} x^{10} + \frac{455}{9} \, a^{3} b^{12} x^{9} + \frac{3003}{8} \, a^{5} b^{10} x^{8} + \frac{6435}{7} \, a^{7} b^{8} x^{7} + \frac{5005}{6} \, a^{9} b^{6} x^{6} + 273 \, a^{11} b^{4} x^{5} + \frac{105}{4} \, a^{13} b^{2} x^{4} + \frac{1}{3} \, a^{15} x^{3} + \frac{2}{20349} \, {\left(969 \, b^{15} x^{10} + 112455 \, a^{2} b^{13} x^{9} + 1633905 \, a^{4} b^{11} x^{8} + 6789783 \, a^{6} b^{9} x^{7} + 10072755 \, a^{8} b^{7} x^{6} + 5555277 \, a^{10} b^{5} x^{5} + 1028755 \, a^{12} b^{3} x^{4} + 43605 \, a^{14} b x^{3}\right)} \sqrt{x}"," ",0,"3/2*a*b^14*x^10 + 455/9*a^3*b^12*x^9 + 3003/8*a^5*b^10*x^8 + 6435/7*a^7*b^8*x^7 + 5005/6*a^9*b^6*x^6 + 273*a^11*b^4*x^5 + 105/4*a^13*b^2*x^4 + 1/3*a^15*x^3 + 2/20349*(969*b^15*x^10 + 112455*a^2*b^13*x^9 + 1633905*a^4*b^11*x^8 + 6789783*a^6*b^9*x^7 + 10072755*a^8*b^7*x^6 + 5555277*a^10*b^5*x^5 + 1028755*a^12*b^3*x^4 + 43605*a^14*b*x^3)*sqrt(x)","A",0
2173,1,173,0,0.775131," ","integrate(x*(a+b*x^(1/2))^15,x, algorithm=""fricas"")","\frac{5}{3} \, a b^{14} x^{9} + \frac{455}{8} \, a^{3} b^{12} x^{8} + 429 \, a^{5} b^{10} x^{7} + \frac{2145}{2} \, a^{7} b^{8} x^{6} + 1001 \, a^{9} b^{6} x^{5} + \frac{1365}{4} \, a^{11} b^{4} x^{4} + 35 \, a^{13} b^{2} x^{3} + \frac{1}{2} \, a^{15} x^{2} + \frac{2}{969} \, {\left(51 \, b^{15} x^{9} + 5985 \, a^{2} b^{13} x^{8} + 88179 \, a^{4} b^{11} x^{7} + 373065 \, a^{6} b^{9} x^{6} + 566865 \, a^{8} b^{7} x^{5} + 323323 \, a^{10} b^{5} x^{4} + 62985 \, a^{12} b^{3} x^{3} + 2907 \, a^{14} b x^{2}\right)} \sqrt{x}"," ",0,"5/3*a*b^14*x^9 + 455/8*a^3*b^12*x^8 + 429*a^5*b^10*x^7 + 2145/2*a^7*b^8*x^6 + 1001*a^9*b^6*x^5 + 1365/4*a^11*b^4*x^4 + 35*a^13*b^2*x^3 + 1/2*a^15*x^2 + 2/969*(51*b^15*x^9 + 5985*a^2*b^13*x^8 + 88179*a^4*b^11*x^7 + 373065*a^6*b^9*x^6 + 566865*a^8*b^7*x^5 + 323323*a^10*b^5*x^4 + 62985*a^12*b^3*x^3 + 2907*a^14*b*x^2)*sqrt(x)","B",0
2174,1,167,0,0.890119," ","integrate((a+b*x^(1/2))^15,x, algorithm=""fricas"")","\frac{15}{8} \, a b^{14} x^{8} + 65 \, a^{3} b^{12} x^{7} + \frac{1001}{2} \, a^{5} b^{10} x^{6} + 1287 \, a^{7} b^{8} x^{5} + \frac{5005}{4} \, a^{9} b^{6} x^{4} + 455 \, a^{11} b^{4} x^{3} + \frac{105}{2} \, a^{13} b^{2} x^{2} + a^{15} x + \frac{2}{17} \, {\left(b^{15} x^{8} + 119 \, a^{2} b^{13} x^{7} + 1785 \, a^{4} b^{11} x^{6} + 7735 \, a^{6} b^{9} x^{5} + 12155 \, a^{8} b^{7} x^{4} + 7293 \, a^{10} b^{5} x^{3} + 1547 \, a^{12} b^{3} x^{2} + 85 \, a^{14} b x\right)} \sqrt{x}"," ",0,"15/8*a*b^14*x^8 + 65*a^3*b^12*x^7 + 1001/2*a^5*b^10*x^6 + 1287*a^7*b^8*x^5 + 5005/4*a^9*b^6*x^4 + 455*a^11*b^4*x^3 + 105/2*a^13*b^2*x^2 + a^15*x + 2/17*(b^15*x^8 + 119*a^2*b^13*x^7 + 1785*a^4*b^11*x^6 + 7735*a^6*b^9*x^5 + 12155*a^8*b^7*x^4 + 7293*a^10*b^5*x^3 + 1547*a^12*b^3*x^2 + 85*a^14*b*x)*sqrt(x)","B",0
2175,1,167,0,0.912798," ","integrate((a+b*x^(1/2))^15/x,x, algorithm=""fricas"")","\frac{15}{7} \, a b^{14} x^{7} + \frac{455}{6} \, a^{3} b^{12} x^{6} + \frac{3003}{5} \, a^{5} b^{10} x^{5} + \frac{6435}{4} \, a^{7} b^{8} x^{4} + \frac{5005}{3} \, a^{9} b^{6} x^{3} + \frac{1365}{2} \, a^{11} b^{4} x^{2} + 105 \, a^{13} b^{2} x + 2 \, a^{15} \log\left(\sqrt{x}\right) + \frac{2}{45045} \, {\left(3003 \, b^{15} x^{7} + 363825 \, a^{2} b^{13} x^{6} + 5589675 \, a^{4} b^{11} x^{5} + 25050025 \, a^{6} b^{9} x^{4} + 41409225 \, a^{8} b^{7} x^{3} + 27054027 \, a^{10} b^{5} x^{2} + 6831825 \, a^{12} b^{3} x + 675675 \, a^{14} b\right)} \sqrt{x}"," ",0,"15/7*a*b^14*x^7 + 455/6*a^3*b^12*x^6 + 3003/5*a^5*b^10*x^5 + 6435/4*a^7*b^8*x^4 + 5005/3*a^9*b^6*x^3 + 1365/2*a^11*b^4*x^2 + 105*a^13*b^2*x + 2*a^15*log(sqrt(x)) + 2/45045*(3003*b^15*x^7 + 363825*a^2*b^13*x^6 + 5589675*a^4*b^11*x^5 + 25050025*a^6*b^9*x^4 + 41409225*a^8*b^7*x^3 + 27054027*a^10*b^5*x^2 + 6831825*a^12*b^3*x + 675675*a^14*b)*sqrt(x)","A",0
2176,1,172,0,0.795318," ","integrate((a+b*x^(1/2))^15/x^2,x, algorithm=""fricas"")","\frac{4290 \, a b^{14} x^{7} + 156156 \, a^{3} b^{12} x^{6} + 1288287 \, a^{5} b^{10} x^{5} + 3680820 \, a^{7} b^{8} x^{4} + 4294290 \, a^{9} b^{6} x^{3} + 2342340 \, a^{11} b^{4} x^{2} + 360360 \, a^{13} b^{2} x \log\left(\sqrt{x}\right) - 1716 \, a^{15} + 8 \, {\left(33 \, b^{15} x^{7} + 4095 \, a^{2} b^{13} x^{6} + 65065 \, a^{4} b^{11} x^{5} + 306735 \, a^{6} b^{9} x^{4} + 552123 \, a^{8} b^{7} x^{3} + 429429 \, a^{10} b^{5} x^{2} + 195195 \, a^{12} b^{3} x - 6435 \, a^{14} b\right)} \sqrt{x}}{1716 \, x}"," ",0,"1/1716*(4290*a*b^14*x^7 + 156156*a^3*b^12*x^6 + 1288287*a^5*b^10*x^5 + 3680820*a^7*b^8*x^4 + 4294290*a^9*b^6*x^3 + 2342340*a^11*b^4*x^2 + 360360*a^13*b^2*x*log(sqrt(x)) - 1716*a^15 + 8*(33*b^15*x^7 + 4095*a^2*b^13*x^6 + 65065*a^4*b^11*x^5 + 306735*a^6*b^9*x^4 + 552123*a^8*b^7*x^3 + 429429*a^10*b^5*x^2 + 195195*a^12*b^3*x - 6435*a^14*b)*sqrt(x))/x","A",0
2177,1,172,0,0.849864," ","integrate((a+b*x^(1/2))^15/x^3,x, algorithm=""fricas"")","\frac{396 \, a b^{14} x^{7} + 15015 \, a^{3} b^{12} x^{6} + 132132 \, a^{5} b^{10} x^{5} + 424710 \, a^{7} b^{8} x^{4} + 660660 \, a^{9} b^{6} x^{3} + 360360 \, a^{11} b^{4} x^{2} \log\left(\sqrt{x}\right) - 13860 \, a^{13} b^{2} x - 66 \, a^{15} + 8 \, {\left(3 \, b^{15} x^{7} + 385 \, a^{2} b^{13} x^{6} + 6435 \, a^{4} b^{11} x^{5} + 33033 \, a^{6} b^{9} x^{4} + 70785 \, a^{8} b^{7} x^{3} + 99099 \, a^{10} b^{5} x^{2} - 15015 \, a^{12} b^{3} x - 165 \, a^{14} b\right)} \sqrt{x}}{132 \, x^{2}}"," ",0,"1/132*(396*a*b^14*x^7 + 15015*a^3*b^12*x^6 + 132132*a^5*b^10*x^5 + 424710*a^7*b^8*x^4 + 660660*a^9*b^6*x^3 + 360360*a^11*b^4*x^2*log(sqrt(x)) - 13860*a^13*b^2*x - 66*a^15 + 8*(3*b^15*x^7 + 385*a^2*b^13*x^6 + 6435*a^4*b^11*x^5 + 33033*a^6*b^9*x^4 + 70785*a^8*b^7*x^3 + 99099*a^10*b^5*x^2 - 15015*a^12*b^3*x - 165*a^14*b)*sqrt(x))/x^2","A",0
2178,1,171,0,0.884120," ","integrate((a+b*x^(1/2))^15/x^4,x, algorithm=""fricas"")","\frac{135 \, a b^{14} x^{7} + 5460 \, a^{3} b^{12} x^{6} + 54054 \, a^{5} b^{10} x^{5} + 231660 \, a^{7} b^{8} x^{4} + 360360 \, a^{9} b^{6} x^{3} \log\left(\sqrt{x}\right) - 49140 \, a^{11} b^{4} x^{2} - 1890 \, a^{13} b^{2} x - 12 \, a^{15} + 8 \, {\left(b^{15} x^{7} + 135 \, a^{2} b^{13} x^{6} + 2457 \, a^{4} b^{11} x^{5} + 15015 \, a^{6} b^{9} x^{4} + 57915 \, a^{8} b^{7} x^{3} - 27027 \, a^{10} b^{5} x^{2} - 1365 \, a^{12} b^{3} x - 27 \, a^{14} b\right)} \sqrt{x}}{36 \, x^{3}}"," ",0,"1/36*(135*a*b^14*x^7 + 5460*a^3*b^12*x^6 + 54054*a^5*b^10*x^5 + 231660*a^7*b^8*x^4 + 360360*a^9*b^6*x^3*log(sqrt(x)) - 49140*a^11*b^4*x^2 - 1890*a^13*b^2*x - 12*a^15 + 8*(b^15*x^7 + 135*a^2*b^13*x^6 + 2457*a^4*b^11*x^5 + 15015*a^6*b^9*x^4 + 57915*a^8*b^7*x^3 - 27027*a^10*b^5*x^2 - 1365*a^12*b^3*x - 27*a^14*b)*sqrt(x))/x^3","A",0
2179,1,172,0,0.892754," ","integrate((a+b*x^(1/2))^15/x^6,x, algorithm=""fricas"")","\frac{450 \, a b^{14} x^{7} + 27300 \, a^{3} b^{12} x^{6} + 360360 \, a^{5} b^{10} x^{5} \log\left(\sqrt{x}\right) - 386100 \, a^{7} b^{8} x^{4} - 150150 \, a^{9} b^{6} x^{3} - 27300 \, a^{11} b^{4} x^{2} - 1575 \, a^{13} b^{2} x - 12 \, a^{15} + 8 \, {\left(3 \, b^{15} x^{7} + 525 \, a^{2} b^{13} x^{6} + 20475 \, a^{4} b^{11} x^{5} - 75075 \, a^{6} b^{9} x^{4} - 32175 \, a^{8} b^{7} x^{3} - 9009 \, a^{10} b^{5} x^{2} - 975 \, a^{12} b^{3} x - 25 \, a^{14} b\right)} \sqrt{x}}{60 \, x^{5}}"," ",0,"1/60*(450*a*b^14*x^7 + 27300*a^3*b^12*x^6 + 360360*a^5*b^10*x^5*log(sqrt(x)) - 386100*a^7*b^8*x^4 - 150150*a^9*b^6*x^3 - 27300*a^11*b^4*x^2 - 1575*a^13*b^2*x - 12*a^15 + 8*(3*b^15*x^7 + 525*a^2*b^13*x^6 + 20475*a^4*b^11*x^5 - 75075*a^6*b^9*x^4 - 32175*a^8*b^7*x^3 - 9009*a^10*b^5*x^2 - 975*a^12*b^3*x - 25*a^14*b)*sqrt(x))/x^5","A",0
2180,1,172,0,0.843797," ","integrate((a+b*x^(1/2))^15/x^7,x, algorithm=""fricas"")","\frac{5940 \, a b^{14} x^{7} + 360360 \, a^{3} b^{12} x^{6} \log\left(\sqrt{x}\right) - 1189188 \, a^{5} b^{10} x^{5} - 1274130 \, a^{7} b^{8} x^{4} - 660660 \, a^{9} b^{6} x^{3} - 135135 \, a^{11} b^{4} x^{2} - 8316 \, a^{13} b^{2} x - 66 \, a^{15} + 8 \, {\left(33 \, b^{15} x^{7} + 10395 \, a^{2} b^{13} x^{6} - 135135 \, a^{4} b^{11} x^{5} - 165165 \, a^{6} b^{9} x^{4} - 127413 \, a^{8} b^{7} x^{3} - 42471 \, a^{10} b^{5} x^{2} - 5005 \, a^{12} b^{3} x - 135 \, a^{14} b\right)} \sqrt{x}}{396 \, x^{6}}"," ",0,"1/396*(5940*a*b^14*x^7 + 360360*a^3*b^12*x^6*log(sqrt(x)) - 1189188*a^5*b^10*x^5 - 1274130*a^7*b^8*x^4 - 660660*a^9*b^6*x^3 - 135135*a^11*b^4*x^2 - 8316*a^13*b^2*x - 66*a^15 + 8*(33*b^15*x^7 + 10395*a^2*b^13*x^6 - 135135*a^4*b^11*x^5 - 165165*a^6*b^9*x^4 - 127413*a^8*b^7*x^3 - 42471*a^10*b^5*x^2 - 5005*a^12*b^3*x - 135*a^14*b)*sqrt(x))/x^6","A",0
2181,1,172,0,0.750267," ","integrate((a+b*x^(1/2))^15/x^8,x, algorithm=""fricas"")","\frac{360360 \, a b^{14} x^{7} \log\left(\sqrt{x}\right) - 5465460 \, a^{3} b^{12} x^{6} - 18036018 \, a^{5} b^{10} x^{5} - 25765740 \, a^{7} b^{8} x^{4} - 15030015 \, a^{9} b^{6} x^{3} - 3279276 \, a^{11} b^{4} x^{2} - 210210 \, a^{13} b^{2} x - 1716 \, a^{15} + 8 \, {\left(3003 \, b^{15} x^{7} - 315315 \, a^{2} b^{13} x^{6} - 1366365 \, a^{4} b^{11} x^{5} - 3006003 \, a^{6} b^{9} x^{4} - 2760615 \, a^{8} b^{7} x^{3} - 1002001 \, a^{10} b^{5} x^{2} - 124215 \, a^{12} b^{3} x - 3465 \, a^{14} b\right)} \sqrt{x}}{12012 \, x^{7}}"," ",0,"1/12012*(360360*a*b^14*x^7*log(sqrt(x)) - 5465460*a^3*b^12*x^6 - 18036018*a^5*b^10*x^5 - 25765740*a^7*b^8*x^4 - 15030015*a^9*b^6*x^3 - 3279276*a^11*b^4*x^2 - 210210*a^13*b^2*x - 1716*a^15 + 8*(3003*b^15*x^7 - 315315*a^2*b^13*x^6 - 1366365*a^4*b^11*x^5 - 3006003*a^6*b^9*x^4 - 2760615*a^8*b^7*x^3 - 1002001*a^10*b^5*x^2 - 124215*a^12*b^3*x - 3465*a^14*b)*sqrt(x))/x^7","A",0
2182,1,164,0,0.738214," ","integrate((a+b*x^(1/2))^15/x^9,x, algorithm=""fricas"")","-\frac{120 \, a b^{14} x^{7} + 1820 \, a^{3} b^{12} x^{6} + 8008 \, a^{5} b^{10} x^{5} + 12870 \, a^{7} b^{8} x^{4} + 8008 \, a^{9} b^{6} x^{3} + 1820 \, a^{11} b^{4} x^{2} + 120 \, a^{13} b^{2} x + a^{15} + 16 \, {\left(b^{15} x^{7} + 35 \, a^{2} b^{13} x^{6} + 273 \, a^{4} b^{11} x^{5} + 715 \, a^{6} b^{9} x^{4} + 715 \, a^{8} b^{7} x^{3} + 273 \, a^{10} b^{5} x^{2} + 35 \, a^{12} b^{3} x + a^{14} b\right)} \sqrt{x}}{8 \, x^{8}}"," ",0,"-1/8*(120*a*b^14*x^7 + 1820*a^3*b^12*x^6 + 8008*a^5*b^10*x^5 + 12870*a^7*b^8*x^4 + 8008*a^9*b^6*x^3 + 1820*a^11*b^4*x^2 + 120*a^13*b^2*x + a^15 + 16*(b^15*x^7 + 35*a^2*b^13*x^6 + 273*a^4*b^11*x^5 + 715*a^6*b^9*x^4 + 715*a^8*b^7*x^3 + 273*a^10*b^5*x^2 + 35*a^12*b^3*x + a^14*b)*sqrt(x))/x^8","B",0
2183,1,168,0,0.863712," ","integrate((a+b*x^(1/2))^15/x^10,x, algorithm=""fricas"")","-\frac{9180 \, a b^{14} x^{7} + 185640 \, a^{3} b^{12} x^{6} + 918918 \, a^{5} b^{10} x^{5} + 1575288 \, a^{7} b^{8} x^{4} + 1021020 \, a^{9} b^{6} x^{3} + 238680 \, a^{11} b^{4} x^{2} + 16065 \, a^{13} b^{2} x + 136 \, a^{15} + 16 \, {\left(51 \, b^{15} x^{7} + 3213 \, a^{2} b^{13} x^{6} + 29835 \, a^{4} b^{11} x^{5} + 85085 \, a^{6} b^{9} x^{4} + 89505 \, a^{8} b^{7} x^{3} + 35343 \, a^{10} b^{5} x^{2} + 4641 \, a^{12} b^{3} x + 135 \, a^{14} b\right)} \sqrt{x}}{1224 \, x^{9}}"," ",0,"-1/1224*(9180*a*b^14*x^7 + 185640*a^3*b^12*x^6 + 918918*a^5*b^10*x^5 + 1575288*a^7*b^8*x^4 + 1021020*a^9*b^6*x^3 + 238680*a^11*b^4*x^2 + 16065*a^13*b^2*x + 136*a^15 + 16*(51*b^15*x^7 + 3213*a^2*b^13*x^6 + 29835*a^4*b^11*x^5 + 85085*a^6*b^9*x^4 + 89505*a^8*b^7*x^3 + 35343*a^10*b^5*x^2 + 4641*a^12*b^3*x + 135*a^14*b)*sqrt(x))/x^9","B",0
2184,1,168,0,0.724163," ","integrate((a+b*x^(1/2))^15/x^11,x, algorithm=""fricas"")","-\frac{193800 \, a b^{14} x^{7} + 4408950 \, a^{3} b^{12} x^{6} + 23279256 \, a^{5} b^{10} x^{5} + 41570100 \, a^{7} b^{8} x^{4} + 27713400 \, a^{9} b^{6} x^{3} + 6613425 \, a^{11} b^{4} x^{2} + 452200 \, a^{13} b^{2} x + 3876 \, a^{15} + 16 \, {\left(969 \, b^{15} x^{7} + 72675 \, a^{2} b^{13} x^{6} + 734825 \, a^{4} b^{11} x^{5} + 2204475 \, a^{6} b^{9} x^{4} + 2398275 \, a^{8} b^{7} x^{3} + 969969 \, a^{10} b^{5} x^{2} + 129675 \, a^{12} b^{3} x + 3825 \, a^{14} b\right)} \sqrt{x}}{38760 \, x^{10}}"," ",0,"-1/38760*(193800*a*b^14*x^7 + 4408950*a^3*b^12*x^6 + 23279256*a^5*b^10*x^5 + 41570100*a^7*b^8*x^4 + 27713400*a^9*b^6*x^3 + 6613425*a^11*b^4*x^2 + 452200*a^13*b^2*x + 3876*a^15 + 16*(969*b^15*x^7 + 72675*a^2*b^13*x^6 + 734825*a^4*b^11*x^5 + 2204475*a^6*b^9*x^4 + 2398275*a^8*b^7*x^3 + 969969*a^10*b^5*x^2 + 129675*a^12*b^3*x + 3825*a^14*b)*sqrt(x))/x^10","A",0
2185,1,168,0,0.706963," ","integrate((a+b*x^(1/2))^15/x^12,x, algorithm=""fricas"")","-\frac{2238390 \, a b^{14} x^{7} + 54318264 \, a^{3} b^{12} x^{6} + 298750452 \, a^{5} b^{10} x^{5} + 548725320 \, a^{7} b^{8} x^{4} + 373438065 \, a^{9} b^{6} x^{3} + 90530440 \, a^{11} b^{4} x^{2} + 6267492 \, a^{13} b^{2} x + 54264 \, a^{15} + 16 \, {\left(10659 \, b^{15} x^{7} + 870485 \, a^{2} b^{13} x^{6} + 9258795 \, a^{4} b^{11} x^{5} + 28726005 \, a^{6} b^{9} x^{4} + 32008977 \, a^{8} b^{7} x^{3} + 13180167 \, a^{10} b^{5} x^{2} + 1786785 \, a^{12} b^{3} x + 53295 \, a^{14} b\right)} \sqrt{x}}{596904 \, x^{11}}"," ",0,"-1/596904*(2238390*a*b^14*x^7 + 54318264*a^3*b^12*x^6 + 298750452*a^5*b^10*x^5 + 548725320*a^7*b^8*x^4 + 373438065*a^9*b^6*x^3 + 90530440*a^11*b^4*x^2 + 6267492*a^13*b^2*x + 54264*a^15 + 16*(10659*b^15*x^7 + 870485*a^2*b^13*x^6 + 9258795*a^4*b^11*x^5 + 28726005*a^6*b^9*x^4 + 32008977*a^8*b^7*x^3 + 13180167*a^10*b^5*x^2 + 1786785*a^12*b^3*x + 53295*a^14*b)*sqrt(x))/x^11","A",0
2186,1,168,0,0.823344," ","integrate((a+b*x^(1/2))^15/x^13,x, algorithm=""fricas"")","-\frac{17651304 \, a b^{14} x^{7} + 446185740 \, a^{3} b^{12} x^{6} + 2524136472 \, a^{5} b^{10} x^{5} + 4732755885 \, a^{7} b^{8} x^{4} + 3272028760 \, a^{9} b^{6} x^{3} + 803134332 \, a^{11} b^{4} x^{2} + 56163240 \, a^{13} b^{2} x + 490314 \, a^{15} + 16 \, {\left(81719 \, b^{15} x^{7} + 7020405 \, a^{2} b^{13} x^{6} + 77224455 \, a^{4} b^{11} x^{5} + 245402157 \, a^{6} b^{9} x^{4} + 278397405 \, a^{8} b^{7} x^{3} + 116243127 \, a^{10} b^{5} x^{2} + 15935205 \, a^{12} b^{3} x + 479655 \, a^{14} b\right)} \sqrt{x}}{5883768 \, x^{12}}"," ",0,"-1/5883768*(17651304*a*b^14*x^7 + 446185740*a^3*b^12*x^6 + 2524136472*a^5*b^10*x^5 + 4732755885*a^7*b^8*x^4 + 3272028760*a^9*b^6*x^3 + 803134332*a^11*b^4*x^2 + 56163240*a^13*b^2*x + 490314*a^15 + 16*(81719*b^15*x^7 + 7020405*a^2*b^13*x^6 + 77224455*a^4*b^11*x^5 + 245402157*a^6*b^9*x^4 + 278397405*a^8*b^7*x^3 + 116243127*a^10*b^5*x^2 + 15935205*a^12*b^3*x + 479655*a^14*b)*sqrt(x))/x^12","A",0
2187,1,168,0,0.746498," ","integrate((a+b*x^(1/2))^15/x^14,x, algorithm=""fricas"")","-\frac{106234700 \, a b^{14} x^{7} + 2762102200 \, a^{3} b^{12} x^{6} + 15951140205 \, a^{5} b^{10} x^{5} + 30383124200 \, a^{7} b^{8} x^{4} + 21268186940 \, a^{9} b^{6} x^{3} + 5273104200 \, a^{11} b^{4} x^{2} + 371821450 \, a^{13} b^{2} x + 3268760 \, a^{15} + 16 \, {\left(482885 \, b^{15} x^{7} + 42902475 \, a^{2} b^{13} x^{6} + 483367885 \, a^{4} b^{11} x^{5} + 1563837275 \, a^{6} b^{9} x^{4} + 1799000775 \, a^{8} b^{7} x^{3} + 759578105 \, a^{10} b^{5} x^{2} + 105079975 \, a^{12} b^{3} x + 3187041 \, a^{14} b\right)} \sqrt{x}}{42493880 \, x^{13}}"," ",0,"-1/42493880*(106234700*a*b^14*x^7 + 2762102200*a^3*b^12*x^6 + 15951140205*a^5*b^10*x^5 + 30383124200*a^7*b^8*x^4 + 21268186940*a^9*b^6*x^3 + 5273104200*a^11*b^4*x^2 + 371821450*a^13*b^2*x + 3268760*a^15 + 16*(482885*b^15*x^7 + 42902475*a^2*b^13*x^6 + 483367885*a^4*b^11*x^5 + 1563837275*a^6*b^9*x^4 + 1799000775*a^8*b^7*x^3 + 759578105*a^10*b^5*x^2 + 105079975*a^12*b^3*x + 3187041*a^14*b)*sqrt(x))/x^13","A",0
2188,1,168,0,0.856920," ","integrate((a+b*x^(1/2))^15/x^15,x, algorithm=""fricas"")","-\frac{521515800 \, a b^{14} x^{7} + 13841898525 \, a^{3} b^{12} x^{6} + 81205804680 \, a^{5} b^{10} x^{5} + 156611194740 \, a^{7} b^{8} x^{4} + 110735188200 \, a^{9} b^{6} x^{3} + 27683797050 \, a^{11} b^{4} x^{2} + 1965713400 \, a^{13} b^{2} x + 17383860 \, a^{15} + 16 \, {\left(2340135 \, b^{15} x^{7} + 212952285 \, a^{2} b^{13} x^{6} + 2442687975 \, a^{4} b^{11} x^{5} + 8013730725 \, a^{6} b^{9} x^{4} + 9322094925 \, a^{8} b^{7} x^{3} + 3972023055 \, a^{10} b^{5} x^{2} + 553675941 \, a^{12} b^{3} x + 16900975 \, a^{14} b\right)} \sqrt{x}}{243374040 \, x^{14}}"," ",0,"-1/243374040*(521515800*a*b^14*x^7 + 13841898525*a^3*b^12*x^6 + 81205804680*a^5*b^10*x^5 + 156611194740*a^7*b^8*x^4 + 110735188200*a^9*b^6*x^3 + 27683797050*a^11*b^4*x^2 + 1965713400*a^13*b^2*x + 17383860*a^15 + 16*(2340135*b^15*x^7 + 212952285*a^2*b^13*x^6 + 2442687975*a^4*b^11*x^5 + 8013730725*a^6*b^9*x^4 + 9322094925*a^8*b^7*x^3 + 3972023055*a^10*b^5*x^2 + 553675941*a^12*b^3*x + 16900975*a^14*b)*sqrt(x))/x^14","A",0
2189,1,168,0,0.829425," ","integrate((a+b*x^(1/2))^15/x^16,x, algorithm=""fricas"")","-\frac{2181340125 \, a b^{14} x^{7} + 58815393000 \, a^{3} b^{12} x^{6} + 349363434420 \, a^{5} b^{10} x^{5} + 680578119000 \, a^{7} b^{8} x^{4} + 485226992250 \, a^{9} b^{6} x^{3} + 122155047000 \, a^{11} b^{4} x^{2} + 8725360500 \, a^{13} b^{2} x + 77558760 \, a^{15} + 16 \, {\left(9694845 \, b^{15} x^{7} + 898198875 \, a^{2} b^{13} x^{6} + 10447471125 \, a^{4} b^{11} x^{5} + 34659070875 \, a^{6} b^{9} x^{4} + 40686735375 \, a^{8} b^{7} x^{3} + 17468171721 \, a^{10} b^{5} x^{2} + 2450641375 \, a^{12} b^{3} x + 75218625 \, a^{14} b\right)} \sqrt{x}}{1163381400 \, x^{15}}"," ",0,"-1/1163381400*(2181340125*a*b^14*x^7 + 58815393000*a^3*b^12*x^6 + 349363434420*a^5*b^10*x^5 + 680578119000*a^7*b^8*x^4 + 485226992250*a^9*b^6*x^3 + 122155047000*a^11*b^4*x^2 + 8725360500*a^13*b^2*x + 77558760*a^15 + 16*(9694845*b^15*x^7 + 898198875*a^2*b^13*x^6 + 10447471125*a^4*b^11*x^5 + 34659070875*a^6*b^9*x^4 + 40686735375*a^8*b^7*x^3 + 17468171721*a^10*b^5*x^2 + 2450641375*a^12*b^3*x + 75218625*a^14*b)*sqrt(x))/x^15","A",0
2190,1,168,0,0.720289," ","integrate((a+b*x^(1/2))^15/x^17,x, algorithm=""fricas"")","-\frac{8014405200 \, a b^{14} x^{7} + 218793261960 \, a^{3} b^{12} x^{6} + 1312759571760 \, a^{5} b^{10} x^{5} + 2578634873100 \, a^{7} b^{8} x^{4} + 1851327601200 \, a^{9} b^{6} x^{3} + 468842704200 \, a^{11} b^{4} x^{2} + 33660501840 \, a^{13} b^{2} x + 300540195 \, a^{15} + 32 \, {\left(17678835 \, b^{15} x^{7} + 1660880025 \, a^{2} b^{13} x^{6} + 19535112675 \, a^{4} b^{11} x^{5} + 65400159825 \, a^{6} b^{9} x^{4} + 77359046193 \, a^{8} b^{7} x^{3} + 33426748355 \, a^{10} b^{5} x^{2} + 4715372025 \, a^{12} b^{3} x + 145422675 \, a^{14} b\right)} \sqrt{x}}{4808643120 \, x^{16}}"," ",0,"-1/4808643120*(8014405200*a*b^14*x^7 + 218793261960*a^3*b^12*x^6 + 1312759571760*a^5*b^10*x^5 + 2578634873100*a^7*b^8*x^4 + 1851327601200*a^9*b^6*x^3 + 468842704200*a^11*b^4*x^2 + 33660501840*a^13*b^2*x + 300540195*a^15 + 32*(17678835*b^15*x^7 + 1660880025*a^2*b^13*x^6 + 19535112675*a^4*b^11*x^5 + 65400159825*a^6*b^9*x^4 + 77359046193*a^8*b^7*x^3 + 33426748355*a^10*b^5*x^2 + 4715372025*a^12*b^3*x + 145422675*a^14*b)*sqrt(x))/x^16","A",0
2191,1,88,0,0.819493," ","integrate(x^3/(a+b*x^(1/2)),x, algorithm=""fricas"")","-\frac{70 \, a b^{6} x^{3} + 105 \, a^{3} b^{4} x^{2} + 210 \, a^{5} b^{2} x + 420 \, a^{7} \log\left(b \sqrt{x} + a\right) - 4 \, {\left(15 \, b^{7} x^{3} + 21 \, a^{2} b^{5} x^{2} + 35 \, a^{4} b^{3} x + 105 \, a^{6} b\right)} \sqrt{x}}{210 \, b^{8}}"," ",0,"-1/210*(70*a*b^6*x^3 + 105*a^3*b^4*x^2 + 210*a^5*b^2*x + 420*a^7*log(b*sqrt(x) + a) - 4*(15*b^7*x^3 + 21*a^2*b^5*x^2 + 35*a^4*b^3*x + 105*a^6*b)*sqrt(x))/b^8","A",0
2192,1,66,0,0.636388," ","integrate(x^2/(a+b*x^(1/2)),x, algorithm=""fricas"")","-\frac{15 \, a b^{4} x^{2} + 30 \, a^{3} b^{2} x + 60 \, a^{5} \log\left(b \sqrt{x} + a\right) - 4 \, {\left(3 \, b^{5} x^{2} + 5 \, a^{2} b^{3} x + 15 \, a^{4} b\right)} \sqrt{x}}{30 \, b^{6}}"," ",0,"-1/30*(15*a*b^4*x^2 + 30*a^3*b^2*x + 60*a^5*log(b*sqrt(x) + a) - 4*(3*b^5*x^2 + 5*a^2*b^3*x + 15*a^4*b)*sqrt(x))/b^6","A",0
2193,1,43,0,0.927269," ","integrate(x/(a+b*x^(1/2)),x, algorithm=""fricas"")","-\frac{3 \, a b^{2} x + 6 \, a^{3} \log\left(b \sqrt{x} + a\right) - 2 \, {\left(b^{3} x + 3 \, a^{2} b\right)} \sqrt{x}}{3 \, b^{4}}"," ",0,"-1/3*(3*a*b^2*x + 6*a^3*log(b*sqrt(x) + a) - 2*(b^3*x + 3*a^2*b)*sqrt(x))/b^4","A",0
2194,1,22,0,1.031076," ","integrate(1/(a+b*x^(1/2)),x, algorithm=""fricas"")","-\frac{2 \, {\left(a \log\left(b \sqrt{x} + a\right) - b \sqrt{x}\right)}}{b^{2}}"," ",0,"-2*(a*log(b*sqrt(x) + a) - b*sqrt(x))/b^2","A",0
2195,1,20,0,0.865283," ","integrate(1/x/(a+b*x^(1/2)),x, algorithm=""fricas"")","-\frac{2 \, {\left(\log\left(b \sqrt{x} + a\right) - \log\left(\sqrt{x}\right)\right)}}{a}"," ",0,"-2*(log(b*sqrt(x) + a) - log(sqrt(x)))/a","A",0
2196,1,43,0,0.741259," ","integrate(1/x^2/(a+b*x^(1/2)),x, algorithm=""fricas"")","-\frac{2 \, b^{2} x \log\left(b \sqrt{x} + a\right) - 2 \, b^{2} x \log\left(\sqrt{x}\right) - 2 \, a b \sqrt{x} + a^{2}}{a^{3} x}"," ",0,"-(2*b^2*x*log(b*sqrt(x) + a) - 2*b^2*x*log(sqrt(x)) - 2*a*b*sqrt(x) + a^2)/(a^3*x)","A",0
2197,1,69,0,0.847813," ","integrate(1/x^3/(a+b*x^(1/2)),x, algorithm=""fricas"")","-\frac{12 \, b^{4} x^{2} \log\left(b \sqrt{x} + a\right) - 12 \, b^{4} x^{2} \log\left(\sqrt{x}\right) + 6 \, a^{2} b^{2} x + 3 \, a^{4} - 4 \, {\left(3 \, a b^{3} x + a^{3} b\right)} \sqrt{x}}{6 \, a^{5} x^{2}}"," ",0,"-1/6*(12*b^4*x^2*log(b*sqrt(x) + a) - 12*b^4*x^2*log(sqrt(x)) + 6*a^2*b^2*x + 3*a^4 - 4*(3*a*b^3*x + a^3*b)*sqrt(x))/(a^5*x^2)","A",0
2198,1,92,0,1.099724," ","integrate(1/x^4/(a+b*x^(1/2)),x, algorithm=""fricas"")","-\frac{60 \, b^{6} x^{3} \log\left(b \sqrt{x} + a\right) - 60 \, b^{6} x^{3} \log\left(\sqrt{x}\right) + 30 \, a^{2} b^{4} x^{2} + 15 \, a^{4} b^{2} x + 10 \, a^{6} - 4 \, {\left(15 \, a b^{5} x^{2} + 5 \, a^{3} b^{3} x + 3 \, a^{5} b\right)} \sqrt{x}}{30 \, a^{7} x^{3}}"," ",0,"-1/30*(60*b^6*x^3*log(b*sqrt(x) + a) - 60*b^6*x^3*log(sqrt(x)) + 30*a^2*b^4*x^2 + 15*a^4*b^2*x + 10*a^6 - 4*(15*a*b^5*x^2 + 5*a^3*b^3*x + 3*a^5*b)*sqrt(x))/(a^7*x^3)","A",0
2199,1,128,0,0.918915," ","integrate(x^3/(a+b*x^(1/2))^2,x, algorithm=""fricas"")","\frac{10 \, b^{8} x^{4} + 35 \, a^{2} b^{6} x^{3} + 105 \, a^{4} b^{4} x^{2} - 150 \, a^{6} b^{2} x - 60 \, a^{8} + 420 \, {\left(a^{6} b^{2} x - a^{8}\right)} \log\left(b \sqrt{x} + a\right) - 4 \, {\left(6 \, a b^{7} x^{3} + 14 \, a^{3} b^{5} x^{2} + 70 \, a^{5} b^{3} x - 105 \, a^{7} b\right)} \sqrt{x}}{30 \, {\left(b^{10} x - a^{2} b^{8}\right)}}"," ",0,"1/30*(10*b^8*x^4 + 35*a^2*b^6*x^3 + 105*a^4*b^4*x^2 - 150*a^6*b^2*x - 60*a^8 + 420*(a^6*b^2*x - a^8)*log(b*sqrt(x) + a) - 4*(6*a*b^7*x^3 + 14*a^3*b^5*x^2 + 70*a^5*b^3*x - 105*a^7*b)*sqrt(x))/(b^10*x - a^2*b^8)","A",0
2200,1,106,0,0.816749," ","integrate(x^2/(a+b*x^(1/2))^2,x, algorithm=""fricas"")","\frac{3 \, b^{6} x^{3} + 15 \, a^{2} b^{4} x^{2} - 18 \, a^{4} b^{2} x - 12 \, a^{6} + 60 \, {\left(a^{4} b^{2} x - a^{6}\right)} \log\left(b \sqrt{x} + a\right) - 4 \, {\left(2 \, a b^{5} x^{2} + 10 \, a^{3} b^{3} x - 15 \, a^{5} b\right)} \sqrt{x}}{6 \, {\left(b^{8} x - a^{2} b^{6}\right)}}"," ",0,"1/6*(3*b^6*x^3 + 15*a^2*b^4*x^2 - 18*a^4*b^2*x - 12*a^6 + 60*(a^4*b^2*x - a^6)*log(b*sqrt(x) + a) - 4*(2*a*b^5*x^2 + 10*a^3*b^3*x - 15*a^5*b)*sqrt(x))/(b^8*x - a^2*b^6)","A",0
2201,1,82,0,1.020167," ","integrate(x/(a+b*x^(1/2))^2,x, algorithm=""fricas"")","\frac{b^{4} x^{2} - a^{2} b^{2} x - 2 \, a^{4} + 6 \, {\left(a^{2} b^{2} x - a^{4}\right)} \log\left(b \sqrt{x} + a\right) - 2 \, {\left(2 \, a b^{3} x - 3 \, a^{3} b\right)} \sqrt{x}}{b^{6} x - a^{2} b^{4}}"," ",0,"(b^4*x^2 - a^2*b^2*x - 2*a^4 + 6*(a^2*b^2*x - a^4)*log(b*sqrt(x) + a) - 2*(2*a*b^3*x - 3*a^3*b)*sqrt(x))/(b^6*x - a^2*b^4)","A",0
2202,1,50,0,0.925367," ","integrate(1/(a+b*x^(1/2))^2,x, algorithm=""fricas"")","\frac{2 \, {\left(a b \sqrt{x} - a^{2} + {\left(b^{2} x - a^{2}\right)} \log\left(b \sqrt{x} + a\right)\right)}}{b^{4} x - a^{2} b^{2}}"," ",0,"2*(a*b*sqrt(x) - a^2 + (b^2*x - a^2)*log(b*sqrt(x) + a))/(b^4*x - a^2*b^2)","A",0
2203,1,67,0,1.161200," ","integrate(1/x/(a+b*x^(1/2))^2,x, algorithm=""fricas"")","\frac{2 \, {\left(a b \sqrt{x} - a^{2} - {\left(b^{2} x - a^{2}\right)} \log\left(b \sqrt{x} + a\right) + {\left(b^{2} x - a^{2}\right)} \log\left(\sqrt{x}\right)\right)}}{a^{2} b^{2} x - a^{4}}"," ",0,"2*(a*b*sqrt(x) - a^2 - (b^2*x - a^2)*log(b*sqrt(x) + a) + (b^2*x - a^2)*log(sqrt(x)))/(a^2*b^2*x - a^4)","A",0
2204,1,105,0,0.785487," ","integrate(1/x^2/(a+b*x^(1/2))^2,x, algorithm=""fricas"")","-\frac{3 \, a^{2} b^{2} x - a^{4} + 6 \, {\left(b^{4} x^{2} - a^{2} b^{2} x\right)} \log\left(b \sqrt{x} + a\right) - 6 \, {\left(b^{4} x^{2} - a^{2} b^{2} x\right)} \log\left(\sqrt{x}\right) - 2 \, {\left(3 \, a b^{3} x - 2 \, a^{3} b\right)} \sqrt{x}}{a^{4} b^{2} x^{2} - a^{6} x}"," ",0,"-(3*a^2*b^2*x - a^4 + 6*(b^4*x^2 - a^2*b^2*x)*log(b*sqrt(x) + a) - 6*(b^4*x^2 - a^2*b^2*x)*log(sqrt(x)) - 2*(3*a*b^3*x - 2*a^3*b)*sqrt(x))/(a^4*b^2*x^2 - a^6*x)","A",0
2205,1,133,0,0.881703," ","integrate(1/x^3/(a+b*x^(1/2))^2,x, algorithm=""fricas"")","-\frac{30 \, a^{2} b^{4} x^{2} - 15 \, a^{4} b^{2} x - 3 \, a^{6} + 60 \, {\left(b^{6} x^{3} - a^{2} b^{4} x^{2}\right)} \log\left(b \sqrt{x} + a\right) - 60 \, {\left(b^{6} x^{3} - a^{2} b^{4} x^{2}\right)} \log\left(\sqrt{x}\right) - 4 \, {\left(15 \, a b^{5} x^{2} - 10 \, a^{3} b^{3} x - 2 \, a^{5} b\right)} \sqrt{x}}{6 \, {\left(a^{6} b^{2} x^{3} - a^{8} x^{2}\right)}}"," ",0,"-1/6*(30*a^2*b^4*x^2 - 15*a^4*b^2*x - 3*a^6 + 60*(b^6*x^3 - a^2*b^4*x^2)*log(b*sqrt(x) + a) - 60*(b^6*x^3 - a^2*b^4*x^2)*log(sqrt(x)) - 4*(15*a*b^5*x^2 - 10*a^3*b^3*x - 2*a^5*b)*sqrt(x))/(a^6*b^2*x^3 - a^8*x^2)","A",0
2206,1,155,0,0.675200," ","integrate(1/x^4/(a+b*x^(1/2))^2,x, algorithm=""fricas"")","-\frac{210 \, a^{2} b^{6} x^{3} - 105 \, a^{4} b^{4} x^{2} - 35 \, a^{6} b^{2} x - 10 \, a^{8} + 420 \, {\left(b^{8} x^{4} - a^{2} b^{6} x^{3}\right)} \log\left(b \sqrt{x} + a\right) - 420 \, {\left(b^{8} x^{4} - a^{2} b^{6} x^{3}\right)} \log\left(\sqrt{x}\right) - 4 \, {\left(105 \, a b^{7} x^{3} - 70 \, a^{3} b^{5} x^{2} - 14 \, a^{5} b^{3} x - 6 \, a^{7} b\right)} \sqrt{x}}{30 \, {\left(a^{8} b^{2} x^{4} - a^{10} x^{3}\right)}}"," ",0,"-1/30*(210*a^2*b^6*x^3 - 105*a^4*b^4*x^2 - 35*a^6*b^2*x - 10*a^8 + 420*(b^8*x^4 - a^2*b^6*x^3)*log(b*sqrt(x) + a) - 420*(b^8*x^4 - a^2*b^6*x^3)*log(sqrt(x)) - 4*(105*a*b^7*x^3 - 70*a^3*b^5*x^2 - 14*a^5*b^3*x - 6*a^7*b)*sqrt(x))/(a^8*b^2*x^4 - a^10*x^3)","A",0
2207,1,157,0,0.643264," ","integrate(x^3/(a+b*x^(1/2))^3,x, algorithm=""fricas"")","-\frac{15 \, a b^{8} x^{4} + 70 \, a^{3} b^{6} x^{3} - 185 \, a^{5} b^{4} x^{2} - 50 \, a^{7} b^{2} x + 130 \, a^{9} + 420 \, {\left(a^{5} b^{4} x^{2} - 2 \, a^{7} b^{2} x + a^{9}\right)} \log\left(b \sqrt{x} + a\right) - 4 \, {\left(b^{9} x^{4} + 8 \, a^{2} b^{7} x^{3} + 56 \, a^{4} b^{5} x^{2} - 175 \, a^{6} b^{3} x + 105 \, a^{8} b\right)} \sqrt{x}}{10 \, {\left(b^{12} x^{2} - 2 \, a^{2} b^{10} x + a^{4} b^{8}\right)}}"," ",0,"-1/10*(15*a*b^8*x^4 + 70*a^3*b^6*x^3 - 185*a^5*b^4*x^2 - 50*a^7*b^2*x + 130*a^9 + 420*(a^5*b^4*x^2 - 2*a^7*b^2*x + a^9)*log(b*sqrt(x) + a) - 4*(b^9*x^4 + 8*a^2*b^7*x^3 + 56*a^4*b^5*x^2 - 175*a^6*b^3*x + 105*a^8*b)*sqrt(x))/(b^12*x^2 - 2*a^2*b^10*x + a^4*b^8)","A",0
2208,1,135,0,0.716949," ","integrate(x^2/(a+b*x^(1/2))^3,x, algorithm=""fricas"")","-\frac{9 \, a b^{6} x^{3} - 18 \, a^{3} b^{4} x^{2} - 24 \, a^{5} b^{2} x + 27 \, a^{7} + 60 \, {\left(a^{3} b^{4} x^{2} - 2 \, a^{5} b^{2} x + a^{7}\right)} \log\left(b \sqrt{x} + a\right) - 2 \, {\left(b^{7} x^{3} + 16 \, a^{2} b^{5} x^{2} - 50 \, a^{4} b^{3} x + 30 \, a^{6} b\right)} \sqrt{x}}{3 \, {\left(b^{10} x^{2} - 2 \, a^{2} b^{8} x + a^{4} b^{6}\right)}}"," ",0,"-1/3*(9*a*b^6*x^3 - 18*a^3*b^4*x^2 - 24*a^5*b^2*x + 27*a^7 + 60*(a^3*b^4*x^2 - 2*a^5*b^2*x + a^7)*log(b*sqrt(x) + a) - 2*(b^7*x^3 + 16*a^2*b^5*x^2 - 50*a^4*b^3*x + 30*a^6*b)*sqrt(x))/(b^10*x^2 - 2*a^2*b^8*x + a^4*b^6)","A",0
2209,1,101,0,0.679541," ","integrate(x/(a+b*x^(1/2))^3,x, algorithm=""fricas"")","\frac{7 \, a^{3} b^{2} x - 5 \, a^{5} - 6 \, {\left(a b^{4} x^{2} - 2 \, a^{3} b^{2} x + a^{5}\right)} \log\left(b \sqrt{x} + a\right) + 2 \, {\left(b^{5} x^{2} - 5 \, a^{2} b^{3} x + 3 \, a^{4} b\right)} \sqrt{x}}{b^{8} x^{2} - 2 \, a^{2} b^{6} x + a^{4} b^{4}}"," ",0,"(7*a^3*b^2*x - 5*a^5 - 6*(a*b^4*x^2 - 2*a^3*b^2*x + a^5)*log(b*sqrt(x) + a) + 2*(b^5*x^2 - 5*a^2*b^3*x + 3*a^4*b)*sqrt(x))/(b^8*x^2 - 2*a^2*b^6*x + a^4*b^4)","A",0
2210,1,47,0,0.892715," ","integrate(1/(a+b*x^(1/2))^3,x, algorithm=""fricas"")","-\frac{2 \, b^{3} x^{\frac{3}{2}} - 3 \, a b^{2} x + a^{3}}{b^{6} x^{2} - 2 \, a^{2} b^{4} x + a^{4} b^{2}}"," ",0,"-(2*b^3*x^(3/2) - 3*a*b^2*x + a^3)/(b^6*x^2 - 2*a^2*b^4*x + a^4*b^2)","B",0
2211,1,115,0,0.896676," ","integrate(1/x/(a+b*x^(1/2))^3,x, algorithm=""fricas"")","-\frac{a^{2} b^{2} x - 3 \, a^{4} + 2 \, {\left(b^{4} x^{2} - 2 \, a^{2} b^{2} x + a^{4}\right)} \log\left(b \sqrt{x} + a\right) - 2 \, {\left(b^{4} x^{2} - 2 \, a^{2} b^{2} x + a^{4}\right)} \log\left(\sqrt{x}\right) - 2 \, {\left(a b^{3} x - 2 \, a^{3} b\right)} \sqrt{x}}{a^{3} b^{4} x^{2} - 2 \, a^{5} b^{2} x + a^{7}}"," ",0,"-(a^2*b^2*x - 3*a^4 + 2*(b^4*x^2 - 2*a^2*b^2*x + a^4)*log(b*sqrt(x) + a) - 2*(b^4*x^2 - 2*a^2*b^2*x + a^4)*log(sqrt(x)) - 2*(a*b^3*x - 2*a^3*b)*sqrt(x))/(a^3*b^4*x^2 - 2*a^5*b^2*x + a^7)","B",0
2212,1,155,0,0.683893," ","integrate(1/x^2/(a+b*x^(1/2))^3,x, algorithm=""fricas"")","-\frac{6 \, a^{2} b^{4} x^{2} - 9 \, a^{4} b^{2} x + a^{6} + 12 \, {\left(b^{6} x^{3} - 2 \, a^{2} b^{4} x^{2} + a^{4} b^{2} x\right)} \log\left(b \sqrt{x} + a\right) - 12 \, {\left(b^{6} x^{3} - 2 \, a^{2} b^{4} x^{2} + a^{4} b^{2} x\right)} \log\left(\sqrt{x}\right) - 2 \, {\left(6 \, a b^{5} x^{2} - 10 \, a^{3} b^{3} x + 3 \, a^{5} b\right)} \sqrt{x}}{a^{5} b^{4} x^{3} - 2 \, a^{7} b^{2} x^{2} + a^{9} x}"," ",0,"-(6*a^2*b^4*x^2 - 9*a^4*b^2*x + a^6 + 12*(b^6*x^3 - 2*a^2*b^4*x^2 + a^4*b^2*x)*log(b*sqrt(x) + a) - 12*(b^6*x^3 - 2*a^2*b^4*x^2 + a^4*b^2*x)*log(sqrt(x)) - 2*(6*a*b^5*x^2 - 10*a^3*b^3*x + 3*a^5*b)*sqrt(x))/(a^5*b^4*x^3 - 2*a^7*b^2*x^2 + a^9*x)","B",0
2213,1,182,0,0.730998," ","integrate(1/x^3/(a+b*x^(1/2))^3,x, algorithm=""fricas"")","-\frac{30 \, a^{2} b^{6} x^{3} - 45 \, a^{4} b^{4} x^{2} + 10 \, a^{6} b^{2} x + a^{8} + 60 \, {\left(b^{8} x^{4} - 2 \, a^{2} b^{6} x^{3} + a^{4} b^{4} x^{2}\right)} \log\left(b \sqrt{x} + a\right) - 60 \, {\left(b^{8} x^{4} - 2 \, a^{2} b^{6} x^{3} + a^{4} b^{4} x^{2}\right)} \log\left(\sqrt{x}\right) - 4 \, {\left(15 \, a b^{7} x^{3} - 25 \, a^{3} b^{5} x^{2} + 8 \, a^{5} b^{3} x + a^{7} b\right)} \sqrt{x}}{2 \, {\left(a^{7} b^{4} x^{4} - 2 \, a^{9} b^{2} x^{3} + a^{11} x^{2}\right)}}"," ",0,"-1/2*(30*a^2*b^6*x^3 - 45*a^4*b^4*x^2 + 10*a^6*b^2*x + a^8 + 60*(b^8*x^4 - 2*a^2*b^6*x^3 + a^4*b^4*x^2)*log(b*sqrt(x) + a) - 60*(b^8*x^4 - 2*a^2*b^6*x^3 + a^4*b^4*x^2)*log(sqrt(x)) - 4*(15*a*b^7*x^3 - 25*a^3*b^5*x^2 + 8*a^5*b^3*x + a^7*b)*sqrt(x))/(a^7*b^4*x^4 - 2*a^9*b^2*x^3 + a^11*x^2)","A",0
2214,1,207,0,0.586497," ","integrate(1/x^4/(a+b*x^(1/2))^3,x, algorithm=""fricas"")","-\frac{420 \, a^{2} b^{8} x^{4} - 630 \, a^{4} b^{6} x^{3} + 140 \, a^{6} b^{4} x^{2} + 35 \, a^{8} b^{2} x + 5 \, a^{10} + 840 \, {\left(b^{10} x^{5} - 2 \, a^{2} b^{8} x^{4} + a^{4} b^{6} x^{3}\right)} \log\left(b \sqrt{x} + a\right) - 840 \, {\left(b^{10} x^{5} - 2 \, a^{2} b^{8} x^{4} + a^{4} b^{6} x^{3}\right)} \log\left(\sqrt{x}\right) - 2 \, {\left(420 \, a b^{9} x^{4} - 700 \, a^{3} b^{7} x^{3} + 224 \, a^{5} b^{5} x^{2} + 32 \, a^{7} b^{3} x + 9 \, a^{9} b\right)} \sqrt{x}}{15 \, {\left(a^{9} b^{4} x^{5} - 2 \, a^{11} b^{2} x^{4} + a^{13} x^{3}\right)}}"," ",0,"-1/15*(420*a^2*b^8*x^4 - 630*a^4*b^6*x^3 + 140*a^6*b^4*x^2 + 35*a^8*b^2*x + 5*a^10 + 840*(b^10*x^5 - 2*a^2*b^8*x^4 + a^4*b^6*x^3)*log(b*sqrt(x) + a) - 840*(b^10*x^5 - 2*a^2*b^8*x^4 + a^4*b^6*x^3)*log(sqrt(x)) - 2*(420*a*b^9*x^4 - 700*a^3*b^7*x^3 + 224*a^5*b^5*x^2 + 32*a^7*b^3*x + 9*a^9*b)*sqrt(x))/(a^9*b^4*x^5 - 2*a^11*b^2*x^4 + a^13*x^3)","A",0
2215,1,245,0,0.852555," ","integrate(x^4/(a+b*x^(1/2))^5,x, algorithm=""fricas"")","-\frac{25 \, a b^{12} x^{6} + 250 \, a^{3} b^{10} x^{5} - 1250 \, a^{5} b^{8} x^{4} - 40 \, a^{7} b^{6} x^{3} + 3840 \, a^{9} b^{4} x^{2} - 4240 \, a^{11} b^{2} x + 1375 \, a^{13} + 2520 \, {\left(a^{5} b^{8} x^{4} - 4 \, a^{7} b^{6} x^{3} + 6 \, a^{9} b^{4} x^{2} - 4 \, a^{11} b^{2} x + a^{13}\right)} \log\left(b \sqrt{x} + a\right) - 4 \, {\left(b^{13} x^{6} + 21 \, a^{2} b^{11} x^{5} + 256 \, a^{4} b^{9} x^{4} - 1674 \, a^{6} b^{7} x^{3} + 3066 \, a^{8} b^{5} x^{2} - 2310 \, a^{10} b^{3} x + 630 \, a^{12} b\right)} \sqrt{x}}{10 \, {\left(b^{18} x^{4} - 4 \, a^{2} b^{16} x^{3} + 6 \, a^{4} b^{14} x^{2} - 4 \, a^{6} b^{12} x + a^{8} b^{10}\right)}}"," ",0,"-1/10*(25*a*b^12*x^6 + 250*a^3*b^10*x^5 - 1250*a^5*b^8*x^4 - 40*a^7*b^6*x^3 + 3840*a^9*b^4*x^2 - 4240*a^11*b^2*x + 1375*a^13 + 2520*(a^5*b^8*x^4 - 4*a^7*b^6*x^3 + 6*a^9*b^4*x^2 - 4*a^11*b^2*x + a^13)*log(b*sqrt(x) + a) - 4*(b^13*x^6 + 21*a^2*b^11*x^5 + 256*a^4*b^9*x^4 - 1674*a^6*b^7*x^3 + 3066*a^8*b^5*x^2 - 2310*a^10*b^3*x + 630*a^12*b)*sqrt(x))/(b^18*x^4 - 4*a^2*b^16*x^3 + 6*a^4*b^14*x^2 - 4*a^6*b^12*x + a^8*b^10)","A",0
2216,1,223,0,0.861271," ","integrate(x^3/(a+b*x^(1/2))^5,x, algorithm=""fricas"")","-\frac{30 \, a b^{10} x^{5} - 120 \, a^{3} b^{8} x^{4} - 366 \, a^{5} b^{6} x^{3} + 1179 \, a^{7} b^{4} x^{2} - 1066 \, a^{9} b^{2} x + 319 \, a^{11} + 420 \, {\left(a^{3} b^{8} x^{4} - 4 \, a^{5} b^{6} x^{3} + 6 \, a^{7} b^{4} x^{2} - 4 \, a^{9} b^{2} x + a^{11}\right)} \log\left(b \sqrt{x} + a\right) - 4 \, {\left(b^{11} x^{5} + 41 \, a^{2} b^{9} x^{4} - 279 \, a^{4} b^{7} x^{3} + 511 \, a^{6} b^{5} x^{2} - 385 \, a^{8} b^{3} x + 105 \, a^{10} b\right)} \sqrt{x}}{6 \, {\left(b^{16} x^{4} - 4 \, a^{2} b^{14} x^{3} + 6 \, a^{4} b^{12} x^{2} - 4 \, a^{6} b^{10} x + a^{8} b^{8}\right)}}"," ",0,"-1/6*(30*a*b^10*x^5 - 120*a^3*b^8*x^4 - 366*a^5*b^6*x^3 + 1179*a^7*b^4*x^2 - 1066*a^9*b^2*x + 319*a^11 + 420*(a^3*b^8*x^4 - 4*a^5*b^6*x^3 + 6*a^7*b^4*x^2 - 4*a^9*b^2*x + a^11)*log(b*sqrt(x) + a) - 4*(b^11*x^5 + 41*a^2*b^9*x^4 - 279*a^4*b^7*x^3 + 511*a^6*b^5*x^2 - 385*a^8*b^3*x + 105*a^10*b)*sqrt(x))/(b^16*x^4 - 4*a^2*b^14*x^3 + 6*a^4*b^12*x^2 - 4*a^6*b^10*x + a^8*b^8)","B",0
2217,1,191,0,0.868817," ","integrate(x^2/(a+b*x^(1/2))^5,x, algorithm=""fricas"")","\frac{180 \, a^{3} b^{6} x^{3} - 357 \, a^{5} b^{4} x^{2} + 278 \, a^{7} b^{2} x - 77 \, a^{9} - 60 \, {\left(a b^{8} x^{4} - 4 \, a^{3} b^{6} x^{3} + 6 \, a^{5} b^{4} x^{2} - 4 \, a^{7} b^{2} x + a^{9}\right)} \log\left(b \sqrt{x} + a\right) + 4 \, {\left(3 \, b^{9} x^{4} - 42 \, a^{2} b^{7} x^{3} + 73 \, a^{4} b^{5} x^{2} - 55 \, a^{6} b^{3} x + 15 \, a^{8} b\right)} \sqrt{x}}{6 \, {\left(b^{14} x^{4} - 4 \, a^{2} b^{12} x^{3} + 6 \, a^{4} b^{10} x^{2} - 4 \, a^{6} b^{8} x + a^{8} b^{6}\right)}}"," ",0,"1/6*(180*a^3*b^6*x^3 - 357*a^5*b^4*x^2 + 278*a^7*b^2*x - 77*a^9 - 60*(a*b^8*x^4 - 4*a^3*b^6*x^3 + 6*a^5*b^4*x^2 - 4*a^7*b^2*x + a^9)*log(b*sqrt(x) + a) + 4*(3*b^9*x^4 - 42*a^2*b^7*x^3 + 73*a^4*b^5*x^2 - 55*a^6*b^3*x + 15*a^8*b)*sqrt(x))/(b^14*x^4 - 4*a^2*b^12*x^3 + 6*a^4*b^10*x^2 - 4*a^6*b^8*x + a^8*b^6)","B",0
2218,1,108,0,0.789345," ","integrate(x/(a+b*x^(1/2))^5,x, algorithm=""fricas"")","\frac{10 \, a b^{6} x^{3} - 5 \, a^{3} b^{4} x^{2} + 4 \, a^{5} b^{2} x - a^{7} - 4 \, {\left(b^{7} x^{3} + a^{2} b^{5} x^{2}\right)} \sqrt{x}}{2 \, {\left(b^{12} x^{4} - 4 \, a^{2} b^{10} x^{3} + 6 \, a^{4} b^{8} x^{2} - 4 \, a^{6} b^{6} x + a^{8} b^{4}\right)}}"," ",0,"1/2*(10*a*b^6*x^3 - 5*a^3*b^4*x^2 + 4*a^5*b^2*x - a^7 - 4*(b^7*x^3 + a^2*b^5*x^2)*sqrt(x))/(b^12*x^4 - 4*a^2*b^10*x^3 + 6*a^4*b^8*x^2 - 4*a^6*b^6*x + a^8*b^4)","B",0
2219,1,96,0,0.808922," ","integrate(1/(a+b*x^(1/2))^5,x, algorithm=""fricas"")","\frac{15 \, a b^{4} x^{2} + 10 \, a^{3} b^{2} x - a^{5} - 4 \, {\left(b^{5} x^{2} + 5 \, a^{2} b^{3} x\right)} \sqrt{x}}{6 \, {\left(b^{10} x^{4} - 4 \, a^{2} b^{8} x^{3} + 6 \, a^{4} b^{6} x^{2} - 4 \, a^{6} b^{4} x + a^{8} b^{2}\right)}}"," ",0,"1/6*(15*a*b^4*x^2 + 10*a^3*b^2*x - a^5 - 4*(b^5*x^2 + 5*a^2*b^3*x)*sqrt(x))/(b^10*x^4 - 4*a^2*b^8*x^3 + 6*a^4*b^6*x^2 - 4*a^6*b^4*x + a^8*b^2)","B",0
2220,1,227,0,0.860291," ","integrate(1/x/(a+b*x^(1/2))^5,x, algorithm=""fricas"")","-\frac{6 \, a^{2} b^{6} x^{3} - 21 \, a^{4} b^{4} x^{2} + 16 \, a^{6} b^{2} x - 25 \, a^{8} + 12 \, {\left(b^{8} x^{4} - 4 \, a^{2} b^{6} x^{3} + 6 \, a^{4} b^{4} x^{2} - 4 \, a^{6} b^{2} x + a^{8}\right)} \log\left(b \sqrt{x} + a\right) - 12 \, {\left(b^{8} x^{4} - 4 \, a^{2} b^{6} x^{3} + 6 \, a^{4} b^{4} x^{2} - 4 \, a^{6} b^{2} x + a^{8}\right)} \log\left(\sqrt{x}\right) - 4 \, {\left(3 \, a b^{7} x^{3} - 11 \, a^{3} b^{5} x^{2} + 14 \, a^{5} b^{3} x - 12 \, a^{7} b\right)} \sqrt{x}}{6 \, {\left(a^{5} b^{8} x^{4} - 4 \, a^{7} b^{6} x^{3} + 6 \, a^{9} b^{4} x^{2} - 4 \, a^{11} b^{2} x + a^{13}\right)}}"," ",0,"-1/6*(6*a^2*b^6*x^3 - 21*a^4*b^4*x^2 + 16*a^6*b^2*x - 25*a^8 + 12*(b^8*x^4 - 4*a^2*b^6*x^3 + 6*a^4*b^4*x^2 - 4*a^6*b^2*x + a^8)*log(b*sqrt(x) + a) - 12*(b^8*x^4 - 4*a^2*b^6*x^3 + 6*a^4*b^4*x^2 - 4*a^6*b^2*x + a^8)*log(sqrt(x)) - 4*(3*a*b^7*x^3 - 11*a^3*b^5*x^2 + 14*a^5*b^3*x - 12*a^7*b)*sqrt(x))/(a^5*b^8*x^4 - 4*a^7*b^6*x^3 + 6*a^9*b^4*x^2 - 4*a^11*b^2*x + a^13)","B",0
2221,1,267,0,0.876085," ","integrate(1/x^2/(a+b*x^(1/2))^5,x, algorithm=""fricas"")","-\frac{30 \, a^{2} b^{8} x^{4} - 105 \, a^{4} b^{6} x^{3} + 130 \, a^{6} b^{4} x^{2} - 65 \, a^{8} b^{2} x + 2 \, a^{10} + 60 \, {\left(b^{10} x^{5} - 4 \, a^{2} b^{8} x^{4} + 6 \, a^{4} b^{6} x^{3} - 4 \, a^{6} b^{4} x^{2} + a^{8} b^{2} x\right)} \log\left(b \sqrt{x} + a\right) - 60 \, {\left(b^{10} x^{5} - 4 \, a^{2} b^{8} x^{4} + 6 \, a^{4} b^{6} x^{3} - 4 \, a^{6} b^{4} x^{2} + a^{8} b^{2} x\right)} \log\left(\sqrt{x}\right) - 4 \, {\left(15 \, a b^{9} x^{4} - 55 \, a^{3} b^{7} x^{3} + 73 \, a^{5} b^{5} x^{2} - 40 \, a^{7} b^{3} x + 5 \, a^{9} b\right)} \sqrt{x}}{2 \, {\left(a^{7} b^{8} x^{5} - 4 \, a^{9} b^{6} x^{4} + 6 \, a^{11} b^{4} x^{3} - 4 \, a^{13} b^{2} x^{2} + a^{15} x\right)}}"," ",0,"-1/2*(30*a^2*b^8*x^4 - 105*a^4*b^6*x^3 + 130*a^6*b^4*x^2 - 65*a^8*b^2*x + 2*a^10 + 60*(b^10*x^5 - 4*a^2*b^8*x^4 + 6*a^4*b^6*x^3 - 4*a^6*b^4*x^2 + a^8*b^2*x)*log(b*sqrt(x) + a) - 60*(b^10*x^5 - 4*a^2*b^8*x^4 + 6*a^4*b^6*x^3 - 4*a^6*b^4*x^2 + a^8*b^2*x)*log(sqrt(x)) - 4*(15*a*b^9*x^4 - 55*a^3*b^7*x^3 + 73*a^5*b^5*x^2 - 40*a^7*b^3*x + 5*a^9*b)*sqrt(x))/(a^7*b^8*x^5 - 4*a^9*b^6*x^4 + 6*a^11*b^4*x^3 - 4*a^13*b^2*x^2 + a^15*x)","B",0
2222,1,295,0,0.911821," ","integrate(1/x^3/(a+b*x^(1/2))^5,x, algorithm=""fricas"")","-\frac{420 \, a^{2} b^{10} x^{5} - 1470 \, a^{4} b^{8} x^{4} + 1820 \, a^{6} b^{6} x^{3} - 875 \, a^{8} b^{4} x^{2} + 78 \, a^{10} b^{2} x + 3 \, a^{12} + 840 \, {\left(b^{12} x^{6} - 4 \, a^{2} b^{10} x^{5} + 6 \, a^{4} b^{8} x^{4} - 4 \, a^{6} b^{6} x^{3} + a^{8} b^{4} x^{2}\right)} \log\left(b \sqrt{x} + a\right) - 840 \, {\left(b^{12} x^{6} - 4 \, a^{2} b^{10} x^{5} + 6 \, a^{4} b^{8} x^{4} - 4 \, a^{6} b^{6} x^{3} + a^{8} b^{4} x^{2}\right)} \log\left(\sqrt{x}\right) - 4 \, {\left(210 \, a b^{11} x^{5} - 770 \, a^{3} b^{9} x^{4} + 1022 \, a^{5} b^{7} x^{3} - 558 \, a^{7} b^{5} x^{2} + 85 \, a^{9} b^{3} x + 5 \, a^{11} b\right)} \sqrt{x}}{6 \, {\left(a^{9} b^{8} x^{6} - 4 \, a^{11} b^{6} x^{5} + 6 \, a^{13} b^{4} x^{4} - 4 \, a^{15} b^{2} x^{3} + a^{17} x^{2}\right)}}"," ",0,"-1/6*(420*a^2*b^10*x^5 - 1470*a^4*b^8*x^4 + 1820*a^6*b^6*x^3 - 875*a^8*b^4*x^2 + 78*a^10*b^2*x + 3*a^12 + 840*(b^12*x^6 - 4*a^2*b^10*x^5 + 6*a^4*b^8*x^4 - 4*a^6*b^6*x^3 + a^8*b^4*x^2)*log(b*sqrt(x) + a) - 840*(b^12*x^6 - 4*a^2*b^10*x^5 + 6*a^4*b^8*x^4 - 4*a^6*b^6*x^3 + a^8*b^4*x^2)*log(sqrt(x)) - 4*(210*a*b^11*x^5 - 770*a^3*b^9*x^4 + 1022*a^5*b^7*x^3 - 558*a^7*b^5*x^2 + 85*a^9*b^3*x + 5*a^11*b)*sqrt(x))/(a^9*b^8*x^6 - 4*a^11*b^6*x^5 + 6*a^13*b^4*x^4 - 4*a^15*b^2*x^3 + a^17*x^2)","B",0
2223,1,370,0,0.812160," ","integrate(x^5/(a+b*x^(1/2))^8,x, algorithm=""fricas"")","\frac{21 \, b^{18} x^{9} + 1365 \, a^{2} b^{16} x^{8} - 10143 \, a^{4} b^{14} x^{7} - 27195 \, a^{6} b^{12} x^{6} + 227094 \, a^{8} b^{10} x^{5} - 540190 \, a^{10} b^{8} x^{4} + 661465 \, a^{12} b^{6} x^{3} - 455091 \, a^{14} b^{4} x^{2} + 167867 \, a^{16} b^{2} x - 25961 \, a^{18} + 27720 \, {\left(a^{4} b^{14} x^{7} - 7 \, a^{6} b^{12} x^{6} + 21 \, a^{8} b^{10} x^{5} - 35 \, a^{10} b^{8} x^{4} + 35 \, a^{12} b^{6} x^{3} - 21 \, a^{14} b^{4} x^{2} + 7 \, a^{16} b^{2} x - a^{18}\right)} \log\left(b \sqrt{x} + a\right) - 8 \, {\left(28 \, a b^{17} x^{8} + 1064 \, a^{3} b^{15} x^{7} - 13083 \, a^{5} b^{13} x^{6} + 48580 \, a^{7} b^{11} x^{5} - 92323 \, a^{9} b^{9} x^{4} + 101376 \, a^{11} b^{7} x^{3} - 65373 \, a^{13} b^{5} x^{2} + 23100 \, a^{15} b^{3} x - 3465 \, a^{17} b\right)} \sqrt{x}}{42 \, {\left(b^{26} x^{7} - 7 \, a^{2} b^{24} x^{6} + 21 \, a^{4} b^{22} x^{5} - 35 \, a^{6} b^{20} x^{4} + 35 \, a^{8} b^{18} x^{3} - 21 \, a^{10} b^{16} x^{2} + 7 \, a^{12} b^{14} x - a^{14} b^{12}\right)}}"," ",0,"1/42*(21*b^18*x^9 + 1365*a^2*b^16*x^8 - 10143*a^4*b^14*x^7 - 27195*a^6*b^12*x^6 + 227094*a^8*b^10*x^5 - 540190*a^10*b^8*x^4 + 661465*a^12*b^6*x^3 - 455091*a^14*b^4*x^2 + 167867*a^16*b^2*x - 25961*a^18 + 27720*(a^4*b^14*x^7 - 7*a^6*b^12*x^6 + 21*a^8*b^10*x^5 - 35*a^10*b^8*x^4 + 35*a^12*b^6*x^3 - 21*a^14*b^4*x^2 + 7*a^16*b^2*x - a^18)*log(b*sqrt(x) + a) - 8*(28*a*b^17*x^8 + 1064*a^3*b^15*x^7 - 13083*a^5*b^13*x^6 + 48580*a^7*b^11*x^5 - 92323*a^9*b^9*x^4 + 101376*a^11*b^7*x^3 - 65373*a^13*b^5*x^2 + 23100*a^15*b^3*x - 3465*a^17*b)*sqrt(x))/(b^26*x^7 - 7*a^2*b^24*x^6 + 21*a^4*b^22*x^5 - 35*a^6*b^20*x^4 + 35*a^8*b^18*x^3 - 21*a^10*b^16*x^2 + 7*a^12*b^14*x - a^14*b^12)","B",0
2224,1,348,0,0.799758," ","integrate(x^4/(a+b*x^(1/2))^8,x, algorithm=""fricas"")","\frac{35 \, b^{16} x^{8} - 245 \, a^{2} b^{14} x^{7} - 9555 \, a^{4} b^{12} x^{6} + 41405 \, a^{6} b^{10} x^{5} - 83720 \, a^{8} b^{8} x^{4} + 94745 \, a^{10} b^{6} x^{3} - 62139 \, a^{12} b^{4} x^{2} + 22183 \, a^{14} b^{2} x - 3349 \, a^{16} + 2520 \, {\left(a^{2} b^{14} x^{7} - 7 \, a^{4} b^{12} x^{6} + 21 \, a^{6} b^{10} x^{5} - 35 \, a^{8} b^{8} x^{4} + 35 \, a^{10} b^{6} x^{3} - 21 \, a^{12} b^{4} x^{2} + 7 \, a^{14} b^{2} x - a^{16}\right)} \log\left(b \sqrt{x} + a\right) - 8 \, {\left(70 \, a b^{15} x^{7} - 1225 \, a^{3} b^{13} x^{6} + 4410 \, a^{5} b^{11} x^{5} - 8393 \, a^{7} b^{9} x^{4} + 9216 \, a^{9} b^{7} x^{3} - 5943 \, a^{11} b^{5} x^{2} + 2100 \, a^{13} b^{3} x - 315 \, a^{15} b\right)} \sqrt{x}}{35 \, {\left(b^{24} x^{7} - 7 \, a^{2} b^{22} x^{6} + 21 \, a^{4} b^{20} x^{5} - 35 \, a^{6} b^{18} x^{4} + 35 \, a^{8} b^{16} x^{3} - 21 \, a^{10} b^{14} x^{2} + 7 \, a^{12} b^{12} x - a^{14} b^{10}\right)}}"," ",0,"1/35*(35*b^16*x^8 - 245*a^2*b^14*x^7 - 9555*a^4*b^12*x^6 + 41405*a^6*b^10*x^5 - 83720*a^8*b^8*x^4 + 94745*a^10*b^6*x^3 - 62139*a^12*b^4*x^2 + 22183*a^14*b^2*x - 3349*a^16 + 2520*(a^2*b^14*x^7 - 7*a^4*b^12*x^6 + 21*a^6*b^10*x^5 - 35*a^8*b^8*x^4 + 35*a^10*b^6*x^3 - 21*a^12*b^4*x^2 + 7*a^14*b^2*x - a^16)*log(b*sqrt(x) + a) - 8*(70*a*b^15*x^7 - 1225*a^3*b^13*x^6 + 4410*a^5*b^11*x^5 - 8393*a^7*b^9*x^4 + 9216*a^9*b^7*x^3 - 5943*a^11*b^5*x^2 + 2100*a^13*b^3*x - 315*a^15*b)*sqrt(x))/(b^24*x^7 - 7*a^2*b^22*x^6 + 21*a^4*b^20*x^5 - 35*a^6*b^18*x^4 + 35*a^8*b^16*x^3 - 21*a^10*b^14*x^2 + 7*a^12*b^12*x - a^14*b^10)","B",0
2225,1,315,0,0.753195," ","integrate(x^3/(a+b*x^(1/2))^8,x, algorithm=""fricas"")","-\frac{7350 \, a^{2} b^{12} x^{6} - 16905 \, a^{4} b^{10} x^{5} + 32585 \, a^{6} b^{8} x^{4} - 34370 \, a^{8} b^{6} x^{3} + 21504 \, a^{10} b^{4} x^{2} - 7413 \, a^{12} b^{2} x + 1089 \, a^{14} - 420 \, {\left(b^{14} x^{7} - 7 \, a^{2} b^{12} x^{6} + 21 \, a^{4} b^{10} x^{5} - 35 \, a^{6} b^{8} x^{4} + 35 \, a^{8} b^{6} x^{3} - 21 \, a^{10} b^{4} x^{2} + 7 \, a^{12} b^{2} x - a^{14}\right)} \log\left(b \sqrt{x} + a\right) - 4 \, {\left(735 \, a b^{13} x^{6} - 980 \, a^{3} b^{11} x^{5} + 2891 \, a^{5} b^{9} x^{4} - 3072 \, a^{7} b^{7} x^{3} + 1981 \, a^{9} b^{5} x^{2} - 700 \, a^{11} b^{3} x + 105 \, a^{13} b\right)} \sqrt{x}}{210 \, {\left(b^{22} x^{7} - 7 \, a^{2} b^{20} x^{6} + 21 \, a^{4} b^{18} x^{5} - 35 \, a^{6} b^{16} x^{4} + 35 \, a^{8} b^{14} x^{3} - 21 \, a^{10} b^{12} x^{2} + 7 \, a^{12} b^{10} x - a^{14} b^{8}\right)}}"," ",0,"-1/210*(7350*a^2*b^12*x^6 - 16905*a^4*b^10*x^5 + 32585*a^6*b^8*x^4 - 34370*a^8*b^6*x^3 + 21504*a^10*b^4*x^2 - 7413*a^12*b^2*x + 1089*a^14 - 420*(b^14*x^7 - 7*a^2*b^12*x^6 + 21*a^4*b^10*x^5 - 35*a^6*b^8*x^4 + 35*a^8*b^6*x^3 - 21*a^10*b^4*x^2 + 7*a^12*b^2*x - a^14)*log(b*sqrt(x) + a) - 4*(735*a*b^13*x^6 - 980*a^3*b^11*x^5 + 2891*a^5*b^9*x^4 - 3072*a^7*b^7*x^3 + 1981*a^9*b^5*x^2 - 700*a^11*b^3*x + 105*a^13*b)*sqrt(x))/(b^22*x^7 - 7*a^2*b^20*x^6 + 21*a^4*b^18*x^5 - 35*a^6*b^16*x^4 + 35*a^8*b^14*x^3 - 21*a^10*b^12*x^2 + 7*a^12*b^10*x - a^14*b^8)","B",0
2226,1,188,0,0.920416," ","integrate(x^2/(a+b*x^(1/2))^8,x, algorithm=""fricas"")","-\frac{21 \, b^{12} x^{6} + 231 \, a^{2} b^{10} x^{5} + 105 \, a^{4} b^{8} x^{4} + 42 \, a^{6} b^{6} x^{3} - 21 \, a^{8} b^{4} x^{2} + 7 \, a^{10} b^{2} x - a^{12} - 16 \, {\left(7 \, a b^{11} x^{5} + 14 \, a^{3} b^{9} x^{4} + 3 \, a^{5} b^{7} x^{3}\right)} \sqrt{x}}{21 \, {\left(b^{20} x^{7} - 7 \, a^{2} b^{18} x^{6} + 21 \, a^{4} b^{16} x^{5} - 35 \, a^{6} b^{14} x^{4} + 35 \, a^{8} b^{12} x^{3} - 21 \, a^{10} b^{10} x^{2} + 7 \, a^{12} b^{8} x - a^{14} b^{6}\right)}}"," ",0,"-1/21*(21*b^12*x^6 + 231*a^2*b^10*x^5 + 105*a^4*b^8*x^4 + 42*a^6*b^6*x^3 - 21*a^8*b^4*x^2 + 7*a^10*b^2*x - a^12 - 16*(7*a*b^11*x^5 + 14*a^3*b^9*x^4 + 3*a^5*b^7*x^3)*sqrt(x))/(b^20*x^7 - 7*a^2*b^18*x^6 + 21*a^4*b^16*x^5 - 35*a^6*b^14*x^4 + 35*a^8*b^12*x^3 - 21*a^10*b^10*x^2 + 7*a^12*b^8*x - a^14*b^6)","B",0
2227,1,177,0,0.561003," ","integrate(x/(a+b*x^(1/2))^8,x, algorithm=""fricas"")","-\frac{35 \, b^{10} x^{5} + 595 \, a^{2} b^{8} x^{4} + 630 \, a^{4} b^{6} x^{3} + 14 \, a^{6} b^{4} x^{2} + 7 \, a^{8} b^{2} x - a^{10} - 32 \, {\left(7 \, a b^{9} x^{4} + 26 \, a^{3} b^{7} x^{3} + 7 \, a^{5} b^{5} x^{2}\right)} \sqrt{x}}{70 \, {\left(b^{18} x^{7} - 7 \, a^{2} b^{16} x^{6} + 21 \, a^{4} b^{14} x^{5} - 35 \, a^{6} b^{12} x^{4} + 35 \, a^{8} b^{10} x^{3} - 21 \, a^{10} b^{8} x^{2} + 7 \, a^{12} b^{6} x - a^{14} b^{4}\right)}}"," ",0,"-1/70*(35*b^10*x^5 + 595*a^2*b^8*x^4 + 630*a^4*b^6*x^3 + 14*a^6*b^4*x^2 + 7*a^8*b^2*x - a^10 - 32*(7*a*b^9*x^4 + 26*a^3*b^7*x^3 + 7*a^5*b^5*x^2)*sqrt(x))/(b^18*x^7 - 7*a^2*b^16*x^6 + 21*a^4*b^14*x^5 - 35*a^6*b^12*x^4 + 35*a^8*b^10*x^3 - 21*a^10*b^8*x^2 + 7*a^12*b^6*x - a^14*b^4)","B",0
2228,1,164,0,0.878938," ","integrate(1/(a+b*x^(1/2))^8,x, algorithm=""fricas"")","-\frac{7 \, b^{8} x^{4} + 140 \, a^{2} b^{6} x^{3} + 210 \, a^{4} b^{4} x^{2} + 28 \, a^{6} b^{2} x - a^{8} - 16 \, {\left(3 \, a b^{7} x^{3} + 14 \, a^{3} b^{5} x^{2} + 7 \, a^{5} b^{3} x\right)} \sqrt{x}}{21 \, {\left(b^{16} x^{7} - 7 \, a^{2} b^{14} x^{6} + 21 \, a^{4} b^{12} x^{5} - 35 \, a^{6} b^{10} x^{4} + 35 \, a^{8} b^{8} x^{3} - 21 \, a^{10} b^{6} x^{2} + 7 \, a^{12} b^{4} x - a^{14} b^{2}\right)}}"," ",0,"-1/21*(7*b^8*x^4 + 140*a^2*b^6*x^3 + 210*a^4*b^4*x^2 + 28*a^6*b^2*x - a^8 - 16*(3*a*b^7*x^3 + 14*a^3*b^5*x^2 + 7*a^5*b^3*x)*sqrt(x))/(b^16*x^7 - 7*a^2*b^14*x^6 + 21*a^4*b^12*x^5 - 35*a^6*b^10*x^4 + 35*a^8*b^8*x^3 - 21*a^10*b^6*x^2 + 7*a^12*b^4*x - a^14*b^2)","B",0
2229,1,398,0,0.517778," ","integrate(1/x/(a+b*x^(1/2))^8,x, algorithm=""fricas"")","-\frac{210 \, a^{2} b^{12} x^{6} - 1365 \, a^{4} b^{10} x^{5} + 3745 \, a^{6} b^{8} x^{4} - 5530 \, a^{8} b^{6} x^{3} + 5964 \, a^{10} b^{4} x^{2} - 273 \, a^{12} b^{2} x + 1089 \, a^{14} + 420 \, {\left(b^{14} x^{7} - 7 \, a^{2} b^{12} x^{6} + 21 \, a^{4} b^{10} x^{5} - 35 \, a^{6} b^{8} x^{4} + 35 \, a^{8} b^{6} x^{3} - 21 \, a^{10} b^{4} x^{2} + 7 \, a^{12} b^{2} x - a^{14}\right)} \log\left(b \sqrt{x} + a\right) - 420 \, {\left(b^{14} x^{7} - 7 \, a^{2} b^{12} x^{6} + 21 \, a^{4} b^{10} x^{5} - 35 \, a^{6} b^{8} x^{4} + 35 \, a^{8} b^{6} x^{3} - 21 \, a^{10} b^{4} x^{2} + 7 \, a^{12} b^{2} x - a^{14}\right)} \log\left(\sqrt{x}\right) - 4 \, {\left(105 \, a b^{13} x^{6} - 700 \, a^{3} b^{11} x^{5} + 1981 \, a^{5} b^{9} x^{4} - 3072 \, a^{7} b^{7} x^{3} + 2891 \, a^{9} b^{5} x^{2} - 980 \, a^{11} b^{3} x + 735 \, a^{13} b\right)} \sqrt{x}}{210 \, {\left(a^{8} b^{14} x^{7} - 7 \, a^{10} b^{12} x^{6} + 21 \, a^{12} b^{10} x^{5} - 35 \, a^{14} b^{8} x^{4} + 35 \, a^{16} b^{6} x^{3} - 21 \, a^{18} b^{4} x^{2} + 7 \, a^{20} b^{2} x - a^{22}\right)}}"," ",0,"-1/210*(210*a^2*b^12*x^6 - 1365*a^4*b^10*x^5 + 3745*a^6*b^8*x^4 - 5530*a^8*b^6*x^3 + 5964*a^10*b^4*x^2 - 273*a^12*b^2*x + 1089*a^14 + 420*(b^14*x^7 - 7*a^2*b^12*x^6 + 21*a^4*b^10*x^5 - 35*a^6*b^8*x^4 + 35*a^8*b^6*x^3 - 21*a^10*b^4*x^2 + 7*a^12*b^2*x - a^14)*log(b*sqrt(x) + a) - 420*(b^14*x^7 - 7*a^2*b^12*x^6 + 21*a^4*b^10*x^5 - 35*a^6*b^8*x^4 + 35*a^8*b^6*x^3 - 21*a^10*b^4*x^2 + 7*a^12*b^2*x - a^14)*log(sqrt(x)) - 4*(105*a*b^13*x^6 - 700*a^3*b^11*x^5 + 1981*a^5*b^9*x^4 - 3072*a^7*b^7*x^3 + 2891*a^9*b^5*x^2 - 980*a^11*b^3*x + 735*a^13*b)*sqrt(x))/(a^8*b^14*x^7 - 7*a^10*b^12*x^6 + 21*a^12*b^10*x^5 - 35*a^14*b^8*x^4 + 35*a^16*b^6*x^3 - 21*a^18*b^4*x^2 + 7*a^20*b^2*x - a^22)","B",0
2230,1,435,0,0.716080," ","integrate(1/x^2/(a+b*x^(1/2))^8,x, algorithm=""fricas"")","-\frac{1260 \, a^{2} b^{14} x^{7} - 8190 \, a^{4} b^{12} x^{6} + 22470 \, a^{6} b^{10} x^{5} - 33495 \, a^{8} b^{8} x^{4} + 28924 \, a^{10} b^{6} x^{3} - 13888 \, a^{12} b^{4} x^{2} + 3594 \, a^{14} b^{2} x - 35 \, a^{16} + 2520 \, {\left(b^{16} x^{8} - 7 \, a^{2} b^{14} x^{7} + 21 \, a^{4} b^{12} x^{6} - 35 \, a^{6} b^{10} x^{5} + 35 \, a^{8} b^{8} x^{4} - 21 \, a^{10} b^{6} x^{3} + 7 \, a^{12} b^{4} x^{2} - a^{14} b^{2} x\right)} \log\left(b \sqrt{x} + a\right) - 2520 \, {\left(b^{16} x^{8} - 7 \, a^{2} b^{14} x^{7} + 21 \, a^{4} b^{12} x^{6} - 35 \, a^{6} b^{10} x^{5} + 35 \, a^{8} b^{8} x^{4} - 21 \, a^{10} b^{6} x^{3} + 7 \, a^{12} b^{4} x^{2} - a^{14} b^{2} x\right)} \log\left(\sqrt{x}\right) - 8 \, {\left(315 \, a b^{15} x^{7} - 2100 \, a^{3} b^{13} x^{6} + 5943 \, a^{5} b^{11} x^{5} - 9216 \, a^{7} b^{9} x^{4} + 8393 \, a^{9} b^{7} x^{3} - 4410 \, a^{11} b^{5} x^{2} + 1225 \, a^{13} b^{3} x - 70 \, a^{15} b\right)} \sqrt{x}}{35 \, {\left(a^{10} b^{14} x^{8} - 7 \, a^{12} b^{12} x^{7} + 21 \, a^{14} b^{10} x^{6} - 35 \, a^{16} b^{8} x^{5} + 35 \, a^{18} b^{6} x^{4} - 21 \, a^{20} b^{4} x^{3} + 7 \, a^{22} b^{2} x^{2} - a^{24} x\right)}}"," ",0,"-1/35*(1260*a^2*b^14*x^7 - 8190*a^4*b^12*x^6 + 22470*a^6*b^10*x^5 - 33495*a^8*b^8*x^4 + 28924*a^10*b^6*x^3 - 13888*a^12*b^4*x^2 + 3594*a^14*b^2*x - 35*a^16 + 2520*(b^16*x^8 - 7*a^2*b^14*x^7 + 21*a^4*b^12*x^6 - 35*a^6*b^10*x^5 + 35*a^8*b^8*x^4 - 21*a^10*b^6*x^3 + 7*a^12*b^4*x^2 - a^14*b^2*x)*log(b*sqrt(x) + a) - 2520*(b^16*x^8 - 7*a^2*b^14*x^7 + 21*a^4*b^12*x^6 - 35*a^6*b^10*x^5 + 35*a^8*b^8*x^4 - 21*a^10*b^6*x^3 + 7*a^12*b^4*x^2 - a^14*b^2*x)*log(sqrt(x)) - 8*(315*a*b^15*x^7 - 2100*a^3*b^13*x^6 + 5943*a^5*b^11*x^5 - 9216*a^7*b^9*x^4 + 8393*a^9*b^7*x^3 - 4410*a^11*b^5*x^2 + 1225*a^13*b^3*x - 70*a^15*b)*sqrt(x))/(a^10*b^14*x^8 - 7*a^12*b^12*x^7 + 21*a^14*b^10*x^6 - 35*a^16*b^8*x^5 + 35*a^18*b^6*x^4 - 21*a^20*b^4*x^3 + 7*a^22*b^2*x^2 - a^24*x)","B",0
2231,1,463,0,0.748725," ","integrate(1/x^3/(a+b*x^(1/2))^8,x, algorithm=""fricas"")","-\frac{13860 \, a^{2} b^{16} x^{8} - 90090 \, a^{4} b^{14} x^{7} + 247170 \, a^{6} b^{12} x^{6} - 368445 \, a^{8} b^{10} x^{5} + 318087 \, a^{10} b^{8} x^{4} - 154532 \, a^{12} b^{6} x^{3} + 36104 \, a^{14} b^{4} x^{2} - 1365 \, a^{16} b^{2} x - 21 \, a^{18} + 27720 \, {\left(b^{18} x^{9} - 7 \, a^{2} b^{16} x^{8} + 21 \, a^{4} b^{14} x^{7} - 35 \, a^{6} b^{12} x^{6} + 35 \, a^{8} b^{10} x^{5} - 21 \, a^{10} b^{8} x^{4} + 7 \, a^{12} b^{6} x^{3} - a^{14} b^{4} x^{2}\right)} \log\left(b \sqrt{x} + a\right) - 27720 \, {\left(b^{18} x^{9} - 7 \, a^{2} b^{16} x^{8} + 21 \, a^{4} b^{14} x^{7} - 35 \, a^{6} b^{12} x^{6} + 35 \, a^{8} b^{10} x^{5} - 21 \, a^{10} b^{8} x^{4} + 7 \, a^{12} b^{6} x^{3} - a^{14} b^{4} x^{2}\right)} \log\left(\sqrt{x}\right) - 8 \, {\left(3465 \, a b^{17} x^{8} - 23100 \, a^{3} b^{15} x^{7} + 65373 \, a^{5} b^{13} x^{6} - 101376 \, a^{7} b^{11} x^{5} + 92323 \, a^{9} b^{9} x^{4} - 48580 \, a^{11} b^{7} x^{3} + 13083 \, a^{13} b^{5} x^{2} - 1064 \, a^{15} b^{3} x - 28 \, a^{17} b\right)} \sqrt{x}}{42 \, {\left(a^{12} b^{14} x^{9} - 7 \, a^{14} b^{12} x^{8} + 21 \, a^{16} b^{10} x^{7} - 35 \, a^{18} b^{8} x^{6} + 35 \, a^{20} b^{6} x^{5} - 21 \, a^{22} b^{4} x^{4} + 7 \, a^{24} b^{2} x^{3} - a^{26} x^{2}\right)}}"," ",0,"-1/42*(13860*a^2*b^16*x^8 - 90090*a^4*b^14*x^7 + 247170*a^6*b^12*x^6 - 368445*a^8*b^10*x^5 + 318087*a^10*b^8*x^4 - 154532*a^12*b^6*x^3 + 36104*a^14*b^4*x^2 - 1365*a^16*b^2*x - 21*a^18 + 27720*(b^18*x^9 - 7*a^2*b^16*x^8 + 21*a^4*b^14*x^7 - 35*a^6*b^12*x^6 + 35*a^8*b^10*x^5 - 21*a^10*b^8*x^4 + 7*a^12*b^6*x^3 - a^14*b^4*x^2)*log(b*sqrt(x) + a) - 27720*(b^18*x^9 - 7*a^2*b^16*x^8 + 21*a^4*b^14*x^7 - 35*a^6*b^12*x^6 + 35*a^8*b^10*x^5 - 21*a^10*b^8*x^4 + 7*a^12*b^6*x^3 - a^14*b^4*x^2)*log(sqrt(x)) - 8*(3465*a*b^17*x^8 - 23100*a^3*b^15*x^7 + 65373*a^5*b^13*x^6 - 101376*a^7*b^11*x^5 + 92323*a^9*b^9*x^4 - 48580*a^11*b^7*x^3 + 13083*a^13*b^5*x^2 - 1064*a^15*b^3*x - 28*a^17*b)*sqrt(x))/(a^12*b^14*x^9 - 7*a^14*b^12*x^8 + 21*a^16*b^10*x^7 - 35*a^18*b^8*x^6 + 35*a^20*b^6*x^5 - 21*a^22*b^4*x^4 + 7*a^24*b^2*x^3 - a^26*x^2)","B",0
2232,1,15,0,0.698945," ","integrate(1/x/(2+b*x^(1/2)),x, algorithm=""fricas"")","-\log\left(b \sqrt{x} + 2\right) + \log\left(\sqrt{x}\right)"," ",0,"-log(b*sqrt(x) + 2) + log(sqrt(x))","A",0
2233,1,77,0,0.829006," ","integrate(x^2*(a+b*x^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{4 \, {\left(693 \, b^{6} x^{3} - 70 \, a^{2} b^{4} x^{2} - 96 \, a^{4} b^{2} x - 256 \, a^{6} + {\left(63 \, a b^{5} x^{2} + 80 \, a^{3} b^{3} x + 128 \, a^{5} b\right)} \sqrt{x}\right)} \sqrt{b \sqrt{x} + a}}{9009 \, b^{6}}"," ",0,"4/9009*(693*b^6*x^3 - 70*a^2*b^4*x^2 - 96*a^4*b^2*x - 256*a^6 + (63*a*b^5*x^2 + 80*a^3*b^3*x + 128*a^5*b)*sqrt(x))*sqrt(b*sqrt(x) + a)/b^6","A",0
2234,1,55,0,2.879519," ","integrate(x*(a+b*x^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{4 \, {\left(35 \, b^{4} x^{2} - 6 \, a^{2} b^{2} x - 16 \, a^{4} + {\left(5 \, a b^{3} x + 8 \, a^{3} b\right)} \sqrt{x}\right)} \sqrt{b \sqrt{x} + a}}{315 \, b^{4}}"," ",0,"4/315*(35*b^4*x^2 - 6*a^2*b^2*x - 16*a^4 + (5*a*b^3*x + 8*a^3*b)*sqrt(x))*sqrt(b*sqrt(x) + a)/b^4","A",0
2235,1,32,0,0.785402," ","integrate((a+b*x^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{4 \, {\left(3 \, b^{2} x + a b \sqrt{x} - 2 \, a^{2}\right)} \sqrt{b \sqrt{x} + a}}{15 \, b^{2}}"," ",0,"4/15*(3*b^2*x + a*b*sqrt(x) - 2*a^2)*sqrt(b*sqrt(x) + a)/b^2","A",0
2236,1,88,0,2.963999," ","integrate((a+b*x^(1/2))^(1/2)/x,x, algorithm=""fricas"")","\left[2 \, \sqrt{a} \log\left(\frac{b x - 2 \, \sqrt{b \sqrt{x} + a} \sqrt{a} \sqrt{x} + 2 \, a \sqrt{x}}{x}\right) + 4 \, \sqrt{b \sqrt{x} + a}, 4 \, \sqrt{-a} \arctan\left(\frac{\sqrt{b \sqrt{x} + a} \sqrt{-a}}{a}\right) + 4 \, \sqrt{b \sqrt{x} + a}\right]"," ",0,"[2*sqrt(a)*log((b*x - 2*sqrt(b*sqrt(x) + a)*sqrt(a)*sqrt(x) + 2*a*sqrt(x))/x) + 4*sqrt(b*sqrt(x) + a), 4*sqrt(-a)*arctan(sqrt(b*sqrt(x) + a)*sqrt(-a)/a) + 4*sqrt(b*sqrt(x) + a)]","A",0
2237,1,133,0,0.891336," ","integrate((a+b*x^(1/2))^(1/2)/x^2,x, algorithm=""fricas"")","\left[\frac{\sqrt{a} b^{2} x \log\left(\frac{b x + 2 \, \sqrt{b \sqrt{x} + a} \sqrt{a} \sqrt{x} + 2 \, a \sqrt{x}}{x}\right) - 2 \, {\left(a b \sqrt{x} + 2 \, a^{2}\right)} \sqrt{b \sqrt{x} + a}}{4 \, a^{2} x}, -\frac{\sqrt{-a} b^{2} x \arctan\left(\frac{\sqrt{b \sqrt{x} + a} \sqrt{-a}}{a}\right) + {\left(a b \sqrt{x} + 2 \, a^{2}\right)} \sqrt{b \sqrt{x} + a}}{2 \, a^{2} x}\right]"," ",0,"[1/4*(sqrt(a)*b^2*x*log((b*x + 2*sqrt(b*sqrt(x) + a)*sqrt(a)*sqrt(x) + 2*a*sqrt(x))/x) - 2*(a*b*sqrt(x) + 2*a^2)*sqrt(b*sqrt(x) + a))/(a^2*x), -1/2*(sqrt(-a)*b^2*x*arctan(sqrt(b*sqrt(x) + a)*sqrt(-a)/a) + (a*b*sqrt(x) + 2*a^2)*sqrt(b*sqrt(x) + a))/(a^2*x)]","A",0
2238,1,184,0,0.839146," ","integrate((a+b*x^(1/2))^(1/2)/x^3,x, algorithm=""fricas"")","\left[\frac{15 \, \sqrt{a} b^{4} x^{2} \log\left(\frac{b x + 2 \, \sqrt{b \sqrt{x} + a} \sqrt{a} \sqrt{x} + 2 \, a \sqrt{x}}{x}\right) + 2 \, {\left(10 \, a^{2} b^{2} x - 48 \, a^{4} - {\left(15 \, a b^{3} x + 8 \, a^{3} b\right)} \sqrt{x}\right)} \sqrt{b \sqrt{x} + a}}{192 \, a^{4} x^{2}}, -\frac{15 \, \sqrt{-a} b^{4} x^{2} \arctan\left(\frac{\sqrt{b \sqrt{x} + a} \sqrt{-a}}{a}\right) - {\left(10 \, a^{2} b^{2} x - 48 \, a^{4} - {\left(15 \, a b^{3} x + 8 \, a^{3} b\right)} \sqrt{x}\right)} \sqrt{b \sqrt{x} + a}}{96 \, a^{4} x^{2}}\right]"," ",0,"[1/192*(15*sqrt(a)*b^4*x^2*log((b*x + 2*sqrt(b*sqrt(x) + a)*sqrt(a)*sqrt(x) + 2*a*sqrt(x))/x) + 2*(10*a^2*b^2*x - 48*a^4 - (15*a*b^3*x + 8*a^3*b)*sqrt(x))*sqrt(b*sqrt(x) + a))/(a^4*x^2), -1/96*(15*sqrt(-a)*b^4*x^2*arctan(sqrt(b*sqrt(x) + a)*sqrt(-a)/a) - (10*a^2*b^2*x - 48*a^4 - (15*a*b^3*x + 8*a^3*b)*sqrt(x))*sqrt(b*sqrt(x) + a))/(a^4*x^2)]","A",0
2239,1,67,0,0.800038," ","integrate(x^2/(a+b*x^(1/2))^(1/2),x, algorithm=""fricas"")","-\frac{4 \, {\left(70 \, a b^{4} x^{2} + 96 \, a^{3} b^{2} x + 256 \, a^{5} - {\left(63 \, b^{5} x^{2} + 80 \, a^{2} b^{3} x + 128 \, a^{4} b\right)} \sqrt{x}\right)} \sqrt{b \sqrt{x} + a}}{693 \, b^{6}}"," ",0,"-4/693*(70*a*b^4*x^2 + 96*a^3*b^2*x + 256*a^5 - (63*b^5*x^2 + 80*a^2*b^3*x + 128*a^4*b)*sqrt(x))*sqrt(b*sqrt(x) + a)/b^6","A",0
2240,1,45,0,0.848911," ","integrate(x/(a+b*x^(1/2))^(1/2),x, algorithm=""fricas"")","-\frac{4 \, {\left(6 \, a b^{2} x + 16 \, a^{3} - {\left(5 \, b^{3} x + 8 \, a^{2} b\right)} \sqrt{x}\right)} \sqrt{b \sqrt{x} + a}}{35 \, b^{4}}"," ",0,"-4/35*(6*a*b^2*x + 16*a^3 - (5*b^3*x + 8*a^2*b)*sqrt(x))*sqrt(b*sqrt(x) + a)/b^4","A",0
2241,1,23,0,0.859869," ","integrate(1/(a+b*x^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{4 \, \sqrt{b \sqrt{x} + a} {\left(b \sqrt{x} - 2 \, a\right)}}{3 \, b^{2}}"," ",0,"4/3*sqrt(b*sqrt(x) + a)*(b*sqrt(x) - 2*a)/b^2","A",0
2242,1,67,0,0.871561," ","integrate(1/x/(a+b*x^(1/2))^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, \log\left(\frac{b x - 2 \, \sqrt{b \sqrt{x} + a} \sqrt{a} \sqrt{x} + 2 \, a \sqrt{x}}{x}\right)}{\sqrt{a}}, \frac{4 \, \sqrt{-a} \arctan\left(\frac{\sqrt{b \sqrt{x} + a} \sqrt{-a}}{a}\right)}{a}\right]"," ",0,"[2*log((b*x - 2*sqrt(b*sqrt(x) + a)*sqrt(a)*sqrt(x) + 2*a*sqrt(x))/x)/sqrt(a), 4*sqrt(-a)*arctan(sqrt(b*sqrt(x) + a)*sqrt(-a)/a)/a]","A",0
2243,1,137,0,0.916011," ","integrate(1/x^2/(a+b*x^(1/2))^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{a} b^{2} x \log\left(\frac{b x - 2 \, \sqrt{b \sqrt{x} + a} \sqrt{a} \sqrt{x} + 2 \, a \sqrt{x}}{x}\right) + 2 \, {\left(3 \, a b \sqrt{x} - 2 \, a^{2}\right)} \sqrt{b \sqrt{x} + a}}{4 \, a^{3} x}, \frac{3 \, \sqrt{-a} b^{2} x \arctan\left(\frac{\sqrt{b \sqrt{x} + a} \sqrt{-a}}{a}\right) + {\left(3 \, a b \sqrt{x} - 2 \, a^{2}\right)} \sqrt{b \sqrt{x} + a}}{2 \, a^{3} x}\right]"," ",0,"[1/4*(3*sqrt(a)*b^2*x*log((b*x - 2*sqrt(b*sqrt(x) + a)*sqrt(a)*sqrt(x) + 2*a*sqrt(x))/x) + 2*(3*a*b*sqrt(x) - 2*a^2)*sqrt(b*sqrt(x) + a))/(a^3*x), 1/2*(3*sqrt(-a)*b^2*x*arctan(sqrt(b*sqrt(x) + a)*sqrt(-a)/a) + (3*a*b*sqrt(x) - 2*a^2)*sqrt(b*sqrt(x) + a))/(a^3*x)]","A",0
2244,1,184,0,0.918267," ","integrate(1/x^3/(a+b*x^(1/2))^(1/2),x, algorithm=""fricas"")","\left[\frac{105 \, \sqrt{a} b^{4} x^{2} \log\left(\frac{b x - 2 \, \sqrt{b \sqrt{x} + a} \sqrt{a} \sqrt{x} + 2 \, a \sqrt{x}}{x}\right) - 2 \, {\left(70 \, a^{2} b^{2} x + 48 \, a^{4} - 7 \, {\left(15 \, a b^{3} x + 8 \, a^{3} b\right)} \sqrt{x}\right)} \sqrt{b \sqrt{x} + a}}{192 \, a^{5} x^{2}}, \frac{105 \, \sqrt{-a} b^{4} x^{2} \arctan\left(\frac{\sqrt{b \sqrt{x} + a} \sqrt{-a}}{a}\right) - {\left(70 \, a^{2} b^{2} x + 48 \, a^{4} - 7 \, {\left(15 \, a b^{3} x + 8 \, a^{3} b\right)} \sqrt{x}\right)} \sqrt{b \sqrt{x} + a}}{96 \, a^{5} x^{2}}\right]"," ",0,"[1/192*(105*sqrt(a)*b^4*x^2*log((b*x - 2*sqrt(b*sqrt(x) + a)*sqrt(a)*sqrt(x) + 2*a*sqrt(x))/x) - 2*(70*a^2*b^2*x + 48*a^4 - 7*(15*a*b^3*x + 8*a^3*b)*sqrt(x))*sqrt(b*sqrt(x) + a))/(a^5*x^2), 1/96*(105*sqrt(-a)*b^4*x^2*arctan(sqrt(b*sqrt(x) + a)*sqrt(-a)/a) - (70*a^2*b^2*x + 48*a^4 - 7*(15*a*b^3*x + 8*a^3*b)*sqrt(x))*sqrt(b*sqrt(x) + a))/(a^5*x^2)]","A",0
2245,1,98,0,0.938196," ","integrate(x^(1/2)*(a+b*x^(1/2))^n,x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, a^{3} + {\left(a b^{2} n^{2} + a b^{2} n\right)} x - {\left(2 \, a^{2} b n - {\left(b^{3} n^{2} + 3 \, b^{3} n + 2 \, b^{3}\right)} x\right)} \sqrt{x}\right)} {\left(b \sqrt{x} + a\right)}^{n}}{b^{3} n^{3} + 6 \, b^{3} n^{2} + 11 \, b^{3} n + 6 \, b^{3}}"," ",0,"2*(2*a^3 + (a*b^2*n^2 + a*b^2*n)*x - (2*a^2*b*n - (b^3*n^2 + 3*b^3*n + 2*b^3)*x)*sqrt(x))*(b*sqrt(x) + a)^n/(b^3*n^3 + 6*b^3*n^2 + 11*b^3*n + 6*b^3)","A",0
2246,1,25,0,0.903113," ","integrate((a+b*x^(1/2))^n/x^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(b \sqrt{x} + a\right)} {\left(b \sqrt{x} + a\right)}^{n}}{b n + b}"," ",0,"2*(b*sqrt(x) + a)*(b*sqrt(x) + a)^n/(b*n + b)","A",0
2247,1,7,0,0.718428," ","integrate((1+x^(1/2))/x^(1/2),x, algorithm=""fricas"")","x + 2 \, \sqrt{x}"," ",0,"x + 2*sqrt(x)","A",0
2248,1,12,0,0.664681," ","integrate((1+x^(1/2))^2/x^(1/2),x, algorithm=""fricas"")","\frac{2}{3} \, {\left(x + 3\right)} \sqrt{x} + 2 \, x"," ",0,"2/3*(x + 3)*sqrt(x) + 2*x","A",0
2249,1,17,0,0.788228," ","integrate((1+x^(1/2))^3/x^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, x^{2} + 2 \, {\left(x + 1\right)} \sqrt{x} + 3 \, x"," ",0,"1/2*x^2 + 2*(x + 1)*sqrt(x) + 3*x","A",0
2250,1,15,0,0.597717," ","integrate(x^(1/2)/(1+x^(1/2)),x, algorithm=""fricas"")","x - 2 \, \sqrt{x} + 2 \, \log\left(\sqrt{x} + 1\right)"," ",0,"x - 2*sqrt(x) + 2*log(sqrt(x) + 1)","A",0
2251,1,8,0,0.829209," ","integrate(1/x^(1/2)/(1+x^(1/2)),x, algorithm=""fricas"")","2 \, \log\left(\sqrt{x} + 1\right)"," ",0,"2*log(sqrt(x) + 1)","A",0
2252,1,12,0,0.785964," ","integrate(1/x^(1/2)/(1+x^(1/2))^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(\sqrt{x} - 1\right)}}{x - 1}"," ",0,"-2*(sqrt(x) - 1)/(x - 1)","A",0
2253,1,20,0,0.741466," ","integrate(1/x^(1/2)/(1+x^(1/2))^3,x, algorithm=""fricas"")","-\frac{x - 2 \, \sqrt{x} + 1}{x^{2} - 2 \, x + 1}"," ",0,"-(x - 2*sqrt(x) + 1)/(x^2 - 2*x + 1)","B",0
2254,1,23,0,0.562415," ","integrate(x^(1/2)*(1+x^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{4}{105} \, {\left({\left(15 \, x - 4\right)} \sqrt{x} + 3 \, x + 8\right)} \sqrt{\sqrt{x} + 1}"," ",0,"4/105*((15*x - 4)*sqrt(x) + 3*x + 8)*sqrt(sqrt(x) + 1)","A",0
2255,1,9,0,0.747041," ","integrate((1+x^(1/2))^(1/2)/x^(1/2),x, algorithm=""fricas"")","\frac{4}{3} \, {\left(\sqrt{x} + 1\right)}^{\frac{3}{2}}"," ",0,"4/3*(sqrt(x) + 1)^(3/2)","A",0
2256,1,50,0,0.827696," ","integrate(x^(1/3)/(1+x^(1/2)),x, algorithm=""fricas"")","2 \, \sqrt{3} \arctan\left(\frac{2}{3} \, \sqrt{3} x^{\frac{1}{6}} - \frac{1}{3} \, \sqrt{3}\right) + \frac{6}{5} \, x^{\frac{5}{6}} - 3 \, x^{\frac{1}{3}} + \log\left(x^{\frac{1}{3}} - x^{\frac{1}{6}} + 1\right) - 2 \, \log\left(x^{\frac{1}{6}} + 1\right)"," ",0,"2*sqrt(3)*arctan(2/3*sqrt(3)*x^(1/6) - 1/3*sqrt(3)) + 6/5*x^(5/6) - 3*x^(1/3) + log(x^(1/3) - x^(1/6) + 1) - 2*log(x^(1/6) + 1)","A",0
2257,1,260,0,0.885987," ","integrate(x^m*(a+b*x^(1/2))^4,x, algorithm=""fricas"")","\frac{{\left({\left(4 \, b^{4} m^{4} + 28 \, b^{4} m^{3} + 71 \, b^{4} m^{2} + 77 \, b^{4} m + 30 \, b^{4}\right)} x^{3} + 6 \, {\left(4 \, a^{2} b^{2} m^{4} + 32 \, a^{2} b^{2} m^{3} + 91 \, a^{2} b^{2} m^{2} + 108 \, a^{2} b^{2} m + 45 \, a^{2} b^{2}\right)} x^{2} + {\left(4 \, a^{4} m^{4} + 36 \, a^{4} m^{3} + 119 \, a^{4} m^{2} + 171 \, a^{4} m + 90 \, a^{4}\right)} x + 8 \, {\left({\left(2 \, a b^{3} m^{4} + 15 \, a b^{3} m^{3} + 40 \, a b^{3} m^{2} + 45 \, a b^{3} m + 18 \, a b^{3}\right)} x^{2} + {\left(2 \, a^{3} b m^{4} + 17 \, a^{3} b m^{3} + 52 \, a^{3} b m^{2} + 67 \, a^{3} b m + 30 \, a^{3} b\right)} x\right)} \sqrt{x}\right)} x^{m}}{4 \, m^{5} + 40 \, m^{4} + 155 \, m^{3} + 290 \, m^{2} + 261 \, m + 90}"," ",0,"((4*b^4*m^4 + 28*b^4*m^3 + 71*b^4*m^2 + 77*b^4*m + 30*b^4)*x^3 + 6*(4*a^2*b^2*m^4 + 32*a^2*b^2*m^3 + 91*a^2*b^2*m^2 + 108*a^2*b^2*m + 45*a^2*b^2)*x^2 + (4*a^4*m^4 + 36*a^4*m^3 + 119*a^4*m^2 + 171*a^4*m + 90*a^4)*x + 8*((2*a*b^3*m^4 + 15*a*b^3*m^3 + 40*a*b^3*m^2 + 45*a*b^3*m + 18*a*b^3)*x^2 + (2*a^3*b*m^4 + 17*a^3*b*m^3 + 52*a^3*b*m^2 + 67*a^3*b*m + 30*a^3*b)*x)*sqrt(x))*x^m/(4*m^5 + 40*m^4 + 155*m^3 + 290*m^2 + 261*m + 90)","B",0
2258,1,167,0,0.891177," ","integrate(x^m*(a+b*x^(1/2))^3,x, algorithm=""fricas"")","\frac{{\left(3 \, {\left(4 \, a b^{2} m^{3} + 20 \, a b^{2} m^{2} + 31 \, a b^{2} m + 15 \, a b^{2}\right)} x^{2} + {\left(4 \, a^{3} m^{3} + 24 \, a^{3} m^{2} + 47 \, a^{3} m + 30 \, a^{3}\right)} x + 2 \, {\left({\left(2 \, b^{3} m^{3} + 9 \, b^{3} m^{2} + 13 \, b^{3} m + 6 \, b^{3}\right)} x^{2} + 3 \, {\left(2 \, a^{2} b m^{3} + 11 \, a^{2} b m^{2} + 19 \, a^{2} b m + 10 \, a^{2} b\right)} x\right)} \sqrt{x}\right)} x^{m}}{4 \, m^{4} + 28 \, m^{3} + 71 \, m^{2} + 77 \, m + 30}"," ",0,"(3*(4*a*b^2*m^3 + 20*a*b^2*m^2 + 31*a*b^2*m + 15*a*b^2)*x^2 + (4*a^3*m^3 + 24*a^3*m^2 + 47*a^3*m + 30*a^3)*x + 2*((2*b^3*m^3 + 9*b^3*m^2 + 13*b^3*m + 6*b^3)*x^2 + 3*(2*a^2*b*m^3 + 11*a^2*b*m^2 + 19*a^2*b*m + 10*a^2*b)*x)*sqrt(x))*x^m/(4*m^4 + 28*m^3 + 71*m^2 + 77*m + 30)","B",0
2259,1,89,0,0.854028," ","integrate(x^m*(a+b*x^(1/2))^2,x, algorithm=""fricas"")","\frac{{\left({\left(2 \, b^{2} m^{2} + 5 \, b^{2} m + 3 \, b^{2}\right)} x^{2} + 4 \, {\left(a b m^{2} + 3 \, a b m + 2 \, a b\right)} x^{\frac{3}{2}} + {\left(2 \, a^{2} m^{2} + 7 \, a^{2} m + 6 \, a^{2}\right)} x\right)} x^{m}}{2 \, m^{3} + 9 \, m^{2} + 13 \, m + 6}"," ",0,"((2*b^2*m^2 + 5*b^2*m + 3*b^2)*x^2 + 4*(a*b*m^2 + 3*a*b*m + 2*a*b)*x^(3/2) + (2*a^2*m^2 + 7*a^2*m + 6*a^2)*x)*x^m/(2*m^3 + 9*m^2 + 13*m + 6)","A",0
2260,1,37,0,0.820885," ","integrate(x^m*(a+b*x^(1/2)),x, algorithm=""fricas"")","\frac{{\left(2 \, {\left(b m + b\right)} x^{\frac{3}{2}} + {\left(2 \, a m + 3 \, a\right)} x\right)} x^{m}}{2 \, m^{2} + 5 \, m + 3}"," ",0,"(2*(b*m + b)*x^(3/2) + (2*a*m + 3*a)*x)*x^m/(2*m^2 + 5*m + 3)","A",0
2261,0,0,0,0.774443," ","integrate(x^m/(a+b*x^(1/2)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \sqrt{x} x^{m} - a x^{m}}{b^{2} x - a^{2}}, x\right)"," ",0,"integral((b*sqrt(x)*x^m - a*x^m)/(b^2*x - a^2), x)","F",0
2262,0,0,0,0.848000," ","integrate(x^m/(a+b*x^(1/2))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{2 \, a b \sqrt{x} x^{m} - {\left(b^{2} x + a^{2}\right)} x^{m}}{b^{4} x^{2} - 2 \, a^{2} b^{2} x + a^{4}}, x\right)"," ",0,"integral(-(2*a*b*sqrt(x)*x^m - (b^2*x + a^2)*x^m)/(b^4*x^2 - 2*a^2*b^2*x + a^4), x)","F",0
2263,-2,0,0,0.000000," ","integrate(x^m*(a+b*x^(1/2))^p,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   alglogextint: unimplemented","F(-2)",0
2264,1,458,0,0.994108," ","integrate(x^3*(a+b*x^(1/2))^p,x, algorithm=""fricas"")","-\frac{2 \, {\left(5040 \, a^{8} - {\left(b^{8} p^{7} + 28 \, b^{8} p^{6} + 322 \, b^{8} p^{5} + 1960 \, b^{8} p^{4} + 6769 \, b^{8} p^{3} + 13132 \, b^{8} p^{2} + 13068 \, b^{8} p + 5040 \, b^{8}\right)} x^{4} + 7 \, {\left(a^{2} b^{6} p^{6} + 15 \, a^{2} b^{6} p^{5} + 85 \, a^{2} b^{6} p^{4} + 225 \, a^{2} b^{6} p^{3} + 274 \, a^{2} b^{6} p^{2} + 120 \, a^{2} b^{6} p\right)} x^{3} + 210 \, {\left(a^{4} b^{4} p^{4} + 6 \, a^{4} b^{4} p^{3} + 11 \, a^{4} b^{4} p^{2} + 6 \, a^{4} b^{4} p\right)} x^{2} + 2520 \, {\left(a^{6} b^{2} p^{2} + a^{6} b^{2} p\right)} x - {\left(5040 \, a^{7} b p + {\left(a b^{7} p^{7} + 21 \, a b^{7} p^{6} + 175 \, a b^{7} p^{5} + 735 \, a b^{7} p^{4} + 1624 \, a b^{7} p^{3} + 1764 \, a b^{7} p^{2} + 720 \, a b^{7} p\right)} x^{3} + 42 \, {\left(a^{3} b^{5} p^{5} + 10 \, a^{3} b^{5} p^{4} + 35 \, a^{3} b^{5} p^{3} + 50 \, a^{3} b^{5} p^{2} + 24 \, a^{3} b^{5} p\right)} x^{2} + 840 \, {\left(a^{5} b^{3} p^{3} + 3 \, a^{5} b^{3} p^{2} + 2 \, a^{5} b^{3} p\right)} x\right)} \sqrt{x}\right)} {\left(b \sqrt{x} + a\right)}^{p}}{b^{8} p^{8} + 36 \, b^{8} p^{7} + 546 \, b^{8} p^{6} + 4536 \, b^{8} p^{5} + 22449 \, b^{8} p^{4} + 67284 \, b^{8} p^{3} + 118124 \, b^{8} p^{2} + 109584 \, b^{8} p + 40320 \, b^{8}}"," ",0,"-2*(5040*a^8 - (b^8*p^7 + 28*b^8*p^6 + 322*b^8*p^5 + 1960*b^8*p^4 + 6769*b^8*p^3 + 13132*b^8*p^2 + 13068*b^8*p + 5040*b^8)*x^4 + 7*(a^2*b^6*p^6 + 15*a^2*b^6*p^5 + 85*a^2*b^6*p^4 + 225*a^2*b^6*p^3 + 274*a^2*b^6*p^2 + 120*a^2*b^6*p)*x^3 + 210*(a^4*b^4*p^4 + 6*a^4*b^4*p^3 + 11*a^4*b^4*p^2 + 6*a^4*b^4*p)*x^2 + 2520*(a^6*b^2*p^2 + a^6*b^2*p)*x - (5040*a^7*b*p + (a*b^7*p^7 + 21*a*b^7*p^6 + 175*a*b^7*p^5 + 735*a*b^7*p^4 + 1624*a*b^7*p^3 + 1764*a*b^7*p^2 + 720*a*b^7*p)*x^3 + 42*(a^3*b^5*p^5 + 10*a^3*b^5*p^4 + 35*a^3*b^5*p^3 + 50*a^3*b^5*p^2 + 24*a^3*b^5*p)*x^2 + 840*(a^5*b^3*p^3 + 3*a^5*b^3*p^2 + 2*a^5*b^3*p)*x)*sqrt(x))*(b*sqrt(x) + a)^p/(b^8*p^8 + 36*b^8*p^7 + 546*b^8*p^6 + 4536*b^8*p^5 + 22449*b^8*p^4 + 67284*b^8*p^3 + 118124*b^8*p^2 + 109584*b^8*p + 40320*b^8)","B",0
2265,1,281,0,0.977717," ","integrate(x^2*(a+b*x^(1/2))^p,x, algorithm=""fricas"")","-\frac{2 \, {\left(120 \, a^{6} - {\left(b^{6} p^{5} + 15 \, b^{6} p^{4} + 85 \, b^{6} p^{3} + 225 \, b^{6} p^{2} + 274 \, b^{6} p + 120 \, b^{6}\right)} x^{3} + 5 \, {\left(a^{2} b^{4} p^{4} + 6 \, a^{2} b^{4} p^{3} + 11 \, a^{2} b^{4} p^{2} + 6 \, a^{2} b^{4} p\right)} x^{2} + 60 \, {\left(a^{4} b^{2} p^{2} + a^{4} b^{2} p\right)} x - {\left(120 \, a^{5} b p + {\left(a b^{5} p^{5} + 10 \, a b^{5} p^{4} + 35 \, a b^{5} p^{3} + 50 \, a b^{5} p^{2} + 24 \, a b^{5} p\right)} x^{2} + 20 \, {\left(a^{3} b^{3} p^{3} + 3 \, a^{3} b^{3} p^{2} + 2 \, a^{3} b^{3} p\right)} x\right)} \sqrt{x}\right)} {\left(b \sqrt{x} + a\right)}^{p}}{b^{6} p^{6} + 21 \, b^{6} p^{5} + 175 \, b^{6} p^{4} + 735 \, b^{6} p^{3} + 1624 \, b^{6} p^{2} + 1764 \, b^{6} p + 720 \, b^{6}}"," ",0,"-2*(120*a^6 - (b^6*p^5 + 15*b^6*p^4 + 85*b^6*p^3 + 225*b^6*p^2 + 274*b^6*p + 120*b^6)*x^3 + 5*(a^2*b^4*p^4 + 6*a^2*b^4*p^3 + 11*a^2*b^4*p^2 + 6*a^2*b^4*p)*x^2 + 60*(a^4*b^2*p^2 + a^4*b^2*p)*x - (120*a^5*b*p + (a*b^5*p^5 + 10*a*b^5*p^4 + 35*a*b^5*p^3 + 50*a*b^5*p^2 + 24*a*b^5*p)*x^2 + 20*(a^3*b^3*p^3 + 3*a^3*b^3*p^2 + 2*a^3*b^3*p)*x)*sqrt(x))*(b*sqrt(x) + a)^p/(b^6*p^6 + 21*b^6*p^5 + 175*b^6*p^4 + 735*b^6*p^3 + 1624*b^6*p^2 + 1764*b^6*p + 720*b^6)","B",0
2266,1,148,0,1.201949," ","integrate(x*(a+b*x^(1/2))^p,x, algorithm=""fricas"")","-\frac{2 \, {\left(6 \, a^{4} - {\left(b^{4} p^{3} + 6 \, b^{4} p^{2} + 11 \, b^{4} p + 6 \, b^{4}\right)} x^{2} + 3 \, {\left(a^{2} b^{2} p^{2} + a^{2} b^{2} p\right)} x - {\left(6 \, a^{3} b p + {\left(a b^{3} p^{3} + 3 \, a b^{3} p^{2} + 2 \, a b^{3} p\right)} x\right)} \sqrt{x}\right)} {\left(b \sqrt{x} + a\right)}^{p}}{b^{4} p^{4} + 10 \, b^{4} p^{3} + 35 \, b^{4} p^{2} + 50 \, b^{4} p + 24 \, b^{4}}"," ",0,"-2*(6*a^4 - (b^4*p^3 + 6*b^4*p^2 + 11*b^4*p + 6*b^4)*x^2 + 3*(a^2*b^2*p^2 + a^2*b^2*p)*x - (6*a^3*b*p + (a*b^3*p^3 + 3*a*b^3*p^2 + 2*a*b^3*p)*x)*sqrt(x))*(b*sqrt(x) + a)^p/(b^4*p^4 + 10*b^4*p^3 + 35*b^4*p^2 + 50*b^4*p + 24*b^4)","A",0
2267,1,56,0,1.009779," ","integrate((a+b*x^(1/2))^p,x, algorithm=""fricas"")","\frac{2 \, {\left(a b p \sqrt{x} - a^{2} + {\left(b^{2} p + b^{2}\right)} x\right)} {\left(b \sqrt{x} + a\right)}^{p}}{b^{2} p^{2} + 3 \, b^{2} p + 2 \, b^{2}}"," ",0,"2*(a*b*p*sqrt(x) - a^2 + (b^2*p + b^2)*x)*(b*sqrt(x) + a)^p/(b^2*p^2 + 3*b^2*p + 2*b^2)","A",0
2268,0,0,0,1.264591," ","integrate((a+b*x^(1/2))^p/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \sqrt{x} + a\right)}^{p}}{x}, x\right)"," ",0,"integral((b*sqrt(x) + a)^p/x, x)","F",0
2269,0,0,0,1.611559," ","integrate((a+b*x^(1/2))^p/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \sqrt{x} + a\right)}^{p}}{x^{2}}, x\right)"," ",0,"integral((b*sqrt(x) + a)^p/x^2, x)","F",0
2270,1,8,0,1.777829," ","integrate(x^(1/2)/(1+x^(3/2)),x, algorithm=""fricas"")","\frac{2}{3} \, \log\left(x^{\frac{3}{2}} + 1\right)"," ",0,"2/3*log(x^(3/2) + 1)","A",0
2271,-1,0,0,0.000000," ","integrate(x^3/(a+b*x^(3/2))^(2/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2272,-1,0,0,0.000000," ","integrate(1/(a+b*x^(3/2))^(2/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2273,1,27,0,2.207089," ","integrate(1/x^3/(a+b*x^(3/2))^(2/3),x, algorithm=""fricas"")","\frac{{\left(3 \, b x^{\frac{3}{2}} - a\right)} {\left(b x^{\frac{3}{2}} + a\right)}^{\frac{1}{3}}}{2 \, a^{2} x^{2}}"," ",0,"1/2*(3*b*x^(3/2) - a)*(b*x^(3/2) + a)^(1/3)/(a^2*x^2)","A",0
2274,1,53,0,2.100031," ","integrate(1/x^6/(a+b*x^(3/2))^(2/3),x, algorithm=""fricas"")","-\frac{{\left(27 \, a b^{2} x^{3} + 14 \, a^{3} - 9 \, {\left(9 \, b^{3} x^{4} + 2 \, a^{2} b x\right)} \sqrt{x}\right)} {\left(b x^{\frac{3}{2}} + a\right)}^{\frac{1}{3}}}{70 \, a^{4} x^{5}}"," ",0,"-1/70*(27*a*b^2*x^3 + 14*a^3 - 9*(9*b^3*x^4 + 2*a^2*b*x)*sqrt(x))*(b*x^(3/2) + a)^(1/3)/(a^4*x^5)","A",0
2275,1,75,0,2.170838," ","integrate(1/x^9/(a+b*x^(3/2))^(2/3),x, algorithm=""fricas"")","-\frac{{\left(243 \, a b^{4} x^{6} + 126 \, a^{3} b^{2} x^{3} + 91 \, a^{5} - 3 \, {\left(243 \, b^{5} x^{7} + 54 \, a^{2} b^{3} x^{4} + 35 \, a^{4} b x\right)} \sqrt{x}\right)} {\left(b x^{\frac{3}{2}} + a\right)}^{\frac{1}{3}}}{728 \, a^{6} x^{8}}"," ",0,"-1/728*(243*a*b^4*x^6 + 126*a^3*b^2*x^3 + 91*a^5 - 3*(243*b^5*x^7 + 54*a^2*b^3*x^4 + 35*a^4*b*x)*sqrt(x))*(b*x^(3/2) + a)^(1/3)/(a^6*x^8)","A",0
2276,1,72,0,2.077632," ","integrate(x^8/(a+b*x^(3/2))^(2/3),x, algorithm=""fricas"")","-\frac{{\left(105 \, a b^{4} x^{6} + 162 \, a^{3} b^{2} x^{3} + 729 \, a^{5} - {\left(91 \, b^{5} x^{7} + 126 \, a^{2} b^{3} x^{4} + 243 \, a^{4} b x\right)} \sqrt{x}\right)} {\left(b x^{\frac{3}{2}} + a\right)}^{\frac{1}{3}}}{728 \, b^{6}}"," ",0,"-1/728*(105*a*b^4*x^6 + 162*a^3*b^2*x^3 + 729*a^5 - (91*b^5*x^7 + 126*a^2*b^3*x^4 + 243*a^4*b*x)*sqrt(x))*(b*x^(3/2) + a)^(1/3)/b^6","A",0
2277,1,50,0,1.662069," ","integrate(x^5/(a+b*x^(3/2))^(2/3),x, algorithm=""fricas"")","-\frac{{\left(18 \, a b^{2} x^{3} + 81 \, a^{3} - {\left(14 \, b^{3} x^{4} + 27 \, a^{2} b x\right)} \sqrt{x}\right)} {\left(b x^{\frac{3}{2}} + a\right)}^{\frac{1}{3}}}{70 \, b^{4}}"," ",0,"-1/70*(18*a*b^2*x^3 + 81*a^3 - (14*b^3*x^4 + 27*a^2*b*x)*sqrt(x))*(b*x^(3/2) + a)^(1/3)/b^4","A",0
2278,1,23,0,1.216855," ","integrate(x^2/(a+b*x^(3/2))^(2/3),x, algorithm=""fricas"")","\frac{{\left(b x^{\frac{3}{2}} + a\right)}^{\frac{1}{3}} {\left(b x^{\frac{3}{2}} - 3 \, a\right)}}{2 \, b^{2}}"," ",0,"1/2*(b*x^(3/2) + a)^(1/3)*(b*x^(3/2) - 3*a)/b^2","A",0
2279,-1,0,0,0.000000," ","integrate(1/x/(a+b*x^(3/2))^(2/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2280,-1,0,0,0.000000," ","integrate(1/x^4/(a+b*x^(3/2))^(2/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2281,0,0,0,4.779203," ","integrate(x^4/(a+b*x^(3/2))^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{\frac{11}{2}} - a x^{4}\right)} {\left(b x^{\frac{3}{2}} + a\right)}^{\frac{1}{3}}}{b^{2} x^{3} - a^{2}}, x\right)"," ",0,"integral((b*x^(11/2) - a*x^4)*(b*x^(3/2) + a)^(1/3)/(b^2*x^3 - a^2), x)","F",0
2282,0,0,0,4.730810," ","integrate(x/(a+b*x^(3/2))^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{\frac{5}{2}} - a x\right)} {\left(b x^{\frac{3}{2}} + a\right)}^{\frac{1}{3}}}{b^{2} x^{3} - a^{2}}, x\right)"," ",0,"integral((b*x^(5/2) - a*x)*(b*x^(3/2) + a)^(1/3)/(b^2*x^3 - a^2), x)","F",0
2283,0,0,0,3.571002," ","integrate(1/x^2/(a+b*x^(3/2))^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{\frac{3}{2}} + a\right)}^{\frac{1}{3}} {\left(b x^{\frac{3}{2}} - a\right)}}{b^{2} x^{5} - a^{2} x^{2}}, x\right)"," ",0,"integral((b*x^(3/2) + a)^(1/3)*(b*x^(3/2) - a)/(b^2*x^5 - a^2*x^2), x)","F",0
2284,0,0,0,4.274482," ","integrate(1/x^5/(a+b*x^(3/2))^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{\frac{3}{2}} + a\right)}^{\frac{1}{3}} {\left(b x^{\frac{3}{2}} - a\right)}}{b^{2} x^{8} - a^{2} x^{5}}, x\right)"," ",0,"integral((b*x^(3/2) + a)^(1/3)*(b*x^(3/2) - a)/(b^2*x^8 - a^2*x^5), x)","F",0
2285,1,13,0,1.035244," ","integrate((a+b*x^(1/3))*x^4,x, algorithm=""fricas"")","\frac{3}{16} \, b x^{\frac{16}{3}} + \frac{1}{5} \, a x^{5}"," ",0,"3/16*b*x^(16/3) + 1/5*a*x^5","A",0
2286,1,13,0,1.022712," ","integrate((a+b*x^(1/3))*x^3,x, algorithm=""fricas"")","\frac{3}{13} \, b x^{\frac{13}{3}} + \frac{1}{4} \, a x^{4}"," ",0,"3/13*b*x^(13/3) + 1/4*a*x^4","A",0
2287,1,13,0,1.056163," ","integrate((a+b*x^(1/3))*x^2,x, algorithm=""fricas"")","\frac{3}{10} \, b x^{\frac{10}{3}} + \frac{1}{3} \, a x^{3}"," ",0,"3/10*b*x^(10/3) + 1/3*a*x^3","A",0
2288,1,13,0,1.087877," ","integrate((a+b*x^(1/3))*x,x, algorithm=""fricas"")","\frac{3}{7} \, b x^{\frac{7}{3}} + \frac{1}{2} \, a x^{2}"," ",0,"3/7*b*x^(7/3) + 1/2*a*x^2","A",0
2289,1,10,0,1.038672," ","integrate(a+b*x^(1/3),x, algorithm=""fricas"")","\frac{3}{4} \, b x^{\frac{4}{3}} + a x"," ",0,"3/4*b*x^(4/3) + a*x","A",0
2290,1,14,0,1.065889," ","integrate((a+b*x^(1/3))/x,x, algorithm=""fricas"")","3 \, a \log\left(x^{\frac{1}{3}}\right) + 3 \, b x^{\frac{1}{3}}"," ",0,"3*a*log(x^(1/3)) + 3*b*x^(1/3)","A",0
2291,1,15,0,1.084194," ","integrate((a+b*x^(1/3))/x^2,x, algorithm=""fricas"")","-\frac{3 \, b x^{\frac{1}{3}} + 2 \, a}{2 \, x}"," ",0,"-1/2*(3*b*x^(1/3) + 2*a)/x","A",0
2292,1,15,0,0.816379," ","integrate((a+b*x^(1/3))/x^3,x, algorithm=""fricas"")","-\frac{6 \, b x^{\frac{1}{3}} + 5 \, a}{10 \, x^{2}}"," ",0,"-1/10*(6*b*x^(1/3) + 5*a)/x^2","A",0
2293,1,15,0,0.615274," ","integrate((a+b*x^(1/3))/x^4,x, algorithm=""fricas"")","-\frac{9 \, b x^{\frac{1}{3}} + 8 \, a}{24 \, x^{3}}"," ",0,"-1/24*(9*b*x^(1/3) + 8*a)/x^3","A",0
2294,1,24,0,0.865375," ","integrate((a+b*x^(1/3))^2*x^4,x, algorithm=""fricas"")","\frac{3}{17} \, b^{2} x^{\frac{17}{3}} + \frac{3}{8} \, a b x^{\frac{16}{3}} + \frac{1}{5} \, a^{2} x^{5}"," ",0,"3/17*b^2*x^(17/3) + 3/8*a*b*x^(16/3) + 1/5*a^2*x^5","A",0
2295,1,24,0,0.671307," ","integrate((a+b*x^(1/3))^2*x^3,x, algorithm=""fricas"")","\frac{3}{14} \, b^{2} x^{\frac{14}{3}} + \frac{6}{13} \, a b x^{\frac{13}{3}} + \frac{1}{4} \, a^{2} x^{4}"," ",0,"3/14*b^2*x^(14/3) + 6/13*a*b*x^(13/3) + 1/4*a^2*x^4","A",0
2296,1,24,0,0.711165," ","integrate((a+b*x^(1/3))^2*x^2,x, algorithm=""fricas"")","\frac{3}{11} \, b^{2} x^{\frac{11}{3}} + \frac{3}{5} \, a b x^{\frac{10}{3}} + \frac{1}{3} \, a^{2} x^{3}"," ",0,"3/11*b^2*x^(11/3) + 3/5*a*b*x^(10/3) + 1/3*a^2*x^3","A",0
2297,1,24,0,0.621437," ","integrate((a+b*x^(1/3))^2*x,x, algorithm=""fricas"")","\frac{3}{8} \, b^{2} x^{\frac{8}{3}} + \frac{6}{7} \, a b x^{\frac{7}{3}} + \frac{1}{2} \, a^{2} x^{2}"," ",0,"3/8*b^2*x^(8/3) + 6/7*a*b*x^(7/3) + 1/2*a^2*x^2","A",0
2298,1,21,0,0.926632," ","integrate((a+b*x^(1/3))^2,x, algorithm=""fricas"")","\frac{3}{5} \, b^{2} x^{\frac{5}{3}} + \frac{3}{2} \, a b x^{\frac{4}{3}} + a^{2} x"," ",0,"3/5*b^2*x^(5/3) + 3/2*a*b*x^(4/3) + a^2*x","A",0
2299,1,25,0,0.934357," ","integrate((a+b*x^(1/3))^2/x,x, algorithm=""fricas"")","3 \, a^{2} \log\left(x^{\frac{1}{3}}\right) + \frac{3}{2} \, b^{2} x^{\frac{2}{3}} + 6 \, a b x^{\frac{1}{3}}"," ",0,"3*a^2*log(x^(1/3)) + 3/2*b^2*x^(2/3) + 6*a*b*x^(1/3)","A",0
2300,1,24,0,0.870323," ","integrate((a+b*x^(1/3))^2/x^2,x, algorithm=""fricas"")","-\frac{3 \, b^{2} x^{\frac{2}{3}} + 3 \, a b x^{\frac{1}{3}} + a^{2}}{x}"," ",0,"-(3*b^2*x^(2/3) + 3*a*b*x^(1/3) + a^2)/x","A",0
2301,1,26,0,1.018153," ","integrate((a+b*x^(1/3))^2/x^3,x, algorithm=""fricas"")","-\frac{15 \, b^{2} x^{\frac{2}{3}} + 24 \, a b x^{\frac{1}{3}} + 10 \, a^{2}}{20 \, x^{2}}"," ",0,"-1/20*(15*b^2*x^(2/3) + 24*a*b*x^(1/3) + 10*a^2)/x^2","A",0
2302,1,26,0,0.623522," ","integrate((a+b*x^(1/3))^2/x^4,x, algorithm=""fricas"")","-\frac{36 \, b^{2} x^{\frac{2}{3}} + 63 \, a b x^{\frac{1}{3}} + 28 \, a^{2}}{84 \, x^{3}}"," ",0,"-1/84*(36*b^2*x^(2/3) + 63*a*b*x^(1/3) + 28*a^2)/x^3","A",0
2303,1,35,0,0.639061," ","integrate((a+b*x^(1/3))^3*x^4,x, algorithm=""fricas"")","\frac{1}{6} \, b^{3} x^{6} + \frac{9}{17} \, a b^{2} x^{\frac{17}{3}} + \frac{9}{16} \, a^{2} b x^{\frac{16}{3}} + \frac{1}{5} \, a^{3} x^{5}"," ",0,"1/6*b^3*x^6 + 9/17*a*b^2*x^(17/3) + 9/16*a^2*b*x^(16/3) + 1/5*a^3*x^5","A",0
2304,1,35,0,0.938435," ","integrate((a+b*x^(1/3))^3*x^3,x, algorithm=""fricas"")","\frac{1}{5} \, b^{3} x^{5} + \frac{9}{14} \, a b^{2} x^{\frac{14}{3}} + \frac{9}{13} \, a^{2} b x^{\frac{13}{3}} + \frac{1}{4} \, a^{3} x^{4}"," ",0,"1/5*b^3*x^5 + 9/14*a*b^2*x^(14/3) + 9/13*a^2*b*x^(13/3) + 1/4*a^3*x^4","A",0
2305,1,35,0,0.989678," ","integrate((a+b*x^(1/3))^3*x^2,x, algorithm=""fricas"")","\frac{1}{4} \, b^{3} x^{4} + \frac{9}{11} \, a b^{2} x^{\frac{11}{3}} + \frac{9}{10} \, a^{2} b x^{\frac{10}{3}} + \frac{1}{3} \, a^{3} x^{3}"," ",0,"1/4*b^3*x^4 + 9/11*a*b^2*x^(11/3) + 9/10*a^2*b*x^(10/3) + 1/3*a^3*x^3","A",0
2306,1,35,0,0.905103," ","integrate((a+b*x^(1/3))^3*x,x, algorithm=""fricas"")","\frac{1}{3} \, b^{3} x^{3} + \frac{9}{8} \, a b^{2} x^{\frac{8}{3}} + \frac{9}{7} \, a^{2} b x^{\frac{7}{3}} + \frac{1}{2} \, a^{3} x^{2}"," ",0,"1/3*b^3*x^3 + 9/8*a*b^2*x^(8/3) + 9/7*a^2*b*x^(7/3) + 1/2*a^3*x^2","A",0
2307,1,32,0,1.038415," ","integrate((a+b*x^(1/3))^3,x, algorithm=""fricas"")","\frac{1}{2} \, b^{3} x^{2} + \frac{9}{5} \, a b^{2} x^{\frac{5}{3}} + \frac{9}{4} \, a^{2} b x^{\frac{4}{3}} + a^{3} x"," ",0,"1/2*b^3*x^2 + 9/5*a*b^2*x^(5/3) + 9/4*a^2*b*x^(4/3) + a^3*x","A",0
2308,1,33,0,1.103266," ","integrate((a+b*x^(1/3))^3/x,x, algorithm=""fricas"")","b^{3} x + 3 \, a^{3} \log\left(x^{\frac{1}{3}}\right) + \frac{9}{2} \, a b^{2} x^{\frac{2}{3}} + 9 \, a^{2} b x^{\frac{1}{3}}"," ",0,"b^3*x + 3*a^3*log(x^(1/3)) + 9/2*a*b^2*x^(2/3) + 9*a^2*b*x^(1/3)","A",0
2309,1,39,0,0.921310," ","integrate((a+b*x^(1/3))^3/x^2,x, algorithm=""fricas"")","\frac{6 \, b^{3} x \log\left(x^{\frac{1}{3}}\right) - 18 \, a b^{2} x^{\frac{2}{3}} - 9 \, a^{2} b x^{\frac{1}{3}} - 2 \, a^{3}}{2 \, x}"," ",0,"1/2*(6*b^3*x*log(x^(1/3)) - 18*a*b^2*x^(2/3) - 9*a^2*b*x^(1/3) - 2*a^3)/x","A",0
2310,1,35,0,1.074406," ","integrate((a+b*x^(1/3))^3/x^3,x, algorithm=""fricas"")","-\frac{20 \, b^{3} x + 45 \, a b^{2} x^{\frac{2}{3}} + 36 \, a^{2} b x^{\frac{1}{3}} + 10 \, a^{3}}{20 \, x^{2}}"," ",0,"-1/20*(20*b^3*x + 45*a*b^2*x^(2/3) + 36*a^2*b*x^(1/3) + 10*a^3)/x^2","A",0
2311,1,35,0,1.139254," ","integrate((a+b*x^(1/3))^3/x^4,x, algorithm=""fricas"")","-\frac{84 \, b^{3} x + 216 \, a b^{2} x^{\frac{2}{3}} + 189 \, a^{2} b x^{\frac{1}{3}} + 56 \, a^{3}}{168 \, x^{3}}"," ",0,"-1/168*(84*b^3*x + 216*a*b^2*x^(2/3) + 189*a^2*b*x^(1/3) + 56*a^3)/x^3","A",0
2312,1,69,0,0.956563," ","integrate((a+b*x^(1/3))^5*x^4,x, algorithm=""fricas"")","\frac{5}{3} \, a^{2} b^{3} x^{6} + \frac{1}{5} \, a^{5} x^{5} + \frac{3}{340} \, {\left(17 \, b^{5} x^{6} + 200 \, a^{3} b^{2} x^{5}\right)} x^{\frac{2}{3}} + \frac{15}{304} \, {\left(16 \, a b^{4} x^{6} + 19 \, a^{4} b x^{5}\right)} x^{\frac{1}{3}}"," ",0,"5/3*a^2*b^3*x^6 + 1/5*a^5*x^5 + 3/340*(17*b^5*x^6 + 200*a^3*b^2*x^5)*x^(2/3) + 15/304*(16*a*b^4*x^6 + 19*a^4*b*x^5)*x^(1/3)","A",0
2313,1,69,0,0.937047," ","integrate((a+b*x^(1/3))^5*x^3,x, algorithm=""fricas"")","2 \, a^{2} b^{3} x^{5} + \frac{1}{4} \, a^{5} x^{4} + \frac{3}{119} \, {\left(7 \, b^{5} x^{5} + 85 \, a^{3} b^{2} x^{4}\right)} x^{\frac{2}{3}} + \frac{15}{208} \, {\left(13 \, a b^{4} x^{5} + 16 \, a^{4} b x^{4}\right)} x^{\frac{1}{3}}"," ",0,"2*a^2*b^3*x^5 + 1/4*a^5*x^4 + 3/119*(7*b^5*x^5 + 85*a^3*b^2*x^4)*x^(2/3) + 15/208*(13*a*b^4*x^5 + 16*a^4*b*x^4)*x^(1/3)","A",0
2314,1,69,0,1.074589," ","integrate((a+b*x^(1/3))^5*x^2,x, algorithm=""fricas"")","\frac{5}{2} \, a^{2} b^{3} x^{4} + \frac{1}{3} \, a^{5} x^{3} + \frac{3}{154} \, {\left(11 \, b^{5} x^{4} + 140 \, a^{3} b^{2} x^{3}\right)} x^{\frac{2}{3}} + \frac{3}{26} \, {\left(10 \, a b^{4} x^{4} + 13 \, a^{4} b x^{3}\right)} x^{\frac{1}{3}}"," ",0,"5/2*a^2*b^3*x^4 + 1/3*a^5*x^3 + 3/154*(11*b^5*x^4 + 140*a^3*b^2*x^3)*x^(2/3) + 3/26*(10*a*b^4*x^4 + 13*a^4*b*x^3)*x^(1/3)","A",0
2315,1,69,0,1.044451," ","integrate((a+b*x^(1/3))^5*x,x, algorithm=""fricas"")","\frac{10}{3} \, a^{2} b^{3} x^{3} + \frac{1}{2} \, a^{5} x^{2} + \frac{3}{44} \, {\left(4 \, b^{5} x^{3} + 55 \, a^{3} b^{2} x^{2}\right)} x^{\frac{2}{3}} + \frac{3}{14} \, {\left(7 \, a b^{4} x^{3} + 10 \, a^{4} b x^{2}\right)} x^{\frac{1}{3}}"," ",0,"10/3*a^2*b^3*x^3 + 1/2*a^5*x^2 + 3/44*(4*b^5*x^3 + 55*a^3*b^2*x^2)*x^(2/3) + 3/14*(7*a*b^4*x^3 + 10*a^4*b*x^2)*x^(1/3)","A",0
2316,1,61,0,1.099196," ","integrate((a+b*x^(1/3))^5,x, algorithm=""fricas"")","5 \, a^{2} b^{3} x^{2} + a^{5} x + \frac{3}{8} \, {\left(b^{5} x^{2} + 16 \, a^{3} b^{2} x\right)} x^{\frac{2}{3}} + \frac{15}{28} \, {\left(4 \, a b^{4} x^{2} + 7 \, a^{4} b x\right)} x^{\frac{1}{3}}"," ",0,"5*a^2*b^3*x^2 + a^5*x + 3/8*(b^5*x^2 + 16*a^3*b^2*x)*x^(2/3) + 15/28*(4*a*b^4*x^2 + 7*a^4*b*x)*x^(1/3)","A",0
2317,1,56,0,0.870558," ","integrate((a+b*x^(1/3))^5/x,x, algorithm=""fricas"")","10 \, a^{2} b^{3} x + 3 \, a^{5} \log\left(x^{\frac{1}{3}}\right) + \frac{3}{5} \, {\left(b^{5} x + 25 \, a^{3} b^{2}\right)} x^{\frac{2}{3}} + \frac{15}{4} \, {\left(a b^{4} x + 4 \, a^{4} b\right)} x^{\frac{1}{3}}"," ",0,"10*a^2*b^3*x + 3*a^5*log(x^(1/3)) + 3/5*(b^5*x + 25*a^3*b^2)*x^(2/3) + 15/4*(a*b^4*x + 4*a^4*b)*x^(1/3)","A",0
2318,1,62,0,0.772053," ","integrate((a+b*x^(1/3))^5/x^2,x, algorithm=""fricas"")","\frac{60 \, a^{2} b^{3} x \log\left(x^{\frac{1}{3}}\right) - 2 \, a^{5} + 3 \, {\left(b^{5} x - 20 \, a^{3} b^{2}\right)} x^{\frac{2}{3}} + 15 \, {\left(2 \, a b^{4} x - a^{4} b\right)} x^{\frac{1}{3}}}{2 \, x}"," ",0,"1/2*(60*a^2*b^3*x*log(x^(1/3)) - 2*a^5 + 3*(b^5*x - 20*a^3*b^2)*x^(2/3) + 15*(2*a*b^4*x - a^4*b)*x^(1/3))/x","A",0
2319,1,57,0,0.802217," ","integrate((a+b*x^(1/3))^5/x^3,x, algorithm=""fricas"")","-\frac{20 \, a^{2} b^{3} x + a^{5} + 3 \, {\left(2 \, b^{5} x + 5 \, a^{3} b^{2}\right)} x^{\frac{2}{3}} + 3 \, {\left(5 \, a b^{4} x + 2 \, a^{4} b\right)} x^{\frac{1}{3}}}{2 \, x^{2}}"," ",0,"-1/2*(20*a^2*b^3*x + a^5 + 3*(2*b^5*x + 5*a^3*b^2)*x^(2/3) + 3*(5*a*b^4*x + 2*a^4*b)*x^(1/3))/x^2","B",0
2320,1,59,0,0.814378," ","integrate((a+b*x^(1/3))^5/x^4,x, algorithm=""fricas"")","-\frac{840 \, a^{2} b^{3} x + 56 \, a^{5} + 18 \, {\left(7 \, b^{5} x + 40 \, a^{3} b^{2}\right)} x^{\frac{2}{3}} + 63 \, {\left(8 \, a b^{4} x + 5 \, a^{4} b\right)} x^{\frac{1}{3}}}{168 \, x^{3}}"," ",0,"-1/168*(840*a^2*b^3*x + 56*a^5 + 18*(7*b^5*x + 40*a^3*b^2)*x^(2/3) + 63*(8*a*b^4*x + 5*a^4*b)*x^(1/3))/x^3","A",0
2321,1,58,0,0.696486," ","integrate((a+b*x^(1/3))^5/x^5,x, algorithm=""fricas"")","-\frac{6160 \, a^{2} b^{3} x + 462 \, a^{5} + 792 \, {\left(b^{5} x + 7 \, a^{3} b^{2}\right)} x^{\frac{2}{3}} + 315 \, {\left(11 \, a b^{4} x + 8 \, a^{4} b\right)} x^{\frac{1}{3}}}{1848 \, x^{4}}"," ",0,"-1/1848*(6160*a^2*b^3*x + 462*a^5 + 792*(b^5*x + 7*a^3*b^2)*x^(2/3) + 315*(11*a*b^4*x + 8*a^4*b)*x^(1/3))/x^4","A",0
2322,1,59,0,0.937445," ","integrate((a+b*x^(1/3))^5/x^6,x, algorithm=""fricas"")","-\frac{25025 \, a^{2} b^{3} x + 2002 \, a^{5} + 231 \, {\left(13 \, b^{5} x + 100 \, a^{3} b^{2}\right)} x^{\frac{2}{3}} + 975 \, {\left(14 \, a b^{4} x + 11 \, a^{4} b\right)} x^{\frac{1}{3}}}{10010 \, x^{5}}"," ",0,"-1/10010*(25025*a^2*b^3*x + 2002*a^5 + 231*(13*b^5*x + 100*a^3*b^2)*x^(2/3) + 975*(14*a*b^4*x + 11*a^4*b)*x^(1/3))/x^5","A",0
2323,1,59,0,0.900949," ","integrate((a+b*x^(1/3))^5/x^7,x, algorithm=""fricas"")","-\frac{74256 \, a^{2} b^{3} x + 6188 \, a^{5} + 1071 \, {\left(8 \, b^{5} x + 65 \, a^{3} b^{2}\right)} x^{\frac{2}{3}} + 2340 \, {\left(17 \, a b^{4} x + 14 \, a^{4} b\right)} x^{\frac{1}{3}}}{37128 \, x^{6}}"," ",0,"-1/37128*(74256*a^2*b^3*x + 6188*a^5 + 1071*(8*b^5*x + 65*a^3*b^2)*x^(2/3) + 2340*(17*a*b^4*x + 14*a^4*b)*x^(1/3))/x^6","A",0
2324,1,124,0,0.761449," ","integrate((a+b*x^(1/3))^10*x^4,x, algorithm=""fricas"")","\frac{5}{4} \, a b^{9} x^{8} + 30 \, a^{4} b^{6} x^{7} + 20 \, a^{7} b^{3} x^{6} + \frac{1}{5} \, a^{10} x^{5} + \frac{27}{1955} \, {\left(425 \, a^{2} b^{8} x^{7} + 2737 \, a^{5} b^{5} x^{6} + 575 \, a^{8} b^{2} x^{5}\right)} x^{\frac{2}{3}} + \frac{3}{41800} \, {\left(1672 \, b^{10} x^{8} + 228000 \, a^{3} b^{7} x^{7} + 462000 \, a^{6} b^{4} x^{6} + 26125 \, a^{9} b x^{5}\right)} x^{\frac{1}{3}}"," ",0,"5/4*a*b^9*x^8 + 30*a^4*b^6*x^7 + 20*a^7*b^3*x^6 + 1/5*a^10*x^5 + 27/1955*(425*a^2*b^8*x^7 + 2737*a^5*b^5*x^6 + 575*a^8*b^2*x^5)*x^(2/3) + 3/41800*(1672*b^10*x^8 + 228000*a^3*b^7*x^7 + 462000*a^6*b^4*x^6 + 26125*a^9*b*x^5)*x^(1/3)","A",0
2325,1,124,0,0.774617," ","integrate((a+b*x^(1/3))^10*x^3,x, algorithm=""fricas"")","\frac{10}{7} \, a b^{9} x^{7} + 35 \, a^{4} b^{6} x^{6} + 24 \, a^{7} b^{3} x^{5} + \frac{1}{4} \, a^{10} x^{4} + \frac{27}{476} \, {\left(119 \, a^{2} b^{8} x^{6} + 784 \, a^{5} b^{5} x^{5} + 170 \, a^{8} b^{2} x^{4}\right)} x^{\frac{2}{3}} + \frac{3}{21736} \, {\left(988 \, b^{10} x^{7} + 137280 \, a^{3} b^{7} x^{6} + 285285 \, a^{6} b^{4} x^{5} + 16720 \, a^{9} b x^{4}\right)} x^{\frac{1}{3}}"," ",0,"10/7*a*b^9*x^7 + 35*a^4*b^6*x^6 + 24*a^7*b^3*x^5 + 1/4*a^10*x^4 + 27/476*(119*a^2*b^8*x^6 + 784*a^5*b^5*x^5 + 170*a^8*b^2*x^4)*x^(2/3) + 3/21736*(988*b^10*x^7 + 137280*a^3*b^7*x^6 + 285285*a^6*b^4*x^5 + 16720*a^9*b*x^4)*x^(1/3)","A",0
2326,1,124,0,0.607610," ","integrate((a+b*x^(1/3))^10*x^2,x, algorithm=""fricas"")","\frac{5}{3} \, a b^{9} x^{6} + 42 \, a^{4} b^{6} x^{5} + 30 \, a^{7} b^{3} x^{4} + \frac{1}{3} \, a^{10} x^{3} + \frac{27}{187} \, {\left(55 \, a^{2} b^{8} x^{5} + 374 \, a^{5} b^{5} x^{4} + 85 \, a^{8} b^{2} x^{3}\right)} x^{\frac{2}{3}} + \frac{3}{494} \, {\left(26 \, b^{10} x^{6} + 3705 \, a^{3} b^{7} x^{5} + 7980 \, a^{6} b^{4} x^{4} + 494 \, a^{9} b x^{3}\right)} x^{\frac{1}{3}}"," ",0,"5/3*a*b^9*x^6 + 42*a^4*b^6*x^5 + 30*a^7*b^3*x^4 + 1/3*a^10*x^3 + 27/187*(55*a^2*b^8*x^5 + 374*a^5*b^5*x^4 + 85*a^8*b^2*x^3)*x^(2/3) + 3/494*(26*b^10*x^6 + 3705*a^3*b^7*x^5 + 7980*a^6*b^4*x^4 + 494*a^9*b*x^3)*x^(1/3)","A",0
2327,1,124,0,0.748609," ","integrate((a+b*x^(1/3))^10*x,x, algorithm=""fricas"")","2 \, a b^{9} x^{5} + \frac{105}{2} \, a^{4} b^{6} x^{4} + 40 \, a^{7} b^{3} x^{3} + \frac{1}{2} \, a^{10} x^{2} + \frac{27}{616} \, {\left(220 \, a^{2} b^{8} x^{4} + 1568 \, a^{5} b^{5} x^{3} + 385 \, a^{8} b^{2} x^{2}\right)} x^{\frac{2}{3}} + \frac{3}{1456} \, {\left(91 \, b^{10} x^{5} + 13440 \, a^{3} b^{7} x^{4} + 30576 \, a^{6} b^{4} x^{3} + 2080 \, a^{9} b x^{2}\right)} x^{\frac{1}{3}}"," ",0,"2*a*b^9*x^5 + 105/2*a^4*b^6*x^4 + 40*a^7*b^3*x^3 + 1/2*a^10*x^2 + 27/616*(220*a^2*b^8*x^4 + 1568*a^5*b^5*x^3 + 385*a^8*b^2*x^2)*x^(2/3) + 3/1456*(91*b^10*x^5 + 13440*a^3*b^7*x^4 + 30576*a^6*b^4*x^3 + 2080*a^9*b*x^2)*x^(1/3)","A",0
2328,1,117,0,0.903970," ","integrate((a+b*x^(1/3))^10,x, algorithm=""fricas"")","\frac{5}{2} \, a b^{9} x^{4} + 70 \, a^{4} b^{6} x^{3} + 60 \, a^{7} b^{3} x^{2} + a^{10} x + \frac{27}{22} \, {\left(10 \, a^{2} b^{8} x^{3} + 77 \, a^{5} b^{5} x^{2} + 22 \, a^{8} b^{2} x\right)} x^{\frac{2}{3}} + \frac{3}{26} \, {\left(2 \, b^{10} x^{4} + 312 \, a^{3} b^{7} x^{3} + 780 \, a^{6} b^{4} x^{2} + 65 \, a^{9} b x\right)} x^{\frac{1}{3}}"," ",0,"5/2*a*b^9*x^4 + 70*a^4*b^6*x^3 + 60*a^7*b^3*x^2 + a^10*x + 27/22*(10*a^2*b^8*x^3 + 77*a^5*b^5*x^2 + 22*a^8*b^2*x)*x^(2/3) + 3/26*(2*b^10*x^4 + 312*a^3*b^7*x^3 + 780*a^6*b^4*x^2 + 65*a^9*b*x)*x^(1/3)","B",0
2329,1,113,0,0.854048," ","integrate((a+b*x^(1/3))^10/x,x, algorithm=""fricas"")","\frac{10}{3} \, a b^{9} x^{3} + 105 \, a^{4} b^{6} x^{2} + 120 \, a^{7} b^{3} x + 3 \, a^{10} \log\left(x^{\frac{1}{3}}\right) + \frac{27}{40} \, {\left(25 \, a^{2} b^{8} x^{2} + 224 \, a^{5} b^{5} x + 100 \, a^{8} b^{2}\right)} x^{\frac{2}{3}} + \frac{3}{70} \, {\left(7 \, b^{10} x^{3} + 1200 \, a^{3} b^{7} x^{2} + 3675 \, a^{6} b^{4} x + 700 \, a^{9} b\right)} x^{\frac{1}{3}}"," ",0,"10/3*a*b^9*x^3 + 105*a^4*b^6*x^2 + 120*a^7*b^3*x + 3*a^10*log(x^(1/3)) + 27/40*(25*a^2*b^8*x^2 + 224*a^5*b^5*x + 100*a^8*b^2)*x^(2/3) + 3/70*(7*b^10*x^3 + 1200*a^3*b^7*x^2 + 3675*a^6*b^4*x + 700*a^9*b)*x^(1/3)","A",0
2330,1,116,0,1.108112," ","integrate((a+b*x^(1/3))^10/x^2,x, algorithm=""fricas"")","\frac{35 \, a b^{9} x^{3} + 1470 \, a^{4} b^{6} x^{2} + 2520 \, a^{7} b^{3} x \log\left(x^{\frac{1}{3}}\right) - 7 \, a^{10} + 189 \, {\left(a^{2} b^{8} x^{2} + 14 \, a^{5} b^{5} x - 5 \, a^{8} b^{2}\right)} x^{\frac{2}{3}} + 3 \, {\left(b^{10} x^{3} + 210 \, a^{3} b^{7} x^{2} + 1470 \, a^{6} b^{4} x - 35 \, a^{9} b\right)} x^{\frac{1}{3}}}{7 \, x}"," ",0,"1/7*(35*a*b^9*x^3 + 1470*a^4*b^6*x^2 + 2520*a^7*b^3*x*log(x^(1/3)) - 7*a^10 + 189*(a^2*b^8*x^2 + 14*a^5*b^5*x - 5*a^8*b^2)*x^(2/3) + 3*(b^10*x^3 + 210*a^3*b^7*x^2 + 1470*a^6*b^4*x - 35*a^9*b)*x^(1/3))/x","A",0
2331,1,117,0,0.782748," ","integrate((a+b*x^(1/3))^10/x^3,x, algorithm=""fricas"")","\frac{40 \, a b^{9} x^{3} + 2520 \, a^{4} b^{6} x^{2} \log\left(x^{\frac{1}{3}}\right) - 480 \, a^{7} b^{3} x - 2 \, a^{10} + 27 \, {\left(10 \, a^{2} b^{8} x^{2} - 112 \, a^{5} b^{5} x - 5 \, a^{8} b^{2}\right)} x^{\frac{2}{3}} + 3 \, {\left(b^{10} x^{3} + 480 \, a^{3} b^{7} x^{2} - 420 \, a^{6} b^{4} x - 8 \, a^{9} b\right)} x^{\frac{1}{3}}}{4 \, x^{2}}"," ",0,"1/4*(40*a*b^9*x^3 + 2520*a^4*b^6*x^2*log(x^(1/3)) - 480*a^7*b^3*x - 2*a^10 + 27*(10*a^2*b^8*x^2 - 112*a^5*b^5*x - 5*a^8*b^2)*x^(2/3) + 3*(b^10*x^3 + 480*a^3*b^7*x^2 - 420*a^6*b^4*x - 8*a^9*b)*x^(1/3))/x^2","A",0
2332,1,118,0,0.650201," ","integrate((a+b*x^(1/3))^10/x^4,x, algorithm=""fricas"")","\frac{2520 \, a b^{9} x^{3} \log\left(x^{\frac{1}{3}}\right) - 17640 \, a^{4} b^{6} x^{2} - 5040 \, a^{7} b^{3} x - 28 \, a^{10} - 324 \, {\left(35 \, a^{2} b^{8} x^{2} + 49 \, a^{5} b^{5} x + 5 \, a^{8} b^{2}\right)} x^{\frac{2}{3}} + 63 \, {\left(4 \, b^{10} x^{3} - 240 \, a^{3} b^{7} x^{2} - 168 \, a^{6} b^{4} x - 5 \, a^{9} b\right)} x^{\frac{1}{3}}}{84 \, x^{3}}"," ",0,"1/84*(2520*a*b^9*x^3*log(x^(1/3)) - 17640*a^4*b^6*x^2 - 5040*a^7*b^3*x - 28*a^10 - 324*(35*a^2*b^8*x^2 + 49*a^5*b^5*x + 5*a^8*b^2)*x^(2/3) + 63*(4*b^10*x^3 - 240*a^3*b^7*x^2 - 168*a^6*b^4*x - 5*a^9*b)*x^(1/3))/x^3","A",0
2333,1,114,0,0.857600," ","integrate((a+b*x^(1/3))^10/x^5,x, algorithm=""fricas"")","-\frac{440 \, a b^{9} x^{3} + 4620 \, a^{4} b^{6} x^{2} + 1760 \, a^{7} b^{3} x + 11 \, a^{10} + 297 \, {\left(5 \, a^{2} b^{8} x^{2} + 16 \, a^{5} b^{5} x + 2 \, a^{8} b^{2}\right)} x^{\frac{2}{3}} + 3 \, {\left(22 \, b^{10} x^{3} + 1056 \, a^{3} b^{7} x^{2} + 1155 \, a^{6} b^{4} x + 40 \, a^{9} b\right)} x^{\frac{1}{3}}}{44 \, x^{4}}"," ",0,"-1/44*(440*a*b^9*x^3 + 4620*a^4*b^6*x^2 + 1760*a^7*b^3*x + 11*a^10 + 297*(5*a^2*b^8*x^2 + 16*a^5*b^5*x + 2*a^8*b^2)*x^(2/3) + 3*(22*b^10*x^3 + 1056*a^3*b^7*x^2 + 1155*a^6*b^4*x + 40*a^9*b)*x^(1/3))/x^4","B",0
2334,1,114,0,0.811158," ","integrate((a+b*x^(1/3))^10/x^6,x, algorithm=""fricas"")","-\frac{25025 \, a b^{9} x^{3} + 350350 \, a^{4} b^{6} x^{2} + 150150 \, a^{7} b^{3} x + 1001 \, a^{10} + 297 \, {\left(325 \, a^{2} b^{8} x^{2} + 1274 \, a^{5} b^{5} x + 175 \, a^{8} b^{2}\right)} x^{\frac{2}{3}} + 39 \, {\left(77 \, b^{10} x^{3} + 5775 \, a^{3} b^{7} x^{2} + 7350 \, a^{6} b^{4} x + 275 \, a^{9} b\right)} x^{\frac{1}{3}}}{5005 \, x^{5}}"," ",0,"-1/5005*(25025*a*b^9*x^3 + 350350*a^4*b^6*x^2 + 150150*a^7*b^3*x + 1001*a^10 + 297*(325*a^2*b^8*x^2 + 1274*a^5*b^5*x + 175*a^8*b^2)*x^(2/3) + 39*(77*b^10*x^3 + 5775*a^3*b^7*x^2 + 7350*a^6*b^4*x + 275*a^9*b)*x^(1/3))/x^5","A",0
2335,1,114,0,0.864409," ","integrate((a+b*x^(1/3))^10/x^7,x, algorithm=""fricas"")","-\frac{388960 \, a b^{9} x^{3} + 6126120 \, a^{4} b^{6} x^{2} + 2800512 \, a^{7} b^{3} x + 19448 \, a^{10} + 15147 \, {\left(104 \, a^{2} b^{8} x^{2} + 448 \, a^{5} b^{5} x + 65 \, a^{8} b^{2}\right)} x^{\frac{2}{3}} + 234 \, {\left(187 \, b^{10} x^{3} + 16320 \, a^{3} b^{7} x^{2} + 22440 \, a^{6} b^{4} x + 880 \, a^{9} b\right)} x^{\frac{1}{3}}}{116688 \, x^{6}}"," ",0,"-1/116688*(388960*a*b^9*x^3 + 6126120*a^4*b^6*x^2 + 2800512*a^7*b^3*x + 19448*a^10 + 15147*(104*a^2*b^8*x^2 + 448*a^5*b^5*x + 65*a^8*b^2)*x^(2/3) + 234*(187*b^10*x^3 + 16320*a^3*b^7*x^2 + 22440*a^6*b^4*x + 880*a^9*b)*x^(1/3))/x^6","A",0
2336,1,114,0,0.853938," ","integrate((a+b*x^(1/3))^10/x^8,x, algorithm=""fricas"")","-\frac{3233230 \, a b^{9} x^{3} + 54318264 \, a^{4} b^{6} x^{2} + 25865840 \, a^{7} b^{3} x + 184756 \, a^{10} + 35343 \, {\left(380 \, a^{2} b^{8} x^{2} + 1729 \, a^{5} b^{5} x + 260 \, a^{8} b^{2}\right)} x^{\frac{2}{3}} + 1482 \, {\left(238 \, b^{10} x^{3} + 22440 \, a^{3} b^{7} x^{2} + 32340 \, a^{6} b^{4} x + 1309 \, a^{9} b\right)} x^{\frac{1}{3}}}{1293292 \, x^{7}}"," ",0,"-1/1293292*(3233230*a*b^9*x^3 + 54318264*a^4*b^6*x^2 + 25865840*a^7*b^3*x + 184756*a^10 + 35343*(380*a^2*b^8*x^2 + 1729*a^5*b^5*x + 260*a^8*b^2)*x^(2/3) + 1482*(238*b^10*x^3 + 22440*a^3*b^7*x^2 + 32340*a^6*b^4*x + 1309*a^9*b)*x^(1/3))/x^7","A",0
2337,1,114,0,0.857531," ","integrate((a+b*x^(1/3))^10/x^9,x, algorithm=""fricas"")","-\frac{18305056 \, a b^{9} x^{3} + 320338480 \, a^{4} b^{6} x^{2} + 156900480 \, a^{7} b^{3} x + 1144066 \, a^{10} + 73899 \, {\left(1045 \, a^{2} b^{8} x^{2} + 4928 \, a^{5} b^{5} x + 760 \, a^{8} b^{2}\right)} x^{\frac{2}{3}} + 5016 \, {\left(391 \, b^{10} x^{3} + 38640 \, a^{3} b^{7} x^{2} + 57477 \, a^{6} b^{4} x + 2380 \, a^{9} b\right)} x^{\frac{1}{3}}}{9152528 \, x^{8}}"," ",0,"-1/9152528*(18305056*a*b^9*x^3 + 320338480*a^4*b^6*x^2 + 156900480*a^7*b^3*x + 1144066*a^10 + 73899*(1045*a^2*b^8*x^2 + 4928*a^5*b^5*x + 760*a^8*b^2)*x^(2/3) + 5016*(391*b^10*x^3 + 38640*a^3*b^7*x^2 + 57477*a^6*b^4*x + 2380*a^9*b)*x^(1/3))/x^8","A",0
2338,1,114,0,1.024418," ","integrate((a+b*x^(1/3))^10/x^10,x, algorithm=""fricas"")","-\frac{79676025 \, a b^{9} x^{3} + 1434168450 \, a^{4} b^{6} x^{2} + 717084225 \, a^{7} b^{3} x + 5311735 \, a^{10} + 1235169 \, {\left(275 \, a^{2} b^{8} x^{2} + 1330 \, a^{5} b^{5} x + 209 \, a^{8} b^{2}\right)} x^{\frac{2}{3}} + 28215 \, {\left(299 \, b^{10} x^{3} + 30498 \, a^{3} b^{7} x^{2} + 46410 \, a^{6} b^{4} x + 1955 \, a^{9} b\right)} x^{\frac{1}{3}}}{47805615 \, x^{9}}"," ",0,"-1/47805615*(79676025*a*b^9*x^3 + 1434168450*a^4*b^6*x^2 + 717084225*a^7*b^3*x + 5311735*a^10 + 1235169*(275*a^2*b^8*x^2 + 1330*a^5*b^5*x + 209*a^8*b^2)*x^(2/3) + 28215*(299*b^10*x^3 + 30498*a^3*b^7*x^2 + 46410*a^6*b^4*x + 1955*a^9*b)*x^(1/3))/x^9","A",0
2339,1,179,0,0.807064," ","integrate((a+b*x^(1/3))^15*x^5,x, algorithm=""fricas"")","\frac{1}{11} \, b^{15} x^{11} + \frac{91}{2} \, a^{3} b^{12} x^{10} + \frac{5005}{9} \, a^{6} b^{9} x^{9} + \frac{5005}{8} \, a^{9} b^{6} x^{8} + 65 \, a^{12} b^{3} x^{7} + \frac{1}{6} \, a^{15} x^{6} + \frac{9}{21344} \, {\left(3335 \, a b^{14} x^{10} + 334880 \, a^{4} b^{11} x^{9} + 1760880 \, a^{7} b^{8} x^{8} + 928928 \, a^{10} b^{5} x^{7} + 37352 \, a^{13} b^{2} x^{6}\right)} x^{\frac{2}{3}} + \frac{9}{129580} \, {\left(146300 \, a^{2} b^{13} x^{10} + 4632485 \, a^{5} b^{10} x^{9} + 11117964 \, a^{8} b^{7} x^{8} + 2679950 \, a^{11} b^{4} x^{7} + 34100 \, a^{14} b x^{6}\right)} x^{\frac{1}{3}}"," ",0,"1/11*b^15*x^11 + 91/2*a^3*b^12*x^10 + 5005/9*a^6*b^9*x^9 + 5005/8*a^9*b^6*x^8 + 65*a^12*b^3*x^7 + 1/6*a^15*x^6 + 9/21344*(3335*a*b^14*x^10 + 334880*a^4*b^11*x^9 + 1760880*a^7*b^8*x^8 + 928928*a^10*b^5*x^7 + 37352*a^13*b^2*x^6)*x^(2/3) + 9/129580*(146300*a^2*b^13*x^10 + 4632485*a^5*b^10*x^9 + 11117964*a^8*b^7*x^8 + 2679950*a^11*b^4*x^7 + 34100*a^14*b*x^6)*x^(1/3)","A",0
2340,1,179,0,0.890747," ","integrate((a+b*x^(1/3))^15*x^4,x, algorithm=""fricas"")","\frac{1}{10} \, b^{15} x^{10} + \frac{455}{9} \, a^{3} b^{12} x^{9} + \frac{5005}{8} \, a^{6} b^{9} x^{8} + 715 \, a^{9} b^{6} x^{7} + \frac{455}{6} \, a^{12} b^{3} x^{6} + \frac{1}{5} \, a^{15} x^{5} + \frac{9}{226780} \, {\left(39100 \, a b^{14} x^{9} + 3968650 \, a^{4} b^{11} x^{8} + 21149700 \, a^{7} b^{8} x^{7} + 11350339 \, a^{10} b^{5} x^{6} + 466900 \, a^{13} b^{2} x^{5}\right)} x^{\frac{2}{3}} + \frac{9}{7600} \, {\left(9500 \, a^{2} b^{13} x^{9} + 304304 \, a^{5} b^{10} x^{8} + 741000 \, a^{8} b^{7} x^{7} + 182000 \, a^{11} b^{4} x^{6} + 2375 \, a^{14} b x^{5}\right)} x^{\frac{1}{3}}"," ",0,"1/10*b^15*x^10 + 455/9*a^3*b^12*x^9 + 5005/8*a^6*b^9*x^8 + 715*a^9*b^6*x^7 + 455/6*a^12*b^3*x^6 + 1/5*a^15*x^5 + 9/226780*(39100*a*b^14*x^9 + 3968650*a^4*b^11*x^8 + 21149700*a^7*b^8*x^7 + 11350339*a^10*b^5*x^6 + 466900*a^13*b^2*x^5)*x^(2/3) + 9/7600*(9500*a^2*b^13*x^9 + 304304*a^5*b^10*x^8 + 741000*a^8*b^7*x^7 + 182000*a^11*b^4*x^6 + 2375*a^14*b*x^5)*x^(1/3)","A",0
2341,1,179,0,0.895453," ","integrate((a+b*x^(1/3))^15*x^3,x, algorithm=""fricas"")","\frac{1}{9} \, b^{15} x^{9} + \frac{455}{8} \, a^{3} b^{12} x^{8} + 715 \, a^{6} b^{9} x^{7} + \frac{5005}{6} \, a^{9} b^{6} x^{6} + 91 \, a^{12} b^{3} x^{5} + \frac{1}{4} \, a^{15} x^{4} + \frac{9}{20332} \, {\left(3910 \, a b^{14} x^{8} + 402220 \, a^{4} b^{11} x^{7} + 2180607 \, a^{7} b^{8} x^{6} + 1197196 \, a^{10} b^{5} x^{5} + 50830 \, a^{13} b^{2} x^{4}\right)} x^{\frac{2}{3}} + \frac{9}{19760} \, {\left(27664 \, a^{2} b^{13} x^{8} + 899080 \, a^{5} b^{10} x^{7} + 2230800 \, a^{8} b^{7} x^{6} + 561925 \, a^{11} b^{4} x^{5} + 7600 \, a^{14} b x^{4}\right)} x^{\frac{1}{3}}"," ",0,"1/9*b^15*x^9 + 455/8*a^3*b^12*x^8 + 715*a^6*b^9*x^7 + 5005/6*a^9*b^6*x^6 + 91*a^12*b^3*x^5 + 1/4*a^15*x^4 + 9/20332*(3910*a*b^14*x^8 + 402220*a^4*b^11*x^7 + 2180607*a^7*b^8*x^6 + 1197196*a^10*b^5*x^5 + 50830*a^13*b^2*x^4)*x^(2/3) + 9/19760*(27664*a^2*b^13*x^8 + 899080*a^5*b^10*x^7 + 2230800*a^8*b^7*x^6 + 561925*a^11*b^4*x^5 + 7600*a^14*b*x^4)*x^(1/3)","A",0
2342,1,179,0,0.668739," ","integrate((a+b*x^(1/3))^15*x^2,x, algorithm=""fricas"")","\frac{1}{8} \, b^{15} x^{8} + 65 \, a^{3} b^{12} x^{7} + \frac{5005}{6} \, a^{6} b^{9} x^{6} + 1001 \, a^{9} b^{6} x^{5} + \frac{455}{4} \, a^{12} b^{3} x^{4} + \frac{1}{3} \, a^{15} x^{3} + \frac{9}{17204} \, {\left(3740 \, a b^{14} x^{7} + 391391 \, a^{4} b^{11} x^{6} + 2170740 \, a^{7} b^{8} x^{5} + 1230086 \, a^{10} b^{5} x^{4} + 54740 \, a^{13} b^{2} x^{3}\right)} x^{\frac{2}{3}} + \frac{9}{3344} \, {\left(5320 \, a^{2} b^{13} x^{7} + 176176 \, a^{5} b^{10} x^{6} + 448305 \, a^{8} b^{7} x^{5} + 117040 \, a^{11} b^{4} x^{4} + 1672 \, a^{14} b x^{3}\right)} x^{\frac{1}{3}}"," ",0,"1/8*b^15*x^8 + 65*a^3*b^12*x^7 + 5005/6*a^6*b^9*x^6 + 1001*a^9*b^6*x^5 + 455/4*a^12*b^3*x^4 + 1/3*a^15*x^3 + 9/17204*(3740*a*b^14*x^7 + 391391*a^4*b^11*x^6 + 2170740*a^7*b^8*x^5 + 1230086*a^10*b^5*x^4 + 54740*a^13*b^2*x^3)*x^(2/3) + 9/3344*(5320*a^2*b^13*x^7 + 176176*a^5*b^10*x^6 + 448305*a^8*b^7*x^5 + 117040*a^11*b^4*x^4 + 1672*a^14*b*x^3)*x^(1/3)","A",0
2343,1,179,0,0.706863," ","integrate((a+b*x^(1/3))^15*x,x, algorithm=""fricas"")","\frac{1}{7} \, b^{15} x^{7} + \frac{455}{6} \, a^{3} b^{12} x^{6} + 1001 \, a^{6} b^{9} x^{5} + \frac{5005}{4} \, a^{9} b^{6} x^{4} + \frac{455}{3} \, a^{12} b^{3} x^{3} + \frac{1}{2} \, a^{15} x^{2} + \frac{9}{952} \, {\left(238 \, a b^{14} x^{6} + 25480 \, a^{4} b^{11} x^{5} + 145860 \, a^{7} b^{8} x^{4} + 86632 \, a^{10} b^{5} x^{3} + 4165 \, a^{13} b^{2} x^{2}\right)} x^{\frac{2}{3}} + \frac{9}{2128} \, {\left(3920 \, a^{2} b^{13} x^{6} + 133133 \, a^{5} b^{10} x^{5} + 351120 \, a^{8} b^{7} x^{4} + 96824 \, a^{11} b^{4} x^{3} + 1520 \, a^{14} b x^{2}\right)} x^{\frac{1}{3}}"," ",0,"1/7*b^15*x^7 + 455/6*a^3*b^12*x^6 + 1001*a^6*b^9*x^5 + 5005/4*a^9*b^6*x^4 + 455/3*a^12*b^3*x^3 + 1/2*a^15*x^2 + 9/952*(238*a*b^14*x^6 + 25480*a^4*b^11*x^5 + 145860*a^7*b^8*x^4 + 86632*a^10*b^5*x^3 + 4165*a^13*b^2*x^2)*x^(2/3) + 9/2128*(3920*a^2*b^13*x^6 + 133133*a^5*b^10*x^5 + 351120*a^8*b^7*x^4 + 96824*a^11*b^4*x^3 + 1520*a^14*b*x^2)*x^(1/3)","A",0
2344,1,172,0,0.774199," ","integrate((a+b*x^(1/3))^15,x, algorithm=""fricas"")","\frac{1}{6} \, b^{15} x^{6} + 91 \, a^{3} b^{12} x^{5} + \frac{5005}{4} \, a^{6} b^{9} x^{4} + \frac{5005}{3} \, a^{9} b^{6} x^{3} + \frac{455}{2} \, a^{12} b^{3} x^{2} + a^{15} x + \frac{9}{136} \, {\left(40 \, a b^{14} x^{5} + 4420 \, a^{4} b^{11} x^{4} + 26520 \, a^{7} b^{8} x^{3} + 17017 \, a^{10} b^{5} x^{2} + 952 \, a^{13} b^{2} x\right)} x^{\frac{2}{3}} + \frac{9}{16} \, {\left(35 \, a^{2} b^{13} x^{5} + 1232 \, a^{5} b^{10} x^{4} + 3432 \, a^{8} b^{7} x^{3} + 1040 \, a^{11} b^{4} x^{2} + 20 \, a^{14} b x\right)} x^{\frac{1}{3}}"," ",0,"1/6*b^15*x^6 + 91*a^3*b^12*x^5 + 5005/4*a^6*b^9*x^4 + 5005/3*a^9*b^6*x^3 + 455/2*a^12*b^3*x^2 + a^15*x + 9/136*(40*a*b^14*x^5 + 4420*a^4*b^11*x^4 + 26520*a^7*b^8*x^3 + 17017*a^10*b^5*x^2 + 952*a^13*b^2*x)*x^(2/3) + 9/16*(35*a^2*b^13*x^5 + 1232*a^5*b^10*x^4 + 3432*a^8*b^7*x^3 + 1040*a^11*b^4*x^2 + 20*a^14*b*x)*x^(1/3)","B",0
2345,1,168,0,0.854363," ","integrate((a+b*x^(1/3))^15/x,x, algorithm=""fricas"")","\frac{1}{5} \, b^{15} x^{5} + \frac{455}{4} \, a^{3} b^{12} x^{4} + \frac{5005}{3} \, a^{6} b^{9} x^{3} + \frac{5005}{2} \, a^{9} b^{6} x^{2} + 455 \, a^{12} b^{3} x + 3 \, a^{15} \log\left(x^{\frac{1}{3}}\right) + \frac{9}{3080} \, {\left(1100 \, a b^{14} x^{4} + 127400 \, a^{4} b^{11} x^{3} + 825825 \, a^{7} b^{8} x^{2} + 616616 \, a^{10} b^{5} x + 53900 \, a^{13} b^{2}\right)} x^{\frac{2}{3}} + \frac{9}{1820} \, {\left(4900 \, a^{2} b^{13} x^{4} + 182182 \, a^{5} b^{10} x^{3} + 557700 \, a^{8} b^{7} x^{2} + 207025 \, a^{11} b^{4} x + 9100 \, a^{14} b\right)} x^{\frac{1}{3}}"," ",0,"1/5*b^15*x^5 + 455/4*a^3*b^12*x^4 + 5005/3*a^6*b^9*x^3 + 5005/2*a^9*b^6*x^2 + 455*a^12*b^3*x + 3*a^15*log(x^(1/3)) + 9/3080*(1100*a*b^14*x^4 + 127400*a^4*b^11*x^3 + 825825*a^7*b^8*x^2 + 616616*a^10*b^5*x + 53900*a^13*b^2)*x^(2/3) + 9/1820*(4900*a^2*b^13*x^4 + 182182*a^5*b^10*x^3 + 557700*a^8*b^7*x^2 + 207025*a^11*b^4*x + 9100*a^14*b)*x^(1/3)","A",0
2346,1,173,0,0.946995," ","integrate((a+b*x^(1/3))^15/x^2,x, algorithm=""fricas"")","\frac{66 \, b^{15} x^{5} + 40040 \, a^{3} b^{12} x^{4} + 660660 \, a^{6} b^{9} x^{3} + 1321320 \, a^{9} b^{6} x^{2} + 360360 \, a^{12} b^{3} x \log\left(x^{\frac{1}{3}}\right) - 264 \, a^{15} + 27 \, {\left(40 \, a b^{14} x^{4} + 5005 \, a^{4} b^{11} x^{3} + 37752 \, a^{7} b^{8} x^{2} + 44044 \, a^{10} b^{5} x - 3080 \, a^{13} b^{2}\right)} x^{\frac{2}{3}} + 594 \, {\left(14 \, a^{2} b^{13} x^{4} + 572 \, a^{5} b^{10} x^{3} + 2145 \, a^{8} b^{7} x^{2} + 1820 \, a^{11} b^{4} x - 10 \, a^{14} b\right)} x^{\frac{1}{3}}}{264 \, x}"," ",0,"1/264*(66*b^15*x^5 + 40040*a^3*b^12*x^4 + 660660*a^6*b^9*x^3 + 1321320*a^9*b^6*x^2 + 360360*a^12*b^3*x*log(x^(1/3)) - 264*a^15 + 27*(40*a*b^14*x^4 + 5005*a^4*b^11*x^3 + 37752*a^7*b^8*x^2 + 44044*a^10*b^5*x - 3080*a^13*b^2)*x^(2/3) + 594*(14*a^2*b^13*x^4 + 572*a^5*b^10*x^3 + 2145*a^8*b^7*x^2 + 1820*a^11*b^4*x - 10*a^14*b)*x^(1/3))/x","A",0
2347,1,173,0,0.881638," ","integrate((a+b*x^(1/3))^15/x^3,x, algorithm=""fricas"")","\frac{8 \, b^{15} x^{5} + 5460 \, a^{3} b^{12} x^{4} + 120120 \, a^{6} b^{9} x^{3} + 360360 \, a^{9} b^{6} x^{2} \log\left(x^{\frac{1}{3}}\right) - 10920 \, a^{12} b^{3} x - 12 \, a^{15} + 27 \, {\left(5 \, a b^{14} x^{4} + 728 \, a^{4} b^{11} x^{3} + 8580 \, a^{7} b^{8} x^{2} - 8008 \, a^{10} b^{5} x - 70 \, a^{13} b^{2}\right)} x^{\frac{2}{3}} + 54 \, {\left(20 \, a^{2} b^{13} x^{4} + 1001 \, a^{5} b^{10} x^{3} + 8580 \, a^{8} b^{7} x^{2} - 910 \, a^{11} b^{4} x - 4 \, a^{14} b\right)} x^{\frac{1}{3}}}{24 \, x^{2}}"," ",0,"1/24*(8*b^15*x^5 + 5460*a^3*b^12*x^4 + 120120*a^6*b^9*x^3 + 360360*a^9*b^6*x^2*log(x^(1/3)) - 10920*a^12*b^3*x - 12*a^15 + 27*(5*a*b^14*x^4 + 728*a^4*b^11*x^3 + 8580*a^7*b^8*x^2 - 8008*a^10*b^5*x - 70*a^13*b^2)*x^(2/3) + 54*(20*a^2*b^13*x^4 + 1001*a^5*b^10*x^3 + 8580*a^8*b^7*x^2 - 910*a^11*b^4*x - 4*a^14*b)*x^(1/3))/x^2","A",0
2348,1,173,0,0.594011," ","integrate((a+b*x^(1/3))^15/x^4,x, algorithm=""fricas"")","\frac{12 \, b^{15} x^{5} + 10920 \, a^{3} b^{12} x^{4} + 360360 \, a^{6} b^{9} x^{3} \log\left(x^{\frac{1}{3}}\right) - 120120 \, a^{9} b^{6} x^{2} - 5460 \, a^{12} b^{3} x - 8 \, a^{15} + 54 \, {\left(4 \, a b^{14} x^{4} + 910 \, a^{4} b^{11} x^{3} - 8580 \, a^{7} b^{8} x^{2} - 1001 \, a^{10} b^{5} x - 20 \, a^{13} b^{2}\right)} x^{\frac{2}{3}} + 27 \, {\left(70 \, a^{2} b^{13} x^{4} + 8008 \, a^{5} b^{10} x^{3} - 8580 \, a^{8} b^{7} x^{2} - 728 \, a^{11} b^{4} x - 5 \, a^{14} b\right)} x^{\frac{1}{3}}}{24 \, x^{3}}"," ",0,"1/24*(12*b^15*x^5 + 10920*a^3*b^12*x^4 + 360360*a^6*b^9*x^3*log(x^(1/3)) - 120120*a^9*b^6*x^2 - 5460*a^12*b^3*x - 8*a^15 + 54*(4*a*b^14*x^4 + 910*a^4*b^11*x^3 - 8580*a^7*b^8*x^2 - 1001*a^10*b^5*x - 20*a^13*b^2)*x^(2/3) + 27*(70*a^2*b^13*x^4 + 8008*a^5*b^10*x^3 - 8580*a^8*b^7*x^2 - 728*a^11*b^4*x - 5*a^14*b)*x^(1/3))/x^3","A",0
2349,1,173,0,0.947398," ","integrate((a+b*x^(1/3))^15/x^6,x, algorithm=""fricas"")","\frac{360360 \, b^{15} x^{5} \log\left(x^{\frac{1}{3}}\right) - 54654600 \, a^{3} b^{12} x^{4} - 300600300 \, a^{6} b^{9} x^{3} - 200400200 \, a^{9} b^{6} x^{2} - 13663650 \, a^{12} b^{3} x - 24024 \, a^{15} - 594 \, {\left(9100 \, a b^{14} x^{4} + 207025 \, a^{4} b^{11} x^{3} + 557700 \, a^{7} b^{8} x^{2} + 182182 \, a^{10} b^{5} x + 4900 \, a^{13} b^{2}\right)} x^{\frac{2}{3}} - 351 \, {\left(53900 \, a^{2} b^{13} x^{4} + 616616 \, a^{5} b^{10} x^{3} + 825825 \, a^{8} b^{7} x^{2} + 127400 \, a^{11} b^{4} x + 1100 \, a^{14} b\right)} x^{\frac{1}{3}}}{120120 \, x^{5}}"," ",0,"1/120120*(360360*b^15*x^5*log(x^(1/3)) - 54654600*a^3*b^12*x^4 - 300600300*a^6*b^9*x^3 - 200400200*a^9*b^6*x^2 - 13663650*a^12*b^3*x - 24024*a^15 - 594*(9100*a*b^14*x^4 + 207025*a^4*b^11*x^3 + 557700*a^7*b^8*x^2 + 182182*a^10*b^5*x + 4900*a^13*b^2)*x^(2/3) - 351*(53900*a^2*b^13*x^4 + 616616*a^5*b^10*x^3 + 825825*a^8*b^7*x^2 + 127400*a^11*b^4*x + 1100*a^14*b)*x^(1/3))/x^5","A",0
2350,1,169,0,0.826142," ","integrate((a+b*x^(1/3))^15/x^7,x, algorithm=""fricas"")","-\frac{816 \, b^{15} x^{5} + 185640 \, a^{3} b^{12} x^{4} + 1361360 \, a^{6} b^{9} x^{3} + 1021020 \, a^{9} b^{6} x^{2} + 74256 \, a^{12} b^{3} x + 136 \, a^{15} + 459 \, {\left(20 \, a b^{14} x^{4} + 1040 \, a^{4} b^{11} x^{3} + 3432 \, a^{7} b^{8} x^{2} + 1232 \, a^{10} b^{5} x + 35 \, a^{13} b^{2}\right)} x^{\frac{2}{3}} + 54 \, {\left(952 \, a^{2} b^{13} x^{4} + 17017 \, a^{5} b^{10} x^{3} + 26520 \, a^{8} b^{7} x^{2} + 4420 \, a^{11} b^{4} x + 40 \, a^{14} b\right)} x^{\frac{1}{3}}}{816 \, x^{6}}"," ",0,"-1/816*(816*b^15*x^5 + 185640*a^3*b^12*x^4 + 1361360*a^6*b^9*x^3 + 1021020*a^9*b^6*x^2 + 74256*a^12*b^3*x + 136*a^15 + 459*(20*a*b^14*x^4 + 1040*a^4*b^11*x^3 + 3432*a^7*b^8*x^2 + 1232*a^10*b^5*x + 35*a^13*b^2)*x^(2/3) + 54*(952*a^2*b^13*x^4 + 17017*a^5*b^10*x^3 + 26520*a^8*b^7*x^2 + 4420*a^11*b^4*x + 40*a^14*b)*x^(1/3))/x^6","B",0
2351,1,169,0,1.032650," ","integrate((a+b*x^(1/3))^15/x^8,x, algorithm=""fricas"")","-\frac{54264 \, b^{15} x^{5} + 16460080 \, a^{3} b^{12} x^{4} + 135795660 \, a^{6} b^{9} x^{3} + 108636528 \, a^{9} b^{6} x^{2} + 8230040 \, a^{12} b^{3} x + 15504 \, a^{15} + 459 \, {\left(1520 \, a b^{14} x^{4} + 96824 \, a^{4} b^{11} x^{3} + 351120 \, a^{7} b^{8} x^{2} + 133133 \, a^{10} b^{5} x + 3920 \, a^{13} b^{2}\right)} x^{\frac{2}{3}} + 1026 \, {\left(4165 \, a^{2} b^{13} x^{4} + 86632 \, a^{5} b^{10} x^{3} + 145860 \, a^{8} b^{7} x^{2} + 25480 \, a^{11} b^{4} x + 238 \, a^{14} b\right)} x^{\frac{1}{3}}}{108528 \, x^{7}}"," ",0,"-1/108528*(54264*b^15*x^5 + 16460080*a^3*b^12*x^4 + 135795660*a^6*b^9*x^3 + 108636528*a^9*b^6*x^2 + 8230040*a^12*b^3*x + 15504*a^15 + 459*(1520*a*b^14*x^4 + 96824*a^4*b^11*x^3 + 351120*a^7*b^8*x^2 + 133133*a^10*b^5*x + 3920*a^13*b^2)*x^(2/3) + 1026*(4165*a^2*b^13*x^4 + 86632*a^5*b^10*x^3 + 145860*a^8*b^7*x^2 + 25480*a^11*b^4*x + 238*a^14*b)*x^(1/3))/x^7","A",0
2352,1,169,0,1.017784," ","integrate((a+b*x^(1/3))^15/x^9,x, algorithm=""fricas"")","-\frac{1307504 \, b^{15} x^{5} + 446185740 \, a^{3} b^{12} x^{4} + 3926434512 \, a^{6} b^{9} x^{3} + 3272028760 \, a^{9} b^{6} x^{2} + 254963280 \, a^{12} b^{3} x + 490314 \, a^{15} + 10557 \, {\left(1672 \, a b^{14} x^{4} + 117040 \, a^{4} b^{11} x^{3} + 448305 \, a^{7} b^{8} x^{2} + 176176 \, a^{10} b^{5} x + 5320 \, a^{13} b^{2}\right)} x^{\frac{2}{3}} + 2052 \, {\left(54740 \, a^{2} b^{13} x^{4} + 1230086 \, a^{5} b^{10} x^{3} + 2170740 \, a^{8} b^{7} x^{2} + 391391 \, a^{11} b^{4} x + 3740 \, a^{14} b\right)} x^{\frac{1}{3}}}{3922512 \, x^{8}}"," ",0,"-1/3922512*(1307504*b^15*x^5 + 446185740*a^3*b^12*x^4 + 3926434512*a^6*b^9*x^3 + 3272028760*a^9*b^6*x^2 + 254963280*a^12*b^3*x + 490314*a^15 + 10557*(1672*a*b^14*x^4 + 117040*a^4*b^11*x^3 + 448305*a^7*b^8*x^2 + 176176*a^10*b^5*x + 5320*a^13*b^2)*x^(2/3) + 2052*(54740*a^2*b^13*x^4 + 1230086*a^5*b^10*x^3 + 2170740*a^8*b^7*x^2 + 391391*a^11*b^4*x + 3740*a^14*b)*x^(1/3))/x^8","A",0
2353,1,169,0,0.785293," ","integrate((a+b*x^(1/3))^15/x^10,x, algorithm=""fricas"")","-\frac{17383860 \, b^{15} x^{5} + 6327725040 \, a^{3} b^{12} x^{4} + 58004146200 \, a^{6} b^{9} x^{3} + 49717839600 \, a^{9} b^{6} x^{2} + 3954828150 \, a^{12} b^{3} x + 7726160 \, a^{15} + 31671 \, {\left(7600 \, a b^{14} x^{4} + 561925 \, a^{4} b^{11} x^{3} + 2230800 \, a^{7} b^{8} x^{2} + 899080 \, a^{10} b^{5} x + 27664 \, a^{13} b^{2}\right)} x^{\frac{2}{3}} + 30780 \, {\left(50830 \, a^{2} b^{13} x^{4} + 1197196 \, a^{5} b^{10} x^{3} + 2180607 \, a^{8} b^{7} x^{2} + 402220 \, a^{11} b^{4} x + 3910 \, a^{14} b\right)} x^{\frac{1}{3}}}{69535440 \, x^{9}}"," ",0,"-1/69535440*(17383860*b^15*x^5 + 6327725040*a^3*b^12*x^4 + 58004146200*a^6*b^9*x^3 + 49717839600*a^9*b^6*x^2 + 3954828150*a^12*b^3*x + 7726160*a^15 + 31671*(7600*a*b^14*x^4 + 561925*a^4*b^11*x^3 + 2230800*a^7*b^8*x^2 + 899080*a^10*b^5*x + 27664*a^13*b^2)*x^(2/3) + 30780*(50830*a^2*b^13*x^4 + 1197196*a^5*b^10*x^3 + 2180607*a^8*b^7*x^2 + 402220*a^11*b^4*x + 3910*a^14*b)*x^(1/3))/x^9","A",0
2354,1,169,0,1.090968," ","integrate((a+b*x^(1/3))^15/x^11,x, algorithm=""fricas"")","-\frac{155117520 \, b^{15} x^{5} + 58815393000 \, a^{3} b^{12} x^{4} + 554545134000 \, a^{6} b^{9} x^{3} + 485226992250 \, a^{9} b^{6} x^{2} + 39210262000 \, a^{12} b^{3} x + 77558760 \, a^{15} + 918459 \, {\left(2375 \, a b^{14} x^{4} + 182000 \, a^{4} b^{11} x^{3} + 741000 \, a^{7} b^{8} x^{2} + 304304 \, a^{10} b^{5} x + 9500 \, a^{13} b^{2}\right)} x^{\frac{2}{3}} + 30780 \, {\left(466900 \, a^{2} b^{13} x^{4} + 11350339 \, a^{5} b^{10} x^{3} + 21149700 \, a^{8} b^{7} x^{2} + 3968650 \, a^{11} b^{4} x + 39100 \, a^{14} b\right)} x^{\frac{1}{3}}}{775587600 \, x^{10}}"," ",0,"-1/775587600*(155117520*b^15*x^5 + 58815393000*a^3*b^12*x^4 + 554545134000*a^6*b^9*x^3 + 485226992250*a^9*b^6*x^2 + 39210262000*a^12*b^3*x + 77558760*a^15 + 918459*(2375*a*b^14*x^4 + 182000*a^4*b^11*x^3 + 741000*a^7*b^8*x^2 + 304304*a^10*b^5*x + 9500*a^13*b^2)*x^(2/3) + 30780*(466900*a^2*b^13*x^4 + 11350339*a^5*b^10*x^3 + 21149700*a^8*b^7*x^2 + 3968650*a^11*b^4*x + 39100*a^14*b)*x^(1/3))/x^10","A",0
2355,1,169,0,0.622929," ","integrate((a+b*x^(1/3))^15/x^12,x, algorithm=""fricas"")","-\frac{1037158320 \, b^{15} x^{5} + 404491744800 \, a^{3} b^{12} x^{4} + 3893233043700 \, a^{6} b^{9} x^{3} + 3460651594400 \, a^{9} b^{6} x^{2} + 283144221360 \, a^{12} b^{3} x + 565722720 \, a^{15} + 432216 \, {\left(34100 \, a b^{14} x^{4} + 2679950 \, a^{4} b^{11} x^{3} + 11117964 \, a^{7} b^{8} x^{2} + 4632485 \, a^{10} b^{5} x + 146300 \, a^{13} b^{2}\right)} x^{\frac{2}{3}} + 2623995 \, {\left(37352 \, a^{2} b^{13} x^{4} + 928928 \, a^{5} b^{10} x^{3} + 1760880 \, a^{8} b^{7} x^{2} + 334880 \, a^{11} b^{4} x + 3335 \, a^{14} b\right)} x^{\frac{1}{3}}}{6222949920 \, x^{11}}"," ",0,"-1/6222949920*(1037158320*b^15*x^5 + 404491744800*a^3*b^12*x^4 + 3893233043700*a^6*b^9*x^3 + 3460651594400*a^9*b^6*x^2 + 283144221360*a^12*b^3*x + 565722720*a^15 + 432216*(34100*a*b^14*x^4 + 2679950*a^4*b^11*x^3 + 11117964*a^7*b^8*x^2 + 4632485*a^10*b^5*x + 146300*a^13*b^2)*x^(2/3) + 2623995*(37352*a^2*b^13*x^4 + 928928*a^5*b^10*x^3 + 1760880*a^8*b^7*x^2 + 334880*a^11*b^4*x + 3335*a^14*b)*x^(1/3))/x^11","A",0
2356,1,133,0,0.924714," ","integrate(x^3/(a+b*x^(1/3)),x, algorithm=""fricas"")","\frac{3080 \, a^{2} b^{9} x^{3} - 4620 \, a^{5} b^{6} x^{2} + 9240 \, a^{8} b^{3} x - 27720 \, a^{11} \log\left(b x^{\frac{1}{3}} + a\right) + 63 \, {\left(40 \, b^{11} x^{3} - 55 \, a^{3} b^{8} x^{2} + 88 \, a^{6} b^{5} x - 220 \, a^{9} b^{2}\right)} x^{\frac{2}{3}} - 198 \, {\left(14 \, a b^{10} x^{3} - 20 \, a^{4} b^{7} x^{2} + 35 \, a^{7} b^{4} x - 140 \, a^{10} b\right)} x^{\frac{1}{3}}}{9240 \, b^{12}}"," ",0,"1/9240*(3080*a^2*b^9*x^3 - 4620*a^5*b^6*x^2 + 9240*a^8*b^3*x - 27720*a^11*log(b*x^(1/3) + a) + 63*(40*b^11*x^3 - 55*a^3*b^8*x^2 + 88*a^6*b^5*x - 220*a^9*b^2)*x^(2/3) - 198*(14*a*b^10*x^3 - 20*a^4*b^7*x^2 + 35*a^7*b^4*x - 140*a^10*b)*x^(1/3))/b^12","A",0
2357,1,100,0,0.736863," ","integrate(x^2/(a+b*x^(1/3)),x, algorithm=""fricas"")","\frac{140 \, a^{2} b^{6} x^{2} - 280 \, a^{5} b^{3} x + 840 \, a^{8} \log\left(b x^{\frac{1}{3}} + a\right) + 21 \, {\left(5 \, b^{8} x^{2} - 8 \, a^{3} b^{5} x + 20 \, a^{6} b^{2}\right)} x^{\frac{2}{3}} - 30 \, {\left(4 \, a b^{7} x^{2} - 7 \, a^{4} b^{4} x + 28 \, a^{7} b\right)} x^{\frac{1}{3}}}{280 \, b^{9}}"," ",0,"1/280*(140*a^2*b^6*x^2 - 280*a^5*b^3*x + 840*a^8*log(b*x^(1/3) + a) + 21*(5*b^8*x^2 - 8*a^3*b^5*x + 20*a^6*b^2)*x^(2/3) - 30*(4*a*b^7*x^2 - 7*a^4*b^4*x + 28*a^7*b)*x^(1/3))/b^9","A",0
2358,1,66,0,0.810200," ","integrate(x/(a+b*x^(1/3)),x, algorithm=""fricas"")","\frac{20 \, a^{2} b^{3} x - 60 \, a^{5} \log\left(b x^{\frac{1}{3}} + a\right) + 6 \, {\left(2 \, b^{5} x - 5 \, a^{3} b^{2}\right)} x^{\frac{2}{3}} - 15 \, {\left(a b^{4} x - 4 \, a^{4} b\right)} x^{\frac{1}{3}}}{20 \, b^{6}}"," ",0,"1/20*(20*a^2*b^3*x - 60*a^5*log(b*x^(1/3) + a) + 6*(2*b^5*x - 5*a^3*b^2)*x^(2/3) - 15*(a*b^4*x - 4*a^4*b)*x^(1/3))/b^6","A",0
2359,1,33,0,0.532345," ","integrate(1/(a+b*x^(1/3)),x, algorithm=""fricas"")","\frac{3 \, {\left(2 \, a^{2} \log\left(b x^{\frac{1}{3}} + a\right) + b^{2} x^{\frac{2}{3}} - 2 \, a b x^{\frac{1}{3}}\right)}}{2 \, b^{3}}"," ",0,"3/2*(2*a^2*log(b*x^(1/3) + a) + b^2*x^(2/3) - 2*a*b*x^(1/3))/b^3","A",0
2360,1,20,0,0.794798," ","integrate(1/(a+b*x^(1/3))/x,x, algorithm=""fricas"")","-\frac{3 \, {\left(\log\left(b x^{\frac{1}{3}} + a\right) - \log\left(x^{\frac{1}{3}}\right)\right)}}{a}"," ",0,"-3*(log(b*x^(1/3) + a) - log(x^(1/3)))/a","A",0
2361,1,56,0,1.086358," ","integrate(1/(a+b*x^(1/3))/x^2,x, algorithm=""fricas"")","\frac{6 \, b^{3} x \log\left(b x^{\frac{1}{3}} + a\right) - 6 \, b^{3} x \log\left(x^{\frac{1}{3}}\right) - 6 \, a b^{2} x^{\frac{2}{3}} + 3 \, a^{2} b x^{\frac{1}{3}} - 2 \, a^{3}}{2 \, a^{4} x}"," ",0,"1/2*(6*b^3*x*log(b*x^(1/3) + a) - 6*b^3*x*log(x^(1/3)) - 6*a*b^2*x^(2/3) + 3*a^2*b*x^(1/3) - 2*a^3)/(a^4*x)","A",0
2362,1,93,0,0.957292," ","integrate(1/(a+b*x^(1/3))/x^3,x, algorithm=""fricas"")","-\frac{60 \, b^{6} x^{2} \log\left(b x^{\frac{1}{3}} + a\right) - 60 \, b^{6} x^{2} \log\left(x^{\frac{1}{3}}\right) - 20 \, a^{3} b^{3} x + 10 \, a^{6} - 15 \, {\left(4 \, a b^{5} x - a^{4} b^{2}\right)} x^{\frac{2}{3}} + 6 \, {\left(5 \, a^{2} b^{4} x - 2 \, a^{5} b\right)} x^{\frac{1}{3}}}{20 \, a^{7} x^{2}}"," ",0,"-1/20*(60*b^6*x^2*log(b*x^(1/3) + a) - 60*b^6*x^2*log(x^(1/3)) - 20*a^3*b^3*x + 10*a^6 - 15*(4*a*b^5*x - a^4*b^2)*x^(2/3) + 6*(5*a^2*b^4*x - 2*a^5*b)*x^(1/3))/(a^7*x^2)","A",0
2363,1,126,0,1.119970," ","integrate(1/(a+b*x^(1/3))/x^4,x, algorithm=""fricas"")","\frac{2520 \, b^{9} x^{3} \log\left(b x^{\frac{1}{3}} + a\right) - 2520 \, b^{9} x^{3} \log\left(x^{\frac{1}{3}}\right) - 840 \, a^{3} b^{6} x^{2} + 420 \, a^{6} b^{3} x - 280 \, a^{9} - 90 \, {\left(28 \, a b^{8} x^{2} - 7 \, a^{4} b^{5} x + 4 \, a^{7} b^{2}\right)} x^{\frac{2}{3}} + 63 \, {\left(20 \, a^{2} b^{7} x^{2} - 8 \, a^{5} b^{4} x + 5 \, a^{8} b\right)} x^{\frac{1}{3}}}{840 \, a^{10} x^{3}}"," ",0,"1/840*(2520*b^9*x^3*log(b*x^(1/3) + a) - 2520*b^9*x^3*log(x^(1/3)) - 840*a^3*b^6*x^2 + 420*a^6*b^3*x - 280*a^9 - 90*(28*a*b^8*x^2 - 7*a^4*b^5*x + 4*a^7*b^2)*x^(2/3) + 63*(20*a^2*b^7*x^2 - 8*a^5*b^4*x + 5*a^8*b)*x^(1/3))/(a^10*x^3)","A",0
2364,1,17,0,0.847811," ","integrate(1/(2+b*x^(1/3))/x,x, algorithm=""fricas"")","-\frac{3}{2} \, \log\left(b x^{\frac{1}{3}} + 2\right) + \frac{3}{2} \, \log\left(x^{\frac{1}{3}}\right)"," ",0,"-3/2*log(b*x^(1/3) + 2) + 3/2*log(x^(1/3))","A",0
2365,1,181,0,0.904241," ","integrate(x^3/(a+b*x^(1/3))^2,x, algorithm=""fricas"")","-\frac{560 \, a b^{12} x^{4} - 1540 \, a^{4} b^{9} x^{3} + 4620 \, a^{7} b^{6} x^{2} + 6720 \, a^{10} b^{3} x - 2520 \, a^{13} - 27720 \, {\left(a^{10} b^{3} x + a^{13}\right)} \log\left(b x^{\frac{1}{3}} + a\right) - 63 \, {\left(15 \, a^{2} b^{11} x^{3} - 33 \, a^{5} b^{8} x^{2} + 132 \, a^{8} b^{5} x + 220 \, a^{11} b^{2}\right)} x^{\frac{2}{3}} - 18 \, {\left(14 \, b^{13} x^{4} - 66 \, a^{3} b^{10} x^{3} + 165 \, a^{6} b^{7} x^{2} - 1155 \, a^{9} b^{4} x - 1540 \, a^{12} b\right)} x^{\frac{1}{3}}}{840 \, {\left(b^{15} x + a^{3} b^{12}\right)}}"," ",0,"-1/840*(560*a*b^12*x^4 - 1540*a^4*b^9*x^3 + 4620*a^7*b^6*x^2 + 6720*a^10*b^3*x - 2520*a^13 - 27720*(a^10*b^3*x + a^13)*log(b*x^(1/3) + a) - 63*(15*a^2*b^11*x^3 - 33*a^5*b^8*x^2 + 132*a^8*b^5*x + 220*a^11*b^2)*x^(2/3) - 18*(14*b^13*x^4 - 66*a^3*b^10*x^3 + 165*a^6*b^7*x^2 - 1155*a^9*b^4*x - 1540*a^12*b)*x^(1/3))/(b^15*x + a^3*b^12)","A",0
2366,1,147,0,0.855245," ","integrate(x^2/(a+b*x^(1/3))^2,x, algorithm=""fricas"")","-\frac{35 \, a b^{9} x^{3} - 140 \, a^{4} b^{6} x^{2} - 175 \, a^{7} b^{3} x + 105 \, a^{10} + 840 \, {\left(a^{7} b^{3} x + a^{10}\right)} \log\left(b x^{\frac{1}{3}} + a\right) - 21 \, {\left(3 \, a^{2} b^{8} x^{2} - 12 \, a^{5} b^{5} x - 20 \, a^{8} b^{2}\right)} x^{\frac{2}{3}} - 15 \, {\left(b^{10} x^{3} - 6 \, a^{3} b^{7} x^{2} + 42 \, a^{6} b^{4} x + 56 \, a^{9} b\right)} x^{\frac{1}{3}}}{35 \, {\left(b^{12} x + a^{3} b^{9}\right)}}"," ",0,"-1/35*(35*a*b^9*x^3 - 140*a^4*b^6*x^2 - 175*a^7*b^3*x + 105*a^10 + 840*(a^7*b^3*x + a^10)*log(b*x^(1/3) + a) - 21*(3*a^2*b^8*x^2 - 12*a^5*b^5*x - 20*a^8*b^2)*x^(2/3) - 15*(b^10*x^3 - 6*a^3*b^7*x^2 + 42*a^6*b^4*x + 56*a^9*b)*x^(1/3))/(b^12*x + a^3*b^9)","A",0
2367,1,114,0,0.864520," ","integrate(x/(a+b*x^(1/3))^2,x, algorithm=""fricas"")","-\frac{8 \, a b^{6} x^{2} + 8 \, a^{4} b^{3} x - 12 \, a^{7} - 60 \, {\left(a^{4} b^{3} x + a^{7}\right)} \log\left(b x^{\frac{1}{3}} + a\right) - 6 \, {\left(3 \, a^{2} b^{5} x + 5 \, a^{5} b^{2}\right)} x^{\frac{2}{3}} - 3 \, {\left(b^{7} x^{2} - 15 \, a^{3} b^{4} x - 20 \, a^{6} b\right)} x^{\frac{1}{3}}}{4 \, {\left(b^{9} x + a^{3} b^{6}\right)}}"," ",0,"-1/4*(8*a*b^6*x^2 + 8*a^4*b^3*x - 12*a^7 - 60*(a^4*b^3*x + a^7)*log(b*x^(1/3) + a) - 6*(3*a^2*b^5*x + 5*a^5*b^2)*x^(2/3) - 3*(b^7*x^2 - 15*a^3*b^4*x - 20*a^6*b)*x^(1/3))/(b^9*x + a^3*b^6)","A",0
2368,1,68,0,0.860393," ","integrate(1/(a+b*x^(1/3))^2,x, algorithm=""fricas"")","-\frac{3 \, {\left(a^{2} b^{2} x^{\frac{2}{3}} + a^{4} + 2 \, {\left(a b^{3} x + a^{4}\right)} \log\left(b x^{\frac{1}{3}} + a\right) - {\left(b^{4} x + 2 \, a^{3} b\right)} x^{\frac{1}{3}}\right)}}{b^{6} x + a^{3} b^{3}}"," ",0,"-3*(a^2*b^2*x^(2/3) + a^4 + 2*(a*b^3*x + a^4)*log(b*x^(1/3) + a) - (b^4*x + 2*a^3*b)*x^(1/3))/(b^6*x + a^3*b^3)","A",0
2369,1,70,0,0.516070," ","integrate(1/(a+b*x^(1/3))^2/x,x, algorithm=""fricas"")","\frac{3 \, {\left(a b^{2} x^{\frac{2}{3}} - a^{2} b x^{\frac{1}{3}} + a^{3} - {\left(b^{3} x + a^{3}\right)} \log\left(b x^{\frac{1}{3}} + a\right) + {\left(b^{3} x + a^{3}\right)} \log\left(x^{\frac{1}{3}}\right)\right)}}{a^{2} b^{3} x + a^{5}}"," ",0,"3*(a*b^2*x^(2/3) - a^2*b*x^(1/3) + a^3 - (b^3*x + a^3)*log(b*x^(1/3) + a) + (b^3*x + a^3)*log(x^(1/3)))/(a^2*b^3*x + a^5)","B",0
2370,1,122,0,0.877832," ","integrate(1/(a+b*x^(1/3))^2/x^2,x, algorithm=""fricas"")","-\frac{4 \, a^{3} b^{3} x + a^{6} - 12 \, {\left(b^{6} x^{2} + a^{3} b^{3} x\right)} \log\left(b x^{\frac{1}{3}} + a\right) + 12 \, {\left(b^{6} x^{2} + a^{3} b^{3} x\right)} \log\left(x^{\frac{1}{3}}\right) + 3 \, {\left(4 \, a b^{5} x + 3 \, a^{4} b^{2}\right)} x^{\frac{2}{3}} - 3 \, {\left(2 \, a^{2} b^{4} x + a^{5} b\right)} x^{\frac{1}{3}}}{a^{5} b^{3} x^{2} + a^{8} x}"," ",0,"-(4*a^3*b^3*x + a^6 - 12*(b^6*x^2 + a^3*b^3*x)*log(b*x^(1/3) + a) + 12*(b^6*x^2 + a^3*b^3*x)*log(x^(1/3)) + 3*(4*a*b^5*x + 3*a^4*b^2)*x^(2/3) - 3*(2*a^2*b^4*x + a^5*b)*x^(1/3))/(a^5*b^3*x^2 + a^8*x)","A",0
2371,1,164,0,0.864331," ","integrate(1/(a+b*x^(1/3))^2/x^3,x, algorithm=""fricas"")","\frac{140 \, a^{3} b^{6} x^{2} + 70 \, a^{6} b^{3} x - 10 \, a^{9} - 420 \, {\left(b^{9} x^{3} + a^{3} b^{6} x^{2}\right)} \log\left(b x^{\frac{1}{3}} + a\right) + 420 \, {\left(b^{9} x^{3} + a^{3} b^{6} x^{2}\right)} \log\left(x^{\frac{1}{3}}\right) + 15 \, {\left(28 \, a b^{8} x^{2} + 21 \, a^{4} b^{5} x - 3 \, a^{7} b^{2}\right)} x^{\frac{2}{3}} - 6 \, {\left(35 \, a^{2} b^{7} x^{2} + 21 \, a^{5} b^{4} x - 4 \, a^{8} b\right)} x^{\frac{1}{3}}}{20 \, {\left(a^{8} b^{3} x^{3} + a^{11} x^{2}\right)}}"," ",0,"1/20*(140*a^3*b^6*x^2 + 70*a^6*b^3*x - 10*a^9 - 420*(b^9*x^3 + a^3*b^6*x^2)*log(b*x^(1/3) + a) + 420*(b^9*x^3 + a^3*b^6*x^2)*log(x^(1/3)) + 15*(28*a*b^8*x^2 + 21*a^4*b^5*x - 3*a^7*b^2)*x^(2/3) - 6*(35*a^2*b^7*x^2 + 21*a^5*b^4*x - 4*a^8*b)*x^(1/3))/(a^8*b^3*x^3 + a^11*x^2)","A",0
2372,1,196,0,0.795769," ","integrate(1/(a+b*x^(1/3))^2/x^4,x, algorithm=""fricas"")","-\frac{840 \, a^{3} b^{9} x^{3} + 420 \, a^{6} b^{6} x^{2} - 140 \, a^{9} b^{3} x + 28 \, a^{12} - 2520 \, {\left(b^{12} x^{4} + a^{3} b^{9} x^{3}\right)} \log\left(b x^{\frac{1}{3}} + a\right) + 2520 \, {\left(b^{12} x^{4} + a^{3} b^{9} x^{3}\right)} \log\left(x^{\frac{1}{3}}\right) + 18 \, {\left(140 \, a b^{11} x^{3} + 105 \, a^{4} b^{8} x^{2} - 15 \, a^{7} b^{5} x + 6 \, a^{10} b^{2}\right)} x^{\frac{2}{3}} - 63 \, {\left(20 \, a^{2} b^{10} x^{3} + 12 \, a^{5} b^{7} x^{2} - 3 \, a^{8} b^{4} x + a^{11} b\right)} x^{\frac{1}{3}}}{84 \, {\left(a^{11} b^{3} x^{4} + a^{14} x^{3}\right)}}"," ",0,"-1/84*(840*a^3*b^9*x^3 + 420*a^6*b^6*x^2 - 140*a^9*b^3*x + 28*a^12 - 2520*(b^12*x^4 + a^3*b^9*x^3)*log(b*x^(1/3) + a) + 2520*(b^12*x^4 + a^3*b^9*x^3)*log(x^(1/3)) + 18*(140*a*b^11*x^3 + 105*a^4*b^8*x^2 - 15*a^7*b^5*x + 6*a^10*b^2)*x^(2/3) - 63*(20*a^2*b^10*x^3 + 12*a^5*b^7*x^2 - 3*a^8*b^4*x + a^11*b)*x^(1/3))/(a^11*b^3*x^4 + a^14*x^3)","A",0
2373,1,225,0,0.531294," ","integrate(x^3/(a+b*x^(1/3))^3,x, algorithm=""fricas"")","\frac{56 \, b^{15} x^{5} - 728 \, a^{3} b^{12} x^{4} + 3080 \, a^{6} b^{9} x^{3} + 8568 \, a^{9} b^{6} x^{2} - 1344 \, a^{12} b^{3} x - 5292 \, a^{15} - 27720 \, {\left(a^{9} b^{6} x^{2} + 2 \, a^{12} b^{3} x + a^{15}\right)} \log\left(b x^{\frac{1}{3}} + a\right) - 63 \, {\left(3 \, a b^{14} x^{4} - 18 \, a^{4} b^{11} x^{3} + 99 \, a^{7} b^{8} x^{2} + 352 \, a^{10} b^{5} x + 220 \, a^{13} b^{2}\right)} x^{\frac{2}{3}} + 18 \, {\left(24 \, a^{2} b^{13} x^{4} - 99 \, a^{5} b^{10} x^{3} + 990 \, a^{8} b^{7} x^{2} + 2695 \, a^{11} b^{4} x + 1540 \, a^{14} b\right)} x^{\frac{1}{3}}}{168 \, {\left(b^{18} x^{2} + 2 \, a^{3} b^{15} x + a^{6} b^{12}\right)}}"," ",0,"1/168*(56*b^15*x^5 - 728*a^3*b^12*x^4 + 3080*a^6*b^9*x^3 + 8568*a^9*b^6*x^2 - 1344*a^12*b^3*x - 5292*a^15 - 27720*(a^9*b^6*x^2 + 2*a^12*b^3*x + a^15)*log(b*x^(1/3) + a) - 63*(3*a*b^14*x^4 - 18*a^4*b^11*x^3 + 99*a^7*b^8*x^2 + 352*a^10*b^5*x + 220*a^13*b^2)*x^(2/3) + 18*(24*a^2*b^13*x^4 - 99*a^5*b^10*x^3 + 990*a^8*b^7*x^2 + 2695*a^11*b^4*x + 1540*a^14*b)*x^(1/3))/(b^18*x^2 + 2*a^3*b^15*x + a^6*b^12)","A",0
2374,1,192,0,0.848717," ","integrate(x^2/(a+b*x^(1/3))^3,x, algorithm=""fricas"")","\frac{5 \, b^{12} x^{4} - 90 \, a^{3} b^{9} x^{3} - 195 \, a^{6} b^{6} x^{2} + 170 \, a^{9} b^{3} x + 225 \, a^{12} + 840 \, {\left(a^{6} b^{6} x^{2} + 2 \, a^{9} b^{3} x + a^{12}\right)} \log\left(b x^{\frac{1}{3}} + a\right) - 3 \, {\left(6 \, a b^{11} x^{3} - 63 \, a^{4} b^{8} x^{2} - 224 \, a^{7} b^{5} x - 140 \, a^{10} b^{2}\right)} x^{\frac{2}{3}} + 15 \, {\left(3 \, a^{2} b^{10} x^{3} - 36 \, a^{5} b^{7} x^{2} - 98 \, a^{8} b^{4} x - 56 \, a^{11} b\right)} x^{\frac{1}{3}}}{10 \, {\left(b^{15} x^{2} + 2 \, a^{3} b^{12} x + a^{6} b^{9}\right)}}"," ",0,"1/10*(5*b^12*x^4 - 90*a^3*b^9*x^3 - 195*a^6*b^6*x^2 + 170*a^9*b^3*x + 225*a^12 + 840*(a^6*b^6*x^2 + 2*a^9*b^3*x + a^12)*log(b*x^(1/3) + a) - 3*(6*a*b^11*x^3 - 63*a^4*b^8*x^2 - 224*a^7*b^5*x - 140*a^10*b^2)*x^(2/3) + 15*(3*a^2*b^10*x^3 - 36*a^5*b^7*x^2 - 98*a^8*b^4*x - 56*a^11*b)*x^(1/3))/(b^15*x^2 + 2*a^3*b^12*x + a^6*b^9)","A",0
2375,1,159,0,0.764218," ","integrate(x/(a+b*x^(1/3))^3,x, algorithm=""fricas"")","\frac{2 \, b^{9} x^{3} + 4 \, a^{3} b^{6} x^{2} - 34 \, a^{6} b^{3} x - 27 \, a^{9} - 60 \, {\left(a^{3} b^{6} x^{2} + 2 \, a^{6} b^{3} x + a^{9}\right)} \log\left(b x^{\frac{1}{3}} + a\right) - 3 \, {\left(3 \, a b^{8} x^{2} + 16 \, a^{4} b^{5} x + 10 \, a^{7} b^{2}\right)} x^{\frac{2}{3}} + 3 \, {\left(12 \, a^{2} b^{7} x^{2} + 35 \, a^{5} b^{4} x + 20 \, a^{8} b\right)} x^{\frac{1}{3}}}{2 \, {\left(b^{12} x^{2} + 2 \, a^{3} b^{9} x + a^{6} b^{6}\right)}}"," ",0,"1/2*(2*b^9*x^3 + 4*a^3*b^6*x^2 - 34*a^6*b^3*x - 27*a^9 - 60*(a^3*b^6*x^2 + 2*a^6*b^3*x + a^9)*log(b*x^(1/3) + a) - 3*(3*a*b^8*x^2 + 16*a^4*b^5*x + 10*a^7*b^2)*x^(2/3) + 3*(12*a^2*b^7*x^2 + 35*a^5*b^4*x + 20*a^8*b)*x^(1/3))/(b^12*x^2 + 2*a^3*b^9*x + a^6*b^6)","B",0
2376,1,113,0,0.780125," ","integrate(1/(a+b*x^(1/3))^3,x, algorithm=""fricas"")","\frac{3 \, {\left(6 \, a^{3} b^{3} x + 3 \, a^{6} + 2 \, {\left(b^{6} x^{2} + 2 \, a^{3} b^{3} x + a^{6}\right)} \log\left(b x^{\frac{1}{3}} + a\right) + {\left(4 \, a b^{5} x + a^{4} b^{2}\right)} x^{\frac{2}{3}} - {\left(5 \, a^{2} b^{4} x + 2 \, a^{5} b\right)} x^{\frac{1}{3}}\right)}}{2 \, {\left(b^{9} x^{2} + 2 \, a^{3} b^{6} x + a^{6} b^{3}\right)}}"," ",0,"3/2*(6*a^3*b^3*x + 3*a^6 + 2*(b^6*x^2 + 2*a^3*b^3*x + a^6)*log(b*x^(1/3) + a) + (4*a*b^5*x + a^4*b^2)*x^(2/3) - (5*a^2*b^4*x + 2*a^5*b)*x^(1/3))/(b^9*x^2 + 2*a^3*b^6*x + a^6*b^3)","B",0
2377,1,129,0,0.839600," ","integrate(1/(a+b*x^(1/3))^3/x,x, algorithm=""fricas"")","\frac{3 \, {\left(3 \, a^{6} - 2 \, {\left(b^{6} x^{2} + 2 \, a^{3} b^{3} x + a^{6}\right)} \log\left(b x^{\frac{1}{3}} + a\right) + 2 \, {\left(b^{6} x^{2} + 2 \, a^{3} b^{3} x + a^{6}\right)} \log\left(x^{\frac{1}{3}}\right) + {\left(2 \, a b^{5} x + 5 \, a^{4} b^{2}\right)} x^{\frac{2}{3}} - {\left(a^{2} b^{4} x + 4 \, a^{5} b\right)} x^{\frac{1}{3}}\right)}}{2 \, {\left(a^{3} b^{6} x^{2} + 2 \, a^{6} b^{3} x + a^{9}\right)}}"," ",0,"3/2*(3*a^6 - 2*(b^6*x^2 + 2*a^3*b^3*x + a^6)*log(b*x^(1/3) + a) + 2*(b^6*x^2 + 2*a^3*b^3*x + a^6)*log(x^(1/3)) + (2*a*b^5*x + 5*a^4*b^2)*x^(2/3) - (a^2*b^4*x + 4*a^5*b)*x^(1/3))/(a^3*b^6*x^2 + 2*a^6*b^3*x + a^9)","B",0
2378,1,191,0,0.858647," ","integrate(1/(a+b*x^(1/3))^3/x^2,x, algorithm=""fricas"")","-\frac{20 \, a^{3} b^{6} x^{2} + 31 \, a^{6} b^{3} x + 2 \, a^{9} - 60 \, {\left(b^{9} x^{3} + 2 \, a^{3} b^{6} x^{2} + a^{6} b^{3} x\right)} \log\left(b x^{\frac{1}{3}} + a\right) + 60 \, {\left(b^{9} x^{3} + 2 \, a^{3} b^{6} x^{2} + a^{6} b^{3} x\right)} \log\left(x^{\frac{1}{3}}\right) + 3 \, {\left(20 \, a b^{8} x^{2} + 35 \, a^{4} b^{5} x + 12 \, a^{7} b^{2}\right)} x^{\frac{2}{3}} - 3 \, {\left(10 \, a^{2} b^{7} x^{2} + 16 \, a^{5} b^{4} x + 3 \, a^{8} b\right)} x^{\frac{1}{3}}}{2 \, {\left(a^{6} b^{6} x^{3} + 2 \, a^{9} b^{3} x^{2} + a^{12} x\right)}}"," ",0,"-1/2*(20*a^3*b^6*x^2 + 31*a^6*b^3*x + 2*a^9 - 60*(b^9*x^3 + 2*a^3*b^6*x^2 + a^6*b^3*x)*log(b*x^(1/3) + a) + 60*(b^9*x^3 + 2*a^3*b^6*x^2 + a^6*b^3*x)*log(x^(1/3)) + 3*(20*a*b^8*x^2 + 35*a^4*b^5*x + 12*a^7*b^2)*x^(2/3) - 3*(10*a^2*b^7*x^2 + 16*a^5*b^4*x + 3*a^8*b)*x^(1/3))/(a^6*b^6*x^3 + 2*a^9*b^3*x^2 + a^12*x)","B",0
2379,1,230,0,0.650666," ","integrate(1/(a+b*x^(1/3))^3/x^3,x, algorithm=""fricas"")","\frac{280 \, a^{3} b^{9} x^{3} + 420 \, a^{6} b^{6} x^{2} + 90 \, a^{9} b^{3} x - 5 \, a^{12} - 840 \, {\left(b^{12} x^{4} + 2 \, a^{3} b^{9} x^{3} + a^{6} b^{6} x^{2}\right)} \log\left(b x^{\frac{1}{3}} + a\right) + 840 \, {\left(b^{12} x^{4} + 2 \, a^{3} b^{9} x^{3} + a^{6} b^{6} x^{2}\right)} \log\left(x^{\frac{1}{3}}\right) + 15 \, {\left(56 \, a b^{11} x^{3} + 98 \, a^{4} b^{8} x^{2} + 36 \, a^{7} b^{5} x - 3 \, a^{10} b^{2}\right)} x^{\frac{2}{3}} - 3 \, {\left(140 \, a^{2} b^{10} x^{3} + 224 \, a^{5} b^{7} x^{2} + 63 \, a^{8} b^{4} x - 6 \, a^{11} b\right)} x^{\frac{1}{3}}}{10 \, {\left(a^{9} b^{6} x^{4} + 2 \, a^{12} b^{3} x^{3} + a^{15} x^{2}\right)}}"," ",0,"1/10*(280*a^3*b^9*x^3 + 420*a^6*b^6*x^2 + 90*a^9*b^3*x - 5*a^12 - 840*(b^12*x^4 + 2*a^3*b^9*x^3 + a^6*b^6*x^2)*log(b*x^(1/3) + a) + 840*(b^12*x^4 + 2*a^3*b^9*x^3 + a^6*b^6*x^2)*log(x^(1/3)) + 15*(56*a*b^11*x^3 + 98*a^4*b^8*x^2 + 36*a^7*b^5*x - 3*a^10*b^2)*x^(2/3) - 3*(140*a^2*b^10*x^3 + 224*a^5*b^7*x^2 + 63*a^8*b^4*x - 6*a^11*b)*x^(1/3))/(a^9*b^6*x^4 + 2*a^12*b^3*x^3 + a^15*x^2)","A",0
2380,1,263,0,0.818328," ","integrate(1/(a+b*x^(1/3))^3/x^4,x, algorithm=""fricas"")","-\frac{9240 \, a^{3} b^{12} x^{4} + 13860 \, a^{6} b^{9} x^{3} + 3080 \, a^{9} b^{6} x^{2} - 728 \, a^{12} b^{3} x + 56 \, a^{15} - 27720 \, {\left(b^{15} x^{5} + 2 \, a^{3} b^{12} x^{4} + a^{6} b^{9} x^{3}\right)} \log\left(b x^{\frac{1}{3}} + a\right) + 27720 \, {\left(b^{15} x^{5} + 2 \, a^{3} b^{12} x^{4} + a^{6} b^{9} x^{3}\right)} \log\left(x^{\frac{1}{3}}\right) + 18 \, {\left(1540 \, a b^{14} x^{4} + 2695 \, a^{4} b^{11} x^{3} + 990 \, a^{7} b^{8} x^{2} - 99 \, a^{10} b^{5} x + 24 \, a^{13} b^{2}\right)} x^{\frac{2}{3}} - 63 \, {\left(220 \, a^{2} b^{13} x^{4} + 352 \, a^{5} b^{10} x^{3} + 99 \, a^{8} b^{7} x^{2} - 18 \, a^{11} b^{4} x + 3 \, a^{14} b\right)} x^{\frac{1}{3}}}{168 \, {\left(a^{12} b^{6} x^{5} + 2 \, a^{15} b^{3} x^{4} + a^{18} x^{3}\right)}}"," ",0,"-1/168*(9240*a^3*b^12*x^4 + 13860*a^6*b^9*x^3 + 3080*a^9*b^6*x^2 - 728*a^12*b^3*x + 56*a^15 - 27720*(b^15*x^5 + 2*a^3*b^12*x^4 + a^6*b^9*x^3)*log(b*x^(1/3) + a) + 27720*(b^15*x^5 + 2*a^3*b^12*x^4 + a^6*b^9*x^3)*log(x^(1/3)) + 18*(1540*a*b^14*x^4 + 2695*a^4*b^11*x^3 + 990*a^7*b^8*x^2 - 99*a^10*b^5*x + 24*a^13*b^2)*x^(2/3) - 63*(220*a^2*b^13*x^4 + 352*a^5*b^10*x^3 + 99*a^8*b^7*x^2 - 18*a^11*b^4*x + 3*a^14*b)*x^(1/3))/(a^12*b^6*x^5 + 2*a^15*b^3*x^4 + a^18*x^3)","A",0
2381,1,21,0,0.822816," ","integrate(1/(1+x^(1/3))^(1/2),x, algorithm=""fricas"")","\frac{2}{5} \, {\left(3 \, x^{\frac{2}{3}} - 4 \, x^{\frac{1}{3}} + 8\right)} \sqrt{x^{\frac{1}{3}} + 1}"," ",0,"2/5*(3*x^(2/3) - 4*x^(1/3) + 8)*sqrt(x^(1/3) + 1)","A",0
2382,1,23,0,1.128386," ","integrate(1/(1+x^(1/3))/x^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, x \arctan\left(x^{\frac{1}{6}}\right) + 3 \, x^{\frac{5}{6}} - \sqrt{x}\right)}}{x}"," ",0,"2*(3*x*arctan(x^(1/6)) + 3*x^(5/6) - sqrt(x))/x","A",0
2383,1,25,0,0.855892," ","integrate(x^(2/3)/(1+x^(1/3)),x, algorithm=""fricas"")","\frac{3}{4} \, {\left(x - 4\right)} x^{\frac{1}{3}} - x + \frac{3}{2} \, x^{\frac{2}{3}} + 3 \, \log\left(x^{\frac{1}{3}} + 1\right)"," ",0,"3/4*(x - 4)*x^(1/3) - x + 3/2*x^(2/3) + 3*log(x^(1/3) + 1)","A",0
2384,1,12,0,0.599766," ","integrate(1/(1+x^(2/3)),x, algorithm=""fricas"")","3 \, x^{\frac{1}{3}} - 3 \, \arctan\left(x^{\frac{1}{3}}\right)"," ",0,"3*x^(1/3) - 3*arctan(x^(1/3))","A",0
2385,1,8,0,0.859034," ","integrate(1/(1+x^(2/3))/x^(1/3),x, algorithm=""fricas"")","\frac{3}{2} \, \log\left(x^{\frac{2}{3}} + 1\right)"," ",0,"3/2*log(x^(2/3) + 1)","A",0
2386,1,6,0,0.667557," ","integrate(1/(1+x^(2/3))/x^(2/3),x, algorithm=""fricas"")","3 \, \arctan\left(x^{\frac{1}{3}}\right)"," ",0,"3*arctan(x^(1/3))","A",0
2387,1,7,0,2.847425," ","integrate((-1+x^(2/3))^(1/2)/x^(1/3),x, algorithm=""fricas"")","{\left(x^{\frac{2}{3}} - 1\right)}^{\frac{3}{2}}"," ",0,"(x^(2/3) - 1)^(3/2)","A",0
2388,1,19,0,2.647847," ","integrate((1+x^(2/3))^(3/2)/x^(1/3),x, algorithm=""fricas"")","\frac{3}{5} \, {\left(x^{\frac{4}{3}} + 2 \, x^{\frac{2}{3}} + 1\right)} \sqrt{x^{\frac{2}{3}} + 1}"," ",0,"3/5*(x^(4/3) + 2*x^(2/3) + 1)*sqrt(x^(2/3) + 1)","B",0
2389,1,125,0,0.919122," ","integrate(x^(1/2)/(1+x^(2/3)),x, algorithm=""fricas"")","-3 \, \sqrt{2} \arctan\left(\sqrt{2} \sqrt{\sqrt{2} x^{\frac{1}{6}} + x^{\frac{1}{3}} + 1} - \sqrt{2} x^{\frac{1}{6}} - 1\right) - 3 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} \sqrt{-4 \, \sqrt{2} x^{\frac{1}{6}} + 4 \, x^{\frac{1}{3}} + 4} - \sqrt{2} x^{\frac{1}{6}} + 1\right) + \frac{3}{4} \, \sqrt{2} \log\left(4 \, \sqrt{2} x^{\frac{1}{6}} + 4 \, x^{\frac{1}{3}} + 4\right) - \frac{3}{4} \, \sqrt{2} \log\left(-4 \, \sqrt{2} x^{\frac{1}{6}} + 4 \, x^{\frac{1}{3}} + 4\right) + \frac{6}{5} \, x^{\frac{5}{6}} - 6 \, x^{\frac{1}{6}}"," ",0,"-3*sqrt(2)*arctan(sqrt(2)*sqrt(sqrt(2)*x^(1/6) + x^(1/3) + 1) - sqrt(2)*x^(1/6) - 1) - 3*sqrt(2)*arctan(1/2*sqrt(2)*sqrt(-4*sqrt(2)*x^(1/6) + 4*x^(1/3) + 4) - sqrt(2)*x^(1/6) + 1) + 3/4*sqrt(2)*log(4*sqrt(2)*x^(1/6) + 4*x^(1/3) + 4) - 3/4*sqrt(2)*log(-4*sqrt(2)*x^(1/6) + 4*x^(1/3) + 4) + 6/5*x^(5/6) - 6*x^(1/6)","A",0
2390,1,638,0,3.391656," ","integrate(x^(1/3)/(-1+x^(5/6)),x, algorithm=""fricas"")","\frac{1}{10} \, {\left(3 \, \sqrt{5} - \sqrt{-\frac{27}{4} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{2} + \frac{9}{2} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} + \sqrt{5} - 3\right)} {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} - \frac{27}{4} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)}^{2} + 18 \, \sqrt{2} \sqrt{\sqrt{5} - 5} + 18 \, \sqrt{5} - 90} - 3\right)} \log\left(\frac{9}{4} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{2} + \frac{9}{4} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)}^{2} + 3 \, \sqrt{-\frac{27}{4} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{2} + \frac{9}{2} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} + \sqrt{5} - 3\right)} {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} - \frac{27}{4} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)}^{2} + 18 \, \sqrt{2} \sqrt{\sqrt{5} - 5} + 18 \, \sqrt{5} - 90} {\left(\sqrt{5} - 1\right)} + 72 \, x^{\frac{1}{6}} + 36\right) + \frac{1}{10} \, {\left(3 \, \sqrt{5} + \sqrt{-\frac{27}{4} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{2} + \frac{9}{2} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} + \sqrt{5} - 3\right)} {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} - \frac{27}{4} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)}^{2} + 18 \, \sqrt{2} \sqrt{\sqrt{5} - 5} + 18 \, \sqrt{5} - 90} - 3\right)} \log\left(\frac{9}{4} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{2} + \frac{9}{4} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)}^{2} - 3 \, \sqrt{-\frac{27}{4} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{2} + \frac{9}{2} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} + \sqrt{5} - 3\right)} {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} - \frac{27}{4} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)}^{2} + 18 \, \sqrt{2} \sqrt{\sqrt{5} - 5} + 18 \, \sqrt{5} - 90} {\left(\sqrt{5} - 1\right)} + 72 \, x^{\frac{1}{6}} + 36\right) - \frac{3}{10} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)} \log\left(-\frac{9}{4} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} + \sqrt{5} + 1\right)}^{2} + 36 \, x^{\frac{1}{6}}\right) + \frac{3}{10} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)} \log\left(-\frac{9}{4} \, {\left(\sqrt{2} \sqrt{\sqrt{5} - 5} - \sqrt{5} - 1\right)}^{2} + 36 \, x^{\frac{1}{6}}\right) + 2 \, \sqrt{x} + \frac{6}{5} \, \log\left(x^{\frac{1}{6}} - 1\right)"," ",0,"1/10*(3*sqrt(5) - sqrt(-27/4*(sqrt(2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^2 + 9/2*(sqrt(2)*sqrt(sqrt(5) - 5) + sqrt(5) - 3)*(sqrt(2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1) - 27/4*(sqrt(2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)^2 + 18*sqrt(2)*sqrt(sqrt(5) - 5) + 18*sqrt(5) - 90) - 3)*log(9/4*(sqrt(2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^2 + 9/4*(sqrt(2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)^2 + 3*sqrt(-27/4*(sqrt(2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^2 + 9/2*(sqrt(2)*sqrt(sqrt(5) - 5) + sqrt(5) - 3)*(sqrt(2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1) - 27/4*(sqrt(2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)^2 + 18*sqrt(2)*sqrt(sqrt(5) - 5) + 18*sqrt(5) - 90)*(sqrt(5) - 1) + 72*x^(1/6) + 36) + 1/10*(3*sqrt(5) + sqrt(-27/4*(sqrt(2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^2 + 9/2*(sqrt(2)*sqrt(sqrt(5) - 5) + sqrt(5) - 3)*(sqrt(2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1) - 27/4*(sqrt(2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)^2 + 18*sqrt(2)*sqrt(sqrt(5) - 5) + 18*sqrt(5) - 90) - 3)*log(9/4*(sqrt(2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^2 + 9/4*(sqrt(2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)^2 - 3*sqrt(-27/4*(sqrt(2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^2 + 9/2*(sqrt(2)*sqrt(sqrt(5) - 5) + sqrt(5) - 3)*(sqrt(2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1) - 27/4*(sqrt(2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)^2 + 18*sqrt(2)*sqrt(sqrt(5) - 5) + 18*sqrt(5) - 90)*(sqrt(5) - 1) + 72*x^(1/6) + 36) - 3/10*(sqrt(2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)*log(-9/4*(sqrt(2)*sqrt(sqrt(5) - 5) + sqrt(5) + 1)^2 + 36*x^(1/6)) + 3/10*(sqrt(2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)*log(-9/4*(sqrt(2)*sqrt(sqrt(5) - 5) - sqrt(5) - 1)^2 + 36*x^(1/6)) + 2*sqrt(x) + 6/5*log(x^(1/6) - 1)","B",0
2391,1,63,0,0.630826," ","integrate((3-1/x^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{1}{6} \, {\left(6 \, x - \sqrt{x}\right)} \sqrt{\frac{3 \, x - \sqrt{x}}{x}} + \frac{1}{36} \, \sqrt{3} \log\left(2 \, \sqrt{3} \sqrt{x} \sqrt{\frac{3 \, x - \sqrt{x}}{x}} - 6 \, \sqrt{x} + 1\right)"," ",0,"1/6*(6*x - sqrt(x))*sqrt((3*x - sqrt(x))/x) + 1/36*sqrt(3)*log(2*sqrt(3)*sqrt(x)*sqrt((3*x - sqrt(x))/x) - 6*sqrt(x) + 1)","A",0
2392,1,55,0,0.880397," ","integrate(1/(1+1/x^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, {\left(2 \, x - 3 \, \sqrt{x}\right)} \sqrt{\frac{x + \sqrt{x}}{x}} + \frac{3}{4} \, \log\left(\sqrt{\frac{x + \sqrt{x}}{x}} + 1\right) - \frac{3}{4} \, \log\left(\sqrt{\frac{x + \sqrt{x}}{x}} - 1\right)"," ",0,"1/2*(2*x - 3*sqrt(x))*sqrt((x + sqrt(x))/x) + 3/4*log(sqrt((x + sqrt(x))/x) + 1) - 3/4*log(sqrt((x + sqrt(x))/x) - 1)","A",0
2393,-1,0,0,0.000000," ","integrate((a+b/x^(3/2))^(2/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2394,1,13,0,1.077617," ","integrate((a+b/x^(1/3))*x^4,x, algorithm=""fricas"")","\frac{1}{5} \, a x^{5} + \frac{3}{14} \, b x^{\frac{14}{3}}"," ",0,"1/5*a*x^5 + 3/14*b*x^(14/3)","A",0
2395,1,13,0,1.084622," ","integrate((a+b/x^(1/3))*x^3,x, algorithm=""fricas"")","\frac{1}{4} \, a x^{4} + \frac{3}{11} \, b x^{\frac{11}{3}}"," ",0,"1/4*a*x^4 + 3/11*b*x^(11/3)","A",0
2396,1,13,0,0.726846," ","integrate((a+b/x^(1/3))*x^2,x, algorithm=""fricas"")","\frac{1}{3} \, a x^{3} + \frac{3}{8} \, b x^{\frac{8}{3}}"," ",0,"1/3*a*x^3 + 3/8*b*x^(8/3)","A",0
2397,1,13,0,0.985096," ","integrate((a+b/x^(1/3))*x,x, algorithm=""fricas"")","\frac{1}{2} \, a x^{2} + \frac{3}{5} \, b x^{\frac{5}{3}}"," ",0,"1/2*a*x^2 + 3/5*b*x^(5/3)","A",0
2398,1,10,0,1.037227," ","integrate(a+b/x^(1/3),x, algorithm=""fricas"")","a x + \frac{3}{2} \, b x^{\frac{2}{3}}"," ",0,"a*x + 3/2*b*x^(2/3)","A",0
2399,1,19,0,0.639619," ","integrate((a+b/x^(1/3))/x,x, algorithm=""fricas"")","\frac{3 \, {\left(a x \log\left(x^{\frac{1}{3}}\right) - b x^{\frac{2}{3}}\right)}}{x}"," ",0,"3*(a*x*log(x^(1/3)) - b*x^(2/3))/x","A",0
2400,1,16,0,0.765139," ","integrate((a+b/x^(1/3))/x^2,x, algorithm=""fricas"")","-\frac{4 \, a x + 3 \, b x^{\frac{2}{3}}}{4 \, x^{2}}"," ",0,"-1/4*(4*a*x + 3*b*x^(2/3))/x^2","A",0
2401,1,16,0,0.875671," ","integrate((a+b/x^(1/3))/x^3,x, algorithm=""fricas"")","-\frac{7 \, a x + 6 \, b x^{\frac{2}{3}}}{14 \, x^{3}}"," ",0,"-1/14*(7*a*x + 6*b*x^(2/3))/x^3","A",0
2402,1,16,0,0.878115," ","integrate((a+b/x^(1/3))/x^4,x, algorithm=""fricas"")","-\frac{10 \, a x + 9 \, b x^{\frac{2}{3}}}{30 \, x^{4}}"," ",0,"-1/30*(10*a*x + 9*b*x^(2/3))/x^4","A",0
2403,1,24,0,0.817366," ","integrate((a+b/x^(1/3))^2*x^4,x, algorithm=""fricas"")","\frac{1}{5} \, a^{2} x^{5} + \frac{3}{7} \, a b x^{\frac{14}{3}} + \frac{3}{13} \, b^{2} x^{\frac{13}{3}}"," ",0,"1/5*a^2*x^5 + 3/7*a*b*x^(14/3) + 3/13*b^2*x^(13/3)","A",0
2404,1,24,0,0.741224," ","integrate((a+b/x^(1/3))^2*x^3,x, algorithm=""fricas"")","\frac{1}{4} \, a^{2} x^{4} + \frac{6}{11} \, a b x^{\frac{11}{3}} + \frac{3}{10} \, b^{2} x^{\frac{10}{3}}"," ",0,"1/4*a^2*x^4 + 6/11*a*b*x^(11/3) + 3/10*b^2*x^(10/3)","A",0
2405,1,24,0,0.945312," ","integrate((a+b/x^(1/3))^2*x^2,x, algorithm=""fricas"")","\frac{1}{3} \, a^{2} x^{3} + \frac{3}{4} \, a b x^{\frac{8}{3}} + \frac{3}{7} \, b^{2} x^{\frac{7}{3}}"," ",0,"1/3*a^2*x^3 + 3/4*a*b*x^(8/3) + 3/7*b^2*x^(7/3)","A",0
2406,1,24,0,0.907597," ","integrate((a+b/x^(1/3))^2*x,x, algorithm=""fricas"")","\frac{1}{2} \, a^{2} x^{2} + \frac{6}{5} \, a b x^{\frac{5}{3}} + \frac{3}{4} \, b^{2} x^{\frac{4}{3}}"," ",0,"1/2*a^2*x^2 + 6/5*a*b*x^(5/3) + 3/4*b^2*x^(4/3)","A",0
2407,1,21,0,1.092489," ","integrate((a+b/x^(1/3))^2,x, algorithm=""fricas"")","a^{2} x + 3 \, a b x^{\frac{2}{3}} + 3 \, b^{2} x^{\frac{1}{3}}"," ",0,"a^2*x + 3*a*b*x^(2/3) + 3*b^2*x^(1/3)","A",0
2408,1,31,0,0.849434," ","integrate((a+b/x^(1/3))^2/x,x, algorithm=""fricas"")","\frac{3 \, {\left(2 \, a^{2} x \log\left(x^{\frac{1}{3}}\right) - 4 \, a b x^{\frac{2}{3}} - b^{2} x^{\frac{1}{3}}\right)}}{2 \, x}"," ",0,"3/2*(2*a^2*x*log(x^(1/3)) - 4*a*b*x^(2/3) - b^2*x^(1/3))/x","A",0
2409,1,27,0,0.795682," ","integrate((a+b/x^(1/3))^2/x^2,x, algorithm=""fricas"")","-\frac{10 \, a^{2} x + 15 \, a b x^{\frac{2}{3}} + 6 \, b^{2} x^{\frac{1}{3}}}{10 \, x^{2}}"," ",0,"-1/10*(10*a^2*x + 15*a*b*x^(2/3) + 6*b^2*x^(1/3))/x^2","A",0
2410,1,27,0,0.736314," ","integrate((a+b/x^(1/3))^2/x^3,x, algorithm=""fricas"")","-\frac{28 \, a^{2} x + 48 \, a b x^{\frac{2}{3}} + 21 \, b^{2} x^{\frac{1}{3}}}{56 \, x^{3}}"," ",0,"-1/56*(28*a^2*x + 48*a*b*x^(2/3) + 21*b^2*x^(1/3))/x^3","A",0
2411,1,27,0,0.969194," ","integrate((a+b/x^(1/3))^2/x^4,x, algorithm=""fricas"")","-\frac{55 \, a^{2} x + 99 \, a b x^{\frac{2}{3}} + 45 \, b^{2} x^{\frac{1}{3}}}{165 \, x^{4}}"," ",0,"-1/165*(55*a^2*x + 99*a*b*x^(2/3) + 45*b^2*x^(1/3))/x^4","A",0
2412,1,35,0,0.827039," ","integrate((a+b/x^(1/3))^3*x^4,x, algorithm=""fricas"")","\frac{1}{5} \, a^{3} x^{5} + \frac{9}{14} \, a^{2} b x^{\frac{14}{3}} + \frac{9}{13} \, a b^{2} x^{\frac{13}{3}} + \frac{1}{4} \, b^{3} x^{4}"," ",0,"1/5*a^3*x^5 + 9/14*a^2*b*x^(14/3) + 9/13*a*b^2*x^(13/3) + 1/4*b^3*x^4","A",0
2413,1,35,0,0.813483," ","integrate((a+b/x^(1/3))^3*x^3,x, algorithm=""fricas"")","\frac{1}{4} \, a^{3} x^{4} + \frac{9}{11} \, a^{2} b x^{\frac{11}{3}} + \frac{9}{10} \, a b^{2} x^{\frac{10}{3}} + \frac{1}{3} \, b^{3} x^{3}"," ",0,"1/4*a^3*x^4 + 9/11*a^2*b*x^(11/3) + 9/10*a*b^2*x^(10/3) + 1/3*b^3*x^3","A",0
2414,1,35,0,0.663659," ","integrate((a+b/x^(1/3))^3*x^2,x, algorithm=""fricas"")","\frac{1}{3} \, a^{3} x^{3} + \frac{9}{8} \, a^{2} b x^{\frac{8}{3}} + \frac{9}{7} \, a b^{2} x^{\frac{7}{3}} + \frac{1}{2} \, b^{3} x^{2}"," ",0,"1/3*a^3*x^3 + 9/8*a^2*b*x^(8/3) + 9/7*a*b^2*x^(7/3) + 1/2*b^3*x^2","A",0
2415,1,32,0,0.588597," ","integrate((a+b/x^(1/3))^3*x,x, algorithm=""fricas"")","\frac{1}{2} \, a^{3} x^{2} + \frac{9}{5} \, a^{2} b x^{\frac{5}{3}} + \frac{9}{4} \, a b^{2} x^{\frac{4}{3}} + b^{3} x"," ",0,"1/2*a^3*x^2 + 9/5*a^2*b*x^(5/3) + 9/4*a*b^2*x^(4/3) + b^3*x","A",0
2416,1,33,0,0.622516," ","integrate((a+b/x^(1/3))^3,x, algorithm=""fricas"")","a^{3} x + 3 \, b^{3} \log\left(x^{\frac{1}{3}}\right) + \frac{9}{2} \, a^{2} b x^{\frac{2}{3}} + 9 \, a b^{2} x^{\frac{1}{3}}"," ",0,"a^3*x + 3*b^3*log(x^(1/3)) + 9/2*a^2*b*x^(2/3) + 9*a*b^2*x^(1/3)","A",0
2417,1,39,0,0.970160," ","integrate((a+b/x^(1/3))^3/x,x, algorithm=""fricas"")","\frac{6 \, a^{3} x \log\left(x^{\frac{1}{3}}\right) - 18 \, a^{2} b x^{\frac{2}{3}} - 9 \, a b^{2} x^{\frac{1}{3}} - 2 \, b^{3}}{2 \, x}"," ",0,"1/2*(6*a^3*x*log(x^(1/3)) - 18*a^2*b*x^(2/3) - 9*a*b^2*x^(1/3) - 2*b^3)/x","A",0
2418,1,35,0,0.702190," ","integrate((a+b/x^(1/3))^3/x^2,x, algorithm=""fricas"")","-\frac{20 \, a^{3} x + 45 \, a^{2} b x^{\frac{2}{3}} + 36 \, a b^{2} x^{\frac{1}{3}} + 10 \, b^{3}}{20 \, x^{2}}"," ",0,"-1/20*(20*a^3*x + 45*a^2*b*x^(2/3) + 36*a*b^2*x^(1/3) + 10*b^3)/x^2","A",0
2419,1,35,0,0.785093," ","integrate((a+b/x^(1/3))^3/x^3,x, algorithm=""fricas"")","-\frac{84 \, a^{3} x + 216 \, a^{2} b x^{\frac{2}{3}} + 189 \, a b^{2} x^{\frac{1}{3}} + 56 \, b^{3}}{168 \, x^{3}}"," ",0,"-1/168*(84*a^3*x + 216*a^2*b*x^(2/3) + 189*a*b^2*x^(1/3) + 56*b^3)/x^3","A",0
2420,1,35,0,0.609584," ","integrate((a+b/x^(1/3))^3/x^4,x, algorithm=""fricas"")","-\frac{220 \, a^{3} x + 594 \, a^{2} b x^{\frac{2}{3}} + 540 \, a b^{2} x^{\frac{1}{3}} + 165 \, b^{3}}{660 \, x^{4}}"," ",0,"-1/660*(220*a^3*x + 594*a^2*b*x^(2/3) + 540*a*b^2*x^(1/3) + 165*b^3)/x^4","A",0
2421,1,111,0,0.940142," ","integrate(x^2/(a+b/x^(1/3)),x, algorithm=""fricas"")","\frac{280 \, a^{9} x^{3} - 420 \, a^{6} b^{3} x^{2} + 840 \, a^{3} b^{6} x - 2520 \, b^{9} \log\left(a x^{\frac{1}{3}} + b\right) - 63 \, {\left(5 \, a^{8} b x^{2} - 8 \, a^{5} b^{4} x + 20 \, a^{2} b^{7}\right)} x^{\frac{2}{3}} + 90 \, {\left(4 \, a^{7} b^{2} x^{2} - 7 \, a^{4} b^{5} x + 28 \, a b^{8}\right)} x^{\frac{1}{3}}}{840 \, a^{10}}"," ",0,"1/840*(280*a^9*x^3 - 420*a^6*b^3*x^2 + 840*a^3*b^6*x - 2520*b^9*log(a*x^(1/3) + b) - 63*(5*a^8*b*x^2 - 8*a^5*b^4*x + 20*a^2*b^7)*x^(2/3) + 90*(4*a^7*b^2*x^2 - 7*a^4*b^5*x + 28*a*b^8)*x^(1/3))/a^10","A",0
2422,1,77,0,1.063018," ","integrate(x/(a+b/x^(1/3)),x, algorithm=""fricas"")","\frac{10 \, a^{6} x^{2} - 20 \, a^{3} b^{3} x + 60 \, b^{6} \log\left(a x^{\frac{1}{3}} + b\right) - 6 \, {\left(2 \, a^{5} b x - 5 \, a^{2} b^{4}\right)} x^{\frac{2}{3}} + 15 \, {\left(a^{4} b^{2} x - 4 \, a b^{5}\right)} x^{\frac{1}{3}}}{20 \, a^{7}}"," ",0,"1/20*(10*a^6*x^2 - 20*a^3*b^3*x + 60*b^6*log(a*x^(1/3) + b) - 6*(2*a^5*b*x - 5*a^2*b^4)*x^(2/3) + 15*(a^4*b^2*x - 4*a*b^5)*x^(1/3))/a^7","A",0
2423,1,43,0,1.165507," ","integrate(1/(a+b/x^(1/3)),x, algorithm=""fricas"")","\frac{2 \, a^{3} x - 6 \, b^{3} \log\left(a x^{\frac{1}{3}} + b\right) - 3 \, a^{2} b x^{\frac{2}{3}} + 6 \, a b^{2} x^{\frac{1}{3}}}{2 \, a^{4}}"," ",0,"1/2*(2*a^3*x - 6*b^3*log(a*x^(1/3) + b) - 3*a^2*b*x^(2/3) + 6*a*b^2*x^(1/3))/a^4","A",0
2424,1,13,0,1.127082," ","integrate(1/(a+b/x^(1/3))/x,x, algorithm=""fricas"")","\frac{3 \, \log\left(a x^{\frac{1}{3}} + b\right)}{a}"," ",0,"3*log(a*x^(1/3) + b)/a","A",0
2425,1,47,0,0.902244," ","integrate(1/(a+b/x^(1/3))/x^2,x, algorithm=""fricas"")","-\frac{3 \, {\left(2 \, a^{2} x \log\left(a x^{\frac{1}{3}} + b\right) - 2 \, a^{2} x \log\left(x^{\frac{1}{3}}\right) - 2 \, a b x^{\frac{2}{3}} + b^{2} x^{\frac{1}{3}}\right)}}{2 \, b^{3} x}"," ",0,"-3/2*(2*a^2*x*log(a*x^(1/3) + b) - 2*a^2*x*log(x^(1/3)) - 2*a*b*x^(2/3) + b^2*x^(1/3))/(b^3*x)","A",0
2426,1,85,0,1.117713," ","integrate(1/(a+b/x^(1/3))/x^3,x, algorithm=""fricas"")","\frac{60 \, a^{5} x^{2} \log\left(a x^{\frac{1}{3}} + b\right) - 60 \, a^{5} x^{2} \log\left(x^{\frac{1}{3}}\right) - 20 \, a^{2} b^{3} x - 15 \, {\left(4 \, a^{4} b x - a b^{4}\right)} x^{\frac{2}{3}} + 6 \, {\left(5 \, a^{3} b^{2} x - 2 \, b^{5}\right)} x^{\frac{1}{3}}}{20 \, b^{6} x^{2}}"," ",0,"1/20*(60*a^5*x^2*log(a*x^(1/3) + b) - 60*a^5*x^2*log(x^(1/3)) - 20*a^2*b^3*x - 15*(4*a^4*b*x - a*b^4)*x^(2/3) + 6*(5*a^3*b^2*x - 2*b^5)*x^(1/3))/(b^6*x^2)","A",0
2427,1,118,0,0.781276," ","integrate(1/(a+b/x^(1/3))/x^4,x, algorithm=""fricas"")","-\frac{840 \, a^{8} x^{3} \log\left(a x^{\frac{1}{3}} + b\right) - 840 \, a^{8} x^{3} \log\left(x^{\frac{1}{3}}\right) - 280 \, a^{5} b^{3} x^{2} + 140 \, a^{2} b^{6} x - 30 \, {\left(28 \, a^{7} b x^{2} - 7 \, a^{4} b^{4} x + 4 \, a b^{7}\right)} x^{\frac{2}{3}} + 21 \, {\left(20 \, a^{6} b^{2} x^{2} - 8 \, a^{3} b^{5} x + 5 \, b^{8}\right)} x^{\frac{1}{3}}}{280 \, b^{9} x^{3}}"," ",0,"-1/280*(840*a^8*x^3*log(a*x^(1/3) + b) - 840*a^8*x^3*log(x^(1/3)) - 280*a^5*b^3*x^2 + 140*a^2*b^6*x - 30*(28*a^7*b*x^2 - 7*a^4*b^4*x + 4*a*b^7)*x^(2/3) + 21*(20*a^6*b^2*x^2 - 8*a^3*b^5*x + 5*b^8)*x^(1/3))/(b^9*x^3)","A",0
2428,1,151,0,0.813152," ","integrate(1/(a+b/x^(1/3))/x^5,x, algorithm=""fricas"")","\frac{27720 \, a^{11} x^{4} \log\left(a x^{\frac{1}{3}} + b\right) - 27720 \, a^{11} x^{4} \log\left(x^{\frac{1}{3}}\right) - 9240 \, a^{8} b^{3} x^{3} + 4620 \, a^{5} b^{6} x^{2} - 3080 \, a^{2} b^{9} x - 198 \, {\left(140 \, a^{10} b x^{3} - 35 \, a^{7} b^{4} x^{2} + 20 \, a^{4} b^{7} x - 14 \, a b^{10}\right)} x^{\frac{2}{3}} + 63 \, {\left(220 \, a^{9} b^{2} x^{3} - 88 \, a^{6} b^{5} x^{2} + 55 \, a^{3} b^{8} x - 40 \, b^{11}\right)} x^{\frac{1}{3}}}{9240 \, b^{12} x^{4}}"," ",0,"1/9240*(27720*a^11*x^4*log(a*x^(1/3) + b) - 27720*a^11*x^4*log(x^(1/3)) - 9240*a^8*b^3*x^3 + 4620*a^5*b^6*x^2 - 3080*a^2*b^9*x - 198*(140*a^10*b*x^3 - 35*a^7*b^4*x^2 + 20*a^4*b^7*x - 14*a*b^10)*x^(2/3) + 63*(220*a^9*b^2*x^3 - 88*a^6*b^5*x^2 + 55*a^3*b^8*x - 40*b^11)*x^(1/3))/(b^12*x^4)","A",0
2429,1,169,0,0.824929," ","integrate(x^2/(a+b/x^(1/3))^2,x, algorithm=""fricas"")","\frac{28 \, a^{12} x^{4} - 140 \, a^{9} b^{3} x^{3} + 420 \, a^{6} b^{6} x^{2} + 588 \, a^{3} b^{9} x - 252 \, b^{12} - 2520 \, {\left(a^{3} b^{9} x + b^{12}\right)} \log\left(a x^{\frac{1}{3}} + b\right) - 63 \, {\left(a^{11} b x^{3} - 3 \, a^{8} b^{4} x^{2} + 12 \, a^{5} b^{7} x + 20 \, a^{2} b^{10}\right)} x^{\frac{2}{3}} + 18 \, {\left(6 \, a^{10} b^{2} x^{3} - 15 \, a^{7} b^{5} x^{2} + 105 \, a^{4} b^{8} x + 140 \, a b^{11}\right)} x^{\frac{1}{3}}}{84 \, {\left(a^{14} x + a^{11} b^{3}\right)}}"," ",0,"1/84*(28*a^12*x^4 - 140*a^9*b^3*x^3 + 420*a^6*b^6*x^2 + 588*a^3*b^9*x - 252*b^12 - 2520*(a^3*b^9*x + b^12)*log(a*x^(1/3) + b) - 63*(a^11*b*x^3 - 3*a^8*b^4*x^2 + 12*a^5*b^7*x + 20*a^2*b^10)*x^(2/3) + 18*(6*a^10*b^2*x^3 - 15*a^7*b^5*x^2 + 105*a^4*b^8*x + 140*a*b^11)*x^(1/3))/(a^14*x + a^11*b^3)","A",0
2430,1,137,0,0.855439," ","integrate(x/(a+b/x^(1/3))^2,x, algorithm=""fricas"")","\frac{10 \, a^{9} x^{3} - 70 \, a^{6} b^{3} x^{2} - 80 \, a^{3} b^{6} x + 60 \, b^{9} + 420 \, {\left(a^{3} b^{6} x + b^{9}\right)} \log\left(a x^{\frac{1}{3}} + b\right) - 6 \, {\left(4 \, a^{8} b x^{2} - 21 \, a^{5} b^{4} x - 35 \, a^{2} b^{7}\right)} x^{\frac{2}{3}} + 15 \, {\left(3 \, a^{7} b^{2} x^{2} - 21 \, a^{4} b^{5} x - 28 \, a b^{8}\right)} x^{\frac{1}{3}}}{20 \, {\left(a^{11} x + a^{8} b^{3}\right)}}"," ",0,"1/20*(10*a^9*x^3 - 70*a^6*b^3*x^2 - 80*a^3*b^6*x + 60*b^9 + 420*(a^3*b^6*x + b^9)*log(a*x^(1/3) + b) - 6*(4*a^8*b*x^2 - 21*a^5*b^4*x - 35*a^2*b^7)*x^(2/3) + 15*(3*a^7*b^2*x^2 - 21*a^4*b^5*x - 28*a*b^8)*x^(1/3))/(a^11*x + a^8*b^3)","A",0
2431,1,100,0,0.821557," ","integrate(1/(a+b/x^(1/3))^2,x, algorithm=""fricas"")","\frac{a^{6} x^{2} + a^{3} b^{3} x - 3 \, b^{6} - 12 \, {\left(a^{3} b^{3} x + b^{6}\right)} \log\left(a x^{\frac{1}{3}} + b\right) - 3 \, {\left(a^{5} b x + 2 \, a^{2} b^{4}\right)} x^{\frac{2}{3}} + 3 \, {\left(3 \, a^{4} b^{2} x + 4 \, a b^{5}\right)} x^{\frac{1}{3}}}{a^{8} x + a^{5} b^{3}}"," ",0,"(a^6*x^2 + a^3*b^3*x - 3*b^6 - 12*(a^3*b^3*x + b^6)*log(a*x^(1/3) + b) - 3*(a^5*b*x + 2*a^2*b^4)*x^(2/3) + 3*(3*a^4*b^2*x + 4*a*b^5)*x^(1/3))/(a^8*x + a^5*b^3)","A",0
2432,1,56,0,0.892714," ","integrate(1/(a+b/x^(1/3))^2/x,x, algorithm=""fricas"")","\frac{3 \, {\left(a^{2} b x^{\frac{2}{3}} - a b^{2} x^{\frac{1}{3}} + b^{3} + {\left(a^{3} x + b^{3}\right)} \log\left(a x^{\frac{1}{3}} + b\right)\right)}}{a^{5} x + a^{2} b^{3}}"," ",0,"3*(a^2*b*x^(2/3) - a*b^2*x^(1/3) + b^3 + (a^3*x + b^3)*log(a*x^(1/3) + b))/(a^5*x + a^2*b^3)","A",0
2433,1,98,0,1.021549," ","integrate(1/(a+b/x^(1/3))^2/x^2,x, algorithm=""fricas"")","\frac{3 \, {\left(a^{2} b^{2} x^{\frac{4}{3}} - a b^{3} x + 2 \, {\left(a^{4} x^{2} + a b^{3} x\right)} \log\left(a x^{\frac{1}{3}} + b\right) - 2 \, {\left(a^{4} x^{2} + a b^{3} x\right)} \log\left(x^{\frac{1}{3}}\right) - {\left(2 \, a^{3} b x + b^{4}\right)} x^{\frac{2}{3}}\right)}}{a^{3} b^{3} x^{2} + b^{6} x}"," ",0,"3*(a^2*b^2*x^(4/3) - a*b^3*x + 2*(a^4*x^2 + a*b^3*x)*log(a*x^(1/3) + b) - 2*(a^4*x^2 + a*b^3*x)*log(x^(1/3)) - (2*a^3*b*x + b^4)*x^(2/3))/(a^3*b^3*x^2 + b^6*x)","B",0
2434,1,148,0,0.764338," ","integrate(1/(a+b/x^(1/3))^2/x^3,x, algorithm=""fricas"")","\frac{20 \, a^{4} b^{3} x^{2} + 8 \, a b^{6} x - 60 \, {\left(a^{7} x^{3} + a^{4} b^{3} x^{2}\right)} \log\left(a x^{\frac{1}{3}} + b\right) + 60 \, {\left(a^{7} x^{3} + a^{4} b^{3} x^{2}\right)} \log\left(x^{\frac{1}{3}}\right) + 3 \, {\left(20 \, a^{6} b x^{2} + 15 \, a^{3} b^{4} x - b^{7}\right)} x^{\frac{2}{3}} - 6 \, {\left(5 \, a^{5} b^{2} x^{2} + 3 \, a^{2} b^{5} x\right)} x^{\frac{1}{3}}}{4 \, {\left(a^{3} b^{6} x^{3} + b^{9} x^{2}\right)}}"," ",0,"1/4*(20*a^4*b^3*x^2 + 8*a*b^6*x - 60*(a^7*x^3 + a^4*b^3*x^2)*log(a*x^(1/3) + b) + 60*(a^7*x^3 + a^4*b^3*x^2)*log(x^(1/3)) + 3*(20*a^6*b*x^2 + 15*a^3*b^4*x - b^7)*x^(2/3) - 6*(5*a^5*b^2*x^2 + 3*a^2*b^5*x)*x^(1/3))/(a^3*b^6*x^3 + b^9*x^2)","A",0
2435,1,179,0,0.839956," ","integrate(1/(a+b/x^(1/3))^2/x^4,x, algorithm=""fricas"")","-\frac{280 \, a^{7} b^{3} x^{3} + 140 \, a^{4} b^{6} x^{2} - 35 \, a b^{9} x - 840 \, {\left(a^{10} x^{4} + a^{7} b^{3} x^{3}\right)} \log\left(a x^{\frac{1}{3}} + b\right) + 840 \, {\left(a^{10} x^{4} + a^{7} b^{3} x^{3}\right)} \log\left(x^{\frac{1}{3}}\right) + 15 \, {\left(56 \, a^{9} b x^{3} + 42 \, a^{6} b^{4} x^{2} - 6 \, a^{3} b^{7} x + b^{10}\right)} x^{\frac{2}{3}} - 21 \, {\left(20 \, a^{8} b^{2} x^{3} + 12 \, a^{5} b^{5} x^{2} - 3 \, a^{2} b^{8} x\right)} x^{\frac{1}{3}}}{35 \, {\left(a^{3} b^{9} x^{4} + b^{12} x^{3}\right)}}"," ",0,"-1/35*(280*a^7*b^3*x^3 + 140*a^4*b^6*x^2 - 35*a*b^9*x - 840*(a^10*x^4 + a^7*b^3*x^3)*log(a*x^(1/3) + b) + 840*(a^10*x^4 + a^7*b^3*x^3)*log(x^(1/3)) + 15*(56*a^9*b*x^3 + 42*a^6*b^4*x^2 - 6*a^3*b^7*x + b^10)*x^(2/3) - 21*(20*a^8*b^2*x^3 + 12*a^5*b^5*x^2 - 3*a^2*b^8*x)*x^(1/3))/(a^3*b^9*x^4 + b^12*x^3)","A",0
2436,1,214,0,0.742211," ","integrate(1/(a+b/x^(1/3))^2/x^5,x, algorithm=""fricas"")","\frac{9240 \, a^{10} b^{3} x^{4} + 4620 \, a^{7} b^{6} x^{3} - 1540 \, a^{4} b^{9} x^{2} + 560 \, a b^{12} x - 27720 \, {\left(a^{13} x^{5} + a^{10} b^{3} x^{4}\right)} \log\left(a x^{\frac{1}{3}} + b\right) + 27720 \, {\left(a^{13} x^{5} + a^{10} b^{3} x^{4}\right)} \log\left(x^{\frac{1}{3}}\right) + 18 \, {\left(1540 \, a^{12} b x^{4} + 1155 \, a^{9} b^{4} x^{3} - 165 \, a^{6} b^{7} x^{2} + 66 \, a^{3} b^{10} x - 14 \, b^{13}\right)} x^{\frac{2}{3}} - 63 \, {\left(220 \, a^{11} b^{2} x^{4} + 132 \, a^{8} b^{5} x^{3} - 33 \, a^{5} b^{8} x^{2} + 15 \, a^{2} b^{11} x\right)} x^{\frac{1}{3}}}{840 \, {\left(a^{3} b^{12} x^{5} + b^{15} x^{4}\right)}}"," ",0,"1/840*(9240*a^10*b^3*x^4 + 4620*a^7*b^6*x^3 - 1540*a^4*b^9*x^2 + 560*a*b^12*x - 27720*(a^13*x^5 + a^10*b^3*x^4)*log(a*x^(1/3) + b) + 27720*(a^13*x^5 + a^10*b^3*x^4)*log(x^(1/3)) + 18*(1540*a^12*b*x^4 + 1155*a^9*b^4*x^3 - 165*a^6*b^7*x^2 + 66*a^3*b^10*x - 14*b^13)*x^(2/3) - 63*(220*a^11*b^2*x^4 + 132*a^8*b^5*x^3 - 33*a^5*b^8*x^2 + 15*a^2*b^11*x)*x^(1/3))/(a^3*b^12*x^5 + b^15*x^4)","A",0
2437,1,225,0,0.870384," ","integrate(x^2/(a+b/x^(1/3))^3,x, algorithm=""fricas"")","\frac{56 \, a^{15} x^{5} - 728 \, a^{12} b^{3} x^{4} + 3080 \, a^{9} b^{6} x^{3} + 8568 \, a^{6} b^{9} x^{2} - 1344 \, a^{3} b^{12} x - 5292 \, b^{15} - 27720 \, {\left(a^{6} b^{9} x^{2} + 2 \, a^{3} b^{12} x + b^{15}\right)} \log\left(a x^{\frac{1}{3}} + b\right) - 63 \, {\left(3 \, a^{14} b x^{4} - 18 \, a^{11} b^{4} x^{3} + 99 \, a^{8} b^{7} x^{2} + 352 \, a^{5} b^{10} x + 220 \, a^{2} b^{13}\right)} x^{\frac{2}{3}} + 18 \, {\left(24 \, a^{13} b^{2} x^{4} - 99 \, a^{10} b^{5} x^{3} + 990 \, a^{7} b^{8} x^{2} + 2695 \, a^{4} b^{11} x + 1540 \, a b^{14}\right)} x^{\frac{1}{3}}}{168 \, {\left(a^{18} x^{2} + 2 \, a^{15} b^{3} x + a^{12} b^{6}\right)}}"," ",0,"1/168*(56*a^15*x^5 - 728*a^12*b^3*x^4 + 3080*a^9*b^6*x^3 + 8568*a^6*b^9*x^2 - 1344*a^3*b^12*x - 5292*b^15 - 27720*(a^6*b^9*x^2 + 2*a^3*b^12*x + b^15)*log(a*x^(1/3) + b) - 63*(3*a^14*b*x^4 - 18*a^11*b^4*x^3 + 99*a^8*b^7*x^2 + 352*a^5*b^10*x + 220*a^2*b^13)*x^(2/3) + 18*(24*a^13*b^2*x^4 - 99*a^10*b^5*x^3 + 990*a^7*b^8*x^2 + 2695*a^4*b^11*x + 1540*a*b^14)*x^(1/3))/(a^18*x^2 + 2*a^15*b^3*x + a^12*b^6)","A",0
2438,1,192,0,0.769745," ","integrate(x/(a+b/x^(1/3))^3,x, algorithm=""fricas"")","\frac{5 \, a^{12} x^{4} - 90 \, a^{9} b^{3} x^{3} - 195 \, a^{6} b^{6} x^{2} + 170 \, a^{3} b^{9} x + 225 \, b^{12} + 840 \, {\left(a^{6} b^{6} x^{2} + 2 \, a^{3} b^{9} x + b^{12}\right)} \log\left(a x^{\frac{1}{3}} + b\right) - 3 \, {\left(6 \, a^{11} b x^{3} - 63 \, a^{8} b^{4} x^{2} - 224 \, a^{5} b^{7} x - 140 \, a^{2} b^{10}\right)} x^{\frac{2}{3}} + 15 \, {\left(3 \, a^{10} b^{2} x^{3} - 36 \, a^{7} b^{5} x^{2} - 98 \, a^{4} b^{8} x - 56 \, a b^{11}\right)} x^{\frac{1}{3}}}{10 \, {\left(a^{15} x^{2} + 2 \, a^{12} b^{3} x + a^{9} b^{6}\right)}}"," ",0,"1/10*(5*a^12*x^4 - 90*a^9*b^3*x^3 - 195*a^6*b^6*x^2 + 170*a^3*b^9*x + 225*b^12 + 840*(a^6*b^6*x^2 + 2*a^3*b^9*x + b^12)*log(a*x^(1/3) + b) - 3*(6*a^11*b*x^3 - 63*a^8*b^4*x^2 - 224*a^5*b^7*x - 140*a^2*b^10)*x^(2/3) + 15*(3*a^10*b^2*x^3 - 36*a^7*b^5*x^2 - 98*a^4*b^8*x - 56*a*b^11)*x^(1/3))/(a^15*x^2 + 2*a^12*b^3*x + a^9*b^6)","A",0
2439,1,159,0,1.195325," ","integrate(1/(a+b/x^(1/3))^3,x, algorithm=""fricas"")","\frac{2 \, a^{9} x^{3} + 4 \, a^{6} b^{3} x^{2} - 34 \, a^{3} b^{6} x - 27 \, b^{9} - 60 \, {\left(a^{6} b^{3} x^{2} + 2 \, a^{3} b^{6} x + b^{9}\right)} \log\left(a x^{\frac{1}{3}} + b\right) - 3 \, {\left(3 \, a^{8} b x^{2} + 16 \, a^{5} b^{4} x + 10 \, a^{2} b^{7}\right)} x^{\frac{2}{3}} + 3 \, {\left(12 \, a^{7} b^{2} x^{2} + 35 \, a^{4} b^{5} x + 20 \, a b^{8}\right)} x^{\frac{1}{3}}}{2 \, {\left(a^{12} x^{2} + 2 \, a^{9} b^{3} x + a^{6} b^{6}\right)}}"," ",0,"1/2*(2*a^9*x^3 + 4*a^6*b^3*x^2 - 34*a^3*b^6*x - 27*b^9 - 60*(a^6*b^3*x^2 + 2*a^3*b^6*x + b^9)*log(a*x^(1/3) + b) - 3*(3*a^8*b*x^2 + 16*a^5*b^4*x + 10*a^2*b^7)*x^(2/3) + 3*(12*a^7*b^2*x^2 + 35*a^4*b^5*x + 20*a*b^8)*x^(1/3))/(a^12*x^2 + 2*a^9*b^3*x + a^6*b^6)","A",0
2440,1,113,0,1.056821," ","integrate(1/(a+b/x^(1/3))^3/x,x, algorithm=""fricas"")","\frac{3 \, {\left(6 \, a^{3} b^{3} x + 3 \, b^{6} + 2 \, {\left(a^{6} x^{2} + 2 \, a^{3} b^{3} x + b^{6}\right)} \log\left(a x^{\frac{1}{3}} + b\right) + {\left(4 \, a^{5} b x + a^{2} b^{4}\right)} x^{\frac{2}{3}} - {\left(5 \, a^{4} b^{2} x + 2 \, a b^{5}\right)} x^{\frac{1}{3}}\right)}}{2 \, {\left(a^{9} x^{2} + 2 \, a^{6} b^{3} x + a^{3} b^{6}\right)}}"," ",0,"3/2*(6*a^3*b^3*x + 3*b^6 + 2*(a^6*x^2 + 2*a^3*b^3*x + b^6)*log(a*x^(1/3) + b) + (4*a^5*b*x + a^2*b^4)*x^(2/3) - (5*a^4*b^2*x + 2*a*b^5)*x^(1/3))/(a^9*x^2 + 2*a^6*b^3*x + a^3*b^6)","B",0
2441,1,129,0,1.132967," ","integrate(1/(a+b/x^(1/3))^3/x^2,x, algorithm=""fricas"")","\frac{3 \, {\left(3 \, b^{6} - 2 \, {\left(a^{6} x^{2} + 2 \, a^{3} b^{3} x + b^{6}\right)} \log\left(a x^{\frac{1}{3}} + b\right) + 2 \, {\left(a^{6} x^{2} + 2 \, a^{3} b^{3} x + b^{6}\right)} \log\left(x^{\frac{1}{3}}\right) + {\left(2 \, a^{5} b x + 5 \, a^{2} b^{4}\right)} x^{\frac{2}{3}} - {\left(a^{4} b^{2} x + 4 \, a b^{5}\right)} x^{\frac{1}{3}}\right)}}{2 \, {\left(a^{6} b^{3} x^{2} + 2 \, a^{3} b^{6} x + b^{9}\right)}}"," ",0,"3/2*(3*b^6 - 2*(a^6*x^2 + 2*a^3*b^3*x + b^6)*log(a*x^(1/3) + b) + 2*(a^6*x^2 + 2*a^3*b^3*x + b^6)*log(x^(1/3)) + (2*a^5*b*x + 5*a^2*b^4)*x^(2/3) - (a^4*b^2*x + 4*a*b^5)*x^(1/3))/(a^6*b^3*x^2 + 2*a^3*b^6*x + b^9)","B",0
2442,1,191,0,0.974669," ","integrate(1/(a+b/x^(1/3))^3/x^3,x, algorithm=""fricas"")","-\frac{20 \, a^{6} b^{3} x^{2} + 31 \, a^{3} b^{6} x + 2 \, b^{9} - 60 \, {\left(a^{9} x^{3} + 2 \, a^{6} b^{3} x^{2} + a^{3} b^{6} x\right)} \log\left(a x^{\frac{1}{3}} + b\right) + 60 \, {\left(a^{9} x^{3} + 2 \, a^{6} b^{3} x^{2} + a^{3} b^{6} x\right)} \log\left(x^{\frac{1}{3}}\right) + 3 \, {\left(20 \, a^{8} b x^{2} + 35 \, a^{5} b^{4} x + 12 \, a^{2} b^{7}\right)} x^{\frac{2}{3}} - 3 \, {\left(10 \, a^{7} b^{2} x^{2} + 16 \, a^{4} b^{5} x + 3 \, a b^{8}\right)} x^{\frac{1}{3}}}{2 \, {\left(a^{6} b^{6} x^{3} + 2 \, a^{3} b^{9} x^{2} + b^{12} x\right)}}"," ",0,"-1/2*(20*a^6*b^3*x^2 + 31*a^3*b^6*x + 2*b^9 - 60*(a^9*x^3 + 2*a^6*b^3*x^2 + a^3*b^6*x)*log(a*x^(1/3) + b) + 60*(a^9*x^3 + 2*a^6*b^3*x^2 + a^3*b^6*x)*log(x^(1/3)) + 3*(20*a^8*b*x^2 + 35*a^5*b^4*x + 12*a^2*b^7)*x^(2/3) - 3*(10*a^7*b^2*x^2 + 16*a^4*b^5*x + 3*a*b^8)*x^(1/3))/(a^6*b^6*x^3 + 2*a^3*b^9*x^2 + b^12*x)","B",0
2443,1,230,0,0.664014," ","integrate(1/(a+b/x^(1/3))^3/x^4,x, algorithm=""fricas"")","\frac{280 \, a^{9} b^{3} x^{3} + 420 \, a^{6} b^{6} x^{2} + 90 \, a^{3} b^{9} x - 5 \, b^{12} - 840 \, {\left(a^{12} x^{4} + 2 \, a^{9} b^{3} x^{3} + a^{6} b^{6} x^{2}\right)} \log\left(a x^{\frac{1}{3}} + b\right) + 840 \, {\left(a^{12} x^{4} + 2 \, a^{9} b^{3} x^{3} + a^{6} b^{6} x^{2}\right)} \log\left(x^{\frac{1}{3}}\right) + 15 \, {\left(56 \, a^{11} b x^{3} + 98 \, a^{8} b^{4} x^{2} + 36 \, a^{5} b^{7} x - 3 \, a^{2} b^{10}\right)} x^{\frac{2}{3}} - 3 \, {\left(140 \, a^{10} b^{2} x^{3} + 224 \, a^{7} b^{5} x^{2} + 63 \, a^{4} b^{8} x - 6 \, a b^{11}\right)} x^{\frac{1}{3}}}{10 \, {\left(a^{6} b^{9} x^{4} + 2 \, a^{3} b^{12} x^{3} + b^{15} x^{2}\right)}}"," ",0,"1/10*(280*a^9*b^3*x^3 + 420*a^6*b^6*x^2 + 90*a^3*b^9*x - 5*b^12 - 840*(a^12*x^4 + 2*a^9*b^3*x^3 + a^6*b^6*x^2)*log(a*x^(1/3) + b) + 840*(a^12*x^4 + 2*a^9*b^3*x^3 + a^6*b^6*x^2)*log(x^(1/3)) + 15*(56*a^11*b*x^3 + 98*a^8*b^4*x^2 + 36*a^5*b^7*x - 3*a^2*b^10)*x^(2/3) - 3*(140*a^10*b^2*x^3 + 224*a^7*b^5*x^2 + 63*a^4*b^8*x - 6*a*b^11)*x^(1/3))/(a^6*b^9*x^4 + 2*a^3*b^12*x^3 + b^15*x^2)","A",0
2444,1,263,0,0.978271," ","integrate(1/(a+b/x^(1/3))^3/x^5,x, algorithm=""fricas"")","-\frac{9240 \, a^{12} b^{3} x^{4} + 13860 \, a^{9} b^{6} x^{3} + 3080 \, a^{6} b^{9} x^{2} - 728 \, a^{3} b^{12} x + 56 \, b^{15} - 27720 \, {\left(a^{15} x^{5} + 2 \, a^{12} b^{3} x^{4} + a^{9} b^{6} x^{3}\right)} \log\left(a x^{\frac{1}{3}} + b\right) + 27720 \, {\left(a^{15} x^{5} + 2 \, a^{12} b^{3} x^{4} + a^{9} b^{6} x^{3}\right)} \log\left(x^{\frac{1}{3}}\right) + 18 \, {\left(1540 \, a^{14} b x^{4} + 2695 \, a^{11} b^{4} x^{3} + 990 \, a^{8} b^{7} x^{2} - 99 \, a^{5} b^{10} x + 24 \, a^{2} b^{13}\right)} x^{\frac{2}{3}} - 63 \, {\left(220 \, a^{13} b^{2} x^{4} + 352 \, a^{10} b^{5} x^{3} + 99 \, a^{7} b^{8} x^{2} - 18 \, a^{4} b^{11} x + 3 \, a b^{14}\right)} x^{\frac{1}{3}}}{168 \, {\left(a^{6} b^{12} x^{5} + 2 \, a^{3} b^{15} x^{4} + b^{18} x^{3}\right)}}"," ",0,"-1/168*(9240*a^12*b^3*x^4 + 13860*a^9*b^6*x^3 + 3080*a^6*b^9*x^2 - 728*a^3*b^12*x + 56*b^15 - 27720*(a^15*x^5 + 2*a^12*b^3*x^4 + a^9*b^6*x^3)*log(a*x^(1/3) + b) + 27720*(a^15*x^5 + 2*a^12*b^3*x^4 + a^9*b^6*x^3)*log(x^(1/3)) + 18*(1540*a^14*b*x^4 + 2695*a^11*b^4*x^3 + 990*a^8*b^7*x^2 - 99*a^5*b^10*x + 24*a^2*b^13)*x^(2/3) - 63*(220*a^13*b^2*x^4 + 352*a^10*b^5*x^3 + 99*a^7*b^8*x^2 - 18*a^4*b^11*x + 3*a*b^14)*x^(1/3))/(a^6*b^12*x^5 + 2*a^3*b^15*x^4 + b^18*x^3)","A",0
2445,1,27,0,1.220060," ","integrate(1/(1+b/x^(1/3)),x, algorithm=""fricas"")","-3 \, b^{3} \log\left(b + x^{\frac{1}{3}}\right) + 3 \, b^{2} x^{\frac{1}{3}} - \frac{3}{2} \, b x^{\frac{2}{3}} + x"," ",0,"-3*b^3*log(b + x^(1/3)) + 3*b^2*x^(1/3) - 3/2*b*x^(2/3) + x","A",0
2446,-1,0,0,0.000000," ","integrate(x^(2/3)*(1+x^(5/3))^(2/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2447,-1,0,0,0.000000," ","integrate(x^(7/3)*(a^(10/3)-x^(10/3))^(19/7),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2448,1,29,0,0.984611," ","integrate(1/(1+x^(1/5)),x, algorithm=""fricas"")","\frac{5}{4} \, x^{\frac{4}{5}} - \frac{5}{3} \, x^{\frac{3}{5}} + \frac{5}{2} \, x^{\frac{2}{5}} - 5 \, x^{\frac{1}{5}} + 5 \, \log\left(x^{\frac{1}{5}} + 1\right)"," ",0,"5/4*x^(4/5) - 5/3*x^(3/5) + 5/2*x^(2/5) - 5*x^(1/5) + 5*log(x^(1/5) + 1)","A",0
2449,-1,0,0,0.000000," ","integrate(1/x^(1/5)/(1+x^(4/5))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2450,-1,0,0,0.000000," ","integrate((a+b/x^(3/5))^(2/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2451,1,28,0,1.913216," ","integrate(x^3*(a+b*x^n),x, algorithm=""fricas"")","\frac{4 \, b x^{4} x^{n} + {\left(a n + 4 \, a\right)} x^{4}}{4 \, {\left(n + 4\right)}}"," ",0,"1/4*(4*b*x^4*x^n + (a*n + 4*a)*x^4)/(n + 4)","A",0
2452,1,28,0,0.988041," ","integrate(x^2*(a+b*x^n),x, algorithm=""fricas"")","\frac{3 \, b x^{3} x^{n} + {\left(a n + 3 \, a\right)} x^{3}}{3 \, {\left(n + 3\right)}}"," ",0,"1/3*(3*b*x^3*x^n + (a*n + 3*a)*x^3)/(n + 3)","A",0
2453,1,28,0,1.091445," ","integrate(x*(a+b*x^n),x, algorithm=""fricas"")","\frac{2 \, b x^{2} x^{n} + {\left(a n + 2 \, a\right)} x^{2}}{2 \, {\left(n + 2\right)}}"," ",0,"1/2*(2*b*x^2*x^n + (a*n + 2*a)*x^2)/(n + 2)","A",0
2454,1,20,0,1.138323," ","integrate(a+b*x^n,x, algorithm=""fricas"")","\frac{b x x^{n} + {\left(a n + a\right)} x}{n + 1}"," ",0,"(b*x*x^n + (a*n + a)*x)/(n + 1)","A",0
2455,1,15,0,0.976292," ","integrate((a+b*x^n)/x,x, algorithm=""fricas"")","\frac{a n \log\left(x\right) + b x^{n}}{n}"," ",0,"(a*n*log(x) + b*x^n)/n","A",0
2456,1,23,0,1.075370," ","integrate((a+b*x^n)/x^2,x, algorithm=""fricas"")","-\frac{a n - b x^{n} - a}{{\left(n - 1\right)} x}"," ",0,"-(a*n - b*x^n - a)/((n - 1)*x)","A",0
2457,1,23,0,0.738173," ","integrate((a+b*x^n)/x^3,x, algorithm=""fricas"")","-\frac{a n - 2 \, b x^{n} - 2 \, a}{2 \, {\left(n - 2\right)} x^{2}}"," ",0,"-1/2*(a*n - 2*b*x^n - 2*a)/((n - 2)*x^2)","A",0
2458,1,74,0,0.922342," ","integrate(x^3*(a+b*x^n)^2,x, algorithm=""fricas"")","\frac{2 \, {\left(b^{2} n + 4 \, b^{2}\right)} x^{4} x^{2 \, n} + 8 \, {\left(a b n + 2 \, a b\right)} x^{4} x^{n} + {\left(a^{2} n^{2} + 6 \, a^{2} n + 8 \, a^{2}\right)} x^{4}}{4 \, {\left(n^{2} + 6 \, n + 8\right)}}"," ",0,"1/4*(2*(b^2*n + 4*b^2)*x^4*x^(2*n) + 8*(a*b*n + 2*a*b)*x^4*x^n + (a^2*n^2 + 6*a^2*n + 8*a^2)*x^4)/(n^2 + 6*n + 8)","A",0
2459,1,78,0,0.798128," ","integrate(x^2*(a+b*x^n)^2,x, algorithm=""fricas"")","\frac{3 \, {\left(b^{2} n + 3 \, b^{2}\right)} x^{3} x^{2 \, n} + 6 \, {\left(2 \, a b n + 3 \, a b\right)} x^{3} x^{n} + {\left(2 \, a^{2} n^{2} + 9 \, a^{2} n + 9 \, a^{2}\right)} x^{3}}{3 \, {\left(2 \, n^{2} + 9 \, n + 9\right)}}"," ",0,"1/3*(3*(b^2*n + 3*b^2)*x^3*x^(2*n) + 6*(2*a*b*n + 3*a*b)*x^3*x^n + (2*a^2*n^2 + 9*a^2*n + 9*a^2)*x^3)/(2*n^2 + 9*n + 9)","A",0
2460,1,72,0,0.643908," ","integrate(x*(a+b*x^n)^2,x, algorithm=""fricas"")","\frac{{\left(b^{2} n + 2 \, b^{2}\right)} x^{2} x^{2 \, n} + 4 \, {\left(a b n + a b\right)} x^{2} x^{n} + {\left(a^{2} n^{2} + 3 \, a^{2} n + 2 \, a^{2}\right)} x^{2}}{2 \, {\left(n^{2} + 3 \, n + 2\right)}}"," ",0,"1/2*((b^2*n + 2*b^2)*x^2*x^(2*n) + 4*(a*b*n + a*b)*x^2*x^n + (a^2*n^2 + 3*a^2*n + 2*a^2)*x^2)/(n^2 + 3*n + 2)","A",0
2461,1,65,0,0.954711," ","integrate((a+b*x^n)^2,x, algorithm=""fricas"")","\frac{{\left(b^{2} n + b^{2}\right)} x x^{2 \, n} + 2 \, {\left(2 \, a b n + a b\right)} x x^{n} + {\left(2 \, a^{2} n^{2} + 3 \, a^{2} n + a^{2}\right)} x}{2 \, n^{2} + 3 \, n + 1}"," ",0,"((b^2*n + b^2)*x*x^(2*n) + 2*(2*a*b*n + a*b)*x*x^n + (2*a^2*n^2 + 3*a^2*n + a^2)*x)/(2*n^2 + 3*n + 1)","A",0
2462,1,30,0,0.880290," ","integrate((a+b*x^n)^2/x,x, algorithm=""fricas"")","\frac{2 \, a^{2} n \log\left(x\right) + b^{2} x^{2 \, n} + 4 \, a b x^{n}}{2 \, n}"," ",0,"1/2*(2*a^2*n*log(x) + b^2*x^(2*n) + 4*a*b*x^n)/n","A",0
2463,1,68,0,0.781486," ","integrate((a+b*x^n)^2/x^2,x, algorithm=""fricas"")","-\frac{2 \, a^{2} n^{2} - 3 \, a^{2} n + a^{2} - {\left(b^{2} n - b^{2}\right)} x^{2 \, n} - 2 \, {\left(2 \, a b n - a b\right)} x^{n}}{{\left(2 \, n^{2} - 3 \, n + 1\right)} x}"," ",0,"-(2*a^2*n^2 - 3*a^2*n + a^2 - (b^2*n - b^2)*x^(2*n) - 2*(2*a*b*n - a*b)*x^n)/((2*n^2 - 3*n + 1)*x)","A",0
2464,1,66,0,1.143717," ","integrate((a+b*x^n)^2/x^3,x, algorithm=""fricas"")","-\frac{a^{2} n^{2} - 3 \, a^{2} n + 2 \, a^{2} - {\left(b^{2} n - 2 \, b^{2}\right)} x^{2 \, n} - 4 \, {\left(a b n - a b\right)} x^{n}}{2 \, {\left(n^{2} - 3 \, n + 2\right)} x^{2}}"," ",0,"-1/2*(a^2*n^2 - 3*a^2*n + 2*a^2 - (b^2*n - 2*b^2)*x^(2*n) - 4*(a*b*n - a*b)*x^n)/((n^2 - 3*n + 2)*x^2)","A",0
2465,1,145,0,0.904050," ","integrate(x^3*(a+b*x^n)^3,x, algorithm=""fricas"")","\frac{4 \, {\left(b^{3} n^{2} + 6 \, b^{3} n + 8 \, b^{3}\right)} x^{4} x^{3 \, n} + 6 \, {\left(3 \, a b^{2} n^{2} + 16 \, a b^{2} n + 16 \, a b^{2}\right)} x^{4} x^{2 \, n} + 12 \, {\left(3 \, a^{2} b n^{2} + 10 \, a^{2} b n + 8 \, a^{2} b\right)} x^{4} x^{n} + {\left(3 \, a^{3} n^{3} + 22 \, a^{3} n^{2} + 48 \, a^{3} n + 32 \, a^{3}\right)} x^{4}}{4 \, {\left(3 \, n^{3} + 22 \, n^{2} + 48 \, n + 32\right)}}"," ",0,"1/4*(4*(b^3*n^2 + 6*b^3*n + 8*b^3)*x^4*x^(3*n) + 6*(3*a*b^2*n^2 + 16*a*b^2*n + 16*a*b^2)*x^4*x^(2*n) + 12*(3*a^2*b*n^2 + 10*a^2*b*n + 8*a^2*b)*x^4*x^n + (3*a^3*n^3 + 22*a^3*n^2 + 48*a^3*n + 32*a^3)*x^4)/(3*n^3 + 22*n^2 + 48*n + 32)","B",0
2466,1,144,0,0.900831," ","integrate(x^2*(a+b*x^n)^3,x, algorithm=""fricas"")","\frac{{\left(2 \, b^{3} n^{2} + 9 \, b^{3} n + 9 \, b^{3}\right)} x^{3} x^{3 \, n} + 9 \, {\left(a b^{2} n^{2} + 4 \, a b^{2} n + 3 \, a b^{2}\right)} x^{3} x^{2 \, n} + 9 \, {\left(2 \, a^{2} b n^{2} + 5 \, a^{2} b n + 3 \, a^{2} b\right)} x^{3} x^{n} + {\left(2 \, a^{3} n^{3} + 11 \, a^{3} n^{2} + 18 \, a^{3} n + 9 \, a^{3}\right)} x^{3}}{3 \, {\left(2 \, n^{3} + 11 \, n^{2} + 18 \, n + 9\right)}}"," ",0,"1/3*((2*b^3*n^2 + 9*b^3*n + 9*b^3)*x^3*x^(3*n) + 9*(a*b^2*n^2 + 4*a*b^2*n + 3*a*b^2)*x^3*x^(2*n) + 9*(2*a^2*b*n^2 + 5*a^2*b*n + 3*a^2*b)*x^3*x^n + (2*a^3*n^3 + 11*a^3*n^2 + 18*a^3*n + 9*a^3)*x^3)/(2*n^3 + 11*n^2 + 18*n + 9)","B",0
2467,1,145,0,1.162711," ","integrate(x*(a+b*x^n)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(b^{3} n^{2} + 3 \, b^{3} n + 2 \, b^{3}\right)} x^{2} x^{3 \, n} + 3 \, {\left(3 \, a b^{2} n^{2} + 8 \, a b^{2} n + 4 \, a b^{2}\right)} x^{2} x^{2 \, n} + 6 \, {\left(3 \, a^{2} b n^{2} + 5 \, a^{2} b n + 2 \, a^{2} b\right)} x^{2} x^{n} + {\left(3 \, a^{3} n^{3} + 11 \, a^{3} n^{2} + 12 \, a^{3} n + 4 \, a^{3}\right)} x^{2}}{2 \, {\left(3 \, n^{3} + 11 \, n^{2} + 12 \, n + 4\right)}}"," ",0,"1/2*(2*(b^3*n^2 + 3*b^3*n + 2*b^3)*x^2*x^(3*n) + 3*(3*a*b^2*n^2 + 8*a*b^2*n + 4*a*b^2)*x^2*x^(2*n) + 6*(3*a^2*b*n^2 + 5*a^2*b*n + 2*a^2*b)*x^2*x^n + (3*a^3*n^3 + 11*a^3*n^2 + 12*a^3*n + 4*a^3)*x^2)/(3*n^3 + 11*n^2 + 12*n + 4)","B",0
2468,1,130,0,1.241208," ","integrate((a+b*x^n)^3,x, algorithm=""fricas"")","\frac{{\left(2 \, b^{3} n^{2} + 3 \, b^{3} n + b^{3}\right)} x x^{3 \, n} + 3 \, {\left(3 \, a b^{2} n^{2} + 4 \, a b^{2} n + a b^{2}\right)} x x^{2 \, n} + 3 \, {\left(6 \, a^{2} b n^{2} + 5 \, a^{2} b n + a^{2} b\right)} x x^{n} + {\left(6 \, a^{3} n^{3} + 11 \, a^{3} n^{2} + 6 \, a^{3} n + a^{3}\right)} x}{6 \, n^{3} + 11 \, n^{2} + 6 \, n + 1}"," ",0,"((2*b^3*n^2 + 3*b^3*n + b^3)*x*x^(3*n) + 3*(3*a*b^2*n^2 + 4*a*b^2*n + a*b^2)*x*x^(2*n) + 3*(6*a^2*b*n^2 + 5*a^2*b*n + a^2*b)*x*x^n + (6*a^3*n^3 + 11*a^3*n^2 + 6*a^3*n + a^3)*x)/(6*n^3 + 11*n^2 + 6*n + 1)","B",0
2469,1,44,0,0.898339," ","integrate((a+b*x^n)^3/x,x, algorithm=""fricas"")","\frac{6 \, a^{3} n \log\left(x\right) + 2 \, b^{3} x^{3 \, n} + 9 \, a b^{2} x^{2 \, n} + 18 \, a^{2} b x^{n}}{6 \, n}"," ",0,"1/6*(6*a^3*n*log(x) + 2*b^3*x^(3*n) + 9*a*b^2*x^(2*n) + 18*a^2*b*x^n)/n","A",0
2470,1,131,0,1.344824," ","integrate((a+b*x^n)^3/x^2,x, algorithm=""fricas"")","-\frac{6 \, a^{3} n^{3} - 11 \, a^{3} n^{2} + 6 \, a^{3} n - a^{3} - {\left(2 \, b^{3} n^{2} - 3 \, b^{3} n + b^{3}\right)} x^{3 \, n} - 3 \, {\left(3 \, a b^{2} n^{2} - 4 \, a b^{2} n + a b^{2}\right)} x^{2 \, n} - 3 \, {\left(6 \, a^{2} b n^{2} - 5 \, a^{2} b n + a^{2} b\right)} x^{n}}{{\left(6 \, n^{3} - 11 \, n^{2} + 6 \, n - 1\right)} x}"," ",0,"-(6*a^3*n^3 - 11*a^3*n^2 + 6*a^3*n - a^3 - (2*b^3*n^2 - 3*b^3*n + b^3)*x^(3*n) - 3*(3*a*b^2*n^2 - 4*a*b^2*n + a*b^2)*x^(2*n) - 3*(6*a^2*b*n^2 - 5*a^2*b*n + a^2*b)*x^n)/((6*n^3 - 11*n^2 + 6*n - 1)*x)","B",0
2471,1,134,0,1.120162," ","integrate((a+b*x^n)^3/x^3,x, algorithm=""fricas"")","-\frac{3 \, a^{3} n^{3} - 11 \, a^{3} n^{2} + 12 \, a^{3} n - 4 \, a^{3} - 2 \, {\left(b^{3} n^{2} - 3 \, b^{3} n + 2 \, b^{3}\right)} x^{3 \, n} - 3 \, {\left(3 \, a b^{2} n^{2} - 8 \, a b^{2} n + 4 \, a b^{2}\right)} x^{2 \, n} - 6 \, {\left(3 \, a^{2} b n^{2} - 5 \, a^{2} b n + 2 \, a^{2} b\right)} x^{n}}{2 \, {\left(3 \, n^{3} - 11 \, n^{2} + 12 \, n - 4\right)} x^{2}}"," ",0,"-1/2*(3*a^3*n^3 - 11*a^3*n^2 + 12*a^3*n - 4*a^3 - 2*(b^3*n^2 - 3*b^3*n + 2*b^3)*x^(3*n) - 3*(3*a*b^2*n^2 - 8*a*b^2*n + 4*a*b^2)*x^(2*n) - 6*(3*a^2*b*n^2 - 5*a^2*b*n + 2*a^2*b)*x^n)/((3*n^3 - 11*n^2 + 12*n - 4)*x^2)","B",0
2472,0,0,0,1.028688," ","integrate(x/(a+b*x^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{b x^{n} + a}, x\right)"," ",0,"integral(x/(b*x^n + a), x)","F",0
2473,0,0,0,0.826246," ","integrate(1/(a+b*x^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b x^{n} + a}, x\right)"," ",0,"integral(1/(b*x^n + a), x)","F",0
2474,1,22,0,1.218062," ","integrate(1/x/(a+b*x^n),x, algorithm=""fricas"")","\frac{n \log\left(x\right) - \log\left(b x^{n} + a\right)}{a n}"," ",0,"(n*log(x) - log(b*x^n + a))/(a*n)","A",0
2475,0,0,0,0.925837," ","integrate(1/x^2/(a+b*x^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b x^{2} x^{n} + a x^{2}}, x\right)"," ",0,"integral(1/(b*x^2*x^n + a*x^2), x)","F",0
2476,0,0,0,0.961325," ","integrate(1/x^3/(a+b*x^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b x^{3} x^{n} + a x^{3}}, x\right)"," ",0,"integral(1/(b*x^3*x^n + a*x^3), x)","F",0
2477,0,0,0,0.929920," ","integrate(x/(a+b*x^n)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}}, x\right)"," ",0,"integral(x/(b^2*x^(2*n) + 2*a*b*x^n + a^2), x)","F",0
2478,0,0,0,0.919102," ","integrate(1/(a+b*x^n)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}}, x\right)"," ",0,"integral(1/(b^2*x^(2*n) + 2*a*b*x^n + a^2), x)","F",0
2479,1,50,0,1.039559," ","integrate(1/x/(a+b*x^n)^2,x, algorithm=""fricas"")","\frac{b n x^{n} \log\left(x\right) + a n \log\left(x\right) - {\left(b x^{n} + a\right)} \log\left(b x^{n} + a\right) + a}{a^{2} b n x^{n} + a^{3} n}"," ",0,"(b*n*x^n*log(x) + a*n*log(x) - (b*x^n + a)*log(b*x^n + a) + a)/(a^2*b*n*x^n + a^3*n)","A",0
2480,0,0,0,1.028927," ","integrate(1/x^2/(a+b*x^n)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{2} x^{2} x^{2 \, n} + 2 \, a b x^{2} x^{n} + a^{2} x^{2}}, x\right)"," ",0,"integral(1/(b^2*x^2*x^(2*n) + 2*a*b*x^2*x^n + a^2*x^2), x)","F",0
2481,0,0,0,0.930690," ","integrate(1/x^3/(a+b*x^n)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{2} x^{3} x^{2 \, n} + 2 \, a b x^{3} x^{n} + a^{2} x^{3}}, x\right)"," ",0,"integral(1/(b^2*x^3*x^(2*n) + 2*a*b*x^3*x^n + a^2*x^3), x)","F",0
2482,0,0,0,1.041851," ","integrate(x/(a+b*x^n)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{b^{3} x^{3 \, n} + 3 \, a b^{2} x^{2 \, n} + 3 \, a^{2} b x^{n} + a^{3}}, x\right)"," ",0,"integral(x/(b^3*x^(3*n) + 3*a*b^2*x^(2*n) + 3*a^2*b*x^n + a^3), x)","F",0
2483,0,0,0,1.364411," ","integrate(1/(a+b*x^n)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{3} x^{3 \, n} + 3 \, a b^{2} x^{2 \, n} + 3 \, a^{2} b x^{n} + a^{3}}, x\right)"," ",0,"integral(1/(b^3*x^(3*n) + 3*a*b^2*x^(2*n) + 3*a^2*b*x^n + a^3), x)","F",0
2484,1,106,0,1.607022," ","integrate(1/x/(a+b*x^n)^3,x, algorithm=""fricas"")","\frac{2 \, b^{2} n x^{2 \, n} \log\left(x\right) + 2 \, a^{2} n \log\left(x\right) + 3 \, a^{2} + 2 \, {\left(2 \, a b n \log\left(x\right) + a b\right)} x^{n} - 2 \, {\left(b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}\right)} \log\left(b x^{n} + a\right)}{2 \, {\left(a^{3} b^{2} n x^{2 \, n} + 2 \, a^{4} b n x^{n} + a^{5} n\right)}}"," ",0,"1/2*(2*b^2*n*x^(2*n)*log(x) + 2*a^2*n*log(x) + 3*a^2 + 2*(2*a*b*n*log(x) + a*b)*x^n - 2*(b^2*x^(2*n) + 2*a*b*x^n + a^2)*log(b*x^n + a))/(a^3*b^2*n*x^(2*n) + 2*a^4*b*n*x^n + a^5*n)","A",0
2485,0,0,0,0.922436," ","integrate(1/x^2/(a+b*x^n)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{3} x^{2} x^{3 \, n} + 3 \, a b^{2} x^{2} x^{2 \, n} + 3 \, a^{2} b x^{2} x^{n} + a^{3} x^{2}}, x\right)"," ",0,"integral(1/(b^3*x^2*x^(3*n) + 3*a*b^2*x^2*x^(2*n) + 3*a^2*b*x^2*x^n + a^3*x^2), x)","F",0
2486,0,0,0,0.802136," ","integrate(1/x^3/(a+b*x^n)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{3} x^{3} x^{3 \, n} + 3 \, a b^{2} x^{3} x^{2 \, n} + 3 \, a^{2} b x^{3} x^{n} + a^{3} x^{3}}, x\right)"," ",0,"integral(1/(b^3*x^3*x^(3*n) + 3*a*b^2*x^3*x^(2*n) + 3*a^2*b*x^3*x^n + a^3*x^3), x)","F",0
2487,-2,0,0,0.000000," ","integrate(x*(a+b*x^n)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
2488,-2,0,0,0.000000," ","integrate((a+b*x^n)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
2489,1,91,0,0.816386," ","integrate((a+b*x^n)^(1/2)/x,x, algorithm=""fricas"")","\left[\frac{\sqrt{a} \log\left(\frac{b x^{n} - 2 \, \sqrt{b x^{n} + a} \sqrt{a} + 2 \, a}{x^{n}}\right) + 2 \, \sqrt{b x^{n} + a}}{n}, \frac{2 \, {\left(\sqrt{-a} \arctan\left(\frac{\sqrt{b x^{n} + a} \sqrt{-a}}{a}\right) + \sqrt{b x^{n} + a}\right)}}{n}\right]"," ",0,"[(sqrt(a)*log((b*x^n - 2*sqrt(b*x^n + a)*sqrt(a) + 2*a)/x^n) + 2*sqrt(b*x^n + a))/n, 2*(sqrt(-a)*arctan(sqrt(b*x^n + a)*sqrt(-a)/a) + sqrt(b*x^n + a))/n]","A",0
2490,-2,0,0,0.000000," ","integrate((a+b*x^n)^(1/2)/x^2,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
2491,-2,0,0,0.000000," ","integrate((a+b*x^n)^(1/2)/x^3,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
2492,-2,0,0,0.000000," ","integrate(x*(a+b*x^n)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
2493,-2,0,0,0.000000," ","integrate((a+b*x^n)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
2494,1,114,0,1.908051," ","integrate((a+b*x^n)^(3/2)/x,x, algorithm=""fricas"")","\left[\frac{3 \, a^{\frac{3}{2}} \log\left(\frac{b x^{n} - 2 \, \sqrt{b x^{n} + a} \sqrt{a} + 2 \, a}{x^{n}}\right) + 2 \, {\left(b x^{n} + 4 \, a\right)} \sqrt{b x^{n} + a}}{3 \, n}, \frac{2 \, {\left(3 \, \sqrt{-a} a \arctan\left(\frac{\sqrt{b x^{n} + a} \sqrt{-a}}{a}\right) + {\left(b x^{n} + 4 \, a\right)} \sqrt{b x^{n} + a}\right)}}{3 \, n}\right]"," ",0,"[1/3*(3*a^(3/2)*log((b*x^n - 2*sqrt(b*x^n + a)*sqrt(a) + 2*a)/x^n) + 2*(b*x^n + 4*a)*sqrt(b*x^n + a))/n, 2/3*(3*sqrt(-a)*a*arctan(sqrt(b*x^n + a)*sqrt(-a)/a) + (b*x^n + 4*a)*sqrt(b*x^n + a))/n]","A",0
2495,-2,0,0,0.000000," ","integrate((a+b*x^n)^(3/2)/x^2,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
2496,-2,0,0,0.000000," ","integrate((a+b*x^n)^(3/2)/x^3,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
2497,-2,0,0,0.000000," ","integrate(x*(a+b*x^n)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
2498,-2,0,0,0.000000," ","integrate((a+b*x^n)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
2499,1,144,0,1.357157," ","integrate((a+b*x^n)^(5/2)/x,x, algorithm=""fricas"")","\left[\frac{15 \, a^{\frac{5}{2}} \log\left(\frac{b x^{n} - 2 \, \sqrt{b x^{n} + a} \sqrt{a} + 2 \, a}{x^{n}}\right) + 2 \, {\left(3 \, b^{2} x^{2 \, n} + 11 \, a b x^{n} + 23 \, a^{2}\right)} \sqrt{b x^{n} + a}}{15 \, n}, \frac{2 \, {\left(15 \, \sqrt{-a} a^{2} \arctan\left(\frac{\sqrt{b x^{n} + a} \sqrt{-a}}{a}\right) + {\left(3 \, b^{2} x^{2 \, n} + 11 \, a b x^{n} + 23 \, a^{2}\right)} \sqrt{b x^{n} + a}\right)}}{15 \, n}\right]"," ",0,"[1/15*(15*a^(5/2)*log((b*x^n - 2*sqrt(b*x^n + a)*sqrt(a) + 2*a)/x^n) + 2*(3*b^2*x^(2*n) + 11*a*b*x^n + 23*a^2)*sqrt(b*x^n + a))/n, 2/15*(15*sqrt(-a)*a^2*arctan(sqrt(b*x^n + a)*sqrt(-a)/a) + (3*b^2*x^(2*n) + 11*a*b*x^n + 23*a^2)*sqrt(b*x^n + a))/n]","A",0
2500,-2,0,0,0.000000," ","integrate((a+b*x^n)^(5/2)/x^2,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
2501,-2,0,0,0.000000," ","integrate((a+b*x^n)^(5/2)/x^3,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
2502,-2,0,0,0.000000," ","integrate(x/(a+b*x^n)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
2503,-2,0,0,0.000000," ","integrate(1/(a+b*x^n)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
2504,1,70,0,1.354921," ","integrate(1/x/(a+b*x^n)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{b x^{n} - 2 \, \sqrt{b x^{n} + a} \sqrt{a} + 2 \, a}{x^{n}}\right)}{\sqrt{a} n}, \frac{2 \, \sqrt{-a} \arctan\left(\frac{\sqrt{b x^{n} + a} \sqrt{-a}}{a}\right)}{a n}\right]"," ",0,"[log((b*x^n - 2*sqrt(b*x^n + a)*sqrt(a) + 2*a)/x^n)/(sqrt(a)*n), 2*sqrt(-a)*arctan(sqrt(b*x^n + a)*sqrt(-a)/a)/(a*n)]","A",0
2505,-2,0,0,0.000000," ","integrate(1/x^2/(a+b*x^n)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
2506,-2,0,0,0.000000," ","integrate(1/x^3/(a+b*x^n)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
2507,-2,0,0,0.000000," ","integrate(x/(a+b*x^n)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
2508,-2,0,0,0.000000," ","integrate(1/(a+b*x^n)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
2509,1,144,0,0.942864," ","integrate(1/x/(a+b*x^n)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(\sqrt{a} b x^{n} + a^{\frac{3}{2}}\right)} \log\left(\frac{b x^{n} - 2 \, \sqrt{b x^{n} + a} \sqrt{a} + 2 \, a}{x^{n}}\right) + 2 \, \sqrt{b x^{n} + a} a}{a^{2} b n x^{n} + a^{3} n}, \frac{2 \, {\left({\left(\sqrt{-a} b x^{n} + \sqrt{-a} a\right)} \arctan\left(\frac{\sqrt{b x^{n} + a} \sqrt{-a}}{a}\right) + \sqrt{b x^{n} + a} a\right)}}{a^{2} b n x^{n} + a^{3} n}\right]"," ",0,"[((sqrt(a)*b*x^n + a^(3/2))*log((b*x^n - 2*sqrt(b*x^n + a)*sqrt(a) + 2*a)/x^n) + 2*sqrt(b*x^n + a)*a)/(a^2*b*n*x^n + a^3*n), 2*((sqrt(-a)*b*x^n + sqrt(-a)*a)*arctan(sqrt(b*x^n + a)*sqrt(-a)/a) + sqrt(b*x^n + a)*a)/(a^2*b*n*x^n + a^3*n)]","A",0
2510,-2,0,0,0.000000," ","integrate(1/x^2/(a+b*x^n)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
2511,-2,0,0,0.000000," ","integrate(1/x^3/(a+b*x^n)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
2512,-2,0,0,0.000000," ","integrate(x/(a+b*x^n)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
2513,-2,0,0,0.000000," ","integrate(1/(a+b*x^n)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
2514,1,230,0,0.919183," ","integrate(1/x/(a+b*x^n)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(\sqrt{a} b^{2} x^{2 \, n} + 2 \, a^{\frac{3}{2}} b x^{n} + a^{\frac{5}{2}}\right)} \log\left(\frac{b x^{n} - 2 \, \sqrt{b x^{n} + a} \sqrt{a} + 2 \, a}{x^{n}}\right) + 2 \, {\left(3 \, a b x^{n} + 4 \, a^{2}\right)} \sqrt{b x^{n} + a}}{3 \, {\left(a^{3} b^{2} n x^{2 \, n} + 2 \, a^{4} b n x^{n} + a^{5} n\right)}}, \frac{2 \, {\left(3 \, {\left(\sqrt{-a} b^{2} x^{2 \, n} + 2 \, \sqrt{-a} a b x^{n} + \sqrt{-a} a^{2}\right)} \arctan\left(\frac{\sqrt{b x^{n} + a} \sqrt{-a}}{a}\right) + {\left(3 \, a b x^{n} + 4 \, a^{2}\right)} \sqrt{b x^{n} + a}\right)}}{3 \, {\left(a^{3} b^{2} n x^{2 \, n} + 2 \, a^{4} b n x^{n} + a^{5} n\right)}}\right]"," ",0,"[1/3*(3*(sqrt(a)*b^2*x^(2*n) + 2*a^(3/2)*b*x^n + a^(5/2))*log((b*x^n - 2*sqrt(b*x^n + a)*sqrt(a) + 2*a)/x^n) + 2*(3*a*b*x^n + 4*a^2)*sqrt(b*x^n + a))/(a^3*b^2*n*x^(2*n) + 2*a^4*b*n*x^n + a^5*n), 2/3*(3*(sqrt(-a)*b^2*x^(2*n) + 2*sqrt(-a)*a*b*x^n + sqrt(-a)*a^2)*arctan(sqrt(b*x^n + a)*sqrt(-a)/a) + (3*a*b*x^n + 4*a^2)*sqrt(b*x^n + a))/(a^3*b^2*n*x^(2*n) + 2*a^4*b*n*x^n + a^5*n)]","A",0
2515,-2,0,0,0.000000," ","integrate(1/x^2/(a+b*x^n)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
2516,-2,0,0,0.000000," ","integrate(1/x^3/(a+b*x^n)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
2517,1,106,0,0.826700," ","integrate((a+b*x^n)^(1/3)/x,x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} a^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} {\left(b x^{n} + a\right)}^{\frac{1}{3}} a^{\frac{2}{3}} + \sqrt{3} a}{3 \, a}\right) + a^{\frac{1}{3}} \log\left({\left(b x^{n} + a\right)}^{\frac{2}{3}} + {\left(b x^{n} + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + a^{\frac{2}{3}}\right) - 2 \, a^{\frac{1}{3}} \log\left({\left(b x^{n} + a\right)}^{\frac{1}{3}} - a^{\frac{1}{3}}\right) - 6 \, {\left(b x^{n} + a\right)}^{\frac{1}{3}}}{2 \, n}"," ",0,"-1/2*(2*sqrt(3)*a^(1/3)*arctan(1/3*(2*sqrt(3)*(b*x^n + a)^(1/3)*a^(2/3) + sqrt(3)*a)/a) + a^(1/3)*log((b*x^n + a)^(2/3) + (b*x^n + a)^(1/3)*a^(1/3) + a^(2/3)) - 2*a^(1/3)*log((b*x^n + a)^(1/3) - a^(1/3)) - 6*(b*x^n + a)^(1/3))/n","A",0
2518,1,22,0,0.947172," ","integrate(x^(-1+4*n)*(a+b*x^n),x, algorithm=""fricas"")","\frac{4 \, b x^{5 \, n} + 5 \, a x^{4 \, n}}{20 \, n}"," ",0,"1/20*(4*b*x^(5*n) + 5*a*x^(4*n))/n","A",0
2519,1,22,0,0.934628," ","integrate(x^(-1+3*n)*(a+b*x^n),x, algorithm=""fricas"")","\frac{3 \, b x^{4 \, n} + 4 \, a x^{3 \, n}}{12 \, n}"," ",0,"1/12*(3*b*x^(4*n) + 4*a*x^(3*n))/n","A",0
2520,1,22,0,1.287223," ","integrate(x^(-1+2*n)*(a+b*x^n),x, algorithm=""fricas"")","\frac{2 \, b x^{3 \, n} + 3 \, a x^{2 \, n}}{6 \, n}"," ",0,"1/6*(2*b*x^(3*n) + 3*a*x^(2*n))/n","A",0
2521,1,19,0,0.579232," ","integrate(x^(-1+n)*(a+b*x^n),x, algorithm=""fricas"")","\frac{b x^{2 \, n} + 2 \, a x^{n}}{2 \, n}"," ",0,"1/2*(b*x^(2*n) + 2*a*x^n)/n","A",0
2522,1,15,0,0.671722," ","integrate((a+b*x^n)/x,x, algorithm=""fricas"")","\frac{a n \log\left(x\right) + b x^{n}}{n}"," ",0,"(a*n*log(x) + b*x^n)/n","A",0
2523,1,21,0,0.804465," ","integrate(x^(-1-n)*(a+b*x^n),x, algorithm=""fricas"")","\frac{b n x^{n} \log\left(x\right) - a}{n x^{n}}"," ",0,"(b*n*x^n*log(x) - a)/(n*x^n)","A",0
2524,1,20,0,0.744807," ","integrate(x^(-1-2*n)*(a+b*x^n),x, algorithm=""fricas"")","-\frac{2 \, b x^{n} + a}{2 \, n x^{2 \, n}}"," ",0,"-1/2*(2*b*x^n + a)/(n*x^(2*n))","A",0
2525,1,22,0,0.861372," ","integrate(x^(-1-3*n)*(a+b*x^n),x, algorithm=""fricas"")","-\frac{3 \, b x^{n} + 2 \, a}{6 \, n x^{3 \, n}}"," ",0,"-1/6*(3*b*x^n + 2*a)/(n*x^(3*n))","A",0
2526,1,22,0,0.528746," ","integrate(x^(-1-4*n)*(a+b*x^n),x, algorithm=""fricas"")","-\frac{4 \, b x^{n} + 3 \, a}{12 \, n x^{4 \, n}}"," ",0,"-1/12*(4*b*x^n + 3*a)/(n*x^(4*n))","A",0
2527,1,22,0,0.939507," ","integrate(x^(-1-5*n)*(a+b*x^n),x, algorithm=""fricas"")","-\frac{5 \, b x^{n} + 4 \, a}{20 \, n x^{5 \, n}}"," ",0,"-1/20*(5*b*x^n + 4*a)/(n*x^(5*n))","A",0
2528,1,35,0,0.739005," ","integrate(x^(-1+4*n)*(a+b*x^n)^2,x, algorithm=""fricas"")","\frac{10 \, b^{2} x^{6 \, n} + 24 \, a b x^{5 \, n} + 15 \, a^{2} x^{4 \, n}}{60 \, n}"," ",0,"1/60*(10*b^2*x^(6*n) + 24*a*b*x^(5*n) + 15*a^2*x^(4*n))/n","A",0
2529,1,35,0,0.905356," ","integrate(x^(-1+3*n)*(a+b*x^n)^2,x, algorithm=""fricas"")","\frac{6 \, b^{2} x^{5 \, n} + 15 \, a b x^{4 \, n} + 10 \, a^{2} x^{3 \, n}}{30 \, n}"," ",0,"1/30*(6*b^2*x^(5*n) + 15*a*b*x^(4*n) + 10*a^2*x^(3*n))/n","A",0
2530,1,35,0,0.776132," ","integrate(x^(-1+2*n)*(a+b*x^n)^2,x, algorithm=""fricas"")","\frac{3 \, b^{2} x^{4 \, n} + 8 \, a b x^{3 \, n} + 6 \, a^{2} x^{2 \, n}}{12 \, n}"," ",0,"1/12*(3*b^2*x^(4*n) + 8*a*b*x^(3*n) + 6*a^2*x^(2*n))/n","A",0
2531,1,32,0,0.958857," ","integrate(x^(-1+n)*(a+b*x^n)^2,x, algorithm=""fricas"")","\frac{b^{2} x^{3 \, n} + 3 \, a b x^{2 \, n} + 3 \, a^{2} x^{n}}{3 \, n}"," ",0,"1/3*(b^2*x^(3*n) + 3*a*b*x^(2*n) + 3*a^2*x^n)/n","A",0
2532,1,30,0,0.844877," ","integrate((a+b*x^n)^2/x,x, algorithm=""fricas"")","\frac{2 \, a^{2} n \log\left(x\right) + b^{2} x^{2 \, n} + 4 \, a b x^{n}}{2 \, n}"," ",0,"1/2*(2*a^2*n*log(x) + b^2*x^(2*n) + 4*a*b*x^n)/n","A",0
2533,1,34,0,0.803793," ","integrate(x^(-1-n)*(a+b*x^n)^2,x, algorithm=""fricas"")","\frac{2 \, a b n x^{n} \log\left(x\right) + b^{2} x^{2 \, n} - a^{2}}{n x^{n}}"," ",0,"(2*a*b*n*x^n*log(x) + b^2*x^(2*n) - a^2)/(n*x^n)","A",0
2534,1,38,0,0.860946," ","integrate(x^(-1-2*n)*(a+b*x^n)^2,x, algorithm=""fricas"")","\frac{2 \, b^{2} n x^{2 \, n} \log\left(x\right) - 4 \, a b x^{n} - a^{2}}{2 \, n x^{2 \, n}}"," ",0,"1/2*(2*b^2*n*x^(2*n)*log(x) - 4*a*b*x^n - a^2)/(n*x^(2*n))","A",0
2535,1,33,0,0.668318," ","integrate(x^(-1-3*n)*(a+b*x^n)^2,x, algorithm=""fricas"")","-\frac{3 \, b^{2} x^{2 \, n} + 3 \, a b x^{n} + a^{2}}{3 \, n x^{3 \, n}}"," ",0,"-1/3*(3*b^2*x^(2*n) + 3*a*b*x^n + a^2)/(n*x^(3*n))","A",0
2536,1,35,0,0.912993," ","integrate(x^(-1-4*n)*(a+b*x^n)^2,x, algorithm=""fricas"")","-\frac{6 \, b^{2} x^{2 \, n} + 8 \, a b x^{n} + 3 \, a^{2}}{12 \, n x^{4 \, n}}"," ",0,"-1/12*(6*b^2*x^(2*n) + 8*a*b*x^n + 3*a^2)/(n*x^(4*n))","A",0
2537,1,35,0,0.869847," ","integrate(x^(-1-5*n)*(a+b*x^n)^2,x, algorithm=""fricas"")","-\frac{10 \, b^{2} x^{2 \, n} + 15 \, a b x^{n} + 6 \, a^{2}}{30 \, n x^{5 \, n}}"," ",0,"-1/30*(10*b^2*x^(2*n) + 15*a*b*x^n + 6*a^2)/(n*x^(5*n))","A",0
2538,1,35,0,0.980445," ","integrate(x^(-1-6*n)*(a+b*x^n)^2,x, algorithm=""fricas"")","-\frac{15 \, b^{2} x^{2 \, n} + 24 \, a b x^{n} + 10 \, a^{2}}{60 \, n x^{6 \, n}}"," ",0,"-1/60*(15*b^2*x^(2*n) + 24*a*b*x^n + 10*a^2)/(n*x^(6*n))","A",0
2539,1,48,0,0.775847," ","integrate(x^(-1+4*n)*(a+b*x^n)^3,x, algorithm=""fricas"")","\frac{20 \, b^{3} x^{7 \, n} + 70 \, a b^{2} x^{6 \, n} + 84 \, a^{2} b x^{5 \, n} + 35 \, a^{3} x^{4 \, n}}{140 \, n}"," ",0,"1/140*(20*b^3*x^(7*n) + 70*a*b^2*x^(6*n) + 84*a^2*b*x^(5*n) + 35*a^3*x^(4*n))/n","A",0
2540,1,48,0,0.891231," ","integrate(x^(-1+3*n)*(a+b*x^n)^3,x, algorithm=""fricas"")","\frac{10 \, b^{3} x^{6 \, n} + 36 \, a b^{2} x^{5 \, n} + 45 \, a^{2} b x^{4 \, n} + 20 \, a^{3} x^{3 \, n}}{60 \, n}"," ",0,"1/60*(10*b^3*x^(6*n) + 36*a*b^2*x^(5*n) + 45*a^2*b*x^(4*n) + 20*a^3*x^(3*n))/n","A",0
2541,1,48,0,0.813739," ","integrate(x^(-1+2*n)*(a+b*x^n)^3,x, algorithm=""fricas"")","\frac{4 \, b^{3} x^{5 \, n} + 15 \, a b^{2} x^{4 \, n} + 20 \, a^{2} b x^{3 \, n} + 10 \, a^{3} x^{2 \, n}}{20 \, n}"," ",0,"1/20*(4*b^3*x^(5*n) + 15*a*b^2*x^(4*n) + 20*a^2*b*x^(3*n) + 10*a^3*x^(2*n))/n","A",0
2542,1,45,0,0.884919," ","integrate(x^(-1+n)*(a+b*x^n)^3,x, algorithm=""fricas"")","\frac{b^{3} x^{4 \, n} + 4 \, a b^{2} x^{3 \, n} + 6 \, a^{2} b x^{2 \, n} + 4 \, a^{3} x^{n}}{4 \, n}"," ",0,"1/4*(b^3*x^(4*n) + 4*a*b^2*x^(3*n) + 6*a^2*b*x^(2*n) + 4*a^3*x^n)/n","B",0
2543,1,44,0,0.572011," ","integrate((a+b*x^n)^3/x,x, algorithm=""fricas"")","\frac{6 \, a^{3} n \log\left(x\right) + 2 \, b^{3} x^{3 \, n} + 9 \, a b^{2} x^{2 \, n} + 18 \, a^{2} b x^{n}}{6 \, n}"," ",0,"1/6*(6*a^3*n*log(x) + 2*b^3*x^(3*n) + 9*a*b^2*x^(2*n) + 18*a^2*b*x^n)/n","A",0
2544,1,48,0,0.840999," ","integrate(x^(-1-n)*(a+b*x^n)^3,x, algorithm=""fricas"")","\frac{6 \, a^{2} b n x^{n} \log\left(x\right) + b^{3} x^{3 \, n} + 6 \, a b^{2} x^{2 \, n} - 2 \, a^{3}}{2 \, n x^{n}}"," ",0,"1/2*(6*a^2*b*n*x^n*log(x) + b^3*x^(3*n) + 6*a*b^2*x^(2*n) - 2*a^3)/(n*x^n)","A",0
2545,1,51,0,0.548578," ","integrate(x^(-1-2*n)*(a+b*x^n)^3,x, algorithm=""fricas"")","\frac{6 \, a b^{2} n x^{2 \, n} \log\left(x\right) + 2 \, b^{3} x^{3 \, n} - 6 \, a^{2} b x^{n} - a^{3}}{2 \, n x^{2 \, n}}"," ",0,"1/2*(6*a*b^2*n*x^(2*n)*log(x) + 2*b^3*x^(3*n) - 6*a^2*b*x^n - a^3)/(n*x^(2*n))","A",0
2546,1,51,0,0.871817," ","integrate(x^(-1-3*n)*(a+b*x^n)^3,x, algorithm=""fricas"")","\frac{6 \, b^{3} n x^{3 \, n} \log\left(x\right) - 18 \, a b^{2} x^{2 \, n} - 9 \, a^{2} b x^{n} - 2 \, a^{3}}{6 \, n x^{3 \, n}}"," ",0,"1/6*(6*b^3*n*x^(3*n)*log(x) - 18*a*b^2*x^(2*n) - 9*a^2*b*x^n - 2*a^3)/(n*x^(3*n))","A",0
2547,1,46,0,0.703549," ","integrate(x^(-1-4*n)*(a+b*x^n)^3,x, algorithm=""fricas"")","-\frac{4 \, b^{3} x^{3 \, n} + 6 \, a b^{2} x^{2 \, n} + 4 \, a^{2} b x^{n} + a^{3}}{4 \, n x^{4 \, n}}"," ",0,"-1/4*(4*b^3*x^(3*n) + 6*a*b^2*x^(2*n) + 4*a^2*b*x^n + a^3)/(n*x^(4*n))","A",0
2548,1,48,0,0.639408," ","integrate(x^(-1-5*n)*(a+b*x^n)^3,x, algorithm=""fricas"")","-\frac{10 \, b^{3} x^{3 \, n} + 20 \, a b^{2} x^{2 \, n} + 15 \, a^{2} b x^{n} + 4 \, a^{3}}{20 \, n x^{5 \, n}}"," ",0,"-1/20*(10*b^3*x^(3*n) + 20*a*b^2*x^(2*n) + 15*a^2*b*x^n + 4*a^3)/(n*x^(5*n))","A",0
2549,1,48,0,0.941869," ","integrate(x^(-1-6*n)*(a+b*x^n)^3,x, algorithm=""fricas"")","-\frac{20 \, b^{3} x^{3 \, n} + 45 \, a b^{2} x^{2 \, n} + 36 \, a^{2} b x^{n} + 10 \, a^{3}}{60 \, n x^{6 \, n}}"," ",0,"-1/60*(20*b^3*x^(3*n) + 45*a*b^2*x^(2*n) + 36*a^2*b*x^n + 10*a^3)/(n*x^(6*n))","A",0
2550,1,48,0,0.843392," ","integrate(x^(-1-7*n)*(a+b*x^n)^3,x, algorithm=""fricas"")","-\frac{35 \, b^{3} x^{3 \, n} + 84 \, a b^{2} x^{2 \, n} + 70 \, a^{2} b x^{n} + 20 \, a^{3}}{140 \, n x^{7 \, n}}"," ",0,"-1/140*(35*b^3*x^(3*n) + 84*a*b^2*x^(2*n) + 70*a^2*b*x^n + 20*a^3)/(n*x^(7*n))","A",0
2551,1,74,0,0.879999," ","integrate(x^(-1+4*n)*(a+b*x^n)^5,x, algorithm=""fricas"")","\frac{56 \, b^{5} x^{9 \, n} + 315 \, a b^{4} x^{8 \, n} + 720 \, a^{2} b^{3} x^{7 \, n} + 840 \, a^{3} b^{2} x^{6 \, n} + 504 \, a^{4} b x^{5 \, n} + 126 \, a^{5} x^{4 \, n}}{504 \, n}"," ",0,"1/504*(56*b^5*x^(9*n) + 315*a*b^4*x^(8*n) + 720*a^2*b^3*x^(7*n) + 840*a^3*b^2*x^(6*n) + 504*a^4*b*x^(5*n) + 126*a^5*x^(4*n))/n","A",0
2552,1,74,0,0.872132," ","integrate(x^(-1+3*n)*(a+b*x^n)^5,x, algorithm=""fricas"")","\frac{21 \, b^{5} x^{8 \, n} + 120 \, a b^{4} x^{7 \, n} + 280 \, a^{2} b^{3} x^{6 \, n} + 336 \, a^{3} b^{2} x^{5 \, n} + 210 \, a^{4} b x^{4 \, n} + 56 \, a^{5} x^{3 \, n}}{168 \, n}"," ",0,"1/168*(21*b^5*x^(8*n) + 120*a*b^4*x^(7*n) + 280*a^2*b^3*x^(6*n) + 336*a^3*b^2*x^(5*n) + 210*a^4*b*x^(4*n) + 56*a^5*x^(3*n))/n","A",0
2553,1,74,0,0.885520," ","integrate(x^(-1+2*n)*(a+b*x^n)^5,x, algorithm=""fricas"")","\frac{6 \, b^{5} x^{7 \, n} + 35 \, a b^{4} x^{6 \, n} + 84 \, a^{2} b^{3} x^{5 \, n} + 105 \, a^{3} b^{2} x^{4 \, n} + 70 \, a^{4} b x^{3 \, n} + 21 \, a^{5} x^{2 \, n}}{42 \, n}"," ",0,"1/42*(6*b^5*x^(7*n) + 35*a*b^4*x^(6*n) + 84*a^2*b^3*x^(5*n) + 105*a^3*b^2*x^(4*n) + 70*a^4*b*x^(3*n) + 21*a^5*x^(2*n))/n","B",0
2554,1,71,0,0.886099," ","integrate(x^(-1+n)*(a+b*x^n)^5,x, algorithm=""fricas"")","\frac{b^{5} x^{6 \, n} + 6 \, a b^{4} x^{5 \, n} + 15 \, a^{2} b^{3} x^{4 \, n} + 20 \, a^{3} b^{2} x^{3 \, n} + 15 \, a^{4} b x^{2 \, n} + 6 \, a^{5} x^{n}}{6 \, n}"," ",0,"1/6*(b^5*x^(6*n) + 6*a*b^4*x^(5*n) + 15*a^2*b^3*x^(4*n) + 20*a^3*b^2*x^(3*n) + 15*a^4*b*x^(2*n) + 6*a^5*x^n)/n","B",0
2555,1,70,0,1.070257," ","integrate((a+b*x^n)^5/x,x, algorithm=""fricas"")","\frac{60 \, a^{5} n \log\left(x\right) + 12 \, b^{5} x^{5 \, n} + 75 \, a b^{4} x^{4 \, n} + 200 \, a^{2} b^{3} x^{3 \, n} + 300 \, a^{3} b^{2} x^{2 \, n} + 300 \, a^{4} b x^{n}}{60 \, n}"," ",0,"1/60*(60*a^5*n*log(x) + 12*b^5*x^(5*n) + 75*a*b^4*x^(4*n) + 200*a^2*b^3*x^(3*n) + 300*a^3*b^2*x^(2*n) + 300*a^4*b*x^n)/n","A",0
2556,1,75,0,0.887657," ","integrate(x^(-1-n)*(a+b*x^n)^5,x, algorithm=""fricas"")","\frac{60 \, a^{4} b n x^{n} \log\left(x\right) + 3 \, b^{5} x^{5 \, n} + 20 \, a b^{4} x^{4 \, n} + 60 \, a^{2} b^{3} x^{3 \, n} + 120 \, a^{3} b^{2} x^{2 \, n} - 12 \, a^{5}}{12 \, n x^{n}}"," ",0,"1/12*(60*a^4*b*n*x^n*log(x) + 3*b^5*x^(5*n) + 20*a*b^4*x^(4*n) + 60*a^2*b^3*x^(3*n) + 120*a^3*b^2*x^(2*n) - 12*a^5)/(n*x^n)","A",0
2557,1,77,0,0.929579," ","integrate(x^(-1-2*n)*(a+b*x^n)^5,x, algorithm=""fricas"")","\frac{60 \, a^{3} b^{2} n x^{2 \, n} \log\left(x\right) + 2 \, b^{5} x^{5 \, n} + 15 \, a b^{4} x^{4 \, n} + 60 \, a^{2} b^{3} x^{3 \, n} - 30 \, a^{4} b x^{n} - 3 \, a^{5}}{6 \, n x^{2 \, n}}"," ",0,"1/6*(60*a^3*b^2*n*x^(2*n)*log(x) + 2*b^5*x^(5*n) + 15*a*b^4*x^(4*n) + 60*a^2*b^3*x^(3*n) - 30*a^4*b*x^n - 3*a^5)/(n*x^(2*n))","A",0
2558,1,77,0,0.747922," ","integrate(x^(-1-3*n)*(a+b*x^n)^5,x, algorithm=""fricas"")","\frac{60 \, a^{2} b^{3} n x^{3 \, n} \log\left(x\right) + 3 \, b^{5} x^{5 \, n} + 30 \, a b^{4} x^{4 \, n} - 60 \, a^{3} b^{2} x^{2 \, n} - 15 \, a^{4} b x^{n} - 2 \, a^{5}}{6 \, n x^{3 \, n}}"," ",0,"1/6*(60*a^2*b^3*n*x^(3*n)*log(x) + 3*b^5*x^(5*n) + 30*a*b^4*x^(4*n) - 60*a^3*b^2*x^(2*n) - 15*a^4*b*x^n - 2*a^5)/(n*x^(3*n))","A",0
2559,1,77,0,0.826997," ","integrate(x^(-1-4*n)*(a+b*x^n)^5,x, algorithm=""fricas"")","\frac{60 \, a b^{4} n x^{4 \, n} \log\left(x\right) + 12 \, b^{5} x^{5 \, n} - 120 \, a^{2} b^{3} x^{3 \, n} - 60 \, a^{3} b^{2} x^{2 \, n} - 20 \, a^{4} b x^{n} - 3 \, a^{5}}{12 \, n x^{4 \, n}}"," ",0,"1/12*(60*a*b^4*n*x^(4*n)*log(x) + 12*b^5*x^(5*n) - 120*a^2*b^3*x^(3*n) - 60*a^3*b^2*x^(2*n) - 20*a^4*b*x^n - 3*a^5)/(n*x^(4*n))","A",0
2560,1,77,0,0.870265," ","integrate(x^(-1-5*n)*(a+b*x^n)^5,x, algorithm=""fricas"")","\frac{60 \, b^{5} n x^{5 \, n} \log\left(x\right) - 300 \, a b^{4} x^{4 \, n} - 300 \, a^{2} b^{3} x^{3 \, n} - 200 \, a^{3} b^{2} x^{2 \, n} - 75 \, a^{4} b x^{n} - 12 \, a^{5}}{60 \, n x^{5 \, n}}"," ",0,"1/60*(60*b^5*n*x^(5*n)*log(x) - 300*a*b^4*x^(4*n) - 300*a^2*b^3*x^(3*n) - 200*a^3*b^2*x^(2*n) - 75*a^4*b*x^n - 12*a^5)/(n*x^(5*n))","A",0
2561,1,72,0,0.726241," ","integrate(x^(-1-6*n)*(a+b*x^n)^5,x, algorithm=""fricas"")","-\frac{6 \, b^{5} x^{5 \, n} + 15 \, a b^{4} x^{4 \, n} + 20 \, a^{2} b^{3} x^{3 \, n} + 15 \, a^{3} b^{2} x^{2 \, n} + 6 \, a^{4} b x^{n} + a^{5}}{6 \, n x^{6 \, n}}"," ",0,"-1/6*(6*b^5*x^(5*n) + 15*a*b^4*x^(4*n) + 20*a^2*b^3*x^(3*n) + 15*a^3*b^2*x^(2*n) + 6*a^4*b*x^n + a^5)/(n*x^(6*n))","B",0
2562,1,74,0,0.830751," ","integrate(x^(-1-7*n)*(a+b*x^n)^5,x, algorithm=""fricas"")","-\frac{21 \, b^{5} x^{5 \, n} + 70 \, a b^{4} x^{4 \, n} + 105 \, a^{2} b^{3} x^{3 \, n} + 84 \, a^{3} b^{2} x^{2 \, n} + 35 \, a^{4} b x^{n} + 6 \, a^{5}}{42 \, n x^{7 \, n}}"," ",0,"-1/42*(21*b^5*x^(5*n) + 70*a*b^4*x^(4*n) + 105*a^2*b^3*x^(3*n) + 84*a^3*b^2*x^(2*n) + 35*a^4*b*x^n + 6*a^5)/(n*x^(7*n))","A",0
2563,1,74,0,0.908336," ","integrate(x^(-1-8*n)*(a+b*x^n)^5,x, algorithm=""fricas"")","-\frac{56 \, b^{5} x^{5 \, n} + 210 \, a b^{4} x^{4 \, n} + 336 \, a^{2} b^{3} x^{3 \, n} + 280 \, a^{3} b^{2} x^{2 \, n} + 120 \, a^{4} b x^{n} + 21 \, a^{5}}{168 \, n x^{8 \, n}}"," ",0,"-1/168*(56*b^5*x^(5*n) + 210*a*b^4*x^(4*n) + 336*a^2*b^3*x^(3*n) + 280*a^3*b^2*x^(2*n) + 120*a^4*b*x^n + 21*a^5)/(n*x^(8*n))","A",0
2564,1,74,0,0.735549," ","integrate(x^(-1-9*n)*(a+b*x^n)^5,x, algorithm=""fricas"")","-\frac{126 \, b^{5} x^{5 \, n} + 504 \, a b^{4} x^{4 \, n} + 840 \, a^{2} b^{3} x^{3 \, n} + 720 \, a^{3} b^{2} x^{2 \, n} + 315 \, a^{4} b x^{n} + 56 \, a^{5}}{504 \, n x^{9 \, n}}"," ",0,"-1/504*(126*b^5*x^(5*n) + 504*a*b^4*x^(4*n) + 840*a^2*b^3*x^(3*n) + 720*a^3*b^2*x^(2*n) + 315*a^4*b*x^n + 56*a^5)/(n*x^(9*n))","A",0
2565,1,74,0,0.787770," ","integrate(x^(-1-10*n)*(a+b*x^n)^5,x, algorithm=""fricas"")","-\frac{252 \, b^{5} x^{5 \, n} + 1050 \, a b^{4} x^{4 \, n} + 1800 \, a^{2} b^{3} x^{3 \, n} + 1575 \, a^{3} b^{2} x^{2 \, n} + 700 \, a^{4} b x^{n} + 126 \, a^{5}}{1260 \, n x^{10 \, n}}"," ",0,"-1/1260*(252*b^5*x^(5*n) + 1050*a*b^4*x^(4*n) + 1800*a^2*b^3*x^(3*n) + 1575*a^3*b^2*x^(2*n) + 700*a^4*b*x^n + 126*a^5)/(n*x^(10*n))","A",0
2566,1,113,0,0.649624," ","integrate(x^(-1+9*n)*(a+b*x^n)^8,x, algorithm=""fricas"")","\frac{12870 \, b^{8} x^{17 \, n} + 109395 \, a b^{7} x^{16 \, n} + 408408 \, a^{2} b^{6} x^{15 \, n} + 875160 \, a^{3} b^{5} x^{14 \, n} + 1178100 \, a^{4} b^{4} x^{13 \, n} + 1021020 \, a^{5} b^{3} x^{12 \, n} + 556920 \, a^{6} b^{2} x^{11 \, n} + 175032 \, a^{7} b x^{10 \, n} + 24310 \, a^{8} x^{9 \, n}}{218790 \, n}"," ",0,"1/218790*(12870*b^8*x^(17*n) + 109395*a*b^7*x^(16*n) + 408408*a^2*b^6*x^(15*n) + 875160*a^3*b^5*x^(14*n) + 1178100*a^4*b^4*x^(13*n) + 1021020*a^5*b^3*x^(12*n) + 556920*a^6*b^2*x^(11*n) + 175032*a^7*b*x^(10*n) + 24310*a^8*x^(9*n))/n","A",0
2567,1,113,0,0.993045," ","integrate(x^(-1+8*n)*(a+b*x^n)^8,x, algorithm=""fricas"")","\frac{6435 \, b^{8} x^{16 \, n} + 54912 \, a b^{7} x^{15 \, n} + 205920 \, a^{2} b^{6} x^{14 \, n} + 443520 \, a^{3} b^{5} x^{13 \, n} + 600600 \, a^{4} b^{4} x^{12 \, n} + 524160 \, a^{5} b^{3} x^{11 \, n} + 288288 \, a^{6} b^{2} x^{10 \, n} + 91520 \, a^{7} b x^{9 \, n} + 12870 \, a^{8} x^{8 \, n}}{102960 \, n}"," ",0,"1/102960*(6435*b^8*x^(16*n) + 54912*a*b^7*x^(15*n) + 205920*a^2*b^6*x^(14*n) + 443520*a^3*b^5*x^(13*n) + 600600*a^4*b^4*x^(12*n) + 524160*a^5*b^3*x^(11*n) + 288288*a^6*b^2*x^(10*n) + 91520*a^7*b*x^(9*n) + 12870*a^8*x^(8*n))/n","A",0
2568,1,113,0,1.199486," ","integrate(x^(-1+7*n)*(a+b*x^n)^8,x, algorithm=""fricas"")","\frac{3003 \, b^{8} x^{15 \, n} + 25740 \, a b^{7} x^{14 \, n} + 97020 \, a^{2} b^{6} x^{13 \, n} + 210210 \, a^{3} b^{5} x^{12 \, n} + 286650 \, a^{4} b^{4} x^{11 \, n} + 252252 \, a^{5} b^{3} x^{10 \, n} + 140140 \, a^{6} b^{2} x^{9 \, n} + 45045 \, a^{7} b x^{8 \, n} + 6435 \, a^{8} x^{7 \, n}}{45045 \, n}"," ",0,"1/45045*(3003*b^8*x^(15*n) + 25740*a*b^7*x^(14*n) + 97020*a^2*b^6*x^(13*n) + 210210*a^3*b^5*x^(12*n) + 286650*a^4*b^4*x^(11*n) + 252252*a^5*b^3*x^(10*n) + 140140*a^6*b^2*x^(9*n) + 45045*a^7*b*x^(8*n) + 6435*a^8*x^(7*n))/n","A",0
2569,1,113,0,0.872724," ","integrate(x^(-1+6*n)*(a+b*x^n)^8,x, algorithm=""fricas"")","\frac{1287 \, b^{8} x^{14 \, n} + 11088 \, a b^{7} x^{13 \, n} + 42042 \, a^{2} b^{6} x^{12 \, n} + 91728 \, a^{3} b^{5} x^{11 \, n} + 126126 \, a^{4} b^{4} x^{10 \, n} + 112112 \, a^{5} b^{3} x^{9 \, n} + 63063 \, a^{6} b^{2} x^{8 \, n} + 20592 \, a^{7} b x^{7 \, n} + 3003 \, a^{8} x^{6 \, n}}{18018 \, n}"," ",0,"1/18018*(1287*b^8*x^(14*n) + 11088*a*b^7*x^(13*n) + 42042*a^2*b^6*x^(12*n) + 91728*a^3*b^5*x^(11*n) + 126126*a^4*b^4*x^(10*n) + 112112*a^5*b^3*x^(9*n) + 63063*a^6*b^2*x^(8*n) + 20592*a^7*b*x^(7*n) + 3003*a^8*x^(6*n))/n","A",0
2570,1,113,0,0.902465," ","integrate(x^(-1+5*n)*(a+b*x^n)^8,x, algorithm=""fricas"")","\frac{495 \, b^{8} x^{13 \, n} + 4290 \, a b^{7} x^{12 \, n} + 16380 \, a^{2} b^{6} x^{11 \, n} + 36036 \, a^{3} b^{5} x^{10 \, n} + 50050 \, a^{4} b^{4} x^{9 \, n} + 45045 \, a^{5} b^{3} x^{8 \, n} + 25740 \, a^{6} b^{2} x^{7 \, n} + 8580 \, a^{7} b x^{6 \, n} + 1287 \, a^{8} x^{5 \, n}}{6435 \, n}"," ",0,"1/6435*(495*b^8*x^(13*n) + 4290*a*b^7*x^(12*n) + 16380*a^2*b^6*x^(11*n) + 36036*a^3*b^5*x^(10*n) + 50050*a^4*b^4*x^(9*n) + 45045*a^5*b^3*x^(8*n) + 25740*a^6*b^2*x^(7*n) + 8580*a^7*b*x^(6*n) + 1287*a^8*x^(5*n))/n","A",0
2571,1,113,0,0.789972," ","integrate(x^(-1+4*n)*(a+b*x^n)^8,x, algorithm=""fricas"")","\frac{165 \, b^{8} x^{12 \, n} + 1440 \, a b^{7} x^{11 \, n} + 5544 \, a^{2} b^{6} x^{10 \, n} + 12320 \, a^{3} b^{5} x^{9 \, n} + 17325 \, a^{4} b^{4} x^{8 \, n} + 15840 \, a^{5} b^{3} x^{7 \, n} + 9240 \, a^{6} b^{2} x^{6 \, n} + 3168 \, a^{7} b x^{5 \, n} + 495 \, a^{8} x^{4 \, n}}{1980 \, n}"," ",0,"1/1980*(165*b^8*x^(12*n) + 1440*a*b^7*x^(11*n) + 5544*a^2*b^6*x^(10*n) + 12320*a^3*b^5*x^(9*n) + 17325*a^4*b^4*x^(8*n) + 15840*a^5*b^3*x^(7*n) + 9240*a^6*b^2*x^(6*n) + 3168*a^7*b*x^(5*n) + 495*a^8*x^(4*n))/n","A",0
2572,1,113,0,0.739563," ","integrate(x^(-1+3*n)*(a+b*x^n)^8,x, algorithm=""fricas"")","\frac{45 \, b^{8} x^{11 \, n} + 396 \, a b^{7} x^{10 \, n} + 1540 \, a^{2} b^{6} x^{9 \, n} + 3465 \, a^{3} b^{5} x^{8 \, n} + 4950 \, a^{4} b^{4} x^{7 \, n} + 4620 \, a^{5} b^{3} x^{6 \, n} + 2772 \, a^{6} b^{2} x^{5 \, n} + 990 \, a^{7} b x^{4 \, n} + 165 \, a^{8} x^{3 \, n}}{495 \, n}"," ",0,"1/495*(45*b^8*x^(11*n) + 396*a*b^7*x^(10*n) + 1540*a^2*b^6*x^(9*n) + 3465*a^3*b^5*x^(8*n) + 4950*a^4*b^4*x^(7*n) + 4620*a^5*b^3*x^(6*n) + 2772*a^6*b^2*x^(5*n) + 990*a^7*b*x^(4*n) + 165*a^8*x^(3*n))/n","B",0
2573,1,113,0,0.552145," ","integrate(x^(-1+2*n)*(a+b*x^n)^8,x, algorithm=""fricas"")","\frac{9 \, b^{8} x^{10 \, n} + 80 \, a b^{7} x^{9 \, n} + 315 \, a^{2} b^{6} x^{8 \, n} + 720 \, a^{3} b^{5} x^{7 \, n} + 1050 \, a^{4} b^{4} x^{6 \, n} + 1008 \, a^{5} b^{3} x^{5 \, n} + 630 \, a^{6} b^{2} x^{4 \, n} + 240 \, a^{7} b x^{3 \, n} + 45 \, a^{8} x^{2 \, n}}{90 \, n}"," ",0,"1/90*(9*b^8*x^(10*n) + 80*a*b^7*x^(9*n) + 315*a^2*b^6*x^(8*n) + 720*a^3*b^5*x^(7*n) + 1050*a^4*b^4*x^(6*n) + 1008*a^5*b^3*x^(5*n) + 630*a^6*b^2*x^(4*n) + 240*a^7*b*x^(3*n) + 45*a^8*x^(2*n))/n","B",0
2574,1,110,0,0.847292," ","integrate(x^(-1+n)*(a+b*x^n)^8,x, algorithm=""fricas"")","\frac{b^{8} x^{9 \, n} + 9 \, a b^{7} x^{8 \, n} + 36 \, a^{2} b^{6} x^{7 \, n} + 84 \, a^{3} b^{5} x^{6 \, n} + 126 \, a^{4} b^{4} x^{5 \, n} + 126 \, a^{5} b^{3} x^{4 \, n} + 84 \, a^{6} b^{2} x^{3 \, n} + 36 \, a^{7} b x^{2 \, n} + 9 \, a^{8} x^{n}}{9 \, n}"," ",0,"1/9*(b^8*x^(9*n) + 9*a*b^7*x^(8*n) + 36*a^2*b^6*x^(7*n) + 84*a^3*b^5*x^(6*n) + 126*a^4*b^4*x^(5*n) + 126*a^5*b^3*x^(4*n) + 84*a^6*b^2*x^(3*n) + 36*a^7*b*x^(2*n) + 9*a^8*x^n)/n","B",0
2575,1,109,0,0.842371," ","integrate((a+b*x^n)^8/x,x, algorithm=""fricas"")","\frac{840 \, a^{8} n \log\left(x\right) + 105 \, b^{8} x^{8 \, n} + 960 \, a b^{7} x^{7 \, n} + 3920 \, a^{2} b^{6} x^{6 \, n} + 9408 \, a^{3} b^{5} x^{5 \, n} + 14700 \, a^{4} b^{4} x^{4 \, n} + 15680 \, a^{5} b^{3} x^{3 \, n} + 11760 \, a^{6} b^{2} x^{2 \, n} + 6720 \, a^{7} b x^{n}}{840 \, n}"," ",0,"1/840*(840*a^8*n*log(x) + 105*b^8*x^(8*n) + 960*a*b^7*x^(7*n) + 3920*a^2*b^6*x^(6*n) + 9408*a^3*b^5*x^(5*n) + 14700*a^4*b^4*x^(4*n) + 15680*a^5*b^3*x^(3*n) + 11760*a^6*b^2*x^(2*n) + 6720*a^7*b*x^n)/n","A",0
2576,1,114,0,0.835834," ","integrate(x^(-1-n)*(a+b*x^n)^8,x, algorithm=""fricas"")","\frac{840 \, a^{7} b n x^{n} \log\left(x\right) + 15 \, b^{8} x^{8 \, n} + 140 \, a b^{7} x^{7 \, n} + 588 \, a^{2} b^{6} x^{6 \, n} + 1470 \, a^{3} b^{5} x^{5 \, n} + 2450 \, a^{4} b^{4} x^{4 \, n} + 2940 \, a^{5} b^{3} x^{3 \, n} + 2940 \, a^{6} b^{2} x^{2 \, n} - 105 \, a^{8}}{105 \, n x^{n}}"," ",0,"1/105*(840*a^7*b*n*x^n*log(x) + 15*b^8*x^(8*n) + 140*a*b^7*x^(7*n) + 588*a^2*b^6*x^(6*n) + 1470*a^3*b^5*x^(5*n) + 2450*a^4*b^4*x^(4*n) + 2940*a^5*b^3*x^(3*n) + 2940*a^6*b^2*x^(2*n) - 105*a^8)/(n*x^n)","A",0
2577,1,116,0,0.830230," ","integrate(x^(-1-2*n)*(a+b*x^n)^8,x, algorithm=""fricas"")","\frac{840 \, a^{6} b^{2} n x^{2 \, n} \log\left(x\right) + 5 \, b^{8} x^{8 \, n} + 48 \, a b^{7} x^{7 \, n} + 210 \, a^{2} b^{6} x^{6 \, n} + 560 \, a^{3} b^{5} x^{5 \, n} + 1050 \, a^{4} b^{4} x^{4 \, n} + 1680 \, a^{5} b^{3} x^{3 \, n} - 240 \, a^{7} b x^{n} - 15 \, a^{8}}{30 \, n x^{2 \, n}}"," ",0,"1/30*(840*a^6*b^2*n*x^(2*n)*log(x) + 5*b^8*x^(8*n) + 48*a*b^7*x^(7*n) + 210*a^2*b^6*x^(6*n) + 560*a^3*b^5*x^(5*n) + 1050*a^4*b^4*x^(4*n) + 1680*a^5*b^3*x^(3*n) - 240*a^7*b*x^n - 15*a^8)/(n*x^(2*n))","A",0
2578,1,116,0,0.899610," ","integrate(x^(-1-3*n)*(a+b*x^n)^8,x, algorithm=""fricas"")","\frac{840 \, a^{5} b^{3} n x^{3 \, n} \log\left(x\right) + 3 \, b^{8} x^{8 \, n} + 30 \, a b^{7} x^{7 \, n} + 140 \, a^{2} b^{6} x^{6 \, n} + 420 \, a^{3} b^{5} x^{5 \, n} + 1050 \, a^{4} b^{4} x^{4 \, n} - 420 \, a^{6} b^{2} x^{2 \, n} - 60 \, a^{7} b x^{n} - 5 \, a^{8}}{15 \, n x^{3 \, n}}"," ",0,"1/15*(840*a^5*b^3*n*x^(3*n)*log(x) + 3*b^8*x^(8*n) + 30*a*b^7*x^(7*n) + 140*a^2*b^6*x^(6*n) + 420*a^3*b^5*x^(5*n) + 1050*a^4*b^4*x^(4*n) - 420*a^6*b^2*x^(2*n) - 60*a^7*b*x^n - 5*a^8)/(n*x^(3*n))","A",0
2579,1,116,0,0.996408," ","integrate(x^(-1-4*n)*(a+b*x^n)^8,x, algorithm=""fricas"")","\frac{840 \, a^{4} b^{4} n x^{4 \, n} \log\left(x\right) + 3 \, b^{8} x^{8 \, n} + 32 \, a b^{7} x^{7 \, n} + 168 \, a^{2} b^{6} x^{6 \, n} + 672 \, a^{3} b^{5} x^{5 \, n} - 672 \, a^{5} b^{3} x^{3 \, n} - 168 \, a^{6} b^{2} x^{2 \, n} - 32 \, a^{7} b x^{n} - 3 \, a^{8}}{12 \, n x^{4 \, n}}"," ",0,"1/12*(840*a^4*b^4*n*x^(4*n)*log(x) + 3*b^8*x^(8*n) + 32*a*b^7*x^(7*n) + 168*a^2*b^6*x^(6*n) + 672*a^3*b^5*x^(5*n) - 672*a^5*b^3*x^(3*n) - 168*a^6*b^2*x^(2*n) - 32*a^7*b*x^n - 3*a^8)/(n*x^(4*n))","A",0
2580,1,116,0,0.677975," ","integrate(x^(-1-5*n)*(a+b*x^n)^8,x, algorithm=""fricas"")","\frac{840 \, a^{3} b^{5} n x^{5 \, n} \log\left(x\right) + 5 \, b^{8} x^{8 \, n} + 60 \, a b^{7} x^{7 \, n} + 420 \, a^{2} b^{6} x^{6 \, n} - 1050 \, a^{4} b^{4} x^{4 \, n} - 420 \, a^{5} b^{3} x^{3 \, n} - 140 \, a^{6} b^{2} x^{2 \, n} - 30 \, a^{7} b x^{n} - 3 \, a^{8}}{15 \, n x^{5 \, n}}"," ",0,"1/15*(840*a^3*b^5*n*x^(5*n)*log(x) + 5*b^8*x^(8*n) + 60*a*b^7*x^(7*n) + 420*a^2*b^6*x^(6*n) - 1050*a^4*b^4*x^(4*n) - 420*a^5*b^3*x^(3*n) - 140*a^6*b^2*x^(2*n) - 30*a^7*b*x^n - 3*a^8)/(n*x^(5*n))","A",0
2581,1,116,0,1.205157," ","integrate(x^(-1-6*n)*(a+b*x^n)^8,x, algorithm=""fricas"")","\frac{840 \, a^{2} b^{6} n x^{6 \, n} \log\left(x\right) + 15 \, b^{8} x^{8 \, n} + 240 \, a b^{7} x^{7 \, n} - 1680 \, a^{3} b^{5} x^{5 \, n} - 1050 \, a^{4} b^{4} x^{4 \, n} - 560 \, a^{5} b^{3} x^{3 \, n} - 210 \, a^{6} b^{2} x^{2 \, n} - 48 \, a^{7} b x^{n} - 5 \, a^{8}}{30 \, n x^{6 \, n}}"," ",0,"1/30*(840*a^2*b^6*n*x^(6*n)*log(x) + 15*b^8*x^(8*n) + 240*a*b^7*x^(7*n) - 1680*a^3*b^5*x^(5*n) - 1050*a^4*b^4*x^(4*n) - 560*a^5*b^3*x^(3*n) - 210*a^6*b^2*x^(2*n) - 48*a^7*b*x^n - 5*a^8)/(n*x^(6*n))","A",0
2582,1,116,0,1.002777," ","integrate(x^(-1-7*n)*(a+b*x^n)^8,x, algorithm=""fricas"")","\frac{840 \, a b^{7} n x^{7 \, n} \log\left(x\right) + 105 \, b^{8} x^{8 \, n} - 2940 \, a^{2} b^{6} x^{6 \, n} - 2940 \, a^{3} b^{5} x^{5 \, n} - 2450 \, a^{4} b^{4} x^{4 \, n} - 1470 \, a^{5} b^{3} x^{3 \, n} - 588 \, a^{6} b^{2} x^{2 \, n} - 140 \, a^{7} b x^{n} - 15 \, a^{8}}{105 \, n x^{7 \, n}}"," ",0,"1/105*(840*a*b^7*n*x^(7*n)*log(x) + 105*b^8*x^(8*n) - 2940*a^2*b^6*x^(6*n) - 2940*a^3*b^5*x^(5*n) - 2450*a^4*b^4*x^(4*n) - 1470*a^5*b^3*x^(3*n) - 588*a^6*b^2*x^(2*n) - 140*a^7*b*x^n - 15*a^8)/(n*x^(7*n))","A",0
2583,1,116,0,0.925384," ","integrate(x^(-1-8*n)*(a+b*x^n)^8,x, algorithm=""fricas"")","\frac{840 \, b^{8} n x^{8 \, n} \log\left(x\right) - 6720 \, a b^{7} x^{7 \, n} - 11760 \, a^{2} b^{6} x^{6 \, n} - 15680 \, a^{3} b^{5} x^{5 \, n} - 14700 \, a^{4} b^{4} x^{4 \, n} - 9408 \, a^{5} b^{3} x^{3 \, n} - 3920 \, a^{6} b^{2} x^{2 \, n} - 960 \, a^{7} b x^{n} - 105 \, a^{8}}{840 \, n x^{8 \, n}}"," ",0,"1/840*(840*b^8*n*x^(8*n)*log(x) - 6720*a*b^7*x^(7*n) - 11760*a^2*b^6*x^(6*n) - 15680*a^3*b^5*x^(5*n) - 14700*a^4*b^4*x^(4*n) - 9408*a^5*b^3*x^(3*n) - 3920*a^6*b^2*x^(2*n) - 960*a^7*b*x^n - 105*a^8)/(n*x^(8*n))","A",0
2584,1,111,0,1.543484," ","integrate(x^(-1-9*n)*(a+b*x^n)^8,x, algorithm=""fricas"")","-\frac{9 \, b^{8} x^{8 \, n} + 36 \, a b^{7} x^{7 \, n} + 84 \, a^{2} b^{6} x^{6 \, n} + 126 \, a^{3} b^{5} x^{5 \, n} + 126 \, a^{4} b^{4} x^{4 \, n} + 84 \, a^{5} b^{3} x^{3 \, n} + 36 \, a^{6} b^{2} x^{2 \, n} + 9 \, a^{7} b x^{n} + a^{8}}{9 \, n x^{9 \, n}}"," ",0,"-1/9*(9*b^8*x^(8*n) + 36*a*b^7*x^(7*n) + 84*a^2*b^6*x^(6*n) + 126*a^3*b^5*x^(5*n) + 126*a^4*b^4*x^(4*n) + 84*a^5*b^3*x^(3*n) + 36*a^6*b^2*x^(2*n) + 9*a^7*b*x^n + a^8)/(n*x^(9*n))","B",0
2585,1,113,0,0.926576," ","integrate(x^(-1-10*n)*(a+b*x^n)^8,x, algorithm=""fricas"")","-\frac{45 \, b^{8} x^{8 \, n} + 240 \, a b^{7} x^{7 \, n} + 630 \, a^{2} b^{6} x^{6 \, n} + 1008 \, a^{3} b^{5} x^{5 \, n} + 1050 \, a^{4} b^{4} x^{4 \, n} + 720 \, a^{5} b^{3} x^{3 \, n} + 315 \, a^{6} b^{2} x^{2 \, n} + 80 \, a^{7} b x^{n} + 9 \, a^{8}}{90 \, n x^{10 \, n}}"," ",0,"-1/90*(45*b^8*x^(8*n) + 240*a*b^7*x^(7*n) + 630*a^2*b^6*x^(6*n) + 1008*a^3*b^5*x^(5*n) + 1050*a^4*b^4*x^(4*n) + 720*a^5*b^3*x^(3*n) + 315*a^6*b^2*x^(2*n) + 80*a^7*b*x^n + 9*a^8)/(n*x^(10*n))","B",0
2586,1,113,0,1.007748," ","integrate(x^(-1-11*n)*(a+b*x^n)^8,x, algorithm=""fricas"")","-\frac{165 \, b^{8} x^{8 \, n} + 990 \, a b^{7} x^{7 \, n} + 2772 \, a^{2} b^{6} x^{6 \, n} + 4620 \, a^{3} b^{5} x^{5 \, n} + 4950 \, a^{4} b^{4} x^{4 \, n} + 3465 \, a^{5} b^{3} x^{3 \, n} + 1540 \, a^{6} b^{2} x^{2 \, n} + 396 \, a^{7} b x^{n} + 45 \, a^{8}}{495 \, n x^{11 \, n}}"," ",0,"-1/495*(165*b^8*x^(8*n) + 990*a*b^7*x^(7*n) + 2772*a^2*b^6*x^(6*n) + 4620*a^3*b^5*x^(5*n) + 4950*a^4*b^4*x^(4*n) + 3465*a^5*b^3*x^(3*n) + 1540*a^6*b^2*x^(2*n) + 396*a^7*b*x^n + 45*a^8)/(n*x^(11*n))","A",0
2587,1,113,0,1.081374," ","integrate(x^(-1-12*n)*(a+b*x^n)^8,x, algorithm=""fricas"")","-\frac{495 \, b^{8} x^{8 \, n} + 3168 \, a b^{7} x^{7 \, n} + 9240 \, a^{2} b^{6} x^{6 \, n} + 15840 \, a^{3} b^{5} x^{5 \, n} + 17325 \, a^{4} b^{4} x^{4 \, n} + 12320 \, a^{5} b^{3} x^{3 \, n} + 5544 \, a^{6} b^{2} x^{2 \, n} + 1440 \, a^{7} b x^{n} + 165 \, a^{8}}{1980 \, n x^{12 \, n}}"," ",0,"-1/1980*(495*b^8*x^(8*n) + 3168*a*b^7*x^(7*n) + 9240*a^2*b^6*x^(6*n) + 15840*a^3*b^5*x^(5*n) + 17325*a^4*b^4*x^(4*n) + 12320*a^5*b^3*x^(3*n) + 5544*a^6*b^2*x^(2*n) + 1440*a^7*b*x^n + 165*a^8)/(n*x^(12*n))","A",0
2588,1,113,0,1.757349," ","integrate(x^(-1-13*n)*(a+b*x^n)^8,x, algorithm=""fricas"")","-\frac{1287 \, b^{8} x^{8 \, n} + 8580 \, a b^{7} x^{7 \, n} + 25740 \, a^{2} b^{6} x^{6 \, n} + 45045 \, a^{3} b^{5} x^{5 \, n} + 50050 \, a^{4} b^{4} x^{4 \, n} + 36036 \, a^{5} b^{3} x^{3 \, n} + 16380 \, a^{6} b^{2} x^{2 \, n} + 4290 \, a^{7} b x^{n} + 495 \, a^{8}}{6435 \, n x^{13 \, n}}"," ",0,"-1/6435*(1287*b^8*x^(8*n) + 8580*a*b^7*x^(7*n) + 25740*a^2*b^6*x^(6*n) + 45045*a^3*b^5*x^(5*n) + 50050*a^4*b^4*x^(4*n) + 36036*a^5*b^3*x^(3*n) + 16380*a^6*b^2*x^(2*n) + 4290*a^7*b*x^n + 495*a^8)/(n*x^(13*n))","A",0
2589,1,113,0,0.823021," ","integrate(x^(-1-14*n)*(a+b*x^n)^8,x, algorithm=""fricas"")","-\frac{3003 \, b^{8} x^{8 \, n} + 20592 \, a b^{7} x^{7 \, n} + 63063 \, a^{2} b^{6} x^{6 \, n} + 112112 \, a^{3} b^{5} x^{5 \, n} + 126126 \, a^{4} b^{4} x^{4 \, n} + 91728 \, a^{5} b^{3} x^{3 \, n} + 42042 \, a^{6} b^{2} x^{2 \, n} + 11088 \, a^{7} b x^{n} + 1287 \, a^{8}}{18018 \, n x^{14 \, n}}"," ",0,"-1/18018*(3003*b^8*x^(8*n) + 20592*a*b^7*x^(7*n) + 63063*a^2*b^6*x^(6*n) + 112112*a^3*b^5*x^(5*n) + 126126*a^4*b^4*x^(4*n) + 91728*a^5*b^3*x^(3*n) + 42042*a^6*b^2*x^(2*n) + 11088*a^7*b*x^n + 1287*a^8)/(n*x^(14*n))","A",0
2590,1,113,0,1.511652," ","integrate(x^(-1-15*n)*(a+b*x^n)^8,x, algorithm=""fricas"")","-\frac{6435 \, b^{8} x^{8 \, n} + 45045 \, a b^{7} x^{7 \, n} + 140140 \, a^{2} b^{6} x^{6 \, n} + 252252 \, a^{3} b^{5} x^{5 \, n} + 286650 \, a^{4} b^{4} x^{4 \, n} + 210210 \, a^{5} b^{3} x^{3 \, n} + 97020 \, a^{6} b^{2} x^{2 \, n} + 25740 \, a^{7} b x^{n} + 3003 \, a^{8}}{45045 \, n x^{15 \, n}}"," ",0,"-1/45045*(6435*b^8*x^(8*n) + 45045*a*b^7*x^(7*n) + 140140*a^2*b^6*x^(6*n) + 252252*a^3*b^5*x^(5*n) + 286650*a^4*b^4*x^(4*n) + 210210*a^5*b^3*x^(3*n) + 97020*a^6*b^2*x^(2*n) + 25740*a^7*b*x^n + 3003*a^8)/(n*x^(15*n))","A",0
2591,1,214,0,0.779184," ","integrate(x^(-1+n)*(a+b*x^n)^16,x, algorithm=""fricas"")","\frac{b^{16} x^{17 \, n} + 17 \, a b^{15} x^{16 \, n} + 136 \, a^{2} b^{14} x^{15 \, n} + 680 \, a^{3} b^{13} x^{14 \, n} + 2380 \, a^{4} b^{12} x^{13 \, n} + 6188 \, a^{5} b^{11} x^{12 \, n} + 12376 \, a^{6} b^{10} x^{11 \, n} + 19448 \, a^{7} b^{9} x^{10 \, n} + 24310 \, a^{8} b^{8} x^{9 \, n} + 24310 \, a^{9} b^{7} x^{8 \, n} + 19448 \, a^{10} b^{6} x^{7 \, n} + 12376 \, a^{11} b^{5} x^{6 \, n} + 6188 \, a^{12} b^{4} x^{5 \, n} + 2380 \, a^{13} b^{3} x^{4 \, n} + 680 \, a^{14} b^{2} x^{3 \, n} + 136 \, a^{15} b x^{2 \, n} + 17 \, a^{16} x^{n}}{17 \, n}"," ",0,"1/17*(b^16*x^(17*n) + 17*a*b^15*x^(16*n) + 136*a^2*b^14*x^(15*n) + 680*a^3*b^13*x^(14*n) + 2380*a^4*b^12*x^(13*n) + 6188*a^5*b^11*x^(12*n) + 12376*a^6*b^10*x^(11*n) + 19448*a^7*b^9*x^(10*n) + 24310*a^8*b^8*x^(9*n) + 24310*a^9*b^7*x^(8*n) + 19448*a^10*b^6*x^(7*n) + 12376*a^11*b^5*x^(6*n) + 6188*a^12*b^4*x^(5*n) + 2380*a^13*b^3*x^(4*n) + 680*a^14*b^2*x^(3*n) + 136*a^15*b*x^(2*n) + 17*a^16*x^n)/n","B",0
2592,1,134,0,0.518292," ","integrate(x^12*(b*x^13+a)^12,x, algorithm=""fricas"")","\frac{1}{169} x^{169} b^{12} + \frac{1}{13} x^{156} b^{11} a + \frac{6}{13} x^{143} b^{10} a^{2} + \frac{22}{13} x^{130} b^{9} a^{3} + \frac{55}{13} x^{117} b^{8} a^{4} + \frac{99}{13} x^{104} b^{7} a^{5} + \frac{132}{13} x^{91} b^{6} a^{6} + \frac{132}{13} x^{78} b^{5} a^{7} + \frac{99}{13} x^{65} b^{4} a^{8} + \frac{55}{13} x^{52} b^{3} a^{9} + \frac{22}{13} x^{39} b^{2} a^{10} + \frac{6}{13} x^{26} b a^{11} + \frac{1}{13} x^{13} a^{12}"," ",0,"1/169*x^169*b^12 + 1/13*x^156*b^11*a + 6/13*x^143*b^10*a^2 + 22/13*x^130*b^9*a^3 + 55/13*x^117*b^8*a^4 + 99/13*x^104*b^7*a^5 + 132/13*x^91*b^6*a^6 + 132/13*x^78*b^5*a^7 + 99/13*x^65*b^4*a^8 + 55/13*x^52*b^3*a^9 + 22/13*x^39*b^2*a^10 + 6/13*x^26*b*a^11 + 1/13*x^13*a^12","B",0
2593,1,134,0,0.406321," ","integrate(x^24*(b*x^25+a)^12,x, algorithm=""fricas"")","\frac{1}{325} x^{325} b^{12} + \frac{1}{25} x^{300} b^{11} a + \frac{6}{25} x^{275} b^{10} a^{2} + \frac{22}{25} x^{250} b^{9} a^{3} + \frac{11}{5} x^{225} b^{8} a^{4} + \frac{99}{25} x^{200} b^{7} a^{5} + \frac{132}{25} x^{175} b^{6} a^{6} + \frac{132}{25} x^{150} b^{5} a^{7} + \frac{99}{25} x^{125} b^{4} a^{8} + \frac{11}{5} x^{100} b^{3} a^{9} + \frac{22}{25} x^{75} b^{2} a^{10} + \frac{6}{25} x^{50} b a^{11} + \frac{1}{25} x^{25} a^{12}"," ",0,"1/325*x^325*b^12 + 1/25*x^300*b^11*a + 6/25*x^275*b^10*a^2 + 22/25*x^250*b^9*a^3 + 11/5*x^225*b^8*a^4 + 99/25*x^200*b^7*a^5 + 132/25*x^175*b^6*a^6 + 132/25*x^150*b^5*a^7 + 99/25*x^125*b^4*a^8 + 11/5*x^100*b^3*a^9 + 22/25*x^75*b^2*a^10 + 6/25*x^50*b*a^11 + 1/25*x^25*a^12","B",0
2594,1,134,0,0.667554," ","integrate(x^36*(b*x^37+a)^12,x, algorithm=""fricas"")","\frac{1}{481} x^{481} b^{12} + \frac{1}{37} x^{444} b^{11} a + \frac{6}{37} x^{407} b^{10} a^{2} + \frac{22}{37} x^{370} b^{9} a^{3} + \frac{55}{37} x^{333} b^{8} a^{4} + \frac{99}{37} x^{296} b^{7} a^{5} + \frac{132}{37} x^{259} b^{6} a^{6} + \frac{132}{37} x^{222} b^{5} a^{7} + \frac{99}{37} x^{185} b^{4} a^{8} + \frac{55}{37} x^{148} b^{3} a^{9} + \frac{22}{37} x^{111} b^{2} a^{10} + \frac{6}{37} x^{74} b a^{11} + \frac{1}{37} x^{37} a^{12}"," ",0,"1/481*x^481*b^12 + 1/37*x^444*b^11*a + 6/37*x^407*b^10*a^2 + 22/37*x^370*b^9*a^3 + 55/37*x^333*b^8*a^4 + 99/37*x^296*b^7*a^5 + 132/37*x^259*b^6*a^6 + 132/37*x^222*b^5*a^7 + 99/37*x^185*b^4*a^8 + 55/37*x^148*b^3*a^9 + 22/37*x^111*b^2*a^10 + 6/37*x^74*b*a^11 + 1/37*x^37*a^12","B",0
2595,1,194,0,0.951475," ","integrate(x^(12*m)*(a+b*x^(1+12*m))^12,x, algorithm=""fricas"")","\frac{b^{12} x^{156 \, m + 13} + 13 \, a b^{11} x^{144 \, m + 12} + 78 \, a^{2} b^{10} x^{132 \, m + 11} + 286 \, a^{3} b^{9} x^{120 \, m + 10} + 715 \, a^{4} b^{8} x^{108 \, m + 9} + 1287 \, a^{5} b^{7} x^{96 \, m + 8} + 1716 \, a^{6} b^{6} x^{84 \, m + 7} + 1716 \, a^{7} b^{5} x^{72 \, m + 6} + 1287 \, a^{8} b^{4} x^{60 \, m + 5} + 715 \, a^{9} b^{3} x^{48 \, m + 4} + 286 \, a^{10} b^{2} x^{36 \, m + 3} + 78 \, a^{11} b x^{24 \, m + 2} + 13 \, a^{12} x^{12 \, m + 1}}{13 \, {\left(12 \, m + 1\right)}}"," ",0,"1/13*(b^12*x^(156*m + 13) + 13*a*b^11*x^(144*m + 12) + 78*a^2*b^10*x^(132*m + 11) + 286*a^3*b^9*x^(120*m + 10) + 715*a^4*b^8*x^(108*m + 9) + 1287*a^5*b^7*x^(96*m + 8) + 1716*a^6*b^6*x^(84*m + 7) + 1716*a^7*b^5*x^(72*m + 6) + 1287*a^8*b^4*x^(60*m + 5) + 715*a^9*b^3*x^(48*m + 4) + 286*a^10*b^2*x^(36*m + 3) + 78*a^11*b*x^(24*m + 2) + 13*a^12*x^(12*m + 1))/(12*m + 1)","B",0
2596,1,194,0,1.032530," ","integrate(x^(12*m)*(a+b*x^(1+12*m))^12,x, algorithm=""fricas"")","\frac{b^{12} x^{156 \, m + 13} + 13 \, a b^{11} x^{144 \, m + 12} + 78 \, a^{2} b^{10} x^{132 \, m + 11} + 286 \, a^{3} b^{9} x^{120 \, m + 10} + 715 \, a^{4} b^{8} x^{108 \, m + 9} + 1287 \, a^{5} b^{7} x^{96 \, m + 8} + 1716 \, a^{6} b^{6} x^{84 \, m + 7} + 1716 \, a^{7} b^{5} x^{72 \, m + 6} + 1287 \, a^{8} b^{4} x^{60 \, m + 5} + 715 \, a^{9} b^{3} x^{48 \, m + 4} + 286 \, a^{10} b^{2} x^{36 \, m + 3} + 78 \, a^{11} b x^{24 \, m + 2} + 13 \, a^{12} x^{12 \, m + 1}}{13 \, {\left(12 \, m + 1\right)}}"," ",0,"1/13*(b^12*x^(156*m + 13) + 13*a*b^11*x^(144*m + 12) + 78*a^2*b^10*x^(132*m + 11) + 286*a^3*b^9*x^(120*m + 10) + 715*a^4*b^8*x^(108*m + 9) + 1287*a^5*b^7*x^(96*m + 8) + 1716*a^6*b^6*x^(84*m + 7) + 1716*a^7*b^5*x^(72*m + 6) + 1287*a^8*b^4*x^(60*m + 5) + 715*a^9*b^3*x^(48*m + 4) + 286*a^10*b^2*x^(36*m + 3) + 78*a^11*b*x^(24*m + 2) + 13*a^12*x^(12*m + 1))/(12*m + 1)","B",0
2597,1,65,0,0.899518," ","integrate(x^(-1+5*n)/(a+b*x^n),x, algorithm=""fricas"")","\frac{3 \, b^{4} x^{4 \, n} - 4 \, a b^{3} x^{3 \, n} + 6 \, a^{2} b^{2} x^{2 \, n} - 12 \, a^{3} b x^{n} + 12 \, a^{4} \log\left(b x^{n} + a\right)}{12 \, b^{5} n}"," ",0,"1/12*(3*b^4*x^(4*n) - 4*a*b^3*x^(3*n) + 6*a^2*b^2*x^(2*n) - 12*a^3*b*x^n + 12*a^4*log(b*x^n + a))/(b^5*n)","A",0
2598,1,52,0,1.173809," ","integrate(x^(-1+4*n)/(a+b*x^n),x, algorithm=""fricas"")","\frac{2 \, b^{3} x^{3 \, n} - 3 \, a b^{2} x^{2 \, n} + 6 \, a^{2} b x^{n} - 6 \, a^{3} \log\left(b x^{n} + a\right)}{6 \, b^{4} n}"," ",0,"1/6*(2*b^3*x^(3*n) - 3*a*b^2*x^(2*n) + 6*a^2*b*x^n - 6*a^3*log(b*x^n + a))/(b^4*n)","A",0
2599,1,38,0,1.172624," ","integrate(x^(-1+3*n)/(a+b*x^n),x, algorithm=""fricas"")","\frac{b^{2} x^{2 \, n} - 2 \, a b x^{n} + 2 \, a^{2} \log\left(b x^{n} + a\right)}{2 \, b^{3} n}"," ",0,"1/2*(b^2*x^(2*n) - 2*a*b*x^n + 2*a^2*log(b*x^n + a))/(b^3*n)","A",0
2600,1,24,0,1.258045," ","integrate(x^(-1+2*n)/(a+b*x^n),x, algorithm=""fricas"")","\frac{b x^{n} - a \log\left(b x^{n} + a\right)}{b^{2} n}"," ",0,"(b*x^n - a*log(b*x^n + a))/(b^2*n)","A",0
2601,1,15,0,0.850430," ","integrate(x^(-1+n)/(a+b*x^n),x, algorithm=""fricas"")","\frac{\log\left(b x^{n} + a\right)}{b n}"," ",0,"log(b*x^n + a)/(b*n)","A",0
2602,1,22,0,0.904203," ","integrate(1/x/(a+b*x^n),x, algorithm=""fricas"")","\frac{n \log\left(x\right) - \log\left(b x^{n} + a\right)}{a n}"," ",0,"(n*log(x) - log(b*x^n + a))/(a*n)","A",0
2603,1,37,0,1.086311," ","integrate(x^(-1-n)/(a+b*x^n),x, algorithm=""fricas"")","-\frac{b n x^{n} \log\left(x\right) - b x^{n} \log\left(b x^{n} + a\right) + a}{a^{2} n x^{n}}"," ",0,"-(b*n*x^n*log(x) - b*x^n*log(b*x^n + a) + a)/(a^2*n*x^n)","A",0
2604,1,59,0,1.005485," ","integrate(x^(-1-2*n)/(a+b*x^n),x, algorithm=""fricas"")","\frac{2 \, b^{2} n x^{2 \, n} \log\left(x\right) - 2 \, b^{2} x^{2 \, n} \log\left(b x^{n} + a\right) + 2 \, a b x^{n} - a^{2}}{2 \, a^{3} n x^{2 \, n}}"," ",0,"1/2*(2*b^2*n*x^(2*n)*log(x) - 2*b^2*x^(2*n)*log(b*x^n + a) + 2*a*b*x^n - a^2)/(a^3*n*x^(2*n))","A",0
2605,1,72,0,0.628451," ","integrate(x^(-1-3*n)/(a+b*x^n),x, algorithm=""fricas"")","-\frac{6 \, b^{3} n x^{3 \, n} \log\left(x\right) - 6 \, b^{3} x^{3 \, n} \log\left(b x^{n} + a\right) + 6 \, a b^{2} x^{2 \, n} - 3 \, a^{2} b x^{n} + 2 \, a^{3}}{6 \, a^{4} n x^{3 \, n}}"," ",0,"-1/6*(6*b^3*n*x^(3*n)*log(x) - 6*b^3*x^(3*n)*log(b*x^n + a) + 6*a*b^2*x^(2*n) - 3*a^2*b*x^n + 2*a^3)/(a^4*n*x^(3*n))","A",0
2606,1,65,0,0.622166," ","integrate(x^(-1+5*n)/(a+b*x^n),x, algorithm=""fricas"")","\frac{3 \, b^{4} x^{4 \, n} - 4 \, a b^{3} x^{3 \, n} + 6 \, a^{2} b^{2} x^{2 \, n} - 12 \, a^{3} b x^{n} + 12 \, a^{4} \log\left(b x^{n} + a\right)}{12 \, b^{5} n}"," ",0,"1/12*(3*b^4*x^(4*n) - 4*a*b^3*x^(3*n) + 6*a^2*b^2*x^(2*n) - 12*a^3*b*x^n + 12*a^4*log(b*x^n + a))/(b^5*n)","A",0
2607,1,52,0,0.901269," ","integrate(x^(-1+4*n)/(a+b*x^n),x, algorithm=""fricas"")","\frac{2 \, b^{3} x^{3 \, n} - 3 \, a b^{2} x^{2 \, n} + 6 \, a^{2} b x^{n} - 6 \, a^{3} \log\left(b x^{n} + a\right)}{6 \, b^{4} n}"," ",0,"1/6*(2*b^3*x^(3*n) - 3*a*b^2*x^(2*n) + 6*a^2*b*x^n - 6*a^3*log(b*x^n + a))/(b^4*n)","A",0
2608,1,38,0,1.002820," ","integrate(x^(-1+3*n)/(a+b*x^n),x, algorithm=""fricas"")","\frac{b^{2} x^{2 \, n} - 2 \, a b x^{n} + 2 \, a^{2} \log\left(b x^{n} + a\right)}{2 \, b^{3} n}"," ",0,"1/2*(b^2*x^(2*n) - 2*a*b*x^n + 2*a^2*log(b*x^n + a))/(b^3*n)","A",0
2609,1,24,0,0.885719," ","integrate(x^(-1+2*n)/(a+b*x^n),x, algorithm=""fricas"")","\frac{b x^{n} - a \log\left(b x^{n} + a\right)}{b^{2} n}"," ",0,"(b*x^n - a*log(b*x^n + a))/(b^2*n)","A",0
2610,1,15,0,1.165450," ","integrate(x^(-1+n)/(a+b*x^n),x, algorithm=""fricas"")","\frac{\log\left(b x^{n} + a\right)}{b n}"," ",0,"log(b*x^n + a)/(b*n)","A",0
2611,1,22,0,1.215136," ","integrate(1/x/(a+b*x^n),x, algorithm=""fricas"")","\frac{n \log\left(x\right) - \log\left(b x^{n} + a\right)}{a n}"," ",0,"(n*log(x) - log(b*x^n + a))/(a*n)","A",0
2612,1,37,0,1.131206," ","integrate(x^(-1-n)/(a+b*x^n),x, algorithm=""fricas"")","-\frac{b n x^{n} \log\left(x\right) - b x^{n} \log\left(b x^{n} + a\right) + a}{a^{2} n x^{n}}"," ",0,"-(b*n*x^n*log(x) - b*x^n*log(b*x^n + a) + a)/(a^2*n*x^n)","A",0
2613,1,59,0,1.138036," ","integrate(x^(-1-2*n)/(a+b*x^n),x, algorithm=""fricas"")","\frac{2 \, b^{2} n x^{2 \, n} \log\left(x\right) - 2 \, b^{2} x^{2 \, n} \log\left(b x^{n} + a\right) + 2 \, a b x^{n} - a^{2}}{2 \, a^{3} n x^{2 \, n}}"," ",0,"1/2*(2*b^2*n*x^(2*n)*log(x) - 2*b^2*x^(2*n)*log(b*x^n + a) + 2*a*b*x^n - a^2)/(a^3*n*x^(2*n))","A",0
2614,1,72,0,1.058447," ","integrate(x^(-1-3*n)/(a+b*x^n),x, algorithm=""fricas"")","-\frac{6 \, b^{3} n x^{3 \, n} \log\left(x\right) - 6 \, b^{3} x^{3 \, n} \log\left(b x^{n} + a\right) + 6 \, a b^{2} x^{2 \, n} - 3 \, a^{2} b x^{n} + 2 \, a^{3}}{6 \, a^{4} n x^{3 \, n}}"," ",0,"-1/6*(6*b^3*n*x^(3*n)*log(x) - 6*b^3*x^(3*n)*log(b*x^n + a) + 6*a*b^2*x^(2*n) - 3*a^2*b*x^n + 2*a^3)/(a^4*n*x^(3*n))","A",0
2615,1,55,0,1.410784," ","integrate(x^(-1+5*n)/(2+b*x^n),x, algorithm=""fricas"")","\frac{3 \, b^{4} x^{4 \, n} - 8 \, b^{3} x^{3 \, n} + 24 \, b^{2} x^{2 \, n} - 96 \, b x^{n} + 192 \, \log\left(b x^{n} + 2\right)}{12 \, b^{5} n}"," ",0,"1/12*(3*b^4*x^(4*n) - 8*b^3*x^(3*n) + 24*b^2*x^(2*n) - 96*b*x^n + 192*log(b*x^n + 2))/(b^5*n)","A",0
2616,1,44,0,1.469297," ","integrate(x^(-1+4*n)/(2+b*x^n),x, algorithm=""fricas"")","\frac{b^{3} x^{3 \, n} - 3 \, b^{2} x^{2 \, n} + 12 \, b x^{n} - 24 \, \log\left(b x^{n} + 2\right)}{3 \, b^{4} n}"," ",0,"1/3*(b^3*x^(3*n) - 3*b^2*x^(2*n) + 12*b*x^n - 24*log(b*x^n + 2))/(b^4*n)","A",0
2617,1,34,0,1.373324," ","integrate(x^(-1+3*n)/(2+b*x^n),x, algorithm=""fricas"")","\frac{b^{2} x^{2 \, n} - 4 \, b x^{n} + 8 \, \log\left(b x^{n} + 2\right)}{2 \, b^{3} n}"," ",0,"1/2*(b^2*x^(2*n) - 4*b*x^n + 8*log(b*x^n + 2))/(b^3*n)","A",0
2618,1,23,0,0.734603," ","integrate(x^(-1+2*n)/(2+b*x^n),x, algorithm=""fricas"")","\frac{b x^{n} - 2 \, \log\left(b x^{n} + 2\right)}{b^{2} n}"," ",0,"(b*x^n - 2*log(b*x^n + 2))/(b^2*n)","A",0
2619,1,15,0,1.064820," ","integrate(x^(-1+n)/(2+b*x^n),x, algorithm=""fricas"")","\frac{\log\left(b x^{n} + 2\right)}{b n}"," ",0,"log(b*x^n + 2)/(b*n)","A",0
2620,1,20,0,1.339188," ","integrate(1/x/(2+b*x^n),x, algorithm=""fricas"")","\frac{n \log\left(x\right) - \log\left(b x^{n} + 2\right)}{2 \, n}"," ",0,"1/2*(n*log(x) - log(b*x^n + 2))/n","A",0
2621,1,34,0,1.337754," ","integrate(x^(-1-n)/(2+b*x^n),x, algorithm=""fricas"")","-\frac{b n x^{n} \log\left(x\right) - b x^{n} \log\left(b x^{n} + 2\right) + 2}{4 \, n x^{n}}"," ",0,"-1/4*(b*n*x^n*log(x) - b*x^n*log(b*x^n + 2) + 2)/(n*x^n)","A",0
2622,1,50,0,0.745507," ","integrate(x^(-1-2*n)/(2+b*x^n),x, algorithm=""fricas"")","\frac{b^{2} n x^{2 \, n} \log\left(x\right) - b^{2} x^{2 \, n} \log\left(b x^{n} + 2\right) + 2 \, b x^{n} - 2}{8 \, n x^{2 \, n}}"," ",0,"1/8*(b^2*n*x^(2*n)*log(x) - b^2*x^(2*n)*log(b*x^n + 2) + 2*b*x^n - 2)/(n*x^(2*n))","A",0
2623,1,61,0,1.081022," ","integrate(x^(-1-3*n)/(2+b*x^n),x, algorithm=""fricas"")","-\frac{3 \, b^{3} n x^{3 \, n} \log\left(x\right) - 3 \, b^{3} x^{3 \, n} \log\left(b x^{n} + 2\right) + 6 \, b^{2} x^{2 \, n} - 6 \, b x^{n} + 8}{48 \, n x^{3 \, n}}"," ",0,"-1/48*(3*b^3*n*x^(3*n)*log(x) - 3*b^3*x^(3*n)*log(b*x^n + 2) + 6*b^2*x^(2*n) - 6*b*x^n + 8)/(n*x^(3*n))","A",0
2624,1,76,0,1.013810," ","integrate(x^(-1+4*n)/(a+b*x^n)^2,x, algorithm=""fricas"")","\frac{b^{3} x^{3 \, n} - 3 \, a b^{2} x^{2 \, n} - 4 \, a^{2} b x^{n} + 2 \, a^{3} + 6 \, {\left(a^{2} b x^{n} + a^{3}\right)} \log\left(b x^{n} + a\right)}{2 \, {\left(b^{5} n x^{n} + a b^{4} n\right)}}"," ",0,"1/2*(b^3*x^(3*n) - 3*a*b^2*x^(2*n) - 4*a^2*b*x^n + 2*a^3 + 6*(a^2*b*x^n + a^3)*log(b*x^n + a))/(b^5*n*x^n + a*b^4*n)","A",0
2625,1,59,0,0.701132," ","integrate(x^(-1+3*n)/(a+b*x^n)^2,x, algorithm=""fricas"")","\frac{b^{2} x^{2 \, n} + a b x^{n} - a^{2} - 2 \, {\left(a b x^{n} + a^{2}\right)} \log\left(b x^{n} + a\right)}{b^{4} n x^{n} + a b^{3} n}"," ",0,"(b^2*x^(2*n) + a*b*x^n - a^2 - 2*(a*b*x^n + a^2)*log(b*x^n + a))/(b^4*n*x^n + a*b^3*n)","A",0
2626,1,36,0,0.842831," ","integrate(x^(-1+2*n)/(a+b*x^n)^2,x, algorithm=""fricas"")","\frac{{\left(b x^{n} + a\right)} \log\left(b x^{n} + a\right) + a}{b^{3} n x^{n} + a b^{2} n}"," ",0,"((b*x^n + a)*log(b*x^n + a) + a)/(b^3*n*x^n + a*b^2*n)","A",0
2627,1,17,0,0.662870," ","integrate(x^(-1+n)/(a+b*x^n)^2,x, algorithm=""fricas"")","-\frac{1}{b^{2} n x^{n} + a b n}"," ",0,"-1/(b^2*n*x^n + a*b*n)","A",0
2628,1,50,0,0.971333," ","integrate(1/x/(a+b*x^n)^2,x, algorithm=""fricas"")","\frac{b n x^{n} \log\left(x\right) + a n \log\left(x\right) - {\left(b x^{n} + a\right)} \log\left(b x^{n} + a\right) + a}{a^{2} b n x^{n} + a^{3} n}"," ",0,"(b*n*x^n*log(x) + a*n*log(x) - (b*x^n + a)*log(b*x^n + a) + a)/(a^2*b*n*x^n + a^3*n)","A",0
2629,1,82,0,0.851445," ","integrate(x^(-1-n)/(a+b*x^n)^2,x, algorithm=""fricas"")","-\frac{2 \, b^{2} n x^{2 \, n} \log\left(x\right) + a^{2} + 2 \, {\left(a b n \log\left(x\right) + a b\right)} x^{n} - 2 \, {\left(b^{2} x^{2 \, n} + a b x^{n}\right)} \log\left(b x^{n} + a\right)}{a^{3} b n x^{2 \, n} + a^{4} n x^{n}}"," ",0,"-(2*b^2*n*x^(2*n)*log(x) + a^2 + 2*(a*b*n*log(x) + a*b)*x^n - 2*(b^2*x^(2*n) + a*b*x^n)*log(b*x^n + a))/(a^3*b*n*x^(2*n) + a^4*n*x^n)","A",0
2630,1,105,0,0.804218," ","integrate(x^(-1-2*n)/(a+b*x^n)^2,x, algorithm=""fricas"")","\frac{6 \, b^{3} n x^{3 \, n} \log\left(x\right) + 3 \, a^{2} b x^{n} - a^{3} + 6 \, {\left(a b^{2} n \log\left(x\right) + a b^{2}\right)} x^{2 \, n} - 6 \, {\left(b^{3} x^{3 \, n} + a b^{2} x^{2 \, n}\right)} \log\left(b x^{n} + a\right)}{2 \, {\left(a^{4} b n x^{3 \, n} + a^{5} n x^{2 \, n}\right)}}"," ",0,"1/2*(6*b^3*n*x^(3*n)*log(x) + 3*a^2*b*x^n - a^3 + 6*(a*b^2*n*log(x) + a*b^2)*x^(2*n) - 6*(b^3*x^(3*n) + a*b^2*x^(2*n))*log(b*x^n + a))/(a^4*b*n*x^(3*n) + a^5*n*x^(2*n))","A",0
2631,1,116,0,1.038381," ","integrate(x^(-1-3*n)/(a+b*x^n)^2,x, algorithm=""fricas"")","-\frac{12 \, b^{4} n x^{4 \, n} \log\left(x\right) + 6 \, a^{2} b^{2} x^{2 \, n} - 2 \, a^{3} b x^{n} + a^{4} + 12 \, {\left(a b^{3} n \log\left(x\right) + a b^{3}\right)} x^{3 \, n} - 12 \, {\left(b^{4} x^{4 \, n} + a b^{3} x^{3 \, n}\right)} \log\left(b x^{n} + a\right)}{3 \, {\left(a^{5} b n x^{4 \, n} + a^{6} n x^{3 \, n}\right)}}"," ",0,"-1/3*(12*b^4*n*x^(4*n)*log(x) + 6*a^2*b^2*x^(2*n) - 2*a^3*b*x^n + a^4 + 12*(a*b^3*n*log(x) + a*b^3)*x^(3*n) - 12*(b^4*x^(4*n) + a*b^3*x^(3*n))*log(b*x^n + a))/(a^5*b*n*x^(4*n) + a^6*n*x^(3*n))","A",0
2632,1,102,0,0.870976," ","integrate(x^(-1+4*n)/(a+b*x^n)^3,x, algorithm=""fricas"")","\frac{2 \, b^{3} x^{3 \, n} + 4 \, a b^{2} x^{2 \, n} - 4 \, a^{2} b x^{n} - 5 \, a^{3} - 6 \, {\left(a b^{2} x^{2 \, n} + 2 \, a^{2} b x^{n} + a^{3}\right)} \log\left(b x^{n} + a\right)}{2 \, {\left(b^{6} n x^{2 \, n} + 2 \, a b^{5} n x^{n} + a^{2} b^{4} n\right)}}"," ",0,"1/2*(2*b^3*x^(3*n) + 4*a*b^2*x^(2*n) - 4*a^2*b*x^n - 5*a^3 - 6*(a*b^2*x^(2*n) + 2*a^2*b*x^n + a^3)*log(b*x^n + a))/(b^6*n*x^(2*n) + 2*a*b^5*n*x^n + a^2*b^4*n)","A",0
2633,1,76,0,1.388832," ","integrate(x^(-1+3*n)/(a+b*x^n)^3,x, algorithm=""fricas"")","\frac{4 \, a b x^{n} + 3 \, a^{2} + 2 \, {\left(b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}\right)} \log\left(b x^{n} + a\right)}{2 \, {\left(b^{5} n x^{2 \, n} + 2 \, a b^{4} n x^{n} + a^{2} b^{3} n\right)}}"," ",0,"1/2*(4*a*b*x^n + 3*a^2 + 2*(b^2*x^(2*n) + 2*a*b*x^n + a^2)*log(b*x^n + a))/(b^5*n*x^(2*n) + 2*a*b^4*n*x^n + a^2*b^3*n)","A",0
2634,1,41,0,1.217856," ","integrate(x^(-1+2*n)/(a+b*x^n)^3,x, algorithm=""fricas"")","-\frac{2 \, b x^{n} + a}{2 \, {\left(b^{4} n x^{2 \, n} + 2 \, a b^{3} n x^{n} + a^{2} b^{2} n\right)}}"," ",0,"-1/2*(2*b*x^n + a)/(b^4*n*x^(2*n) + 2*a*b^3*n*x^n + a^2*b^2*n)","A",0
2635,1,31,0,0.765795," ","integrate(x^(-1+n)/(a+b*x^n)^3,x, algorithm=""fricas"")","-\frac{1}{2 \, {\left(b^{3} n x^{2 \, n} + 2 \, a b^{2} n x^{n} + a^{2} b n\right)}}"," ",0,"-1/2/(b^3*n*x^(2*n) + 2*a*b^2*n*x^n + a^2*b*n)","A",0
2636,1,106,0,0.851772," ","integrate(1/x/(a+b*x^n)^3,x, algorithm=""fricas"")","\frac{2 \, b^{2} n x^{2 \, n} \log\left(x\right) + 2 \, a^{2} n \log\left(x\right) + 3 \, a^{2} + 2 \, {\left(2 \, a b n \log\left(x\right) + a b\right)} x^{n} - 2 \, {\left(b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}\right)} \log\left(b x^{n} + a\right)}{2 \, {\left(a^{3} b^{2} n x^{2 \, n} + 2 \, a^{4} b n x^{n} + a^{5} n\right)}}"," ",0,"1/2*(2*b^2*n*x^(2*n)*log(x) + 2*a^2*n*log(x) + 3*a^2 + 2*(2*a*b*n*log(x) + a*b)*x^n - 2*(b^2*x^(2*n) + 2*a*b*x^n + a^2)*log(b*x^n + a))/(a^3*b^2*n*x^(2*n) + 2*a^4*b*n*x^n + a^5*n)","A",0
2637,1,139,0,1.198446," ","integrate(x^(-1-n)/(a+b*x^n)^3,x, algorithm=""fricas"")","-\frac{6 \, b^{3} n x^{3 \, n} \log\left(x\right) + 2 \, a^{3} + 6 \, {\left(2 \, a b^{2} n \log\left(x\right) + a b^{2}\right)} x^{2 \, n} + 3 \, {\left(2 \, a^{2} b n \log\left(x\right) + 3 \, a^{2} b\right)} x^{n} - 6 \, {\left(b^{3} x^{3 \, n} + 2 \, a b^{2} x^{2 \, n} + a^{2} b x^{n}\right)} \log\left(b x^{n} + a\right)}{2 \, {\left(a^{4} b^{2} n x^{3 \, n} + 2 \, a^{5} b n x^{2 \, n} + a^{6} n x^{n}\right)}}"," ",0,"-1/2*(6*b^3*n*x^(3*n)*log(x) + 2*a^3 + 6*(2*a*b^2*n*log(x) + a*b^2)*x^(2*n) + 3*(2*a^2*b*n*log(x) + 3*a^2*b)*x^n - 6*(b^3*x^(3*n) + 2*a*b^2*x^(2*n) + a^2*b*x^n)*log(b*x^n + a))/(a^4*b^2*n*x^(3*n) + 2*a^5*b*n*x^(2*n) + a^6*n*x^n)","A",0
2638,1,160,0,1.375257," ","integrate(x^(-1-2*n)/(a+b*x^n)^3,x, algorithm=""fricas"")","\frac{12 \, b^{4} n x^{4 \, n} \log\left(x\right) + 4 \, a^{3} b x^{n} - a^{4} + 12 \, {\left(2 \, a b^{3} n \log\left(x\right) + a b^{3}\right)} x^{3 \, n} + 6 \, {\left(2 \, a^{2} b^{2} n \log\left(x\right) + 3 \, a^{2} b^{2}\right)} x^{2 \, n} - 12 \, {\left(b^{4} x^{4 \, n} + 2 \, a b^{3} x^{3 \, n} + a^{2} b^{2} x^{2 \, n}\right)} \log\left(b x^{n} + a\right)}{2 \, {\left(a^{5} b^{2} n x^{4 \, n} + 2 \, a^{6} b n x^{3 \, n} + a^{7} n x^{2 \, n}\right)}}"," ",0,"1/2*(12*b^4*n*x^(4*n)*log(x) + 4*a^3*b*x^n - a^4 + 12*(2*a*b^3*n*log(x) + a*b^3)*x^(3*n) + 6*(2*a^2*b^2*n*log(x) + 3*a^2*b^2)*x^(2*n) - 12*(b^4*x^(4*n) + 2*a*b^3*x^(3*n) + a^2*b^2*x^(2*n))*log(b*x^n + a))/(a^5*b^2*n*x^(4*n) + 2*a^6*b*n*x^(3*n) + a^7*n*x^(2*n))","A",0
2639,1,130,0,1.379156," ","integrate(x^(-1-1/2*n)/(a+b*x^n),x, algorithm=""fricas"")","\left[-\frac{2 \, x x^{-\frac{1}{2} \, n - 1} - \sqrt{-\frac{b}{a}} \log\left(\frac{a x^{2} x^{-n - 2} + 2 \, a x x^{-\frac{1}{2} \, n - 1} \sqrt{-\frac{b}{a}} - b}{a x^{2} x^{-n - 2} + b}\right)}{a n}, -\frac{2 \, {\left(x x^{-\frac{1}{2} \, n - 1} + \sqrt{\frac{b}{a}} \arctan\left(\frac{\sqrt{\frac{b}{a}}}{x x^{-\frac{1}{2} \, n - 1}}\right)\right)}}{a n}\right]"," ",0,"[-(2*x*x^(-1/2*n - 1) - sqrt(-b/a)*log((a*x^2*x^(-n - 2) + 2*a*x*x^(-1/2*n - 1)*sqrt(-b/a) - b)/(a*x^2*x^(-n - 2) + b)))/(a*n), -2*(x*x^(-1/2*n - 1) + sqrt(b/a)*arctan(sqrt(b/a)/(x*x^(-1/2*n - 1))))/(a*n)]","A",0
2640,1,178,0,1.655366," ","integrate(x^(-1-2/3*n)/(a+b*x^n),x, algorithm=""fricas"")","-\frac{3 \, x x^{-\frac{2}{3} \, n - 1} - 2 \, \sqrt{3} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} a \sqrt{x} x^{-\frac{1}{3} \, n - \frac{1}{2}} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} + \sqrt{3} b}{3 \, b}\right) + \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(-\frac{a \sqrt{x} x^{-\frac{1}{3} \, n - \frac{1}{2}} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}} - b x x^{-\frac{2}{3} \, n - 1} + b \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}}}{x}\right) - 2 \, \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(\frac{b x x^{-\frac{1}{3} \, n - \frac{1}{2}} + a \sqrt{x} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}}}{x}\right)}{2 \, a n}"," ",0,"-1/2*(3*x*x^(-2/3*n - 1) - 2*sqrt(3)*(-b^2/a^2)^(1/3)*arctan(1/3*(2*sqrt(3)*a*sqrt(x)*x^(-1/3*n - 1/2)*(-b^2/a^2)^(1/3) + sqrt(3)*b)/b) + (-b^2/a^2)^(1/3)*log(-(a*sqrt(x)*x^(-1/3*n - 1/2)*(-b^2/a^2)^(2/3) - b*x*x^(-2/3*n - 1) + b*(-b^2/a^2)^(1/3))/x) - 2*(-b^2/a^2)^(1/3)*log((b*x*x^(-1/3*n - 1/2) + a*sqrt(x)*(-b^2/a^2)^(2/3))/x))/(a*n)","A",0
2641,1,261,0,1.405251," ","integrate(x^(-1-3/4*n)/(a+b*x^n),x, algorithm=""fricas"")","-\frac{12 \, a n \left(-\frac{b^{3}}{a^{7} n^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{a^{2} b^{2} n x^{\frac{1}{3}} x^{-\frac{1}{4} \, n - \frac{1}{3}} \left(-\frac{b^{3}}{a^{7} n^{4}}\right)^{\frac{1}{4}} - a^{2} n x^{\frac{1}{3}} \sqrt{-\frac{a^{3} b^{3} n^{2} x^{\frac{1}{3}} \sqrt{-\frac{b^{3}}{a^{7} n^{4}}} - b^{4} x x^{-\frac{1}{2} \, n - \frac{2}{3}}}{x}} \left(-\frac{b^{3}}{a^{7} n^{4}}\right)^{\frac{1}{4}}}{b^{3}}\right) - 3 \, a n \left(-\frac{b^{3}}{a^{7} n^{4}}\right)^{\frac{1}{4}} \log\left(\frac{a^{5} n^{3} x^{\frac{2}{3}} \left(-\frac{b^{3}}{a^{7} n^{4}}\right)^{\frac{3}{4}} + b^{2} x x^{-\frac{1}{4} \, n - \frac{1}{3}}}{x}\right) + 3 \, a n \left(-\frac{b^{3}}{a^{7} n^{4}}\right)^{\frac{1}{4}} \log\left(-\frac{a^{5} n^{3} x^{\frac{2}{3}} \left(-\frac{b^{3}}{a^{7} n^{4}}\right)^{\frac{3}{4}} - b^{2} x x^{-\frac{1}{4} \, n - \frac{1}{3}}}{x}\right) + 4 \, x x^{-\frac{3}{4} \, n - 1}}{3 \, a n}"," ",0,"-1/3*(12*a*n*(-b^3/(a^7*n^4))^(1/4)*arctan(-(a^2*b^2*n*x^(1/3)*x^(-1/4*n - 1/3)*(-b^3/(a^7*n^4))^(1/4) - a^2*n*x^(1/3)*sqrt(-(a^3*b^3*n^2*x^(1/3)*sqrt(-b^3/(a^7*n^4)) - b^4*x*x^(-1/2*n - 2/3))/x)*(-b^3/(a^7*n^4))^(1/4))/b^3) - 3*a*n*(-b^3/(a^7*n^4))^(1/4)*log((a^5*n^3*x^(2/3)*(-b^3/(a^7*n^4))^(3/4) + b^2*x*x^(-1/4*n - 1/3))/x) + 3*a*n*(-b^3/(a^7*n^4))^(1/4)*log(-(a^5*n^3*x^(2/3)*(-b^3/(a^7*n^4))^(3/4) - b^2*x*x^(-1/4*n - 1/3))/x) + 4*x*x^(-3/4*n - 1))/(a*n)","A",0
2642,1,37,0,1.055479," ","integrate(x^(-1-n)/(a+b*x^n),x, algorithm=""fricas"")","-\frac{b n x^{n} \log\left(x\right) - b x^{n} \log\left(b x^{n} + a\right) + a}{a^{2} n x^{n}}"," ",0,"-(b*n*x^n*log(x) - b*x^n*log(b*x^n + a) + a)/(a^2*n*x^n)","A",0
2643,1,130,0,1.111862," ","integrate(x^(-1-1/2*n)/(a+b*x^n),x, algorithm=""fricas"")","\left[-\frac{2 \, x x^{-\frac{1}{2} \, n - 1} - \sqrt{-\frac{b}{a}} \log\left(\frac{a x^{2} x^{-n - 2} + 2 \, a x x^{-\frac{1}{2} \, n - 1} \sqrt{-\frac{b}{a}} - b}{a x^{2} x^{-n - 2} + b}\right)}{a n}, -\frac{2 \, {\left(x x^{-\frac{1}{2} \, n - 1} + \sqrt{\frac{b}{a}} \arctan\left(\frac{\sqrt{\frac{b}{a}}}{x x^{-\frac{1}{2} \, n - 1}}\right)\right)}}{a n}\right]"," ",0,"[-(2*x*x^(-1/2*n - 1) - sqrt(-b/a)*log((a*x^2*x^(-n - 2) + 2*a*x*x^(-1/2*n - 1)*sqrt(-b/a) - b)/(a*x^2*x^(-n - 2) + b)))/(a*n), -2*(x*x^(-1/2*n - 1) + sqrt(b/a)*arctan(sqrt(b/a)/(x*x^(-1/2*n - 1))))/(a*n)]","A",0
2644,1,145,0,1.243001," ","integrate(x^(-1-1/3*n)/(a+b*x^n),x, algorithm=""fricas"")","-\frac{6 \, x x^{-\frac{1}{3} \, n - 1} - 2 \, \sqrt{3} \left(\frac{b}{a}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} a x x^{-\frac{1}{3} \, n - 1} \left(\frac{b}{a}\right)^{\frac{2}{3}} - \sqrt{3} b}{3 \, b}\right) - 2 \, \left(\frac{b}{a}\right)^{\frac{1}{3}} \log\left(\frac{x x^{-\frac{1}{3} \, n - 1} + \left(\frac{b}{a}\right)^{\frac{1}{3}}}{x}\right) + \left(\frac{b}{a}\right)^{\frac{1}{3}} \log\left(\frac{x^{2} x^{-\frac{2}{3} \, n - 2} - x x^{-\frac{1}{3} \, n - 1} \left(\frac{b}{a}\right)^{\frac{1}{3}} + \left(\frac{b}{a}\right)^{\frac{2}{3}}}{x^{2}}\right)}{2 \, a n}"," ",0,"-1/2*(6*x*x^(-1/3*n - 1) - 2*sqrt(3)*(b/a)^(1/3)*arctan(1/3*(2*sqrt(3)*a*x*x^(-1/3*n - 1)*(b/a)^(2/3) - sqrt(3)*b)/b) - 2*(b/a)^(1/3)*log((x*x^(-1/3*n - 1) + (b/a)^(1/3))/x) + (b/a)^(1/3)*log((x^2*x^(-2/3*n - 2) - x*x^(-1/3*n - 1)*(b/a)^(1/3) + (b/a)^(2/3))/x^2))/(a*n)","A",0
2645,1,211,0,1.558732," ","integrate(x^(-1-1/4*n)/(a+b*x^n),x, algorithm=""fricas"")","\frac{4 \, a n \left(-\frac{b}{a^{5} n^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{a^{4} n^{3} x x^{-\frac{1}{4} \, n - 1} \left(-\frac{b}{a^{5} n^{4}}\right)^{\frac{3}{4}} - a^{4} n^{3} x \sqrt{\frac{a^{2} n^{2} \sqrt{-\frac{b}{a^{5} n^{4}}} + x^{2} x^{-\frac{1}{2} \, n - 2}}{x^{2}}} \left(-\frac{b}{a^{5} n^{4}}\right)^{\frac{3}{4}}}{b}\right) + a n \left(-\frac{b}{a^{5} n^{4}}\right)^{\frac{1}{4}} \log\left(\frac{a n \left(-\frac{b}{a^{5} n^{4}}\right)^{\frac{1}{4}} + x x^{-\frac{1}{4} \, n - 1}}{x}\right) - a n \left(-\frac{b}{a^{5} n^{4}}\right)^{\frac{1}{4}} \log\left(-\frac{a n \left(-\frac{b}{a^{5} n^{4}}\right)^{\frac{1}{4}} - x x^{-\frac{1}{4} \, n - 1}}{x}\right) - 4 \, x x^{-\frac{1}{4} \, n - 1}}{a n}"," ",0,"(4*a*n*(-b/(a^5*n^4))^(1/4)*arctan(-(a^4*n^3*x*x^(-1/4*n - 1)*(-b/(a^5*n^4))^(3/4) - a^4*n^3*x*sqrt((a^2*n^2*sqrt(-b/(a^5*n^4)) + x^2*x^(-1/2*n - 2))/x^2)*(-b/(a^5*n^4))^(3/4))/b) + a*n*(-b/(a^5*n^4))^(1/4)*log((a*n*(-b/(a^5*n^4))^(1/4) + x*x^(-1/4*n - 1))/x) - a*n*(-b/(a^5*n^4))^(1/4)*log(-(a*n*(-b/(a^5*n^4))^(1/4) - x*x^(-1/4*n - 1))/x) - 4*x*x^(-1/4*n - 1))/(a*n)","A",0
2646,1,251,0,1.160385," ","integrate(x^(-1-3/2*n)/(a+b*x^n),x, algorithm=""fricas"")","\left[-\frac{2 \, a x x^{-\frac{3}{2} \, n - 1} - 3 \, b \sqrt{-\frac{b}{a}} \log\left(-\frac{2 \, a^{3} x^{\frac{5}{3}} x^{-\frac{5}{2} \, n - \frac{5}{3}} \sqrt{-\frac{b}{a}} - a^{3} x^{2} x^{-3 \, n - 2} - 2 \, a^{2} b x x^{-\frac{3}{2} \, n - 1} \sqrt{-\frac{b}{a}} + 2 \, a^{2} b x^{\frac{4}{3}} x^{-2 \, n - \frac{4}{3}} + 2 \, a b^{2} x^{\frac{1}{3}} x^{-\frac{1}{2} \, n - \frac{1}{3}} \sqrt{-\frac{b}{a}} - 2 \, a b^{2} x^{\frac{2}{3}} x^{-n - \frac{2}{3}} + b^{3}}{a^{3} x^{2} x^{-3 \, n - 2} + b^{3}}\right) - 6 \, b x^{\frac{1}{3}} x^{-\frac{1}{2} \, n - \frac{1}{3}}}{3 \, a^{2} n}, -\frac{2 \, {\left(a x x^{-\frac{3}{2} \, n - 1} - 3 \, b \sqrt{\frac{b}{a}} \arctan\left(\frac{\sqrt{\frac{b}{a}}}{x^{\frac{1}{3}} x^{-\frac{1}{2} \, n - \frac{1}{3}}}\right) - 3 \, b x^{\frac{1}{3}} x^{-\frac{1}{2} \, n - \frac{1}{3}}\right)}}{3 \, a^{2} n}\right]"," ",0,"[-1/3*(2*a*x*x^(-3/2*n - 1) - 3*b*sqrt(-b/a)*log(-(2*a^3*x^(5/3)*x^(-5/2*n - 5/3)*sqrt(-b/a) - a^3*x^2*x^(-3*n - 2) - 2*a^2*b*x*x^(-3/2*n - 1)*sqrt(-b/a) + 2*a^2*b*x^(4/3)*x^(-2*n - 4/3) + 2*a*b^2*x^(1/3)*x^(-1/2*n - 1/3)*sqrt(-b/a) - 2*a*b^2*x^(2/3)*x^(-n - 2/3) + b^3)/(a^3*x^2*x^(-3*n - 2) + b^3)) - 6*b*x^(1/3)*x^(-1/2*n - 1/3))/(a^2*n), -2/3*(a*x*x^(-3/2*n - 1) - 3*b*sqrt(b/a)*arctan(sqrt(b/a)/(x^(1/3)*x^(-1/2*n - 1/3))) - 3*b*x^(1/3)*x^(-1/2*n - 1/3))/(a^2*n)]","A",0
2647,1,180,0,1.667088," ","integrate(x^(-1-4/3*n)/(a+b*x^n),x, algorithm=""fricas"")","-\frac{3 \, a x x^{-\frac{4}{3} \, n - 1} - 4 \, \sqrt{3} b \left(-\frac{b}{a}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} a x^{\frac{1}{4}} x^{-\frac{1}{3} \, n - \frac{1}{4}} \left(-\frac{b}{a}\right)^{\frac{2}{3}} - \sqrt{3} b}{3 \, b}\right) + 2 \, b \left(-\frac{b}{a}\right)^{\frac{1}{3}} \log\left(\frac{x^{\frac{3}{4}} x^{-\frac{1}{3} \, n - \frac{1}{4}} \left(-\frac{b}{a}\right)^{\frac{1}{3}} + x x^{-\frac{2}{3} \, n - \frac{1}{2}} + \sqrt{x} \left(-\frac{b}{a}\right)^{\frac{2}{3}}}{x}\right) - 4 \, b \left(-\frac{b}{a}\right)^{\frac{1}{3}} \log\left(\frac{x x^{-\frac{1}{3} \, n - \frac{1}{4}} - x^{\frac{3}{4}} \left(-\frac{b}{a}\right)^{\frac{1}{3}}}{x}\right) - 12 \, b x^{\frac{1}{4}} x^{-\frac{1}{3} \, n - \frac{1}{4}}}{4 \, a^{2} n}"," ",0,"-1/4*(3*a*x*x^(-4/3*n - 1) - 4*sqrt(3)*b*(-b/a)^(1/3)*arctan(1/3*(2*sqrt(3)*a*x^(1/4)*x^(-1/3*n - 1/4)*(-b/a)^(2/3) - sqrt(3)*b)/b) + 2*b*(-b/a)^(1/3)*log((x^(3/4)*x^(-1/3*n - 1/4)*(-b/a)^(1/3) + x*x^(-2/3*n - 1/2) + sqrt(x)*(-b/a)^(2/3))/x) - 4*b*(-b/a)^(1/3)*log((x*x^(-1/3*n - 1/4) - x^(3/4)*(-b/a)^(1/3))/x) - 12*b*x^(1/4)*x^(-1/3*n - 1/4))/(a^2*n)","A",0
2648,1,270,0,1.760178," ","integrate(x^(-1-5/4*n)/(a+b*x^n),x, algorithm=""fricas"")","-\frac{20 \, a^{2} n \left(-\frac{b^{5}}{a^{9} n^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{a^{7} b n^{3} x^{\frac{1}{5}} x^{-\frac{1}{4} \, n - \frac{1}{5}} \left(-\frac{b^{5}}{a^{9} n^{4}}\right)^{\frac{3}{4}} - a^{7} n^{3} x^{\frac{1}{5}} \sqrt{\frac{a^{4} n^{2} x^{\frac{3}{5}} \sqrt{-\frac{b^{5}}{a^{9} n^{4}}} + b^{2} x x^{-\frac{1}{2} \, n - \frac{2}{5}}}{x}} \left(-\frac{b^{5}}{a^{9} n^{4}}\right)^{\frac{3}{4}}}{b^{5}}\right) + 5 \, a^{2} n \left(-\frac{b^{5}}{a^{9} n^{4}}\right)^{\frac{1}{4}} \log\left(\frac{a^{2} n x^{\frac{4}{5}} \left(-\frac{b^{5}}{a^{9} n^{4}}\right)^{\frac{1}{4}} + b x x^{-\frac{1}{4} \, n - \frac{1}{5}}}{x}\right) - 5 \, a^{2} n \left(-\frac{b^{5}}{a^{9} n^{4}}\right)^{\frac{1}{4}} \log\left(-\frac{a^{2} n x^{\frac{4}{5}} \left(-\frac{b^{5}}{a^{9} n^{4}}\right)^{\frac{1}{4}} - b x x^{-\frac{1}{4} \, n - \frac{1}{5}}}{x}\right) + 4 \, a x x^{-\frac{5}{4} \, n - 1} - 20 \, b x^{\frac{1}{5}} x^{-\frac{1}{4} \, n - \frac{1}{5}}}{5 \, a^{2} n}"," ",0,"-1/5*(20*a^2*n*(-b^5/(a^9*n^4))^(1/4)*arctan(-(a^7*b*n^3*x^(1/5)*x^(-1/4*n - 1/5)*(-b^5/(a^9*n^4))^(3/4) - a^7*n^3*x^(1/5)*sqrt((a^4*n^2*x^(3/5)*sqrt(-b^5/(a^9*n^4)) + b^2*x*x^(-1/2*n - 2/5))/x)*(-b^5/(a^9*n^4))^(3/4))/b^5) + 5*a^2*n*(-b^5/(a^9*n^4))^(1/4)*log((a^2*n*x^(4/5)*(-b^5/(a^9*n^4))^(1/4) + b*x*x^(-1/4*n - 1/5))/x) - 5*a^2*n*(-b^5/(a^9*n^4))^(1/4)*log(-(a^2*n*x^(4/5)*(-b^5/(a^9*n^4))^(1/4) - b*x*x^(-1/4*n - 1/5))/x) + 4*a*x*x^(-5/4*n - 1) - 20*b*x^(1/5)*x^(-1/4*n - 1/5))/(a^2*n)","A",0
2649,1,66,0,1.099597," ","integrate(x^(-1+4*n)*(a+b*x^n)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, b^{4} x^{4 \, n} + 5 \, a b^{3} x^{3 \, n} - 6 \, a^{2} b^{2} x^{2 \, n} + 8 \, a^{3} b x^{n} - 16 \, a^{4}\right)} \sqrt{b x^{n} + a}}{315 \, b^{4} n}"," ",0,"2/315*(35*b^4*x^(4*n) + 5*a*b^3*x^(3*n) - 6*a^2*b^2*x^(2*n) + 8*a^3*b*x^n - 16*a^4)*sqrt(b*x^n + a)/(b^4*n)","A",0
2650,1,53,0,1.109671," ","integrate(x^(-1+3*n)*(a+b*x^n)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, b^{3} x^{3 \, n} + 3 \, a b^{2} x^{2 \, n} - 4 \, a^{2} b x^{n} + 8 \, a^{3}\right)} \sqrt{b x^{n} + a}}{105 \, b^{3} n}"," ",0,"2/105*(15*b^3*x^(3*n) + 3*a*b^2*x^(2*n) - 4*a^2*b*x^n + 8*a^3)*sqrt(b*x^n + a)/(b^3*n)","A",0
2651,1,39,0,1.266200," ","integrate(x^(-1+2*n)*(a+b*x^n)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, b^{2} x^{2 \, n} + a b x^{n} - 2 \, a^{2}\right)} \sqrt{b x^{n} + a}}{15 \, b^{2} n}"," ",0,"2/15*(3*b^2*x^(2*n) + a*b*x^n - 2*a^2)*sqrt(b*x^n + a)/(b^2*n)","A",0
2652,1,17,0,1.287800," ","integrate(x^(-1+n)*(a+b*x^n)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(b x^{n} + a\right)}^{\frac{3}{2}}}{3 \, b n}"," ",0,"2/3*(b*x^n + a)^(3/2)/(b*n)","A",0
2653,1,91,0,0.867635," ","integrate((a+b*x^n)^(1/2)/x,x, algorithm=""fricas"")","\left[\frac{\sqrt{a} \log\left(\frac{b x^{n} - 2 \, \sqrt{b x^{n} + a} \sqrt{a} + 2 \, a}{x^{n}}\right) + 2 \, \sqrt{b x^{n} + a}}{n}, \frac{2 \, {\left(\sqrt{-a} \arctan\left(\frac{\sqrt{b x^{n} + a} \sqrt{-a}}{a}\right) + \sqrt{b x^{n} + a}\right)}}{n}\right]"," ",0,"[(sqrt(a)*log((b*x^n - 2*sqrt(b*x^n + a)*sqrt(a) + 2*a)/x^n) + 2*sqrt(b*x^n + a))/n, 2*(sqrt(-a)*arctan(sqrt(b*x^n + a)*sqrt(-a)/a) + sqrt(b*x^n + a))/n]","A",0
2654,1,119,0,0.981919," ","integrate(x^(-1-n)*(a+b*x^n)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a} b x^{n} \log\left(\frac{b x^{n} - 2 \, \sqrt{b x^{n} + a} \sqrt{a} + 2 \, a}{x^{n}}\right) - 2 \, \sqrt{b x^{n} + a} a}{2 \, a n x^{n}}, \frac{\sqrt{-a} b x^{n} \arctan\left(\frac{\sqrt{b x^{n} + a} \sqrt{-a}}{a}\right) - \sqrt{b x^{n} + a} a}{a n x^{n}}\right]"," ",0,"[1/2*(sqrt(a)*b*x^n*log((b*x^n - 2*sqrt(b*x^n + a)*sqrt(a) + 2*a)/x^n) - 2*sqrt(b*x^n + a)*a)/(a*n*x^n), (sqrt(-a)*b*x^n*arctan(sqrt(b*x^n + a)*sqrt(-a)/a) - sqrt(b*x^n + a)*a)/(a*n*x^n)]","A",0
2655,1,153,0,1.684946," ","integrate(x^(-1-2*n)*(a+b*x^n)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a} b^{2} x^{2 \, n} \log\left(\frac{b x^{n} + 2 \, \sqrt{b x^{n} + a} \sqrt{a} + 2 \, a}{x^{n}}\right) - 2 \, {\left(a b x^{n} + 2 \, a^{2}\right)} \sqrt{b x^{n} + a}}{8 \, a^{2} n x^{2 \, n}}, -\frac{\sqrt{-a} b^{2} x^{2 \, n} \arctan\left(\frac{\sqrt{b x^{n} + a} \sqrt{-a}}{a}\right) + {\left(a b x^{n} + 2 \, a^{2}\right)} \sqrt{b x^{n} + a}}{4 \, a^{2} n x^{2 \, n}}\right]"," ",0,"[1/8*(sqrt(a)*b^2*x^(2*n)*log((b*x^n + 2*sqrt(b*x^n + a)*sqrt(a) + 2*a)/x^n) - 2*(a*b*x^n + 2*a^2)*sqrt(b*x^n + a))/(a^2*n*x^(2*n)), -1/4*(sqrt(-a)*b^2*x^(2*n)*arctan(sqrt(b*x^n + a)*sqrt(-a)/a) + (a*b*x^n + 2*a^2)*sqrt(b*x^n + a))/(a^2*n*x^(2*n))]","A",0
2656,1,183,0,1.567338," ","integrate(x^(-1-3*n)*(a+b*x^n)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{a} b^{3} x^{3 \, n} \log\left(\frac{b x^{n} - 2 \, \sqrt{b x^{n} + a} \sqrt{a} + 2 \, a}{x^{n}}\right) + 2 \, {\left(3 \, a b^{2} x^{2 \, n} - 2 \, a^{2} b x^{n} - 8 \, a^{3}\right)} \sqrt{b x^{n} + a}}{48 \, a^{3} n x^{3 \, n}}, \frac{3 \, \sqrt{-a} b^{3} x^{3 \, n} \arctan\left(\frac{\sqrt{b x^{n} + a} \sqrt{-a}}{a}\right) + {\left(3 \, a b^{2} x^{2 \, n} - 2 \, a^{2} b x^{n} - 8 \, a^{3}\right)} \sqrt{b x^{n} + a}}{24 \, a^{3} n x^{3 \, n}}\right]"," ",0,"[1/48*(3*sqrt(a)*b^3*x^(3*n)*log((b*x^n - 2*sqrt(b*x^n + a)*sqrt(a) + 2*a)/x^n) + 2*(3*a*b^2*x^(2*n) - 2*a^2*b*x^n - 8*a^3)*sqrt(b*x^n + a))/(a^3*n*x^(3*n)), 1/24*(3*sqrt(-a)*b^3*x^(3*n)*arctan(sqrt(b*x^n + a)*sqrt(-a)/a) + (3*a*b^2*x^(2*n) - 2*a^2*b*x^n - 8*a^3)*sqrt(b*x^n + a))/(a^3*n*x^(3*n))]","A",0
2657,1,209,0,1.503027," ","integrate(x^(-1-4*n)*(a+b*x^n)^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, \sqrt{a} b^{4} x^{4 \, n} \log\left(\frac{b x^{n} + 2 \, \sqrt{b x^{n} + a} \sqrt{a} + 2 \, a}{x^{n}}\right) - 2 \, {\left(15 \, a b^{3} x^{3 \, n} - 10 \, a^{2} b^{2} x^{2 \, n} + 8 \, a^{3} b x^{n} + 48 \, a^{4}\right)} \sqrt{b x^{n} + a}}{384 \, a^{4} n x^{4 \, n}}, -\frac{15 \, \sqrt{-a} b^{4} x^{4 \, n} \arctan\left(\frac{\sqrt{b x^{n} + a} \sqrt{-a}}{a}\right) + {\left(15 \, a b^{3} x^{3 \, n} - 10 \, a^{2} b^{2} x^{2 \, n} + 8 \, a^{3} b x^{n} + 48 \, a^{4}\right)} \sqrt{b x^{n} + a}}{192 \, a^{4} n x^{4 \, n}}\right]"," ",0,"[1/384*(15*sqrt(a)*b^4*x^(4*n)*log((b*x^n + 2*sqrt(b*x^n + a)*sqrt(a) + 2*a)/x^n) - 2*(15*a*b^3*x^(3*n) - 10*a^2*b^2*x^(2*n) + 8*a^3*b*x^n + 48*a^4)*sqrt(b*x^n + a))/(a^4*n*x^(4*n)), -1/192*(15*sqrt(-a)*b^4*x^(4*n)*arctan(sqrt(b*x^n + a)*sqrt(-a)/a) + (15*a*b^3*x^(3*n) - 10*a^2*b^2*x^(2*n) + 8*a^3*b*x^n + 48*a^4)*sqrt(b*x^n + a))/(a^4*n*x^(4*n))]","A",0
2658,1,53,0,1.231877," ","integrate(x^(-1+4*n)/(a+b*x^n)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, b^{3} x^{3 \, n} - 6 \, a b^{2} x^{2 \, n} + 8 \, a^{2} b x^{n} - 16 \, a^{3}\right)} \sqrt{b x^{n} + a}}{35 \, b^{4} n}"," ",0,"2/35*(5*b^3*x^(3*n) - 6*a*b^2*x^(2*n) + 8*a^2*b*x^n - 16*a^3)*sqrt(b*x^n + a)/(b^4*n)","A",0
2659,1,40,0,1.200921," ","integrate(x^(-1+3*n)/(a+b*x^n)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, b^{2} x^{2 \, n} - 4 \, a b x^{n} + 8 \, a^{2}\right)} \sqrt{b x^{n} + a}}{15 \, b^{3} n}"," ",0,"2/15*(3*b^2*x^(2*n) - 4*a*b*x^n + 8*a^2)*sqrt(b*x^n + a)/(b^3*n)","A",0
2660,1,26,0,0.949923," ","integrate(x^(-1+2*n)/(a+b*x^n)^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{b x^{n} + a} {\left(b x^{n} - 2 \, a\right)}}{3 \, b^{2} n}"," ",0,"2/3*sqrt(b*x^n + a)*(b*x^n - 2*a)/(b^2*n)","A",0
2661,1,17,0,0.824985," ","integrate(x^(-1+n)/(a+b*x^n)^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{b x^{n} + a}}{b n}"," ",0,"2*sqrt(b*x^n + a)/(b*n)","A",0
2662,1,70,0,1.414849," ","integrate(1/x/(a+b*x^n)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{b x^{n} - 2 \, \sqrt{b x^{n} + a} \sqrt{a} + 2 \, a}{x^{n}}\right)}{\sqrt{a} n}, \frac{2 \, \sqrt{-a} \arctan\left(\frac{\sqrt{b x^{n} + a} \sqrt{-a}}{a}\right)}{a n}\right]"," ",0,"[log((b*x^n - 2*sqrt(b*x^n + a)*sqrt(a) + 2*a)/x^n)/(sqrt(a)*n), 2*sqrt(-a)*arctan(sqrt(b*x^n + a)*sqrt(-a)/a)/(a*n)]","A",0
2663,1,119,0,0.913561," ","integrate(x^(-1-n)/(a+b*x^n)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a} b x^{n} \log\left(\frac{b x^{n} + 2 \, \sqrt{b x^{n} + a} \sqrt{a} + 2 \, a}{x^{n}}\right) - 2 \, \sqrt{b x^{n} + a} a}{2 \, a^{2} n x^{n}}, -\frac{\sqrt{-a} b x^{n} \arctan\left(\frac{\sqrt{b x^{n} + a} \sqrt{-a}}{a}\right) + \sqrt{b x^{n} + a} a}{a^{2} n x^{n}}\right]"," ",0,"[1/2*(sqrt(a)*b*x^n*log((b*x^n + 2*sqrt(b*x^n + a)*sqrt(a) + 2*a)/x^n) - 2*sqrt(b*x^n + a)*a)/(a^2*n*x^n), -(sqrt(-a)*b*x^n*arctan(sqrt(b*x^n + a)*sqrt(-a)/a) + sqrt(b*x^n + a)*a)/(a^2*n*x^n)]","A",0
2664,1,157,0,0.988396," ","integrate(x^(-1-2*n)/(a+b*x^n)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{a} b^{2} x^{2 \, n} \log\left(\frac{b x^{n} - 2 \, \sqrt{b x^{n} + a} \sqrt{a} + 2 \, a}{x^{n}}\right) + 2 \, {\left(3 \, a b x^{n} - 2 \, a^{2}\right)} \sqrt{b x^{n} + a}}{8 \, a^{3} n x^{2 \, n}}, \frac{3 \, \sqrt{-a} b^{2} x^{2 \, n} \arctan\left(\frac{\sqrt{b x^{n} + a} \sqrt{-a}}{a}\right) + {\left(3 \, a b x^{n} - 2 \, a^{2}\right)} \sqrt{b x^{n} + a}}{4 \, a^{3} n x^{2 \, n}}\right]"," ",0,"[1/8*(3*sqrt(a)*b^2*x^(2*n)*log((b*x^n - 2*sqrt(b*x^n + a)*sqrt(a) + 2*a)/x^n) + 2*(3*a*b*x^n - 2*a^2)*sqrt(b*x^n + a))/(a^3*n*x^(2*n)), 1/4*(3*sqrt(-a)*b^2*x^(2*n)*arctan(sqrt(b*x^n + a)*sqrt(-a)/a) + (3*a*b*x^n - 2*a^2)*sqrt(b*x^n + a))/(a^3*n*x^(2*n))]","A",0
2665,1,183,0,1.191821," ","integrate(x^(-1-3*n)/(a+b*x^n)^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, \sqrt{a} b^{3} x^{3 \, n} \log\left(\frac{b x^{n} + 2 \, \sqrt{b x^{n} + a} \sqrt{a} + 2 \, a}{x^{n}}\right) - 2 \, {\left(15 \, a b^{2} x^{2 \, n} - 10 \, a^{2} b x^{n} + 8 \, a^{3}\right)} \sqrt{b x^{n} + a}}{48 \, a^{4} n x^{3 \, n}}, -\frac{15 \, \sqrt{-a} b^{3} x^{3 \, n} \arctan\left(\frac{\sqrt{b x^{n} + a} \sqrt{-a}}{a}\right) + {\left(15 \, a b^{2} x^{2 \, n} - 10 \, a^{2} b x^{n} + 8 \, a^{3}\right)} \sqrt{b x^{n} + a}}{24 \, a^{4} n x^{3 \, n}}\right]"," ",0,"[1/48*(15*sqrt(a)*b^3*x^(3*n)*log((b*x^n + 2*sqrt(b*x^n + a)*sqrt(a) + 2*a)/x^n) - 2*(15*a*b^2*x^(2*n) - 10*a^2*b*x^n + 8*a^3)*sqrt(b*x^n + a))/(a^4*n*x^(3*n)), -1/24*(15*sqrt(-a)*b^3*x^(3*n)*arctan(sqrt(b*x^n + a)*sqrt(-a)/a) + (15*a*b^2*x^(2*n) - 10*a^2*b*x^n + 8*a^3)*sqrt(b*x^n + a))/(a^4*n*x^(3*n))]","A",0
2666,1,209,0,1.073696," ","integrate(x^(-1-4*n)/(a+b*x^n)^(1/2),x, algorithm=""fricas"")","\left[\frac{105 \, \sqrt{a} b^{4} x^{4 \, n} \log\left(\frac{b x^{n} - 2 \, \sqrt{b x^{n} + a} \sqrt{a} + 2 \, a}{x^{n}}\right) + 2 \, {\left(105 \, a b^{3} x^{3 \, n} - 70 \, a^{2} b^{2} x^{2 \, n} + 56 \, a^{3} b x^{n} - 48 \, a^{4}\right)} \sqrt{b x^{n} + a}}{384 \, a^{5} n x^{4 \, n}}, \frac{105 \, \sqrt{-a} b^{4} x^{4 \, n} \arctan\left(\frac{\sqrt{b x^{n} + a} \sqrt{-a}}{a}\right) + {\left(105 \, a b^{3} x^{3 \, n} - 70 \, a^{2} b^{2} x^{2 \, n} + 56 \, a^{3} b x^{n} - 48 \, a^{4}\right)} \sqrt{b x^{n} + a}}{192 \, a^{5} n x^{4 \, n}}\right]"," ",0,"[1/384*(105*sqrt(a)*b^4*x^(4*n)*log((b*x^n - 2*sqrt(b*x^n + a)*sqrt(a) + 2*a)/x^n) + 2*(105*a*b^3*x^(3*n) - 70*a^2*b^2*x^(2*n) + 56*a^3*b*x^n - 48*a^4)*sqrt(b*x^n + a))/(a^5*n*x^(4*n)), 1/192*(105*sqrt(-a)*b^4*x^(4*n)*arctan(sqrt(b*x^n + a)*sqrt(-a)/a) + (105*a*b^3*x^(3*n) - 70*a^2*b^2*x^(2*n) + 56*a^3*b*x^n - 48*a^4)*sqrt(b*x^n + a))/(a^5*n*x^(4*n))]","A",0
2667,1,362,0,1.092751," ","integrate(x^m*(a+b*x^n)^3,x, algorithm=""fricas"")","\frac{{\left(b^{3} m^{3} + 3 \, b^{3} m^{2} + 3 \, b^{3} m + b^{3} + 2 \, {\left(b^{3} m + b^{3}\right)} n^{2} + 3 \, {\left(b^{3} m^{2} + 2 \, b^{3} m + b^{3}\right)} n\right)} x x^{m} x^{3 \, n} + 3 \, {\left(a b^{2} m^{3} + 3 \, a b^{2} m^{2} + 3 \, a b^{2} m + a b^{2} + 3 \, {\left(a b^{2} m + a b^{2}\right)} n^{2} + 4 \, {\left(a b^{2} m^{2} + 2 \, a b^{2} m + a b^{2}\right)} n\right)} x x^{m} x^{2 \, n} + 3 \, {\left(a^{2} b m^{3} + 3 \, a^{2} b m^{2} + 3 \, a^{2} b m + a^{2} b + 6 \, {\left(a^{2} b m + a^{2} b\right)} n^{2} + 5 \, {\left(a^{2} b m^{2} + 2 \, a^{2} b m + a^{2} b\right)} n\right)} x x^{m} x^{n} + {\left(a^{3} m^{3} + 6 \, a^{3} n^{3} + 3 \, a^{3} m^{2} + 3 \, a^{3} m + a^{3} + 11 \, {\left(a^{3} m + a^{3}\right)} n^{2} + 6 \, {\left(a^{3} m^{2} + 2 \, a^{3} m + a^{3}\right)} n\right)} x x^{m}}{m^{4} + 6 \, {\left(m + 1\right)} n^{3} + 4 \, m^{3} + 11 \, {\left(m^{2} + 2 \, m + 1\right)} n^{2} + 6 \, m^{2} + 6 \, {\left(m^{3} + 3 \, m^{2} + 3 \, m + 1\right)} n + 4 \, m + 1}"," ",0,"((b^3*m^3 + 3*b^3*m^2 + 3*b^3*m + b^3 + 2*(b^3*m + b^3)*n^2 + 3*(b^3*m^2 + 2*b^3*m + b^3)*n)*x*x^m*x^(3*n) + 3*(a*b^2*m^3 + 3*a*b^2*m^2 + 3*a*b^2*m + a*b^2 + 3*(a*b^2*m + a*b^2)*n^2 + 4*(a*b^2*m^2 + 2*a*b^2*m + a*b^2)*n)*x*x^m*x^(2*n) + 3*(a^2*b*m^3 + 3*a^2*b*m^2 + 3*a^2*b*m + a^2*b + 6*(a^2*b*m + a^2*b)*n^2 + 5*(a^2*b*m^2 + 2*a^2*b*m + a^2*b)*n)*x*x^m*x^n + (a^3*m^3 + 6*a^3*n^3 + 3*a^3*m^2 + 3*a^3*m + a^3 + 11*(a^3*m + a^3)*n^2 + 6*(a^3*m^2 + 2*a^3*m + a^3)*n)*x*x^m)/(m^4 + 6*(m + 1)*n^3 + 4*m^3 + 11*(m^2 + 2*m + 1)*n^2 + 6*m^2 + 6*(m^3 + 3*m^2 + 3*m + 1)*n + 4*m + 1)","B",0
2668,1,151,0,0.926890," ","integrate(x^m*(a+b*x^n)^2,x, algorithm=""fricas"")","\frac{{\left(b^{2} m^{2} + 2 \, b^{2} m + b^{2} + {\left(b^{2} m + b^{2}\right)} n\right)} x x^{m} x^{2 \, n} + 2 \, {\left(a b m^{2} + 2 \, a b m + a b + 2 \, {\left(a b m + a b\right)} n\right)} x x^{m} x^{n} + {\left(a^{2} m^{2} + 2 \, a^{2} n^{2} + 2 \, a^{2} m + a^{2} + 3 \, {\left(a^{2} m + a^{2}\right)} n\right)} x x^{m}}{m^{3} + 2 \, {\left(m + 1\right)} n^{2} + 3 \, m^{2} + 3 \, {\left(m^{2} + 2 \, m + 1\right)} n + 3 \, m + 1}"," ",0,"((b^2*m^2 + 2*b^2*m + b^2 + (b^2*m + b^2)*n)*x*x^m*x^(2*n) + 2*(a*b*m^2 + 2*a*b*m + a*b + 2*(a*b*m + a*b)*n)*x*x^m*x^n + (a^2*m^2 + 2*a^2*n^2 + 2*a^2*m + a^2 + 3*(a^2*m + a^2)*n)*x*x^m)/(m^3 + 2*(m + 1)*n^2 + 3*m^2 + 3*(m^2 + 2*m + 1)*n + 3*m + 1)","B",0
2669,1,43,0,0.917953," ","integrate(x^m*(a+b*x^n),x, algorithm=""fricas"")","\frac{{\left(b m + b\right)} x x^{m} x^{n} + {\left(a m + a n + a\right)} x x^{m}}{m^{2} + {\left(m + 1\right)} n + 2 \, m + 1}"," ",0,"((b*m + b)*x*x^m*x^n + (a*m + a*n + a)*x*x^m)/(m^2 + (m + 1)*n + 2*m + 1)","A",0
2670,0,0,0,0.808382," ","integrate(x^m/(a+b*x^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{b x^{n} + a}, x\right)"," ",0,"integral(x^m/(b*x^n + a), x)","F",0
2671,0,0,0,0.894175," ","integrate(x^m/(a+b*x^n)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}}, x\right)"," ",0,"integral(x^m/(b^2*x^(2*n) + 2*a*b*x^n + a^2), x)","F",0
2672,0,0,0,1.050657," ","integrate(x^m/(a+b*x^n)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{b^{3} x^{3 \, n} + 3 \, a b^{2} x^{2 \, n} + 3 \, a^{2} b x^{n} + a^{3}}, x\right)"," ",0,"integral(x^m/(b^3*x^(3*n) + 3*a*b^2*x^(2*n) + 3*a^2*b*x^n + a^3), x)","F",0
2673,-2,0,0,0.000000," ","integrate(x^m*(a+b*x^n)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
2674,-2,0,0,0.000000," ","integrate(x^m*(a+b*x^n)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
2675,-2,0,0,0.000000," ","integrate(x^m/(a+b*x^n)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
2676,-2,0,0,0.000000," ","integrate(x^m/(a+b*x^n)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
2677,-2,0,0,0.000000," ","integrate(x^m/(a+b*x^n)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
2678,-2,0,0,0.000000," ","integrate(x^(3+2*n)/(a+b*x^n)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
2679,-2,0,0,0.000000," ","integrate(x^(3+n)/(a+b*x^n)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
2680,-2,0,0,0.000000," ","integrate(x^(3-n)/(a+b*x^n)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
2681,-2,0,0,0.000000," ","integrate(x^(3-2*n)/(a+b*x^n)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
2682,-2,0,0,0.000000," ","integrate(x^(m+2*n)/(a+b*x^n)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
2683,-2,0,0,0.000000," ","integrate(x^(m+n)/(a+b*x^n)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
2684,-2,0,0,0.000000," ","integrate(x^(m-n)/(a+b*x^n)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
2685,-2,0,0,0.000000," ","integrate(x^(m-2*n)/(a+b*x^n)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
2686,-2,0,0,0.000000," ","integrate(-1/2*b*n*x^(-1+m+n)/(a+b*x^n)^(3/2)+m*x^(-1+m)/(a+b*x^n)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
2687,1,175,0,0.732497," ","integrate(x^(-1+7/2*n)/(a+b*x^n)^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, a^{3} \sqrt{b} \log\left(2 \, \sqrt{b x^{n} + a} \sqrt{b} x^{\frac{1}{2} \, n} - 2 \, b x^{n} - a\right) + 2 \, {\left(8 \, b^{3} x^{\frac{5}{2} \, n} - 10 \, a b^{2} x^{\frac{3}{2} \, n} + 15 \, a^{2} b x^{\frac{1}{2} \, n}\right)} \sqrt{b x^{n} + a}}{48 \, b^{4} n}, \frac{15 \, a^{3} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x^{\frac{1}{2} \, n}}{\sqrt{b x^{n} + a}}\right) + {\left(8 \, b^{3} x^{\frac{5}{2} \, n} - 10 \, a b^{2} x^{\frac{3}{2} \, n} + 15 \, a^{2} b x^{\frac{1}{2} \, n}\right)} \sqrt{b x^{n} + a}}{24 \, b^{4} n}\right]"," ",0,"[1/48*(15*a^3*sqrt(b)*log(2*sqrt(b*x^n + a)*sqrt(b)*x^(1/2*n) - 2*b*x^n - a) + 2*(8*b^3*x^(5/2*n) - 10*a*b^2*x^(3/2*n) + 15*a^2*b*x^(1/2*n))*sqrt(b*x^n + a))/(b^4*n), 1/24*(15*a^3*sqrt(-b)*arctan(sqrt(-b)*x^(1/2*n)/sqrt(b*x^n + a)) + (8*b^3*x^(5/2*n) - 10*a*b^2*x^(3/2*n) + 15*a^2*b*x^(1/2*n))*sqrt(b*x^n + a))/(b^4*n)]","A",0
2688,1,150,0,0.897821," ","integrate(x^(-1+5/2*n)/(a+b*x^n)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, a^{2} \sqrt{b} \log\left(-2 \, \sqrt{b x^{n} + a} \sqrt{b} x^{\frac{1}{2} \, n} - 2 \, b x^{n} - a\right) + 2 \, {\left(2 \, b^{2} x^{\frac{3}{2} \, n} - 3 \, a b x^{\frac{1}{2} \, n}\right)} \sqrt{b x^{n} + a}}{8 \, b^{3} n}, -\frac{3 \, a^{2} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x^{\frac{1}{2} \, n}}{\sqrt{b x^{n} + a}}\right) - {\left(2 \, b^{2} x^{\frac{3}{2} \, n} - 3 \, a b x^{\frac{1}{2} \, n}\right)} \sqrt{b x^{n} + a}}{4 \, b^{3} n}\right]"," ",0,"[1/8*(3*a^2*sqrt(b)*log(-2*sqrt(b*x^n + a)*sqrt(b)*x^(1/2*n) - 2*b*x^n - a) + 2*(2*b^2*x^(3/2*n) - 3*a*b*x^(1/2*n))*sqrt(b*x^n + a))/(b^3*n), -1/4*(3*a^2*sqrt(-b)*arctan(sqrt(-b)*x^(1/2*n)/sqrt(b*x^n + a)) - (2*b^2*x^(3/2*n) - 3*a*b*x^(1/2*n))*sqrt(b*x^n + a))/(b^3*n)]","A",0
2689,1,114,0,1.214969," ","integrate(x^(-1+3/2*n)/(a+b*x^n)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{b x^{n} + a} b x^{\frac{1}{2} \, n} + a \sqrt{b} \log\left(2 \, \sqrt{b x^{n} + a} \sqrt{b} x^{\frac{1}{2} \, n} - 2 \, b x^{n} - a\right)}{2 \, b^{2} n}, \frac{\sqrt{b x^{n} + a} b x^{\frac{1}{2} \, n} + a \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x^{\frac{1}{2} \, n}}{\sqrt{b x^{n} + a}}\right)}{b^{2} n}\right]"," ",0,"[1/2*(2*sqrt(b*x^n + a)*b*x^(1/2*n) + a*sqrt(b)*log(2*sqrt(b*x^n + a)*sqrt(b)*x^(1/2*n) - 2*b*x^n - a))/(b^2*n), (sqrt(b*x^n + a)*b*x^(1/2*n) + a*sqrt(-b)*arctan(sqrt(-b)*x^(1/2*n)/sqrt(b*x^n + a)))/(b^2*n)]","A",0
2690,-2,0,0,0.000000," ","integrate(x^(-1+1/2*n)/(a+b*x^n)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
2691,-2,0,0,0.000000," ","integrate(x^(-1-1/2*n)/(a+b*x^n)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
2692,-2,0,0,0.000000," ","integrate(x^(-1-3/2*n)/(a+b*x^n)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
2693,-2,0,0,0.000000," ","integrate(x^(-1-5/2*n)/(a+b*x^n)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
2694,-2,0,0,0.000000," ","integrate(x^(-1-7/2*n)/(a+b*x^n)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
2695,-2,0,0,0.000000," ","integrate(x^m/(a+b*x^(-2+m))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
2696,-2,0,0,0.000000," ","integrate(x^m/(a+b*x^(2-m))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
2697,-2,0,0,0.000000," ","integrate(6*a*x^2/b/(4+m)/(a+b*x^(-2+m))^(1/2)+x^m/(a+b*x^(-2+m))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
2698,1,16,0,0.882896," ","integrate(1/2*x^(-1+m)*(2*a*m+b*(2*m-n)*x^n)/(a+b*x^n)^(3/2),x, algorithm=""fricas"")","\frac{x x^{m - 1}}{\sqrt{b x^{n} + a}}"," ",0,"x*x^(m - 1)/sqrt(b*x^n + a)","A",0
2699,-2,0,0,0.000000," ","integrate(-1/2*b*n*x^(-1+m+n)/(a+b*x^n)^(3/2)+m*x^(-1+m)/(a+b*x^n)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
2700,-2,0,0,0.000000," ","integrate(x^m/(a+b*x^(3+3*m))^(1/3),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
2701,-2,0,0,0.000000," ","integrate(x^m*(a+b/(x^(3/2+3/2*m)))^(2/3),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
2702,-2,0,0,0.000000," ","integrate(x^(-1+1/3*n)/(a+b*x^n)^(1/3),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
2703,-2,0,0,0.000000," ","integrate(x^(-1-2/3*n)*(a+b*x^n)^(2/3),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
2704,0,0,0,0.653599," ","integrate(x^m*(a+b*x^n)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{n} + a\right)}^{p} x^{m}, x\right)"," ",0,"integral((b*x^n + a)^p*x^m, x)","F",0
2705,1,192,0,0.798362," ","integrate((a+b*x^n)^(-4-1/n),x, algorithm=""fricas"")","\frac{6 \, b^{4} n^{3} x x^{4 \, n} + 6 \, {\left(4 \, a b^{3} n^{3} + a b^{3} n^{2}\right)} x x^{3 \, n} + 3 \, {\left(12 \, a^{2} b^{2} n^{3} + 7 \, a^{2} b^{2} n^{2} + a^{2} b^{2} n\right)} x x^{2 \, n} + {\left(24 \, a^{3} b n^{3} + 26 \, a^{3} b n^{2} + 9 \, a^{3} b n + a^{3} b\right)} x x^{n} + {\left(6 \, a^{4} n^{3} + 11 \, a^{4} n^{2} + 6 \, a^{4} n + a^{4}\right)} x}{{\left(6 \, a^{4} n^{3} + 11 \, a^{4} n^{2} + 6 \, a^{4} n + a^{4}\right)} {\left(b x^{n} + a\right)}^{\frac{4 \, n + 1}{n}}}"," ",0,"(6*b^4*n^3*x*x^(4*n) + 6*(4*a*b^3*n^3 + a*b^3*n^2)*x*x^(3*n) + 3*(12*a^2*b^2*n^3 + 7*a^2*b^2*n^2 + a^2*b^2*n)*x*x^(2*n) + (24*a^3*b*n^3 + 26*a^3*b*n^2 + 9*a^3*b*n + a^3*b)*x*x^n + (6*a^4*n^3 + 11*a^4*n^2 + 6*a^4*n + a^4)*x)/((6*a^4*n^3 + 11*a^4*n^2 + 6*a^4*n + a^4)*(b*x^n + a)^((4*n + 1)/n))","A",0
2706,1,126,0,0.961414," ","integrate((a+b*x^n)^(-3-1/n),x, algorithm=""fricas"")","\frac{2 \, b^{3} n^{2} x x^{3 \, n} + 2 \, {\left(3 \, a b^{2} n^{2} + a b^{2} n\right)} x x^{2 \, n} + {\left(6 \, a^{2} b n^{2} + 5 \, a^{2} b n + a^{2} b\right)} x x^{n} + {\left(2 \, a^{3} n^{2} + 3 \, a^{3} n + a^{3}\right)} x}{{\left(2 \, a^{3} n^{2} + 3 \, a^{3} n + a^{3}\right)} {\left(b x^{n} + a\right)}^{\frac{3 \, n + 1}{n}}}"," ",0,"(2*b^3*n^2*x*x^(3*n) + 2*(3*a*b^2*n^2 + a*b^2*n)*x*x^(2*n) + (6*a^2*b*n^2 + 5*a^2*b*n + a^2*b)*x*x^n + (2*a^3*n^2 + 3*a^3*n + a^3)*x)/((2*a^3*n^2 + 3*a^3*n + a^3)*(b*x^n + a)^((3*n + 1)/n))","A",0
2707,1,68,0,0.986934," ","integrate((a+b*x^n)^(-2-1/n),x, algorithm=""fricas"")","\frac{b^{2} n x x^{2 \, n} + {\left(2 \, a b n + a b\right)} x x^{n} + {\left(a^{2} n + a^{2}\right)} x}{{\left(a^{2} n + a^{2}\right)} {\left(b x^{n} + a\right)}^{\frac{2 \, n + 1}{n}}}"," ",0,"(b^2*n*x*x^(2*n) + (2*a*b*n + a*b)*x*x^n + (a^2*n + a^2)*x)/((a^2*n + a^2)*(b*x^n + a)^((2*n + 1)/n))","A",0
2708,1,31,0,0.761116," ","integrate((a+b*x^n)^(-1-1/n),x, algorithm=""fricas"")","\frac{b x x^{n} + a x}{{\left(b x^{n} + a\right)}^{\frac{n + 1}{n}} a}"," ",0,"(b*x*x^n + a*x)/((b*x^n + a)^((n + 1)/n)*a)","A",0
2709,0,0,0,0.806059," ","integrate(1/((a+b*x^n)^(1/n)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(b x^{n} + a\right)}^{\left(\frac{1}{n}\right)}}, x\right)"," ",0,"integral(1/((b*x^n + a)^(1/n)), x)","F",0
2710,0,0,0,0.849076," ","integrate((a+b*x^n)^(1-1/n),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{n} + a\right)}^{\frac{n - 1}{n}}, x\right)"," ",0,"integral((b*x^n + a)^((n - 1)/n), x)","F",0
2711,0,0,0,0.947057," ","integrate((a+b*x^n)^(2-1/n),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{n} + a\right)}^{\frac{2 \, n - 1}{n}}, x\right)"," ",0,"integral((b*x^n + a)^((2*n - 1)/n), x)","F",0
2712,1,24,0,1.055853," ","integrate(x^m*(b*x^n)^p,x, algorithm=""fricas"")","\frac{x x^{m} e^{\left(n p \log\left(x\right) + p \log\left(b\right)\right)}}{n p + m + 1}"," ",0,"x*x^m*e^(n*p*log(x) + p*log(b))/(n*p + m + 1)","A",0
2713,1,22,0,0.671170," ","integrate(x^2*(b*x^n)^p,x, algorithm=""fricas"")","\frac{x^{3} e^{\left(n p \log\left(x\right) + p \log\left(b\right)\right)}}{n p + 3}"," ",0,"x^3*e^(n*p*log(x) + p*log(b))/(n*p + 3)","A",0
2714,1,22,0,0.528460," ","integrate(x*(b*x^n)^p,x, algorithm=""fricas"")","\frac{x^{2} e^{\left(n p \log\left(x\right) + p \log\left(b\right)\right)}}{n p + 2}"," ",0,"x^2*e^(n*p*log(x) + p*log(b))/(n*p + 2)","A",0
2715,1,20,0,0.454626," ","integrate((b*x^n)^p,x, algorithm=""fricas"")","\frac{x e^{\left(n p \log\left(x\right) + p \log\left(b\right)\right)}}{n p + 1}"," ",0,"x*e^(n*p*log(x) + p*log(b))/(n*p + 1)","A",0
2716,1,18,0,0.550777," ","integrate((b*x^n)^p/x,x, algorithm=""fricas"")","\frac{e^{\left(n p \log\left(x\right) + p \log\left(b\right)\right)}}{n p}"," ",0,"e^(n*p*log(x) + p*log(b))/(n*p)","A",0
2717,1,22,0,0.814113," ","integrate((b*x^n)^p/x^2,x, algorithm=""fricas"")","\frac{e^{\left(n p \log\left(x\right) + p \log\left(b\right)\right)}}{{\left(n p - 1\right)} x}"," ",0,"e^(n*p*log(x) + p*log(b))/((n*p - 1)*x)","A",0
2718,1,22,0,0.532353," ","integrate((b*x^n)^p/x^3,x, algorithm=""fricas"")","\frac{e^{\left(n p \log\left(x\right) + p \log\left(b\right)\right)}}{{\left(n p - 2\right)} x^{2}}"," ",0,"e^(n*p*log(x) + p*log(b))/((n*p - 2)*x^2)","A",0
2719,1,22,0,0.934640," ","integrate((b*x^n)^p/x^4,x, algorithm=""fricas"")","\frac{e^{\left(n p \log\left(x\right) + p \log\left(b\right)\right)}}{{\left(n p - 3\right)} x^{3}}"," ",0,"e^(n*p*log(x) + p*log(b))/((n*p - 3)*x^3)","A",0
2720,1,27,0,0.487465," ","integrate(x^(-1+n)*(a+b*x^n)^p,x, algorithm=""fricas"")","\frac{{\left(b x^{n} + a\right)} {\left(b x^{n} + a\right)}^{p}}{b n p + b n}"," ",0,"(b*x^n + a)*(b*x^n + a)^p/(b*n*p + b*n)","A",0
2721,1,62,0,0.750311," ","integrate(x^(-1+2*n)*(a+b*x^n)^p,x, algorithm=""fricas"")","\frac{{\left(a b p x^{n} - a^{2} + {\left(b^{2} p + b^{2}\right)} x^{2 \, n}\right)} {\left(b x^{n} + a\right)}^{p}}{b^{2} n p^{2} + 3 \, b^{2} n p + 2 \, b^{2} n}"," ",0,"(a*b*p*x^n - a^2 + (b^2*p + b^2)*x^(2*n))*(b*x^n + a)^p/(b^2*n*p^2 + 3*b^2*n*p + 2*b^2*n)","A",0
2722,1,108,0,0.607125," ","integrate(x^(-1+3*n)*(a+b*x^n)^p,x, algorithm=""fricas"")","-\frac{{\left(2 \, a^{2} b p x^{n} - 2 \, a^{3} - {\left(b^{3} p^{2} + 3 \, b^{3} p + 2 \, b^{3}\right)} x^{3 \, n} - {\left(a b^{2} p^{2} + a b^{2} p\right)} x^{2 \, n}\right)} {\left(b x^{n} + a\right)}^{p}}{b^{3} n p^{3} + 6 \, b^{3} n p^{2} + 11 \, b^{3} n p + 6 \, b^{3} n}"," ",0,"-(2*a^2*b*p*x^n - 2*a^3 - (b^3*p^2 + 3*b^3*p + 2*b^3)*x^(3*n) - (a*b^2*p^2 + a*b^2*p)*x^(2*n))*(b*x^n + a)^p/(b^3*n*p^3 + 6*b^3*n*p^2 + 11*b^3*n*p + 6*b^3*n)","A",0
2723,1,158,0,0.636384," ","integrate(x^(-1+4*n)*(a+b*x^n)^p,x, algorithm=""fricas"")","\frac{{\left(6 \, a^{3} b p x^{n} - 6 \, a^{4} + {\left(b^{4} p^{3} + 6 \, b^{4} p^{2} + 11 \, b^{4} p + 6 \, b^{4}\right)} x^{4 \, n} + {\left(a b^{3} p^{3} + 3 \, a b^{3} p^{2} + 2 \, a b^{3} p\right)} x^{3 \, n} - 3 \, {\left(a^{2} b^{2} p^{2} + a^{2} b^{2} p\right)} x^{2 \, n}\right)} {\left(b x^{n} + a\right)}^{p}}{b^{4} n p^{4} + 10 \, b^{4} n p^{3} + 35 \, b^{4} n p^{2} + 50 \, b^{4} n p + 24 \, b^{4} n}"," ",0,"(6*a^3*b*p*x^n - 6*a^4 + (b^4*p^3 + 6*b^4*p^2 + 11*b^4*p + 6*b^4)*x^(4*n) + (a*b^3*p^3 + 3*a*b^3*p^2 + 2*a*b^3*p)*x^(3*n) - 3*(a^2*b^2*p^2 + a^2*b^2*p)*x^(2*n))*(b*x^n + a)^p/(b^4*n*p^4 + 10*b^4*n*p^3 + 35*b^4*n*p^2 + 50*b^4*n*p + 24*b^4*n)","A",0
2724,1,53,0,0.542418," ","integrate(x^(-n*p-n-1)*(a+b*x^n)^p,x, algorithm=""fricas"")","-\frac{{\left(b x x^{-n p - n - 1} x^{n} + a x x^{-n p - n - 1}\right)} {\left(b x^{n} + a\right)}^{p}}{a n p + a n}"," ",0,"-(b*x*x^(-n*p - n - 1)*x^n + a*x*x^(-n*p - n - 1))*(b*x^n + a)^p/(a*n*p + a*n)","A",0
2725,1,111,0,0.705398," ","integrate(x^(-1-9*n)*(a+b*x^n)^8,x, algorithm=""fricas"")","-\frac{9 \, b^{8} x^{8 \, n} + 36 \, a b^{7} x^{7 \, n} + 84 \, a^{2} b^{6} x^{6 \, n} + 126 \, a^{3} b^{5} x^{5 \, n} + 126 \, a^{4} b^{4} x^{4 \, n} + 84 \, a^{5} b^{3} x^{3 \, n} + 36 \, a^{6} b^{2} x^{2 \, n} + 9 \, a^{7} b x^{n} + a^{8}}{9 \, n x^{9 \, n}}"," ",0,"-1/9*(9*b^8*x^(8*n) + 36*a*b^7*x^(7*n) + 84*a^2*b^6*x^(6*n) + 126*a^3*b^5*x^(5*n) + 126*a^4*b^4*x^(4*n) + 84*a^5*b^3*x^(3*n) + 36*a^6*b^2*x^(2*n) + 9*a^7*b*x^n + a^8)/(n*x^(9*n))","B",0
2726,1,34,0,0.677686," ","integrate(x^(-4-3*p)*(b*x^3+a)^p,x, algorithm=""fricas"")","-\frac{{\left(b x^{4} + a x\right)} {\left(b x^{3} + a\right)}^{p} x^{-3 \, p - 4}}{3 \, {\left(a p + a\right)}}"," ",0,"-1/3*(b*x^4 + a*x)*(b*x^3 + a)^p*x^(-3*p - 4)/(a*p + a)","A",0
2727,1,90,0,0.527483," ","integrate((b*x^3+a)^8/x^28,x, algorithm=""fricas"")","-\frac{9 \, b^{8} x^{24} + 36 \, a b^{7} x^{21} + 84 \, a^{2} b^{6} x^{18} + 126 \, a^{3} b^{5} x^{15} + 126 \, a^{4} b^{4} x^{12} + 84 \, a^{5} b^{3} x^{9} + 36 \, a^{6} b^{2} x^{6} + 9 \, a^{7} b x^{3} + a^{8}}{27 \, x^{27}}"," ",0,"-1/27*(9*b^8*x^24 + 36*a*b^7*x^21 + 84*a^2*b^6*x^18 + 126*a^3*b^5*x^15 + 126*a^4*b^4*x^12 + 84*a^5*b^3*x^9 + 36*a^6*b^2*x^6 + 9*a^7*b*x^3 + a^8)/x^27","B",0
2728,1,22,0,0.825222," ","integrate(1/x/(a+b*x^n),x, algorithm=""fricas"")","\frac{n \log\left(x\right) - \log\left(b x^{n} + a\right)}{a n}"," ",0,"(n*log(x) - log(b*x^n + a))/(a*n)","A",0
2729,1,18,0,0.677149," ","integrate(1/x/(b*x^3+a),x, algorithm=""fricas"")","-\frac{\log\left(b x^{3} + a\right) - 3 \, \log\left(x\right)}{3 \, a}"," ",0,"-1/3*(log(b*x^3 + a) - 3*log(x))/a","A",0
2730,1,192,0,0.611040," ","integrate(1/((a+b*x^n)^((1+4*n)/n)),x, algorithm=""fricas"")","\frac{6 \, b^{4} n^{3} x x^{4 \, n} + 6 \, {\left(4 \, a b^{3} n^{3} + a b^{3} n^{2}\right)} x x^{3 \, n} + 3 \, {\left(12 \, a^{2} b^{2} n^{3} + 7 \, a^{2} b^{2} n^{2} + a^{2} b^{2} n\right)} x x^{2 \, n} + {\left(24 \, a^{3} b n^{3} + 26 \, a^{3} b n^{2} + 9 \, a^{3} b n + a^{3} b\right)} x x^{n} + {\left(6 \, a^{4} n^{3} + 11 \, a^{4} n^{2} + 6 \, a^{4} n + a^{4}\right)} x}{{\left(6 \, a^{4} n^{3} + 11 \, a^{4} n^{2} + 6 \, a^{4} n + a^{4}\right)} {\left(b x^{n} + a\right)}^{\frac{4 \, n + 1}{n}}}"," ",0,"(6*b^4*n^3*x*x^(4*n) + 6*(4*a*b^3*n^3 + a*b^3*n^2)*x*x^(3*n) + 3*(12*a^2*b^2*n^3 + 7*a^2*b^2*n^2 + a^2*b^2*n)*x*x^(2*n) + (24*a^3*b*n^3 + 26*a^3*b*n^2 + 9*a^3*b*n + a^3*b)*x*x^n + (6*a^4*n^3 + 11*a^4*n^2 + 6*a^4*n + a^4)*x)/((6*a^4*n^3 + 11*a^4*n^2 + 6*a^4*n + a^4)*(b*x^n + a)^((4*n + 1)/n))","A",0
2731,1,126,0,0.601501," ","integrate(1/((a+b*x^n)^((1+3*n)/n)),x, algorithm=""fricas"")","\frac{2 \, b^{3} n^{2} x x^{3 \, n} + 2 \, {\left(3 \, a b^{2} n^{2} + a b^{2} n\right)} x x^{2 \, n} + {\left(6 \, a^{2} b n^{2} + 5 \, a^{2} b n + a^{2} b\right)} x x^{n} + {\left(2 \, a^{3} n^{2} + 3 \, a^{3} n + a^{3}\right)} x}{{\left(2 \, a^{3} n^{2} + 3 \, a^{3} n + a^{3}\right)} {\left(b x^{n} + a\right)}^{\frac{3 \, n + 1}{n}}}"," ",0,"(2*b^3*n^2*x*x^(3*n) + 2*(3*a*b^2*n^2 + a*b^2*n)*x*x^(2*n) + (6*a^2*b*n^2 + 5*a^2*b*n + a^2*b)*x*x^n + (2*a^3*n^2 + 3*a^3*n + a^3)*x)/((2*a^3*n^2 + 3*a^3*n + a^3)*(b*x^n + a)^((3*n + 1)/n))","A",0
2732,1,68,0,0.522966," ","integrate(1/((a+b*x^n)^((1+2*n)/n)),x, algorithm=""fricas"")","\frac{b^{2} n x x^{2 \, n} + {\left(2 \, a b n + a b\right)} x x^{n} + {\left(a^{2} n + a^{2}\right)} x}{{\left(a^{2} n + a^{2}\right)} {\left(b x^{n} + a\right)}^{\frac{2 \, n + 1}{n}}}"," ",0,"(b^2*n*x*x^(2*n) + (2*a*b*n + a*b)*x*x^n + (a^2*n + a^2)*x)/((a^2*n + a^2)*(b*x^n + a)^((2*n + 1)/n))","A",0
2733,1,31,0,0.800862," ","integrate(1/((a+b*x^n)^((1+n)/n)),x, algorithm=""fricas"")","\frac{b x x^{n} + a x}{{\left(b x^{n} + a\right)}^{\frac{n + 1}{n}} a}"," ",0,"(b*x*x^n + a*x)/((b*x^n + a)^((n + 1)/n)*a)","A",0
2734,0,0,0,0.823763," ","integrate(1/((a+b*x^n)^(1/n)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(b x^{n} + a\right)}^{\left(\frac{1}{n}\right)}}, x\right)"," ",0,"integral(1/((b*x^n + a)^(1/n)), x)","F",0
2735,0,0,0,0.758491," ","integrate(1/((a+b*x^n)^((1-n)/n)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{n} + a\right)}^{\frac{n - 1}{n}}, x\right)"," ",0,"integral((b*x^n + a)^((n - 1)/n), x)","F",0
2736,0,0,0,0.673954," ","integrate(1/((a+b*x^n)^((1-2*n)/n)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{n} + a\right)}^{\frac{2 \, n - 1}{n}}, x\right)"," ",0,"integral((b*x^n + a)^((2*n - 1)/n), x)","F",0
2737,1,15,0,0.502601," ","integrate(1/x/(a+b/(x^n)),x, algorithm=""fricas"")","\frac{\log\left(a x^{n} + b\right)}{a n}"," ",0,"log(a*x^n + b)/(a*n)","A",0
2738,1,18,0,0.601660," ","integrate(x^m/(a+b*x^(1+m)),x, algorithm=""fricas"")","\frac{\log\left(b x^{m + 1} + a\right)}{b m + b}"," ",0,"log(b*x^(m + 1) + a)/(b*m + b)","A",0
2739,1,35,0,0.618910," ","integrate(x^m*(a+b*x^(1+m))^n,x, algorithm=""fricas"")","\frac{{\left(b x^{m + 1} + a\right)} {\left(b x^{m + 1} + a\right)}^{n}}{b m + {\left(b m + b\right)} n + b}"," ",0,"(b*x^(m + 1) + a)*(b*x^(m + 1) + a)^n/(b*m + (b*m + b)*n + b)","A",0
2740,1,58,0,0.684678," ","integrate(x^m*(a+b*x^(2+2*m))^3,x, algorithm=""fricas"")","\frac{5 \, b^{3} x^{7} x^{7 \, m} + 21 \, a b^{2} x^{5} x^{5 \, m} + 35 \, a^{2} b x^{3} x^{3 \, m} + 35 \, a^{3} x x^{m}}{35 \, {\left(m + 1\right)}}"," ",0,"1/35*(5*b^3*x^7*x^(7*m) + 21*a*b^2*x^5*x^(5*m) + 35*a^2*b*x^3*x^(3*m) + 35*a^3*x*x^m)/(m + 1)","A",0
2741,1,42,0,0.744139," ","integrate(x^m*(a+b*x^(2+2*m))^2,x, algorithm=""fricas"")","\frac{3 \, b^{2} x^{5} x^{5 \, m} + 10 \, a b x^{3} x^{3 \, m} + 15 \, a^{2} x x^{m}}{15 \, {\left(m + 1\right)}}"," ",0,"1/15*(3*b^2*x^5*x^(5*m) + 10*a*b*x^3*x^(3*m) + 15*a^2*x*x^m)/(m + 1)","A",0
2742,1,25,0,0.812594," ","integrate(x^m*(a+b*x^(2+2*m)),x, algorithm=""fricas"")","\frac{b x^{3} x^{3 \, m} + 3 \, a x x^{m}}{3 \, {\left(m + 1\right)}}"," ",0,"1/3*(b*x^3*x^(3*m) + 3*a*x*x^m)/(m + 1)","A",0
2743,1,96,0,0.583759," ","integrate(x^m/(a+b*x^(2+2*m)),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a b} \log\left(\frac{b x^{2} x^{2 \, m} - 2 \, \sqrt{-a b} x x^{m} - a}{b x^{2} x^{2 \, m} + a}\right)}{2 \, {\left(a b m + a b\right)}}, -\frac{\sqrt{a b} \arctan\left(\frac{\sqrt{a b}}{b x x^{m}}\right)}{a b m + a b}\right]"," ",0,"[-1/2*sqrt(-a*b)*log((b*x^2*x^(2*m) - 2*sqrt(-a*b)*x*x^m - a)/(b*x^2*x^(2*m) + a))/(a*b*m + a*b), -sqrt(a*b)*arctan(sqrt(a*b)/(b*x*x^m))/(a*b*m + a*b)]","A",0
2744,1,212,0,0.643808," ","integrate(x^m/(a+b*x^(2+2*m))^2,x, algorithm=""fricas"")","\left[\frac{2 \, a b x x^{m} - {\left(\sqrt{-a b} b x^{2} x^{2 \, m} + \sqrt{-a b} a\right)} \log\left(\frac{b x^{2} x^{2 \, m} - 2 \, \sqrt{-a b} x x^{m} - a}{b x^{2} x^{2 \, m} + a}\right)}{4 \, {\left(a^{3} b m + a^{3} b + {\left(a^{2} b^{2} m + a^{2} b^{2}\right)} x^{2} x^{2 \, m}\right)}}, \frac{a b x x^{m} - {\left(\sqrt{a b} b x^{2} x^{2 \, m} + \sqrt{a b} a\right)} \arctan\left(\frac{\sqrt{a b}}{b x x^{m}}\right)}{2 \, {\left(a^{3} b m + a^{3} b + {\left(a^{2} b^{2} m + a^{2} b^{2}\right)} x^{2} x^{2 \, m}\right)}}\right]"," ",0,"[1/4*(2*a*b*x*x^m - (sqrt(-a*b)*b*x^2*x^(2*m) + sqrt(-a*b)*a)*log((b*x^2*x^(2*m) - 2*sqrt(-a*b)*x*x^m - a)/(b*x^2*x^(2*m) + a)))/(a^3*b*m + a^3*b + (a^2*b^2*m + a^2*b^2)*x^2*x^(2*m)), 1/2*(a*b*x*x^m - (sqrt(a*b)*b*x^2*x^(2*m) + sqrt(a*b)*a)*arctan(sqrt(a*b)/(b*x*x^m)))/(a^3*b*m + a^3*b + (a^2*b^2*m + a^2*b^2)*x^2*x^(2*m))]","A",0
2745,1,340,0,0.911912," ","integrate(x^m/(a+b*x^(2+2*m))^3,x, algorithm=""fricas"")","\left[\frac{6 \, a b^{2} x^{3} x^{3 \, m} + 10 \, a^{2} b x x^{m} - 3 \, {\left(\sqrt{-a b} b^{2} x^{4} x^{4 \, m} + 2 \, \sqrt{-a b} a b x^{2} x^{2 \, m} + \sqrt{-a b} a^{2}\right)} \log\left(\frac{b x^{2} x^{2 \, m} - 2 \, \sqrt{-a b} x x^{m} - a}{b x^{2} x^{2 \, m} + a}\right)}{16 \, {\left(a^{5} b m + a^{5} b + {\left(a^{3} b^{3} m + a^{3} b^{3}\right)} x^{4} x^{4 \, m} + 2 \, {\left(a^{4} b^{2} m + a^{4} b^{2}\right)} x^{2} x^{2 \, m}\right)}}, \frac{3 \, a b^{2} x^{3} x^{3 \, m} + 5 \, a^{2} b x x^{m} - 3 \, {\left(\sqrt{a b} b^{2} x^{4} x^{4 \, m} + 2 \, \sqrt{a b} a b x^{2} x^{2 \, m} + \sqrt{a b} a^{2}\right)} \arctan\left(\frac{\sqrt{a b}}{b x x^{m}}\right)}{8 \, {\left(a^{5} b m + a^{5} b + {\left(a^{3} b^{3} m + a^{3} b^{3}\right)} x^{4} x^{4 \, m} + 2 \, {\left(a^{4} b^{2} m + a^{4} b^{2}\right)} x^{2} x^{2 \, m}\right)}}\right]"," ",0,"[1/16*(6*a*b^2*x^3*x^(3*m) + 10*a^2*b*x*x^m - 3*(sqrt(-a*b)*b^2*x^4*x^(4*m) + 2*sqrt(-a*b)*a*b*x^2*x^(2*m) + sqrt(-a*b)*a^2)*log((b*x^2*x^(2*m) - 2*sqrt(-a*b)*x*x^m - a)/(b*x^2*x^(2*m) + a)))/(a^5*b*m + a^5*b + (a^3*b^3*m + a^3*b^3)*x^4*x^(4*m) + 2*(a^4*b^2*m + a^4*b^2)*x^2*x^(2*m)), 1/8*(3*a*b^2*x^3*x^(3*m) + 5*a^2*b*x*x^m - 3*(sqrt(a*b)*b^2*x^4*x^(4*m) + 2*sqrt(a*b)*a*b*x^2*x^(2*m) + sqrt(a*b)*a^2)*arctan(sqrt(a*b)/(b*x*x^m)))/(a^5*b*m + a^5*b + (a^3*b^3*m + a^3*b^3)*x^4*x^(4*m) + 2*(a^4*b^2*m + a^4*b^2)*x^2*x^(2*m))]","A",0
2746,-2,0,0,0.000000," ","integrate(x^m*(a+b*x^(2+2*m))^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
2747,-2,0,0,0.000000," ","integrate(x^m*(a+b*x^(2+2*m))^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
2748,-2,0,0,0.000000," ","integrate(x^m*(a+b*x^(2+2*m))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
2749,-2,0,0,0.000000," ","integrate(x^m/(a+b*x^(2+2*m))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
2750,1,47,0,0.689408," ","integrate(x^m/(a+b*x^(2+2*m))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{b x^{2} x^{2 \, m} + a} x x^{m}}{{\left(a b m + a b\right)} x^{2} x^{2 \, m} + a^{2} m + a^{2}}"," ",0,"sqrt(b*x^2*x^(2*m) + a)*x*x^m/((a*b*m + a*b)*x^2*x^(2*m) + a^2*m + a^2)","A",0
2751,1,93,0,1.016399," ","integrate(x^m/(a+b*x^(2+2*m))^(5/2),x, algorithm=""fricas"")","\frac{{\left(2 \, b x^{3} x^{3 \, m} + 3 \, a x x^{m}\right)} \sqrt{b x^{2} x^{2 \, m} + a}}{3 \, {\left({\left(a^{2} b^{2} m + a^{2} b^{2}\right)} x^{4} x^{4 \, m} + a^{4} m + a^{4} + 2 \, {\left(a^{3} b m + a^{3} b\right)} x^{2} x^{2 \, m}\right)}}"," ",0,"1/3*(2*b*x^3*x^(3*m) + 3*a*x*x^m)*sqrt(b*x^2*x^(2*m) + a)/((a^2*b^2*m + a^2*b^2)*x^4*x^(4*m) + a^4*m + a^4 + 2*(a^3*b*m + a^3*b)*x^2*x^(2*m))","A",0
2752,1,135,0,0.957476," ","integrate(x^m/(a+b*x^(2+2*m))^(7/2),x, algorithm=""fricas"")","\frac{{\left(8 \, b^{2} x^{5} x^{5 \, m} + 20 \, a b x^{3} x^{3 \, m} + 15 \, a^{2} x x^{m}\right)} \sqrt{b x^{2} x^{2 \, m} + a}}{15 \, {\left({\left(a^{3} b^{3} m + a^{3} b^{3}\right)} x^{6} x^{6 \, m} + a^{6} m + a^{6} + 3 \, {\left(a^{4} b^{2} m + a^{4} b^{2}\right)} x^{4} x^{4 \, m} + 3 \, {\left(a^{5} b m + a^{5} b\right)} x^{2} x^{2 \, m}\right)}}"," ",0,"1/15*(8*b^2*x^5*x^(5*m) + 20*a*b*x^3*x^(3*m) + 15*a^2*x*x^m)*sqrt(b*x^2*x^(2*m) + a)/((a^3*b^3*m + a^3*b^3)*x^6*x^(6*m) + a^6*m + a^6 + 3*(a^4*b^2*m + a^4*b^2)*x^4*x^(4*m) + 3*(a^5*b*m + a^5*b)*x^2*x^(2*m))","A",0
2753,1,16,0,0.999355," ","integrate(x^n*(1+x^(1+n))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(x^{n + 1} + 1\right)}^{\frac{3}{2}}}{3 \, {\left(n + 1\right)}}"," ",0,"2/3*(x^(n + 1) + 1)^(3/2)/(n + 1)","A",0
2754,1,18,0,0.943440," ","integrate(x^n*(a^2+x^(1+n))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(a^{2} + x^{n + 1}\right)}^{\frac{3}{2}}}{3 \, {\left(n + 1\right)}}"," ",0,"2/3*(a^2 + x^(n + 1))^(3/2)/(n + 1)","A",0
2755,1,172,0,0.665499," ","integrate((c*x)^m*(a+b*x^n)^2,x, algorithm=""fricas"")","\frac{{\left(b^{2} m^{2} + 2 \, b^{2} m + b^{2} + {\left(b^{2} m + b^{2}\right)} n\right)} x x^{2 \, n} e^{\left(m \log\left(c\right) + m \log\left(x\right)\right)} + 2 \, {\left(a b m^{2} + 2 \, a b m + a b + 2 \, {\left(a b m + a b\right)} n\right)} x x^{n} e^{\left(m \log\left(c\right) + m \log\left(x\right)\right)} + {\left(a^{2} m^{2} + 2 \, a^{2} n^{2} + 2 \, a^{2} m + a^{2} + 3 \, {\left(a^{2} m + a^{2}\right)} n\right)} x e^{\left(m \log\left(c\right) + m \log\left(x\right)\right)}}{m^{3} + 2 \, {\left(m + 1\right)} n^{2} + 3 \, m^{2} + 3 \, {\left(m^{2} + 2 \, m + 1\right)} n + 3 \, m + 1}"," ",0,"((b^2*m^2 + 2*b^2*m + b^2 + (b^2*m + b^2)*n)*x*x^(2*n)*e^(m*log(c) + m*log(x)) + 2*(a*b*m^2 + 2*a*b*m + a*b + 2*(a*b*m + a*b)*n)*x*x^n*e^(m*log(c) + m*log(x)) + (a^2*m^2 + 2*a^2*n^2 + 2*a^2*m + a^2 + 3*(a^2*m + a^2)*n)*x*e^(m*log(c) + m*log(x)))/(m^3 + 2*(m + 1)*n^2 + 3*m^2 + 3*(m^2 + 2*m + 1)*n + 3*m + 1)","B",0
2756,1,87,0,0.829810," ","integrate((c*x)^m*(b*x^3+a)^2,x, algorithm=""fricas"")","\frac{{\left({\left(b^{2} m^{2} + 5 \, b^{2} m + 4 \, b^{2}\right)} x^{7} + 2 \, {\left(a b m^{2} + 8 \, a b m + 7 \, a b\right)} x^{4} + {\left(a^{2} m^{2} + 11 \, a^{2} m + 28 \, a^{2}\right)} x\right)} \left(c x\right)^{m}}{m^{3} + 12 \, m^{2} + 39 \, m + 28}"," ",0,"((b^2*m^2 + 5*b^2*m + 4*b^2)*x^7 + 2*(a*b*m^2 + 8*a*b*m + 7*a*b)*x^4 + (a^2*m^2 + 11*a^2*m + 28*a^2)*x)*(c*x)^m/(m^3 + 12*m^2 + 39*m + 28)","A",0
2757,1,87,0,0.873031," ","integrate((c*x)^m*(b*x^2+a)^2,x, algorithm=""fricas"")","\frac{{\left({\left(b^{2} m^{2} + 4 \, b^{2} m + 3 \, b^{2}\right)} x^{5} + 2 \, {\left(a b m^{2} + 6 \, a b m + 5 \, a b\right)} x^{3} + {\left(a^{2} m^{2} + 8 \, a^{2} m + 15 \, a^{2}\right)} x\right)} \left(c x\right)^{m}}{m^{3} + 9 \, m^{2} + 23 \, m + 15}"," ",0,"((b^2*m^2 + 4*b^2*m + 3*b^2)*x^5 + 2*(a*b*m^2 + 6*a*b*m + 5*a*b)*x^3 + (a^2*m^2 + 8*a^2*m + 15*a^2)*x)*(c*x)^m/(m^3 + 9*m^2 + 23*m + 15)","A",0
2758,1,87,0,0.890928," ","integrate((c*x)^m*(b*x+a)^2,x, algorithm=""fricas"")","\frac{{\left({\left(b^{2} m^{2} + 3 \, b^{2} m + 2 \, b^{2}\right)} x^{3} + 2 \, {\left(a b m^{2} + 4 \, a b m + 3 \, a b\right)} x^{2} + {\left(a^{2} m^{2} + 5 \, a^{2} m + 6 \, a^{2}\right)} x\right)} \left(c x\right)^{m}}{m^{3} + 6 \, m^{2} + 11 \, m + 6}"," ",0,"((b^2*m^2 + 3*b^2*m + 2*b^2)*x^3 + 2*(a*b*m^2 + 4*a*b*m + 3*a*b)*x^2 + (a^2*m^2 + 5*a^2*m + 6*a^2)*x)*(c*x)^m/(m^3 + 6*m^2 + 11*m + 6)","A",0
2759,1,63,0,0.696000," ","integrate((a+b/x)^2*(c*x)^m,x, algorithm=""fricas"")","\frac{{\left(b^{2} m^{2} + b^{2} m + {\left(a^{2} m^{2} - a^{2} m\right)} x^{2} + 2 \, {\left(a b m^{2} - a b\right)} x\right)} \left(c x\right)^{m}}{{\left(m^{3} - m\right)} x}"," ",0,"(b^2*m^2 + b^2*m + (a^2*m^2 - a^2*m)*x^2 + 2*(a*b*m^2 - a*b)*x)*(c*x)^m/((m^3 - m)*x)","A",0
2760,1,81,0,0.847219," ","integrate((a+b/x^2)^2*(c*x)^m,x, algorithm=""fricas"")","\frac{{\left({\left(a^{2} m^{2} - 4 \, a^{2} m + 3 \, a^{2}\right)} x^{4} + b^{2} m^{2} + 2 \, {\left(a b m^{2} - 2 \, a b m - 3 \, a b\right)} x^{2} - b^{2}\right)} \left(c x\right)^{m}}{{\left(m^{3} - 3 \, m^{2} - m + 3\right)} x^{3}}"," ",0,"((a^2*m^2 - 4*a^2*m + 3*a^2)*x^4 + b^2*m^2 + 2*(a*b*m^2 - 2*a*b*m - 3*a*b)*x^2 - b^2)*(c*x)^m/((m^3 - 3*m^2 - m + 3)*x^3)","A",0
2761,1,87,0,1.040174," ","integrate((a+b/x^3)^2*(c*x)^m,x, algorithm=""fricas"")","\frac{{\left({\left(a^{2} m^{2} - 7 \, a^{2} m + 10 \, a^{2}\right)} x^{6} + b^{2} m^{2} + 2 \, {\left(a b m^{2} - 4 \, a b m - 5 \, a b\right)} x^{3} - b^{2} m - 2 \, b^{2}\right)} \left(c x\right)^{m}}{{\left(m^{3} - 6 \, m^{2} + 3 \, m + 10\right)} x^{5}}"," ",0,"((a^2*m^2 - 7*a^2*m + 10*a^2)*x^6 + b^2*m^2 + 2*(a*b*m^2 - 4*a*b*m - 5*a*b)*x^3 - b^2*m - 2*b^2)*(c*x)^m/((m^3 - 6*m^2 + 3*m + 10)*x^5)","A",0
2762,1,225,0,1.205101," ","integrate((c*x)^(-1-1/2*n)/(a+b*x^n),x, algorithm=""fricas"")","\left[-\frac{2 \, x e^{\left(-\frac{1}{2} \, {\left(n + 2\right)} \log\left(c\right) - \frac{1}{2} \, {\left(n + 2\right)} \log\left(x\right)\right)} - \sqrt{-\frac{b c^{-n - 2}}{a}} \log\left(\frac{a x^{2} e^{\left(-{\left(n + 2\right)} \log\left(c\right) - {\left(n + 2\right)} \log\left(x\right)\right)} + 2 \, a \sqrt{-\frac{b c^{-n - 2}}{a}} x e^{\left(-\frac{1}{2} \, {\left(n + 2\right)} \log\left(c\right) - \frac{1}{2} \, {\left(n + 2\right)} \log\left(x\right)\right)} - b c^{-n - 2}}{a x^{2} e^{\left(-{\left(n + 2\right)} \log\left(c\right) - {\left(n + 2\right)} \log\left(x\right)\right)} + b c^{-n - 2}}\right)}{a n}, -\frac{2 \, {\left(x e^{\left(-\frac{1}{2} \, {\left(n + 2\right)} \log\left(c\right) - \frac{1}{2} \, {\left(n + 2\right)} \log\left(x\right)\right)} + \sqrt{\frac{b c^{-n - 2}}{a}} \arctan\left(\frac{\sqrt{\frac{b c^{-n - 2}}{a}} e^{\left(\frac{1}{2} \, {\left(n + 2\right)} \log\left(c\right) + \frac{1}{2} \, {\left(n + 2\right)} \log\left(x\right)\right)}}{x}\right)\right)}}{a n}\right]"," ",0,"[-(2*x*e^(-1/2*(n + 2)*log(c) - 1/2*(n + 2)*log(x)) - sqrt(-b*c^(-n - 2)/a)*log((a*x^2*e^(-(n + 2)*log(c) - (n + 2)*log(x)) + 2*a*sqrt(-b*c^(-n - 2)/a)*x*e^(-1/2*(n + 2)*log(c) - 1/2*(n + 2)*log(x)) - b*c^(-n - 2))/(a*x^2*e^(-(n + 2)*log(c) - (n + 2)*log(x)) + b*c^(-n - 2))))/(a*n), -2*(x*e^(-1/2*(n + 2)*log(c) - 1/2*(n + 2)*log(x)) + sqrt(b*c^(-n - 2)/a)*arctan(sqrt(b*c^(-n - 2)/a)*e^(1/2*(n + 2)*log(c) + 1/2*(n + 2)*log(x))/x))/(a*n)]","A",0
2763,1,329,0,1.425466," ","integrate((c*x)^(-1-2/3*n)/(a+b*x^n),x, algorithm=""fricas"")","-\frac{3 \, x e^{\left(-\frac{1}{3} \, {\left(2 \, n + 3\right)} \log\left(c\right) - \frac{1}{3} \, {\left(2 \, n + 3\right)} \log\left(x\right)\right)} - 2 \, \sqrt{3} \left(-\frac{b^{2} c^{-2 \, n - 3}}{a^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} a \left(-\frac{b^{2} c^{-2 \, n - 3}}{a^{2}}\right)^{\frac{1}{3}} \sqrt{x} e^{\left(-\frac{1}{6} \, {\left(2 \, n + 3\right)} \log\left(c\right) - \frac{1}{6} \, {\left(2 \, n + 3\right)} \log\left(x\right)\right)} + \sqrt{3} b c^{-n - \frac{3}{2}}}{3 \, b c^{-n - \frac{3}{2}}}\right) - 2 \, \left(-\frac{b^{2} c^{-2 \, n - 3}}{a^{2}}\right)^{\frac{1}{3}} \log\left(\frac{b c^{-n - \frac{3}{2}} x e^{\left(-\frac{1}{6} \, {\left(2 \, n + 3\right)} \log\left(c\right) - \frac{1}{6} \, {\left(2 \, n + 3\right)} \log\left(x\right)\right)} + a \left(-\frac{b^{2} c^{-2 \, n - 3}}{a^{2}}\right)^{\frac{2}{3}} \sqrt{x}}{x}\right) + \left(-\frac{b^{2} c^{-2 \, n - 3}}{a^{2}}\right)^{\frac{1}{3}} \log\left(\frac{b c^{-n - \frac{3}{2}} x e^{\left(-\frac{1}{3} \, {\left(2 \, n + 3\right)} \log\left(c\right) - \frac{1}{3} \, {\left(2 \, n + 3\right)} \log\left(x\right)\right)} - a \left(-\frac{b^{2} c^{-2 \, n - 3}}{a^{2}}\right)^{\frac{2}{3}} \sqrt{x} e^{\left(-\frac{1}{6} \, {\left(2 \, n + 3\right)} \log\left(c\right) - \frac{1}{6} \, {\left(2 \, n + 3\right)} \log\left(x\right)\right)} - b c^{-n - \frac{3}{2}} \left(-\frac{b^{2} c^{-2 \, n - 3}}{a^{2}}\right)^{\frac{1}{3}}}{x}\right)}{2 \, a n}"," ",0,"-1/2*(3*x*e^(-1/3*(2*n + 3)*log(c) - 1/3*(2*n + 3)*log(x)) - 2*sqrt(3)*(-b^2*c^(-2*n - 3)/a^2)^(1/3)*arctan(1/3*(2*sqrt(3)*a*(-b^2*c^(-2*n - 3)/a^2)^(1/3)*sqrt(x)*e^(-1/6*(2*n + 3)*log(c) - 1/6*(2*n + 3)*log(x)) + sqrt(3)*b*c^(-n - 3/2))/(b*c^(-n - 3/2))) - 2*(-b^2*c^(-2*n - 3)/a^2)^(1/3)*log((b*c^(-n - 3/2)*x*e^(-1/6*(2*n + 3)*log(c) - 1/6*(2*n + 3)*log(x)) + a*(-b^2*c^(-2*n - 3)/a^2)^(2/3)*sqrt(x))/x) + (-b^2*c^(-2*n - 3)/a^2)^(1/3)*log((b*c^(-n - 3/2)*x*e^(-1/3*(2*n + 3)*log(c) - 1/3*(2*n + 3)*log(x)) - a*(-b^2*c^(-2*n - 3)/a^2)^(2/3)*sqrt(x)*e^(-1/6*(2*n + 3)*log(c) - 1/6*(2*n + 3)*log(x)) - b*c^(-n - 3/2)*(-b^2*c^(-2*n - 3)/a^2)^(1/3))/x))/(a*n)","A",0
2764,1,426,0,2.524022," ","integrate((c*x)^(-1-3/4*n)/(a+b*x^n),x, algorithm=""fricas"")","-\frac{12 \, a n \left(-\frac{b^{3} c^{-3 \, n - 4}}{a^{7} n^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{a^{2} b^{2} c^{-2 \, n - \frac{8}{3}} n x^{\frac{1}{3}} \left(-\frac{b^{3} c^{-3 \, n - 4}}{a^{7} n^{4}}\right)^{\frac{1}{4}} e^{\left(-\frac{1}{12} \, {\left(3 \, n + 4\right)} \log\left(c\right) - \frac{1}{12} \, {\left(3 \, n + 4\right)} \log\left(x\right)\right)} - a^{2} n x^{\frac{1}{3}} \sqrt{-\frac{a^{3} b^{3} c^{-3 \, n - 4} n^{2} x^{\frac{1}{3}} \sqrt{-\frac{b^{3} c^{-3 \, n - 4}}{a^{7} n^{4}}} - b^{4} c^{-4 \, n - \frac{16}{3}} x e^{\left(-\frac{1}{6} \, {\left(3 \, n + 4\right)} \log\left(c\right) - \frac{1}{6} \, {\left(3 \, n + 4\right)} \log\left(x\right)\right)}}{x}} \left(-\frac{b^{3} c^{-3 \, n - 4}}{a^{7} n^{4}}\right)^{\frac{1}{4}}}{b^{3} c^{-3 \, n - 4}}\right) - 3 \, a n \left(-\frac{b^{3} c^{-3 \, n - 4}}{a^{7} n^{4}}\right)^{\frac{1}{4}} \log\left(\frac{a^{5} n^{3} x^{\frac{2}{3}} \left(-\frac{b^{3} c^{-3 \, n - 4}}{a^{7} n^{4}}\right)^{\frac{3}{4}} + b^{2} c^{-2 \, n - \frac{8}{3}} x e^{\left(-\frac{1}{12} \, {\left(3 \, n + 4\right)} \log\left(c\right) - \frac{1}{12} \, {\left(3 \, n + 4\right)} \log\left(x\right)\right)}}{x}\right) + 3 \, a n \left(-\frac{b^{3} c^{-3 \, n - 4}}{a^{7} n^{4}}\right)^{\frac{1}{4}} \log\left(-\frac{a^{5} n^{3} x^{\frac{2}{3}} \left(-\frac{b^{3} c^{-3 \, n - 4}}{a^{7} n^{4}}\right)^{\frac{3}{4}} - b^{2} c^{-2 \, n - \frac{8}{3}} x e^{\left(-\frac{1}{12} \, {\left(3 \, n + 4\right)} \log\left(c\right) - \frac{1}{12} \, {\left(3 \, n + 4\right)} \log\left(x\right)\right)}}{x}\right) + 4 \, x e^{\left(-\frac{1}{4} \, {\left(3 \, n + 4\right)} \log\left(c\right) - \frac{1}{4} \, {\left(3 \, n + 4\right)} \log\left(x\right)\right)}}{3 \, a n}"," ",0,"-1/3*(12*a*n*(-b^3*c^(-3*n - 4)/(a^7*n^4))^(1/4)*arctan(-(a^2*b^2*c^(-2*n - 8/3)*n*x^(1/3)*(-b^3*c^(-3*n - 4)/(a^7*n^4))^(1/4)*e^(-1/12*(3*n + 4)*log(c) - 1/12*(3*n + 4)*log(x)) - a^2*n*x^(1/3)*sqrt(-(a^3*b^3*c^(-3*n - 4)*n^2*x^(1/3)*sqrt(-b^3*c^(-3*n - 4)/(a^7*n^4)) - b^4*c^(-4*n - 16/3)*x*e^(-1/6*(3*n + 4)*log(c) - 1/6*(3*n + 4)*log(x)))/x)*(-b^3*c^(-3*n - 4)/(a^7*n^4))^(1/4))/(b^3*c^(-3*n - 4))) - 3*a*n*(-b^3*c^(-3*n - 4)/(a^7*n^4))^(1/4)*log((a^5*n^3*x^(2/3)*(-b^3*c^(-3*n - 4)/(a^7*n^4))^(3/4) + b^2*c^(-2*n - 8/3)*x*e^(-1/12*(3*n + 4)*log(c) - 1/12*(3*n + 4)*log(x)))/x) + 3*a*n*(-b^3*c^(-3*n - 4)/(a^7*n^4))^(1/4)*log(-(a^5*n^3*x^(2/3)*(-b^3*c^(-3*n - 4)/(a^7*n^4))^(3/4) - b^2*c^(-2*n - 8/3)*x*e^(-1/12*(3*n + 4)*log(c) - 1/12*(3*n + 4)*log(x)))/x) + 4*x*e^(-1/4*(3*n + 4)*log(c) - 1/4*(3*n + 4)*log(x)))/(a*n)","A",0
2765,1,59,0,0.995187," ","integrate((c*x)^(-1-n)/(a+b*x^n),x, algorithm=""fricas"")","-\frac{b c^{-n - 1} n x^{n} \log\left(x\right) - b c^{-n - 1} x^{n} \log\left(b x^{n} + a\right) + a c^{-n - 1}}{a^{2} n x^{n}}"," ",0,"-(b*c^(-n - 1)*n*x^n*log(x) - b*c^(-n - 1)*x^n*log(b*x^n + a) + a*c^(-n - 1))/(a^2*n*x^n)","A",0
2766,1,225,0,0.958178," ","integrate((c*x)^(-1-1/2*n)/(a+b*x^n),x, algorithm=""fricas"")","\left[-\frac{2 \, x e^{\left(-\frac{1}{2} \, {\left(n + 2\right)} \log\left(c\right) - \frac{1}{2} \, {\left(n + 2\right)} \log\left(x\right)\right)} - \sqrt{-\frac{b c^{-n - 2}}{a}} \log\left(\frac{a x^{2} e^{\left(-{\left(n + 2\right)} \log\left(c\right) - {\left(n + 2\right)} \log\left(x\right)\right)} + 2 \, a \sqrt{-\frac{b c^{-n - 2}}{a}} x e^{\left(-\frac{1}{2} \, {\left(n + 2\right)} \log\left(c\right) - \frac{1}{2} \, {\left(n + 2\right)} \log\left(x\right)\right)} - b c^{-n - 2}}{a x^{2} e^{\left(-{\left(n + 2\right)} \log\left(c\right) - {\left(n + 2\right)} \log\left(x\right)\right)} + b c^{-n - 2}}\right)}{a n}, -\frac{2 \, {\left(x e^{\left(-\frac{1}{2} \, {\left(n + 2\right)} \log\left(c\right) - \frac{1}{2} \, {\left(n + 2\right)} \log\left(x\right)\right)} + \sqrt{\frac{b c^{-n - 2}}{a}} \arctan\left(\frac{\sqrt{\frac{b c^{-n - 2}}{a}} e^{\left(\frac{1}{2} \, {\left(n + 2\right)} \log\left(c\right) + \frac{1}{2} \, {\left(n + 2\right)} \log\left(x\right)\right)}}{x}\right)\right)}}{a n}\right]"," ",0,"[-(2*x*e^(-1/2*(n + 2)*log(c) - 1/2*(n + 2)*log(x)) - sqrt(-b*c^(-n - 2)/a)*log((a*x^2*e^(-(n + 2)*log(c) - (n + 2)*log(x)) + 2*a*sqrt(-b*c^(-n - 2)/a)*x*e^(-1/2*(n + 2)*log(c) - 1/2*(n + 2)*log(x)) - b*c^(-n - 2))/(a*x^2*e^(-(n + 2)*log(c) - (n + 2)*log(x)) + b*c^(-n - 2))))/(a*n), -2*(x*e^(-1/2*(n + 2)*log(c) - 1/2*(n + 2)*log(x)) + sqrt(b*c^(-n - 2)/a)*arctan(sqrt(b*c^(-n - 2)/a)*e^(1/2*(n + 2)*log(c) + 1/2*(n + 2)*log(x))/x))/(a*n)]","A",0
2767,1,255,0,0.713301," ","integrate((c*x)^(-1-1/3*n)/(a+b*x^n),x, algorithm=""fricas"")","-\frac{6 \, x e^{\left(-\frac{1}{3} \, {\left(n + 3\right)} \log\left(c\right) - \frac{1}{3} \, {\left(n + 3\right)} \log\left(x\right)\right)} - 2 \, \sqrt{3} \left(\frac{b c^{-n - 3}}{a}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} a \left(\frac{b c^{-n - 3}}{a}\right)^{\frac{2}{3}} x e^{\left(-\frac{1}{3} \, {\left(n + 3\right)} \log\left(c\right) - \frac{1}{3} \, {\left(n + 3\right)} \log\left(x\right)\right)} - \sqrt{3} b c^{-n - 3}}{3 \, b c^{-n - 3}}\right) - 2 \, \left(\frac{b c^{-n - 3}}{a}\right)^{\frac{1}{3}} \log\left(\frac{x e^{\left(-\frac{1}{3} \, {\left(n + 3\right)} \log\left(c\right) - \frac{1}{3} \, {\left(n + 3\right)} \log\left(x\right)\right)} + \left(\frac{b c^{-n - 3}}{a}\right)^{\frac{1}{3}}}{x}\right) + \left(\frac{b c^{-n - 3}}{a}\right)^{\frac{1}{3}} \log\left(\frac{x^{2} e^{\left(-\frac{2}{3} \, {\left(n + 3\right)} \log\left(c\right) - \frac{2}{3} \, {\left(n + 3\right)} \log\left(x\right)\right)} - \left(\frac{b c^{-n - 3}}{a}\right)^{\frac{1}{3}} x e^{\left(-\frac{1}{3} \, {\left(n + 3\right)} \log\left(c\right) - \frac{1}{3} \, {\left(n + 3\right)} \log\left(x\right)\right)} + \left(\frac{b c^{-n - 3}}{a}\right)^{\frac{2}{3}}}{x^{2}}\right)}{2 \, a n}"," ",0,"-1/2*(6*x*e^(-1/3*(n + 3)*log(c) - 1/3*(n + 3)*log(x)) - 2*sqrt(3)*(b*c^(-n - 3)/a)^(1/3)*arctan(1/3*(2*sqrt(3)*a*(b*c^(-n - 3)/a)^(2/3)*x*e^(-1/3*(n + 3)*log(c) - 1/3*(n + 3)*log(x)) - sqrt(3)*b*c^(-n - 3))/(b*c^(-n - 3))) - 2*(b*c^(-n - 3)/a)^(1/3)*log((x*e^(-1/3*(n + 3)*log(c) - 1/3*(n + 3)*log(x)) + (b*c^(-n - 3)/a)^(1/3))/x) + (b*c^(-n - 3)/a)^(1/3)*log((x^2*e^(-2/3*(n + 3)*log(c) - 2/3*(n + 3)*log(x)) - (b*c^(-n - 3)/a)^(1/3)*x*e^(-1/3*(n + 3)*log(c) - 1/3*(n + 3)*log(x)) + (b*c^(-n - 3)/a)^(2/3))/x^2))/(a*n)","A",0
2768,1,321,0,0.916073," ","integrate((c*x)^(-1-1/4*n)/(a+b*x^n),x, algorithm=""fricas"")","\frac{4 \, a n \left(-\frac{b c^{-n - 4}}{a^{5} n^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{a^{4} n^{3} x \left(-\frac{b c^{-n - 4}}{a^{5} n^{4}}\right)^{\frac{3}{4}} e^{\left(-\frac{1}{4} \, {\left(n + 4\right)} \log\left(c\right) - \frac{1}{4} \, {\left(n + 4\right)} \log\left(x\right)\right)} - a^{4} n^{3} x \sqrt{\frac{a^{2} n^{2} \sqrt{-\frac{b c^{-n - 4}}{a^{5} n^{4}}} + x^{2} e^{\left(-\frac{1}{2} \, {\left(n + 4\right)} \log\left(c\right) - \frac{1}{2} \, {\left(n + 4\right)} \log\left(x\right)\right)}}{x^{2}}} \left(-\frac{b c^{-n - 4}}{a^{5} n^{4}}\right)^{\frac{3}{4}}}{b c^{-n - 4}}\right) + a n \left(-\frac{b c^{-n - 4}}{a^{5} n^{4}}\right)^{\frac{1}{4}} \log\left(\frac{a n \left(-\frac{b c^{-n - 4}}{a^{5} n^{4}}\right)^{\frac{1}{4}} + x e^{\left(-\frac{1}{4} \, {\left(n + 4\right)} \log\left(c\right) - \frac{1}{4} \, {\left(n + 4\right)} \log\left(x\right)\right)}}{x}\right) - a n \left(-\frac{b c^{-n - 4}}{a^{5} n^{4}}\right)^{\frac{1}{4}} \log\left(-\frac{a n \left(-\frac{b c^{-n - 4}}{a^{5} n^{4}}\right)^{\frac{1}{4}} - x e^{\left(-\frac{1}{4} \, {\left(n + 4\right)} \log\left(c\right) - \frac{1}{4} \, {\left(n + 4\right)} \log\left(x\right)\right)}}{x}\right) - 4 \, x e^{\left(-\frac{1}{4} \, {\left(n + 4\right)} \log\left(c\right) - \frac{1}{4} \, {\left(n + 4\right)} \log\left(x\right)\right)}}{a n}"," ",0,"(4*a*n*(-b*c^(-n - 4)/(a^5*n^4))^(1/4)*arctan(-(a^4*n^3*x*(-b*c^(-n - 4)/(a^5*n^4))^(3/4)*e^(-1/4*(n + 4)*log(c) - 1/4*(n + 4)*log(x)) - a^4*n^3*x*sqrt((a^2*n^2*sqrt(-b*c^(-n - 4)/(a^5*n^4)) + x^2*e^(-1/2*(n + 4)*log(c) - 1/2*(n + 4)*log(x)))/x^2)*(-b*c^(-n - 4)/(a^5*n^4))^(3/4))/(b*c^(-n - 4))) + a*n*(-b*c^(-n - 4)/(a^5*n^4))^(1/4)*log((a*n*(-b*c^(-n - 4)/(a^5*n^4))^(1/4) + x*e^(-1/4*(n + 4)*log(c) - 1/4*(n + 4)*log(x)))/x) - a*n*(-b*c^(-n - 4)/(a^5*n^4))^(1/4)*log(-(a*n*(-b*c^(-n - 4)/(a^5*n^4))^(1/4) - x*e^(-1/4*(n + 4)*log(c) - 1/4*(n + 4)*log(x)))/x) - 4*x*e^(-1/4*(n + 4)*log(c) - 1/4*(n + 4)*log(x)))/(a*n)","A",0
2769,1,492,0,1.241755," ","integrate((c*x)^(-1-3/2*n)/(a+b*x^n),x, algorithm=""fricas"")","\left[\frac{3 \, b c^{-n - \frac{2}{3}} \sqrt{-\frac{b c^{-n - \frac{2}{3}}}{a}} \log\left(-\frac{2 \, a^{2} b c^{-n - \frac{2}{3}} x^{\frac{4}{3}} e^{\left(-\frac{2}{3} \, {\left(3 \, n + 2\right)} \log\left(c\right) - \frac{2}{3} \, {\left(3 \, n + 2\right)} \log\left(x\right)\right)} - a^{3} x^{2} e^{\left(-{\left(3 \, n + 2\right)} \log\left(c\right) - {\left(3 \, n + 2\right)} \log\left(x\right)\right)} - 2 \, a b^{2} c^{-2 \, n - \frac{4}{3}} x^{\frac{2}{3}} e^{\left(-\frac{1}{3} \, {\left(3 \, n + 2\right)} \log\left(c\right) - \frac{1}{3} \, {\left(3 \, n + 2\right)} \log\left(x\right)\right)} + b^{3} c^{-3 \, n - 2} - 2 \, {\left(a^{2} b c^{-n - \frac{2}{3}} x e^{\left(-\frac{1}{2} \, {\left(3 \, n + 2\right)} \log\left(c\right) - \frac{1}{2} \, {\left(3 \, n + 2\right)} \log\left(x\right)\right)} - a^{3} x^{\frac{5}{3}} e^{\left(-\frac{5}{6} \, {\left(3 \, n + 2\right)} \log\left(c\right) - \frac{5}{6} \, {\left(3 \, n + 2\right)} \log\left(x\right)\right)} - a b^{2} c^{-2 \, n - \frac{4}{3}} x^{\frac{1}{3}} e^{\left(-\frac{1}{6} \, {\left(3 \, n + 2\right)} \log\left(c\right) - \frac{1}{6} \, {\left(3 \, n + 2\right)} \log\left(x\right)\right)}\right)} \sqrt{-\frac{b c^{-n - \frac{2}{3}}}{a}}}{a^{3} x^{2} e^{\left(-{\left(3 \, n + 2\right)} \log\left(c\right) - {\left(3 \, n + 2\right)} \log\left(x\right)\right)} + b^{3} c^{-3 \, n - 2}}\right) + 6 \, b c^{-n - \frac{2}{3}} x^{\frac{1}{3}} e^{\left(-\frac{1}{6} \, {\left(3 \, n + 2\right)} \log\left(c\right) - \frac{1}{6} \, {\left(3 \, n + 2\right)} \log\left(x\right)\right)} - 2 \, a x e^{\left(-\frac{1}{2} \, {\left(3 \, n + 2\right)} \log\left(c\right) - \frac{1}{2} \, {\left(3 \, n + 2\right)} \log\left(x\right)\right)}}{3 \, a^{2} n}, \frac{2 \, {\left(3 \, b c^{-n - \frac{2}{3}} \sqrt{\frac{b c^{-n - \frac{2}{3}}}{a}} \arctan\left(\frac{\sqrt{\frac{b c^{-n - \frac{2}{3}}}{a}} e^{\left(\frac{1}{6} \, {\left(3 \, n + 2\right)} \log\left(c\right) + \frac{1}{6} \, {\left(3 \, n + 2\right)} \log\left(x\right)\right)}}{x^{\frac{1}{3}}}\right) + 3 \, b c^{-n - \frac{2}{3}} x^{\frac{1}{3}} e^{\left(-\frac{1}{6} \, {\left(3 \, n + 2\right)} \log\left(c\right) - \frac{1}{6} \, {\left(3 \, n + 2\right)} \log\left(x\right)\right)} - a x e^{\left(-\frac{1}{2} \, {\left(3 \, n + 2\right)} \log\left(c\right) - \frac{1}{2} \, {\left(3 \, n + 2\right)} \log\left(x\right)\right)}\right)}}{3 \, a^{2} n}\right]"," ",0,"[1/3*(3*b*c^(-n - 2/3)*sqrt(-b*c^(-n - 2/3)/a)*log(-(2*a^2*b*c^(-n - 2/3)*x^(4/3)*e^(-2/3*(3*n + 2)*log(c) - 2/3*(3*n + 2)*log(x)) - a^3*x^2*e^(-(3*n + 2)*log(c) - (3*n + 2)*log(x)) - 2*a*b^2*c^(-2*n - 4/3)*x^(2/3)*e^(-1/3*(3*n + 2)*log(c) - 1/3*(3*n + 2)*log(x)) + b^3*c^(-3*n - 2) - 2*(a^2*b*c^(-n - 2/3)*x*e^(-1/2*(3*n + 2)*log(c) - 1/2*(3*n + 2)*log(x)) - a^3*x^(5/3)*e^(-5/6*(3*n + 2)*log(c) - 5/6*(3*n + 2)*log(x)) - a*b^2*c^(-2*n - 4/3)*x^(1/3)*e^(-1/6*(3*n + 2)*log(c) - 1/6*(3*n + 2)*log(x)))*sqrt(-b*c^(-n - 2/3)/a))/(a^3*x^2*e^(-(3*n + 2)*log(c) - (3*n + 2)*log(x)) + b^3*c^(-3*n - 2))) + 6*b*c^(-n - 2/3)*x^(1/3)*e^(-1/6*(3*n + 2)*log(c) - 1/6*(3*n + 2)*log(x)) - 2*a*x*e^(-1/2*(3*n + 2)*log(c) - 1/2*(3*n + 2)*log(x)))/(a^2*n), 2/3*(3*b*c^(-n - 2/3)*sqrt(b*c^(-n - 2/3)/a)*arctan(sqrt(b*c^(-n - 2/3)/a)*e^(1/6*(3*n + 2)*log(c) + 1/6*(3*n + 2)*log(x))/x^(1/3)) + 3*b*c^(-n - 2/3)*x^(1/3)*e^(-1/6*(3*n + 2)*log(c) - 1/6*(3*n + 2)*log(x)) - a*x*e^(-1/2*(3*n + 2)*log(c) - 1/2*(3*n + 2)*log(x)))/(a^2*n)]","A",0
2770,1,351,0,1.898670," ","integrate((c*x)^(-1-4/3*n)/(a+b*x^n),x, algorithm=""fricas"")","\frac{4 \, \sqrt{3} b c^{-n - \frac{3}{4}} \left(-\frac{b c^{-n - \frac{3}{4}}}{a}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} a \left(-\frac{b c^{-n - \frac{3}{4}}}{a}\right)^{\frac{2}{3}} x^{\frac{1}{4}} e^{\left(-\frac{1}{12} \, {\left(4 \, n + 3\right)} \log\left(c\right) - \frac{1}{12} \, {\left(4 \, n + 3\right)} \log\left(x\right)\right)} - \sqrt{3} b c^{-n - \frac{3}{4}}}{3 \, b c^{-n - \frac{3}{4}}}\right) - 2 \, b c^{-n - \frac{3}{4}} \left(-\frac{b c^{-n - \frac{3}{4}}}{a}\right)^{\frac{1}{3}} \log\left(\frac{\left(-\frac{b c^{-n - \frac{3}{4}}}{a}\right)^{\frac{1}{3}} x^{\frac{3}{4}} e^{\left(-\frac{1}{12} \, {\left(4 \, n + 3\right)} \log\left(c\right) - \frac{1}{12} \, {\left(4 \, n + 3\right)} \log\left(x\right)\right)} + x e^{\left(-\frac{1}{6} \, {\left(4 \, n + 3\right)} \log\left(c\right) - \frac{1}{6} \, {\left(4 \, n + 3\right)} \log\left(x\right)\right)} + \left(-\frac{b c^{-n - \frac{3}{4}}}{a}\right)^{\frac{2}{3}} \sqrt{x}}{x}\right) + 4 \, b c^{-n - \frac{3}{4}} \left(-\frac{b c^{-n - \frac{3}{4}}}{a}\right)^{\frac{1}{3}} \log\left(\frac{x e^{\left(-\frac{1}{12} \, {\left(4 \, n + 3\right)} \log\left(c\right) - \frac{1}{12} \, {\left(4 \, n + 3\right)} \log\left(x\right)\right)} - \left(-\frac{b c^{-n - \frac{3}{4}}}{a}\right)^{\frac{1}{3}} x^{\frac{3}{4}}}{x}\right) + 12 \, b c^{-n - \frac{3}{4}} x^{\frac{1}{4}} e^{\left(-\frac{1}{12} \, {\left(4 \, n + 3\right)} \log\left(c\right) - \frac{1}{12} \, {\left(4 \, n + 3\right)} \log\left(x\right)\right)} - 3 \, a x e^{\left(-\frac{1}{3} \, {\left(4 \, n + 3\right)} \log\left(c\right) - \frac{1}{3} \, {\left(4 \, n + 3\right)} \log\left(x\right)\right)}}{4 \, a^{2} n}"," ",0,"1/4*(4*sqrt(3)*b*c^(-n - 3/4)*(-b*c^(-n - 3/4)/a)^(1/3)*arctan(1/3*(2*sqrt(3)*a*(-b*c^(-n - 3/4)/a)^(2/3)*x^(1/4)*e^(-1/12*(4*n + 3)*log(c) - 1/12*(4*n + 3)*log(x)) - sqrt(3)*b*c^(-n - 3/4))/(b*c^(-n - 3/4))) - 2*b*c^(-n - 3/4)*(-b*c^(-n - 3/4)/a)^(1/3)*log(((-b*c^(-n - 3/4)/a)^(1/3)*x^(3/4)*e^(-1/12*(4*n + 3)*log(c) - 1/12*(4*n + 3)*log(x)) + x*e^(-1/6*(4*n + 3)*log(c) - 1/6*(4*n + 3)*log(x)) + (-b*c^(-n - 3/4)/a)^(2/3)*sqrt(x))/x) + 4*b*c^(-n - 3/4)*(-b*c^(-n - 3/4)/a)^(1/3)*log((x*e^(-1/12*(4*n + 3)*log(c) - 1/12*(4*n + 3)*log(x)) - (-b*c^(-n - 3/4)/a)^(1/3)*x^(3/4))/x) + 12*b*c^(-n - 3/4)*x^(1/4)*e^(-1/12*(4*n + 3)*log(c) - 1/12*(4*n + 3)*log(x)) - 3*a*x*e^(-1/3*(4*n + 3)*log(c) - 1/3*(4*n + 3)*log(x)))/(a^2*n)","A",0
2771,1,448,0,4.385012," ","integrate((c*x)^(-1-5/4*n)/(a+b*x^n),x, algorithm=""fricas"")","-\frac{20 \, a^{2} n \left(-\frac{b^{5} c^{-5 \, n - 4}}{a^{9} n^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{a^{7} b c^{-n - \frac{4}{5}} n^{3} x^{\frac{1}{5}} \left(-\frac{b^{5} c^{-5 \, n - 4}}{a^{9} n^{4}}\right)^{\frac{3}{4}} e^{\left(-\frac{1}{20} \, {\left(5 \, n + 4\right)} \log\left(c\right) - \frac{1}{20} \, {\left(5 \, n + 4\right)} \log\left(x\right)\right)} - a^{7} n^{3} x^{\frac{1}{5}} \sqrt{\frac{a^{4} n^{2} x^{\frac{3}{5}} \sqrt{-\frac{b^{5} c^{-5 \, n - 4}}{a^{9} n^{4}}} + b^{2} c^{-2 \, n - \frac{8}{5}} x e^{\left(-\frac{1}{10} \, {\left(5 \, n + 4\right)} \log\left(c\right) - \frac{1}{10} \, {\left(5 \, n + 4\right)} \log\left(x\right)\right)}}{x}} \left(-\frac{b^{5} c^{-5 \, n - 4}}{a^{9} n^{4}}\right)^{\frac{3}{4}}}{b^{5} c^{-5 \, n - 4}}\right) + 5 \, a^{2} n \left(-\frac{b^{5} c^{-5 \, n - 4}}{a^{9} n^{4}}\right)^{\frac{1}{4}} \log\left(\frac{a^{2} n x^{\frac{4}{5}} \left(-\frac{b^{5} c^{-5 \, n - 4}}{a^{9} n^{4}}\right)^{\frac{1}{4}} + b c^{-n - \frac{4}{5}} x e^{\left(-\frac{1}{20} \, {\left(5 \, n + 4\right)} \log\left(c\right) - \frac{1}{20} \, {\left(5 \, n + 4\right)} \log\left(x\right)\right)}}{x}\right) - 5 \, a^{2} n \left(-\frac{b^{5} c^{-5 \, n - 4}}{a^{9} n^{4}}\right)^{\frac{1}{4}} \log\left(-\frac{a^{2} n x^{\frac{4}{5}} \left(-\frac{b^{5} c^{-5 \, n - 4}}{a^{9} n^{4}}\right)^{\frac{1}{4}} - b c^{-n - \frac{4}{5}} x e^{\left(-\frac{1}{20} \, {\left(5 \, n + 4\right)} \log\left(c\right) - \frac{1}{20} \, {\left(5 \, n + 4\right)} \log\left(x\right)\right)}}{x}\right) - 20 \, b c^{-n - \frac{4}{5}} x^{\frac{1}{5}} e^{\left(-\frac{1}{20} \, {\left(5 \, n + 4\right)} \log\left(c\right) - \frac{1}{20} \, {\left(5 \, n + 4\right)} \log\left(x\right)\right)} + 4 \, a x e^{\left(-\frac{1}{4} \, {\left(5 \, n + 4\right)} \log\left(c\right) - \frac{1}{4} \, {\left(5 \, n + 4\right)} \log\left(x\right)\right)}}{5 \, a^{2} n}"," ",0,"-1/5*(20*a^2*n*(-b^5*c^(-5*n - 4)/(a^9*n^4))^(1/4)*arctan(-(a^7*b*c^(-n - 4/5)*n^3*x^(1/5)*(-b^5*c^(-5*n - 4)/(a^9*n^4))^(3/4)*e^(-1/20*(5*n + 4)*log(c) - 1/20*(5*n + 4)*log(x)) - a^7*n^3*x^(1/5)*sqrt((a^4*n^2*x^(3/5)*sqrt(-b^5*c^(-5*n - 4)/(a^9*n^4)) + b^2*c^(-2*n - 8/5)*x*e^(-1/10*(5*n + 4)*log(c) - 1/10*(5*n + 4)*log(x)))/x)*(-b^5*c^(-5*n - 4)/(a^9*n^4))^(3/4))/(b^5*c^(-5*n - 4))) + 5*a^2*n*(-b^5*c^(-5*n - 4)/(a^9*n^4))^(1/4)*log((a^2*n*x^(4/5)*(-b^5*c^(-5*n - 4)/(a^9*n^4))^(1/4) + b*c^(-n - 4/5)*x*e^(-1/20*(5*n + 4)*log(c) - 1/20*(5*n + 4)*log(x)))/x) - 5*a^2*n*(-b^5*c^(-5*n - 4)/(a^9*n^4))^(1/4)*log(-(a^2*n*x^(4/5)*(-b^5*c^(-5*n - 4)/(a^9*n^4))^(1/4) - b*c^(-n - 4/5)*x*e^(-1/20*(5*n + 4)*log(c) - 1/20*(5*n + 4)*log(x)))/x) - 20*b*c^(-n - 4/5)*x^(1/5)*e^(-1/20*(5*n + 4)*log(c) - 1/20*(5*n + 4)*log(x)) + 4*a*x*e^(-1/4*(5*n + 4)*log(c) - 1/4*(5*n + 4)*log(x)))/(a^2*n)","A",0
2772,0,0,0,0.970676," ","integrate((c*x)^(4+n)/(a+b*x^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(c x\right)^{n + 4}}{b x^{n} + a}, x\right)"," ",0,"integral((c*x)^(n + 4)/(b*x^n + a), x)","F",0
2773,0,0,0,0.878554," ","integrate((c*x)^(3+n)/(a+b*x^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(c x\right)^{n + 3}}{b x^{n} + a}, x\right)"," ",0,"integral((c*x)^(n + 3)/(b*x^n + a), x)","F",0
2774,0,0,0,0.845491," ","integrate((c*x)^(2+n)/(a+b*x^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(c x\right)^{n + 2}}{b x^{n} + a}, x\right)"," ",0,"integral((c*x)^(n + 2)/(b*x^n + a), x)","F",0
2775,0,0,0,1.078209," ","integrate((c*x)^(1+n)/(a+b*x^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(c x\right)^{n + 1}}{b x^{n} + a}, x\right)"," ",0,"integral((c*x)^(n + 1)/(b*x^n + a), x)","F",0
2776,0,0,0,1.013515," ","integrate((c*x)^n/(a+b*x^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(c x\right)^{n}}{b x^{n} + a}, x\right)"," ",0,"integral((c*x)^n/(b*x^n + a), x)","F",0
2777,1,20,0,0.844522," ","integrate((c*x)^(-1+n)/(a+b*x^n),x, algorithm=""fricas"")","\frac{c^{n - 1} \log\left(b x^{n} + a\right)}{b n}"," ",0,"c^(n - 1)*log(b*x^n + a)/(b*n)","A",0
2778,0,0,0,1.246087," ","integrate((c*x)^(-2+n)/(a+b*x^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(c x\right)^{n - 2}}{b x^{n} + a}, x\right)"," ",0,"integral((c*x)^(n - 2)/(b*x^n + a), x)","F",0
2779,0,0,0,0.854448," ","integrate((c*x)^(-3+n)/(a+b*x^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(c x\right)^{n - 3}}{b x^{n} + a}, x\right)"," ",0,"integral((c*x)^(n - 3)/(b*x^n + a), x)","F",0
2780,1,22,0,0.892564," ","integrate((c*x)^(-1+n)/(a+b*x^n)^2,x, algorithm=""fricas"")","-\frac{c^{n - 1}}{b^{2} n x^{n} + a b n}"," ",0,"-c^(n - 1)/(b^2*n*x^n + a*b*n)","A",0
2781,1,231,0,1.178301," ","integrate((c*x)^(-1+7/2*n)/(a+b*x^n)^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, a^{3} \sqrt{b} c^{\frac{7}{2} \, n - 1} \log\left(2 \, \sqrt{b x^{n} + a} \sqrt{b} x^{\frac{1}{2} \, n} - 2 \, b x^{n} - a\right) + 2 \, {\left(8 \, b^{3} c^{\frac{7}{2} \, n - 1} x^{\frac{5}{2} \, n} - 10 \, a b^{2} c^{\frac{7}{2} \, n - 1} x^{\frac{3}{2} \, n} + 15 \, a^{2} b c^{\frac{7}{2} \, n - 1} x^{\frac{1}{2} \, n}\right)} \sqrt{b x^{n} + a}}{48 \, b^{4} n}, \frac{15 \, a^{3} \sqrt{-b} c^{\frac{7}{2} \, n - 1} \arctan\left(\frac{\sqrt{-b} x^{\frac{1}{2} \, n}}{\sqrt{b x^{n} + a}}\right) + {\left(8 \, b^{3} c^{\frac{7}{2} \, n - 1} x^{\frac{5}{2} \, n} - 10 \, a b^{2} c^{\frac{7}{2} \, n - 1} x^{\frac{3}{2} \, n} + 15 \, a^{2} b c^{\frac{7}{2} \, n - 1} x^{\frac{1}{2} \, n}\right)} \sqrt{b x^{n} + a}}{24 \, b^{4} n}\right]"," ",0,"[1/48*(15*a^3*sqrt(b)*c^(7/2*n - 1)*log(2*sqrt(b*x^n + a)*sqrt(b)*x^(1/2*n) - 2*b*x^n - a) + 2*(8*b^3*c^(7/2*n - 1)*x^(5/2*n) - 10*a*b^2*c^(7/2*n - 1)*x^(3/2*n) + 15*a^2*b*c^(7/2*n - 1)*x^(1/2*n))*sqrt(b*x^n + a))/(b^4*n), 1/24*(15*a^3*sqrt(-b)*c^(7/2*n - 1)*arctan(sqrt(-b)*x^(1/2*n)/sqrt(b*x^n + a)) + (8*b^3*c^(7/2*n - 1)*x^(5/2*n) - 10*a*b^2*c^(7/2*n - 1)*x^(3/2*n) + 15*a^2*b*c^(7/2*n - 1)*x^(1/2*n))*sqrt(b*x^n + a))/(b^4*n)]","A",0
2782,1,192,0,1.190350," ","integrate((c*x)^(-1+5/2*n)/(a+b*x^n)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, a^{2} \sqrt{b} c^{\frac{5}{2} \, n - 1} \log\left(-2 \, \sqrt{b x^{n} + a} \sqrt{b} x^{\frac{1}{2} \, n} - 2 \, b x^{n} - a\right) + 2 \, {\left(2 \, b^{2} c^{\frac{5}{2} \, n - 1} x^{\frac{3}{2} \, n} - 3 \, a b c^{\frac{5}{2} \, n - 1} x^{\frac{1}{2} \, n}\right)} \sqrt{b x^{n} + a}}{8 \, b^{3} n}, -\frac{3 \, a^{2} \sqrt{-b} c^{\frac{5}{2} \, n - 1} \arctan\left(\frac{\sqrt{-b} x^{\frac{1}{2} \, n}}{\sqrt{b x^{n} + a}}\right) - {\left(2 \, b^{2} c^{\frac{5}{2} \, n - 1} x^{\frac{3}{2} \, n} - 3 \, a b c^{\frac{5}{2} \, n - 1} x^{\frac{1}{2} \, n}\right)} \sqrt{b x^{n} + a}}{4 \, b^{3} n}\right]"," ",0,"[1/8*(3*a^2*sqrt(b)*c^(5/2*n - 1)*log(-2*sqrt(b*x^n + a)*sqrt(b)*x^(1/2*n) - 2*b*x^n - a) + 2*(2*b^2*c^(5/2*n - 1)*x^(3/2*n) - 3*a*b*c^(5/2*n - 1)*x^(1/2*n))*sqrt(b*x^n + a))/(b^3*n), -1/4*(3*a^2*sqrt(-b)*c^(5/2*n - 1)*arctan(sqrt(-b)*x^(1/2*n)/sqrt(b*x^n + a)) - (2*b^2*c^(5/2*n - 1)*x^(3/2*n) - 3*a*b*c^(5/2*n - 1)*x^(1/2*n))*sqrt(b*x^n + a))/(b^3*n)]","A",0
2783,1,142,0,1.223315," ","integrate((c*x)^(-1+3/2*n)/(a+b*x^n)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{b x^{n} + a} b c^{\frac{3}{2} \, n - 1} x^{\frac{1}{2} \, n} + a \sqrt{b} c^{\frac{3}{2} \, n - 1} \log\left(2 \, \sqrt{b x^{n} + a} \sqrt{b} x^{\frac{1}{2} \, n} - 2 \, b x^{n} - a\right)}{2 \, b^{2} n}, \frac{\sqrt{b x^{n} + a} b c^{\frac{3}{2} \, n - 1} x^{\frac{1}{2} \, n} + a \sqrt{-b} c^{\frac{3}{2} \, n - 1} \arctan\left(\frac{\sqrt{-b} x^{\frac{1}{2} \, n}}{\sqrt{b x^{n} + a}}\right)}{b^{2} n}\right]"," ",0,"[1/2*(2*sqrt(b*x^n + a)*b*c^(3/2*n - 1)*x^(1/2*n) + a*sqrt(b)*c^(3/2*n - 1)*log(2*sqrt(b*x^n + a)*sqrt(b)*x^(1/2*n) - 2*b*x^n - a))/(b^2*n), (sqrt(b*x^n + a)*b*c^(3/2*n - 1)*x^(1/2*n) + a*sqrt(-b)*c^(3/2*n - 1)*arctan(sqrt(-b)*x^(1/2*n)/sqrt(b*x^n + a)))/(b^2*n)]","A",0
2784,-2,0,0,0.000000," ","integrate((c*x)^(-1+1/2*n)/(a+b*x^n)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
2785,-2,0,0,0.000000," ","integrate((c*x)^(-1-1/2*n)/(a+b*x^n)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
2786,-2,0,0,0.000000," ","integrate((c*x)^(-1-3/2*n)/(a+b*x^n)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
2787,-2,0,0,0.000000," ","integrate((c*x)^(-1-5/2*n)/(a+b*x^n)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
2788,-2,0,0,0.000000," ","integrate((c*x)^(-1-7/2*n)/(a+b*x^n)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
2789,0,0,0,1.484775," ","integrate((c*x)^m*(a+b*x^n)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{n} + a\right)}^{p} \left(c x\right)^{m}, x\right)"," ",0,"integral((b*x^n + a)^p*(c*x)^m, x)","F",0
2790,0,0,0,0.981001," ","integrate((c*x)^(3*n)*(a+b*x^n)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{n} + a\right)}^{p} \left(c x\right)^{3 \, n}, x\right)"," ",0,"integral((b*x^n + a)^p*(c*x)^(3*n), x)","F",0
2791,0,0,0,1.148063," ","integrate((c*x)^(2*n)*(a+b*x^n)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{n} + a\right)}^{p} \left(c x\right)^{2 \, n}, x\right)"," ",0,"integral((b*x^n + a)^p*(c*x)^(2*n), x)","F",0
2792,0,0,0,1.004228," ","integrate((c*x)^n*(a+b*x^n)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{n} + a\right)}^{p} \left(c x\right)^{n}, x\right)"," ",0,"integral((b*x^n + a)^p*(c*x)^n, x)","F",0
2793,0,0,0,1.007020," ","integrate((a+b*x^n)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{n} + a\right)}^{p}, x\right)"," ",0,"integral((b*x^n + a)^p, x)","F",0
2794,0,0,0,1.244622," ","integrate((a+b*x^n)^p/((c*x)^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{n} + a\right)}^{p}}{\left(c x\right)^{n}}, x\right)"," ",0,"integral((b*x^n + a)^p/(c*x)^n, x)","F",0
2795,0,0,0,1.061313," ","integrate((a+b*x^n)^p/((c*x)^(2*n)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{n} + a\right)}^{p}}{\left(c x\right)^{2 \, n}}, x\right)"," ",0,"integral((b*x^n + a)^p/(c*x)^(2*n), x)","F",0
2796,0,0,0,0.868596," ","integrate((a+b*x^n)^p/((c*x)^(3*n)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{n} + a\right)}^{p}}{\left(c x\right)^{3 \, n}}, x\right)"," ",0,"integral((b*x^n + a)^p/(c*x)^(3*n), x)","F",0
2797,0,0,0,1.101330," ","integrate((c*x)^(-n*p-1)*(a+b*x^n)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{n} + a\right)}^{p} \left(c x\right)^{-n p - 1}, x\right)"," ",0,"integral((b*x^n + a)^p*(c*x)^(-n*p - 1), x)","F",0
2798,1,75,0,0.837788," ","integrate((c*x)^(-n*p-n-1)*(a+b*x^n)^p,x, algorithm=""fricas"")","-\frac{{\left(b x x^{n} e^{\left(-{\left(n p + n + 1\right)} \log\left(c\right) - {\left(n p + n + 1\right)} \log\left(x\right)\right)} + a x e^{\left(-{\left(n p + n + 1\right)} \log\left(c\right) - {\left(n p + n + 1\right)} \log\left(x\right)\right)}\right)} {\left(b x^{n} + a\right)}^{p}}{a n p + a n}"," ",0,"-(b*x*x^n*e^(-(n*p + n + 1)*log(c) - (n*p + n + 1)*log(x)) + a*x*e^(-(n*p + n + 1)*log(c) - (n*p + n + 1)*log(x)))*(b*x^n + a)^p/(a*n*p + a*n)","A",0
2799,1,144,0,1.027603," ","integrate((c*x)^(-n*p-2*n-1)*(a+b*x^n)^p,x, algorithm=""fricas"")","-\frac{{\left(a b p x x^{n} e^{\left(-{\left(n p + 2 \, n + 1\right)} \log\left(c\right) - {\left(n p + 2 \, n + 1\right)} \log\left(x\right)\right)} - b^{2} x x^{2 \, n} e^{\left(-{\left(n p + 2 \, n + 1\right)} \log\left(c\right) - {\left(n p + 2 \, n + 1\right)} \log\left(x\right)\right)} + {\left(a^{2} p + a^{2}\right)} x e^{\left(-{\left(n p + 2 \, n + 1\right)} \log\left(c\right) - {\left(n p + 2 \, n + 1\right)} \log\left(x\right)\right)}\right)} {\left(b x^{n} + a\right)}^{p}}{a^{2} n p^{2} + 3 \, a^{2} n p + 2 \, a^{2} n}"," ",0,"-(a*b*p*x*x^n*e^(-(n*p + 2*n + 1)*log(c) - (n*p + 2*n + 1)*log(x)) - b^2*x*x^(2*n)*e^(-(n*p + 2*n + 1)*log(c) - (n*p + 2*n + 1)*log(x)) + (a^2*p + a^2)*x*e^(-(n*p + 2*n + 1)*log(c) - (n*p + 2*n + 1)*log(x)))*(b*x^n + a)^p/(a^2*n*p^2 + 3*a^2*n*p + 2*a^2*n)","A",0
2800,1,215,0,0.795094," ","integrate((c*x)^(-n*p-3*n-1)*(a+b*x^n)^p,x, algorithm=""fricas"")","\frac{{\left(2 \, a b^{2} p x x^{2 \, n} e^{\left(-{\left(n p + 3 \, n + 1\right)} \log\left(c\right) - {\left(n p + 3 \, n + 1\right)} \log\left(x\right)\right)} - 2 \, b^{3} x x^{3 \, n} e^{\left(-{\left(n p + 3 \, n + 1\right)} \log\left(c\right) - {\left(n p + 3 \, n + 1\right)} \log\left(x\right)\right)} - {\left(a^{2} b p^{2} + a^{2} b p\right)} x x^{n} e^{\left(-{\left(n p + 3 \, n + 1\right)} \log\left(c\right) - {\left(n p + 3 \, n + 1\right)} \log\left(x\right)\right)} - {\left(a^{3} p^{2} + 3 \, a^{3} p + 2 \, a^{3}\right)} x e^{\left(-{\left(n p + 3 \, n + 1\right)} \log\left(c\right) - {\left(n p + 3 \, n + 1\right)} \log\left(x\right)\right)}\right)} {\left(b x^{n} + a\right)}^{p}}{a^{3} n p^{3} + 6 \, a^{3} n p^{2} + 11 \, a^{3} n p + 6 \, a^{3} n}"," ",0,"(2*a*b^2*p*x*x^(2*n)*e^(-(n*p + 3*n + 1)*log(c) - (n*p + 3*n + 1)*log(x)) - 2*b^3*x*x^(3*n)*e^(-(n*p + 3*n + 1)*log(c) - (n*p + 3*n + 1)*log(x)) - (a^2*b*p^2 + a^2*b*p)*x*x^n*e^(-(n*p + 3*n + 1)*log(c) - (n*p + 3*n + 1)*log(x)) - (a^3*p^2 + 3*a^3*p + 2*a^3)*x*e^(-(n*p + 3*n + 1)*log(c) - (n*p + 3*n + 1)*log(x)))*(b*x^n + a)^p/(a^3*n*p^3 + 6*a^3*n*p^2 + 11*a^3*n*p + 6*a^3*n)","A",0
2801,1,294,0,1.294944," ","integrate((c*x)^(-n*p-4*n-1)*(a+b*x^n)^p,x, algorithm=""fricas"")","-\frac{{\left(6 \, a b^{3} p x x^{3 \, n} e^{\left(-{\left(n p + 4 \, n + 1\right)} \log\left(c\right) - {\left(n p + 4 \, n + 1\right)} \log\left(x\right)\right)} - 6 \, b^{4} x x^{4 \, n} e^{\left(-{\left(n p + 4 \, n + 1\right)} \log\left(c\right) - {\left(n p + 4 \, n + 1\right)} \log\left(x\right)\right)} - 3 \, {\left(a^{2} b^{2} p^{2} + a^{2} b^{2} p\right)} x x^{2 \, n} e^{\left(-{\left(n p + 4 \, n + 1\right)} \log\left(c\right) - {\left(n p + 4 \, n + 1\right)} \log\left(x\right)\right)} + {\left(a^{3} b p^{3} + 3 \, a^{3} b p^{2} + 2 \, a^{3} b p\right)} x x^{n} e^{\left(-{\left(n p + 4 \, n + 1\right)} \log\left(c\right) - {\left(n p + 4 \, n + 1\right)} \log\left(x\right)\right)} + {\left(a^{4} p^{3} + 6 \, a^{4} p^{2} + 11 \, a^{4} p + 6 \, a^{4}\right)} x e^{\left(-{\left(n p + 4 \, n + 1\right)} \log\left(c\right) - {\left(n p + 4 \, n + 1\right)} \log\left(x\right)\right)}\right)} {\left(b x^{n} + a\right)}^{p}}{a^{4} n p^{4} + 10 \, a^{4} n p^{3} + 35 \, a^{4} n p^{2} + 50 \, a^{4} n p + 24 \, a^{4} n}"," ",0,"-(6*a*b^3*p*x*x^(3*n)*e^(-(n*p + 4*n + 1)*log(c) - (n*p + 4*n + 1)*log(x)) - 6*b^4*x*x^(4*n)*e^(-(n*p + 4*n + 1)*log(c) - (n*p + 4*n + 1)*log(x)) - 3*(a^2*b^2*p^2 + a^2*b^2*p)*x*x^(2*n)*e^(-(n*p + 4*n + 1)*log(c) - (n*p + 4*n + 1)*log(x)) + (a^3*b*p^3 + 3*a^3*b*p^2 + 2*a^3*b*p)*x*x^n*e^(-(n*p + 4*n + 1)*log(c) - (n*p + 4*n + 1)*log(x)) + (a^4*p^3 + 6*a^4*p^2 + 11*a^4*p + 6*a^4)*x*e^(-(n*p + 4*n + 1)*log(c) - (n*p + 4*n + 1)*log(x)))*(b*x^n + a)^p/(a^4*n*p^4 + 10*a^4*n*p^3 + 35*a^4*n*p^2 + 50*a^4*n*p + 24*a^4*n)","A",0
2802,1,103,0,1.301777," ","integrate((c*(b*x+a)^2)^(5/2),x, algorithm=""fricas"")","\frac{{\left(b^{5} c^{2} x^{6} + 6 \, a b^{4} c^{2} x^{5} + 15 \, a^{2} b^{3} c^{2} x^{4} + 20 \, a^{3} b^{2} c^{2} x^{3} + 15 \, a^{4} b c^{2} x^{2} + 6 \, a^{5} c^{2} x\right)} \sqrt{b^{2} c x^{2} + 2 \, a b c x + a^{2} c}}{6 \, {\left(b x + a\right)}}"," ",0,"1/6*(b^5*c^2*x^6 + 6*a*b^4*c^2*x^5 + 15*a^2*b^3*c^2*x^4 + 20*a^3*b^2*c^2*x^3 + 15*a^4*b*c^2*x^2 + 6*a^5*c^2*x)*sqrt(b^2*c*x^2 + 2*a*b*c*x + a^2*c)/(b*x + a)","B",0
2803,1,67,0,1.393840," ","integrate((c*(b*x+a)^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left(b^{3} c x^{4} + 4 \, a b^{2} c x^{3} + 6 \, a^{2} b c x^{2} + 4 \, a^{3} c x\right)} \sqrt{b^{2} c x^{2} + 2 \, a b c x + a^{2} c}}{4 \, {\left(b x + a\right)}}"," ",0,"1/4*(b^3*c*x^4 + 4*a*b^2*c*x^3 + 6*a^2*b*c*x^2 + 4*a^3*c*x)*sqrt(b^2*c*x^2 + 2*a*b*c*x + a^2*c)/(b*x + a)","B",0
2804,1,41,0,0.905149," ","integrate((c*(b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{b^{2} c x^{2} + 2 \, a b c x + a^{2} c} {\left(b x^{2} + 2 \, a x\right)}}{2 \, {\left(b x + a\right)}}"," ",0,"1/2*sqrt(b^2*c*x^2 + 2*a*b*c*x + a^2*c)*(b*x^2 + 2*a*x)/(b*x + a)","A",0
2805,1,42,0,1.228809," ","integrate(1/(c*(b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{b^{2} c x^{2} + 2 \, a b c x + a^{2} c} \log\left(b x + a\right)}{b^{2} c x + a b c}"," ",0,"sqrt(b^2*c*x^2 + 2*a*b*c*x + a^2*c)*log(b*x + a)/(b^2*c*x + a*b*c)","A",0
2806,1,69,0,1.288456," ","integrate(1/(c*(b*x+a)^2)^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{b^{2} c x^{2} + 2 \, a b c x + a^{2} c}}{2 \, {\left(b^{4} c^{2} x^{3} + 3 \, a b^{3} c^{2} x^{2} + 3 \, a^{2} b^{2} c^{2} x + a^{3} b c^{2}\right)}}"," ",0,"-1/2*sqrt(b^2*c*x^2 + 2*a*b*c*x + a^2*c)/(b^4*c^2*x^3 + 3*a*b^3*c^2*x^2 + 3*a^2*b^2*c^2*x + a^3*b*c^2)","B",0
2807,1,97,0,1.193582," ","integrate(1/(c*(b*x+a)^2)^(5/2),x, algorithm=""fricas"")","-\frac{\sqrt{b^{2} c x^{2} + 2 \, a b c x + a^{2} c}}{4 \, {\left(b^{6} c^{3} x^{5} + 5 \, a b^{5} c^{3} x^{4} + 10 \, a^{2} b^{4} c^{3} x^{3} + 10 \, a^{3} b^{3} c^{3} x^{2} + 5 \, a^{4} b^{2} c^{3} x + a^{5} b c^{3}\right)}}"," ",0,"-1/4*sqrt(b^2*c*x^2 + 2*a*b*c*x + a^2*c)/(b^6*c^3*x^5 + 5*a*b^5*c^3*x^4 + 10*a^2*b^4*c^3*x^3 + 10*a^3*b^3*c^3*x^2 + 5*a^4*b^2*c^3*x + a^5*b*c^3)","B",0
2808,1,9,0,1.033282," ","integrate(((3+5*x)^2)^(1/2),x, algorithm=""fricas"")","\frac{5}{2} \, x^{2} + 3 \, x"," ",0,"5/2*x^2 + 3*x","A",0
2809,1,9,0,1.306592," ","integrate(((6+10*x)^2)^(1/2),x, algorithm=""fricas"")","5 \, x^{2} + 6 \, x"," ",0,"5*x^2 + 6*x","A",0
2810,1,8,0,1.051675," ","integrate(1/((3+5*x)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{5} \, \log\left(5 \, x + 3\right)"," ",0,"1/5*log(5*x + 3)","A",0
2811,1,8,0,1.015911," ","integrate(1/((6+10*x)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{10} \, \log\left(5 \, x + 3\right)"," ",0,"1/10*log(5*x + 3)","A",0
2812,1,6,0,0.824651," ","integrate(1/(-(2+3*x)^2)^(1/2),x, algorithm=""fricas"")","-\frac{1}{3} i \, \log\left(x + \frac{2}{3}\right)"," ",0,"-1/3*I*log(x + 2/3)","C",0
2813,1,135,0,0.820741," ","integrate((c*(b*x+a)^3)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(b^{7} c^{2} x^{7} + 7 \, a b^{6} c^{2} x^{6} + 21 \, a^{2} b^{5} c^{2} x^{5} + 35 \, a^{3} b^{4} c^{2} x^{4} + 35 \, a^{4} b^{3} c^{2} x^{3} + 21 \, a^{5} b^{2} c^{2} x^{2} + 7 \, a^{6} b c^{2} x + a^{7} c^{2}\right)} \sqrt{b^{3} c x^{3} + 3 \, a b^{2} c x^{2} + 3 \, a^{2} b c x + a^{3} c}}{17 \, b}"," ",0,"2/17*(b^7*c^2*x^7 + 7*a*b^6*c^2*x^6 + 21*a^2*b^5*c^2*x^5 + 35*a^3*b^4*c^2*x^4 + 35*a^4*b^3*c^2*x^3 + 21*a^5*b^2*c^2*x^2 + 7*a^6*b*c^2*x + a^7*c^2)*sqrt(b^3*c*x^3 + 3*a*b^2*c*x^2 + 3*a^2*b*c*x + a^3*c)/b","B",0
2814,1,83,0,1.030104," ","integrate((c*(b*x+a)^3)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(b^{4} c x^{4} + 4 \, a b^{3} c x^{3} + 6 \, a^{2} b^{2} c x^{2} + 4 \, a^{3} b c x + a^{4} c\right)} \sqrt{b^{3} c x^{3} + 3 \, a b^{2} c x^{2} + 3 \, a^{2} b c x + a^{3} c}}{11 \, b}"," ",0,"2/11*(b^4*c*x^4 + 4*a*b^3*c*x^3 + 6*a^2*b^2*c*x^2 + 4*a^3*b*c*x + a^4*c)*sqrt(b^3*c*x^3 + 3*a*b^2*c*x^2 + 3*a^2*b*c*x + a^3*c)/b","B",0
2815,1,44,0,0.805246," ","integrate((c*(b*x+a)^3)^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{b^{3} c x^{3} + 3 \, a b^{2} c x^{2} + 3 \, a^{2} b c x + a^{3} c} {\left(b x + a\right)}}{5 \, b}"," ",0,"2/5*sqrt(b^3*c*x^3 + 3*a*b^2*c*x^2 + 3*a^2*b*c*x + a^3*c)*(b*x + a)/b","B",0
2816,1,61,0,0.908991," ","integrate(1/(c*(b*x+a)^3)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{b^{3} c x^{3} + 3 \, a b^{2} c x^{2} + 3 \, a^{2} b c x + a^{3} c}}{b^{3} c x^{2} + 2 \, a b^{2} c x + a^{2} b c}"," ",0,"-2*sqrt(b^3*c*x^3 + 3*a*b^2*c*x^2 + 3*a^2*b*c*x + a^3*c)/(b^3*c*x^2 + 2*a*b^2*c*x + a^2*b*c)","B",0
2817,1,109,0,1.097344," ","integrate(1/(c*(b*x+a)^3)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{b^{3} c x^{3} + 3 \, a b^{2} c x^{2} + 3 \, a^{2} b c x + a^{3} c}}{7 \, {\left(b^{6} c^{2} x^{5} + 5 \, a b^{5} c^{2} x^{4} + 10 \, a^{2} b^{4} c^{2} x^{3} + 10 \, a^{3} b^{3} c^{2} x^{2} + 5 \, a^{4} b^{2} c^{2} x + a^{5} b c^{2}\right)}}"," ",0,"-2/7*sqrt(b^3*c*x^3 + 3*a*b^2*c*x^2 + 3*a^2*b*c*x + a^3*c)/(b^6*c^2*x^5 + 5*a*b^5*c^2*x^4 + 10*a^2*b^4*c^2*x^3 + 10*a^3*b^3*c^2*x^2 + 5*a^4*b^2*c^2*x + a^5*b*c^2)","B",0
2818,1,151,0,0.918103," ","integrate(1/(c*(b*x+a)^3)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{b^{3} c x^{3} + 3 \, a b^{2} c x^{2} + 3 \, a^{2} b c x + a^{3} c}}{13 \, {\left(b^{9} c^{3} x^{8} + 8 \, a b^{8} c^{3} x^{7} + 28 \, a^{2} b^{7} c^{3} x^{6} + 56 \, a^{3} b^{6} c^{3} x^{5} + 70 \, a^{4} b^{5} c^{3} x^{4} + 56 \, a^{5} b^{4} c^{3} x^{3} + 28 \, a^{6} b^{3} c^{3} x^{2} + 8 \, a^{7} b^{2} c^{3} x + a^{8} b c^{3}\right)}}"," ",0,"-2/13*sqrt(b^3*c*x^3 + 3*a*b^2*c*x^2 + 3*a^2*b*c*x + a^3*c)/(b^9*c^3*x^8 + 8*a*b^8*c^3*x^7 + 28*a^2*b^7*c^3*x^6 + 56*a^3*b^6*c^3*x^5 + 70*a^4*b^5*c^3*x^4 + 56*a^5*b^4*c^3*x^3 + 28*a^6*b^3*c^3*x^2 + 8*a^7*b^2*c^3*x + a^8*b*c^3)","B",0
2819,1,27,0,0.690821," ","integrate((c/(b*x+a))^(5/2),x, algorithm=""fricas"")","-\frac{2 \, c^{2} \sqrt{\frac{c}{b x + a}}}{3 \, {\left(b^{2} x + a b\right)}}"," ",0,"-2/3*c^2*sqrt(c/(b*x + a))/(b^2*x + a*b)","A",0
2820,1,17,0,0.915334," ","integrate((c/(b*x+a))^(3/2),x, algorithm=""fricas"")","-\frac{2 \, c \sqrt{\frac{c}{b x + a}}}{b}"," ",0,"-2*c*sqrt(c/(b*x + a))/b","A",0
2821,1,21,0,0.685181," ","integrate((c/(b*x+a))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(b x + a\right)} \sqrt{\frac{c}{b x + a}}}{b}"," ",0,"2*(b*x + a)*sqrt(c/(b*x + a))/b","A",0
2822,1,35,0,1.018378," ","integrate(1/(c/(b*x+a))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)} \sqrt{\frac{c}{b x + a}}}{3 \, b c}"," ",0,"2/3*(b^2*x^2 + 2*a*b*x + a^2)*sqrt(c/(b*x + a))/(b*c)","A",0
2823,1,46,0,0.882987," ","integrate(1/(c/(b*x+a))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3}\right)} \sqrt{\frac{c}{b x + a}}}{5 \, b c^{2}}"," ",0,"2/5*(b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x + a^3)*sqrt(c/(b*x + a))/(b*c^2)","A",0
2824,1,57,0,0.993581," ","integrate(1/(c/(b*x+a))^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(b^{4} x^{4} + 4 \, a b^{3} x^{3} + 6 \, a^{2} b^{2} x^{2} + 4 \, a^{3} b x + a^{4}\right)} \sqrt{\frac{c}{b x + a}}}{7 \, b c^{3}}"," ",0,"2/7*(b^4*x^4 + 4*a*b^3*x^3 + 6*a^2*b^2*x^2 + 4*a^3*b*x + a^4)*sqrt(c/(b*x + a))/(b*c^3)","B",0
2825,1,60,0,0.977695," ","integrate((c/(b*x+a)^2)^(5/2),x, algorithm=""fricas"")","-\frac{c^{2} \sqrt{\frac{c}{b^{2} x^{2} + 2 \, a b x + a^{2}}}}{4 \, {\left(b^{4} x^{3} + 3 \, a b^{3} x^{2} + 3 \, a^{2} b^{2} x + a^{3} b\right)}}"," ",0,"-1/4*c^2*sqrt(c/(b^2*x^2 + 2*a*b*x + a^2))/(b^4*x^3 + 3*a*b^3*x^2 + 3*a^2*b^2*x + a^3*b)","B",0
2826,1,36,0,1.331063," ","integrate((c/(b*x+a)^2)^(3/2),x, algorithm=""fricas"")","-\frac{c \sqrt{\frac{c}{b^{2} x^{2} + 2 \, a b x + a^{2}}}}{2 \, {\left(b^{2} x + a b\right)}}"," ",0,"-1/2*c*sqrt(c/(b^2*x^2 + 2*a*b*x + a^2))/(b^2*x + a*b)","A",0
2827,1,37,0,1.180244," ","integrate((c/(b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{{\left(b x + a\right)} \sqrt{\frac{c}{b^{2} x^{2} + 2 \, a b x + a^{2}}} \log\left(b x + a\right)}{b}"," ",0,"(b*x + a)*sqrt(c/(b^2*x^2 + 2*a*b*x + a^2))*log(b*x + a)/b","A",0
2828,1,48,0,1.025028," ","integrate(1/(c/(b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{{\left(b^{2} x^{3} + 3 \, a b x^{2} + 2 \, a^{2} x\right)} \sqrt{\frac{c}{b^{2} x^{2} + 2 \, a b x + a^{2}}}}{2 \, c}"," ",0,"1/2*(b^2*x^3 + 3*a*b*x^2 + 2*a^2*x)*sqrt(c/(b^2*x^2 + 2*a*b*x + a^2))/c","B",0
2829,1,70,0,1.192029," ","integrate(1/(c/(b*x+a)^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left(b^{4} x^{5} + 5 \, a b^{3} x^{4} + 10 \, a^{2} b^{2} x^{3} + 10 \, a^{3} b x^{2} + 4 \, a^{4} x\right)} \sqrt{\frac{c}{b^{2} x^{2} + 2 \, a b x + a^{2}}}}{4 \, c^{2}}"," ",0,"1/4*(b^4*x^5 + 5*a*b^3*x^4 + 10*a^2*b^2*x^3 + 10*a^3*b*x^2 + 4*a^4*x)*sqrt(c/(b^2*x^2 + 2*a*b*x + a^2))/c^2","B",0
2830,1,92,0,0.836935," ","integrate(1/(c/(b*x+a)^2)^(5/2),x, algorithm=""fricas"")","\frac{{\left(b^{6} x^{7} + 7 \, a b^{5} x^{6} + 21 \, a^{2} b^{4} x^{5} + 35 \, a^{3} b^{3} x^{4} + 35 \, a^{4} b^{2} x^{3} + 21 \, a^{5} b x^{2} + 6 \, a^{6} x\right)} \sqrt{\frac{c}{b^{2} x^{2} + 2 \, a b x + a^{2}}}}{6 \, c^{3}}"," ",0,"1/6*(b^6*x^7 + 7*a*b^5*x^6 + 21*a^2*b^4*x^5 + 35*a^3*b^3*x^4 + 35*a^4*b^2*x^3 + 21*a^5*b*x^2 + 6*a^6*x)*sqrt(c/(b^2*x^2 + 2*a*b*x + a^2))/c^3","B",0
2831,1,93,0,0.827218," ","integrate((c/(b*x+a)^3)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, c^{2} \sqrt{\frac{c}{b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3}}}}{13 \, {\left(b^{6} x^{5} + 5 \, a b^{5} x^{4} + 10 \, a^{2} b^{4} x^{3} + 10 \, a^{3} b^{3} x^{2} + 5 \, a^{4} b^{2} x + a^{5} b\right)}}"," ",0,"-2/13*c^2*sqrt(c/(b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x + a^3))/(b^6*x^5 + 5*a*b^5*x^4 + 10*a^2*b^4*x^3 + 10*a^3*b^3*x^2 + 5*a^4*b^2*x + a^5*b)","B",0
2832,1,58,0,1.043500," ","integrate((c/(b*x+a)^3)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, c \sqrt{\frac{c}{b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3}}}}{7 \, {\left(b^{3} x^{2} + 2 \, a b^{2} x + a^{2} b\right)}}"," ",0,"-2/7*c*sqrt(c/(b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x + a^3))/(b^3*x^2 + 2*a*b^2*x + a^2*b)","B",0
2833,1,43,0,0.595614," ","integrate((c/(b*x+a)^3)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(b x + a\right)} \sqrt{\frac{c}{b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3}}}}{b}"," ",0,"-2*(b*x + a)*sqrt(c/(b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x + a^3))/b","B",0
2834,1,79,0,1.066434," ","integrate(1/(c/(b*x+a)^3)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(b^{4} x^{4} + 4 \, a b^{3} x^{3} + 6 \, a^{2} b^{2} x^{2} + 4 \, a^{3} b x + a^{4}\right)} \sqrt{\frac{c}{b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3}}}}{5 \, b c}"," ",0,"2/5*(b^4*x^4 + 4*a*b^3*x^3 + 6*a^2*b^2*x^2 + 4*a^3*b*x + a^4)*sqrt(c/(b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x + a^3))/(b*c)","B",0
2835,1,112,0,0.852511," ","integrate(1/(c/(b*x+a)^3)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(b^{7} x^{7} + 7 \, a b^{6} x^{6} + 21 \, a^{2} b^{5} x^{5} + 35 \, a^{3} b^{4} x^{4} + 35 \, a^{4} b^{3} x^{3} + 21 \, a^{5} b^{2} x^{2} + 7 \, a^{6} b x + a^{7}\right)} \sqrt{\frac{c}{b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3}}}}{11 \, b c^{2}}"," ",0,"2/11*(b^7*x^7 + 7*a*b^6*x^6 + 21*a^2*b^5*x^5 + 35*a^3*b^4*x^4 + 35*a^4*b^3*x^3 + 21*a^5*b^2*x^2 + 7*a^6*b*x + a^7)*sqrt(c/(b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x + a^3))/(b*c^2)","B",0
2836,1,145,0,1.059716," ","integrate(1/(c/(b*x+a)^3)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(b^{10} x^{10} + 10 \, a b^{9} x^{9} + 45 \, a^{2} b^{8} x^{8} + 120 \, a^{3} b^{7} x^{7} + 210 \, a^{4} b^{6} x^{6} + 252 \, a^{5} b^{5} x^{5} + 210 \, a^{6} b^{4} x^{4} + 120 \, a^{7} b^{3} x^{3} + 45 \, a^{8} b^{2} x^{2} + 10 \, a^{9} b x + a^{10}\right)} \sqrt{\frac{c}{b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3}}}}{17 \, b c^{3}}"," ",0,"2/17*(b^10*x^10 + 10*a*b^9*x^9 + 45*a^2*b^8*x^8 + 120*a^3*b^7*x^7 + 210*a^4*b^6*x^6 + 252*a^5*b^5*x^5 + 210*a^6*b^4*x^4 + 120*a^7*b^3*x^3 + 45*a^8*b^2*x^2 + 10*a^9*b*x + a^10)*sqrt(c/(b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x + a^3))/(b*c^3)","B",0
2837,1,37,0,1.164761," ","integrate((c*(b*x+a)^(3/2))^(2/3),x, algorithm=""fricas"")","\frac{{\left(b x^{2} + 2 \, a x\right)} \left({\left(b c x + a c\right)} \sqrt{b x + a}\right)^{\frac{2}{3}}}{2 \, {\left(b x + a\right)}}"," ",0,"1/2*(b*x^2 + 2*a*x)*((b*c*x + a*c)*sqrt(b*x + a))^(2/3)/(b*x + a)","A",0
2838,1,17,0,1.180360," ","integrate((c*(b*x+a)^(2/3))^(3/2),x, algorithm=""fricas"")","\frac{1}{2} \, {\left(b c x^{2} + 2 \, a c x\right)} \sqrt{c}"," ",0,"1/2*(b*c*x^2 + 2*a*c*x)*sqrt(c)","A",0
2839,1,51,0,1.608572," ","integrate(1/(c/(b*x+a)^(3/2))^(2/3),x, algorithm=""fricas"")","\frac{{\left(b x^{2} + 2 \, a x\right)} \sqrt{b x + a} \left(\frac{\sqrt{b x + a} c}{b^{2} x^{2} + 2 \, a b x + a^{2}}\right)^{\frac{1}{3}}}{2 \, c}"," ",0,"1/2*(b*x^2 + 2*a*x)*sqrt(b*x + a)*(sqrt(b*x + a)*c/(b^2*x^2 + 2*a*b*x + a^2))^(1/3)/c","B",0
2840,1,15,0,0.582641," ","integrate(1/(c/(b*x+a)^(2/3))^(3/2),x, algorithm=""fricas"")","\frac{b x^{2} + 2 \, a x}{2 \, c^{\frac{3}{2}}}"," ",0,"1/2*(b*x^2 + 2*a*x)/c^(3/2)","A",0
2841,1,93,0,0.894168," ","integrate((d*x+c)^3*(a+b*(d*x+c)^2),x, algorithm=""fricas"")","\frac{1}{6} x^{6} d^{5} b + x^{5} d^{4} c b + \frac{5}{2} x^{4} d^{3} c^{2} b + \frac{10}{3} x^{3} d^{2} c^{3} b + \frac{5}{2} x^{2} d c^{4} b + \frac{1}{4} x^{4} d^{3} a + x c^{5} b + x^{3} d^{2} c a + \frac{3}{2} x^{2} d c^{2} a + x c^{3} a"," ",0,"1/6*x^6*d^5*b + x^5*d^4*c*b + 5/2*x^4*d^3*c^2*b + 10/3*x^3*d^2*c^3*b + 5/2*x^2*d*c^4*b + 1/4*x^4*d^3*a + x*c^5*b + x^3*d^2*c*a + 3/2*x^2*d*c^2*a + x*c^3*a","B",0
2842,1,207,0,0.450378," ","integrate((d*x+c)^3*(a+b*(d*x+c)^2)^2,x, algorithm=""fricas"")","\frac{1}{8} x^{8} d^{7} b^{2} + x^{7} d^{6} c b^{2} + \frac{7}{2} x^{6} d^{5} c^{2} b^{2} + 7 x^{5} d^{4} c^{3} b^{2} + \frac{35}{4} x^{4} d^{3} c^{4} b^{2} + \frac{1}{3} x^{6} d^{5} b a + 7 x^{3} d^{2} c^{5} b^{2} + 2 x^{5} d^{4} c b a + \frac{7}{2} x^{2} d c^{6} b^{2} + 5 x^{4} d^{3} c^{2} b a + x c^{7} b^{2} + \frac{20}{3} x^{3} d^{2} c^{3} b a + 5 x^{2} d c^{4} b a + \frac{1}{4} x^{4} d^{3} a^{2} + 2 x c^{5} b a + x^{3} d^{2} c a^{2} + \frac{3}{2} x^{2} d c^{2} a^{2} + x c^{3} a^{2}"," ",0,"1/8*x^8*d^7*b^2 + x^7*d^6*c*b^2 + 7/2*x^6*d^5*c^2*b^2 + 7*x^5*d^4*c^3*b^2 + 35/4*x^4*d^3*c^4*b^2 + 1/3*x^6*d^5*b*a + 7*x^3*d^2*c^5*b^2 + 2*x^5*d^4*c*b*a + 7/2*x^2*d*c^6*b^2 + 5*x^4*d^3*c^2*b*a + x*c^7*b^2 + 20/3*x^3*d^2*c^3*b*a + 5*x^2*d*c^4*b*a + 1/4*x^4*d^3*a^2 + 2*x*c^5*b*a + x^3*d^2*c*a^2 + 3/2*x^2*d*c^2*a^2 + x*c^3*a^2","B",0
2843,1,355,0,0.580010," ","integrate((d*x+c)^3*(a+b*(d*x+c)^2)^3,x, algorithm=""fricas"")","\frac{1}{10} x^{10} d^{9} b^{3} + x^{9} d^{8} c b^{3} + \frac{9}{2} x^{8} d^{7} c^{2} b^{3} + 12 x^{7} d^{6} c^{3} b^{3} + 21 x^{6} d^{5} c^{4} b^{3} + \frac{3}{8} x^{8} d^{7} b^{2} a + \frac{126}{5} x^{5} d^{4} c^{5} b^{3} + 3 x^{7} d^{6} c b^{2} a + 21 x^{4} d^{3} c^{6} b^{3} + \frac{21}{2} x^{6} d^{5} c^{2} b^{2} a + 12 x^{3} d^{2} c^{7} b^{3} + 21 x^{5} d^{4} c^{3} b^{2} a + \frac{9}{2} x^{2} d c^{8} b^{3} + \frac{105}{4} x^{4} d^{3} c^{4} b^{2} a + \frac{1}{2} x^{6} d^{5} b a^{2} + x c^{9} b^{3} + 21 x^{3} d^{2} c^{5} b^{2} a + 3 x^{5} d^{4} c b a^{2} + \frac{21}{2} x^{2} d c^{6} b^{2} a + \frac{15}{2} x^{4} d^{3} c^{2} b a^{2} + 3 x c^{7} b^{2} a + 10 x^{3} d^{2} c^{3} b a^{2} + \frac{15}{2} x^{2} d c^{4} b a^{2} + \frac{1}{4} x^{4} d^{3} a^{3} + 3 x c^{5} b a^{2} + x^{3} d^{2} c a^{3} + \frac{3}{2} x^{2} d c^{2} a^{3} + x c^{3} a^{3}"," ",0,"1/10*x^10*d^9*b^3 + x^9*d^8*c*b^3 + 9/2*x^8*d^7*c^2*b^3 + 12*x^7*d^6*c^3*b^3 + 21*x^6*d^5*c^4*b^3 + 3/8*x^8*d^7*b^2*a + 126/5*x^5*d^4*c^5*b^3 + 3*x^7*d^6*c*b^2*a + 21*x^4*d^3*c^6*b^3 + 21/2*x^6*d^5*c^2*b^2*a + 12*x^3*d^2*c^7*b^3 + 21*x^5*d^4*c^3*b^2*a + 9/2*x^2*d*c^8*b^3 + 105/4*x^4*d^3*c^4*b^2*a + 1/2*x^6*d^5*b*a^2 + x*c^9*b^3 + 21*x^3*d^2*c^5*b^2*a + 3*x^5*d^4*c*b*a^2 + 21/2*x^2*d*c^6*b^2*a + 15/2*x^4*d^3*c^2*b*a^2 + 3*x*c^7*b^2*a + 10*x^3*d^2*c^3*b*a^2 + 15/2*x^2*d*c^4*b*a^2 + 1/4*x^4*d^3*a^3 + 3*x*c^5*b*a^2 + x^3*d^2*c*a^3 + 3/2*x^2*d*c^2*a^3 + x*c^3*a^3","B",0
2844,1,11,0,1.667078," ","integrate((2+x)/(1+(2+x)^2),x, algorithm=""fricas"")","\frac{1}{2} \, \log\left(x^{2} + 4 \, x + 5\right)"," ",0,"1/2*log(x^2 + 4*x + 5)","A",0
2845,1,12,0,1.059400," ","integrate((2+x)/(1+(2+x)^2)^2,x, algorithm=""fricas"")","-\frac{1}{2 \, {\left(x^{2} + 4 \, x + 5\right)}}"," ",0,"-1/2/(x^2 + 4*x + 5)","A",0
2846,1,22,0,1.072726," ","integrate((2+x)/(1+(2+x)^2)^3,x, algorithm=""fricas"")","-\frac{1}{4 \, {\left(x^{4} + 8 \, x^{3} + 26 \, x^{2} + 40 \, x + 25\right)}}"," ",0,"-1/4/(x^4 + 8*x^3 + 26*x^2 + 40*x + 25)","A",0
2847,1,438,0,0.969033," ","integrate((d*x+c)^5*(a+b*(d*x+c)^2)^p,x, algorithm=""fricas"")","\frac{{\left(2 \, b^{3} c^{6} + {\left(b^{3} d^{6} p^{2} + 3 \, b^{3} d^{6} p + 2 \, b^{3} d^{6}\right)} x^{6} + 6 \, {\left(b^{3} c d^{5} p^{2} + 3 \, b^{3} c d^{5} p + 2 \, b^{3} c d^{5}\right)} x^{5} + {\left(30 \, b^{3} c^{2} d^{4} + {\left(15 \, b^{3} c^{2} + a b^{2}\right)} d^{4} p^{2} + {\left(45 \, b^{3} c^{2} + a b^{2}\right)} d^{4} p\right)} x^{4} + 4 \, {\left(10 \, b^{3} c^{3} d^{3} + {\left(5 \, b^{3} c^{3} + a b^{2} c\right)} d^{3} p^{2} + {\left(15 \, b^{3} c^{3} + a b^{2} c\right)} d^{3} p\right)} x^{3} + 2 \, a^{3} + {\left(b^{3} c^{6} + a b^{2} c^{4}\right)} p^{2} + {\left(30 \, b^{3} c^{4} d^{2} + 3 \, {\left(5 \, b^{3} c^{4} + 2 \, a b^{2} c^{2}\right)} d^{2} p^{2} + {\left(45 \, b^{3} c^{4} + 6 \, a b^{2} c^{2} - 2 \, a^{2} b\right)} d^{2} p\right)} x^{2} + {\left(3 \, b^{3} c^{6} + a b^{2} c^{4} - 2 \, a^{2} b c^{2}\right)} p + 2 \, {\left(6 \, b^{3} c^{5} d + {\left(3 \, b^{3} c^{5} + 2 \, a b^{2} c^{3}\right)} d p^{2} + {\left(9 \, b^{3} c^{5} + 2 \, a b^{2} c^{3} - 2 \, a^{2} b c\right)} d p\right)} x\right)} {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a\right)}^{p}}{2 \, {\left(b^{3} d p^{3} + 6 \, b^{3} d p^{2} + 11 \, b^{3} d p + 6 \, b^{3} d\right)}}"," ",0,"1/2*(2*b^3*c^6 + (b^3*d^6*p^2 + 3*b^3*d^6*p + 2*b^3*d^6)*x^6 + 6*(b^3*c*d^5*p^2 + 3*b^3*c*d^5*p + 2*b^3*c*d^5)*x^5 + (30*b^3*c^2*d^4 + (15*b^3*c^2 + a*b^2)*d^4*p^2 + (45*b^3*c^2 + a*b^2)*d^4*p)*x^4 + 4*(10*b^3*c^3*d^3 + (5*b^3*c^3 + a*b^2*c)*d^3*p^2 + (15*b^3*c^3 + a*b^2*c)*d^3*p)*x^3 + 2*a^3 + (b^3*c^6 + a*b^2*c^4)*p^2 + (30*b^3*c^4*d^2 + 3*(5*b^3*c^4 + 2*a*b^2*c^2)*d^2*p^2 + (45*b^3*c^4 + 6*a*b^2*c^2 - 2*a^2*b)*d^2*p)*x^2 + (3*b^3*c^6 + a*b^2*c^4 - 2*a^2*b*c^2)*p + 2*(6*b^3*c^5*d + (3*b^3*c^5 + 2*a*b^2*c^3)*d*p^2 + (9*b^3*c^5 + 2*a*b^2*c^3 - 2*a^2*b*c)*d*p)*x)*(b*d^2*x^2 + 2*b*c*d*x + b*c^2 + a)^p/(b^3*d*p^3 + 6*b^3*d*p^2 + 11*b^3*d*p + 6*b^3*d)","B",0
2848,0,0,0,1.007349," ","integrate((d*x+c)^4*(a+b*(d*x+c)^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(d^{4} x^{4} + 4 \, c d^{3} x^{3} + 6 \, c^{2} d^{2} x^{2} + 4 \, c^{3} d x + c^{4}\right)} {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a\right)}^{p}, x\right)"," ",0,"integral((d^4*x^4 + 4*c*d^3*x^3 + 6*c^2*d^2*x^2 + 4*c^3*d*x + c^4)*(b*d^2*x^2 + 2*b*c*d*x + b*c^2 + a)^p, x)","F",0
2849,1,183,0,1.641127," ","integrate((d*x+c)^3*(a+b*(d*x+c)^2)^p,x, algorithm=""fricas"")","\frac{{\left(b^{2} c^{4} + {\left(b^{2} d^{4} p + b^{2} d^{4}\right)} x^{4} + 4 \, {\left(b^{2} c d^{3} p + b^{2} c d^{3}\right)} x^{3} + {\left(6 \, b^{2} c^{2} d^{2} + {\left(6 \, b^{2} c^{2} + a b\right)} d^{2} p\right)} x^{2} - a^{2} + {\left(b^{2} c^{4} + a b c^{2}\right)} p + 2 \, {\left(2 \, b^{2} c^{3} d + {\left(2 \, b^{2} c^{3} + a b c\right)} d p\right)} x\right)} {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a\right)}^{p}}{2 \, {\left(b^{2} d p^{2} + 3 \, b^{2} d p + 2 \, b^{2} d\right)}}"," ",0,"1/2*(b^2*c^4 + (b^2*d^4*p + b^2*d^4)*x^4 + 4*(b^2*c*d^3*p + b^2*c*d^3)*x^3 + (6*b^2*c^2*d^2 + (6*b^2*c^2 + a*b)*d^2*p)*x^2 - a^2 + (b^2*c^4 + a*b*c^2)*p + 2*(2*b^2*c^3*d + (2*b^2*c^3 + a*b*c)*d*p)*x)*(b*d^2*x^2 + 2*b*c*d*x + b*c^2 + a)^p/(b^2*d*p^2 + 3*b^2*d*p + 2*b^2*d)","B",0
2850,0,0,0,0.978596," ","integrate((d*x+c)^2*(a+b*(d*x+c)^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(d^{2} x^{2} + 2 \, c d x + c^{2}\right)} {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a\right)}^{p}, x\right)"," ",0,"integral((d^2*x^2 + 2*c*d*x + c^2)*(b*d^2*x^2 + 2*b*c*d*x + b*c^2 + a)^p, x)","F",0
2851,1,56,0,1.044121," ","integrate((d*x+c)*(a+b*(d*x+c)^2)^p,x, algorithm=""fricas"")","\frac{{\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a\right)} {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a\right)}^{p}}{2 \, {\left(b d p + b d\right)}}"," ",0,"1/2*(b*d^2*x^2 + 2*b*c*d*x + b*c^2 + a)*(b*d^2*x^2 + 2*b*c*d*x + b*c^2 + a)^p/(b*d*p + b*d)","A",0
2852,0,0,0,1.188547," ","integrate((a+b*(d*x+c)^2)^p/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a\right)}^{p}}{d x + c}, x\right)"," ",0,"integral((b*d^2*x^2 + 2*b*c*d*x + b*c^2 + a)^p/(d*x + c), x)","F",0
2853,1,105,0,1.180068," ","integrate((d*x+c)^3*(a+b*(d*x+c)^3),x, algorithm=""fricas"")","\frac{1}{7} x^{7} d^{6} b + x^{6} d^{5} c b + 3 x^{5} d^{4} c^{2} b + 5 x^{4} d^{3} c^{3} b + 5 x^{3} d^{2} c^{4} b + 3 x^{2} d c^{5} b + x c^{6} b + \frac{1}{4} x^{4} d^{3} a + x^{3} d^{2} c a + \frac{3}{2} x^{2} d c^{2} a + x c^{3} a"," ",0,"1/7*x^7*d^6*b + x^6*d^5*c*b + 3*x^5*d^4*c^2*b + 5*x^4*d^3*c^3*b + 5*x^3*d^2*c^4*b + 3*x^2*d*c^5*b + x*c^6*b + 1/4*x^4*d^3*a + x^3*d^2*c*a + 3/2*x^2*d*c^2*a + x*c^3*a","B",0
2854,1,248,0,0.778524," ","integrate((d*x+c)^3*(a+b*(d*x+c)^3)^2,x, algorithm=""fricas"")","\frac{1}{10} x^{10} d^{9} b^{2} + x^{9} d^{8} c b^{2} + \frac{9}{2} x^{8} d^{7} c^{2} b^{2} + 12 x^{7} d^{6} c^{3} b^{2} + 21 x^{6} d^{5} c^{4} b^{2} + \frac{126}{5} x^{5} d^{4} c^{5} b^{2} + 21 x^{4} d^{3} c^{6} b^{2} + \frac{2}{7} x^{7} d^{6} b a + 12 x^{3} d^{2} c^{7} b^{2} + 2 x^{6} d^{5} c b a + \frac{9}{2} x^{2} d c^{8} b^{2} + 6 x^{5} d^{4} c^{2} b a + x c^{9} b^{2} + 10 x^{4} d^{3} c^{3} b a + 10 x^{3} d^{2} c^{4} b a + 6 x^{2} d c^{5} b a + 2 x c^{6} b a + \frac{1}{4} x^{4} d^{3} a^{2} + x^{3} d^{2} c a^{2} + \frac{3}{2} x^{2} d c^{2} a^{2} + x c^{3} a^{2}"," ",0,"1/10*x^10*d^9*b^2 + x^9*d^8*c*b^2 + 9/2*x^8*d^7*c^2*b^2 + 12*x^7*d^6*c^3*b^2 + 21*x^6*d^5*c^4*b^2 + 126/5*x^5*d^4*c^5*b^2 + 21*x^4*d^3*c^6*b^2 + 2/7*x^7*d^6*b*a + 12*x^3*d^2*c^7*b^2 + 2*x^6*d^5*c*b*a + 9/2*x^2*d*c^8*b^2 + 6*x^5*d^4*c^2*b*a + x*c^9*b^2 + 10*x^4*d^3*c^3*b*a + 10*x^3*d^2*c^4*b*a + 6*x^2*d*c^5*b*a + 2*x*c^6*b*a + 1/4*x^4*d^3*a^2 + x^3*d^2*c*a^2 + 3/2*x^2*d*c^2*a^2 + x*c^3*a^2","B",0
2855,1,442,0,1.226641," ","integrate((d*x+c)^3*(a+b*(d*x+c)^3)^3,x, algorithm=""fricas"")","\frac{1}{13} x^{13} d^{12} b^{3} + x^{12} d^{11} c b^{3} + 6 x^{11} d^{10} c^{2} b^{3} + 22 x^{10} d^{9} c^{3} b^{3} + 55 x^{9} d^{8} c^{4} b^{3} + 99 x^{8} d^{7} c^{5} b^{3} + 132 x^{7} d^{6} c^{6} b^{3} + \frac{3}{10} x^{10} d^{9} b^{2} a + 132 x^{6} d^{5} c^{7} b^{3} + 3 x^{9} d^{8} c b^{2} a + 99 x^{5} d^{4} c^{8} b^{3} + \frac{27}{2} x^{8} d^{7} c^{2} b^{2} a + 55 x^{4} d^{3} c^{9} b^{3} + 36 x^{7} d^{6} c^{3} b^{2} a + 22 x^{3} d^{2} c^{10} b^{3} + 63 x^{6} d^{5} c^{4} b^{2} a + 6 x^{2} d c^{11} b^{3} + \frac{378}{5} x^{5} d^{4} c^{5} b^{2} a + x c^{12} b^{3} + 63 x^{4} d^{3} c^{6} b^{2} a + \frac{3}{7} x^{7} d^{6} b a^{2} + 36 x^{3} d^{2} c^{7} b^{2} a + 3 x^{6} d^{5} c b a^{2} + \frac{27}{2} x^{2} d c^{8} b^{2} a + 9 x^{5} d^{4} c^{2} b a^{2} + 3 x c^{9} b^{2} a + 15 x^{4} d^{3} c^{3} b a^{2} + 15 x^{3} d^{2} c^{4} b a^{2} + 9 x^{2} d c^{5} b a^{2} + 3 x c^{6} b a^{2} + \frac{1}{4} x^{4} d^{3} a^{3} + x^{3} d^{2} c a^{3} + \frac{3}{2} x^{2} d c^{2} a^{3} + x c^{3} a^{3}"," ",0,"1/13*x^13*d^12*b^3 + x^12*d^11*c*b^3 + 6*x^11*d^10*c^2*b^3 + 22*x^10*d^9*c^3*b^3 + 55*x^9*d^8*c^4*b^3 + 99*x^8*d^7*c^5*b^3 + 132*x^7*d^6*c^6*b^3 + 3/10*x^10*d^9*b^2*a + 132*x^6*d^5*c^7*b^3 + 3*x^9*d^8*c*b^2*a + 99*x^5*d^4*c^8*b^3 + 27/2*x^8*d^7*c^2*b^2*a + 55*x^4*d^3*c^9*b^3 + 36*x^7*d^6*c^3*b^2*a + 22*x^3*d^2*c^10*b^3 + 63*x^6*d^5*c^4*b^2*a + 6*x^2*d*c^11*b^3 + 378/5*x^5*d^4*c^5*b^2*a + x*c^12*b^3 + 63*x^4*d^3*c^6*b^2*a + 3/7*x^7*d^6*b*a^2 + 36*x^3*d^2*c^7*b^2*a + 3*x^6*d^5*c*b*a^2 + 27/2*x^2*d*c^8*b^2*a + 9*x^5*d^4*c^2*b*a^2 + 3*x*c^9*b^2*a + 15*x^4*d^3*c^3*b*a^2 + 15*x^3*d^2*c^4*b*a^2 + 9*x^2*d*c^5*b*a^2 + 3*x*c^6*b*a^2 + 1/4*x^4*d^3*a^3 + x^3*d^2*c*a^3 + 3/2*x^2*d*c^2*a^3 + x*c^3*a^3","B",0
2856,1,138,0,0.928733," ","integrate((d*e*x+c*e)^3*(a+b*(d*x+c)^3),x, algorithm=""fricas"")","\frac{1}{7} x^{7} e^{3} d^{6} b + x^{6} e^{3} d^{5} c b + 3 x^{5} e^{3} d^{4} c^{2} b + 5 x^{4} e^{3} d^{3} c^{3} b + 5 x^{3} e^{3} d^{2} c^{4} b + 3 x^{2} e^{3} d c^{5} b + x e^{3} c^{6} b + \frac{1}{4} x^{4} e^{3} d^{3} a + x^{3} e^{3} d^{2} c a + \frac{3}{2} x^{2} e^{3} d c^{2} a + x e^{3} c^{3} a"," ",0,"1/7*x^7*e^3*d^6*b + x^6*e^3*d^5*c*b + 3*x^5*e^3*d^4*c^2*b + 5*x^4*e^3*d^3*c^3*b + 5*x^3*e^3*d^2*c^4*b + 3*x^2*e^3*d*c^5*b + x*e^3*c^6*b + 1/4*x^4*e^3*d^3*a + x^3*e^3*d^2*c*a + 3/2*x^2*e^3*d*c^2*a + x*e^3*c^3*a","B",0
2857,1,311,0,0.815202," ","integrate((d*e*x+c*e)^3*(a+b*(d*x+c)^3)^2,x, algorithm=""fricas"")","\frac{1}{10} x^{10} e^{3} d^{9} b^{2} + x^{9} e^{3} d^{8} c b^{2} + \frac{9}{2} x^{8} e^{3} d^{7} c^{2} b^{2} + 12 x^{7} e^{3} d^{6} c^{3} b^{2} + 21 x^{6} e^{3} d^{5} c^{4} b^{2} + \frac{126}{5} x^{5} e^{3} d^{4} c^{5} b^{2} + 21 x^{4} e^{3} d^{3} c^{6} b^{2} + \frac{2}{7} x^{7} e^{3} d^{6} b a + 12 x^{3} e^{3} d^{2} c^{7} b^{2} + 2 x^{6} e^{3} d^{5} c b a + \frac{9}{2} x^{2} e^{3} d c^{8} b^{2} + 6 x^{5} e^{3} d^{4} c^{2} b a + x e^{3} c^{9} b^{2} + 10 x^{4} e^{3} d^{3} c^{3} b a + 10 x^{3} e^{3} d^{2} c^{4} b a + 6 x^{2} e^{3} d c^{5} b a + 2 x e^{3} c^{6} b a + \frac{1}{4} x^{4} e^{3} d^{3} a^{2} + x^{3} e^{3} d^{2} c a^{2} + \frac{3}{2} x^{2} e^{3} d c^{2} a^{2} + x e^{3} c^{3} a^{2}"," ",0,"1/10*x^10*e^3*d^9*b^2 + x^9*e^3*d^8*c*b^2 + 9/2*x^8*e^3*d^7*c^2*b^2 + 12*x^7*e^3*d^6*c^3*b^2 + 21*x^6*e^3*d^5*c^4*b^2 + 126/5*x^5*e^3*d^4*c^5*b^2 + 21*x^4*e^3*d^3*c^6*b^2 + 2/7*x^7*e^3*d^6*b*a + 12*x^3*e^3*d^2*c^7*b^2 + 2*x^6*e^3*d^5*c*b*a + 9/2*x^2*e^3*d*c^8*b^2 + 6*x^5*e^3*d^4*c^2*b*a + x*e^3*c^9*b^2 + 10*x^4*e^3*d^3*c^3*b*a + 10*x^3*e^3*d^2*c^4*b*a + 6*x^2*e^3*d*c^5*b*a + 2*x*e^3*c^6*b*a + 1/4*x^4*e^3*d^3*a^2 + x^3*e^3*d^2*c*a^2 + 3/2*x^2*e^3*d*c^2*a^2 + x*e^3*c^3*a^2","B",0
2858,1,544,0,1.123553," ","integrate((d*e*x+c*e)^3*(a+b*(d*x+c)^3)^3,x, algorithm=""fricas"")","\frac{1}{13} x^{13} e^{3} d^{12} b^{3} + x^{12} e^{3} d^{11} c b^{3} + 6 x^{11} e^{3} d^{10} c^{2} b^{3} + 22 x^{10} e^{3} d^{9} c^{3} b^{3} + 55 x^{9} e^{3} d^{8} c^{4} b^{3} + 99 x^{8} e^{3} d^{7} c^{5} b^{3} + 132 x^{7} e^{3} d^{6} c^{6} b^{3} + \frac{3}{10} x^{10} e^{3} d^{9} b^{2} a + 132 x^{6} e^{3} d^{5} c^{7} b^{3} + 3 x^{9} e^{3} d^{8} c b^{2} a + 99 x^{5} e^{3} d^{4} c^{8} b^{3} + \frac{27}{2} x^{8} e^{3} d^{7} c^{2} b^{2} a + 55 x^{4} e^{3} d^{3} c^{9} b^{3} + 36 x^{7} e^{3} d^{6} c^{3} b^{2} a + 22 x^{3} e^{3} d^{2} c^{10} b^{3} + 63 x^{6} e^{3} d^{5} c^{4} b^{2} a + 6 x^{2} e^{3} d c^{11} b^{3} + \frac{378}{5} x^{5} e^{3} d^{4} c^{5} b^{2} a + x e^{3} c^{12} b^{3} + 63 x^{4} e^{3} d^{3} c^{6} b^{2} a + \frac{3}{7} x^{7} e^{3} d^{6} b a^{2} + 36 x^{3} e^{3} d^{2} c^{7} b^{2} a + 3 x^{6} e^{3} d^{5} c b a^{2} + \frac{27}{2} x^{2} e^{3} d c^{8} b^{2} a + 9 x^{5} e^{3} d^{4} c^{2} b a^{2} + 3 x e^{3} c^{9} b^{2} a + 15 x^{4} e^{3} d^{3} c^{3} b a^{2} + 15 x^{3} e^{3} d^{2} c^{4} b a^{2} + 9 x^{2} e^{3} d c^{5} b a^{2} + 3 x e^{3} c^{6} b a^{2} + \frac{1}{4} x^{4} e^{3} d^{3} a^{3} + x^{3} e^{3} d^{2} c a^{3} + \frac{3}{2} x^{2} e^{3} d c^{2} a^{3} + x e^{3} c^{3} a^{3}"," ",0,"1/13*x^13*e^3*d^12*b^3 + x^12*e^3*d^11*c*b^3 + 6*x^11*e^3*d^10*c^2*b^3 + 22*x^10*e^3*d^9*c^3*b^3 + 55*x^9*e^3*d^8*c^4*b^3 + 99*x^8*e^3*d^7*c^5*b^3 + 132*x^7*e^3*d^6*c^6*b^3 + 3/10*x^10*e^3*d^9*b^2*a + 132*x^6*e^3*d^5*c^7*b^3 + 3*x^9*e^3*d^8*c*b^2*a + 99*x^5*e^3*d^4*c^8*b^3 + 27/2*x^8*e^3*d^7*c^2*b^2*a + 55*x^4*e^3*d^3*c^9*b^3 + 36*x^7*e^3*d^6*c^3*b^2*a + 22*x^3*e^3*d^2*c^10*b^3 + 63*x^6*e^3*d^5*c^4*b^2*a + 6*x^2*e^3*d*c^11*b^3 + 378/5*x^5*e^3*d^4*c^5*b^2*a + x*e^3*c^12*b^3 + 63*x^4*e^3*d^3*c^6*b^2*a + 3/7*x^7*e^3*d^6*b*a^2 + 36*x^3*e^3*d^2*c^7*b^2*a + 3*x^6*e^3*d^5*c*b*a^2 + 27/2*x^2*e^3*d*c^8*b^2*a + 9*x^5*e^3*d^4*c^2*b*a^2 + 3*x*e^3*c^9*b^2*a + 15*x^4*e^3*d^3*c^3*b*a^2 + 15*x^3*e^3*d^2*c^4*b*a^2 + 9*x^2*e^3*d*c^5*b*a^2 + 3*x*e^3*c^6*b*a^2 + 1/4*x^4*e^3*d^3*a^3 + x^3*e^3*d^2*c*a^3 + 3/2*x^2*e^3*d*c^2*a^3 + x*e^3*c^3*a^3","B",0
2859,1,164,0,0.914166," ","integrate((d*x+c)^4/(a+b*(d*x+c)^3),x, algorithm=""fricas"")","\frac{3 \, d^{2} x^{2} + 6 \, c d x - 2 \, \sqrt{3} \left(\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} {\left(b d x + b c\right)} \left(\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}} - \sqrt{3} a}{3 \, a}\right) - \left(\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}} \log\left(a d^{2} x^{2} + 2 \, a c d x + a c^{2} - {\left(b d x + b c\right)} \left(\frac{a^{2}}{b^{2}}\right)^{\frac{2}{3}} + a \left(\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}}\right) + 2 \, \left(\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}} \log\left(a d x + a c + b \left(\frac{a^{2}}{b^{2}}\right)^{\frac{2}{3}}\right)}{6 \, b d}"," ",0,"1/6*(3*d^2*x^2 + 6*c*d*x - 2*sqrt(3)*(a^2/b^2)^(1/3)*arctan(1/3*(2*sqrt(3)*(b*d*x + b*c)*(a^2/b^2)^(1/3) - sqrt(3)*a)/a) - (a^2/b^2)^(1/3)*log(a*d^2*x^2 + 2*a*c*d*x + a*c^2 - (b*d*x + b*c)*(a^2/b^2)^(2/3) + a*(a^2/b^2)^(1/3)) + 2*(a^2/b^2)^(1/3)*log(a*d*x + a*c + b*(a^2/b^2)^(2/3)))/(b*d)","A",0
2860,1,135,0,0.975651," ","integrate((d*x+c)^3/(a+b*(d*x+c)^3),x, algorithm=""fricas"")","\frac{6 \, d x + 2 \, \sqrt{3} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} {\left(b d x + b c\right)} \left(-\frac{a}{b}\right)^{\frac{2}{3}} - \sqrt{3} a}{3 \, a}\right) - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + {\left(d x + c\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right) + 2 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left(d x + c - \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}{6 \, b d}"," ",0,"1/6*(6*d*x + 2*sqrt(3)*(-a/b)^(1/3)*arctan(1/3*(2*sqrt(3)*(b*d*x + b*c)*(-a/b)^(2/3) - sqrt(3)*a)/a) - (-a/b)^(1/3)*log(d^2*x^2 + 2*c*d*x + c^2 + (d*x + c)*(-a/b)^(1/3) + (-a/b)^(2/3)) + 2*(-a/b)^(1/3)*log(d*x + c - (-a/b)^(1/3)))/(b*d)","A",0
2861,1,42,0,1.818216," ","integrate((d*x+c)^2/(a+b*(d*x+c)^3),x, algorithm=""fricas"")","\frac{\log\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right)}{3 \, b d}"," ",0,"1/3*log(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)/(b*d)","B",0
2862,1,452,0,1.006490," ","integrate((d*x+c)/(a+b*(d*x+c)^3),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{\frac{1}{3}} a b \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \log\left(\frac{2 \, b^{2} d^{3} x^{3} + 6 \, b^{2} c d^{2} x^{2} + 6 \, b^{2} c^{2} d x + 2 \, b^{2} c^{3} - a b + 3 \, \sqrt{\frac{1}{3}} {\left(a b d x + a b c + 2 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} + \left(-a b^{2}\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} - 3 \, \left(-a b^{2}\right)^{\frac{2}{3}} {\left(d x + c\right)}}{b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a}\right) + \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} {\left(b d x + b c\right)} + \left(-a b^{2}\right)^{\frac{2}{3}}\right) - 2 \, \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b d x + b c - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{6 \, a b^{2} d}, \frac{6 \, \sqrt{\frac{1}{3}} a b \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, b d x + 2 \, b c + \left(-a b^{2}\right)^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}}}{b}\right) + \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} {\left(b d x + b c\right)} + \left(-a b^{2}\right)^{\frac{2}{3}}\right) - 2 \, \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b d x + b c - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{6 \, a b^{2} d}\right]"," ",0,"[1/6*(3*sqrt(1/3)*a*b*sqrt((-a*b^2)^(1/3)/a)*log((2*b^2*d^3*x^3 + 6*b^2*c*d^2*x^2 + 6*b^2*c^2*d*x + 2*b^2*c^3 - a*b + 3*sqrt(1/3)*(a*b*d*x + a*b*c + 2*(d^2*x^2 + 2*c*d*x + c^2)*(-a*b^2)^(2/3) + (-a*b^2)^(1/3)*a)*sqrt((-a*b^2)^(1/3)/a) - 3*(-a*b^2)^(2/3)*(d*x + c))/(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)) + (-a*b^2)^(2/3)*log(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 + (-a*b^2)^(1/3)*(b*d*x + b*c) + (-a*b^2)^(2/3)) - 2*(-a*b^2)^(2/3)*log(b*d*x + b*c - (-a*b^2)^(1/3)))/(a*b^2*d), 1/6*(6*sqrt(1/3)*a*b*sqrt(-(-a*b^2)^(1/3)/a)*arctan(sqrt(1/3)*(2*b*d*x + 2*b*c + (-a*b^2)^(1/3))*sqrt(-(-a*b^2)^(1/3)/a)/b) + (-a*b^2)^(2/3)*log(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 + (-a*b^2)^(1/3)*(b*d*x + b*c) + (-a*b^2)^(2/3)) - 2*(-a*b^2)^(2/3)*log(b*d*x + b*c - (-a*b^2)^(1/3)))/(a*b^2*d)]","A",0
2863,1,442,0,1.272650," ","integrate(1/(a+b*(d*x+c)^3),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{\frac{1}{3}} a b \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \log\left(\frac{2 \, a b d^{3} x^{3} + 6 \, a b c d^{2} x^{2} + 6 \, a b c^{2} d x + 2 \, a b c^{3} - a^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, a b d^{2} x^{2} + 4 \, a b c d x + 2 \, a b c^{2} + \left(a^{2} b\right)^{\frac{2}{3}} {\left(d x + c\right)} - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} - 3 \, \left(a^{2} b\right)^{\frac{1}{3}} {\left(a d x + a c\right)}}{b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a}\right) - \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b d^{2} x^{2} + 2 \, a b c d x + a b c^{2} - \left(a^{2} b\right)^{\frac{2}{3}} {\left(d x + c\right)} + \left(a^{2} b\right)^{\frac{1}{3}} a\right) + 2 \, \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b d x + a b c + \left(a^{2} b\right)^{\frac{2}{3}}\right)}{6 \, a^{2} b d}, \frac{6 \, \sqrt{\frac{1}{3}} a b \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(a^{2} b\right)^{\frac{2}{3}} {\left(d x + c\right)} - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{a^{2}}\right) - \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b d^{2} x^{2} + 2 \, a b c d x + a b c^{2} - \left(a^{2} b\right)^{\frac{2}{3}} {\left(d x + c\right)} + \left(a^{2} b\right)^{\frac{1}{3}} a\right) + 2 \, \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b d x + a b c + \left(a^{2} b\right)^{\frac{2}{3}}\right)}{6 \, a^{2} b d}\right]"," ",0,"[1/6*(3*sqrt(1/3)*a*b*sqrt(-(a^2*b)^(1/3)/b)*log((2*a*b*d^3*x^3 + 6*a*b*c*d^2*x^2 + 6*a*b*c^2*d*x + 2*a*b*c^3 - a^2 + 3*sqrt(1/3)*(2*a*b*d^2*x^2 + 4*a*b*c*d*x + 2*a*b*c^2 + (a^2*b)^(2/3)*(d*x + c) - (a^2*b)^(1/3)*a)*sqrt(-(a^2*b)^(1/3)/b) - 3*(a^2*b)^(1/3)*(a*d*x + a*c))/(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)) - (a^2*b)^(2/3)*log(a*b*d^2*x^2 + 2*a*b*c*d*x + a*b*c^2 - (a^2*b)^(2/3)*(d*x + c) + (a^2*b)^(1/3)*a) + 2*(a^2*b)^(2/3)*log(a*b*d*x + a*b*c + (a^2*b)^(2/3)))/(a^2*b*d), 1/6*(6*sqrt(1/3)*a*b*sqrt((a^2*b)^(1/3)/b)*arctan(sqrt(1/3)*(2*(a^2*b)^(2/3)*(d*x + c) - (a^2*b)^(1/3)*a)*sqrt((a^2*b)^(1/3)/b)/a^2) - (a^2*b)^(2/3)*log(a*b*d^2*x^2 + 2*a*b*c*d*x + a*b*c^2 - (a^2*b)^(2/3)*(d*x + c) + (a^2*b)^(1/3)*a) + 2*(a^2*b)^(2/3)*log(a*b*d*x + a*b*c + (a^2*b)^(2/3)))/(a^2*b*d)]","A",0
2864,1,51,0,0.977908," ","integrate(1/(d*x+c)/(a+b*(d*x+c)^3),x, algorithm=""fricas"")","-\frac{\log\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right) - 3 \, \log\left(d x + c\right)}{3 \, a d}"," ",0,"-1/3*(log(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a) - 3*log(d*x + c))/(a*d)","A",0
2865,1,150,0,0.988985," ","integrate(1/(d*x+c)^2/(a+b*(d*x+c)^3),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} {\left(d x + c\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}} \arctan\left(\frac{2}{3} \, \sqrt{3} {\left(d x + c\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}} - \frac{1}{3} \, \sqrt{3}\right) + {\left(d x + c\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}} \log\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} - {\left(a d x + a c\right)} \left(\frac{b}{a}\right)^{\frac{2}{3}} + a \left(\frac{b}{a}\right)^{\frac{1}{3}}\right) - 2 \, {\left(d x + c\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}} \log\left(b d x + b c + a \left(\frac{b}{a}\right)^{\frac{2}{3}}\right) + 6}{6 \, {\left(a d^{2} x + a c d\right)}}"," ",0,"-1/6*(2*sqrt(3)*(d*x + c)*(b/a)^(1/3)*arctan(2/3*sqrt(3)*(d*x + c)*(b/a)^(1/3) - 1/3*sqrt(3)) + (d*x + c)*(b/a)^(1/3)*log(b*d^2*x^2 + 2*b*c*d*x + b*c^2 - (a*d*x + a*c)*(b/a)^(2/3) + a*(b/a)^(1/3)) - 2*(d*x + c)*(b/a)^(1/3)*log(b*d*x + b*c + a*(b/a)^(2/3)) + 6)/(a*d^2*x + a*c*d)","A",0
2866,1,236,0,0.602824," ","integrate(1/(d*x+c)^3/(a+b*(d*x+c)^3),x, algorithm=""fricas"")","\frac{2 \, \sqrt{3} {\left(d^{2} x^{2} + 2 \, c d x + c^{2}\right)} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} {\left(a d x + a c\right)} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}} - \sqrt{3} b}{3 \, b}\right) - {\left(d^{2} x^{2} + 2 \, c d x + c^{2}\right)} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} + a^{2} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}} + {\left(a b d x + a b c\right)} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}}\right) + 2 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2}\right)} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b d x + b c - a \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}}\right) - 3}{6 \, {\left(a d^{3} x^{2} + 2 \, a c d^{2} x + a c^{2} d\right)}}"," ",0,"1/6*(2*sqrt(3)*(d^2*x^2 + 2*c*d*x + c^2)*(-b^2/a^2)^(1/3)*arctan(1/3*(2*sqrt(3)*(a*d*x + a*c)*(-b^2/a^2)^(2/3) - sqrt(3)*b)/b) - (d^2*x^2 + 2*c*d*x + c^2)*(-b^2/a^2)^(1/3)*log(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 + a^2*(-b^2/a^2)^(2/3) + (a*b*d*x + a*b*c)*(-b^2/a^2)^(1/3)) + 2*(d^2*x^2 + 2*c*d*x + c^2)*(-b^2/a^2)^(1/3)*log(b*d*x + b*c - a*(-b^2/a^2)^(1/3)) - 3)/(a*d^3*x^2 + 2*a*c*d^2*x + a*c^2*d)","A",0
2867,1,158,0,1.185245," ","integrate(1/(d*x+c)^4/(a+b*(d*x+c)^3),x, algorithm=""fricas"")","\frac{{\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3}\right)} \log\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right) - 3 \, {\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3}\right)} \log\left(d x + c\right) - a}{3 \, {\left(a^{2} d^{4} x^{3} + 3 \, a^{2} c d^{3} x^{2} + 3 \, a^{2} c^{2} d^{2} x + a^{2} c^{3} d\right)}}"," ",0,"1/3*((b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3)*log(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a) - 3*(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3)*log(d*x + c) - a)/(a^2*d^4*x^3 + 3*a^2*c*d^3*x^2 + 3*a^2*c^2*d^2*x + a^2*c^3*d)","B",0
2868,1,838,0,0.892657," ","integrate((d*x+c)^4/(a+b*(d*x+c)^3)^2,x, algorithm=""fricas"")","\left[-\frac{3 \, a b^{2} d^{2} x^{2} + 6 \, a b^{2} c d x + 3 \, a b^{2} c^{2} - 3 \, \sqrt{\frac{1}{3}} {\left(a b^{2} d^{3} x^{3} + 3 \, a b^{2} c d^{2} x^{2} + 3 \, a b^{2} c^{2} d x + a b^{2} c^{3} + a^{2} b\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \log\left(\frac{2 \, b^{2} d^{3} x^{3} + 6 \, b^{2} c d^{2} x^{2} + 6 \, b^{2} c^{2} d x + 2 \, b^{2} c^{3} - a b + 3 \, \sqrt{\frac{1}{3}} {\left(a b d x + a b c + 2 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} + \left(-a b^{2}\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} - 3 \, \left(-a b^{2}\right)^{\frac{2}{3}} {\left(d x + c\right)}}{b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a}\right) - {\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} {\left(b d x + b c\right)} + \left(-a b^{2}\right)^{\frac{2}{3}}\right) + 2 \, {\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b d x + b c - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{9 \, {\left(a b^{4} d^{4} x^{3} + 3 \, a b^{4} c d^{3} x^{2} + 3 \, a b^{4} c^{2} d^{2} x + {\left(a b^{4} c^{3} + a^{2} b^{3}\right)} d\right)}}, -\frac{3 \, a b^{2} d^{2} x^{2} + 6 \, a b^{2} c d x + 3 \, a b^{2} c^{2} - 6 \, \sqrt{\frac{1}{3}} {\left(a b^{2} d^{3} x^{3} + 3 \, a b^{2} c d^{2} x^{2} + 3 \, a b^{2} c^{2} d x + a b^{2} c^{3} + a^{2} b\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, b d x + 2 \, b c + \left(-a b^{2}\right)^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}}}{b}\right) - {\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} {\left(b d x + b c\right)} + \left(-a b^{2}\right)^{\frac{2}{3}}\right) + 2 \, {\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b d x + b c - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{9 \, {\left(a b^{4} d^{4} x^{3} + 3 \, a b^{4} c d^{3} x^{2} + 3 \, a b^{4} c^{2} d^{2} x + {\left(a b^{4} c^{3} + a^{2} b^{3}\right)} d\right)}}\right]"," ",0,"[-1/9*(3*a*b^2*d^2*x^2 + 6*a*b^2*c*d*x + 3*a*b^2*c^2 - 3*sqrt(1/3)*(a*b^2*d^3*x^3 + 3*a*b^2*c*d^2*x^2 + 3*a*b^2*c^2*d*x + a*b^2*c^3 + a^2*b)*sqrt((-a*b^2)^(1/3)/a)*log((2*b^2*d^3*x^3 + 6*b^2*c*d^2*x^2 + 6*b^2*c^2*d*x + 2*b^2*c^3 - a*b + 3*sqrt(1/3)*(a*b*d*x + a*b*c + 2*(d^2*x^2 + 2*c*d*x + c^2)*(-a*b^2)^(2/3) + (-a*b^2)^(1/3)*a)*sqrt((-a*b^2)^(1/3)/a) - 3*(-a*b^2)^(2/3)*(d*x + c))/(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)) - (b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)*(-a*b^2)^(2/3)*log(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 + (-a*b^2)^(1/3)*(b*d*x + b*c) + (-a*b^2)^(2/3)) + 2*(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)*(-a*b^2)^(2/3)*log(b*d*x + b*c - (-a*b^2)^(1/3)))/(a*b^4*d^4*x^3 + 3*a*b^4*c*d^3*x^2 + 3*a*b^4*c^2*d^2*x + (a*b^4*c^3 + a^2*b^3)*d), -1/9*(3*a*b^2*d^2*x^2 + 6*a*b^2*c*d*x + 3*a*b^2*c^2 - 6*sqrt(1/3)*(a*b^2*d^3*x^3 + 3*a*b^2*c*d^2*x^2 + 3*a*b^2*c^2*d*x + a*b^2*c^3 + a^2*b)*sqrt(-(-a*b^2)^(1/3)/a)*arctan(sqrt(1/3)*(2*b*d*x + 2*b*c + (-a*b^2)^(1/3))*sqrt(-(-a*b^2)^(1/3)/a)/b) - (b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)*(-a*b^2)^(2/3)*log(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 + (-a*b^2)^(1/3)*(b*d*x + b*c) + (-a*b^2)^(2/3)) + 2*(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)*(-a*b^2)^(2/3)*log(b*d*x + b*c - (-a*b^2)^(1/3)))/(a*b^4*d^4*x^3 + 3*a*b^4*c*d^3*x^2 + 3*a*b^4*c^2*d^2*x + (a*b^4*c^3 + a^2*b^3)*d)]","B",0
2869,1,810,0,0.792405," ","integrate((d*x+c)^3/(a+b*(d*x+c)^3)^2,x, algorithm=""fricas"")","\left[-\frac{6 \, a^{2} b d x + 6 \, a^{2} b c - 3 \, \sqrt{\frac{1}{3}} {\left(a b^{2} d^{3} x^{3} + 3 \, a b^{2} c d^{2} x^{2} + 3 \, a b^{2} c^{2} d x + a b^{2} c^{3} + a^{2} b\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \log\left(\frac{2 \, a b d^{3} x^{3} + 6 \, a b c d^{2} x^{2} + 6 \, a b c^{2} d x + 2 \, a b c^{3} - a^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, a b d^{2} x^{2} + 4 \, a b c d x + 2 \, a b c^{2} + \left(a^{2} b\right)^{\frac{2}{3}} {\left(d x + c\right)} - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} - 3 \, \left(a^{2} b\right)^{\frac{1}{3}} {\left(a d x + a c\right)}}{b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a}\right) + {\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b d^{2} x^{2} + 2 \, a b c d x + a b c^{2} - \left(a^{2} b\right)^{\frac{2}{3}} {\left(d x + c\right)} + \left(a^{2} b\right)^{\frac{1}{3}} a\right) - 2 \, {\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b d x + a b c + \left(a^{2} b\right)^{\frac{2}{3}}\right)}{18 \, {\left(a^{2} b^{3} d^{4} x^{3} + 3 \, a^{2} b^{3} c d^{3} x^{2} + 3 \, a^{2} b^{3} c^{2} d^{2} x + {\left(a^{2} b^{3} c^{3} + a^{3} b^{2}\right)} d\right)}}, -\frac{6 \, a^{2} b d x + 6 \, a^{2} b c - 6 \, \sqrt{\frac{1}{3}} {\left(a b^{2} d^{3} x^{3} + 3 \, a b^{2} c d^{2} x^{2} + 3 \, a b^{2} c^{2} d x + a b^{2} c^{3} + a^{2} b\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(a^{2} b\right)^{\frac{2}{3}} {\left(d x + c\right)} - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{a^{2}}\right) + {\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b d^{2} x^{2} + 2 \, a b c d x + a b c^{2} - \left(a^{2} b\right)^{\frac{2}{3}} {\left(d x + c\right)} + \left(a^{2} b\right)^{\frac{1}{3}} a\right) - 2 \, {\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b d x + a b c + \left(a^{2} b\right)^{\frac{2}{3}}\right)}{18 \, {\left(a^{2} b^{3} d^{4} x^{3} + 3 \, a^{2} b^{3} c d^{3} x^{2} + 3 \, a^{2} b^{3} c^{2} d^{2} x + {\left(a^{2} b^{3} c^{3} + a^{3} b^{2}\right)} d\right)}}\right]"," ",0,"[-1/18*(6*a^2*b*d*x + 6*a^2*b*c - 3*sqrt(1/3)*(a*b^2*d^3*x^3 + 3*a*b^2*c*d^2*x^2 + 3*a*b^2*c^2*d*x + a*b^2*c^3 + a^2*b)*sqrt(-(a^2*b)^(1/3)/b)*log((2*a*b*d^3*x^3 + 6*a*b*c*d^2*x^2 + 6*a*b*c^2*d*x + 2*a*b*c^3 - a^2 + 3*sqrt(1/3)*(2*a*b*d^2*x^2 + 4*a*b*c*d*x + 2*a*b*c^2 + (a^2*b)^(2/3)*(d*x + c) - (a^2*b)^(1/3)*a)*sqrt(-(a^2*b)^(1/3)/b) - 3*(a^2*b)^(1/3)*(a*d*x + a*c))/(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)) + (b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)*(a^2*b)^(2/3)*log(a*b*d^2*x^2 + 2*a*b*c*d*x + a*b*c^2 - (a^2*b)^(2/3)*(d*x + c) + (a^2*b)^(1/3)*a) - 2*(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)*(a^2*b)^(2/3)*log(a*b*d*x + a*b*c + (a^2*b)^(2/3)))/(a^2*b^3*d^4*x^3 + 3*a^2*b^3*c*d^3*x^2 + 3*a^2*b^3*c^2*d^2*x + (a^2*b^3*c^3 + a^3*b^2)*d), -1/18*(6*a^2*b*d*x + 6*a^2*b*c - 6*sqrt(1/3)*(a*b^2*d^3*x^3 + 3*a*b^2*c*d^2*x^2 + 3*a*b^2*c^2*d*x + a*b^2*c^3 + a^2*b)*sqrt((a^2*b)^(1/3)/b)*arctan(sqrt(1/3)*(2*(a^2*b)^(2/3)*(d*x + c) - (a^2*b)^(1/3)*a)*sqrt((a^2*b)^(1/3)/b)/a^2) + (b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)*(a^2*b)^(2/3)*log(a*b*d^2*x^2 + 2*a*b*c*d*x + a*b*c^2 - (a^2*b)^(2/3)*(d*x + c) + (a^2*b)^(1/3)*a) - 2*(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)*(a^2*b)^(2/3)*log(a*b*d*x + a*b*c + (a^2*b)^(2/3)))/(a^2*b^3*d^4*x^3 + 3*a^2*b^3*c*d^3*x^2 + 3*a^2*b^3*c^2*d^2*x + (a^2*b^3*c^3 + a^3*b^2)*d)]","B",0
2870,1,52,0,0.860941," ","integrate((d*x+c)^2/(a+b*(d*x+c)^3)^2,x, algorithm=""fricas"")","-\frac{1}{3 \, {\left(b^{2} d^{4} x^{3} + 3 \, b^{2} c d^{3} x^{2} + 3 \, b^{2} c^{2} d^{2} x + {\left(b^{2} c^{3} + a b\right)} d\right)}}"," ",0,"-1/3/(b^2*d^4*x^3 + 3*b^2*c*d^3*x^2 + 3*b^2*c^2*d^2*x + (b^2*c^3 + a*b)*d)","B",0
2871,1,852,0,1.429085," ","integrate((d*x+c)/(a+b*(d*x+c)^3)^2,x, algorithm=""fricas"")","\left[\frac{6 \, a b^{2} d^{2} x^{2} + 12 \, a b^{2} c d x + 6 \, a b^{2} c^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(a b^{2} d^{3} x^{3} + 3 \, a b^{2} c d^{2} x^{2} + 3 \, a b^{2} c^{2} d x + a b^{2} c^{3} + a^{2} b\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \log\left(\frac{2 \, b^{2} d^{3} x^{3} + 6 \, b^{2} c d^{2} x^{2} + 6 \, b^{2} c^{2} d x + 2 \, b^{2} c^{3} - a b + 3 \, \sqrt{\frac{1}{3}} {\left(a b d x + a b c + 2 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} + \left(-a b^{2}\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} - 3 \, \left(-a b^{2}\right)^{\frac{2}{3}} {\left(d x + c\right)}}{b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a}\right) + {\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} {\left(b d x + b c\right)} + \left(-a b^{2}\right)^{\frac{2}{3}}\right) - 2 \, {\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b d x + b c - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{18 \, {\left(a^{2} b^{3} d^{4} x^{3} + 3 \, a^{2} b^{3} c d^{3} x^{2} + 3 \, a^{2} b^{3} c^{2} d^{2} x + {\left(a^{2} b^{3} c^{3} + a^{3} b^{2}\right)} d\right)}}, \frac{6 \, a b^{2} d^{2} x^{2} + 12 \, a b^{2} c d x + 6 \, a b^{2} c^{2} + 6 \, \sqrt{\frac{1}{3}} {\left(a b^{2} d^{3} x^{3} + 3 \, a b^{2} c d^{2} x^{2} + 3 \, a b^{2} c^{2} d x + a b^{2} c^{3} + a^{2} b\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, b d x + 2 \, b c + \left(-a b^{2}\right)^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}}}{b}\right) + {\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} {\left(b d x + b c\right)} + \left(-a b^{2}\right)^{\frac{2}{3}}\right) - 2 \, {\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b d x + b c - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{18 \, {\left(a^{2} b^{3} d^{4} x^{3} + 3 \, a^{2} b^{3} c d^{3} x^{2} + 3 \, a^{2} b^{3} c^{2} d^{2} x + {\left(a^{2} b^{3} c^{3} + a^{3} b^{2}\right)} d\right)}}\right]"," ",0,"[1/18*(6*a*b^2*d^2*x^2 + 12*a*b^2*c*d*x + 6*a*b^2*c^2 + 3*sqrt(1/3)*(a*b^2*d^3*x^3 + 3*a*b^2*c*d^2*x^2 + 3*a*b^2*c^2*d*x + a*b^2*c^3 + a^2*b)*sqrt((-a*b^2)^(1/3)/a)*log((2*b^2*d^3*x^3 + 6*b^2*c*d^2*x^2 + 6*b^2*c^2*d*x + 2*b^2*c^3 - a*b + 3*sqrt(1/3)*(a*b*d*x + a*b*c + 2*(d^2*x^2 + 2*c*d*x + c^2)*(-a*b^2)^(2/3) + (-a*b^2)^(1/3)*a)*sqrt((-a*b^2)^(1/3)/a) - 3*(-a*b^2)^(2/3)*(d*x + c))/(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)) + (b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)*(-a*b^2)^(2/3)*log(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 + (-a*b^2)^(1/3)*(b*d*x + b*c) + (-a*b^2)^(2/3)) - 2*(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)*(-a*b^2)^(2/3)*log(b*d*x + b*c - (-a*b^2)^(1/3)))/(a^2*b^3*d^4*x^3 + 3*a^2*b^3*c*d^3*x^2 + 3*a^2*b^3*c^2*d^2*x + (a^2*b^3*c^3 + a^3*b^2)*d), 1/18*(6*a*b^2*d^2*x^2 + 12*a*b^2*c*d*x + 6*a*b^2*c^2 + 6*sqrt(1/3)*(a*b^2*d^3*x^3 + 3*a*b^2*c*d^2*x^2 + 3*a*b^2*c^2*d*x + a*b^2*c^3 + a^2*b)*sqrt(-(-a*b^2)^(1/3)/a)*arctan(sqrt(1/3)*(2*b*d*x + 2*b*c + (-a*b^2)^(1/3))*sqrt(-(-a*b^2)^(1/3)/a)/b) + (b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)*(-a*b^2)^(2/3)*log(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 + (-a*b^2)^(1/3)*(b*d*x + b*c) + (-a*b^2)^(2/3)) - 2*(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)*(-a*b^2)^(2/3)*log(b*d*x + b*c - (-a*b^2)^(1/3)))/(a^2*b^3*d^4*x^3 + 3*a^2*b^3*c*d^3*x^2 + 3*a^2*b^3*c^2*d^2*x + (a^2*b^3*c^3 + a^3*b^2)*d)]","B",0
2872,1,808,0,1.186228," ","integrate(1/(a+b*(d*x+c)^3)^2,x, algorithm=""fricas"")","\left[\frac{3 \, a^{2} b d x + 3 \, a^{2} b c + 3 \, \sqrt{\frac{1}{3}} {\left(a b^{2} d^{3} x^{3} + 3 \, a b^{2} c d^{2} x^{2} + 3 \, a b^{2} c^{2} d x + a b^{2} c^{3} + a^{2} b\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \log\left(\frac{2 \, a b d^{3} x^{3} + 6 \, a b c d^{2} x^{2} + 6 \, a b c^{2} d x + 2 \, a b c^{3} - a^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, a b d^{2} x^{2} + 4 \, a b c d x + 2 \, a b c^{2} + \left(a^{2} b\right)^{\frac{2}{3}} {\left(d x + c\right)} - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} - 3 \, \left(a^{2} b\right)^{\frac{1}{3}} {\left(a d x + a c\right)}}{b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a}\right) - {\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b d^{2} x^{2} + 2 \, a b c d x + a b c^{2} - \left(a^{2} b\right)^{\frac{2}{3}} {\left(d x + c\right)} + \left(a^{2} b\right)^{\frac{1}{3}} a\right) + 2 \, {\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b d x + a b c + \left(a^{2} b\right)^{\frac{2}{3}}\right)}{9 \, {\left(a^{3} b^{2} d^{4} x^{3} + 3 \, a^{3} b^{2} c d^{3} x^{2} + 3 \, a^{3} b^{2} c^{2} d^{2} x + {\left(a^{3} b^{2} c^{3} + a^{4} b\right)} d\right)}}, \frac{3 \, a^{2} b d x + 3 \, a^{2} b c + 6 \, \sqrt{\frac{1}{3}} {\left(a b^{2} d^{3} x^{3} + 3 \, a b^{2} c d^{2} x^{2} + 3 \, a b^{2} c^{2} d x + a b^{2} c^{3} + a^{2} b\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(a^{2} b\right)^{\frac{2}{3}} {\left(d x + c\right)} - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{a^{2}}\right) - {\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b d^{2} x^{2} + 2 \, a b c d x + a b c^{2} - \left(a^{2} b\right)^{\frac{2}{3}} {\left(d x + c\right)} + \left(a^{2} b\right)^{\frac{1}{3}} a\right) + 2 \, {\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b d x + a b c + \left(a^{2} b\right)^{\frac{2}{3}}\right)}{9 \, {\left(a^{3} b^{2} d^{4} x^{3} + 3 \, a^{3} b^{2} c d^{3} x^{2} + 3 \, a^{3} b^{2} c^{2} d^{2} x + {\left(a^{3} b^{2} c^{3} + a^{4} b\right)} d\right)}}\right]"," ",0,"[1/9*(3*a^2*b*d*x + 3*a^2*b*c + 3*sqrt(1/3)*(a*b^2*d^3*x^3 + 3*a*b^2*c*d^2*x^2 + 3*a*b^2*c^2*d*x + a*b^2*c^3 + a^2*b)*sqrt(-(a^2*b)^(1/3)/b)*log((2*a*b*d^3*x^3 + 6*a*b*c*d^2*x^2 + 6*a*b*c^2*d*x + 2*a*b*c^3 - a^2 + 3*sqrt(1/3)*(2*a*b*d^2*x^2 + 4*a*b*c*d*x + 2*a*b*c^2 + (a^2*b)^(2/3)*(d*x + c) - (a^2*b)^(1/3)*a)*sqrt(-(a^2*b)^(1/3)/b) - 3*(a^2*b)^(1/3)*(a*d*x + a*c))/(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)) - (b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)*(a^2*b)^(2/3)*log(a*b*d^2*x^2 + 2*a*b*c*d*x + a*b*c^2 - (a^2*b)^(2/3)*(d*x + c) + (a^2*b)^(1/3)*a) + 2*(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)*(a^2*b)^(2/3)*log(a*b*d*x + a*b*c + (a^2*b)^(2/3)))/(a^3*b^2*d^4*x^3 + 3*a^3*b^2*c*d^3*x^2 + 3*a^3*b^2*c^2*d^2*x + (a^3*b^2*c^3 + a^4*b)*d), 1/9*(3*a^2*b*d*x + 3*a^2*b*c + 6*sqrt(1/3)*(a*b^2*d^3*x^3 + 3*a*b^2*c*d^2*x^2 + 3*a*b^2*c^2*d*x + a*b^2*c^3 + a^2*b)*sqrt((a^2*b)^(1/3)/b)*arctan(sqrt(1/3)*(2*(a^2*b)^(2/3)*(d*x + c) - (a^2*b)^(1/3)*a)*sqrt((a^2*b)^(1/3)/b)/a^2) - (b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)*(a^2*b)^(2/3)*log(a*b*d^2*x^2 + 2*a*b*c*d*x + a*b*c^2 - (a^2*b)^(2/3)*(d*x + c) + (a^2*b)^(1/3)*a) + 2*(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)*(a^2*b)^(2/3)*log(a*b*d*x + a*b*c + (a^2*b)^(2/3)))/(a^3*b^2*d^4*x^3 + 3*a^3*b^2*c*d^3*x^2 + 3*a^3*b^2*c^2*d^2*x + (a^3*b^2*c^3 + a^4*b)*d)]","B",0
2873,1,169,0,1.037670," ","integrate(1/(d*x+c)/(a+b*(d*x+c)^3)^2,x, algorithm=""fricas"")","-\frac{{\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right)} \log\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right) - 3 \, {\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right)} \log\left(d x + c\right) - a}{3 \, {\left(a^{2} b d^{4} x^{3} + 3 \, a^{2} b c d^{3} x^{2} + 3 \, a^{2} b c^{2} d^{2} x + {\left(a^{2} b c^{3} + a^{3}\right)} d\right)}}"," ",0,"-1/3*((b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)*log(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a) - 3*(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)*log(d*x + c) - a)/(a^2*b*d^4*x^3 + 3*a^2*b*c*d^3*x^2 + 3*a^2*b*c^2*d^2*x + (a^2*b*c^3 + a^3)*d)","B",0
2874,1,384,0,1.131625," ","integrate(1/(d*x+c)^2/(a+b*(d*x+c)^3)^2,x, algorithm=""fricas"")","-\frac{12 \, b d^{3} x^{3} + 36 \, b c d^{2} x^{2} + 36 \, b c^{2} d x + 12 \, b c^{3} + 4 \, \sqrt{3} {\left(b d^{4} x^{4} + 4 \, b c d^{3} x^{3} + 6 \, b c^{2} d^{2} x^{2} + b c^{4} + {\left(4 \, b c^{3} + a\right)} d x + a c\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}} \arctan\left(\frac{2}{3} \, \sqrt{3} {\left(d x + c\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}} - \frac{1}{3} \, \sqrt{3}\right) + 2 \, {\left(b d^{4} x^{4} + 4 \, b c d^{3} x^{3} + 6 \, b c^{2} d^{2} x^{2} + b c^{4} + {\left(4 \, b c^{3} + a\right)} d x + a c\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}} \log\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} - {\left(a d x + a c\right)} \left(\frac{b}{a}\right)^{\frac{2}{3}} + a \left(\frac{b}{a}\right)^{\frac{1}{3}}\right) - 4 \, {\left(b d^{4} x^{4} + 4 \, b c d^{3} x^{3} + 6 \, b c^{2} d^{2} x^{2} + b c^{4} + {\left(4 \, b c^{3} + a\right)} d x + a c\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}} \log\left(b d x + b c + a \left(\frac{b}{a}\right)^{\frac{2}{3}}\right) + 9 \, a}{9 \, {\left(a^{2} b d^{5} x^{4} + 4 \, a^{2} b c d^{4} x^{3} + 6 \, a^{2} b c^{2} d^{3} x^{2} + {\left(4 \, a^{2} b c^{3} + a^{3}\right)} d^{2} x + {\left(a^{2} b c^{4} + a^{3} c\right)} d\right)}}"," ",0,"-1/9*(12*b*d^3*x^3 + 36*b*c*d^2*x^2 + 36*b*c^2*d*x + 12*b*c^3 + 4*sqrt(3)*(b*d^4*x^4 + 4*b*c*d^3*x^3 + 6*b*c^2*d^2*x^2 + b*c^4 + (4*b*c^3 + a)*d*x + a*c)*(b/a)^(1/3)*arctan(2/3*sqrt(3)*(d*x + c)*(b/a)^(1/3) - 1/3*sqrt(3)) + 2*(b*d^4*x^4 + 4*b*c*d^3*x^3 + 6*b*c^2*d^2*x^2 + b*c^4 + (4*b*c^3 + a)*d*x + a*c)*(b/a)^(1/3)*log(b*d^2*x^2 + 2*b*c*d*x + b*c^2 - (a*d*x + a*c)*(b/a)^(2/3) + a*(b/a)^(1/3)) - 4*(b*d^4*x^4 + 4*b*c*d^3*x^3 + 6*b*c^2*d^2*x^2 + b*c^4 + (4*b*c^3 + a)*d*x + a*c)*(b/a)^(1/3)*log(b*d*x + b*c + a*(b/a)^(2/3)) + 9*a)/(a^2*b*d^5*x^4 + 4*a^2*b*c*d^4*x^3 + 6*a^2*b*c^2*d^3*x^2 + (4*a^2*b*c^3 + a^3)*d^2*x + (a^2*b*c^4 + a^3*c)*d)","B",0
2875,1,509,0,1.568444," ","integrate(1/(d*x+c)^3/(a+b*(d*x+c)^3)^2,x, algorithm=""fricas"")","-\frac{15 \, b d^{3} x^{3} + 45 \, b c d^{2} x^{2} + 45 \, b c^{2} d x + 15 \, b c^{3} - 10 \, \sqrt{3} {\left(b d^{5} x^{5} + 5 \, b c d^{4} x^{4} + 10 \, b c^{2} d^{3} x^{3} + b c^{5} + {\left(10 \, b c^{3} + a\right)} d^{2} x^{2} + a c^{2} + {\left(5 \, b c^{4} + 2 \, a c\right)} d x\right)} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} {\left(a d x + a c\right)} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}} - \sqrt{3} b}{3 \, b}\right) + 5 \, {\left(b d^{5} x^{5} + 5 \, b c d^{4} x^{4} + 10 \, b c^{2} d^{3} x^{3} + b c^{5} + {\left(10 \, b c^{3} + a\right)} d^{2} x^{2} + a c^{2} + {\left(5 \, b c^{4} + 2 \, a c\right)} d x\right)} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} + a^{2} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}} + {\left(a b d x + a b c\right)} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}}\right) - 10 \, {\left(b d^{5} x^{5} + 5 \, b c d^{4} x^{4} + 10 \, b c^{2} d^{3} x^{3} + b c^{5} + {\left(10 \, b c^{3} + a\right)} d^{2} x^{2} + a c^{2} + {\left(5 \, b c^{4} + 2 \, a c\right)} d x\right)} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b d x + b c - a \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}}\right) + 9 \, a}{18 \, {\left(a^{2} b d^{6} x^{5} + 5 \, a^{2} b c d^{5} x^{4} + 10 \, a^{2} b c^{2} d^{4} x^{3} + {\left(10 \, a^{2} b c^{3} + a^{3}\right)} d^{3} x^{2} + {\left(5 \, a^{2} b c^{4} + 2 \, a^{3} c\right)} d^{2} x + {\left(a^{2} b c^{5} + a^{3} c^{2}\right)} d\right)}}"," ",0,"-1/18*(15*b*d^3*x^3 + 45*b*c*d^2*x^2 + 45*b*c^2*d*x + 15*b*c^3 - 10*sqrt(3)*(b*d^5*x^5 + 5*b*c*d^4*x^4 + 10*b*c^2*d^3*x^3 + b*c^5 + (10*b*c^3 + a)*d^2*x^2 + a*c^2 + (5*b*c^4 + 2*a*c)*d*x)*(-b^2/a^2)^(1/3)*arctan(1/3*(2*sqrt(3)*(a*d*x + a*c)*(-b^2/a^2)^(2/3) - sqrt(3)*b)/b) + 5*(b*d^5*x^5 + 5*b*c*d^4*x^4 + 10*b*c^2*d^3*x^3 + b*c^5 + (10*b*c^3 + a)*d^2*x^2 + a*c^2 + (5*b*c^4 + 2*a*c)*d*x)*(-b^2/a^2)^(1/3)*log(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 + a^2*(-b^2/a^2)^(2/3) + (a*b*d*x + a*b*c)*(-b^2/a^2)^(1/3)) - 10*(b*d^5*x^5 + 5*b*c*d^4*x^4 + 10*b*c^2*d^3*x^3 + b*c^5 + (10*b*c^3 + a)*d^2*x^2 + a*c^2 + (5*b*c^4 + 2*a*c)*d*x)*(-b^2/a^2)^(1/3)*log(b*d*x + b*c - a*(-b^2/a^2)^(1/3)) + 9*a)/(a^2*b*d^6*x^5 + 5*a^2*b*c*d^5*x^4 + 10*a^2*b*c^2*d^4*x^3 + (10*a^2*b*c^3 + a^3)*d^3*x^2 + (5*a^2*b*c^4 + 2*a^3*c)*d^2*x + (a^2*b*c^5 + a^3*c^2)*d)","B",0
2876,1,431,0,0.920167," ","integrate(1/(d*x+c)^4/(a+b*(d*x+c)^3)^2,x, algorithm=""fricas"")","-\frac{2 \, a b d^{3} x^{3} + 6 \, a b c d^{2} x^{2} + 6 \, a b c^{2} d x + 2 \, a b c^{3} + a^{2} - 2 \, {\left(b^{2} d^{6} x^{6} + 6 \, b^{2} c d^{5} x^{5} + 15 \, b^{2} c^{2} d^{4} x^{4} + b^{2} c^{6} + {\left(20 \, b^{2} c^{3} + a b\right)} d^{3} x^{3} + a b c^{3} + 3 \, {\left(5 \, b^{2} c^{4} + a b c\right)} d^{2} x^{2} + 3 \, {\left(2 \, b^{2} c^{5} + a b c^{2}\right)} d x\right)} \log\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right) + 6 \, {\left(b^{2} d^{6} x^{6} + 6 \, b^{2} c d^{5} x^{5} + 15 \, b^{2} c^{2} d^{4} x^{4} + b^{2} c^{6} + {\left(20 \, b^{2} c^{3} + a b\right)} d^{3} x^{3} + a b c^{3} + 3 \, {\left(5 \, b^{2} c^{4} + a b c\right)} d^{2} x^{2} + 3 \, {\left(2 \, b^{2} c^{5} + a b c^{2}\right)} d x\right)} \log\left(d x + c\right)}{3 \, {\left(a^{3} b d^{7} x^{6} + 6 \, a^{3} b c d^{6} x^{5} + 15 \, a^{3} b c^{2} d^{5} x^{4} + {\left(20 \, a^{3} b c^{3} + a^{4}\right)} d^{4} x^{3} + 3 \, {\left(5 \, a^{3} b c^{4} + a^{4} c\right)} d^{3} x^{2} + 3 \, {\left(2 \, a^{3} b c^{5} + a^{4} c^{2}\right)} d^{2} x + {\left(a^{3} b c^{6} + a^{4} c^{3}\right)} d\right)}}"," ",0,"-1/3*(2*a*b*d^3*x^3 + 6*a*b*c*d^2*x^2 + 6*a*b*c^2*d*x + 2*a*b*c^3 + a^2 - 2*(b^2*d^6*x^6 + 6*b^2*c*d^5*x^5 + 15*b^2*c^2*d^4*x^4 + b^2*c^6 + (20*b^2*c^3 + a*b)*d^3*x^3 + a*b*c^3 + 3*(5*b^2*c^4 + a*b*c)*d^2*x^2 + 3*(2*b^2*c^5 + a*b*c^2)*d*x)*log(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a) + 6*(b^2*d^6*x^6 + 6*b^2*c*d^5*x^5 + 15*b^2*c^2*d^4*x^4 + b^2*c^6 + (20*b^2*c^3 + a*b)*d^3*x^3 + a*b*c^3 + 3*(5*b^2*c^4 + a*b*c)*d^2*x^2 + 3*(2*b^2*c^5 + a*b*c^2)*d*x)*log(d*x + c))/(a^3*b*d^7*x^6 + 6*a^3*b*c*d^6*x^5 + 15*a^3*b*c^2*d^5*x^4 + (20*a^3*b*c^3 + a^4)*d^4*x^3 + 3*(5*a^3*b*c^4 + a^4*c)*d^3*x^2 + 3*(2*a^3*b*c^5 + a^4*c^2)*d^2*x + (a^3*b*c^6 + a^4*c^3)*d)","B",0
2877,1,1706,0,0.910973," ","integrate((d*x+c)^4/(a+b*(d*x+c)^3)^3,x, algorithm=""fricas"")","\left[\frac{6 \, a b^{3} d^{5} x^{5} + 30 \, a b^{3} c d^{4} x^{4} + 60 \, a b^{3} c^{2} d^{3} x^{3} + 6 \, a b^{3} c^{5} - 3 \, a^{2} b^{2} c^{2} + 3 \, {\left(20 \, a b^{3} c^{3} - a^{2} b^{2}\right)} d^{2} x^{2} + 6 \, {\left(5 \, a b^{3} c^{4} - a^{2} b^{2} c\right)} d x + 3 \, \sqrt{\frac{1}{3}} {\left(a b^{3} d^{6} x^{6} + 6 \, a b^{3} c d^{5} x^{5} + 15 \, a b^{3} c^{2} d^{4} x^{4} + a b^{3} c^{6} + 2 \, a^{2} b^{2} c^{3} + 2 \, {\left(10 \, a b^{3} c^{3} + a^{2} b^{2}\right)} d^{3} x^{3} + 3 \, {\left(5 \, a b^{3} c^{4} + 2 \, a^{2} b^{2} c\right)} d^{2} x^{2} + a^{3} b + 6 \, {\left(a b^{3} c^{5} + a^{2} b^{2} c^{2}\right)} d x\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \log\left(\frac{2 \, b^{2} d^{3} x^{3} + 6 \, b^{2} c d^{2} x^{2} + 6 \, b^{2} c^{2} d x + 2 \, b^{2} c^{3} - a b + 3 \, \sqrt{\frac{1}{3}} {\left(a b d x + a b c + 2 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} + \left(-a b^{2}\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} - 3 \, \left(-a b^{2}\right)^{\frac{2}{3}} {\left(d x + c\right)}}{b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a}\right) + {\left(b^{2} d^{6} x^{6} + 6 \, b^{2} c d^{5} x^{5} + 15 \, b^{2} c^{2} d^{4} x^{4} + b^{2} c^{6} + 2 \, {\left(10 \, b^{2} c^{3} + a b\right)} d^{3} x^{3} + 2 \, a b c^{3} + 3 \, {\left(5 \, b^{2} c^{4} + 2 \, a b c\right)} d^{2} x^{2} + 6 \, {\left(b^{2} c^{5} + a b c^{2}\right)} d x + a^{2}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} {\left(b d x + b c\right)} + \left(-a b^{2}\right)^{\frac{2}{3}}\right) - 2 \, {\left(b^{2} d^{6} x^{6} + 6 \, b^{2} c d^{5} x^{5} + 15 \, b^{2} c^{2} d^{4} x^{4} + b^{2} c^{6} + 2 \, {\left(10 \, b^{2} c^{3} + a b\right)} d^{3} x^{3} + 2 \, a b c^{3} + 3 \, {\left(5 \, b^{2} c^{4} + 2 \, a b c\right)} d^{2} x^{2} + 6 \, {\left(b^{2} c^{5} + a b c^{2}\right)} d x + a^{2}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b d x + b c - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{54 \, {\left(a^{2} b^{5} d^{7} x^{6} + 6 \, a^{2} b^{5} c d^{6} x^{5} + 15 \, a^{2} b^{5} c^{2} d^{5} x^{4} + 2 \, {\left(10 \, a^{2} b^{5} c^{3} + a^{3} b^{4}\right)} d^{4} x^{3} + 3 \, {\left(5 \, a^{2} b^{5} c^{4} + 2 \, a^{3} b^{4} c\right)} d^{3} x^{2} + 6 \, {\left(a^{2} b^{5} c^{5} + a^{3} b^{4} c^{2}\right)} d^{2} x + {\left(a^{2} b^{5} c^{6} + 2 \, a^{3} b^{4} c^{3} + a^{4} b^{3}\right)} d\right)}}, \frac{6 \, a b^{3} d^{5} x^{5} + 30 \, a b^{3} c d^{4} x^{4} + 60 \, a b^{3} c^{2} d^{3} x^{3} + 6 \, a b^{3} c^{5} - 3 \, a^{2} b^{2} c^{2} + 3 \, {\left(20 \, a b^{3} c^{3} - a^{2} b^{2}\right)} d^{2} x^{2} + 6 \, {\left(5 \, a b^{3} c^{4} - a^{2} b^{2} c\right)} d x + 6 \, \sqrt{\frac{1}{3}} {\left(a b^{3} d^{6} x^{6} + 6 \, a b^{3} c d^{5} x^{5} + 15 \, a b^{3} c^{2} d^{4} x^{4} + a b^{3} c^{6} + 2 \, a^{2} b^{2} c^{3} + 2 \, {\left(10 \, a b^{3} c^{3} + a^{2} b^{2}\right)} d^{3} x^{3} + 3 \, {\left(5 \, a b^{3} c^{4} + 2 \, a^{2} b^{2} c\right)} d^{2} x^{2} + a^{3} b + 6 \, {\left(a b^{3} c^{5} + a^{2} b^{2} c^{2}\right)} d x\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, b d x + 2 \, b c + \left(-a b^{2}\right)^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}}}{b}\right) + {\left(b^{2} d^{6} x^{6} + 6 \, b^{2} c d^{5} x^{5} + 15 \, b^{2} c^{2} d^{4} x^{4} + b^{2} c^{6} + 2 \, {\left(10 \, b^{2} c^{3} + a b\right)} d^{3} x^{3} + 2 \, a b c^{3} + 3 \, {\left(5 \, b^{2} c^{4} + 2 \, a b c\right)} d^{2} x^{2} + 6 \, {\left(b^{2} c^{5} + a b c^{2}\right)} d x + a^{2}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} {\left(b d x + b c\right)} + \left(-a b^{2}\right)^{\frac{2}{3}}\right) - 2 \, {\left(b^{2} d^{6} x^{6} + 6 \, b^{2} c d^{5} x^{5} + 15 \, b^{2} c^{2} d^{4} x^{4} + b^{2} c^{6} + 2 \, {\left(10 \, b^{2} c^{3} + a b\right)} d^{3} x^{3} + 2 \, a b c^{3} + 3 \, {\left(5 \, b^{2} c^{4} + 2 \, a b c\right)} d^{2} x^{2} + 6 \, {\left(b^{2} c^{5} + a b c^{2}\right)} d x + a^{2}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b d x + b c - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{54 \, {\left(a^{2} b^{5} d^{7} x^{6} + 6 \, a^{2} b^{5} c d^{6} x^{5} + 15 \, a^{2} b^{5} c^{2} d^{5} x^{4} + 2 \, {\left(10 \, a^{2} b^{5} c^{3} + a^{3} b^{4}\right)} d^{4} x^{3} + 3 \, {\left(5 \, a^{2} b^{5} c^{4} + 2 \, a^{3} b^{4} c\right)} d^{3} x^{2} + 6 \, {\left(a^{2} b^{5} c^{5} + a^{3} b^{4} c^{2}\right)} d^{2} x + {\left(a^{2} b^{5} c^{6} + 2 \, a^{3} b^{4} c^{3} + a^{4} b^{3}\right)} d\right)}}\right]"," ",0,"[1/54*(6*a*b^3*d^5*x^5 + 30*a*b^3*c*d^4*x^4 + 60*a*b^3*c^2*d^3*x^3 + 6*a*b^3*c^5 - 3*a^2*b^2*c^2 + 3*(20*a*b^3*c^3 - a^2*b^2)*d^2*x^2 + 6*(5*a*b^3*c^4 - a^2*b^2*c)*d*x + 3*sqrt(1/3)*(a*b^3*d^6*x^6 + 6*a*b^3*c*d^5*x^5 + 15*a*b^3*c^2*d^4*x^4 + a*b^3*c^6 + 2*a^2*b^2*c^3 + 2*(10*a*b^3*c^3 + a^2*b^2)*d^3*x^3 + 3*(5*a*b^3*c^4 + 2*a^2*b^2*c)*d^2*x^2 + a^3*b + 6*(a*b^3*c^5 + a^2*b^2*c^2)*d*x)*sqrt((-a*b^2)^(1/3)/a)*log((2*b^2*d^3*x^3 + 6*b^2*c*d^2*x^2 + 6*b^2*c^2*d*x + 2*b^2*c^3 - a*b + 3*sqrt(1/3)*(a*b*d*x + a*b*c + 2*(d^2*x^2 + 2*c*d*x + c^2)*(-a*b^2)^(2/3) + (-a*b^2)^(1/3)*a)*sqrt((-a*b^2)^(1/3)/a) - 3*(-a*b^2)^(2/3)*(d*x + c))/(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)) + (b^2*d^6*x^6 + 6*b^2*c*d^5*x^5 + 15*b^2*c^2*d^4*x^4 + b^2*c^6 + 2*(10*b^2*c^3 + a*b)*d^3*x^3 + 2*a*b*c^3 + 3*(5*b^2*c^4 + 2*a*b*c)*d^2*x^2 + 6*(b^2*c^5 + a*b*c^2)*d*x + a^2)*(-a*b^2)^(2/3)*log(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 + (-a*b^2)^(1/3)*(b*d*x + b*c) + (-a*b^2)^(2/3)) - 2*(b^2*d^6*x^6 + 6*b^2*c*d^5*x^5 + 15*b^2*c^2*d^4*x^4 + b^2*c^6 + 2*(10*b^2*c^3 + a*b)*d^3*x^3 + 2*a*b*c^3 + 3*(5*b^2*c^4 + 2*a*b*c)*d^2*x^2 + 6*(b^2*c^5 + a*b*c^2)*d*x + a^2)*(-a*b^2)^(2/3)*log(b*d*x + b*c - (-a*b^2)^(1/3)))/(a^2*b^5*d^7*x^6 + 6*a^2*b^5*c*d^6*x^5 + 15*a^2*b^5*c^2*d^5*x^4 + 2*(10*a^2*b^5*c^3 + a^3*b^4)*d^4*x^3 + 3*(5*a^2*b^5*c^4 + 2*a^3*b^4*c)*d^3*x^2 + 6*(a^2*b^5*c^5 + a^3*b^4*c^2)*d^2*x + (a^2*b^5*c^6 + 2*a^3*b^4*c^3 + a^4*b^3)*d), 1/54*(6*a*b^3*d^5*x^5 + 30*a*b^3*c*d^4*x^4 + 60*a*b^3*c^2*d^3*x^3 + 6*a*b^3*c^5 - 3*a^2*b^2*c^2 + 3*(20*a*b^3*c^3 - a^2*b^2)*d^2*x^2 + 6*(5*a*b^3*c^4 - a^2*b^2*c)*d*x + 6*sqrt(1/3)*(a*b^3*d^6*x^6 + 6*a*b^3*c*d^5*x^5 + 15*a*b^3*c^2*d^4*x^4 + a*b^3*c^6 + 2*a^2*b^2*c^3 + 2*(10*a*b^3*c^3 + a^2*b^2)*d^3*x^3 + 3*(5*a*b^3*c^4 + 2*a^2*b^2*c)*d^2*x^2 + a^3*b + 6*(a*b^3*c^5 + a^2*b^2*c^2)*d*x)*sqrt(-(-a*b^2)^(1/3)/a)*arctan(sqrt(1/3)*(2*b*d*x + 2*b*c + (-a*b^2)^(1/3))*sqrt(-(-a*b^2)^(1/3)/a)/b) + (b^2*d^6*x^6 + 6*b^2*c*d^5*x^5 + 15*b^2*c^2*d^4*x^4 + b^2*c^6 + 2*(10*b^2*c^3 + a*b)*d^3*x^3 + 2*a*b*c^3 + 3*(5*b^2*c^4 + 2*a*b*c)*d^2*x^2 + 6*(b^2*c^5 + a*b*c^2)*d*x + a^2)*(-a*b^2)^(2/3)*log(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 + (-a*b^2)^(1/3)*(b*d*x + b*c) + (-a*b^2)^(2/3)) - 2*(b^2*d^6*x^6 + 6*b^2*c*d^5*x^5 + 15*b^2*c^2*d^4*x^4 + b^2*c^6 + 2*(10*b^2*c^3 + a*b)*d^3*x^3 + 2*a*b*c^3 + 3*(5*b^2*c^4 + 2*a*b*c)*d^2*x^2 + 6*(b^2*c^5 + a*b*c^2)*d*x + a^2)*(-a*b^2)^(2/3)*log(b*d*x + b*c - (-a*b^2)^(1/3)))/(a^2*b^5*d^7*x^6 + 6*a^2*b^5*c*d^6*x^5 + 15*a^2*b^5*c^2*d^5*x^4 + 2*(10*a^2*b^5*c^3 + a^3*b^4)*d^4*x^3 + 3*(5*a^2*b^5*c^4 + 2*a^3*b^4*c)*d^3*x^2 + 6*(a^2*b^5*c^5 + a^3*b^4*c^2)*d^2*x + (a^2*b^5*c^6 + 2*a^3*b^4*c^3 + a^4*b^3)*d)]","B",0
2878,1,1650,0,1.044427," ","integrate((d*x+c)^3/(a+b*(d*x+c)^3)^3,x, algorithm=""fricas"")","\left[\frac{3 \, a^{2} b^{2} d^{4} x^{4} + 12 \, a^{2} b^{2} c d^{3} x^{3} + 18 \, a^{2} b^{2} c^{2} d^{2} x^{2} + 3 \, a^{2} b^{2} c^{4} - 6 \, a^{3} b c + 6 \, {\left(2 \, a^{2} b^{2} c^{3} - a^{3} b\right)} d x + 3 \, \sqrt{\frac{1}{3}} {\left(a b^{3} d^{6} x^{6} + 6 \, a b^{3} c d^{5} x^{5} + 15 \, a b^{3} c^{2} d^{4} x^{4} + a b^{3} c^{6} + 2 \, a^{2} b^{2} c^{3} + 2 \, {\left(10 \, a b^{3} c^{3} + a^{2} b^{2}\right)} d^{3} x^{3} + 3 \, {\left(5 \, a b^{3} c^{4} + 2 \, a^{2} b^{2} c\right)} d^{2} x^{2} + a^{3} b + 6 \, {\left(a b^{3} c^{5} + a^{2} b^{2} c^{2}\right)} d x\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \log\left(\frac{2 \, a b d^{3} x^{3} + 6 \, a b c d^{2} x^{2} + 6 \, a b c^{2} d x + 2 \, a b c^{3} - a^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, a b d^{2} x^{2} + 4 \, a b c d x + 2 \, a b c^{2} + \left(a^{2} b\right)^{\frac{2}{3}} {\left(d x + c\right)} - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} - 3 \, \left(a^{2} b\right)^{\frac{1}{3}} {\left(a d x + a c\right)}}{b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a}\right) - {\left(b^{2} d^{6} x^{6} + 6 \, b^{2} c d^{5} x^{5} + 15 \, b^{2} c^{2} d^{4} x^{4} + b^{2} c^{6} + 2 \, {\left(10 \, b^{2} c^{3} + a b\right)} d^{3} x^{3} + 2 \, a b c^{3} + 3 \, {\left(5 \, b^{2} c^{4} + 2 \, a b c\right)} d^{2} x^{2} + 6 \, {\left(b^{2} c^{5} + a b c^{2}\right)} d x + a^{2}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b d^{2} x^{2} + 2 \, a b c d x + a b c^{2} - \left(a^{2} b\right)^{\frac{2}{3}} {\left(d x + c\right)} + \left(a^{2} b\right)^{\frac{1}{3}} a\right) + 2 \, {\left(b^{2} d^{6} x^{6} + 6 \, b^{2} c d^{5} x^{5} + 15 \, b^{2} c^{2} d^{4} x^{4} + b^{2} c^{6} + 2 \, {\left(10 \, b^{2} c^{3} + a b\right)} d^{3} x^{3} + 2 \, a b c^{3} + 3 \, {\left(5 \, b^{2} c^{4} + 2 \, a b c\right)} d^{2} x^{2} + 6 \, {\left(b^{2} c^{5} + a b c^{2}\right)} d x + a^{2}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b d x + a b c + \left(a^{2} b\right)^{\frac{2}{3}}\right)}{54 \, {\left(a^{3} b^{4} d^{7} x^{6} + 6 \, a^{3} b^{4} c d^{6} x^{5} + 15 \, a^{3} b^{4} c^{2} d^{5} x^{4} + 2 \, {\left(10 \, a^{3} b^{4} c^{3} + a^{4} b^{3}\right)} d^{4} x^{3} + 3 \, {\left(5 \, a^{3} b^{4} c^{4} + 2 \, a^{4} b^{3} c\right)} d^{3} x^{2} + 6 \, {\left(a^{3} b^{4} c^{5} + a^{4} b^{3} c^{2}\right)} d^{2} x + {\left(a^{3} b^{4} c^{6} + 2 \, a^{4} b^{3} c^{3} + a^{5} b^{2}\right)} d\right)}}, \frac{3 \, a^{2} b^{2} d^{4} x^{4} + 12 \, a^{2} b^{2} c d^{3} x^{3} + 18 \, a^{2} b^{2} c^{2} d^{2} x^{2} + 3 \, a^{2} b^{2} c^{4} - 6 \, a^{3} b c + 6 \, {\left(2 \, a^{2} b^{2} c^{3} - a^{3} b\right)} d x + 6 \, \sqrt{\frac{1}{3}} {\left(a b^{3} d^{6} x^{6} + 6 \, a b^{3} c d^{5} x^{5} + 15 \, a b^{3} c^{2} d^{4} x^{4} + a b^{3} c^{6} + 2 \, a^{2} b^{2} c^{3} + 2 \, {\left(10 \, a b^{3} c^{3} + a^{2} b^{2}\right)} d^{3} x^{3} + 3 \, {\left(5 \, a b^{3} c^{4} + 2 \, a^{2} b^{2} c\right)} d^{2} x^{2} + a^{3} b + 6 \, {\left(a b^{3} c^{5} + a^{2} b^{2} c^{2}\right)} d x\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(a^{2} b\right)^{\frac{2}{3}} {\left(d x + c\right)} - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{a^{2}}\right) - {\left(b^{2} d^{6} x^{6} + 6 \, b^{2} c d^{5} x^{5} + 15 \, b^{2} c^{2} d^{4} x^{4} + b^{2} c^{6} + 2 \, {\left(10 \, b^{2} c^{3} + a b\right)} d^{3} x^{3} + 2 \, a b c^{3} + 3 \, {\left(5 \, b^{2} c^{4} + 2 \, a b c\right)} d^{2} x^{2} + 6 \, {\left(b^{2} c^{5} + a b c^{2}\right)} d x + a^{2}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b d^{2} x^{2} + 2 \, a b c d x + a b c^{2} - \left(a^{2} b\right)^{\frac{2}{3}} {\left(d x + c\right)} + \left(a^{2} b\right)^{\frac{1}{3}} a\right) + 2 \, {\left(b^{2} d^{6} x^{6} + 6 \, b^{2} c d^{5} x^{5} + 15 \, b^{2} c^{2} d^{4} x^{4} + b^{2} c^{6} + 2 \, {\left(10 \, b^{2} c^{3} + a b\right)} d^{3} x^{3} + 2 \, a b c^{3} + 3 \, {\left(5 \, b^{2} c^{4} + 2 \, a b c\right)} d^{2} x^{2} + 6 \, {\left(b^{2} c^{5} + a b c^{2}\right)} d x + a^{2}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b d x + a b c + \left(a^{2} b\right)^{\frac{2}{3}}\right)}{54 \, {\left(a^{3} b^{4} d^{7} x^{6} + 6 \, a^{3} b^{4} c d^{6} x^{5} + 15 \, a^{3} b^{4} c^{2} d^{5} x^{4} + 2 \, {\left(10 \, a^{3} b^{4} c^{3} + a^{4} b^{3}\right)} d^{4} x^{3} + 3 \, {\left(5 \, a^{3} b^{4} c^{4} + 2 \, a^{4} b^{3} c\right)} d^{3} x^{2} + 6 \, {\left(a^{3} b^{4} c^{5} + a^{4} b^{3} c^{2}\right)} d^{2} x + {\left(a^{3} b^{4} c^{6} + 2 \, a^{4} b^{3} c^{3} + a^{5} b^{2}\right)} d\right)}}\right]"," ",0,"[1/54*(3*a^2*b^2*d^4*x^4 + 12*a^2*b^2*c*d^3*x^3 + 18*a^2*b^2*c^2*d^2*x^2 + 3*a^2*b^2*c^4 - 6*a^3*b*c + 6*(2*a^2*b^2*c^3 - a^3*b)*d*x + 3*sqrt(1/3)*(a*b^3*d^6*x^6 + 6*a*b^3*c*d^5*x^5 + 15*a*b^3*c^2*d^4*x^4 + a*b^3*c^6 + 2*a^2*b^2*c^3 + 2*(10*a*b^3*c^3 + a^2*b^2)*d^3*x^3 + 3*(5*a*b^3*c^4 + 2*a^2*b^2*c)*d^2*x^2 + a^3*b + 6*(a*b^3*c^5 + a^2*b^2*c^2)*d*x)*sqrt(-(a^2*b)^(1/3)/b)*log((2*a*b*d^3*x^3 + 6*a*b*c*d^2*x^2 + 6*a*b*c^2*d*x + 2*a*b*c^3 - a^2 + 3*sqrt(1/3)*(2*a*b*d^2*x^2 + 4*a*b*c*d*x + 2*a*b*c^2 + (a^2*b)^(2/3)*(d*x + c) - (a^2*b)^(1/3)*a)*sqrt(-(a^2*b)^(1/3)/b) - 3*(a^2*b)^(1/3)*(a*d*x + a*c))/(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)) - (b^2*d^6*x^6 + 6*b^2*c*d^5*x^5 + 15*b^2*c^2*d^4*x^4 + b^2*c^6 + 2*(10*b^2*c^3 + a*b)*d^3*x^3 + 2*a*b*c^3 + 3*(5*b^2*c^4 + 2*a*b*c)*d^2*x^2 + 6*(b^2*c^5 + a*b*c^2)*d*x + a^2)*(a^2*b)^(2/3)*log(a*b*d^2*x^2 + 2*a*b*c*d*x + a*b*c^2 - (a^2*b)^(2/3)*(d*x + c) + (a^2*b)^(1/3)*a) + 2*(b^2*d^6*x^6 + 6*b^2*c*d^5*x^5 + 15*b^2*c^2*d^4*x^4 + b^2*c^6 + 2*(10*b^2*c^3 + a*b)*d^3*x^3 + 2*a*b*c^3 + 3*(5*b^2*c^4 + 2*a*b*c)*d^2*x^2 + 6*(b^2*c^5 + a*b*c^2)*d*x + a^2)*(a^2*b)^(2/3)*log(a*b*d*x + a*b*c + (a^2*b)^(2/3)))/(a^3*b^4*d^7*x^6 + 6*a^3*b^4*c*d^6*x^5 + 15*a^3*b^4*c^2*d^5*x^4 + 2*(10*a^3*b^4*c^3 + a^4*b^3)*d^4*x^3 + 3*(5*a^3*b^4*c^4 + 2*a^4*b^3*c)*d^3*x^2 + 6*(a^3*b^4*c^5 + a^4*b^3*c^2)*d^2*x + (a^3*b^4*c^6 + 2*a^4*b^3*c^3 + a^5*b^2)*d), 1/54*(3*a^2*b^2*d^4*x^4 + 12*a^2*b^2*c*d^3*x^3 + 18*a^2*b^2*c^2*d^2*x^2 + 3*a^2*b^2*c^4 - 6*a^3*b*c + 6*(2*a^2*b^2*c^3 - a^3*b)*d*x + 6*sqrt(1/3)*(a*b^3*d^6*x^6 + 6*a*b^3*c*d^5*x^5 + 15*a*b^3*c^2*d^4*x^4 + a*b^3*c^6 + 2*a^2*b^2*c^3 + 2*(10*a*b^3*c^3 + a^2*b^2)*d^3*x^3 + 3*(5*a*b^3*c^4 + 2*a^2*b^2*c)*d^2*x^2 + a^3*b + 6*(a*b^3*c^5 + a^2*b^2*c^2)*d*x)*sqrt((a^2*b)^(1/3)/b)*arctan(sqrt(1/3)*(2*(a^2*b)^(2/3)*(d*x + c) - (a^2*b)^(1/3)*a)*sqrt((a^2*b)^(1/3)/b)/a^2) - (b^2*d^6*x^6 + 6*b^2*c*d^5*x^5 + 15*b^2*c^2*d^4*x^4 + b^2*c^6 + 2*(10*b^2*c^3 + a*b)*d^3*x^3 + 2*a*b*c^3 + 3*(5*b^2*c^4 + 2*a*b*c)*d^2*x^2 + 6*(b^2*c^5 + a*b*c^2)*d*x + a^2)*(a^2*b)^(2/3)*log(a*b*d^2*x^2 + 2*a*b*c*d*x + a*b*c^2 - (a^2*b)^(2/3)*(d*x + c) + (a^2*b)^(1/3)*a) + 2*(b^2*d^6*x^6 + 6*b^2*c*d^5*x^5 + 15*b^2*c^2*d^4*x^4 + b^2*c^6 + 2*(10*b^2*c^3 + a*b)*d^3*x^3 + 2*a*b*c^3 + 3*(5*b^2*c^4 + 2*a*b*c)*d^2*x^2 + 6*(b^2*c^5 + a*b*c^2)*d*x + a^2)*(a^2*b)^(2/3)*log(a*b*d*x + a*b*c + (a^2*b)^(2/3)))/(a^3*b^4*d^7*x^6 + 6*a^3*b^4*c*d^6*x^5 + 15*a^3*b^4*c^2*d^5*x^4 + 2*(10*a^3*b^4*c^3 + a^4*b^3)*d^4*x^3 + 3*(5*a^3*b^4*c^4 + 2*a^4*b^3*c)*d^3*x^2 + 6*(a^3*b^4*c^5 + a^4*b^3*c^2)*d^2*x + (a^3*b^4*c^6 + 2*a^4*b^3*c^3 + a^5*b^2)*d)]","B",0
2879,1,133,0,1.062262," ","integrate((d*x+c)^2/(a+b*(d*x+c)^3)^3,x, algorithm=""fricas"")","-\frac{1}{6 \, {\left(b^{3} d^{7} x^{6} + 6 \, b^{3} c d^{6} x^{5} + 15 \, b^{3} c^{2} d^{5} x^{4} + 2 \, {\left(10 \, b^{3} c^{3} + a b^{2}\right)} d^{4} x^{3} + 3 \, {\left(5 \, b^{3} c^{4} + 2 \, a b^{2} c\right)} d^{3} x^{2} + 6 \, {\left(b^{3} c^{5} + a b^{2} c^{2}\right)} d^{2} x + {\left(b^{3} c^{6} + 2 \, a b^{2} c^{3} + a^{2} b\right)} d\right)}}"," ",0,"-1/6/(b^3*d^7*x^6 + 6*b^3*c*d^6*x^5 + 15*b^3*c^2*d^5*x^4 + 2*(10*b^3*c^3 + a*b^2)*d^4*x^3 + 3*(5*b^3*c^4 + 2*a*b^2*c)*d^3*x^2 + 6*(b^3*c^5 + a*b^2*c^2)*d^2*x + (b^3*c^6 + 2*a*b^2*c^3 + a^2*b)*d)","B",0
2880,1,1708,0,1.052668," ","integrate((d*x+c)/(a+b*(d*x+c)^3)^3,x, algorithm=""fricas"")","\left[\frac{12 \, a b^{3} d^{5} x^{5} + 60 \, a b^{3} c d^{4} x^{4} + 120 \, a b^{3} c^{2} d^{3} x^{3} + 12 \, a b^{3} c^{5} + 21 \, a^{2} b^{2} c^{2} + 3 \, {\left(40 \, a b^{3} c^{3} + 7 \, a^{2} b^{2}\right)} d^{2} x^{2} + 6 \, {\left(10 \, a b^{3} c^{4} + 7 \, a^{2} b^{2} c\right)} d x + 6 \, \sqrt{\frac{1}{3}} {\left(a b^{3} d^{6} x^{6} + 6 \, a b^{3} c d^{5} x^{5} + 15 \, a b^{3} c^{2} d^{4} x^{4} + a b^{3} c^{6} + 2 \, a^{2} b^{2} c^{3} + 2 \, {\left(10 \, a b^{3} c^{3} + a^{2} b^{2}\right)} d^{3} x^{3} + 3 \, {\left(5 \, a b^{3} c^{4} + 2 \, a^{2} b^{2} c\right)} d^{2} x^{2} + a^{3} b + 6 \, {\left(a b^{3} c^{5} + a^{2} b^{2} c^{2}\right)} d x\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \log\left(\frac{2 \, b^{2} d^{3} x^{3} + 6 \, b^{2} c d^{2} x^{2} + 6 \, b^{2} c^{2} d x + 2 \, b^{2} c^{3} - a b + 3 \, \sqrt{\frac{1}{3}} {\left(a b d x + a b c + 2 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} + \left(-a b^{2}\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} - 3 \, \left(-a b^{2}\right)^{\frac{2}{3}} {\left(d x + c\right)}}{b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a}\right) + 2 \, {\left(b^{2} d^{6} x^{6} + 6 \, b^{2} c d^{5} x^{5} + 15 \, b^{2} c^{2} d^{4} x^{4} + b^{2} c^{6} + 2 \, {\left(10 \, b^{2} c^{3} + a b\right)} d^{3} x^{3} + 2 \, a b c^{3} + 3 \, {\left(5 \, b^{2} c^{4} + 2 \, a b c\right)} d^{2} x^{2} + 6 \, {\left(b^{2} c^{5} + a b c^{2}\right)} d x + a^{2}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} {\left(b d x + b c\right)} + \left(-a b^{2}\right)^{\frac{2}{3}}\right) - 4 \, {\left(b^{2} d^{6} x^{6} + 6 \, b^{2} c d^{5} x^{5} + 15 \, b^{2} c^{2} d^{4} x^{4} + b^{2} c^{6} + 2 \, {\left(10 \, b^{2} c^{3} + a b\right)} d^{3} x^{3} + 2 \, a b c^{3} + 3 \, {\left(5 \, b^{2} c^{4} + 2 \, a b c\right)} d^{2} x^{2} + 6 \, {\left(b^{2} c^{5} + a b c^{2}\right)} d x + a^{2}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b d x + b c - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{54 \, {\left(a^{3} b^{4} d^{7} x^{6} + 6 \, a^{3} b^{4} c d^{6} x^{5} + 15 \, a^{3} b^{4} c^{2} d^{5} x^{4} + 2 \, {\left(10 \, a^{3} b^{4} c^{3} + a^{4} b^{3}\right)} d^{4} x^{3} + 3 \, {\left(5 \, a^{3} b^{4} c^{4} + 2 \, a^{4} b^{3} c\right)} d^{3} x^{2} + 6 \, {\left(a^{3} b^{4} c^{5} + a^{4} b^{3} c^{2}\right)} d^{2} x + {\left(a^{3} b^{4} c^{6} + 2 \, a^{4} b^{3} c^{3} + a^{5} b^{2}\right)} d\right)}}, \frac{12 \, a b^{3} d^{5} x^{5} + 60 \, a b^{3} c d^{4} x^{4} + 120 \, a b^{3} c^{2} d^{3} x^{3} + 12 \, a b^{3} c^{5} + 21 \, a^{2} b^{2} c^{2} + 3 \, {\left(40 \, a b^{3} c^{3} + 7 \, a^{2} b^{2}\right)} d^{2} x^{2} + 6 \, {\left(10 \, a b^{3} c^{4} + 7 \, a^{2} b^{2} c\right)} d x + 12 \, \sqrt{\frac{1}{3}} {\left(a b^{3} d^{6} x^{6} + 6 \, a b^{3} c d^{5} x^{5} + 15 \, a b^{3} c^{2} d^{4} x^{4} + a b^{3} c^{6} + 2 \, a^{2} b^{2} c^{3} + 2 \, {\left(10 \, a b^{3} c^{3} + a^{2} b^{2}\right)} d^{3} x^{3} + 3 \, {\left(5 \, a b^{3} c^{4} + 2 \, a^{2} b^{2} c\right)} d^{2} x^{2} + a^{3} b + 6 \, {\left(a b^{3} c^{5} + a^{2} b^{2} c^{2}\right)} d x\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, b d x + 2 \, b c + \left(-a b^{2}\right)^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}}}{b}\right) + 2 \, {\left(b^{2} d^{6} x^{6} + 6 \, b^{2} c d^{5} x^{5} + 15 \, b^{2} c^{2} d^{4} x^{4} + b^{2} c^{6} + 2 \, {\left(10 \, b^{2} c^{3} + a b\right)} d^{3} x^{3} + 2 \, a b c^{3} + 3 \, {\left(5 \, b^{2} c^{4} + 2 \, a b c\right)} d^{2} x^{2} + 6 \, {\left(b^{2} c^{5} + a b c^{2}\right)} d x + a^{2}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} {\left(b d x + b c\right)} + \left(-a b^{2}\right)^{\frac{2}{3}}\right) - 4 \, {\left(b^{2} d^{6} x^{6} + 6 \, b^{2} c d^{5} x^{5} + 15 \, b^{2} c^{2} d^{4} x^{4} + b^{2} c^{6} + 2 \, {\left(10 \, b^{2} c^{3} + a b\right)} d^{3} x^{3} + 2 \, a b c^{3} + 3 \, {\left(5 \, b^{2} c^{4} + 2 \, a b c\right)} d^{2} x^{2} + 6 \, {\left(b^{2} c^{5} + a b c^{2}\right)} d x + a^{2}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b d x + b c - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{54 \, {\left(a^{3} b^{4} d^{7} x^{6} + 6 \, a^{3} b^{4} c d^{6} x^{5} + 15 \, a^{3} b^{4} c^{2} d^{5} x^{4} + 2 \, {\left(10 \, a^{3} b^{4} c^{3} + a^{4} b^{3}\right)} d^{4} x^{3} + 3 \, {\left(5 \, a^{3} b^{4} c^{4} + 2 \, a^{4} b^{3} c\right)} d^{3} x^{2} + 6 \, {\left(a^{3} b^{4} c^{5} + a^{4} b^{3} c^{2}\right)} d^{2} x + {\left(a^{3} b^{4} c^{6} + 2 \, a^{4} b^{3} c^{3} + a^{5} b^{2}\right)} d\right)}}\right]"," ",0,"[1/54*(12*a*b^3*d^5*x^5 + 60*a*b^3*c*d^4*x^4 + 120*a*b^3*c^2*d^3*x^3 + 12*a*b^3*c^5 + 21*a^2*b^2*c^2 + 3*(40*a*b^3*c^3 + 7*a^2*b^2)*d^2*x^2 + 6*(10*a*b^3*c^4 + 7*a^2*b^2*c)*d*x + 6*sqrt(1/3)*(a*b^3*d^6*x^6 + 6*a*b^3*c*d^5*x^5 + 15*a*b^3*c^2*d^4*x^4 + a*b^3*c^6 + 2*a^2*b^2*c^3 + 2*(10*a*b^3*c^3 + a^2*b^2)*d^3*x^3 + 3*(5*a*b^3*c^4 + 2*a^2*b^2*c)*d^2*x^2 + a^3*b + 6*(a*b^3*c^5 + a^2*b^2*c^2)*d*x)*sqrt((-a*b^2)^(1/3)/a)*log((2*b^2*d^3*x^3 + 6*b^2*c*d^2*x^2 + 6*b^2*c^2*d*x + 2*b^2*c^3 - a*b + 3*sqrt(1/3)*(a*b*d*x + a*b*c + 2*(d^2*x^2 + 2*c*d*x + c^2)*(-a*b^2)^(2/3) + (-a*b^2)^(1/3)*a)*sqrt((-a*b^2)^(1/3)/a) - 3*(-a*b^2)^(2/3)*(d*x + c))/(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)) + 2*(b^2*d^6*x^6 + 6*b^2*c*d^5*x^5 + 15*b^2*c^2*d^4*x^4 + b^2*c^6 + 2*(10*b^2*c^3 + a*b)*d^3*x^3 + 2*a*b*c^3 + 3*(5*b^2*c^4 + 2*a*b*c)*d^2*x^2 + 6*(b^2*c^5 + a*b*c^2)*d*x + a^2)*(-a*b^2)^(2/3)*log(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 + (-a*b^2)^(1/3)*(b*d*x + b*c) + (-a*b^2)^(2/3)) - 4*(b^2*d^6*x^6 + 6*b^2*c*d^5*x^5 + 15*b^2*c^2*d^4*x^4 + b^2*c^6 + 2*(10*b^2*c^3 + a*b)*d^3*x^3 + 2*a*b*c^3 + 3*(5*b^2*c^4 + 2*a*b*c)*d^2*x^2 + 6*(b^2*c^5 + a*b*c^2)*d*x + a^2)*(-a*b^2)^(2/3)*log(b*d*x + b*c - (-a*b^2)^(1/3)))/(a^3*b^4*d^7*x^6 + 6*a^3*b^4*c*d^6*x^5 + 15*a^3*b^4*c^2*d^5*x^4 + 2*(10*a^3*b^4*c^3 + a^4*b^3)*d^4*x^3 + 3*(5*a^3*b^4*c^4 + 2*a^4*b^3*c)*d^3*x^2 + 6*(a^3*b^4*c^5 + a^4*b^3*c^2)*d^2*x + (a^3*b^4*c^6 + 2*a^4*b^3*c^3 + a^5*b^2)*d), 1/54*(12*a*b^3*d^5*x^5 + 60*a*b^3*c*d^4*x^4 + 120*a*b^3*c^2*d^3*x^3 + 12*a*b^3*c^5 + 21*a^2*b^2*c^2 + 3*(40*a*b^3*c^3 + 7*a^2*b^2)*d^2*x^2 + 6*(10*a*b^3*c^4 + 7*a^2*b^2*c)*d*x + 12*sqrt(1/3)*(a*b^3*d^6*x^6 + 6*a*b^3*c*d^5*x^5 + 15*a*b^3*c^2*d^4*x^4 + a*b^3*c^6 + 2*a^2*b^2*c^3 + 2*(10*a*b^3*c^3 + a^2*b^2)*d^3*x^3 + 3*(5*a*b^3*c^4 + 2*a^2*b^2*c)*d^2*x^2 + a^3*b + 6*(a*b^3*c^5 + a^2*b^2*c^2)*d*x)*sqrt(-(-a*b^2)^(1/3)/a)*arctan(sqrt(1/3)*(2*b*d*x + 2*b*c + (-a*b^2)^(1/3))*sqrt(-(-a*b^2)^(1/3)/a)/b) + 2*(b^2*d^6*x^6 + 6*b^2*c*d^5*x^5 + 15*b^2*c^2*d^4*x^4 + b^2*c^6 + 2*(10*b^2*c^3 + a*b)*d^3*x^3 + 2*a*b*c^3 + 3*(5*b^2*c^4 + 2*a*b*c)*d^2*x^2 + 6*(b^2*c^5 + a*b*c^2)*d*x + a^2)*(-a*b^2)^(2/3)*log(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 + (-a*b^2)^(1/3)*(b*d*x + b*c) + (-a*b^2)^(2/3)) - 4*(b^2*d^6*x^6 + 6*b^2*c*d^5*x^5 + 15*b^2*c^2*d^4*x^4 + b^2*c^6 + 2*(10*b^2*c^3 + a*b)*d^3*x^3 + 2*a*b*c^3 + 3*(5*b^2*c^4 + 2*a*b*c)*d^2*x^2 + 6*(b^2*c^5 + a*b*c^2)*d*x + a^2)*(-a*b^2)^(2/3)*log(b*d*x + b*c - (-a*b^2)^(1/3)))/(a^3*b^4*d^7*x^6 + 6*a^3*b^4*c*d^6*x^5 + 15*a^3*b^4*c^2*d^5*x^4 + 2*(10*a^3*b^4*c^3 + a^4*b^3)*d^4*x^3 + 3*(5*a^3*b^4*c^4 + 2*a^4*b^3*c)*d^3*x^2 + 6*(a^3*b^4*c^5 + a^4*b^3*c^2)*d^2*x + (a^3*b^4*c^6 + 2*a^4*b^3*c^3 + a^5*b^2)*d)]","B",0
2881,1,1646,0,1.213172," ","integrate(1/(a+b*(d*x+c)^3)^3,x, algorithm=""fricas"")","\left[\frac{15 \, a^{2} b^{2} d^{4} x^{4} + 60 \, a^{2} b^{2} c d^{3} x^{3} + 90 \, a^{2} b^{2} c^{2} d^{2} x^{2} + 15 \, a^{2} b^{2} c^{4} + 24 \, a^{3} b c + 12 \, {\left(5 \, a^{2} b^{2} c^{3} + 2 \, a^{3} b\right)} d x + 15 \, \sqrt{\frac{1}{3}} {\left(a b^{3} d^{6} x^{6} + 6 \, a b^{3} c d^{5} x^{5} + 15 \, a b^{3} c^{2} d^{4} x^{4} + a b^{3} c^{6} + 2 \, a^{2} b^{2} c^{3} + 2 \, {\left(10 \, a b^{3} c^{3} + a^{2} b^{2}\right)} d^{3} x^{3} + 3 \, {\left(5 \, a b^{3} c^{4} + 2 \, a^{2} b^{2} c\right)} d^{2} x^{2} + a^{3} b + 6 \, {\left(a b^{3} c^{5} + a^{2} b^{2} c^{2}\right)} d x\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \log\left(\frac{2 \, a b d^{3} x^{3} + 6 \, a b c d^{2} x^{2} + 6 \, a b c^{2} d x + 2 \, a b c^{3} - a^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, a b d^{2} x^{2} + 4 \, a b c d x + 2 \, a b c^{2} + \left(a^{2} b\right)^{\frac{2}{3}} {\left(d x + c\right)} - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} - 3 \, \left(a^{2} b\right)^{\frac{1}{3}} {\left(a d x + a c\right)}}{b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a}\right) - 5 \, {\left(b^{2} d^{6} x^{6} + 6 \, b^{2} c d^{5} x^{5} + 15 \, b^{2} c^{2} d^{4} x^{4} + b^{2} c^{6} + 2 \, {\left(10 \, b^{2} c^{3} + a b\right)} d^{3} x^{3} + 2 \, a b c^{3} + 3 \, {\left(5 \, b^{2} c^{4} + 2 \, a b c\right)} d^{2} x^{2} + 6 \, {\left(b^{2} c^{5} + a b c^{2}\right)} d x + a^{2}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b d^{2} x^{2} + 2 \, a b c d x + a b c^{2} - \left(a^{2} b\right)^{\frac{2}{3}} {\left(d x + c\right)} + \left(a^{2} b\right)^{\frac{1}{3}} a\right) + 10 \, {\left(b^{2} d^{6} x^{6} + 6 \, b^{2} c d^{5} x^{5} + 15 \, b^{2} c^{2} d^{4} x^{4} + b^{2} c^{6} + 2 \, {\left(10 \, b^{2} c^{3} + a b\right)} d^{3} x^{3} + 2 \, a b c^{3} + 3 \, {\left(5 \, b^{2} c^{4} + 2 \, a b c\right)} d^{2} x^{2} + 6 \, {\left(b^{2} c^{5} + a b c^{2}\right)} d x + a^{2}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b d x + a b c + \left(a^{2} b\right)^{\frac{2}{3}}\right)}{54 \, {\left(a^{4} b^{3} d^{7} x^{6} + 6 \, a^{4} b^{3} c d^{6} x^{5} + 15 \, a^{4} b^{3} c^{2} d^{5} x^{4} + 2 \, {\left(10 \, a^{4} b^{3} c^{3} + a^{5} b^{2}\right)} d^{4} x^{3} + 3 \, {\left(5 \, a^{4} b^{3} c^{4} + 2 \, a^{5} b^{2} c\right)} d^{3} x^{2} + 6 \, {\left(a^{4} b^{3} c^{5} + a^{5} b^{2} c^{2}\right)} d^{2} x + {\left(a^{4} b^{3} c^{6} + 2 \, a^{5} b^{2} c^{3} + a^{6} b\right)} d\right)}}, \frac{15 \, a^{2} b^{2} d^{4} x^{4} + 60 \, a^{2} b^{2} c d^{3} x^{3} + 90 \, a^{2} b^{2} c^{2} d^{2} x^{2} + 15 \, a^{2} b^{2} c^{4} + 24 \, a^{3} b c + 12 \, {\left(5 \, a^{2} b^{2} c^{3} + 2 \, a^{3} b\right)} d x + 30 \, \sqrt{\frac{1}{3}} {\left(a b^{3} d^{6} x^{6} + 6 \, a b^{3} c d^{5} x^{5} + 15 \, a b^{3} c^{2} d^{4} x^{4} + a b^{3} c^{6} + 2 \, a^{2} b^{2} c^{3} + 2 \, {\left(10 \, a b^{3} c^{3} + a^{2} b^{2}\right)} d^{3} x^{3} + 3 \, {\left(5 \, a b^{3} c^{4} + 2 \, a^{2} b^{2} c\right)} d^{2} x^{2} + a^{3} b + 6 \, {\left(a b^{3} c^{5} + a^{2} b^{2} c^{2}\right)} d x\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(a^{2} b\right)^{\frac{2}{3}} {\left(d x + c\right)} - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{a^{2}}\right) - 5 \, {\left(b^{2} d^{6} x^{6} + 6 \, b^{2} c d^{5} x^{5} + 15 \, b^{2} c^{2} d^{4} x^{4} + b^{2} c^{6} + 2 \, {\left(10 \, b^{2} c^{3} + a b\right)} d^{3} x^{3} + 2 \, a b c^{3} + 3 \, {\left(5 \, b^{2} c^{4} + 2 \, a b c\right)} d^{2} x^{2} + 6 \, {\left(b^{2} c^{5} + a b c^{2}\right)} d x + a^{2}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b d^{2} x^{2} + 2 \, a b c d x + a b c^{2} - \left(a^{2} b\right)^{\frac{2}{3}} {\left(d x + c\right)} + \left(a^{2} b\right)^{\frac{1}{3}} a\right) + 10 \, {\left(b^{2} d^{6} x^{6} + 6 \, b^{2} c d^{5} x^{5} + 15 \, b^{2} c^{2} d^{4} x^{4} + b^{2} c^{6} + 2 \, {\left(10 \, b^{2} c^{3} + a b\right)} d^{3} x^{3} + 2 \, a b c^{3} + 3 \, {\left(5 \, b^{2} c^{4} + 2 \, a b c\right)} d^{2} x^{2} + 6 \, {\left(b^{2} c^{5} + a b c^{2}\right)} d x + a^{2}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b d x + a b c + \left(a^{2} b\right)^{\frac{2}{3}}\right)}{54 \, {\left(a^{4} b^{3} d^{7} x^{6} + 6 \, a^{4} b^{3} c d^{6} x^{5} + 15 \, a^{4} b^{3} c^{2} d^{5} x^{4} + 2 \, {\left(10 \, a^{4} b^{3} c^{3} + a^{5} b^{2}\right)} d^{4} x^{3} + 3 \, {\left(5 \, a^{4} b^{3} c^{4} + 2 \, a^{5} b^{2} c\right)} d^{3} x^{2} + 6 \, {\left(a^{4} b^{3} c^{5} + a^{5} b^{2} c^{2}\right)} d^{2} x + {\left(a^{4} b^{3} c^{6} + 2 \, a^{5} b^{2} c^{3} + a^{6} b\right)} d\right)}}\right]"," ",0,"[1/54*(15*a^2*b^2*d^4*x^4 + 60*a^2*b^2*c*d^3*x^3 + 90*a^2*b^2*c^2*d^2*x^2 + 15*a^2*b^2*c^4 + 24*a^3*b*c + 12*(5*a^2*b^2*c^3 + 2*a^3*b)*d*x + 15*sqrt(1/3)*(a*b^3*d^6*x^6 + 6*a*b^3*c*d^5*x^5 + 15*a*b^3*c^2*d^4*x^4 + a*b^3*c^6 + 2*a^2*b^2*c^3 + 2*(10*a*b^3*c^3 + a^2*b^2)*d^3*x^3 + 3*(5*a*b^3*c^4 + 2*a^2*b^2*c)*d^2*x^2 + a^3*b + 6*(a*b^3*c^5 + a^2*b^2*c^2)*d*x)*sqrt(-(a^2*b)^(1/3)/b)*log((2*a*b*d^3*x^3 + 6*a*b*c*d^2*x^2 + 6*a*b*c^2*d*x + 2*a*b*c^3 - a^2 + 3*sqrt(1/3)*(2*a*b*d^2*x^2 + 4*a*b*c*d*x + 2*a*b*c^2 + (a^2*b)^(2/3)*(d*x + c) - (a^2*b)^(1/3)*a)*sqrt(-(a^2*b)^(1/3)/b) - 3*(a^2*b)^(1/3)*(a*d*x + a*c))/(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)) - 5*(b^2*d^6*x^6 + 6*b^2*c*d^5*x^5 + 15*b^2*c^2*d^4*x^4 + b^2*c^6 + 2*(10*b^2*c^3 + a*b)*d^3*x^3 + 2*a*b*c^3 + 3*(5*b^2*c^4 + 2*a*b*c)*d^2*x^2 + 6*(b^2*c^5 + a*b*c^2)*d*x + a^2)*(a^2*b)^(2/3)*log(a*b*d^2*x^2 + 2*a*b*c*d*x + a*b*c^2 - (a^2*b)^(2/3)*(d*x + c) + (a^2*b)^(1/3)*a) + 10*(b^2*d^6*x^6 + 6*b^2*c*d^5*x^5 + 15*b^2*c^2*d^4*x^4 + b^2*c^6 + 2*(10*b^2*c^3 + a*b)*d^3*x^3 + 2*a*b*c^3 + 3*(5*b^2*c^4 + 2*a*b*c)*d^2*x^2 + 6*(b^2*c^5 + a*b*c^2)*d*x + a^2)*(a^2*b)^(2/3)*log(a*b*d*x + a*b*c + (a^2*b)^(2/3)))/(a^4*b^3*d^7*x^6 + 6*a^4*b^3*c*d^6*x^5 + 15*a^4*b^3*c^2*d^5*x^4 + 2*(10*a^4*b^3*c^3 + a^5*b^2)*d^4*x^3 + 3*(5*a^4*b^3*c^4 + 2*a^5*b^2*c)*d^3*x^2 + 6*(a^4*b^3*c^5 + a^5*b^2*c^2)*d^2*x + (a^4*b^3*c^6 + 2*a^5*b^2*c^3 + a^6*b)*d), 1/54*(15*a^2*b^2*d^4*x^4 + 60*a^2*b^2*c*d^3*x^3 + 90*a^2*b^2*c^2*d^2*x^2 + 15*a^2*b^2*c^4 + 24*a^3*b*c + 12*(5*a^2*b^2*c^3 + 2*a^3*b)*d*x + 30*sqrt(1/3)*(a*b^3*d^6*x^6 + 6*a*b^3*c*d^5*x^5 + 15*a*b^3*c^2*d^4*x^4 + a*b^3*c^6 + 2*a^2*b^2*c^3 + 2*(10*a*b^3*c^3 + a^2*b^2)*d^3*x^3 + 3*(5*a*b^3*c^4 + 2*a^2*b^2*c)*d^2*x^2 + a^3*b + 6*(a*b^3*c^5 + a^2*b^2*c^2)*d*x)*sqrt((a^2*b)^(1/3)/b)*arctan(sqrt(1/3)*(2*(a^2*b)^(2/3)*(d*x + c) - (a^2*b)^(1/3)*a)*sqrt((a^2*b)^(1/3)/b)/a^2) - 5*(b^2*d^6*x^6 + 6*b^2*c*d^5*x^5 + 15*b^2*c^2*d^4*x^4 + b^2*c^6 + 2*(10*b^2*c^3 + a*b)*d^3*x^3 + 2*a*b*c^3 + 3*(5*b^2*c^4 + 2*a*b*c)*d^2*x^2 + 6*(b^2*c^5 + a*b*c^2)*d*x + a^2)*(a^2*b)^(2/3)*log(a*b*d^2*x^2 + 2*a*b*c*d*x + a*b*c^2 - (a^2*b)^(2/3)*(d*x + c) + (a^2*b)^(1/3)*a) + 10*(b^2*d^6*x^6 + 6*b^2*c*d^5*x^5 + 15*b^2*c^2*d^4*x^4 + b^2*c^6 + 2*(10*b^2*c^3 + a*b)*d^3*x^3 + 2*a*b*c^3 + 3*(5*b^2*c^4 + 2*a*b*c)*d^2*x^2 + 6*(b^2*c^5 + a*b*c^2)*d*x + a^2)*(a^2*b)^(2/3)*log(a*b*d*x + a*b*c + (a^2*b)^(2/3)))/(a^4*b^3*d^7*x^6 + 6*a^4*b^3*c*d^6*x^5 + 15*a^4*b^3*c^2*d^5*x^4 + 2*(10*a^4*b^3*c^3 + a^5*b^2)*d^4*x^3 + 3*(5*a^4*b^3*c^4 + 2*a^5*b^2*c)*d^3*x^2 + 6*(a^4*b^3*c^5 + a^5*b^2*c^2)*d^2*x + (a^4*b^3*c^6 + 2*a^5*b^2*c^3 + a^6*b)*d)]","B",0
2882,1,467,0,0.852833," ","integrate(1/(d*x+c)/(a+b*(d*x+c)^3)^3,x, algorithm=""fricas"")","\frac{2 \, a b d^{3} x^{3} + 6 \, a b c d^{2} x^{2} + 6 \, a b c^{2} d x + 2 \, a b c^{3} + 3 \, a^{2} - 2 \, {\left(b^{2} d^{6} x^{6} + 6 \, b^{2} c d^{5} x^{5} + 15 \, b^{2} c^{2} d^{4} x^{4} + b^{2} c^{6} + 2 \, {\left(10 \, b^{2} c^{3} + a b\right)} d^{3} x^{3} + 2 \, a b c^{3} + 3 \, {\left(5 \, b^{2} c^{4} + 2 \, a b c\right)} d^{2} x^{2} + 6 \, {\left(b^{2} c^{5} + a b c^{2}\right)} d x + a^{2}\right)} \log\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right) + 6 \, {\left(b^{2} d^{6} x^{6} + 6 \, b^{2} c d^{5} x^{5} + 15 \, b^{2} c^{2} d^{4} x^{4} + b^{2} c^{6} + 2 \, {\left(10 \, b^{2} c^{3} + a b\right)} d^{3} x^{3} + 2 \, a b c^{3} + 3 \, {\left(5 \, b^{2} c^{4} + 2 \, a b c\right)} d^{2} x^{2} + 6 \, {\left(b^{2} c^{5} + a b c^{2}\right)} d x + a^{2}\right)} \log\left(d x + c\right)}{6 \, {\left(a^{3} b^{2} d^{7} x^{6} + 6 \, a^{3} b^{2} c d^{6} x^{5} + 15 \, a^{3} b^{2} c^{2} d^{5} x^{4} + 2 \, {\left(10 \, a^{3} b^{2} c^{3} + a^{4} b\right)} d^{4} x^{3} + 3 \, {\left(5 \, a^{3} b^{2} c^{4} + 2 \, a^{4} b c\right)} d^{3} x^{2} + 6 \, {\left(a^{3} b^{2} c^{5} + a^{4} b c^{2}\right)} d^{2} x + {\left(a^{3} b^{2} c^{6} + 2 \, a^{4} b c^{3} + a^{5}\right)} d\right)}}"," ",0,"1/6*(2*a*b*d^3*x^3 + 6*a*b*c*d^2*x^2 + 6*a*b*c^2*d*x + 2*a*b*c^3 + 3*a^2 - 2*(b^2*d^6*x^6 + 6*b^2*c*d^5*x^5 + 15*b^2*c^2*d^4*x^4 + b^2*c^6 + 2*(10*b^2*c^3 + a*b)*d^3*x^3 + 2*a*b*c^3 + 3*(5*b^2*c^4 + 2*a*b*c)*d^2*x^2 + 6*(b^2*c^5 + a*b*c^2)*d*x + a^2)*log(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a) + 6*(b^2*d^6*x^6 + 6*b^2*c*d^5*x^5 + 15*b^2*c^2*d^4*x^4 + b^2*c^6 + 2*(10*b^2*c^3 + a*b)*d^3*x^3 + 2*a*b*c^3 + 3*(5*b^2*c^4 + 2*a*b*c)*d^2*x^2 + 6*(b^2*c^5 + a*b*c^2)*d*x + a^2)*log(d*x + c))/(a^3*b^2*d^7*x^6 + 6*a^3*b^2*c*d^6*x^5 + 15*a^3*b^2*c^2*d^5*x^4 + 2*(10*a^3*b^2*c^3 + a^4*b)*d^4*x^3 + 3*(5*a^3*b^2*c^4 + 2*a^4*b*c)*d^3*x^2 + 6*(a^3*b^2*c^5 + a^4*b*c^2)*d^2*x + (a^3*b^2*c^6 + 2*a^4*b*c^3 + a^5)*d)","B",0
2883,1,855,0,1.105473," ","integrate(1/(d*x+c)^2/(a+b*(d*x+c)^3)^3,x, algorithm=""fricas"")","-\frac{84 \, b^{2} d^{6} x^{6} + 504 \, b^{2} c d^{5} x^{5} + 1260 \, b^{2} c^{2} d^{4} x^{4} + 84 \, b^{2} c^{6} + 21 \, {\left(80 \, b^{2} c^{3} + 7 \, a b\right)} d^{3} x^{3} + 147 \, a b c^{3} + 63 \, {\left(20 \, b^{2} c^{4} + 7 \, a b c\right)} d^{2} x^{2} + 63 \, {\left(8 \, b^{2} c^{5} + 7 \, a b c^{2}\right)} d x + 28 \, \sqrt{3} {\left(b^{2} d^{7} x^{7} + 7 \, b^{2} c d^{6} x^{6} + 21 \, b^{2} c^{2} d^{5} x^{5} + b^{2} c^{7} + {\left(35 \, b^{2} c^{3} + 2 \, a b\right)} d^{4} x^{4} + {\left(35 \, b^{2} c^{4} + 8 \, a b c\right)} d^{3} x^{3} + 2 \, a b c^{4} + 3 \, {\left(7 \, b^{2} c^{5} + 4 \, a b c^{2}\right)} d^{2} x^{2} + a^{2} c + {\left(7 \, b^{2} c^{6} + 8 \, a b c^{3} + a^{2}\right)} d x\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}} \arctan\left(\frac{2}{3} \, \sqrt{3} {\left(d x + c\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}} - \frac{1}{3} \, \sqrt{3}\right) + 14 \, {\left(b^{2} d^{7} x^{7} + 7 \, b^{2} c d^{6} x^{6} + 21 \, b^{2} c^{2} d^{5} x^{5} + b^{2} c^{7} + {\left(35 \, b^{2} c^{3} + 2 \, a b\right)} d^{4} x^{4} + {\left(35 \, b^{2} c^{4} + 8 \, a b c\right)} d^{3} x^{3} + 2 \, a b c^{4} + 3 \, {\left(7 \, b^{2} c^{5} + 4 \, a b c^{2}\right)} d^{2} x^{2} + a^{2} c + {\left(7 \, b^{2} c^{6} + 8 \, a b c^{3} + a^{2}\right)} d x\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}} \log\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} - {\left(a d x + a c\right)} \left(\frac{b}{a}\right)^{\frac{2}{3}} + a \left(\frac{b}{a}\right)^{\frac{1}{3}}\right) - 28 \, {\left(b^{2} d^{7} x^{7} + 7 \, b^{2} c d^{6} x^{6} + 21 \, b^{2} c^{2} d^{5} x^{5} + b^{2} c^{7} + {\left(35 \, b^{2} c^{3} + 2 \, a b\right)} d^{4} x^{4} + {\left(35 \, b^{2} c^{4} + 8 \, a b c\right)} d^{3} x^{3} + 2 \, a b c^{4} + 3 \, {\left(7 \, b^{2} c^{5} + 4 \, a b c^{2}\right)} d^{2} x^{2} + a^{2} c + {\left(7 \, b^{2} c^{6} + 8 \, a b c^{3} + a^{2}\right)} d x\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}} \log\left(b d x + b c + a \left(\frac{b}{a}\right)^{\frac{2}{3}}\right) + 54 \, a^{2}}{54 \, {\left(a^{3} b^{2} d^{8} x^{7} + 7 \, a^{3} b^{2} c d^{7} x^{6} + 21 \, a^{3} b^{2} c^{2} d^{6} x^{5} + {\left(35 \, a^{3} b^{2} c^{3} + 2 \, a^{4} b\right)} d^{5} x^{4} + {\left(35 \, a^{3} b^{2} c^{4} + 8 \, a^{4} b c\right)} d^{4} x^{3} + 3 \, {\left(7 \, a^{3} b^{2} c^{5} + 4 \, a^{4} b c^{2}\right)} d^{3} x^{2} + {\left(7 \, a^{3} b^{2} c^{6} + 8 \, a^{4} b c^{3} + a^{5}\right)} d^{2} x + {\left(a^{3} b^{2} c^{7} + 2 \, a^{4} b c^{4} + a^{5} c\right)} d\right)}}"," ",0,"-1/54*(84*b^2*d^6*x^6 + 504*b^2*c*d^5*x^5 + 1260*b^2*c^2*d^4*x^4 + 84*b^2*c^6 + 21*(80*b^2*c^3 + 7*a*b)*d^3*x^3 + 147*a*b*c^3 + 63*(20*b^2*c^4 + 7*a*b*c)*d^2*x^2 + 63*(8*b^2*c^5 + 7*a*b*c^2)*d*x + 28*sqrt(3)*(b^2*d^7*x^7 + 7*b^2*c*d^6*x^6 + 21*b^2*c^2*d^5*x^5 + b^2*c^7 + (35*b^2*c^3 + 2*a*b)*d^4*x^4 + (35*b^2*c^4 + 8*a*b*c)*d^3*x^3 + 2*a*b*c^4 + 3*(7*b^2*c^5 + 4*a*b*c^2)*d^2*x^2 + a^2*c + (7*b^2*c^6 + 8*a*b*c^3 + a^2)*d*x)*(b/a)^(1/3)*arctan(2/3*sqrt(3)*(d*x + c)*(b/a)^(1/3) - 1/3*sqrt(3)) + 14*(b^2*d^7*x^7 + 7*b^2*c*d^6*x^6 + 21*b^2*c^2*d^5*x^5 + b^2*c^7 + (35*b^2*c^3 + 2*a*b)*d^4*x^4 + (35*b^2*c^4 + 8*a*b*c)*d^3*x^3 + 2*a*b*c^4 + 3*(7*b^2*c^5 + 4*a*b*c^2)*d^2*x^2 + a^2*c + (7*b^2*c^6 + 8*a*b*c^3 + a^2)*d*x)*(b/a)^(1/3)*log(b*d^2*x^2 + 2*b*c*d*x + b*c^2 - (a*d*x + a*c)*(b/a)^(2/3) + a*(b/a)^(1/3)) - 28*(b^2*d^7*x^7 + 7*b^2*c*d^6*x^6 + 21*b^2*c^2*d^5*x^5 + b^2*c^7 + (35*b^2*c^3 + 2*a*b)*d^4*x^4 + (35*b^2*c^4 + 8*a*b*c)*d^3*x^3 + 2*a*b*c^4 + 3*(7*b^2*c^5 + 4*a*b*c^2)*d^2*x^2 + a^2*c + (7*b^2*c^6 + 8*a*b*c^3 + a^2)*d*x)*(b/a)^(1/3)*log(b*d*x + b*c + a*(b/a)^(2/3)) + 54*a^2)/(a^3*b^2*d^8*x^7 + 7*a^3*b^2*c*d^7*x^6 + 21*a^3*b^2*c^2*d^6*x^5 + (35*a^3*b^2*c^3 + 2*a^4*b)*d^5*x^4 + (35*a^3*b^2*c^4 + 8*a^4*b*c)*d^4*x^3 + 3*(7*a^3*b^2*c^5 + 4*a^4*b*c^2)*d^3*x^2 + (7*a^3*b^2*c^6 + 8*a^4*b*c^3 + a^5)*d^2*x + (a^3*b^2*c^7 + 2*a^4*b*c^4 + a^5*c)*d)","B",0
2884,1,1024,0,1.103090," ","integrate(1/(d*x+c)^3/(a+b*(d*x+c)^3)^3,x, algorithm=""fricas"")","-\frac{60 \, b^{2} d^{6} x^{6} + 360 \, b^{2} c d^{5} x^{5} + 900 \, b^{2} c^{2} d^{4} x^{4} + 60 \, b^{2} c^{6} + 48 \, {\left(25 \, b^{2} c^{3} + 2 \, a b\right)} d^{3} x^{3} + 96 \, a b c^{3} + 36 \, {\left(25 \, b^{2} c^{4} + 8 \, a b c\right)} d^{2} x^{2} + 72 \, {\left(5 \, b^{2} c^{5} + 4 \, a b c^{2}\right)} d x - 40 \, \sqrt{3} {\left(b^{2} d^{8} x^{8} + 8 \, b^{2} c d^{7} x^{7} + 28 \, b^{2} c^{2} d^{6} x^{6} + 2 \, {\left(28 \, b^{2} c^{3} + a b\right)} d^{5} x^{5} + b^{2} c^{8} + 10 \, {\left(7 \, b^{2} c^{4} + a b c\right)} d^{4} x^{4} + 2 \, a b c^{5} + 4 \, {\left(14 \, b^{2} c^{5} + 5 \, a b c^{2}\right)} d^{3} x^{3} + {\left(28 \, b^{2} c^{6} + 20 \, a b c^{3} + a^{2}\right)} d^{2} x^{2} + a^{2} c^{2} + 2 \, {\left(4 \, b^{2} c^{7} + 5 \, a b c^{4} + a^{2} c\right)} d x\right)} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} {\left(a d x + a c\right)} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}} - \sqrt{3} b}{3 \, b}\right) + 20 \, {\left(b^{2} d^{8} x^{8} + 8 \, b^{2} c d^{7} x^{7} + 28 \, b^{2} c^{2} d^{6} x^{6} + 2 \, {\left(28 \, b^{2} c^{3} + a b\right)} d^{5} x^{5} + b^{2} c^{8} + 10 \, {\left(7 \, b^{2} c^{4} + a b c\right)} d^{4} x^{4} + 2 \, a b c^{5} + 4 \, {\left(14 \, b^{2} c^{5} + 5 \, a b c^{2}\right)} d^{3} x^{3} + {\left(28 \, b^{2} c^{6} + 20 \, a b c^{3} + a^{2}\right)} d^{2} x^{2} + a^{2} c^{2} + 2 \, {\left(4 \, b^{2} c^{7} + 5 \, a b c^{4} + a^{2} c\right)} d x\right)} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} + a^{2} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}} + {\left(a b d x + a b c\right)} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}}\right) - 40 \, {\left(b^{2} d^{8} x^{8} + 8 \, b^{2} c d^{7} x^{7} + 28 \, b^{2} c^{2} d^{6} x^{6} + 2 \, {\left(28 \, b^{2} c^{3} + a b\right)} d^{5} x^{5} + b^{2} c^{8} + 10 \, {\left(7 \, b^{2} c^{4} + a b c\right)} d^{4} x^{4} + 2 \, a b c^{5} + 4 \, {\left(14 \, b^{2} c^{5} + 5 \, a b c^{2}\right)} d^{3} x^{3} + {\left(28 \, b^{2} c^{6} + 20 \, a b c^{3} + a^{2}\right)} d^{2} x^{2} + a^{2} c^{2} + 2 \, {\left(4 \, b^{2} c^{7} + 5 \, a b c^{4} + a^{2} c\right)} d x\right)} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b d x + b c - a \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}}\right) + 27 \, a^{2}}{54 \, {\left(a^{3} b^{2} d^{9} x^{8} + 8 \, a^{3} b^{2} c d^{8} x^{7} + 28 \, a^{3} b^{2} c^{2} d^{7} x^{6} + 2 \, {\left(28 \, a^{3} b^{2} c^{3} + a^{4} b\right)} d^{6} x^{5} + 10 \, {\left(7 \, a^{3} b^{2} c^{4} + a^{4} b c\right)} d^{5} x^{4} + 4 \, {\left(14 \, a^{3} b^{2} c^{5} + 5 \, a^{4} b c^{2}\right)} d^{4} x^{3} + {\left(28 \, a^{3} b^{2} c^{6} + 20 \, a^{4} b c^{3} + a^{5}\right)} d^{3} x^{2} + 2 \, {\left(4 \, a^{3} b^{2} c^{7} + 5 \, a^{4} b c^{4} + a^{5} c\right)} d^{2} x + {\left(a^{3} b^{2} c^{8} + 2 \, a^{4} b c^{5} + a^{5} c^{2}\right)} d\right)}}"," ",0,"-1/54*(60*b^2*d^6*x^6 + 360*b^2*c*d^5*x^5 + 900*b^2*c^2*d^4*x^4 + 60*b^2*c^6 + 48*(25*b^2*c^3 + 2*a*b)*d^3*x^3 + 96*a*b*c^3 + 36*(25*b^2*c^4 + 8*a*b*c)*d^2*x^2 + 72*(5*b^2*c^5 + 4*a*b*c^2)*d*x - 40*sqrt(3)*(b^2*d^8*x^8 + 8*b^2*c*d^7*x^7 + 28*b^2*c^2*d^6*x^6 + 2*(28*b^2*c^3 + a*b)*d^5*x^5 + b^2*c^8 + 10*(7*b^2*c^4 + a*b*c)*d^4*x^4 + 2*a*b*c^5 + 4*(14*b^2*c^5 + 5*a*b*c^2)*d^3*x^3 + (28*b^2*c^6 + 20*a*b*c^3 + a^2)*d^2*x^2 + a^2*c^2 + 2*(4*b^2*c^7 + 5*a*b*c^4 + a^2*c)*d*x)*(-b^2/a^2)^(1/3)*arctan(1/3*(2*sqrt(3)*(a*d*x + a*c)*(-b^2/a^2)^(2/3) - sqrt(3)*b)/b) + 20*(b^2*d^8*x^8 + 8*b^2*c*d^7*x^7 + 28*b^2*c^2*d^6*x^6 + 2*(28*b^2*c^3 + a*b)*d^5*x^5 + b^2*c^8 + 10*(7*b^2*c^4 + a*b*c)*d^4*x^4 + 2*a*b*c^5 + 4*(14*b^2*c^5 + 5*a*b*c^2)*d^3*x^3 + (28*b^2*c^6 + 20*a*b*c^3 + a^2)*d^2*x^2 + a^2*c^2 + 2*(4*b^2*c^7 + 5*a*b*c^4 + a^2*c)*d*x)*(-b^2/a^2)^(1/3)*log(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 + a^2*(-b^2/a^2)^(2/3) + (a*b*d*x + a*b*c)*(-b^2/a^2)^(1/3)) - 40*(b^2*d^8*x^8 + 8*b^2*c*d^7*x^7 + 28*b^2*c^2*d^6*x^6 + 2*(28*b^2*c^3 + a*b)*d^5*x^5 + b^2*c^8 + 10*(7*b^2*c^4 + a*b*c)*d^4*x^4 + 2*a*b*c^5 + 4*(14*b^2*c^5 + 5*a*b*c^2)*d^3*x^3 + (28*b^2*c^6 + 20*a*b*c^3 + a^2)*d^2*x^2 + a^2*c^2 + 2*(4*b^2*c^7 + 5*a*b*c^4 + a^2*c)*d*x)*(-b^2/a^2)^(1/3)*log(b*d*x + b*c - a*(-b^2/a^2)^(1/3)) + 27*a^2)/(a^3*b^2*d^9*x^8 + 8*a^3*b^2*c*d^8*x^7 + 28*a^3*b^2*c^2*d^7*x^6 + 2*(28*a^3*b^2*c^3 + a^4*b)*d^6*x^5 + 10*(7*a^3*b^2*c^4 + a^4*b*c)*d^5*x^4 + 4*(14*a^3*b^2*c^5 + 5*a^4*b*c^2)*d^4*x^3 + (28*a^3*b^2*c^6 + 20*a^4*b*c^3 + a^5)*d^3*x^2 + 2*(4*a^3*b^2*c^7 + 5*a^4*b*c^4 + a^5*c)*d^2*x + (a^3*b^2*c^8 + 2*a^4*b*c^5 + a^5*c^2)*d)","B",0
2885,1,889,0,1.150407," ","integrate(1/(d*x+c)^4/(a+b*(d*x+c)^3)^3,x, algorithm=""fricas"")","-\frac{6 \, a b^{2} d^{6} x^{6} + 36 \, a b^{2} c d^{5} x^{5} + 90 \, a b^{2} c^{2} d^{4} x^{4} + 6 \, a b^{2} c^{6} + 3 \, {\left(40 \, a b^{2} c^{3} + 3 \, a^{2} b\right)} d^{3} x^{3} + 9 \, a^{2} b c^{3} + 9 \, {\left(10 \, a b^{2} c^{4} + 3 \, a^{2} b c\right)} d^{2} x^{2} + 2 \, a^{3} + 9 \, {\left(4 \, a b^{2} c^{5} + 3 \, a^{2} b c^{2}\right)} d x - 6 \, {\left(b^{3} d^{9} x^{9} + 9 \, b^{3} c d^{8} x^{8} + 36 \, b^{3} c^{2} d^{7} x^{7} + 2 \, {\left(42 \, b^{3} c^{3} + a b^{2}\right)} d^{6} x^{6} + b^{3} c^{9} + 6 \, {\left(21 \, b^{3} c^{4} + 2 \, a b^{2} c\right)} d^{5} x^{5} + 2 \, a b^{2} c^{6} + 6 \, {\left(21 \, b^{3} c^{5} + 5 \, a b^{2} c^{2}\right)} d^{4} x^{4} + {\left(84 \, b^{3} c^{6} + 40 \, a b^{2} c^{3} + a^{2} b\right)} d^{3} x^{3} + a^{2} b c^{3} + 3 \, {\left(12 \, b^{3} c^{7} + 10 \, a b^{2} c^{4} + a^{2} b c\right)} d^{2} x^{2} + 3 \, {\left(3 \, b^{3} c^{8} + 4 \, a b^{2} c^{5} + a^{2} b c^{2}\right)} d x\right)} \log\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right) + 18 \, {\left(b^{3} d^{9} x^{9} + 9 \, b^{3} c d^{8} x^{8} + 36 \, b^{3} c^{2} d^{7} x^{7} + 2 \, {\left(42 \, b^{3} c^{3} + a b^{2}\right)} d^{6} x^{6} + b^{3} c^{9} + 6 \, {\left(21 \, b^{3} c^{4} + 2 \, a b^{2} c\right)} d^{5} x^{5} + 2 \, a b^{2} c^{6} + 6 \, {\left(21 \, b^{3} c^{5} + 5 \, a b^{2} c^{2}\right)} d^{4} x^{4} + {\left(84 \, b^{3} c^{6} + 40 \, a b^{2} c^{3} + a^{2} b\right)} d^{3} x^{3} + a^{2} b c^{3} + 3 \, {\left(12 \, b^{3} c^{7} + 10 \, a b^{2} c^{4} + a^{2} b c\right)} d^{2} x^{2} + 3 \, {\left(3 \, b^{3} c^{8} + 4 \, a b^{2} c^{5} + a^{2} b c^{2}\right)} d x\right)} \log\left(d x + c\right)}{6 \, {\left(a^{4} b^{2} d^{10} x^{9} + 9 \, a^{4} b^{2} c d^{9} x^{8} + 36 \, a^{4} b^{2} c^{2} d^{8} x^{7} + 2 \, {\left(42 \, a^{4} b^{2} c^{3} + a^{5} b\right)} d^{7} x^{6} + 6 \, {\left(21 \, a^{4} b^{2} c^{4} + 2 \, a^{5} b c\right)} d^{6} x^{5} + 6 \, {\left(21 \, a^{4} b^{2} c^{5} + 5 \, a^{5} b c^{2}\right)} d^{5} x^{4} + {\left(84 \, a^{4} b^{2} c^{6} + 40 \, a^{5} b c^{3} + a^{6}\right)} d^{4} x^{3} + 3 \, {\left(12 \, a^{4} b^{2} c^{7} + 10 \, a^{5} b c^{4} + a^{6} c\right)} d^{3} x^{2} + 3 \, {\left(3 \, a^{4} b^{2} c^{8} + 4 \, a^{5} b c^{5} + a^{6} c^{2}\right)} d^{2} x + {\left(a^{4} b^{2} c^{9} + 2 \, a^{5} b c^{6} + a^{6} c^{3}\right)} d\right)}}"," ",0,"-1/6*(6*a*b^2*d^6*x^6 + 36*a*b^2*c*d^5*x^5 + 90*a*b^2*c^2*d^4*x^4 + 6*a*b^2*c^6 + 3*(40*a*b^2*c^3 + 3*a^2*b)*d^3*x^3 + 9*a^2*b*c^3 + 9*(10*a*b^2*c^4 + 3*a^2*b*c)*d^2*x^2 + 2*a^3 + 9*(4*a*b^2*c^5 + 3*a^2*b*c^2)*d*x - 6*(b^3*d^9*x^9 + 9*b^3*c*d^8*x^8 + 36*b^3*c^2*d^7*x^7 + 2*(42*b^3*c^3 + a*b^2)*d^6*x^6 + b^3*c^9 + 6*(21*b^3*c^4 + 2*a*b^2*c)*d^5*x^5 + 2*a*b^2*c^6 + 6*(21*b^3*c^5 + 5*a*b^2*c^2)*d^4*x^4 + (84*b^3*c^6 + 40*a*b^2*c^3 + a^2*b)*d^3*x^3 + a^2*b*c^3 + 3*(12*b^3*c^7 + 10*a*b^2*c^4 + a^2*b*c)*d^2*x^2 + 3*(3*b^3*c^8 + 4*a*b^2*c^5 + a^2*b*c^2)*d*x)*log(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a) + 18*(b^3*d^9*x^9 + 9*b^3*c*d^8*x^8 + 36*b^3*c^2*d^7*x^7 + 2*(42*b^3*c^3 + a*b^2)*d^6*x^6 + b^3*c^9 + 6*(21*b^3*c^4 + 2*a*b^2*c)*d^5*x^5 + 2*a*b^2*c^6 + 6*(21*b^3*c^5 + 5*a*b^2*c^2)*d^4*x^4 + (84*b^3*c^6 + 40*a*b^2*c^3 + a^2*b)*d^3*x^3 + a^2*b*c^3 + 3*(12*b^3*c^7 + 10*a*b^2*c^4 + a^2*b*c)*d^2*x^2 + 3*(3*b^3*c^8 + 4*a*b^2*c^5 + a^2*b*c^2)*d*x)*log(d*x + c))/(a^4*b^2*d^10*x^9 + 9*a^4*b^2*c*d^9*x^8 + 36*a^4*b^2*c^2*d^8*x^7 + 2*(42*a^4*b^2*c^3 + a^5*b)*d^7*x^6 + 6*(21*a^4*b^2*c^4 + 2*a^5*b*c)*d^6*x^5 + 6*(21*a^4*b^2*c^5 + 5*a^5*b*c^2)*d^5*x^4 + (84*a^4*b^2*c^6 + 40*a^5*b*c^3 + a^6)*d^4*x^3 + 3*(12*a^4*b^2*c^7 + 10*a^5*b*c^4 + a^6*c)*d^3*x^2 + 3*(3*a^4*b^2*c^8 + 4*a^5*b*c^5 + a^6*c^2)*d^2*x + (a^4*b^2*c^9 + 2*a^5*b*c^6 + a^6*c^3)*d)","B",0
2886,1,179,0,0.848154," ","integrate((d*e*x+c*e)^4/(a+b*(d*x+c)^3),x, algorithm=""fricas"")","\frac{3 \, d^{2} e^{4} x^{2} + 6 \, c d e^{4} x - 2 \, \sqrt{3} e^{4} \left(\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} {\left(b d x + b c\right)} \left(\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}} - \sqrt{3} a}{3 \, a}\right) - e^{4} \left(\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}} \log\left(a d^{2} x^{2} + 2 \, a c d x + a c^{2} - {\left(b d x + b c\right)} \left(\frac{a^{2}}{b^{2}}\right)^{\frac{2}{3}} + a \left(\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}}\right) + 2 \, e^{4} \left(\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}} \log\left(a d x + a c + b \left(\frac{a^{2}}{b^{2}}\right)^{\frac{2}{3}}\right)}{6 \, b d}"," ",0,"1/6*(3*d^2*e^4*x^2 + 6*c*d*e^4*x - 2*sqrt(3)*e^4*(a^2/b^2)^(1/3)*arctan(1/3*(2*sqrt(3)*(b*d*x + b*c)*(a^2/b^2)^(1/3) - sqrt(3)*a)/a) - e^4*(a^2/b^2)^(1/3)*log(a*d^2*x^2 + 2*a*c*d*x + a*c^2 - (b*d*x + b*c)*(a^2/b^2)^(2/3) + a*(a^2/b^2)^(1/3)) + 2*e^4*(a^2/b^2)^(1/3)*log(a*d*x + a*c + b*(a^2/b^2)^(2/3)))/(b*d)","A",0
2887,1,147,0,0.704681," ","integrate((d*e*x+c*e)^3/(a+b*(d*x+c)^3),x, algorithm=""fricas"")","\frac{6 \, d e^{3} x + 2 \, \sqrt{3} e^{3} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} {\left(b d x + b c\right)} \left(-\frac{a}{b}\right)^{\frac{2}{3}} - \sqrt{3} a}{3 \, a}\right) - e^{3} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + {\left(d x + c\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right) + 2 \, e^{3} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left(d x + c - \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}{6 \, b d}"," ",0,"1/6*(6*d*e^3*x + 2*sqrt(3)*e^3*(-a/b)^(1/3)*arctan(1/3*(2*sqrt(3)*(b*d*x + b*c)*(-a/b)^(2/3) - sqrt(3)*a)/a) - e^3*(-a/b)^(1/3)*log(d^2*x^2 + 2*c*d*x + c^2 + (d*x + c)*(-a/b)^(1/3) + (-a/b)^(2/3)) + 2*e^3*(-a/b)^(1/3)*log(d*x + c - (-a/b)^(1/3)))/(b*d)","A",0
2888,1,45,0,0.888103," ","integrate((d*e*x+c*e)^2/(a+b*(d*x+c)^3),x, algorithm=""fricas"")","\frac{e^{2} \log\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right)}{3 \, b d}"," ",0,"1/3*e^2*log(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)/(b*d)","A",0
2889,1,458,0,0.992675," ","integrate((d*e*x+c*e)/(a+b*(d*x+c)^3),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{\frac{1}{3}} a b e \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \log\left(\frac{2 \, b^{2} d^{3} x^{3} + 6 \, b^{2} c d^{2} x^{2} + 6 \, b^{2} c^{2} d x + 2 \, b^{2} c^{3} - a b + 3 \, \sqrt{\frac{1}{3}} {\left(a b d x + a b c + 2 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} + \left(-a b^{2}\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} - 3 \, \left(-a b^{2}\right)^{\frac{2}{3}} {\left(d x + c\right)}}{b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a}\right) + \left(-a b^{2}\right)^{\frac{2}{3}} e \log\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} {\left(b d x + b c\right)} + \left(-a b^{2}\right)^{\frac{2}{3}}\right) - 2 \, \left(-a b^{2}\right)^{\frac{2}{3}} e \log\left(b d x + b c - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{6 \, a b^{2} d}, \frac{6 \, \sqrt{\frac{1}{3}} a b e \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, b d x + 2 \, b c + \left(-a b^{2}\right)^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}}}{b}\right) + \left(-a b^{2}\right)^{\frac{2}{3}} e \log\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} {\left(b d x + b c\right)} + \left(-a b^{2}\right)^{\frac{2}{3}}\right) - 2 \, \left(-a b^{2}\right)^{\frac{2}{3}} e \log\left(b d x + b c - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{6 \, a b^{2} d}\right]"," ",0,"[1/6*(3*sqrt(1/3)*a*b*e*sqrt((-a*b^2)^(1/3)/a)*log((2*b^2*d^3*x^3 + 6*b^2*c*d^2*x^2 + 6*b^2*c^2*d*x + 2*b^2*c^3 - a*b + 3*sqrt(1/3)*(a*b*d*x + a*b*c + 2*(d^2*x^2 + 2*c*d*x + c^2)*(-a*b^2)^(2/3) + (-a*b^2)^(1/3)*a)*sqrt((-a*b^2)^(1/3)/a) - 3*(-a*b^2)^(2/3)*(d*x + c))/(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)) + (-a*b^2)^(2/3)*e*log(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 + (-a*b^2)^(1/3)*(b*d*x + b*c) + (-a*b^2)^(2/3)) - 2*(-a*b^2)^(2/3)*e*log(b*d*x + b*c - (-a*b^2)^(1/3)))/(a*b^2*d), 1/6*(6*sqrt(1/3)*a*b*e*sqrt(-(-a*b^2)^(1/3)/a)*arctan(sqrt(1/3)*(2*b*d*x + 2*b*c + (-a*b^2)^(1/3))*sqrt(-(-a*b^2)^(1/3)/a)/b) + (-a*b^2)^(2/3)*e*log(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 + (-a*b^2)^(1/3)*(b*d*x + b*c) + (-a*b^2)^(2/3)) - 2*(-a*b^2)^(2/3)*e*log(b*d*x + b*c - (-a*b^2)^(1/3)))/(a*b^2*d)]","A",0
2890,1,54,0,1.013671," ","integrate(1/(d*e*x+c*e)/(a+b*(d*x+c)^3),x, algorithm=""fricas"")","-\frac{\log\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right) - 3 \, \log\left(d x + c\right)}{3 \, a d e}"," ",0,"-1/3*(log(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a) - 3*log(d*x + c))/(a*d*e)","A",0
2891,1,156,0,0.900460," ","integrate(1/(d*e*x+c*e)^2/(a+b*(d*x+c)^3),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} {\left(d x + c\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}} \arctan\left(\frac{2}{3} \, \sqrt{3} {\left(d x + c\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}} - \frac{1}{3} \, \sqrt{3}\right) + {\left(d x + c\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}} \log\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} - {\left(a d x + a c\right)} \left(\frac{b}{a}\right)^{\frac{2}{3}} + a \left(\frac{b}{a}\right)^{\frac{1}{3}}\right) - 2 \, {\left(d x + c\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}} \log\left(b d x + b c + a \left(\frac{b}{a}\right)^{\frac{2}{3}}\right) + 6}{6 \, {\left(a d^{2} e^{2} x + a c d e^{2}\right)}}"," ",0,"-1/6*(2*sqrt(3)*(d*x + c)*(b/a)^(1/3)*arctan(2/3*sqrt(3)*(d*x + c)*(b/a)^(1/3) - 1/3*sqrt(3)) + (d*x + c)*(b/a)^(1/3)*log(b*d^2*x^2 + 2*b*c*d*x + b*c^2 - (a*d*x + a*c)*(b/a)^(2/3) + a*(b/a)^(1/3)) - 2*(d*x + c)*(b/a)^(1/3)*log(b*d*x + b*c + a*(b/a)^(2/3)) + 6)/(a*d^2*e^2*x + a*c*d*e^2)","A",0
2892,1,245,0,0.800294," ","integrate(1/(d*e*x+c*e)^3/(a+b*(d*x+c)^3),x, algorithm=""fricas"")","\frac{2 \, \sqrt{3} {\left(d^{2} x^{2} + 2 \, c d x + c^{2}\right)} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} {\left(a d x + a c\right)} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}} - \sqrt{3} b}{3 \, b}\right) - {\left(d^{2} x^{2} + 2 \, c d x + c^{2}\right)} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} + a^{2} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}} + {\left(a b d x + a b c\right)} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}}\right) + 2 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2}\right)} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b d x + b c - a \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}}\right) - 3}{6 \, {\left(a d^{3} e^{3} x^{2} + 2 \, a c d^{2} e^{3} x + a c^{2} d e^{3}\right)}}"," ",0,"1/6*(2*sqrt(3)*(d^2*x^2 + 2*c*d*x + c^2)*(-b^2/a^2)^(1/3)*arctan(1/3*(2*sqrt(3)*(a*d*x + a*c)*(-b^2/a^2)^(2/3) - sqrt(3)*b)/b) - (d^2*x^2 + 2*c*d*x + c^2)*(-b^2/a^2)^(1/3)*log(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 + a^2*(-b^2/a^2)^(2/3) + (a*b*d*x + a*b*c)*(-b^2/a^2)^(1/3)) + 2*(d^2*x^2 + 2*c*d*x + c^2)*(-b^2/a^2)^(1/3)*log(b*d*x + b*c - a*(-b^2/a^2)^(1/3)) - 3)/(a*d^3*e^3*x^2 + 2*a*c*d^2*e^3*x + a*c^2*d*e^3)","A",0
2893,1,170,0,0.934459," ","integrate(1/(d*e*x+c*e)^4/(a+b*(d*x+c)^3),x, algorithm=""fricas"")","\frac{{\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3}\right)} \log\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right) - 3 \, {\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3}\right)} \log\left(d x + c\right) - a}{3 \, {\left(a^{2} d^{4} e^{4} x^{3} + 3 \, a^{2} c d^{3} e^{4} x^{2} + 3 \, a^{2} c^{2} d^{2} e^{4} x + a^{2} c^{3} d e^{4}\right)}}"," ",0,"1/3*((b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3)*log(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a) - 3*(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3)*log(d*x + c) - a)/(a^2*d^4*e^4*x^3 + 3*a^2*c*d^3*e^4*x^2 + 3*a^2*c^2*d^2*e^4*x + a^2*c^3*d*e^4)","B",0
2894,1,940,0,1.558596," ","integrate((d*e*x+c*e)^4/(a+b*(d*x+c)^3)^2,x, algorithm=""fricas"")","\left[-\frac{3 \, a b^{2} d^{2} e^{4} x^{2} + 6 \, a b^{2} c d e^{4} x + 3 \, a b^{2} c^{2} e^{4} - 3 \, \sqrt{\frac{1}{3}} {\left(a b^{2} d^{3} e^{4} x^{3} + 3 \, a b^{2} c d^{2} e^{4} x^{2} + 3 \, a b^{2} c^{2} d e^{4} x + {\left(a b^{2} c^{3} + a^{2} b\right)} e^{4}\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \log\left(\frac{2 \, b^{2} d^{3} x^{3} + 6 \, b^{2} c d^{2} x^{2} + 6 \, b^{2} c^{2} d x + 2 \, b^{2} c^{3} - a b + 3 \, \sqrt{\frac{1}{3}} {\left(a b d x + a b c + 2 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} + \left(-a b^{2}\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} - 3 \, \left(-a b^{2}\right)^{\frac{2}{3}} {\left(d x + c\right)}}{b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a}\right) - {\left(b d^{3} e^{4} x^{3} + 3 \, b c d^{2} e^{4} x^{2} + 3 \, b c^{2} d e^{4} x + {\left(b c^{3} + a\right)} e^{4}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} {\left(b d x + b c\right)} + \left(-a b^{2}\right)^{\frac{2}{3}}\right) + 2 \, {\left(b d^{3} e^{4} x^{3} + 3 \, b c d^{2} e^{4} x^{2} + 3 \, b c^{2} d e^{4} x + {\left(b c^{3} + a\right)} e^{4}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b d x + b c - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{9 \, {\left(a b^{4} d^{4} x^{3} + 3 \, a b^{4} c d^{3} x^{2} + 3 \, a b^{4} c^{2} d^{2} x + {\left(a b^{4} c^{3} + a^{2} b^{3}\right)} d\right)}}, -\frac{3 \, a b^{2} d^{2} e^{4} x^{2} + 6 \, a b^{2} c d e^{4} x + 3 \, a b^{2} c^{2} e^{4} - 6 \, \sqrt{\frac{1}{3}} {\left(a b^{2} d^{3} e^{4} x^{3} + 3 \, a b^{2} c d^{2} e^{4} x^{2} + 3 \, a b^{2} c^{2} d e^{4} x + {\left(a b^{2} c^{3} + a^{2} b\right)} e^{4}\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, b d x + 2 \, b c + \left(-a b^{2}\right)^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}}}{b}\right) - {\left(b d^{3} e^{4} x^{3} + 3 \, b c d^{2} e^{4} x^{2} + 3 \, b c^{2} d e^{4} x + {\left(b c^{3} + a\right)} e^{4}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} {\left(b d x + b c\right)} + \left(-a b^{2}\right)^{\frac{2}{3}}\right) + 2 \, {\left(b d^{3} e^{4} x^{3} + 3 \, b c d^{2} e^{4} x^{2} + 3 \, b c^{2} d e^{4} x + {\left(b c^{3} + a\right)} e^{4}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b d x + b c - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{9 \, {\left(a b^{4} d^{4} x^{3} + 3 \, a b^{4} c d^{3} x^{2} + 3 \, a b^{4} c^{2} d^{2} x + {\left(a b^{4} c^{3} + a^{2} b^{3}\right)} d\right)}}\right]"," ",0,"[-1/9*(3*a*b^2*d^2*e^4*x^2 + 6*a*b^2*c*d*e^4*x + 3*a*b^2*c^2*e^4 - 3*sqrt(1/3)*(a*b^2*d^3*e^4*x^3 + 3*a*b^2*c*d^2*e^4*x^2 + 3*a*b^2*c^2*d*e^4*x + (a*b^2*c^3 + a^2*b)*e^4)*sqrt((-a*b^2)^(1/3)/a)*log((2*b^2*d^3*x^3 + 6*b^2*c*d^2*x^2 + 6*b^2*c^2*d*x + 2*b^2*c^3 - a*b + 3*sqrt(1/3)*(a*b*d*x + a*b*c + 2*(d^2*x^2 + 2*c*d*x + c^2)*(-a*b^2)^(2/3) + (-a*b^2)^(1/3)*a)*sqrt((-a*b^2)^(1/3)/a) - 3*(-a*b^2)^(2/3)*(d*x + c))/(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)) - (b*d^3*e^4*x^3 + 3*b*c*d^2*e^4*x^2 + 3*b*c^2*d*e^4*x + (b*c^3 + a)*e^4)*(-a*b^2)^(2/3)*log(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 + (-a*b^2)^(1/3)*(b*d*x + b*c) + (-a*b^2)^(2/3)) + 2*(b*d^3*e^4*x^3 + 3*b*c*d^2*e^4*x^2 + 3*b*c^2*d*e^4*x + (b*c^3 + a)*e^4)*(-a*b^2)^(2/3)*log(b*d*x + b*c - (-a*b^2)^(1/3)))/(a*b^4*d^4*x^3 + 3*a*b^4*c*d^3*x^2 + 3*a*b^4*c^2*d^2*x + (a*b^4*c^3 + a^2*b^3)*d), -1/9*(3*a*b^2*d^2*e^4*x^2 + 6*a*b^2*c*d*e^4*x + 3*a*b^2*c^2*e^4 - 6*sqrt(1/3)*(a*b^2*d^3*e^4*x^3 + 3*a*b^2*c*d^2*e^4*x^2 + 3*a*b^2*c^2*d*e^4*x + (a*b^2*c^3 + a^2*b)*e^4)*sqrt(-(-a*b^2)^(1/3)/a)*arctan(sqrt(1/3)*(2*b*d*x + 2*b*c + (-a*b^2)^(1/3))*sqrt(-(-a*b^2)^(1/3)/a)/b) - (b*d^3*e^4*x^3 + 3*b*c*d^2*e^4*x^2 + 3*b*c^2*d*e^4*x + (b*c^3 + a)*e^4)*(-a*b^2)^(2/3)*log(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 + (-a*b^2)^(1/3)*(b*d*x + b*c) + (-a*b^2)^(2/3)) + 2*(b*d^3*e^4*x^3 + 3*b*c*d^2*e^4*x^2 + 3*b*c^2*d*e^4*x + (b*c^3 + a)*e^4)*(-a*b^2)^(2/3)*log(b*d*x + b*c - (-a*b^2)^(1/3)))/(a*b^4*d^4*x^3 + 3*a*b^4*c*d^3*x^2 + 3*a*b^4*c^2*d^2*x + (a*b^4*c^3 + a^2*b^3)*d)]","B",0
2895,1,906,0,1.071436," ","integrate((d*e*x+c*e)^3/(a+b*(d*x+c)^3)^2,x, algorithm=""fricas"")","\left[-\frac{6 \, a^{2} b d e^{3} x + 6 \, a^{2} b c e^{3} - 3 \, \sqrt{\frac{1}{3}} {\left(a b^{2} d^{3} e^{3} x^{3} + 3 \, a b^{2} c d^{2} e^{3} x^{2} + 3 \, a b^{2} c^{2} d e^{3} x + {\left(a b^{2} c^{3} + a^{2} b\right)} e^{3}\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \log\left(\frac{2 \, a b d^{3} x^{3} + 6 \, a b c d^{2} x^{2} + 6 \, a b c^{2} d x + 2 \, a b c^{3} - a^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, a b d^{2} x^{2} + 4 \, a b c d x + 2 \, a b c^{2} + \left(a^{2} b\right)^{\frac{2}{3}} {\left(d x + c\right)} - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} - 3 \, \left(a^{2} b\right)^{\frac{1}{3}} {\left(a d x + a c\right)}}{b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a}\right) + {\left(b d^{3} e^{3} x^{3} + 3 \, b c d^{2} e^{3} x^{2} + 3 \, b c^{2} d e^{3} x + {\left(b c^{3} + a\right)} e^{3}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b d^{2} x^{2} + 2 \, a b c d x + a b c^{2} - \left(a^{2} b\right)^{\frac{2}{3}} {\left(d x + c\right)} + \left(a^{2} b\right)^{\frac{1}{3}} a\right) - 2 \, {\left(b d^{3} e^{3} x^{3} + 3 \, b c d^{2} e^{3} x^{2} + 3 \, b c^{2} d e^{3} x + {\left(b c^{3} + a\right)} e^{3}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b d x + a b c + \left(a^{2} b\right)^{\frac{2}{3}}\right)}{18 \, {\left(a^{2} b^{3} d^{4} x^{3} + 3 \, a^{2} b^{3} c d^{3} x^{2} + 3 \, a^{2} b^{3} c^{2} d^{2} x + {\left(a^{2} b^{3} c^{3} + a^{3} b^{2}\right)} d\right)}}, -\frac{6 \, a^{2} b d e^{3} x + 6 \, a^{2} b c e^{3} - 6 \, \sqrt{\frac{1}{3}} {\left(a b^{2} d^{3} e^{3} x^{3} + 3 \, a b^{2} c d^{2} e^{3} x^{2} + 3 \, a b^{2} c^{2} d e^{3} x + {\left(a b^{2} c^{3} + a^{2} b\right)} e^{3}\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(a^{2} b\right)^{\frac{2}{3}} {\left(d x + c\right)} - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{a^{2}}\right) + {\left(b d^{3} e^{3} x^{3} + 3 \, b c d^{2} e^{3} x^{2} + 3 \, b c^{2} d e^{3} x + {\left(b c^{3} + a\right)} e^{3}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b d^{2} x^{2} + 2 \, a b c d x + a b c^{2} - \left(a^{2} b\right)^{\frac{2}{3}} {\left(d x + c\right)} + \left(a^{2} b\right)^{\frac{1}{3}} a\right) - 2 \, {\left(b d^{3} e^{3} x^{3} + 3 \, b c d^{2} e^{3} x^{2} + 3 \, b c^{2} d e^{3} x + {\left(b c^{3} + a\right)} e^{3}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b d x + a b c + \left(a^{2} b\right)^{\frac{2}{3}}\right)}{18 \, {\left(a^{2} b^{3} d^{4} x^{3} + 3 \, a^{2} b^{3} c d^{3} x^{2} + 3 \, a^{2} b^{3} c^{2} d^{2} x + {\left(a^{2} b^{3} c^{3} + a^{3} b^{2}\right)} d\right)}}\right]"," ",0,"[-1/18*(6*a^2*b*d*e^3*x + 6*a^2*b*c*e^3 - 3*sqrt(1/3)*(a*b^2*d^3*e^3*x^3 + 3*a*b^2*c*d^2*e^3*x^2 + 3*a*b^2*c^2*d*e^3*x + (a*b^2*c^3 + a^2*b)*e^3)*sqrt(-(a^2*b)^(1/3)/b)*log((2*a*b*d^3*x^3 + 6*a*b*c*d^2*x^2 + 6*a*b*c^2*d*x + 2*a*b*c^3 - a^2 + 3*sqrt(1/3)*(2*a*b*d^2*x^2 + 4*a*b*c*d*x + 2*a*b*c^2 + (a^2*b)^(2/3)*(d*x + c) - (a^2*b)^(1/3)*a)*sqrt(-(a^2*b)^(1/3)/b) - 3*(a^2*b)^(1/3)*(a*d*x + a*c))/(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)) + (b*d^3*e^3*x^3 + 3*b*c*d^2*e^3*x^2 + 3*b*c^2*d*e^3*x + (b*c^3 + a)*e^3)*(a^2*b)^(2/3)*log(a*b*d^2*x^2 + 2*a*b*c*d*x + a*b*c^2 - (a^2*b)^(2/3)*(d*x + c) + (a^2*b)^(1/3)*a) - 2*(b*d^3*e^3*x^3 + 3*b*c*d^2*e^3*x^2 + 3*b*c^2*d*e^3*x + (b*c^3 + a)*e^3)*(a^2*b)^(2/3)*log(a*b*d*x + a*b*c + (a^2*b)^(2/3)))/(a^2*b^3*d^4*x^3 + 3*a^2*b^3*c*d^3*x^2 + 3*a^2*b^3*c^2*d^2*x + (a^2*b^3*c^3 + a^3*b^2)*d), -1/18*(6*a^2*b*d*e^3*x + 6*a^2*b*c*e^3 - 6*sqrt(1/3)*(a*b^2*d^3*e^3*x^3 + 3*a*b^2*c*d^2*e^3*x^2 + 3*a*b^2*c^2*d*e^3*x + (a*b^2*c^3 + a^2*b)*e^3)*sqrt((a^2*b)^(1/3)/b)*arctan(sqrt(1/3)*(2*(a^2*b)^(2/3)*(d*x + c) - (a^2*b)^(1/3)*a)*sqrt((a^2*b)^(1/3)/b)/a^2) + (b*d^3*e^3*x^3 + 3*b*c*d^2*e^3*x^2 + 3*b*c^2*d*e^3*x + (b*c^3 + a)*e^3)*(a^2*b)^(2/3)*log(a*b*d^2*x^2 + 2*a*b*c*d*x + a*b*c^2 - (a^2*b)^(2/3)*(d*x + c) + (a^2*b)^(1/3)*a) - 2*(b*d^3*e^3*x^3 + 3*b*c*d^2*e^3*x^2 + 3*b*c^2*d*e^3*x + (b*c^3 + a)*e^3)*(a^2*b)^(2/3)*log(a*b*d*x + a*b*c + (a^2*b)^(2/3)))/(a^2*b^3*d^4*x^3 + 3*a^2*b^3*c*d^3*x^2 + 3*a^2*b^3*c^2*d^2*x + (a^2*b^3*c^3 + a^3*b^2)*d)]","B",0
2896,1,55,0,1.199341," ","integrate((d*e*x+c*e)^2/(a+b*(d*x+c)^3)^2,x, algorithm=""fricas"")","-\frac{e^{2}}{3 \, {\left(b^{2} d^{4} x^{3} + 3 \, b^{2} c d^{3} x^{2} + 3 \, b^{2} c^{2} d^{2} x + {\left(b^{2} c^{3} + a b\right)} d\right)}}"," ",0,"-1/3*e^2/(b^2*d^4*x^3 + 3*b^2*c*d^3*x^2 + 3*b^2*c^2*d^2*x + (b^2*c^3 + a*b)*d)","B",0
2897,1,894,0,1.019681," ","integrate((d*e*x+c*e)/(a+b*(d*x+c)^3)^2,x, algorithm=""fricas"")","\left[\frac{6 \, a b^{2} d^{2} e x^{2} + 12 \, a b^{2} c d e x + 6 \, a b^{2} c^{2} e + 3 \, \sqrt{\frac{1}{3}} {\left(a b^{2} d^{3} e x^{3} + 3 \, a b^{2} c d^{2} e x^{2} + 3 \, a b^{2} c^{2} d e x + {\left(a b^{2} c^{3} + a^{2} b\right)} e\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \log\left(\frac{2 \, b^{2} d^{3} x^{3} + 6 \, b^{2} c d^{2} x^{2} + 6 \, b^{2} c^{2} d x + 2 \, b^{2} c^{3} - a b + 3 \, \sqrt{\frac{1}{3}} {\left(a b d x + a b c + 2 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} + \left(-a b^{2}\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} - 3 \, \left(-a b^{2}\right)^{\frac{2}{3}} {\left(d x + c\right)}}{b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a}\right) + {\left(b d^{3} e x^{3} + 3 \, b c d^{2} e x^{2} + 3 \, b c^{2} d e x + {\left(b c^{3} + a\right)} e\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} {\left(b d x + b c\right)} + \left(-a b^{2}\right)^{\frac{2}{3}}\right) - 2 \, {\left(b d^{3} e x^{3} + 3 \, b c d^{2} e x^{2} + 3 \, b c^{2} d e x + {\left(b c^{3} + a\right)} e\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b d x + b c - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{18 \, {\left(a^{2} b^{3} d^{4} x^{3} + 3 \, a^{2} b^{3} c d^{3} x^{2} + 3 \, a^{2} b^{3} c^{2} d^{2} x + {\left(a^{2} b^{3} c^{3} + a^{3} b^{2}\right)} d\right)}}, \frac{6 \, a b^{2} d^{2} e x^{2} + 12 \, a b^{2} c d e x + 6 \, a b^{2} c^{2} e + 6 \, \sqrt{\frac{1}{3}} {\left(a b^{2} d^{3} e x^{3} + 3 \, a b^{2} c d^{2} e x^{2} + 3 \, a b^{2} c^{2} d e x + {\left(a b^{2} c^{3} + a^{2} b\right)} e\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, b d x + 2 \, b c + \left(-a b^{2}\right)^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}}}{b}\right) + {\left(b d^{3} e x^{3} + 3 \, b c d^{2} e x^{2} + 3 \, b c^{2} d e x + {\left(b c^{3} + a\right)} e\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} {\left(b d x + b c\right)} + \left(-a b^{2}\right)^{\frac{2}{3}}\right) - 2 \, {\left(b d^{3} e x^{3} + 3 \, b c d^{2} e x^{2} + 3 \, b c^{2} d e x + {\left(b c^{3} + a\right)} e\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b d x + b c - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{18 \, {\left(a^{2} b^{3} d^{4} x^{3} + 3 \, a^{2} b^{3} c d^{3} x^{2} + 3 \, a^{2} b^{3} c^{2} d^{2} x + {\left(a^{2} b^{3} c^{3} + a^{3} b^{2}\right)} d\right)}}\right]"," ",0,"[1/18*(6*a*b^2*d^2*e*x^2 + 12*a*b^2*c*d*e*x + 6*a*b^2*c^2*e + 3*sqrt(1/3)*(a*b^2*d^3*e*x^3 + 3*a*b^2*c*d^2*e*x^2 + 3*a*b^2*c^2*d*e*x + (a*b^2*c^3 + a^2*b)*e)*sqrt((-a*b^2)^(1/3)/a)*log((2*b^2*d^3*x^3 + 6*b^2*c*d^2*x^2 + 6*b^2*c^2*d*x + 2*b^2*c^3 - a*b + 3*sqrt(1/3)*(a*b*d*x + a*b*c + 2*(d^2*x^2 + 2*c*d*x + c^2)*(-a*b^2)^(2/3) + (-a*b^2)^(1/3)*a)*sqrt((-a*b^2)^(1/3)/a) - 3*(-a*b^2)^(2/3)*(d*x + c))/(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)) + (b*d^3*e*x^3 + 3*b*c*d^2*e*x^2 + 3*b*c^2*d*e*x + (b*c^3 + a)*e)*(-a*b^2)^(2/3)*log(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 + (-a*b^2)^(1/3)*(b*d*x + b*c) + (-a*b^2)^(2/3)) - 2*(b*d^3*e*x^3 + 3*b*c*d^2*e*x^2 + 3*b*c^2*d*e*x + (b*c^3 + a)*e)*(-a*b^2)^(2/3)*log(b*d*x + b*c - (-a*b^2)^(1/3)))/(a^2*b^3*d^4*x^3 + 3*a^2*b^3*c*d^3*x^2 + 3*a^2*b^3*c^2*d^2*x + (a^2*b^3*c^3 + a^3*b^2)*d), 1/18*(6*a*b^2*d^2*e*x^2 + 12*a*b^2*c*d*e*x + 6*a*b^2*c^2*e + 6*sqrt(1/3)*(a*b^2*d^3*e*x^3 + 3*a*b^2*c*d^2*e*x^2 + 3*a*b^2*c^2*d*e*x + (a*b^2*c^3 + a^2*b)*e)*sqrt(-(-a*b^2)^(1/3)/a)*arctan(sqrt(1/3)*(2*b*d*x + 2*b*c + (-a*b^2)^(1/3))*sqrt(-(-a*b^2)^(1/3)/a)/b) + (b*d^3*e*x^3 + 3*b*c*d^2*e*x^2 + 3*b*c^2*d*e*x + (b*c^3 + a)*e)*(-a*b^2)^(2/3)*log(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 + (-a*b^2)^(1/3)*(b*d*x + b*c) + (-a*b^2)^(2/3)) - 2*(b*d^3*e*x^3 + 3*b*c*d^2*e*x^2 + 3*b*c^2*d*e*x + (b*c^3 + a)*e)*(-a*b^2)^(2/3)*log(b*d*x + b*c - (-a*b^2)^(1/3)))/(a^2*b^3*d^4*x^3 + 3*a^2*b^3*c*d^3*x^2 + 3*a^2*b^3*c^2*d^2*x + (a^2*b^3*c^3 + a^3*b^2)*d)]","B",0
2898,1,173,0,0.933787," ","integrate(1/(d*e*x+c*e)/(a+b*(d*x+c)^3)^2,x, algorithm=""fricas"")","-\frac{{\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right)} \log\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right) - 3 \, {\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right)} \log\left(d x + c\right) - a}{3 \, {\left(a^{2} b d^{4} e x^{3} + 3 \, a^{2} b c d^{3} e x^{2} + 3 \, a^{2} b c^{2} d^{2} e x + {\left(a^{2} b c^{3} + a^{3}\right)} d e\right)}}"," ",0,"-1/3*((b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)*log(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a) - 3*(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)*log(d*x + c) - a)/(a^2*b*d^4*e*x^3 + 3*a^2*b*c*d^3*e*x^2 + 3*a^2*b*c^2*d^2*e*x + (a^2*b*c^3 + a^3)*d*e)","B",0
2899,1,399,0,1.239994," ","integrate(1/(d*e*x+c*e)^2/(a+b*(d*x+c)^3)^2,x, algorithm=""fricas"")","-\frac{12 \, b d^{3} x^{3} + 36 \, b c d^{2} x^{2} + 36 \, b c^{2} d x + 12 \, b c^{3} + 4 \, \sqrt{3} {\left(b d^{4} x^{4} + 4 \, b c d^{3} x^{3} + 6 \, b c^{2} d^{2} x^{2} + b c^{4} + {\left(4 \, b c^{3} + a\right)} d x + a c\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}} \arctan\left(\frac{2}{3} \, \sqrt{3} {\left(d x + c\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}} - \frac{1}{3} \, \sqrt{3}\right) + 2 \, {\left(b d^{4} x^{4} + 4 \, b c d^{3} x^{3} + 6 \, b c^{2} d^{2} x^{2} + b c^{4} + {\left(4 \, b c^{3} + a\right)} d x + a c\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}} \log\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} - {\left(a d x + a c\right)} \left(\frac{b}{a}\right)^{\frac{2}{3}} + a \left(\frac{b}{a}\right)^{\frac{1}{3}}\right) - 4 \, {\left(b d^{4} x^{4} + 4 \, b c d^{3} x^{3} + 6 \, b c^{2} d^{2} x^{2} + b c^{4} + {\left(4 \, b c^{3} + a\right)} d x + a c\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}} \log\left(b d x + b c + a \left(\frac{b}{a}\right)^{\frac{2}{3}}\right) + 9 \, a}{9 \, {\left(a^{2} b d^{5} e^{2} x^{4} + 4 \, a^{2} b c d^{4} e^{2} x^{3} + 6 \, a^{2} b c^{2} d^{3} e^{2} x^{2} + {\left(4 \, a^{2} b c^{3} + a^{3}\right)} d^{2} e^{2} x + {\left(a^{2} b c^{4} + a^{3} c\right)} d e^{2}\right)}}"," ",0,"-1/9*(12*b*d^3*x^3 + 36*b*c*d^2*x^2 + 36*b*c^2*d*x + 12*b*c^3 + 4*sqrt(3)*(b*d^4*x^4 + 4*b*c*d^3*x^3 + 6*b*c^2*d^2*x^2 + b*c^4 + (4*b*c^3 + a)*d*x + a*c)*(b/a)^(1/3)*arctan(2/3*sqrt(3)*(d*x + c)*(b/a)^(1/3) - 1/3*sqrt(3)) + 2*(b*d^4*x^4 + 4*b*c*d^3*x^3 + 6*b*c^2*d^2*x^2 + b*c^4 + (4*b*c^3 + a)*d*x + a*c)*(b/a)^(1/3)*log(b*d^2*x^2 + 2*b*c*d*x + b*c^2 - (a*d*x + a*c)*(b/a)^(2/3) + a*(b/a)^(1/3)) - 4*(b*d^4*x^4 + 4*b*c*d^3*x^3 + 6*b*c^2*d^2*x^2 + b*c^4 + (4*b*c^3 + a)*d*x + a*c)*(b/a)^(1/3)*log(b*d*x + b*c + a*(b/a)^(2/3)) + 9*a)/(a^2*b*d^5*e^2*x^4 + 4*a^2*b*c*d^4*e^2*x^3 + 6*a^2*b*c^2*d^3*e^2*x^2 + (4*a^2*b*c^3 + a^3)*d^2*e^2*x + (a^2*b*c^4 + a^3*c)*d*e^2)","B",0
2900,1,527,0,1.205408," ","integrate(1/(d*e*x+c*e)^3/(a+b*(d*x+c)^3)^2,x, algorithm=""fricas"")","-\frac{15 \, b d^{3} x^{3} + 45 \, b c d^{2} x^{2} + 45 \, b c^{2} d x + 15 \, b c^{3} - 10 \, \sqrt{3} {\left(b d^{5} x^{5} + 5 \, b c d^{4} x^{4} + 10 \, b c^{2} d^{3} x^{3} + b c^{5} + {\left(10 \, b c^{3} + a\right)} d^{2} x^{2} + a c^{2} + {\left(5 \, b c^{4} + 2 \, a c\right)} d x\right)} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} {\left(a d x + a c\right)} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}} - \sqrt{3} b}{3 \, b}\right) + 5 \, {\left(b d^{5} x^{5} + 5 \, b c d^{4} x^{4} + 10 \, b c^{2} d^{3} x^{3} + b c^{5} + {\left(10 \, b c^{3} + a\right)} d^{2} x^{2} + a c^{2} + {\left(5 \, b c^{4} + 2 \, a c\right)} d x\right)} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} + a^{2} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}} + {\left(a b d x + a b c\right)} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}}\right) - 10 \, {\left(b d^{5} x^{5} + 5 \, b c d^{4} x^{4} + 10 \, b c^{2} d^{3} x^{3} + b c^{5} + {\left(10 \, b c^{3} + a\right)} d^{2} x^{2} + a c^{2} + {\left(5 \, b c^{4} + 2 \, a c\right)} d x\right)} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b d x + b c - a \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}}\right) + 9 \, a}{18 \, {\left(a^{2} b d^{6} e^{3} x^{5} + 5 \, a^{2} b c d^{5} e^{3} x^{4} + 10 \, a^{2} b c^{2} d^{4} e^{3} x^{3} + {\left(10 \, a^{2} b c^{3} + a^{3}\right)} d^{3} e^{3} x^{2} + {\left(5 \, a^{2} b c^{4} + 2 \, a^{3} c\right)} d^{2} e^{3} x + {\left(a^{2} b c^{5} + a^{3} c^{2}\right)} d e^{3}\right)}}"," ",0,"-1/18*(15*b*d^3*x^3 + 45*b*c*d^2*x^2 + 45*b*c^2*d*x + 15*b*c^3 - 10*sqrt(3)*(b*d^5*x^5 + 5*b*c*d^4*x^4 + 10*b*c^2*d^3*x^3 + b*c^5 + (10*b*c^3 + a)*d^2*x^2 + a*c^2 + (5*b*c^4 + 2*a*c)*d*x)*(-b^2/a^2)^(1/3)*arctan(1/3*(2*sqrt(3)*(a*d*x + a*c)*(-b^2/a^2)^(2/3) - sqrt(3)*b)/b) + 5*(b*d^5*x^5 + 5*b*c*d^4*x^4 + 10*b*c^2*d^3*x^3 + b*c^5 + (10*b*c^3 + a)*d^2*x^2 + a*c^2 + (5*b*c^4 + 2*a*c)*d*x)*(-b^2/a^2)^(1/3)*log(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 + a^2*(-b^2/a^2)^(2/3) + (a*b*d*x + a*b*c)*(-b^2/a^2)^(1/3)) - 10*(b*d^5*x^5 + 5*b*c*d^4*x^4 + 10*b*c^2*d^3*x^3 + b*c^5 + (10*b*c^3 + a)*d^2*x^2 + a*c^2 + (5*b*c^4 + 2*a*c)*d*x)*(-b^2/a^2)^(1/3)*log(b*d*x + b*c - a*(-b^2/a^2)^(1/3)) + 9*a)/(a^2*b*d^6*e^3*x^5 + 5*a^2*b*c*d^5*e^3*x^4 + 10*a^2*b*c^2*d^4*e^3*x^3 + (10*a^2*b*c^3 + a^3)*d^3*e^3*x^2 + (5*a^2*b*c^4 + 2*a^3*c)*d^2*e^3*x + (a^2*b*c^5 + a^3*c^2)*d*e^3)","B",0
2901,1,452,0,0.988089," ","integrate(1/(d*e*x+c*e)^4/(a+b*(d*x+c)^3)^2,x, algorithm=""fricas"")","-\frac{2 \, a b d^{3} x^{3} + 6 \, a b c d^{2} x^{2} + 6 \, a b c^{2} d x + 2 \, a b c^{3} + a^{2} - 2 \, {\left(b^{2} d^{6} x^{6} + 6 \, b^{2} c d^{5} x^{5} + 15 \, b^{2} c^{2} d^{4} x^{4} + b^{2} c^{6} + {\left(20 \, b^{2} c^{3} + a b\right)} d^{3} x^{3} + a b c^{3} + 3 \, {\left(5 \, b^{2} c^{4} + a b c\right)} d^{2} x^{2} + 3 \, {\left(2 \, b^{2} c^{5} + a b c^{2}\right)} d x\right)} \log\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right) + 6 \, {\left(b^{2} d^{6} x^{6} + 6 \, b^{2} c d^{5} x^{5} + 15 \, b^{2} c^{2} d^{4} x^{4} + b^{2} c^{6} + {\left(20 \, b^{2} c^{3} + a b\right)} d^{3} x^{3} + a b c^{3} + 3 \, {\left(5 \, b^{2} c^{4} + a b c\right)} d^{2} x^{2} + 3 \, {\left(2 \, b^{2} c^{5} + a b c^{2}\right)} d x\right)} \log\left(d x + c\right)}{3 \, {\left(a^{3} b d^{7} e^{4} x^{6} + 6 \, a^{3} b c d^{6} e^{4} x^{5} + 15 \, a^{3} b c^{2} d^{5} e^{4} x^{4} + {\left(20 \, a^{3} b c^{3} + a^{4}\right)} d^{4} e^{4} x^{3} + 3 \, {\left(5 \, a^{3} b c^{4} + a^{4} c\right)} d^{3} e^{4} x^{2} + 3 \, {\left(2 \, a^{3} b c^{5} + a^{4} c^{2}\right)} d^{2} e^{4} x + {\left(a^{3} b c^{6} + a^{4} c^{3}\right)} d e^{4}\right)}}"," ",0,"-1/3*(2*a*b*d^3*x^3 + 6*a*b*c*d^2*x^2 + 6*a*b*c^2*d*x + 2*a*b*c^3 + a^2 - 2*(b^2*d^6*x^6 + 6*b^2*c*d^5*x^5 + 15*b^2*c^2*d^4*x^4 + b^2*c^6 + (20*b^2*c^3 + a*b)*d^3*x^3 + a*b*c^3 + 3*(5*b^2*c^4 + a*b*c)*d^2*x^2 + 3*(2*b^2*c^5 + a*b*c^2)*d*x)*log(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a) + 6*(b^2*d^6*x^6 + 6*b^2*c*d^5*x^5 + 15*b^2*c^2*d^4*x^4 + b^2*c^6 + (20*b^2*c^3 + a*b)*d^3*x^3 + a*b*c^3 + 3*(5*b^2*c^4 + a*b*c)*d^2*x^2 + 3*(2*b^2*c^5 + a*b*c^2)*d*x)*log(d*x + c))/(a^3*b*d^7*e^4*x^6 + 6*a^3*b*c*d^6*e^4*x^5 + 15*a^3*b*c^2*d^5*e^4*x^4 + (20*a^3*b*c^3 + a^4)*d^4*e^4*x^3 + 3*(5*a^3*b*c^4 + a^4*c)*d^3*e^4*x^2 + 3*(2*a^3*b*c^5 + a^4*c^2)*d^2*e^4*x + (a^3*b*c^6 + a^4*c^3)*d*e^4)","B",0
2902,1,1886,0,1.104997," ","integrate((d*e*x+c*e)^4/(a+b*(d*x+c)^3)^3,x, algorithm=""fricas"")","\left[\frac{6 \, a b^{3} d^{5} e^{4} x^{5} + 30 \, a b^{3} c d^{4} e^{4} x^{4} + 60 \, a b^{3} c^{2} d^{3} e^{4} x^{3} + 3 \, {\left(20 \, a b^{3} c^{3} - a^{2} b^{2}\right)} d^{2} e^{4} x^{2} + 6 \, {\left(5 \, a b^{3} c^{4} - a^{2} b^{2} c\right)} d e^{4} x + 3 \, {\left(2 \, a b^{3} c^{5} - a^{2} b^{2} c^{2}\right)} e^{4} + 3 \, \sqrt{\frac{1}{3}} {\left(a b^{3} d^{6} e^{4} x^{6} + 6 \, a b^{3} c d^{5} e^{4} x^{5} + 15 \, a b^{3} c^{2} d^{4} e^{4} x^{4} + 2 \, {\left(10 \, a b^{3} c^{3} + a^{2} b^{2}\right)} d^{3} e^{4} x^{3} + 3 \, {\left(5 \, a b^{3} c^{4} + 2 \, a^{2} b^{2} c\right)} d^{2} e^{4} x^{2} + 6 \, {\left(a b^{3} c^{5} + a^{2} b^{2} c^{2}\right)} d e^{4} x + {\left(a b^{3} c^{6} + 2 \, a^{2} b^{2} c^{3} + a^{3} b\right)} e^{4}\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \log\left(\frac{2 \, b^{2} d^{3} x^{3} + 6 \, b^{2} c d^{2} x^{2} + 6 \, b^{2} c^{2} d x + 2 \, b^{2} c^{3} - a b + 3 \, \sqrt{\frac{1}{3}} {\left(a b d x + a b c + 2 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} + \left(-a b^{2}\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} - 3 \, \left(-a b^{2}\right)^{\frac{2}{3}} {\left(d x + c\right)}}{b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a}\right) + {\left(b^{2} d^{6} e^{4} x^{6} + 6 \, b^{2} c d^{5} e^{4} x^{5} + 15 \, b^{2} c^{2} d^{4} e^{4} x^{4} + 2 \, {\left(10 \, b^{2} c^{3} + a b\right)} d^{3} e^{4} x^{3} + 3 \, {\left(5 \, b^{2} c^{4} + 2 \, a b c\right)} d^{2} e^{4} x^{2} + 6 \, {\left(b^{2} c^{5} + a b c^{2}\right)} d e^{4} x + {\left(b^{2} c^{6} + 2 \, a b c^{3} + a^{2}\right)} e^{4}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} {\left(b d x + b c\right)} + \left(-a b^{2}\right)^{\frac{2}{3}}\right) - 2 \, {\left(b^{2} d^{6} e^{4} x^{6} + 6 \, b^{2} c d^{5} e^{4} x^{5} + 15 \, b^{2} c^{2} d^{4} e^{4} x^{4} + 2 \, {\left(10 \, b^{2} c^{3} + a b\right)} d^{3} e^{4} x^{3} + 3 \, {\left(5 \, b^{2} c^{4} + 2 \, a b c\right)} d^{2} e^{4} x^{2} + 6 \, {\left(b^{2} c^{5} + a b c^{2}\right)} d e^{4} x + {\left(b^{2} c^{6} + 2 \, a b c^{3} + a^{2}\right)} e^{4}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b d x + b c - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{54 \, {\left(a^{2} b^{5} d^{7} x^{6} + 6 \, a^{2} b^{5} c d^{6} x^{5} + 15 \, a^{2} b^{5} c^{2} d^{5} x^{4} + 2 \, {\left(10 \, a^{2} b^{5} c^{3} + a^{3} b^{4}\right)} d^{4} x^{3} + 3 \, {\left(5 \, a^{2} b^{5} c^{4} + 2 \, a^{3} b^{4} c\right)} d^{3} x^{2} + 6 \, {\left(a^{2} b^{5} c^{5} + a^{3} b^{4} c^{2}\right)} d^{2} x + {\left(a^{2} b^{5} c^{6} + 2 \, a^{3} b^{4} c^{3} + a^{4} b^{3}\right)} d\right)}}, \frac{6 \, a b^{3} d^{5} e^{4} x^{5} + 30 \, a b^{3} c d^{4} e^{4} x^{4} + 60 \, a b^{3} c^{2} d^{3} e^{4} x^{3} + 3 \, {\left(20 \, a b^{3} c^{3} - a^{2} b^{2}\right)} d^{2} e^{4} x^{2} + 6 \, {\left(5 \, a b^{3} c^{4} - a^{2} b^{2} c\right)} d e^{4} x + 3 \, {\left(2 \, a b^{3} c^{5} - a^{2} b^{2} c^{2}\right)} e^{4} + 6 \, \sqrt{\frac{1}{3}} {\left(a b^{3} d^{6} e^{4} x^{6} + 6 \, a b^{3} c d^{5} e^{4} x^{5} + 15 \, a b^{3} c^{2} d^{4} e^{4} x^{4} + 2 \, {\left(10 \, a b^{3} c^{3} + a^{2} b^{2}\right)} d^{3} e^{4} x^{3} + 3 \, {\left(5 \, a b^{3} c^{4} + 2 \, a^{2} b^{2} c\right)} d^{2} e^{4} x^{2} + 6 \, {\left(a b^{3} c^{5} + a^{2} b^{2} c^{2}\right)} d e^{4} x + {\left(a b^{3} c^{6} + 2 \, a^{2} b^{2} c^{3} + a^{3} b\right)} e^{4}\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, b d x + 2 \, b c + \left(-a b^{2}\right)^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}}}{b}\right) + {\left(b^{2} d^{6} e^{4} x^{6} + 6 \, b^{2} c d^{5} e^{4} x^{5} + 15 \, b^{2} c^{2} d^{4} e^{4} x^{4} + 2 \, {\left(10 \, b^{2} c^{3} + a b\right)} d^{3} e^{4} x^{3} + 3 \, {\left(5 \, b^{2} c^{4} + 2 \, a b c\right)} d^{2} e^{4} x^{2} + 6 \, {\left(b^{2} c^{5} + a b c^{2}\right)} d e^{4} x + {\left(b^{2} c^{6} + 2 \, a b c^{3} + a^{2}\right)} e^{4}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} {\left(b d x + b c\right)} + \left(-a b^{2}\right)^{\frac{2}{3}}\right) - 2 \, {\left(b^{2} d^{6} e^{4} x^{6} + 6 \, b^{2} c d^{5} e^{4} x^{5} + 15 \, b^{2} c^{2} d^{4} e^{4} x^{4} + 2 \, {\left(10 \, b^{2} c^{3} + a b\right)} d^{3} e^{4} x^{3} + 3 \, {\left(5 \, b^{2} c^{4} + 2 \, a b c\right)} d^{2} e^{4} x^{2} + 6 \, {\left(b^{2} c^{5} + a b c^{2}\right)} d e^{4} x + {\left(b^{2} c^{6} + 2 \, a b c^{3} + a^{2}\right)} e^{4}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b d x + b c - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{54 \, {\left(a^{2} b^{5} d^{7} x^{6} + 6 \, a^{2} b^{5} c d^{6} x^{5} + 15 \, a^{2} b^{5} c^{2} d^{5} x^{4} + 2 \, {\left(10 \, a^{2} b^{5} c^{3} + a^{3} b^{4}\right)} d^{4} x^{3} + 3 \, {\left(5 \, a^{2} b^{5} c^{4} + 2 \, a^{3} b^{4} c\right)} d^{3} x^{2} + 6 \, {\left(a^{2} b^{5} c^{5} + a^{3} b^{4} c^{2}\right)} d^{2} x + {\left(a^{2} b^{5} c^{6} + 2 \, a^{3} b^{4} c^{3} + a^{4} b^{3}\right)} d\right)}}\right]"," ",0,"[1/54*(6*a*b^3*d^5*e^4*x^5 + 30*a*b^3*c*d^4*e^4*x^4 + 60*a*b^3*c^2*d^3*e^4*x^3 + 3*(20*a*b^3*c^3 - a^2*b^2)*d^2*e^4*x^2 + 6*(5*a*b^3*c^4 - a^2*b^2*c)*d*e^4*x + 3*(2*a*b^3*c^5 - a^2*b^2*c^2)*e^4 + 3*sqrt(1/3)*(a*b^3*d^6*e^4*x^6 + 6*a*b^3*c*d^5*e^4*x^5 + 15*a*b^3*c^2*d^4*e^4*x^4 + 2*(10*a*b^3*c^3 + a^2*b^2)*d^3*e^4*x^3 + 3*(5*a*b^3*c^4 + 2*a^2*b^2*c)*d^2*e^4*x^2 + 6*(a*b^3*c^5 + a^2*b^2*c^2)*d*e^4*x + (a*b^3*c^6 + 2*a^2*b^2*c^3 + a^3*b)*e^4)*sqrt((-a*b^2)^(1/3)/a)*log((2*b^2*d^3*x^3 + 6*b^2*c*d^2*x^2 + 6*b^2*c^2*d*x + 2*b^2*c^3 - a*b + 3*sqrt(1/3)*(a*b*d*x + a*b*c + 2*(d^2*x^2 + 2*c*d*x + c^2)*(-a*b^2)^(2/3) + (-a*b^2)^(1/3)*a)*sqrt((-a*b^2)^(1/3)/a) - 3*(-a*b^2)^(2/3)*(d*x + c))/(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)) + (b^2*d^6*e^4*x^6 + 6*b^2*c*d^5*e^4*x^5 + 15*b^2*c^2*d^4*e^4*x^4 + 2*(10*b^2*c^3 + a*b)*d^3*e^4*x^3 + 3*(5*b^2*c^4 + 2*a*b*c)*d^2*e^4*x^2 + 6*(b^2*c^5 + a*b*c^2)*d*e^4*x + (b^2*c^6 + 2*a*b*c^3 + a^2)*e^4)*(-a*b^2)^(2/3)*log(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 + (-a*b^2)^(1/3)*(b*d*x + b*c) + (-a*b^2)^(2/3)) - 2*(b^2*d^6*e^4*x^6 + 6*b^2*c*d^5*e^4*x^5 + 15*b^2*c^2*d^4*e^4*x^4 + 2*(10*b^2*c^3 + a*b)*d^3*e^4*x^3 + 3*(5*b^2*c^4 + 2*a*b*c)*d^2*e^4*x^2 + 6*(b^2*c^5 + a*b*c^2)*d*e^4*x + (b^2*c^6 + 2*a*b*c^3 + a^2)*e^4)*(-a*b^2)^(2/3)*log(b*d*x + b*c - (-a*b^2)^(1/3)))/(a^2*b^5*d^7*x^6 + 6*a^2*b^5*c*d^6*x^5 + 15*a^2*b^5*c^2*d^5*x^4 + 2*(10*a^2*b^5*c^3 + a^3*b^4)*d^4*x^3 + 3*(5*a^2*b^5*c^4 + 2*a^3*b^4*c)*d^3*x^2 + 6*(a^2*b^5*c^5 + a^3*b^4*c^2)*d^2*x + (a^2*b^5*c^6 + 2*a^3*b^4*c^3 + a^4*b^3)*d), 1/54*(6*a*b^3*d^5*e^4*x^5 + 30*a*b^3*c*d^4*e^4*x^4 + 60*a*b^3*c^2*d^3*e^4*x^3 + 3*(20*a*b^3*c^3 - a^2*b^2)*d^2*e^4*x^2 + 6*(5*a*b^3*c^4 - a^2*b^2*c)*d*e^4*x + 3*(2*a*b^3*c^5 - a^2*b^2*c^2)*e^4 + 6*sqrt(1/3)*(a*b^3*d^6*e^4*x^6 + 6*a*b^3*c*d^5*e^4*x^5 + 15*a*b^3*c^2*d^4*e^4*x^4 + 2*(10*a*b^3*c^3 + a^2*b^2)*d^3*e^4*x^3 + 3*(5*a*b^3*c^4 + 2*a^2*b^2*c)*d^2*e^4*x^2 + 6*(a*b^3*c^5 + a^2*b^2*c^2)*d*e^4*x + (a*b^3*c^6 + 2*a^2*b^2*c^3 + a^3*b)*e^4)*sqrt(-(-a*b^2)^(1/3)/a)*arctan(sqrt(1/3)*(2*b*d*x + 2*b*c + (-a*b^2)^(1/3))*sqrt(-(-a*b^2)^(1/3)/a)/b) + (b^2*d^6*e^4*x^6 + 6*b^2*c*d^5*e^4*x^5 + 15*b^2*c^2*d^4*e^4*x^4 + 2*(10*b^2*c^3 + a*b)*d^3*e^4*x^3 + 3*(5*b^2*c^4 + 2*a*b*c)*d^2*e^4*x^2 + 6*(b^2*c^5 + a*b*c^2)*d*e^4*x + (b^2*c^6 + 2*a*b*c^3 + a^2)*e^4)*(-a*b^2)^(2/3)*log(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 + (-a*b^2)^(1/3)*(b*d*x + b*c) + (-a*b^2)^(2/3)) - 2*(b^2*d^6*e^4*x^6 + 6*b^2*c*d^5*e^4*x^5 + 15*b^2*c^2*d^4*e^4*x^4 + 2*(10*b^2*c^3 + a*b)*d^3*e^4*x^3 + 3*(5*b^2*c^4 + 2*a*b*c)*d^2*e^4*x^2 + 6*(b^2*c^5 + a*b*c^2)*d*e^4*x + (b^2*c^6 + 2*a*b*c^3 + a^2)*e^4)*(-a*b^2)^(2/3)*log(b*d*x + b*c - (-a*b^2)^(1/3)))/(a^2*b^5*d^7*x^6 + 6*a^2*b^5*c*d^6*x^5 + 15*a^2*b^5*c^2*d^5*x^4 + 2*(10*a^2*b^5*c^3 + a^3*b^4)*d^4*x^3 + 3*(5*a^2*b^5*c^4 + 2*a^3*b^4*c)*d^3*x^2 + 6*(a^2*b^5*c^5 + a^3*b^4*c^2)*d^2*x + (a^2*b^5*c^6 + 2*a^3*b^4*c^3 + a^4*b^3)*d)]","B",0
2903,1,1822,0,1.470365," ","integrate((d*e*x+c*e)^3/(a+b*(d*x+c)^3)^3,x, algorithm=""fricas"")","\left[\frac{3 \, a^{2} b^{2} d^{4} e^{3} x^{4} + 12 \, a^{2} b^{2} c d^{3} e^{3} x^{3} + 18 \, a^{2} b^{2} c^{2} d^{2} e^{3} x^{2} + 6 \, {\left(2 \, a^{2} b^{2} c^{3} - a^{3} b\right)} d e^{3} x + 3 \, {\left(a^{2} b^{2} c^{4} - 2 \, a^{3} b c\right)} e^{3} + 3 \, \sqrt{\frac{1}{3}} {\left(a b^{3} d^{6} e^{3} x^{6} + 6 \, a b^{3} c d^{5} e^{3} x^{5} + 15 \, a b^{3} c^{2} d^{4} e^{3} x^{4} + 2 \, {\left(10 \, a b^{3} c^{3} + a^{2} b^{2}\right)} d^{3} e^{3} x^{3} + 3 \, {\left(5 \, a b^{3} c^{4} + 2 \, a^{2} b^{2} c\right)} d^{2} e^{3} x^{2} + 6 \, {\left(a b^{3} c^{5} + a^{2} b^{2} c^{2}\right)} d e^{3} x + {\left(a b^{3} c^{6} + 2 \, a^{2} b^{2} c^{3} + a^{3} b\right)} e^{3}\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \log\left(\frac{2 \, a b d^{3} x^{3} + 6 \, a b c d^{2} x^{2} + 6 \, a b c^{2} d x + 2 \, a b c^{3} - a^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, a b d^{2} x^{2} + 4 \, a b c d x + 2 \, a b c^{2} + \left(a^{2} b\right)^{\frac{2}{3}} {\left(d x + c\right)} - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} - 3 \, \left(a^{2} b\right)^{\frac{1}{3}} {\left(a d x + a c\right)}}{b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a}\right) - {\left(b^{2} d^{6} e^{3} x^{6} + 6 \, b^{2} c d^{5} e^{3} x^{5} + 15 \, b^{2} c^{2} d^{4} e^{3} x^{4} + 2 \, {\left(10 \, b^{2} c^{3} + a b\right)} d^{3} e^{3} x^{3} + 3 \, {\left(5 \, b^{2} c^{4} + 2 \, a b c\right)} d^{2} e^{3} x^{2} + 6 \, {\left(b^{2} c^{5} + a b c^{2}\right)} d e^{3} x + {\left(b^{2} c^{6} + 2 \, a b c^{3} + a^{2}\right)} e^{3}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b d^{2} x^{2} + 2 \, a b c d x + a b c^{2} - \left(a^{2} b\right)^{\frac{2}{3}} {\left(d x + c\right)} + \left(a^{2} b\right)^{\frac{1}{3}} a\right) + 2 \, {\left(b^{2} d^{6} e^{3} x^{6} + 6 \, b^{2} c d^{5} e^{3} x^{5} + 15 \, b^{2} c^{2} d^{4} e^{3} x^{4} + 2 \, {\left(10 \, b^{2} c^{3} + a b\right)} d^{3} e^{3} x^{3} + 3 \, {\left(5 \, b^{2} c^{4} + 2 \, a b c\right)} d^{2} e^{3} x^{2} + 6 \, {\left(b^{2} c^{5} + a b c^{2}\right)} d e^{3} x + {\left(b^{2} c^{6} + 2 \, a b c^{3} + a^{2}\right)} e^{3}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b d x + a b c + \left(a^{2} b\right)^{\frac{2}{3}}\right)}{54 \, {\left(a^{3} b^{4} d^{7} x^{6} + 6 \, a^{3} b^{4} c d^{6} x^{5} + 15 \, a^{3} b^{4} c^{2} d^{5} x^{4} + 2 \, {\left(10 \, a^{3} b^{4} c^{3} + a^{4} b^{3}\right)} d^{4} x^{3} + 3 \, {\left(5 \, a^{3} b^{4} c^{4} + 2 \, a^{4} b^{3} c\right)} d^{3} x^{2} + 6 \, {\left(a^{3} b^{4} c^{5} + a^{4} b^{3} c^{2}\right)} d^{2} x + {\left(a^{3} b^{4} c^{6} + 2 \, a^{4} b^{3} c^{3} + a^{5} b^{2}\right)} d\right)}}, \frac{3 \, a^{2} b^{2} d^{4} e^{3} x^{4} + 12 \, a^{2} b^{2} c d^{3} e^{3} x^{3} + 18 \, a^{2} b^{2} c^{2} d^{2} e^{3} x^{2} + 6 \, {\left(2 \, a^{2} b^{2} c^{3} - a^{3} b\right)} d e^{3} x + 3 \, {\left(a^{2} b^{2} c^{4} - 2 \, a^{3} b c\right)} e^{3} + 6 \, \sqrt{\frac{1}{3}} {\left(a b^{3} d^{6} e^{3} x^{6} + 6 \, a b^{3} c d^{5} e^{3} x^{5} + 15 \, a b^{3} c^{2} d^{4} e^{3} x^{4} + 2 \, {\left(10 \, a b^{3} c^{3} + a^{2} b^{2}\right)} d^{3} e^{3} x^{3} + 3 \, {\left(5 \, a b^{3} c^{4} + 2 \, a^{2} b^{2} c\right)} d^{2} e^{3} x^{2} + 6 \, {\left(a b^{3} c^{5} + a^{2} b^{2} c^{2}\right)} d e^{3} x + {\left(a b^{3} c^{6} + 2 \, a^{2} b^{2} c^{3} + a^{3} b\right)} e^{3}\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(a^{2} b\right)^{\frac{2}{3}} {\left(d x + c\right)} - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{a^{2}}\right) - {\left(b^{2} d^{6} e^{3} x^{6} + 6 \, b^{2} c d^{5} e^{3} x^{5} + 15 \, b^{2} c^{2} d^{4} e^{3} x^{4} + 2 \, {\left(10 \, b^{2} c^{3} + a b\right)} d^{3} e^{3} x^{3} + 3 \, {\left(5 \, b^{2} c^{4} + 2 \, a b c\right)} d^{2} e^{3} x^{2} + 6 \, {\left(b^{2} c^{5} + a b c^{2}\right)} d e^{3} x + {\left(b^{2} c^{6} + 2 \, a b c^{3} + a^{2}\right)} e^{3}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b d^{2} x^{2} + 2 \, a b c d x + a b c^{2} - \left(a^{2} b\right)^{\frac{2}{3}} {\left(d x + c\right)} + \left(a^{2} b\right)^{\frac{1}{3}} a\right) + 2 \, {\left(b^{2} d^{6} e^{3} x^{6} + 6 \, b^{2} c d^{5} e^{3} x^{5} + 15 \, b^{2} c^{2} d^{4} e^{3} x^{4} + 2 \, {\left(10 \, b^{2} c^{3} + a b\right)} d^{3} e^{3} x^{3} + 3 \, {\left(5 \, b^{2} c^{4} + 2 \, a b c\right)} d^{2} e^{3} x^{2} + 6 \, {\left(b^{2} c^{5} + a b c^{2}\right)} d e^{3} x + {\left(b^{2} c^{6} + 2 \, a b c^{3} + a^{2}\right)} e^{3}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b d x + a b c + \left(a^{2} b\right)^{\frac{2}{3}}\right)}{54 \, {\left(a^{3} b^{4} d^{7} x^{6} + 6 \, a^{3} b^{4} c d^{6} x^{5} + 15 \, a^{3} b^{4} c^{2} d^{5} x^{4} + 2 \, {\left(10 \, a^{3} b^{4} c^{3} + a^{4} b^{3}\right)} d^{4} x^{3} + 3 \, {\left(5 \, a^{3} b^{4} c^{4} + 2 \, a^{4} b^{3} c\right)} d^{3} x^{2} + 6 \, {\left(a^{3} b^{4} c^{5} + a^{4} b^{3} c^{2}\right)} d^{2} x + {\left(a^{3} b^{4} c^{6} + 2 \, a^{4} b^{3} c^{3} + a^{5} b^{2}\right)} d\right)}}\right]"," ",0,"[1/54*(3*a^2*b^2*d^4*e^3*x^4 + 12*a^2*b^2*c*d^3*e^3*x^3 + 18*a^2*b^2*c^2*d^2*e^3*x^2 + 6*(2*a^2*b^2*c^3 - a^3*b)*d*e^3*x + 3*(a^2*b^2*c^4 - 2*a^3*b*c)*e^3 + 3*sqrt(1/3)*(a*b^3*d^6*e^3*x^6 + 6*a*b^3*c*d^5*e^3*x^5 + 15*a*b^3*c^2*d^4*e^3*x^4 + 2*(10*a*b^3*c^3 + a^2*b^2)*d^3*e^3*x^3 + 3*(5*a*b^3*c^4 + 2*a^2*b^2*c)*d^2*e^3*x^2 + 6*(a*b^3*c^5 + a^2*b^2*c^2)*d*e^3*x + (a*b^3*c^6 + 2*a^2*b^2*c^3 + a^3*b)*e^3)*sqrt(-(a^2*b)^(1/3)/b)*log((2*a*b*d^3*x^3 + 6*a*b*c*d^2*x^2 + 6*a*b*c^2*d*x + 2*a*b*c^3 - a^2 + 3*sqrt(1/3)*(2*a*b*d^2*x^2 + 4*a*b*c*d*x + 2*a*b*c^2 + (a^2*b)^(2/3)*(d*x + c) - (a^2*b)^(1/3)*a)*sqrt(-(a^2*b)^(1/3)/b) - 3*(a^2*b)^(1/3)*(a*d*x + a*c))/(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)) - (b^2*d^6*e^3*x^6 + 6*b^2*c*d^5*e^3*x^5 + 15*b^2*c^2*d^4*e^3*x^4 + 2*(10*b^2*c^3 + a*b)*d^3*e^3*x^3 + 3*(5*b^2*c^4 + 2*a*b*c)*d^2*e^3*x^2 + 6*(b^2*c^5 + a*b*c^2)*d*e^3*x + (b^2*c^6 + 2*a*b*c^3 + a^2)*e^3)*(a^2*b)^(2/3)*log(a*b*d^2*x^2 + 2*a*b*c*d*x + a*b*c^2 - (a^2*b)^(2/3)*(d*x + c) + (a^2*b)^(1/3)*a) + 2*(b^2*d^6*e^3*x^6 + 6*b^2*c*d^5*e^3*x^5 + 15*b^2*c^2*d^4*e^3*x^4 + 2*(10*b^2*c^3 + a*b)*d^3*e^3*x^3 + 3*(5*b^2*c^4 + 2*a*b*c)*d^2*e^3*x^2 + 6*(b^2*c^5 + a*b*c^2)*d*e^3*x + (b^2*c^6 + 2*a*b*c^3 + a^2)*e^3)*(a^2*b)^(2/3)*log(a*b*d*x + a*b*c + (a^2*b)^(2/3)))/(a^3*b^4*d^7*x^6 + 6*a^3*b^4*c*d^6*x^5 + 15*a^3*b^4*c^2*d^5*x^4 + 2*(10*a^3*b^4*c^3 + a^4*b^3)*d^4*x^3 + 3*(5*a^3*b^4*c^4 + 2*a^4*b^3*c)*d^3*x^2 + 6*(a^3*b^4*c^5 + a^4*b^3*c^2)*d^2*x + (a^3*b^4*c^6 + 2*a^4*b^3*c^3 + a^5*b^2)*d), 1/54*(3*a^2*b^2*d^4*e^3*x^4 + 12*a^2*b^2*c*d^3*e^3*x^3 + 18*a^2*b^2*c^2*d^2*e^3*x^2 + 6*(2*a^2*b^2*c^3 - a^3*b)*d*e^3*x + 3*(a^2*b^2*c^4 - 2*a^3*b*c)*e^3 + 6*sqrt(1/3)*(a*b^3*d^6*e^3*x^6 + 6*a*b^3*c*d^5*e^3*x^5 + 15*a*b^3*c^2*d^4*e^3*x^4 + 2*(10*a*b^3*c^3 + a^2*b^2)*d^3*e^3*x^3 + 3*(5*a*b^3*c^4 + 2*a^2*b^2*c)*d^2*e^3*x^2 + 6*(a*b^3*c^5 + a^2*b^2*c^2)*d*e^3*x + (a*b^3*c^6 + 2*a^2*b^2*c^3 + a^3*b)*e^3)*sqrt((a^2*b)^(1/3)/b)*arctan(sqrt(1/3)*(2*(a^2*b)^(2/3)*(d*x + c) - (a^2*b)^(1/3)*a)*sqrt((a^2*b)^(1/3)/b)/a^2) - (b^2*d^6*e^3*x^6 + 6*b^2*c*d^5*e^3*x^5 + 15*b^2*c^2*d^4*e^3*x^4 + 2*(10*b^2*c^3 + a*b)*d^3*e^3*x^3 + 3*(5*b^2*c^4 + 2*a*b*c)*d^2*e^3*x^2 + 6*(b^2*c^5 + a*b*c^2)*d*e^3*x + (b^2*c^6 + 2*a*b*c^3 + a^2)*e^3)*(a^2*b)^(2/3)*log(a*b*d^2*x^2 + 2*a*b*c*d*x + a*b*c^2 - (a^2*b)^(2/3)*(d*x + c) + (a^2*b)^(1/3)*a) + 2*(b^2*d^6*e^3*x^6 + 6*b^2*c*d^5*e^3*x^5 + 15*b^2*c^2*d^4*e^3*x^4 + 2*(10*b^2*c^3 + a*b)*d^3*e^3*x^3 + 3*(5*b^2*c^4 + 2*a*b*c)*d^2*e^3*x^2 + 6*(b^2*c^5 + a*b*c^2)*d*e^3*x + (b^2*c^6 + 2*a*b*c^3 + a^2)*e^3)*(a^2*b)^(2/3)*log(a*b*d*x + a*b*c + (a^2*b)^(2/3)))/(a^3*b^4*d^7*x^6 + 6*a^3*b^4*c*d^6*x^5 + 15*a^3*b^4*c^2*d^5*x^4 + 2*(10*a^3*b^4*c^3 + a^4*b^3)*d^4*x^3 + 3*(5*a^3*b^4*c^4 + 2*a^4*b^3*c)*d^3*x^2 + 6*(a^3*b^4*c^5 + a^4*b^3*c^2)*d^2*x + (a^3*b^4*c^6 + 2*a^4*b^3*c^3 + a^5*b^2)*d)]","B",0
2904,1,136,0,0.840624," ","integrate((d*e*x+c*e)^2/(a+b*(d*x+c)^3)^3,x, algorithm=""fricas"")","-\frac{e^{2}}{6 \, {\left(b^{3} d^{7} x^{6} + 6 \, b^{3} c d^{6} x^{5} + 15 \, b^{3} c^{2} d^{5} x^{4} + 2 \, {\left(10 \, b^{3} c^{3} + a b^{2}\right)} d^{4} x^{3} + 3 \, {\left(5 \, b^{3} c^{4} + 2 \, a b^{2} c\right)} d^{3} x^{2} + 6 \, {\left(b^{3} c^{5} + a b^{2} c^{2}\right)} d^{2} x + {\left(b^{3} c^{6} + 2 \, a b^{2} c^{3} + a^{2} b\right)} d\right)}}"," ",0,"-1/6*e^2/(b^3*d^7*x^6 + 6*b^3*c*d^6*x^5 + 15*b^3*c^2*d^5*x^4 + 2*(10*b^3*c^3 + a*b^2)*d^4*x^3 + 3*(5*b^3*c^4 + 2*a*b^2*c)*d^3*x^2 + 6*(b^3*c^5 + a*b^2*c^2)*d^2*x + (b^3*c^6 + 2*a*b^2*c^3 + a^2*b)*d)","B",0
2905,1,1780,0,1.085205," ","integrate((d*e*x+c*e)/(a+b*(d*x+c)^3)^3,x, algorithm=""fricas"")","\left[\frac{12 \, a b^{3} d^{5} e x^{5} + 60 \, a b^{3} c d^{4} e x^{4} + 120 \, a b^{3} c^{2} d^{3} e x^{3} + 3 \, {\left(40 \, a b^{3} c^{3} + 7 \, a^{2} b^{2}\right)} d^{2} e x^{2} + 6 \, {\left(10 \, a b^{3} c^{4} + 7 \, a^{2} b^{2} c\right)} d e x + 6 \, \sqrt{\frac{1}{3}} {\left(a b^{3} d^{6} e x^{6} + 6 \, a b^{3} c d^{5} e x^{5} + 15 \, a b^{3} c^{2} d^{4} e x^{4} + 2 \, {\left(10 \, a b^{3} c^{3} + a^{2} b^{2}\right)} d^{3} e x^{3} + 3 \, {\left(5 \, a b^{3} c^{4} + 2 \, a^{2} b^{2} c\right)} d^{2} e x^{2} + 6 \, {\left(a b^{3} c^{5} + a^{2} b^{2} c^{2}\right)} d e x + {\left(a b^{3} c^{6} + 2 \, a^{2} b^{2} c^{3} + a^{3} b\right)} e\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \log\left(\frac{2 \, b^{2} d^{3} x^{3} + 6 \, b^{2} c d^{2} x^{2} + 6 \, b^{2} c^{2} d x + 2 \, b^{2} c^{3} - a b + 3 \, \sqrt{\frac{1}{3}} {\left(a b d x + a b c + 2 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} + \left(-a b^{2}\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} - 3 \, \left(-a b^{2}\right)^{\frac{2}{3}} {\left(d x + c\right)}}{b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a}\right) + 2 \, {\left(b^{2} d^{6} e x^{6} + 6 \, b^{2} c d^{5} e x^{5} + 15 \, b^{2} c^{2} d^{4} e x^{4} + 2 \, {\left(10 \, b^{2} c^{3} + a b\right)} d^{3} e x^{3} + 3 \, {\left(5 \, b^{2} c^{4} + 2 \, a b c\right)} d^{2} e x^{2} + 6 \, {\left(b^{2} c^{5} + a b c^{2}\right)} d e x + {\left(b^{2} c^{6} + 2 \, a b c^{3} + a^{2}\right)} e\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} {\left(b d x + b c\right)} + \left(-a b^{2}\right)^{\frac{2}{3}}\right) - 4 \, {\left(b^{2} d^{6} e x^{6} + 6 \, b^{2} c d^{5} e x^{5} + 15 \, b^{2} c^{2} d^{4} e x^{4} + 2 \, {\left(10 \, b^{2} c^{3} + a b\right)} d^{3} e x^{3} + 3 \, {\left(5 \, b^{2} c^{4} + 2 \, a b c\right)} d^{2} e x^{2} + 6 \, {\left(b^{2} c^{5} + a b c^{2}\right)} d e x + {\left(b^{2} c^{6} + 2 \, a b c^{3} + a^{2}\right)} e\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b d x + b c - \left(-a b^{2}\right)^{\frac{1}{3}}\right) + 3 \, {\left(4 \, a b^{3} c^{5} + 7 \, a^{2} b^{2} c^{2}\right)} e}{54 \, {\left(a^{3} b^{4} d^{7} x^{6} + 6 \, a^{3} b^{4} c d^{6} x^{5} + 15 \, a^{3} b^{4} c^{2} d^{5} x^{4} + 2 \, {\left(10 \, a^{3} b^{4} c^{3} + a^{4} b^{3}\right)} d^{4} x^{3} + 3 \, {\left(5 \, a^{3} b^{4} c^{4} + 2 \, a^{4} b^{3} c\right)} d^{3} x^{2} + 6 \, {\left(a^{3} b^{4} c^{5} + a^{4} b^{3} c^{2}\right)} d^{2} x + {\left(a^{3} b^{4} c^{6} + 2 \, a^{4} b^{3} c^{3} + a^{5} b^{2}\right)} d\right)}}, \frac{12 \, a b^{3} d^{5} e x^{5} + 60 \, a b^{3} c d^{4} e x^{4} + 120 \, a b^{3} c^{2} d^{3} e x^{3} + 3 \, {\left(40 \, a b^{3} c^{3} + 7 \, a^{2} b^{2}\right)} d^{2} e x^{2} + 6 \, {\left(10 \, a b^{3} c^{4} + 7 \, a^{2} b^{2} c\right)} d e x + 12 \, \sqrt{\frac{1}{3}} {\left(a b^{3} d^{6} e x^{6} + 6 \, a b^{3} c d^{5} e x^{5} + 15 \, a b^{3} c^{2} d^{4} e x^{4} + 2 \, {\left(10 \, a b^{3} c^{3} + a^{2} b^{2}\right)} d^{3} e x^{3} + 3 \, {\left(5 \, a b^{3} c^{4} + 2 \, a^{2} b^{2} c\right)} d^{2} e x^{2} + 6 \, {\left(a b^{3} c^{5} + a^{2} b^{2} c^{2}\right)} d e x + {\left(a b^{3} c^{6} + 2 \, a^{2} b^{2} c^{3} + a^{3} b\right)} e\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, b d x + 2 \, b c + \left(-a b^{2}\right)^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}}}{b}\right) + 2 \, {\left(b^{2} d^{6} e x^{6} + 6 \, b^{2} c d^{5} e x^{5} + 15 \, b^{2} c^{2} d^{4} e x^{4} + 2 \, {\left(10 \, b^{2} c^{3} + a b\right)} d^{3} e x^{3} + 3 \, {\left(5 \, b^{2} c^{4} + 2 \, a b c\right)} d^{2} e x^{2} + 6 \, {\left(b^{2} c^{5} + a b c^{2}\right)} d e x + {\left(b^{2} c^{6} + 2 \, a b c^{3} + a^{2}\right)} e\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} {\left(b d x + b c\right)} + \left(-a b^{2}\right)^{\frac{2}{3}}\right) - 4 \, {\left(b^{2} d^{6} e x^{6} + 6 \, b^{2} c d^{5} e x^{5} + 15 \, b^{2} c^{2} d^{4} e x^{4} + 2 \, {\left(10 \, b^{2} c^{3} + a b\right)} d^{3} e x^{3} + 3 \, {\left(5 \, b^{2} c^{4} + 2 \, a b c\right)} d^{2} e x^{2} + 6 \, {\left(b^{2} c^{5} + a b c^{2}\right)} d e x + {\left(b^{2} c^{6} + 2 \, a b c^{3} + a^{2}\right)} e\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b d x + b c - \left(-a b^{2}\right)^{\frac{1}{3}}\right) + 3 \, {\left(4 \, a b^{3} c^{5} + 7 \, a^{2} b^{2} c^{2}\right)} e}{54 \, {\left(a^{3} b^{4} d^{7} x^{6} + 6 \, a^{3} b^{4} c d^{6} x^{5} + 15 \, a^{3} b^{4} c^{2} d^{5} x^{4} + 2 \, {\left(10 \, a^{3} b^{4} c^{3} + a^{4} b^{3}\right)} d^{4} x^{3} + 3 \, {\left(5 \, a^{3} b^{4} c^{4} + 2 \, a^{4} b^{3} c\right)} d^{3} x^{2} + 6 \, {\left(a^{3} b^{4} c^{5} + a^{4} b^{3} c^{2}\right)} d^{2} x + {\left(a^{3} b^{4} c^{6} + 2 \, a^{4} b^{3} c^{3} + a^{5} b^{2}\right)} d\right)}}\right]"," ",0,"[1/54*(12*a*b^3*d^5*e*x^5 + 60*a*b^3*c*d^4*e*x^4 + 120*a*b^3*c^2*d^3*e*x^3 + 3*(40*a*b^3*c^3 + 7*a^2*b^2)*d^2*e*x^2 + 6*(10*a*b^3*c^4 + 7*a^2*b^2*c)*d*e*x + 6*sqrt(1/3)*(a*b^3*d^6*e*x^6 + 6*a*b^3*c*d^5*e*x^5 + 15*a*b^3*c^2*d^4*e*x^4 + 2*(10*a*b^3*c^3 + a^2*b^2)*d^3*e*x^3 + 3*(5*a*b^3*c^4 + 2*a^2*b^2*c)*d^2*e*x^2 + 6*(a*b^3*c^5 + a^2*b^2*c^2)*d*e*x + (a*b^3*c^6 + 2*a^2*b^2*c^3 + a^3*b)*e)*sqrt((-a*b^2)^(1/3)/a)*log((2*b^2*d^3*x^3 + 6*b^2*c*d^2*x^2 + 6*b^2*c^2*d*x + 2*b^2*c^3 - a*b + 3*sqrt(1/3)*(a*b*d*x + a*b*c + 2*(d^2*x^2 + 2*c*d*x + c^2)*(-a*b^2)^(2/3) + (-a*b^2)^(1/3)*a)*sqrt((-a*b^2)^(1/3)/a) - 3*(-a*b^2)^(2/3)*(d*x + c))/(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)) + 2*(b^2*d^6*e*x^6 + 6*b^2*c*d^5*e*x^5 + 15*b^2*c^2*d^4*e*x^4 + 2*(10*b^2*c^3 + a*b)*d^3*e*x^3 + 3*(5*b^2*c^4 + 2*a*b*c)*d^2*e*x^2 + 6*(b^2*c^5 + a*b*c^2)*d*e*x + (b^2*c^6 + 2*a*b*c^3 + a^2)*e)*(-a*b^2)^(2/3)*log(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 + (-a*b^2)^(1/3)*(b*d*x + b*c) + (-a*b^2)^(2/3)) - 4*(b^2*d^6*e*x^6 + 6*b^2*c*d^5*e*x^5 + 15*b^2*c^2*d^4*e*x^4 + 2*(10*b^2*c^3 + a*b)*d^3*e*x^3 + 3*(5*b^2*c^4 + 2*a*b*c)*d^2*e*x^2 + 6*(b^2*c^5 + a*b*c^2)*d*e*x + (b^2*c^6 + 2*a*b*c^3 + a^2)*e)*(-a*b^2)^(2/3)*log(b*d*x + b*c - (-a*b^2)^(1/3)) + 3*(4*a*b^3*c^5 + 7*a^2*b^2*c^2)*e)/(a^3*b^4*d^7*x^6 + 6*a^3*b^4*c*d^6*x^5 + 15*a^3*b^4*c^2*d^5*x^4 + 2*(10*a^3*b^4*c^3 + a^4*b^3)*d^4*x^3 + 3*(5*a^3*b^4*c^4 + 2*a^4*b^3*c)*d^3*x^2 + 6*(a^3*b^4*c^5 + a^4*b^3*c^2)*d^2*x + (a^3*b^4*c^6 + 2*a^4*b^3*c^3 + a^5*b^2)*d), 1/54*(12*a*b^3*d^5*e*x^5 + 60*a*b^3*c*d^4*e*x^4 + 120*a*b^3*c^2*d^3*e*x^3 + 3*(40*a*b^3*c^3 + 7*a^2*b^2)*d^2*e*x^2 + 6*(10*a*b^3*c^4 + 7*a^2*b^2*c)*d*e*x + 12*sqrt(1/3)*(a*b^3*d^6*e*x^6 + 6*a*b^3*c*d^5*e*x^5 + 15*a*b^3*c^2*d^4*e*x^4 + 2*(10*a*b^3*c^3 + a^2*b^2)*d^3*e*x^3 + 3*(5*a*b^3*c^4 + 2*a^2*b^2*c)*d^2*e*x^2 + 6*(a*b^3*c^5 + a^2*b^2*c^2)*d*e*x + (a*b^3*c^6 + 2*a^2*b^2*c^3 + a^3*b)*e)*sqrt(-(-a*b^2)^(1/3)/a)*arctan(sqrt(1/3)*(2*b*d*x + 2*b*c + (-a*b^2)^(1/3))*sqrt(-(-a*b^2)^(1/3)/a)/b) + 2*(b^2*d^6*e*x^6 + 6*b^2*c*d^5*e*x^5 + 15*b^2*c^2*d^4*e*x^4 + 2*(10*b^2*c^3 + a*b)*d^3*e*x^3 + 3*(5*b^2*c^4 + 2*a*b*c)*d^2*e*x^2 + 6*(b^2*c^5 + a*b*c^2)*d*e*x + (b^2*c^6 + 2*a*b*c^3 + a^2)*e)*(-a*b^2)^(2/3)*log(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 + (-a*b^2)^(1/3)*(b*d*x + b*c) + (-a*b^2)^(2/3)) - 4*(b^2*d^6*e*x^6 + 6*b^2*c*d^5*e*x^5 + 15*b^2*c^2*d^4*e*x^4 + 2*(10*b^2*c^3 + a*b)*d^3*e*x^3 + 3*(5*b^2*c^4 + 2*a*b*c)*d^2*e*x^2 + 6*(b^2*c^5 + a*b*c^2)*d*e*x + (b^2*c^6 + 2*a*b*c^3 + a^2)*e)*(-a*b^2)^(2/3)*log(b*d*x + b*c - (-a*b^2)^(1/3)) + 3*(4*a*b^3*c^5 + 7*a^2*b^2*c^2)*e)/(a^3*b^4*d^7*x^6 + 6*a^3*b^4*c*d^6*x^5 + 15*a^3*b^4*c^2*d^5*x^4 + 2*(10*a^3*b^4*c^3 + a^4*b^3)*d^4*x^3 + 3*(5*a^3*b^4*c^4 + 2*a^4*b^3*c)*d^3*x^2 + 6*(a^3*b^4*c^5 + a^4*b^3*c^2)*d^2*x + (a^3*b^4*c^6 + 2*a^4*b^3*c^3 + a^5*b^2)*d)]","B",0
2906,1,474,0,0.798834," ","integrate(1/(d*e*x+c*e)/(a+b*(d*x+c)^3)^3,x, algorithm=""fricas"")","\frac{2 \, a b d^{3} x^{3} + 6 \, a b c d^{2} x^{2} + 6 \, a b c^{2} d x + 2 \, a b c^{3} + 3 \, a^{2} - 2 \, {\left(b^{2} d^{6} x^{6} + 6 \, b^{2} c d^{5} x^{5} + 15 \, b^{2} c^{2} d^{4} x^{4} + b^{2} c^{6} + 2 \, {\left(10 \, b^{2} c^{3} + a b\right)} d^{3} x^{3} + 2 \, a b c^{3} + 3 \, {\left(5 \, b^{2} c^{4} + 2 \, a b c\right)} d^{2} x^{2} + 6 \, {\left(b^{2} c^{5} + a b c^{2}\right)} d x + a^{2}\right)} \log\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right) + 6 \, {\left(b^{2} d^{6} x^{6} + 6 \, b^{2} c d^{5} x^{5} + 15 \, b^{2} c^{2} d^{4} x^{4} + b^{2} c^{6} + 2 \, {\left(10 \, b^{2} c^{3} + a b\right)} d^{3} x^{3} + 2 \, a b c^{3} + 3 \, {\left(5 \, b^{2} c^{4} + 2 \, a b c\right)} d^{2} x^{2} + 6 \, {\left(b^{2} c^{5} + a b c^{2}\right)} d x + a^{2}\right)} \log\left(d x + c\right)}{6 \, {\left(a^{3} b^{2} d^{7} e x^{6} + 6 \, a^{3} b^{2} c d^{6} e x^{5} + 15 \, a^{3} b^{2} c^{2} d^{5} e x^{4} + 2 \, {\left(10 \, a^{3} b^{2} c^{3} + a^{4} b\right)} d^{4} e x^{3} + 3 \, {\left(5 \, a^{3} b^{2} c^{4} + 2 \, a^{4} b c\right)} d^{3} e x^{2} + 6 \, {\left(a^{3} b^{2} c^{5} + a^{4} b c^{2}\right)} d^{2} e x + {\left(a^{3} b^{2} c^{6} + 2 \, a^{4} b c^{3} + a^{5}\right)} d e\right)}}"," ",0,"1/6*(2*a*b*d^3*x^3 + 6*a*b*c*d^2*x^2 + 6*a*b*c^2*d*x + 2*a*b*c^3 + 3*a^2 - 2*(b^2*d^6*x^6 + 6*b^2*c*d^5*x^5 + 15*b^2*c^2*d^4*x^4 + b^2*c^6 + 2*(10*b^2*c^3 + a*b)*d^3*x^3 + 2*a*b*c^3 + 3*(5*b^2*c^4 + 2*a*b*c)*d^2*x^2 + 6*(b^2*c^5 + a*b*c^2)*d*x + a^2)*log(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a) + 6*(b^2*d^6*x^6 + 6*b^2*c*d^5*x^5 + 15*b^2*c^2*d^4*x^4 + b^2*c^6 + 2*(10*b^2*c^3 + a*b)*d^3*x^3 + 2*a*b*c^3 + 3*(5*b^2*c^4 + 2*a*b*c)*d^2*x^2 + 6*(b^2*c^5 + a*b*c^2)*d*x + a^2)*log(d*x + c))/(a^3*b^2*d^7*e*x^6 + 6*a^3*b^2*c*d^6*e*x^5 + 15*a^3*b^2*c^2*d^5*e*x^4 + 2*(10*a^3*b^2*c^3 + a^4*b)*d^4*e*x^3 + 3*(5*a^3*b^2*c^4 + 2*a^4*b*c)*d^3*e*x^2 + 6*(a^3*b^2*c^5 + a^4*b*c^2)*d^2*e*x + (a^3*b^2*c^6 + 2*a^4*b*c^3 + a^5)*d*e)","B",0
2907,1,879,0,1.080524," ","integrate(1/(d*e*x+c*e)^2/(a+b*(d*x+c)^3)^3,x, algorithm=""fricas"")","-\frac{84 \, b^{2} d^{6} x^{6} + 504 \, b^{2} c d^{5} x^{5} + 1260 \, b^{2} c^{2} d^{4} x^{4} + 84 \, b^{2} c^{6} + 21 \, {\left(80 \, b^{2} c^{3} + 7 \, a b\right)} d^{3} x^{3} + 147 \, a b c^{3} + 63 \, {\left(20 \, b^{2} c^{4} + 7 \, a b c\right)} d^{2} x^{2} + 63 \, {\left(8 \, b^{2} c^{5} + 7 \, a b c^{2}\right)} d x + 28 \, \sqrt{3} {\left(b^{2} d^{7} x^{7} + 7 \, b^{2} c d^{6} x^{6} + 21 \, b^{2} c^{2} d^{5} x^{5} + b^{2} c^{7} + {\left(35 \, b^{2} c^{3} + 2 \, a b\right)} d^{4} x^{4} + {\left(35 \, b^{2} c^{4} + 8 \, a b c\right)} d^{3} x^{3} + 2 \, a b c^{4} + 3 \, {\left(7 \, b^{2} c^{5} + 4 \, a b c^{2}\right)} d^{2} x^{2} + a^{2} c + {\left(7 \, b^{2} c^{6} + 8 \, a b c^{3} + a^{2}\right)} d x\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}} \arctan\left(\frac{2}{3} \, \sqrt{3} {\left(d x + c\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}} - \frac{1}{3} \, \sqrt{3}\right) + 14 \, {\left(b^{2} d^{7} x^{7} + 7 \, b^{2} c d^{6} x^{6} + 21 \, b^{2} c^{2} d^{5} x^{5} + b^{2} c^{7} + {\left(35 \, b^{2} c^{3} + 2 \, a b\right)} d^{4} x^{4} + {\left(35 \, b^{2} c^{4} + 8 \, a b c\right)} d^{3} x^{3} + 2 \, a b c^{4} + 3 \, {\left(7 \, b^{2} c^{5} + 4 \, a b c^{2}\right)} d^{2} x^{2} + a^{2} c + {\left(7 \, b^{2} c^{6} + 8 \, a b c^{3} + a^{2}\right)} d x\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}} \log\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} - {\left(a d x + a c\right)} \left(\frac{b}{a}\right)^{\frac{2}{3}} + a \left(\frac{b}{a}\right)^{\frac{1}{3}}\right) - 28 \, {\left(b^{2} d^{7} x^{7} + 7 \, b^{2} c d^{6} x^{6} + 21 \, b^{2} c^{2} d^{5} x^{5} + b^{2} c^{7} + {\left(35 \, b^{2} c^{3} + 2 \, a b\right)} d^{4} x^{4} + {\left(35 \, b^{2} c^{4} + 8 \, a b c\right)} d^{3} x^{3} + 2 \, a b c^{4} + 3 \, {\left(7 \, b^{2} c^{5} + 4 \, a b c^{2}\right)} d^{2} x^{2} + a^{2} c + {\left(7 \, b^{2} c^{6} + 8 \, a b c^{3} + a^{2}\right)} d x\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}} \log\left(b d x + b c + a \left(\frac{b}{a}\right)^{\frac{2}{3}}\right) + 54 \, a^{2}}{54 \, {\left(a^{3} b^{2} d^{8} e^{2} x^{7} + 7 \, a^{3} b^{2} c d^{7} e^{2} x^{6} + 21 \, a^{3} b^{2} c^{2} d^{6} e^{2} x^{5} + {\left(35 \, a^{3} b^{2} c^{3} + 2 \, a^{4} b\right)} d^{5} e^{2} x^{4} + {\left(35 \, a^{3} b^{2} c^{4} + 8 \, a^{4} b c\right)} d^{4} e^{2} x^{3} + 3 \, {\left(7 \, a^{3} b^{2} c^{5} + 4 \, a^{4} b c^{2}\right)} d^{3} e^{2} x^{2} + {\left(7 \, a^{3} b^{2} c^{6} + 8 \, a^{4} b c^{3} + a^{5}\right)} d^{2} e^{2} x + {\left(a^{3} b^{2} c^{7} + 2 \, a^{4} b c^{4} + a^{5} c\right)} d e^{2}\right)}}"," ",0,"-1/54*(84*b^2*d^6*x^6 + 504*b^2*c*d^5*x^5 + 1260*b^2*c^2*d^4*x^4 + 84*b^2*c^6 + 21*(80*b^2*c^3 + 7*a*b)*d^3*x^3 + 147*a*b*c^3 + 63*(20*b^2*c^4 + 7*a*b*c)*d^2*x^2 + 63*(8*b^2*c^5 + 7*a*b*c^2)*d*x + 28*sqrt(3)*(b^2*d^7*x^7 + 7*b^2*c*d^6*x^6 + 21*b^2*c^2*d^5*x^5 + b^2*c^7 + (35*b^2*c^3 + 2*a*b)*d^4*x^4 + (35*b^2*c^4 + 8*a*b*c)*d^3*x^3 + 2*a*b*c^4 + 3*(7*b^2*c^5 + 4*a*b*c^2)*d^2*x^2 + a^2*c + (7*b^2*c^6 + 8*a*b*c^3 + a^2)*d*x)*(b/a)^(1/3)*arctan(2/3*sqrt(3)*(d*x + c)*(b/a)^(1/3) - 1/3*sqrt(3)) + 14*(b^2*d^7*x^7 + 7*b^2*c*d^6*x^6 + 21*b^2*c^2*d^5*x^5 + b^2*c^7 + (35*b^2*c^3 + 2*a*b)*d^4*x^4 + (35*b^2*c^4 + 8*a*b*c)*d^3*x^3 + 2*a*b*c^4 + 3*(7*b^2*c^5 + 4*a*b*c^2)*d^2*x^2 + a^2*c + (7*b^2*c^6 + 8*a*b*c^3 + a^2)*d*x)*(b/a)^(1/3)*log(b*d^2*x^2 + 2*b*c*d*x + b*c^2 - (a*d*x + a*c)*(b/a)^(2/3) + a*(b/a)^(1/3)) - 28*(b^2*d^7*x^7 + 7*b^2*c*d^6*x^6 + 21*b^2*c^2*d^5*x^5 + b^2*c^7 + (35*b^2*c^3 + 2*a*b)*d^4*x^4 + (35*b^2*c^4 + 8*a*b*c)*d^3*x^3 + 2*a*b*c^4 + 3*(7*b^2*c^5 + 4*a*b*c^2)*d^2*x^2 + a^2*c + (7*b^2*c^6 + 8*a*b*c^3 + a^2)*d*x)*(b/a)^(1/3)*log(b*d*x + b*c + a*(b/a)^(2/3)) + 54*a^2)/(a^3*b^2*d^8*e^2*x^7 + 7*a^3*b^2*c*d^7*e^2*x^6 + 21*a^3*b^2*c^2*d^6*e^2*x^5 + (35*a^3*b^2*c^3 + 2*a^4*b)*d^5*e^2*x^4 + (35*a^3*b^2*c^4 + 8*a^4*b*c)*d^4*e^2*x^3 + 3*(7*a^3*b^2*c^5 + 4*a^4*b*c^2)*d^3*e^2*x^2 + (7*a^3*b^2*c^6 + 8*a^4*b*c^3 + a^5)*d^2*e^2*x + (a^3*b^2*c^7 + 2*a^4*b*c^4 + a^5*c)*d*e^2)","B",0
2908,1,1051,0,1.336040," ","integrate(1/(d*e*x+c*e)^3/(a+b*(d*x+c)^3)^3,x, algorithm=""fricas"")","-\frac{60 \, b^{2} d^{6} x^{6} + 360 \, b^{2} c d^{5} x^{5} + 900 \, b^{2} c^{2} d^{4} x^{4} + 60 \, b^{2} c^{6} + 48 \, {\left(25 \, b^{2} c^{3} + 2 \, a b\right)} d^{3} x^{3} + 96 \, a b c^{3} + 36 \, {\left(25 \, b^{2} c^{4} + 8 \, a b c\right)} d^{2} x^{2} + 72 \, {\left(5 \, b^{2} c^{5} + 4 \, a b c^{2}\right)} d x - 40 \, \sqrt{3} {\left(b^{2} d^{8} x^{8} + 8 \, b^{2} c d^{7} x^{7} + 28 \, b^{2} c^{2} d^{6} x^{6} + 2 \, {\left(28 \, b^{2} c^{3} + a b\right)} d^{5} x^{5} + b^{2} c^{8} + 10 \, {\left(7 \, b^{2} c^{4} + a b c\right)} d^{4} x^{4} + 2 \, a b c^{5} + 4 \, {\left(14 \, b^{2} c^{5} + 5 \, a b c^{2}\right)} d^{3} x^{3} + {\left(28 \, b^{2} c^{6} + 20 \, a b c^{3} + a^{2}\right)} d^{2} x^{2} + a^{2} c^{2} + 2 \, {\left(4 \, b^{2} c^{7} + 5 \, a b c^{4} + a^{2} c\right)} d x\right)} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} {\left(a d x + a c\right)} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}} - \sqrt{3} b}{3 \, b}\right) + 20 \, {\left(b^{2} d^{8} x^{8} + 8 \, b^{2} c d^{7} x^{7} + 28 \, b^{2} c^{2} d^{6} x^{6} + 2 \, {\left(28 \, b^{2} c^{3} + a b\right)} d^{5} x^{5} + b^{2} c^{8} + 10 \, {\left(7 \, b^{2} c^{4} + a b c\right)} d^{4} x^{4} + 2 \, a b c^{5} + 4 \, {\left(14 \, b^{2} c^{5} + 5 \, a b c^{2}\right)} d^{3} x^{3} + {\left(28 \, b^{2} c^{6} + 20 \, a b c^{3} + a^{2}\right)} d^{2} x^{2} + a^{2} c^{2} + 2 \, {\left(4 \, b^{2} c^{7} + 5 \, a b c^{4} + a^{2} c\right)} d x\right)} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} + a^{2} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}} + {\left(a b d x + a b c\right)} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}}\right) - 40 \, {\left(b^{2} d^{8} x^{8} + 8 \, b^{2} c d^{7} x^{7} + 28 \, b^{2} c^{2} d^{6} x^{6} + 2 \, {\left(28 \, b^{2} c^{3} + a b\right)} d^{5} x^{5} + b^{2} c^{8} + 10 \, {\left(7 \, b^{2} c^{4} + a b c\right)} d^{4} x^{4} + 2 \, a b c^{5} + 4 \, {\left(14 \, b^{2} c^{5} + 5 \, a b c^{2}\right)} d^{3} x^{3} + {\left(28 \, b^{2} c^{6} + 20 \, a b c^{3} + a^{2}\right)} d^{2} x^{2} + a^{2} c^{2} + 2 \, {\left(4 \, b^{2} c^{7} + 5 \, a b c^{4} + a^{2} c\right)} d x\right)} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b d x + b c - a \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}}\right) + 27 \, a^{2}}{54 \, {\left(a^{3} b^{2} d^{9} e^{3} x^{8} + 8 \, a^{3} b^{2} c d^{8} e^{3} x^{7} + 28 \, a^{3} b^{2} c^{2} d^{7} e^{3} x^{6} + 2 \, {\left(28 \, a^{3} b^{2} c^{3} + a^{4} b\right)} d^{6} e^{3} x^{5} + 10 \, {\left(7 \, a^{3} b^{2} c^{4} + a^{4} b c\right)} d^{5} e^{3} x^{4} + 4 \, {\left(14 \, a^{3} b^{2} c^{5} + 5 \, a^{4} b c^{2}\right)} d^{4} e^{3} x^{3} + {\left(28 \, a^{3} b^{2} c^{6} + 20 \, a^{4} b c^{3} + a^{5}\right)} d^{3} e^{3} x^{2} + 2 \, {\left(4 \, a^{3} b^{2} c^{7} + 5 \, a^{4} b c^{4} + a^{5} c\right)} d^{2} e^{3} x + {\left(a^{3} b^{2} c^{8} + 2 \, a^{4} b c^{5} + a^{5} c^{2}\right)} d e^{3}\right)}}"," ",0,"-1/54*(60*b^2*d^6*x^6 + 360*b^2*c*d^5*x^5 + 900*b^2*c^2*d^4*x^4 + 60*b^2*c^6 + 48*(25*b^2*c^3 + 2*a*b)*d^3*x^3 + 96*a*b*c^3 + 36*(25*b^2*c^4 + 8*a*b*c)*d^2*x^2 + 72*(5*b^2*c^5 + 4*a*b*c^2)*d*x - 40*sqrt(3)*(b^2*d^8*x^8 + 8*b^2*c*d^7*x^7 + 28*b^2*c^2*d^6*x^6 + 2*(28*b^2*c^3 + a*b)*d^5*x^5 + b^2*c^8 + 10*(7*b^2*c^4 + a*b*c)*d^4*x^4 + 2*a*b*c^5 + 4*(14*b^2*c^5 + 5*a*b*c^2)*d^3*x^3 + (28*b^2*c^6 + 20*a*b*c^3 + a^2)*d^2*x^2 + a^2*c^2 + 2*(4*b^2*c^7 + 5*a*b*c^4 + a^2*c)*d*x)*(-b^2/a^2)^(1/3)*arctan(1/3*(2*sqrt(3)*(a*d*x + a*c)*(-b^2/a^2)^(2/3) - sqrt(3)*b)/b) + 20*(b^2*d^8*x^8 + 8*b^2*c*d^7*x^7 + 28*b^2*c^2*d^6*x^6 + 2*(28*b^2*c^3 + a*b)*d^5*x^5 + b^2*c^8 + 10*(7*b^2*c^4 + a*b*c)*d^4*x^4 + 2*a*b*c^5 + 4*(14*b^2*c^5 + 5*a*b*c^2)*d^3*x^3 + (28*b^2*c^6 + 20*a*b*c^3 + a^2)*d^2*x^2 + a^2*c^2 + 2*(4*b^2*c^7 + 5*a*b*c^4 + a^2*c)*d*x)*(-b^2/a^2)^(1/3)*log(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 + a^2*(-b^2/a^2)^(2/3) + (a*b*d*x + a*b*c)*(-b^2/a^2)^(1/3)) - 40*(b^2*d^8*x^8 + 8*b^2*c*d^7*x^7 + 28*b^2*c^2*d^6*x^6 + 2*(28*b^2*c^3 + a*b)*d^5*x^5 + b^2*c^8 + 10*(7*b^2*c^4 + a*b*c)*d^4*x^4 + 2*a*b*c^5 + 4*(14*b^2*c^5 + 5*a*b*c^2)*d^3*x^3 + (28*b^2*c^6 + 20*a*b*c^3 + a^2)*d^2*x^2 + a^2*c^2 + 2*(4*b^2*c^7 + 5*a*b*c^4 + a^2*c)*d*x)*(-b^2/a^2)^(1/3)*log(b*d*x + b*c - a*(-b^2/a^2)^(1/3)) + 27*a^2)/(a^3*b^2*d^9*e^3*x^8 + 8*a^3*b^2*c*d^8*e^3*x^7 + 28*a^3*b^2*c^2*d^7*e^3*x^6 + 2*(28*a^3*b^2*c^3 + a^4*b)*d^6*e^3*x^5 + 10*(7*a^3*b^2*c^4 + a^4*b*c)*d^5*e^3*x^4 + 4*(14*a^3*b^2*c^5 + 5*a^4*b*c^2)*d^4*e^3*x^3 + (28*a^3*b^2*c^6 + 20*a^4*b*c^3 + a^5)*d^3*e^3*x^2 + 2*(4*a^3*b^2*c^7 + 5*a^4*b*c^4 + a^5*c)*d^2*e^3*x + (a^3*b^2*c^8 + 2*a^4*b*c^5 + a^5*c^2)*d*e^3)","B",0
2909,1,919,0,1.095367," ","integrate(1/(d*e*x+c*e)^4/(a+b*(d*x+c)^3)^3,x, algorithm=""fricas"")","-\frac{6 \, a b^{2} d^{6} x^{6} + 36 \, a b^{2} c d^{5} x^{5} + 90 \, a b^{2} c^{2} d^{4} x^{4} + 6 \, a b^{2} c^{6} + 3 \, {\left(40 \, a b^{2} c^{3} + 3 \, a^{2} b\right)} d^{3} x^{3} + 9 \, a^{2} b c^{3} + 9 \, {\left(10 \, a b^{2} c^{4} + 3 \, a^{2} b c\right)} d^{2} x^{2} + 2 \, a^{3} + 9 \, {\left(4 \, a b^{2} c^{5} + 3 \, a^{2} b c^{2}\right)} d x - 6 \, {\left(b^{3} d^{9} x^{9} + 9 \, b^{3} c d^{8} x^{8} + 36 \, b^{3} c^{2} d^{7} x^{7} + 2 \, {\left(42 \, b^{3} c^{3} + a b^{2}\right)} d^{6} x^{6} + b^{3} c^{9} + 6 \, {\left(21 \, b^{3} c^{4} + 2 \, a b^{2} c\right)} d^{5} x^{5} + 2 \, a b^{2} c^{6} + 6 \, {\left(21 \, b^{3} c^{5} + 5 \, a b^{2} c^{2}\right)} d^{4} x^{4} + {\left(84 \, b^{3} c^{6} + 40 \, a b^{2} c^{3} + a^{2} b\right)} d^{3} x^{3} + a^{2} b c^{3} + 3 \, {\left(12 \, b^{3} c^{7} + 10 \, a b^{2} c^{4} + a^{2} b c\right)} d^{2} x^{2} + 3 \, {\left(3 \, b^{3} c^{8} + 4 \, a b^{2} c^{5} + a^{2} b c^{2}\right)} d x\right)} \log\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right) + 18 \, {\left(b^{3} d^{9} x^{9} + 9 \, b^{3} c d^{8} x^{8} + 36 \, b^{3} c^{2} d^{7} x^{7} + 2 \, {\left(42 \, b^{3} c^{3} + a b^{2}\right)} d^{6} x^{6} + b^{3} c^{9} + 6 \, {\left(21 \, b^{3} c^{4} + 2 \, a b^{2} c\right)} d^{5} x^{5} + 2 \, a b^{2} c^{6} + 6 \, {\left(21 \, b^{3} c^{5} + 5 \, a b^{2} c^{2}\right)} d^{4} x^{4} + {\left(84 \, b^{3} c^{6} + 40 \, a b^{2} c^{3} + a^{2} b\right)} d^{3} x^{3} + a^{2} b c^{3} + 3 \, {\left(12 \, b^{3} c^{7} + 10 \, a b^{2} c^{4} + a^{2} b c\right)} d^{2} x^{2} + 3 \, {\left(3 \, b^{3} c^{8} + 4 \, a b^{2} c^{5} + a^{2} b c^{2}\right)} d x\right)} \log\left(d x + c\right)}{6 \, {\left(a^{4} b^{2} d^{10} e^{4} x^{9} + 9 \, a^{4} b^{2} c d^{9} e^{4} x^{8} + 36 \, a^{4} b^{2} c^{2} d^{8} e^{4} x^{7} + 2 \, {\left(42 \, a^{4} b^{2} c^{3} + a^{5} b\right)} d^{7} e^{4} x^{6} + 6 \, {\left(21 \, a^{4} b^{2} c^{4} + 2 \, a^{5} b c\right)} d^{6} e^{4} x^{5} + 6 \, {\left(21 \, a^{4} b^{2} c^{5} + 5 \, a^{5} b c^{2}\right)} d^{5} e^{4} x^{4} + {\left(84 \, a^{4} b^{2} c^{6} + 40 \, a^{5} b c^{3} + a^{6}\right)} d^{4} e^{4} x^{3} + 3 \, {\left(12 \, a^{4} b^{2} c^{7} + 10 \, a^{5} b c^{4} + a^{6} c\right)} d^{3} e^{4} x^{2} + 3 \, {\left(3 \, a^{4} b^{2} c^{8} + 4 \, a^{5} b c^{5} + a^{6} c^{2}\right)} d^{2} e^{4} x + {\left(a^{4} b^{2} c^{9} + 2 \, a^{5} b c^{6} + a^{6} c^{3}\right)} d e^{4}\right)}}"," ",0,"-1/6*(6*a*b^2*d^6*x^6 + 36*a*b^2*c*d^5*x^5 + 90*a*b^2*c^2*d^4*x^4 + 6*a*b^2*c^6 + 3*(40*a*b^2*c^3 + 3*a^2*b)*d^3*x^3 + 9*a^2*b*c^3 + 9*(10*a*b^2*c^4 + 3*a^2*b*c)*d^2*x^2 + 2*a^3 + 9*(4*a*b^2*c^5 + 3*a^2*b*c^2)*d*x - 6*(b^3*d^9*x^9 + 9*b^3*c*d^8*x^8 + 36*b^3*c^2*d^7*x^7 + 2*(42*b^3*c^3 + a*b^2)*d^6*x^6 + b^3*c^9 + 6*(21*b^3*c^4 + 2*a*b^2*c)*d^5*x^5 + 2*a*b^2*c^6 + 6*(21*b^3*c^5 + 5*a*b^2*c^2)*d^4*x^4 + (84*b^3*c^6 + 40*a*b^2*c^3 + a^2*b)*d^3*x^3 + a^2*b*c^3 + 3*(12*b^3*c^7 + 10*a*b^2*c^4 + a^2*b*c)*d^2*x^2 + 3*(3*b^3*c^8 + 4*a*b^2*c^5 + a^2*b*c^2)*d*x)*log(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a) + 18*(b^3*d^9*x^9 + 9*b^3*c*d^8*x^8 + 36*b^3*c^2*d^7*x^7 + 2*(42*b^3*c^3 + a*b^2)*d^6*x^6 + b^3*c^9 + 6*(21*b^3*c^4 + 2*a*b^2*c)*d^5*x^5 + 2*a*b^2*c^6 + 6*(21*b^3*c^5 + 5*a*b^2*c^2)*d^4*x^4 + (84*b^3*c^6 + 40*a*b^2*c^3 + a^2*b)*d^3*x^3 + a^2*b*c^3 + 3*(12*b^3*c^7 + 10*a*b^2*c^4 + a^2*b*c)*d^2*x^2 + 3*(3*b^3*c^8 + 4*a*b^2*c^5 + a^2*b*c^2)*d*x)*log(d*x + c))/(a^4*b^2*d^10*e^4*x^9 + 9*a^4*b^2*c*d^9*e^4*x^8 + 36*a^4*b^2*c^2*d^8*e^4*x^7 + 2*(42*a^4*b^2*c^3 + a^5*b)*d^7*e^4*x^6 + 6*(21*a^4*b^2*c^4 + 2*a^5*b*c)*d^6*e^4*x^5 + 6*(21*a^4*b^2*c^5 + 5*a^5*b*c^2)*d^5*e^4*x^4 + (84*a^4*b^2*c^6 + 40*a^5*b*c^3 + a^6)*d^4*e^4*x^3 + 3*(12*a^4*b^2*c^7 + 10*a^5*b*c^4 + a^6*c)*d^3*e^4*x^2 + 3*(3*a^4*b^2*c^8 + 4*a^5*b*c^5 + a^6*c^2)*d^2*e^4*x + (a^4*b^2*c^9 + 2*a^5*b*c^6 + a^6*c^3)*d*e^4)","B",0
2910,1,104,0,0.569081," ","integrate((d*x+c)^3*(a+b*(d*x+c)^4)^p,x, algorithm=""fricas"")","\frac{{\left(b d^{4} x^{4} + 4 \, b c d^{3} x^{3} + 6 \, b c^{2} d^{2} x^{2} + 4 \, b c^{3} d x + b c^{4} + a\right)} {\left(b d^{4} x^{4} + 4 \, b c d^{3} x^{3} + 6 \, b c^{2} d^{2} x^{2} + 4 \, b c^{3} d x + b c^{4} + a\right)}^{p}}{4 \, {\left(b d p + b d\right)}}"," ",0,"1/4*(b*d^4*x^4 + 4*b*c*d^3*x^3 + 6*b*c^2*d^2*x^2 + 4*b*c^3*d*x + b*c^4 + a)*(b*d^4*x^4 + 4*b*c*d^3*x^3 + 6*b*c^2*d^2*x^2 + 4*b*c^3*d*x + b*c^4 + a)^p/(b*d*p + b*d)","B",0
2911,1,117,0,0.828115," ","integrate((d*x+c)^3*(a+b*(d*x+c)^4),x, algorithm=""fricas"")","\frac{1}{8} x^{8} d^{7} b + x^{7} d^{6} c b + \frac{7}{2} x^{6} d^{5} c^{2} b + 7 x^{5} d^{4} c^{3} b + \frac{35}{4} x^{4} d^{3} c^{4} b + 7 x^{3} d^{2} c^{5} b + \frac{7}{2} x^{2} d c^{6} b + x c^{7} b + \frac{1}{4} x^{4} d^{3} a + x^{3} d^{2} c a + \frac{3}{2} x^{2} d c^{2} a + x c^{3} a"," ",0,"1/8*x^8*d^7*b + x^7*d^6*c*b + 7/2*x^6*d^5*c^2*b + 7*x^5*d^4*c^3*b + 35/4*x^4*d^3*c^4*b + 7*x^3*d^2*c^5*b + 7/2*x^2*d*c^6*b + x*c^7*b + 1/4*x^4*d^3*a + x^3*d^2*c*a + 3/2*x^2*d*c^2*a + x*c^3*a","B",0
2912,1,289,0,0.670640," ","integrate((d*x+c)^3*(a+b*(d*x+c)^4)^2,x, algorithm=""fricas"")","\frac{1}{12} x^{12} d^{11} b^{2} + x^{11} d^{10} c b^{2} + \frac{11}{2} x^{10} d^{9} c^{2} b^{2} + \frac{55}{3} x^{9} d^{8} c^{3} b^{2} + \frac{165}{4} x^{8} d^{7} c^{4} b^{2} + 66 x^{7} d^{6} c^{5} b^{2} + 77 x^{6} d^{5} c^{6} b^{2} + 66 x^{5} d^{4} c^{7} b^{2} + \frac{165}{4} x^{4} d^{3} c^{8} b^{2} + \frac{1}{4} x^{8} d^{7} b a + \frac{55}{3} x^{3} d^{2} c^{9} b^{2} + 2 x^{7} d^{6} c b a + \frac{11}{2} x^{2} d c^{10} b^{2} + 7 x^{6} d^{5} c^{2} b a + x c^{11} b^{2} + 14 x^{5} d^{4} c^{3} b a + \frac{35}{2} x^{4} d^{3} c^{4} b a + 14 x^{3} d^{2} c^{5} b a + 7 x^{2} d c^{6} b a + 2 x c^{7} b a + \frac{1}{4} x^{4} d^{3} a^{2} + x^{3} d^{2} c a^{2} + \frac{3}{2} x^{2} d c^{2} a^{2} + x c^{3} a^{2}"," ",0,"1/12*x^12*d^11*b^2 + x^11*d^10*c*b^2 + 11/2*x^10*d^9*c^2*b^2 + 55/3*x^9*d^8*c^3*b^2 + 165/4*x^8*d^7*c^4*b^2 + 66*x^7*d^6*c^5*b^2 + 77*x^6*d^5*c^6*b^2 + 66*x^5*d^4*c^7*b^2 + 165/4*x^4*d^3*c^8*b^2 + 1/4*x^8*d^7*b*a + 55/3*x^3*d^2*c^9*b^2 + 2*x^7*d^6*c*b*a + 11/2*x^2*d*c^10*b^2 + 7*x^6*d^5*c^2*b*a + x*c^11*b^2 + 14*x^5*d^4*c^3*b*a + 35/2*x^4*d^3*c^4*b*a + 14*x^3*d^2*c^5*b*a + 7*x^2*d*c^6*b*a + 2*x*c^7*b*a + 1/4*x^4*d^3*a^2 + x^3*d^2*c*a^2 + 3/2*x^2*d*c^2*a^2 + x*c^3*a^2","B",0
2913,1,529,0,0.840738," ","integrate((d*x+c)^3*(a+b*(d*x+c)^4)^3,x, algorithm=""fricas"")","\frac{1}{16} x^{16} d^{15} b^{3} + x^{15} d^{14} c b^{3} + \frac{15}{2} x^{14} d^{13} c^{2} b^{3} + 35 x^{13} d^{12} c^{3} b^{3} + \frac{455}{4} x^{12} d^{11} c^{4} b^{3} + 273 x^{11} d^{10} c^{5} b^{3} + \frac{1001}{2} x^{10} d^{9} c^{6} b^{3} + 715 x^{9} d^{8} c^{7} b^{3} + \frac{6435}{8} x^{8} d^{7} c^{8} b^{3} + \frac{1}{4} x^{12} d^{11} b^{2} a + 715 x^{7} d^{6} c^{9} b^{3} + 3 x^{11} d^{10} c b^{2} a + \frac{1001}{2} x^{6} d^{5} c^{10} b^{3} + \frac{33}{2} x^{10} d^{9} c^{2} b^{2} a + 273 x^{5} d^{4} c^{11} b^{3} + 55 x^{9} d^{8} c^{3} b^{2} a + \frac{455}{4} x^{4} d^{3} c^{12} b^{3} + \frac{495}{4} x^{8} d^{7} c^{4} b^{2} a + 35 x^{3} d^{2} c^{13} b^{3} + 198 x^{7} d^{6} c^{5} b^{2} a + \frac{15}{2} x^{2} d c^{14} b^{3} + 231 x^{6} d^{5} c^{6} b^{2} a + x c^{15} b^{3} + 198 x^{5} d^{4} c^{7} b^{2} a + \frac{495}{4} x^{4} d^{3} c^{8} b^{2} a + \frac{3}{8} x^{8} d^{7} b a^{2} + 55 x^{3} d^{2} c^{9} b^{2} a + 3 x^{7} d^{6} c b a^{2} + \frac{33}{2} x^{2} d c^{10} b^{2} a + \frac{21}{2} x^{6} d^{5} c^{2} b a^{2} + 3 x c^{11} b^{2} a + 21 x^{5} d^{4} c^{3} b a^{2} + \frac{105}{4} x^{4} d^{3} c^{4} b a^{2} + 21 x^{3} d^{2} c^{5} b a^{2} + \frac{21}{2} x^{2} d c^{6} b a^{2} + 3 x c^{7} b a^{2} + \frac{1}{4} x^{4} d^{3} a^{3} + x^{3} d^{2} c a^{3} + \frac{3}{2} x^{2} d c^{2} a^{3} + x c^{3} a^{3}"," ",0,"1/16*x^16*d^15*b^3 + x^15*d^14*c*b^3 + 15/2*x^14*d^13*c^2*b^3 + 35*x^13*d^12*c^3*b^3 + 455/4*x^12*d^11*c^4*b^3 + 273*x^11*d^10*c^5*b^3 + 1001/2*x^10*d^9*c^6*b^3 + 715*x^9*d^8*c^7*b^3 + 6435/8*x^8*d^7*c^8*b^3 + 1/4*x^12*d^11*b^2*a + 715*x^7*d^6*c^9*b^3 + 3*x^11*d^10*c*b^2*a + 1001/2*x^6*d^5*c^10*b^3 + 33/2*x^10*d^9*c^2*b^2*a + 273*x^5*d^4*c^11*b^3 + 55*x^9*d^8*c^3*b^2*a + 455/4*x^4*d^3*c^12*b^3 + 495/4*x^8*d^7*c^4*b^2*a + 35*x^3*d^2*c^13*b^3 + 198*x^7*d^6*c^5*b^2*a + 15/2*x^2*d*c^14*b^3 + 231*x^6*d^5*c^6*b^2*a + x*c^15*b^3 + 198*x^5*d^4*c^7*b^2*a + 495/4*x^4*d^3*c^8*b^2*a + 3/8*x^8*d^7*b*a^2 + 55*x^3*d^2*c^9*b^2*a + 3*x^7*d^6*c*b*a^2 + 33/2*x^2*d*c^10*b^2*a + 21/2*x^6*d^5*c^2*b*a^2 + 3*x*c^11*b^2*a + 21*x^5*d^4*c^3*b*a^2 + 105/4*x^4*d^3*c^4*b*a^2 + 21*x^3*d^2*c^5*b*a^2 + 21/2*x^2*d*c^6*b*a^2 + 3*x*c^7*b*a^2 + 1/4*x^4*d^3*a^3 + x^3*d^2*c*a^3 + 3/2*x^2*d*c^2*a^3 + x*c^3*a^3","B",0
2914,1,54,0,0.880159," ","integrate((d*x+c)^3/(a+b*(d*x+c)^4),x, algorithm=""fricas"")","\frac{\log\left(b d^{4} x^{4} + 4 \, b c d^{3} x^{3} + 6 \, b c^{2} d^{2} x^{2} + 4 \, b c^{3} d x + b c^{4} + a\right)}{4 \, b d}"," ",0,"1/4*log(b*d^4*x^4 + 4*b*c*d^3*x^3 + 6*b*c^2*d^2*x^2 + 4*b*c^3*d*x + b*c^4 + a)/(b*d)","B",0
2915,1,66,0,0.837907," ","integrate((d*x+c)^3/(a+b*(d*x+c)^4)^2,x, algorithm=""fricas"")","-\frac{1}{4 \, {\left(b^{2} d^{5} x^{4} + 4 \, b^{2} c d^{4} x^{3} + 6 \, b^{2} c^{2} d^{3} x^{2} + 4 \, b^{2} c^{3} d^{2} x + {\left(b^{2} c^{4} + a b\right)} d\right)}}"," ",0,"-1/4/(b^2*d^5*x^4 + 4*b^2*c*d^4*x^3 + 6*b^2*c^2*d^3*x^2 + 4*b^2*c^3*d^2*x + (b^2*c^4 + a*b)*d)","B",0
2916,1,172,0,0.642181," ","integrate((d*x+c)^3/(a+b*(d*x+c)^4)^3,x, algorithm=""fricas"")","-\frac{1}{8 \, {\left(b^{3} d^{9} x^{8} + 8 \, b^{3} c d^{8} x^{7} + 28 \, b^{3} c^{2} d^{7} x^{6} + 56 \, b^{3} c^{3} d^{6} x^{5} + 2 \, {\left(35 \, b^{3} c^{4} + a b^{2}\right)} d^{5} x^{4} + 8 \, {\left(7 \, b^{3} c^{5} + a b^{2} c\right)} d^{4} x^{3} + 4 \, {\left(7 \, b^{3} c^{6} + 3 \, a b^{2} c^{2}\right)} d^{3} x^{2} + 8 \, {\left(b^{3} c^{7} + a b^{2} c^{3}\right)} d^{2} x + {\left(b^{3} c^{8} + 2 \, a b^{2} c^{4} + a^{2} b\right)} d\right)}}"," ",0,"-1/8/(b^3*d^9*x^8 + 8*b^3*c*d^8*x^7 + 28*b^3*c^2*d^7*x^6 + 56*b^3*c^3*d^6*x^5 + 2*(35*b^3*c^4 + a*b^2)*d^5*x^4 + 8*(7*b^3*c^5 + a*b^2*c)*d^4*x^3 + 4*(7*b^3*c^6 + 3*a*b^2*c^2)*d^3*x^2 + 8*(b^3*c^7 + a*b^2*c^3)*d^2*x + (b^3*c^8 + 2*a*b^2*c^4 + a^2*b)*d)","B",0
2917,0,0,0,0.817042," ","integrate(1/(a+b*(d*x+c)^4)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{b d^{4} x^{4} + 4 \, b c d^{3} x^{3} + 6 \, b c^{2} d^{2} x^{2} + 4 \, b c^{3} d x + b c^{4} + a}}, x\right)"," ",0,"integral(1/sqrt(b*d^4*x^4 + 4*b*c*d^3*x^3 + 6*b*c^2*d^2*x^2 + 4*b*c^3*d*x + b*c^4 + a), x)","F",0
2918,0,0,0,1.272221," ","integrate(x/(a+b*(d*x+c)^4)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{\sqrt{b d^{4} x^{4} + 4 \, b c d^{3} x^{3} + 6 \, b c^{2} d^{2} x^{2} + 4 \, b c^{3} d x + b c^{4} + a}}, x\right)"," ",0,"integral(x/sqrt(b*d^4*x^4 + 4*b*c*d^3*x^3 + 6*b*c^2*d^2*x^2 + 4*b*c^3*d*x + b*c^4 + a), x)","F",0
2919,-2,0,0,0.000000," ","integrate((d*x)^m*(a+b*(c*x)^(3/2))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   alglogextint: unimplemented","F(-2)",0
2920,-2,0,0,0.000000," ","integrate((d*x)^m*(a+b*(c*x)^(1/2))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   alglogextint: unimplemented","F(-2)",0
2921,-2,0,0,0.000000," ","integrate((d*x)^m*(a+b/(c*x)^(1/2))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   alglogextint: unimplemented","F(-2)",0
2922,-2,0,0,0.000000," ","integrate((d*x)^m*(a+b/(c*x)^(3/2))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   alglogextint: unimplemented","F(-2)",0
2923,0,0,0,0.954881," ","integrate((d*x)^m*(a+b*(c*x)^n)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(\left(c x\right)^{n} b + a\right)}^{p} \left(d x\right)^{m}, x\right)"," ",0,"integral(((c*x)^n*b + a)^p*(d*x)^m, x)","F",0
2924,0,0,0,0.874814," ","integrate(x^2*(a+b*(c*x)^n)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(\left(c x\right)^{n} b + a\right)}^{p} x^{2}, x\right)"," ",0,"integral(((c*x)^n*b + a)^p*x^2, x)","F",0
2925,0,0,0,0.916909," ","integrate(x*(a+b*(c*x)^n)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(\left(c x\right)^{n} b + a\right)}^{p} x, x\right)"," ",0,"integral(((c*x)^n*b + a)^p*x, x)","F",0
2926,0,0,0,0.902860," ","integrate((a+b*(c*x)^n)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(\left(c x\right)^{n} b + a\right)}^{p}, x\right)"," ",0,"integral(((c*x)^n*b + a)^p, x)","F",0
2927,0,0,0,0.886915," ","integrate((a+b*(c*x)^n)^p/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(\left(c x\right)^{n} b + a\right)}^{p}}{x}, x\right)"," ",0,"integral(((c*x)^n*b + a)^p/x, x)","F",0
2928,0,0,0,0.959720," ","integrate((a+b*(c*x)^n)^p/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(\left(c x\right)^{n} b + a\right)}^{p}}{x^{2}}, x\right)"," ",0,"integral(((c*x)^n*b + a)^p/x^2, x)","F",0
2929,1,48,0,0.902670," ","integrate(1/(1+(x^2)^(3/2)),x, algorithm=""fricas"")","\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{2}{3} \, \sqrt{3} \sqrt{x^{2}} - \frac{1}{3} \, \sqrt{3}\right) - \frac{1}{6} \, \log\left(x^{2} - \sqrt{x^{2}} + 1\right) + \frac{1}{3} \, \log\left(\sqrt{x^{2}} + 1\right)"," ",0,"1/3*sqrt(3)*arctan(2/3*sqrt(3)*sqrt(x^2) - 1/3*sqrt(3)) - 1/6*log(x^2 - sqrt(x^2) + 1) + 1/3*log(sqrt(x^2) + 1)","A",0
2930,1,103,0,0.961253," ","integrate(x^5*(a+b*(c*x^2)^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(693 \, b^{6} c^{3} x^{6} - 70 \, a^{2} b^{4} c^{2} x^{4} - 96 \, a^{4} b^{2} c x^{2} - 256 \, a^{6} + {\left(63 \, a b^{5} c^{2} x^{4} + 80 \, a^{3} b^{3} c x^{2} + 128 \, a^{5} b\right)} \sqrt{c x^{2}}\right)} \sqrt{\sqrt{c x^{2}} b + a}}{9009 \, b^{6} c^{3}}"," ",0,"2/9009*(693*b^6*c^3*x^6 - 70*a^2*b^4*c^2*x^4 - 96*a^4*b^2*c*x^2 - 256*a^6 + (63*a*b^5*c^2*x^4 + 80*a^3*b^3*c*x^2 + 128*a^5*b)*sqrt(c*x^2))*sqrt(sqrt(c*x^2)*b + a)/(b^6*c^3)","A",0
2931,1,75,0,0.641114," ","integrate(x^3*(a+b*(c*x^2)^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, b^{4} c^{2} x^{4} - 6 \, a^{2} b^{2} c x^{2} - 16 \, a^{4} + {\left(5 \, a b^{3} c x^{2} + 8 \, a^{3} b\right)} \sqrt{c x^{2}}\right)} \sqrt{\sqrt{c x^{2}} b + a}}{315 \, b^{4} c^{2}}"," ",0,"2/315*(35*b^4*c^2*x^4 - 6*a^2*b^2*c*x^2 - 16*a^4 + (5*a*b^3*c*x^2 + 8*a^3*b)*sqrt(c*x^2))*sqrt(sqrt(c*x^2)*b + a)/(b^4*c^2)","A",0
2932,1,46,0,0.855007," ","integrate(x*(a+b*(c*x^2)^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, b^{2} c x^{2} + \sqrt{c x^{2}} a b - 2 \, a^{2}\right)} \sqrt{\sqrt{c x^{2}} b + a}}{15 \, b^{2} c}"," ",0,"2/15*(3*b^2*c*x^2 + sqrt(c*x^2)*a*b - 2*a^2)*sqrt(sqrt(c*x^2)*b + a)/(b^2*c)","A",0
2933,1,114,0,0.834900," ","integrate((a+b*(c*x^2)^(1/2))^(1/2)/x,x, algorithm=""fricas"")","\left[\sqrt{a} \log\left(\frac{b c x^{2} - 2 \, \sqrt{c x^{2}} \sqrt{\sqrt{c x^{2}} b + a} \sqrt{a} + 2 \, \sqrt{c x^{2}} a}{x^{2}}\right) + 2 \, \sqrt{\sqrt{c x^{2}} b + a}, 2 \, \sqrt{-a} \arctan\left(\frac{\sqrt{\sqrt{c x^{2}} b + a} \sqrt{-a}}{a}\right) + 2 \, \sqrt{\sqrt{c x^{2}} b + a}\right]"," ",0,"[sqrt(a)*log((b*c*x^2 - 2*sqrt(c*x^2)*sqrt(sqrt(c*x^2)*b + a)*sqrt(a) + 2*sqrt(c*x^2)*a)/x^2) + 2*sqrt(sqrt(c*x^2)*b + a), 2*sqrt(-a)*arctan(sqrt(sqrt(c*x^2)*b + a)*sqrt(-a)/a) + 2*sqrt(sqrt(c*x^2)*b + a)]","A",0
2934,1,174,0,0.580396," ","integrate((a+b*(c*x^2)^(1/2))^(1/2)/x^3,x, algorithm=""fricas"")","\left[\frac{\sqrt{a} b^{2} c x^{2} \log\left(\frac{b c x^{2} + 2 \, \sqrt{c x^{2}} \sqrt{\sqrt{c x^{2}} b + a} \sqrt{a} + 2 \, \sqrt{c x^{2}} a}{x^{2}}\right) - 2 \, {\left(\sqrt{c x^{2}} a b + 2 \, a^{2}\right)} \sqrt{\sqrt{c x^{2}} b + a}}{8 \, a^{2} x^{2}}, -\frac{\sqrt{-a} b^{2} c x^{2} \arctan\left(\frac{\sqrt{\sqrt{c x^{2}} b + a} \sqrt{-a}}{a}\right) + {\left(\sqrt{c x^{2}} a b + 2 \, a^{2}\right)} \sqrt{\sqrt{c x^{2}} b + a}}{4 \, a^{2} x^{2}}\right]"," ",0,"[1/8*(sqrt(a)*b^2*c*x^2*log((b*c*x^2 + 2*sqrt(c*x^2)*sqrt(sqrt(c*x^2)*b + a)*sqrt(a) + 2*sqrt(c*x^2)*a)/x^2) - 2*(sqrt(c*x^2)*a*b + 2*a^2)*sqrt(sqrt(c*x^2)*b + a))/(a^2*x^2), -1/4*(sqrt(-a)*b^2*c*x^2*arctan(sqrt(sqrt(c*x^2)*b + a)*sqrt(-a)/a) + (sqrt(c*x^2)*a*b + 2*a^2)*sqrt(sqrt(c*x^2)*b + a))/(a^2*x^2)]","A",0
2935,1,237,0,0.681123," ","integrate((a+b*(c*x^2)^(1/2))^(1/2)/x^5,x, algorithm=""fricas"")","\left[\frac{15 \, \sqrt{a} b^{4} c^{2} x^{4} \log\left(\frac{b c x^{2} + 2 \, \sqrt{c x^{2}} \sqrt{\sqrt{c x^{2}} b + a} \sqrt{a} + 2 \, \sqrt{c x^{2}} a}{x^{2}}\right) + 2 \, {\left(10 \, a^{2} b^{2} c x^{2} - 48 \, a^{4} - {\left(15 \, a b^{3} c x^{2} + 8 \, a^{3} b\right)} \sqrt{c x^{2}}\right)} \sqrt{\sqrt{c x^{2}} b + a}}{384 \, a^{4} x^{4}}, -\frac{15 \, \sqrt{-a} b^{4} c^{2} x^{4} \arctan\left(\frac{\sqrt{\sqrt{c x^{2}} b + a} \sqrt{-a}}{a}\right) - {\left(10 \, a^{2} b^{2} c x^{2} - 48 \, a^{4} - {\left(15 \, a b^{3} c x^{2} + 8 \, a^{3} b\right)} \sqrt{c x^{2}}\right)} \sqrt{\sqrt{c x^{2}} b + a}}{192 \, a^{4} x^{4}}\right]"," ",0,"[1/384*(15*sqrt(a)*b^4*c^2*x^4*log((b*c*x^2 + 2*sqrt(c*x^2)*sqrt(sqrt(c*x^2)*b + a)*sqrt(a) + 2*sqrt(c*x^2)*a)/x^2) + 2*(10*a^2*b^2*c*x^2 - 48*a^4 - (15*a*b^3*c*x^2 + 8*a^3*b)*sqrt(c*x^2))*sqrt(sqrt(c*x^2)*b + a))/(a^4*x^4), -1/192*(15*sqrt(-a)*b^4*c^2*x^4*arctan(sqrt(sqrt(c*x^2)*b + a)*sqrt(-a)/a) - (10*a^2*b^2*c*x^2 - 48*a^4 - (15*a*b^3*c*x^2 + 8*a^3*b)*sqrt(c*x^2))*sqrt(sqrt(c*x^2)*b + a))/(a^4*x^4)]","A",0
2936,1,98,0,0.821188," ","integrate(x^4*(a+b*(c*x^2)^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(315 \, b^{5} c^{3} x^{6} - 40 \, a^{2} b^{3} c^{2} x^{4} - 64 \, a^{4} b c x^{2} + {\left(35 \, a b^{4} c^{2} x^{4} + 48 \, a^{3} b^{2} c x^{2} + 128 \, a^{5}\right)} \sqrt{c x^{2}}\right)} \sqrt{\sqrt{c x^{2}} b + a}}{3465 \, b^{5} c^{3} x}"," ",0,"2/3465*(315*b^5*c^3*x^6 - 40*a^2*b^3*c^2*x^4 - 64*a^4*b*c*x^2 + (35*a*b^4*c^2*x^4 + 48*a^3*b^2*c*x^2 + 128*a^5)*sqrt(c*x^2))*sqrt(sqrt(c*x^2)*b + a)/(b^5*c^3*x)","A",0
2937,1,70,0,0.623393," ","integrate(x^2*(a+b*(c*x^2)^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, b^{3} c^{2} x^{4} - 4 \, a^{2} b c x^{2} + {\left(3 \, a b^{2} c x^{2} + 8 \, a^{3}\right)} \sqrt{c x^{2}}\right)} \sqrt{\sqrt{c x^{2}} b + a}}{105 \, b^{3} c^{2} x}"," ",0,"2/105*(15*b^3*c^2*x^4 - 4*a^2*b*c*x^2 + (3*a*b^2*c*x^2 + 8*a^3)*sqrt(c*x^2))*sqrt(sqrt(c*x^2)*b + a)/(b^3*c^2*x)","A",0
2938,1,40,0,0.849312," ","integrate((a+b*(c*x^2)^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(b c x^{2} + \sqrt{c x^{2}} a\right)} \sqrt{\sqrt{c x^{2}} b + a}}{3 \, b c x}"," ",0,"2/3*(b*c*x^2 + sqrt(c*x^2)*a)*sqrt(sqrt(c*x^2)*b + a)/(b*c*x)","A",0
2939,1,180,0,0.696911," ","integrate((a+b*(c*x^2)^(1/2))^(1/2)/x^2,x, algorithm=""fricas"")","\left[\frac{b x \sqrt{\frac{c}{a}} \log\left(\frac{b c x^{2} - 2 \, \sqrt{\sqrt{c x^{2}} b + a} a x \sqrt{\frac{c}{a}} + 2 \, \sqrt{c x^{2}} a}{x^{2}}\right) - 2 \, \sqrt{\sqrt{c x^{2}} b + a}}{2 \, x}, -\frac{b x \sqrt{-\frac{c}{a}} \arctan\left(-\frac{{\left(a b c x^{2} \sqrt{-\frac{c}{a}} - \sqrt{c x^{2}} a^{2} \sqrt{-\frac{c}{a}}\right)} \sqrt{\sqrt{c x^{2}} b + a}}{b^{2} c^{2} x^{3} - a^{2} c x}\right) + \sqrt{\sqrt{c x^{2}} b + a}}{x}\right]"," ",0,"[1/2*(b*x*sqrt(c/a)*log((b*c*x^2 - 2*sqrt(sqrt(c*x^2)*b + a)*a*x*sqrt(c/a) + 2*sqrt(c*x^2)*a)/x^2) - 2*sqrt(sqrt(c*x^2)*b + a))/x, -(b*x*sqrt(-c/a)*arctan(-(a*b*c*x^2*sqrt(-c/a) - sqrt(c*x^2)*a^2*sqrt(-c/a))*sqrt(sqrt(c*x^2)*b + a)/(b^2*c^2*x^3 - a^2*c*x)) + sqrt(sqrt(c*x^2)*b + a))/x]","A",0
2940,1,252,0,0.838291," ","integrate((a+b*(c*x^2)^(1/2))^(1/2)/x^4,x, algorithm=""fricas"")","\left[\frac{3 \, b^{3} c x^{3} \sqrt{\frac{c}{a}} \log\left(\frac{b c x^{2} - 2 \, \sqrt{\sqrt{c x^{2}} b + a} a x \sqrt{\frac{c}{a}} + 2 \, \sqrt{c x^{2}} a}{x^{2}}\right) + 2 \, {\left(3 \, b^{2} c x^{2} - 2 \, \sqrt{c x^{2}} a b - 8 \, a^{2}\right)} \sqrt{\sqrt{c x^{2}} b + a}}{48 \, a^{2} x^{3}}, -\frac{3 \, b^{3} c x^{3} \sqrt{-\frac{c}{a}} \arctan\left(-\frac{{\left(a b c x^{2} \sqrt{-\frac{c}{a}} - \sqrt{c x^{2}} a^{2} \sqrt{-\frac{c}{a}}\right)} \sqrt{\sqrt{c x^{2}} b + a}}{b^{2} c^{2} x^{3} - a^{2} c x}\right) - {\left(3 \, b^{2} c x^{2} - 2 \, \sqrt{c x^{2}} a b - 8 \, a^{2}\right)} \sqrt{\sqrt{c x^{2}} b + a}}{24 \, a^{2} x^{3}}\right]"," ",0,"[1/48*(3*b^3*c*x^3*sqrt(c/a)*log((b*c*x^2 - 2*sqrt(sqrt(c*x^2)*b + a)*a*x*sqrt(c/a) + 2*sqrt(c*x^2)*a)/x^2) + 2*(3*b^2*c*x^2 - 2*sqrt(c*x^2)*a*b - 8*a^2)*sqrt(sqrt(c*x^2)*b + a))/(a^2*x^3), -1/24*(3*b^3*c*x^3*sqrt(-c/a)*arctan(-(a*b*c*x^2*sqrt(-c/a) - sqrt(c*x^2)*a^2*sqrt(-c/a))*sqrt(sqrt(c*x^2)*b + a)/(b^2*c^2*x^3 - a^2*c*x)) - (3*b^2*c*x^2 - 2*sqrt(c*x^2)*a*b - 8*a^2)*sqrt(sqrt(c*x^2)*b + a))/(a^2*x^3)]","A",0
2941,1,314,0,0.672390," ","integrate((a+b*(c*x^2)^(1/2))^(1/2)/x^6,x, algorithm=""fricas"")","\left[\frac{105 \, b^{5} c^{2} x^{5} \sqrt{\frac{c}{a}} \log\left(\frac{b c x^{2} - 2 \, \sqrt{\sqrt{c x^{2}} b + a} a x \sqrt{\frac{c}{a}} + 2 \, \sqrt{c x^{2}} a}{x^{2}}\right) + 2 \, {\left(105 \, b^{4} c^{2} x^{4} + 56 \, a^{2} b^{2} c x^{2} - 384 \, a^{4} - 2 \, {\left(35 \, a b^{3} c x^{2} + 24 \, a^{3} b\right)} \sqrt{c x^{2}}\right)} \sqrt{\sqrt{c x^{2}} b + a}}{3840 \, a^{4} x^{5}}, -\frac{105 \, b^{5} c^{2} x^{5} \sqrt{-\frac{c}{a}} \arctan\left(-\frac{{\left(a b c x^{2} \sqrt{-\frac{c}{a}} - \sqrt{c x^{2}} a^{2} \sqrt{-\frac{c}{a}}\right)} \sqrt{\sqrt{c x^{2}} b + a}}{b^{2} c^{2} x^{3} - a^{2} c x}\right) - {\left(105 \, b^{4} c^{2} x^{4} + 56 \, a^{2} b^{2} c x^{2} - 384 \, a^{4} - 2 \, {\left(35 \, a b^{3} c x^{2} + 24 \, a^{3} b\right)} \sqrt{c x^{2}}\right)} \sqrt{\sqrt{c x^{2}} b + a}}{1920 \, a^{4} x^{5}}\right]"," ",0,"[1/3840*(105*b^5*c^2*x^5*sqrt(c/a)*log((b*c*x^2 - 2*sqrt(sqrt(c*x^2)*b + a)*a*x*sqrt(c/a) + 2*sqrt(c*x^2)*a)/x^2) + 2*(105*b^4*c^2*x^4 + 56*a^2*b^2*c*x^2 - 384*a^4 - 2*(35*a*b^3*c*x^2 + 24*a^3*b)*sqrt(c*x^2))*sqrt(sqrt(c*x^2)*b + a))/(a^4*x^5), -1/1920*(105*b^5*c^2*x^5*sqrt(-c/a)*arctan(-(a*b*c*x^2*sqrt(-c/a) - sqrt(c*x^2)*a^2*sqrt(-c/a))*sqrt(sqrt(c*x^2)*b + a)/(b^2*c^2*x^3 - a^2*c*x)) - (105*b^4*c^2*x^4 + 56*a^2*b^2*c*x^2 - 384*a^4 - 2*(35*a*b^3*c*x^2 + 24*a^3*b)*sqrt(c*x^2))*sqrt(sqrt(c*x^2)*b + a))/(a^4*x^5)]","A",0
2942,1,78,0,0.658361," ","integrate(x^8*(a+b*(c*x^2)^(3/2))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, b^{3} c^{5} x^{10} - 4 \, a^{2} b c^{2} x^{4} + {\left(3 \, a b^{2} c^{3} x^{6} + 8 \, a^{3}\right)} \sqrt{c x^{2}}\right)} \sqrt{\sqrt{c x^{2}} b c x^{2} + a}}{315 \, b^{3} c^{5} x}"," ",0,"2/315*(15*b^3*c^5*x^10 - 4*a^2*b*c^2*x^4 + (3*a*b^2*c^3*x^6 + 8*a^3)*sqrt(c*x^2))*sqrt(sqrt(c*x^2)*b*c*x^2 + a)/(b^3*c^5*x)","A",0
2943,1,56,0,0.821141," ","integrate(x^5*(a+b*(c*x^2)^(3/2))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, b^{2} c^{3} x^{6} + \sqrt{c x^{2}} a b c x^{2} - 2 \, a^{2}\right)} \sqrt{\sqrt{c x^{2}} b c x^{2} + a}}{45 \, b^{2} c^{3}}"," ",0,"2/45*(3*b^2*c^3*x^6 + sqrt(c*x^2)*a*b*c*x^2 - 2*a^2)*sqrt(sqrt(c*x^2)*b*c*x^2 + a)/(b^2*c^3)","A",0
2944,1,46,0,0.742027," ","integrate(x^2*(a+b*(c*x^2)^(3/2))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(b c^{2} x^{4} + \sqrt{c x^{2}} a\right)} \sqrt{\sqrt{c x^{2}} b c x^{2} + a}}{9 \, b c^{2} x}"," ",0,"2/9*(b*c^2*x^4 + sqrt(c*x^2)*a)*sqrt(sqrt(c*x^2)*b*c*x^2 + a)/(b*c^2*x)","A",0
2945,1,133,0,0.854254," ","integrate((a+b*(c*x^2)^(3/2))^(1/2)/x,x, algorithm=""fricas"")","\left[\frac{1}{3} \, \sqrt{a} \log\left(\frac{b c^{2} x^{4} - 2 \, \sqrt{\sqrt{c x^{2}} b c x^{2} + a} \sqrt{c x^{2}} \sqrt{a} + 2 \, \sqrt{c x^{2}} a}{x^{4}}\right) + \frac{2}{3} \, \sqrt{\sqrt{c x^{2}} b c x^{2} + a}, \frac{2}{3} \, \sqrt{-a} \arctan\left(\frac{\sqrt{\sqrt{c x^{2}} b c x^{2} + a} \sqrt{-a}}{a}\right) + \frac{2}{3} \, \sqrt{\sqrt{c x^{2}} b c x^{2} + a}\right]"," ",0,"[1/3*sqrt(a)*log((b*c^2*x^4 - 2*sqrt(sqrt(c*x^2)*b*c*x^2 + a)*sqrt(c*x^2)*sqrt(a) + 2*sqrt(c*x^2)*a)/x^4) + 2/3*sqrt(sqrt(c*x^2)*b*c*x^2 + a), 2/3*sqrt(-a)*arctan(sqrt(sqrt(c*x^2)*b*c*x^2 + a)*sqrt(-a)/a) + 2/3*sqrt(sqrt(c*x^2)*b*c*x^2 + a)]","A",0
2946,1,206,0,1.019196," ","integrate((a+b*(c*x^2)^(3/2))^(1/2)/x^4,x, algorithm=""fricas"")","\left[\frac{b c x^{3} \sqrt{\frac{c}{a}} \log\left(\frac{b c^{2} x^{4} - 2 \, \sqrt{\sqrt{c x^{2}} b c x^{2} + a} a x \sqrt{\frac{c}{a}} + 2 \, \sqrt{c x^{2}} a}{x^{4}}\right) - 2 \, \sqrt{\sqrt{c x^{2}} b c x^{2} + a}}{6 \, x^{3}}, -\frac{b c x^{3} \sqrt{-\frac{c}{a}} \arctan\left(-\frac{{\left(a b c^{2} x^{4} \sqrt{-\frac{c}{a}} - \sqrt{c x^{2}} a^{2} \sqrt{-\frac{c}{a}}\right)} \sqrt{\sqrt{c x^{2}} b c x^{2} + a}}{b^{2} c^{4} x^{7} - a^{2} c x}\right) + \sqrt{\sqrt{c x^{2}} b c x^{2} + a}}{3 \, x^{3}}\right]"," ",0,"[1/6*(b*c*x^3*sqrt(c/a)*log((b*c^2*x^4 - 2*sqrt(sqrt(c*x^2)*b*c*x^2 + a)*a*x*sqrt(c/a) + 2*sqrt(c*x^2)*a)/x^4) - 2*sqrt(sqrt(c*x^2)*b*c*x^2 + a))/x^3, -1/3*(b*c*x^3*sqrt(-c/a)*arctan(-(a*b*c^2*x^4*sqrt(-c/a) - sqrt(c*x^2)*a^2*sqrt(-c/a))*sqrt(sqrt(c*x^2)*b*c*x^2 + a)/(b^2*c^4*x^7 - a^2*c*x)) + sqrt(sqrt(c*x^2)*b*c*x^2 + a))/x^3]","A",0
2947,0,0,0,1.051016," ","integrate(x^3*(a+b*(c*x^2)^(3/2))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{\sqrt{c x^{2}} b c x^{2} + a} x^{3}, x\right)"," ",0,"integral(sqrt(sqrt(c*x^2)*b*c*x^2 + a)*x^3, x)","F",0
2948,0,0,0,0.734093," ","integrate((a+b*(c*x^2)^(3/2))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{\sqrt{c x^{2}} b c x^{2} + a}, x\right)"," ",0,"integral(sqrt(sqrt(c*x^2)*b*c*x^2 + a), x)","F",0
2949,0,0,0,0.855555," ","integrate((a+b*(c*x^2)^(3/2))^(1/2)/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\sqrt{c x^{2}} b c x^{2} + a}}{x^{3}}, x\right)"," ",0,"integral(sqrt(sqrt(c*x^2)*b*c*x^2 + a)/x^3, x)","F",0
2950,0,0,0,0.912820," ","integrate((a+b*(c*x^2)^(3/2))^(1/2)/x^6,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\sqrt{c x^{2}} b c x^{2} + a}}{x^{6}}, x\right)"," ",0,"integral(sqrt(sqrt(c*x^2)*b*c*x^2 + a)/x^6, x)","F",0
2951,0,0,0,0.880305," ","integrate(x^4*(a+b*(c*x^2)^(3/2))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{\sqrt{c x^{2}} b c x^{2} + a} x^{4}, x\right)"," ",0,"integral(sqrt(sqrt(c*x^2)*b*c*x^2 + a)*x^4, x)","F",0
2952,0,0,0,0.995897," ","integrate(x*(a+b*(c*x^2)^(3/2))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{\sqrt{c x^{2}} b c x^{2} + a} x, x\right)"," ",0,"integral(sqrt(sqrt(c*x^2)*b*c*x^2 + a)*x, x)","F",0
2953,0,0,0,7.786335," ","integrate((a+b*(c*x^2)^(3/2))^(1/2)/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\sqrt{c x^{2}} b c x^{2} + a}}{x^{2}}, x\right)"," ",0,"integral(sqrt(sqrt(c*x^2)*b*c*x^2 + a)/x^2, x)","F",0
2954,0,0,0,1.055830," ","integrate((a+b*(c*x^2)^(3/2))^(1/2)/x^5,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\sqrt{c x^{2}} b c x^{2} + a}}{x^{5}}, x\right)"," ",0,"integral(sqrt(sqrt(c*x^2)*b*c*x^2 + a)/x^5, x)","F",0
2955,0,0,0,1.072359," ","integrate((d*x)^m*(a+b*(c*x^2)^(3/2))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{\sqrt{c x^{2}} b c x^{2} + a} \left(d x\right)^{m}, x\right)"," ",0,"integral(sqrt(sqrt(c*x^2)*b*c*x^2 + a)*(d*x)^m, x)","F",0
2956,0,0,0,0.897682," ","integrate((d*x)^m*(a+b*(c*x^2)^(1/2))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{\sqrt{c x^{2}} b + a} \left(d x\right)^{m}, x\right)"," ",0,"integral(sqrt(sqrt(c*x^2)*b + a)*(d*x)^m, x)","F",0
2957,0,0,0,1.381021," ","integrate((d*x)^m*(a+b/(c*x^2)^(1/2))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\left(d x\right)^{m} \sqrt{\frac{a c x^{2} + \sqrt{c x^{2}} b}{c x^{2}}}, x\right)"," ",0,"integral((d*x)^m*sqrt((a*c*x^2 + sqrt(c*x^2)*b)/(c*x^2)), x)","F",0
2958,0,0,0,1.794119," ","integrate((d*x)^m*(a+b/(c*x^2)^(3/2))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\left(d x\right)^{m} \sqrt{\frac{a c^{2} x^{4} + \sqrt{c x^{2}} b}{c^{2} x^{4}}}, x\right)"," ",0,"integral((d*x)^m*sqrt((a*c^2*x^4 + sqrt(c*x^2)*b)/(c^2*x^4)), x)","F",0
2959,1,6,0,0.825125," ","integrate(1/(1+(x^3)^(2/3)),x, algorithm=""fricas"")","\arctan\left({\left(x^{3}\right)}^{\frac{1}{3}}\right)"," ",0,"arctan((x^3)^(1/3))","A",0
2960,1,75,0,1.032275," ","integrate(x^5*(a+b*(c*x^3)^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{4 \, {\left(35 \, b^{4} c^{2} x^{6} - 6 \, a^{2} b^{2} c x^{3} - 16 \, a^{4} + {\left(5 \, a b^{3} c x^{3} + 8 \, a^{3} b\right)} \sqrt{c x^{3}}\right)} \sqrt{\sqrt{c x^{3}} b + a}}{945 \, b^{4} c^{2}}"," ",0,"4/945*(35*b^4*c^2*x^6 - 6*a^2*b^2*c*x^3 - 16*a^4 + (5*a*b^3*c*x^3 + 8*a^3*b)*sqrt(c*x^3))*sqrt(sqrt(c*x^3)*b + a)/(b^4*c^2)","A",0
2961,1,46,0,0.913902," ","integrate(x^2*(a+b*(c*x^3)^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{4 \, {\left(3 \, b^{2} c x^{3} + \sqrt{c x^{3}} a b - 2 \, a^{2}\right)} \sqrt{\sqrt{c x^{3}} b + a}}{45 \, b^{2} c}"," ",0,"4/45*(3*b^2*c*x^3 + sqrt(c*x^3)*a*b - 2*a^2)*sqrt(sqrt(c*x^3)*b + a)/(b^2*c)","A",0
2962,-1,0,0,0.000000," ","integrate((a+b*(c*x^3)^(1/2))^(1/2)/x,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2963,-1,0,0,0.000000," ","integrate((a+b*(c*x^3)^(1/2))^(1/2)/x^4,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2964,0,0,0,10.210391," ","integrate(x*(a+b*(c*x^3)^(1/2))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{\sqrt{c x^{3}} b + a} x, x\right)"," ",0,"integral(sqrt(sqrt(c*x^3)*b + a)*x, x)","F",0
2965,0,0,0,9.764795," ","integrate((a+b*(c*x^3)^(1/2))^(1/2)/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\sqrt{c x^{3}} b + a}}{x^{2}}, x\right)"," ",0,"integral(sqrt(sqrt(c*x^3)*b + a)/x^2, x)","F",0
2966,0,0,0,9.097601," ","integrate((a+b*(c*x^3)^(1/2))^(1/2)/x^5,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\sqrt{c x^{3}} b + a}}{x^{5}}, x\right)"," ",0,"integral(sqrt(sqrt(c*x^3)*b + a)/x^5, x)","F",0
2967,0,0,0,11.180865," ","integrate(x^3*(a+b*(c*x^3)^(1/2))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{\sqrt{c x^{3}} b + a} x^{3}, x\right)"," ",0,"integral(sqrt(sqrt(c*x^3)*b + a)*x^3, x)","F",0
2968,0,0,0,12.135209," ","integrate((a+b*(c*x^3)^(1/2))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{\sqrt{c x^{3}} b + a}, x\right)"," ",0,"integral(sqrt(sqrt(c*x^3)*b + a), x)","F",0
2969,0,0,0,11.062404," ","integrate((a+b*(c*x^3)^(1/2))^(1/2)/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\sqrt{c x^{3}} b + a}}{x^{3}}, x\right)"," ",0,"integral(sqrt(sqrt(c*x^3)*b + a)/x^3, x)","F",0
2970,1,87,0,10.336481," ","integrate(x^17*(a+b*(c*x^3)^(3/2))^(1/2),x, algorithm=""fricas"")","\frac{4 \, {\left(35 \, b^{4} c^{6} x^{18} - 6 \, a^{2} b^{2} c^{3} x^{9} - 16 \, a^{4} + {\left(5 \, a b^{3} c^{4} x^{12} + 8 \, a^{3} b c x^{3}\right)} \sqrt{c x^{3}}\right)} \sqrt{\sqrt{c x^{3}} b c x^{3} + a}}{2835 \, b^{4} c^{6}}"," ",0,"4/2835*(35*b^4*c^6*x^18 - 6*a^2*b^2*c^3*x^9 - 16*a^4 + (5*a*b^3*c^4*x^12 + 8*a^3*b*c*x^3)*sqrt(c*x^3))*sqrt(sqrt(c*x^3)*b*c*x^3 + a)/(b^4*c^6)","A",0
2971,1,56,0,5.911615," ","integrate(x^8*(a+b*(c*x^3)^(3/2))^(1/2),x, algorithm=""fricas"")","\frac{4 \, {\left(3 \, b^{2} c^{3} x^{9} + \sqrt{c x^{3}} a b c x^{3} - 2 \, a^{2}\right)} \sqrt{\sqrt{c x^{3}} b c x^{3} + a}}{135 \, b^{2} c^{3}}"," ",0,"4/135*(3*b^2*c^3*x^9 + sqrt(c*x^3)*a*b*c*x^3 - 2*a^2)*sqrt(sqrt(c*x^3)*b*c*x^3 + a)/(b^2*c^3)","A",0
2972,-1,0,0,0.000000," ","integrate((a+b*(c*x^3)^(3/2))^(1/2)/x,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2973,-1,0,0,0.000000," ","integrate((a+b*(c*x^3)^(3/2))^(1/2)/x^10,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2974,0,0,0,3.733709," ","integrate(x^2*(a+b*(c*x^3)^(3/2))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{\sqrt{c x^{3}} b c x^{3} + a} x^{2}, x\right)"," ",0,"integral(sqrt(sqrt(c*x^3)*b*c*x^3 + a)*x^2, x)","F",0
2975,-1,0,0,0.000000," ","integrate(x^9*(a+b*(c*x^3)^(3/2))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2976,-1,0,0,0.000000," ","integrate((a+b*(c*x^3)^(3/2))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2977,-1,0,0,0.000000," ","integrate((a+b*(c*x^3)^(3/2))^(1/2)/x^9,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2978,-2,0,0,0.000000," ","integrate((d*x)^m*(a+b*(c*x^3)^(3/2))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   alglogextint: unimplemented","F(-2)",0
2979,-2,0,0,0.000000," ","integrate((d*x)^m*(a+b*(c*x^3)^(1/2))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   alglogextint: unimplemented","F(-2)",0
2980,-2,0,0,0.000000," ","integrate((d*x)^m*(a+b/(c*x^3)^(1/2))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   alglogextint: unimplemented","F(-2)",0
2981,-2,0,0,0.000000," ","integrate((d*x)^m*(a+b/(c*x^3)^(3/2))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   alglogextint: unimplemented","F(-2)",0
2982,1,224,0,1.530655," ","integrate(x*(a+b*(c/x)^(1/2))^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, \sqrt{a} b^{4} c^{2} \log\left(-2 \, \sqrt{b \sqrt{\frac{c}{x}} + a} \sqrt{a} x \sqrt{\frac{c}{x}} + 2 \, a x \sqrt{\frac{c}{x}} + b c\right) - 2 \, {\left(10 \, a^{2} b^{2} c x - 48 \, a^{4} x^{2} - {\left(15 \, a b^{3} c x + 8 \, a^{3} b x^{2}\right)} \sqrt{\frac{c}{x}}\right)} \sqrt{b \sqrt{\frac{c}{x}} + a}}{192 \, a^{4}}, \frac{15 \, \sqrt{-a} b^{4} c^{2} \arctan\left(\frac{\sqrt{b \sqrt{\frac{c}{x}} + a} \sqrt{-a}}{a}\right) - {\left(10 \, a^{2} b^{2} c x - 48 \, a^{4} x^{2} - {\left(15 \, a b^{3} c x + 8 \, a^{3} b x^{2}\right)} \sqrt{\frac{c}{x}}\right)} \sqrt{b \sqrt{\frac{c}{x}} + a}}{96 \, a^{4}}\right]"," ",0,"[1/192*(15*sqrt(a)*b^4*c^2*log(-2*sqrt(b*sqrt(c/x) + a)*sqrt(a)*x*sqrt(c/x) + 2*a*x*sqrt(c/x) + b*c) - 2*(10*a^2*b^2*c*x - 48*a^4*x^2 - (15*a*b^3*c*x + 8*a^3*b*x^2)*sqrt(c/x))*sqrt(b*sqrt(c/x) + a))/a^4, 1/96*(15*sqrt(-a)*b^4*c^2*arctan(sqrt(b*sqrt(c/x) + a)*sqrt(-a)/a) - (10*a^2*b^2*c*x - 48*a^4*x^2 - (15*a*b^3*c*x + 8*a^3*b*x^2)*sqrt(c/x))*sqrt(b*sqrt(c/x) + a))/a^4]","A",0
2983,1,161,0,1.641042," ","integrate((a+b*(c/x)^(1/2))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a} b^{2} c \log\left(-2 \, \sqrt{b \sqrt{\frac{c}{x}} + a} \sqrt{a} x \sqrt{\frac{c}{x}} + 2 \, a x \sqrt{\frac{c}{x}} + b c\right) + 2 \, {\left(a b x \sqrt{\frac{c}{x}} + 2 \, a^{2} x\right)} \sqrt{b \sqrt{\frac{c}{x}} + a}}{4 \, a^{2}}, \frac{\sqrt{-a} b^{2} c \arctan\left(\frac{\sqrt{b \sqrt{\frac{c}{x}} + a} \sqrt{-a}}{a}\right) + {\left(a b x \sqrt{\frac{c}{x}} + 2 \, a^{2} x\right)} \sqrt{b \sqrt{\frac{c}{x}} + a}}{2 \, a^{2}}\right]"," ",0,"[1/4*(sqrt(a)*b^2*c*log(-2*sqrt(b*sqrt(c/x) + a)*sqrt(a)*x*sqrt(c/x) + 2*a*x*sqrt(c/x) + b*c) + 2*(a*b*x*sqrt(c/x) + 2*a^2*x)*sqrt(b*sqrt(c/x) + a))/a^2, 1/2*(sqrt(-a)*b^2*c*arctan(sqrt(b*sqrt(c/x) + a)*sqrt(-a)/a) + (a*b*x*sqrt(c/x) + 2*a^2*x)*sqrt(b*sqrt(c/x) + a))/a^2]","A",0
2984,1,110,0,1.507398," ","integrate((a+b*(c/x)^(1/2))^(1/2)/x,x, algorithm=""fricas"")","\left[2 \, \sqrt{a} \log\left(2 \, \sqrt{b \sqrt{\frac{c}{x}} + a} \sqrt{a} x \sqrt{\frac{c}{x}} + 2 \, a x \sqrt{\frac{c}{x}} + b c\right) - 4 \, \sqrt{b \sqrt{\frac{c}{x}} + a}, -4 \, \sqrt{-a} \arctan\left(\frac{\sqrt{b \sqrt{\frac{c}{x}} + a} \sqrt{-a}}{a}\right) - 4 \, \sqrt{b \sqrt{\frac{c}{x}} + a}\right]"," ",0,"[2*sqrt(a)*log(2*sqrt(b*sqrt(c/x) + a)*sqrt(a)*x*sqrt(c/x) + 2*a*x*sqrt(c/x) + b*c) - 4*sqrt(b*sqrt(c/x) + a), -4*sqrt(-a)*arctan(sqrt(b*sqrt(c/x) + a)*sqrt(-a)/a) - 4*sqrt(b*sqrt(c/x) + a)]","A",0
2985,1,48,0,1.287222," ","integrate((a+b*(c/x)^(1/2))^(1/2)/x^2,x, algorithm=""fricas"")","-\frac{4 \, {\left(a b x \sqrt{\frac{c}{x}} + 3 \, b^{2} c - 2 \, a^{2} x\right)} \sqrt{b \sqrt{\frac{c}{x}} + a}}{15 \, b^{2} c x}"," ",0,"-4/15*(a*b*x*sqrt(c/x) + 3*b^2*c - 2*a^2*x)*sqrt(b*sqrt(c/x) + a)/(b^2*c*x)","A",0
2986,1,77,0,1.198839," ","integrate((a+b*(c/x)^(1/2))^(1/2)/x^3,x, algorithm=""fricas"")","-\frac{4 \, {\left(35 \, b^{4} c^{2} - 6 \, a^{2} b^{2} c x - 16 \, a^{4} x^{2} + {\left(5 \, a b^{3} c x + 8 \, a^{3} b x^{2}\right)} \sqrt{\frac{c}{x}}\right)} \sqrt{b \sqrt{\frac{c}{x}} + a}}{315 \, b^{4} c^{2} x^{2}}"," ",0,"-4/315*(35*b^4*c^2 - 6*a^2*b^2*c*x - 16*a^4*x^2 + (5*a*b^3*c*x + 8*a^3*b*x^2)*sqrt(c/x))*sqrt(b*sqrt(c/x) + a)/(b^4*c^2*x^2)","A",0
2987,1,105,0,1.427662," ","integrate((a+b*(c/x)^(1/2))^(1/2)/x^4,x, algorithm=""fricas"")","-\frac{4 \, {\left(693 \, b^{6} c^{3} - 70 \, a^{2} b^{4} c^{2} x - 96 \, a^{4} b^{2} c x^{2} - 256 \, a^{6} x^{3} + {\left(63 \, a b^{5} c^{2} x + 80 \, a^{3} b^{3} c x^{2} + 128 \, a^{5} b x^{3}\right)} \sqrt{\frac{c}{x}}\right)} \sqrt{b \sqrt{\frac{c}{x}} + a}}{9009 \, b^{6} c^{3} x^{3}}"," ",0,"-4/9009*(693*b^6*c^3 - 70*a^2*b^4*c^2*x - 96*a^4*b^2*c*x^2 - 256*a^6*x^3 + (63*a*b^5*c^2*x + 80*a^3*b^3*c*x^2 + 128*a^5*b*x^3)*sqrt(c/x))*sqrt(b*sqrt(c/x) + a)/(b^6*c^3*x^3)","A",0
2988,1,224,0,1.476074," ","integrate(x/(a+b*(c/x)^(1/2))^(1/2),x, algorithm=""fricas"")","\left[\frac{105 \, \sqrt{a} b^{4} c^{2} \log\left(2 \, \sqrt{b \sqrt{\frac{c}{x}} + a} \sqrt{a} x \sqrt{\frac{c}{x}} + 2 \, a x \sqrt{\frac{c}{x}} + b c\right) + 2 \, {\left(70 \, a^{2} b^{2} c x + 48 \, a^{4} x^{2} - 7 \, {\left(15 \, a b^{3} c x + 8 \, a^{3} b x^{2}\right)} \sqrt{\frac{c}{x}}\right)} \sqrt{b \sqrt{\frac{c}{x}} + a}}{192 \, a^{5}}, -\frac{105 \, \sqrt{-a} b^{4} c^{2} \arctan\left(\frac{\sqrt{b \sqrt{\frac{c}{x}} + a} \sqrt{-a}}{a}\right) - {\left(70 \, a^{2} b^{2} c x + 48 \, a^{4} x^{2} - 7 \, {\left(15 \, a b^{3} c x + 8 \, a^{3} b x^{2}\right)} \sqrt{\frac{c}{x}}\right)} \sqrt{b \sqrt{\frac{c}{x}} + a}}{96 \, a^{5}}\right]"," ",0,"[1/192*(105*sqrt(a)*b^4*c^2*log(2*sqrt(b*sqrt(c/x) + a)*sqrt(a)*x*sqrt(c/x) + 2*a*x*sqrt(c/x) + b*c) + 2*(70*a^2*b^2*c*x + 48*a^4*x^2 - 7*(15*a*b^3*c*x + 8*a^3*b*x^2)*sqrt(c/x))*sqrt(b*sqrt(c/x) + a))/a^5, -1/96*(105*sqrt(-a)*b^4*c^2*arctan(sqrt(b*sqrt(c/x) + a)*sqrt(-a)/a) - (70*a^2*b^2*c*x + 48*a^4*x^2 - 7*(15*a*b^3*c*x + 8*a^3*b*x^2)*sqrt(c/x))*sqrt(b*sqrt(c/x) + a))/a^5]","A",0
2989,1,165,0,1.479426," ","integrate(1/(a+b*(c/x)^(1/2))^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{a} b^{2} c \log\left(2 \, \sqrt{b \sqrt{\frac{c}{x}} + a} \sqrt{a} x \sqrt{\frac{c}{x}} + 2 \, a x \sqrt{\frac{c}{x}} + b c\right) - 2 \, {\left(3 \, a b x \sqrt{\frac{c}{x}} - 2 \, a^{2} x\right)} \sqrt{b \sqrt{\frac{c}{x}} + a}}{4 \, a^{3}}, -\frac{3 \, \sqrt{-a} b^{2} c \arctan\left(\frac{\sqrt{b \sqrt{\frac{c}{x}} + a} \sqrt{-a}}{a}\right) + {\left(3 \, a b x \sqrt{\frac{c}{x}} - 2 \, a^{2} x\right)} \sqrt{b \sqrt{\frac{c}{x}} + a}}{2 \, a^{3}}\right]"," ",0,"[1/4*(3*sqrt(a)*b^2*c*log(2*sqrt(b*sqrt(c/x) + a)*sqrt(a)*x*sqrt(c/x) + 2*a*x*sqrt(c/x) + b*c) - 2*(3*a*b*x*sqrt(c/x) - 2*a^2*x)*sqrt(b*sqrt(c/x) + a))/a^3, -1/2*(3*sqrt(-a)*b^2*c*arctan(sqrt(b*sqrt(c/x) + a)*sqrt(-a)/a) + (3*a*b*x*sqrt(c/x) - 2*a^2*x)*sqrt(b*sqrt(c/x) + a))/a^3]","A",0
2990,1,81,0,1.400731," ","integrate(1/x/(a+b*(c/x)^(1/2))^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, \log\left(2 \, \sqrt{b \sqrt{\frac{c}{x}} + a} \sqrt{a} x \sqrt{\frac{c}{x}} + 2 \, a x \sqrt{\frac{c}{x}} + b c\right)}{\sqrt{a}}, -\frac{4 \, \sqrt{-a} \arctan\left(\frac{\sqrt{b \sqrt{\frac{c}{x}} + a} \sqrt{-a}}{a}\right)}{a}\right]"," ",0,"[2*log(2*sqrt(b*sqrt(c/x) + a)*sqrt(a)*x*sqrt(c/x) + 2*a*x*sqrt(c/x) + b*c)/sqrt(a), -4*sqrt(-a)*arctan(sqrt(b*sqrt(c/x) + a)*sqrt(-a)/a)/a]","A",0
2991,1,34,0,1.476767," ","integrate(1/x^2/(a+b*(c/x)^(1/2))^(1/2),x, algorithm=""fricas"")","-\frac{4 \, \sqrt{b \sqrt{\frac{c}{x}} + a} {\left(b \sqrt{\frac{c}{x}} - 2 \, a\right)}}{3 \, b^{2} c}"," ",0,"-4/3*sqrt(b*sqrt(c/x) + a)*(b*sqrt(c/x) - 2*a)/(b^2*c)","A",0
2992,1,61,0,1.230531," ","integrate(1/x^3/(a+b*(c/x)^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{4 \, {\left(6 \, a b^{2} c + 16 \, a^{3} x - {\left(5 \, b^{3} c + 8 \, a^{2} b x\right)} \sqrt{\frac{c}{x}}\right)} \sqrt{b \sqrt{\frac{c}{x}} + a}}{35 \, b^{4} c^{2} x}"," ",0,"4/35*(6*a*b^2*c + 16*a^3*x - (5*b^3*c + 8*a^2*b*x)*sqrt(c/x))*sqrt(b*sqrt(c/x) + a)/(b^4*c^2*x)","A",0
2993,1,89,0,1.322260," ","integrate(1/x^4/(a+b*(c/x)^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{4 \, {\left(70 \, a b^{4} c^{2} + 96 \, a^{3} b^{2} c x + 256 \, a^{5} x^{2} - {\left(63 \, b^{5} c^{2} + 80 \, a^{2} b^{3} c x + 128 \, a^{4} b x^{2}\right)} \sqrt{\frac{c}{x}}\right)} \sqrt{b \sqrt{\frac{c}{x}} + a}}{693 \, b^{6} c^{3} x^{2}}"," ",0,"4/693*(70*a*b^4*c^2 + 96*a^3*b^2*c*x + 256*a^5*x^2 - (63*b^5*c^2 + 80*a^2*b^3*c*x + 128*a^4*b*x^2)*sqrt(c/x))*sqrt(b*sqrt(c/x) + a)/(b^6*c^3*x^2)","A",0
2994,1,55,0,1.127725," ","integrate(1/(1+(1/x)^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, {\left(2 \, x - 3 \, \sqrt{x}\right)} \sqrt{\frac{x + \sqrt{x}}{x}} + \frac{3}{4} \, \log\left(\sqrt{\frac{x + \sqrt{x}}{x}} + 1\right) - \frac{3}{4} \, \log\left(\sqrt{\frac{x + \sqrt{x}}{x}} - 1\right)"," ",0,"1/2*(2*x - 3*sqrt(x))*sqrt((x + sqrt(x))/x) + 3/4*log(sqrt((x + sqrt(x))/x) + 1) - 3/4*log(sqrt((x + sqrt(x))/x) - 1)","A",0
2995,-2,0,0,0.000000," ","integrate((d*x)^m*(a+b*(c/x)^(3/2))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   alglogextint: unimplemented","F(-2)",0
2996,-2,0,0,0.000000," ","integrate((d*x)^m*(a+b*(c/x)^(1/2))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   alglogextint: unimplemented","F(-2)",0
2997,-2,0,0,0.000000," ","integrate((d*x)^m*(a+b/(c/x)^(1/2))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   alglogextint: unimplemented","F(-2)",0
2998,-2,0,0,0.000000," ","integrate((d*x)^m*(a+b/(c/x)^(3/2))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   alglogextint: unimplemented","F(-2)",0
2999,-2,0,0,0.000000," ","integrate((d*x)^m/(a+b*(c/x)^(3/2))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   alglogextint: unimplemented","F(-2)",0
3000,-2,0,0,0.000000," ","integrate((d*x)^m/(a+b*(c/x)^(1/2))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   alglogextint: unimplemented","F(-2)",0
3001,-2,0,0,0.000000," ","integrate((d*x)^m/(a+b/(c/x)^(1/2))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   alglogextint: unimplemented","F(-2)",0
3002,-2,0,0,0.000000," ","integrate((d*x)^m/(a+b/(c/x)^(3/2))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   alglogextint: unimplemented","F(-2)",0
3003,1,15,0,1.455770," ","integrate(a+b*(c*x^n)^(1/n),x, algorithm=""fricas"")","\frac{1}{2} \, b c^{\left(\frac{1}{n}\right)} x^{2} + a x"," ",0,"1/2*b*c^(1/n)*x^2 + a*x","A",0
3004,1,32,0,1.073149," ","integrate((a+b*(c*x^n)^(1/n))^2,x, algorithm=""fricas"")","\frac{1}{3} \, b^{2} c^{\frac{2}{n}} x^{3} + a b c^{\left(\frac{1}{n}\right)} x^{2} + a^{2} x"," ",0,"1/3*b^2*c^(2/n)*x^3 + a*b*c^(1/n)*x^2 + a^2*x","A",0
3005,1,50,0,1.438730," ","integrate((a+b*(c*x^n)^(1/n))^3,x, algorithm=""fricas"")","\frac{1}{4} \, b^{3} c^{\frac{3}{n}} x^{4} + a b^{2} c^{\frac{2}{n}} x^{3} + \frac{3}{2} \, a^{2} b c^{\left(\frac{1}{n}\right)} x^{2} + a^{3} x"," ",0,"1/4*b^3*c^(3/n)*x^4 + a*b^2*c^(2/n)*x^3 + 3/2*a^2*b*c^(1/n)*x^2 + a^3*x","A",0
3006,1,74,0,1.235394," ","integrate(x^3/(a+b*(c*x^n)^(1/n)),x, algorithm=""fricas"")","\frac{2 \, b^{3} c^{\frac{3}{n}} x^{3} - 3 \, a b^{2} c^{\frac{2}{n}} x^{2} + 6 \, a^{2} b c^{\left(\frac{1}{n}\right)} x - 6 \, a^{3} \log\left(b c^{\left(\frac{1}{n}\right)} x + a\right)}{6 \, b^{4} c^{\frac{4}{n}}}"," ",0,"1/6*(2*b^3*c^(3/n)*x^3 - 3*a*b^2*c^(2/n)*x^2 + 6*a^2*b*c^(1/n)*x - 6*a^3*log(b*c^(1/n)*x + a))/(b^4*c^(4/n))","A",0
3007,1,55,0,1.199039," ","integrate(x^2/(a+b*(c*x^n)^(1/n)),x, algorithm=""fricas"")","\frac{b^{2} c^{\frac{2}{n}} x^{2} - 2 \, a b c^{\left(\frac{1}{n}\right)} x + 2 \, a^{2} \log\left(b c^{\left(\frac{1}{n}\right)} x + a\right)}{2 \, b^{3} c^{\frac{3}{n}}}"," ",0,"1/2*(b^2*c^(2/n)*x^2 - 2*a*b*c^(1/n)*x + 2*a^2*log(b*c^(1/n)*x + a))/(b^3*c^(3/n))","A",0
3008,1,36,0,1.774938," ","integrate(x/(a+b*(c*x^n)^(1/n)),x, algorithm=""fricas"")","\frac{b c^{\left(\frac{1}{n}\right)} x - a \log\left(b c^{\left(\frac{1}{n}\right)} x + a\right)}{b^{2} c^{\frac{2}{n}}}"," ",0,"(b*c^(1/n)*x - a*log(b*c^(1/n)*x + a))/(b^2*c^(2/n))","A",0
3009,1,22,0,1.063219," ","integrate(1/(a+b*(c*x^n)^(1/n)),x, algorithm=""fricas"")","\frac{\log\left(b c^{\left(\frac{1}{n}\right)} x + a\right)}{b c^{\left(\frac{1}{n}\right)}}"," ",0,"log(b*c^(1/n)*x + a)/(b*c^(1/n))","A",0
3010,1,21,0,1.530832," ","integrate(1/x/(a+b*(c*x^n)^(1/n)),x, algorithm=""fricas"")","-\frac{\log\left(b c^{\left(\frac{1}{n}\right)} x + a\right) - \log\left(x\right)}{a}"," ",0,"-(log(b*c^(1/n)*x + a) - log(x))/a","A",0
3011,1,41,0,0.951518," ","integrate(1/x^2/(a+b*(c*x^n)^(1/n)),x, algorithm=""fricas"")","\frac{b c^{\left(\frac{1}{n}\right)} x \log\left(b c^{\left(\frac{1}{n}\right)} x + a\right) - b c^{\left(\frac{1}{n}\right)} x \log\left(x\right) - a}{a^{2} x}"," ",0,"(b*c^(1/n)*x*log(b*c^(1/n)*x + a) - b*c^(1/n)*x*log(x) - a)/(a^2*x)","A",0
3012,1,65,0,0.993744," ","integrate(1/x^3/(a+b*(c*x^n)^(1/n)),x, algorithm=""fricas"")","-\frac{2 \, b^{2} c^{\frac{2}{n}} x^{2} \log\left(b c^{\left(\frac{1}{n}\right)} x + a\right) - 2 \, b^{2} c^{\frac{2}{n}} x^{2} \log\left(x\right) - 2 \, a b c^{\left(\frac{1}{n}\right)} x + a^{2}}{2 \, a^{3} x^{2}}"," ",0,"-1/2*(2*b^2*c^(2/n)*x^2*log(b*c^(1/n)*x + a) - 2*b^2*c^(2/n)*x^2*log(x) - 2*a*b*c^(1/n)*x + a^2)/(a^3*x^2)","A",0
3013,1,105,0,1.182263," ","integrate(x^3/(a+b*(c*x^n)^(1/n))^2,x, algorithm=""fricas"")","\frac{b^{3} c^{\frac{3}{n}} x^{3} - 3 \, a b^{2} c^{\frac{2}{n}} x^{2} - 4 \, a^{2} b c^{\left(\frac{1}{n}\right)} x + 2 \, a^{3} + 6 \, {\left(a^{2} b c^{\left(\frac{1}{n}\right)} x + a^{3}\right)} \log\left(b c^{\left(\frac{1}{n}\right)} x + a\right)}{2 \, {\left(b^{5} c^{\frac{5}{n}} x + a b^{4} c^{\frac{4}{n}}\right)}}"," ",0,"1/2*(b^3*c^(3/n)*x^3 - 3*a*b^2*c^(2/n)*x^2 - 4*a^2*b*c^(1/n)*x + 2*a^3 + 6*(a^2*b*c^(1/n)*x + a^3)*log(b*c^(1/n)*x + a))/(b^5*c^(5/n)*x + a*b^4*c^(4/n))","A",0
3014,1,83,0,0.917495," ","integrate(x^2/(a+b*(c*x^n)^(1/n))^2,x, algorithm=""fricas"")","\frac{b^{2} c^{\frac{2}{n}} x^{2} + a b c^{\left(\frac{1}{n}\right)} x - a^{2} - 2 \, {\left(a b c^{\left(\frac{1}{n}\right)} x + a^{2}\right)} \log\left(b c^{\left(\frac{1}{n}\right)} x + a\right)}{b^{4} c^{\frac{4}{n}} x + a b^{3} c^{\frac{3}{n}}}"," ",0,"(b^2*c^(2/n)*x^2 + a*b*c^(1/n)*x - a^2 - 2*(a*b*c^(1/n)*x + a^2)*log(b*c^(1/n)*x + a))/(b^4*c^(4/n)*x + a*b^3*c^(3/n))","A",0
3015,1,52,0,1.108108," ","integrate(x/(a+b*(c*x^n)^(1/n))^2,x, algorithm=""fricas"")","\frac{{\left(b c^{\left(\frac{1}{n}\right)} x + a\right)} \log\left(b c^{\left(\frac{1}{n}\right)} x + a\right) + a}{b^{3} c^{\frac{3}{n}} x + a b^{2} c^{\frac{2}{n}}}"," ",0,"((b*c^(1/n)*x + a)*log(b*c^(1/n)*x + a) + a)/(b^3*c^(3/n)*x + a*b^2*c^(2/n))","A",0
3016,1,25,0,0.940546," ","integrate(1/(a+b*(c*x^n)^(1/n))^2,x, algorithm=""fricas"")","-\frac{1}{b^{2} c^{\frac{2}{n}} x + a b c^{\left(\frac{1}{n}\right)}}"," ",0,"-1/(b^2*c^(2/n)*x + a*b*c^(1/n))","A",0
3017,1,57,0,1.081521," ","integrate(1/x/(a+b*(c*x^n)^(1/n))^2,x, algorithm=""fricas"")","\frac{b c^{\left(\frac{1}{n}\right)} x \log\left(x\right) - {\left(b c^{\left(\frac{1}{n}\right)} x + a\right)} \log\left(b c^{\left(\frac{1}{n}\right)} x + a\right) + a \log\left(x\right) + a}{a^{2} b c^{\left(\frac{1}{n}\right)} x + a^{3}}"," ",0,"(b*c^(1/n)*x*log(x) - (b*c^(1/n)*x + a)*log(b*c^(1/n)*x + a) + a*log(x) + a)/(a^2*b*c^(1/n)*x + a^3)","A",0
3018,1,99,0,0.943300," ","integrate(1/x^2/(a+b*(c*x^n)^(1/n))^2,x, algorithm=""fricas"")","-\frac{2 \, b^{2} c^{\frac{2}{n}} x^{2} \log\left(x\right) + a^{2} + 2 \, {\left(a b x \log\left(x\right) + a b x\right)} c^{\left(\frac{1}{n}\right)} - 2 \, {\left(b^{2} c^{\frac{2}{n}} x^{2} + a b c^{\left(\frac{1}{n}\right)} x\right)} \log\left(b c^{\left(\frac{1}{n}\right)} x + a\right)}{a^{3} b c^{\left(\frac{1}{n}\right)} x^{2} + a^{4} x}"," ",0,"-(2*b^2*c^(2/n)*x^2*log(x) + a^2 + 2*(a*b*x*log(x) + a*b*x)*c^(1/n) - 2*(b^2*c^(2/n)*x^2 + a*b*c^(1/n)*x)*log(b*c^(1/n)*x + a))/(a^3*b*c^(1/n)*x^2 + a^4*x)","A",0
3019,1,131,0,1.166777," ","integrate(1/x^3/(a+b*(c*x^n)^(1/n))^2,x, algorithm=""fricas"")","\frac{6 \, b^{3} c^{\frac{3}{n}} x^{3} \log\left(x\right) + 3 \, a^{2} b c^{\left(\frac{1}{n}\right)} x - a^{3} + 6 \, {\left(a b^{2} x^{2} \log\left(x\right) + a b^{2} x^{2}\right)} c^{\frac{2}{n}} - 6 \, {\left(b^{3} c^{\frac{3}{n}} x^{3} + a b^{2} c^{\frac{2}{n}} x^{2}\right)} \log\left(b c^{\left(\frac{1}{n}\right)} x + a\right)}{2 \, {\left(a^{4} b c^{\left(\frac{1}{n}\right)} x^{3} + a^{5} x^{2}\right)}}"," ",0,"1/2*(6*b^3*c^(3/n)*x^3*log(x) + 3*a^2*b*c^(1/n)*x - a^3 + 6*(a*b^2*x^2*log(x) + a*b^2*x^2)*c^(2/n) - 6*(b^3*c^(3/n)*x^3 + a*b^2*c^(2/n)*x^2)*log(b*c^(1/n)*x + a))/(a^4*b*c^(1/n)*x^3 + a^5*x^2)","A",0
3020,1,43,0,0.983263," ","integrate(1/(a+b*(c*x^n)^(1/n))^3,x, algorithm=""fricas"")","-\frac{1}{2 \, {\left(b^{3} c^{\frac{3}{n}} x^{2} + 2 \, a b^{2} c^{\frac{2}{n}} x + a^{2} b c^{\left(\frac{1}{n}\right)}\right)}}"," ",0,"-1/2/(b^3*c^(3/n)*x^2 + 2*a*b^2*c^(2/n)*x + a^2*b*c^(1/n))","A",0
3021,1,16,0,0.821751," ","integrate(x/(1+(x^n)^(1/n))^2,x, algorithm=""fricas"")","\frac{{\left(x + 1\right)} \log\left(x + 1\right) + 1}{x + 1}"," ",0,"((x + 1)*log(x + 1) + 1)/(x + 1)","A",0
3022,1,183,0,1.301731," ","integrate(x^3*(a+b*(c*x^n)^(1/n))^p,x, algorithm=""fricas"")","\frac{{\left(6 \, a^{3} b c^{\left(\frac{1}{n}\right)} p x + {\left(b^{4} p^{3} + 6 \, b^{4} p^{2} + 11 \, b^{4} p + 6 \, b^{4}\right)} c^{\frac{4}{n}} x^{4} + {\left(a b^{3} p^{3} + 3 \, a b^{3} p^{2} + 2 \, a b^{3} p\right)} c^{\frac{3}{n}} x^{3} - 6 \, a^{4} - 3 \, {\left(a^{2} b^{2} p^{2} + a^{2} b^{2} p\right)} c^{\frac{2}{n}} x^{2}\right)} {\left(b c^{\left(\frac{1}{n}\right)} x + a\right)}^{p}}{{\left(b^{4} p^{4} + 10 \, b^{4} p^{3} + 35 \, b^{4} p^{2} + 50 \, b^{4} p + 24 \, b^{4}\right)} c^{\frac{4}{n}}}"," ",0,"(6*a^3*b*c^(1/n)*p*x + (b^4*p^3 + 6*b^4*p^2 + 11*b^4*p + 6*b^4)*c^(4/n)*x^4 + (a*b^3*p^3 + 3*a*b^3*p^2 + 2*a*b^3*p)*c^(3/n)*x^3 - 6*a^4 - 3*(a^2*b^2*p^2 + a^2*b^2*p)*c^(2/n)*x^2)*(b*c^(1/n)*x + a)^p/((b^4*p^4 + 10*b^4*p^3 + 35*b^4*p^2 + 50*b^4*p + 24*b^4)*c^(4/n))","A",0
3023,1,129,0,0.757293," ","integrate(x^2*(a+b*(c*x^n)^(1/n))^p,x, algorithm=""fricas"")","-\frac{{\left(2 \, a^{2} b c^{\left(\frac{1}{n}\right)} p x - {\left(b^{3} p^{2} + 3 \, b^{3} p + 2 \, b^{3}\right)} c^{\frac{3}{n}} x^{3} - {\left(a b^{2} p^{2} + a b^{2} p\right)} c^{\frac{2}{n}} x^{2} - 2 \, a^{3}\right)} {\left(b c^{\left(\frac{1}{n}\right)} x + a\right)}^{p}}{{\left(b^{3} p^{3} + 6 \, b^{3} p^{2} + 11 \, b^{3} p + 6 \, b^{3}\right)} c^{\frac{3}{n}}}"," ",0,"-(2*a^2*b*c^(1/n)*p*x - (b^3*p^2 + 3*b^3*p + 2*b^3)*c^(3/n)*x^3 - (a*b^2*p^2 + a*b^2*p)*c^(2/n)*x^2 - 2*a^3)*(b*c^(1/n)*x + a)^p/((b^3*p^3 + 6*b^3*p^2 + 11*b^3*p + 6*b^3)*c^(3/n))","A",0
3024,1,79,0,1.254531," ","integrate(x*(a+b*(c*x^n)^(1/n))^p,x, algorithm=""fricas"")","\frac{{\left(a b c^{\left(\frac{1}{n}\right)} p x + {\left(b^{2} p + b^{2}\right)} c^{\frac{2}{n}} x^{2} - a^{2}\right)} {\left(b c^{\left(\frac{1}{n}\right)} x + a\right)}^{p}}{{\left(b^{2} p^{2} + 3 \, b^{2} p + 2 \, b^{2}\right)} c^{\frac{2}{n}}}"," ",0,"(a*b*c^(1/n)*p*x + (b^2*p + b^2)*c^(2/n)*x^2 - a^2)*(b*c^(1/n)*x + a)^p/((b^2*p^2 + 3*b^2*p + 2*b^2)*c^(2/n))","A",0
3025,1,37,0,1.217073," ","integrate((a+b*(c*x^n)^(1/n))^p,x, algorithm=""fricas"")","\frac{{\left(b c^{\left(\frac{1}{n}\right)} x + a\right)} {\left(b c^{\left(\frac{1}{n}\right)} x + a\right)}^{p}}{{\left(b p + b\right)} c^{\left(\frac{1}{n}\right)}}"," ",0,"(b*c^(1/n)*x + a)*(b*c^(1/n)*x + a)^p/((b*p + b)*c^(1/n))","A",0
3026,0,0,0,1.483822," ","integrate((a+b*(c*x^n)^(1/n))^p/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(\left(c x^{n}\right)^{\left(\frac{1}{n}\right)} b + a\right)}^{p}}{x}, x\right)"," ",0,"integral(((c*x^n)^(1/n)*b + a)^p/x, x)","F",0
3027,0,0,0,0.962706," ","integrate((a+b*(c*x^n)^(1/n))^p/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(\left(c x^{n}\right)^{\left(\frac{1}{n}\right)} b + a\right)}^{p}}{x^{2}}, x\right)"," ",0,"integral(((c*x^n)^(1/n)*b + a)^p/x^2, x)","F",0
3028,1,52,0,1.258646," ","integrate((a+b*(c*x^n)^(2/n))^3,x, algorithm=""fricas"")","\frac{1}{7} \, b^{3} c^{\frac{6}{n}} x^{7} + \frac{3}{5} \, a b^{2} c^{\frac{4}{n}} x^{5} + a^{2} b c^{\frac{2}{n}} x^{3} + a^{3} x"," ",0,"1/7*b^3*c^(6/n)*x^7 + 3/5*a*b^2*c^(4/n)*x^5 + a^2*b*c^(2/n)*x^3 + a^3*x","A",0
3029,1,35,0,0.942326," ","integrate((a+b*(c*x^n)^(2/n))^2,x, algorithm=""fricas"")","\frac{1}{5} \, b^{2} c^{\frac{4}{n}} x^{5} + \frac{2}{3} \, a b c^{\frac{2}{n}} x^{3} + a^{2} x"," ",0,"1/5*b^2*c^(4/n)*x^5 + 2/3*a*b*c^(2/n)*x^3 + a^2*x","A",0
3030,1,17,0,1.223535," ","integrate(a+b*(c*x^n)^(2/n),x, algorithm=""fricas"")","\frac{1}{3} \, b c^{\frac{2}{n}} x^{3} + a x"," ",0,"1/3*b*c^(2/n)*x^3 + a*x","A",0
3031,1,127,0,0.967584," ","integrate(1/(a+b*(c*x^n)^(2/n)),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a b c^{\frac{2}{n}}} \log\left(\frac{b c^{\frac{2}{n}} x^{2} - 2 \, \sqrt{-a b c^{\frac{2}{n}}} x - a}{b c^{\frac{2}{n}} x^{2} + a}\right)}{2 \, a b c^{\frac{2}{n}}}, \frac{\sqrt{a b c^{\frac{2}{n}}} \arctan\left(\frac{\sqrt{a b c^{\frac{2}{n}}} x}{a}\right)}{a b c^{\frac{2}{n}}}\right]"," ",0,"[-1/2*sqrt(-a*b*c^(2/n))*log((b*c^(2/n)*x^2 - 2*sqrt(-a*b*c^(2/n))*x - a)/(b*c^(2/n)*x^2 + a))/(a*b*c^(2/n)), sqrt(a*b*c^(2/n))*arctan(sqrt(a*b*c^(2/n))*x/a)/(a*b*c^(2/n))]","A",0
3032,1,218,0,1.301591," ","integrate(1/(a+b*(c*x^n)^(2/n))^2,x, algorithm=""fricas"")","\left[\frac{2 \, a b c^{\frac{2}{n}} x - {\left(b c^{\frac{2}{n}} x^{2} + a\right)} \sqrt{-a b c^{\frac{2}{n}}} \log\left(\frac{b c^{\frac{2}{n}} x^{2} - 2 \, \sqrt{-a b c^{\frac{2}{n}}} x - a}{b c^{\frac{2}{n}} x^{2} + a}\right)}{4 \, {\left(a^{2} b^{2} c^{\frac{4}{n}} x^{2} + a^{3} b c^{\frac{2}{n}}\right)}}, \frac{a b c^{\frac{2}{n}} x + {\left(b c^{\frac{2}{n}} x^{2} + a\right)} \sqrt{a b c^{\frac{2}{n}}} \arctan\left(\frac{\sqrt{a b c^{\frac{2}{n}}} x}{a}\right)}{2 \, {\left(a^{2} b^{2} c^{\frac{4}{n}} x^{2} + a^{3} b c^{\frac{2}{n}}\right)}}\right]"," ",0,"[1/4*(2*a*b*c^(2/n)*x - (b*c^(2/n)*x^2 + a)*sqrt(-a*b*c^(2/n))*log((b*c^(2/n)*x^2 - 2*sqrt(-a*b*c^(2/n))*x - a)/(b*c^(2/n)*x^2 + a)))/(a^2*b^2*c^(4/n)*x^2 + a^3*b*c^(2/n)), 1/2*(a*b*c^(2/n)*x + (b*c^(2/n)*x^2 + a)*sqrt(a*b*c^(2/n))*arctan(sqrt(a*b*c^(2/n))*x/a))/(a^2*b^2*c^(4/n)*x^2 + a^3*b*c^(2/n))]","A",0
3033,1,328,0,0.962486," ","integrate(1/(a+b*(c*x^n)^(2/n))^3,x, algorithm=""fricas"")","\left[\frac{6 \, a b^{2} c^{\frac{4}{n}} x^{3} + 10 \, a^{2} b c^{\frac{2}{n}} x - 3 \, {\left(b^{2} c^{\frac{4}{n}} x^{4} + 2 \, a b c^{\frac{2}{n}} x^{2} + a^{2}\right)} \sqrt{-a b c^{\frac{2}{n}}} \log\left(\frac{b c^{\frac{2}{n}} x^{2} - 2 \, \sqrt{-a b c^{\frac{2}{n}}} x - a}{b c^{\frac{2}{n}} x^{2} + a}\right)}{16 \, {\left(a^{3} b^{3} c^{\frac{6}{n}} x^{4} + 2 \, a^{4} b^{2} c^{\frac{4}{n}} x^{2} + a^{5} b c^{\frac{2}{n}}\right)}}, \frac{3 \, a b^{2} c^{\frac{4}{n}} x^{3} + 5 \, a^{2} b c^{\frac{2}{n}} x + 3 \, {\left(b^{2} c^{\frac{4}{n}} x^{4} + 2 \, a b c^{\frac{2}{n}} x^{2} + a^{2}\right)} \sqrt{a b c^{\frac{2}{n}}} \arctan\left(\frac{\sqrt{a b c^{\frac{2}{n}}} x}{a}\right)}{8 \, {\left(a^{3} b^{3} c^{\frac{6}{n}} x^{4} + 2 \, a^{4} b^{2} c^{\frac{4}{n}} x^{2} + a^{5} b c^{\frac{2}{n}}\right)}}\right]"," ",0,"[1/16*(6*a*b^2*c^(4/n)*x^3 + 10*a^2*b*c^(2/n)*x - 3*(b^2*c^(4/n)*x^4 + 2*a*b*c^(2/n)*x^2 + a^2)*sqrt(-a*b*c^(2/n))*log((b*c^(2/n)*x^2 - 2*sqrt(-a*b*c^(2/n))*x - a)/(b*c^(2/n)*x^2 + a)))/(a^3*b^3*c^(6/n)*x^4 + 2*a^4*b^2*c^(4/n)*x^2 + a^5*b*c^(2/n)), 1/8*(3*a*b^2*c^(4/n)*x^3 + 5*a^2*b*c^(2/n)*x + 3*(b^2*c^(4/n)*x^4 + 2*a*b*c^(2/n)*x^2 + a^2)*sqrt(a*b*c^(2/n))*arctan(sqrt(a*b*c^(2/n))*x/a))/(a^3*b^3*c^(6/n)*x^4 + 2*a^4*b^2*c^(4/n)*x^2 + a^5*b*c^(2/n))]","A",0
3034,1,6,0,1.010838," ","integrate(1/(1+4*(x^4)^(1/2)),x, algorithm=""fricas"")","\frac{1}{2} \, \arctan\left(2 \, x\right)"," ",0,"1/2*arctan(2*x)","A",0
3035,1,17,0,1.354438," ","integrate(1/(1-4*(x^4)^(1/2)),x, algorithm=""fricas"")","\frac{1}{4} \, \log\left(2 \, x + 1\right) - \frac{1}{4} \, \log\left(2 \, x - 1\right)"," ",0,"1/4*log(2*x + 1) - 1/4*log(2*x - 1)","A",0
3036,1,6,0,0.882721," ","integrate(1/(1+4*(x^6)^(1/3)),x, algorithm=""fricas"")","\frac{1}{2} \, \arctan\left(2 \, x\right)"," ",0,"1/2*arctan(2*x)","A",0
3037,1,17,0,1.698359," ","integrate(1/(1-4*(x^6)^(1/3)),x, algorithm=""fricas"")","\frac{1}{4} \, \log\left(2 \, x + 1\right) - \frac{1}{4} \, \log\left(2 \, x - 1\right)"," ",0,"1/4*log(2*x + 1) - 1/4*log(2*x - 1)","A",0
3038,1,6,0,1.021228," ","integrate(1/(1+4*(x^(2*n))^(1/n)),x, algorithm=""fricas"")","\frac{1}{2} \, \arctan\left(2 \, x\right)"," ",0,"1/2*arctan(2*x)","A",0
3039,1,17,0,0.901277," ","integrate(1/(1-4*(x^(2*n))^(1/n)),x, algorithm=""fricas"")","\frac{1}{4} \, \log\left(2 \, x + 1\right) - \frac{1}{4} \, \log\left(2 \, x - 1\right)"," ",0,"1/4*log(2*x + 1) - 1/4*log(2*x - 1)","A",0
3040,1,53,0,1.184883," ","integrate((a+b*(c*x^n)^(3/n))^3,x, algorithm=""fricas"")","\frac{1}{10} \, b^{3} c^{\frac{9}{n}} x^{10} + \frac{3}{7} \, a b^{2} c^{\frac{6}{n}} x^{7} + \frac{3}{4} \, a^{2} b c^{\frac{3}{n}} x^{4} + a^{3} x"," ",0,"1/10*b^3*c^(9/n)*x^10 + 3/7*a*b^2*c^(6/n)*x^7 + 3/4*a^2*b*c^(3/n)*x^4 + a^3*x","A",0
3041,1,35,0,0.669511," ","integrate((a+b*(c*x^n)^(3/n))^2,x, algorithm=""fricas"")","\frac{1}{7} \, b^{2} c^{\frac{6}{n}} x^{7} + \frac{1}{2} \, a b c^{\frac{3}{n}} x^{4} + a^{2} x"," ",0,"1/7*b^2*c^(6/n)*x^7 + 1/2*a*b*c^(3/n)*x^4 + a^2*x","A",0
3042,1,17,0,0.829192," ","integrate(a+b*(c*x^n)^(3/n),x, algorithm=""fricas"")","\frac{1}{4} \, b c^{\frac{3}{n}} x^{4} + a x"," ",0,"1/4*b*c^(3/n)*x^4 + a*x","A",0
3043,1,549,0,0.816970," ","integrate(1/(a+b*(c*x^n)^(3/n)),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{\frac{1}{3}} a b c^{\frac{3}{n}} \sqrt{-\frac{\left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{1}{3}}}{b c^{\frac{3}{n}}}} \log\left(\frac{2 \, a b c^{\frac{3}{n}} x^{3} - 3 \, \left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{1}{3}} a x - a^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, a b c^{\frac{3}{n}} x^{2} + \left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{2}{3}} x - \left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{1}{3}} a\right)} \sqrt{-\frac{\left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{1}{3}}}{b c^{\frac{3}{n}}}}}{b c^{\frac{3}{n}} x^{3} + a}\right) - \left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{2}{3}} \log\left(a b c^{\frac{3}{n}} x^{2} - \left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{2}{3}} x + \left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{1}{3}} a\right) + 2 \, \left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{2}{3}} \log\left(a b c^{\frac{3}{n}} x + \left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{2}{3}}\right)}{6 \, a^{2} b c^{\frac{3}{n}}}, \frac{6 \, \sqrt{\frac{1}{3}} a b c^{\frac{3}{n}} \sqrt{\frac{\left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{1}{3}}}{b c^{\frac{3}{n}}}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{2}{3}} x - \left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{1}{3}}}{b c^{\frac{3}{n}}}}}{a^{2}}\right) - \left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{2}{3}} \log\left(a b c^{\frac{3}{n}} x^{2} - \left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{2}{3}} x + \left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{1}{3}} a\right) + 2 \, \left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{2}{3}} \log\left(a b c^{\frac{3}{n}} x + \left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{2}{3}}\right)}{6 \, a^{2} b c^{\frac{3}{n}}}\right]"," ",0,"[1/6*(3*sqrt(1/3)*a*b*c^(3/n)*sqrt(-(a^2*b*c^(3/n))^(1/3)/(b*c^(3/n)))*log((2*a*b*c^(3/n)*x^3 - 3*(a^2*b*c^(3/n))^(1/3)*a*x - a^2 + 3*sqrt(1/3)*(2*a*b*c^(3/n)*x^2 + (a^2*b*c^(3/n))^(2/3)*x - (a^2*b*c^(3/n))^(1/3)*a)*sqrt(-(a^2*b*c^(3/n))^(1/3)/(b*c^(3/n))))/(b*c^(3/n)*x^3 + a)) - (a^2*b*c^(3/n))^(2/3)*log(a*b*c^(3/n)*x^2 - (a^2*b*c^(3/n))^(2/3)*x + (a^2*b*c^(3/n))^(1/3)*a) + 2*(a^2*b*c^(3/n))^(2/3)*log(a*b*c^(3/n)*x + (a^2*b*c^(3/n))^(2/3)))/(a^2*b*c^(3/n)), 1/6*(6*sqrt(1/3)*a*b*c^(3/n)*sqrt((a^2*b*c^(3/n))^(1/3)/(b*c^(3/n)))*arctan(sqrt(1/3)*(2*(a^2*b*c^(3/n))^(2/3)*x - (a^2*b*c^(3/n))^(1/3)*a)*sqrt((a^2*b*c^(3/n))^(1/3)/(b*c^(3/n)))/a^2) - (a^2*b*c^(3/n))^(2/3)*log(a*b*c^(3/n)*x^2 - (a^2*b*c^(3/n))^(2/3)*x + (a^2*b*c^(3/n))^(1/3)*a) + 2*(a^2*b*c^(3/n))^(2/3)*log(a*b*c^(3/n)*x + (a^2*b*c^(3/n))^(2/3)))/(a^2*b*c^(3/n))]","A",0
3044,1,705,0,0.955074," ","integrate(1/(a+b*(c*x^n)^(3/n))^2,x, algorithm=""fricas"")","\left[\frac{3 \, a^{2} b c^{\frac{3}{n}} x + 3 \, \sqrt{\frac{1}{3}} {\left(a b^{2} c^{\frac{6}{n}} x^{3} + a^{2} b c^{\frac{3}{n}}\right)} \sqrt{-\frac{\left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{1}{3}}}{b c^{\frac{3}{n}}}} \log\left(\frac{2 \, a b c^{\frac{3}{n}} x^{3} - 3 \, \left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{1}{3}} a x - a^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, a b c^{\frac{3}{n}} x^{2} + \left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{2}{3}} x - \left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{1}{3}} a\right)} \sqrt{-\frac{\left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{1}{3}}}{b c^{\frac{3}{n}}}}}{b c^{\frac{3}{n}} x^{3} + a}\right) - {\left(b c^{\frac{3}{n}} x^{3} + a\right)} \left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{2}{3}} \log\left(a b c^{\frac{3}{n}} x^{2} - \left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{2}{3}} x + \left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{1}{3}} a\right) + 2 \, {\left(b c^{\frac{3}{n}} x^{3} + a\right)} \left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{2}{3}} \log\left(a b c^{\frac{3}{n}} x + \left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{2}{3}}\right)}{9 \, {\left(a^{3} b^{2} c^{\frac{6}{n}} x^{3} + a^{4} b c^{\frac{3}{n}}\right)}}, \frac{3 \, a^{2} b c^{\frac{3}{n}} x + 6 \, \sqrt{\frac{1}{3}} {\left(a b^{2} c^{\frac{6}{n}} x^{3} + a^{2} b c^{\frac{3}{n}}\right)} \sqrt{\frac{\left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{1}{3}}}{b c^{\frac{3}{n}}}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{2}{3}} x - \left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{1}{3}}}{b c^{\frac{3}{n}}}}}{a^{2}}\right) - {\left(b c^{\frac{3}{n}} x^{3} + a\right)} \left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{2}{3}} \log\left(a b c^{\frac{3}{n}} x^{2} - \left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{2}{3}} x + \left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{1}{3}} a\right) + 2 \, {\left(b c^{\frac{3}{n}} x^{3} + a\right)} \left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{2}{3}} \log\left(a b c^{\frac{3}{n}} x + \left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{2}{3}}\right)}{9 \, {\left(a^{3} b^{2} c^{\frac{6}{n}} x^{3} + a^{4} b c^{\frac{3}{n}}\right)}}\right]"," ",0,"[1/9*(3*a^2*b*c^(3/n)*x + 3*sqrt(1/3)*(a*b^2*c^(6/n)*x^3 + a^2*b*c^(3/n))*sqrt(-(a^2*b*c^(3/n))^(1/3)/(b*c^(3/n)))*log((2*a*b*c^(3/n)*x^3 - 3*(a^2*b*c^(3/n))^(1/3)*a*x - a^2 + 3*sqrt(1/3)*(2*a*b*c^(3/n)*x^2 + (a^2*b*c^(3/n))^(2/3)*x - (a^2*b*c^(3/n))^(1/3)*a)*sqrt(-(a^2*b*c^(3/n))^(1/3)/(b*c^(3/n))))/(b*c^(3/n)*x^3 + a)) - (b*c^(3/n)*x^3 + a)*(a^2*b*c^(3/n))^(2/3)*log(a*b*c^(3/n)*x^2 - (a^2*b*c^(3/n))^(2/3)*x + (a^2*b*c^(3/n))^(1/3)*a) + 2*(b*c^(3/n)*x^3 + a)*(a^2*b*c^(3/n))^(2/3)*log(a*b*c^(3/n)*x + (a^2*b*c^(3/n))^(2/3)))/(a^3*b^2*c^(6/n)*x^3 + a^4*b*c^(3/n)), 1/9*(3*a^2*b*c^(3/n)*x + 6*sqrt(1/3)*(a*b^2*c^(6/n)*x^3 + a^2*b*c^(3/n))*sqrt((a^2*b*c^(3/n))^(1/3)/(b*c^(3/n)))*arctan(sqrt(1/3)*(2*(a^2*b*c^(3/n))^(2/3)*x - (a^2*b*c^(3/n))^(1/3)*a)*sqrt((a^2*b*c^(3/n))^(1/3)/(b*c^(3/n)))/a^2) - (b*c^(3/n)*x^3 + a)*(a^2*b*c^(3/n))^(2/3)*log(a*b*c^(3/n)*x^2 - (a^2*b*c^(3/n))^(2/3)*x + (a^2*b*c^(3/n))^(1/3)*a) + 2*(b*c^(3/n)*x^3 + a)*(a^2*b*c^(3/n))^(2/3)*log(a*b*c^(3/n)*x + (a^2*b*c^(3/n))^(2/3)))/(a^3*b^2*c^(6/n)*x^3 + a^4*b*c^(3/n))]","A",0
3045,1,885,0,0.733478," ","integrate(1/(a+b*(c*x^n)^(3/n))^3,x, algorithm=""fricas"")","\left[\frac{15 \, a^{2} b^{2} c^{\frac{6}{n}} x^{4} + 24 \, a^{3} b c^{\frac{3}{n}} x + 15 \, \sqrt{\frac{1}{3}} {\left(a b^{3} c^{\frac{9}{n}} x^{6} + 2 \, a^{2} b^{2} c^{\frac{6}{n}} x^{3} + a^{3} b c^{\frac{3}{n}}\right)} \sqrt{-\frac{\left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{1}{3}}}{b c^{\frac{3}{n}}}} \log\left(\frac{2 \, a b c^{\frac{3}{n}} x^{3} - 3 \, \left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{1}{3}} a x - a^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, a b c^{\frac{3}{n}} x^{2} + \left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{2}{3}} x - \left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{1}{3}} a\right)} \sqrt{-\frac{\left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{1}{3}}}{b c^{\frac{3}{n}}}}}{b c^{\frac{3}{n}} x^{3} + a}\right) - 5 \, {\left(b^{2} c^{\frac{6}{n}} x^{6} + 2 \, a b c^{\frac{3}{n}} x^{3} + a^{2}\right)} \left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{2}{3}} \log\left(a b c^{\frac{3}{n}} x^{2} - \left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{2}{3}} x + \left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{1}{3}} a\right) + 10 \, {\left(b^{2} c^{\frac{6}{n}} x^{6} + 2 \, a b c^{\frac{3}{n}} x^{3} + a^{2}\right)} \left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{2}{3}} \log\left(a b c^{\frac{3}{n}} x + \left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{2}{3}}\right)}{54 \, {\left(a^{4} b^{3} c^{\frac{9}{n}} x^{6} + 2 \, a^{5} b^{2} c^{\frac{6}{n}} x^{3} + a^{6} b c^{\frac{3}{n}}\right)}}, \frac{15 \, a^{2} b^{2} c^{\frac{6}{n}} x^{4} + 24 \, a^{3} b c^{\frac{3}{n}} x + 30 \, \sqrt{\frac{1}{3}} {\left(a b^{3} c^{\frac{9}{n}} x^{6} + 2 \, a^{2} b^{2} c^{\frac{6}{n}} x^{3} + a^{3} b c^{\frac{3}{n}}\right)} \sqrt{\frac{\left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{1}{3}}}{b c^{\frac{3}{n}}}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{2}{3}} x - \left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{1}{3}}}{b c^{\frac{3}{n}}}}}{a^{2}}\right) - 5 \, {\left(b^{2} c^{\frac{6}{n}} x^{6} + 2 \, a b c^{\frac{3}{n}} x^{3} + a^{2}\right)} \left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{2}{3}} \log\left(a b c^{\frac{3}{n}} x^{2} - \left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{2}{3}} x + \left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{1}{3}} a\right) + 10 \, {\left(b^{2} c^{\frac{6}{n}} x^{6} + 2 \, a b c^{\frac{3}{n}} x^{3} + a^{2}\right)} \left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{2}{3}} \log\left(a b c^{\frac{3}{n}} x + \left(a^{2} b c^{\frac{3}{n}}\right)^{\frac{2}{3}}\right)}{54 \, {\left(a^{4} b^{3} c^{\frac{9}{n}} x^{6} + 2 \, a^{5} b^{2} c^{\frac{6}{n}} x^{3} + a^{6} b c^{\frac{3}{n}}\right)}}\right]"," ",0,"[1/54*(15*a^2*b^2*c^(6/n)*x^4 + 24*a^3*b*c^(3/n)*x + 15*sqrt(1/3)*(a*b^3*c^(9/n)*x^6 + 2*a^2*b^2*c^(6/n)*x^3 + a^3*b*c^(3/n))*sqrt(-(a^2*b*c^(3/n))^(1/3)/(b*c^(3/n)))*log((2*a*b*c^(3/n)*x^3 - 3*(a^2*b*c^(3/n))^(1/3)*a*x - a^2 + 3*sqrt(1/3)*(2*a*b*c^(3/n)*x^2 + (a^2*b*c^(3/n))^(2/3)*x - (a^2*b*c^(3/n))^(1/3)*a)*sqrt(-(a^2*b*c^(3/n))^(1/3)/(b*c^(3/n))))/(b*c^(3/n)*x^3 + a)) - 5*(b^2*c^(6/n)*x^6 + 2*a*b*c^(3/n)*x^3 + a^2)*(a^2*b*c^(3/n))^(2/3)*log(a*b*c^(3/n)*x^2 - (a^2*b*c^(3/n))^(2/3)*x + (a^2*b*c^(3/n))^(1/3)*a) + 10*(b^2*c^(6/n)*x^6 + 2*a*b*c^(3/n)*x^3 + a^2)*(a^2*b*c^(3/n))^(2/3)*log(a*b*c^(3/n)*x + (a^2*b*c^(3/n))^(2/3)))/(a^4*b^3*c^(9/n)*x^6 + 2*a^5*b^2*c^(6/n)*x^3 + a^6*b*c^(3/n)), 1/54*(15*a^2*b^2*c^(6/n)*x^4 + 24*a^3*b*c^(3/n)*x + 30*sqrt(1/3)*(a*b^3*c^(9/n)*x^6 + 2*a^2*b^2*c^(6/n)*x^3 + a^3*b*c^(3/n))*sqrt((a^2*b*c^(3/n))^(1/3)/(b*c^(3/n)))*arctan(sqrt(1/3)*(2*(a^2*b*c^(3/n))^(2/3)*x - (a^2*b*c^(3/n))^(1/3)*a)*sqrt((a^2*b*c^(3/n))^(1/3)/(b*c^(3/n)))/a^2) - 5*(b^2*c^(6/n)*x^6 + 2*a*b*c^(3/n)*x^3 + a^2)*(a^2*b*c^(3/n))^(2/3)*log(a*b*c^(3/n)*x^2 - (a^2*b*c^(3/n))^(2/3)*x + (a^2*b*c^(3/n))^(1/3)*a) + 10*(b^2*c^(6/n)*x^6 + 2*a*b*c^(3/n)*x^3 + a^2)*(a^2*b*c^(3/n))^(2/3)*log(a*b*c^(3/n)*x + (a^2*b*c^(3/n))^(2/3)))/(a^4*b^3*c^(9/n)*x^6 + 2*a^5*b^2*c^(6/n)*x^3 + a^6*b*c^(3/n))]","B",0
3046,0,0,0,0.891012," ","integrate((d*x)^m*(a+b*(c*x^q)^n)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(\left(c x^{q}\right)^{n} b + a\right)}^{p} \left(d x\right)^{m}, x\right)"," ",0,"integral(((c*x^q)^n*b + a)^p*(d*x)^m, x)","F",0
3047,0,0,0,0.860986," ","integrate(x^2*(a+b*(c*x^q)^n)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(\left(c x^{q}\right)^{n} b + a\right)}^{p} x^{2}, x\right)"," ",0,"integral(((c*x^q)^n*b + a)^p*x^2, x)","F",0
3048,0,0,0,0.802179," ","integrate(x*(a+b*(c*x^q)^n)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(\left(c x^{q}\right)^{n} b + a\right)}^{p} x, x\right)"," ",0,"integral(((c*x^q)^n*b + a)^p*x, x)","F",0
3049,0,0,0,1.018646," ","integrate((a+b*(c*x^q)^n)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(\left(c x^{q}\right)^{n} b + a\right)}^{p}, x\right)"," ",0,"integral(((c*x^q)^n*b + a)^p, x)","F",0
3050,0,0,0,0.801360," ","integrate((a+b*(c*x^q)^n)^p/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(\left(c x^{q}\right)^{n} b + a\right)}^{p}}{x}, x\right)"," ",0,"integral(((c*x^q)^n*b + a)^p/x, x)","F",0
3051,0,0,0,0.784349," ","integrate((a+b*(c*x^q)^n)^p/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(\left(c x^{q}\right)^{n} b + a\right)}^{p}}{x^{2}}, x\right)"," ",0,"integral(((c*x^q)^n*b + a)^p/x^2, x)","F",0
3052,-2,0,0,0.000000," ","integrate(x^m*(a+c/x+b*(d/x)^(1/2))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   alglogextint: unimplemented","F(-2)",0
3053,-1,0,0,0.000000," ","integrate(x^2*(a+c/x+b*(d/x)^(1/2))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3054,-1,0,0,0.000000," ","integrate(x*(a+c/x+b*(d/x)^(1/2))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3055,-1,0,0,0.000000," ","integrate((a+c/x+b*(d/x)^(1/2))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3056,-1,0,0,0.000000," ","integrate((a+c/x+b*(d/x)^(1/2))^(1/2)/x,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3057,-1,0,0,0.000000," ","integrate((a+c/x+b*(d/x)^(1/2))^(1/2)/x^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3058,-1,0,0,0.000000," ","integrate((a+c/x+b*(d/x)^(1/2))^(1/2)/x^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3059,-1,0,0,0.000000," ","integrate((a+c/x+b*(d/x)^(1/2))^(1/2)/x^4,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3060,-2,0,0,0.000000," ","integrate(x^m/(a+c/x+b*(d/x)^(1/2))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   alglogextint: unimplemented","F(-2)",0
3061,-1,0,0,0.000000," ","integrate(x^2/(a+c/x+b*(d/x)^(1/2))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3062,-1,0,0,0.000000," ","integrate(x/(a+c/x+b*(d/x)^(1/2))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3063,-1,0,0,0.000000," ","integrate(1/(a+c/x+b*(d/x)^(1/2))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3064,-1,0,0,0.000000," ","integrate(1/x/(a+c/x+b*(d/x)^(1/2))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3065,-1,0,0,0.000000," ","integrate(1/x^2/(a+c/x+b*(d/x)^(1/2))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3066,-1,0,0,0.000000," ","integrate(1/x^3/(a+c/x+b*(d/x)^(1/2))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3067,-1,0,0,0.000000," ","integrate(1/x^4/(a+c/x+b*(d/x)^(1/2))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3068,1,18,0,1.062827," ","integrate((1/x+(1/x)^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{4}{3} \, {\left(x + \sqrt{x}\right)} \sqrt{\frac{\sqrt{x} + 1}{x}}"," ",0,"4/3*(x + sqrt(x))*sqrt((sqrt(x) + 1)/x)","A",0
3069,1,94,0,4.940472," ","integrate((2+1/x+(1/x)^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{1}{4} \, {\left(4 \, x + \sqrt{x}\right)} \sqrt{\frac{2 \, x + \sqrt{x} + 1}{x}} + \frac{7}{64} \, \sqrt{2} \log\left(-2048 \, x^{2} - 64 \, {\left(32 \, x + 9\right)} \sqrt{x} - 8 \, {\left(3 \, \sqrt{2} {\left(32 \, x + 3\right)} \sqrt{x} + 4 \, \sqrt{2} {\left(32 \, x^{2} + 13 \, x\right)}\right)} \sqrt{\frac{2 \, x + \sqrt{x} + 1}{x}} - 1664 \, x - 113\right)"," ",0,"1/4*(4*x + sqrt(x))*sqrt((2*x + sqrt(x) + 1)/x) + 7/64*sqrt(2)*log(-2048*x^2 - 64*(32*x + 9)*sqrt(x) - 8*(3*sqrt(2)*(32*x + 3)*sqrt(x) + 4*sqrt(2)*(32*x^2 + 13*x))*sqrt((2*x + sqrt(x) + 1)/x) - 1664*x - 113)","B",0
3070,1,77,0,1.003432," ","integrate((c*x^n)^(1/n)*(a+b*(c*x^n)^(1/n))^p,x, algorithm=""fricas"")","\frac{{\left(a b c^{\left(\frac{1}{n}\right)} p x + {\left(b^{2} p + b^{2}\right)} c^{\frac{2}{n}} x^{2} - a^{2}\right)} {\left(b c^{\left(\frac{1}{n}\right)} x + a\right)}^{p}}{{\left(b^{2} p^{2} + 3 \, b^{2} p + 2 \, b^{2}\right)} c^{\left(\frac{1}{n}\right)}}"," ",0,"(a*b*c^(1/n)*p*x + (b^2*p + b^2)*c^(2/n)*x^2 - a^2)*(b*c^(1/n)*x + a)^p/((b^2*p^2 + 3*b^2*p + 2*b^2)*c^(1/n))","A",0
3071,1,60,0,0.718494," ","integrate((c*x^n)^(1/n)*(a+b*(c*x^n)^(1/n))^3,x, algorithm=""fricas"")","\frac{1}{5} \, b^{3} c^{\frac{4}{n}} x^{5} + \frac{3}{4} \, a b^{2} c^{\frac{3}{n}} x^{4} + a^{2} b c^{\frac{2}{n}} x^{3} + \frac{1}{2} \, a^{3} c^{\left(\frac{1}{n}\right)} x^{2}"," ",0,"1/5*b^3*c^(4/n)*x^5 + 3/4*a*b^2*c^(3/n)*x^4 + a^2*b*c^(2/n)*x^3 + 1/2*a^3*c^(1/n)*x^2","A",0
3072,1,43,0,0.911928," ","integrate((c*x^n)^(1/n)*(a+b*(c*x^n)^(1/n))^2,x, algorithm=""fricas"")","\frac{1}{4} \, b^{2} c^{\frac{3}{n}} x^{4} + \frac{2}{3} \, a b c^{\frac{2}{n}} x^{3} + \frac{1}{2} \, a^{2} c^{\left(\frac{1}{n}\right)} x^{2}"," ",0,"1/4*b^2*c^(3/n)*x^4 + 2/3*a*b*c^(2/n)*x^3 + 1/2*a^2*c^(1/n)*x^2","A",0
3073,1,25,0,1.000839," ","integrate((c*x^n)^(1/n)*(a+b*(c*x^n)^(1/n)),x, algorithm=""fricas"")","\frac{1}{3} \, b c^{\frac{2}{n}} x^{3} + \frac{1}{2} \, a c^{\left(\frac{1}{n}\right)} x^{2}"," ",0,"1/3*b*c^(2/n)*x^3 + 1/2*a*c^(1/n)*x^2","A",0
3074,1,34,0,0.722145," ","integrate((c*x^n)^(1/n)/(a+b*(c*x^n)^(1/n)),x, algorithm=""fricas"")","\frac{b c^{\left(\frac{1}{n}\right)} x - a \log\left(b c^{\left(\frac{1}{n}\right)} x + a\right)}{b^{2} c^{\left(\frac{1}{n}\right)}}"," ",0,"(b*c^(1/n)*x - a*log(b*c^(1/n)*x + a))/(b^2*c^(1/n))","A",0
3075,1,50,0,0.709848," ","integrate((c*x^n)^(1/n)/(a+b*(c*x^n)^(1/n))^2,x, algorithm=""fricas"")","\frac{{\left(b c^{\left(\frac{1}{n}\right)} x + a\right)} \log\left(b c^{\left(\frac{1}{n}\right)} x + a\right) + a}{b^{3} c^{\frac{2}{n}} x + a b^{2} c^{\left(\frac{1}{n}\right)}}"," ",0,"((b*c^(1/n)*x + a)*log(b*c^(1/n)*x + a) + a)/(b^3*c^(2/n)*x + a*b^2*c^(1/n))","A",0
3076,1,56,0,1.019268," ","integrate((c*x^n)^(1/n)/(a+b*(c*x^n)^(1/n))^3,x, algorithm=""fricas"")","-\frac{2 \, b c^{\left(\frac{1}{n}\right)} x + a}{2 \, {\left(b^{4} c^{\frac{3}{n}} x^{2} + 2 \, a b^{3} c^{\frac{2}{n}} x + a^{2} b^{2} c^{\left(\frac{1}{n}\right)}\right)}}"," ",0,"-1/2*(2*b*c^(1/n)*x + a)/(b^4*c^(3/n)*x^2 + 2*a*b^3*c^(2/n)*x + a^2*b^2*c^(1/n))","A",0
3077,1,74,0,0.859278," ","integrate((c*x^n)^(1/n)/(a+b*(c*x^n)^(1/n))^4,x, algorithm=""fricas"")","-\frac{3 \, b c^{\left(\frac{1}{n}\right)} x + a}{6 \, {\left(b^{5} c^{\frac{4}{n}} x^{3} + 3 \, a b^{4} c^{\frac{3}{n}} x^{2} + 3 \, a^{2} b^{3} c^{\frac{2}{n}} x + a^{3} b^{2} c^{\left(\frac{1}{n}\right)}\right)}}"," ",0,"-1/6*(3*b*c^(1/n)*x + a)/(b^5*c^(4/n)*x^3 + 3*a*b^4*c^(3/n)*x^2 + 3*a^2*b^3*c^(2/n)*x + a^3*b^2*c^(1/n))","A",0
3078,1,92,0,0.837149," ","integrate((c*x^n)^(1/n)/(a+b*(c*x^n)^(1/n))^5,x, algorithm=""fricas"")","-\frac{4 \, b c^{\left(\frac{1}{n}\right)} x + a}{12 \, {\left(b^{6} c^{\frac{5}{n}} x^{4} + 4 \, a b^{5} c^{\frac{4}{n}} x^{3} + 6 \, a^{2} b^{4} c^{\frac{3}{n}} x^{2} + 4 \, a^{3} b^{3} c^{\frac{2}{n}} x + a^{4} b^{2} c^{\left(\frac{1}{n}\right)}\right)}}"," ",0,"-1/12*(4*b*c^(1/n)*x + a)/(b^6*c^(5/n)*x^4 + 4*a*b^5*c^(4/n)*x^3 + 6*a^2*b^4*c^(3/n)*x^2 + 4*a^3*b^3*c^(2/n)*x + a^4*b^2*c^(1/n))","A",0
