1,1,22,0,0.0071705,"\int (b x)^p (c x)^m \, dx","Int[(b*x)^p*(c*x)^m,x]","\frac{(b x)^{p+1} (c x)^m}{b (m+p+1)}","\frac{(b x)^{p+1} (c x)^m}{b (m+p+1)}",1,"((b*x)^(1 + p)*(c*x)^m)/(b*(1 + m + p))","A",2,2,11,0.1818,1,"{20, 32}"
2,1,16,0,0.0015588,"\int x^3 \sqrt{b x^2} \, dx","Int[x^3*Sqrt[b*x^2],x]","\frac{1}{5} x^4 \sqrt{b x^2}","\frac{1}{5} x^4 \sqrt{b x^2}",1,"(x^4*Sqrt[b*x^2])/5","A",2,2,13,0.1538,1,"{15, 30}"
3,1,16,0,0.0017026,"\int x^2 \sqrt{b x^2} \, dx","Int[x^2*Sqrt[b*x^2],x]","\frac{1}{4} x^3 \sqrt{b x^2}","\frac{1}{4} x^3 \sqrt{b x^2}",1,"(x^3*Sqrt[b*x^2])/4","A",2,2,13,0.1538,1,"{15, 30}"
4,1,16,0,0.0016844,"\int x \sqrt{b x^2} \, dx","Int[x*Sqrt[b*x^2],x]","\frac{1}{3} x^2 \sqrt{b x^2}","\frac{1}{3} x^2 \sqrt{b x^2}",1,"(x^2*Sqrt[b*x^2])/3","A",2,2,11,0.1818,1,"{15, 30}"
5,1,14,0,0.0015243,"\int \sqrt{b x^2} \, dx","Int[Sqrt[b*x^2],x]","\frac{1}{2} x \sqrt{b x^2}","\frac{1}{2} x \sqrt{b x^2}",1,"(x*Sqrt[b*x^2])/2","A",2,2,9,0.2222,1,"{15, 30}"
6,1,9,0,0.0008505,"\int \frac{\sqrt{b x^2}}{x} \, dx","Int[Sqrt[b*x^2]/x,x]","\sqrt{b x^2}","\sqrt{b x^2}",1,"Sqrt[b*x^2]","A",2,2,13,0.1538,1,"{15, 8}"
7,1,15,0,0.0013557,"\int \frac{\sqrt{b x^2}}{x^2} \, dx","Int[Sqrt[b*x^2]/x^2,x]","\frac{\sqrt{b x^2} \log (x)}{x}","\frac{\sqrt{b x^2} \log (x)}{x}",1,"(Sqrt[b*x^2]*Log[x])/x","A",2,2,13,0.1538,1,"{15, 29}"
8,1,14,0,0.0015441,"\int \frac{\sqrt{b x^2}}{x^3} \, dx","Int[Sqrt[b*x^2]/x^3,x]","-\frac{\sqrt{b x^2}}{x^2}","-\frac{\sqrt{b x^2}}{x^2}",1,"-(Sqrt[b*x^2]/x^2)","A",2,2,13,0.1538,1,"{15, 30}"
9,1,16,0,0.0014777,"\int \frac{\sqrt{b x^2}}{x^4} \, dx","Int[Sqrt[b*x^2]/x^4,x]","-\frac{\sqrt{b x^2}}{2 x^3}","-\frac{\sqrt{b x^2}}{2 x^3}",1,"-Sqrt[b*x^2]/(2*x^3)","A",2,2,13,0.1538,1,"{15, 30}"
10,1,16,0,0.001575,"\int \frac{\sqrt{b x^2}}{x^5} \, dx","Int[Sqrt[b*x^2]/x^5,x]","-\frac{\sqrt{b x^2}}{3 x^4}","-\frac{\sqrt{b x^2}}{3 x^4}",1,"-Sqrt[b*x^2]/(3*x^4)","A",2,2,13,0.1538,1,"{15, 30}"
11,1,14,0,0.001058,"\int \left(x^2\right)^{3/2} \, dx","Int[(x^2)^(3/2),x]","\frac{1}{4} x^3 \sqrt{x^2}","\frac{1}{4} x^3 \sqrt{x^2}",1,"(x^3*Sqrt[x^2])/4","A",2,2,7,0.2857,1,"{15, 30}"
12,1,17,0,0.0016268,"\int x^2 \left(b x^2\right)^{3/2} \, dx","Int[x^2*(b*x^2)^(3/2),x]","\frac{1}{6} b x^5 \sqrt{b x^2}","\frac{1}{6} b x^5 \sqrt{b x^2}",1,"(b*x^5*Sqrt[b*x^2])/6","A",2,2,13,0.1538,1,"{15, 30}"
13,1,17,0,0.0015975,"\int x \left(b x^2\right)^{3/2} \, dx","Int[x*(b*x^2)^(3/2),x]","\frac{1}{5} b x^4 \sqrt{b x^2}","\frac{1}{5} b x^4 \sqrt{b x^2}",1,"(b*x^4*Sqrt[b*x^2])/5","A",2,2,11,0.1818,1,"{15, 30}"
14,1,17,0,0.0015696,"\int \left(b x^2\right)^{3/2} \, dx","Int[(b*x^2)^(3/2),x]","\frac{1}{4} b x^3 \sqrt{b x^2}","\frac{1}{4} b x^3 \sqrt{b x^2}",1,"(b*x^3*Sqrt[b*x^2])/4","A",2,2,9,0.2222,1,"{15, 30}"
15,1,17,0,0.0016634,"\int \frac{\left(b x^2\right)^{3/2}}{x} \, dx","Int[(b*x^2)^(3/2)/x,x]","\frac{1}{3} b x^2 \sqrt{b x^2}","\frac{1}{3} b x^2 \sqrt{b x^2}",1,"(b*x^2*Sqrt[b*x^2])/3","A",2,2,13,0.1538,1,"{15, 30}"
16,1,15,0,0.0015888,"\int \frac{\left(b x^2\right)^{3/2}}{x^2} \, dx","Int[(b*x^2)^(3/2)/x^2,x]","\frac{1}{2} b x \sqrt{b x^2}","\frac{1}{2} b x \sqrt{b x^2}",1,"(b*x*Sqrt[b*x^2])/2","A",2,2,13,0.1538,1,"{15, 30}"
17,1,11,0,0.0010735,"\int \frac{\left(b x^2\right)^{3/2}}{x^3} \, dx","Int[(b*x^2)^(3/2)/x^3,x]","b \sqrt{b x^2}","b \sqrt{b x^2}",1,"b*Sqrt[b*x^2]","A",2,2,13,0.1538,1,"{15, 8}"
18,1,16,0,0.0014149,"\int \frac{\left(b x^2\right)^{3/2}}{x^4} \, dx","Int[(b*x^2)^(3/2)/x^4,x]","\frac{b \sqrt{b x^2} \log (x)}{x}","\frac{b \sqrt{b x^2} \log (x)}{x}",1,"(b*Sqrt[b*x^2]*Log[x])/x","A",2,2,13,0.1538,1,"{15, 29}"
19,1,15,0,0.0016574,"\int \frac{\left(b x^2\right)^{3/2}}{x^5} \, dx","Int[(b*x^2)^(3/2)/x^5,x]","-\frac{b \sqrt{b x^2}}{x^2}","-\frac{b \sqrt{b x^2}}{x^2}",1,"-((b*Sqrt[b*x^2])/x^2)","A",2,2,13,0.1538,1,"{15, 30}"
20,1,17,0,0.001592,"\int \frac{\left(b x^2\right)^{3/2}}{x^6} \, dx","Int[(b*x^2)^(3/2)/x^6,x]","-\frac{b \sqrt{b x^2}}{2 x^3}","-\frac{b \sqrt{b x^2}}{2 x^3}",1,"-(b*Sqrt[b*x^2])/(2*x^3)","A",2,2,13,0.1538,1,"{15, 30}"
21,1,17,0,0.0016539,"\int \frac{\left(b x^2\right)^{3/2}}{x^7} \, dx","Int[(b*x^2)^(3/2)/x^7,x]","-\frac{b \sqrt{b x^2}}{3 x^4}","-\frac{b \sqrt{b x^2}}{3 x^4}",1,"-(b*Sqrt[b*x^2])/(3*x^4)","A",2,2,13,0.1538,1,"{15, 30}"
22,1,14,0,0.0010279,"\int \left(x^2\right)^{5/2} \, dx","Int[(x^2)^(5/2),x]","\frac{1}{6} x^5 \sqrt{x^2}","\frac{1}{6} x^5 \sqrt{x^2}",1,"(x^5*Sqrt[x^2])/6","A",2,2,7,0.2857,1,"{15, 30}"
23,1,19,0,0.0017408,"\int x \left(b x^2\right)^{5/2} \, dx","Int[x*(b*x^2)^(5/2),x]","\frac{1}{7} b^2 x^6 \sqrt{b x^2}","\frac{1}{7} b^2 x^6 \sqrt{b x^2}",1,"(b^2*x^6*Sqrt[b*x^2])/7","A",2,2,11,0.1818,1,"{15, 30}"
24,1,19,0,0.0017534,"\int \left(b x^2\right)^{5/2} \, dx","Int[(b*x^2)^(5/2),x]","\frac{1}{6} b^2 x^5 \sqrt{b x^2}","\frac{1}{6} b^2 x^5 \sqrt{b x^2}",1,"(b^2*x^5*Sqrt[b*x^2])/6","A",2,2,9,0.2222,1,"{15, 30}"
25,1,19,0,0.0018269,"\int \frac{\left(b x^2\right)^{5/2}}{x} \, dx","Int[(b*x^2)^(5/2)/x,x]","\frac{1}{5} b^2 x^4 \sqrt{b x^2}","\frac{1}{5} b^2 x^4 \sqrt{b x^2}",1,"(b^2*x^4*Sqrt[b*x^2])/5","A",2,2,13,0.1538,1,"{15, 30}"
26,1,19,0,0.0018087,"\int \frac{\left(b x^2\right)^{5/2}}{x^2} \, dx","Int[(b*x^2)^(5/2)/x^2,x]","\frac{1}{4} b^2 x^3 \sqrt{b x^2}","\frac{1}{4} b^2 x^3 \sqrt{b x^2}",1,"(b^2*x^3*Sqrt[b*x^2])/4","A",2,2,13,0.1538,1,"{15, 30}"
27,1,19,0,0.0018727,"\int \frac{\left(b x^2\right)^{5/2}}{x^3} \, dx","Int[(b*x^2)^(5/2)/x^3,x]","\frac{1}{3} b^2 x^2 \sqrt{b x^2}","\frac{1}{3} b^2 x^2 \sqrt{b x^2}",1,"(b^2*x^2*Sqrt[b*x^2])/3","A",2,2,13,0.1538,1,"{15, 30}"
28,1,17,0,0.0017405,"\int \frac{\left(b x^2\right)^{5/2}}{x^4} \, dx","Int[(b*x^2)^(5/2)/x^4,x]","\frac{1}{2} b^2 x \sqrt{b x^2}","\frac{1}{2} b^2 x \sqrt{b x^2}",1,"(b^2*x*Sqrt[b*x^2])/2","A",2,2,13,0.1538,1,"{15, 30}"
29,1,13,0,0.0012499,"\int \frac{\left(b x^2\right)^{5/2}}{x^5} \, dx","Int[(b*x^2)^(5/2)/x^5,x]","b^2 \sqrt{b x^2}","b^2 \sqrt{b x^2}",1,"b^2*Sqrt[b*x^2]","A",2,2,13,0.1538,1,"{15, 8}"
30,1,18,0,0.0016462,"\int \frac{\left(b x^2\right)^{5/2}}{x^6} \, dx","Int[(b*x^2)^(5/2)/x^6,x]","\frac{b^2 \sqrt{b x^2} \log (x)}{x}","\frac{b^2 \sqrt{b x^2} \log (x)}{x}",1,"(b^2*Sqrt[b*x^2]*Log[x])/x","A",2,2,13,0.1538,1,"{15, 29}"
31,1,17,0,0.0018603,"\int \frac{\left(b x^2\right)^{5/2}}{x^7} \, dx","Int[(b*x^2)^(5/2)/x^7,x]","-\frac{b^2 \sqrt{b x^2}}{x^2}","-\frac{b^2 \sqrt{b x^2}}{x^2}",1,"-((b^2*Sqrt[b*x^2])/x^2)","A",2,2,13,0.1538,1,"{15, 30}"
32,1,19,0,0.0018092,"\int \frac{\left(b x^2\right)^{5/2}}{x^8} \, dx","Int[(b*x^2)^(5/2)/x^8,x]","-\frac{b^2 \sqrt{b x^2}}{2 x^3}","-\frac{b^2 \sqrt{b x^2}}{2 x^3}",1,"-(b^2*Sqrt[b*x^2])/(2*x^3)","A",2,2,13,0.1538,1,"{15, 30}"
33,1,19,0,0.0018539,"\int \frac{\left(b x^2\right)^{5/2}}{x^9} \, dx","Int[(b*x^2)^(5/2)/x^9,x]","-\frac{b^2 \sqrt{b x^2}}{3 x^4}","-\frac{b^2 \sqrt{b x^2}}{3 x^4}",1,"-(b^2*Sqrt[b*x^2])/(3*x^4)","A",2,2,13,0.1538,1,"{15, 30}"
34,1,14,0,0.0010921,"\int \left(x^2\right)^{7/2} \, dx","Int[(x^2)^(7/2),x]","\frac{1}{8} x^7 \sqrt{x^2}","\frac{1}{8} x^7 \sqrt{x^2}",1,"(x^7*Sqrt[x^2])/8","A",2,2,7,0.2857,1,"{15, 30}"
35,1,16,0,0.0017573,"\int \frac{x^3}{\sqrt{b x^2}} \, dx","Int[x^3/Sqrt[b*x^2],x]","\frac{x^4}{3 \sqrt{b x^2}}","\frac{x^4}{3 \sqrt{b x^2}}",1,"x^4/(3*Sqrt[b*x^2])","A",2,2,13,0.1538,1,"{15, 30}"
36,1,13,0,0.0012854,"\int \frac{x}{\sqrt{b x^2}} \, dx","Int[x/Sqrt[b*x^2],x]","\frac{x^2}{\sqrt{b x^2}}","\frac{x^2}{\sqrt{b x^2}}",1,"x^2/Sqrt[b*x^2]","A",2,2,11,0.1818,1,"{15, 8}"
37,1,11,0,0.0013983,"\int \frac{1}{x \sqrt{b x^2}} \, dx","Int[1/(x*Sqrt[b*x^2]),x]","-\frac{1}{\sqrt{b x^2}}","-\frac{1}{\sqrt{b x^2}}",1,"-(1/Sqrt[b*x^2])","A",2,2,13,0.1538,1,"{15, 30}"
38,1,16,0,0.0014343,"\int \frac{1}{x^3 \sqrt{b x^2}} \, dx","Int[1/(x^3*Sqrt[b*x^2]),x]","-\frac{1}{3 x^2 \sqrt{b x^2}}","-\frac{1}{3 x^2 \sqrt{b x^2}}",1,"-1/(3*x^2*Sqrt[b*x^2])","A",2,2,13,0.1538,1,"{15, 30}"
39,1,16,0,0.0015693,"\int \frac{x^2}{\sqrt{b x^2}} \, dx","Int[x^2/Sqrt[b*x^2],x]","\frac{x^3}{2 \sqrt{b x^2}}","\frac{x^3}{2 \sqrt{b x^2}}",1,"x^3/(2*Sqrt[b*x^2])","A",2,2,13,0.1538,1,"{15, 30}"
40,1,13,0,0.0011591,"\int \frac{1}{\sqrt{b x^2}} \, dx","Int[1/Sqrt[b*x^2],x]","\frac{x \log (x)}{\sqrt{b x^2}}","\frac{x \log (x)}{\sqrt{b x^2}}",1,"(x*Log[x])/Sqrt[b*x^2]","A",2,2,9,0.2222,1,"{15, 29}"
41,1,16,0,0.0014971,"\int \frac{1}{x^2 \sqrt{b x^2}} \, dx","Int[1/(x^2*Sqrt[b*x^2]),x]","-\frac{1}{2 x \sqrt{b x^2}}","-\frac{1}{2 x \sqrt{b x^2}}",1,"-1/(2*x*Sqrt[b*x^2])","A",2,2,13,0.1538,1,"{15, 30}"
42,1,19,0,0.0017836,"\int \frac{x^5}{\left(b x^2\right)^{3/2}} \, dx","Int[x^5/(b*x^2)^(3/2),x]","\frac{x^4}{3 b \sqrt{b x^2}}","\frac{x^4}{3 b \sqrt{b x^2}}",1,"x^4/(3*b*Sqrt[b*x^2])","A",2,2,13,0.1538,1,"{15, 30}"
43,1,16,0,0.0014285,"\int \frac{x^3}{\left(b x^2\right)^{3/2}} \, dx","Int[x^3/(b*x^2)^(3/2),x]","\frac{x^2}{b \sqrt{b x^2}}","\frac{x^2}{b \sqrt{b x^2}}",1,"x^2/(b*Sqrt[b*x^2])","A",2,2,13,0.1538,1,"{15, 8}"
44,1,14,0,0.0016773,"\int \frac{x}{\left(b x^2\right)^{3/2}} \, dx","Int[x/(b*x^2)^(3/2),x]","-\frac{1}{b \sqrt{b x^2}}","-\frac{1}{b \sqrt{b x^2}}",1,"-(1/(b*Sqrt[b*x^2]))","A",2,2,11,0.1818,1,"{15, 30}"
45,1,19,0,0.0017707,"\int \frac{1}{x \left(b x^2\right)^{3/2}} \, dx","Int[1/(x*(b*x^2)^(3/2)),x]","-\frac{1}{3 b x^2 \sqrt{b x^2}}","-\frac{1}{3 b x^2 \sqrt{b x^2}}",1,"-1/(3*b*x^2*Sqrt[b*x^2])","A",2,2,13,0.1538,1,"{15, 30}"
46,1,19,0,0.0018358,"\int \frac{1}{x^3 \left(b x^2\right)^{3/2}} \, dx","Int[1/(x^3*(b*x^2)^(3/2)),x]","-\frac{1}{5 b x^4 \sqrt{b x^2}}","-\frac{1}{5 b x^4 \sqrt{b x^2}}",1,"-1/(5*b*x^4*Sqrt[b*x^2])","A",2,2,13,0.1538,1,"{15, 30}"
47,1,19,0,0.0017462,"\int \frac{x^6}{\left(b x^2\right)^{3/2}} \, dx","Int[x^6/(b*x^2)^(3/2),x]","\frac{x^5}{4 b \sqrt{b x^2}}","\frac{x^5}{4 b \sqrt{b x^2}}",1,"x^5/(4*b*Sqrt[b*x^2])","A",2,2,13,0.1538,1,"{15, 30}"
48,1,19,0,0.0017728,"\int \frac{x^4}{\left(b x^2\right)^{3/2}} \, dx","Int[x^4/(b*x^2)^(3/2),x]","\frac{x^3}{2 b \sqrt{b x^2}}","\frac{x^3}{2 b \sqrt{b x^2}}",1,"x^3/(2*b*Sqrt[b*x^2])","A",2,2,13,0.1538,1,"{15, 30}"
49,1,16,0,0.0015001,"\int \frac{x^2}{\left(b x^2\right)^{3/2}} \, dx","Int[x^2/(b*x^2)^(3/2),x]","\frac{x \log (x)}{b \sqrt{b x^2}}","\frac{x \log (x)}{b \sqrt{b x^2}}",1,"(x*Log[x])/(b*Sqrt[b*x^2])","A",2,2,13,0.1538,1,"{15, 29}"
50,1,19,0,0.0016886,"\int \frac{1}{\left(b x^2\right)^{3/2}} \, dx","Int[(b*x^2)^(-3/2),x]","-\frac{1}{2 b x \sqrt{b x^2}}","-\frac{1}{2 b x \sqrt{b x^2}}",1,"-1/(2*b*x*Sqrt[b*x^2])","A",2,2,9,0.2222,1,"{15, 30}"
51,1,19,0,0.0017734,"\int \frac{1}{x^2 \left(b x^2\right)^{3/2}} \, dx","Int[1/(x^2*(b*x^2)^(3/2)),x]","-\frac{1}{4 b x^3 \sqrt{b x^2}}","-\frac{1}{4 b x^3 \sqrt{b x^2}}",1,"-1/(4*b*x^3*Sqrt[b*x^2])","A",2,2,13,0.1538,1,"{15, 30}"
52,1,19,0,0.0021009,"\int \frac{x^7}{\left(b x^2\right)^{5/2}} \, dx","Int[x^7/(b*x^2)^(5/2),x]","\frac{x^4}{3 b^2 \sqrt{b x^2}}","\frac{x^4}{3 b^2 \sqrt{b x^2}}",1,"x^4/(3*b^2*Sqrt[b*x^2])","A",2,2,13,0.1538,1,"{15, 30}"
53,1,16,0,0.0013776,"\int \frac{x^5}{\left(b x^2\right)^{5/2}} \, dx","Int[x^5/(b*x^2)^(5/2),x]","\frac{x^2}{b^2 \sqrt{b x^2}}","\frac{x^2}{b^2 \sqrt{b x^2}}",1,"x^2/(b^2*Sqrt[b*x^2])","A",2,2,13,0.1538,1,"{15, 8}"
54,1,14,0,0.0016415,"\int \frac{x^3}{\left(b x^2\right)^{5/2}} \, dx","Int[x^3/(b*x^2)^(5/2),x]","-\frac{1}{b^2 \sqrt{b x^2}}","-\frac{1}{b^2 \sqrt{b x^2}}",1,"-(1/(b^2*Sqrt[b*x^2]))","A",2,2,13,0.1538,1,"{15, 30}"
55,1,19,0,0.0018456,"\int \frac{x}{\left(b x^2\right)^{5/2}} \, dx","Int[x/(b*x^2)^(5/2),x]","-\frac{1}{3 b^2 x^2 \sqrt{b x^2}}","-\frac{1}{3 b^2 x^2 \sqrt{b x^2}}",1,"-1/(3*b^2*x^2*Sqrt[b*x^2])","A",2,2,11,0.1818,1,"{15, 30}"
56,1,19,0,0.0017918,"\int \frac{1}{x \left(b x^2\right)^{5/2}} \, dx","Int[1/(x*(b*x^2)^(5/2)),x]","-\frac{1}{5 b^2 x^4 \sqrt{b x^2}}","-\frac{1}{5 b^2 x^4 \sqrt{b x^2}}",1,"-1/(5*b^2*x^4*Sqrt[b*x^2])","A",2,2,13,0.1538,1,"{15, 30}"
57,1,19,0,0.0018147,"\int \frac{x^6}{\left(b x^2\right)^{5/2}} \, dx","Int[x^6/(b*x^2)^(5/2),x]","\frac{x^3}{2 b^2 \sqrt{b x^2}}","\frac{x^3}{2 b^2 \sqrt{b x^2}}",1,"x^3/(2*b^2*Sqrt[b*x^2])","A",2,2,13,0.1538,1,"{15, 30}"
58,1,16,0,0.0015386,"\int \frac{x^4}{\left(b x^2\right)^{5/2}} \, dx","Int[x^4/(b*x^2)^(5/2),x]","\frac{x \log (x)}{b^2 \sqrt{b x^2}}","\frac{x \log (x)}{b^2 \sqrt{b x^2}}",1,"(x*Log[x])/(b^2*Sqrt[b*x^2])","A",2,2,13,0.1538,1,"{15, 29}"
59,1,19,0,0.0018013,"\int \frac{x^2}{\left(b x^2\right)^{5/2}} \, dx","Int[x^2/(b*x^2)^(5/2),x]","-\frac{1}{2 b^2 x \sqrt{b x^2}}","-\frac{1}{2 b^2 x \sqrt{b x^2}}",1,"-1/(2*b^2*x*Sqrt[b*x^2])","A",2,2,13,0.1538,1,"{15, 30}"
60,1,19,0,0.0017482,"\int \frac{1}{\left(b x^2\right)^{5/2}} \, dx","Int[(b*x^2)^(-5/2),x]","-\frac{1}{4 b^2 x^3 \sqrt{b x^2}}","-\frac{1}{4 b^2 x^3 \sqrt{b x^2}}",1,"-1/(4*b^2*x^3*Sqrt[b*x^2])","A",2,2,9,0.2222,1,"{15, 30}"
61,1,19,0,0.0018788,"\int \frac{1}{x^2 \left(b x^2\right)^{5/2}} \, dx","Int[1/(x^2*(b*x^2)^(5/2)),x]","-\frac{1}{6 b^2 x^5 \sqrt{b x^2}}","-\frac{1}{6 b^2 x^5 \sqrt{b x^2}}",1,"-1/(6*b^2*x^5*Sqrt[b*x^2])","A",2,2,13,0.1538,1,"{15, 30}"
62,1,29,0,0.0098853,"\int (c x)^m \left(b x^2\right)^{3/2} \, dx","Int[(c*x)^m*(b*x^2)^(3/2),x]","\frac{b \sqrt{b x^2} (c x)^{m+4}}{c^4 (m+4) x}","\frac{b \sqrt{b x^2} (c x)^{m+4}}{c^4 (m+4) x}",1,"(b*(c*x)^(4 + m)*Sqrt[b*x^2])/(c^4*(4 + m)*x)","A",3,3,15,0.2000,1,"{15, 16, 32}"
63,1,28,0,0.0090569,"\int (c x)^m \sqrt{b x^2} \, dx","Int[(c*x)^m*Sqrt[b*x^2],x]","\frac{\sqrt{b x^2} (c x)^{m+2}}{c^2 (m+2) x}","\frac{\sqrt{b x^2} (c x)^{m+2}}{c^2 (m+2) x}",1,"((c*x)^(2 + m)*Sqrt[b*x^2])/(c^2*(2 + m)*x)","A",3,3,15,0.2000,1,"{15, 16, 32}"
64,1,19,0,0.0049172,"\int \frac{(c x)^m}{\sqrt{b x^2}} \, dx","Int[(c*x)^m/Sqrt[b*x^2],x]","\frac{x (c x)^m}{m \sqrt{b x^2}}","\frac{x (c x)^m}{m \sqrt{b x^2}}",1,"(x*(c*x)^m)/(m*Sqrt[b*x^2])","A",3,3,15,0.2000,1,"{15, 16, 32}"
65,1,32,0,0.0119664,"\int \frac{(c x)^m}{\left(b x^2\right)^{3/2}} \, dx","Int[(c*x)^m/(b*x^2)^(3/2),x]","-\frac{c^2 x (c x)^{m-2}}{b (2-m) \sqrt{b x^2}}","-\frac{c^2 x (c x)^{m-2}}{b (2-m) \sqrt{b x^2}}",1,"-((c^2*x*(c*x)^(-2 + m))/(b*(2 - m)*Sqrt[b*x^2]))","A",3,3,15,0.2000,1,"{15, 16, 32}"
66,1,21,0,0.0055522,"\int x^m \left(b x^2\right)^p \, dx","Int[x^m*(b*x^2)^p,x]","\frac{x^{m+1} \left(b x^2\right)^p}{m+2 p+1}","\frac{x^{m+1} \left(b x^2\right)^p}{m+2 p+1}",1,"(x^(1 + m)*(b*x^2)^p)/(1 + m + 2*p)","A",2,2,11,0.1818,1,"{15, 30}"
67,1,22,0,0.0054969,"\int (c x)^m \left(b x^2\right)^p \, dx","Int[(c*x)^m*(b*x^2)^p,x]","\frac{x \left(b x^2\right)^p (c x)^m}{m+2 p+1}","\frac{x \left(b x^2\right)^p (c x)^m}{m+2 p+1}",1,"(x*(c*x)^m*(b*x^2)^p)/(1 + m + 2*p)","A",3,3,13,0.2308,1,"{15, 20, 30}"
68,1,13,0,0.0024992,"\int x^{-1-2 p} \left(x^2\right)^p \, dx","Int[x^(-1 - 2*p)*(x^2)^p,x]","x^{-2 p} \left(x^2\right)^p \log (x)","x^{-2 p} \left(x^2\right)^p \log (x)",1,"((x^2)^p*Log[x])/x^(2*p)","A",2,2,13,0.1538,1,"{15, 29}"
69,1,19,0,0.0050369,"\int x^3 \left(b x^2\right)^p \, dx","Int[x^3*(b*x^2)^p,x]","\frac{x^4 \left(b x^2\right)^p}{2 (p+2)}","\frac{x^4 \left(b x^2\right)^p}{2 (p+2)}",1,"(x^4*(b*x^2)^p)/(2*(2 + p))","A",2,2,11,0.1818,1,"{15, 30}"
70,1,18,0,0.0043131,"\int x^2 \left(b x^2\right)^p \, dx","Int[x^2*(b*x^2)^p,x]","\frac{x^3 \left(b x^2\right)^p}{2 p+3}","\frac{x^3 \left(b x^2\right)^p}{2 p+3}",1,"(x^3*(b*x^2)^p)/(3 + 2*p)","A",2,2,11,0.1818,1,"{15, 30}"
71,1,19,0,0.0046985,"\int x \left(b x^2\right)^p \, dx","Int[x*(b*x^2)^p,x]","\frac{x^2 \left(b x^2\right)^p}{2 (p+1)}","\frac{x^2 \left(b x^2\right)^p}{2 (p+1)}",1,"(x^2*(b*x^2)^p)/(2*(1 + p))","A",2,2,9,0.2222,1,"{15, 30}"
72,1,16,0,0.0043056,"\int \left(b x^2\right)^p \, dx","Int[(b*x^2)^p,x]","\frac{x \left(b x^2\right)^p}{2 p+1}","\frac{x \left(b x^2\right)^p}{2 p+1}",1,"(x*(b*x^2)^p)/(1 + 2*p)","A",2,2,7,0.2857,1,"{15, 30}"
73,1,14,0,0.0028232,"\int \frac{\left(b x^2\right)^p}{x} \, dx","Int[(b*x^2)^p/x,x]","\frac{\left(b x^2\right)^p}{2 p}","\frac{\left(b x^2\right)^p}{2 p}",1,"(b*x^2)^p/(2*p)","A",2,2,11,0.1818,1,"{15, 30}"
74,1,19,0,0.0059464,"\int \frac{\left(b x^2\right)^p}{x^2} \, dx","Int[(b*x^2)^p/x^2,x]","-\frac{\left(b x^2\right)^p}{(1-2 p) x}","-\frac{\left(b x^2\right)^p}{(1-2 p) x}",1,"-((b*x^2)^p/((1 - 2*p)*x))","A",2,2,11,0.1818,1,"{15, 30}"
75,1,21,0,0.0051819,"\int \frac{\left(b x^2\right)^p}{x^3} \, dx","Int[(b*x^2)^p/x^3,x]","-\frac{\left(b x^2\right)^p}{2 (1-p) x^2}","-\frac{\left(b x^2\right)^p}{2 (1-p) x^2}",1,"-(b*x^2)^p/(2*(1 - p)*x^2)","A",2,2,11,0.1818,1,"{15, 30}"
76,1,19,0,0.0059692,"\int \frac{\left(b x^2\right)^p}{x^4} \, dx","Int[(b*x^2)^p/x^4,x]","-\frac{\left(b x^2\right)^p}{(3-2 p) x^3}","-\frac{\left(b x^2\right)^p}{(3-2 p) x^3}",1,"-((b*x^2)^p/((3 - 2*p)*x^3))","A",2,2,11,0.1818,1,"{15, 30}"
77,1,14,0,0.0015145,"\int \sqrt{b x^3} \, dx","Int[Sqrt[b*x^3],x]","\frac{2}{5} x \sqrt{b x^3}","\frac{2}{5} x \sqrt{b x^3}",1,"(2*x*Sqrt[b*x^3])/5","A",2,2,9,0.2222,1,"{15, 30}"
78,1,14,0,0.0014066,"\int \sqrt{b x^2} \, dx","Int[Sqrt[b*x^2],x]","\frac{1}{2} x \sqrt{b x^2}","\frac{1}{2} x \sqrt{b x^2}",1,"(x*Sqrt[b*x^2])/2","A",2,2,9,0.2222,1,"{15, 30}"
79,1,14,0,0.0012822,"\int \sqrt{b x} \, dx","Int[Sqrt[b*x],x]","\frac{2 (b x)^{3/2}}{3 b}","\frac{2 (b x)^{3/2}}{3 b}",1,"(2*(b*x)^(3/2))/(3*b)","A",1,1,7,0.1429,1,"{32}"
80,1,12,0,0.001497,"\int \sqrt{\frac{b}{x}} \, dx","Int[Sqrt[b/x],x]","2 x \sqrt{\frac{b}{x}}","2 x \sqrt{\frac{b}{x}}",1,"2*Sqrt[b/x]*x","A",2,2,9,0.2222,1,"{15, 30}"
81,1,13,0,0.0025132,"\int \sqrt{\frac{b}{x^2}} \, dx","Int[Sqrt[b/x^2],x]","x \sqrt{\frac{b}{x^2}} \log (x)","x \sqrt{\frac{b}{x^2}} \log (x)",1,"Sqrt[b/x^2]*x*Log[x]","A",2,2,9,0.2222,1,"{15, 29}"
82,1,12,0,0.0016037,"\int \sqrt{\frac{b}{x^3}} \, dx","Int[Sqrt[b/x^3],x]","-2 x \sqrt{\frac{b}{x^3}}","-2 x \sqrt{\frac{b}{x^3}}",1,"-2*Sqrt[b/x^3]*x","A",2,2,9,0.2222,1,"{15, 30}"
83,1,17,0,0.0016906,"\int \left(b x^3\right)^{3/2} \, dx","Int[(b*x^3)^(3/2),x]","\frac{2}{11} b x^4 \sqrt{b x^3}","\frac{2}{11} b x^4 \sqrt{b x^3}",1,"(2*b*x^4*Sqrt[b*x^3])/11","A",2,2,9,0.2222,1,"{15, 30}"
84,1,17,0,0.0017307,"\int \left(b x^2\right)^{3/2} \, dx","Int[(b*x^2)^(3/2),x]","\frac{1}{4} b x^3 \sqrt{b x^2}","\frac{1}{4} b x^3 \sqrt{b x^2}",1,"(b*x^3*Sqrt[b*x^2])/4","A",2,2,9,0.2222,1,"{15, 30}"
85,1,14,0,0.0013268,"\int (b x)^{3/2} \, dx","Int[(b*x)^(3/2),x]","\frac{2 (b x)^{5/2}}{5 b}","\frac{2 (b x)^{5/2}}{5 b}",1,"(2*(b*x)^(5/2))/(5*b)","A",1,1,7,0.1429,1,"{32}"
86,1,12,0,0.0016709,"\int \left(\frac{b}{x}\right)^{3/2} \, dx","Int[(b/x)^(3/2),x]","-2 b \sqrt{\frac{b}{x}}","-2 b \sqrt{\frac{b}{x}}",1,"-2*b*Sqrt[b/x]","A",2,2,9,0.2222,1,"{15, 30}"
87,1,17,0,0.0017096,"\int \left(\frac{b}{x^2}\right)^{3/2} \, dx","Int[(b/x^2)^(3/2),x]","-\frac{b \sqrt{\frac{b}{x^2}}}{2 x}","-\frac{b \sqrt{\frac{b}{x^2}}}{2 x}",1,"-(b*Sqrt[b/x^2])/(2*x)","A",2,2,9,0.2222,1,"{15, 30}"
88,1,17,0,0.0017197,"\int \left(\frac{b}{x^3}\right)^{3/2} \, dx","Int[(b/x^3)^(3/2),x]","-\frac{2 b \sqrt{\frac{b}{x^3}}}{7 x^2}","-\frac{2 b \sqrt{\frac{b}{x^3}}}{7 x^2}",1,"(-2*b*Sqrt[b/x^3])/(7*x^2)","A",2,2,9,0.2222,1,"{15, 30}"
89,1,12,0,0.0014569,"\int \frac{1}{\sqrt{b x^3}} \, dx","Int[1/Sqrt[b*x^3],x]","-\frac{2 x}{\sqrt{b x^3}}","-\frac{2 x}{\sqrt{b x^3}}",1,"(-2*x)/Sqrt[b*x^3]","A",2,2,9,0.2222,1,"{15, 30}"
90,1,13,0,0.0012351,"\int \frac{1}{\sqrt{b x^2}} \, dx","Int[1/Sqrt[b*x^2],x]","\frac{x \log (x)}{\sqrt{b x^2}}","\frac{x \log (x)}{\sqrt{b x^2}}",1,"(x*Log[x])/Sqrt[b*x^2]","A",2,2,9,0.2222,1,"{15, 29}"
91,1,12,0,0.0011501,"\int \frac{1}{\sqrt{b x}} \, dx","Int[1/Sqrt[b*x],x]","\frac{2 \sqrt{b x}}{b}","\frac{2 \sqrt{b x}}{b}",1,"(2*Sqrt[b*x])/b","A",1,1,7,0.1429,1,"{32}"
92,1,14,0,0.0015289,"\int \frac{1}{\sqrt{\frac{b}{x}}} \, dx","Int[1/Sqrt[b/x],x]","\frac{2 x}{3 \sqrt{\frac{b}{x}}}","\frac{2 x}{3 \sqrt{\frac{b}{x}}}",1,"(2*x)/(3*Sqrt[b/x])","A",2,2,9,0.2222,1,"{15, 30}"
93,1,14,0,0.0014358,"\int \frac{1}{\sqrt{\frac{b}{x^2}}} \, dx","Int[1/Sqrt[b/x^2],x]","\frac{x}{2 \sqrt{\frac{b}{x^2}}}","\frac{x}{2 \sqrt{\frac{b}{x^2}}}",1,"x/(2*Sqrt[b/x^2])","A",2,2,9,0.2222,1,"{15, 30}"
94,1,14,0,0.0014239,"\int \frac{1}{\sqrt{\frac{b}{x^3}}} \, dx","Int[1/Sqrt[b/x^3],x]","\frac{2 x}{5 \sqrt{\frac{b}{x^3}}}","\frac{2 x}{5 \sqrt{\frac{b}{x^3}}}",1,"(2*x)/(5*Sqrt[b/x^3])","A",2,2,9,0.2222,1,"{15, 30}"
95,1,19,0,0.0017849,"\int \frac{1}{\left(b x^3\right)^{3/2}} \, dx","Int[(b*x^3)^(-3/2),x]","-\frac{2}{7 b x^2 \sqrt{b x^3}}","-\frac{2}{7 b x^2 \sqrt{b x^3}}",1,"-2/(7*b*x^2*Sqrt[b*x^3])","A",2,2,9,0.2222,1,"{15, 30}"
96,1,19,0,0.00183,"\int \frac{1}{\left(b x^2\right)^{3/2}} \, dx","Int[(b*x^2)^(-3/2),x]","-\frac{1}{2 b x \sqrt{b x^2}}","-\frac{1}{2 b x \sqrt{b x^2}}",1,"-1/(2*b*x*Sqrt[b*x^2])","A",2,2,9,0.2222,1,"{15, 30}"
97,1,12,0,0.0012317,"\int \frac{1}{(b x)^{3/2}} \, dx","Int[(b*x)^(-3/2),x]","-\frac{2}{b \sqrt{b x}}","-\frac{2}{b \sqrt{b x}}",1,"-2/(b*Sqrt[b*x])","A",1,1,7,0.1429,1,"{32}"
98,1,19,0,0.0020271,"\int \frac{1}{\left(\frac{b}{x}\right)^{3/2}} \, dx","Int[(b/x)^(-3/2),x]","\frac{2 x^2}{5 b \sqrt{\frac{b}{x}}}","\frac{2 x^2}{5 b \sqrt{\frac{b}{x}}}",1,"(2*x^2)/(5*b*Sqrt[b/x])","A",2,2,9,0.2222,1,"{15, 30}"
99,1,19,0,0.0020934,"\int \frac{1}{\left(\frac{b}{x^2}\right)^{3/2}} \, dx","Int[(b/x^2)^(-3/2),x]","\frac{x^3}{4 b \sqrt{\frac{b}{x^2}}}","\frac{x^3}{4 b \sqrt{\frac{b}{x^2}}}",1,"x^3/(4*b*Sqrt[b/x^2])","A",2,2,9,0.2222,1,"{15, 30}"
100,1,19,0,0.0020722,"\int \frac{1}{\left(\frac{b}{x^3}\right)^{3/2}} \, dx","Int[(b/x^3)^(-3/2),x]","\frac{2 x^4}{11 b \sqrt{\frac{b}{x^3}}}","\frac{2 x^4}{11 b \sqrt{\frac{b}{x^3}}}",1,"(2*x^4)/(11*b*Sqrt[b/x^3])","A",2,2,9,0.2222,1,"{15, 30}"
101,1,17,0,0.0047795,"\int \sqrt[3]{b x^n} \, dx","Int[(b*x^n)^(1/3),x]","\frac{3 x \sqrt[3]{b x^n}}{n+3}","\frac{3 x \sqrt[3]{b x^n}}{n+3}",1,"(3*x*(b*x^n)^(1/3))/(3 + n)","A",2,2,9,0.2222,1,"{15, 30}"
102,1,14,0,0.0013163,"\int \sqrt[3]{b x^3} \, dx","Int[(b*x^3)^(1/3),x]","\frac{1}{2} x \sqrt[3]{b x^3}","\frac{1}{2} x \sqrt[3]{b x^3}",1,"(x*(b*x^3)^(1/3))/2","A",2,2,9,0.2222,1,"{15, 30}"
103,1,14,0,0.0015132,"\int \sqrt[3]{b x^2} \, dx","Int[(b*x^2)^(1/3),x]","\frac{3}{5} x \sqrt[3]{b x^2}","\frac{3}{5} x \sqrt[3]{b x^2}",1,"(3*x*(b*x^2)^(1/3))/5","A",2,2,9,0.2222,1,"{15, 30}"
104,1,14,0,0.0012486,"\int \sqrt[3]{b x} \, dx","Int[(b*x)^(1/3),x]","\frac{3 (b x)^{4/3}}{4 b}","\frac{3 (b x)^{4/3}}{4 b}",1,"(3*(b*x)^(4/3))/(4*b)","A",1,1,7,0.1429,1,"{32}"
105,1,14,0,0.0016445,"\int \sqrt[3]{\frac{b}{x}} \, dx","Int[(b/x)^(1/3),x]","\frac{3}{2} x \sqrt[3]{\frac{b}{x}}","\frac{3}{2} x \sqrt[3]{\frac{b}{x}}",1,"(3*(b/x)^(1/3)*x)/2","A",2,2,9,0.2222,1,"{15, 30}"
106,1,12,0,0.0015893,"\int \sqrt[3]{\frac{b}{x^2}} \, dx","Int[(b/x^2)^(1/3),x]","3 x \sqrt[3]{\frac{b}{x^2}}","3 x \sqrt[3]{\frac{b}{x^2}}",1,"3*(b/x^2)^(1/3)*x","A",2,2,9,0.2222,1,"{15, 30}"
107,1,13,0,0.002619,"\int \sqrt[3]{\frac{b}{x^3}} \, dx","Int[(b/x^3)^(1/3),x]","x \sqrt[3]{\frac{b}{x^3}} \log (x)","x \sqrt[3]{\frac{b}{x^3}} \log (x)",1,"(b/x^3)^(1/3)*x*Log[x]","A",2,2,9,0.2222,1,"{15, 29}"
108,1,12,0,0.0016192,"\int \sqrt[3]{\frac{b}{x^4}} \, dx","Int[(b/x^4)^(1/3),x]","-3 x \sqrt[3]{\frac{b}{x^4}}","-3 x \sqrt[3]{\frac{b}{x^4}}",1,"-3*(b/x^4)^(1/3)*x","A",2,2,9,0.2222,1,"{15, 30}"
109,1,19,0,0.0050974,"\int \left(b x^n\right)^{2/3} \, dx","Int[(b*x^n)^(2/3),x]","\frac{3 x \left(b x^n\right)^{2/3}}{2 n+3}","\frac{3 x \left(b x^n\right)^{2/3}}{2 n+3}",1,"(3*x*(b*x^n)^(2/3))/(3 + 2*n)","A",2,2,9,0.2222,1,"{15, 30}"
110,1,14,0,0.0014176,"\int \left(b x^2\right)^{2/3} \, dx","Int[(b*x^2)^(2/3),x]","\frac{3}{7} x \left(b x^2\right)^{2/3}","\frac{3}{7} x \left(b x^2\right)^{2/3}",1,"(3*x*(b*x^2)^(2/3))/7","A",2,2,9,0.2222,1,"{15, 30}"
111,1,14,0,0.0011246,"\int (b x)^{2/3} \, dx","Int[(b*x)^(2/3),x]","\frac{3 (b x)^{5/3}}{5 b}","\frac{3 (b x)^{5/3}}{5 b}",1,"(3*(b*x)^(5/3))/(5*b)","A",1,1,7,0.1429,1,"{32}"
112,1,12,0,0.0014171,"\int \left(\frac{b}{x}\right)^{2/3} \, dx","Int[(b/x)^(2/3),x]","3 x \left(\frac{b}{x}\right)^{2/3}","3 x \left(\frac{b}{x}\right)^{2/3}",1,"3*(b/x)^(2/3)*x","A",2,2,9,0.2222,1,"{15, 30}"
113,1,12,0,0.0014199,"\int \left(\frac{b}{x^2}\right)^{2/3} \, dx","Int[(b/x^2)^(2/3),x]","-3 x \left(\frac{b}{x^2}\right)^{2/3}","-3 x \left(\frac{b}{x^2}\right)^{2/3}",1,"-3*(b/x^2)^(2/3)*x","A",2,2,9,0.2222,1,"{15, 30}"
114,1,12,0,0.0014428,"\int \left(\frac{b}{x^3}\right)^{2/3} \, dx","Int[(b/x^3)^(2/3),x]","x \left(-\left(\frac{b}{x^3}\right)^{2/3}\right)","x \left(-\left(\frac{b}{x^3}\right)^{2/3}\right)",1,"-((b/x^3)^(2/3)*x)","A",2,2,9,0.2222,1,"{15, 30}"
115,1,14,0,0.0015081,"\int \left(\frac{b}{x^4}\right)^{2/3} \, dx","Int[(b/x^4)^(2/3),x]","-\frac{3}{5} x \left(\frac{b}{x^4}\right)^{2/3}","-\frac{3}{5} x \left(\frac{b}{x^4}\right)^{2/3}",1,"(-3*(b/x^4)^(2/3)*x)/5","A",2,2,9,0.2222,1,"{15, 30}"
116,1,19,0,0.0055366,"\int \frac{1}{\sqrt[3]{b x^n}} \, dx","Int[(b*x^n)^(-1/3),x]","\frac{3 x}{(3-n) \sqrt[3]{b x^n}}","\frac{3 x}{(3-n) \sqrt[3]{b x^n}}",1,"(3*x)/((3 - n)*(b*x^n)^(1/3))","A",2,2,9,0.2222,1,"{15, 30}"
117,1,12,0,0.0014454,"\int \frac{1}{\sqrt[3]{b x^4}} \, dx","Int[(b*x^4)^(-1/3),x]","-\frac{3 x}{\sqrt[3]{b x^4}}","-\frac{3 x}{\sqrt[3]{b x^4}}",1,"(-3*x)/(b*x^4)^(1/3)","A",2,2,9,0.2222,1,"{15, 30}"
118,1,13,0,0.0013001,"\int \frac{1}{\sqrt[3]{b x^3}} \, dx","Int[(b*x^3)^(-1/3),x]","\frac{x \log (x)}{\sqrt[3]{b x^3}}","\frac{x \log (x)}{\sqrt[3]{b x^3}}",1,"(x*Log[x])/(b*x^3)^(1/3)","A",2,2,9,0.2222,1,"{15, 29}"
119,1,12,0,0.0013559,"\int \frac{1}{\sqrt[3]{b x^2}} \, dx","Int[(b*x^2)^(-1/3),x]","\frac{3 x}{\sqrt[3]{b x^2}}","\frac{3 x}{\sqrt[3]{b x^2}}",1,"(3*x)/(b*x^2)^(1/3)","A",2,2,9,0.2222,1,"{15, 30}"
120,1,14,0,0.0013512,"\int \frac{1}{\sqrt[3]{b x}} \, dx","Int[(b*x)^(-1/3),x]","\frac{3 (b x)^{2/3}}{2 b}","\frac{3 (b x)^{2/3}}{2 b}",1,"(3*(b*x)^(2/3))/(2*b)","A",1,1,7,0.1429,1,"{32}"
121,1,14,0,0.0015995,"\int \frac{1}{\sqrt[3]{\frac{b}{x}}} \, dx","Int[(b/x)^(-1/3),x]","\frac{3 x}{4 \sqrt[3]{\frac{b}{x}}}","\frac{3 x}{4 \sqrt[3]{\frac{b}{x}}}",1,"(3*x)/(4*(b/x)^(1/3))","A",2,2,9,0.2222,1,"{15, 30}"
122,1,14,0,0.0014599,"\int \frac{1}{\sqrt[3]{\frac{b}{x^2}}} \, dx","Int[(b/x^2)^(-1/3),x]","\frac{3 x}{5 \sqrt[3]{\frac{b}{x^2}}}","\frac{3 x}{5 \sqrt[3]{\frac{b}{x^2}}}",1,"(3*x)/(5*(b/x^2)^(1/3))","A",2,2,9,0.2222,1,"{15, 30}"
123,1,14,0,0.0013602,"\int \frac{1}{\sqrt[3]{\frac{b}{x^3}}} \, dx","Int[(b/x^3)^(-1/3),x]","\frac{x}{2 \sqrt[3]{\frac{b}{x^3}}}","\frac{x}{2 \sqrt[3]{\frac{b}{x^3}}}",1,"x/(2*(b/x^3)^(1/3))","A",2,2,9,0.2222,1,"{15, 30}"
124,1,19,0,0.0054536,"\int \frac{1}{\left(b x^n\right)^{2/3}} \, dx","Int[(b*x^n)^(-2/3),x]","\frac{3 x}{(3-2 n) \left(b x^n\right)^{2/3}}","\frac{3 x}{(3-2 n) \left(b x^n\right)^{2/3}}",1,"(3*x)/((3 - 2*n)*(b*x^n)^(2/3))","A",2,2,9,0.2222,1,"{15, 30}"
125,1,12,0,0.0013575,"\int \frac{1}{\left(b x^3\right)^{2/3}} \, dx","Int[(b*x^3)^(-2/3),x]","-\frac{x}{\left(b x^3\right)^{2/3}}","-\frac{x}{\left(b x^3\right)^{2/3}}",1,"-(x/(b*x^3)^(2/3))","A",2,2,9,0.2222,1,"{15, 30}"
126,1,12,0,0.0013542,"\int \frac{1}{\left(b x^2\right)^{2/3}} \, dx","Int[(b*x^2)^(-2/3),x]","-\frac{3 x}{\left(b x^2\right)^{2/3}}","-\frac{3 x}{\left(b x^2\right)^{2/3}}",1,"(-3*x)/(b*x^2)^(2/3)","A",2,2,9,0.2222,1,"{15, 30}"
127,1,12,0,0.0013403,"\int \frac{1}{(b x)^{2/3}} \, dx","Int[(b*x)^(-2/3),x]","\frac{3 \sqrt[3]{b x}}{b}","\frac{3 \sqrt[3]{b x}}{b}",1,"(3*(b*x)^(1/3))/b","A",1,1,7,0.1429,1,"{32}"
128,1,14,0,0.001393,"\int \frac{1}{\left(\frac{b}{x}\right)^{2/3}} \, dx","Int[(b/x)^(-2/3),x]","\frac{3 x}{5 \left(\frac{b}{x}\right)^{2/3}}","\frac{3 x}{5 \left(\frac{b}{x}\right)^{2/3}}",1,"(3*x)/(5*(b/x)^(2/3))","A",2,2,9,0.2222,1,"{15, 30}"
129,1,14,0,0.0013713,"\int \frac{1}{\left(\frac{b}{x^2}\right)^{2/3}} \, dx","Int[(b/x^2)^(-2/3),x]","\frac{3 x}{7 \left(\frac{b}{x^2}\right)^{2/3}}","\frac{3 x}{7 \left(\frac{b}{x^2}\right)^{2/3}}",1,"(3*x)/(7*(b/x^2)^(2/3))","A",2,2,9,0.2222,1,"{15, 30}"
130,1,14,0,0.001497,"\int \frac{1}{\left(\frac{b}{x^3}\right)^{2/3}} \, dx","Int[(b/x^3)^(-2/3),x]","\frac{x}{3 \left(\frac{b}{x^3}\right)^{2/3}}","\frac{x}{3 \left(\frac{b}{x^3}\right)^{2/3}}",1,"x/(3*(b/x^3)^(2/3))","A",2,2,9,0.2222,1,"{15, 30}"
131,1,19,0,0.0050222,"\int x^2 \sqrt{b x^n} \, dx","Int[x^2*Sqrt[b*x^n],x]","\frac{2 x^3 \sqrt{b x^n}}{n+6}","\frac{2 x^3 \sqrt{b x^n}}{n+6}",1,"(2*x^3*Sqrt[b*x^n])/(6 + n)","A",2,2,13,0.1538,1,"{15, 30}"
132,1,19,0,0.0050968,"\int x \sqrt{b x^n} \, dx","Int[x*Sqrt[b*x^n],x]","\frac{2 x^2 \sqrt{b x^n}}{n+4}","\frac{2 x^2 \sqrt{b x^n}}{n+4}",1,"(2*x^2*Sqrt[b*x^n])/(4 + n)","A",2,2,11,0.1818,1,"{15, 30}"
133,1,17,0,0.004238,"\int \sqrt{b x^n} \, dx","Int[Sqrt[b*x^n],x]","\frac{2 x \sqrt{b x^n}}{n+2}","\frac{2 x \sqrt{b x^n}}{n+2}",1,"(2*x*Sqrt[b*x^n])/(2 + n)","A",2,2,9,0.2222,1,"{15, 30}"
134,1,14,0,0.0032852,"\int \frac{\sqrt{b x^n}}{x} \, dx","Int[Sqrt[b*x^n]/x,x]","\frac{2 \sqrt{b x^n}}{n}","\frac{2 \sqrt{b x^n}}{n}",1,"(2*Sqrt[b*x^n])/n","A",2,2,13,0.1538,1,"{15, 30}"
135,1,21,0,0.0052112,"\int \frac{\sqrt{b x^n}}{x^2} \, dx","Int[Sqrt[b*x^n]/x^2,x]","-\frac{2 \sqrt{b x^n}}{(2-n) x}","-\frac{2 \sqrt{b x^n}}{(2-n) x}",1,"(-2*Sqrt[b*x^n])/((2 - n)*x)","A",2,2,13,0.1538,1,"{15, 30}"
136,1,21,0,0.0053926,"\int \frac{\sqrt{b x^n}}{x^3} \, dx","Int[Sqrt[b*x^n]/x^3,x]","-\frac{2 \sqrt{b x^n}}{(4-n) x^2}","-\frac{2 \sqrt{b x^n}}{(4-n) x^2}",1,"(-2*Sqrt[b*x^n])/((4 - n)*x^2)","A",2,2,13,0.1538,1,"{15, 30}"
137,1,24,0,0.0061238,"\int x \left(b x^n\right)^{3/2} \, dx","Int[x*(b*x^n)^(3/2),x]","\frac{2 b x^{n+2} \sqrt{b x^n}}{3 n+4}","\frac{2 b x^{n+2} \sqrt{b x^n}}{3 n+4}",1,"(2*b*x^(2 + n)*Sqrt[b*x^n])/(4 + 3*n)","A",2,2,11,0.1818,1,"{15, 30}"
138,1,24,0,0.0054126,"\int \left(b x^n\right)^{3/2} \, dx","Int[(b*x^n)^(3/2),x]","\frac{2 b x^{n+1} \sqrt{b x^n}}{3 n+2}","\frac{2 b x^{n+1} \sqrt{b x^n}}{3 n+2}",1,"(2*b*x^(1 + n)*Sqrt[b*x^n])/(2 + 3*n)","A",2,2,9,0.2222,1,"{15, 30}"
139,1,20,0,0.0034291,"\int \frac{\left(b x^n\right)^{3/2}}{x} \, dx","Int[(b*x^n)^(3/2)/x,x]","\frac{2 b x^n \sqrt{b x^n}}{3 n}","\frac{2 b x^n \sqrt{b x^n}}{3 n}",1,"(2*b*x^n*Sqrt[b*x^n])/(3*n)","A",2,2,13,0.1538,1,"{15, 30}"
140,1,24,0,0.0068027,"\int \frac{\left(b x^n\right)^{3/2}}{x^2} \, dx","Int[(b*x^n)^(3/2)/x^2,x]","-\frac{2 b x^{n-1} \sqrt{b x^n}}{2-3 n}","-\frac{2 b x^{n-1} \sqrt{b x^n}}{2-3 n}",1,"(-2*b*x^(-1 + n)*Sqrt[b*x^n])/(2 - 3*n)","A",2,2,13,0.1538,1,"{15, 30}"
141,1,24,0,0.0067825,"\int \frac{\left(b x^n\right)^{3/2}}{x^3} \, dx","Int[(b*x^n)^(3/2)/x^3,x]","-\frac{2 b x^{n-2} \sqrt{b x^n}}{4-3 n}","-\frac{2 b x^{n-2} \sqrt{b x^n}}{4-3 n}",1,"(-2*b*x^(-2 + n)*Sqrt[b*x^n])/(4 - 3*n)","A",2,2,13,0.1538,1,"{15, 30}"
142,1,26,0,0.0054398,"\int \frac{\left(b x^n\right)^{3/2}}{x^4} \, dx","Int[(b*x^n)^(3/2)/x^4,x]","-\frac{2 b x^{n-3} \sqrt{b x^n}}{3 (2-n)}","-\frac{2 b x^{n-3} \sqrt{b x^n}}{3 (2-n)}",1,"(-2*b*x^(-3 + n)*Sqrt[b*x^n])/(3*(2 - n))","A",2,2,13,0.1538,1,"{15, 30}"
143,1,21,0,0.005397,"\int \frac{x^2}{\sqrt{b x^n}} \, dx","Int[x^2/Sqrt[b*x^n],x]","\frac{2 x^3}{(6-n) \sqrt{b x^n}}","\frac{2 x^3}{(6-n) \sqrt{b x^n}}",1,"(2*x^3)/((6 - n)*Sqrt[b*x^n])","A",2,2,13,0.1538,1,"{15, 30}"
144,1,21,0,0.0040158,"\int \frac{x}{\sqrt{b x^n}} \, dx","Int[x/Sqrt[b*x^n],x]","\frac{2 x^2}{(4-n) \sqrt{b x^n}}","\frac{2 x^2}{(4-n) \sqrt{b x^n}}",1,"(2*x^2)/((4 - n)*Sqrt[b*x^n])","A",2,2,11,0.1818,1,"{15, 30}"
145,1,19,0,0.0039118,"\int \frac{1}{\sqrt{b x^n}} \, dx","Int[1/Sqrt[b*x^n],x]","\frac{2 x}{(2-n) \sqrt{b x^n}}","\frac{2 x}{(2-n) \sqrt{b x^n}}",1,"(2*x)/((2 - n)*Sqrt[b*x^n])","A",2,2,9,0.2222,1,"{15, 30}"
146,1,14,0,0.0029323,"\int \frac{1}{x \sqrt{b x^n}} \, dx","Int[1/(x*Sqrt[b*x^n]),x]","-\frac{2}{n \sqrt{b x^n}}","-\frac{2}{n \sqrt{b x^n}}",1,"-2/(n*Sqrt[b*x^n])","A",2,2,13,0.1538,1,"{15, 30}"
147,1,19,0,0.0038447,"\int \frac{1}{x^2 \sqrt{b x^n}} \, dx","Int[1/(x^2*Sqrt[b*x^n]),x]","-\frac{2}{(n+2) x \sqrt{b x^n}}","-\frac{2}{(n+2) x \sqrt{b x^n}}",1,"-2/((2 + n)*x*Sqrt[b*x^n])","A",2,2,13,0.1538,1,"{15, 30}"
148,1,19,0,0.0038454,"\int \frac{1}{x^3 \sqrt{b x^n}} \, dx","Int[1/(x^3*Sqrt[b*x^n]),x]","-\frac{2}{(n+4) x^2 \sqrt{b x^n}}","-\frac{2}{(n+4) x^2 \sqrt{b x^n}}",1,"-2/((4 + n)*x^2*Sqrt[b*x^n])","A",2,2,13,0.1538,1,"{15, 30}"
149,1,30,0,0.0078502,"\int \frac{x^2}{\left(b x^n\right)^{3/2}} \, dx","Int[x^2/(b*x^n)^(3/2),x]","\frac{2 x^{3-n}}{3 b (2-n) \sqrt{b x^n}}","\frac{2 x^{3-n}}{3 b (2-n) \sqrt{b x^n}}",1,"(2*x^(3 - n))/(3*b*(2 - n)*Sqrt[b*x^n])","A",2,2,13,0.1538,1,"{15, 30}"
150,1,28,0,0.007607,"\int \frac{x}{\left(b x^n\right)^{3/2}} \, dx","Int[x/(b*x^n)^(3/2),x]","\frac{2 x^{2-n}}{b (4-3 n) \sqrt{b x^n}}","\frac{2 x^{2-n}}{b (4-3 n) \sqrt{b x^n}}",1,"(2*x^(2 - n))/(b*(4 - 3*n)*Sqrt[b*x^n])","A",2,2,11,0.1818,1,"{15, 30}"
151,1,28,0,0.0063945,"\int \frac{1}{\left(b x^n\right)^{3/2}} \, dx","Int[(b*x^n)^(-3/2),x]","\frac{2 x^{1-n}}{b (2-3 n) \sqrt{b x^n}}","\frac{2 x^{1-n}}{b (2-3 n) \sqrt{b x^n}}",1,"(2*x^(1 - n))/(b*(2 - 3*n)*Sqrt[b*x^n])","A",2,2,9,0.2222,1,"{15, 30}"
152,1,24,0,0.003785,"\int \frac{1}{x \left(b x^n\right)^{3/2}} \, dx","Int[1/(x*(b*x^n)^(3/2)),x]","-\frac{2 x^{-n}}{3 b n \sqrt{b x^n}}","-\frac{2 x^{-n}}{3 b n \sqrt{b x^n}}",1,"-2/(3*b*n*x^n*Sqrt[b*x^n])","A",2,2,13,0.1538,1,"{15, 30}"
153,1,28,0,0.0066267,"\int \frac{1}{x^2 \left(b x^n\right)^{3/2}} \, dx","Int[1/(x^2*(b*x^n)^(3/2)),x]","-\frac{2 x^{-n-1}}{b (3 n+2) \sqrt{b x^n}}","-\frac{2 x^{-n-1}}{b (3 n+2) \sqrt{b x^n}}",1,"(-2*x^(-1 - n))/(b*(2 + 3*n)*Sqrt[b*x^n])","A",2,2,13,0.1538,1,"{15, 30}"
154,1,28,0,0.0069323,"\int \frac{1}{x^3 \left(b x^n\right)^{3/2}} \, dx","Int[1/(x^3*(b*x^n)^(3/2)),x]","-\frac{2 x^{-n-2}}{b (3 n+4) \sqrt{b x^n}}","-\frac{2 x^{-n-2}}{b (3 n+4) \sqrt{b x^n}}",1,"(-2*x^(-2 - n))/(b*(4 + 3*n)*Sqrt[b*x^n])","A",2,2,13,0.1538,1,"{15, 30}"
155,1,28,0,0.0064715,"\int \frac{1}{x^4 \left(b x^n\right)^{3/2}} \, dx","Int[1/(x^4*(b*x^n)^(3/2)),x]","-\frac{2 x^{-n-3}}{3 b (n+2) \sqrt{b x^n}}","-\frac{2 x^{-n-3}}{3 b (n+2) \sqrt{b x^n}}",1,"(-2*x^(-3 - n))/(3*b*(2 + n)*Sqrt[b*x^n])","A",2,2,13,0.1538,1,"{15, 30}"
156,1,32,0,0.0100261,"\int \frac{x^m}{\left(a x^n\right)^{3/2}} \, dx","Int[x^m/(a*x^n)^(3/2),x]","\frac{2 x^{m-n+1}}{a (2 m-3 n+2) \sqrt{a x^n}}","\frac{2 x^{m-n+1}}{a (2 m-3 n+2) \sqrt{a x^n}}",1,"(2*x^(1 + m - n))/(a*(2 + 2*m - 3*n)*Sqrt[a*x^n])","A",2,2,13,0.1538,1,"{15, 30}"
157,1,36,0,0.0070287,"\int \frac{(c x)^m}{\left(a x^n\right)^{3/2}} \, dx","Int[(c*x)^m/(a*x^n)^(3/2),x]","\frac{2 x^{1-n} (c x)^m}{a (2 m-3 n+2) \sqrt{a x^n}}","\frac{2 x^{1-n} (c x)^m}{a (2 m-3 n+2) \sqrt{a x^n}}",1,"(2*x^(1 - n)*(c*x)^m)/(a*(2 + 2*m - 3*n)*Sqrt[a*x^n])","A",3,3,15,0.2000,1,"{15, 20, 30}"
158,1,28,0,0.0077379,"\int x^m \left(b x^n\right)^{3/2} \, dx","Int[x^m*(b*x^n)^(3/2),x]","\frac{2 b \sqrt{b x^n} x^{m+n+1}}{2 m+3 n+2}","\frac{2 b \sqrt{b x^n} x^{m+n+1}}{2 m+3 n+2}",1,"(2*b*x^(1 + m + n)*Sqrt[b*x^n])/(2 + 2*m + 3*n)","A",2,2,13,0.1538,1,"{15, 30}"
159,1,24,0,0.0072219,"\int x^m \sqrt{b x^n} \, dx","Int[x^m*Sqrt[b*x^n],x]","\frac{2 x^{m+1} \sqrt{b x^n}}{2 m+n+2}","\frac{2 x^{m+1} \sqrt{b x^n}}{2 m+n+2}",1,"(2*x^(1 + m)*Sqrt[b*x^n])/(2 + 2*m + n)","A",2,2,13,0.1538,1,"{15, 30}"
160,1,26,0,0.0075513,"\int \frac{x^m}{\sqrt{b x^n}} \, dx","Int[x^m/Sqrt[b*x^n],x]","\frac{2 x^{m+1}}{(2 m-n+2) \sqrt{b x^n}}","\frac{2 x^{m+1}}{(2 m-n+2) \sqrt{b x^n}}",1,"(2*x^(1 + m))/((2 + 2*m - n)*Sqrt[b*x^n])","A",2,2,13,0.1538,1,"{15, 30}"
161,1,32,0,0.0061174,"\int \frac{x^m}{\left(b x^n\right)^{3/2}} \, dx","Int[x^m/(b*x^n)^(3/2),x]","\frac{2 x^{m-n+1}}{b (2 m-3 n+2) \sqrt{b x^n}}","\frac{2 x^{m-n+1}}{b (2 m-3 n+2) \sqrt{b x^n}}",1,"(2*x^(1 + m - n))/(b*(2 + 2*m - 3*n)*Sqrt[b*x^n])","A",2,2,13,0.1538,1,"{15, 30}"
162,1,36,0,0.0133699,"\int (c x)^m \left(b x^n\right)^{5/2} \, dx","Int[(c*x)^m*(b*x^n)^(5/2),x]","\frac{2 b^2 x^{2 n+1} \sqrt{b x^n} (c x)^m}{2 m+5 n+2}","\frac{2 \left(b x^n\right)^{5/2} (c x)^{m+1}}{c (2 m+5 n+2)}",1,"(2*b^2*x^(1 + 2*n)*(c*x)^m*Sqrt[b*x^n])/(2 + 2*m + 5*n)","A",3,3,15,0.2000,1,"{15, 20, 30}"
163,1,32,0,0.0068314,"\int (c x)^m \left(b x^n\right)^{3/2} \, dx","Int[(c*x)^m*(b*x^n)^(3/2),x]","\frac{2 b x^{n+1} \sqrt{b x^n} (c x)^m}{2 m+3 n+2}","\frac{2 b x^{n+1} \sqrt{b x^n} (c x)^m}{2 m+3 n+2}",1,"(2*b*x^(1 + n)*(c*x)^m*Sqrt[b*x^n])/(2 + 2*m + 3*n)","A",3,3,15,0.2000,1,"{15, 20, 30}"
164,1,25,0,0.005874,"\int (c x)^m \sqrt{b x^n} \, dx","Int[(c*x)^m*Sqrt[b*x^n],x]","\frac{2 x \sqrt{b x^n} (c x)^m}{2 m+n+2}","\frac{2 \sqrt{b x^n} (c x)^{m+1}}{c (2 m+n+2)}",1,"(2*x*(c*x)^m*Sqrt[b*x^n])/(2 + 2*m + n)","A",3,3,15,0.2000,1,"{15, 20, 30}"
165,1,27,0,0.0059093,"\int \frac{(c x)^m}{\sqrt{b x^n}} \, dx","Int[(c*x)^m/Sqrt[b*x^n],x]","\frac{2 x (c x)^m}{(2 m-n+2) \sqrt{b x^n}}","\frac{2 x (c x)^m}{(2 m-n+2) \sqrt{b x^n}}",1,"(2*x*(c*x)^m)/((2 + 2*m - n)*Sqrt[b*x^n])","A",3,3,15,0.2000,1,"{15, 20, 30}"
166,1,36,0,0.006889,"\int \frac{(c x)^m}{\left(b x^n\right)^{3/2}} \, dx","Int[(c*x)^m/(b*x^n)^(3/2),x]","\frac{2 x^{1-n} (c x)^m}{b (2 m-3 n+2) \sqrt{b x^n}}","\frac{2 x^{1-n} (c x)^m}{b (2 m-3 n+2) \sqrt{b x^n}}",1,"(2*x^(1 - n)*(c*x)^m)/(b*(2 + 2*m - 3*n)*Sqrt[b*x^n])","A",3,3,15,0.2000,1,"{15, 20, 30}"
167,1,36,0,0.0125394,"\int \frac{(c x)^m}{\left(b x^n\right)^{5/2}} \, dx","Int[(c*x)^m/(b*x^n)^(5/2),x]","\frac{2 x^{1-2 n} (c x)^m}{b^2 (2 m-5 n+2) \sqrt{b x^n}}","\frac{2 x^{1-2 n} (c x)^m}{b^2 (2 m-5 n+2) \sqrt{b x^n}}",1,"(2*x^(1 - 2*n)*(c*x)^m)/(b^2*(2 + 2*m - 5*n)*Sqrt[b*x^n])","A",3,3,15,0.2000,1,"{15, 20, 30}"
168,1,20,0,0.0020854,"\int x^{-1-\frac{3 n}{2}} \left(b x^n\right)^{3/2} \, dx","Int[x^(-1 - (3*n)/2)*(b*x^n)^(3/2),x]","b x^{-n/2} \log (x) \sqrt{b x^n}","b x^{-n/2} \log (x) \sqrt{b x^n}",1,"(b*Sqrt[b*x^n]*Log[x])/x^(n/2)","A",2,2,19,0.1053,1,"{15, 29}"
169,1,19,0,0.0029187,"\int x^{-1-\frac{n}{2}} \sqrt{b x^n} \, dx","Int[x^(-1 - n/2)*Sqrt[b*x^n],x]","x^{-n/2} \log (x) \sqrt{b x^n}","x^{-n/2} \log (x) \sqrt{b x^n}",1,"(Sqrt[b*x^n]*Log[x])/x^(n/2)","A",2,2,19,0.1053,1,"{15, 29}"
170,1,19,0,0.0025012,"\int \frac{x^{-1+\frac{n}{2}}}{\sqrt{b x^n}} \, dx","Int[x^(-1 + n/2)/Sqrt[b*x^n],x]","\frac{x^{n/2} \log (x)}{\sqrt{b x^n}}","\frac{x^{n/2} \log (x)}{\sqrt{b x^n}}",1,"(x^(n/2)*Log[x])/Sqrt[b*x^n]","A",2,2,19,0.1053,1,"{15, 29}"
171,1,22,0,0.0018731,"\int \frac{x^{-1+\frac{3 n}{2}}}{\left(b x^n\right)^{3/2}} \, dx","Int[x^(-1 + (3*n)/2)/(b*x^n)^(3/2),x]","\frac{x^{n/2} \log (x)}{b \sqrt{b x^n}}","\frac{x^{n/2} \log (x)}{b \sqrt{b x^n}}",1,"(x^(n/2)*Log[x])/(b*Sqrt[b*x^n])","A",2,2,19,0.1053,1,"{15, 29}"
172,1,21,0,0.0055734,"\int x^m \left(b x^n\right)^p \, dx","Int[x^m*(b*x^n)^p,x]","\frac{x^{m+1} \left(b x^n\right)^p}{m+n p+1}","\frac{x^{m+1} \left(b x^n\right)^p}{m+n p+1}",1,"(x^(1 + m)*(b*x^n)^p)/(1 + m + n*p)","A",2,2,11,0.1818,1,"{15, 30}"
173,1,22,0,0.0053109,"\int (c x)^m \left(b x^n\right)^p \, dx","Int[(c*x)^m*(b*x^n)^p,x]","\frac{x (c x)^m \left(b x^n\right)^p}{m+n p+1}","\frac{(c x)^{m+1} \left(b x^n\right)^p}{c (m+n p+1)}",1,"(x*(c*x)^m*(b*x^n)^p)/(1 + m + n*p)","A",3,3,13,0.2308,1,"{15, 20, 30}"
174,1,18,0,0.0053697,"\int x^2 \left(b x^n\right)^p \, dx","Int[x^2*(b*x^n)^p,x]","\frac{x^3 \left(b x^n\right)^p}{n p+3}","\frac{x^3 \left(b x^n\right)^p}{n p+3}",1,"(x^3*(b*x^n)^p)/(3 + n*p)","A",2,2,11,0.1818,1,"{15, 30}"
175,1,18,0,0.0046938,"\int x \left(b x^n\right)^p \, dx","Int[x*(b*x^n)^p,x]","\frac{x^2 \left(b x^n\right)^p}{n p+2}","\frac{x^2 \left(b x^n\right)^p}{n p+2}",1,"(x^2*(b*x^n)^p)/(2 + n*p)","A",2,2,9,0.2222,1,"{15, 30}"
176,1,16,0,0.0046513,"\int \left(b x^n\right)^p \, dx","Int[(b*x^n)^p,x]","\frac{x \left(b x^n\right)^p}{n p+1}","\frac{x \left(b x^n\right)^p}{n p+1}",1,"(x*(b*x^n)^p)/(1 + n*p)","A",2,2,7,0.2857,1,"{15, 30}"
177,1,14,0,0.0036984,"\int \frac{\left(b x^n\right)^p}{x} \, dx","Int[(b*x^n)^p/x,x]","\frac{\left(b x^n\right)^p}{n p}","\frac{\left(b x^n\right)^p}{n p}",1,"(b*x^n)^p/(n*p)","A",2,2,11,0.1818,1,"{15, 30}"
178,1,20,0,0.0073168,"\int \frac{\left(b x^n\right)^p}{x^2} \, dx","Int[(b*x^n)^p/x^2,x]","-\frac{\left(b x^n\right)^p}{x (1-n p)}","-\frac{\left(b x^n\right)^p}{x (1-n p)}",1,"-((b*x^n)^p/((1 - n*p)*x))","A",2,2,11,0.1818,1,"{15, 30}"
179,1,20,0,0.006346,"\int \frac{\left(b x^n\right)^p}{x^3} \, dx","Int[(b*x^n)^p/x^3,x]","-\frac{\left(b x^n\right)^p}{x^2 (2-n p)}","-\frac{\left(b x^n\right)^p}{x^2 (2-n p)}",1,"-((b*x^n)^p/((2 - n*p)*x^2))","A",2,2,11,0.1818,1,"{15, 30}"
180,1,20,0,0.0026378,"\int x^m \left(a x^n\right)^{-1/n} \, dx","Int[x^m/(a*x^n)^n^(-1),x]","\frac{x^{m+1} \left(a x^n\right)^{-1/n}}{m}","\frac{x^{m+1} \left(a x^n\right)^{-1/n}}{m}",1,"x^(1 + m)/(m*(a*x^n)^n^(-1))","A",2,2,15,0.1333,1,"{15, 30}"
181,1,21,0,0.0045587,"\int (c x)^m \left(a x^n\right)^{-1/n} \, dx","Int[(c*x)^m/(a*x^n)^n^(-1),x]","\frac{x \left(a x^n\right)^{-1/n} (c x)^m}{m}","\frac{x \left(a x^n\right)^{-1/n} (c x)^m}{m}",1,"(x*(c*x)^m)/(m*(a*x^n)^n^(-1))","A",3,3,17,0.1765,1,"{15, 16, 32}"
182,1,18,0,0.001827,"\int x^2 \left(a x^n\right)^{-1/n} \, dx","Int[x^2/(a*x^n)^n^(-1),x]","\frac{1}{2} x^3 \left(a x^n\right)^{-1/n}","\frac{1}{2} x^3 \left(a x^n\right)^{-1/n}",1,"x^3/(2*(a*x^n)^n^(-1))","A",2,2,15,0.1333,1,"{15, 30}"
183,1,15,0,0.0014573,"\int x \left(a x^n\right)^{-1/n} \, dx","Int[x/(a*x^n)^n^(-1),x]","x^2 \left(a x^n\right)^{-1/n}","x^2 \left(a x^n\right)^{-1/n}",1,"x^2/(a*x^n)^n^(-1)","A",2,2,13,0.1538,1,"{15, 8}"
184,1,15,0,0.0015194,"\int \left(a x^n\right)^{-1/n} \, dx","Int[(a*x^n)^(-n^(-1)),x]","x \log (x) \left(a x^n\right)^{-1/n}","x \log (x) \left(a x^n\right)^{-1/n}",1,"(x*Log[x])/(a*x^n)^n^(-1)","A",2,2,11,0.1818,1,"{15, 29}"
185,1,13,0,0.0016147,"\int \frac{\left(a x^n\right)^{-1/n}}{x} \, dx","Int[1/(x*(a*x^n)^n^(-1)),x]","-\left(a x^n\right)^{-1/n}","-\left(a x^n\right)^{-1/n}",1,"-(a*x^n)^(-n^(-1))","A",2,2,15,0.1333,1,"{15, 30}"
186,1,18,0,0.0017376,"\int \frac{\left(a x^n\right)^{-1/n}}{x^2} \, dx","Int[1/(x^2*(a*x^n)^n^(-1)),x]","-\frac{\left(a x^n\right)^{-1/n}}{2 x}","-\frac{\left(a x^n\right)^{-1/n}}{2 x}",1,"-1/(2*x*(a*x^n)^n^(-1))","A",2,2,15,0.1333,1,"{15, 30}"
187,1,22,0,0.0034739,"\int x^m \left(a x^n\right)^{-\frac{1+m}{n}} \, dx","Int[x^m/(a*x^n)^((1 + m)/n),x]","x^{m+1} \log (x) \left(a x^n\right)^{-\frac{m+1}{n}}","x^{m+1} \log (x) \left(a x^n\right)^{-\frac{m+1}{n}}",1,"(x^(1 + m)*Log[x])/(a*x^n)^((1 + m)/n)","A",2,2,18,0.1111,1,"{15, 29}"
188,1,16,0,0.0031623,"\int x^{-1-n p} \left(a x^n\right)^p \, dx","Int[x^(-1 - n*p)*(a*x^n)^p,x]","\log (x) x^{-n p} \left(a x^n\right)^p","\log (x) x^{-n p} \left(a x^n\right)^p",1,"((a*x^n)^p*Log[x])/x^(n*p)","A",2,2,16,0.1250,1,"{15, 29}"
189,1,26,0,0.0451479,"\int x^m \left(a \left(b x^n\right)^p\right)^q \, dx","Int[x^m*(a*(b*x^n)^p)^q,x]","\frac{x^{m+1} \left(a \left(b x^n\right)^p\right)^q}{m+n p q+1}","\frac{x^{m+1} \left(a \left(b x^n\right)^p\right)^q}{m+n p q+1}",1,"(x^(1 + m)*(a*(b*x^n)^p)^q)/(1 + m + n*p*q)","A",2,2,15,0.1333,1,"{6679, 30}"
190,1,23,0,0.0460035,"\int x^2 \left(a \left(b x^n\right)^p\right)^q \, dx","Int[x^2*(a*(b*x^n)^p)^q,x]","\frac{x^3 \left(a \left(b x^n\right)^p\right)^q}{n p q+3}","\frac{x^3 \left(a \left(b x^n\right)^p\right)^q}{n p q+3}",1,"(x^3*(a*(b*x^n)^p)^q)/(3 + n*p*q)","A",2,2,15,0.1333,1,"{6679, 30}"
191,1,23,0,0.028609,"\int x \left(a \left(b x^n\right)^p\right)^q \, dx","Int[x*(a*(b*x^n)^p)^q,x]","\frac{x^2 \left(a \left(b x^n\right)^p\right)^q}{n p q+2}","\frac{x^2 \left(a \left(b x^n\right)^p\right)^q}{n p q+2}",1,"(x^2*(a*(b*x^n)^p)^q)/(2 + n*p*q)","A",2,2,13,0.1538,1,"{6679, 30}"
192,1,21,0,0.0141064,"\int \left(a \left(b x^n\right)^p\right)^q \, dx","Int[(a*(b*x^n)^p)^q,x]","\frac{x \left(a \left(b x^n\right)^p\right)^q}{n p q+1}","\frac{x \left(a \left(b x^n\right)^p\right)^q}{n p q+1}",1,"(x*(a*(b*x^n)^p)^q)/(1 + n*p*q)","A",2,2,11,0.1818,1,"{6679, 30}"
193,1,21,0,0.044548,"\int \frac{\left(a \left(b x^n\right)^p\right)^q}{x} \, dx","Int[(a*(b*x^n)^p)^q/x,x]","\frac{\left(a \left(b x^n\right)^p\right)^q}{n p q}","\frac{\left(a \left(b x^n\right)^p\right)^q}{n p q}",1,"(a*(b*x^n)^p)^q/(n*p*q)","A",2,2,15,0.1333,1,"{6679, 30}"
194,1,25,0,0.0452928,"\int \frac{\left(a \left(b x^n\right)^p\right)^q}{x^2} \, dx","Int[(a*(b*x^n)^p)^q/x^2,x]","-\frac{\left(a \left(b x^n\right)^p\right)^q}{x (1-n p q)}","-\frac{\left(a \left(b x^n\right)^p\right)^q}{x (1-n p q)}",1,"-((a*(b*x^n)^p)^q/((1 - n*p*q)*x))","A",2,2,15,0.1333,1,"{6679, 30}"
195,1,25,0,0.0454394,"\int \frac{\left(a \left(b x^n\right)^p\right)^q}{x^3} \, dx","Int[(a*(b*x^n)^p)^q/x^3,x]","-\frac{\left(a \left(b x^n\right)^p\right)^q}{x^2 (2-n p q)}","-\frac{\left(a \left(b x^n\right)^p\right)^q}{x^2 (2-n p q)}",1,"-((a*(b*x^n)^p)^q/((2 - n*p*q)*x^2))","A",2,2,15,0.1333,1,"{6679, 30}"
196,1,25,0,0.0499666,"\int x^2 \left(a \left(b x^m\right)^n\right)^{-\frac{1}{m n}} \, dx","Int[x^2/(a*(b*x^m)^n)^(1/(m*n)),x]","\frac{1}{2} x^3 \left(a \left(b x^m\right)^n\right)^{-\frac{1}{m n}}","\frac{1}{2} x^3 \left(a \left(b x^m\right)^n\right)^{-\frac{1}{m n}}",1,"x^3/(2*(a*(b*x^m)^n)^(1/(m*n)))","A",2,2,22,0.09091,1,"{6679, 30}"
197,1,22,0,0.0287356,"\int x \left(a \left(b x^m\right)^n\right)^{-\frac{1}{m n}} \, dx","Int[x/(a*(b*x^m)^n)^(1/(m*n)),x]","x^2 \left(a \left(b x^m\right)^n\right)^{-\frac{1}{m n}}","x^2 \left(a \left(b x^m\right)^n\right)^{-\frac{1}{m n}}",1,"x^2/(a*(b*x^m)^n)^(1/(m*n))","A",2,2,20,0.1000,1,"{6679, 8}"
198,1,22,0,0.0109022,"\int \left(a \left(b x^m\right)^n\right)^{-\frac{1}{m n}} \, dx","Int[(a*(b*x^m)^n)^(-(1/(m*n))),x]","x \log (x) \left(a \left(b x^m\right)^n\right)^{-\frac{1}{m n}}","x \log (x) \left(a \left(b x^m\right)^n\right)^{-\frac{1}{m n}}",1,"(x*Log[x])/(a*(b*x^m)^n)^(1/(m*n))","A",2,2,18,0.1111,1,"{6679, 29}"
199,1,20,0,0.0442031,"\int \frac{\left(a \left(b x^m\right)^n\right)^{-\frac{1}{m n}}}{x} \, dx","Int[1/(x*(a*(b*x^m)^n)^(1/(m*n))),x]","-\left(a \left(b x^m\right)^n\right)^{-\frac{1}{m n}}","-\left(a \left(b x^m\right)^n\right)^{-\frac{1}{m n}}",1,"-(a*(b*x^m)^n)^(-(1/(m*n)))","A",2,2,22,0.09091,1,"{6679, 30}"
200,1,25,0,0.0432139,"\int \frac{\left(a \left(b x^m\right)^n\right)^{-\frac{1}{m n}}}{x^2} \, dx","Int[1/(x^2*(a*(b*x^m)^n)^(1/(m*n))),x]","-\frac{\left(a \left(b x^m\right)^n\right)^{-\frac{1}{m n}}}{2 x}","-\frac{\left(a \left(b x^m\right)^n\right)^{-\frac{1}{m n}}}{2 x}",1,"-1/(2*x*(a*(b*x^m)^n)^(1/(m*n)))","A",2,2,22,0.09091,1,"{6679, 30}"
201,1,24,0,0.0427497,"\int x^{2-n p q} \left(a \left(b x^n\right)^p\right)^q \, dx","Int[x^(2 - n*p*q)*(a*(b*x^n)^p)^q,x]","\frac{1}{3} x^{3-n p q} \left(a \left(b x^n\right)^p\right)^q","\frac{1}{3} x^{3-n p q} \left(a \left(b x^n\right)^p\right)^q",1,"(x^(3 - n*p*q)*(a*(b*x^n)^p)^q)/3","A",2,2,21,0.09524,1,"{6679, 30}"
202,1,24,0,0.0421745,"\int x^{1-n p q} \left(a \left(b x^n\right)^p\right)^q \, dx","Int[x^(1 - n*p*q)*(a*(b*x^n)^p)^q,x]","\frac{1}{2} x^{2-n p q} \left(a \left(b x^n\right)^p\right)^q","\frac{1}{2} x^{2-n p q} \left(a \left(b x^n\right)^p\right)^q",1,"(x^(2 - n*p*q)*(a*(b*x^n)^p)^q)/2","A",2,2,21,0.09524,1,"{6679, 30}"
203,1,21,0,0.0429259,"\int x^{-n p q} \left(a \left(b x^n\right)^p\right)^q \, dx","Int[(a*(b*x^n)^p)^q/x^(n*p*q),x]","x^{1-n p q} \left(a \left(b x^n\right)^p\right)^q","x^{1-n p q} \left(a \left(b x^n\right)^p\right)^q",1,"x^(1 - n*p*q)*(a*(b*x^n)^p)^q","A",2,2,19,0.1053,1,"{6679, 8}"
204,1,21,0,0.0436247,"\int x^{-1-n p q} \left(a \left(b x^n\right)^p\right)^q \, dx","Int[x^(-1 - n*p*q)*(a*(b*x^n)^p)^q,x]","\log (x) x^{-n p q} \left(a \left(b x^n\right)^p\right)^q","\log (x) x^{-n p q} \left(a \left(b x^n\right)^p\right)^q",1,"((a*(b*x^n)^p)^q*Log[x])/x^(n*p*q)","A",2,2,21,0.09524,1,"{6679, 29}"
205,1,22,0,0.0420725,"\int x^{-2-n p q} \left(a \left(b x^n\right)^p\right)^q \, dx","Int[x^(-2 - n*p*q)*(a*(b*x^n)^p)^q,x]","-x^{-n p q-1} \left(a \left(b x^n\right)^p\right)^q","-x^{-n p q-1} \left(a \left(b x^n\right)^p\right)^q",1,"-(x^(-1 - n*p*q)*(a*(b*x^n)^p)^q)","A",2,2,21,0.09524,1,"{6679, 30}"
206,1,17,0,0.0048759,"\int x^3 \left(a+b x^3\right) \, dx","Int[x^3*(a + b*x^3),x]","\frac{a x^4}{4}+\frac{b x^7}{7}","\frac{a x^4}{4}+\frac{b x^7}{7}",1,"(a*x^4)/4 + (b*x^7)/7","A",2,1,11,0.09091,1,"{14}"
207,1,17,0,0.0044511,"\int x^2 \left(a+b x^3\right) \, dx","Int[x^2*(a + b*x^3),x]","\frac{a x^3}{3}+\frac{b x^6}{6}","\frac{a x^3}{3}+\frac{b x^6}{6}",1,"(a*x^3)/3 + (b*x^6)/6","A",2,1,11,0.09091,1,"{14}"
208,1,17,0,0.0046148,"\int x \left(a+b x^3\right) \, dx","Int[x*(a + b*x^3),x]","\frac{a x^2}{2}+\frac{b x^5}{5}","\frac{a x^2}{2}+\frac{b x^5}{5}",1,"(a*x^2)/2 + (b*x^5)/5","A",2,1,9,0.1111,1,"{14}"
209,1,12,0,0.0022618,"\int \left(a+b x^3\right) \, dx","Int[a + b*x^3,x]","a x+\frac{b x^4}{4}","a x+\frac{b x^4}{4}",1,"a*x + (b*x^4)/4","A",1,0,7,0,1,"{}"
210,1,13,0,0.003704,"\int \frac{a+b x^3}{x} \, dx","Int[(a + b*x^3)/x,x]","a \log (x)+\frac{b x^3}{3}","a \log (x)+\frac{b x^3}{3}",1,"(b*x^3)/3 + a*Log[x]","A",2,1,11,0.09091,1,"{14}"
211,1,15,0,0.0045238,"\int \frac{a+b x^3}{x^2} \, dx","Int[(a + b*x^3)/x^2,x]","\frac{b x^2}{2}-\frac{a}{x}","\frac{b x^2}{2}-\frac{a}{x}",1,"-(a/x) + (b*x^2)/2","A",2,1,11,0.09091,1,"{14}"
212,1,12,0,0.0040152,"\int \frac{a+b x^3}{x^3} \, dx","Int[(a + b*x^3)/x^3,x]","b x-\frac{a}{2 x^2}","b x-\frac{a}{2 x^2}",1,"-a/(2*x^2) + b*x","A",2,1,11,0.09091,1,"{14}"
213,1,13,0,0.0042974,"\int \frac{a+b x^3}{x^4} \, dx","Int[(a + b*x^3)/x^4,x]","b \log (x)-\frac{a}{3 x^3}","b \log (x)-\frac{a}{3 x^3}",1,"-a/(3*x^3) + b*Log[x]","A",2,1,11,0.09091,1,"{14}"
214,1,15,0,0.0044847,"\int \frac{a+b x^3}{x^5} \, dx","Int[(a + b*x^3)/x^5,x]","-\frac{a}{4 x^4}-\frac{b}{x}","-\frac{a}{4 x^4}-\frac{b}{x}",1,"-a/(4*x^4) - b/x","A",2,1,11,0.09091,1,"{14}"
215,1,17,0,0.0045445,"\int \frac{a+b x^3}{x^6} \, dx","Int[(a + b*x^3)/x^6,x]","-\frac{a}{5 x^5}-\frac{b}{2 x^2}","-\frac{a}{5 x^5}-\frac{b}{2 x^2}",1,"-a/(5*x^5) - b/(2*x^2)","A",2,1,11,0.09091,1,"{14}"
216,1,17,0,0.0049774,"\int \frac{a+b x^3}{x^7} \, dx","Int[(a + b*x^3)/x^7,x]","-\frac{a}{6 x^6}-\frac{b}{3 x^3}","-\frac{a}{6 x^6}-\frac{b}{3 x^3}",1,"-a/(6*x^6) - b/(3*x^3)","A",2,1,11,0.09091,1,"{14}"
217,1,17,0,0.0045915,"\int \frac{a+b x^3}{x^8} \, dx","Int[(a + b*x^3)/x^8,x]","-\frac{a}{7 x^7}-\frac{b}{4 x^4}","-\frac{a}{7 x^7}-\frac{b}{4 x^4}",1,"-a/(7*x^7) - b/(4*x^4)","A",2,1,11,0.09091,1,"{14}"
218,1,30,0,0.0097121,"\int x^4 \left(a+b x^3\right)^2 \, dx","Int[x^4*(a + b*x^3)^2,x]","\frac{a^2 x^5}{5}+\frac{1}{4} a b x^8+\frac{b^2 x^{11}}{11}","\frac{a^2 x^5}{5}+\frac{1}{4} a b x^8+\frac{b^2 x^{11}}{11}",1,"(a^2*x^5)/5 + (a*b*x^8)/4 + (b^2*x^11)/11","A",2,1,13,0.07692,1,"{270}"
219,1,30,0,0.0093571,"\int x^3 \left(a+b x^3\right)^2 \, dx","Int[x^3*(a + b*x^3)^2,x]","\frac{a^2 x^4}{4}+\frac{2}{7} a b x^7+\frac{b^2 x^{10}}{10}","\frac{a^2 x^4}{4}+\frac{2}{7} a b x^7+\frac{b^2 x^{10}}{10}",1,"(a^2*x^4)/4 + (2*a*b*x^7)/7 + (b^2*x^10)/10","A",2,1,13,0.07692,1,"{270}"
220,1,16,0,0.0026883,"\int x^2 \left(a+b x^3\right)^2 \, dx","Int[x^2*(a + b*x^3)^2,x]","\frac{\left(a+b x^3\right)^3}{9 b}","\frac{\left(a+b x^3\right)^3}{9 b}",1,"(a + b*x^3)^3/(9*b)","A",1,1,13,0.07692,1,"{261}"
221,1,30,0,0.0088576,"\int x \left(a+b x^3\right)^2 \, dx","Int[x*(a + b*x^3)^2,x]","\frac{a^2 x^2}{2}+\frac{2}{5} a b x^5+\frac{b^2 x^8}{8}","\frac{a^2 x^2}{2}+\frac{2}{5} a b x^5+\frac{b^2 x^8}{8}",1,"(a^2*x^2)/2 + (2*a*b*x^5)/5 + (b^2*x^8)/8","A",2,1,11,0.09091,1,"{270}"
222,1,25,0,0.006953,"\int \left(a+b x^3\right)^2 \, dx","Int[(a + b*x^3)^2,x]","a^2 x+\frac{1}{2} a b x^4+\frac{b^2 x^7}{7}","a^2 x+\frac{1}{2} a b x^4+\frac{b^2 x^7}{7}",1,"a^2*x + (a*b*x^4)/2 + (b^2*x^7)/7","A",2,1,9,0.1111,1,"{194}"
223,1,26,0,0.0120073,"\int \frac{\left(a+b x^3\right)^2}{x} \, dx","Int[(a + b*x^3)^2/x,x]","a^2 \log (x)+\frac{2}{3} a b x^3+\frac{b^2 x^6}{6}","a^2 \log (x)+\frac{2}{3} a b x^3+\frac{b^2 x^6}{6}",1,"(2*a*b*x^3)/3 + (b^2*x^6)/6 + a^2*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
224,1,25,0,0.009013,"\int \frac{\left(a+b x^3\right)^2}{x^2} \, dx","Int[(a + b*x^3)^2/x^2,x]","-\frac{a^2}{x}+a b x^2+\frac{b^2 x^5}{5}","-\frac{a^2}{x}+a b x^2+\frac{b^2 x^5}{5}",1,"-(a^2/x) + a*b*x^2 + (b^2*x^5)/5","A",2,1,13,0.07692,1,"{270}"
225,1,26,0,0.0087787,"\int \frac{\left(a+b x^3\right)^2}{x^3} \, dx","Int[(a + b*x^3)^2/x^3,x]","-\frac{a^2}{2 x^2}+2 a b x+\frac{b^2 x^4}{4}","-\frac{a^2}{2 x^2}+2 a b x+\frac{b^2 x^4}{4}",1,"-a^2/(2*x^2) + 2*a*b*x + (b^2*x^4)/4","A",2,1,13,0.07692,1,"{270}"
226,1,27,0,0.0128269,"\int \frac{\left(a+b x^3\right)^2}{x^4} \, dx","Int[(a + b*x^3)^2/x^4,x]","-\frac{a^2}{3 x^3}+2 a b \log (x)+\frac{b^2 x^3}{3}","-\frac{a^2}{3 x^3}+2 a b \log (x)+\frac{b^2 x^3}{3}",1,"-a^2/(3*x^3) + (b^2*x^3)/3 + 2*a*b*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
227,1,28,0,0.0094556,"\int \frac{\left(a+b x^3\right)^2}{x^5} \, dx","Int[(a + b*x^3)^2/x^5,x]","-\frac{a^2}{4 x^4}-\frac{2 a b}{x}+\frac{b^2 x^2}{2}","-\frac{a^2}{4 x^4}-\frac{2 a b}{x}+\frac{b^2 x^2}{2}",1,"-a^2/(4*x^4) - (2*a*b)/x + (b^2*x^2)/2","A",2,1,13,0.07692,1,"{270}"
228,1,23,0,0.009359,"\int \frac{\left(a+b x^3\right)^2}{x^6} \, dx","Int[(a + b*x^3)^2/x^6,x]","-\frac{a^2}{5 x^5}-\frac{a b}{x^2}+b^2 x","-\frac{a^2}{5 x^5}-\frac{a b}{x^2}+b^2 x",1,"-a^2/(5*x^5) - (a*b)/x^2 + b^2*x","A",2,1,13,0.07692,1,"{270}"
229,1,26,0,0.0130423,"\int \frac{\left(a+b x^3\right)^2}{x^7} \, dx","Int[(a + b*x^3)^2/x^7,x]","-\frac{a^2}{6 x^6}-\frac{2 a b}{3 x^3}+b^2 \log (x)","-\frac{a^2}{6 x^6}-\frac{2 a b}{3 x^3}+b^2 \log (x)",1,"-a^2/(6*x^6) - (2*a*b)/(3*x^3) + b^2*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
230,1,28,0,0.0098012,"\int \frac{\left(a+b x^3\right)^2}{x^8} \, dx","Int[(a + b*x^3)^2/x^8,x]","-\frac{a^2}{7 x^7}-\frac{a b}{2 x^4}-\frac{b^2}{x}","-\frac{a^2}{7 x^7}-\frac{a b}{2 x^4}-\frac{b^2}{x}",1,"-a^2/(7*x^7) - (a*b)/(2*x^4) - b^2/x","A",2,1,13,0.07692,1,"{270}"
231,1,30,0,0.0095963,"\int \frac{\left(a+b x^3\right)^2}{x^9} \, dx","Int[(a + b*x^3)^2/x^9,x]","-\frac{a^2}{8 x^8}-\frac{2 a b}{5 x^5}-\frac{b^2}{2 x^2}","-\frac{a^2}{8 x^8}-\frac{2 a b}{5 x^5}-\frac{b^2}{2 x^2}",1,"-a^2/(8*x^8) - (2*a*b)/(5*x^5) - b^2/(2*x^2)","A",2,1,13,0.07692,1,"{270}"
232,1,19,0,0.0033423,"\int \frac{\left(a+b x^3\right)^2}{x^{10}} \, dx","Int[(a + b*x^3)^2/x^10,x]","-\frac{\left(a+b x^3\right)^3}{9 a x^9}","-\frac{\left(a+b x^3\right)^3}{9 a x^9}",1,"-(a + b*x^3)^3/(9*a*x^9)","A",1,1,13,0.07692,1,"{264}"
233,1,30,0,0.0103513,"\int \frac{\left(a+b x^3\right)^2}{x^{11}} \, dx","Int[(a + b*x^3)^2/x^11,x]","-\frac{a^2}{10 x^{10}}-\frac{2 a b}{7 x^7}-\frac{b^2}{4 x^4}","-\frac{a^2}{10 x^{10}}-\frac{2 a b}{7 x^7}-\frac{b^2}{4 x^4}",1,"-a^2/(10*x^10) - (2*a*b)/(7*x^7) - b^2/(4*x^4)","A",2,1,13,0.07692,1,"{270}"
234,1,30,0,0.0098668,"\int \frac{\left(a+b x^3\right)^2}{x^{12}} \, dx","Int[(a + b*x^3)^2/x^12,x]","-\frac{a^2}{11 x^{11}}-\frac{a b}{4 x^8}-\frac{b^2}{5 x^5}","-\frac{a^2}{11 x^{11}}-\frac{a b}{4 x^8}-\frac{b^2}{5 x^5}",1,"-a^2/(11*x^11) - (a*b)/(4*x^8) - b^2/(5*x^5)","A",2,1,13,0.07692,1,"{270}"
235,1,30,0,0.0135996,"\int \frac{\left(a+b x^3\right)^2}{x^{13}} \, dx","Int[(a + b*x^3)^2/x^13,x]","-\frac{a^2}{12 x^{12}}-\frac{2 a b}{9 x^9}-\frac{b^2}{6 x^6}","-\frac{a^2}{12 x^{12}}-\frac{2 a b}{9 x^9}-\frac{b^2}{6 x^6}",1,"-a^2/(12*x^12) - (2*a*b)/(9*x^9) - b^2/(6*x^6)","A",3,2,13,0.1538,1,"{266, 43}"
236,1,43,0,0.0273662,"\int x^{14} \left(a+b x^3\right)^3 \, dx","Int[x^14*(a + b*x^3)^3,x]","\frac{1}{6} a^2 b x^{18}+\frac{a^3 x^{15}}{15}+\frac{1}{7} a b^2 x^{21}+\frac{b^3 x^{24}}{24}","\frac{1}{6} a^2 b x^{18}+\frac{a^3 x^{15}}{15}+\frac{1}{7} a b^2 x^{21}+\frac{b^3 x^{24}}{24}",1,"(a^3*x^15)/15 + (a^2*b*x^18)/6 + (a*b^2*x^21)/7 + (b^3*x^24)/24","A",3,2,13,0.1538,1,"{266, 43}"
237,1,43,0,0.0248982,"\int x^{11} \left(a+b x^3\right)^3 \, dx","Int[x^11*(a + b*x^3)^3,x]","\frac{1}{5} a^2 b x^{15}+\frac{a^3 x^{12}}{12}+\frac{1}{6} a b^2 x^{18}+\frac{b^3 x^{21}}{21}","\frac{1}{5} a^2 b x^{15}+\frac{a^3 x^{12}}{12}+\frac{1}{6} a b^2 x^{18}+\frac{b^3 x^{21}}{21}",1,"(a^3*x^12)/12 + (a^2*b*x^15)/5 + (a*b^2*x^18)/6 + (b^3*x^21)/21","A",3,2,13,0.1538,1,"{266, 43}"
238,1,43,0,0.024537,"\int x^8 \left(a+b x^3\right)^3 \, dx","Int[x^8*(a + b*x^3)^3,x]","\frac{1}{4} a^2 b x^{12}+\frac{a^3 x^9}{9}+\frac{1}{5} a b^2 x^{15}+\frac{b^3 x^{18}}{18}","\frac{1}{4} a^2 b x^{12}+\frac{a^3 x^9}{9}+\frac{1}{5} a b^2 x^{15}+\frac{b^3 x^{18}}{18}",1,"(a^3*x^9)/9 + (a^2*b*x^12)/4 + (a*b^2*x^15)/5 + (b^3*x^18)/18","A",3,2,13,0.1538,1,"{266, 43}"
239,1,34,0,0.0304055,"\int x^5 \left(a+b x^3\right)^3 \, dx","Int[x^5*(a + b*x^3)^3,x]","\frac{\left(a+b x^3\right)^5}{15 b^2}-\frac{a \left(a+b x^3\right)^4}{12 b^2}","\frac{\left(a+b x^3\right)^5}{15 b^2}-\frac{a \left(a+b x^3\right)^4}{12 b^2}",1,"-(a*(a + b*x^3)^4)/(12*b^2) + (a + b*x^3)^5/(15*b^2)","A",3,2,13,0.1538,1,"{266, 43}"
240,1,16,0,0.0029147,"\int x^2 \left(a+b x^3\right)^3 \, dx","Int[x^2*(a + b*x^3)^3,x]","\frac{\left(a+b x^3\right)^4}{12 b}","\frac{\left(a+b x^3\right)^4}{12 b}",1,"(a + b*x^3)^4/(12*b)","A",1,1,13,0.07692,1,"{261}"
241,1,36,0,0.0192102,"\int \frac{\left(a+b x^3\right)^3}{x} \, dx","Int[(a + b*x^3)^3/x,x]","a^2 b x^3+a^3 \log (x)+\frac{1}{2} a b^2 x^6+\frac{b^3 x^9}{9}","a^2 b x^3+a^3 \log (x)+\frac{1}{2} a b^2 x^6+\frac{b^3 x^9}{9}",1,"a^2*b*x^3 + (a*b^2*x^6)/2 + (b^3*x^9)/9 + a^3*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
242,1,37,0,0.0202246,"\int \frac{\left(a+b x^3\right)^3}{x^4} \, dx","Int[(a + b*x^3)^3/x^4,x]","3 a^2 b \log (x)-\frac{a^3}{3 x^3}+a b^2 x^3+\frac{b^3 x^6}{6}","3 a^2 b \log (x)-\frac{a^3}{3 x^3}+a b^2 x^3+\frac{b^3 x^6}{6}",1,"-a^3/(3*x^3) + a*b^2*x^3 + (b^3*x^6)/6 + 3*a^2*b*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
243,1,38,0,0.0183484,"\int \frac{\left(a+b x^3\right)^3}{x^7} \, dx","Int[(a + b*x^3)^3/x^7,x]","-\frac{a^2 b}{x^3}-\frac{a^3}{6 x^6}+3 a b^2 \log (x)+\frac{b^3 x^3}{3}","-\frac{a^2 b}{x^3}-\frac{a^3}{6 x^6}+3 a b^2 \log (x)+\frac{b^3 x^3}{3}",1,"-a^3/(6*x^6) - (a^2*b)/x^3 + (b^3*x^3)/3 + 3*a*b^2*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
244,1,37,0,0.017969,"\int \frac{\left(a+b x^3\right)^3}{x^{10}} \, dx","Int[(a + b*x^3)^3/x^10,x]","-\frac{a^2 b}{2 x^6}-\frac{a^3}{9 x^9}-\frac{a b^2}{x^3}+b^3 \log (x)","-\frac{a^2 b}{2 x^6}-\frac{a^3}{9 x^9}-\frac{a b^2}{x^3}+b^3 \log (x)",1,"-a^3/(9*x^9) - (a^2*b)/(2*x^6) - (a*b^2)/x^3 + b^3*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
245,1,19,0,0.0030226,"\int \frac{\left(a+b x^3\right)^3}{x^{13}} \, dx","Int[(a + b*x^3)^3/x^13,x]","-\frac{\left(a+b x^3\right)^4}{12 a x^{12}}","-\frac{\left(a+b x^3\right)^4}{12 a x^{12}}",1,"-(a + b*x^3)^4/(12*a*x^12)","A",1,1,13,0.07692,1,"{264}"
246,1,40,0,0.0166418,"\int \frac{\left(a+b x^3\right)^3}{x^{16}} \, dx","Int[(a + b*x^3)^3/x^16,x]","\frac{b \left(a+b x^3\right)^4}{60 a^2 x^{12}}-\frac{\left(a+b x^3\right)^4}{15 a x^{15}}","\frac{b \left(a+b x^3\right)^4}{60 a^2 x^{12}}-\frac{\left(a+b x^3\right)^4}{15 a x^{15}}",1,"-(a + b*x^3)^4/(15*a*x^15) + (b*(a + b*x^3)^4)/(60*a^2*x^12)","A",3,3,13,0.2308,1,"{266, 45, 37}"
247,1,43,0,0.0184389,"\int \frac{\left(a+b x^3\right)^3}{x^{19}} \, dx","Int[(a + b*x^3)^3/x^19,x]","-\frac{a^2 b}{5 x^{15}}-\frac{a^3}{18 x^{18}}-\frac{a b^2}{4 x^{12}}-\frac{b^3}{9 x^9}","-\frac{a^2 b}{5 x^{15}}-\frac{a^3}{18 x^{18}}-\frac{a b^2}{4 x^{12}}-\frac{b^3}{9 x^9}",1,"-a^3/(18*x^18) - (a^2*b)/(5*x^15) - (a*b^2)/(4*x^12) - b^3/(9*x^9)","A",3,2,13,0.1538,1,"{266, 43}"
248,1,43,0,0.0185465,"\int \frac{\left(a+b x^3\right)^3}{x^{22}} \, dx","Int[(a + b*x^3)^3/x^22,x]","-\frac{a^2 b}{6 x^{18}}-\frac{a^3}{21 x^{21}}-\frac{a b^2}{5 x^{15}}-\frac{b^3}{12 x^{12}}","-\frac{a^2 b}{6 x^{18}}-\frac{a^3}{21 x^{21}}-\frac{a b^2}{5 x^{15}}-\frac{b^3}{12 x^{12}}",1,"-a^3/(21*x^21) - (a^2*b)/(6*x^18) - (a*b^2)/(5*x^15) - b^3/(12*x^12)","A",3,2,13,0.1538,1,"{266, 43}"
249,1,43,0,0.0151228,"\int x^4 \left(a+b x^3\right)^3 \, dx","Int[x^4*(a + b*x^3)^3,x]","\frac{3}{8} a^2 b x^8+\frac{a^3 x^5}{5}+\frac{3}{11} a b^2 x^{11}+\frac{b^3 x^{14}}{14}","\frac{3}{8} a^2 b x^8+\frac{a^3 x^5}{5}+\frac{3}{11} a b^2 x^{11}+\frac{b^3 x^{14}}{14}",1,"(a^3*x^5)/5 + (3*a^2*b*x^8)/8 + (3*a*b^2*x^11)/11 + (b^3*x^14)/14","A",2,1,13,0.07692,1,"{270}"
250,1,43,0,0.0138194,"\int x^3 \left(a+b x^3\right)^3 \, dx","Int[x^3*(a + b*x^3)^3,x]","\frac{3}{7} a^2 b x^7+\frac{a^3 x^4}{4}+\frac{3}{10} a b^2 x^{10}+\frac{b^3 x^{13}}{13}","\frac{3}{7} a^2 b x^7+\frac{a^3 x^4}{4}+\frac{3}{10} a b^2 x^{10}+\frac{b^3 x^{13}}{13}",1,"(a^3*x^4)/4 + (3*a^2*b*x^7)/7 + (3*a*b^2*x^10)/10 + (b^3*x^13)/13","A",2,1,13,0.07692,1,"{270}"
251,1,43,0,0.0136601,"\int x \left(a+b x^3\right)^3 \, dx","Int[x*(a + b*x^3)^3,x]","\frac{3}{5} a^2 b x^5+\frac{a^3 x^2}{2}+\frac{3}{8} a b^2 x^8+\frac{b^3 x^{11}}{11}","\frac{3}{5} a^2 b x^5+\frac{a^3 x^2}{2}+\frac{3}{8} a b^2 x^8+\frac{b^3 x^{11}}{11}",1,"(a^3*x^2)/2 + (3*a^2*b*x^5)/5 + (3*a*b^2*x^8)/8 + (b^3*x^11)/11","A",2,1,11,0.09091,1,"{270}"
252,1,38,0,0.0108652,"\int \left(a+b x^3\right)^3 \, dx","Int[(a + b*x^3)^3,x]","\frac{3}{4} a^2 b x^4+a^3 x+\frac{3}{7} a b^2 x^7+\frac{b^3 x^{10}}{10}","\frac{3}{4} a^2 b x^4+a^3 x+\frac{3}{7} a b^2 x^7+\frac{b^3 x^{10}}{10}",1,"a^3*x + (3*a^2*b*x^4)/4 + (3*a*b^2*x^7)/7 + (b^3*x^10)/10","A",2,1,9,0.1111,1,"{194}"
253,1,41,0,0.0137518,"\int \frac{\left(a+b x^3\right)^3}{x^2} \, dx","Int[(a + b*x^3)^3/x^2,x]","\frac{3}{2} a^2 b x^2-\frac{a^3}{x}+\frac{3}{5} a b^2 x^5+\frac{b^3 x^8}{8}","\frac{3}{2} a^2 b x^2-\frac{a^3}{x}+\frac{3}{5} a b^2 x^5+\frac{b^3 x^8}{8}",1,"-(a^3/x) + (3*a^2*b*x^2)/2 + (3*a*b^2*x^5)/5 + (b^3*x^8)/8","A",2,1,13,0.07692,1,"{270}"
254,1,39,0,0.0132737,"\int \frac{\left(a+b x^3\right)^3}{x^3} \, dx","Int[(a + b*x^3)^3/x^3,x]","3 a^2 b x-\frac{a^3}{2 x^2}+\frac{3}{4} a b^2 x^4+\frac{b^3 x^7}{7}","3 a^2 b x-\frac{a^3}{2 x^2}+\frac{3}{4} a b^2 x^4+\frac{b^3 x^7}{7}",1,"-a^3/(2*x^2) + 3*a^2*b*x + (3*a*b^2*x^4)/4 + (b^3*x^7)/7","A",2,1,13,0.07692,1,"{270}"
255,1,41,0,0.0148853,"\int \frac{\left(a+b x^3\right)^3}{x^5} \, dx","Int[(a + b*x^3)^3/x^5,x]","-\frac{3 a^2 b}{x}-\frac{a^3}{4 x^4}+\frac{3}{2} a b^2 x^2+\frac{b^3 x^5}{5}","-\frac{3 a^2 b}{x}-\frac{a^3}{4 x^4}+\frac{3}{2} a b^2 x^2+\frac{b^3 x^5}{5}",1,"-a^3/(4*x^4) - (3*a^2*b)/x + (3*a*b^2*x^2)/2 + (b^3*x^5)/5","A",2,1,13,0.07692,1,"{270}"
256,1,39,0,0.012512,"\int \frac{\left(a+b x^3\right)^3}{x^6} \, dx","Int[(a + b*x^3)^3/x^6,x]","-\frac{3 a^2 b}{2 x^2}-\frac{a^3}{5 x^5}+3 a b^2 x+\frac{b^3 x^4}{4}","-\frac{3 a^2 b}{2 x^2}-\frac{a^3}{5 x^5}+3 a b^2 x+\frac{b^3 x^4}{4}",1,"-a^3/(5*x^5) - (3*a^2*b)/(2*x^2) + 3*a*b^2*x + (b^3*x^4)/4","A",2,1,13,0.07692,1,"{270}"
257,1,41,0,0.0129814,"\int \frac{\left(a+b x^3\right)^3}{x^8} \, dx","Int[(a + b*x^3)^3/x^8,x]","-\frac{3 a^2 b}{4 x^4}-\frac{a^3}{7 x^7}-\frac{3 a b^2}{x}+\frac{b^3 x^2}{2}","-\frac{3 a^2 b}{4 x^4}-\frac{a^3}{7 x^7}-\frac{3 a b^2}{x}+\frac{b^3 x^2}{2}",1,"-a^3/(7*x^7) - (3*a^2*b)/(4*x^4) - (3*a*b^2)/x + (b^3*x^2)/2","A",2,1,13,0.07692,1,"{270}"
258,1,69,0,0.0460839,"\int x^{17} \left(a+b x^3\right)^5 \, dx","Int[x^17*(a + b*x^3)^5,x]","\frac{10}{27} a^2 b^3 x^{27}+\frac{5}{12} a^3 b^2 x^{24}+\frac{5}{21} a^4 b x^{21}+\frac{a^5 x^{18}}{18}+\frac{1}{6} a b^4 x^{30}+\frac{b^5 x^{33}}{33}","\frac{10}{27} a^2 b^3 x^{27}+\frac{5}{12} a^3 b^2 x^{24}+\frac{5}{21} a^4 b x^{21}+\frac{a^5 x^{18}}{18}+\frac{1}{6} a b^4 x^{30}+\frac{b^5 x^{33}}{33}",1,"(a^5*x^18)/18 + (5*a^4*b*x^21)/21 + (5*a^3*b^2*x^24)/12 + (10*a^2*b^3*x^27)/27 + (a*b^4*x^30)/6 + (b^5*x^33)/33","A",3,2,13,0.1538,1,"{266, 43}"
259,1,69,0,0.0420508,"\int x^{14} \left(a+b x^3\right)^5 \, dx","Int[x^14*(a + b*x^3)^5,x]","\frac{5}{12} a^2 b^3 x^{24}+\frac{10}{21} a^3 b^2 x^{21}+\frac{5}{18} a^4 b x^{18}+\frac{a^5 x^{15}}{15}+\frac{5}{27} a b^4 x^{27}+\frac{b^5 x^{30}}{30}","\frac{5}{12} a^2 b^3 x^{24}+\frac{10}{21} a^3 b^2 x^{21}+\frac{5}{18} a^4 b x^{18}+\frac{a^5 x^{15}}{15}+\frac{5}{27} a b^4 x^{27}+\frac{b^5 x^{30}}{30}",1,"(a^5*x^15)/15 + (5*a^4*b*x^18)/18 + (10*a^3*b^2*x^21)/21 + (5*a^2*b^3*x^24)/12 + (5*a*b^4*x^27)/27 + (b^5*x^30)/30","A",3,2,13,0.1538,1,"{266, 43}"
260,1,72,0,0.0908243,"\int x^{11} \left(a+b x^3\right)^5 \, dx","Int[x^11*(a + b*x^3)^5,x]","\frac{a^2 \left(a+b x^3\right)^7}{7 b^4}-\frac{a^3 \left(a+b x^3\right)^6}{18 b^4}+\frac{\left(a+b x^3\right)^9}{27 b^4}-\frac{a \left(a+b x^3\right)^8}{8 b^4}","\frac{a^2 \left(a+b x^3\right)^7}{7 b^4}-\frac{a^3 \left(a+b x^3\right)^6}{18 b^4}+\frac{\left(a+b x^3\right)^9}{27 b^4}-\frac{a \left(a+b x^3\right)^8}{8 b^4}",1,"-(a^3*(a + b*x^3)^6)/(18*b^4) + (a^2*(a + b*x^3)^7)/(7*b^4) - (a*(a + b*x^3)^8)/(8*b^4) + (a + b*x^3)^9/(27*b^4)","A",3,2,13,0.1538,1,"{266, 43}"
261,1,53,0,0.0637328,"\int x^8 \left(a+b x^3\right)^5 \, dx","Int[x^8*(a + b*x^3)^5,x]","\frac{a^2 \left(a+b x^3\right)^6}{18 b^3}+\frac{\left(a+b x^3\right)^8}{24 b^3}-\frac{2 a \left(a+b x^3\right)^7}{21 b^3}","\frac{a^2 \left(a+b x^3\right)^6}{18 b^3}+\frac{\left(a+b x^3\right)^8}{24 b^3}-\frac{2 a \left(a+b x^3\right)^7}{21 b^3}",1,"(a^2*(a + b*x^3)^6)/(18*b^3) - (2*a*(a + b*x^3)^7)/(21*b^3) + (a + b*x^3)^8/(24*b^3)","A",3,2,13,0.1538,1,"{266, 43}"
262,1,34,0,0.0363607,"\int x^5 \left(a+b x^3\right)^5 \, dx","Int[x^5*(a + b*x^3)^5,x]","\frac{\left(a+b x^3\right)^7}{21 b^2}-\frac{a \left(a+b x^3\right)^6}{18 b^2}","\frac{\left(a+b x^3\right)^7}{21 b^2}-\frac{a \left(a+b x^3\right)^6}{18 b^2}",1,"-(a*(a + b*x^3)^6)/(18*b^2) + (a + b*x^3)^7/(21*b^2)","A",3,2,13,0.1538,1,"{266, 43}"
263,1,16,0,0.0028552,"\int x^2 \left(a+b x^3\right)^5 \, dx","Int[x^2*(a + b*x^3)^5,x]","\frac{\left(a+b x^3\right)^6}{18 b}","\frac{\left(a+b x^3\right)^6}{18 b}",1,"(a + b*x^3)^6/(18*b)","A",1,1,13,0.07692,1,"{261}"
264,1,65,0,0.0333262,"\int \frac{\left(a+b x^3\right)^5}{x} \, dx","Int[(a + b*x^3)^5/x,x]","\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 (x)+\frac{5}{12} a b^4 x^{12}+\frac{b^5 x^{15}}{15}","\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 (x)+\frac{5}{12} a b^4 x^{12}+\frac{b^5 x^{15}}{15}",1,"(5*a^4*b*x^3)/3 + (5*a^3*b^2*x^6)/3 + (10*a^2*b^3*x^9)/9 + (5*a*b^4*x^12)/12 + (b^5*x^15)/15 + a^5*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
265,1,66,0,0.0363388,"\int \frac{\left(a+b x^3\right)^5}{x^4} \, dx","Int[(a + b*x^3)^5/x^4,x]","\frac{5}{3} a^2 b^3 x^6+\frac{10}{3} a^3 b^2 x^3+5 a^4 b \log (x)-\frac{a^5}{3 x^3}+\frac{5}{9} a b^4 x^9+\frac{b^5 x^{12}}{12}","\frac{5}{3} a^2 b^3 x^6+\frac{10}{3} a^3 b^2 x^3+5 a^4 b \log (x)-\frac{a^5}{3 x^3}+\frac{5}{9} a b^4 x^9+\frac{b^5 x^{12}}{12}",1,"-a^5/(3*x^3) + (10*a^3*b^2*x^3)/3 + (5*a^2*b^3*x^6)/3 + (5*a*b^4*x^9)/9 + (b^5*x^12)/12 + 5*a^4*b*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
266,1,66,0,0.0344692,"\int \frac{\left(a+b x^3\right)^5}{x^7} \, dx","Int[(a + b*x^3)^5/x^7,x]","\frac{10}{3} a^2 b^3 x^3+10 a^3 b^2 \log (x)-\frac{5 a^4 b}{3 x^3}-\frac{a^5}{6 x^6}+\frac{5}{6} a b^4 x^6+\frac{b^5 x^9}{9}","\frac{10}{3} a^2 b^3 x^3+10 a^3 b^2 \log (x)-\frac{5 a^4 b}{3 x^3}-\frac{a^5}{6 x^6}+\frac{5}{6} a b^4 x^6+\frac{b^5 x^9}{9}",1,"-a^5/(6*x^6) - (5*a^4*b)/(3*x^3) + (10*a^2*b^3*x^3)/3 + (5*a*b^4*x^6)/6 + (b^5*x^9)/9 + 10*a^3*b^2*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
267,1,66,0,0.0331047,"\int \frac{\left(a+b x^3\right)^5}{x^{10}} \, dx","Int[(a + b*x^3)^5/x^10,x]","-\frac{10 a^3 b^2}{3 x^3}+10 a^2 b^3 \log (x)-\frac{5 a^4 b}{6 x^6}-\frac{a^5}{9 x^9}+\frac{5}{3} a b^4 x^3+\frac{b^5 x^6}{6}","-\frac{10 a^3 b^2}{3 x^3}+10 a^2 b^3 \log (x)-\frac{5 a^4 b}{6 x^6}-\frac{a^5}{9 x^9}+\frac{5}{3} a b^4 x^3+\frac{b^5 x^6}{6}",1,"-a^5/(9*x^9) - (5*a^4*b)/(6*x^6) - (10*a^3*b^2)/(3*x^3) + (5*a*b^4*x^3)/3 + (b^5*x^6)/6 + 10*a^2*b^3*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
268,1,66,0,0.0307271,"\int \frac{\left(a+b x^3\right)^5}{x^{13}} \, dx","Int[(a + b*x^3)^5/x^13,x]","-\frac{5 a^3 b^2}{3 x^6}-\frac{10 a^2 b^3}{3 x^3}-\frac{5 a^4 b}{9 x^9}-\frac{a^5}{12 x^{12}}+5 a b^4 \log (x)+\frac{b^5 x^3}{3}","-\frac{5 a^3 b^2}{3 x^6}-\frac{10 a^2 b^3}{3 x^3}-\frac{5 a^4 b}{9 x^9}-\frac{a^5}{12 x^{12}}+5 a b^4 \log (x)+\frac{b^5 x^3}{3}",1,"-a^5/(12*x^12) - (5*a^4*b)/(9*x^9) - (5*a^3*b^2)/(3*x^6) - (10*a^2*b^3)/(3*x^3) + (b^5*x^3)/3 + 5*a*b^4*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
269,1,65,0,0.0310776,"\int \frac{\left(a+b x^3\right)^5}{x^{16}} \, dx","Int[(a + b*x^3)^5/x^16,x]","-\frac{10 a^3 b^2}{9 x^9}-\frac{5 a^2 b^3}{3 x^6}-\frac{5 a^4 b}{12 x^{12}}-\frac{a^5}{15 x^{15}}-\frac{5 a b^4}{3 x^3}+b^5 \log (x)","-\frac{10 a^3 b^2}{9 x^9}-\frac{5 a^2 b^3}{3 x^6}-\frac{5 a^4 b}{12 x^{12}}-\frac{a^5}{15 x^{15}}-\frac{5 a b^4}{3 x^3}+b^5 \log (x)",1,"-a^5/(15*x^15) - (5*a^4*b)/(12*x^12) - (10*a^3*b^2)/(9*x^9) - (5*a^2*b^3)/(3*x^6) - (5*a*b^4)/(3*x^3) + b^5*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
270,1,19,0,0.0031309,"\int \frac{\left(a+b x^3\right)^5}{x^{19}} \, dx","Int[(a + b*x^3)^5/x^19,x]","-\frac{\left(a+b x^3\right)^6}{18 a x^{18}}","-\frac{\left(a+b x^3\right)^6}{18 a x^{18}}",1,"-(a + b*x^3)^6/(18*a*x^18)","A",1,1,13,0.07692,1,"{264}"
271,1,40,0,0.0168073,"\int \frac{\left(a+b x^3\right)^5}{x^{22}} \, dx","Int[(a + b*x^3)^5/x^22,x]","\frac{b \left(a+b x^3\right)^6}{126 a^2 x^{18}}-\frac{\left(a+b x^3\right)^6}{21 a x^{21}}","\frac{b \left(a+b x^3\right)^6}{126 a^2 x^{18}}-\frac{\left(a+b x^3\right)^6}{21 a x^{21}}",1,"-(a + b*x^3)^6/(21*a*x^21) + (b*(a + b*x^3)^6)/(126*a^2*x^18)","A",3,3,13,0.2308,1,"{266, 45, 37}"
272,1,62,0,0.0280182,"\int \frac{\left(a+b x^3\right)^5}{x^{25}} \, dx","Int[(a + b*x^3)^5/x^25,x]","-\frac{b^2 \left(a+b x^3\right)^6}{504 a^3 x^{18}}+\frac{b \left(a+b x^3\right)^6}{84 a^2 x^{21}}-\frac{\left(a+b x^3\right)^6}{24 a x^{24}}","-\frac{b^2 \left(a+b x^3\right)^6}{504 a^3 x^{18}}+\frac{b \left(a+b x^3\right)^6}{84 a^2 x^{21}}-\frac{\left(a+b x^3\right)^6}{24 a x^{24}}",1,"-(a + b*x^3)^6/(24*a*x^24) + (b*(a + b*x^3)^6)/(84*a^2*x^21) - (b^2*(a + b*x^3)^6)/(504*a^3*x^18)","A",4,3,13,0.2308,1,"{266, 45, 37}"
273,1,69,0,0.0310307,"\int \frac{\left(a+b x^3\right)^5}{x^{28}} \, dx","Int[(a + b*x^3)^5/x^28,x]","-\frac{10 a^3 b^2}{21 x^{21}}-\frac{5 a^2 b^3}{9 x^{18}}-\frac{5 a^4 b}{24 x^{24}}-\frac{a^5}{27 x^{27}}-\frac{a b^4}{3 x^{15}}-\frac{b^5}{12 x^{12}}","-\frac{10 a^3 b^2}{21 x^{21}}-\frac{5 a^2 b^3}{9 x^{18}}-\frac{5 a^4 b}{24 x^{24}}-\frac{a^5}{27 x^{27}}-\frac{a b^4}{3 x^{15}}-\frac{b^5}{12 x^{12}}",1,"-a^5/(27*x^27) - (5*a^4*b)/(24*x^24) - (10*a^3*b^2)/(21*x^21) - (5*a^2*b^3)/(9*x^18) - (a*b^4)/(3*x^15) - b^5/(12*x^12)","A",3,2,13,0.1538,1,"{266, 43}"
274,1,69,0,0.0299066,"\int \frac{\left(a+b x^3\right)^5}{x^{31}} \, dx","Int[(a + b*x^3)^5/x^31,x]","-\frac{5 a^3 b^2}{12 x^{24}}-\frac{10 a^2 b^3}{21 x^{21}}-\frac{5 a^4 b}{27 x^{27}}-\frac{a^5}{30 x^{30}}-\frac{5 a b^4}{18 x^{18}}-\frac{b^5}{15 x^{15}}","-\frac{5 a^3 b^2}{12 x^{24}}-\frac{10 a^2 b^3}{21 x^{21}}-\frac{5 a^4 b}{27 x^{27}}-\frac{a^5}{30 x^{30}}-\frac{5 a b^4}{18 x^{18}}-\frac{b^5}{15 x^{15}}",1,"-a^5/(30*x^30) - (5*a^4*b)/(27*x^27) - (5*a^3*b^2)/(12*x^24) - (10*a^2*b^3)/(21*x^21) - (5*a*b^4)/(18*x^18) - b^5/(15*x^15)","A",3,2,13,0.1538,1,"{266, 43}"
275,1,69,0,0.024613,"\int x^4 \left(a+b x^3\right)^5 \, dx","Int[x^4*(a + b*x^3)^5,x]","\frac{5}{7} a^2 b^3 x^{14}+\frac{10}{11} a^3 b^2 x^{11}+\frac{5}{8} a^4 b x^8+\frac{a^5 x^5}{5}+\frac{5}{17} a b^4 x^{17}+\frac{b^5 x^{20}}{20}","\frac{5}{7} a^2 b^3 x^{14}+\frac{10}{11} a^3 b^2 x^{11}+\frac{5}{8} a^4 b x^8+\frac{a^5 x^5}{5}+\frac{5}{17} a b^4 x^{17}+\frac{b^5 x^{20}}{20}",1,"(a^5*x^5)/5 + (5*a^4*b*x^8)/8 + (10*a^3*b^2*x^11)/11 + (5*a^2*b^3*x^14)/7 + (5*a*b^4*x^17)/17 + (b^5*x^20)/20","A",2,1,13,0.07692,1,"{270}"
276,1,66,0,0.0221241,"\int x^3 \left(a+b x^3\right)^5 \, dx","Int[x^3*(a + b*x^3)^5,x]","\frac{10}{13} a^2 b^3 x^{13}+a^3 b^2 x^{10}+\frac{5}{7} a^4 b x^7+\frac{a^5 x^4}{4}+\frac{5}{16} a b^4 x^{16}+\frac{b^5 x^{19}}{19}","\frac{10}{13} a^2 b^3 x^{13}+a^3 b^2 x^{10}+\frac{5}{7} a^4 b x^7+\frac{a^5 x^4}{4}+\frac{5}{16} a b^4 x^{16}+\frac{b^5 x^{19}}{19}",1,"(a^5*x^4)/4 + (5*a^4*b*x^7)/7 + a^3*b^2*x^10 + (10*a^2*b^3*x^13)/13 + (5*a*b^4*x^16)/16 + (b^5*x^19)/19","A",2,1,13,0.07692,1,"{270}"
277,1,66,0,0.0234117,"\int x \left(a+b x^3\right)^5 \, dx","Int[x*(a + b*x^3)^5,x]","\frac{10}{11} a^2 b^3 x^{11}+\frac{5}{4} a^3 b^2 x^8+a^4 b x^5+\frac{a^5 x^2}{2}+\frac{5}{14} a b^4 x^{14}+\frac{b^5 x^{17}}{17}","\frac{10}{11} a^2 b^3 x^{11}+\frac{5}{4} a^3 b^2 x^8+a^4 b x^5+\frac{a^5 x^2}{2}+\frac{5}{14} a b^4 x^{14}+\frac{b^5 x^{17}}{17}",1,"(a^5*x^2)/2 + a^4*b*x^5 + (5*a^3*b^2*x^8)/4 + (10*a^2*b^3*x^11)/11 + (5*a*b^4*x^14)/14 + (b^5*x^17)/17","A",2,1,11,0.09091,1,"{270}"
278,1,61,0,0.0193903,"\int \left(a+b x^3\right)^5 \, dx","Int[(a + b*x^3)^5,x]","a^2 b^3 x^{10}+\frac{10}{7} a^3 b^2 x^7+\frac{5}{4} a^4 b x^4+a^5 x+\frac{5}{13} a b^4 x^{13}+\frac{b^5 x^{16}}{16}","a^2 b^3 x^{10}+\frac{10}{7} a^3 b^2 x^7+\frac{5}{4} a^4 b x^4+a^5 x+\frac{5}{13} a b^4 x^{13}+\frac{b^5 x^{16}}{16}",1,"a^5*x + (5*a^4*b*x^4)/4 + (10*a^3*b^2*x^7)/7 + a^2*b^3*x^10 + (5*a*b^4*x^13)/13 + (b^5*x^16)/16","A",2,1,9,0.1111,1,"{194}"
279,1,65,0,0.0224125,"\int \frac{\left(a+b x^3\right)^5}{x^2} \, dx","Int[(a + b*x^3)^5/x^2,x]","\frac{5}{4} a^2 b^3 x^8+2 a^3 b^2 x^5+\frac{5}{2} a^4 b x^2-\frac{a^5}{x}+\frac{5}{11} a b^4 x^{11}+\frac{b^5 x^{14}}{14}","\frac{5}{4} a^2 b^3 x^8+2 a^3 b^2 x^5+\frac{5}{2} a^4 b x^2-\frac{a^5}{x}+\frac{5}{11} a b^4 x^{11}+\frac{b^5 x^{14}}{14}",1,"-(a^5/x) + (5*a^4*b*x^2)/2 + 2*a^3*b^2*x^5 + (5*a^2*b^3*x^8)/4 + (5*a*b^4*x^11)/11 + (b^5*x^14)/14","A",2,1,13,0.07692,1,"{270}"
280,1,65,0,0.0221762,"\int \frac{\left(a+b x^3\right)^5}{x^3} \, dx","Int[(a + b*x^3)^5/x^3,x]","\frac{10}{7} a^2 b^3 x^7+\frac{5}{2} a^3 b^2 x^4+5 a^4 b x-\frac{a^5}{2 x^2}+\frac{1}{2} a b^4 x^{10}+\frac{b^5 x^{13}}{13}","\frac{10}{7} a^2 b^3 x^7+\frac{5}{2} a^3 b^2 x^4+5 a^4 b x-\frac{a^5}{2 x^2}+\frac{1}{2} a b^4 x^{10}+\frac{b^5 x^{13}}{13}",1,"-a^5/(2*x^2) + 5*a^4*b*x + (5*a^3*b^2*x^4)/2 + (10*a^2*b^3*x^7)/7 + (a*b^4*x^10)/2 + (b^5*x^13)/13","A",2,1,13,0.07692,1,"{270}"
281,1,63,0,0.0234461,"\int \frac{\left(a+b x^3\right)^5}{x^5} \, dx","Int[(a + b*x^3)^5/x^5,x]","2 a^2 b^3 x^5+5 a^3 b^2 x^2-\frac{5 a^4 b}{x}-\frac{a^5}{4 x^4}+\frac{5}{8} a b^4 x^8+\frac{b^5 x^{11}}{11}","2 a^2 b^3 x^5+5 a^3 b^2 x^2-\frac{5 a^4 b}{x}-\frac{a^5}{4 x^4}+\frac{5}{8} a b^4 x^8+\frac{b^5 x^{11}}{11}",1,"-a^5/(4*x^4) - (5*a^4*b)/x + 5*a^3*b^2*x^2 + 2*a^2*b^3*x^5 + (5*a*b^4*x^8)/8 + (b^5*x^11)/11","A",2,1,13,0.07692,1,"{270}"
282,1,65,0,0.0213671,"\int \frac{\left(a+b x^3\right)^5}{x^6} \, dx","Int[(a + b*x^3)^5/x^6,x]","\frac{5}{2} a^2 b^3 x^4+10 a^3 b^2 x-\frac{5 a^4 b}{2 x^2}-\frac{a^5}{5 x^5}+\frac{5}{7} a b^4 x^7+\frac{b^5 x^{10}}{10}","\frac{5}{2} a^2 b^3 x^4+10 a^3 b^2 x-\frac{5 a^4 b}{2 x^2}-\frac{a^5}{5 x^5}+\frac{5}{7} a b^4 x^7+\frac{b^5 x^{10}}{10}",1,"-a^5/(5*x^5) - (5*a^4*b)/(2*x^2) + 10*a^3*b^2*x + (5*a^2*b^3*x^4)/2 + (5*a*b^4*x^7)/7 + (b^5*x^10)/10","A",2,1,13,0.07692,1,"{270}"
283,1,62,0,0.0231554,"\int \frac{\left(a+b x^3\right)^5}{x^8} \, dx","Int[(a + b*x^3)^5/x^8,x]","5 a^2 b^3 x^2-\frac{10 a^3 b^2}{x}-\frac{5 a^4 b}{4 x^4}-\frac{a^5}{7 x^7}+a b^4 x^5+\frac{b^5 x^8}{8}","5 a^2 b^3 x^2-\frac{10 a^3 b^2}{x}-\frac{5 a^4 b}{4 x^4}-\frac{a^5}{7 x^7}+a b^4 x^5+\frac{b^5 x^8}{8}",1,"-a^5/(7*x^7) - (5*a^4*b)/(4*x^4) - (10*a^3*b^2)/x + 5*a^2*b^3*x^2 + a*b^4*x^5 + (b^5*x^8)/8","A",2,1,13,0.07692,1,"{270}"
284,1,61,0,0.0224884,"\int \frac{\left(a+b x^3\right)^5}{x^9} \, dx","Int[(a + b*x^3)^5/x^9,x]","-\frac{5 a^3 b^2}{x^2}+10 a^2 b^3 x-\frac{a^4 b}{x^5}-\frac{a^5}{8 x^8}+\frac{5}{4} a b^4 x^4+\frac{b^5 x^7}{7}","-\frac{5 a^3 b^2}{x^2}+10 a^2 b^3 x-\frac{a^4 b}{x^5}-\frac{a^5}{8 x^8}+\frac{5}{4} a b^4 x^4+\frac{b^5 x^7}{7}",1,"-a^5/(8*x^8) - (a^4*b)/x^5 - (5*a^3*b^2)/x^2 + 10*a^2*b^3*x + (5*a*b^4*x^4)/4 + (b^5*x^7)/7","A",2,1,13,0.07692,1,"{270}"
285,1,129,0,0.2164763,"\int x^{20} \left(a+b x^3\right)^8 \, dx","Int[x^20*(a + b*x^3)^8,x]","\frac{5 a^2 \left(a+b x^3\right)^{13}}{13 b^7}-\frac{5 a^3 \left(a+b x^3\right)^{12}}{9 b^7}+\frac{5 a^4 \left(a+b x^3\right)^{11}}{11 b^7}-\frac{a^5 \left(a+b x^3\right)^{10}}{5 b^7}+\frac{a^6 \left(a+b x^3\right)^9}{27 b^7}+\frac{\left(a+b x^3\right)^{15}}{45 b^7}-\frac{a \left(a+b x^3\right)^{14}}{7 b^7}","\frac{5 a^2 \left(a+b x^3\right)^{13}}{13 b^7}-\frac{5 a^3 \left(a+b x^3\right)^{12}}{9 b^7}+\frac{5 a^4 \left(a+b x^3\right)^{11}}{11 b^7}-\frac{a^5 \left(a+b x^3\right)^{10}}{5 b^7}+\frac{a^6 \left(a+b x^3\right)^9}{27 b^7}+\frac{\left(a+b x^3\right)^{15}}{45 b^7}-\frac{a \left(a+b x^3\right)^{14}}{7 b^7}",1,"(a^6*(a + b*x^3)^9)/(27*b^7) - (a^5*(a + b*x^3)^10)/(5*b^7) + (5*a^4*(a + b*x^3)^11)/(11*b^7) - (5*a^3*(a + b*x^3)^12)/(9*b^7) + (5*a^2*(a + b*x^3)^13)/(13*b^7) - (a*(a + b*x^3)^14)/(7*b^7) + (a + b*x^3)^15/(45*b^7)","A",3,2,13,0.1538,1,"{266, 43}"
286,1,110,0,0.1726127,"\int x^{17} \left(a+b x^3\right)^8 \, dx","Int[x^17*(a + b*x^3)^8,x]","\frac{5 a^2 \left(a+b x^3\right)^{12}}{18 b^6}-\frac{10 a^3 \left(a+b x^3\right)^{11}}{33 b^6}+\frac{a^4 \left(a+b x^3\right)^{10}}{6 b^6}-\frac{a^5 \left(a+b x^3\right)^9}{27 b^6}+\frac{\left(a+b x^3\right)^{14}}{42 b^6}-\frac{5 a \left(a+b x^3\right)^{13}}{39 b^6}","\frac{5 a^2 \left(a+b x^3\right)^{12}}{18 b^6}-\frac{10 a^3 \left(a+b x^3\right)^{11}}{33 b^6}+\frac{a^4 \left(a+b x^3\right)^{10}}{6 b^6}-\frac{a^5 \left(a+b x^3\right)^9}{27 b^6}+\frac{\left(a+b x^3\right)^{14}}{42 b^6}-\frac{5 a \left(a+b x^3\right)^{13}}{39 b^6}",1,"-(a^5*(a + b*x^3)^9)/(27*b^6) + (a^4*(a + b*x^3)^10)/(6*b^6) - (10*a^3*(a + b*x^3)^11)/(33*b^6) + (5*a^2*(a + b*x^3)^12)/(18*b^6) - (5*a*(a + b*x^3)^13)/(39*b^6) + (a + b*x^3)^14/(42*b^6)","A",3,2,13,0.1538,1,"{266, 43}"
287,1,91,0,0.1403578,"\int x^{14} \left(a+b x^3\right)^8 \, dx","Int[x^14*(a + b*x^3)^8,x]","\frac{2 a^2 \left(a+b x^3\right)^{11}}{11 b^5}-\frac{2 a^3 \left(a+b x^3\right)^{10}}{15 b^5}+\frac{a^4 \left(a+b x^3\right)^9}{27 b^5}+\frac{\left(a+b x^3\right)^{13}}{39 b^5}-\frac{a \left(a+b x^3\right)^{12}}{9 b^5}","\frac{2 a^2 \left(a+b x^3\right)^{11}}{11 b^5}-\frac{2 a^3 \left(a+b x^3\right)^{10}}{15 b^5}+\frac{a^4 \left(a+b x^3\right)^9}{27 b^5}+\frac{\left(a+b x^3\right)^{13}}{39 b^5}-\frac{a \left(a+b x^3\right)^{12}}{9 b^5}",1,"(a^4*(a + b*x^3)^9)/(27*b^5) - (2*a^3*(a + b*x^3)^10)/(15*b^5) + (2*a^2*(a + b*x^3)^11)/(11*b^5) - (a*(a + b*x^3)^12)/(9*b^5) + (a + b*x^3)^13/(39*b^5)","A",3,2,13,0.1538,1,"{266, 43}"
288,1,72,0,0.1099872,"\int x^{11} \left(a+b x^3\right)^8 \, dx","Int[x^11*(a + b*x^3)^8,x]","\frac{a^2 \left(a+b x^3\right)^{10}}{10 b^4}-\frac{a^3 \left(a+b x^3\right)^9}{27 b^4}+\frac{\left(a+b x^3\right)^{12}}{36 b^4}-\frac{a \left(a+b x^3\right)^{11}}{11 b^4}","\frac{a^2 \left(a+b x^3\right)^{10}}{10 b^4}-\frac{a^3 \left(a+b x^3\right)^9}{27 b^4}+\frac{\left(a+b x^3\right)^{12}}{36 b^4}-\frac{a \left(a+b x^3\right)^{11}}{11 b^4}",1,"-(a^3*(a + b*x^3)^9)/(27*b^4) + (a^2*(a + b*x^3)^10)/(10*b^4) - (a*(a + b*x^3)^11)/(11*b^4) + (a + b*x^3)^12/(36*b^4)","A",3,2,13,0.1538,1,"{266, 43}"
289,1,53,0,0.0794962,"\int x^8 \left(a+b x^3\right)^8 \, dx","Int[x^8*(a + b*x^3)^8,x]","\frac{a^2 \left(a+b x^3\right)^9}{27 b^3}+\frac{\left(a+b x^3\right)^{11}}{33 b^3}-\frac{a \left(a+b x^3\right)^{10}}{15 b^3}","\frac{a^2 \left(a+b x^3\right)^9}{27 b^3}+\frac{\left(a+b x^3\right)^{11}}{33 b^3}-\frac{a \left(a+b x^3\right)^{10}}{15 b^3}",1,"(a^2*(a + b*x^3)^9)/(27*b^3) - (a*(a + b*x^3)^10)/(15*b^3) + (a + b*x^3)^11/(33*b^3)","A",3,2,13,0.1538,1,"{266, 43}"
290,1,34,0,0.0429557,"\int x^5 \left(a+b x^3\right)^8 \, dx","Int[x^5*(a + b*x^3)^8,x]","\frac{\left(a+b x^3\right)^{10}}{30 b^2}-\frac{a \left(a+b x^3\right)^9}{27 b^2}","\frac{\left(a+b x^3\right)^{10}}{30 b^2}-\frac{a \left(a+b x^3\right)^9}{27 b^2}",1,"-(a*(a + b*x^3)^9)/(27*b^2) + (a + b*x^3)^10/(30*b^2)","A",3,2,13,0.1538,1,"{266, 43}"
291,1,16,0,0.0028053,"\int x^2 \left(a+b x^3\right)^8 \, dx","Int[x^2*(a + b*x^3)^8,x]","\frac{\left(a+b x^3\right)^9}{27 b}","\frac{\left(a+b x^3\right)^9}{27 b}",1,"(a + b*x^3)^9/(27*b)","A",1,1,13,0.07692,1,"{261}"
292,1,104,0,0.0551169,"\int \frac{\left(a+b x^3\right)^8}{x} \, dx","Int[(a + b*x^3)^8/x,x]","\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 (x)+\frac{8}{21} a b^7 x^{21}+\frac{b^8 x^{24}}{24}","\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 (x)+\frac{8}{21} a b^7 x^{21}+\frac{b^8 x^{24}}{24}",1,"(8*a^7*b*x^3)/3 + (14*a^6*b^2*x^6)/3 + (56*a^5*b^3*x^9)/9 + (35*a^4*b^4*x^12)/6 + (56*a^3*b^5*x^15)/15 + (14*a^2*b^6*x^18)/9 + (8*a*b^7*x^21)/21 + (b^8*x^24)/24 + a^8*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
293,1,105,0,0.0582046,"\int \frac{\left(a+b x^3\right)^8}{x^4} \, dx","Int[(a + b*x^3)^8/x^4,x]","\frac{28}{15} a^2 b^6 x^{15}+\frac{14}{3} a^3 b^5 x^{12}+\frac{70}{9} a^4 b^4 x^9+\frac{28}{3} a^5 b^3 x^6+\frac{28}{3} a^6 b^2 x^3+8 a^7 b \log (x)-\frac{a^8}{3 x^3}+\frac{4}{9} a b^7 x^{18}+\frac{b^8 x^{21}}{21}","\frac{28}{15} a^2 b^6 x^{15}+\frac{14}{3} a^3 b^5 x^{12}+\frac{70}{9} a^4 b^4 x^9+\frac{28}{3} a^5 b^3 x^6+\frac{28}{3} a^6 b^2 x^3+8 a^7 b \log (x)-\frac{a^8}{3 x^3}+\frac{4}{9} a b^7 x^{18}+\frac{b^8 x^{21}}{21}",1,"-a^8/(3*x^3) + (28*a^6*b^2*x^3)/3 + (28*a^5*b^3*x^6)/3 + (70*a^4*b^4*x^9)/9 + (14*a^3*b^5*x^12)/3 + (28*a^2*b^6*x^15)/15 + (4*a*b^7*x^18)/9 + (b^8*x^21)/21 + 8*a^7*b*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
294,1,105,0,0.0584267,"\int \frac{\left(a+b x^3\right)^8}{x^7} \, dx","Int[(a + b*x^3)^8/x^7,x]","\frac{7}{3} a^2 b^6 x^{12}+\frac{56}{9} a^3 b^5 x^9+\frac{35}{3} a^4 b^4 x^6+\frac{56}{3} a^5 b^3 x^3+28 a^6 b^2 \log (x)-\frac{8 a^7 b}{3 x^3}-\frac{a^8}{6 x^6}+\frac{8}{15} a b^7 x^{15}+\frac{b^8 x^{18}}{18}","\frac{7}{3} a^2 b^6 x^{12}+\frac{56}{9} a^3 b^5 x^9+\frac{35}{3} a^4 b^4 x^6+\frac{56}{3} a^5 b^3 x^3+28 a^6 b^2 \log (x)-\frac{8 a^7 b}{3 x^3}-\frac{a^8}{6 x^6}+\frac{8}{15} a b^7 x^{15}+\frac{b^8 x^{18}}{18}",1,"-a^8/(6*x^6) - (8*a^7*b)/(3*x^3) + (56*a^5*b^3*x^3)/3 + (35*a^4*b^4*x^6)/3 + (56*a^3*b^5*x^9)/9 + (7*a^2*b^6*x^12)/3 + (8*a*b^7*x^15)/15 + (b^8*x^18)/18 + 28*a^6*b^2*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
295,1,105,0,0.0556131,"\int \frac{\left(a+b x^3\right)^8}{x^{10}} \, dx","Int[(a + b*x^3)^8/x^10,x]","\frac{28}{9} a^2 b^6 x^9+\frac{28}{3} a^3 b^5 x^6+\frac{70}{3} a^4 b^4 x^3-\frac{28 a^6 b^2}{3 x^3}+56 a^5 b^3 \log (x)-\frac{4 a^7 b}{3 x^6}-\frac{a^8}{9 x^9}+\frac{2}{3} a b^7 x^{12}+\frac{b^8 x^{15}}{15}","\frac{28}{9} a^2 b^6 x^9+\frac{28}{3} a^3 b^5 x^6+\frac{70}{3} a^4 b^4 x^3-\frac{28 a^6 b^2}{3 x^3}+56 a^5 b^3 \log (x)-\frac{4 a^7 b}{3 x^6}-\frac{a^8}{9 x^9}+\frac{2}{3} a b^7 x^{12}+\frac{b^8 x^{15}}{15}",1,"-a^8/(9*x^9) - (4*a^7*b)/(3*x^6) - (28*a^6*b^2)/(3*x^3) + (70*a^4*b^4*x^3)/3 + (28*a^3*b^5*x^6)/3 + (28*a^2*b^6*x^9)/9 + (2*a*b^7*x^12)/3 + (b^8*x^15)/15 + 56*a^5*b^3*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
296,1,105,0,0.0560571,"\int \frac{\left(a+b x^3\right)^8}{x^{13}} \, dx","Int[(a + b*x^3)^8/x^13,x]","\frac{14}{3} a^2 b^6 x^6+\frac{56}{3} a^3 b^5 x^3-\frac{56 a^5 b^3}{3 x^3}-\frac{14 a^6 b^2}{3 x^6}+70 a^4 b^4 \log (x)-\frac{8 a^7 b}{9 x^9}-\frac{a^8}{12 x^{12}}+\frac{8}{9} a b^7 x^9+\frac{b^8 x^{12}}{12}","\frac{14}{3} a^2 b^6 x^6+\frac{56}{3} a^3 b^5 x^3-\frac{56 a^5 b^3}{3 x^3}-\frac{14 a^6 b^2}{3 x^6}+70 a^4 b^4 \log (x)-\frac{8 a^7 b}{9 x^9}-\frac{a^8}{12 x^{12}}+\frac{8}{9} a b^7 x^9+\frac{b^8 x^{12}}{12}",1,"-a^8/(12*x^12) - (8*a^7*b)/(9*x^9) - (14*a^6*b^2)/(3*x^6) - (56*a^5*b^3)/(3*x^3) + (56*a^3*b^5*x^3)/3 + (14*a^2*b^6*x^6)/3 + (8*a*b^7*x^9)/9 + (b^8*x^12)/12 + 70*a^4*b^4*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
297,1,105,0,0.0598809,"\int \frac{\left(a+b x^3\right)^8}{x^{16}} \, dx","Int[(a + b*x^3)^8/x^16,x]","\frac{28}{3} a^2 b^6 x^3-\frac{70 a^4 b^4}{3 x^3}-\frac{28 a^5 b^3}{3 x^6}-\frac{28 a^6 b^2}{9 x^9}+56 a^3 b^5 \log (x)-\frac{2 a^7 b}{3 x^{12}}-\frac{a^8}{15 x^{15}}+\frac{4}{3} a b^7 x^6+\frac{b^8 x^9}{9}","\frac{28}{3} a^2 b^6 x^3-\frac{70 a^4 b^4}{3 x^3}-\frac{28 a^5 b^3}{3 x^6}-\frac{28 a^6 b^2}{9 x^9}+56 a^3 b^5 \log (x)-\frac{2 a^7 b}{3 x^{12}}-\frac{a^8}{15 x^{15}}+\frac{4}{3} a b^7 x^6+\frac{b^8 x^9}{9}",1,"-a^8/(15*x^15) - (2*a^7*b)/(3*x^12) - (28*a^6*b^2)/(9*x^9) - (28*a^5*b^3)/(3*x^6) - (70*a^4*b^4)/(3*x^3) + (28*a^2*b^6*x^3)/3 + (4*a*b^7*x^6)/3 + (b^8*x^9)/9 + 56*a^3*b^5*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
298,1,105,0,0.0553437,"\int \frac{\left(a+b x^3\right)^8}{x^{19}} \, dx","Int[(a + b*x^3)^8/x^19,x]","-\frac{7 a^6 b^2}{3 x^{12}}-\frac{56 a^5 b^3}{9 x^9}-\frac{35 a^4 b^4}{3 x^6}-\frac{56 a^3 b^5}{3 x^3}+28 a^2 b^6 \log (x)-\frac{8 a^7 b}{15 x^{15}}-\frac{a^8}{18 x^{18}}+\frac{8}{3} a b^7 x^3+\frac{b^8 x^6}{6}","-\frac{7 a^6 b^2}{3 x^{12}}-\frac{56 a^5 b^3}{9 x^9}-\frac{35 a^4 b^4}{3 x^6}-\frac{56 a^3 b^5}{3 x^3}+28 a^2 b^6 \log (x)-\frac{8 a^7 b}{15 x^{15}}-\frac{a^8}{18 x^{18}}+\frac{8}{3} a b^7 x^3+\frac{b^8 x^6}{6}",1,"-a^8/(18*x^18) - (8*a^7*b)/(15*x^15) - (7*a^6*b^2)/(3*x^12) - (56*a^5*b^3)/(9*x^9) - (35*a^4*b^4)/(3*x^6) - (56*a^3*b^5)/(3*x^3) + (8*a*b^7*x^3)/3 + (b^8*x^6)/6 + 28*a^2*b^6*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
299,1,105,0,0.0538065,"\int \frac{\left(a+b x^3\right)^8}{x^{22}} \, dx","Int[(a + b*x^3)^8/x^22,x]","-\frac{28 a^6 b^2}{15 x^{15}}-\frac{14 a^5 b^3}{3 x^{12}}-\frac{70 a^4 b^4}{9 x^9}-\frac{28 a^3 b^5}{3 x^6}-\frac{28 a^2 b^6}{3 x^3}-\frac{4 a^7 b}{9 x^{18}}-\frac{a^8}{21 x^{21}}+8 a b^7 \log (x)+\frac{b^8 x^3}{3}","-\frac{28 a^6 b^2}{15 x^{15}}-\frac{14 a^5 b^3}{3 x^{12}}-\frac{70 a^4 b^4}{9 x^9}-\frac{28 a^3 b^5}{3 x^6}-\frac{28 a^2 b^6}{3 x^3}-\frac{4 a^7 b}{9 x^{18}}-\frac{a^8}{21 x^{21}}+8 a b^7 \log (x)+\frac{b^8 x^3}{3}",1,"-a^8/(21*x^21) - (4*a^7*b)/(9*x^18) - (28*a^6*b^2)/(15*x^15) - (14*a^5*b^3)/(3*x^12) - (70*a^4*b^4)/(9*x^9) - (28*a^3*b^5)/(3*x^6) - (28*a^2*b^6)/(3*x^3) + (b^8*x^3)/3 + 8*a*b^7*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
300,1,104,0,0.0507342,"\int \frac{\left(a+b x^3\right)^8}{x^{25}} \, dx","Int[(a + b*x^3)^8/x^25,x]","-\frac{14 a^6 b^2}{9 x^{18}}-\frac{56 a^5 b^3}{15 x^{15}}-\frac{35 a^4 b^4}{6 x^{12}}-\frac{56 a^3 b^5}{9 x^9}-\frac{14 a^2 b^6}{3 x^6}-\frac{8 a^7 b}{21 x^{21}}-\frac{a^8}{24 x^{24}}-\frac{8 a b^7}{3 x^3}+b^8 \log (x)","-\frac{14 a^6 b^2}{9 x^{18}}-\frac{56 a^5 b^3}{15 x^{15}}-\frac{35 a^4 b^4}{6 x^{12}}-\frac{56 a^3 b^5}{9 x^9}-\frac{14 a^2 b^6}{3 x^6}-\frac{8 a^7 b}{21 x^{21}}-\frac{a^8}{24 x^{24}}-\frac{8 a b^7}{3 x^3}+b^8 \log (x)",1,"-a^8/(24*x^24) - (8*a^7*b)/(21*x^21) - (14*a^6*b^2)/(9*x^18) - (56*a^5*b^3)/(15*x^15) - (35*a^4*b^4)/(6*x^12) - (56*a^3*b^5)/(9*x^9) - (14*a^2*b^6)/(3*x^6) - (8*a*b^7)/(3*x^3) + b^8*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
301,1,19,0,0.0031577,"\int \frac{\left(a+b x^3\right)^8}{x^{28}} \, dx","Int[(a + b*x^3)^8/x^28,x]","-\frac{\left(a+b x^3\right)^9}{27 a x^{27}}","-\frac{\left(a+b x^3\right)^9}{27 a x^{27}}",1,"-(a + b*x^3)^9/(27*a*x^27)","A",1,1,13,0.07692,1,"{264}"
302,1,40,0,0.0176665,"\int \frac{\left(a+b x^3\right)^8}{x^{31}} \, dx","Int[(a + b*x^3)^8/x^31,x]","\frac{b \left(a+b x^3\right)^9}{270 a^2 x^{27}}-\frac{\left(a+b x^3\right)^9}{30 a x^{30}}","\frac{b \left(a+b x^3\right)^9}{270 a^2 x^{27}}-\frac{\left(a+b x^3\right)^9}{30 a x^{30}}",1,"-(a + b*x^3)^9/(30*a*x^30) + (b*(a + b*x^3)^9)/(270*a^2*x^27)","A",3,3,13,0.2308,1,"{266, 45, 37}"
303,1,62,0,0.0267899,"\int \frac{\left(a+b x^3\right)^8}{x^{34}} \, dx","Int[(a + b*x^3)^8/x^34,x]","-\frac{b^2 \left(a+b x^3\right)^9}{1485 a^3 x^{27}}+\frac{b \left(a+b x^3\right)^9}{165 a^2 x^{30}}-\frac{\left(a+b x^3\right)^9}{33 a x^{33}}","-\frac{b^2 \left(a+b x^3\right)^9}{1485 a^3 x^{27}}+\frac{b \left(a+b x^3\right)^9}{165 a^2 x^{30}}-\frac{\left(a+b x^3\right)^9}{33 a x^{33}}",1,"-(a + b*x^3)^9/(33*a*x^33) + (b*(a + b*x^3)^9)/(165*a^2*x^30) - (b^2*(a + b*x^3)^9)/(1485*a^3*x^27)","A",4,3,13,0.2308,1,"{266, 45, 37}"
304,1,84,0,0.0393221,"\int \frac{\left(a+b x^3\right)^8}{x^{37}} \, dx","Int[(a + b*x^3)^8/x^37,x]","\frac{b^3 \left(a+b x^3\right)^9}{5940 a^4 x^{27}}-\frac{b^2 \left(a+b x^3\right)^9}{660 a^3 x^{30}}+\frac{b \left(a+b x^3\right)^9}{132 a^2 x^{33}}-\frac{\left(a+b x^3\right)^9}{36 a x^{36}}","\frac{b^3 \left(a+b x^3\right)^9}{5940 a^4 x^{27}}-\frac{b^2 \left(a+b x^3\right)^9}{660 a^3 x^{30}}+\frac{b \left(a+b x^3\right)^9}{132 a^2 x^{33}}-\frac{\left(a+b x^3\right)^9}{36 a x^{36}}",1,"-(a + b*x^3)^9/(36*a*x^36) + (b*(a + b*x^3)^9)/(132*a^2*x^33) - (b^2*(a + b*x^3)^9)/(660*a^3*x^30) + (b^3*(a + b*x^3)^9)/(5940*a^4*x^27)","A",5,3,13,0.2308,1,"{266, 45, 37}"
305,1,106,0,0.0521462,"\int \frac{\left(a+b x^3\right)^8}{x^{40}} \, dx","Int[(a + b*x^3)^8/x^40,x]","-\frac{b^4 \left(a+b x^3\right)^9}{19305 a^5 x^{27}}+\frac{b^3 \left(a+b x^3\right)^9}{2145 a^4 x^{30}}-\frac{b^2 \left(a+b x^3\right)^9}{429 a^3 x^{33}}+\frac{b \left(a+b x^3\right)^9}{117 a^2 x^{36}}-\frac{\left(a+b x^3\right)^9}{39 a x^{39}}","-\frac{b^4 \left(a+b x^3\right)^9}{19305 a^5 x^{27}}+\frac{b^3 \left(a+b x^3\right)^9}{2145 a^4 x^{30}}-\frac{b^2 \left(a+b x^3\right)^9}{429 a^3 x^{33}}+\frac{b \left(a+b x^3\right)^9}{117 a^2 x^{36}}-\frac{\left(a+b x^3\right)^9}{39 a x^{39}}",1,"-(a + b*x^3)^9/(39*a*x^39) + (b*(a + b*x^3)^9)/(117*a^2*x^36) - (b^2*(a + b*x^3)^9)/(429*a^3*x^33) + (b^3*(a + b*x^3)^9)/(2145*a^4*x^30) - (b^4*(a + b*x^3)^9)/(19305*a^5*x^27)","A",6,3,13,0.2308,1,"{266, 45, 37}"
306,1,108,0,0.05092,"\int \frac{\left(a+b x^3\right)^8}{x^{43}} \, dx","Int[(a + b*x^3)^8/x^43,x]","-\frac{7 a^6 b^2}{9 x^{36}}-\frac{56 a^5 b^3}{33 x^{33}}-\frac{7 a^4 b^4}{3 x^{30}}-\frac{56 a^3 b^5}{27 x^{27}}-\frac{7 a^2 b^6}{6 x^{24}}-\frac{8 a^7 b}{39 x^{39}}-\frac{a^8}{42 x^{42}}-\frac{8 a b^7}{21 x^{21}}-\frac{b^8}{18 x^{18}}","-\frac{7 a^6 b^2}{9 x^{36}}-\frac{56 a^5 b^3}{33 x^{33}}-\frac{7 a^4 b^4}{3 x^{30}}-\frac{56 a^3 b^5}{27 x^{27}}-\frac{7 a^2 b^6}{6 x^{24}}-\frac{8 a^7 b}{39 x^{39}}-\frac{a^8}{42 x^{42}}-\frac{8 a b^7}{21 x^{21}}-\frac{b^8}{18 x^{18}}",1,"-a^8/(42*x^42) - (8*a^7*b)/(39*x^39) - (7*a^6*b^2)/(9*x^36) - (56*a^5*b^3)/(33*x^33) - (7*a^4*b^4)/(3*x^30) - (56*a^3*b^5)/(27*x^27) - (7*a^2*b^6)/(6*x^24) - (8*a*b^7)/(21*x^21) - b^8/(18*x^18)","A",3,2,13,0.1538,1,"{266, 43}"
307,1,108,0,0.0492615,"\int \frac{\left(a+b x^3\right)^8}{x^{46}} \, dx","Int[(a + b*x^3)^8/x^46,x]","-\frac{28 a^6 b^2}{39 x^{39}}-\frac{14 a^5 b^3}{9 x^{36}}-\frac{70 a^4 b^4}{33 x^{33}}-\frac{28 a^3 b^5}{15 x^{30}}-\frac{28 a^2 b^6}{27 x^{27}}-\frac{4 a^7 b}{21 x^{42}}-\frac{a^8}{45 x^{45}}-\frac{a b^7}{3 x^{24}}-\frac{b^8}{21 x^{21}}","-\frac{28 a^6 b^2}{39 x^{39}}-\frac{14 a^5 b^3}{9 x^{36}}-\frac{70 a^4 b^4}{33 x^{33}}-\frac{28 a^3 b^5}{15 x^{30}}-\frac{28 a^2 b^6}{27 x^{27}}-\frac{4 a^7 b}{21 x^{42}}-\frac{a^8}{45 x^{45}}-\frac{a b^7}{3 x^{24}}-\frac{b^8}{21 x^{21}}",1,"-a^8/(45*x^45) - (4*a^7*b)/(21*x^42) - (28*a^6*b^2)/(39*x^39) - (14*a^5*b^3)/(9*x^36) - (70*a^4*b^4)/(33*x^33) - (28*a^3*b^5)/(15*x^30) - (28*a^2*b^6)/(27*x^27) - (a*b^7)/(3*x^24) - b^8/(21*x^21)","A",3,2,13,0.1538,1,"{266, 43}"
308,1,103,0,0.0449214,"\int x^4 \left(a+b x^3\right)^8 \, dx","Int[x^4*(a + b*x^3)^8,x]","\frac{28}{23} a^2 b^6 x^{23}+\frac{14}{5} a^3 b^5 x^{20}+\frac{70}{17} a^4 b^4 x^{17}+4 a^5 b^3 x^{14}+\frac{28}{11} a^6 b^2 x^{11}+a^7 b x^8+\frac{a^8 x^5}{5}+\frac{4}{13} a b^7 x^{26}+\frac{b^8 x^{29}}{29}","\frac{28}{23} a^2 b^6 x^{23}+\frac{14}{5} a^3 b^5 x^{20}+\frac{70}{17} a^4 b^4 x^{17}+4 a^5 b^3 x^{14}+\frac{28}{11} a^6 b^2 x^{11}+a^7 b x^8+\frac{a^8 x^5}{5}+\frac{4}{13} a b^7 x^{26}+\frac{b^8 x^{29}}{29}",1,"(a^8*x^5)/5 + a^7*b*x^8 + (28*a^6*b^2*x^11)/11 + 4*a^5*b^3*x^14 + (70*a^4*b^4*x^17)/17 + (14*a^3*b^5*x^20)/5 + (28*a^2*b^6*x^23)/23 + (4*a*b^7*x^26)/13 + (b^8*x^29)/29","A",2,1,13,0.07692,1,"{270}"
309,1,108,0,0.0388762,"\int x^3 \left(a+b x^3\right)^8 \, dx","Int[x^3*(a + b*x^3)^8,x]","\frac{14}{11} a^2 b^6 x^{22}+\frac{56}{19} a^3 b^5 x^{19}+\frac{35}{8} a^4 b^4 x^{16}+\frac{56}{13} a^5 b^3 x^{13}+\frac{14}{5} a^6 b^2 x^{10}+\frac{8}{7} a^7 b x^7+\frac{a^8 x^4}{4}+\frac{8}{25} a b^7 x^{25}+\frac{b^8 x^{28}}{28}","\frac{14}{11} a^2 b^6 x^{22}+\frac{56}{19} a^3 b^5 x^{19}+\frac{35}{8} a^4 b^4 x^{16}+\frac{56}{13} a^5 b^3 x^{13}+\frac{14}{5} a^6 b^2 x^{10}+\frac{8}{7} a^7 b x^7+\frac{a^8 x^4}{4}+\frac{8}{25} a b^7 x^{25}+\frac{b^8 x^{28}}{28}",1,"(a^8*x^4)/4 + (8*a^7*b*x^7)/7 + (14*a^6*b^2*x^10)/5 + (56*a^5*b^3*x^13)/13 + (35*a^4*b^4*x^16)/8 + (56*a^3*b^5*x^19)/19 + (14*a^2*b^6*x^22)/11 + (8*a*b^7*x^25)/25 + (b^8*x^28)/28","A",2,1,13,0.07692,1,"{270}"
310,1,106,0,0.038971,"\int x \left(a+b x^3\right)^8 \, dx","Int[x*(a + b*x^3)^8,x]","\frac{7}{5} a^2 b^6 x^{20}+\frac{56}{17} a^3 b^5 x^{17}+5 a^4 b^4 x^{14}+\frac{56}{11} a^5 b^3 x^{11}+\frac{7}{2} a^6 b^2 x^8+\frac{8}{5} a^7 b x^5+\frac{a^8 x^2}{2}+\frac{8}{23} a b^7 x^{23}+\frac{b^8 x^{26}}{26}","\frac{7}{5} a^2 b^6 x^{20}+\frac{56}{17} a^3 b^5 x^{17}+5 a^4 b^4 x^{14}+\frac{56}{11} a^5 b^3 x^{11}+\frac{7}{2} a^6 b^2 x^8+\frac{8}{5} a^7 b x^5+\frac{a^8 x^2}{2}+\frac{8}{23} a b^7 x^{23}+\frac{b^8 x^{26}}{26}",1,"(a^8*x^2)/2 + (8*a^7*b*x^5)/5 + (7*a^6*b^2*x^8)/2 + (56*a^5*b^3*x^11)/11 + 5*a^4*b^4*x^14 + (56*a^3*b^5*x^17)/17 + (7*a^2*b^6*x^20)/5 + (8*a*b^7*x^23)/23 + (b^8*x^26)/26","A",2,1,11,0.09091,1,"{270}"
311,1,99,0,0.037282,"\int \left(a+b x^3\right)^8 \, dx","Int[(a + b*x^3)^8,x]","\frac{28}{19} a^2 b^6 x^{19}+\frac{7}{2} a^3 b^5 x^{16}+\frac{70}{13} a^4 b^4 x^{13}+\frac{28}{5} a^5 b^3 x^{10}+4 a^6 b^2 x^7+2 a^7 b x^4+a^8 x+\frac{4}{11} a b^7 x^{22}+\frac{b^8 x^{25}}{25}","\frac{28}{19} a^2 b^6 x^{19}+\frac{7}{2} a^3 b^5 x^{16}+\frac{70}{13} a^4 b^4 x^{13}+\frac{28}{5} a^5 b^3 x^{10}+4 a^6 b^2 x^7+2 a^7 b x^4+a^8 x+\frac{4}{11} a b^7 x^{22}+\frac{b^8 x^{25}}{25}",1,"a^8*x + 2*a^7*b*x^4 + 4*a^6*b^2*x^7 + (28*a^5*b^3*x^10)/5 + (70*a^4*b^4*x^13)/13 + (7*a^3*b^5*x^16)/2 + (28*a^2*b^6*x^19)/19 + (4*a*b^7*x^22)/11 + (b^8*x^25)/25","A",2,1,9,0.1111,1,"{194}"
312,1,100,0,0.0395976,"\int \frac{\left(a+b x^3\right)^8}{x^2} \, dx","Int[(a + b*x^3)^8/x^2,x]","\frac{28}{17} a^2 b^6 x^{17}+4 a^3 b^5 x^{14}+\frac{70}{11} a^4 b^4 x^{11}+7 a^5 b^3 x^8+\frac{28}{5} a^6 b^2 x^5+4 a^7 b x^2-\frac{a^8}{x}+\frac{2}{5} a b^7 x^{20}+\frac{b^8 x^{23}}{23}","\frac{28}{17} a^2 b^6 x^{17}+4 a^3 b^5 x^{14}+\frac{70}{11} a^4 b^4 x^{11}+7 a^5 b^3 x^8+\frac{28}{5} a^6 b^2 x^5+4 a^7 b x^2-\frac{a^8}{x}+\frac{2}{5} a b^7 x^{20}+\frac{b^8 x^{23}}{23}",1,"-(a^8/x) + 4*a^7*b*x^2 + (28*a^6*b^2*x^5)/5 + 7*a^5*b^3*x^8 + (70*a^4*b^4*x^11)/11 + 4*a^3*b^5*x^14 + (28*a^2*b^6*x^17)/17 + (2*a*b^7*x^20)/5 + (b^8*x^23)/23","A",2,1,13,0.07692,1,"{270}"
313,1,98,0,0.0371823,"\int \frac{\left(a+b x^3\right)^8}{x^3} \, dx","Int[(a + b*x^3)^8/x^3,x]","\frac{7}{4} a^2 b^6 x^{16}+\frac{56}{13} a^3 b^5 x^{13}+7 a^4 b^4 x^{10}+8 a^5 b^3 x^7+7 a^6 b^2 x^4+8 a^7 b x-\frac{a^8}{2 x^2}+\frac{8}{19} a b^7 x^{19}+\frac{b^8 x^{22}}{22}","\frac{7}{4} a^2 b^6 x^{16}+\frac{56}{13} a^3 b^5 x^{13}+7 a^4 b^4 x^{10}+8 a^5 b^3 x^7+7 a^6 b^2 x^4+8 a^7 b x-\frac{a^8}{2 x^2}+\frac{8}{19} a b^7 x^{19}+\frac{b^8 x^{22}}{22}",1,"-a^8/(2*x^2) + 8*a^7*b*x + 7*a^6*b^2*x^4 + 8*a^5*b^3*x^7 + 7*a^4*b^4*x^10 + (56*a^3*b^5*x^13)/13 + (7*a^2*b^6*x^16)/4 + (8*a*b^7*x^19)/19 + (b^8*x^22)/22","A",2,1,13,0.07692,1,"{270}"
314,1,102,0,0.0375903,"\int \frac{\left(a+b x^3\right)^8}{x^5} \, dx","Int[(a + b*x^3)^8/x^5,x]","2 a^2 b^6 x^{14}+\frac{56}{11} a^3 b^5 x^{11}+\frac{35}{4} a^4 b^4 x^8+\frac{56}{5} a^5 b^3 x^5+14 a^6 b^2 x^2-\frac{8 a^7 b}{x}-\frac{a^8}{4 x^4}+\frac{8}{17} a b^7 x^{17}+\frac{b^8 x^{20}}{20}","2 a^2 b^6 x^{14}+\frac{56}{11} a^3 b^5 x^{11}+\frac{35}{4} a^4 b^4 x^8+\frac{56}{5} a^5 b^3 x^5+14 a^6 b^2 x^2-\frac{8 a^7 b}{x}-\frac{a^8}{4 x^4}+\frac{8}{17} a b^7 x^{17}+\frac{b^8 x^{20}}{20}",1,"-a^8/(4*x^4) - (8*a^7*b)/x + 14*a^6*b^2*x^2 + (56*a^5*b^3*x^5)/5 + (35*a^4*b^4*x^8)/4 + (56*a^3*b^5*x^11)/11 + 2*a^2*b^6*x^14 + (8*a*b^7*x^17)/17 + (b^8*x^20)/20","A",2,1,13,0.07692,1,"{270}"
315,1,98,0,0.0364757,"\int \frac{\left(a+b x^3\right)^8}{x^6} \, dx","Int[(a + b*x^3)^8/x^6,x]","\frac{28}{13} a^2 b^6 x^{13}+\frac{28}{5} a^3 b^5 x^{10}+10 a^4 b^4 x^7+14 a^5 b^3 x^4+28 a^6 b^2 x-\frac{4 a^7 b}{x^2}-\frac{a^8}{5 x^5}+\frac{1}{2} a b^7 x^{16}+\frac{b^8 x^{19}}{19}","\frac{28}{13} a^2 b^6 x^{13}+\frac{28}{5} a^3 b^5 x^{10}+10 a^4 b^4 x^7+14 a^5 b^3 x^4+28 a^6 b^2 x-\frac{4 a^7 b}{x^2}-\frac{a^8}{5 x^5}+\frac{1}{2} a b^7 x^{16}+\frac{b^8 x^{19}}{19}",1,"-a^8/(5*x^5) - (4*a^7*b)/x^2 + 28*a^6*b^2*x + 14*a^5*b^3*x^4 + 10*a^4*b^4*x^7 + (28*a^3*b^5*x^10)/5 + (28*a^2*b^6*x^13)/13 + (a*b^7*x^16)/2 + (b^8*x^19)/19","A",2,1,13,0.07692,1,"{270}"
316,1,98,0,0.0371253,"\int \frac{\left(a+b x^3\right)^8}{x^8} \, dx","Int[(a + b*x^3)^8/x^8,x]","\frac{28}{11} a^2 b^6 x^{11}+7 a^3 b^5 x^8+14 a^4 b^4 x^5+28 a^5 b^3 x^2-\frac{28 a^6 b^2}{x}-\frac{2 a^7 b}{x^4}-\frac{a^8}{7 x^7}+\frac{4}{7} a b^7 x^{14}+\frac{b^8 x^{17}}{17}","\frac{28}{11} a^2 b^6 x^{11}+7 a^3 b^5 x^8+14 a^4 b^4 x^5+28 a^5 b^3 x^2-\frac{28 a^6 b^2}{x}-\frac{2 a^7 b}{x^4}-\frac{a^8}{7 x^7}+\frac{4}{7} a b^7 x^{14}+\frac{b^8 x^{17}}{17}",1,"-a^8/(7*x^7) - (2*a^7*b)/x^4 - (28*a^6*b^2)/x + 28*a^5*b^3*x^2 + 14*a^4*b^4*x^5 + 7*a^3*b^5*x^8 + (28*a^2*b^6*x^11)/11 + (4*a*b^7*x^14)/7 + (b^8*x^17)/17","A",2,1,13,0.07692,1,"{270}"
317,1,100,0,0.0358057,"\int \frac{\left(a+b x^3\right)^8}{x^9} \, dx","Int[(a + b*x^3)^8/x^9,x]","\frac{14}{5} a^2 b^6 x^{10}+8 a^3 b^5 x^7+\frac{35}{2} a^4 b^4 x^4-\frac{14 a^6 b^2}{x^2}+56 a^5 b^3 x-\frac{8 a^7 b}{5 x^5}-\frac{a^8}{8 x^8}+\frac{8}{13} a b^7 x^{13}+\frac{b^8 x^{16}}{16}","\frac{14}{5} a^2 b^6 x^{10}+8 a^3 b^5 x^7+\frac{35}{2} a^4 b^4 x^4-\frac{14 a^6 b^2}{x^2}+56 a^5 b^3 x-\frac{8 a^7 b}{5 x^5}-\frac{a^8}{8 x^8}+\frac{8}{13} a b^7 x^{13}+\frac{b^8 x^{16}}{16}",1,"-a^8/(8*x^8) - (8*a^7*b)/(5*x^5) - (14*a^6*b^2)/x^2 + 56*a^5*b^3*x + (35*a^4*b^4*x^4)/2 + 8*a^3*b^5*x^7 + (14*a^2*b^6*x^10)/5 + (8*a*b^7*x^13)/13 + (b^8*x^16)/16","A",2,1,13,0.07692,1,"{270}"
318,1,40,0,0.0255807,"\int \frac{x^8}{a+b x^3} \, dx","Int[x^8/(a + b*x^3),x]","\frac{a^2 \log \left(a+b x^3\right)}{3 b^3}-\frac{a x^3}{3 b^2}+\frac{x^6}{6 b}","\frac{a^2 \log \left(a+b x^3\right)}{3 b^3}-\frac{a x^3}{3 b^2}+\frac{x^6}{6 b}",1,"-(a*x^3)/(3*b^2) + x^6/(6*b) + (a^2*Log[a + b*x^3])/(3*b^3)","A",3,2,13,0.1538,1,"{266, 43}"
319,1,27,0,0.0169171,"\int \frac{x^5}{a+b x^3} \, dx","Int[x^5/(a + b*x^3),x]","\frac{x^3}{3 b}-\frac{a \log \left(a+b x^3\right)}{3 b^2}","\frac{x^3}{3 b}-\frac{a \log \left(a+b x^3\right)}{3 b^2}",1,"x^3/(3*b) - (a*Log[a + b*x^3])/(3*b^2)","A",3,2,13,0.1538,1,"{266, 43}"
320,1,15,0,0.0035428,"\int \frac{x^2}{a+b x^3} \, dx","Int[x^2/(a + b*x^3),x]","\frac{\log \left(a+b x^3\right)}{3 b}","\frac{\log \left(a+b x^3\right)}{3 b}",1,"Log[a + b*x^3]/(3*b)","A",1,1,13,0.07692,1,"{260}"
321,1,22,0,0.0102264,"\int \frac{1}{x \left(a+b x^3\right)} \, dx","Int[1/(x*(a + b*x^3)),x]","\frac{\log (x)}{a}-\frac{\log \left(a+b x^3\right)}{3 a}","\frac{\log (x)}{a}-\frac{\log \left(a+b x^3\right)}{3 a}",1,"Log[x]/a - Log[a + b*x^3]/(3*a)","A",4,4,13,0.3077,1,"{266, 36, 29, 31}"
322,1,35,0,0.0212956,"\int \frac{1}{x^4 \left(a+b x^3\right)} \, dx","Int[1/(x^4*(a + b*x^3)),x]","\frac{b \log \left(a+b x^3\right)}{3 a^2}-\frac{b \log (x)}{a^2}-\frac{1}{3 a x^3}","\frac{b \log \left(a+b x^3\right)}{3 a^2}-\frac{b \log (x)}{a^2}-\frac{1}{3 a x^3}",1,"-1/(3*a*x^3) - (b*Log[x])/a^2 + (b*Log[a + b*x^3])/(3*a^2)","A",3,2,13,0.1538,1,"{266, 44}"
323,1,124,0,0.0834253,"\int \frac{x^4}{a+b x^3} \, dx","Int[x^4/(a + b*x^3),x]","-\frac{a^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 b^{5/3}}+\frac{a^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 b^{5/3}}+\frac{a^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^{5/3}}+\frac{x^2}{2 b}","-\frac{a^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 b^{5/3}}+\frac{a^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 b^{5/3}}+\frac{a^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^{5/3}}+\frac{x^2}{2 b}",1,"x^2/(2*b) + (a^(2/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*b^(5/3)) + (a^(2/3)*Log[a^(1/3) + b^(1/3)*x])/(3*b^(5/3)) - (a^(2/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*b^(5/3))","A",7,7,13,0.5385,1,"{321, 292, 31, 634, 617, 204, 628}"
324,1,119,0,0.0682103,"\int \frac{x^3}{a+b x^3} \, dx","Int[x^3/(a + b*x^3),x]","\frac{\sqrt[3]{a} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 b^{4/3}}-\frac{\sqrt[3]{a} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 b^{4/3}}+\frac{\sqrt[3]{a} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^{4/3}}+\frac{x}{b}","\frac{\sqrt[3]{a} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 b^{4/3}}-\frac{\sqrt[3]{a} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 b^{4/3}}+\frac{\sqrt[3]{a} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^{4/3}}+\frac{x}{b}",1,"x/b + (a^(1/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*b^(4/3)) - (a^(1/3)*Log[a^(1/3) + b^(1/3)*x])/(3*b^(4/3)) + (a^(1/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*b^(4/3))","A",7,7,13,0.5385,1,"{321, 200, 31, 634, 617, 204, 628}"
325,1,115,0,0.0496066,"\int \frac{x}{a+b x^3} \, dx","Int[x/(a + b*x^3),x]","\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 \sqrt[3]{a} b^{2/3}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 \sqrt[3]{a} b^{2/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} \sqrt[3]{a} b^{2/3}}","\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 \sqrt[3]{a} b^{2/3}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 \sqrt[3]{a} b^{2/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} \sqrt[3]{a} b^{2/3}}",1,"-(ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))]/(Sqrt[3]*a^(1/3)*b^(2/3))) - Log[a^(1/3) + b^(1/3)*x]/(3*a^(1/3)*b^(2/3)) + Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2]/(6*a^(1/3)*b^(2/3))","A",6,6,11,0.5455,1,"{292, 31, 634, 617, 204, 628}"
326,1,115,0,0.0507357,"\int \frac{1}{a+b x^3} \, dx","Int[(a + b*x^3)^(-1),x]","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{2/3} \sqrt[3]{b}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{2/3} \sqrt[3]{b}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} \sqrt[3]{b}}","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{2/3} \sqrt[3]{b}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{2/3} \sqrt[3]{b}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} \sqrt[3]{b}}",1,"-(ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))]/(Sqrt[3]*a^(2/3)*b^(1/3))) + Log[a^(1/3) + b^(1/3)*x]/(3*a^(2/3)*b^(1/3)) - Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2]/(6*a^(2/3)*b^(1/3))","A",6,6,9,0.6667,1,"{200, 31, 634, 617, 204, 628}"
327,1,122,0,0.0619413,"\int \frac{1}{x^2 \left(a+b x^3\right)} \, dx","Int[1/(x^2*(a + b*x^3)),x]","-\frac{\sqrt[3]{b} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{4/3}}+\frac{\sqrt[3]{b} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{4/3}}+\frac{\sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{4/3}}-\frac{1}{a x}","-\frac{\sqrt[3]{b} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{4/3}}+\frac{\sqrt[3]{b} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{4/3}}+\frac{\sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{4/3}}-\frac{1}{a x}",1,"-(1/(a*x)) + (b^(1/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(4/3)) + (b^(1/3)*Log[a^(1/3) + b^(1/3)*x])/(3*a^(4/3)) - (b^(1/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(4/3))","A",7,7,13,0.5385,1,"{325, 292, 31, 634, 617, 204, 628}"
328,1,124,0,0.06516,"\int \frac{1}{x^3 \left(a+b x^3\right)} \, dx","Int[1/(x^3*(a + b*x^3)),x]","\frac{b^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{5/3}}-\frac{b^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{5/3}}+\frac{b^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{5/3}}-\frac{1}{2 a x^2}","\frac{b^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{5/3}}-\frac{b^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{5/3}}+\frac{b^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{5/3}}-\frac{1}{2 a x^2}",1,"-1/(2*a*x^2) + (b^(2/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(5/3)) - (b^(2/3)*Log[a^(1/3) + b^(1/3)*x])/(3*a^(5/3)) + (b^(2/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(5/3))","A",7,7,13,0.5385,1,"{325, 200, 31, 634, 617, 204, 628}"
329,1,46,0,0.0303931,"\int \frac{x^8}{\left(a+b x^3\right)^2} \, dx","Int[x^8/(a + b*x^3)^2,x]","-\frac{a^2}{3 b^3 \left(a+b x^3\right)}-\frac{2 a \log \left(a+b x^3\right)}{3 b^3}+\frac{x^3}{3 b^2}","-\frac{a^2}{3 b^3 \left(a+b x^3\right)}-\frac{2 a \log \left(a+b x^3\right)}{3 b^3}+\frac{x^3}{3 b^2}",1,"x^3/(3*b^2) - a^2/(3*b^3*(a + b*x^3)) - (2*a*Log[a + b*x^3])/(3*b^3)","A",3,2,13,0.1538,1,"{266, 43}"
330,1,33,0,0.0247502,"\int \frac{x^5}{\left(a+b x^3\right)^2} \, dx","Int[x^5/(a + b*x^3)^2,x]","\frac{a}{3 b^2 \left(a+b x^3\right)}+\frac{\log \left(a+b x^3\right)}{3 b^2}","\frac{a}{3 b^2 \left(a+b x^3\right)}+\frac{\log \left(a+b x^3\right)}{3 b^2}",1,"a/(3*b^2*(a + b*x^3)) + Log[a + b*x^3]/(3*b^2)","A",3,2,13,0.1538,1,"{266, 43}"
331,1,16,0,0.0033311,"\int \frac{x^2}{\left(a+b x^3\right)^2} \, dx","Int[x^2/(a + b*x^3)^2,x]","-\frac{1}{3 b \left(a+b x^3\right)}","-\frac{1}{3 b \left(a+b x^3\right)}",1,"-1/(3*b*(a + b*x^3))","A",1,1,13,0.07692,1,"{261}"
332,1,38,0,0.0258655,"\int \frac{1}{x \left(a+b x^3\right)^2} \, dx","Int[1/(x*(a + b*x^3)^2),x]","-\frac{\log \left(a+b x^3\right)}{3 a^2}+\frac{\log (x)}{a^2}+\frac{1}{3 a \left(a+b x^3\right)}","-\frac{\log \left(a+b x^3\right)}{3 a^2}+\frac{\log (x)}{a^2}+\frac{1}{3 a \left(a+b x^3\right)}",1,"1/(3*a*(a + b*x^3)) + Log[x]/a^2 - Log[a + b*x^3]/(3*a^2)","A",3,2,13,0.1538,1,"{266, 44}"
333,1,52,0,0.035635,"\int \frac{1}{x^4 \left(a+b x^3\right)^2} \, dx","Int[1/(x^4*(a + b*x^3)^2),x]","-\frac{b}{3 a^2 \left(a+b x^3\right)}+\frac{2 b \log \left(a+b x^3\right)}{3 a^3}-\frac{2 b \log (x)}{a^3}-\frac{1}{3 a^2 x^3}","-\frac{b}{3 a^2 \left(a+b x^3\right)}+\frac{2 b \log \left(a+b x^3\right)}{3 a^3}-\frac{2 b \log (x)}{a^3}-\frac{1}{3 a^2 x^3}",1,"-1/(3*a^2*x^3) - b/(3*a^2*(a + b*x^3)) - (2*b*Log[x])/a^3 + (2*b*Log[a + b*x^3])/(3*a^3)","A",3,2,13,0.1538,1,"{266, 44}"
334,1,136,0,0.0651125,"\int \frac{x^4}{\left(a+b x^3\right)^2} \, dx","Int[x^4/(a + b*x^3)^2,x]","\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{9 \sqrt[3]{a} b^{5/3}}-\frac{2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 \sqrt[3]{a} b^{5/3}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} \sqrt[3]{a} b^{5/3}}-\frac{x^2}{3 b \left(a+b x^3\right)}","\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{9 \sqrt[3]{a} b^{5/3}}-\frac{2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 \sqrt[3]{a} b^{5/3}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} \sqrt[3]{a} b^{5/3}}-\frac{x^2}{3 b \left(a+b x^3\right)}",1,"-x^2/(3*b*(a + b*x^3)) - (2*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(1/3)*b^(5/3)) - (2*Log[a^(1/3) + b^(1/3)*x])/(9*a^(1/3)*b^(5/3)) + Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2]/(9*a^(1/3)*b^(5/3))","A",7,7,13,0.5385,1,"{288, 292, 31, 634, 617, 204, 628}"
335,1,134,0,0.0644192,"\int \frac{x^3}{\left(a+b x^3\right)^2} \, dx","Int[x^3/(a + b*x^3)^2,x]","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{18 a^{2/3} b^{4/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{2/3} b^{4/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{2/3} b^{4/3}}-\frac{x}{3 b \left(a+b x^3\right)}","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{18 a^{2/3} b^{4/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{2/3} b^{4/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{2/3} b^{4/3}}-\frac{x}{3 b \left(a+b x^3\right)}",1,"-x/(3*b*(a + b*x^3)) - ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))]/(3*Sqrt[3]*a^(2/3)*b^(4/3)) + Log[a^(1/3) + b^(1/3)*x]/(9*a^(2/3)*b^(4/3)) - Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2]/(18*a^(2/3)*b^(4/3))","A",7,7,13,0.5385,1,"{288, 200, 31, 634, 617, 204, 628}"
336,1,136,0,0.0629304,"\int \frac{x}{\left(a+b x^3\right)^2} \, dx","Int[x/(a + b*x^3)^2,x]","\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{18 a^{4/3} b^{2/3}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{4/3} b^{2/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{4/3} b^{2/3}}+\frac{x^2}{3 a \left(a+b x^3\right)}","\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{18 a^{4/3} b^{2/3}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{4/3} b^{2/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{4/3} b^{2/3}}+\frac{x^2}{3 a \left(a+b x^3\right)}",1,"x^2/(3*a*(a + b*x^3)) - ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))]/(3*Sqrt[3]*a^(4/3)*b^(2/3)) - Log[a^(1/3) + b^(1/3)*x]/(9*a^(4/3)*b^(2/3)) + Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2]/(18*a^(4/3)*b^(2/3))","A",7,7,11,0.6364,1,"{290, 292, 31, 634, 617, 204, 628}"
337,1,134,0,0.0633538,"\int \frac{1}{\left(a+b x^3\right)^2} \, dx","Int[(a + b*x^3)^(-2),x]","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{9 a^{5/3} \sqrt[3]{b}}+\frac{2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{5/3} \sqrt[3]{b}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{5/3} \sqrt[3]{b}}+\frac{x}{3 a \left(a+b x^3\right)}","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{9 a^{5/3} \sqrt[3]{b}}+\frac{2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{5/3} \sqrt[3]{b}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{5/3} \sqrt[3]{b}}+\frac{x}{3 a \left(a+b x^3\right)}",1,"x/(3*a*(a + b*x^3)) - (2*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(5/3)*b^(1/3)) + (2*Log[a^(1/3) + b^(1/3)*x])/(9*a^(5/3)*b^(1/3)) - Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2]/(9*a^(5/3)*b^(1/3))","A",7,7,9,0.7778,1,"{199, 200, 31, 634, 617, 204, 628}"
338,1,146,0,0.0774414,"\int \frac{1}{x^2 \left(a+b x^3\right)^2} \, dx","Int[1/(x^2*(a + b*x^3)^2),x]","-\frac{2 \sqrt[3]{b} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{9 a^{7/3}}+\frac{4 \sqrt[3]{b} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{7/3}}+\frac{4 \sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{7/3}}-\frac{4}{3 a^2 x}+\frac{1}{3 a x \left(a+b x^3\right)}","-\frac{2 \sqrt[3]{b} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{9 a^{7/3}}+\frac{4 \sqrt[3]{b} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{7/3}}+\frac{4 \sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{7/3}}-\frac{4}{3 a^2 x}+\frac{1}{3 a x \left(a+b x^3\right)}",1,"-4/(3*a^2*x) + 1/(3*a*x*(a + b*x^3)) + (4*b^(1/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(7/3)) + (4*b^(1/3)*Log[a^(1/3) + b^(1/3)*x])/(9*a^(7/3)) - (2*b^(1/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(9*a^(7/3))","A",8,8,13,0.6154,1,"{290, 325, 292, 31, 634, 617, 204, 628}"
339,1,146,0,0.0775369,"\int \frac{1}{x^3 \left(a+b x^3\right)^2} \, dx","Int[1/(x^3*(a + b*x^3)^2),x]","\frac{5 b^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{18 a^{8/3}}-\frac{5 b^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{8/3}}+\frac{5 b^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{8/3}}-\frac{5}{6 a^2 x^2}+\frac{1}{3 a x^2 \left(a+b x^3\right)}","\frac{5 b^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{18 a^{8/3}}-\frac{5 b^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{8/3}}+\frac{5 b^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{8/3}}-\frac{5}{6 a^2 x^2}+\frac{1}{3 a x^2 \left(a+b x^3\right)}",1,"-5/(6*a^2*x^2) + 1/(3*a*x^2*(a + b*x^3)) + (5*b^(2/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(8/3)) - (5*b^(2/3)*Log[a^(1/3) + b^(1/3)*x])/(9*a^(8/3)) + (5*b^(2/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(18*a^(8/3))","A",8,8,13,0.6154,1,"{290, 325, 200, 31, 634, 617, 204, 628}"
340,1,61,0,0.048149,"\int \frac{x^{11}}{\left(a+b x^3\right)^3} \, dx","Int[x^11/(a + b*x^3)^3,x]","\frac{a^3}{6 b^4 \left(a+b x^3\right)^2}-\frac{a^2}{b^4 \left(a+b x^3\right)}-\frac{a \log \left(a+b x^3\right)}{b^4}+\frac{x^3}{3 b^3}","\frac{a^3}{6 b^4 \left(a+b x^3\right)^2}-\frac{a^2}{b^4 \left(a+b x^3\right)}-\frac{a \log \left(a+b x^3\right)}{b^4}+\frac{x^3}{3 b^3}",1,"x^3/(3*b^3) + a^3/(6*b^4*(a + b*x^3)^2) - a^2/(b^4*(a + b*x^3)) - (a*Log[a + b*x^3])/b^4","A",3,2,13,0.1538,1,"{266, 43}"
341,1,52,0,0.0373049,"\int \frac{x^8}{\left(a+b x^3\right)^3} \, dx","Int[x^8/(a + b*x^3)^3,x]","-\frac{a^2}{6 b^3 \left(a+b x^3\right)^2}+\frac{2 a}{3 b^3 \left(a+b x^3\right)}+\frac{\log \left(a+b x^3\right)}{3 b^3}","-\frac{a^2}{6 b^3 \left(a+b x^3\right)^2}+\frac{2 a}{3 b^3 \left(a+b x^3\right)}+\frac{\log \left(a+b x^3\right)}{3 b^3}",1,"-a^2/(6*b^3*(a + b*x^3)^2) + (2*a)/(3*b^3*(a + b*x^3)) + Log[a + b*x^3]/(3*b^3)","A",3,2,13,0.1538,1,"{266, 43}"
342,1,19,0,0.0034208,"\int \frac{x^5}{\left(a+b x^3\right)^3} \, dx","Int[x^5/(a + b*x^3)^3,x]","\frac{x^6}{6 a \left(a+b x^3\right)^2}","\frac{x^6}{6 a \left(a+b x^3\right)^2}",1,"x^6/(6*a*(a + b*x^3)^2)","A",1,1,13,0.07692,1,"{264}"
343,1,16,0,0.0032999,"\int \frac{x^2}{\left(a+b x^3\right)^3} \, dx","Int[x^2/(a + b*x^3)^3,x]","-\frac{1}{6 b \left(a+b x^3\right)^2}","-\frac{1}{6 b \left(a+b x^3\right)^2}",1,"-1/(6*b*(a + b*x^3)^2)","A",1,1,13,0.07692,1,"{261}"
344,1,54,0,0.0364858,"\int \frac{1}{x \left(a+b x^3\right)^3} \, dx","Int[1/(x*(a + b*x^3)^3),x]","\frac{1}{3 a^2 \left(a+b x^3\right)}-\frac{\log \left(a+b x^3\right)}{3 a^3}+\frac{\log (x)}{a^3}+\frac{1}{6 a \left(a+b x^3\right)^2}","\frac{1}{3 a^2 \left(a+b x^3\right)}-\frac{\log \left(a+b x^3\right)}{3 a^3}+\frac{\log (x)}{a^3}+\frac{1}{6 a \left(a+b x^3\right)^2}",1,"1/(6*a*(a + b*x^3)^2) + 1/(3*a^2*(a + b*x^3)) + Log[x]/a^3 - Log[a + b*x^3]/(3*a^3)","A",3,2,13,0.1538,1,"{266, 44}"
345,1,66,0,0.0487344,"\int \frac{1}{x^4 \left(a+b x^3\right)^3} \, dx","Int[1/(x^4*(a + b*x^3)^3),x]","-\frac{2 b}{3 a^3 \left(a+b x^3\right)}-\frac{b}{6 a^2 \left(a+b x^3\right)^2}+\frac{b \log \left(a+b x^3\right)}{a^4}-\frac{3 b \log (x)}{a^4}-\frac{1}{3 a^3 x^3}","-\frac{2 b}{3 a^3 \left(a+b x^3\right)}-\frac{b}{6 a^2 \left(a+b x^3\right)^2}+\frac{b \log \left(a+b x^3\right)}{a^4}-\frac{3 b \log (x)}{a^4}-\frac{1}{3 a^3 x^3}",1,"-1/(3*a^3*x^3) - b/(6*a^2*(a + b*x^3)^2) - (2*b)/(3*a^3*(a + b*x^3)) - (3*b*Log[x])/a^4 + (b*Log[a + b*x^3])/a^4","A",3,2,13,0.1538,1,"{266, 44}"
346,1,155,0,0.0785695,"\int \frac{x^7}{\left(a+b x^3\right)^3} \, dx","Int[x^7/(a + b*x^3)^3,x]","\frac{5 \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{54 \sqrt[3]{a} b^{8/3}}-\frac{5 x^2}{18 b^2 \left(a+b x^3\right)}-\frac{5 \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 \sqrt[3]{a} b^{8/3}}-\frac{5 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} \sqrt[3]{a} b^{8/3}}-\frac{x^5}{6 b \left(a+b x^3\right)^2}","\frac{5 \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{54 \sqrt[3]{a} b^{8/3}}-\frac{5 x^2}{18 b^2 \left(a+b x^3\right)}-\frac{5 \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 \sqrt[3]{a} b^{8/3}}-\frac{5 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} \sqrt[3]{a} b^{8/3}}-\frac{x^5}{6 b \left(a+b x^3\right)^2}",1,"-x^5/(6*b*(a + b*x^3)^2) - (5*x^2)/(18*b^2*(a + b*x^3)) - (5*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(1/3)*b^(8/3)) - (5*Log[a^(1/3) + b^(1/3)*x])/(27*a^(1/3)*b^(8/3)) + (5*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(54*a^(1/3)*b^(8/3))","A",8,7,13,0.5385,1,"{288, 292, 31, 634, 617, 204, 628}"
347,1,153,0,0.0764082,"\int \frac{x^6}{\left(a+b x^3\right)^3} \, dx","Int[x^6/(a + b*x^3)^3,x]","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{27 a^{2/3} b^{7/3}}+\frac{2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{2/3} b^{7/3}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{2/3} b^{7/3}}-\frac{2 x}{9 b^2 \left(a+b x^3\right)}-\frac{x^4}{6 b \left(a+b x^3\right)^2}","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{27 a^{2/3} b^{7/3}}+\frac{2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{2/3} b^{7/3}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{2/3} b^{7/3}}-\frac{2 x}{9 b^2 \left(a+b x^3\right)}-\frac{x^4}{6 b \left(a+b x^3\right)^2}",1,"-x^4/(6*b*(a + b*x^3)^2) - (2*x)/(9*b^2*(a + b*x^3)) - (2*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(2/3)*b^(7/3)) + (2*Log[a^(1/3) + b^(1/3)*x])/(27*a^(2/3)*b^(7/3)) - Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2]/(27*a^(2/3)*b^(7/3))","A",8,7,13,0.5385,1,"{288, 200, 31, 634, 617, 204, 628}"
348,1,158,0,0.076943,"\int \frac{x^4}{\left(a+b x^3\right)^3} \, dx","Int[x^4/(a + b*x^3)^3,x]","\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{54 a^{4/3} b^{5/3}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{4/3} b^{5/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{4/3} b^{5/3}}+\frac{x^2}{9 a b \left(a+b x^3\right)}-\frac{x^2}{6 b \left(a+b x^3\right)^2}","\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{54 a^{4/3} b^{5/3}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{4/3} b^{5/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{4/3} b^{5/3}}+\frac{x^2}{9 a b \left(a+b x^3\right)}-\frac{x^2}{6 b \left(a+b x^3\right)^2}",1,"-x^2/(6*b*(a + b*x^3)^2) + x^2/(9*a*b*(a + b*x^3)) - ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))]/(9*Sqrt[3]*a^(4/3)*b^(5/3)) - Log[a^(1/3) + b^(1/3)*x]/(27*a^(4/3)*b^(5/3)) + Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2]/(54*a^(4/3)*b^(5/3))","A",8,8,13,0.6154,1,"{288, 290, 292, 31, 634, 617, 204, 628}"
349,1,154,0,0.0770565,"\int \frac{x^3}{\left(a+b x^3\right)^3} \, dx","Int[x^3/(a + b*x^3)^3,x]","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{54 a^{5/3} b^{4/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{5/3} b^{4/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{5/3} b^{4/3}}+\frac{x}{18 a b \left(a+b x^3\right)}-\frac{x}{6 b \left(a+b x^3\right)^2}","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{54 a^{5/3} b^{4/3}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{5/3} b^{4/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{5/3} b^{4/3}}+\frac{x}{18 a b \left(a+b x^3\right)}-\frac{x}{6 b \left(a+b x^3\right)^2}",1,"-x/(6*b*(a + b*x^3)^2) + x/(18*a*b*(a + b*x^3)) - ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))]/(9*Sqrt[3]*a^(5/3)*b^(4/3)) + Log[a^(1/3) + b^(1/3)*x]/(27*a^(5/3)*b^(4/3)) - Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2]/(54*a^(5/3)*b^(4/3))","A",8,8,13,0.6154,1,"{288, 199, 200, 31, 634, 617, 204, 628}"
350,1,155,0,0.076143,"\int \frac{x}{\left(a+b x^3\right)^3} \, dx","Int[x/(a + b*x^3)^3,x]","\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{27 a^{7/3} b^{2/3}}-\frac{2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{7/3} b^{2/3}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{7/3} b^{2/3}}+\frac{2 x^2}{9 a^2 \left(a+b x^3\right)}+\frac{x^2}{6 a \left(a+b x^3\right)^2}","\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{27 a^{7/3} b^{2/3}}-\frac{2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{7/3} b^{2/3}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{7/3} b^{2/3}}+\frac{2 x^2}{9 a^2 \left(a+b x^3\right)}+\frac{x^2}{6 a \left(a+b x^3\right)^2}",1,"x^2/(6*a*(a + b*x^3)^2) + (2*x^2)/(9*a^2*(a + b*x^3)) - (2*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(7/3)*b^(2/3)) - (2*Log[a^(1/3) + b^(1/3)*x])/(27*a^(7/3)*b^(2/3)) + Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2]/(27*a^(7/3)*b^(2/3))","A",8,7,11,0.6364,1,"{290, 292, 31, 634, 617, 204, 628}"
351,1,151,0,0.0776701,"\int \frac{1}{\left(a+b x^3\right)^3} \, dx","Int[(a + b*x^3)^(-3),x]","-\frac{5 \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{54 a^{8/3} \sqrt[3]{b}}+\frac{5 x}{18 a^2 \left(a+b x^3\right)}+\frac{5 \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{8/3} \sqrt[3]{b}}-\frac{5 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{8/3} \sqrt[3]{b}}+\frac{x}{6 a \left(a+b x^3\right)^2}","-\frac{5 \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{54 a^{8/3} \sqrt[3]{b}}+\frac{5 x}{18 a^2 \left(a+b x^3\right)}+\frac{5 \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{8/3} \sqrt[3]{b}}-\frac{5 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{8/3} \sqrt[3]{b}}+\frac{x}{6 a \left(a+b x^3\right)^2}",1,"x/(6*a*(a + b*x^3)^2) + (5*x)/(18*a^2*(a + b*x^3)) - (5*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(8/3)*b^(1/3)) + (5*Log[a^(1/3) + b^(1/3)*x])/(27*a^(8/3)*b^(1/3)) - (5*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(54*a^(8/3)*b^(1/3))","A",8,7,9,0.7778,1,"{199, 200, 31, 634, 617, 204, 628}"
352,1,41,0,0.0293576,"\int \frac{x^8}{a-b x^3} \, dx","Int[x^8/(a - b*x^3),x]","-\frac{a^2 \log \left(a-b x^3\right)}{3 b^3}-\frac{a x^3}{3 b^2}-\frac{x^6}{6 b}","-\frac{a^2 \log \left(a-b x^3\right)}{3 b^3}-\frac{a x^3}{3 b^2}-\frac{x^6}{6 b}",1,"-(a*x^3)/(3*b^2) - x^6/(6*b) - (a^2*Log[a - b*x^3])/(3*b^3)","A",3,2,14,0.1429,1,"{266, 43}"
353,1,28,0,0.0193602,"\int \frac{x^5}{a-b x^3} \, dx","Int[x^5/(a - b*x^3),x]","-\frac{a \log \left(a-b x^3\right)}{3 b^2}-\frac{x^3}{3 b}","-\frac{a \log \left(a-b x^3\right)}{3 b^2}-\frac{x^3}{3 b}",1,"-x^3/(3*b) - (a*Log[a - b*x^3])/(3*b^2)","A",3,2,14,0.1429,1,"{266, 43}"
354,1,16,0,0.0034309,"\int \frac{x^2}{a-b x^3} \, dx","Int[x^2/(a - b*x^3),x]","-\frac{\log \left(a-b x^3\right)}{3 b}","-\frac{\log \left(a-b x^3\right)}{3 b}",1,"-Log[a - b*x^3]/(3*b)","A",1,1,14,0.07143,1,"{260}"
355,1,23,0,0.0114506,"\int \frac{1}{x \left(a-b x^3\right)} \, dx","Int[1/(x*(a - b*x^3)),x]","\frac{\log (x)}{a}-\frac{\log \left(a-b x^3\right)}{3 a}","\frac{\log (x)}{a}-\frac{\log \left(a-b x^3\right)}{3 a}",1,"Log[x]/a - Log[a - b*x^3]/(3*a)","A",4,4,14,0.2857,1,"{266, 36, 29, 31}"
356,1,35,0,0.0220054,"\int \frac{1}{x^4 \left(a-b x^3\right)} \, dx","Int[1/(x^4*(a - b*x^3)),x]","-\frac{b \log \left(a-b x^3\right)}{3 a^2}+\frac{b \log (x)}{a^2}-\frac{1}{3 a x^3}","-\frac{b \log \left(a-b x^3\right)}{3 a^2}+\frac{b \log (x)}{a^2}-\frac{1}{3 a x^3}",1,"-1/(3*a*x^3) + (b*Log[x])/a^2 - (b*Log[a - b*x^3])/(3*a^2)","A",3,2,14,0.1429,1,"{266, 44}"
357,1,125,0,0.066276,"\int \frac{x^4}{a-b x^3} \, dx","Int[x^4/(a - b*x^3),x]","\frac{a^{2/3} \log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 b^{5/3}}-\frac{a^{2/3} \log \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{3 b^{5/3}}-\frac{a^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}+2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^{5/3}}-\frac{x^2}{2 b}","\frac{a^{2/3} \log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 b^{5/3}}-\frac{a^{2/3} \log \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{3 b^{5/3}}-\frac{a^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}+2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^{5/3}}-\frac{x^2}{2 b}",1,"-x^2/(2*b) - (a^(2/3)*ArcTan[(a^(1/3) + 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*b^(5/3)) - (a^(2/3)*Log[a^(1/3) - b^(1/3)*x])/(3*b^(5/3)) + (a^(2/3)*Log[a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*b^(5/3))","A",7,7,14,0.5000,1,"{321, 292, 31, 634, 617, 204, 628}"
358,1,120,0,0.0603309,"\int \frac{x^3}{a-b x^3} \, dx","Int[x^3/(a - b*x^3),x]","\frac{\sqrt[3]{a} \log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 b^{4/3}}-\frac{\sqrt[3]{a} \log \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{3 b^{4/3}}+\frac{\sqrt[3]{a} \tan ^{-1}\left(\frac{\sqrt[3]{a}+2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^{4/3}}-\frac{x}{b}","\frac{\sqrt[3]{a} \log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 b^{4/3}}-\frac{\sqrt[3]{a} \log \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{3 b^{4/3}}+\frac{\sqrt[3]{a} \tan ^{-1}\left(\frac{\sqrt[3]{a}+2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^{4/3}}-\frac{x}{b}",1,"-(x/b) + (a^(1/3)*ArcTan[(a^(1/3) + 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*b^(4/3)) - (a^(1/3)*Log[a^(1/3) - b^(1/3)*x])/(3*b^(4/3)) + (a^(1/3)*Log[a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*b^(4/3))","A",7,7,14,0.5000,1,"{321, 200, 31, 634, 617, 204, 628}"
359,1,115,0,0.0501204,"\int \frac{x}{a-b x^3} \, dx","Int[x/(a - b*x^3),x]","\frac{\log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 \sqrt[3]{a} b^{2/3}}-\frac{\log \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{3 \sqrt[3]{a} b^{2/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}+2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} \sqrt[3]{a} b^{2/3}}","\frac{\log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 \sqrt[3]{a} b^{2/3}}-\frac{\log \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{3 \sqrt[3]{a} b^{2/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}+2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} \sqrt[3]{a} b^{2/3}}",1,"-(ArcTan[(a^(1/3) + 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))]/(Sqrt[3]*a^(1/3)*b^(2/3))) - Log[a^(1/3) - b^(1/3)*x]/(3*a^(1/3)*b^(2/3)) + Log[a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2]/(6*a^(1/3)*b^(2/3))","A",6,6,12,0.5000,1,"{292, 31, 634, 617, 204, 628}"
360,1,114,0,0.046836,"\int \frac{1}{a-b x^3} \, dx","Int[(a - b*x^3)^(-1),x]","\frac{\log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{2/3} \sqrt[3]{b}}-\frac{\log \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{3 a^{2/3} \sqrt[3]{b}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}+2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} \sqrt[3]{b}}","\frac{\log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{2/3} \sqrt[3]{b}}-\frac{\log \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{3 a^{2/3} \sqrt[3]{b}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}+2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} \sqrt[3]{b}}",1,"ArcTan[(a^(1/3) + 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))]/(Sqrt[3]*a^(2/3)*b^(1/3)) - Log[a^(1/3) - b^(1/3)*x]/(3*a^(2/3)*b^(1/3)) + Log[a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2]/(6*a^(2/3)*b^(1/3))","A",6,6,10,0.6000,1,"{200, 31, 634, 617, 204, 628}"
361,1,123,0,0.0608481,"\int \frac{1}{x^2 \left(a-b x^3\right)} \, dx","Int[1/(x^2*(a - b*x^3)),x]","\frac{\sqrt[3]{b} \log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{4/3}}-\frac{\sqrt[3]{b} \log \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{3 a^{4/3}}-\frac{\sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt[3]{a}+2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{4/3}}-\frac{1}{a x}","\frac{\sqrt[3]{b} \log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{4/3}}-\frac{\sqrt[3]{b} \log \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{3 a^{4/3}}-\frac{\sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt[3]{a}+2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{4/3}}-\frac{1}{a x}",1,"-(1/(a*x)) - (b^(1/3)*ArcTan[(a^(1/3) + 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(4/3)) - (b^(1/3)*Log[a^(1/3) - b^(1/3)*x])/(3*a^(4/3)) + (b^(1/3)*Log[a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(4/3))","A",7,7,14,0.5000,1,"{325, 292, 31, 634, 617, 204, 628}"
362,1,124,0,0.0625653,"\int \frac{1}{x^3 \left(a-b x^3\right)} \, dx","Int[1/(x^3*(a - b*x^3)),x]","\frac{b^{2/3} \log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{5/3}}-\frac{b^{2/3} \log \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{3 a^{5/3}}+\frac{b^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}+2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{5/3}}-\frac{1}{2 a x^2}","\frac{b^{2/3} \log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{5/3}}-\frac{b^{2/3} \log \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{3 a^{5/3}}+\frac{b^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}+2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{5/3}}-\frac{1}{2 a x^2}",1,"-1/(2*a*x^2) + (b^(2/3)*ArcTan[(a^(1/3) + 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(5/3)) - (b^(2/3)*Log[a^(1/3) - b^(1/3)*x])/(3*a^(5/3)) + (b^(2/3)*Log[a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(5/3))","A",7,7,14,0.5000,1,"{325, 200, 31, 634, 617, 204, 628}"
363,1,125,0,0.085638,"\int \frac{1}{1+a+b x^3} \, dx","Int[(1 + a + b*x^3)^(-1),x]","-\frac{\log \left(-\sqrt[3]{a+1} \sqrt[3]{b} x+(a+1)^{2/3}+b^{2/3} x^2\right)}{6 (a+1)^{2/3} \sqrt[3]{b}}+\frac{\log \left(\sqrt[3]{a+1}+\sqrt[3]{b} x\right)}{3 (a+1)^{2/3} \sqrt[3]{b}}-\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+1}}}{\sqrt{3}}\right)}{\sqrt{3} (a+1)^{2/3} \sqrt[3]{b}}","-\frac{\log \left(-\sqrt[3]{a+1} \sqrt[3]{b} x+(a+1)^{2/3}+b^{2/3} x^2\right)}{6 (a+1)^{2/3} \sqrt[3]{b}}+\frac{\log \left(\sqrt[3]{a+1}+\sqrt[3]{b} x\right)}{3 (a+1)^{2/3} \sqrt[3]{b}}-\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+1}}}{\sqrt{3}}\right)}{\sqrt{3} (a+1)^{2/3} \sqrt[3]{b}}",1,"-(ArcTan[(1 - (2*b^(1/3)*x)/(1 + a)^(1/3))/Sqrt[3]]/(Sqrt[3]*(1 + a)^(2/3)*b^(1/3))) + Log[(1 + a)^(1/3) + b^(1/3)*x]/(3*(1 + a)^(2/3)*b^(1/3)) - Log[(1 + a)^(2/3) - (1 + a)^(1/3)*b^(1/3)*x + b^(2/3)*x^2]/(6*(1 + a)^(2/3)*b^(1/3))","A",6,6,10,0.6000,1,"{200, 31, 634, 617, 204, 628}"
364,1,124,0,0.0582614,"\int \frac{1}{1+a-b x^3} \, dx","Int[(1 + a - b*x^3)^(-1),x]","\frac{\log \left(\sqrt[3]{a+1} \sqrt[3]{b} x+(a+1)^{2/3}+b^{2/3} x^2\right)}{6 (a+1)^{2/3} \sqrt[3]{b}}-\frac{\log \left(\sqrt[3]{a+1}-\sqrt[3]{b} x\right)}{3 (a+1)^{2/3} \sqrt[3]{b}}+\frac{\tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+1}}+1}{\sqrt{3}}\right)}{\sqrt{3} (a+1)^{2/3} \sqrt[3]{b}}","\frac{\log \left(\sqrt[3]{a+1} \sqrt[3]{b} x+(a+1)^{2/3}+b^{2/3} x^2\right)}{6 (a+1)^{2/3} \sqrt[3]{b}}-\frac{\log \left(\sqrt[3]{a+1}-\sqrt[3]{b} x\right)}{3 (a+1)^{2/3} \sqrt[3]{b}}+\frac{\tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+1}}+1}{\sqrt{3}}\right)}{\sqrt{3} (a+1)^{2/3} \sqrt[3]{b}}",1,"ArcTan[(1 + (2*b^(1/3)*x)/(1 + a)^(1/3))/Sqrt[3]]/(Sqrt[3]*(1 + a)^(2/3)*b^(1/3)) - Log[(1 + a)^(1/3) - b^(1/3)*x]/(3*(1 + a)^(2/3)*b^(1/3)) + Log[(1 + a)^(2/3) + (1 + a)^(1/3)*b^(1/3)*x + b^(2/3)*x^2]/(6*(1 + a)^(2/3)*b^(1/3))","A",6,6,11,0.5455,1,"{200, 31, 634, 617, 204, 628}"
365,1,139,0,0.0977801,"\int \frac{1}{-1+a+b x^3} \, dx","Int[(-1 + a + b*x^3)^(-1),x]","-\frac{\log \left(\sqrt[3]{1-a} \sqrt[3]{b} x+(1-a)^{2/3}+b^{2/3} x^2\right)}{6 (1-a)^{2/3} \sqrt[3]{b}}+\frac{\log \left(\sqrt[3]{1-a}-\sqrt[3]{b} x\right)}{3 (1-a)^{2/3} \sqrt[3]{b}}-\frac{\tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{1-a}}+1}{\sqrt{3}}\right)}{\sqrt{3} (1-a)^{2/3} \sqrt[3]{b}}","-\frac{\log \left(\sqrt[3]{1-a} \sqrt[3]{b} x+(1-a)^{2/3}+b^{2/3} x^2\right)}{6 (1-a)^{2/3} \sqrt[3]{b}}+\frac{\log \left(\sqrt[3]{1-a}-\sqrt[3]{b} x\right)}{3 (1-a)^{2/3} \sqrt[3]{b}}-\frac{\tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{1-a}}+1}{\sqrt{3}}\right)}{\sqrt{3} (1-a)^{2/3} \sqrt[3]{b}}",1,"-(ArcTan[(1 + (2*b^(1/3)*x)/(1 - a)^(1/3))/Sqrt[3]]/(Sqrt[3]*(1 - a)^(2/3)*b^(1/3))) + Log[(1 - a)^(1/3) - b^(1/3)*x]/(3*(1 - a)^(2/3)*b^(1/3)) - Log[(1 - a)^(2/3) + (1 - a)^(1/3)*b^(1/3)*x + b^(2/3)*x^2]/(6*(1 - a)^(2/3)*b^(1/3))","A",6,6,10,0.6000,1,"{200, 31, 634, 617, 204, 628}"
366,1,138,0,0.0675966,"\int \frac{1}{-1+a-b x^3} \, dx","Int[(-1 + a - b*x^3)^(-1),x]","\frac{\log \left(-\sqrt[3]{1-a} \sqrt[3]{b} x+(1-a)^{2/3}+b^{2/3} x^2\right)}{6 (1-a)^{2/3} \sqrt[3]{b}}-\frac{\log \left(\sqrt[3]{1-a}+\sqrt[3]{b} x\right)}{3 (1-a)^{2/3} \sqrt[3]{b}}+\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} x}{\sqrt[3]{1-a}}}{\sqrt{3}}\right)}{\sqrt{3} (1-a)^{2/3} \sqrt[3]{b}}","\frac{\log \left(-\sqrt[3]{1-a} \sqrt[3]{b} x+(1-a)^{2/3}+b^{2/3} x^2\right)}{6 (1-a)^{2/3} \sqrt[3]{b}}-\frac{\log \left(\sqrt[3]{1-a}+\sqrt[3]{b} x\right)}{3 (1-a)^{2/3} \sqrt[3]{b}}+\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} x}{\sqrt[3]{1-a}}}{\sqrt{3}}\right)}{\sqrt{3} (1-a)^{2/3} \sqrt[3]{b}}",1,"ArcTan[(1 - (2*b^(1/3)*x)/(1 - a)^(1/3))/Sqrt[3]]/(Sqrt[3]*(1 - a)^(2/3)*b^(1/3)) - Log[(1 - a)^(1/3) + b^(1/3)*x]/(3*(1 - a)^(2/3)*b^(1/3)) + Log[(1 - a)^(2/3) - (1 - a)^(1/3)*b^(1/3)*x + b^(2/3)*x^2]/(6*(1 - a)^(2/3)*b^(1/3))","A",6,6,11,0.5455,1,"{200, 31, 634, 617, 204, 628}"
367,1,10,0,0.0061983,"\int \frac{\sqrt{x}}{1+x^3} \, dx","Int[Sqrt[x]/(1 + x^3),x]","\frac{2}{3} \tan ^{-1}\left(x^{3/2}\right)","\frac{2}{3} \tan ^{-1}\left(x^{3/2}\right)",1,"(2*ArcTan[x^(3/2)])/3","A",3,3,13,0.2308,1,"{329, 275, 203}"
368,1,80,0,0.0447942,"\int x^{11} \sqrt{a+b x^3} \, dx","Int[x^11*Sqrt[a + b*x^3],x]","\frac{2 a^2 \left(a+b x^3\right)^{5/2}}{5 b^4}-\frac{2 a^3 \left(a+b x^3\right)^{3/2}}{9 b^4}+\frac{2 \left(a+b x^3\right)^{9/2}}{27 b^4}-\frac{2 a \left(a+b x^3\right)^{7/2}}{7 b^4}","\frac{2 a^2 \left(a+b x^3\right)^{5/2}}{5 b^4}-\frac{2 a^3 \left(a+b x^3\right)^{3/2}}{9 b^4}+\frac{2 \left(a+b x^3\right)^{9/2}}{27 b^4}-\frac{2 a \left(a+b x^3\right)^{7/2}}{7 b^4}",1,"(-2*a^3*(a + b*x^3)^(3/2))/(9*b^4) + (2*a^2*(a + b*x^3)^(5/2))/(5*b^4) - (2*a*(a + b*x^3)^(7/2))/(7*b^4) + (2*(a + b*x^3)^(9/2))/(27*b^4)","A",3,2,15,0.1333,1,"{266, 43}"
369,1,59,0,0.035611,"\int x^8 \sqrt{a+b x^3} \, dx","Int[x^8*Sqrt[a + b*x^3],x]","\frac{2 a^2 \left(a+b x^3\right)^{3/2}}{9 b^3}+\frac{2 \left(a+b x^3\right)^{7/2}}{21 b^3}-\frac{4 a \left(a+b x^3\right)^{5/2}}{15 b^3}","\frac{2 a^2 \left(a+b x^3\right)^{3/2}}{9 b^3}+\frac{2 \left(a+b x^3\right)^{7/2}}{21 b^3}-\frac{4 a \left(a+b x^3\right)^{5/2}}{15 b^3}",1,"(2*a^2*(a + b*x^3)^(3/2))/(9*b^3) - (4*a*(a + b*x^3)^(5/2))/(15*b^3) + (2*(a + b*x^3)^(7/2))/(21*b^3)","A",3,2,15,0.1333,1,"{266, 43}"
370,1,38,0,0.0224393,"\int x^5 \sqrt{a+b x^3} \, dx","Int[x^5*Sqrt[a + b*x^3],x]","\frac{2 \left(a+b x^3\right)^{5/2}}{15 b^2}-\frac{2 a \left(a+b x^3\right)^{3/2}}{9 b^2}","\frac{2 \left(a+b x^3\right)^{5/2}}{15 b^2}-\frac{2 a \left(a+b x^3\right)^{3/2}}{9 b^2}",1,"(-2*a*(a + b*x^3)^(3/2))/(9*b^2) + (2*(a + b*x^3)^(5/2))/(15*b^2)","A",3,2,15,0.1333,1,"{266, 43}"
371,1,18,0,0.0040069,"\int x^2 \sqrt{a+b x^3} \, dx","Int[x^2*Sqrt[a + b*x^3],x]","\frac{2 \left(a+b x^3\right)^{3/2}}{9 b}","\frac{2 \left(a+b x^3\right)^{3/2}}{9 b}",1,"(2*(a + b*x^3)^(3/2))/(9*b)","A",1,1,15,0.06667,1,"{261}"
372,1,43,0,0.025524,"\int \frac{\sqrt{a+b x^3}}{x} \, dx","Int[Sqrt[a + b*x^3]/x,x]","\frac{2}{3} \sqrt{a+b x^3}-\frac{2}{3} \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)","\frac{2}{3} \sqrt{a+b x^3}-\frac{2}{3} \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)",1,"(2*Sqrt[a + b*x^3])/3 - (2*Sqrt[a]*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/3","A",4,4,15,0.2667,1,"{266, 50, 63, 208}"
373,1,47,0,0.0266854,"\int \frac{\sqrt{a+b x^3}}{x^4} \, dx","Int[Sqrt[a + b*x^3]/x^4,x]","-\frac{\sqrt{a+b x^3}}{3 x^3}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{3 \sqrt{a}}","-\frac{\sqrt{a+b x^3}}{3 x^3}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{3 \sqrt{a}}",1,"-Sqrt[a + b*x^3]/(3*x^3) - (b*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/(3*Sqrt[a])","A",4,4,15,0.2667,1,"{266, 47, 63, 208}"
374,1,71,0,0.0370353,"\int \frac{\sqrt{a+b x^3}}{x^7} \, dx","Int[Sqrt[a + b*x^3]/x^7,x]","\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{12 a^{3/2}}-\frac{b \sqrt{a+b x^3}}{12 a x^3}-\frac{\sqrt{a+b x^3}}{6 x^6}","\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{12 a^{3/2}}-\frac{b \sqrt{a+b x^3}}{12 a x^3}-\frac{\sqrt{a+b x^3}}{6 x^6}",1,"-Sqrt[a + b*x^3]/(6*x^6) - (b*Sqrt[a + b*x^3])/(12*a*x^3) + (b^2*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/(12*a^(3/2))","A",5,5,15,0.3333,1,"{266, 47, 51, 63, 208}"
375,1,95,0,0.0532572,"\int \frac{\sqrt{a+b x^3}}{x^{10}} \, dx","Int[Sqrt[a + b*x^3]/x^10,x]","\frac{b^2 \sqrt{a+b x^3}}{24 a^2 x^3}-\frac{b^3 \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{24 a^{5/2}}-\frac{b \sqrt{a+b x^3}}{36 a x^6}-\frac{\sqrt{a+b x^3}}{9 x^9}","\frac{b^2 \sqrt{a+b x^3}}{24 a^2 x^3}-\frac{b^3 \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{24 a^{5/2}}-\frac{b \sqrt{a+b x^3}}{36 a x^6}-\frac{\sqrt{a+b x^3}}{9 x^9}",1,"-Sqrt[a + b*x^3]/(9*x^9) - (b*Sqrt[a + b*x^3])/(36*a*x^6) + (b^2*Sqrt[a + b*x^3])/(24*a^2*x^3) - (b^3*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/(24*a^(5/2))","A",6,5,15,0.3333,1,"{266, 47, 51, 63, 208}"
376,1,275,0,0.1237479,"\int x^6 \sqrt{a+b x^3} \, dx","Int[x^6*Sqrt[a + b*x^3],x]","-\frac{48 a^2 x \sqrt{a+b x^3}}{935 b^2}+\frac{32\ 3^{3/4} \sqrt{2+\sqrt{3}} a^3 \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{935 b^{7/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2}{17} x^7 \sqrt{a+b x^3}+\frac{6 a x^4 \sqrt{a+b x^3}}{187 b}","-\frac{48 a^2 x \sqrt{a+b x^3}}{935 b^2}+\frac{32\ 3^{3/4} \sqrt{2+\sqrt{3}} a^3 \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{935 b^{7/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2}{17} x^7 \sqrt{a+b x^3}+\frac{6 a x^4 \sqrt{a+b x^3}}{187 b}",1,"(-48*a^2*x*Sqrt[a + b*x^3])/(935*b^2) + (6*a*x^4*Sqrt[a + b*x^3])/(187*b) + (2*x^7*Sqrt[a + b*x^3])/17 + (32*3^(3/4)*Sqrt[2 + Sqrt[3]]*a^3*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(935*b^(7/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",4,3,15,0.2000,1,"{279, 321, 218}"
377,1,251,0,0.069921,"\int x^3 \sqrt{a+b x^3} \, dx","Int[x^3*Sqrt[a + b*x^3],x]","-\frac{4\ 3^{3/4} \sqrt{2+\sqrt{3}} a^2 \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{55 b^{4/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2}{11} x^4 \sqrt{a+b x^3}+\frac{6 a x \sqrt{a+b x^3}}{55 b}","-\frac{4\ 3^{3/4} \sqrt{2+\sqrt{3}} a^2 \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{55 b^{4/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2}{11} x^4 \sqrt{a+b x^3}+\frac{6 a x \sqrt{a+b x^3}}{55 b}",1,"(6*a*x*Sqrt[a + b*x^3])/(55*b) + (2*x^4*Sqrt[a + b*x^3])/11 - (4*3^(3/4)*Sqrt[2 + Sqrt[3]]*a^2*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(55*b^(4/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",3,3,15,0.2000,1,"{279, 321, 218}"
378,1,227,0,0.0404463,"\int \sqrt{a+b x^3} \, dx","Int[Sqrt[a + b*x^3],x]","\frac{2\ 3^{3/4} \sqrt{2+\sqrt{3}} a \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{5 \sqrt[3]{b} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2}{5} x \sqrt{a+b x^3}","\frac{2\ 3^{3/4} \sqrt{2+\sqrt{3}} a \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{5 \sqrt[3]{b} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2}{5} x \sqrt{a+b x^3}",1,"(2*x*Sqrt[a + b*x^3])/5 + (2*3^(3/4)*Sqrt[2 + Sqrt[3]]*a*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(5*b^(1/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",2,2,11,0.1818,1,"{195, 218}"
379,1,228,0,0.0417935,"\int \frac{\sqrt{a+b x^3}}{x^3} \, dx","Int[Sqrt[a + b*x^3]/x^3,x]","\frac{3^{3/4} \sqrt{2+\sqrt{3}} b^{2/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\sqrt{a+b x^3}}{2 x^2}","\frac{3^{3/4} \sqrt{2+\sqrt{3}} b^{2/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\sqrt{a+b x^3}}{2 x^2}",1,"-Sqrt[a + b*x^3]/(2*x^2) + (3^(3/4)*Sqrt[2 + Sqrt[3]]*b^(2/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(2*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",2,2,15,0.1333,1,"{277, 218}"
380,1,253,0,0.0692936,"\int \frac{\sqrt{a+b x^3}}{x^6} \, dx","Int[Sqrt[a + b*x^3]/x^6,x]","-\frac{3^{3/4} \sqrt{2+\sqrt{3}} b^{5/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{20 a \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{3 b \sqrt{a+b x^3}}{20 a x^2}-\frac{\sqrt{a+b x^3}}{5 x^5}","-\frac{3^{3/4} \sqrt{2+\sqrt{3}} b^{5/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{20 a \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{3 b \sqrt{a+b x^3}}{20 a x^2}-\frac{\sqrt{a+b x^3}}{5 x^5}",1,"-Sqrt[a + b*x^3]/(5*x^5) - (3*b*Sqrt[a + b*x^3])/(20*a*x^2) - (3^(3/4)*Sqrt[2 + Sqrt[3]]*b^(5/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(20*a*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",3,3,15,0.2000,1,"{277, 325, 218}"
381,1,277,0,0.0979007,"\int \frac{\sqrt{a+b x^3}}{x^9} \, dx","Int[Sqrt[a + b*x^3]/x^9,x]","\frac{21 b^2 \sqrt{a+b x^3}}{320 a^2 x^2}+\frac{7\ 3^{3/4} \sqrt{2+\sqrt{3}} b^{8/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{320 a^2 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{3 b \sqrt{a+b x^3}}{80 a x^5}-\frac{\sqrt{a+b x^3}}{8 x^8}","\frac{21 b^2 \sqrt{a+b x^3}}{320 a^2 x^2}+\frac{7\ 3^{3/4} \sqrt{2+\sqrt{3}} b^{8/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{320 a^2 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{3 b \sqrt{a+b x^3}}{80 a x^5}-\frac{\sqrt{a+b x^3}}{8 x^8}",1,"-Sqrt[a + b*x^3]/(8*x^8) - (3*b*Sqrt[a + b*x^3])/(80*a*x^5) + (21*b^2*Sqrt[a + b*x^3])/(320*a^2*x^2) + (7*3^(3/4)*Sqrt[2 + Sqrt[3]]*b^(8/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(320*a^2*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",4,3,15,0.2000,1,"{277, 325, 218}"
382,1,535,0,0.298441,"\int x^7 \sqrt{a+b x^3} \, dx","Int[x^7*Sqrt[a + b*x^3],x]","-\frac{60 a^2 x^2 \sqrt{a+b x^3}}{1729 b^2}+\frac{240 a^3 \sqrt{a+b x^3}}{1729 b^{8/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{80 \sqrt{2} 3^{3/4} a^{10/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{1729 b^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{120 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{10/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{1729 b^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2}{19} x^8 \sqrt{a+b x^3}+\frac{6 a x^5 \sqrt{a+b x^3}}{247 b}","-\frac{60 a^2 x^2 \sqrt{a+b x^3}}{1729 b^2}+\frac{240 a^3 \sqrt{a+b x^3}}{1729 b^{8/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{80 \sqrt{2} 3^{3/4} a^{10/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{1729 b^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{120 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{10/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{1729 b^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2}{19} x^8 \sqrt{a+b x^3}+\frac{6 a x^5 \sqrt{a+b x^3}}{247 b}",1,"(-60*a^2*x^2*Sqrt[a + b*x^3])/(1729*b^2) + (6*a*x^5*Sqrt[a + b*x^3])/(247*b) + (2*x^8*Sqrt[a + b*x^3])/19 + (240*a^3*Sqrt[a + b*x^3])/(1729*b^(8/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (120*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(10/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(1729*b^(8/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (80*Sqrt[2]*3^(3/4)*a^(10/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(1729*b^(8/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",6,5,15,0.3333,1,"{279, 321, 303, 218, 1877}"
383,1,511,0,0.2014701,"\int x^4 \sqrt{a+b x^3} \, dx","Int[x^4*Sqrt[a + b*x^3],x]","-\frac{24 a^2 \sqrt{a+b x^3}}{91 b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{8 \sqrt{2} 3^{3/4} a^{7/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{91 b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{12 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{7/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{91 b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2}{13} x^5 \sqrt{a+b x^3}+\frac{6 a x^2 \sqrt{a+b x^3}}{91 b}","-\frac{24 a^2 \sqrt{a+b x^3}}{91 b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{8 \sqrt{2} 3^{3/4} a^{7/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{91 b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{12 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{7/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{91 b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2}{13} x^5 \sqrt{a+b x^3}+\frac{6 a x^2 \sqrt{a+b x^3}}{91 b}",1,"(6*a*x^2*Sqrt[a + b*x^3])/(91*b) + (2*x^5*Sqrt[a + b*x^3])/13 - (24*a^2*Sqrt[a + b*x^3])/(91*b^(5/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) + (12*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(7/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(91*b^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) - (8*Sqrt[2]*3^(3/4)*a^(7/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(91*b^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",5,5,15,0.3333,1,"{279, 321, 303, 218, 1877}"
384,1,487,0,0.1470706,"\int x \sqrt{a+b x^3} \, dx","Int[x*Sqrt[a + b*x^3],x]","\frac{2 \sqrt{2} 3^{3/4} a^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{7 b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{7 b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{6 a \sqrt{a+b x^3}}{7 b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{2}{7} x^2 \sqrt{a+b x^3}","\frac{2 \sqrt{2} 3^{3/4} a^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{7 b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{7 b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{6 a \sqrt{a+b x^3}}{7 b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{2}{7} x^2 \sqrt{a+b x^3}",1,"(2*x^2*Sqrt[a + b*x^3])/7 + (6*a*Sqrt[a + b*x^3])/(7*b^(2/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(4/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(7*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (2*Sqrt[2]*3^(3/4)*a^(4/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(7*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",4,4,13,0.3077,1,"{279, 303, 218, 1877}"
385,1,479,0,0.1438506,"\int \frac{\sqrt{a+b x^3}}{x^2} \, dx","Int[Sqrt[a + b*x^3]/x^2,x]","\frac{\sqrt{2} 3^{3/4} \sqrt[3]{a} \sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{\sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} \sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\sqrt{a+b x^3}}{x}+\frac{3 \sqrt[3]{b} \sqrt{a+b x^3}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x}","\frac{\sqrt{2} 3^{3/4} \sqrt[3]{a} \sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{\sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} \sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\sqrt{a+b x^3}}{x}+\frac{3 \sqrt[3]{b} \sqrt{a+b x^3}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x}",1,"-(Sqrt[a + b*x^3]/x) + (3*b^(1/3)*Sqrt[a + b*x^3])/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x) - (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(1/3)*b^(1/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(2*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (Sqrt[2]*3^(3/4)*a^(1/3)*b^(1/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",4,4,15,0.2667,1,"{277, 303, 218, 1877}"
386,1,511,0,0.2010435,"\int \frac{\sqrt{a+b x^3}}{x^5} \, dx","Int[Sqrt[a + b*x^3]/x^5,x]","\frac{3^{3/4} b^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{4 \sqrt{2} a^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} b^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{16 a^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{3 b^{4/3} \sqrt{a+b x^3}}{8 a \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{3 b \sqrt{a+b x^3}}{8 a x}-\frac{\sqrt{a+b x^3}}{4 x^4}","\frac{3^{3/4} b^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{4 \sqrt{2} a^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} b^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{16 a^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{3 b^{4/3} \sqrt{a+b x^3}}{8 a \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{3 b \sqrt{a+b x^3}}{8 a x}-\frac{\sqrt{a+b x^3}}{4 x^4}",1,"-Sqrt[a + b*x^3]/(4*x^4) - (3*b*Sqrt[a + b*x^3])/(8*a*x) + (3*b^(4/3)*Sqrt[a + b*x^3])/(8*a*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*b^(4/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(16*a^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (3^(3/4)*b^(4/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(4*Sqrt[2]*a^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",5,5,15,0.3333,1,"{277, 325, 303, 218, 1877}"
387,1,80,0,0.0469948,"\int x^{11} \left(a+b x^3\right)^{3/2} \, dx","Int[x^11*(a + b*x^3)^(3/2),x]","\frac{2 a^2 \left(a+b x^3\right)^{7/2}}{7 b^4}-\frac{2 a^3 \left(a+b x^3\right)^{5/2}}{15 b^4}+\frac{2 \left(a+b x^3\right)^{11/2}}{33 b^4}-\frac{2 a \left(a+b x^3\right)^{9/2}}{9 b^4}","\frac{2 a^2 \left(a+b x^3\right)^{7/2}}{7 b^4}-\frac{2 a^3 \left(a+b x^3\right)^{5/2}}{15 b^4}+\frac{2 \left(a+b x^3\right)^{11/2}}{33 b^4}-\frac{2 a \left(a+b x^3\right)^{9/2}}{9 b^4}",1,"(-2*a^3*(a + b*x^3)^(5/2))/(15*b^4) + (2*a^2*(a + b*x^3)^(7/2))/(7*b^4) - (2*a*(a + b*x^3)^(9/2))/(9*b^4) + (2*(a + b*x^3)^(11/2))/(33*b^4)","A",3,2,15,0.1333,1,"{266, 43}"
388,1,59,0,0.0352062,"\int x^8 \left(a+b x^3\right)^{3/2} \, dx","Int[x^8*(a + b*x^3)^(3/2),x]","\frac{2 a^2 \left(a+b x^3\right)^{5/2}}{15 b^3}+\frac{2 \left(a+b x^3\right)^{9/2}}{27 b^3}-\frac{4 a \left(a+b x^3\right)^{7/2}}{21 b^3}","\frac{2 a^2 \left(a+b x^3\right)^{5/2}}{15 b^3}+\frac{2 \left(a+b x^3\right)^{9/2}}{27 b^3}-\frac{4 a \left(a+b x^3\right)^{7/2}}{21 b^3}",1,"(2*a^2*(a + b*x^3)^(5/2))/(15*b^3) - (4*a*(a + b*x^3)^(7/2))/(21*b^3) + (2*(a + b*x^3)^(9/2))/(27*b^3)","A",3,2,15,0.1333,1,"{266, 43}"
389,1,38,0,0.0238234,"\int x^5 \left(a+b x^3\right)^{3/2} \, dx","Int[x^5*(a + b*x^3)^(3/2),x]","\frac{2 \left(a+b x^3\right)^{7/2}}{21 b^2}-\frac{2 a \left(a+b x^3\right)^{5/2}}{15 b^2}","\frac{2 \left(a+b x^3\right)^{7/2}}{21 b^2}-\frac{2 a \left(a+b x^3\right)^{5/2}}{15 b^2}",1,"(-2*a*(a + b*x^3)^(5/2))/(15*b^2) + (2*(a + b*x^3)^(7/2))/(21*b^2)","A",3,2,15,0.1333,1,"{266, 43}"
390,1,18,0,0.0046283,"\int x^2 \left(a+b x^3\right)^{3/2} \, dx","Int[x^2*(a + b*x^3)^(3/2),x]","\frac{2 \left(a+b x^3\right)^{5/2}}{15 b}","\frac{2 \left(a+b x^3\right)^{5/2}}{15 b}",1,"(2*(a + b*x^3)^(5/2))/(15*b)","A",1,1,15,0.06667,1,"{261}"
391,1,59,0,0.0343941,"\int \frac{\left(a+b x^3\right)^{3/2}}{x} \, dx","Int[(a + b*x^3)^(3/2)/x,x]","-\frac{2}{3} a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)+\frac{2}{3} a \sqrt{a+b x^3}+\frac{2}{9} \left(a+b x^3\right)^{3/2}","-\frac{2}{3} a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)+\frac{2}{3} a \sqrt{a+b x^3}+\frac{2}{9} \left(a+b x^3\right)^{3/2}",1,"(2*a*Sqrt[a + b*x^3])/3 + (2*(a + b*x^3)^(3/2))/9 - (2*a^(3/2)*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/3","A",5,4,15,0.2667,1,"{266, 50, 63, 208}"
392,1,58,0,0.0359271,"\int \frac{\left(a+b x^3\right)^{3/2}}{x^4} \, dx","Int[(a + b*x^3)^(3/2)/x^4,x]","-\frac{\left(a+b x^3\right)^{3/2}}{3 x^3}+b \sqrt{a+b x^3}-\sqrt{a} b \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)","-\frac{\left(a+b x^3\right)^{3/2}}{3 x^3}+b \sqrt{a+b x^3}-\sqrt{a} b \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)",1,"b*Sqrt[a + b*x^3] - (a + b*x^3)^(3/2)/(3*x^3) - Sqrt[a]*b*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]]","A",5,5,15,0.3333,1,"{266, 47, 50, 63, 208}"
393,1,68,0,0.039009,"\int \frac{\left(a+b x^3\right)^{3/2}}{x^7} \, dx","Int[(a + b*x^3)^(3/2)/x^7,x]","-\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{4 \sqrt{a}}-\frac{b \sqrt{a+b x^3}}{4 x^3}-\frac{\left(a+b x^3\right)^{3/2}}{6 x^6}","-\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{4 \sqrt{a}}-\frac{b \sqrt{a+b x^3}}{4 x^3}-\frac{\left(a+b x^3\right)^{3/2}}{6 x^6}",1,"-(b*Sqrt[a + b*x^3])/(4*x^3) - (a + b*x^3)^(3/2)/(6*x^6) - (b^2*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/(4*Sqrt[a])","A",5,4,15,0.2667,1,"{266, 47, 63, 208}"
394,1,296,0,0.1280329,"\int x^6 \left(a+b x^3\right)^{3/2} \, dx","Int[x^6*(a + b*x^3)^(3/2),x]","-\frac{432 a^3 x \sqrt{a+b x^3}}{21505 b^2}+\frac{288\ 3^{3/4} \sqrt{2+\sqrt{3}} a^4 \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{21505 b^{7/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{54 a^2 x^4 \sqrt{a+b x^3}}{4301 b}+\frac{2}{23} x^7 \left(a+b x^3\right)^{3/2}+\frac{18}{391} a x^7 \sqrt{a+b x^3}","-\frac{432 a^3 x \sqrt{a+b x^3}}{21505 b^2}+\frac{288\ 3^{3/4} \sqrt{2+\sqrt{3}} a^4 \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{21505 b^{7/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{54 a^2 x^4 \sqrt{a+b x^3}}{4301 b}+\frac{2}{23} x^7 \left(a+b x^3\right)^{3/2}+\frac{18}{391} a x^7 \sqrt{a+b x^3}",1,"(-432*a^3*x*Sqrt[a + b*x^3])/(21505*b^2) + (54*a^2*x^4*Sqrt[a + b*x^3])/(4301*b) + (18*a*x^7*Sqrt[a + b*x^3])/391 + (2*x^7*(a + b*x^3)^(3/2))/23 + (288*3^(3/4)*Sqrt[2 + Sqrt[3]]*a^4*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(21505*b^(7/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",5,3,15,0.2000,1,"{279, 321, 218}"
395,1,272,0,0.0938804,"\int x^3 \left(a+b x^3\right)^{3/2} \, dx","Int[x^3*(a + b*x^3)^(3/2),x]","-\frac{36\ 3^{3/4} \sqrt{2+\sqrt{3}} a^3 \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{935 b^{4/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{54 a^2 x \sqrt{a+b x^3}}{935 b}+\frac{2}{17} x^4 \left(a+b x^3\right)^{3/2}+\frac{18}{187} a x^4 \sqrt{a+b x^3}","-\frac{36\ 3^{3/4} \sqrt{2+\sqrt{3}} a^3 \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{935 b^{4/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{54 a^2 x \sqrt{a+b x^3}}{935 b}+\frac{2}{17} x^4 \left(a+b x^3\right)^{3/2}+\frac{18}{187} a x^4 \sqrt{a+b x^3}",1,"(54*a^2*x*Sqrt[a + b*x^3])/(935*b) + (18*a*x^4*Sqrt[a + b*x^3])/187 + (2*x^4*(a + b*x^3)^(3/2))/17 - (36*3^(3/4)*Sqrt[2 + Sqrt[3]]*a^3*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(935*b^(4/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",4,3,15,0.2000,1,"{279, 321, 218}"
396,1,246,0,0.0625514,"\int \left(a+b x^3\right)^{3/2} \, dx","Int[(a + b*x^3)^(3/2),x]","\frac{18\ 3^{3/4} \sqrt{2+\sqrt{3}} a^2 \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{55 \sqrt[3]{b} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{18}{55} a x \sqrt{a+b x^3}+\frac{2}{11} x \left(a+b x^3\right)^{3/2}","\frac{18\ 3^{3/4} \sqrt{2+\sqrt{3}} a^2 \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{55 \sqrt[3]{b} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{18}{55} a x \sqrt{a+b x^3}+\frac{2}{11} x \left(a+b x^3\right)^{3/2}",1,"(18*a*x*Sqrt[a + b*x^3])/55 + (2*x*(a + b*x^3)^(3/2))/11 + (18*3^(3/4)*Sqrt[2 + Sqrt[3]]*a^2*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(55*b^(1/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",3,2,11,0.1818,1,"{195, 218}"
397,1,246,0,0.0627232,"\int \frac{\left(a+b x^3\right)^{3/2}}{x^3} \, dx","Int[(a + b*x^3)^(3/2)/x^3,x]","\frac{9\ 3^{3/4} \sqrt{2+\sqrt{3}} a b^{2/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{10 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\left(a+b x^3\right)^{3/2}}{2 x^2}+\frac{9}{10} b x \sqrt{a+b x^3}","\frac{9\ 3^{3/4} \sqrt{2+\sqrt{3}} a b^{2/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{10 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\left(a+b x^3\right)^{3/2}}{2 x^2}+\frac{9}{10} b x \sqrt{a+b x^3}",1,"(9*b*x*Sqrt[a + b*x^3])/10 - (a + b*x^3)^(3/2)/(2*x^2) + (9*3^(3/4)*Sqrt[2 + Sqrt[3]]*a*b^(2/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(10*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",3,3,15,0.2000,1,"{277, 195, 218}"
398,1,247,0,0.0649385,"\int \frac{\left(a+b x^3\right)^{3/2}}{x^6} \, dx","Int[(a + b*x^3)^(3/2)/x^6,x]","\frac{9\ 3^{3/4} \sqrt{2+\sqrt{3}} b^{5/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{20 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{9 b \sqrt{a+b x^3}}{20 x^2}-\frac{\left(a+b x^3\right)^{3/2}}{5 x^5}","\frac{9\ 3^{3/4} \sqrt{2+\sqrt{3}} b^{5/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{20 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{9 b \sqrt{a+b x^3}}{20 x^2}-\frac{\left(a+b x^3\right)^{3/2}}{5 x^5}",1,"(-9*b*Sqrt[a + b*x^3])/(20*x^2) - (a + b*x^3)^(3/2)/(5*x^5) + (9*3^(3/4)*Sqrt[2 + Sqrt[3]]*b^(5/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(20*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",3,2,15,0.1333,1,"{277, 218}"
399,1,556,0,0.3043754,"\int x^7 \left(a+b x^3\right)^{3/2} \, dx","Int[x^7*(a + b*x^3)^(3/2),x]","-\frac{108 a^3 x^2 \sqrt{a+b x^3}}{8645 b^2}+\frac{432 a^4 \sqrt{a+b x^3}}{8645 b^{8/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{144 \sqrt{2} 3^{3/4} a^{13/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{8645 b^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{216 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{13/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{8645 b^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{54 a^2 x^5 \sqrt{a+b x^3}}{6175 b}+\frac{2}{25} x^8 \left(a+b x^3\right)^{3/2}+\frac{18}{475} a x^8 \sqrt{a+b x^3}","-\frac{108 a^3 x^2 \sqrt{a+b x^3}}{8645 b^2}+\frac{432 a^4 \sqrt{a+b x^3}}{8645 b^{8/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{144 \sqrt{2} 3^{3/4} a^{13/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{8645 b^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{216 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{13/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{8645 b^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{54 a^2 x^5 \sqrt{a+b x^3}}{6175 b}+\frac{2}{25} x^8 \left(a+b x^3\right)^{3/2}+\frac{18}{475} a x^8 \sqrt{a+b x^3}",1,"(-108*a^3*x^2*Sqrt[a + b*x^3])/(8645*b^2) + (54*a^2*x^5*Sqrt[a + b*x^3])/(6175*b) + (18*a*x^8*Sqrt[a + b*x^3])/475 + (432*a^4*Sqrt[a + b*x^3])/(8645*b^(8/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) + (2*x^8*(a + b*x^3)^(3/2))/25 - (216*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(13/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(8645*b^(8/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (144*Sqrt[2]*3^(3/4)*a^(13/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(8645*b^(8/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",7,5,15,0.3333,1,"{279, 321, 303, 218, 1877}"
400,1,532,0,0.2441263,"\int x^4 \left(a+b x^3\right)^{3/2} \, dx","Int[x^4*(a + b*x^3)^(3/2),x]","-\frac{216 a^3 \sqrt{a+b x^3}}{1729 b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{72 \sqrt{2} 3^{3/4} a^{10/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{1729 b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{108 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{10/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{1729 b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{54 a^2 x^2 \sqrt{a+b x^3}}{1729 b}+\frac{2}{19} x^5 \left(a+b x^3\right)^{3/2}+\frac{18}{247} a x^5 \sqrt{a+b x^3}","-\frac{216 a^3 \sqrt{a+b x^3}}{1729 b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{72 \sqrt{2} 3^{3/4} a^{10/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{1729 b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{108 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{10/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{1729 b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{54 a^2 x^2 \sqrt{a+b x^3}}{1729 b}+\frac{2}{19} x^5 \left(a+b x^3\right)^{3/2}+\frac{18}{247} a x^5 \sqrt{a+b x^3}",1,"(54*a^2*x^2*Sqrt[a + b*x^3])/(1729*b) + (18*a*x^5*Sqrt[a + b*x^3])/247 - (216*a^3*Sqrt[a + b*x^3])/(1729*b^(5/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) + (2*x^5*(a + b*x^3)^(3/2))/19 + (108*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(10/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(1729*b^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) - (72*Sqrt[2]*3^(3/4)*a^(10/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(1729*b^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",6,5,15,0.3333,1,"{279, 321, 303, 218, 1877}"
401,1,508,0,0.1875079,"\int x \left(a+b x^3\right)^{3/2} \, dx","Int[x*(a + b*x^3)^(3/2),x]","\frac{54 a^2 \sqrt{a+b x^3}}{91 b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{18 \sqrt{2} 3^{3/4} a^{7/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{91 b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{27 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{7/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{91 b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{18}{91} a x^2 \sqrt{a+b x^3}+\frac{2}{13} x^2 \left(a+b x^3\right)^{3/2}","\frac{54 a^2 \sqrt{a+b x^3}}{91 b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{18 \sqrt{2} 3^{3/4} a^{7/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{91 b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{27 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{7/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{91 b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{18}{91} a x^2 \sqrt{a+b x^3}+\frac{2}{13} x^2 \left(a+b x^3\right)^{3/2}",1,"(18*a*x^2*Sqrt[a + b*x^3])/91 + (54*a^2*Sqrt[a + b*x^3])/(91*b^(2/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) + (2*x^2*(a + b*x^3)^(3/2))/13 - (27*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(7/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(91*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (18*Sqrt[2]*3^(3/4)*a^(7/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(91*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",5,4,13,0.3077,1,"{279, 303, 218, 1877}"
402,1,504,0,0.1921876,"\int \frac{\left(a+b x^3\right)^{3/2}}{x^2} \, dx","Int[(a + b*x^3)^(3/2)/x^2,x]","\frac{9 \sqrt{2} 3^{3/4} a^{4/3} \sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{7 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{27 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{4/3} \sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{14 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{9}{7} b x^2 \sqrt{a+b x^3}+\frac{27 a \sqrt[3]{b} \sqrt{a+b x^3}}{7 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{\left(a+b x^3\right)^{3/2}}{x}","\frac{9 \sqrt{2} 3^{3/4} a^{4/3} \sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{7 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{27 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{4/3} \sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{14 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{9}{7} b x^2 \sqrt{a+b x^3}+\frac{27 a \sqrt[3]{b} \sqrt{a+b x^3}}{7 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{\left(a+b x^3\right)^{3/2}}{x}",1,"(9*b*x^2*Sqrt[a + b*x^3])/7 + (27*a*b^(1/3)*Sqrt[a + b*x^3])/(7*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (a + b*x^3)^(3/2)/x - (27*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(4/3)*b^(1/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(14*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (9*Sqrt[2]*3^(3/4)*a^(4/3)*b^(1/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(7*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",5,5,15,0.3333,1,"{277, 279, 303, 218, 1877}"
403,1,505,0,0.1874761,"\int \frac{\left(a+b x^3\right)^{3/2}}{x^5} \, dx","Int[(a + b*x^3)^(3/2)/x^5,x]","\frac{9\ 3^{3/4} \sqrt[3]{a} b^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{4 \sqrt{2} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{27 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} b^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{16 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{27 b^{4/3} \sqrt{a+b x^3}}{8 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{\left(a+b x^3\right)^{3/2}}{4 x^4}-\frac{9 b \sqrt{a+b x^3}}{8 x}","\frac{9\ 3^{3/4} \sqrt[3]{a} b^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{4 \sqrt{2} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{27 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} b^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{16 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{27 b^{4/3} \sqrt{a+b x^3}}{8 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{\left(a+b x^3\right)^{3/2}}{4 x^4}-\frac{9 b \sqrt{a+b x^3}}{8 x}",1,"(-9*b*Sqrt[a + b*x^3])/(8*x) + (27*b^(4/3)*Sqrt[a + b*x^3])/(8*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (a + b*x^3)^(3/2)/(4*x^4) - (27*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(1/3)*b^(4/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(16*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (9*3^(3/4)*a^(1/3)*b^(4/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(4*Sqrt[2]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",5,4,15,0.2667,1,"{277, 303, 218, 1877}"
404,1,80,0,0.0442464,"\int \frac{x^{11}}{\sqrt{a+b x^3}} \, dx","Int[x^11/Sqrt[a + b*x^3],x]","\frac{2 a^2 \left(a+b x^3\right)^{3/2}}{3 b^4}-\frac{2 a^3 \sqrt{a+b x^3}}{3 b^4}+\frac{2 \left(a+b x^3\right)^{7/2}}{21 b^4}-\frac{2 a \left(a+b x^3\right)^{5/2}}{5 b^4}","\frac{2 a^2 \left(a+b x^3\right)^{3/2}}{3 b^4}-\frac{2 a^3 \sqrt{a+b x^3}}{3 b^4}+\frac{2 \left(a+b x^3\right)^{7/2}}{21 b^4}-\frac{2 a \left(a+b x^3\right)^{5/2}}{5 b^4}",1,"(-2*a^3*Sqrt[a + b*x^3])/(3*b^4) + (2*a^2*(a + b*x^3)^(3/2))/(3*b^4) - (2*a*(a + b*x^3)^(5/2))/(5*b^4) + (2*(a + b*x^3)^(7/2))/(21*b^4)","A",3,2,15,0.1333,1,"{266, 43}"
405,1,59,0,0.0338344,"\int \frac{x^8}{\sqrt{a+b x^3}} \, dx","Int[x^8/Sqrt[a + b*x^3],x]","\frac{2 a^2 \sqrt{a+b x^3}}{3 b^3}+\frac{2 \left(a+b x^3\right)^{5/2}}{15 b^3}-\frac{4 a \left(a+b x^3\right)^{3/2}}{9 b^3}","\frac{2 a^2 \sqrt{a+b x^3}}{3 b^3}+\frac{2 \left(a+b x^3\right)^{5/2}}{15 b^3}-\frac{4 a \left(a+b x^3\right)^{3/2}}{9 b^3}",1,"(2*a^2*Sqrt[a + b*x^3])/(3*b^3) - (4*a*(a + b*x^3)^(3/2))/(9*b^3) + (2*(a + b*x^3)^(5/2))/(15*b^3)","A",3,2,15,0.1333,1,"{266, 43}"
406,1,38,0,0.0229955,"\int \frac{x^5}{\sqrt{a+b x^3}} \, dx","Int[x^5/Sqrt[a + b*x^3],x]","\frac{2 \left(a+b x^3\right)^{3/2}}{9 b^2}-\frac{2 a \sqrt{a+b x^3}}{3 b^2}","\frac{2 \left(a+b x^3\right)^{3/2}}{9 b^2}-\frac{2 a \sqrt{a+b x^3}}{3 b^2}",1,"(-2*a*Sqrt[a + b*x^3])/(3*b^2) + (2*(a + b*x^3)^(3/2))/(9*b^2)","A",3,2,15,0.1333,1,"{266, 43}"
407,1,18,0,0.0045655,"\int \frac{x^2}{\sqrt{a+b x^3}} \, dx","Int[x^2/Sqrt[a + b*x^3],x]","\frac{2 \sqrt{a+b x^3}}{3 b}","\frac{2 \sqrt{a+b x^3}}{3 b}",1,"(2*Sqrt[a + b*x^3])/(3*b)","A",1,1,15,0.06667,1,"{261}"
408,1,27,0,0.0170935,"\int \frac{1}{x \sqrt{a+b x^3}} \, dx","Int[1/(x*Sqrt[a + b*x^3]),x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{3 \sqrt{a}}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{3 \sqrt{a}}",1,"(-2*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/(3*Sqrt[a])","A",3,3,15,0.2000,1,"{266, 63, 208}"
409,1,50,0,0.0264228,"\int \frac{1}{x^4 \sqrt{a+b x^3}} \, dx","Int[1/(x^4*Sqrt[a + b*x^3]),x]","\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{3 a^{3/2}}-\frac{\sqrt{a+b x^3}}{3 a x^3}","\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{3 a^{3/2}}-\frac{\sqrt{a+b x^3}}{3 a x^3}",1,"-Sqrt[a + b*x^3]/(3*a*x^3) + (b*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/(3*a^(3/2))","A",4,4,15,0.2667,1,"{266, 51, 63, 208}"
410,1,74,0,0.0381319,"\int \frac{1}{x^7 \sqrt{a+b x^3}} \, dx","Int[1/(x^7*Sqrt[a + b*x^3]),x]","-\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{4 a^{5/2}}+\frac{b \sqrt{a+b x^3}}{4 a^2 x^3}-\frac{\sqrt{a+b x^3}}{6 a x^6}","-\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{4 a^{5/2}}+\frac{b \sqrt{a+b x^3}}{4 a^2 x^3}-\frac{\sqrt{a+b x^3}}{6 a x^6}",1,"-Sqrt[a + b*x^3]/(6*a*x^6) + (b*Sqrt[a + b*x^3])/(4*a^2*x^3) - (b^2*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/(4*a^(5/2))","A",5,4,15,0.2667,1,"{266, 51, 63, 208}"
411,1,254,0,0.0666739,"\int \frac{x^6}{\sqrt{a+b x^3}} \, dx","Int[x^6/Sqrt[a + b*x^3],x]","\frac{32 \sqrt{2+\sqrt{3}} a^2 \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{55 \sqrt[4]{3} b^{7/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{16 a x \sqrt{a+b x^3}}{55 b^2}+\frac{2 x^4 \sqrt{a+b x^3}}{11 b}","\frac{32 \sqrt{2+\sqrt{3}} a^2 \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{55 \sqrt[4]{3} b^{7/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{16 a x \sqrt{a+b x^3}}{55 b^2}+\frac{2 x^4 \sqrt{a+b x^3}}{11 b}",1,"(-16*a*x*Sqrt[a + b*x^3])/(55*b^2) + (2*x^4*Sqrt[a + b*x^3])/(11*b) + (32*Sqrt[2 + Sqrt[3]]*a^2*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(55*3^(1/4)*b^(7/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",3,2,15,0.1333,1,"{321, 218}"
412,1,230,0,0.0408032,"\int \frac{x^3}{\sqrt{a+b x^3}} \, dx","Int[x^3/Sqrt[a + b*x^3],x]","\frac{2 x \sqrt{a+b x^3}}{5 b}-\frac{4 \sqrt{2+\sqrt{3}} a \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{5 \sqrt[4]{3} b^{4/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}","\frac{2 x \sqrt{a+b x^3}}{5 b}-\frac{4 \sqrt{2+\sqrt{3}} a \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{5 \sqrt[4]{3} b^{4/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}",1,"(2*x*Sqrt[a + b*x^3])/(5*b) - (4*Sqrt[2 + Sqrt[3]]*a*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(5*3^(1/4)*b^(4/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",2,2,15,0.1333,1,"{321, 218}"
413,1,207,0,0.0184218,"\int \frac{1}{\sqrt{a+b x^3}} \, dx","Int[1/Sqrt[a + b*x^3],x]","\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt[3]{b} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}","\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt[3]{b} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}",1,"(2*Sqrt[2 + Sqrt[3]]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3^(1/4)*b^(1/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",1,1,11,0.09091,1,"{218}"
414,1,234,0,0.041705,"\int \frac{1}{x^3 \sqrt{a+b x^3}} \, dx","Int[1/(x^3*Sqrt[a + b*x^3]),x]","-\frac{\sqrt{2+\sqrt{3}} b^{2/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt[4]{3} a \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\sqrt{a+b x^3}}{2 a x^2}","-\frac{\sqrt{2+\sqrt{3}} b^{2/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt[4]{3} a \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\sqrt{a+b x^3}}{2 a x^2}",1,"-Sqrt[a + b*x^3]/(2*a*x^2) - (Sqrt[2 + Sqrt[3]]*b^(2/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(2*3^(1/4)*a*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",2,2,15,0.1333,1,"{325, 218}"
415,1,256,0,0.0671831,"\int \frac{1}{x^6 \sqrt{a+b x^3}} \, dx","Int[1/(x^6*Sqrt[a + b*x^3]),x]","\frac{7 \sqrt{2+\sqrt{3}} b^{5/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{20 \sqrt[4]{3} a^2 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{7 b \sqrt{a+b x^3}}{20 a^2 x^2}-\frac{\sqrt{a+b x^3}}{5 a x^5}","\frac{7 \sqrt{2+\sqrt{3}} b^{5/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{20 \sqrt[4]{3} a^2 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{7 b \sqrt{a+b x^3}}{20 a^2 x^2}-\frac{\sqrt{a+b x^3}}{5 a x^5}",1,"-Sqrt[a + b*x^3]/(5*a*x^5) + (7*b*Sqrt[a + b*x^3])/(20*a^2*x^2) + (7*Sqrt[2 + Sqrt[3]]*b^(5/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(20*3^(1/4)*a^2*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",3,2,15,0.1333,1,"{325, 218}"
416,1,514,0,0.1959439,"\int \frac{x^7}{\sqrt{a+b x^3}} \, dx","Int[x^7/Sqrt[a + b*x^3],x]","\frac{80 a^2 \sqrt{a+b x^3}}{91 b^{8/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{80 \sqrt{2} a^{7/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{91 \sqrt[4]{3} b^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{40 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{7/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{91 b^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{20 a x^2 \sqrt{a+b x^3}}{91 b^2}+\frac{2 x^5 \sqrt{a+b x^3}}{13 b}","\frac{80 a^2 \sqrt{a+b x^3}}{91 b^{8/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{80 \sqrt{2} a^{7/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{91 \sqrt[4]{3} b^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{40 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{7/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{91 b^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{20 a x^2 \sqrt{a+b x^3}}{91 b^2}+\frac{2 x^5 \sqrt{a+b x^3}}{13 b}",1,"(-20*a*x^2*Sqrt[a + b*x^3])/(91*b^2) + (2*x^5*Sqrt[a + b*x^3])/(13*b) + (80*a^2*Sqrt[a + b*x^3])/(91*b^(8/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (40*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(7/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(91*b^(8/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (80*Sqrt[2]*a^(7/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(91*3^(1/4)*b^(8/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",5,4,15,0.2667,1,"{321, 303, 218, 1877}"
417,1,490,0,0.1455753,"\int \frac{x^4}{\sqrt{a+b x^3}} \, dx","Int[x^4/Sqrt[a + b*x^3],x]","-\frac{8 \sqrt{2} a^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{7 \sqrt[4]{3} b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{4 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{7 b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{8 a \sqrt{a+b x^3}}{7 b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{2 x^2 \sqrt{a+b x^3}}{7 b}","-\frac{8 \sqrt{2} a^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{7 \sqrt[4]{3} b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{4 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{7 b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{8 a \sqrt{a+b x^3}}{7 b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{2 x^2 \sqrt{a+b x^3}}{7 b}",1,"(2*x^2*Sqrt[a + b*x^3])/(7*b) - (8*a*Sqrt[a + b*x^3])/(7*b^(5/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) + (4*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(4/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(7*b^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) - (8*Sqrt[2]*a^(4/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(7*3^(1/4)*b^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",4,4,15,0.2667,1,"{321, 303, 218, 1877}"
418,1,462,0,0.0998305,"\int \frac{x}{\sqrt{a+b x^3}} \, dx","Int[x/Sqrt[a + b*x^3],x]","\frac{2 \sqrt{2} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 \sqrt{a+b x^3}}{b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}","\frac{2 \sqrt{2} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 \sqrt{a+b x^3}}{b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}",1,"(2*Sqrt[a + b*x^3])/(b^(2/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(1/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (2*Sqrt[2]*a^(1/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3^(1/4)*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",3,3,13,0.2308,1,"{303, 218, 1877}"
419,1,484,0,0.1415381,"\int \frac{1}{x^2 \sqrt{a+b x^3}} \, dx","Int[1/(x^2*Sqrt[a + b*x^3]),x]","\frac{\sqrt{2} \sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} a^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{2 a^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\sqrt{a+b x^3}}{a x}+\frac{\sqrt[3]{b} \sqrt{a+b x^3}}{a \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}","\frac{\sqrt{2} \sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} a^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{2 a^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\sqrt{a+b x^3}}{a x}+\frac{\sqrt[3]{b} \sqrt{a+b x^3}}{a \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}",1,"-(Sqrt[a + b*x^3]/(a*x)) + (b^(1/3)*Sqrt[a + b*x^3])/(a*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (3^(1/4)*Sqrt[2 - Sqrt[3]]*b^(1/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(2*a^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (Sqrt[2]*b^(1/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3^(1/4)*a^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",4,4,15,0.2667,1,"{325, 303, 218, 1877}"
420,1,514,0,0.1907012,"\int \frac{1}{x^5 \sqrt{a+b x^3}} \, dx","Int[1/(x^5*Sqrt[a + b*x^3]),x]","-\frac{5 b^{4/3} \sqrt{a+b x^3}}{8 a^2 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{5 b^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{4 \sqrt{2} \sqrt[4]{3} a^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{5 \sqrt[4]{3} \sqrt{2-\sqrt{3}} b^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{16 a^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{5 b \sqrt{a+b x^3}}{8 a^2 x}-\frac{\sqrt{a+b x^3}}{4 a x^4}","-\frac{5 b^{4/3} \sqrt{a+b x^3}}{8 a^2 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{5 b^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{4 \sqrt{2} \sqrt[4]{3} a^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{5 \sqrt[4]{3} \sqrt{2-\sqrt{3}} b^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{16 a^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{5 b \sqrt{a+b x^3}}{8 a^2 x}-\frac{\sqrt{a+b x^3}}{4 a x^4}",1,"-Sqrt[a + b*x^3]/(4*a*x^4) + (5*b*Sqrt[a + b*x^3])/(8*a^2*x) - (5*b^(4/3)*Sqrt[a + b*x^3])/(8*a^2*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) + (5*3^(1/4)*Sqrt[2 - Sqrt[3]]*b^(4/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(16*a^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) - (5*b^(4/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(4*Sqrt[2]*3^(1/4)*a^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",5,4,15,0.2667,1,"{325, 303, 218, 1877}"
421,1,78,0,0.0437219,"\int \frac{x^{11}}{\left(a+b x^3\right)^{3/2}} \, dx","Int[x^11/(a + b*x^3)^(3/2),x]","\frac{2 a^3}{3 b^4 \sqrt{a+b x^3}}+\frac{2 a^2 \sqrt{a+b x^3}}{b^4}-\frac{2 a \left(a+b x^3\right)^{3/2}}{3 b^4}+\frac{2 \left(a+b x^3\right)^{5/2}}{15 b^4}","\frac{2 a^3}{3 b^4 \sqrt{a+b x^3}}+\frac{2 a^2 \sqrt{a+b x^3}}{b^4}-\frac{2 a \left(a+b x^3\right)^{3/2}}{3 b^4}+\frac{2 \left(a+b x^3\right)^{5/2}}{15 b^4}",1,"(2*a^3)/(3*b^4*Sqrt[a + b*x^3]) + (2*a^2*Sqrt[a + b*x^3])/b^4 - (2*a*(a + b*x^3)^(3/2))/(3*b^4) + (2*(a + b*x^3)^(5/2))/(15*b^4)","A",3,2,15,0.1333,1,"{266, 43}"
422,1,59,0,0.0342384,"\int \frac{x^8}{\left(a+b x^3\right)^{3/2}} \, dx","Int[x^8/(a + b*x^3)^(3/2),x]","-\frac{2 a^2}{3 b^3 \sqrt{a+b x^3}}-\frac{4 a \sqrt{a+b x^3}}{3 b^3}+\frac{2 \left(a+b x^3\right)^{3/2}}{9 b^3}","-\frac{2 a^2}{3 b^3 \sqrt{a+b x^3}}-\frac{4 a \sqrt{a+b x^3}}{3 b^3}+\frac{2 \left(a+b x^3\right)^{3/2}}{9 b^3}",1,"(-2*a^2)/(3*b^3*Sqrt[a + b*x^3]) - (4*a*Sqrt[a + b*x^3])/(3*b^3) + (2*(a + b*x^3)^(3/2))/(9*b^3)","A",3,2,15,0.1333,1,"{266, 43}"
423,1,38,0,0.0225487,"\int \frac{x^5}{\left(a+b x^3\right)^{3/2}} \, dx","Int[x^5/(a + b*x^3)^(3/2),x]","\frac{2 a}{3 b^2 \sqrt{a+b x^3}}+\frac{2 \sqrt{a+b x^3}}{3 b^2}","\frac{2 a}{3 b^2 \sqrt{a+b x^3}}+\frac{2 \sqrt{a+b x^3}}{3 b^2}",1,"(2*a)/(3*b^2*Sqrt[a + b*x^3]) + (2*Sqrt[a + b*x^3])/(3*b^2)","A",3,2,15,0.1333,1,"{266, 43}"
424,1,18,0,0.0046769,"\int \frac{x^2}{\left(a+b x^3\right)^{3/2}} \, dx","Int[x^2/(a + b*x^3)^(3/2),x]","-\frac{2}{3 b \sqrt{a+b x^3}}","-\frac{2}{3 b \sqrt{a+b x^3}}",1,"-2/(3*b*Sqrt[a + b*x^3])","A",1,1,15,0.06667,1,"{261}"
425,1,46,0,0.0257106,"\int \frac{1}{x \left(a+b x^3\right)^{3/2}} \, dx","Int[1/(x*(a + b*x^3)^(3/2)),x]","\frac{2}{3 a \sqrt{a+b x^3}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{3 a^{3/2}}","\frac{2}{3 a \sqrt{a+b x^3}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{3 a^{3/2}}",1,"2/(3*a*Sqrt[a + b*x^3]) - (2*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/(3*a^(3/2))","A",4,4,15,0.2667,1,"{266, 51, 63, 208}"
426,1,66,0,0.0375877,"\int \frac{1}{x^4 \left(a+b x^3\right)^{3/2}} \, dx","Int[1/(x^4*(a + b*x^3)^(3/2)),x]","-\frac{\sqrt{a+b x^3}}{a^2 x^3}+\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{a^{5/2}}+\frac{2}{3 a x^3 \sqrt{a+b x^3}}","-\frac{b}{a^2 \sqrt{a+b x^3}}+\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{a^{5/2}}-\frac{1}{3 a x^3 \sqrt{a+b x^3}}",1,"2/(3*a*x^3*Sqrt[a + b*x^3]) - Sqrt[a + b*x^3]/(a^2*x^3) + (b*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/a^(5/2)","A",5,4,15,0.2667,1,"{266, 51, 63, 208}"
427,1,95,0,0.050526,"\int \frac{1}{x^7 \left(a+b x^3\right)^{3/2}} \, dx","Int[1/(x^7*(a + b*x^3)^(3/2)),x]","-\frac{5 b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{4 a^{7/2}}+\frac{5 b \sqrt{a+b x^3}}{4 a^3 x^3}-\frac{5 \sqrt{a+b x^3}}{6 a^2 x^6}+\frac{2}{3 a x^6 \sqrt{a+b x^3}}","\frac{5 b^2}{4 a^3 \sqrt{a+b x^3}}-\frac{5 b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{4 a^{7/2}}+\frac{5 b}{12 a^2 x^3 \sqrt{a+b x^3}}-\frac{1}{6 a x^6 \sqrt{a+b x^3}}",1,"2/(3*a*x^6*Sqrt[a + b*x^3]) - (5*Sqrt[a + b*x^3])/(6*a^2*x^6) + (5*b*Sqrt[a + b*x^3])/(4*a^3*x^3) - (5*b^2*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/(4*a^(7/2))","A",6,4,15,0.2667,1,"{266, 51, 63, 208}"
428,1,251,0,0.0674615,"\int \frac{x^6}{\left(a+b x^3\right)^{3/2}} \, dx","Int[x^6/(a + b*x^3)^(3/2),x]","-\frac{32 \sqrt{2+\sqrt{3}} a \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{15 \sqrt[4]{3} b^{7/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{16 x \sqrt{a+b x^3}}{15 b^2}-\frac{2 x^4}{3 b \sqrt{a+b x^3}}","-\frac{32 \sqrt{2+\sqrt{3}} a \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{15 \sqrt[4]{3} b^{7/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{16 x \sqrt{a+b x^3}}{15 b^2}-\frac{2 x^4}{3 b \sqrt{a+b x^3}}",1,"(-2*x^4)/(3*b*Sqrt[a + b*x^3]) + (16*x*Sqrt[a + b*x^3])/(15*b^2) - (32*Sqrt[2 + Sqrt[3]]*a*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(15*3^(1/4)*b^(7/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",3,3,15,0.2000,1,"{288, 321, 218}"
429,1,229,0,0.0430155,"\int \frac{x^3}{\left(a+b x^3\right)^{3/2}} \, dx","Int[x^3/(a + b*x^3)^(3/2),x]","\frac{4 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} b^{4/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2 x}{3 b \sqrt{a+b x^3}}","\frac{4 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} b^{4/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2 x}{3 b \sqrt{a+b x^3}}",1,"(-2*x)/(3*b*Sqrt[a + b*x^3]) + (4*Sqrt[2 + Sqrt[3]]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*b^(4/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",2,2,15,0.1333,1,"{288, 218}"
430,1,232,0,0.0395791,"\int \frac{1}{\left(a+b x^3\right)^{3/2}} \, dx","Int[(a + b*x^3)^(-3/2),x]","\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} a \sqrt[3]{b} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 x}{3 a \sqrt{a+b x^3}}","\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} a \sqrt[3]{b} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 x}{3 a \sqrt{a+b x^3}}",1,"(2*x)/(3*a*Sqrt[a + b*x^3]) + (2*Sqrt[2 + Sqrt[3]]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*a*b^(1/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",2,2,11,0.1818,1,"{199, 218}"
431,1,255,0,0.0667766,"\int \frac{1}{x^3 \left(a+b x^3\right)^{3/2}} \, dx","Int[1/(x^3*(a + b*x^3)^(3/2)),x]","-\frac{7 \sqrt{2+\sqrt{3}} b^{2/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{6 \sqrt[4]{3} a^2 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{7 \sqrt{a+b x^3}}{6 a^2 x^2}+\frac{2}{3 a x^2 \sqrt{a+b x^3}}","-\frac{7 \sqrt{2+\sqrt{3}} b^{2/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{6 \sqrt[4]{3} a^2 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{7 \sqrt{a+b x^3}}{6 a^2 x^2}+\frac{2}{3 a x^2 \sqrt{a+b x^3}}",1,"2/(3*a*x^2*Sqrt[a + b*x^3]) - (7*Sqrt[a + b*x^3])/(6*a^2*x^2) - (7*Sqrt[2 + Sqrt[3]]*b^(2/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(6*3^(1/4)*a^2*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",3,3,15,0.2000,1,"{290, 325, 218}"
432,1,277,0,0.0939251,"\int \frac{1}{x^6 \left(a+b x^3\right)^{3/2}} \, dx","Int[1/(x^6*(a + b*x^3)^(3/2)),x]","\frac{91 \sqrt{2+\sqrt{3}} b^{5/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{60 \sqrt[4]{3} a^3 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{91 b \sqrt{a+b x^3}}{60 a^3 x^2}-\frac{13 \sqrt{a+b x^3}}{15 a^2 x^5}+\frac{2}{3 a x^5 \sqrt{a+b x^3}}","\frac{91 \sqrt{2+\sqrt{3}} b^{5/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{60 \sqrt[4]{3} a^3 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{91 b \sqrt{a+b x^3}}{60 a^3 x^2}-\frac{13 \sqrt{a+b x^3}}{15 a^2 x^5}+\frac{2}{3 a x^5 \sqrt{a+b x^3}}",1,"2/(3*a*x^5*Sqrt[a + b*x^3]) - (13*Sqrt[a + b*x^3])/(15*a^2*x^5) + (91*b*Sqrt[a + b*x^3])/(60*a^3*x^2) + (91*Sqrt[2 + Sqrt[3]]*b^(5/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(60*3^(1/4)*a^3*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",4,3,15,0.2000,1,"{290, 325, 218}"
433,1,511,0,0.1948235,"\int \frac{x^7}{\left(a+b x^3\right)^{3/2}} \, dx","Int[x^7/(a + b*x^3)^(3/2),x]","-\frac{80 \sqrt{2} a^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{21 \sqrt[4]{3} b^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{40 \sqrt{2-\sqrt{3}} a^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{7\ 3^{3/4} b^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{20 x^2 \sqrt{a+b x^3}}{21 b^2}-\frac{80 a \sqrt{a+b x^3}}{21 b^{8/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{2 x^5}{3 b \sqrt{a+b x^3}}","-\frac{80 \sqrt{2} a^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{21 \sqrt[4]{3} b^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{40 \sqrt{2-\sqrt{3}} a^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{7\ 3^{3/4} b^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{20 x^2 \sqrt{a+b x^3}}{21 b^2}-\frac{80 a \sqrt{a+b x^3}}{21 b^{8/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{2 x^5}{3 b \sqrt{a+b x^3}}",1,"(-2*x^5)/(3*b*Sqrt[a + b*x^3]) + (20*x^2*Sqrt[a + b*x^3])/(21*b^2) - (80*a*Sqrt[a + b*x^3])/(21*b^(8/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) + (40*Sqrt[2 - Sqrt[3]]*a^(4/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(7*3^(3/4)*b^(8/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) - (80*Sqrt[2]*a^(4/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(21*3^(1/4)*b^(8/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",5,5,15,0.3333,1,"{288, 321, 303, 218, 1877}"
434,1,487,0,0.1488701,"\int \frac{x^4}{\left(a+b x^3\right)^{3/2}} \, dx","Int[x^4/(a + b*x^3)^(3/2),x]","\frac{8 \sqrt{2} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{4 \sqrt{2-\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3^{3/4} b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{8 \sqrt{a+b x^3}}{3 b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{2 x^2}{3 b \sqrt{a+b x^3}}","\frac{8 \sqrt{2} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{4 \sqrt{2-\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3^{3/4} b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{8 \sqrt{a+b x^3}}{3 b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{2 x^2}{3 b \sqrt{a+b x^3}}",1,"(-2*x^2)/(3*b*Sqrt[a + b*x^3]) + (8*Sqrt[a + b*x^3])/(3*b^(5/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (4*Sqrt[2 - Sqrt[3]]*a^(1/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3^(3/4)*b^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (8*Sqrt[2]*a^(1/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*b^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",4,4,15,0.2667,1,"{288, 303, 218, 1877}"
435,1,489,0,0.1475969,"\int \frac{x}{\left(a+b x^3\right)^{3/2}} \, dx","Int[x/(a + b*x^3)^(3/2),x]","-\frac{2 \sqrt{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} a^{2/3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{\sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3^{3/4} a^{2/3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2 \sqrt{a+b x^3}}{3 a b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{2 x^2}{3 a \sqrt{a+b x^3}}","-\frac{2 \sqrt{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} a^{2/3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{\sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3^{3/4} a^{2/3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2 \sqrt{a+b x^3}}{3 a b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{2 x^2}{3 a \sqrt{a+b x^3}}",1,"(2*x^2)/(3*a*Sqrt[a + b*x^3]) - (2*Sqrt[a + b*x^3])/(3*a*b^(2/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) + (Sqrt[2 - Sqrt[3]]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3^(3/4)*a^(2/3)*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) - (2*Sqrt[2]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*a^(2/3)*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",4,4,13,0.3077,1,"{290, 303, 218, 1877}"
436,1,513,0,0.191643,"\int \frac{1}{x^2 \left(a+b x^3\right)^{3/2}} \, dx","Int[1/(x^2*(a + b*x^3)^(3/2)),x]","\frac{5 \sqrt{2} \sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} a^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{5 \sqrt{2-\sqrt{3}} \sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{2\ 3^{3/4} a^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{5 \sqrt{a+b x^3}}{3 a^2 x}+\frac{5 \sqrt[3]{b} \sqrt{a+b x^3}}{3 a^2 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{2}{3 a x \sqrt{a+b x^3}}","\frac{5 \sqrt{2} \sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} a^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{5 \sqrt{2-\sqrt{3}} \sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{2\ 3^{3/4} a^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{5 \sqrt{a+b x^3}}{3 a^2 x}+\frac{5 \sqrt[3]{b} \sqrt{a+b x^3}}{3 a^2 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{2}{3 a x \sqrt{a+b x^3}}",1,"2/(3*a*x*Sqrt[a + b*x^3]) - (5*Sqrt[a + b*x^3])/(3*a^2*x) + (5*b^(1/3)*Sqrt[a + b*x^3])/(3*a^2*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (5*Sqrt[2 - Sqrt[3]]*b^(1/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(2*3^(3/4)*a^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (5*Sqrt[2]*b^(1/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*a^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",5,5,15,0.3333,1,"{290, 325, 303, 218, 1877}"
437,1,535,0,0.2466944,"\int \frac{1}{x^5 \left(a+b x^3\right)^{3/2}} \, dx","Int[1/(x^5*(a + b*x^3)^(3/2)),x]","-\frac{55 b^{4/3} \sqrt{a+b x^3}}{24 a^3 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{55 b^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{12 \sqrt{2} \sqrt[4]{3} a^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{55 \sqrt{2-\sqrt{3}} b^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{16\ 3^{3/4} a^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{55 b \sqrt{a+b x^3}}{24 a^3 x}-\frac{11 \sqrt{a+b x^3}}{12 a^2 x^4}+\frac{2}{3 a x^4 \sqrt{a+b x^3}}","-\frac{55 b^{4/3} \sqrt{a+b x^3}}{24 a^3 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{55 b^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{12 \sqrt{2} \sqrt[4]{3} a^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{55 \sqrt{2-\sqrt{3}} b^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{16\ 3^{3/4} a^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{55 b \sqrt{a+b x^3}}{24 a^3 x}-\frac{11 \sqrt{a+b x^3}}{12 a^2 x^4}+\frac{2}{3 a x^4 \sqrt{a+b x^3}}",1,"2/(3*a*x^4*Sqrt[a + b*x^3]) - (11*Sqrt[a + b*x^3])/(12*a^2*x^4) + (55*b*Sqrt[a + b*x^3])/(24*a^3*x) - (55*b^(4/3)*Sqrt[a + b*x^3])/(24*a^3*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) + (55*Sqrt[2 - Sqrt[3]]*b^(4/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(16*3^(3/4)*a^(8/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) - (55*b^(4/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(12*Sqrt[2]*3^(1/4)*a^(8/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",6,5,15,0.3333,1,"{290, 325, 303, 218, 1877}"
438,1,53,0,0.0178267,"\int \frac{x^{11}}{\sqrt{1+x^3}} \, dx","Int[x^11/Sqrt[1 + x^3],x]","\frac{2}{21} \left(x^3+1\right)^{7/2}-\frac{2}{5} \left(x^3+1\right)^{5/2}+\frac{2}{3} \left(x^3+1\right)^{3/2}-\frac{2 \sqrt{x^3+1}}{3}","\frac{2}{21} \left(x^3+1\right)^{7/2}-\frac{2}{5} \left(x^3+1\right)^{5/2}+\frac{2}{3} \left(x^3+1\right)^{3/2}-\frac{2 \sqrt{x^3+1}}{3}",1,"(-2*Sqrt[1 + x^3])/3 + (2*(1 + x^3)^(3/2))/3 - (2*(1 + x^3)^(5/2))/5 + (2*(1 + x^3)^(7/2))/21","A",3,2,13,0.1538,1,"{266, 43}"
439,1,40,0,0.0146081,"\int \frac{x^8}{\sqrt{1+x^3}} \, dx","Int[x^8/Sqrt[1 + x^3],x]","\frac{2}{15} \left(x^3+1\right)^{5/2}-\frac{4}{9} \left(x^3+1\right)^{3/2}+\frac{2 \sqrt{x^3+1}}{3}","\frac{2}{15} \left(x^3+1\right)^{5/2}-\frac{4}{9} \left(x^3+1\right)^{3/2}+\frac{2 \sqrt{x^3+1}}{3}",1,"(2*Sqrt[1 + x^3])/3 - (4*(1 + x^3)^(3/2))/9 + (2*(1 + x^3)^(5/2))/15","A",3,2,13,0.1538,1,"{266, 43}"
440,1,27,0,0.0102721,"\int \frac{x^5}{\sqrt{1+x^3}} \, dx","Int[x^5/Sqrt[1 + x^3],x]","\frac{2}{9} \left(x^3+1\right)^{3/2}-\frac{2 \sqrt{x^3+1}}{3}","\frac{2}{9} \left(x^3+1\right)^{3/2}-\frac{2 \sqrt{x^3+1}}{3}",1,"(-2*Sqrt[1 + x^3])/3 + (2*(1 + x^3)^(3/2))/9","A",3,2,13,0.1538,1,"{266, 43}"
441,1,13,0,0.0025572,"\int \frac{x^2}{\sqrt{1+x^3}} \, dx","Int[x^2/Sqrt[1 + x^3],x]","\frac{2 \sqrt{x^3+1}}{3}","\frac{2 \sqrt{x^3+1}}{3}",1,"(2*Sqrt[1 + x^3])/3","A",1,1,13,0.07692,1,"{261}"
442,1,14,0,0.0067682,"\int \frac{1}{x \sqrt{1+x^3}} \, dx","Int[1/(x*Sqrt[1 + x^3]),x]","-\frac{2}{3} \tanh ^{-1}\left(\sqrt{x^3+1}\right)","-\frac{2}{3} \tanh ^{-1}\left(\sqrt{x^3+1}\right)",1,"(-2*ArcTanh[Sqrt[1 + x^3]])/3","A",3,3,13,0.2308,1,"{266, 63, 207}"
443,1,31,0,0.0106171,"\int \frac{1}{x^4 \sqrt{1+x^3}} \, dx","Int[1/(x^4*Sqrt[1 + x^3]),x]","\frac{1}{3} \tanh ^{-1}\left(\sqrt{x^3+1}\right)-\frac{\sqrt{x^3+1}}{3 x^3}","\frac{1}{3} \tanh ^{-1}\left(\sqrt{x^3+1}\right)-\frac{\sqrt{x^3+1}}{3 x^3}",1,"-Sqrt[1 + x^3]/(3*x^3) + ArcTanh[Sqrt[1 + x^3]]/3","A",4,4,13,0.3077,1,"{266, 51, 63, 207}"
444,1,47,0,0.016173,"\int \frac{1}{x^7 \sqrt{1+x^3}} \, dx","Int[1/(x^7*Sqrt[1 + x^3]),x]","\frac{\sqrt{x^3+1}}{4 x^3}-\frac{\sqrt{x^3+1}}{6 x^6}-\frac{1}{4} \tanh ^{-1}\left(\sqrt{x^3+1}\right)","\frac{\sqrt{x^3+1}}{4 x^3}-\frac{\sqrt{x^3+1}}{6 x^6}-\frac{1}{4} \tanh ^{-1}\left(\sqrt{x^3+1}\right)",1,"-Sqrt[1 + x^3]/(6*x^6) + Sqrt[1 + x^3]/(4*x^3) - ArcTanh[Sqrt[1 + x^3]]/4","A",5,4,13,0.3077,1,"{266, 51, 63, 207}"
445,1,63,0,0.0201826,"\int \frac{1}{x^{10} \sqrt{1+x^3}} \, dx","Int[1/(x^10*Sqrt[1 + x^3]),x]","-\frac{5 \sqrt{x^3+1}}{24 x^3}+\frac{5 \sqrt{x^3+1}}{36 x^6}-\frac{\sqrt{x^3+1}}{9 x^9}+\frac{5}{24} \tanh ^{-1}\left(\sqrt{x^3+1}\right)","-\frac{5 \sqrt{x^3+1}}{24 x^3}+\frac{5 \sqrt{x^3+1}}{36 x^6}-\frac{\sqrt{x^3+1}}{9 x^9}+\frac{5}{24} \tanh ^{-1}\left(\sqrt{x^3+1}\right)",1,"-Sqrt[1 + x^3]/(9*x^9) + (5*Sqrt[1 + x^3])/(36*x^6) - (5*Sqrt[1 + x^3])/(24*x^3) + (5*ArcTanh[Sqrt[1 + x^3]])/24","A",6,4,13,0.3077,1,"{266, 51, 63, 207}"
446,1,136,0,0.0340231,"\int \frac{x^6}{\sqrt{1+x^3}} \, dx","Int[x^6/Sqrt[1 + x^3],x]","\frac{2}{11} \sqrt{x^3+1} x^4-\frac{16}{55} \sqrt{x^3+1} x+\frac{32 \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{55 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}","\frac{2}{11} \sqrt{x^3+1} x^4-\frac{16}{55} \sqrt{x^3+1} x+\frac{32 \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{55 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}",1,"(-16*x*Sqrt[1 + x^3])/55 + (2*x^4*Sqrt[1 + x^3])/11 + (32*Sqrt[2 + Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(55*3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3])","A",3,2,13,0.1538,1,"{321, 218}"
447,1,120,0,0.0169843,"\int \frac{x^3}{\sqrt{1+x^3}} \, dx","Int[x^3/Sqrt[1 + x^3],x]","\frac{2}{5} x \sqrt{x^3+1}-\frac{4 \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{5 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}","\frac{2}{5} x \sqrt{x^3+1}-\frac{4 \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{5 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}",1,"(2*x*Sqrt[1 + x^3])/5 - (4*Sqrt[2 + Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(5*3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3])","A",2,2,13,0.1538,1,"{321, 218}"
448,1,103,0,0.0074325,"\int \frac{1}{\sqrt{1+x^3}} \, dx","Int[1/Sqrt[1 + x^3],x]","\frac{2 \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}","\frac{2 \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}",1,"(2*Sqrt[2 + Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3])","A",1,1,9,0.1111,1,"{218}"
449,1,122,0,0.0172496,"\int \frac{1}{x^3 \sqrt{1+x^3}} \, dx","Int[1/(x^3*Sqrt[1 + x^3]),x]","-\frac{\sqrt{x^3+1}}{2 x^2}-\frac{\sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}","-\frac{\sqrt{x^3+1}}{2 x^2}-\frac{\sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}",1,"-Sqrt[1 + x^3]/(2*x^2) - (Sqrt[2 + Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(2*3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3])","A",2,2,13,0.1538,1,"{325, 218}"
450,1,138,0,0.0274403,"\int \frac{1}{x^6 \sqrt{1+x^3}} \, dx","Int[1/(x^6*Sqrt[1 + x^3]),x]","\frac{7 \sqrt{x^3+1}}{20 x^2}-\frac{\sqrt{x^3+1}}{5 x^5}+\frac{7 \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{20 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}","\frac{7 \sqrt{x^3+1}}{20 x^2}-\frac{\sqrt{x^3+1}}{5 x^5}+\frac{7 \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{20 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}",1,"-Sqrt[1 + x^3]/(5*x^5) + (7*Sqrt[1 + x^3])/(20*x^2) + (7*Sqrt[2 + Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(20*3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3])","A",3,2,13,0.1538,1,"{325, 218}"
451,1,262,0,0.0701099,"\int \frac{x^7}{\sqrt{1+x^3}} \, dx","Int[x^7/Sqrt[1 + x^3],x]","\frac{2}{13} \sqrt{x^3+1} x^5-\frac{20}{91} \sqrt{x^3+1} x^2+\frac{80 \sqrt{x^3+1}}{91 \left(x+\sqrt{3}+1\right)}+\frac{80 \sqrt{2} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{91 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}-\frac{40 \sqrt[4]{3} \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{91 \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}","\frac{2}{13} \sqrt{x^3+1} x^5-\frac{20}{91} \sqrt{x^3+1} x^2+\frac{80 \sqrt{x^3+1}}{91 \left(x+\sqrt{3}+1\right)}+\frac{80 \sqrt{2} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{91 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}-\frac{40 \sqrt[4]{3} \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{91 \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}",1,"(-20*x^2*Sqrt[1 + x^3])/91 + (2*x^5*Sqrt[1 + x^3])/13 + (80*Sqrt[1 + x^3])/(91*(1 + Sqrt[3] + x)) - (40*3^(1/4)*Sqrt[2 - Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticE[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(91*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3]) + (80*Sqrt[2]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(91*3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3])","A",5,4,13,0.3077,1,"{321, 303, 218, 1877}"
452,1,246,0,0.0490425,"\int \frac{x^4}{\sqrt{1+x^3}} \, dx","Int[x^4/Sqrt[1 + x^3],x]","\frac{2}{7} \sqrt{x^3+1} x^2-\frac{8 \sqrt{x^3+1}}{7 \left(x+\sqrt{3}+1\right)}-\frac{8 \sqrt{2} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{7 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}+\frac{4 \sqrt[4]{3} \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{7 \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}","\frac{2}{7} \sqrt{x^3+1} x^2-\frac{8 \sqrt{x^3+1}}{7 \left(x+\sqrt{3}+1\right)}-\frac{8 \sqrt{2} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{7 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}+\frac{4 \sqrt[4]{3} \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{7 \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}",1,"(2*x^2*Sqrt[1 + x^3])/7 - (8*Sqrt[1 + x^3])/(7*(1 + Sqrt[3] + x)) + (4*3^(1/4)*Sqrt[2 - Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticE[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(7*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3]) - (8*Sqrt[2]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(7*3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3])","A",4,4,13,0.3077,1,"{321, 303, 218, 1877}"
453,1,224,0,0.0331502,"\int \frac{x}{\sqrt{1+x^3}} \, dx","Int[x/Sqrt[1 + x^3],x]","\frac{2 \sqrt{x^3+1}}{x+\sqrt{3}+1}+\frac{2 \sqrt{2} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}","\frac{2 \sqrt{x^3+1}}{x+\sqrt{3}+1}+\frac{2 \sqrt{2} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}",1,"(2*Sqrt[1 + x^3])/(1 + Sqrt[3] + x) - (3^(1/4)*Sqrt[2 - Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticE[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3]) + (2*Sqrt[2]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3])","A",3,3,11,0.2727,1,"{303, 218, 1877}"
454,1,238,0,0.0534705,"\int \frac{1}{x^2 \sqrt{1+x^3}} \, dx","Int[1/(x^2*Sqrt[1 + x^3]),x]","-\frac{\sqrt{x^3+1}}{x}+\frac{\sqrt{x^3+1}}{x+\sqrt{3}+1}+\frac{\sqrt{2} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}","-\frac{\sqrt{x^3+1}}{x}+\frac{\sqrt{x^3+1}}{x+\sqrt{3}+1}+\frac{\sqrt{2} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}",1,"-(Sqrt[1 + x^3]/x) + Sqrt[1 + x^3]/(1 + Sqrt[3] + x) - (3^(1/4)*Sqrt[2 - Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticE[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(2*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3]) + (Sqrt[2]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3])","A",4,4,13,0.3077,1,"{325, 303, 218, 1877}"
455,1,262,0,0.0660223,"\int \frac{1}{x^5 \sqrt{1+x^3}} \, dx","Int[1/(x^5*Sqrt[1 + x^3]),x]","\frac{5 \sqrt{x^3+1}}{8 x}-\frac{5 \sqrt{x^3+1}}{8 \left(x+\sqrt{3}+1\right)}-\frac{\sqrt{x^3+1}}{4 x^4}-\frac{5 (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{4 \sqrt{2} \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}+\frac{5 \sqrt[4]{3} \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{16 \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}","\frac{5 \sqrt{x^3+1}}{8 x}-\frac{5 \sqrt{x^3+1}}{8 \left(x+\sqrt{3}+1\right)}-\frac{\sqrt{x^3+1}}{4 x^4}-\frac{5 (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{4 \sqrt{2} \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}+\frac{5 \sqrt[4]{3} \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{16 \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}",1,"-Sqrt[1 + x^3]/(4*x^4) + (5*Sqrt[1 + x^3])/(8*x) - (5*Sqrt[1 + x^3])/(8*(1 + Sqrt[3] + x)) + (5*3^(1/4)*Sqrt[2 - Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticE[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(16*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3]) - (5*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(4*Sqrt[2]*3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3])","A",5,4,13,0.3077,1,"{325, 303, 218, 1877}"
456,1,61,0,0.0240009,"\int \frac{x^{11}}{\sqrt{1-x^3}} \, dx","Int[x^11/Sqrt[1 - x^3],x]","\frac{2}{21} \left(1-x^3\right)^{7/2}-\frac{2}{5} \left(1-x^3\right)^{5/2}+\frac{2}{3} \left(1-x^3\right)^{3/2}-\frac{2 \sqrt{1-x^3}}{3}","\frac{2}{21} \left(1-x^3\right)^{7/2}-\frac{2}{5} \left(1-x^3\right)^{5/2}+\frac{2}{3} \left(1-x^3\right)^{3/2}-\frac{2 \sqrt{1-x^3}}{3}",1,"(-2*Sqrt[1 - x^3])/3 + (2*(1 - x^3)^(3/2))/3 - (2*(1 - x^3)^(5/2))/5 + (2*(1 - x^3)^(7/2))/21","A",3,2,15,0.1333,1,"{266, 43}"
457,1,46,0,0.0186933,"\int \frac{x^8}{\sqrt{1-x^3}} \, dx","Int[x^8/Sqrt[1 - x^3],x]","-\frac{2}{15} \left(1-x^3\right)^{5/2}+\frac{4}{9} \left(1-x^3\right)^{3/2}-\frac{2 \sqrt{1-x^3}}{3}","-\frac{2}{15} \left(1-x^3\right)^{5/2}+\frac{4}{9} \left(1-x^3\right)^{3/2}-\frac{2 \sqrt{1-x^3}}{3}",1,"(-2*Sqrt[1 - x^3])/3 + (4*(1 - x^3)^(3/2))/9 - (2*(1 - x^3)^(5/2))/15","A",3,2,15,0.1333,1,"{266, 43}"
458,1,31,0,0.0133722,"\int \frac{x^5}{\sqrt{1-x^3}} \, dx","Int[x^5/Sqrt[1 - x^3],x]","\frac{2}{9} \left(1-x^3\right)^{3/2}-\frac{2 \sqrt{1-x^3}}{3}","\frac{2}{9} \left(1-x^3\right)^{3/2}-\frac{2 \sqrt{1-x^3}}{3}",1,"(-2*Sqrt[1 - x^3])/3 + (2*(1 - x^3)^(3/2))/9","A",3,2,15,0.1333,1,"{266, 43}"
459,1,15,0,0.0028425,"\int \frac{x^2}{\sqrt{1-x^3}} \, dx","Int[x^2/Sqrt[1 - x^3],x]","-\frac{2}{3} \sqrt{1-x^3}","-\frac{2}{3} \sqrt{1-x^3}",1,"(-2*Sqrt[1 - x^3])/3","A",1,1,15,0.06667,1,"{261}"
460,1,16,0,0.0081268,"\int \frac{1}{x \sqrt{1-x^3}} \, dx","Int[1/(x*Sqrt[1 - x^3]),x]","-\frac{2}{3} \tanh ^{-1}\left(\sqrt{1-x^3}\right)","-\frac{2}{3} \tanh ^{-1}\left(\sqrt{1-x^3}\right)",1,"(-2*ArcTanh[Sqrt[1 - x^3]])/3","A",3,3,15,0.2000,1,"{266, 63, 206}"
461,1,35,0,0.0143049,"\int \frac{1}{x^4 \sqrt{1-x^3}} \, dx","Int[1/(x^4*Sqrt[1 - x^3]),x]","-\frac{\sqrt{1-x^3}}{3 x^3}-\frac{1}{3} \tanh ^{-1}\left(\sqrt{1-x^3}\right)","-\frac{\sqrt{1-x^3}}{3 x^3}-\frac{1}{3} \tanh ^{-1}\left(\sqrt{1-x^3}\right)",1,"-Sqrt[1 - x^3]/(3*x^3) - ArcTanh[Sqrt[1 - x^3]]/3","A",4,4,15,0.2667,1,"{266, 51, 63, 206}"
462,1,53,0,0.0204685,"\int \frac{1}{x^7 \sqrt{1-x^3}} \, dx","Int[1/(x^7*Sqrt[1 - x^3]),x]","-\frac{\sqrt{1-x^3}}{4 x^3}-\frac{\sqrt{1-x^3}}{6 x^6}-\frac{1}{4} \tanh ^{-1}\left(\sqrt{1-x^3}\right)","-\frac{\sqrt{1-x^3}}{4 x^3}-\frac{\sqrt{1-x^3}}{6 x^6}-\frac{1}{4} \tanh ^{-1}\left(\sqrt{1-x^3}\right)",1,"-Sqrt[1 - x^3]/(6*x^6) - Sqrt[1 - x^3]/(4*x^3) - ArcTanh[Sqrt[1 - x^3]]/4","A",5,4,15,0.2667,1,"{266, 51, 63, 206}"
463,1,71,0,0.0280834,"\int \frac{1}{x^{10} \sqrt{1-x^3}} \, dx","Int[1/(x^10*Sqrt[1 - x^3]),x]","-\frac{5 \sqrt{1-x^3}}{24 x^3}-\frac{5 \sqrt{1-x^3}}{36 x^6}-\frac{\sqrt{1-x^3}}{9 x^9}-\frac{5}{24} \tanh ^{-1}\left(\sqrt{1-x^3}\right)","-\frac{5 \sqrt{1-x^3}}{24 x^3}-\frac{5 \sqrt{1-x^3}}{36 x^6}-\frac{\sqrt{1-x^3}}{9 x^9}-\frac{5}{24} \tanh ^{-1}\left(\sqrt{1-x^3}\right)",1,"-Sqrt[1 - x^3]/(9*x^9) - (5*Sqrt[1 - x^3])/(36*x^6) - (5*Sqrt[1 - x^3])/(24*x^3) - (5*ArcTanh[Sqrt[1 - x^3]])/24","A",6,4,15,0.2667,1,"{266, 51, 63, 206}"
464,1,152,0,0.0381576,"\int \frac{x^6}{\sqrt{1-x^3}} \, dx","Int[x^6/Sqrt[1 - x^3],x]","-\frac{2}{11} \sqrt{1-x^3} x^4-\frac{16}{55} \sqrt{1-x^3} x-\frac{32 \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{55 \sqrt[4]{3} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}","-\frac{2}{11} \sqrt{1-x^3} x^4-\frac{16}{55} \sqrt{1-x^3} x-\frac{32 \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{55 \sqrt[4]{3} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}",1,"(-16*x*Sqrt[1 - x^3])/55 - (2*x^4*Sqrt[1 - x^3])/11 - (32*Sqrt[2 + Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] - x)/(1 + Sqrt[3] - x)], -7 - 4*Sqrt[3]])/(55*3^(1/4)*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[1 - x^3])","A",3,2,15,0.1333,1,"{321, 218}"
465,1,134,0,0.0206643,"\int \frac{x^3}{\sqrt{1-x^3}} \, dx","Int[x^3/Sqrt[1 - x^3],x]","-\frac{2}{5} \sqrt{1-x^3} x-\frac{4 \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{5 \sqrt[4]{3} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}","-\frac{2}{5} \sqrt{1-x^3} x-\frac{4 \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{5 \sqrt[4]{3} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}",1,"(-2*x*Sqrt[1 - x^3])/5 - (4*Sqrt[2 + Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] - x)/(1 + Sqrt[3] - x)], -7 - 4*Sqrt[3]])/(5*3^(1/4)*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[1 - x^3])","A",2,2,15,0.1333,1,"{321, 218}"
466,1,115,0,0.009101,"\int \frac{1}{\sqrt{1-x^3}} \, dx","Int[1/Sqrt[1 - x^3],x]","-\frac{2 \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}","-\frac{2 \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}",1,"(-2*Sqrt[2 + Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] - x)/(1 + Sqrt[3] - x)], -7 - 4*Sqrt[3]])/(3^(1/4)*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[1 - x^3])","A",1,1,11,0.09091,1,"{218}"
467,1,136,0,0.0210201,"\int \frac{1}{x^3 \sqrt{1-x^3}} \, dx","Int[1/(x^3*Sqrt[1 - x^3]),x]","-\frac{\sqrt{1-x^3}}{2 x^2}-\frac{\sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt[4]{3} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}","-\frac{\sqrt{1-x^3}}{2 x^2}-\frac{\sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt[4]{3} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}",1,"-Sqrt[1 - x^3]/(2*x^2) - (Sqrt[2 + Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] - x)/(1 + Sqrt[3] - x)], -7 - 4*Sqrt[3]])/(2*3^(1/4)*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[1 - x^3])","A",2,2,15,0.1333,1,"{325, 218}"
468,1,154,0,0.0328632,"\int \frac{1}{x^6 \sqrt{1-x^3}} \, dx","Int[1/(x^6*Sqrt[1 - x^3]),x]","-\frac{7 \sqrt{1-x^3}}{20 x^2}-\frac{\sqrt{1-x^3}}{5 x^5}-\frac{7 \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{20 \sqrt[4]{3} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}","-\frac{7 \sqrt{1-x^3}}{20 x^2}-\frac{\sqrt{1-x^3}}{5 x^5}-\frac{7 \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{20 \sqrt[4]{3} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}",1,"-Sqrt[1 - x^3]/(5*x^5) - (7*Sqrt[1 - x^3])/(20*x^2) - (7*Sqrt[2 + Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] - x)/(1 + Sqrt[3] - x)], -7 - 4*Sqrt[3]])/(20*3^(1/4)*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[1 - x^3])","A",3,2,15,0.1333,1,"{325, 218}"
469,1,294,0,0.0849482,"\int \frac{x^7}{\sqrt{1-x^3}} \, dx","Int[x^7/Sqrt[1 - x^3],x]","-\frac{2}{13} \sqrt{1-x^3} x^5-\frac{20}{91} \sqrt{1-x^3} x^2+\frac{80 \sqrt{1-x^3}}{91 \left(-x+\sqrt{3}+1\right)}+\frac{80 \sqrt{2} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{91 \sqrt[4]{3} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}-\frac{40 \sqrt[4]{3} \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{91 \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}","-\frac{2}{13} \sqrt{1-x^3} x^5-\frac{20}{91} \sqrt{1-x^3} x^2+\frac{80 \sqrt{1-x^3}}{91 \left(-x+\sqrt{3}+1\right)}+\frac{80 \sqrt{2} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{91 \sqrt[4]{3} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}-\frac{40 \sqrt[4]{3} \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{91 \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}",1,"(80*Sqrt[1 - x^3])/(91*(1 + Sqrt[3] - x)) - (20*x^2*Sqrt[1 - x^3])/91 - (2*x^5*Sqrt[1 - x^3])/13 - (40*3^(1/4)*Sqrt[2 - Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*EllipticE[ArcSin[(1 - Sqrt[3] - x)/(1 + Sqrt[3] - x)], -7 - 4*Sqrt[3]])/(91*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[1 - x^3]) + (80*Sqrt[2]*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] - x)/(1 + Sqrt[3] - x)], -7 - 4*Sqrt[3]])/(91*3^(1/4)*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[1 - x^3])","A",5,4,15,0.2667,1,"{321, 303, 218, 1877}"
470,1,276,0,0.0608835,"\int \frac{x^4}{\sqrt{1-x^3}} \, dx","Int[x^4/Sqrt[1 - x^3],x]","-\frac{2}{7} \sqrt{1-x^3} x^2+\frac{8 \sqrt{1-x^3}}{7 \left(-x+\sqrt{3}+1\right)}+\frac{8 \sqrt{2} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{7 \sqrt[4]{3} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}-\frac{4 \sqrt[4]{3} \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{7 \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}","-\frac{2}{7} \sqrt{1-x^3} x^2+\frac{8 \sqrt{1-x^3}}{7 \left(-x+\sqrt{3}+1\right)}+\frac{8 \sqrt{2} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{7 \sqrt[4]{3} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}-\frac{4 \sqrt[4]{3} \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{7 \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}",1,"(8*Sqrt[1 - x^3])/(7*(1 + Sqrt[3] - x)) - (2*x^2*Sqrt[1 - x^3])/7 - (4*3^(1/4)*Sqrt[2 - Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*EllipticE[ArcSin[(1 - Sqrt[3] - x)/(1 + Sqrt[3] - x)], -7 - 4*Sqrt[3]])/(7*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[1 - x^3]) + (8*Sqrt[2]*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] - x)/(1 + Sqrt[3] - x)], -7 - 4*Sqrt[3]])/(7*3^(1/4)*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[1 - x^3])","A",4,4,15,0.2667,1,"{321, 303, 218, 1877}"
471,1,252,0,0.0408051,"\int \frac{x}{\sqrt{1-x^3}} \, dx","Int[x/Sqrt[1 - x^3],x]","\frac{2 \sqrt{1-x^3}}{-x+\sqrt{3}+1}+\frac{2 \sqrt{2} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}","\frac{2 \sqrt{1-x^3}}{-x+\sqrt{3}+1}+\frac{2 \sqrt{2} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}",1,"(2*Sqrt[1 - x^3])/(1 + Sqrt[3] - x) - (3^(1/4)*Sqrt[2 - Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*EllipticE[ArcSin[(1 - Sqrt[3] - x)/(1 + Sqrt[3] - x)], -7 - 4*Sqrt[3]])/(Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[1 - x^3]) + (2*Sqrt[2]*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] - x)/(1 + Sqrt[3] - x)], -7 - 4*Sqrt[3]])/(3^(1/4)*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[1 - x^3])","A",3,3,13,0.2308,1,"{303, 218, 1877}"
472,1,270,0,0.0624255,"\int \frac{1}{x^2 \sqrt{1-x^3}} \, dx","Int[1/(x^2*Sqrt[1 - x^3]),x]","-\frac{\sqrt{1-x^3}}{-x+\sqrt{3}+1}-\frac{\sqrt{1-x^3}}{x}-\frac{\sqrt{2} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}+\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}","-\frac{\sqrt{1-x^3}}{-x+\sqrt{3}+1}-\frac{\sqrt{1-x^3}}{x}-\frac{\sqrt{2} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}+\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}",1,"-(Sqrt[1 - x^3]/(1 + Sqrt[3] - x)) - Sqrt[1 - x^3]/x + (3^(1/4)*Sqrt[2 - Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*EllipticE[ArcSin[(1 - Sqrt[3] - x)/(1 + Sqrt[3] - x)], -7 - 4*Sqrt[3]])/(2*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[1 - x^3]) - (Sqrt[2]*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] - x)/(1 + Sqrt[3] - x)], -7 - 4*Sqrt[3]])/(3^(1/4)*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[1 - x^3])","A",4,4,15,0.2667,1,"{325, 303, 218, 1877}"
473,1,294,0,0.0845049,"\int \frac{1}{x^5 \sqrt{1-x^3}} \, dx","Int[1/(x^5*Sqrt[1 - x^3]),x]","-\frac{5 \sqrt{1-x^3}}{8 \left(-x+\sqrt{3}+1\right)}-\frac{5 \sqrt{1-x^3}}{8 x}-\frac{\sqrt{1-x^3}}{4 x^4}-\frac{5 (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{4 \sqrt{2} \sqrt[4]{3} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}+\frac{5 \sqrt[4]{3} \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{16 \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}","-\frac{5 \sqrt{1-x^3}}{8 \left(-x+\sqrt{3}+1\right)}-\frac{5 \sqrt{1-x^3}}{8 x}-\frac{\sqrt{1-x^3}}{4 x^4}-\frac{5 (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{4 \sqrt{2} \sqrt[4]{3} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}+\frac{5 \sqrt[4]{3} \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{16 \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}",1,"(-5*Sqrt[1 - x^3])/(8*(1 + Sqrt[3] - x)) - Sqrt[1 - x^3]/(4*x^4) - (5*Sqrt[1 - x^3])/(8*x) + (5*3^(1/4)*Sqrt[2 - Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*EllipticE[ArcSin[(1 - Sqrt[3] - x)/(1 + Sqrt[3] - x)], -7 - 4*Sqrt[3]])/(16*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[1 - x^3]) - (5*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] - x)/(1 + Sqrt[3] - x)], -7 - 4*Sqrt[3]])/(4*Sqrt[2]*3^(1/4)*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[1 - x^3])","A",5,4,15,0.2667,1,"{325, 303, 218, 1877}"
474,1,53,0,0.0171603,"\int \frac{x^{11}}{\sqrt{-1+x^3}} \, dx","Int[x^11/Sqrt[-1 + x^3],x]","\frac{2}{21} \left(x^3-1\right)^{7/2}+\frac{2}{5} \left(x^3-1\right)^{5/2}+\frac{2}{3} \left(x^3-1\right)^{3/2}+\frac{2 \sqrt{x^3-1}}{3}","\frac{2}{21} \left(x^3-1\right)^{7/2}+\frac{2}{5} \left(x^3-1\right)^{5/2}+\frac{2}{3} \left(x^3-1\right)^{3/2}+\frac{2 \sqrt{x^3-1}}{3}",1,"(2*Sqrt[-1 + x^3])/3 + (2*(-1 + x^3)^(3/2))/3 + (2*(-1 + x^3)^(5/2))/5 + (2*(-1 + x^3)^(7/2))/21","A",3,2,13,0.1538,1,"{266, 43}"
475,1,40,0,0.0142532,"\int \frac{x^8}{\sqrt{-1+x^3}} \, dx","Int[x^8/Sqrt[-1 + x^3],x]","\frac{2}{15} \left(x^3-1\right)^{5/2}+\frac{4}{9} \left(x^3-1\right)^{3/2}+\frac{2 \sqrt{x^3-1}}{3}","\frac{2}{15} \left(x^3-1\right)^{5/2}+\frac{4}{9} \left(x^3-1\right)^{3/2}+\frac{2 \sqrt{x^3-1}}{3}",1,"(2*Sqrt[-1 + x^3])/3 + (4*(-1 + x^3)^(3/2))/9 + (2*(-1 + x^3)^(5/2))/15","A",3,2,13,0.1538,1,"{266, 43}"
476,1,27,0,0.0097768,"\int \frac{x^5}{\sqrt{-1+x^3}} \, dx","Int[x^5/Sqrt[-1 + x^3],x]","\frac{2}{9} \left(x^3-1\right)^{3/2}+\frac{2 \sqrt{x^3-1}}{3}","\frac{2}{9} \left(x^3-1\right)^{3/2}+\frac{2 \sqrt{x^3-1}}{3}",1,"(2*Sqrt[-1 + x^3])/3 + (2*(-1 + x^3)^(3/2))/9","A",3,2,13,0.1538,1,"{266, 43}"
477,1,13,0,0.0024092,"\int \frac{x^2}{\sqrt{-1+x^3}} \, dx","Int[x^2/Sqrt[-1 + x^3],x]","\frac{2 \sqrt{x^3-1}}{3}","\frac{2 \sqrt{x^3-1}}{3}",1,"(2*Sqrt[-1 + x^3])/3","A",1,1,13,0.07692,1,"{261}"
478,1,14,0,0.0064262,"\int \frac{1}{x \sqrt{-1+x^3}} \, dx","Int[1/(x*Sqrt[-1 + x^3]),x]","\frac{2}{3} \tan ^{-1}\left(\sqrt{x^3-1}\right)","\frac{2}{3} \tan ^{-1}\left(\sqrt{x^3-1}\right)",1,"(2*ArcTan[Sqrt[-1 + x^3]])/3","A",3,3,13,0.2308,1,"{266, 63, 203}"
479,1,31,0,0.0107069,"\int \frac{1}{x^4 \sqrt{-1+x^3}} \, dx","Int[1/(x^4*Sqrt[-1 + x^3]),x]","\frac{\sqrt{x^3-1}}{3 x^3}+\frac{1}{3} \tan ^{-1}\left(\sqrt{x^3-1}\right)","\frac{\sqrt{x^3-1}}{3 x^3}+\frac{1}{3} \tan ^{-1}\left(\sqrt{x^3-1}\right)",1,"Sqrt[-1 + x^3]/(3*x^3) + ArcTan[Sqrt[-1 + x^3]]/3","A",4,4,13,0.3077,1,"{266, 51, 63, 203}"
480,1,47,0,0.014413,"\int \frac{1}{x^7 \sqrt{-1+x^3}} \, dx","Int[1/(x^7*Sqrt[-1 + x^3]),x]","\frac{\sqrt{x^3-1}}{4 x^3}+\frac{\sqrt{x^3-1}}{6 x^6}+\frac{1}{4} \tan ^{-1}\left(\sqrt{x^3-1}\right)","\frac{\sqrt{x^3-1}}{4 x^3}+\frac{\sqrt{x^3-1}}{6 x^6}+\frac{1}{4} \tan ^{-1}\left(\sqrt{x^3-1}\right)",1,"Sqrt[-1 + x^3]/(6*x^6) + Sqrt[-1 + x^3]/(4*x^3) + ArcTan[Sqrt[-1 + x^3]]/4","A",5,4,13,0.3077,1,"{266, 51, 63, 203}"
481,1,63,0,0.0194304,"\int \frac{1}{x^{10} \sqrt{-1+x^3}} \, dx","Int[1/(x^10*Sqrt[-1 + x^3]),x]","\frac{5 \sqrt{x^3-1}}{24 x^3}+\frac{5 \sqrt{x^3-1}}{36 x^6}+\frac{\sqrt{x^3-1}}{9 x^9}+\frac{5}{24} \tan ^{-1}\left(\sqrt{x^3-1}\right)","\frac{5 \sqrt{x^3-1}}{24 x^3}+\frac{5 \sqrt{x^3-1}}{36 x^6}+\frac{\sqrt{x^3-1}}{9 x^9}+\frac{5}{24} \tan ^{-1}\left(\sqrt{x^3-1}\right)",1,"Sqrt[-1 + x^3]/(9*x^9) + (5*Sqrt[-1 + x^3])/(36*x^6) + (5*Sqrt[-1 + x^3])/(24*x^3) + (5*ArcTan[Sqrt[-1 + x^3]])/24","A",6,4,13,0.3077,1,"{266, 51, 63, 203}"
482,1,153,0,0.0365812,"\int \frac{x^6}{\sqrt{-1+x^3}} \, dx","Int[x^6/Sqrt[-1 + x^3],x]","\frac{2}{11} \sqrt{x^3-1} x^4+\frac{16}{55} \sqrt{x^3-1} x-\frac{32 \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{55 \sqrt[4]{3} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}","\frac{2}{11} \sqrt{x^3-1} x^4+\frac{16}{55} \sqrt{x^3-1} x-\frac{32 \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{55 \sqrt[4]{3} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}",1,"(16*x*Sqrt[-1 + x^3])/55 + (2*x^4*Sqrt[-1 + x^3])/11 - (32*Sqrt[2 - Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(55*3^(1/4)*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3])","A",3,2,13,0.1538,1,"{321, 219}"
483,1,137,0,0.0203478,"\int \frac{x^3}{\sqrt{-1+x^3}} \, dx","Int[x^3/Sqrt[-1 + x^3],x]","\frac{2}{5} x \sqrt{x^3-1}-\frac{4 \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{5 \sqrt[4]{3} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}","\frac{2}{5} x \sqrt{x^3-1}-\frac{4 \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{5 \sqrt[4]{3} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}",1,"(2*x*Sqrt[-1 + x^3])/5 - (4*Sqrt[2 - Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(5*3^(1/4)*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3])","A",2,2,13,0.1538,1,"{321, 219}"
484,1,120,0,0.0087963,"\int \frac{1}{\sqrt{-1+x^3}} \, dx","Int[1/Sqrt[-1 + x^3],x]","-\frac{2 \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}","-\frac{2 \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}",1,"(-2*Sqrt[2 - Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(3^(1/4)*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3])","A",1,1,9,0.1111,1,"{219}"
485,1,139,0,0.0199751,"\int \frac{1}{x^3 \sqrt{-1+x^3}} \, dx","Int[1/(x^3*Sqrt[-1 + x^3]),x]","\frac{\sqrt{x^3-1}}{2 x^2}-\frac{\sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{2 \sqrt[4]{3} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}","\frac{\sqrt{x^3-1}}{2 x^2}-\frac{\sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{2 \sqrt[4]{3} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}",1,"Sqrt[-1 + x^3]/(2*x^2) - (Sqrt[2 - Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(2*3^(1/4)*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3])","A",2,2,13,0.1538,1,"{325, 219}"
486,1,155,0,0.0333066,"\int \frac{1}{x^6 \sqrt{-1+x^3}} \, dx","Int[1/(x^6*Sqrt[-1 + x^3]),x]","\frac{7 \sqrt{x^3-1}}{20 x^2}+\frac{\sqrt{x^3-1}}{5 x^5}-\frac{7 \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{20 \sqrt[4]{3} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}","\frac{7 \sqrt{x^3-1}}{20 x^2}+\frac{\sqrt{x^3-1}}{5 x^5}-\frac{7 \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{20 \sqrt[4]{3} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}",1,"Sqrt[-1 + x^3]/(5*x^5) + (7*Sqrt[-1 + x^3])/(20*x^2) - (7*Sqrt[2 - Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(20*3^(1/4)*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3])","A",3,2,13,0.1538,1,"{325, 219}"
487,1,294,0,0.0820525,"\int \frac{x^7}{\sqrt{-1+x^3}} \, dx","Int[x^7/Sqrt[-1 + x^3],x]","\frac{2}{13} \sqrt{x^3-1} x^5+\frac{20}{91} \sqrt{x^3-1} x^2-\frac{80 \sqrt{x^3-1}}{91 \left(-x-\sqrt{3}+1\right)}-\frac{80 \sqrt{2} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{91 \sqrt[4]{3} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}+\frac{40 \sqrt[4]{3} \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{91 \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}","\frac{2}{13} \sqrt{x^3-1} x^5+\frac{20}{91} \sqrt{x^3-1} x^2-\frac{80 \sqrt{x^3-1}}{91 \left(-x-\sqrt{3}+1\right)}-\frac{80 \sqrt{2} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{91 \sqrt[4]{3} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}+\frac{40 \sqrt[4]{3} \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{91 \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}",1,"(-80*Sqrt[-1 + x^3])/(91*(1 - Sqrt[3] - x)) + (20*x^2*Sqrt[-1 + x^3])/91 + (2*x^5*Sqrt[-1 + x^3])/13 + (40*3^(1/4)*Sqrt[2 + Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticE[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(91*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3]) - (80*Sqrt[2]*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(91*3^(1/4)*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3])","A",5,4,13,0.3077,1,"{321, 304, 219, 1879}"
488,1,278,0,0.0575174,"\int \frac{x^4}{\sqrt{-1+x^3}} \, dx","Int[x^4/Sqrt[-1 + x^3],x]","\frac{2}{7} \sqrt{x^3-1} x^2-\frac{8 \sqrt{x^3-1}}{7 \left(-x-\sqrt{3}+1\right)}-\frac{8 \sqrt{2} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{7 \sqrt[4]{3} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}+\frac{4 \sqrt[4]{3} \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{7 \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}","\frac{2}{7} \sqrt{x^3-1} x^2-\frac{8 \sqrt{x^3-1}}{7 \left(-x-\sqrt{3}+1\right)}-\frac{8 \sqrt{2} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{7 \sqrt[4]{3} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}+\frac{4 \sqrt[4]{3} \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{7 \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}",1,"(-8*Sqrt[-1 + x^3])/(7*(1 - Sqrt[3] - x)) + (2*x^2*Sqrt[-1 + x^3])/7 + (4*3^(1/4)*Sqrt[2 + Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticE[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(7*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3]) - (8*Sqrt[2]*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(7*3^(1/4)*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3])","A",4,4,13,0.3077,1,"{321, 304, 219, 1879}"
489,1,255,0,0.0375745,"\int \frac{x}{\sqrt{-1+x^3}} \, dx","Int[x/Sqrt[-1 + x^3],x]","-\frac{2 \sqrt{x^3-1}}{-x-\sqrt{3}+1}-\frac{2 \sqrt{2} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}+\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}","-\frac{2 \sqrt{x^3-1}}{-x-\sqrt{3}+1}-\frac{2 \sqrt{2} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}+\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}",1,"(-2*Sqrt[-1 + x^3])/(1 - Sqrt[3] - x) + (3^(1/4)*Sqrt[2 + Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticE[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3]) - (2*Sqrt[2]*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(3^(1/4)*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3])","A",3,3,11,0.2727,1,"{304, 219, 1879}"
490,1,269,0,0.0575192,"\int \frac{1}{x^2 \sqrt{-1+x^3}} \, dx","Int[1/(x^2*Sqrt[-1 + x^3]),x]","\frac{\sqrt{x^3-1}}{-x-\sqrt{3}+1}+\frac{\sqrt{x^3-1}}{x}+\frac{\sqrt{2} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}-\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{2 \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}","\frac{\sqrt{x^3-1}}{-x-\sqrt{3}+1}+\frac{\sqrt{x^3-1}}{x}+\frac{\sqrt{2} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}-\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{2 \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}",1,"Sqrt[-1 + x^3]/(1 - Sqrt[3] - x) + Sqrt[-1 + x^3]/x - (3^(1/4)*Sqrt[2 + Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticE[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(2*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3]) + (Sqrt[2]*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(3^(1/4)*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3])","A",4,4,13,0.3077,1,"{325, 304, 219, 1879}"
491,1,294,0,0.0775788,"\int \frac{1}{x^5 \sqrt{-1+x^3}} \, dx","Int[1/(x^5*Sqrt[-1 + x^3]),x]","\frac{5 \sqrt{x^3-1}}{8 \left(-x-\sqrt{3}+1\right)}+\frac{5 \sqrt{x^3-1}}{8 x}+\frac{\sqrt{x^3-1}}{4 x^4}+\frac{5 (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{4 \sqrt{2} \sqrt[4]{3} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}-\frac{5 \sqrt[4]{3} \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{16 \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}","\frac{5 \sqrt{x^3-1}}{8 \left(-x-\sqrt{3}+1\right)}+\frac{5 \sqrt{x^3-1}}{8 x}+\frac{\sqrt{x^3-1}}{4 x^4}+\frac{5 (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{4 \sqrt{2} \sqrt[4]{3} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}-\frac{5 \sqrt[4]{3} \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{16 \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}",1,"(5*Sqrt[-1 + x^3])/(8*(1 - Sqrt[3] - x)) + Sqrt[-1 + x^3]/(4*x^4) + (5*Sqrt[-1 + x^3])/(8*x) - (5*3^(1/4)*Sqrt[2 + Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticE[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(16*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3]) + (5*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(4*Sqrt[2]*3^(1/4)*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3])","A",5,4,13,0.3077,1,"{325, 304, 219, 1879}"
492,1,61,0,0.0248423,"\int \frac{x^{11}}{\sqrt{-1-x^3}} \, dx","Int[x^11/Sqrt[-1 - x^3],x]","\frac{2}{21} \left(-x^3-1\right)^{7/2}+\frac{2}{5} \left(-x^3-1\right)^{5/2}+\frac{2}{3} \left(-x^3-1\right)^{3/2}+\frac{2}{3} \sqrt{-x^3-1}","\frac{2}{21} \left(-x^3-1\right)^{7/2}+\frac{2}{5} \left(-x^3-1\right)^{5/2}+\frac{2}{3} \left(-x^3-1\right)^{3/2}+\frac{2}{3} \sqrt{-x^3-1}",1,"(2*Sqrt[-1 - x^3])/3 + (2*(-1 - x^3)^(3/2))/3 + (2*(-1 - x^3)^(5/2))/5 + (2*(-1 - x^3)^(7/2))/21","A",3,2,15,0.1333,1,"{266, 43}"
493,1,46,0,0.0185338,"\int \frac{x^8}{\sqrt{-1-x^3}} \, dx","Int[x^8/Sqrt[-1 - x^3],x]","-\frac{2}{15} \left(-x^3-1\right)^{5/2}-\frac{4}{9} \left(-x^3-1\right)^{3/2}-\frac{2}{3} \sqrt{-x^3-1}","-\frac{2}{15} \left(-x^3-1\right)^{5/2}-\frac{4}{9} \left(-x^3-1\right)^{3/2}-\frac{2}{3} \sqrt{-x^3-1}",1,"(-2*Sqrt[-1 - x^3])/3 - (4*(-1 - x^3)^(3/2))/9 - (2*(-1 - x^3)^(5/2))/15","A",3,2,15,0.1333,1,"{266, 43}"
494,1,31,0,0.0144815,"\int \frac{x^5}{\sqrt{-1-x^3}} \, dx","Int[x^5/Sqrt[-1 - x^3],x]","\frac{2}{9} \left(-x^3-1\right)^{3/2}+\frac{2}{3} \sqrt{-x^3-1}","\frac{2}{9} \left(-x^3-1\right)^{3/2}+\frac{2}{3} \sqrt{-x^3-1}",1,"(2*Sqrt[-1 - x^3])/3 + (2*(-1 - x^3)^(3/2))/9","A",3,2,15,0.1333,1,"{266, 43}"
495,1,15,0,0.0028506,"\int \frac{x^2}{\sqrt{-1-x^3}} \, dx","Int[x^2/Sqrt[-1 - x^3],x]","-\frac{2}{3} \sqrt{-x^3-1}","-\frac{2}{3} \sqrt{-x^3-1}",1,"(-2*Sqrt[-1 - x^3])/3","A",1,1,15,0.06667,1,"{261}"
496,1,16,0,0.0083577,"\int \frac{1}{x \sqrt{-1-x^3}} \, dx","Int[1/(x*Sqrt[-1 - x^3]),x]","\frac{2}{3} \tan ^{-1}\left(\sqrt{-x^3-1}\right)","\frac{2}{3} \tan ^{-1}\left(\sqrt{-x^3-1}\right)",1,"(2*ArcTan[Sqrt[-1 - x^3]])/3","A",3,3,15,0.2000,1,"{266, 63, 204}"
497,1,35,0,0.0147958,"\int \frac{1}{x^4 \sqrt{-1-x^3}} \, dx","Int[1/(x^4*Sqrt[-1 - x^3]),x]","\frac{\sqrt{-x^3-1}}{3 x^3}-\frac{1}{3} \tan ^{-1}\left(\sqrt{-x^3-1}\right)","\frac{\sqrt{-x^3-1}}{3 x^3}-\frac{1}{3} \tan ^{-1}\left(\sqrt{-x^3-1}\right)",1,"Sqrt[-1 - x^3]/(3*x^3) - ArcTan[Sqrt[-1 - x^3]]/3","A",4,4,15,0.2667,1,"{266, 51, 63, 204}"
498,1,53,0,0.0198301,"\int \frac{1}{x^7 \sqrt{-1-x^3}} \, dx","Int[1/(x^7*Sqrt[-1 - x^3]),x]","-\frac{\sqrt{-x^3-1}}{4 x^3}+\frac{\sqrt{-x^3-1}}{6 x^6}+\frac{1}{4} \tan ^{-1}\left(\sqrt{-x^3-1}\right)","-\frac{\sqrt{-x^3-1}}{4 x^3}+\frac{\sqrt{-x^3-1}}{6 x^6}+\frac{1}{4} \tan ^{-1}\left(\sqrt{-x^3-1}\right)",1,"Sqrt[-1 - x^3]/(6*x^6) - Sqrt[-1 - x^3]/(4*x^3) + ArcTan[Sqrt[-1 - x^3]]/4","A",5,4,15,0.2667,1,"{266, 51, 63, 204}"
499,1,71,0,0.0279848,"\int \frac{1}{x^{10} \sqrt{-1-x^3}} \, dx","Int[1/(x^10*Sqrt[-1 - x^3]),x]","\frac{5 \sqrt{-x^3-1}}{24 x^3}-\frac{5 \sqrt{-x^3-1}}{36 x^6}+\frac{\sqrt{-x^3-1}}{9 x^9}-\frac{5}{24} \tan ^{-1}\left(\sqrt{-x^3-1}\right)","\frac{5 \sqrt{-x^3-1}}{24 x^3}-\frac{5 \sqrt{-x^3-1}}{36 x^6}+\frac{\sqrt{-x^3-1}}{9 x^9}-\frac{5}{24} \tan ^{-1}\left(\sqrt{-x^3-1}\right)",1,"Sqrt[-1 - x^3]/(9*x^9) - (5*Sqrt[-1 - x^3])/(36*x^6) + (5*Sqrt[-1 - x^3])/(24*x^3) - (5*ArcTan[Sqrt[-1 - x^3]])/24","A",6,4,15,0.2667,1,"{266, 51, 63, 204}"
500,1,149,0,0.0368375,"\int \frac{x^6}{\sqrt{-1-x^3}} \, dx","Int[x^6/Sqrt[-1 - x^3],x]","-\frac{2}{11} \sqrt{-x^3-1} x^4+\frac{16}{55} \sqrt{-x^3-1} x+\frac{32 \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{55 \sqrt[4]{3} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}","-\frac{2}{11} \sqrt{-x^3-1} x^4+\frac{16}{55} \sqrt{-x^3-1} x+\frac{32 \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{55 \sqrt[4]{3} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}",1,"(16*x*Sqrt[-1 - x^3])/55 - (2*x^4*Sqrt[-1 - x^3])/11 + (32*Sqrt[2 - Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 - Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] + x)/(1 - Sqrt[3] + x)], -7 + 4*Sqrt[3]])/(55*3^(1/4)*Sqrt[-((1 + x)/(1 - Sqrt[3] + x)^2)]*Sqrt[-1 - x^3])","A",3,2,15,0.1333,1,"{321, 219}"
501,1,131,0,0.0184333,"\int \frac{x^3}{\sqrt{-1-x^3}} \, dx","Int[x^3/Sqrt[-1 - x^3],x]","-\frac{2}{5} \sqrt{-x^3-1} x-\frac{4 \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{5 \sqrt[4]{3} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}","-\frac{2}{5} \sqrt{-x^3-1} x-\frac{4 \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{5 \sqrt[4]{3} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}",1,"(-2*x*Sqrt[-1 - x^3])/5 - (4*Sqrt[2 - Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 - Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] + x)/(1 - Sqrt[3] + x)], -7 + 4*Sqrt[3]])/(5*3^(1/4)*Sqrt[-((1 + x)/(1 - Sqrt[3] + x)^2)]*Sqrt[-1 - x^3])","A",2,2,15,0.1333,1,"{321, 219}"
502,1,112,0,0.0079803,"\int \frac{1}{\sqrt{-1-x^3}} \, dx","Int[1/Sqrt[-1 - x^3],x]","\frac{2 \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}","\frac{2 \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}",1,"(2*Sqrt[2 - Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 - Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] + x)/(1 - Sqrt[3] + x)], -7 + 4*Sqrt[3]])/(3^(1/4)*Sqrt[-((1 + x)/(1 - Sqrt[3] + x)^2)]*Sqrt[-1 - x^3])","A",1,1,11,0.09091,1,"{219}"
503,1,133,0,0.0183783,"\int \frac{1}{x^3 \sqrt{-1-x^3}} \, dx","Int[1/(x^3*Sqrt[-1 - x^3]),x]","\frac{\sqrt{-x^3-1}}{2 x^2}-\frac{\sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{2 \sqrt[4]{3} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}","\frac{\sqrt{-x^3-1}}{2 x^2}-\frac{\sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{2 \sqrt[4]{3} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}",1,"Sqrt[-1 - x^3]/(2*x^2) - (Sqrt[2 - Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 - Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] + x)/(1 - Sqrt[3] + x)], -7 + 4*Sqrt[3]])/(2*3^(1/4)*Sqrt[-((1 + x)/(1 - Sqrt[3] + x)^2)]*Sqrt[-1 - x^3])","A",2,2,15,0.1333,1,"{325, 219}"
504,1,151,0,0.0310589,"\int \frac{1}{x^6 \sqrt{-1-x^3}} \, dx","Int[1/(x^6*Sqrt[-1 - x^3]),x]","-\frac{7 \sqrt{-x^3-1}}{20 x^2}+\frac{\sqrt{-x^3-1}}{5 x^5}+\frac{7 \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{20 \sqrt[4]{3} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}","-\frac{7 \sqrt{-x^3-1}}{20 x^2}+\frac{\sqrt{-x^3-1}}{5 x^5}+\frac{7 \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{20 \sqrt[4]{3} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}",1,"Sqrt[-1 - x^3]/(5*x^5) - (7*Sqrt[-1 - x^3])/(20*x^2) + (7*Sqrt[2 - Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 - Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] + x)/(1 - Sqrt[3] + x)], -7 + 4*Sqrt[3]])/(20*3^(1/4)*Sqrt[-((1 + x)/(1 - Sqrt[3] + x)^2)]*Sqrt[-1 - x^3])","A",3,2,15,0.1333,1,"{325, 219}"
505,1,282,0,0.0759533,"\int \frac{x^7}{\sqrt{-1-x^3}} \, dx","Int[x^7/Sqrt[-1 - x^3],x]","-\frac{2}{13} \sqrt{-x^3-1} x^5+\frac{20}{91} \sqrt{-x^3-1} x^2-\frac{80 \sqrt{-x^3-1}}{91 \left(x-\sqrt{3}+1\right)}-\frac{80 \sqrt{2} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{91 \sqrt[4]{3} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}+\frac{40 \sqrt[4]{3} \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{91 \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}","-\frac{2}{13} \sqrt{-x^3-1} x^5+\frac{20}{91} \sqrt{-x^3-1} x^2-\frac{80 \sqrt{-x^3-1}}{91 \left(x-\sqrt{3}+1\right)}-\frac{80 \sqrt{2} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{91 \sqrt[4]{3} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}+\frac{40 \sqrt[4]{3} \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{91 \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}",1,"(20*x^2*Sqrt[-1 - x^3])/91 - (2*x^5*Sqrt[-1 - x^3])/13 - (80*Sqrt[-1 - x^3])/(91*(1 - Sqrt[3] + x)) + (40*3^(1/4)*Sqrt[2 + Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 - Sqrt[3] + x)^2]*EllipticE[ArcSin[(1 + Sqrt[3] + x)/(1 - Sqrt[3] + x)], -7 + 4*Sqrt[3]])/(91*Sqrt[-((1 + x)/(1 - Sqrt[3] + x)^2)]*Sqrt[-1 - x^3]) - (80*Sqrt[2]*(1 + x)*Sqrt[(1 - x + x^2)/(1 - Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] + x)/(1 - Sqrt[3] + x)], -7 + 4*Sqrt[3]])/(91*3^(1/4)*Sqrt[-((1 + x)/(1 - Sqrt[3] + x)^2)]*Sqrt[-1 - x^3])","A",5,4,15,0.2667,1,"{321, 304, 219, 1879}"
506,1,264,0,0.0543119,"\int \frac{x^4}{\sqrt{-1-x^3}} \, dx","Int[x^4/Sqrt[-1 - x^3],x]","-\frac{2}{7} \sqrt{-x^3-1} x^2+\frac{8 \sqrt{-x^3-1}}{7 \left(x-\sqrt{3}+1\right)}+\frac{8 \sqrt{2} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{7 \sqrt[4]{3} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}-\frac{4 \sqrt[4]{3} \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{7 \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}","-\frac{2}{7} \sqrt{-x^3-1} x^2+\frac{8 \sqrt{-x^3-1}}{7 \left(x-\sqrt{3}+1\right)}+\frac{8 \sqrt{2} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{7 \sqrt[4]{3} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}-\frac{4 \sqrt[4]{3} \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{7 \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}",1,"(-2*x^2*Sqrt[-1 - x^3])/7 + (8*Sqrt[-1 - x^3])/(7*(1 - Sqrt[3] + x)) - (4*3^(1/4)*Sqrt[2 + Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 - Sqrt[3] + x)^2]*EllipticE[ArcSin[(1 + Sqrt[3] + x)/(1 - Sqrt[3] + x)], -7 + 4*Sqrt[3]])/(7*Sqrt[-((1 + x)/(1 - Sqrt[3] + x)^2)]*Sqrt[-1 - x^3]) + (8*Sqrt[2]*(1 + x)*Sqrt[(1 - x + x^2)/(1 - Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] + x)/(1 - Sqrt[3] + x)], -7 + 4*Sqrt[3]])/(7*3^(1/4)*Sqrt[-((1 + x)/(1 - Sqrt[3] + x)^2)]*Sqrt[-1 - x^3])","A",4,4,15,0.2667,1,"{321, 304, 219, 1879}"
507,1,239,0,0.0356602,"\int \frac{x}{\sqrt{-1-x^3}} \, dx","Int[x/Sqrt[-1 - x^3],x]","-\frac{2 \sqrt{-x^3-1}}{x-\sqrt{3}+1}-\frac{2 \sqrt{2} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}+\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}","-\frac{2 \sqrt{-x^3-1}}{x-\sqrt{3}+1}-\frac{2 \sqrt{2} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}+\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}",1,"(-2*Sqrt[-1 - x^3])/(1 - Sqrt[3] + x) + (3^(1/4)*Sqrt[2 + Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 - Sqrt[3] + x)^2]*EllipticE[ArcSin[(1 + Sqrt[3] + x)/(1 - Sqrt[3] + x)], -7 + 4*Sqrt[3]])/(Sqrt[-((1 + x)/(1 - Sqrt[3] + x)^2)]*Sqrt[-1 - x^3]) - (2*Sqrt[2]*(1 + x)*Sqrt[(1 - x + x^2)/(1 - Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] + x)/(1 - Sqrt[3] + x)], -7 + 4*Sqrt[3]])/(3^(1/4)*Sqrt[-((1 + x)/(1 - Sqrt[3] + x)^2)]*Sqrt[-1 - x^3])","A",3,3,13,0.2308,1,"{304, 219, 1879}"
508,1,257,0,0.053921,"\int \frac{1}{x^2 \sqrt{-1-x^3}} \, dx","Int[1/(x^2*Sqrt[-1 - x^3]),x]","\frac{\sqrt{-x^3-1}}{x}-\frac{\sqrt{-x^3-1}}{x-\sqrt{3}+1}-\frac{\sqrt{2} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}+\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{2 \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}","\frac{\sqrt{-x^3-1}}{x}-\frac{\sqrt{-x^3-1}}{x-\sqrt{3}+1}-\frac{\sqrt{2} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}+\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{2 \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}",1,"Sqrt[-1 - x^3]/x - Sqrt[-1 - x^3]/(1 - Sqrt[3] + x) + (3^(1/4)*Sqrt[2 + Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 - Sqrt[3] + x)^2]*EllipticE[ArcSin[(1 + Sqrt[3] + x)/(1 - Sqrt[3] + x)], -7 + 4*Sqrt[3]])/(2*Sqrt[-((1 + x)/(1 - Sqrt[3] + x)^2)]*Sqrt[-1 - x^3]) - (Sqrt[2]*(1 + x)*Sqrt[(1 - x + x^2)/(1 - Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] + x)/(1 - Sqrt[3] + x)], -7 + 4*Sqrt[3]])/(3^(1/4)*Sqrt[-((1 + x)/(1 - Sqrt[3] + x)^2)]*Sqrt[-1 - x^3])","A",4,4,15,0.2667,1,"{325, 304, 219, 1879}"
509,1,282,0,0.0735309,"\int \frac{1}{x^5 \sqrt{-1-x^3}} \, dx","Int[1/(x^5*Sqrt[-1 - x^3]),x]","-\frac{5 \sqrt{-x^3-1}}{8 x}+\frac{5 \sqrt{-x^3-1}}{8 \left(x-\sqrt{3}+1\right)}+\frac{\sqrt{-x^3-1}}{4 x^4}+\frac{5 (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{4 \sqrt{2} \sqrt[4]{3} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}-\frac{5 \sqrt[4]{3} \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{16 \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}","-\frac{5 \sqrt{-x^3-1}}{8 x}+\frac{5 \sqrt{-x^3-1}}{8 \left(x-\sqrt{3}+1\right)}+\frac{\sqrt{-x^3-1}}{4 x^4}+\frac{5 (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{4 \sqrt{2} \sqrt[4]{3} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}-\frac{5 \sqrt[4]{3} \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{16 \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}",1,"Sqrt[-1 - x^3]/(4*x^4) - (5*Sqrt[-1 - x^3])/(8*x) + (5*Sqrt[-1 - x^3])/(8*(1 - Sqrt[3] + x)) - (5*3^(1/4)*Sqrt[2 + Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 - Sqrt[3] + x)^2]*EllipticE[ArcSin[(1 + Sqrt[3] + x)/(1 - Sqrt[3] + x)], -7 + 4*Sqrt[3]])/(16*Sqrt[-((1 + x)/(1 - Sqrt[3] + x)^2)]*Sqrt[-1 - x^3]) + (5*(1 + x)*Sqrt[(1 - x + x^2)/(1 - Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] + x)/(1 - Sqrt[3] + x)], -7 + 4*Sqrt[3]])/(4*Sqrt[2]*3^(1/4)*Sqrt[-((1 + x)/(1 - Sqrt[3] + x)^2)]*Sqrt[-1 - x^3])","A",5,4,15,0.2667,1,"{325, 304, 219, 1879}"
510,1,80,0,0.04404,"\int x^{11} \sqrt[3]{a+b x^3} \, dx","Int[x^11*(a + b*x^3)^(1/3),x]","\frac{3 a^2 \left(a+b x^3\right)^{7/3}}{7 b^4}-\frac{a^3 \left(a+b x^3\right)^{4/3}}{4 b^4}+\frac{\left(a+b x^3\right)^{13/3}}{13 b^4}-\frac{3 a \left(a+b x^3\right)^{10/3}}{10 b^4}","\frac{3 a^2 \left(a+b x^3\right)^{7/3}}{7 b^4}-\frac{a^3 \left(a+b x^3\right)^{4/3}}{4 b^4}+\frac{\left(a+b x^3\right)^{13/3}}{13 b^4}-\frac{3 a \left(a+b x^3\right)^{10/3}}{10 b^4}",1,"-(a^3*(a + b*x^3)^(4/3))/(4*b^4) + (3*a^2*(a + b*x^3)^(7/3))/(7*b^4) - (3*a*(a + b*x^3)^(10/3))/(10*b^4) + (a + b*x^3)^(13/3)/(13*b^4)","A",3,2,15,0.1333,1,"{266, 43}"
511,1,59,0,0.0321434,"\int x^8 \sqrt[3]{a+b x^3} \, dx","Int[x^8*(a + b*x^3)^(1/3),x]","\frac{a^2 \left(a+b x^3\right)^{4/3}}{4 b^3}+\frac{\left(a+b x^3\right)^{10/3}}{10 b^3}-\frac{2 a \left(a+b x^3\right)^{7/3}}{7 b^3}","\frac{a^2 \left(a+b x^3\right)^{4/3}}{4 b^3}+\frac{\left(a+b x^3\right)^{10/3}}{10 b^3}-\frac{2 a \left(a+b x^3\right)^{7/3}}{7 b^3}",1,"(a^2*(a + b*x^3)^(4/3))/(4*b^3) - (2*a*(a + b*x^3)^(7/3))/(7*b^3) + (a + b*x^3)^(10/3)/(10*b^3)","A",3,2,15,0.1333,1,"{266, 43}"
512,1,38,0,0.0222906,"\int x^5 \sqrt[3]{a+b x^3} \, dx","Int[x^5*(a + b*x^3)^(1/3),x]","\frac{\left(a+b x^3\right)^{7/3}}{7 b^2}-\frac{a \left(a+b x^3\right)^{4/3}}{4 b^2}","\frac{\left(a+b x^3\right)^{7/3}}{7 b^2}-\frac{a \left(a+b x^3\right)^{4/3}}{4 b^2}",1,"-(a*(a + b*x^3)^(4/3))/(4*b^2) + (a + b*x^3)^(7/3)/(7*b^2)","A",3,2,15,0.1333,1,"{266, 43}"
513,1,18,0,0.0037848,"\int x^2 \sqrt[3]{a+b x^3} \, dx","Int[x^2*(a + b*x^3)^(1/3),x]","\frac{\left(a+b x^3\right)^{4/3}}{4 b}","\frac{\left(a+b x^3\right)^{4/3}}{4 b}",1,"(a + b*x^3)^(4/3)/(4*b)","A",1,1,15,0.06667,1,"{261}"
514,1,95,0,0.0693723,"\int \frac{\sqrt[3]{a+b x^3}}{x} \, dx","Int[(a + b*x^3)^(1/3)/x,x]","\sqrt[3]{a+b x^3}+\frac{1}{2} \sqrt[3]{a} \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)-\frac{\sqrt[3]{a} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3}}-\frac{1}{2} \sqrt[3]{a} \log (x)","\sqrt[3]{a+b x^3}+\frac{1}{2} \sqrt[3]{a} \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)-\frac{\sqrt[3]{a} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3}}-\frac{1}{2} \sqrt[3]{a} \log (x)",1,"(a + b*x^3)^(1/3) - (a^(1/3)*ArcTan[(a^(1/3) + 2*(a + b*x^3)^(1/3))/(Sqrt[3]*a^(1/3))])/Sqrt[3] - (a^(1/3)*Log[x])/2 + (a^(1/3)*Log[a^(1/3) - (a + b*x^3)^(1/3)])/2","A",6,6,15,0.4000,1,"{266, 50, 57, 617, 204, 31}"
515,1,107,0,0.0644006,"\int \frac{\sqrt[3]{a+b x^3}}{x^4} \, dx","Int[(a + b*x^3)^(1/3)/x^4,x]","\frac{b \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{6 a^{2/3}}-\frac{b \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{2/3}}-\frac{b \log (x)}{6 a^{2/3}}-\frac{\sqrt[3]{a+b x^3}}{3 x^3}","\frac{b \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{6 a^{2/3}}-\frac{b \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{2/3}}-\frac{b \log (x)}{6 a^{2/3}}-\frac{\sqrt[3]{a+b x^3}}{3 x^3}",1,"-(a + b*x^3)^(1/3)/(3*x^3) - (b*ArcTan[(a^(1/3) + 2*(a + b*x^3)^(1/3))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(2/3)) - (b*Log[x])/(6*a^(2/3)) + (b*Log[a^(1/3) - (a + b*x^3)^(1/3)])/(6*a^(2/3))","A",6,6,15,0.4000,1,"{266, 47, 57, 617, 204, 31}"
516,1,173,0,0.1004946,"\int x^4 \sqrt[3]{a+b x^3} \, dx","Int[x^4*(a + b*x^3)^(1/3),x]","\frac{a^2 \log \left(1-\frac{\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}\right)}{27 b^{5/3}}-\frac{a^2 \log \left(\frac{b^{2/3} x^2}{\left(a+b x^3\right)^{2/3}}+\frac{\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1\right)}{54 b^{5/3}}+\frac{a^2 \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{9 \sqrt{3} b^{5/3}}+\frac{1}{6} x^5 \sqrt[3]{a+b x^3}+\frac{a x^2 \sqrt[3]{a+b x^3}}{18 b}","\frac{a^2 \log \left(\sqrt[3]{b} x-\sqrt[3]{a+b x^3}\right)}{18 b^{5/3}}+\frac{a^2 \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{9 \sqrt{3} b^{5/3}}+\frac{1}{6} x^5 \sqrt[3]{a+b x^3}+\frac{a x^2 \sqrt[3]{a+b x^3}}{18 b}",1,"(a*x^2*(a + b*x^3)^(1/3))/(18*b) + (x^5*(a + b*x^3)^(1/3))/6 + (a^2*ArcTan[(1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/Sqrt[3]])/(9*Sqrt[3]*b^(5/3)) + (a^2*Log[1 - (b^(1/3)*x)/(a + b*x^3)^(1/3)])/(27*b^(5/3)) - (a^2*Log[1 + (b^(2/3)*x^2)/(a + b*x^3)^(2/3) + (b^(1/3)*x)/(a + b*x^3)^(1/3)])/(54*b^(5/3))","A",9,9,15,0.6000,1,"{279, 321, 331, 292, 31, 634, 617, 204, 628}"
517,1,145,0,0.0670141,"\int x \sqrt[3]{a+b x^3} \, dx","Int[x*(a + b*x^3)^(1/3),x]","-\frac{a \log \left(1-\frac{\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}\right)}{9 b^{2/3}}+\frac{a \log \left(\frac{b^{2/3} x^2}{\left(a+b x^3\right)^{2/3}}+\frac{\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1\right)}{18 b^{2/3}}-\frac{a \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} b^{2/3}}+\frac{1}{3} x^2 \sqrt[3]{a+b x^3}","-\frac{a \log \left(\sqrt[3]{b} x-\sqrt[3]{a+b x^3}\right)}{6 b^{2/3}}-\frac{a \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} b^{2/3}}+\frac{1}{3} x^2 \sqrt[3]{a+b x^3}",1,"(x^2*(a + b*x^3)^(1/3))/3 - (a*ArcTan[(1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/Sqrt[3]])/(3*Sqrt[3]*b^(2/3)) - (a*Log[1 - (b^(1/3)*x)/(a + b*x^3)^(1/3)])/(9*b^(2/3)) + (a*Log[1 + (b^(2/3)*x^2)/(a + b*x^3)^(2/3) + (b^(1/3)*x)/(a + b*x^3)^(1/3)])/(18*b^(2/3))","A",8,8,13,0.6154,1,"{279, 331, 292, 31, 634, 617, 204, 628}"
518,1,138,0,0.0695022,"\int \frac{\sqrt[3]{a+b x^3}}{x^2} \, dx","Int[(a + b*x^3)^(1/3)/x^2,x]","\frac{1}{6} \sqrt[3]{b} \log \left(\frac{b^{2/3} x^2}{\left(a+b x^3\right)^{2/3}}+\frac{\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1\right)-\frac{\sqrt[3]{a+b x^3}}{x}-\frac{1}{3} \sqrt[3]{b} \log \left(1-\frac{\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}\right)-\frac{\sqrt[3]{b} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3}}","-\frac{\sqrt[3]{a+b x^3}}{x}-\frac{1}{2} \sqrt[3]{b} \log \left(\sqrt[3]{b} x-\sqrt[3]{a+b x^3}\right)-\frac{\sqrt[3]{b} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3}}",1,"-((a + b*x^3)^(1/3)/x) - (b^(1/3)*ArcTan[(1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/Sqrt[3]])/Sqrt[3] - (b^(1/3)*Log[1 - (b^(1/3)*x)/(a + b*x^3)^(1/3)])/3 + (b^(1/3)*Log[1 + (b^(2/3)*x^2)/(a + b*x^3)^(2/3) + (b^(1/3)*x)/(a + b*x^3)^(1/3)])/6","A",8,8,15,0.5333,1,"{277, 331, 292, 31, 634, 617, 204, 628}"
519,1,21,0,0.0044863,"\int \frac{\sqrt[3]{a+b x^3}}{x^5} \, dx","Int[(a + b*x^3)^(1/3)/x^5,x]","-\frac{\left(a+b x^3\right)^{4/3}}{4 a x^4}","-\frac{\left(a+b x^3\right)^{4/3}}{4 a x^4}",1,"-(a + b*x^3)^(4/3)/(4*a*x^4)","A",1,1,15,0.06667,1,"{264}"
520,1,44,0,0.0108102,"\int \frac{\sqrt[3]{a+b x^3}}{x^8} \, dx","Int[(a + b*x^3)^(1/3)/x^8,x]","\frac{3 b \left(a+b x^3\right)^{4/3}}{28 a^2 x^4}-\frac{\left(a+b x^3\right)^{4/3}}{7 a x^7}","\frac{3 b \left(a+b x^3\right)^{4/3}}{28 a^2 x^4}-\frac{\left(a+b x^3\right)^{4/3}}{7 a x^7}",1,"-(a + b*x^3)^(4/3)/(7*a*x^7) + (3*b*(a + b*x^3)^(4/3))/(28*a^2*x^4)","A",2,2,15,0.1333,1,"{271, 264}"
521,1,68,0,0.0194384,"\int \frac{\sqrt[3]{a+b x^3}}{x^{11}} \, dx","Int[(a + b*x^3)^(1/3)/x^11,x]","-\frac{9 b^2 \left(a+b x^3\right)^{4/3}}{140 a^3 x^4}+\frac{3 b \left(a+b x^3\right)^{4/3}}{35 a^2 x^7}-\frac{\left(a+b x^3\right)^{4/3}}{10 a x^{10}}","-\frac{9 b^2 \left(a+b x^3\right)^{4/3}}{140 a^3 x^4}+\frac{3 b \left(a+b x^3\right)^{4/3}}{35 a^2 x^7}-\frac{\left(a+b x^3\right)^{4/3}}{10 a x^{10}}",1,"-(a + b*x^3)^(4/3)/(10*a*x^10) + (3*b*(a + b*x^3)^(4/3))/(35*a^2*x^7) - (9*b^2*(a + b*x^3)^(4/3))/(140*a^3*x^4)","A",3,2,15,0.1333,1,"{271, 264}"
522,1,92,0,0.0304313,"\int \frac{\sqrt[3]{a+b x^3}}{x^{14}} \, dx","Int[(a + b*x^3)^(1/3)/x^14,x]","\frac{81 b^3 \left(a+b x^3\right)^{4/3}}{1820 a^4 x^4}-\frac{27 b^2 \left(a+b x^3\right)^{4/3}}{455 a^3 x^7}+\frac{9 b \left(a+b x^3\right)^{4/3}}{130 a^2 x^{10}}-\frac{\left(a+b x^3\right)^{4/3}}{13 a x^{13}}","\frac{81 b^3 \left(a+b x^3\right)^{4/3}}{1820 a^4 x^4}-\frac{27 b^2 \left(a+b x^3\right)^{4/3}}{455 a^3 x^7}+\frac{9 b \left(a+b x^3\right)^{4/3}}{130 a^2 x^{10}}-\frac{\left(a+b x^3\right)^{4/3}}{13 a x^{13}}",1,"-(a + b*x^3)^(4/3)/(13*a*x^13) + (9*b*(a + b*x^3)^(4/3))/(130*a^2*x^10) - (27*b^2*(a + b*x^3)^(4/3))/(455*a^3*x^7) + (81*b^3*(a + b*x^3)^(4/3))/(1820*a^4*x^4)","A",4,2,15,0.1333,1,"{271, 264}"
523,1,51,0,0.0158705,"\int x^3 \sqrt[3]{a+b x^3} \, dx","Int[x^3*(a + b*x^3)^(1/3),x]","\frac{x^4 \sqrt[3]{a+b x^3} \, _2F_1\left(-\frac{1}{3},\frac{4}{3};\frac{7}{3};-\frac{b x^3}{a}\right)}{4 \sqrt[3]{\frac{b x^3}{a}+1}}","\frac{x^4 \left(a+b x^3\right)^{4/3} \, _2F_1\left(1,\frac{8}{3};\frac{7}{3};-\frac{b x^3}{a}\right)}{4 a}",1,"(x^4*(a + b*x^3)^(1/3)*Hypergeometric2F1[-1/3, 4/3, 7/3, -((b*x^3)/a)])/(4*(1 + (b*x^3)/a)^(1/3))","A",2,2,15,0.1333,1,"{365, 364}"
524,1,46,0,0.0085533,"\int \sqrt[3]{a+b x^3} \, dx","Int[(a + b*x^3)^(1/3),x]","\frac{x \sqrt[3]{a+b x^3} \, _2F_1\left(-\frac{1}{3},\frac{1}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{\sqrt[3]{\frac{b x^3}{a}+1}}","\frac{x \left(a+b x^3\right)^{4/3} \, _2F_1\left(1,\frac{5}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{a}",1,"(x*(a + b*x^3)^(1/3)*Hypergeometric2F1[-1/3, 1/3, 4/3, -((b*x^3)/a)])/(1 + (b*x^3)/a)^(1/3)","A",2,2,11,0.1818,1,"{246, 245}"
525,1,51,0,0.0150014,"\int \frac{\sqrt[3]{a+b x^3}}{x^3} \, dx","Int[(a + b*x^3)^(1/3)/x^3,x]","-\frac{\sqrt[3]{a+b x^3} \, _2F_1\left(-\frac{2}{3},-\frac{1}{3};\frac{1}{3};-\frac{b x^3}{a}\right)}{2 x^2 \sqrt[3]{\frac{b x^3}{a}+1}}","-\frac{\left(a+b x^3\right)^{4/3} \, _2F_1\left(\frac{2}{3},1;\frac{1}{3};-\frac{b x^3}{a}\right)}{2 a x^2}",1,"-((a + b*x^3)^(1/3)*Hypergeometric2F1[-2/3, -1/3, 1/3, -((b*x^3)/a)])/(2*x^2*(1 + (b*x^3)/a)^(1/3))","A",2,2,15,0.1333,1,"{365, 364}"
526,1,51,0,0.0168332,"\int \frac{\sqrt[3]{a+b x^3}}{x^6} \, dx","Int[(a + b*x^3)^(1/3)/x^6,x]","-\frac{\sqrt[3]{a+b x^3} \, _2F_1\left(-\frac{5}{3},-\frac{1}{3};-\frac{2}{3};-\frac{b x^3}{a}\right)}{5 x^5 \sqrt[3]{\frac{b x^3}{a}+1}}","-\frac{\left(a+b x^3\right)^{4/3} \, _2F_1\left(-\frac{1}{3},1;-\frac{2}{3};-\frac{b x^3}{a}\right)}{5 a x^5}",1,"-((a + b*x^3)^(1/3)*Hypergeometric2F1[-5/3, -1/3, -2/3, -((b*x^3)/a)])/(5*x^5*(1 + (b*x^3)/a)^(1/3))","A",2,2,15,0.1333,1,"{365, 364}"
527,1,80,0,0.0489658,"\int x^{11} \left(a+b x^3\right)^{2/3} \, dx","Int[x^11*(a + b*x^3)^(2/3),x]","\frac{3 a^2 \left(a+b x^3\right)^{8/3}}{8 b^4}-\frac{a^3 \left(a+b x^3\right)^{5/3}}{5 b^4}+\frac{\left(a+b x^3\right)^{14/3}}{14 b^4}-\frac{3 a \left(a+b x^3\right)^{11/3}}{11 b^4}","\frac{3 a^2 \left(a+b x^3\right)^{8/3}}{8 b^4}-\frac{a^3 \left(a+b x^3\right)^{5/3}}{5 b^4}+\frac{\left(a+b x^3\right)^{14/3}}{14 b^4}-\frac{3 a \left(a+b x^3\right)^{11/3}}{11 b^4}",1,"-(a^3*(a + b*x^3)^(5/3))/(5*b^4) + (3*a^2*(a + b*x^3)^(8/3))/(8*b^4) - (3*a*(a + b*x^3)^(11/3))/(11*b^4) + (a + b*x^3)^(14/3)/(14*b^4)","A",3,2,15,0.1333,1,"{266, 43}"
528,1,59,0,0.0343528,"\int x^8 \left(a+b x^3\right)^{2/3} \, dx","Int[x^8*(a + b*x^3)^(2/3),x]","\frac{a^2 \left(a+b x^3\right)^{5/3}}{5 b^3}+\frac{\left(a+b x^3\right)^{11/3}}{11 b^3}-\frac{a \left(a+b x^3\right)^{8/3}}{4 b^3}","\frac{a^2 \left(a+b x^3\right)^{5/3}}{5 b^3}+\frac{\left(a+b x^3\right)^{11/3}}{11 b^3}-\frac{a \left(a+b x^3\right)^{8/3}}{4 b^3}",1,"(a^2*(a + b*x^3)^(5/3))/(5*b^3) - (a*(a + b*x^3)^(8/3))/(4*b^3) + (a + b*x^3)^(11/3)/(11*b^3)","A",3,2,15,0.1333,1,"{266, 43}"
529,1,38,0,0.0228097,"\int x^5 \left(a+b x^3\right)^{2/3} \, dx","Int[x^5*(a + b*x^3)^(2/3),x]","\frac{\left(a+b x^3\right)^{8/3}}{8 b^2}-\frac{a \left(a+b x^3\right)^{5/3}}{5 b^2}","\frac{\left(a+b x^3\right)^{8/3}}{8 b^2}-\frac{a \left(a+b x^3\right)^{5/3}}{5 b^2}",1,"-(a*(a + b*x^3)^(5/3))/(5*b^2) + (a + b*x^3)^(8/3)/(8*b^2)","A",3,2,15,0.1333,1,"{266, 43}"
530,1,18,0,0.0045089,"\int x^2 \left(a+b x^3\right)^{2/3} \, dx","Int[x^2*(a + b*x^3)^(2/3),x]","\frac{\left(a+b x^3\right)^{5/3}}{5 b}","\frac{\left(a+b x^3\right)^{5/3}}{5 b}",1,"(a + b*x^3)^(5/3)/(5*b)","A",1,1,15,0.06667,1,"{261}"
531,1,98,0,0.0664979,"\int \frac{\left(a+b x^3\right)^{2/3}}{x} \, dx","Int[(a + b*x^3)^(2/3)/x,x]","\frac{1}{2} a^{2/3} \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)+\frac{a^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3}}-\frac{1}{2} a^{2/3} \log (x)+\frac{1}{2} \left(a+b x^3\right)^{2/3}","\frac{1}{2} a^{2/3} \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)+\frac{a^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3}}-\frac{1}{2} a^{2/3} \log (x)+\frac{1}{2} \left(a+b x^3\right)^{2/3}",1,"(a + b*x^3)^(2/3)/2 + (a^(2/3)*ArcTan[(a^(1/3) + 2*(a + b*x^3)^(1/3))/(Sqrt[3]*a^(1/3))])/Sqrt[3] - (a^(2/3)*Log[x])/2 + (a^(2/3)*Log[a^(1/3) - (a + b*x^3)^(1/3)])/2","A",6,6,15,0.4000,1,"{266, 50, 55, 617, 204, 31}"
532,1,107,0,0.0639311,"\int \frac{\left(a+b x^3\right)^{2/3}}{x^4} \, dx","Int[(a + b*x^3)^(2/3)/x^4,x]","-\frac{\left(a+b x^3\right)^{2/3}}{3 x^3}+\frac{b \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{3 \sqrt[3]{a}}+\frac{2 b \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} \sqrt[3]{a}}-\frac{b \log (x)}{3 \sqrt[3]{a}}","-\frac{\left(a+b x^3\right)^{2/3}}{3 x^3}+\frac{b \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{3 \sqrt[3]{a}}+\frac{2 b \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} \sqrt[3]{a}}-\frac{b \log (x)}{3 \sqrt[3]{a}}",1,"-(a + b*x^3)^(2/3)/(3*x^3) + (2*b*ArcTan[(a^(1/3) + 2*(a + b*x^3)^(1/3))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(1/3)) - (b*Log[x])/(3*a^(1/3)) + (b*Log[a^(1/3) - (a + b*x^3)^(1/3)])/(3*a^(1/3))","A",6,6,15,0.4000,1,"{266, 47, 55, 617, 204, 31}"
533,1,51,0,0.0153125,"\int x^4 \left(a+b x^3\right)^{2/3} \, dx","Int[x^4*(a + b*x^3)^(2/3),x]","\frac{x^5 \left(a+b x^3\right)^{2/3} \, _2F_1\left(-\frac{2}{3},\frac{5}{3};\frac{8}{3};-\frac{b x^3}{a}\right)}{5 \left(\frac{b x^3}{a}+1\right)^{2/3}}","\frac{x^5 \left(a+b x^3\right)^{5/3} \, _2F_1\left(1,\frac{10}{3};\frac{8}{3};-\frac{b x^3}{a}\right)}{5 a}",1,"(x^5*(a + b*x^3)^(2/3)*Hypergeometric2F1[-2/3, 5/3, 8/3, -((b*x^3)/a)])/(5*(1 + (b*x^3)/a)^(2/3))","A",2,2,15,0.1333,1,"{365, 364}"
534,1,51,0,0.0128214,"\int x \left(a+b x^3\right)^{2/3} \, dx","Int[x*(a + b*x^3)^(2/3),x]","\frac{x^2 \left(a+b x^3\right)^{2/3} \, _2F_1\left(-\frac{2}{3},\frac{2}{3};\frac{5}{3};-\frac{b x^3}{a}\right)}{2 \left(\frac{b x^3}{a}+1\right)^{2/3}}","\frac{x^2 \left(a+b x^3\right)^{5/3} \, _2F_1\left(1,\frac{7}{3};\frac{5}{3};-\frac{b x^3}{a}\right)}{2 a}",1,"(x^2*(a + b*x^3)^(2/3)*Hypergeometric2F1[-2/3, 2/3, 5/3, -((b*x^3)/a)])/(2*(1 + (b*x^3)/a)^(2/3))","A",2,2,13,0.1538,1,"{365, 364}"
535,1,49,0,0.0161101,"\int \frac{\left(a+b x^3\right)^{2/3}}{x^2} \, dx","Int[(a + b*x^3)^(2/3)/x^2,x]","-\frac{\left(a+b x^3\right)^{2/3} \, _2F_1\left(-\frac{2}{3},-\frac{1}{3};\frac{2}{3};-\frac{b x^3}{a}\right)}{x \left(\frac{b x^3}{a}+1\right)^{2/3}}","-\frac{\left(a+b x^3\right)^{5/3} \, _2F_1\left(1,\frac{4}{3};\frac{2}{3};-\frac{b x^3}{a}\right)}{a x}",1,"-(((a + b*x^3)^(2/3)*Hypergeometric2F1[-2/3, -1/3, 2/3, -((b*x^3)/a)])/(x*(1 + (b*x^3)/a)^(2/3)))","A",2,2,15,0.1333,1,"{365, 364}"
536,1,51,0,0.0159126,"\int \frac{\left(a+b x^3\right)^{2/3}}{x^5} \, dx","Int[(a + b*x^3)^(2/3)/x^5,x]","-\frac{\left(a+b x^3\right)^{2/3} \, _2F_1\left(-\frac{4}{3},-\frac{2}{3};-\frac{1}{3};-\frac{b x^3}{a}\right)}{4 x^4 \left(\frac{b x^3}{a}+1\right)^{2/3}}","-\frac{\left(a+b x^3\right)^{5/3} \, _2F_1\left(\frac{1}{3},1;-\frac{1}{3};-\frac{b x^3}{a}\right)}{4 a x^4}",1,"-((a + b*x^3)^(2/3)*Hypergeometric2F1[-4/3, -2/3, -1/3, -((b*x^3)/a)])/(4*x^4*(1 + (b*x^3)/a)^(2/3))","A",2,2,15,0.1333,1,"{365, 364}"
537,1,117,0,0.0356335,"\int x^3 \left(a+b x^3\right)^{2/3} \, dx","Int[x^3*(a + b*x^3)^(2/3),x]","\frac{a^2 \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{18 b^{4/3}}-\frac{a^2 \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{9 \sqrt{3} b^{4/3}}+\frac{1}{6} x^4 \left(a+b x^3\right)^{2/3}+\frac{a x \left(a+b x^3\right)^{2/3}}{9 b}","\frac{a^2 \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{18 b^{4/3}}-\frac{a^2 \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{9 \sqrt{3} b^{4/3}}+\frac{1}{6} x^4 \left(a+b x^3\right)^{2/3}+\frac{a x \left(a+b x^3\right)^{2/3}}{9 b}",1,"(a*x*(a + b*x^3)^(2/3))/(9*b) + (x^4*(a + b*x^3)^(2/3))/6 - (a^2*ArcTan[(1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/Sqrt[3]])/(9*Sqrt[3]*b^(4/3)) + (a^2*Log[-(b^(1/3)*x) + (a + b*x^3)^(1/3)])/(18*b^(4/3))","A",3,3,15,0.2000,1,"{279, 321, 239}"
538,1,91,0,0.0165869,"\int \left(a+b x^3\right)^{2/3} \, dx","Int[(a + b*x^3)^(2/3),x]","\frac{1}{3} x \left(a+b x^3\right)^{2/3}-\frac{a \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{3 \sqrt[3]{b}}+\frac{2 a \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} \sqrt[3]{b}}","\frac{1}{3} x \left(a+b x^3\right)^{2/3}-\frac{a \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{3 \sqrt[3]{b}}+\frac{2 a \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} \sqrt[3]{b}}",1,"(x*(a + b*x^3)^(2/3))/3 + (2*a*ArcTan[(1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/Sqrt[3]])/(3*Sqrt[3]*b^(1/3)) - (a*Log[-(b^(1/3)*x) + (a + b*x^3)^(1/3)])/(3*b^(1/3))","A",2,2,11,0.1818,1,"{195, 239}"
539,1,88,0,0.0191102,"\int \frac{\left(a+b x^3\right)^{2/3}}{x^3} \, dx","Int[(a + b*x^3)^(2/3)/x^3,x]","-\frac{1}{2} b^{2/3} \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)+\frac{b^{2/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\left(a+b x^3\right)^{2/3}}{2 x^2}","-\frac{1}{2} b^{2/3} \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)+\frac{b^{2/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\left(a+b x^3\right)^{2/3}}{2 x^2}",1,"-(a + b*x^3)^(2/3)/(2*x^2) + (b^(2/3)*ArcTan[(1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/Sqrt[3]])/Sqrt[3] - (b^(2/3)*Log[-(b^(1/3)*x) + (a + b*x^3)^(1/3)])/2","A",2,2,15,0.1333,1,"{277, 239}"
540,1,21,0,0.0052076,"\int \frac{\left(a+b x^3\right)^{2/3}}{x^6} \, dx","Int[(a + b*x^3)^(2/3)/x^6,x]","-\frac{\left(a+b x^3\right)^{5/3}}{5 a x^5}","-\frac{\left(a+b x^3\right)^{5/3}}{5 a x^5}",1,"-(a + b*x^3)^(5/3)/(5*a*x^5)","A",1,1,15,0.06667,1,"{264}"
541,1,44,0,0.0109494,"\int \frac{\left(a+b x^3\right)^{2/3}}{x^9} \, dx","Int[(a + b*x^3)^(2/3)/x^9,x]","\frac{3 b \left(a+b x^3\right)^{5/3}}{40 a^2 x^5}-\frac{\left(a+b x^3\right)^{5/3}}{8 a x^8}","\frac{3 b \left(a+b x^3\right)^{5/3}}{40 a^2 x^5}-\frac{\left(a+b x^3\right)^{5/3}}{8 a x^8}",1,"-(a + b*x^3)^(5/3)/(8*a*x^8) + (3*b*(a + b*x^3)^(5/3))/(40*a^2*x^5)","A",2,2,15,0.1333,1,"{271, 264}"
542,1,68,0,0.0191239,"\int \frac{\left(a+b x^3\right)^{2/3}}{x^{12}} \, dx","Int[(a + b*x^3)^(2/3)/x^12,x]","-\frac{9 b^2 \left(a+b x^3\right)^{5/3}}{220 a^3 x^5}+\frac{3 b \left(a+b x^3\right)^{5/3}}{44 a^2 x^8}-\frac{\left(a+b x^3\right)^{5/3}}{11 a x^{11}}","-\frac{9 b^2 \left(a+b x^3\right)^{5/3}}{220 a^3 x^5}+\frac{3 b \left(a+b x^3\right)^{5/3}}{44 a^2 x^8}-\frac{\left(a+b x^3\right)^{5/3}}{11 a x^{11}}",1,"-(a + b*x^3)^(5/3)/(11*a*x^11) + (3*b*(a + b*x^3)^(5/3))/(44*a^2*x^8) - (9*b^2*(a + b*x^3)^(5/3))/(220*a^3*x^5)","A",3,2,15,0.1333,1,"{271, 264}"
543,1,46,0,0.019694,"\int x^8 \left(1-x^3\right)^{6/5} \, dx","Int[x^8*(1 - x^3)^(6/5),x]","-\frac{5}{63} \left(1-x^3\right)^{21/5}+\frac{5}{24} \left(1-x^3\right)^{16/5}-\frac{5}{33} \left(1-x^3\right)^{11/5}","-\frac{5}{63} \left(1-x^3\right)^{21/5}+\frac{5}{24} \left(1-x^3\right)^{16/5}-\frac{5}{33} \left(1-x^3\right)^{11/5}",1,"(-5*(1 - x^3)^(11/5))/33 + (5*(1 - x^3)^(16/5))/24 - (5*(1 - x^3)^(21/5))/63","A",3,2,15,0.1333,1,"{266, 43}"
544,1,80,0,0.0450665,"\int \frac{x^{11}}{\sqrt[3]{a+b x^3}} \, dx","Int[x^11/(a + b*x^3)^(1/3),x]","\frac{3 a^2 \left(a+b x^3\right)^{5/3}}{5 b^4}-\frac{a^3 \left(a+b x^3\right)^{2/3}}{2 b^4}+\frac{\left(a+b x^3\right)^{11/3}}{11 b^4}-\frac{3 a \left(a+b x^3\right)^{8/3}}{8 b^4}","\frac{3 a^2 \left(a+b x^3\right)^{5/3}}{5 b^4}-\frac{a^3 \left(a+b x^3\right)^{2/3}}{2 b^4}+\frac{\left(a+b x^3\right)^{11/3}}{11 b^4}-\frac{3 a \left(a+b x^3\right)^{8/3}}{8 b^4}",1,"-(a^3*(a + b*x^3)^(2/3))/(2*b^4) + (3*a^2*(a + b*x^3)^(5/3))/(5*b^4) - (3*a*(a + b*x^3)^(8/3))/(8*b^4) + (a + b*x^3)^(11/3)/(11*b^4)","A",3,2,15,0.1333,1,"{266, 43}"
545,1,59,0,0.0349255,"\int \frac{x^8}{\sqrt[3]{a+b x^3}} \, dx","Int[x^8/(a + b*x^3)^(1/3),x]","\frac{a^2 \left(a+b x^3\right)^{2/3}}{2 b^3}+\frac{\left(a+b x^3\right)^{8/3}}{8 b^3}-\frac{2 a \left(a+b x^3\right)^{5/3}}{5 b^3}","\frac{a^2 \left(a+b x^3\right)^{2/3}}{2 b^3}+\frac{\left(a+b x^3\right)^{8/3}}{8 b^3}-\frac{2 a \left(a+b x^3\right)^{5/3}}{5 b^3}",1,"(a^2*(a + b*x^3)^(2/3))/(2*b^3) - (2*a*(a + b*x^3)^(5/3))/(5*b^3) + (a + b*x^3)^(8/3)/(8*b^3)","A",3,2,15,0.1333,1,"{266, 43}"
546,1,38,0,0.0222965,"\int \frac{x^5}{\sqrt[3]{a+b x^3}} \, dx","Int[x^5/(a + b*x^3)^(1/3),x]","\frac{\left(a+b x^3\right)^{5/3}}{5 b^2}-\frac{a \left(a+b x^3\right)^{2/3}}{2 b^2}","\frac{\left(a+b x^3\right)^{5/3}}{5 b^2}-\frac{a \left(a+b x^3\right)^{2/3}}{2 b^2}",1,"-(a*(a + b*x^3)^(2/3))/(2*b^2) + (a + b*x^3)^(5/3)/(5*b^2)","A",3,2,15,0.1333,1,"{266, 43}"
547,1,18,0,0.0044997,"\int \frac{x^2}{\sqrt[3]{a+b x^3}} \, dx","Int[x^2/(a + b*x^3)^(1/3),x]","\frac{\left(a+b x^3\right)^{2/3}}{2 b}","\frac{\left(a+b x^3\right)^{2/3}}{2 b}",1,"(a + b*x^3)^(2/3)/(2*b)","A",1,1,15,0.06667,1,"{261}"
548,1,83,0,0.0506088,"\int \frac{1}{x \sqrt[3]{a+b x^3}} \, dx","Int[1/(x*(a + b*x^3)^(1/3)),x]","\frac{\log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{2 \sqrt[3]{a}}+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} \sqrt[3]{a}}-\frac{\log (x)}{2 \sqrt[3]{a}}","\frac{\log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{2 \sqrt[3]{a}}+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} \sqrt[3]{a}}-\frac{\log (x)}{2 \sqrt[3]{a}}",1,"ArcTan[(a^(1/3) + 2*(a + b*x^3)^(1/3))/(Sqrt[3]*a^(1/3))]/(Sqrt[3]*a^(1/3)) - Log[x]/(2*a^(1/3)) + Log[a^(1/3) - (a + b*x^3)^(1/3)]/(2*a^(1/3))","A",5,5,15,0.3333,1,"{266, 55, 617, 204, 31}"
549,1,110,0,0.0688638,"\int \frac{1}{x^4 \sqrt[3]{a+b x^3}} \, dx","Int[1/(x^4*(a + b*x^3)^(1/3)),x]","-\frac{b \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{6 a^{4/3}}-\frac{b \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{4/3}}+\frac{b \log (x)}{6 a^{4/3}}-\frac{\left(a+b x^3\right)^{2/3}}{3 a x^3}","-\frac{b \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{6 a^{4/3}}-\frac{b \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{4/3}}+\frac{b \log (x)}{6 a^{4/3}}-\frac{\left(a+b x^3\right)^{2/3}}{3 a x^3}",1,"-(a + b*x^3)^(2/3)/(3*a*x^3) - (b*ArcTan[(a^(1/3) + 2*(a + b*x^3)^(1/3))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(4/3)) + (b*Log[x])/(6*a^(4/3)) - (b*Log[a^(1/3) - (a + b*x^3)^(1/3)])/(6*a^(4/3))","A",6,6,15,0.4000,1,"{266, 51, 55, 617, 204, 31}"
550,1,51,0,0.0143734,"\int \frac{x^7}{\sqrt[3]{a+b x^3}} \, dx","Int[x^7/(a + b*x^3)^(1/3),x]","\frac{x^8 \sqrt[3]{\frac{b x^3}{a}+1} \, _2F_1\left(\frac{1}{3},\frac{8}{3};\frac{11}{3};-\frac{b x^3}{a}\right)}{8 \sqrt[3]{a+b x^3}}","\frac{x^8 \left(a+b x^3\right)^{2/3} \, _2F_1\left(1,\frac{10}{3};\frac{11}{3};-\frac{b x^3}{a}\right)}{8 a}",1,"(x^8*(1 + (b*x^3)/a)^(1/3)*Hypergeometric2F1[1/3, 8/3, 11/3, -((b*x^3)/a)])/(8*(a + b*x^3)^(1/3))","A",2,2,15,0.1333,1,"{365, 364}"
551,1,51,0,0.0159755,"\int \frac{x^4}{\sqrt[3]{a+b x^3}} \, dx","Int[x^4/(a + b*x^3)^(1/3),x]","\frac{x^5 \sqrt[3]{\frac{b x^3}{a}+1} \, _2F_1\left(\frac{1}{3},\frac{5}{3};\frac{8}{3};-\frac{b x^3}{a}\right)}{5 \sqrt[3]{a+b x^3}}","\frac{x^5 \left(a+b x^3\right)^{2/3} \, _2F_1\left(1,\frac{7}{3};\frac{8}{3};-\frac{b x^3}{a}\right)}{5 a}",1,"(x^5*(1 + (b*x^3)/a)^(1/3)*Hypergeometric2F1[1/3, 5/3, 8/3, -((b*x^3)/a)])/(5*(a + b*x^3)^(1/3))","A",2,2,15,0.1333,1,"{365, 364}"
552,1,51,0,0.0121902,"\int \frac{x}{\sqrt[3]{a+b x^3}} \, dx","Int[x/(a + b*x^3)^(1/3),x]","\frac{x^2 \sqrt[3]{\frac{b x^3}{a}+1} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{5}{3};-\frac{b x^3}{a}\right)}{2 \sqrt[3]{a+b x^3}}","\frac{x^2 \left(a+b x^3\right)^{2/3} \, _2F_1\left(1,\frac{4}{3};\frac{5}{3};-\frac{b x^3}{a}\right)}{2 a}",1,"(x^2*(1 + (b*x^3)/a)^(1/3)*Hypergeometric2F1[1/3, 2/3, 5/3, -((b*x^3)/a)])/(2*(a + b*x^3)^(1/3))","A",2,2,13,0.1538,1,"{365, 364}"
553,1,49,0,0.0158883,"\int \frac{1}{x^2 \sqrt[3]{a+b x^3}} \, dx","Int[1/(x^2*(a + b*x^3)^(1/3)),x]","-\frac{\sqrt[3]{\frac{b x^3}{a}+1} \, _2F_1\left(-\frac{1}{3},\frac{1}{3};\frac{2}{3};-\frac{b x^3}{a}\right)}{x \sqrt[3]{a+b x^3}}","-\frac{\left(a+b x^3\right)^{2/3} \, _2F_1\left(\frac{1}{3},1;\frac{2}{3};-\frac{b x^3}{a}\right)}{a x}",1,"-(((1 + (b*x^3)/a)^(1/3)*Hypergeometric2F1[-1/3, 1/3, 2/3, -((b*x^3)/a)])/(x*(a + b*x^3)^(1/3)))","A",2,2,15,0.1333,1,"{365, 364}"
554,1,51,0,0.0150739,"\int \frac{1}{x^5 \sqrt[3]{a+b x^3}} \, dx","Int[1/(x^5*(a + b*x^3)^(1/3)),x]","-\frac{\sqrt[3]{\frac{b x^3}{a}+1} \, _2F_1\left(-\frac{4}{3},\frac{1}{3};-\frac{1}{3};-\frac{b x^3}{a}\right)}{4 x^4 \sqrt[3]{a+b x^3}}","-\frac{\left(a+b x^3\right)^{2/3} \, _2F_1\left(-\frac{2}{3},1;-\frac{1}{3};-\frac{b x^3}{a}\right)}{4 a x^4}",1,"-((1 + (b*x^3)/a)^(1/3)*Hypergeometric2F1[-4/3, 1/3, -1/3, -((b*x^3)/a)])/(4*x^4*(a + b*x^3)^(1/3))","A",2,2,15,0.1333,1,"{365, 364}"
555,1,94,0,0.0188949,"\int \frac{x^3}{\sqrt[3]{a+b x^3}} \, dx","Int[x^3/(a + b*x^3)^(1/3),x]","\frac{a \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{6 b^{4/3}}-\frac{a \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} b^{4/3}}+\frac{x \left(a+b x^3\right)^{2/3}}{3 b}","\frac{a \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{6 b^{4/3}}-\frac{a \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} b^{4/3}}+\frac{x \left(a+b x^3\right)^{2/3}}{3 b}",1,"(x*(a + b*x^3)^(2/3))/(3*b) - (a*ArcTan[(1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/Sqrt[3]])/(3*Sqrt[3]*b^(4/3)) + (a*Log[-(b^(1/3)*x) + (a + b*x^3)^(1/3)])/(6*b^(4/3))","A",2,2,15,0.1333,1,"{321, 239}"
556,1,70,0,0.007904,"\int \frac{1}{\sqrt[3]{a+b x^3}} \, dx","Int[(a + b*x^3)^(-1/3),x]","\frac{\tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{b}}-\frac{\log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{2 \sqrt[3]{b}}","\frac{\tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{b}}-\frac{\log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{2 \sqrt[3]{b}}",1,"ArcTan[(1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/Sqrt[3]]/(Sqrt[3]*b^(1/3)) - Log[-(b^(1/3)*x) + (a + b*x^3)^(1/3)]/(2*b^(1/3))","A",1,1,11,0.09091,1,"{239}"
557,1,21,0,0.0048383,"\int \frac{1}{x^3 \sqrt[3]{a+b x^3}} \, dx","Int[1/(x^3*(a + b*x^3)^(1/3)),x]","-\frac{\left(a+b x^3\right)^{2/3}}{2 a x^2}","-\frac{\left(a+b x^3\right)^{2/3}}{2 a x^2}",1,"-(a + b*x^3)^(2/3)/(2*a*x^2)","A",1,1,15,0.06667,1,"{264}"
558,1,44,0,0.010515,"\int \frac{1}{x^6 \sqrt[3]{a+b x^3}} \, dx","Int[1/(x^6*(a + b*x^3)^(1/3)),x]","\frac{3 b \left(a+b x^3\right)^{2/3}}{10 a^2 x^2}-\frac{\left(a+b x^3\right)^{2/3}}{5 a x^5}","\frac{3 b \left(a+b x^3\right)^{2/3}}{10 a^2 x^2}-\frac{\left(a+b x^3\right)^{2/3}}{5 a x^5}",1,"-(a + b*x^3)^(2/3)/(5*a*x^5) + (3*b*(a + b*x^3)^(2/3))/(10*a^2*x^2)","A",2,2,15,0.1333,1,"{271, 264}"
559,1,68,0,0.0176911,"\int \frac{1}{x^9 \sqrt[3]{a+b x^3}} \, dx","Int[1/(x^9*(a + b*x^3)^(1/3)),x]","-\frac{9 b^2 \left(a+b x^3\right)^{2/3}}{40 a^3 x^2}+\frac{3 b \left(a+b x^3\right)^{2/3}}{20 a^2 x^5}-\frac{\left(a+b x^3\right)^{2/3}}{8 a x^8}","-\frac{9 b^2 \left(a+b x^3\right)^{2/3}}{40 a^3 x^2}+\frac{3 b \left(a+b x^3\right)^{2/3}}{20 a^2 x^5}-\frac{\left(a+b x^3\right)^{2/3}}{8 a x^8}",1,"-(a + b*x^3)^(2/3)/(8*a*x^8) + (3*b*(a + b*x^3)^(2/3))/(20*a^2*x^5) - (9*b^2*(a + b*x^3)^(2/3))/(40*a^3*x^2)","A",3,2,15,0.1333,1,"{271, 264}"
560,1,92,0,0.0289558,"\int \frac{1}{x^{12} \sqrt[3]{a+b x^3}} \, dx","Int[1/(x^12*(a + b*x^3)^(1/3)),x]","\frac{81 b^3 \left(a+b x^3\right)^{2/3}}{440 a^4 x^2}-\frac{27 b^2 \left(a+b x^3\right)^{2/3}}{220 a^3 x^5}+\frac{9 b \left(a+b x^3\right)^{2/3}}{88 a^2 x^8}-\frac{\left(a+b x^3\right)^{2/3}}{11 a x^{11}}","\frac{81 b^3 \left(a+b x^3\right)^{2/3}}{440 a^4 x^2}-\frac{27 b^2 \left(a+b x^3\right)^{2/3}}{220 a^3 x^5}+\frac{9 b \left(a+b x^3\right)^{2/3}}{88 a^2 x^8}-\frac{\left(a+b x^3\right)^{2/3}}{11 a x^{11}}",1,"-(a + b*x^3)^(2/3)/(11*a*x^11) + (9*b*(a + b*x^3)^(2/3))/(88*a^2*x^8) - (27*b^2*(a + b*x^3)^(2/3))/(220*a^3*x^5) + (81*b^3*(a + b*x^3)^(2/3))/(440*a^4*x^2)","A",4,2,15,0.1333,1,"{271, 264}"
561,1,78,0,0.0444571,"\int \frac{x^{11}}{\left(a+b x^3\right)^{2/3}} \, dx","Int[x^11/(a + b*x^3)^(2/3),x]","\frac{3 a^2 \left(a+b x^3\right)^{4/3}}{4 b^4}-\frac{a^3 \sqrt[3]{a+b x^3}}{b^4}+\frac{\left(a+b x^3\right)^{10/3}}{10 b^4}-\frac{3 a \left(a+b x^3\right)^{7/3}}{7 b^4}","\frac{3 a^2 \left(a+b x^3\right)^{4/3}}{4 b^4}-\frac{a^3 \sqrt[3]{a+b x^3}}{b^4}+\frac{\left(a+b x^3\right)^{10/3}}{10 b^4}-\frac{3 a \left(a+b x^3\right)^{7/3}}{7 b^4}",1,"-((a^3*(a + b*x^3)^(1/3))/b^4) + (3*a^2*(a + b*x^3)^(4/3))/(4*b^4) - (3*a*(a + b*x^3)^(7/3))/(7*b^4) + (a + b*x^3)^(10/3)/(10*b^4)","A",3,2,15,0.1333,1,"{266, 43}"
562,1,56,0,0.0330715,"\int \frac{x^8}{\left(a+b x^3\right)^{2/3}} \, dx","Int[x^8/(a + b*x^3)^(2/3),x]","\frac{a^2 \sqrt[3]{a+b x^3}}{b^3}+\frac{\left(a+b x^3\right)^{7/3}}{7 b^3}-\frac{a \left(a+b x^3\right)^{4/3}}{2 b^3}","\frac{a^2 \sqrt[3]{a+b x^3}}{b^3}+\frac{\left(a+b x^3\right)^{7/3}}{7 b^3}-\frac{a \left(a+b x^3\right)^{4/3}}{2 b^3}",1,"(a^2*(a + b*x^3)^(1/3))/b^3 - (a*(a + b*x^3)^(4/3))/(2*b^3) + (a + b*x^3)^(7/3)/(7*b^3)","A",3,2,15,0.1333,1,"{266, 43}"
563,1,36,0,0.0219188,"\int \frac{x^5}{\left(a+b x^3\right)^{2/3}} \, dx","Int[x^5/(a + b*x^3)^(2/3),x]","\frac{\left(a+b x^3\right)^{4/3}}{4 b^2}-\frac{a \sqrt[3]{a+b x^3}}{b^2}","\frac{\left(a+b x^3\right)^{4/3}}{4 b^2}-\frac{a \sqrt[3]{a+b x^3}}{b^2}",1,"-((a*(a + b*x^3)^(1/3))/b^2) + (a + b*x^3)^(4/3)/(4*b^2)","A",3,2,15,0.1333,1,"{266, 43}"
564,1,15,0,0.004248,"\int \frac{x^2}{\left(a+b x^3\right)^{2/3}} \, dx","Int[x^2/(a + b*x^3)^(2/3),x]","\frac{\sqrt[3]{a+b x^3}}{b}","\frac{\sqrt[3]{a+b x^3}}{b}",1,"(a + b*x^3)^(1/3)/b","A",1,1,15,0.06667,1,"{261}"
565,1,84,0,0.0490152,"\int \frac{1}{x \left(a+b x^3\right)^{2/3}} \, dx","Int[1/(x*(a + b*x^3)^(2/3)),x]","\frac{\log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{2 a^{2/3}}-\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3}}-\frac{\log (x)}{2 a^{2/3}}","\frac{\log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{2 a^{2/3}}-\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3}}-\frac{\log (x)}{2 a^{2/3}}",1,"-(ArcTan[(a^(1/3) + 2*(a + b*x^3)^(1/3))/(Sqrt[3]*a^(1/3))]/(Sqrt[3]*a^(2/3))) - Log[x]/(2*a^(2/3)) + Log[a^(1/3) - (a + b*x^3)^(1/3)]/(2*a^(2/3))","A",5,5,15,0.3333,1,"{266, 57, 617, 204, 31}"
566,1,110,0,0.0668387,"\int \frac{1}{x^4 \left(a+b x^3\right)^{2/3}} \, dx","Int[1/(x^4*(a + b*x^3)^(2/3)),x]","-\frac{b \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{3 a^{5/3}}+\frac{2 b \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{5/3}}+\frac{b \log (x)}{3 a^{5/3}}-\frac{\sqrt[3]{a+b x^3}}{3 a x^3}","-\frac{b \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{3 a^{5/3}}+\frac{2 b \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{5/3}}+\frac{b \log (x)}{3 a^{5/3}}-\frac{\sqrt[3]{a+b x^3}}{3 a x^3}",1,"-(a + b*x^3)^(1/3)/(3*a*x^3) + (2*b*ArcTan[(a^(1/3) + 2*(a + b*x^3)^(1/3))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(5/3)) + (b*Log[x])/(3*a^(5/3)) - (b*Log[a^(1/3) - (a + b*x^3)^(1/3)])/(3*a^(5/3))","A",6,6,15,0.4000,1,"{266, 51, 57, 617, 204, 31}"
567,1,176,0,0.091355,"\int \frac{x^7}{\left(a+b x^3\right)^{2/3}} \, dx","Int[x^7/(a + b*x^3)^(2/3),x]","-\frac{5 a^2 \log \left(1-\frac{\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}\right)}{27 b^{8/3}}+\frac{5 a^2 \log \left(\frac{b^{2/3} x^2}{\left(a+b x^3\right)^{2/3}}+\frac{\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1\right)}{54 b^{8/3}}-\frac{5 a^2 \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{9 \sqrt{3} b^{8/3}}-\frac{5 a x^2 \sqrt[3]{a+b x^3}}{18 b^2}+\frac{x^5 \sqrt[3]{a+b x^3}}{6 b}","-\frac{5 a^2 \log \left(\sqrt[3]{b} x-\sqrt[3]{a+b x^3}\right)}{18 b^{8/3}}-\frac{5 a^2 \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{9 \sqrt{3} b^{8/3}}-\frac{5 a x^2 \sqrt[3]{a+b x^3}}{18 b^2}+\frac{x^5 \sqrt[3]{a+b x^3}}{6 b}",1,"(-5*a*x^2*(a + b*x^3)^(1/3))/(18*b^2) + (x^5*(a + b*x^3)^(1/3))/(6*b) - (5*a^2*ArcTan[(1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/Sqrt[3]])/(9*Sqrt[3]*b^(8/3)) - (5*a^2*Log[1 - (b^(1/3)*x)/(a + b*x^3)^(1/3)])/(27*b^(8/3)) + (5*a^2*Log[1 + (b^(2/3)*x^2)/(a + b*x^3)^(2/3) + (b^(1/3)*x)/(a + b*x^3)^(1/3)])/(54*b^(8/3))","A",9,8,15,0.5333,1,"{321, 331, 292, 31, 634, 617, 204, 628}"
568,1,148,0,0.0688983,"\int \frac{x^4}{\left(a+b x^3\right)^{2/3}} \, dx","Int[x^4/(a + b*x^3)^(2/3),x]","\frac{2 a \log \left(1-\frac{\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}\right)}{9 b^{5/3}}-\frac{a \log \left(\frac{b^{2/3} x^2}{\left(a+b x^3\right)^{2/3}}+\frac{\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1\right)}{9 b^{5/3}}+\frac{2 a \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} b^{5/3}}+\frac{x^2 \sqrt[3]{a+b x^3}}{3 b}","\frac{a \log \left(\sqrt[3]{b} x-\sqrt[3]{a+b x^3}\right)}{3 b^{5/3}}+\frac{2 a \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} b^{5/3}}+\frac{x^2 \sqrt[3]{a+b x^3}}{3 b}",1,"(x^2*(a + b*x^3)^(1/3))/(3*b) + (2*a*ArcTan[(1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/Sqrt[3]])/(3*Sqrt[3]*b^(5/3)) + (2*a*Log[1 - (b^(1/3)*x)/(a + b*x^3)^(1/3)])/(9*b^(5/3)) - (a*Log[1 + (b^(2/3)*x^2)/(a + b*x^3)^(2/3) + (b^(1/3)*x)/(a + b*x^3)^(1/3)])/(9*b^(5/3))","A",8,8,15,0.5333,1,"{321, 331, 292, 31, 634, 617, 204, 628}"
569,1,122,0,0.0530405,"\int \frac{x}{\left(a+b x^3\right)^{2/3}} \, dx","Int[x/(a + b*x^3)^(2/3),x]","-\frac{\log \left(1-\frac{\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}\right)}{3 b^{2/3}}+\frac{\log \left(\frac{b^{2/3} x^2}{\left(a+b x^3\right)^{2/3}}+\frac{\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1\right)}{6 b^{2/3}}-\frac{\tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} b^{2/3}}","-\frac{\log \left(\sqrt[3]{b} x-\sqrt[3]{a+b x^3}\right)}{2 b^{2/3}}-\frac{\tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} b^{2/3}}",1,"-(ArcTan[(1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/Sqrt[3]]/(Sqrt[3]*b^(2/3))) - Log[1 - (b^(1/3)*x)/(a + b*x^3)^(1/3)]/(3*b^(2/3)) + Log[1 + (b^(2/3)*x^2)/(a + b*x^3)^(2/3) + (b^(1/3)*x)/(a + b*x^3)^(1/3)]/(6*b^(2/3))","A",7,7,13,0.5385,1,"{331, 292, 31, 634, 617, 204, 628}"
570,1,19,0,0.0048431,"\int \frac{1}{x^2 \left(a+b x^3\right)^{2/3}} \, dx","Int[1/(x^2*(a + b*x^3)^(2/3)),x]","-\frac{\sqrt[3]{a+b x^3}}{a x}","-\frac{\sqrt[3]{a+b x^3}}{a x}",1,"-((a + b*x^3)^(1/3)/(a*x))","A",1,1,15,0.06667,1,"{264}"
571,1,44,0,0.0111215,"\int \frac{1}{x^5 \left(a+b x^3\right)^{2/3}} \, dx","Int[1/(x^5*(a + b*x^3)^(2/3)),x]","\frac{3 b \sqrt[3]{a+b x^3}}{4 a^2 x}-\frac{\sqrt[3]{a+b x^3}}{4 a x^4}","\frac{3 b \sqrt[3]{a+b x^3}}{4 a^2 x}-\frac{\sqrt[3]{a+b x^3}}{4 a x^4}",1,"-(a + b*x^3)^(1/3)/(4*a*x^4) + (3*b*(a + b*x^3)^(1/3))/(4*a^2*x)","A",2,2,15,0.1333,1,"{271, 264}"
572,1,68,0,0.0201348,"\int \frac{1}{x^8 \left(a+b x^3\right)^{2/3}} \, dx","Int[1/(x^8*(a + b*x^3)^(2/3)),x]","-\frac{9 b^2 \sqrt[3]{a+b x^3}}{14 a^3 x}+\frac{3 b \sqrt[3]{a+b x^3}}{14 a^2 x^4}-\frac{\sqrt[3]{a+b x^3}}{7 a x^7}","-\frac{9 b^2 \sqrt[3]{a+b x^3}}{14 a^3 x}+\frac{3 b \sqrt[3]{a+b x^3}}{14 a^2 x^4}-\frac{\sqrt[3]{a+b x^3}}{7 a x^7}",1,"-(a + b*x^3)^(1/3)/(7*a*x^7) + (3*b*(a + b*x^3)^(1/3))/(14*a^2*x^4) - (9*b^2*(a + b*x^3)^(1/3))/(14*a^3*x)","A",3,2,15,0.1333,1,"{271, 264}"
573,1,92,0,0.0305809,"\int \frac{1}{x^{11} \left(a+b x^3\right)^{2/3}} \, dx","Int[1/(x^11*(a + b*x^3)^(2/3)),x]","\frac{81 b^3 \sqrt[3]{a+b x^3}}{140 a^4 x}-\frac{27 b^2 \sqrt[3]{a+b x^3}}{140 a^3 x^4}+\frac{9 b \sqrt[3]{a+b x^3}}{70 a^2 x^7}-\frac{\sqrt[3]{a+b x^3}}{10 a x^{10}}","\frac{81 b^3 \sqrt[3]{a+b x^3}}{140 a^4 x}-\frac{27 b^2 \sqrt[3]{a+b x^3}}{140 a^3 x^4}+\frac{9 b \sqrt[3]{a+b x^3}}{70 a^2 x^7}-\frac{\sqrt[3]{a+b x^3}}{10 a x^{10}}",1,"-(a + b*x^3)^(1/3)/(10*a*x^10) + (9*b*(a + b*x^3)^(1/3))/(70*a^2*x^7) - (27*b^2*(a + b*x^3)^(1/3))/(140*a^3*x^4) + (81*b^3*(a + b*x^3)^(1/3))/(140*a^4*x)","A",4,2,15,0.1333,1,"{271, 264}"
574,1,51,0,0.0158768,"\int \frac{x^6}{\left(a+b x^3\right)^{2/3}} \, dx","Int[x^6/(a + b*x^3)^(2/3),x]","\frac{x^7 \left(\frac{b x^3}{a}+1\right)^{2/3} \, _2F_1\left(\frac{2}{3},\frac{7}{3};\frac{10}{3};-\frac{b x^3}{a}\right)}{7 \left(a+b x^3\right)^{2/3}}","\frac{x^7 \sqrt[3]{a+b x^3} \, _2F_1\left(1,\frac{8}{3};\frac{10}{3};-\frac{b x^3}{a}\right)}{7 a}",1,"(x^7*(1 + (b*x^3)/a)^(2/3)*Hypergeometric2F1[2/3, 7/3, 10/3, -((b*x^3)/a)])/(7*(a + b*x^3)^(2/3))","A",2,2,15,0.1333,1,"{365, 364}"
575,1,51,0,0.0167299,"\int \frac{x^3}{\left(a+b x^3\right)^{2/3}} \, dx","Int[x^3/(a + b*x^3)^(2/3),x]","\frac{x^4 \left(\frac{b x^3}{a}+1\right)^{2/3} \, _2F_1\left(\frac{2}{3},\frac{4}{3};\frac{7}{3};-\frac{b x^3}{a}\right)}{4 \left(a+b x^3\right)^{2/3}}","\frac{x^4 \sqrt[3]{a+b x^3} \, _2F_1\left(1,\frac{5}{3};\frac{7}{3};-\frac{b x^3}{a}\right)}{4 a}",1,"(x^4*(1 + (b*x^3)/a)^(2/3)*Hypergeometric2F1[2/3, 4/3, 7/3, -((b*x^3)/a)])/(4*(a + b*x^3)^(2/3))","A",2,2,15,0.1333,1,"{365, 364}"
576,1,46,0,0.0090233,"\int \frac{1}{\left(a+b x^3\right)^{2/3}} \, dx","Int[(a + b*x^3)^(-2/3),x]","\frac{x \left(\frac{b x^3}{a}+1\right)^{2/3} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{\left(a+b x^3\right)^{2/3}}","\frac{x \sqrt[3]{a+b x^3} \, _2F_1\left(\frac{2}{3},1;\frac{4}{3};-\frac{b x^3}{a}\right)}{a}",1,"(x*(1 + (b*x^3)/a)^(2/3)*Hypergeometric2F1[1/3, 2/3, 4/3, -((b*x^3)/a)])/(a + b*x^3)^(2/3)","A",2,2,11,0.1818,1,"{246, 245}"
577,1,51,0,0.0170219,"\int \frac{1}{x^3 \left(a+b x^3\right)^{2/3}} \, dx","Int[1/(x^3*(a + b*x^3)^(2/3)),x]","-\frac{\left(\frac{b x^3}{a}+1\right)^{2/3} \, _2F_1\left(-\frac{2}{3},\frac{2}{3};\frac{1}{3};-\frac{b x^3}{a}\right)}{2 x^2 \left(a+b x^3\right)^{2/3}}","-\frac{\sqrt[3]{a+b x^3} \, _2F_1\left(-\frac{1}{3},1;\frac{1}{3};-\frac{b x^3}{a}\right)}{2 a x^2}",1,"-((1 + (b*x^3)/a)^(2/3)*Hypergeometric2F1[-2/3, 2/3, 1/3, -((b*x^3)/a)])/(2*x^2*(a + b*x^3)^(2/3))","A",2,2,15,0.1333,1,"{365, 364}"
578,1,51,0,0.0161575,"\int \frac{1}{x^6 \left(a+b x^3\right)^{2/3}} \, dx","Int[1/(x^6*(a + b*x^3)^(2/3)),x]","-\frac{\left(\frac{b x^3}{a}+1\right)^{2/3} \, _2F_1\left(-\frac{5}{3},\frac{2}{3};-\frac{2}{3};-\frac{b x^3}{a}\right)}{5 x^5 \left(a+b x^3\right)^{2/3}}","-\frac{\sqrt[3]{a+b x^3} \, _2F_1\left(-\frac{4}{3},1;-\frac{2}{3};-\frac{b x^3}{a}\right)}{5 a x^5}",1,"-((1 + (b*x^3)/a)^(2/3)*Hypergeometric2F1[-5/3, 2/3, -2/3, -((b*x^3)/a)])/(5*x^5*(a + b*x^3)^(2/3))","A",2,2,15,0.1333,1,"{365, 364}"
579,1,72,0,0.0100193,"\int \frac{1}{\sqrt[3]{a-b x^3}} \, dx","Int[(a - b*x^3)^(-1/3),x]","\frac{\log \left(\sqrt[3]{a-b x^3}+\sqrt[3]{b} x\right)}{2 \sqrt[3]{b}}-\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a-b x^3}}}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{b}}","\frac{\log \left(\sqrt[3]{a-b x^3}+\sqrt[3]{b} x\right)}{2 \sqrt[3]{b}}-\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a-b x^3}}}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{b}}",1,"-(ArcTan[(1 - (2*b^(1/3)*x)/(a - b*x^3)^(1/3))/Sqrt[3]]/(Sqrt[3]*b^(1/3))) + Log[b^(1/3)*x + (a - b*x^3)^(1/3)]/(2*b^(1/3))","A",1,1,12,0.08333,1,"{239}"
580,1,46,0,0.0050076,"\int \frac{1}{\sqrt[3]{2+x^3}} \, dx","Int[(2 + x^3)^(-1/3),x]","\frac{\tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3+2}}+1}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{1}{2} \log \left(\sqrt[3]{x^3+2}-x\right)","\frac{\tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3+2}}+1}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{1}{2} \log \left(\sqrt[3]{x^3+2}-x\right)",1,"ArcTan[(1 + (2*x)/(2 + x^3)^(1/3))/Sqrt[3]]/Sqrt[3] - Log[-x + (2 + x^3)^(1/3)]/2","A",1,1,9,0.1111,1,"{239}"
581,1,87,0,0.0411156,"\int \frac{x}{\left(1-x^3\right)^{2/3}} \, dx","Int[x/(1 - x^3)^(2/3),x]","\frac{1}{6} \log \left(\frac{x^2}{\left(1-x^3\right)^{2/3}}-\frac{x}{\sqrt[3]{1-x^3}}+1\right)-\frac{1}{3} \log \left(\frac{x}{\sqrt[3]{1-x^3}}+1\right)-\frac{\tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt{3}}","-\frac{1}{2} \log \left(-\sqrt[3]{1-x^3}-x\right)-\frac{\tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt{3}}",1,"-(ArcTan[(1 - (2*x)/(1 - x^3)^(1/3))/Sqrt[3]]/Sqrt[3]) + Log[1 + x^2/(1 - x^3)^(2/3) - x/(1 - x^3)^(1/3)]/6 - Log[1 + x/(1 - x^3)^(1/3)]/3","A",7,7,13,0.5385,1,"{331, 292, 31, 634, 618, 204, 628}"
582,1,13,0,0.0026733,"\int \frac{x^2}{\sqrt[4]{2+x^3}} \, dx","Int[x^2/(2 + x^3)^(1/4),x]","\frac{4}{9} \left(x^3+2\right)^{3/4}","\frac{4}{9} \left(x^3+2\right)^{3/4}",1,"(4*(2 + x^3)^(3/4))/9","A",1,1,13,0.07692,1,"{261}"
583,1,151,0,0.0756078,"\int x^m \left(a+b x^3\right)^8 \, dx","Int[x^m*(a + b*x^3)^8,x]","\frac{28 a^6 b^2 x^{m+7}}{m+7}+\frac{56 a^5 b^3 x^{m+10}}{m+10}+\frac{70 a^4 b^4 x^{m+13}}{m+13}+\frac{56 a^3 b^5 x^{m+16}}{m+16}+\frac{28 a^2 b^6 x^{m+19}}{m+19}+\frac{8 a^7 b x^{m+4}}{m+4}+\frac{a^8 x^{m+1}}{m+1}+\frac{8 a b^7 x^{m+22}}{m+22}+\frac{b^8 x^{m+25}}{m+25}","\frac{28 a^6 b^2 x^{m+7}}{m+7}+\frac{56 a^5 b^3 x^{m+10}}{m+10}+\frac{70 a^4 b^4 x^{m+13}}{m+13}+\frac{56 a^3 b^5 x^{m+16}}{m+16}+\frac{28 a^2 b^6 x^{m+19}}{m+19}+\frac{8 a^7 b x^{m+4}}{m+4}+\frac{a^8 x^{m+1}}{m+1}+\frac{8 a b^7 x^{m+22}}{m+22}+\frac{b^8 x^{m+25}}{m+25}",1,"(a^8*x^(1 + m))/(1 + m) + (8*a^7*b*x^(4 + m))/(4 + m) + (28*a^6*b^2*x^(7 + m))/(7 + m) + (56*a^5*b^3*x^(10 + m))/(10 + m) + (70*a^4*b^4*x^(13 + m))/(13 + m) + (56*a^3*b^5*x^(16 + m))/(16 + m) + (28*a^2*b^6*x^(19 + m))/(19 + m) + (8*a*b^7*x^(22 + m))/(22 + m) + (b^8*x^(25 + m))/(25 + m)","A",2,1,13,0.07692,1,"{270}"
584,1,97,0,0.0370078,"\int x^m \left(a+b x^3\right)^5 \, dx","Int[x^m*(a + b*x^3)^5,x]","\frac{10 a^3 b^2 x^{m+7}}{m+7}+\frac{10 a^2 b^3 x^{m+10}}{m+10}+\frac{5 a^4 b x^{m+4}}{m+4}+\frac{a^5 x^{m+1}}{m+1}+\frac{5 a b^4 x^{m+13}}{m+13}+\frac{b^5 x^{m+16}}{m+16}","\frac{10 a^3 b^2 x^{m+7}}{m+7}+\frac{10 a^2 b^3 x^{m+10}}{m+10}+\frac{5 a^4 b x^{m+4}}{m+4}+\frac{a^5 x^{m+1}}{m+1}+\frac{5 a b^4 x^{m+13}}{m+13}+\frac{b^5 x^{m+16}}{m+16}",1,"(a^5*x^(1 + m))/(1 + m) + (5*a^4*b*x^(4 + m))/(4 + m) + (10*a^3*b^2*x^(7 + m))/(7 + m) + (10*a^2*b^3*x^(10 + m))/(10 + m) + (5*a*b^4*x^(13 + m))/(13 + m) + (b^5*x^(16 + m))/(16 + m)","A",2,1,13,0.07692,1,"{270}"
585,1,61,0,0.0218334,"\int x^m \left(a+b x^3\right)^3 \, dx","Int[x^m*(a + b*x^3)^3,x]","\frac{3 a^2 b x^{m+4}}{m+4}+\frac{a^3 x^{m+1}}{m+1}+\frac{3 a b^2 x^{m+7}}{m+7}+\frac{b^3 x^{m+10}}{m+10}","\frac{3 a^2 b x^{m+4}}{m+4}+\frac{a^3 x^{m+1}}{m+1}+\frac{3 a b^2 x^{m+7}}{m+7}+\frac{b^3 x^{m+10}}{m+10}",1,"(a^3*x^(1 + m))/(1 + m) + (3*a^2*b*x^(4 + m))/(4 + m) + (3*a*b^2*x^(7 + m))/(7 + m) + (b^3*x^(10 + m))/(10 + m)","A",2,1,13,0.07692,1,"{270}"
586,1,43,0,0.0144864,"\int x^m \left(a+b x^3\right)^2 \, dx","Int[x^m*(a + b*x^3)^2,x]","\frac{a^2 x^{m+1}}{m+1}+\frac{2 a b x^{m+4}}{m+4}+\frac{b^2 x^{m+7}}{m+7}","\frac{a^2 x^{m+1}}{m+1}+\frac{2 a b x^{m+4}}{m+4}+\frac{b^2 x^{m+7}}{m+7}",1,"(a^2*x^(1 + m))/(1 + m) + (2*a*b*x^(4 + m))/(4 + m) + (b^2*x^(7 + m))/(7 + m)","A",2,1,13,0.07692,1,"{270}"
587,1,25,0,0.0072057,"\int x^m \left(a+b x^3\right) \, dx","Int[x^m*(a + b*x^3),x]","\frac{a x^{m+1}}{m+1}+\frac{b x^{m+4}}{m+4}","\frac{a x^{m+1}}{m+1}+\frac{b x^{m+4}}{m+4}",1,"(a*x^(1 + m))/(1 + m) + (b*x^(4 + m))/(4 + m)","A",2,1,11,0.09091,1,"{14}"
588,1,39,0,0.0084455,"\int \frac{x^m}{a+b x^3} \, dx","Int[x^m/(a + b*x^3),x]","\frac{x^{m+1} \, _2F_1\left(1,\frac{m+1}{3};\frac{m+4}{3};-\frac{b x^3}{a}\right)}{a (m+1)}","\frac{x^{m+1} \, _2F_1\left(1,\frac{m+1}{3};\frac{m+4}{3};-\frac{b x^3}{a}\right)}{a (m+1)}",1,"(x^(1 + m)*Hypergeometric2F1[1, (1 + m)/3, (4 + m)/3, -((b*x^3)/a)])/(a*(1 + m))","A",1,1,13,0.07692,1,"{364}"
589,1,39,0,0.0078223,"\int \frac{x^m}{\left(a+b x^3\right)^2} \, dx","Int[x^m/(a + b*x^3)^2,x]","\frac{x^{m+1} \, _2F_1\left(2,\frac{m+1}{3};\frac{m+4}{3};-\frac{b x^3}{a}\right)}{a^2 (m+1)}","\frac{x^{m+1} \, _2F_1\left(2,\frac{m+1}{3};\frac{m+4}{3};-\frac{b x^3}{a}\right)}{a^2 (m+1)}",1,"(x^(1 + m)*Hypergeometric2F1[2, (1 + m)/3, (4 + m)/3, -((b*x^3)/a)])/(a^2*(1 + m))","A",1,1,13,0.07692,1,"{364}"
590,1,39,0,0.0081129,"\int \frac{x^m}{\left(a+b x^3\right)^3} \, dx","Int[x^m/(a + b*x^3)^3,x]","\frac{x^{m+1} \, _2F_1\left(3,\frac{m+1}{3};\frac{m+4}{3};-\frac{b x^3}{a}\right)}{a^3 (m+1)}","\frac{x^{m+1} \, _2F_1\left(3,\frac{m+1}{3};\frac{m+4}{3};-\frac{b x^3}{a}\right)}{a^3 (m+1)}",1,"(x^(1 + m)*Hypergeometric2F1[3, (1 + m)/3, (4 + m)/3, -((b*x^3)/a)])/(a^3*(1 + m))","A",1,1,13,0.07692,1,"{364}"
591,1,64,0,0.0197573,"\int x^m \left(a+b x^3\right)^{3/2} \, dx","Int[x^m*(a + b*x^3)^(3/2),x]","\frac{a x^{m+1} \sqrt{a+b x^3} \, _2F_1\left(-\frac{3}{2},\frac{m+1}{3};\frac{m+4}{3};-\frac{b x^3}{a}\right)}{(m+1) \sqrt{\frac{b x^3}{a}+1}}","\frac{a x^{m+1} \sqrt{a+b x^3} \, _2F_1\left(-\frac{3}{2},\frac{m+1}{3};\frac{m+4}{3};-\frac{b x^3}{a}\right)}{(m+1) \sqrt{\frac{b x^3}{a}+1}}",1,"(a*x^(1 + m)*Sqrt[a + b*x^3]*Hypergeometric2F1[-3/2, (1 + m)/3, (4 + m)/3, -((b*x^3)/a)])/((1 + m)*Sqrt[1 + (b*x^3)/a])","A",2,2,15,0.1333,1,"{365, 364}"
592,1,63,0,0.0178059,"\int x^m \sqrt{a+b x^3} \, dx","Int[x^m*Sqrt[a + b*x^3],x]","\frac{x^{m+1} \sqrt{a+b x^3} \, _2F_1\left(-\frac{1}{2},\frac{m+1}{3};\frac{m+4}{3};-\frac{b x^3}{a}\right)}{(m+1) \sqrt{\frac{b x^3}{a}+1}}","\frac{x^{m+1} \sqrt{a+b x^3} \, _2F_1\left(-\frac{1}{2},\frac{m+1}{3};\frac{m+4}{3};-\frac{b x^3}{a}\right)}{(m+1) \sqrt{\frac{b x^3}{a}+1}}",1,"(x^(1 + m)*Sqrt[a + b*x^3]*Hypergeometric2F1[-1/2, (1 + m)/3, (4 + m)/3, -((b*x^3)/a)])/((1 + m)*Sqrt[1 + (b*x^3)/a])","A",2,2,15,0.1333,1,"{365, 364}"
593,1,63,0,0.0180777,"\int \frac{x^m}{\sqrt{a+b x^3}} \, dx","Int[x^m/Sqrt[a + b*x^3],x]","\frac{x^{m+1} \sqrt{\frac{b x^3}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{3};\frac{m+4}{3};-\frac{b x^3}{a}\right)}{(m+1) \sqrt{a+b x^3}}","\frac{x^{m+1} \sqrt{a+b x^3} \, _2F_1\left(1,\frac{1}{6} (2 m+5);\frac{m+4}{3};-\frac{b x^3}{a}\right)}{a (m+1)}",1,"(x^(1 + m)*Sqrt[1 + (b*x^3)/a]*Hypergeometric2F1[1/2, (1 + m)/3, (4 + m)/3, -((b*x^3)/a)])/((1 + m)*Sqrt[a + b*x^3])","A",2,2,15,0.1333,1,"{365, 364}"
594,1,66,0,0.018984,"\int \frac{x^m}{\left(a+b x^3\right)^{3/2}} \, dx","Int[x^m/(a + b*x^3)^(3/2),x]","\frac{x^{m+1} \sqrt{\frac{b x^3}{a}+1} \, _2F_1\left(\frac{3}{2},\frac{m+1}{3};\frac{m+4}{3};-\frac{b x^3}{a}\right)}{a (m+1) \sqrt{a+b x^3}}","\frac{x^{m+1} \sqrt{\frac{b x^3}{a}+1} \, _2F_1\left(\frac{3}{2},\frac{m+1}{3};\frac{m+4}{3};-\frac{b x^3}{a}\right)}{a (m+1) \sqrt{a+b x^3}}",1,"(x^(1 + m)*Sqrt[1 + (b*x^3)/a]*Hypergeometric2F1[3/2, (1 + m)/3, (4 + m)/3, -((b*x^3)/a)])/(a*(1 + m)*Sqrt[a + b*x^3])","A",2,2,15,0.1333,1,"{365, 364}"
595,1,69,0,0.0229611,"\int (c x)^m \left(a+b x^3\right)^{4/3} \, dx","Int[(c*x)^m*(a + b*x^3)^(4/3),x]","\frac{a \sqrt[3]{a+b x^3} (c x)^{m+1} \, _2F_1\left(-\frac{4}{3},\frac{m+1}{3};\frac{m+4}{3};-\frac{b x^3}{a}\right)}{c (m+1) \sqrt[3]{\frac{b x^3}{a}+1}}","\frac{a \sqrt[3]{a+b x^3} (c x)^{m+1} \, _2F_1\left(-\frac{4}{3},\frac{m+1}{3};\frac{m+4}{3};-\frac{b x^3}{a}\right)}{c (m+1) \sqrt[3]{\frac{b x^3}{a}+1}}",1,"(a*(c*x)^(1 + m)*(a + b*x^3)^(1/3)*Hypergeometric2F1[-4/3, (1 + m)/3, (4 + m)/3, -((b*x^3)/a)])/(c*(1 + m)*(1 + (b*x^3)/a)^(1/3))","A",2,2,17,0.1176,1,"{365, 364}"
596,1,68,0,0.0217224,"\int (c x)^m \left(a+b x^3\right)^{2/3} \, dx","Int[(c*x)^m*(a + b*x^3)^(2/3),x]","\frac{\left(a+b x^3\right)^{2/3} (c x)^{m+1} \, _2F_1\left(-\frac{2}{3},\frac{m+1}{3};\frac{m+4}{3};-\frac{b x^3}{a}\right)}{c (m+1) \left(\frac{b x^3}{a}+1\right)^{2/3}}","\frac{(c x)^{m+1} \left(a+b c^3 x^3\right)^{5/3} \, _2F_1\left(1,\frac{m+6}{3};\frac{m+4}{3};-\frac{b c^3 x^3}{a}\right)}{a c (m+1)}",1,"((c*x)^(1 + m)*(a + b*x^3)^(2/3)*Hypergeometric2F1[-2/3, (1 + m)/3, (4 + m)/3, -((b*x^3)/a)])/(c*(1 + m)*(1 + (b*x^3)/a)^(2/3))","A",2,2,17,0.1176,1,"{365, 364}"
597,1,68,0,0.0191093,"\int (c x)^m \sqrt[3]{a+b x^3} \, dx","Int[(c*x)^m*(a + b*x^3)^(1/3),x]","\frac{\sqrt[3]{a+b x^3} (c x)^{m+1} \, _2F_1\left(-\frac{1}{3},\frac{m+1}{3};\frac{m+4}{3};-\frac{b x^3}{a}\right)}{c (m+1) \sqrt[3]{\frac{b x^3}{a}+1}}","\frac{(c x)^{m+1} \left(a+b c^3 x^3\right)^{4/3} \, _2F_1\left(1,\frac{m+5}{3};\frac{m+4}{3};-\frac{b c^3 x^3}{a}\right)}{a c (m+1)}",1,"((c*x)^(1 + m)*(a + b*x^3)^(1/3)*Hypergeometric2F1[-1/3, (1 + m)/3, (4 + m)/3, -((b*x^3)/a)])/(c*(1 + m)*(1 + (b*x^3)/a)^(1/3))","A",2,2,17,0.1176,1,"{365, 364}"
598,1,66,0,0.0176311,"\int (c x)^m \left(a+b x^3\right)^p \, dx","Int[(c*x)^m*(a + b*x^3)^p,x]","\frac{(c x)^{m+1} \left(a+b x^3\right)^p \left(\frac{b x^3}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+1}{3},-p;\frac{m+4}{3};-\frac{b x^3}{a}\right)}{c (m+1)}","\frac{(c x)^{m+1} \left(a+b x^3\right)^p \left(\frac{b x^3}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+1}{3},-p;\frac{m+4}{3};-\frac{b x^3}{a}\right)}{c (m+1)}",1,"((c*x)^(1 + m)*(a + b*x^3)^p*Hypergeometric2F1[(1 + m)/3, -p, (4 + m)/3, -((b*x^3)/a)])/(c*(1 + m)*(1 + (b*x^3)/a)^p)","A",2,2,15,0.1333,1,"{365, 364}"
599,1,23,0,0.0061137,"\int x^2 \left(a+b x^3\right)^p \, dx","Int[x^2*(a + b*x^3)^p,x]","\frac{\left(a+b x^3\right)^{p+1}}{3 b (p+1)}","\frac{\left(a+b x^3\right)^{p+1}}{3 b (p+1)}",1,"(a + b*x^3)^(1 + p)/(3*b*(1 + p))","A",1,1,13,0.07692,1,"{261}"
600,1,48,0,0.028962,"\int x^5 \left(a+b x^3\right)^p \, dx","Int[x^5*(a + b*x^3)^p,x]","\frac{\left(a+b x^3\right)^{p+2}}{3 b^2 (p+2)}-\frac{a \left(a+b x^3\right)^{p+1}}{3 b^2 (p+1)}","\frac{\left(a+b x^3\right)^{p+2}}{3 b^2 (p+2)}-\frac{a \left(a+b x^3\right)^{p+1}}{3 b^2 (p+1)}",1,"-(a*(a + b*x^3)^(1 + p))/(3*b^2*(1 + p)) + (a + b*x^3)^(2 + p)/(3*b^2*(2 + p))","A",3,2,13,0.1538,1,"{266, 43}"
601,1,74,0,0.0441732,"\int x^8 \left(a+b x^3\right)^p \, dx","Int[x^8*(a + b*x^3)^p,x]","\frac{a^2 \left(a+b x^3\right)^{p+1}}{3 b^3 (p+1)}-\frac{2 a \left(a+b x^3\right)^{p+2}}{3 b^3 (p+2)}+\frac{\left(a+b x^3\right)^{p+3}}{3 b^3 (p+3)}","\frac{a^2 \left(a+b x^3\right)^{p+1}}{3 b^3 (p+1)}-\frac{2 a \left(a+b x^3\right)^{p+2}}{3 b^3 (p+2)}+\frac{\left(a+b x^3\right)^{p+3}}{3 b^3 (p+3)}",1,"(a^2*(a + b*x^3)^(1 + p))/(3*b^3*(1 + p)) - (2*a*(a + b*x^3)^(2 + p))/(3*b^3*(2 + p)) + (a + b*x^3)^(3 + p)/(3*b^3*(3 + p))","A",3,2,13,0.1538,1,"{266, 43}"
602,1,95,0,0.0595246,"\int x^{11} \left(a+b x^3\right)^p \, dx","Int[x^11*(a + b*x^3)^p,x]","-\frac{a^3 \left(a+b x^3\right)^{p+1}}{3 b^4 (p+1)}+\frac{a^2 \left(a+b x^3\right)^{p+2}}{b^4 (p+2)}-\frac{a \left(a+b x^3\right)^{p+3}}{b^4 (p+3)}+\frac{\left(a+b x^3\right)^{p+4}}{3 b^4 (p+4)}","-\frac{a^3 \left(a+b x^3\right)^{p+1}}{3 b^4 (p+1)}+\frac{a^2 \left(a+b x^3\right)^{p+2}}{b^4 (p+2)}-\frac{a \left(a+b x^3\right)^{p+3}}{b^4 (p+3)}+\frac{\left(a+b x^3\right)^{p+4}}{3 b^4 (p+4)}",1,"-(a^3*(a + b*x^3)^(1 + p))/(3*b^4*(1 + p)) + (a^2*(a + b*x^3)^(2 + p))/(b^4*(2 + p)) - (a*(a + b*x^3)^(3 + p))/(b^4*(3 + p)) + (a + b*x^3)^(4 + p)/(3*b^4*(4 + p))","A",3,2,13,0.1538,1,"{266, 43}"
603,1,25,0,0.0075716,"\int x^m \left(a+b x^4\right) \, dx","Int[x^m*(a + b*x^4),x]","\frac{a x^{m+1}}{m+1}+\frac{b x^{m+5}}{m+5}","\frac{a x^{m+1}}{m+1}+\frac{b x^{m+5}}{m+5}",1,"(a*x^(1 + m))/(1 + m) + (b*x^(5 + m))/(5 + m)","A",2,1,11,0.09091,1,"{14}"
604,1,17,0,0.0052271,"\int x^5 \left(a+b x^4\right) \, dx","Int[x^5*(a + b*x^4),x]","\frac{a x^6}{6}+\frac{b x^{10}}{10}","\frac{a x^6}{6}+\frac{b x^{10}}{10}",1,"(a*x^6)/6 + (b*x^10)/10","A",2,1,11,0.09091,1,"{14}"
605,1,17,0,0.0052259,"\int x^4 \left(a+b x^4\right) \, dx","Int[x^4*(a + b*x^4),x]","\frac{a x^5}{5}+\frac{b x^9}{9}","\frac{a x^5}{5}+\frac{b x^9}{9}",1,"(a*x^5)/5 + (b*x^9)/9","A",2,1,11,0.09091,1,"{14}"
606,1,17,0,0.0047609,"\int x^3 \left(a+b x^4\right) \, dx","Int[x^3*(a + b*x^4),x]","\frac{a x^4}{4}+\frac{b x^8}{8}","\frac{a x^4}{4}+\frac{b x^8}{8}",1,"(a*x^4)/4 + (b*x^8)/8","A",2,1,11,0.09091,1,"{14}"
607,1,17,0,0.0053618,"\int x^2 \left(a+b x^4\right) \, dx","Int[x^2*(a + b*x^4),x]","\frac{a x^3}{3}+\frac{b x^7}{7}","\frac{a x^3}{3}+\frac{b x^7}{7}",1,"(a*x^3)/3 + (b*x^7)/7","A",2,1,11,0.09091,1,"{14}"
608,1,17,0,0.0047628,"\int x \left(a+b x^4\right) \, dx","Int[x*(a + b*x^4),x]","\frac{a x^2}{2}+\frac{b x^6}{6}","\frac{a x^2}{2}+\frac{b x^6}{6}",1,"(a*x^2)/2 + (b*x^6)/6","A",2,1,9,0.1111,1,"{14}"
609,1,12,0,0.0021382,"\int \left(a+b x^4\right) \, dx","Int[a + b*x^4,x]","a x+\frac{b x^5}{5}","a x+\frac{b x^5}{5}",1,"a*x + (b*x^5)/5","A",1,0,7,0,1,"{}"
610,1,13,0,0.0036848,"\int \frac{a+b x^4}{x} \, dx","Int[(a + b*x^4)/x,x]","a \log (x)+\frac{b x^4}{4}","a \log (x)+\frac{b x^4}{4}",1,"(b*x^4)/4 + a*Log[x]","A",2,1,11,0.09091,1,"{14}"
611,1,15,0,0.0045657,"\int \frac{a+b x^4}{x^2} \, dx","Int[(a + b*x^4)/x^2,x]","\frac{b x^3}{3}-\frac{a}{x}","\frac{b x^3}{3}-\frac{a}{x}",1,"-(a/x) + (b*x^3)/3","A",2,1,11,0.09091,1,"{14}"
612,1,17,0,0.0046726,"\int \frac{a+b x^4}{x^3} \, dx","Int[(a + b*x^4)/x^3,x]","\frac{b x^2}{2}-\frac{a}{2 x^2}","\frac{b x^2}{2}-\frac{a}{2 x^2}",1,"-a/(2*x^2) + (b*x^2)/2","A",2,1,11,0.09091,1,"{14}"
613,1,12,0,0.0042222,"\int \frac{a+b x^4}{x^4} \, dx","Int[(a + b*x^4)/x^4,x]","b x-\frac{a}{3 x^3}","b x-\frac{a}{3 x^3}",1,"-a/(3*x^3) + b*x","A",2,1,11,0.09091,1,"{14}"
614,1,13,0,0.0046414,"\int \frac{a+b x^4}{x^5} \, dx","Int[(a + b*x^4)/x^5,x]","b \log (x)-\frac{a}{4 x^4}","b \log (x)-\frac{a}{4 x^4}",1,"-a/(4*x^4) + b*Log[x]","A",2,1,11,0.09091,1,"{14}"
615,1,15,0,0.0048259,"\int \frac{a+b x^4}{x^6} \, dx","Int[(a + b*x^4)/x^6,x]","-\frac{a}{5 x^5}-\frac{b}{x}","-\frac{a}{5 x^5}-\frac{b}{x}",1,"-a/(5*x^5) - b/x","A",2,1,11,0.09091,1,"{14}"
616,1,17,0,0.0049891,"\int \frac{a+b x^4}{x^7} \, dx","Int[(a + b*x^4)/x^7,x]","-\frac{a}{6 x^6}-\frac{b}{2 x^2}","-\frac{a}{6 x^6}-\frac{b}{2 x^2}",1,"-a/(6*x^6) - b/(2*x^2)","A",2,1,11,0.09091,1,"{14}"
617,1,17,0,0.0046928,"\int \frac{a+b x^4}{x^8} \, dx","Int[(a + b*x^4)/x^8,x]","-\frac{a}{7 x^7}-\frac{b}{3 x^3}","-\frac{a}{7 x^7}-\frac{b}{3 x^3}",1,"-a/(7*x^7) - b/(3*x^3)","A",2,1,11,0.09091,1,"{14}"
618,1,17,0,0.0048534,"\int \frac{a+b x^4}{x^9} \, dx","Int[(a + b*x^4)/x^9,x]","-\frac{a}{8 x^8}-\frac{b}{4 x^4}","-\frac{a}{8 x^8}-\frac{b}{4 x^4}",1,"-a/(8*x^8) - b/(4*x^4)","A",2,1,11,0.09091,1,"{14}"
619,1,17,0,0.0047332,"\int \frac{a+b x^4}{x^{10}} \, dx","Int[(a + b*x^4)/x^10,x]","-\frac{a}{9 x^9}-\frac{b}{5 x^5}","-\frac{a}{9 x^9}-\frac{b}{5 x^5}",1,"-a/(9*x^9) - b/(5*x^5)","A",2,1,11,0.09091,1,"{14}"
620,1,43,0,0.0149535,"\int x^m \left(a+b x^4\right)^2 \, dx","Int[x^m*(a + b*x^4)^2,x]","\frac{a^2 x^{m+1}}{m+1}+\frac{2 a b x^{m+5}}{m+5}+\frac{b^2 x^{m+9}}{m+9}","\frac{a^2 x^{m+1}}{m+1}+\frac{2 a b x^{m+5}}{m+5}+\frac{b^2 x^{m+9}}{m+9}",1,"(a^2*x^(1 + m))/(1 + m) + (2*a*b*x^(5 + m))/(5 + m) + (b^2*x^(9 + m))/(9 + m)","A",2,1,13,0.07692,1,"{270}"
621,1,30,0,0.0100878,"\int x^5 \left(a+b x^4\right)^2 \, dx","Int[x^5*(a + b*x^4)^2,x]","\frac{a^2 x^6}{6}+\frac{1}{5} a b x^{10}+\frac{b^2 x^{14}}{14}","\frac{a^2 x^6}{6}+\frac{1}{5} a b x^{10}+\frac{b^2 x^{14}}{14}",1,"(a^2*x^6)/6 + (a*b*x^10)/5 + (b^2*x^14)/14","A",2,1,13,0.07692,1,"{270}"
622,1,30,0,0.0100323,"\int x^4 \left(a+b x^4\right)^2 \, dx","Int[x^4*(a + b*x^4)^2,x]","\frac{a^2 x^5}{5}+\frac{2}{9} a b x^9+\frac{b^2 x^{13}}{13}","\frac{a^2 x^5}{5}+\frac{2}{9} a b x^9+\frac{b^2 x^{13}}{13}",1,"(a^2*x^5)/5 + (2*a*b*x^9)/9 + (b^2*x^13)/13","A",2,1,13,0.07692,1,"{270}"
623,1,16,0,0.0029175,"\int x^3 \left(a+b x^4\right)^2 \, dx","Int[x^3*(a + b*x^4)^2,x]","\frac{\left(a+b x^4\right)^3}{12 b}","\frac{\left(a+b x^4\right)^3}{12 b}",1,"(a + b*x^4)^3/(12*b)","A",1,1,13,0.07692,1,"{261}"
624,1,30,0,0.0097477,"\int x^2 \left(a+b x^4\right)^2 \, dx","Int[x^2*(a + b*x^4)^2,x]","\frac{a^2 x^3}{3}+\frac{2}{7} a b x^7+\frac{b^2 x^{11}}{11}","\frac{a^2 x^3}{3}+\frac{2}{7} a b x^7+\frac{b^2 x^{11}}{11}",1,"(a^2*x^3)/3 + (2*a*b*x^7)/7 + (b^2*x^11)/11","A",2,1,13,0.07692,1,"{270}"
625,1,30,0,0.0091989,"\int x \left(a+b x^4\right)^2 \, dx","Int[x*(a + b*x^4)^2,x]","\frac{a^2 x^2}{2}+\frac{1}{3} a b x^6+\frac{b^2 x^{10}}{10}","\frac{a^2 x^2}{2}+\frac{1}{3} a b x^6+\frac{b^2 x^{10}}{10}",1,"(a^2*x^2)/2 + (a*b*x^6)/3 + (b^2*x^10)/10","A",2,1,11,0.09091,1,"{270}"
626,1,25,0,0.0070385,"\int \left(a+b x^4\right)^2 \, dx","Int[(a + b*x^4)^2,x]","a^2 x+\frac{2}{5} a b x^5+\frac{b^2 x^9}{9}","a^2 x+\frac{2}{5} a b x^5+\frac{b^2 x^9}{9}",1,"a^2*x + (2*a*b*x^5)/5 + (b^2*x^9)/9","A",2,1,9,0.1111,1,"{194}"
627,1,26,0,0.0122927,"\int \frac{\left(a+b x^4\right)^2}{x} \, dx","Int[(a + b*x^4)^2/x,x]","a^2 \log (x)+\frac{1}{2} a b x^4+\frac{b^2 x^8}{8}","a^2 \log (x)+\frac{1}{2} a b x^4+\frac{b^2 x^8}{8}",1,"(a*b*x^4)/2 + (b^2*x^8)/8 + a^2*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
628,1,28,0,0.0094924,"\int \frac{\left(a+b x^4\right)^2}{x^2} \, dx","Int[(a + b*x^4)^2/x^2,x]","-\frac{a^2}{x}+\frac{2}{3} a b x^3+\frac{b^2 x^7}{7}","-\frac{a^2}{x}+\frac{2}{3} a b x^3+\frac{b^2 x^7}{7}",1,"-(a^2/x) + (2*a*b*x^3)/3 + (b^2*x^7)/7","A",2,1,13,0.07692,1,"{270}"
629,1,27,0,0.0093361,"\int \frac{\left(a+b x^4\right)^2}{x^3} \, dx","Int[(a + b*x^4)^2/x^3,x]","-\frac{a^2}{2 x^2}+a b x^2+\frac{b^2 x^6}{6}","-\frac{a^2}{2 x^2}+a b x^2+\frac{b^2 x^6}{6}",1,"-a^2/(2*x^2) + a*b*x^2 + (b^2*x^6)/6","A",2,1,13,0.07692,1,"{270}"
630,1,26,0,0.0087323,"\int \frac{\left(a+b x^4\right)^2}{x^4} \, dx","Int[(a + b*x^4)^2/x^4,x]","-\frac{a^2}{3 x^3}+2 a b x+\frac{b^2 x^5}{5}","-\frac{a^2}{3 x^3}+2 a b x+\frac{b^2 x^5}{5}",1,"-a^2/(3*x^3) + 2*a*b*x + (b^2*x^5)/5","A",2,1,13,0.07692,1,"{270}"
631,1,27,0,0.0132604,"\int \frac{\left(a+b x^4\right)^2}{x^5} \, dx","Int[(a + b*x^4)^2/x^5,x]","-\frac{a^2}{4 x^4}+2 a b \log (x)+\frac{b^2 x^4}{4}","-\frac{a^2}{4 x^4}+2 a b \log (x)+\frac{b^2 x^4}{4}",1,"-a^2/(4*x^4) + (b^2*x^4)/4 + 2*a*b*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
632,1,61,0,0.0202695,"\int x^m \left(a+b x^4\right)^3 \, dx","Int[x^m*(a + b*x^4)^3,x]","\frac{3 a^2 b x^{m+5}}{m+5}+\frac{a^3 x^{m+1}}{m+1}+\frac{3 a b^2 x^{m+9}}{m+9}+\frac{b^3 x^{m+13}}{m+13}","\frac{3 a^2 b x^{m+5}}{m+5}+\frac{a^3 x^{m+1}}{m+1}+\frac{3 a b^2 x^{m+9}}{m+9}+\frac{b^3 x^{m+13}}{m+13}",1,"(a^3*x^(1 + m))/(1 + m) + (3*a^2*b*x^(5 + m))/(5 + m) + (3*a*b^2*x^(9 + m))/(9 + m) + (b^3*x^(13 + m))/(13 + m)","A",2,1,13,0.07692,1,"{270}"
633,1,43,0,0.0146323,"\int x^5 \left(a+b x^4\right)^3 \, dx","Int[x^5*(a + b*x^4)^3,x]","\frac{3}{10} a^2 b x^{10}+\frac{a^3 x^6}{6}+\frac{3}{14} a b^2 x^{14}+\frac{b^3 x^{18}}{18}","\frac{3}{10} a^2 b x^{10}+\frac{a^3 x^6}{6}+\frac{3}{14} a b^2 x^{14}+\frac{b^3 x^{18}}{18}",1,"(a^3*x^6)/6 + (3*a^2*b*x^10)/10 + (3*a*b^2*x^14)/14 + (b^3*x^18)/18","A",2,1,13,0.07692,1,"{270}"
634,1,43,0,0.0144689,"\int x^4 \left(a+b x^4\right)^3 \, dx","Int[x^4*(a + b*x^4)^3,x]","\frac{1}{3} a^2 b x^9+\frac{a^3 x^5}{5}+\frac{3}{13} a b^2 x^{13}+\frac{b^3 x^{17}}{17}","\frac{1}{3} a^2 b x^9+\frac{a^3 x^5}{5}+\frac{3}{13} a b^2 x^{13}+\frac{b^3 x^{17}}{17}",1,"(a^3*x^5)/5 + (a^2*b*x^9)/3 + (3*a*b^2*x^13)/13 + (b^3*x^17)/17","A",2,1,13,0.07692,1,"{270}"
635,1,16,0,0.0029122,"\int x^3 \left(a+b x^4\right)^3 \, dx","Int[x^3*(a + b*x^4)^3,x]","\frac{\left(a+b x^4\right)^4}{16 b}","\frac{\left(a+b x^4\right)^4}{16 b}",1,"(a + b*x^4)^4/(16*b)","A",1,1,13,0.07692,1,"{261}"
636,1,43,0,0.0138865,"\int x^2 \left(a+b x^4\right)^3 \, dx","Int[x^2*(a + b*x^4)^3,x]","\frac{3}{7} a^2 b x^7+\frac{a^3 x^3}{3}+\frac{3}{11} a b^2 x^{11}+\frac{b^3 x^{15}}{15}","\frac{3}{7} a^2 b x^7+\frac{a^3 x^3}{3}+\frac{3}{11} a b^2 x^{11}+\frac{b^3 x^{15}}{15}",1,"(a^3*x^3)/3 + (3*a^2*b*x^7)/7 + (3*a*b^2*x^11)/11 + (b^3*x^15)/15","A",2,1,13,0.07692,1,"{270}"
637,1,43,0,0.013336,"\int x \left(a+b x^4\right)^3 \, dx","Int[x*(a + b*x^4)^3,x]","\frac{1}{2} a^2 b x^6+\frac{a^3 x^2}{2}+\frac{3}{10} a b^2 x^{10}+\frac{b^3 x^{14}}{14}","\frac{1}{2} a^2 b x^6+\frac{a^3 x^2}{2}+\frac{3}{10} a b^2 x^{10}+\frac{b^3 x^{14}}{14}",1,"(a^3*x^2)/2 + (a^2*b*x^6)/2 + (3*a*b^2*x^10)/10 + (b^3*x^14)/14","A",2,1,11,0.09091,1,"{270}"
638,1,38,0,0.0109337,"\int \left(a+b x^4\right)^3 \, dx","Int[(a + b*x^4)^3,x]","\frac{3}{5} a^2 b x^5+a^3 x+\frac{1}{3} a b^2 x^9+\frac{b^3 x^{13}}{13}","\frac{3}{5} a^2 b x^5+a^3 x+\frac{1}{3} a b^2 x^9+\frac{b^3 x^{13}}{13}",1,"a^3*x + (3*a^2*b*x^5)/5 + (a*b^2*x^9)/3 + (b^3*x^13)/13","A",2,1,9,0.1111,1,"{194}"
639,1,39,0,0.0182281,"\int \frac{\left(a+b x^4\right)^3}{x} \, dx","Int[(a + b*x^4)^3/x,x]","\frac{3}{4} a^2 b x^4+a^3 \log (x)+\frac{3}{8} a b^2 x^8+\frac{b^3 x^{12}}{12}","\frac{3}{4} a^2 b x^4+a^3 \log (x)+\frac{3}{8} a b^2 x^8+\frac{b^3 x^{12}}{12}",1,"(3*a^2*b*x^4)/4 + (3*a*b^2*x^8)/8 + (b^3*x^12)/12 + a^3*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
640,1,38,0,0.0129084,"\int \frac{\left(a+b x^4\right)^3}{x^2} \, dx","Int[(a + b*x^4)^3/x^2,x]","a^2 b x^3-\frac{a^3}{x}+\frac{3}{7} a b^2 x^7+\frac{b^3 x^{11}}{11}","a^2 b x^3-\frac{a^3}{x}+\frac{3}{7} a b^2 x^7+\frac{b^3 x^{11}}{11}",1,"-(a^3/x) + a^2*b*x^3 + (3*a*b^2*x^7)/7 + (b^3*x^11)/11","A",2,1,13,0.07692,1,"{270}"
641,1,43,0,0.0135031,"\int \frac{\left(a+b x^4\right)^3}{x^3} \, dx","Int[(a + b*x^4)^3/x^3,x]","\frac{3}{2} a^2 b x^2-\frac{a^3}{2 x^2}+\frac{1}{2} a b^2 x^6+\frac{b^3 x^{10}}{10}","\frac{3}{2} a^2 b x^2-\frac{a^3}{2 x^2}+\frac{1}{2} a b^2 x^6+\frac{b^3 x^{10}}{10}",1,"-a^3/(2*x^2) + (3*a^2*b*x^2)/2 + (a*b^2*x^6)/2 + (b^3*x^10)/10","A",2,1,13,0.07692,1,"{270}"
642,1,39,0,0.0139555,"\int \frac{\left(a+b x^4\right)^3}{x^4} \, dx","Int[(a + b*x^4)^3/x^4,x]","3 a^2 b x-\frac{a^3}{3 x^3}+\frac{3}{5} a b^2 x^5+\frac{b^3 x^9}{9}","3 a^2 b x-\frac{a^3}{3 x^3}+\frac{3}{5} a b^2 x^5+\frac{b^3 x^9}{9}",1,"-a^3/(3*x^3) + 3*a^2*b*x + (3*a*b^2*x^5)/5 + (b^3*x^9)/9","A",2,1,13,0.07692,1,"{270}"
643,1,40,0,0.0214073,"\int \frac{\left(a+b x^4\right)^3}{x^5} \, dx","Int[(a + b*x^4)^3/x^5,x]","3 a^2 b \log (x)-\frac{a^3}{4 x^4}+\frac{3}{4} a b^2 x^4+\frac{b^3 x^8}{8}","3 a^2 b \log (x)-\frac{a^3}{4 x^4}+\frac{3}{4} a b^2 x^4+\frac{b^3 x^8}{8}",1,"-a^3/(4*x^4) + (3*a*b^2*x^4)/4 + (b^3*x^8)/8 + 3*a^2*b*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
644,1,51,0,0.0306201,"\int \frac{x^9}{a+c x^4} \, dx","Int[x^9/(a + c*x^4),x]","\frac{a^{3/2} \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{2 c^{5/2}}-\frac{a x^2}{2 c^2}+\frac{x^6}{6 c}","\frac{a^{3/2} \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{2 c^{5/2}}-\frac{a x^2}{2 c^2}+\frac{x^6}{6 c}",1,"-(a*x^2)/(2*c^2) + x^6/(6*c) + (a^(3/2)*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(2*c^(5/2))","A",4,3,13,0.2308,1,"{275, 302, 205}"
645,1,27,0,0.019002,"\int \frac{x^7}{a+c x^4} \, dx","Int[x^7/(a + c*x^4),x]","\frac{x^4}{4 c}-\frac{a \log \left(a+c x^4\right)}{4 c^2}","\frac{x^4}{4 c}-\frac{a \log \left(a+c x^4\right)}{4 c^2}",1,"x^4/(4*c) - (a*Log[a + c*x^4])/(4*c^2)","A",3,2,13,0.1538,1,"{266, 43}"
646,1,40,0,0.0204349,"\int \frac{x^5}{a+c x^4} \, dx","Int[x^5/(a + c*x^4),x]","\frac{x^2}{2 c}-\frac{\sqrt{a} \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{2 c^{3/2}}","\frac{x^2}{2 c}-\frac{\sqrt{a} \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{2 c^{3/2}}",1,"x^2/(2*c) - (Sqrt[a]*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(2*c^(3/2))","A",3,3,13,0.2308,1,"{275, 321, 205}"
647,1,15,0,0.0032196,"\int \frac{x^3}{a+c x^4} \, dx","Int[x^3/(a + c*x^4),x]","\frac{\log \left(a+c x^4\right)}{4 c}","\frac{\log \left(a+c x^4\right)}{4 c}",1,"Log[a + c*x^4]/(4*c)","A",1,1,13,0.07692,1,"{260}"
648,1,29,0,0.0104272,"\int \frac{x}{a+c x^4} \, dx","Int[x/(a + c*x^4),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{2 \sqrt{a} \sqrt{c}}","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{2 \sqrt{a} \sqrt{c}}",1,"ArcTan[(Sqrt[c]*x^2)/Sqrt[a]]/(2*Sqrt[a]*Sqrt[c])","A",2,2,11,0.1818,1,"{275, 205}"
649,1,22,0,0.0106017,"\int \frac{1}{x \left(a+c x^4\right)} \, dx","Int[1/(x*(a + c*x^4)),x]","\frac{\log (x)}{a}-\frac{\log \left(a+c x^4\right)}{4 a}","\frac{\log (x)}{a}-\frac{\log \left(a+c x^4\right)}{4 a}",1,"Log[x]/a - Log[a + c*x^4]/(4*a)","A",4,4,13,0.3077,1,"{266, 36, 29, 31}"
650,1,40,0,0.0173497,"\int \frac{1}{x^3 \left(a+c x^4\right)} \, dx","Int[1/(x^3*(a + c*x^4)),x]","-\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{2 a^{3/2}}-\frac{1}{2 a x^2}","-\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{2 a^{3/2}}-\frac{1}{2 a x^2}",1,"-1/(2*a*x^2) - (Sqrt[c]*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(2*a^(3/2))","A",3,3,13,0.2308,1,"{275, 325, 205}"
651,1,35,0,0.0231348,"\int \frac{1}{x^5 \left(a+c x^4\right)} \, dx","Int[1/(x^5*(a + c*x^4)),x]","\frac{c \log \left(a+c x^4\right)}{4 a^2}-\frac{c \log (x)}{a^2}-\frac{1}{4 a x^4}","\frac{c \log \left(a+c x^4\right)}{4 a^2}-\frac{c \log (x)}{a^2}-\frac{1}{4 a x^4}",1,"-1/(4*a*x^4) - (c*Log[x])/a^2 + (c*Log[a + c*x^4])/(4*a^2)","A",3,2,13,0.1538,1,"{266, 44}"
652,1,51,0,0.0263047,"\int \frac{1}{x^7 \left(a+c x^4\right)} \, dx","Int[1/(x^7*(a + c*x^4)),x]","\frac{c^{3/2} \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{2 a^{5/2}}+\frac{c}{2 a^2 x^2}-\frac{1}{6 a x^6}","\frac{c^{3/2} \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{2 a^{5/2}}+\frac{c}{2 a^2 x^2}-\frac{1}{6 a x^6}",1,"-1/(6*a*x^6) + c/(2*a^2*x^2) + (c^(3/2)*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(2*a^(5/2))","A",4,3,13,0.2308,1,"{275, 325, 205}"
653,1,190,0,0.1422401,"\int \frac{x^4}{a+c x^4} \, dx","Int[x^4/(a + c*x^4),x]","\frac{\sqrt[4]{a} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} c^{5/4}}-\frac{\sqrt[4]{a} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} c^{5/4}}+\frac{\sqrt[4]{a} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} c^{5/4}}-\frac{\sqrt[4]{a} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} c^{5/4}}+\frac{x}{c}","\frac{\sqrt[4]{a} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} c^{5/4}}-\frac{\sqrt[4]{a} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} c^{5/4}}+\frac{\sqrt[4]{a} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} c^{5/4}}-\frac{\sqrt[4]{a} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} c^{5/4}}+\frac{x}{c}",1,"x/c + (a^(1/4)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*c^(5/4)) - (a^(1/4)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*c^(5/4)) + (a^(1/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(4*Sqrt[2]*c^(5/4)) - (a^(1/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(4*Sqrt[2]*c^(5/4))","A",10,7,13,0.5385,1,"{321, 211, 1165, 628, 1162, 617, 204}"
654,1,185,0,0.1072947,"\int \frac{x^2}{a+c x^4} \, dx","Int[x^2/(a + c*x^4),x]","\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} \sqrt[4]{a} c^{3/4}}-\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} \sqrt[4]{a} c^{3/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} \sqrt[4]{a} c^{3/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} \sqrt[4]{a} c^{3/4}}","\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} \sqrt[4]{a} c^{3/4}}-\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} \sqrt[4]{a} c^{3/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} \sqrt[4]{a} c^{3/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} \sqrt[4]{a} c^{3/4}}",1,"-ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)]/(2*Sqrt[2]*a^(1/4)*c^(3/4)) + ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)]/(2*Sqrt[2]*a^(1/4)*c^(3/4)) + Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2]/(4*Sqrt[2]*a^(1/4)*c^(3/4)) - Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2]/(4*Sqrt[2]*a^(1/4)*c^(3/4))","A",9,6,13,0.4615,1,"{297, 1162, 617, 204, 1165, 628}"
655,1,185,0,0.0998309,"\int \frac{1}{a+c x^4} \, dx","Int[(a + c*x^4)^(-1),x]","-\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} \sqrt[4]{c}}+\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} \sqrt[4]{c}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{c}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{c}}","-\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} \sqrt[4]{c}}+\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} \sqrt[4]{c}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{c}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{c}}",1,"-ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)]/(2*Sqrt[2]*a^(3/4)*c^(1/4)) + ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)]/(2*Sqrt[2]*a^(3/4)*c^(1/4)) - Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2]/(4*Sqrt[2]*a^(3/4)*c^(1/4)) + Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2]/(4*Sqrt[2]*a^(3/4)*c^(1/4))","A",9,6,9,0.6667,1,"{211, 1165, 628, 1162, 617, 204}"
656,1,193,0,0.12092,"\int \frac{1}{x^2 \left(a+c x^4\right)} \, dx","Int[1/(x^2*(a + c*x^4)),x]","-\frac{\sqrt[4]{c} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{5/4}}+\frac{\sqrt[4]{c} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{5/4}}+\frac{\sqrt[4]{c} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{5/4}}-\frac{\sqrt[4]{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{5/4}}-\frac{1}{a x}","-\frac{\sqrt[4]{c} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{5/4}}+\frac{\sqrt[4]{c} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{5/4}}+\frac{\sqrt[4]{c} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{5/4}}-\frac{\sqrt[4]{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{5/4}}-\frac{1}{a x}",1,"-(1/(a*x)) + (c^(1/4)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(5/4)) - (c^(1/4)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(5/4)) - (c^(1/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(4*Sqrt[2]*a^(5/4)) + (c^(1/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(4*Sqrt[2]*a^(5/4))","A",10,7,13,0.5385,1,"{325, 297, 1162, 617, 204, 1165, 628}"
657,1,195,0,0.1187285,"\int \frac{1}{x^4 \left(a+c x^4\right)} \, dx","Int[1/(x^4*(a + c*x^4)),x]","\frac{c^{3/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{7/4}}-\frac{c^{3/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{7/4}}+\frac{c^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{7/4}}-\frac{c^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{7/4}}-\frac{1}{3 a x^3}","\frac{c^{3/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{7/4}}-\frac{c^{3/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{7/4}}+\frac{c^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{7/4}}-\frac{c^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{7/4}}-\frac{1}{3 a x^3}",1,"-1/(3*a*x^3) + (c^(3/4)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(7/4)) - (c^(3/4)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(7/4)) + (c^(3/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(4*Sqrt[2]*a^(7/4)) - (c^(3/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(4*Sqrt[2]*a^(7/4))","A",10,7,13,0.5385,1,"{325, 211, 1165, 628, 1162, 617, 204}"
658,1,46,0,0.0325363,"\int \frac{x^{11}}{\left(a+c x^4\right)^2} \, dx","Int[x^11/(a + c*x^4)^2,x]","-\frac{a^2}{4 c^3 \left(a+c x^4\right)}-\frac{a \log \left(a+c x^4\right)}{2 c^3}+\frac{x^4}{4 c^2}","-\frac{a^2}{4 c^3 \left(a+c x^4\right)}-\frac{a \log \left(a+c x^4\right)}{2 c^3}+\frac{x^4}{4 c^2}",1,"x^4/(4*c^2) - a^2/(4*c^3*(a + c*x^4)) - (a*Log[a + c*x^4])/(2*c^3)","A",3,2,13,0.1538,1,"{266, 43}"
659,1,59,0,0.031221,"\int \frac{x^9}{\left(a+c x^4\right)^2} \, dx","Int[x^9/(a + c*x^4)^2,x]","-\frac{3 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{4 c^{5/2}}-\frac{x^6}{4 c \left(a+c x^4\right)}+\frac{3 x^2}{4 c^2}","-\frac{3 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{4 c^{5/2}}-\frac{x^6}{4 c \left(a+c x^4\right)}+\frac{3 x^2}{4 c^2}",1,"(3*x^2)/(4*c^2) - x^6/(4*c*(a + c*x^4)) - (3*Sqrt[a]*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(4*c^(5/2))","A",4,4,13,0.3077,1,"{275, 288, 321, 205}"
660,1,33,0,0.0238308,"\int \frac{x^7}{\left(a+c x^4\right)^2} \, dx","Int[x^7/(a + c*x^4)^2,x]","\frac{a}{4 c^2 \left(a+c x^4\right)}+\frac{\log \left(a+c x^4\right)}{4 c^2}","\frac{a}{4 c^2 \left(a+c x^4\right)}+\frac{\log \left(a+c x^4\right)}{4 c^2}",1,"a/(4*c^2*(a + c*x^4)) + Log[a + c*x^4]/(4*c^2)","A",3,2,13,0.1538,1,"{266, 43}"
661,1,49,0,0.0235347,"\int \frac{x^5}{\left(a+c x^4\right)^2} \, dx","Int[x^5/(a + c*x^4)^2,x]","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{4 \sqrt{a} c^{3/2}}-\frac{x^2}{4 c \left(a+c x^4\right)}","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{4 \sqrt{a} c^{3/2}}-\frac{x^2}{4 c \left(a+c x^4\right)}",1,"-x^2/(4*c*(a + c*x^4)) + ArcTan[(Sqrt[c]*x^2)/Sqrt[a]]/(4*Sqrt[a]*c^(3/2))","A",3,3,13,0.2308,1,"{275, 288, 205}"
662,1,16,0,0.0034657,"\int \frac{x^3}{\left(a+c x^4\right)^2} \, dx","Int[x^3/(a + c*x^4)^2,x]","-\frac{1}{4 c \left(a+c x^4\right)}","-\frac{1}{4 c \left(a+c x^4\right)}",1,"-1/(4*c*(a + c*x^4))","A",1,1,13,0.07692,1,"{261}"
663,1,49,0,0.0210504,"\int \frac{x}{\left(a+c x^4\right)^2} \, dx","Int[x/(a + c*x^4)^2,x]","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{4 a^{3/2} \sqrt{c}}+\frac{x^2}{4 a \left(a+c x^4\right)}","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{4 a^{3/2} \sqrt{c}}+\frac{x^2}{4 a \left(a+c x^4\right)}",1,"x^2/(4*a*(a + c*x^4)) + ArcTan[(Sqrt[c]*x^2)/Sqrt[a]]/(4*a^(3/2)*Sqrt[c])","A",3,3,11,0.2727,1,"{275, 199, 205}"
664,1,38,0,0.0258131,"\int \frac{1}{x \left(a+c x^4\right)^2} \, dx","Int[1/(x*(a + c*x^4)^2),x]","-\frac{\log \left(a+c x^4\right)}{4 a^2}+\frac{\log (x)}{a^2}+\frac{1}{4 a \left(a+c x^4\right)}","-\frac{\log \left(a+c x^4\right)}{4 a^2}+\frac{\log (x)}{a^2}+\frac{1}{4 a \left(a+c x^4\right)}",1,"1/(4*a*(a + c*x^4)) + Log[x]/a^2 - Log[a + c*x^4]/(4*a^2)","A",3,2,13,0.1538,1,"{266, 44}"
665,1,59,0,0.0314795,"\int \frac{1}{x^3 \left(a+c x^4\right)^2} \, dx","Int[1/(x^3*(a + c*x^4)^2),x]","-\frac{3 \sqrt{c} \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{4 a^{5/2}}-\frac{3}{4 a^2 x^2}+\frac{1}{4 a x^2 \left(a+c x^4\right)}","-\frac{3 \sqrt{c} \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{4 a^{5/2}}-\frac{3}{4 a^2 x^2}+\frac{1}{4 a x^2 \left(a+c x^4\right)}",1,"-3/(4*a^2*x^2) + 1/(4*a*x^2*(a + c*x^4)) - (3*Sqrt[c]*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(4*a^(5/2))","A",4,4,13,0.3077,1,"{275, 290, 325, 205}"
666,1,204,0,0.1258635,"\int \frac{x^6}{\left(a+c x^4\right)^2} \, dx","Int[x^6/(a + c*x^4)^2,x]","\frac{3 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} \sqrt[4]{a} c^{7/4}}-\frac{3 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} \sqrt[4]{a} c^{7/4}}-\frac{3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} \sqrt[4]{a} c^{7/4}}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} \sqrt[4]{a} c^{7/4}}-\frac{x^3}{4 c \left(a+c x^4\right)}","\frac{3 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} \sqrt[4]{a} c^{7/4}}-\frac{3 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} \sqrt[4]{a} c^{7/4}}-\frac{3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} \sqrt[4]{a} c^{7/4}}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} \sqrt[4]{a} c^{7/4}}-\frac{x^3}{4 c \left(a+c x^4\right)}",1,"-x^3/(4*c*(a + c*x^4)) - (3*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(1/4)*c^(7/4)) + (3*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(1/4)*c^(7/4)) + (3*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(16*Sqrt[2]*a^(1/4)*c^(7/4)) - (3*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(16*Sqrt[2]*a^(1/4)*c^(7/4))","A",10,7,13,0.5385,1,"{288, 297, 1162, 617, 204, 1165, 628}"
667,1,202,0,0.119729,"\int \frac{x^4}{\left(a+c x^4\right)^2} \, dx","Int[x^4/(a + c*x^4)^2,x]","-\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{3/4} c^{5/4}}+\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{3/4} c^{5/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{3/4} c^{5/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{3/4} c^{5/4}}-\frac{x}{4 c \left(a+c x^4\right)}","-\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{3/4} c^{5/4}}+\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{3/4} c^{5/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{3/4} c^{5/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{3/4} c^{5/4}}-\frac{x}{4 c \left(a+c x^4\right)}",1,"-x/(4*c*(a + c*x^4)) - ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)]/(8*Sqrt[2]*a^(3/4)*c^(5/4)) + ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)]/(8*Sqrt[2]*a^(3/4)*c^(5/4)) - Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2]/(16*Sqrt[2]*a^(3/4)*c^(5/4)) + Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2]/(16*Sqrt[2]*a^(3/4)*c^(5/4))","A",10,7,13,0.5385,1,"{288, 211, 1165, 628, 1162, 617, 204}"
668,1,204,0,0.119539,"\int \frac{x^2}{\left(a+c x^4\right)^2} \, dx","Int[x^2/(a + c*x^4)^2,x]","\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{5/4} c^{3/4}}-\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{5/4} c^{3/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{5/4} c^{3/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{5/4} c^{3/4}}+\frac{x^3}{4 a \left(a+c x^4\right)}","\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{5/4} c^{3/4}}-\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{5/4} c^{3/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{5/4} c^{3/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{5/4} c^{3/4}}+\frac{x^3}{4 a \left(a+c x^4\right)}",1,"x^3/(4*a*(a + c*x^4)) - ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)]/(8*Sqrt[2]*a^(5/4)*c^(3/4)) + ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)]/(8*Sqrt[2]*a^(5/4)*c^(3/4)) + Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2]/(16*Sqrt[2]*a^(5/4)*c^(3/4)) - Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2]/(16*Sqrt[2]*a^(5/4)*c^(3/4))","A",10,7,13,0.5385,1,"{290, 297, 1162, 617, 204, 1165, 628}"
669,1,202,0,0.1193063,"\int \frac{1}{\left(a+c x^4\right)^2} \, dx","Int[(a + c*x^4)^(-2),x]","-\frac{3 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{7/4} \sqrt[4]{c}}+\frac{3 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{7/4} \sqrt[4]{c}}-\frac{3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{7/4} \sqrt[4]{c}}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{7/4} \sqrt[4]{c}}+\frac{x}{4 a \left(a+c x^4\right)}","-\frac{3 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{7/4} \sqrt[4]{c}}+\frac{3 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{7/4} \sqrt[4]{c}}-\frac{3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{7/4} \sqrt[4]{c}}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{7/4} \sqrt[4]{c}}+\frac{x}{4 a \left(a+c x^4\right)}",1,"x/(4*a*(a + c*x^4)) - (3*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*c^(1/4)) + (3*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*c^(1/4)) - (3*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(16*Sqrt[2]*a^(7/4)*c^(1/4)) + (3*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(16*Sqrt[2]*a^(7/4)*c^(1/4))","A",10,7,9,0.7778,1,"{199, 211, 1165, 628, 1162, 617, 204}"
670,1,214,0,0.1372345,"\int \frac{1}{x^2 \left(a+c x^4\right)^2} \, dx","Int[1/(x^2*(a + c*x^4)^2),x]","-\frac{5 \sqrt[4]{c} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{9/4}}+\frac{5 \sqrt[4]{c} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{9/4}}+\frac{5 \sqrt[4]{c} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{9/4}}-\frac{5 \sqrt[4]{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{9/4}}-\frac{5}{4 a^2 x}+\frac{1}{4 a x \left(a+c x^4\right)}","-\frac{5 \sqrt[4]{c} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{9/4}}+\frac{5 \sqrt[4]{c} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{9/4}}+\frac{5 \sqrt[4]{c} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{9/4}}-\frac{5 \sqrt[4]{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{9/4}}-\frac{5}{4 a^2 x}+\frac{1}{4 a x \left(a+c x^4\right)}",1,"-5/(4*a^2*x) + 1/(4*a*x*(a + c*x^4)) + (5*c^(1/4)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(9/4)) - (5*c^(1/4)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(9/4)) - (5*c^(1/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(16*Sqrt[2]*a^(9/4)) + (5*c^(1/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(16*Sqrt[2]*a^(9/4))","A",11,8,13,0.6154,1,"{290, 325, 297, 1162, 617, 204, 1165, 628}"
671,1,214,0,0.1369876,"\int \frac{1}{x^4 \left(a+c x^4\right)^2} \, dx","Int[1/(x^4*(a + c*x^4)^2),x]","\frac{7 c^{3/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{11/4}}-\frac{7 c^{3/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{11/4}}+\frac{7 c^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{11/4}}-\frac{7 c^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{11/4}}-\frac{7}{12 a^2 x^3}+\frac{1}{4 a x^3 \left(a+c x^4\right)}","\frac{7 c^{3/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{11/4}}-\frac{7 c^{3/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{11/4}}+\frac{7 c^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{11/4}}-\frac{7 c^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{11/4}}-\frac{7}{12 a^2 x^3}+\frac{1}{4 a x^3 \left(a+c x^4\right)}",1,"-7/(12*a^2*x^3) + 1/(4*a*x^3*(a + c*x^4)) + (7*c^(3/4)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(11/4)) - (7*c^(3/4)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(11/4)) + (7*c^(3/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(16*Sqrt[2]*a^(11/4)) - (7*c^(3/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(16*Sqrt[2]*a^(11/4))","A",11,8,13,0.6154,1,"{290, 325, 211, 1165, 628, 1162, 617, 204}"
672,1,52,0,0.0362498,"\int \frac{x^{11}}{\left(a+c x^4\right)^3} \, dx","Int[x^11/(a + c*x^4)^3,x]","-\frac{a^2}{8 c^3 \left(a+c x^4\right)^2}+\frac{a}{2 c^3 \left(a+c x^4\right)}+\frac{\log \left(a+c x^4\right)}{4 c^3}","-\frac{a^2}{8 c^3 \left(a+c x^4\right)^2}+\frac{a}{2 c^3 \left(a+c x^4\right)}+\frac{\log \left(a+c x^4\right)}{4 c^3}",1,"-a^2/(8*c^3*(a + c*x^4)^2) + a/(2*c^3*(a + c*x^4)) + Log[a + c*x^4]/(4*c^3)","A",3,2,13,0.1538,1,"{266, 43}"
673,1,68,0,0.035788,"\int \frac{x^9}{\left(a+c x^4\right)^3} \, dx","Int[x^9/(a + c*x^4)^3,x]","-\frac{3 x^2}{16 c^2 \left(a+c x^4\right)}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{16 \sqrt{a} c^{5/2}}-\frac{x^6}{8 c \left(a+c x^4\right)^2}","-\frac{3 x^2}{16 c^2 \left(a+c x^4\right)}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{16 \sqrt{a} c^{5/2}}-\frac{x^6}{8 c \left(a+c x^4\right)^2}",1,"-x^6/(8*c*(a + c*x^4)^2) - (3*x^2)/(16*c^2*(a + c*x^4)) + (3*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(16*Sqrt[a]*c^(5/2))","A",4,3,13,0.2308,1,"{275, 288, 205}"
674,1,19,0,0.0035922,"\int \frac{x^7}{\left(a+c x^4\right)^3} \, dx","Int[x^7/(a + c*x^4)^3,x]","\frac{x^8}{8 a \left(a+c x^4\right)^2}","\frac{x^8}{8 a \left(a+c x^4\right)^2}",1,"x^8/(8*a*(a + c*x^4)^2)","A",1,1,13,0.07692,1,"{264}"
675,1,71,0,0.0346298,"\int \frac{x^5}{\left(a+c x^4\right)^3} \, dx","Int[x^5/(a + c*x^4)^3,x]","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{16 a^{3/2} c^{3/2}}+\frac{x^2}{16 a c \left(a+c x^4\right)}-\frac{x^2}{8 c \left(a+c x^4\right)^2}","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{16 a^{3/2} c^{3/2}}+\frac{x^2}{16 a c \left(a+c x^4\right)}-\frac{x^2}{8 c \left(a+c x^4\right)^2}",1,"-x^2/(8*c*(a + c*x^4)^2) + x^2/(16*a*c*(a + c*x^4)) + ArcTan[(Sqrt[c]*x^2)/Sqrt[a]]/(16*a^(3/2)*c^(3/2))","A",4,4,13,0.3077,1,"{275, 288, 199, 205}"
676,1,16,0,0.0032871,"\int \frac{x^3}{\left(a+c x^4\right)^3} \, dx","Int[x^3/(a + c*x^4)^3,x]","-\frac{1}{8 c \left(a+c x^4\right)^2}","-\frac{1}{8 c \left(a+c x^4\right)^2}",1,"-1/(8*c*(a + c*x^4)^2)","A",1,1,13,0.07692,1,"{261}"
677,1,68,0,0.0313811,"\int \frac{x}{\left(a+c x^4\right)^3} \, dx","Int[x/(a + c*x^4)^3,x]","\frac{3 x^2}{16 a^2 \left(a+c x^4\right)}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{16 a^{5/2} \sqrt{c}}+\frac{x^2}{8 a \left(a+c x^4\right)^2}","\frac{3 x^2}{16 a^2 \left(a+c x^4\right)}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{16 a^{5/2} \sqrt{c}}+\frac{x^2}{8 a \left(a+c x^4\right)^2}",1,"x^2/(8*a*(a + c*x^4)^2) + (3*x^2)/(16*a^2*(a + c*x^4)) + (3*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(16*a^(5/2)*Sqrt[c])","A",4,3,11,0.2727,1,"{275, 199, 205}"
678,1,54,0,0.0366971,"\int \frac{1}{x \left(a+c x^4\right)^3} \, dx","Int[1/(x*(a + c*x^4)^3),x]","\frac{1}{4 a^2 \left(a+c x^4\right)}-\frac{\log \left(a+c x^4\right)}{4 a^3}+\frac{\log (x)}{a^3}+\frac{1}{8 a \left(a+c x^4\right)^2}","\frac{1}{4 a^2 \left(a+c x^4\right)}-\frac{\log \left(a+c x^4\right)}{4 a^3}+\frac{\log (x)}{a^3}+\frac{1}{8 a \left(a+c x^4\right)^2}",1,"1/(8*a*(a + c*x^4)^2) + 1/(4*a^2*(a + c*x^4)) + Log[x]/a^3 - Log[a + c*x^4]/(4*a^3)","A",3,2,13,0.1538,1,"{266, 44}"
679,1,78,0,0.0432071,"\int \frac{1}{x^3 \left(a+c x^4\right)^3} \, dx","Int[1/(x^3*(a + c*x^4)^3),x]","\frac{5}{16 a^2 x^2 \left(a+c x^4\right)}-\frac{15 \sqrt{c} \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{16 a^{7/2}}-\frac{15}{16 a^3 x^2}+\frac{1}{8 a x^2 \left(a+c x^4\right)^2}","\frac{5}{16 a^2 x^2 \left(a+c x^4\right)}-\frac{15 \sqrt{c} \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{16 a^{7/2}}-\frac{15}{16 a^3 x^2}+\frac{1}{8 a x^2 \left(a+c x^4\right)^2}",1,"-15/(16*a^3*x^2) + 1/(8*a*x^2*(a + c*x^4)^2) + 5/(16*a^2*x^2*(a + c*x^4)) - (15*Sqrt[c]*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(16*a^(7/2))","A",5,4,13,0.3077,1,"{275, 290, 325, 205}"
680,1,223,0,0.1423275,"\int \frac{x^{10}}{\left(a+c x^4\right)^3} \, dx","Int[x^10/(a + c*x^4)^3,x]","-\frac{7 x^3}{32 c^2 \left(a+c x^4\right)}+\frac{21 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{128 \sqrt{2} \sqrt[4]{a} c^{11/4}}-\frac{21 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{128 \sqrt{2} \sqrt[4]{a} c^{11/4}}-\frac{21 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{64 \sqrt{2} \sqrt[4]{a} c^{11/4}}+\frac{21 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{64 \sqrt{2} \sqrt[4]{a} c^{11/4}}-\frac{x^7}{8 c \left(a+c x^4\right)^2}","-\frac{7 x^3}{32 c^2 \left(a+c x^4\right)}+\frac{21 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{128 \sqrt{2} \sqrt[4]{a} c^{11/4}}-\frac{21 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{128 \sqrt{2} \sqrt[4]{a} c^{11/4}}-\frac{21 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{64 \sqrt{2} \sqrt[4]{a} c^{11/4}}+\frac{21 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{64 \sqrt{2} \sqrt[4]{a} c^{11/4}}-\frac{x^7}{8 c \left(a+c x^4\right)^2}",1,"-x^7/(8*c*(a + c*x^4)^2) - (7*x^3)/(32*c^2*(a + c*x^4)) - (21*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(64*Sqrt[2]*a^(1/4)*c^(11/4)) + (21*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(64*Sqrt[2]*a^(1/4)*c^(11/4)) + (21*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(128*Sqrt[2]*a^(1/4)*c^(11/4)) - (21*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(128*Sqrt[2]*a^(1/4)*c^(11/4))","A",11,7,13,0.5385,1,"{288, 297, 1162, 617, 204, 1165, 628}"
681,1,221,0,0.1379434,"\int \frac{x^8}{\left(a+c x^4\right)^3} \, dx","Int[x^8/(a + c*x^4)^3,x]","-\frac{5 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{128 \sqrt{2} a^{3/4} c^{9/4}}+\frac{5 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{128 \sqrt{2} a^{3/4} c^{9/4}}-\frac{5 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{64 \sqrt{2} a^{3/4} c^{9/4}}+\frac{5 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{64 \sqrt{2} a^{3/4} c^{9/4}}-\frac{5 x}{32 c^2 \left(a+c x^4\right)}-\frac{x^5}{8 c \left(a+c x^4\right)^2}","-\frac{5 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{128 \sqrt{2} a^{3/4} c^{9/4}}+\frac{5 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{128 \sqrt{2} a^{3/4} c^{9/4}}-\frac{5 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{64 \sqrt{2} a^{3/4} c^{9/4}}+\frac{5 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{64 \sqrt{2} a^{3/4} c^{9/4}}-\frac{5 x}{32 c^2 \left(a+c x^4\right)}-\frac{x^5}{8 c \left(a+c x^4\right)^2}",1,"-x^5/(8*c*(a + c*x^4)^2) - (5*x)/(32*c^2*(a + c*x^4)) - (5*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(64*Sqrt[2]*a^(3/4)*c^(9/4)) + (5*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(64*Sqrt[2]*a^(3/4)*c^(9/4)) - (5*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(128*Sqrt[2]*a^(3/4)*c^(9/4)) + (5*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(128*Sqrt[2]*a^(3/4)*c^(9/4))","A",11,7,13,0.5385,1,"{288, 211, 1165, 628, 1162, 617, 204}"
682,1,226,0,0.1401599,"\int \frac{x^6}{\left(a+c x^4\right)^3} \, dx","Int[x^6/(a + c*x^4)^3,x]","\frac{3 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{128 \sqrt{2} a^{5/4} c^{7/4}}-\frac{3 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{128 \sqrt{2} a^{5/4} c^{7/4}}-\frac{3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{64 \sqrt{2} a^{5/4} c^{7/4}}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{64 \sqrt{2} a^{5/4} c^{7/4}}+\frac{3 x^3}{32 a c \left(a+c x^4\right)}-\frac{x^3}{8 c \left(a+c x^4\right)^2}","\frac{3 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{128 \sqrt{2} a^{5/4} c^{7/4}}-\frac{3 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{128 \sqrt{2} a^{5/4} c^{7/4}}-\frac{3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{64 \sqrt{2} a^{5/4} c^{7/4}}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{64 \sqrt{2} a^{5/4} c^{7/4}}+\frac{3 x^3}{32 a c \left(a+c x^4\right)}-\frac{x^3}{8 c \left(a+c x^4\right)^2}",1,"-x^3/(8*c*(a + c*x^4)^2) + (3*x^3)/(32*a*c*(a + c*x^4)) - (3*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(64*Sqrt[2]*a^(5/4)*c^(7/4)) + (3*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(64*Sqrt[2]*a^(5/4)*c^(7/4)) + (3*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(128*Sqrt[2]*a^(5/4)*c^(7/4)) - (3*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(128*Sqrt[2]*a^(5/4)*c^(7/4))","A",11,8,13,0.6154,1,"{288, 290, 297, 1162, 617, 204, 1165, 628}"
683,1,222,0,0.1408409,"\int \frac{x^4}{\left(a+c x^4\right)^3} \, dx","Int[x^4/(a + c*x^4)^3,x]","-\frac{3 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{128 \sqrt{2} a^{7/4} c^{5/4}}+\frac{3 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{128 \sqrt{2} a^{7/4} c^{5/4}}-\frac{3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{64 \sqrt{2} a^{7/4} c^{5/4}}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{64 \sqrt{2} a^{7/4} c^{5/4}}+\frac{x}{32 a c \left(a+c x^4\right)}-\frac{x}{8 c \left(a+c x^4\right)^2}","-\frac{3 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{128 \sqrt{2} a^{7/4} c^{5/4}}+\frac{3 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{128 \sqrt{2} a^{7/4} c^{5/4}}-\frac{3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{64 \sqrt{2} a^{7/4} c^{5/4}}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{64 \sqrt{2} a^{7/4} c^{5/4}}+\frac{x}{32 a c \left(a+c x^4\right)}-\frac{x}{8 c \left(a+c x^4\right)^2}",1,"-x/(8*c*(a + c*x^4)^2) + x/(32*a*c*(a + c*x^4)) - (3*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(64*Sqrt[2]*a^(7/4)*c^(5/4)) + (3*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(64*Sqrt[2]*a^(7/4)*c^(5/4)) - (3*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(128*Sqrt[2]*a^(7/4)*c^(5/4)) + (3*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(128*Sqrt[2]*a^(7/4)*c^(5/4))","A",11,8,13,0.6154,1,"{288, 199, 211, 1165, 628, 1162, 617, 204}"
684,1,223,0,0.1444612,"\int \frac{x^2}{\left(a+c x^4\right)^3} \, dx","Int[x^2/(a + c*x^4)^3,x]","\frac{5 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{128 \sqrt{2} a^{9/4} c^{3/4}}-\frac{5 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{128 \sqrt{2} a^{9/4} c^{3/4}}-\frac{5 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{64 \sqrt{2} a^{9/4} c^{3/4}}+\frac{5 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{64 \sqrt{2} a^{9/4} c^{3/4}}+\frac{5 x^3}{32 a^2 \left(a+c x^4\right)}+\frac{x^3}{8 a \left(a+c x^4\right)^2}","\frac{5 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{128 \sqrt{2} a^{9/4} c^{3/4}}-\frac{5 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{128 \sqrt{2} a^{9/4} c^{3/4}}-\frac{5 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{64 \sqrt{2} a^{9/4} c^{3/4}}+\frac{5 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{64 \sqrt{2} a^{9/4} c^{3/4}}+\frac{5 x^3}{32 a^2 \left(a+c x^4\right)}+\frac{x^3}{8 a \left(a+c x^4\right)^2}",1,"x^3/(8*a*(a + c*x^4)^2) + (5*x^3)/(32*a^2*(a + c*x^4)) - (5*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(64*Sqrt[2]*a^(9/4)*c^(3/4)) + (5*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(64*Sqrt[2]*a^(9/4)*c^(3/4)) + (5*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(128*Sqrt[2]*a^(9/4)*c^(3/4)) - (5*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(128*Sqrt[2]*a^(9/4)*c^(3/4))","A",11,7,13,0.5385,1,"{290, 297, 1162, 617, 204, 1165, 628}"
685,1,219,0,0.1363503,"\int \frac{1}{\left(a+c x^4\right)^3} \, dx","Int[(a + c*x^4)^(-3),x]","\frac{7 x}{32 a^2 \left(a+c x^4\right)}-\frac{21 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{128 \sqrt{2} a^{11/4} \sqrt[4]{c}}+\frac{21 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{128 \sqrt{2} a^{11/4} \sqrt[4]{c}}-\frac{21 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{64 \sqrt{2} a^{11/4} \sqrt[4]{c}}+\frac{21 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{64 \sqrt{2} a^{11/4} \sqrt[4]{c}}+\frac{x}{8 a \left(a+c x^4\right)^2}","\frac{7 x}{32 a^2 \left(a+c x^4\right)}-\frac{21 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{128 \sqrt{2} a^{11/4} \sqrt[4]{c}}+\frac{21 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{128 \sqrt{2} a^{11/4} \sqrt[4]{c}}-\frac{21 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{64 \sqrt{2} a^{11/4} \sqrt[4]{c}}+\frac{21 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{64 \sqrt{2} a^{11/4} \sqrt[4]{c}}+\frac{x}{8 a \left(a+c x^4\right)^2}",1,"x/(8*a*(a + c*x^4)^2) + (7*x)/(32*a^2*(a + c*x^4)) - (21*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(64*Sqrt[2]*a^(11/4)*c^(1/4)) + (21*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(64*Sqrt[2]*a^(11/4)*c^(1/4)) - (21*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(128*Sqrt[2]*a^(11/4)*c^(1/4)) + (21*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(128*Sqrt[2]*a^(11/4)*c^(1/4))","A",11,7,9,0.7778,1,"{199, 211, 1165, 628, 1162, 617, 204}"
686,1,233,0,0.1611812,"\int \frac{1}{x^2 \left(a+c x^4\right)^3} \, dx","Int[1/(x^2*(a + c*x^4)^3),x]","\frac{9}{32 a^2 x \left(a+c x^4\right)}-\frac{45 \sqrt[4]{c} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{128 \sqrt{2} a^{13/4}}+\frac{45 \sqrt[4]{c} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{128 \sqrt{2} a^{13/4}}+\frac{45 \sqrt[4]{c} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{64 \sqrt{2} a^{13/4}}-\frac{45 \sqrt[4]{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{64 \sqrt{2} a^{13/4}}-\frac{45}{32 a^3 x}+\frac{1}{8 a x \left(a+c x^4\right)^2}","\frac{9}{32 a^2 x \left(a+c x^4\right)}-\frac{45 \sqrt[4]{c} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{128 \sqrt{2} a^{13/4}}+\frac{45 \sqrt[4]{c} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{128 \sqrt{2} a^{13/4}}+\frac{45 \sqrt[4]{c} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{64 \sqrt{2} a^{13/4}}-\frac{45 \sqrt[4]{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{64 \sqrt{2} a^{13/4}}-\frac{45}{32 a^3 x}+\frac{1}{8 a x \left(a+c x^4\right)^2}",1,"-45/(32*a^3*x) + 1/(8*a*x*(a + c*x^4)^2) + 9/(32*a^2*x*(a + c*x^4)) + (45*c^(1/4)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(64*Sqrt[2]*a^(13/4)) - (45*c^(1/4)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(64*Sqrt[2]*a^(13/4)) - (45*c^(1/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(128*Sqrt[2]*a^(13/4)) + (45*c^(1/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(128*Sqrt[2]*a^(13/4))","A",12,8,13,0.6154,1,"{290, 325, 297, 1162, 617, 204, 1165, 628}"
687,1,38,0,0.0219432,"\int \frac{x^9}{2+3 x^4} \, dx","Int[x^9/(2 + 3*x^4),x]","\frac{x^6}{18}-\frac{x^2}{9}+\frac{1}{9} \sqrt{\frac{2}{3}} \tan ^{-1}\left(\sqrt{\frac{3}{2}} x^2\right)","\frac{x^6}{18}-\frac{x^2}{9}+\frac{1}{9} \sqrt{\frac{2}{3}} \tan ^{-1}\left(\sqrt{\frac{3}{2}} x^2\right)",1,"-x^2/9 + x^6/18 + (Sqrt[2/3]*ArcTan[Sqrt[3/2]*x^2])/9","A",4,3,13,0.2308,1,"{275, 302, 203}"
688,1,20,0,0.0127968,"\int \frac{x^7}{2+3 x^4} \, dx","Int[x^7/(2 + 3*x^4),x]","\frac{x^4}{12}-\frac{1}{18} \log \left(3 x^4+2\right)","\frac{x^4}{12}-\frac{1}{18} \log \left(3 x^4+2\right)",1,"x^4/12 - Log[2 + 3*x^4]/18","A",3,2,13,0.1538,1,"{266, 43}"
689,1,29,0,0.0134381,"\int \frac{x^5}{2+3 x^4} \, dx","Int[x^5/(2 + 3*x^4),x]","\frac{x^2}{6}-\frac{\tan ^{-1}\left(\sqrt{\frac{3}{2}} x^2\right)}{3 \sqrt{6}}","\frac{x^2}{6}-\frac{\tan ^{-1}\left(\sqrt{\frac{3}{2}} x^2\right)}{3 \sqrt{6}}",1,"x^2/6 - ArcTan[Sqrt[3/2]*x^2]/(3*Sqrt[6])","A",3,3,13,0.2308,1,"{275, 321, 203}"
690,1,12,0,0.0025986,"\int \frac{x^3}{2+3 x^4} \, dx","Int[x^3/(2 + 3*x^4),x]","\frac{1}{12} \log \left(3 x^4+2\right)","\frac{1}{12} \log \left(3 x^4+2\right)",1,"Log[2 + 3*x^4]/12","A",1,1,13,0.07692,1,"{260}"
691,1,21,0,0.0076428,"\int \frac{x}{2+3 x^4} \, dx","Int[x/(2 + 3*x^4),x]","\frac{\tan ^{-1}\left(\sqrt{\frac{3}{2}} x^2\right)}{2 \sqrt{6}}","\frac{\tan ^{-1}\left(\sqrt{\frac{3}{2}} x^2\right)}{2 \sqrt{6}}",1,"ArcTan[Sqrt[3/2]*x^2]/(2*Sqrt[6])","A",2,2,11,0.1818,1,"{275, 203}"
692,1,19,0,0.0081227,"\int \frac{1}{x \left(2+3 x^4\right)} \, dx","Int[1/(x*(2 + 3*x^4)),x]","\frac{\log (x)}{2}-\frac{1}{8} \log \left(3 x^4+2\right)","\frac{\log (x)}{2}-\frac{1}{8} \log \left(3 x^4+2\right)",1,"Log[x]/2 - Log[2 + 3*x^4]/8","A",4,4,13,0.3077,1,"{266, 36, 29, 31}"
693,1,31,0,0.0118667,"\int \frac{1}{x^3 \left(2+3 x^4\right)} \, dx","Int[1/(x^3*(2 + 3*x^4)),x]","-\frac{1}{4 x^2}-\frac{1}{4} \sqrt{\frac{3}{2}} \tan ^{-1}\left(\sqrt{\frac{3}{2}} x^2\right)","-\frac{1}{4 x^2}-\frac{1}{4} \sqrt{\frac{3}{2}} \tan ^{-1}\left(\sqrt{\frac{3}{2}} x^2\right)",1,"-1/(4*x^2) - (Sqrt[3/2]*ArcTan[Sqrt[3/2]*x^2])/4","A",3,3,13,0.2308,1,"{275, 325, 203}"
694,1,104,0,0.0952704,"\int \frac{x^6}{2+3 x^4} \, dx","Int[x^6/(2 + 3*x^4),x]","\frac{x^3}{9}-\frac{\log \left(3 x^2-6^{3/4} x+\sqrt{6}\right)}{6\ 6^{3/4}}+\frac{\log \left(3 x^2+6^{3/4} x+\sqrt{6}\right)}{6\ 6^{3/4}}+\frac{\tan ^{-1}\left(1-\sqrt[4]{6} x\right)}{3\ 6^{3/4}}-\frac{\tan ^{-1}\left(\sqrt[4]{6} x+1\right)}{3\ 6^{3/4}}","\frac{x^3}{9}-\frac{\log \left(3 x^2-6^{3/4} x+\sqrt{6}\right)}{6\ 6^{3/4}}+\frac{\log \left(3 x^2+6^{3/4} x+\sqrt{6}\right)}{6\ 6^{3/4}}+\frac{\tan ^{-1}\left(1-\sqrt[4]{6} x\right)}{3\ 6^{3/4}}-\frac{\tan ^{-1}\left(\sqrt[4]{6} x+1\right)}{3\ 6^{3/4}}",1,"x^3/9 + ArcTan[1 - 6^(1/4)*x]/(3*6^(3/4)) - ArcTan[1 + 6^(1/4)*x]/(3*6^(3/4)) - Log[Sqrt[6] - 6^(3/4)*x + 3*x^2]/(6*6^(3/4)) + Log[Sqrt[6] + 6^(3/4)*x + 3*x^2]/(6*6^(3/4))","A",10,7,13,0.5385,1,"{321, 297, 1162, 617, 204, 1165, 628}"
695,1,102,0,0.0751092,"\int \frac{x^4}{2+3 x^4} \, dx","Int[x^4/(2 + 3*x^4),x]","\frac{\log \left(3 x^2-6^{3/4} x+\sqrt{6}\right)}{12 \sqrt[4]{6}}-\frac{\log \left(3 x^2+6^{3/4} x+\sqrt{6}\right)}{12 \sqrt[4]{6}}+\frac{x}{3}+\frac{\tan ^{-1}\left(1-\sqrt[4]{6} x\right)}{6 \sqrt[4]{6}}-\frac{\tan ^{-1}\left(\sqrt[4]{6} x+1\right)}{6 \sqrt[4]{6}}","\frac{\log \left(3 x^2-6^{3/4} x+\sqrt{6}\right)}{12 \sqrt[4]{6}}-\frac{\log \left(3 x^2+6^{3/4} x+\sqrt{6}\right)}{12 \sqrt[4]{6}}+\frac{x}{3}+\frac{\tan ^{-1}\left(1-\sqrt[4]{6} x\right)}{6 \sqrt[4]{6}}-\frac{\tan ^{-1}\left(\sqrt[4]{6} x+1\right)}{6 \sqrt[4]{6}}",1,"x/3 + ArcTan[1 - 6^(1/4)*x]/(6*6^(1/4)) - ArcTan[1 + 6^(1/4)*x]/(6*6^(1/4)) + Log[Sqrt[6] - 6^(3/4)*x + 3*x^2]/(12*6^(1/4)) - Log[Sqrt[6] + 6^(3/4)*x + 3*x^2]/(12*6^(1/4))","A",10,7,13,0.5385,1,"{321, 211, 1165, 628, 1162, 617, 204}"
696,1,97,0,0.067842,"\int \frac{x^2}{2+3 x^4} \, dx","Int[x^2/(2 + 3*x^4),x]","\frac{\log \left(3 x^2-6^{3/4} x+\sqrt{6}\right)}{4\ 6^{3/4}}-\frac{\log \left(3 x^2+6^{3/4} x+\sqrt{6}\right)}{4\ 6^{3/4}}-\frac{\tan ^{-1}\left(1-\sqrt[4]{6} x\right)}{2\ 6^{3/4}}+\frac{\tan ^{-1}\left(\sqrt[4]{6} x+1\right)}{2\ 6^{3/4}}","\frac{\log \left(3 x^2-6^{3/4} x+\sqrt{6}\right)}{4\ 6^{3/4}}-\frac{\log \left(3 x^2+6^{3/4} x+\sqrt{6}\right)}{4\ 6^{3/4}}-\frac{\tan ^{-1}\left(1-\sqrt[4]{6} x\right)}{2\ 6^{3/4}}+\frac{\tan ^{-1}\left(\sqrt[4]{6} x+1\right)}{2\ 6^{3/4}}",1,"-ArcTan[1 - 6^(1/4)*x]/(2*6^(3/4)) + ArcTan[1 + 6^(1/4)*x]/(2*6^(3/4)) + Log[Sqrt[6] - 6^(3/4)*x + 3*x^2]/(4*6^(3/4)) - Log[Sqrt[6] + 6^(3/4)*x + 3*x^2]/(4*6^(3/4))","A",9,6,13,0.4615,1,"{297, 1162, 617, 204, 1165, 628}"
697,1,97,0,0.0652577,"\int \frac{1}{2+3 x^4} \, dx","Int[(2 + 3*x^4)^(-1),x]","-\frac{\log \left(3 x^2-6^{3/4} x+\sqrt{6}\right)}{8 \sqrt[4]{6}}+\frac{\log \left(3 x^2+6^{3/4} x+\sqrt{6}\right)}{8 \sqrt[4]{6}}-\frac{\tan ^{-1}\left(1-\sqrt[4]{6} x\right)}{4 \sqrt[4]{6}}+\frac{\tan ^{-1}\left(\sqrt[4]{6} x+1\right)}{4 \sqrt[4]{6}}","-\frac{\log \left(3 x^2-6^{3/4} x+\sqrt{6}\right)}{8 \sqrt[4]{6}}+\frac{\log \left(3 x^2+6^{3/4} x+\sqrt{6}\right)}{8 \sqrt[4]{6}}-\frac{\tan ^{-1}\left(1-\sqrt[4]{6} x\right)}{4 \sqrt[4]{6}}+\frac{\tan ^{-1}\left(\sqrt[4]{6} x+1\right)}{4 \sqrt[4]{6}}",1,"-ArcTan[1 - 6^(1/4)*x]/(4*6^(1/4)) + ArcTan[1 + 6^(1/4)*x]/(4*6^(1/4)) - Log[Sqrt[6] - 6^(3/4)*x + 3*x^2]/(8*6^(1/4)) + Log[Sqrt[6] + 6^(3/4)*x + 3*x^2]/(8*6^(1/4))","A",9,6,9,0.6667,1,"{211, 1165, 628, 1162, 617, 204}"
698,1,124,0,0.0760307,"\int \frac{1}{x^2 \left(2+3 x^4\right)} \, dx","Int[1/(x^2*(2 + 3*x^4)),x]","-\frac{\sqrt[4]{3} \log \left(3 x^2-6^{3/4} x+\sqrt{6}\right)}{8\ 2^{3/4}}+\frac{\sqrt[4]{3} \log \left(3 x^2+6^{3/4} x+\sqrt{6}\right)}{8\ 2^{3/4}}-\frac{1}{2 x}+\frac{\sqrt[4]{3} \tan ^{-1}\left(1-\sqrt[4]{6} x\right)}{4\ 2^{3/4}}-\frac{\sqrt[4]{3} \tan ^{-1}\left(\sqrt[4]{6} x+1\right)}{4\ 2^{3/4}}","-\frac{\sqrt[4]{3} \log \left(3 x^2-6^{3/4} x+\sqrt{6}\right)}{8\ 2^{3/4}}+\frac{\sqrt[4]{3} \log \left(3 x^2+6^{3/4} x+\sqrt{6}\right)}{8\ 2^{3/4}}-\frac{1}{2 x}+\frac{\sqrt[4]{3} \tan ^{-1}\left(1-\sqrt[4]{6} x\right)}{4\ 2^{3/4}}-\frac{\sqrt[4]{3} \tan ^{-1}\left(\sqrt[4]{6} x+1\right)}{4\ 2^{3/4}}",1,"-1/(2*x) + (3^(1/4)*ArcTan[1 - 6^(1/4)*x])/(4*2^(3/4)) - (3^(1/4)*ArcTan[1 + 6^(1/4)*x])/(4*2^(3/4)) - (3^(1/4)*Log[Sqrt[6] - 6^(3/4)*x + 3*x^2])/(8*2^(3/4)) + (3^(1/4)*Log[Sqrt[6] + 6^(3/4)*x + 3*x^2])/(8*2^(3/4))","A",10,7,13,0.5385,1,"{325, 297, 1162, 617, 204, 1165, 628}"
699,1,13,0,0.0025883,"\int \frac{x^3}{\left(2+3 x^4\right)^2} \, dx","Int[x^3/(2 + 3*x^4)^2,x]","-\frac{1}{12 \left(3 x^4+2\right)}","-\frac{1}{12 \left(3 x^4+2\right)}",1,"-1/(12*(2 + 3*x^4))","A",1,1,13,0.07692,1,"{261}"
700,1,38,0,0.0134294,"\int \frac{x}{\left(2+3 x^4\right)^2} \, dx","Int[x/(2 + 3*x^4)^2,x]","\frac{x^2}{8 \left(3 x^4+2\right)}+\frac{\tan ^{-1}\left(\sqrt{\frac{3}{2}} x^2\right)}{8 \sqrt{6}}","\frac{x^2}{8 \left(3 x^4+2\right)}+\frac{\tan ^{-1}\left(\sqrt{\frac{3}{2}} x^2\right)}{8 \sqrt{6}}",1,"x^2/(8*(2 + 3*x^4)) + ArcTan[Sqrt[3/2]*x^2]/(8*Sqrt[6])","A",3,3,11,0.2727,1,"{275, 199, 203}"
701,1,32,0,0.0199567,"\int \frac{1}{x \left(2+3 x^4\right)^2} \, dx","Int[1/(x*(2 + 3*x^4)^2),x]","\frac{1}{8 \left(3 x^4+2\right)}-\frac{1}{16} \log \left(3 x^4+2\right)+\frac{\log (x)}{4}","\frac{1}{8 \left(3 x^4+2\right)}-\frac{1}{16} \log \left(3 x^4+2\right)+\frac{\log (x)}{4}",1,"1/(8*(2 + 3*x^4)) + Log[x]/4 - Log[2 + 3*x^4]/16","A",3,2,13,0.1538,1,"{266, 44}"
702,1,47,0,0.0204528,"\int \frac{1}{x^3 \left(2+3 x^4\right)^2} \, dx","Int[1/(x^3*(2 + 3*x^4)^2),x]","\frac{1}{8 x^2 \left(3 x^4+2\right)}-\frac{3}{16 x^2}-\frac{3}{16} \sqrt{\frac{3}{2}} \tan ^{-1}\left(\sqrt{\frac{3}{2}} x^2\right)","\frac{1}{8 x^2 \left(3 x^4+2\right)}-\frac{3}{16 x^2}-\frac{3}{16} \sqrt{\frac{3}{2}} \tan ^{-1}\left(\sqrt{\frac{3}{2}} x^2\right)",1,"-3/(16*x^2) + 1/(8*x^2*(2 + 3*x^4)) - (3*Sqrt[3/2]*ArcTan[Sqrt[3/2]*x^2])/16","A",4,4,13,0.3077,1,"{275, 290, 325, 203}"
703,1,111,0,0.0764342,"\int \frac{x^4}{\left(2+3 x^4\right)^2} \, dx","Int[x^4/(2 + 3*x^4)^2,x]","-\frac{x}{12 \left(3 x^4+2\right)}-\frac{\log \left(3 x^2-6^{3/4} x+\sqrt{6}\right)}{96 \sqrt[4]{6}}+\frac{\log \left(3 x^2+6^{3/4} x+\sqrt{6}\right)}{96 \sqrt[4]{6}}-\frac{\tan ^{-1}\left(1-\sqrt[4]{6} x\right)}{48 \sqrt[4]{6}}+\frac{\tan ^{-1}\left(\sqrt[4]{6} x+1\right)}{48 \sqrt[4]{6}}","-\frac{x}{12 \left(3 x^4+2\right)}-\frac{\log \left(3 x^2-6^{3/4} x+\sqrt{6}\right)}{96 \sqrt[4]{6}}+\frac{\log \left(3 x^2+6^{3/4} x+\sqrt{6}\right)}{96 \sqrt[4]{6}}-\frac{\tan ^{-1}\left(1-\sqrt[4]{6} x\right)}{48 \sqrt[4]{6}}+\frac{\tan ^{-1}\left(\sqrt[4]{6} x+1\right)}{48 \sqrt[4]{6}}",1,"-x/(12*(2 + 3*x^4)) - ArcTan[1 - 6^(1/4)*x]/(48*6^(1/4)) + ArcTan[1 + 6^(1/4)*x]/(48*6^(1/4)) - Log[Sqrt[6] - 6^(3/4)*x + 3*x^2]/(96*6^(1/4)) + Log[Sqrt[6] + 6^(3/4)*x + 3*x^2]/(96*6^(1/4))","A",10,7,13,0.5385,1,"{288, 211, 1165, 628, 1162, 617, 204}"
704,1,113,0,0.0759393,"\int \frac{x^2}{\left(2+3 x^4\right)^2} \, dx","Int[x^2/(2 + 3*x^4)^2,x]","\frac{x^3}{8 \left(3 x^4+2\right)}+\frac{\log \left(3 x^2-6^{3/4} x+\sqrt{6}\right)}{32\ 6^{3/4}}-\frac{\log \left(3 x^2+6^{3/4} x+\sqrt{6}\right)}{32\ 6^{3/4}}-\frac{\tan ^{-1}\left(1-\sqrt[4]{6} x\right)}{16\ 6^{3/4}}+\frac{\tan ^{-1}\left(\sqrt[4]{6} x+1\right)}{16\ 6^{3/4}}","\frac{x^3}{8 \left(3 x^4+2\right)}+\frac{\log \left(3 x^2-6^{3/4} x+\sqrt{6}\right)}{32\ 6^{3/4}}-\frac{\log \left(3 x^2+6^{3/4} x+\sqrt{6}\right)}{32\ 6^{3/4}}-\frac{\tan ^{-1}\left(1-\sqrt[4]{6} x\right)}{16\ 6^{3/4}}+\frac{\tan ^{-1}\left(\sqrt[4]{6} x+1\right)}{16\ 6^{3/4}}",1,"x^3/(8*(2 + 3*x^4)) - ArcTan[1 - 6^(1/4)*x]/(16*6^(3/4)) + ArcTan[1 + 6^(1/4)*x]/(16*6^(3/4)) + Log[Sqrt[6] - 6^(3/4)*x + 3*x^2]/(32*6^(3/4)) - Log[Sqrt[6] + 6^(3/4)*x + 3*x^2]/(32*6^(3/4))","A",10,7,13,0.5385,1,"{290, 297, 1162, 617, 204, 1165, 628}"
705,1,131,0,0.0739224,"\int \frac{1}{\left(2+3 x^4\right)^2} \, dx","Int[(2 + 3*x^4)^(-2),x]","\frac{x}{8 \left(3 x^4+2\right)}-\frac{3^{3/4} \log \left(3 x^2-6^{3/4} x+\sqrt{6}\right)}{64 \sqrt[4]{2}}+\frac{3^{3/4} \log \left(3 x^2+6^{3/4} x+\sqrt{6}\right)}{64 \sqrt[4]{2}}-\frac{3^{3/4} \tan ^{-1}\left(1-\sqrt[4]{6} x\right)}{32 \sqrt[4]{2}}+\frac{3^{3/4} \tan ^{-1}\left(\sqrt[4]{6} x+1\right)}{32 \sqrt[4]{2}}","\frac{x}{8 \left(3 x^4+2\right)}-\frac{3^{3/4} \log \left(3 x^2-6^{3/4} x+\sqrt{6}\right)}{64 \sqrt[4]{2}}+\frac{3^{3/4} \log \left(3 x^2+6^{3/4} x+\sqrt{6}\right)}{64 \sqrt[4]{2}}-\frac{3^{3/4} \tan ^{-1}\left(1-\sqrt[4]{6} x\right)}{32 \sqrt[4]{2}}+\frac{3^{3/4} \tan ^{-1}\left(\sqrt[4]{6} x+1\right)}{32 \sqrt[4]{2}}",1,"x/(8*(2 + 3*x^4)) - (3^(3/4)*ArcTan[1 - 6^(1/4)*x])/(32*2^(1/4)) + (3^(3/4)*ArcTan[1 + 6^(1/4)*x])/(32*2^(1/4)) - (3^(3/4)*Log[Sqrt[6] - 6^(3/4)*x + 3*x^2])/(64*2^(1/4)) + (3^(3/4)*Log[Sqrt[6] + 6^(3/4)*x + 3*x^2])/(64*2^(1/4))","A",10,7,9,0.7778,1,"{199, 211, 1165, 628, 1162, 617, 204}"
706,1,140,0,0.0845571,"\int \frac{1}{x^2 \left(2+3 x^4\right)^2} \, dx","Int[1/(x^2*(2 + 3*x^4)^2),x]","\frac{1}{8 x \left(3 x^4+2\right)}-\frac{5 \sqrt[4]{3} \log \left(3 x^2-6^{3/4} x+\sqrt{6}\right)}{64\ 2^{3/4}}+\frac{5 \sqrt[4]{3} \log \left(3 x^2+6^{3/4} x+\sqrt{6}\right)}{64\ 2^{3/4}}-\frac{5}{16 x}+\frac{5 \sqrt[4]{3} \tan ^{-1}\left(1-\sqrt[4]{6} x\right)}{32\ 2^{3/4}}-\frac{5 \sqrt[4]{3} \tan ^{-1}\left(\sqrt[4]{6} x+1\right)}{32\ 2^{3/4}}","\frac{1}{8 x \left(3 x^4+2\right)}-\frac{5 \sqrt[4]{3} \log \left(3 x^2-6^{3/4} x+\sqrt{6}\right)}{64\ 2^{3/4}}+\frac{5 \sqrt[4]{3} \log \left(3 x^2+6^{3/4} x+\sqrt{6}\right)}{64\ 2^{3/4}}-\frac{5}{16 x}+\frac{5 \sqrt[4]{3} \tan ^{-1}\left(1-\sqrt[4]{6} x\right)}{32\ 2^{3/4}}-\frac{5 \sqrt[4]{3} \tan ^{-1}\left(\sqrt[4]{6} x+1\right)}{32\ 2^{3/4}}",1,"-5/(16*x) + 1/(8*x*(2 + 3*x^4)) + (5*3^(1/4)*ArcTan[1 - 6^(1/4)*x])/(32*2^(3/4)) - (5*3^(1/4)*ArcTan[1 + 6^(1/4)*x])/(32*2^(3/4)) - (5*3^(1/4)*Log[Sqrt[6] - 6^(3/4)*x + 3*x^2])/(64*2^(3/4)) + (5*3^(1/4)*Log[Sqrt[6] + 6^(3/4)*x + 3*x^2])/(64*2^(3/4))","A",11,8,13,0.6154,1,"{290, 325, 297, 1162, 617, 204, 1165, 628}"
707,1,133,0,0.0789787,"\int \frac{x^2}{3+x^4} \, dx","Int[x^2/(3 + x^4),x]","\frac{\log \left(x^2-\sqrt{2} \sqrt[4]{3} x+\sqrt{3}\right)}{4 \sqrt{2} \sqrt[4]{3}}-\frac{\log \left(x^2+\sqrt{2} \sqrt[4]{3} x+\sqrt{3}\right)}{4 \sqrt{2} \sqrt[4]{3}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} x}{\sqrt[4]{3}}\right)}{2 \sqrt{2} \sqrt[4]{3}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt[4]{3}}+1\right)}{2 \sqrt{2} \sqrt[4]{3}}","\frac{\log \left(x^2-\sqrt{2} \sqrt[4]{3} x+\sqrt{3}\right)}{4 \sqrt{2} \sqrt[4]{3}}-\frac{\log \left(x^2+\sqrt{2} \sqrt[4]{3} x+\sqrt{3}\right)}{4 \sqrt{2} \sqrt[4]{3}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} x}{\sqrt[4]{3}}\right)}{2 \sqrt{2} \sqrt[4]{3}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt[4]{3}}+1\right)}{2 \sqrt{2} \sqrt[4]{3}}",1,"-ArcTan[1 - (Sqrt[2]*x)/3^(1/4)]/(2*Sqrt[2]*3^(1/4)) + ArcTan[1 + (Sqrt[2]*x)/3^(1/4)]/(2*Sqrt[2]*3^(1/4)) + Log[Sqrt[3] - Sqrt[2]*3^(1/4)*x + x^2]/(4*Sqrt[2]*3^(1/4)) - Log[Sqrt[3] + Sqrt[2]*3^(1/4)*x + x^2]/(4*Sqrt[2]*3^(1/4))","A",9,6,11,0.5455,1,"{297, 1162, 617, 204, 1165, 628}"
708,1,83,0,0.0724358,"\int \frac{1}{1+a+(-1+a) x^4} \, dx","Int[(1 + a + (-1 + a)*x^4)^(-1),x]","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{1-a} x}{\sqrt[4]{a+1}}\right)}{2 \sqrt{a+1} \sqrt[4]{1-a^2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{1-a} x}{\sqrt[4]{a+1}}\right)}{2 \sqrt{a+1} \sqrt[4]{1-a^2}}","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{1-a} x}{\sqrt[4]{a+1}}\right)}{2 \sqrt{a+1} \sqrt[4]{1-a^2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{1-a} x}{\sqrt[4]{a+1}}\right)}{2 \sqrt{a+1} \sqrt[4]{1-a^2}}",1,"ArcTan[((1 - a)^(1/4)*x)/(1 + a)^(1/4)]/(2*Sqrt[1 + a]*(1 - a^2)^(1/4)) + ArcTanh[((1 - a)^(1/4)*x)/(1 + a)^(1/4)]/(2*Sqrt[1 + a]*(1 - a^2)^(1/4))","A",3,3,12,0.2500,1,"{212, 208, 205}"
709,1,79,0,0.0604985,"\int \frac{1}{2 a+2 b+x^4} \, dx","Int[(2*a + 2*b + x^4)^(-1),x]","-\frac{\tan ^{-1}\left(\frac{x}{\sqrt[4]{2} \sqrt[4]{-a-b}}\right)}{2\ 2^{3/4} (-a-b)^{3/4}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt[4]{2} \sqrt[4]{-a-b}}\right)}{2\ 2^{3/4} (-a-b)^{3/4}}","-\frac{\tan ^{-1}\left(\frac{x}{\sqrt[4]{2} \sqrt[4]{-a-b}}\right)}{2\ 2^{3/4} (-a-b)^{3/4}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt[4]{2} \sqrt[4]{-a-b}}\right)}{2\ 2^{3/4} (-a-b)^{3/4}}",1,"-ArcTan[x/(2^(1/4)*(-a - b)^(1/4))]/(2*2^(3/4)*(-a - b)^(3/4)) - ArcTanh[x/(2^(1/4)*(-a - b)^(1/4))]/(2*2^(3/4)*(-a - b)^(3/4))","A",3,3,12,0.2500,1,"{212, 206, 203}"
710,1,79,0,0.0301928,"\int \frac{1}{2 (a+b)+x^4} \, dx","Int[(2*(a + b) + x^4)^(-1),x]","-\frac{\tan ^{-1}\left(\frac{x}{\sqrt[4]{2} \sqrt[4]{-a-b}}\right)}{2\ 2^{3/4} (-a-b)^{3/4}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt[4]{2} \sqrt[4]{-a-b}}\right)}{2\ 2^{3/4} (-a-b)^{3/4}}","-\frac{\tan ^{-1}\left(\frac{x}{\sqrt[4]{2} \sqrt[4]{-a-b}}\right)}{2\ 2^{3/4} (-a-b)^{3/4}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt[4]{2} \sqrt[4]{-a-b}}\right)}{2\ 2^{3/4} (-a-b)^{3/4}}",1,"-ArcTan[x/(2^(1/4)*(-a - b)^(1/4))]/(2*2^(3/4)*(-a - b)^(3/4)) - ArcTanh[x/(2^(1/4)*(-a - b)^(1/4))]/(2*2^(3/4)*(-a - b)^(3/4))","A",3,3,11,0.2727,1,"{212, 206, 203}"
711,1,33,0,0.0223402,"\int \frac{x}{2 a+2 b+x^4} \, dx","Int[x/(2*a + 2*b + x^4),x]","\frac{\tan ^{-1}\left(\frac{x^2}{\sqrt{2} \sqrt{a+b}}\right)}{2 \sqrt{2} \sqrt{a+b}}","\frac{\tan ^{-1}\left(\frac{x^2}{\sqrt{2} \sqrt{a+b}}\right)}{2 \sqrt{2} \sqrt{a+b}}",1,"ArcTan[x^2/(Sqrt[2]*Sqrt[a + b])]/(2*Sqrt[2]*Sqrt[a + b])","A",2,2,14,0.1429,1,"{275, 203}"
712,1,33,0,0.0120248,"\int \frac{x}{2 (a+b)+x^4} \, dx","Int[x/(2*(a + b) + x^4),x]","\frac{\tan ^{-1}\left(\frac{x^2}{\sqrt{2} \sqrt{a+b}}\right)}{2 \sqrt{2} \sqrt{a+b}}","\frac{\tan ^{-1}\left(\frac{x^2}{\sqrt{2} \sqrt{a+b}}\right)}{2 \sqrt{2} \sqrt{a+b}}",1,"ArcTan[x^2/(Sqrt[2]*Sqrt[a + b])]/(2*Sqrt[2]*Sqrt[a + b])","A",2,2,13,0.1538,1,"{275, 203}"
713,1,79,0,0.0255669,"\int \frac{x^2}{2 a+2 b+x^4} \, dx","Int[x^2/(2*a + 2*b + x^4),x]","\frac{\tan ^{-1}\left(\frac{x}{\sqrt[4]{2} \sqrt[4]{-a-b}}\right)}{2 \sqrt[4]{2} \sqrt[4]{-a-b}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt[4]{2} \sqrt[4]{-a-b}}\right)}{2 \sqrt[4]{2} \sqrt[4]{-a-b}}","\frac{\tan ^{-1}\left(\frac{x}{\sqrt[4]{2} \sqrt[4]{-a-b}}\right)}{2 \sqrt[4]{2} \sqrt[4]{-a-b}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt[4]{2} \sqrt[4]{-a-b}}\right)}{2 \sqrt[4]{2} \sqrt[4]{-a-b}}",1,"ArcTan[x/(2^(1/4)*(-a - b)^(1/4))]/(2*2^(1/4)*(-a - b)^(1/4)) - ArcTanh[x/(2^(1/4)*(-a - b)^(1/4))]/(2*2^(1/4)*(-a - b)^(1/4))","A",3,3,16,0.1875,1,"{298, 203, 206}"
714,1,79,0,0.0242379,"\int \frac{x^2}{2 (a+b)+x^4} \, dx","Int[x^2/(2*(a + b) + x^4),x]","\frac{\tan ^{-1}\left(\frac{x}{\sqrt[4]{2} \sqrt[4]{-a-b}}\right)}{2 \sqrt[4]{2} \sqrt[4]{-a-b}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt[4]{2} \sqrt[4]{-a-b}}\right)}{2 \sqrt[4]{2} \sqrt[4]{-a-b}}","\frac{\tan ^{-1}\left(\frac{x}{\sqrt[4]{2} \sqrt[4]{-a-b}}\right)}{2 \sqrt[4]{2} \sqrt[4]{-a-b}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt[4]{2} \sqrt[4]{-a-b}}\right)}{2 \sqrt[4]{2} \sqrt[4]{-a-b}}",1,"ArcTan[x/(2^(1/4)*(-a - b)^(1/4))]/(2*2^(1/4)*(-a - b)^(1/4)) - ArcTanh[x/(2^(1/4)*(-a - b)^(1/4))]/(2*2^(1/4)*(-a - b)^(1/4))","A",3,3,15,0.2000,1,"{298, 203, 206}"
715,1,14,0,0.0034531,"\int \frac{x^3}{2 a+2 b+x^4} \, dx","Int[x^3/(2*a + 2*b + x^4),x]","\frac{1}{4} \log \left(2 (a+b)+x^4\right)","\frac{1}{4} \log \left(2 (a+b)+x^4\right)",1,"Log[2*(a + b) + x^4]/4","A",1,1,16,0.06250,1,"{260}"
716,1,14,0,0.0030743,"\int \frac{x^3}{2 (a+b)+x^4} \, dx","Int[x^3/(2*(a + b) + x^4),x]","\frac{1}{4} \log \left(2 (a+b)+x^4\right)","\frac{1}{4} \log \left(2 (a+b)+x^4\right)",1,"Log[2*(a + b) + x^4]/4","A",1,1,15,0.06667,1,"{260}"
717,1,21,0,0.0043785,"\int x^{5/2} \left(a+c x^4\right) \, dx","Int[x^(5/2)*(a + c*x^4),x]","\frac{2}{7} a x^{7/2}+\frac{2}{15} c x^{15/2}","\frac{2}{7} a x^{7/2}+\frac{2}{15} c x^{15/2}",1,"(2*a*x^(7/2))/7 + (2*c*x^(15/2))/15","A",2,1,13,0.07692,1,"{14}"
718,1,21,0,0.0042359,"\int x^{3/2} \left(a+c x^4\right) \, dx","Int[x^(3/2)*(a + c*x^4),x]","\frac{2}{5} a x^{5/2}+\frac{2}{13} c x^{13/2}","\frac{2}{5} a x^{5/2}+\frac{2}{13} c x^{13/2}",1,"(2*a*x^(5/2))/5 + (2*c*x^(13/2))/13","A",2,1,13,0.07692,1,"{14}"
719,1,21,0,0.0039089,"\int \sqrt{x} \left(a+c x^4\right) \, dx","Int[Sqrt[x]*(a + c*x^4),x]","\frac{2}{3} a x^{3/2}+\frac{2}{11} c x^{11/2}","\frac{2}{3} a x^{3/2}+\frac{2}{11} c x^{11/2}",1,"(2*a*x^(3/2))/3 + (2*c*x^(11/2))/11","A",2,1,13,0.07692,1,"{14}"
720,1,19,0,0.0040556,"\int \frac{a+c x^4}{\sqrt{x}} \, dx","Int[(a + c*x^4)/Sqrt[x],x]","2 a \sqrt{x}+\frac{2}{9} c x^{9/2}","2 a \sqrt{x}+\frac{2}{9} c x^{9/2}",1,"2*a*Sqrt[x] + (2*c*x^(9/2))/9","A",2,1,13,0.07692,1,"{14}"
721,1,19,0,0.003801,"\int \frac{a+c x^4}{x^{3/2}} \, dx","Int[(a + c*x^4)/x^(3/2),x]","\frac{2}{7} c x^{7/2}-\frac{2 a}{\sqrt{x}}","\frac{2}{7} c x^{7/2}-\frac{2 a}{\sqrt{x}}",1,"(-2*a)/Sqrt[x] + (2*c*x^(7/2))/7","A",2,1,13,0.07692,1,"{14}"
722,1,21,0,0.0041378,"\int \frac{a+c x^4}{x^{5/2}} \, dx","Int[(a + c*x^4)/x^(5/2),x]","\frac{2}{5} c x^{5/2}-\frac{2 a}{3 x^{3/2}}","\frac{2}{5} c x^{5/2}-\frac{2 a}{3 x^{3/2}}",1,"(-2*a)/(3*x^(3/2)) + (2*c*x^(5/2))/5","A",2,1,13,0.07692,1,"{14}"
723,1,21,0,0.0041887,"\int \frac{a+c x^4}{x^{7/2}} \, dx","Int[(a + c*x^4)/x^(7/2),x]","\frac{2}{3} c x^{3/2}-\frac{2 a}{5 x^{5/2}}","\frac{2}{3} c x^{3/2}-\frac{2 a}{5 x^{5/2}}",1,"(-2*a)/(5*x^(5/2)) + (2*c*x^(3/2))/3","A",2,1,13,0.07692,1,"{14}"
724,1,36,0,0.0086518,"\int x^{5/2} \left(a+c x^4\right)^2 \, dx","Int[x^(5/2)*(a + c*x^4)^2,x]","\frac{2}{7} a^2 x^{7/2}+\frac{4}{15} a c x^{15/2}+\frac{2}{23} c^2 x^{23/2}","\frac{2}{7} a^2 x^{7/2}+\frac{4}{15} a c x^{15/2}+\frac{2}{23} c^2 x^{23/2}",1,"(2*a^2*x^(7/2))/7 + (4*a*c*x^(15/2))/15 + (2*c^2*x^(23/2))/23","A",2,1,15,0.06667,1,"{270}"
725,1,36,0,0.0083541,"\int x^{3/2} \left(a+c x^4\right)^2 \, dx","Int[x^(3/2)*(a + c*x^4)^2,x]","\frac{2}{5} a^2 x^{5/2}+\frac{4}{13} a c x^{13/2}+\frac{2}{21} c^2 x^{21/2}","\frac{2}{5} a^2 x^{5/2}+\frac{4}{13} a c x^{13/2}+\frac{2}{21} c^2 x^{21/2}",1,"(2*a^2*x^(5/2))/5 + (4*a*c*x^(13/2))/13 + (2*c^2*x^(21/2))/21","A",2,1,15,0.06667,1,"{270}"
726,1,36,0,0.0082749,"\int \sqrt{x} \left(a+c x^4\right)^2 \, dx","Int[Sqrt[x]*(a + c*x^4)^2,x]","\frac{2}{3} a^2 x^{3/2}+\frac{4}{11} a c x^{11/2}+\frac{2}{19} c^2 x^{19/2}","\frac{2}{3} a^2 x^{3/2}+\frac{4}{11} a c x^{11/2}+\frac{2}{19} c^2 x^{19/2}",1,"(2*a^2*x^(3/2))/3 + (4*a*c*x^(11/2))/11 + (2*c^2*x^(19/2))/19","A",2,1,15,0.06667,1,"{270}"
727,1,34,0,0.0081666,"\int \frac{\left(a+c x^4\right)^2}{\sqrt{x}} \, dx","Int[(a + c*x^4)^2/Sqrt[x],x]","2 a^2 \sqrt{x}+\frac{4}{9} a c x^{9/2}+\frac{2}{17} c^2 x^{17/2}","2 a^2 \sqrt{x}+\frac{4}{9} a c x^{9/2}+\frac{2}{17} c^2 x^{17/2}",1,"2*a^2*Sqrt[x] + (4*a*c*x^(9/2))/9 + (2*c^2*x^(17/2))/17","A",2,1,15,0.06667,1,"{270}"
728,1,34,0,0.0081777,"\int \frac{\left(a+c x^4\right)^2}{x^{3/2}} \, dx","Int[(a + c*x^4)^2/x^(3/2),x]","-\frac{2 a^2}{\sqrt{x}}+\frac{4}{7} a c x^{7/2}+\frac{2}{15} c^2 x^{15/2}","-\frac{2 a^2}{\sqrt{x}}+\frac{4}{7} a c x^{7/2}+\frac{2}{15} c^2 x^{15/2}",1,"(-2*a^2)/Sqrt[x] + (4*a*c*x^(7/2))/7 + (2*c^2*x^(15/2))/15","A",2,1,15,0.06667,1,"{270}"
729,1,36,0,0.0094453,"\int \frac{\left(a+c x^4\right)^2}{x^{5/2}} \, dx","Int[(a + c*x^4)^2/x^(5/2),x]","-\frac{2 a^2}{3 x^{3/2}}+\frac{4}{5} a c x^{5/2}+\frac{2}{13} c^2 x^{13/2}","-\frac{2 a^2}{3 x^{3/2}}+\frac{4}{5} a c x^{5/2}+\frac{2}{13} c^2 x^{13/2}",1,"(-2*a^2)/(3*x^(3/2)) + (4*a*c*x^(5/2))/5 + (2*c^2*x^(13/2))/13","A",2,1,15,0.06667,1,"{270}"
730,1,36,0,0.0081328,"\int \frac{\left(a+c x^4\right)^2}{x^{7/2}} \, dx","Int[(a + c*x^4)^2/x^(7/2),x]","-\frac{2 a^2}{5 x^{5/2}}+\frac{4}{3} a c x^{3/2}+\frac{2}{11} c^2 x^{11/2}","-\frac{2 a^2}{5 x^{5/2}}+\frac{4}{3} a c x^{3/2}+\frac{2}{11} c^2 x^{11/2}",1,"(-2*a^2)/(5*x^(5/2)) + (4*a*c*x^(3/2))/3 + (2*c^2*x^(11/2))/11","A",2,1,15,0.06667,1,"{270}"
731,1,51,0,0.0127232,"\int x^{5/2} \left(a+c x^4\right)^3 \, dx","Int[x^(5/2)*(a + c*x^4)^3,x]","\frac{2}{5} a^2 c x^{15/2}+\frac{2}{7} a^3 x^{7/2}+\frac{6}{23} a c^2 x^{23/2}+\frac{2}{31} c^3 x^{31/2}","\frac{2}{5} a^2 c x^{15/2}+\frac{2}{7} a^3 x^{7/2}+\frac{6}{23} a c^2 x^{23/2}+\frac{2}{31} c^3 x^{31/2}",1,"(2*a^3*x^(7/2))/7 + (2*a^2*c*x^(15/2))/5 + (6*a*c^2*x^(23/2))/23 + (2*c^3*x^(31/2))/31","A",2,1,15,0.06667,1,"{270}"
732,1,51,0,0.0125475,"\int x^{3/2} \left(a+c x^4\right)^3 \, dx","Int[x^(3/2)*(a + c*x^4)^3,x]","\frac{6}{13} a^2 c x^{13/2}+\frac{2}{5} a^3 x^{5/2}+\frac{2}{7} a c^2 x^{21/2}+\frac{2}{29} c^3 x^{29/2}","\frac{6}{13} a^2 c x^{13/2}+\frac{2}{5} a^3 x^{5/2}+\frac{2}{7} a c^2 x^{21/2}+\frac{2}{29} c^3 x^{29/2}",1,"(2*a^3*x^(5/2))/5 + (6*a^2*c*x^(13/2))/13 + (2*a*c^2*x^(21/2))/7 + (2*c^3*x^(29/2))/29","A",2,1,15,0.06667,1,"{270}"
733,1,51,0,0.0124144,"\int \sqrt{x} \left(a+c x^4\right)^3 \, dx","Int[Sqrt[x]*(a + c*x^4)^3,x]","\frac{6}{11} a^2 c x^{11/2}+\frac{2}{3} a^3 x^{3/2}+\frac{6}{19} a c^2 x^{19/2}+\frac{2}{27} c^3 x^{27/2}","\frac{6}{11} a^2 c x^{11/2}+\frac{2}{3} a^3 x^{3/2}+\frac{6}{19} a c^2 x^{19/2}+\frac{2}{27} c^3 x^{27/2}",1,"(2*a^3*x^(3/2))/3 + (6*a^2*c*x^(11/2))/11 + (6*a*c^2*x^(19/2))/19 + (2*c^3*x^(27/2))/27","A",2,1,15,0.06667,1,"{270}"
734,1,49,0,0.0120546,"\int \frac{\left(a+c x^4\right)^3}{\sqrt{x}} \, dx","Int[(a + c*x^4)^3/Sqrt[x],x]","\frac{2}{3} a^2 c x^{9/2}+2 a^3 \sqrt{x}+\frac{6}{17} a c^2 x^{17/2}+\frac{2}{25} c^3 x^{25/2}","\frac{2}{3} a^2 c x^{9/2}+2 a^3 \sqrt{x}+\frac{6}{17} a c^2 x^{17/2}+\frac{2}{25} c^3 x^{25/2}",1,"2*a^3*Sqrt[x] + (2*a^2*c*x^(9/2))/3 + (6*a*c^2*x^(17/2))/17 + (2*c^3*x^(25/2))/25","A",2,1,15,0.06667,1,"{270}"
735,1,49,0,0.0127762,"\int \frac{\left(a+c x^4\right)^3}{x^{3/2}} \, dx","Int[(a + c*x^4)^3/x^(3/2),x]","\frac{6}{7} a^2 c x^{7/2}-\frac{2 a^3}{\sqrt{x}}+\frac{2}{5} a c^2 x^{15/2}+\frac{2}{23} c^3 x^{23/2}","\frac{6}{7} a^2 c x^{7/2}-\frac{2 a^3}{\sqrt{x}}+\frac{2}{5} a c^2 x^{15/2}+\frac{2}{23} c^3 x^{23/2}",1,"(-2*a^3)/Sqrt[x] + (6*a^2*c*x^(7/2))/7 + (2*a*c^2*x^(15/2))/5 + (2*c^3*x^(23/2))/23","A",2,1,15,0.06667,1,"{270}"
736,1,51,0,0.0124189,"\int \frac{\left(a+c x^4\right)^3}{x^{5/2}} \, dx","Int[(a + c*x^4)^3/x^(5/2),x]","\frac{6}{5} a^2 c x^{5/2}-\frac{2 a^3}{3 x^{3/2}}+\frac{6}{13} a c^2 x^{13/2}+\frac{2}{21} c^3 x^{21/2}","\frac{6}{5} a^2 c x^{5/2}-\frac{2 a^3}{3 x^{3/2}}+\frac{6}{13} a c^2 x^{13/2}+\frac{2}{21} c^3 x^{21/2}",1,"(-2*a^3)/(3*x^(3/2)) + (6*a^2*c*x^(5/2))/5 + (6*a*c^2*x^(13/2))/13 + (2*c^3*x^(21/2))/21","A",2,1,15,0.06667,1,"{270}"
737,1,49,0,0.0115815,"\int \frac{\left(a+c x^4\right)^3}{x^{7/2}} \, dx","Int[(a + c*x^4)^3/x^(7/2),x]","2 a^2 c x^{3/2}-\frac{2 a^3}{5 x^{5/2}}+\frac{6}{11} a c^2 x^{11/2}+\frac{2}{19} c^3 x^{19/2}","2 a^2 c x^{3/2}-\frac{2 a^3}{5 x^{5/2}}+\frac{6}{11} a c^2 x^{11/2}+\frac{2}{19} c^3 x^{19/2}",1,"(-2*a^3)/(5*x^(5/2)) + 2*a^2*c*x^(3/2) + (6*a*c^2*x^(11/2))/11 + (2*c^3*x^(19/2))/19","A",2,1,15,0.06667,1,"{270}"
738,1,299,0,0.3762232,"\int \frac{x^{9/2}}{a+c x^4} \, dx","Int[x^(9/2)/(a + c*x^4),x]","-\frac{(-a)^{3/8} \log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{4 \sqrt{2} c^{11/8}}+\frac{(-a)^{3/8} \log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{4 \sqrt{2} c^{11/8}}+\frac{(-a)^{3/8} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{2 \sqrt{2} c^{11/8}}-\frac{(-a)^{3/8} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}+1\right)}{2 \sqrt{2} c^{11/8}}+\frac{(-a)^{3/8} \tan ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{2 c^{11/8}}-\frac{(-a)^{3/8} \tanh ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{2 c^{11/8}}+\frac{2 x^{3/2}}{3 c}","-\frac{(-a)^{3/8} \log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{4 \sqrt{2} c^{11/8}}+\frac{(-a)^{3/8} \log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{4 \sqrt{2} c^{11/8}}+\frac{(-a)^{3/8} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{2 \sqrt{2} c^{11/8}}-\frac{(-a)^{3/8} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}+1\right)}{2 \sqrt{2} c^{11/8}}+\frac{(-a)^{3/8} \tan ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{2 c^{11/8}}-\frac{(-a)^{3/8} \tanh ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{2 c^{11/8}}+\frac{2 x^{3/2}}{3 c}",1,"(2*x^(3/2))/(3*c) + ((-a)^(3/8)*ArcTan[1 - (Sqrt[2]*c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(2*Sqrt[2]*c^(11/8)) - ((-a)^(3/8)*ArcTan[1 + (Sqrt[2]*c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(2*Sqrt[2]*c^(11/8)) + ((-a)^(3/8)*ArcTan[(c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(2*c^(11/8)) - ((-a)^(3/8)*ArcTanh[(c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(2*c^(11/8)) - ((-a)^(3/8)*Log[(-a)^(1/4) - Sqrt[2]*(-a)^(1/8)*c^(1/8)*Sqrt[x] + c^(1/4)*x])/(4*Sqrt[2]*c^(11/8)) + ((-a)^(3/8)*Log[(-a)^(1/4) + Sqrt[2]*(-a)^(1/8)*c^(1/8)*Sqrt[x] + c^(1/4)*x])/(4*Sqrt[2]*c^(11/8))","A",15,12,15,0.8000,1,"{321, 329, 300, 297, 1162, 617, 204, 1165, 628, 298, 205, 208}"
739,1,297,0,0.2889148,"\int \frac{x^{7/2}}{a+c x^4} \, dx","Int[x^(7/2)/(a + c*x^4),x]","\frac{\sqrt[8]{-a} \log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{4 \sqrt{2} c^{9/8}}-\frac{\sqrt[8]{-a} \log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{4 \sqrt{2} c^{9/8}}+\frac{\sqrt[8]{-a} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{2 \sqrt{2} c^{9/8}}-\frac{\sqrt[8]{-a} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}+1\right)}{2 \sqrt{2} c^{9/8}}-\frac{\sqrt[8]{-a} \tan ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{2 c^{9/8}}-\frac{\sqrt[8]{-a} \tanh ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{2 c^{9/8}}+\frac{2 \sqrt{x}}{c}","\frac{\sqrt[8]{-a} \log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{4 \sqrt{2} c^{9/8}}-\frac{\sqrt[8]{-a} \log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{4 \sqrt{2} c^{9/8}}+\frac{\sqrt[8]{-a} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{2 \sqrt{2} c^{9/8}}-\frac{\sqrt[8]{-a} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}+1\right)}{2 \sqrt{2} c^{9/8}}-\frac{\sqrt[8]{-a} \tan ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{2 c^{9/8}}-\frac{\sqrt[8]{-a} \tanh ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{2 c^{9/8}}+\frac{2 \sqrt{x}}{c}",1,"(2*Sqrt[x])/c + ((-a)^(1/8)*ArcTan[1 - (Sqrt[2]*c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(2*Sqrt[2]*c^(9/8)) - ((-a)^(1/8)*ArcTan[1 + (Sqrt[2]*c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(2*Sqrt[2]*c^(9/8)) - ((-a)^(1/8)*ArcTan[(c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(2*c^(9/8)) - ((-a)^(1/8)*ArcTanh[(c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(2*c^(9/8)) + ((-a)^(1/8)*Log[(-a)^(1/4) - Sqrt[2]*(-a)^(1/8)*c^(1/8)*Sqrt[x] + c^(1/4)*x])/(4*Sqrt[2]*c^(9/8)) - ((-a)^(1/8)*Log[(-a)^(1/4) + Sqrt[2]*(-a)^(1/8)*c^(1/8)*Sqrt[x] + c^(1/4)*x])/(4*Sqrt[2]*c^(9/8))","A",15,12,15,0.8000,1,"{321, 329, 214, 212, 208, 205, 211, 1165, 628, 1162, 617, 204}"
740,1,287,0,0.2347906,"\int \frac{x^{5/2}}{a+c x^4} \, dx","Int[x^(5/2)/(a + c*x^4),x]","\frac{\log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{4 \sqrt{2} \sqrt[8]{-a} c^{7/8}}-\frac{\log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{4 \sqrt{2} \sqrt[8]{-a} c^{7/8}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{2 \sqrt{2} \sqrt[8]{-a} c^{7/8}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}+1\right)}{2 \sqrt{2} \sqrt[8]{-a} c^{7/8}}+\frac{\tan ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{2 \sqrt[8]{-a} c^{7/8}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{2 \sqrt[8]{-a} c^{7/8}}","\frac{\log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{4 \sqrt{2} \sqrt[8]{-a} c^{7/8}}-\frac{\log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{4 \sqrt{2} \sqrt[8]{-a} c^{7/8}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{2 \sqrt{2} \sqrt[8]{-a} c^{7/8}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}+1\right)}{2 \sqrt{2} \sqrt[8]{-a} c^{7/8}}+\frac{\tan ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{2 \sqrt[8]{-a} c^{7/8}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{2 \sqrt[8]{-a} c^{7/8}}",1,"-ArcTan[1 - (Sqrt[2]*c^(1/8)*Sqrt[x])/(-a)^(1/8)]/(2*Sqrt[2]*(-a)^(1/8)*c^(7/8)) + ArcTan[1 + (Sqrt[2]*c^(1/8)*Sqrt[x])/(-a)^(1/8)]/(2*Sqrt[2]*(-a)^(1/8)*c^(7/8)) + ArcTan[(c^(1/8)*Sqrt[x])/(-a)^(1/8)]/(2*(-a)^(1/8)*c^(7/8)) - ArcTanh[(c^(1/8)*Sqrt[x])/(-a)^(1/8)]/(2*(-a)^(1/8)*c^(7/8)) + Log[(-a)^(1/4) - Sqrt[2]*(-a)^(1/8)*c^(1/8)*Sqrt[x] + c^(1/4)*x]/(4*Sqrt[2]*(-a)^(1/8)*c^(7/8)) - Log[(-a)^(1/4) + Sqrt[2]*(-a)^(1/8)*c^(1/8)*Sqrt[x] + c^(1/4)*x]/(4*Sqrt[2]*(-a)^(1/8)*c^(7/8))","A",14,11,15,0.7333,1,"{329, 301, 297, 1162, 617, 204, 1165, 628, 298, 205, 208}"
741,1,287,0,0.2330869,"\int \frac{x^{3/2}}{a+c x^4} \, dx","Int[x^(3/2)/(a + c*x^4),x]","-\frac{\log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{4 \sqrt{2} (-a)^{3/8} c^{5/8}}+\frac{\log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{4 \sqrt{2} (-a)^{3/8} c^{5/8}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{2 \sqrt{2} (-a)^{3/8} c^{5/8}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}+1\right)}{2 \sqrt{2} (-a)^{3/8} c^{5/8}}-\frac{\tan ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{2 (-a)^{3/8} c^{5/8}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{2 (-a)^{3/8} c^{5/8}}","-\frac{\log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{4 \sqrt{2} (-a)^{3/8} c^{5/8}}+\frac{\log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{4 \sqrt{2} (-a)^{3/8} c^{5/8}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{2 \sqrt{2} (-a)^{3/8} c^{5/8}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}+1\right)}{2 \sqrt{2} (-a)^{3/8} c^{5/8}}-\frac{\tan ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{2 (-a)^{3/8} c^{5/8}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{2 (-a)^{3/8} c^{5/8}}",1,"-ArcTan[1 - (Sqrt[2]*c^(1/8)*Sqrt[x])/(-a)^(1/8)]/(2*Sqrt[2]*(-a)^(3/8)*c^(5/8)) + ArcTan[1 + (Sqrt[2]*c^(1/8)*Sqrt[x])/(-a)^(1/8)]/(2*Sqrt[2]*(-a)^(3/8)*c^(5/8)) - ArcTan[(c^(1/8)*Sqrt[x])/(-a)^(1/8)]/(2*(-a)^(3/8)*c^(5/8)) - ArcTanh[(c^(1/8)*Sqrt[x])/(-a)^(1/8)]/(2*(-a)^(3/8)*c^(5/8)) - Log[(-a)^(1/4) - Sqrt[2]*(-a)^(1/8)*c^(1/8)*Sqrt[x] + c^(1/4)*x]/(4*Sqrt[2]*(-a)^(3/8)*c^(5/8)) + Log[(-a)^(1/4) + Sqrt[2]*(-a)^(1/8)*c^(1/8)*Sqrt[x] + c^(1/4)*x]/(4*Sqrt[2]*(-a)^(3/8)*c^(5/8))","A",14,11,15,0.7333,1,"{329, 301, 211, 1165, 628, 1162, 617, 204, 212, 208, 205}"
742,1,287,0,0.2392183,"\int \frac{\sqrt{x}}{a+c x^4} \, dx","Int[Sqrt[x]/(a + c*x^4),x]","-\frac{\log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{4 \sqrt{2} (-a)^{5/8} c^{3/8}}+\frac{\log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{4 \sqrt{2} (-a)^{5/8} c^{3/8}}+\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{2 \sqrt{2} (-a)^{5/8} c^{3/8}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}+1\right)}{2 \sqrt{2} (-a)^{5/8} c^{3/8}}+\frac{\tan ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{2 (-a)^{5/8} c^{3/8}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{2 (-a)^{5/8} c^{3/8}}","-\frac{\log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{4 \sqrt{2} (-a)^{5/8} c^{3/8}}+\frac{\log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{4 \sqrt{2} (-a)^{5/8} c^{3/8}}+\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{2 \sqrt{2} (-a)^{5/8} c^{3/8}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}+1\right)}{2 \sqrt{2} (-a)^{5/8} c^{3/8}}+\frac{\tan ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{2 (-a)^{5/8} c^{3/8}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{2 (-a)^{5/8} c^{3/8}}",1,"ArcTan[1 - (Sqrt[2]*c^(1/8)*Sqrt[x])/(-a)^(1/8)]/(2*Sqrt[2]*(-a)^(5/8)*c^(3/8)) - ArcTan[1 + (Sqrt[2]*c^(1/8)*Sqrt[x])/(-a)^(1/8)]/(2*Sqrt[2]*(-a)^(5/8)*c^(3/8)) + ArcTan[(c^(1/8)*Sqrt[x])/(-a)^(1/8)]/(2*(-a)^(5/8)*c^(3/8)) - ArcTanh[(c^(1/8)*Sqrt[x])/(-a)^(1/8)]/(2*(-a)^(5/8)*c^(3/8)) - Log[(-a)^(1/4) - Sqrt[2]*(-a)^(1/8)*c^(1/8)*Sqrt[x] + c^(1/4)*x]/(4*Sqrt[2]*(-a)^(5/8)*c^(3/8)) + Log[(-a)^(1/4) + Sqrt[2]*(-a)^(1/8)*c^(1/8)*Sqrt[x] + c^(1/4)*x]/(4*Sqrt[2]*(-a)^(5/8)*c^(3/8))","A",14,11,15,0.7333,1,"{329, 300, 297, 1162, 617, 204, 1165, 628, 298, 205, 208}"
743,1,287,0,0.2237207,"\int \frac{1}{\sqrt{x} \left(a+c x^4\right)} \, dx","Int[1/(Sqrt[x]*(a + c*x^4)),x]","\frac{\log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{4 \sqrt{2} (-a)^{7/8} \sqrt[8]{c}}-\frac{\log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{4 \sqrt{2} (-a)^{7/8} \sqrt[8]{c}}+\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{2 \sqrt{2} (-a)^{7/8} \sqrt[8]{c}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}+1\right)}{2 \sqrt{2} (-a)^{7/8} \sqrt[8]{c}}-\frac{\tan ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{2 (-a)^{7/8} \sqrt[8]{c}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{2 (-a)^{7/8} \sqrt[8]{c}}","\frac{\log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{4 \sqrt{2} (-a)^{7/8} \sqrt[8]{c}}-\frac{\log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{4 \sqrt{2} (-a)^{7/8} \sqrt[8]{c}}+\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{2 \sqrt{2} (-a)^{7/8} \sqrt[8]{c}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}+1\right)}{2 \sqrt{2} (-a)^{7/8} \sqrt[8]{c}}-\frac{\tan ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{2 (-a)^{7/8} \sqrt[8]{c}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{2 (-a)^{7/8} \sqrt[8]{c}}",1,"ArcTan[1 - (Sqrt[2]*c^(1/8)*Sqrt[x])/(-a)^(1/8)]/(2*Sqrt[2]*(-a)^(7/8)*c^(1/8)) - ArcTan[1 + (Sqrt[2]*c^(1/8)*Sqrt[x])/(-a)^(1/8)]/(2*Sqrt[2]*(-a)^(7/8)*c^(1/8)) - ArcTan[(c^(1/8)*Sqrt[x])/(-a)^(1/8)]/(2*(-a)^(7/8)*c^(1/8)) - ArcTanh[(c^(1/8)*Sqrt[x])/(-a)^(1/8)]/(2*(-a)^(7/8)*c^(1/8)) + Log[(-a)^(1/4) - Sqrt[2]*(-a)^(1/8)*c^(1/8)*Sqrt[x] + c^(1/4)*x]/(4*Sqrt[2]*(-a)^(7/8)*c^(1/8)) - Log[(-a)^(1/4) + Sqrt[2]*(-a)^(1/8)*c^(1/8)*Sqrt[x] + c^(1/4)*x]/(4*Sqrt[2]*(-a)^(7/8)*c^(1/8))","A",14,11,15,0.7333,1,"{329, 214, 212, 208, 205, 211, 1165, 628, 1162, 617, 204}"
744,1,297,0,0.2738119,"\int \frac{1}{x^{3/2} \left(a+c x^4\right)} \, dx","Int[1/(x^(3/2)*(a + c*x^4)),x]","\frac{\sqrt[8]{c} \log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{4 \sqrt{2} (-a)^{9/8}}-\frac{\sqrt[8]{c} \log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{4 \sqrt{2} (-a)^{9/8}}-\frac{\sqrt[8]{c} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{2 \sqrt{2} (-a)^{9/8}}+\frac{\sqrt[8]{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}+1\right)}{2 \sqrt{2} (-a)^{9/8}}+\frac{\sqrt[8]{c} \tan ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{2 (-a)^{9/8}}-\frac{\sqrt[8]{c} \tanh ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{2 (-a)^{9/8}}-\frac{2}{a \sqrt{x}}","\frac{\sqrt[8]{c} \log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{4 \sqrt{2} (-a)^{9/8}}-\frac{\sqrt[8]{c} \log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{4 \sqrt{2} (-a)^{9/8}}-\frac{\sqrt[8]{c} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{2 \sqrt{2} (-a)^{9/8}}+\frac{\sqrt[8]{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}+1\right)}{2 \sqrt{2} (-a)^{9/8}}+\frac{\sqrt[8]{c} \tan ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{2 (-a)^{9/8}}-\frac{\sqrt[8]{c} \tanh ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{2 (-a)^{9/8}}-\frac{2}{a \sqrt{x}}",1,"-2/(a*Sqrt[x]) - (c^(1/8)*ArcTan[1 - (Sqrt[2]*c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(2*Sqrt[2]*(-a)^(9/8)) + (c^(1/8)*ArcTan[1 + (Sqrt[2]*c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(2*Sqrt[2]*(-a)^(9/8)) + (c^(1/8)*ArcTan[(c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(2*(-a)^(9/8)) - (c^(1/8)*ArcTanh[(c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(2*(-a)^(9/8)) + (c^(1/8)*Log[(-a)^(1/4) - Sqrt[2]*(-a)^(1/8)*c^(1/8)*Sqrt[x] + c^(1/4)*x])/(4*Sqrt[2]*(-a)^(9/8)) - (c^(1/8)*Log[(-a)^(1/4) + Sqrt[2]*(-a)^(1/8)*c^(1/8)*Sqrt[x] + c^(1/4)*x])/(4*Sqrt[2]*(-a)^(9/8))","A",15,12,15,0.8000,1,"{325, 329, 301, 297, 1162, 617, 204, 1165, 628, 298, 205, 208}"
745,1,299,0,0.2856888,"\int \frac{1}{x^{5/2} \left(a+c x^4\right)} \, dx","Int[1/(x^(5/2)*(a + c*x^4)),x]","-\frac{c^{3/8} \log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{4 \sqrt{2} (-a)^{11/8}}+\frac{c^{3/8} \log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{4 \sqrt{2} (-a)^{11/8}}-\frac{c^{3/8} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{2 \sqrt{2} (-a)^{11/8}}+\frac{c^{3/8} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}+1\right)}{2 \sqrt{2} (-a)^{11/8}}-\frac{c^{3/8} \tan ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{2 (-a)^{11/8}}-\frac{c^{3/8} \tanh ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{2 (-a)^{11/8}}-\frac{2}{3 a x^{3/2}}","-\frac{c^{3/8} \log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{4 \sqrt{2} (-a)^{11/8}}+\frac{c^{3/8} \log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{4 \sqrt{2} (-a)^{11/8}}-\frac{c^{3/8} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{2 \sqrt{2} (-a)^{11/8}}+\frac{c^{3/8} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}+1\right)}{2 \sqrt{2} (-a)^{11/8}}-\frac{c^{3/8} \tan ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{2 (-a)^{11/8}}-\frac{c^{3/8} \tanh ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{2 (-a)^{11/8}}-\frac{2}{3 a x^{3/2}}",1,"-2/(3*a*x^(3/2)) - (c^(3/8)*ArcTan[1 - (Sqrt[2]*c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(2*Sqrt[2]*(-a)^(11/8)) + (c^(3/8)*ArcTan[1 + (Sqrt[2]*c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(2*Sqrt[2]*(-a)^(11/8)) - (c^(3/8)*ArcTan[(c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(2*(-a)^(11/8)) - (c^(3/8)*ArcTanh[(c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(2*(-a)^(11/8)) - (c^(3/8)*Log[(-a)^(1/4) - Sqrt[2]*(-a)^(1/8)*c^(1/8)*Sqrt[x] + c^(1/4)*x])/(4*Sqrt[2]*(-a)^(11/8)) + (c^(3/8)*Log[(-a)^(1/4) + Sqrt[2]*(-a)^(1/8)*c^(1/8)*Sqrt[x] + c^(1/4)*x])/(4*Sqrt[2]*(-a)^(11/8))","A",15,12,15,0.8000,1,"{325, 329, 301, 211, 1165, 628, 1162, 617, 204, 212, 208, 205}"
746,1,308,0,0.2686577,"\int \frac{x^{13/2}}{\left(a+c x^4\right)^2} \, dx","Int[x^(13/2)/(a + c*x^4)^2,x]","\frac{7 \log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{32 \sqrt{2} \sqrt[8]{-a} c^{15/8}}-\frac{7 \log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{32 \sqrt{2} \sqrt[8]{-a} c^{15/8}}-\frac{7 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 \sqrt{2} \sqrt[8]{-a} c^{15/8}}+\frac{7 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}+1\right)}{16 \sqrt{2} \sqrt[8]{-a} c^{15/8}}+\frac{7 \tan ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 \sqrt[8]{-a} c^{15/8}}-\frac{7 \tanh ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 \sqrt[8]{-a} c^{15/8}}-\frac{x^{7/2}}{4 c \left(a+c x^4\right)}","\frac{7 \log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{32 \sqrt{2} \sqrt[8]{-a} c^{15/8}}-\frac{7 \log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{32 \sqrt{2} \sqrt[8]{-a} c^{15/8}}-\frac{7 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 \sqrt{2} \sqrt[8]{-a} c^{15/8}}+\frac{7 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}+1\right)}{16 \sqrt{2} \sqrt[8]{-a} c^{15/8}}+\frac{7 \tan ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 \sqrt[8]{-a} c^{15/8}}-\frac{7 \tanh ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 \sqrt[8]{-a} c^{15/8}}-\frac{x^{7/2}}{4 c \left(a+c x^4\right)}",1,"-x^(7/2)/(4*c*(a + c*x^4)) - (7*ArcTan[1 - (Sqrt[2]*c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(16*Sqrt[2]*(-a)^(1/8)*c^(15/8)) + (7*ArcTan[1 + (Sqrt[2]*c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(16*Sqrt[2]*(-a)^(1/8)*c^(15/8)) + (7*ArcTan[(c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(16*(-a)^(1/8)*c^(15/8)) - (7*ArcTanh[(c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(16*(-a)^(1/8)*c^(15/8)) + (7*Log[(-a)^(1/4) - Sqrt[2]*(-a)^(1/8)*c^(1/8)*Sqrt[x] + c^(1/4)*x])/(32*Sqrt[2]*(-a)^(1/8)*c^(15/8)) - (7*Log[(-a)^(1/4) + Sqrt[2]*(-a)^(1/8)*c^(1/8)*Sqrt[x] + c^(1/4)*x])/(32*Sqrt[2]*(-a)^(1/8)*c^(15/8))","A",15,12,15,0.8000,1,"{288, 329, 301, 297, 1162, 617, 204, 1165, 628, 298, 205, 208}"
747,1,308,0,0.25079,"\int \frac{x^{11/2}}{\left(a+c x^4\right)^2} \, dx","Int[x^(11/2)/(a + c*x^4)^2,x]","-\frac{5 \log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{32 \sqrt{2} (-a)^{3/8} c^{13/8}}+\frac{5 \log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{32 \sqrt{2} (-a)^{3/8} c^{13/8}}-\frac{5 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 \sqrt{2} (-a)^{3/8} c^{13/8}}+\frac{5 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}+1\right)}{16 \sqrt{2} (-a)^{3/8} c^{13/8}}-\frac{5 \tan ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 (-a)^{3/8} c^{13/8}}-\frac{5 \tanh ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 (-a)^{3/8} c^{13/8}}-\frac{x^{5/2}}{4 c \left(a+c x^4\right)}","-\frac{5 \log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{32 \sqrt{2} (-a)^{3/8} c^{13/8}}+\frac{5 \log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{32 \sqrt{2} (-a)^{3/8} c^{13/8}}-\frac{5 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 \sqrt{2} (-a)^{3/8} c^{13/8}}+\frac{5 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}+1\right)}{16 \sqrt{2} (-a)^{3/8} c^{13/8}}-\frac{5 \tan ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 (-a)^{3/8} c^{13/8}}-\frac{5 \tanh ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 (-a)^{3/8} c^{13/8}}-\frac{x^{5/2}}{4 c \left(a+c x^4\right)}",1,"-x^(5/2)/(4*c*(a + c*x^4)) - (5*ArcTan[1 - (Sqrt[2]*c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(16*Sqrt[2]*(-a)^(3/8)*c^(13/8)) + (5*ArcTan[1 + (Sqrt[2]*c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(16*Sqrt[2]*(-a)^(3/8)*c^(13/8)) - (5*ArcTan[(c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(16*(-a)^(3/8)*c^(13/8)) - (5*ArcTanh[(c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(16*(-a)^(3/8)*c^(13/8)) - (5*Log[(-a)^(1/4) - Sqrt[2]*(-a)^(1/8)*c^(1/8)*Sqrt[x] + c^(1/4)*x])/(32*Sqrt[2]*(-a)^(3/8)*c^(13/8)) + (5*Log[(-a)^(1/4) + Sqrt[2]*(-a)^(1/8)*c^(1/8)*Sqrt[x] + c^(1/4)*x])/(32*Sqrt[2]*(-a)^(3/8)*c^(13/8))","A",15,12,15,0.8000,1,"{288, 329, 301, 211, 1165, 628, 1162, 617, 204, 212, 208, 205}"
748,1,308,0,0.2538303,"\int \frac{x^{9/2}}{\left(a+c x^4\right)^2} \, dx","Int[x^(9/2)/(a + c*x^4)^2,x]","-\frac{3 \log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{32 \sqrt{2} (-a)^{5/8} c^{11/8}}+\frac{3 \log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{32 \sqrt{2} (-a)^{5/8} c^{11/8}}+\frac{3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 \sqrt{2} (-a)^{5/8} c^{11/8}}-\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}+1\right)}{16 \sqrt{2} (-a)^{5/8} c^{11/8}}+\frac{3 \tan ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 (-a)^{5/8} c^{11/8}}-\frac{3 \tanh ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 (-a)^{5/8} c^{11/8}}-\frac{x^{3/2}}{4 c \left(a+c x^4\right)}","-\frac{3 \log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{32 \sqrt{2} (-a)^{5/8} c^{11/8}}+\frac{3 \log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{32 \sqrt{2} (-a)^{5/8} c^{11/8}}+\frac{3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 \sqrt{2} (-a)^{5/8} c^{11/8}}-\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}+1\right)}{16 \sqrt{2} (-a)^{5/8} c^{11/8}}+\frac{3 \tan ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 (-a)^{5/8} c^{11/8}}-\frac{3 \tanh ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 (-a)^{5/8} c^{11/8}}-\frac{x^{3/2}}{4 c \left(a+c x^4\right)}",1,"-x^(3/2)/(4*c*(a + c*x^4)) + (3*ArcTan[1 - (Sqrt[2]*c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(16*Sqrt[2]*(-a)^(5/8)*c^(11/8)) - (3*ArcTan[1 + (Sqrt[2]*c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(16*Sqrt[2]*(-a)^(5/8)*c^(11/8)) + (3*ArcTan[(c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(16*(-a)^(5/8)*c^(11/8)) - (3*ArcTanh[(c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(16*(-a)^(5/8)*c^(11/8)) - (3*Log[(-a)^(1/4) - Sqrt[2]*(-a)^(1/8)*c^(1/8)*Sqrt[x] + c^(1/4)*x])/(32*Sqrt[2]*(-a)^(5/8)*c^(11/8)) + (3*Log[(-a)^(1/4) + Sqrt[2]*(-a)^(1/8)*c^(1/8)*Sqrt[x] + c^(1/4)*x])/(32*Sqrt[2]*(-a)^(5/8)*c^(11/8))","A",15,12,15,0.8000,1,"{288, 329, 300, 297, 1162, 617, 204, 1165, 628, 298, 205, 208}"
749,1,308,0,0.2472115,"\int \frac{x^{7/2}}{\left(a+c x^4\right)^2} \, dx","Int[x^(7/2)/(a + c*x^4)^2,x]","\frac{\log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{32 \sqrt{2} (-a)^{7/8} c^{9/8}}-\frac{\log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{32 \sqrt{2} (-a)^{7/8} c^{9/8}}+\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 \sqrt{2} (-a)^{7/8} c^{9/8}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}+1\right)}{16 \sqrt{2} (-a)^{7/8} c^{9/8}}-\frac{\tan ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 (-a)^{7/8} c^{9/8}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 (-a)^{7/8} c^{9/8}}-\frac{\sqrt{x}}{4 c \left(a+c x^4\right)}","\frac{\log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{32 \sqrt{2} (-a)^{7/8} c^{9/8}}-\frac{\log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{32 \sqrt{2} (-a)^{7/8} c^{9/8}}+\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 \sqrt{2} (-a)^{7/8} c^{9/8}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}+1\right)}{16 \sqrt{2} (-a)^{7/8} c^{9/8}}-\frac{\tan ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 (-a)^{7/8} c^{9/8}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 (-a)^{7/8} c^{9/8}}-\frac{\sqrt{x}}{4 c \left(a+c x^4\right)}",1,"-Sqrt[x]/(4*c*(a + c*x^4)) + ArcTan[1 - (Sqrt[2]*c^(1/8)*Sqrt[x])/(-a)^(1/8)]/(16*Sqrt[2]*(-a)^(7/8)*c^(9/8)) - ArcTan[1 + (Sqrt[2]*c^(1/8)*Sqrt[x])/(-a)^(1/8)]/(16*Sqrt[2]*(-a)^(7/8)*c^(9/8)) - ArcTan[(c^(1/8)*Sqrt[x])/(-a)^(1/8)]/(16*(-a)^(7/8)*c^(9/8)) - ArcTanh[(c^(1/8)*Sqrt[x])/(-a)^(1/8)]/(16*(-a)^(7/8)*c^(9/8)) + Log[(-a)^(1/4) - Sqrt[2]*(-a)^(1/8)*c^(1/8)*Sqrt[x] + c^(1/4)*x]/(32*Sqrt[2]*(-a)^(7/8)*c^(9/8)) - Log[(-a)^(1/4) + Sqrt[2]*(-a)^(1/8)*c^(1/8)*Sqrt[x] + c^(1/4)*x]/(32*Sqrt[2]*(-a)^(7/8)*c^(9/8))","A",15,12,15,0.8000,1,"{288, 329, 214, 212, 208, 205, 211, 1165, 628, 1162, 617, 204}"
750,1,308,0,0.2511688,"\int \frac{x^{5/2}}{\left(a+c x^4\right)^2} \, dx","Int[x^(5/2)/(a + c*x^4)^2,x]","-\frac{\log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{32 \sqrt{2} (-a)^{9/8} c^{7/8}}+\frac{\log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{32 \sqrt{2} (-a)^{9/8} c^{7/8}}+\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 \sqrt{2} (-a)^{9/8} c^{7/8}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}+1\right)}{16 \sqrt{2} (-a)^{9/8} c^{7/8}}-\frac{\tan ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 (-a)^{9/8} c^{7/8}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 (-a)^{9/8} c^{7/8}}+\frac{x^{7/2}}{4 a \left(a+c x^4\right)}","-\frac{\log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{32 \sqrt{2} (-a)^{9/8} c^{7/8}}+\frac{\log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{32 \sqrt{2} (-a)^{9/8} c^{7/8}}+\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 \sqrt{2} (-a)^{9/8} c^{7/8}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}+1\right)}{16 \sqrt{2} (-a)^{9/8} c^{7/8}}-\frac{\tan ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 (-a)^{9/8} c^{7/8}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 (-a)^{9/8} c^{7/8}}+\frac{x^{7/2}}{4 a \left(a+c x^4\right)}",1,"x^(7/2)/(4*a*(a + c*x^4)) + ArcTan[1 - (Sqrt[2]*c^(1/8)*Sqrt[x])/(-a)^(1/8)]/(16*Sqrt[2]*(-a)^(9/8)*c^(7/8)) - ArcTan[1 + (Sqrt[2]*c^(1/8)*Sqrt[x])/(-a)^(1/8)]/(16*Sqrt[2]*(-a)^(9/8)*c^(7/8)) - ArcTan[(c^(1/8)*Sqrt[x])/(-a)^(1/8)]/(16*(-a)^(9/8)*c^(7/8)) + ArcTanh[(c^(1/8)*Sqrt[x])/(-a)^(1/8)]/(16*(-a)^(9/8)*c^(7/8)) - Log[(-a)^(1/4) - Sqrt[2]*(-a)^(1/8)*c^(1/8)*Sqrt[x] + c^(1/4)*x]/(32*Sqrt[2]*(-a)^(9/8)*c^(7/8)) + Log[(-a)^(1/4) + Sqrt[2]*(-a)^(1/8)*c^(1/8)*Sqrt[x] + c^(1/4)*x]/(32*Sqrt[2]*(-a)^(9/8)*c^(7/8))","A",15,12,15,0.8000,1,"{290, 329, 301, 297, 1162, 617, 204, 1165, 628, 298, 205, 208}"
751,1,308,0,0.2606252,"\int \frac{x^{3/2}}{\left(a+c x^4\right)^2} \, dx","Int[x^(3/2)/(a + c*x^4)^2,x]","\frac{3 \log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{32 \sqrt{2} (-a)^{11/8} c^{5/8}}-\frac{3 \log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{32 \sqrt{2} (-a)^{11/8} c^{5/8}}+\frac{3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 \sqrt{2} (-a)^{11/8} c^{5/8}}-\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}+1\right)}{16 \sqrt{2} (-a)^{11/8} c^{5/8}}+\frac{3 \tan ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 (-a)^{11/8} c^{5/8}}+\frac{3 \tanh ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 (-a)^{11/8} c^{5/8}}+\frac{x^{5/2}}{4 a \left(a+c x^4\right)}","\frac{3 \log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{32 \sqrt{2} (-a)^{11/8} c^{5/8}}-\frac{3 \log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{32 \sqrt{2} (-a)^{11/8} c^{5/8}}+\frac{3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 \sqrt{2} (-a)^{11/8} c^{5/8}}-\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}+1\right)}{16 \sqrt{2} (-a)^{11/8} c^{5/8}}+\frac{3 \tan ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 (-a)^{11/8} c^{5/8}}+\frac{3 \tanh ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 (-a)^{11/8} c^{5/8}}+\frac{x^{5/2}}{4 a \left(a+c x^4\right)}",1,"x^(5/2)/(4*a*(a + c*x^4)) + (3*ArcTan[1 - (Sqrt[2]*c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(16*Sqrt[2]*(-a)^(11/8)*c^(5/8)) - (3*ArcTan[1 + (Sqrt[2]*c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(16*Sqrt[2]*(-a)^(11/8)*c^(5/8)) + (3*ArcTan[(c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(16*(-a)^(11/8)*c^(5/8)) + (3*ArcTanh[(c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(16*(-a)^(11/8)*c^(5/8)) + (3*Log[(-a)^(1/4) - Sqrt[2]*(-a)^(1/8)*c^(1/8)*Sqrt[x] + c^(1/4)*x])/(32*Sqrt[2]*(-a)^(11/8)*c^(5/8)) - (3*Log[(-a)^(1/4) + Sqrt[2]*(-a)^(1/8)*c^(1/8)*Sqrt[x] + c^(1/4)*x])/(32*Sqrt[2]*(-a)^(11/8)*c^(5/8))","A",15,12,15,0.8000,1,"{290, 329, 301, 211, 1165, 628, 1162, 617, 204, 212, 208, 205}"
752,1,308,0,0.2938952,"\int \frac{\sqrt{x}}{\left(a+c x^4\right)^2} \, dx","Int[Sqrt[x]/(a + c*x^4)^2,x]","\frac{5 \log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{32 \sqrt{2} (-a)^{13/8} c^{3/8}}-\frac{5 \log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{32 \sqrt{2} (-a)^{13/8} c^{3/8}}-\frac{5 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 \sqrt{2} (-a)^{13/8} c^{3/8}}+\frac{5 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}+1\right)}{16 \sqrt{2} (-a)^{13/8} c^{3/8}}-\frac{5 \tan ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 (-a)^{13/8} c^{3/8}}+\frac{5 \tanh ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 (-a)^{13/8} c^{3/8}}+\frac{x^{3/2}}{4 a \left(a+c x^4\right)}","\frac{5 \log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{32 \sqrt{2} (-a)^{13/8} c^{3/8}}-\frac{5 \log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{32 \sqrt{2} (-a)^{13/8} c^{3/8}}-\frac{5 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 \sqrt{2} (-a)^{13/8} c^{3/8}}+\frac{5 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}+1\right)}{16 \sqrt{2} (-a)^{13/8} c^{3/8}}-\frac{5 \tan ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 (-a)^{13/8} c^{3/8}}+\frac{5 \tanh ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 (-a)^{13/8} c^{3/8}}+\frac{x^{3/2}}{4 a \left(a+c x^4\right)}",1,"x^(3/2)/(4*a*(a + c*x^4)) - (5*ArcTan[1 - (Sqrt[2]*c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(16*Sqrt[2]*(-a)^(13/8)*c^(3/8)) + (5*ArcTan[1 + (Sqrt[2]*c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(16*Sqrt[2]*(-a)^(13/8)*c^(3/8)) - (5*ArcTan[(c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(16*(-a)^(13/8)*c^(3/8)) + (5*ArcTanh[(c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(16*(-a)^(13/8)*c^(3/8)) + (5*Log[(-a)^(1/4) - Sqrt[2]*(-a)^(1/8)*c^(1/8)*Sqrt[x] + c^(1/4)*x])/(32*Sqrt[2]*(-a)^(13/8)*c^(3/8)) - (5*Log[(-a)^(1/4) + Sqrt[2]*(-a)^(1/8)*c^(1/8)*Sqrt[x] + c^(1/4)*x])/(32*Sqrt[2]*(-a)^(13/8)*c^(3/8))","A",15,12,15,0.8000,1,"{290, 329, 300, 297, 1162, 617, 204, 1165, 628, 298, 205, 208}"
753,1,308,0,0.2661093,"\int \frac{1}{\sqrt{x} \left(a+c x^4\right)^2} \, dx","Int[1/(Sqrt[x]*(a + c*x^4)^2),x]","\frac{\sqrt{x}}{4 a \left(a+c x^4\right)}-\frac{7 \log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{32 \sqrt{2} (-a)^{15/8} \sqrt[8]{c}}+\frac{7 \log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{32 \sqrt{2} (-a)^{15/8} \sqrt[8]{c}}-\frac{7 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 \sqrt{2} (-a)^{15/8} \sqrt[8]{c}}+\frac{7 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}+1\right)}{16 \sqrt{2} (-a)^{15/8} \sqrt[8]{c}}+\frac{7 \tan ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 (-a)^{15/8} \sqrt[8]{c}}+\frac{7 \tanh ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 (-a)^{15/8} \sqrt[8]{c}}","\frac{\sqrt{x}}{4 a \left(a+c x^4\right)}-\frac{7 \log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{32 \sqrt{2} (-a)^{15/8} \sqrt[8]{c}}+\frac{7 \log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{32 \sqrt{2} (-a)^{15/8} \sqrt[8]{c}}-\frac{7 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 \sqrt{2} (-a)^{15/8} \sqrt[8]{c}}+\frac{7 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}+1\right)}{16 \sqrt{2} (-a)^{15/8} \sqrt[8]{c}}+\frac{7 \tan ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 (-a)^{15/8} \sqrt[8]{c}}+\frac{7 \tanh ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 (-a)^{15/8} \sqrt[8]{c}}",1,"Sqrt[x]/(4*a*(a + c*x^4)) - (7*ArcTan[1 - (Sqrt[2]*c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(16*Sqrt[2]*(-a)^(15/8)*c^(1/8)) + (7*ArcTan[1 + (Sqrt[2]*c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(16*Sqrt[2]*(-a)^(15/8)*c^(1/8)) + (7*ArcTan[(c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(16*(-a)^(15/8)*c^(1/8)) + (7*ArcTanh[(c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(16*(-a)^(15/8)*c^(1/8)) - (7*Log[(-a)^(1/4) - Sqrt[2]*(-a)^(1/8)*c^(1/8)*Sqrt[x] + c^(1/4)*x])/(32*Sqrt[2]*(-a)^(15/8)*c^(1/8)) + (7*Log[(-a)^(1/4) + Sqrt[2]*(-a)^(1/8)*c^(1/8)*Sqrt[x] + c^(1/4)*x])/(32*Sqrt[2]*(-a)^(15/8)*c^(1/8))","A",15,12,15,0.8000,1,"{290, 329, 214, 212, 208, 205, 211, 1165, 628, 1162, 617, 204}"
754,1,320,0,0.2985696,"\int \frac{1}{x^{3/2} \left(a+c x^4\right)^2} \, dx","Int[1/(x^(3/2)*(a + c*x^4)^2),x]","-\frac{9}{4 a^2 \sqrt{x}}+\frac{1}{4 a \sqrt{x} \left(a+c x^4\right)}-\frac{9 \sqrt[8]{c} \log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{32 \sqrt{2} (-a)^{17/8}}+\frac{9 \sqrt[8]{c} \log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{32 \sqrt{2} (-a)^{17/8}}+\frac{9 \sqrt[8]{c} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 \sqrt{2} (-a)^{17/8}}-\frac{9 \sqrt[8]{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}+1\right)}{16 \sqrt{2} (-a)^{17/8}}-\frac{9 \sqrt[8]{c} \tan ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 (-a)^{17/8}}+\frac{9 \sqrt[8]{c} \tanh ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 (-a)^{17/8}}","-\frac{9}{4 a^2 \sqrt{x}}+\frac{1}{4 a \sqrt{x} \left(a+c x^4\right)}-\frac{9 \sqrt[8]{c} \log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{32 \sqrt{2} (-a)^{17/8}}+\frac{9 \sqrt[8]{c} \log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{32 \sqrt{2} (-a)^{17/8}}+\frac{9 \sqrt[8]{c} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 \sqrt{2} (-a)^{17/8}}-\frac{9 \sqrt[8]{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}+1\right)}{16 \sqrt{2} (-a)^{17/8}}-\frac{9 \sqrt[8]{c} \tan ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 (-a)^{17/8}}+\frac{9 \sqrt[8]{c} \tanh ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{16 (-a)^{17/8}}",1,"-9/(4*a^2*Sqrt[x]) + 1/(4*a*Sqrt[x]*(a + c*x^4)) + (9*c^(1/8)*ArcTan[1 - (Sqrt[2]*c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(16*Sqrt[2]*(-a)^(17/8)) - (9*c^(1/8)*ArcTan[1 + (Sqrt[2]*c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(16*Sqrt[2]*(-a)^(17/8)) - (9*c^(1/8)*ArcTan[(c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(16*(-a)^(17/8)) + (9*c^(1/8)*ArcTanh[(c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(16*(-a)^(17/8)) - (9*c^(1/8)*Log[(-a)^(1/4) - Sqrt[2]*(-a)^(1/8)*c^(1/8)*Sqrt[x] + c^(1/4)*x])/(32*Sqrt[2]*(-a)^(17/8)) + (9*c^(1/8)*Log[(-a)^(1/4) + Sqrt[2]*(-a)^(1/8)*c^(1/8)*Sqrt[x] + c^(1/4)*x])/(32*Sqrt[2]*(-a)^(17/8))","A",16,13,15,0.8667,1,"{290, 325, 329, 301, 297, 1162, 617, 204, 1165, 628, 298, 205, 208}"
755,1,329,0,0.2826887,"\int \frac{x^{15/2}}{\left(a+c x^4\right)^3} \, dx","Int[x^(15/2)/(a + c*x^4)^3,x]","-\frac{9 \sqrt{x}}{64 c^2 \left(a+c x^4\right)}+\frac{9 \log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{512 \sqrt{2} (-a)^{7/8} c^{17/8}}-\frac{9 \log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{512 \sqrt{2} (-a)^{7/8} c^{17/8}}+\frac{9 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 \sqrt{2} (-a)^{7/8} c^{17/8}}-\frac{9 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}+1\right)}{256 \sqrt{2} (-a)^{7/8} c^{17/8}}-\frac{9 \tan ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 (-a)^{7/8} c^{17/8}}-\frac{9 \tanh ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 (-a)^{7/8} c^{17/8}}-\frac{x^{9/2}}{8 c \left(a+c x^4\right)^2}","-\frac{9 \sqrt{x}}{64 c^2 \left(a+c x^4\right)}+\frac{9 \log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{512 \sqrt{2} (-a)^{7/8} c^{17/8}}-\frac{9 \log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{512 \sqrt{2} (-a)^{7/8} c^{17/8}}+\frac{9 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 \sqrt{2} (-a)^{7/8} c^{17/8}}-\frac{9 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}+1\right)}{256 \sqrt{2} (-a)^{7/8} c^{17/8}}-\frac{9 \tan ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 (-a)^{7/8} c^{17/8}}-\frac{9 \tanh ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 (-a)^{7/8} c^{17/8}}-\frac{x^{9/2}}{8 c \left(a+c x^4\right)^2}",1,"-x^(9/2)/(8*c*(a + c*x^4)^2) - (9*Sqrt[x])/(64*c^2*(a + c*x^4)) + (9*ArcTan[1 - (Sqrt[2]*c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(256*Sqrt[2]*(-a)^(7/8)*c^(17/8)) - (9*ArcTan[1 + (Sqrt[2]*c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(256*Sqrt[2]*(-a)^(7/8)*c^(17/8)) - (9*ArcTan[(c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(256*(-a)^(7/8)*c^(17/8)) - (9*ArcTanh[(c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(256*(-a)^(7/8)*c^(17/8)) + (9*Log[(-a)^(1/4) - Sqrt[2]*(-a)^(1/8)*c^(1/8)*Sqrt[x] + c^(1/4)*x])/(512*Sqrt[2]*(-a)^(7/8)*c^(17/8)) - (9*Log[(-a)^(1/4) + Sqrt[2]*(-a)^(1/8)*c^(1/8)*Sqrt[x] + c^(1/4)*x])/(512*Sqrt[2]*(-a)^(7/8)*c^(17/8))","A",16,12,15,0.8000,1,"{288, 329, 214, 212, 208, 205, 211, 1165, 628, 1162, 617, 204}"
756,1,332,0,0.2859738,"\int \frac{x^{13/2}}{\left(a+c x^4\right)^3} \, dx","Int[x^(13/2)/(a + c*x^4)^3,x]","-\frac{7 \log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{512 \sqrt{2} (-a)^{9/8} c^{15/8}}+\frac{7 \log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{512 \sqrt{2} (-a)^{9/8} c^{15/8}}+\frac{7 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 \sqrt{2} (-a)^{9/8} c^{15/8}}-\frac{7 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}+1\right)}{256 \sqrt{2} (-a)^{9/8} c^{15/8}}-\frac{7 \tan ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 (-a)^{9/8} c^{15/8}}+\frac{7 \tanh ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 (-a)^{9/8} c^{15/8}}+\frac{7 x^{7/2}}{64 a c \left(a+c x^4\right)}-\frac{x^{7/2}}{8 c \left(a+c x^4\right)^2}","-\frac{7 \log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{512 \sqrt{2} (-a)^{9/8} c^{15/8}}+\frac{7 \log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{512 \sqrt{2} (-a)^{9/8} c^{15/8}}+\frac{7 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 \sqrt{2} (-a)^{9/8} c^{15/8}}-\frac{7 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}+1\right)}{256 \sqrt{2} (-a)^{9/8} c^{15/8}}-\frac{7 \tan ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 (-a)^{9/8} c^{15/8}}+\frac{7 \tanh ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 (-a)^{9/8} c^{15/8}}+\frac{7 x^{7/2}}{64 a c \left(a+c x^4\right)}-\frac{x^{7/2}}{8 c \left(a+c x^4\right)^2}",1,"-x^(7/2)/(8*c*(a + c*x^4)^2) + (7*x^(7/2))/(64*a*c*(a + c*x^4)) + (7*ArcTan[1 - (Sqrt[2]*c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(256*Sqrt[2]*(-a)^(9/8)*c^(15/8)) - (7*ArcTan[1 + (Sqrt[2]*c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(256*Sqrt[2]*(-a)^(9/8)*c^(15/8)) - (7*ArcTan[(c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(256*(-a)^(9/8)*c^(15/8)) + (7*ArcTanh[(c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(256*(-a)^(9/8)*c^(15/8)) - (7*Log[(-a)^(1/4) - Sqrt[2]*(-a)^(1/8)*c^(1/8)*Sqrt[x] + c^(1/4)*x])/(512*Sqrt[2]*(-a)^(9/8)*c^(15/8)) + (7*Log[(-a)^(1/4) + Sqrt[2]*(-a)^(1/8)*c^(1/8)*Sqrt[x] + c^(1/4)*x])/(512*Sqrt[2]*(-a)^(9/8)*c^(15/8))","A",16,13,15,0.8667,1,"{288, 290, 329, 301, 297, 1162, 617, 204, 1165, 628, 298, 205, 208}"
757,1,332,0,0.2976151,"\int \frac{x^{11/2}}{\left(a+c x^4\right)^3} \, dx","Int[x^(11/2)/(a + c*x^4)^3,x]","\frac{15 \log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{512 \sqrt{2} (-a)^{11/8} c^{13/8}}-\frac{15 \log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{512 \sqrt{2} (-a)^{11/8} c^{13/8}}+\frac{15 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 \sqrt{2} (-a)^{11/8} c^{13/8}}-\frac{15 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}+1\right)}{256 \sqrt{2} (-a)^{11/8} c^{13/8}}+\frac{15 \tan ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 (-a)^{11/8} c^{13/8}}+\frac{15 \tanh ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 (-a)^{11/8} c^{13/8}}+\frac{5 x^{5/2}}{64 a c \left(a+c x^4\right)}-\frac{x^{5/2}}{8 c \left(a+c x^4\right)^2}","\frac{15 \log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{512 \sqrt{2} (-a)^{11/8} c^{13/8}}-\frac{15 \log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{512 \sqrt{2} (-a)^{11/8} c^{13/8}}+\frac{15 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 \sqrt{2} (-a)^{11/8} c^{13/8}}-\frac{15 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}+1\right)}{256 \sqrt{2} (-a)^{11/8} c^{13/8}}+\frac{15 \tan ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 (-a)^{11/8} c^{13/8}}+\frac{15 \tanh ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 (-a)^{11/8} c^{13/8}}+\frac{5 x^{5/2}}{64 a c \left(a+c x^4\right)}-\frac{x^{5/2}}{8 c \left(a+c x^4\right)^2}",1,"-x^(5/2)/(8*c*(a + c*x^4)^2) + (5*x^(5/2))/(64*a*c*(a + c*x^4)) + (15*ArcTan[1 - (Sqrt[2]*c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(256*Sqrt[2]*(-a)^(11/8)*c^(13/8)) - (15*ArcTan[1 + (Sqrt[2]*c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(256*Sqrt[2]*(-a)^(11/8)*c^(13/8)) + (15*ArcTan[(c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(256*(-a)^(11/8)*c^(13/8)) + (15*ArcTanh[(c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(256*(-a)^(11/8)*c^(13/8)) + (15*Log[(-a)^(1/4) - Sqrt[2]*(-a)^(1/8)*c^(1/8)*Sqrt[x] + c^(1/4)*x])/(512*Sqrt[2]*(-a)^(11/8)*c^(13/8)) - (15*Log[(-a)^(1/4) + Sqrt[2]*(-a)^(1/8)*c^(1/8)*Sqrt[x] + c^(1/4)*x])/(512*Sqrt[2]*(-a)^(11/8)*c^(13/8))","A",16,13,15,0.8667,1,"{288, 290, 329, 301, 211, 1165, 628, 1162, 617, 204, 212, 208, 205}"
758,1,332,0,0.3040562,"\int \frac{x^{9/2}}{\left(a+c x^4\right)^3} \, dx","Int[x^(9/2)/(a + c*x^4)^3,x]","\frac{15 \log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{512 \sqrt{2} (-a)^{13/8} c^{11/8}}-\frac{15 \log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{512 \sqrt{2} (-a)^{13/8} c^{11/8}}-\frac{15 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 \sqrt{2} (-a)^{13/8} c^{11/8}}+\frac{15 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}+1\right)}{256 \sqrt{2} (-a)^{13/8} c^{11/8}}-\frac{15 \tan ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 (-a)^{13/8} c^{11/8}}+\frac{15 \tanh ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 (-a)^{13/8} c^{11/8}}+\frac{3 x^{3/2}}{64 a c \left(a+c x^4\right)}-\frac{x^{3/2}}{8 c \left(a+c x^4\right)^2}","\frac{15 \log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{512 \sqrt{2} (-a)^{13/8} c^{11/8}}-\frac{15 \log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{512 \sqrt{2} (-a)^{13/8} c^{11/8}}-\frac{15 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 \sqrt{2} (-a)^{13/8} c^{11/8}}+\frac{15 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}+1\right)}{256 \sqrt{2} (-a)^{13/8} c^{11/8}}-\frac{15 \tan ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 (-a)^{13/8} c^{11/8}}+\frac{15 \tanh ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 (-a)^{13/8} c^{11/8}}+\frac{3 x^{3/2}}{64 a c \left(a+c x^4\right)}-\frac{x^{3/2}}{8 c \left(a+c x^4\right)^2}",1,"-x^(3/2)/(8*c*(a + c*x^4)^2) + (3*x^(3/2))/(64*a*c*(a + c*x^4)) - (15*ArcTan[1 - (Sqrt[2]*c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(256*Sqrt[2]*(-a)^(13/8)*c^(11/8)) + (15*ArcTan[1 + (Sqrt[2]*c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(256*Sqrt[2]*(-a)^(13/8)*c^(11/8)) - (15*ArcTan[(c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(256*(-a)^(13/8)*c^(11/8)) + (15*ArcTanh[(c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(256*(-a)^(13/8)*c^(11/8)) + (15*Log[(-a)^(1/4) - Sqrt[2]*(-a)^(1/8)*c^(1/8)*Sqrt[x] + c^(1/4)*x])/(512*Sqrt[2]*(-a)^(13/8)*c^(11/8)) - (15*Log[(-a)^(1/4) + Sqrt[2]*(-a)^(1/8)*c^(1/8)*Sqrt[x] + c^(1/4)*x])/(512*Sqrt[2]*(-a)^(13/8)*c^(11/8))","A",16,13,15,0.8667,1,"{288, 290, 329, 300, 297, 1162, 617, 204, 1165, 628, 298, 205, 208}"
759,1,332,0,0.2897906,"\int \frac{x^{7/2}}{\left(a+c x^4\right)^3} \, dx","Int[x^(7/2)/(a + c*x^4)^3,x]","-\frac{7 \log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{512 \sqrt{2} (-a)^{15/8} c^{9/8}}+\frac{7 \log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{512 \sqrt{2} (-a)^{15/8} c^{9/8}}-\frac{7 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 \sqrt{2} (-a)^{15/8} c^{9/8}}+\frac{7 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}+1\right)}{256 \sqrt{2} (-a)^{15/8} c^{9/8}}+\frac{7 \tan ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 (-a)^{15/8} c^{9/8}}+\frac{7 \tanh ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 (-a)^{15/8} c^{9/8}}+\frac{\sqrt{x}}{64 a c \left(a+c x^4\right)}-\frac{\sqrt{x}}{8 c \left(a+c x^4\right)^2}","-\frac{7 \log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{512 \sqrt{2} (-a)^{15/8} c^{9/8}}+\frac{7 \log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{512 \sqrt{2} (-a)^{15/8} c^{9/8}}-\frac{7 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 \sqrt{2} (-a)^{15/8} c^{9/8}}+\frac{7 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}+1\right)}{256 \sqrt{2} (-a)^{15/8} c^{9/8}}+\frac{7 \tan ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 (-a)^{15/8} c^{9/8}}+\frac{7 \tanh ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 (-a)^{15/8} c^{9/8}}+\frac{\sqrt{x}}{64 a c \left(a+c x^4\right)}-\frac{\sqrt{x}}{8 c \left(a+c x^4\right)^2}",1,"-Sqrt[x]/(8*c*(a + c*x^4)^2) + Sqrt[x]/(64*a*c*(a + c*x^4)) - (7*ArcTan[1 - (Sqrt[2]*c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(256*Sqrt[2]*(-a)^(15/8)*c^(9/8)) + (7*ArcTan[1 + (Sqrt[2]*c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(256*Sqrt[2]*(-a)^(15/8)*c^(9/8)) + (7*ArcTan[(c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(256*(-a)^(15/8)*c^(9/8)) + (7*ArcTanh[(c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(256*(-a)^(15/8)*c^(9/8)) - (7*Log[(-a)^(1/4) - Sqrt[2]*(-a)^(1/8)*c^(1/8)*Sqrt[x] + c^(1/4)*x])/(512*Sqrt[2]*(-a)^(15/8)*c^(9/8)) + (7*Log[(-a)^(1/4) + Sqrt[2]*(-a)^(1/8)*c^(1/8)*Sqrt[x] + c^(1/4)*x])/(512*Sqrt[2]*(-a)^(15/8)*c^(9/8))","A",16,13,15,0.8667,1,"{288, 290, 329, 214, 212, 208, 205, 211, 1165, 628, 1162, 617, 204}"
760,1,329,0,0.3081812,"\int \frac{x^{5/2}}{\left(a+c x^4\right)^3} \, dx","Int[x^(5/2)/(a + c*x^4)^3,x]","\frac{9 x^{7/2}}{64 a^2 \left(a+c x^4\right)}+\frac{9 \log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{512 \sqrt{2} (-a)^{17/8} c^{7/8}}-\frac{9 \log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{512 \sqrt{2} (-a)^{17/8} c^{7/8}}-\frac{9 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 \sqrt{2} (-a)^{17/8} c^{7/8}}+\frac{9 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}+1\right)}{256 \sqrt{2} (-a)^{17/8} c^{7/8}}+\frac{9 \tan ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 (-a)^{17/8} c^{7/8}}-\frac{9 \tanh ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 (-a)^{17/8} c^{7/8}}+\frac{x^{7/2}}{8 a \left(a+c x^4\right)^2}","\frac{9 x^{7/2}}{64 a^2 \left(a+c x^4\right)}+\frac{9 \log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{512 \sqrt{2} (-a)^{17/8} c^{7/8}}-\frac{9 \log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{512 \sqrt{2} (-a)^{17/8} c^{7/8}}-\frac{9 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 \sqrt{2} (-a)^{17/8} c^{7/8}}+\frac{9 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}+1\right)}{256 \sqrt{2} (-a)^{17/8} c^{7/8}}+\frac{9 \tan ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 (-a)^{17/8} c^{7/8}}-\frac{9 \tanh ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 (-a)^{17/8} c^{7/8}}+\frac{x^{7/2}}{8 a \left(a+c x^4\right)^2}",1,"x^(7/2)/(8*a*(a + c*x^4)^2) + (9*x^(7/2))/(64*a^2*(a + c*x^4)) - (9*ArcTan[1 - (Sqrt[2]*c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(256*Sqrt[2]*(-a)^(17/8)*c^(7/8)) + (9*ArcTan[1 + (Sqrt[2]*c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(256*Sqrt[2]*(-a)^(17/8)*c^(7/8)) + (9*ArcTan[(c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(256*(-a)^(17/8)*c^(7/8)) - (9*ArcTanh[(c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(256*(-a)^(17/8)*c^(7/8)) + (9*Log[(-a)^(1/4) - Sqrt[2]*(-a)^(1/8)*c^(1/8)*Sqrt[x] + c^(1/4)*x])/(512*Sqrt[2]*(-a)^(17/8)*c^(7/8)) - (9*Log[(-a)^(1/4) + Sqrt[2]*(-a)^(1/8)*c^(1/8)*Sqrt[x] + c^(1/4)*x])/(512*Sqrt[2]*(-a)^(17/8)*c^(7/8))","A",16,12,15,0.8000,1,"{290, 329, 301, 297, 1162, 617, 204, 1165, 628, 298, 205, 208}"
761,1,329,0,0.3032336,"\int \frac{x^{3/2}}{\left(a+c x^4\right)^3} \, dx","Int[x^(3/2)/(a + c*x^4)^3,x]","\frac{11 x^{5/2}}{64 a^2 \left(a+c x^4\right)}-\frac{33 \log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{512 \sqrt{2} (-a)^{19/8} c^{5/8}}+\frac{33 \log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{512 \sqrt{2} (-a)^{19/8} c^{5/8}}-\frac{33 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 \sqrt{2} (-a)^{19/8} c^{5/8}}+\frac{33 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}+1\right)}{256 \sqrt{2} (-a)^{19/8} c^{5/8}}-\frac{33 \tan ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 (-a)^{19/8} c^{5/8}}-\frac{33 \tanh ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 (-a)^{19/8} c^{5/8}}+\frac{x^{5/2}}{8 a \left(a+c x^4\right)^2}","\frac{11 x^{5/2}}{64 a^2 \left(a+c x^4\right)}-\frac{33 \log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{512 \sqrt{2} (-a)^{19/8} c^{5/8}}+\frac{33 \log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{512 \sqrt{2} (-a)^{19/8} c^{5/8}}-\frac{33 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 \sqrt{2} (-a)^{19/8} c^{5/8}}+\frac{33 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}+1\right)}{256 \sqrt{2} (-a)^{19/8} c^{5/8}}-\frac{33 \tan ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 (-a)^{19/8} c^{5/8}}-\frac{33 \tanh ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 (-a)^{19/8} c^{5/8}}+\frac{x^{5/2}}{8 a \left(a+c x^4\right)^2}",1,"x^(5/2)/(8*a*(a + c*x^4)^2) + (11*x^(5/2))/(64*a^2*(a + c*x^4)) - (33*ArcTan[1 - (Sqrt[2]*c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(256*Sqrt[2]*(-a)^(19/8)*c^(5/8)) + (33*ArcTan[1 + (Sqrt[2]*c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(256*Sqrt[2]*(-a)^(19/8)*c^(5/8)) - (33*ArcTan[(c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(256*(-a)^(19/8)*c^(5/8)) - (33*ArcTanh[(c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(256*(-a)^(19/8)*c^(5/8)) - (33*Log[(-a)^(1/4) - Sqrt[2]*(-a)^(1/8)*c^(1/8)*Sqrt[x] + c^(1/4)*x])/(512*Sqrt[2]*(-a)^(19/8)*c^(5/8)) + (33*Log[(-a)^(1/4) + Sqrt[2]*(-a)^(1/8)*c^(1/8)*Sqrt[x] + c^(1/4)*x])/(512*Sqrt[2]*(-a)^(19/8)*c^(5/8))","A",16,12,15,0.8000,1,"{290, 329, 301, 211, 1165, 628, 1162, 617, 204, 212, 208, 205}"
762,1,329,0,0.3129492,"\int \frac{\sqrt{x}}{\left(a+c x^4\right)^3} \, dx","Int[Sqrt[x]/(a + c*x^4)^3,x]","\frac{13 x^{3/2}}{64 a^2 \left(a+c x^4\right)}-\frac{65 \log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{512 \sqrt{2} (-a)^{21/8} c^{3/8}}+\frac{65 \log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{512 \sqrt{2} (-a)^{21/8} c^{3/8}}+\frac{65 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 \sqrt{2} (-a)^{21/8} c^{3/8}}-\frac{65 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}+1\right)}{256 \sqrt{2} (-a)^{21/8} c^{3/8}}+\frac{65 \tan ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 (-a)^{21/8} c^{3/8}}-\frac{65 \tanh ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 (-a)^{21/8} c^{3/8}}+\frac{x^{3/2}}{8 a \left(a+c x^4\right)^2}","\frac{13 x^{3/2}}{64 a^2 \left(a+c x^4\right)}-\frac{65 \log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{512 \sqrt{2} (-a)^{21/8} c^{3/8}}+\frac{65 \log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{512 \sqrt{2} (-a)^{21/8} c^{3/8}}+\frac{65 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 \sqrt{2} (-a)^{21/8} c^{3/8}}-\frac{65 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}+1\right)}{256 \sqrt{2} (-a)^{21/8} c^{3/8}}+\frac{65 \tan ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 (-a)^{21/8} c^{3/8}}-\frac{65 \tanh ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 (-a)^{21/8} c^{3/8}}+\frac{x^{3/2}}{8 a \left(a+c x^4\right)^2}",1,"x^(3/2)/(8*a*(a + c*x^4)^2) + (13*x^(3/2))/(64*a^2*(a + c*x^4)) + (65*ArcTan[1 - (Sqrt[2]*c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(256*Sqrt[2]*(-a)^(21/8)*c^(3/8)) - (65*ArcTan[1 + (Sqrt[2]*c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(256*Sqrt[2]*(-a)^(21/8)*c^(3/8)) + (65*ArcTan[(c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(256*(-a)^(21/8)*c^(3/8)) - (65*ArcTanh[(c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(256*(-a)^(21/8)*c^(3/8)) - (65*Log[(-a)^(1/4) - Sqrt[2]*(-a)^(1/8)*c^(1/8)*Sqrt[x] + c^(1/4)*x])/(512*Sqrt[2]*(-a)^(21/8)*c^(3/8)) + (65*Log[(-a)^(1/4) + Sqrt[2]*(-a)^(1/8)*c^(1/8)*Sqrt[x] + c^(1/4)*x])/(512*Sqrt[2]*(-a)^(21/8)*c^(3/8))","A",16,12,15,0.8000,1,"{290, 329, 300, 297, 1162, 617, 204, 1165, 628, 298, 205, 208}"
763,1,329,0,0.3025571,"\int \frac{1}{\sqrt{x} \left(a+c x^4\right)^3} \, dx","Int[1/(Sqrt[x]*(a + c*x^4)^3),x]","\frac{15 \sqrt{x}}{64 a^2 \left(a+c x^4\right)}+\frac{\sqrt{x}}{8 a \left(a+c x^4\right)^2}+\frac{105 \log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{512 \sqrt{2} (-a)^{23/8} \sqrt[8]{c}}-\frac{105 \log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{512 \sqrt{2} (-a)^{23/8} \sqrt[8]{c}}+\frac{105 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 \sqrt{2} (-a)^{23/8} \sqrt[8]{c}}-\frac{105 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}+1\right)}{256 \sqrt{2} (-a)^{23/8} \sqrt[8]{c}}-\frac{105 \tan ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 (-a)^{23/8} \sqrt[8]{c}}-\frac{105 \tanh ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 (-a)^{23/8} \sqrt[8]{c}}","\frac{15 \sqrt{x}}{64 a^2 \left(a+c x^4\right)}+\frac{\sqrt{x}}{8 a \left(a+c x^4\right)^2}+\frac{105 \log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{512 \sqrt{2} (-a)^{23/8} \sqrt[8]{c}}-\frac{105 \log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{c} \sqrt{x}+\sqrt[4]{-a}+\sqrt[4]{c} x\right)}{512 \sqrt{2} (-a)^{23/8} \sqrt[8]{c}}+\frac{105 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 \sqrt{2} (-a)^{23/8} \sqrt[8]{c}}-\frac{105 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}+1\right)}{256 \sqrt{2} (-a)^{23/8} \sqrt[8]{c}}-\frac{105 \tan ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 (-a)^{23/8} \sqrt[8]{c}}-\frac{105 \tanh ^{-1}\left(\frac{\sqrt[8]{c} \sqrt{x}}{\sqrt[8]{-a}}\right)}{256 (-a)^{23/8} \sqrt[8]{c}}",1,"Sqrt[x]/(8*a*(a + c*x^4)^2) + (15*Sqrt[x])/(64*a^2*(a + c*x^4)) + (105*ArcTan[1 - (Sqrt[2]*c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(256*Sqrt[2]*(-a)^(23/8)*c^(1/8)) - (105*ArcTan[1 + (Sqrt[2]*c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(256*Sqrt[2]*(-a)^(23/8)*c^(1/8)) - (105*ArcTan[(c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(256*(-a)^(23/8)*c^(1/8)) - (105*ArcTanh[(c^(1/8)*Sqrt[x])/(-a)^(1/8)])/(256*(-a)^(23/8)*c^(1/8)) + (105*Log[(-a)^(1/4) - Sqrt[2]*(-a)^(1/8)*c^(1/8)*Sqrt[x] + c^(1/4)*x])/(512*Sqrt[2]*(-a)^(23/8)*c^(1/8)) - (105*Log[(-a)^(1/4) + Sqrt[2]*(-a)^(1/8)*c^(1/8)*Sqrt[x] + c^(1/4)*x])/(512*Sqrt[2]*(-a)^(23/8)*c^(1/8))","A",16,12,15,0.8000,1,"{290, 329, 214, 212, 208, 205, 211, 1165, 628, 1162, 617, 204}"
764,1,59,0,0.0346376,"\int x^{11} \sqrt{a+c x^4} \, dx","Int[x^11*Sqrt[a + c*x^4],x]","\frac{a^2 \left(a+c x^4\right)^{3/2}}{6 c^3}+\frac{\left(a+c x^4\right)^{7/2}}{14 c^3}-\frac{a \left(a+c x^4\right)^{5/2}}{5 c^3}","\frac{a^2 \left(a+c x^4\right)^{3/2}}{6 c^3}+\frac{\left(a+c x^4\right)^{7/2}}{14 c^3}-\frac{a \left(a+c x^4\right)^{5/2}}{5 c^3}",1,"(a^2*(a + c*x^4)^(3/2))/(6*c^3) - (a*(a + c*x^4)^(5/2))/(5*c^3) + (a + c*x^4)^(7/2)/(14*c^3)","A",3,2,15,0.1333,1,"{266, 43}"
765,1,38,0,0.0227148,"\int x^7 \sqrt{a+c x^4} \, dx","Int[x^7*Sqrt[a + c*x^4],x]","\frac{\left(a+c x^4\right)^{5/2}}{10 c^2}-\frac{a \left(a+c x^4\right)^{3/2}}{6 c^2}","\frac{\left(a+c x^4\right)^{5/2}}{10 c^2}-\frac{a \left(a+c x^4\right)^{3/2}}{6 c^2}",1,"-(a*(a + c*x^4)^(3/2))/(6*c^2) + (a + c*x^4)^(5/2)/(10*c^2)","A",3,2,15,0.1333,1,"{266, 43}"
766,1,18,0,0.0044399,"\int x^3 \sqrt{a+c x^4} \, dx","Int[x^3*Sqrt[a + c*x^4],x]","\frac{\left(a+c x^4\right)^{3/2}}{6 c}","\frac{\left(a+c x^4\right)^{3/2}}{6 c}",1,"(a + c*x^4)^(3/2)/(6*c)","A",1,1,15,0.06667,1,"{261}"
767,1,43,0,0.0264348,"\int \frac{\sqrt{a+c x^4}}{x} \, dx","Int[Sqrt[a + c*x^4]/x,x]","\frac{1}{2} \sqrt{a+c x^4}-\frac{1}{2} \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+c x^4}}{\sqrt{a}}\right)","\frac{1}{2} \sqrt{a+c x^4}-\frac{1}{2} \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+c x^4}}{\sqrt{a}}\right)",1,"Sqrt[a + c*x^4]/2 - (Sqrt[a]*ArcTanh[Sqrt[a + c*x^4]/Sqrt[a]])/2","A",4,4,15,0.2667,1,"{266, 50, 63, 208}"
768,1,47,0,0.0263731,"\int \frac{\sqrt{a+c x^4}}{x^5} \, dx","Int[Sqrt[a + c*x^4]/x^5,x]","-\frac{\sqrt{a+c x^4}}{4 x^4}-\frac{c \tanh ^{-1}\left(\frac{\sqrt{a+c x^4}}{\sqrt{a}}\right)}{4 \sqrt{a}}","-\frac{\sqrt{a+c x^4}}{4 x^4}-\frac{c \tanh ^{-1}\left(\frac{\sqrt{a+c x^4}}{\sqrt{a}}\right)}{4 \sqrt{a}}",1,"-Sqrt[a + c*x^4]/(4*x^4) - (c*ArcTanh[Sqrt[a + c*x^4]/Sqrt[a]])/(4*Sqrt[a])","A",4,4,15,0.2667,1,"{266, 47, 63, 208}"
769,1,71,0,0.0392335,"\int \frac{\sqrt{a+c x^4}}{x^9} \, dx","Int[Sqrt[a + c*x^4]/x^9,x]","\frac{c^2 \tanh ^{-1}\left(\frac{\sqrt{a+c x^4}}{\sqrt{a}}\right)}{16 a^{3/2}}-\frac{c \sqrt{a+c x^4}}{16 a x^4}-\frac{\sqrt{a+c x^4}}{8 x^8}","\frac{c^2 \tanh ^{-1}\left(\frac{\sqrt{a+c x^4}}{\sqrt{a}}\right)}{16 a^{3/2}}-\frac{c \sqrt{a+c x^4}}{16 a x^4}-\frac{\sqrt{a+c x^4}}{8 x^8}",1,"-Sqrt[a + c*x^4]/(8*x^8) - (c*Sqrt[a + c*x^4])/(16*a*x^4) + (c^2*ArcTanh[Sqrt[a + c*x^4]/Sqrt[a]])/(16*a^(3/2))","A",5,5,15,0.3333,1,"{266, 47, 51, 63, 208}"
770,1,74,0,0.0461811,"\int x^5 \sqrt{a+c x^4} \, dx","Int[x^5*Sqrt[a + c*x^4],x]","-\frac{a^2 \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a+c x^4}}\right)}{16 c^{3/2}}+\frac{1}{8} x^6 \sqrt{a+c x^4}+\frac{a x^2 \sqrt{a+c x^4}}{16 c}","-\frac{a^2 \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a+c x^4}}\right)}{16 c^{3/2}}+\frac{1}{8} x^6 \sqrt{a+c x^4}+\frac{a x^2 \sqrt{a+c x^4}}{16 c}",1,"(a*x^2*Sqrt[a + c*x^4])/(16*c) + (x^6*Sqrt[a + c*x^4])/8 - (a^2*ArcTanh[(Sqrt[c]*x^2)/Sqrt[a + c*x^4]])/(16*c^(3/2))","A",5,5,15,0.3333,1,"{275, 279, 321, 217, 206}"
771,1,50,0,0.0248935,"\int x \sqrt{a+c x^4} \, dx","Int[x*Sqrt[a + c*x^4],x]","\frac{1}{4} x^2 \sqrt{a+c x^4}+\frac{a \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a+c x^4}}\right)}{4 \sqrt{c}}","\frac{1}{4} x^2 \sqrt{a+c x^4}+\frac{a \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a+c x^4}}\right)}{4 \sqrt{c}}",1,"(x^2*Sqrt[a + c*x^4])/4 + (a*ArcTanh[(Sqrt[c]*x^2)/Sqrt[a + c*x^4]])/(4*Sqrt[c])","A",4,4,13,0.3077,1,"{275, 195, 217, 206}"
772,1,49,0,0.0257567,"\int \frac{\sqrt{a+c x^4}}{x^3} \, dx","Int[Sqrt[a + c*x^4]/x^3,x]","\frac{1}{2} \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a+c x^4}}\right)-\frac{\sqrt{a+c x^4}}{2 x^2}","\frac{1}{2} \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a+c x^4}}\right)-\frac{\sqrt{a+c x^4}}{2 x^2}",1,"-Sqrt[a + c*x^4]/(2*x^2) + (Sqrt[c]*ArcTanh[(Sqrt[c]*x^2)/Sqrt[a + c*x^4]])/2","A",4,4,15,0.2667,1,"{275, 277, 217, 206}"
773,1,21,0,0.0042621,"\int \frac{\sqrt{a+c x^4}}{x^7} \, dx","Int[Sqrt[a + c*x^4]/x^7,x]","-\frac{\left(a+c x^4\right)^{3/2}}{6 a x^6}","-\frac{\left(a+c x^4\right)^{3/2}}{6 a x^6}",1,"-(a + c*x^4)^(3/2)/(6*a*x^6)","A",1,1,15,0.06667,1,"{264}"
774,1,44,0,0.0106655,"\int \frac{\sqrt{a+c x^4}}{x^{11}} \, dx","Int[Sqrt[a + c*x^4]/x^11,x]","\frac{c \left(a+c x^4\right)^{3/2}}{15 a^2 x^6}-\frac{\left(a+c x^4\right)^{3/2}}{10 a x^{10}}","\frac{c \left(a+c x^4\right)^{3/2}}{15 a^2 x^6}-\frac{\left(a+c x^4\right)^{3/2}}{10 a x^{10}}",1,"-(a + c*x^4)^(3/2)/(10*a*x^10) + (c*(a + c*x^4)^(3/2))/(15*a^2*x^6)","A",2,2,15,0.1333,1,"{271, 264}"
775,1,68,0,0.0185057,"\int \frac{\sqrt{a+c x^4}}{x^{15}} \, dx","Int[Sqrt[a + c*x^4]/x^15,x]","-\frac{4 c^2 \left(a+c x^4\right)^{3/2}}{105 a^3 x^6}+\frac{2 c \left(a+c x^4\right)^{3/2}}{35 a^2 x^{10}}-\frac{\left(a+c x^4\right)^{3/2}}{14 a x^{14}}","-\frac{4 c^2 \left(a+c x^4\right)^{3/2}}{105 a^3 x^6}+\frac{2 c \left(a+c x^4\right)^{3/2}}{35 a^2 x^{10}}-\frac{\left(a+c x^4\right)^{3/2}}{14 a x^{14}}",1,"-(a + c*x^4)^(3/2)/(14*a*x^14) + (2*c*(a + c*x^4)^(3/2))/(35*a^2*x^10) - (4*c^2*(a + c*x^4)^(3/2))/(105*a^3*x^6)","A",3,2,15,0.1333,1,"{271, 264}"
776,1,127,0,0.0410729,"\int x^4 \sqrt{a+c x^4} \, dx","Int[x^4*Sqrt[a + c*x^4],x]","-\frac{a^{7/4} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{21 c^{5/4} \sqrt{a+c x^4}}+\frac{1}{7} x^5 \sqrt{a+c x^4}+\frac{2 a x \sqrt{a+c x^4}}{21 c}","-\frac{a^{7/4} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{21 c^{5/4} \sqrt{a+c x^4}}+\frac{1}{7} x^5 \sqrt{a+c x^4}+\frac{2 a x \sqrt{a+c x^4}}{21 c}",1,"(2*a*x*Sqrt[a + c*x^4])/(21*c) + (x^5*Sqrt[a + c*x^4])/7 - (a^(7/4)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(21*c^(5/4)*Sqrt[a + c*x^4])","A",3,3,15,0.2000,1,"{279, 321, 220}"
777,1,105,0,0.0184156,"\int \sqrt{a+c x^4} \, dx","Int[Sqrt[a + c*x^4],x]","\frac{a^{3/4} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{3 \sqrt[4]{c} \sqrt{a+c x^4}}+\frac{1}{3} x \sqrt{a+c x^4}","\frac{a^{3/4} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{3 \sqrt[4]{c} \sqrt{a+c x^4}}+\frac{1}{3} x \sqrt{a+c x^4}",1,"(x*Sqrt[a + c*x^4])/3 + (a^(3/4)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(3*c^(1/4)*Sqrt[a + c*x^4])","A",2,2,11,0.1818,1,"{195, 220}"
778,1,107,0,0.0216233,"\int \frac{\sqrt{a+c x^4}}{x^4} \, dx","Int[Sqrt[a + c*x^4]/x^4,x]","\frac{c^{3/4} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{3 \sqrt[4]{a} \sqrt{a+c x^4}}-\frac{\sqrt{a+c x^4}}{3 x^3}","\frac{c^{3/4} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{3 \sqrt[4]{a} \sqrt{a+c x^4}}-\frac{\sqrt{a+c x^4}}{3 x^3}",1,"-Sqrt[a + c*x^4]/(3*x^3) + (c^(3/4)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(3*a^(1/4)*Sqrt[a + c*x^4])","A",2,2,15,0.1333,1,"{277, 220}"
779,1,129,0,0.0346284,"\int \frac{\sqrt{a+c x^4}}{x^8} \, dx","Int[Sqrt[a + c*x^4]/x^8,x]","-\frac{c^{7/4} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{21 a^{5/4} \sqrt{a+c x^4}}-\frac{2 c \sqrt{a+c x^4}}{21 a x^3}-\frac{\sqrt{a+c x^4}}{7 x^7}","-\frac{c^{7/4} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{21 a^{5/4} \sqrt{a+c x^4}}-\frac{2 c \sqrt{a+c x^4}}{21 a x^3}-\frac{\sqrt{a+c x^4}}{7 x^7}",1,"-Sqrt[a + c*x^4]/(7*x^7) - (2*c*Sqrt[a + c*x^4])/(21*a*x^3) - (c^(7/4)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(21*a^(5/4)*Sqrt[a + c*x^4])","A",3,3,15,0.2000,1,"{277, 325, 220}"
780,1,234,0,0.0721215,"\int x^2 \sqrt{a+c x^4} \, dx","Int[x^2*Sqrt[a + c*x^4],x]","\frac{a^{5/4} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 c^{3/4} \sqrt{a+c x^4}}-\frac{2 a^{5/4} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 c^{3/4} \sqrt{a+c x^4}}+\frac{1}{5} x^3 \sqrt{a+c x^4}+\frac{2 a x \sqrt{a+c x^4}}{5 \sqrt{c} \left(\sqrt{a}+\sqrt{c} x^2\right)}","\frac{a^{5/4} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 c^{3/4} \sqrt{a+c x^4}}-\frac{2 a^{5/4} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 c^{3/4} \sqrt{a+c x^4}}+\frac{1}{5} x^3 \sqrt{a+c x^4}+\frac{2 a x \sqrt{a+c x^4}}{5 \sqrt{c} \left(\sqrt{a}+\sqrt{c} x^2\right)}",1,"(x^3*Sqrt[a + c*x^4])/5 + (2*a*x*Sqrt[a + c*x^4])/(5*Sqrt[c]*(Sqrt[a] + Sqrt[c]*x^2)) - (2*a^(5/4)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(5*c^(3/4)*Sqrt[a + c*x^4]) + (a^(5/4)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(5*c^(3/4)*Sqrt[a + c*x^4])","A",4,4,15,0.2667,1,"{279, 305, 220, 1196}"
781,1,224,0,0.0662573,"\int \frac{\sqrt{a+c x^4}}{x^2} \, dx","Int[Sqrt[a + c*x^4]/x^2,x]","\frac{2 \sqrt{c} x \sqrt{a+c x^4}}{\sqrt{a}+\sqrt{c} x^2}-\frac{\sqrt{a+c x^4}}{x}+\frac{\sqrt[4]{a} \sqrt[4]{c} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{\sqrt{a+c x^4}}-\frac{2 \sqrt[4]{a} \sqrt[4]{c} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{\sqrt{a+c x^4}}","\frac{2 \sqrt{c} x \sqrt{a+c x^4}}{\sqrt{a}+\sqrt{c} x^2}-\frac{\sqrt{a+c x^4}}{x}+\frac{\sqrt[4]{a} \sqrt[4]{c} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{\sqrt{a+c x^4}}-\frac{2 \sqrt[4]{a} \sqrt[4]{c} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{\sqrt{a+c x^4}}",1,"-(Sqrt[a + c*x^4]/x) + (2*Sqrt[c]*x*Sqrt[a + c*x^4])/(Sqrt[a] + Sqrt[c]*x^2) - (2*a^(1/4)*c^(1/4)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/Sqrt[a + c*x^4] + (a^(1/4)*c^(1/4)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/Sqrt[a + c*x^4]","A",4,4,15,0.2667,1,"{277, 305, 220, 1196}"
782,1,258,0,0.0896084,"\int \frac{\sqrt{a+c x^4}}{x^6} \, dx","Int[Sqrt[a + c*x^4]/x^6,x]","\frac{c^{5/4} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 a^{3/4} \sqrt{a+c x^4}}-\frac{2 c^{5/4} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 a^{3/4} \sqrt{a+c x^4}}+\frac{2 c^{3/2} x \sqrt{a+c x^4}}{5 a \left(\sqrt{a}+\sqrt{c} x^2\right)}-\frac{2 c \sqrt{a+c x^4}}{5 a x}-\frac{\sqrt{a+c x^4}}{5 x^5}","\frac{c^{5/4} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 a^{3/4} \sqrt{a+c x^4}}-\frac{2 c^{5/4} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 a^{3/4} \sqrt{a+c x^4}}+\frac{2 c^{3/2} x \sqrt{a+c x^4}}{5 a \left(\sqrt{a}+\sqrt{c} x^2\right)}-\frac{2 c \sqrt{a+c x^4}}{5 a x}-\frac{\sqrt{a+c x^4}}{5 x^5}",1,"-Sqrt[a + c*x^4]/(5*x^5) - (2*c*Sqrt[a + c*x^4])/(5*a*x) + (2*c^(3/2)*x*Sqrt[a + c*x^4])/(5*a*(Sqrt[a] + Sqrt[c]*x^2)) - (2*c^(5/4)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(5*a^(3/4)*Sqrt[a + c*x^4]) + (c^(5/4)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(5*a^(3/4)*Sqrt[a + c*x^4])","A",5,5,15,0.3333,1,"{277, 325, 305, 220, 1196}"
783,1,59,0,0.0342912,"\int x^{11} \left(a+c x^4\right)^{3/2} \, dx","Int[x^11*(a + c*x^4)^(3/2),x]","\frac{a^2 \left(a+c x^4\right)^{5/2}}{10 c^3}+\frac{\left(a+c x^4\right)^{9/2}}{18 c^3}-\frac{a \left(a+c x^4\right)^{7/2}}{7 c^3}","\frac{a^2 \left(a+c x^4\right)^{5/2}}{10 c^3}+\frac{\left(a+c x^4\right)^{9/2}}{18 c^3}-\frac{a \left(a+c x^4\right)^{7/2}}{7 c^3}",1,"(a^2*(a + c*x^4)^(5/2))/(10*c^3) - (a*(a + c*x^4)^(7/2))/(7*c^3) + (a + c*x^4)^(9/2)/(18*c^3)","A",3,2,15,0.1333,1,"{266, 43}"
784,1,38,0,0.023506,"\int x^7 \left(a+c x^4\right)^{3/2} \, dx","Int[x^7*(a + c*x^4)^(3/2),x]","\frac{\left(a+c x^4\right)^{7/2}}{14 c^2}-\frac{a \left(a+c x^4\right)^{5/2}}{10 c^2}","\frac{\left(a+c x^4\right)^{7/2}}{14 c^2}-\frac{a \left(a+c x^4\right)^{5/2}}{10 c^2}",1,"-(a*(a + c*x^4)^(5/2))/(10*c^2) + (a + c*x^4)^(7/2)/(14*c^2)","A",3,2,15,0.1333,1,"{266, 43}"
785,1,18,0,0.0048617,"\int x^3 \left(a+c x^4\right)^{3/2} \, dx","Int[x^3*(a + c*x^4)^(3/2),x]","\frac{\left(a+c x^4\right)^{5/2}}{10 c}","\frac{\left(a+c x^4\right)^{5/2}}{10 c}",1,"(a + c*x^4)^(5/2)/(10*c)","A",1,1,15,0.06667,1,"{261}"
786,1,59,0,0.0347514,"\int \frac{\left(a+c x^4\right)^{3/2}}{x} \, dx","Int[(a + c*x^4)^(3/2)/x,x]","-\frac{1}{2} a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+c x^4}}{\sqrt{a}}\right)+\frac{1}{2} a \sqrt{a+c x^4}+\frac{1}{6} \left(a+c x^4\right)^{3/2}","-\frac{1}{2} a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+c x^4}}{\sqrt{a}}\right)+\frac{1}{2} a \sqrt{a+c x^4}+\frac{1}{6} \left(a+c x^4\right)^{3/2}",1,"(a*Sqrt[a + c*x^4])/2 + (a + c*x^4)^(3/2)/6 - (a^(3/2)*ArcTanh[Sqrt[a + c*x^4]/Sqrt[a]])/2","A",5,4,15,0.2667,1,"{266, 50, 63, 208}"
787,1,63,0,0.0377259,"\int \frac{\left(a+c x^4\right)^{3/2}}{x^5} \, dx","Int[(a + c*x^4)^(3/2)/x^5,x]","-\frac{\left(a+c x^4\right)^{3/2}}{4 x^4}+\frac{3}{4} c \sqrt{a+c x^4}-\frac{3}{4} \sqrt{a} c \tanh ^{-1}\left(\frac{\sqrt{a+c x^4}}{\sqrt{a}}\right)","-\frac{\left(a+c x^4\right)^{3/2}}{4 x^4}+\frac{3}{4} c \sqrt{a+c x^4}-\frac{3}{4} \sqrt{a} c \tanh ^{-1}\left(\frac{\sqrt{a+c x^4}}{\sqrt{a}}\right)",1,"(3*c*Sqrt[a + c*x^4])/4 - (a + c*x^4)^(3/2)/(4*x^4) - (3*Sqrt[a]*c*ArcTanh[Sqrt[a + c*x^4]/Sqrt[a]])/4","A",5,5,15,0.3333,1,"{266, 47, 50, 63, 208}"
788,1,68,0,0.0385098,"\int \frac{\left(a+c x^4\right)^{3/2}}{x^9} \, dx","Int[(a + c*x^4)^(3/2)/x^9,x]","-\frac{3 c^2 \tanh ^{-1}\left(\frac{\sqrt{a+c x^4}}{\sqrt{a}}\right)}{16 \sqrt{a}}-\frac{3 c \sqrt{a+c x^4}}{16 x^4}-\frac{\left(a+c x^4\right)^{3/2}}{8 x^8}","-\frac{3 c^2 \tanh ^{-1}\left(\frac{\sqrt{a+c x^4}}{\sqrt{a}}\right)}{16 \sqrt{a}}-\frac{3 c \sqrt{a+c x^4}}{16 x^4}-\frac{\left(a+c x^4\right)^{3/2}}{8 x^8}",1,"(-3*c*Sqrt[a + c*x^4])/(16*x^4) - (a + c*x^4)^(3/2)/(8*x^8) - (3*c^2*ArcTanh[Sqrt[a + c*x^4]/Sqrt[a]])/(16*Sqrt[a])","A",5,4,15,0.2667,1,"{266, 47, 63, 208}"
789,1,95,0,0.0591329,"\int x^5 \left(a+c x^4\right)^{3/2} \, dx","Int[x^5*(a + c*x^4)^(3/2),x]","-\frac{a^3 \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a+c x^4}}\right)}{32 c^{3/2}}+\frac{a^2 x^2 \sqrt{a+c x^4}}{32 c}+\frac{1}{12} x^6 \left(a+c x^4\right)^{3/2}+\frac{1}{16} a x^6 \sqrt{a+c x^4}","-\frac{a^3 \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a+c x^4}}\right)}{32 c^{3/2}}+\frac{a^2 x^2 \sqrt{a+c x^4}}{32 c}+\frac{1}{12} x^6 \left(a+c x^4\right)^{3/2}+\frac{1}{16} a x^6 \sqrt{a+c x^4}",1,"(a^2*x^2*Sqrt[a + c*x^4])/(32*c) + (a*x^6*Sqrt[a + c*x^4])/16 + (x^6*(a + c*x^4)^(3/2))/12 - (a^3*ArcTanh[(Sqrt[c]*x^2)/Sqrt[a + c*x^4]])/(32*c^(3/2))","A",6,5,15,0.3333,1,"{275, 279, 321, 217, 206}"
790,1,71,0,0.0359085,"\int x \left(a+c x^4\right)^{3/2} \, dx","Int[x*(a + c*x^4)^(3/2),x]","\frac{3 a^2 \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a+c x^4}}\right)}{16 \sqrt{c}}+\frac{3}{16} a x^2 \sqrt{a+c x^4}+\frac{1}{8} x^2 \left(a+c x^4\right)^{3/2}","\frac{3 a^2 \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a+c x^4}}\right)}{16 \sqrt{c}}+\frac{3}{16} a x^2 \sqrt{a+c x^4}+\frac{1}{8} x^2 \left(a+c x^4\right)^{3/2}",1,"(3*a*x^2*Sqrt[a + c*x^4])/16 + (x^2*(a + c*x^4)^(3/2))/8 + (3*a^2*ArcTanh[(Sqrt[c]*x^2)/Sqrt[a + c*x^4]])/(16*Sqrt[c])","A",5,4,13,0.3077,1,"{275, 195, 217, 206}"
791,1,69,0,0.0389532,"\int \frac{\left(a+c x^4\right)^{3/2}}{x^3} \, dx","Int[(a + c*x^4)^(3/2)/x^3,x]","\frac{3}{4} c x^2 \sqrt{a+c x^4}-\frac{\left(a+c x^4\right)^{3/2}}{2 x^2}+\frac{3}{4} a \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a+c x^4}}\right)","\frac{3}{4} c x^2 \sqrt{a+c x^4}-\frac{\left(a+c x^4\right)^{3/2}}{2 x^2}+\frac{3}{4} a \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a+c x^4}}\right)",1,"(3*c*x^2*Sqrt[a + c*x^4])/4 - (a + c*x^4)^(3/2)/(2*x^2) + (3*a*Sqrt[c]*ArcTanh[(Sqrt[c]*x^2)/Sqrt[a + c*x^4]])/4","A",5,5,15,0.3333,1,"{275, 277, 195, 217, 206}"
792,1,68,0,0.0410732,"\int \frac{\left(a+c x^4\right)^{3/2}}{x^7} \, dx","Int[(a + c*x^4)^(3/2)/x^7,x]","\frac{1}{2} c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a+c x^4}}\right)-\frac{c \sqrt{a+c x^4}}{2 x^2}-\frac{\left(a+c x^4\right)^{3/2}}{6 x^6}","\frac{1}{2} c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a+c x^4}}\right)-\frac{c \sqrt{a+c x^4}}{2 x^2}-\frac{\left(a+c x^4\right)^{3/2}}{6 x^6}",1,"-(c*Sqrt[a + c*x^4])/(2*x^2) - (a + c*x^4)^(3/2)/(6*x^6) + (c^(3/2)*ArcTanh[(Sqrt[c]*x^2)/Sqrt[a + c*x^4]])/2","A",5,4,15,0.2667,1,"{275, 277, 217, 206}"
793,1,21,0,0.0047694,"\int \frac{\left(a+c x^4\right)^{3/2}}{x^{11}} \, dx","Int[(a + c*x^4)^(3/2)/x^11,x]","-\frac{\left(a+c x^4\right)^{5/2}}{10 a x^{10}}","-\frac{\left(a+c x^4\right)^{5/2}}{10 a x^{10}}",1,"-(a + c*x^4)^(5/2)/(10*a*x^10)","A",1,1,15,0.06667,1,"{264}"
794,1,44,0,0.0107889,"\int \frac{\left(a+c x^4\right)^{3/2}}{x^{15}} \, dx","Int[(a + c*x^4)^(3/2)/x^15,x]","\frac{c \left(a+c x^4\right)^{5/2}}{35 a^2 x^{10}}-\frac{\left(a+c x^4\right)^{5/2}}{14 a x^{14}}","\frac{c \left(a+c x^4\right)^{5/2}}{35 a^2 x^{10}}-\frac{\left(a+c x^4\right)^{5/2}}{14 a x^{14}}",1,"-(a + c*x^4)^(5/2)/(14*a*x^14) + (c*(a + c*x^4)^(5/2))/(35*a^2*x^10)","A",2,2,15,0.1333,1,"{271, 264}"
795,1,68,0,0.0188366,"\int \frac{\left(a+c x^4\right)^{3/2}}{x^{19}} \, dx","Int[(a + c*x^4)^(3/2)/x^19,x]","-\frac{4 c^2 \left(a+c x^4\right)^{5/2}}{315 a^3 x^{10}}+\frac{2 c \left(a+c x^4\right)^{5/2}}{63 a^2 x^{14}}-\frac{\left(a+c x^4\right)^{5/2}}{18 a x^{18}}","-\frac{4 c^2 \left(a+c x^4\right)^{5/2}}{315 a^3 x^{10}}+\frac{2 c \left(a+c x^4\right)^{5/2}}{63 a^2 x^{14}}-\frac{\left(a+c x^4\right)^{5/2}}{18 a x^{18}}",1,"-(a + c*x^4)^(5/2)/(18*a*x^18) + (2*c*(a + c*x^4)^(5/2))/(63*a^2*x^14) - (4*c^2*(a + c*x^4)^(5/2))/(315*a^3*x^10)","A",3,2,15,0.1333,1,"{271, 264}"
796,1,148,0,0.0478541,"\int x^4 \left(a+c x^4\right)^{3/2} \, dx","Int[x^4*(a + c*x^4)^(3/2),x]","-\frac{2 a^{11/4} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{77 c^{5/4} \sqrt{a+c x^4}}+\frac{4 a^2 x \sqrt{a+c x^4}}{77 c}+\frac{1}{11} x^5 \left(a+c x^4\right)^{3/2}+\frac{6}{77} a x^5 \sqrt{a+c x^4}","-\frac{2 a^{11/4} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{77 c^{5/4} \sqrt{a+c x^4}}+\frac{4 a^2 x \sqrt{a+c x^4}}{77 c}+\frac{1}{11} x^5 \left(a+c x^4\right)^{3/2}+\frac{6}{77} a x^5 \sqrt{a+c x^4}",1,"(4*a^2*x*Sqrt[a + c*x^4])/(77*c) + (6*a*x^5*Sqrt[a + c*x^4])/77 + (x^5*(a + c*x^4)^(3/2))/11 - (2*a^(11/4)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(77*c^(5/4)*Sqrt[a + c*x^4])","A",4,3,15,0.2000,1,"{279, 321, 220}"
797,1,122,0,0.0275611,"\int \left(a+c x^4\right)^{3/2} \, dx","Int[(a + c*x^4)^(3/2),x]","\frac{2 a^{7/4} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{7 \sqrt[4]{c} \sqrt{a+c x^4}}+\frac{2}{7} a x \sqrt{a+c x^4}+\frac{1}{7} x \left(a+c x^4\right)^{3/2}","\frac{2 a^{7/4} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{7 \sqrt[4]{c} \sqrt{a+c x^4}}+\frac{2}{7} a x \sqrt{a+c x^4}+\frac{1}{7} x \left(a+c x^4\right)^{3/2}",1,"(2*a*x*Sqrt[a + c*x^4])/7 + (x*(a + c*x^4)^(3/2))/7 + (2*a^(7/4)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(7*c^(1/4)*Sqrt[a + c*x^4])","A",3,2,11,0.1818,1,"{195, 220}"
798,1,124,0,0.0300392,"\int \frac{\left(a+c x^4\right)^{3/2}}{x^4} \, dx","Int[(a + c*x^4)^(3/2)/x^4,x]","\frac{2 a^{3/4} c^{3/4} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{3 \sqrt{a+c x^4}}-\frac{\left(a+c x^4\right)^{3/2}}{3 x^3}+\frac{2}{3} c x \sqrt{a+c x^4}","\frac{2 a^{3/4} c^{3/4} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{3 \sqrt{a+c x^4}}-\frac{\left(a+c x^4\right)^{3/2}}{3 x^3}+\frac{2}{3} c x \sqrt{a+c x^4}",1,"(2*c*x*Sqrt[a + c*x^4])/3 - (a + c*x^4)^(3/2)/(3*x^3) + (2*a^(3/4)*c^(3/4)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(3*Sqrt[a + c*x^4])","A",3,3,15,0.2000,1,"{277, 195, 220}"
799,1,126,0,0.0322656,"\int \frac{\left(a+c x^4\right)^{3/2}}{x^8} \, dx","Int[(a + c*x^4)^(3/2)/x^8,x]","\frac{2 c^{7/4} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{7 \sqrt[4]{a} \sqrt{a+c x^4}}-\frac{2 c \sqrt{a+c x^4}}{7 x^3}-\frac{\left(a+c x^4\right)^{3/2}}{7 x^7}","\frac{2 c^{7/4} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{7 \sqrt[4]{a} \sqrt{a+c x^4}}-\frac{2 c \sqrt{a+c x^4}}{7 x^3}-\frac{\left(a+c x^4\right)^{3/2}}{7 x^7}",1,"(-2*c*Sqrt[a + c*x^4])/(7*x^3) - (a + c*x^4)^(3/2)/(7*x^7) + (2*c^(7/4)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(7*a^(1/4)*Sqrt[a + c*x^4])","A",3,2,15,0.1333,1,"{277, 220}"
800,1,255,0,0.0861974,"\int x^2 \left(a+c x^4\right)^{3/2} \, dx","Int[x^2*(a + c*x^4)^(3/2),x]","\frac{2 a^{9/4} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 c^{3/4} \sqrt{a+c x^4}}-\frac{4 a^{9/4} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 c^{3/4} \sqrt{a+c x^4}}+\frac{4 a^2 x \sqrt{a+c x^4}}{15 \sqrt{c} \left(\sqrt{a}+\sqrt{c} x^2\right)}+\frac{1}{9} x^3 \left(a+c x^4\right)^{3/2}+\frac{2}{15} a x^3 \sqrt{a+c x^4}","\frac{2 a^{9/4} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 c^{3/4} \sqrt{a+c x^4}}-\frac{4 a^{9/4} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 c^{3/4} \sqrt{a+c x^4}}+\frac{4 a^2 x \sqrt{a+c x^4}}{15 \sqrt{c} \left(\sqrt{a}+\sqrt{c} x^2\right)}+\frac{1}{9} x^3 \left(a+c x^4\right)^{3/2}+\frac{2}{15} a x^3 \sqrt{a+c x^4}",1,"(2*a*x^3*Sqrt[a + c*x^4])/15 + (4*a^2*x*Sqrt[a + c*x^4])/(15*Sqrt[c]*(Sqrt[a] + Sqrt[c]*x^2)) + (x^3*(a + c*x^4)^(3/2))/9 - (4*a^(9/4)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(15*c^(3/4)*Sqrt[a + c*x^4]) + (2*a^(9/4)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(15*c^(3/4)*Sqrt[a + c*x^4])","A",5,4,15,0.2667,1,"{279, 305, 220, 1196}"
801,1,251,0,0.0879687,"\int \frac{\left(a+c x^4\right)^{3/2}}{x^2} \, dx","Int[(a + c*x^4)^(3/2)/x^2,x]","\frac{6 a^{5/4} \sqrt[4]{c} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 \sqrt{a+c x^4}}-\frac{12 a^{5/4} \sqrt[4]{c} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 \sqrt{a+c x^4}}+\frac{6}{5} c x^3 \sqrt{a+c x^4}+\frac{12 a \sqrt{c} x \sqrt{a+c x^4}}{5 \left(\sqrt{a}+\sqrt{c} x^2\right)}-\frac{\left(a+c x^4\right)^{3/2}}{x}","\frac{6 a^{5/4} \sqrt[4]{c} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 \sqrt{a+c x^4}}-\frac{12 a^{5/4} \sqrt[4]{c} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 \sqrt{a+c x^4}}+\frac{6}{5} c x^3 \sqrt{a+c x^4}+\frac{12 a \sqrt{c} x \sqrt{a+c x^4}}{5 \left(\sqrt{a}+\sqrt{c} x^2\right)}-\frac{\left(a+c x^4\right)^{3/2}}{x}",1,"(6*c*x^3*Sqrt[a + c*x^4])/5 + (12*a*Sqrt[c]*x*Sqrt[a + c*x^4])/(5*(Sqrt[a] + Sqrt[c]*x^2)) - (a + c*x^4)^(3/2)/x - (12*a^(5/4)*c^(1/4)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(5*Sqrt[a + c*x^4]) + (6*a^(5/4)*c^(1/4)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(5*Sqrt[a + c*x^4])","A",5,5,15,0.3333,1,"{277, 279, 305, 220, 1196}"
802,1,252,0,0.0855572,"\int \frac{\left(a+c x^4\right)^{3/2}}{x^6} \, dx","Int[(a + c*x^4)^(3/2)/x^6,x]","\frac{12 c^{3/2} x \sqrt{a+c x^4}}{5 \left(\sqrt{a}+\sqrt{c} x^2\right)}+\frac{6 \sqrt[4]{a} c^{5/4} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 \sqrt{a+c x^4}}-\frac{12 \sqrt[4]{a} c^{5/4} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 \sqrt{a+c x^4}}-\frac{6 c \sqrt{a+c x^4}}{5 x}-\frac{\left(a+c x^4\right)^{3/2}}{5 x^5}","\frac{12 c^{3/2} x \sqrt{a+c x^4}}{5 \left(\sqrt{a}+\sqrt{c} x^2\right)}+\frac{6 \sqrt[4]{a} c^{5/4} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 \sqrt{a+c x^4}}-\frac{12 \sqrt[4]{a} c^{5/4} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 \sqrt{a+c x^4}}-\frac{6 c \sqrt{a+c x^4}}{5 x}-\frac{\left(a+c x^4\right)^{3/2}}{5 x^5}",1,"(-6*c*Sqrt[a + c*x^4])/(5*x) + (12*c^(3/2)*x*Sqrt[a + c*x^4])/(5*(Sqrt[a] + Sqrt[c]*x^2)) - (a + c*x^4)^(3/2)/(5*x^5) - (12*a^(1/4)*c^(5/4)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(5*Sqrt[a + c*x^4]) + (6*a^(1/4)*c^(5/4)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(5*Sqrt[a + c*x^4])","A",5,4,15,0.2667,1,"{277, 305, 220, 1196}"
803,1,72,0,0.0107769,"\int \left(1+x^4\right)^{3/2} \, dx","Int[(1 + x^4)^(3/2),x]","\frac{1}{7} x \left(x^4+1\right)^{3/2}+\frac{2}{7} x \sqrt{x^4+1}+\frac{2 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{7 \sqrt{x^4+1}}","\frac{1}{7} x \left(x^4+1\right)^{3/2}+\frac{2}{7} x \sqrt{x^4+1}+\frac{2 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{7 \sqrt{x^4+1}}",1,"(2*x*Sqrt[1 + x^4])/7 + (x*(1 + x^4)^(3/2))/7 + (2*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(7*Sqrt[1 + x^4])","A",3,2,9,0.2222,1,"{195, 220}"
804,1,41,0,0.0057027,"\int \left(1-x^4\right)^{3/2} \, dx","Int[(1 - x^4)^(3/2),x]","\frac{1}{7} x \left(1-x^4\right)^{3/2}+\frac{2}{7} x \sqrt{1-x^4}+\frac{4}{7} F\left(\left.\sin ^{-1}(x)\right|-1\right)","\frac{1}{7} x \left(1-x^4\right)^{3/2}+\frac{2}{7} x \sqrt{1-x^4}+\frac{4}{7} F\left(\left.\sin ^{-1}(x)\right|-1\right)",1,"(2*x*Sqrt[1 - x^4])/7 + (x*(1 - x^4)^(3/2))/7 + (4*EllipticF[ArcSin[x], -1])/7","A",3,2,11,0.1818,1,"{195, 221}"
805,1,31,0,0.0148999,"\int x^7 \sqrt{5+3 x^4} \, dx","Int[x^7*Sqrt[5 + 3*x^4],x]","\frac{1}{90} \left(3 x^4+5\right)^{5/2}-\frac{5}{54} \left(3 x^4+5\right)^{3/2}","\frac{1}{90} \left(3 x^4+5\right)^{5/2}-\frac{5}{54} \left(3 x^4+5\right)^{3/2}",1,"(-5*(5 + 3*x^4)^(3/2))/54 + (5 + 3*x^4)^(5/2)/90","A",3,2,15,0.1333,1,"{266, 43}"
806,1,13,0,0.0023835,"\int x^3 \sqrt{5+x^4} \, dx","Int[x^3*Sqrt[5 + x^4],x]","\frac{1}{6} \left(x^4+5\right)^{3/2}","\frac{1}{6} \left(x^4+5\right)^{3/2}",1,"(5 + x^4)^(3/2)/6","A",1,1,13,0.07692,1,"{261}"
807,1,40,0,0.0138261,"\int x \sqrt{3+2 x^4} \, dx","Int[x*Sqrt[3 + 2*x^4],x]","\frac{1}{4} \sqrt{2 x^4+3} x^2+\frac{3 \sinh ^{-1}\left(\sqrt{\frac{2}{3}} x^2\right)}{4 \sqrt{2}}","\frac{1}{4} \sqrt{2 x^4+3} x^2+\frac{3 \sinh ^{-1}\left(\sqrt{\frac{2}{3}} x^2\right)}{4 \sqrt{2}}",1,"(x^2*Sqrt[3 + 2*x^4])/4 + (3*ArcSinh[Sqrt[2/3]*x^2])/(4*Sqrt[2])","A",3,3,13,0.2308,1,"{275, 195, 215}"
808,1,35,0,0.0107706,"\int x \sqrt{-2+x^4} \, dx","Int[x*Sqrt[-2 + x^4],x]","\frac{1}{4} x^2 \sqrt{x^4-2}-\frac{1}{2} \tanh ^{-1}\left(\frac{x^2}{\sqrt{x^4-2}}\right)","\frac{1}{4} x^2 \sqrt{x^4-2}-\frac{1}{2} \tanh ^{-1}\left(\frac{x^2}{\sqrt{x^4-2}}\right)",1,"(x^2*Sqrt[-2 + x^4])/4 - ArcTanh[x^2/Sqrt[-2 + x^4]]/2","A",4,4,11,0.3636,1,"{275, 195, 217, 206}"
809,1,58,0,0.0073908,"\int \sqrt{1+x^4} \, dx","Int[Sqrt[1 + x^4],x]","\frac{1}{3} \sqrt{x^4+1} x+\frac{\left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{3 \sqrt{x^4+1}}","\frac{1}{3} \sqrt{x^4+1} x+\frac{\left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{3 \sqrt{x^4+1}}",1,"(x*Sqrt[1 + x^4])/3 + ((1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(3*Sqrt[1 + x^4])","A",2,2,9,0.2222,1,"{195, 220}"
810,1,25,0,0.0030338,"\int \sqrt{1-x^4} \, dx","Int[Sqrt[1 - x^4],x]","\frac{1}{3} \sqrt{1-x^4} x+\frac{2}{3} F\left(\left.\sin ^{-1}(x)\right|-1\right)","\frac{1}{3} \sqrt{1-x^4} x+\frac{2}{3} F\left(\left.\sin ^{-1}(x)\right|-1\right)",1,"(x*Sqrt[1 - x^4])/3 + (2*EllipticF[ArcSin[x], -1])/3","A",2,2,11,0.1818,1,"{195, 221}"
811,1,59,0,0.0327336,"\int \frac{x^{11}}{\sqrt{a+b x^4}} \, dx","Int[x^11/Sqrt[a + b*x^4],x]","\frac{a^2 \sqrt{a+b x^4}}{2 b^3}+\frac{\left(a+b x^4\right)^{5/2}}{10 b^3}-\frac{a \left(a+b x^4\right)^{3/2}}{3 b^3}","\frac{a^2 \sqrt{a+b x^4}}{2 b^3}+\frac{\left(a+b x^4\right)^{5/2}}{10 b^3}-\frac{a \left(a+b x^4\right)^{3/2}}{3 b^3}",1,"(a^2*Sqrt[a + b*x^4])/(2*b^3) - (a*(a + b*x^4)^(3/2))/(3*b^3) + (a + b*x^4)^(5/2)/(10*b^3)","A",3,2,15,0.1333,1,"{266, 43}"
812,1,38,0,0.0221903,"\int \frac{x^7}{\sqrt{a+b x^4}} \, dx","Int[x^7/Sqrt[a + b*x^4],x]","\frac{\left(a+b x^4\right)^{3/2}}{6 b^2}-\frac{a \sqrt{a+b x^4}}{2 b^2}","\frac{\left(a+b x^4\right)^{3/2}}{6 b^2}-\frac{a \sqrt{a+b x^4}}{2 b^2}",1,"-(a*Sqrt[a + b*x^4])/(2*b^2) + (a + b*x^4)^(3/2)/(6*b^2)","A",3,2,15,0.1333,1,"{266, 43}"
813,1,18,0,0.0044366,"\int \frac{x^3}{\sqrt{a+b x^4}} \, dx","Int[x^3/Sqrt[a + b*x^4],x]","\frac{\sqrt{a+b x^4}}{2 b}","\frac{\sqrt{a+b x^4}}{2 b}",1,"Sqrt[a + b*x^4]/(2*b)","A",1,1,15,0.06667,1,"{261}"
814,1,27,0,0.0167404,"\int \frac{1}{x \sqrt{a+b x^4}} \, dx","Int[1/(x*Sqrt[a + b*x^4]),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)}{2 \sqrt{a}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)}{2 \sqrt{a}}",1,"-ArcTanh[Sqrt[a + b*x^4]/Sqrt[a]]/(2*Sqrt[a])","A",3,3,15,0.2000,1,"{266, 63, 208}"
815,1,50,0,0.0259341,"\int \frac{1}{x^5 \sqrt{a+b x^4}} \, dx","Int[1/(x^5*Sqrt[a + b*x^4]),x]","\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)}{4 a^{3/2}}-\frac{\sqrt{a+b x^4}}{4 a x^4}","\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)}{4 a^{3/2}}-\frac{\sqrt{a+b x^4}}{4 a x^4}",1,"-Sqrt[a + b*x^4]/(4*a*x^4) + (b*ArcTanh[Sqrt[a + b*x^4]/Sqrt[a]])/(4*a^(3/2))","A",4,4,15,0.2667,1,"{266, 51, 63, 208}"
816,1,53,0,0.0280935,"\int \frac{x^5}{\sqrt{a+b x^4}} \, dx","Int[x^5/Sqrt[a + b*x^4],x]","\frac{x^2 \sqrt{a+b x^4}}{4 b}-\frac{a \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{4 b^{3/2}}","\frac{x^2 \sqrt{a+b x^4}}{4 b}-\frac{a \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{4 b^{3/2}}",1,"(x^2*Sqrt[a + b*x^4])/(4*b) - (a*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a + b*x^4]])/(4*b^(3/2))","A",4,4,15,0.2667,1,"{275, 321, 217, 206}"
817,1,30,0,0.0147117,"\int \frac{x}{\sqrt{a+b x^4}} \, dx","Int[x/Sqrt[a + b*x^4],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{2 \sqrt{b}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{2 \sqrt{b}}",1,"ArcTanh[(Sqrt[b]*x^2)/Sqrt[a + b*x^4]]/(2*Sqrt[b])","A",3,3,13,0.2308,1,"{275, 217, 206}"
818,1,21,0,0.0042104,"\int \frac{1}{x^3 \sqrt{a+b x^4}} \, dx","Int[1/(x^3*Sqrt[a + b*x^4]),x]","-\frac{\sqrt{a+b x^4}}{2 a x^2}","-\frac{\sqrt{a+b x^4}}{2 a x^2}",1,"-Sqrt[a + b*x^4]/(2*a*x^2)","A",1,1,15,0.06667,1,"{264}"
819,1,44,0,0.0101492,"\int \frac{1}{x^7 \sqrt{a+b x^4}} \, dx","Int[1/(x^7*Sqrt[a + b*x^4]),x]","\frac{b \sqrt{a+b x^4}}{3 a^2 x^2}-\frac{\sqrt{a+b x^4}}{6 a x^6}","\frac{b \sqrt{a+b x^4}}{3 a^2 x^2}-\frac{\sqrt{a+b x^4}}{6 a x^6}",1,"-Sqrt[a + b*x^4]/(6*a*x^6) + (b*Sqrt[a + b*x^4])/(3*a^2*x^2)","A",2,2,15,0.1333,1,"{271, 264}"
820,1,68,0,0.0190767,"\int \frac{1}{x^{11} \sqrt{a+b x^4}} \, dx","Int[1/(x^11*Sqrt[a + b*x^4]),x]","-\frac{4 b^2 \sqrt{a+b x^4}}{15 a^3 x^2}+\frac{2 b \sqrt{a+b x^4}}{15 a^2 x^6}-\frac{\sqrt{a+b x^4}}{10 a x^{10}}","-\frac{4 b^2 \sqrt{a+b x^4}}{15 a^3 x^2}+\frac{2 b \sqrt{a+b x^4}}{15 a^2 x^6}-\frac{\sqrt{a+b x^4}}{10 a x^{10}}",1,"-Sqrt[a + b*x^4]/(10*a*x^10) + (2*b*Sqrt[a + b*x^4])/(15*a^2*x^6) - (4*b^2*Sqrt[a + b*x^4])/(15*a^3*x^2)","A",3,2,15,0.1333,1,"{271, 264}"
821,1,130,0,0.0411811,"\int \frac{x^8}{\sqrt{a+b x^4}} \, dx","Int[x^8/Sqrt[a + b*x^4],x]","\frac{5 a^{7/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{42 b^{9/4} \sqrt{a+b x^4}}-\frac{5 a x \sqrt{a+b x^4}}{21 b^2}+\frac{x^5 \sqrt{a+b x^4}}{7 b}","\frac{5 a^{7/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{42 b^{9/4} \sqrt{a+b x^4}}-\frac{5 a x \sqrt{a+b x^4}}{21 b^2}+\frac{x^5 \sqrt{a+b x^4}}{7 b}",1,"(-5*a*x*Sqrt[a + b*x^4])/(21*b^2) + (x^5*Sqrt[a + b*x^4])/(7*b) + (5*a^(7/4)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(42*b^(9/4)*Sqrt[a + b*x^4])","A",3,2,15,0.1333,1,"{321, 220}"
822,1,108,0,0.0207992,"\int \frac{x^4}{\sqrt{a+b x^4}} \, dx","Int[x^4/Sqrt[a + b*x^4],x]","\frac{x \sqrt{a+b x^4}}{3 b}-\frac{a^{3/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{6 b^{5/4} \sqrt{a+b x^4}}","\frac{x \sqrt{a+b x^4}}{3 b}-\frac{a^{3/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{6 b^{5/4} \sqrt{a+b x^4}}",1,"(x*Sqrt[a + b*x^4])/(3*b) - (a^(3/4)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(6*b^(5/4)*Sqrt[a + b*x^4])","A",2,2,15,0.1333,1,"{321, 220}"
823,1,88,0,0.009741,"\int \frac{1}{\sqrt{a+b x^4}} \, dx","Int[1/Sqrt[a + b*x^4],x]","\frac{\left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a} \sqrt[4]{b} \sqrt{a+b x^4}}","\frac{\left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a} \sqrt[4]{b} \sqrt{a+b x^4}}",1,"((Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(2*a^(1/4)*b^(1/4)*Sqrt[a + b*x^4])","A",1,1,11,0.09091,1,"{220}"
824,1,110,0,0.0251748,"\int \frac{1}{x^4 \sqrt{a+b x^4}} \, dx","Int[1/(x^4*Sqrt[a + b*x^4]),x]","-\frac{b^{3/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{6 a^{5/4} \sqrt{a+b x^4}}-\frac{\sqrt{a+b x^4}}{3 a x^3}","-\frac{b^{3/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{6 a^{5/4} \sqrt{a+b x^4}}-\frac{\sqrt{a+b x^4}}{3 a x^3}",1,"-Sqrt[a + b*x^4]/(3*a*x^3) - (b^(3/4)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(6*a^(5/4)*Sqrt[a + b*x^4])","A",2,2,15,0.1333,1,"{325, 220}"
825,1,132,0,0.0360192,"\int \frac{1}{x^8 \sqrt{a+b x^4}} \, dx","Int[1/(x^8*Sqrt[a + b*x^4]),x]","\frac{5 b^{7/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{42 a^{9/4} \sqrt{a+b x^4}}+\frac{5 b \sqrt{a+b x^4}}{21 a^2 x^3}-\frac{\sqrt{a+b x^4}}{7 a x^7}","\frac{5 b^{7/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{42 a^{9/4} \sqrt{a+b x^4}}+\frac{5 b \sqrt{a+b x^4}}{21 a^2 x^3}-\frac{\sqrt{a+b x^4}}{7 a x^7}",1,"-Sqrt[a + b*x^4]/(7*a*x^7) + (5*b*Sqrt[a + b*x^4])/(21*a^2*x^3) + (5*b^(7/4)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(42*a^(9/4)*Sqrt[a + b*x^4])","A",3,2,15,0.1333,1,"{325, 220}"
826,1,261,0,0.0918937,"\int \frac{x^{10}}{\sqrt{a+b x^4}} \, dx","Int[x^10/Sqrt[a + b*x^4],x]","\frac{7 a^2 x \sqrt{a+b x^4}}{15 b^{5/2} \left(\sqrt{a}+\sqrt{b} x^2\right)}+\frac{7 a^{9/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{30 b^{11/4} \sqrt{a+b x^4}}-\frac{7 a^{9/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 b^{11/4} \sqrt{a+b x^4}}-\frac{7 a x^3 \sqrt{a+b x^4}}{45 b^2}+\frac{x^7 \sqrt{a+b x^4}}{9 b}","\frac{7 a^2 x \sqrt{a+b x^4}}{15 b^{5/2} \left(\sqrt{a}+\sqrt{b} x^2\right)}+\frac{7 a^{9/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{30 b^{11/4} \sqrt{a+b x^4}}-\frac{7 a^{9/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 b^{11/4} \sqrt{a+b x^4}}-\frac{7 a x^3 \sqrt{a+b x^4}}{45 b^2}+\frac{x^7 \sqrt{a+b x^4}}{9 b}",1,"(-7*a*x^3*Sqrt[a + b*x^4])/(45*b^2) + (x^7*Sqrt[a + b*x^4])/(9*b) + (7*a^2*x*Sqrt[a + b*x^4])/(15*b^(5/2)*(Sqrt[a] + Sqrt[b]*x^2)) - (7*a^(9/4)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(15*b^(11/4)*Sqrt[a + b*x^4]) + (7*a^(9/4)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(30*b^(11/4)*Sqrt[a + b*x^4])","A",5,4,15,0.2667,1,"{321, 305, 220, 1196}"
827,1,237,0,0.0666207,"\int \frac{x^6}{\sqrt{a+b x^4}} \, dx","Int[x^6/Sqrt[a + b*x^4],x]","-\frac{3 a^{5/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{10 b^{7/4} \sqrt{a+b x^4}}+\frac{3 a^{5/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 b^{7/4} \sqrt{a+b x^4}}-\frac{3 a x \sqrt{a+b x^4}}{5 b^{3/2} \left(\sqrt{a}+\sqrt{b} x^2\right)}+\frac{x^3 \sqrt{a+b x^4}}{5 b}","-\frac{3 a^{5/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{10 b^{7/4} \sqrt{a+b x^4}}+\frac{3 a^{5/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 b^{7/4} \sqrt{a+b x^4}}-\frac{3 a x \sqrt{a+b x^4}}{5 b^{3/2} \left(\sqrt{a}+\sqrt{b} x^2\right)}+\frac{x^3 \sqrt{a+b x^4}}{5 b}",1,"(x^3*Sqrt[a + b*x^4])/(5*b) - (3*a*x*Sqrt[a + b*x^4])/(5*b^(3/2)*(Sqrt[a] + Sqrt[b]*x^2)) + (3*a^(5/4)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(5*b^(7/4)*Sqrt[a + b*x^4]) - (3*a^(5/4)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(10*b^(7/4)*Sqrt[a + b*x^4])","A",4,4,15,0.2667,1,"{321, 305, 220, 1196}"
828,1,210,0,0.0463466,"\int \frac{x^2}{\sqrt{a+b x^4}} \, dx","Int[x^2/Sqrt[a + b*x^4],x]","\frac{\sqrt[4]{a} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 b^{3/4} \sqrt{a+b x^4}}-\frac{\sqrt[4]{a} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{b^{3/4} \sqrt{a+b x^4}}+\frac{x \sqrt{a+b x^4}}{\sqrt{b} \left(\sqrt{a}+\sqrt{b} x^2\right)}","\frac{\sqrt[4]{a} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 b^{3/4} \sqrt{a+b x^4}}-\frac{\sqrt[4]{a} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{b^{3/4} \sqrt{a+b x^4}}+\frac{x \sqrt{a+b x^4}}{\sqrt{b} \left(\sqrt{a}+\sqrt{b} x^2\right)}",1,"(x*Sqrt[a + b*x^4])/(Sqrt[b]*(Sqrt[a] + Sqrt[b]*x^2)) - (a^(1/4)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(b^(3/4)*Sqrt[a + b*x^4]) + (a^(1/4)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(2*b^(3/4)*Sqrt[a + b*x^4])","A",3,3,15,0.2000,1,"{305, 220, 1196}"
829,1,232,0,0.0666828,"\int \frac{1}{x^2 \sqrt{a+b x^4}} \, dx","Int[1/(x^2*Sqrt[a + b*x^4]),x]","\frac{\sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{3/4} \sqrt{a+b x^4}}-\frac{\sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{a^{3/4} \sqrt{a+b x^4}}+\frac{\sqrt{b} x \sqrt{a+b x^4}}{a \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{\sqrt{a+b x^4}}{a x}","\frac{\sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{3/4} \sqrt{a+b x^4}}-\frac{\sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{a^{3/4} \sqrt{a+b x^4}}+\frac{\sqrt{b} x \sqrt{a+b x^4}}{a \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{\sqrt{a+b x^4}}{a x}",1,"-(Sqrt[a + b*x^4]/(a*x)) + (Sqrt[b]*x*Sqrt[a + b*x^4])/(a*(Sqrt[a] + Sqrt[b]*x^2)) - (b^(1/4)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(a^(3/4)*Sqrt[a + b*x^4]) + (b^(1/4)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(2*a^(3/4)*Sqrt[a + b*x^4])","A",4,4,15,0.2667,1,"{325, 305, 220, 1196}"
830,1,261,0,0.0921261,"\int \frac{1}{x^6 \sqrt{a+b x^4}} \, dx","Int[1/(x^6*Sqrt[a + b*x^4]),x]","-\frac{3 b^{3/2} x \sqrt{a+b x^4}}{5 a^2 \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{3 b^{5/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{10 a^{7/4} \sqrt{a+b x^4}}+\frac{3 b^{5/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 a^{7/4} \sqrt{a+b x^4}}+\frac{3 b \sqrt{a+b x^4}}{5 a^2 x}-\frac{\sqrt{a+b x^4}}{5 a x^5}","-\frac{3 b^{3/2} x \sqrt{a+b x^4}}{5 a^2 \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{3 b^{5/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{10 a^{7/4} \sqrt{a+b x^4}}+\frac{3 b^{5/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 a^{7/4} \sqrt{a+b x^4}}+\frac{3 b \sqrt{a+b x^4}}{5 a^2 x}-\frac{\sqrt{a+b x^4}}{5 a x^5}",1,"-Sqrt[a + b*x^4]/(5*a*x^5) + (3*b*Sqrt[a + b*x^4])/(5*a^2*x) - (3*b^(3/2)*x*Sqrt[a + b*x^4])/(5*a^2*(Sqrt[a] + Sqrt[b]*x^2)) + (3*b^(5/4)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(5*a^(7/4)*Sqrt[a + b*x^4]) - (3*b^(5/4)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(10*a^(7/4)*Sqrt[a + b*x^4])","A",5,4,15,0.2667,1,"{325, 305, 220, 1196}"
831,1,62,0,0.0351539,"\int \frac{x^{11}}{\sqrt{a-b x^4}} \, dx","Int[x^11/Sqrt[a - b*x^4],x]","-\frac{a^2 \sqrt{a-b x^4}}{2 b^3}-\frac{\left(a-b x^4\right)^{5/2}}{10 b^3}+\frac{a \left(a-b x^4\right)^{3/2}}{3 b^3}","-\frac{a^2 \sqrt{a-b x^4}}{2 b^3}-\frac{\left(a-b x^4\right)^{5/2}}{10 b^3}+\frac{a \left(a-b x^4\right)^{3/2}}{3 b^3}",1,"-(a^2*Sqrt[a - b*x^4])/(2*b^3) + (a*(a - b*x^4)^(3/2))/(3*b^3) - (a - b*x^4)^(5/2)/(10*b^3)","A",3,2,16,0.1250,1,"{266, 43}"
832,1,40,0,0.0236956,"\int \frac{x^7}{\sqrt{a-b x^4}} \, dx","Int[x^7/Sqrt[a - b*x^4],x]","\frac{\left(a-b x^4\right)^{3/2}}{6 b^2}-\frac{a \sqrt{a-b x^4}}{2 b^2}","\frac{\left(a-b x^4\right)^{3/2}}{6 b^2}-\frac{a \sqrt{a-b x^4}}{2 b^2}",1,"-(a*Sqrt[a - b*x^4])/(2*b^2) + (a - b*x^4)^(3/2)/(6*b^2)","A",3,2,16,0.1250,1,"{266, 43}"
833,1,19,0,0.0043524,"\int \frac{x^3}{\sqrt{a-b x^4}} \, dx","Int[x^3/Sqrt[a - b*x^4],x]","-\frac{\sqrt{a-b x^4}}{2 b}","-\frac{\sqrt{a-b x^4}}{2 b}",1,"-Sqrt[a - b*x^4]/(2*b)","A",1,1,16,0.06250,1,"{261}"
834,1,28,0,0.0180761,"\int \frac{1}{x \sqrt{a-b x^4}} \, dx","Int[1/(x*Sqrt[a - b*x^4]),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a-b x^4}}{\sqrt{a}}\right)}{2 \sqrt{a}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a-b x^4}}{\sqrt{a}}\right)}{2 \sqrt{a}}",1,"-ArcTanh[Sqrt[a - b*x^4]/Sqrt[a]]/(2*Sqrt[a])","A",3,3,16,0.1875,1,"{266, 63, 208}"
835,1,52,0,0.0283322,"\int \frac{1}{x^5 \sqrt{a-b x^4}} \, dx","Int[1/(x^5*Sqrt[a - b*x^4]),x]","-\frac{b \tanh ^{-1}\left(\frac{\sqrt{a-b x^4}}{\sqrt{a}}\right)}{4 a^{3/2}}-\frac{\sqrt{a-b x^4}}{4 a x^4}","-\frac{b \tanh ^{-1}\left(\frac{\sqrt{a-b x^4}}{\sqrt{a}}\right)}{4 a^{3/2}}-\frac{\sqrt{a-b x^4}}{4 a x^4}",1,"-Sqrt[a - b*x^4]/(4*a*x^4) - (b*ArcTanh[Sqrt[a - b*x^4]/Sqrt[a]])/(4*a^(3/2))","A",4,4,16,0.2500,1,"{266, 51, 63, 208}"
836,1,55,0,0.029561,"\int \frac{x^5}{\sqrt{a-b x^4}} \, dx","Int[x^5/Sqrt[a - b*x^4],x]","\frac{a \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}\right)}{4 b^{3/2}}-\frac{x^2 \sqrt{a-b x^4}}{4 b}","\frac{a \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}\right)}{4 b^{3/2}}-\frac{x^2 \sqrt{a-b x^4}}{4 b}",1,"-(x^2*Sqrt[a - b*x^4])/(4*b) + (a*ArcTan[(Sqrt[b]*x^2)/Sqrt[a - b*x^4]])/(4*b^(3/2))","A",4,4,16,0.2500,1,"{275, 321, 217, 203}"
837,1,31,0,0.0142488,"\int \frac{x}{\sqrt{a-b x^4}} \, dx","Int[x/Sqrt[a - b*x^4],x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}\right)}{2 \sqrt{b}}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}\right)}{2 \sqrt{b}}",1,"ArcTan[(Sqrt[b]*x^2)/Sqrt[a - b*x^4]]/(2*Sqrt[b])","A",3,3,14,0.2143,1,"{275, 217, 203}"
838,1,22,0,0.0044414,"\int \frac{1}{x^3 \sqrt{a-b x^4}} \, dx","Int[1/(x^3*Sqrt[a - b*x^4]),x]","-\frac{\sqrt{a-b x^4}}{2 a x^2}","-\frac{\sqrt{a-b x^4}}{2 a x^2}",1,"-Sqrt[a - b*x^4]/(2*a*x^2)","A",1,1,16,0.06250,1,"{264}"
839,1,46,0,0.0109992,"\int \frac{1}{x^7 \sqrt{a-b x^4}} \, dx","Int[1/(x^7*Sqrt[a - b*x^4]),x]","-\frac{b \sqrt{a-b x^4}}{3 a^2 x^2}-\frac{\sqrt{a-b x^4}}{6 a x^6}","-\frac{b \sqrt{a-b x^4}}{3 a^2 x^2}-\frac{\sqrt{a-b x^4}}{6 a x^6}",1,"-Sqrt[a - b*x^4]/(6*a*x^6) - (b*Sqrt[a - b*x^4])/(3*a^2*x^2)","A",2,2,16,0.1250,1,"{271, 264}"
840,1,71,0,0.0187645,"\int \frac{1}{x^{11} \sqrt{a-b x^4}} \, dx","Int[1/(x^11*Sqrt[a - b*x^4]),x]","-\frac{4 b^2 \sqrt{a-b x^4}}{15 a^3 x^2}-\frac{2 b \sqrt{a-b x^4}}{15 a^2 x^6}-\frac{\sqrt{a-b x^4}}{10 a x^{10}}","-\frac{4 b^2 \sqrt{a-b x^4}}{15 a^3 x^2}-\frac{2 b \sqrt{a-b x^4}}{15 a^2 x^6}-\frac{\sqrt{a-b x^4}}{10 a x^{10}}",1,"-Sqrt[a - b*x^4]/(10*a*x^10) - (2*b*Sqrt[a - b*x^4])/(15*a^2*x^6) - (4*b^2*Sqrt[a - b*x^4])/(15*a^3*x^2)","A",3,2,16,0.1250,1,"{271, 264}"
841,1,100,0,0.0341451,"\int \frac{x^8}{\sqrt{a-b x^4}} \, dx","Int[x^8/Sqrt[a - b*x^4],x]","\frac{5 a^{9/4} \sqrt{1-\frac{b x^4}{a}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{21 b^{9/4} \sqrt{a-b x^4}}-\frac{5 a x \sqrt{a-b x^4}}{21 b^2}-\frac{x^5 \sqrt{a-b x^4}}{7 b}","\frac{5 a^{9/4} \sqrt{1-\frac{b x^4}{a}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{21 b^{9/4} \sqrt{a-b x^4}}-\frac{5 a x \sqrt{a-b x^4}}{21 b^2}-\frac{x^5 \sqrt{a-b x^4}}{7 b}",1,"(-5*a*x*Sqrt[a - b*x^4])/(21*b^2) - (x^5*Sqrt[a - b*x^4])/(7*b) + (5*a^(9/4)*Sqrt[1 - (b*x^4)/a]*EllipticF[ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(21*b^(9/4)*Sqrt[a - b*x^4])","A",4,3,16,0.1875,1,"{321, 224, 221}"
842,1,77,0,0.0201801,"\int \frac{x^4}{\sqrt{a-b x^4}} \, dx","Int[x^4/Sqrt[a - b*x^4],x]","\frac{a^{5/4} \sqrt{1-\frac{b x^4}{a}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{3 b^{5/4} \sqrt{a-b x^4}}-\frac{x \sqrt{a-b x^4}}{3 b}","\frac{a^{5/4} \sqrt{1-\frac{b x^4}{a}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{3 b^{5/4} \sqrt{a-b x^4}}-\frac{x \sqrt{a-b x^4}}{3 b}",1,"-(x*Sqrt[a - b*x^4])/(3*b) + (a^(5/4)*Sqrt[1 - (b*x^4)/a]*EllipticF[ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(3*b^(5/4)*Sqrt[a - b*x^4])","A",3,3,16,0.1875,1,"{321, 224, 221}"
843,1,53,0,0.0113811,"\int \frac{1}{\sqrt{a-b x^4}} \, dx","Int[1/Sqrt[a - b*x^4],x]","\frac{\sqrt[4]{a} \sqrt{1-\frac{b x^4}{a}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{\sqrt[4]{b} \sqrt{a-b x^4}}","\frac{\sqrt[4]{a} \sqrt{1-\frac{b x^4}{a}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{\sqrt[4]{b} \sqrt{a-b x^4}}",1,"(a^(1/4)*Sqrt[1 - (b*x^4)/a]*EllipticF[ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(b^(1/4)*Sqrt[a - b*x^4])","A",2,2,12,0.1667,1,"{224, 221}"
844,1,79,0,0.0209344,"\int \frac{1}{x^4 \sqrt{a-b x^4}} \, dx","Int[1/(x^4*Sqrt[a - b*x^4]),x]","\frac{b^{3/4} \sqrt{1-\frac{b x^4}{a}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{3 a^{3/4} \sqrt{a-b x^4}}-\frac{\sqrt{a-b x^4}}{3 a x^3}","\frac{b^{3/4} \sqrt{1-\frac{b x^4}{a}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{3 a^{3/4} \sqrt{a-b x^4}}-\frac{\sqrt{a-b x^4}}{3 a x^3}",1,"-Sqrt[a - b*x^4]/(3*a*x^3) + (b^(3/4)*Sqrt[1 - (b*x^4)/a]*EllipticF[ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(3*a^(3/4)*Sqrt[a - b*x^4])","A",3,3,16,0.1875,1,"{325, 224, 221}"
845,1,102,0,0.033461,"\int \frac{1}{x^8 \sqrt{a-b x^4}} \, dx","Int[1/(x^8*Sqrt[a - b*x^4]),x]","\frac{5 b^{7/4} \sqrt{1-\frac{b x^4}{a}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{21 a^{7/4} \sqrt{a-b x^4}}-\frac{5 b \sqrt{a-b x^4}}{21 a^2 x^3}-\frac{\sqrt{a-b x^4}}{7 a x^7}","\frac{5 b^{7/4} \sqrt{1-\frac{b x^4}{a}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{21 a^{7/4} \sqrt{a-b x^4}}-\frac{5 b \sqrt{a-b x^4}}{21 a^2 x^3}-\frac{\sqrt{a-b x^4}}{7 a x^7}",1,"-Sqrt[a - b*x^4]/(7*a*x^7) - (5*b*Sqrt[a - b*x^4])/(21*a^2*x^3) + (5*b^(7/4)*Sqrt[1 - (b*x^4)/a]*EllipticF[ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(21*a^(7/4)*Sqrt[a - b*x^4])","A",4,3,16,0.1875,1,"{325, 224, 221}"
846,1,158,0,0.0945325,"\int \frac{x^{10}}{\sqrt{a-b x^4}} \, dx","Int[x^10/Sqrt[a - b*x^4],x]","-\frac{7 a^{11/4} \sqrt{1-\frac{b x^4}{a}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{15 b^{11/4} \sqrt{a-b x^4}}+\frac{7 a^{11/4} \sqrt{1-\frac{b x^4}{a}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{15 b^{11/4} \sqrt{a-b x^4}}-\frac{7 a x^3 \sqrt{a-b x^4}}{45 b^2}-\frac{x^7 \sqrt{a-b x^4}}{9 b}","-\frac{7 a^{11/4} \sqrt{1-\frac{b x^4}{a}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{15 b^{11/4} \sqrt{a-b x^4}}+\frac{7 a^{11/4} \sqrt{1-\frac{b x^4}{a}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{15 b^{11/4} \sqrt{a-b x^4}}-\frac{7 a x^3 \sqrt{a-b x^4}}{45 b^2}-\frac{x^7 \sqrt{a-b x^4}}{9 b}",1,"(-7*a*x^3*Sqrt[a - b*x^4])/(45*b^2) - (x^7*Sqrt[a - b*x^4])/(9*b) + (7*a^(11/4)*Sqrt[1 - (b*x^4)/a]*EllipticE[ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(15*b^(11/4)*Sqrt[a - b*x^4]) - (7*a^(11/4)*Sqrt[1 - (b*x^4)/a]*EllipticF[ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(15*b^(11/4)*Sqrt[a - b*x^4])","A",8,7,16,0.4375,1,"{321, 307, 224, 221, 1200, 1199, 424}"
847,1,135,0,0.0770988,"\int \frac{x^6}{\sqrt{a-b x^4}} \, dx","Int[x^6/Sqrt[a - b*x^4],x]","-\frac{3 a^{7/4} \sqrt{1-\frac{b x^4}{a}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{5 b^{7/4} \sqrt{a-b x^4}}+\frac{3 a^{7/4} \sqrt{1-\frac{b x^4}{a}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{5 b^{7/4} \sqrt{a-b x^4}}-\frac{x^3 \sqrt{a-b x^4}}{5 b}","-\frac{3 a^{7/4} \sqrt{1-\frac{b x^4}{a}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{5 b^{7/4} \sqrt{a-b x^4}}+\frac{3 a^{7/4} \sqrt{1-\frac{b x^4}{a}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{5 b^{7/4} \sqrt{a-b x^4}}-\frac{x^3 \sqrt{a-b x^4}}{5 b}",1,"-(x^3*Sqrt[a - b*x^4])/(5*b) + (3*a^(7/4)*Sqrt[1 - (b*x^4)/a]*EllipticE[ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(5*b^(7/4)*Sqrt[a - b*x^4]) - (3*a^(7/4)*Sqrt[1 - (b*x^4)/a]*EllipticF[ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(5*b^(7/4)*Sqrt[a - b*x^4])","A",7,7,16,0.4375,1,"{321, 307, 224, 221, 1200, 1199, 424}"
848,1,108,0,0.0640952,"\int \frac{x^2}{\sqrt{a-b x^4}} \, dx","Int[x^2/Sqrt[a - b*x^4],x]","\frac{a^{3/4} \sqrt{1-\frac{b x^4}{a}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{b^{3/4} \sqrt{a-b x^4}}-\frac{a^{3/4} \sqrt{1-\frac{b x^4}{a}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{b^{3/4} \sqrt{a-b x^4}}","\frac{a^{3/4} \sqrt{1-\frac{b x^4}{a}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{b^{3/4} \sqrt{a-b x^4}}-\frac{a^{3/4} \sqrt{1-\frac{b x^4}{a}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{b^{3/4} \sqrt{a-b x^4}}",1,"(a^(3/4)*Sqrt[1 - (b*x^4)/a]*EllipticE[ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(b^(3/4)*Sqrt[a - b*x^4]) - (a^(3/4)*Sqrt[1 - (b*x^4)/a]*EllipticF[ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(b^(3/4)*Sqrt[a - b*x^4])","A",6,6,16,0.3750,1,"{307, 224, 221, 1200, 1199, 424}"
849,1,128,0,0.0768875,"\int \frac{1}{x^2 \sqrt{a-b x^4}} \, dx","Int[1/(x^2*Sqrt[a - b*x^4]),x]","-\frac{\sqrt{a-b x^4}}{a x}+\frac{\sqrt[4]{b} \sqrt{1-\frac{b x^4}{a}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{\sqrt[4]{a} \sqrt{a-b x^4}}-\frac{\sqrt[4]{b} \sqrt{1-\frac{b x^4}{a}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{\sqrt[4]{a} \sqrt{a-b x^4}}","-\frac{\sqrt{a-b x^4}}{a x}+\frac{\sqrt[4]{b} \sqrt{1-\frac{b x^4}{a}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{\sqrt[4]{a} \sqrt{a-b x^4}}-\frac{\sqrt[4]{b} \sqrt{1-\frac{b x^4}{a}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{\sqrt[4]{a} \sqrt{a-b x^4}}",1,"-(Sqrt[a - b*x^4]/(a*x)) - (b^(1/4)*Sqrt[1 - (b*x^4)/a]*EllipticE[ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(a^(1/4)*Sqrt[a - b*x^4]) + (b^(1/4)*Sqrt[1 - (b*x^4)/a]*EllipticF[ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(a^(1/4)*Sqrt[a - b*x^4])","A",7,7,16,0.4375,1,"{325, 307, 224, 221, 1200, 1199, 424}"
850,1,158,0,0.091197,"\int \frac{1}{x^6 \sqrt{a-b x^4}} \, dx","Int[1/(x^6*Sqrt[a - b*x^4]),x]","\frac{3 b^{5/4} \sqrt{1-\frac{b x^4}{a}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{5 a^{5/4} \sqrt{a-b x^4}}-\frac{3 b^{5/4} \sqrt{1-\frac{b x^4}{a}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{5 a^{5/4} \sqrt{a-b x^4}}-\frac{3 b \sqrt{a-b x^4}}{5 a^2 x}-\frac{\sqrt{a-b x^4}}{5 a x^5}","\frac{3 b^{5/4} \sqrt{1-\frac{b x^4}{a}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{5 a^{5/4} \sqrt{a-b x^4}}-\frac{3 b^{5/4} \sqrt{1-\frac{b x^4}{a}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)\right|-1\right)}{5 a^{5/4} \sqrt{a-b x^4}}-\frac{3 b \sqrt{a-b x^4}}{5 a^2 x}-\frac{\sqrt{a-b x^4}}{5 a x^5}",1,"-Sqrt[a - b*x^4]/(5*a*x^5) - (3*b*Sqrt[a - b*x^4])/(5*a^2*x) - (3*b^(5/4)*Sqrt[1 - (b*x^4)/a]*EllipticE[ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(5*a^(5/4)*Sqrt[a - b*x^4]) + (3*b^(5/4)*Sqrt[1 - (b*x^4)/a]*EllipticF[ArcSin[(b^(1/4)*x)/a^(1/4)], -1])/(5*a^(5/4)*Sqrt[a - b*x^4])","A",8,7,16,0.4375,1,"{325, 307, 224, 221, 1200, 1199, 424}"
851,1,57,0,0.0326121,"\int \frac{x^{11}}{\left(a+b x^4\right)^{3/2}} \, dx","Int[x^11/(a + b*x^4)^(3/2),x]","-\frac{a^2}{2 b^3 \sqrt{a+b x^4}}-\frac{a \sqrt{a+b x^4}}{b^3}+\frac{\left(a+b x^4\right)^{3/2}}{6 b^3}","-\frac{a^2}{2 b^3 \sqrt{a+b x^4}}-\frac{a \sqrt{a+b x^4}}{b^3}+\frac{\left(a+b x^4\right)^{3/2}}{6 b^3}",1,"-a^2/(2*b^3*Sqrt[a + b*x^4]) - (a*Sqrt[a + b*x^4])/b^3 + (a + b*x^4)^(3/2)/(6*b^3)","A",3,2,15,0.1333,1,"{266, 43}"
852,1,38,0,0.0221735,"\int \frac{x^7}{\left(a+b x^4\right)^{3/2}} \, dx","Int[x^7/(a + b*x^4)^(3/2),x]","\frac{a}{2 b^2 \sqrt{a+b x^4}}+\frac{\sqrt{a+b x^4}}{2 b^2}","\frac{a}{2 b^2 \sqrt{a+b x^4}}+\frac{\sqrt{a+b x^4}}{2 b^2}",1,"a/(2*b^2*Sqrt[a + b*x^4]) + Sqrt[a + b*x^4]/(2*b^2)","A",3,2,15,0.1333,1,"{266, 43}"
853,1,18,0,0.0045454,"\int \frac{x^3}{\left(a+b x^4\right)^{3/2}} \, dx","Int[x^3/(a + b*x^4)^(3/2),x]","-\frac{1}{2 b \sqrt{a+b x^4}}","-\frac{1}{2 b \sqrt{a+b x^4}}",1,"-1/(2*b*Sqrt[a + b*x^4])","A",1,1,15,0.06667,1,"{261}"
854,1,46,0,0.0266344,"\int \frac{1}{x \left(a+b x^4\right)^{3/2}} \, dx","Int[1/(x*(a + b*x^4)^(3/2)),x]","\frac{1}{2 a \sqrt{a+b x^4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)}{2 a^{3/2}}","\frac{1}{2 a \sqrt{a+b x^4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)}{2 a^{3/2}}",1,"1/(2*a*Sqrt[a + b*x^4]) - ArcTanh[Sqrt[a + b*x^4]/Sqrt[a]]/(2*a^(3/2))","A",4,4,15,0.2667,1,"{266, 51, 63, 208}"
855,1,71,0,0.0376518,"\int \frac{1}{x^5 \left(a+b x^4\right)^{3/2}} \, dx","Int[1/(x^5*(a + b*x^4)^(3/2)),x]","-\frac{3 \sqrt{a+b x^4}}{4 a^2 x^4}+\frac{3 b \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)}{4 a^{5/2}}+\frac{1}{2 a x^4 \sqrt{a+b x^4}}","-\frac{3 b}{4 a^2 \sqrt{a+b x^4}}+\frac{3 b \tanh ^{-1}\left(\frac{\sqrt{a+b x^4}}{\sqrt{a}}\right)}{4 a^{5/2}}-\frac{1}{4 a x^4 \sqrt{a+b x^4}}",1,"1/(2*a*x^4*Sqrt[a + b*x^4]) - (3*Sqrt[a + b*x^4])/(4*a^2*x^4) + (3*b*ArcTanh[Sqrt[a + b*x^4]/Sqrt[a]])/(4*a^(5/2))","A",5,4,15,0.2667,1,"{266, 51, 63, 208}"
856,1,74,0,0.045765,"\int \frac{x^9}{\left(a+b x^4\right)^{3/2}} \, dx","Int[x^9/(a + b*x^4)^(3/2),x]","\frac{3 x^2 \sqrt{a+b x^4}}{4 b^2}-\frac{3 a \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{4 b^{5/2}}-\frac{x^6}{2 b \sqrt{a+b x^4}}","\frac{3 x^2 \sqrt{a+b x^4}}{4 b^2}-\frac{3 a \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{4 b^{5/2}}-\frac{x^6}{2 b \sqrt{a+b x^4}}",1,"-x^6/(2*b*Sqrt[a + b*x^4]) + (3*x^2*Sqrt[a + b*x^4])/(4*b^2) - (3*a*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a + b*x^4]])/(4*b^(5/2))","A",5,5,15,0.3333,1,"{275, 288, 321, 217, 206}"
857,1,52,0,0.0286138,"\int \frac{x^5}{\left(a+b x^4\right)^{3/2}} \, dx","Int[x^5/(a + b*x^4)^(3/2),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{2 b^{3/2}}-\frac{x^2}{2 b \sqrt{a+b x^4}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{2 b^{3/2}}-\frac{x^2}{2 b \sqrt{a+b x^4}}",1,"-x^2/(2*b*Sqrt[a + b*x^4]) + ArcTanh[(Sqrt[b]*x^2)/Sqrt[a + b*x^4]]/(2*b^(3/2))","A",4,4,15,0.2667,1,"{275, 288, 217, 206}"
858,1,21,0,0.0036308,"\int \frac{x}{\left(a+b x^4\right)^{3/2}} \, dx","Int[x/(a + b*x^4)^(3/2),x]","\frac{x^2}{2 a \sqrt{a+b x^4}}","\frac{x^2}{2 a \sqrt{a+b x^4}}",1,"x^2/(2*a*Sqrt[a + b*x^4])","A",1,1,13,0.07692,1,"{264}"
859,1,42,0,0.0102541,"\int \frac{1}{x^3 \left(a+b x^4\right)^{3/2}} \, dx","Int[1/(x^3*(a + b*x^4)^(3/2)),x]","-\frac{b x^2}{a^2 \sqrt{a+b x^4}}-\frac{1}{2 a x^2 \sqrt{a+b x^4}}","-\frac{b x^2}{a^2 \sqrt{a+b x^4}}-\frac{1}{2 a x^2 \sqrt{a+b x^4}}",1,"-1/(2*a*x^2*Sqrt[a + b*x^4]) - (b*x^2)/(a^2*Sqrt[a + b*x^4])","A",2,2,15,0.1333,1,"{271, 264}"
860,1,68,0,0.0177637,"\int \frac{1}{x^7 \left(a+b x^4\right)^{3/2}} \, dx","Int[1/(x^7*(a + b*x^4)^(3/2)),x]","\frac{4 b^2 x^2}{3 a^3 \sqrt{a+b x^4}}+\frac{2 b}{3 a^2 x^2 \sqrt{a+b x^4}}-\frac{1}{6 a x^6 \sqrt{a+b x^4}}","\frac{4 b^2 x^2}{3 a^3 \sqrt{a+b x^4}}+\frac{2 b}{3 a^2 x^2 \sqrt{a+b x^4}}-\frac{1}{6 a x^6 \sqrt{a+b x^4}}",1,"-1/(6*a*x^6*Sqrt[a + b*x^4]) + (2*b)/(3*a^2*x^2*Sqrt[a + b*x^4]) + (4*b^2*x^2)/(3*a^3*Sqrt[a + b*x^4])","A",3,2,15,0.1333,1,"{271, 264}"
861,1,151,0,0.0515274,"\int \frac{x^{12}}{\left(a+b x^4\right)^{3/2}} \, dx","Int[x^12/(a + b*x^4)^(3/2),x]","\frac{15 a^{7/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{28 b^{13/4} \sqrt{a+b x^4}}+\frac{9 x^5 \sqrt{a+b x^4}}{14 b^2}-\frac{15 a x \sqrt{a+b x^4}}{14 b^3}-\frac{x^9}{2 b \sqrt{a+b x^4}}","\frac{15 a^{7/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{28 b^{13/4} \sqrt{a+b x^4}}+\frac{9 x^5 \sqrt{a+b x^4}}{14 b^2}-\frac{15 a x \sqrt{a+b x^4}}{14 b^3}-\frac{x^9}{2 b \sqrt{a+b x^4}}",1,"-x^9/(2*b*Sqrt[a + b*x^4]) - (15*a*x*Sqrt[a + b*x^4])/(14*b^3) + (9*x^5*Sqrt[a + b*x^4])/(14*b^2) + (15*a^(7/4)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(28*b^(13/4)*Sqrt[a + b*x^4])","A",4,3,15,0.2000,1,"{288, 321, 220}"
862,1,129,0,0.0348788,"\int \frac{x^8}{\left(a+b x^4\right)^{3/2}} \, dx","Int[x^8/(a + b*x^4)^(3/2),x]","-\frac{5 a^{3/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{12 b^{9/4} \sqrt{a+b x^4}}+\frac{5 x \sqrt{a+b x^4}}{6 b^2}-\frac{x^5}{2 b \sqrt{a+b x^4}}","-\frac{5 a^{3/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{12 b^{9/4} \sqrt{a+b x^4}}+\frac{5 x \sqrt{a+b x^4}}{6 b^2}-\frac{x^5}{2 b \sqrt{a+b x^4}}",1,"-x^5/(2*b*Sqrt[a + b*x^4]) + (5*x*Sqrt[a + b*x^4])/(6*b^2) - (5*a^(3/4)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(12*b^(9/4)*Sqrt[a + b*x^4])","A",3,3,15,0.2000,1,"{288, 321, 220}"
863,1,108,0,0.0213572,"\int \frac{x^4}{\left(a+b x^4\right)^{3/2}} \, dx","Int[x^4/(a + b*x^4)^(3/2),x]","\frac{\left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{a} b^{5/4} \sqrt{a+b x^4}}-\frac{x}{2 b \sqrt{a+b x^4}}","\frac{\left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{a} b^{5/4} \sqrt{a+b x^4}}-\frac{x}{2 b \sqrt{a+b x^4}}",1,"-x/(2*b*Sqrt[a + b*x^4]) + ((Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(4*a^(1/4)*b^(5/4)*Sqrt[a + b*x^4])","A",2,2,15,0.1333,1,"{288, 220}"
864,1,108,0,0.0188733,"\int \frac{1}{\left(a+b x^4\right)^{3/2}} \, dx","Int[(a + b*x^4)^(-3/2),x]","\frac{\left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 a^{5/4} \sqrt[4]{b} \sqrt{a+b x^4}}+\frac{x}{2 a \sqrt{a+b x^4}}","\frac{\left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 a^{5/4} \sqrt[4]{b} \sqrt{a+b x^4}}+\frac{x}{2 a \sqrt{a+b x^4}}",1,"x/(2*a*Sqrt[a + b*x^4]) + ((Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(4*a^(5/4)*b^(1/4)*Sqrt[a + b*x^4])","A",2,2,11,0.1818,1,"{199, 220}"
865,1,131,0,0.0353922,"\int \frac{1}{x^4 \left(a+b x^4\right)^{3/2}} \, dx","Int[1/(x^4*(a + b*x^4)^(3/2)),x]","-\frac{5 b^{3/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{12 a^{9/4} \sqrt{a+b x^4}}-\frac{5 \sqrt{a+b x^4}}{6 a^2 x^3}+\frac{1}{2 a x^3 \sqrt{a+b x^4}}","-\frac{5 b^{3/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{12 a^{9/4} \sqrt{a+b x^4}}-\frac{5 \sqrt{a+b x^4}}{6 a^2 x^3}+\frac{1}{2 a x^3 \sqrt{a+b x^4}}",1,"1/(2*a*x^3*Sqrt[a + b*x^4]) - (5*Sqrt[a + b*x^4])/(6*a^2*x^3) - (5*b^(3/4)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(12*a^(9/4)*Sqrt[a + b*x^4])","A",3,3,15,0.2000,1,"{290, 325, 220}"
866,1,153,0,0.0503625,"\int \frac{1}{x^8 \left(a+b x^4\right)^{3/2}} \, dx","Int[1/(x^8*(a + b*x^4)^(3/2)),x]","\frac{15 b^{7/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{28 a^{13/4} \sqrt{a+b x^4}}+\frac{15 b \sqrt{a+b x^4}}{14 a^3 x^3}-\frac{9 \sqrt{a+b x^4}}{14 a^2 x^7}+\frac{1}{2 a x^7 \sqrt{a+b x^4}}","\frac{15 b^{7/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{28 a^{13/4} \sqrt{a+b x^4}}+\frac{15 b \sqrt{a+b x^4}}{14 a^3 x^3}-\frac{9 \sqrt{a+b x^4}}{14 a^2 x^7}+\frac{1}{2 a x^7 \sqrt{a+b x^4}}",1,"1/(2*a*x^7*Sqrt[a + b*x^4]) - (9*Sqrt[a + b*x^4])/(14*a^2*x^7) + (15*b*Sqrt[a + b*x^4])/(14*a^3*x^3) + (15*b^(7/4)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(28*a^(13/4)*Sqrt[a + b*x^4])","A",4,3,15,0.2000,1,"{290, 325, 220}"
867,1,282,0,0.1145512,"\int \frac{x^{14}}{\left(a+b x^4\right)^{3/2}} \, dx","Int[x^14/(a + b*x^4)^(3/2),x]","\frac{77 a^2 x \sqrt{a+b x^4}}{30 b^{7/2} \left(\sqrt{a}+\sqrt{b} x^2\right)}+\frac{77 a^{9/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{60 b^{15/4} \sqrt{a+b x^4}}-\frac{77 a^{9/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{30 b^{15/4} \sqrt{a+b x^4}}+\frac{11 x^7 \sqrt{a+b x^4}}{18 b^2}-\frac{77 a x^3 \sqrt{a+b x^4}}{90 b^3}-\frac{x^{11}}{2 b \sqrt{a+b x^4}}","\frac{77 a^2 x \sqrt{a+b x^4}}{30 b^{7/2} \left(\sqrt{a}+\sqrt{b} x^2\right)}+\frac{77 a^{9/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{60 b^{15/4} \sqrt{a+b x^4}}-\frac{77 a^{9/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{30 b^{15/4} \sqrt{a+b x^4}}+\frac{11 x^7 \sqrt{a+b x^4}}{18 b^2}-\frac{77 a x^3 \sqrt{a+b x^4}}{90 b^3}-\frac{x^{11}}{2 b \sqrt{a+b x^4}}",1,"-x^11/(2*b*Sqrt[a + b*x^4]) - (77*a*x^3*Sqrt[a + b*x^4])/(90*b^3) + (11*x^7*Sqrt[a + b*x^4])/(18*b^2) + (77*a^2*x*Sqrt[a + b*x^4])/(30*b^(7/2)*(Sqrt[a] + Sqrt[b]*x^2)) - (77*a^(9/4)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(30*b^(15/4)*Sqrt[a + b*x^4]) + (77*a^(9/4)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(60*b^(15/4)*Sqrt[a + b*x^4])","A",6,5,15,0.3333,1,"{288, 321, 305, 220, 1196}"
868,1,258,0,0.0876296,"\int \frac{x^{10}}{\left(a+b x^4\right)^{3/2}} \, dx","Int[x^10/(a + b*x^4)^(3/2),x]","-\frac{21 a^{5/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{20 b^{11/4} \sqrt{a+b x^4}}+\frac{21 a^{5/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{10 b^{11/4} \sqrt{a+b x^4}}+\frac{7 x^3 \sqrt{a+b x^4}}{10 b^2}-\frac{21 a x \sqrt{a+b x^4}}{10 b^{5/2} \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{x^7}{2 b \sqrt{a+b x^4}}","-\frac{21 a^{5/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{20 b^{11/4} \sqrt{a+b x^4}}+\frac{21 a^{5/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{10 b^{11/4} \sqrt{a+b x^4}}+\frac{7 x^3 \sqrt{a+b x^4}}{10 b^2}-\frac{21 a x \sqrt{a+b x^4}}{10 b^{5/2} \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{x^7}{2 b \sqrt{a+b x^4}}",1,"-x^7/(2*b*Sqrt[a + b*x^4]) + (7*x^3*Sqrt[a + b*x^4])/(10*b^2) - (21*a*x*Sqrt[a + b*x^4])/(10*b^(5/2)*(Sqrt[a] + Sqrt[b]*x^2)) + (21*a^(5/4)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(10*b^(11/4)*Sqrt[a + b*x^4]) - (21*a^(5/4)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(20*b^(11/4)*Sqrt[a + b*x^4])","A",5,5,15,0.3333,1,"{288, 321, 305, 220, 1196}"
869,1,236,0,0.066738,"\int \frac{x^6}{\left(a+b x^4\right)^{3/2}} \, dx","Int[x^6/(a + b*x^4)^(3/2),x]","\frac{3 x \sqrt{a+b x^4}}{2 b^{3/2} \left(\sqrt{a}+\sqrt{b} x^2\right)}+\frac{3 \sqrt[4]{a} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 b^{7/4} \sqrt{a+b x^4}}-\frac{3 \sqrt[4]{a} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 b^{7/4} \sqrt{a+b x^4}}-\frac{x^3}{2 b \sqrt{a+b x^4}}","\frac{3 x \sqrt{a+b x^4}}{2 b^{3/2} \left(\sqrt{a}+\sqrt{b} x^2\right)}+\frac{3 \sqrt[4]{a} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 b^{7/4} \sqrt{a+b x^4}}-\frac{3 \sqrt[4]{a} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 b^{7/4} \sqrt{a+b x^4}}-\frac{x^3}{2 b \sqrt{a+b x^4}}",1,"-x^3/(2*b*Sqrt[a + b*x^4]) + (3*x*Sqrt[a + b*x^4])/(2*b^(3/2)*(Sqrt[a] + Sqrt[b]*x^2)) - (3*a^(1/4)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(2*b^(7/4)*Sqrt[a + b*x^4]) + (3*a^(1/4)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(4*b^(7/4)*Sqrt[a + b*x^4])","A",4,4,15,0.2667,1,"{288, 305, 220, 1196}"
870,1,239,0,0.0687683,"\int \frac{x^2}{\left(a+b x^4\right)^{3/2}} \, dx","Int[x^2/(a + b*x^4)^(3/2),x]","-\frac{\left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 a^{3/4} b^{3/4} \sqrt{a+b x^4}}+\frac{\left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{3/4} b^{3/4} \sqrt{a+b x^4}}+\frac{x^3}{2 a \sqrt{a+b x^4}}-\frac{x \sqrt{a+b x^4}}{2 a \sqrt{b} \left(\sqrt{a}+\sqrt{b} x^2\right)}","-\frac{\left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 a^{3/4} b^{3/4} \sqrt{a+b x^4}}+\frac{\left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{3/4} b^{3/4} \sqrt{a+b x^4}}+\frac{x^3}{2 a \sqrt{a+b x^4}}-\frac{x \sqrt{a+b x^4}}{2 a \sqrt{b} \left(\sqrt{a}+\sqrt{b} x^2\right)}",1,"x^3/(2*a*Sqrt[a + b*x^4]) - (x*Sqrt[a + b*x^4])/(2*a*Sqrt[b]*(Sqrt[a] + Sqrt[b]*x^2)) + ((Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(2*a^(3/4)*b^(3/4)*Sqrt[a + b*x^4]) - ((Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(4*a^(3/4)*b^(3/4)*Sqrt[a + b*x^4])","A",4,4,15,0.2667,1,"{290, 305, 220, 1196}"
871,1,260,0,0.0889881,"\int \frac{1}{x^2 \left(a+b x^4\right)^{3/2}} \, dx","Int[1/(x^2*(a + b*x^4)^(3/2)),x]","\frac{3 \sqrt{b} x \sqrt{a+b x^4}}{2 a^2 \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{3 \sqrt{a+b x^4}}{2 a^2 x}+\frac{3 \sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 a^{7/4} \sqrt{a+b x^4}}-\frac{3 \sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{7/4} \sqrt{a+b x^4}}+\frac{1}{2 a x \sqrt{a+b x^4}}","\frac{3 \sqrt{b} x \sqrt{a+b x^4}}{2 a^2 \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{3 \sqrt{a+b x^4}}{2 a^2 x}+\frac{3 \sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 a^{7/4} \sqrt{a+b x^4}}-\frac{3 \sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{7/4} \sqrt{a+b x^4}}+\frac{1}{2 a x \sqrt{a+b x^4}}",1,"1/(2*a*x*Sqrt[a + b*x^4]) - (3*Sqrt[a + b*x^4])/(2*a^2*x) + (3*Sqrt[b]*x*Sqrt[a + b*x^4])/(2*a^2*(Sqrt[a] + Sqrt[b]*x^2)) - (3*b^(1/4)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(2*a^(7/4)*Sqrt[a + b*x^4]) + (3*b^(1/4)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(4*a^(7/4)*Sqrt[a + b*x^4])","A",5,5,15,0.3333,1,"{290, 325, 305, 220, 1196}"
872,1,282,0,0.1156969,"\int \frac{1}{x^6 \left(a+b x^4\right)^{3/2}} \, dx","Int[1/(x^6*(a + b*x^4)^(3/2)),x]","-\frac{21 b^{3/2} x \sqrt{a+b x^4}}{10 a^3 \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{21 b^{5/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{20 a^{11/4} \sqrt{a+b x^4}}+\frac{21 b^{5/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{10 a^{11/4} \sqrt{a+b x^4}}+\frac{21 b \sqrt{a+b x^4}}{10 a^3 x}-\frac{7 \sqrt{a+b x^4}}{10 a^2 x^5}+\frac{1}{2 a x^5 \sqrt{a+b x^4}}","-\frac{21 b^{3/2} x \sqrt{a+b x^4}}{10 a^3 \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{21 b^{5/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{20 a^{11/4} \sqrt{a+b x^4}}+\frac{21 b^{5/4} \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{10 a^{11/4} \sqrt{a+b x^4}}+\frac{21 b \sqrt{a+b x^4}}{10 a^3 x}-\frac{7 \sqrt{a+b x^4}}{10 a^2 x^5}+\frac{1}{2 a x^5 \sqrt{a+b x^4}}",1,"1/(2*a*x^5*Sqrt[a + b*x^4]) - (7*Sqrt[a + b*x^4])/(10*a^2*x^5) + (21*b*Sqrt[a + b*x^4])/(10*a^3*x) - (21*b^(3/2)*x*Sqrt[a + b*x^4])/(10*a^3*(Sqrt[a] + Sqrt[b]*x^2)) + (21*b^(5/4)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticE[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(10*a^(11/4)*Sqrt[a + b*x^4]) - (21*b^(5/4)*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(20*a^(11/4)*Sqrt[a + b*x^4])","A",6,5,15,0.3333,1,"{290, 325, 305, 220, 1196}"
873,1,127,0,0.0283282,"\int \frac{1}{\left(a+b x^4\right)^{5/2}} \, dx","Int[(a + b*x^4)^(-5/2),x]","\frac{5 x}{12 a^2 \sqrt{a+b x^4}}+\frac{5 \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{24 a^{9/4} \sqrt[4]{b} \sqrt{a+b x^4}}+\frac{x}{6 a \left(a+b x^4\right)^{3/2}}","\frac{5 x}{12 a^2 \sqrt{a+b x^4}}+\frac{5 \left(\sqrt{a}+\sqrt{b} x^2\right) \sqrt{\frac{a+b x^4}{\left(\sqrt{a}+\sqrt{b} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{24 a^{9/4} \sqrt[4]{b} \sqrt{a+b x^4}}+\frac{x}{6 a \left(a+b x^4\right)^{3/2}}",1,"x/(6*a*(a + b*x^4)^(3/2)) + (5*x)/(12*a^2*Sqrt[a + b*x^4]) + (5*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(24*a^(9/4)*b^(1/4)*Sqrt[a + b*x^4])","A",3,2,11,0.1818,1,"{199, 220}"
874,1,46,0,0.0201704,"\int \frac{x^{11}}{\sqrt{1-x^4}} \, dx","Int[x^11/Sqrt[1 - x^4],x]","-\frac{1}{10} \left(1-x^4\right)^{5/2}+\frac{1}{3} \left(1-x^4\right)^{3/2}-\frac{\sqrt{1-x^4}}{2}","-\frac{1}{10} \left(1-x^4\right)^{5/2}+\frac{1}{3} \left(1-x^4\right)^{3/2}-\frac{\sqrt{1-x^4}}{2}",1,"-Sqrt[1 - x^4]/2 + (1 - x^4)^(3/2)/3 - (1 - x^4)^(5/2)/10","A",3,2,15,0.1333,1,"{266, 43}"
875,1,31,0,0.0146928,"\int \frac{x^7}{\sqrt{1-x^4}} \, dx","Int[x^7/Sqrt[1 - x^4],x]","\frac{1}{6} \left(1-x^4\right)^{3/2}-\frac{\sqrt{1-x^4}}{2}","\frac{1}{6} \left(1-x^4\right)^{3/2}-\frac{\sqrt{1-x^4}}{2}",1,"-Sqrt[1 - x^4]/2 + (1 - x^4)^(3/2)/6","A",3,2,15,0.1333,1,"{266, 43}"
876,1,15,0,0.0029978,"\int \frac{x^3}{\sqrt{1-x^4}} \, dx","Int[x^3/Sqrt[1 - x^4],x]","-\frac{1}{2} \sqrt{1-x^4}","-\frac{1}{2} \sqrt{1-x^4}",1,"-Sqrt[1 - x^4]/2","A",1,1,15,0.06667,1,"{261}"
877,1,16,0,0.0085582,"\int \frac{1}{x \sqrt{1-x^4}} \, dx","Int[1/(x*Sqrt[1 - x^4]),x]","-\frac{1}{2} \tanh ^{-1}\left(\sqrt{1-x^4}\right)","-\frac{1}{2} \tanh ^{-1}\left(\sqrt{1-x^4}\right)",1,"-ArcTanh[Sqrt[1 - x^4]]/2","A",3,3,15,0.2000,1,"{266, 63, 206}"
878,1,35,0,0.0144941,"\int \frac{1}{x^5 \sqrt{1-x^4}} \, dx","Int[1/(x^5*Sqrt[1 - x^4]),x]","-\frac{\sqrt{1-x^4}}{4 x^4}-\frac{1}{4} \tanh ^{-1}\left(\sqrt{1-x^4}\right)","-\frac{\sqrt{1-x^4}}{4 x^4}-\frac{1}{4} \tanh ^{-1}\left(\sqrt{1-x^4}\right)",1,"-Sqrt[1 - x^4]/(4*x^4) - ArcTanh[Sqrt[1 - x^4]]/4","A",4,4,15,0.2667,1,"{266, 51, 63, 206}"
879,1,27,0,0.0116118,"\int \frac{x^5}{\sqrt{1-x^4}} \, dx","Int[x^5/Sqrt[1 - x^4],x]","\frac{1}{4} \sin ^{-1}\left(x^2\right)-\frac{1}{4} x^2 \sqrt{1-x^4}","\frac{1}{4} \sin ^{-1}\left(x^2\right)-\frac{1}{4} x^2 \sqrt{1-x^4}",1,"-(x^2*Sqrt[1 - x^4])/4 + ArcSin[x^2]/4","A",3,3,15,0.2000,1,"{275, 321, 216}"
880,1,8,0,0.0029568,"\int \frac{x}{\sqrt{1-x^4}} \, dx","Int[x/Sqrt[1 - x^4],x]","\frac{1}{2} \sin ^{-1}\left(x^2\right)","\frac{1}{2} \sin ^{-1}\left(x^2\right)",1,"ArcSin[x^2]/2","A",2,2,13,0.1538,1,"{275, 216}"
881,1,18,0,0.003119,"\int \frac{1}{x^3 \sqrt{1-x^4}} \, dx","Int[1/(x^3*Sqrt[1 - x^4]),x]","-\frac{\sqrt{1-x^4}}{2 x^2}","-\frac{\sqrt{1-x^4}}{2 x^2}",1,"-Sqrt[1 - x^4]/(2*x^2)","A",1,1,15,0.06667,1,"{264}"
882,1,37,0,0.0074301,"\int \frac{1}{x^7 \sqrt{1-x^4}} \, dx","Int[1/(x^7*Sqrt[1 - x^4]),x]","-\frac{\sqrt{1-x^4}}{3 x^2}-\frac{\sqrt{1-x^4}}{6 x^6}","-\frac{\sqrt{1-x^4}}{3 x^2}-\frac{\sqrt{1-x^4}}{6 x^6}",1,"-Sqrt[1 - x^4]/(6*x^6) - Sqrt[1 - x^4]/(3*x^2)","A",2,2,15,0.1333,1,"{271, 264}"
883,1,55,0,0.0121978,"\int \frac{1}{x^{11} \sqrt{1-x^4}} \, dx","Int[1/(x^11*Sqrt[1 - x^4]),x]","-\frac{4 \sqrt{1-x^4}}{15 x^2}-\frac{2 \sqrt{1-x^4}}{15 x^6}-\frac{\sqrt{1-x^4}}{10 x^{10}}","-\frac{4 \sqrt{1-x^4}}{15 x^2}-\frac{2 \sqrt{1-x^4}}{15 x^6}-\frac{\sqrt{1-x^4}}{10 x^{10}}",1,"-Sqrt[1 - x^4]/(10*x^10) - (2*Sqrt[1 - x^4])/(15*x^6) - (4*Sqrt[1 - x^4])/(15*x^2)","A",3,2,15,0.1333,1,"{271, 264}"
884,1,43,0,0.0091225,"\int \frac{x^8}{\sqrt{1-x^4}} \, dx","Int[x^8/Sqrt[1 - x^4],x]","-\frac{1}{7} \sqrt{1-x^4} x^5-\frac{5}{21} \sqrt{1-x^4} x+\frac{5}{21} F\left(\left.\sin ^{-1}(x)\right|-1\right)","-\frac{1}{7} \sqrt{1-x^4} x^5-\frac{5}{21} \sqrt{1-x^4} x+\frac{5}{21} F\left(\left.\sin ^{-1}(x)\right|-1\right)",1,"(-5*x*Sqrt[1 - x^4])/21 - (x^5*Sqrt[1 - x^4])/7 + (5*EllipticF[ArcSin[x], -1])/21","A",3,2,15,0.1333,1,"{321, 221}"
885,1,25,0,0.0048619,"\int \frac{x^4}{\sqrt{1-x^4}} \, dx","Int[x^4/Sqrt[1 - x^4],x]","\frac{1}{3} F\left(\left.\sin ^{-1}(x)\right|-1\right)-\frac{1}{3} x \sqrt{1-x^4}","\frac{1}{3} F\left(\left.\sin ^{-1}(x)\right|-1\right)-\frac{1}{3} x \sqrt{1-x^4}",1,"-(x*Sqrt[1 - x^4])/3 + EllipticF[ArcSin[x], -1]/3","A",2,2,15,0.1333,1,"{321, 221}"
886,1,4,0,0.0013657,"\int \frac{1}{\sqrt{1-x^4}} \, dx","Int[1/Sqrt[1 - x^4],x]","F\left(\left.\sin ^{-1}(x)\right|-1\right)","F\left(\left.\sin ^{-1}(x)\right|-1\right)",1,"EllipticF[ArcSin[x], -1]","A",1,1,11,0.09091,1,"{221}"
887,1,27,0,0.0048177,"\int \frac{1}{x^4 \sqrt{1-x^4}} \, dx","Int[1/(x^4*Sqrt[1 - x^4]),x]","\frac{1}{3} F\left(\left.\sin ^{-1}(x)\right|-1\right)-\frac{\sqrt{1-x^4}}{3 x^3}","\frac{1}{3} F\left(\left.\sin ^{-1}(x)\right|-1\right)-\frac{\sqrt{1-x^4}}{3 x^3}",1,"-Sqrt[1 - x^4]/(3*x^3) + EllipticF[ArcSin[x], -1]/3","A",2,2,15,0.1333,1,"{325, 221}"
888,1,45,0,0.0092758,"\int \frac{1}{x^8 \sqrt{1-x^4}} \, dx","Int[1/(x^8*Sqrt[1 - x^4]),x]","-\frac{5 \sqrt{1-x^4}}{21 x^3}-\frac{\sqrt{1-x^4}}{7 x^7}+\frac{5}{21} F\left(\left.\sin ^{-1}(x)\right|-1\right)","-\frac{5 \sqrt{1-x^4}}{21 x^3}-\frac{\sqrt{1-x^4}}{7 x^7}+\frac{5}{21} F\left(\left.\sin ^{-1}(x)\right|-1\right)",1,"-Sqrt[1 - x^4]/(7*x^7) - (5*Sqrt[1 - x^4])/(21*x^3) + (5*EllipticF[ArcSin[x], -1])/21","A",3,2,15,0.1333,1,"{325, 221}"
889,1,53,0,0.0212611,"\int \frac{x^{10}}{\sqrt{1-x^4}} \, dx","Int[x^10/Sqrt[1 - x^4],x]","-\frac{1}{9} \sqrt{1-x^4} x^7-\frac{7}{45} \sqrt{1-x^4} x^3-\frac{7}{15} F\left(\left.\sin ^{-1}(x)\right|-1\right)+\frac{7}{15} E\left(\left.\sin ^{-1}(x)\right|-1\right)","-\frac{1}{9} \sqrt{1-x^4} x^7-\frac{7}{45} \sqrt{1-x^4} x^3-\frac{7}{15} F\left(\left.\sin ^{-1}(x)\right|-1\right)+\frac{7}{15} E\left(\left.\sin ^{-1}(x)\right|-1\right)",1,"(-7*x^3*Sqrt[1 - x^4])/45 - (x^7*Sqrt[1 - x^4])/9 + (7*EllipticE[ArcSin[x], -1])/15 - (7*EllipticF[ArcSin[x], -1])/15","A",6,5,15,0.3333,1,"{321, 307, 221, 1181, 424}"
890,1,35,0,0.0162421,"\int \frac{x^6}{\sqrt{1-x^4}} \, dx","Int[x^6/Sqrt[1 - x^4],x]","-\frac{1}{5} \sqrt{1-x^4} x^3-\frac{3}{5} F\left(\left.\sin ^{-1}(x)\right|-1\right)+\frac{3}{5} E\left(\left.\sin ^{-1}(x)\right|-1\right)","-\frac{1}{5} \sqrt{1-x^4} x^3-\frac{3}{5} F\left(\left.\sin ^{-1}(x)\right|-1\right)+\frac{3}{5} E\left(\left.\sin ^{-1}(x)\right|-1\right)",1,"-(x^3*Sqrt[1 - x^4])/5 + (3*EllipticE[ArcSin[x], -1])/5 - (3*EllipticF[ArcSin[x], -1])/5","A",5,5,15,0.3333,1,"{321, 307, 221, 1181, 424}"
891,1,11,0,0.0120484,"\int \frac{x^2}{\sqrt{1-x^4}} \, dx","Int[x^2/Sqrt[1 - x^4],x]","E\left(\left.\sin ^{-1}(x)\right|-1\right)-F\left(\left.\sin ^{-1}(x)\right|-1\right)","E\left(\left.\sin ^{-1}(x)\right|-1\right)-F\left(\left.\sin ^{-1}(x)\right|-1\right)",1,"EllipticE[ArcSin[x], -1] - EllipticF[ArcSin[x], -1]","A",4,4,15,0.2667,1,"{307, 221, 1181, 424}"
892,1,27,0,0.0157373,"\int \frac{1}{x^2 \sqrt{1-x^4}} \, dx","Int[1/(x^2*Sqrt[1 - x^4]),x]","-\frac{\sqrt{1-x^4}}{x}+F\left(\left.\sin ^{-1}(x)\right|-1\right)-E\left(\left.\sin ^{-1}(x)\right|-1\right)","-\frac{\sqrt{1-x^4}}{x}+F\left(\left.\sin ^{-1}(x)\right|-1\right)-E\left(\left.\sin ^{-1}(x)\right|-1\right)",1,"-(Sqrt[1 - x^4]/x) - EllipticE[ArcSin[x], -1] + EllipticF[ArcSin[x], -1]","A",5,5,15,0.3333,1,"{325, 307, 221, 1181, 424}"
893,1,53,0,0.0202259,"\int \frac{1}{x^6 \sqrt{1-x^4}} \, dx","Int[1/(x^6*Sqrt[1 - x^4]),x]","-\frac{3 \sqrt{1-x^4}}{5 x}-\frac{\sqrt{1-x^4}}{5 x^5}+\frac{3}{5} F\left(\left.\sin ^{-1}(x)\right|-1\right)-\frac{3}{5} E\left(\left.\sin ^{-1}(x)\right|-1\right)","-\frac{3 \sqrt{1-x^4}}{5 x}-\frac{\sqrt{1-x^4}}{5 x^5}+\frac{3}{5} F\left(\left.\sin ^{-1}(x)\right|-1\right)-\frac{3}{5} E\left(\left.\sin ^{-1}(x)\right|-1\right)",1,"-Sqrt[1 - x^4]/(5*x^5) - (3*Sqrt[1 - x^4])/(5*x) - (3*EllipticE[ArcSin[x], -1])/5 + (3*EllipticF[ArcSin[x], -1])/5","A",6,5,15,0.3333,1,"{325, 307, 221, 1181, 424}"
894,1,42,0,0.0184253,"\int \frac{x^{11}}{\left(1-x^4\right)^{3/2}} \, dx","Int[x^11/(1 - x^4)^(3/2),x]","-\frac{1}{6} \left(1-x^4\right)^{3/2}+\sqrt{1-x^4}+\frac{1}{2 \sqrt{1-x^4}}","-\frac{1}{6} \left(1-x^4\right)^{3/2}+\sqrt{1-x^4}+\frac{1}{2 \sqrt{1-x^4}}",1,"1/(2*Sqrt[1 - x^4]) + Sqrt[1 - x^4] - (1 - x^4)^(3/2)/6","A",3,2,15,0.1333,1,"{266, 43}"
895,1,31,0,0.0138459,"\int \frac{x^7}{\left(1-x^4\right)^{3/2}} \, dx","Int[x^7/(1 - x^4)^(3/2),x]","\frac{\sqrt{1-x^4}}{2}+\frac{1}{2 \sqrt{1-x^4}}","\frac{\sqrt{1-x^4}}{2}+\frac{1}{2 \sqrt{1-x^4}}",1,"1/(2*Sqrt[1 - x^4]) + Sqrt[1 - x^4]/2","A",3,2,15,0.1333,1,"{266, 43}"
896,1,15,0,0.0036682,"\int \frac{x^3}{\left(1-x^4\right)^{3/2}} \, dx","Int[x^3/(1 - x^4)^(3/2),x]","\frac{1}{2 \sqrt{1-x^4}}","\frac{1}{2 \sqrt{1-x^4}}",1,"1/(2*Sqrt[1 - x^4])","A",1,1,15,0.06667,1,"{261}"
897,1,32,0,0.0143036,"\int \frac{1}{x \left(1-x^4\right)^{3/2}} \, dx","Int[1/(x*(1 - x^4)^(3/2)),x]","\frac{1}{2 \sqrt{1-x^4}}-\frac{1}{2} \tanh ^{-1}\left(\sqrt{1-x^4}\right)","\frac{1}{2 \sqrt{1-x^4}}-\frac{1}{2} \tanh ^{-1}\left(\sqrt{1-x^4}\right)",1,"1/(2*Sqrt[1 - x^4]) - ArcTanh[Sqrt[1 - x^4]]/2","A",4,4,15,0.2667,1,"{266, 51, 63, 206}"
898,1,53,0,0.0222809,"\int \frac{1}{x^5 \left(1-x^4\right)^{3/2}} \, dx","Int[1/(x^5*(1 - x^4)^(3/2)),x]","-\frac{3 \sqrt{1-x^4}}{4 x^4}+\frac{1}{2 x^4 \sqrt{1-x^4}}-\frac{3}{4} \tanh ^{-1}\left(\sqrt{1-x^4}\right)","-\frac{1}{4 x^4 \sqrt{1-x^4}}+\frac{3}{4 \sqrt{1-x^4}}-\frac{3}{4} \tanh ^{-1}\left(\sqrt{1-x^4}\right)",1,"1/(2*x^4*Sqrt[1 - x^4]) - (3*Sqrt[1 - x^4])/(4*x^4) - (3*ArcTanh[Sqrt[1 - x^4]])/4","A",5,4,15,0.2667,1,"{266, 51, 63, 206}"
899,1,45,0,0.0193598,"\int \frac{x^9}{\left(1-x^4\right)^{3/2}} \, dx","Int[x^9/(1 - x^4)^(3/2),x]","\frac{x^6}{2 \sqrt{1-x^4}}+\frac{3}{4} \sqrt{1-x^4} x^2-\frac{3}{4} \sin ^{-1}\left(x^2\right)","\frac{x^6}{2 \sqrt{1-x^4}}+\frac{3}{4} \sqrt{1-x^4} x^2-\frac{3}{4} \sin ^{-1}\left(x^2\right)",1,"x^6/(2*Sqrt[1 - x^4]) + (3*x^2*Sqrt[1 - x^4])/4 - (3*ArcSin[x^2])/4","A",4,4,15,0.2667,1,"{275, 288, 321, 216}"
900,1,27,0,0.0118562,"\int \frac{x^5}{\left(1-x^4\right)^{3/2}} \, dx","Int[x^5/(1 - x^4)^(3/2),x]","\frac{x^2}{2 \sqrt{1-x^4}}-\frac{1}{2} \sin ^{-1}\left(x^2\right)","\frac{x^2}{2 \sqrt{1-x^4}}-\frac{1}{2} \sin ^{-1}\left(x^2\right)",1,"x^2/(2*Sqrt[1 - x^4]) - ArcSin[x^2]/2","A",3,3,15,0.2000,1,"{275, 288, 216}"
901,1,18,0,0.0026559,"\int \frac{x}{\left(1-x^4\right)^{3/2}} \, dx","Int[x/(1 - x^4)^(3/2),x]","\frac{x^2}{2 \sqrt{1-x^4}}","\frac{x^2}{2 \sqrt{1-x^4}}",1,"x^2/(2*Sqrt[1 - x^4])","A",1,1,13,0.07692,1,"{264}"
902,1,34,0,0.0071093,"\int \frac{1}{x^3 \left(1-x^4\right)^{3/2}} \, dx","Int[1/(x^3*(1 - x^4)^(3/2)),x]","\frac{x^2}{\sqrt{1-x^4}}-\frac{1}{2 x^2 \sqrt{1-x^4}}","\frac{x^2}{\sqrt{1-x^4}}-\frac{1}{2 x^2 \sqrt{1-x^4}}",1,"-1/(2*x^2*Sqrt[1 - x^4]) + x^2/Sqrt[1 - x^4]","A",2,2,15,0.1333,1,"{271, 264}"
903,1,55,0,0.0122783,"\int \frac{1}{x^7 \left(1-x^4\right)^{3/2}} \, dx","Int[1/(x^7*(1 - x^4)^(3/2)),x]","\frac{4 x^2}{3 \sqrt{1-x^4}}-\frac{2}{3 \sqrt{1-x^4} x^2}-\frac{1}{6 \sqrt{1-x^4} x^6}","\frac{4 x^2}{3 \sqrt{1-x^4}}-\frac{2}{3 \sqrt{1-x^4} x^2}-\frac{1}{6 \sqrt{1-x^4} x^6}",1,"-1/(6*x^6*Sqrt[1 - x^4]) - 2/(3*x^2*Sqrt[1 - x^4]) + (4*x^2)/(3*Sqrt[1 - x^4])","A",3,2,15,0.1333,1,"{271, 264}"
904,1,61,0,0.0153233,"\int \frac{x^{12}}{\left(1-x^4\right)^{3/2}} \, dx","Int[x^12/(1 - x^4)^(3/2),x]","\frac{x^9}{2 \sqrt{1-x^4}}+\frac{9}{14} \sqrt{1-x^4} x^5+\frac{15}{14} \sqrt{1-x^4} x-\frac{15}{14} F\left(\left.\sin ^{-1}(x)\right|-1\right)","\frac{x^9}{2 \sqrt{1-x^4}}+\frac{9}{14} \sqrt{1-x^4} x^5+\frac{15}{14} \sqrt{1-x^4} x-\frac{15}{14} F\left(\left.\sin ^{-1}(x)\right|-1\right)",1,"x^9/(2*Sqrt[1 - x^4]) + (15*x*Sqrt[1 - x^4])/14 + (9*x^5*Sqrt[1 - x^4])/14 - (15*EllipticF[ArcSin[x], -1])/14","A",4,3,15,0.2000,1,"{288, 321, 221}"
905,1,43,0,0.0095008,"\int \frac{x^8}{\left(1-x^4\right)^{3/2}} \, dx","Int[x^8/(1 - x^4)^(3/2),x]","\frac{x^5}{2 \sqrt{1-x^4}}+\frac{5}{6} \sqrt{1-x^4} x-\frac{5}{6} F\left(\left.\sin ^{-1}(x)\right|-1\right)","\frac{x^5}{2 \sqrt{1-x^4}}+\frac{5}{6} \sqrt{1-x^4} x-\frac{5}{6} F\left(\left.\sin ^{-1}(x)\right|-1\right)",1,"x^5/(2*Sqrt[1 - x^4]) + (5*x*Sqrt[1 - x^4])/6 - (5*EllipticF[ArcSin[x], -1])/6","A",3,3,15,0.2000,1,"{288, 321, 221}"
906,1,25,0,0.0048987,"\int \frac{x^4}{\left(1-x^4\right)^{3/2}} \, dx","Int[x^4/(1 - x^4)^(3/2),x]","\frac{x}{2 \sqrt{1-x^4}}-\frac{1}{2} F\left(\left.\sin ^{-1}(x)\right|-1\right)","\frac{x}{2 \sqrt{1-x^4}}-\frac{1}{2} F\left(\left.\sin ^{-1}(x)\right|-1\right)",1,"x/(2*Sqrt[1 - x^4]) - EllipticF[ArcSin[x], -1]/2","A",2,2,15,0.1333,1,"{288, 221}"
907,1,25,0,0.0029822,"\int \frac{1}{\left(1-x^4\right)^{3/2}} \, dx","Int[(1 - x^4)^(-3/2),x]","\frac{x}{2 \sqrt{1-x^4}}+\frac{1}{2} F\left(\left.\sin ^{-1}(x)\right|-1\right)","\frac{x}{2 \sqrt{1-x^4}}+\frac{1}{2} F\left(\left.\sin ^{-1}(x)\right|-1\right)",1,"x/(2*Sqrt[1 - x^4]) + EllipticF[ArcSin[x], -1]/2","A",2,2,11,0.1818,1,"{199, 221}"
908,1,45,0,0.0097015,"\int \frac{1}{x^4 \left(1-x^4\right)^{3/2}} \, dx","Int[1/(x^4*(1 - x^4)^(3/2)),x]","-\frac{5 \sqrt{1-x^4}}{6 x^3}+\frac{1}{2 x^3 \sqrt{1-x^4}}+\frac{5}{6} F\left(\left.\sin ^{-1}(x)\right|-1\right)","-\frac{5 \sqrt{1-x^4}}{6 x^3}+\frac{1}{2 x^3 \sqrt{1-x^4}}+\frac{5}{6} F\left(\left.\sin ^{-1}(x)\right|-1\right)",1,"1/(2*x^3*Sqrt[1 - x^4]) - (5*Sqrt[1 - x^4])/(6*x^3) + (5*EllipticF[ArcSin[x], -1])/6","A",3,3,15,0.2000,1,"{290, 325, 221}"
909,1,63,0,0.0148437,"\int \frac{1}{x^8 \left(1-x^4\right)^{3/2}} \, dx","Int[1/(x^8*(1 - x^4)^(3/2)),x]","-\frac{15 \sqrt{1-x^4}}{14 x^3}-\frac{9 \sqrt{1-x^4}}{14 x^7}+\frac{1}{2 x^7 \sqrt{1-x^4}}+\frac{15}{14} F\left(\left.\sin ^{-1}(x)\right|-1\right)","-\frac{15 \sqrt{1-x^4}}{14 x^3}-\frac{9 \sqrt{1-x^4}}{14 x^7}+\frac{1}{2 x^7 \sqrt{1-x^4}}+\frac{15}{14} F\left(\left.\sin ^{-1}(x)\right|-1\right)",1,"1/(2*x^7*Sqrt[1 - x^4]) - (9*Sqrt[1 - x^4])/(14*x^7) - (15*Sqrt[1 - x^4])/(14*x^3) + (15*EllipticF[ArcSin[x], -1])/14","A",4,3,15,0.2000,1,"{290, 325, 221}"
910,1,71,0,0.0268503,"\int \frac{x^{14}}{\left(1-x^4\right)^{3/2}} \, dx","Int[x^14/(1 - x^4)^(3/2),x]","\frac{x^{11}}{2 \sqrt{1-x^4}}+\frac{11}{18} \sqrt{1-x^4} x^7+\frac{77}{90} \sqrt{1-x^4} x^3+\frac{77}{30} F\left(\left.\sin ^{-1}(x)\right|-1\right)-\frac{77}{30} E\left(\left.\sin ^{-1}(x)\right|-1\right)","\frac{x^{11}}{2 \sqrt{1-x^4}}+\frac{11}{18} \sqrt{1-x^4} x^7+\frac{77}{90} \sqrt{1-x^4} x^3+\frac{77}{30} F\left(\left.\sin ^{-1}(x)\right|-1\right)-\frac{77}{30} E\left(\left.\sin ^{-1}(x)\right|-1\right)",1,"x^11/(2*Sqrt[1 - x^4]) + (77*x^3*Sqrt[1 - x^4])/90 + (11*x^7*Sqrt[1 - x^4])/18 - (77*EllipticE[ArcSin[x], -1])/30 + (77*EllipticF[ArcSin[x], -1])/30","A",7,6,15,0.4000,1,"{288, 321, 307, 221, 1181, 424}"
911,1,53,0,0.0210173,"\int \frac{x^{10}}{\left(1-x^4\right)^{3/2}} \, dx","Int[x^10/(1 - x^4)^(3/2),x]","\frac{x^7}{2 \sqrt{1-x^4}}+\frac{7}{10} \sqrt{1-x^4} x^3+\frac{21}{10} F\left(\left.\sin ^{-1}(x)\right|-1\right)-\frac{21}{10} E\left(\left.\sin ^{-1}(x)\right|-1\right)","\frac{x^7}{2 \sqrt{1-x^4}}+\frac{7}{10} \sqrt{1-x^4} x^3+\frac{21}{10} F\left(\left.\sin ^{-1}(x)\right|-1\right)-\frac{21}{10} E\left(\left.\sin ^{-1}(x)\right|-1\right)",1,"x^7/(2*Sqrt[1 - x^4]) + (7*x^3*Sqrt[1 - x^4])/10 - (21*EllipticE[ArcSin[x], -1])/10 + (21*EllipticF[ArcSin[x], -1])/10","A",6,6,15,0.4000,1,"{288, 321, 307, 221, 1181, 424}"
912,1,35,0,0.0165171,"\int \frac{x^6}{\left(1-x^4\right)^{3/2}} \, dx","Int[x^6/(1 - x^4)^(3/2),x]","\frac{x^3}{2 \sqrt{1-x^4}}+\frac{3}{2} F\left(\left.\sin ^{-1}(x)\right|-1\right)-\frac{3}{2} E\left(\left.\sin ^{-1}(x)\right|-1\right)","\frac{x^3}{2 \sqrt{1-x^4}}+\frac{3}{2} F\left(\left.\sin ^{-1}(x)\right|-1\right)-\frac{3}{2} E\left(\left.\sin ^{-1}(x)\right|-1\right)",1,"x^3/(2*Sqrt[1 - x^4]) - (3*EllipticE[ArcSin[x], -1])/2 + (3*EllipticF[ArcSin[x], -1])/2","A",5,5,15,0.3333,1,"{288, 307, 221, 1181, 424}"
913,1,35,0,0.0163181,"\int \frac{x^2}{\left(1-x^4\right)^{3/2}} \, dx","Int[x^2/(1 - x^4)^(3/2),x]","\frac{x^3}{2 \sqrt{1-x^4}}+\frac{1}{2} F\left(\left.\sin ^{-1}(x)\right|-1\right)-\frac{1}{2} E\left(\left.\sin ^{-1}(x)\right|-1\right)","\frac{x^3}{2 \sqrt{1-x^4}}+\frac{1}{2} F\left(\left.\sin ^{-1}(x)\right|-1\right)-\frac{1}{2} E\left(\left.\sin ^{-1}(x)\right|-1\right)",1,"x^3/(2*Sqrt[1 - x^4]) - EllipticE[ArcSin[x], -1]/2 + EllipticF[ArcSin[x], -1]/2","A",5,5,15,0.3333,1,"{290, 307, 221, 1181, 424}"
914,1,53,0,0.0204178,"\int \frac{1}{x^2 \left(1-x^4\right)^{3/2}} \, dx","Int[1/(x^2*(1 - x^4)^(3/2)),x]","-\frac{3 \sqrt{1-x^4}}{2 x}+\frac{1}{2 x \sqrt{1-x^4}}+\frac{3}{2} F\left(\left.\sin ^{-1}(x)\right|-1\right)-\frac{3}{2} E\left(\left.\sin ^{-1}(x)\right|-1\right)","-\frac{3 \sqrt{1-x^4}}{2 x}+\frac{1}{2 x \sqrt{1-x^4}}+\frac{3}{2} F\left(\left.\sin ^{-1}(x)\right|-1\right)-\frac{3}{2} E\left(\left.\sin ^{-1}(x)\right|-1\right)",1,"1/(2*x*Sqrt[1 - x^4]) - (3*Sqrt[1 - x^4])/(2*x) - (3*EllipticE[ArcSin[x], -1])/2 + (3*EllipticF[ArcSin[x], -1])/2","A",6,6,15,0.4000,1,"{290, 325, 307, 221, 1181, 424}"
915,1,71,0,0.0263981,"\int \frac{1}{x^6 \left(1-x^4\right)^{3/2}} \, dx","Int[1/(x^6*(1 - x^4)^(3/2)),x]","-\frac{21 \sqrt{1-x^4}}{10 x}-\frac{7 \sqrt{1-x^4}}{10 x^5}+\frac{1}{2 x^5 \sqrt{1-x^4}}+\frac{21}{10} F\left(\left.\sin ^{-1}(x)\right|-1\right)-\frac{21}{10} E\left(\left.\sin ^{-1}(x)\right|-1\right)","-\frac{21 \sqrt{1-x^4}}{10 x}-\frac{7 \sqrt{1-x^4}}{10 x^5}+\frac{1}{2 x^5 \sqrt{1-x^4}}+\frac{21}{10} F\left(\left.\sin ^{-1}(x)\right|-1\right)-\frac{21}{10} E\left(\left.\sin ^{-1}(x)\right|-1\right)",1,"1/(2*x^5*Sqrt[1 - x^4]) - (7*Sqrt[1 - x^4])/(10*x^5) - (21*Sqrt[1 - x^4])/(10*x) - (21*EllipticE[ArcSin[x], -1])/10 + (21*EllipticF[ArcSin[x], -1])/10","A",7,6,15,0.4000,1,"{290, 325, 307, 221, 1181, 424}"
916,1,41,0,0.0057407,"\int \frac{1}{\left(1-x^4\right)^{5/2}} \, dx","Int[(1 - x^4)^(-5/2),x]","\frac{5 x}{12 \sqrt{1-x^4}}+\frac{x}{6 \left(1-x^4\right)^{3/2}}+\frac{5}{12} F\left(\left.\sin ^{-1}(x)\right|-1\right)","\frac{5 x}{12 \sqrt{1-x^4}}+\frac{x}{6 \left(1-x^4\right)^{3/2}}+\frac{5}{12} F\left(\left.\sin ^{-1}(x)\right|-1\right)",1,"x/(6*(1 - x^4)^(3/2)) + (5*x)/(12*Sqrt[1 - x^4]) + (5*EllipticF[ArcSin[x], -1])/12","A",3,2,11,0.1818,1,"{199, 221}"
917,1,40,0,0.0143273,"\int \frac{x^{11}}{\sqrt{1+x^4}} \, dx","Int[x^11/Sqrt[1 + x^4],x]","\frac{1}{10} \left(x^4+1\right)^{5/2}-\frac{1}{3} \left(x^4+1\right)^{3/2}+\frac{\sqrt{x^4+1}}{2}","\frac{1}{10} \left(x^4+1\right)^{5/2}-\frac{1}{3} \left(x^4+1\right)^{3/2}+\frac{\sqrt{x^4+1}}{2}",1,"Sqrt[1 + x^4]/2 - (1 + x^4)^(3/2)/3 + (1 + x^4)^(5/2)/10","A",3,2,13,0.1538,1,"{266, 43}"
918,1,27,0,0.0098072,"\int \frac{x^7}{\sqrt{1+x^4}} \, dx","Int[x^7/Sqrt[1 + x^4],x]","\frac{1}{6} \left(x^4+1\right)^{3/2}-\frac{\sqrt{x^4+1}}{2}","\frac{1}{6} \left(x^4+1\right)^{3/2}-\frac{\sqrt{x^4+1}}{2}",1,"-Sqrt[1 + x^4]/2 + (1 + x^4)^(3/2)/6","A",3,2,13,0.1538,1,"{266, 43}"
919,1,13,0,0.0024358,"\int \frac{x^3}{\sqrt{1+x^4}} \, dx","Int[x^3/Sqrt[1 + x^4],x]","\frac{\sqrt{x^4+1}}{2}","\frac{\sqrt{x^4+1}}{2}",1,"Sqrt[1 + x^4]/2","A",1,1,13,0.07692,1,"{261}"
920,1,14,0,0.0065767,"\int \frac{1}{x \sqrt{1+x^4}} \, dx","Int[1/(x*Sqrt[1 + x^4]),x]","-\frac{1}{2} \tanh ^{-1}\left(\sqrt{x^4+1}\right)","-\frac{1}{2} \tanh ^{-1}\left(\sqrt{x^4+1}\right)",1,"-ArcTanh[Sqrt[1 + x^4]]/2","A",3,3,13,0.2308,1,"{266, 63, 207}"
921,1,31,0,0.0108621,"\int \frac{1}{x^5 \sqrt{1+x^4}} \, dx","Int[1/(x^5*Sqrt[1 + x^4]),x]","\frac{1}{4} \tanh ^{-1}\left(\sqrt{x^4+1}\right)-\frac{\sqrt{x^4+1}}{4 x^4}","\frac{1}{4} \tanh ^{-1}\left(\sqrt{x^4+1}\right)-\frac{\sqrt{x^4+1}}{4 x^4}",1,"-Sqrt[1 + x^4]/(4*x^4) + ArcTanh[Sqrt[1 + x^4]]/4","A",4,4,13,0.3077,1,"{266, 51, 63, 207}"
922,1,25,0,0.0087406,"\int \frac{x^5}{\sqrt{1+x^4}} \, dx","Int[x^5/Sqrt[1 + x^4],x]","\frac{1}{4} x^2 \sqrt{x^4+1}-\frac{1}{4} \sinh ^{-1}\left(x^2\right)","\frac{1}{4} x^2 \sqrt{x^4+1}-\frac{1}{4} \sinh ^{-1}\left(x^2\right)",1,"(x^2*Sqrt[1 + x^4])/4 - ArcSinh[x^2]/4","A",3,3,13,0.2308,1,"{275, 321, 215}"
923,1,8,0,0.0026005,"\int \frac{x}{\sqrt{1+x^4}} \, dx","Int[x/Sqrt[1 + x^4],x]","\frac{1}{2} \sinh ^{-1}\left(x^2\right)","\frac{1}{2} \sinh ^{-1}\left(x^2\right)",1,"ArcSinh[x^2]/2","A",2,2,11,0.1818,1,"{275, 215}"
924,1,16,0,0.0026284,"\int \frac{1}{x^3 \sqrt{1+x^4}} \, dx","Int[1/(x^3*Sqrt[1 + x^4]),x]","-\frac{\sqrt{x^4+1}}{2 x^2}","-\frac{\sqrt{x^4+1}}{2 x^2}",1,"-Sqrt[1 + x^4]/(2*x^2)","A",1,1,13,0.07692,1,"{264}"
925,1,33,0,0.005913,"\int \frac{1}{x^7 \sqrt{1+x^4}} \, dx","Int[1/(x^7*Sqrt[1 + x^4]),x]","\frac{\sqrt{x^4+1}}{3 x^2}-\frac{\sqrt{x^4+1}}{6 x^6}","\frac{\sqrt{x^4+1}}{3 x^2}-\frac{\sqrt{x^4+1}}{6 x^6}",1,"-Sqrt[1 + x^4]/(6*x^6) + Sqrt[1 + x^4]/(3*x^2)","A",2,2,13,0.1538,1,"{271, 264}"
926,1,49,0,0.0098078,"\int \frac{1}{x^{11} \sqrt{1+x^4}} \, dx","Int[1/(x^11*Sqrt[1 + x^4]),x]","-\frac{4 \sqrt{x^4+1}}{15 x^2}+\frac{2 \sqrt{x^4+1}}{15 x^6}-\frac{\sqrt{x^4+1}}{10 x^{10}}","-\frac{4 \sqrt{x^4+1}}{15 x^2}+\frac{2 \sqrt{x^4+1}}{15 x^6}-\frac{\sqrt{x^4+1}}{10 x^{10}}",1,"-Sqrt[1 + x^4]/(10*x^10) + (2*Sqrt[1 + x^4])/(15*x^6) - (4*Sqrt[1 + x^4])/(15*x^2)","A",3,2,13,0.1538,1,"{271, 264}"
927,1,74,0,0.0143709,"\int \frac{x^8}{\sqrt{1+x^4}} \, dx","Int[x^8/Sqrt[1 + x^4],x]","\frac{1}{7} \sqrt{x^4+1} x^5-\frac{5}{21} \sqrt{x^4+1} x+\frac{5 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{42 \sqrt{x^4+1}}","\frac{1}{7} \sqrt{x^4+1} x^5-\frac{5}{21} \sqrt{x^4+1} x+\frac{5 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{42 \sqrt{x^4+1}}",1,"(-5*x*Sqrt[1 + x^4])/21 + (x^5*Sqrt[1 + x^4])/7 + (5*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(42*Sqrt[1 + x^4])","A",3,2,13,0.1538,1,"{321, 220}"
928,1,58,0,0.0090074,"\int \frac{x^4}{\sqrt{1+x^4}} \, dx","Int[x^4/Sqrt[1 + x^4],x]","\frac{1}{3} x \sqrt{x^4+1}-\frac{\left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{6 \sqrt{x^4+1}}","\frac{1}{3} x \sqrt{x^4+1}-\frac{\left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{6 \sqrt{x^4+1}}",1,"(x*Sqrt[1 + x^4])/3 - ((1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(6*Sqrt[1 + x^4])","A",2,2,13,0.1538,1,"{321, 220}"
929,1,43,0,0.0030825,"\int \frac{1}{\sqrt{1+x^4}} \, dx","Int[1/Sqrt[1 + x^4],x]","\frac{\left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{2 \sqrt{x^4+1}}","\frac{\left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{2 \sqrt{x^4+1}}",1,"((1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(2*Sqrt[1 + x^4])","A",1,1,9,0.1111,1,"{220}"
930,1,60,0,0.008139,"\int \frac{1}{x^4 \sqrt{1+x^4}} \, dx","Int[1/(x^4*Sqrt[1 + x^4]),x]","-\frac{\sqrt{x^4+1}}{3 x^3}-\frac{\left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{6 \sqrt{x^4+1}}","-\frac{\sqrt{x^4+1}}{3 x^3}-\frac{\left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{6 \sqrt{x^4+1}}",1,"-Sqrt[1 + x^4]/(3*x^3) - ((1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(6*Sqrt[1 + x^4])","A",2,2,13,0.1538,1,"{325, 220}"
931,1,76,0,0.0155506,"\int \frac{1}{x^8 \sqrt{1+x^4}} \, dx","Int[1/(x^8*Sqrt[1 + x^4]),x]","\frac{5 \sqrt{x^4+1}}{21 x^3}-\frac{\sqrt{x^4+1}}{7 x^7}+\frac{5 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{42 \sqrt{x^4+1}}","\frac{5 \sqrt{x^4+1}}{21 x^3}-\frac{\sqrt{x^4+1}}{7 x^7}+\frac{5 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{42 \sqrt{x^4+1}}",1,"-Sqrt[1 + x^4]/(7*x^7) + (5*Sqrt[1 + x^4])/(21*x^3) + (5*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(42*Sqrt[1 + x^4])","A",3,2,13,0.1538,1,"{325, 220}"
932,1,140,0,0.0309806,"\int \frac{x^{10}}{\sqrt{1+x^4}} \, dx","Int[x^10/Sqrt[1 + x^4],x]","\frac{1}{9} \sqrt{x^4+1} x^7-\frac{7}{45} \sqrt{x^4+1} x^3+\frac{7 \sqrt{x^4+1} x}{15 \left(x^2+1\right)}+\frac{7 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{30 \sqrt{x^4+1}}-\frac{7 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{15 \sqrt{x^4+1}}","\frac{1}{9} \sqrt{x^4+1} x^7-\frac{7}{45} \sqrt{x^4+1} x^3+\frac{7 \sqrt{x^4+1} x}{15 \left(x^2+1\right)}+\frac{7 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{30 \sqrt{x^4+1}}-\frac{7 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{15 \sqrt{x^4+1}}",1,"(-7*x^3*Sqrt[1 + x^4])/45 + (x^7*Sqrt[1 + x^4])/9 + (7*x*Sqrt[1 + x^4])/(15*(1 + x^2)) - (7*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticE[2*ArcTan[x], 1/2])/(15*Sqrt[1 + x^4]) + (7*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(30*Sqrt[1 + x^4])","A",5,4,13,0.3077,1,"{321, 305, 220, 1196}"
933,1,124,0,0.0219355,"\int \frac{x^6}{\sqrt{1+x^4}} \, dx","Int[x^6/Sqrt[1 + x^4],x]","\frac{1}{5} \sqrt{x^4+1} x^3-\frac{3 \sqrt{x^4+1} x}{5 \left(x^2+1\right)}-\frac{3 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{10 \sqrt{x^4+1}}+\frac{3 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{5 \sqrt{x^4+1}}","\frac{1}{5} \sqrt{x^4+1} x^3-\frac{3 \sqrt{x^4+1} x}{5 \left(x^2+1\right)}-\frac{3 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{10 \sqrt{x^4+1}}+\frac{3 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{5 \sqrt{x^4+1}}",1,"(x^3*Sqrt[1 + x^4])/5 - (3*x*Sqrt[1 + x^4])/(5*(1 + x^2)) + (3*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticE[2*ArcTan[x], 1/2])/(5*Sqrt[1 + x^4]) - (3*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(10*Sqrt[1 + x^4])","A",4,4,13,0.3077,1,"{321, 305, 220, 1196}"
934,1,103,0,0.0126818,"\int \frac{x^2}{\sqrt{1+x^4}} \, dx","Int[x^2/Sqrt[1 + x^4],x]","\frac{\sqrt{x^4+1} x}{x^2+1}+\frac{\left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{2 \sqrt{x^4+1}}-\frac{\left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{x^4+1}}","\frac{\sqrt{x^4+1} x}{x^2+1}+\frac{\left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{2 \sqrt{x^4+1}}-\frac{\left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{x^4+1}}",1,"(x*Sqrt[1 + x^4])/(1 + x^2) - ((1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticE[2*ArcTan[x], 1/2])/Sqrt[1 + x^4] + ((1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(2*Sqrt[1 + x^4])","A",3,3,13,0.2308,1,"{305, 220, 1196}"
935,1,117,0,0.0149928,"\int \frac{1}{x^2 \sqrt{1+x^4}} \, dx","Int[1/(x^2*Sqrt[1 + x^4]),x]","\frac{\sqrt{x^4+1} x}{x^2+1}-\frac{\sqrt{x^4+1}}{x}+\frac{\left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{2 \sqrt{x^4+1}}-\frac{\left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{x^4+1}}","\frac{\sqrt{x^4+1} x}{x^2+1}-\frac{\sqrt{x^4+1}}{x}+\frac{\left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{2 \sqrt{x^4+1}}-\frac{\left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{x^4+1}}",1,"-(Sqrt[1 + x^4]/x) + (x*Sqrt[1 + x^4])/(1 + x^2) - ((1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticE[2*ArcTan[x], 1/2])/Sqrt[1 + x^4] + ((1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(2*Sqrt[1 + x^4])","A",4,4,13,0.3077,1,"{325, 305, 220, 1196}"
936,1,140,0,0.0238988,"\int \frac{1}{x^6 \sqrt{1+x^4}} \, dx","Int[1/(x^6*Sqrt[1 + x^4]),x]","-\frac{3 \sqrt{x^4+1} x}{5 \left(x^2+1\right)}+\frac{3 \sqrt{x^4+1}}{5 x}-\frac{\sqrt{x^4+1}}{5 x^5}-\frac{3 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{10 \sqrt{x^4+1}}+\frac{3 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{5 \sqrt{x^4+1}}","-\frac{3 \sqrt{x^4+1} x}{5 \left(x^2+1\right)}+\frac{3 \sqrt{x^4+1}}{5 x}-\frac{\sqrt{x^4+1}}{5 x^5}-\frac{3 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{10 \sqrt{x^4+1}}+\frac{3 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{5 \sqrt{x^4+1}}",1,"-Sqrt[1 + x^4]/(5*x^5) + (3*Sqrt[1 + x^4])/(5*x) - (3*x*Sqrt[1 + x^4])/(5*(1 + x^2)) + (3*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticE[2*ArcTan[x], 1/2])/(5*Sqrt[1 + x^4]) - (3*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(10*Sqrt[1 + x^4])","A",5,4,13,0.3077,1,"{325, 305, 220, 1196}"
937,1,38,0,0.0137624,"\int \frac{x^{11}}{\left(1+x^4\right)^{3/2}} \, dx","Int[x^11/(1 + x^4)^(3/2),x]","\frac{1}{6} \left(x^4+1\right)^{3/2}-\sqrt{x^4+1}-\frac{1}{2 \sqrt{x^4+1}}","\frac{1}{6} \left(x^4+1\right)^{3/2}-\sqrt{x^4+1}-\frac{1}{2 \sqrt{x^4+1}}",1,"-1/(2*Sqrt[1 + x^4]) - Sqrt[1 + x^4] + (1 + x^4)^(3/2)/6","A",3,2,13,0.1538,1,"{266, 43}"
938,1,27,0,0.0096739,"\int \frac{x^7}{\left(1+x^4\right)^{3/2}} \, dx","Int[x^7/(1 + x^4)^(3/2),x]","\frac{\sqrt{x^4+1}}{2}+\frac{1}{2 \sqrt{x^4+1}}","\frac{\sqrt{x^4+1}}{2}+\frac{1}{2 \sqrt{x^4+1}}",1,"1/(2*Sqrt[1 + x^4]) + Sqrt[1 + x^4]/2","A",3,2,13,0.1538,1,"{266, 43}"
939,1,13,0,0.0026001,"\int \frac{x^3}{\left(1+x^4\right)^{3/2}} \, dx","Int[x^3/(1 + x^4)^(3/2),x]","-\frac{1}{2 \sqrt{x^4+1}}","-\frac{1}{2 \sqrt{x^4+1}}",1,"-1/(2*Sqrt[1 + x^4])","A",1,1,13,0.07692,1,"{261}"
940,1,28,0,0.0111564,"\int \frac{1}{x \left(1+x^4\right)^{3/2}} \, dx","Int[1/(x*(1 + x^4)^(3/2)),x]","\frac{1}{2 \sqrt{x^4+1}}-\frac{1}{2} \tanh ^{-1}\left(\sqrt{x^4+1}\right)","\frac{1}{2 \sqrt{x^4+1}}-\frac{1}{2} \tanh ^{-1}\left(\sqrt{x^4+1}\right)",1,"1/(2*Sqrt[1 + x^4]) - ArcTanh[Sqrt[1 + x^4]]/2","A",4,4,13,0.3077,1,"{266, 51, 63, 207}"
941,1,47,0,0.0153616,"\int \frac{1}{x^5 \left(1+x^4\right)^{3/2}} \, dx","Int[1/(x^5*(1 + x^4)^(3/2)),x]","-\frac{3 \sqrt{x^4+1}}{4 x^4}+\frac{1}{2 x^4 \sqrt{x^4+1}}+\frac{3}{4} \tanh ^{-1}\left(\sqrt{x^4+1}\right)","-\frac{1}{4 x^4 \sqrt{x^4+1}}-\frac{3}{4 \sqrt{x^4+1}}+\frac{3}{4} \tanh ^{-1}\left(\sqrt{x^4+1}\right)",1,"1/(2*x^4*Sqrt[1 + x^4]) - (3*Sqrt[1 + x^4])/(4*x^4) + (3*ArcTanh[Sqrt[1 + x^4]])/4","A",5,4,13,0.3077,1,"{266, 51, 63, 207}"
942,1,41,0,0.01531,"\int \frac{x^9}{\left(1+x^4\right)^{3/2}} \, dx","Int[x^9/(1 + x^4)^(3/2),x]","-\frac{x^6}{2 \sqrt{x^4+1}}+\frac{3}{4} \sqrt{x^4+1} x^2-\frac{3}{4} \sinh ^{-1}\left(x^2\right)","-\frac{x^6}{2 \sqrt{x^4+1}}+\frac{3}{4} \sqrt{x^4+1} x^2-\frac{3}{4} \sinh ^{-1}\left(x^2\right)",1,"-x^6/(2*Sqrt[1 + x^4]) + (3*x^2*Sqrt[1 + x^4])/4 - (3*ArcSinh[x^2])/4","A",4,4,13,0.3077,1,"{275, 288, 321, 215}"
943,1,25,0,0.0089134,"\int \frac{x^5}{\left(1+x^4\right)^{3/2}} \, dx","Int[x^5/(1 + x^4)^(3/2),x]","\frac{1}{2} \sinh ^{-1}\left(x^2\right)-\frac{x^2}{2 \sqrt{x^4+1}}","\frac{1}{2} \sinh ^{-1}\left(x^2\right)-\frac{x^2}{2 \sqrt{x^4+1}}",1,"-x^2/(2*Sqrt[1 + x^4]) + ArcSinh[x^2]/2","A",3,3,13,0.2308,1,"{275, 288, 215}"
944,1,16,0,0.0022335,"\int \frac{x}{\left(1+x^4\right)^{3/2}} \, dx","Int[x/(1 + x^4)^(3/2),x]","\frac{x^2}{2 \sqrt{x^4+1}}","\frac{x^2}{2 \sqrt{x^4+1}}",1,"x^2/(2*Sqrt[1 + x^4])","A",1,1,11,0.09091,1,"{264}"
945,1,31,0,0.0059413,"\int \frac{1}{x^3 \left(1+x^4\right)^{3/2}} \, dx","Int[1/(x^3*(1 + x^4)^(3/2)),x]","-\frac{x^2}{\sqrt{x^4+1}}-\frac{1}{2 \sqrt{x^4+1} x^2}","-\frac{x^2}{\sqrt{x^4+1}}-\frac{1}{2 \sqrt{x^4+1} x^2}",1,"-1/(2*x^2*Sqrt[1 + x^4]) - x^2/Sqrt[1 + x^4]","A",2,2,13,0.1538,1,"{271, 264}"
946,1,49,0,0.010478,"\int \frac{1}{x^7 \left(1+x^4\right)^{3/2}} \, dx","Int[1/(x^7*(1 + x^4)^(3/2)),x]","\frac{4 x^2}{3 \sqrt{x^4+1}}+\frac{2}{3 \sqrt{x^4+1} x^2}-\frac{1}{6 \sqrt{x^4+1} x^6}","\frac{4 x^2}{3 \sqrt{x^4+1}}+\frac{2}{3 \sqrt{x^4+1} x^2}-\frac{1}{6 \sqrt{x^4+1} x^6}",1,"-1/(6*x^6*Sqrt[1 + x^4]) + 2/(3*x^2*Sqrt[1 + x^4]) + (4*x^2)/(3*Sqrt[1 + x^4])","A",3,2,13,0.1538,1,"{271, 264}"
947,1,90,0,0.0199829,"\int \frac{x^{12}}{\left(1+x^4\right)^{3/2}} \, dx","Int[x^12/(1 + x^4)^(3/2),x]","-\frac{x^9}{2 \sqrt{x^4+1}}+\frac{9}{14} \sqrt{x^4+1} x^5-\frac{15}{14} \sqrt{x^4+1} x+\frac{15 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{28 \sqrt{x^4+1}}","-\frac{x^9}{2 \sqrt{x^4+1}}+\frac{9}{14} \sqrt{x^4+1} x^5-\frac{15}{14} \sqrt{x^4+1} x+\frac{15 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{28 \sqrt{x^4+1}}",1,"-x^9/(2*Sqrt[1 + x^4]) - (15*x*Sqrt[1 + x^4])/14 + (9*x^5*Sqrt[1 + x^4])/14 + (15*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(28*Sqrt[1 + x^4])","A",4,3,13,0.2308,1,"{288, 321, 220}"
948,1,74,0,0.0143724,"\int \frac{x^8}{\left(1+x^4\right)^{3/2}} \, dx","Int[x^8/(1 + x^4)^(3/2),x]","-\frac{x^5}{2 \sqrt{x^4+1}}+\frac{5}{6} \sqrt{x^4+1} x-\frac{5 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{12 \sqrt{x^4+1}}","-\frac{x^5}{2 \sqrt{x^4+1}}+\frac{5}{6} \sqrt{x^4+1} x-\frac{5 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{12 \sqrt{x^4+1}}",1,"-x^5/(2*Sqrt[1 + x^4]) + (5*x*Sqrt[1 + x^4])/6 - (5*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(12*Sqrt[1 + x^4])","A",3,3,13,0.2308,1,"{288, 321, 220}"
949,1,58,0,0.0086073,"\int \frac{x^4}{\left(1+x^4\right)^{3/2}} \, dx","Int[x^4/(1 + x^4)^(3/2),x]","\frac{\left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{4 \sqrt{x^4+1}}-\frac{x}{2 \sqrt{x^4+1}}","\frac{\left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{4 \sqrt{x^4+1}}-\frac{x}{2 \sqrt{x^4+1}}",1,"-x/(2*Sqrt[1 + x^4]) + ((1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(4*Sqrt[1 + x^4])","A",2,2,13,0.1538,1,"{288, 220}"
950,1,58,0,0.0065369,"\int \frac{1}{\left(1+x^4\right)^{3/2}} \, dx","Int[(1 + x^4)^(-3/2),x]","\frac{x}{2 \sqrt{x^4+1}}+\frac{\left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{4 \sqrt{x^4+1}}","\frac{x}{2 \sqrt{x^4+1}}+\frac{\left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{4 \sqrt{x^4+1}}",1,"x/(2*Sqrt[1 + x^4]) + ((1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(4*Sqrt[1 + x^4])","A",2,2,9,0.2222,1,"{199, 220}"
951,1,76,0,0.0146343,"\int \frac{1}{x^4 \left(1+x^4\right)^{3/2}} \, dx","Int[1/(x^4*(1 + x^4)^(3/2)),x]","-\frac{5 \sqrt{x^4+1}}{6 x^3}+\frac{1}{2 x^3 \sqrt{x^4+1}}-\frac{5 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{12 \sqrt{x^4+1}}","-\frac{5 \sqrt{x^4+1}}{6 x^3}+\frac{1}{2 x^3 \sqrt{x^4+1}}-\frac{5 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{12 \sqrt{x^4+1}}",1,"1/(2*x^3*Sqrt[1 + x^4]) - (5*Sqrt[1 + x^4])/(6*x^3) - (5*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(12*Sqrt[1 + x^4])","A",3,3,13,0.2308,1,"{290, 325, 220}"
952,1,92,0,0.0212835,"\int \frac{1}{x^8 \left(1+x^4\right)^{3/2}} \, dx","Int[1/(x^8*(1 + x^4)^(3/2)),x]","\frac{15 \sqrt{x^4+1}}{14 x^3}-\frac{9 \sqrt{x^4+1}}{14 x^7}+\frac{1}{2 x^7 \sqrt{x^4+1}}+\frac{15 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{28 \sqrt{x^4+1}}","\frac{15 \sqrt{x^4+1}}{14 x^3}-\frac{9 \sqrt{x^4+1}}{14 x^7}+\frac{1}{2 x^7 \sqrt{x^4+1}}+\frac{15 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{28 \sqrt{x^4+1}}",1,"1/(2*x^7*Sqrt[1 + x^4]) - (9*Sqrt[1 + x^4])/(14*x^7) + (15*Sqrt[1 + x^4])/(14*x^3) + (15*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(28*Sqrt[1 + x^4])","A",4,3,13,0.2308,1,"{290, 325, 220}"
953,1,156,0,0.0402486,"\int \frac{x^{14}}{\left(1+x^4\right)^{3/2}} \, dx","Int[x^14/(1 + x^4)^(3/2),x]","-\frac{x^{11}}{2 \sqrt{x^4+1}}+\frac{11}{18} \sqrt{x^4+1} x^7-\frac{77}{90} \sqrt{x^4+1} x^3+\frac{77 \sqrt{x^4+1} x}{30 \left(x^2+1\right)}+\frac{77 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{60 \sqrt{x^4+1}}-\frac{77 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{30 \sqrt{x^4+1}}","-\frac{x^{11}}{2 \sqrt{x^4+1}}+\frac{11}{18} \sqrt{x^4+1} x^7-\frac{77}{90} \sqrt{x^4+1} x^3+\frac{77 \sqrt{x^4+1} x}{30 \left(x^2+1\right)}+\frac{77 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{60 \sqrt{x^4+1}}-\frac{77 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{30 \sqrt{x^4+1}}",1,"-x^11/(2*Sqrt[1 + x^4]) - (77*x^3*Sqrt[1 + x^4])/90 + (11*x^7*Sqrt[1 + x^4])/18 + (77*x*Sqrt[1 + x^4])/(30*(1 + x^2)) - (77*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticE[2*ArcTan[x], 1/2])/(30*Sqrt[1 + x^4]) + (77*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(60*Sqrt[1 + x^4])","A",6,5,13,0.3846,1,"{288, 321, 305, 220, 1196}"
954,1,140,0,0.031527,"\int \frac{x^{10}}{\left(1+x^4\right)^{3/2}} \, dx","Int[x^10/(1 + x^4)^(3/2),x]","-\frac{x^7}{2 \sqrt{x^4+1}}+\frac{7}{10} \sqrt{x^4+1} x^3-\frac{21 \sqrt{x^4+1} x}{10 \left(x^2+1\right)}-\frac{21 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{20 \sqrt{x^4+1}}+\frac{21 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{10 \sqrt{x^4+1}}","-\frac{x^7}{2 \sqrt{x^4+1}}+\frac{7}{10} \sqrt{x^4+1} x^3-\frac{21 \sqrt{x^4+1} x}{10 \left(x^2+1\right)}-\frac{21 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{20 \sqrt{x^4+1}}+\frac{21 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{10 \sqrt{x^4+1}}",1,"-x^7/(2*Sqrt[1 + x^4]) + (7*x^3*Sqrt[1 + x^4])/10 - (21*x*Sqrt[1 + x^4])/(10*(1 + x^2)) + (21*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticE[2*ArcTan[x], 1/2])/(10*Sqrt[1 + x^4]) - (21*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(20*Sqrt[1 + x^4])","A",5,5,13,0.3846,1,"{288, 321, 305, 220, 1196}"
955,1,124,0,0.0212209,"\int \frac{x^6}{\left(1+x^4\right)^{3/2}} \, dx","Int[x^6/(1 + x^4)^(3/2),x]","-\frac{x^3}{2 \sqrt{x^4+1}}+\frac{3 \sqrt{x^4+1} x}{2 \left(x^2+1\right)}+\frac{3 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{4 \sqrt{x^4+1}}-\frac{3 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{2 \sqrt{x^4+1}}","-\frac{x^3}{2 \sqrt{x^4+1}}+\frac{3 \sqrt{x^4+1} x}{2 \left(x^2+1\right)}+\frac{3 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{4 \sqrt{x^4+1}}-\frac{3 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{2 \sqrt{x^4+1}}",1,"-x^3/(2*Sqrt[1 + x^4]) + (3*x*Sqrt[1 + x^4])/(2*(1 + x^2)) - (3*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticE[2*ArcTan[x], 1/2])/(2*Sqrt[1 + x^4]) + (3*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(4*Sqrt[1 + x^4])","A",4,4,13,0.3077,1,"{288, 305, 220, 1196}"
956,1,124,0,0.0207975,"\int \frac{x^2}{\left(1+x^4\right)^{3/2}} \, dx","Int[x^2/(1 + x^4)^(3/2),x]","\frac{x^3}{2 \sqrt{x^4+1}}-\frac{\sqrt{x^4+1} x}{2 \left(x^2+1\right)}-\frac{\left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{4 \sqrt{x^4+1}}+\frac{\left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{2 \sqrt{x^4+1}}","\frac{x^3}{2 \sqrt{x^4+1}}-\frac{\sqrt{x^4+1} x}{2 \left(x^2+1\right)}-\frac{\left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{4 \sqrt{x^4+1}}+\frac{\left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{2 \sqrt{x^4+1}}",1,"x^3/(2*Sqrt[1 + x^4]) - (x*Sqrt[1 + x^4])/(2*(1 + x^2)) + ((1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticE[2*ArcTan[x], 1/2])/(2*Sqrt[1 + x^4]) - ((1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(4*Sqrt[1 + x^4])","A",4,4,13,0.3077,1,"{290, 305, 220, 1196}"
957,1,140,0,0.0245369,"\int \frac{1}{x^2 \left(1+x^4\right)^{3/2}} \, dx","Int[1/(x^2*(1 + x^4)^(3/2)),x]","\frac{3 \sqrt{x^4+1} x}{2 \left(x^2+1\right)}-\frac{3 \sqrt{x^4+1}}{2 x}+\frac{1}{2 \sqrt{x^4+1} x}+\frac{3 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{4 \sqrt{x^4+1}}-\frac{3 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{2 \sqrt{x^4+1}}","\frac{3 \sqrt{x^4+1} x}{2 \left(x^2+1\right)}-\frac{3 \sqrt{x^4+1}}{2 x}+\frac{1}{2 \sqrt{x^4+1} x}+\frac{3 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{4 \sqrt{x^4+1}}-\frac{3 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{2 \sqrt{x^4+1}}",1,"1/(2*x*Sqrt[1 + x^4]) - (3*Sqrt[1 + x^4])/(2*x) + (3*x*Sqrt[1 + x^4])/(2*(1 + x^2)) - (3*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticE[2*ArcTan[x], 1/2])/(2*Sqrt[1 + x^4]) + (3*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(4*Sqrt[1 + x^4])","A",5,5,13,0.3846,1,"{290, 325, 305, 220, 1196}"
958,1,156,0,0.0344749,"\int \frac{1}{x^6 \left(1+x^4\right)^{3/2}} \, dx","Int[1/(x^6*(1 + x^4)^(3/2)),x]","-\frac{21 \sqrt{x^4+1} x}{10 \left(x^2+1\right)}+\frac{21 \sqrt{x^4+1}}{10 x}-\frac{7 \sqrt{x^4+1}}{10 x^5}+\frac{1}{2 \sqrt{x^4+1} x^5}-\frac{21 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{20 \sqrt{x^4+1}}+\frac{21 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{10 \sqrt{x^4+1}}","-\frac{21 \sqrt{x^4+1} x}{10 \left(x^2+1\right)}+\frac{21 \sqrt{x^4+1}}{10 x}-\frac{7 \sqrt{x^4+1}}{10 x^5}+\frac{1}{2 \sqrt{x^4+1} x^5}-\frac{21 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{20 \sqrt{x^4+1}}+\frac{21 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{10 \sqrt{x^4+1}}",1,"1/(2*x^5*Sqrt[1 + x^4]) - (7*Sqrt[1 + x^4])/(10*x^5) + (21*Sqrt[1 + x^4])/(10*x) - (21*x*Sqrt[1 + x^4])/(10*(1 + x^2)) + (21*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticE[2*ArcTan[x], 1/2])/(10*Sqrt[1 + x^4]) - (21*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(20*Sqrt[1 + x^4])","A",6,5,13,0.3846,1,"{290, 325, 305, 220, 1196}"
959,1,72,0,0.010459,"\int \frac{1}{\left(1+x^4\right)^{5/2}} \, dx","Int[(1 + x^4)^(-5/2),x]","\frac{5 x}{12 \sqrt{x^4+1}}+\frac{x}{6 \left(x^4+1\right)^{3/2}}+\frac{5 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{24 \sqrt{x^4+1}}","\frac{5 x}{12 \sqrt{x^4+1}}+\frac{x}{6 \left(x^4+1\right)^{3/2}}+\frac{5 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{24 \sqrt{x^4+1}}",1,"x/(6*(1 + x^4)^(3/2)) + (5*x)/(12*Sqrt[1 + x^4]) + (5*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(24*Sqrt[1 + x^4])","A",3,2,9,0.2222,1,"{199, 220}"
960,1,29,0,0.0136172,"\int \frac{x^7}{\sqrt{16-x^4}} \, dx","Int[x^7/Sqrt[16 - x^4],x]","\frac{1}{6} \left(16-x^4\right)^{3/2}-8 \sqrt{16-x^4}","\frac{1}{6} \left(16-x^4\right)^{3/2}-8 \sqrt{16-x^4}",1,"-8*Sqrt[16 - x^4] + (16 - x^4)^(3/2)/6","A",3,2,15,0.1333,1,"{266, 43}"
961,1,29,0,0.0140243,"\int \frac{x^5}{\sqrt{16-x^4}} \, dx","Int[x^5/Sqrt[16 - x^4],x]","4 \sin ^{-1}\left(\frac{x^2}{4}\right)-\frac{1}{4} x^2 \sqrt{16-x^4}","4 \sin ^{-1}\left(\frac{x^2}{4}\right)-\frac{1}{4} x^2 \sqrt{16-x^4}",1,"-(x^2*Sqrt[16 - x^4])/4 + 4*ArcSin[x^2/4]","A",3,3,15,0.2000,1,"{275, 321, 216}"
962,1,15,0,0.0029264,"\int \frac{x^3}{\sqrt{16-x^4}} \, dx","Int[x^3/Sqrt[16 - x^4],x]","-\frac{1}{2} \sqrt{16-x^4}","-\frac{1}{2} \sqrt{16-x^4}",1,"-Sqrt[16 - x^4]/2","A",1,1,15,0.06667,1,"{261}"
963,1,12,0,0.0041662,"\int \frac{x}{\sqrt{16-x^4}} \, dx","Int[x/Sqrt[16 - x^4],x]","\frac{1}{2} \sin ^{-1}\left(\frac{x^2}{4}\right)","\frac{1}{2} \sin ^{-1}\left(\frac{x^2}{4}\right)",1,"ArcSin[x^2/4]/2","A",2,2,13,0.1538,1,"{275, 216}"
964,1,20,0,0.01006,"\int \frac{1}{x \sqrt{16-x^4}} \, dx","Int[1/(x*Sqrt[16 - x^4]),x]","-\frac{1}{8} \tanh ^{-1}\left(\frac{\sqrt{16-x^4}}{4}\right)","-\frac{1}{8} \tanh ^{-1}\left(\frac{\sqrt{16-x^4}}{4}\right)",1,"-ArcTanh[Sqrt[16 - x^4]/4]/8","A",3,3,15,0.2000,1,"{266, 63, 206}"
965,1,18,0,0.0032332,"\int \frac{1}{x^3 \sqrt{16-x^4}} \, dx","Int[1/(x^3*Sqrt[16 - x^4]),x]","-\frac{\sqrt{16-x^4}}{32 x^2}","-\frac{\sqrt{16-x^4}}{32 x^2}",1,"-Sqrt[16 - x^4]/(32*x^2)","A",1,1,15,0.06667,1,"{264}"
966,1,39,0,0.0158811,"\int \frac{1}{x^5 \sqrt{16-x^4}} \, dx","Int[1/(x^5*Sqrt[16 - x^4]),x]","-\frac{\sqrt{16-x^4}}{64 x^4}-\frac{1}{256} \tanh ^{-1}\left(\frac{\sqrt{16-x^4}}{4}\right)","-\frac{\sqrt{16-x^4}}{64 x^4}-\frac{1}{256} \tanh ^{-1}\left(\frac{\sqrt{16-x^4}}{4}\right)",1,"-Sqrt[16 - x^4]/(64*x^4) - ArcTanh[Sqrt[16 - x^4]/4]/256","A",4,4,15,0.2667,1,"{266, 51, 63, 206}"
967,1,37,0,0.0076976,"\int \frac{1}{x^7 \sqrt{16-x^4}} \, dx","Int[1/(x^7*Sqrt[16 - x^4]),x]","-\frac{\sqrt{16-x^4}}{768 x^2}-\frac{\sqrt{16-x^4}}{96 x^6}","-\frac{\sqrt{16-x^4}}{768 x^2}-\frac{\sqrt{16-x^4}}{96 x^6}",1,"-Sqrt[16 - x^4]/(96*x^6) - Sqrt[16 - x^4]/(768*x^2)","A",2,2,15,0.1333,1,"{271, 264}"
968,1,43,0,0.0201656,"\int \frac{x^6}{\sqrt{16-x^4}} \, dx","Int[x^6/Sqrt[16 - x^4],x]","-\frac{1}{5} \sqrt{16-x^4} x^3-\frac{96}{5} F\left(\left.\sin ^{-1}\left(\frac{x}{2}\right)\right|-1\right)+\frac{96}{5} E\left(\left.\sin ^{-1}\left(\frac{x}{2}\right)\right|-1\right)","-\frac{1}{5} \sqrt{16-x^4} x^3-\frac{96}{5} F\left(\left.\sin ^{-1}\left(\frac{x}{2}\right)\right|-1\right)+\frac{96}{5} E\left(\left.\sin ^{-1}\left(\frac{x}{2}\right)\right|-1\right)",1,"-(x^3*Sqrt[16 - x^4])/5 + (96*EllipticE[ArcSin[x/2], -1])/5 - (96*EllipticF[ArcSin[x/2], -1])/5","A",6,6,15,0.4000,1,"{321, 307, 221, 1181, 21, 424}"
969,1,29,0,0.0057608,"\int \frac{x^4}{\sqrt{16-x^4}} \, dx","Int[x^4/Sqrt[16 - x^4],x]","\frac{8}{3} F\left(\left.\sin ^{-1}\left(\frac{x}{2}\right)\right|-1\right)-\frac{1}{3} x \sqrt{16-x^4}","\frac{8}{3} F\left(\left.\sin ^{-1}\left(\frac{x}{2}\right)\right|-1\right)-\frac{1}{3} x \sqrt{16-x^4}",1,"-(x*Sqrt[16 - x^4])/3 + (8*EllipticF[ArcSin[x/2], -1])/3","A",2,2,15,0.1333,1,"{321, 221}"
970,1,21,0,0.0152457,"\int \frac{x^2}{\sqrt{16-x^4}} \, dx","Int[x^2/Sqrt[16 - x^4],x]","2 E\left(\left.\sin ^{-1}\left(\frac{x}{2}\right)\right|-1\right)-2 F\left(\left.\sin ^{-1}\left(\frac{x}{2}\right)\right|-1\right)","2 E\left(\left.\sin ^{-1}\left(\frac{x}{2}\right)\right|-1\right)-2 F\left(\left.\sin ^{-1}\left(\frac{x}{2}\right)\right|-1\right)",1,"2*EllipticE[ArcSin[x/2], -1] - 2*EllipticF[ArcSin[x/2], -1]","A",5,5,15,0.3333,1,"{307, 221, 1181, 21, 424}"
971,1,12,0,0.0016934,"\int \frac{1}{\sqrt{16-x^4}} \, dx","Int[1/Sqrt[16 - x^4],x]","\frac{1}{2} F\left(\left.\sin ^{-1}\left(\frac{x}{2}\right)\right|-1\right)","\frac{1}{2} F\left(\left.\sin ^{-1}\left(\frac{x}{2}\right)\right|-1\right)",1,"EllipticF[ArcSin[x/2], -1]/2","A",1,1,11,0.09091,1,"{221}"
972,1,43,0,0.0198747,"\int \frac{1}{x^2 \sqrt{16-x^4}} \, dx","Int[1/(x^2*Sqrt[16 - x^4]),x]","-\frac{\sqrt{16-x^4}}{16 x}+\frac{1}{8} F\left(\left.\sin ^{-1}\left(\frac{x}{2}\right)\right|-1\right)-\frac{1}{8} E\left(\left.\sin ^{-1}\left(\frac{x}{2}\right)\right|-1\right)","-\frac{\sqrt{16-x^4}}{16 x}+\frac{1}{8} F\left(\left.\sin ^{-1}\left(\frac{x}{2}\right)\right|-1\right)-\frac{1}{8} E\left(\left.\sin ^{-1}\left(\frac{x}{2}\right)\right|-1\right)",1,"-Sqrt[16 - x^4]/(16*x) - EllipticE[ArcSin[x/2], -1]/8 + EllipticF[ArcSin[x/2], -1]/8","A",6,6,15,0.4000,1,"{325, 307, 221, 1181, 21, 424}"
973,1,31,0,0.0055191,"\int \frac{1}{x^4 \sqrt{16-x^4}} \, dx","Int[1/(x^4*Sqrt[16 - x^4]),x]","\frac{1}{96} F\left(\left.\sin ^{-1}\left(\frac{x}{2}\right)\right|-1\right)-\frac{\sqrt{16-x^4}}{48 x^3}","\frac{1}{96} F\left(\left.\sin ^{-1}\left(\frac{x}{2}\right)\right|-1\right)-\frac{\sqrt{16-x^4}}{48 x^3}",1,"-Sqrt[16 - x^4]/(48*x^3) + EllipticF[ArcSin[x/2], -1]/96","A",2,2,15,0.1333,1,"{325, 221}"
974,1,18,0,0.0070415,"\int \frac{x}{\sqrt{-4+x^4}} \, dx","Int[x/Sqrt[-4 + x^4],x]","\frac{1}{2} \tanh ^{-1}\left(\frac{x^2}{\sqrt{x^4-4}}\right)","\frac{1}{2} \tanh ^{-1}\left(\frac{x^2}{\sqrt{x^4-4}}\right)",1,"ArcTanh[x^2/Sqrt[-4 + x^4]]/2","A",3,3,11,0.2727,1,"{275, 217, 206}"
975,1,12,0,0.0037786,"\int \frac{x}{\sqrt{4+x^4}} \, dx","Int[x/Sqrt[4 + x^4],x]","\frac{1}{2} \sinh ^{-1}\left(\frac{x^2}{2}\right)","\frac{1}{2} \sinh ^{-1}\left(\frac{x^2}{2}\right)",1,"ArcSinh[x^2/2]/2","A",2,2,11,0.1818,1,"{275, 215}"
976,1,14,0,0.0068633,"\int \frac{1}{x \sqrt{-1+x^4}} \, dx","Int[1/(x*Sqrt[-1 + x^4]),x]","\frac{1}{2} \tan ^{-1}\left(\sqrt{x^4-1}\right)","\frac{1}{2} \tan ^{-1}\left(\sqrt{x^4-1}\right)",1,"ArcTan[Sqrt[-1 + x^4]]/2","A",3,3,13,0.2308,1,"{266, 63, 203}"
977,1,72,0,0.0091386,"\int \frac{x^4}{\sqrt{-1+x^4}} \, dx","Int[x^4/Sqrt[-1 + x^4],x]","\frac{1}{3} \sqrt{x^4-1} x+\frac{\sqrt{x^2-1} \sqrt{x^2+1} F\left(\sin ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^2-1}}\right)|\frac{1}{2}\right)}{3 \sqrt{2} \sqrt{x^4-1}}","\frac{1}{3} \sqrt{x^4-1} x+\frac{\sqrt{x^2-1} \sqrt{x^2+1} F\left(\sin ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^2-1}}\right)|\frac{1}{2}\right)}{3 \sqrt{2} \sqrt{x^4-1}}",1,"(x*Sqrt[-1 + x^4])/3 + (Sqrt[-1 + x^2]*Sqrt[1 + x^2]*EllipticF[ArcSin[(Sqrt[2]*x)/Sqrt[-1 + x^2]], 1/2])/(3*Sqrt[2]*Sqrt[-1 + x^4])","A",2,2,13,0.1538,1,"{321, 222}"
978,1,54,0,0.0037157,"\int \frac{1}{\sqrt{-1+x^4}} \, dx","Int[1/Sqrt[-1 + x^4],x]","\frac{\sqrt{x^2-1} \sqrt{x^2+1} F\left(\sin ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^2-1}}\right)|\frac{1}{2}\right)}{\sqrt{2} \sqrt{x^4-1}}","\frac{\sqrt{x^2-1} \sqrt{x^2+1} F\left(\sin ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^2-1}}\right)|\frac{1}{2}\right)}{\sqrt{2} \sqrt{x^4-1}}",1,"(Sqrt[-1 + x^2]*Sqrt[1 + x^2]*EllipticF[ArcSin[(Sqrt[2]*x)/Sqrt[-1 + x^2]], 1/2])/(Sqrt[2]*Sqrt[-1 + x^4])","A",1,1,9,0.1111,1,"{222}"
979,1,74,0,0.0093243,"\int \frac{1}{x^4 \sqrt{-1+x^4}} \, dx","Int[1/(x^4*Sqrt[-1 + x^4]),x]","\frac{\sqrt{x^4-1}}{3 x^3}+\frac{\sqrt{x^2-1} \sqrt{x^2+1} F\left(\sin ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^2-1}}\right)|\frac{1}{2}\right)}{3 \sqrt{2} \sqrt{x^4-1}}","\frac{\sqrt{x^4-1}}{3 x^3}+\frac{\sqrt{x^2-1} \sqrt{x^2+1} F\left(\sin ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^2-1}}\right)|\frac{1}{2}\right)}{3 \sqrt{2} \sqrt{x^4-1}}",1,"Sqrt[-1 + x^4]/(3*x^3) + (Sqrt[-1 + x^2]*Sqrt[1 + x^2]*EllipticF[ArcSin[(Sqrt[2]*x)/Sqrt[-1 + x^2]], 1/2])/(3*Sqrt[2]*Sqrt[-1 + x^4])","A",2,2,13,0.1538,1,"{325, 222}"
980,1,150,0,0.0232515,"\int \frac{x^6}{\sqrt{-1+x^4}} \, dx","Int[x^6/Sqrt[-1 + x^4],x]","\frac{1}{5} \sqrt{x^4-1} x^3+\frac{3 \left(x^2+1\right) x}{5 \sqrt{x^4-1}}+\frac{3 \sqrt{x^2-1} \sqrt{x^2+1} F\left(\sin ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^2-1}}\right)|\frac{1}{2}\right)}{5 \sqrt{2} \sqrt{x^4-1}}-\frac{3 \sqrt{2} \sqrt{x^2-1} \sqrt{x^2+1} E\left(\sin ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^2-1}}\right)|\frac{1}{2}\right)}{5 \sqrt{x^4-1}}","\frac{1}{5} \sqrt{x^4-1} x^3+\frac{3 \left(x^2+1\right) x}{5 \sqrt{x^4-1}}+\frac{3 \sqrt{x^2-1} \sqrt{x^2+1} F\left(\sin ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^2-1}}\right)|\frac{1}{2}\right)}{5 \sqrt{2} \sqrt{x^4-1}}-\frac{3 \sqrt{2} \sqrt{x^2-1} \sqrt{x^2+1} E\left(\sin ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^2-1}}\right)|\frac{1}{2}\right)}{5 \sqrt{x^4-1}}",1,"(3*x*(1 + x^2))/(5*Sqrt[-1 + x^4]) + (x^3*Sqrt[-1 + x^4])/5 - (3*Sqrt[2]*Sqrt[-1 + x^2]*Sqrt[1 + x^2]*EllipticE[ArcSin[(Sqrt[2]*x)/Sqrt[-1 + x^2]], 1/2])/(5*Sqrt[-1 + x^4]) + (3*Sqrt[-1 + x^2]*Sqrt[1 + x^2]*EllipticF[ArcSin[(Sqrt[2]*x)/Sqrt[-1 + x^2]], 1/2])/(5*Sqrt[2]*Sqrt[-1 + x^4])","A",4,4,13,0.3077,1,"{321, 306, 222, 1185}"
981,1,126,0,0.0131219,"\int \frac{x^2}{\sqrt{-1+x^4}} \, dx","Int[x^2/Sqrt[-1 + x^4],x]","\frac{x \left(x^2+1\right)}{\sqrt{x^4-1}}+\frac{\sqrt{x^2-1} \sqrt{x^2+1} F\left(\sin ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^2-1}}\right)|\frac{1}{2}\right)}{\sqrt{2} \sqrt{x^4-1}}-\frac{\sqrt{2} \sqrt{x^2-1} \sqrt{x^2+1} E\left(\sin ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^2-1}}\right)|\frac{1}{2}\right)}{\sqrt{x^4-1}}","\frac{x \left(x^2+1\right)}{\sqrt{x^4-1}}+\frac{\sqrt{x^2-1} \sqrt{x^2+1} F\left(\sin ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^2-1}}\right)|\frac{1}{2}\right)}{\sqrt{2} \sqrt{x^4-1}}-\frac{\sqrt{2} \sqrt{x^2-1} \sqrt{x^2+1} E\left(\sin ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^2-1}}\right)|\frac{1}{2}\right)}{\sqrt{x^4-1}}",1,"(x*(1 + x^2))/Sqrt[-1 + x^4] - (Sqrt[2]*Sqrt[-1 + x^2]*Sqrt[1 + x^2]*EllipticE[ArcSin[(Sqrt[2]*x)/Sqrt[-1 + x^2]], 1/2])/Sqrt[-1 + x^4] + (Sqrt[-1 + x^2]*Sqrt[1 + x^2]*EllipticF[ArcSin[(Sqrt[2]*x)/Sqrt[-1 + x^2]], 1/2])/(Sqrt[2]*Sqrt[-1 + x^4])","A",3,3,13,0.2308,1,"{306, 222, 1185}"
982,1,140,0,0.0162141,"\int \frac{1}{x^2 \sqrt{-1+x^4}} \, dx","Int[1/(x^2*Sqrt[-1 + x^4]),x]","-\frac{x \left(x^2+1\right)}{\sqrt{x^4-1}}+\frac{\sqrt{x^4-1}}{x}-\frac{\sqrt{x^2-1} \sqrt{x^2+1} F\left(\sin ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^2-1}}\right)|\frac{1}{2}\right)}{\sqrt{2} \sqrt{x^4-1}}+\frac{\sqrt{2} \sqrt{x^2-1} \sqrt{x^2+1} E\left(\sin ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^2-1}}\right)|\frac{1}{2}\right)}{\sqrt{x^4-1}}","-\frac{x \left(x^2+1\right)}{\sqrt{x^4-1}}+\frac{\sqrt{x^4-1}}{x}-\frac{\sqrt{x^2-1} \sqrt{x^2+1} F\left(\sin ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^2-1}}\right)|\frac{1}{2}\right)}{\sqrt{2} \sqrt{x^4-1}}+\frac{\sqrt{2} \sqrt{x^2-1} \sqrt{x^2+1} E\left(\sin ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^2-1}}\right)|\frac{1}{2}\right)}{\sqrt{x^4-1}}",1,"-((x*(1 + x^2))/Sqrt[-1 + x^4]) + Sqrt[-1 + x^4]/x + (Sqrt[2]*Sqrt[-1 + x^2]*Sqrt[1 + x^2]*EllipticE[ArcSin[(Sqrt[2]*x)/Sqrt[-1 + x^2]], 1/2])/Sqrt[-1 + x^4] - (Sqrt[-1 + x^2]*Sqrt[1 + x^2]*EllipticF[ArcSin[(Sqrt[2]*x)/Sqrt[-1 + x^2]], 1/2])/(Sqrt[2]*Sqrt[-1 + x^4])","A",4,4,13,0.3077,1,"{325, 306, 222, 1185}"
983,1,48,0,0.0336314,"\int \frac{x^2}{\sqrt{3-2 x^4}} \, dx","Int[x^2/Sqrt[3 - 2*x^4],x]","\frac{\sqrt[4]{3} E\left(\left.\sin ^{-1}\left(\sqrt[4]{\frac{2}{3}} x\right)\right|-1\right)}{2^{3/4}}-\frac{\sqrt[4]{3} F\left(\left.\sin ^{-1}\left(\sqrt[4]{\frac{2}{3}} x\right)\right|-1\right)}{2^{3/4}}","\frac{\sqrt[4]{3} E\left(\left.\sin ^{-1}\left(\sqrt[4]{\frac{2}{3}} x\right)\right|-1\right)}{2^{3/4}}-\frac{\sqrt[4]{3} F\left(\left.\sin ^{-1}\left(\sqrt[4]{\frac{2}{3}} x\right)\right|-1\right)}{2^{3/4}}",1,"(3^(1/4)*EllipticE[ArcSin[(2/3)^(1/4)*x], -1])/2^(3/4) - (3^(1/4)*EllipticF[ArcSin[(2/3)^(1/4)*x], -1])/2^(3/4)","A",5,5,15,0.3333,1,"{307, 221, 1181, 21, 424}"
984,1,54,0,0.0467568,"\int \frac{x^2}{\sqrt{3-b x^4}} \, dx","Int[x^2/Sqrt[3 - b*x^4],x]","\frac{\sqrt[4]{3} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{3}}\right)\right|-1\right)}{b^{3/4}}-\frac{\sqrt[4]{3} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{3}}\right)\right|-1\right)}{b^{3/4}}","\frac{\sqrt[4]{3} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{3}}\right)\right|-1\right)}{b^{3/4}}-\frac{\sqrt[4]{3} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{3}}\right)\right|-1\right)}{b^{3/4}}",1,"(3^(1/4)*EllipticE[ArcSin[(b^(1/4)*x)/3^(1/4)], -1])/b^(3/4) - (3^(1/4)*EllipticF[ArcSin[(b^(1/4)*x)/3^(1/4)], -1])/b^(3/4)","A",4,4,16,0.2500,1,"{307, 221, 1199, 424}"
985,1,27,0,0.0102084,"\int x^7 \sqrt[3]{1+x^4} \, dx","Int[x^7*(1 + x^4)^(1/3),x]","\frac{3}{28} \left(x^4+1\right)^{7/3}-\frac{3}{16} \left(x^4+1\right)^{4/3}","\frac{3}{28} \left(x^4+1\right)^{7/3}-\frac{3}{16} \left(x^4+1\right)^{4/3}",1,"(-3*(1 + x^4)^(4/3))/16 + (3*(1 + x^4)^(7/3))/28","A",3,2,13,0.1538,1,"{266, 43}"
986,1,13,0,0.0030519,"\int \frac{x^3}{\left(1+x^4\right)^{4/3}} \, dx","Int[x^3/(1 + x^4)^(4/3),x]","-\frac{3}{4 \sqrt[3]{x^4+1}}","-\frac{3}{4 \sqrt[3]{x^4+1}}",1,"-3/(4*(1 + x^4)^(1/3))","A",1,1,13,0.07692,1,"{261}"
987,1,13,0,0.0026967,"\int \frac{x^3}{\sqrt[3]{1+x^4}} \, dx","Int[x^3/(1 + x^4)^(1/3),x]","\frac{3}{8} \left(x^4+1\right)^{2/3}","\frac{3}{8} \left(x^4+1\right)^{2/3}",1,"(3*(1 + x^4)^(2/3))/8","A",1,1,13,0.07692,1,"{261}"
988,1,101,0,0.0587497,"\int x^{19} \sqrt[4]{a+b x^4} \, dx","Int[x^19*(a + b*x^4)^(1/4),x]","\frac{6 a^2 \left(a+b x^4\right)^{13/4}}{13 b^5}-\frac{4 a^3 \left(a+b x^4\right)^{9/4}}{9 b^5}+\frac{a^4 \left(a+b x^4\right)^{5/4}}{5 b^5}+\frac{\left(a+b x^4\right)^{21/4}}{21 b^5}-\frac{4 a \left(a+b x^4\right)^{17/4}}{17 b^5}","\frac{6 a^2 \left(a+b x^4\right)^{13/4}}{13 b^5}-\frac{4 a^3 \left(a+b x^4\right)^{9/4}}{9 b^5}+\frac{a^4 \left(a+b x^4\right)^{5/4}}{5 b^5}+\frac{\left(a+b x^4\right)^{21/4}}{21 b^5}-\frac{4 a \left(a+b x^4\right)^{17/4}}{17 b^5}",1,"(a^4*(a + b*x^4)^(5/4))/(5*b^5) - (4*a^3*(a + b*x^4)^(9/4))/(9*b^5) + (6*a^2*(a + b*x^4)^(13/4))/(13*b^5) - (4*a*(a + b*x^4)^(17/4))/(17*b^5) + (a + b*x^4)^(21/4)/(21*b^5)","A",3,2,15,0.1333,1,"{266, 43}"
989,1,80,0,0.0444452,"\int x^{15} \sqrt[4]{a+b x^4} \, dx","Int[x^15*(a + b*x^4)^(1/4),x]","\frac{a^2 \left(a+b x^4\right)^{9/4}}{3 b^4}-\frac{a^3 \left(a+b x^4\right)^{5/4}}{5 b^4}+\frac{\left(a+b x^4\right)^{17/4}}{17 b^4}-\frac{3 a \left(a+b x^4\right)^{13/4}}{13 b^4}","\frac{a^2 \left(a+b x^4\right)^{9/4}}{3 b^4}-\frac{a^3 \left(a+b x^4\right)^{5/4}}{5 b^4}+\frac{\left(a+b x^4\right)^{17/4}}{17 b^4}-\frac{3 a \left(a+b x^4\right)^{13/4}}{13 b^4}",1,"-(a^3*(a + b*x^4)^(5/4))/(5*b^4) + (a^2*(a + b*x^4)^(9/4))/(3*b^4) - (3*a*(a + b*x^4)^(13/4))/(13*b^4) + (a + b*x^4)^(17/4)/(17*b^4)","A",3,2,15,0.1333,1,"{266, 43}"
990,1,59,0,0.0339833,"\int x^{11} \sqrt[4]{a+b x^4} \, dx","Int[x^11*(a + b*x^4)^(1/4),x]","\frac{a^2 \left(a+b x^4\right)^{5/4}}{5 b^3}+\frac{\left(a+b x^4\right)^{13/4}}{13 b^3}-\frac{2 a \left(a+b x^4\right)^{9/4}}{9 b^3}","\frac{a^2 \left(a+b x^4\right)^{5/4}}{5 b^3}+\frac{\left(a+b x^4\right)^{13/4}}{13 b^3}-\frac{2 a \left(a+b x^4\right)^{9/4}}{9 b^3}",1,"(a^2*(a + b*x^4)^(5/4))/(5*b^3) - (2*a*(a + b*x^4)^(9/4))/(9*b^3) + (a + b*x^4)^(13/4)/(13*b^3)","A",3,2,15,0.1333,1,"{266, 43}"
991,1,38,0,0.0225679,"\int x^7 \sqrt[4]{a+b x^4} \, dx","Int[x^7*(a + b*x^4)^(1/4),x]","\frac{\left(a+b x^4\right)^{9/4}}{9 b^2}-\frac{a \left(a+b x^4\right)^{5/4}}{5 b^2}","\frac{\left(a+b x^4\right)^{9/4}}{9 b^2}-\frac{a \left(a+b x^4\right)^{5/4}}{5 b^2}",1,"-(a*(a + b*x^4)^(5/4))/(5*b^2) + (a + b*x^4)^(9/4)/(9*b^2)","A",3,2,15,0.1333,1,"{266, 43}"
992,1,18,0,0.0038969,"\int x^3 \sqrt[4]{a+b x^4} \, dx","Int[x^3*(a + b*x^4)^(1/4),x]","\frac{\left(a+b x^4\right)^{5/4}}{5 b}","\frac{\left(a+b x^4\right)^{5/4}}{5 b}",1,"(a + b*x^4)^(5/4)/(5*b)","A",1,1,15,0.06667,1,"{261}"
993,1,66,0,0.043224,"\int \frac{\sqrt[4]{a+b x^4}}{x} \, dx","Int[(a + b*x^4)^(1/4)/x,x]","\sqrt[4]{a+b x^4}-\frac{1}{2} \sqrt[4]{a} \tan ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)-\frac{1}{2} \sqrt[4]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)","\sqrt[4]{a+b x^4}-\frac{1}{2} \sqrt[4]{a} \tan ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)-\frac{1}{2} \sqrt[4]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)",1,"(a + b*x^4)^(1/4) - (a^(1/4)*ArcTan[(a + b*x^4)^(1/4)/a^(1/4)])/2 - (a^(1/4)*ArcTanh[(a + b*x^4)^(1/4)/a^(1/4)])/2","A",6,6,15,0.4000,1,"{266, 50, 63, 212, 206, 203}"
994,1,75,0,0.044144,"\int \frac{\sqrt[4]{a+b x^4}}{x^5} \, dx","Int[(a + b*x^4)^(1/4)/x^5,x]","-\frac{b \tan ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{8 a^{3/4}}-\frac{b \tanh ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{8 a^{3/4}}-\frac{\sqrt[4]{a+b x^4}}{4 x^4}","-\frac{b \tan ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{8 a^{3/4}}-\frac{b \tanh ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{8 a^{3/4}}-\frac{\sqrt[4]{a+b x^4}}{4 x^4}",1,"-(a + b*x^4)^(1/4)/(4*x^4) - (b*ArcTan[(a + b*x^4)^(1/4)/a^(1/4)])/(8*a^(3/4)) - (b*ArcTanh[(a + b*x^4)^(1/4)/a^(1/4)])/(8*a^(3/4))","A",6,6,15,0.4000,1,"{266, 47, 63, 212, 206, 203}"
995,1,101,0,0.0593026,"\int \frac{\sqrt[4]{a+b x^4}}{x^9} \, dx","Int[(a + b*x^4)^(1/4)/x^9,x]","\frac{3 b^2 \tan ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{64 a^{7/4}}+\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{64 a^{7/4}}-\frac{b \sqrt[4]{a+b x^4}}{32 a x^4}-\frac{\sqrt[4]{a+b x^4}}{8 x^8}","\frac{3 b^2 \tan ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{64 a^{7/4}}+\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{64 a^{7/4}}-\frac{b \sqrt[4]{a+b x^4}}{32 a x^4}-\frac{\sqrt[4]{a+b x^4}}{8 x^8}",1,"-(a + b*x^4)^(1/4)/(8*x^8) - (b*(a + b*x^4)^(1/4))/(32*a*x^4) + (3*b^2*ArcTan[(a + b*x^4)^(1/4)/a^(1/4)])/(64*a^(7/4)) + (3*b^2*ArcTanh[(a + b*x^4)^(1/4)/a^(1/4)])/(64*a^(7/4))","A",7,7,15,0.4667,1,"{266, 47, 51, 63, 212, 206, 203}"
996,1,125,0,0.0837615,"\int x^9 \sqrt[4]{a+b x^4} \, dx","Int[x^9*(a + b*x^4)^(1/4),x]","-\frac{2 a^2 x^2 \sqrt[4]{a+b x^4}}{77 b^2}+\frac{4 a^{7/2} \left(\frac{b x^4}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{77 b^{5/2} \left(a+b x^4\right)^{3/4}}+\frac{1}{11} x^{10} \sqrt[4]{a+b x^4}+\frac{a x^6 \sqrt[4]{a+b x^4}}{77 b}","-\frac{2 a^2 x^2 \sqrt[4]{a+b x^4}}{77 b^2}+\frac{4 a^{7/2} \left(\frac{b x^4}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{77 b^{5/2} \left(a+b x^4\right)^{3/4}}+\frac{1}{11} x^{10} \sqrt[4]{a+b x^4}+\frac{a x^6 \sqrt[4]{a+b x^4}}{77 b}",1,"(-2*a^2*x^2*(a + b*x^4)^(1/4))/(77*b^2) + (a*x^6*(a + b*x^4)^(1/4))/(77*b) + (x^10*(a + b*x^4)^(1/4))/11 + (4*a^(7/2)*(1 + (b*x^4)/a)^(3/4)*EllipticF[ArcTan[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(77*b^(5/2)*(a + b*x^4)^(3/4))","A",6,5,15,0.3333,1,"{275, 279, 321, 233, 231}"
997,1,101,0,0.0623637,"\int x^5 \sqrt[4]{a+b x^4} \, dx","Int[x^5*(a + b*x^4)^(1/4),x]","-\frac{2 a^{5/2} \left(\frac{b x^4}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{21 b^{3/2} \left(a+b x^4\right)^{3/4}}+\frac{1}{7} x^6 \sqrt[4]{a+b x^4}+\frac{a x^2 \sqrt[4]{a+b x^4}}{21 b}","-\frac{2 a^{5/2} \left(\frac{b x^4}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{21 b^{3/2} \left(a+b x^4\right)^{3/4}}+\frac{1}{7} x^6 \sqrt[4]{a+b x^4}+\frac{a x^2 \sqrt[4]{a+b x^4}}{21 b}",1,"(a*x^2*(a + b*x^4)^(1/4))/(21*b) + (x^6*(a + b*x^4)^(1/4))/7 - (2*a^(5/2)*(1 + (b*x^4)/a)^(3/4)*EllipticF[ArcTan[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(21*b^(3/2)*(a + b*x^4)^(3/4))","A",5,5,15,0.3333,1,"{275, 279, 321, 233, 231}"
998,1,79,0,0.0411113,"\int x \sqrt[4]{a+b x^4} \, dx","Int[x*(a + b*x^4)^(1/4),x]","\frac{a^{3/2} \left(\frac{b x^4}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{3 \sqrt{b} \left(a+b x^4\right)^{3/4}}+\frac{1}{3} x^2 \sqrt[4]{a+b x^4}","\frac{a^{3/2} \left(\frac{b x^4}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{3 \sqrt{b} \left(a+b x^4\right)^{3/4}}+\frac{1}{3} x^2 \sqrt[4]{a+b x^4}",1,"(x^2*(a + b*x^4)^(1/4))/3 + (a^(3/2)*(1 + (b*x^4)/a)^(3/4)*EllipticF[ArcTan[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(3*Sqrt[b]*(a + b*x^4)^(3/4))","A",4,4,13,0.3077,1,"{275, 195, 233, 231}"
999,1,79,0,0.0466232,"\int \frac{\sqrt[4]{a+b x^4}}{x^3} \, dx","Int[(a + b*x^4)^(1/4)/x^3,x]","\frac{\sqrt{a} \sqrt{b} \left(\frac{b x^4}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{2 \left(a+b x^4\right)^{3/4}}-\frac{\sqrt[4]{a+b x^4}}{2 x^2}","\frac{\sqrt{a} \sqrt{b} \left(\frac{b x^4}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{2 \left(a+b x^4\right)^{3/4}}-\frac{\sqrt[4]{a+b x^4}}{2 x^2}",1,"-(a + b*x^4)^(1/4)/(2*x^2) + (Sqrt[a]*Sqrt[b]*(1 + (b*x^4)/a)^(3/4)*EllipticF[ArcTan[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(2*(a + b*x^4)^(3/4))","A",4,4,15,0.2667,1,"{275, 277, 233, 231}"
1000,1,101,0,0.0644072,"\int \frac{\sqrt[4]{a+b x^4}}{x^7} \, dx","Int[(a + b*x^4)^(1/4)/x^7,x]","-\frac{b^{3/2} \left(\frac{b x^4}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{12 \sqrt{a} \left(a+b x^4\right)^{3/4}}-\frac{b \sqrt[4]{a+b x^4}}{12 a x^2}-\frac{\sqrt[4]{a+b x^4}}{6 x^6}","-\frac{b^{3/2} \left(\frac{b x^4}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{12 \sqrt{a} \left(a+b x^4\right)^{3/4}}-\frac{b \sqrt[4]{a+b x^4}}{12 a x^2}-\frac{\sqrt[4]{a+b x^4}}{6 x^6}",1,"-(a + b*x^4)^(1/4)/(6*x^6) - (b*(a + b*x^4)^(1/4))/(12*a*x^2) - (b^(3/2)*(1 + (b*x^4)/a)^(3/4)*EllipticF[ArcTan[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(12*Sqrt[a]*(a + b*x^4)^(3/4))","A",5,5,15,0.3333,1,"{275, 277, 325, 233, 231}"
1001,1,125,0,0.0828897,"\int \frac{\sqrt[4]{a+b x^4}}{x^{11}} \, dx","Int[(a + b*x^4)^(1/4)/x^11,x]","\frac{b^2 \sqrt[4]{a+b x^4}}{24 a^2 x^2}+\frac{b^{5/2} \left(\frac{b x^4}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{24 a^{3/2} \left(a+b x^4\right)^{3/4}}-\frac{b \sqrt[4]{a+b x^4}}{60 a x^6}-\frac{\sqrt[4]{a+b x^4}}{10 x^{10}}","\frac{b^2 \sqrt[4]{a+b x^4}}{24 a^2 x^2}+\frac{b^{5/2} \left(\frac{b x^4}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{24 a^{3/2} \left(a+b x^4\right)^{3/4}}-\frac{b \sqrt[4]{a+b x^4}}{60 a x^6}-\frac{\sqrt[4]{a+b x^4}}{10 x^{10}}",1,"-(a + b*x^4)^(1/4)/(10*x^10) - (b*(a + b*x^4)^(1/4))/(60*a*x^6) + (b^2*(a + b*x^4)^(1/4))/(24*a^2*x^2) + (b^(5/2)*(1 + (b*x^4)/a)^(3/4)*EllipticF[ArcTan[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(24*a^(3/2)*(a + b*x^4)^(3/4))","A",6,5,15,0.3333,1,"{275, 277, 325, 233, 231}"
1002,1,103,0,0.0382135,"\int x^6 \sqrt[4]{a+b x^4} \, dx","Int[x^6*(a + b*x^4)^(1/4),x]","\frac{3 a^2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{64 b^{7/4}}-\frac{3 a^2 \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{64 b^{7/4}}+\frac{1}{8} x^7 \sqrt[4]{a+b x^4}+\frac{a x^3 \sqrt[4]{a+b x^4}}{32 b}","\frac{3 a^2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{64 b^{7/4}}-\frac{3 a^2 \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{64 b^{7/4}}+\frac{1}{8} x^7 \sqrt[4]{a+b x^4}+\frac{a x^3 \sqrt[4]{a+b x^4}}{32 b}",1,"(a*x^3*(a + b*x^4)^(1/4))/(32*b) + (x^7*(a + b*x^4)^(1/4))/8 + (3*a^2*ArcTan[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/(64*b^(7/4)) - (3*a^2*ArcTanh[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/(64*b^(7/4))","A",6,6,15,0.4000,1,"{279, 321, 331, 298, 203, 206}"
1003,1,77,0,0.0245646,"\int x^2 \sqrt[4]{a+b x^4} \, dx","Int[x^2*(a + b*x^4)^(1/4),x]","-\frac{a \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{8 b^{3/4}}+\frac{a \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{8 b^{3/4}}+\frac{1}{4} x^3 \sqrt[4]{a+b x^4}","-\frac{a \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{8 b^{3/4}}+\frac{a \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{8 b^{3/4}}+\frac{1}{4} x^3 \sqrt[4]{a+b x^4}",1,"(x^3*(a + b*x^4)^(1/4))/4 - (a*ArcTan[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/(8*b^(3/4)) + (a*ArcTanh[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/(8*b^(3/4))","A",5,5,15,0.3333,1,"{279, 331, 298, 203, 206}"
1004,1,73,0,0.0243003,"\int \frac{\sqrt[4]{a+b x^4}}{x^2} \, dx","Int[(a + b*x^4)^(1/4)/x^2,x]","-\frac{\sqrt[4]{a+b x^4}}{x}-\frac{1}{2} \sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)+\frac{1}{2} \sqrt[4]{b} \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)","-\frac{\sqrt[4]{a+b x^4}}{x}-\frac{1}{2} \sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)+\frac{1}{2} \sqrt[4]{b} \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)",1,"-((a + b*x^4)^(1/4)/x) - (b^(1/4)*ArcTan[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/2 + (b^(1/4)*ArcTanh[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/2","A",5,5,15,0.3333,1,"{277, 331, 298, 203, 206}"
1005,1,21,0,0.0047634,"\int \frac{\sqrt[4]{a+b x^4}}{x^6} \, dx","Int[(a + b*x^4)^(1/4)/x^6,x]","-\frac{\left(a+b x^4\right)^{5/4}}{5 a x^5}","-\frac{\left(a+b x^4\right)^{5/4}}{5 a x^5}",1,"-(a + b*x^4)^(5/4)/(5*a*x^5)","A",1,1,15,0.06667,1,"{264}"
1006,1,44,0,0.0100388,"\int \frac{\sqrt[4]{a+b x^4}}{x^{10}} \, dx","Int[(a + b*x^4)^(1/4)/x^10,x]","\frac{4 b \left(a+b x^4\right)^{5/4}}{45 a^2 x^5}-\frac{\left(a+b x^4\right)^{5/4}}{9 a x^9}","\frac{4 b \left(a+b x^4\right)^{5/4}}{45 a^2 x^5}-\frac{\left(a+b x^4\right)^{5/4}}{9 a x^9}",1,"-(a + b*x^4)^(5/4)/(9*a*x^9) + (4*b*(a + b*x^4)^(5/4))/(45*a^2*x^5)","A",2,2,15,0.1333,1,"{271, 264}"
1007,1,68,0,0.0190968,"\int \frac{\sqrt[4]{a+b x^4}}{x^{14}} \, dx","Int[(a + b*x^4)^(1/4)/x^14,x]","-\frac{32 b^2 \left(a+b x^4\right)^{5/4}}{585 a^3 x^5}+\frac{8 b \left(a+b x^4\right)^{5/4}}{117 a^2 x^9}-\frac{\left(a+b x^4\right)^{5/4}}{13 a x^{13}}","-\frac{32 b^2 \left(a+b x^4\right)^{5/4}}{585 a^3 x^5}+\frac{8 b \left(a+b x^4\right)^{5/4}}{117 a^2 x^9}-\frac{\left(a+b x^4\right)^{5/4}}{13 a x^{13}}",1,"-(a + b*x^4)^(5/4)/(13*a*x^13) + (8*b*(a + b*x^4)^(5/4))/(117*a^2*x^9) - (32*b^2*(a + b*x^4)^(5/4))/(585*a^3*x^5)","A",3,2,15,0.1333,1,"{271, 264}"
1008,1,92,0,0.0267598,"\int \frac{\sqrt[4]{a+b x^4}}{x^{18}} \, dx","Int[(a + b*x^4)^(1/4)/x^18,x]","\frac{128 b^3 \left(a+b x^4\right)^{5/4}}{3315 a^4 x^5}-\frac{32 b^2 \left(a+b x^4\right)^{5/4}}{663 a^3 x^9}+\frac{12 b \left(a+b x^4\right)^{5/4}}{221 a^2 x^{13}}-\frac{\left(a+b x^4\right)^{5/4}}{17 a x^{17}}","\frac{128 b^3 \left(a+b x^4\right)^{5/4}}{3315 a^4 x^5}-\frac{32 b^2 \left(a+b x^4\right)^{5/4}}{663 a^3 x^9}+\frac{12 b \left(a+b x^4\right)^{5/4}}{221 a^2 x^{13}}-\frac{\left(a+b x^4\right)^{5/4}}{17 a x^{17}}",1,"-(a + b*x^4)^(5/4)/(17*a*x^17) + (12*b*(a + b*x^4)^(5/4))/(221*a^2*x^13) - (32*b^2*(a + b*x^4)^(5/4))/(663*a^3*x^9) + (128*b^3*(a + b*x^4)^(5/4))/(3315*a^4*x^5)","A",4,2,15,0.1333,1,"{271, 264}"
1009,1,150,0,0.0741586,"\int x^{12} \sqrt[4]{a+b x^4} \, dx","Int[x^12*(a + b*x^4)^(1/4),x]","-\frac{3 a^2 x^5 \sqrt[4]{a+b x^4}}{280 b^2}+\frac{3 a^3 x \sqrt[4]{a+b x^4}}{112 b^3}+\frac{3 a^{7/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{112 b^{5/2} \left(a+b x^4\right)^{3/4}}+\frac{1}{14} x^{13} \sqrt[4]{a+b x^4}+\frac{a x^9 \sqrt[4]{a+b x^4}}{140 b}","-\frac{3 a^2 x^5 \sqrt[4]{a+b x^4}}{280 b^2}+\frac{3 a^3 x \sqrt[4]{a+b x^4}}{112 b^3}+\frac{3 a^{7/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{112 b^{5/2} \left(a+b x^4\right)^{3/4}}+\frac{1}{14} x^{13} \sqrt[4]{a+b x^4}+\frac{a x^9 \sqrt[4]{a+b x^4}}{140 b}",1,"(3*a^3*x*(a + b*x^4)^(1/4))/(112*b^3) - (3*a^2*x^5*(a + b*x^4)^(1/4))/(280*b^2) + (a*x^9*(a + b*x^4)^(1/4))/(140*b) + (x^13*(a + b*x^4)^(1/4))/14 + (3*a^(7/2)*(1 + a/(b*x^4))^(3/4)*x^3*EllipticF[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(112*b^(5/2)*(a + b*x^4)^(3/4))","A",8,6,15,0.4000,1,"{279, 321, 237, 335, 275, 231}"
1010,1,126,0,0.0561152,"\int x^8 \sqrt[4]{a+b x^4} \, dx","Int[x^8*(a + b*x^4)^(1/4),x]","-\frac{a^2 x \sqrt[4]{a+b x^4}}{24 b^2}-\frac{a^{5/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{24 b^{3/2} \left(a+b x^4\right)^{3/4}}+\frac{1}{10} x^9 \sqrt[4]{a+b x^4}+\frac{a x^5 \sqrt[4]{a+b x^4}}{60 b}","-\frac{a^2 x \sqrt[4]{a+b x^4}}{24 b^2}-\frac{a^{5/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{24 b^{3/2} \left(a+b x^4\right)^{3/4}}+\frac{1}{10} x^9 \sqrt[4]{a+b x^4}+\frac{a x^5 \sqrt[4]{a+b x^4}}{60 b}",1,"-(a^2*x*(a + b*x^4)^(1/4))/(24*b^2) + (a*x^5*(a + b*x^4)^(1/4))/(60*b) + (x^9*(a + b*x^4)^(1/4))/10 - (a^(5/2)*(1 + a/(b*x^4))^(3/4)*x^3*EllipticF[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(24*b^(3/2)*(a + b*x^4)^(3/4))","A",7,6,15,0.4000,1,"{279, 321, 237, 335, 275, 231}"
1011,1,102,0,0.044762,"\int x^4 \sqrt[4]{a+b x^4} \, dx","Int[x^4*(a + b*x^4)^(1/4),x]","\frac{a^{3/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{12 \sqrt{b} \left(a+b x^4\right)^{3/4}}+\frac{1}{6} x^5 \sqrt[4]{a+b x^4}+\frac{a x \sqrt[4]{a+b x^4}}{12 b}","\frac{a^{3/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{12 \sqrt{b} \left(a+b x^4\right)^{3/4}}+\frac{1}{6} x^5 \sqrt[4]{a+b x^4}+\frac{a x \sqrt[4]{a+b x^4}}{12 b}",1,"(a*x*(a + b*x^4)^(1/4))/(12*b) + (x^5*(a + b*x^4)^(1/4))/6 + (a^(3/2)*(1 + a/(b*x^4))^(3/4)*x^3*EllipticF[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(12*Sqrt[b]*(a + b*x^4)^(3/4))","A",6,6,15,0.4000,1,"{279, 321, 237, 335, 275, 231}"
1012,1,80,0,0.0316619,"\int \sqrt[4]{a+b x^4} \, dx","Int[(a + b*x^4)^(1/4),x]","\frac{1}{2} x \sqrt[4]{a+b x^4}-\frac{\sqrt{a} \sqrt{b} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{2 \left(a+b x^4\right)^{3/4}}","\frac{1}{2} x \sqrt[4]{a+b x^4}-\frac{\sqrt{a} \sqrt{b} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{2 \left(a+b x^4\right)^{3/4}}",1,"(x*(a + b*x^4)^(1/4))/2 - (Sqrt[a]*Sqrt[b]*(1 + a/(b*x^4))^(3/4)*x^3*EllipticF[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(2*(a + b*x^4)^(3/4))","A",5,5,11,0.4545,1,"{195, 237, 335, 275, 231}"
1013,1,82,0,0.0340621,"\int \frac{\sqrt[4]{a+b x^4}}{x^4} \, dx","Int[(a + b*x^4)^(1/4)/x^4,x]","-\frac{b^{3/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{3 \sqrt{a} \left(a+b x^4\right)^{3/4}}-\frac{\sqrt[4]{a+b x^4}}{3 x^3}","-\frac{b^{3/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{3 \sqrt{a} \left(a+b x^4\right)^{3/4}}-\frac{\sqrt[4]{a+b x^4}}{3 x^3}",1,"-(a + b*x^4)^(1/4)/(3*x^3) - (b^(3/2)*(1 + a/(b*x^4))^(3/4)*x^3*EllipticF[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(3*Sqrt[a]*(a + b*x^4)^(3/4))","A",5,5,15,0.3333,1,"{277, 237, 335, 275, 231}"
1014,1,104,0,0.0466352,"\int \frac{\sqrt[4]{a+b x^4}}{x^8} \, dx","Int[(a + b*x^4)^(1/4)/x^8,x]","\frac{2 b^{5/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{21 a^{3/2} \left(a+b x^4\right)^{3/4}}-\frac{b \sqrt[4]{a+b x^4}}{21 a x^3}-\frac{\sqrt[4]{a+b x^4}}{7 x^7}","\frac{2 b^{5/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{21 a^{3/2} \left(a+b x^4\right)^{3/4}}-\frac{b \sqrt[4]{a+b x^4}}{21 a x^3}-\frac{\sqrt[4]{a+b x^4}}{7 x^7}",1,"-(a + b*x^4)^(1/4)/(7*x^7) - (b*(a + b*x^4)^(1/4))/(21*a*x^3) + (2*b^(5/2)*(1 + a/(b*x^4))^(3/4)*x^3*EllipticF[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(21*a^(3/2)*(a + b*x^4)^(3/4))","A",6,6,15,0.4000,1,"{277, 325, 237, 335, 275, 231}"
1015,1,128,0,0.060442,"\int \frac{\sqrt[4]{a+b x^4}}{x^{12}} \, dx","Int[(a + b*x^4)^(1/4)/x^12,x]","\frac{2 b^2 \sqrt[4]{a+b x^4}}{77 a^2 x^3}-\frac{4 b^{7/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{77 a^{5/2} \left(a+b x^4\right)^{3/4}}-\frac{b \sqrt[4]{a+b x^4}}{77 a x^7}-\frac{\sqrt[4]{a+b x^4}}{11 x^{11}}","\frac{2 b^2 \sqrt[4]{a+b x^4}}{77 a^2 x^3}-\frac{4 b^{7/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{77 a^{5/2} \left(a+b x^4\right)^{3/4}}-\frac{b \sqrt[4]{a+b x^4}}{77 a x^7}-\frac{\sqrt[4]{a+b x^4}}{11 x^{11}}",1,"-(a + b*x^4)^(1/4)/(11*x^11) - (b*(a + b*x^4)^(1/4))/(77*a*x^7) + (2*b^2*(a + b*x^4)^(1/4))/(77*a^2*x^3) - (4*b^(7/2)*(1 + a/(b*x^4))^(3/4)*x^3*EllipticF[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(77*a^(5/2)*(a + b*x^4)^(3/4))","A",7,6,15,0.4000,1,"{277, 325, 237, 335, 275, 231}"
1016,1,152,0,0.0775219,"\int \frac{\sqrt[4]{a+b x^4}}{x^{16}} \, dx","Int[(a + b*x^4)^(1/4)/x^16,x]","-\frac{4 b^3 \sqrt[4]{a+b x^4}}{231 a^3 x^3}+\frac{2 b^2 \sqrt[4]{a+b x^4}}{231 a^2 x^7}+\frac{8 b^{9/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{231 a^{7/2} \left(a+b x^4\right)^{3/4}}-\frac{b \sqrt[4]{a+b x^4}}{165 a x^{11}}-\frac{\sqrt[4]{a+b x^4}}{15 x^{15}}","-\frac{4 b^3 \sqrt[4]{a+b x^4}}{231 a^3 x^3}+\frac{2 b^2 \sqrt[4]{a+b x^4}}{231 a^2 x^7}+\frac{8 b^{9/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{231 a^{7/2} \left(a+b x^4\right)^{3/4}}-\frac{b \sqrt[4]{a+b x^4}}{165 a x^{11}}-\frac{\sqrt[4]{a+b x^4}}{15 x^{15}}",1,"-(a + b*x^4)^(1/4)/(15*x^15) - (b*(a + b*x^4)^(1/4))/(165*a*x^11) + (2*b^2*(a + b*x^4)^(1/4))/(231*a^2*x^7) - (4*b^3*(a + b*x^4)^(1/4))/(231*a^3*x^3) + (8*b^(9/2)*(1 + a/(b*x^4))^(3/4)*x^3*EllipticF[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(231*a^(7/2)*(a + b*x^4)^(3/4))","A",8,6,15,0.4000,1,"{277, 325, 237, 335, 275, 231}"
1017,1,101,0,0.0569821,"\int x^{19} \left(a+b x^4\right)^{3/4} \, dx","Int[x^19*(a + b*x^4)^(3/4),x]","\frac{2 a^2 \left(a+b x^4\right)^{15/4}}{5 b^5}-\frac{4 a^3 \left(a+b x^4\right)^{11/4}}{11 b^5}+\frac{a^4 \left(a+b x^4\right)^{7/4}}{7 b^5}+\frac{\left(a+b x^4\right)^{23/4}}{23 b^5}-\frac{4 a \left(a+b x^4\right)^{19/4}}{19 b^5}","\frac{2 a^2 \left(a+b x^4\right)^{15/4}}{5 b^5}-\frac{4 a^3 \left(a+b x^4\right)^{11/4}}{11 b^5}+\frac{a^4 \left(a+b x^4\right)^{7/4}}{7 b^5}+\frac{\left(a+b x^4\right)^{23/4}}{23 b^5}-\frac{4 a \left(a+b x^4\right)^{19/4}}{19 b^5}",1,"(a^4*(a + b*x^4)^(7/4))/(7*b^5) - (4*a^3*(a + b*x^4)^(11/4))/(11*b^5) + (2*a^2*(a + b*x^4)^(15/4))/(5*b^5) - (4*a*(a + b*x^4)^(19/4))/(19*b^5) + (a + b*x^4)^(23/4)/(23*b^5)","A",3,2,15,0.1333,1,"{266, 43}"
1018,1,80,0,0.0465933,"\int x^{15} \left(a+b x^4\right)^{3/4} \, dx","Int[x^15*(a + b*x^4)^(3/4),x]","\frac{3 a^2 \left(a+b x^4\right)^{11/4}}{11 b^4}-\frac{a^3 \left(a+b x^4\right)^{7/4}}{7 b^4}+\frac{\left(a+b x^4\right)^{19/4}}{19 b^4}-\frac{a \left(a+b x^4\right)^{15/4}}{5 b^4}","\frac{3 a^2 \left(a+b x^4\right)^{11/4}}{11 b^4}-\frac{a^3 \left(a+b x^4\right)^{7/4}}{7 b^4}+\frac{\left(a+b x^4\right)^{19/4}}{19 b^4}-\frac{a \left(a+b x^4\right)^{15/4}}{5 b^4}",1,"-(a^3*(a + b*x^4)^(7/4))/(7*b^4) + (3*a^2*(a + b*x^4)^(11/4))/(11*b^4) - (a*(a + b*x^4)^(15/4))/(5*b^4) + (a + b*x^4)^(19/4)/(19*b^4)","A",3,2,15,0.1333,1,"{266, 43}"
1019,1,59,0,0.0340583,"\int x^{11} \left(a+b x^4\right)^{3/4} \, dx","Int[x^11*(a + b*x^4)^(3/4),x]","\frac{a^2 \left(a+b x^4\right)^{7/4}}{7 b^3}+\frac{\left(a+b x^4\right)^{15/4}}{15 b^3}-\frac{2 a \left(a+b x^4\right)^{11/4}}{11 b^3}","\frac{a^2 \left(a+b x^4\right)^{7/4}}{7 b^3}+\frac{\left(a+b x^4\right)^{15/4}}{15 b^3}-\frac{2 a \left(a+b x^4\right)^{11/4}}{11 b^3}",1,"(a^2*(a + b*x^4)^(7/4))/(7*b^3) - (2*a*(a + b*x^4)^(11/4))/(11*b^3) + (a + b*x^4)^(15/4)/(15*b^3)","A",3,2,15,0.1333,1,"{266, 43}"
1020,1,38,0,0.0234202,"\int x^7 \left(a+b x^4\right)^{3/4} \, dx","Int[x^7*(a + b*x^4)^(3/4),x]","\frac{\left(a+b x^4\right)^{11/4}}{11 b^2}-\frac{a \left(a+b x^4\right)^{7/4}}{7 b^2}","\frac{\left(a+b x^4\right)^{11/4}}{11 b^2}-\frac{a \left(a+b x^4\right)^{7/4}}{7 b^2}",1,"-(a*(a + b*x^4)^(7/4))/(7*b^2) + (a + b*x^4)^(11/4)/(11*b^2)","A",3,2,15,0.1333,1,"{266, 43}"
1021,1,18,0,0.0047501,"\int x^3 \left(a+b x^4\right)^{3/4} \, dx","Int[x^3*(a + b*x^4)^(3/4),x]","\frac{\left(a+b x^4\right)^{7/4}}{7 b}","\frac{\left(a+b x^4\right)^{7/4}}{7 b}",1,"(a + b*x^4)^(7/4)/(7*b)","A",1,1,15,0.06667,1,"{261}"
1022,1,70,0,0.0463159,"\int \frac{\left(a+b x^4\right)^{3/4}}{x} \, dx","Int[(a + b*x^4)^(3/4)/x,x]","\frac{1}{2} a^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)-\frac{1}{2} a^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)+\frac{1}{3} \left(a+b x^4\right)^{3/4}","\frac{1}{2} a^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)-\frac{1}{2} a^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)+\frac{1}{3} \left(a+b x^4\right)^{3/4}",1,"(a + b*x^4)^(3/4)/3 + (a^(3/4)*ArcTan[(a + b*x^4)^(1/4)/a^(1/4)])/2 - (a^(3/4)*ArcTanh[(a + b*x^4)^(1/4)/a^(1/4)])/2","A",6,6,15,0.4000,1,"{266, 50, 63, 298, 203, 206}"
1023,1,75,0,0.0467913,"\int \frac{\left(a+b x^4\right)^{3/4}}{x^5} \, dx","Int[(a + b*x^4)^(3/4)/x^5,x]","-\frac{\left(a+b x^4\right)^{3/4}}{4 x^4}+\frac{3 b \tan ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{8 \sqrt[4]{a}}-\frac{3 b \tanh ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{8 \sqrt[4]{a}}","-\frac{\left(a+b x^4\right)^{3/4}}{4 x^4}+\frac{3 b \tan ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{8 \sqrt[4]{a}}-\frac{3 b \tanh ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{8 \sqrt[4]{a}}",1,"-(a + b*x^4)^(3/4)/(4*x^4) + (3*b*ArcTan[(a + b*x^4)^(1/4)/a^(1/4)])/(8*a^(1/4)) - (3*b*ArcTanh[(a + b*x^4)^(1/4)/a^(1/4)])/(8*a^(1/4))","A",6,6,15,0.4000,1,"{266, 47, 63, 298, 203, 206}"
1024,1,101,0,0.0594983,"\int \frac{\left(a+b x^4\right)^{3/4}}{x^9} \, dx","Int[(a + b*x^4)^(3/4)/x^9,x]","-\frac{3 b^2 \tan ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{64 a^{5/4}}+\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{64 a^{5/4}}-\frac{3 b \left(a+b x^4\right)^{3/4}}{32 a x^4}-\frac{\left(a+b x^4\right)^{3/4}}{8 x^8}","-\frac{3 b^2 \tan ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{64 a^{5/4}}+\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{64 a^{5/4}}-\frac{3 b \left(a+b x^4\right)^{3/4}}{32 a x^4}-\frac{\left(a+b x^4\right)^{3/4}}{8 x^8}",1,"-(a + b*x^4)^(3/4)/(8*x^8) - (3*b*(a + b*x^4)^(3/4))/(32*a*x^4) - (3*b^2*ArcTan[(a + b*x^4)^(1/4)/a^(1/4)])/(64*a^(5/4)) + (3*b^2*ArcTanh[(a + b*x^4)^(1/4)/a^(1/4)])/(64*a^(5/4))","A",7,7,15,0.4667,1,"{266, 47, 51, 63, 298, 203, 206}"
1025,1,149,0,0.0982427,"\int x^9 \left(a+b x^4\right)^{3/4} \, dx","Int[x^9*(a + b*x^4)^(3/4),x]","-\frac{2 a^2 x^2 \left(a+b x^4\right)^{3/4}}{65 b^2}+\frac{4 a^3 x^2}{65 b^2 \sqrt[4]{a+b x^4}}-\frac{4 a^{7/2} \sqrt[4]{\frac{b x^4}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{65 b^{5/2} \sqrt[4]{a+b x^4}}+\frac{1}{13} x^{10} \left(a+b x^4\right)^{3/4}+\frac{a x^6 \left(a+b x^4\right)^{3/4}}{39 b}","-\frac{2 a^2 x^2 \left(a+b x^4\right)^{3/4}}{65 b^2}+\frac{4 a^3 x^2}{65 b^2 \sqrt[4]{a+b x^4}}-\frac{4 a^{7/2} \sqrt[4]{\frac{b x^4}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{65 b^{5/2} \sqrt[4]{a+b x^4}}+\frac{1}{13} x^{10} \left(a+b x^4\right)^{3/4}+\frac{a x^6 \left(a+b x^4\right)^{3/4}}{39 b}",1,"(4*a^3*x^2)/(65*b^2*(a + b*x^4)^(1/4)) - (2*a^2*x^2*(a + b*x^4)^(3/4))/(65*b^2) + (a*x^6*(a + b*x^4)^(3/4))/(39*b) + (x^10*(a + b*x^4)^(3/4))/13 - (4*a^(7/2)*(1 + (b*x^4)/a)^(1/4)*EllipticE[ArcTan[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(65*b^(5/2)*(a + b*x^4)^(1/4))","A",7,6,15,0.4000,1,"{275, 279, 321, 229, 227, 196}"
1026,1,125,0,0.0751214,"\int x^5 \left(a+b x^4\right)^{3/4} \, dx","Int[x^5*(a + b*x^4)^(3/4),x]","\frac{2 a^{5/2} \sqrt[4]{\frac{b x^4}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{15 b^{3/2} \sqrt[4]{a+b x^4}}-\frac{2 a^2 x^2}{15 b \sqrt[4]{a+b x^4}}+\frac{1}{9} x^6 \left(a+b x^4\right)^{3/4}+\frac{a x^2 \left(a+b x^4\right)^{3/4}}{15 b}","\frac{2 a^{5/2} \sqrt[4]{\frac{b x^4}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{15 b^{3/2} \sqrt[4]{a+b x^4}}-\frac{2 a^2 x^2}{15 b \sqrt[4]{a+b x^4}}+\frac{1}{9} x^6 \left(a+b x^4\right)^{3/4}+\frac{a x^2 \left(a+b x^4\right)^{3/4}}{15 b}",1,"(-2*a^2*x^2)/(15*b*(a + b*x^4)^(1/4)) + (a*x^2*(a + b*x^4)^(3/4))/(15*b) + (x^6*(a + b*x^4)^(3/4))/9 + (2*a^(5/2)*(1 + (b*x^4)/a)^(1/4)*EllipticE[ArcTan[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(15*b^(3/2)*(a + b*x^4)^(1/4))","A",6,6,15,0.4000,1,"{275, 279, 321, 229, 227, 196}"
1027,1,98,0,0.0496406,"\int x \left(a+b x^4\right)^{3/4} \, dx","Int[x*(a + b*x^4)^(3/4),x]","-\frac{3 a^{3/2} \sqrt[4]{\frac{b x^4}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{5 \sqrt{b} \sqrt[4]{a+b x^4}}+\frac{1}{5} x^2 \left(a+b x^4\right)^{3/4}+\frac{3 a x^2}{5 \sqrt[4]{a+b x^4}}","-\frac{3 a^{3/2} \sqrt[4]{\frac{b x^4}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{5 \sqrt{b} \sqrt[4]{a+b x^4}}+\frac{1}{5} x^2 \left(a+b x^4\right)^{3/4}+\frac{3 a x^2}{5 \sqrt[4]{a+b x^4}}",1,"(3*a*x^2)/(5*(a + b*x^4)^(1/4)) + (x^2*(a + b*x^4)^(3/4))/5 - (3*a^(3/2)*(1 + (b*x^4)/a)^(1/4)*EllipticE[ArcTan[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(5*Sqrt[b]*(a + b*x^4)^(1/4))","A",5,5,13,0.3846,1,"{275, 195, 229, 227, 196}"
1028,1,98,0,0.0544473,"\int \frac{\left(a+b x^4\right)^{3/4}}{x^3} \, dx","Int[(a + b*x^4)^(3/4)/x^3,x]","\frac{3 b x^2}{2 \sqrt[4]{a+b x^4}}-\frac{\left(a+b x^4\right)^{3/4}}{2 x^2}-\frac{3 \sqrt{a} \sqrt{b} \sqrt[4]{\frac{b x^4}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{2 \sqrt[4]{a+b x^4}}","\frac{3 b x^2}{2 \sqrt[4]{a+b x^4}}-\frac{\left(a+b x^4\right)^{3/4}}{2 x^2}-\frac{3 \sqrt{a} \sqrt{b} \sqrt[4]{\frac{b x^4}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{2 \sqrt[4]{a+b x^4}}",1,"(3*b*x^2)/(2*(a + b*x^4)^(1/4)) - (a + b*x^4)^(3/4)/(2*x^2) - (3*Sqrt[a]*Sqrt[b]*(1 + (b*x^4)/a)^(1/4)*EllipticE[ArcTan[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(2*(a + b*x^4)^(1/4))","A",5,5,15,0.3333,1,"{275, 277, 229, 227, 196}"
1029,1,125,0,0.0725773,"\int \frac{\left(a+b x^4\right)^{3/4}}{x^7} \, dx","Int[(a + b*x^4)^(3/4)/x^7,x]","\frac{b^2 x^2}{4 a \sqrt[4]{a+b x^4}}-\frac{b^{3/2} \sqrt[4]{\frac{b x^4}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{4 \sqrt{a} \sqrt[4]{a+b x^4}}-\frac{b \left(a+b x^4\right)^{3/4}}{4 a x^2}-\frac{\left(a+b x^4\right)^{3/4}}{6 x^6}","\frac{b^2 x^2}{4 a \sqrt[4]{a+b x^4}}-\frac{b^{3/2} \sqrt[4]{\frac{b x^4}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{4 \sqrt{a} \sqrt[4]{a+b x^4}}-\frac{b \left(a+b x^4\right)^{3/4}}{4 a x^2}-\frac{\left(a+b x^4\right)^{3/4}}{6 x^6}",1,"(b^2*x^2)/(4*a*(a + b*x^4)^(1/4)) - (a + b*x^4)^(3/4)/(6*x^6) - (b*(a + b*x^4)^(3/4))/(4*a*x^2) - (b^(3/2)*(1 + (b*x^4)/a)^(1/4)*EllipticE[ArcTan[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(4*Sqrt[a]*(a + b*x^4)^(1/4))","A",6,6,15,0.4000,1,"{275, 277, 325, 229, 227, 196}"
1030,1,149,0,0.0940012,"\int \frac{\left(a+b x^4\right)^{3/4}}{x^{11}} \, dx","Int[(a + b*x^4)^(3/4)/x^11,x]","-\frac{3 b^3 x^2}{40 a^2 \sqrt[4]{a+b x^4}}+\frac{3 b^2 \left(a+b x^4\right)^{3/4}}{40 a^2 x^2}+\frac{3 b^{5/2} \sqrt[4]{\frac{b x^4}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{40 a^{3/2} \sqrt[4]{a+b x^4}}-\frac{b \left(a+b x^4\right)^{3/4}}{20 a x^6}-\frac{\left(a+b x^4\right)^{3/4}}{10 x^{10}}","-\frac{3 b^3 x^2}{40 a^2 \sqrt[4]{a+b x^4}}+\frac{3 b^2 \left(a+b x^4\right)^{3/4}}{40 a^2 x^2}+\frac{3 b^{5/2} \sqrt[4]{\frac{b x^4}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{40 a^{3/2} \sqrt[4]{a+b x^4}}-\frac{b \left(a+b x^4\right)^{3/4}}{20 a x^6}-\frac{\left(a+b x^4\right)^{3/4}}{10 x^{10}}",1,"(-3*b^3*x^2)/(40*a^2*(a + b*x^4)^(1/4)) - (a + b*x^4)^(3/4)/(10*x^10) - (b*(a + b*x^4)^(3/4))/(20*a*x^6) + (3*b^2*(a + b*x^4)^(3/4))/(40*a^2*x^2) + (3*b^(5/2)*(1 + (b*x^4)/a)^(1/4)*EllipticE[ArcTan[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(40*a^(3/2)*(a + b*x^4)^(1/4))","A",7,6,15,0.4000,1,"{275, 277, 325, 229, 227, 196}"
1031,1,149,0,0.0609087,"\int x^{12} \left(a+b x^4\right)^{3/4} \, dx","Int[x^12*(a + b*x^4)^(3/4),x]","-\frac{9 a^2 x^5 \left(a+b x^4\right)^{3/4}}{512 b^2}+\frac{45 a^3 x \left(a+b x^4\right)^{3/4}}{2048 b^3}-\frac{45 a^4 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{4096 b^{13/4}}-\frac{45 a^4 \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{4096 b^{13/4}}+\frac{1}{16} x^{13} \left(a+b x^4\right)^{3/4}+\frac{a x^9 \left(a+b x^4\right)^{3/4}}{64 b}","-\frac{9 a^2 x^5 \left(a+b x^4\right)^{3/4}}{512 b^2}+\frac{45 a^3 x \left(a+b x^4\right)^{3/4}}{2048 b^3}-\frac{45 a^4 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{4096 b^{13/4}}-\frac{45 a^4 \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{4096 b^{13/4}}+\frac{1}{16} x^{13} \left(a+b x^4\right)^{3/4}+\frac{a x^9 \left(a+b x^4\right)^{3/4}}{64 b}",1,"(45*a^3*x*(a + b*x^4)^(3/4))/(2048*b^3) - (9*a^2*x^5*(a + b*x^4)^(3/4))/(512*b^2) + (a*x^9*(a + b*x^4)^(3/4))/(64*b) + (x^13*(a + b*x^4)^(3/4))/16 - (45*a^4*ArcTan[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/(4096*b^(13/4)) - (45*a^4*ArcTanh[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/(4096*b^(13/4))","A",8,6,15,0.4000,1,"{279, 321, 240, 212, 206, 203}"
1032,1,125,0,0.0450163,"\int x^8 \left(a+b x^4\right)^{3/4} \, dx","Int[x^8*(a + b*x^4)^(3/4),x]","-\frac{5 a^2 x \left(a+b x^4\right)^{3/4}}{128 b^2}+\frac{5 a^3 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{256 b^{9/4}}+\frac{5 a^3 \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{256 b^{9/4}}+\frac{1}{12} x^9 \left(a+b x^4\right)^{3/4}+\frac{a x^5 \left(a+b x^4\right)^{3/4}}{32 b}","-\frac{5 a^2 x \left(a+b x^4\right)^{3/4}}{128 b^2}+\frac{5 a^3 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{256 b^{9/4}}+\frac{5 a^3 \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{256 b^{9/4}}+\frac{1}{12} x^9 \left(a+b x^4\right)^{3/4}+\frac{a x^5 \left(a+b x^4\right)^{3/4}}{32 b}",1,"(-5*a^2*x*(a + b*x^4)^(3/4))/(128*b^2) + (a*x^5*(a + b*x^4)^(3/4))/(32*b) + (x^9*(a + b*x^4)^(3/4))/12 + (5*a^3*ArcTan[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/(256*b^(9/4)) + (5*a^3*ArcTanh[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/(256*b^(9/4))","A",7,6,15,0.4000,1,"{279, 321, 240, 212, 206, 203}"
1033,1,101,0,0.0321504,"\int x^4 \left(a+b x^4\right)^{3/4} \, dx","Int[x^4*(a + b*x^4)^(3/4),x]","-\frac{3 a^2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{64 b^{5/4}}-\frac{3 a^2 \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{64 b^{5/4}}+\frac{1}{8} x^5 \left(a+b x^4\right)^{3/4}+\frac{3 a x \left(a+b x^4\right)^{3/4}}{32 b}","-\frac{3 a^2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{64 b^{5/4}}-\frac{3 a^2 \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{64 b^{5/4}}+\frac{1}{8} x^5 \left(a+b x^4\right)^{3/4}+\frac{3 a x \left(a+b x^4\right)^{3/4}}{32 b}",1,"(3*a*x*(a + b*x^4)^(3/4))/(32*b) + (x^5*(a + b*x^4)^(3/4))/8 - (3*a^2*ArcTan[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/(64*b^(5/4)) - (3*a^2*ArcTanh[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/(64*b^(5/4))","A",6,6,15,0.4000,1,"{279, 321, 240, 212, 206, 203}"
1034,1,75,0,0.0188698,"\int \left(a+b x^4\right)^{3/4} \, dx","Int[(a + b*x^4)^(3/4),x]","\frac{1}{4} x \left(a+b x^4\right)^{3/4}+\frac{3 a \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{8 \sqrt[4]{b}}+\frac{3 a \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{8 \sqrt[4]{b}}","\frac{1}{4} x \left(a+b x^4\right)^{3/4}+\frac{3 a \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{8 \sqrt[4]{b}}+\frac{3 a \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{8 \sqrt[4]{b}}",1,"(x*(a + b*x^4)^(3/4))/4 + (3*a*ArcTan[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/(8*b^(1/4)) + (3*a*ArcTanh[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/(8*b^(1/4))","A",5,5,11,0.4545,1,"{195, 240, 212, 206, 203}"
1035,1,75,0,0.0218054,"\int \frac{\left(a+b x^4\right)^{3/4}}{x^4} \, dx","Int[(a + b*x^4)^(3/4)/x^4,x]","\frac{1}{2} b^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)+\frac{1}{2} b^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)-\frac{\left(a+b x^4\right)^{3/4}}{3 x^3}","\frac{1}{2} b^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)+\frac{1}{2} b^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)-\frac{\left(a+b x^4\right)^{3/4}}{3 x^3}",1,"-(a + b*x^4)^(3/4)/(3*x^3) + (b^(3/4)*ArcTan[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/2 + (b^(3/4)*ArcTanh[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/2","A",5,5,15,0.3333,1,"{277, 240, 212, 206, 203}"
1036,1,21,0,0.0044587,"\int \frac{\left(a+b x^4\right)^{3/4}}{x^8} \, dx","Int[(a + b*x^4)^(3/4)/x^8,x]","-\frac{\left(a+b x^4\right)^{7/4}}{7 a x^7}","-\frac{\left(a+b x^4\right)^{7/4}}{7 a x^7}",1,"-(a + b*x^4)^(7/4)/(7*a*x^7)","A",1,1,15,0.06667,1,"{264}"
1037,1,44,0,0.0109337,"\int \frac{\left(a+b x^4\right)^{3/4}}{x^{12}} \, dx","Int[(a + b*x^4)^(3/4)/x^12,x]","\frac{4 b \left(a+b x^4\right)^{7/4}}{77 a^2 x^7}-\frac{\left(a+b x^4\right)^{7/4}}{11 a x^{11}}","\frac{4 b \left(a+b x^4\right)^{7/4}}{77 a^2 x^7}-\frac{\left(a+b x^4\right)^{7/4}}{11 a x^{11}}",1,"-(a + b*x^4)^(7/4)/(11*a*x^11) + (4*b*(a + b*x^4)^(7/4))/(77*a^2*x^7)","A",2,2,15,0.1333,1,"{271, 264}"
1038,1,68,0,0.0195247,"\int \frac{\left(a+b x^4\right)^{3/4}}{x^{16}} \, dx","Int[(a + b*x^4)^(3/4)/x^16,x]","-\frac{32 b^2 \left(a+b x^4\right)^{7/4}}{1155 a^3 x^7}+\frac{8 b \left(a+b x^4\right)^{7/4}}{165 a^2 x^{11}}-\frac{\left(a+b x^4\right)^{7/4}}{15 a x^{15}}","-\frac{32 b^2 \left(a+b x^4\right)^{7/4}}{1155 a^3 x^7}+\frac{8 b \left(a+b x^4\right)^{7/4}}{165 a^2 x^{11}}-\frac{\left(a+b x^4\right)^{7/4}}{15 a x^{15}}",1,"-(a + b*x^4)^(7/4)/(15*a*x^15) + (8*b*(a + b*x^4)^(7/4))/(165*a^2*x^11) - (32*b^2*(a + b*x^4)^(7/4))/(1155*a^3*x^7)","A",3,2,15,0.1333,1,"{271, 264}"
1039,1,92,0,0.0277969,"\int \frac{\left(a+b x^4\right)^{3/4}}{x^{20}} \, dx","Int[(a + b*x^4)^(3/4)/x^20,x]","\frac{128 b^3 \left(a+b x^4\right)^{7/4}}{7315 a^4 x^7}-\frac{32 b^2 \left(a+b x^4\right)^{7/4}}{1045 a^3 x^{11}}+\frac{4 b \left(a+b x^4\right)^{7/4}}{95 a^2 x^{15}}-\frac{\left(a+b x^4\right)^{7/4}}{19 a x^{19}}","\frac{128 b^3 \left(a+b x^4\right)^{7/4}}{7315 a^4 x^7}-\frac{32 b^2 \left(a+b x^4\right)^{7/4}}{1045 a^3 x^{11}}+\frac{4 b \left(a+b x^4\right)^{7/4}}{95 a^2 x^{15}}-\frac{\left(a+b x^4\right)^{7/4}}{19 a x^{19}}",1,"-(a + b*x^4)^(7/4)/(19*a*x^19) + (4*b*(a + b*x^4)^(7/4))/(95*a^2*x^15) - (32*b^2*(a + b*x^4)^(7/4))/(1045*a^3*x^11) + (128*b^3*(a + b*x^4)^(7/4))/(7315*a^4*x^7)","A",4,2,15,0.1333,1,"{271, 264}"
1040,1,150,0,0.0709193,"\int x^{10} \left(a+b x^4\right)^{3/4} \, dx","Int[x^10*(a + b*x^4)^(3/4),x]","-\frac{a^2 x^3 \left(a+b x^4\right)^{3/4}}{40 b^2}+\frac{3 a^3 x^3}{80 b^2 \sqrt[4]{a+b x^4}}+\frac{3 a^{7/2} x \sqrt[4]{\frac{a}{b x^4}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{80 b^{5/2} \sqrt[4]{a+b x^4}}+\frac{1}{14} x^{11} \left(a+b x^4\right)^{3/4}+\frac{3 a x^7 \left(a+b x^4\right)^{3/4}}{140 b}","-\frac{a^2 x^3 \left(a+b x^4\right)^{3/4}}{40 b^2}+\frac{3 a^3 x^3}{80 b^2 \sqrt[4]{a+b x^4}}+\frac{3 a^{7/2} x \sqrt[4]{\frac{a}{b x^4}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{80 b^{5/2} \sqrt[4]{a+b x^4}}+\frac{1}{14} x^{11} \left(a+b x^4\right)^{3/4}+\frac{3 a x^7 \left(a+b x^4\right)^{3/4}}{140 b}",1,"(3*a^3*x^3)/(80*b^2*(a + b*x^4)^(1/4)) - (a^2*x^3*(a + b*x^4)^(3/4))/(40*b^2) + (3*a*x^7*(a + b*x^4)^(3/4))/(140*b) + (x^11*(a + b*x^4)^(3/4))/14 + (3*a^(7/2)*(1 + a/(b*x^4))^(1/4)*x*EllipticE[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(80*b^(5/2)*(a + b*x^4)^(1/4))","A",8,7,15,0.4667,1,"{279, 321, 310, 281, 335, 275, 196}"
1041,1,126,0,0.0573729,"\int x^6 \left(a+b x^4\right)^{3/4} \, dx","Int[x^6*(a + b*x^4)^(3/4),x]","-\frac{3 a^{5/2} x \sqrt[4]{\frac{a}{b x^4}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{40 b^{3/2} \sqrt[4]{a+b x^4}}-\frac{3 a^2 x^3}{40 b \sqrt[4]{a+b x^4}}+\frac{1}{10} x^7 \left(a+b x^4\right)^{3/4}+\frac{a x^3 \left(a+b x^4\right)^{3/4}}{20 b}","-\frac{3 a^{5/2} x \sqrt[4]{\frac{a}{b x^4}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{40 b^{3/2} \sqrt[4]{a+b x^4}}-\frac{3 a^2 x^3}{40 b \sqrt[4]{a+b x^4}}+\frac{1}{10} x^7 \left(a+b x^4\right)^{3/4}+\frac{a x^3 \left(a+b x^4\right)^{3/4}}{20 b}",1,"(-3*a^2*x^3)/(40*b*(a + b*x^4)^(1/4)) + (a*x^3*(a + b*x^4)^(3/4))/(20*b) + (x^7*(a + b*x^4)^(3/4))/10 - (3*a^(5/2)*(1 + a/(b*x^4))^(1/4)*x*EllipticE[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(40*b^(3/2)*(a + b*x^4)^(1/4))","A",7,7,15,0.4667,1,"{279, 321, 310, 281, 335, 275, 196}"
1042,1,99,0,0.047035,"\int x^2 \left(a+b x^4\right)^{3/4} \, dx","Int[x^2*(a + b*x^4)^(3/4),x]","\frac{a^{3/2} x \sqrt[4]{\frac{a}{b x^4}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{4 \sqrt{b} \sqrt[4]{a+b x^4}}+\frac{1}{6} x^3 \left(a+b x^4\right)^{3/4}+\frac{a x^3}{4 \sqrt[4]{a+b x^4}}","\frac{a^{3/2} x \sqrt[4]{\frac{a}{b x^4}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{4 \sqrt{b} \sqrt[4]{a+b x^4}}+\frac{1}{6} x^3 \left(a+b x^4\right)^{3/4}+\frac{a x^3}{4 \sqrt[4]{a+b x^4}}",1,"(a*x^3)/(4*(a + b*x^4)^(1/4)) + (x^3*(a + b*x^4)^(3/4))/6 + (a^(3/2)*(1 + a/(b*x^4))^(1/4)*x*EllipticE[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(4*Sqrt[b]*(a + b*x^4)^(1/4))","A",6,6,15,0.4000,1,"{279, 310, 281, 335, 275, 196}"
1043,1,97,0,0.0465699,"\int \frac{\left(a+b x^4\right)^{3/4}}{x^2} \, dx","Int[(a + b*x^4)^(3/4)/x^2,x]","\frac{3 b x^3}{2 \sqrt[4]{a+b x^4}}-\frac{\left(a+b x^4\right)^{3/4}}{x}+\frac{3 \sqrt{a} \sqrt{b} x \sqrt[4]{\frac{a}{b x^4}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{2 \sqrt[4]{a+b x^4}}","\frac{3 b x^3}{2 \sqrt[4]{a+b x^4}}-\frac{\left(a+b x^4\right)^{3/4}}{x}+\frac{3 \sqrt{a} \sqrt{b} x \sqrt[4]{\frac{a}{b x^4}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{2 \sqrt[4]{a+b x^4}}",1,"(3*b*x^3)/(2*(a + b*x^4)^(1/4)) - (a + b*x^4)^(3/4)/x + (3*Sqrt[a]*Sqrt[b]*(1 + a/(b*x^4))^(1/4)*x*EllipticE[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(2*(a + b*x^4)^(1/4))","A",6,6,15,0.4000,1,"{277, 310, 281, 335, 275, 196}"
1044,1,99,0,0.0470486,"\int \frac{\left(a+b x^4\right)^{3/4}}{x^6} \, dx","Int[(a + b*x^4)^(3/4)/x^6,x]","\frac{3 b^{3/2} x \sqrt[4]{\frac{a}{b x^4}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{5 \sqrt{a} \sqrt[4]{a+b x^4}}-\frac{3 b}{5 x \sqrt[4]{a+b x^4}}-\frac{\left(a+b x^4\right)^{3/4}}{5 x^5}","\frac{3 b^{3/2} x \sqrt[4]{\frac{a}{b x^4}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{5 \sqrt{a} \sqrt[4]{a+b x^4}}-\frac{3 b}{5 x \sqrt[4]{a+b x^4}}-\frac{\left(a+b x^4\right)^{3/4}}{5 x^5}",1,"(-3*b)/(5*x*(a + b*x^4)^(1/4)) - (a + b*x^4)^(3/4)/(5*x^5) + (3*b^(3/2)*(1 + a/(b*x^4))^(1/4)*x*EllipticE[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(5*Sqrt[a]*(a + b*x^4)^(1/4))","A",6,6,15,0.4000,1,"{277, 312, 281, 335, 275, 196}"
1045,1,126,0,0.0580357,"\int \frac{\left(a+b x^4\right)^{3/4}}{x^{10}} \, dx","Int[(a + b*x^4)^(3/4)/x^10,x]","-\frac{2 b^{5/2} x \sqrt[4]{\frac{a}{b x^4}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{15 a^{3/2} \sqrt[4]{a+b x^4}}+\frac{2 b^2}{15 a x \sqrt[4]{a+b x^4}}-\frac{b \left(a+b x^4\right)^{3/4}}{15 a x^5}-\frac{\left(a+b x^4\right)^{3/4}}{9 x^9}","-\frac{2 b^{5/2} x \sqrt[4]{\frac{a}{b x^4}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{15 a^{3/2} \sqrt[4]{a+b x^4}}+\frac{2 b^2}{15 a x \sqrt[4]{a+b x^4}}-\frac{b \left(a+b x^4\right)^{3/4}}{15 a x^5}-\frac{\left(a+b x^4\right)^{3/4}}{9 x^9}",1,"(2*b^2)/(15*a*x*(a + b*x^4)^(1/4)) - (a + b*x^4)^(3/4)/(9*x^9) - (b*(a + b*x^4)^(3/4))/(15*a*x^5) - (2*b^(5/2)*(1 + a/(b*x^4))^(1/4)*x*EllipticE[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(15*a^(3/2)*(a + b*x^4)^(1/4))","A",7,7,15,0.4667,1,"{277, 325, 312, 281, 335, 275, 196}"
1046,1,150,0,0.0711166,"\int \frac{\left(a+b x^4\right)^{3/4}}{x^{14}} \, dx","Int[(a + b*x^4)^(3/4)/x^14,x]","-\frac{4 b^3}{65 a^2 x \sqrt[4]{a+b x^4}}+\frac{2 b^2 \left(a+b x^4\right)^{3/4}}{65 a^2 x^5}+\frac{4 b^{7/2} x \sqrt[4]{\frac{a}{b x^4}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{65 a^{5/2} \sqrt[4]{a+b x^4}}-\frac{b \left(a+b x^4\right)^{3/4}}{39 a x^9}-\frac{\left(a+b x^4\right)^{3/4}}{13 x^{13}}","-\frac{4 b^3}{65 a^2 x \sqrt[4]{a+b x^4}}+\frac{2 b^2 \left(a+b x^4\right)^{3/4}}{65 a^2 x^5}+\frac{4 b^{7/2} x \sqrt[4]{\frac{a}{b x^4}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{65 a^{5/2} \sqrt[4]{a+b x^4}}-\frac{b \left(a+b x^4\right)^{3/4}}{39 a x^9}-\frac{\left(a+b x^4\right)^{3/4}}{13 x^{13}}",1,"(-4*b^3)/(65*a^2*x*(a + b*x^4)^(1/4)) - (a + b*x^4)^(3/4)/(13*x^13) - (b*(a + b*x^4)^(3/4))/(39*a*x^9) + (2*b^2*(a + b*x^4)^(3/4))/(65*a^2*x^5) + (4*b^(7/2)*(1 + a/(b*x^4))^(1/4)*x*EllipticE[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(65*a^(5/2)*(a + b*x^4)^(1/4))","A",8,7,15,0.4667,1,"{277, 325, 312, 281, 335, 275, 196}"
1047,1,101,0,0.0539924,"\int x^{19} \left(a+b x^4\right)^{5/4} \, dx","Int[x^19*(a + b*x^4)^(5/4),x]","\frac{6 a^2 \left(a+b x^4\right)^{17/4}}{17 b^5}-\frac{4 a^3 \left(a+b x^4\right)^{13/4}}{13 b^5}+\frac{a^4 \left(a+b x^4\right)^{9/4}}{9 b^5}+\frac{\left(a+b x^4\right)^{25/4}}{25 b^5}-\frac{4 a \left(a+b x^4\right)^{21/4}}{21 b^5}","\frac{6 a^2 \left(a+b x^4\right)^{17/4}}{17 b^5}-\frac{4 a^3 \left(a+b x^4\right)^{13/4}}{13 b^5}+\frac{a^4 \left(a+b x^4\right)^{9/4}}{9 b^5}+\frac{\left(a+b x^4\right)^{25/4}}{25 b^5}-\frac{4 a \left(a+b x^4\right)^{21/4}}{21 b^5}",1,"(a^4*(a + b*x^4)^(9/4))/(9*b^5) - (4*a^3*(a + b*x^4)^(13/4))/(13*b^5) + (6*a^2*(a + b*x^4)^(17/4))/(17*b^5) - (4*a*(a + b*x^4)^(21/4))/(21*b^5) + (a + b*x^4)^(25/4)/(25*b^5)","A",3,2,15,0.1333,1,"{266, 43}"
1048,1,80,0,0.0435236,"\int x^{15} \left(a+b x^4\right)^{5/4} \, dx","Int[x^15*(a + b*x^4)^(5/4),x]","\frac{3 a^2 \left(a+b x^4\right)^{13/4}}{13 b^4}-\frac{a^3 \left(a+b x^4\right)^{9/4}}{9 b^4}+\frac{\left(a+b x^4\right)^{21/4}}{21 b^4}-\frac{3 a \left(a+b x^4\right)^{17/4}}{17 b^4}","\frac{3 a^2 \left(a+b x^4\right)^{13/4}}{13 b^4}-\frac{a^3 \left(a+b x^4\right)^{9/4}}{9 b^4}+\frac{\left(a+b x^4\right)^{21/4}}{21 b^4}-\frac{3 a \left(a+b x^4\right)^{17/4}}{17 b^4}",1,"-(a^3*(a + b*x^4)^(9/4))/(9*b^4) + (3*a^2*(a + b*x^4)^(13/4))/(13*b^4) - (3*a*(a + b*x^4)^(17/4))/(17*b^4) + (a + b*x^4)^(21/4)/(21*b^4)","A",3,2,15,0.1333,1,"{266, 43}"
1049,1,59,0,0.0320943,"\int x^{11} \left(a+b x^4\right)^{5/4} \, dx","Int[x^11*(a + b*x^4)^(5/4),x]","\frac{a^2 \left(a+b x^4\right)^{9/4}}{9 b^3}+\frac{\left(a+b x^4\right)^{17/4}}{17 b^3}-\frac{2 a \left(a+b x^4\right)^{13/4}}{13 b^3}","\frac{a^2 \left(a+b x^4\right)^{9/4}}{9 b^3}+\frac{\left(a+b x^4\right)^{17/4}}{17 b^3}-\frac{2 a \left(a+b x^4\right)^{13/4}}{13 b^3}",1,"(a^2*(a + b*x^4)^(9/4))/(9*b^3) - (2*a*(a + b*x^4)^(13/4))/(13*b^3) + (a + b*x^4)^(17/4)/(17*b^3)","A",3,2,15,0.1333,1,"{266, 43}"
1050,1,38,0,0.021901,"\int x^7 \left(a+b x^4\right)^{5/4} \, dx","Int[x^7*(a + b*x^4)^(5/4),x]","\frac{\left(a+b x^4\right)^{13/4}}{13 b^2}-\frac{a \left(a+b x^4\right)^{9/4}}{9 b^2}","\frac{\left(a+b x^4\right)^{13/4}}{13 b^2}-\frac{a \left(a+b x^4\right)^{9/4}}{9 b^2}",1,"-(a*(a + b*x^4)^(9/4))/(9*b^2) + (a + b*x^4)^(13/4)/(13*b^2)","A",3,2,15,0.1333,1,"{266, 43}"
1051,1,18,0,0.0041643,"\int x^3 \left(a+b x^4\right)^{5/4} \, dx","Int[x^3*(a + b*x^4)^(5/4),x]","\frac{\left(a+b x^4\right)^{9/4}}{9 b}","\frac{\left(a+b x^4\right)^{9/4}}{9 b}",1,"(a + b*x^4)^(9/4)/(9*b)","A",1,1,15,0.06667,1,"{261}"
1052,1,83,0,0.0519887,"\int \frac{\left(a+b x^4\right)^{5/4}}{x} \, dx","Int[(a + b*x^4)^(5/4)/x,x]","-\frac{1}{2} a^{5/4} \tan ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)-\frac{1}{2} a^{5/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)+a \sqrt[4]{a+b x^4}+\frac{1}{5} \left(a+b x^4\right)^{5/4}","-\frac{1}{2} a^{5/4} \tan ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)-\frac{1}{2} a^{5/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)+a \sqrt[4]{a+b x^4}+\frac{1}{5} \left(a+b x^4\right)^{5/4}",1,"a*(a + b*x^4)^(1/4) + (a + b*x^4)^(5/4)/5 - (a^(5/4)*ArcTan[(a + b*x^4)^(1/4)/a^(1/4)])/2 - (a^(5/4)*ArcTanh[(a + b*x^4)^(1/4)/a^(1/4)])/2","A",7,6,15,0.4000,1,"{266, 50, 63, 212, 206, 203}"
1053,1,91,0,0.0529128,"\int \frac{\left(a+b x^4\right)^{5/4}}{x^5} \, dx","Int[(a + b*x^4)^(5/4)/x^5,x]","-\frac{\left(a+b x^4\right)^{5/4}}{4 x^4}+\frac{5}{4} b \sqrt[4]{a+b x^4}-\frac{5}{8} \sqrt[4]{a} b \tan ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)-\frac{5}{8} \sqrt[4]{a} b \tanh ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)","-\frac{\left(a+b x^4\right)^{5/4}}{4 x^4}+\frac{5}{4} b \sqrt[4]{a+b x^4}-\frac{5}{8} \sqrt[4]{a} b \tan ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)-\frac{5}{8} \sqrt[4]{a} b \tanh ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)",1,"(5*b*(a + b*x^4)^(1/4))/4 - (a + b*x^4)^(5/4)/(4*x^4) - (5*a^(1/4)*b*ArcTan[(a + b*x^4)^(1/4)/a^(1/4)])/8 - (5*a^(1/4)*b*ArcTanh[(a + b*x^4)^(1/4)/a^(1/4)])/8","A",7,7,15,0.4667,1,"{266, 47, 50, 63, 212, 206, 203}"
1054,1,98,0,0.0566003,"\int \frac{\left(a+b x^4\right)^{5/4}}{x^9} \, dx","Int[(a + b*x^4)^(5/4)/x^9,x]","-\frac{5 b^2 \tan ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{64 a^{3/4}}-\frac{5 b^2 \tanh ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{64 a^{3/4}}-\frac{5 b \sqrt[4]{a+b x^4}}{32 x^4}-\frac{\left(a+b x^4\right)^{5/4}}{8 x^8}","-\frac{5 b^2 \tan ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{64 a^{3/4}}-\frac{5 b^2 \tanh ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{64 a^{3/4}}-\frac{5 b \sqrt[4]{a+b x^4}}{32 x^4}-\frac{\left(a+b x^4\right)^{5/4}}{8 x^8}",1,"(-5*b*(a + b*x^4)^(1/4))/(32*x^4) - (a + b*x^4)^(5/4)/(8*x^8) - (5*b^2*ArcTan[(a + b*x^4)^(1/4)/a^(1/4)])/(64*a^(3/4)) - (5*b^2*ArcTanh[(a + b*x^4)^(1/4)/a^(1/4)])/(64*a^(3/4))","A",7,6,15,0.4000,1,"{266, 47, 63, 212, 206, 203}"
1055,1,146,0,0.1030485,"\int x^9 \left(a+b x^4\right)^{5/4} \, dx","Int[x^9*(a + b*x^4)^(5/4),x]","-\frac{2 a^3 x^2 \sqrt[4]{a+b x^4}}{231 b^2}+\frac{4 a^{9/2} \left(\frac{b x^4}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{231 b^{5/2} \left(a+b x^4\right)^{3/4}}+\frac{a^2 x^6 \sqrt[4]{a+b x^4}}{231 b}+\frac{1}{15} x^{10} \left(a+b x^4\right)^{5/4}+\frac{1}{33} a x^{10} \sqrt[4]{a+b x^4}","-\frac{2 a^3 x^2 \sqrt[4]{a+b x^4}}{231 b^2}+\frac{4 a^{9/2} \left(\frac{b x^4}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{231 b^{5/2} \left(a+b x^4\right)^{3/4}}+\frac{a^2 x^6 \sqrt[4]{a+b x^4}}{231 b}+\frac{1}{15} x^{10} \left(a+b x^4\right)^{5/4}+\frac{1}{33} a x^{10} \sqrt[4]{a+b x^4}",1,"(-2*a^3*x^2*(a + b*x^4)^(1/4))/(231*b^2) + (a^2*x^6*(a + b*x^4)^(1/4))/(231*b) + (a*x^10*(a + b*x^4)^(1/4))/33 + (x^10*(a + b*x^4)^(5/4))/15 + (4*a^(9/2)*(1 + (b*x^4)/a)^(3/4)*EllipticF[ArcTan[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(231*b^(5/2)*(a + b*x^4)^(3/4))","A",7,5,15,0.3333,1,"{275, 279, 321, 233, 231}"
1056,1,122,0,0.0792693,"\int x^5 \left(a+b x^4\right)^{5/4} \, dx","Int[x^5*(a + b*x^4)^(5/4),x]","-\frac{10 a^{7/2} \left(\frac{b x^4}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{231 b^{3/2} \left(a+b x^4\right)^{3/4}}+\frac{5 a^2 x^2 \sqrt[4]{a+b x^4}}{231 b}+\frac{1}{11} x^6 \left(a+b x^4\right)^{5/4}+\frac{5}{77} a x^6 \sqrt[4]{a+b x^4}","-\frac{10 a^{7/2} \left(\frac{b x^4}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{231 b^{3/2} \left(a+b x^4\right)^{3/4}}+\frac{5 a^2 x^2 \sqrt[4]{a+b x^4}}{231 b}+\frac{1}{11} x^6 \left(a+b x^4\right)^{5/4}+\frac{5}{77} a x^6 \sqrt[4]{a+b x^4}",1,"(5*a^2*x^2*(a + b*x^4)^(1/4))/(231*b) + (5*a*x^6*(a + b*x^4)^(1/4))/77 + (x^6*(a + b*x^4)^(5/4))/11 - (10*a^(7/2)*(1 + (b*x^4)/a)^(3/4)*EllipticF[ArcTan[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(231*b^(3/2)*(a + b*x^4)^(3/4))","A",6,5,15,0.3333,1,"{275, 279, 321, 233, 231}"
1057,1,98,0,0.0551144,"\int x \left(a+b x^4\right)^{5/4} \, dx","Int[x*(a + b*x^4)^(5/4),x]","\frac{5 a^{5/2} \left(\frac{b x^4}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{21 \sqrt{b} \left(a+b x^4\right)^{3/4}}+\frac{5}{21} a x^2 \sqrt[4]{a+b x^4}+\frac{1}{7} x^2 \left(a+b x^4\right)^{5/4}","\frac{5 a^{5/2} \left(\frac{b x^4}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{21 \sqrt{b} \left(a+b x^4\right)^{3/4}}+\frac{5}{21} a x^2 \sqrt[4]{a+b x^4}+\frac{1}{7} x^2 \left(a+b x^4\right)^{5/4}",1,"(5*a*x^2*(a + b*x^4)^(1/4))/21 + (x^2*(a + b*x^4)^(5/4))/7 + (5*a^(5/2)*(1 + (b*x^4)/a)^(3/4)*EllipticF[ArcTan[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(21*Sqrt[b]*(a + b*x^4)^(3/4))","A",5,4,13,0.3077,1,"{275, 195, 233, 231}"
1058,1,98,0,0.059825,"\int \frac{\left(a+b x^4\right)^{5/4}}{x^3} \, dx","Int[(a + b*x^4)^(5/4)/x^3,x]","\frac{5 a^{3/2} \sqrt{b} \left(\frac{b x^4}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{6 \left(a+b x^4\right)^{3/4}}+\frac{5}{6} b x^2 \sqrt[4]{a+b x^4}-\frac{\left(a+b x^4\right)^{5/4}}{2 x^2}","\frac{5 a^{3/2} \sqrt{b} \left(\frac{b x^4}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{6 \left(a+b x^4\right)^{3/4}}+\frac{5}{6} b x^2 \sqrt[4]{a+b x^4}-\frac{\left(a+b x^4\right)^{5/4}}{2 x^2}",1,"(5*b*x^2*(a + b*x^4)^(1/4))/6 - (a + b*x^4)^(5/4)/(2*x^2) + (5*a^(3/2)*Sqrt[b]*(1 + (b*x^4)/a)^(3/4)*EllipticF[ArcTan[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(6*(a + b*x^4)^(3/4))","A",5,5,15,0.3333,1,"{275, 277, 195, 233, 231}"
1059,1,98,0,0.0611447,"\int \frac{\left(a+b x^4\right)^{5/4}}{x^7} \, dx","Int[(a + b*x^4)^(5/4)/x^7,x]","\frac{5 \sqrt{a} b^{3/2} \left(\frac{b x^4}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{12 \left(a+b x^4\right)^{3/4}}-\frac{5 b \sqrt[4]{a+b x^4}}{12 x^2}-\frac{\left(a+b x^4\right)^{5/4}}{6 x^6}","\frac{5 \sqrt{a} b^{3/2} \left(\frac{b x^4}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{12 \left(a+b x^4\right)^{3/4}}-\frac{5 b \sqrt[4]{a+b x^4}}{12 x^2}-\frac{\left(a+b x^4\right)^{5/4}}{6 x^6}",1,"(-5*b*(a + b*x^4)^(1/4))/(12*x^2) - (a + b*x^4)^(5/4)/(6*x^6) + (5*Sqrt[a]*b^(3/2)*(1 + (b*x^4)/a)^(3/4)*EllipticF[ArcTan[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(12*(a + b*x^4)^(3/4))","A",5,4,15,0.2667,1,"{275, 277, 233, 231}"
1060,1,122,0,0.0783831,"\int \frac{\left(a+b x^4\right)^{5/4}}{x^{11}} \, dx","Int[(a + b*x^4)^(5/4)/x^11,x]","-\frac{b^2 \sqrt[4]{a+b x^4}}{24 a x^2}-\frac{b^{5/2} \left(\frac{b x^4}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{24 \sqrt{a} \left(a+b x^4\right)^{3/4}}-\frac{b \sqrt[4]{a+b x^4}}{12 x^6}-\frac{\left(a+b x^4\right)^{5/4}}{10 x^{10}}","-\frac{b^2 \sqrt[4]{a+b x^4}}{24 a x^2}-\frac{b^{5/2} \left(\frac{b x^4}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{24 \sqrt{a} \left(a+b x^4\right)^{3/4}}-\frac{b \sqrt[4]{a+b x^4}}{12 x^6}-\frac{\left(a+b x^4\right)^{5/4}}{10 x^{10}}",1,"-(b*(a + b*x^4)^(1/4))/(12*x^6) - (b^2*(a + b*x^4)^(1/4))/(24*a*x^2) - (a + b*x^4)^(5/4)/(10*x^10) - (b^(5/2)*(1 + (b*x^4)/a)^(3/4)*EllipticF[ArcTan[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(24*Sqrt[a]*(a + b*x^4)^(3/4))","A",6,5,15,0.3333,1,"{275, 277, 325, 233, 231}"
1061,1,146,0,0.100437,"\int \frac{\left(a+b x^4\right)^{5/4}}{x^{15}} \, dx","Int[(a + b*x^4)^(5/4)/x^15,x]","\frac{5 b^3 \sqrt[4]{a+b x^4}}{336 a^2 x^2}+\frac{5 b^{7/2} \left(\frac{b x^4}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{336 a^{3/2} \left(a+b x^4\right)^{3/4}}-\frac{b^2 \sqrt[4]{a+b x^4}}{168 a x^6}-\frac{b \sqrt[4]{a+b x^4}}{28 x^{10}}-\frac{\left(a+b x^4\right)^{5/4}}{14 x^{14}}","\frac{5 b^3 \sqrt[4]{a+b x^4}}{336 a^2 x^2}+\frac{5 b^{7/2} \left(\frac{b x^4}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{336 a^{3/2} \left(a+b x^4\right)^{3/4}}-\frac{b^2 \sqrt[4]{a+b x^4}}{168 a x^6}-\frac{b \sqrt[4]{a+b x^4}}{28 x^{10}}-\frac{\left(a+b x^4\right)^{5/4}}{14 x^{14}}",1,"-(b*(a + b*x^4)^(1/4))/(28*x^10) - (b^2*(a + b*x^4)^(1/4))/(168*a*x^6) + (5*b^3*(a + b*x^4)^(1/4))/(336*a^2*x^2) - (a + b*x^4)^(5/4)/(14*x^14) + (5*b^(7/2)*(1 + (b*x^4)/a)^(3/4)*EllipticF[ArcTan[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(336*a^(3/2)*(a + b*x^4)^(3/4))","A",7,5,15,0.3333,1,"{275, 277, 325, 233, 231}"
1062,1,148,0,0.0641264,"\int x^{10} \left(a+b x^4\right)^{5/4} \, dx","Int[x^10*(a + b*x^4)^(5/4),x]","-\frac{35 a^3 x^3 \sqrt[4]{a+b x^4}}{6144 b^2}-\frac{35 a^4 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{4096 b^{11/4}}+\frac{35 a^4 \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{4096 b^{11/4}}+\frac{5 a^2 x^7 \sqrt[4]{a+b x^4}}{1536 b}+\frac{1}{16} x^{11} \left(a+b x^4\right)^{5/4}+\frac{5}{192} a x^{11} \sqrt[4]{a+b x^4}","-\frac{35 a^3 x^3 \sqrt[4]{a+b x^4}}{6144 b^2}-\frac{35 a^4 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{4096 b^{11/4}}+\frac{35 a^4 \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{4096 b^{11/4}}+\frac{5 a^2 x^7 \sqrt[4]{a+b x^4}}{1536 b}+\frac{1}{16} x^{11} \left(a+b x^4\right)^{5/4}+\frac{5}{192} a x^{11} \sqrt[4]{a+b x^4}",1,"(-35*a^3*x^3*(a + b*x^4)^(1/4))/(6144*b^2) + (5*a^2*x^7*(a + b*x^4)^(1/4))/(1536*b) + (5*a*x^11*(a + b*x^4)^(1/4))/192 + (x^11*(a + b*x^4)^(5/4))/16 - (35*a^4*ArcTan[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/(4096*b^(11/4)) + (35*a^4*ArcTanh[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/(4096*b^(11/4))","A",8,6,15,0.4000,1,"{279, 321, 331, 298, 203, 206}"
1063,1,124,0,0.0504509,"\int x^6 \left(a+b x^4\right)^{5/4} \, dx","Int[x^6*(a + b*x^4)^(5/4),x]","\frac{5 a^3 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{256 b^{7/4}}-\frac{5 a^3 \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{256 b^{7/4}}+\frac{5 a^2 x^3 \sqrt[4]{a+b x^4}}{384 b}+\frac{1}{12} x^7 \left(a+b x^4\right)^{5/4}+\frac{5}{96} a x^7 \sqrt[4]{a+b x^4}","\frac{5 a^3 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{256 b^{7/4}}-\frac{5 a^3 \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{256 b^{7/4}}+\frac{5 a^2 x^3 \sqrt[4]{a+b x^4}}{384 b}+\frac{1}{12} x^7 \left(a+b x^4\right)^{5/4}+\frac{5}{96} a x^7 \sqrt[4]{a+b x^4}",1,"(5*a^2*x^3*(a + b*x^4)^(1/4))/(384*b) + (5*a*x^7*(a + b*x^4)^(1/4))/96 + (x^7*(a + b*x^4)^(5/4))/12 + (5*a^3*ArcTan[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/(256*b^(7/4)) - (5*a^3*ArcTanh[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/(256*b^(7/4))","A",7,6,15,0.4000,1,"{279, 321, 331, 298, 203, 206}"
1064,1,100,0,0.0370888,"\int x^2 \left(a+b x^4\right)^{5/4} \, dx","Int[x^2*(a + b*x^4)^(5/4),x]","-\frac{5 a^2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{64 b^{3/4}}+\frac{5 a^2 \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{64 b^{3/4}}+\frac{1}{8} x^3 \left(a+b x^4\right)^{5/4}+\frac{5}{32} a x^3 \sqrt[4]{a+b x^4}","-\frac{5 a^2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{64 b^{3/4}}+\frac{5 a^2 \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{64 b^{3/4}}+\frac{1}{8} x^3 \left(a+b x^4\right)^{5/4}+\frac{5}{32} a x^3 \sqrt[4]{a+b x^4}",1,"(5*a*x^3*(a + b*x^4)^(1/4))/32 + (x^3*(a + b*x^4)^(5/4))/8 - (5*a^2*ArcTan[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/(64*b^(3/4)) + (5*a^2*ArcTanh[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/(64*b^(3/4))","A",6,5,15,0.3333,1,"{279, 331, 298, 203, 206}"
1065,1,94,0,0.0357187,"\int \frac{\left(a+b x^4\right)^{5/4}}{x^2} \, dx","Int[(a + b*x^4)^(5/4)/x^2,x]","\frac{5}{4} b x^3 \sqrt[4]{a+b x^4}-\frac{\left(a+b x^4\right)^{5/4}}{x}-\frac{5}{8} a \sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)+\frac{5}{8} a \sqrt[4]{b} \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)","\frac{5}{4} b x^3 \sqrt[4]{a+b x^4}-\frac{\left(a+b x^4\right)^{5/4}}{x}-\frac{5}{8} a \sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)+\frac{5}{8} a \sqrt[4]{b} \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)",1,"(5*b*x^3*(a + b*x^4)^(1/4))/4 - (a + b*x^4)^(5/4)/x - (5*a*b^(1/4)*ArcTan[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/8 + (5*a*b^(1/4)*ArcTanh[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/8","A",6,6,15,0.4000,1,"{277, 279, 331, 298, 203, 206}"
1066,1,92,0,0.0345465,"\int \frac{\left(a+b x^4\right)^{5/4}}{x^6} \, dx","Int[(a + b*x^4)^(5/4)/x^6,x]","-\frac{1}{2} b^{5/4} \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)+\frac{1}{2} b^{5/4} \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)-\frac{b \sqrt[4]{a+b x^4}}{x}-\frac{\left(a+b x^4\right)^{5/4}}{5 x^5}","-\frac{1}{2} b^{5/4} \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)+\frac{1}{2} b^{5/4} \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)-\frac{b \sqrt[4]{a+b x^4}}{x}-\frac{\left(a+b x^4\right)^{5/4}}{5 x^5}",1,"-((b*(a + b*x^4)^(1/4))/x) - (a + b*x^4)^(5/4)/(5*x^5) - (b^(5/4)*ArcTan[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/2 + (b^(5/4)*ArcTanh[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/2","A",6,5,15,0.3333,1,"{277, 331, 298, 203, 206}"
1067,1,21,0,0.0045641,"\int \frac{\left(a+b x^4\right)^{5/4}}{x^{10}} \, dx","Int[(a + b*x^4)^(5/4)/x^10,x]","-\frac{\left(a+b x^4\right)^{9/4}}{9 a x^9}","-\frac{\left(a+b x^4\right)^{9/4}}{9 a x^9}",1,"-(a + b*x^4)^(9/4)/(9*a*x^9)","A",1,1,15,0.06667,1,"{264}"
1068,1,44,0,0.0108018,"\int \frac{\left(a+b x^4\right)^{5/4}}{x^{14}} \, dx","Int[(a + b*x^4)^(5/4)/x^14,x]","\frac{4 b \left(a+b x^4\right)^{9/4}}{117 a^2 x^9}-\frac{\left(a+b x^4\right)^{9/4}}{13 a x^{13}}","\frac{4 b \left(a+b x^4\right)^{9/4}}{117 a^2 x^9}-\frac{\left(a+b x^4\right)^{9/4}}{13 a x^{13}}",1,"-(a + b*x^4)^(9/4)/(13*a*x^13) + (4*b*(a + b*x^4)^(9/4))/(117*a^2*x^9)","A",2,2,15,0.1333,1,"{271, 264}"
1069,1,68,0,0.019809,"\int \frac{\left(a+b x^4\right)^{5/4}}{x^{18}} \, dx","Int[(a + b*x^4)^(5/4)/x^18,x]","-\frac{32 b^2 \left(a+b x^4\right)^{9/4}}{1989 a^3 x^9}+\frac{8 b \left(a+b x^4\right)^{9/4}}{221 a^2 x^{13}}-\frac{\left(a+b x^4\right)^{9/4}}{17 a x^{17}}","-\frac{32 b^2 \left(a+b x^4\right)^{9/4}}{1989 a^3 x^9}+\frac{8 b \left(a+b x^4\right)^{9/4}}{221 a^2 x^{13}}-\frac{\left(a+b x^4\right)^{9/4}}{17 a x^{17}}",1,"-(a + b*x^4)^(9/4)/(17*a*x^17) + (8*b*(a + b*x^4)^(9/4))/(221*a^2*x^13) - (32*b^2*(a + b*x^4)^(9/4))/(1989*a^3*x^9)","A",3,2,15,0.1333,1,"{271, 264}"
1070,1,92,0,0.028267,"\int \frac{\left(a+b x^4\right)^{5/4}}{x^{22}} \, dx","Int[(a + b*x^4)^(5/4)/x^22,x]","\frac{128 b^3 \left(a+b x^4\right)^{9/4}}{13923 a^4 x^9}-\frac{32 b^2 \left(a+b x^4\right)^{9/4}}{1547 a^3 x^{13}}+\frac{4 b \left(a+b x^4\right)^{9/4}}{119 a^2 x^{17}}-\frac{\left(a+b x^4\right)^{9/4}}{21 a x^{21}}","\frac{128 b^3 \left(a+b x^4\right)^{9/4}}{13923 a^4 x^9}-\frac{32 b^2 \left(a+b x^4\right)^{9/4}}{1547 a^3 x^{13}}+\frac{4 b \left(a+b x^4\right)^{9/4}}{119 a^2 x^{17}}-\frac{\left(a+b x^4\right)^{9/4}}{21 a x^{21}}",1,"-(a + b*x^4)^(9/4)/(21*a*x^21) + (4*b*(a + b*x^4)^(9/4))/(119*a^2*x^17) - (32*b^2*(a + b*x^4)^(9/4))/(1547*a^3*x^13) + (128*b^3*(a + b*x^4)^(9/4))/(13923*a^4*x^9)","A",4,2,15,0.1333,1,"{271, 264}"
1071,1,171,0,0.087997,"\int x^{12} \left(a+b x^4\right)^{5/4} \, dx","Int[x^12*(a + b*x^4)^(5/4),x]","-\frac{a^3 x^5 \sqrt[4]{a+b x^4}}{336 b^2}+\frac{5 a^4 x \sqrt[4]{a+b x^4}}{672 b^3}+\frac{5 a^{9/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{672 b^{5/2} \left(a+b x^4\right)^{3/4}}+\frac{a^2 x^9 \sqrt[4]{a+b x^4}}{504 b}+\frac{1}{18} x^{13} \left(a+b x^4\right)^{5/4}+\frac{5}{252} a x^{13} \sqrt[4]{a+b x^4}","-\frac{a^3 x^5 \sqrt[4]{a+b x^4}}{336 b^2}+\frac{5 a^4 x \sqrt[4]{a+b x^4}}{672 b^3}+\frac{5 a^{9/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{672 b^{5/2} \left(a+b x^4\right)^{3/4}}+\frac{a^2 x^9 \sqrt[4]{a+b x^4}}{504 b}+\frac{1}{18} x^{13} \left(a+b x^4\right)^{5/4}+\frac{5}{252} a x^{13} \sqrt[4]{a+b x^4}",1,"(5*a^4*x*(a + b*x^4)^(1/4))/(672*b^3) - (a^3*x^5*(a + b*x^4)^(1/4))/(336*b^2) + (a^2*x^9*(a + b*x^4)^(1/4))/(504*b) + (5*a*x^13*(a + b*x^4)^(1/4))/252 + (x^13*(a + b*x^4)^(5/4))/18 + (5*a^(9/2)*(1 + a/(b*x^4))^(3/4)*x^3*EllipticF[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(672*b^(5/2)*(a + b*x^4)^(3/4))","A",9,6,15,0.4000,1,"{279, 321, 237, 335, 275, 231}"
1072,1,147,0,0.0692857,"\int x^8 \left(a+b x^4\right)^{5/4} \, dx","Int[x^8*(a + b*x^4)^(5/4),x]","-\frac{5 a^3 x \sqrt[4]{a+b x^4}}{336 b^2}-\frac{5 a^{7/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{336 b^{3/2} \left(a+b x^4\right)^{3/4}}+\frac{a^2 x^5 \sqrt[4]{a+b x^4}}{168 b}+\frac{1}{14} x^9 \left(a+b x^4\right)^{5/4}+\frac{1}{28} a x^9 \sqrt[4]{a+b x^4}","-\frac{5 a^3 x \sqrt[4]{a+b x^4}}{336 b^2}-\frac{5 a^{7/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{336 b^{3/2} \left(a+b x^4\right)^{3/4}}+\frac{a^2 x^5 \sqrt[4]{a+b x^4}}{168 b}+\frac{1}{14} x^9 \left(a+b x^4\right)^{5/4}+\frac{1}{28} a x^9 \sqrt[4]{a+b x^4}",1,"(-5*a^3*x*(a + b*x^4)^(1/4))/(336*b^2) + (a^2*x^5*(a + b*x^4)^(1/4))/(168*b) + (a*x^9*(a + b*x^4)^(1/4))/28 + (x^9*(a + b*x^4)^(5/4))/14 - (5*a^(7/2)*(1 + a/(b*x^4))^(3/4)*x^3*EllipticF[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(336*b^(3/2)*(a + b*x^4)^(3/4))","A",8,6,15,0.4000,1,"{279, 321, 237, 335, 275, 231}"
1073,1,123,0,0.0562202,"\int x^4 \left(a+b x^4\right)^{5/4} \, dx","Int[x^4*(a + b*x^4)^(5/4),x]","\frac{a^2 x \sqrt[4]{a+b x^4}}{24 b}+\frac{a^{5/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{24 \sqrt{b} \left(a+b x^4\right)^{3/4}}+\frac{1}{10} x^5 \left(a+b x^4\right)^{5/4}+\frac{1}{12} a x^5 \sqrt[4]{a+b x^4}","\frac{a^2 x \sqrt[4]{a+b x^4}}{24 b}+\frac{a^{5/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{24 \sqrt{b} \left(a+b x^4\right)^{3/4}}+\frac{1}{10} x^5 \left(a+b x^4\right)^{5/4}+\frac{1}{12} a x^5 \sqrt[4]{a+b x^4}",1,"(a^2*x*(a + b*x^4)^(1/4))/(24*b) + (a*x^5*(a + b*x^4)^(1/4))/12 + (x^5*(a + b*x^4)^(5/4))/10 + (a^(5/2)*(1 + a/(b*x^4))^(3/4)*x^3*EllipticF[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(24*Sqrt[b]*(a + b*x^4)^(3/4))","A",7,6,15,0.4000,1,"{279, 321, 237, 335, 275, 231}"
1074,1,97,0,0.0383726,"\int \left(a+b x^4\right)^{5/4} \, dx","Int[(a + b*x^4)^(5/4),x]","-\frac{5 a^{3/2} \sqrt{b} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{12 \left(a+b x^4\right)^{3/4}}+\frac{1}{6} x \left(a+b x^4\right)^{5/4}+\frac{5}{12} a x \sqrt[4]{a+b x^4}","-\frac{5 a^{3/2} \sqrt{b} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{12 \left(a+b x^4\right)^{3/4}}+\frac{1}{6} x \left(a+b x^4\right)^{5/4}+\frac{5}{12} a x \sqrt[4]{a+b x^4}",1,"(5*a*x*(a + b*x^4)^(1/4))/12 + (x*(a + b*x^4)^(5/4))/6 - (5*a^(3/2)*Sqrt[b]*(1 + a/(b*x^4))^(3/4)*x^3*EllipticF[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(12*(a + b*x^4)^(3/4))","A",6,5,11,0.4545,1,"{195, 237, 335, 275, 231}"
1075,1,99,0,0.0405582,"\int \frac{\left(a+b x^4\right)^{5/4}}{x^4} \, dx","Int[(a + b*x^4)^(5/4)/x^4,x]","-\frac{5 \sqrt{a} b^{3/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{6 \left(a+b x^4\right)^{3/4}}+\frac{5}{6} b x \sqrt[4]{a+b x^4}-\frac{\left(a+b x^4\right)^{5/4}}{3 x^3}","-\frac{5 \sqrt{a} b^{3/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{6 \left(a+b x^4\right)^{3/4}}+\frac{5}{6} b x \sqrt[4]{a+b x^4}-\frac{\left(a+b x^4\right)^{5/4}}{3 x^3}",1,"(5*b*x*(a + b*x^4)^(1/4))/6 - (a + b*x^4)^(5/4)/(3*x^3) - (5*Sqrt[a]*b^(3/2)*(1 + a/(b*x^4))^(3/4)*x^3*EllipticF[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(6*(a + b*x^4)^(3/4))","A",6,6,15,0.4000,1,"{277, 195, 237, 335, 275, 231}"
1076,1,101,0,0.0441044,"\int \frac{\left(a+b x^4\right)^{5/4}}{x^8} \, dx","Int[(a + b*x^4)^(5/4)/x^8,x]","-\frac{5 b^{5/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{21 \sqrt{a} \left(a+b x^4\right)^{3/4}}-\frac{5 b \sqrt[4]{a+b x^4}}{21 x^3}-\frac{\left(a+b x^4\right)^{5/4}}{7 x^7}","-\frac{5 b^{5/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{21 \sqrt{a} \left(a+b x^4\right)^{3/4}}-\frac{5 b \sqrt[4]{a+b x^4}}{21 x^3}-\frac{\left(a+b x^4\right)^{5/4}}{7 x^7}",1,"(-5*b*(a + b*x^4)^(1/4))/(21*x^3) - (a + b*x^4)^(5/4)/(7*x^7) - (5*b^(5/2)*(1 + a/(b*x^4))^(3/4)*x^3*EllipticF[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(21*Sqrt[a]*(a + b*x^4)^(3/4))","A",6,5,15,0.3333,1,"{277, 237, 335, 275, 231}"
1077,1,125,0,0.0545783,"\int \frac{\left(a+b x^4\right)^{5/4}}{x^{12}} \, dx","Int[(a + b*x^4)^(5/4)/x^12,x]","\frac{10 b^{7/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{231 a^{3/2} \left(a+b x^4\right)^{3/4}}-\frac{5 b^2 \sqrt[4]{a+b x^4}}{231 a x^3}-\frac{5 b \sqrt[4]{a+b x^4}}{77 x^7}-\frac{\left(a+b x^4\right)^{5/4}}{11 x^{11}}","\frac{10 b^{7/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{231 a^{3/2} \left(a+b x^4\right)^{3/4}}-\frac{5 b^2 \sqrt[4]{a+b x^4}}{231 a x^3}-\frac{5 b \sqrt[4]{a+b x^4}}{77 x^7}-\frac{\left(a+b x^4\right)^{5/4}}{11 x^{11}}",1,"(-5*b*(a + b*x^4)^(1/4))/(77*x^7) - (5*b^2*(a + b*x^4)^(1/4))/(231*a*x^3) - (a + b*x^4)^(5/4)/(11*x^11) + (10*b^(7/2)*(1 + a/(b*x^4))^(3/4)*x^3*EllipticF[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(231*a^(3/2)*(a + b*x^4)^(3/4))","A",7,6,15,0.4000,1,"{277, 325, 237, 335, 275, 231}"
1078,1,149,0,0.07019,"\int \frac{\left(a+b x^4\right)^{5/4}}{x^{16}} \, dx","Int[(a + b*x^4)^(5/4)/x^16,x]","\frac{2 b^3 \sqrt[4]{a+b x^4}}{231 a^2 x^3}-\frac{4 b^{9/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{231 a^{5/2} \left(a+b x^4\right)^{3/4}}-\frac{b^2 \sqrt[4]{a+b x^4}}{231 a x^7}-\frac{b \sqrt[4]{a+b x^4}}{33 x^{11}}-\frac{\left(a+b x^4\right)^{5/4}}{15 x^{15}}","\frac{2 b^3 \sqrt[4]{a+b x^4}}{231 a^2 x^3}-\frac{4 b^{9/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{231 a^{5/2} \left(a+b x^4\right)^{3/4}}-\frac{b^2 \sqrt[4]{a+b x^4}}{231 a x^7}-\frac{b \sqrt[4]{a+b x^4}}{33 x^{11}}-\frac{\left(a+b x^4\right)^{5/4}}{15 x^{15}}",1,"-(b*(a + b*x^4)^(1/4))/(33*x^11) - (b^2*(a + b*x^4)^(1/4))/(231*a*x^7) + (2*b^3*(a + b*x^4)^(1/4))/(231*a^2*x^3) - (a + b*x^4)^(5/4)/(15*x^15) - (4*b^(9/2)*(1 + a/(b*x^4))^(3/4)*x^3*EllipticF[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(231*a^(5/2)*(a + b*x^4)^(3/4))","A",8,6,15,0.4000,1,"{277, 325, 237, 335, 275, 231}"
1079,1,96,0,0.0256012,"\int \left(a+b x^4\right)^{7/4} \, dx","Int[(a + b*x^4)^(7/4),x]","\frac{21 a^2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{64 \sqrt[4]{b}}+\frac{21 a^2 \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{64 \sqrt[4]{b}}+\frac{7}{32} a x \left(a+b x^4\right)^{3/4}+\frac{1}{8} x \left(a+b x^4\right)^{7/4}","\frac{21 a^2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{64 \sqrt[4]{b}}+\frac{21 a^2 \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{64 \sqrt[4]{b}}+\frac{7}{32} a x \left(a+b x^4\right)^{3/4}+\frac{1}{8} x \left(a+b x^4\right)^{7/4}",1,"(7*a*x*(a + b*x^4)^(3/4))/32 + (x*(a + b*x^4)^(7/4))/8 + (21*a^2*ArcTan[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/(64*b^(1/4)) + (21*a^2*ArcTanh[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/(64*b^(1/4))","A",6,5,11,0.4545,1,"{195, 240, 212, 206, 203}"
1080,1,101,0,0.0534013,"\int \frac{x^{19}}{\sqrt[4]{a+b x^4}} \, dx","Int[x^19/(a + b*x^4)^(1/4),x]","\frac{6 a^2 \left(a+b x^4\right)^{11/4}}{11 b^5}-\frac{4 a^3 \left(a+b x^4\right)^{7/4}}{7 b^5}+\frac{a^4 \left(a+b x^4\right)^{3/4}}{3 b^5}+\frac{\left(a+b x^4\right)^{19/4}}{19 b^5}-\frac{4 a \left(a+b x^4\right)^{15/4}}{15 b^5}","\frac{6 a^2 \left(a+b x^4\right)^{11/4}}{11 b^5}-\frac{4 a^3 \left(a+b x^4\right)^{7/4}}{7 b^5}+\frac{a^4 \left(a+b x^4\right)^{3/4}}{3 b^5}+\frac{\left(a+b x^4\right)^{19/4}}{19 b^5}-\frac{4 a \left(a+b x^4\right)^{15/4}}{15 b^5}",1,"(a^4*(a + b*x^4)^(3/4))/(3*b^5) - (4*a^3*(a + b*x^4)^(7/4))/(7*b^5) + (6*a^2*(a + b*x^4)^(11/4))/(11*b^5) - (4*a*(a + b*x^4)^(15/4))/(15*b^5) + (a + b*x^4)^(19/4)/(19*b^5)","A",3,2,15,0.1333,1,"{266, 43}"
1081,1,80,0,0.0425469,"\int \frac{x^{15}}{\sqrt[4]{a+b x^4}} \, dx","Int[x^15/(a + b*x^4)^(1/4),x]","\frac{3 a^2 \left(a+b x^4\right)^{7/4}}{7 b^4}-\frac{a^3 \left(a+b x^4\right)^{3/4}}{3 b^4}+\frac{\left(a+b x^4\right)^{15/4}}{15 b^4}-\frac{3 a \left(a+b x^4\right)^{11/4}}{11 b^4}","\frac{3 a^2 \left(a+b x^4\right)^{7/4}}{7 b^4}-\frac{a^3 \left(a+b x^4\right)^{3/4}}{3 b^4}+\frac{\left(a+b x^4\right)^{15/4}}{15 b^4}-\frac{3 a \left(a+b x^4\right)^{11/4}}{11 b^4}",1,"-(a^3*(a + b*x^4)^(3/4))/(3*b^4) + (3*a^2*(a + b*x^4)^(7/4))/(7*b^4) - (3*a*(a + b*x^4)^(11/4))/(11*b^4) + (a + b*x^4)^(15/4)/(15*b^4)","A",3,2,15,0.1333,1,"{266, 43}"
1082,1,59,0,0.0327176,"\int \frac{x^{11}}{\sqrt[4]{a+b x^4}} \, dx","Int[x^11/(a + b*x^4)^(1/4),x]","\frac{a^2 \left(a+b x^4\right)^{3/4}}{3 b^3}+\frac{\left(a+b x^4\right)^{11/4}}{11 b^3}-\frac{2 a \left(a+b x^4\right)^{7/4}}{7 b^3}","\frac{a^2 \left(a+b x^4\right)^{3/4}}{3 b^3}+\frac{\left(a+b x^4\right)^{11/4}}{11 b^3}-\frac{2 a \left(a+b x^4\right)^{7/4}}{7 b^3}",1,"(a^2*(a + b*x^4)^(3/4))/(3*b^3) - (2*a*(a + b*x^4)^(7/4))/(7*b^3) + (a + b*x^4)^(11/4)/(11*b^3)","A",3,2,15,0.1333,1,"{266, 43}"
1083,1,38,0,0.0211263,"\int \frac{x^7}{\sqrt[4]{a+b x^4}} \, dx","Int[x^7/(a + b*x^4)^(1/4),x]","\frac{\left(a+b x^4\right)^{7/4}}{7 b^2}-\frac{a \left(a+b x^4\right)^{3/4}}{3 b^2}","\frac{\left(a+b x^4\right)^{7/4}}{7 b^2}-\frac{a \left(a+b x^4\right)^{3/4}}{3 b^2}",1,"-(a*(a + b*x^4)^(3/4))/(3*b^2) + (a + b*x^4)^(7/4)/(7*b^2)","A",3,2,15,0.1333,1,"{266, 43}"
1084,1,18,0,0.0040828,"\int \frac{x^3}{\sqrt[4]{a+b x^4}} \, dx","Int[x^3/(a + b*x^4)^(1/4),x]","\frac{\left(a+b x^4\right)^{3/4}}{3 b}","\frac{\left(a+b x^4\right)^{3/4}}{3 b}",1,"(a + b*x^4)^(3/4)/(3*b)","A",1,1,15,0.06667,1,"{261}"
1085,1,55,0,0.0321208,"\int \frac{1}{x \sqrt[4]{a+b x^4}} \, dx","Int[1/(x*(a + b*x^4)^(1/4)),x]","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{2 \sqrt[4]{a}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{2 \sqrt[4]{a}}","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{2 \sqrt[4]{a}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{2 \sqrt[4]{a}}",1,"ArcTan[(a + b*x^4)^(1/4)/a^(1/4)]/(2*a^(1/4)) - ArcTanh[(a + b*x^4)^(1/4)/a^(1/4)]/(2*a^(1/4))","A",5,5,15,0.3333,1,"{266, 63, 298, 203, 206}"
1086,1,78,0,0.0452031,"\int \frac{1}{x^5 \sqrt[4]{a+b x^4}} \, dx","Int[1/(x^5*(a + b*x^4)^(1/4)),x]","-\frac{b \tan ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{8 a^{5/4}}+\frac{b \tanh ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{8 a^{5/4}}-\frac{\left(a+b x^4\right)^{3/4}}{4 a x^4}","-\frac{b \tan ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{8 a^{5/4}}+\frac{b \tanh ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{8 a^{5/4}}-\frac{\left(a+b x^4\right)^{3/4}}{4 a x^4}",1,"-(a + b*x^4)^(3/4)/(4*a*x^4) - (b*ArcTan[(a + b*x^4)^(1/4)/a^(1/4)])/(8*a^(5/4)) + (b*ArcTanh[(a + b*x^4)^(1/4)/a^(1/4)])/(8*a^(5/4))","A",6,6,15,0.4000,1,"{266, 51, 63, 298, 203, 206}"
1087,1,104,0,0.0610391,"\int \frac{1}{x^9 \sqrt[4]{a+b x^4}} \, dx","Int[1/(x^9*(a + b*x^4)^(1/4)),x]","\frac{5 b^2 \tan ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{64 a^{9/4}}-\frac{5 b^2 \tanh ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{64 a^{9/4}}+\frac{5 b \left(a+b x^4\right)^{3/4}}{32 a^2 x^4}-\frac{\left(a+b x^4\right)^{3/4}}{8 a x^8}","\frac{5 b^2 \tan ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{64 a^{9/4}}-\frac{5 b^2 \tanh ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{64 a^{9/4}}+\frac{5 b \left(a+b x^4\right)^{3/4}}{32 a^2 x^4}-\frac{\left(a+b x^4\right)^{3/4}}{8 a x^8}",1,"-(a + b*x^4)^(3/4)/(8*a*x^8) + (5*b*(a + b*x^4)^(3/4))/(32*a^2*x^4) + (5*b^2*ArcTan[(a + b*x^4)^(1/4)/a^(1/4)])/(64*a^(9/4)) - (5*b^2*ArcTanh[(a + b*x^4)^(1/4)/a^(1/4)])/(64*a^(9/4))","A",7,6,15,0.4000,1,"{266, 51, 63, 298, 203, 206}"
1088,1,152,0,0.0985127,"\int \frac{x^{13}}{\sqrt[4]{a+b x^4}} \, dx","Int[x^13/(a + b*x^4)^(1/4),x]","\frac{4 a^2 x^2 \left(a+b x^4\right)^{3/4}}{39 b^3}-\frac{8 a^3 x^2}{39 b^3 \sqrt[4]{a+b x^4}}+\frac{8 a^{7/2} \sqrt[4]{\frac{b x^4}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{39 b^{7/2} \sqrt[4]{a+b x^4}}-\frac{10 a x^6 \left(a+b x^4\right)^{3/4}}{117 b^2}+\frac{x^{10} \left(a+b x^4\right)^{3/4}}{13 b}","\frac{4 a^2 x^2 \left(a+b x^4\right)^{3/4}}{39 b^3}-\frac{8 a^3 x^2}{39 b^3 \sqrt[4]{a+b x^4}}+\frac{8 a^{7/2} \sqrt[4]{\frac{b x^4}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{39 b^{7/2} \sqrt[4]{a+b x^4}}-\frac{10 a x^6 \left(a+b x^4\right)^{3/4}}{117 b^2}+\frac{x^{10} \left(a+b x^4\right)^{3/4}}{13 b}",1,"(-8*a^3*x^2)/(39*b^3*(a + b*x^4)^(1/4)) + (4*a^2*x^2*(a + b*x^4)^(3/4))/(39*b^3) - (10*a*x^6*(a + b*x^4)^(3/4))/(117*b^2) + (x^10*(a + b*x^4)^(3/4))/(13*b) + (8*a^(7/2)*(1 + (b*x^4)/a)^(1/4)*EllipticE[ArcTan[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(39*b^(7/2)*(a + b*x^4)^(1/4))","A",7,5,15,0.3333,1,"{275, 321, 229, 227, 196}"
1089,1,128,0,0.0741468,"\int \frac{x^9}{\sqrt[4]{a+b x^4}} \, dx","Int[x^9/(a + b*x^4)^(1/4),x]","\frac{4 a^2 x^2}{15 b^2 \sqrt[4]{a+b x^4}}-\frac{4 a^{5/2} \sqrt[4]{\frac{b x^4}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{15 b^{5/2} \sqrt[4]{a+b x^4}}-\frac{2 a x^2 \left(a+b x^4\right)^{3/4}}{15 b^2}+\frac{x^6 \left(a+b x^4\right)^{3/4}}{9 b}","\frac{4 a^2 x^2}{15 b^2 \sqrt[4]{a+b x^4}}-\frac{4 a^{5/2} \sqrt[4]{\frac{b x^4}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{15 b^{5/2} \sqrt[4]{a+b x^4}}-\frac{2 a x^2 \left(a+b x^4\right)^{3/4}}{15 b^2}+\frac{x^6 \left(a+b x^4\right)^{3/4}}{9 b}",1,"(4*a^2*x^2)/(15*b^2*(a + b*x^4)^(1/4)) - (2*a*x^2*(a + b*x^4)^(3/4))/(15*b^2) + (x^6*(a + b*x^4)^(3/4))/(9*b) - (4*a^(5/2)*(1 + (b*x^4)/a)^(1/4)*EllipticE[ArcTan[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(15*b^(5/2)*(a + b*x^4)^(1/4))","A",6,5,15,0.3333,1,"{275, 321, 229, 227, 196}"
1090,1,104,0,0.0562071,"\int \frac{x^5}{\sqrt[4]{a+b x^4}} \, dx","Int[x^5/(a + b*x^4)^(1/4),x]","\frac{2 a^{3/2} \sqrt[4]{\frac{b x^4}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{5 b^{3/2} \sqrt[4]{a+b x^4}}+\frac{x^2 \left(a+b x^4\right)^{3/4}}{5 b}-\frac{2 a x^2}{5 b \sqrt[4]{a+b x^4}}","\frac{2 a^{3/2} \sqrt[4]{\frac{b x^4}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{5 b^{3/2} \sqrt[4]{a+b x^4}}+\frac{x^2 \left(a+b x^4\right)^{3/4}}{5 b}-\frac{2 a x^2}{5 b \sqrt[4]{a+b x^4}}",1,"(-2*a*x^2)/(5*b*(a + b*x^4)^(1/4)) + (x^2*(a + b*x^4)^(3/4))/(5*b) + (2*a^(3/2)*(1 + (b*x^4)/a)^(1/4)*EllipticE[ArcTan[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(5*b^(3/2)*(a + b*x^4)^(1/4))","A",5,5,15,0.3333,1,"{275, 321, 229, 227, 196}"
1091,1,74,0,0.0377393,"\int \frac{x}{\sqrt[4]{a+b x^4}} \, dx","Int[x/(a + b*x^4)^(1/4),x]","\frac{x^2}{\sqrt[4]{a+b x^4}}-\frac{\sqrt{a} \sqrt[4]{\frac{b x^4}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{\sqrt{b} \sqrt[4]{a+b x^4}}","\frac{x^2}{\sqrt[4]{a+b x^4}}-\frac{\sqrt{a} \sqrt[4]{\frac{b x^4}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{\sqrt{b} \sqrt[4]{a+b x^4}}",1,"x^2/(a + b*x^4)^(1/4) - (Sqrt[a]*(1 + (b*x^4)/a)^(1/4)*EllipticE[ArcTan[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(Sqrt[b]*(a + b*x^4)^(1/4))","A",4,4,13,0.3077,1,"{275, 229, 227, 196}"
1092,1,104,0,0.0537696,"\int \frac{1}{x^3 \sqrt[4]{a+b x^4}} \, dx","Int[1/(x^3*(a + b*x^4)^(1/4)),x]","\frac{b x^2}{2 a \sqrt[4]{a+b x^4}}-\frac{\left(a+b x^4\right)^{3/4}}{2 a x^2}-\frac{\sqrt{b} \sqrt[4]{\frac{b x^4}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{2 \sqrt{a} \sqrt[4]{a+b x^4}}","\frac{b x^2}{2 a \sqrt[4]{a+b x^4}}-\frac{\left(a+b x^4\right)^{3/4}}{2 a x^2}-\frac{\sqrt{b} \sqrt[4]{\frac{b x^4}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{2 \sqrt{a} \sqrt[4]{a+b x^4}}",1,"(b*x^2)/(2*a*(a + b*x^4)^(1/4)) - (a + b*x^4)^(3/4)/(2*a*x^2) - (Sqrt[b]*(1 + (b*x^4)/a)^(1/4)*EllipticE[ArcTan[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(2*Sqrt[a]*(a + b*x^4)^(1/4))","A",5,5,15,0.3333,1,"{275, 325, 229, 227, 196}"
1093,1,128,0,0.0738232,"\int \frac{1}{x^7 \sqrt[4]{a+b x^4}} \, dx","Int[1/(x^7*(a + b*x^4)^(1/4)),x]","-\frac{b^2 x^2}{4 a^2 \sqrt[4]{a+b x^4}}+\frac{b^{3/2} \sqrt[4]{\frac{b x^4}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{4 a^{3/2} \sqrt[4]{a+b x^4}}+\frac{b \left(a+b x^4\right)^{3/4}}{4 a^2 x^2}-\frac{\left(a+b x^4\right)^{3/4}}{6 a x^6}","-\frac{b^2 x^2}{4 a^2 \sqrt[4]{a+b x^4}}+\frac{b^{3/2} \sqrt[4]{\frac{b x^4}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{4 a^{3/2} \sqrt[4]{a+b x^4}}+\frac{b \left(a+b x^4\right)^{3/4}}{4 a^2 x^2}-\frac{\left(a+b x^4\right)^{3/4}}{6 a x^6}",1,"-(b^2*x^2)/(4*a^2*(a + b*x^4)^(1/4)) - (a + b*x^4)^(3/4)/(6*a*x^6) + (b*(a + b*x^4)^(3/4))/(4*a^2*x^2) + (b^(3/2)*(1 + (b*x^4)/a)^(1/4)*EllipticE[ArcTan[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(4*a^(3/2)*(a + b*x^4)^(1/4))","A",6,5,15,0.3333,1,"{275, 325, 229, 227, 196}"
1094,1,152,0,0.0954142,"\int \frac{1}{x^{11} \sqrt[4]{a+b x^4}} \, dx","Int[1/(x^11*(a + b*x^4)^(1/4)),x]","\frac{7 b^3 x^2}{40 a^3 \sqrt[4]{a+b x^4}}-\frac{7 b^2 \left(a+b x^4\right)^{3/4}}{40 a^3 x^2}-\frac{7 b^{5/2} \sqrt[4]{\frac{b x^4}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{40 a^{5/2} \sqrt[4]{a+b x^4}}+\frac{7 b \left(a+b x^4\right)^{3/4}}{60 a^2 x^6}-\frac{\left(a+b x^4\right)^{3/4}}{10 a x^{10}}","\frac{7 b^3 x^2}{40 a^3 \sqrt[4]{a+b x^4}}-\frac{7 b^2 \left(a+b x^4\right)^{3/4}}{40 a^3 x^2}-\frac{7 b^{5/2} \sqrt[4]{\frac{b x^4}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{40 a^{5/2} \sqrt[4]{a+b x^4}}+\frac{7 b \left(a+b x^4\right)^{3/4}}{60 a^2 x^6}-\frac{\left(a+b x^4\right)^{3/4}}{10 a x^{10}}",1,"(7*b^3*x^2)/(40*a^3*(a + b*x^4)^(1/4)) - (a + b*x^4)^(3/4)/(10*a*x^10) + (7*b*(a + b*x^4)^(3/4))/(60*a^2*x^6) - (7*b^2*(a + b*x^4)^(3/4))/(40*a^3*x^2) - (7*b^(5/2)*(1 + (b*x^4)/a)^(1/4)*EllipticE[ArcTan[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(40*a^(5/2)*(a + b*x^4)^(1/4))","A",7,5,15,0.3333,1,"{275, 325, 229, 227, 196}"
1095,1,104,0,0.0314346,"\int \frac{x^8}{\sqrt[4]{a+b x^4}} \, dx","Int[x^8/(a + b*x^4)^(1/4),x]","\frac{5 a^2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{64 b^{9/4}}+\frac{5 a^2 \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{64 b^{9/4}}-\frac{5 a x \left(a+b x^4\right)^{3/4}}{32 b^2}+\frac{x^5 \left(a+b x^4\right)^{3/4}}{8 b}","\frac{5 a^2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{64 b^{9/4}}+\frac{5 a^2 \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{64 b^{9/4}}-\frac{5 a x \left(a+b x^4\right)^{3/4}}{32 b^2}+\frac{x^5 \left(a+b x^4\right)^{3/4}}{8 b}",1,"(-5*a*x*(a + b*x^4)^(3/4))/(32*b^2) + (x^5*(a + b*x^4)^(3/4))/(8*b) + (5*a^2*ArcTan[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/(64*b^(9/4)) + (5*a^2*ArcTanh[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/(64*b^(9/4))","A",6,5,15,0.3333,1,"{321, 240, 212, 206, 203}"
1096,1,78,0,0.0219084,"\int \frac{x^4}{\sqrt[4]{a+b x^4}} \, dx","Int[x^4/(a + b*x^4)^(1/4),x]","-\frac{a \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{8 b^{5/4}}-\frac{a \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{8 b^{5/4}}+\frac{x \left(a+b x^4\right)^{3/4}}{4 b}","-\frac{a \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{8 b^{5/4}}-\frac{a \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{8 b^{5/4}}+\frac{x \left(a+b x^4\right)^{3/4}}{4 b}",1,"(x*(a + b*x^4)^(3/4))/(4*b) - (a*ArcTan[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/(8*b^(5/4)) - (a*ArcTanh[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/(8*b^(5/4))","A",5,5,15,0.3333,1,"{321, 240, 212, 206, 203}"
1097,1,57,0,0.013011,"\int \frac{1}{\sqrt[4]{a+b x^4}} \, dx","Int[(a + b*x^4)^(-1/4),x]","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{2 \sqrt[4]{b}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{2 \sqrt[4]{b}}","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{2 \sqrt[4]{b}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{2 \sqrt[4]{b}}",1,"ArcTan[(b^(1/4)*x)/(a + b*x^4)^(1/4)]/(2*b^(1/4)) + ArcTanh[(b^(1/4)*x)/(a + b*x^4)^(1/4)]/(2*b^(1/4))","A",4,4,11,0.3636,1,"{240, 212, 206, 203}"
1098,1,21,0,0.0047528,"\int \frac{1}{x^4 \sqrt[4]{a+b x^4}} \, dx","Int[1/(x^4*(a + b*x^4)^(1/4)),x]","-\frac{\left(a+b x^4\right)^{3/4}}{3 a x^3}","-\frac{\left(a+b x^4\right)^{3/4}}{3 a x^3}",1,"-(a + b*x^4)^(3/4)/(3*a*x^3)","A",1,1,15,0.06667,1,"{264}"
1099,1,44,0,0.0101368,"\int \frac{1}{x^8 \sqrt[4]{a+b x^4}} \, dx","Int[1/(x^8*(a + b*x^4)^(1/4)),x]","\frac{4 b \left(a+b x^4\right)^{3/4}}{21 a^2 x^3}-\frac{\left(a+b x^4\right)^{3/4}}{7 a x^7}","\frac{4 b \left(a+b x^4\right)^{3/4}}{21 a^2 x^3}-\frac{\left(a+b x^4\right)^{3/4}}{7 a x^7}",1,"-(a + b*x^4)^(3/4)/(7*a*x^7) + (4*b*(a + b*x^4)^(3/4))/(21*a^2*x^3)","A",2,2,15,0.1333,1,"{271, 264}"
1100,1,68,0,0.0179517,"\int \frac{1}{x^{12} \sqrt[4]{a+b x^4}} \, dx","Int[1/(x^12*(a + b*x^4)^(1/4)),x]","-\frac{32 b^2 \left(a+b x^4\right)^{3/4}}{231 a^3 x^3}+\frac{8 b \left(a+b x^4\right)^{3/4}}{77 a^2 x^7}-\frac{\left(a+b x^4\right)^{3/4}}{11 a x^{11}}","-\frac{32 b^2 \left(a+b x^4\right)^{3/4}}{231 a^3 x^3}+\frac{8 b \left(a+b x^4\right)^{3/4}}{77 a^2 x^7}-\frac{\left(a+b x^4\right)^{3/4}}{11 a x^{11}}",1,"-(a + b*x^4)^(3/4)/(11*a*x^11) + (8*b*(a + b*x^4)^(3/4))/(77*a^2*x^7) - (32*b^2*(a + b*x^4)^(3/4))/(231*a^3*x^3)","A",3,2,15,0.1333,1,"{271, 264}"
1101,1,92,0,0.0283792,"\int \frac{1}{x^{16} \sqrt[4]{a+b x^4}} \, dx","Int[1/(x^16*(a + b*x^4)^(1/4)),x]","\frac{128 b^3 \left(a+b x^4\right)^{3/4}}{1155 a^4 x^3}-\frac{32 b^2 \left(a+b x^4\right)^{3/4}}{385 a^3 x^7}+\frac{4 b \left(a+b x^4\right)^{3/4}}{55 a^2 x^{11}}-\frac{\left(a+b x^4\right)^{3/4}}{15 a x^{15}}","\frac{128 b^3 \left(a+b x^4\right)^{3/4}}{1155 a^4 x^3}-\frac{32 b^2 \left(a+b x^4\right)^{3/4}}{385 a^3 x^7}+\frac{4 b \left(a+b x^4\right)^{3/4}}{55 a^2 x^{11}}-\frac{\left(a+b x^4\right)^{3/4}}{15 a x^{15}}",1,"-(a + b*x^4)^(3/4)/(15*a*x^15) + (4*b*(a + b*x^4)^(3/4))/(55*a^2*x^11) - (32*b^2*(a + b*x^4)^(3/4))/(385*a^3*x^7) + (128*b^3*(a + b*x^4)^(3/4))/(1155*a^4*x^3)","A",4,2,15,0.1333,1,"{271, 264}"
1102,1,116,0,0.0430372,"\int \frac{1}{x^{20} \sqrt[4]{a+b x^4}} \, dx","Int[1/(x^20*(a + b*x^4)^(1/4)),x]","-\frac{2048 b^4 \left(a+b x^4\right)^{3/4}}{21945 a^5 x^3}+\frac{512 b^3 \left(a+b x^4\right)^{3/4}}{7315 a^4 x^7}-\frac{64 b^2 \left(a+b x^4\right)^{3/4}}{1045 a^3 x^{11}}+\frac{16 b \left(a+b x^4\right)^{3/4}}{285 a^2 x^{15}}-\frac{\left(a+b x^4\right)^{3/4}}{19 a x^{19}}","-\frac{2048 b^4 \left(a+b x^4\right)^{3/4}}{21945 a^5 x^3}+\frac{512 b^3 \left(a+b x^4\right)^{3/4}}{7315 a^4 x^7}-\frac{64 b^2 \left(a+b x^4\right)^{3/4}}{1045 a^3 x^{11}}+\frac{16 b \left(a+b x^4\right)^{3/4}}{285 a^2 x^{15}}-\frac{\left(a+b x^4\right)^{3/4}}{19 a x^{19}}",1,"-(a + b*x^4)^(3/4)/(19*a*x^19) + (16*b*(a + b*x^4)^(3/4))/(285*a^2*x^15) - (64*b^2*(a + b*x^4)^(3/4))/(1045*a^3*x^11) + (512*b^3*(a + b*x^4)^(3/4))/(7315*a^4*x^7) - (2048*b^4*(a + b*x^4)^(3/4))/(21945*a^5*x^3)","A",5,2,15,0.1333,1,"{271, 264}"
1103,1,129,0,0.0597346,"\int \frac{x^{10}}{\sqrt[4]{a+b x^4}} \, dx","Int[x^10/(a + b*x^4)^(1/4),x]","\frac{7 a^2 x^3}{40 b^2 \sqrt[4]{a+b x^4}}+\frac{7 a^{5/2} x \sqrt[4]{\frac{a}{b x^4}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{40 b^{5/2} \sqrt[4]{a+b x^4}}-\frac{7 a x^3 \left(a+b x^4\right)^{3/4}}{60 b^2}+\frac{x^7 \left(a+b x^4\right)^{3/4}}{10 b}","\frac{7 a^2 x^3}{40 b^2 \sqrt[4]{a+b x^4}}+\frac{7 a^{5/2} x \sqrt[4]{\frac{a}{b x^4}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{40 b^{5/2} \sqrt[4]{a+b x^4}}-\frac{7 a x^3 \left(a+b x^4\right)^{3/4}}{60 b^2}+\frac{x^7 \left(a+b x^4\right)^{3/4}}{10 b}",1,"(7*a^2*x^3)/(40*b^2*(a + b*x^4)^(1/4)) - (7*a*x^3*(a + b*x^4)^(3/4))/(60*b^2) + (x^7*(a + b*x^4)^(3/4))/(10*b) + (7*a^(5/2)*(1 + a/(b*x^4))^(1/4)*x*EllipticE[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(40*b^(5/2)*(a + b*x^4)^(1/4))","A",7,6,15,0.4000,1,"{321, 310, 281, 335, 275, 196}"
1104,1,105,0,0.0457805,"\int \frac{x^6}{\sqrt[4]{a+b x^4}} \, dx","Int[x^6/(a + b*x^4)^(1/4),x]","-\frac{a^{3/2} x \sqrt[4]{\frac{a}{b x^4}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{4 b^{3/2} \sqrt[4]{a+b x^4}}+\frac{x^3 \left(a+b x^4\right)^{3/4}}{6 b}-\frac{a x^3}{4 b \sqrt[4]{a+b x^4}}","-\frac{a^{3/2} x \sqrt[4]{\frac{a}{b x^4}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{4 b^{3/2} \sqrt[4]{a+b x^4}}+\frac{x^3 \left(a+b x^4\right)^{3/4}}{6 b}-\frac{a x^3}{4 b \sqrt[4]{a+b x^4}}",1,"-(a*x^3)/(4*b*(a + b*x^4)^(1/4)) + (x^3*(a + b*x^4)^(3/4))/(6*b) - (a^(3/2)*(1 + a/(b*x^4))^(1/4)*x*EllipticE[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(4*b^(3/2)*(a + b*x^4)^(1/4))","A",6,6,15,0.4000,1,"{321, 310, 281, 335, 275, 196}"
1105,1,80,0,0.040962,"\int \frac{x^2}{\sqrt[4]{a+b x^4}} \, dx","Int[x^2/(a + b*x^4)^(1/4),x]","\frac{x^3}{2 \sqrt[4]{a+b x^4}}+\frac{\sqrt{a} x \sqrt[4]{\frac{a}{b x^4}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{2 \sqrt{b} \sqrt[4]{a+b x^4}}","\frac{x^3}{2 \sqrt[4]{a+b x^4}}+\frac{\sqrt{a} x \sqrt[4]{\frac{a}{b x^4}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{2 \sqrt{b} \sqrt[4]{a+b x^4}}",1,"x^3/(2*(a + b*x^4)^(1/4)) + (Sqrt[a]*(1 + a/(b*x^4))^(1/4)*x*EllipticE[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(2*Sqrt[b]*(a + b*x^4)^(1/4))","A",5,5,15,0.3333,1,"{310, 281, 335, 275, 196}"
1106,1,75,0,0.0373939,"\int \frac{1}{x^2 \sqrt[4]{a+b x^4}} \, dx","Int[1/(x^2*(a + b*x^4)^(1/4)),x]","\frac{\sqrt{b} x \sqrt[4]{\frac{a}{b x^4}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{\sqrt{a} \sqrt[4]{a+b x^4}}-\frac{1}{x \sqrt[4]{a+b x^4}}","\frac{\sqrt{b} x \sqrt[4]{\frac{a}{b x^4}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{\sqrt{a} \sqrt[4]{a+b x^4}}-\frac{1}{x \sqrt[4]{a+b x^4}}",1,"-(1/(x*(a + b*x^4)^(1/4))) + (Sqrt[b]*(1 + a/(b*x^4))^(1/4)*x*EllipticE[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(Sqrt[a]*(a + b*x^4)^(1/4))","A",5,5,15,0.3333,1,"{312, 281, 335, 275, 196}"
1107,1,105,0,0.0489841,"\int \frac{1}{x^6 \sqrt[4]{a+b x^4}} \, dx","Int[1/(x^6*(a + b*x^4)^(1/4)),x]","-\frac{2 b^{3/2} x \sqrt[4]{\frac{a}{b x^4}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{5 a^{3/2} \sqrt[4]{a+b x^4}}+\frac{2 b}{5 a x \sqrt[4]{a+b x^4}}-\frac{\left(a+b x^4\right)^{3/4}}{5 a x^5}","-\frac{2 b^{3/2} x \sqrt[4]{\frac{a}{b x^4}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{5 a^{3/2} \sqrt[4]{a+b x^4}}+\frac{2 b}{5 a x \sqrt[4]{a+b x^4}}-\frac{\left(a+b x^4\right)^{3/4}}{5 a x^5}",1,"(2*b)/(5*a*x*(a + b*x^4)^(1/4)) - (a + b*x^4)^(3/4)/(5*a*x^5) - (2*b^(3/2)*(1 + a/(b*x^4))^(1/4)*x*EllipticE[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(5*a^(3/2)*(a + b*x^4)^(1/4))","A",6,6,15,0.4000,1,"{325, 312, 281, 335, 275, 196}"
1108,1,129,0,0.0592237,"\int \frac{1}{x^{10} \sqrt[4]{a+b x^4}} \, dx","Int[1/(x^10*(a + b*x^4)^(1/4)),x]","-\frac{4 b^2}{15 a^2 x \sqrt[4]{a+b x^4}}+\frac{4 b^{5/2} x \sqrt[4]{\frac{a}{b x^4}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{15 a^{5/2} \sqrt[4]{a+b x^4}}+\frac{2 b \left(a+b x^4\right)^{3/4}}{15 a^2 x^5}-\frac{\left(a+b x^4\right)^{3/4}}{9 a x^9}","-\frac{4 b^2}{15 a^2 x \sqrt[4]{a+b x^4}}+\frac{4 b^{5/2} x \sqrt[4]{\frac{a}{b x^4}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{15 a^{5/2} \sqrt[4]{a+b x^4}}+\frac{2 b \left(a+b x^4\right)^{3/4}}{15 a^2 x^5}-\frac{\left(a+b x^4\right)^{3/4}}{9 a x^9}",1,"(-4*b^2)/(15*a^2*x*(a + b*x^4)^(1/4)) - (a + b*x^4)^(3/4)/(9*a*x^9) + (2*b*(a + b*x^4)^(3/4))/(15*a^2*x^5) + (4*b^(5/2)*(1 + a/(b*x^4))^(1/4)*x*EllipticE[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(15*a^(5/2)*(a + b*x^4)^(1/4))","A",7,6,15,0.4000,1,"{325, 312, 281, 335, 275, 196}"
1109,1,153,0,0.0735035,"\int \frac{1}{x^{14} \sqrt[4]{a+b x^4}} \, dx","Int[1/(x^14*(a + b*x^4)^(1/4)),x]","\frac{8 b^3}{39 a^3 x \sqrt[4]{a+b x^4}}-\frac{4 b^2 \left(a+b x^4\right)^{3/4}}{39 a^3 x^5}-\frac{8 b^{7/2} x \sqrt[4]{\frac{a}{b x^4}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{39 a^{7/2} \sqrt[4]{a+b x^4}}+\frac{10 b \left(a+b x^4\right)^{3/4}}{117 a^2 x^9}-\frac{\left(a+b x^4\right)^{3/4}}{13 a x^{13}}","\frac{8 b^3}{39 a^3 x \sqrt[4]{a+b x^4}}-\frac{4 b^2 \left(a+b x^4\right)^{3/4}}{39 a^3 x^5}-\frac{8 b^{7/2} x \sqrt[4]{\frac{a}{b x^4}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{39 a^{7/2} \sqrt[4]{a+b x^4}}+\frac{10 b \left(a+b x^4\right)^{3/4}}{117 a^2 x^9}-\frac{\left(a+b x^4\right)^{3/4}}{13 a x^{13}}",1,"(8*b^3)/(39*a^3*x*(a + b*x^4)^(1/4)) - (a + b*x^4)^(3/4)/(13*a*x^13) + (10*b*(a + b*x^4)^(3/4))/(117*a^2*x^9) - (4*b^2*(a + b*x^4)^(3/4))/(39*a^3*x^5) - (8*b^(7/2)*(1 + a/(b*x^4))^(1/4)*x*EllipticE[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(39*a^(7/2)*(a + b*x^4)^(1/4))","A",8,6,15,0.4000,1,"{325, 312, 281, 335, 275, 196}"
1110,1,98,0,0.0543862,"\int \frac{x^{19}}{\left(a+b x^4\right)^{3/4}} \, dx","Int[x^19/(a + b*x^4)^(3/4),x]","\frac{2 a^2 \left(a+b x^4\right)^{9/4}}{3 b^5}-\frac{4 a^3 \left(a+b x^4\right)^{5/4}}{5 b^5}+\frac{a^4 \sqrt[4]{a+b x^4}}{b^5}+\frac{\left(a+b x^4\right)^{17/4}}{17 b^5}-\frac{4 a \left(a+b x^4\right)^{13/4}}{13 b^5}","\frac{2 a^2 \left(a+b x^4\right)^{9/4}}{3 b^5}-\frac{4 a^3 \left(a+b x^4\right)^{5/4}}{5 b^5}+\frac{a^4 \sqrt[4]{a+b x^4}}{b^5}+\frac{\left(a+b x^4\right)^{17/4}}{17 b^5}-\frac{4 a \left(a+b x^4\right)^{13/4}}{13 b^5}",1,"(a^4*(a + b*x^4)^(1/4))/b^5 - (4*a^3*(a + b*x^4)^(5/4))/(5*b^5) + (2*a^2*(a + b*x^4)^(9/4))/(3*b^5) - (4*a*(a + b*x^4)^(13/4))/(13*b^5) + (a + b*x^4)^(17/4)/(17*b^5)","A",3,2,15,0.1333,1,"{266, 43}"
1111,1,78,0,0.0449799,"\int \frac{x^{15}}{\left(a+b x^4\right)^{3/4}} \, dx","Int[x^15/(a + b*x^4)^(3/4),x]","\frac{3 a^2 \left(a+b x^4\right)^{5/4}}{5 b^4}-\frac{a^3 \sqrt[4]{a+b x^4}}{b^4}+\frac{\left(a+b x^4\right)^{13/4}}{13 b^4}-\frac{a \left(a+b x^4\right)^{9/4}}{3 b^4}","\frac{3 a^2 \left(a+b x^4\right)^{5/4}}{5 b^4}-\frac{a^3 \sqrt[4]{a+b x^4}}{b^4}+\frac{\left(a+b x^4\right)^{13/4}}{13 b^4}-\frac{a \left(a+b x^4\right)^{9/4}}{3 b^4}",1,"-((a^3*(a + b*x^4)^(1/4))/b^4) + (3*a^2*(a + b*x^4)^(5/4))/(5*b^4) - (a*(a + b*x^4)^(9/4))/(3*b^4) + (a + b*x^4)^(13/4)/(13*b^4)","A",3,2,15,0.1333,1,"{266, 43}"
1112,1,56,0,0.0322967,"\int \frac{x^{11}}{\left(a+b x^4\right)^{3/4}} \, dx","Int[x^11/(a + b*x^4)^(3/4),x]","\frac{a^2 \sqrt[4]{a+b x^4}}{b^3}+\frac{\left(a+b x^4\right)^{9/4}}{9 b^3}-\frac{2 a \left(a+b x^4\right)^{5/4}}{5 b^3}","\frac{a^2 \sqrt[4]{a+b x^4}}{b^3}+\frac{\left(a+b x^4\right)^{9/4}}{9 b^3}-\frac{2 a \left(a+b x^4\right)^{5/4}}{5 b^3}",1,"(a^2*(a + b*x^4)^(1/4))/b^3 - (2*a*(a + b*x^4)^(5/4))/(5*b^3) + (a + b*x^4)^(9/4)/(9*b^3)","A",3,2,15,0.1333,1,"{266, 43}"
1113,1,36,0,0.0211734,"\int \frac{x^7}{\left(a+b x^4\right)^{3/4}} \, dx","Int[x^7/(a + b*x^4)^(3/4),x]","\frac{\left(a+b x^4\right)^{5/4}}{5 b^2}-\frac{a \sqrt[4]{a+b x^4}}{b^2}","\frac{\left(a+b x^4\right)^{5/4}}{5 b^2}-\frac{a \sqrt[4]{a+b x^4}}{b^2}",1,"-((a*(a + b*x^4)^(1/4))/b^2) + (a + b*x^4)^(5/4)/(5*b^2)","A",3,2,15,0.1333,1,"{266, 43}"
1114,1,15,0,0.0041534,"\int \frac{x^3}{\left(a+b x^4\right)^{3/4}} \, dx","Int[x^3/(a + b*x^4)^(3/4),x]","\frac{\sqrt[4]{a+b x^4}}{b}","\frac{\sqrt[4]{a+b x^4}}{b}",1,"(a + b*x^4)^(1/4)/b","A",1,1,15,0.06667,1,"{261}"
1115,1,55,0,0.0314953,"\int \frac{1}{x \left(a+b x^4\right)^{3/4}} \, dx","Int[1/(x*(a + b*x^4)^(3/4)),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{2 a^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{2 a^{3/4}}","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{2 a^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{2 a^{3/4}}",1,"-ArcTan[(a + b*x^4)^(1/4)/a^(1/4)]/(2*a^(3/4)) - ArcTanh[(a + b*x^4)^(1/4)/a^(1/4)]/(2*a^(3/4))","A",5,5,15,0.3333,1,"{266, 63, 212, 206, 203}"
1116,1,78,0,0.0450485,"\int \frac{1}{x^5 \left(a+b x^4\right)^{3/4}} \, dx","Int[1/(x^5*(a + b*x^4)^(3/4)),x]","\frac{3 b \tan ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{8 a^{7/4}}+\frac{3 b \tanh ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{8 a^{7/4}}-\frac{\sqrt[4]{a+b x^4}}{4 a x^4}","\frac{3 b \tan ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{8 a^{7/4}}+\frac{3 b \tanh ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{8 a^{7/4}}-\frac{\sqrt[4]{a+b x^4}}{4 a x^4}",1,"-(a + b*x^4)^(1/4)/(4*a*x^4) + (3*b*ArcTan[(a + b*x^4)^(1/4)/a^(1/4)])/(8*a^(7/4)) + (3*b*ArcTanh[(a + b*x^4)^(1/4)/a^(1/4)])/(8*a^(7/4))","A",6,6,15,0.4000,1,"{266, 51, 63, 212, 206, 203}"
1117,1,104,0,0.0611489,"\int \frac{1}{x^9 \left(a+b x^4\right)^{3/4}} \, dx","Int[1/(x^9*(a + b*x^4)^(3/4)),x]","-\frac{21 b^2 \tan ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{64 a^{11/4}}-\frac{21 b^2 \tanh ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{64 a^{11/4}}+\frac{7 b \sqrt[4]{a+b x^4}}{32 a^2 x^4}-\frac{\sqrt[4]{a+b x^4}}{8 a x^8}","-\frac{21 b^2 \tan ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{64 a^{11/4}}-\frac{21 b^2 \tanh ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{64 a^{11/4}}+\frac{7 b \sqrt[4]{a+b x^4}}{32 a^2 x^4}-\frac{\sqrt[4]{a+b x^4}}{8 a x^8}",1,"-(a + b*x^4)^(1/4)/(8*a*x^8) + (7*b*(a + b*x^4)^(1/4))/(32*a^2*x^4) - (21*b^2*ArcTan[(a + b*x^4)^(1/4)/a^(1/4)])/(64*a^(11/4)) - (21*b^2*ArcTanh[(a + b*x^4)^(1/4)/a^(1/4)])/(64*a^(11/4))","A",7,6,15,0.4000,1,"{266, 51, 63, 212, 206, 203}"
1118,1,128,0,0.0817333,"\int \frac{x^{13}}{\left(a+b x^4\right)^{3/4}} \, dx","Int[x^13/(a + b*x^4)^(3/4),x]","\frac{20 a^2 x^2 \sqrt[4]{a+b x^4}}{77 b^3}-\frac{40 a^{7/2} \left(\frac{b x^4}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{77 b^{7/2} \left(a+b x^4\right)^{3/4}}-\frac{10 a x^6 \sqrt[4]{a+b x^4}}{77 b^2}+\frac{x^{10} \sqrt[4]{a+b x^4}}{11 b}","\frac{20 a^2 x^2 \sqrt[4]{a+b x^4}}{77 b^3}-\frac{40 a^{7/2} \left(\frac{b x^4}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{77 b^{7/2} \left(a+b x^4\right)^{3/4}}-\frac{10 a x^6 \sqrt[4]{a+b x^4}}{77 b^2}+\frac{x^{10} \sqrt[4]{a+b x^4}}{11 b}",1,"(20*a^2*x^2*(a + b*x^4)^(1/4))/(77*b^3) - (10*a*x^6*(a + b*x^4)^(1/4))/(77*b^2) + (x^10*(a + b*x^4)^(1/4))/(11*b) - (40*a^(7/2)*(1 + (b*x^4)/a)^(3/4)*EllipticF[ArcTan[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(77*b^(7/2)*(a + b*x^4)^(3/4))","A",6,4,15,0.2667,1,"{275, 321, 233, 231}"
1119,1,104,0,0.0637318,"\int \frac{x^9}{\left(a+b x^4\right)^{3/4}} \, dx","Int[x^9/(a + b*x^4)^(3/4),x]","\frac{4 a^{5/2} \left(\frac{b x^4}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{7 b^{5/2} \left(a+b x^4\right)^{3/4}}-\frac{2 a x^2 \sqrt[4]{a+b x^4}}{7 b^2}+\frac{x^6 \sqrt[4]{a+b x^4}}{7 b}","\frac{4 a^{5/2} \left(\frac{b x^4}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{7 b^{5/2} \left(a+b x^4\right)^{3/4}}-\frac{2 a x^2 \sqrt[4]{a+b x^4}}{7 b^2}+\frac{x^6 \sqrt[4]{a+b x^4}}{7 b}",1,"(-2*a*x^2*(a + b*x^4)^(1/4))/(7*b^2) + (x^6*(a + b*x^4)^(1/4))/(7*b) + (4*a^(5/2)*(1 + (b*x^4)/a)^(3/4)*EllipticF[ArcTan[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(7*b^(5/2)*(a + b*x^4)^(3/4))","A",5,4,15,0.2667,1,"{275, 321, 233, 231}"
1120,1,82,0,0.045413,"\int \frac{x^5}{\left(a+b x^4\right)^{3/4}} \, dx","Int[x^5/(a + b*x^4)^(3/4),x]","\frac{x^2 \sqrt[4]{a+b x^4}}{3 b}-\frac{2 a^{3/2} \left(\frac{b x^4}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{3 b^{3/2} \left(a+b x^4\right)^{3/4}}","\frac{x^2 \sqrt[4]{a+b x^4}}{3 b}-\frac{2 a^{3/2} \left(\frac{b x^4}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{3 b^{3/2} \left(a+b x^4\right)^{3/4}}",1,"(x^2*(a + b*x^4)^(1/4))/(3*b) - (2*a^(3/2)*(1 + (b*x^4)/a)^(3/4)*EllipticF[ArcTan[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(3*b^(3/2)*(a + b*x^4)^(3/4))","A",4,4,15,0.2667,1,"{275, 321, 233, 231}"
1121,1,57,0,0.0311582,"\int \frac{x}{\left(a+b x^4\right)^{3/4}} \, dx","Int[x/(a + b*x^4)^(3/4),x]","\frac{\sqrt{a} \left(\frac{b x^4}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{\sqrt{b} \left(a+b x^4\right)^{3/4}}","\frac{\sqrt{a} \left(\frac{b x^4}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{\sqrt{b} \left(a+b x^4\right)^{3/4}}",1,"(Sqrt[a]*(1 + (b*x^4)/a)^(3/4)*EllipticF[ArcTan[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(Sqrt[b]*(a + b*x^4)^(3/4))","A",3,3,13,0.2308,1,"{275, 233, 231}"
1122,1,82,0,0.0454305,"\int \frac{1}{x^3 \left(a+b x^4\right)^{3/4}} \, dx","Int[1/(x^3*(a + b*x^4)^(3/4)),x]","-\frac{\sqrt[4]{a+b x^4}}{2 a x^2}-\frac{\sqrt{b} \left(\frac{b x^4}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{2 \sqrt{a} \left(a+b x^4\right)^{3/4}}","-\frac{\sqrt[4]{a+b x^4}}{2 a x^2}-\frac{\sqrt{b} \left(\frac{b x^4}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{2 \sqrt{a} \left(a+b x^4\right)^{3/4}}",1,"-(a + b*x^4)^(1/4)/(2*a*x^2) - (Sqrt[b]*(1 + (b*x^4)/a)^(3/4)*EllipticF[ArcTan[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(2*Sqrt[a]*(a + b*x^4)^(3/4))","A",4,4,15,0.2667,1,"{275, 325, 233, 231}"
1123,1,104,0,0.0628616,"\int \frac{1}{x^7 \left(a+b x^4\right)^{3/4}} \, dx","Int[1/(x^7*(a + b*x^4)^(3/4)),x]","\frac{5 b^{3/2} \left(\frac{b x^4}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{12 a^{3/2} \left(a+b x^4\right)^{3/4}}+\frac{5 b \sqrt[4]{a+b x^4}}{12 a^2 x^2}-\frac{\sqrt[4]{a+b x^4}}{6 a x^6}","\frac{5 b^{3/2} \left(\frac{b x^4}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{12 a^{3/2} \left(a+b x^4\right)^{3/4}}+\frac{5 b \sqrt[4]{a+b x^4}}{12 a^2 x^2}-\frac{\sqrt[4]{a+b x^4}}{6 a x^6}",1,"-(a + b*x^4)^(1/4)/(6*a*x^6) + (5*b*(a + b*x^4)^(1/4))/(12*a^2*x^2) + (5*b^(3/2)*(1 + (b*x^4)/a)^(3/4)*EllipticF[ArcTan[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(12*a^(3/2)*(a + b*x^4)^(3/4))","A",5,4,15,0.2667,1,"{275, 325, 233, 231}"
1124,1,128,0,0.0826996,"\int \frac{1}{x^{11} \left(a+b x^4\right)^{3/4}} \, dx","Int[1/(x^11*(a + b*x^4)^(3/4)),x]","-\frac{3 b^2 \sqrt[4]{a+b x^4}}{8 a^3 x^2}-\frac{3 b^{5/2} \left(\frac{b x^4}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{8 a^{5/2} \left(a+b x^4\right)^{3/4}}+\frac{3 b \sqrt[4]{a+b x^4}}{20 a^2 x^6}-\frac{\sqrt[4]{a+b x^4}}{10 a x^{10}}","-\frac{3 b^2 \sqrt[4]{a+b x^4}}{8 a^3 x^2}-\frac{3 b^{5/2} \left(\frac{b x^4}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{8 a^{5/2} \left(a+b x^4\right)^{3/4}}+\frac{3 b \sqrt[4]{a+b x^4}}{20 a^2 x^6}-\frac{\sqrt[4]{a+b x^4}}{10 a x^{10}}",1,"-(a + b*x^4)^(1/4)/(10*a*x^10) + (3*b*(a + b*x^4)^(1/4))/(20*a^2*x^6) - (3*b^2*(a + b*x^4)^(1/4))/(8*a^3*x^2) - (3*b^(5/2)*(1 + (b*x^4)/a)^(3/4)*EllipticF[ArcTan[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(8*a^(5/2)*(a + b*x^4)^(3/4))","A",6,4,15,0.2667,1,"{275, 325, 233, 231}"
1125,1,106,0,0.0371375,"\int \frac{x^{10}}{\left(a+b x^4\right)^{3/4}} \, dx","Int[x^10/(a + b*x^4)^(3/4),x]","-\frac{21 a^2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{64 b^{11/4}}+\frac{21 a^2 \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{64 b^{11/4}}-\frac{7 a x^3 \sqrt[4]{a+b x^4}}{32 b^2}+\frac{x^7 \sqrt[4]{a+b x^4}}{8 b}","-\frac{21 a^2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{64 b^{11/4}}+\frac{21 a^2 \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{64 b^{11/4}}-\frac{7 a x^3 \sqrt[4]{a+b x^4}}{32 b^2}+\frac{x^7 \sqrt[4]{a+b x^4}}{8 b}",1,"(-7*a*x^3*(a + b*x^4)^(1/4))/(32*b^2) + (x^7*(a + b*x^4)^(1/4))/(8*b) - (21*a^2*ArcTan[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/(64*b^(11/4)) + (21*a^2*ArcTanh[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/(64*b^(11/4))","A",6,5,15,0.3333,1,"{321, 331, 298, 203, 206}"
1126,1,80,0,0.0251478,"\int \frac{x^6}{\left(a+b x^4\right)^{3/4}} \, dx","Int[x^6/(a + b*x^4)^(3/4),x]","\frac{3 a \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{8 b^{7/4}}-\frac{3 a \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{8 b^{7/4}}+\frac{x^3 \sqrt[4]{a+b x^4}}{4 b}","\frac{3 a \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{8 b^{7/4}}-\frac{3 a \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{8 b^{7/4}}+\frac{x^3 \sqrt[4]{a+b x^4}}{4 b}",1,"(x^3*(a + b*x^4)^(1/4))/(4*b) + (3*a*ArcTan[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/(8*b^(7/4)) - (3*a*ArcTanh[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/(8*b^(7/4))","A",5,5,15,0.3333,1,"{321, 331, 298, 203, 206}"
1127,1,57,0,0.0214927,"\int \frac{x^2}{\left(a+b x^4\right)^{3/4}} \, dx","Int[x^2/(a + b*x^4)^(3/4),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{2 b^{3/4}}-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{2 b^{3/4}}","\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{2 b^{3/4}}-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{2 b^{3/4}}",1,"-ArcTan[(b^(1/4)*x)/(a + b*x^4)^(1/4)]/(2*b^(3/4)) + ArcTanh[(b^(1/4)*x)/(a + b*x^4)^(1/4)]/(2*b^(3/4))","A",4,4,15,0.2667,1,"{331, 298, 203, 206}"
1128,1,19,0,0.0063483,"\int \frac{1}{x^2 \left(a+b x^4\right)^{3/4}} \, dx","Int[1/(x^2*(a + b*x^4)^(3/4)),x]","-\frac{\sqrt[4]{a+b x^4}}{a x}","-\frac{\sqrt[4]{a+b x^4}}{a x}",1,"-((a + b*x^4)^(1/4)/(a*x))","A",1,1,15,0.06667,1,"{264}"
1129,1,44,0,0.0118411,"\int \frac{1}{x^6 \left(a+b x^4\right)^{3/4}} \, dx","Int[1/(x^6*(a + b*x^4)^(3/4)),x]","\frac{4 b \sqrt[4]{a+b x^4}}{5 a^2 x}-\frac{\sqrt[4]{a+b x^4}}{5 a x^5}","\frac{4 b \sqrt[4]{a+b x^4}}{5 a^2 x}-\frac{\sqrt[4]{a+b x^4}}{5 a x^5}",1,"-(a + b*x^4)^(1/4)/(5*a*x^5) + (4*b*(a + b*x^4)^(1/4))/(5*a^2*x)","A",2,2,15,0.1333,1,"{271, 264}"
1130,1,68,0,0.0210661,"\int \frac{1}{x^{10} \left(a+b x^4\right)^{3/4}} \, dx","Int[1/(x^10*(a + b*x^4)^(3/4)),x]","-\frac{32 b^2 \sqrt[4]{a+b x^4}}{45 a^3 x}+\frac{8 b \sqrt[4]{a+b x^4}}{45 a^2 x^5}-\frac{\sqrt[4]{a+b x^4}}{9 a x^9}","-\frac{32 b^2 \sqrt[4]{a+b x^4}}{45 a^3 x}+\frac{8 b \sqrt[4]{a+b x^4}}{45 a^2 x^5}-\frac{\sqrt[4]{a+b x^4}}{9 a x^9}",1,"-(a + b*x^4)^(1/4)/(9*a*x^9) + (8*b*(a + b*x^4)^(1/4))/(45*a^2*x^5) - (32*b^2*(a + b*x^4)^(1/4))/(45*a^3*x)","A",3,2,15,0.1333,1,"{271, 264}"
1131,1,92,0,0.0286821,"\int \frac{1}{x^{14} \left(a+b x^4\right)^{3/4}} \, dx","Int[1/(x^14*(a + b*x^4)^(3/4)),x]","\frac{128 b^3 \sqrt[4]{a+b x^4}}{195 a^4 x}-\frac{32 b^2 \sqrt[4]{a+b x^4}}{195 a^3 x^5}+\frac{4 b \sqrt[4]{a+b x^4}}{39 a^2 x^9}-\frac{\sqrt[4]{a+b x^4}}{13 a x^{13}}","\frac{128 b^3 \sqrt[4]{a+b x^4}}{195 a^4 x}-\frac{32 b^2 \sqrt[4]{a+b x^4}}{195 a^3 x^5}+\frac{4 b \sqrt[4]{a+b x^4}}{39 a^2 x^9}-\frac{\sqrt[4]{a+b x^4}}{13 a x^{13}}",1,"-(a + b*x^4)^(1/4)/(13*a*x^13) + (4*b*(a + b*x^4)^(1/4))/(39*a^2*x^9) - (32*b^2*(a + b*x^4)^(1/4))/(195*a^3*x^5) + (128*b^3*(a + b*x^4)^(1/4))/(195*a^4*x)","A",4,2,15,0.1333,1,"{271, 264}"
1132,1,129,0,0.0585965,"\int \frac{x^{12}}{\left(a+b x^4\right)^{3/4}} \, dx","Int[x^12/(a + b*x^4)^(3/4),x]","\frac{3 a^2 x \sqrt[4]{a+b x^4}}{8 b^3}+\frac{3 a^{5/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{8 b^{5/2} \left(a+b x^4\right)^{3/4}}-\frac{3 a x^5 \sqrt[4]{a+b x^4}}{20 b^2}+\frac{x^9 \sqrt[4]{a+b x^4}}{10 b}","\frac{3 a^2 x \sqrt[4]{a+b x^4}}{8 b^3}+\frac{3 a^{5/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{8 b^{5/2} \left(a+b x^4\right)^{3/4}}-\frac{3 a x^5 \sqrt[4]{a+b x^4}}{20 b^2}+\frac{x^9 \sqrt[4]{a+b x^4}}{10 b}",1,"(3*a^2*x*(a + b*x^4)^(1/4))/(8*b^3) - (3*a*x^5*(a + b*x^4)^(1/4))/(20*b^2) + (x^9*(a + b*x^4)^(1/4))/(10*b) + (3*a^(5/2)*(1 + a/(b*x^4))^(3/4)*x^3*EllipticF[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(8*b^(5/2)*(a + b*x^4)^(3/4))","A",7,5,15,0.3333,1,"{321, 237, 335, 275, 231}"
1133,1,105,0,0.0436661,"\int \frac{x^8}{\left(a+b x^4\right)^{3/4}} \, dx","Int[x^8/(a + b*x^4)^(3/4),x]","-\frac{5 a^{3/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{12 b^{3/2} \left(a+b x^4\right)^{3/4}}-\frac{5 a x \sqrt[4]{a+b x^4}}{12 b^2}+\frac{x^5 \sqrt[4]{a+b x^4}}{6 b}","-\frac{5 a^{3/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{12 b^{3/2} \left(a+b x^4\right)^{3/4}}-\frac{5 a x \sqrt[4]{a+b x^4}}{12 b^2}+\frac{x^5 \sqrt[4]{a+b x^4}}{6 b}",1,"(-5*a*x*(a + b*x^4)^(1/4))/(12*b^2) + (x^5*(a + b*x^4)^(1/4))/(6*b) - (5*a^(3/2)*(1 + a/(b*x^4))^(3/4)*x^3*EllipticF[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(12*b^(3/2)*(a + b*x^4)^(3/4))","A",6,5,15,0.3333,1,"{321, 237, 335, 275, 231}"
1134,1,83,0,0.0331245,"\int \frac{x^4}{\left(a+b x^4\right)^{3/4}} \, dx","Int[x^4/(a + b*x^4)^(3/4),x]","\frac{x \sqrt[4]{a+b x^4}}{2 b}+\frac{\sqrt{a} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{2 \sqrt{b} \left(a+b x^4\right)^{3/4}}","\frac{x \sqrt[4]{a+b x^4}}{2 b}+\frac{\sqrt{a} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{2 \sqrt{b} \left(a+b x^4\right)^{3/4}}",1,"(x*(a + b*x^4)^(1/4))/(2*b) + (Sqrt[a]*(1 + a/(b*x^4))^(3/4)*x^3*EllipticF[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(2*Sqrt[b]*(a + b*x^4)^(3/4))","A",5,5,15,0.3333,1,"{321, 237, 335, 275, 231}"
1135,1,61,0,0.024496,"\int \frac{1}{\left(a+b x^4\right)^{3/4}} \, dx","Int[(a + b*x^4)^(-3/4),x]","-\frac{\sqrt{b} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{\sqrt{a} \left(a+b x^4\right)^{3/4}}","-\frac{\sqrt{b} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{\sqrt{a} \left(a+b x^4\right)^{3/4}}",1,"-((Sqrt[b]*(1 + a/(b*x^4))^(3/4)*x^3*EllipticF[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(Sqrt[a]*(a + b*x^4)^(3/4)))","A",4,4,11,0.3636,1,"{237, 335, 275, 231}"
1136,1,85,0,0.0339459,"\int \frac{1}{x^4 \left(a+b x^4\right)^{3/4}} \, dx","Int[1/(x^4*(a + b*x^4)^(3/4)),x]","\frac{2 b^{3/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{3 a^{3/2} \left(a+b x^4\right)^{3/4}}-\frac{\sqrt[4]{a+b x^4}}{3 a x^3}","\frac{2 b^{3/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{3 a^{3/2} \left(a+b x^4\right)^{3/4}}-\frac{\sqrt[4]{a+b x^4}}{3 a x^3}",1,"-(a + b*x^4)^(1/4)/(3*a*x^3) + (2*b^(3/2)*(1 + a/(b*x^4))^(3/4)*x^3*EllipticF[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(3*a^(3/2)*(a + b*x^4)^(3/4))","A",5,5,15,0.3333,1,"{325, 237, 335, 275, 231}"
1137,1,107,0,0.0453221,"\int \frac{1}{x^8 \left(a+b x^4\right)^{3/4}} \, dx","Int[1/(x^8*(a + b*x^4)^(3/4)),x]","-\frac{4 b^{5/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{7 a^{5/2} \left(a+b x^4\right)^{3/4}}+\frac{2 b \sqrt[4]{a+b x^4}}{7 a^2 x^3}-\frac{\sqrt[4]{a+b x^4}}{7 a x^7}","-\frac{4 b^{5/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{7 a^{5/2} \left(a+b x^4\right)^{3/4}}+\frac{2 b \sqrt[4]{a+b x^4}}{7 a^2 x^3}-\frac{\sqrt[4]{a+b x^4}}{7 a x^7}",1,"-(a + b*x^4)^(1/4)/(7*a*x^7) + (2*b*(a + b*x^4)^(1/4))/(7*a^2*x^3) - (4*b^(5/2)*(1 + a/(b*x^4))^(3/4)*x^3*EllipticF[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(7*a^(5/2)*(a + b*x^4)^(3/4))","A",6,5,15,0.3333,1,"{325, 237, 335, 275, 231}"
1138,1,131,0,0.0566277,"\int \frac{1}{x^{12} \left(a+b x^4\right)^{3/4}} \, dx","Int[1/(x^12*(a + b*x^4)^(3/4)),x]","-\frac{20 b^2 \sqrt[4]{a+b x^4}}{77 a^3 x^3}+\frac{40 b^{7/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{77 a^{7/2} \left(a+b x^4\right)^{3/4}}+\frac{10 b \sqrt[4]{a+b x^4}}{77 a^2 x^7}-\frac{\sqrt[4]{a+b x^4}}{11 a x^{11}}","-\frac{20 b^2 \sqrt[4]{a+b x^4}}{77 a^3 x^3}+\frac{40 b^{7/2} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{77 a^{7/2} \left(a+b x^4\right)^{3/4}}+\frac{10 b \sqrt[4]{a+b x^4}}{77 a^2 x^7}-\frac{\sqrt[4]{a+b x^4}}{11 a x^{11}}",1,"-(a + b*x^4)^(1/4)/(11*a*x^11) + (10*b*(a + b*x^4)^(1/4))/(77*a^2*x^7) - (20*b^2*(a + b*x^4)^(1/4))/(77*a^3*x^3) + (40*b^(7/2)*(1 + a/(b*x^4))^(3/4)*x^3*EllipticF[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(77*a^(7/2)*(a + b*x^4)^(3/4))","A",7,5,15,0.3333,1,"{325, 237, 335, 275, 231}"
1139,1,99,0,0.0540024,"\int \frac{x^{19}}{\left(a+b x^4\right)^{5/4}} \, dx","Int[x^19/(a + b*x^4)^(5/4),x]","-\frac{a^4}{b^5 \sqrt[4]{a+b x^4}}-\frac{4 a^3 \left(a+b x^4\right)^{3/4}}{3 b^5}+\frac{6 a^2 \left(a+b x^4\right)^{7/4}}{7 b^5}-\frac{4 a \left(a+b x^4\right)^{11/4}}{11 b^5}+\frac{\left(a+b x^4\right)^{15/4}}{15 b^5}","-\frac{a^4}{b^5 \sqrt[4]{a+b x^4}}-\frac{4 a^3 \left(a+b x^4\right)^{3/4}}{3 b^5}+\frac{6 a^2 \left(a+b x^4\right)^{7/4}}{7 b^5}-\frac{4 a \left(a+b x^4\right)^{11/4}}{11 b^5}+\frac{\left(a+b x^4\right)^{15/4}}{15 b^5}",1,"-(a^4/(b^5*(a + b*x^4)^(1/4))) - (4*a^3*(a + b*x^4)^(3/4))/(3*b^5) + (6*a^2*(a + b*x^4)^(7/4))/(7*b^5) - (4*a*(a + b*x^4)^(11/4))/(11*b^5) + (a + b*x^4)^(15/4)/(15*b^5)","A",3,2,15,0.1333,1,"{266, 43}"
1140,1,74,0,0.0439708,"\int \frac{x^{15}}{\left(a+b x^4\right)^{5/4}} \, dx","Int[x^15/(a + b*x^4)^(5/4),x]","\frac{a^3}{b^4 \sqrt[4]{a+b x^4}}+\frac{a^2 \left(a+b x^4\right)^{3/4}}{b^4}-\frac{3 a \left(a+b x^4\right)^{7/4}}{7 b^4}+\frac{\left(a+b x^4\right)^{11/4}}{11 b^4}","\frac{a^3}{b^4 \sqrt[4]{a+b x^4}}+\frac{a^2 \left(a+b x^4\right)^{3/4}}{b^4}-\frac{3 a \left(a+b x^4\right)^{7/4}}{7 b^4}+\frac{\left(a+b x^4\right)^{11/4}}{11 b^4}",1,"a^3/(b^4*(a + b*x^4)^(1/4)) + (a^2*(a + b*x^4)^(3/4))/b^4 - (3*a*(a + b*x^4)^(7/4))/(7*b^4) + (a + b*x^4)^(11/4)/(11*b^4)","A",3,2,15,0.1333,1,"{266, 43}"
1141,1,57,0,0.0334128,"\int \frac{x^{11}}{\left(a+b x^4\right)^{5/4}} \, dx","Int[x^11/(a + b*x^4)^(5/4),x]","-\frac{a^2}{b^3 \sqrt[4]{a+b x^4}}-\frac{2 a \left(a+b x^4\right)^{3/4}}{3 b^3}+\frac{\left(a+b x^4\right)^{7/4}}{7 b^3}","-\frac{a^2}{b^3 \sqrt[4]{a+b x^4}}-\frac{2 a \left(a+b x^4\right)^{3/4}}{3 b^3}+\frac{\left(a+b x^4\right)^{7/4}}{7 b^3}",1,"-(a^2/(b^3*(a + b*x^4)^(1/4))) - (2*a*(a + b*x^4)^(3/4))/(3*b^3) + (a + b*x^4)^(7/4)/(7*b^3)","A",3,2,15,0.1333,1,"{266, 43}"
1142,1,35,0,0.0213331,"\int \frac{x^7}{\left(a+b x^4\right)^{5/4}} \, dx","Int[x^7/(a + b*x^4)^(5/4),x]","\frac{a}{b^2 \sqrt[4]{a+b x^4}}+\frac{\left(a+b x^4\right)^{3/4}}{3 b^2}","\frac{a}{b^2 \sqrt[4]{a+b x^4}}+\frac{\left(a+b x^4\right)^{3/4}}{3 b^2}",1,"a/(b^2*(a + b*x^4)^(1/4)) + (a + b*x^4)^(3/4)/(3*b^2)","A",3,2,15,0.1333,1,"{266, 43}"
1143,1,16,0,0.0044063,"\int \frac{x^3}{\left(a+b x^4\right)^{5/4}} \, dx","Int[x^3/(a + b*x^4)^(5/4),x]","-\frac{1}{b \sqrt[4]{a+b x^4}}","-\frac{1}{b \sqrt[4]{a+b x^4}}",1,"-(1/(b*(a + b*x^4)^(1/4)))","A",1,1,15,0.06667,1,"{261}"
1144,1,70,0,0.0443256,"\int \frac{1}{x \left(a+b x^4\right)^{5/4}} \, dx","Int[1/(x*(a + b*x^4)^(5/4)),x]","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{2 a^{5/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{2 a^{5/4}}+\frac{1}{a \sqrt[4]{a+b x^4}}","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{2 a^{5/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{2 a^{5/4}}+\frac{1}{a \sqrt[4]{a+b x^4}}",1,"1/(a*(a + b*x^4)^(1/4)) + ArcTan[(a + b*x^4)^(1/4)/a^(1/4)]/(2*a^(5/4)) - ArcTanh[(a + b*x^4)^(1/4)/a^(1/4)]/(2*a^(5/4))","A",6,6,15,0.4000,1,"{266, 51, 63, 298, 203, 206}"
1145,1,96,0,0.059758,"\int \frac{1}{x^5 \left(a+b x^4\right)^{5/4}} \, dx","Int[1/(x^5*(a + b*x^4)^(5/4)),x]","-\frac{5 \left(a+b x^4\right)^{3/4}}{4 a^2 x^4}-\frac{5 b \tan ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{8 a^{9/4}}+\frac{5 b \tanh ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{8 a^{9/4}}+\frac{1}{a x^4 \sqrt[4]{a+b x^4}}","-\frac{5 b}{4 a^2 \sqrt[4]{a+b x^4}}-\frac{5 b \tan ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{8 a^{9/4}}+\frac{5 b \tanh ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{8 a^{9/4}}-\frac{1}{4 a x^4 \sqrt[4]{a+b x^4}}",1,"1/(a*x^4*(a + b*x^4)^(1/4)) - (5*(a + b*x^4)^(3/4))/(4*a^2*x^4) - (5*b*ArcTan[(a + b*x^4)^(1/4)/a^(1/4)])/(8*a^(9/4)) + (5*b*ArcTanh[(a + b*x^4)^(1/4)/a^(1/4)])/(8*a^(9/4))","A",7,6,15,0.4000,1,"{266, 51, 63, 298, 203, 206}"
1146,1,122,0,0.075702,"\int \frac{1}{x^9 \left(a+b x^4\right)^{5/4}} \, dx","Int[1/(x^9*(a + b*x^4)^(5/4)),x]","\frac{45 b^2 \tan ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{64 a^{13/4}}-\frac{45 b^2 \tanh ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{64 a^{13/4}}+\frac{45 b \left(a+b x^4\right)^{3/4}}{32 a^3 x^4}-\frac{9 \left(a+b x^4\right)^{3/4}}{8 a^2 x^8}+\frac{1}{a x^8 \sqrt[4]{a+b x^4}}","\frac{45 b^2}{32 a^3 \sqrt[4]{a+b x^4}}+\frac{45 b^2 \tan ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{64 a^{13/4}}-\frac{45 b^2 \tanh ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)}{64 a^{13/4}}+\frac{9 b}{32 a^2 x^4 \sqrt[4]{a+b x^4}}-\frac{1}{8 a x^8 \sqrt[4]{a+b x^4}}",1,"1/(a*x^8*(a + b*x^4)^(1/4)) - (9*(a + b*x^4)^(3/4))/(8*a^2*x^8) + (45*b*(a + b*x^4)^(3/4))/(32*a^3*x^4) + (45*b^2*ArcTan[(a + b*x^4)^(1/4)/a^(1/4)])/(64*a^(13/4)) - (45*b^2*ArcTanh[(a + b*x^4)^(1/4)/a^(1/4)])/(64*a^(13/4))","A",8,6,15,0.4000,1,"{266, 51, 63, 298, 203, 206}"
1147,1,128,0,0.0851698,"\int \frac{x^{13}}{\left(a+b x^4\right)^{5/4}} \, dx","Int[x^13/(a + b*x^4)^(5/4),x]","\frac{4 a^2 x^2}{3 b^3 \sqrt[4]{a+b x^4}}-\frac{8 a^{5/2} \sqrt[4]{\frac{b x^4}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{3 b^{7/2} \sqrt[4]{a+b x^4}}-\frac{2 a x^6}{9 b^2 \sqrt[4]{a+b x^4}}+\frac{x^{10}}{9 b \sqrt[4]{a+b x^4}}","\frac{4 a^2 x^2}{3 b^3 \sqrt[4]{a+b x^4}}-\frac{8 a^{5/2} \sqrt[4]{\frac{b x^4}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{3 b^{7/2} \sqrt[4]{a+b x^4}}-\frac{2 a x^6}{9 b^2 \sqrt[4]{a+b x^4}}+\frac{x^{10}}{9 b \sqrt[4]{a+b x^4}}",1,"(4*a^2*x^2)/(3*b^3*(a + b*x^4)^(1/4)) - (2*a*x^6)/(9*b^2*(a + b*x^4)^(1/4)) + x^10/(9*b*(a + b*x^4)^(1/4)) - (8*a^(5/2)*(1 + (b*x^4)/a)^(1/4)*EllipticE[ArcTan[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(3*b^(7/2)*(a + b*x^4)^(1/4))","A",6,4,15,0.2667,1,"{275, 285, 197, 196}"
1148,1,104,0,0.0646542,"\int \frac{x^9}{\left(a+b x^4\right)^{5/4}} \, dx","Int[x^9/(a + b*x^4)^(5/4),x]","\frac{12 a^{3/2} \sqrt[4]{\frac{b x^4}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{5 b^{5/2} \sqrt[4]{a+b x^4}}-\frac{6 a x^2}{5 b^2 \sqrt[4]{a+b x^4}}+\frac{x^6}{5 b \sqrt[4]{a+b x^4}}","\frac{12 a^{3/2} \sqrt[4]{\frac{b x^4}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{5 b^{5/2} \sqrt[4]{a+b x^4}}-\frac{6 a x^2}{5 b^2 \sqrt[4]{a+b x^4}}+\frac{x^6}{5 b \sqrt[4]{a+b x^4}}",1,"(-6*a*x^2)/(5*b^2*(a + b*x^4)^(1/4)) + x^6/(5*b*(a + b*x^4)^(1/4)) + (12*a^(3/2)*(1 + (b*x^4)/a)^(1/4)*EllipticE[ArcTan[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(5*b^(5/2)*(a + b*x^4)^(1/4))","A",5,4,15,0.2667,1,"{275, 285, 197, 196}"
1149,1,77,0,0.0474708,"\int \frac{x^5}{\left(a+b x^4\right)^{5/4}} \, dx","Int[x^5/(a + b*x^4)^(5/4),x]","\frac{x^2}{b \sqrt[4]{a+b x^4}}-\frac{2 \sqrt{a} \sqrt[4]{\frac{b x^4}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{b^{3/2} \sqrt[4]{a+b x^4}}","\frac{x^2}{b \sqrt[4]{a+b x^4}}-\frac{2 \sqrt{a} \sqrt[4]{\frac{b x^4}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{b^{3/2} \sqrt[4]{a+b x^4}}",1,"x^2/(b*(a + b*x^4)^(1/4)) - (2*Sqrt[a]*(1 + (b*x^4)/a)^(1/4)*EllipticE[ArcTan[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(b^(3/2)*(a + b*x^4)^(1/4))","A",4,4,15,0.2667,1,"{275, 285, 197, 196}"
1150,1,57,0,0.0300586,"\int \frac{x}{\left(a+b x^4\right)^{5/4}} \, dx","Int[x/(a + b*x^4)^(5/4),x]","\frac{\sqrt[4]{\frac{b x^4}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{\sqrt{a} \sqrt{b} \sqrt[4]{a+b x^4}}","\frac{\sqrt[4]{\frac{b x^4}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{\sqrt{a} \sqrt{b} \sqrt[4]{a+b x^4}}",1,"((1 + (b*x^4)/a)^(1/4)*EllipticE[ArcTan[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(Sqrt[a]*Sqrt[b]*(a + b*x^4)^(1/4))","A",3,3,13,0.2308,1,"{275, 197, 196}"
1151,1,82,0,0.0471722,"\int \frac{1}{x^3 \left(a+b x^4\right)^{5/4}} \, dx","Int[1/(x^3*(a + b*x^4)^(5/4)),x]","-\frac{3 \sqrt{b} \sqrt[4]{\frac{b x^4}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{2 a^{3/2} \sqrt[4]{a+b x^4}}-\frac{1}{2 a x^2 \sqrt[4]{a+b x^4}}","-\frac{3 \sqrt{b} \sqrt[4]{\frac{b x^4}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{2 a^{3/2} \sqrt[4]{a+b x^4}}-\frac{1}{2 a x^2 \sqrt[4]{a+b x^4}}",1,"-1/(2*a*x^2*(a + b*x^4)^(1/4)) - (3*Sqrt[b]*(1 + (b*x^4)/a)^(1/4)*EllipticE[ArcTan[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(2*a^(3/2)*(a + b*x^4)^(1/4))","A",4,4,15,0.2667,1,"{275, 286, 197, 196}"
1152,1,104,0,0.0639458,"\int \frac{1}{x^7 \left(a+b x^4\right)^{5/4}} \, dx","Int[1/(x^7*(a + b*x^4)^(5/4)),x]","\frac{7 b^{3/2} \sqrt[4]{\frac{b x^4}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{4 a^{5/2} \sqrt[4]{a+b x^4}}+\frac{7 b}{12 a^2 x^2 \sqrt[4]{a+b x^4}}-\frac{1}{6 a x^6 \sqrt[4]{a+b x^4}}","\frac{7 b^{3/2} \sqrt[4]{\frac{b x^4}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{4 a^{5/2} \sqrt[4]{a+b x^4}}+\frac{7 b}{12 a^2 x^2 \sqrt[4]{a+b x^4}}-\frac{1}{6 a x^6 \sqrt[4]{a+b x^4}}",1,"-1/(6*a*x^6*(a + b*x^4)^(1/4)) + (7*b)/(12*a^2*x^2*(a + b*x^4)^(1/4)) + (7*b^(3/2)*(1 + (b*x^4)/a)^(1/4)*EllipticE[ArcTan[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(4*a^(5/2)*(a + b*x^4)^(1/4))","A",5,4,15,0.2667,1,"{275, 286, 197, 196}"
1153,1,128,0,0.0820153,"\int \frac{1}{x^{11} \left(a+b x^4\right)^{5/4}} \, dx","Int[1/(x^11*(a + b*x^4)^(5/4)),x]","-\frac{77 b^2}{120 a^3 x^2 \sqrt[4]{a+b x^4}}-\frac{77 b^{5/2} \sqrt[4]{\frac{b x^4}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{40 a^{7/2} \sqrt[4]{a+b x^4}}+\frac{11 b}{60 a^2 x^6 \sqrt[4]{a+b x^4}}-\frac{1}{10 a x^{10} \sqrt[4]{a+b x^4}}","-\frac{77 b^2}{120 a^3 x^2 \sqrt[4]{a+b x^4}}-\frac{77 b^{5/2} \sqrt[4]{\frac{b x^4}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{40 a^{7/2} \sqrt[4]{a+b x^4}}+\frac{11 b}{60 a^2 x^6 \sqrt[4]{a+b x^4}}-\frac{1}{10 a x^{10} \sqrt[4]{a+b x^4}}",1,"-1/(10*a*x^10*(a + b*x^4)^(1/4)) + (11*b)/(60*a^2*x^6*(a + b*x^4)^(1/4)) - (77*b^2)/(120*a^3*x^2*(a + b*x^4)^(1/4)) - (77*b^(5/2)*(1 + (b*x^4)/a)^(1/4)*EllipticE[ArcTan[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(40*a^(7/2)*(a + b*x^4)^(1/4))","A",6,4,15,0.2667,1,"{275, 286, 197, 196}"
1154,1,123,0,0.0451936,"\int \frac{x^{12}}{\left(a+b x^4\right)^{5/4}} \, dx","Int[x^12/(a + b*x^4)^(5/4),x]","\frac{45 a^2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{64 b^{13/4}}+\frac{45 a^2 \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{64 b^{13/4}}+\frac{9 x^5 \left(a+b x^4\right)^{3/4}}{8 b^2}-\frac{45 a x \left(a+b x^4\right)^{3/4}}{32 b^3}-\frac{x^9}{b \sqrt[4]{a+b x^4}}","\frac{45 a^2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{64 b^{13/4}}+\frac{45 a^2 \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{64 b^{13/4}}+\frac{9 x^5 \left(a+b x^4\right)^{3/4}}{8 b^2}-\frac{45 a x \left(a+b x^4\right)^{3/4}}{32 b^3}-\frac{x^9}{b \sqrt[4]{a+b x^4}}",1,"-(x^9/(b*(a + b*x^4)^(1/4))) - (45*a*x*(a + b*x^4)^(3/4))/(32*b^3) + (9*x^5*(a + b*x^4)^(3/4))/(8*b^2) + (45*a^2*ArcTan[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/(64*b^(13/4)) + (45*a^2*ArcTanh[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/(64*b^(13/4))","A",7,6,15,0.4000,1,"{288, 321, 240, 212, 206, 203}"
1155,1,97,0,0.0311875,"\int \frac{x^8}{\left(a+b x^4\right)^{5/4}} \, dx","Int[x^8/(a + b*x^4)^(5/4),x]","\frac{5 x \left(a+b x^4\right)^{3/4}}{4 b^2}-\frac{5 a \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{8 b^{9/4}}-\frac{5 a \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{8 b^{9/4}}-\frac{x^5}{b \sqrt[4]{a+b x^4}}","\frac{5 x \left(a+b x^4\right)^{3/4}}{4 b^2}-\frac{5 a \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{8 b^{9/4}}-\frac{5 a \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{8 b^{9/4}}-\frac{x^5}{b \sqrt[4]{a+b x^4}}",1,"-(x^5/(b*(a + b*x^4)^(1/4))) + (5*x*(a + b*x^4)^(3/4))/(4*b^2) - (5*a*ArcTan[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/(8*b^(9/4)) - (5*a*ArcTanh[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/(8*b^(9/4))","A",6,6,15,0.4000,1,"{288, 321, 240, 212, 206, 203}"
1156,1,74,0,0.0219148,"\int \frac{x^4}{\left(a+b x^4\right)^{5/4}} \, dx","Int[x^4/(a + b*x^4)^(5/4),x]","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{2 b^{5/4}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{2 b^{5/4}}-\frac{x}{b \sqrt[4]{a+b x^4}}","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{2 b^{5/4}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{2 b^{5/4}}-\frac{x}{b \sqrt[4]{a+b x^4}}",1,"-(x/(b*(a + b*x^4)^(1/4))) + ArcTan[(b^(1/4)*x)/(a + b*x^4)^(1/4)]/(2*b^(5/4)) + ArcTanh[(b^(1/4)*x)/(a + b*x^4)^(1/4)]/(2*b^(5/4))","A",5,5,15,0.3333,1,"{288, 240, 212, 206, 203}"
1157,1,16,0,0.0019039,"\int \frac{1}{\left(a+b x^4\right)^{5/4}} \, dx","Int[(a + b*x^4)^(-5/4),x]","\frac{x}{a \sqrt[4]{a+b x^4}}","\frac{x}{a \sqrt[4]{a+b x^4}}",1,"x/(a*(a + b*x^4)^(1/4))","A",1,1,11,0.09091,1,"{191}"
1158,1,42,0,0.007843,"\int \frac{1}{x^4 \left(a+b x^4\right)^{5/4}} \, dx","Int[1/(x^4*(a + b*x^4)^(5/4)),x]","-\frac{4 b x}{3 a^2 \sqrt[4]{a+b x^4}}-\frac{1}{3 a x^3 \sqrt[4]{a+b x^4}}","-\frac{4 b x}{3 a^2 \sqrt[4]{a+b x^4}}-\frac{1}{3 a x^3 \sqrt[4]{a+b x^4}}",1,"-1/(3*a*x^3*(a + b*x^4)^(1/4)) - (4*b*x)/(3*a^2*(a + b*x^4)^(1/4))","A",2,2,15,0.1333,1,"{271, 191}"
1159,1,66,0,0.0160023,"\int \frac{1}{x^8 \left(a+b x^4\right)^{5/4}} \, dx","Int[1/(x^8*(a + b*x^4)^(5/4)),x]","\frac{32 b^2 x}{21 a^3 \sqrt[4]{a+b x^4}}+\frac{8 b}{21 a^2 x^3 \sqrt[4]{a+b x^4}}-\frac{1}{7 a x^7 \sqrt[4]{a+b x^4}}","\frac{32 b^2 x}{21 a^3 \sqrt[4]{a+b x^4}}+\frac{8 b}{21 a^2 x^3 \sqrt[4]{a+b x^4}}-\frac{1}{7 a x^7 \sqrt[4]{a+b x^4}}",1,"-1/(7*a*x^7*(a + b*x^4)^(1/4)) + (8*b)/(21*a^2*x^3*(a + b*x^4)^(1/4)) + (32*b^2*x)/(21*a^3*(a + b*x^4)^(1/4))","A",3,2,15,0.1333,1,"{271, 191}"
1160,1,90,0,0.0260121,"\int \frac{1}{x^{12} \left(a+b x^4\right)^{5/4}} \, dx","Int[1/(x^12*(a + b*x^4)^(5/4)),x]","-\frac{128 b^3 x}{77 a^4 \sqrt[4]{a+b x^4}}-\frac{32 b^2}{77 a^3 x^3 \sqrt[4]{a+b x^4}}+\frac{12 b}{77 a^2 x^7 \sqrt[4]{a+b x^4}}-\frac{1}{11 a x^{11} \sqrt[4]{a+b x^4}}","-\frac{128 b^3 x}{77 a^4 \sqrt[4]{a+b x^4}}-\frac{32 b^2}{77 a^3 x^3 \sqrt[4]{a+b x^4}}+\frac{12 b}{77 a^2 x^7 \sqrt[4]{a+b x^4}}-\frac{1}{11 a x^{11} \sqrt[4]{a+b x^4}}",1,"-1/(11*a*x^11*(a + b*x^4)^(1/4)) + (12*b)/(77*a^2*x^7*(a + b*x^4)^(1/4)) - (32*b^2)/(77*a^3*x^3*(a + b*x^4)^(1/4)) - (128*b^3*x)/(77*a^4*(a + b*x^4)^(1/4))","A",4,2,15,0.1333,1,"{271, 191}"
1161,1,114,0,0.0395808,"\int \frac{1}{x^{16} \left(a+b x^4\right)^{5/4}} \, dx","Int[1/(x^16*(a + b*x^4)^(5/4)),x]","\frac{2048 b^4 x}{1155 a^5 \sqrt[4]{a+b x^4}}+\frac{512 b^3}{1155 a^4 x^3 \sqrt[4]{a+b x^4}}-\frac{64 b^2}{385 a^3 x^7 \sqrt[4]{a+b x^4}}+\frac{16 b}{165 a^2 x^{11} \sqrt[4]{a+b x^4}}-\frac{1}{15 a x^{15} \sqrt[4]{a+b x^4}}","\frac{2048 b^4 x}{1155 a^5 \sqrt[4]{a+b x^4}}+\frac{512 b^3}{1155 a^4 x^3 \sqrt[4]{a+b x^4}}-\frac{64 b^2}{385 a^3 x^7 \sqrt[4]{a+b x^4}}+\frac{16 b}{165 a^2 x^{11} \sqrt[4]{a+b x^4}}-\frac{1}{15 a x^{15} \sqrt[4]{a+b x^4}}",1,"-1/(15*a*x^15*(a + b*x^4)^(1/4)) + (16*b)/(165*a^2*x^11*(a + b*x^4)^(1/4)) - (64*b^2)/(385*a^3*x^7*(a + b*x^4)^(1/4)) + (512*b^3)/(1155*a^4*x^3*(a + b*x^4)^(1/4)) + (2048*b^4*x)/(1155*a^5*(a + b*x^4)^(1/4))","A",5,2,15,0.1333,1,"{271, 191}"
1162,1,129,0,0.0619913,"\int \frac{x^{14}}{\left(a+b x^4\right)^{5/4}} \, dx","Int[x^14/(a + b*x^4)^(5/4),x]","\frac{77 a^2 x^3}{120 b^3 \sqrt[4]{a+b x^4}}+\frac{77 a^{5/2} x \sqrt[4]{\frac{a}{b x^4}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{40 b^{7/2} \sqrt[4]{a+b x^4}}-\frac{11 a x^7}{60 b^2 \sqrt[4]{a+b x^4}}+\frac{x^{11}}{10 b \sqrt[4]{a+b x^4}}","\frac{77 a^2 x^3}{120 b^3 \sqrt[4]{a+b x^4}}+\frac{77 a^{5/2} x \sqrt[4]{\frac{a}{b x^4}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{40 b^{7/2} \sqrt[4]{a+b x^4}}-\frac{11 a x^7}{60 b^2 \sqrt[4]{a+b x^4}}+\frac{x^{11}}{10 b \sqrt[4]{a+b x^4}}",1,"(77*a^2*x^3)/(120*b^3*(a + b*x^4)^(1/4)) - (11*a*x^7)/(60*b^2*(a + b*x^4)^(1/4)) + x^11/(10*b*(a + b*x^4)^(1/4)) + (77*a^(5/2)*(1 + a/(b*x^4))^(1/4)*x*EllipticE[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(40*b^(7/2)*(a + b*x^4)^(1/4))","A",7,5,15,0.3333,1,"{282, 281, 335, 275, 196}"
1163,1,105,0,0.0493878,"\int \frac{x^{10}}{\left(a+b x^4\right)^{5/4}} \, dx","Int[x^10/(a + b*x^4)^(5/4),x]","-\frac{7 a^{3/2} x \sqrt[4]{\frac{a}{b x^4}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{4 b^{5/2} \sqrt[4]{a+b x^4}}-\frac{7 a x^3}{12 b^2 \sqrt[4]{a+b x^4}}+\frac{x^7}{6 b \sqrt[4]{a+b x^4}}","-\frac{7 a^{3/2} x \sqrt[4]{\frac{a}{b x^4}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{4 b^{5/2} \sqrt[4]{a+b x^4}}-\frac{7 a x^3}{12 b^2 \sqrt[4]{a+b x^4}}+\frac{x^7}{6 b \sqrt[4]{a+b x^4}}",1,"(-7*a*x^3)/(12*b^2*(a + b*x^4)^(1/4)) + x^7/(6*b*(a + b*x^4)^(1/4)) - (7*a^(3/2)*(1 + a/(b*x^4))^(1/4)*x*EllipticE[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(4*b^(5/2)*(a + b*x^4)^(1/4))","A",6,5,15,0.3333,1,"{282, 281, 335, 275, 196}"
1164,1,83,0,0.0370882,"\int \frac{x^6}{\left(a+b x^4\right)^{5/4}} \, dx","Int[x^6/(a + b*x^4)^(5/4),x]","\frac{3 \sqrt{a} x \sqrt[4]{\frac{a}{b x^4}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{2 b^{3/2} \sqrt[4]{a+b x^4}}+\frac{x^3}{2 b \sqrt[4]{a+b x^4}}","\frac{3 \sqrt{a} x \sqrt[4]{\frac{a}{b x^4}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{2 b^{3/2} \sqrt[4]{a+b x^4}}+\frac{x^3}{2 b \sqrt[4]{a+b x^4}}",1,"x^3/(2*b*(a + b*x^4)^(1/4)) + (3*Sqrt[a]*(1 + a/(b*x^4))^(1/4)*x*EllipticE[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(2*b^(3/2)*(a + b*x^4)^(1/4))","A",5,5,15,0.3333,1,"{282, 281, 335, 275, 196}"
1165,1,59,0,0.0279974,"\int \frac{x^2}{\left(a+b x^4\right)^{5/4}} \, dx","Int[x^2/(a + b*x^4)^(5/4),x]","-\frac{x \sqrt[4]{\frac{a}{b x^4}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{\sqrt{a} \sqrt{b} \sqrt[4]{a+b x^4}}","-\frac{x \sqrt[4]{\frac{a}{b x^4}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{\sqrt{a} \sqrt{b} \sqrt[4]{a+b x^4}}",1,"-(((1 + a/(b*x^4))^(1/4)*x*EllipticE[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(Sqrt[a]*Sqrt[b]*(a + b*x^4)^(1/4)))","A",4,4,15,0.2667,1,"{281, 335, 275, 196}"
1166,1,79,0,0.037294,"\int \frac{1}{x^2 \left(a+b x^4\right)^{5/4}} \, dx","Int[1/(x^2*(a + b*x^4)^(5/4)),x]","\frac{2 \sqrt{b} x \sqrt[4]{\frac{a}{b x^4}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{a^{3/2} \sqrt[4]{a+b x^4}}-\frac{1}{a x \sqrt[4]{a+b x^4}}","\frac{2 \sqrt{b} x \sqrt[4]{\frac{a}{b x^4}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{a^{3/2} \sqrt[4]{a+b x^4}}-\frac{1}{a x \sqrt[4]{a+b x^4}}",1,"-(1/(a*x*(a + b*x^4)^(1/4))) + (2*Sqrt[b]*(1 + a/(b*x^4))^(1/4)*x*EllipticE[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(a^(3/2)*(a + b*x^4)^(1/4))","A",5,5,15,0.3333,1,"{283, 281, 335, 275, 196}"
1167,1,105,0,0.0484748,"\int \frac{1}{x^6 \left(a+b x^4\right)^{5/4}} \, dx","Int[1/(x^6*(a + b*x^4)^(5/4)),x]","-\frac{12 b^{3/2} x \sqrt[4]{\frac{a}{b x^4}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{5 a^{5/2} \sqrt[4]{a+b x^4}}+\frac{6 b}{5 a^2 x \sqrt[4]{a+b x^4}}-\frac{1}{5 a x^5 \sqrt[4]{a+b x^4}}","-\frac{12 b^{3/2} x \sqrt[4]{\frac{a}{b x^4}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{5 a^{5/2} \sqrt[4]{a+b x^4}}+\frac{6 b}{5 a^2 x \sqrt[4]{a+b x^4}}-\frac{1}{5 a x^5 \sqrt[4]{a+b x^4}}",1,"-1/(5*a*x^5*(a + b*x^4)^(1/4)) + (6*b)/(5*a^2*x*(a + b*x^4)^(1/4)) - (12*b^(3/2)*(1 + a/(b*x^4))^(1/4)*x*EllipticE[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(5*a^(5/2)*(a + b*x^4)^(1/4))","A",6,5,15,0.3333,1,"{283, 281, 335, 275, 196}"
1168,1,129,0,0.0634339,"\int \frac{1}{x^{10} \left(a+b x^4\right)^{5/4}} \, dx","Int[1/(x^10*(a + b*x^4)^(5/4)),x]","-\frac{4 b^2}{3 a^3 x \sqrt[4]{a+b x^4}}+\frac{8 b^{5/2} x \sqrt[4]{\frac{a}{b x^4}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{3 a^{7/2} \sqrt[4]{a+b x^4}}+\frac{2 b}{9 a^2 x^5 \sqrt[4]{a+b x^4}}-\frac{1}{9 a x^9 \sqrt[4]{a+b x^4}}","-\frac{4 b^2}{3 a^3 x \sqrt[4]{a+b x^4}}+\frac{8 b^{5/2} x \sqrt[4]{\frac{a}{b x^4}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{3 a^{7/2} \sqrt[4]{a+b x^4}}+\frac{2 b}{9 a^2 x^5 \sqrt[4]{a+b x^4}}-\frac{1}{9 a x^9 \sqrt[4]{a+b x^4}}",1,"-1/(9*a*x^9*(a + b*x^4)^(1/4)) + (2*b)/(9*a^2*x^5*(a + b*x^4)^(1/4)) - (4*b^2)/(3*a^3*x*(a + b*x^4)^(1/4)) + (8*b^(5/2)*(1 + a/(b*x^4))^(1/4)*x*EllipticE[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(3*a^(7/2)*(a + b*x^4)^(1/4))","A",7,5,15,0.3333,1,"{283, 281, 335, 275, 196}"
1169,1,153,0,0.0808795,"\int \frac{1}{x^{14} \left(a+b x^4\right)^{5/4}} \, dx","Int[1/(x^14*(a + b*x^4)^(5/4)),x]","\frac{56 b^3}{39 a^4 x \sqrt[4]{a+b x^4}}-\frac{28 b^2}{117 a^3 x^5 \sqrt[4]{a+b x^4}}-\frac{112 b^{7/2} x \sqrt[4]{\frac{a}{b x^4}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{39 a^{9/2} \sqrt[4]{a+b x^4}}+\frac{14 b}{117 a^2 x^9 \sqrt[4]{a+b x^4}}-\frac{1}{13 a x^{13} \sqrt[4]{a+b x^4}}","\frac{56 b^3}{39 a^4 x \sqrt[4]{a+b x^4}}-\frac{28 b^2}{117 a^3 x^5 \sqrt[4]{a+b x^4}}-\frac{112 b^{7/2} x \sqrt[4]{\frac{a}{b x^4}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{39 a^{9/2} \sqrt[4]{a+b x^4}}+\frac{14 b}{117 a^2 x^9 \sqrt[4]{a+b x^4}}-\frac{1}{13 a x^{13} \sqrt[4]{a+b x^4}}",1,"-1/(13*a*x^13*(a + b*x^4)^(1/4)) + (14*b)/(117*a^2*x^9*(a + b*x^4)^(1/4)) - (28*b^2)/(117*a^3*x^5*(a + b*x^4)^(1/4)) + (56*b^3)/(39*a^4*x*(a + b*x^4)^(1/4)) - (112*b^(7/2)*(1 + a/(b*x^4))^(1/4)*x*EllipticE[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(39*a^(9/2)*(a + b*x^4)^(1/4))","A",8,5,15,0.3333,1,"{283, 281, 335, 275, 196}"
1170,1,83,0,0.0314403,"\int \frac{1}{\left(a+b x^4\right)^{7/4}} \, dx","Int[(a + b*x^4)^(-7/4),x]","\frac{x}{3 a \left(a+b x^4\right)^{3/4}}-\frac{2 \sqrt{b} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{3 a^{3/2} \left(a+b x^4\right)^{3/4}}","\frac{x}{3 a \left(a+b x^4\right)^{3/4}}-\frac{2 \sqrt{b} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{3 a^{3/2} \left(a+b x^4\right)^{3/4}}",1,"x/(3*a*(a + b*x^4)^(3/4)) - (2*Sqrt[b]*(1 + a/(b*x^4))^(3/4)*x^3*EllipticF[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(3*a^(3/2)*(a + b*x^4)^(3/4))","A",5,5,11,0.4545,1,"{199, 237, 335, 275, 231}"
1171,1,39,0,0.0051588,"\int \frac{1}{\left(a+b x^4\right)^{9/4}} \, dx","Int[(a + b*x^4)^(-9/4),x]","\frac{4 x}{5 a^2 \sqrt[4]{a+b x^4}}+\frac{x}{5 a \left(a+b x^4\right)^{5/4}}","\frac{4 x}{5 a^2 \sqrt[4]{a+b x^4}}+\frac{x}{5 a \left(a+b x^4\right)^{5/4}}",1,"x/(5*a*(a + b*x^4)^(5/4)) + (4*x)/(5*a^2*(a + b*x^4)^(1/4))","A",2,2,11,0.1818,1,"{192, 191}"
1172,1,102,0,0.0398733,"\int \frac{1}{\left(a+b x^4\right)^{11/4}} \, dx","Int[(a + b*x^4)^(-11/4),x]","\frac{2 x}{7 a^2 \left(a+b x^4\right)^{3/4}}-\frac{4 \sqrt{b} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{7 a^{5/2} \left(a+b x^4\right)^{3/4}}+\frac{x}{7 a \left(a+b x^4\right)^{7/4}}","\frac{2 x}{7 a^2 \left(a+b x^4\right)^{3/4}}-\frac{4 \sqrt{b} x^3 \left(\frac{a}{b x^4}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{7 a^{5/2} \left(a+b x^4\right)^{3/4}}+\frac{x}{7 a \left(a+b x^4\right)^{7/4}}",1,"x/(7*a*(a + b*x^4)^(7/4)) + (2*x)/(7*a^2*(a + b*x^4)^(3/4)) - (4*Sqrt[b]*(1 + a/(b*x^4))^(3/4)*x^3*EllipticF[ArcCot[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(7*a^(5/2)*(a + b*x^4)^(3/4))","A",6,5,11,0.4545,1,"{199, 237, 335, 275, 231}"
1173,1,58,0,0.0098094,"\int \frac{1}{\left(a+b x^4\right)^{13/4}} \, dx","Int[(a + b*x^4)^(-13/4),x]","\frac{32 x}{45 a^3 \sqrt[4]{a+b x^4}}+\frac{8 x}{45 a^2 \left(a+b x^4\right)^{5/4}}+\frac{x}{9 a \left(a+b x^4\right)^{9/4}}","\frac{32 x}{45 a^3 \sqrt[4]{a+b x^4}}+\frac{8 x}{45 a^2 \left(a+b x^4\right)^{5/4}}+\frac{x}{9 a \left(a+b x^4\right)^{9/4}}",1,"x/(9*a*(a + b*x^4)^(9/4)) + (8*x)/(45*a^2*(a + b*x^4)^(5/4)) + (32*x)/(45*a^3*(a + b*x^4)^(1/4))","A",3,2,11,0.1818,1,"{192, 191}"
1174,1,77,0,0.0159634,"\int \frac{1}{\left(a+b x^4\right)^{17/4}} \, dx","Int[(a + b*x^4)^(-17/4),x]","\frac{128 x}{195 a^4 \sqrt[4]{a+b x^4}}+\frac{32 x}{195 a^3 \left(a+b x^4\right)^{5/4}}+\frac{4 x}{39 a^2 \left(a+b x^4\right)^{9/4}}+\frac{x}{13 a \left(a+b x^4\right)^{13/4}}","\frac{128 x}{195 a^4 \sqrt[4]{a+b x^4}}+\frac{32 x}{195 a^3 \left(a+b x^4\right)^{5/4}}+\frac{4 x}{39 a^2 \left(a+b x^4\right)^{9/4}}+\frac{x}{13 a \left(a+b x^4\right)^{13/4}}",1,"x/(13*a*(a + b*x^4)^(13/4)) + (4*x)/(39*a^2*(a + b*x^4)^(9/4)) + (32*x)/(195*a^3*(a + b*x^4)^(5/4)) + (128*x)/(195*a^4*(a + b*x^4)^(1/4))","A",4,2,11,0.1818,1,"{192, 191}"
1175,1,106,0,0.0569475,"\int x^{19} \sqrt[4]{a-b x^4} \, dx","Int[x^19*(a - b*x^4)^(1/4),x]","-\frac{6 a^2 \left(a-b x^4\right)^{13/4}}{13 b^5}+\frac{4 a^3 \left(a-b x^4\right)^{9/4}}{9 b^5}-\frac{a^4 \left(a-b x^4\right)^{5/4}}{5 b^5}-\frac{\left(a-b x^4\right)^{21/4}}{21 b^5}+\frac{4 a \left(a-b x^4\right)^{17/4}}{17 b^5}","-\frac{6 a^2 \left(a-b x^4\right)^{13/4}}{13 b^5}+\frac{4 a^3 \left(a-b x^4\right)^{9/4}}{9 b^5}-\frac{a^4 \left(a-b x^4\right)^{5/4}}{5 b^5}-\frac{\left(a-b x^4\right)^{21/4}}{21 b^5}+\frac{4 a \left(a-b x^4\right)^{17/4}}{17 b^5}",1,"-(a^4*(a - b*x^4)^(5/4))/(5*b^5) + (4*a^3*(a - b*x^4)^(9/4))/(9*b^5) - (6*a^2*(a - b*x^4)^(13/4))/(13*b^5) + (4*a*(a - b*x^4)^(17/4))/(17*b^5) - (a - b*x^4)^(21/4)/(21*b^5)","A",3,2,16,0.1250,1,"{266, 43}"
1176,1,84,0,0.0459359,"\int x^{15} \sqrt[4]{a-b x^4} \, dx","Int[x^15*(a - b*x^4)^(1/4),x]","\frac{a^2 \left(a-b x^4\right)^{9/4}}{3 b^4}-\frac{a^3 \left(a-b x^4\right)^{5/4}}{5 b^4}+\frac{\left(a-b x^4\right)^{17/4}}{17 b^4}-\frac{3 a \left(a-b x^4\right)^{13/4}}{13 b^4}","\frac{a^2 \left(a-b x^4\right)^{9/4}}{3 b^4}-\frac{a^3 \left(a-b x^4\right)^{5/4}}{5 b^4}+\frac{\left(a-b x^4\right)^{17/4}}{17 b^4}-\frac{3 a \left(a-b x^4\right)^{13/4}}{13 b^4}",1,"-(a^3*(a - b*x^4)^(5/4))/(5*b^4) + (a^2*(a - b*x^4)^(9/4))/(3*b^4) - (3*a*(a - b*x^4)^(13/4))/(13*b^4) + (a - b*x^4)^(17/4)/(17*b^4)","A",3,2,16,0.1250,1,"{266, 43}"
1177,1,62,0,0.0342731,"\int x^{11} \sqrt[4]{a-b x^4} \, dx","Int[x^11*(a - b*x^4)^(1/4),x]","-\frac{a^2 \left(a-b x^4\right)^{5/4}}{5 b^3}-\frac{\left(a-b x^4\right)^{13/4}}{13 b^3}+\frac{2 a \left(a-b x^4\right)^{9/4}}{9 b^3}","-\frac{a^2 \left(a-b x^4\right)^{5/4}}{5 b^3}-\frac{\left(a-b x^4\right)^{13/4}}{13 b^3}+\frac{2 a \left(a-b x^4\right)^{9/4}}{9 b^3}",1,"-(a^2*(a - b*x^4)^(5/4))/(5*b^3) + (2*a*(a - b*x^4)^(9/4))/(9*b^3) - (a - b*x^4)^(13/4)/(13*b^3)","A",3,2,16,0.1250,1,"{266, 43}"
1178,1,40,0,0.0230262,"\int x^7 \sqrt[4]{a-b x^4} \, dx","Int[x^7*(a - b*x^4)^(1/4),x]","\frac{\left(a-b x^4\right)^{9/4}}{9 b^2}-\frac{a \left(a-b x^4\right)^{5/4}}{5 b^2}","\frac{\left(a-b x^4\right)^{9/4}}{9 b^2}-\frac{a \left(a-b x^4\right)^{5/4}}{5 b^2}",1,"-(a*(a - b*x^4)^(5/4))/(5*b^2) + (a - b*x^4)^(9/4)/(9*b^2)","A",3,2,16,0.1250,1,"{266, 43}"
1179,1,19,0,0.0045606,"\int x^3 \sqrt[4]{a-b x^4} \, dx","Int[x^3*(a - b*x^4)^(1/4),x]","-\frac{\left(a-b x^4\right)^{5/4}}{5 b}","-\frac{\left(a-b x^4\right)^{5/4}}{5 b}",1,"-(a - b*x^4)^(5/4)/(5*b)","A",1,1,16,0.06250,1,"{261}"
1180,1,69,0,0.0432912,"\int \frac{\sqrt[4]{a-b x^4}}{x} \, dx","Int[(a - b*x^4)^(1/4)/x,x]","\sqrt[4]{a-b x^4}-\frac{1}{2} \sqrt[4]{a} \tan ^{-1}\left(\frac{\sqrt[4]{a-b x^4}}{\sqrt[4]{a}}\right)-\frac{1}{2} \sqrt[4]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{a-b x^4}}{\sqrt[4]{a}}\right)","\sqrt[4]{a-b x^4}-\frac{1}{2} \sqrt[4]{a} \tan ^{-1}\left(\frac{\sqrt[4]{a-b x^4}}{\sqrt[4]{a}}\right)-\frac{1}{2} \sqrt[4]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{a-b x^4}}{\sqrt[4]{a}}\right)",1,"(a - b*x^4)^(1/4) - (a^(1/4)*ArcTan[(a - b*x^4)^(1/4)/a^(1/4)])/2 - (a^(1/4)*ArcTanh[(a - b*x^4)^(1/4)/a^(1/4)])/2","A",6,6,16,0.3750,1,"{266, 50, 63, 212, 206, 203}"
1181,1,78,0,0.0431871,"\int \frac{\sqrt[4]{a-b x^4}}{x^5} \, dx","Int[(a - b*x^4)^(1/4)/x^5,x]","\frac{b \tan ^{-1}\left(\frac{\sqrt[4]{a-b x^4}}{\sqrt[4]{a}}\right)}{8 a^{3/4}}+\frac{b \tanh ^{-1}\left(\frac{\sqrt[4]{a-b x^4}}{\sqrt[4]{a}}\right)}{8 a^{3/4}}-\frac{\sqrt[4]{a-b x^4}}{4 x^4}","\frac{b \tan ^{-1}\left(\frac{\sqrt[4]{a-b x^4}}{\sqrt[4]{a}}\right)}{8 a^{3/4}}+\frac{b \tanh ^{-1}\left(\frac{\sqrt[4]{a-b x^4}}{\sqrt[4]{a}}\right)}{8 a^{3/4}}-\frac{\sqrt[4]{a-b x^4}}{4 x^4}",1,"-(a - b*x^4)^(1/4)/(4*x^4) + (b*ArcTan[(a - b*x^4)^(1/4)/a^(1/4)])/(8*a^(3/4)) + (b*ArcTanh[(a - b*x^4)^(1/4)/a^(1/4)])/(8*a^(3/4))","A",6,6,16,0.3750,1,"{266, 47, 63, 212, 206, 203}"
1182,1,105,0,0.0578054,"\int \frac{\sqrt[4]{a-b x^4}}{x^9} \, dx","Int[(a - b*x^4)^(1/4)/x^9,x]","\frac{3 b^2 \tan ^{-1}\left(\frac{\sqrt[4]{a-b x^4}}{\sqrt[4]{a}}\right)}{64 a^{7/4}}+\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt[4]{a-b x^4}}{\sqrt[4]{a}}\right)}{64 a^{7/4}}+\frac{b \sqrt[4]{a-b x^4}}{32 a x^4}-\frac{\sqrt[4]{a-b x^4}}{8 x^8}","\frac{3 b^2 \tan ^{-1}\left(\frac{\sqrt[4]{a-b x^4}}{\sqrt[4]{a}}\right)}{64 a^{7/4}}+\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt[4]{a-b x^4}}{\sqrt[4]{a}}\right)}{64 a^{7/4}}+\frac{b \sqrt[4]{a-b x^4}}{32 a x^4}-\frac{\sqrt[4]{a-b x^4}}{8 x^8}",1,"-(a - b*x^4)^(1/4)/(8*x^8) + (b*(a - b*x^4)^(1/4))/(32*a*x^4) + (3*b^2*ArcTan[(a - b*x^4)^(1/4)/a^(1/4)])/(64*a^(7/4)) + (3*b^2*ArcTanh[(a - b*x^4)^(1/4)/a^(1/4)])/(64*a^(7/4))","A",7,7,16,0.4375,1,"{266, 47, 51, 63, 212, 206, 203}"
1183,1,130,0,0.0834779,"\int x^9 \sqrt[4]{a-b x^4} \, dx","Int[x^9*(a - b*x^4)^(1/4),x]","-\frac{2 a^2 x^2 \sqrt[4]{a-b x^4}}{77 b^2}+\frac{4 a^{7/2} \left(1-\frac{b x^4}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{77 b^{5/2} \left(a-b x^4\right)^{3/4}}+\frac{1}{11} x^{10} \sqrt[4]{a-b x^4}-\frac{a x^6 \sqrt[4]{a-b x^4}}{77 b}","-\frac{2 a^2 x^2 \sqrt[4]{a-b x^4}}{77 b^2}+\frac{4 a^{7/2} \left(1-\frac{b x^4}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{77 b^{5/2} \left(a-b x^4\right)^{3/4}}+\frac{1}{11} x^{10} \sqrt[4]{a-b x^4}-\frac{a x^6 \sqrt[4]{a-b x^4}}{77 b}",1,"(-2*a^2*x^2*(a - b*x^4)^(1/4))/(77*b^2) - (a*x^6*(a - b*x^4)^(1/4))/(77*b) + (x^10*(a - b*x^4)^(1/4))/11 + (4*a^(7/2)*(1 - (b*x^4)/a)^(3/4)*EllipticF[ArcSin[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(77*b^(5/2)*(a - b*x^4)^(3/4))","A",6,5,16,0.3125,1,"{275, 279, 321, 233, 232}"
1184,1,105,0,0.0635742,"\int x^5 \sqrt[4]{a-b x^4} \, dx","Int[x^5*(a - b*x^4)^(1/4),x]","\frac{2 a^{5/2} \left(1-\frac{b x^4}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{21 b^{3/2} \left(a-b x^4\right)^{3/4}}+\frac{1}{7} x^6 \sqrt[4]{a-b x^4}-\frac{a x^2 \sqrt[4]{a-b x^4}}{21 b}","\frac{2 a^{5/2} \left(1-\frac{b x^4}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{21 b^{3/2} \left(a-b x^4\right)^{3/4}}+\frac{1}{7} x^6 \sqrt[4]{a-b x^4}-\frac{a x^2 \sqrt[4]{a-b x^4}}{21 b}",1,"-(a*x^2*(a - b*x^4)^(1/4))/(21*b) + (x^6*(a - b*x^4)^(1/4))/7 + (2*a^(5/2)*(1 - (b*x^4)/a)^(3/4)*EllipticF[ArcSin[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(21*b^(3/2)*(a - b*x^4)^(3/4))","A",5,5,16,0.3125,1,"{275, 279, 321, 233, 232}"
1185,1,82,0,0.0427203,"\int x \sqrt[4]{a-b x^4} \, dx","Int[x*(a - b*x^4)^(1/4),x]","\frac{a^{3/2} \left(1-\frac{b x^4}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{3 \sqrt{b} \left(a-b x^4\right)^{3/4}}+\frac{1}{3} x^2 \sqrt[4]{a-b x^4}","\frac{a^{3/2} \left(1-\frac{b x^4}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{3 \sqrt{b} \left(a-b x^4\right)^{3/4}}+\frac{1}{3} x^2 \sqrt[4]{a-b x^4}",1,"(x^2*(a - b*x^4)^(1/4))/3 + (a^(3/2)*(1 - (b*x^4)/a)^(3/4)*EllipticF[ArcSin[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(3*Sqrt[b]*(a - b*x^4)^(3/4))","A",4,4,14,0.2857,1,"{275, 195, 233, 232}"
1186,1,82,0,0.0467652,"\int \frac{\sqrt[4]{a-b x^4}}{x^3} \, dx","Int[(a - b*x^4)^(1/4)/x^3,x]","-\frac{\sqrt[4]{a-b x^4}}{2 x^2}-\frac{\sqrt{a} \sqrt{b} \left(1-\frac{b x^4}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{2 \left(a-b x^4\right)^{3/4}}","-\frac{\sqrt[4]{a-b x^4}}{2 x^2}-\frac{\sqrt{a} \sqrt{b} \left(1-\frac{b x^4}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{2 \left(a-b x^4\right)^{3/4}}",1,"-(a - b*x^4)^(1/4)/(2*x^2) - (Sqrt[a]*Sqrt[b]*(1 - (b*x^4)/a)^(3/4)*EllipticF[ArcSin[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(2*(a - b*x^4)^(3/4))","A",4,4,16,0.2500,1,"{275, 277, 233, 232}"
1187,1,105,0,0.0630944,"\int \frac{\sqrt[4]{a-b x^4}}{x^7} \, dx","Int[(a - b*x^4)^(1/4)/x^7,x]","-\frac{b^{3/2} \left(1-\frac{b x^4}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{12 \sqrt{a} \left(a-b x^4\right)^{3/4}}+\frac{b \sqrt[4]{a-b x^4}}{12 a x^2}-\frac{\sqrt[4]{a-b x^4}}{6 x^6}","-\frac{b^{3/2} \left(1-\frac{b x^4}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{12 \sqrt{a} \left(a-b x^4\right)^{3/4}}+\frac{b \sqrt[4]{a-b x^4}}{12 a x^2}-\frac{\sqrt[4]{a-b x^4}}{6 x^6}",1,"-(a - b*x^4)^(1/4)/(6*x^6) + (b*(a - b*x^4)^(1/4))/(12*a*x^2) - (b^(3/2)*(1 - (b*x^4)/a)^(3/4)*EllipticF[ArcSin[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(12*Sqrt[a]*(a - b*x^4)^(3/4))","A",5,5,16,0.3125,1,"{275, 277, 325, 233, 232}"
1188,1,130,0,0.0854398,"\int \frac{\sqrt[4]{a-b x^4}}{x^{11}} \, dx","Int[(a - b*x^4)^(1/4)/x^11,x]","\frac{b^2 \sqrt[4]{a-b x^4}}{24 a^2 x^2}-\frac{b^{5/2} \left(1-\frac{b x^4}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{24 a^{3/2} \left(a-b x^4\right)^{3/4}}+\frac{b \sqrt[4]{a-b x^4}}{60 a x^6}-\frac{\sqrt[4]{a-b x^4}}{10 x^{10}}","\frac{b^2 \sqrt[4]{a-b x^4}}{24 a^2 x^2}-\frac{b^{5/2} \left(1-\frac{b x^4}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{24 a^{3/2} \left(a-b x^4\right)^{3/4}}+\frac{b \sqrt[4]{a-b x^4}}{60 a x^6}-\frac{\sqrt[4]{a-b x^4}}{10 x^{10}}",1,"-(a - b*x^4)^(1/4)/(10*x^10) + (b*(a - b*x^4)^(1/4))/(60*a*x^6) + (b^2*(a - b*x^4)^(1/4))/(24*a^2*x^2) - (b^(5/2)*(1 - (b*x^4)/a)^(3/4)*EllipticF[ArcSin[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(24*a^(3/2)*(a - b*x^4)^(3/4))","A",6,5,16,0.3125,1,"{275, 277, 325, 233, 232}"
1189,1,263,0,0.1578046,"\int x^6 \sqrt[4]{a-b x^4} \, dx","Int[x^6*(a - b*x^4)^(1/4),x]","\frac{3 a^2 \log \left(\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{128 \sqrt{2} b^{7/4}}-\frac{3 a^2 \log \left(\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}+\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{128 \sqrt{2} b^{7/4}}-\frac{3 a^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}\right)}{64 \sqrt{2} b^{7/4}}+\frac{3 a^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{64 \sqrt{2} b^{7/4}}+\frac{1}{8} x^7 \sqrt[4]{a-b x^4}-\frac{a x^3 \sqrt[4]{a-b x^4}}{32 b}","\frac{3 a^2 \log \left(\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{128 \sqrt{2} b^{7/4}}-\frac{3 a^2 \log \left(\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}+\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{128 \sqrt{2} b^{7/4}}-\frac{3 a^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}\right)}{64 \sqrt{2} b^{7/4}}+\frac{3 a^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{64 \sqrt{2} b^{7/4}}+\frac{1}{8} x^7 \sqrt[4]{a-b x^4}-\frac{a x^3 \sqrt[4]{a-b x^4}}{32 b}",1,"-(a*x^3*(a - b*x^4)^(1/4))/(32*b) + (x^7*(a - b*x^4)^(1/4))/8 - (3*a^2*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/(a - b*x^4)^(1/4)])/(64*Sqrt[2]*b^(7/4)) + (3*a^2*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/(a - b*x^4)^(1/4)])/(64*Sqrt[2]*b^(7/4)) + (3*a^2*Log[1 + (Sqrt[b]*x^2)/Sqrt[a - b*x^4] - (Sqrt[2]*b^(1/4)*x)/(a - b*x^4)^(1/4)])/(128*Sqrt[2]*b^(7/4)) - (3*a^2*Log[1 + (Sqrt[b]*x^2)/Sqrt[a - b*x^4] + (Sqrt[2]*b^(1/4)*x)/(a - b*x^4)^(1/4)])/(128*Sqrt[2]*b^(7/4))","A",12,9,16,0.5625,1,"{279, 321, 331, 297, 1162, 617, 204, 1165, 628}"
1190,1,232,0,0.1107041,"\int x^2 \sqrt[4]{a-b x^4} \, dx","Int[x^2*(a - b*x^4)^(1/4),x]","\frac{a \log \left(\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{16 \sqrt{2} b^{3/4}}-\frac{a \log \left(\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}+\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{16 \sqrt{2} b^{3/4}}-\frac{a \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}\right)}{8 \sqrt{2} b^{3/4}}+\frac{a \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{8 \sqrt{2} b^{3/4}}+\frac{1}{4} x^3 \sqrt[4]{a-b x^4}","\frac{a \log \left(\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{16 \sqrt{2} b^{3/4}}-\frac{a \log \left(\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}+\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{16 \sqrt{2} b^{3/4}}-\frac{a \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}\right)}{8 \sqrt{2} b^{3/4}}+\frac{a \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{8 \sqrt{2} b^{3/4}}+\frac{1}{4} x^3 \sqrt[4]{a-b x^4}",1,"(x^3*(a - b*x^4)^(1/4))/4 - (a*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/(a - b*x^4)^(1/4)])/(8*Sqrt[2]*b^(3/4)) + (a*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/(a - b*x^4)^(1/4)])/(8*Sqrt[2]*b^(3/4)) + (a*Log[1 + (Sqrt[b]*x^2)/Sqrt[a - b*x^4] - (Sqrt[2]*b^(1/4)*x)/(a - b*x^4)^(1/4)])/(16*Sqrt[2]*b^(3/4)) - (a*Log[1 + (Sqrt[b]*x^2)/Sqrt[a - b*x^4] + (Sqrt[2]*b^(1/4)*x)/(a - b*x^4)^(1/4)])/(16*Sqrt[2]*b^(3/4))","A",11,8,16,0.5000,1,"{279, 331, 297, 1162, 617, 204, 1165, 628}"
1191,1,226,0,0.1107742,"\int \frac{\sqrt[4]{a-b x^4}}{x^2} \, dx","Int[(a - b*x^4)^(1/4)/x^2,x]","-\frac{\sqrt[4]{a-b x^4}}{x}-\frac{\sqrt[4]{b} \log \left(\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{4 \sqrt{2}}+\frac{\sqrt[4]{b} \log \left(\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}+\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{4 \sqrt{2}}+\frac{\sqrt[4]{b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}\right)}{2 \sqrt{2}}-\frac{\sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{2 \sqrt{2}}","-\frac{\sqrt[4]{a-b x^4}}{x}-\frac{\sqrt[4]{b} \log \left(\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{4 \sqrt{2}}+\frac{\sqrt[4]{b} \log \left(\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}+\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{4 \sqrt{2}}+\frac{\sqrt[4]{b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}\right)}{2 \sqrt{2}}-\frac{\sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{2 \sqrt{2}}",1,"-((a - b*x^4)^(1/4)/x) + (b^(1/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/(a - b*x^4)^(1/4)])/(2*Sqrt[2]) - (b^(1/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/(a - b*x^4)^(1/4)])/(2*Sqrt[2]) - (b^(1/4)*Log[1 + (Sqrt[b]*x^2)/Sqrt[a - b*x^4] - (Sqrt[2]*b^(1/4)*x)/(a - b*x^4)^(1/4)])/(4*Sqrt[2]) + (b^(1/4)*Log[1 + (Sqrt[b]*x^2)/Sqrt[a - b*x^4] + (Sqrt[2]*b^(1/4)*x)/(a - b*x^4)^(1/4)])/(4*Sqrt[2])","A",11,8,16,0.5000,1,"{277, 331, 297, 1162, 617, 204, 1165, 628}"
1192,1,22,0,0.0044349,"\int \frac{\sqrt[4]{a-b x^4}}{x^6} \, dx","Int[(a - b*x^4)^(1/4)/x^6,x]","-\frac{\left(a-b x^4\right)^{5/4}}{5 a x^5}","-\frac{\left(a-b x^4\right)^{5/4}}{5 a x^5}",1,"-(a - b*x^4)^(5/4)/(5*a*x^5)","A",1,1,16,0.06250,1,"{264}"
1193,1,46,0,0.0107183,"\int \frac{\sqrt[4]{a-b x^4}}{x^{10}} \, dx","Int[(a - b*x^4)^(1/4)/x^10,x]","-\frac{4 b \left(a-b x^4\right)^{5/4}}{45 a^2 x^5}-\frac{\left(a-b x^4\right)^{5/4}}{9 a x^9}","-\frac{4 b \left(a-b x^4\right)^{5/4}}{45 a^2 x^5}-\frac{\left(a-b x^4\right)^{5/4}}{9 a x^9}",1,"-(a - b*x^4)^(5/4)/(9*a*x^9) - (4*b*(a - b*x^4)^(5/4))/(45*a^2*x^5)","A",2,2,16,0.1250,1,"{271, 264}"
1194,1,71,0,0.0190207,"\int \frac{\sqrt[4]{a-b x^4}}{x^{14}} \, dx","Int[(a - b*x^4)^(1/4)/x^14,x]","-\frac{32 b^2 \left(a-b x^4\right)^{5/4}}{585 a^3 x^5}-\frac{8 b \left(a-b x^4\right)^{5/4}}{117 a^2 x^9}-\frac{\left(a-b x^4\right)^{5/4}}{13 a x^{13}}","-\frac{32 b^2 \left(a-b x^4\right)^{5/4}}{585 a^3 x^5}-\frac{8 b \left(a-b x^4\right)^{5/4}}{117 a^2 x^9}-\frac{\left(a-b x^4\right)^{5/4}}{13 a x^{13}}",1,"-(a - b*x^4)^(5/4)/(13*a*x^13) - (8*b*(a - b*x^4)^(5/4))/(117*a^2*x^9) - (32*b^2*(a - b*x^4)^(5/4))/(585*a^3*x^5)","A",3,2,16,0.1250,1,"{271, 264}"
1195,1,96,0,0.0290444,"\int \frac{\sqrt[4]{a-b x^4}}{x^{18}} \, dx","Int[(a - b*x^4)^(1/4)/x^18,x]","-\frac{128 b^3 \left(a-b x^4\right)^{5/4}}{3315 a^4 x^5}-\frac{32 b^2 \left(a-b x^4\right)^{5/4}}{663 a^3 x^9}-\frac{12 b \left(a-b x^4\right)^{5/4}}{221 a^2 x^{13}}-\frac{\left(a-b x^4\right)^{5/4}}{17 a x^{17}}","-\frac{128 b^3 \left(a-b x^4\right)^{5/4}}{3315 a^4 x^5}-\frac{32 b^2 \left(a-b x^4\right)^{5/4}}{663 a^3 x^9}-\frac{12 b \left(a-b x^4\right)^{5/4}}{221 a^2 x^{13}}-\frac{\left(a-b x^4\right)^{5/4}}{17 a x^{17}}",1,"-(a - b*x^4)^(5/4)/(17*a*x^17) - (12*b*(a - b*x^4)^(5/4))/(221*a^2*x^13) - (32*b^2*(a - b*x^4)^(5/4))/(663*a^3*x^9) - (128*b^3*(a - b*x^4)^(5/4))/(3315*a^4*x^5)","A",4,2,16,0.1250,1,"{271, 264}"
1196,1,156,0,0.0774046,"\int x^{12} \sqrt[4]{a-b x^4} \, dx","Int[x^12*(a - b*x^4)^(1/4),x]","-\frac{3 a^2 x^5 \sqrt[4]{a-b x^4}}{280 b^2}-\frac{3 a^3 x \sqrt[4]{a-b x^4}}{112 b^3}-\frac{3 a^{7/2} x^3 \left(1-\frac{a}{b x^4}\right)^{3/4} F\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{112 b^{5/2} \left(a-b x^4\right)^{3/4}}+\frac{1}{14} x^{13} \sqrt[4]{a-b x^4}-\frac{a x^9 \sqrt[4]{a-b x^4}}{140 b}","-\frac{3 a^2 x^5 \sqrt[4]{a-b x^4}}{280 b^2}-\frac{3 a^3 x \sqrt[4]{a-b x^4}}{112 b^3}-\frac{3 a^{7/2} x^3 \left(1-\frac{a}{b x^4}\right)^{3/4} F\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{112 b^{5/2} \left(a-b x^4\right)^{3/4}}+\frac{1}{14} x^{13} \sqrt[4]{a-b x^4}-\frac{a x^9 \sqrt[4]{a-b x^4}}{140 b}",1,"(-3*a^3*x*(a - b*x^4)^(1/4))/(112*b^3) - (3*a^2*x^5*(a - b*x^4)^(1/4))/(280*b^2) - (a*x^9*(a - b*x^4)^(1/4))/(140*b) + (x^13*(a - b*x^4)^(1/4))/14 - (3*a^(7/2)*(1 - a/(b*x^4))^(3/4)*x^3*EllipticF[ArcCsc[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(112*b^(5/2)*(a - b*x^4)^(3/4))","A",8,6,16,0.3750,1,"{279, 321, 237, 335, 275, 232}"
1197,1,131,0,0.0638393,"\int x^8 \sqrt[4]{a-b x^4} \, dx","Int[x^8*(a - b*x^4)^(1/4),x]","-\frac{a^2 x \sqrt[4]{a-b x^4}}{24 b^2}-\frac{a^{5/2} x^3 \left(1-\frac{a}{b x^4}\right)^{3/4} F\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{24 b^{3/2} \left(a-b x^4\right)^{3/4}}+\frac{1}{10} x^9 \sqrt[4]{a-b x^4}-\frac{a x^5 \sqrt[4]{a-b x^4}}{60 b}","-\frac{a^2 x \sqrt[4]{a-b x^4}}{24 b^2}-\frac{a^{5/2} x^3 \left(1-\frac{a}{b x^4}\right)^{3/4} F\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{24 b^{3/2} \left(a-b x^4\right)^{3/4}}+\frac{1}{10} x^9 \sqrt[4]{a-b x^4}-\frac{a x^5 \sqrt[4]{a-b x^4}}{60 b}",1,"-(a^2*x*(a - b*x^4)^(1/4))/(24*b^2) - (a*x^5*(a - b*x^4)^(1/4))/(60*b) + (x^9*(a - b*x^4)^(1/4))/10 - (a^(5/2)*(1 - a/(b*x^4))^(3/4)*x^3*EllipticF[ArcCsc[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(24*b^(3/2)*(a - b*x^4)^(3/4))","A",7,6,16,0.3750,1,"{279, 321, 237, 335, 275, 232}"
1198,1,106,0,0.0467996,"\int x^4 \sqrt[4]{a-b x^4} \, dx","Int[x^4*(a - b*x^4)^(1/4),x]","-\frac{a^{3/2} x^3 \left(1-\frac{a}{b x^4}\right)^{3/4} F\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{12 \sqrt{b} \left(a-b x^4\right)^{3/4}}+\frac{1}{6} x^5 \sqrt[4]{a-b x^4}-\frac{a x \sqrt[4]{a-b x^4}}{12 b}","-\frac{a^{3/2} x^3 \left(1-\frac{a}{b x^4}\right)^{3/4} F\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{12 \sqrt{b} \left(a-b x^4\right)^{3/4}}+\frac{1}{6} x^5 \sqrt[4]{a-b x^4}-\frac{a x \sqrt[4]{a-b x^4}}{12 b}",1,"-(a*x*(a - b*x^4)^(1/4))/(12*b) + (x^5*(a - b*x^4)^(1/4))/6 - (a^(3/2)*(1 - a/(b*x^4))^(3/4)*x^3*EllipticF[ArcCsc[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(12*Sqrt[b]*(a - b*x^4)^(3/4))","A",6,6,16,0.3750,1,"{279, 321, 237, 335, 275, 232}"
1199,1,83,0,0.0326889,"\int \sqrt[4]{a-b x^4} \, dx","Int[(a - b*x^4)^(1/4),x]","\frac{1}{2} x \sqrt[4]{a-b x^4}-\frac{\sqrt{a} \sqrt{b} x^3 \left(1-\frac{a}{b x^4}\right)^{3/4} F\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{2 \left(a-b x^4\right)^{3/4}}","\frac{1}{2} x \sqrt[4]{a-b x^4}-\frac{\sqrt{a} \sqrt{b} x^3 \left(1-\frac{a}{b x^4}\right)^{3/4} F\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{2 \left(a-b x^4\right)^{3/4}}",1,"(x*(a - b*x^4)^(1/4))/2 - (Sqrt[a]*Sqrt[b]*(1 - a/(b*x^4))^(3/4)*x^3*EllipticF[ArcCsc[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(2*(a - b*x^4)^(3/4))","A",5,5,12,0.4167,1,"{195, 237, 335, 275, 232}"
1200,1,85,0,0.0339662,"\int \frac{\sqrt[4]{a-b x^4}}{x^4} \, dx","Int[(a - b*x^4)^(1/4)/x^4,x]","\frac{b^{3/2} x^3 \left(1-\frac{a}{b x^4}\right)^{3/4} F\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{3 \sqrt{a} \left(a-b x^4\right)^{3/4}}-\frac{\sqrt[4]{a-b x^4}}{3 x^3}","\frac{b^{3/2} x^3 \left(1-\frac{a}{b x^4}\right)^{3/4} F\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{3 \sqrt{a} \left(a-b x^4\right)^{3/4}}-\frac{\sqrt[4]{a-b x^4}}{3 x^3}",1,"-(a - b*x^4)^(1/4)/(3*x^3) + (b^(3/2)*(1 - a/(b*x^4))^(3/4)*x^3*EllipticF[ArcCsc[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(3*Sqrt[a]*(a - b*x^4)^(3/4))","A",5,5,16,0.3125,1,"{277, 237, 335, 275, 232}"
1201,1,108,0,0.0459606,"\int \frac{\sqrt[4]{a-b x^4}}{x^8} \, dx","Int[(a - b*x^4)^(1/4)/x^8,x]","\frac{2 b^{5/2} x^3 \left(1-\frac{a}{b x^4}\right)^{3/4} F\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{21 a^{3/2} \left(a-b x^4\right)^{3/4}}+\frac{b \sqrt[4]{a-b x^4}}{21 a x^3}-\frac{\sqrt[4]{a-b x^4}}{7 x^7}","\frac{2 b^{5/2} x^3 \left(1-\frac{a}{b x^4}\right)^{3/4} F\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{21 a^{3/2} \left(a-b x^4\right)^{3/4}}+\frac{b \sqrt[4]{a-b x^4}}{21 a x^3}-\frac{\sqrt[4]{a-b x^4}}{7 x^7}",1,"-(a - b*x^4)^(1/4)/(7*x^7) + (b*(a - b*x^4)^(1/4))/(21*a*x^3) + (2*b^(5/2)*(1 - a/(b*x^4))^(3/4)*x^3*EllipticF[ArcCsc[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(21*a^(3/2)*(a - b*x^4)^(3/4))","A",6,6,16,0.3750,1,"{277, 325, 237, 335, 275, 232}"
1202,1,133,0,0.0614957,"\int \frac{\sqrt[4]{a-b x^4}}{x^{12}} \, dx","Int[(a - b*x^4)^(1/4)/x^12,x]","\frac{2 b^2 \sqrt[4]{a-b x^4}}{77 a^2 x^3}+\frac{4 b^{7/2} x^3 \left(1-\frac{a}{b x^4}\right)^{3/4} F\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{77 a^{5/2} \left(a-b x^4\right)^{3/4}}+\frac{b \sqrt[4]{a-b x^4}}{77 a x^7}-\frac{\sqrt[4]{a-b x^4}}{11 x^{11}}","\frac{2 b^2 \sqrt[4]{a-b x^4}}{77 a^2 x^3}+\frac{4 b^{7/2} x^3 \left(1-\frac{a}{b x^4}\right)^{3/4} F\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{77 a^{5/2} \left(a-b x^4\right)^{3/4}}+\frac{b \sqrt[4]{a-b x^4}}{77 a x^7}-\frac{\sqrt[4]{a-b x^4}}{11 x^{11}}",1,"-(a - b*x^4)^(1/4)/(11*x^11) + (b*(a - b*x^4)^(1/4))/(77*a*x^7) + (2*b^2*(a - b*x^4)^(1/4))/(77*a^2*x^3) + (4*b^(7/2)*(1 - a/(b*x^4))^(3/4)*x^3*EllipticF[ArcCsc[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(77*a^(5/2)*(a - b*x^4)^(3/4))","A",7,6,16,0.3750,1,"{277, 325, 237, 335, 275, 232}"
1203,1,158,0,0.0778504,"\int \frac{\sqrt[4]{a-b x^4}}{x^{16}} \, dx","Int[(a - b*x^4)^(1/4)/x^16,x]","\frac{4 b^3 \sqrt[4]{a-b x^4}}{231 a^3 x^3}+\frac{2 b^2 \sqrt[4]{a-b x^4}}{231 a^2 x^7}+\frac{8 b^{9/2} x^3 \left(1-\frac{a}{b x^4}\right)^{3/4} F\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{231 a^{7/2} \left(a-b x^4\right)^{3/4}}+\frac{b \sqrt[4]{a-b x^4}}{165 a x^{11}}-\frac{\sqrt[4]{a-b x^4}}{15 x^{15}}","\frac{4 b^3 \sqrt[4]{a-b x^4}}{231 a^3 x^3}+\frac{2 b^2 \sqrt[4]{a-b x^4}}{231 a^2 x^7}+\frac{8 b^{9/2} x^3 \left(1-\frac{a}{b x^4}\right)^{3/4} F\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{231 a^{7/2} \left(a-b x^4\right)^{3/4}}+\frac{b \sqrt[4]{a-b x^4}}{165 a x^{11}}-\frac{\sqrt[4]{a-b x^4}}{15 x^{15}}",1,"-(a - b*x^4)^(1/4)/(15*x^15) + (b*(a - b*x^4)^(1/4))/(165*a*x^11) + (2*b^2*(a - b*x^4)^(1/4))/(231*a^2*x^7) + (4*b^3*(a - b*x^4)^(1/4))/(231*a^3*x^3) + (8*b^(9/2)*(1 - a/(b*x^4))^(3/4)*x^3*EllipticF[ArcCsc[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(231*a^(7/2)*(a - b*x^4)^(3/4))","A",8,6,16,0.3750,1,"{277, 325, 237, 335, 275, 232}"
1204,1,106,0,0.0571342,"\int \frac{x^{19}}{\sqrt[4]{a-b x^4}} \, dx","Int[x^19/(a - b*x^4)^(1/4),x]","-\frac{6 a^2 \left(a-b x^4\right)^{11/4}}{11 b^5}+\frac{4 a^3 \left(a-b x^4\right)^{7/4}}{7 b^5}-\frac{a^4 \left(a-b x^4\right)^{3/4}}{3 b^5}-\frac{\left(a-b x^4\right)^{19/4}}{19 b^5}+\frac{4 a \left(a-b x^4\right)^{15/4}}{15 b^5}","-\frac{6 a^2 \left(a-b x^4\right)^{11/4}}{11 b^5}+\frac{4 a^3 \left(a-b x^4\right)^{7/4}}{7 b^5}-\frac{a^4 \left(a-b x^4\right)^{3/4}}{3 b^5}-\frac{\left(a-b x^4\right)^{19/4}}{19 b^5}+\frac{4 a \left(a-b x^4\right)^{15/4}}{15 b^5}",1,"-(a^4*(a - b*x^4)^(3/4))/(3*b^5) + (4*a^3*(a - b*x^4)^(7/4))/(7*b^5) - (6*a^2*(a - b*x^4)^(11/4))/(11*b^5) + (4*a*(a - b*x^4)^(15/4))/(15*b^5) - (a - b*x^4)^(19/4)/(19*b^5)","A",3,2,16,0.1250,1,"{266, 43}"
1205,1,84,0,0.0460536,"\int \frac{x^{15}}{\sqrt[4]{a-b x^4}} \, dx","Int[x^15/(a - b*x^4)^(1/4),x]","\frac{3 a^2 \left(a-b x^4\right)^{7/4}}{7 b^4}-\frac{a^3 \left(a-b x^4\right)^{3/4}}{3 b^4}+\frac{\left(a-b x^4\right)^{15/4}}{15 b^4}-\frac{3 a \left(a-b x^4\right)^{11/4}}{11 b^4}","\frac{3 a^2 \left(a-b x^4\right)^{7/4}}{7 b^4}-\frac{a^3 \left(a-b x^4\right)^{3/4}}{3 b^4}+\frac{\left(a-b x^4\right)^{15/4}}{15 b^4}-\frac{3 a \left(a-b x^4\right)^{11/4}}{11 b^4}",1,"-(a^3*(a - b*x^4)^(3/4))/(3*b^4) + (3*a^2*(a - b*x^4)^(7/4))/(7*b^4) - (3*a*(a - b*x^4)^(11/4))/(11*b^4) + (a - b*x^4)^(15/4)/(15*b^4)","A",3,2,16,0.1250,1,"{266, 43}"
1206,1,62,0,0.0337152,"\int \frac{x^{11}}{\sqrt[4]{a-b x^4}} \, dx","Int[x^11/(a - b*x^4)^(1/4),x]","-\frac{a^2 \left(a-b x^4\right)^{3/4}}{3 b^3}-\frac{\left(a-b x^4\right)^{11/4}}{11 b^3}+\frac{2 a \left(a-b x^4\right)^{7/4}}{7 b^3}","-\frac{a^2 \left(a-b x^4\right)^{3/4}}{3 b^3}-\frac{\left(a-b x^4\right)^{11/4}}{11 b^3}+\frac{2 a \left(a-b x^4\right)^{7/4}}{7 b^3}",1,"-(a^2*(a - b*x^4)^(3/4))/(3*b^3) + (2*a*(a - b*x^4)^(7/4))/(7*b^3) - (a - b*x^4)^(11/4)/(11*b^3)","A",3,2,16,0.1250,1,"{266, 43}"
1207,1,40,0,0.0225616,"\int \frac{x^7}{\sqrt[4]{a-b x^4}} \, dx","Int[x^7/(a - b*x^4)^(1/4),x]","\frac{\left(a-b x^4\right)^{7/4}}{7 b^2}-\frac{a \left(a-b x^4\right)^{3/4}}{3 b^2}","\frac{\left(a-b x^4\right)^{7/4}}{7 b^2}-\frac{a \left(a-b x^4\right)^{3/4}}{3 b^2}",1,"-(a*(a - b*x^4)^(3/4))/(3*b^2) + (a - b*x^4)^(7/4)/(7*b^2)","A",3,2,16,0.1250,1,"{266, 43}"
1208,1,19,0,0.0041099,"\int \frac{x^3}{\sqrt[4]{a-b x^4}} \, dx","Int[x^3/(a - b*x^4)^(1/4),x]","-\frac{\left(a-b x^4\right)^{3/4}}{3 b}","-\frac{\left(a-b x^4\right)^{3/4}}{3 b}",1,"-(a - b*x^4)^(3/4)/(3*b)","A",1,1,16,0.06250,1,"{261}"
1209,1,57,0,0.0347115,"\int \frac{1}{x \sqrt[4]{a-b x^4}} \, dx","Int[1/(x*(a - b*x^4)^(1/4)),x]","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a-b x^4}}{\sqrt[4]{a}}\right)}{2 \sqrt[4]{a}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a-b x^4}}{\sqrt[4]{a}}\right)}{2 \sqrt[4]{a}}","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a-b x^4}}{\sqrt[4]{a}}\right)}{2 \sqrt[4]{a}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a-b x^4}}{\sqrt[4]{a}}\right)}{2 \sqrt[4]{a}}",1,"ArcTan[(a - b*x^4)^(1/4)/a^(1/4)]/(2*a^(1/4)) - ArcTanh[(a - b*x^4)^(1/4)/a^(1/4)]/(2*a^(1/4))","A",5,5,16,0.3125,1,"{266, 63, 298, 203, 206}"
1210,1,81,0,0.0473019,"\int \frac{1}{x^5 \sqrt[4]{a-b x^4}} \, dx","Int[1/(x^5*(a - b*x^4)^(1/4)),x]","\frac{b \tan ^{-1}\left(\frac{\sqrt[4]{a-b x^4}}{\sqrt[4]{a}}\right)}{8 a^{5/4}}-\frac{b \tanh ^{-1}\left(\frac{\sqrt[4]{a-b x^4}}{\sqrt[4]{a}}\right)}{8 a^{5/4}}-\frac{\left(a-b x^4\right)^{3/4}}{4 a x^4}","\frac{b \tan ^{-1}\left(\frac{\sqrt[4]{a-b x^4}}{\sqrt[4]{a}}\right)}{8 a^{5/4}}-\frac{b \tanh ^{-1}\left(\frac{\sqrt[4]{a-b x^4}}{\sqrt[4]{a}}\right)}{8 a^{5/4}}-\frac{\left(a-b x^4\right)^{3/4}}{4 a x^4}",1,"-(a - b*x^4)^(3/4)/(4*a*x^4) + (b*ArcTan[(a - b*x^4)^(1/4)/a^(1/4)])/(8*a^(5/4)) - (b*ArcTanh[(a - b*x^4)^(1/4)/a^(1/4)])/(8*a^(5/4))","A",6,6,16,0.3750,1,"{266, 51, 63, 298, 203, 206}"
1211,1,108,0,0.0612817,"\int \frac{1}{x^9 \sqrt[4]{a-b x^4}} \, dx","Int[1/(x^9*(a - b*x^4)^(1/4)),x]","\frac{5 b^2 \tan ^{-1}\left(\frac{\sqrt[4]{a-b x^4}}{\sqrt[4]{a}}\right)}{64 a^{9/4}}-\frac{5 b^2 \tanh ^{-1}\left(\frac{\sqrt[4]{a-b x^4}}{\sqrt[4]{a}}\right)}{64 a^{9/4}}-\frac{5 b \left(a-b x^4\right)^{3/4}}{32 a^2 x^4}-\frac{\left(a-b x^4\right)^{3/4}}{8 a x^8}","\frac{5 b^2 \tan ^{-1}\left(\frac{\sqrt[4]{a-b x^4}}{\sqrt[4]{a}}\right)}{64 a^{9/4}}-\frac{5 b^2 \tanh ^{-1}\left(\frac{\sqrt[4]{a-b x^4}}{\sqrt[4]{a}}\right)}{64 a^{9/4}}-\frac{5 b \left(a-b x^4\right)^{3/4}}{32 a^2 x^4}-\frac{\left(a-b x^4\right)^{3/4}}{8 a x^8}",1,"-(a - b*x^4)^(3/4)/(8*a*x^8) - (5*b*(a - b*x^4)^(3/4))/(32*a^2*x^4) + (5*b^2*ArcTan[(a - b*x^4)^(1/4)/a^(1/4)])/(64*a^(9/4)) - (5*b^2*ArcTanh[(a - b*x^4)^(1/4)/a^(1/4)])/(64*a^(9/4))","A",7,6,16,0.3750,1,"{266, 51, 63, 298, 203, 206}"
1212,1,133,0,0.0846476,"\int \frac{x^{13}}{\sqrt[4]{a-b x^4}} \, dx","Int[x^13/(a - b*x^4)^(1/4),x]","-\frac{4 a^2 x^2 \left(a-b x^4\right)^{3/4}}{39 b^3}+\frac{8 a^{7/2} \sqrt[4]{1-\frac{b x^4}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{39 b^{7/2} \sqrt[4]{a-b x^4}}-\frac{10 a x^6 \left(a-b x^4\right)^{3/4}}{117 b^2}-\frac{x^{10} \left(a-b x^4\right)^{3/4}}{13 b}","-\frac{4 a^2 x^2 \left(a-b x^4\right)^{3/4}}{39 b^3}+\frac{8 a^{7/2} \sqrt[4]{1-\frac{b x^4}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{39 b^{7/2} \sqrt[4]{a-b x^4}}-\frac{10 a x^6 \left(a-b x^4\right)^{3/4}}{117 b^2}-\frac{x^{10} \left(a-b x^4\right)^{3/4}}{13 b}",1,"(-4*a^2*x^2*(a - b*x^4)^(3/4))/(39*b^3) - (10*a*x^6*(a - b*x^4)^(3/4))/(117*b^2) - (x^10*(a - b*x^4)^(3/4))/(13*b) + (8*a^(7/2)*(1 - (b*x^4)/a)^(1/4)*EllipticE[ArcSin[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(39*b^(7/2)*(a - b*x^4)^(1/4))","A",6,4,16,0.2500,1,"{275, 321, 229, 228}"
1213,1,108,0,0.0650337,"\int \frac{x^9}{\sqrt[4]{a-b x^4}} \, dx","Int[x^9/(a - b*x^4)^(1/4),x]","\frac{4 a^{5/2} \sqrt[4]{1-\frac{b x^4}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{15 b^{5/2} \sqrt[4]{a-b x^4}}-\frac{2 a x^2 \left(a-b x^4\right)^{3/4}}{15 b^2}-\frac{x^6 \left(a-b x^4\right)^{3/4}}{9 b}","\frac{4 a^{5/2} \sqrt[4]{1-\frac{b x^4}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{15 b^{5/2} \sqrt[4]{a-b x^4}}-\frac{2 a x^2 \left(a-b x^4\right)^{3/4}}{15 b^2}-\frac{x^6 \left(a-b x^4\right)^{3/4}}{9 b}",1,"(-2*a*x^2*(a - b*x^4)^(3/4))/(15*b^2) - (x^6*(a - b*x^4)^(3/4))/(9*b) + (4*a^(5/2)*(1 - (b*x^4)/a)^(1/4)*EllipticE[ArcSin[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(15*b^(5/2)*(a - b*x^4)^(1/4))","A",5,4,16,0.2500,1,"{275, 321, 229, 228}"
1214,1,85,0,0.046735,"\int \frac{x^5}{\sqrt[4]{a-b x^4}} \, dx","Int[x^5/(a - b*x^4)^(1/4),x]","\frac{2 a^{3/2} \sqrt[4]{1-\frac{b x^4}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{5 b^{3/2} \sqrt[4]{a-b x^4}}-\frac{x^2 \left(a-b x^4\right)^{3/4}}{5 b}","\frac{2 a^{3/2} \sqrt[4]{1-\frac{b x^4}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{5 b^{3/2} \sqrt[4]{a-b x^4}}-\frac{x^2 \left(a-b x^4\right)^{3/4}}{5 b}",1,"-(x^2*(a - b*x^4)^(3/4))/(5*b) + (2*a^(3/2)*(1 - (b*x^4)/a)^(1/4)*EllipticE[ArcSin[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(5*b^(3/2)*(a - b*x^4)^(1/4))","A",4,4,16,0.2500,1,"{275, 321, 229, 228}"
1215,1,59,0,0.0300433,"\int \frac{x}{\sqrt[4]{a-b x^4}} \, dx","Int[x/(a - b*x^4)^(1/4),x]","\frac{\sqrt{a} \sqrt[4]{1-\frac{b x^4}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{\sqrt{b} \sqrt[4]{a-b x^4}}","\frac{\sqrt{a} \sqrt[4]{1-\frac{b x^4}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{\sqrt{b} \sqrt[4]{a-b x^4}}",1,"(Sqrt[a]*(1 - (b*x^4)/a)^(1/4)*EllipticE[ArcSin[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(Sqrt[b]*(a - b*x^4)^(1/4))","A",3,3,14,0.2143,1,"{275, 229, 228}"
1216,1,85,0,0.0495269,"\int \frac{1}{x^3 \sqrt[4]{a-b x^4}} \, dx","Int[1/(x^3*(a - b*x^4)^(1/4)),x]","-\frac{\left(a-b x^4\right)^{3/4}}{2 a x^2}-\frac{\sqrt{b} \sqrt[4]{1-\frac{b x^4}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{2 \sqrt{a} \sqrt[4]{a-b x^4}}","-\frac{\left(a-b x^4\right)^{3/4}}{2 a x^2}-\frac{\sqrt{b} \sqrt[4]{1-\frac{b x^4}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{2 \sqrt{a} \sqrt[4]{a-b x^4}}",1,"-(a - b*x^4)^(3/4)/(2*a*x^2) - (Sqrt[b]*(1 - (b*x^4)/a)^(1/4)*EllipticE[ArcSin[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(2*Sqrt[a]*(a - b*x^4)^(1/4))","A",4,4,16,0.2500,1,"{275, 325, 229, 228}"
1217,1,108,0,0.0659651,"\int \frac{1}{x^7 \sqrt[4]{a-b x^4}} \, dx","Int[1/(x^7*(a - b*x^4)^(1/4)),x]","-\frac{b^{3/2} \sqrt[4]{1-\frac{b x^4}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{4 a^{3/2} \sqrt[4]{a-b x^4}}-\frac{b \left(a-b x^4\right)^{3/4}}{4 a^2 x^2}-\frac{\left(a-b x^4\right)^{3/4}}{6 a x^6}","-\frac{b^{3/2} \sqrt[4]{1-\frac{b x^4}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{4 a^{3/2} \sqrt[4]{a-b x^4}}-\frac{b \left(a-b x^4\right)^{3/4}}{4 a^2 x^2}-\frac{\left(a-b x^4\right)^{3/4}}{6 a x^6}",1,"-(a - b*x^4)^(3/4)/(6*a*x^6) - (b*(a - b*x^4)^(3/4))/(4*a^2*x^2) - (b^(3/2)*(1 - (b*x^4)/a)^(1/4)*EllipticE[ArcSin[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(4*a^(3/2)*(a - b*x^4)^(1/4))","A",5,4,16,0.2500,1,"{275, 325, 229, 228}"
1218,1,133,0,0.0854562,"\int \frac{1}{x^{11} \sqrt[4]{a-b x^4}} \, dx","Int[1/(x^11*(a - b*x^4)^(1/4)),x]","-\frac{7 b^2 \left(a-b x^4\right)^{3/4}}{40 a^3 x^2}-\frac{7 b^{5/2} \sqrt[4]{1-\frac{b x^4}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{40 a^{5/2} \sqrt[4]{a-b x^4}}-\frac{7 b \left(a-b x^4\right)^{3/4}}{60 a^2 x^6}-\frac{\left(a-b x^4\right)^{3/4}}{10 a x^{10}}","-\frac{7 b^2 \left(a-b x^4\right)^{3/4}}{40 a^3 x^2}-\frac{7 b^{5/2} \sqrt[4]{1-\frac{b x^4}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{40 a^{5/2} \sqrt[4]{a-b x^4}}-\frac{7 b \left(a-b x^4\right)^{3/4}}{60 a^2 x^6}-\frac{\left(a-b x^4\right)^{3/4}}{10 a x^{10}}",1,"-(a - b*x^4)^(3/4)/(10*a*x^10) - (7*b*(a - b*x^4)^(3/4))/(60*a^2*x^6) - (7*b^2*(a - b*x^4)^(3/4))/(40*a^3*x^2) - (7*b^(5/2)*(1 - (b*x^4)/a)^(1/4)*EllipticE[ArcSin[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(40*a^(5/2)*(a - b*x^4)^(1/4))","A",6,4,16,0.2500,1,"{275, 325, 229, 228}"
1219,1,264,0,0.135438,"\int \frac{x^8}{\sqrt[4]{a-b x^4}} \, dx","Int[x^8/(a - b*x^4)^(1/4),x]","-\frac{5 a^2 \log \left(\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{128 \sqrt{2} b^{9/4}}+\frac{5 a^2 \log \left(\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}+\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{128 \sqrt{2} b^{9/4}}-\frac{5 a^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}\right)}{64 \sqrt{2} b^{9/4}}+\frac{5 a^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{64 \sqrt{2} b^{9/4}}-\frac{5 a x \left(a-b x^4\right)^{3/4}}{32 b^2}-\frac{x^5 \left(a-b x^4\right)^{3/4}}{8 b}","-\frac{5 a^2 \log \left(\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{128 \sqrt{2} b^{9/4}}+\frac{5 a^2 \log \left(\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}+\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{128 \sqrt{2} b^{9/4}}-\frac{5 a^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}\right)}{64 \sqrt{2} b^{9/4}}+\frac{5 a^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{64 \sqrt{2} b^{9/4}}-\frac{5 a x \left(a-b x^4\right)^{3/4}}{32 b^2}-\frac{x^5 \left(a-b x^4\right)^{3/4}}{8 b}",1,"(-5*a*x*(a - b*x^4)^(3/4))/(32*b^2) - (x^5*(a - b*x^4)^(3/4))/(8*b) - (5*a^2*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/(a - b*x^4)^(1/4)])/(64*Sqrt[2]*b^(9/4)) + (5*a^2*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/(a - b*x^4)^(1/4)])/(64*Sqrt[2]*b^(9/4)) - (5*a^2*Log[1 + (Sqrt[b]*x^2)/Sqrt[a - b*x^4] - (Sqrt[2]*b^(1/4)*x)/(a - b*x^4)^(1/4)])/(128*Sqrt[2]*b^(9/4)) + (5*a^2*Log[1 + (Sqrt[b]*x^2)/Sqrt[a - b*x^4] + (Sqrt[2]*b^(1/4)*x)/(a - b*x^4)^(1/4)])/(128*Sqrt[2]*b^(9/4))","A",12,8,16,0.5000,1,"{321, 240, 211, 1165, 628, 1162, 617, 204}"
1220,1,233,0,0.1093681,"\int \frac{x^4}{\sqrt[4]{a-b x^4}} \, dx","Int[x^4/(a - b*x^4)^(1/4),x]","-\frac{a \log \left(\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{16 \sqrt{2} b^{5/4}}+\frac{a \log \left(\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}+\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{16 \sqrt{2} b^{5/4}}-\frac{a \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}\right)}{8 \sqrt{2} b^{5/4}}+\frac{a \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{8 \sqrt{2} b^{5/4}}-\frac{x \left(a-b x^4\right)^{3/4}}{4 b}","-\frac{a \log \left(\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{16 \sqrt{2} b^{5/4}}+\frac{a \log \left(\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}+\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{16 \sqrt{2} b^{5/4}}-\frac{a \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}\right)}{8 \sqrt{2} b^{5/4}}+\frac{a \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{8 \sqrt{2} b^{5/4}}-\frac{x \left(a-b x^4\right)^{3/4}}{4 b}",1,"-(x*(a - b*x^4)^(3/4))/(4*b) - (a*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/(a - b*x^4)^(1/4)])/(8*Sqrt[2]*b^(5/4)) + (a*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/(a - b*x^4)^(1/4)])/(8*Sqrt[2]*b^(5/4)) - (a*Log[1 + (Sqrt[b]*x^2)/Sqrt[a - b*x^4] - (Sqrt[2]*b^(1/4)*x)/(a - b*x^4)^(1/4)])/(16*Sqrt[2]*b^(5/4)) + (a*Log[1 + (Sqrt[b]*x^2)/Sqrt[a - b*x^4] + (Sqrt[2]*b^(1/4)*x)/(a - b*x^4)^(1/4)])/(16*Sqrt[2]*b^(5/4))","A",11,8,16,0.5000,1,"{321, 240, 211, 1165, 628, 1162, 617, 204}"
1221,1,209,0,0.0872729,"\int \frac{1}{\sqrt[4]{a-b x^4}} \, dx","Int[(a - b*x^4)^(-1/4),x]","-\frac{\log \left(\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{4 \sqrt{2} \sqrt[4]{b}}+\frac{\log \left(\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}+\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{4 \sqrt{2} \sqrt[4]{b}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}\right)}{2 \sqrt{2} \sqrt[4]{b}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{2 \sqrt{2} \sqrt[4]{b}}","-\frac{\log \left(\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{4 \sqrt{2} \sqrt[4]{b}}+\frac{\log \left(\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}+\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{4 \sqrt{2} \sqrt[4]{b}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}\right)}{2 \sqrt{2} \sqrt[4]{b}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{2 \sqrt{2} \sqrt[4]{b}}",1,"-ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/(a - b*x^4)^(1/4)]/(2*Sqrt[2]*b^(1/4)) + ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/(a - b*x^4)^(1/4)]/(2*Sqrt[2]*b^(1/4)) - Log[1 + (Sqrt[b]*x^2)/Sqrt[a - b*x^4] - (Sqrt[2]*b^(1/4)*x)/(a - b*x^4)^(1/4)]/(4*Sqrt[2]*b^(1/4)) + Log[1 + (Sqrt[b]*x^2)/Sqrt[a - b*x^4] + (Sqrt[2]*b^(1/4)*x)/(a - b*x^4)^(1/4)]/(4*Sqrt[2]*b^(1/4))","A",10,7,12,0.5833,1,"{240, 211, 1165, 628, 1162, 617, 204}"
1222,1,22,0,0.0046507,"\int \frac{1}{x^4 \sqrt[4]{a-b x^4}} \, dx","Int[1/(x^4*(a - b*x^4)^(1/4)),x]","-\frac{\left(a-b x^4\right)^{3/4}}{3 a x^3}","-\frac{\left(a-b x^4\right)^{3/4}}{3 a x^3}",1,"-(a - b*x^4)^(3/4)/(3*a*x^3)","A",1,1,16,0.06250,1,"{264}"
1223,1,46,0,0.0105069,"\int \frac{1}{x^8 \sqrt[4]{a-b x^4}} \, dx","Int[1/(x^8*(a - b*x^4)^(1/4)),x]","-\frac{4 b \left(a-b x^4\right)^{3/4}}{21 a^2 x^3}-\frac{\left(a-b x^4\right)^{3/4}}{7 a x^7}","-\frac{4 b \left(a-b x^4\right)^{3/4}}{21 a^2 x^3}-\frac{\left(a-b x^4\right)^{3/4}}{7 a x^7}",1,"-(a - b*x^4)^(3/4)/(7*a*x^7) - (4*b*(a - b*x^4)^(3/4))/(21*a^2*x^3)","A",2,2,16,0.1250,1,"{271, 264}"
1224,1,71,0,0.018884,"\int \frac{1}{x^{12} \sqrt[4]{a-b x^4}} \, dx","Int[1/(x^12*(a - b*x^4)^(1/4)),x]","-\frac{32 b^2 \left(a-b x^4\right)^{3/4}}{231 a^3 x^3}-\frac{8 b \left(a-b x^4\right)^{3/4}}{77 a^2 x^7}-\frac{\left(a-b x^4\right)^{3/4}}{11 a x^{11}}","-\frac{32 b^2 \left(a-b x^4\right)^{3/4}}{231 a^3 x^3}-\frac{8 b \left(a-b x^4\right)^{3/4}}{77 a^2 x^7}-\frac{\left(a-b x^4\right)^{3/4}}{11 a x^{11}}",1,"-(a - b*x^4)^(3/4)/(11*a*x^11) - (8*b*(a - b*x^4)^(3/4))/(77*a^2*x^7) - (32*b^2*(a - b*x^4)^(3/4))/(231*a^3*x^3)","A",3,2,16,0.1250,1,"{271, 264}"
1225,1,96,0,0.0283588,"\int \frac{1}{x^{16} \sqrt[4]{a-b x^4}} \, dx","Int[1/(x^16*(a - b*x^4)^(1/4)),x]","-\frac{128 b^3 \left(a-b x^4\right)^{3/4}}{1155 a^4 x^3}-\frac{32 b^2 \left(a-b x^4\right)^{3/4}}{385 a^3 x^7}-\frac{4 b \left(a-b x^4\right)^{3/4}}{55 a^2 x^{11}}-\frac{\left(a-b x^4\right)^{3/4}}{15 a x^{15}}","-\frac{128 b^3 \left(a-b x^4\right)^{3/4}}{1155 a^4 x^3}-\frac{32 b^2 \left(a-b x^4\right)^{3/4}}{385 a^3 x^7}-\frac{4 b \left(a-b x^4\right)^{3/4}}{55 a^2 x^{11}}-\frac{\left(a-b x^4\right)^{3/4}}{15 a x^{15}}",1,"-(a - b*x^4)^(3/4)/(15*a*x^15) - (4*b*(a - b*x^4)^(3/4))/(55*a^2*x^11) - (32*b^2*(a - b*x^4)^(3/4))/(385*a^3*x^7) - (128*b^3*(a - b*x^4)^(3/4))/(1155*a^4*x^3)","A",4,2,16,0.1250,1,"{271, 264}"
1226,1,121,0,0.0411944,"\int \frac{1}{x^{20} \sqrt[4]{a-b x^4}} \, dx","Int[1/(x^20*(a - b*x^4)^(1/4)),x]","-\frac{2048 b^4 \left(a-b x^4\right)^{3/4}}{21945 a^5 x^3}-\frac{512 b^3 \left(a-b x^4\right)^{3/4}}{7315 a^4 x^7}-\frac{64 b^2 \left(a-b x^4\right)^{3/4}}{1045 a^3 x^{11}}-\frac{16 b \left(a-b x^4\right)^{3/4}}{285 a^2 x^{15}}-\frac{\left(a-b x^4\right)^{3/4}}{19 a x^{19}}","-\frac{2048 b^4 \left(a-b x^4\right)^{3/4}}{21945 a^5 x^3}-\frac{512 b^3 \left(a-b x^4\right)^{3/4}}{7315 a^4 x^7}-\frac{64 b^2 \left(a-b x^4\right)^{3/4}}{1045 a^3 x^{11}}-\frac{16 b \left(a-b x^4\right)^{3/4}}{285 a^2 x^{15}}-\frac{\left(a-b x^4\right)^{3/4}}{19 a x^{19}}",1,"-(a - b*x^4)^(3/4)/(19*a*x^19) - (16*b*(a - b*x^4)^(3/4))/(285*a^2*x^15) - (64*b^2*(a - b*x^4)^(3/4))/(1045*a^3*x^11) - (512*b^3*(a - b*x^4)^(3/4))/(7315*a^4*x^7) - (2048*b^4*(a - b*x^4)^(3/4))/(21945*a^5*x^3)","A",5,2,16,0.1250,1,"{271, 264}"
1227,1,134,0,0.0614109,"\int \frac{x^{10}}{\sqrt[4]{a-b x^4}} \, dx","Int[x^10/(a - b*x^4)^(1/4),x]","-\frac{7 a^2 \left(a-b x^4\right)^{3/4}}{40 b^3 x}+\frac{7 a^{5/2} x \sqrt[4]{1-\frac{a}{b x^4}} E\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{40 b^{5/2} \sqrt[4]{a-b x^4}}-\frac{7 a x^3 \left(a-b x^4\right)^{3/4}}{60 b^2}-\frac{x^7 \left(a-b x^4\right)^{3/4}}{10 b}","-\frac{7 a^2 \left(a-b x^4\right)^{3/4}}{40 b^3 x}+\frac{7 a^{5/2} x \sqrt[4]{1-\frac{a}{b x^4}} E\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{40 b^{5/2} \sqrt[4]{a-b x^4}}-\frac{7 a x^3 \left(a-b x^4\right)^{3/4}}{60 b^2}-\frac{x^7 \left(a-b x^4\right)^{3/4}}{10 b}",1,"(-7*a^2*(a - b*x^4)^(3/4))/(40*b^3*x) - (7*a*x^3*(a - b*x^4)^(3/4))/(60*b^2) - (x^7*(a - b*x^4)^(3/4))/(10*b) + (7*a^(5/2)*(1 - a/(b*x^4))^(1/4)*x*EllipticE[ArcCsc[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(40*b^(5/2)*(a - b*x^4)^(1/4))","A",7,6,16,0.3750,1,"{321, 311, 313, 335, 275, 228}"
1228,1,109,0,0.047434,"\int \frac{x^6}{\sqrt[4]{a-b x^4}} \, dx","Int[x^6/(a - b*x^4)^(1/4),x]","\frac{a^{3/2} x \sqrt[4]{1-\frac{a}{b x^4}} E\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{4 b^{3/2} \sqrt[4]{a-b x^4}}-\frac{a \left(a-b x^4\right)^{3/4}}{4 b^2 x}-\frac{x^3 \left(a-b x^4\right)^{3/4}}{6 b}","\frac{a^{3/2} x \sqrt[4]{1-\frac{a}{b x^4}} E\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{4 b^{3/2} \sqrt[4]{a-b x^4}}-\frac{a \left(a-b x^4\right)^{3/4}}{4 b^2 x}-\frac{x^3 \left(a-b x^4\right)^{3/4}}{6 b}",1,"-(a*(a - b*x^4)^(3/4))/(4*b^2*x) - (x^3*(a - b*x^4)^(3/4))/(6*b) + (a^(3/2)*(1 - a/(b*x^4))^(1/4)*x*EllipticE[ArcCsc[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(4*b^(3/2)*(a - b*x^4)^(1/4))","A",6,6,16,0.3750,1,"{321, 311, 313, 335, 275, 228}"
1229,1,86,0,0.0375278,"\int \frac{x^2}{\sqrt[4]{a-b x^4}} \, dx","Int[x^2/(a - b*x^4)^(1/4),x]","\frac{\sqrt{a} x \sqrt[4]{1-\frac{a}{b x^4}} E\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{2 \sqrt{b} \sqrt[4]{a-b x^4}}-\frac{\left(a-b x^4\right)^{3/4}}{2 b x}","\frac{\sqrt{a} x \sqrt[4]{1-\frac{a}{b x^4}} E\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{2 \sqrt{b} \sqrt[4]{a-b x^4}}-\frac{\left(a-b x^4\right)^{3/4}}{2 b x}",1,"-(a - b*x^4)^(3/4)/(2*b*x) + (Sqrt[a]*(1 - a/(b*x^4))^(1/4)*x*EllipticE[ArcCsc[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(2*Sqrt[b]*(a - b*x^4)^(1/4))","A",5,5,16,0.3125,1,"{311, 313, 335, 275, 228}"
1230,1,61,0,0.0280738,"\int \frac{1}{x^2 \sqrt[4]{a-b x^4}} \, dx","Int[1/(x^2*(a - b*x^4)^(1/4)),x]","-\frac{\sqrt{b} x \sqrt[4]{1-\frac{a}{b x^4}} E\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{\sqrt{a} \sqrt[4]{a-b x^4}}","-\frac{\sqrt{b} x \sqrt[4]{1-\frac{a}{b x^4}} E\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{\sqrt{a} \sqrt[4]{a-b x^4}}",1,"-((Sqrt[b]*(1 - a/(b*x^4))^(1/4)*x*EllipticE[ArcCsc[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(Sqrt[a]*(a - b*x^4)^(1/4)))","A",4,4,16,0.2500,1,"{313, 335, 275, 228}"
1231,1,86,0,0.0370405,"\int \frac{1}{x^6 \sqrt[4]{a-b x^4}} \, dx","Int[1/(x^6*(a - b*x^4)^(1/4)),x]","-\frac{2 b^{3/2} x \sqrt[4]{1-\frac{a}{b x^4}} E\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{5 a^{3/2} \sqrt[4]{a-b x^4}}-\frac{\left(a-b x^4\right)^{3/4}}{5 a x^5}","-\frac{2 b^{3/2} x \sqrt[4]{1-\frac{a}{b x^4}} E\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{5 a^{3/2} \sqrt[4]{a-b x^4}}-\frac{\left(a-b x^4\right)^{3/4}}{5 a x^5}",1,"-(a - b*x^4)^(3/4)/(5*a*x^5) - (2*b^(3/2)*(1 - a/(b*x^4))^(1/4)*x*EllipticE[ArcCsc[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(5*a^(3/2)*(a - b*x^4)^(1/4))","A",5,5,16,0.3125,1,"{325, 313, 335, 275, 228}"
1232,1,109,0,0.0487805,"\int \frac{1}{x^{10} \sqrt[4]{a-b x^4}} \, dx","Int[1/(x^10*(a - b*x^4)^(1/4)),x]","-\frac{4 b^{5/2} x \sqrt[4]{1-\frac{a}{b x^4}} E\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{15 a^{5/2} \sqrt[4]{a-b x^4}}-\frac{2 b \left(a-b x^4\right)^{3/4}}{15 a^2 x^5}-\frac{\left(a-b x^4\right)^{3/4}}{9 a x^9}","-\frac{4 b^{5/2} x \sqrt[4]{1-\frac{a}{b x^4}} E\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{15 a^{5/2} \sqrt[4]{a-b x^4}}-\frac{2 b \left(a-b x^4\right)^{3/4}}{15 a^2 x^5}-\frac{\left(a-b x^4\right)^{3/4}}{9 a x^9}",1,"-(a - b*x^4)^(3/4)/(9*a*x^9) - (2*b*(a - b*x^4)^(3/4))/(15*a^2*x^5) - (4*b^(5/2)*(1 - a/(b*x^4))^(1/4)*x*EllipticE[ArcCsc[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(15*a^(5/2)*(a - b*x^4)^(1/4))","A",6,5,16,0.3125,1,"{325, 313, 335, 275, 228}"
1233,1,134,0,0.0639307,"\int \frac{1}{x^{14} \sqrt[4]{a-b x^4}} \, dx","Int[1/(x^14*(a - b*x^4)^(1/4)),x]","-\frac{4 b^2 \left(a-b x^4\right)^{3/4}}{39 a^3 x^5}-\frac{8 b^{7/2} x \sqrt[4]{1-\frac{a}{b x^4}} E\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{39 a^{7/2} \sqrt[4]{a-b x^4}}-\frac{10 b \left(a-b x^4\right)^{3/4}}{117 a^2 x^9}-\frac{\left(a-b x^4\right)^{3/4}}{13 a x^{13}}","-\frac{4 b^2 \left(a-b x^4\right)^{3/4}}{39 a^3 x^5}-\frac{8 b^{7/2} x \sqrt[4]{1-\frac{a}{b x^4}} E\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{39 a^{7/2} \sqrt[4]{a-b x^4}}-\frac{10 b \left(a-b x^4\right)^{3/4}}{117 a^2 x^9}-\frac{\left(a-b x^4\right)^{3/4}}{13 a x^{13}}",1,"-(a - b*x^4)^(3/4)/(13*a*x^13) - (10*b*(a - b*x^4)^(3/4))/(117*a^2*x^9) - (4*b^2*(a - b*x^4)^(3/4))/(39*a^3*x^5) - (8*b^(7/2)*(1 - a/(b*x^4))^(1/4)*x*EllipticE[ArcCsc[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(39*a^(7/2)*(a - b*x^4)^(1/4))","A",7,5,16,0.3125,1,"{325, 313, 335, 275, 228}"
1234,1,104,0,0.0552531,"\int \frac{x^{19}}{\left(a-b x^4\right)^{3/4}} \, dx","Int[x^19/(a - b*x^4)^(3/4),x]","-\frac{2 a^2 \left(a-b x^4\right)^{9/4}}{3 b^5}+\frac{4 a^3 \left(a-b x^4\right)^{5/4}}{5 b^5}-\frac{a^4 \sqrt[4]{a-b x^4}}{b^5}-\frac{\left(a-b x^4\right)^{17/4}}{17 b^5}+\frac{4 a \left(a-b x^4\right)^{13/4}}{13 b^5}","-\frac{2 a^2 \left(a-b x^4\right)^{9/4}}{3 b^5}+\frac{4 a^3 \left(a-b x^4\right)^{5/4}}{5 b^5}-\frac{a^4 \sqrt[4]{a-b x^4}}{b^5}-\frac{\left(a-b x^4\right)^{17/4}}{17 b^5}+\frac{4 a \left(a-b x^4\right)^{13/4}}{13 b^5}",1,"-((a^4*(a - b*x^4)^(1/4))/b^5) + (4*a^3*(a - b*x^4)^(5/4))/(5*b^5) - (2*a^2*(a - b*x^4)^(9/4))/(3*b^5) + (4*a*(a - b*x^4)^(13/4))/(13*b^5) - (a - b*x^4)^(17/4)/(17*b^5)","A",3,2,16,0.1250,1,"{266, 43}"
1235,1,82,0,0.0461735,"\int \frac{x^{15}}{\left(a-b x^4\right)^{3/4}} \, dx","Int[x^15/(a - b*x^4)^(3/4),x]","\frac{3 a^2 \left(a-b x^4\right)^{5/4}}{5 b^4}-\frac{a^3 \sqrt[4]{a-b x^4}}{b^4}+\frac{\left(a-b x^4\right)^{13/4}}{13 b^4}-\frac{a \left(a-b x^4\right)^{9/4}}{3 b^4}","\frac{3 a^2 \left(a-b x^4\right)^{5/4}}{5 b^4}-\frac{a^3 \sqrt[4]{a-b x^4}}{b^4}+\frac{\left(a-b x^4\right)^{13/4}}{13 b^4}-\frac{a \left(a-b x^4\right)^{9/4}}{3 b^4}",1,"-((a^3*(a - b*x^4)^(1/4))/b^4) + (3*a^2*(a - b*x^4)^(5/4))/(5*b^4) - (a*(a - b*x^4)^(9/4))/(3*b^4) + (a - b*x^4)^(13/4)/(13*b^4)","A",3,2,16,0.1250,1,"{266, 43}"
1236,1,60,0,0.0335839,"\int \frac{x^{11}}{\left(a-b x^4\right)^{3/4}} \, dx","Int[x^11/(a - b*x^4)^(3/4),x]","-\frac{a^2 \sqrt[4]{a-b x^4}}{b^3}-\frac{\left(a-b x^4\right)^{9/4}}{9 b^3}+\frac{2 a \left(a-b x^4\right)^{5/4}}{5 b^3}","-\frac{a^2 \sqrt[4]{a-b x^4}}{b^3}-\frac{\left(a-b x^4\right)^{9/4}}{9 b^3}+\frac{2 a \left(a-b x^4\right)^{5/4}}{5 b^3}",1,"-((a^2*(a - b*x^4)^(1/4))/b^3) + (2*a*(a - b*x^4)^(5/4))/(5*b^3) - (a - b*x^4)^(9/4)/(9*b^3)","A",3,2,16,0.1250,1,"{266, 43}"
1237,1,38,0,0.0228438,"\int \frac{x^7}{\left(a-b x^4\right)^{3/4}} \, dx","Int[x^7/(a - b*x^4)^(3/4),x]","\frac{\left(a-b x^4\right)^{5/4}}{5 b^2}-\frac{a \sqrt[4]{a-b x^4}}{b^2}","\frac{\left(a-b x^4\right)^{5/4}}{5 b^2}-\frac{a \sqrt[4]{a-b x^4}}{b^2}",1,"-((a*(a - b*x^4)^(1/4))/b^2) + (a - b*x^4)^(5/4)/(5*b^2)","A",3,2,16,0.1250,1,"{266, 43}"
1238,1,17,0,0.0043918,"\int \frac{x^3}{\left(a-b x^4\right)^{3/4}} \, dx","Int[x^3/(a - b*x^4)^(3/4),x]","-\frac{\sqrt[4]{a-b x^4}}{b}","-\frac{\sqrt[4]{a-b x^4}}{b}",1,"-((a - b*x^4)^(1/4)/b)","A",1,1,16,0.06250,1,"{261}"
1239,1,57,0,0.0325523,"\int \frac{1}{x \left(a-b x^4\right)^{3/4}} \, dx","Int[1/(x*(a - b*x^4)^(3/4)),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a-b x^4}}{\sqrt[4]{a}}\right)}{2 a^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a-b x^4}}{\sqrt[4]{a}}\right)}{2 a^{3/4}}","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a-b x^4}}{\sqrt[4]{a}}\right)}{2 a^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a-b x^4}}{\sqrt[4]{a}}\right)}{2 a^{3/4}}",1,"-ArcTan[(a - b*x^4)^(1/4)/a^(1/4)]/(2*a^(3/4)) - ArcTanh[(a - b*x^4)^(1/4)/a^(1/4)]/(2*a^(3/4))","A",5,5,16,0.3125,1,"{266, 63, 212, 206, 203}"
1240,1,81,0,0.0446181,"\int \frac{1}{x^5 \left(a-b x^4\right)^{3/4}} \, dx","Int[1/(x^5*(a - b*x^4)^(3/4)),x]","-\frac{3 b \tan ^{-1}\left(\frac{\sqrt[4]{a-b x^4}}{\sqrt[4]{a}}\right)}{8 a^{7/4}}-\frac{3 b \tanh ^{-1}\left(\frac{\sqrt[4]{a-b x^4}}{\sqrt[4]{a}}\right)}{8 a^{7/4}}-\frac{\sqrt[4]{a-b x^4}}{4 a x^4}","-\frac{3 b \tan ^{-1}\left(\frac{\sqrt[4]{a-b x^4}}{\sqrt[4]{a}}\right)}{8 a^{7/4}}-\frac{3 b \tanh ^{-1}\left(\frac{\sqrt[4]{a-b x^4}}{\sqrt[4]{a}}\right)}{8 a^{7/4}}-\frac{\sqrt[4]{a-b x^4}}{4 a x^4}",1,"-(a - b*x^4)^(1/4)/(4*a*x^4) - (3*b*ArcTan[(a - b*x^4)^(1/4)/a^(1/4)])/(8*a^(7/4)) - (3*b*ArcTanh[(a - b*x^4)^(1/4)/a^(1/4)])/(8*a^(7/4))","A",6,6,16,0.3750,1,"{266, 51, 63, 212, 206, 203}"
1241,1,108,0,0.0590348,"\int \frac{1}{x^9 \left(a-b x^4\right)^{3/4}} \, dx","Int[1/(x^9*(a - b*x^4)^(3/4)),x]","-\frac{21 b^2 \tan ^{-1}\left(\frac{\sqrt[4]{a-b x^4}}{\sqrt[4]{a}}\right)}{64 a^{11/4}}-\frac{21 b^2 \tanh ^{-1}\left(\frac{\sqrt[4]{a-b x^4}}{\sqrt[4]{a}}\right)}{64 a^{11/4}}-\frac{7 b \sqrt[4]{a-b x^4}}{32 a^2 x^4}-\frac{\sqrt[4]{a-b x^4}}{8 a x^8}","-\frac{21 b^2 \tan ^{-1}\left(\frac{\sqrt[4]{a-b x^4}}{\sqrt[4]{a}}\right)}{64 a^{11/4}}-\frac{21 b^2 \tanh ^{-1}\left(\frac{\sqrt[4]{a-b x^4}}{\sqrt[4]{a}}\right)}{64 a^{11/4}}-\frac{7 b \sqrt[4]{a-b x^4}}{32 a^2 x^4}-\frac{\sqrt[4]{a-b x^4}}{8 a x^8}",1,"-(a - b*x^4)^(1/4)/(8*a*x^8) - (7*b*(a - b*x^4)^(1/4))/(32*a^2*x^4) - (21*b^2*ArcTan[(a - b*x^4)^(1/4)/a^(1/4)])/(64*a^(11/4)) - (21*b^2*ArcTanh[(a - b*x^4)^(1/4)/a^(1/4)])/(64*a^(11/4))","A",7,6,16,0.3750,1,"{266, 51, 63, 212, 206, 203}"
1242,1,133,0,0.085963,"\int \frac{x^{13}}{\left(a-b x^4\right)^{3/4}} \, dx","Int[x^13/(a - b*x^4)^(3/4),x]","-\frac{20 a^2 x^2 \sqrt[4]{a-b x^4}}{77 b^3}+\frac{40 a^{7/2} \left(1-\frac{b x^4}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{77 b^{7/2} \left(a-b x^4\right)^{3/4}}-\frac{10 a x^6 \sqrt[4]{a-b x^4}}{77 b^2}-\frac{x^{10} \sqrt[4]{a-b x^4}}{11 b}","-\frac{20 a^2 x^2 \sqrt[4]{a-b x^4}}{77 b^3}+\frac{40 a^{7/2} \left(1-\frac{b x^4}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{77 b^{7/2} \left(a-b x^4\right)^{3/4}}-\frac{10 a x^6 \sqrt[4]{a-b x^4}}{77 b^2}-\frac{x^{10} \sqrt[4]{a-b x^4}}{11 b}",1,"(-20*a^2*x^2*(a - b*x^4)^(1/4))/(77*b^3) - (10*a*x^6*(a - b*x^4)^(1/4))/(77*b^2) - (x^10*(a - b*x^4)^(1/4))/(11*b) + (40*a^(7/2)*(1 - (b*x^4)/a)^(3/4)*EllipticF[ArcSin[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(77*b^(7/2)*(a - b*x^4)^(3/4))","A",6,4,16,0.2500,1,"{275, 321, 233, 232}"
1243,1,108,0,0.0648372,"\int \frac{x^9}{\left(a-b x^4\right)^{3/4}} \, dx","Int[x^9/(a - b*x^4)^(3/4),x]","\frac{4 a^{5/2} \left(1-\frac{b x^4}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{7 b^{5/2} \left(a-b x^4\right)^{3/4}}-\frac{2 a x^2 \sqrt[4]{a-b x^4}}{7 b^2}-\frac{x^6 \sqrt[4]{a-b x^4}}{7 b}","\frac{4 a^{5/2} \left(1-\frac{b x^4}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{7 b^{5/2} \left(a-b x^4\right)^{3/4}}-\frac{2 a x^2 \sqrt[4]{a-b x^4}}{7 b^2}-\frac{x^6 \sqrt[4]{a-b x^4}}{7 b}",1,"(-2*a*x^2*(a - b*x^4)^(1/4))/(7*b^2) - (x^6*(a - b*x^4)^(1/4))/(7*b) + (4*a^(5/2)*(1 - (b*x^4)/a)^(3/4)*EllipticF[ArcSin[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(7*b^(5/2)*(a - b*x^4)^(3/4))","A",5,4,16,0.2500,1,"{275, 321, 233, 232}"
1244,1,85,0,0.0488086,"\int \frac{x^5}{\left(a-b x^4\right)^{3/4}} \, dx","Int[x^5/(a - b*x^4)^(3/4),x]","\frac{2 a^{3/2} \left(1-\frac{b x^4}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{3 b^{3/2} \left(a-b x^4\right)^{3/4}}-\frac{x^2 \sqrt[4]{a-b x^4}}{3 b}","\frac{2 a^{3/2} \left(1-\frac{b x^4}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{3 b^{3/2} \left(a-b x^4\right)^{3/4}}-\frac{x^2 \sqrt[4]{a-b x^4}}{3 b}",1,"-(x^2*(a - b*x^4)^(1/4))/(3*b) + (2*a^(3/2)*(1 - (b*x^4)/a)^(3/4)*EllipticF[ArcSin[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(3*b^(3/2)*(a - b*x^4)^(3/4))","A",4,4,16,0.2500,1,"{275, 321, 233, 232}"
1245,1,59,0,0.0318083,"\int \frac{x}{\left(a-b x^4\right)^{3/4}} \, dx","Int[x/(a - b*x^4)^(3/4),x]","\frac{\sqrt{a} \left(1-\frac{b x^4}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{\sqrt{b} \left(a-b x^4\right)^{3/4}}","\frac{\sqrt{a} \left(1-\frac{b x^4}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{\sqrt{b} \left(a-b x^4\right)^{3/4}}",1,"(Sqrt[a]*(1 - (b*x^4)/a)^(3/4)*EllipticF[ArcSin[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(Sqrt[b]*(a - b*x^4)^(3/4))","A",3,3,14,0.2143,1,"{275, 233, 232}"
1246,1,85,0,0.0463563,"\int \frac{1}{x^3 \left(a-b x^4\right)^{3/4}} \, dx","Int[1/(x^3*(a - b*x^4)^(3/4)),x]","\frac{\sqrt{b} \left(1-\frac{b x^4}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{2 \sqrt{a} \left(a-b x^4\right)^{3/4}}-\frac{\sqrt[4]{a-b x^4}}{2 a x^2}","\frac{\sqrt{b} \left(1-\frac{b x^4}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{2 \sqrt{a} \left(a-b x^4\right)^{3/4}}-\frac{\sqrt[4]{a-b x^4}}{2 a x^2}",1,"-(a - b*x^4)^(1/4)/(2*a*x^2) + (Sqrt[b]*(1 - (b*x^4)/a)^(3/4)*EllipticF[ArcSin[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(2*Sqrt[a]*(a - b*x^4)^(3/4))","A",4,4,16,0.2500,1,"{275, 325, 233, 232}"
1247,1,108,0,0.0675386,"\int \frac{1}{x^7 \left(a-b x^4\right)^{3/4}} \, dx","Int[1/(x^7*(a - b*x^4)^(3/4)),x]","\frac{5 b^{3/2} \left(1-\frac{b x^4}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{12 a^{3/2} \left(a-b x^4\right)^{3/4}}-\frac{5 b \sqrt[4]{a-b x^4}}{12 a^2 x^2}-\frac{\sqrt[4]{a-b x^4}}{6 a x^6}","\frac{5 b^{3/2} \left(1-\frac{b x^4}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{12 a^{3/2} \left(a-b x^4\right)^{3/4}}-\frac{5 b \sqrt[4]{a-b x^4}}{12 a^2 x^2}-\frac{\sqrt[4]{a-b x^4}}{6 a x^6}",1,"-(a - b*x^4)^(1/4)/(6*a*x^6) - (5*b*(a - b*x^4)^(1/4))/(12*a^2*x^2) + (5*b^(3/2)*(1 - (b*x^4)/a)^(3/4)*EllipticF[ArcSin[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(12*a^(3/2)*(a - b*x^4)^(3/4))","A",5,4,16,0.2500,1,"{275, 325, 233, 232}"
1248,1,133,0,0.0859719,"\int \frac{1}{x^{11} \left(a-b x^4\right)^{3/4}} \, dx","Int[1/(x^11*(a - b*x^4)^(3/4)),x]","-\frac{3 b^2 \sqrt[4]{a-b x^4}}{8 a^3 x^2}+\frac{3 b^{5/2} \left(1-\frac{b x^4}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{8 a^{5/2} \left(a-b x^4\right)^{3/4}}-\frac{3 b \sqrt[4]{a-b x^4}}{20 a^2 x^6}-\frac{\sqrt[4]{a-b x^4}}{10 a x^{10}}","-\frac{3 b^2 \sqrt[4]{a-b x^4}}{8 a^3 x^2}+\frac{3 b^{5/2} \left(1-\frac{b x^4}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{8 a^{5/2} \left(a-b x^4\right)^{3/4}}-\frac{3 b \sqrt[4]{a-b x^4}}{20 a^2 x^6}-\frac{\sqrt[4]{a-b x^4}}{10 a x^{10}}",1,"-(a - b*x^4)^(1/4)/(10*a*x^10) - (3*b*(a - b*x^4)^(1/4))/(20*a^2*x^6) - (3*b^2*(a - b*x^4)^(1/4))/(8*a^3*x^2) + (3*b^(5/2)*(1 - (b*x^4)/a)^(3/4)*EllipticF[ArcSin[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(8*a^(5/2)*(a - b*x^4)^(3/4))","A",6,4,16,0.2500,1,"{275, 325, 233, 232}"
1249,1,266,0,0.140351,"\int \frac{x^{10}}{\left(a-b x^4\right)^{3/4}} \, dx","Int[x^10/(a - b*x^4)^(3/4),x]","\frac{21 a^2 \log \left(\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{128 \sqrt{2} b^{11/4}}-\frac{21 a^2 \log \left(\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}+\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{128 \sqrt{2} b^{11/4}}-\frac{21 a^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}\right)}{64 \sqrt{2} b^{11/4}}+\frac{21 a^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{64 \sqrt{2} b^{11/4}}-\frac{7 a x^3 \sqrt[4]{a-b x^4}}{32 b^2}-\frac{x^7 \sqrt[4]{a-b x^4}}{8 b}","\frac{21 a^2 \log \left(\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{128 \sqrt{2} b^{11/4}}-\frac{21 a^2 \log \left(\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}+\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{128 \sqrt{2} b^{11/4}}-\frac{21 a^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}\right)}{64 \sqrt{2} b^{11/4}}+\frac{21 a^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{64 \sqrt{2} b^{11/4}}-\frac{7 a x^3 \sqrt[4]{a-b x^4}}{32 b^2}-\frac{x^7 \sqrt[4]{a-b x^4}}{8 b}",1,"(-7*a*x^3*(a - b*x^4)^(1/4))/(32*b^2) - (x^7*(a - b*x^4)^(1/4))/(8*b) - (21*a^2*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/(a - b*x^4)^(1/4)])/(64*Sqrt[2]*b^(11/4)) + (21*a^2*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/(a - b*x^4)^(1/4)])/(64*Sqrt[2]*b^(11/4)) + (21*a^2*Log[1 + (Sqrt[b]*x^2)/Sqrt[a - b*x^4] - (Sqrt[2]*b^(1/4)*x)/(a - b*x^4)^(1/4)])/(128*Sqrt[2]*b^(11/4)) - (21*a^2*Log[1 + (Sqrt[b]*x^2)/Sqrt[a - b*x^4] + (Sqrt[2]*b^(1/4)*x)/(a - b*x^4)^(1/4)])/(128*Sqrt[2]*b^(11/4))","A",12,8,16,0.5000,1,"{321, 331, 297, 1162, 617, 204, 1165, 628}"
1250,1,235,0,0.1095264,"\int \frac{x^6}{\left(a-b x^4\right)^{3/4}} \, dx","Int[x^6/(a - b*x^4)^(3/4),x]","\frac{3 a \log \left(\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{16 \sqrt{2} b^{7/4}}-\frac{3 a \log \left(\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}+\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{16 \sqrt{2} b^{7/4}}-\frac{3 a \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}\right)}{8 \sqrt{2} b^{7/4}}+\frac{3 a \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{8 \sqrt{2} b^{7/4}}-\frac{x^3 \sqrt[4]{a-b x^4}}{4 b}","\frac{3 a \log \left(\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{16 \sqrt{2} b^{7/4}}-\frac{3 a \log \left(\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}+\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{16 \sqrt{2} b^{7/4}}-\frac{3 a \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}\right)}{8 \sqrt{2} b^{7/4}}+\frac{3 a \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{8 \sqrt{2} b^{7/4}}-\frac{x^3 \sqrt[4]{a-b x^4}}{4 b}",1,"-(x^3*(a - b*x^4)^(1/4))/(4*b) - (3*a*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/(a - b*x^4)^(1/4)])/(8*Sqrt[2]*b^(7/4)) + (3*a*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/(a - b*x^4)^(1/4)])/(8*Sqrt[2]*b^(7/4)) + (3*a*Log[1 + (Sqrt[b]*x^2)/Sqrt[a - b*x^4] - (Sqrt[2]*b^(1/4)*x)/(a - b*x^4)^(1/4)])/(16*Sqrt[2]*b^(7/4)) - (3*a*Log[1 + (Sqrt[b]*x^2)/Sqrt[a - b*x^4] + (Sqrt[2]*b^(1/4)*x)/(a - b*x^4)^(1/4)])/(16*Sqrt[2]*b^(7/4))","A",11,8,16,0.5000,1,"{321, 331, 297, 1162, 617, 204, 1165, 628}"
1251,1,209,0,0.0877794,"\int \frac{x^2}{\left(a-b x^4\right)^{3/4}} \, dx","Int[x^2/(a - b*x^4)^(3/4),x]","\frac{\log \left(\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{4 \sqrt{2} b^{3/4}}-\frac{\log \left(\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}+\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{4 \sqrt{2} b^{3/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}\right)}{2 \sqrt{2} b^{3/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{2 \sqrt{2} b^{3/4}}","\frac{\log \left(\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{4 \sqrt{2} b^{3/4}}-\frac{\log \left(\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}+\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{4 \sqrt{2} b^{3/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}\right)}{2 \sqrt{2} b^{3/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)}{2 \sqrt{2} b^{3/4}}",1,"-ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/(a - b*x^4)^(1/4)]/(2*Sqrt[2]*b^(3/4)) + ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/(a - b*x^4)^(1/4)]/(2*Sqrt[2]*b^(3/4)) + Log[1 + (Sqrt[b]*x^2)/Sqrt[a - b*x^4] - (Sqrt[2]*b^(1/4)*x)/(a - b*x^4)^(1/4)]/(4*Sqrt[2]*b^(3/4)) - Log[1 + (Sqrt[b]*x^2)/Sqrt[a - b*x^4] + (Sqrt[2]*b^(1/4)*x)/(a - b*x^4)^(1/4)]/(4*Sqrt[2]*b^(3/4))","A",10,7,16,0.4375,1,"{331, 297, 1162, 617, 204, 1165, 628}"
1252,1,20,0,0.004762,"\int \frac{1}{x^2 \left(a-b x^4\right)^{3/4}} \, dx","Int[1/(x^2*(a - b*x^4)^(3/4)),x]","-\frac{\sqrt[4]{a-b x^4}}{a x}","-\frac{\sqrt[4]{a-b x^4}}{a x}",1,"-((a - b*x^4)^(1/4)/(a*x))","A",1,1,16,0.06250,1,"{264}"
1253,1,46,0,0.0115406,"\int \frac{1}{x^6 \left(a-b x^4\right)^{3/4}} \, dx","Int[1/(x^6*(a - b*x^4)^(3/4)),x]","-\frac{4 b \sqrt[4]{a-b x^4}}{5 a^2 x}-\frac{\sqrt[4]{a-b x^4}}{5 a x^5}","-\frac{4 b \sqrt[4]{a-b x^4}}{5 a^2 x}-\frac{\sqrt[4]{a-b x^4}}{5 a x^5}",1,"-(a - b*x^4)^(1/4)/(5*a*x^5) - (4*b*(a - b*x^4)^(1/4))/(5*a^2*x)","A",2,2,16,0.1250,1,"{271, 264}"
1254,1,71,0,0.0193996,"\int \frac{1}{x^{10} \left(a-b x^4\right)^{3/4}} \, dx","Int[1/(x^10*(a - b*x^4)^(3/4)),x]","-\frac{32 b^2 \sqrt[4]{a-b x^4}}{45 a^3 x}-\frac{8 b \sqrt[4]{a-b x^4}}{45 a^2 x^5}-\frac{\sqrt[4]{a-b x^4}}{9 a x^9}","-\frac{32 b^2 \sqrt[4]{a-b x^4}}{45 a^3 x}-\frac{8 b \sqrt[4]{a-b x^4}}{45 a^2 x^5}-\frac{\sqrt[4]{a-b x^4}}{9 a x^9}",1,"-(a - b*x^4)^(1/4)/(9*a*x^9) - (8*b*(a - b*x^4)^(1/4))/(45*a^2*x^5) - (32*b^2*(a - b*x^4)^(1/4))/(45*a^3*x)","A",3,2,16,0.1250,1,"{271, 264}"
1255,1,96,0,0.0295717,"\int \frac{1}{x^{14} \left(a-b x^4\right)^{3/4}} \, dx","Int[1/(x^14*(a - b*x^4)^(3/4)),x]","-\frac{128 b^3 \sqrt[4]{a-b x^4}}{195 a^4 x}-\frac{32 b^2 \sqrt[4]{a-b x^4}}{195 a^3 x^5}-\frac{4 b \sqrt[4]{a-b x^4}}{39 a^2 x^9}-\frac{\sqrt[4]{a-b x^4}}{13 a x^{13}}","-\frac{128 b^3 \sqrt[4]{a-b x^4}}{195 a^4 x}-\frac{32 b^2 \sqrt[4]{a-b x^4}}{195 a^3 x^5}-\frac{4 b \sqrt[4]{a-b x^4}}{39 a^2 x^9}-\frac{\sqrt[4]{a-b x^4}}{13 a x^{13}}",1,"-(a - b*x^4)^(1/4)/(13*a*x^13) - (4*b*(a - b*x^4)^(1/4))/(39*a^2*x^9) - (32*b^2*(a - b*x^4)^(1/4))/(195*a^3*x^5) - (128*b^3*(a - b*x^4)^(1/4))/(195*a^4*x)","A",4,2,16,0.1250,1,"{271, 264}"
1256,1,134,0,0.061248,"\int \frac{x^{12}}{\left(a-b x^4\right)^{3/4}} \, dx","Int[x^12/(a - b*x^4)^(3/4),x]","-\frac{3 a^2 x \sqrt[4]{a-b x^4}}{8 b^3}-\frac{3 a^{5/2} x^3 \left(1-\frac{a}{b x^4}\right)^{3/4} F\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{8 b^{5/2} \left(a-b x^4\right)^{3/4}}-\frac{3 a x^5 \sqrt[4]{a-b x^4}}{20 b^2}-\frac{x^9 \sqrt[4]{a-b x^4}}{10 b}","-\frac{3 a^2 x \sqrt[4]{a-b x^4}}{8 b^3}-\frac{3 a^{5/2} x^3 \left(1-\frac{a}{b x^4}\right)^{3/4} F\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{8 b^{5/2} \left(a-b x^4\right)^{3/4}}-\frac{3 a x^5 \sqrt[4]{a-b x^4}}{20 b^2}-\frac{x^9 \sqrt[4]{a-b x^4}}{10 b}",1,"(-3*a^2*x*(a - b*x^4)^(1/4))/(8*b^3) - (3*a*x^5*(a - b*x^4)^(1/4))/(20*b^2) - (x^9*(a - b*x^4)^(1/4))/(10*b) - (3*a^(5/2)*(1 - a/(b*x^4))^(3/4)*x^3*EllipticF[ArcCsc[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(8*b^(5/2)*(a - b*x^4)^(3/4))","A",7,5,16,0.3125,1,"{321, 237, 335, 275, 232}"
1257,1,109,0,0.0477997,"\int \frac{x^8}{\left(a-b x^4\right)^{3/4}} \, dx","Int[x^8/(a - b*x^4)^(3/4),x]","-\frac{5 a^{3/2} x^3 \left(1-\frac{a}{b x^4}\right)^{3/4} F\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{12 b^{3/2} \left(a-b x^4\right)^{3/4}}-\frac{5 a x \sqrt[4]{a-b x^4}}{12 b^2}-\frac{x^5 \sqrt[4]{a-b x^4}}{6 b}","-\frac{5 a^{3/2} x^3 \left(1-\frac{a}{b x^4}\right)^{3/4} F\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{12 b^{3/2} \left(a-b x^4\right)^{3/4}}-\frac{5 a x \sqrt[4]{a-b x^4}}{12 b^2}-\frac{x^5 \sqrt[4]{a-b x^4}}{6 b}",1,"(-5*a*x*(a - b*x^4)^(1/4))/(12*b^2) - (x^5*(a - b*x^4)^(1/4))/(6*b) - (5*a^(3/2)*(1 - a/(b*x^4))^(3/4)*x^3*EllipticF[ArcCsc[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(12*b^(3/2)*(a - b*x^4)^(3/4))","A",6,5,16,0.3125,1,"{321, 237, 335, 275, 232}"
1258,1,86,0,0.0356865,"\int \frac{x^4}{\left(a-b x^4\right)^{3/4}} \, dx","Int[x^4/(a - b*x^4)^(3/4),x]","-\frac{x \sqrt[4]{a-b x^4}}{2 b}-\frac{\sqrt{a} x^3 \left(1-\frac{a}{b x^4}\right)^{3/4} F\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{2 \sqrt{b} \left(a-b x^4\right)^{3/4}}","-\frac{x \sqrt[4]{a-b x^4}}{2 b}-\frac{\sqrt{a} x^3 \left(1-\frac{a}{b x^4}\right)^{3/4} F\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{2 \sqrt{b} \left(a-b x^4\right)^{3/4}}",1,"-(x*(a - b*x^4)^(1/4))/(2*b) - (Sqrt[a]*(1 - a/(b*x^4))^(3/4)*x^3*EllipticF[ArcCsc[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(2*Sqrt[b]*(a - b*x^4)^(3/4))","A",5,5,16,0.3125,1,"{321, 237, 335, 275, 232}"
1259,1,63,0,0.026208,"\int \frac{1}{\left(a-b x^4\right)^{3/4}} \, dx","Int[(a - b*x^4)^(-3/4),x]","-\frac{\sqrt{b} x^3 \left(1-\frac{a}{b x^4}\right)^{3/4} F\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{\sqrt{a} \left(a-b x^4\right)^{3/4}}","-\frac{\sqrt{b} x^3 \left(1-\frac{a}{b x^4}\right)^{3/4} F\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{\sqrt{a} \left(a-b x^4\right)^{3/4}}",1,"-((Sqrt[b]*(1 - a/(b*x^4))^(3/4)*x^3*EllipticF[ArcCsc[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(Sqrt[a]*(a - b*x^4)^(3/4)))","A",4,4,12,0.3333,1,"{237, 335, 275, 232}"
1260,1,88,0,0.0365147,"\int \frac{1}{x^4 \left(a-b x^4\right)^{3/4}} \, dx","Int[1/(x^4*(a - b*x^4)^(3/4)),x]","-\frac{2 b^{3/2} x^3 \left(1-\frac{a}{b x^4}\right)^{3/4} F\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{3 a^{3/2} \left(a-b x^4\right)^{3/4}}-\frac{\sqrt[4]{a-b x^4}}{3 a x^3}","-\frac{2 b^{3/2} x^3 \left(1-\frac{a}{b x^4}\right)^{3/4} F\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{3 a^{3/2} \left(a-b x^4\right)^{3/4}}-\frac{\sqrt[4]{a-b x^4}}{3 a x^3}",1,"-(a - b*x^4)^(1/4)/(3*a*x^3) - (2*b^(3/2)*(1 - a/(b*x^4))^(3/4)*x^3*EllipticF[ArcCsc[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(3*a^(3/2)*(a - b*x^4)^(3/4))","A",5,5,16,0.3125,1,"{325, 237, 335, 275, 232}"
1261,1,111,0,0.0486328,"\int \frac{1}{x^8 \left(a-b x^4\right)^{3/4}} \, dx","Int[1/(x^8*(a - b*x^4)^(3/4)),x]","-\frac{4 b^{5/2} x^3 \left(1-\frac{a}{b x^4}\right)^{3/4} F\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{7 a^{5/2} \left(a-b x^4\right)^{3/4}}-\frac{2 b \sqrt[4]{a-b x^4}}{7 a^2 x^3}-\frac{\sqrt[4]{a-b x^4}}{7 a x^7}","-\frac{4 b^{5/2} x^3 \left(1-\frac{a}{b x^4}\right)^{3/4} F\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{7 a^{5/2} \left(a-b x^4\right)^{3/4}}-\frac{2 b \sqrt[4]{a-b x^4}}{7 a^2 x^3}-\frac{\sqrt[4]{a-b x^4}}{7 a x^7}",1,"-(a - b*x^4)^(1/4)/(7*a*x^7) - (2*b*(a - b*x^4)^(1/4))/(7*a^2*x^3) - (4*b^(5/2)*(1 - a/(b*x^4))^(3/4)*x^3*EllipticF[ArcCsc[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(7*a^(5/2)*(a - b*x^4)^(3/4))","A",6,5,16,0.3125,1,"{325, 237, 335, 275, 232}"
1262,1,136,0,0.0598432,"\int \frac{1}{x^{12} \left(a-b x^4\right)^{3/4}} \, dx","Int[1/(x^12*(a - b*x^4)^(3/4)),x]","-\frac{20 b^2 \sqrt[4]{a-b x^4}}{77 a^3 x^3}-\frac{40 b^{7/2} x^3 \left(1-\frac{a}{b x^4}\right)^{3/4} F\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{77 a^{7/2} \left(a-b x^4\right)^{3/4}}-\frac{10 b \sqrt[4]{a-b x^4}}{77 a^2 x^7}-\frac{\sqrt[4]{a-b x^4}}{11 a x^{11}}","-\frac{20 b^2 \sqrt[4]{a-b x^4}}{77 a^3 x^3}-\frac{40 b^{7/2} x^3 \left(1-\frac{a}{b x^4}\right)^{3/4} F\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{77 a^{7/2} \left(a-b x^4\right)^{3/4}}-\frac{10 b \sqrt[4]{a-b x^4}}{77 a^2 x^7}-\frac{\sqrt[4]{a-b x^4}}{11 a x^{11}}",1,"-(a - b*x^4)^(1/4)/(11*a*x^11) - (10*b*(a - b*x^4)^(1/4))/(77*a^2*x^7) - (20*b^2*(a - b*x^4)^(1/4))/(77*a^3*x^3) - (40*b^(7/2)*(1 - a/(b*x^4))^(3/4)*x^3*EllipticF[ArcCsc[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(77*a^(7/2)*(a - b*x^4)^(3/4))","A",7,5,16,0.3125,1,"{325, 237, 335, 275, 232}"
1263,1,81,0,0.0387146,"\int \frac{x^2}{\left(a-b x^4\right)^{5/4}} \, dx","Int[x^2/(a - b*x^4)^(5/4),x]","\frac{1}{b x \sqrt[4]{a-b x^4}}-\frac{x \sqrt[4]{1-\frac{a}{b x^4}} E\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{\sqrt{a} \sqrt{b} \sqrt[4]{a-b x^4}}","\frac{1}{b x \sqrt[4]{a-b x^4}}-\frac{x \sqrt[4]{1-\frac{a}{b x^4}} E\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)\right|2\right)}{\sqrt{a} \sqrt{b} \sqrt[4]{a-b x^4}}",1,"1/(b*x*(a - b*x^4)^(1/4)) - ((1 - a/(b*x^4))^(1/4)*x*EllipticE[ArcCsc[(Sqrt[b]*x^2)/Sqrt[a]]/2, 2])/(Sqrt[a]*Sqrt[b]*(a - b*x^4)^(1/4))","A",5,5,16,0.3125,1,"{287, 313, 335, 275, 228}"
1264,1,48,0,0.0265116,"\int x^7 \left(a+b x^4\right)^p \, dx","Int[x^7*(a + b*x^4)^p,x]","\frac{\left(a+b x^4\right)^{p+2}}{4 b^2 (p+2)}-\frac{a \left(a+b x^4\right)^{p+1}}{4 b^2 (p+1)}","\frac{\left(a+b x^4\right)^{p+2}}{4 b^2 (p+2)}-\frac{a \left(a+b x^4\right)^{p+1}}{4 b^2 (p+1)}",1,"-(a*(a + b*x^4)^(1 + p))/(4*b^2*(1 + p)) + (a + b*x^4)^(2 + p)/(4*b^2*(2 + p))","A",3,2,13,0.1538,1,"{266, 43}"
1265,1,23,0,0.0040387,"\int x^3 \left(a+b x^4\right)^p \, dx","Int[x^3*(a + b*x^4)^p,x]","\frac{\left(a+b x^4\right)^{p+1}}{4 b (p+1)}","\frac{\left(a+b x^4\right)^{p+1}}{4 b (p+1)}",1,"(a + b*x^4)^(1 + p)/(4*b*(1 + p))","A",1,1,13,0.07692,1,"{261}"
1266,1,41,0,0.0199358,"\int \frac{\left(a+b x^4\right)^p}{x} \, dx","Int[(a + b*x^4)^p/x,x]","-\frac{\left(a+b x^4\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{b x^4}{a}+1\right)}{4 a (p+1)}","-\frac{\left(a+b x^4\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{b x^4}{a}+1\right)}{4 a (p+1)}",1,"-((a + b*x^4)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, 1 + (b*x^4)/a])/(4*a*(1 + p))","A",2,2,13,0.1538,1,"{266, 65}"
1267,1,66,0,0.0455001,"\int \frac{x^{24}}{a+b x^5} \, dx","Int[x^24/(a + b*x^5),x]","\frac{a^2 x^{10}}{10 b^3}-\frac{a^3 x^5}{5 b^4}+\frac{a^4 \log \left(a+b x^5\right)}{5 b^5}-\frac{a x^{15}}{15 b^2}+\frac{x^{20}}{20 b}","\frac{a^2 x^{10}}{10 b^3}-\frac{a^3 x^5}{5 b^4}+\frac{a^4 \log \left(a+b x^5\right)}{5 b^5}-\frac{a x^{15}}{15 b^2}+\frac{x^{20}}{20 b}",1,"-(a^3*x^5)/(5*b^4) + (a^2*x^10)/(10*b^3) - (a*x^15)/(15*b^2) + x^20/(20*b) + (a^4*Log[a + b*x^5])/(5*b^5)","A",3,2,13,0.1538,1,"{266, 43}"
1268,1,53,0,0.034639,"\int \frac{x^{19}}{a+b x^5} \, dx","Int[x^19/(a + b*x^5),x]","\frac{a^2 x^5}{5 b^3}-\frac{a^3 \log \left(a+b x^5\right)}{5 b^4}-\frac{a x^{10}}{10 b^2}+\frac{x^{15}}{15 b}","\frac{a^2 x^5}{5 b^3}-\frac{a^3 \log \left(a+b x^5\right)}{5 b^4}-\frac{a x^{10}}{10 b^2}+\frac{x^{15}}{15 b}",1,"(a^2*x^5)/(5*b^3) - (a*x^10)/(10*b^2) + x^15/(15*b) - (a^3*Log[a + b*x^5])/(5*b^4)","A",3,2,13,0.1538,1,"{266, 43}"
1269,1,40,0,0.0248146,"\int \frac{x^{14}}{a+b x^5} \, dx","Int[x^14/(a + b*x^5),x]","\frac{a^2 \log \left(a+b x^5\right)}{5 b^3}-\frac{a x^5}{5 b^2}+\frac{x^{10}}{10 b}","\frac{a^2 \log \left(a+b x^5\right)}{5 b^3}-\frac{a x^5}{5 b^2}+\frac{x^{10}}{10 b}",1,"-(a*x^5)/(5*b^2) + x^10/(10*b) + (a^2*Log[a + b*x^5])/(5*b^3)","A",3,2,13,0.1538,1,"{266, 43}"
1270,1,27,0,0.0181518,"\int \frac{x^9}{a+b x^5} \, dx","Int[x^9/(a + b*x^5),x]","\frac{x^5}{5 b}-\frac{a \log \left(a+b x^5\right)}{5 b^2}","\frac{x^5}{5 b}-\frac{a \log \left(a+b x^5\right)}{5 b^2}",1,"x^5/(5*b) - (a*Log[a + b*x^5])/(5*b^2)","A",3,2,13,0.1538,1,"{266, 43}"
1271,1,15,0,0.0032536,"\int \frac{x^4}{a+b x^5} \, dx","Int[x^4/(a + b*x^5),x]","\frac{\log \left(a+b x^5\right)}{5 b}","\frac{\log \left(a+b x^5\right)}{5 b}",1,"Log[a + b*x^5]/(5*b)","A",1,1,13,0.07692,1,"{260}"
1272,1,22,0,0.0104789,"\int \frac{1}{x \left(a+b x^5\right)} \, dx","Int[1/(x*(a + b*x^5)),x]","\frac{\log (x)}{a}-\frac{\log \left(a+b x^5\right)}{5 a}","\frac{\log (x)}{a}-\frac{\log \left(a+b x^5\right)}{5 a}",1,"Log[x]/a - Log[a + b*x^5]/(5*a)","A",4,4,13,0.3077,1,"{266, 36, 29, 31}"
1273,1,35,0,0.02158,"\int \frac{1}{x^6 \left(a+b x^5\right)} \, dx","Int[1/(x^6*(a + b*x^5)),x]","\frac{b \log \left(a+b x^5\right)}{5 a^2}-\frac{b \log (x)}{a^2}-\frac{1}{5 a x^5}","\frac{b \log \left(a+b x^5\right)}{5 a^2}-\frac{b \log (x)}{a^2}-\frac{1}{5 a x^5}",1,"-1/(5*a*x^5) - (b*Log[x])/a^2 + (b*Log[a + b*x^5])/(5*a^2)","A",3,2,13,0.1538,1,"{266, 44}"
1274,1,49,0,0.0267747,"\int \frac{1}{x^{11} \left(a+b x^5\right)} \, dx","Int[1/(x^11*(a + b*x^5)),x]","-\frac{b^2 \log \left(a+b x^5\right)}{5 a^3}+\frac{b^2 \log (x)}{a^3}+\frac{b}{5 a^2 x^5}-\frac{1}{10 a x^{10}}","-\frac{b^2 \log \left(a+b x^5\right)}{5 a^3}+\frac{b^2 \log (x)}{a^3}+\frac{b}{5 a^2 x^5}-\frac{1}{10 a x^{10}}",1,"-1/(10*a*x^10) + b/(5*a^2*x^5) + (b^2*Log[x])/a^3 - (b^2*Log[a + b*x^5])/(5*a^3)","A",3,2,13,0.1538,1,"{266, 44}"
1275,1,63,0,0.0325913,"\int \frac{1}{x^{16} \left(a+b x^5\right)} \, dx","Int[1/(x^16*(a + b*x^5)),x]","-\frac{b^2}{5 a^3 x^5}+\frac{b^3 \log \left(a+b x^5\right)}{5 a^4}-\frac{b^3 \log (x)}{a^4}+\frac{b}{10 a^2 x^{10}}-\frac{1}{15 a x^{15}}","-\frac{b^2}{5 a^3 x^5}+\frac{b^3 \log \left(a+b x^5\right)}{5 a^4}-\frac{b^3 \log (x)}{a^4}+\frac{b}{10 a^2 x^{10}}-\frac{1}{15 a x^{15}}",1,"-1/(15*a*x^15) + b/(10*a^2*x^10) - b^2/(5*a^3*x^5) - (b^3*Log[x])/a^4 + (b^3*Log[a + b*x^5])/(5*a^4)","A",3,2,13,0.1538,1,"{266, 44}"
1276,1,305,0,0.63845,"\int \frac{1}{a+b x^5} \, dx","Int[(a + b*x^5)^(-1),x]","-\frac{\left(1-\sqrt{5}\right) \log \left(a^{2/5}-\frac{1}{2} \left(1-\sqrt{5}\right) \sqrt[5]{a} \sqrt[5]{b} x+b^{2/5} x^2\right)}{20 a^{4/5} \sqrt[5]{b}}-\frac{\left(1+\sqrt{5}\right) \log \left(a^{2/5}-\frac{1}{2} \left(1+\sqrt{5}\right) \sqrt[5]{a} \sqrt[5]{b} x+b^{2/5} x^2\right)}{20 a^{4/5} \sqrt[5]{b}}+\frac{\log \left(\sqrt[5]{a}+\sqrt[5]{b} x\right)}{5 a^{4/5} \sqrt[5]{b}}+\frac{\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\frac{2 \sqrt{\frac{2}{5+\sqrt{5}}} \sqrt[5]{b} x}{\sqrt[5]{a}}+\sqrt{\frac{1}{5} \left(5-2 \sqrt{5}\right)}\right)}{5 a^{4/5} \sqrt[5]{b}}-\frac{\sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \tan ^{-1}\left(\sqrt{\frac{1}{5} \left(5+2 \sqrt{5}\right)}-\frac{\sqrt{\frac{2}{5} \left(5+\sqrt{5}\right)} \sqrt[5]{b} x}{\sqrt[5]{a}}\right)}{5 a^{4/5} \sqrt[5]{b}}","-\frac{\left(1-\sqrt{5}\right) \log \left(2 a^{2/5}-\left(1-\sqrt{5}\right) \sqrt[5]{a} \sqrt[5]{b} x+2 b^{2/5} x^2\right)}{20 a^{4/5} \sqrt[5]{b}}-\frac{\left(1+\sqrt{5}\right) \log \left(2 a^{2/5}-\left(1+\sqrt{5}\right) \sqrt[5]{a} \sqrt[5]{b} x+2 b^{2/5} x^2\right)}{20 a^{4/5} \sqrt[5]{b}}+\frac{\log \left(\sqrt[5]{a}+\sqrt[5]{b} x\right)}{5 a^{4/5} \sqrt[5]{b}}-\frac{\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\frac{\left(1-\sqrt{5}\right) \sqrt[5]{a}-4 \sqrt[5]{b} x}{\sqrt{2 \left(5+\sqrt{5}\right)} \sqrt[5]{a}}\right)}{5 a^{4/5} \sqrt[5]{b}}-\frac{\sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \tan ^{-1}\left(\frac{\left(1+\sqrt{5}\right) \sqrt[5]{a}-4 \sqrt[5]{b} x}{\sqrt{2 \left(5-\sqrt{5}\right)} \sqrt[5]{a}}\right)}{5 a^{4/5} \sqrt[5]{b}}",1,"(Sqrt[(5 + Sqrt[5])/2]*ArcTan[Sqrt[(5 - 2*Sqrt[5])/5] + (2*Sqrt[2/(5 + Sqrt[5])]*b^(1/5)*x)/a^(1/5)])/(5*a^(4/5)*b^(1/5)) - (Sqrt[(5 - Sqrt[5])/2]*ArcTan[Sqrt[(5 + 2*Sqrt[5])/5] - (Sqrt[(2*(5 + Sqrt[5]))/5]*b^(1/5)*x)/a^(1/5)])/(5*a^(4/5)*b^(1/5)) + Log[a^(1/5) + b^(1/5)*x]/(5*a^(4/5)*b^(1/5)) - ((1 - Sqrt[5])*Log[a^(2/5) - ((1 - Sqrt[5])*a^(1/5)*b^(1/5)*x)/2 + b^(2/5)*x^2])/(20*a^(4/5)*b^(1/5)) - ((1 + Sqrt[5])*Log[a^(2/5) - ((1 + Sqrt[5])*a^(1/5)*b^(1/5)*x)/2 + b^(2/5)*x^2])/(20*a^(4/5)*b^(1/5))","A",6,6,9,0.6667,0,"{201, 634, 618, 204, 628, 31}"
1277,1,72,0,0.0583653,"\int \frac{x^{24}}{\left(a+b x^5\right)^2} \, dx","Int[x^24/(a + b*x^5)^2,x]","\frac{3 a^2 x^5}{5 b^4}-\frac{a^4}{5 b^5 \left(a+b x^5\right)}-\frac{4 a^3 \log \left(a+b x^5\right)}{5 b^5}-\frac{a x^{10}}{5 b^3}+\frac{x^{15}}{15 b^2}","\frac{3 a^2 x^5}{5 b^4}-\frac{a^4}{5 b^5 \left(a+b x^5\right)}-\frac{4 a^3 \log \left(a+b x^5\right)}{5 b^5}-\frac{a x^{10}}{5 b^3}+\frac{x^{15}}{15 b^2}",1,"(3*a^2*x^5)/(5*b^4) - (a*x^10)/(5*b^3) + x^15/(15*b^2) - a^4/(5*b^5*(a + b*x^5)) - (4*a^3*Log[a + b*x^5])/(5*b^5)","A",3,2,13,0.1538,1,"{266, 43}"
1278,1,59,0,0.0453078,"\int \frac{x^{19}}{\left(a+b x^5\right)^2} \, dx","Int[x^19/(a + b*x^5)^2,x]","\frac{a^3}{5 b^4 \left(a+b x^5\right)}+\frac{3 a^2 \log \left(a+b x^5\right)}{5 b^4}-\frac{2 a x^5}{5 b^3}+\frac{x^{10}}{10 b^2}","\frac{a^3}{5 b^4 \left(a+b x^5\right)}+\frac{3 a^2 \log \left(a+b x^5\right)}{5 b^4}-\frac{2 a x^5}{5 b^3}+\frac{x^{10}}{10 b^2}",1,"(-2*a*x^5)/(5*b^3) + x^10/(10*b^2) + a^3/(5*b^4*(a + b*x^5)) + (3*a^2*Log[a + b*x^5])/(5*b^4)","A",3,2,13,0.1538,1,"{266, 43}"
1279,1,46,0,0.0335878,"\int \frac{x^{14}}{\left(a+b x^5\right)^2} \, dx","Int[x^14/(a + b*x^5)^2,x]","-\frac{a^2}{5 b^3 \left(a+b x^5\right)}-\frac{2 a \log \left(a+b x^5\right)}{5 b^3}+\frac{x^5}{5 b^2}","-\frac{a^2}{5 b^3 \left(a+b x^5\right)}-\frac{2 a \log \left(a+b x^5\right)}{5 b^3}+\frac{x^5}{5 b^2}",1,"x^5/(5*b^2) - a^2/(5*b^3*(a + b*x^5)) - (2*a*Log[a + b*x^5])/(5*b^3)","A",3,2,13,0.1538,1,"{266, 43}"
1280,1,33,0,0.0247409,"\int \frac{x^9}{\left(a+b x^5\right)^2} \, dx","Int[x^9/(a + b*x^5)^2,x]","\frac{a}{5 b^2 \left(a+b x^5\right)}+\frac{\log \left(a+b x^5\right)}{5 b^2}","\frac{a}{5 b^2 \left(a+b x^5\right)}+\frac{\log \left(a+b x^5\right)}{5 b^2}",1,"a/(5*b^2*(a + b*x^5)) + Log[a + b*x^5]/(5*b^2)","A",3,2,13,0.1538,1,"{266, 43}"
1281,1,16,0,0.0035658,"\int \frac{x^4}{\left(a+b x^5\right)^2} \, dx","Int[x^4/(a + b*x^5)^2,x]","-\frac{1}{5 b \left(a+b x^5\right)}","-\frac{1}{5 b \left(a+b x^5\right)}",1,"-1/(5*b*(a + b*x^5))","A",1,1,13,0.07692,1,"{261}"
1282,1,38,0,0.0275933,"\int \frac{1}{x \left(a+b x^5\right)^2} \, dx","Int[1/(x*(a + b*x^5)^2),x]","-\frac{\log \left(a+b x^5\right)}{5 a^2}+\frac{\log (x)}{a^2}+\frac{1}{5 a \left(a+b x^5\right)}","-\frac{\log \left(a+b x^5\right)}{5 a^2}+\frac{\log (x)}{a^2}+\frac{1}{5 a \left(a+b x^5\right)}",1,"1/(5*a*(a + b*x^5)) + Log[x]/a^2 - Log[a + b*x^5]/(5*a^2)","A",3,2,13,0.1538,1,"{266, 44}"
1283,1,52,0,0.0367611,"\int \frac{1}{x^6 \left(a+b x^5\right)^2} \, dx","Int[1/(x^6*(a + b*x^5)^2),x]","-\frac{b}{5 a^2 \left(a+b x^5\right)}+\frac{2 b \log \left(a+b x^5\right)}{5 a^3}-\frac{2 b \log (x)}{a^3}-\frac{1}{5 a^2 x^5}","-\frac{b}{5 a^2 \left(a+b x^5\right)}+\frac{2 b \log \left(a+b x^5\right)}{5 a^3}-\frac{2 b \log (x)}{a^3}-\frac{1}{5 a^2 x^5}",1,"-1/(5*a^2*x^5) - b/(5*a^2*(a + b*x^5)) - (2*b*Log[x])/a^3 + (2*b*Log[a + b*x^5])/(5*a^3)","A",3,2,13,0.1538,1,"{266, 44}"
1284,1,69,0,0.0469586,"\int \frac{1}{x^{11} \left(a+b x^5\right)^2} \, dx","Int[1/(x^11*(a + b*x^5)^2),x]","\frac{b^2}{5 a^3 \left(a+b x^5\right)}-\frac{3 b^2 \log \left(a+b x^5\right)}{5 a^4}+\frac{3 b^2 \log (x)}{a^4}+\frac{2 b}{5 a^3 x^5}-\frac{1}{10 a^2 x^{10}}","\frac{b^2}{5 a^3 \left(a+b x^5\right)}-\frac{3 b^2 \log \left(a+b x^5\right)}{5 a^4}+\frac{3 b^2 \log (x)}{a^4}+\frac{2 b}{5 a^3 x^5}-\frac{1}{10 a^2 x^{10}}",1,"-1/(10*a^2*x^10) + (2*b)/(5*a^3*x^5) + b^2/(5*a^3*(a + b*x^5)) + (3*b^2*Log[x])/a^4 - (3*b^2*Log[a + b*x^5])/(5*a^4)","A",3,2,13,0.1538,1,"{266, 44}"
1285,1,34,0,0.0198526,"\int \frac{x^{14}}{2 b+b x^5} \, dx","Int[x^14/(2*b + b*x^5),x]","\frac{x^{10}}{10 b}-\frac{2 x^5}{5 b}+\frac{4 \log \left(x^5+2\right)}{5 b}","\frac{x^{10}}{10 b}-\frac{2 x^5}{5 b}+\frac{4 \log \left(x^5+2\right)}{5 b}",1,"(-2*x^5)/(5*b) + x^10/(10*b) + (4*Log[2 + x^5])/(5*b)","A",3,2,15,0.1333,1,"{266, 43}"
1286,1,24,0,0.0138791,"\int \frac{x^9}{2 b+b x^5} \, dx","Int[x^9/(2*b + b*x^5),x]","\frac{x^5}{5 b}-\frac{2 \log \left(x^5+2\right)}{5 b}","\frac{x^5}{5 b}-\frac{2 \log \left(x^5+2\right)}{5 b}",1,"x^5/(5*b) - (2*Log[2 + x^5])/(5*b)","A",3,2,15,0.1333,1,"{266, 43}"
1287,1,13,0,0.0030126,"\int \frac{x^4}{2 b+b x^5} \, dx","Int[x^4/(2*b + b*x^5),x]","\frac{\log \left(x^5+2\right)}{5 b}","\frac{\log \left(x^5+2\right)}{5 b}",1,"Log[2 + x^5]/(5*b)","A",1,1,15,0.06667,1,"{260}"
1288,1,23,0,0.0087873,"\int \frac{1}{x \left(2 b+b x^5\right)} \, dx","Int[1/(x*(2*b + b*x^5)),x]","\frac{\log (x)}{2 b}-\frac{\log \left(x^5+2\right)}{10 b}","\frac{\log (x)}{2 b}-\frac{\log \left(x^5+2\right)}{10 b}",1,"Log[x]/(2*b) - Log[2 + x^5]/(10*b)","A",4,4,15,0.2667,1,"{266, 36, 29, 31}"
1289,1,33,0,0.0181239,"\int \frac{1}{x^6 \left(2 b+b x^5\right)} \, dx","Int[1/(x^6*(2*b + b*x^5)),x]","-\frac{1}{10 b x^5}+\frac{\log \left(x^5+2\right)}{20 b}-\frac{\log (x)}{4 b}","-\frac{1}{10 b x^5}+\frac{\log \left(x^5+2\right)}{20 b}-\frac{\log (x)}{4 b}",1,"-1/(10*b*x^5) - Log[x]/(4*b) + Log[2 + x^5]/(20*b)","A",3,2,15,0.1333,1,"{266, 44}"
1290,1,36,0,0.0245118,"\int \frac{x^{14}}{3+b x^5} \, dx","Int[x^14/(3 + b*x^5),x]","-\frac{3 x^5}{5 b^2}+\frac{9 \log \left(b x^5+3\right)}{5 b^3}+\frac{x^{10}}{10 b}","-\frac{3 x^5}{5 b^2}+\frac{9 \log \left(b x^5+3\right)}{5 b^3}+\frac{x^{10}}{10 b}",1,"(-3*x^5)/(5*b^2) + x^10/(10*b) + (9*Log[3 + b*x^5])/(5*b^3)","A",3,2,13,0.1538,1,"{266, 43}"
1291,1,26,0,0.0164288,"\int \frac{x^9}{3+b x^5} \, dx","Int[x^9/(3 + b*x^5),x]","\frac{x^5}{5 b}-\frac{3 \log \left(b x^5+3\right)}{5 b^2}","\frac{x^5}{5 b}-\frac{3 \log \left(b x^5+3\right)}{5 b^2}",1,"x^5/(5*b) - (3*Log[3 + b*x^5])/(5*b^2)","A",3,2,13,0.1538,1,"{266, 43}"
1292,1,15,0,0.0033289,"\int \frac{x^4}{3+b x^5} \, dx","Int[x^4/(3 + b*x^5),x]","\frac{\log \left(b x^5+3\right)}{5 b}","\frac{\log \left(b x^5+3\right)}{5 b}",1,"Log[3 + b*x^5]/(5*b)","A",1,1,13,0.07692,1,"{260}"
1293,1,19,0,0.0094368,"\int \frac{1}{x \left(3+b x^5\right)} \, dx","Int[1/(x*(3 + b*x^5)),x]","\frac{\log (x)}{3}-\frac{1}{15} \log \left(b x^5+3\right)","\frac{\log (x)}{3}-\frac{1}{15} \log \left(b x^5+3\right)",1,"Log[x]/3 - Log[3 + b*x^5]/15","A",4,4,13,0.3077,1,"{266, 36, 29, 31}"
1294,1,28,0,0.0185472,"\int \frac{1}{x^6 \left(3+b x^5\right)} \, dx","Int[1/(x^6*(3 + b*x^5)),x]","\frac{1}{45} b \log \left(b x^5+3\right)-\frac{1}{9} b \log (x)-\frac{1}{15 x^5}","\frac{1}{45} b \log \left(b x^5+3\right)-\frac{1}{9} b \log (x)-\frac{1}{15 x^5}",1,"-1/(15*x^5) - (b*Log[x])/9 + (b*Log[3 + b*x^5])/45","A",3,2,13,0.1538,1,"{266, 44}"
1295,1,25,0,0.0118298,"\int \frac{x^{14}}{1+x^5} \, dx","Int[x^14/(1 + x^5),x]","\frac{x^{10}}{10}-\frac{x^5}{5}+\frac{1}{5} \log \left(x^5+1\right)","\frac{x^{10}}{10}-\frac{x^5}{5}+\frac{1}{5} \log \left(x^5+1\right)",1,"-x^5/5 + x^10/10 + Log[1 + x^5]/5","A",3,2,11,0.1818,1,"{266, 43}"
1296,1,18,0,0.0080608,"\int \frac{x^9}{1+x^5} \, dx","Int[x^9/(1 + x^5),x]","\frac{x^5}{5}-\frac{1}{5} \log \left(x^5+1\right)","\frac{x^5}{5}-\frac{1}{5} \log \left(x^5+1\right)",1,"x^5/5 - Log[1 + x^5]/5","A",3,2,11,0.1818,1,"{266, 43}"
1297,1,10,0,0.0022468,"\int \frac{x^4}{1+x^5} \, dx","Int[x^4/(1 + x^5),x]","\frac{1}{5} \log \left(x^5+1\right)","\frac{1}{5} \log \left(x^5+1\right)",1,"Log[1 + x^5]/5","A",1,1,11,0.09091,1,"{260}"
1298,1,13,0,0.0047985,"\int \frac{1}{x \left(1+x^5\right)} \, dx","Int[1/(x*(1 + x^5)),x]","\log (x)-\frac{1}{5} \log \left(x^5+1\right)","\log (x)-\frac{1}{5} \log \left(x^5+1\right)",1,"Log[x] - Log[1 + x^5]/5","A",4,4,11,0.3636,1,"{266, 36, 29, 31}"
1299,1,22,0,0.0096588,"\int \frac{1}{x^6 \left(1+x^5\right)} \, dx","Int[1/(x^6*(1 + x^5)),x]","-\frac{1}{5 x^5}+\frac{1}{5} \log \left(x^5+1\right)-\log (x)","-\frac{1}{5 x^5}+\frac{1}{5} \log \left(x^5+1\right)-\log (x)",1,"-1/(5*x^5) - Log[x] + Log[1 + x^5]/5","A",3,2,11,0.1818,1,"{266, 44}"
1300,1,186,0,0.2286271,"\int \frac{x^5}{1+x^5} \, dx","Int[x^5/(1 + x^5),x]","\frac{1}{20} \left(1-\sqrt{5}\right) \log \left(x^2-\frac{1}{2} \left(1-\sqrt{5}\right) x+1\right)+\frac{1}{20} \left(1+\sqrt{5}\right) \log \left(x^2-\frac{1}{2} \left(1+\sqrt{5}\right) x+1\right)+x-\frac{1}{5} \log (x+1)-\frac{1}{5} \sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} \tan ^{-1}\left(2 \sqrt{\frac{2}{5+\sqrt{5}}} x+\sqrt{\frac{1}{5} \left(5-2 \sqrt{5}\right)}\right)+\frac{1}{5} \sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \tan ^{-1}\left(\sqrt{\frac{1}{5} \left(5+2 \sqrt{5}\right)}-\sqrt{\frac{2}{5} \left(5+\sqrt{5}\right)} x\right)","\frac{1}{20} \left(1-\sqrt{5}\right) \log \left(x^2-\frac{1}{2} \left(1-\sqrt{5}\right) x+1\right)+\frac{1}{20} \left(1+\sqrt{5}\right) \log \left(x^2-\frac{1}{2} \left(1+\sqrt{5}\right) x+1\right)+x-\frac{1}{5} \log (x+1)-\frac{1}{5} \sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} \tan ^{-1}\left(2 \sqrt{\frac{2}{5+\sqrt{5}}} x+\sqrt{\frac{1}{5} \left(5-2 \sqrt{5}\right)}\right)+\frac{1}{5} \sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \tan ^{-1}\left(\sqrt{\frac{1}{5} \left(5+2 \sqrt{5}\right)}-\sqrt{\frac{2}{5} \left(5+\sqrt{5}\right)} x\right)",1,"x - (Sqrt[(5 + Sqrt[5])/2]*ArcTan[Sqrt[(5 - 2*Sqrt[5])/5] + 2*Sqrt[2/(5 + Sqrt[5])]*x])/5 + (Sqrt[(5 - Sqrt[5])/2]*ArcTan[Sqrt[(5 + 2*Sqrt[5])/5] - Sqrt[(2*(5 + Sqrt[5]))/5]*x])/5 - Log[1 + x]/5 + ((1 - Sqrt[5])*Log[1 - ((1 - Sqrt[5])*x)/2 + x^2])/20 + ((1 + Sqrt[5])*Log[1 - ((1 + Sqrt[5])*x)/2 + x^2])/20","A",7,7,11,0.6364,1,"{321, 201, 634, 618, 204, 628, 31}"
1301,1,185,0,0.2739289,"\int \frac{x^3}{1+x^5} \, dx","Int[x^3/(1 + x^5),x]","\frac{1}{20} \left(1-\sqrt{5}\right) \log \left(x^2-\frac{1}{2} \left(1-\sqrt{5}\right) x+1\right)+\frac{1}{20} \left(1+\sqrt{5}\right) \log \left(x^2-\frac{1}{2} \left(1+\sqrt{5}\right) x+1\right)-\frac{1}{5} \log (x+1)+\frac{1}{5} \sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} \tan ^{-1}\left(2 \sqrt{\frac{2}{5+\sqrt{5}}} x+\sqrt{\frac{1}{5} \left(5-2 \sqrt{5}\right)}\right)-\frac{1}{5} \sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \tan ^{-1}\left(\sqrt{\frac{1}{5} \left(5+2 \sqrt{5}\right)}-\sqrt{\frac{2}{5} \left(5+\sqrt{5}\right)} x\right)","\frac{1}{20} \left(1-\sqrt{5}\right) \log \left(x^2-\frac{1}{2} \left(1-\sqrt{5}\right) x+1\right)+\frac{1}{20} \left(1+\sqrt{5}\right) \log \left(x^2-\frac{1}{2} \left(1+\sqrt{5}\right) x+1\right)-\frac{1}{5} \log (x+1)+\frac{1}{5} \sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} \tan ^{-1}\left(2 \sqrt{\frac{2}{5+\sqrt{5}}} x+\sqrt{\frac{1}{5} \left(5-2 \sqrt{5}\right)}\right)-\frac{1}{5} \sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \tan ^{-1}\left(\sqrt{\frac{1}{5} \left(5+2 \sqrt{5}\right)}-\sqrt{\frac{2}{5} \left(5+\sqrt{5}\right)} x\right)",1,"(Sqrt[(5 + Sqrt[5])/2]*ArcTan[Sqrt[(5 - 2*Sqrt[5])/5] + 2*Sqrt[2/(5 + Sqrt[5])]*x])/5 - (Sqrt[(5 - Sqrt[5])/2]*ArcTan[Sqrt[(5 + 2*Sqrt[5])/5] - Sqrt[(2*(5 + Sqrt[5]))/5]*x])/5 - Log[1 + x]/5 + ((1 - Sqrt[5])*Log[1 - ((1 - Sqrt[5])*x)/2 + x^2])/20 + ((1 + Sqrt[5])*Log[1 - ((1 + Sqrt[5])*x)/2 + x^2])/20","A",6,6,11,0.5455,1,"{293, 634, 618, 204, 628, 31}"
1302,1,185,0,0.2935699,"\int \frac{x^2}{1+x^5} \, dx","Int[x^2/(1 + x^5),x]","-\frac{1}{20} \left(1+\sqrt{5}\right) \log \left(x^2-\frac{1}{2} \left(1-\sqrt{5}\right) x+1\right)-\frac{1}{20} \left(1-\sqrt{5}\right) \log \left(x^2-\frac{1}{2} \left(1+\sqrt{5}\right) x+1\right)+\frac{1}{5} \log (x+1)-\frac{1}{5} \sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \tan ^{-1}\left(2 \sqrt{\frac{2}{5+\sqrt{5}}} x+\sqrt{\frac{1}{5} \left(5-2 \sqrt{5}\right)}\right)-\frac{1}{5} \sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\sqrt{\frac{1}{5} \left(5+2 \sqrt{5}\right)}-\sqrt{\frac{2}{5} \left(5+\sqrt{5}\right)} x\right)","-\frac{1}{20} \left(1+\sqrt{5}\right) \log \left(x^2-\frac{1}{2} \left(1-\sqrt{5}\right) x+1\right)-\frac{1}{20} \left(1-\sqrt{5}\right) \log \left(x^2-\frac{1}{2} \left(1+\sqrt{5}\right) x+1\right)+\frac{1}{5} \log (x+1)-\frac{1}{5} \sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \tan ^{-1}\left(2 \sqrt{\frac{2}{5+\sqrt{5}}} x+\sqrt{\frac{1}{5} \left(5-2 \sqrt{5}\right)}\right)-\frac{1}{5} \sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\sqrt{\frac{1}{5} \left(5+2 \sqrt{5}\right)}-\sqrt{\frac{2}{5} \left(5+\sqrt{5}\right)} x\right)",1,"-(Sqrt[(5 - Sqrt[5])/2]*ArcTan[Sqrt[(5 - 2*Sqrt[5])/5] + 2*Sqrt[2/(5 + Sqrt[5])]*x])/5 - (Sqrt[(5 + Sqrt[5])/2]*ArcTan[Sqrt[(5 + 2*Sqrt[5])/5] - Sqrt[(2*(5 + Sqrt[5]))/5]*x])/5 + Log[1 + x]/5 - ((1 + Sqrt[5])*Log[1 - ((1 - Sqrt[5])*x)/2 + x^2])/20 - ((1 - Sqrt[5])*Log[1 - ((1 + Sqrt[5])*x)/2 + x^2])/20","A",6,6,11,0.5455,1,"{293, 634, 618, 204, 628, 31}"
1303,1,185,0,0.2217492,"\int \frac{x}{1+x^5} \, dx","Int[x/(1 + x^5),x]","\frac{1}{20} \left(1+\sqrt{5}\right) \log \left(x^2-\frac{1}{2} \left(1-\sqrt{5}\right) x+1\right)+\frac{1}{20} \left(1-\sqrt{5}\right) \log \left(x^2-\frac{1}{2} \left(1+\sqrt{5}\right) x+1\right)-\frac{1}{5} \log (x+1)-\frac{1}{5} \sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \tan ^{-1}\left(2 \sqrt{\frac{2}{5+\sqrt{5}}} x+\sqrt{\frac{1}{5} \left(5-2 \sqrt{5}\right)}\right)-\frac{1}{5} \sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\sqrt{\frac{1}{5} \left(5+2 \sqrt{5}\right)}-\sqrt{\frac{2}{5} \left(5+\sqrt{5}\right)} x\right)","\frac{1}{20} \left(1+\sqrt{5}\right) \log \left(x^2-\frac{1}{2} \left(1-\sqrt{5}\right) x+1\right)+\frac{1}{20} \left(1-\sqrt{5}\right) \log \left(x^2-\frac{1}{2} \left(1+\sqrt{5}\right) x+1\right)-\frac{1}{5} \log (x+1)-\frac{1}{5} \sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \tan ^{-1}\left(2 \sqrt{\frac{2}{5+\sqrt{5}}} x+\sqrt{\frac{1}{5} \left(5-2 \sqrt{5}\right)}\right)-\frac{1}{5} \sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\sqrt{\frac{1}{5} \left(5+2 \sqrt{5}\right)}-\sqrt{\frac{2}{5} \left(5+\sqrt{5}\right)} x\right)",1,"-(Sqrt[(5 - Sqrt[5])/2]*ArcTan[Sqrt[(5 - 2*Sqrt[5])/5] + 2*Sqrt[2/(5 + Sqrt[5])]*x])/5 - (Sqrt[(5 + Sqrt[5])/2]*ArcTan[Sqrt[(5 + 2*Sqrt[5])/5] - Sqrt[(2*(5 + Sqrt[5]))/5]*x])/5 - Log[1 + x]/5 + ((1 + Sqrt[5])*Log[1 - ((1 - Sqrt[5])*x)/2 + x^2])/20 + ((1 - Sqrt[5])*Log[1 - ((1 + Sqrt[5])*x)/2 + x^2])/20","A",6,6,9,0.6667,1,"{293, 634, 618, 204, 628, 31}"
1304,1,185,0,0.1930066,"\int \frac{1}{1+x^5} \, dx","Int[(1 + x^5)^(-1),x]","-\frac{1}{20} \left(1-\sqrt{5}\right) \log \left(x^2-\frac{1}{2} \left(1-\sqrt{5}\right) x+1\right)-\frac{1}{20} \left(1+\sqrt{5}\right) \log \left(x^2-\frac{1}{2} \left(1+\sqrt{5}\right) x+1\right)+\frac{1}{5} \log (x+1)+\frac{1}{5} \sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} \tan ^{-1}\left(2 \sqrt{\frac{2}{5+\sqrt{5}}} x+\sqrt{\frac{1}{5} \left(5-2 \sqrt{5}\right)}\right)-\frac{1}{5} \sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \tan ^{-1}\left(\sqrt{\frac{1}{5} \left(5+2 \sqrt{5}\right)}-\sqrt{\frac{2}{5} \left(5+\sqrt{5}\right)} x\right)","-\frac{1}{20} \left(1-\sqrt{5}\right) \log \left(x^2-\frac{1}{2} \left(1-\sqrt{5}\right) x+1\right)-\frac{1}{20} \left(1+\sqrt{5}\right) \log \left(x^2-\frac{1}{2} \left(1+\sqrt{5}\right) x+1\right)+\frac{1}{5} \log (x+1)-\frac{1}{5} \sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\frac{-4 x-\sqrt{5}+1}{\sqrt{2 \left(5+\sqrt{5}\right)}}\right)-\frac{1}{5} \sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \tan ^{-1}\left(\frac{1}{2} \sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} \left(-4 x+\sqrt{5}+1\right)\right)",1,"(Sqrt[(5 + Sqrt[5])/2]*ArcTan[Sqrt[(5 - 2*Sqrt[5])/5] + 2*Sqrt[2/(5 + Sqrt[5])]*x])/5 - (Sqrt[(5 - Sqrt[5])/2]*ArcTan[Sqrt[(5 + 2*Sqrt[5])/5] - Sqrt[(2*(5 + Sqrt[5]))/5]*x])/5 + Log[1 + x]/5 - ((1 - Sqrt[5])*Log[1 - ((1 - Sqrt[5])*x)/2 + x^2])/20 - ((1 + Sqrt[5])*Log[1 - ((1 + Sqrt[5])*x)/2 + x^2])/20","A",6,6,7,0.8571,0,"{201, 634, 618, 204, 628, 31}"
1305,1,190,0,0.2943847,"\int \frac{1}{x^2 \left(1+x^5\right)} \, dx","Int[1/(x^2*(1 + x^5)),x]","-\frac{1}{20} \left(1-\sqrt{5}\right) \log \left(x^2-\frac{1}{2} \left(1-\sqrt{5}\right) x+1\right)-\frac{1}{20} \left(1+\sqrt{5}\right) \log \left(x^2-\frac{1}{2} \left(1+\sqrt{5}\right) x+1\right)-\frac{1}{x}+\frac{1}{5} \log (x+1)-\frac{1}{5} \sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} \tan ^{-1}\left(2 \sqrt{\frac{2}{5+\sqrt{5}}} x+\sqrt{\frac{1}{5} \left(5-2 \sqrt{5}\right)}\right)+\frac{1}{5} \sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \tan ^{-1}\left(\sqrt{\frac{1}{5} \left(5+2 \sqrt{5}\right)}-\sqrt{\frac{2}{5} \left(5+\sqrt{5}\right)} x\right)","-\frac{1}{20} \left(1-\sqrt{5}\right) \log \left(x^2-\frac{1}{2} \left(1-\sqrt{5}\right) x+1\right)-\frac{1}{20} \left(1+\sqrt{5}\right) \log \left(x^2-\frac{1}{2} \left(1+\sqrt{5}\right) x+1\right)-\frac{1}{x}+\frac{1}{5} \log (x+1)-\frac{1}{5} \sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} \tan ^{-1}\left(2 \sqrt{\frac{2}{5+\sqrt{5}}} x+\sqrt{\frac{1}{5} \left(5-2 \sqrt{5}\right)}\right)+\frac{1}{5} \sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \tan ^{-1}\left(\sqrt{\frac{1}{5} \left(5+2 \sqrt{5}\right)}-\sqrt{\frac{2}{5} \left(5+\sqrt{5}\right)} x\right)",1,"-x^(-1) - (Sqrt[(5 + Sqrt[5])/2]*ArcTan[Sqrt[(5 - 2*Sqrt[5])/5] + 2*Sqrt[2/(5 + Sqrt[5])]*x])/5 + (Sqrt[(5 - Sqrt[5])/2]*ArcTan[Sqrt[(5 + 2*Sqrt[5])/5] - Sqrt[(2*(5 + Sqrt[5]))/5]*x])/5 + Log[1 + x]/5 - ((1 - Sqrt[5])*Log[1 - ((1 - Sqrt[5])*x)/2 + x^2])/20 - ((1 + Sqrt[5])*Log[1 - ((1 + Sqrt[5])*x)/2 + x^2])/20","A",7,7,11,0.6364,1,"{325, 293, 634, 618, 204, 628, 31}"
1306,1,192,0,0.276318,"\int \frac{1}{x^3 \left(1+x^5\right)} \, dx","Int[1/(x^3*(1 + x^5)),x]","-\frac{1}{2 x^2}+\frac{1}{20} \left(1+\sqrt{5}\right) \log \left(x^2-\frac{1}{2} \left(1-\sqrt{5}\right) x+1\right)+\frac{1}{20} \left(1-\sqrt{5}\right) \log \left(x^2-\frac{1}{2} \left(1+\sqrt{5}\right) x+1\right)-\frac{1}{5} \log (x+1)+\frac{1}{5} \sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \tan ^{-1}\left(2 \sqrt{\frac{2}{5+\sqrt{5}}} x+\sqrt{\frac{1}{5} \left(5-2 \sqrt{5}\right)}\right)+\frac{1}{5} \sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\sqrt{\frac{1}{5} \left(5+2 \sqrt{5}\right)}-\sqrt{\frac{2}{5} \left(5+\sqrt{5}\right)} x\right)","-\frac{1}{2 x^2}+\frac{1}{20} \left(1+\sqrt{5}\right) \log \left(x^2-\frac{1}{2} \left(1-\sqrt{5}\right) x+1\right)+\frac{1}{20} \left(1-\sqrt{5}\right) \log \left(x^2-\frac{1}{2} \left(1+\sqrt{5}\right) x+1\right)-\frac{1}{5} \log (x+1)+\frac{1}{5} \sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \tan ^{-1}\left(2 \sqrt{\frac{2}{5+\sqrt{5}}} x+\sqrt{\frac{1}{5} \left(5-2 \sqrt{5}\right)}\right)+\frac{1}{5} \sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\sqrt{\frac{1}{5} \left(5+2 \sqrt{5}\right)}-\sqrt{\frac{2}{5} \left(5+\sqrt{5}\right)} x\right)",1,"-1/(2*x^2) + (Sqrt[(5 - Sqrt[5])/2]*ArcTan[Sqrt[(5 - 2*Sqrt[5])/5] + 2*Sqrt[2/(5 + Sqrt[5])]*x])/5 + (Sqrt[(5 + Sqrt[5])/2]*ArcTan[Sqrt[(5 + 2*Sqrt[5])/5] - Sqrt[(2*(5 + Sqrt[5]))/5]*x])/5 - Log[1 + x]/5 + ((1 + Sqrt[5])*Log[1 - ((1 - Sqrt[5])*x)/2 + x^2])/20 + ((1 - Sqrt[5])*Log[1 - ((1 + Sqrt[5])*x)/2 + x^2])/20","A",7,7,11,0.6364,1,"{325, 293, 634, 618, 204, 628, 31}"
1307,1,192,0,0.2274581,"\int \frac{1}{x^4 \left(1+x^5\right)} \, dx","Int[1/(x^4*(1 + x^5)),x]","-\frac{1}{3 x^3}-\frac{1}{20} \left(1+\sqrt{5}\right) \log \left(x^2-\frac{1}{2} \left(1-\sqrt{5}\right) x+1\right)-\frac{1}{20} \left(1-\sqrt{5}\right) \log \left(x^2-\frac{1}{2} \left(1+\sqrt{5}\right) x+1\right)+\frac{1}{5} \log (x+1)+\frac{1}{5} \sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \tan ^{-1}\left(2 \sqrt{\frac{2}{5+\sqrt{5}}} x+\sqrt{\frac{1}{5} \left(5-2 \sqrt{5}\right)}\right)+\frac{1}{5} \sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\sqrt{\frac{1}{5} \left(5+2 \sqrt{5}\right)}-\sqrt{\frac{2}{5} \left(5+\sqrt{5}\right)} x\right)","-\frac{1}{3 x^3}-\frac{1}{20} \left(1+\sqrt{5}\right) \log \left(x^2-\frac{1}{2} \left(1-\sqrt{5}\right) x+1\right)-\frac{1}{20} \left(1-\sqrt{5}\right) \log \left(x^2-\frac{1}{2} \left(1+\sqrt{5}\right) x+1\right)+\frac{1}{5} \log (x+1)+\frac{1}{5} \sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \tan ^{-1}\left(2 \sqrt{\frac{2}{5+\sqrt{5}}} x+\sqrt{\frac{1}{5} \left(5-2 \sqrt{5}\right)}\right)+\frac{1}{5} \sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\sqrt{\frac{1}{5} \left(5+2 \sqrt{5}\right)}-\sqrt{\frac{2}{5} \left(5+\sqrt{5}\right)} x\right)",1,"-1/(3*x^3) + (Sqrt[(5 - Sqrt[5])/2]*ArcTan[Sqrt[(5 - 2*Sqrt[5])/5] + 2*Sqrt[2/(5 + Sqrt[5])]*x])/5 + (Sqrt[(5 + Sqrt[5])/2]*ArcTan[Sqrt[(5 + 2*Sqrt[5])/5] - Sqrt[(2*(5 + Sqrt[5]))/5]*x])/5 + Log[1 + x]/5 - ((1 + Sqrt[5])*Log[1 - ((1 - Sqrt[5])*x)/2 + x^2])/20 - ((1 - Sqrt[5])*Log[1 - ((1 + Sqrt[5])*x)/2 + x^2])/20","A",7,7,11,0.6364,1,"{325, 293, 634, 618, 204, 628, 31}"
1308,1,83,0,0.0455901,"\int \frac{x^{23/2}}{\sqrt{a+b x^5}} \, dx","Int[x^(23/2)/Sqrt[a + b*x^5],x]","\frac{3 a^2 \tanh ^{-1}\left(\frac{\sqrt{b} x^{5/2}}{\sqrt{a+b x^5}}\right)}{20 b^{5/2}}-\frac{3 a x^{5/2} \sqrt{a+b x^5}}{20 b^2}+\frac{x^{15/2} \sqrt{a+b x^5}}{10 b}","\frac{3 a^2 \tanh ^{-1}\left(\frac{\sqrt{b} x^{5/2}}{\sqrt{a+b x^5}}\right)}{20 b^{5/2}}-\frac{3 a x^{5/2} \sqrt{a+b x^5}}{20 b^2}+\frac{x^{15/2} \sqrt{a+b x^5}}{10 b}",1,"(-3*a*x^(5/2)*Sqrt[a + b*x^5])/(20*b^2) + (x^(15/2)*Sqrt[a + b*x^5])/(10*b) + (3*a^2*ArcTanh[(Sqrt[b]*x^(5/2))/Sqrt[a + b*x^5]])/(20*b^(5/2))","A",6,5,17,0.2941,1,"{321, 329, 275, 217, 206}"
1309,1,57,0,0.0358856,"\int \frac{x^{13/2}}{\sqrt{a+b x^5}} \, dx","Int[x^(13/2)/Sqrt[a + b*x^5],x]","\frac{x^{5/2} \sqrt{a+b x^5}}{5 b}-\frac{a \tanh ^{-1}\left(\frac{\sqrt{b} x^{5/2}}{\sqrt{a+b x^5}}\right)}{5 b^{3/2}}","\frac{x^{5/2} \sqrt{a+b x^5}}{5 b}-\frac{a \tanh ^{-1}\left(\frac{\sqrt{b} x^{5/2}}{\sqrt{a+b x^5}}\right)}{5 b^{3/2}}",1,"(x^(5/2)*Sqrt[a + b*x^5])/(5*b) - (a*ArcTanh[(Sqrt[b]*x^(5/2))/Sqrt[a + b*x^5]])/(5*b^(3/2))","A",5,5,17,0.2941,1,"{321, 329, 275, 217, 206}"
1310,1,32,0,0.0289824,"\int \frac{x^{3/2}}{\sqrt{a+b x^5}} \, dx","Int[x^(3/2)/Sqrt[a + b*x^5],x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} x^{5/2}}{\sqrt{a+b x^5}}\right)}{5 \sqrt{b}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} x^{5/2}}{\sqrt{a+b x^5}}\right)}{5 \sqrt{b}}",1,"(2*ArcTanh[(Sqrt[b]*x^(5/2))/Sqrt[a + b*x^5]])/(5*Sqrt[b])","A",4,4,17,0.2353,1,"{329, 275, 217, 206}"
1311,1,23,0,0.0047669,"\int \frac{1}{x^{7/2} \sqrt{a+b x^5}} \, dx","Int[1/(x^(7/2)*Sqrt[a + b*x^5]),x]","-\frac{2 \sqrt{a+b x^5}}{5 a x^{5/2}}","-\frac{2 \sqrt{a+b x^5}}{5 a x^{5/2}}",1,"(-2*Sqrt[a + b*x^5])/(5*a*x^(5/2))","A",1,1,17,0.05882,1,"{264}"
1312,1,48,0,0.0116512,"\int \frac{1}{x^{17/2} \sqrt{a+b x^5}} \, dx","Int[1/(x^(17/2)*Sqrt[a + b*x^5]),x]","\frac{4 b \sqrt{a+b x^5}}{15 a^2 x^{5/2}}-\frac{2 \sqrt{a+b x^5}}{15 a x^{15/2}}","\frac{4 b \sqrt{a+b x^5}}{15 a^2 x^{5/2}}-\frac{2 \sqrt{a+b x^5}}{15 a x^{15/2}}",1,"(-2*Sqrt[a + b*x^5])/(15*a*x^(15/2)) + (4*b*Sqrt[a + b*x^5])/(15*a^2*x^(5/2))","A",2,2,17,0.1176,1,"{271, 264}"
1313,1,47,0,0.014652,"\int \frac{x^{23/2}}{\sqrt{1+x^5}} \, dx","Int[x^(23/2)/Sqrt[1 + x^5],x]","\frac{1}{10} \sqrt{x^5+1} x^{15/2}-\frac{3}{20} \sqrt{x^5+1} x^{5/2}+\frac{3}{20} \sinh ^{-1}\left(x^{5/2}\right)","\frac{1}{10} \sqrt{x^5+1} x^{15/2}-\frac{3}{20} \sqrt{x^5+1} x^{5/2}+\frac{3}{20} \sinh ^{-1}\left(x^{5/2}\right)",1,"(-3*x^(5/2)*Sqrt[1 + x^5])/20 + (x^(15/2)*Sqrt[1 + x^5])/10 + (3*ArcSinh[x^(5/2)])/20","A",5,4,15,0.2667,1,"{321, 329, 275, 215}"
1314,1,29,0,0.0102985,"\int \frac{x^{13/2}}{\sqrt{1+x^5}} \, dx","Int[x^(13/2)/Sqrt[1 + x^5],x]","\frac{1}{5} x^{5/2} \sqrt{x^5+1}-\frac{1}{5} \sinh ^{-1}\left(x^{5/2}\right)","\frac{1}{5} x^{5/2} \sqrt{x^5+1}-\frac{1}{5} \sinh ^{-1}\left(x^{5/2}\right)",1,"(x^(5/2)*Sqrt[1 + x^5])/5 - ArcSinh[x^(5/2)]/5","A",4,4,15,0.2667,1,"{321, 329, 275, 215}"
1315,1,10,0,0.0067993,"\int \frac{x^{3/2}}{\sqrt{1+x^5}} \, dx","Int[x^(3/2)/Sqrt[1 + x^5],x]","\frac{2}{5} \sinh ^{-1}\left(x^{5/2}\right)","\frac{2}{5} \sinh ^{-1}\left(x^{5/2}\right)",1,"(2*ArcSinh[x^(5/2)])/5","A",3,3,15,0.2000,1,"{329, 275, 215}"
1316,1,18,0,0.0029125,"\int \frac{1}{x^{7/2} \sqrt{1+x^5}} \, dx","Int[1/(x^(7/2)*Sqrt[1 + x^5]),x]","-\frac{2 \sqrt{x^5+1}}{5 x^{5/2}}","-\frac{2 \sqrt{x^5+1}}{5 x^{5/2}}",1,"(-2*Sqrt[1 + x^5])/(5*x^(5/2))","A",1,1,15,0.06667,1,"{264}"
1317,1,37,0,0.0067844,"\int \frac{1}{x^{17/2} \sqrt{1+x^5}} \, dx","Int[1/(x^(17/2)*Sqrt[1 + x^5]),x]","\frac{4 \sqrt{x^5+1}}{15 x^{5/2}}-\frac{2 \sqrt{x^5+1}}{15 x^{15/2}}","\frac{4 \sqrt{x^5+1}}{15 x^{5/2}}-\frac{2 \sqrt{x^5+1}}{15 x^{15/2}}",1,"(-2*Sqrt[1 + x^5])/(15*x^(15/2)) + (4*Sqrt[1 + x^5])/(15*x^(5/2))","A",2,2,15,0.1333,1,"{271, 264}"
1318,1,40,0,0.0208056,"\int \frac{x^8}{a+b x^6} \, dx","Int[x^8/(a + b*x^6),x]","\frac{x^3}{3 b}-\frac{\sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b} x^3}{\sqrt{a}}\right)}{3 b^{3/2}}","\frac{x^3}{3 b}-\frac{\sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b} x^3}{\sqrt{a}}\right)}{3 b^{3/2}}",1,"x^3/(3*b) - (Sqrt[a]*ArcTan[(Sqrt[b]*x^3)/Sqrt[a]])/(3*b^(3/2))","A",3,3,13,0.2308,1,"{275, 321, 205}"
1319,1,133,0,0.1224305,"\int \frac{x^7}{a+b x^6} \, dx","Int[x^7/(a + b*x^6),x]","\frac{\sqrt[3]{a} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x^2+b^{2/3} x^4\right)}{12 b^{4/3}}-\frac{\sqrt[3]{a} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{6 b^{4/3}}+\frac{\sqrt[3]{a} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x^2}{\sqrt{3} \sqrt[3]{a}}\right)}{2 \sqrt{3} b^{4/3}}+\frac{x^2}{2 b}","\frac{\sqrt[3]{a} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x^2+b^{2/3} x^4\right)}{12 b^{4/3}}-\frac{\sqrt[3]{a} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{6 b^{4/3}}+\frac{\sqrt[3]{a} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x^2}{\sqrt{3} \sqrt[3]{a}}\right)}{2 \sqrt{3} b^{4/3}}+\frac{x^2}{2 b}",1,"x^2/(2*b) + (a^(1/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x^2)/(Sqrt[3]*a^(1/3))])/(2*Sqrt[3]*b^(4/3)) - (a^(1/3)*Log[a^(1/3) + b^(1/3)*x^2])/(6*b^(4/3)) + (a^(1/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x^2 + b^(2/3)*x^4])/(12*b^(4/3))","A",8,8,13,0.6154,1,"{275, 321, 200, 31, 634, 617, 204, 628}"
1320,1,220,0,0.4232483,"\int \frac{x^6}{a+b x^6} \, dx","Int[x^6/(a + b*x^6),x]","\frac{\sqrt[6]{a} \log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{4 \sqrt{3} b^{7/6}}-\frac{\sqrt[6]{a} \log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{4 \sqrt{3} b^{7/6}}-\frac{\sqrt[6]{a} \tan ^{-1}\left(\frac{\sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{3 b^{7/6}}+\frac{\sqrt[6]{a} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a}-2 \sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{6 b^{7/6}}-\frac{\sqrt[6]{a} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a}+2 \sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{6 b^{7/6}}+\frac{x}{b}","\frac{\sqrt[6]{a} \log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{4 \sqrt{3} b^{7/6}}-\frac{\sqrt[6]{a} \log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{4 \sqrt{3} b^{7/6}}-\frac{\sqrt[6]{a} \tan ^{-1}\left(\frac{\sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{3 b^{7/6}}+\frac{\sqrt[6]{a} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a}-2 \sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{6 b^{7/6}}-\frac{\sqrt[6]{a} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a}+2 \sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{6 b^{7/6}}+\frac{x}{b}",1,"x/b - (a^(1/6)*ArcTan[(b^(1/6)*x)/a^(1/6)])/(3*b^(7/6)) + (a^(1/6)*ArcTan[(Sqrt[3]*a^(1/6) - 2*b^(1/6)*x)/a^(1/6)])/(6*b^(7/6)) - (a^(1/6)*ArcTan[(Sqrt[3]*a^(1/6) + 2*b^(1/6)*x)/a^(1/6)])/(6*b^(7/6)) + (a^(1/6)*Log[a^(1/3) - Sqrt[3]*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2])/(4*Sqrt[3]*b^(7/6)) - (a^(1/6)*Log[a^(1/3) + Sqrt[3]*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2])/(4*Sqrt[3]*b^(7/6))","A",11,7,13,0.5385,1,"{321, 209, 634, 618, 204, 628, 205}"
1321,1,15,0,0.0035342,"\int \frac{x^5}{a+b x^6} \, dx","Int[x^5/(a + b*x^6),x]","\frac{\log \left(a+b x^6\right)}{6 b}","\frac{\log \left(a+b x^6\right)}{6 b}",1,"Log[a + b*x^6]/(6*b)","A",1,1,13,0.07692,1,"{260}"
1322,1,215,0,0.4845034,"\int \frac{x^4}{a+b x^6} \, dx","Int[x^4/(a + b*x^6),x]","\frac{\log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{4 \sqrt{3} \sqrt[6]{a} b^{5/6}}-\frac{\log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{4 \sqrt{3} \sqrt[6]{a} b^{5/6}}+\frac{\tan ^{-1}\left(\frac{\sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{3 \sqrt[6]{a} b^{5/6}}-\frac{\tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a}-2 \sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{6 \sqrt[6]{a} b^{5/6}}+\frac{\tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a}+2 \sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{6 \sqrt[6]{a} b^{5/6}}","\frac{\log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{4 \sqrt{3} \sqrt[6]{a} b^{5/6}}-\frac{\log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{4 \sqrt{3} \sqrt[6]{a} b^{5/6}}+\frac{\tan ^{-1}\left(\frac{\sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{3 \sqrt[6]{a} b^{5/6}}-\frac{\tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a}-2 \sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{6 \sqrt[6]{a} b^{5/6}}+\frac{\tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a}+2 \sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{6 \sqrt[6]{a} b^{5/6}}",1,"ArcTan[(b^(1/6)*x)/a^(1/6)]/(3*a^(1/6)*b^(5/6)) - ArcTan[(Sqrt[3]*a^(1/6) - 2*b^(1/6)*x)/a^(1/6)]/(6*a^(1/6)*b^(5/6)) + ArcTan[(Sqrt[3]*a^(1/6) + 2*b^(1/6)*x)/a^(1/6)]/(6*a^(1/6)*b^(5/6)) + Log[a^(1/3) - Sqrt[3]*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2]/(4*Sqrt[3]*a^(1/6)*b^(5/6)) - Log[a^(1/3) + Sqrt[3]*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2]/(4*Sqrt[3]*a^(1/6)*b^(5/6))","A",10,6,13,0.4615,1,"{295, 634, 618, 204, 628, 205}"
1323,1,123,0,0.0921261,"\int \frac{x^3}{a+b x^6} \, dx","Int[x^3/(a + b*x^6),x]","\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x^2+b^{2/3} x^4\right)}{12 \sqrt[3]{a} b^{2/3}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{6 \sqrt[3]{a} b^{2/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x^2}{\sqrt{3} \sqrt[3]{a}}\right)}{2 \sqrt{3} \sqrt[3]{a} b^{2/3}}","\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x^2+b^{2/3} x^4\right)}{12 \sqrt[3]{a} b^{2/3}}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{6 \sqrt[3]{a} b^{2/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x^2}{\sqrt{3} \sqrt[3]{a}}\right)}{2 \sqrt{3} \sqrt[3]{a} b^{2/3}}",1,"-ArcTan[(a^(1/3) - 2*b^(1/3)*x^2)/(Sqrt[3]*a^(1/3))]/(2*Sqrt[3]*a^(1/3)*b^(2/3)) - Log[a^(1/3) + b^(1/3)*x^2]/(6*a^(1/3)*b^(2/3)) + Log[a^(2/3) - a^(1/3)*b^(1/3)*x^2 + b^(2/3)*x^4]/(12*a^(1/3)*b^(2/3))","A",7,7,13,0.5385,1,"{275, 292, 31, 634, 617, 204, 628}"
1324,1,29,0,0.0121066,"\int \frac{x^2}{a+b x^6} \, dx","Int[x^2/(a + b*x^6),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x^3}{\sqrt{a}}\right)}{3 \sqrt{a} \sqrt{b}}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x^3}{\sqrt{a}}\right)}{3 \sqrt{a} \sqrt{b}}",1,"ArcTan[(Sqrt[b]*x^3)/Sqrt[a]]/(3*Sqrt[a]*Sqrt[b])","A",2,2,13,0.1538,1,"{275, 205}"
1325,1,123,0,0.0868375,"\int \frac{x}{a+b x^6} \, dx","Int[x/(a + b*x^6),x]","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x^2+b^{2/3} x^4\right)}{12 a^{2/3} \sqrt[3]{b}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{6 a^{2/3} \sqrt[3]{b}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x^2}{\sqrt{3} \sqrt[3]{a}}\right)}{2 \sqrt{3} a^{2/3} \sqrt[3]{b}}","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x^2+b^{2/3} x^4\right)}{12 a^{2/3} \sqrt[3]{b}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{6 a^{2/3} \sqrt[3]{b}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x^2}{\sqrt{3} \sqrt[3]{a}}\right)}{2 \sqrt{3} a^{2/3} \sqrt[3]{b}}",1,"-ArcTan[(a^(1/3) - 2*b^(1/3)*x^2)/(Sqrt[3]*a^(1/3))]/(2*Sqrt[3]*a^(2/3)*b^(1/3)) + Log[a^(1/3) + b^(1/3)*x^2]/(6*a^(2/3)*b^(1/3)) - Log[a^(2/3) - a^(1/3)*b^(1/3)*x^2 + b^(2/3)*x^4]/(12*a^(2/3)*b^(1/3))","A",7,7,11,0.6364,1,"{275, 200, 31, 634, 617, 204, 628}"
1326,1,215,0,0.3982417,"\int \frac{1}{a+b x^6} \, dx","Int[(a + b*x^6)^(-1),x]","-\frac{\log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{4 \sqrt{3} a^{5/6} \sqrt[6]{b}}+\frac{\log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{4 \sqrt{3} a^{5/6} \sqrt[6]{b}}+\frac{\tan ^{-1}\left(\frac{\sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{3 a^{5/6} \sqrt[6]{b}}-\frac{\tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a}-2 \sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{6 a^{5/6} \sqrt[6]{b}}+\frac{\tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a}+2 \sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{6 a^{5/6} \sqrt[6]{b}}","-\frac{\log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{4 \sqrt{3} a^{5/6} \sqrt[6]{b}}+\frac{\log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{4 \sqrt{3} a^{5/6} \sqrt[6]{b}}+\frac{\tan ^{-1}\left(\frac{\sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{3 a^{5/6} \sqrt[6]{b}}-\frac{\tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a}-2 \sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{6 a^{5/6} \sqrt[6]{b}}+\frac{\tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a}+2 \sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{6 a^{5/6} \sqrt[6]{b}}",1,"ArcTan[(b^(1/6)*x)/a^(1/6)]/(3*a^(5/6)*b^(1/6)) - ArcTan[(Sqrt[3]*a^(1/6) - 2*b^(1/6)*x)/a^(1/6)]/(6*a^(5/6)*b^(1/6)) + ArcTan[(Sqrt[3]*a^(1/6) + 2*b^(1/6)*x)/a^(1/6)]/(6*a^(5/6)*b^(1/6)) - Log[a^(1/3) - Sqrt[3]*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2]/(4*Sqrt[3]*a^(5/6)*b^(1/6)) + Log[a^(1/3) + Sqrt[3]*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2]/(4*Sqrt[3]*a^(5/6)*b^(1/6))","A",10,6,9,0.6667,1,"{209, 634, 618, 204, 628, 205}"
1327,1,22,0,0.0113709,"\int \frac{1}{x \left(a+b x^6\right)} \, dx","Int[1/(x*(a + b*x^6)),x]","\frac{\log (x)}{a}-\frac{\log \left(a+b x^6\right)}{6 a}","\frac{\log (x)}{a}-\frac{\log \left(a+b x^6\right)}{6 a}",1,"Log[x]/a - Log[a + b*x^6]/(6*a)","A",4,4,13,0.3077,1,"{266, 36, 29, 31}"
1328,1,223,0,0.4799362,"\int \frac{1}{x^2 \left(a+b x^6\right)} \, dx","Int[1/(x^2*(a + b*x^6)),x]","-\frac{\sqrt[6]{b} \log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{4 \sqrt{3} a^{7/6}}+\frac{\sqrt[6]{b} \log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{4 \sqrt{3} a^{7/6}}-\frac{\sqrt[6]{b} \tan ^{-1}\left(\frac{\sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{3 a^{7/6}}+\frac{\sqrt[6]{b} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a}-2 \sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{6 a^{7/6}}-\frac{\sqrt[6]{b} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a}+2 \sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{6 a^{7/6}}-\frac{1}{a x}","-\frac{\sqrt[6]{b} \log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{4 \sqrt{3} a^{7/6}}+\frac{\sqrt[6]{b} \log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{4 \sqrt{3} a^{7/6}}-\frac{\sqrt[6]{b} \tan ^{-1}\left(\frac{\sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{3 a^{7/6}}+\frac{\sqrt[6]{b} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a}-2 \sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{6 a^{7/6}}-\frac{\sqrt[6]{b} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a}+2 \sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{6 a^{7/6}}-\frac{1}{a x}",1,"-(1/(a*x)) - (b^(1/6)*ArcTan[(b^(1/6)*x)/a^(1/6)])/(3*a^(7/6)) + (b^(1/6)*ArcTan[(Sqrt[3]*a^(1/6) - 2*b^(1/6)*x)/a^(1/6)])/(6*a^(7/6)) - (b^(1/6)*ArcTan[(Sqrt[3]*a^(1/6) + 2*b^(1/6)*x)/a^(1/6)])/(6*a^(7/6)) - (b^(1/6)*Log[a^(1/3) - Sqrt[3]*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2])/(4*Sqrt[3]*a^(7/6)) + (b^(1/6)*Log[a^(1/3) + Sqrt[3]*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2])/(4*Sqrt[3]*a^(7/6))","A",11,7,13,0.5385,1,"{325, 295, 634, 618, 204, 628, 205}"
1329,1,133,0,0.1047052,"\int \frac{1}{x^3 \left(a+b x^6\right)} \, dx","Int[1/(x^3*(a + b*x^6)),x]","-\frac{\sqrt[3]{b} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x^2+b^{2/3} x^4\right)}{12 a^{4/3}}+\frac{\sqrt[3]{b} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{6 a^{4/3}}+\frac{\sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x^2}{\sqrt{3} \sqrt[3]{a}}\right)}{2 \sqrt{3} a^{4/3}}-\frac{1}{2 a x^2}","-\frac{\sqrt[3]{b} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x^2+b^{2/3} x^4\right)}{12 a^{4/3}}+\frac{\sqrt[3]{b} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{6 a^{4/3}}+\frac{\sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x^2}{\sqrt{3} \sqrt[3]{a}}\right)}{2 \sqrt{3} a^{4/3}}-\frac{1}{2 a x^2}",1,"-1/(2*a*x^2) + (b^(1/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x^2)/(Sqrt[3]*a^(1/3))])/(2*Sqrt[3]*a^(4/3)) + (b^(1/3)*Log[a^(1/3) + b^(1/3)*x^2])/(6*a^(4/3)) - (b^(1/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x^2 + b^(2/3)*x^4])/(12*a^(4/3))","A",8,8,13,0.6154,1,"{275, 325, 292, 31, 634, 617, 204, 628}"
1330,1,40,0,0.0187189,"\int \frac{1}{x^4 \left(a+b x^6\right)} \, dx","Int[1/(x^4*(a + b*x^6)),x]","-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} x^3}{\sqrt{a}}\right)}{3 a^{3/2}}-\frac{1}{3 a x^3}","-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} x^3}{\sqrt{a}}\right)}{3 a^{3/2}}-\frac{1}{3 a x^3}",1,"-1/(3*a*x^3) - (Sqrt[b]*ArcTan[(Sqrt[b]*x^3)/Sqrt[a]])/(3*a^(3/2))","A",3,3,13,0.2308,1,"{275, 325, 205}"
1331,1,49,0,0.0236848,"\int \frac{x^8}{\left(a+b x^6\right)^2} \, dx","Int[x^8/(a + b*x^6)^2,x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x^3}{\sqrt{a}}\right)}{6 \sqrt{a} b^{3/2}}-\frac{x^3}{6 b \left(a+b x^6\right)}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x^3}{\sqrt{a}}\right)}{6 \sqrt{a} b^{3/2}}-\frac{x^3}{6 b \left(a+b x^6\right)}",1,"-x^3/(6*b*(a + b*x^6)) + ArcTan[(Sqrt[b]*x^3)/Sqrt[a]]/(6*Sqrt[a]*b^(3/2))","A",3,3,13,0.2308,1,"{275, 288, 205}"
1332,1,142,0,0.1064253,"\int \frac{x^7}{\left(a+b x^6\right)^2} \, dx","Int[x^7/(a + b*x^6)^2,x]","\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{18 a^{2/3} b^{4/3}}-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x^2+b^{2/3} x^4\right)}{36 a^{2/3} b^{4/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x^2}{\sqrt{3} \sqrt[3]{a}}\right)}{6 \sqrt{3} a^{2/3} b^{4/3}}-\frac{x^2}{6 b \left(a+b x^6\right)}","\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{18 a^{2/3} b^{4/3}}-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x^2+b^{2/3} x^4\right)}{36 a^{2/3} b^{4/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x^2}{\sqrt{3} \sqrt[3]{a}}\right)}{6 \sqrt{3} a^{2/3} b^{4/3}}-\frac{x^2}{6 b \left(a+b x^6\right)}",1,"-x^2/(6*b*(a + b*x^6)) - ArcTan[(a^(1/3) - 2*b^(1/3)*x^2)/(Sqrt[3]*a^(1/3))]/(6*Sqrt[3]*a^(2/3)*b^(4/3)) + Log[a^(1/3) + b^(1/3)*x^2]/(18*a^(2/3)*b^(4/3)) - Log[a^(2/3) - a^(1/3)*b^(1/3)*x^2 + b^(2/3)*x^4]/(36*a^(2/3)*b^(4/3))","A",8,8,13,0.6154,1,"{275, 288, 200, 31, 634, 617, 204, 628}"
1333,1,232,0,0.4192705,"\int \frac{x^6}{\left(a+b x^6\right)^2} \, dx","Int[x^6/(a + b*x^6)^2,x]","-\frac{\log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{24 \sqrt{3} a^{5/6} b^{7/6}}+\frac{\log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{24 \sqrt{3} a^{5/6} b^{7/6}}+\frac{\tan ^{-1}\left(\frac{\sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{18 a^{5/6} b^{7/6}}-\frac{\tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a}-2 \sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{36 a^{5/6} b^{7/6}}+\frac{\tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a}+2 \sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{36 a^{5/6} b^{7/6}}-\frac{x}{6 b \left(a+b x^6\right)}","-\frac{\log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{24 \sqrt{3} a^{5/6} b^{7/6}}+\frac{\log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{24 \sqrt{3} a^{5/6} b^{7/6}}+\frac{\tan ^{-1}\left(\frac{\sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{18 a^{5/6} b^{7/6}}-\frac{\tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a}-2 \sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{36 a^{5/6} b^{7/6}}+\frac{\tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a}+2 \sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{36 a^{5/6} b^{7/6}}-\frac{x}{6 b \left(a+b x^6\right)}",1,"-x/(6*b*(a + b*x^6)) + ArcTan[(b^(1/6)*x)/a^(1/6)]/(18*a^(5/6)*b^(7/6)) - ArcTan[(Sqrt[3]*a^(1/6) - 2*b^(1/6)*x)/a^(1/6)]/(36*a^(5/6)*b^(7/6)) + ArcTan[(Sqrt[3]*a^(1/6) + 2*b^(1/6)*x)/a^(1/6)]/(36*a^(5/6)*b^(7/6)) - Log[a^(1/3) - Sqrt[3]*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2]/(24*Sqrt[3]*a^(5/6)*b^(7/6)) + Log[a^(1/3) + Sqrt[3]*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2]/(24*Sqrt[3]*a^(5/6)*b^(7/6))","A",11,7,13,0.5385,1,"{288, 209, 634, 618, 204, 628, 205}"
1334,1,16,0,0.0033566,"\int \frac{x^5}{\left(a+b x^6\right)^2} \, dx","Int[x^5/(a + b*x^6)^2,x]","-\frac{1}{6 b \left(a+b x^6\right)}","-\frac{1}{6 b \left(a+b x^6\right)}",1,"-1/(6*b*(a + b*x^6))","A",1,1,13,0.07692,1,"{261}"
1335,1,234,0,0.4831828,"\int \frac{x^4}{\left(a+b x^6\right)^2} \, dx","Int[x^4/(a + b*x^6)^2,x]","\frac{\log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{24 \sqrt{3} a^{7/6} b^{5/6}}-\frac{\log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{24 \sqrt{3} a^{7/6} b^{5/6}}+\frac{\tan ^{-1}\left(\frac{\sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{18 a^{7/6} b^{5/6}}-\frac{\tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a}-2 \sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{36 a^{7/6} b^{5/6}}+\frac{\tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a}+2 \sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{36 a^{7/6} b^{5/6}}+\frac{x^5}{6 a \left(a+b x^6\right)}","\frac{\log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{24 \sqrt{3} a^{7/6} b^{5/6}}-\frac{\log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{24 \sqrt{3} a^{7/6} b^{5/6}}+\frac{\tan ^{-1}\left(\frac{\sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{18 a^{7/6} b^{5/6}}-\frac{\tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a}-2 \sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{36 a^{7/6} b^{5/6}}+\frac{\tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a}+2 \sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{36 a^{7/6} b^{5/6}}+\frac{x^5}{6 a \left(a+b x^6\right)}",1,"x^5/(6*a*(a + b*x^6)) + ArcTan[(b^(1/6)*x)/a^(1/6)]/(18*a^(7/6)*b^(5/6)) - ArcTan[(Sqrt[3]*a^(1/6) - 2*b^(1/6)*x)/a^(1/6)]/(36*a^(7/6)*b^(5/6)) + ArcTan[(Sqrt[3]*a^(1/6) + 2*b^(1/6)*x)/a^(1/6)]/(36*a^(7/6)*b^(5/6)) + Log[a^(1/3) - Sqrt[3]*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2]/(24*Sqrt[3]*a^(7/6)*b^(5/6)) - Log[a^(1/3) + Sqrt[3]*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2]/(24*Sqrt[3]*a^(7/6)*b^(5/6))","A",11,7,13,0.5385,1,"{290, 295, 634, 618, 204, 628, 205}"
1336,1,142,0,0.1093502,"\int \frac{x^3}{\left(a+b x^6\right)^2} \, dx","Int[x^3/(a + b*x^6)^2,x]","-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{18 a^{4/3} b^{2/3}}+\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x^2+b^{2/3} x^4\right)}{36 a^{4/3} b^{2/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x^2}{\sqrt{3} \sqrt[3]{a}}\right)}{6 \sqrt{3} a^{4/3} b^{2/3}}+\frac{x^4}{6 a \left(a+b x^6\right)}","-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{18 a^{4/3} b^{2/3}}+\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x^2+b^{2/3} x^4\right)}{36 a^{4/3} b^{2/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x^2}{\sqrt{3} \sqrt[3]{a}}\right)}{6 \sqrt{3} a^{4/3} b^{2/3}}+\frac{x^4}{6 a \left(a+b x^6\right)}",1,"x^4/(6*a*(a + b*x^6)) - ArcTan[(a^(1/3) - 2*b^(1/3)*x^2)/(Sqrt[3]*a^(1/3))]/(6*Sqrt[3]*a^(4/3)*b^(2/3)) - Log[a^(1/3) + b^(1/3)*x^2]/(18*a^(4/3)*b^(2/3)) + Log[a^(2/3) - a^(1/3)*b^(1/3)*x^2 + b^(2/3)*x^4]/(36*a^(4/3)*b^(2/3))","A",8,8,13,0.6154,1,"{275, 290, 292, 31, 634, 617, 204, 628}"
1337,1,49,0,0.0222814,"\int \frac{x^2}{\left(a+b x^6\right)^2} \, dx","Int[x^2/(a + b*x^6)^2,x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x^3}{\sqrt{a}}\right)}{6 a^{3/2} \sqrt{b}}+\frac{x^3}{6 a \left(a+b x^6\right)}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x^3}{\sqrt{a}}\right)}{6 a^{3/2} \sqrt{b}}+\frac{x^3}{6 a \left(a+b x^6\right)}",1,"x^3/(6*a*(a + b*x^6)) + ArcTan[(Sqrt[b]*x^3)/Sqrt[a]]/(6*a^(3/2)*Sqrt[b])","A",3,3,13,0.2308,1,"{275, 199, 205}"
1338,1,142,0,0.1036092,"\int \frac{x}{\left(a+b x^6\right)^2} \, dx","Int[x/(a + b*x^6)^2,x]","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x^2+b^{2/3} x^4\right)}{18 a^{5/3} \sqrt[3]{b}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{9 a^{5/3} \sqrt[3]{b}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x^2}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{5/3} \sqrt[3]{b}}+\frac{x^2}{6 a \left(a+b x^6\right)}","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x^2+b^{2/3} x^4\right)}{18 a^{5/3} \sqrt[3]{b}}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{9 a^{5/3} \sqrt[3]{b}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x^2}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{5/3} \sqrt[3]{b}}+\frac{x^2}{6 a \left(a+b x^6\right)}",1,"x^2/(6*a*(a + b*x^6)) - ArcTan[(a^(1/3) - 2*b^(1/3)*x^2)/(Sqrt[3]*a^(1/3))]/(3*Sqrt[3]*a^(5/3)*b^(1/3)) + Log[a^(1/3) + b^(1/3)*x^2]/(9*a^(5/3)*b^(1/3)) - Log[a^(2/3) - a^(1/3)*b^(1/3)*x^2 + b^(2/3)*x^4]/(18*a^(5/3)*b^(1/3))","A",8,8,11,0.7273,1,"{275, 199, 200, 31, 634, 617, 204, 628}"
1339,1,232,0,0.3969522,"\int \frac{1}{\left(a+b x^6\right)^2} \, dx","Int[(a + b*x^6)^(-2),x]","-\frac{5 \log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{24 \sqrt{3} a^{11/6} \sqrt[6]{b}}+\frac{5 \log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{24 \sqrt{3} a^{11/6} \sqrt[6]{b}}+\frac{5 \tan ^{-1}\left(\frac{\sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{18 a^{11/6} \sqrt[6]{b}}-\frac{5 \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a}-2 \sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{36 a^{11/6} \sqrt[6]{b}}+\frac{5 \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a}+2 \sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{36 a^{11/6} \sqrt[6]{b}}+\frac{x}{6 a \left(a+b x^6\right)}","-\frac{5 \log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{24 \sqrt{3} a^{11/6} \sqrt[6]{b}}+\frac{5 \log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{24 \sqrt{3} a^{11/6} \sqrt[6]{b}}+\frac{5 \tan ^{-1}\left(\frac{\sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{18 a^{11/6} \sqrt[6]{b}}-\frac{5 \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a}-2 \sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{36 a^{11/6} \sqrt[6]{b}}+\frac{5 \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a}+2 \sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{36 a^{11/6} \sqrt[6]{b}}+\frac{x}{6 a \left(a+b x^6\right)}",1,"x/(6*a*(a + b*x^6)) + (5*ArcTan[(b^(1/6)*x)/a^(1/6)])/(18*a^(11/6)*b^(1/6)) - (5*ArcTan[(Sqrt[3]*a^(1/6) - 2*b^(1/6)*x)/a^(1/6)])/(36*a^(11/6)*b^(1/6)) + (5*ArcTan[(Sqrt[3]*a^(1/6) + 2*b^(1/6)*x)/a^(1/6)])/(36*a^(11/6)*b^(1/6)) - (5*Log[a^(1/3) - Sqrt[3]*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2])/(24*Sqrt[3]*a^(11/6)*b^(1/6)) + (5*Log[a^(1/3) + Sqrt[3]*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2])/(24*Sqrt[3]*a^(11/6)*b^(1/6))","A",11,7,9,0.7778,1,"{199, 209, 634, 618, 204, 628, 205}"
1340,1,38,0,0.0280392,"\int \frac{1}{x \left(a+b x^6\right)^2} \, dx","Int[1/(x*(a + b*x^6)^2),x]","-\frac{\log \left(a+b x^6\right)}{6 a^2}+\frac{\log (x)}{a^2}+\frac{1}{6 a \left(a+b x^6\right)}","-\frac{\log \left(a+b x^6\right)}{6 a^2}+\frac{\log (x)}{a^2}+\frac{1}{6 a \left(a+b x^6\right)}",1,"1/(6*a*(a + b*x^6)) + Log[x]/a^2 - Log[a + b*x^6]/(6*a^2)","A",3,2,13,0.1538,1,"{266, 44}"
1341,1,244,0,0.4977615,"\int \frac{1}{x^2 \left(a+b x^6\right)^2} \, dx","Int[1/(x^2*(a + b*x^6)^2),x]","-\frac{7 \sqrt[6]{b} \log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{24 \sqrt{3} a^{13/6}}+\frac{7 \sqrt[6]{b} \log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{24 \sqrt{3} a^{13/6}}-\frac{7 \sqrt[6]{b} \tan ^{-1}\left(\frac{\sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{18 a^{13/6}}+\frac{7 \sqrt[6]{b} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a}-2 \sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{36 a^{13/6}}-\frac{7 \sqrt[6]{b} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a}+2 \sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{36 a^{13/6}}-\frac{7}{6 a^2 x}+\frac{1}{6 a x \left(a+b x^6\right)}","-\frac{7 \sqrt[6]{b} \log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{24 \sqrt{3} a^{13/6}}+\frac{7 \sqrt[6]{b} \log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{24 \sqrt{3} a^{13/6}}-\frac{7 \sqrt[6]{b} \tan ^{-1}\left(\frac{\sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{18 a^{13/6}}+\frac{7 \sqrt[6]{b} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a}-2 \sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{36 a^{13/6}}-\frac{7 \sqrt[6]{b} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a}+2 \sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{36 a^{13/6}}-\frac{7}{6 a^2 x}+\frac{1}{6 a x \left(a+b x^6\right)}",1,"-7/(6*a^2*x) + 1/(6*a*x*(a + b*x^6)) - (7*b^(1/6)*ArcTan[(b^(1/6)*x)/a^(1/6)])/(18*a^(13/6)) + (7*b^(1/6)*ArcTan[(Sqrt[3]*a^(1/6) - 2*b^(1/6)*x)/a^(1/6)])/(36*a^(13/6)) - (7*b^(1/6)*ArcTan[(Sqrt[3]*a^(1/6) + 2*b^(1/6)*x)/a^(1/6)])/(36*a^(13/6)) - (7*b^(1/6)*Log[a^(1/3) - Sqrt[3]*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2])/(24*Sqrt[3]*a^(13/6)) + (7*b^(1/6)*Log[a^(1/3) + Sqrt[3]*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2])/(24*Sqrt[3]*a^(13/6))","A",12,8,13,0.6154,1,"{290, 325, 295, 634, 618, 204, 628, 205}"
1342,1,152,0,0.1290186,"\int \frac{1}{x^3 \left(a+b x^6\right)^2} \, dx","Int[1/(x^3*(a + b*x^6)^2),x]","-\frac{\sqrt[3]{b} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x^2+b^{2/3} x^4\right)}{9 a^{7/3}}+\frac{2 \sqrt[3]{b} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{9 a^{7/3}}+\frac{2 \sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x^2}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{7/3}}-\frac{2}{3 a^2 x^2}+\frac{1}{6 a x^2 \left(a+b x^6\right)}","-\frac{\sqrt[3]{b} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x^2+b^{2/3} x^4\right)}{9 a^{7/3}}+\frac{2 \sqrt[3]{b} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{9 a^{7/3}}+\frac{2 \sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x^2}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{7/3}}-\frac{2}{3 a^2 x^2}+\frac{1}{6 a x^2 \left(a+b x^6\right)}",1,"-2/(3*a^2*x^2) + 1/(6*a*x^2*(a + b*x^6)) + (2*b^(1/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x^2)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(7/3)) + (2*b^(1/3)*Log[a^(1/3) + b^(1/3)*x^2])/(9*a^(7/3)) - (b^(1/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x^2 + b^(2/3)*x^4])/(9*a^(7/3))","A",9,9,13,0.6923,1,"{275, 290, 325, 292, 31, 634, 617, 204, 628}"
1343,1,59,0,0.031776,"\int \frac{1}{x^4 \left(a+b x^6\right)^2} \, dx","Int[1/(x^4*(a + b*x^6)^2),x]","-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} x^3}{\sqrt{a}}\right)}{2 a^{5/2}}-\frac{1}{2 a^2 x^3}+\frac{1}{6 a x^3 \left(a+b x^6\right)}","-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} x^3}{\sqrt{a}}\right)}{2 a^{5/2}}-\frac{1}{2 a^2 x^3}+\frac{1}{6 a x^3 \left(a+b x^6\right)}",1,"-1/(2*a^2*x^3) + 1/(6*a*x^3*(a + b*x^6)) - (Sqrt[b]*ArcTan[(Sqrt[b]*x^3)/Sqrt[a]])/(2*a^(5/2))","A",4,4,13,0.3077,1,"{275, 290, 325, 205}"
1344,1,16,0,0.007649,"\int \frac{x^8}{1-x^6} \, dx","Int[x^8/(1 - x^6),x]","\frac{1}{3} \tanh ^{-1}\left(x^3\right)-\frac{x^3}{3}","\frac{1}{3} \tanh ^{-1}\left(x^3\right)-\frac{x^3}{3}",1,"-x^3/3 + ArcTanh[x^3]/3","A",3,3,13,0.2308,1,"{275, 321, 206}"
1345,1,56,0,0.0413207,"\int \frac{x^7}{1-x^6} \, dx","Int[x^7/(1 - x^6),x]","-\frac{x^2}{2}-\frac{1}{6} \log \left(1-x^2\right)+\frac{1}{12} \log \left(x^4+x^2+1\right)+\frac{\tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)}{2 \sqrt{3}}","-\frac{x^2}{2}-\frac{1}{6} \log \left(1-x^2\right)+\frac{1}{12} \log \left(x^4+x^2+1\right)+\frac{\tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)}{2 \sqrt{3}}",1,"-x^2/2 + ArcTan[(1 + 2*x^2)/Sqrt[3]]/(2*Sqrt[3]) - Log[1 - x^2]/6 + Log[1 + x^2 + x^4]/12","A",8,8,13,0.6154,1,"{275, 321, 200, 31, 634, 618, 204, 628}"
1346,1,76,0,0.1089114,"\int \frac{x^6}{1-x^6} \, dx","Int[x^6/(1 - x^6),x]","-\frac{1}{12} \log \left(x^2-x+1\right)+\frac{1}{12} \log \left(x^2+x+1\right)-x-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{1}{3} \tanh ^{-1}(x)","\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{1-x^2}\right)}{2 \sqrt{3}}+\frac{1}{6} \tanh ^{-1}\left(\frac{x}{x^2+1}\right)-x+\frac{1}{3} \tanh ^{-1}(x)",1,"-x - ArcTan[(1 - 2*x)/Sqrt[3]]/(2*Sqrt[3]) + ArcTan[(1 + 2*x)/Sqrt[3]]/(2*Sqrt[3]) + ArcTanh[x]/3 - Log[1 - x + x^2]/12 + Log[1 + x + x^2]/12","A",11,7,13,0.5385,1,"{321, 210, 634, 618, 204, 628, 206}"
1347,1,12,0,0.0025075,"\int \frac{x^5}{1-x^6} \, dx","Int[x^5/(1 - x^6),x]","-\frac{1}{6} \log \left(1-x^6\right)","-\frac{1}{6} \log \left(1-x^6\right)",1,"-Log[1 - x^6]/6","A",1,1,13,0.07692,1,"{260}"
1348,1,73,0,0.1486024,"\int \frac{x^4}{1-x^6} \, dx","Int[x^4/(1 - x^6),x]","-\frac{1}{12} \log \left(x^2-x+1\right)+\frac{1}{12} \log \left(x^2+x+1\right)+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{1}{3} \tanh ^{-1}(x)","-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{1-x^2}\right)}{2 \sqrt{3}}+\frac{1}{6} \tanh ^{-1}\left(\frac{x}{x^2+1}\right)+\frac{1}{3} \tanh ^{-1}(x)",1,"ArcTan[(1 - 2*x)/Sqrt[3]]/(2*Sqrt[3]) - ArcTan[(1 + 2*x)/Sqrt[3]]/(2*Sqrt[3]) + ArcTanh[x]/3 - Log[1 - x + x^2]/12 + Log[1 + x + x^2]/12","A",10,6,13,0.4615,1,"{296, 634, 618, 204, 628, 206}"
1349,1,49,0,0.0367543,"\int \frac{x^3}{1-x^6} \, dx","Int[x^3/(1 - x^6),x]","-\frac{1}{6} \log \left(1-x^2\right)+\frac{1}{12} \log \left(x^4+x^2+1\right)-\frac{\tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)}{2 \sqrt{3}}","-\frac{1}{6} \log \left(1-x^2\right)+\frac{1}{12} \log \left(x^4+x^2+1\right)-\frac{\tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)}{2 \sqrt{3}}",1,"-ArcTan[(1 + 2*x^2)/Sqrt[3]]/(2*Sqrt[3]) - Log[1 - x^2]/6 + Log[1 + x^2 + x^4]/12","A",7,7,13,0.5385,1,"{275, 292, 31, 634, 618, 204, 628}"
1350,1,8,0,0.0037426,"\int \frac{x^2}{1-x^6} \, dx","Int[x^2/(1 - x^6),x]","\frac{1}{3} \tanh ^{-1}\left(x^3\right)","\frac{1}{3} \tanh ^{-1}\left(x^3\right)",1,"ArcTanh[x^3]/3","A",2,2,13,0.1538,1,"{275, 206}"
1351,1,49,0,0.0356634,"\int \frac{x}{1-x^6} \, dx","Int[x/(1 - x^6),x]","-\frac{1}{6} \log \left(1-x^2\right)+\frac{1}{12} \log \left(x^4+x^2+1\right)+\frac{\tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)}{2 \sqrt{3}}","-\frac{1}{6} \log \left(1-x^2\right)+\frac{1}{12} \log \left(x^4+x^2+1\right)+\frac{\tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)}{2 \sqrt{3}}",1,"ArcTan[(1 + 2*x^2)/Sqrt[3]]/(2*Sqrt[3]) - Log[1 - x^2]/6 + Log[1 + x^2 + x^4]/12","A",7,7,11,0.6364,1,"{275, 200, 31, 634, 618, 204, 628}"
1352,1,73,0,0.1036422,"\int \frac{1}{1-x^6} \, dx","Int[(1 - x^6)^(-1),x]","-\frac{1}{12} \log \left(x^2-x+1\right)+\frac{1}{12} \log \left(x^2+x+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{1}{3} \tanh ^{-1}(x)","\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{1-x^2}\right)}{2 \sqrt{3}}+\frac{1}{6} \tanh ^{-1}\left(\frac{x}{x^2+1}\right)+\frac{1}{3} \tanh ^{-1}(x)",1,"-ArcTan[(1 - 2*x)/Sqrt[3]]/(2*Sqrt[3]) + ArcTan[(1 + 2*x)/Sqrt[3]]/(2*Sqrt[3]) + ArcTanh[x]/3 - Log[1 - x + x^2]/12 + Log[1 + x + x^2]/12","A",10,6,9,0.6667,1,"{210, 634, 618, 204, 628, 206}"
1353,1,15,0,0.007056,"\int \frac{1}{x \left(1-x^6\right)} \, dx","Int[1/(x*(1 - x^6)),x]","\log (x)-\frac{1}{6} \log \left(1-x^6\right)","\log (x)-\frac{1}{6} \log \left(1-x^6\right)",1,"Log[x] - Log[1 - x^6]/6","A",4,4,13,0.3077,1,"{266, 36, 31, 29}"
1354,1,78,0,0.1492134,"\int \frac{1}{x^2 \left(1-x^6\right)} \, dx","Int[1/(x^2*(1 - x^6)),x]","-\frac{1}{12} \log \left(x^2-x+1\right)+\frac{1}{12} \log \left(x^2+x+1\right)-\frac{1}{x}+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{1}{3} \tanh ^{-1}(x)","-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{1-x^2}\right)}{2 \sqrt{3}}+\frac{1}{6} \tanh ^{-1}\left(\frac{x}{x^2+1}\right)-\frac{1}{x}+\frac{1}{3} \tanh ^{-1}(x)",1,"-x^(-1) + ArcTan[(1 - 2*x)/Sqrt[3]]/(2*Sqrt[3]) - ArcTan[(1 + 2*x)/Sqrt[3]]/(2*Sqrt[3]) + ArcTanh[x]/3 - Log[1 - x + x^2]/12 + Log[1 + x + x^2]/12","A",11,7,13,0.5385,1,"{325, 296, 634, 618, 204, 628, 206}"
1355,1,56,0,0.0401109,"\int \frac{1}{x^3 \left(1-x^6\right)} \, dx","Int[1/(x^3*(1 - x^6)),x]","-\frac{1}{2 x^2}-\frac{1}{6} \log \left(1-x^2\right)+\frac{1}{12} \log \left(x^4+x^2+1\right)-\frac{\tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)}{2 \sqrt{3}}","-\frac{1}{2 x^2}-\frac{1}{6} \log \left(1-x^2\right)+\frac{1}{12} \log \left(x^4+x^2+1\right)-\frac{\tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)}{2 \sqrt{3}}",1,"-1/(2*x^2) - ArcTan[(1 + 2*x^2)/Sqrt[3]]/(2*Sqrt[3]) - Log[1 - x^2]/6 + Log[1 + x^2 + x^4]/12","A",8,8,13,0.6154,1,"{275, 325, 292, 31, 634, 618, 204, 628}"
1356,1,16,0,0.0068052,"\int \frac{1}{x^4 \left(1-x^6\right)} \, dx","Int[1/(x^4*(1 - x^6)),x]","\frac{1}{3} \tanh ^{-1}\left(x^3\right)-\frac{1}{3 x^3}","\frac{1}{3} \tanh ^{-1}\left(x^3\right)-\frac{1}{3 x^3}",1,"-1/(3*x^3) + ArcTanh[x^3]/3","A",3,3,13,0.2308,1,"{275, 325, 206}"
1357,1,56,0,0.0381724,"\int \frac{1}{x^5 \left(1-x^6\right)} \, dx","Int[1/(x^5*(1 - x^6)),x]","-\frac{1}{4 x^4}-\frac{1}{6} \log \left(1-x^2\right)+\frac{1}{12} \log \left(x^4+x^2+1\right)+\frac{\tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)}{2 \sqrt{3}}","-\frac{1}{4 x^4}-\frac{1}{6} \log \left(1-x^2\right)+\frac{1}{12} \log \left(x^4+x^2+1\right)+\frac{\tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)}{2 \sqrt{3}}",1,"-1/(4*x^4) + ArcTan[(1 + 2*x^2)/Sqrt[3]]/(2*Sqrt[3]) - Log[1 - x^2]/6 + Log[1 + x^2 + x^4]/12","A",8,8,13,0.6154,1,"{275, 325, 200, 31, 634, 618, 204, 628}"
1358,1,80,0,0.1100311,"\int \frac{1}{x^6 \left(1-x^6\right)} \, dx","Int[1/(x^6*(1 - x^6)),x]","-\frac{1}{5 x^5}-\frac{1}{12} \log \left(x^2-x+1\right)+\frac{1}{12} \log \left(x^2+x+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{1}{3} \tanh ^{-1}(x)","-\frac{1}{5 x^5}-\frac{1}{12} \log \left(x^2-x+1\right)+\frac{1}{12} \log \left(x^2+x+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{1}{3} \tanh ^{-1}(x)",1,"-1/(5*x^5) - ArcTan[(1 - 2*x)/Sqrt[3]]/(2*Sqrt[3]) + ArcTan[(1 + 2*x)/Sqrt[3]]/(2*Sqrt[3]) + ArcTanh[x]/3 - Log[1 - x + x^2]/12 + Log[1 + x + x^2]/12","A",11,7,13,0.5385,1,"{325, 210, 634, 618, 204, 628, 206}"
1359,1,22,0,0.0121714,"\int \frac{1}{x^7 \left(1-x^6\right)} \, dx","Int[1/(x^7*(1 - x^6)),x]","-\frac{1}{6 x^6}-\frac{1}{6} \log \left(1-x^6\right)+\log (x)","-\frac{1}{6 x^6}-\frac{1}{6} \log \left(1-x^6\right)+\log (x)",1,"-1/(6*x^6) + Log[x] - Log[1 - x^6]/6","A",3,2,13,0.1538,1,"{266, 44}"
1360,1,85,0,0.1474896,"\int \frac{1}{x^8 \left(1-x^6\right)} \, dx","Int[1/(x^8*(1 - x^6)),x]","-\frac{1}{7 x^7}-\frac{1}{12} \log \left(x^2-x+1\right)+\frac{1}{12} \log \left(x^2+x+1\right)-\frac{1}{x}+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{1}{3} \tanh ^{-1}(x)","-\frac{1}{7 x^7}-\frac{1}{12} \log \left(x^2-x+1\right)+\frac{1}{12} \log \left(x^2+x+1\right)-\frac{1}{x}+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{1}{3} \tanh ^{-1}(x)",1,"-1/(7*x^7) - x^(-1) + ArcTan[(1 - 2*x)/Sqrt[3]]/(2*Sqrt[3]) - ArcTan[(1 + 2*x)/Sqrt[3]]/(2*Sqrt[3]) + ArcTanh[x]/3 - Log[1 - x + x^2]/12 + Log[1 + x + x^2]/12","A",12,7,13,0.5385,1,"{325, 296, 634, 618, 204, 628, 206}"
1361,1,16,0,0.0058482,"\int \frac{x^8}{1+x^6} \, dx","Int[x^8/(1 + x^6),x]","\frac{x^3}{3}-\frac{1}{3} \tan ^{-1}\left(x^3\right)","\frac{x^3}{3}-\frac{1}{3} \tan ^{-1}\left(x^3\right)",1,"x^3/3 - ArcTan[x^3]/3","A",3,3,11,0.2727,1,"{275, 321, 203}"
1362,1,56,0,0.0428234,"\int \frac{x^7}{1+x^6} \, dx","Int[x^7/(1 + x^6),x]","\frac{x^2}{2}-\frac{1}{6} \log \left(x^2+1\right)+\frac{1}{12} \log \left(x^4-x^2+1\right)+\frac{\tan ^{-1}\left(\frac{1-2 x^2}{\sqrt{3}}\right)}{2 \sqrt{3}}","\frac{x^2}{2}-\frac{1}{6} \log \left(x^2+1\right)+\frac{1}{12} \log \left(x^4-x^2+1\right)+\frac{\tan ^{-1}\left(\frac{1-2 x^2}{\sqrt{3}}\right)}{2 \sqrt{3}}",1,"x^2/2 + ArcTan[(1 - 2*x^2)/Sqrt[3]]/(2*Sqrt[3]) - Log[1 + x^2]/6 + Log[1 - x^2 + x^4]/12","A",8,8,11,0.7273,1,"{275, 321, 200, 31, 634, 618, 204, 628}"
1363,1,81,0,0.1723584,"\int \frac{x^6}{1+x^6} \, dx","Int[x^6/(1 + x^6),x]","\frac{\log \left(x^2-\sqrt{3} x+1\right)}{4 \sqrt{3}}-\frac{\log \left(x^2+\sqrt{3} x+1\right)}{4 \sqrt{3}}+x+\frac{1}{6} \tan ^{-1}\left(\sqrt{3}-2 x\right)-\frac{1}{3} \tan ^{-1}(x)-\frac{1}{6} \tan ^{-1}\left(2 x+\sqrt{3}\right)","\frac{\log \left(x^2-\sqrt{3} x+1\right)}{4 \sqrt{3}}-\frac{\log \left(x^2+\sqrt{3} x+1\right)}{4 \sqrt{3}}+x+\frac{1}{6} \tan ^{-1}\left(\sqrt{3}-2 x\right)-\frac{1}{3} \tan ^{-1}(x)-\frac{1}{6} \tan ^{-1}\left(2 x+\sqrt{3}\right)",1,"x + ArcTan[Sqrt[3] - 2*x]/6 - ArcTan[x]/3 - ArcTan[Sqrt[3] + 2*x]/6 + Log[1 - Sqrt[3]*x + x^2]/(4*Sqrt[3]) - Log[1 + Sqrt[3]*x + x^2]/(4*Sqrt[3])","A",11,7,11,0.6364,1,"{321, 209, 634, 618, 204, 628, 203}"
1364,1,10,0,0.0022023,"\int \frac{x^5}{1+x^6} \, dx","Int[x^5/(1 + x^6),x]","\frac{1}{6} \log \left(x^6+1\right)","\frac{1}{6} \log \left(x^6+1\right)",1,"Log[1 + x^6]/6","A",1,1,11,0.09091,1,"{260}"
1365,1,80,0,0.2447163,"\int \frac{x^4}{1+x^6} \, dx","Int[x^4/(1 + x^6),x]","\frac{\log \left(x^2-\sqrt{3} x+1\right)}{4 \sqrt{3}}-\frac{\log \left(x^2+\sqrt{3} x+1\right)}{4 \sqrt{3}}-\frac{1}{6} \tan ^{-1}\left(\sqrt{3}-2 x\right)+\frac{1}{3} \tan ^{-1}(x)+\frac{1}{6} \tan ^{-1}\left(2 x+\sqrt{3}\right)","\frac{\log \left(x^2-\sqrt{3} x+1\right)}{4 \sqrt{3}}-\frac{\log \left(x^2+\sqrt{3} x+1\right)}{4 \sqrt{3}}-\frac{1}{6} \tan ^{-1}\left(\sqrt{3}-2 x\right)+\frac{1}{3} \tan ^{-1}(x)+\frac{1}{6} \tan ^{-1}\left(2 x+\sqrt{3}\right)",1,"-ArcTan[Sqrt[3] - 2*x]/6 + ArcTan[x]/3 + ArcTan[Sqrt[3] + 2*x]/6 + Log[1 - Sqrt[3]*x + x^2]/(4*Sqrt[3]) - Log[1 + Sqrt[3]*x + x^2]/(4*Sqrt[3])","A",10,6,11,0.5455,1,"{295, 634, 618, 204, 628, 203}"
1366,1,49,0,0.0392486,"\int \frac{x^3}{1+x^6} \, dx","Int[x^3/(1 + x^6),x]","-\frac{1}{6} \log \left(x^2+1\right)+\frac{1}{12} \log \left(x^4-x^2+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 x^2}{\sqrt{3}}\right)}{2 \sqrt{3}}","-\frac{1}{6} \log \left(x^2+1\right)+\frac{1}{12} \log \left(x^4-x^2+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 x^2}{\sqrt{3}}\right)}{2 \sqrt{3}}",1,"-ArcTan[(1 - 2*x^2)/Sqrt[3]]/(2*Sqrt[3]) - Log[1 + x^2]/6 + Log[1 - x^2 + x^4]/12","A",7,7,11,0.6364,1,"{275, 292, 31, 634, 618, 204, 628}"
1367,1,8,0,0.0033608,"\int \frac{x^2}{1+x^6} \, dx","Int[x^2/(1 + x^6),x]","\frac{1}{3} \tan ^{-1}\left(x^3\right)","\frac{1}{3} \tan ^{-1}\left(x^3\right)",1,"ArcTan[x^3]/3","A",2,2,11,0.1818,1,"{275, 203}"
1368,1,49,0,0.0367808,"\int \frac{x}{1+x^6} \, dx","Int[x/(1 + x^6),x]","\frac{1}{6} \log \left(x^2+1\right)-\frac{1}{12} \log \left(x^4-x^2+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 x^2}{\sqrt{3}}\right)}{2 \sqrt{3}}","\frac{1}{6} \log \left(x^2+1\right)-\frac{1}{12} \log \left(x^4-x^2+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 x^2}{\sqrt{3}}\right)}{2 \sqrt{3}}",1,"-ArcTan[(1 - 2*x^2)/Sqrt[3]]/(2*Sqrt[3]) + Log[1 + x^2]/6 - Log[1 - x^2 + x^4]/12","A",7,7,9,0.7778,1,"{275, 200, 31, 634, 618, 204, 628}"
1369,1,80,0,0.1709314,"\int \frac{1}{1+x^6} \, dx","Int[(1 + x^6)^(-1),x]","-\frac{\log \left(x^2-\sqrt{3} x+1\right)}{4 \sqrt{3}}+\frac{\log \left(x^2+\sqrt{3} x+1\right)}{4 \sqrt{3}}-\frac{1}{6} \tan ^{-1}\left(\sqrt{3}-2 x\right)+\frac{1}{3} \tan ^{-1}(x)+\frac{1}{6} \tan ^{-1}\left(2 x+\sqrt{3}\right)","-\frac{\log \left(x^2-\sqrt{3} x+1\right)}{4 \sqrt{3}}+\frac{\log \left(x^2+\sqrt{3} x+1\right)}{4 \sqrt{3}}-\frac{1}{6} \tan ^{-1}\left(\sqrt{3}-2 x\right)+\frac{1}{3} \tan ^{-1}(x)+\frac{1}{6} \tan ^{-1}\left(2 x+\sqrt{3}\right)",1,"-ArcTan[Sqrt[3] - 2*x]/6 + ArcTan[x]/3 + ArcTan[Sqrt[3] + 2*x]/6 - Log[1 - Sqrt[3]*x + x^2]/(4*Sqrt[3]) + Log[1 + Sqrt[3]*x + x^2]/(4*Sqrt[3])","A",10,6,7,0.8571,1,"{209, 634, 618, 204, 628, 203}"
1370,1,13,0,0.0050972,"\int \frac{1}{x \left(1+x^6\right)} \, dx","Int[1/(x*(1 + x^6)),x]","\log (x)-\frac{1}{6} \log \left(x^6+1\right)","\log (x)-\frac{1}{6} \log \left(x^6+1\right)",1,"Log[x] - Log[1 + x^6]/6","A",4,4,11,0.3636,1,"{266, 36, 29, 31}"
1371,1,85,0,0.2497217,"\int \frac{1}{x^2 \left(1+x^6\right)} \, dx","Int[1/(x^2*(1 + x^6)),x]","-\frac{\log \left(x^2-\sqrt{3} x+1\right)}{4 \sqrt{3}}+\frac{\log \left(x^2+\sqrt{3} x+1\right)}{4 \sqrt{3}}-\frac{1}{x}+\frac{1}{6} \tan ^{-1}\left(\sqrt{3}-2 x\right)-\frac{1}{3} \tan ^{-1}(x)-\frac{1}{6} \tan ^{-1}\left(2 x+\sqrt{3}\right)","-\frac{\log \left(x^2-\sqrt{3} x+1\right)}{4 \sqrt{3}}+\frac{\log \left(x^2+\sqrt{3} x+1\right)}{4 \sqrt{3}}-\frac{1}{x}+\frac{1}{6} \tan ^{-1}\left(\sqrt{3}-2 x\right)-\frac{1}{3} \tan ^{-1}(x)-\frac{1}{6} \tan ^{-1}\left(2 x+\sqrt{3}\right)",1,"-x^(-1) + ArcTan[Sqrt[3] - 2*x]/6 - ArcTan[x]/3 - ArcTan[Sqrt[3] + 2*x]/6 - Log[1 - Sqrt[3]*x + x^2]/(4*Sqrt[3]) + Log[1 + Sqrt[3]*x + x^2]/(4*Sqrt[3])","A",11,7,11,0.6364,1,"{325, 295, 634, 618, 204, 628, 203}"
1372,1,56,0,0.0413397,"\int \frac{1}{x^3 \left(1+x^6\right)} \, dx","Int[1/(x^3*(1 + x^6)),x]","-\frac{1}{2 x^2}+\frac{1}{6} \log \left(x^2+1\right)-\frac{1}{12} \log \left(x^4-x^2+1\right)+\frac{\tan ^{-1}\left(\frac{1-2 x^2}{\sqrt{3}}\right)}{2 \sqrt{3}}","-\frac{1}{2 x^2}+\frac{1}{6} \log \left(x^2+1\right)-\frac{1}{12} \log \left(x^4-x^2+1\right)+\frac{\tan ^{-1}\left(\frac{1-2 x^2}{\sqrt{3}}\right)}{2 \sqrt{3}}",1,"-1/(2*x^2) + ArcTan[(1 - 2*x^2)/Sqrt[3]]/(2*Sqrt[3]) + Log[1 + x^2]/6 - Log[1 - x^2 + x^4]/12","A",8,8,11,0.7273,1,"{275, 325, 292, 31, 634, 618, 204, 628}"
1373,1,16,0,0.0064709,"\int \frac{1}{x^4 \left(1+x^6\right)} \, dx","Int[1/(x^4*(1 + x^6)),x]","-\frac{1}{3 x^3}-\frac{1}{3} \tan ^{-1}\left(x^3\right)","-\frac{1}{3 x^3}-\frac{1}{3} \tan ^{-1}\left(x^3\right)",1,"-1/(3*x^3) - ArcTan[x^3]/3","A",3,3,11,0.2727,1,"{275, 325, 203}"
1374,1,56,0,0.0409842,"\int \frac{1}{x^5 \left(1+x^6\right)} \, dx","Int[1/(x^5*(1 + x^6)),x]","-\frac{1}{4 x^4}-\frac{1}{6} \log \left(x^2+1\right)+\frac{1}{12} \log \left(x^4-x^2+1\right)+\frac{\tan ^{-1}\left(\frac{1-2 x^2}{\sqrt{3}}\right)}{2 \sqrt{3}}","-\frac{1}{4 x^4}-\frac{1}{6} \log \left(x^2+1\right)+\frac{1}{12} \log \left(x^4-x^2+1\right)+\frac{\tan ^{-1}\left(\frac{1-2 x^2}{\sqrt{3}}\right)}{2 \sqrt{3}}",1,"-1/(4*x^4) + ArcTan[(1 - 2*x^2)/Sqrt[3]]/(2*Sqrt[3]) - Log[1 + x^2]/6 + Log[1 - x^2 + x^4]/12","A",8,8,11,0.7273,1,"{275, 325, 200, 31, 634, 618, 204, 628}"
1375,1,87,0,0.1742826,"\int \frac{1}{x^6 \left(1+x^6\right)} \, dx","Int[1/(x^6*(1 + x^6)),x]","-\frac{1}{5 x^5}+\frac{\log \left(x^2-\sqrt{3} x+1\right)}{4 \sqrt{3}}-\frac{\log \left(x^2+\sqrt{3} x+1\right)}{4 \sqrt{3}}+\frac{1}{6} \tan ^{-1}\left(\sqrt{3}-2 x\right)-\frac{1}{3} \tan ^{-1}(x)-\frac{1}{6} \tan ^{-1}\left(2 x+\sqrt{3}\right)","-\frac{1}{5 x^5}+\frac{\log \left(x^2-\sqrt{3} x+1\right)}{4 \sqrt{3}}-\frac{\log \left(x^2+\sqrt{3} x+1\right)}{4 \sqrt{3}}+\frac{1}{6} \tan ^{-1}\left(\sqrt{3}-2 x\right)-\frac{1}{3} \tan ^{-1}(x)-\frac{1}{6} \tan ^{-1}\left(2 x+\sqrt{3}\right)",1,"-1/(5*x^5) + ArcTan[Sqrt[3] - 2*x]/6 - ArcTan[x]/3 - ArcTan[Sqrt[3] + 2*x]/6 + Log[1 - Sqrt[3]*x + x^2]/(4*Sqrt[3]) - Log[1 + Sqrt[3]*x + x^2]/(4*Sqrt[3])","A",11,7,11,0.6364,1,"{325, 209, 634, 618, 204, 628, 203}"
1376,1,22,0,0.0104281,"\int \frac{1}{x^7 \left(1+x^6\right)} \, dx","Int[1/(x^7*(1 + x^6)),x]","-\frac{1}{6 x^6}+\frac{1}{6} \log \left(x^6+1\right)-\log (x)","-\frac{1}{6 x^6}+\frac{1}{6} \log \left(x^6+1\right)-\log (x)",1,"-1/(6*x^6) - Log[x] + Log[1 + x^6]/6","A",3,2,11,0.1818,1,"{266, 44}"
1377,1,90,0,0.2473533,"\int \frac{1}{x^8 \left(1+x^6\right)} \, dx","Int[1/(x^8*(1 + x^6)),x]","-\frac{1}{7 x^7}+\frac{\log \left(x^2-\sqrt{3} x+1\right)}{4 \sqrt{3}}-\frac{\log \left(x^2+\sqrt{3} x+1\right)}{4 \sqrt{3}}+\frac{1}{x}-\frac{1}{6} \tan ^{-1}\left(\sqrt{3}-2 x\right)+\frac{1}{3} \tan ^{-1}(x)+\frac{1}{6} \tan ^{-1}\left(2 x+\sqrt{3}\right)","-\frac{1}{7 x^7}+\frac{\log \left(x^2-\sqrt{3} x+1\right)}{4 \sqrt{3}}-\frac{\log \left(x^2+\sqrt{3} x+1\right)}{4 \sqrt{3}}+\frac{1}{x}-\frac{1}{6} \tan ^{-1}\left(\sqrt{3}-2 x\right)+\frac{1}{3} \tan ^{-1}(x)+\frac{1}{6} \tan ^{-1}\left(2 x+\sqrt{3}\right)",1,"-1/(7*x^7) + x^(-1) - ArcTan[Sqrt[3] - 2*x]/6 + ArcTan[x]/3 + ArcTan[Sqrt[3] + 2*x]/6 + Log[1 - Sqrt[3]*x + x^2]/(4*Sqrt[3]) - Log[1 + Sqrt[3]*x + x^2]/(4*Sqrt[3])","A",12,7,11,0.6364,1,"{325, 295, 634, 618, 204, 628, 203}"
1378,1,167,0,0.2795774,"\int \frac{1}{2-3 x^6} \, dx","Int[(2 - 3*x^6)^(-1),x]","-\frac{\log \left(\sqrt[3]{3} x^2-\sqrt[6]{6} x+\sqrt[3]{2}\right)}{12\ 2^{5/6} \sqrt[6]{3}}+\frac{\log \left(\sqrt[3]{3} x^2+\sqrt[6]{6} x+\sqrt[3]{2}\right)}{12\ 2^{5/6} \sqrt[6]{3}}-\frac{\tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2^{5/6} x}{\sqrt[3]{3}}\right)}{2\ 2^{5/6} 3^{2/3}}+\frac{\tan ^{-1}\left(\frac{2^{5/6} x}{\sqrt[3]{3}}+\frac{1}{\sqrt{3}}\right)}{2\ 2^{5/6} 3^{2/3}}+\frac{\tanh ^{-1}\left(\sqrt[6]{\frac{3}{2}} x\right)}{3\ 2^{5/6} \sqrt[6]{3}}","-\frac{\log \left(\sqrt[3]{3} x^2-\sqrt[6]{6} x+\sqrt[3]{2}\right)}{12\ 2^{5/6} \sqrt[6]{3}}+\frac{\log \left(\sqrt[3]{3} x^2+\sqrt[6]{6} x+\sqrt[3]{2}\right)}{12\ 2^{5/6} \sqrt[6]{3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[6]{6}-2 \sqrt[3]{3} x}{\sqrt[6]{2} 3^{2/3}}\right)}{2\ 2^{5/6} 3^{2/3}}+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{3} x+\sqrt[6]{6}}{\sqrt[6]{2} 3^{2/3}}\right)}{2\ 2^{5/6} 3^{2/3}}+\frac{\tanh ^{-1}\left(\sqrt[6]{\frac{3}{2}} x\right)}{3\ 2^{5/6} \sqrt[6]{3}}",1,"-ArcTan[1/Sqrt[3] - (2^(5/6)*x)/3^(1/3)]/(2*2^(5/6)*3^(2/3)) + ArcTan[1/Sqrt[3] + (2^(5/6)*x)/3^(1/3)]/(2*2^(5/6)*3^(2/3)) + ArcTanh[(3/2)^(1/6)*x]/(3*2^(5/6)*3^(1/6)) - Log[2^(1/3) - 6^(1/6)*x + 3^(1/3)*x^2]/(12*2^(5/6)*3^(1/6)) + Log[2^(1/3) + 6^(1/6)*x + 3^(1/3)*x^2]/(12*2^(5/6)*3^(1/6))","A",10,6,9,0.6667,1,"{210, 634, 618, 204, 628, 206}"
1379,1,244,0,0.3043259,"\int \frac{\sqrt[3]{x}}{1-x^6} \, dx","Int[x^(1/3)/(1 - x^6),x]","-\frac{1}{6} \log \left(1-x^{2/3}\right)+\frac{1}{12} \log \left(x^{4/3}+x^{2/3}+1\right)-\frac{\tan ^{-1}\left(\frac{2 x^{2/3}+1}{\sqrt{3}}\right)}{2 \sqrt{3}}-\frac{1}{6} \cos \left(\frac{2 \pi }{9}\right) \log \left(x^{4/3}+2 x^{2/3} \cos \left(\frac{\pi }{9}\right)+1\right)+\frac{1}{6} \cos \left(\frac{\pi }{9}\right) \log \left(x^{4/3}-2 x^{2/3} \sin \left(\frac{\pi }{18}\right)+1\right)-\frac{1}{6} \sin \left(\frac{\pi }{18}\right) \log \left(x^{4/3}-2 x^{2/3} \cos \left(\frac{2 \pi }{9}\right)+1\right)+\frac{1}{3} \cos \left(\frac{\pi }{18}\right) \tan ^{-1}\left(\csc \left(\frac{2 \pi }{9}\right) \left(x^{2/3}-\cos \left(\frac{2 \pi }{9}\right)\right)\right)+\frac{1}{3} \sin \left(\frac{\pi }{9}\right) \tan ^{-1}\left(\sec \left(\frac{\pi }{18}\right) \left(x^{2/3}-\sin \left(\frac{\pi }{18}\right)\right)\right)-\frac{1}{3} \sin \left(\frac{2 \pi }{9}\right) \tan ^{-1}\left(\csc \left(\frac{\pi }{9}\right) \left(x^{2/3}+\cos \left(\frac{\pi }{9}\right)\right)\right)","-\frac{1}{6} \log \left(1-x^{2/3}\right)+\frac{1}{12} \log \left(x^{4/3}+x^{2/3}+1\right)-\frac{\tan ^{-1}\left(\frac{2 x^{2/3}+1}{\sqrt{3}}\right)}{2 \sqrt{3}}-\frac{1}{6} \cos \left(\frac{2 \pi }{9}\right) \log \left(x^{4/3}+2 x^{2/3} \cos \left(\frac{\pi }{9}\right)+1\right)+\frac{1}{6} \cos \left(\frac{\pi }{9}\right) \log \left(x^{4/3}-2 x^{2/3} \sin \left(\frac{\pi }{18}\right)+1\right)-\frac{1}{6} \sin \left(\frac{\pi }{18}\right) \log \left(x^{4/3}-2 x^{2/3} \cos \left(\frac{2 \pi }{9}\right)+1\right)+\frac{1}{3} \cos \left(\frac{\pi }{18}\right) \tan ^{-1}\left(\csc \left(\frac{2 \pi }{9}\right) \left(x^{2/3}-\cos \left(\frac{2 \pi }{9}\right)\right)\right)+\frac{1}{3} \sin \left(\frac{\pi }{9}\right) \tan ^{-1}\left(\sec \left(\frac{\pi }{18}\right) \left(x^{2/3}-\sin \left(\frac{\pi }{18}\right)\right)\right)-\frac{1}{3} \sin \left(\frac{2 \pi }{9}\right) \tan ^{-1}\left(\csc \left(\frac{\pi }{9}\right) \left(x^{2/3}+\cos \left(\frac{\pi }{9}\right)\right)\right)",1,"-ArcTan[(1 + 2*x^(2/3))/Sqrt[3]]/(2*Sqrt[3]) + (ArcTan[(x^(2/3) - Cos[(2*Pi)/9])*Csc[(2*Pi)/9]]*Cos[Pi/18])/3 - Log[1 - x^(2/3)]/6 + Log[1 + x^(2/3) + x^(4/3)]/12 - (Cos[(2*Pi)/9]*Log[1 + x^(4/3) + 2*x^(2/3)*Cos[Pi/9]])/6 + (Cos[Pi/9]*Log[1 + x^(4/3) - 2*x^(2/3)*Sin[Pi/18]])/6 - (Log[1 + x^(4/3) - 2*x^(2/3)*Cos[(2*Pi)/9]]*Sin[Pi/18])/6 + (ArcTan[Sec[Pi/18]*(x^(2/3) - Sin[Pi/18])]*Sin[Pi/9])/3 - (ArcTan[(x^(2/3) + Cos[Pi/9])*Csc[Pi/9]]*Sin[(2*Pi)/9])/3","A",8,8,15,0.5333,1,"{329, 275, 294, 634, 618, 204, 628, 31}"
1380,1,58,0,0.0290294,"\int x^8 \sqrt{-1+4 x^6} \, dx","Int[x^8*Sqrt[-1 + 4*x^6],x]","\frac{1}{12} \sqrt{4 x^6-1} x^9-\frac{1}{96} \sqrt{4 x^6-1} x^3-\frac{1}{192} \tanh ^{-1}\left(\frac{2 x^3}{\sqrt{4 x^6-1}}\right)","\frac{1}{12} \sqrt{4 x^6-1} x^9-\frac{1}{96} \sqrt{4 x^6-1} x^3-\frac{1}{192} \tanh ^{-1}\left(\frac{2 x^3}{\sqrt{4 x^6-1}}\right)",1,"-(x^3*Sqrt[-1 + 4*x^6])/96 + (x^9*Sqrt[-1 + 4*x^6])/12 - ArcTanh[(2*x^3)/Sqrt[-1 + 4*x^6]]/192","A",5,5,15,0.3333,1,"{275, 279, 321, 217, 206}"
1381,1,17,0,0.003434,"\int x^5 \sqrt{a^6-x^6} \, dx","Int[x^5*Sqrt[a^6 - x^6],x]","-\frac{1}{9} \left(a^6-x^6\right)^{3/2}","-\frac{1}{9} \left(a^6-x^6\right)^{3/2}",1,"-(a^6 - x^6)^(3/2)/9","A",1,1,17,0.05882,1,"{261}"
1382,1,35,0,0.0118392,"\int x^2 \sqrt{-2+x^6} \, dx","Int[x^2*Sqrt[-2 + x^6],x]","\frac{1}{6} x^3 \sqrt{x^6-2}-\frac{1}{3} \tanh ^{-1}\left(\frac{x^3}{\sqrt{x^6-2}}\right)","\frac{1}{6} x^3 \sqrt{x^6-2}-\frac{1}{3} \tanh ^{-1}\left(\frac{x^3}{\sqrt{x^6-2}}\right)",1,"(x^3*Sqrt[-2 + x^6])/6 - ArcTanh[x^3/Sqrt[-2 + x^6]]/3","A",4,4,13,0.3077,1,"{275, 195, 217, 206}"
1383,1,53,0,0.0212099,"\int \frac{x^{23}}{\sqrt{2+x^6}} \, dx","Int[x^23/Sqrt[2 + x^6],x]","\frac{1}{21} \left(x^6+2\right)^{7/2}-\frac{2}{5} \left(x^6+2\right)^{5/2}+\frac{4}{3} \left(x^6+2\right)^{3/2}-\frac{8 \sqrt{x^6+2}}{3}","\frac{1}{21} \left(x^6+2\right)^{7/2}-\frac{2}{5} \left(x^6+2\right)^{5/2}+\frac{4}{3} \left(x^6+2\right)^{3/2}-\frac{8 \sqrt{x^6+2}}{3}",1,"(-8*Sqrt[2 + x^6])/3 + (4*(2 + x^6)^(3/2))/3 - (2*(2 + x^6)^(5/2))/5 + (2 + x^6)^(7/2)/21","A",3,2,13,0.1538,1,"{266, 43}"
1384,1,40,0,0.0147073,"\int \frac{x^{17}}{\sqrt{2+x^6}} \, dx","Int[x^17/Sqrt[2 + x^6],x]","\frac{1}{15} \left(x^6+2\right)^{5/2}-\frac{4}{9} \left(x^6+2\right)^{3/2}+\frac{4 \sqrt{x^6+2}}{3}","\frac{1}{15} \left(x^6+2\right)^{5/2}-\frac{4}{9} \left(x^6+2\right)^{3/2}+\frac{4 \sqrt{x^6+2}}{3}",1,"(4*Sqrt[2 + x^6])/3 - (4*(2 + x^6)^(3/2))/9 + (2 + x^6)^(5/2)/15","A",3,2,13,0.1538,1,"{266, 43}"
1385,1,27,0,0.0109,"\int \frac{x^{11}}{\sqrt{2+x^6}} \, dx","Int[x^11/Sqrt[2 + x^6],x]","\frac{1}{9} \left(x^6+2\right)^{3/2}-\frac{2 \sqrt{x^6+2}}{3}","\frac{1}{9} \left(x^6+2\right)^{3/2}-\frac{2 \sqrt{x^6+2}}{3}",1,"(-2*Sqrt[2 + x^6])/3 + (2 + x^6)^(3/2)/9","A",3,2,13,0.1538,1,"{266, 43}"
1386,1,13,0,0.0026282,"\int \frac{x^5}{\sqrt{2+x^6}} \, dx","Int[x^5/Sqrt[2 + x^6],x]","\frac{\sqrt{x^6+2}}{3}","\frac{\sqrt{x^6+2}}{3}",1,"Sqrt[2 + x^6]/3","A",1,1,13,0.07692,1,"{261}"
1387,1,25,0,0.0118845,"\int \frac{1}{x \sqrt{2+x^6}} \, dx","Int[1/(x*Sqrt[2 + x^6]),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{x^6+2}}{\sqrt{2}}\right)}{3 \sqrt{2}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{x^6+2}}{\sqrt{2}}\right)}{3 \sqrt{2}}",1,"-ArcTanh[Sqrt[2 + x^6]/Sqrt[2]]/(3*Sqrt[2])","A",3,3,13,0.2308,1,"{266, 63, 207}"
1388,1,42,0,0.017391,"\int \frac{1}{x^7 \sqrt{2+x^6}} \, dx","Int[1/(x^7*Sqrt[2 + x^6]),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{x^6+2}}{\sqrt{2}}\right)}{12 \sqrt{2}}-\frac{\sqrt{x^6+2}}{12 x^6}","\frac{\tanh ^{-1}\left(\frac{\sqrt{x^6+2}}{\sqrt{2}}\right)}{12 \sqrt{2}}-\frac{\sqrt{x^6+2}}{12 x^6}",1,"-Sqrt[2 + x^6]/(12*x^6) + ArcTanh[Sqrt[2 + x^6]/Sqrt[2]]/(12*Sqrt[2])","A",4,4,13,0.3077,1,"{266, 51, 63, 207}"
1389,1,58,0,0.023114,"\int \frac{1}{x^{13} \sqrt{2+x^6}} \, dx","Int[1/(x^13*Sqrt[2 + x^6]),x]","\frac{\sqrt{x^6+2}}{32 x^6}-\frac{\sqrt{x^6+2}}{24 x^{12}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{x^6+2}}{\sqrt{2}}\right)}{32 \sqrt{2}}","\frac{\sqrt{x^6+2}}{32 x^6}-\frac{\sqrt{x^6+2}}{24 x^{12}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{x^6+2}}{\sqrt{2}}\right)}{32 \sqrt{2}}",1,"-Sqrt[2 + x^6]/(24*x^12) + Sqrt[2 + x^6]/(32*x^6) - ArcTanh[Sqrt[2 + x^6]/Sqrt[2]]/(32*Sqrt[2])","A",5,4,13,0.3077,1,"{266, 51, 63, 207}"
1390,1,47,0,0.0197368,"\int \frac{x^{14}}{\sqrt{2+x^6}} \, dx","Int[x^14/Sqrt[2 + x^6],x]","\frac{1}{12} \sqrt{x^6+2} x^9-\frac{1}{4} \sqrt{x^6+2} x^3+\frac{1}{2} \sinh ^{-1}\left(\frac{x^3}{\sqrt{2}}\right)","\frac{1}{12} \sqrt{x^6+2} x^9-\frac{1}{4} \sqrt{x^6+2} x^3+\frac{1}{2} \sinh ^{-1}\left(\frac{x^3}{\sqrt{2}}\right)",1,"-(x^3*Sqrt[2 + x^6])/4 + (x^9*Sqrt[2 + x^6])/12 + ArcSinh[x^3/Sqrt[2]]/2","A",4,3,13,0.2308,1,"{275, 321, 215}"
1391,1,31,0,0.0116619,"\int \frac{x^8}{\sqrt{2+x^6}} \, dx","Int[x^8/Sqrt[2 + x^6],x]","\frac{1}{6} x^3 \sqrt{x^6+2}-\frac{1}{3} \sinh ^{-1}\left(\frac{x^3}{\sqrt{2}}\right)","\frac{1}{6} x^3 \sqrt{x^6+2}-\frac{1}{3} \sinh ^{-1}\left(\frac{x^3}{\sqrt{2}}\right)",1,"(x^3*Sqrt[2 + x^6])/6 - ArcSinh[x^3/Sqrt[2]]/3","A",3,3,13,0.2308,1,"{275, 321, 215}"
1392,1,14,0,0.00582,"\int \frac{x^2}{\sqrt{2+x^6}} \, dx","Int[x^2/Sqrt[2 + x^6],x]","\frac{1}{3} \sinh ^{-1}\left(\frac{x^3}{\sqrt{2}}\right)","\frac{1}{3} \sinh ^{-1}\left(\frac{x^3}{\sqrt{2}}\right)",1,"ArcSinh[x^3/Sqrt[2]]/3","A",2,2,13,0.1538,1,"{275, 215}"
1393,1,16,0,0.0030968,"\int \frac{1}{x^4 \sqrt{2+x^6}} \, dx","Int[1/(x^4*Sqrt[2 + x^6]),x]","-\frac{\sqrt{x^6+2}}{6 x^3}","-\frac{\sqrt{x^6+2}}{6 x^3}",1,"-Sqrt[2 + x^6]/(6*x^3)","A",1,1,13,0.07692,1,"{264}"
1394,1,33,0,0.0062895,"\int \frac{1}{x^{10} \sqrt{2+x^6}} \, dx","Int[1/(x^10*Sqrt[2 + x^6]),x]","\frac{\sqrt{x^6+2}}{18 x^3}-\frac{\sqrt{x^6+2}}{18 x^9}","\frac{\sqrt{x^6+2}}{18 x^3}-\frac{\sqrt{x^6+2}}{18 x^9}",1,"-Sqrt[2 + x^6]/(18*x^9) + Sqrt[2 + x^6]/(18*x^3)","A",2,2,13,0.1538,1,"{271, 264}"
1395,1,49,0,0.0100154,"\int \frac{1}{x^{16} \sqrt{2+x^6}} \, dx","Int[1/(x^16*Sqrt[2 + x^6]),x]","-\frac{\sqrt{x^6+2}}{45 x^3}+\frac{\sqrt{x^6+2}}{45 x^9}-\frac{\sqrt{x^6+2}}{30 x^{15}}","-\frac{\sqrt{x^6+2}}{45 x^3}+\frac{\sqrt{x^6+2}}{45 x^9}-\frac{\sqrt{x^6+2}}{30 x^{15}}",1,"-Sqrt[2 + x^6]/(30*x^15) + Sqrt[2 + x^6]/(45*x^9) - Sqrt[2 + x^6]/(45*x^3)","A",3,2,13,0.1538,1,"{271, 264}"
1396,1,186,0,0.1285749,"\int \frac{x^7}{\sqrt{2+x^6}} \, dx","Int[x^7/Sqrt[2 + x^6],x]","\frac{1}{5} x^2 \sqrt{x^6+2}-\frac{2\ 2^{5/6} \sqrt{2+\sqrt{3}} \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} F\left(\sin ^{-1}\left(\frac{x^2+\sqrt[3]{2} \left(1-\sqrt{3}\right)}{x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)}\right)|-7-4 \sqrt{3}\right)}{5 \sqrt[4]{3} \sqrt{\frac{x^2+\sqrt[3]{2}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} \sqrt{x^6+2}}","\frac{1}{5} x^2 \sqrt{x^6+2}-\frac{2\ 2^{5/6} \sqrt{2+\sqrt{3}} \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} F\left(\sin ^{-1}\left(\frac{x^2+\sqrt[3]{2} \left(1-\sqrt{3}\right)}{x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)}\right)|-7-4 \sqrt{3}\right)}{5 \sqrt[4]{3} \sqrt{\frac{x^2+\sqrt[3]{2}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} \sqrt{x^6+2}}",1,"(x^2*Sqrt[2 + x^6])/5 - (2*2^(5/6)*Sqrt[2 + Sqrt[3]]*(2^(1/3) + x^2)*Sqrt[(2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3)*(1 + Sqrt[3]) + x^2)^2]*EllipticF[ArcSin[(2^(1/3)*(1 - Sqrt[3]) + x^2)/(2^(1/3)*(1 + Sqrt[3]) + x^2)], -7 - 4*Sqrt[3]])/(5*3^(1/4)*Sqrt[(2^(1/3) + x^2)/(2^(1/3)*(1 + Sqrt[3]) + x^2)^2]*Sqrt[2 + x^6])","A",3,3,13,0.2308,1,"{275, 321, 218}"
1397,1,166,0,0.0696663,"\int \frac{x}{\sqrt{2+x^6}} \, dx","Int[x/Sqrt[2 + x^6],x]","\frac{\sqrt{2+\sqrt{3}} \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} F\left(\sin ^{-1}\left(\frac{x^2+\sqrt[3]{2} \left(1-\sqrt{3}\right)}{x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)}\right)|-7-4 \sqrt{3}\right)}{\sqrt[6]{2} \sqrt[4]{3} \sqrt{\frac{x^2+\sqrt[3]{2}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} \sqrt{x^6+2}}","\frac{\sqrt{2+\sqrt{3}} \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} F\left(\sin ^{-1}\left(\frac{x^2+\sqrt[3]{2} \left(1-\sqrt{3}\right)}{x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)}\right)|-7-4 \sqrt{3}\right)}{\sqrt[6]{2} \sqrt[4]{3} \sqrt{\frac{x^2+\sqrt[3]{2}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} \sqrt{x^6+2}}",1,"(Sqrt[2 + Sqrt[3]]*(2^(1/3) + x^2)*Sqrt[(2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3)*(1 + Sqrt[3]) + x^2)^2]*EllipticF[ArcSin[(2^(1/3)*(1 - Sqrt[3]) + x^2)/(2^(1/3)*(1 + Sqrt[3]) + x^2)], -7 - 4*Sqrt[3]])/(2^(1/6)*3^(1/4)*Sqrt[(2^(1/3) + x^2)/(2^(1/3)*(1 + Sqrt[3]) + x^2)^2]*Sqrt[2 + x^6])","A",2,2,11,0.1818,1,"{275, 218}"
1398,1,186,0,0.0914403,"\int \frac{1}{x^5 \sqrt{2+x^6}} \, dx","Int[1/(x^5*Sqrt[2 + x^6]),x]","-\frac{\sqrt{x^6+2}}{8 x^4}-\frac{\sqrt{2+\sqrt{3}} \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} F\left(\sin ^{-1}\left(\frac{x^2+\sqrt[3]{2} \left(1-\sqrt{3}\right)}{x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)}\right)|-7-4 \sqrt{3}\right)}{8 \sqrt[6]{2} \sqrt[4]{3} \sqrt{\frac{x^2+\sqrt[3]{2}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} \sqrt{x^6+2}}","-\frac{\sqrt{x^6+2}}{8 x^4}-\frac{\sqrt{2+\sqrt{3}} \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} F\left(\sin ^{-1}\left(\frac{x^2+\sqrt[3]{2} \left(1-\sqrt{3}\right)}{x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)}\right)|-7-4 \sqrt{3}\right)}{8 \sqrt[6]{2} \sqrt[4]{3} \sqrt{\frac{x^2+\sqrt[3]{2}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} \sqrt{x^6+2}}",1,"-Sqrt[2 + x^6]/(8*x^4) - (Sqrt[2 + Sqrt[3]]*(2^(1/3) + x^2)*Sqrt[(2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3)*(1 + Sqrt[3]) + x^2)^2]*EllipticF[ArcSin[(2^(1/3)*(1 - Sqrt[3]) + x^2)/(2^(1/3)*(1 + Sqrt[3]) + x^2)], -7 - 4*Sqrt[3]])/(8*2^(1/6)*3^(1/4)*Sqrt[(2^(1/3) + x^2)/(2^(1/3)*(1 + Sqrt[3]) + x^2)^2]*Sqrt[2 + x^6])","A",3,3,13,0.2308,1,"{275, 325, 218}"
1399,1,179,0,0.0474975,"\int \frac{x^6}{\sqrt{2+x^6}} \, dx","Int[x^6/Sqrt[2 + x^6],x]","\frac{1}{4} x \sqrt{x^6+2}-\frac{x \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) x^2+\sqrt[3]{2}}{\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{4 \sqrt[3]{2} \sqrt[4]{3} \sqrt{\frac{x^2 \left(x^2+\sqrt[3]{2}\right)}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} \sqrt{x^6+2}}","\frac{1}{4} x \sqrt{x^6+2}-\frac{x \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) x^2+\sqrt[3]{2}}{\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{4 \sqrt[3]{2} \sqrt[4]{3} \sqrt{\frac{x^2 \left(x^2+\sqrt[3]{2}\right)}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} \sqrt{x^6+2}}",1,"(x*Sqrt[2 + x^6])/4 - (x*(2^(1/3) + x^2)*Sqrt[(2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3) + (1 + Sqrt[3])*x^2)^2]*EllipticF[ArcCos[(2^(1/3) + (1 - Sqrt[3])*x^2)/(2^(1/3) + (1 + Sqrt[3])*x^2)], (2 + Sqrt[3])/4])/(4*2^(1/3)*3^(1/4)*Sqrt[(x^2*(2^(1/3) + x^2))/(2^(1/3) + (1 + Sqrt[3])*x^2)^2]*Sqrt[2 + x^6])","A",2,2,13,0.1538,1,"{321, 225}"
1400,1,164,0,0.0140648,"\int \frac{1}{\sqrt{2+x^6}} \, dx","Int[1/Sqrt[2 + x^6],x]","\frac{x \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) x^2+\sqrt[3]{2}}{\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{2 \sqrt[3]{2} \sqrt[4]{3} \sqrt{\frac{x^2 \left(x^2+\sqrt[3]{2}\right)}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} \sqrt{x^6+2}}","\frac{x \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) x^2+\sqrt[3]{2}}{\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{2 \sqrt[3]{2} \sqrt[4]{3} \sqrt{\frac{x^2 \left(x^2+\sqrt[3]{2}\right)}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} \sqrt{x^6+2}}",1,"(x*(2^(1/3) + x^2)*Sqrt[(2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3) + (1 + Sqrt[3])*x^2)^2]*EllipticF[ArcCos[(2^(1/3) + (1 - Sqrt[3])*x^2)/(2^(1/3) + (1 + Sqrt[3])*x^2)], (2 + Sqrt[3])/4])/(2*2^(1/3)*3^(1/4)*Sqrt[(x^2*(2^(1/3) + x^2))/(2^(1/3) + (1 + Sqrt[3])*x^2)^2]*Sqrt[2 + x^6])","A",1,1,9,0.1111,1,"{225}"
1401,1,181,0,0.0302554,"\int \frac{1}{x^6 \sqrt{2+x^6}} \, dx","Int[1/(x^6*Sqrt[2 + x^6]),x]","-\frac{\sqrt{x^6+2}}{10 x^5}-\frac{x \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) x^2+\sqrt[3]{2}}{\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{10 \sqrt[3]{2} \sqrt[4]{3} \sqrt{\frac{x^2 \left(x^2+\sqrt[3]{2}\right)}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} \sqrt{x^6+2}}","-\frac{\sqrt{x^6+2}}{10 x^5}-\frac{x \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) x^2+\sqrt[3]{2}}{\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{10 \sqrt[3]{2} \sqrt[4]{3} \sqrt{\frac{x^2 \left(x^2+\sqrt[3]{2}\right)}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} \sqrt{x^6+2}}",1,"-Sqrt[2 + x^6]/(10*x^5) - (x*(2^(1/3) + x^2)*Sqrt[(2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3) + (1 + Sqrt[3])*x^2)^2]*EllipticF[ArcCos[(2^(1/3) + (1 - Sqrt[3])*x^2)/(2^(1/3) + (1 + Sqrt[3])*x^2)], (2 + Sqrt[3])/4])/(10*2^(1/3)*3^(1/4)*Sqrt[(x^2*(2^(1/3) + x^2))/(2^(1/3) + (1 + Sqrt[3])*x^2)^2]*Sqrt[2 + x^6])","A",2,2,13,0.1538,1,"{325, 225}"
1402,1,378,0,0.2106686,"\int \frac{x^9}{\sqrt{2+x^6}} \, dx","Int[x^9/Sqrt[2 + x^6],x]","\frac{1}{7} \sqrt{x^6+2} x^4-\frac{8 \sqrt{x^6+2}}{7 \left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)}-\frac{8\ 2^{2/3} \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} F\left(\sin ^{-1}\left(\frac{x^2+\sqrt[3]{2} \left(1-\sqrt{3}\right)}{x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)}\right)|-7-4 \sqrt{3}\right)}{7 \sqrt[4]{3} \sqrt{\frac{x^2+\sqrt[3]{2}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} \sqrt{x^6+2}}+\frac{4 \sqrt[6]{2} \sqrt[4]{3} \sqrt{2-\sqrt{3}} \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} E\left(\sin ^{-1}\left(\frac{x^2+\sqrt[3]{2} \left(1-\sqrt{3}\right)}{x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)}\right)|-7-4 \sqrt{3}\right)}{7 \sqrt{\frac{x^2+\sqrt[3]{2}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} \sqrt{x^6+2}}","\frac{1}{7} \sqrt{x^6+2} x^4-\frac{8 \sqrt{x^6+2}}{7 \left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)}-\frac{8\ 2^{2/3} \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} F\left(\sin ^{-1}\left(\frac{x^2+\sqrt[3]{2} \left(1-\sqrt{3}\right)}{x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)}\right)|-7-4 \sqrt{3}\right)}{7 \sqrt[4]{3} \sqrt{\frac{x^2+\sqrt[3]{2}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} \sqrt{x^6+2}}+\frac{4 \sqrt[6]{2} \sqrt[4]{3} \sqrt{2-\sqrt{3}} \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} E\left(\sin ^{-1}\left(\frac{x^2+\sqrt[3]{2} \left(1-\sqrt{3}\right)}{x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)}\right)|-7-4 \sqrt{3}\right)}{7 \sqrt{\frac{x^2+\sqrt[3]{2}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} \sqrt{x^6+2}}",1,"(x^4*Sqrt[2 + x^6])/7 - (8*Sqrt[2 + x^6])/(7*(2^(1/3)*(1 + Sqrt[3]) + x^2)) + (4*2^(1/6)*3^(1/4)*Sqrt[2 - Sqrt[3]]*(2^(1/3) + x^2)*Sqrt[(2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3)*(1 + Sqrt[3]) + x^2)^2]*EllipticE[ArcSin[(2^(1/3)*(1 - Sqrt[3]) + x^2)/(2^(1/3)*(1 + Sqrt[3]) + x^2)], -7 - 4*Sqrt[3]])/(7*Sqrt[(2^(1/3) + x^2)/(2^(1/3)*(1 + Sqrt[3]) + x^2)^2]*Sqrt[2 + x^6]) - (8*2^(2/3)*(2^(1/3) + x^2)*Sqrt[(2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3)*(1 + Sqrt[3]) + x^2)^2]*EllipticF[ArcSin[(2^(1/3)*(1 - Sqrt[3]) + x^2)/(2^(1/3)*(1 + Sqrt[3]) + x^2)], -7 - 4*Sqrt[3]])/(7*3^(1/4)*Sqrt[(2^(1/3) + x^2)/(2^(1/3)*(1 + Sqrt[3]) + x^2)^2]*Sqrt[2 + x^6])","A",5,5,13,0.3846,1,"{275, 321, 303, 218, 1877}"
1403,1,354,0,0.1755966,"\int \frac{x^3}{\sqrt{2+x^6}} \, dx","Int[x^3/Sqrt[2 + x^6],x]","\frac{\sqrt{x^6+2}}{x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)}+\frac{2^{2/3} \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} F\left(\sin ^{-1}\left(\frac{x^2+\sqrt[3]{2} \left(1-\sqrt{3}\right)}{x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{x^2+\sqrt[3]{2}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} \sqrt{x^6+2}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} E\left(\sin ^{-1}\left(\frac{x^2+\sqrt[3]{2} \left(1-\sqrt{3}\right)}{x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)}\right)|-7-4 \sqrt{3}\right)}{2^{5/6} \sqrt{\frac{x^2+\sqrt[3]{2}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} \sqrt{x^6+2}}","\frac{\sqrt{x^6+2}}{x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)}+\frac{2^{2/3} \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} F\left(\sin ^{-1}\left(\frac{x^2+\sqrt[3]{2} \left(1-\sqrt{3}\right)}{x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{x^2+\sqrt[3]{2}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} \sqrt{x^6+2}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} E\left(\sin ^{-1}\left(\frac{x^2+\sqrt[3]{2} \left(1-\sqrt{3}\right)}{x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)}\right)|-7-4 \sqrt{3}\right)}{2^{5/6} \sqrt{\frac{x^2+\sqrt[3]{2}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} \sqrt{x^6+2}}",1,"Sqrt[2 + x^6]/(2^(1/3)*(1 + Sqrt[3]) + x^2) - (3^(1/4)*Sqrt[2 - Sqrt[3]]*(2^(1/3) + x^2)*Sqrt[(2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3)*(1 + Sqrt[3]) + x^2)^2]*EllipticE[ArcSin[(2^(1/3)*(1 - Sqrt[3]) + x^2)/(2^(1/3)*(1 + Sqrt[3]) + x^2)], -7 - 4*Sqrt[3]])/(2^(5/6)*Sqrt[(2^(1/3) + x^2)/(2^(1/3)*(1 + Sqrt[3]) + x^2)^2]*Sqrt[2 + x^6]) + (2^(2/3)*(2^(1/3) + x^2)*Sqrt[(2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3)*(1 + Sqrt[3]) + x^2)^2]*EllipticF[ArcSin[(2^(1/3)*(1 - Sqrt[3]) + x^2)/(2^(1/3)*(1 + Sqrt[3]) + x^2)], -7 - 4*Sqrt[3]])/(3^(1/4)*Sqrt[(2^(1/3) + x^2)/(2^(1/3)*(1 + Sqrt[3]) + x^2)^2]*Sqrt[2 + x^6])","A",4,4,13,0.3077,1,"{275, 303, 218, 1877}"
1404,1,378,0,0.1928838,"\int \frac{1}{x^3 \sqrt{2+x^6}} \, dx","Int[1/(x^3*Sqrt[2 + x^6]),x]","\frac{\sqrt{x^6+2}}{4 \left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)}-\frac{\sqrt{x^6+2}}{4 x^2}+\frac{\left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} F\left(\sin ^{-1}\left(\frac{x^2+\sqrt[3]{2} \left(1-\sqrt{3}\right)}{x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt[3]{2} \sqrt[4]{3} \sqrt{\frac{x^2+\sqrt[3]{2}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} \sqrt{x^6+2}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} E\left(\sin ^{-1}\left(\frac{x^2+\sqrt[3]{2} \left(1-\sqrt{3}\right)}{x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)}\right)|-7-4 \sqrt{3}\right)}{4\ 2^{5/6} \sqrt{\frac{x^2+\sqrt[3]{2}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} \sqrt{x^6+2}}","\frac{\sqrt{x^6+2}}{4 \left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)}-\frac{\sqrt{x^6+2}}{4 x^2}+\frac{\left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} F\left(\sin ^{-1}\left(\frac{x^2+\sqrt[3]{2} \left(1-\sqrt{3}\right)}{x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt[3]{2} \sqrt[4]{3} \sqrt{\frac{x^2+\sqrt[3]{2}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} \sqrt{x^6+2}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} E\left(\sin ^{-1}\left(\frac{x^2+\sqrt[3]{2} \left(1-\sqrt{3}\right)}{x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)}\right)|-7-4 \sqrt{3}\right)}{4\ 2^{5/6} \sqrt{\frac{x^2+\sqrt[3]{2}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} \sqrt{x^6+2}}",1,"-Sqrt[2 + x^6]/(4*x^2) + Sqrt[2 + x^6]/(4*(2^(1/3)*(1 + Sqrt[3]) + x^2)) - (3^(1/4)*Sqrt[2 - Sqrt[3]]*(2^(1/3) + x^2)*Sqrt[(2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3)*(1 + Sqrt[3]) + x^2)^2]*EllipticE[ArcSin[(2^(1/3)*(1 - Sqrt[3]) + x^2)/(2^(1/3)*(1 + Sqrt[3]) + x^2)], -7 - 4*Sqrt[3]])/(4*2^(5/6)*Sqrt[(2^(1/3) + x^2)/(2^(1/3)*(1 + Sqrt[3]) + x^2)^2]*Sqrt[2 + x^6]) + ((2^(1/3) + x^2)*Sqrt[(2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3)*(1 + Sqrt[3]) + x^2)^2]*EllipticF[ArcSin[(2^(1/3)*(1 - Sqrt[3]) + x^2)/(2^(1/3)*(1 + Sqrt[3]) + x^2)], -7 - 4*Sqrt[3]])/(2*2^(1/3)*3^(1/4)*Sqrt[(2^(1/3) + x^2)/(2^(1/3)*(1 + Sqrt[3]) + x^2)^2]*Sqrt[2 + x^6])","A",5,5,13,0.3846,1,"{275, 325, 303, 218, 1877}"
1405,1,394,0,0.1305666,"\int \frac{x^{10}}{\sqrt{2+x^6}} \, dx","Int[x^10/Sqrt[2 + x^6],x]","\frac{1}{8} \sqrt{x^6+2} x^5-\frac{5 \left(1+\sqrt{3}\right) \sqrt{x^6+2} x}{8 \left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)}+\frac{5 \left(1-\sqrt{3}\right) \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} x F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) x^2+\sqrt[3]{2}}{\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{8\ 2^{2/3} \sqrt[4]{3} \sqrt{\frac{x^2 \left(x^2+\sqrt[3]{2}\right)}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} \sqrt{x^6+2}}+\frac{5 \sqrt[4]{3} \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} x E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) x^2+\sqrt[3]{2}}{\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{4\ 2^{2/3} \sqrt{\frac{x^2 \left(x^2+\sqrt[3]{2}\right)}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} \sqrt{x^6+2}}","\frac{1}{8} \sqrt{x^6+2} x^5-\frac{5 \left(1+\sqrt{3}\right) \sqrt{x^6+2} x}{8 \left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)}+\frac{5 \left(1-\sqrt{3}\right) \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} x F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) x^2+\sqrt[3]{2}}{\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{8\ 2^{2/3} \sqrt[4]{3} \sqrt{\frac{x^2 \left(x^2+\sqrt[3]{2}\right)}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} \sqrt{x^6+2}}+\frac{5 \sqrt[4]{3} \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} x E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) x^2+\sqrt[3]{2}}{\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{4\ 2^{2/3} \sqrt{\frac{x^2 \left(x^2+\sqrt[3]{2}\right)}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} \sqrt{x^6+2}}",1,"(x^5*Sqrt[2 + x^6])/8 - (5*(1 + Sqrt[3])*x*Sqrt[2 + x^6])/(8*(2^(1/3) + (1 + Sqrt[3])*x^2)) + (5*3^(1/4)*x*(2^(1/3) + x^2)*Sqrt[(2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3) + (1 + Sqrt[3])*x^2)^2]*EllipticE[ArcCos[(2^(1/3) + (1 - Sqrt[3])*x^2)/(2^(1/3) + (1 + Sqrt[3])*x^2)], (2 + Sqrt[3])/4])/(4*2^(2/3)*Sqrt[(x^2*(2^(1/3) + x^2))/(2^(1/3) + (1 + Sqrt[3])*x^2)^2]*Sqrt[2 + x^6]) + (5*(1 - Sqrt[3])*x*(2^(1/3) + x^2)*Sqrt[(2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3) + (1 + Sqrt[3])*x^2)^2]*EllipticF[ArcCos[(2^(1/3) + (1 - Sqrt[3])*x^2)/(2^(1/3) + (1 + Sqrt[3])*x^2)], (2 + Sqrt[3])/4])/(8*2^(2/3)*3^(1/4)*Sqrt[(x^2*(2^(1/3) + x^2))/(2^(1/3) + (1 + Sqrt[3])*x^2)^2]*Sqrt[2 + x^6])","A",4,4,13,0.3077,1,"{321, 308, 225, 1881}"
1406,1,376,0,0.0796318,"\int \frac{x^4}{\sqrt{2+x^6}} \, dx","Int[x^4/Sqrt[2 + x^6],x]","\frac{\left(1+\sqrt{3}\right) \sqrt{x^6+2} x}{2 \left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)}-\frac{\left(1-\sqrt{3}\right) \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} x F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) x^2+\sqrt[3]{2}}{\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{2\ 2^{2/3} \sqrt[4]{3} \sqrt{\frac{x^2 \left(x^2+\sqrt[3]{2}\right)}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} \sqrt{x^6+2}}-\frac{\sqrt[4]{3} \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} x E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) x^2+\sqrt[3]{2}}{\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{2^{2/3} \sqrt{\frac{x^2 \left(x^2+\sqrt[3]{2}\right)}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} \sqrt{x^6+2}}","\frac{\left(1+\sqrt{3}\right) \sqrt{x^6+2} x}{2 \left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)}-\frac{\left(1-\sqrt{3}\right) \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} x F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) x^2+\sqrt[3]{2}}{\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{2\ 2^{2/3} \sqrt[4]{3} \sqrt{\frac{x^2 \left(x^2+\sqrt[3]{2}\right)}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} \sqrt{x^6+2}}-\frac{\sqrt[4]{3} \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} x E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) x^2+\sqrt[3]{2}}{\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{2^{2/3} \sqrt{\frac{x^2 \left(x^2+\sqrt[3]{2}\right)}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} \sqrt{x^6+2}}",1,"((1 + Sqrt[3])*x*Sqrt[2 + x^6])/(2*(2^(1/3) + (1 + Sqrt[3])*x^2)) - (3^(1/4)*x*(2^(1/3) + x^2)*Sqrt[(2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3) + (1 + Sqrt[3])*x^2)^2]*EllipticE[ArcCos[(2^(1/3) + (1 - Sqrt[3])*x^2)/(2^(1/3) + (1 + Sqrt[3])*x^2)], (2 + Sqrt[3])/4])/(2^(2/3)*Sqrt[(x^2*(2^(1/3) + x^2))/(2^(1/3) + (1 + Sqrt[3])*x^2)^2]*Sqrt[2 + x^6]) - ((1 - Sqrt[3])*x*(2^(1/3) + x^2)*Sqrt[(2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3) + (1 + Sqrt[3])*x^2)^2]*EllipticF[ArcCos[(2^(1/3) + (1 - Sqrt[3])*x^2)/(2^(1/3) + (1 + Sqrt[3])*x^2)], (2 + Sqrt[3])/4])/(2*2^(2/3)*3^(1/4)*Sqrt[(x^2*(2^(1/3) + x^2))/(2^(1/3) + (1 + Sqrt[3])*x^2)^2]*Sqrt[2 + x^6])","A",3,3,13,0.2308,1,"{308, 225, 1881}"
1407,1,392,0,0.0797777,"\int \frac{1}{x^2 \sqrt{2+x^6}} \, dx","Int[1/(x^2*Sqrt[2 + x^6]),x]","\frac{\left(1+\sqrt{3}\right) \sqrt{x^6+2} x}{2 \left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)}-\frac{\sqrt{x^6+2}}{2 x}-\frac{\left(1-\sqrt{3}\right) \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} x F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) x^2+\sqrt[3]{2}}{\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{2\ 2^{2/3} \sqrt[4]{3} \sqrt{\frac{x^2 \left(x^2+\sqrt[3]{2}\right)}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} \sqrt{x^6+2}}-\frac{\sqrt[4]{3} \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} x E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) x^2+\sqrt[3]{2}}{\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{2^{2/3} \sqrt{\frac{x^2 \left(x^2+\sqrt[3]{2}\right)}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} \sqrt{x^6+2}}","\frac{\left(1+\sqrt{3}\right) \sqrt{x^6+2} x}{2 \left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)}-\frac{\sqrt{x^6+2}}{2 x}-\frac{\left(1-\sqrt{3}\right) \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} x F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) x^2+\sqrt[3]{2}}{\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{2\ 2^{2/3} \sqrt[4]{3} \sqrt{\frac{x^2 \left(x^2+\sqrt[3]{2}\right)}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} \sqrt{x^6+2}}-\frac{\sqrt[4]{3} \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} x E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) x^2+\sqrt[3]{2}}{\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{2^{2/3} \sqrt{\frac{x^2 \left(x^2+\sqrt[3]{2}\right)}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} \sqrt{x^6+2}}",1,"-Sqrt[2 + x^6]/(2*x) + ((1 + Sqrt[3])*x*Sqrt[2 + x^6])/(2*(2^(1/3) + (1 + Sqrt[3])*x^2)) - (3^(1/4)*x*(2^(1/3) + x^2)*Sqrt[(2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3) + (1 + Sqrt[3])*x^2)^2]*EllipticE[ArcCos[(2^(1/3) + (1 - Sqrt[3])*x^2)/(2^(1/3) + (1 + Sqrt[3])*x^2)], (2 + Sqrt[3])/4])/(2^(2/3)*Sqrt[(x^2*(2^(1/3) + x^2))/(2^(1/3) + (1 + Sqrt[3])*x^2)^2]*Sqrt[2 + x^6]) - ((1 - Sqrt[3])*x*(2^(1/3) + x^2)*Sqrt[(2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3) + (1 + Sqrt[3])*x^2)^2]*EllipticF[ArcCos[(2^(1/3) + (1 - Sqrt[3])*x^2)/(2^(1/3) + (1 + Sqrt[3])*x^2)], (2 + Sqrt[3])/4])/(2*2^(2/3)*3^(1/4)*Sqrt[(x^2*(2^(1/3) + x^2))/(2^(1/3) + (1 + Sqrt[3])*x^2)^2]*Sqrt[2 + x^6])","A",4,4,13,0.3077,1,"{325, 308, 225, 1881}"
1408,1,51,0,0.0183523,"\int \frac{x^{23}}{\left(2+x^6\right)^{3/2}} \, dx","Int[x^23/(2 + x^6)^(3/2),x]","\frac{1}{15} \left(x^6+2\right)^{5/2}-\frac{2}{3} \left(x^6+2\right)^{3/2}+4 \sqrt{x^6+2}+\frac{8}{3 \sqrt{x^6+2}}","\frac{1}{15} \left(x^6+2\right)^{5/2}-\frac{2}{3} \left(x^6+2\right)^{3/2}+4 \sqrt{x^6+2}+\frac{8}{3 \sqrt{x^6+2}}",1,"8/(3*Sqrt[2 + x^6]) + 4*Sqrt[2 + x^6] - (2*(2 + x^6)^(3/2))/3 + (2 + x^6)^(5/2)/15","A",3,2,13,0.1538,1,"{266, 43}"
1409,1,40,0,0.0152648,"\int \frac{x^{17}}{\left(2+x^6\right)^{3/2}} \, dx","Int[x^17/(2 + x^6)^(3/2),x]","\frac{1}{9} \left(x^6+2\right)^{3/2}-\frac{4 \sqrt{x^6+2}}{3}-\frac{4}{3 \sqrt{x^6+2}}","\frac{1}{9} \left(x^6+2\right)^{3/2}-\frac{4 \sqrt{x^6+2}}{3}-\frac{4}{3 \sqrt{x^6+2}}",1,"-4/(3*Sqrt[2 + x^6]) - (4*Sqrt[2 + x^6])/3 + (2 + x^6)^(3/2)/9","A",3,2,13,0.1538,1,"{266, 43}"
1410,1,27,0,0.0108826,"\int \frac{x^{11}}{\left(2+x^6\right)^{3/2}} \, dx","Int[x^11/(2 + x^6)^(3/2),x]","\frac{\sqrt{x^6+2}}{3}+\frac{2}{3 \sqrt{x^6+2}}","\frac{\sqrt{x^6+2}}{3}+\frac{2}{3 \sqrt{x^6+2}}",1,"2/(3*Sqrt[2 + x^6]) + Sqrt[2 + x^6]/3","A",3,2,13,0.1538,1,"{266, 43}"
1411,1,13,0,0.002953,"\int \frac{x^5}{\left(2+x^6\right)^{3/2}} \, dx","Int[x^5/(2 + x^6)^(3/2),x]","-\frac{1}{3 \sqrt{x^6+2}}","-\frac{1}{3 \sqrt{x^6+2}}",1,"-1/(3*Sqrt[2 + x^6])","A",1,1,13,0.07692,1,"{261}"
1412,1,39,0,0.01586,"\int \frac{1}{x \left(2+x^6\right)^{3/2}} \, dx","Int[1/(x*(2 + x^6)^(3/2)),x]","\frac{1}{6 \sqrt{x^6+2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{x^6+2}}{\sqrt{2}}\right)}{6 \sqrt{2}}","\frac{1}{6 \sqrt{x^6+2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{x^6+2}}{\sqrt{2}}\right)}{6 \sqrt{2}}",1,"1/(6*Sqrt[2 + x^6]) - ArcTanh[Sqrt[2 + x^6]/Sqrt[2]]/(6*Sqrt[2])","A",4,4,13,0.3077,1,"{266, 51, 63, 207}"
1413,1,58,0,0.0228854,"\int \frac{1}{x^7 \left(2+x^6\right)^{3/2}} \, dx","Int[1/(x^7*(2 + x^6)^(3/2)),x]","-\frac{\sqrt{x^6+2}}{8 x^6}+\frac{1}{6 x^6 \sqrt{x^6+2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{x^6+2}}{\sqrt{2}}\right)}{8 \sqrt{2}}","-\frac{1}{12 x^6 \sqrt{x^6+2}}-\frac{1}{8 \sqrt{x^6+2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{x^6+2}}{\sqrt{2}}\right)}{8 \sqrt{2}}",1,"1/(6*x^6*Sqrt[2 + x^6]) - Sqrt[2 + x^6]/(8*x^6) + ArcTanh[Sqrt[2 + x^6]/Sqrt[2]]/(8*Sqrt[2])","A",5,4,13,0.3077,1,"{266, 51, 63, 207}"
1414,1,74,0,0.0303197,"\int \frac{1}{x^{13} \left(2+x^6\right)^{3/2}} \, dx","Int[1/(x^13*(2 + x^6)^(3/2)),x]","\frac{5 \sqrt{x^6+2}}{64 x^6}-\frac{5 \sqrt{x^6+2}}{48 x^{12}}+\frac{1}{6 x^{12} \sqrt{x^6+2}}-\frac{5 \tanh ^{-1}\left(\frac{\sqrt{x^6+2}}{\sqrt{2}}\right)}{64 \sqrt{2}}","\frac{5}{96 x^6 \sqrt{x^6+2}}-\frac{1}{24 x^{12} \sqrt{x^6+2}}+\frac{5}{64 \sqrt{x^6+2}}-\frac{5 \tanh ^{-1}\left(\frac{\sqrt{x^6+2}}{\sqrt{2}}\right)}{64 \sqrt{2}}",1,"1/(6*x^12*Sqrt[2 + x^6]) - (5*Sqrt[2 + x^6])/(48*x^12) + (5*Sqrt[2 + x^6])/(64*x^6) - (5*ArcTanh[Sqrt[2 + x^6]/Sqrt[2]])/(64*Sqrt[2])","A",6,4,13,0.3077,1,"{266, 51, 63, 207}"
1415,1,45,0,0.0188832,"\int \frac{x^{14}}{\left(2+x^6\right)^{3/2}} \, dx","Int[x^14/(2 + x^6)^(3/2),x]","-\frac{x^9}{3 \sqrt{x^6+2}}+\frac{1}{2} \sqrt{x^6+2} x^3-\sinh ^{-1}\left(\frac{x^3}{\sqrt{2}}\right)","-\frac{x^9}{3 \sqrt{x^6+2}}+\frac{1}{2} \sqrt{x^6+2} x^3-\sinh ^{-1}\left(\frac{x^3}{\sqrt{2}}\right)",1,"-x^9/(3*Sqrt[2 + x^6]) + (x^3*Sqrt[2 + x^6])/2 - ArcSinh[x^3/Sqrt[2]]","A",4,4,13,0.3077,1,"{275, 288, 321, 215}"
1416,1,31,0,0.012157,"\int \frac{x^8}{\left(2+x^6\right)^{3/2}} \, dx","Int[x^8/(2 + x^6)^(3/2),x]","\frac{1}{3} \sinh ^{-1}\left(\frac{x^3}{\sqrt{2}}\right)-\frac{x^3}{3 \sqrt{x^6+2}}","\frac{1}{3} \sinh ^{-1}\left(\frac{x^3}{\sqrt{2}}\right)-\frac{x^3}{3 \sqrt{x^6+2}}",1,"-x^3/(3*Sqrt[2 + x^6]) + ArcSinh[x^3/Sqrt[2]]/3","A",3,3,13,0.2308,1,"{275, 288, 215}"
1417,1,16,0,0.0030059,"\int \frac{x^2}{\left(2+x^6\right)^{3/2}} \, dx","Int[x^2/(2 + x^6)^(3/2),x]","\frac{x^3}{6 \sqrt{x^6+2}}","\frac{x^3}{6 \sqrt{x^6+2}}",1,"x^3/(6*Sqrt[2 + x^6])","A",1,1,13,0.07692,1,"{264}"
1418,1,33,0,0.0062853,"\int \frac{1}{x^4 \left(2+x^6\right)^{3/2}} \, dx","Int[1/(x^4*(2 + x^6)^(3/2)),x]","-\frac{x^3}{6 \sqrt{x^6+2}}-\frac{1}{6 \sqrt{x^6+2} x^3}","-\frac{x^3}{6 \sqrt{x^6+2}}-\frac{1}{6 \sqrt{x^6+2} x^3}",1,"-1/(6*x^3*Sqrt[2 + x^6]) - x^3/(6*Sqrt[2 + x^6])","A",2,2,13,0.1538,1,"{271, 264}"
1419,1,49,0,0.0103437,"\int \frac{1}{x^{10} \left(2+x^6\right)^{3/2}} \, dx","Int[1/(x^10*(2 + x^6)^(3/2)),x]","\frac{x^3}{9 \sqrt{x^6+2}}+\frac{1}{9 \sqrt{x^6+2} x^3}-\frac{1}{18 \sqrt{x^6+2} x^9}","\frac{x^3}{9 \sqrt{x^6+2}}+\frac{1}{9 \sqrt{x^6+2} x^3}-\frac{1}{18 \sqrt{x^6+2} x^9}",1,"-1/(18*x^9*Sqrt[2 + x^6]) + 1/(9*x^3*Sqrt[2 + x^6]) + x^3/(9*Sqrt[2 + x^6])","A",3,2,13,0.1538,1,"{271, 264}"
1420,1,202,0,0.1030486,"\int \frac{x^{13}}{\left(2+x^6\right)^{3/2}} \, dx","Int[x^13/(2 + x^6)^(3/2),x]","-\frac{x^8}{3 \sqrt{x^6+2}}+\frac{8}{15} \sqrt{x^6+2} x^2-\frac{16\ 2^{5/6} \sqrt{2+\sqrt{3}} \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} F\left(\sin ^{-1}\left(\frac{x^2+\sqrt[3]{2} \left(1-\sqrt{3}\right)}{x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)}\right)|-7-4 \sqrt{3}\right)}{15 \sqrt[4]{3} \sqrt{\frac{x^2+\sqrt[3]{2}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} \sqrt{x^6+2}}","-\frac{x^8}{3 \sqrt{x^6+2}}+\frac{8}{15} \sqrt{x^6+2} x^2-\frac{16\ 2^{5/6} \sqrt{2+\sqrt{3}} \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} F\left(\sin ^{-1}\left(\frac{x^2+\sqrt[3]{2} \left(1-\sqrt{3}\right)}{x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)}\right)|-7-4 \sqrt{3}\right)}{15 \sqrt[4]{3} \sqrt{\frac{x^2+\sqrt[3]{2}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} \sqrt{x^6+2}}",1,"-x^8/(3*Sqrt[2 + x^6]) + (8*x^2*Sqrt[2 + x^6])/15 - (16*2^(5/6)*Sqrt[2 + Sqrt[3]]*(2^(1/3) + x^2)*Sqrt[(2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3)*(1 + Sqrt[3]) + x^2)^2]*EllipticF[ArcSin[(2^(1/3)*(1 - Sqrt[3]) + x^2)/(2^(1/3)*(1 + Sqrt[3]) + x^2)], -7 - 4*Sqrt[3]])/(15*3^(1/4)*Sqrt[(2^(1/3) + x^2)/(2^(1/3)*(1 + Sqrt[3]) + x^2)^2]*Sqrt[2 + x^6])","A",4,4,13,0.3077,1,"{275, 288, 321, 218}"
1421,1,186,0,0.0863903,"\int \frac{x^7}{\left(2+x^6\right)^{3/2}} \, dx","Int[x^7/(2 + x^6)^(3/2),x]","\frac{2^{5/6} \sqrt{2+\sqrt{3}} \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} F\left(\sin ^{-1}\left(\frac{x^2+\sqrt[3]{2} \left(1-\sqrt{3}\right)}{x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{\frac{x^2+\sqrt[3]{2}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} \sqrt{x^6+2}}-\frac{x^2}{3 \sqrt{x^6+2}}","\frac{2^{5/6} \sqrt{2+\sqrt{3}} \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} F\left(\sin ^{-1}\left(\frac{x^2+\sqrt[3]{2} \left(1-\sqrt{3}\right)}{x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{\frac{x^2+\sqrt[3]{2}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} \sqrt{x^6+2}}-\frac{x^2}{3 \sqrt{x^6+2}}",1,"-x^2/(3*Sqrt[2 + x^6]) + (2^(5/6)*Sqrt[2 + Sqrt[3]]*(2^(1/3) + x^2)*Sqrt[(2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3)*(1 + Sqrt[3]) + x^2)^2]*EllipticF[ArcSin[(2^(1/3)*(1 - Sqrt[3]) + x^2)/(2^(1/3)*(1 + Sqrt[3]) + x^2)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*Sqrt[(2^(1/3) + x^2)/(2^(1/3)*(1 + Sqrt[3]) + x^2)^2]*Sqrt[2 + x^6])","A",3,3,13,0.2308,1,"{275, 288, 218}"
1422,1,186,0,0.0826325,"\int \frac{x}{\left(2+x^6\right)^{3/2}} \, dx","Int[x/(2 + x^6)^(3/2),x]","\frac{x^2}{6 \sqrt{x^6+2}}+\frac{\sqrt{2+\sqrt{3}} \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} F\left(\sin ^{-1}\left(\frac{x^2+\sqrt[3]{2} \left(1-\sqrt{3}\right)}{x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)}\right)|-7-4 \sqrt{3}\right)}{6 \sqrt[6]{2} \sqrt[4]{3} \sqrt{\frac{x^2+\sqrt[3]{2}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} \sqrt{x^6+2}}","\frac{x^2}{6 \sqrt{x^6+2}}+\frac{\sqrt{2+\sqrt{3}} \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} F\left(\sin ^{-1}\left(\frac{x^2+\sqrt[3]{2} \left(1-\sqrt{3}\right)}{x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)}\right)|-7-4 \sqrt{3}\right)}{6 \sqrt[6]{2} \sqrt[4]{3} \sqrt{\frac{x^2+\sqrt[3]{2}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} \sqrt{x^6+2}}",1,"x^2/(6*Sqrt[2 + x^6]) + (Sqrt[2 + Sqrt[3]]*(2^(1/3) + x^2)*Sqrt[(2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3)*(1 + Sqrt[3]) + x^2)^2]*EllipticF[ArcSin[(2^(1/3)*(1 - Sqrt[3]) + x^2)/(2^(1/3)*(1 + Sqrt[3]) + x^2)], -7 - 4*Sqrt[3]])/(6*2^(1/6)*3^(1/4)*Sqrt[(2^(1/3) + x^2)/(2^(1/3)*(1 + Sqrt[3]) + x^2)^2]*Sqrt[2 + x^6])","A",3,3,11,0.2727,1,"{275, 199, 218}"
1423,1,202,0,0.1020648,"\int \frac{1}{x^5 \left(2+x^6\right)^{3/2}} \, dx","Int[1/(x^5*(2 + x^6)^(3/2)),x]","-\frac{7 \sqrt{x^6+2}}{48 x^4}+\frac{1}{6 x^4 \sqrt{x^6+2}}-\frac{7 \sqrt{2+\sqrt{3}} \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} F\left(\sin ^{-1}\left(\frac{x^2+\sqrt[3]{2} \left(1-\sqrt{3}\right)}{x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)}\right)|-7-4 \sqrt{3}\right)}{48 \sqrt[6]{2} \sqrt[4]{3} \sqrt{\frac{x^2+\sqrt[3]{2}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} \sqrt{x^6+2}}","-\frac{7 \sqrt{x^6+2}}{48 x^4}+\frac{1}{6 x^4 \sqrt{x^6+2}}-\frac{7 \sqrt{2+\sqrt{3}} \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} F\left(\sin ^{-1}\left(\frac{x^2+\sqrt[3]{2} \left(1-\sqrt{3}\right)}{x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)}\right)|-7-4 \sqrt{3}\right)}{48 \sqrt[6]{2} \sqrt[4]{3} \sqrt{\frac{x^2+\sqrt[3]{2}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} \sqrt{x^6+2}}",1,"1/(6*x^4*Sqrt[2 + x^6]) - (7*Sqrt[2 + x^6])/(48*x^4) - (7*Sqrt[2 + Sqrt[3]]*(2^(1/3) + x^2)*Sqrt[(2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3)*(1 + Sqrt[3]) + x^2)^2]*EllipticF[ArcSin[(2^(1/3)*(1 - Sqrt[3]) + x^2)/(2^(1/3)*(1 + Sqrt[3]) + x^2)], -7 - 4*Sqrt[3]])/(48*2^(1/6)*3^(1/4)*Sqrt[(2^(1/3) + x^2)/(2^(1/3)*(1 + Sqrt[3]) + x^2)^2]*Sqrt[2 + x^6])","A",4,4,13,0.3077,1,"{275, 290, 325, 218}"
1424,1,195,0,0.0454726,"\int \frac{x^{12}}{\left(2+x^6\right)^{3/2}} \, dx","Int[x^12/(2 + x^6)^(3/2),x]","-\frac{x^7}{3 \sqrt{x^6+2}}+\frac{7}{12} \sqrt{x^6+2} x-\frac{7 \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} x F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) x^2+\sqrt[3]{2}}{\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{12 \sqrt[3]{2} \sqrt[4]{3} \sqrt{\frac{x^2 \left(x^2+\sqrt[3]{2}\right)}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} \sqrt{x^6+2}}","-\frac{x^7}{3 \sqrt{x^6+2}}+\frac{7}{12} \sqrt{x^6+2} x-\frac{7 \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} x F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) x^2+\sqrt[3]{2}}{\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{12 \sqrt[3]{2} \sqrt[4]{3} \sqrt{\frac{x^2 \left(x^2+\sqrt[3]{2}\right)}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} \sqrt{x^6+2}}",1,"-x^7/(3*Sqrt[2 + x^6]) + (7*x*Sqrt[2 + x^6])/12 - (7*x*(2^(1/3) + x^2)*Sqrt[(2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3) + (1 + Sqrt[3])*x^2)^2]*EllipticF[ArcCos[(2^(1/3) + (1 - Sqrt[3])*x^2)/(2^(1/3) + (1 + Sqrt[3])*x^2)], (2 + Sqrt[3])/4])/(12*2^(1/3)*3^(1/4)*Sqrt[(x^2*(2^(1/3) + x^2))/(2^(1/3) + (1 + Sqrt[3])*x^2)^2]*Sqrt[2 + x^6])","A",3,3,13,0.2308,1,"{288, 321, 225}"
1425,1,179,0,0.0299589,"\int \frac{x^6}{\left(2+x^6\right)^{3/2}} \, dx","Int[x^6/(2 + x^6)^(3/2),x]","\frac{x \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) x^2+\sqrt[3]{2}}{\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{6 \sqrt[3]{2} \sqrt[4]{3} \sqrt{\frac{x^2 \left(x^2+\sqrt[3]{2}\right)}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} \sqrt{x^6+2}}-\frac{x}{3 \sqrt{x^6+2}}","\frac{x \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) x^2+\sqrt[3]{2}}{\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{6 \sqrt[3]{2} \sqrt[4]{3} \sqrt{\frac{x^2 \left(x^2+\sqrt[3]{2}\right)}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} \sqrt{x^6+2}}-\frac{x}{3 \sqrt{x^6+2}}",1,"-x/(3*Sqrt[2 + x^6]) + (x*(2^(1/3) + x^2)*Sqrt[(2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3) + (1 + Sqrt[3])*x^2)^2]*EllipticF[ArcCos[(2^(1/3) + (1 - Sqrt[3])*x^2)/(2^(1/3) + (1 + Sqrt[3])*x^2)], (2 + Sqrt[3])/4])/(6*2^(1/3)*3^(1/4)*Sqrt[(x^2*(2^(1/3) + x^2))/(2^(1/3) + (1 + Sqrt[3])*x^2)^2]*Sqrt[2 + x^6])","A",2,2,13,0.1538,1,"{288, 225}"
1426,1,179,0,0.0270916,"\int \frac{1}{\left(2+x^6\right)^{3/2}} \, dx","Int[(2 + x^6)^(-3/2),x]","\frac{x}{6 \sqrt{x^6+2}}+\frac{\left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} x F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) x^2+\sqrt[3]{2}}{\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{6 \sqrt[3]{2} \sqrt[4]{3} \sqrt{\frac{x^2 \left(x^2+\sqrt[3]{2}\right)}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} \sqrt{x^6+2}}","\frac{x}{6 \sqrt{x^6+2}}+\frac{\left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} x F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) x^2+\sqrt[3]{2}}{\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{6 \sqrt[3]{2} \sqrt[4]{3} \sqrt{\frac{x^2 \left(x^2+\sqrt[3]{2}\right)}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} \sqrt{x^6+2}}",1,"x/(6*Sqrt[2 + x^6]) + (x*(2^(1/3) + x^2)*Sqrt[(2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3) + (1 + Sqrt[3])*x^2)^2]*EllipticF[ArcCos[(2^(1/3) + (1 - Sqrt[3])*x^2)/(2^(1/3) + (1 + Sqrt[3])*x^2)], (2 + Sqrt[3])/4])/(6*2^(1/3)*3^(1/4)*Sqrt[(x^2*(2^(1/3) + x^2))/(2^(1/3) + (1 + Sqrt[3])*x^2)^2]*Sqrt[2 + x^6])","A",2,2,9,0.2222,1,"{199, 225}"
1427,1,197,0,0.04583,"\int \frac{1}{x^6 \left(2+x^6\right)^{3/2}} \, dx","Int[1/(x^6*(2 + x^6)^(3/2)),x]","-\frac{2 \sqrt{x^6+2}}{15 x^5}+\frac{1}{6 x^5 \sqrt{x^6+2}}-\frac{2^{2/3} x \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) x^2+\sqrt[3]{2}}{\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{15 \sqrt[4]{3} \sqrt{\frac{x^2 \left(x^2+\sqrt[3]{2}\right)}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} \sqrt{x^6+2}}","-\frac{2 \sqrt{x^6+2}}{15 x^5}+\frac{1}{6 x^5 \sqrt{x^6+2}}-\frac{2^{2/3} x \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) x^2+\sqrt[3]{2}}{\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{15 \sqrt[4]{3} \sqrt{\frac{x^2 \left(x^2+\sqrt[3]{2}\right)}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} \sqrt{x^6+2}}",1,"1/(6*x^5*Sqrt[2 + x^6]) - (2*Sqrt[2 + x^6])/(15*x^5) - (2^(2/3)*x*(2^(1/3) + x^2)*Sqrt[(2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3) + (1 + Sqrt[3])*x^2)^2]*EllipticF[ArcCos[(2^(1/3) + (1 - Sqrt[3])*x^2)/(2^(1/3) + (1 + Sqrt[3])*x^2)], (2 + Sqrt[3])/4])/(15*3^(1/4)*Sqrt[(x^2*(2^(1/3) + x^2))/(2^(1/3) + (1 + Sqrt[3])*x^2)^2]*Sqrt[2 + x^6])","A",3,3,13,0.2308,1,"{290, 325, 225}"
1428,1,394,0,0.2220808,"\int \frac{x^{15}}{\left(2+x^6\right)^{3/2}} \, dx","Int[x^15/(2 + x^6)^(3/2),x]","-\frac{x^{10}}{3 \sqrt{x^6+2}}+\frac{10}{21} \sqrt{x^6+2} x^4-\frac{80 \sqrt{x^6+2}}{21 \left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)}-\frac{80\ 2^{2/3} \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} F\left(\sin ^{-1}\left(\frac{x^2+\sqrt[3]{2} \left(1-\sqrt{3}\right)}{x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)}\right)|-7-4 \sqrt{3}\right)}{21 \sqrt[4]{3} \sqrt{\frac{x^2+\sqrt[3]{2}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} \sqrt{x^6+2}}+\frac{40 \sqrt[6]{2} \sqrt{2-\sqrt{3}} \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} E\left(\sin ^{-1}\left(\frac{x^2+\sqrt[3]{2} \left(1-\sqrt{3}\right)}{x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)}\right)|-7-4 \sqrt{3}\right)}{7\ 3^{3/4} \sqrt{\frac{x^2+\sqrt[3]{2}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} \sqrt{x^6+2}}","-\frac{x^{10}}{3 \sqrt{x^6+2}}+\frac{10}{21} \sqrt{x^6+2} x^4-\frac{80 \sqrt{x^6+2}}{21 \left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)}-\frac{80\ 2^{2/3} \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} F\left(\sin ^{-1}\left(\frac{x^2+\sqrt[3]{2} \left(1-\sqrt{3}\right)}{x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)}\right)|-7-4 \sqrt{3}\right)}{21 \sqrt[4]{3} \sqrt{\frac{x^2+\sqrt[3]{2}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} \sqrt{x^6+2}}+\frac{40 \sqrt[6]{2} \sqrt{2-\sqrt{3}} \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} E\left(\sin ^{-1}\left(\frac{x^2+\sqrt[3]{2} \left(1-\sqrt{3}\right)}{x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)}\right)|-7-4 \sqrt{3}\right)}{7\ 3^{3/4} \sqrt{\frac{x^2+\sqrt[3]{2}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} \sqrt{x^6+2}}",1,"-x^10/(3*Sqrt[2 + x^6]) + (10*x^4*Sqrt[2 + x^6])/21 - (80*Sqrt[2 + x^6])/(21*(2^(1/3)*(1 + Sqrt[3]) + x^2)) + (40*2^(1/6)*Sqrt[2 - Sqrt[3]]*(2^(1/3) + x^2)*Sqrt[(2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3)*(1 + Sqrt[3]) + x^2)^2]*EllipticE[ArcSin[(2^(1/3)*(1 - Sqrt[3]) + x^2)/(2^(1/3)*(1 + Sqrt[3]) + x^2)], -7 - 4*Sqrt[3]])/(7*3^(3/4)*Sqrt[(2^(1/3) + x^2)/(2^(1/3)*(1 + Sqrt[3]) + x^2)^2]*Sqrt[2 + x^6]) - (80*2^(2/3)*(2^(1/3) + x^2)*Sqrt[(2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3)*(1 + Sqrt[3]) + x^2)^2]*EllipticF[ArcSin[(2^(1/3)*(1 - Sqrt[3]) + x^2)/(2^(1/3)*(1 + Sqrt[3]) + x^2)], -7 - 4*Sqrt[3]])/(21*3^(1/4)*Sqrt[(2^(1/3) + x^2)/(2^(1/3)*(1 + Sqrt[3]) + x^2)^2]*Sqrt[2 + x^6])","A",6,6,13,0.4615,1,"{275, 288, 321, 303, 218, 1877}"
1429,1,376,0,0.1914853,"\int \frac{x^9}{\left(2+x^6\right)^{3/2}} \, dx","Int[x^9/(2 + x^6)^(3/2),x]","-\frac{x^4}{3 \sqrt{x^6+2}}+\frac{4 \sqrt{x^6+2}}{3 \left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)}+\frac{4\ 2^{2/3} \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} F\left(\sin ^{-1}\left(\frac{x^2+\sqrt[3]{2} \left(1-\sqrt{3}\right)}{x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{\frac{x^2+\sqrt[3]{2}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} \sqrt{x^6+2}}-\frac{2 \sqrt[6]{2} \sqrt{2-\sqrt{3}} \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} E\left(\sin ^{-1}\left(\frac{x^2+\sqrt[3]{2} \left(1-\sqrt{3}\right)}{x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)}\right)|-7-4 \sqrt{3}\right)}{3^{3/4} \sqrt{\frac{x^2+\sqrt[3]{2}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} \sqrt{x^6+2}}","-\frac{x^4}{3 \sqrt{x^6+2}}+\frac{4 \sqrt{x^6+2}}{3 \left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)}+\frac{4\ 2^{2/3} \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} F\left(\sin ^{-1}\left(\frac{x^2+\sqrt[3]{2} \left(1-\sqrt{3}\right)}{x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{\frac{x^2+\sqrt[3]{2}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} \sqrt{x^6+2}}-\frac{2 \sqrt[6]{2} \sqrt{2-\sqrt{3}} \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} E\left(\sin ^{-1}\left(\frac{x^2+\sqrt[3]{2} \left(1-\sqrt{3}\right)}{x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)}\right)|-7-4 \sqrt{3}\right)}{3^{3/4} \sqrt{\frac{x^2+\sqrt[3]{2}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} \sqrt{x^6+2}}",1,"-x^4/(3*Sqrt[2 + x^6]) + (4*Sqrt[2 + x^6])/(3*(2^(1/3)*(1 + Sqrt[3]) + x^2)) - (2*2^(1/6)*Sqrt[2 - Sqrt[3]]*(2^(1/3) + x^2)*Sqrt[(2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3)*(1 + Sqrt[3]) + x^2)^2]*EllipticE[ArcSin[(2^(1/3)*(1 - Sqrt[3]) + x^2)/(2^(1/3)*(1 + Sqrt[3]) + x^2)], -7 - 4*Sqrt[3]])/(3^(3/4)*Sqrt[(2^(1/3) + x^2)/(2^(1/3)*(1 + Sqrt[3]) + x^2)^2]*Sqrt[2 + x^6]) + (4*2^(2/3)*(2^(1/3) + x^2)*Sqrt[(2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3)*(1 + Sqrt[3]) + x^2)^2]*EllipticF[ArcSin[(2^(1/3)*(1 - Sqrt[3]) + x^2)/(2^(1/3)*(1 + Sqrt[3]) + x^2)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*Sqrt[(2^(1/3) + x^2)/(2^(1/3)*(1 + Sqrt[3]) + x^2)^2]*Sqrt[2 + x^6])","A",5,5,13,0.3846,1,"{275, 288, 303, 218, 1877}"
1430,1,378,0,0.1870572,"\int \frac{x^3}{\left(2+x^6\right)^{3/2}} \, dx","Int[x^3/(2 + x^6)^(3/2),x]","\frac{x^4}{6 \sqrt{x^6+2}}-\frac{\sqrt{x^6+2}}{6 \left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)}-\frac{\left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} F\left(\sin ^{-1}\left(\frac{x^2+\sqrt[3]{2} \left(1-\sqrt{3}\right)}{x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[3]{2} \sqrt[4]{3} \sqrt{\frac{x^2+\sqrt[3]{2}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} \sqrt{x^6+2}}+\frac{\sqrt{2-\sqrt{3}} \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} E\left(\sin ^{-1}\left(\frac{x^2+\sqrt[3]{2} \left(1-\sqrt{3}\right)}{x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)}\right)|-7-4 \sqrt{3}\right)}{2\ 2^{5/6} 3^{3/4} \sqrt{\frac{x^2+\sqrt[3]{2}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} \sqrt{x^6+2}}","\frac{x^4}{6 \sqrt{x^6+2}}-\frac{\sqrt{x^6+2}}{6 \left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)}-\frac{\left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} F\left(\sin ^{-1}\left(\frac{x^2+\sqrt[3]{2} \left(1-\sqrt{3}\right)}{x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[3]{2} \sqrt[4]{3} \sqrt{\frac{x^2+\sqrt[3]{2}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} \sqrt{x^6+2}}+\frac{\sqrt{2-\sqrt{3}} \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} E\left(\sin ^{-1}\left(\frac{x^2+\sqrt[3]{2} \left(1-\sqrt{3}\right)}{x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)}\right)|-7-4 \sqrt{3}\right)}{2\ 2^{5/6} 3^{3/4} \sqrt{\frac{x^2+\sqrt[3]{2}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} \sqrt{x^6+2}}",1,"x^4/(6*Sqrt[2 + x^6]) - Sqrt[2 + x^6]/(6*(2^(1/3)*(1 + Sqrt[3]) + x^2)) + (Sqrt[2 - Sqrt[3]]*(2^(1/3) + x^2)*Sqrt[(2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3)*(1 + Sqrt[3]) + x^2)^2]*EllipticE[ArcSin[(2^(1/3)*(1 - Sqrt[3]) + x^2)/(2^(1/3)*(1 + Sqrt[3]) + x^2)], -7 - 4*Sqrt[3]])/(2*2^(5/6)*3^(3/4)*Sqrt[(2^(1/3) + x^2)/(2^(1/3)*(1 + Sqrt[3]) + x^2)^2]*Sqrt[2 + x^6]) - ((2^(1/3) + x^2)*Sqrt[(2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3)*(1 + Sqrt[3]) + x^2)^2]*EllipticF[ArcSin[(2^(1/3)*(1 - Sqrt[3]) + x^2)/(2^(1/3)*(1 + Sqrt[3]) + x^2)], -7 - 4*Sqrt[3]])/(3*2^(1/3)*3^(1/4)*Sqrt[(2^(1/3) + x^2)/(2^(1/3)*(1 + Sqrt[3]) + x^2)^2]*Sqrt[2 + x^6])","A",5,5,13,0.3846,1,"{275, 290, 303, 218, 1877}"
1431,1,394,0,0.2209986,"\int \frac{1}{x^3 \left(2+x^6\right)^{3/2}} \, dx","Int[1/(x^3*(2 + x^6)^(3/2)),x]","\frac{5 \sqrt{x^6+2}}{24 \left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)}-\frac{5 \sqrt{x^6+2}}{24 x^2}+\frac{1}{6 x^2 \sqrt{x^6+2}}+\frac{5 \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} F\left(\sin ^{-1}\left(\frac{x^2+\sqrt[3]{2} \left(1-\sqrt{3}\right)}{x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)}\right)|-7-4 \sqrt{3}\right)}{12 \sqrt[3]{2} \sqrt[4]{3} \sqrt{\frac{x^2+\sqrt[3]{2}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} \sqrt{x^6+2}}-\frac{5 \sqrt{2-\sqrt{3}} \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} E\left(\sin ^{-1}\left(\frac{x^2+\sqrt[3]{2} \left(1-\sqrt{3}\right)}{x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)}\right)|-7-4 \sqrt{3}\right)}{8\ 2^{5/6} 3^{3/4} \sqrt{\frac{x^2+\sqrt[3]{2}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} \sqrt{x^6+2}}","\frac{5 \sqrt{x^6+2}}{24 \left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)}-\frac{5 \sqrt{x^6+2}}{24 x^2}+\frac{1}{6 x^2 \sqrt{x^6+2}}+\frac{5 \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} F\left(\sin ^{-1}\left(\frac{x^2+\sqrt[3]{2} \left(1-\sqrt{3}\right)}{x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)}\right)|-7-4 \sqrt{3}\right)}{12 \sqrt[3]{2} \sqrt[4]{3} \sqrt{\frac{x^2+\sqrt[3]{2}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} \sqrt{x^6+2}}-\frac{5 \sqrt{2-\sqrt{3}} \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} E\left(\sin ^{-1}\left(\frac{x^2+\sqrt[3]{2} \left(1-\sqrt{3}\right)}{x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)}\right)|-7-4 \sqrt{3}\right)}{8\ 2^{5/6} 3^{3/4} \sqrt{\frac{x^2+\sqrt[3]{2}}{\left(x^2+\sqrt[3]{2} \left(1+\sqrt{3}\right)\right)^2}} \sqrt{x^6+2}}",1,"1/(6*x^2*Sqrt[2 + x^6]) - (5*Sqrt[2 + x^6])/(24*x^2) + (5*Sqrt[2 + x^6])/(24*(2^(1/3)*(1 + Sqrt[3]) + x^2)) - (5*Sqrt[2 - Sqrt[3]]*(2^(1/3) + x^2)*Sqrt[(2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3)*(1 + Sqrt[3]) + x^2)^2]*EllipticE[ArcSin[(2^(1/3)*(1 - Sqrt[3]) + x^2)/(2^(1/3)*(1 + Sqrt[3]) + x^2)], -7 - 4*Sqrt[3]])/(8*2^(5/6)*3^(3/4)*Sqrt[(2^(1/3) + x^2)/(2^(1/3)*(1 + Sqrt[3]) + x^2)^2]*Sqrt[2 + x^6]) + (5*(2^(1/3) + x^2)*Sqrt[(2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3)*(1 + Sqrt[3]) + x^2)^2]*EllipticF[ArcSin[(2^(1/3)*(1 - Sqrt[3]) + x^2)/(2^(1/3)*(1 + Sqrt[3]) + x^2)], -7 - 4*Sqrt[3]])/(12*2^(1/3)*3^(1/4)*Sqrt[(2^(1/3) + x^2)/(2^(1/3)*(1 + Sqrt[3]) + x^2)^2]*Sqrt[2 + x^6])","A",6,6,13,0.4615,1,"{275, 290, 325, 303, 218, 1877}"
1432,1,392,0,0.1106391,"\int \frac{x^{10}}{\left(2+x^6\right)^{3/2}} \, dx","Int[x^10/(2 + x^6)^(3/2),x]","-\frac{x^5}{3 \sqrt{x^6+2}}+\frac{5 \left(1+\sqrt{3}\right) \sqrt{x^6+2} x}{6 \left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)}-\frac{5 \left(1-\sqrt{3}\right) \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} x F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) x^2+\sqrt[3]{2}}{\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{6\ 2^{2/3} \sqrt[4]{3} \sqrt{\frac{x^2 \left(x^2+\sqrt[3]{2}\right)}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} \sqrt{x^6+2}}-\frac{5 \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} x E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) x^2+\sqrt[3]{2}}{\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{2^{2/3} 3^{3/4} \sqrt{\frac{x^2 \left(x^2+\sqrt[3]{2}\right)}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} \sqrt{x^6+2}}","-\frac{x^5}{3 \sqrt{x^6+2}}+\frac{5 \left(1+\sqrt{3}\right) \sqrt{x^6+2} x}{6 \left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)}-\frac{5 \left(1-\sqrt{3}\right) \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} x F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) x^2+\sqrt[3]{2}}{\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{6\ 2^{2/3} \sqrt[4]{3} \sqrt{\frac{x^2 \left(x^2+\sqrt[3]{2}\right)}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} \sqrt{x^6+2}}-\frac{5 \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} x E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) x^2+\sqrt[3]{2}}{\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{2^{2/3} 3^{3/4} \sqrt{\frac{x^2 \left(x^2+\sqrt[3]{2}\right)}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} \sqrt{x^6+2}}",1,"-x^5/(3*Sqrt[2 + x^6]) + (5*(1 + Sqrt[3])*x*Sqrt[2 + x^6])/(6*(2^(1/3) + (1 + Sqrt[3])*x^2)) - (5*x*(2^(1/3) + x^2)*Sqrt[(2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3) + (1 + Sqrt[3])*x^2)^2]*EllipticE[ArcCos[(2^(1/3) + (1 - Sqrt[3])*x^2)/(2^(1/3) + (1 + Sqrt[3])*x^2)], (2 + Sqrt[3])/4])/(2^(2/3)*3^(3/4)*Sqrt[(x^2*(2^(1/3) + x^2))/(2^(1/3) + (1 + Sqrt[3])*x^2)^2]*Sqrt[2 + x^6]) - (5*(1 - Sqrt[3])*x*(2^(1/3) + x^2)*Sqrt[(2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3) + (1 + Sqrt[3])*x^2)^2]*EllipticF[ArcCos[(2^(1/3) + (1 - Sqrt[3])*x^2)/(2^(1/3) + (1 + Sqrt[3])*x^2)], (2 + Sqrt[3])/4])/(6*2^(2/3)*3^(1/4)*Sqrt[(x^2*(2^(1/3) + x^2))/(2^(1/3) + (1 + Sqrt[3])*x^2)^2]*Sqrt[2 + x^6])","A",4,4,13,0.3077,1,"{288, 308, 225, 1881}"
1433,1,391,0,0.1108874,"\int \frac{x^4}{\left(2+x^6\right)^{3/2}} \, dx","Int[x^4/(2 + x^6)^(3/2),x]","\frac{x^5}{6 \sqrt{x^6+2}}-\frac{\left(1+\sqrt{3}\right) \sqrt{x^6+2} x}{6 \left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)}+\frac{\left(1-\sqrt{3}\right) \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} x F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) x^2+\sqrt[3]{2}}{\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{6\ 2^{2/3} \sqrt[4]{3} \sqrt{\frac{x^2 \left(x^2+\sqrt[3]{2}\right)}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} \sqrt{x^6+2}}+\frac{\left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} x E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) x^2+\sqrt[3]{2}}{\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{2^{2/3} 3^{3/4} \sqrt{\frac{x^2 \left(x^2+\sqrt[3]{2}\right)}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} \sqrt{x^6+2}}","\frac{x^5}{6 \sqrt{x^6+2}}-\frac{\left(1+\sqrt{3}\right) \sqrt{x^6+2} x}{6 \left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)}+\frac{\left(1-\sqrt{3}\right) \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} x F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) x^2+\sqrt[3]{2}}{\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{6\ 2^{2/3} \sqrt[4]{3} \sqrt{\frac{x^2 \left(x^2+\sqrt[3]{2}\right)}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} \sqrt{x^6+2}}+\frac{\left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} x E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) x^2+\sqrt[3]{2}}{\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{2^{2/3} 3^{3/4} \sqrt{\frac{x^2 \left(x^2+\sqrt[3]{2}\right)}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} \sqrt{x^6+2}}",1,"x^5/(6*Sqrt[2 + x^6]) - ((1 + Sqrt[3])*x*Sqrt[2 + x^6])/(6*(2^(1/3) + (1 + Sqrt[3])*x^2)) + (x*(2^(1/3) + x^2)*Sqrt[(2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3) + (1 + Sqrt[3])*x^2)^2]*EllipticE[ArcCos[(2^(1/3) + (1 - Sqrt[3])*x^2)/(2^(1/3) + (1 + Sqrt[3])*x^2)], (2 + Sqrt[3])/4])/(2^(2/3)*3^(3/4)*Sqrt[(x^2*(2^(1/3) + x^2))/(2^(1/3) + (1 + Sqrt[3])*x^2)^2]*Sqrt[2 + x^6]) + ((1 - Sqrt[3])*x*(2^(1/3) + x^2)*Sqrt[(2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3) + (1 + Sqrt[3])*x^2)^2]*EllipticF[ArcCos[(2^(1/3) + (1 - Sqrt[3])*x^2)/(2^(1/3) + (1 + Sqrt[3])*x^2)], (2 + Sqrt[3])/4])/(6*2^(2/3)*3^(1/4)*Sqrt[(x^2*(2^(1/3) + x^2))/(2^(1/3) + (1 + Sqrt[3])*x^2)^2]*Sqrt[2 + x^6])","A",4,4,13,0.3077,1,"{290, 308, 225, 1881}"
1434,1,408,0,0.1127159,"\int \frac{1}{x^2 \left(2+x^6\right)^{3/2}} \, dx","Int[1/(x^2*(2 + x^6)^(3/2)),x]","\frac{\left(1+\sqrt{3}\right) \sqrt{x^6+2} x}{3 \left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)}-\frac{\sqrt{x^6+2}}{3 x}+\frac{1}{6 \sqrt{x^6+2} x}-\frac{\left(1-\sqrt{3}\right) \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} x F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) x^2+\sqrt[3]{2}}{\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{3\ 2^{2/3} \sqrt[4]{3} \sqrt{\frac{x^2 \left(x^2+\sqrt[3]{2}\right)}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} \sqrt{x^6+2}}-\frac{\sqrt[3]{2} \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} x E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) x^2+\sqrt[3]{2}}{\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{3^{3/4} \sqrt{\frac{x^2 \left(x^2+\sqrt[3]{2}\right)}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} \sqrt{x^6+2}}","\frac{\left(1+\sqrt{3}\right) \sqrt{x^6+2} x}{3 \left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)}-\frac{\sqrt{x^6+2}}{3 x}+\frac{1}{6 \sqrt{x^6+2} x}-\frac{\left(1-\sqrt{3}\right) \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} x F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) x^2+\sqrt[3]{2}}{\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{3\ 2^{2/3} \sqrt[4]{3} \sqrt{\frac{x^2 \left(x^2+\sqrt[3]{2}\right)}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} \sqrt{x^6+2}}-\frac{\sqrt[3]{2} \left(x^2+\sqrt[3]{2}\right) \sqrt{\frac{x^4-\sqrt[3]{2} x^2+2^{2/3}}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} x E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) x^2+\sqrt[3]{2}}{\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{3^{3/4} \sqrt{\frac{x^2 \left(x^2+\sqrt[3]{2}\right)}{\left(\left(1+\sqrt{3}\right) x^2+\sqrt[3]{2}\right)^2}} \sqrt{x^6+2}}",1,"1/(6*x*Sqrt[2 + x^6]) - Sqrt[2 + x^6]/(3*x) + ((1 + Sqrt[3])*x*Sqrt[2 + x^6])/(3*(2^(1/3) + (1 + Sqrt[3])*x^2)) - (2^(1/3)*x*(2^(1/3) + x^2)*Sqrt[(2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3) + (1 + Sqrt[3])*x^2)^2]*EllipticE[ArcCos[(2^(1/3) + (1 - Sqrt[3])*x^2)/(2^(1/3) + (1 + Sqrt[3])*x^2)], (2 + Sqrt[3])/4])/(3^(3/4)*Sqrt[(x^2*(2^(1/3) + x^2))/(2^(1/3) + (1 + Sqrt[3])*x^2)^2]*Sqrt[2 + x^6]) - ((1 - Sqrt[3])*x*(2^(1/3) + x^2)*Sqrt[(2^(2/3) - 2^(1/3)*x^2 + x^4)/(2^(1/3) + (1 + Sqrt[3])*x^2)^2]*EllipticF[ArcCos[(2^(1/3) + (1 - Sqrt[3])*x^2)/(2^(1/3) + (1 + Sqrt[3])*x^2)], (2 + Sqrt[3])/4])/(3*2^(2/3)*3^(1/4)*Sqrt[(x^2*(2^(1/3) + x^2))/(2^(1/3) + (1 + Sqrt[3])*x^2)^2]*Sqrt[2 + x^6])","A",5,5,13,0.3846,1,"{290, 325, 308, 225, 1881}"
1435,1,25,0,0.0076143,"\int x^m \left(a+b x^7\right) \, dx","Int[x^m*(a + b*x^7),x]","\frac{a x^{m+1}}{m+1}+\frac{b x^{m+8}}{m+8}","\frac{a x^{m+1}}{m+1}+\frac{b x^{m+8}}{m+8}",1,"(a*x^(1 + m))/(1 + m) + (b*x^(8 + m))/(8 + m)","A",2,1,11,0.09091,1,"{14}"
1436,1,17,0,0.0049247,"\int x^8 \left(a+b x^7\right) \, dx","Int[x^8*(a + b*x^7),x]","\frac{a x^9}{9}+\frac{b x^{16}}{16}","\frac{a x^9}{9}+\frac{b x^{16}}{16}",1,"(a*x^9)/9 + (b*x^16)/16","A",2,1,11,0.09091,1,"{14}"
1437,1,13,0,0.0045949,"\int \frac{a+b x^7}{x^8} \, dx","Int[(a + b*x^7)/x^8,x]","b \log (x)-\frac{a}{7 x^7}","b \log (x)-\frac{a}{7 x^7}",1,"-a/(7*x^7) + b*Log[x]","A",2,1,11,0.09091,1,"{14}"
1438,1,43,0,0.0170874,"\int x^m \left(a+b x^7\right)^2 \, dx","Int[x^m*(a + b*x^7)^2,x]","\frac{a^2 x^{m+1}}{m+1}+\frac{2 a b x^{m+8}}{m+8}+\frac{b^2 x^{m+15}}{m+15}","\frac{a^2 x^{m+1}}{m+1}+\frac{2 a b x^{m+8}}{m+8}+\frac{b^2 x^{m+15}}{m+15}",1,"(a^2*x^(1 + m))/(1 + m) + (2*a*b*x^(8 + m))/(8 + m) + (b^2*x^(15 + m))/(15 + m)","A",2,1,13,0.07692,1,"{270}"
1439,1,30,0,0.0115207,"\int x^8 \left(a+b x^7\right)^2 \, dx","Int[x^8*(a + b*x^7)^2,x]","\frac{a^2 x^9}{9}+\frac{1}{8} a b x^{16}+\frac{b^2 x^{23}}{23}","\frac{a^2 x^9}{9}+\frac{1}{8} a b x^{16}+\frac{b^2 x^{23}}{23}",1,"(a^2*x^9)/9 + (a*b*x^16)/8 + (b^2*x^23)/23","A",2,1,13,0.07692,1,"{270}"
1440,1,27,0,0.0144491,"\int \frac{\left(a+b x^7\right)^2}{x^8} \, dx","Int[(a + b*x^7)^2/x^8,x]","-\frac{a^2}{7 x^7}+2 a b \log (x)+\frac{b^2 x^7}{7}","-\frac{a^2}{7 x^7}+2 a b \log (x)+\frac{b^2 x^7}{7}",1,"-a^2/(7*x^7) + (b^2*x^7)/7 + 2*a*b*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
1441,1,39,0,0.0085292,"\int \frac{x^m}{a+b x^7} \, dx","Int[x^m/(a + b*x^7),x]","\frac{x^{m+1} \, _2F_1\left(1,\frac{m+1}{7};\frac{m+8}{7};-\frac{b x^7}{a}\right)}{a (m+1)}","\frac{x^{m+1} \, _2F_1\left(1,\frac{m+1}{7};\frac{m+8}{7};-\frac{b x^7}{a}\right)}{a (m+1)}",1,"(x^(1 + m)*Hypergeometric2F1[1, (1 + m)/7, (8 + m)/7, -((b*x^7)/a)])/(a*(1 + m))","A",1,1,13,0.07692,1,"{364}"
1442,1,15,0,0.0037124,"\int \frac{x^6}{a+b x^7} \, dx","Int[x^6/(a + b*x^7),x]","\frac{\log \left(a+b x^7\right)}{7 b}","\frac{\log \left(a+b x^7\right)}{7 b}",1,"Log[a + b*x^7]/(7*b)","A",1,1,13,0.07692,1,"{260}"
1443,1,335,0,0.5359895,"\int \frac{1}{a+b x^7} \, dx","Int[(a + b*x^7)^(-1),x]","\frac{\sin \left(\frac{3 \pi }{14}\right) \log \left(a^{2/7}+2 \sqrt[7]{a} \sqrt[7]{b} x \sin \left(\frac{3 \pi }{14}\right)+b^{2/7} x^2\right)}{7 a^{6/7} \sqrt[7]{b}}-\frac{\sin \left(\frac{\pi }{14}\right) \log \left(a^{2/7}-2 \sqrt[7]{a} \sqrt[7]{b} x \sin \left(\frac{\pi }{14}\right)+b^{2/7} x^2\right)}{7 a^{6/7} \sqrt[7]{b}}-\frac{\cos \left(\frac{\pi }{7}\right) \log \left(a^{2/7}-2 \sqrt[7]{a} \sqrt[7]{b} x \cos \left(\frac{\pi }{7}\right)+b^{2/7} x^2\right)}{7 a^{6/7} \sqrt[7]{b}}+\frac{\log \left(\sqrt[7]{a}+\sqrt[7]{b} x\right)}{7 a^{6/7} \sqrt[7]{b}}+\frac{2 \cos \left(\frac{3 \pi }{14}\right) \tan ^{-1}\left(\frac{\sqrt[7]{b} x \sec \left(\frac{3 \pi }{14}\right)}{\sqrt[7]{a}}+\tan \left(\frac{3 \pi }{14}\right)\right)}{7 a^{6/7} \sqrt[7]{b}}+\frac{2 \cos \left(\frac{\pi }{14}\right) \tan ^{-1}\left(\frac{\sqrt[7]{b} x \sec \left(\frac{\pi }{14}\right)}{\sqrt[7]{a}}-\tan \left(\frac{\pi }{14}\right)\right)}{7 a^{6/7} \sqrt[7]{b}}-\frac{2 \sin \left(\frac{\pi }{7}\right) \tan ^{-1}\left(\cot \left(\frac{\pi }{7}\right)-\frac{\sqrt[7]{b} x \csc \left(\frac{\pi }{7}\right)}{\sqrt[7]{a}}\right)}{7 a^{6/7} \sqrt[7]{b}}","\frac{\sin \left(\frac{3 \pi }{14}\right) \log \left(a^{2/7}+2 \sqrt[7]{a} \sqrt[7]{b} x \sin \left(\frac{3 \pi }{14}\right)+b^{2/7} x^2\right)}{7 a^{6/7} \sqrt[7]{b}}-\frac{\sin \left(\frac{\pi }{14}\right) \log \left(a^{2/7}-2 \sqrt[7]{a} \sqrt[7]{b} x \sin \left(\frac{\pi }{14}\right)+b^{2/7} x^2\right)}{7 a^{6/7} \sqrt[7]{b}}-\frac{\cos \left(\frac{\pi }{7}\right) \log \left(a^{2/7}-2 \sqrt[7]{a} \sqrt[7]{b} x \cos \left(\frac{\pi }{7}\right)+b^{2/7} x^2\right)}{7 a^{6/7} \sqrt[7]{b}}+\frac{\log \left(\sqrt[7]{a}+\sqrt[7]{b} x\right)}{7 a^{6/7} \sqrt[7]{b}}+\frac{2 \cos \left(\frac{3 \pi }{14}\right) \tan ^{-1}\left(\frac{\sqrt[7]{b} x \sec \left(\frac{3 \pi }{14}\right)}{\sqrt[7]{a}}+\tan \left(\frac{3 \pi }{14}\right)\right)}{7 a^{6/7} \sqrt[7]{b}}+\frac{2 \cos \left(\frac{\pi }{14}\right) \tan ^{-1}\left(\frac{\sqrt[7]{b} x \sec \left(\frac{\pi }{14}\right)}{\sqrt[7]{a}}-\tan \left(\frac{\pi }{14}\right)\right)}{7 a^{6/7} \sqrt[7]{b}}-\frac{2 \sin \left(\frac{\pi }{7}\right) \tan ^{-1}\left(\cot \left(\frac{\pi }{7}\right)-\frac{\sqrt[7]{b} x \csc \left(\frac{\pi }{7}\right)}{\sqrt[7]{a}}\right)}{7 a^{6/7} \sqrt[7]{b}}",1,"(2*ArcTan[(b^(1/7)*x*Sec[Pi/14])/a^(1/7) - Tan[Pi/14]]*Cos[Pi/14])/(7*a^(6/7)*b^(1/7)) + (2*ArcTan[(b^(1/7)*x*Sec[(3*Pi)/14])/a^(1/7) + Tan[(3*Pi)/14]]*Cos[(3*Pi)/14])/(7*a^(6/7)*b^(1/7)) + Log[a^(1/7) + b^(1/7)*x]/(7*a^(6/7)*b^(1/7)) - (Cos[Pi/7]*Log[a^(2/7) + b^(2/7)*x^2 - 2*a^(1/7)*b^(1/7)*x*Cos[Pi/7]])/(7*a^(6/7)*b^(1/7)) - (Log[a^(2/7) + b^(2/7)*x^2 - 2*a^(1/7)*b^(1/7)*x*Sin[Pi/14]]*Sin[Pi/14])/(7*a^(6/7)*b^(1/7)) - (2*ArcTan[Cot[Pi/7] - (b^(1/7)*x*Csc[Pi/7])/a^(1/7)]*Sin[Pi/7])/(7*a^(6/7)*b^(1/7)) + (Log[a^(2/7) + b^(2/7)*x^2 + 2*a^(1/7)*b^(1/7)*x*Sin[(3*Pi)/14]]*Sin[(3*Pi)/14])/(7*a^(6/7)*b^(1/7))","A",6,6,9,0.6667,1,"{201, 634, 618, 204, 628, 31}"
1444,1,22,0,0.0121988,"\int \frac{1}{x \left(a+b x^7\right)} \, dx","Int[1/(x*(a + b*x^7)),x]","\frac{\log (x)}{a}-\frac{\log \left(a+b x^7\right)}{7 a}","\frac{\log (x)}{a}-\frac{\log \left(a+b x^7\right)}{7 a}",1,"Log[x]/a - Log[a + b*x^7]/(7*a)","A",4,4,13,0.3077,1,"{266, 36, 29, 31}"
1445,1,38,0,0.008287,"\int \frac{x^m}{a-b x^7} \, dx","Int[x^m/(a - b*x^7),x]","\frac{x^{m+1} \, _2F_1\left(1,\frac{m+1}{7};\frac{m+8}{7};\frac{b x^7}{a}\right)}{a (m+1)}","\frac{x^{m+1} \, _2F_1\left(1,\frac{m+1}{7};\frac{m+8}{7};\frac{b x^7}{a}\right)}{a (m+1)}",1,"(x^(1 + m)*Hypergeometric2F1[1, (1 + m)/7, (8 + m)/7, (b*x^7)/a])/(a*(1 + m))","A",1,1,14,0.07143,1,"{364}"
1446,1,16,0,0.0037889,"\int \frac{x^6}{a-b x^7} \, dx","Int[x^6/(a - b*x^7),x]","-\frac{\log \left(a-b x^7\right)}{7 b}","-\frac{\log \left(a-b x^7\right)}{7 b}",1,"-Log[a - b*x^7]/(7*b)","A",1,1,14,0.07143,1,"{260}"
1447,1,335,0,0.4376132,"\int \frac{1}{a-b x^7} \, dx","Int[(a - b*x^7)^(-1),x]","-\frac{\sin \left(\frac{3 \pi }{14}\right) \log \left(a^{2/7}-2 \sqrt[7]{a} \sqrt[7]{b} x \sin \left(\frac{3 \pi }{14}\right)+b^{2/7} x^2\right)}{7 a^{6/7} \sqrt[7]{b}}+\frac{\sin \left(\frac{\pi }{14}\right) \log \left(a^{2/7}+2 \sqrt[7]{a} \sqrt[7]{b} x \sin \left(\frac{\pi }{14}\right)+b^{2/7} x^2\right)}{7 a^{6/7} \sqrt[7]{b}}+\frac{\cos \left(\frac{\pi }{7}\right) \log \left(a^{2/7}+2 \sqrt[7]{a} \sqrt[7]{b} x \cos \left(\frac{\pi }{7}\right)+b^{2/7} x^2\right)}{7 a^{6/7} \sqrt[7]{b}}-\frac{\log \left(\sqrt[7]{a}-\sqrt[7]{b} x\right)}{7 a^{6/7} \sqrt[7]{b}}+\frac{2 \cos \left(\frac{3 \pi }{14}\right) \tan ^{-1}\left(\frac{\sqrt[7]{b} x \sec \left(\frac{3 \pi }{14}\right)}{\sqrt[7]{a}}-\tan \left(\frac{3 \pi }{14}\right)\right)}{7 a^{6/7} \sqrt[7]{b}}+\frac{2 \cos \left(\frac{\pi }{14}\right) \tan ^{-1}\left(\frac{\sqrt[7]{b} x \sec \left(\frac{\pi }{14}\right)}{\sqrt[7]{a}}+\tan \left(\frac{\pi }{14}\right)\right)}{7 a^{6/7} \sqrt[7]{b}}+\frac{2 \sin \left(\frac{\pi }{7}\right) \tan ^{-1}\left(\frac{\sqrt[7]{b} x \csc \left(\frac{\pi }{7}\right)}{\sqrt[7]{a}}+\cot \left(\frac{\pi }{7}\right)\right)}{7 a^{6/7} \sqrt[7]{b}}","-\frac{\sin \left(\frac{3 \pi }{14}\right) \log \left(a^{2/7}-2 \sqrt[7]{a} \sqrt[7]{b} x \sin \left(\frac{3 \pi }{14}\right)+b^{2/7} x^2\right)}{7 a^{6/7} \sqrt[7]{b}}+\frac{\sin \left(\frac{\pi }{14}\right) \log \left(a^{2/7}+2 \sqrt[7]{a} \sqrt[7]{b} x \sin \left(\frac{\pi }{14}\right)+b^{2/7} x^2\right)}{7 a^{6/7} \sqrt[7]{b}}+\frac{\cos \left(\frac{\pi }{7}\right) \log \left(a^{2/7}+2 \sqrt[7]{a} \sqrt[7]{b} x \cos \left(\frac{\pi }{7}\right)+b^{2/7} x^2\right)}{7 a^{6/7} \sqrt[7]{b}}-\frac{\log \left(\sqrt[7]{a}-\sqrt[7]{b} x\right)}{7 a^{6/7} \sqrt[7]{b}}+\frac{2 \cos \left(\frac{3 \pi }{14}\right) \tan ^{-1}\left(\frac{\sqrt[7]{b} x \sec \left(\frac{3 \pi }{14}\right)}{\sqrt[7]{a}}-\tan \left(\frac{3 \pi }{14}\right)\right)}{7 a^{6/7} \sqrt[7]{b}}+\frac{2 \cos \left(\frac{\pi }{14}\right) \tan ^{-1}\left(\frac{\sqrt[7]{b} x \sec \left(\frac{\pi }{14}\right)}{\sqrt[7]{a}}+\tan \left(\frac{\pi }{14}\right)\right)}{7 a^{6/7} \sqrt[7]{b}}+\frac{2 \sin \left(\frac{\pi }{7}\right) \tan ^{-1}\left(\frac{\sqrt[7]{b} x \csc \left(\frac{\pi }{7}\right)}{\sqrt[7]{a}}+\cot \left(\frac{\pi }{7}\right)\right)}{7 a^{6/7} \sqrt[7]{b}}",1,"(2*ArcTan[(b^(1/7)*x*Sec[Pi/14])/a^(1/7) + Tan[Pi/14]]*Cos[Pi/14])/(7*a^(6/7)*b^(1/7)) + (2*ArcTan[(b^(1/7)*x*Sec[(3*Pi)/14])/a^(1/7) - Tan[(3*Pi)/14]]*Cos[(3*Pi)/14])/(7*a^(6/7)*b^(1/7)) - Log[a^(1/7) - b^(1/7)*x]/(7*a^(6/7)*b^(1/7)) + (Cos[Pi/7]*Log[a^(2/7) + b^(2/7)*x^2 + 2*a^(1/7)*b^(1/7)*x*Cos[Pi/7]])/(7*a^(6/7)*b^(1/7)) + (Log[a^(2/7) + b^(2/7)*x^2 + 2*a^(1/7)*b^(1/7)*x*Sin[Pi/14]]*Sin[Pi/14])/(7*a^(6/7)*b^(1/7)) + (2*ArcTan[Cot[Pi/7] + (b^(1/7)*x*Csc[Pi/7])/a^(1/7)]*Sin[Pi/7])/(7*a^(6/7)*b^(1/7)) - (Log[a^(2/7) + b^(2/7)*x^2 - 2*a^(1/7)*b^(1/7)*x*Sin[(3*Pi)/14]]*Sin[(3*Pi)/14])/(7*a^(6/7)*b^(1/7))","A",6,6,10,0.6000,1,"{202, 634, 618, 204, 628, 31}"
1448,1,23,0,0.0135315,"\int \frac{1}{x \left(a-b x^7\right)} \, dx","Int[1/(x*(a - b*x^7)),x]","\frac{\log (x)}{a}-\frac{\log \left(a-b x^7\right)}{7 a}","\frac{\log (x)}{a}-\frac{\log \left(a-b x^7\right)}{7 a}",1,"Log[x]/a - Log[a - b*x^7]/(7*a)","A",4,4,14,0.2857,1,"{266, 36, 29, 31}"
1449,1,166,0,0.1421185,"\int \frac{1}{1-x^7} \, dx","Int[(1 - x^7)^(-1),x]","-\frac{1}{7} \sin \left(\frac{3 \pi }{14}\right) \log \left(x^2-2 x \sin \left(\frac{3 \pi }{14}\right)+1\right)+\frac{1}{7} \sin \left(\frac{\pi }{14}\right) \log \left(x^2+2 x \sin \left(\frac{\pi }{14}\right)+1\right)+\frac{1}{7} \cos \left(\frac{\pi }{7}\right) \log \left(x^2+2 x \cos \left(\frac{\pi }{7}\right)+1\right)-\frac{1}{7} \log (1-x)+\frac{2}{7} \sin \left(\frac{\pi }{7}\right) \tan ^{-1}\left(\csc \left(\frac{\pi }{7}\right) \left(x+\cos \left(\frac{\pi }{7}\right)\right)\right)+\frac{2}{7} \cos \left(\frac{3 \pi }{14}\right) \tan ^{-1}\left(\sec \left(\frac{3 \pi }{14}\right) \left(x-\sin \left(\frac{3 \pi }{14}\right)\right)\right)+\frac{2}{7} \cos \left(\frac{\pi }{14}\right) \tan ^{-1}\left(\sec \left(\frac{\pi }{14}\right) \left(x+\sin \left(\frac{\pi }{14}\right)\right)\right)","-\frac{1}{7} \sin \left(\frac{3 \pi }{14}\right) \log \left(x^2-2 x \sin \left(\frac{3 \pi }{14}\right)+1\right)+\frac{1}{7} \sin \left(\frac{\pi }{14}\right) \log \left(x^2+2 x \sin \left(\frac{\pi }{14}\right)+1\right)+\frac{1}{7} \cos \left(\frac{\pi }{7}\right) \log \left(x^2+2 x \cos \left(\frac{\pi }{7}\right)+1\right)-\frac{1}{7} \log (1-x)+\frac{2}{7} \sin \left(\frac{\pi }{7}\right) \tan ^{-1}\left(\csc \left(\frac{\pi }{7}\right) \left(x+\cos \left(\frac{\pi }{7}\right)\right)\right)+\frac{2}{7} \cos \left(\frac{3 \pi }{14}\right) \tan ^{-1}\left(\sec \left(\frac{3 \pi }{14}\right) \left(x-\sin \left(\frac{3 \pi }{14}\right)\right)\right)+\frac{2}{7} \cos \left(\frac{\pi }{14}\right) \tan ^{-1}\left(\sec \left(\frac{\pi }{14}\right) \left(x+\sin \left(\frac{\pi }{14}\right)\right)\right)",1,"(2*ArcTan[Sec[Pi/14]*(x + Sin[Pi/14])]*Cos[Pi/14])/7 + (2*ArcTan[Sec[(3*Pi)/14]*(x - Sin[(3*Pi)/14])]*Cos[(3*Pi)/14])/7 - Log[1 - x]/7 + (Cos[Pi/7]*Log[1 + x^2 + 2*x*Cos[Pi/7]])/7 + (Log[1 + x^2 + 2*x*Sin[Pi/14]]*Sin[Pi/14])/7 + (2*ArcTan[(x + Cos[Pi/7])*Csc[Pi/7]]*Sin[Pi/7])/7 - (Log[1 + x^2 - 2*x*Sin[(3*Pi)/14]]*Sin[(3*Pi)/14])/7","A",6,6,9,0.6667,1,"{202, 634, 618, 204, 628, 31}"
1450,1,165,0,0.1390252,"\int \frac{1}{1+x^7} \, dx","Int[(1 + x^7)^(-1),x]","\frac{1}{7} \sin \left(\frac{3 \pi }{14}\right) \log \left(x^2+2 x \sin \left(\frac{3 \pi }{14}\right)+1\right)-\frac{1}{7} \sin \left(\frac{\pi }{14}\right) \log \left(x^2-2 x \sin \left(\frac{\pi }{14}\right)+1\right)-\frac{1}{7} \cos \left(\frac{\pi }{7}\right) \log \left(x^2-2 x \cos \left(\frac{\pi }{7}\right)+1\right)+\frac{1}{7} \log (x+1)+\frac{2}{7} \cos \left(\frac{3 \pi }{14}\right) \tan ^{-1}\left(x \sec \left(\frac{3 \pi }{14}\right)+\tan \left(\frac{3 \pi }{14}\right)\right)+\frac{2}{7} \cos \left(\frac{\pi }{14}\right) \tan ^{-1}\left(x \sec \left(\frac{\pi }{14}\right)-\tan \left(\frac{\pi }{14}\right)\right)-\frac{2}{7} \sin \left(\frac{\pi }{7}\right) \tan ^{-1}\left(\cot \left(\frac{\pi }{7}\right)-x \csc \left(\frac{\pi }{7}\right)\right)","\frac{1}{7} \sin \left(\frac{3 \pi }{14}\right) \log \left(x^2+2 x \sin \left(\frac{3 \pi }{14}\right)+1\right)-\frac{1}{7} \sin \left(\frac{\pi }{14}\right) \log \left(x^2-2 x \sin \left(\frac{\pi }{14}\right)+1\right)-\frac{1}{7} \cos \left(\frac{\pi }{7}\right) \log \left(x^2-2 x \cos \left(\frac{\pi }{7}\right)+1\right)+\frac{1}{7} \log (x+1)+\frac{2}{7} \cos \left(\frac{3 \pi }{14}\right) \tan ^{-1}\left(x \sec \left(\frac{3 \pi }{14}\right)+\tan \left(\frac{3 \pi }{14}\right)\right)+\frac{2}{7} \cos \left(\frac{\pi }{14}\right) \tan ^{-1}\left(x \sec \left(\frac{\pi }{14}\right)-\tan \left(\frac{\pi }{14}\right)\right)-\frac{2}{7} \sin \left(\frac{\pi }{7}\right) \tan ^{-1}\left(\cot \left(\frac{\pi }{7}\right)-x \csc \left(\frac{\pi }{7}\right)\right)",1,"(2*ArcTan[x*Sec[Pi/14] - Tan[Pi/14]]*Cos[Pi/14])/7 + (2*ArcTan[x*Sec[(3*Pi)/14] + Tan[(3*Pi)/14]]*Cos[(3*Pi)/14])/7 + Log[1 + x]/7 - (Cos[Pi/7]*Log[1 + x^2 - 2*x*Cos[Pi/7]])/7 - (Log[1 + x^2 - 2*x*Sin[Pi/14]]*Sin[Pi/14])/7 - (2*ArcTan[Cot[Pi/7] - x*Csc[Pi/7]]*Sin[Pi/7])/7 + (Log[1 + x^2 + 2*x*Sin[(3*Pi)/14]]*Sin[(3*Pi)/14])/7","A",6,6,7,0.8571,1,"{201, 634, 618, 204, 628, 31}"
1451,1,203,0,0.1939761,"\int \frac{x^9}{a+b x^8} \, dx","Int[x^9/(a + b*x^8),x]","\frac{\sqrt[4]{a} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x^2+\sqrt{a}+\sqrt{b} x^4\right)}{8 \sqrt{2} b^{5/4}}-\frac{\sqrt[4]{a} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x^2+\sqrt{a}+\sqrt{b} x^4\right)}{8 \sqrt{2} b^{5/4}}+\frac{\sqrt[4]{a} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x^2}{\sqrt[4]{a}}\right)}{4 \sqrt{2} b^{5/4}}-\frac{\sqrt[4]{a} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x^2}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} b^{5/4}}+\frac{x^2}{2 b}","\frac{\sqrt[4]{a} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x^2+\sqrt{a}+\sqrt{b} x^4\right)}{8 \sqrt{2} b^{5/4}}-\frac{\sqrt[4]{a} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x^2+\sqrt{a}+\sqrt{b} x^4\right)}{8 \sqrt{2} b^{5/4}}+\frac{\sqrt[4]{a} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x^2}{\sqrt[4]{a}}\right)}{4 \sqrt{2} b^{5/4}}-\frac{\sqrt[4]{a} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x^2}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} b^{5/4}}+\frac{x^2}{2 b}",1,"x^2/(2*b) + (a^(1/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*x^2)/a^(1/4)])/(4*Sqrt[2]*b^(5/4)) - (a^(1/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*x^2)/a^(1/4)])/(4*Sqrt[2]*b^(5/4)) + (a^(1/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x^2 + Sqrt[b]*x^4])/(8*Sqrt[2]*b^(5/4)) - (a^(1/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x^2 + Sqrt[b]*x^4])/(8*Sqrt[2]*b^(5/4))","A",11,8,13,0.6154,1,"{275, 321, 211, 1165, 628, 1162, 617, 204}"
1452,1,15,0,0.0033045,"\int \frac{x^7}{a+b x^8} \, dx","Int[x^7/(a + b*x^8),x]","\frac{\log \left(a+b x^8\right)}{8 b}","\frac{\log \left(a+b x^8\right)}{8 b}",1,"Log[a + b*x^8]/(8*b)","A",1,1,13,0.07692,1,"{260}"
1453,1,193,0,0.1559448,"\int \frac{x^5}{a+b x^8} \, dx","Int[x^5/(a + b*x^8),x]","\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x^2+\sqrt{a}+\sqrt{b} x^4\right)}{8 \sqrt{2} \sqrt[4]{a} b^{3/4}}-\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x^2+\sqrt{a}+\sqrt{b} x^4\right)}{8 \sqrt{2} \sqrt[4]{a} b^{3/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x^2}{\sqrt[4]{a}}\right)}{4 \sqrt{2} \sqrt[4]{a} b^{3/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x^2}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} \sqrt[4]{a} b^{3/4}}","\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x^2+\sqrt{a}+\sqrt{b} x^4\right)}{8 \sqrt{2} \sqrt[4]{a} b^{3/4}}-\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x^2+\sqrt{a}+\sqrt{b} x^4\right)}{8 \sqrt{2} \sqrt[4]{a} b^{3/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x^2}{\sqrt[4]{a}}\right)}{4 \sqrt{2} \sqrt[4]{a} b^{3/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x^2}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} \sqrt[4]{a} b^{3/4}}",1,"-ArcTan[1 - (Sqrt[2]*b^(1/4)*x^2)/a^(1/4)]/(4*Sqrt[2]*a^(1/4)*b^(3/4)) + ArcTan[1 + (Sqrt[2]*b^(1/4)*x^2)/a^(1/4)]/(4*Sqrt[2]*a^(1/4)*b^(3/4)) + Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x^2 + Sqrt[b]*x^4]/(8*Sqrt[2]*a^(1/4)*b^(3/4)) - Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x^2 + Sqrt[b]*x^4]/(8*Sqrt[2]*a^(1/4)*b^(3/4))","A",10,7,13,0.5385,1,"{275, 297, 1162, 617, 204, 1165, 628}"
1454,1,29,0,0.0123792,"\int \frac{x^3}{a+b x^8} \, dx","Int[x^3/(a + b*x^8),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x^4}{\sqrt{a}}\right)}{4 \sqrt{a} \sqrt{b}}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x^4}{\sqrt{a}}\right)}{4 \sqrt{a} \sqrt{b}}",1,"ArcTan[(Sqrt[b]*x^4)/Sqrt[a]]/(4*Sqrt[a]*Sqrt[b])","A",2,2,13,0.1538,1,"{275, 205}"
1455,1,193,0,0.1543853,"\int \frac{x}{a+b x^8} \, dx","Int[x/(a + b*x^8),x]","-\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x^2+\sqrt{a}+\sqrt{b} x^4\right)}{8 \sqrt{2} a^{3/4} \sqrt[4]{b}}+\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x^2+\sqrt{a}+\sqrt{b} x^4\right)}{8 \sqrt{2} a^{3/4} \sqrt[4]{b}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x^2}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{3/4} \sqrt[4]{b}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x^2}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{3/4} \sqrt[4]{b}}","-\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x^2+\sqrt{a}+\sqrt{b} x^4\right)}{8 \sqrt{2} a^{3/4} \sqrt[4]{b}}+\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x^2+\sqrt{a}+\sqrt{b} x^4\right)}{8 \sqrt{2} a^{3/4} \sqrt[4]{b}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x^2}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{3/4} \sqrt[4]{b}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x^2}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{3/4} \sqrt[4]{b}}",1,"-ArcTan[1 - (Sqrt[2]*b^(1/4)*x^2)/a^(1/4)]/(4*Sqrt[2]*a^(3/4)*b^(1/4)) + ArcTan[1 + (Sqrt[2]*b^(1/4)*x^2)/a^(1/4)]/(4*Sqrt[2]*a^(3/4)*b^(1/4)) - Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x^2 + Sqrt[b]*x^4]/(8*Sqrt[2]*a^(3/4)*b^(1/4)) + Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x^2 + Sqrt[b]*x^4]/(8*Sqrt[2]*a^(3/4)*b^(1/4))","A",10,7,11,0.6364,1,"{275, 211, 1165, 628, 1162, 617, 204}"
1456,1,22,0,0.0111383,"\int \frac{1}{x \left(a+b x^8\right)} \, dx","Int[1/(x*(a + b*x^8)),x]","\frac{\log (x)}{a}-\frac{\log \left(a+b x^8\right)}{8 a}","\frac{\log (x)}{a}-\frac{\log \left(a+b x^8\right)}{8 a}",1,"Log[x]/a - Log[a + b*x^8]/(8*a)","A",4,4,13,0.3077,1,"{266, 36, 29, 31}"
1457,1,203,0,0.1748042,"\int \frac{1}{x^3 \left(a+b x^8\right)} \, dx","Int[1/(x^3*(a + b*x^8)),x]","-\frac{\sqrt[4]{b} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x^2+\sqrt{a}+\sqrt{b} x^4\right)}{8 \sqrt{2} a^{5/4}}+\frac{\sqrt[4]{b} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x^2+\sqrt{a}+\sqrt{b} x^4\right)}{8 \sqrt{2} a^{5/4}}+\frac{\sqrt[4]{b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x^2}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{5/4}}-\frac{\sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x^2}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{5/4}}-\frac{1}{2 a x^2}","-\frac{\sqrt[4]{b} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x^2+\sqrt{a}+\sqrt{b} x^4\right)}{8 \sqrt{2} a^{5/4}}+\frac{\sqrt[4]{b} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x^2+\sqrt{a}+\sqrt{b} x^4\right)}{8 \sqrt{2} a^{5/4}}+\frac{\sqrt[4]{b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x^2}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{5/4}}-\frac{\sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x^2}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{5/4}}-\frac{1}{2 a x^2}",1,"-1/(2*a*x^2) + (b^(1/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*x^2)/a^(1/4)])/(4*Sqrt[2]*a^(5/4)) - (b^(1/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*x^2)/a^(1/4)])/(4*Sqrt[2]*a^(5/4)) - (b^(1/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x^2 + Sqrt[b]*x^4])/(8*Sqrt[2]*a^(5/4)) + (b^(1/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x^2 + Sqrt[b]*x^4])/(8*Sqrt[2]*a^(5/4))","A",11,8,13,0.6154,1,"{275, 325, 297, 1162, 617, 204, 1165, 628}"
1458,1,40,0,0.0207813,"\int \frac{1}{x^5 \left(a+b x^8\right)} \, dx","Int[1/(x^5*(a + b*x^8)),x]","-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} x^4}{\sqrt{a}}\right)}{4 a^{3/2}}-\frac{1}{4 a x^4}","-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} x^4}{\sqrt{a}}\right)}{4 a^{3/2}}-\frac{1}{4 a x^4}",1,"-1/(4*a*x^4) - (Sqrt[b]*ArcTan[(Sqrt[b]*x^4)/Sqrt[a]])/(4*a^(3/2))","A",3,3,13,0.2308,1,"{275, 325, 205}"
1459,1,203,0,0.1819641,"\int \frac{1}{x^7 \left(a+b x^8\right)} \, dx","Int[1/(x^7*(a + b*x^8)),x]","\frac{b^{3/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x^2+\sqrt{a}+\sqrt{b} x^4\right)}{8 \sqrt{2} a^{7/4}}-\frac{b^{3/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x^2+\sqrt{a}+\sqrt{b} x^4\right)}{8 \sqrt{2} a^{7/4}}+\frac{b^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x^2}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{7/4}}-\frac{b^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x^2}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{7/4}}-\frac{1}{6 a x^6}","\frac{b^{3/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x^2+\sqrt{a}+\sqrt{b} x^4\right)}{8 \sqrt{2} a^{7/4}}-\frac{b^{3/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x^2+\sqrt{a}+\sqrt{b} x^4\right)}{8 \sqrt{2} a^{7/4}}+\frac{b^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x^2}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{7/4}}-\frac{b^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x^2}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{7/4}}-\frac{1}{6 a x^6}",1,"-1/(6*a*x^6) + (b^(3/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*x^2)/a^(1/4)])/(4*Sqrt[2]*a^(7/4)) - (b^(3/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*x^2)/a^(1/4)])/(4*Sqrt[2]*a^(7/4)) + (b^(3/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x^2 + Sqrt[b]*x^4])/(8*Sqrt[2]*a^(7/4)) - (b^(3/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x^2 + Sqrt[b]*x^4])/(8*Sqrt[2]*a^(7/4))","A",11,8,13,0.6154,1,"{275, 325, 211, 1165, 628, 1162, 617, 204}"
1460,1,35,0,0.0242778,"\int \frac{1}{x^9 \left(a+b x^8\right)} \, dx","Int[1/(x^9*(a + b*x^8)),x]","\frac{b \log \left(a+b x^8\right)}{8 a^2}-\frac{b \log (x)}{a^2}-\frac{1}{8 a x^8}","\frac{b \log \left(a+b x^8\right)}{8 a^2}-\frac{b \log (x)}{a^2}-\frac{1}{8 a x^8}",1,"-1/(8*a*x^8) - (b*Log[x])/a^2 + (b*Log[a + b*x^8])/(8*a^2)","A",3,2,13,0.1538,1,"{266, 44}"
1461,1,272,0,0.29687,"\int \frac{x^8}{a+b x^8} \, dx","Int[x^8/(a + b*x^8),x]","\frac{\sqrt[8]{-a} \log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{b} x+\sqrt[4]{-a}+\sqrt[4]{b} x^2\right)}{8 \sqrt{2} b^{9/8}}-\frac{\sqrt[8]{-a} \log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{b} x+\sqrt[4]{-a}+\sqrt[4]{b} x^2\right)}{8 \sqrt{2} b^{9/8}}-\frac{\sqrt[8]{-a} \tan ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 b^{9/8}}+\frac{\sqrt[8]{-a} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 \sqrt{2} b^{9/8}}-\frac{\sqrt[8]{-a} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{b} x}{\sqrt[8]{-a}}+1\right)}{4 \sqrt{2} b^{9/8}}-\frac{\sqrt[8]{-a} \tanh ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 b^{9/8}}+\frac{x}{b}","\frac{\sqrt[8]{-a} \log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{b} x+\sqrt[4]{-a}+\sqrt[4]{b} x^2\right)}{8 \sqrt{2} b^{9/8}}-\frac{\sqrt[8]{-a} \log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{b} x+\sqrt[4]{-a}+\sqrt[4]{b} x^2\right)}{8 \sqrt{2} b^{9/8}}-\frac{\sqrt[8]{-a} \tan ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 b^{9/8}}+\frac{\sqrt[8]{-a} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 \sqrt{2} b^{9/8}}-\frac{\sqrt[8]{-a} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{b} x}{\sqrt[8]{-a}}+1\right)}{4 \sqrt{2} b^{9/8}}-\frac{\sqrt[8]{-a} \tanh ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 b^{9/8}}+\frac{x}{b}",1,"x/b - ((-a)^(1/8)*ArcTan[(b^(1/8)*x)/(-a)^(1/8)])/(4*b^(9/8)) + ((-a)^(1/8)*ArcTan[1 - (Sqrt[2]*b^(1/8)*x)/(-a)^(1/8)])/(4*Sqrt[2]*b^(9/8)) - ((-a)^(1/8)*ArcTan[1 + (Sqrt[2]*b^(1/8)*x)/(-a)^(1/8)])/(4*Sqrt[2]*b^(9/8)) - ((-a)^(1/8)*ArcTanh[(b^(1/8)*x)/(-a)^(1/8)])/(4*b^(9/8)) + ((-a)^(1/8)*Log[(-a)^(1/4) - Sqrt[2]*(-a)^(1/8)*b^(1/8)*x + b^(1/4)*x^2])/(8*Sqrt[2]*b^(9/8)) - ((-a)^(1/8)*Log[(-a)^(1/4) + Sqrt[2]*(-a)^(1/8)*b^(1/8)*x + b^(1/4)*x^2])/(8*Sqrt[2]*b^(9/8))","A",14,11,13,0.8462,1,"{321, 214, 212, 208, 205, 211, 1165, 628, 1162, 617, 204}"
1462,1,267,0,0.2025834,"\int \frac{x^6}{a+b x^8} \, dx","Int[x^6/(a + b*x^8),x]","\frac{\log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{b} x+\sqrt[4]{-a}+\sqrt[4]{b} x^2\right)}{8 \sqrt{2} \sqrt[8]{-a} b^{7/8}}-\frac{\log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{b} x+\sqrt[4]{-a}+\sqrt[4]{b} x^2\right)}{8 \sqrt{2} \sqrt[8]{-a} b^{7/8}}+\frac{\tan ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 \sqrt[8]{-a} b^{7/8}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 \sqrt{2} \sqrt[8]{-a} b^{7/8}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{b} x}{\sqrt[8]{-a}}+1\right)}{4 \sqrt{2} \sqrt[8]{-a} b^{7/8}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 \sqrt[8]{-a} b^{7/8}}","\frac{\log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{b} x+\sqrt[4]{-a}+\sqrt[4]{b} x^2\right)}{8 \sqrt{2} \sqrt[8]{-a} b^{7/8}}-\frac{\log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{b} x+\sqrt[4]{-a}+\sqrt[4]{b} x^2\right)}{8 \sqrt{2} \sqrt[8]{-a} b^{7/8}}+\frac{\tan ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 \sqrt[8]{-a} b^{7/8}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 \sqrt{2} \sqrt[8]{-a} b^{7/8}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{b} x}{\sqrt[8]{-a}}+1\right)}{4 \sqrt{2} \sqrt[8]{-a} b^{7/8}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 \sqrt[8]{-a} b^{7/8}}",1,"ArcTan[(b^(1/8)*x)/(-a)^(1/8)]/(4*(-a)^(1/8)*b^(7/8)) - ArcTan[1 - (Sqrt[2]*b^(1/8)*x)/(-a)^(1/8)]/(4*Sqrt[2]*(-a)^(1/8)*b^(7/8)) + ArcTan[1 + (Sqrt[2]*b^(1/8)*x)/(-a)^(1/8)]/(4*Sqrt[2]*(-a)^(1/8)*b^(7/8)) - ArcTanh[(b^(1/8)*x)/(-a)^(1/8)]/(4*(-a)^(1/8)*b^(7/8)) + Log[(-a)^(1/4) - Sqrt[2]*(-a)^(1/8)*b^(1/8)*x + b^(1/4)*x^2]/(8*Sqrt[2]*(-a)^(1/8)*b^(7/8)) - Log[(-a)^(1/4) + Sqrt[2]*(-a)^(1/8)*b^(1/8)*x + b^(1/4)*x^2]/(8*Sqrt[2]*(-a)^(1/8)*b^(7/8))","A",13,10,13,0.7692,1,"{301, 297, 1162, 617, 204, 1165, 628, 298, 205, 208}"
1463,1,267,0,0.1889729,"\int \frac{x^4}{a+b x^8} \, dx","Int[x^4/(a + b*x^8),x]","-\frac{\log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{b} x+\sqrt[4]{-a}+\sqrt[4]{b} x^2\right)}{8 \sqrt{2} (-a)^{3/8} b^{5/8}}+\frac{\log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{b} x+\sqrt[4]{-a}+\sqrt[4]{b} x^2\right)}{8 \sqrt{2} (-a)^{3/8} b^{5/8}}-\frac{\tan ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 (-a)^{3/8} b^{5/8}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 \sqrt{2} (-a)^{3/8} b^{5/8}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{b} x}{\sqrt[8]{-a}}+1\right)}{4 \sqrt{2} (-a)^{3/8} b^{5/8}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 (-a)^{3/8} b^{5/8}}","-\frac{\log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{b} x+\sqrt[4]{-a}+\sqrt[4]{b} x^2\right)}{8 \sqrt{2} (-a)^{3/8} b^{5/8}}+\frac{\log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{b} x+\sqrt[4]{-a}+\sqrt[4]{b} x^2\right)}{8 \sqrt{2} (-a)^{3/8} b^{5/8}}-\frac{\tan ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 (-a)^{3/8} b^{5/8}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 \sqrt{2} (-a)^{3/8} b^{5/8}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{b} x}{\sqrt[8]{-a}}+1\right)}{4 \sqrt{2} (-a)^{3/8} b^{5/8}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 (-a)^{3/8} b^{5/8}}",1,"-ArcTan[(b^(1/8)*x)/(-a)^(1/8)]/(4*(-a)^(3/8)*b^(5/8)) - ArcTan[1 - (Sqrt[2]*b^(1/8)*x)/(-a)^(1/8)]/(4*Sqrt[2]*(-a)^(3/8)*b^(5/8)) + ArcTan[1 + (Sqrt[2]*b^(1/8)*x)/(-a)^(1/8)]/(4*Sqrt[2]*(-a)^(3/8)*b^(5/8)) - ArcTanh[(b^(1/8)*x)/(-a)^(1/8)]/(4*(-a)^(3/8)*b^(5/8)) - Log[(-a)^(1/4) - Sqrt[2]*(-a)^(1/8)*b^(1/8)*x + b^(1/4)*x^2]/(8*Sqrt[2]*(-a)^(3/8)*b^(5/8)) + Log[(-a)^(1/4) + Sqrt[2]*(-a)^(1/8)*b^(1/8)*x + b^(1/4)*x^2]/(8*Sqrt[2]*(-a)^(3/8)*b^(5/8))","A",13,10,13,0.7692,1,"{301, 211, 1165, 628, 1162, 617, 204, 212, 208, 205}"
1464,1,267,0,0.1944296,"\int \frac{x^2}{a+b x^8} \, dx","Int[x^2/(a + b*x^8),x]","-\frac{\log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{b} x+\sqrt[4]{-a}+\sqrt[4]{b} x^2\right)}{8 \sqrt{2} (-a)^{5/8} b^{3/8}}+\frac{\log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{b} x+\sqrt[4]{-a}+\sqrt[4]{b} x^2\right)}{8 \sqrt{2} (-a)^{5/8} b^{3/8}}+\frac{\tan ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 (-a)^{5/8} b^{3/8}}+\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 \sqrt{2} (-a)^{5/8} b^{3/8}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{b} x}{\sqrt[8]{-a}}+1\right)}{4 \sqrt{2} (-a)^{5/8} b^{3/8}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 (-a)^{5/8} b^{3/8}}","-\frac{\log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{b} x+\sqrt[4]{-a}+\sqrt[4]{b} x^2\right)}{8 \sqrt{2} (-a)^{5/8} b^{3/8}}+\frac{\log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{b} x+\sqrt[4]{-a}+\sqrt[4]{b} x^2\right)}{8 \sqrt{2} (-a)^{5/8} b^{3/8}}+\frac{\tan ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 (-a)^{5/8} b^{3/8}}+\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 \sqrt{2} (-a)^{5/8} b^{3/8}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{b} x}{\sqrt[8]{-a}}+1\right)}{4 \sqrt{2} (-a)^{5/8} b^{3/8}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 (-a)^{5/8} b^{3/8}}",1,"ArcTan[(b^(1/8)*x)/(-a)^(1/8)]/(4*(-a)^(5/8)*b^(3/8)) + ArcTan[1 - (Sqrt[2]*b^(1/8)*x)/(-a)^(1/8)]/(4*Sqrt[2]*(-a)^(5/8)*b^(3/8)) - ArcTan[1 + (Sqrt[2]*b^(1/8)*x)/(-a)^(1/8)]/(4*Sqrt[2]*(-a)^(5/8)*b^(3/8)) - ArcTanh[(b^(1/8)*x)/(-a)^(1/8)]/(4*(-a)^(5/8)*b^(3/8)) - Log[(-a)^(1/4) - Sqrt[2]*(-a)^(1/8)*b^(1/8)*x + b^(1/4)*x^2]/(8*Sqrt[2]*(-a)^(5/8)*b^(3/8)) + Log[(-a)^(1/4) + Sqrt[2]*(-a)^(1/8)*b^(1/8)*x + b^(1/4)*x^2]/(8*Sqrt[2]*(-a)^(5/8)*b^(3/8))","A",13,10,13,0.7692,1,"{300, 297, 1162, 617, 204, 1165, 628, 298, 205, 208}"
1465,1,267,0,0.1835759,"\int \frac{1}{a+b x^8} \, dx","Int[(a + b*x^8)^(-1),x]","\frac{\log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{b} x+\sqrt[4]{-a}+\sqrt[4]{b} x^2\right)}{8 \sqrt{2} (-a)^{7/8} \sqrt[8]{b}}-\frac{\log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{b} x+\sqrt[4]{-a}+\sqrt[4]{b} x^2\right)}{8 \sqrt{2} (-a)^{7/8} \sqrt[8]{b}}-\frac{\tan ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 (-a)^{7/8} \sqrt[8]{b}}+\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 \sqrt{2} (-a)^{7/8} \sqrt[8]{b}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{b} x}{\sqrt[8]{-a}}+1\right)}{4 \sqrt{2} (-a)^{7/8} \sqrt[8]{b}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 (-a)^{7/8} \sqrt[8]{b}}","\frac{\log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{b} x+\sqrt[4]{-a}+\sqrt[4]{b} x^2\right)}{8 \sqrt{2} (-a)^{7/8} \sqrt[8]{b}}-\frac{\log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{b} x+\sqrt[4]{-a}+\sqrt[4]{b} x^2\right)}{8 \sqrt{2} (-a)^{7/8} \sqrt[8]{b}}-\frac{\tan ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 (-a)^{7/8} \sqrt[8]{b}}+\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 \sqrt{2} (-a)^{7/8} \sqrt[8]{b}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{b} x}{\sqrt[8]{-a}}+1\right)}{4 \sqrt{2} (-a)^{7/8} \sqrt[8]{b}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 (-a)^{7/8} \sqrt[8]{b}}",1,"-ArcTan[(b^(1/8)*x)/(-a)^(1/8)]/(4*(-a)^(7/8)*b^(1/8)) + ArcTan[1 - (Sqrt[2]*b^(1/8)*x)/(-a)^(1/8)]/(4*Sqrt[2]*(-a)^(7/8)*b^(1/8)) - ArcTan[1 + (Sqrt[2]*b^(1/8)*x)/(-a)^(1/8)]/(4*Sqrt[2]*(-a)^(7/8)*b^(1/8)) - ArcTanh[(b^(1/8)*x)/(-a)^(1/8)]/(4*(-a)^(7/8)*b^(1/8)) + Log[(-a)^(1/4) - Sqrt[2]*(-a)^(1/8)*b^(1/8)*x + b^(1/4)*x^2]/(8*Sqrt[2]*(-a)^(7/8)*b^(1/8)) - Log[(-a)^(1/4) + Sqrt[2]*(-a)^(1/8)*b^(1/8)*x + b^(1/4)*x^2]/(8*Sqrt[2]*(-a)^(7/8)*b^(1/8))","A",13,10,9,1.111,1,"{214, 212, 208, 205, 211, 1165, 628, 1162, 617, 204}"
1466,1,275,0,0.2282841,"\int \frac{1}{x^2 \left(a+b x^8\right)} \, dx","Int[1/(x^2*(a + b*x^8)),x]","\frac{\sqrt[8]{b} \log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{b} x+\sqrt[4]{-a}+\sqrt[4]{b} x^2\right)}{8 \sqrt{2} (-a)^{9/8}}-\frac{\sqrt[8]{b} \log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{b} x+\sqrt[4]{-a}+\sqrt[4]{b} x^2\right)}{8 \sqrt{2} (-a)^{9/8}}+\frac{\sqrt[8]{b} \tan ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 (-a)^{9/8}}-\frac{\sqrt[8]{b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 \sqrt{2} (-a)^{9/8}}+\frac{\sqrt[8]{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{b} x}{\sqrt[8]{-a}}+1\right)}{4 \sqrt{2} (-a)^{9/8}}-\frac{\sqrt[8]{b} \tanh ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 (-a)^{9/8}}-\frac{1}{a x}","\frac{\sqrt[8]{b} \log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{b} x+\sqrt[4]{-a}+\sqrt[4]{b} x^2\right)}{8 \sqrt{2} (-a)^{9/8}}-\frac{\sqrt[8]{b} \log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{b} x+\sqrt[4]{-a}+\sqrt[4]{b} x^2\right)}{8 \sqrt{2} (-a)^{9/8}}+\frac{\sqrt[8]{b} \tan ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 (-a)^{9/8}}-\frac{\sqrt[8]{b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 \sqrt{2} (-a)^{9/8}}+\frac{\sqrt[8]{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{b} x}{\sqrt[8]{-a}}+1\right)}{4 \sqrt{2} (-a)^{9/8}}-\frac{\sqrt[8]{b} \tanh ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 (-a)^{9/8}}-\frac{1}{a x}",1,"-(1/(a*x)) + (b^(1/8)*ArcTan[(b^(1/8)*x)/(-a)^(1/8)])/(4*(-a)^(9/8)) - (b^(1/8)*ArcTan[1 - (Sqrt[2]*b^(1/8)*x)/(-a)^(1/8)])/(4*Sqrt[2]*(-a)^(9/8)) + (b^(1/8)*ArcTan[1 + (Sqrt[2]*b^(1/8)*x)/(-a)^(1/8)])/(4*Sqrt[2]*(-a)^(9/8)) - (b^(1/8)*ArcTanh[(b^(1/8)*x)/(-a)^(1/8)])/(4*(-a)^(9/8)) + (b^(1/8)*Log[(-a)^(1/4) - Sqrt[2]*(-a)^(1/8)*b^(1/8)*x + b^(1/4)*x^2])/(8*Sqrt[2]*(-a)^(9/8)) - (b^(1/8)*Log[(-a)^(1/4) + Sqrt[2]*(-a)^(1/8)*b^(1/8)*x + b^(1/4)*x^2])/(8*Sqrt[2]*(-a)^(9/8))","A",14,11,13,0.8462,1,"{325, 301, 297, 1162, 617, 204, 1165, 628, 298, 205, 208}"
1467,1,277,0,0.2265533,"\int \frac{1}{x^4 \left(a+b x^8\right)} \, dx","Int[1/(x^4*(a + b*x^8)),x]","-\frac{b^{3/8} \log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{b} x+\sqrt[4]{-a}+\sqrt[4]{b} x^2\right)}{8 \sqrt{2} (-a)^{11/8}}+\frac{b^{3/8} \log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{b} x+\sqrt[4]{-a}+\sqrt[4]{b} x^2\right)}{8 \sqrt{2} (-a)^{11/8}}-\frac{b^{3/8} \tan ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 (-a)^{11/8}}-\frac{b^{3/8} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 \sqrt{2} (-a)^{11/8}}+\frac{b^{3/8} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{b} x}{\sqrt[8]{-a}}+1\right)}{4 \sqrt{2} (-a)^{11/8}}-\frac{b^{3/8} \tanh ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 (-a)^{11/8}}-\frac{1}{3 a x^3}","-\frac{b^{3/8} \log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{b} x+\sqrt[4]{-a}+\sqrt[4]{b} x^2\right)}{8 \sqrt{2} (-a)^{11/8}}+\frac{b^{3/8} \log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{b} x+\sqrt[4]{-a}+\sqrt[4]{b} x^2\right)}{8 \sqrt{2} (-a)^{11/8}}-\frac{b^{3/8} \tan ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 (-a)^{11/8}}-\frac{b^{3/8} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 \sqrt{2} (-a)^{11/8}}+\frac{b^{3/8} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{b} x}{\sqrt[8]{-a}}+1\right)}{4 \sqrt{2} (-a)^{11/8}}-\frac{b^{3/8} \tanh ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 (-a)^{11/8}}-\frac{1}{3 a x^3}",1,"-1/(3*a*x^3) - (b^(3/8)*ArcTan[(b^(1/8)*x)/(-a)^(1/8)])/(4*(-a)^(11/8)) - (b^(3/8)*ArcTan[1 - (Sqrt[2]*b^(1/8)*x)/(-a)^(1/8)])/(4*Sqrt[2]*(-a)^(11/8)) + (b^(3/8)*ArcTan[1 + (Sqrt[2]*b^(1/8)*x)/(-a)^(1/8)])/(4*Sqrt[2]*(-a)^(11/8)) - (b^(3/8)*ArcTanh[(b^(1/8)*x)/(-a)^(1/8)])/(4*(-a)^(11/8)) - (b^(3/8)*Log[(-a)^(1/4) - Sqrt[2]*(-a)^(1/8)*b^(1/8)*x + b^(1/4)*x^2])/(8*Sqrt[2]*(-a)^(11/8)) + (b^(3/8)*Log[(-a)^(1/4) + Sqrt[2]*(-a)^(1/8)*b^(1/8)*x + b^(1/4)*x^2])/(8*Sqrt[2]*(-a)^(11/8))","A",14,11,13,0.8462,1,"{325, 301, 211, 1165, 628, 1162, 617, 204, 212, 208, 205}"
1468,1,277,0,0.2328155,"\int \frac{1}{x^6 \left(a+b x^8\right)} \, dx","Int[1/(x^6*(a + b*x^8)),x]","-\frac{b^{5/8} \log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{b} x+\sqrt[4]{-a}+\sqrt[4]{b} x^2\right)}{8 \sqrt{2} (-a)^{13/8}}+\frac{b^{5/8} \log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{b} x+\sqrt[4]{-a}+\sqrt[4]{b} x^2\right)}{8 \sqrt{2} (-a)^{13/8}}+\frac{b^{5/8} \tan ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 (-a)^{13/8}}+\frac{b^{5/8} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 \sqrt{2} (-a)^{13/8}}-\frac{b^{5/8} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{b} x}{\sqrt[8]{-a}}+1\right)}{4 \sqrt{2} (-a)^{13/8}}-\frac{b^{5/8} \tanh ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 (-a)^{13/8}}-\frac{1}{5 a x^5}","-\frac{b^{5/8} \log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{b} x+\sqrt[4]{-a}+\sqrt[4]{b} x^2\right)}{8 \sqrt{2} (-a)^{13/8}}+\frac{b^{5/8} \log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{b} x+\sqrt[4]{-a}+\sqrt[4]{b} x^2\right)}{8 \sqrt{2} (-a)^{13/8}}+\frac{b^{5/8} \tan ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 (-a)^{13/8}}+\frac{b^{5/8} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 \sqrt{2} (-a)^{13/8}}-\frac{b^{5/8} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{b} x}{\sqrt[8]{-a}}+1\right)}{4 \sqrt{2} (-a)^{13/8}}-\frac{b^{5/8} \tanh ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 (-a)^{13/8}}-\frac{1}{5 a x^5}",1,"-1/(5*a*x^5) + (b^(5/8)*ArcTan[(b^(1/8)*x)/(-a)^(1/8)])/(4*(-a)^(13/8)) + (b^(5/8)*ArcTan[1 - (Sqrt[2]*b^(1/8)*x)/(-a)^(1/8)])/(4*Sqrt[2]*(-a)^(13/8)) - (b^(5/8)*ArcTan[1 + (Sqrt[2]*b^(1/8)*x)/(-a)^(1/8)])/(4*Sqrt[2]*(-a)^(13/8)) - (b^(5/8)*ArcTanh[(b^(1/8)*x)/(-a)^(1/8)])/(4*(-a)^(13/8)) - (b^(5/8)*Log[(-a)^(1/4) - Sqrt[2]*(-a)^(1/8)*b^(1/8)*x + b^(1/4)*x^2])/(8*Sqrt[2]*(-a)^(13/8)) + (b^(5/8)*Log[(-a)^(1/4) + Sqrt[2]*(-a)^(1/8)*b^(1/8)*x + b^(1/4)*x^2])/(8*Sqrt[2]*(-a)^(13/8))","A",14,11,13,0.8462,1,"{325, 300, 297, 1162, 617, 204, 1165, 628, 298, 205, 208}"
1469,1,277,0,0.2419187,"\int \frac{1}{x^8 \left(a+b x^8\right)} \, dx","Int[1/(x^8*(a + b*x^8)),x]","\frac{b^{7/8} \log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{b} x+\sqrt[4]{-a}+\sqrt[4]{b} x^2\right)}{8 \sqrt{2} (-a)^{15/8}}-\frac{b^{7/8} \log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{b} x+\sqrt[4]{-a}+\sqrt[4]{b} x^2\right)}{8 \sqrt{2} (-a)^{15/8}}-\frac{b^{7/8} \tan ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 (-a)^{15/8}}+\frac{b^{7/8} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 \sqrt{2} (-a)^{15/8}}-\frac{b^{7/8} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{b} x}{\sqrt[8]{-a}}+1\right)}{4 \sqrt{2} (-a)^{15/8}}-\frac{b^{7/8} \tanh ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 (-a)^{15/8}}-\frac{1}{7 a x^7}","\frac{b^{7/8} \log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{b} x+\sqrt[4]{-a}+\sqrt[4]{b} x^2\right)}{8 \sqrt{2} (-a)^{15/8}}-\frac{b^{7/8} \log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{b} x+\sqrt[4]{-a}+\sqrt[4]{b} x^2\right)}{8 \sqrt{2} (-a)^{15/8}}-\frac{b^{7/8} \tan ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 (-a)^{15/8}}+\frac{b^{7/8} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 \sqrt{2} (-a)^{15/8}}-\frac{b^{7/8} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{b} x}{\sqrt[8]{-a}}+1\right)}{4 \sqrt{2} (-a)^{15/8}}-\frac{b^{7/8} \tanh ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt[8]{-a}}\right)}{4 (-a)^{15/8}}-\frac{1}{7 a x^7}",1,"-1/(7*a*x^7) - (b^(7/8)*ArcTan[(b^(1/8)*x)/(-a)^(1/8)])/(4*(-a)^(15/8)) + (b^(7/8)*ArcTan[1 - (Sqrt[2]*b^(1/8)*x)/(-a)^(1/8)])/(4*Sqrt[2]*(-a)^(15/8)) - (b^(7/8)*ArcTan[1 + (Sqrt[2]*b^(1/8)*x)/(-a)^(1/8)])/(4*Sqrt[2]*(-a)^(15/8)) - (b^(7/8)*ArcTanh[(b^(1/8)*x)/(-a)^(1/8)])/(4*(-a)^(15/8)) + (b^(7/8)*Log[(-a)^(1/4) - Sqrt[2]*(-a)^(1/8)*b^(1/8)*x + b^(1/4)*x^2])/(8*Sqrt[2]*(-a)^(15/8)) - (b^(7/8)*Log[(-a)^(1/4) + Sqrt[2]*(-a)^(1/8)*b^(1/8)*x + b^(1/4)*x^2])/(8*Sqrt[2]*(-a)^(15/8))","A",14,11,13,0.8462,1,"{325, 214, 212, 208, 205, 211, 1165, 628, 1162, 617, 204}"
1470,1,239,0,0.1688806,"\int \frac{1}{a-b x^8} \, dx","Int[(a - b*x^8)^(-1),x]","-\frac{\log \left(-\sqrt{2} \sqrt[8]{a} \sqrt[8]{b} x+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)}{8 \sqrt{2} a^{7/8} \sqrt[8]{b}}+\frac{\log \left(\sqrt{2} \sqrt[8]{a} \sqrt[8]{b} x+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)}{8 \sqrt{2} a^{7/8} \sqrt[8]{b}}+\frac{\tan ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt[8]{a}}\right)}{4 a^{7/8} \sqrt[8]{b}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{b} x}{\sqrt[8]{a}}\right)}{4 \sqrt{2} a^{7/8} \sqrt[8]{b}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{b} x}{\sqrt[8]{a}}+1\right)}{4 \sqrt{2} a^{7/8} \sqrt[8]{b}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt[8]{a}}\right)}{4 a^{7/8} \sqrt[8]{b}}","-\frac{\log \left(-\sqrt{2} \sqrt[8]{a} \sqrt[8]{b} x+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)}{8 \sqrt{2} a^{7/8} \sqrt[8]{b}}+\frac{\log \left(\sqrt{2} \sqrt[8]{a} \sqrt[8]{b} x+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)}{8 \sqrt{2} a^{7/8} \sqrt[8]{b}}+\frac{\tan ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt[8]{a}}\right)}{4 a^{7/8} \sqrt[8]{b}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{b} x}{\sqrt[8]{a}}\right)}{4 \sqrt{2} a^{7/8} \sqrt[8]{b}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{b} x}{\sqrt[8]{a}}+1\right)}{4 \sqrt{2} a^{7/8} \sqrt[8]{b}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt[8]{a}}\right)}{4 a^{7/8} \sqrt[8]{b}}",1,"ArcTan[(b^(1/8)*x)/a^(1/8)]/(4*a^(7/8)*b^(1/8)) - ArcTan[1 - (Sqrt[2]*b^(1/8)*x)/a^(1/8)]/(4*Sqrt[2]*a^(7/8)*b^(1/8)) + ArcTan[1 + (Sqrt[2]*b^(1/8)*x)/a^(1/8)]/(4*Sqrt[2]*a^(7/8)*b^(1/8)) + ArcTanh[(b^(1/8)*x)/a^(1/8)]/(4*a^(7/8)*b^(1/8)) - Log[a^(1/4) - Sqrt[2]*a^(1/8)*b^(1/8)*x + b^(1/4)*x^2]/(8*Sqrt[2]*a^(7/8)*b^(1/8)) + Log[a^(1/4) + Sqrt[2]*a^(1/8)*b^(1/8)*x + b^(1/4)*x^2]/(8*Sqrt[2]*a^(7/8)*b^(1/8))","A",13,10,10,1.000,1,"{214, 212, 208, 205, 211, 1165, 628, 1162, 617, 204}"
1471,1,24,0,0.0111475,"\int \frac{x^9}{1-x^8} \, dx","Int[x^9/(1 - x^8),x]","-\frac{x^2}{2}+\frac{1}{4} \tan ^{-1}\left(x^2\right)+\frac{1}{4} \tanh ^{-1}\left(x^2\right)","-\frac{x^2}{2}+\frac{1}{4} \tan ^{-1}\left(x^2\right)+\frac{1}{4} \tanh ^{-1}\left(x^2\right)",1,"-x^2/2 + ArcTan[x^2]/4 + ArcTanh[x^2]/4","A",5,5,13,0.3846,1,"{275, 321, 212, 206, 203}"
1472,1,12,0,0.0025672,"\int \frac{x^7}{1-x^8} \, dx","Int[x^7/(1 - x^8),x]","-\frac{1}{8} \log \left(1-x^8\right)","-\frac{1}{8} \log \left(1-x^8\right)",1,"-Log[1 - x^8]/8","A",1,1,13,0.07692,1,"{260}"
1473,1,17,0,0.0088476,"\int \frac{x^5}{1-x^8} \, dx","Int[x^5/(1 - x^8),x]","\frac{1}{4} \tanh ^{-1}\left(x^2\right)-\frac{1}{4} \tan ^{-1}\left(x^2\right)","\frac{1}{4} \tanh ^{-1}\left(x^2\right)-\frac{1}{4} \tan ^{-1}\left(x^2\right)",1,"-ArcTan[x^2]/4 + ArcTanh[x^2]/4","A",4,4,13,0.3077,1,"{275, 298, 203, 206}"
1474,1,8,0,0.0041538,"\int \frac{x^3}{1-x^8} \, dx","Int[x^3/(1 - x^8),x]","\frac{1}{4} \tanh ^{-1}\left(x^4\right)","\frac{1}{4} \tanh ^{-1}\left(x^4\right)",1,"ArcTanh[x^4]/4","A",2,2,13,0.1538,1,"{275, 206}"
1475,1,17,0,0.0062195,"\int \frac{x}{1-x^8} \, dx","Int[x/(1 - x^8),x]","\frac{1}{4} \tan ^{-1}\left(x^2\right)+\frac{1}{4} \tanh ^{-1}\left(x^2\right)","\frac{1}{4} \tan ^{-1}\left(x^2\right)+\frac{1}{4} \tanh ^{-1}\left(x^2\right)",1,"ArcTan[x^2]/4 + ArcTanh[x^2]/4","A",4,4,11,0.3636,1,"{275, 212, 206, 203}"
1476,1,15,0,0.007262,"\int \frac{1}{x \left(1-x^8\right)} \, dx","Int[1/(x*(1 - x^8)),x]","\log (x)-\frac{1}{8} \log \left(1-x^8\right)","\log (x)-\frac{1}{8} \log \left(1-x^8\right)",1,"Log[x] - Log[1 - x^8]/8","A",4,4,13,0.3077,1,"{266, 36, 31, 29}"
1477,1,24,0,0.0110137,"\int \frac{1}{x^3 \left(1-x^8\right)} \, dx","Int[1/(x^3*(1 - x^8)),x]","-\frac{1}{2 x^2}-\frac{1}{4} \tan ^{-1}\left(x^2\right)+\frac{1}{4} \tanh ^{-1}\left(x^2\right)","-\frac{1}{2 x^2}-\frac{1}{4} \tan ^{-1}\left(x^2\right)+\frac{1}{4} \tanh ^{-1}\left(x^2\right)",1,"-1/(2*x^2) - ArcTan[x^2]/4 + ArcTanh[x^2]/4","A",5,5,13,0.3846,1,"{275, 325, 298, 203, 206}"
1478,1,16,0,0.0071306,"\int \frac{1}{x^5 \left(1-x^8\right)} \, dx","Int[1/(x^5*(1 - x^8)),x]","\frac{1}{4} \tanh ^{-1}\left(x^4\right)-\frac{1}{4 x^4}","\frac{1}{4} \tanh ^{-1}\left(x^4\right)-\frac{1}{4 x^4}",1,"-1/(4*x^4) + ArcTanh[x^4]/4","A",3,3,13,0.2308,1,"{275, 325, 206}"
1479,1,24,0,0.0096274,"\int \frac{1}{x^7 \left(1-x^8\right)} \, dx","Int[1/(x^7*(1 - x^8)),x]","-\frac{1}{6 x^6}+\frac{1}{4} \tan ^{-1}\left(x^2\right)+\frac{1}{4} \tanh ^{-1}\left(x^2\right)","-\frac{1}{6 x^6}+\frac{1}{4} \tan ^{-1}\left(x^2\right)+\frac{1}{4} \tanh ^{-1}\left(x^2\right)",1,"-1/(6*x^6) + ArcTan[x^2]/4 + ArcTanh[x^2]/4","A",5,5,13,0.3846,1,"{275, 325, 212, 206, 203}"
1480,1,22,0,0.0111236,"\int \frac{1}{x^9 \left(1-x^8\right)} \, dx","Int[1/(x^9*(1 - x^8)),x]","-\frac{1}{8 x^8}-\frac{1}{8} \log \left(1-x^8\right)+\log (x)","-\frac{1}{8 x^8}-\frac{1}{8} \log \left(1-x^8\right)+\log (x)",1,"-1/(8*x^8) + Log[x] - Log[1 - x^8]/8","A",3,2,13,0.1538,1,"{266, 44}"
1481,1,100,0,0.0519064,"\int \frac{x^8}{1-x^8} \, dx","Int[x^8/(1 - x^8),x]","-\frac{\log \left(x^2-\sqrt{2} x+1\right)}{8 \sqrt{2}}+\frac{\log \left(x^2+\sqrt{2} x+1\right)}{8 \sqrt{2}}-x+\frac{1}{4} \tan ^{-1}(x)-\frac{\tan ^{-1}\left(1-\sqrt{2} x\right)}{4 \sqrt{2}}+\frac{\tan ^{-1}\left(\sqrt{2} x+1\right)}{4 \sqrt{2}}+\frac{1}{4} \tanh ^{-1}(x)","-\frac{\log \left(x^2-\sqrt{2} x+1\right)}{8 \sqrt{2}}+\frac{\log \left(x^2+\sqrt{2} x+1\right)}{8 \sqrt{2}}-x+\frac{1}{4} \tan ^{-1}(x)-\frac{\tan ^{-1}\left(1-\sqrt{2} x\right)}{4 \sqrt{2}}+\frac{\tan ^{-1}\left(\sqrt{2} x+1\right)}{4 \sqrt{2}}+\frac{1}{4} \tanh ^{-1}(x)",1,"-x + ArcTan[x]/4 - ArcTan[1 - Sqrt[2]*x]/(4*Sqrt[2]) + ArcTan[1 + Sqrt[2]*x]/(4*Sqrt[2]) + ArcTanh[x]/4 - Log[1 - Sqrt[2]*x + x^2]/(8*Sqrt[2]) + Log[1 + Sqrt[2]*x + x^2]/(8*Sqrt[2])","A",14,11,13,0.8462,1,"{321, 214, 212, 206, 203, 211, 1165, 628, 1162, 617, 204}"
1482,1,97,0,0.0531369,"\int \frac{x^6}{1-x^8} \, dx","Int[x^6/(1 - x^8),x]","-\frac{\log \left(x^2-\sqrt{2} x+1\right)}{8 \sqrt{2}}+\frac{\log \left(x^2+\sqrt{2} x+1\right)}{8 \sqrt{2}}-\frac{1}{4} \tan ^{-1}(x)+\frac{\tan ^{-1}\left(1-\sqrt{2} x\right)}{4 \sqrt{2}}-\frac{\tan ^{-1}\left(\sqrt{2} x+1\right)}{4 \sqrt{2}}+\frac{1}{4} \tanh ^{-1}(x)","-\frac{\log \left(x^2-\sqrt{2} x+1\right)}{8 \sqrt{2}}+\frac{\log \left(x^2+\sqrt{2} x+1\right)}{8 \sqrt{2}}-\frac{1}{4} \tan ^{-1}(x)+\frac{\tan ^{-1}\left(1-\sqrt{2} x\right)}{4 \sqrt{2}}-\frac{\tan ^{-1}\left(\sqrt{2} x+1\right)}{4 \sqrt{2}}+\frac{1}{4} \tanh ^{-1}(x)",1,"-ArcTan[x]/4 + ArcTan[1 - Sqrt[2]*x]/(4*Sqrt[2]) - ArcTan[1 + Sqrt[2]*x]/(4*Sqrt[2]) + ArcTanh[x]/4 - Log[1 - Sqrt[2]*x + x^2]/(8*Sqrt[2]) + Log[1 + Sqrt[2]*x + x^2]/(8*Sqrt[2])","A",13,10,13,0.7692,1,"{301, 297, 1162, 617, 204, 1165, 628, 298, 203, 206}"
1483,1,97,0,0.0525867,"\int \frac{x^4}{1-x^8} \, dx","Int[x^4/(1 - x^8),x]","\frac{\log \left(x^2-\sqrt{2} x+1\right)}{8 \sqrt{2}}-\frac{\log \left(x^2+\sqrt{2} x+1\right)}{8 \sqrt{2}}+\frac{1}{4} \tan ^{-1}(x)+\frac{\tan ^{-1}\left(1-\sqrt{2} x\right)}{4 \sqrt{2}}-\frac{\tan ^{-1}\left(\sqrt{2} x+1\right)}{4 \sqrt{2}}+\frac{1}{4} \tanh ^{-1}(x)","\frac{\log \left(x^2-\sqrt{2} x+1\right)}{8 \sqrt{2}}-\frac{\log \left(x^2+\sqrt{2} x+1\right)}{8 \sqrt{2}}+\frac{1}{4} \tan ^{-1}(x)+\frac{\tan ^{-1}\left(1-\sqrt{2} x\right)}{4 \sqrt{2}}-\frac{\tan ^{-1}\left(\sqrt{2} x+1\right)}{4 \sqrt{2}}+\frac{1}{4} \tanh ^{-1}(x)",1,"ArcTan[x]/4 + ArcTan[1 - Sqrt[2]*x]/(4*Sqrt[2]) - ArcTan[1 + Sqrt[2]*x]/(4*Sqrt[2]) + ArcTanh[x]/4 + Log[1 - Sqrt[2]*x + x^2]/(8*Sqrt[2]) - Log[1 + Sqrt[2]*x + x^2]/(8*Sqrt[2])","A",13,10,13,0.7692,1,"{301, 211, 1165, 628, 1162, 617, 204, 212, 206, 203}"
1484,1,97,0,0.0517584,"\int \frac{x^2}{1-x^8} \, dx","Int[x^2/(1 - x^8),x]","\frac{\log \left(x^2-\sqrt{2} x+1\right)}{8 \sqrt{2}}-\frac{\log \left(x^2+\sqrt{2} x+1\right)}{8 \sqrt{2}}-\frac{1}{4} \tan ^{-1}(x)-\frac{\tan ^{-1}\left(1-\sqrt{2} x\right)}{4 \sqrt{2}}+\frac{\tan ^{-1}\left(\sqrt{2} x+1\right)}{4 \sqrt{2}}+\frac{1}{4} \tanh ^{-1}(x)","\frac{\log \left(x^2-\sqrt{2} x+1\right)}{8 \sqrt{2}}-\frac{\log \left(x^2+\sqrt{2} x+1\right)}{8 \sqrt{2}}-\frac{1}{4} \tan ^{-1}(x)-\frac{\tan ^{-1}\left(1-\sqrt{2} x\right)}{4 \sqrt{2}}+\frac{\tan ^{-1}\left(\sqrt{2} x+1\right)}{4 \sqrt{2}}+\frac{1}{4} \tanh ^{-1}(x)",1,"-ArcTan[x]/4 - ArcTan[1 - Sqrt[2]*x]/(4*Sqrt[2]) + ArcTan[1 + Sqrt[2]*x]/(4*Sqrt[2]) + ArcTanh[x]/4 + Log[1 - Sqrt[2]*x + x^2]/(8*Sqrt[2]) - Log[1 + Sqrt[2]*x + x^2]/(8*Sqrt[2])","A",13,10,13,0.7692,1,"{300, 297, 1162, 617, 204, 1165, 628, 298, 203, 206}"
1485,1,97,0,0.0495969,"\int \frac{1}{1-x^8} \, dx","Int[(1 - x^8)^(-1),x]","-\frac{\log \left(x^2-\sqrt{2} x+1\right)}{8 \sqrt{2}}+\frac{\log \left(x^2+\sqrt{2} x+1\right)}{8 \sqrt{2}}+\frac{1}{4} \tan ^{-1}(x)-\frac{\tan ^{-1}\left(1-\sqrt{2} x\right)}{4 \sqrt{2}}+\frac{\tan ^{-1}\left(\sqrt{2} x+1\right)}{4 \sqrt{2}}+\frac{1}{4} \tanh ^{-1}(x)","-\frac{\log \left(x^2-\sqrt{2} x+1\right)}{8 \sqrt{2}}+\frac{\log \left(x^2+\sqrt{2} x+1\right)}{8 \sqrt{2}}+\frac{1}{4} \tan ^{-1}(x)-\frac{\tan ^{-1}\left(1-\sqrt{2} x\right)}{4 \sqrt{2}}+\frac{\tan ^{-1}\left(\sqrt{2} x+1\right)}{4 \sqrt{2}}+\frac{1}{4} \tanh ^{-1}(x)",1,"ArcTan[x]/4 - ArcTan[1 - Sqrt[2]*x]/(4*Sqrt[2]) + ArcTan[1 + Sqrt[2]*x]/(4*Sqrt[2]) + ArcTanh[x]/4 - Log[1 - Sqrt[2]*x + x^2]/(8*Sqrt[2]) + Log[1 + Sqrt[2]*x + x^2]/(8*Sqrt[2])","A",13,10,9,1.111,1,"{214, 212, 206, 203, 211, 1165, 628, 1162, 617, 204}"
1486,1,102,0,0.0556487,"\int \frac{1}{x^2 \left(1-x^8\right)} \, dx","Int[1/(x^2*(1 - x^8)),x]","-\frac{\log \left(x^2-\sqrt{2} x+1\right)}{8 \sqrt{2}}+\frac{\log \left(x^2+\sqrt{2} x+1\right)}{8 \sqrt{2}}-\frac{1}{x}-\frac{1}{4} \tan ^{-1}(x)+\frac{\tan ^{-1}\left(1-\sqrt{2} x\right)}{4 \sqrt{2}}-\frac{\tan ^{-1}\left(\sqrt{2} x+1\right)}{4 \sqrt{2}}+\frac{1}{4} \tanh ^{-1}(x)","-\frac{\log \left(x^2-\sqrt{2} x+1\right)}{8 \sqrt{2}}+\frac{\log \left(x^2+\sqrt{2} x+1\right)}{8 \sqrt{2}}-\frac{1}{x}-\frac{1}{4} \tan ^{-1}(x)+\frac{\tan ^{-1}\left(1-\sqrt{2} x\right)}{4 \sqrt{2}}-\frac{\tan ^{-1}\left(\sqrt{2} x+1\right)}{4 \sqrt{2}}+\frac{1}{4} \tanh ^{-1}(x)",1,"-x^(-1) - ArcTan[x]/4 + ArcTan[1 - Sqrt[2]*x]/(4*Sqrt[2]) - ArcTan[1 + Sqrt[2]*x]/(4*Sqrt[2]) + ArcTanh[x]/4 - Log[1 - Sqrt[2]*x + x^2]/(8*Sqrt[2]) + Log[1 + Sqrt[2]*x + x^2]/(8*Sqrt[2])","A",14,11,13,0.8462,1,"{325, 301, 297, 1162, 617, 204, 1165, 628, 298, 203, 206}"
1487,1,104,0,0.0515215,"\int \frac{1}{x^4 \left(1-x^8\right)} \, dx","Int[1/(x^4*(1 - x^8)),x]","-\frac{1}{3 x^3}+\frac{\log \left(x^2-\sqrt{2} x+1\right)}{8 \sqrt{2}}-\frac{\log \left(x^2+\sqrt{2} x+1\right)}{8 \sqrt{2}}+\frac{1}{4} \tan ^{-1}(x)+\frac{\tan ^{-1}\left(1-\sqrt{2} x\right)}{4 \sqrt{2}}-\frac{\tan ^{-1}\left(\sqrt{2} x+1\right)}{4 \sqrt{2}}+\frac{1}{4} \tanh ^{-1}(x)","-\frac{1}{3 x^3}+\frac{\log \left(x^2-\sqrt{2} x+1\right)}{8 \sqrt{2}}-\frac{\log \left(x^2+\sqrt{2} x+1\right)}{8 \sqrt{2}}+\frac{1}{4} \tan ^{-1}(x)+\frac{\tan ^{-1}\left(1-\sqrt{2} x\right)}{4 \sqrt{2}}-\frac{\tan ^{-1}\left(\sqrt{2} x+1\right)}{4 \sqrt{2}}+\frac{1}{4} \tanh ^{-1}(x)",1,"-1/(3*x^3) + ArcTan[x]/4 + ArcTan[1 - Sqrt[2]*x]/(4*Sqrt[2]) - ArcTan[1 + Sqrt[2]*x]/(4*Sqrt[2]) + ArcTanh[x]/4 + Log[1 - Sqrt[2]*x + x^2]/(8*Sqrt[2]) - Log[1 + Sqrt[2]*x + x^2]/(8*Sqrt[2])","A",14,11,13,0.8462,1,"{325, 301, 211, 1165, 628, 1162, 617, 204, 212, 206, 203}"
1488,1,104,0,0.0532422,"\int \frac{1}{x^6 \left(1-x^8\right)} \, dx","Int[1/(x^6*(1 - x^8)),x]","-\frac{1}{5 x^5}+\frac{\log \left(x^2-\sqrt{2} x+1\right)}{8 \sqrt{2}}-\frac{\log \left(x^2+\sqrt{2} x+1\right)}{8 \sqrt{2}}-\frac{1}{4} \tan ^{-1}(x)-\frac{\tan ^{-1}\left(1-\sqrt{2} x\right)}{4 \sqrt{2}}+\frac{\tan ^{-1}\left(\sqrt{2} x+1\right)}{4 \sqrt{2}}+\frac{1}{4} \tanh ^{-1}(x)","-\frac{1}{5 x^5}+\frac{\log \left(x^2-\sqrt{2} x+1\right)}{8 \sqrt{2}}-\frac{\log \left(x^2+\sqrt{2} x+1\right)}{8 \sqrt{2}}-\frac{1}{4} \tan ^{-1}(x)-\frac{\tan ^{-1}\left(1-\sqrt{2} x\right)}{4 \sqrt{2}}+\frac{\tan ^{-1}\left(\sqrt{2} x+1\right)}{4 \sqrt{2}}+\frac{1}{4} \tanh ^{-1}(x)",1,"-1/(5*x^5) - ArcTan[x]/4 - ArcTan[1 - Sqrt[2]*x]/(4*Sqrt[2]) + ArcTan[1 + Sqrt[2]*x]/(4*Sqrt[2]) + ArcTanh[x]/4 + Log[1 - Sqrt[2]*x + x^2]/(8*Sqrt[2]) - Log[1 + Sqrt[2]*x + x^2]/(8*Sqrt[2])","A",14,11,13,0.8462,1,"{325, 300, 297, 1162, 617, 204, 1165, 628, 298, 203, 206}"
1489,1,104,0,0.0520038,"\int \frac{1}{x^8 \left(1-x^8\right)} \, dx","Int[1/(x^8*(1 - x^8)),x]","-\frac{1}{7 x^7}-\frac{\log \left(x^2-\sqrt{2} x+1\right)}{8 \sqrt{2}}+\frac{\log \left(x^2+\sqrt{2} x+1\right)}{8 \sqrt{2}}+\frac{1}{4} \tan ^{-1}(x)-\frac{\tan ^{-1}\left(1-\sqrt{2} x\right)}{4 \sqrt{2}}+\frac{\tan ^{-1}\left(\sqrt{2} x+1\right)}{4 \sqrt{2}}+\frac{1}{4} \tanh ^{-1}(x)","-\frac{1}{7 x^7}-\frac{\log \left(x^2-\sqrt{2} x+1\right)}{8 \sqrt{2}}+\frac{\log \left(x^2+\sqrt{2} x+1\right)}{8 \sqrt{2}}+\frac{1}{4} \tan ^{-1}(x)-\frac{\tan ^{-1}\left(1-\sqrt{2} x\right)}{4 \sqrt{2}}+\frac{\tan ^{-1}\left(\sqrt{2} x+1\right)}{4 \sqrt{2}}+\frac{1}{4} \tanh ^{-1}(x)",1,"-1/(7*x^7) + ArcTan[x]/4 - ArcTan[1 - Sqrt[2]*x]/(4*Sqrt[2]) + ArcTan[1 + Sqrt[2]*x]/(4*Sqrt[2]) + ArcTanh[x]/4 - Log[1 - Sqrt[2]*x + x^2]/(8*Sqrt[2]) + Log[1 + Sqrt[2]*x + x^2]/(8*Sqrt[2])","A",14,11,13,0.8462,1,"{325, 214, 212, 206, 203, 211, 1165, 628, 1162, 617, 204}"
1490,1,100,0,0.0645671,"\int \frac{x^9}{1+x^8} \, dx","Int[x^9/(1 + x^8),x]","\frac{x^2}{2}+\frac{\log \left(x^4-\sqrt{2} x^2+1\right)}{8 \sqrt{2}}-\frac{\log \left(x^4+\sqrt{2} x^2+1\right)}{8 \sqrt{2}}+\frac{\tan ^{-1}\left(1-\sqrt{2} x^2\right)}{4 \sqrt{2}}-\frac{\tan ^{-1}\left(\sqrt{2} x^2+1\right)}{4 \sqrt{2}}","\frac{x^2}{2}+\frac{\log \left(x^4-\sqrt{2} x^2+1\right)}{8 \sqrt{2}}-\frac{\log \left(x^4+\sqrt{2} x^2+1\right)}{8 \sqrt{2}}+\frac{\tan ^{-1}\left(1-\sqrt{2} x^2\right)}{4 \sqrt{2}}-\frac{\tan ^{-1}\left(\sqrt{2} x^2+1\right)}{4 \sqrt{2}}",1,"x^2/2 + ArcTan[1 - Sqrt[2]*x^2]/(4*Sqrt[2]) - ArcTan[1 + Sqrt[2]*x^2]/(4*Sqrt[2]) + Log[1 - Sqrt[2]*x^2 + x^4]/(8*Sqrt[2]) - Log[1 + Sqrt[2]*x^2 + x^4]/(8*Sqrt[2])","A",11,8,11,0.7273,1,"{275, 321, 211, 1165, 628, 1162, 617, 204}"
1491,1,10,0,0.002044,"\int \frac{x^7}{1+x^8} \, dx","Int[x^7/(1 + x^8),x]","\frac{1}{8} \log \left(x^8+1\right)","\frac{1}{8} \log \left(x^8+1\right)",1,"Log[1 + x^8]/8","A",1,1,11,0.09091,1,"{260}"
1492,1,93,0,0.0630532,"\int \frac{x^5}{1+x^8} \, dx","Int[x^5/(1 + x^8),x]","\frac{\log \left(x^4-\sqrt{2} x^2+1\right)}{8 \sqrt{2}}-\frac{\log \left(x^4+\sqrt{2} x^2+1\right)}{8 \sqrt{2}}-\frac{\tan ^{-1}\left(1-\sqrt{2} x^2\right)}{4 \sqrt{2}}+\frac{\tan ^{-1}\left(\sqrt{2} x^2+1\right)}{4 \sqrt{2}}","\frac{\log \left(x^4-\sqrt{2} x^2+1\right)}{8 \sqrt{2}}-\frac{\log \left(x^4+\sqrt{2} x^2+1\right)}{8 \sqrt{2}}-\frac{\tan ^{-1}\left(1-\sqrt{2} x^2\right)}{4 \sqrt{2}}+\frac{\tan ^{-1}\left(\sqrt{2} x^2+1\right)}{4 \sqrt{2}}",1,"-ArcTan[1 - Sqrt[2]*x^2]/(4*Sqrt[2]) + ArcTan[1 + Sqrt[2]*x^2]/(4*Sqrt[2]) + Log[1 - Sqrt[2]*x^2 + x^4]/(8*Sqrt[2]) - Log[1 + Sqrt[2]*x^2 + x^4]/(8*Sqrt[2])","A",10,7,11,0.6364,1,"{275, 297, 1162, 617, 204, 1165, 628}"
1493,1,8,0,0.0029167,"\int \frac{x^3}{1+x^8} \, dx","Int[x^3/(1 + x^8),x]","\frac{1}{4} \tan ^{-1}\left(x^4\right)","\frac{1}{4} \tan ^{-1}\left(x^4\right)",1,"ArcTan[x^4]/4","A",2,2,11,0.1818,1,"{275, 203}"
1494,1,93,0,0.0617393,"\int \frac{x}{1+x^8} \, dx","Int[x/(1 + x^8),x]","-\frac{\log \left(x^4-\sqrt{2} x^2+1\right)}{8 \sqrt{2}}+\frac{\log \left(x^4+\sqrt{2} x^2+1\right)}{8 \sqrt{2}}-\frac{\tan ^{-1}\left(1-\sqrt{2} x^2\right)}{4 \sqrt{2}}+\frac{\tan ^{-1}\left(\sqrt{2} x^2+1\right)}{4 \sqrt{2}}","-\frac{\log \left(x^4-\sqrt{2} x^2+1\right)}{8 \sqrt{2}}+\frac{\log \left(x^4+\sqrt{2} x^2+1\right)}{8 \sqrt{2}}-\frac{\tan ^{-1}\left(1-\sqrt{2} x^2\right)}{4 \sqrt{2}}+\frac{\tan ^{-1}\left(\sqrt{2} x^2+1\right)}{4 \sqrt{2}}",1,"-ArcTan[1 - Sqrt[2]*x^2]/(4*Sqrt[2]) + ArcTan[1 + Sqrt[2]*x^2]/(4*Sqrt[2]) - Log[1 - Sqrt[2]*x^2 + x^4]/(8*Sqrt[2]) + Log[1 + Sqrt[2]*x^2 + x^4]/(8*Sqrt[2])","A",10,7,9,0.7778,1,"{275, 211, 1165, 628, 1162, 617, 204}"
1495,1,13,0,0.0049444,"\int \frac{1}{x \left(1+x^8\right)} \, dx","Int[1/(x*(1 + x^8)),x]","\log (x)-\frac{1}{8} \log \left(x^8+1\right)","\log (x)-\frac{1}{8} \log \left(x^8+1\right)",1,"Log[x] - Log[1 + x^8]/8","A",4,4,11,0.3636,1,"{266, 36, 29, 31}"
1496,1,100,0,0.0656631,"\int \frac{1}{x^3 \left(1+x^8\right)} \, dx","Int[1/(x^3*(1 + x^8)),x]","-\frac{1}{2 x^2}-\frac{\log \left(x^4-\sqrt{2} x^2+1\right)}{8 \sqrt{2}}+\frac{\log \left(x^4+\sqrt{2} x^2+1\right)}{8 \sqrt{2}}+\frac{\tan ^{-1}\left(1-\sqrt{2} x^2\right)}{4 \sqrt{2}}-\frac{\tan ^{-1}\left(\sqrt{2} x^2+1\right)}{4 \sqrt{2}}","-\frac{1}{2 x^2}-\frac{\log \left(x^4-\sqrt{2} x^2+1\right)}{8 \sqrt{2}}+\frac{\log \left(x^4+\sqrt{2} x^2+1\right)}{8 \sqrt{2}}+\frac{\tan ^{-1}\left(1-\sqrt{2} x^2\right)}{4 \sqrt{2}}-\frac{\tan ^{-1}\left(\sqrt{2} x^2+1\right)}{4 \sqrt{2}}",1,"-1/(2*x^2) + ArcTan[1 - Sqrt[2]*x^2]/(4*Sqrt[2]) - ArcTan[1 + Sqrt[2]*x^2]/(4*Sqrt[2]) - Log[1 - Sqrt[2]*x^2 + x^4]/(8*Sqrt[2]) + Log[1 + Sqrt[2]*x^2 + x^4]/(8*Sqrt[2])","A",11,8,11,0.7273,1,"{275, 325, 297, 1162, 617, 204, 1165, 628}"
1497,1,16,0,0.0059629,"\int \frac{1}{x^5 \left(1+x^8\right)} \, dx","Int[1/(x^5*(1 + x^8)),x]","-\frac{1}{4 x^4}-\frac{1}{4} \tan ^{-1}\left(x^4\right)","-\frac{1}{4 x^4}-\frac{1}{4} \tan ^{-1}\left(x^4\right)",1,"-1/(4*x^4) - ArcTan[x^4]/4","A",3,3,11,0.2727,1,"{275, 325, 203}"
1498,1,100,0,0.0665876,"\int \frac{1}{x^7 \left(1+x^8\right)} \, dx","Int[1/(x^7*(1 + x^8)),x]","-\frac{1}{6 x^6}+\frac{\log \left(x^4-\sqrt{2} x^2+1\right)}{8 \sqrt{2}}-\frac{\log \left(x^4+\sqrt{2} x^2+1\right)}{8 \sqrt{2}}+\frac{\tan ^{-1}\left(1-\sqrt{2} x^2\right)}{4 \sqrt{2}}-\frac{\tan ^{-1}\left(\sqrt{2} x^2+1\right)}{4 \sqrt{2}}","-\frac{1}{6 x^6}+\frac{\log \left(x^4-\sqrt{2} x^2+1\right)}{8 \sqrt{2}}-\frac{\log \left(x^4+\sqrt{2} x^2+1\right)}{8 \sqrt{2}}+\frac{\tan ^{-1}\left(1-\sqrt{2} x^2\right)}{4 \sqrt{2}}-\frac{\tan ^{-1}\left(\sqrt{2} x^2+1\right)}{4 \sqrt{2}}",1,"-1/(6*x^6) + ArcTan[1 - Sqrt[2]*x^2]/(4*Sqrt[2]) - ArcTan[1 + Sqrt[2]*x^2]/(4*Sqrt[2]) + Log[1 - Sqrt[2]*x^2 + x^4]/(8*Sqrt[2]) - Log[1 + Sqrt[2]*x^2 + x^4]/(8*Sqrt[2])","A",11,8,11,0.7273,1,"{275, 325, 211, 1165, 628, 1162, 617, 204}"
1499,1,22,0,0.0097526,"\int \frac{1}{x^9 \left(1+x^8\right)} \, dx","Int[1/(x^9*(1 + x^8)),x]","-\frac{1}{8 x^8}+\frac{1}{8} \log \left(x^8+1\right)-\log (x)","-\frac{1}{8 x^8}+\frac{1}{8} \log \left(x^8+1\right)-\log (x)",1,"-1/(8*x^8) - Log[x] + Log[1 + x^8]/8","A",3,2,11,0.1818,1,"{266, 44}"
1500,1,340,0,0.3187971,"\int \frac{x^8}{1+x^8} \, dx","Int[x^8/(1 + x^8),x]","\frac{1}{16} \sqrt{2-\sqrt{2}} \log \left(x^2-\sqrt{2-\sqrt{2}} x+1\right)-\frac{1}{16} \sqrt{2-\sqrt{2}} \log \left(x^2+\sqrt{2-\sqrt{2}} x+1\right)+\frac{1}{16} \sqrt{2+\sqrt{2}} \log \left(x^2-\sqrt{2+\sqrt{2}} x+1\right)-\frac{1}{16} \sqrt{2+\sqrt{2}} \log \left(x^2+\sqrt{2+\sqrt{2}} x+1\right)+x+\frac{\tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}}-2 x}{\sqrt{2+\sqrt{2}}}\right)}{4 \sqrt{2 \left(2-\sqrt{2}\right)}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}}-2 x}{\sqrt{2-\sqrt{2}}}\right)}{4 \sqrt{2 \left(2+\sqrt{2}\right)}}-\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2-\sqrt{2}}}{\sqrt{2+\sqrt{2}}}\right)}{4 \sqrt{2 \left(2-\sqrt{2}\right)}}-\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2+\sqrt{2}}}{\sqrt{2-\sqrt{2}}}\right)}{4 \sqrt{2 \left(2+\sqrt{2}\right)}}","\frac{1}{16} \sqrt{2-\sqrt{2}} \log \left(x^2-\sqrt{2-\sqrt{2}} x+1\right)-\frac{1}{16} \sqrt{2-\sqrt{2}} \log \left(x^2+\sqrt{2-\sqrt{2}} x+1\right)+\frac{1}{16} \sqrt{2+\sqrt{2}} \log \left(x^2-\sqrt{2+\sqrt{2}} x+1\right)-\frac{1}{16} \sqrt{2+\sqrt{2}} \log \left(x^2+\sqrt{2+\sqrt{2}} x+1\right)+x+\frac{\tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}}-2 x}{\sqrt{2+\sqrt{2}}}\right)}{4 \sqrt{2 \left(2-\sqrt{2}\right)}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}}-2 x}{\sqrt{2-\sqrt{2}}}\right)}{4 \sqrt{2 \left(2+\sqrt{2}\right)}}-\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2-\sqrt{2}}}{\sqrt{2+\sqrt{2}}}\right)}{4 \sqrt{2 \left(2-\sqrt{2}\right)}}-\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2+\sqrt{2}}}{\sqrt{2-\sqrt{2}}}\right)}{4 \sqrt{2 \left(2+\sqrt{2}\right)}}",1,"x + ArcTan[(Sqrt[2 - Sqrt[2]] - 2*x)/Sqrt[2 + Sqrt[2]]]/(4*Sqrt[2*(2 - Sqrt[2])]) + ArcTan[(Sqrt[2 + Sqrt[2]] - 2*x)/Sqrt[2 - Sqrt[2]]]/(4*Sqrt[2*(2 + Sqrt[2])]) - ArcTan[(Sqrt[2 - Sqrt[2]] + 2*x)/Sqrt[2 + Sqrt[2]]]/(4*Sqrt[2*(2 - Sqrt[2])]) - ArcTan[(Sqrt[2 + Sqrt[2]] + 2*x)/Sqrt[2 - Sqrt[2]]]/(4*Sqrt[2*(2 + Sqrt[2])]) + (Sqrt[2 - Sqrt[2]]*Log[1 - Sqrt[2 - Sqrt[2]]*x + x^2])/16 - (Sqrt[2 - Sqrt[2]]*Log[1 + Sqrt[2 - Sqrt[2]]*x + x^2])/16 + (Sqrt[2 + Sqrt[2]]*Log[1 - Sqrt[2 + Sqrt[2]]*x + x^2])/16 - (Sqrt[2 + Sqrt[2]]*Log[1 + Sqrt[2 + Sqrt[2]]*x + x^2])/16","A",20,7,11,0.6364,1,"{321, 213, 1169, 634, 618, 204, 628}"
1501,1,339,0,0.2070594,"\int \frac{x^6}{1+x^8} \, dx","Int[x^6/(1 + x^8),x]","\frac{1}{16} \sqrt{2-\sqrt{2}} \log \left(x^2-\sqrt{2-\sqrt{2}} x+1\right)-\frac{1}{16} \sqrt{2-\sqrt{2}} \log \left(x^2+\sqrt{2-\sqrt{2}} x+1\right)+\frac{1}{16} \sqrt{2+\sqrt{2}} \log \left(x^2-\sqrt{2+\sqrt{2}} x+1\right)-\frac{1}{16} \sqrt{2+\sqrt{2}} \log \left(x^2+\sqrt{2+\sqrt{2}} x+1\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}}-2 x}{\sqrt{2+\sqrt{2}}}\right)}{4 \sqrt{2 \left(2-\sqrt{2}\right)}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}}-2 x}{\sqrt{2-\sqrt{2}}}\right)}{4 \sqrt{2 \left(2+\sqrt{2}\right)}}+\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2-\sqrt{2}}}{\sqrt{2+\sqrt{2}}}\right)}{4 \sqrt{2 \left(2-\sqrt{2}\right)}}+\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2+\sqrt{2}}}{\sqrt{2-\sqrt{2}}}\right)}{4 \sqrt{2 \left(2+\sqrt{2}\right)}}","\frac{1}{16} \sqrt{2-\sqrt{2}} \log \left(x^2-\sqrt{2-\sqrt{2}} x+1\right)-\frac{1}{16} \sqrt{2-\sqrt{2}} \log \left(x^2+\sqrt{2-\sqrt{2}} x+1\right)+\frac{1}{16} \sqrt{2+\sqrt{2}} \log \left(x^2-\sqrt{2+\sqrt{2}} x+1\right)-\frac{1}{16} \sqrt{2+\sqrt{2}} \log \left(x^2+\sqrt{2+\sqrt{2}} x+1\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}}-2 x}{\sqrt{2+\sqrt{2}}}\right)}{4 \sqrt{2 \left(2-\sqrt{2}\right)}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}}-2 x}{\sqrt{2-\sqrt{2}}}\right)}{4 \sqrt{2 \left(2+\sqrt{2}\right)}}+\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2-\sqrt{2}}}{\sqrt{2+\sqrt{2}}}\right)}{4 \sqrt{2 \left(2-\sqrt{2}\right)}}+\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2+\sqrt{2}}}{\sqrt{2-\sqrt{2}}}\right)}{4 \sqrt{2 \left(2+\sqrt{2}\right)}}",1,"-ArcTan[(Sqrt[2 - Sqrt[2]] - 2*x)/Sqrt[2 + Sqrt[2]]]/(4*Sqrt[2*(2 - Sqrt[2])]) - ArcTan[(Sqrt[2 + Sqrt[2]] - 2*x)/Sqrt[2 - Sqrt[2]]]/(4*Sqrt[2*(2 + Sqrt[2])]) + ArcTan[(Sqrt[2 - Sqrt[2]] + 2*x)/Sqrt[2 + Sqrt[2]]]/(4*Sqrt[2*(2 - Sqrt[2])]) + ArcTan[(Sqrt[2 + Sqrt[2]] + 2*x)/Sqrt[2 - Sqrt[2]]]/(4*Sqrt[2*(2 + Sqrt[2])]) + (Sqrt[2 - Sqrt[2]]*Log[1 - Sqrt[2 - Sqrt[2]]*x + x^2])/16 - (Sqrt[2 - Sqrt[2]]*Log[1 + Sqrt[2 - Sqrt[2]]*x + x^2])/16 + (Sqrt[2 + Sqrt[2]]*Log[1 - Sqrt[2 + Sqrt[2]]*x + x^2])/16 - (Sqrt[2 + Sqrt[2]]*Log[1 + Sqrt[2 + Sqrt[2]]*x + x^2])/16","A",21,7,11,0.6364,1,"{299, 1122, 1169, 634, 618, 204, 628}"
1502,1,347,0,0.186792,"\int \frac{x^4}{1+x^8} \, dx","Int[x^4/(1 + x^8),x]","-\frac{\log \left(x^2-\sqrt{2-\sqrt{2}} x+1\right)}{8 \sqrt{2 \left(2-\sqrt{2}\right)}}+\frac{\log \left(x^2+\sqrt{2-\sqrt{2}} x+1\right)}{8 \sqrt{2 \left(2-\sqrt{2}\right)}}+\frac{\log \left(x^2-\sqrt{2+\sqrt{2}} x+1\right)}{8 \sqrt{2 \left(2+\sqrt{2}\right)}}-\frac{\log \left(x^2+\sqrt{2+\sqrt{2}} x+1\right)}{8 \sqrt{2 \left(2+\sqrt{2}\right)}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}}-2 x}{\sqrt{2+\sqrt{2}}}\right)}{4 \sqrt{2 \left(2+\sqrt{2}\right)}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}}-2 x}{\sqrt{2-\sqrt{2}}}\right)}{4 \sqrt{2 \left(2-\sqrt{2}\right)}}-\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2-\sqrt{2}}}{\sqrt{2+\sqrt{2}}}\right)}{4 \sqrt{2 \left(2+\sqrt{2}\right)}}+\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2+\sqrt{2}}}{\sqrt{2-\sqrt{2}}}\right)}{4 \sqrt{2 \left(2-\sqrt{2}\right)}}","-\frac{\log \left(x^2-\sqrt{2-\sqrt{2}} x+1\right)}{8 \sqrt{2 \left(2-\sqrt{2}\right)}}+\frac{\log \left(x^2+\sqrt{2-\sqrt{2}} x+1\right)}{8 \sqrt{2 \left(2-\sqrt{2}\right)}}+\frac{\log \left(x^2-\sqrt{2+\sqrt{2}} x+1\right)}{8 \sqrt{2 \left(2+\sqrt{2}\right)}}-\frac{\log \left(x^2+\sqrt{2+\sqrt{2}} x+1\right)}{8 \sqrt{2 \left(2+\sqrt{2}\right)}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}}-2 x}{\sqrt{2+\sqrt{2}}}\right)}{4 \sqrt{2 \left(2+\sqrt{2}\right)}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}}-2 x}{\sqrt{2-\sqrt{2}}}\right)}{4 \sqrt{2 \left(2-\sqrt{2}\right)}}-\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2-\sqrt{2}}}{\sqrt{2+\sqrt{2}}}\right)}{4 \sqrt{2 \left(2+\sqrt{2}\right)}}+\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2+\sqrt{2}}}{\sqrt{2-\sqrt{2}}}\right)}{4 \sqrt{2 \left(2-\sqrt{2}\right)}}",1,"ArcTan[(Sqrt[2 - Sqrt[2]] - 2*x)/Sqrt[2 + Sqrt[2]]]/(4*Sqrt[2*(2 + Sqrt[2])]) - ArcTan[(Sqrt[2 + Sqrt[2]] - 2*x)/Sqrt[2 - Sqrt[2]]]/(4*Sqrt[2*(2 - Sqrt[2])]) - ArcTan[(Sqrt[2 - Sqrt[2]] + 2*x)/Sqrt[2 + Sqrt[2]]]/(4*Sqrt[2*(2 + Sqrt[2])]) + ArcTan[(Sqrt[2 + Sqrt[2]] + 2*x)/Sqrt[2 - Sqrt[2]]]/(4*Sqrt[2*(2 - Sqrt[2])]) - Log[1 - Sqrt[2 - Sqrt[2]]*x + x^2]/(8*Sqrt[2*(2 - Sqrt[2])]) + Log[1 + Sqrt[2 - Sqrt[2]]*x + x^2]/(8*Sqrt[2*(2 - Sqrt[2])]) + Log[1 - Sqrt[2 + Sqrt[2]]*x + x^2]/(8*Sqrt[2*(2 + Sqrt[2])]) - Log[1 + Sqrt[2 + Sqrt[2]]*x + x^2]/(8*Sqrt[2*(2 + Sqrt[2])])","A",19,7,11,0.6364,1,"{299, 1127, 1161, 618, 204, 1164, 628}"
1503,1,339,0,0.2000264,"\int \frac{x^2}{1+x^8} \, dx","Int[x^2/(1 + x^8),x]","\frac{\log \left(x^2-\sqrt{2-\sqrt{2}} x+1\right)}{8 \sqrt{2 \left(2-\sqrt{2}\right)}}-\frac{\log \left(x^2+\sqrt{2-\sqrt{2}} x+1\right)}{8 \sqrt{2 \left(2-\sqrt{2}\right)}}-\frac{\log \left(x^2-\sqrt{2+\sqrt{2}} x+1\right)}{8 \sqrt{2 \left(2+\sqrt{2}\right)}}+\frac{\log \left(x^2+\sqrt{2+\sqrt{2}} x+1\right)}{8 \sqrt{2 \left(2+\sqrt{2}\right)}}+\frac{1}{8} \sqrt{2-\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}}-2 x}{\sqrt{2+\sqrt{2}}}\right)-\frac{1}{8} \sqrt{2+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}}-2 x}{\sqrt{2-\sqrt{2}}}\right)-\frac{1}{8} \sqrt{2-\sqrt{2}} \tan ^{-1}\left(\frac{2 x+\sqrt{2-\sqrt{2}}}{\sqrt{2+\sqrt{2}}}\right)+\frac{1}{8} \sqrt{2+\sqrt{2}} \tan ^{-1}\left(\frac{2 x+\sqrt{2+\sqrt{2}}}{\sqrt{2-\sqrt{2}}}\right)","\frac{\log \left(x^2-\sqrt{2-\sqrt{2}} x+1\right)}{8 \sqrt{2 \left(2-\sqrt{2}\right)}}-\frac{\log \left(x^2+\sqrt{2-\sqrt{2}} x+1\right)}{8 \sqrt{2 \left(2-\sqrt{2}\right)}}-\frac{\log \left(x^2-\sqrt{2+\sqrt{2}} x+1\right)}{8 \sqrt{2 \left(2+\sqrt{2}\right)}}+\frac{\log \left(x^2+\sqrt{2+\sqrt{2}} x+1\right)}{8 \sqrt{2 \left(2+\sqrt{2}\right)}}+\frac{1}{8} \sqrt{2-\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}}-2 x}{\sqrt{2+\sqrt{2}}}\right)-\frac{1}{8} \sqrt{2+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}}-2 x}{\sqrt{2-\sqrt{2}}}\right)-\frac{1}{8} \sqrt{2-\sqrt{2}} \tan ^{-1}\left(\frac{2 x+\sqrt{2-\sqrt{2}}}{\sqrt{2+\sqrt{2}}}\right)+\frac{1}{8} \sqrt{2+\sqrt{2}} \tan ^{-1}\left(\frac{2 x+\sqrt{2+\sqrt{2}}}{\sqrt{2-\sqrt{2}}}\right)",1,"(Sqrt[2 - Sqrt[2]]*ArcTan[(Sqrt[2 - Sqrt[2]] - 2*x)/Sqrt[2 + Sqrt[2]]])/8 - (Sqrt[2 + Sqrt[2]]*ArcTan[(Sqrt[2 + Sqrt[2]] - 2*x)/Sqrt[2 - Sqrt[2]]])/8 - (Sqrt[2 - Sqrt[2]]*ArcTan[(Sqrt[2 - Sqrt[2]] + 2*x)/Sqrt[2 + Sqrt[2]]])/8 + (Sqrt[2 + Sqrt[2]]*ArcTan[(Sqrt[2 + Sqrt[2]] + 2*x)/Sqrt[2 - Sqrt[2]]])/8 + Log[1 - Sqrt[2 - Sqrt[2]]*x + x^2]/(8*Sqrt[2*(2 - Sqrt[2])]) - Log[1 + Sqrt[2 - Sqrt[2]]*x + x^2]/(8*Sqrt[2*(2 - Sqrt[2])]) - Log[1 - Sqrt[2 + Sqrt[2]]*x + x^2]/(8*Sqrt[2*(2 + Sqrt[2])]) + Log[1 + Sqrt[2 + Sqrt[2]]*x + x^2]/(8*Sqrt[2*(2 + Sqrt[2])])","A",19,6,11,0.5455,1,"{299, 1094, 634, 618, 204, 628}"
1504,1,339,0,0.1933772,"\int \frac{1}{1+x^8} \, dx","Int[(1 + x^8)^(-1),x]","-\frac{1}{16} \sqrt{2-\sqrt{2}} \log \left(x^2-\sqrt{2-\sqrt{2}} x+1\right)+\frac{1}{16} \sqrt{2-\sqrt{2}} \log \left(x^2+\sqrt{2-\sqrt{2}} x+1\right)-\frac{1}{16} \sqrt{2+\sqrt{2}} \log \left(x^2-\sqrt{2+\sqrt{2}} x+1\right)+\frac{1}{16} \sqrt{2+\sqrt{2}} \log \left(x^2+\sqrt{2+\sqrt{2}} x+1\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}}-2 x}{\sqrt{2+\sqrt{2}}}\right)}{4 \sqrt{2 \left(2-\sqrt{2}\right)}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}}-2 x}{\sqrt{2-\sqrt{2}}}\right)}{4 \sqrt{2 \left(2+\sqrt{2}\right)}}+\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2-\sqrt{2}}}{\sqrt{2+\sqrt{2}}}\right)}{4 \sqrt{2 \left(2-\sqrt{2}\right)}}+\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2+\sqrt{2}}}{\sqrt{2-\sqrt{2}}}\right)}{4 \sqrt{2 \left(2+\sqrt{2}\right)}}","-\frac{1}{16} \sqrt{2-\sqrt{2}} \log \left(x^2-\sqrt{2-\sqrt{2}} x+1\right)+\frac{1}{16} \sqrt{2-\sqrt{2}} \log \left(x^2+\sqrt{2-\sqrt{2}} x+1\right)-\frac{1}{16} \sqrt{2+\sqrt{2}} \log \left(x^2-\sqrt{2+\sqrt{2}} x+1\right)+\frac{1}{16} \sqrt{2+\sqrt{2}} \log \left(x^2+\sqrt{2+\sqrt{2}} x+1\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}}-2 x}{\sqrt{2+\sqrt{2}}}\right)}{4 \sqrt{2 \left(2-\sqrt{2}\right)}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}}-2 x}{\sqrt{2-\sqrt{2}}}\right)}{4 \sqrt{2 \left(2+\sqrt{2}\right)}}+\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2-\sqrt{2}}}{\sqrt{2+\sqrt{2}}}\right)}{4 \sqrt{2 \left(2-\sqrt{2}\right)}}+\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2+\sqrt{2}}}{\sqrt{2-\sqrt{2}}}\right)}{4 \sqrt{2 \left(2+\sqrt{2}\right)}}",1,"-ArcTan[(Sqrt[2 - Sqrt[2]] - 2*x)/Sqrt[2 + Sqrt[2]]]/(4*Sqrt[2*(2 - Sqrt[2])]) - ArcTan[(Sqrt[2 + Sqrt[2]] - 2*x)/Sqrt[2 - Sqrt[2]]]/(4*Sqrt[2*(2 + Sqrt[2])]) + ArcTan[(Sqrt[2 - Sqrt[2]] + 2*x)/Sqrt[2 + Sqrt[2]]]/(4*Sqrt[2*(2 - Sqrt[2])]) + ArcTan[(Sqrt[2 + Sqrt[2]] + 2*x)/Sqrt[2 - Sqrt[2]]]/(4*Sqrt[2*(2 + Sqrt[2])]) - (Sqrt[2 - Sqrt[2]]*Log[1 - Sqrt[2 - Sqrt[2]]*x + x^2])/16 + (Sqrt[2 - Sqrt[2]]*Log[1 + Sqrt[2 - Sqrt[2]]*x + x^2])/16 - (Sqrt[2 + Sqrt[2]]*Log[1 - Sqrt[2 + Sqrt[2]]*x + x^2])/16 + (Sqrt[2 + Sqrt[2]]*Log[1 + Sqrt[2 + Sqrt[2]]*x + x^2])/16","A",19,6,7,0.8571,1,"{213, 1169, 634, 618, 204, 628}"
1505,1,344,0,0.1931161,"\int \frac{1}{x^2 \left(1+x^8\right)} \, dx","Int[1/(x^2*(1 + x^8)),x]","-\frac{1}{16} \sqrt{2-\sqrt{2}} \log \left(x^2-\sqrt{2-\sqrt{2}} x+1\right)+\frac{1}{16} \sqrt{2-\sqrt{2}} \log \left(x^2+\sqrt{2-\sqrt{2}} x+1\right)-\frac{1}{16} \sqrt{2+\sqrt{2}} \log \left(x^2-\sqrt{2+\sqrt{2}} x+1\right)+\frac{1}{16} \sqrt{2+\sqrt{2}} \log \left(x^2+\sqrt{2+\sqrt{2}} x+1\right)-\frac{1}{x}+\frac{\tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}}-2 x}{\sqrt{2+\sqrt{2}}}\right)}{4 \sqrt{2 \left(2-\sqrt{2}\right)}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}}-2 x}{\sqrt{2-\sqrt{2}}}\right)}{4 \sqrt{2 \left(2+\sqrt{2}\right)}}-\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2-\sqrt{2}}}{\sqrt{2+\sqrt{2}}}\right)}{4 \sqrt{2 \left(2-\sqrt{2}\right)}}-\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2+\sqrt{2}}}{\sqrt{2-\sqrt{2}}}\right)}{4 \sqrt{2 \left(2+\sqrt{2}\right)}}","-\frac{1}{16} \sqrt{2-\sqrt{2}} \log \left(x^2-\sqrt{2-\sqrt{2}} x+1\right)+\frac{1}{16} \sqrt{2-\sqrt{2}} \log \left(x^2+\sqrt{2-\sqrt{2}} x+1\right)-\frac{1}{16} \sqrt{2+\sqrt{2}} \log \left(x^2-\sqrt{2+\sqrt{2}} x+1\right)+\frac{1}{16} \sqrt{2+\sqrt{2}} \log \left(x^2+\sqrt{2+\sqrt{2}} x+1\right)-\frac{1}{x}+\frac{\tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}}-2 x}{\sqrt{2+\sqrt{2}}}\right)}{4 \sqrt{2 \left(2-\sqrt{2}\right)}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}}-2 x}{\sqrt{2-\sqrt{2}}}\right)}{4 \sqrt{2 \left(2+\sqrt{2}\right)}}-\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2-\sqrt{2}}}{\sqrt{2+\sqrt{2}}}\right)}{4 \sqrt{2 \left(2-\sqrt{2}\right)}}-\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2+\sqrt{2}}}{\sqrt{2-\sqrt{2}}}\right)}{4 \sqrt{2 \left(2+\sqrt{2}\right)}}",1,"-x^(-1) + ArcTan[(Sqrt[2 - Sqrt[2]] - 2*x)/Sqrt[2 + Sqrt[2]]]/(4*Sqrt[2*(2 - Sqrt[2])]) + ArcTan[(Sqrt[2 + Sqrt[2]] - 2*x)/Sqrt[2 - Sqrt[2]]]/(4*Sqrt[2*(2 + Sqrt[2])]) - ArcTan[(Sqrt[2 - Sqrt[2]] + 2*x)/Sqrt[2 + Sqrt[2]]]/(4*Sqrt[2*(2 - Sqrt[2])]) - ArcTan[(Sqrt[2 + Sqrt[2]] + 2*x)/Sqrt[2 - Sqrt[2]]]/(4*Sqrt[2*(2 + Sqrt[2])]) - (Sqrt[2 - Sqrt[2]]*Log[1 - Sqrt[2 - Sqrt[2]]*x + x^2])/16 + (Sqrt[2 - Sqrt[2]]*Log[1 + Sqrt[2 - Sqrt[2]]*x + x^2])/16 - (Sqrt[2 + Sqrt[2]]*Log[1 - Sqrt[2 + Sqrt[2]]*x + x^2])/16 + (Sqrt[2 + Sqrt[2]]*Log[1 + Sqrt[2 + Sqrt[2]]*x + x^2])/16","A",22,8,11,0.7273,1,"{325, 299, 1122, 1169, 634, 618, 204, 628}"
1506,1,354,0,0.1867171,"\int \frac{1}{x^4 \left(1+x^8\right)} \, dx","Int[1/(x^4*(1 + x^8)),x]","-\frac{1}{3 x^3}+\frac{\log \left(x^2-\sqrt{2-\sqrt{2}} x+1\right)}{8 \sqrt{2 \left(2-\sqrt{2}\right)}}-\frac{\log \left(x^2+\sqrt{2-\sqrt{2}} x+1\right)}{8 \sqrt{2 \left(2-\sqrt{2}\right)}}-\frac{\log \left(x^2-\sqrt{2+\sqrt{2}} x+1\right)}{8 \sqrt{2 \left(2+\sqrt{2}\right)}}+\frac{\log \left(x^2+\sqrt{2+\sqrt{2}} x+1\right)}{8 \sqrt{2 \left(2+\sqrt{2}\right)}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}}-2 x}{\sqrt{2+\sqrt{2}}}\right)}{4 \sqrt{2 \left(2+\sqrt{2}\right)}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}}-2 x}{\sqrt{2-\sqrt{2}}}\right)}{4 \sqrt{2 \left(2-\sqrt{2}\right)}}+\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2-\sqrt{2}}}{\sqrt{2+\sqrt{2}}}\right)}{4 \sqrt{2 \left(2+\sqrt{2}\right)}}-\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2+\sqrt{2}}}{\sqrt{2-\sqrt{2}}}\right)}{4 \sqrt{2 \left(2-\sqrt{2}\right)}}","-\frac{1}{3 x^3}+\frac{\log \left(x^2-\sqrt{2-\sqrt{2}} x+1\right)}{8 \sqrt{2 \left(2-\sqrt{2}\right)}}-\frac{\log \left(x^2+\sqrt{2-\sqrt{2}} x+1\right)}{8 \sqrt{2 \left(2-\sqrt{2}\right)}}-\frac{\log \left(x^2-\sqrt{2+\sqrt{2}} x+1\right)}{8 \sqrt{2 \left(2+\sqrt{2}\right)}}+\frac{\log \left(x^2+\sqrt{2+\sqrt{2}} x+1\right)}{8 \sqrt{2 \left(2+\sqrt{2}\right)}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}}-2 x}{\sqrt{2+\sqrt{2}}}\right)}{4 \sqrt{2 \left(2+\sqrt{2}\right)}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}}-2 x}{\sqrt{2-\sqrt{2}}}\right)}{4 \sqrt{2 \left(2-\sqrt{2}\right)}}+\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2-\sqrt{2}}}{\sqrt{2+\sqrt{2}}}\right)}{4 \sqrt{2 \left(2+\sqrt{2}\right)}}-\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2+\sqrt{2}}}{\sqrt{2-\sqrt{2}}}\right)}{4 \sqrt{2 \left(2-\sqrt{2}\right)}}",1,"-1/(3*x^3) - ArcTan[(Sqrt[2 - Sqrt[2]] - 2*x)/Sqrt[2 + Sqrt[2]]]/(4*Sqrt[2*(2 + Sqrt[2])]) + ArcTan[(Sqrt[2 + Sqrt[2]] - 2*x)/Sqrt[2 - Sqrt[2]]]/(4*Sqrt[2*(2 - Sqrt[2])]) + ArcTan[(Sqrt[2 - Sqrt[2]] + 2*x)/Sqrt[2 + Sqrt[2]]]/(4*Sqrt[2*(2 + Sqrt[2])]) - ArcTan[(Sqrt[2 + Sqrt[2]] + 2*x)/Sqrt[2 - Sqrt[2]]]/(4*Sqrt[2*(2 - Sqrt[2])]) + Log[1 - Sqrt[2 - Sqrt[2]]*x + x^2]/(8*Sqrt[2*(2 - Sqrt[2])]) - Log[1 + Sqrt[2 - Sqrt[2]]*x + x^2]/(8*Sqrt[2*(2 - Sqrt[2])]) - Log[1 - Sqrt[2 + Sqrt[2]]*x + x^2]/(8*Sqrt[2*(2 + Sqrt[2])]) + Log[1 + Sqrt[2 + Sqrt[2]]*x + x^2]/(8*Sqrt[2*(2 + Sqrt[2])])","A",20,8,11,0.7273,1,"{325, 299, 1127, 1161, 618, 204, 1164, 628}"
1507,1,346,0,0.1655065,"\int \frac{1}{x^6 \left(1+x^8\right)} \, dx","Int[1/(x^6*(1 + x^8)),x]","-\frac{1}{5 x^5}-\frac{\log \left(x^2-\sqrt{2-\sqrt{2}} x+1\right)}{8 \sqrt{2 \left(2-\sqrt{2}\right)}}+\frac{\log \left(x^2+\sqrt{2-\sqrt{2}} x+1\right)}{8 \sqrt{2 \left(2-\sqrt{2}\right)}}+\frac{\log \left(x^2-\sqrt{2+\sqrt{2}} x+1\right)}{8 \sqrt{2 \left(2+\sqrt{2}\right)}}-\frac{\log \left(x^2+\sqrt{2+\sqrt{2}} x+1\right)}{8 \sqrt{2 \left(2+\sqrt{2}\right)}}-\frac{1}{8} \sqrt{2-\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}}-2 x}{\sqrt{2+\sqrt{2}}}\right)+\frac{1}{8} \sqrt{2+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}}-2 x}{\sqrt{2-\sqrt{2}}}\right)+\frac{1}{8} \sqrt{2-\sqrt{2}} \tan ^{-1}\left(\frac{2 x+\sqrt{2-\sqrt{2}}}{\sqrt{2+\sqrt{2}}}\right)-\frac{1}{8} \sqrt{2+\sqrt{2}} \tan ^{-1}\left(\frac{2 x+\sqrt{2+\sqrt{2}}}{\sqrt{2-\sqrt{2}}}\right)","-\frac{1}{5 x^5}-\frac{\log \left(x^2-\sqrt{2-\sqrt{2}} x+1\right)}{8 \sqrt{2 \left(2-\sqrt{2}\right)}}+\frac{\log \left(x^2+\sqrt{2-\sqrt{2}} x+1\right)}{8 \sqrt{2 \left(2-\sqrt{2}\right)}}+\frac{\log \left(x^2-\sqrt{2+\sqrt{2}} x+1\right)}{8 \sqrt{2 \left(2+\sqrt{2}\right)}}-\frac{\log \left(x^2+\sqrt{2+\sqrt{2}} x+1\right)}{8 \sqrt{2 \left(2+\sqrt{2}\right)}}-\frac{1}{8} \sqrt{2-\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}}-2 x}{\sqrt{2+\sqrt{2}}}\right)+\frac{1}{8} \sqrt{2+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}}-2 x}{\sqrt{2-\sqrt{2}}}\right)+\frac{1}{8} \sqrt{2-\sqrt{2}} \tan ^{-1}\left(\frac{2 x+\sqrt{2-\sqrt{2}}}{\sqrt{2+\sqrt{2}}}\right)-\frac{1}{8} \sqrt{2+\sqrt{2}} \tan ^{-1}\left(\frac{2 x+\sqrt{2+\sqrt{2}}}{\sqrt{2-\sqrt{2}}}\right)",1,"-1/(5*x^5) - (Sqrt[2 - Sqrt[2]]*ArcTan[(Sqrt[2 - Sqrt[2]] - 2*x)/Sqrt[2 + Sqrt[2]]])/8 + (Sqrt[2 + Sqrt[2]]*ArcTan[(Sqrt[2 + Sqrt[2]] - 2*x)/Sqrt[2 - Sqrt[2]]])/8 + (Sqrt[2 - Sqrt[2]]*ArcTan[(Sqrt[2 - Sqrt[2]] + 2*x)/Sqrt[2 + Sqrt[2]]])/8 - (Sqrt[2 + Sqrt[2]]*ArcTan[(Sqrt[2 + Sqrt[2]] + 2*x)/Sqrt[2 - Sqrt[2]]])/8 - Log[1 - Sqrt[2 - Sqrt[2]]*x + x^2]/(8*Sqrt[2*(2 - Sqrt[2])]) + Log[1 + Sqrt[2 - Sqrt[2]]*x + x^2]/(8*Sqrt[2*(2 - Sqrt[2])]) + Log[1 - Sqrt[2 + Sqrt[2]]*x + x^2]/(8*Sqrt[2*(2 + Sqrt[2])]) - Log[1 + Sqrt[2 + Sqrt[2]]*x + x^2]/(8*Sqrt[2*(2 + Sqrt[2])])","A",20,7,11,0.6364,1,"{325, 299, 1094, 634, 618, 204, 628}"
1508,1,346,0,0.185894,"\int \frac{1}{x^8 \left(1+x^8\right)} \, dx","Int[1/(x^8*(1 + x^8)),x]","-\frac{1}{7 x^7}+\frac{1}{16} \sqrt{2-\sqrt{2}} \log \left(x^2-\sqrt{2-\sqrt{2}} x+1\right)-\frac{1}{16} \sqrt{2-\sqrt{2}} \log \left(x^2+\sqrt{2-\sqrt{2}} x+1\right)+\frac{1}{16} \sqrt{2+\sqrt{2}} \log \left(x^2-\sqrt{2+\sqrt{2}} x+1\right)-\frac{1}{16} \sqrt{2+\sqrt{2}} \log \left(x^2+\sqrt{2+\sqrt{2}} x+1\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}}-2 x}{\sqrt{2+\sqrt{2}}}\right)}{4 \sqrt{2 \left(2-\sqrt{2}\right)}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}}-2 x}{\sqrt{2-\sqrt{2}}}\right)}{4 \sqrt{2 \left(2+\sqrt{2}\right)}}-\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2-\sqrt{2}}}{\sqrt{2+\sqrt{2}}}\right)}{4 \sqrt{2 \left(2-\sqrt{2}\right)}}-\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2+\sqrt{2}}}{\sqrt{2-\sqrt{2}}}\right)}{4 \sqrt{2 \left(2+\sqrt{2}\right)}}","-\frac{1}{7 x^7}+\frac{1}{16} \sqrt{2-\sqrt{2}} \log \left(x^2-\sqrt{2-\sqrt{2}} x+1\right)-\frac{1}{16} \sqrt{2-\sqrt{2}} \log \left(x^2+\sqrt{2-\sqrt{2}} x+1\right)+\frac{1}{16} \sqrt{2+\sqrt{2}} \log \left(x^2-\sqrt{2+\sqrt{2}} x+1\right)-\frac{1}{16} \sqrt{2+\sqrt{2}} \log \left(x^2+\sqrt{2+\sqrt{2}} x+1\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}}-2 x}{\sqrt{2+\sqrt{2}}}\right)}{4 \sqrt{2 \left(2-\sqrt{2}\right)}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}}-2 x}{\sqrt{2-\sqrt{2}}}\right)}{4 \sqrt{2 \left(2+\sqrt{2}\right)}}-\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2-\sqrt{2}}}{\sqrt{2+\sqrt{2}}}\right)}{4 \sqrt{2 \left(2-\sqrt{2}\right)}}-\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2+\sqrt{2}}}{\sqrt{2-\sqrt{2}}}\right)}{4 \sqrt{2 \left(2+\sqrt{2}\right)}}",1,"-1/(7*x^7) + ArcTan[(Sqrt[2 - Sqrt[2]] - 2*x)/Sqrt[2 + Sqrt[2]]]/(4*Sqrt[2*(2 - Sqrt[2])]) + ArcTan[(Sqrt[2 + Sqrt[2]] - 2*x)/Sqrt[2 - Sqrt[2]]]/(4*Sqrt[2*(2 + Sqrt[2])]) - ArcTan[(Sqrt[2 - Sqrt[2]] + 2*x)/Sqrt[2 + Sqrt[2]]]/(4*Sqrt[2*(2 - Sqrt[2])]) - ArcTan[(Sqrt[2 + Sqrt[2]] + 2*x)/Sqrt[2 - Sqrt[2]]]/(4*Sqrt[2*(2 + Sqrt[2])]) + (Sqrt[2 - Sqrt[2]]*Log[1 - Sqrt[2 - Sqrt[2]]*x + x^2])/16 - (Sqrt[2 - Sqrt[2]]*Log[1 + Sqrt[2 - Sqrt[2]]*x + x^2])/16 + (Sqrt[2 + Sqrt[2]]*Log[1 - Sqrt[2 + Sqrt[2]]*x + x^2])/16 - (Sqrt[2 + Sqrt[2]]*Log[1 + Sqrt[2 + Sqrt[2]]*x + x^2])/16","A",20,7,11,0.6364,1,"{325, 213, 1169, 634, 618, 204, 628}"
1509,1,25,0,0.0076866,"\int x^3 \sqrt{1+x^8} \, dx","Int[x^3*Sqrt[1 + x^8],x]","\frac{1}{8} \sqrt{x^8+1} x^4+\frac{1}{8} \sinh ^{-1}\left(x^4\right)","\frac{1}{8} \sqrt{x^8+1} x^4+\frac{1}{8} \sinh ^{-1}\left(x^4\right)",1,"(x^4*Sqrt[1 + x^8])/8 + ArcSinh[x^4]/8","A",3,3,13,0.2308,1,"{275, 195, 215}"
1510,1,62,0,0.0245337,"\int x \sqrt{1+x^8} \, dx","Int[x*Sqrt[1 + x^8],x]","\frac{1}{6} \sqrt{x^8+1} x^2+\frac{\left(x^4+1\right) \sqrt{\frac{x^8+1}{\left(x^4+1\right)^2}} F\left(2 \tan ^{-1}\left(x^2\right)|\frac{1}{2}\right)}{6 \sqrt{x^8+1}}","\frac{1}{6} \sqrt{x^8+1} x^2+\frac{\left(x^4+1\right) \sqrt{\frac{x^8+1}{\left(x^4+1\right)^2}} F\left(2 \tan ^{-1}\left(x^2\right)|\frac{1}{2}\right)}{6 \sqrt{x^8+1}}",1,"(x^2*Sqrt[1 + x^8])/6 + ((1 + x^4)*Sqrt[(1 + x^8)/(1 + x^4)^2]*EllipticF[2*ArcTan[x^2], 1/2])/(6*Sqrt[1 + x^8])","A",3,3,11,0.2727,1,"{275, 195, 220}"
1511,1,28,0,0.0109673,"\int \frac{\sqrt{1+x^8}}{x} \, dx","Int[Sqrt[1 + x^8]/x,x]","\frac{\sqrt{x^8+1}}{4}-\frac{1}{4} \tanh ^{-1}\left(\sqrt{x^8+1}\right)","\frac{\sqrt{x^8+1}}{4}-\frac{1}{4} \tanh ^{-1}\left(\sqrt{x^8+1}\right)",1,"Sqrt[1 + x^8]/4 - ArcTanh[Sqrt[1 + x^8]]/4","A",4,4,13,0.3077,1,"{266, 50, 63, 207}"
1512,1,125,0,0.0546132,"\int \frac{\sqrt{1+x^8}}{x^3} \, dx","Int[Sqrt[1 + x^8]/x^3,x]","\frac{\sqrt{x^8+1} x^2}{x^4+1}-\frac{\sqrt{x^8+1}}{2 x^2}+\frac{\left(x^4+1\right) \sqrt{\frac{x^8+1}{\left(x^4+1\right)^2}} F\left(2 \tan ^{-1}\left(x^2\right)|\frac{1}{2}\right)}{2 \sqrt{x^8+1}}-\frac{\left(x^4+1\right) \sqrt{\frac{x^8+1}{\left(x^4+1\right)^2}} E\left(2 \tan ^{-1}\left(x^2\right)|\frac{1}{2}\right)}{\sqrt{x^8+1}}","\frac{\sqrt{x^8+1} x^2}{x^4+1}-\frac{\sqrt{x^8+1}}{2 x^2}+\frac{\left(x^4+1\right) \sqrt{\frac{x^8+1}{\left(x^4+1\right)^2}} F\left(2 \tan ^{-1}\left(x^2\right)|\frac{1}{2}\right)}{2 \sqrt{x^8+1}}-\frac{\left(x^4+1\right) \sqrt{\frac{x^8+1}{\left(x^4+1\right)^2}} E\left(2 \tan ^{-1}\left(x^2\right)|\frac{1}{2}\right)}{\sqrt{x^8+1}}",1,"-Sqrt[1 + x^8]/(2*x^2) + (x^2*Sqrt[1 + x^8])/(1 + x^4) - ((1 + x^4)*Sqrt[(1 + x^8)/(1 + x^4)^2]*EllipticE[2*ArcTan[x^2], 1/2])/Sqrt[1 + x^8] + ((1 + x^4)*Sqrt[(1 + x^8)/(1 + x^4)^2]*EllipticF[2*ArcTan[x^2], 1/2])/(2*Sqrt[1 + x^8])","A",5,5,13,0.3846,1,"{275, 277, 305, 220, 1196}"
1513,1,35,0,0.0120813,"\int x^3 \sqrt{-2+x^8} \, dx","Int[x^3*Sqrt[-2 + x^8],x]","\frac{1}{8} x^4 \sqrt{x^8-2}-\frac{1}{4} \tanh ^{-1}\left(\frac{x^4}{\sqrt{x^8-2}}\right)","\frac{1}{8} x^4 \sqrt{x^8-2}-\frac{1}{4} \tanh ^{-1}\left(\frac{x^4}{\sqrt{x^8-2}}\right)",1,"(x^4*Sqrt[-2 + x^8])/8 - ArcTanh[x^4/Sqrt[-2 + x^8]]/4","A",4,4,13,0.3077,1,"{275, 195, 217, 206}"
1514,1,41,0,0.0162791,"\int \frac{x^{19}}{\sqrt{1+x^8}} \, dx","Int[x^19/Sqrt[1 + x^8],x]","\frac{1}{16} \sqrt{x^8+1} x^{12}-\frac{3}{32} \sqrt{x^8+1} x^4+\frac{3}{32} \sinh ^{-1}\left(x^4\right)","\frac{1}{16} \sqrt{x^8+1} x^{12}-\frac{3}{32} \sqrt{x^8+1} x^4+\frac{3}{32} \sinh ^{-1}\left(x^4\right)",1,"(-3*x^4*Sqrt[1 + x^8])/32 + (x^12*Sqrt[1 + x^8])/16 + (3*ArcSinh[x^4])/32","A",4,3,13,0.2308,1,"{275, 321, 215}"
1515,1,27,0,0.0104585,"\int \frac{x^{15}}{\sqrt{1+x^8}} \, dx","Int[x^15/Sqrt[1 + x^8],x]","\frac{1}{12} \left(x^8+1\right)^{3/2}-\frac{\sqrt{x^8+1}}{4}","\frac{1}{12} \left(x^8+1\right)^{3/2}-\frac{\sqrt{x^8+1}}{4}",1,"-Sqrt[1 + x^8]/4 + (1 + x^8)^(3/2)/12","A",3,2,13,0.1538,1,"{266, 43}"
1516,1,25,0,0.0095592,"\int \frac{x^{11}}{\sqrt{1+x^8}} \, dx","Int[x^11/Sqrt[1 + x^8],x]","\frac{1}{8} x^4 \sqrt{x^8+1}-\frac{1}{8} \sinh ^{-1}\left(x^4\right)","\frac{1}{8} x^4 \sqrt{x^8+1}-\frac{1}{8} \sinh ^{-1}\left(x^4\right)",1,"(x^4*Sqrt[1 + x^8])/8 - ArcSinh[x^4]/8","A",3,3,13,0.2308,1,"{275, 321, 215}"
1517,1,13,0,0.0025551,"\int \frac{x^7}{\sqrt{1+x^8}} \, dx","Int[x^7/Sqrt[1 + x^8],x]","\frac{\sqrt{x^8+1}}{4}","\frac{\sqrt{x^8+1}}{4}",1,"Sqrt[1 + x^8]/4","A",1,1,13,0.07692,1,"{261}"
1518,1,8,0,0.0033625,"\int \frac{x^3}{\sqrt{1+x^8}} \, dx","Int[x^3/Sqrt[1 + x^8],x]","\frac{1}{4} \sinh ^{-1}\left(x^4\right)","\frac{1}{4} \sinh ^{-1}\left(x^4\right)",1,"ArcSinh[x^4]/4","A",2,2,13,0.1538,1,"{275, 215}"
1519,1,14,0,0.0068982,"\int \frac{1}{x \sqrt{1+x^8}} \, dx","Int[1/(x*Sqrt[1 + x^8]),x]","-\frac{1}{4} \tanh ^{-1}\left(\sqrt{x^8+1}\right)","-\frac{1}{4} \tanh ^{-1}\left(\sqrt{x^8+1}\right)",1,"-ArcTanh[Sqrt[1 + x^8]]/4","A",3,3,13,0.2308,1,"{266, 63, 207}"
1520,1,16,0,0.0028306,"\int \frac{1}{x^5 \sqrt{1+x^8}} \, dx","Int[1/(x^5*Sqrt[1 + x^8]),x]","-\frac{\sqrt{x^8+1}}{4 x^4}","-\frac{\sqrt{x^8+1}}{4 x^4}",1,"-Sqrt[1 + x^8]/(4*x^4)","A",1,1,13,0.07692,1,"{264}"
1521,1,31,0,0.0110578,"\int \frac{1}{x^9 \sqrt{1+x^8}} \, dx","Int[1/(x^9*Sqrt[1 + x^8]),x]","\frac{1}{8} \tanh ^{-1}\left(\sqrt{x^8+1}\right)-\frac{\sqrt{x^8+1}}{8 x^8}","\frac{1}{8} \tanh ^{-1}\left(\sqrt{x^8+1}\right)-\frac{\sqrt{x^8+1}}{8 x^8}",1,"-Sqrt[1 + x^8]/(8*x^8) + ArcTanh[Sqrt[1 + x^8]]/8","A",4,4,13,0.3077,1,"{266, 51, 63, 207}"
1522,1,33,0,0.00632,"\int \frac{1}{x^{13} \sqrt{1+x^8}} \, dx","Int[1/(x^13*Sqrt[1 + x^8]),x]","\frac{\sqrt{x^8+1}}{6 x^4}-\frac{\sqrt{x^8+1}}{12 x^{12}}","\frac{\sqrt{x^8+1}}{6 x^4}-\frac{\sqrt{x^8+1}}{12 x^{12}}",1,"-Sqrt[1 + x^8]/(12*x^12) + Sqrt[1 + x^8]/(6*x^4)","A",2,2,13,0.1538,1,"{271, 264}"
1523,1,47,0,0.0163496,"\int \frac{1}{x^{17} \sqrt{1+x^8}} \, dx","Int[1/(x^17*Sqrt[1 + x^8]),x]","\frac{3 \sqrt{x^8+1}}{32 x^8}-\frac{\sqrt{x^8+1}}{16 x^{16}}-\frac{3}{32} \tanh ^{-1}\left(\sqrt{x^8+1}\right)","\frac{3 \sqrt{x^8+1}}{32 x^8}-\frac{\sqrt{x^8+1}}{16 x^{16}}-\frac{3}{32} \tanh ^{-1}\left(\sqrt{x^8+1}\right)",1,"-Sqrt[1 + x^8]/(16*x^16) + (3*Sqrt[1 + x^8])/(32*x^8) - (3*ArcTanh[Sqrt[1 + x^8]])/32","A",5,4,13,0.3077,1,"{266, 51, 63, 207}"
1524,1,130,0,0.0529887,"\int \frac{x^{13}}{\sqrt{1+x^8}} \, dx","Int[x^13/Sqrt[1 + x^8],x]","\frac{1}{10} \sqrt{x^8+1} x^6-\frac{3 \sqrt{x^8+1} x^2}{10 \left(x^4+1\right)}-\frac{3 \left(x^4+1\right) \sqrt{\frac{x^8+1}{\left(x^4+1\right)^2}} F\left(2 \tan ^{-1}\left(x^2\right)|\frac{1}{2}\right)}{20 \sqrt{x^8+1}}+\frac{3 \left(x^4+1\right) \sqrt{\frac{x^8+1}{\left(x^4+1\right)^2}} E\left(2 \tan ^{-1}\left(x^2\right)|\frac{1}{2}\right)}{10 \sqrt{x^8+1}}","\frac{1}{10} \sqrt{x^8+1} x^6-\frac{3 \sqrt{x^8+1} x^2}{10 \left(x^4+1\right)}-\frac{3 \left(x^4+1\right) \sqrt{\frac{x^8+1}{\left(x^4+1\right)^2}} F\left(2 \tan ^{-1}\left(x^2\right)|\frac{1}{2}\right)}{20 \sqrt{x^8+1}}+\frac{3 \left(x^4+1\right) \sqrt{\frac{x^8+1}{\left(x^4+1\right)^2}} E\left(2 \tan ^{-1}\left(x^2\right)|\frac{1}{2}\right)}{10 \sqrt{x^8+1}}",1,"(x^6*Sqrt[1 + x^8])/10 - (3*x^2*Sqrt[1 + x^8])/(10*(1 + x^4)) + (3*(1 + x^4)*Sqrt[(1 + x^8)/(1 + x^4)^2]*EllipticE[2*ArcTan[x^2], 1/2])/(10*Sqrt[1 + x^8]) - (3*(1 + x^4)*Sqrt[(1 + x^8)/(1 + x^4)^2]*EllipticF[2*ArcTan[x^2], 1/2])/(20*Sqrt[1 + x^8])","A",5,5,13,0.3846,1,"{275, 321, 305, 220, 1196}"
1525,1,62,0,0.0239049,"\int \frac{x^9}{\sqrt{1+x^8}} \, dx","Int[x^9/Sqrt[1 + x^8],x]","\frac{1}{6} x^2 \sqrt{x^8+1}-\frac{\left(x^4+1\right) \sqrt{\frac{x^8+1}{\left(x^4+1\right)^2}} F\left(2 \tan ^{-1}\left(x^2\right)|\frac{1}{2}\right)}{12 \sqrt{x^8+1}}","\frac{1}{6} x^2 \sqrt{x^8+1}-\frac{\left(x^4+1\right) \sqrt{\frac{x^8+1}{\left(x^4+1\right)^2}} F\left(2 \tan ^{-1}\left(x^2\right)|\frac{1}{2}\right)}{12 \sqrt{x^8+1}}",1,"(x^2*Sqrt[1 + x^8])/6 - ((1 + x^4)*Sqrt[(1 + x^8)/(1 + x^4)^2]*EllipticF[2*ArcTan[x^2], 1/2])/(12*Sqrt[1 + x^8])","A",3,3,13,0.2308,1,"{275, 321, 220}"
1526,1,114,0,0.0407318,"\int \frac{x^5}{\sqrt{1+x^8}} \, dx","Int[x^5/Sqrt[1 + x^8],x]","\frac{\sqrt{x^8+1} x^2}{2 \left(x^4+1\right)}+\frac{\left(x^4+1\right) \sqrt{\frac{x^8+1}{\left(x^4+1\right)^2}} F\left(2 \tan ^{-1}\left(x^2\right)|\frac{1}{2}\right)}{4 \sqrt{x^8+1}}-\frac{\left(x^4+1\right) \sqrt{\frac{x^8+1}{\left(x^4+1\right)^2}} E\left(2 \tan ^{-1}\left(x^2\right)|\frac{1}{2}\right)}{2 \sqrt{x^8+1}}","\frac{\sqrt{x^8+1} x^2}{2 \left(x^4+1\right)}+\frac{\left(x^4+1\right) \sqrt{\frac{x^8+1}{\left(x^4+1\right)^2}} F\left(2 \tan ^{-1}\left(x^2\right)|\frac{1}{2}\right)}{4 \sqrt{x^8+1}}-\frac{\left(x^4+1\right) \sqrt{\frac{x^8+1}{\left(x^4+1\right)^2}} E\left(2 \tan ^{-1}\left(x^2\right)|\frac{1}{2}\right)}{2 \sqrt{x^8+1}}",1,"(x^2*Sqrt[1 + x^8])/(2*(1 + x^4)) - ((1 + x^4)*Sqrt[(1 + x^8)/(1 + x^4)^2]*EllipticE[2*ArcTan[x^2], 1/2])/(2*Sqrt[1 + x^8]) + ((1 + x^4)*Sqrt[(1 + x^8)/(1 + x^4)^2]*EllipticF[2*ArcTan[x^2], 1/2])/(4*Sqrt[1 + x^8])","A",4,4,13,0.3077,1,"{275, 305, 220, 1196}"
1527,1,45,0,0.0152446,"\int \frac{x}{\sqrt{1+x^8}} \, dx","Int[x/Sqrt[1 + x^8],x]","\frac{\left(x^4+1\right) \sqrt{\frac{x^8+1}{\left(x^4+1\right)^2}} F\left(2 \tan ^{-1}\left(x^2\right)|\frac{1}{2}\right)}{4 \sqrt{x^8+1}}","\frac{\left(x^4+1\right) \sqrt{\frac{x^8+1}{\left(x^4+1\right)^2}} F\left(2 \tan ^{-1}\left(x^2\right)|\frac{1}{2}\right)}{4 \sqrt{x^8+1}}",1,"((1 + x^4)*Sqrt[(1 + x^8)/(1 + x^4)^2]*EllipticF[2*ArcTan[x^2], 1/2])/(4*Sqrt[1 + x^8])","A",2,2,11,0.1818,1,"{275, 220}"
1528,1,130,0,0.0457453,"\int \frac{1}{x^3 \sqrt{1+x^8}} \, dx","Int[1/(x^3*Sqrt[1 + x^8]),x]","\frac{\sqrt{x^8+1} x^2}{2 \left(x^4+1\right)}-\frac{\sqrt{x^8+1}}{2 x^2}+\frac{\left(x^4+1\right) \sqrt{\frac{x^8+1}{\left(x^4+1\right)^2}} F\left(2 \tan ^{-1}\left(x^2\right)|\frac{1}{2}\right)}{4 \sqrt{x^8+1}}-\frac{\left(x^4+1\right) \sqrt{\frac{x^8+1}{\left(x^4+1\right)^2}} E\left(2 \tan ^{-1}\left(x^2\right)|\frac{1}{2}\right)}{2 \sqrt{x^8+1}}","\frac{\sqrt{x^8+1} x^2}{2 \left(x^4+1\right)}-\frac{\sqrt{x^8+1}}{2 x^2}+\frac{\left(x^4+1\right) \sqrt{\frac{x^8+1}{\left(x^4+1\right)^2}} F\left(2 \tan ^{-1}\left(x^2\right)|\frac{1}{2}\right)}{4 \sqrt{x^8+1}}-\frac{\left(x^4+1\right) \sqrt{\frac{x^8+1}{\left(x^4+1\right)^2}} E\left(2 \tan ^{-1}\left(x^2\right)|\frac{1}{2}\right)}{2 \sqrt{x^8+1}}",1,"-Sqrt[1 + x^8]/(2*x^2) + (x^2*Sqrt[1 + x^8])/(2*(1 + x^4)) - ((1 + x^4)*Sqrt[(1 + x^8)/(1 + x^4)^2]*EllipticE[2*ArcTan[x^2], 1/2])/(2*Sqrt[1 + x^8]) + ((1 + x^4)*Sqrt[(1 + x^8)/(1 + x^4)^2]*EllipticF[2*ArcTan[x^2], 1/2])/(4*Sqrt[1 + x^8])","A",5,5,13,0.3846,1,"{275, 325, 305, 220, 1196}"
1529,1,62,0,0.0244289,"\int \frac{1}{x^7 \sqrt{1+x^8}} \, dx","Int[1/(x^7*Sqrt[1 + x^8]),x]","-\frac{\sqrt{x^8+1}}{6 x^6}-\frac{\left(x^4+1\right) \sqrt{\frac{x^8+1}{\left(x^4+1\right)^2}} F\left(2 \tan ^{-1}\left(x^2\right)|\frac{1}{2}\right)}{12 \sqrt{x^8+1}}","-\frac{\sqrt{x^8+1}}{6 x^6}-\frac{\left(x^4+1\right) \sqrt{\frac{x^8+1}{\left(x^4+1\right)^2}} F\left(2 \tan ^{-1}\left(x^2\right)|\frac{1}{2}\right)}{12 \sqrt{x^8+1}}",1,"-Sqrt[1 + x^8]/(6*x^6) - ((1 + x^4)*Sqrt[(1 + x^8)/(1 + x^4)^2]*EllipticF[2*ArcTan[x^2], 1/2])/(12*Sqrt[1 + x^8])","A",3,3,13,0.2308,1,"{275, 325, 220}"
1530,1,239,0,0.0671675,"\int \frac{x^{10}}{\sqrt{1+x^8}} \, dx","Int[x^10/Sqrt[1 + x^8],x]","\frac{1}{7} \sqrt{x^8+1} x^3+\frac{3 \sqrt{\frac{\left(x^2+1\right)^2}{x^2}} \sqrt{-\frac{x^8+1}{x^4}} x^3 F\left(\sin ^{-1}\left(\frac{1}{2} \sqrt{-\frac{\sqrt{2} x^4-2 x^2+\sqrt{2}}{x^2}}\right)|-2 \left(1-\sqrt{2}\right)\right)}{14 \sqrt{2+\sqrt{2}} \left(x^2+1\right) \sqrt{x^8+1}}+\frac{3 \sqrt{-\frac{\left(1-x^2\right)^2}{x^2}} \sqrt{-\frac{x^8+1}{x^4}} x^3 F\left(\sin ^{-1}\left(\frac{1}{2} \sqrt{\frac{\sqrt{2} x^4+2 x^2+\sqrt{2}}{x^2}}\right)|-2 \left(1-\sqrt{2}\right)\right)}{14 \sqrt{2+\sqrt{2}} \left(1-x^2\right) \sqrt{x^8+1}}","\frac{1}{7} \sqrt{x^8+1} x^3+\frac{3 \sqrt{\frac{\left(x^2+1\right)^2}{x^2}} \sqrt{-\frac{x^8+1}{x^4}} x^3 F\left(\sin ^{-1}\left(\frac{1}{2} \sqrt{-\frac{\sqrt{2} x^4-2 x^2+\sqrt{2}}{x^2}}\right)|-2 \left(1-\sqrt{2}\right)\right)}{14 \sqrt{2+\sqrt{2}} \left(x^2+1\right) \sqrt{x^8+1}}+\frac{3 \sqrt{-\frac{\left(1-x^2\right)^2}{x^2}} \sqrt{-\frac{x^8+1}{x^4}} x^3 F\left(\sin ^{-1}\left(\frac{1}{2} \sqrt{\frac{\sqrt{2} x^4+2 x^2+\sqrt{2}}{x^2}}\right)|-2 \left(1-\sqrt{2}\right)\right)}{14 \sqrt{2+\sqrt{2}} \left(1-x^2\right) \sqrt{x^8+1}}",1,"(x^3*Sqrt[1 + x^8])/7 + (3*x^3*Sqrt[(1 + x^2)^2/x^2]*Sqrt[-((1 + x^8)/x^4)]*EllipticF[ArcSin[Sqrt[-((Sqrt[2] - 2*x^2 + Sqrt[2]*x^4)/x^2)]/2], -2*(1 - Sqrt[2])])/(14*Sqrt[2 + Sqrt[2]]*(1 + x^2)*Sqrt[1 + x^8]) + (3*x^3*Sqrt[-((1 - x^2)^2/x^2)]*Sqrt[-((1 + x^8)/x^4)]*EllipticF[ArcSin[Sqrt[(Sqrt[2] + 2*x^2 + Sqrt[2]*x^4)/x^2]/2], -2*(1 - Sqrt[2])])/(14*Sqrt[2 + Sqrt[2]]*(1 - x^2)*Sqrt[1 + x^8])","A",4,3,13,0.2308,1,"{321, 309, 1883}"
1531,1,237,0,0.0614129,"\int \frac{x^8}{\sqrt{1+x^8}} \, dx","Int[x^8/Sqrt[1 + x^8],x]","\frac{1}{5} \sqrt{x^8+1} x-\frac{\sqrt{\frac{\left(x^2+1\right)^2}{x^2}} \sqrt{-\frac{x^8+1}{x^4}} x^3 F\left(\sin ^{-1}\left(\frac{1}{2} \sqrt{-\frac{\sqrt{2} x^4-2 x^2+\sqrt{2}}{x^2}}\right)|-2 \left(1-\sqrt{2}\right)\right)}{10 \sqrt{2+\sqrt{2}} \left(x^2+1\right) \sqrt{x^8+1}}+\frac{\sqrt{-\frac{\left(1-x^2\right)^2}{x^2}} \sqrt{-\frac{x^8+1}{x^4}} x^3 F\left(\sin ^{-1}\left(\frac{1}{2} \sqrt{\frac{\sqrt{2} x^4+2 x^2+\sqrt{2}}{x^2}}\right)|-2 \left(1-\sqrt{2}\right)\right)}{10 \sqrt{2+\sqrt{2}} \left(1-x^2\right) \sqrt{x^8+1}}","\frac{1}{5} \sqrt{x^8+1} x-\frac{\sqrt{\frac{\left(x^2+1\right)^2}{x^2}} \sqrt{-\frac{x^8+1}{x^4}} x^3 F\left(\sin ^{-1}\left(\frac{1}{2} \sqrt{-\frac{\sqrt{2} x^4-2 x^2+\sqrt{2}}{x^2}}\right)|-2 \left(1-\sqrt{2}\right)\right)}{10 \sqrt{2+\sqrt{2}} \left(x^2+1\right) \sqrt{x^8+1}}+\frac{\sqrt{-\frac{\left(1-x^2\right)^2}{x^2}} \sqrt{-\frac{x^8+1}{x^4}} x^3 F\left(\sin ^{-1}\left(\frac{1}{2} \sqrt{\frac{\sqrt{2} x^4+2 x^2+\sqrt{2}}{x^2}}\right)|-2 \left(1-\sqrt{2}\right)\right)}{10 \sqrt{2+\sqrt{2}} \left(1-x^2\right) \sqrt{x^8+1}}",1,"(x*Sqrt[1 + x^8])/5 - (x^3*Sqrt[(1 + x^2)^2/x^2]*Sqrt[-((1 + x^8)/x^4)]*EllipticF[ArcSin[Sqrt[-((Sqrt[2] - 2*x^2 + Sqrt[2]*x^4)/x^2)]/2], -2*(1 - Sqrt[2])])/(10*Sqrt[2 + Sqrt[2]]*(1 + x^2)*Sqrt[1 + x^8]) + (x^3*Sqrt[-((1 - x^2)^2/x^2)]*Sqrt[-((1 + x^8)/x^4)]*EllipticF[ArcSin[Sqrt[(Sqrt[2] + 2*x^2 + Sqrt[2]*x^4)/x^2]/2], -2*(1 - Sqrt[2])])/(10*Sqrt[2 + Sqrt[2]]*(1 - x^2)*Sqrt[1 + x^8])","A",4,3,13,0.2308,1,"{321, 226, 1883}"
1532,1,22,0,0.0043918,"\int \frac{x^6}{\sqrt{1+x^8}} \, dx","Int[x^6/Sqrt[1 + x^8],x]","\frac{1}{7} x^7 \, _2F_1\left(\frac{1}{2},\frac{7}{8};\frac{15}{8};-x^8\right)","\frac{1}{7} x^7 \, _2F_1\left(\frac{1}{2},\frac{7}{8};\frac{15}{8};-x^8\right)",1,"(x^7*Hypergeometric2F1[1/2, 7/8, 15/8, -x^8])/7","A",1,1,13,0.07692,1,"{364}"
1533,1,22,0,0.0049126,"\int \frac{x^4}{\sqrt{1+x^8}} \, dx","Int[x^4/Sqrt[1 + x^8],x]","\frac{1}{5} x^5 \, _2F_1\left(\frac{1}{2},\frac{5}{8};\frac{13}{8};-x^8\right)","\frac{1}{5} x^5 \, _2F_1\left(\frac{1}{2},\frac{5}{8};\frac{13}{8};-x^8\right)",1,"(x^5*Hypergeometric2F1[1/2, 5/8, 13/8, -x^8])/5","A",1,1,13,0.07692,1,"{364}"
1534,1,223,0,0.0476937,"\int \frac{x^2}{\sqrt{1+x^8}} \, dx","Int[x^2/Sqrt[1 + x^8],x]","-\frac{\sqrt{\frac{\left(x^2+1\right)^2}{x^2}} \sqrt{-\frac{x^8+1}{x^4}} x^3 F\left(\sin ^{-1}\left(\frac{1}{2} \sqrt{-\frac{\sqrt{2} x^4-2 x^2+\sqrt{2}}{x^2}}\right)|-2 \left(1-\sqrt{2}\right)\right)}{2 \sqrt{2+\sqrt{2}} \left(x^2+1\right) \sqrt{x^8+1}}-\frac{\sqrt{-\frac{\left(1-x^2\right)^2}{x^2}} \sqrt{-\frac{x^8+1}{x^4}} x^3 F\left(\sin ^{-1}\left(\frac{1}{2} \sqrt{\frac{\sqrt{2} x^4+2 x^2+\sqrt{2}}{x^2}}\right)|-2 \left(1-\sqrt{2}\right)\right)}{2 \sqrt{2+\sqrt{2}} \left(1-x^2\right) \sqrt{x^8+1}}","-\frac{\sqrt{\frac{\left(x^2+1\right)^2}{x^2}} \sqrt{-\frac{x^8+1}{x^4}} x^3 F\left(\sin ^{-1}\left(\frac{1}{2} \sqrt{-\frac{\sqrt{2} x^4-2 x^2+\sqrt{2}}{x^2}}\right)|-2 \left(1-\sqrt{2}\right)\right)}{2 \sqrt{2+\sqrt{2}} \left(x^2+1\right) \sqrt{x^8+1}}-\frac{\sqrt{-\frac{\left(1-x^2\right)^2}{x^2}} \sqrt{-\frac{x^8+1}{x^4}} x^3 F\left(\sin ^{-1}\left(\frac{1}{2} \sqrt{\frac{\sqrt{2} x^4+2 x^2+\sqrt{2}}{x^2}}\right)|-2 \left(1-\sqrt{2}\right)\right)}{2 \sqrt{2+\sqrt{2}} \left(1-x^2\right) \sqrt{x^8+1}}",1,"-(x^3*Sqrt[(1 + x^2)^2/x^2]*Sqrt[-((1 + x^8)/x^4)]*EllipticF[ArcSin[Sqrt[-((Sqrt[2] - 2*x^2 + Sqrt[2]*x^4)/x^2)]/2], -2*(1 - Sqrt[2])])/(2*Sqrt[2 + Sqrt[2]]*(1 + x^2)*Sqrt[1 + x^8]) - (x^3*Sqrt[-((1 - x^2)^2/x^2)]*Sqrt[-((1 + x^8)/x^4)]*EllipticF[ArcSin[Sqrt[(Sqrt[2] + 2*x^2 + Sqrt[2]*x^4)/x^2]/2], -2*(1 - Sqrt[2])])/(2*Sqrt[2 + Sqrt[2]]*(1 - x^2)*Sqrt[1 + x^8])","A",3,2,13,0.1538,1,"{309, 1883}"
1535,1,223,0,0.0457847,"\int \frac{1}{\sqrt{1+x^8}} \, dx","Int[1/Sqrt[1 + x^8],x]","\frac{x^3 \sqrt{\frac{\left(x^2+1\right)^2}{x^2}} \sqrt{-\frac{x^8+1}{x^4}} F\left(\sin ^{-1}\left(\frac{1}{2} \sqrt{-\frac{\sqrt{2} x^4-2 x^2+\sqrt{2}}{x^2}}\right)|-2 \left(1-\sqrt{2}\right)\right)}{2 \sqrt{2+\sqrt{2}} \left(x^2+1\right) \sqrt{x^8+1}}-\frac{x^3 \sqrt{-\frac{\left(1-x^2\right)^2}{x^2}} \sqrt{-\frac{x^8+1}{x^4}} F\left(\sin ^{-1}\left(\frac{1}{2} \sqrt{\frac{\sqrt{2} x^4+2 x^2+\sqrt{2}}{x^2}}\right)|-2 \left(1-\sqrt{2}\right)\right)}{2 \sqrt{2+\sqrt{2}} \left(1-x^2\right) \sqrt{x^8+1}}","\frac{x^3 \sqrt{\frac{\left(x^2+1\right)^2}{x^2}} \sqrt{-\frac{x^8+1}{x^4}} F\left(\sin ^{-1}\left(\frac{1}{2} \sqrt{-\frac{\sqrt{2} x^4-2 x^2+\sqrt{2}}{x^2}}\right)|-2 \left(1-\sqrt{2}\right)\right)}{2 \sqrt{2+\sqrt{2}} \left(x^2+1\right) \sqrt{x^8+1}}-\frac{x^3 \sqrt{-\frac{\left(1-x^2\right)^2}{x^2}} \sqrt{-\frac{x^8+1}{x^4}} F\left(\sin ^{-1}\left(\frac{1}{2} \sqrt{\frac{\sqrt{2} x^4+2 x^2+\sqrt{2}}{x^2}}\right)|-2 \left(1-\sqrt{2}\right)\right)}{2 \sqrt{2+\sqrt{2}} \left(1-x^2\right) \sqrt{x^8+1}}",1,"(x^3*Sqrt[(1 + x^2)^2/x^2]*Sqrt[-((1 + x^8)/x^4)]*EllipticF[ArcSin[Sqrt[-((Sqrt[2] - 2*x^2 + Sqrt[2]*x^4)/x^2)]/2], -2*(1 - Sqrt[2])])/(2*Sqrt[2 + Sqrt[2]]*(1 + x^2)*Sqrt[1 + x^8]) - (x^3*Sqrt[-((1 - x^2)^2/x^2)]*Sqrt[-((1 + x^8)/x^4)]*EllipticF[ArcSin[Sqrt[(Sqrt[2] + 2*x^2 + Sqrt[2]*x^4)/x^2]/2], -2*(1 - Sqrt[2])])/(2*Sqrt[2 + Sqrt[2]]*(1 - x^2)*Sqrt[1 + x^8])","A",3,2,9,0.2222,1,"{226, 1883}"
1536,1,37,0,0.0086354,"\int \frac{1}{x^2 \sqrt{1+x^8}} \, dx","Int[1/(x^2*Sqrt[1 + x^8]),x]","\frac{3}{7} x^7 \, _2F_1\left(\frac{1}{2},\frac{7}{8};\frac{15}{8};-x^8\right)-\frac{\sqrt{x^8+1}}{x}","\frac{3}{7} x^7 \, _2F_1\left(\frac{1}{2},\frac{7}{8};\frac{15}{8};-x^8\right)-\frac{\sqrt{x^8+1}}{x}",1,"-(Sqrt[1 + x^8]/x) + (3*x^7*Hypergeometric2F1[1/2, 7/8, 15/8, -x^8])/7","A",2,2,13,0.1538,1,"{325, 364}"
1537,1,39,0,0.0084266,"\int \frac{1}{x^4 \sqrt{1+x^8}} \, dx","Int[1/(x^4*Sqrt[1 + x^8]),x]","\frac{1}{15} x^5 \, _2F_1\left(\frac{1}{2},\frac{5}{8};\frac{13}{8};-x^8\right)-\frac{\sqrt{x^8+1}}{3 x^3}","\frac{1}{15} x^5 \, _2F_1\left(\frac{1}{2},\frac{5}{8};\frac{13}{8};-x^8\right)-\frac{\sqrt{x^8+1}}{3 x^3}",1,"-Sqrt[1 + x^8]/(3*x^3) + (x^5*Hypergeometric2F1[1/2, 5/8, 13/8, -x^8])/15","A",2,2,13,0.1538,1,"{325, 364}"
1538,1,239,0,0.0644307,"\int \frac{1}{x^6 \sqrt{1+x^8}} \, dx","Int[1/(x^6*Sqrt[1 + x^8]),x]","-\frac{\sqrt{x^8+1}}{5 x^5}+\frac{\sqrt{\frac{\left(x^2+1\right)^2}{x^2}} \sqrt{-\frac{x^8+1}{x^4}} x^3 F\left(\sin ^{-1}\left(\frac{1}{2} \sqrt{-\frac{\sqrt{2} x^4-2 x^2+\sqrt{2}}{x^2}}\right)|-2 \left(1-\sqrt{2}\right)\right)}{10 \sqrt{2+\sqrt{2}} \left(x^2+1\right) \sqrt{x^8+1}}+\frac{\sqrt{-\frac{\left(1-x^2\right)^2}{x^2}} \sqrt{-\frac{x^8+1}{x^4}} x^3 F\left(\sin ^{-1}\left(\frac{1}{2} \sqrt{\frac{\sqrt{2} x^4+2 x^2+\sqrt{2}}{x^2}}\right)|-2 \left(1-\sqrt{2}\right)\right)}{10 \sqrt{2+\sqrt{2}} \left(1-x^2\right) \sqrt{x^8+1}}","-\frac{\sqrt{x^8+1}}{5 x^5}+\frac{\sqrt{\frac{\left(x^2+1\right)^2}{x^2}} \sqrt{-\frac{x^8+1}{x^4}} x^3 F\left(\sin ^{-1}\left(\frac{1}{2} \sqrt{-\frac{\sqrt{2} x^4-2 x^2+\sqrt{2}}{x^2}}\right)|-2 \left(1-\sqrt{2}\right)\right)}{10 \sqrt{2+\sqrt{2}} \left(x^2+1\right) \sqrt{x^8+1}}+\frac{\sqrt{-\frac{\left(1-x^2\right)^2}{x^2}} \sqrt{-\frac{x^8+1}{x^4}} x^3 F\left(\sin ^{-1}\left(\frac{1}{2} \sqrt{\frac{\sqrt{2} x^4+2 x^2+\sqrt{2}}{x^2}}\right)|-2 \left(1-\sqrt{2}\right)\right)}{10 \sqrt{2+\sqrt{2}} \left(1-x^2\right) \sqrt{x^8+1}}",1,"-Sqrt[1 + x^8]/(5*x^5) + (x^3*Sqrt[(1 + x^2)^2/x^2]*Sqrt[-((1 + x^8)/x^4)]*EllipticF[ArcSin[Sqrt[-((Sqrt[2] - 2*x^2 + Sqrt[2]*x^4)/x^2)]/2], -2*(1 - Sqrt[2])])/(10*Sqrt[2 + Sqrt[2]]*(1 + x^2)*Sqrt[1 + x^8]) + (x^3*Sqrt[-((1 - x^2)^2/x^2)]*Sqrt[-((1 + x^8)/x^4)]*EllipticF[ArcSin[Sqrt[(Sqrt[2] + 2*x^2 + Sqrt[2]*x^4)/x^2]/2], -2*(1 - Sqrt[2])])/(10*Sqrt[2 + Sqrt[2]]*(1 - x^2)*Sqrt[1 + x^8])","A",4,3,13,0.2308,1,"{325, 309, 1883}"
1539,1,239,0,0.0611552,"\int \frac{1}{x^8 \sqrt{1+x^8}} \, dx","Int[1/(x^8*Sqrt[1 + x^8]),x]","-\frac{\sqrt{x^8+1}}{7 x^7}-\frac{3 \sqrt{\frac{\left(x^2+1\right)^2}{x^2}} \sqrt{-\frac{x^8+1}{x^4}} x^3 F\left(\sin ^{-1}\left(\frac{1}{2} \sqrt{-\frac{\sqrt{2} x^4-2 x^2+\sqrt{2}}{x^2}}\right)|-2 \left(1-\sqrt{2}\right)\right)}{14 \sqrt{2+\sqrt{2}} \left(x^2+1\right) \sqrt{x^8+1}}+\frac{3 \sqrt{-\frac{\left(1-x^2\right)^2}{x^2}} \sqrt{-\frac{x^8+1}{x^4}} x^3 F\left(\sin ^{-1}\left(\frac{1}{2} \sqrt{\frac{\sqrt{2} x^4+2 x^2+\sqrt{2}}{x^2}}\right)|-2 \left(1-\sqrt{2}\right)\right)}{14 \sqrt{2+\sqrt{2}} \left(1-x^2\right) \sqrt{x^8+1}}","-\frac{\sqrt{x^8+1}}{7 x^7}-\frac{3 \sqrt{\frac{\left(x^2+1\right)^2}{x^2}} \sqrt{-\frac{x^8+1}{x^4}} x^3 F\left(\sin ^{-1}\left(\frac{1}{2} \sqrt{-\frac{\sqrt{2} x^4-2 x^2+\sqrt{2}}{x^2}}\right)|-2 \left(1-\sqrt{2}\right)\right)}{14 \sqrt{2+\sqrt{2}} \left(x^2+1\right) \sqrt{x^8+1}}+\frac{3 \sqrt{-\frac{\left(1-x^2\right)^2}{x^2}} \sqrt{-\frac{x^8+1}{x^4}} x^3 F\left(\sin ^{-1}\left(\frac{1}{2} \sqrt{\frac{\sqrt{2} x^4+2 x^2+\sqrt{2}}{x^2}}\right)|-2 \left(1-\sqrt{2}\right)\right)}{14 \sqrt{2+\sqrt{2}} \left(1-x^2\right) \sqrt{x^8+1}}",1,"-Sqrt[1 + x^8]/(7*x^7) - (3*x^3*Sqrt[(1 + x^2)^2/x^2]*Sqrt[-((1 + x^8)/x^4)]*EllipticF[ArcSin[Sqrt[-((Sqrt[2] - 2*x^2 + Sqrt[2]*x^4)/x^2)]/2], -2*(1 - Sqrt[2])])/(14*Sqrt[2 + Sqrt[2]]*(1 + x^2)*Sqrt[1 + x^8]) + (3*x^3*Sqrt[-((1 - x^2)^2/x^2)]*Sqrt[-((1 + x^8)/x^4)]*EllipticF[ArcSin[Sqrt[(Sqrt[2] + 2*x^2 + Sqrt[2]*x^4)/x^2]/2], -2*(1 - Sqrt[2])])/(14*Sqrt[2 + Sqrt[2]]*(1 - x^2)*Sqrt[1 + x^8])","A",4,3,13,0.2308,1,"{325, 226, 1883}"
1540,1,325,0,0.2092609,"\int \frac{1}{1-x^{10}} \, dx","Int[(1 - x^10)^(-1),x]","-\frac{1}{40} \left(1-\sqrt{5}\right) \log \left(x^2-\frac{1}{2} \left(1-\sqrt{5}\right) x+1\right)+\frac{1}{40} \left(1-\sqrt{5}\right) \log \left(x^2+\frac{1}{2} \left(1-\sqrt{5}\right) x+1\right)-\frac{1}{40} \left(1+\sqrt{5}\right) \log \left(x^2-\frac{1}{2} \left(1+\sqrt{5}\right) x+1\right)+\frac{1}{40} \left(1+\sqrt{5}\right) \log \left(x^2+\frac{1}{2} \left(1+\sqrt{5}\right) x+1\right)-\frac{1}{10} \sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\frac{-4 x-\sqrt{5}+1}{\sqrt{2 \left(5+\sqrt{5}\right)}}\right)-\frac{1}{10} \sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \tan ^{-1}\left(\frac{1}{2} \sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} \left(-4 x+\sqrt{5}+1\right)\right)+\frac{1}{10} \sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\frac{4 x-\sqrt{5}+1}{\sqrt{2 \left(5+\sqrt{5}\right)}}\right)+\frac{1}{10} \sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \tan ^{-1}\left(\frac{1}{2} \sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} \left(4 x+\sqrt{5}+1\right)\right)+\frac{1}{5} \tanh ^{-1}(x)","\frac{1}{20} \sqrt{10-2 \sqrt{5}} \tan ^{-1}\left(\frac{\sqrt{10-2 \sqrt{5}} x}{2 \left(1-x^2\right)}\right)+\frac{1}{20} \sqrt{10+2 \sqrt{5}} \tan ^{-1}\left(\frac{\sqrt{10+2 \sqrt{5}} x}{2 \left(1-x^2\right)}\right)+\frac{1}{20} \left(1-\sqrt{5}\right) \tanh ^{-1}\left(\frac{\left(1-\sqrt{5}\right) x}{2 \left(x^2+1\right)}\right)+\frac{1}{20} \left(1+\sqrt{5}\right) \tanh ^{-1}\left(\frac{\left(1+\sqrt{5}\right) x}{2 \left(x^2+1\right)}\right)+\frac{1}{5} \tanh ^{-1}(x)",1,"-(Sqrt[(5 + Sqrt[5])/2]*ArcTan[(1 - Sqrt[5] - 4*x)/Sqrt[2*(5 + Sqrt[5])]])/10 - (Sqrt[(5 - Sqrt[5])/2]*ArcTan[(Sqrt[(5 + Sqrt[5])/10]*(1 + Sqrt[5] - 4*x))/2])/10 + (Sqrt[(5 + Sqrt[5])/2]*ArcTan[(1 - Sqrt[5] + 4*x)/Sqrt[2*(5 + Sqrt[5])]])/10 + (Sqrt[(5 - Sqrt[5])/2]*ArcTan[(Sqrt[(5 + Sqrt[5])/10]*(1 + Sqrt[5] + 4*x))/2])/10 + ArcTanh[x]/5 - ((1 - Sqrt[5])*Log[1 - ((1 - Sqrt[5])*x)/2 + x^2])/40 + ((1 - Sqrt[5])*Log[1 + ((1 - Sqrt[5])*x)/2 + x^2])/40 - ((1 + Sqrt[5])*Log[1 - ((1 + Sqrt[5])*x)/2 + x^2])/40 + ((1 + Sqrt[5])*Log[1 + ((1 + Sqrt[5])*x)/2 + x^2])/40","A",10,6,9,0.6667,1,"{210, 634, 618, 204, 628, 206}"
1541,1,8,0,0.0040674,"\int \frac{x^4}{\sqrt{1-x^{10}}} \, dx","Int[x^4/Sqrt[1 - x^10],x]","\frac{1}{5} \sin ^{-1}\left(x^5\right)","\frac{1}{5} \sin ^{-1}\left(x^5\right)",1,"ArcSin[x^5]/5","A",2,2,15,0.1333,1,"{275, 216}"
1542,1,18,0,0.0077767,"\int \frac{x^4}{\sqrt{-2+x^{10}}} \, dx","Int[x^4/Sqrt[-2 + x^10],x]","\frac{1}{5} \tanh ^{-1}\left(\frac{x^5}{\sqrt{x^{10}-2}}\right)","\frac{1}{5} \tanh ^{-1}\left(\frac{x^5}{\sqrt{x^{10}-2}}\right)",1,"ArcTanh[x^5/Sqrt[-2 + x^10]]/5","A",3,3,13,0.2308,1,"{275, 217, 206}"
1543,1,12,0,0.004958,"\int \frac{x^5}{9+x^{12}} \, dx","Int[x^5/(9 + x^12),x]","\frac{1}{18} \tan ^{-1}\left(\frac{x^6}{3}\right)","\frac{1}{18} \tan ^{-1}\left(\frac{x^6}{3}\right)",1,"ArcTan[x^6/3]/18","A",2,2,11,0.1818,1,"{275, 203}"
1544,1,12,0,0.0054283,"\int \frac{x^5}{9-x^{12}} \, dx","Int[x^5/(9 - x^12),x]","\frac{1}{18} \tanh ^{-1}\left(\frac{x^6}{3}\right)","\frac{1}{18} \tanh ^{-1}\left(\frac{x^6}{3}\right)",1,"ArcTanh[x^6/3]/18","A",2,2,13,0.1538,1,"{275, 206}"
1545,1,29,0,0.0090506,"\int x^5 \sqrt{9+x^{12}} \, dx","Int[x^5*Sqrt[9 + x^12],x]","\frac{1}{12} \sqrt{x^{12}+9} x^6+\frac{3}{4} \sinh ^{-1}\left(\frac{x^6}{3}\right)","\frac{1}{12} \sqrt{x^{12}+9} x^6+\frac{3}{4} \sinh ^{-1}\left(\frac{x^6}{3}\right)",1,"(x^6*Sqrt[9 + x^12])/12 + (3*ArcSinh[x^6/3])/4","A",3,3,13,0.2308,1,"{275, 195, 215}"
1546,1,17,0,0.0114011,"\int \left(a+\frac{b}{x}\right) x^6 \, dx","Int[(a + b/x)*x^6,x]","\frac{a x^7}{7}+\frac{b x^6}{6}","\frac{a x^7}{7}+\frac{b x^6}{6}",1,"(b*x^6)/6 + (a*x^7)/7","A",2,1,11,0.09091,1,"{14}"
1547,1,17,0,0.0097291,"\int \left(a+\frac{b}{x}\right) x^5 \, dx","Int[(a + b/x)*x^5,x]","\frac{a x^6}{6}+\frac{b x^5}{5}","\frac{a x^6}{6}+\frac{b x^5}{5}",1,"(b*x^5)/5 + (a*x^6)/6","A",2,1,11,0.09091,1,"{14}"
1548,1,17,0,0.0091237,"\int \left(a+\frac{b}{x}\right) x^4 \, dx","Int[(a + b/x)*x^4,x]","\frac{a x^5}{5}+\frac{b x^4}{4}","\frac{a x^5}{5}+\frac{b x^4}{4}",1,"(b*x^4)/4 + (a*x^5)/5","A",2,1,11,0.09091,1,"{14}"
1549,1,17,0,0.0076346,"\int \left(a+\frac{b}{x}\right) x^3 \, dx","Int[(a + b/x)*x^3,x]","\frac{a x^4}{4}+\frac{b x^3}{3}","\frac{a x^4}{4}+\frac{b x^3}{3}",1,"(b*x^3)/3 + (a*x^4)/4","A",2,1,11,0.09091,1,"{14}"
1550,1,17,0,0.006411,"\int \left(a+\frac{b}{x}\right) x^2 \, dx","Int[(a + b/x)*x^2,x]","\frac{a x^3}{3}+\frac{b x^2}{2}","\frac{a x^3}{3}+\frac{b x^2}{2}",1,"(b*x^2)/2 + (a*x^3)/3","A",2,1,11,0.09091,1,"{14}"
1551,1,12,0,0.0037697,"\int \left(a+\frac{b}{x}\right) x \, dx","Int[(a + b/x)*x,x]","\frac{a x^2}{2}+b x","\frac{a x^2}{2}+b x",1,"b*x + (a*x^2)/2","A",2,1,9,0.1111,1,"{14}"
1552,1,8,0,0.0019793,"\int \left(a+\frac{b}{x}\right) \, dx","Int[a + b/x,x]","a x+b \log (x)","a x+b \log (x)",1,"a*x + b*Log[x]","A",1,0,7,0,1,"{}"
1553,1,11,0,0.0046539,"\int \frac{a+\frac{b}{x}}{x} \, dx","Int[(a + b/x)/x,x]","a \log (x)-\frac{b}{x}","a \log (x)-\frac{b}{x}",1,"-(b/x) + a*Log[x]","A",2,1,11,0.09091,1,"{14}"
1554,1,15,0,0.0047808,"\int \frac{a+\frac{b}{x}}{x^2} \, dx","Int[(a + b/x)/x^2,x]","-\frac{a}{x}-\frac{b}{2 x^2}","-\frac{a}{x}-\frac{b}{2 x^2}",1,"-b/(2*x^2) - a/x","A",2,1,11,0.09091,1,"{14}"
1555,1,17,0,0.0048012,"\int \frac{a+\frac{b}{x}}{x^3} \, dx","Int[(a + b/x)/x^3,x]","-\frac{a}{2 x^2}-\frac{b}{3 x^3}","-\frac{a}{2 x^2}-\frac{b}{3 x^3}",1,"-b/(3*x^3) - a/(2*x^2)","A",2,1,11,0.09091,1,"{14}"
1556,1,17,0,0.0048105,"\int \frac{a+\frac{b}{x}}{x^4} \, dx","Int[(a + b/x)/x^4,x]","-\frac{a}{3 x^3}-\frac{b}{4 x^4}","-\frac{a}{3 x^3}-\frac{b}{4 x^4}",1,"-b/(4*x^4) - a/(3*x^3)","A",2,1,11,0.09091,1,"{14}"
1557,1,17,0,0.0047732,"\int \frac{a+\frac{b}{x}}{x^5} \, dx","Int[(a + b/x)/x^5,x]","-\frac{a}{4 x^4}-\frac{b}{5 x^5}","-\frac{a}{4 x^4}-\frac{b}{5 x^5}",1,"-b/(5*x^5) - a/(4*x^4)","A",2,1,11,0.09091,1,"{14}"
1558,1,17,0,0.004701,"\int \frac{a+\frac{b}{x}}{x^6} \, dx","Int[(a + b/x)/x^6,x]","-\frac{a}{5 x^5}-\frac{b}{6 x^6}","-\frac{a}{5 x^5}-\frac{b}{6 x^6}",1,"-b/(6*x^6) - a/(5*x^5)","A",2,1,11,0.09091,1,"{14}"
1559,1,30,0,0.0140427,"\int \left(a+\frac{b}{x}\right)^2 x^5 \, dx","Int[(a + b/x)^2*x^5,x]","\frac{a^2 x^6}{6}+\frac{2}{5} a b x^5+\frac{b^2 x^4}{4}","\frac{a^2 x^6}{6}+\frac{2}{5} a b x^5+\frac{b^2 x^4}{4}",1,"(b^2*x^4)/4 + (2*a*b*x^5)/5 + (a^2*x^6)/6","A",3,2,13,0.1538,1,"{263, 43}"
1560,1,30,0,0.013179,"\int \left(a+\frac{b}{x}\right)^2 x^4 \, dx","Int[(a + b/x)^2*x^4,x]","\frac{a^2 x^5}{5}+\frac{1}{2} a b x^4+\frac{b^2 x^3}{3}","\frac{a^2 x^5}{5}+\frac{1}{2} a b x^4+\frac{b^2 x^3}{3}",1,"(b^2*x^3)/3 + (a*b*x^4)/2 + (a^2*x^5)/5","A",3,2,13,0.1538,1,"{263, 43}"
1561,1,30,0,0.012121,"\int \left(a+\frac{b}{x}\right)^2 x^3 \, dx","Int[(a + b/x)^2*x^3,x]","\frac{a^2 x^4}{4}+\frac{2}{3} a b x^3+\frac{b^2 x^2}{2}","\frac{a^2 x^4}{4}+\frac{2}{3} a b x^3+\frac{b^2 x^2}{2}",1,"(b^2*x^2)/2 + (2*a*b*x^3)/3 + (a^2*x^4)/4","A",3,2,13,0.1538,1,"{263, 43}"
1562,1,14,0,0.00388,"\int \left(a+\frac{b}{x}\right)^2 x^2 \, dx","Int[(a + b/x)^2*x^2,x]","\frac{(a x+b)^3}{3 a}","\frac{(a x+b)^3}{3 a}",1,"(b + a*x)^3/(3*a)","A",2,2,13,0.1538,1,"{263, 32}"
1563,1,22,0,0.0080695,"\int \left(a+\frac{b}{x}\right)^2 x \, dx","Int[(a + b/x)^2*x,x]","\frac{a^2 x^2}{2}+2 a b x+b^2 \log (x)","\frac{a^2 x^2}{2}+2 a b x+b^2 \log (x)",1,"2*a*b*x + (a^2*x^2)/2 + b^2*Log[x]","A",3,2,11,0.1818,1,"{263, 43}"
1564,1,20,0,0.0087427,"\int \left(a+\frac{b}{x}\right)^2 \, dx","Int[(a + b/x)^2,x]","a^2 x+2 a b \log (x)-\frac{b^2}{x}","a^2 x+2 a b \log (x)-\frac{b^2}{x}",1,"-(b^2/x) + a^2*x + 2*a*b*Log[x]","A",3,2,9,0.2222,1,"{193, 43}"
1565,1,24,0,0.0105294,"\int \frac{\left(a+\frac{b}{x}\right)^2}{x} \, dx","Int[(a + b/x)^2/x,x]","a^2 \log (x)-\frac{2 a b}{x}-\frac{b^2}{2 x^2}","a^2 \log (x)-\frac{2 a b}{x}-\frac{b^2}{2 x^2}",1,"-b^2/(2*x^2) - (2*a*b)/x + a^2*Log[x]","A",3,2,13,0.1538,1,"{263, 43}"
1566,1,16,0,0.0034732,"\int \frac{\left(a+\frac{b}{x}\right)^2}{x^2} \, dx","Int[(a + b/x)^2/x^2,x]","-\frac{\left(a+\frac{b}{x}\right)^3}{3 b}","-\frac{\left(a+\frac{b}{x}\right)^3}{3 b}",1,"-(a + b/x)^3/(3*b)","A",1,1,13,0.07692,1,"{261}"
1567,1,30,0,0.01058,"\int \frac{\left(a+\frac{b}{x}\right)^2}{x^3} \, dx","Int[(a + b/x)^2/x^3,x]","-\frac{a^2}{2 x^2}-\frac{2 a b}{3 x^3}-\frac{b^2}{4 x^4}","-\frac{a^2}{2 x^2}-\frac{2 a b}{3 x^3}-\frac{b^2}{4 x^4}",1,"-b^2/(4*x^4) - (2*a*b)/(3*x^3) - a^2/(2*x^2)","A",3,2,13,0.1538,1,"{263, 43}"
1568,1,30,0,0.0106251,"\int \frac{\left(a+\frac{b}{x}\right)^2}{x^4} \, dx","Int[(a + b/x)^2/x^4,x]","-\frac{a^2}{3 x^3}-\frac{a b}{2 x^4}-\frac{b^2}{5 x^5}","-\frac{a^2}{3 x^3}-\frac{a b}{2 x^4}-\frac{b^2}{5 x^5}",1,"-b^2/(5*x^5) - (a*b)/(2*x^4) - a^2/(3*x^3)","A",3,2,13,0.1538,1,"{263, 43}"
1569,1,30,0,0.0106383,"\int \frac{\left(a+\frac{b}{x}\right)^2}{x^5} \, dx","Int[(a + b/x)^2/x^5,x]","-\frac{a^2}{4 x^4}-\frac{2 a b}{5 x^5}-\frac{b^2}{6 x^6}","-\frac{a^2}{4 x^4}-\frac{2 a b}{5 x^5}-\frac{b^2}{6 x^6}",1,"-b^2/(6*x^6) - (2*a*b)/(5*x^5) - a^2/(4*x^4)","A",3,2,13,0.1538,1,"{263, 43}"
1570,1,43,0,0.0199591,"\int \left(a+\frac{b}{x}\right)^3 x^6 \, dx","Int[(a + b/x)^3*x^6,x]","\frac{1}{2} a^2 b x^6+\frac{a^3 x^7}{7}+\frac{3}{5} a b^2 x^5+\frac{b^3 x^4}{4}","\frac{1}{2} a^2 b x^6+\frac{a^3 x^7}{7}+\frac{3}{5} a b^2 x^5+\frac{b^3 x^4}{4}",1,"(b^3*x^4)/4 + (3*a*b^2*x^5)/5 + (a^2*b*x^6)/2 + (a^3*x^7)/7","A",3,2,13,0.1538,1,"{263, 43}"
1571,1,43,0,0.0176521,"\int \left(a+\frac{b}{x}\right)^3 x^5 \, dx","Int[(a + b/x)^3*x^5,x]","\frac{3}{5} a^2 b x^5+\frac{a^3 x^6}{6}+\frac{3}{4} a b^2 x^4+\frac{b^3 x^3}{3}","\frac{3}{5} a^2 b x^5+\frac{a^3 x^6}{6}+\frac{3}{4} a b^2 x^4+\frac{b^3 x^3}{3}",1,"(b^3*x^3)/3 + (3*a*b^2*x^4)/4 + (3*a^2*b*x^5)/5 + (a^3*x^6)/6","A",3,2,13,0.1538,1,"{263, 43}"
1572,1,30,0,0.0099667,"\int \left(a+\frac{b}{x}\right)^3 x^4 \, dx","Int[(a + b/x)^3*x^4,x]","\frac{(a x+b)^5}{5 a^2}-\frac{b (a x+b)^4}{4 a^2}","\frac{(a x+b)^5}{5 a^2}-\frac{b (a x+b)^4}{4 a^2}",1,"-(b*(b + a*x)^4)/(4*a^2) + (b + a*x)^5/(5*a^2)","A",3,2,13,0.1538,1,"{263, 43}"
1573,1,14,0,0.0040203,"\int \left(a+\frac{b}{x}\right)^3 x^3 \, dx","Int[(a + b/x)^3*x^3,x]","\frac{(a x+b)^4}{4 a}","\frac{(a x+b)^4}{4 a}",1,"(b + a*x)^4/(4*a)","A",2,2,13,0.1538,1,"{263, 32}"
1574,1,35,0,0.011661,"\int \left(a+\frac{b}{x}\right)^3 x^2 \, dx","Int[(a + b/x)^3*x^2,x]","\frac{3}{2} a^2 b x^2+\frac{a^3 x^3}{3}+3 a b^2 x+b^3 \log (x)","\frac{3}{2} a^2 b x^2+\frac{a^3 x^3}{3}+3 a b^2 x+b^3 \log (x)",1,"3*a*b^2*x + (3*a^2*b*x^2)/2 + (a^3*x^3)/3 + b^3*Log[x]","A",3,2,13,0.1538,1,"{263, 43}"
1575,1,34,0,0.0140042,"\int \left(a+\frac{b}{x}\right)^3 x \, dx","Int[(a + b/x)^3*x,x]","3 a^2 b x+\frac{a^3 x^2}{2}+3 a b^2 \log (x)-\frac{b^3}{x}","3 a^2 b x+\frac{a^3 x^2}{2}+3 a b^2 \log (x)-\frac{b^3}{x}",1,"-(b^3/x) + 3*a^2*b*x + (a^3*x^2)/2 + 3*a*b^2*Log[x]","A",3,2,11,0.1818,1,"{263, 43}"
1576,1,33,0,0.0125911,"\int \left(a+\frac{b}{x}\right)^3 \, dx","Int[(a + b/x)^3,x]","3 a^2 b \log (x)+a^3 x-\frac{3 a b^2}{x}-\frac{b^3}{2 x^2}","3 a^2 b \log (x)+a^3 x-\frac{3 a b^2}{x}-\frac{b^3}{2 x^2}",1,"-b^3/(2*x^2) - (3*a*b^2)/x + a^3*x + 3*a^2*b*Log[x]","A",3,2,9,0.2222,1,"{193, 43}"
1577,1,37,0,0.014899,"\int \frac{\left(a+\frac{b}{x}\right)^3}{x} \, dx","Int[(a + b/x)^3/x,x]","-\frac{3 a^2 b}{x}+a^3 \log (x)-\frac{3 a b^2}{2 x^2}-\frac{b^3}{3 x^3}","-\frac{3 a^2 b}{x}+a^3 \log (x)-\frac{3 a b^2}{2 x^2}-\frac{b^3}{3 x^3}",1,"-b^3/(3*x^3) - (3*a*b^2)/(2*x^2) - (3*a^2*b)/x + a^3*Log[x]","A",3,2,13,0.1538,1,"{263, 43}"
1578,1,16,0,0.0034446,"\int \frac{\left(a+\frac{b}{x}\right)^3}{x^2} \, dx","Int[(a + b/x)^3/x^2,x]","-\frac{\left(a+\frac{b}{x}\right)^4}{4 b}","-\frac{\left(a+\frac{b}{x}\right)^4}{4 b}",1,"-(a + b/x)^4/(4*b)","A",1,1,13,0.07692,1,"{261}"
1579,1,36,0,0.0071368,"\int \frac{\left(a+\frac{b}{x}\right)^3}{x^3} \, dx","Int[(a + b/x)^3/x^3,x]","\frac{a (a x+b)^4}{20 b^2 x^4}-\frac{(a x+b)^4}{5 b x^5}","\frac{a (a x+b)^4}{20 b^2 x^4}-\frac{(a x+b)^4}{5 b x^5}",1,"-(b + a*x)^4/(5*b*x^5) + (a*(b + a*x)^4)/(20*b^2*x^4)","A",3,3,13,0.2308,1,"{263, 45, 37}"
1580,1,43,0,0.0149324,"\int \frac{\left(a+\frac{b}{x}\right)^3}{x^4} \, dx","Int[(a + b/x)^3/x^4,x]","-\frac{3 a^2 b}{4 x^4}-\frac{a^3}{3 x^3}-\frac{3 a b^2}{5 x^5}-\frac{b^3}{6 x^6}","-\frac{3 a^2 b}{4 x^4}-\frac{a^3}{3 x^3}-\frac{3 a b^2}{5 x^5}-\frac{b^3}{6 x^6}",1,"-b^3/(6*x^6) - (3*a*b^2)/(5*x^5) - (3*a^2*b)/(4*x^4) - a^3/(3*x^3)","A",3,2,13,0.1538,1,"{263, 43}"
1581,1,43,0,0.0149061,"\int \frac{\left(a+\frac{b}{x}\right)^3}{x^5} \, dx","Int[(a + b/x)^3/x^5,x]","-\frac{3 a^2 b}{5 x^5}-\frac{a^3}{4 x^4}-\frac{a b^2}{2 x^6}-\frac{b^3}{7 x^7}","-\frac{3 a^2 b}{5 x^5}-\frac{a^3}{4 x^4}-\frac{a b^2}{2 x^6}-\frac{b^3}{7 x^7}",1,"-b^3/(7*x^7) - (a*b^2)/(2*x^6) - (3*a^2*b)/(5*x^5) - a^3/(4*x^4)","A",3,2,13,0.1538,1,"{263, 43}"
1582,1,43,0,0.0145501,"\int \frac{\left(a+\frac{b}{x}\right)^3}{x^6} \, dx","Int[(a + b/x)^3/x^6,x]","-\frac{a^2 b}{2 x^6}-\frac{a^3}{5 x^5}-\frac{3 a b^2}{7 x^7}-\frac{b^3}{8 x^8}","-\frac{a^2 b}{2 x^6}-\frac{a^3}{5 x^5}-\frac{3 a b^2}{7 x^7}-\frac{b^3}{8 x^8}",1,"-b^3/(8*x^8) - (3*a*b^2)/(7*x^7) - (a^2*b)/(2*x^6) - a^3/(5*x^5)","A",3,2,13,0.1538,1,"{263, 43}"
1583,1,106,0,0.0569334,"\int \left(a+\frac{b}{x}\right)^8 x^{16} \, dx","Int[(a + b/x)^8*x^16,x]","\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{1}{2} a^7 b x^{16}+\frac{a^8 x^{17}}{17}+\frac{4}{5} a b^7 x^{10}+\frac{b^8 x^9}{9}","\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{1}{2} a^7 b x^{16}+\frac{a^8 x^{17}}{17}+\frac{4}{5} a b^7 x^{10}+\frac{b^8 x^9}{9}",1,"(b^8*x^9)/9 + (4*a*b^7*x^10)/5 + (28*a^2*b^6*x^11)/11 + (14*a^3*b^5*x^12)/3 + (70*a^4*b^4*x^13)/13 + 4*a^5*b^3*x^14 + (28*a^6*b^2*x^15)/15 + (a^7*b*x^16)/2 + (a^8*x^17)/17","A",3,2,13,0.1538,1,"{263, 43}"
1584,1,106,0,0.0479001,"\int \left(a+\frac{b}{x}\right)^8 x^{15} \, dx","Int[(a + b/x)^8*x^15,x]","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}{15} a^7 b x^{15}+\frac{a^8 x^{16}}{16}+\frac{8}{9} a b^7 x^9+\frac{b^8 x^8}{8}","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}{15} a^7 b x^{15}+\frac{a^8 x^{16}}{16}+\frac{8}{9} a b^7 x^9+\frac{b^8 x^8}{8}",1,"(b^8*x^8)/8 + (8*a*b^7*x^9)/9 + (14*a^2*b^6*x^10)/5 + (56*a^3*b^5*x^11)/11 + (35*a^4*b^4*x^12)/6 + (56*a^5*b^3*x^13)/13 + 2*a^6*b^2*x^14 + (8*a^7*b*x^15)/15 + (a^8*x^16)/16","A",3,2,13,0.1538,1,"{263, 43}"
1585,1,98,0,0.044195,"\int \left(a+\frac{b}{x}\right)^8 x^{13} \, dx","Int[(a + b/x)^8*x^13,x]","\frac{5 b^2 (a x+b)^{12}}{6 a^6}-\frac{10 b^3 (a x+b)^{11}}{11 a^6}+\frac{b^4 (a x+b)^{10}}{2 a^6}-\frac{b^5 (a x+b)^9}{9 a^6}+\frac{(a x+b)^{14}}{14 a^6}-\frac{5 b (a x+b)^{13}}{13 a^6}","\frac{5 b^2 (a x+b)^{12}}{6 a^6}-\frac{10 b^3 (a x+b)^{11}}{11 a^6}+\frac{b^4 (a x+b)^{10}}{2 a^6}-\frac{b^5 (a x+b)^9}{9 a^6}+\frac{(a x+b)^{14}}{14 a^6}-\frac{5 b (a x+b)^{13}}{13 a^6}",1,"-(b^5*(b + a*x)^9)/(9*a^6) + (b^4*(b + a*x)^10)/(2*a^6) - (10*b^3*(b + a*x)^11)/(11*a^6) + (5*b^2*(b + a*x)^12)/(6*a^6) - (5*b*(b + a*x)^13)/(13*a^6) + (b + a*x)^14/(14*a^6)","A",3,2,13,0.1538,1,"{263, 43}"
1586,1,81,0,0.0376675,"\int \left(a+\frac{b}{x}\right)^8 x^{12} \, dx","Int[(a + b/x)^8*x^12,x]","\frac{6 b^2 (a x+b)^{11}}{11 a^5}-\frac{2 b^3 (a x+b)^{10}}{5 a^5}+\frac{b^4 (a x+b)^9}{9 a^5}+\frac{(a x+b)^{13}}{13 a^5}-\frac{b (a x+b)^{12}}{3 a^5}","\frac{6 b^2 (a x+b)^{11}}{11 a^5}-\frac{2 b^3 (a x+b)^{10}}{5 a^5}+\frac{b^4 (a x+b)^9}{9 a^5}+\frac{(a x+b)^{13}}{13 a^5}-\frac{b (a x+b)^{12}}{3 a^5}",1,"(b^4*(b + a*x)^9)/(9*a^5) - (2*b^3*(b + a*x)^10)/(5*a^5) + (6*b^2*(b + a*x)^11)/(11*a^5) - (b*(b + a*x)^12)/(3*a^5) + (b + a*x)^13/(13*a^5)","A",3,2,13,0.1538,1,"{263, 43}"
1587,1,64,0,0.0334422,"\int \left(a+\frac{b}{x}\right)^8 x^{11} \, dx","Int[(a + b/x)^8*x^11,x]","\frac{3 b^2 (a x+b)^{10}}{10 a^4}-\frac{b^3 (a x+b)^9}{9 a^4}+\frac{(a x+b)^{12}}{12 a^4}-\frac{3 b (a x+b)^{11}}{11 a^4}","\frac{3 b^2 (a x+b)^{10}}{10 a^4}-\frac{b^3 (a x+b)^9}{9 a^4}+\frac{(a x+b)^{12}}{12 a^4}-\frac{3 b (a x+b)^{11}}{11 a^4}",1,"-(b^3*(b + a*x)^9)/(9*a^4) + (3*b^2*(b + a*x)^10)/(10*a^4) - (3*b*(b + a*x)^11)/(11*a^4) + (b + a*x)^12/(12*a^4)","A",3,2,13,0.1538,1,"{263, 43}"
1588,1,47,0,0.0282751,"\int \left(a+\frac{b}{x}\right)^8 x^{10} \, dx","Int[(a + b/x)^8*x^10,x]","\frac{b^2 (a x+b)^9}{9 a^3}+\frac{(a x+b)^{11}}{11 a^3}-\frac{b (a x+b)^{10}}{5 a^3}","\frac{b^2 (a x+b)^9}{9 a^3}+\frac{(a x+b)^{11}}{11 a^3}-\frac{b (a x+b)^{10}}{5 a^3}",1,"(b^2*(b + a*x)^9)/(9*a^3) - (b*(b + a*x)^10)/(5*a^3) + (b + a*x)^11/(11*a^3)","A",3,2,13,0.1538,1,"{263, 43}"
1589,1,30,0,0.0102484,"\int \left(a+\frac{b}{x}\right)^8 x^9 \, dx","Int[(a + b/x)^8*x^9,x]","\frac{(a x+b)^{10}}{10 a^2}-\frac{b (a x+b)^9}{9 a^2}","\frac{(a x+b)^{10}}{10 a^2}-\frac{b (a x+b)^9}{9 a^2}",1,"-(b*(b + a*x)^9)/(9*a^2) + (b + a*x)^10/(10*a^2)","A",3,2,13,0.1538,1,"{263, 43}"
1590,1,14,0,0.0038971,"\int \left(a+\frac{b}{x}\right)^8 x^8 \, dx","Int[(a + b/x)^8*x^8,x]","\frac{(a x+b)^9}{9 a}","\frac{(a x+b)^9}{9 a}",1,"(b + a*x)^9/(9*a)","A",2,2,13,0.1538,1,"{263, 32}"
1591,1,98,0,0.0357748,"\int \left(a+\frac{b}{x}\right)^8 x^7 \, dx","Int[(a + b/x)^8*x^7,x]","14 a^2 b^6 x^2+\frac{56}{3} a^3 b^5 x^3+\frac{35}{2} a^4 b^4 x^4+\frac{56}{5} a^5 b^3 x^5+\frac{14}{3} a^6 b^2 x^6+\frac{8}{7} a^7 b x^7+\frac{a^8 x^8}{8}+8 a b^7 x+b^8 \log (x)","14 a^2 b^6 x^2+\frac{56}{3} a^3 b^5 x^3+\frac{35}{2} a^4 b^4 x^4+\frac{56}{5} a^5 b^3 x^5+\frac{14}{3} a^6 b^2 x^6+\frac{8}{7} a^7 b x^7+\frac{a^8 x^8}{8}+8 a b^7 x+b^8 \log (x)",1,"8*a*b^7*x + 14*a^2*b^6*x^2 + (56*a^3*b^5*x^3)/3 + (35*a^4*b^4*x^4)/2 + (56*a^5*b^3*x^5)/5 + (14*a^6*b^2*x^6)/3 + (8*a^7*b*x^7)/7 + (a^8*x^8)/8 + b^8*Log[x]","A",3,2,13,0.1538,1,"{263, 43}"
1592,1,95,0,0.039522,"\int \left(a+\frac{b}{x}\right)^8 x^6 \, dx","Int[(a + b/x)^8*x^6,x]","\frac{28}{5} a^6 b^2 x^5+14 a^5 b^3 x^4+\frac{70}{3} a^4 b^4 x^3+28 a^3 b^5 x^2+28 a^2 b^6 x+\frac{4}{3} a^7 b x^6+\frac{a^8 x^7}{7}+8 a b^7 \log (x)-\frac{b^8}{x}","\frac{28}{5} a^6 b^2 x^5+14 a^5 b^3 x^4+\frac{70}{3} a^4 b^4 x^3+28 a^3 b^5 x^2+28 a^2 b^6 x+\frac{4}{3} a^7 b x^6+\frac{a^8 x^7}{7}+8 a b^7 \log (x)-\frac{b^8}{x}",1,"-(b^8/x) + 28*a^2*b^6*x + 28*a^3*b^5*x^2 + (70*a^4*b^4*x^3)/3 + 14*a^5*b^3*x^4 + (28*a^6*b^2*x^5)/5 + (4*a^7*b*x^6)/3 + (a^8*x^7)/7 + 8*a*b^7*Log[x]","A",3,2,13,0.1538,1,"{263, 43}"
1593,1,95,0,0.0389603,"\int \left(a+\frac{b}{x}\right)^8 x^5 \, dx","Int[(a + b/x)^8*x^5,x]","7 a^6 b^2 x^4+\frac{56}{3} a^5 b^3 x^3+35 a^4 b^4 x^2+56 a^3 b^5 x+28 a^2 b^6 \log (x)+\frac{8}{5} a^7 b x^5+\frac{a^8 x^6}{6}-\frac{8 a b^7}{x}-\frac{b^8}{2 x^2}","7 a^6 b^2 x^4+\frac{56}{3} a^5 b^3 x^3+35 a^4 b^4 x^2+56 a^3 b^5 x+28 a^2 b^6 \log (x)+\frac{8}{5} a^7 b x^5+\frac{a^8 x^6}{6}-\frac{8 a b^7}{x}-\frac{b^8}{2 x^2}",1,"-b^8/(2*x^2) - (8*a*b^7)/x + 56*a^3*b^5*x + 35*a^4*b^4*x^2 + (56*a^5*b^3*x^3)/3 + 7*a^6*b^2*x^4 + (8*a^7*b*x^5)/5 + (a^8*x^6)/6 + 28*a^2*b^6*Log[x]","A",3,2,13,0.1538,1,"{263, 43}"
1594,1,93,0,0.0396267,"\int \left(a+\frac{b}{x}\right)^8 x^4 \, dx","Int[(a + b/x)^8*x^4,x]","\frac{28}{3} a^6 b^2 x^3+28 a^5 b^3 x^2+70 a^4 b^4 x-\frac{28 a^2 b^6}{x}+56 a^3 b^5 \log (x)+2 a^7 b x^4+\frac{a^8 x^5}{5}-\frac{4 a b^7}{x^2}-\frac{b^8}{3 x^3}","\frac{28}{3} a^6 b^2 x^3+28 a^5 b^3 x^2+70 a^4 b^4 x-\frac{28 a^2 b^6}{x}+56 a^3 b^5 \log (x)+2 a^7 b x^4+\frac{a^8 x^5}{5}-\frac{4 a b^7}{x^2}-\frac{b^8}{3 x^3}",1,"-b^8/(3*x^3) - (4*a*b^7)/x^2 - (28*a^2*b^6)/x + 70*a^4*b^4*x + 28*a^5*b^3*x^2 + (28*a^6*b^2*x^3)/3 + 2*a^7*b*x^4 + (a^8*x^5)/5 + 56*a^3*b^5*Log[x]","A",3,2,13,0.1538,1,"{263, 43}"
1595,1,95,0,0.0392652,"\int \left(a+\frac{b}{x}\right)^8 x^3 \, dx","Int[(a + b/x)^8*x^3,x]","14 a^6 b^2 x^2-\frac{14 a^2 b^6}{x^2}+56 a^5 b^3 x-\frac{56 a^3 b^5}{x}+70 a^4 b^4 \log (x)+\frac{8}{3} a^7 b x^3+\frac{a^8 x^4}{4}-\frac{8 a b^7}{3 x^3}-\frac{b^8}{4 x^4}","14 a^6 b^2 x^2-\frac{14 a^2 b^6}{x^2}+56 a^5 b^3 x-\frac{56 a^3 b^5}{x}+70 a^4 b^4 \log (x)+\frac{8}{3} a^7 b x^3+\frac{a^8 x^4}{4}-\frac{8 a b^7}{3 x^3}-\frac{b^8}{4 x^4}",1,"-b^8/(4*x^4) - (8*a*b^7)/(3*x^3) - (14*a^2*b^6)/x^2 - (56*a^3*b^5)/x + 56*a^5*b^3*x + 14*a^6*b^2*x^2 + (8*a^7*b*x^3)/3 + (a^8*x^4)/4 + 70*a^4*b^4*Log[x]","A",3,2,13,0.1538,1,"{263, 43}"
1596,1,93,0,0.0431441,"\int \left(a+\frac{b}{x}\right)^8 x^2 \, dx","Int[(a + b/x)^8*x^2,x]","-\frac{28 a^3 b^5}{x^2}-\frac{28 a^2 b^6}{3 x^3}+28 a^6 b^2 x-\frac{70 a^4 b^4}{x}+56 a^5 b^3 \log (x)+4 a^7 b x^2+\frac{a^8 x^3}{3}-\frac{2 a b^7}{x^4}-\frac{b^8}{5 x^5}","-\frac{28 a^3 b^5}{x^2}-\frac{28 a^2 b^6}{3 x^3}+28 a^6 b^2 x-\frac{70 a^4 b^4}{x}+56 a^5 b^3 \log (x)+4 a^7 b x^2+\frac{a^8 x^3}{3}-\frac{2 a b^7}{x^4}-\frac{b^8}{5 x^5}",1,"-b^8/(5*x^5) - (2*a*b^7)/x^4 - (28*a^2*b^6)/(3*x^3) - (28*a^3*b^5)/x^2 - (70*a^4*b^4)/x + 28*a^6*b^2*x + 4*a^7*b*x^2 + (a^8*x^3)/3 + 56*a^5*b^3*Log[x]","A",3,2,13,0.1538,1,"{263, 43}"
1597,1,95,0,0.0392794,"\int \left(a+\frac{b}{x}\right)^8 x \, dx","Int[(a + b/x)^8*x,x]","-\frac{35 a^4 b^4}{x^2}-\frac{56 a^3 b^5}{3 x^3}-\frac{7 a^2 b^6}{x^4}-\frac{56 a^5 b^3}{x}+28 a^6 b^2 \log (x)+8 a^7 b x+\frac{a^8 x^2}{2}-\frac{8 a b^7}{5 x^5}-\frac{b^8}{6 x^6}","-\frac{35 a^4 b^4}{x^2}-\frac{56 a^3 b^5}{3 x^3}-\frac{7 a^2 b^6}{x^4}-\frac{56 a^5 b^3}{x}+28 a^6 b^2 \log (x)+8 a^7 b x+\frac{a^8 x^2}{2}-\frac{8 a b^7}{5 x^5}-\frac{b^8}{6 x^6}",1,"-b^8/(6*x^6) - (8*a*b^7)/(5*x^5) - (7*a^2*b^6)/x^4 - (56*a^3*b^5)/(3*x^3) - (35*a^4*b^4)/x^2 - (56*a^5*b^3)/x + 8*a^7*b*x + (a^8*x^2)/2 + 28*a^6*b^2*Log[x]","A",3,2,11,0.1818,1,"{263, 43}"
1598,1,94,0,0.0395111,"\int \left(a+\frac{b}{x}\right)^8 \, dx","Int[(a + b/x)^8,x]","-\frac{28 a^5 b^3}{x^2}-\frac{70 a^4 b^4}{3 x^3}-\frac{14 a^3 b^5}{x^4}-\frac{28 a^2 b^6}{5 x^5}-\frac{28 a^6 b^2}{x}+8 a^7 b \log (x)+a^8 x-\frac{4 a b^7}{3 x^6}-\frac{b^8}{7 x^7}","-\frac{28 a^5 b^3}{x^2}-\frac{70 a^4 b^4}{3 x^3}-\frac{14 a^3 b^5}{x^4}-\frac{28 a^2 b^6}{5 x^5}-\frac{28 a^6 b^2}{x}+8 a^7 b \log (x)+a^8 x-\frac{4 a b^7}{3 x^6}-\frac{b^8}{7 x^7}",1,"-b^8/(7*x^7) - (4*a*b^7)/(3*x^6) - (28*a^2*b^6)/(5*x^5) - (14*a^3*b^5)/x^4 - (70*a^4*b^4)/(3*x^3) - (28*a^5*b^3)/x^2 - (28*a^6*b^2)/x + a^8*x + 8*a^7*b*Log[x]","A",3,2,9,0.2222,1,"{193, 43}"
1599,1,100,0,0.0420873,"\int \frac{\left(a+\frac{b}{x}\right)^8}{x} \, dx","Int[(a + b/x)^8/x,x]","-\frac{14 a^6 b^2}{x^2}-\frac{56 a^5 b^3}{3 x^3}-\frac{35 a^4 b^4}{2 x^4}-\frac{56 a^3 b^5}{5 x^5}-\frac{14 a^2 b^6}{3 x^6}-\frac{8 a^7 b}{x}+a^8 \log (x)-\frac{8 a b^7}{7 x^7}-\frac{b^8}{8 x^8}","-\frac{14 a^6 b^2}{x^2}-\frac{56 a^5 b^3}{3 x^3}-\frac{35 a^4 b^4}{2 x^4}-\frac{56 a^3 b^5}{5 x^5}-\frac{14 a^2 b^6}{3 x^6}-\frac{8 a^7 b}{x}+a^8 \log (x)-\frac{8 a b^7}{7 x^7}-\frac{b^8}{8 x^8}",1,"-b^8/(8*x^8) - (8*a*b^7)/(7*x^7) - (14*a^2*b^6)/(3*x^6) - (56*a^3*b^5)/(5*x^5) - (35*a^4*b^4)/(2*x^4) - (56*a^5*b^3)/(3*x^3) - (14*a^6*b^2)/x^2 - (8*a^7*b)/x + a^8*Log[x]","A",3,2,13,0.1538,1,"{263, 43}"
1600,1,16,0,0.0034522,"\int \frac{\left(a+\frac{b}{x}\right)^8}{x^2} \, dx","Int[(a + b/x)^8/x^2,x]","-\frac{\left(a+\frac{b}{x}\right)^9}{9 b}","-\frac{\left(a+\frac{b}{x}\right)^9}{9 b}",1,"-(a + b/x)^9/(9*b)","A",1,1,13,0.07692,1,"{261}"
1601,1,36,0,0.0070418,"\int \frac{\left(a+\frac{b}{x}\right)^8}{x^3} \, dx","Int[(a + b/x)^8/x^3,x]","\frac{a (a x+b)^9}{90 b^2 x^9}-\frac{(a x+b)^9}{10 b x^{10}}","\frac{a (a x+b)^9}{90 b^2 x^9}-\frac{(a x+b)^9}{10 b x^{10}}",1,"-(b + a*x)^9/(10*b*x^10) + (a*(b + a*x)^9)/(90*b^2*x^9)","A",3,3,13,0.2308,1,"{263, 45, 37}"
1602,1,56,0,0.0122673,"\int \frac{\left(a+\frac{b}{x}\right)^8}{x^4} \, dx","Int[(a + b/x)^8/x^4,x]","-\frac{a^2 (a x+b)^9}{495 b^3 x^9}+\frac{a (a x+b)^9}{55 b^2 x^{10}}-\frac{(a x+b)^9}{11 b x^{11}}","-\frac{a^2 (a x+b)^9}{495 b^3 x^9}+\frac{a (a x+b)^9}{55 b^2 x^{10}}-\frac{(a x+b)^9}{11 b x^{11}}",1,"-(b + a*x)^9/(11*b*x^11) + (a*(b + a*x)^9)/(55*b^2*x^10) - (a^2*(b + a*x)^9)/(495*b^3*x^9)","A",4,3,13,0.2308,1,"{263, 45, 37}"
1603,1,76,0,0.0187091,"\int \frac{\left(a+\frac{b}{x}\right)^8}{x^5} \, dx","Int[(a + b/x)^8/x^5,x]","\frac{a^3 (a x+b)^9}{1980 b^4 x^9}-\frac{a^2 (a x+b)^9}{220 b^3 x^{10}}+\frac{a (a x+b)^9}{44 b^2 x^{11}}-\frac{(a x+b)^9}{12 b x^{12}}","\frac{a^3 (a x+b)^9}{1980 b^4 x^9}-\frac{a^2 (a x+b)^9}{220 b^3 x^{10}}+\frac{a (a x+b)^9}{44 b^2 x^{11}}-\frac{(a x+b)^9}{12 b x^{12}}",1,"-(b + a*x)^9/(12*b*x^12) + (a*(b + a*x)^9)/(44*b^2*x^11) - (a^2*(b + a*x)^9)/(220*b^3*x^10) + (a^3*(b + a*x)^9)/(1980*b^4*x^9)","A",5,3,13,0.2308,1,"{263, 45, 37}"
1604,1,96,0,0.0274715,"\int \frac{\left(a+\frac{b}{x}\right)^8}{x^6} \, dx","Int[(a + b/x)^8/x^6,x]","-\frac{a^4 (a x+b)^9}{6435 b^5 x^9}+\frac{a^3 (a x+b)^9}{715 b^4 x^{10}}-\frac{a^2 (a x+b)^9}{143 b^3 x^{11}}+\frac{a (a x+b)^9}{39 b^2 x^{12}}-\frac{(a x+b)^9}{13 b x^{13}}","-\frac{a^4 (a x+b)^9}{6435 b^5 x^9}+\frac{a^3 (a x+b)^9}{715 b^4 x^{10}}-\frac{a^2 (a x+b)^9}{143 b^3 x^{11}}+\frac{a (a x+b)^9}{39 b^2 x^{12}}-\frac{(a x+b)^9}{13 b x^{13}}",1,"-(b + a*x)^9/(13*b*x^13) + (a*(b + a*x)^9)/(39*b^2*x^12) - (a^2*(b + a*x)^9)/(143*b^3*x^11) + (a^3*(b + a*x)^9)/(715*b^4*x^10) - (a^4*(b + a*x)^9)/(6435*b^5*x^9)","A",6,3,13,0.2308,1,"{263, 45, 37}"
1605,1,106,0,0.0430039,"\int \frac{\left(a+\frac{b}{x}\right)^8}{x^7} \, dx","Int[(a + b/x)^8/x^7,x]","-\frac{7 a^6 b^2}{2 x^8}-\frac{56 a^5 b^3}{9 x^9}-\frac{7 a^4 b^4}{x^{10}}-\frac{56 a^3 b^5}{11 x^{11}}-\frac{7 a^2 b^6}{3 x^{12}}-\frac{8 a^7 b}{7 x^7}-\frac{a^8}{6 x^6}-\frac{8 a b^7}{13 x^{13}}-\frac{b^8}{14 x^{14}}","-\frac{7 a^6 b^2}{2 x^8}-\frac{56 a^5 b^3}{9 x^9}-\frac{7 a^4 b^4}{x^{10}}-\frac{56 a^3 b^5}{11 x^{11}}-\frac{7 a^2 b^6}{3 x^{12}}-\frac{8 a^7 b}{7 x^7}-\frac{a^8}{6 x^6}-\frac{8 a b^7}{13 x^{13}}-\frac{b^8}{14 x^{14}}",1,"-b^8/(14*x^14) - (8*a*b^7)/(13*x^13) - (7*a^2*b^6)/(3*x^12) - (56*a^3*b^5)/(11*x^11) - (7*a^4*b^4)/x^10 - (56*a^5*b^3)/(9*x^9) - (7*a^6*b^2)/(2*x^8) - (8*a^7*b)/(7*x^7) - a^8/(6*x^6)","A",3,2,13,0.1538,1,"{263, 43}"
1606,1,106,0,0.0407175,"\int \frac{\left(a+\frac{b}{x}\right)^8}{x^8} \, dx","Int[(a + b/x)^8/x^8,x]","-\frac{28 a^6 b^2}{9 x^9}-\frac{28 a^5 b^3}{5 x^{10}}-\frac{70 a^4 b^4}{11 x^{11}}-\frac{14 a^3 b^5}{3 x^{12}}-\frac{28 a^2 b^6}{13 x^{13}}-\frac{a^7 b}{x^8}-\frac{a^8}{7 x^7}-\frac{4 a b^7}{7 x^{14}}-\frac{b^8}{15 x^{15}}","-\frac{28 a^6 b^2}{9 x^9}-\frac{28 a^5 b^3}{5 x^{10}}-\frac{70 a^4 b^4}{11 x^{11}}-\frac{14 a^3 b^5}{3 x^{12}}-\frac{28 a^2 b^6}{13 x^{13}}-\frac{a^7 b}{x^8}-\frac{a^8}{7 x^7}-\frac{4 a b^7}{7 x^{14}}-\frac{b^8}{15 x^{15}}",1,"-b^8/(15*x^15) - (4*a*b^7)/(7*x^14) - (28*a^2*b^6)/(13*x^13) - (14*a^3*b^5)/(3*x^12) - (70*a^4*b^4)/(11*x^11) - (28*a^5*b^3)/(5*x^10) - (28*a^6*b^2)/(9*x^9) - (a^7*b)/x^8 - a^8/(7*x^7)","A",3,2,13,0.1538,1,"{263, 43}"
1607,1,70,0,0.0372933,"\int \frac{x^4}{a+\frac{b}{x}} \, dx","Int[x^4/(a + b/x),x]","-\frac{b^3 x^2}{2 a^4}+\frac{b^2 x^3}{3 a^3}+\frac{b^4 x}{a^5}-\frac{b^5 \log (a x+b)}{a^6}-\frac{b x^4}{4 a^2}+\frac{x^5}{5 a}","-\frac{b^3 x^2}{2 a^4}+\frac{b^2 x^3}{3 a^3}+\frac{b^4 x}{a^5}-\frac{b^5 \log (a x+b)}{a^6}-\frac{b x^4}{4 a^2}+\frac{x^5}{5 a}",1,"(b^4*x)/a^5 - (b^3*x^2)/(2*a^4) + (b^2*x^3)/(3*a^3) - (b*x^4)/(4*a^2) + x^5/(5*a) - (b^5*Log[b + a*x])/a^6","A",3,2,13,0.1538,1,"{263, 43}"
1608,1,57,0,0.0267549,"\int \frac{x^3}{a+\frac{b}{x}} \, dx","Int[x^3/(a + b/x),x]","\frac{b^2 x^2}{2 a^3}-\frac{b^3 x}{a^4}+\frac{b^4 \log (a x+b)}{a^5}-\frac{b x^3}{3 a^2}+\frac{x^4}{4 a}","\frac{b^2 x^2}{2 a^3}-\frac{b^3 x}{a^4}+\frac{b^4 \log (a x+b)}{a^5}-\frac{b x^3}{3 a^2}+\frac{x^4}{4 a}",1,"-((b^3*x)/a^4) + (b^2*x^2)/(2*a^3) - (b*x^3)/(3*a^2) + x^4/(4*a) + (b^4*Log[b + a*x])/a^5","A",3,2,13,0.1538,1,"{263, 43}"
1609,1,44,0,0.0222153,"\int \frac{x^2}{a+\frac{b}{x}} \, dx","Int[x^2/(a + b/x),x]","\frac{b^2 x}{a^3}-\frac{b^3 \log (a x+b)}{a^4}-\frac{b x^2}{2 a^2}+\frac{x^3}{3 a}","\frac{b^2 x}{a^3}-\frac{b^3 \log (a x+b)}{a^4}-\frac{b x^2}{2 a^2}+\frac{x^3}{3 a}",1,"(b^2*x)/a^3 - (b*x^2)/(2*a^2) + x^3/(3*a) - (b^3*Log[b + a*x])/a^4","A",3,2,13,0.1538,1,"{263, 43}"
1610,1,31,0,0.0157775,"\int \frac{x}{a+\frac{b}{x}} \, dx","Int[x/(a + b/x),x]","\frac{b^2 \log (a x+b)}{a^3}-\frac{b x}{a^2}+\frac{x^2}{2 a}","\frac{b^2 \log (a x+b)}{a^3}-\frac{b x}{a^2}+\frac{x^2}{2 a}",1,"-((b*x)/a^2) + x^2/(2*a) + (b^2*Log[b + a*x])/a^3","A",3,2,11,0.1818,1,"{263, 43}"
1611,1,18,0,0.0103014,"\int \frac{1}{a+\frac{b}{x}} \, dx","Int[(a + b/x)^(-1),x]","\frac{x}{a}-\frac{b \log (a x+b)}{a^2}","\frac{x}{a}-\frac{b \log (a x+b)}{a^2}",1,"x/a - (b*Log[b + a*x])/a^2","A",3,2,9,0.2222,1,"{193, 43}"
1612,1,10,0,0.0035947,"\int \frac{1}{\left(a+\frac{b}{x}\right) x} \, dx","Int[1/((a + b/x)*x),x]","\frac{\log (a x+b)}{a}","\frac{\log (a x+b)}{a}",1,"Log[b + a*x]/a","A",2,2,13,0.1538,1,"{263, 31}"
1613,1,13,0,0.0038023,"\int \frac{1}{\left(a+\frac{b}{x}\right) x^2} \, dx","Int[1/((a + b/x)*x^2),x]","-\frac{\log \left(a+\frac{b}{x}\right)}{b}","-\frac{\log \left(a+\frac{b}{x}\right)}{b}",1,"-(Log[a + b/x]/b)","A",1,1,13,0.07692,1,"{260}"
1614,1,28,0,0.0162563,"\int \frac{1}{\left(a+\frac{b}{x}\right) x^3} \, dx","Int[1/((a + b/x)*x^3),x]","-\frac{a \log (x)}{b^2}+\frac{a \log (a x+b)}{b^2}-\frac{1}{b x}","-\frac{a \log (x)}{b^2}+\frac{a \log (a x+b)}{b^2}-\frac{1}{b x}",1,"-(1/(b*x)) - (a*Log[x])/b^2 + (a*Log[b + a*x])/b^2","A",3,2,13,0.1538,1,"{263, 44}"
1615,1,42,0,0.0198733,"\int \frac{1}{\left(a+\frac{b}{x}\right) x^4} \, dx","Int[1/((a + b/x)*x^4),x]","\frac{a^2 \log (x)}{b^3}-\frac{a^2 \log (a x+b)}{b^3}+\frac{a}{b^2 x}-\frac{1}{2 b x^2}","\frac{a^2 \log (x)}{b^3}-\frac{a^2 \log (a x+b)}{b^3}+\frac{a}{b^2 x}-\frac{1}{2 b x^2}",1,"-1/(2*b*x^2) + a/(b^2*x) + (a^2*Log[x])/b^3 - (a^2*Log[b + a*x])/b^3","A",3,2,13,0.1538,1,"{263, 44}"
1616,1,56,0,0.0231498,"\int \frac{1}{\left(a+\frac{b}{x}\right) x^5} \, dx","Int[1/((a + b/x)*x^5),x]","-\frac{a^2}{b^3 x}-\frac{a^3 \log (x)}{b^4}+\frac{a^3 \log (a x+b)}{b^4}+\frac{a}{2 b^2 x^2}-\frac{1}{3 b x^3}","-\frac{a^2}{b^3 x}-\frac{a^3 \log (x)}{b^4}+\frac{a^3 \log (a x+b)}{b^4}+\frac{a}{2 b^2 x^2}-\frac{1}{3 b x^3}",1,"-1/(3*b*x^3) + a/(2*b^2*x^2) - a^2/(b^3*x) - (a^3*Log[x])/b^4 + (a^3*Log[b + a*x])/b^4","A",3,2,13,0.1538,1,"{263, 44}"
1617,1,68,0,0.0303397,"\int \frac{1}{\left(a+\frac{b}{x}\right) x^6} \, dx","Int[1/((a + b/x)*x^6),x]","-\frac{a^2}{2 b^3 x^2}+\frac{a^3}{b^4 x}+\frac{a^4 \log (x)}{b^5}-\frac{a^4 \log (a x+b)}{b^5}+\frac{a}{3 b^2 x^3}-\frac{1}{4 b x^4}","-\frac{a^2}{2 b^3 x^2}+\frac{a^3}{b^4 x}+\frac{a^4 \log (x)}{b^5}-\frac{a^4 \log (a x+b)}{b^5}+\frac{a}{3 b^2 x^3}-\frac{1}{4 b x^4}",1,"-1/(4*b*x^4) + a/(3*b^2*x^3) - a^2/(2*b^3*x^2) + a^3/(b^4*x) + (a^4*Log[x])/b^5 - (a^4*Log[b + a*x])/b^5","A",3,2,13,0.1538,1,"{263, 44}"
1618,1,82,0,0.0342849,"\int \frac{1}{\left(a+\frac{b}{x}\right) x^7} \, dx","Int[1/((a + b/x)*x^7),x]","\frac{a^3}{2 b^4 x^2}-\frac{a^2}{3 b^3 x^3}-\frac{a^4}{b^5 x}-\frac{a^5 \log (x)}{b^6}+\frac{a^5 \log (a x+b)}{b^6}+\frac{a}{4 b^2 x^4}-\frac{1}{5 b x^5}","\frac{a^3}{2 b^4 x^2}-\frac{a^2}{3 b^3 x^3}-\frac{a^4}{b^5 x}-\frac{a^5 \log (x)}{b^6}+\frac{a^5 \log (a x+b)}{b^6}+\frac{a}{4 b^2 x^4}-\frac{1}{5 b x^5}",1,"-1/(5*b*x^5) + a/(4*b^2*x^4) - a^2/(3*b^3*x^3) + a^3/(2*b^4*x^2) - a^4/(b^5*x) - (a^5*Log[x])/b^6 + (a^5*Log[b + a*x])/b^6","A",3,2,13,0.1538,1,"{263, 44}"
1619,1,98,0,0.0655405,"\int \frac{x^5}{\left(a+\frac{b}{x}\right)^2} \, dx","Int[x^5/(a + b/x)^2,x]","\frac{5 b^4 x^2}{2 a^6}-\frac{4 b^3 x^3}{3 a^5}+\frac{3 b^2 x^4}{4 a^4}+\frac{b^7}{a^8 (a x+b)}-\frac{6 b^5 x}{a^7}+\frac{7 b^6 \log (a x+b)}{a^8}-\frac{2 b x^5}{5 a^3}+\frac{x^6}{6 a^2}","\frac{5 b^4 x^2}{2 a^6}-\frac{4 b^3 x^3}{3 a^5}+\frac{3 b^2 x^4}{4 a^4}+\frac{b^7}{a^8 (a x+b)}-\frac{6 b^5 x}{a^7}+\frac{7 b^6 \log (a x+b)}{a^8}-\frac{2 b x^5}{5 a^3}+\frac{x^6}{6 a^2}",1,"(-6*b^5*x)/a^7 + (5*b^4*x^2)/(2*a^6) - (4*b^3*x^3)/(3*a^5) + (3*b^2*x^4)/(4*a^4) - (2*b*x^5)/(5*a^3) + x^6/(6*a^2) + b^7/(a^8*(b + a*x)) + (7*b^6*Log[b + a*x])/a^8","A",3,2,13,0.1538,1,"{263, 43}"
1620,1,81,0,0.0527342,"\int \frac{x^4}{\left(a+\frac{b}{x}\right)^2} \, dx","Int[x^4/(a + b/x)^2,x]","-\frac{2 b^3 x^2}{a^5}+\frac{b^2 x^3}{a^4}-\frac{b^6}{a^7 (a x+b)}+\frac{5 b^4 x}{a^6}-\frac{6 b^5 \log (a x+b)}{a^7}-\frac{b x^4}{2 a^3}+\frac{x^5}{5 a^2}","-\frac{2 b^3 x^2}{a^5}+\frac{b^2 x^3}{a^4}-\frac{b^6}{a^7 (a x+b)}+\frac{5 b^4 x}{a^6}-\frac{6 b^5 \log (a x+b)}{a^7}-\frac{b x^4}{2 a^3}+\frac{x^5}{5 a^2}",1,"(5*b^4*x)/a^6 - (2*b^3*x^2)/a^5 + (b^2*x^3)/a^4 - (b*x^4)/(2*a^3) + x^5/(5*a^2) - b^6/(a^7*(b + a*x)) - (6*b^5*Log[b + a*x])/a^7","A",3,2,13,0.1538,1,"{263, 43}"
1621,1,72,0,0.0478724,"\int \frac{x^3}{\left(a+\frac{b}{x}\right)^2} \, dx","Int[x^3/(a + b/x)^2,x]","\frac{3 b^2 x^2}{2 a^4}+\frac{b^5}{a^6 (a x+b)}-\frac{4 b^3 x}{a^5}+\frac{5 b^4 \log (a x+b)}{a^6}-\frac{2 b x^3}{3 a^3}+\frac{x^4}{4 a^2}","\frac{3 b^2 x^2}{2 a^4}+\frac{b^5}{a^6 (a x+b)}-\frac{4 b^3 x}{a^5}+\frac{5 b^4 \log (a x+b)}{a^6}-\frac{2 b x^3}{3 a^3}+\frac{x^4}{4 a^2}",1,"(-4*b^3*x)/a^5 + (3*b^2*x^2)/(2*a^4) - (2*b*x^3)/(3*a^3) + x^4/(4*a^2) + b^5/(a^6*(b + a*x)) + (5*b^4*Log[b + a*x])/a^6","A",3,2,13,0.1538,1,"{263, 43}"
1622,1,58,0,0.0370357,"\int \frac{x^2}{\left(a+\frac{b}{x}\right)^2} \, dx","Int[x^2/(a + b/x)^2,x]","-\frac{b^4}{a^5 (a x+b)}+\frac{3 b^2 x}{a^4}-\frac{4 b^3 \log (a x+b)}{a^5}-\frac{b x^2}{a^3}+\frac{x^3}{3 a^2}","-\frac{b^4}{a^5 (a x+b)}+\frac{3 b^2 x}{a^4}-\frac{4 b^3 \log (a x+b)}{a^5}-\frac{b x^2}{a^3}+\frac{x^3}{3 a^2}",1,"(3*b^2*x)/a^4 - (b*x^2)/a^3 + x^3/(3*a^2) - b^4/(a^5*(b + a*x)) - (4*b^3*Log[b + a*x])/a^5","A",3,2,13,0.1538,1,"{263, 43}"
1623,1,46,0,0.0281744,"\int \frac{x}{\left(a+\frac{b}{x}\right)^2} \, dx","Int[x/(a + b/x)^2,x]","\frac{b^3}{a^4 (a x+b)}+\frac{3 b^2 \log (a x+b)}{a^4}-\frac{2 b x}{a^3}+\frac{x^2}{2 a^2}","\frac{b^3}{a^4 (a x+b)}+\frac{3 b^2 \log (a x+b)}{a^4}-\frac{2 b x}{a^3}+\frac{x^2}{2 a^2}",1,"(-2*b*x)/a^3 + x^2/(2*a^2) + b^3/(a^4*(b + a*x)) + (3*b^2*Log[b + a*x])/a^4","A",3,2,11,0.1818,1,"{263, 43}"
1624,1,34,0,0.0139466,"\int \frac{1}{\left(a+\frac{b}{x}\right)^2} \, dx","Int[(a + b/x)^(-2),x]","-\frac{2 b \log (a x+b)}{a^3}+\frac{2 x}{a^2}-\frac{x}{a \left(a+\frac{b}{x}\right)}","-\frac{2 b \log (a x+b)}{a^3}+\frac{2 x}{a^2}-\frac{x}{a \left(a+\frac{b}{x}\right)}",1,"(2*x)/a^2 - x/(a*(a + b/x)) - (2*b*Log[b + a*x])/a^3","A",4,3,9,0.3333,1,"{192, 193, 43}"
1625,1,23,0,0.0147991,"\int \frac{1}{\left(a+\frac{b}{x}\right)^2 x} \, dx","Int[1/((a + b/x)^2*x),x]","\frac{b}{a^2 (a x+b)}+\frac{\log (a x+b)}{a^2}","\frac{b}{a^2 (a x+b)}+\frac{\log (a x+b)}{a^2}",1,"b/(a^2*(b + a*x)) + Log[b + a*x]/a^2","A",3,2,13,0.1538,1,"{263, 43}"
1626,1,13,0,0.0035431,"\int \frac{1}{\left(a+\frac{b}{x}\right)^2 x^2} \, dx","Int[1/((a + b/x)^2*x^2),x]","\frac{1}{b \left(a+\frac{b}{x}\right)}","\frac{1}{b \left(a+\frac{b}{x}\right)}",1,"1/(b*(a + b/x))","A",1,1,13,0.07692,1,"{261}"
1627,1,29,0,0.0168673,"\int \frac{1}{\left(a+\frac{b}{x}\right)^2 x^3} \, dx","Int[1/((a + b/x)^2*x^3),x]","-\frac{\log (a x+b)}{b^2}+\frac{1}{b (a x+b)}+\frac{\log (x)}{b^2}","-\frac{\log (a x+b)}{b^2}+\frac{1}{b (a x+b)}+\frac{\log (x)}{b^2}",1,"1/(b*(b + a*x)) + Log[x]/b^2 - Log[b + a*x]/b^2","A",3,2,13,0.1538,1,"{263, 44}"
1628,1,42,0,0.0240158,"\int \frac{1}{\left(a+\frac{b}{x}\right)^2 x^4} \, dx","Int[1/((a + b/x)^2*x^4),x]","-\frac{a}{b^2 (a x+b)}-\frac{2 a \log (x)}{b^3}+\frac{2 a \log (a x+b)}{b^3}-\frac{1}{b^2 x}","-\frac{a}{b^2 (a x+b)}-\frac{2 a \log (x)}{b^3}+\frac{2 a \log (a x+b)}{b^3}-\frac{1}{b^2 x}",1,"-(1/(b^2*x)) - a/(b^2*(b + a*x)) - (2*a*Log[x])/b^3 + (2*a*Log[b + a*x])/b^3","A",3,2,13,0.1538,1,"{263, 44}"
1629,1,58,0,0.0309973,"\int \frac{1}{\left(a+\frac{b}{x}\right)^2 x^5} \, dx","Int[1/((a + b/x)^2*x^5),x]","\frac{a^2}{b^3 (a x+b)}+\frac{3 a^2 \log (x)}{b^4}-\frac{3 a^2 \log (a x+b)}{b^4}+\frac{2 a}{b^3 x}-\frac{1}{2 b^2 x^2}","\frac{a^2}{b^3 (a x+b)}+\frac{3 a^2 \log (x)}{b^4}-\frac{3 a^2 \log (a x+b)}{b^4}+\frac{2 a}{b^3 x}-\frac{1}{2 b^2 x^2}",1,"-1/(2*b^2*x^2) + (2*a)/(b^3*x) + a^2/(b^3*(b + a*x)) + (3*a^2*Log[x])/b^4 - (3*a^2*Log[b + a*x])/b^4","A",3,2,13,0.1538,1,"{263, 44}"
1630,1,69,0,0.0379721,"\int \frac{1}{\left(a+\frac{b}{x}\right)^2 x^6} \, dx","Int[1/((a + b/x)^2*x^6),x]","-\frac{a^3}{b^4 (a x+b)}-\frac{3 a^2}{b^4 x}-\frac{4 a^3 \log (x)}{b^5}+\frac{4 a^3 \log (a x+b)}{b^5}+\frac{a}{b^3 x^2}-\frac{1}{3 b^2 x^3}","-\frac{a^3}{b^4 (a x+b)}-\frac{3 a^2}{b^4 x}-\frac{4 a^3 \log (x)}{b^5}+\frac{4 a^3 \log (a x+b)}{b^5}+\frac{a}{b^3 x^2}-\frac{1}{3 b^2 x^3}",1,"-1/(3*b^2*x^3) + a/(b^3*x^2) - (3*a^2)/(b^4*x) - a^3/(b^4*(b + a*x)) - (4*a^3*Log[x])/b^5 + (4*a^3*Log[b + a*x])/b^5","A",3,2,13,0.1538,1,"{263, 44}"
1631,1,84,0,0.0471178,"\int \frac{1}{\left(a+\frac{b}{x}\right)^2 x^7} \, dx","Int[1/((a + b/x)^2*x^7),x]","-\frac{3 a^2}{2 b^4 x^2}+\frac{a^4}{b^5 (a x+b)}+\frac{4 a^3}{b^5 x}+\frac{5 a^4 \log (x)}{b^6}-\frac{5 a^4 \log (a x+b)}{b^6}+\frac{2 a}{3 b^3 x^3}-\frac{1}{4 b^2 x^4}","-\frac{3 a^2}{2 b^4 x^2}+\frac{a^4}{b^5 (a x+b)}+\frac{4 a^3}{b^5 x}+\frac{5 a^4 \log (x)}{b^6}-\frac{5 a^4 \log (a x+b)}{b^6}+\frac{2 a}{3 b^3 x^3}-\frac{1}{4 b^2 x^4}",1,"-1/(4*b^2*x^4) + (2*a)/(3*b^3*x^3) - (3*a^2)/(2*b^4*x^2) + (4*a^3)/(b^5*x) + a^4/(b^5*(b + a*x)) + (5*a^4*Log[x])/b^6 - (5*a^4*Log[b + a*x])/b^6","A",3,2,13,0.1538,1,"{263, 44}"
1632,1,94,0,0.0548742,"\int \frac{1}{\left(a+\frac{b}{x}\right)^2 x^8} \, dx","Int[1/((a + b/x)^2*x^8),x]","\frac{2 a^3}{b^5 x^2}-\frac{a^2}{b^4 x^3}-\frac{a^5}{b^6 (a x+b)}-\frac{5 a^4}{b^6 x}-\frac{6 a^5 \log (x)}{b^7}+\frac{6 a^5 \log (a x+b)}{b^7}+\frac{a}{2 b^3 x^4}-\frac{1}{5 b^2 x^5}","\frac{2 a^3}{b^5 x^2}-\frac{a^2}{b^4 x^3}-\frac{a^5}{b^6 (a x+b)}-\frac{5 a^4}{b^6 x}-\frac{6 a^5 \log (x)}{b^7}+\frac{6 a^5 \log (a x+b)}{b^7}+\frac{a}{2 b^3 x^4}-\frac{1}{5 b^2 x^5}",1,"-1/(5*b^2*x^5) + a/(2*b^3*x^4) - a^2/(b^4*x^3) + (2*a^3)/(b^5*x^2) - (5*a^4)/(b^6*x) - a^5/(b^6*(b + a*x)) - (6*a^5*Log[x])/b^7 + (6*a^5*Log[b + a*x])/b^7","A",3,2,13,0.1538,1,"{263, 44}"
1633,1,99,0,0.0703092,"\int \frac{x^4}{\left(a+\frac{b}{x}\right)^3} \, dx","Int[x^4/(a + b/x)^3,x]","-\frac{5 b^3 x^2}{a^6}+\frac{2 b^2 x^3}{a^5}+\frac{b^7}{2 a^8 (a x+b)^2}-\frac{7 b^6}{a^8 (a x+b)}+\frac{15 b^4 x}{a^7}-\frac{21 b^5 \log (a x+b)}{a^8}-\frac{3 b x^4}{4 a^4}+\frac{x^5}{5 a^3}","-\frac{5 b^3 x^2}{a^6}+\frac{2 b^2 x^3}{a^5}+\frac{b^7}{2 a^8 (a x+b)^2}-\frac{7 b^6}{a^8 (a x+b)}+\frac{15 b^4 x}{a^7}-\frac{21 b^5 \log (a x+b)}{a^8}-\frac{3 b x^4}{4 a^4}+\frac{x^5}{5 a^3}",1,"(15*b^4*x)/a^7 - (5*b^3*x^2)/a^6 + (2*b^2*x^3)/a^5 - (3*b*x^4)/(4*a^4) + x^5/(5*a^3) + b^7/(2*a^8*(b + a*x)^2) - (7*b^6)/(a^8*(b + a*x)) - (21*b^5*Log[b + a*x])/a^8","A",3,2,13,0.1538,1,"{263, 43}"
1634,1,86,0,0.0562362,"\int \frac{x^3}{\left(a+\frac{b}{x}\right)^3} \, dx","Int[x^3/(a + b/x)^3,x]","\frac{3 b^2 x^2}{a^5}-\frac{b^6}{2 a^7 (a x+b)^2}+\frac{6 b^5}{a^7 (a x+b)}-\frac{10 b^3 x}{a^6}+\frac{15 b^4 \log (a x+b)}{a^7}-\frac{b x^3}{a^4}+\frac{x^4}{4 a^3}","\frac{3 b^2 x^2}{a^5}-\frac{b^6}{2 a^7 (a x+b)^2}+\frac{6 b^5}{a^7 (a x+b)}-\frac{10 b^3 x}{a^6}+\frac{15 b^4 \log (a x+b)}{a^7}-\frac{b x^3}{a^4}+\frac{x^4}{4 a^3}",1,"(-10*b^3*x)/a^6 + (3*b^2*x^2)/a^5 - (b*x^3)/a^4 + x^4/(4*a^3) - b^6/(2*a^7*(b + a*x)^2) + (6*b^5)/(a^7*(b + a*x)) + (15*b^4*Log[b + a*x])/a^7","A",3,2,13,0.1538,1,"{263, 43}"
1635,1,77,0,0.0491546,"\int \frac{x^2}{\left(a+\frac{b}{x}\right)^3} \, dx","Int[x^2/(a + b/x)^3,x]","\frac{b^5}{2 a^6 (a x+b)^2}-\frac{5 b^4}{a^6 (a x+b)}+\frac{6 b^2 x}{a^5}-\frac{10 b^3 \log (a x+b)}{a^6}-\frac{3 b x^2}{2 a^4}+\frac{x^3}{3 a^3}","\frac{b^5}{2 a^6 (a x+b)^2}-\frac{5 b^4}{a^6 (a x+b)}+\frac{6 b^2 x}{a^5}-\frac{10 b^3 \log (a x+b)}{a^6}-\frac{3 b x^2}{2 a^4}+\frac{x^3}{3 a^3}",1,"(6*b^2*x)/a^5 - (3*b*x^2)/(2*a^4) + x^3/(3*a^3) + b^5/(2*a^6*(b + a*x)^2) - (5*b^4)/(a^6*(b + a*x)) - (10*b^3*Log[b + a*x])/a^6","A",3,2,13,0.1538,1,"{263, 43}"
1636,1,64,0,0.0367898,"\int \frac{x}{\left(a+\frac{b}{x}\right)^3} \, dx","Int[x/(a + b/x)^3,x]","-\frac{b^4}{2 a^5 (a x+b)^2}+\frac{4 b^3}{a^5 (a x+b)}+\frac{6 b^2 \log (a x+b)}{a^5}-\frac{3 b x}{a^4}+\frac{x^2}{2 a^3}","-\frac{b^4}{2 a^5 (a x+b)^2}+\frac{4 b^3}{a^5 (a x+b)}+\frac{6 b^2 \log (a x+b)}{a^5}-\frac{3 b x}{a^4}+\frac{x^2}{2 a^3}",1,"(-3*b*x)/a^4 + x^2/(2*a^3) - b^4/(2*a^5*(b + a*x)^2) + (4*b^3)/(a^5*(b + a*x)) + (6*b^2*Log[b + a*x])/a^5","A",3,2,11,0.1818,1,"{263, 43}"
1637,1,53,0,0.0202364,"\int \frac{1}{\left(a+\frac{b}{x}\right)^3} \, dx","Int[(a + b/x)^(-3),x]","-\frac{3 x}{2 a^2 \left(a+\frac{b}{x}\right)}-\frac{3 b \log (a x+b)}{a^4}+\frac{3 x}{a^3}-\frac{x}{2 a \left(a+\frac{b}{x}\right)^2}","-\frac{3 x}{2 a^2 \left(a+\frac{b}{x}\right)}-\frac{3 b \log (a x+b)}{a^4}+\frac{3 x}{a^3}-\frac{x}{2 a \left(a+\frac{b}{x}\right)^2}",1,"(3*x)/a^3 - x/(2*a*(a + b/x)^2) - (3*x)/(2*a^2*(a + b/x)) - (3*b*Log[b + a*x])/a^4","A",5,3,9,0.3333,1,"{192, 193, 43}"
1638,1,41,0,0.0222989,"\int \frac{1}{\left(a+\frac{b}{x}\right)^3 x} \, dx","Int[1/((a + b/x)^3*x),x]","-\frac{b^2}{2 a^3 (a x+b)^2}+\frac{2 b}{a^3 (a x+b)}+\frac{\log (a x+b)}{a^3}","-\frac{b^2}{2 a^3 (a x+b)^2}+\frac{2 b}{a^3 (a x+b)}+\frac{\log (a x+b)}{a^3}",1,"-b^2/(2*a^3*(b + a*x)^2) + (2*b)/(a^3*(b + a*x)) + Log[b + a*x]/a^3","A",3,2,13,0.1538,1,"{263, 43}"
1639,1,16,0,0.0037841,"\int \frac{1}{\left(a+\frac{b}{x}\right)^3 x^2} \, dx","Int[1/((a + b/x)^3*x^2),x]","\frac{1}{2 b \left(a+\frac{b}{x}\right)^2}","\frac{1}{2 b \left(a+\frac{b}{x}\right)^2}",1,"1/(2*b*(a + b/x)^2)","A",1,1,13,0.07692,1,"{261}"
1640,1,14,0,0.0037481,"\int \frac{1}{\left(a+\frac{b}{x}\right)^3 x^3} \, dx","Int[1/((a + b/x)^3*x^3),x]","-\frac{1}{2 a (a x+b)^2}","-\frac{1}{2 a (a x+b)^2}",1,"-1/(2*a*(b + a*x)^2)","A",2,2,13,0.1538,1,"{263, 32}"
1641,1,43,0,0.0231611,"\int \frac{1}{\left(a+\frac{b}{x}\right)^3 x^4} \, dx","Int[1/((a + b/x)^3*x^4),x]","\frac{1}{b^2 (a x+b)}-\frac{\log (a x+b)}{b^3}+\frac{1}{2 b (a x+b)^2}+\frac{\log (x)}{b^3}","\frac{1}{b^2 (a x+b)}-\frac{\log (a x+b)}{b^3}+\frac{1}{2 b (a x+b)^2}+\frac{\log (x)}{b^3}",1,"1/(2*b*(b + a*x)^2) + 1/(b^2*(b + a*x)) + Log[x]/b^3 - Log[b + a*x]/b^3","A",3,2,13,0.1538,1,"{263, 44}"
1642,1,57,0,0.0316528,"\int \frac{1}{\left(a+\frac{b}{x}\right)^3 x^5} \, dx","Int[1/((a + b/x)^3*x^5),x]","-\frac{2 a}{b^3 (a x+b)}-\frac{a}{2 b^2 (a x+b)^2}-\frac{3 a \log (x)}{b^4}+\frac{3 a \log (a x+b)}{b^4}-\frac{1}{b^3 x}","-\frac{2 a}{b^3 (a x+b)}-\frac{a}{2 b^2 (a x+b)^2}-\frac{3 a \log (x)}{b^4}+\frac{3 a \log (a x+b)}{b^4}-\frac{1}{b^3 x}",1,"-(1/(b^3*x)) - a/(2*b^2*(b + a*x)^2) - (2*a)/(b^3*(b + a*x)) - (3*a*Log[x])/b^4 + (3*a*Log[b + a*x])/b^4","A",3,2,13,0.1538,1,"{263, 44}"
1643,1,76,0,0.0402006,"\int \frac{1}{\left(a+\frac{b}{x}\right)^3 x^6} \, dx","Int[1/((a + b/x)^3*x^6),x]","\frac{3 a^2}{b^4 (a x+b)}+\frac{a^2}{2 b^3 (a x+b)^2}+\frac{6 a^2 \log (x)}{b^5}-\frac{6 a^2 \log (a x+b)}{b^5}+\frac{3 a}{b^4 x}-\frac{1}{2 b^3 x^2}","\frac{3 a^2}{b^4 (a x+b)}+\frac{a^2}{2 b^3 (a x+b)^2}+\frac{6 a^2 \log (x)}{b^5}-\frac{6 a^2 \log (a x+b)}{b^5}+\frac{3 a}{b^4 x}-\frac{1}{2 b^3 x^2}",1,"-1/(2*b^3*x^2) + (3*a)/(b^4*x) + a^2/(2*b^3*(b + a*x)^2) + (3*a^2)/(b^4*(b + a*x)) + (6*a^2*Log[x])/b^5 - (6*a^2*Log[b + a*x])/b^5","A",3,2,13,0.1538,1,"{263, 44}"
1644,1,89,0,0.0486551,"\int \frac{1}{\left(a+\frac{b}{x}\right)^3 x^7} \, dx","Int[1/((a + b/x)^3*x^7),x]","-\frac{4 a^3}{b^5 (a x+b)}-\frac{a^3}{2 b^4 (a x+b)^2}-\frac{6 a^2}{b^5 x}-\frac{10 a^3 \log (x)}{b^6}+\frac{10 a^3 \log (a x+b)}{b^6}+\frac{3 a}{2 b^4 x^2}-\frac{1}{3 b^3 x^3}","-\frac{4 a^3}{b^5 (a x+b)}-\frac{a^3}{2 b^4 (a x+b)^2}-\frac{6 a^2}{b^5 x}-\frac{10 a^3 \log (x)}{b^6}+\frac{10 a^3 \log (a x+b)}{b^6}+\frac{3 a}{2 b^4 x^2}-\frac{1}{3 b^3 x^3}",1,"-1/(3*b^3*x^3) + (3*a)/(2*b^4*x^2) - (6*a^2)/(b^5*x) - a^3/(2*b^4*(b + a*x)^2) - (4*a^3)/(b^5*(b + a*x)) - (10*a^3*Log[x])/b^6 + (10*a^3*Log[b + a*x])/b^6","A",3,2,13,0.1538,1,"{263, 44}"
1645,1,97,0,0.0567562,"\int \frac{1}{\left(a+\frac{b}{x}\right)^3 x^8} \, dx","Int[1/((a + b/x)^3*x^8),x]","-\frac{3 a^2}{b^5 x^2}+\frac{5 a^4}{b^6 (a x+b)}+\frac{a^4}{2 b^5 (a x+b)^2}+\frac{10 a^3}{b^6 x}+\frac{15 a^4 \log (x)}{b^7}-\frac{15 a^4 \log (a x+b)}{b^7}+\frac{a}{b^4 x^3}-\frac{1}{4 b^3 x^4}","-\frac{3 a^2}{b^5 x^2}+\frac{5 a^4}{b^6 (a x+b)}+\frac{a^4}{2 b^5 (a x+b)^2}+\frac{10 a^3}{b^6 x}+\frac{15 a^4 \log (x)}{b^7}-\frac{15 a^4 \log (a x+b)}{b^7}+\frac{a}{b^4 x^3}-\frac{1}{4 b^3 x^4}",1,"-1/(4*b^3*x^4) + a/(b^4*x^3) - (3*a^2)/(b^5*x^2) + (10*a^3)/(b^6*x) + a^4/(2*b^5*(b + a*x)^2) + (5*a^4)/(b^6*(b + a*x)) + (15*a^4*Log[x])/b^7 - (15*a^4*Log[b + a*x])/b^7","A",3,2,13,0.1538,1,"{263, 44}"
1646,1,111,0,0.0671547,"\int \frac{1}{\left(a+\frac{b}{x}\right)^3 x^9} \, dx","Int[1/((a + b/x)^3*x^9),x]","\frac{5 a^3}{b^6 x^2}-\frac{2 a^2}{b^5 x^3}-\frac{6 a^5}{b^7 (a x+b)}-\frac{a^5}{2 b^6 (a x+b)^2}-\frac{15 a^4}{b^7 x}-\frac{21 a^5 \log (x)}{b^8}+\frac{21 a^5 \log (a x+b)}{b^8}+\frac{3 a}{4 b^4 x^4}-\frac{1}{5 b^3 x^5}","\frac{5 a^3}{b^6 x^2}-\frac{2 a^2}{b^5 x^3}-\frac{6 a^5}{b^7 (a x+b)}-\frac{a^5}{2 b^6 (a x+b)^2}-\frac{15 a^4}{b^7 x}-\frac{21 a^5 \log (x)}{b^8}+\frac{21 a^5 \log (a x+b)}{b^8}+\frac{3 a}{4 b^4 x^4}-\frac{1}{5 b^3 x^5}",1,"-1/(5*b^3*x^5) + (3*a)/(4*b^4*x^4) - (2*a^2)/(b^5*x^3) + (5*a^3)/(b^6*x^2) - (15*a^4)/(b^7*x) - a^5/(2*b^6*(b + a*x)^2) - (6*a^5)/(b^7*(b + a*x)) - (21*a^5*Log[x])/b^8 + (21*a^5*Log[b + a*x])/b^8","A",3,2,13,0.1538,1,"{263, 44}"
1647,1,21,0,0.0042015,"\int \left(a+\frac{b}{x}\right) x^{5/2} \, dx","Int[(a + b/x)*x^(5/2),x]","\frac{2}{7} a x^{7/2}+\frac{2}{5} b x^{5/2}","\frac{2}{7} a x^{7/2}+\frac{2}{5} b x^{5/2}",1,"(2*b*x^(5/2))/5 + (2*a*x^(7/2))/7","A",2,1,13,0.07692,1,"{14}"
1648,1,21,0,0.0044522,"\int \left(a+\frac{b}{x}\right) x^{3/2} \, dx","Int[(a + b/x)*x^(3/2),x]","\frac{2}{5} a x^{5/2}+\frac{2}{3} b x^{3/2}","\frac{2}{5} a x^{5/2}+\frac{2}{3} b x^{3/2}",1,"(2*b*x^(3/2))/3 + (2*a*x^(5/2))/5","A",2,1,13,0.07692,1,"{14}"
1649,1,19,0,0.0043763,"\int \left(a+\frac{b}{x}\right) \sqrt{x} \, dx","Int[(a + b/x)*Sqrt[x],x]","\frac{2}{3} a x^{3/2}+2 b \sqrt{x}","\frac{2}{3} a x^{3/2}+2 b \sqrt{x}",1,"2*b*Sqrt[x] + (2*a*x^(3/2))/3","A",2,1,13,0.07692,1,"{14}"
1650,1,17,0,0.0042461,"\int \frac{a+\frac{b}{x}}{\sqrt{x}} \, dx","Int[(a + b/x)/Sqrt[x],x]","2 a \sqrt{x}-\frac{2 b}{\sqrt{x}}","2 a \sqrt{x}-\frac{2 b}{\sqrt{x}}",1,"(-2*b)/Sqrt[x] + 2*a*Sqrt[x]","A",2,1,13,0.07692,1,"{14}"
1651,1,19,0,0.0040228,"\int \frac{a+\frac{b}{x}}{x^{3/2}} \, dx","Int[(a + b/x)/x^(3/2),x]","-\frac{2 a}{\sqrt{x}}-\frac{2 b}{3 x^{3/2}}","-\frac{2 a}{\sqrt{x}}-\frac{2 b}{3 x^{3/2}}",1,"(-2*b)/(3*x^(3/2)) - (2*a)/Sqrt[x]","A",2,1,13,0.07692,1,"{14}"
1652,1,21,0,0.0039515,"\int \frac{a+\frac{b}{x}}{x^{5/2}} \, dx","Int[(a + b/x)/x^(5/2),x]","-\frac{2 a}{3 x^{3/2}}-\frac{2 b}{5 x^{5/2}}","-\frac{2 a}{3 x^{3/2}}-\frac{2 b}{5 x^{5/2}}",1,"(-2*b)/(5*x^(5/2)) - (2*a)/(3*x^(3/2))","A",2,1,13,0.07692,1,"{14}"
1653,1,36,0,0.0098707,"\int \left(a+\frac{b}{x}\right)^2 x^{5/2} \, dx","Int[(a + b/x)^2*x^(5/2),x]","\frac{2}{7} a^2 x^{7/2}+\frac{4}{5} a b x^{5/2}+\frac{2}{3} b^2 x^{3/2}","\frac{2}{7} a^2 x^{7/2}+\frac{4}{5} a b x^{5/2}+\frac{2}{3} b^2 x^{3/2}",1,"(2*b^2*x^(3/2))/3 + (4*a*b*x^(5/2))/5 + (2*a^2*x^(7/2))/7","A",3,2,15,0.1333,1,"{263, 43}"
1654,1,34,0,0.0092085,"\int \left(a+\frac{b}{x}\right)^2 x^{3/2} \, dx","Int[(a + b/x)^2*x^(3/2),x]","\frac{2}{5} a^2 x^{5/2}+\frac{4}{3} a b x^{3/2}+2 b^2 \sqrt{x}","\frac{2}{5} a^2 x^{5/2}+\frac{4}{3} a b x^{3/2}+2 b^2 \sqrt{x}",1,"2*b^2*Sqrt[x] + (4*a*b*x^(3/2))/3 + (2*a^2*x^(5/2))/5","A",3,2,15,0.1333,1,"{263, 43}"
1655,1,32,0,0.0092571,"\int \left(a+\frac{b}{x}\right)^2 \sqrt{x} \, dx","Int[(a + b/x)^2*Sqrt[x],x]","\frac{2}{3} a^2 x^{3/2}+4 a b \sqrt{x}-\frac{2 b^2}{\sqrt{x}}","\frac{2}{3} a^2 x^{3/2}+4 a b \sqrt{x}-\frac{2 b^2}{\sqrt{x}}",1,"(-2*b^2)/Sqrt[x] + 4*a*b*Sqrt[x] + (2*a^2*x^(3/2))/3","A",3,2,15,0.1333,1,"{263, 43}"
1656,1,32,0,0.0091209,"\int \frac{\left(a+\frac{b}{x}\right)^2}{\sqrt{x}} \, dx","Int[(a + b/x)^2/Sqrt[x],x]","2 a^2 \sqrt{x}-\frac{4 a b}{\sqrt{x}}-\frac{2 b^2}{3 x^{3/2}}","2 a^2 \sqrt{x}-\frac{4 a b}{\sqrt{x}}-\frac{2 b^2}{3 x^{3/2}}",1,"(-2*b^2)/(3*x^(3/2)) - (4*a*b)/Sqrt[x] + 2*a^2*Sqrt[x]","A",3,2,15,0.1333,1,"{263, 43}"
1657,1,34,0,0.0092866,"\int \frac{\left(a+\frac{b}{x}\right)^2}{x^{3/2}} \, dx","Int[(a + b/x)^2/x^(3/2),x]","-\frac{2 a^2}{\sqrt{x}}-\frac{4 a b}{3 x^{3/2}}-\frac{2 b^2}{5 x^{5/2}}","-\frac{2 a^2}{\sqrt{x}}-\frac{4 a b}{3 x^{3/2}}-\frac{2 b^2}{5 x^{5/2}}",1,"(-2*b^2)/(5*x^(5/2)) - (4*a*b)/(3*x^(3/2)) - (2*a^2)/Sqrt[x]","A",3,2,15,0.1333,1,"{263, 43}"
1658,1,36,0,0.0093189,"\int \frac{\left(a+\frac{b}{x}\right)^2}{x^{5/2}} \, dx","Int[(a + b/x)^2/x^(5/2),x]","-\frac{2 a^2}{3 x^{3/2}}-\frac{4 a b}{5 x^{5/2}}-\frac{2 b^2}{7 x^{7/2}}","-\frac{2 a^2}{3 x^{3/2}}-\frac{4 a b}{5 x^{5/2}}-\frac{2 b^2}{7 x^{7/2}}",1,"(-2*b^2)/(7*x^(7/2)) - (4*a*b)/(5*x^(5/2)) - (2*a^2)/(3*x^(3/2))","A",3,2,15,0.1333,1,"{263, 43}"
1659,1,47,0,0.0127937,"\int \left(a+\frac{b}{x}\right)^3 x^{5/2} \, dx","Int[(a + b/x)^3*x^(5/2),x]","\frac{6}{5} a^2 b x^{5/2}+\frac{2}{7} a^3 x^{7/2}+2 a b^2 x^{3/2}+2 b^3 \sqrt{x}","\frac{6}{5} a^2 b x^{5/2}+\frac{2}{7} a^3 x^{7/2}+2 a b^2 x^{3/2}+2 b^3 \sqrt{x}",1,"2*b^3*Sqrt[x] + 2*a*b^2*x^(3/2) + (6*a^2*b*x^(5/2))/5 + (2*a^3*x^(7/2))/7","A",3,2,15,0.1333,1,"{263, 43}"
1660,1,45,0,0.0124484,"\int \left(a+\frac{b}{x}\right)^3 x^{3/2} \, dx","Int[(a + b/x)^3*x^(3/2),x]","2 a^2 b x^{3/2}+\frac{2}{5} a^3 x^{5/2}+6 a b^2 \sqrt{x}-\frac{2 b^3}{\sqrt{x}}","2 a^2 b x^{3/2}+\frac{2}{5} a^3 x^{5/2}+6 a b^2 \sqrt{x}-\frac{2 b^3}{\sqrt{x}}",1,"(-2*b^3)/Sqrt[x] + 6*a*b^2*Sqrt[x] + 2*a^2*b*x^(3/2) + (2*a^3*x^(5/2))/5","A",3,2,15,0.1333,1,"{263, 43}"
1661,1,47,0,0.0130861,"\int \left(a+\frac{b}{x}\right)^3 \sqrt{x} \, dx","Int[(a + b/x)^3*Sqrt[x],x]","6 a^2 b \sqrt{x}+\frac{2}{3} a^3 x^{3/2}-\frac{6 a b^2}{\sqrt{x}}-\frac{2 b^3}{3 x^{3/2}}","6 a^2 b \sqrt{x}+\frac{2}{3} a^3 x^{3/2}-\frac{6 a b^2}{\sqrt{x}}-\frac{2 b^3}{3 x^{3/2}}",1,"(-2*b^3)/(3*x^(3/2)) - (6*a*b^2)/Sqrt[x] + 6*a^2*b*Sqrt[x] + (2*a^3*x^(3/2))/3","A",3,2,15,0.1333,1,"{263, 43}"
1662,1,45,0,0.0131865,"\int \frac{\left(a+\frac{b}{x}\right)^3}{\sqrt{x}} \, dx","Int[(a + b/x)^3/Sqrt[x],x]","-\frac{6 a^2 b}{\sqrt{x}}+2 a^3 \sqrt{x}-\frac{2 a b^2}{x^{3/2}}-\frac{2 b^3}{5 x^{5/2}}","-\frac{6 a^2 b}{\sqrt{x}}+2 a^3 \sqrt{x}-\frac{2 a b^2}{x^{3/2}}-\frac{2 b^3}{5 x^{5/2}}",1,"(-2*b^3)/(5*x^(5/2)) - (2*a*b^2)/x^(3/2) - (6*a^2*b)/Sqrt[x] + 2*a^3*Sqrt[x]","A",3,2,15,0.1333,1,"{263, 43}"
1663,1,47,0,0.0126803,"\int \frac{\left(a+\frac{b}{x}\right)^3}{x^{3/2}} \, dx","Int[(a + b/x)^3/x^(3/2),x]","-\frac{2 a^2 b}{x^{3/2}}-\frac{2 a^3}{\sqrt{x}}-\frac{6 a b^2}{5 x^{5/2}}-\frac{2 b^3}{7 x^{7/2}}","-\frac{2 a^2 b}{x^{3/2}}-\frac{2 a^3}{\sqrt{x}}-\frac{6 a b^2}{5 x^{5/2}}-\frac{2 b^3}{7 x^{7/2}}",1,"(-2*b^3)/(7*x^(7/2)) - (6*a*b^2)/(5*x^(5/2)) - (2*a^2*b)/x^(3/2) - (2*a^3)/Sqrt[x]","A",3,2,15,0.1333,1,"{263, 43}"
1664,1,51,0,0.0133382,"\int \frac{\left(a+\frac{b}{x}\right)^3}{x^{5/2}} \, dx","Int[(a + b/x)^3/x^(5/2),x]","-\frac{6 a^2 b}{5 x^{5/2}}-\frac{2 a^3}{3 x^{3/2}}-\frac{6 a b^2}{7 x^{7/2}}-\frac{2 b^3}{9 x^{9/2}}","-\frac{6 a^2 b}{5 x^{5/2}}-\frac{2 a^3}{3 x^{3/2}}-\frac{6 a b^2}{7 x^{7/2}}-\frac{2 b^3}{9 x^{9/2}}",1,"(-2*b^3)/(9*x^(9/2)) - (6*a*b^2)/(7*x^(7/2)) - (6*a^2*b)/(5*x^(5/2)) - (2*a^3)/(3*x^(3/2))","A",3,2,15,0.1333,1,"{263, 43}"
1665,1,83,0,0.0355053,"\int \frac{x^{5/2}}{a+\frac{b}{x}} \, dx","Int[x^(5/2)/(a + b/x),x]","\frac{2 b^2 x^{3/2}}{3 a^3}-\frac{2 b^3 \sqrt{x}}{a^4}+\frac{2 b^{7/2} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{a^{9/2}}-\frac{2 b x^{5/2}}{5 a^2}+\frac{2 x^{7/2}}{7 a}","\frac{2 b^2 x^{3/2}}{3 a^3}-\frac{2 b^3 \sqrt{x}}{a^4}+\frac{2 b^{7/2} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{a^{9/2}}-\frac{2 b x^{5/2}}{5 a^2}+\frac{2 x^{7/2}}{7 a}",1,"(-2*b^3*Sqrt[x])/a^4 + (2*b^2*x^(3/2))/(3*a^3) - (2*b*x^(5/2))/(5*a^2) + (2*x^(7/2))/(7*a) + (2*b^(7/2)*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]])/a^(9/2)","A",7,4,15,0.2667,1,"{263, 50, 63, 205}"
1666,1,68,0,0.0232231,"\int \frac{x^{3/2}}{a+\frac{b}{x}} \, dx","Int[x^(3/2)/(a + b/x),x]","\frac{2 b^2 \sqrt{x}}{a^3}-\frac{2 b^{5/2} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{a^{7/2}}-\frac{2 b x^{3/2}}{3 a^2}+\frac{2 x^{5/2}}{5 a}","\frac{2 b^2 \sqrt{x}}{a^3}-\frac{2 b^{5/2} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{a^{7/2}}-\frac{2 b x^{3/2}}{3 a^2}+\frac{2 x^{5/2}}{5 a}",1,"(2*b^2*Sqrt[x])/a^3 - (2*b*x^(3/2))/(3*a^2) + (2*x^(5/2))/(5*a) - (2*b^(5/2)*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]])/a^(7/2)","A",6,4,15,0.2667,1,"{263, 50, 63, 205}"
1667,1,53,0,0.0181793,"\int \frac{\sqrt{x}}{a+\frac{b}{x}} \, dx","Int[Sqrt[x]/(a + b/x),x]","\frac{2 b^{3/2} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{a^{5/2}}-\frac{2 b \sqrt{x}}{a^2}+\frac{2 x^{3/2}}{3 a}","\frac{2 b^{3/2} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{a^{5/2}}-\frac{2 b \sqrt{x}}{a^2}+\frac{2 x^{3/2}}{3 a}",1,"(-2*b*Sqrt[x])/a^2 + (2*x^(3/2))/(3*a) + (2*b^(3/2)*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]])/a^(5/2)","A",5,4,15,0.2667,1,"{263, 50, 63, 205}"
1668,1,40,0,0.013709,"\int \frac{1}{\left(a+\frac{b}{x}\right) \sqrt{x}} \, dx","Int[1/((a + b/x)*Sqrt[x]),x]","\frac{2 \sqrt{x}}{a}-\frac{2 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{a^{3/2}}","\frac{2 \sqrt{x}}{a}-\frac{2 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{a^{3/2}}",1,"(2*Sqrt[x])/a - (2*Sqrt[b]*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]])/a^(3/2)","A",4,4,15,0.2667,1,"{263, 50, 63, 205}"
1669,1,29,0,0.0103555,"\int \frac{1}{\left(a+\frac{b}{x}\right) x^{3/2}} \, dx","Int[1/((a + b/x)*x^(3/2)),x]","\frac{2 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{\sqrt{a} \sqrt{b}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{\sqrt{a} \sqrt{b}}",1,"(2*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]])/(Sqrt[a]*Sqrt[b])","A",3,3,15,0.2000,1,"{263, 63, 205}"
1670,1,40,0,0.0149488,"\int \frac{1}{\left(a+\frac{b}{x}\right) x^{5/2}} \, dx","Int[1/((a + b/x)*x^(5/2)),x]","-\frac{2 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{b^{3/2}}-\frac{2}{b \sqrt{x}}","-\frac{2 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{b^{3/2}}-\frac{2}{b \sqrt{x}}",1,"-2/(b*Sqrt[x]) - (2*Sqrt[a]*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]])/b^(3/2)","A",4,4,15,0.2667,1,"{263, 51, 63, 205}"
1671,1,53,0,0.0187194,"\int \frac{1}{\left(a+\frac{b}{x}\right) x^{7/2}} \, dx","Int[1/((a + b/x)*x^(7/2)),x]","\frac{2 a^{3/2} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{b^{5/2}}+\frac{2 a}{b^2 \sqrt{x}}-\frac{2}{3 b x^{3/2}}","\frac{2 a^{3/2} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{b^{5/2}}+\frac{2 a}{b^2 \sqrt{x}}-\frac{2}{3 b x^{3/2}}",1,"-2/(3*b*x^(3/2)) + (2*a)/(b^2*Sqrt[x]) + (2*a^(3/2)*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]])/b^(5/2)","A",5,4,15,0.2667,1,"{263, 51, 63, 205}"
1672,1,68,0,0.0253934,"\int \frac{1}{\left(a+\frac{b}{x}\right) x^{9/2}} \, dx","Int[1/((a + b/x)*x^(9/2)),x]","-\frac{2 a^2}{b^3 \sqrt{x}}-\frac{2 a^{5/2} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{b^{7/2}}+\frac{2 a}{3 b^2 x^{3/2}}-\frac{2}{5 b x^{5/2}}","-\frac{2 a^2}{b^3 \sqrt{x}}-\frac{2 a^{5/2} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{b^{7/2}}+\frac{2 a}{3 b^2 x^{3/2}}-\frac{2}{5 b x^{5/2}}",1,"-2/(5*b*x^(5/2)) + (2*a)/(3*b^2*x^(3/2)) - (2*a^2)/(b^3*Sqrt[x]) - (2*a^(5/2)*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]])/b^(7/2)","A",6,4,15,0.2667,1,"{263, 51, 63, 205}"
1673,1,98,0,0.0406906,"\int \frac{x^{5/2}}{\left(a+\frac{b}{x}\right)^2} \, dx","Int[x^(5/2)/(a + b/x)^2,x]","\frac{3 b^2 x^{3/2}}{a^4}-\frac{9 b^3 \sqrt{x}}{a^5}+\frac{9 b^{7/2} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{a^{11/2}}-\frac{9 b x^{5/2}}{5 a^3}+\frac{9 x^{7/2}}{7 a^2}-\frac{x^{9/2}}{a (a x+b)}","\frac{3 b^2 x^{3/2}}{a^4}-\frac{9 b^3 \sqrt{x}}{a^5}+\frac{9 b^{7/2} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{a^{11/2}}-\frac{9 b x^{5/2}}{5 a^3}+\frac{9 x^{7/2}}{7 a^2}-\frac{x^{9/2}}{a (a x+b)}",1,"(-9*b^3*Sqrt[x])/a^5 + (3*b^2*x^(3/2))/a^4 - (9*b*x^(5/2))/(5*a^3) + (9*x^(7/2))/(7*a^2) - x^(9/2)/(a*(b + a*x)) + (9*b^(7/2)*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]])/a^(11/2)","A",8,5,15,0.3333,1,"{263, 47, 50, 63, 205}"
1674,1,85,0,0.0334017,"\int \frac{x^{3/2}}{\left(a+\frac{b}{x}\right)^2} \, dx","Int[x^(3/2)/(a + b/x)^2,x]","\frac{7 b^2 \sqrt{x}}{a^4}-\frac{7 b^{5/2} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{a^{9/2}}-\frac{7 b x^{3/2}}{3 a^3}+\frac{7 x^{5/2}}{5 a^2}-\frac{x^{7/2}}{a (a x+b)}","\frac{7 b^2 \sqrt{x}}{a^4}-\frac{7 b^{5/2} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{a^{9/2}}-\frac{7 b x^{3/2}}{3 a^3}+\frac{7 x^{5/2}}{5 a^2}-\frac{x^{7/2}}{a (a x+b)}",1,"(7*b^2*Sqrt[x])/a^4 - (7*b*x^(3/2))/(3*a^3) + (7*x^(5/2))/(5*a^2) - x^(7/2)/(a*(b + a*x)) - (7*b^(5/2)*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]])/a^(9/2)","A",7,5,15,0.3333,1,"{263, 47, 50, 63, 205}"
1675,1,70,0,0.023811,"\int \frac{\sqrt{x}}{\left(a+\frac{b}{x}\right)^2} \, dx","Int[Sqrt[x]/(a + b/x)^2,x]","\frac{5 b^{3/2} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{a^{7/2}}-\frac{5 b \sqrt{x}}{a^3}+\frac{5 x^{3/2}}{3 a^2}-\frac{x^{5/2}}{a (a x+b)}","\frac{5 b^{3/2} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{a^{7/2}}-\frac{5 b \sqrt{x}}{a^3}+\frac{5 x^{3/2}}{3 a^2}-\frac{x^{5/2}}{a (a x+b)}",1,"(-5*b*Sqrt[x])/a^3 + (5*x^(3/2))/(3*a^2) - x^(5/2)/(a*(b + a*x)) + (5*b^(3/2)*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]])/a^(7/2)","A",6,5,15,0.3333,1,"{263, 47, 50, 63, 205}"
1676,1,57,0,0.0192307,"\int \frac{1}{\left(a+\frac{b}{x}\right)^2 \sqrt{x}} \, dx","Int[1/((a + b/x)^2*Sqrt[x]),x]","-\frac{3 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{a^{5/2}}+\frac{3 \sqrt{x}}{a^2}-\frac{x^{3/2}}{a (a x+b)}","-\frac{3 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{a^{5/2}}+\frac{3 \sqrt{x}}{a^2}-\frac{x^{3/2}}{a (a x+b)}",1,"(3*Sqrt[x])/a^2 - x^(3/2)/(a*(b + a*x)) - (3*Sqrt[b]*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]])/a^(5/2)","A",5,5,15,0.3333,1,"{263, 47, 50, 63, 205}"
1677,1,46,0,0.0158499,"\int \frac{1}{\left(a+\frac{b}{x}\right)^2 x^{3/2}} \, dx","Int[1/((a + b/x)^2*x^(3/2)),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{a^{3/2} \sqrt{b}}-\frac{\sqrt{x}}{a (a x+b)}","\frac{\tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{a^{3/2} \sqrt{b}}-\frac{\sqrt{x}}{a (a x+b)}",1,"-(Sqrt[x]/(a*(b + a*x))) + ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]]/(a^(3/2)*Sqrt[b])","A",4,4,15,0.2667,1,"{263, 47, 63, 205}"
1678,1,45,0,0.0157653,"\int \frac{1}{\left(a+\frac{b}{x}\right)^2 x^{5/2}} \, dx","Int[1/((a + b/x)^2*x^(5/2)),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{\sqrt{a} b^{3/2}}+\frac{\sqrt{x}}{b (a x+b)}","\frac{\tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{\sqrt{a} b^{3/2}}+\frac{\sqrt{x}}{b (a x+b)}",1,"Sqrt[x]/(b*(b + a*x)) + ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]]/(Sqrt[a]*b^(3/2))","A",4,4,15,0.2667,1,"{263, 51, 63, 205}"
1679,1,56,0,0.0191806,"\int \frac{1}{\left(a+\frac{b}{x}\right)^2 x^{7/2}} \, dx","Int[1/((a + b/x)^2*x^(7/2)),x]","-\frac{3 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{b^{5/2}}+\frac{1}{b \sqrt{x} (a x+b)}-\frac{3}{b^2 \sqrt{x}}","-\frac{3 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{b^{5/2}}+\frac{1}{b \sqrt{x} (a x+b)}-\frac{3}{b^2 \sqrt{x}}",1,"-3/(b^2*Sqrt[x]) + 1/(b*Sqrt[x]*(b + a*x)) - (3*Sqrt[a]*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]])/b^(5/2)","A",5,4,15,0.2667,1,"{263, 51, 63, 205}"
1680,1,69,0,0.0242281,"\int \frac{1}{\left(a+\frac{b}{x}\right)^2 x^{9/2}} \, dx","Int[1/((a + b/x)^2*x^(9/2)),x]","\frac{5 a^{3/2} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{b^{7/2}}+\frac{5 a}{b^3 \sqrt{x}}+\frac{1}{b x^{3/2} (a x+b)}-\frac{5}{3 b^2 x^{3/2}}","\frac{5 a^{3/2} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{b^{7/2}}+\frac{5 a}{b^3 \sqrt{x}}+\frac{1}{b x^{3/2} (a x+b)}-\frac{5}{3 b^2 x^{3/2}}",1,"-5/(3*b^2*x^(3/2)) + (5*a)/(b^3*Sqrt[x]) + 1/(b*x^(3/2)*(b + a*x)) + (5*a^(3/2)*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]])/b^(7/2)","A",6,4,15,0.2667,1,"{263, 51, 63, 205}"
1681,1,84,0,0.032364,"\int \frac{1}{\left(a+\frac{b}{x}\right)^2 x^{11/2}} \, dx","Int[1/((a + b/x)^2*x^(11/2)),x]","-\frac{7 a^2}{b^4 \sqrt{x}}-\frac{7 a^{5/2} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{b^{9/2}}+\frac{7 a}{3 b^3 x^{3/2}}+\frac{1}{b x^{5/2} (a x+b)}-\frac{7}{5 b^2 x^{5/2}}","-\frac{7 a^2}{b^4 \sqrt{x}}-\frac{7 a^{5/2} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{b^{9/2}}+\frac{7 a}{3 b^3 x^{3/2}}+\frac{1}{b x^{5/2} (a x+b)}-\frac{7}{5 b^2 x^{5/2}}",1,"-7/(5*b^2*x^(5/2)) + (7*a)/(3*b^3*x^(3/2)) - (7*a^2)/(b^4*Sqrt[x]) + 1/(b*x^(5/2)*(b + a*x)) - (7*a^(5/2)*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]])/b^(9/2)","A",7,4,15,0.2667,1,"{263, 51, 63, 205}"
1682,1,110,0,0.0413503,"\int \frac{x^{3/2}}{\left(a+\frac{b}{x}\right)^3} \, dx","Int[x^(3/2)/(a + b/x)^3,x]","\frac{63 b^2 \sqrt{x}}{4 a^5}-\frac{63 b^{5/2} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{4 a^{11/2}}-\frac{9 x^{7/2}}{4 a^2 (a x+b)}-\frac{21 b x^{3/2}}{4 a^4}+\frac{63 x^{5/2}}{20 a^3}-\frac{x^{9/2}}{2 a (a x+b)^2}","\frac{63 b^2 \sqrt{x}}{4 a^5}-\frac{63 b^{5/2} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{4 a^{11/2}}-\frac{9 x^{7/2}}{4 a^2 (a x+b)}-\frac{21 b x^{3/2}}{4 a^4}+\frac{63 x^{5/2}}{20 a^3}-\frac{x^{9/2}}{2 a (a x+b)^2}",1,"(63*b^2*Sqrt[x])/(4*a^5) - (21*b*x^(3/2))/(4*a^4) + (63*x^(5/2))/(20*a^3) - x^(9/2)/(2*a*(b + a*x)^2) - (9*x^(7/2))/(4*a^2*(b + a*x)) - (63*b^(5/2)*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]])/(4*a^(11/2))","A",8,5,15,0.3333,1,"{263, 47, 50, 63, 205}"
1683,1,95,0,0.0336625,"\int \frac{\sqrt{x}}{\left(a+\frac{b}{x}\right)^3} \, dx","Int[Sqrt[x]/(a + b/x)^3,x]","\frac{35 b^{3/2} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{4 a^{9/2}}-\frac{7 x^{5/2}}{4 a^2 (a x+b)}-\frac{35 b \sqrt{x}}{4 a^4}+\frac{35 x^{3/2}}{12 a^3}-\frac{x^{7/2}}{2 a (a x+b)^2}","\frac{35 b^{3/2} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{4 a^{9/2}}-\frac{7 x^{5/2}}{4 a^2 (a x+b)}-\frac{35 b \sqrt{x}}{4 a^4}+\frac{35 x^{3/2}}{12 a^3}-\frac{x^{7/2}}{2 a (a x+b)^2}",1,"(-35*b*Sqrt[x])/(4*a^4) + (35*x^(3/2))/(12*a^3) - x^(7/2)/(2*a*(b + a*x)^2) - (7*x^(5/2))/(4*a^2*(b + a*x)) + (35*b^(3/2)*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]])/(4*a^(9/2))","A",7,5,15,0.3333,1,"{263, 47, 50, 63, 205}"
1684,1,82,0,0.0250705,"\int \frac{1}{\left(a+\frac{b}{x}\right)^3 \sqrt{x}} \, dx","Int[1/((a + b/x)^3*Sqrt[x]),x]","-\frac{5 x^{3/2}}{4 a^2 (a x+b)}-\frac{15 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{4 a^{7/2}}+\frac{15 \sqrt{x}}{4 a^3}-\frac{x^{5/2}}{2 a (a x+b)^2}","-\frac{5 x^{3/2}}{4 a^2 (a x+b)}-\frac{15 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{4 a^{7/2}}+\frac{15 \sqrt{x}}{4 a^3}-\frac{x^{5/2}}{2 a (a x+b)^2}",1,"(15*Sqrt[x])/(4*a^3) - x^(5/2)/(2*a*(b + a*x)^2) - (5*x^(3/2))/(4*a^2*(b + a*x)) - (15*Sqrt[b]*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]])/(4*a^(7/2))","A",6,5,15,0.3333,1,"{263, 47, 50, 63, 205}"
1685,1,70,0,0.0220354,"\int \frac{1}{\left(a+\frac{b}{x}\right)^3 x^{3/2}} \, dx","Int[1/((a + b/x)^3*x^(3/2)),x]","-\frac{3 \sqrt{x}}{4 a^2 (a x+b)}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{4 a^{5/2} \sqrt{b}}-\frac{x^{3/2}}{2 a (a x+b)^2}","-\frac{3 \sqrt{x}}{4 a^2 (a x+b)}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{4 a^{5/2} \sqrt{b}}-\frac{x^{3/2}}{2 a (a x+b)^2}",1,"-x^(3/2)/(2*a*(b + a*x)^2) - (3*Sqrt[x])/(4*a^2*(b + a*x)) + (3*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]])/(4*a^(5/2)*Sqrt[b])","A",5,4,15,0.2667,1,"{263, 47, 63, 205}"
1686,1,73,0,0.0222098,"\int \frac{1}{\left(a+\frac{b}{x}\right)^3 x^{5/2}} \, dx","Int[1/((a + b/x)^3*x^(5/2)),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{4 a^{3/2} b^{3/2}}+\frac{\sqrt{x}}{4 a b (a x+b)}-\frac{\sqrt{x}}{2 a (a x+b)^2}","\frac{\tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{4 a^{3/2} b^{3/2}}+\frac{\sqrt{x}}{4 a b (a x+b)}-\frac{\sqrt{x}}{2 a (a x+b)^2}",1,"-Sqrt[x]/(2*a*(b + a*x)^2) + Sqrt[x]/(4*a*b*(b + a*x)) + ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]]/(4*a^(3/2)*b^(3/2))","A",5,5,15,0.3333,1,"{263, 47, 51, 63, 205}"
1687,1,70,0,0.0233464,"\int \frac{1}{\left(a+\frac{b}{x}\right)^3 x^{7/2}} \, dx","Int[1/((a + b/x)^3*x^(7/2)),x]","\frac{3 \sqrt{x}}{4 b^2 (a x+b)}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{4 \sqrt{a} b^{5/2}}+\frac{\sqrt{x}}{2 b (a x+b)^2}","\frac{3 \sqrt{x}}{4 b^2 (a x+b)}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{4 \sqrt{a} b^{5/2}}+\frac{\sqrt{x}}{2 b (a x+b)^2}",1,"Sqrt[x]/(2*b*(b + a*x)^2) + (3*Sqrt[x])/(4*b^2*(b + a*x)) + (3*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]])/(4*Sqrt[a]*b^(5/2))","A",5,4,15,0.2667,1,"{263, 51, 63, 205}"
1688,1,82,0,0.0286377,"\int \frac{1}{\left(a+\frac{b}{x}\right)^3 x^{9/2}} \, dx","Int[1/((a + b/x)^3*x^(9/2)),x]","\frac{5}{4 b^2 \sqrt{x} (a x+b)}-\frac{15 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{4 b^{7/2}}+\frac{1}{2 b \sqrt{x} (a x+b)^2}-\frac{15}{4 b^3 \sqrt{x}}","\frac{5}{4 b^2 \sqrt{x} (a x+b)}-\frac{15 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{4 b^{7/2}}+\frac{1}{2 b \sqrt{x} (a x+b)^2}-\frac{15}{4 b^3 \sqrt{x}}",1,"-15/(4*b^3*Sqrt[x]) + 1/(2*b*Sqrt[x]*(b + a*x)^2) + 5/(4*b^2*Sqrt[x]*(b + a*x)) - (15*Sqrt[a]*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]])/(4*b^(7/2))","A",6,4,15,0.2667,1,"{263, 51, 63, 205}"
1689,1,95,0,0.0324622,"\int \frac{1}{\left(a+\frac{b}{x}\right)^3 x^{11/2}} \, dx","Int[1/((a + b/x)^3*x^(11/2)),x]","\frac{35 a^{3/2} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{4 b^{9/2}}+\frac{7}{4 b^2 x^{3/2} (a x+b)}+\frac{35 a}{4 b^4 \sqrt{x}}+\frac{1}{2 b x^{3/2} (a x+b)^2}-\frac{35}{12 b^3 x^{3/2}}","\frac{35 a^{3/2} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{4 b^{9/2}}+\frac{7}{4 b^2 x^{3/2} (a x+b)}+\frac{35 a}{4 b^4 \sqrt{x}}+\frac{1}{2 b x^{3/2} (a x+b)^2}-\frac{35}{12 b^3 x^{3/2}}",1,"-35/(12*b^3*x^(3/2)) + (35*a)/(4*b^4*Sqrt[x]) + 1/(2*b*x^(3/2)*(b + a*x)^2) + 7/(4*b^2*x^(3/2)*(b + a*x)) + (35*a^(3/2)*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]])/(4*b^(9/2))","A",7,4,15,0.2667,1,"{263, 51, 63, 205}"
1690,1,110,0,0.0430688,"\int \frac{1}{\left(a+\frac{b}{x}\right)^3 x^{13/2}} \, dx","Int[1/((a + b/x)^3*x^(13/2)),x]","-\frac{63 a^2}{4 b^5 \sqrt{x}}-\frac{63 a^{5/2} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{4 b^{11/2}}+\frac{21 a}{4 b^4 x^{3/2}}+\frac{9}{4 b^2 x^{5/2} (a x+b)}+\frac{1}{2 b x^{5/2} (a x+b)^2}-\frac{63}{20 b^3 x^{5/2}}","-\frac{63 a^2}{4 b^5 \sqrt{x}}-\frac{63 a^{5/2} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{4 b^{11/2}}+\frac{21 a}{4 b^4 x^{3/2}}+\frac{9}{4 b^2 x^{5/2} (a x+b)}+\frac{1}{2 b x^{5/2} (a x+b)^2}-\frac{63}{20 b^3 x^{5/2}}",1,"-63/(20*b^3*x^(5/2)) + (21*a)/(4*b^4*x^(3/2)) - (63*a^2)/(4*b^5*Sqrt[x]) + 1/(2*b*x^(5/2)*(b + a*x)^2) + 9/(4*b^2*x^(5/2)*(b + a*x)) - (63*a^(5/2)*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]])/(4*b^(11/2))","A",8,4,15,0.2667,1,"{263, 51, 63, 205}"
1691,1,117,0,0.0549252,"\int \sqrt{a+\frac{b}{x}} x^3 \, dx","Int[Sqrt[a + b/x]*x^3,x]","-\frac{5 b^2 x^2 \sqrt{a+\frac{b}{x}}}{96 a^2}+\frac{5 b^3 x \sqrt{a+\frac{b}{x}}}{64 a^3}-\frac{5 b^4 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{64 a^{7/2}}+\frac{b x^3 \sqrt{a+\frac{b}{x}}}{24 a}+\frac{1}{4} x^4 \sqrt{a+\frac{b}{x}}","-\frac{5 b^2 x^2 \sqrt{a+\frac{b}{x}}}{96 a^2}+\frac{5 b^3 x \sqrt{a+\frac{b}{x}}}{64 a^3}-\frac{5 b^4 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{64 a^{7/2}}+\frac{b x^3 \sqrt{a+\frac{b}{x}}}{24 a}+\frac{1}{4} x^4 \sqrt{a+\frac{b}{x}}",1,"(5*b^3*Sqrt[a + b/x]*x)/(64*a^3) - (5*b^2*Sqrt[a + b/x]*x^2)/(96*a^2) + (b*Sqrt[a + b/x]*x^3)/(24*a) + (Sqrt[a + b/x]*x^4)/4 - (5*b^4*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/(64*a^(7/2))","A",7,5,15,0.3333,1,"{266, 47, 51, 63, 208}"
1692,1,93,0,0.0393377,"\int \sqrt{a+\frac{b}{x}} x^2 \, dx","Int[Sqrt[a + b/x]*x^2,x]","-\frac{b^2 x \sqrt{a+\frac{b}{x}}}{8 a^2}+\frac{b^3 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{8 a^{5/2}}+\frac{b x^2 \sqrt{a+\frac{b}{x}}}{12 a}+\frac{1}{3} x^3 \sqrt{a+\frac{b}{x}}","-\frac{b^2 x \sqrt{a+\frac{b}{x}}}{8 a^2}+\frac{b^3 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{8 a^{5/2}}+\frac{b x^2 \sqrt{a+\frac{b}{x}}}{12 a}+\frac{1}{3} x^3 \sqrt{a+\frac{b}{x}}",1,"-(b^2*Sqrt[a + b/x]*x)/(8*a^2) + (b*Sqrt[a + b/x]*x^2)/(12*a) + (Sqrt[a + b/x]*x^3)/3 + (b^3*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/(8*a^(5/2))","A",6,5,15,0.3333,1,"{266, 47, 51, 63, 208}"
1693,1,69,0,0.0274541,"\int \sqrt{a+\frac{b}{x}} x \, dx","Int[Sqrt[a + b/x]*x,x]","-\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{4 a^{3/2}}+\frac{1}{2} x^2 \sqrt{a+\frac{b}{x}}+\frac{b x \sqrt{a+\frac{b}{x}}}{4 a}","-\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{4 a^{3/2}}+\frac{1}{2} x^2 \sqrt{a+\frac{b}{x}}+\frac{b x \sqrt{a+\frac{b}{x}}}{4 a}",1,"(b*Sqrt[a + b/x]*x)/(4*a) + (Sqrt[a + b/x]*x^2)/2 - (b^2*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/(4*a^(3/2))","A",5,5,13,0.3846,1,"{266, 47, 51, 63, 208}"
1694,1,39,0,0.0173824,"\int \sqrt{a+\frac{b}{x}} \, dx","Int[Sqrt[a + b/x],x]","x \sqrt{a+\frac{b}{x}}+\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{\sqrt{a}}","x \sqrt{a+\frac{b}{x}}+\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{\sqrt{a}}",1,"Sqrt[a + b/x]*x + (b*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/Sqrt[a]","A",4,4,11,0.3636,1,"{242, 47, 63, 208}"
1695,1,39,0,0.0192805,"\int \frac{\sqrt{a+\frac{b}{x}}}{x} \, dx","Int[Sqrt[a + b/x]/x,x]","2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)-2 \sqrt{a+\frac{b}{x}}","2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)-2 \sqrt{a+\frac{b}{x}}",1,"-2*Sqrt[a + b/x] + 2*Sqrt[a]*ArcTanh[Sqrt[a + b/x]/Sqrt[a]]","A",4,4,15,0.2667,1,"{266, 50, 63, 208}"
1696,1,18,0,0.0054849,"\int \frac{\sqrt{a+\frac{b}{x}}}{x^2} \, dx","Int[Sqrt[a + b/x]/x^2,x]","-\frac{2 \left(a+\frac{b}{x}\right)^{3/2}}{3 b}","-\frac{2 \left(a+\frac{b}{x}\right)^{3/2}}{3 b}",1,"(-2*(a + b/x)^(3/2))/(3*b)","A",1,1,15,0.06667,1,"{261}"
1697,1,38,0,0.0174295,"\int \frac{\sqrt{a+\frac{b}{x}}}{x^3} \, dx","Int[Sqrt[a + b/x]/x^3,x]","\frac{2 a \left(a+\frac{b}{x}\right)^{3/2}}{3 b^2}-\frac{2 \left(a+\frac{b}{x}\right)^{5/2}}{5 b^2}","\frac{2 a \left(a+\frac{b}{x}\right)^{3/2}}{3 b^2}-\frac{2 \left(a+\frac{b}{x}\right)^{5/2}}{5 b^2}",1,"(2*a*(a + b/x)^(3/2))/(3*b^2) - (2*(a + b/x)^(5/2))/(5*b^2)","A",3,2,15,0.1333,1,"{266, 43}"
1698,1,59,0,0.0251826,"\int \frac{\sqrt{a+\frac{b}{x}}}{x^4} \, dx","Int[Sqrt[a + b/x]/x^4,x]","-\frac{2 a^2 \left(a+\frac{b}{x}\right)^{3/2}}{3 b^3}-\frac{2 \left(a+\frac{b}{x}\right)^{7/2}}{7 b^3}+\frac{4 a \left(a+\frac{b}{x}\right)^{5/2}}{5 b^3}","-\frac{2 a^2 \left(a+\frac{b}{x}\right)^{3/2}}{3 b^3}-\frac{2 \left(a+\frac{b}{x}\right)^{7/2}}{7 b^3}+\frac{4 a \left(a+\frac{b}{x}\right)^{5/2}}{5 b^3}",1,"(-2*a^2*(a + b/x)^(3/2))/(3*b^3) + (4*a*(a + b/x)^(5/2))/(5*b^3) - (2*(a + b/x)^(7/2))/(7*b^3)","A",3,2,15,0.1333,1,"{266, 43}"
1699,1,80,0,0.0326512,"\int \frac{\sqrt{a+\frac{b}{x}}}{x^5} \, dx","Int[Sqrt[a + b/x]/x^5,x]","-\frac{6 a^2 \left(a+\frac{b}{x}\right)^{5/2}}{5 b^4}+\frac{2 a^3 \left(a+\frac{b}{x}\right)^{3/2}}{3 b^4}-\frac{2 \left(a+\frac{b}{x}\right)^{9/2}}{9 b^4}+\frac{6 a \left(a+\frac{b}{x}\right)^{7/2}}{7 b^4}","-\frac{6 a^2 \left(a+\frac{b}{x}\right)^{5/2}}{5 b^4}+\frac{2 a^3 \left(a+\frac{b}{x}\right)^{3/2}}{3 b^4}-\frac{2 \left(a+\frac{b}{x}\right)^{9/2}}{9 b^4}+\frac{6 a \left(a+\frac{b}{x}\right)^{7/2}}{7 b^4}",1,"(2*a^3*(a + b/x)^(3/2))/(3*b^4) - (6*a^2*(a + b/x)^(5/2))/(5*b^4) + (6*a*(a + b/x)^(7/2))/(7*b^4) - (2*(a + b/x)^(9/2))/(9*b^4)","A",3,2,15,0.1333,1,"{266, 43}"
1700,1,101,0,0.0425936,"\int \frac{\sqrt{a+\frac{b}{x}}}{x^6} \, dx","Int[Sqrt[a + b/x]/x^6,x]","-\frac{12 a^2 \left(a+\frac{b}{x}\right)^{7/2}}{7 b^5}+\frac{8 a^3 \left(a+\frac{b}{x}\right)^{5/2}}{5 b^5}-\frac{2 a^4 \left(a+\frac{b}{x}\right)^{3/2}}{3 b^5}-\frac{2 \left(a+\frac{b}{x}\right)^{11/2}}{11 b^5}+\frac{8 a \left(a+\frac{b}{x}\right)^{9/2}}{9 b^5}","-\frac{12 a^2 \left(a+\frac{b}{x}\right)^{7/2}}{7 b^5}+\frac{8 a^3 \left(a+\frac{b}{x}\right)^{5/2}}{5 b^5}-\frac{2 a^4 \left(a+\frac{b}{x}\right)^{3/2}}{3 b^5}-\frac{2 \left(a+\frac{b}{x}\right)^{11/2}}{11 b^5}+\frac{8 a \left(a+\frac{b}{x}\right)^{9/2}}{9 b^5}",1,"(-2*a^4*(a + b/x)^(3/2))/(3*b^5) + (8*a^3*(a + b/x)^(5/2))/(5*b^5) - (12*a^2*(a + b/x)^(7/2))/(7*b^5) + (8*a*(a + b/x)^(9/2))/(9*b^5) - (2*(a + b/x)^(11/2))/(11*b^5)","A",3,2,15,0.1333,1,"{266, 43}"
1701,1,114,0,0.0518756,"\int \left(a+\frac{b}{x}\right)^{3/2} x^3 \, dx","Int[(a + b/x)^(3/2)*x^3,x]","-\frac{3 b^3 x \sqrt{a+\frac{b}{x}}}{64 a^2}+\frac{3 b^4 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{64 a^{5/2}}+\frac{b^2 x^2 \sqrt{a+\frac{b}{x}}}{32 a}+\frac{1}{8} b x^3 \sqrt{a+\frac{b}{x}}+\frac{1}{4} x^4 \left(a+\frac{b}{x}\right)^{3/2}","-\frac{3 b^3 x \sqrt{a+\frac{b}{x}}}{64 a^2}+\frac{3 b^4 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{64 a^{5/2}}+\frac{b^2 x^2 \sqrt{a+\frac{b}{x}}}{32 a}+\frac{1}{8} b x^3 \sqrt{a+\frac{b}{x}}+\frac{1}{4} x^4 \left(a+\frac{b}{x}\right)^{3/2}",1,"(-3*b^3*Sqrt[a + b/x]*x)/(64*a^2) + (b^2*Sqrt[a + b/x]*x^2)/(32*a) + (b*Sqrt[a + b/x]*x^3)/8 + ((a + b/x)^(3/2)*x^4)/4 + (3*b^4*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/(64*a^(5/2))","A",7,5,15,0.3333,1,"{266, 47, 51, 63, 208}"
1702,1,90,0,0.0391332,"\int \left(a+\frac{b}{x}\right)^{3/2} x^2 \, dx","Int[(a + b/x)^(3/2)*x^2,x]","-\frac{b^3 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{8 a^{3/2}}+\frac{b^2 x \sqrt{a+\frac{b}{x}}}{8 a}+\frac{1}{4} b x^2 \sqrt{a+\frac{b}{x}}+\frac{1}{3} x^3 \left(a+\frac{b}{x}\right)^{3/2}","-\frac{b^3 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{8 a^{3/2}}+\frac{b^2 x \sqrt{a+\frac{b}{x}}}{8 a}+\frac{1}{4} b x^2 \sqrt{a+\frac{b}{x}}+\frac{1}{3} x^3 \left(a+\frac{b}{x}\right)^{3/2}",1,"(b^2*Sqrt[a + b/x]*x)/(8*a) + (b*Sqrt[a + b/x]*x^2)/4 + ((a + b/x)^(3/2)*x^3)/3 - (b^3*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/(8*a^(3/2))","A",6,5,15,0.3333,1,"{266, 47, 51, 63, 208}"
1703,1,66,0,0.0276017,"\int \left(a+\frac{b}{x}\right)^{3/2} x \, dx","Int[(a + b/x)^(3/2)*x,x]","\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{4 \sqrt{a}}+\frac{1}{2} x^2 \left(a+\frac{b}{x}\right)^{3/2}+\frac{3}{4} b x \sqrt{a+\frac{b}{x}}","\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{4 \sqrt{a}}+\frac{1}{2} x^2 \left(a+\frac{b}{x}\right)^{3/2}+\frac{3}{4} b x \sqrt{a+\frac{b}{x}}",1,"(3*b*Sqrt[a + b/x]*x)/4 + ((a + b/x)^(3/2)*x^2)/2 + (3*b^2*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/(4*Sqrt[a])","A",5,4,13,0.3077,1,"{266, 47, 63, 208}"
1704,1,54,0,0.0241782,"\int \left(a+\frac{b}{x}\right)^{3/2} \, dx","Int[(a + b/x)^(3/2),x]","x \left(a+\frac{b}{x}\right)^{3/2}-3 b \sqrt{a+\frac{b}{x}}+3 \sqrt{a} b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)","x \left(a+\frac{b}{x}\right)^{3/2}-3 b \sqrt{a+\frac{b}{x}}+3 \sqrt{a} b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)",1,"-3*b*Sqrt[a + b/x] + (a + b/x)^(3/2)*x + 3*Sqrt[a]*b*ArcTanh[Sqrt[a + b/x]/Sqrt[a]]","A",5,5,11,0.4545,1,"{242, 47, 50, 63, 208}"
1705,1,55,0,0.0269337,"\int \frac{\left(a+\frac{b}{x}\right)^{3/2}}{x} \, dx","Int[(a + b/x)^(3/2)/x,x]","2 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)-2 a \sqrt{a+\frac{b}{x}}-\frac{2}{3} \left(a+\frac{b}{x}\right)^{3/2}","2 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)-2 a \sqrt{a+\frac{b}{x}}-\frac{2}{3} \left(a+\frac{b}{x}\right)^{3/2}",1,"-2*a*Sqrt[a + b/x] - (2*(a + b/x)^(3/2))/3 + 2*a^(3/2)*ArcTanh[Sqrt[a + b/x]/Sqrt[a]]","A",5,4,15,0.2667,1,"{266, 50, 63, 208}"
1706,1,18,0,0.0059618,"\int \frac{\left(a+\frac{b}{x}\right)^{3/2}}{x^2} \, dx","Int[(a + b/x)^(3/2)/x^2,x]","-\frac{2 \left(a+\frac{b}{x}\right)^{5/2}}{5 b}","-\frac{2 \left(a+\frac{b}{x}\right)^{5/2}}{5 b}",1,"(-2*(a + b/x)^(5/2))/(5*b)","A",1,1,15,0.06667,1,"{261}"
1707,1,38,0,0.0175401,"\int \frac{\left(a+\frac{b}{x}\right)^{3/2}}{x^3} \, dx","Int[(a + b/x)^(3/2)/x^3,x]","\frac{2 a \left(a+\frac{b}{x}\right)^{5/2}}{5 b^2}-\frac{2 \left(a+\frac{b}{x}\right)^{7/2}}{7 b^2}","\frac{2 a \left(a+\frac{b}{x}\right)^{5/2}}{5 b^2}-\frac{2 \left(a+\frac{b}{x}\right)^{7/2}}{7 b^2}",1,"(2*a*(a + b/x)^(5/2))/(5*b^2) - (2*(a + b/x)^(7/2))/(7*b^2)","A",3,2,15,0.1333,1,"{266, 43}"
1708,1,59,0,0.0256244,"\int \frac{\left(a+\frac{b}{x}\right)^{3/2}}{x^4} \, dx","Int[(a + b/x)^(3/2)/x^4,x]","-\frac{2 a^2 \left(a+\frac{b}{x}\right)^{5/2}}{5 b^3}-\frac{2 \left(a+\frac{b}{x}\right)^{9/2}}{9 b^3}+\frac{4 a \left(a+\frac{b}{x}\right)^{7/2}}{7 b^3}","-\frac{2 a^2 \left(a+\frac{b}{x}\right)^{5/2}}{5 b^3}-\frac{2 \left(a+\frac{b}{x}\right)^{9/2}}{9 b^3}+\frac{4 a \left(a+\frac{b}{x}\right)^{7/2}}{7 b^3}",1,"(-2*a^2*(a + b/x)^(5/2))/(5*b^3) + (4*a*(a + b/x)^(7/2))/(7*b^3) - (2*(a + b/x)^(9/2))/(9*b^3)","A",3,2,15,0.1333,1,"{266, 43}"
1709,1,80,0,0.0338428,"\int \frac{\left(a+\frac{b}{x}\right)^{3/2}}{x^5} \, dx","Int[(a + b/x)^(3/2)/x^5,x]","-\frac{6 a^2 \left(a+\frac{b}{x}\right)^{7/2}}{7 b^4}+\frac{2 a^3 \left(a+\frac{b}{x}\right)^{5/2}}{5 b^4}-\frac{2 \left(a+\frac{b}{x}\right)^{11/2}}{11 b^4}+\frac{2 a \left(a+\frac{b}{x}\right)^{9/2}}{3 b^4}","-\frac{6 a^2 \left(a+\frac{b}{x}\right)^{7/2}}{7 b^4}+\frac{2 a^3 \left(a+\frac{b}{x}\right)^{5/2}}{5 b^4}-\frac{2 \left(a+\frac{b}{x}\right)^{11/2}}{11 b^4}+\frac{2 a \left(a+\frac{b}{x}\right)^{9/2}}{3 b^4}",1,"(2*a^3*(a + b/x)^(5/2))/(5*b^4) - (6*a^2*(a + b/x)^(7/2))/(7*b^4) + (2*a*(a + b/x)^(9/2))/(3*b^4) - (2*(a + b/x)^(11/2))/(11*b^4)","A",3,2,15,0.1333,1,"{266, 43}"
1710,1,101,0,0.040455,"\int \frac{\left(a+\frac{b}{x}\right)^{3/2}}{x^6} \, dx","Int[(a + b/x)^(3/2)/x^6,x]","-\frac{4 a^2 \left(a+\frac{b}{x}\right)^{9/2}}{3 b^5}+\frac{8 a^3 \left(a+\frac{b}{x}\right)^{7/2}}{7 b^5}-\frac{2 a^4 \left(a+\frac{b}{x}\right)^{5/2}}{5 b^5}-\frac{2 \left(a+\frac{b}{x}\right)^{13/2}}{13 b^5}+\frac{8 a \left(a+\frac{b}{x}\right)^{11/2}}{11 b^5}","-\frac{4 a^2 \left(a+\frac{b}{x}\right)^{9/2}}{3 b^5}+\frac{8 a^3 \left(a+\frac{b}{x}\right)^{7/2}}{7 b^5}-\frac{2 a^4 \left(a+\frac{b}{x}\right)^{5/2}}{5 b^5}-\frac{2 \left(a+\frac{b}{x}\right)^{13/2}}{13 b^5}+\frac{8 a \left(a+\frac{b}{x}\right)^{11/2}}{11 b^5}",1,"(-2*a^4*(a + b/x)^(5/2))/(5*b^5) + (8*a^3*(a + b/x)^(7/2))/(7*b^5) - (4*a^2*(a + b/x)^(9/2))/(3*b^5) + (8*a*(a + b/x)^(11/2))/(11*b^5) - (2*(a + b/x)^(13/2))/(13*b^5)","A",3,2,15,0.1333,1,"{266, 43}"
1711,1,122,0,0.0507715,"\int \frac{\left(a+\frac{b}{x}\right)^{3/2}}{x^7} \, dx","Int[(a + b/x)^(3/2)/x^7,x]","-\frac{20 a^2 \left(a+\frac{b}{x}\right)^{11/2}}{11 b^6}+\frac{20 a^3 \left(a+\frac{b}{x}\right)^{9/2}}{9 b^6}-\frac{10 a^4 \left(a+\frac{b}{x}\right)^{7/2}}{7 b^6}+\frac{2 a^5 \left(a+\frac{b}{x}\right)^{5/2}}{5 b^6}-\frac{2 \left(a+\frac{b}{x}\right)^{15/2}}{15 b^6}+\frac{10 a \left(a+\frac{b}{x}\right)^{13/2}}{13 b^6}","-\frac{20 a^2 \left(a+\frac{b}{x}\right)^{11/2}}{11 b^6}+\frac{20 a^3 \left(a+\frac{b}{x}\right)^{9/2}}{9 b^6}-\frac{10 a^4 \left(a+\frac{b}{x}\right)^{7/2}}{7 b^6}+\frac{2 a^5 \left(a+\frac{b}{x}\right)^{5/2}}{5 b^6}-\frac{2 \left(a+\frac{b}{x}\right)^{15/2}}{15 b^6}+\frac{10 a \left(a+\frac{b}{x}\right)^{13/2}}{13 b^6}",1,"(2*a^5*(a + b/x)^(5/2))/(5*b^6) - (10*a^4*(a + b/x)^(7/2))/(7*b^6) + (20*a^3*(a + b/x)^(9/2))/(9*b^6) - (20*a^2*(a + b/x)^(11/2))/(11*b^6) + (10*a*(a + b/x)^(13/2))/(13*b^6) - (2*(a + b/x)^(15/2))/(15*b^6)","A",3,2,15,0.1333,1,"{266, 43}"
1712,1,111,0,0.0516641,"\int \left(a+\frac{b}{x}\right)^{5/2} x^3 \, dx","Int[(a + b/x)^(5/2)*x^3,x]","-\frac{5 b^4 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{64 a^{3/2}}+\frac{5}{32} b^2 x^2 \sqrt{a+\frac{b}{x}}+\frac{5 b^3 x \sqrt{a+\frac{b}{x}}}{64 a}+\frac{5}{24} b x^3 \left(a+\frac{b}{x}\right)^{3/2}+\frac{1}{4} x^4 \left(a+\frac{b}{x}\right)^{5/2}","-\frac{5 b^4 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{64 a^{3/2}}+\frac{5}{32} b^2 x^2 \sqrt{a+\frac{b}{x}}+\frac{5 b^3 x \sqrt{a+\frac{b}{x}}}{64 a}+\frac{5}{24} b x^3 \left(a+\frac{b}{x}\right)^{3/2}+\frac{1}{4} x^4 \left(a+\frac{b}{x}\right)^{5/2}",1,"(5*b^3*Sqrt[a + b/x]*x)/(64*a) + (5*b^2*Sqrt[a + b/x]*x^2)/32 + (5*b*(a + b/x)^(3/2)*x^3)/24 + ((a + b/x)^(5/2)*x^4)/4 - (5*b^4*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/(64*a^(3/2))","A",7,5,15,0.3333,1,"{266, 47, 51, 63, 208}"
1713,1,87,0,0.0375767,"\int \left(a+\frac{b}{x}\right)^{5/2} x^2 \, dx","Int[(a + b/x)^(5/2)*x^2,x]","\frac{5}{8} b^2 x \sqrt{a+\frac{b}{x}}+\frac{5 b^3 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{8 \sqrt{a}}+\frac{5}{12} b x^2 \left(a+\frac{b}{x}\right)^{3/2}+\frac{1}{3} x^3 \left(a+\frac{b}{x}\right)^{5/2}","\frac{5}{8} b^2 x \sqrt{a+\frac{b}{x}}+\frac{5 b^3 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{8 \sqrt{a}}+\frac{5}{12} b x^2 \left(a+\frac{b}{x}\right)^{3/2}+\frac{1}{3} x^3 \left(a+\frac{b}{x}\right)^{5/2}",1,"(5*b^2*Sqrt[a + b/x]*x)/8 + (5*b*(a + b/x)^(3/2)*x^2)/12 + ((a + b/x)^(5/2)*x^3)/3 + (5*b^3*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/(8*Sqrt[a])","A",6,4,15,0.2667,1,"{266, 47, 63, 208}"
1714,1,84,0,0.034874,"\int \left(a+\frac{b}{x}\right)^{5/2} x \, dx","Int[(a + b/x)^(5/2)*x,x]","-\frac{15}{4} b^2 \sqrt{a+\frac{b}{x}}+\frac{15}{4} \sqrt{a} b^2 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)+\frac{1}{2} x^2 \left(a+\frac{b}{x}\right)^{5/2}+\frac{5}{4} b x \left(a+\frac{b}{x}\right)^{3/2}","-\frac{15}{4} b^2 \sqrt{a+\frac{b}{x}}+\frac{15}{4} \sqrt{a} b^2 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)+\frac{1}{2} x^2 \left(a+\frac{b}{x}\right)^{5/2}+\frac{5}{4} b x \left(a+\frac{b}{x}\right)^{3/2}",1,"(-15*b^2*Sqrt[a + b/x])/4 + (5*b*(a + b/x)^(3/2)*x)/4 + ((a + b/x)^(5/2)*x^2)/2 + (15*Sqrt[a]*b^2*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/4","A",6,5,13,0.3846,1,"{266, 47, 50, 63, 208}"
1715,1,71,0,0.0310837,"\int \left(a+\frac{b}{x}\right)^{5/2} \, dx","Int[(a + b/x)^(5/2),x]","5 a^{3/2} b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)+x \left(a+\frac{b}{x}\right)^{5/2}-\frac{5}{3} b \left(a+\frac{b}{x}\right)^{3/2}-5 a b \sqrt{a+\frac{b}{x}}","5 a^{3/2} b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)+x \left(a+\frac{b}{x}\right)^{5/2}-\frac{5}{3} b \left(a+\frac{b}{x}\right)^{3/2}-5 a b \sqrt{a+\frac{b}{x}}",1,"-5*a*b*Sqrt[a + b/x] - (5*b*(a + b/x)^(3/2))/3 + (a + b/x)^(5/2)*x + 5*a^(3/2)*b*ArcTanh[Sqrt[a + b/x]/Sqrt[a]]","A",6,5,11,0.4545,1,"{242, 47, 50, 63, 208}"
1716,1,73,0,0.033514,"\int \frac{\left(a+\frac{b}{x}\right)^{5/2}}{x} \, dx","Int[(a + b/x)^(5/2)/x,x]","-2 a^2 \sqrt{a+\frac{b}{x}}+2 a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)-\frac{2}{3} a \left(a+\frac{b}{x}\right)^{3/2}-\frac{2}{5} \left(a+\frac{b}{x}\right)^{5/2}","-2 a^2 \sqrt{a+\frac{b}{x}}+2 a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)-\frac{2}{3} a \left(a+\frac{b}{x}\right)^{3/2}-\frac{2}{5} \left(a+\frac{b}{x}\right)^{5/2}",1,"-2*a^2*Sqrt[a + b/x] - (2*a*(a + b/x)^(3/2))/3 - (2*(a + b/x)^(5/2))/5 + 2*a^(5/2)*ArcTanh[Sqrt[a + b/x]/Sqrt[a]]","A",6,4,15,0.2667,1,"{266, 50, 63, 208}"
1717,1,18,0,0.0056614,"\int \frac{\left(a+\frac{b}{x}\right)^{5/2}}{x^2} \, dx","Int[(a + b/x)^(5/2)/x^2,x]","-\frac{2 \left(a+\frac{b}{x}\right)^{7/2}}{7 b}","-\frac{2 \left(a+\frac{b}{x}\right)^{7/2}}{7 b}",1,"(-2*(a + b/x)^(7/2))/(7*b)","A",1,1,15,0.06667,1,"{261}"
1718,1,38,0,0.0171105,"\int \frac{\left(a+\frac{b}{x}\right)^{5/2}}{x^3} \, dx","Int[(a + b/x)^(5/2)/x^3,x]","\frac{2 a \left(a+\frac{b}{x}\right)^{7/2}}{7 b^2}-\frac{2 \left(a+\frac{b}{x}\right)^{9/2}}{9 b^2}","\frac{2 a \left(a+\frac{b}{x}\right)^{7/2}}{7 b^2}-\frac{2 \left(a+\frac{b}{x}\right)^{9/2}}{9 b^2}",1,"(2*a*(a + b/x)^(7/2))/(7*b^2) - (2*(a + b/x)^(9/2))/(9*b^2)","A",3,2,15,0.1333,1,"{266, 43}"
1719,1,59,0,0.0242511,"\int \frac{\left(a+\frac{b}{x}\right)^{5/2}}{x^4} \, dx","Int[(a + b/x)^(5/2)/x^4,x]","-\frac{2 a^2 \left(a+\frac{b}{x}\right)^{7/2}}{7 b^3}-\frac{2 \left(a+\frac{b}{x}\right)^{11/2}}{11 b^3}+\frac{4 a \left(a+\frac{b}{x}\right)^{9/2}}{9 b^3}","-\frac{2 a^2 \left(a+\frac{b}{x}\right)^{7/2}}{7 b^3}-\frac{2 \left(a+\frac{b}{x}\right)^{11/2}}{11 b^3}+\frac{4 a \left(a+\frac{b}{x}\right)^{9/2}}{9 b^3}",1,"(-2*a^2*(a + b/x)^(7/2))/(7*b^3) + (4*a*(a + b/x)^(9/2))/(9*b^3) - (2*(a + b/x)^(11/2))/(11*b^3)","A",3,2,15,0.1333,1,"{266, 43}"
1720,1,80,0,0.0320359,"\int \frac{\left(a+\frac{b}{x}\right)^{5/2}}{x^5} \, dx","Int[(a + b/x)^(5/2)/x^5,x]","-\frac{2 a^2 \left(a+\frac{b}{x}\right)^{9/2}}{3 b^4}+\frac{2 a^3 \left(a+\frac{b}{x}\right)^{7/2}}{7 b^4}-\frac{2 \left(a+\frac{b}{x}\right)^{13/2}}{13 b^4}+\frac{6 a \left(a+\frac{b}{x}\right)^{11/2}}{11 b^4}","-\frac{2 a^2 \left(a+\frac{b}{x}\right)^{9/2}}{3 b^4}+\frac{2 a^3 \left(a+\frac{b}{x}\right)^{7/2}}{7 b^4}-\frac{2 \left(a+\frac{b}{x}\right)^{13/2}}{13 b^4}+\frac{6 a \left(a+\frac{b}{x}\right)^{11/2}}{11 b^4}",1,"(2*a^3*(a + b/x)^(7/2))/(7*b^4) - (2*a^2*(a + b/x)^(9/2))/(3*b^4) + (6*a*(a + b/x)^(11/2))/(11*b^4) - (2*(a + b/x)^(13/2))/(13*b^4)","A",3,2,15,0.1333,1,"{266, 43}"
1721,1,101,0,0.0395268,"\int \frac{\left(a+\frac{b}{x}\right)^{5/2}}{x^6} \, dx","Int[(a + b/x)^(5/2)/x^6,x]","-\frac{12 a^2 \left(a+\frac{b}{x}\right)^{11/2}}{11 b^5}+\frac{8 a^3 \left(a+\frac{b}{x}\right)^{9/2}}{9 b^5}-\frac{2 a^4 \left(a+\frac{b}{x}\right)^{7/2}}{7 b^5}-\frac{2 \left(a+\frac{b}{x}\right)^{15/2}}{15 b^5}+\frac{8 a \left(a+\frac{b}{x}\right)^{13/2}}{13 b^5}","-\frac{12 a^2 \left(a+\frac{b}{x}\right)^{11/2}}{11 b^5}+\frac{8 a^3 \left(a+\frac{b}{x}\right)^{9/2}}{9 b^5}-\frac{2 a^4 \left(a+\frac{b}{x}\right)^{7/2}}{7 b^5}-\frac{2 \left(a+\frac{b}{x}\right)^{15/2}}{15 b^5}+\frac{8 a \left(a+\frac{b}{x}\right)^{13/2}}{13 b^5}",1,"(-2*a^4*(a + b/x)^(7/2))/(7*b^5) + (8*a^3*(a + b/x)^(9/2))/(9*b^5) - (12*a^2*(a + b/x)^(11/2))/(11*b^5) + (8*a*(a + b/x)^(13/2))/(13*b^5) - (2*(a + b/x)^(15/2))/(15*b^5)","A",3,2,15,0.1333,1,"{266, 43}"
1722,1,120,0,0.0507232,"\int \frac{x^3}{\sqrt{a+\frac{b}{x}}} \, dx","Int[x^3/Sqrt[a + b/x],x]","\frac{35 b^2 x^2 \sqrt{a+\frac{b}{x}}}{96 a^3}-\frac{35 b^3 x \sqrt{a+\frac{b}{x}}}{64 a^4}+\frac{35 b^4 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{64 a^{9/2}}-\frac{7 b x^3 \sqrt{a+\frac{b}{x}}}{24 a^2}+\frac{x^4 \sqrt{a+\frac{b}{x}}}{4 a}","\frac{35 b^2 x^2 \sqrt{a+\frac{b}{x}}}{96 a^3}-\frac{35 b^3 x \sqrt{a+\frac{b}{x}}}{64 a^4}+\frac{35 b^4 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{64 a^{9/2}}-\frac{7 b x^3 \sqrt{a+\frac{b}{x}}}{24 a^2}+\frac{x^4 \sqrt{a+\frac{b}{x}}}{4 a}",1,"(-35*b^3*Sqrt[a + b/x]*x)/(64*a^4) + (35*b^2*Sqrt[a + b/x]*x^2)/(96*a^3) - (7*b*Sqrt[a + b/x]*x^3)/(24*a^2) + (Sqrt[a + b/x]*x^4)/(4*a) + (35*b^4*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/(64*a^(9/2))","A",7,4,15,0.2667,1,"{266, 51, 63, 208}"
1723,1,96,0,0.039083,"\int \frac{x^2}{\sqrt{a+\frac{b}{x}}} \, dx","Int[x^2/Sqrt[a + b/x],x]","\frac{5 b^2 x \sqrt{a+\frac{b}{x}}}{8 a^3}-\frac{5 b^3 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{8 a^{7/2}}-\frac{5 b x^2 \sqrt{a+\frac{b}{x}}}{12 a^2}+\frac{x^3 \sqrt{a+\frac{b}{x}}}{3 a}","\frac{5 b^2 x \sqrt{a+\frac{b}{x}}}{8 a^3}-\frac{5 b^3 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{8 a^{7/2}}-\frac{5 b x^2 \sqrt{a+\frac{b}{x}}}{12 a^2}+\frac{x^3 \sqrt{a+\frac{b}{x}}}{3 a}",1,"(5*b^2*Sqrt[a + b/x]*x)/(8*a^3) - (5*b*Sqrt[a + b/x]*x^2)/(12*a^2) + (Sqrt[a + b/x]*x^3)/(3*a) - (5*b^3*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/(8*a^(7/2))","A",6,4,15,0.2667,1,"{266, 51, 63, 208}"
1724,1,72,0,0.0273446,"\int \frac{x}{\sqrt{a+\frac{b}{x}}} \, dx","Int[x/Sqrt[a + b/x],x]","\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{4 a^{5/2}}-\frac{3 b x \sqrt{a+\frac{b}{x}}}{4 a^2}+\frac{x^2 \sqrt{a+\frac{b}{x}}}{2 a}","\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{4 a^{5/2}}-\frac{3 b x \sqrt{a+\frac{b}{x}}}{4 a^2}+\frac{x^2 \sqrt{a+\frac{b}{x}}}{2 a}",1,"(-3*b*Sqrt[a + b/x]*x)/(4*a^2) + (Sqrt[a + b/x]*x^2)/(2*a) + (3*b^2*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/(4*a^(5/2))","A",5,4,13,0.3077,1,"{266, 51, 63, 208}"
1725,1,43,0,0.0171796,"\int \frac{1}{\sqrt{a+\frac{b}{x}}} \, dx","Int[1/Sqrt[a + b/x],x]","\frac{x \sqrt{a+\frac{b}{x}}}{a}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{3/2}}","\frac{x \sqrt{a+\frac{b}{x}}}{a}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{3/2}}",1,"(Sqrt[a + b/x]*x)/a - (b*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/a^(3/2)","A",4,4,11,0.3636,1,"{242, 51, 63, 208}"
1726,1,25,0,0.0137432,"\int \frac{1}{\sqrt{a+\frac{b}{x}} x} \, dx","Int[1/(Sqrt[a + b/x]*x),x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{\sqrt{a}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{\sqrt{a}}",1,"(2*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/Sqrt[a]","A",3,3,15,0.2000,1,"{266, 63, 208}"
1727,1,16,0,0.0051254,"\int \frac{1}{\sqrt{a+\frac{b}{x}} x^2} \, dx","Int[1/(Sqrt[a + b/x]*x^2),x]","-\frac{2 \sqrt{a+\frac{b}{x}}}{b}","-\frac{2 \sqrt{a+\frac{b}{x}}}{b}",1,"(-2*Sqrt[a + b/x])/b","A",1,1,15,0.06667,1,"{261}"
1728,1,36,0,0.0160528,"\int \frac{1}{\sqrt{a+\frac{b}{x}} x^3} \, dx","Int[1/(Sqrt[a + b/x]*x^3),x]","\frac{2 a \sqrt{a+\frac{b}{x}}}{b^2}-\frac{2 \left(a+\frac{b}{x}\right)^{3/2}}{3 b^2}","\frac{2 a \sqrt{a+\frac{b}{x}}}{b^2}-\frac{2 \left(a+\frac{b}{x}\right)^{3/2}}{3 b^2}",1,"(2*a*Sqrt[a + b/x])/b^2 - (2*(a + b/x)^(3/2))/(3*b^2)","A",3,2,15,0.1333,1,"{266, 43}"
1729,1,57,0,0.023212,"\int \frac{1}{\sqrt{a+\frac{b}{x}} x^4} \, dx","Int[1/(Sqrt[a + b/x]*x^4),x]","-\frac{2 a^2 \sqrt{a+\frac{b}{x}}}{b^3}-\frac{2 \left(a+\frac{b}{x}\right)^{5/2}}{5 b^3}+\frac{4 a \left(a+\frac{b}{x}\right)^{3/2}}{3 b^3}","-\frac{2 a^2 \sqrt{a+\frac{b}{x}}}{b^3}-\frac{2 \left(a+\frac{b}{x}\right)^{5/2}}{5 b^3}+\frac{4 a \left(a+\frac{b}{x}\right)^{3/2}}{3 b^3}",1,"(-2*a^2*Sqrt[a + b/x])/b^3 + (4*a*(a + b/x)^(3/2))/(3*b^3) - (2*(a + b/x)^(5/2))/(5*b^3)","A",3,2,15,0.1333,1,"{266, 43}"
1730,1,76,0,0.0319035,"\int \frac{1}{\sqrt{a+\frac{b}{x}} x^5} \, dx","Int[1/(Sqrt[a + b/x]*x^5),x]","-\frac{2 a^2 \left(a+\frac{b}{x}\right)^{3/2}}{b^4}+\frac{2 a^3 \sqrt{a+\frac{b}{x}}}{b^4}-\frac{2 \left(a+\frac{b}{x}\right)^{7/2}}{7 b^4}+\frac{6 a \left(a+\frac{b}{x}\right)^{5/2}}{5 b^4}","-\frac{2 a^2 \left(a+\frac{b}{x}\right)^{3/2}}{b^4}+\frac{2 a^3 \sqrt{a+\frac{b}{x}}}{b^4}-\frac{2 \left(a+\frac{b}{x}\right)^{7/2}}{7 b^4}+\frac{6 a \left(a+\frac{b}{x}\right)^{5/2}}{5 b^4}",1,"(2*a^3*Sqrt[a + b/x])/b^4 - (2*a^2*(a + b/x)^(3/2))/b^4 + (6*a*(a + b/x)^(5/2))/(5*b^4) - (2*(a + b/x)^(7/2))/(7*b^4)","A",3,2,15,0.1333,1,"{266, 43}"
1731,1,99,0,0.0385148,"\int \frac{1}{\sqrt{a+\frac{b}{x}} x^6} \, dx","Int[1/(Sqrt[a + b/x]*x^6),x]","-\frac{12 a^2 \left(a+\frac{b}{x}\right)^{5/2}}{5 b^5}+\frac{8 a^3 \left(a+\frac{b}{x}\right)^{3/2}}{3 b^5}-\frac{2 a^4 \sqrt{a+\frac{b}{x}}}{b^5}-\frac{2 \left(a+\frac{b}{x}\right)^{9/2}}{9 b^5}+\frac{8 a \left(a+\frac{b}{x}\right)^{7/2}}{7 b^5}","-\frac{12 a^2 \left(a+\frac{b}{x}\right)^{5/2}}{5 b^5}+\frac{8 a^3 \left(a+\frac{b}{x}\right)^{3/2}}{3 b^5}-\frac{2 a^4 \sqrt{a+\frac{b}{x}}}{b^5}-\frac{2 \left(a+\frac{b}{x}\right)^{9/2}}{9 b^5}+\frac{8 a \left(a+\frac{b}{x}\right)^{7/2}}{7 b^5}",1,"(-2*a^4*Sqrt[a + b/x])/b^5 + (8*a^3*(a + b/x)^(3/2))/(3*b^5) - (12*a^2*(a + b/x)^(5/2))/(5*b^5) + (8*a*(a + b/x)^(7/2))/(7*b^5) - (2*(a + b/x)^(9/2))/(9*b^5)","A",3,2,15,0.1333,1,"{266, 43}"
1732,1,115,0,0.0529987,"\int \frac{x^2}{\left(a+\frac{b}{x}\right)^{3/2}} \, dx","Int[x^2/(a + b/x)^(3/2),x]","\frac{35 b^2 x \sqrt{a+\frac{b}{x}}}{8 a^4}-\frac{35 b^3 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{8 a^{9/2}}-\frac{35 b x^2 \sqrt{a+\frac{b}{x}}}{12 a^3}+\frac{7 x^3 \sqrt{a+\frac{b}{x}}}{3 a^2}-\frac{2 x^3}{a \sqrt{a+\frac{b}{x}}}","\frac{35 b^3}{8 a^4 \sqrt{a+\frac{b}{x}}}+\frac{35 b^2 x}{24 a^3 \sqrt{a+\frac{b}{x}}}-\frac{35 b^3 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{8 a^{9/2}}-\frac{7 b x^2}{12 a^2 \sqrt{a+\frac{b}{x}}}+\frac{x^3}{3 a \sqrt{a+\frac{b}{x}}}",1,"(35*b^2*Sqrt[a + b/x]*x)/(8*a^4) - (35*b*Sqrt[a + b/x]*x^2)/(12*a^3) - (2*x^3)/(a*Sqrt[a + b/x]) + (7*Sqrt[a + b/x]*x^3)/(3*a^2) - (35*b^3*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/(8*a^(9/2))","A",7,4,15,0.2667,1,"{266, 51, 63, 208}"
1733,1,91,0,0.0378823,"\int \frac{x}{\left(a+\frac{b}{x}\right)^{3/2}} \, dx","Int[x/(a + b/x)^(3/2),x]","\frac{15 b^2 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{4 a^{7/2}}+\frac{5 x^2 \sqrt{a+\frac{b}{x}}}{2 a^2}-\frac{15 b x \sqrt{a+\frac{b}{x}}}{4 a^3}-\frac{2 x^2}{a \sqrt{a+\frac{b}{x}}}","-\frac{15 b^2}{4 a^3 \sqrt{a+\frac{b}{x}}}+\frac{15 b^2 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{4 a^{7/2}}-\frac{5 b x}{4 a^2 \sqrt{a+\frac{b}{x}}}+\frac{x^2}{2 a \sqrt{a+\frac{b}{x}}}",1,"(-15*b*Sqrt[a + b/x]*x)/(4*a^3) - (2*x^2)/(a*Sqrt[a + b/x]) + (5*Sqrt[a + b/x]*x^2)/(2*a^2) + (15*b^2*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/(4*a^(7/2))","A",6,4,13,0.3077,1,"{266, 51, 63, 208}"
1734,1,61,0,0.0263445,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{3/2}} \, dx","Int[(a + b/x)^(-3/2),x]","\frac{3 x \sqrt{a+\frac{b}{x}}}{a^2}-\frac{3 b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{5/2}}-\frac{2 x}{a \sqrt{a+\frac{b}{x}}}","\frac{3 b}{a^2 \sqrt{a+\frac{b}{x}}}-\frac{3 b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{5/2}}+\frac{x}{a \sqrt{a+\frac{b}{x}}}",1,"(-2*x)/(a*Sqrt[a + b/x]) + (3*Sqrt[a + b/x]*x)/a^2 - (3*b*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/a^(5/2)","A",5,4,11,0.3636,1,"{242, 51, 63, 208}"
1735,1,42,0,0.0207117,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{3/2} x} \, dx","Int[1/((a + b/x)^(3/2)*x),x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{3/2}}-\frac{2}{a \sqrt{a+\frac{b}{x}}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{3/2}}-\frac{2}{a \sqrt{a+\frac{b}{x}}}",1,"-2/(a*Sqrt[a + b/x]) + (2*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/a^(3/2)","A",4,4,15,0.2667,1,"{266, 51, 63, 208}"
1736,1,16,0,0.0056079,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{3/2} x^2} \, dx","Int[1/((a + b/x)^(3/2)*x^2),x]","\frac{2}{b \sqrt{a+\frac{b}{x}}}","\frac{2}{b \sqrt{a+\frac{b}{x}}}",1,"2/(b*Sqrt[a + b/x])","A",1,1,15,0.06667,1,"{261}"
1737,1,34,0,0.0169184,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{3/2} x^3} \, dx","Int[1/((a + b/x)^(3/2)*x^3),x]","-\frac{2 a}{b^2 \sqrt{a+\frac{b}{x}}}-\frac{2 \sqrt{a+\frac{b}{x}}}{b^2}","-\frac{2 a}{b^2 \sqrt{a+\frac{b}{x}}}-\frac{2 \sqrt{a+\frac{b}{x}}}{b^2}",1,"(-2*a)/(b^2*Sqrt[a + b/x]) - (2*Sqrt[a + b/x])/b^2","A",3,2,15,0.1333,1,"{266, 43}"
1738,1,55,0,0.0249515,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{3/2} x^4} \, dx","Int[1/((a + b/x)^(3/2)*x^4),x]","\frac{2 a^2}{b^3 \sqrt{a+\frac{b}{x}}}+\frac{4 a \sqrt{a+\frac{b}{x}}}{b^3}-\frac{2 \left(a+\frac{b}{x}\right)^{3/2}}{3 b^3}","\frac{2 a^2}{b^3 \sqrt{a+\frac{b}{x}}}+\frac{4 a \sqrt{a+\frac{b}{x}}}{b^3}-\frac{2 \left(a+\frac{b}{x}\right)^{3/2}}{3 b^3}",1,"(2*a^2)/(b^3*Sqrt[a + b/x]) + (4*a*Sqrt[a + b/x])/b^3 - (2*(a + b/x)^(3/2))/(3*b^3)","A",3,2,15,0.1333,1,"{266, 43}"
1739,1,74,0,0.0322883,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{3/2} x^5} \, dx","Int[1/((a + b/x)^(3/2)*x^5),x]","-\frac{2 a^3}{b^4 \sqrt{a+\frac{b}{x}}}-\frac{6 a^2 \sqrt{a+\frac{b}{x}}}{b^4}+\frac{2 a \left(a+\frac{b}{x}\right)^{3/2}}{b^4}-\frac{2 \left(a+\frac{b}{x}\right)^{5/2}}{5 b^4}","-\frac{2 a^3}{b^4 \sqrt{a+\frac{b}{x}}}-\frac{6 a^2 \sqrt{a+\frac{b}{x}}}{b^4}+\frac{2 a \left(a+\frac{b}{x}\right)^{3/2}}{b^4}-\frac{2 \left(a+\frac{b}{x}\right)^{5/2}}{5 b^4}",1,"(-2*a^3)/(b^4*Sqrt[a + b/x]) - (6*a^2*Sqrt[a + b/x])/b^4 + (2*a*(a + b/x)^(3/2))/b^4 - (2*(a + b/x)^(5/2))/(5*b^4)","A",3,2,15,0.1333,1,"{266, 43}"
1740,1,95,0,0.039751,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{3/2} x^6} \, dx","Int[1/((a + b/x)^(3/2)*x^6),x]","\frac{2 a^4}{b^5 \sqrt{a+\frac{b}{x}}}+\frac{8 a^3 \sqrt{a+\frac{b}{x}}}{b^5}-\frac{4 a^2 \left(a+\frac{b}{x}\right)^{3/2}}{b^5}+\frac{8 a \left(a+\frac{b}{x}\right)^{5/2}}{5 b^5}-\frac{2 \left(a+\frac{b}{x}\right)^{7/2}}{7 b^5}","\frac{2 a^4}{b^5 \sqrt{a+\frac{b}{x}}}+\frac{8 a^3 \sqrt{a+\frac{b}{x}}}{b^5}-\frac{4 a^2 \left(a+\frac{b}{x}\right)^{3/2}}{b^5}+\frac{8 a \left(a+\frac{b}{x}\right)^{5/2}}{5 b^5}-\frac{2 \left(a+\frac{b}{x}\right)^{7/2}}{7 b^5}",1,"(2*a^4)/(b^5*Sqrt[a + b/x]) + (8*a^3*Sqrt[a + b/x])/b^5 - (4*a^2*(a + b/x)^(3/2))/b^5 + (8*a*(a + b/x)^(5/2))/(5*b^5) - (2*(a + b/x)^(7/2))/(7*b^5)","A",3,2,15,0.1333,1,"{266, 43}"
1741,1,116,0,0.0487726,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{3/2} x^7} \, dx","Int[1/((a + b/x)^(3/2)*x^7),x]","-\frac{2 a^5}{b^6 \sqrt{a+\frac{b}{x}}}-\frac{10 a^4 \sqrt{a+\frac{b}{x}}}{b^6}+\frac{20 a^3 \left(a+\frac{b}{x}\right)^{3/2}}{3 b^6}-\frac{4 a^2 \left(a+\frac{b}{x}\right)^{5/2}}{b^6}+\frac{10 a \left(a+\frac{b}{x}\right)^{7/2}}{7 b^6}-\frac{2 \left(a+\frac{b}{x}\right)^{9/2}}{9 b^6}","-\frac{2 a^5}{b^6 \sqrt{a+\frac{b}{x}}}-\frac{10 a^4 \sqrt{a+\frac{b}{x}}}{b^6}+\frac{20 a^3 \left(a+\frac{b}{x}\right)^{3/2}}{3 b^6}-\frac{4 a^2 \left(a+\frac{b}{x}\right)^{5/2}}{b^6}+\frac{10 a \left(a+\frac{b}{x}\right)^{7/2}}{7 b^6}-\frac{2 \left(a+\frac{b}{x}\right)^{9/2}}{9 b^6}",1,"(-2*a^5)/(b^6*Sqrt[a + b/x]) - (10*a^4*Sqrt[a + b/x])/b^6 + (20*a^3*(a + b/x)^(3/2))/(3*b^6) - (4*a^2*(a + b/x)^(5/2))/b^6 + (10*a*(a + b/x)^(7/2))/(7*b^6) - (2*(a + b/x)^(9/2))/(9*b^6)","A",3,2,15,0.1333,1,"{266, 43}"
1742,1,134,0,0.0663102,"\int \frac{x^2}{\left(a+\frac{b}{x}\right)^{5/2}} \, dx","Int[x^2/(a + b/x)^(5/2),x]","\frac{105 b^2 x \sqrt{a+\frac{b}{x}}}{8 a^5}-\frac{105 b^3 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{8 a^{11/2}}-\frac{35 b x^2 \sqrt{a+\frac{b}{x}}}{4 a^4}+\frac{7 x^3 \sqrt{a+\frac{b}{x}}}{a^3}-\frac{6 x^3}{a^2 \sqrt{a+\frac{b}{x}}}-\frac{2 x^3}{3 a \left(a+\frac{b}{x}\right)^{3/2}}","\frac{105 b^3}{8 a^5 \sqrt{a+\frac{b}{x}}}+\frac{35 b^3}{8 a^4 \left(a+\frac{b}{x}\right)^{3/2}}+\frac{21 b^2 x}{8 a^3 \left(a+\frac{b}{x}\right)^{3/2}}-\frac{105 b^3 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{8 a^{11/2}}-\frac{3 b x^2}{4 a^2 \left(a+\frac{b}{x}\right)^{3/2}}+\frac{x^3}{3 a \left(a+\frac{b}{x}\right)^{3/2}}",1,"(105*b^2*Sqrt[a + b/x]*x)/(8*a^5) - (35*b*Sqrt[a + b/x]*x^2)/(4*a^4) - (2*x^3)/(3*a*(a + b/x)^(3/2)) - (6*x^3)/(a^2*Sqrt[a + b/x]) + (7*Sqrt[a + b/x]*x^3)/a^3 - (105*b^3*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/(8*a^(11/2))","A",8,4,15,0.2667,1,"{266, 51, 63, 208}"
1743,1,114,0,0.0502586,"\int \frac{x}{\left(a+\frac{b}{x}\right)^{5/2}} \, dx","Int[x/(a + b/x)^(5/2),x]","\frac{35 b^2 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{4 a^{9/2}}+\frac{35 x^2 \sqrt{a+\frac{b}{x}}}{6 a^3}-\frac{14 x^2}{3 a^2 \sqrt{a+\frac{b}{x}}}-\frac{35 b x \sqrt{a+\frac{b}{x}}}{4 a^4}-\frac{2 x^2}{3 a \left(a+\frac{b}{x}\right)^{3/2}}","-\frac{35 b^2}{4 a^4 \sqrt{a+\frac{b}{x}}}-\frac{35 b^2}{12 a^3 \left(a+\frac{b}{x}\right)^{3/2}}+\frac{35 b^2 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{4 a^{9/2}}-\frac{7 b x}{4 a^2 \left(a+\frac{b}{x}\right)^{3/2}}+\frac{x^2}{2 a \left(a+\frac{b}{x}\right)^{3/2}}",1,"(-35*b*Sqrt[a + b/x]*x)/(4*a^4) - (2*x^2)/(3*a*(a + b/x)^(3/2)) - (14*x^2)/(3*a^2*Sqrt[a + b/x]) + (35*Sqrt[a + b/x]*x^2)/(6*a^3) + (35*b^2*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/(4*a^(9/2))","A",7,4,13,0.3077,1,"{266, 51, 63, 208}"
1744,1,82,0,0.0359848,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{5/2}} \, dx","Int[(a + b/x)^(-5/2),x]","\frac{5 x \sqrt{a+\frac{b}{x}}}{a^3}-\frac{10 x}{3 a^2 \sqrt{a+\frac{b}{x}}}-\frac{5 b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{7/2}}-\frac{2 x}{3 a \left(a+\frac{b}{x}\right)^{3/2}}","\frac{5 b}{a^3 \sqrt{a+\frac{b}{x}}}+\frac{5 b}{3 a^2 \left(a+\frac{b}{x}\right)^{3/2}}-\frac{5 b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{7/2}}+\frac{x}{a \left(a+\frac{b}{x}\right)^{3/2}}",1,"(-2*x)/(3*a*(a + b/x)^(3/2)) - (10*x)/(3*a^2*Sqrt[a + b/x]) + (5*Sqrt[a + b/x]*x)/a^3 - (5*b*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/a^(7/2)","A",6,4,11,0.3636,1,"{242, 51, 63, 208}"
1745,1,60,0,0.0291079,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{5/2} x} \, dx","Int[1/((a + b/x)^(5/2)*x),x]","-\frac{2}{a^2 \sqrt{a+\frac{b}{x}}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{5/2}}-\frac{2}{3 a \left(a+\frac{b}{x}\right)^{3/2}}","-\frac{2}{a^2 \sqrt{a+\frac{b}{x}}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{5/2}}-\frac{2}{3 a \left(a+\frac{b}{x}\right)^{3/2}}",1,"-2/(3*a*(a + b/x)^(3/2)) - 2/(a^2*Sqrt[a + b/x]) + (2*ArcTanh[Sqrt[a + b/x]/Sqrt[a]])/a^(5/2)","A",5,4,15,0.2667,1,"{266, 51, 63, 208}"
1746,1,18,0,0.0056434,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{5/2} x^2} \, dx","Int[1/((a + b/x)^(5/2)*x^2),x]","\frac{2}{3 b \left(a+\frac{b}{x}\right)^{3/2}}","\frac{2}{3 b \left(a+\frac{b}{x}\right)^{3/2}}",1,"2/(3*b*(a + b/x)^(3/2))","A",1,1,15,0.06667,1,"{261}"
1747,1,36,0,0.0172852,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{5/2} x^3} \, dx","Int[1/((a + b/x)^(5/2)*x^3),x]","\frac{2}{b^2 \sqrt{a+\frac{b}{x}}}-\frac{2 a}{3 b^2 \left(a+\frac{b}{x}\right)^{3/2}}","\frac{2}{b^2 \sqrt{a+\frac{b}{x}}}-\frac{2 a}{3 b^2 \left(a+\frac{b}{x}\right)^{3/2}}",1,"(-2*a)/(3*b^2*(a + b/x)^(3/2)) + 2/(b^2*Sqrt[a + b/x])","A",3,2,15,0.1333,1,"{266, 43}"
1748,1,55,0,0.0248751,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{5/2} x^4} \, dx","Int[1/((a + b/x)^(5/2)*x^4),x]","\frac{2 a^2}{3 b^3 \left(a+\frac{b}{x}\right)^{3/2}}-\frac{4 a}{b^3 \sqrt{a+\frac{b}{x}}}-\frac{2 \sqrt{a+\frac{b}{x}}}{b^3}","\frac{2 a^2}{3 b^3 \left(a+\frac{b}{x}\right)^{3/2}}-\frac{4 a}{b^3 \sqrt{a+\frac{b}{x}}}-\frac{2 \sqrt{a+\frac{b}{x}}}{b^3}",1,"(2*a^2)/(3*b^3*(a + b/x)^(3/2)) - (4*a)/(b^3*Sqrt[a + b/x]) - (2*Sqrt[a + b/x])/b^3","A",3,2,15,0.1333,1,"{266, 43}"
1749,1,76,0,0.0319017,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{5/2} x^5} \, dx","Int[1/((a + b/x)^(5/2)*x^5),x]","-\frac{2 a^3}{3 b^4 \left(a+\frac{b}{x}\right)^{3/2}}+\frac{6 a^2}{b^4 \sqrt{a+\frac{b}{x}}}+\frac{6 a \sqrt{a+\frac{b}{x}}}{b^4}-\frac{2 \left(a+\frac{b}{x}\right)^{3/2}}{3 b^4}","-\frac{2 a^3}{3 b^4 \left(a+\frac{b}{x}\right)^{3/2}}+\frac{6 a^2}{b^4 \sqrt{a+\frac{b}{x}}}+\frac{6 a \sqrt{a+\frac{b}{x}}}{b^4}-\frac{2 \left(a+\frac{b}{x}\right)^{3/2}}{3 b^4}",1,"(-2*a^3)/(3*b^4*(a + b/x)^(3/2)) + (6*a^2)/(b^4*Sqrt[a + b/x]) + (6*a*Sqrt[a + b/x])/b^4 - (2*(a + b/x)^(3/2))/(3*b^4)","A",3,2,15,0.1333,1,"{266, 43}"
1750,1,97,0,0.0393913,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{5/2} x^6} \, dx","Int[1/((a + b/x)^(5/2)*x^6),x]","\frac{2 a^4}{3 b^5 \left(a+\frac{b}{x}\right)^{3/2}}-\frac{8 a^3}{b^5 \sqrt{a+\frac{b}{x}}}-\frac{12 a^2 \sqrt{a+\frac{b}{x}}}{b^5}+\frac{8 a \left(a+\frac{b}{x}\right)^{3/2}}{3 b^5}-\frac{2 \left(a+\frac{b}{x}\right)^{5/2}}{5 b^5}","\frac{2 a^4}{3 b^5 \left(a+\frac{b}{x}\right)^{3/2}}-\frac{8 a^3}{b^5 \sqrt{a+\frac{b}{x}}}-\frac{12 a^2 \sqrt{a+\frac{b}{x}}}{b^5}+\frac{8 a \left(a+\frac{b}{x}\right)^{3/2}}{3 b^5}-\frac{2 \left(a+\frac{b}{x}\right)^{5/2}}{5 b^5}",1,"(2*a^4)/(3*b^5*(a + b/x)^(3/2)) - (8*a^3)/(b^5*Sqrt[a + b/x]) - (12*a^2*Sqrt[a + b/x])/b^5 + (8*a*(a + b/x)^(3/2))/(3*b^5) - (2*(a + b/x)^(5/2))/(5*b^5)","A",3,2,15,0.1333,1,"{266, 43}"
1751,1,116,0,0.0483134,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{5/2} x^7} \, dx","Int[1/((a + b/x)^(5/2)*x^7),x]","-\frac{2 a^5}{3 b^6 \left(a+\frac{b}{x}\right)^{3/2}}+\frac{10 a^4}{b^6 \sqrt{a+\frac{b}{x}}}+\frac{20 a^3 \sqrt{a+\frac{b}{x}}}{b^6}-\frac{20 a^2 \left(a+\frac{b}{x}\right)^{3/2}}{3 b^6}+\frac{2 a \left(a+\frac{b}{x}\right)^{5/2}}{b^6}-\frac{2 \left(a+\frac{b}{x}\right)^{7/2}}{7 b^6}","-\frac{2 a^5}{3 b^6 \left(a+\frac{b}{x}\right)^{3/2}}+\frac{10 a^4}{b^6 \sqrt{a+\frac{b}{x}}}+\frac{20 a^3 \sqrt{a+\frac{b}{x}}}{b^6}-\frac{20 a^2 \left(a+\frac{b}{x}\right)^{3/2}}{3 b^6}+\frac{2 a \left(a+\frac{b}{x}\right)^{5/2}}{b^6}-\frac{2 \left(a+\frac{b}{x}\right)^{7/2}}{7 b^6}",1,"(-2*a^5)/(3*b^6*(a + b/x)^(3/2)) + (10*a^4)/(b^6*Sqrt[a + b/x]) + (20*a^3*Sqrt[a + b/x])/b^6 - (20*a^2*(a + b/x)^(3/2))/(3*b^6) + (2*a*(a + b/x)^(5/2))/b^6 - (2*(a + b/x)^(7/2))/(7*b^6)","A",3,2,15,0.1333,1,"{266, 43}"
1752,1,100,0,0.031134,"\int \sqrt{a+\frac{b}{x}} x^{7/2} \, dx","Int[Sqrt[a + b/x]*x^(7/2),x]","\frac{16 b^2 x^{5/2} \left(a+\frac{b}{x}\right)^{3/2}}{105 a^3}-\frac{32 b^3 x^{3/2} \left(a+\frac{b}{x}\right)^{3/2}}{315 a^4}-\frac{4 b x^{7/2} \left(a+\frac{b}{x}\right)^{3/2}}{21 a^2}+\frac{2 x^{9/2} \left(a+\frac{b}{x}\right)^{3/2}}{9 a}","\frac{16 b^2 x^{5/2} \left(a+\frac{b}{x}\right)^{3/2}}{105 a^3}-\frac{32 b^3 x^{3/2} \left(a+\frac{b}{x}\right)^{3/2}}{315 a^4}-\frac{4 b x^{7/2} \left(a+\frac{b}{x}\right)^{3/2}}{21 a^2}+\frac{2 x^{9/2} \left(a+\frac{b}{x}\right)^{3/2}}{9 a}",1,"(-32*b^3*(a + b/x)^(3/2)*x^(3/2))/(315*a^4) + (16*b^2*(a + b/x)^(3/2)*x^(5/2))/(105*a^3) - (4*b*(a + b/x)^(3/2)*x^(7/2))/(21*a^2) + (2*(a + b/x)^(3/2)*x^(9/2))/(9*a)","A",4,2,17,0.1176,1,"{271, 264}"
1753,1,74,0,0.021808,"\int \sqrt{a+\frac{b}{x}} x^{5/2} \, dx","Int[Sqrt[a + b/x]*x^(5/2),x]","\frac{16 b^2 x^{3/2} \left(a+\frac{b}{x}\right)^{3/2}}{105 a^3}-\frac{8 b x^{5/2} \left(a+\frac{b}{x}\right)^{3/2}}{35 a^2}+\frac{2 x^{7/2} \left(a+\frac{b}{x}\right)^{3/2}}{7 a}","\frac{16 b^2 x^{3/2} \left(a+\frac{b}{x}\right)^{3/2}}{105 a^3}-\frac{8 b x^{5/2} \left(a+\frac{b}{x}\right)^{3/2}}{35 a^2}+\frac{2 x^{7/2} \left(a+\frac{b}{x}\right)^{3/2}}{7 a}",1,"(16*b^2*(a + b/x)^(3/2)*x^(3/2))/(105*a^3) - (8*b*(a + b/x)^(3/2)*x^(5/2))/(35*a^2) + (2*(a + b/x)^(3/2)*x^(7/2))/(7*a)","A",3,2,17,0.1176,1,"{271, 264}"
1754,1,48,0,0.0123544,"\int \sqrt{a+\frac{b}{x}} x^{3/2} \, dx","Int[Sqrt[a + b/x]*x^(3/2),x]","\frac{2 x^{5/2} \left(a+\frac{b}{x}\right)^{3/2}}{5 a}-\frac{4 b x^{3/2} \left(a+\frac{b}{x}\right)^{3/2}}{15 a^2}","\frac{2 x^{5/2} \left(a+\frac{b}{x}\right)^{3/2}}{5 a}-\frac{4 b x^{3/2} \left(a+\frac{b}{x}\right)^{3/2}}{15 a^2}",1,"(-4*b*(a + b/x)^(3/2)*x^(3/2))/(15*a^2) + (2*(a + b/x)^(3/2)*x^(5/2))/(5*a)","A",2,2,17,0.1176,1,"{271, 264}"
1755,1,23,0,0.0053108,"\int \sqrt{a+\frac{b}{x}} \sqrt{x} \, dx","Int[Sqrt[a + b/x]*Sqrt[x],x]","\frac{2 x^{3/2} \left(a+\frac{b}{x}\right)^{3/2}}{3 a}","\frac{2 x^{3/2} \left(a+\frac{b}{x}\right)^{3/2}}{3 a}",1,"(2*(a + b/x)^(3/2)*x^(3/2))/(3*a)","A",1,1,17,0.05882,1,"{264}"
1756,1,49,0,0.0248701,"\int \frac{\sqrt{a+\frac{b}{x}}}{\sqrt{x}} \, dx","Int[Sqrt[a + b/x]/Sqrt[x],x]","2 \sqrt{x} \sqrt{a+\frac{b}{x}}-2 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)","2 \sqrt{x} \sqrt{a+\frac{b}{x}}-2 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)",1,"2*Sqrt[a + b/x]*Sqrt[x] - 2*Sqrt[b]*ArcTanh[Sqrt[b]/(Sqrt[a + b/x]*Sqrt[x])]","A",4,4,17,0.2353,1,"{337, 277, 217, 206}"
1757,1,50,0,0.0260107,"\int \frac{\sqrt{a+\frac{b}{x}}}{x^{3/2}} \, dx","Int[Sqrt[a + b/x]/x^(3/2),x]","-\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{x}}-\frac{a \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)}{\sqrt{b}}","-\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{x}}-\frac{a \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)}{\sqrt{b}}",1,"-(Sqrt[a + b/x]/Sqrt[x]) - (a*ArcTanh[Sqrt[b]/(Sqrt[a + b/x]*Sqrt[x])])/Sqrt[b]","A",4,4,17,0.2353,1,"{337, 195, 217, 206}"
1758,1,80,0,0.0387153,"\int \frac{\sqrt{a+\frac{b}{x}}}{x^{5/2}} \, dx","Int[Sqrt[a + b/x]/x^(5/2),x]","\frac{a^2 \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)}{4 b^{3/2}}-\frac{\sqrt{a+\frac{b}{x}}}{2 x^{3/2}}-\frac{a \sqrt{a+\frac{b}{x}}}{4 b \sqrt{x}}","\frac{a^2 \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)}{4 b^{3/2}}-\frac{\sqrt{a+\frac{b}{x}}}{2 x^{3/2}}-\frac{a \sqrt{a+\frac{b}{x}}}{4 b \sqrt{x}}",1,"-Sqrt[a + b/x]/(2*x^(3/2)) - (a*Sqrt[a + b/x])/(4*b*Sqrt[x]) + (a^2*ArcTanh[Sqrt[b]/(Sqrt[a + b/x]*Sqrt[x])])/(4*b^(3/2))","A",5,5,17,0.2941,1,"{337, 279, 321, 217, 206}"
1759,1,106,0,0.0548153,"\int \frac{\sqrt{a+\frac{b}{x}}}{x^{7/2}} \, dx","Int[Sqrt[a + b/x]/x^(7/2),x]","\frac{a^2 \sqrt{a+\frac{b}{x}}}{8 b^2 \sqrt{x}}-\frac{a^3 \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)}{8 b^{5/2}}-\frac{a \sqrt{a+\frac{b}{x}}}{12 b x^{3/2}}-\frac{\sqrt{a+\frac{b}{x}}}{3 x^{5/2}}","\frac{a^2 \sqrt{a+\frac{b}{x}}}{8 b^2 \sqrt{x}}-\frac{a^3 \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)}{8 b^{5/2}}-\frac{a \sqrt{a+\frac{b}{x}}}{12 b x^{3/2}}-\frac{\sqrt{a+\frac{b}{x}}}{3 x^{5/2}}",1,"-Sqrt[a + b/x]/(3*x^(5/2)) - (a*Sqrt[a + b/x])/(12*b*x^(3/2)) + (a^2*Sqrt[a + b/x])/(8*b^2*Sqrt[x]) - (a^3*ArcTanh[Sqrt[b]/(Sqrt[a + b/x]*Sqrt[x])])/(8*b^(5/2))","A",6,5,17,0.2941,1,"{337, 279, 321, 217, 206}"
1760,1,100,0,0.0337823,"\int \left(a+\frac{b}{x}\right)^{3/2} x^{9/2} \, dx","Int[(a + b/x)^(3/2)*x^(9/2),x]","\frac{16 b^2 x^{7/2} \left(a+\frac{b}{x}\right)^{5/2}}{231 a^3}-\frac{32 b^3 x^{5/2} \left(a+\frac{b}{x}\right)^{5/2}}{1155 a^4}-\frac{4 b x^{9/2} \left(a+\frac{b}{x}\right)^{5/2}}{33 a^2}+\frac{2 x^{11/2} \left(a+\frac{b}{x}\right)^{5/2}}{11 a}","\frac{16 b^2 x^{7/2} \left(a+\frac{b}{x}\right)^{5/2}}{231 a^3}-\frac{32 b^3 x^{5/2} \left(a+\frac{b}{x}\right)^{5/2}}{1155 a^4}-\frac{4 b x^{9/2} \left(a+\frac{b}{x}\right)^{5/2}}{33 a^2}+\frac{2 x^{11/2} \left(a+\frac{b}{x}\right)^{5/2}}{11 a}",1,"(-32*b^3*(a + b/x)^(5/2)*x^(5/2))/(1155*a^4) + (16*b^2*(a + b/x)^(5/2)*x^(7/2))/(231*a^3) - (4*b*(a + b/x)^(5/2)*x^(9/2))/(33*a^2) + (2*(a + b/x)^(5/2)*x^(11/2))/(11*a)","A",4,2,17,0.1176,1,"{271, 264}"
1761,1,74,0,0.0226424,"\int \left(a+\frac{b}{x}\right)^{3/2} x^{7/2} \, dx","Int[(a + b/x)^(3/2)*x^(7/2),x]","\frac{16 b^2 x^{5/2} \left(a+\frac{b}{x}\right)^{5/2}}{315 a^3}-\frac{8 b x^{7/2} \left(a+\frac{b}{x}\right)^{5/2}}{63 a^2}+\frac{2 x^{9/2} \left(a+\frac{b}{x}\right)^{5/2}}{9 a}","\frac{16 b^2 x^{5/2} \left(a+\frac{b}{x}\right)^{5/2}}{315 a^3}-\frac{8 b x^{7/2} \left(a+\frac{b}{x}\right)^{5/2}}{63 a^2}+\frac{2 x^{9/2} \left(a+\frac{b}{x}\right)^{5/2}}{9 a}",1,"(16*b^2*(a + b/x)^(5/2)*x^(5/2))/(315*a^3) - (8*b*(a + b/x)^(5/2)*x^(7/2))/(63*a^2) + (2*(a + b/x)^(5/2)*x^(9/2))/(9*a)","A",3,2,17,0.1176,1,"{271, 264}"
1762,1,48,0,0.0136551,"\int \left(a+\frac{b}{x}\right)^{3/2} x^{5/2} \, dx","Int[(a + b/x)^(3/2)*x^(5/2),x]","\frac{2 x^{7/2} \left(a+\frac{b}{x}\right)^{5/2}}{7 a}-\frac{4 b x^{5/2} \left(a+\frac{b}{x}\right)^{5/2}}{35 a^2}","\frac{2 x^{7/2} \left(a+\frac{b}{x}\right)^{5/2}}{7 a}-\frac{4 b x^{5/2} \left(a+\frac{b}{x}\right)^{5/2}}{35 a^2}",1,"(-4*b*(a + b/x)^(5/2)*x^(5/2))/(35*a^2) + (2*(a + b/x)^(5/2)*x^(7/2))/(7*a)","A",2,2,17,0.1176,1,"{271, 264}"
1763,1,23,0,0.0056947,"\int \left(a+\frac{b}{x}\right)^{3/2} x^{3/2} \, dx","Int[(a + b/x)^(3/2)*x^(3/2),x]","\frac{2 x^{5/2} \left(a+\frac{b}{x}\right)^{5/2}}{5 a}","\frac{2 x^{5/2} \left(a+\frac{b}{x}\right)^{5/2}}{5 a}",1,"(2*(a + b/x)^(5/2)*x^(5/2))/(5*a)","A",1,1,17,0.05882,1,"{264}"
1764,1,70,0,0.0362546,"\int \left(a+\frac{b}{x}\right)^{3/2} \sqrt{x} \, dx","Int[(a + b/x)^(3/2)*Sqrt[x],x]","-2 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)+\frac{2}{3} x^{3/2} \left(a+\frac{b}{x}\right)^{3/2}+2 b \sqrt{x} \sqrt{a+\frac{b}{x}}","-2 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)+\frac{2}{3} x^{3/2} \left(a+\frac{b}{x}\right)^{3/2}+2 b \sqrt{x} \sqrt{a+\frac{b}{x}}",1,"2*b*Sqrt[a + b/x]*Sqrt[x] + (2*(a + b/x)^(3/2)*x^(3/2))/3 - 2*b^(3/2)*ArcTanh[Sqrt[b]/(Sqrt[a + b/x]*Sqrt[x])]","A",5,4,17,0.2353,1,"{337, 277, 217, 206}"
1765,1,69,0,0.0350443,"\int \frac{\left(a+\frac{b}{x}\right)^{3/2}}{\sqrt{x}} \, dx","Int[(a + b/x)^(3/2)/Sqrt[x],x]","2 \sqrt{x} \left(a+\frac{b}{x}\right)^{3/2}-\frac{3 b \sqrt{a+\frac{b}{x}}}{\sqrt{x}}-3 a \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)","2 \sqrt{x} \left(a+\frac{b}{x}\right)^{3/2}-\frac{3 b \sqrt{a+\frac{b}{x}}}{\sqrt{x}}-3 a \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)",1,"(-3*b*Sqrt[a + b/x])/Sqrt[x] + 2*(a + b/x)^(3/2)*Sqrt[x] - 3*a*Sqrt[b]*ArcTanh[Sqrt[b]/(Sqrt[a + b/x]*Sqrt[x])]","A",5,5,17,0.2941,1,"{337, 277, 195, 217, 206}"
1766,1,77,0,0.0315074,"\int \frac{\left(a+\frac{b}{x}\right)^{3/2}}{x^{3/2}} \, dx","Int[(a + b/x)^(3/2)/x^(3/2),x]","-\frac{3 a^2 \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)}{4 \sqrt{b}}-\frac{3 a \sqrt{a+\frac{b}{x}}}{4 \sqrt{x}}-\frac{\left(a+\frac{b}{x}\right)^{3/2}}{2 \sqrt{x}}","-\frac{3 a^2 \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)}{4 \sqrt{b}}-\frac{3 a \sqrt{a+\frac{b}{x}}}{4 \sqrt{x}}-\frac{\left(a+\frac{b}{x}\right)^{3/2}}{2 \sqrt{x}}",1,"(-3*a*Sqrt[a + b/x])/(4*Sqrt[x]) - (a + b/x)^(3/2)/(2*Sqrt[x]) - (3*a^2*ArcTanh[Sqrt[b]/(Sqrt[a + b/x]*Sqrt[x])])/(4*Sqrt[b])","A",5,4,17,0.2353,1,"{337, 195, 217, 206}"
1767,1,103,0,0.053141,"\int \frac{\left(a+\frac{b}{x}\right)^{3/2}}{x^{5/2}} \, dx","Int[(a + b/x)^(3/2)/x^(5/2),x]","\frac{a^3 \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)}{8 b^{3/2}}-\frac{a^2 \sqrt{a+\frac{b}{x}}}{8 b \sqrt{x}}-\frac{a \sqrt{a+\frac{b}{x}}}{4 x^{3/2}}-\frac{\left(a+\frac{b}{x}\right)^{3/2}}{3 x^{3/2}}","\frac{a^3 \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)}{8 b^{3/2}}-\frac{a^2 \sqrt{a+\frac{b}{x}}}{8 b \sqrt{x}}-\frac{a \sqrt{a+\frac{b}{x}}}{4 x^{3/2}}-\frac{\left(a+\frac{b}{x}\right)^{3/2}}{3 x^{3/2}}",1,"-(a*Sqrt[a + b/x])/(4*x^(3/2)) - (a + b/x)^(3/2)/(3*x^(3/2)) - (a^2*Sqrt[a + b/x])/(8*b*Sqrt[x]) + (a^3*ArcTanh[Sqrt[b]/(Sqrt[a + b/x]*Sqrt[x])])/(8*b^(3/2))","A",6,5,17,0.2941,1,"{337, 279, 321, 217, 206}"
1768,1,100,0,0.0345881,"\int \left(a+\frac{b}{x}\right)^{5/2} x^{11/2} \, dx","Int[(a + b/x)^(5/2)*x^(11/2),x]","\frac{16 b^2 x^{9/2} \left(a+\frac{b}{x}\right)^{7/2}}{429 a^3}-\frac{32 b^3 x^{7/2} \left(a+\frac{b}{x}\right)^{7/2}}{3003 a^4}-\frac{12 b x^{11/2} \left(a+\frac{b}{x}\right)^{7/2}}{143 a^2}+\frac{2 x^{13/2} \left(a+\frac{b}{x}\right)^{7/2}}{13 a}","\frac{16 b^2 x^{9/2} \left(a+\frac{b}{x}\right)^{7/2}}{429 a^3}-\frac{32 b^3 x^{7/2} \left(a+\frac{b}{x}\right)^{7/2}}{3003 a^4}-\frac{12 b x^{11/2} \left(a+\frac{b}{x}\right)^{7/2}}{143 a^2}+\frac{2 x^{13/2} \left(a+\frac{b}{x}\right)^{7/2}}{13 a}",1,"(-32*b^3*(a + b/x)^(7/2)*x^(7/2))/(3003*a^4) + (16*b^2*(a + b/x)^(7/2)*x^(9/2))/(429*a^3) - (12*b*(a + b/x)^(7/2)*x^(11/2))/(143*a^2) + (2*(a + b/x)^(7/2)*x^(13/2))/(13*a)","A",4,2,17,0.1176,1,"{271, 264}"
1769,1,74,0,0.0225016,"\int \left(a+\frac{b}{x}\right)^{5/2} x^{9/2} \, dx","Int[(a + b/x)^(5/2)*x^(9/2),x]","\frac{16 b^2 x^{7/2} \left(a+\frac{b}{x}\right)^{7/2}}{693 a^3}-\frac{8 b x^{9/2} \left(a+\frac{b}{x}\right)^{7/2}}{99 a^2}+\frac{2 x^{11/2} \left(a+\frac{b}{x}\right)^{7/2}}{11 a}","\frac{16 b^2 x^{7/2} \left(a+\frac{b}{x}\right)^{7/2}}{693 a^3}-\frac{8 b x^{9/2} \left(a+\frac{b}{x}\right)^{7/2}}{99 a^2}+\frac{2 x^{11/2} \left(a+\frac{b}{x}\right)^{7/2}}{11 a}",1,"(16*b^2*(a + b/x)^(7/2)*x^(7/2))/(693*a^3) - (8*b*(a + b/x)^(7/2)*x^(9/2))/(99*a^2) + (2*(a + b/x)^(7/2)*x^(11/2))/(11*a)","A",3,2,17,0.1176,1,"{271, 264}"
1770,1,48,0,0.01314,"\int \left(a+\frac{b}{x}\right)^{5/2} x^{7/2} \, dx","Int[(a + b/x)^(5/2)*x^(7/2),x]","\frac{2 x^{9/2} \left(a+\frac{b}{x}\right)^{7/2}}{9 a}-\frac{4 b x^{7/2} \left(a+\frac{b}{x}\right)^{7/2}}{63 a^2}","\frac{2 x^{9/2} \left(a+\frac{b}{x}\right)^{7/2}}{9 a}-\frac{4 b x^{7/2} \left(a+\frac{b}{x}\right)^{7/2}}{63 a^2}",1,"(-4*b*(a + b/x)^(7/2)*x^(7/2))/(63*a^2) + (2*(a + b/x)^(7/2)*x^(9/2))/(9*a)","A",2,2,17,0.1176,1,"{271, 264}"
1771,1,23,0,0.0057093,"\int \left(a+\frac{b}{x}\right)^{5/2} x^{5/2} \, dx","Int[(a + b/x)^(5/2)*x^(5/2),x]","\frac{2 x^{7/2} \left(a+\frac{b}{x}\right)^{7/2}}{7 a}","\frac{2 x^{7/2} \left(a+\frac{b}{x}\right)^{7/2}}{7 a}",1,"(2*(a + b/x)^(7/2)*x^(7/2))/(7*a)","A",1,1,17,0.05882,1,"{264}"
1772,1,93,0,0.0487318,"\int \left(a+\frac{b}{x}\right)^{5/2} x^{3/2} \, dx","Int[(a + b/x)^(5/2)*x^(3/2),x]","2 b^2 \sqrt{x} \sqrt{a+\frac{b}{x}}-2 b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)+\frac{2}{3} b x^{3/2} \left(a+\frac{b}{x}\right)^{3/2}+\frac{2}{5} x^{5/2} \left(a+\frac{b}{x}\right)^{5/2}","2 b^2 \sqrt{x} \sqrt{a+\frac{b}{x}}-2 b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)+\frac{2}{3} b x^{3/2} \left(a+\frac{b}{x}\right)^{3/2}+\frac{2}{5} x^{5/2} \left(a+\frac{b}{x}\right)^{5/2}",1,"2*b^2*Sqrt[a + b/x]*Sqrt[x] + (2*b*(a + b/x)^(3/2)*x^(3/2))/3 + (2*(a + b/x)^(5/2)*x^(5/2))/5 - 2*b^(5/2)*ArcTanh[Sqrt[b]/(Sqrt[a + b/x]*Sqrt[x])]","A",6,4,17,0.2353,1,"{337, 277, 217, 206}"
1773,1,94,0,0.0476009,"\int \left(a+\frac{b}{x}\right)^{5/2} \sqrt{x} \, dx","Int[(a + b/x)^(5/2)*Sqrt[x],x]","-\frac{5 b^2 \sqrt{a+\frac{b}{x}}}{\sqrt{x}}-5 a b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)+\frac{2}{3} x^{3/2} \left(a+\frac{b}{x}\right)^{5/2}+\frac{10}{3} b \sqrt{x} \left(a+\frac{b}{x}\right)^{3/2}","-\frac{5 b^2 \sqrt{a+\frac{b}{x}}}{\sqrt{x}}-5 a b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)+\frac{2}{3} x^{3/2} \left(a+\frac{b}{x}\right)^{5/2}+\frac{10}{3} b \sqrt{x} \left(a+\frac{b}{x}\right)^{3/2}",1,"(-5*b^2*Sqrt[a + b/x])/Sqrt[x] + (10*b*(a + b/x)^(3/2)*Sqrt[x])/3 + (2*(a + b/x)^(5/2)*x^(3/2))/3 - 5*a*b^(3/2)*ArcTanh[Sqrt[b]/(Sqrt[a + b/x]*Sqrt[x])]","A",6,5,17,0.2941,1,"{337, 277, 195, 217, 206}"
1774,1,97,0,0.0457083,"\int \frac{\left(a+\frac{b}{x}\right)^{5/2}}{\sqrt{x}} \, dx","Int[(a + b/x)^(5/2)/Sqrt[x],x]","-\frac{15}{4} a^2 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)+2 \sqrt{x} \left(a+\frac{b}{x}\right)^{5/2}-\frac{5 b \left(a+\frac{b}{x}\right)^{3/2}}{2 \sqrt{x}}-\frac{15 a b \sqrt{a+\frac{b}{x}}}{4 \sqrt{x}}","-\frac{15}{4} a^2 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)+2 \sqrt{x} \left(a+\frac{b}{x}\right)^{5/2}-\frac{5 b \left(a+\frac{b}{x}\right)^{3/2}}{2 \sqrt{x}}-\frac{15 a b \sqrt{a+\frac{b}{x}}}{4 \sqrt{x}}",1,"(-15*a*b*Sqrt[a + b/x])/(4*Sqrt[x]) - (5*b*(a + b/x)^(3/2))/(2*Sqrt[x]) + 2*(a + b/x)^(5/2)*Sqrt[x] - (15*a^2*Sqrt[b]*ArcTanh[Sqrt[b]/(Sqrt[a + b/x]*Sqrt[x])])/4","A",6,5,17,0.2941,1,"{337, 277, 195, 217, 206}"
1775,1,100,0,0.045123,"\int \frac{\left(a+\frac{b}{x}\right)^{5/2}}{x^{3/2}} \, dx","Int[(a + b/x)^(5/2)/x^(3/2),x]","-\frac{5 a^2 \sqrt{a+\frac{b}{x}}}{8 \sqrt{x}}-\frac{5 a^3 \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)}{8 \sqrt{b}}-\frac{5 a \left(a+\frac{b}{x}\right)^{3/2}}{12 \sqrt{x}}-\frac{\left(a+\frac{b}{x}\right)^{5/2}}{3 \sqrt{x}}","-\frac{5 a^2 \sqrt{a+\frac{b}{x}}}{8 \sqrt{x}}-\frac{5 a^3 \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)}{8 \sqrt{b}}-\frac{5 a \left(a+\frac{b}{x}\right)^{3/2}}{12 \sqrt{x}}-\frac{\left(a+\frac{b}{x}\right)^{5/2}}{3 \sqrt{x}}",1,"(-5*a^2*Sqrt[a + b/x])/(8*Sqrt[x]) - (5*a*(a + b/x)^(3/2))/(12*Sqrt[x]) - (a + b/x)^(5/2)/(3*Sqrt[x]) - (5*a^3*ArcTanh[Sqrt[b]/(Sqrt[a + b/x]*Sqrt[x])])/(8*Sqrt[b])","A",6,4,17,0.2353,1,"{337, 195, 217, 206}"
1776,1,126,0,0.0682302,"\int \frac{\left(a+\frac{b}{x}\right)^{5/2}}{x^{5/2}} \, dx","Int[(a + b/x)^(5/2)/x^(5/2),x]","\frac{5 a^4 \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)}{64 b^{3/2}}-\frac{5 a^2 \sqrt{a+\frac{b}{x}}}{32 x^{3/2}}-\frac{5 a^3 \sqrt{a+\frac{b}{x}}}{64 b \sqrt{x}}-\frac{5 a \left(a+\frac{b}{x}\right)^{3/2}}{24 x^{3/2}}-\frac{\left(a+\frac{b}{x}\right)^{5/2}}{4 x^{3/2}}","\frac{5 a^4 \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)}{64 b^{3/2}}-\frac{5 a^2 \sqrt{a+\frac{b}{x}}}{32 x^{3/2}}-\frac{5 a^3 \sqrt{a+\frac{b}{x}}}{64 b \sqrt{x}}-\frac{5 a \left(a+\frac{b}{x}\right)^{3/2}}{24 x^{3/2}}-\frac{\left(a+\frac{b}{x}\right)^{5/2}}{4 x^{3/2}}",1,"(-5*a^2*Sqrt[a + b/x])/(32*x^(3/2)) - (5*a*(a + b/x)^(3/2))/(24*x^(3/2)) - (a + b/x)^(5/2)/(4*x^(3/2)) - (5*a^3*Sqrt[a + b/x])/(64*b*Sqrt[x]) + (5*a^4*ArcTanh[Sqrt[b]/(Sqrt[a + b/x]*Sqrt[x])])/(64*b^(3/2))","A",7,5,17,0.2941,1,"{337, 279, 321, 217, 206}"
1777,1,126,0,0.0441931,"\int \frac{x^{7/2}}{\sqrt{a+\frac{b}{x}}} \, dx","Int[x^(7/2)/Sqrt[a + b/x],x]","\frac{32 b^2 x^{5/2} \sqrt{a+\frac{b}{x}}}{105 a^3}-\frac{128 b^3 x^{3/2} \sqrt{a+\frac{b}{x}}}{315 a^4}+\frac{256 b^4 \sqrt{x} \sqrt{a+\frac{b}{x}}}{315 a^5}-\frac{16 b x^{7/2} \sqrt{a+\frac{b}{x}}}{63 a^2}+\frac{2 x^{9/2} \sqrt{a+\frac{b}{x}}}{9 a}","\frac{32 b^2 x^{5/2} \sqrt{a+\frac{b}{x}}}{105 a^3}-\frac{128 b^3 x^{3/2} \sqrt{a+\frac{b}{x}}}{315 a^4}+\frac{256 b^4 \sqrt{x} \sqrt{a+\frac{b}{x}}}{315 a^5}-\frac{16 b x^{7/2} \sqrt{a+\frac{b}{x}}}{63 a^2}+\frac{2 x^{9/2} \sqrt{a+\frac{b}{x}}}{9 a}",1,"(256*b^4*Sqrt[a + b/x]*Sqrt[x])/(315*a^5) - (128*b^3*Sqrt[a + b/x]*x^(3/2))/(315*a^4) + (32*b^2*Sqrt[a + b/x]*x^(5/2))/(105*a^3) - (16*b*Sqrt[a + b/x]*x^(7/2))/(63*a^2) + (2*Sqrt[a + b/x]*x^(9/2))/(9*a)","A",5,2,17,0.1176,1,"{271, 264}"
1778,1,100,0,0.0312053,"\int \frac{x^{5/2}}{\sqrt{a+\frac{b}{x}}} \, dx","Int[x^(5/2)/Sqrt[a + b/x],x]","\frac{16 b^2 x^{3/2} \sqrt{a+\frac{b}{x}}}{35 a^3}-\frac{32 b^3 \sqrt{x} \sqrt{a+\frac{b}{x}}}{35 a^4}-\frac{12 b x^{5/2} \sqrt{a+\frac{b}{x}}}{35 a^2}+\frac{2 x^{7/2} \sqrt{a+\frac{b}{x}}}{7 a}","\frac{16 b^2 x^{3/2} \sqrt{a+\frac{b}{x}}}{35 a^3}-\frac{32 b^3 \sqrt{x} \sqrt{a+\frac{b}{x}}}{35 a^4}-\frac{12 b x^{5/2} \sqrt{a+\frac{b}{x}}}{35 a^2}+\frac{2 x^{7/2} \sqrt{a+\frac{b}{x}}}{7 a}",1,"(-32*b^3*Sqrt[a + b/x]*Sqrt[x])/(35*a^4) + (16*b^2*Sqrt[a + b/x]*x^(3/2))/(35*a^3) - (12*b*Sqrt[a + b/x]*x^(5/2))/(35*a^2) + (2*Sqrt[a + b/x]*x^(7/2))/(7*a)","A",4,2,17,0.1176,1,"{271, 264}"
1779,1,74,0,0.0210913,"\int \frac{x^{3/2}}{\sqrt{a+\frac{b}{x}}} \, dx","Int[x^(3/2)/Sqrt[a + b/x],x]","\frac{16 b^2 \sqrt{x} \sqrt{a+\frac{b}{x}}}{15 a^3}-\frac{8 b x^{3/2} \sqrt{a+\frac{b}{x}}}{15 a^2}+\frac{2 x^{5/2} \sqrt{a+\frac{b}{x}}}{5 a}","\frac{16 b^2 \sqrt{x} \sqrt{a+\frac{b}{x}}}{15 a^3}-\frac{8 b x^{3/2} \sqrt{a+\frac{b}{x}}}{15 a^2}+\frac{2 x^{5/2} \sqrt{a+\frac{b}{x}}}{5 a}",1,"(16*b^2*Sqrt[a + b/x]*Sqrt[x])/(15*a^3) - (8*b*Sqrt[a + b/x]*x^(3/2))/(15*a^2) + (2*Sqrt[a + b/x]*x^(5/2))/(5*a)","A",3,2,17,0.1176,1,"{271, 264}"
1780,1,48,0,0.0125094,"\int \frac{\sqrt{x}}{\sqrt{a+\frac{b}{x}}} \, dx","Int[Sqrt[x]/Sqrt[a + b/x],x]","\frac{2 x^{3/2} \sqrt{a+\frac{b}{x}}}{3 a}-\frac{4 b \sqrt{x} \sqrt{a+\frac{b}{x}}}{3 a^2}","\frac{2 x^{3/2} \sqrt{a+\frac{b}{x}}}{3 a}-\frac{4 b \sqrt{x} \sqrt{a+\frac{b}{x}}}{3 a^2}",1,"(-4*b*Sqrt[a + b/x]*Sqrt[x])/(3*a^2) + (2*Sqrt[a + b/x]*x^(3/2))/(3*a)","A",2,2,17,0.1176,1,"{271, 264}"
1781,1,21,0,0.005363,"\int \frac{1}{\sqrt{a+\frac{b}{x}} \sqrt{x}} \, dx","Int[1/(Sqrt[a + b/x]*Sqrt[x]),x]","\frac{2 \sqrt{x} \sqrt{a+\frac{b}{x}}}{a}","\frac{2 \sqrt{x} \sqrt{a+\frac{b}{x}}}{a}",1,"(2*Sqrt[a + b/x]*Sqrt[x])/a","A",1,1,17,0.05882,1,"{264}"
1782,1,30,0,0.015364,"\int \frac{1}{\sqrt{a+\frac{b}{x}} x^{3/2}} \, dx","Int[1/(Sqrt[a + b/x]*x^(3/2)),x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)}{\sqrt{b}}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)}{\sqrt{b}}",1,"(-2*ArcTanh[Sqrt[b]/(Sqrt[a + b/x]*Sqrt[x])])/Sqrt[b]","A",3,3,17,0.1765,1,"{337, 217, 206}"
1783,1,52,0,0.0260261,"\int \frac{1}{\sqrt{a+\frac{b}{x}} x^{5/2}} \, dx","Int[1/(Sqrt[a + b/x]*x^(5/2)),x]","\frac{a \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)}{b^{3/2}}-\frac{\sqrt{a+\frac{b}{x}}}{b \sqrt{x}}","\frac{a \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)}{b^{3/2}}-\frac{\sqrt{a+\frac{b}{x}}}{b \sqrt{x}}",1,"-(Sqrt[a + b/x]/(b*Sqrt[x])) + (a*ArcTanh[Sqrt[b]/(Sqrt[a + b/x]*Sqrt[x])])/b^(3/2)","A",4,4,17,0.2353,1,"{337, 321, 217, 206}"
1784,1,83,0,0.0394826,"\int \frac{1}{\sqrt{a+\frac{b}{x}} x^{7/2}} \, dx","Int[1/(Sqrt[a + b/x]*x^(7/2)),x]","-\frac{3 a^2 \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)}{4 b^{5/2}}+\frac{3 a \sqrt{a+\frac{b}{x}}}{4 b^2 \sqrt{x}}-\frac{\sqrt{a+\frac{b}{x}}}{2 b x^{3/2}}","-\frac{3 a^2 \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)}{4 b^{5/2}}+\frac{3 a \sqrt{a+\frac{b}{x}}}{4 b^2 \sqrt{x}}-\frac{\sqrt{a+\frac{b}{x}}}{2 b x^{3/2}}",1,"-Sqrt[a + b/x]/(2*b*x^(3/2)) + (3*a*Sqrt[a + b/x])/(4*b^2*Sqrt[x]) - (3*a^2*ArcTanh[Sqrt[b]/(Sqrt[a + b/x]*Sqrt[x])])/(4*b^(5/2))","A",5,4,17,0.2353,1,"{337, 321, 217, 206}"
1785,1,109,0,0.0536002,"\int \frac{1}{\sqrt{a+\frac{b}{x}} x^{9/2}} \, dx","Int[1/(Sqrt[a + b/x]*x^(9/2)),x]","-\frac{5 a^2 \sqrt{a+\frac{b}{x}}}{8 b^3 \sqrt{x}}+\frac{5 a^3 \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)}{8 b^{7/2}}+\frac{5 a \sqrt{a+\frac{b}{x}}}{12 b^2 x^{3/2}}-\frac{\sqrt{a+\frac{b}{x}}}{3 b x^{5/2}}","-\frac{5 a^2 \sqrt{a+\frac{b}{x}}}{8 b^3 \sqrt{x}}+\frac{5 a^3 \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)}{8 b^{7/2}}+\frac{5 a \sqrt{a+\frac{b}{x}}}{12 b^2 x^{3/2}}-\frac{\sqrt{a+\frac{b}{x}}}{3 b x^{5/2}}",1,"-Sqrt[a + b/x]/(3*b*x^(5/2)) + (5*a*Sqrt[a + b/x])/(12*b^2*x^(3/2)) - (5*a^2*Sqrt[a + b/x])/(8*b^3*Sqrt[x]) + (5*a^3*ArcTanh[Sqrt[b]/(Sqrt[a + b/x]*Sqrt[x])])/(8*b^(7/2))","A",6,4,17,0.2353,1,"{337, 321, 217, 206}"
1786,1,126,0,0.0450926,"\int \frac{x^{5/2}}{\left(a+\frac{b}{x}\right)^{3/2}} \, dx","Int[x^(5/2)/(a + b/x)^(3/2),x]","\frac{32 b^2 x^{3/2}}{35 a^3 \sqrt{a+\frac{b}{x}}}-\frac{256 b^4}{35 a^5 \sqrt{x} \sqrt{a+\frac{b}{x}}}-\frac{128 b^3 \sqrt{x}}{35 a^4 \sqrt{a+\frac{b}{x}}}-\frac{16 b x^{5/2}}{35 a^2 \sqrt{a+\frac{b}{x}}}+\frac{2 x^{7/2}}{7 a \sqrt{a+\frac{b}{x}}}","\frac{32 b^2 x^{3/2}}{35 a^3 \sqrt{a+\frac{b}{x}}}-\frac{256 b^4}{35 a^5 \sqrt{x} \sqrt{a+\frac{b}{x}}}-\frac{128 b^3 \sqrt{x}}{35 a^4 \sqrt{a+\frac{b}{x}}}-\frac{16 b x^{5/2}}{35 a^2 \sqrt{a+\frac{b}{x}}}+\frac{2 x^{7/2}}{7 a \sqrt{a+\frac{b}{x}}}",1,"(-256*b^4)/(35*a^5*Sqrt[a + b/x]*Sqrt[x]) - (128*b^3*Sqrt[x])/(35*a^4*Sqrt[a + b/x]) + (32*b^2*x^(3/2))/(35*a^3*Sqrt[a + b/x]) - (16*b*x^(5/2))/(35*a^2*Sqrt[a + b/x]) + (2*x^(7/2))/(7*a*Sqrt[a + b/x])","A",5,2,17,0.1176,1,"{271, 264}"
1787,1,100,0,0.0333058,"\int \frac{x^{3/2}}{\left(a+\frac{b}{x}\right)^{3/2}} \, dx","Int[x^(3/2)/(a + b/x)^(3/2),x]","\frac{32 b^3}{5 a^4 \sqrt{x} \sqrt{a+\frac{b}{x}}}+\frac{16 b^2 \sqrt{x}}{5 a^3 \sqrt{a+\frac{b}{x}}}-\frac{4 b x^{3/2}}{5 a^2 \sqrt{a+\frac{b}{x}}}+\frac{2 x^{5/2}}{5 a \sqrt{a+\frac{b}{x}}}","\frac{32 b^3}{5 a^4 \sqrt{x} \sqrt{a+\frac{b}{x}}}+\frac{16 b^2 \sqrt{x}}{5 a^3 \sqrt{a+\frac{b}{x}}}-\frac{4 b x^{3/2}}{5 a^2 \sqrt{a+\frac{b}{x}}}+\frac{2 x^{5/2}}{5 a \sqrt{a+\frac{b}{x}}}",1,"(32*b^3)/(5*a^4*Sqrt[a + b/x]*Sqrt[x]) + (16*b^2*Sqrt[x])/(5*a^3*Sqrt[a + b/x]) - (4*b*x^(3/2))/(5*a^2*Sqrt[a + b/x]) + (2*x^(5/2))/(5*a*Sqrt[a + b/x])","A",4,2,17,0.1176,1,"{271, 264}"
1788,1,74,0,0.0227034,"\int \frac{\sqrt{x}}{\left(a+\frac{b}{x}\right)^{3/2}} \, dx","Int[Sqrt[x]/(a + b/x)^(3/2),x]","-\frac{16 b^2}{3 a^3 \sqrt{x} \sqrt{a+\frac{b}{x}}}-\frac{8 b \sqrt{x}}{3 a^2 \sqrt{a+\frac{b}{x}}}+\frac{2 x^{3/2}}{3 a \sqrt{a+\frac{b}{x}}}","-\frac{16 b^2}{3 a^3 \sqrt{x} \sqrt{a+\frac{b}{x}}}-\frac{8 b \sqrt{x}}{3 a^2 \sqrt{a+\frac{b}{x}}}+\frac{2 x^{3/2}}{3 a \sqrt{a+\frac{b}{x}}}",1,"(-16*b^2)/(3*a^3*Sqrt[a + b/x]*Sqrt[x]) - (8*b*Sqrt[x])/(3*a^2*Sqrt[a + b/x]) + (2*x^(3/2))/(3*a*Sqrt[a + b/x])","A",3,2,17,0.1176,1,"{271, 264}"
1789,1,44,0,0.0134833,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{3/2} \sqrt{x}} \, dx","Int[1/((a + b/x)^(3/2)*Sqrt[x]),x]","\frac{4 b}{a^2 \sqrt{x} \sqrt{a+\frac{b}{x}}}+\frac{2 \sqrt{x}}{a \sqrt{a+\frac{b}{x}}}","\frac{4 b}{a^2 \sqrt{x} \sqrt{a+\frac{b}{x}}}+\frac{2 \sqrt{x}}{a \sqrt{a+\frac{b}{x}}}",1,"(4*b)/(a^2*Sqrt[a + b/x]*Sqrt[x]) + (2*Sqrt[x])/(a*Sqrt[a + b/x])","A",2,2,17,0.1176,1,"{271, 264}"
1790,1,21,0,0.0056761,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{3/2} x^{3/2}} \, dx","Int[1/((a + b/x)^(3/2)*x^(3/2)),x]","-\frac{2}{a \sqrt{x} \sqrt{a+\frac{b}{x}}}","-\frac{2}{a \sqrt{x} \sqrt{a+\frac{b}{x}}}",1,"-2/(a*Sqrt[a + b/x]*Sqrt[x])","A",1,1,17,0.05882,1,"{264}"
1791,1,52,0,0.0278075,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{3/2} x^{5/2}} \, dx","Int[1/((a + b/x)^(3/2)*x^(5/2)),x]","\frac{2}{b \sqrt{x} \sqrt{a+\frac{b}{x}}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)}{b^{3/2}}","\frac{2}{b \sqrt{x} \sqrt{a+\frac{b}{x}}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)}{b^{3/2}}",1,"2/(b*Sqrt[a + b/x]*Sqrt[x]) - (2*ArcTanh[Sqrt[b]/(Sqrt[a + b/x]*Sqrt[x])])/b^(3/2)","A",4,4,17,0.2353,1,"{337, 288, 217, 206}"
1792,1,74,0,0.0399742,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{3/2} x^{7/2}} \, dx","Int[1/((a + b/x)^(3/2)*x^(7/2)),x]","-\frac{3 \sqrt{a+\frac{b}{x}}}{b^2 \sqrt{x}}+\frac{3 a \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)}{b^{5/2}}+\frac{2}{b x^{3/2} \sqrt{a+\frac{b}{x}}}","-\frac{3 \sqrt{a+\frac{b}{x}}}{b^2 \sqrt{x}}+\frac{3 a \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)}{b^{5/2}}+\frac{2}{b x^{3/2} \sqrt{a+\frac{b}{x}}}",1,"2/(b*Sqrt[a + b/x]*x^(3/2)) - (3*Sqrt[a + b/x])/(b^2*Sqrt[x]) + (3*a*ArcTanh[Sqrt[b]/(Sqrt[a + b/x]*Sqrt[x])])/b^(5/2)","A",5,5,17,0.2941,1,"{337, 288, 321, 217, 206}"
1793,1,104,0,0.0541592,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{3/2} x^{9/2}} \, dx","Int[1/((a + b/x)^(3/2)*x^(9/2)),x]","-\frac{15 a^2 \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)}{4 b^{7/2}}-\frac{5 \sqrt{a+\frac{b}{x}}}{2 b^2 x^{3/2}}+\frac{15 a \sqrt{a+\frac{b}{x}}}{4 b^3 \sqrt{x}}+\frac{2}{b x^{5/2} \sqrt{a+\frac{b}{x}}}","-\frac{15 a^2 \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)}{4 b^{7/2}}-\frac{5 \sqrt{a+\frac{b}{x}}}{2 b^2 x^{3/2}}+\frac{15 a \sqrt{a+\frac{b}{x}}}{4 b^3 \sqrt{x}}+\frac{2}{b x^{5/2} \sqrt{a+\frac{b}{x}}}",1,"2/(b*Sqrt[a + b/x]*x^(5/2)) - (5*Sqrt[a + b/x])/(2*b^2*x^(3/2)) + (15*a*Sqrt[a + b/x])/(4*b^3*Sqrt[x]) - (15*a^2*ArcTanh[Sqrt[b]/(Sqrt[a + b/x]*Sqrt[x])])/(4*b^(7/2))","A",6,5,17,0.2941,1,"{337, 288, 321, 217, 206}"
1794,1,130,0,0.0707505,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{3/2} x^{11/2}} \, dx","Int[1/((a + b/x)^(3/2)*x^(11/2)),x]","-\frac{35 a^2 \sqrt{a+\frac{b}{x}}}{8 b^4 \sqrt{x}}+\frac{35 a^3 \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)}{8 b^{9/2}}+\frac{35 a \sqrt{a+\frac{b}{x}}}{12 b^3 x^{3/2}}-\frac{7 \sqrt{a+\frac{b}{x}}}{3 b^2 x^{5/2}}+\frac{2}{b x^{7/2} \sqrt{a+\frac{b}{x}}}","-\frac{35 a^2 \sqrt{a+\frac{b}{x}}}{8 b^4 \sqrt{x}}+\frac{35 a^3 \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)}{8 b^{9/2}}+\frac{35 a \sqrt{a+\frac{b}{x}}}{12 b^3 x^{3/2}}-\frac{7 \sqrt{a+\frac{b}{x}}}{3 b^2 x^{5/2}}+\frac{2}{b x^{7/2} \sqrt{a+\frac{b}{x}}}",1,"2/(b*Sqrt[a + b/x]*x^(7/2)) - (7*Sqrt[a + b/x])/(3*b^2*x^(5/2)) + (35*a*Sqrt[a + b/x])/(12*b^3*x^(3/2)) - (35*a^2*Sqrt[a + b/x])/(8*b^4*Sqrt[x]) + (35*a^3*ArcTanh[Sqrt[b]/(Sqrt[a + b/x]*Sqrt[x])])/(8*b^(9/2))","A",7,5,17,0.2941,1,"{337, 288, 321, 217, 206}"
1795,1,152,0,0.062057,"\int \frac{x^{5/2}}{\left(a+\frac{b}{x}\right)^{5/2}} \, dx","Int[x^(5/2)/(a + b/x)^(5/2),x]","-\frac{512 b^5}{21 a^6 x^{3/2} \left(a+\frac{b}{x}\right)^{3/2}}+\frac{32 b^2 x^{3/2}}{21 a^3 \left(a+\frac{b}{x}\right)^{3/2}}-\frac{256 b^4}{7 a^5 \sqrt{x} \left(a+\frac{b}{x}\right)^{3/2}}-\frac{64 b^3 \sqrt{x}}{7 a^4 \left(a+\frac{b}{x}\right)^{3/2}}-\frac{4 b x^{5/2}}{7 a^2 \left(a+\frac{b}{x}\right)^{3/2}}+\frac{2 x^{7/2}}{7 a \left(a+\frac{b}{x}\right)^{3/2}}","-\frac{512 b^5}{21 a^6 x^{3/2} \left(a+\frac{b}{x}\right)^{3/2}}+\frac{32 b^2 x^{3/2}}{21 a^3 \left(a+\frac{b}{x}\right)^{3/2}}-\frac{256 b^4}{7 a^5 \sqrt{x} \left(a+\frac{b}{x}\right)^{3/2}}-\frac{64 b^3 \sqrt{x}}{7 a^4 \left(a+\frac{b}{x}\right)^{3/2}}-\frac{4 b x^{5/2}}{7 a^2 \left(a+\frac{b}{x}\right)^{3/2}}+\frac{2 x^{7/2}}{7 a \left(a+\frac{b}{x}\right)^{3/2}}",1,"(-512*b^5)/(21*a^6*(a + b/x)^(3/2)*x^(3/2)) - (256*b^4)/(7*a^5*(a + b/x)^(3/2)*Sqrt[x]) - (64*b^3*Sqrt[x])/(7*a^4*(a + b/x)^(3/2)) + (32*b^2*x^(3/2))/(21*a^3*(a + b/x)^(3/2)) - (4*b*x^(5/2))/(7*a^2*(a + b/x)^(3/2)) + (2*x^(7/2))/(7*a*(a + b/x)^(3/2))","A",6,2,17,0.1176,1,"{271, 264}"
1796,1,126,0,0.0467119,"\int \frac{x^{3/2}}{\left(a+\frac{b}{x}\right)^{5/2}} \, dx","Int[x^(3/2)/(a + b/x)^(5/2),x]","\frac{256 b^4}{15 a^5 x^{3/2} \left(a+\frac{b}{x}\right)^{3/2}}+\frac{128 b^3}{5 a^4 \sqrt{x} \left(a+\frac{b}{x}\right)^{3/2}}+\frac{32 b^2 \sqrt{x}}{5 a^3 \left(a+\frac{b}{x}\right)^{3/2}}-\frac{16 b x^{3/2}}{15 a^2 \left(a+\frac{b}{x}\right)^{3/2}}+\frac{2 x^{5/2}}{5 a \left(a+\frac{b}{x}\right)^{3/2}}","\frac{256 b^4}{15 a^5 x^{3/2} \left(a+\frac{b}{x}\right)^{3/2}}+\frac{128 b^3}{5 a^4 \sqrt{x} \left(a+\frac{b}{x}\right)^{3/2}}+\frac{32 b^2 \sqrt{x}}{5 a^3 \left(a+\frac{b}{x}\right)^{3/2}}-\frac{16 b x^{3/2}}{15 a^2 \left(a+\frac{b}{x}\right)^{3/2}}+\frac{2 x^{5/2}}{5 a \left(a+\frac{b}{x}\right)^{3/2}}",1,"(256*b^4)/(15*a^5*(a + b/x)^(3/2)*x^(3/2)) + (128*b^3)/(5*a^4*(a + b/x)^(3/2)*Sqrt[x]) + (32*b^2*Sqrt[x])/(5*a^3*(a + b/x)^(3/2)) - (16*b*x^(3/2))/(15*a^2*(a + b/x)^(3/2)) + (2*x^(5/2))/(5*a*(a + b/x)^(3/2))","A",5,2,17,0.1176,1,"{271, 264}"
1797,1,96,0,0.0349012,"\int \frac{\sqrt{x}}{\left(a+\frac{b}{x}\right)^{5/2}} \, dx","Int[Sqrt[x]/(a + b/x)^(5/2),x]","-\frac{32 b^3}{3 a^4 x^{3/2} \left(a+\frac{b}{x}\right)^{3/2}}-\frac{16 b^2}{a^3 \sqrt{x} \left(a+\frac{b}{x}\right)^{3/2}}-\frac{4 b \sqrt{x}}{a^2 \left(a+\frac{b}{x}\right)^{3/2}}+\frac{2 x^{3/2}}{3 a \left(a+\frac{b}{x}\right)^{3/2}}","-\frac{32 b^3}{3 a^4 x^{3/2} \left(a+\frac{b}{x}\right)^{3/2}}-\frac{16 b^2}{a^3 \sqrt{x} \left(a+\frac{b}{x}\right)^{3/2}}-\frac{4 b \sqrt{x}}{a^2 \left(a+\frac{b}{x}\right)^{3/2}}+\frac{2 x^{3/2}}{3 a \left(a+\frac{b}{x}\right)^{3/2}}",1,"(-32*b^3)/(3*a^4*(a + b/x)^(3/2)*x^(3/2)) - (16*b^2)/(a^3*(a + b/x)^(3/2)*Sqrt[x]) - (4*b*Sqrt[x])/(a^2*(a + b/x)^(3/2)) + (2*x^(3/2))/(3*a*(a + b/x)^(3/2))","A",4,2,17,0.1176,1,"{271, 264}"
1798,1,70,0,0.0223814,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{5/2} \sqrt{x}} \, dx","Int[1/((a + b/x)^(5/2)*Sqrt[x]),x]","\frac{16 b^2}{3 a^3 x^{3/2} \left(a+\frac{b}{x}\right)^{3/2}}+\frac{8 b}{a^2 \sqrt{x} \left(a+\frac{b}{x}\right)^{3/2}}+\frac{2 \sqrt{x}}{a \left(a+\frac{b}{x}\right)^{3/2}}","\frac{16 b^2}{3 a^3 x^{3/2} \left(a+\frac{b}{x}\right)^{3/2}}+\frac{8 b}{a^2 \sqrt{x} \left(a+\frac{b}{x}\right)^{3/2}}+\frac{2 \sqrt{x}}{a \left(a+\frac{b}{x}\right)^{3/2}}",1,"(16*b^2)/(3*a^3*(a + b/x)^(3/2)*x^(3/2)) + (8*b)/(a^2*(a + b/x)^(3/2)*Sqrt[x]) + (2*Sqrt[x])/(a*(a + b/x)^(3/2))","A",3,2,17,0.1176,1,"{271, 264}"
1799,1,46,0,0.0132287,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{5/2} x^{3/2}} \, dx","Int[1/((a + b/x)^(5/2)*x^(3/2)),x]","-\frac{4 b}{3 a^2 x^{3/2} \left(a+\frac{b}{x}\right)^{3/2}}-\frac{2}{a \sqrt{x} \left(a+\frac{b}{x}\right)^{3/2}}","-\frac{4 b}{3 a^2 x^{3/2} \left(a+\frac{b}{x}\right)^{3/2}}-\frac{2}{a \sqrt{x} \left(a+\frac{b}{x}\right)^{3/2}}",1,"(-4*b)/(3*a^2*(a + b/x)^(3/2)*x^(3/2)) - 2/(a*(a + b/x)^(3/2)*Sqrt[x])","A",2,2,17,0.1176,1,"{271, 264}"
1800,1,23,0,0.005742,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{5/2} x^{5/2}} \, dx","Int[1/((a + b/x)^(5/2)*x^(5/2)),x]","-\frac{2}{3 a x^{3/2} \left(a+\frac{b}{x}\right)^{3/2}}","-\frac{2}{3 a x^{3/2} \left(a+\frac{b}{x}\right)^{3/2}}",1,"-2/(3*a*(a + b/x)^(3/2)*x^(3/2))","A",1,1,17,0.05882,1,"{264}"
1801,1,75,0,0.0404249,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{5/2} x^{7/2}} \, dx","Int[1/((a + b/x)^(5/2)*x^(7/2)),x]","\frac{2}{b^2 \sqrt{x} \sqrt{a+\frac{b}{x}}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)}{b^{5/2}}+\frac{2}{3 b x^{3/2} \left(a+\frac{b}{x}\right)^{3/2}}","\frac{2}{b^2 \sqrt{x} \sqrt{a+\frac{b}{x}}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)}{b^{5/2}}+\frac{2}{3 b x^{3/2} \left(a+\frac{b}{x}\right)^{3/2}}",1,"2/(3*b*(a + b/x)^(3/2)*x^(3/2)) + 2/(b^2*Sqrt[a + b/x]*Sqrt[x]) - (2*ArcTanh[Sqrt[b]/(Sqrt[a + b/x]*Sqrt[x])])/b^(5/2)","A",5,4,17,0.2353,1,"{337, 288, 217, 206}"
1802,1,99,0,0.0536092,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{5/2} x^{9/2}} \, dx","Int[1/((a + b/x)^(5/2)*x^(9/2)),x]","\frac{10}{3 b^2 x^{3/2} \sqrt{a+\frac{b}{x}}}-\frac{5 \sqrt{a+\frac{b}{x}}}{b^3 \sqrt{x}}+\frac{5 a \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)}{b^{7/2}}+\frac{2}{3 b x^{5/2} \left(a+\frac{b}{x}\right)^{3/2}}","\frac{10}{3 b^2 x^{3/2} \sqrt{a+\frac{b}{x}}}-\frac{5 \sqrt{a+\frac{b}{x}}}{b^3 \sqrt{x}}+\frac{5 a \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)}{b^{7/2}}+\frac{2}{3 b x^{5/2} \left(a+\frac{b}{x}\right)^{3/2}}",1,"2/(3*b*(a + b/x)^(3/2)*x^(5/2)) + 10/(3*b^2*Sqrt[a + b/x]*x^(3/2)) - (5*Sqrt[a + b/x])/(b^3*Sqrt[x]) + (5*a*ArcTanh[Sqrt[b]/(Sqrt[a + b/x]*Sqrt[x])])/b^(7/2)","A",6,5,17,0.2941,1,"{337, 288, 321, 217, 206}"
1803,1,129,0,0.0710331,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{5/2} x^{11/2}} \, dx","Int[1/((a + b/x)^(5/2)*x^(11/2)),x]","-\frac{35 a^2 \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)}{4 b^{9/2}}-\frac{35 \sqrt{a+\frac{b}{x}}}{6 b^3 x^{3/2}}+\frac{14}{3 b^2 x^{5/2} \sqrt{a+\frac{b}{x}}}+\frac{35 a \sqrt{a+\frac{b}{x}}}{4 b^4 \sqrt{x}}+\frac{2}{3 b x^{7/2} \left(a+\frac{b}{x}\right)^{3/2}}","-\frac{35 a^2 \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)}{4 b^{9/2}}-\frac{35 \sqrt{a+\frac{b}{x}}}{6 b^3 x^{3/2}}+\frac{14}{3 b^2 x^{5/2} \sqrt{a+\frac{b}{x}}}+\frac{35 a \sqrt{a+\frac{b}{x}}}{4 b^4 \sqrt{x}}+\frac{2}{3 b x^{7/2} \left(a+\frac{b}{x}\right)^{3/2}}",1,"2/(3*b*(a + b/x)^(3/2)*x^(7/2)) + 14/(3*b^2*Sqrt[a + b/x]*x^(5/2)) - (35*Sqrt[a + b/x])/(6*b^3*x^(3/2)) + (35*a*Sqrt[a + b/x])/(4*b^4*Sqrt[x]) - (35*a^2*ArcTanh[Sqrt[b]/(Sqrt[a + b/x]*Sqrt[x])])/(4*b^(9/2))","A",7,5,17,0.2941,1,"{337, 288, 321, 217, 206}"
1804,1,17,0,0.0045681,"\int \left(a+\frac{b}{x^2}\right) x^6 \, dx","Int[(a + b/x^2)*x^6,x]","\frac{a x^7}{7}+\frac{b x^5}{5}","\frac{a x^7}{7}+\frac{b x^5}{5}",1,"(b*x^5)/5 + (a*x^7)/7","A",2,1,11,0.09091,1,"{14}"
1805,1,17,0,0.0047203,"\int \left(a+\frac{b}{x^2}\right) x^5 \, dx","Int[(a + b/x^2)*x^5,x]","\frac{a x^6}{6}+\frac{b x^4}{4}","\frac{a x^6}{6}+\frac{b x^4}{4}",1,"(b*x^4)/4 + (a*x^6)/6","A",2,1,11,0.09091,1,"{14}"
1806,1,17,0,0.0045602,"\int \left(a+\frac{b}{x^2}\right) x^4 \, dx","Int[(a + b/x^2)*x^4,x]","\frac{a x^5}{5}+\frac{b x^3}{3}","\frac{a x^5}{5}+\frac{b x^3}{3}",1,"(b*x^3)/3 + (a*x^5)/5","A",2,1,11,0.09091,1,"{14}"
1807,1,17,0,0.0045587,"\int \left(a+\frac{b}{x^2}\right) x^3 \, dx","Int[(a + b/x^2)*x^3,x]","\frac{a x^4}{4}+\frac{b x^2}{2}","\frac{a x^4}{4}+\frac{b x^2}{2}",1,"(b*x^2)/2 + (a*x^4)/4","A",2,1,11,0.09091,1,"{14}"
1808,1,12,0,0.0034542,"\int \left(a+\frac{b}{x^2}\right) x^2 \, dx","Int[(a + b/x^2)*x^2,x]","\frac{a x^3}{3}+b x","\frac{a x^3}{3}+b x",1,"b*x + (a*x^3)/3","A",2,1,11,0.09091,1,"{14}"
1809,1,13,0,0.0034573,"\int \left(a+\frac{b}{x^2}\right) x \, dx","Int[(a + b/x^2)*x,x]","\frac{a x^2}{2}+b \log (x)","\frac{a x^2}{2}+b \log (x)",1,"(a*x^2)/2 + b*Log[x]","A",2,1,9,0.1111,1,"{14}"
1810,1,10,0,0.0021625,"\int \left(a+\frac{b}{x^2}\right) \, dx","Int[a + b/x^2,x]","a x-\frac{b}{x}","a x-\frac{b}{x}",1,"-(b/x) + a*x","A",1,0,7,0,1,"{}"
1811,1,13,0,0.0047612,"\int \frac{a+\frac{b}{x^2}}{x} \, dx","Int[(a + b/x^2)/x,x]","a \log (x)-\frac{b}{2 x^2}","a \log (x)-\frac{b}{2 x^2}",1,"-b/(2*x^2) + a*Log[x]","A",2,1,11,0.09091,1,"{14}"
1812,1,15,0,0.0048434,"\int \frac{a+\frac{b}{x^2}}{x^2} \, dx","Int[(a + b/x^2)/x^2,x]","-\frac{a}{x}-\frac{b}{3 x^3}","-\frac{a}{x}-\frac{b}{3 x^3}",1,"-b/(3*x^3) - a/x","A",2,1,11,0.09091,1,"{14}"
1813,1,17,0,0.0050026,"\int \frac{a+\frac{b}{x^2}}{x^3} \, dx","Int[(a + b/x^2)/x^3,x]","-\frac{a}{2 x^2}-\frac{b}{4 x^4}","-\frac{a}{2 x^2}-\frac{b}{4 x^4}",1,"-b/(4*x^4) - a/(2*x^2)","A",2,1,11,0.09091,1,"{14}"
1814,1,17,0,0.0044337,"\int \frac{a+\frac{b}{x^2}}{x^4} \, dx","Int[(a + b/x^2)/x^4,x]","-\frac{a}{3 x^3}-\frac{b}{5 x^5}","-\frac{a}{3 x^3}-\frac{b}{5 x^5}",1,"-b/(5*x^5) - a/(3*x^3)","A",2,1,11,0.09091,1,"{14}"
1815,1,17,0,0.0048508,"\int \frac{a+\frac{b}{x^2}}{x^5} \, dx","Int[(a + b/x^2)/x^5,x]","-\frac{a}{4 x^4}-\frac{b}{6 x^6}","-\frac{a}{4 x^4}-\frac{b}{6 x^6}",1,"-b/(6*x^6) - a/(4*x^4)","A",2,1,11,0.09091,1,"{14}"
1816,1,17,0,0.0047044,"\int \frac{a+\frac{b}{x^2}}{x^6} \, dx","Int[(a + b/x^2)/x^6,x]","-\frac{a}{5 x^5}-\frac{b}{7 x^7}","-\frac{a}{5 x^5}-\frac{b}{7 x^7}",1,"-b/(7*x^7) - a/(5*x^5)","A",2,1,11,0.09091,1,"{14}"
1817,1,30,0,0.0117358,"\int \left(a+\frac{b}{x^2}\right)^2 x^6 \, dx","Int[(a + b/x^2)^2*x^6,x]","\frac{a^2 x^7}{7}+\frac{2}{5} a b x^5+\frac{b^2 x^3}{3}","\frac{a^2 x^7}{7}+\frac{2}{5} a b x^5+\frac{b^2 x^3}{3}",1,"(b^2*x^3)/3 + (2*a*b*x^5)/5 + (a^2*x^7)/7","A",3,2,13,0.1538,1,"{263, 270}"
1818,1,16,0,0.004456,"\int \left(a+\frac{b}{x^2}\right)^2 x^5 \, dx","Int[(a + b/x^2)^2*x^5,x]","\frac{\left(a x^2+b\right)^3}{6 a}","\frac{\left(a x^2+b\right)^3}{6 a}",1,"(b + a*x^2)^3/(6*a)","A",2,2,13,0.1538,1,"{263, 261}"
1819,1,25,0,0.0089196,"\int \left(a+\frac{b}{x^2}\right)^2 x^4 \, dx","Int[(a + b/x^2)^2*x^4,x]","\frac{a^2 x^5}{5}+\frac{2}{3} a b x^3+b^2 x","\frac{a^2 x^5}{5}+\frac{2}{3} a b x^3+b^2 x",1,"b^2*x + (2*a*b*x^3)/3 + (a^2*x^5)/5","A",3,2,13,0.1538,1,"{263, 194}"
1820,1,23,0,0.0139885,"\int \left(a+\frac{b}{x^2}\right)^2 x^3 \, dx","Int[(a + b/x^2)^2*x^3,x]","\frac{a^2 x^4}{4}+a b x^2+b^2 \log (x)","\frac{a^2 x^4}{4}+a b x^2+b^2 \log (x)",1,"a*b*x^2 + (a^2*x^4)/4 + b^2*Log[x]","A",4,3,13,0.2308,1,"{263, 266, 43}"
1821,1,24,0,0.01072,"\int \left(a+\frac{b}{x^2}\right)^2 x^2 \, dx","Int[(a + b/x^2)^2*x^2,x]","\frac{a^2 x^3}{3}+2 a b x-\frac{b^2}{x}","\frac{a^2 x^3}{3}+2 a b x-\frac{b^2}{x}",1,"-(b^2/x) + 2*a*b*x + (a^2*x^3)/3","A",3,2,13,0.1538,1,"{263, 270}"
1822,1,27,0,0.0144858,"\int \left(a+\frac{b}{x^2}\right)^2 x \, dx","Int[(a + b/x^2)^2*x,x]","\frac{a^2 x^2}{2}+2 a b \log (x)-\frac{b^2}{2 x^2}","\frac{a^2 x^2}{2}+2 a b \log (x)-\frac{b^2}{2 x^2}",1,"-b^2/(2*x^2) + (a^2*x^2)/2 + 2*a*b*Log[x]","A",4,3,11,0.2727,1,"{263, 266, 43}"
1823,1,23,0,0.01049,"\int \left(a+\frac{b}{x^2}\right)^2 \, dx","Int[(a + b/x^2)^2,x]","a^2 x-\frac{2 a b}{x}-\frac{b^2}{3 x^3}","a^2 x-\frac{2 a b}{x}-\frac{b^2}{3 x^3}",1,"-b^2/(3*x^3) - (2*a*b)/x + a^2*x","A",3,2,9,0.2222,1,"{193, 270}"
1824,1,24,0,0.0146094,"\int \frac{\left(a+\frac{b}{x^2}\right)^2}{x} \, dx","Int[(a + b/x^2)^2/x,x]","a^2 \log (x)-\frac{a b}{x^2}-\frac{b^2}{4 x^4}","a^2 \log (x)-\frac{a b}{x^2}-\frac{b^2}{4 x^4}",1,"-b^2/(4*x^4) - (a*b)/x^2 + a^2*Log[x]","A",4,3,13,0.2308,1,"{263, 266, 43}"
1825,1,28,0,0.0121368,"\int \frac{\left(a+\frac{b}{x^2}\right)^2}{x^2} \, dx","Int[(a + b/x^2)^2/x^2,x]","-\frac{a^2}{x}-\frac{2 a b}{3 x^3}-\frac{b^2}{5 x^5}","-\frac{a^2}{x}-\frac{2 a b}{3 x^3}-\frac{b^2}{5 x^5}",1,"-b^2/(5*x^5) - (2*a*b)/(3*x^3) - a^2/x","A",3,2,13,0.1538,1,"{263, 270}"
1826,1,16,0,0.0037366,"\int \frac{\left(a+\frac{b}{x^2}\right)^2}{x^3} \, dx","Int[(a + b/x^2)^2/x^3,x]","-\frac{\left(a+\frac{b}{x^2}\right)^3}{6 b}","-\frac{\left(a+\frac{b}{x^2}\right)^3}{6 b}",1,"-(a + b/x^2)^3/(6*b)","A",1,1,13,0.07692,1,"{261}"
1827,1,30,0,0.011996,"\int \frac{\left(a+\frac{b}{x^2}\right)^2}{x^4} \, dx","Int[(a + b/x^2)^2/x^4,x]","-\frac{a^2}{3 x^3}-\frac{2 a b}{5 x^5}-\frac{b^2}{7 x^7}","-\frac{a^2}{3 x^3}-\frac{2 a b}{5 x^5}-\frac{b^2}{7 x^7}",1,"-b^2/(7*x^7) - (2*a*b)/(5*x^5) - a^2/(3*x^3)","A",3,2,13,0.1538,1,"{263, 270}"
1828,1,30,0,0.0149898,"\int \frac{\left(a+\frac{b}{x^2}\right)^2}{x^5} \, dx","Int[(a + b/x^2)^2/x^5,x]","-\frac{a^2}{4 x^4}-\frac{a b}{3 x^6}-\frac{b^2}{8 x^8}","-\frac{a^2}{4 x^4}-\frac{a b}{3 x^6}-\frac{b^2}{8 x^8}",1,"-b^2/(8*x^8) - (a*b)/(3*x^6) - a^2/(4*x^4)","A",4,3,13,0.2308,1,"{263, 266, 43}"
1829,1,30,0,0.0118493,"\int \frac{\left(a+\frac{b}{x^2}\right)^2}{x^6} \, dx","Int[(a + b/x^2)^2/x^6,x]","-\frac{a^2}{5 x^5}-\frac{2 a b}{7 x^7}-\frac{b^2}{9 x^9}","-\frac{a^2}{5 x^5}-\frac{2 a b}{7 x^7}-\frac{b^2}{9 x^9}",1,"-b^2/(9*x^9) - (2*a*b)/(7*x^7) - a^2/(5*x^5)","A",3,2,13,0.1538,1,"{263, 270}"
1830,1,35,0,0.0138719,"\int \left(a+\frac{b}{x^2}\right)^3 x^6 \, dx","Int[(a + b/x^2)^3*x^6,x]","\frac{3}{5} a^2 b x^5+\frac{a^3 x^7}{7}+a b^2 x^3+b^3 x","\frac{3}{5} a^2 b x^5+\frac{a^3 x^7}{7}+a b^2 x^3+b^3 x",1,"b^3*x + a*b^2*x^3 + (3*a^2*b*x^5)/5 + (a^3*x^7)/7","A",3,2,13,0.1538,1,"{263, 194}"
1831,1,39,0,0.0199808,"\int \left(a+\frac{b}{x^2}\right)^3 x^5 \, dx","Int[(a + b/x^2)^3*x^5,x]","\frac{3}{4} a^2 b x^4+\frac{a^3 x^6}{6}+\frac{3}{2} a b^2 x^2+b^3 \log (x)","\frac{3}{4} a^2 b x^4+\frac{a^3 x^6}{6}+\frac{3}{2} a b^2 x^2+b^3 \log (x)",1,"(3*a*b^2*x^2)/2 + (3*a^2*b*x^4)/4 + (a^3*x^6)/6 + b^3*Log[x]","A",4,3,13,0.2308,1,"{263, 266, 43}"
1832,1,34,0,0.0145239,"\int \left(a+\frac{b}{x^2}\right)^3 x^4 \, dx","Int[(a + b/x^2)^3*x^4,x]","a^2 b x^3+\frac{a^3 x^5}{5}+3 a b^2 x-\frac{b^3}{x}","a^2 b x^3+\frac{a^3 x^5}{5}+3 a b^2 x-\frac{b^3}{x}",1,"-(b^3/x) + 3*a*b^2*x + a^2*b*x^3 + (a^3*x^5)/5","A",3,2,13,0.1538,1,"{263, 270}"
1833,1,40,0,0.0224021,"\int \left(a+\frac{b}{x^2}\right)^3 x^3 \, dx","Int[(a + b/x^2)^3*x^3,x]","\frac{3}{2} a^2 b x^2+\frac{a^3 x^4}{4}+3 a b^2 \log (x)-\frac{b^3}{2 x^2}","\frac{3}{2} a^2 b x^2+\frac{a^3 x^4}{4}+3 a b^2 \log (x)-\frac{b^3}{2 x^2}",1,"-b^3/(2*x^2) + (3*a^2*b*x^2)/2 + (a^3*x^4)/4 + 3*a*b^2*Log[x]","A",4,3,13,0.2308,1,"{263, 266, 43}"
1834,1,37,0,0.0153822,"\int \left(a+\frac{b}{x^2}\right)^3 x^2 \, dx","Int[(a + b/x^2)^3*x^2,x]","3 a^2 b x+\frac{a^3 x^3}{3}-\frac{3 a b^2}{x}-\frac{b^3}{3 x^3}","3 a^2 b x+\frac{a^3 x^3}{3}-\frac{3 a b^2}{x}-\frac{b^3}{3 x^3}",1,"-b^3/(3*x^3) - (3*a*b^2)/x + 3*a^2*b*x + (a^3*x^3)/3","A",3,2,13,0.1538,1,"{263, 270}"
1835,1,40,0,0.0196545,"\int \left(a+\frac{b}{x^2}\right)^3 x \, dx","Int[(a + b/x^2)^3*x,x]","3 a^2 b \log (x)+\frac{a^3 x^2}{2}-\frac{3 a b^2}{2 x^2}-\frac{b^3}{4 x^4}","3 a^2 b \log (x)+\frac{a^3 x^2}{2}-\frac{3 a b^2}{2 x^2}-\frac{b^3}{4 x^4}",1,"-b^3/(4*x^4) - (3*a*b^2)/(2*x^2) + (a^3*x^2)/2 + 3*a^2*b*Log[x]","A",4,3,11,0.2727,1,"{263, 266, 43}"
1836,1,34,0,0.0153526,"\int \left(a+\frac{b}{x^2}\right)^3 \, dx","Int[(a + b/x^2)^3,x]","-\frac{3 a^2 b}{x}+a^3 x-\frac{a b^2}{x^3}-\frac{b^3}{5 x^5}","-\frac{3 a^2 b}{x}+a^3 x-\frac{a b^2}{x^3}-\frac{b^3}{5 x^5}",1,"-b^3/(5*x^5) - (a*b^2)/x^3 - (3*a^2*b)/x + a^3*x","A",3,2,9,0.2222,1,"{193, 270}"
1837,1,39,0,0.0208135,"\int \frac{\left(a+\frac{b}{x^2}\right)^3}{x} \, dx","Int[(a + b/x^2)^3/x,x]","-\frac{3 a^2 b}{2 x^2}+a^3 \log (x)-\frac{3 a b^2}{4 x^4}-\frac{b^3}{6 x^6}","-\frac{3 a^2 b}{2 x^2}+a^3 \log (x)-\frac{3 a b^2}{4 x^4}-\frac{b^3}{6 x^6}",1,"-b^3/(6*x^6) - (3*a*b^2)/(4*x^4) - (3*a^2*b)/(2*x^2) + a^3*Log[x]","A",4,3,13,0.2308,1,"{263, 266, 43}"
1838,1,39,0,0.015652,"\int \frac{\left(a+\frac{b}{x^2}\right)^3}{x^2} \, dx","Int[(a + b/x^2)^3/x^2,x]","-\frac{a^2 b}{x^3}-\frac{a^3}{x}-\frac{3 a b^2}{5 x^5}-\frac{b^3}{7 x^7}","-\frac{a^2 b}{x^3}-\frac{a^3}{x}-\frac{3 a b^2}{5 x^5}-\frac{b^3}{7 x^7}",1,"-b^3/(7*x^7) - (3*a*b^2)/(5*x^5) - (a^2*b)/x^3 - a^3/x","A",3,2,13,0.1538,1,"{263, 270}"
1839,1,16,0,0.0037042,"\int \frac{\left(a+\frac{b}{x^2}\right)^3}{x^3} \, dx","Int[(a + b/x^2)^3/x^3,x]","-\frac{\left(a+\frac{b}{x^2}\right)^4}{8 b}","-\frac{\left(a+\frac{b}{x^2}\right)^4}{8 b}",1,"-(a + b/x^2)^4/(8*b)","A",1,1,13,0.07692,1,"{261}"
1840,1,43,0,0.0153341,"\int \frac{\left(a+\frac{b}{x^2}\right)^3}{x^4} \, dx","Int[(a + b/x^2)^3/x^4,x]","-\frac{3 a^2 b}{5 x^5}-\frac{a^3}{3 x^3}-\frac{3 a b^2}{7 x^7}-\frac{b^3}{9 x^9}","-\frac{3 a^2 b}{5 x^5}-\frac{a^3}{3 x^3}-\frac{3 a b^2}{7 x^7}-\frac{b^3}{9 x^9}",1,"-b^3/(9*x^9) - (3*a*b^2)/(7*x^7) - (3*a^2*b)/(5*x^5) - a^3/(3*x^3)","A",3,2,13,0.1538,1,"{263, 270}"
1841,1,40,0,0.0182408,"\int \frac{\left(a+\frac{b}{x^2}\right)^3}{x^5} \, dx","Int[(a + b/x^2)^3/x^5,x]","\frac{a \left(a x^2+b\right)^4}{40 b^2 x^8}-\frac{\left(a x^2+b\right)^4}{10 b x^{10}}","\frac{a \left(a x^2+b\right)^4}{40 b^2 x^8}-\frac{\left(a x^2+b\right)^4}{10 b x^{10}}",1,"-(b + a*x^2)^4/(10*b*x^10) + (a*(b + a*x^2)^4)/(40*b^2*x^8)","A",4,4,13,0.3077,1,"{263, 266, 45, 37}"
1842,1,43,0,0.0154913,"\int \frac{\left(a+\frac{b}{x^2}\right)^3}{x^6} \, dx","Int[(a + b/x^2)^3/x^6,x]","-\frac{3 a^2 b}{7 x^7}-\frac{a^3}{5 x^5}-\frac{a b^2}{3 x^9}-\frac{b^3}{11 x^{11}}","-\frac{3 a^2 b}{7 x^7}-\frac{a^3}{5 x^5}-\frac{a b^2}{3 x^9}-\frac{b^3}{11 x^{11}}",1,"-b^3/(11*x^11) - (a*b^2)/(3*x^9) - (3*a^2*b)/(7*x^7) - a^3/(5*x^5)","A",3,2,13,0.1538,1,"{263, 270}"
1843,1,68,0,0.0279305,"\int \frac{x^6}{a+\frac{b}{x^2}} \, dx","Int[x^6/(a + b/x^2),x]","\frac{b^2 x^3}{3 a^3}-\frac{b^3 x}{a^4}+\frac{b^{7/2} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{a^{9/2}}-\frac{b x^5}{5 a^2}+\frac{x^7}{7 a}","\frac{b^2 x^3}{3 a^3}-\frac{b^3 x}{a^4}+\frac{b^{7/2} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{a^{9/2}}-\frac{b x^5}{5 a^2}+\frac{x^7}{7 a}",1,"-((b^3*x)/a^4) + (b^2*x^3)/(3*a^3) - (b*x^5)/(5*a^2) + x^7/(7*a) + (b^(7/2)*ArcTan[(Sqrt[a]*x)/Sqrt[b]])/a^(9/2)","A",4,3,13,0.2308,1,"{263, 302, 205}"
1844,1,53,0,0.0344523,"\int \frac{x^5}{a+\frac{b}{x^2}} \, dx","Int[x^5/(a + b/x^2),x]","\frac{b^2 x^2}{2 a^3}-\frac{b^3 \log \left(a x^2+b\right)}{2 a^4}-\frac{b x^4}{4 a^2}+\frac{x^6}{6 a}","\frac{b^2 x^2}{2 a^3}-\frac{b^3 \log \left(a x^2+b\right)}{2 a^4}-\frac{b x^4}{4 a^2}+\frac{x^6}{6 a}",1,"(b^2*x^2)/(2*a^3) - (b*x^4)/(4*a^2) + x^6/(6*a) - (b^3*Log[b + a*x^2])/(2*a^4)","A",4,3,13,0.2308,1,"{263, 266, 43}"
1845,1,55,0,0.0244078,"\int \frac{x^4}{a+\frac{b}{x^2}} \, dx","Int[x^4/(a + b/x^2),x]","\frac{b^2 x}{a^3}-\frac{b^{5/2} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{a^{7/2}}-\frac{b x^3}{3 a^2}+\frac{x^5}{5 a}","\frac{b^2 x}{a^3}-\frac{b^{5/2} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{a^{7/2}}-\frac{b x^3}{3 a^2}+\frac{x^5}{5 a}",1,"(b^2*x)/a^3 - (b*x^3)/(3*a^2) + x^5/(5*a) - (b^(5/2)*ArcTan[(Sqrt[a]*x)/Sqrt[b]])/a^(7/2)","A",4,3,13,0.2308,1,"{263, 302, 205}"
1846,1,40,0,0.0256779,"\int \frac{x^3}{a+\frac{b}{x^2}} \, dx","Int[x^3/(a + b/x^2),x]","\frac{b^2 \log \left(a x^2+b\right)}{2 a^3}-\frac{b x^2}{2 a^2}+\frac{x^4}{4 a}","\frac{b^2 \log \left(a x^2+b\right)}{2 a^3}-\frac{b x^2}{2 a^2}+\frac{x^4}{4 a}",1,"-(b*x^2)/(2*a^2) + x^4/(4*a) + (b^2*Log[b + a*x^2])/(2*a^3)","A",4,3,13,0.2308,1,"{263, 266, 43}"
1847,1,42,0,0.0193837,"\int \frac{x^2}{a+\frac{b}{x^2}} \, dx","Int[x^2/(a + b/x^2),x]","\frac{b^{3/2} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{a^{5/2}}-\frac{b x}{a^2}+\frac{x^3}{3 a}","\frac{b^{3/2} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{a^{5/2}}-\frac{b x}{a^2}+\frac{x^3}{3 a}",1,"-((b*x)/a^2) + x^3/(3*a) + (b^(3/2)*ArcTan[(Sqrt[a]*x)/Sqrt[b]])/a^(5/2)","A",4,3,13,0.2308,1,"{263, 302, 205}"
1848,1,27,0,0.0173015,"\int \frac{x}{a+\frac{b}{x^2}} \, dx","Int[x/(a + b/x^2),x]","\frac{x^2}{2 a}-\frac{b \log \left(a x^2+b\right)}{2 a^2}","\frac{x^2}{2 a}-\frac{b \log \left(a x^2+b\right)}{2 a^2}",1,"x^2/(2*a) - (b*Log[b + a*x^2])/(2*a^2)","A",4,3,11,0.2727,1,"{263, 266, 43}"
1849,1,31,0,0.0105006,"\int \frac{1}{a+\frac{b}{x^2}} \, dx","Int[(a + b/x^2)^(-1),x]","\frac{x}{a}-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{a^{3/2}}","\frac{x}{a}-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{a^{3/2}}",1,"x/a - (Sqrt[b]*ArcTan[(Sqrt[a]*x)/Sqrt[b]])/a^(3/2)","A",3,3,9,0.3333,1,"{193, 321, 205}"
1850,1,15,0,0.0048052,"\int \frac{1}{\left(a+\frac{b}{x^2}\right) x} \, dx","Int[1/((a + b/x^2)*x),x]","\frac{\log \left(a x^2+b\right)}{2 a}","\frac{\log \left(a x^2+b\right)}{2 a}",1,"Log[b + a*x^2]/(2*a)","A",2,2,13,0.1538,1,"{263, 260}"
1851,1,24,0,0.0071655,"\int \frac{1}{\left(a+\frac{b}{x^2}\right) x^2} \, dx","Int[1/((a + b/x^2)*x^2),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{\sqrt{a} \sqrt{b}}","\frac{\tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{\sqrt{a} \sqrt{b}}",1,"ArcTan[(Sqrt[a]*x)/Sqrt[b]]/(Sqrt[a]*Sqrt[b])","A",2,2,13,0.1538,1,"{263, 205}"
1852,1,15,0,0.0036942,"\int \frac{1}{\left(a+\frac{b}{x^2}\right) x^3} \, dx","Int[1/((a + b/x^2)*x^3),x]","-\frac{\log \left(a+\frac{b}{x^2}\right)}{2 b}","-\frac{\log \left(a+\frac{b}{x^2}\right)}{2 b}",1,"-Log[a + b/x^2]/(2*b)","A",1,1,13,0.07692,1,"{260}"
1853,1,34,0,0.0118095,"\int \frac{1}{\left(a+\frac{b}{x^2}\right) x^4} \, dx","Int[1/((a + b/x^2)*x^4),x]","-\frac{\sqrt{a} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{b^{3/2}}-\frac{1}{b x}","-\frac{\sqrt{a} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{b^{3/2}}-\frac{1}{b x}",1,"-(1/(b*x)) - (Sqrt[a]*ArcTan[(Sqrt[a]*x)/Sqrt[b]])/b^(3/2)","A",3,3,13,0.2308,1,"{263, 325, 205}"
1854,1,35,0,0.0228595,"\int \frac{1}{\left(a+\frac{b}{x^2}\right) x^5} \, dx","Int[1/((a + b/x^2)*x^5),x]","\frac{a \log \left(a x^2+b\right)}{2 b^2}-\frac{a \log (x)}{b^2}-\frac{1}{2 b x^2}","\frac{a \log \left(a x^2+b\right)}{2 b^2}-\frac{a \log (x)}{b^2}-\frac{1}{2 b x^2}",1,"-1/(2*b*x^2) - (a*Log[x])/b^2 + (a*Log[b + a*x^2])/(2*b^2)","A",4,3,13,0.2308,1,"{263, 266, 44}"
1855,1,43,0,0.0174545,"\int \frac{1}{\left(a+\frac{b}{x^2}\right) x^6} \, dx","Int[1/((a + b/x^2)*x^6),x]","\frac{a^{3/2} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{b^{5/2}}+\frac{a}{b^2 x}-\frac{1}{3 b x^3}","\frac{a^{3/2} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{b^{5/2}}+\frac{a}{b^2 x}-\frac{1}{3 b x^3}",1,"-1/(3*b*x^3) + a/(b^2*x) + (a^(3/2)*ArcTan[(Sqrt[a]*x)/Sqrt[b]])/b^(5/2)","A",4,3,13,0.2308,1,"{263, 325, 205}"
1856,1,49,0,0.0304958,"\int \frac{1}{\left(a+\frac{b}{x^2}\right) x^7} \, dx","Int[1/((a + b/x^2)*x^7),x]","-\frac{a^2 \log \left(a x^2+b\right)}{2 b^3}+\frac{a^2 \log (x)}{b^3}+\frac{a}{2 b^2 x^2}-\frac{1}{4 b x^4}","-\frac{a^2 \log \left(a x^2+b\right)}{2 b^3}+\frac{a^2 \log (x)}{b^3}+\frac{a}{2 b^2 x^2}-\frac{1}{4 b x^4}",1,"-1/(4*b*x^4) + a/(2*b^2*x^2) + (a^2*Log[x])/b^3 - (a^2*Log[b + a*x^2])/(2*b^3)","A",4,3,13,0.2308,1,"{263, 266, 44}"
1857,1,58,0,0.0261248,"\int \frac{1}{\left(a+\frac{b}{x^2}\right) x^8} \, dx","Int[1/((a + b/x^2)*x^8),x]","-\frac{a^2}{b^3 x}-\frac{a^{5/2} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{b^{7/2}}+\frac{a}{3 b^2 x^3}-\frac{1}{5 b x^5}","-\frac{a^2}{b^3 x}-\frac{a^{5/2} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{b^{7/2}}+\frac{a}{3 b^2 x^3}-\frac{1}{5 b x^5}",1,"-1/(5*b*x^5) + a/(3*b^2*x^3) - a^2/(b^3*x) - (a^(5/2)*ArcTan[(Sqrt[a]*x)/Sqrt[b]])/b^(7/2)","A",5,3,13,0.2308,1,"{263, 325, 205}"
1858,1,92,0,0.037117,"\int \frac{x^6}{\left(a+\frac{b}{x^2}\right)^2} \, dx","Int[x^6/(a + b/x^2)^2,x]","\frac{3 b^2 x^3}{2 a^4}-\frac{9 b^3 x}{2 a^5}+\frac{9 b^{7/2} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{2 a^{11/2}}-\frac{9 b x^5}{10 a^3}+\frac{9 x^7}{14 a^2}-\frac{x^9}{2 a \left(a x^2+b\right)}","\frac{3 b^2 x^3}{2 a^4}-\frac{9 b^3 x}{2 a^5}+\frac{9 b^{7/2} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{2 a^{11/2}}-\frac{9 b x^5}{10 a^3}+\frac{9 x^7}{14 a^2}-\frac{x^9}{2 a \left(a x^2+b\right)}",1,"(-9*b^3*x)/(2*a^5) + (3*b^2*x^3)/(2*a^4) - (9*b*x^5)/(10*a^3) + (9*x^7)/(14*a^2) - x^9/(2*a*(b + a*x^2)) + (9*b^(7/2)*ArcTan[(Sqrt[a]*x)/Sqrt[b]])/(2*a^(11/2))","A",5,4,13,0.3077,1,"{263, 288, 302, 205}"
1859,1,70,0,0.0521735,"\int \frac{x^5}{\left(a+\frac{b}{x^2}\right)^2} \, dx","Int[x^5/(a + b/x^2)^2,x]","\frac{3 b^2 x^2}{2 a^4}-\frac{b^4}{2 a^5 \left(a x^2+b\right)}-\frac{2 b^3 \log \left(a x^2+b\right)}{a^5}-\frac{b x^4}{2 a^3}+\frac{x^6}{6 a^2}","\frac{3 b^2 x^2}{2 a^4}-\frac{b^4}{2 a^5 \left(a x^2+b\right)}-\frac{2 b^3 \log \left(a x^2+b\right)}{a^5}-\frac{b x^4}{2 a^3}+\frac{x^6}{6 a^2}",1,"(3*b^2*x^2)/(2*a^4) - (b*x^4)/(2*a^3) + x^6/(6*a^2) - b^4/(2*a^5*(b + a*x^2)) - (2*b^3*Log[b + a*x^2])/a^5","A",4,3,13,0.2308,1,"{263, 266, 43}"
1860,1,79,0,0.0327662,"\int \frac{x^4}{\left(a+\frac{b}{x^2}\right)^2} \, dx","Int[x^4/(a + b/x^2)^2,x]","\frac{7 b^2 x}{2 a^4}-\frac{7 b^{5/2} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{2 a^{9/2}}-\frac{7 b x^3}{6 a^3}+\frac{7 x^5}{10 a^2}-\frac{x^7}{2 a \left(a x^2+b\right)}","\frac{7 b^2 x}{2 a^4}-\frac{7 b^{5/2} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{2 a^{9/2}}-\frac{7 b x^3}{6 a^3}+\frac{7 x^5}{10 a^2}-\frac{x^7}{2 a \left(a x^2+b\right)}",1,"(7*b^2*x)/(2*a^4) - (7*b*x^3)/(6*a^3) + (7*x^5)/(10*a^2) - x^7/(2*a*(b + a*x^2)) - (7*b^(5/2)*ArcTan[(Sqrt[a]*x)/Sqrt[b]])/(2*a^(9/2))","A",5,4,13,0.3077,1,"{263, 288, 302, 205}"
1861,1,57,0,0.0420627,"\int \frac{x^3}{\left(a+\frac{b}{x^2}\right)^2} \, dx","Int[x^3/(a + b/x^2)^2,x]","\frac{b^3}{2 a^4 \left(a x^2+b\right)}+\frac{3 b^2 \log \left(a x^2+b\right)}{2 a^4}-\frac{b x^2}{a^3}+\frac{x^4}{4 a^2}","\frac{b^3}{2 a^4 \left(a x^2+b\right)}+\frac{3 b^2 \log \left(a x^2+b\right)}{2 a^4}-\frac{b x^2}{a^3}+\frac{x^4}{4 a^2}",1,"-((b*x^2)/a^3) + x^4/(4*a^2) + b^3/(2*a^4*(b + a*x^2)) + (3*b^2*Log[b + a*x^2])/(2*a^4)","A",4,3,13,0.2308,1,"{263, 266, 43}"
1862,1,66,0,0.0261688,"\int \frac{x^2}{\left(a+\frac{b}{x^2}\right)^2} \, dx","Int[x^2/(a + b/x^2)^2,x]","\frac{5 b^{3/2} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{2 a^{7/2}}-\frac{5 b x}{2 a^3}+\frac{5 x^3}{6 a^2}-\frac{x^5}{2 a \left(a x^2+b\right)}","\frac{5 b^{3/2} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{2 a^{7/2}}-\frac{5 b x}{2 a^3}+\frac{5 x^3}{6 a^2}-\frac{x^5}{2 a \left(a x^2+b\right)}",1,"(-5*b*x)/(2*a^3) + (5*x^3)/(6*a^2) - x^5/(2*a*(b + a*x^2)) + (5*b^(3/2)*ArcTan[(Sqrt[a]*x)/Sqrt[b]])/(2*a^(7/2))","A",5,4,13,0.3077,1,"{263, 288, 302, 205}"
1863,1,44,0,0.0312199,"\int \frac{x}{\left(a+\frac{b}{x^2}\right)^2} \, dx","Int[x/(a + b/x^2)^2,x]","-\frac{b^2}{2 a^3 \left(a x^2+b\right)}-\frac{b \log \left(a x^2+b\right)}{a^3}+\frac{x^2}{2 a^2}","-\frac{b^2}{2 a^3 \left(a x^2+b\right)}-\frac{b \log \left(a x^2+b\right)}{a^3}+\frac{x^2}{2 a^2}",1,"x^2/(2*a^2) - b^2/(2*a^3*(b + a*x^2)) - (b*Log[b + a*x^2])/a^3","A",4,3,11,0.2727,1,"{263, 266, 43}"
1864,1,55,0,0.0181359,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^2} \, dx","Int[(a + b/x^2)^(-2),x]","-\frac{3 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{2 a^{5/2}}+\frac{3 x}{2 a^2}-\frac{x^3}{2 a \left(a x^2+b\right)}","-\frac{3 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{2 a^{5/2}}+\frac{3 x}{2 a^2}-\frac{x^3}{2 a \left(a x^2+b\right)}",1,"(3*x)/(2*a^2) - x^3/(2*a*(b + a*x^2)) - (3*Sqrt[b]*ArcTan[(Sqrt[a]*x)/Sqrt[b]])/(2*a^(5/2))","A",4,4,9,0.4444,1,"{193, 288, 321, 205}"
1865,1,33,0,0.0241786,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^2 x} \, dx","Int[1/((a + b/x^2)^2*x),x]","\frac{b}{2 a^2 \left(a x^2+b\right)}+\frac{\log \left(a x^2+b\right)}{2 a^2}","\frac{b}{2 a^2 \left(a x^2+b\right)}+\frac{\log \left(a x^2+b\right)}{2 a^2}",1,"b/(2*a^2*(b + a*x^2)) + Log[b + a*x^2]/(2*a^2)","A",4,3,13,0.2308,1,"{263, 266, 43}"
1866,1,45,0,0.013133,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^2 x^2} \, dx","Int[1/((a + b/x^2)^2*x^2),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{2 a^{3/2} \sqrt{b}}-\frac{x}{2 a \left(a x^2+b\right)}","\frac{\tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{2 a^{3/2} \sqrt{b}}-\frac{x}{2 a \left(a x^2+b\right)}",1,"-x/(2*a*(b + a*x^2)) + ArcTan[(Sqrt[a]*x)/Sqrt[b]]/(2*a^(3/2)*Sqrt[b])","A",3,3,13,0.2308,1,"{263, 288, 205}"
1867,1,16,0,0.003838,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^2 x^3} \, dx","Int[1/((a + b/x^2)^2*x^3),x]","\frac{1}{2 b \left(a+\frac{b}{x^2}\right)}","\frac{1}{2 b \left(a+\frac{b}{x^2}\right)}",1,"1/(2*b*(a + b/x^2))","A",1,1,13,0.07692,1,"{261}"
1868,1,45,0,0.0114527,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^2 x^4} \, dx","Int[1/((a + b/x^2)^2*x^4),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{2 \sqrt{a} b^{3/2}}+\frac{x}{2 b \left(a x^2+b\right)}","\frac{\tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{2 \sqrt{a} b^{3/2}}+\frac{x}{2 b \left(a x^2+b\right)}",1,"x/(2*b*(b + a*x^2)) + ArcTan[(Sqrt[a]*x)/Sqrt[b]]/(2*Sqrt[a]*b^(3/2))","A",3,3,13,0.2308,1,"{263, 199, 205}"
1869,1,38,0,0.025249,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^2 x^5} \, dx","Int[1/((a + b/x^2)^2*x^5),x]","-\frac{\log \left(a x^2+b\right)}{2 b^2}+\frac{1}{2 b \left(a x^2+b\right)}+\frac{\log (x)}{b^2}","-\frac{\log \left(a x^2+b\right)}{2 b^2}+\frac{1}{2 b \left(a x^2+b\right)}+\frac{\log (x)}{b^2}",1,"1/(2*b*(b + a*x^2)) + Log[x]/b^2 - Log[b + a*x^2]/(2*b^2)","A",4,3,13,0.2308,1,"{263, 266, 44}"
1870,1,57,0,0.0177912,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^2 x^6} \, dx","Int[1/((a + b/x^2)^2*x^6),x]","-\frac{3 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{2 b^{5/2}}+\frac{1}{2 b x \left(a x^2+b\right)}-\frac{3}{2 b^2 x}","-\frac{3 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{2 b^{5/2}}+\frac{1}{2 b x \left(a x^2+b\right)}-\frac{3}{2 b^2 x}",1,"-3/(2*b^2*x) + 1/(2*b*x*(b + a*x^2)) - (3*Sqrt[a]*ArcTan[(Sqrt[a]*x)/Sqrt[b]])/(2*b^(5/2))","A",4,4,13,0.3077,1,"{263, 290, 325, 205}"
1871,1,49,0,0.0326947,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^2 x^7} \, dx","Int[1/((a + b/x^2)^2*x^7),x]","-\frac{a}{2 b^2 \left(a x^2+b\right)}+\frac{a \log \left(a x^2+b\right)}{b^3}-\frac{2 a \log (x)}{b^3}-\frac{1}{2 b^2 x^2}","-\frac{a}{2 b^2 \left(a x^2+b\right)}+\frac{a \log \left(a x^2+b\right)}{b^3}-\frac{2 a \log (x)}{b^3}-\frac{1}{2 b^2 x^2}",1,"-1/(2*b^2*x^2) - a/(2*b^2*(b + a*x^2)) - (2*a*Log[x])/b^3 + (a*Log[b + a*x^2])/b^3","A",4,3,13,0.2308,1,"{263, 266, 44}"
1872,1,68,0,0.0249115,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^2 x^8} \, dx","Int[1/((a + b/x^2)^2*x^8),x]","\frac{5 a^{3/2} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{2 b^{7/2}}+\frac{5 a}{2 b^3 x}+\frac{1}{2 b x^3 \left(a x^2+b\right)}-\frac{5}{6 b^2 x^3}","\frac{5 a^{3/2} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{2 b^{7/2}}+\frac{5 a}{2 b^3 x}+\frac{1}{2 b x^3 \left(a x^2+b\right)}-\frac{5}{6 b^2 x^3}",1,"-5/(6*b^2*x^3) + (5*a)/(2*b^3*x) + 1/(2*b*x^3*(b + a*x^2)) + (5*a^(3/2)*ArcTan[(Sqrt[a]*x)/Sqrt[b]])/(2*b^(7/2))","A",5,4,13,0.3077,1,"{263, 290, 325, 205}"
1873,1,66,0,0.0424086,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^2 x^9} \, dx","Int[1/((a + b/x^2)^2*x^9),x]","\frac{a^2}{2 b^3 \left(a x^2+b\right)}-\frac{3 a^2 \log \left(a x^2+b\right)}{2 b^4}+\frac{3 a^2 \log (x)}{b^4}+\frac{a}{b^3 x^2}-\frac{1}{4 b^2 x^4}","\frac{a^2}{2 b^3 \left(a x^2+b\right)}-\frac{3 a^2 \log \left(a x^2+b\right)}{2 b^4}+\frac{3 a^2 \log (x)}{b^4}+\frac{a}{b^3 x^2}-\frac{1}{4 b^2 x^4}",1,"-1/(4*b^2*x^4) + a/(b^3*x^2) + a^2/(2*b^3*(b + a*x^2)) + (3*a^2*Log[x])/b^4 - (3*a^2*Log[b + a*x^2])/(2*b^4)","A",4,3,13,0.2308,1,"{263, 266, 44}"
1874,1,87,0,0.0639311,"\int \frac{x^5}{\left(a+\frac{b}{x^2}\right)^3} \, dx","Int[x^5/(a + b/x^2)^3,x]","\frac{3 b^2 x^2}{a^5}-\frac{5 b^4}{2 a^6 \left(a x^2+b\right)}+\frac{b^5}{4 a^6 \left(a x^2+b\right)^2}-\frac{5 b^3 \log \left(a x^2+b\right)}{a^6}-\frac{3 b x^4}{4 a^4}+\frac{x^6}{6 a^3}","\frac{3 b^2 x^2}{a^5}-\frac{5 b^4}{2 a^6 \left(a x^2+b\right)}+\frac{b^5}{4 a^6 \left(a x^2+b\right)^2}-\frac{5 b^3 \log \left(a x^2+b\right)}{a^6}-\frac{3 b x^4}{4 a^4}+\frac{x^6}{6 a^3}",1,"(3*b^2*x^2)/a^5 - (3*b*x^4)/(4*a^4) + x^6/(6*a^3) + b^5/(4*a^6*(b + a*x^2)^2) - (5*b^4)/(2*a^6*(b + a*x^2)) - (5*b^3*Log[b + a*x^2])/a^6","A",4,3,13,0.2308,1,"{263, 266, 43}"
1875,1,98,0,0.0411233,"\int \frac{x^4}{\left(a+\frac{b}{x^2}\right)^3} \, dx","Int[x^4/(a + b/x^2)^3,x]","\frac{63 b^2 x}{8 a^5}-\frac{63 b^{5/2} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{8 a^{11/2}}-\frac{9 x^7}{8 a^2 \left(a x^2+b\right)}-\frac{21 b x^3}{8 a^4}+\frac{63 x^5}{40 a^3}-\frac{x^9}{4 a \left(a x^2+b\right)^2}","\frac{63 b^2 x}{8 a^5}-\frac{63 b^{5/2} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{8 a^{11/2}}-\frac{9 x^7}{8 a^2 \left(a x^2+b\right)}-\frac{21 b x^3}{8 a^4}+\frac{63 x^5}{40 a^3}-\frac{x^9}{4 a \left(a x^2+b\right)^2}",1,"(63*b^2*x)/(8*a^5) - (21*b*x^3)/(8*a^4) + (63*x^5)/(40*a^3) - x^9/(4*a*(b + a*x^2)^2) - (9*x^7)/(8*a^2*(b + a*x^2)) - (63*b^(5/2)*ArcTan[(Sqrt[a]*x)/Sqrt[b]])/(8*a^(11/2))","A",6,4,13,0.3077,1,"{263, 288, 302, 205}"
1876,1,74,0,0.0558214,"\int \frac{x^3}{\left(a+\frac{b}{x^2}\right)^3} \, dx","Int[x^3/(a + b/x^2)^3,x]","-\frac{b^4}{4 a^5 \left(a x^2+b\right)^2}+\frac{2 b^3}{a^5 \left(a x^2+b\right)}+\frac{3 b^2 \log \left(a x^2+b\right)}{a^5}-\frac{3 b x^2}{2 a^4}+\frac{x^4}{4 a^3}","-\frac{b^4}{4 a^5 \left(a x^2+b\right)^2}+\frac{2 b^3}{a^5 \left(a x^2+b\right)}+\frac{3 b^2 \log \left(a x^2+b\right)}{a^5}-\frac{3 b x^2}{2 a^4}+\frac{x^4}{4 a^3}",1,"(-3*b*x^2)/(2*a^4) + x^4/(4*a^3) - b^4/(4*a^5*(b + a*x^2)^2) + (2*b^3)/(a^5*(b + a*x^2)) + (3*b^2*Log[b + a*x^2])/a^5","A",4,3,13,0.2308,1,"{263, 266, 43}"
1877,1,85,0,0.0358001,"\int \frac{x^2}{\left(a+\frac{b}{x^2}\right)^3} \, dx","Int[x^2/(a + b/x^2)^3,x]","\frac{35 b^{3/2} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{8 a^{9/2}}-\frac{7 x^5}{8 a^2 \left(a x^2+b\right)}-\frac{35 b x}{8 a^4}+\frac{35 x^3}{24 a^3}-\frac{x^7}{4 a \left(a x^2+b\right)^2}","\frac{35 b^{3/2} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{8 a^{9/2}}-\frac{7 x^5}{8 a^2 \left(a x^2+b\right)}-\frac{35 b x}{8 a^4}+\frac{35 x^3}{24 a^3}-\frac{x^7}{4 a \left(a x^2+b\right)^2}",1,"(-35*b*x)/(8*a^4) + (35*x^3)/(24*a^3) - x^7/(4*a*(b + a*x^2)^2) - (7*x^5)/(8*a^2*(b + a*x^2)) + (35*b^(3/2)*ArcTan[(Sqrt[a]*x)/Sqrt[b]])/(8*a^(9/2))","A",6,4,13,0.3077,1,"{263, 288, 302, 205}"
1878,1,65,0,0.0456249,"\int \frac{x}{\left(a+\frac{b}{x^2}\right)^3} \, dx","Int[x/(a + b/x^2)^3,x]","\frac{b^3}{4 a^4 \left(a x^2+b\right)^2}-\frac{3 b^2}{2 a^4 \left(a x^2+b\right)}-\frac{3 b \log \left(a x^2+b\right)}{2 a^4}+\frac{x^2}{2 a^3}","\frac{b^3}{4 a^4 \left(a x^2+b\right)^2}-\frac{3 b^2}{2 a^4 \left(a x^2+b\right)}-\frac{3 b \log \left(a x^2+b\right)}{2 a^4}+\frac{x^2}{2 a^3}",1,"x^2/(2*a^3) + b^3/(4*a^4*(b + a*x^2)^2) - (3*b^2)/(2*a^4*(b + a*x^2)) - (3*b*Log[b + a*x^2])/(2*a^4)","A",4,3,11,0.2727,1,"{263, 266, 43}"
1879,1,74,0,0.0253844,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^3} \, dx","Int[(a + b/x^2)^(-3),x]","-\frac{5 x^3}{8 a^2 \left(a x^2+b\right)}-\frac{15 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{8 a^{7/2}}+\frac{15 x}{8 a^3}-\frac{x^5}{4 a \left(a x^2+b\right)^2}","-\frac{5 x^3}{8 a^2 \left(a x^2+b\right)}-\frac{15 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{8 a^{7/2}}+\frac{15 x}{8 a^3}-\frac{x^5}{4 a \left(a x^2+b\right)^2}",1,"(15*x)/(8*a^3) - x^5/(4*a*(b + a*x^2)^2) - (5*x^3)/(8*a^2*(b + a*x^2)) - (15*Sqrt[b]*ArcTan[(Sqrt[a]*x)/Sqrt[b]])/(8*a^(7/2))","A",5,4,9,0.4444,1,"{193, 288, 321, 205}"
1880,1,49,0,0.0352087,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^3 x} \, dx","Int[1/((a + b/x^2)^3*x),x]","-\frac{b^2}{4 a^3 \left(a x^2+b\right)^2}+\frac{b}{a^3 \left(a x^2+b\right)}+\frac{\log \left(a x^2+b\right)}{2 a^3}","-\frac{b^2}{4 a^3 \left(a x^2+b\right)^2}+\frac{b}{a^3 \left(a x^2+b\right)}+\frac{\log \left(a x^2+b\right)}{2 a^3}",1,"-b^2/(4*a^3*(b + a*x^2)^2) + b/(a^3*(b + a*x^2)) + Log[b + a*x^2]/(2*a^3)","A",4,3,13,0.2308,1,"{263, 266, 43}"
1881,1,64,0,0.0200818,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^3 x^2} \, dx","Int[1/((a + b/x^2)^3*x^2),x]","-\frac{3 x}{8 a^2 \left(a x^2+b\right)}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{8 a^{5/2} \sqrt{b}}-\frac{x^3}{4 a \left(a x^2+b\right)^2}","-\frac{3 x}{8 a^2 \left(a x^2+b\right)}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{8 a^{5/2} \sqrt{b}}-\frac{x^3}{4 a \left(a x^2+b\right)^2}",1,"-x^3/(4*a*(b + a*x^2)^2) - (3*x)/(8*a^2*(b + a*x^2)) + (3*ArcTan[(Sqrt[a]*x)/Sqrt[b]])/(8*a^(5/2)*Sqrt[b])","A",4,3,13,0.2308,1,"{263, 288, 205}"
1882,1,16,0,0.0038042,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^3 x^3} \, dx","Int[1/((a + b/x^2)^3*x^3),x]","\frac{1}{4 b \left(a+\frac{b}{x^2}\right)^2}","\frac{1}{4 b \left(a+\frac{b}{x^2}\right)^2}",1,"1/(4*b*(a + b/x^2)^2)","A",1,1,13,0.07692,1,"{261}"
1883,1,65,0,0.0199228,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^3 x^4} \, dx","Int[1/((a + b/x^2)^3*x^4),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{8 a^{3/2} b^{3/2}}+\frac{x}{8 a b \left(a x^2+b\right)}-\frac{x}{4 a \left(a x^2+b\right)^2}","\frac{\tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{8 a^{3/2} b^{3/2}}+\frac{x}{8 a b \left(a x^2+b\right)}-\frac{x}{4 a \left(a x^2+b\right)^2}",1,"-x/(4*a*(b + a*x^2)^2) + x/(8*a*b*(b + a*x^2)) + ArcTan[(Sqrt[a]*x)/Sqrt[b]]/(8*a^(3/2)*b^(3/2))","A",4,4,13,0.3077,1,"{263, 288, 199, 205}"
1884,1,16,0,0.0050669,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^3 x^5} \, dx","Int[1/((a + b/x^2)^3*x^5),x]","-\frac{1}{4 a \left(a x^2+b\right)^2}","-\frac{1}{4 a \left(a x^2+b\right)^2}",1,"-1/(4*a*(b + a*x^2)^2)","A",2,2,13,0.1538,1,"{263, 261}"
1885,1,62,0,0.0170318,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^3 x^6} \, dx","Int[1/((a + b/x^2)^3*x^6),x]","\frac{3 x}{8 b^2 \left(a x^2+b\right)}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{8 \sqrt{a} b^{5/2}}+\frac{x}{4 b \left(a x^2+b\right)^2}","\frac{3 x}{8 b^2 \left(a x^2+b\right)}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{8 \sqrt{a} b^{5/2}}+\frac{x}{4 b \left(a x^2+b\right)^2}",1,"x/(4*b*(b + a*x^2)^2) + (3*x)/(8*b^2*(b + a*x^2)) + (3*ArcTan[(Sqrt[a]*x)/Sqrt[b]])/(8*Sqrt[a]*b^(5/2))","A",4,3,13,0.2308,1,"{263, 199, 205}"
1886,1,54,0,0.035682,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^3 x^7} \, dx","Int[1/((a + b/x^2)^3*x^7),x]","\frac{1}{2 b^2 \left(a x^2+b\right)}-\frac{\log \left(a x^2+b\right)}{2 b^3}+\frac{1}{4 b \left(a x^2+b\right)^2}+\frac{\log (x)}{b^3}","\frac{1}{2 b^2 \left(a x^2+b\right)}-\frac{\log \left(a x^2+b\right)}{2 b^3}+\frac{1}{4 b \left(a x^2+b\right)^2}+\frac{\log (x)}{b^3}",1,"1/(4*b*(b + a*x^2)^2) + 1/(2*b^2*(b + a*x^2)) + Log[x]/b^3 - Log[b + a*x^2]/(2*b^3)","A",4,3,13,0.2308,1,"{263, 266, 44}"
1887,1,76,0,0.0269846,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^3 x^8} \, dx","Int[1/((a + b/x^2)^3*x^8),x]","\frac{5}{8 b^2 x \left(a x^2+b\right)}-\frac{15 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{8 b^{7/2}}+\frac{1}{4 b x \left(a x^2+b\right)^2}-\frac{15}{8 b^3 x}","\frac{5}{8 b^2 x \left(a x^2+b\right)}-\frac{15 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{8 b^{7/2}}+\frac{1}{4 b x \left(a x^2+b\right)^2}-\frac{15}{8 b^3 x}",1,"-15/(8*b^3*x) + 1/(4*b*x*(b + a*x^2)^2) + 5/(8*b^2*x*(b + a*x^2)) - (15*Sqrt[a]*ArcTan[(Sqrt[a]*x)/Sqrt[b]])/(8*b^(7/2))","A",5,4,13,0.3077,1,"{263, 290, 325, 205}"
1888,1,67,0,0.0458847,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^3 x^9} \, dx","Int[1/((a + b/x^2)^3*x^9),x]","-\frac{a}{b^3 \left(a x^2+b\right)}-\frac{a}{4 b^2 \left(a x^2+b\right)^2}+\frac{3 a \log \left(a x^2+b\right)}{2 b^4}-\frac{3 a \log (x)}{b^4}-\frac{1}{2 b^3 x^2}","-\frac{a}{b^3 \left(a x^2+b\right)}-\frac{a}{4 b^2 \left(a x^2+b\right)^2}+\frac{3 a \log \left(a x^2+b\right)}{2 b^4}-\frac{3 a \log (x)}{b^4}-\frac{1}{2 b^3 x^2}",1,"-1/(2*b^3*x^2) - a/(4*b^2*(b + a*x^2)^2) - a/(b^3*(b + a*x^2)) - (3*a*Log[x])/b^4 + (3*a*Log[b + a*x^2])/(2*b^4)","A",4,3,13,0.2308,1,"{263, 266, 44}"
1889,1,87,0,0.0346164,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^3 x^{10}} \, dx","Int[1/((a + b/x^2)^3*x^10),x]","\frac{35 a^{3/2} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{8 b^{9/2}}+\frac{7}{8 b^2 x^3 \left(a x^2+b\right)}+\frac{35 a}{8 b^4 x}+\frac{1}{4 b x^3 \left(a x^2+b\right)^2}-\frac{35}{24 b^3 x^3}","\frac{35 a^{3/2} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{8 b^{9/2}}+\frac{7}{8 b^2 x^3 \left(a x^2+b\right)}+\frac{35 a}{8 b^4 x}+\frac{1}{4 b x^3 \left(a x^2+b\right)^2}-\frac{35}{24 b^3 x^3}",1,"-35/(24*b^3*x^3) + (35*a)/(8*b^4*x) + 1/(4*b*x^3*(b + a*x^2)^2) + 7/(8*b^2*x^3*(b + a*x^2)) + (35*a^(3/2)*ArcTan[(Sqrt[a]*x)/Sqrt[b]])/(8*b^(9/2))","A",6,4,13,0.3077,1,"{263, 290, 325, 205}"
1890,1,86,0,0.0543483,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^3 x^{11}} \, dx","Int[1/((a + b/x^2)^3*x^11),x]","\frac{3 a^2}{2 b^4 \left(a x^2+b\right)}+\frac{a^2}{4 b^3 \left(a x^2+b\right)^2}-\frac{3 a^2 \log \left(a x^2+b\right)}{b^5}+\frac{6 a^2 \log (x)}{b^5}+\frac{3 a}{2 b^4 x^2}-\frac{1}{4 b^3 x^4}","\frac{3 a^2}{2 b^4 \left(a x^2+b\right)}+\frac{a^2}{4 b^3 \left(a x^2+b\right)^2}-\frac{3 a^2 \log \left(a x^2+b\right)}{b^5}+\frac{6 a^2 \log (x)}{b^5}+\frac{3 a}{2 b^4 x^2}-\frac{1}{4 b^3 x^4}",1,"-1/(4*b^3*x^4) + (3*a)/(2*b^4*x^2) + a^2/(4*b^3*(b + a*x^2)^2) + (3*a^2)/(2*b^4*(b + a*x^2)) + (6*a^2*Log[x])/b^5 - (3*a^2*Log[b + a*x^2])/b^5","A",4,3,13,0.2308,1,"{263, 266, 44}"
1891,1,71,0,0.0357065,"\int \sqrt{a+\frac{b}{x^2}} x^3 \, dx","Int[Sqrt[a + b/x^2]*x^3,x]","-\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^2}}}{\sqrt{a}}\right)}{8 a^{3/2}}+\frac{1}{4} x^4 \sqrt{a+\frac{b}{x^2}}+\frac{b x^2 \sqrt{a+\frac{b}{x^2}}}{8 a}","-\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^2}}}{\sqrt{a}}\right)}{8 a^{3/2}}+\frac{1}{4} x^4 \sqrt{a+\frac{b}{x^2}}+\frac{b x^2 \sqrt{a+\frac{b}{x^2}}}{8 a}",1,"(b*Sqrt[a + b/x^2]*x^2)/(8*a) + (Sqrt[a + b/x^2]*x^4)/4 - (b^2*ArcTanh[Sqrt[a + b/x^2]/Sqrt[a]])/(8*a^(3/2))","A",5,5,15,0.3333,1,"{266, 47, 51, 63, 208}"
1892,1,21,0,0.0057577,"\int \sqrt{a+\frac{b}{x^2}} x^2 \, dx","Int[Sqrt[a + b/x^2]*x^2,x]","\frac{x^3 \left(a+\frac{b}{x^2}\right)^{3/2}}{3 a}","\frac{x^3 \left(a+\frac{b}{x^2}\right)^{3/2}}{3 a}",1,"((a + b/x^2)^(3/2)*x^3)/(3*a)","A",1,1,15,0.06667,1,"{264}"
1893,1,47,0,0.0224933,"\int \sqrt{a+\frac{b}{x^2}} x \, dx","Int[Sqrt[a + b/x^2]*x,x]","\frac{1}{2} x^2 \sqrt{a+\frac{b}{x^2}}+\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^2}}}{\sqrt{a}}\right)}{2 \sqrt{a}}","\frac{1}{2} x^2 \sqrt{a+\frac{b}{x^2}}+\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^2}}}{\sqrt{a}}\right)}{2 \sqrt{a}}",1,"(Sqrt[a + b/x^2]*x^2)/2 + (b*ArcTanh[Sqrt[a + b/x^2]/Sqrt[a]])/(2*Sqrt[a])","A",4,4,13,0.3077,1,"{266, 47, 63, 208}"
1894,1,42,0,0.0184578,"\int \sqrt{a+\frac{b}{x^2}} \, dx","Int[Sqrt[a + b/x^2],x]","x \sqrt{a+\frac{b}{x^2}}-\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b}}{x \sqrt{a+\frac{b}{x^2}}}\right)","x \sqrt{a+\frac{b}{x^2}}-\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b}}{x \sqrt{a+\frac{b}{x^2}}}\right)",1,"Sqrt[a + b/x^2]*x - Sqrt[b]*ArcTanh[Sqrt[b]/(Sqrt[a + b/x^2]*x)]","A",4,4,11,0.3636,1,"{242, 277, 217, 206}"
1895,1,38,0,0.0227823,"\int \frac{\sqrt{a+\frac{b}{x^2}}}{x} \, dx","Int[Sqrt[a + b/x^2]/x,x]","\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^2}}}{\sqrt{a}}\right)-\sqrt{a+\frac{b}{x^2}}","\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^2}}}{\sqrt{a}}\right)-\sqrt{a+\frac{b}{x^2}}",1,"-Sqrt[a + b/x^2] + Sqrt[a]*ArcTanh[Sqrt[a + b/x^2]/Sqrt[a]]","A",4,4,15,0.2667,1,"{266, 50, 63, 208}"
1896,1,50,0,0.0204868,"\int \frac{\sqrt{a+\frac{b}{x^2}}}{x^2} \, dx","Int[Sqrt[a + b/x^2]/x^2,x]","-\frac{\sqrt{a+\frac{b}{x^2}}}{2 x}-\frac{a \tanh ^{-1}\left(\frac{\sqrt{b}}{x \sqrt{a+\frac{b}{x^2}}}\right)}{2 \sqrt{b}}","-\frac{\sqrt{a+\frac{b}{x^2}}}{2 x}-\frac{a \tanh ^{-1}\left(\frac{\sqrt{b}}{x \sqrt{a+\frac{b}{x^2}}}\right)}{2 \sqrt{b}}",1,"-Sqrt[a + b/x^2]/(2*x) - (a*ArcTanh[Sqrt[b]/(Sqrt[a + b/x^2]*x)])/(2*Sqrt[b])","A",4,4,15,0.2667,1,"{335, 195, 217, 206}"
1897,1,18,0,0.0059974,"\int \frac{\sqrt{a+\frac{b}{x^2}}}{x^3} \, dx","Int[Sqrt[a + b/x^2]/x^3,x]","-\frac{\left(a+\frac{b}{x^2}\right)^{3/2}}{3 b}","-\frac{\left(a+\frac{b}{x^2}\right)^{3/2}}{3 b}",1,"-(a + b/x^2)^(3/2)/(3*b)","A",1,1,15,0.06667,1,"{261}"
1898,1,74,0,0.0365519,"\int \frac{\sqrt{a+\frac{b}{x^2}}}{x^4} \, dx","Int[Sqrt[a + b/x^2]/x^4,x]","\frac{a^2 \tanh ^{-1}\left(\frac{\sqrt{b}}{x \sqrt{a+\frac{b}{x^2}}}\right)}{8 b^{3/2}}-\frac{a \sqrt{a+\frac{b}{x^2}}}{8 b x}-\frac{\sqrt{a+\frac{b}{x^2}}}{4 x^3}","\frac{a^2 \tanh ^{-1}\left(\frac{\sqrt{b}}{x \sqrt{a+\frac{b}{x^2}}}\right)}{8 b^{3/2}}-\frac{a \sqrt{a+\frac{b}{x^2}}}{8 b x}-\frac{\sqrt{a+\frac{b}{x^2}}}{4 x^3}",1,"-Sqrt[a + b/x^2]/(4*x^3) - (a*Sqrt[a + b/x^2])/(8*b*x) + (a^2*ArcTanh[Sqrt[b]/(Sqrt[a + b/x^2]*x)])/(8*b^(3/2))","A",5,5,15,0.3333,1,"{335, 279, 321, 217, 206}"
1899,1,68,0,0.0346493,"\int \left(a+\frac{b}{x^2}\right)^{3/2} x^3 \, dx","Int[(a + b/x^2)^(3/2)*x^3,x]","\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^2}}}{\sqrt{a}}\right)}{8 \sqrt{a}}+\frac{1}{4} x^4 \left(a+\frac{b}{x^2}\right)^{3/2}+\frac{3}{8} b x^2 \sqrt{a+\frac{b}{x^2}}","\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^2}}}{\sqrt{a}}\right)}{8 \sqrt{a}}+\frac{1}{4} x^4 \left(a+\frac{b}{x^2}\right)^{3/2}+\frac{3}{8} b x^2 \sqrt{a+\frac{b}{x^2}}",1,"(3*b*Sqrt[a + b/x^2]*x^2)/8 + ((a + b/x^2)^(3/2)*x^4)/4 + (3*b^2*ArcTanh[Sqrt[a + b/x^2]/Sqrt[a]])/(8*Sqrt[a])","A",5,4,15,0.2667,1,"{266, 47, 63, 208}"
1900,1,61,0,0.0330456,"\int \left(a+\frac{b}{x^2}\right)^{3/2} x^2 \, dx","Int[(a + b/x^2)^(3/2)*x^2,x]","-b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b}}{x \sqrt{a+\frac{b}{x^2}}}\right)+\frac{1}{3} x^3 \left(a+\frac{b}{x^2}\right)^{3/2}+b x \sqrt{a+\frac{b}{x^2}}","-b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b}}{x \sqrt{a+\frac{b}{x^2}}}\right)+\frac{1}{3} x^3 \left(a+\frac{b}{x^2}\right)^{3/2}+b x \sqrt{a+\frac{b}{x^2}}",1,"b*Sqrt[a + b/x^2]*x + ((a + b/x^2)^(3/2)*x^3)/3 - b^(3/2)*ArcTanh[Sqrt[b]/(Sqrt[a + b/x^2]*x)]","A",5,4,15,0.2667,1,"{335, 277, 217, 206}"
1901,1,63,0,0.030937,"\int \left(a+\frac{b}{x^2}\right)^{3/2} x \, dx","Int[(a + b/x^2)^(3/2)*x,x]","\frac{1}{2} x^2 \left(a+\frac{b}{x^2}\right)^{3/2}-\frac{3}{2} b \sqrt{a+\frac{b}{x^2}}+\frac{3}{2} \sqrt{a} b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^2}}}{\sqrt{a}}\right)","\frac{1}{2} x^2 \left(a+\frac{b}{x^2}\right)^{3/2}-\frac{3}{2} b \sqrt{a+\frac{b}{x^2}}+\frac{3}{2} \sqrt{a} b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^2}}}{\sqrt{a}}\right)",1,"(-3*b*Sqrt[a + b/x^2])/2 + ((a + b/x^2)^(3/2)*x^2)/2 + (3*Sqrt[a]*b*ArcTanh[Sqrt[a + b/x^2]/Sqrt[a]])/2","A",5,5,13,0.3846,1,"{266, 47, 50, 63, 208}"
1902,1,64,0,0.0263427,"\int \left(a+\frac{b}{x^2}\right)^{3/2} \, dx","Int[(a + b/x^2)^(3/2),x]","x \left(a+\frac{b}{x^2}\right)^{3/2}-\frac{3 b \sqrt{a+\frac{b}{x^2}}}{2 x}-\frac{3}{2} a \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b}}{x \sqrt{a+\frac{b}{x^2}}}\right)","x \left(a+\frac{b}{x^2}\right)^{3/2}-\frac{3 b \sqrt{a+\frac{b}{x^2}}}{2 x}-\frac{3}{2} a \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b}}{x \sqrt{a+\frac{b}{x^2}}}\right)",1,"(-3*b*Sqrt[a + b/x^2])/(2*x) + (a + b/x^2)^(3/2)*x - (3*a*Sqrt[b]*ArcTanh[Sqrt[b]/(Sqrt[a + b/x^2]*x)])/2","A",5,5,11,0.4545,1,"{242, 277, 195, 217, 206}"
1903,1,54,0,0.0302899,"\int \frac{\left(a+\frac{b}{x^2}\right)^{3/2}}{x} \, dx","Int[(a + b/x^2)^(3/2)/x,x]","a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^2}}}{\sqrt{a}}\right)-a \sqrt{a+\frac{b}{x^2}}-\frac{1}{3} \left(a+\frac{b}{x^2}\right)^{3/2}","a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^2}}}{\sqrt{a}}\right)-a \sqrt{a+\frac{b}{x^2}}-\frac{1}{3} \left(a+\frac{b}{x^2}\right)^{3/2}",1,"-(a*Sqrt[a + b/x^2]) - (a + b/x^2)^(3/2)/3 + a^(3/2)*ArcTanh[Sqrt[a + b/x^2]/Sqrt[a]]","A",5,4,15,0.2667,1,"{266, 50, 63, 208}"
1904,1,71,0,0.0277239,"\int \frac{\left(a+\frac{b}{x^2}\right)^{3/2}}{x^2} \, dx","Int[(a + b/x^2)^(3/2)/x^2,x]","-\frac{3 a^2 \tanh ^{-1}\left(\frac{\sqrt{b}}{x \sqrt{a+\frac{b}{x^2}}}\right)}{8 \sqrt{b}}-\frac{3 a \sqrt{a+\frac{b}{x^2}}}{8 x}-\frac{\left(a+\frac{b}{x^2}\right)^{3/2}}{4 x}","-\frac{3 a^2 \tanh ^{-1}\left(\frac{\sqrt{b}}{x \sqrt{a+\frac{b}{x^2}}}\right)}{8 \sqrt{b}}-\frac{3 a \sqrt{a+\frac{b}{x^2}}}{8 x}-\frac{\left(a+\frac{b}{x^2}\right)^{3/2}}{4 x}",1,"(-3*a*Sqrt[a + b/x^2])/(8*x) - (a + b/x^2)^(3/2)/(4*x) - (3*a^2*ArcTanh[Sqrt[b]/(Sqrt[a + b/x^2]*x)])/(8*Sqrt[b])","A",5,4,15,0.2667,1,"{335, 195, 217, 206}"
1905,1,18,0,0.0060208,"\int \frac{\left(a+\frac{b}{x^2}\right)^{3/2}}{x^3} \, dx","Int[(a + b/x^2)^(3/2)/x^3,x]","-\frac{\left(a+\frac{b}{x^2}\right)^{5/2}}{5 b}","-\frac{\left(a+\frac{b}{x^2}\right)^{5/2}}{5 b}",1,"-(a + b/x^2)^(5/2)/(5*b)","A",1,1,15,0.06667,1,"{261}"
1906,1,95,0,0.045752,"\int \frac{\left(a+\frac{b}{x^2}\right)^{3/2}}{x^4} \, dx","Int[(a + b/x^2)^(3/2)/x^4,x]","\frac{a^3 \tanh ^{-1}\left(\frac{\sqrt{b}}{x \sqrt{a+\frac{b}{x^2}}}\right)}{16 b^{3/2}}-\frac{a^2 \sqrt{a+\frac{b}{x^2}}}{16 b x}-\frac{a \sqrt{a+\frac{b}{x^2}}}{8 x^3}-\frac{\left(a+\frac{b}{x^2}\right)^{3/2}}{6 x^3}","\frac{a^3 \tanh ^{-1}\left(\frac{\sqrt{b}}{x \sqrt{a+\frac{b}{x^2}}}\right)}{16 b^{3/2}}-\frac{a^2 \sqrt{a+\frac{b}{x^2}}}{16 b x}-\frac{a \sqrt{a+\frac{b}{x^2}}}{8 x^3}-\frac{\left(a+\frac{b}{x^2}\right)^{3/2}}{6 x^3}",1,"-(a*Sqrt[a + b/x^2])/(8*x^3) - (a + b/x^2)^(3/2)/(6*x^3) - (a^2*Sqrt[a + b/x^2])/(16*b*x) + (a^3*ArcTanh[Sqrt[b]/(Sqrt[a + b/x^2]*x)])/(16*b^(3/2))","A",6,5,15,0.3333,1,"{335, 279, 321, 217, 206}"
1907,1,86,0,0.0421809,"\int \left(a+\frac{b}{x^2}\right)^{5/2} x^3 \, dx","Int[(a + b/x^2)^(5/2)*x^3,x]","-\frac{15}{8} b^2 \sqrt{a+\frac{b}{x^2}}+\frac{15}{8} \sqrt{a} b^2 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^2}}}{\sqrt{a}}\right)+\frac{1}{4} x^4 \left(a+\frac{b}{x^2}\right)^{5/2}+\frac{5}{8} b x^2 \left(a+\frac{b}{x^2}\right)^{3/2}","-\frac{15}{8} b^2 \sqrt{a+\frac{b}{x^2}}+\frac{15}{8} \sqrt{a} b^2 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^2}}}{\sqrt{a}}\right)+\frac{1}{4} x^4 \left(a+\frac{b}{x^2}\right)^{5/2}+\frac{5}{8} b x^2 \left(a+\frac{b}{x^2}\right)^{3/2}",1,"(-15*b^2*Sqrt[a + b/x^2])/8 + (5*b*(a + b/x^2)^(3/2)*x^2)/8 + ((a + b/x^2)^(5/2)*x^4)/4 + (15*Sqrt[a]*b^2*ArcTanh[Sqrt[a + b/x^2]/Sqrt[a]])/8","A",6,5,15,0.3333,1,"{266, 47, 50, 63, 208}"
1908,1,88,0,0.0431205,"\int \left(a+\frac{b}{x^2}\right)^{5/2} x^2 \, dx","Int[(a + b/x^2)^(5/2)*x^2,x]","-\frac{5 b^2 \sqrt{a+\frac{b}{x^2}}}{2 x}-\frac{5}{2} a b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b}}{x \sqrt{a+\frac{b}{x^2}}}\right)+\frac{1}{3} x^3 \left(a+\frac{b}{x^2}\right)^{5/2}+\frac{5}{3} b x \left(a+\frac{b}{x^2}\right)^{3/2}","-\frac{5 b^2 \sqrt{a+\frac{b}{x^2}}}{2 x}-\frac{5}{2} a b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b}}{x \sqrt{a+\frac{b}{x^2}}}\right)+\frac{1}{3} x^3 \left(a+\frac{b}{x^2}\right)^{5/2}+\frac{5}{3} b x \left(a+\frac{b}{x^2}\right)^{3/2}",1,"(-5*b^2*Sqrt[a + b/x^2])/(2*x) + (5*b*(a + b/x^2)^(3/2)*x)/3 + ((a + b/x^2)^(5/2)*x^3)/3 - (5*a*b^(3/2)*ArcTanh[Sqrt[b]/(Sqrt[a + b/x^2]*x)])/2","A",6,5,15,0.3333,1,"{335, 277, 195, 217, 206}"
1909,1,80,0,0.0401554,"\int \left(a+\frac{b}{x^2}\right)^{5/2} x \, dx","Int[(a + b/x^2)^(5/2)*x,x]","\frac{5}{2} a^{3/2} b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^2}}}{\sqrt{a}}\right)+\frac{1}{2} x^2 \left(a+\frac{b}{x^2}\right)^{5/2}-\frac{5}{6} b \left(a+\frac{b}{x^2}\right)^{3/2}-\frac{5}{2} a b \sqrt{a+\frac{b}{x^2}}","\frac{5}{2} a^{3/2} b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^2}}}{\sqrt{a}}\right)+\frac{1}{2} x^2 \left(a+\frac{b}{x^2}\right)^{5/2}-\frac{5}{6} b \left(a+\frac{b}{x^2}\right)^{3/2}-\frac{5}{2} a b \sqrt{a+\frac{b}{x^2}}",1,"(-5*a*b*Sqrt[a + b/x^2])/2 - (5*b*(a + b/x^2)^(3/2))/6 + ((a + b/x^2)^(5/2)*x^2)/2 + (5*a^(3/2)*b*ArcTanh[Sqrt[a + b/x^2]/Sqrt[a]])/2","A",6,5,13,0.3846,1,"{266, 47, 50, 63, 208}"
1910,1,86,0,0.0363724,"\int \left(a+\frac{b}{x^2}\right)^{5/2} \, dx","Int[(a + b/x^2)^(5/2),x]","-\frac{15}{8} a^2 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b}}{x \sqrt{a+\frac{b}{x^2}}}\right)+x \left(a+\frac{b}{x^2}\right)^{5/2}-\frac{5 b \left(a+\frac{b}{x^2}\right)^{3/2}}{4 x}-\frac{15 a b \sqrt{a+\frac{b}{x^2}}}{8 x}","-\frac{15}{8} a^2 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b}}{x \sqrt{a+\frac{b}{x^2}}}\right)+x \left(a+\frac{b}{x^2}\right)^{5/2}-\frac{5 b \left(a+\frac{b}{x^2}\right)^{3/2}}{4 x}-\frac{15 a b \sqrt{a+\frac{b}{x^2}}}{8 x}",1,"(-15*a*b*Sqrt[a + b/x^2])/(8*x) - (5*b*(a + b/x^2)^(3/2))/(4*x) + (a + b/x^2)^(5/2)*x - (15*a^2*Sqrt[b]*ArcTanh[Sqrt[b]/(Sqrt[a + b/x^2]*x)])/8","A",6,5,11,0.4545,1,"{242, 277, 195, 217, 206}"
1911,1,72,0,0.0394314,"\int \frac{\left(a+\frac{b}{x^2}\right)^{5/2}}{x} \, dx","Int[(a + b/x^2)^(5/2)/x,x]","-a^2 \sqrt{a+\frac{b}{x^2}}+a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^2}}}{\sqrt{a}}\right)-\frac{1}{3} a \left(a+\frac{b}{x^2}\right)^{3/2}-\frac{1}{5} \left(a+\frac{b}{x^2}\right)^{5/2}","-a^2 \sqrt{a+\frac{b}{x^2}}+a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^2}}}{\sqrt{a}}\right)-\frac{1}{3} a \left(a+\frac{b}{x^2}\right)^{3/2}-\frac{1}{5} \left(a+\frac{b}{x^2}\right)^{5/2}",1,"-(a^2*Sqrt[a + b/x^2]) - (a*(a + b/x^2)^(3/2))/3 - (a + b/x^2)^(5/2)/5 + a^(5/2)*ArcTanh[Sqrt[a + b/x^2]/Sqrt[a]]","A",6,4,15,0.2667,1,"{266, 50, 63, 208}"
1912,1,92,0,0.0373123,"\int \frac{\left(a+\frac{b}{x^2}\right)^{5/2}}{x^2} \, dx","Int[(a + b/x^2)^(5/2)/x^2,x]","-\frac{5 a^2 \sqrt{a+\frac{b}{x^2}}}{16 x}-\frac{5 a^3 \tanh ^{-1}\left(\frac{\sqrt{b}}{x \sqrt{a+\frac{b}{x^2}}}\right)}{16 \sqrt{b}}-\frac{5 a \left(a+\frac{b}{x^2}\right)^{3/2}}{24 x}-\frac{\left(a+\frac{b}{x^2}\right)^{5/2}}{6 x}","-\frac{5 a^2 \sqrt{a+\frac{b}{x^2}}}{16 x}-\frac{5 a^3 \tanh ^{-1}\left(\frac{\sqrt{b}}{x \sqrt{a+\frac{b}{x^2}}}\right)}{16 \sqrt{b}}-\frac{5 a \left(a+\frac{b}{x^2}\right)^{3/2}}{24 x}-\frac{\left(a+\frac{b}{x^2}\right)^{5/2}}{6 x}",1,"(-5*a^2*Sqrt[a + b/x^2])/(16*x) - (5*a*(a + b/x^2)^(3/2))/(24*x) - (a + b/x^2)^(5/2)/(6*x) - (5*a^3*ArcTanh[Sqrt[b]/(Sqrt[a + b/x^2]*x)])/(16*Sqrt[b])","A",6,4,15,0.2667,1,"{335, 195, 217, 206}"
1913,1,18,0,0.0059163,"\int \frac{\left(a+\frac{b}{x^2}\right)^{5/2}}{x^3} \, dx","Int[(a + b/x^2)^(5/2)/x^3,x]","-\frac{\left(a+\frac{b}{x^2}\right)^{7/2}}{7 b}","-\frac{\left(a+\frac{b}{x^2}\right)^{7/2}}{7 b}",1,"-(a + b/x^2)^(7/2)/(7*b)","A",1,1,15,0.06667,1,"{261}"
1914,1,116,0,0.0617103,"\int \frac{\left(a+\frac{b}{x^2}\right)^{5/2}}{x^4} \, dx","Int[(a + b/x^2)^(5/2)/x^4,x]","\frac{5 a^4 \tanh ^{-1}\left(\frac{\sqrt{b}}{x \sqrt{a+\frac{b}{x^2}}}\right)}{128 b^{3/2}}-\frac{5 a^3 \sqrt{a+\frac{b}{x^2}}}{128 b x}-\frac{5 a^2 \sqrt{a+\frac{b}{x^2}}}{64 x^3}-\frac{5 a \left(a+\frac{b}{x^2}\right)^{3/2}}{48 x^3}-\frac{\left(a+\frac{b}{x^2}\right)^{5/2}}{8 x^3}","\frac{5 a^4 \tanh ^{-1}\left(\frac{\sqrt{b}}{x \sqrt{a+\frac{b}{x^2}}}\right)}{128 b^{3/2}}-\frac{5 a^3 \sqrt{a+\frac{b}{x^2}}}{128 b x}-\frac{5 a^2 \sqrt{a+\frac{b}{x^2}}}{64 x^3}-\frac{5 a \left(a+\frac{b}{x^2}\right)^{3/2}}{48 x^3}-\frac{\left(a+\frac{b}{x^2}\right)^{5/2}}{8 x^3}",1,"(-5*a^2*Sqrt[a + b/x^2])/(64*x^3) - (5*a*(a + b/x^2)^(3/2))/(48*x^3) - (a + b/x^2)^(5/2)/(8*x^3) - (5*a^3*Sqrt[a + b/x^2])/(128*b*x) + (5*a^4*ArcTanh[Sqrt[b]/(Sqrt[a + b/x^2]*x)])/(128*b^(3/2))","A",7,5,15,0.3333,1,"{335, 279, 321, 217, 206}"
1915,1,74,0,0.0366002,"\int \frac{x^3}{\sqrt{a+\frac{b}{x^2}}} \, dx","Int[x^3/Sqrt[a + b/x^2],x]","\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^2}}}{\sqrt{a}}\right)}{8 a^{5/2}}-\frac{3 b x^2 \sqrt{a+\frac{b}{x^2}}}{8 a^2}+\frac{x^4 \sqrt{a+\frac{b}{x^2}}}{4 a}","\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^2}}}{\sqrt{a}}\right)}{8 a^{5/2}}-\frac{3 b x^2 \sqrt{a+\frac{b}{x^2}}}{8 a^2}+\frac{x^4 \sqrt{a+\frac{b}{x^2}}}{4 a}",1,"(-3*b*Sqrt[a + b/x^2]*x^2)/(8*a^2) + (Sqrt[a + b/x^2]*x^4)/(4*a) + (3*b^2*ArcTanh[Sqrt[a + b/x^2]/Sqrt[a]])/(8*a^(5/2))","A",5,4,15,0.2667,1,"{266, 51, 63, 208}"
1916,1,50,0,0.0233808,"\int \frac{x}{\sqrt{a+\frac{b}{x^2}}} \, dx","Int[x/Sqrt[a + b/x^2],x]","\frac{x^2 \sqrt{a+\frac{b}{x^2}}}{2 a}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^2}}}{\sqrt{a}}\right)}{2 a^{3/2}}","\frac{x^2 \sqrt{a+\frac{b}{x^2}}}{2 a}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^2}}}{\sqrt{a}}\right)}{2 a^{3/2}}",1,"(Sqrt[a + b/x^2]*x^2)/(2*a) - (b*ArcTanh[Sqrt[a + b/x^2]/Sqrt[a]])/(2*a^(3/2))","A",4,4,13,0.3077,1,"{266, 51, 63, 208}"
1917,1,24,0,0.0170164,"\int \frac{1}{\sqrt{a+\frac{b}{x^2}} x} \, dx","Int[1/(Sqrt[a + b/x^2]*x),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^2}}}{\sqrt{a}}\right)}{\sqrt{a}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^2}}}{\sqrt{a}}\right)}{\sqrt{a}}",1,"ArcTanh[Sqrt[a + b/x^2]/Sqrt[a]]/Sqrt[a]","A",3,3,15,0.2000,1,"{266, 63, 208}"
1918,1,16,0,0.0056214,"\int \frac{1}{\sqrt{a+\frac{b}{x^2}} x^3} \, dx","Int[1/(Sqrt[a + b/x^2]*x^3),x]","-\frac{\sqrt{a+\frac{b}{x^2}}}{b}","-\frac{\sqrt{a+\frac{b}{x^2}}}{b}",1,"-(Sqrt[a + b/x^2]/b)","A",1,1,15,0.06667,1,"{261}"
1919,1,35,0,0.0199261,"\int \frac{1}{\sqrt{a+\frac{b}{x^2}} x^5} \, dx","Int[1/(Sqrt[a + b/x^2]*x^5),x]","\frac{a \sqrt{a+\frac{b}{x^2}}}{b^2}-\frac{\left(a+\frac{b}{x^2}\right)^{3/2}}{3 b^2}","\frac{a \sqrt{a+\frac{b}{x^2}}}{b^2}-\frac{\left(a+\frac{b}{x^2}\right)^{3/2}}{3 b^2}",1,"(a*Sqrt[a + b/x^2])/b^2 - (a + b/x^2)^(3/2)/(3*b^2)","A",3,2,15,0.1333,1,"{266, 43}"
1920,1,57,0,0.0289804,"\int \frac{1}{\sqrt{a+\frac{b}{x^2}} x^7} \, dx","Int[1/(Sqrt[a + b/x^2]*x^7),x]","-\frac{a^2 \sqrt{a+\frac{b}{x^2}}}{b^3}-\frac{\left(a+\frac{b}{x^2}\right)^{5/2}}{5 b^3}+\frac{2 a \left(a+\frac{b}{x^2}\right)^{3/2}}{3 b^3}","-\frac{a^2 \sqrt{a+\frac{b}{x^2}}}{b^3}-\frac{\left(a+\frac{b}{x^2}\right)^{5/2}}{5 b^3}+\frac{2 a \left(a+\frac{b}{x^2}\right)^{3/2}}{3 b^3}",1,"-((a^2*Sqrt[a + b/x^2])/b^3) + (2*a*(a + b/x^2)^(3/2))/(3*b^3) - (a + b/x^2)^(5/2)/(5*b^3)","A",3,2,15,0.1333,1,"{266, 43}"
1921,1,75,0,0.0392734,"\int \frac{1}{\sqrt{a+\frac{b}{x^2}} x^9} \, dx","Int[1/(Sqrt[a + b/x^2]*x^9),x]","-\frac{a^2 \left(a+\frac{b}{x^2}\right)^{3/2}}{b^4}+\frac{a^3 \sqrt{a+\frac{b}{x^2}}}{b^4}-\frac{\left(a+\frac{b}{x^2}\right)^{7/2}}{7 b^4}+\frac{3 a \left(a+\frac{b}{x^2}\right)^{5/2}}{5 b^4}","-\frac{a^2 \left(a+\frac{b}{x^2}\right)^{3/2}}{b^4}+\frac{a^3 \sqrt{a+\frac{b}{x^2}}}{b^4}-\frac{\left(a+\frac{b}{x^2}\right)^{7/2}}{7 b^4}+\frac{3 a \left(a+\frac{b}{x^2}\right)^{5/2}}{5 b^4}",1,"(a^3*Sqrt[a + b/x^2])/b^4 - (a^2*(a + b/x^2)^(3/2))/b^4 + (3*a*(a + b/x^2)^(5/2))/(5*b^4) - (a + b/x^2)^(7/2)/(7*b^4)","A",3,2,15,0.1333,1,"{266, 43}"
1922,1,66,0,0.0189321,"\int \frac{x^4}{\sqrt{a+\frac{b}{x^2}}} \, dx","Int[x^4/Sqrt[a + b/x^2],x]","\frac{8 b^2 x \sqrt{a+\frac{b}{x^2}}}{15 a^3}-\frac{4 b x^3 \sqrt{a+\frac{b}{x^2}}}{15 a^2}+\frac{x^5 \sqrt{a+\frac{b}{x^2}}}{5 a}","\frac{8 b^2 x \sqrt{a+\frac{b}{x^2}}}{15 a^3}-\frac{4 b x^3 \sqrt{a+\frac{b}{x^2}}}{15 a^2}+\frac{x^5 \sqrt{a+\frac{b}{x^2}}}{5 a}",1,"(8*b^2*Sqrt[a + b/x^2]*x)/(15*a^3) - (4*b*Sqrt[a + b/x^2]*x^3)/(15*a^2) + (Sqrt[a + b/x^2]*x^5)/(5*a)","A",3,2,15,0.1333,1,"{271, 191}"
1923,1,42,0,0.0093987,"\int \frac{x^2}{\sqrt{a+\frac{b}{x^2}}} \, dx","Int[x^2/Sqrt[a + b/x^2],x]","\frac{x^3 \sqrt{a+\frac{b}{x^2}}}{3 a}-\frac{2 b x \sqrt{a+\frac{b}{x^2}}}{3 a^2}","\frac{x^3 \sqrt{a+\frac{b}{x^2}}}{3 a}-\frac{2 b x \sqrt{a+\frac{b}{x^2}}}{3 a^2}",1,"(-2*b*Sqrt[a + b/x^2]*x)/(3*a^2) + (Sqrt[a + b/x^2]*x^3)/(3*a)","A",2,2,15,0.1333,1,"{271, 191}"
1924,1,16,0,0.0023042,"\int \frac{1}{\sqrt{a+\frac{b}{x^2}}} \, dx","Int[1/Sqrt[a + b/x^2],x]","\frac{x \sqrt{a+\frac{b}{x^2}}}{a}","\frac{x \sqrt{a+\frac{b}{x^2}}}{a}",1,"(Sqrt[a + b/x^2]*x)/a","A",1,1,11,0.09091,1,"{191}"
1925,1,28,0,0.0135937,"\int \frac{1}{\sqrt{a+\frac{b}{x^2}} x^2} \, dx","Int[1/(Sqrt[a + b/x^2]*x^2),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{b}}{x \sqrt{a+\frac{b}{x^2}}}\right)}{\sqrt{b}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{b}}{x \sqrt{a+\frac{b}{x^2}}}\right)}{\sqrt{b}}",1,"-(ArcTanh[Sqrt[b]/(Sqrt[a + b/x^2]*x)]/Sqrt[b])","A",3,3,15,0.2000,1,"{335, 217, 206}"
1926,1,53,0,0.0231338,"\int \frac{1}{\sqrt{a+\frac{b}{x^2}} x^4} \, dx","Int[1/(Sqrt[a + b/x^2]*x^4),x]","\frac{a \tanh ^{-1}\left(\frac{\sqrt{b}}{x \sqrt{a+\frac{b}{x^2}}}\right)}{2 b^{3/2}}-\frac{\sqrt{a+\frac{b}{x^2}}}{2 b x}","\frac{a \tanh ^{-1}\left(\frac{\sqrt{b}}{x \sqrt{a+\frac{b}{x^2}}}\right)}{2 b^{3/2}}-\frac{\sqrt{a+\frac{b}{x^2}}}{2 b x}",1,"-Sqrt[a + b/x^2]/(2*b*x) + (a*ArcTanh[Sqrt[b]/(Sqrt[a + b/x^2]*x)])/(2*b^(3/2))","A",4,4,15,0.2667,1,"{335, 321, 217, 206}"
1927,1,27,0,0.0180662,"\int \frac{1}{\sqrt{-a+\frac{b}{x^2}} x} \, dx","Int[1/(Sqrt[-a + b/x^2]*x),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{\frac{b}{x^2}-a}}{\sqrt{a}}\right)}{\sqrt{a}}","-\frac{\tan ^{-1}\left(\frac{\sqrt{\frac{b}{x^2}-a}}{\sqrt{a}}\right)}{\sqrt{a}}",1,"-(ArcTan[Sqrt[-a + b/x^2]/Sqrt[a]]/Sqrt[a])","A",3,3,17,0.1765,1,"{266, 63, 205}"
1928,1,20,0,0.0075717,"\int \frac{1}{\sqrt{2+\frac{b}{x^2}} x^2} \, dx","Int[1/(Sqrt[2 + b/x^2]*x^2),x]","-\frac{\text{csch}^{-1}\left(\frac{\sqrt{2} x}{\sqrt{b}}\right)}{\sqrt{b}}","-\frac{\text{csch}^{-1}\left(\frac{\sqrt{2} x}{\sqrt{b}}\right)}{\sqrt{b}}",1,"-(ArcCsch[(Sqrt[2]*x)/Sqrt[b]]/Sqrt[b])","A",2,2,15,0.1333,1,"{335, 215}"
1929,1,20,0,0.0079047,"\int \frac{1}{\sqrt{2-\frac{b}{x^2}} x^2} \, dx","Int[1/(Sqrt[2 - b/x^2]*x^2),x]","-\frac{\csc ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{b}}\right)}{\sqrt{b}}","-\frac{\csc ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{b}}\right)}{\sqrt{b}}",1,"-(ArcCsc[(Sqrt[2]*x)/Sqrt[b]]/Sqrt[b])","A",2,2,16,0.1250,1,"{335, 216}"
1930,1,93,0,0.0454288,"\int \frac{x^3}{\left(a+\frac{b}{x^2}\right)^{3/2}} \, dx","Int[x^3/(a + b/x^2)^(3/2),x]","\frac{15 b^2 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^2}}}{\sqrt{a}}\right)}{8 a^{7/2}}+\frac{5 x^4 \sqrt{a+\frac{b}{x^2}}}{4 a^2}-\frac{15 b x^2 \sqrt{a+\frac{b}{x^2}}}{8 a^3}-\frac{x^4}{a \sqrt{a+\frac{b}{x^2}}}","-\frac{15 b^2}{8 a^3 \sqrt{a+\frac{b}{x^2}}}+\frac{15 b^2 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^2}}}{\sqrt{a}}\right)}{8 a^{7/2}}-\frac{5 b x^2}{8 a^2 \sqrt{a+\frac{b}{x^2}}}+\frac{x^4}{4 a \sqrt{a+\frac{b}{x^2}}}",1,"(-15*b*Sqrt[a + b/x^2]*x^2)/(8*a^3) - x^4/(a*Sqrt[a + b/x^2]) + (5*Sqrt[a + b/x^2]*x^4)/(4*a^2) + (15*b^2*ArcTanh[Sqrt[a + b/x^2]/Sqrt[a]])/(8*a^(7/2))","A",6,4,15,0.2667,1,"{266, 51, 63, 208}"
1931,1,69,0,0.0330882,"\int \frac{x}{\left(a+\frac{b}{x^2}\right)^{3/2}} \, dx","Int[x/(a + b/x^2)^(3/2),x]","\frac{3 x^2 \sqrt{a+\frac{b}{x^2}}}{2 a^2}-\frac{3 b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^2}}}{\sqrt{a}}\right)}{2 a^{5/2}}-\frac{x^2}{a \sqrt{a+\frac{b}{x^2}}}","\frac{3 b}{2 a^2 \sqrt{a+\frac{b}{x^2}}}-\frac{3 b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^2}}}{\sqrt{a}}\right)}{2 a^{5/2}}+\frac{x^2}{2 a \sqrt{a+\frac{b}{x^2}}}",1,"-(x^2/(a*Sqrt[a + b/x^2])) + (3*Sqrt[a + b/x^2]*x^2)/(2*a^2) - (3*b*ArcTanh[Sqrt[a + b/x^2]/Sqrt[a]])/(2*a^(5/2))","A",5,4,13,0.3077,1,"{266, 51, 63, 208}"
1932,1,41,0,0.0236517,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^{3/2} x} \, dx","Int[1/((a + b/x^2)^(3/2)*x),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^2}}}{\sqrt{a}}\right)}{a^{3/2}}-\frac{1}{a \sqrt{a+\frac{b}{x^2}}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^2}}}{\sqrt{a}}\right)}{a^{3/2}}-\frac{1}{a \sqrt{a+\frac{b}{x^2}}}",1,"-(1/(a*Sqrt[a + b/x^2])) + ArcTanh[Sqrt[a + b/x^2]/Sqrt[a]]/a^(3/2)","A",4,4,15,0.2667,1,"{266, 51, 63, 208}"
1933,1,15,0,0.0061414,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^{3/2} x^3} \, dx","Int[1/((a + b/x^2)^(3/2)*x^3),x]","\frac{1}{b \sqrt{a+\frac{b}{x^2}}}","\frac{1}{b \sqrt{a+\frac{b}{x^2}}}",1,"1/(b*Sqrt[a + b/x^2])","A",1,1,15,0.06667,1,"{261}"
1934,1,34,0,0.0217856,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^{3/2} x^5} \, dx","Int[1/((a + b/x^2)^(3/2)*x^5),x]","-\frac{a}{b^2 \sqrt{a+\frac{b}{x^2}}}-\frac{\sqrt{a+\frac{b}{x^2}}}{b^2}","-\frac{a}{b^2 \sqrt{a+\frac{b}{x^2}}}-\frac{\sqrt{a+\frac{b}{x^2}}}{b^2}",1,"-(a/(b^2*Sqrt[a + b/x^2])) - Sqrt[a + b/x^2]/b^2","A",3,2,15,0.1333,1,"{266, 43}"
1935,1,54,0,0.0301785,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^{3/2} x^7} \, dx","Int[1/((a + b/x^2)^(3/2)*x^7),x]","\frac{a^2}{b^3 \sqrt{a+\frac{b}{x^2}}}+\frac{2 a \sqrt{a+\frac{b}{x^2}}}{b^3}-\frac{\left(a+\frac{b}{x^2}\right)^{3/2}}{3 b^3}","\frac{a^2}{b^3 \sqrt{a+\frac{b}{x^2}}}+\frac{2 a \sqrt{a+\frac{b}{x^2}}}{b^3}-\frac{\left(a+\frac{b}{x^2}\right)^{3/2}}{3 b^3}",1,"a^2/(b^3*Sqrt[a + b/x^2]) + (2*a*Sqrt[a + b/x^2])/b^3 - (a + b/x^2)^(3/2)/(3*b^3)","A",3,2,15,0.1333,1,"{266, 43}"
1936,1,73,0,0.0383933,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^{3/2} x^9} \, dx","Int[1/((a + b/x^2)^(3/2)*x^9),x]","-\frac{a^3}{b^4 \sqrt{a+\frac{b}{x^2}}}-\frac{3 a^2 \sqrt{a+\frac{b}{x^2}}}{b^4}+\frac{a \left(a+\frac{b}{x^2}\right)^{3/2}}{b^4}-\frac{\left(a+\frac{b}{x^2}\right)^{5/2}}{5 b^4}","-\frac{a^3}{b^4 \sqrt{a+\frac{b}{x^2}}}-\frac{3 a^2 \sqrt{a+\frac{b}{x^2}}}{b^4}+\frac{a \left(a+\frac{b}{x^2}\right)^{3/2}}{b^4}-\frac{\left(a+\frac{b}{x^2}\right)^{5/2}}{5 b^4}",1,"-(a^3/(b^4*Sqrt[a + b/x^2])) - (3*a^2*Sqrt[a + b/x^2])/b^4 + (a*(a + b/x^2)^(3/2))/b^4 - (a + b/x^2)^(5/2)/(5*b^4)","A",3,2,15,0.1333,1,"{266, 43}"
1937,1,88,0,0.0268412,"\int \frac{x^4}{\left(a+\frac{b}{x^2}\right)^{3/2}} \, dx","Int[x^4/(a + b/x^2)^(3/2),x]","\frac{16 b^2 x \sqrt{a+\frac{b}{x^2}}}{5 a^4}-\frac{8 b^2 x}{5 a^3 \sqrt{a+\frac{b}{x^2}}}-\frac{2 b x^3}{5 a^2 \sqrt{a+\frac{b}{x^2}}}+\frac{x^5}{5 a \sqrt{a+\frac{b}{x^2}}}","\frac{16 b^2 x \sqrt{a+\frac{b}{x^2}}}{5 a^4}-\frac{8 b^2 x}{5 a^3 \sqrt{a+\frac{b}{x^2}}}-\frac{2 b x^3}{5 a^2 \sqrt{a+\frac{b}{x^2}}}+\frac{x^5}{5 a \sqrt{a+\frac{b}{x^2}}}",1,"(-8*b^2*x)/(5*a^3*Sqrt[a + b/x^2]) + (16*b^2*Sqrt[a + b/x^2]*x)/(5*a^4) - (2*b*x^3)/(5*a^2*Sqrt[a + b/x^2]) + x^5/(5*a*Sqrt[a + b/x^2])","A",4,3,15,0.2000,1,"{271, 192, 191}"
1938,1,62,0,0.0162914,"\int \frac{x^2}{\left(a+\frac{b}{x^2}\right)^{3/2}} \, dx","Int[x^2/(a + b/x^2)^(3/2),x]","-\frac{8 b x \sqrt{a+\frac{b}{x^2}}}{3 a^3}+\frac{4 b x}{3 a^2 \sqrt{a+\frac{b}{x^2}}}+\frac{x^3}{3 a \sqrt{a+\frac{b}{x^2}}}","-\frac{8 b x \sqrt{a+\frac{b}{x^2}}}{3 a^3}+\frac{4 b x}{3 a^2 \sqrt{a+\frac{b}{x^2}}}+\frac{x^3}{3 a \sqrt{a+\frac{b}{x^2}}}",1,"(4*b*x)/(3*a^2*Sqrt[a + b/x^2]) - (8*b*Sqrt[a + b/x^2]*x)/(3*a^3) + x^3/(3*a*Sqrt[a + b/x^2])","A",3,3,15,0.2000,1,"{271, 192, 191}"
1939,1,35,0,0.0058369,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^{3/2}} \, dx","Int[(a + b/x^2)^(-3/2),x]","\frac{2 x \sqrt{a+\frac{b}{x^2}}}{a^2}-\frac{x}{a \sqrt{a+\frac{b}{x^2}}}","\frac{2 x \sqrt{a+\frac{b}{x^2}}}{a^2}-\frac{x}{a \sqrt{a+\frac{b}{x^2}}}",1,"-(x/(a*Sqrt[a + b/x^2])) + (2*Sqrt[a + b/x^2]*x)/a^2","A",2,2,11,0.1818,1,"{192, 191}"
1940,1,19,0,0.0065681,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^{3/2} x^2} \, dx","Int[1/((a + b/x^2)^(3/2)*x^2),x]","-\frac{1}{a x \sqrt{a+\frac{b}{x^2}}}","-\frac{1}{a x \sqrt{a+\frac{b}{x^2}}}",1,"-(1/(a*Sqrt[a + b/x^2]*x))","A",1,1,15,0.06667,1,"{264}"
1941,1,47,0,0.0231834,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^{3/2} x^4} \, dx","Int[1/((a + b/x^2)^(3/2)*x^4),x]","\frac{1}{b x \sqrt{a+\frac{b}{x^2}}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{b}}{x \sqrt{a+\frac{b}{x^2}}}\right)}{b^{3/2}}","\frac{1}{b x \sqrt{a+\frac{b}{x^2}}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{b}}{x \sqrt{a+\frac{b}{x^2}}}\right)}{b^{3/2}}",1,"1/(b*Sqrt[a + b/x^2]*x) - ArcTanh[Sqrt[b]/(Sqrt[a + b/x^2]*x)]/b^(3/2)","A",4,4,15,0.2667,1,"{335, 288, 217, 206}"
1942,1,71,0,0.0339055,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^{3/2} x^6} \, dx","Int[1/((a + b/x^2)^(3/2)*x^6),x]","-\frac{3 \sqrt{a+\frac{b}{x^2}}}{2 b^2 x}+\frac{3 a \tanh ^{-1}\left(\frac{\sqrt{b}}{x \sqrt{a+\frac{b}{x^2}}}\right)}{2 b^{5/2}}+\frac{1}{b x^3 \sqrt{a+\frac{b}{x^2}}}","-\frac{3 \sqrt{a+\frac{b}{x^2}}}{2 b^2 x}+\frac{3 a \tanh ^{-1}\left(\frac{\sqrt{b}}{x \sqrt{a+\frac{b}{x^2}}}\right)}{2 b^{5/2}}+\frac{1}{b x^3 \sqrt{a+\frac{b}{x^2}}}",1,"1/(b*Sqrt[a + b/x^2]*x^3) - (3*Sqrt[a + b/x^2])/(2*b^2*x) + (3*a*ArcTanh[Sqrt[b]/(Sqrt[a + b/x^2]*x)])/(2*b^(5/2))","A",5,5,15,0.3333,1,"{335, 288, 321, 217, 206}"
1943,1,95,0,0.0477794,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^{3/2} x^8} \, dx","Int[1/((a + b/x^2)^(3/2)*x^8),x]","-\frac{15 a^2 \tanh ^{-1}\left(\frac{\sqrt{b}}{x \sqrt{a+\frac{b}{x^2}}}\right)}{8 b^{7/2}}+\frac{15 a \sqrt{a+\frac{b}{x^2}}}{8 b^3 x}-\frac{5 \sqrt{a+\frac{b}{x^2}}}{4 b^2 x^3}+\frac{1}{b x^5 \sqrt{a+\frac{b}{x^2}}}","-\frac{15 a^2 \tanh ^{-1}\left(\frac{\sqrt{b}}{x \sqrt{a+\frac{b}{x^2}}}\right)}{8 b^{7/2}}+\frac{15 a \sqrt{a+\frac{b}{x^2}}}{8 b^3 x}-\frac{5 \sqrt{a+\frac{b}{x^2}}}{4 b^2 x^3}+\frac{1}{b x^5 \sqrt{a+\frac{b}{x^2}}}",1,"1/(b*Sqrt[a + b/x^2]*x^5) - (5*Sqrt[a + b/x^2])/(4*b^2*x^3) + (15*a*Sqrt[a + b/x^2])/(8*b^3*x) - (15*a^2*ArcTanh[Sqrt[b]/(Sqrt[a + b/x^2]*x)])/(8*b^(7/2))","A",6,5,15,0.3333,1,"{335, 288, 321, 217, 206}"
1944,1,116,0,0.0594738,"\int \frac{x^3}{\left(a+\frac{b}{x^2}\right)^{5/2}} \, dx","Int[x^3/(a + b/x^2)^(5/2),x]","\frac{35 b^2 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^2}}}{\sqrt{a}}\right)}{8 a^{9/2}}+\frac{35 x^4 \sqrt{a+\frac{b}{x^2}}}{12 a^3}-\frac{7 x^4}{3 a^2 \sqrt{a+\frac{b}{x^2}}}-\frac{35 b x^2 \sqrt{a+\frac{b}{x^2}}}{8 a^4}-\frac{x^4}{3 a \left(a+\frac{b}{x^2}\right)^{3/2}}","-\frac{35 b^2}{8 a^4 \sqrt{a+\frac{b}{x^2}}}-\frac{35 b^2}{24 a^3 \left(a+\frac{b}{x^2}\right)^{3/2}}+\frac{35 b^2 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^2}}}{\sqrt{a}}\right)}{8 a^{9/2}}-\frac{7 b x^2}{8 a^2 \left(a+\frac{b}{x^2}\right)^{3/2}}+\frac{x^4}{4 a \left(a+\frac{b}{x^2}\right)^{3/2}}",1,"(-35*b*Sqrt[a + b/x^2]*x^2)/(8*a^4) - x^4/(3*a*(a + b/x^2)^(3/2)) - (7*x^4)/(3*a^2*Sqrt[a + b/x^2]) + (35*Sqrt[a + b/x^2]*x^4)/(12*a^3) + (35*b^2*ArcTanh[Sqrt[a + b/x^2]/Sqrt[a]])/(8*a^(9/2))","A",7,4,15,0.2667,1,"{266, 51, 63, 208}"
1945,1,92,0,0.0434574,"\int \frac{x}{\left(a+\frac{b}{x^2}\right)^{5/2}} \, dx","Int[x/(a + b/x^2)^(5/2),x]","\frac{5 x^2 \sqrt{a+\frac{b}{x^2}}}{2 a^3}-\frac{5 x^2}{3 a^2 \sqrt{a+\frac{b}{x^2}}}-\frac{5 b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^2}}}{\sqrt{a}}\right)}{2 a^{7/2}}-\frac{x^2}{3 a \left(a+\frac{b}{x^2}\right)^{3/2}}","\frac{5 b}{2 a^3 \sqrt{a+\frac{b}{x^2}}}+\frac{5 b}{6 a^2 \left(a+\frac{b}{x^2}\right)^{3/2}}-\frac{5 b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^2}}}{\sqrt{a}}\right)}{2 a^{7/2}}+\frac{x^2}{2 a \left(a+\frac{b}{x^2}\right)^{3/2}}",1,"-x^2/(3*a*(a + b/x^2)^(3/2)) - (5*x^2)/(3*a^2*Sqrt[a + b/x^2]) + (5*Sqrt[a + b/x^2]*x^2)/(2*a^3) - (5*b*ArcTanh[Sqrt[a + b/x^2]/Sqrt[a]])/(2*a^(7/2))","A",6,4,13,0.3077,1,"{266, 51, 63, 208}"
1946,1,59,0,0.0327098,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^{5/2} x} \, dx","Int[1/((a + b/x^2)^(5/2)*x),x]","-\frac{1}{a^2 \sqrt{a+\frac{b}{x^2}}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^2}}}{\sqrt{a}}\right)}{a^{5/2}}-\frac{1}{3 a \left(a+\frac{b}{x^2}\right)^{3/2}}","-\frac{1}{a^2 \sqrt{a+\frac{b}{x^2}}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^2}}}{\sqrt{a}}\right)}{a^{5/2}}-\frac{1}{3 a \left(a+\frac{b}{x^2}\right)^{3/2}}",1,"-1/(3*a*(a + b/x^2)^(3/2)) - 1/(a^2*Sqrt[a + b/x^2]) + ArcTanh[Sqrt[a + b/x^2]/Sqrt[a]]/a^(5/2)","A",5,4,15,0.2667,1,"{266, 51, 63, 208}"
1947,1,18,0,0.0061118,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^{5/2} x^3} \, dx","Int[1/((a + b/x^2)^(5/2)*x^3),x]","\frac{1}{3 b \left(a+\frac{b}{x^2}\right)^{3/2}}","\frac{1}{3 b \left(a+\frac{b}{x^2}\right)^{3/2}}",1,"1/(3*b*(a + b/x^2)^(3/2))","A",1,1,15,0.06667,1,"{261}"
1948,1,35,0,0.0206982,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^{5/2} x^5} \, dx","Int[1/((a + b/x^2)^(5/2)*x^5),x]","\frac{1}{b^2 \sqrt{a+\frac{b}{x^2}}}-\frac{a}{3 b^2 \left(a+\frac{b}{x^2}\right)^{3/2}}","\frac{1}{b^2 \sqrt{a+\frac{b}{x^2}}}-\frac{a}{3 b^2 \left(a+\frac{b}{x^2}\right)^{3/2}}",1,"-a/(3*b^2*(a + b/x^2)^(3/2)) + 1/(b^2*Sqrt[a + b/x^2])","A",3,2,15,0.1333,1,"{266, 43}"
1949,1,55,0,0.0293698,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^{5/2} x^7} \, dx","Int[1/((a + b/x^2)^(5/2)*x^7),x]","\frac{a^2}{3 b^3 \left(a+\frac{b}{x^2}\right)^{3/2}}-\frac{2 a}{b^3 \sqrt{a+\frac{b}{x^2}}}-\frac{\sqrt{a+\frac{b}{x^2}}}{b^3}","\frac{a^2}{3 b^3 \left(a+\frac{b}{x^2}\right)^{3/2}}-\frac{2 a}{b^3 \sqrt{a+\frac{b}{x^2}}}-\frac{\sqrt{a+\frac{b}{x^2}}}{b^3}",1,"a^2/(3*b^3*(a + b/x^2)^(3/2)) - (2*a)/(b^3*Sqrt[a + b/x^2]) - Sqrt[a + b/x^2]/b^3","A",3,2,15,0.1333,1,"{266, 43}"
1950,1,76,0,0.0404859,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^{5/2} x^9} \, dx","Int[1/((a + b/x^2)^(5/2)*x^9),x]","-\frac{a^3}{3 b^4 \left(a+\frac{b}{x^2}\right)^{3/2}}+\frac{3 a^2}{b^4 \sqrt{a+\frac{b}{x^2}}}+\frac{3 a \sqrt{a+\frac{b}{x^2}}}{b^4}-\frac{\left(a+\frac{b}{x^2}\right)^{3/2}}{3 b^4}","-\frac{a^3}{3 b^4 \left(a+\frac{b}{x^2}\right)^{3/2}}+\frac{3 a^2}{b^4 \sqrt{a+\frac{b}{x^2}}}+\frac{3 a \sqrt{a+\frac{b}{x^2}}}{b^4}-\frac{\left(a+\frac{b}{x^2}\right)^{3/2}}{3 b^4}",1,"-a^3/(3*b^4*(a + b/x^2)^(3/2)) + (3*a^2)/(b^4*Sqrt[a + b/x^2]) + (3*a*Sqrt[a + b/x^2])/b^4 - (a + b/x^2)^(3/2)/(3*b^4)","A",3,2,15,0.1333,1,"{266, 43}"
1951,1,82,0,0.0221335,"\int \frac{x^2}{\left(a+\frac{b}{x^2}\right)^{5/2}} \, dx","Int[x^2/(a + b/x^2)^(5/2),x]","-\frac{16 b x \sqrt{a+\frac{b}{x^2}}}{3 a^4}+\frac{8 b x}{3 a^3 \sqrt{a+\frac{b}{x^2}}}+\frac{2 b x}{3 a^2 \left(a+\frac{b}{x^2}\right)^{3/2}}+\frac{x^3}{3 a \left(a+\frac{b}{x^2}\right)^{3/2}}","-\frac{16 b x \sqrt{a+\frac{b}{x^2}}}{3 a^4}+\frac{8 b x}{3 a^3 \sqrt{a+\frac{b}{x^2}}}+\frac{2 b x}{3 a^2 \left(a+\frac{b}{x^2}\right)^{3/2}}+\frac{x^3}{3 a \left(a+\frac{b}{x^2}\right)^{3/2}}",1,"(2*b*x)/(3*a^2*(a + b/x^2)^(3/2)) + (8*b*x)/(3*a^3*Sqrt[a + b/x^2]) - (16*b*Sqrt[a + b/x^2]*x)/(3*a^4) + x^3/(3*a*(a + b/x^2)^(3/2))","A",4,3,15,0.2000,1,"{271, 192, 191}"
1952,1,58,0,0.0108795,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^{5/2}} \, dx","Int[(a + b/x^2)^(-5/2),x]","\frac{8 x \sqrt{a+\frac{b}{x^2}}}{3 a^3}-\frac{4 x}{3 a^2 \sqrt{a+\frac{b}{x^2}}}-\frac{x}{3 a \left(a+\frac{b}{x^2}\right)^{3/2}}","\frac{8 x \sqrt{a+\frac{b}{x^2}}}{3 a^3}-\frac{4 x}{3 a^2 \sqrt{a+\frac{b}{x^2}}}-\frac{x}{3 a \left(a+\frac{b}{x^2}\right)^{3/2}}",1,"-x/(3*a*(a + b/x^2)^(3/2)) - (4*x)/(3*a^2*Sqrt[a + b/x^2]) + (8*Sqrt[a + b/x^2]*x)/(3*a^3)","A",3,2,11,0.1818,1,"{192, 191}"
1953,1,42,0,0.0139506,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^{5/2} x^2} \, dx","Int[1/((a + b/x^2)^(5/2)*x^2),x]","-\frac{2 b}{3 a^2 x^3 \left(a+\frac{b}{x^2}\right)^{3/2}}-\frac{1}{a x \left(a+\frac{b}{x^2}\right)^{3/2}}","-\frac{2 b}{3 a^2 x^3 \left(a+\frac{b}{x^2}\right)^{3/2}}-\frac{1}{a x \left(a+\frac{b}{x^2}\right)^{3/2}}",1,"(-2*b)/(3*a^2*(a + b/x^2)^(3/2)*x^3) - 1/(a*(a + b/x^2)^(3/2)*x)","A",2,2,15,0.1333,1,"{271, 264}"
1954,1,21,0,0.0061545,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^{5/2} x^4} \, dx","Int[1/((a + b/x^2)^(5/2)*x^4),x]","-\frac{1}{3 a x^3 \left(a+\frac{b}{x^2}\right)^{3/2}}","-\frac{1}{3 a x^3 \left(a+\frac{b}{x^2}\right)^{3/2}}",1,"-1/(3*a*(a + b/x^2)^(3/2)*x^3)","A",1,1,15,0.06667,1,"{264}"
1955,1,68,0,0.0347532,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^{5/2} x^6} \, dx","Int[1/((a + b/x^2)^(5/2)*x^6),x]","\frac{1}{b^2 x \sqrt{a+\frac{b}{x^2}}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{b}}{x \sqrt{a+\frac{b}{x^2}}}\right)}{b^{5/2}}+\frac{1}{3 b x^3 \left(a+\frac{b}{x^2}\right)^{3/2}}","\frac{1}{b^2 x \sqrt{a+\frac{b}{x^2}}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{b}}{x \sqrt{a+\frac{b}{x^2}}}\right)}{b^{5/2}}+\frac{1}{3 b x^3 \left(a+\frac{b}{x^2}\right)^{3/2}}",1,"1/(3*b*(a + b/x^2)^(3/2)*x^3) + 1/(b^2*Sqrt[a + b/x^2]*x) - ArcTanh[Sqrt[b]/(Sqrt[a + b/x^2]*x)]/b^(5/2)","A",5,4,15,0.2667,1,"{335, 288, 217, 206}"
1956,1,95,0,0.0486969,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^{5/2} x^8} \, dx","Int[1/((a + b/x^2)^(5/2)*x^8),x]","-\frac{5 \sqrt{a+\frac{b}{x^2}}}{2 b^3 x}+\frac{5}{3 b^2 x^3 \sqrt{a+\frac{b}{x^2}}}+\frac{5 a \tanh ^{-1}\left(\frac{\sqrt{b}}{x \sqrt{a+\frac{b}{x^2}}}\right)}{2 b^{7/2}}+\frac{1}{3 b x^5 \left(a+\frac{b}{x^2}\right)^{3/2}}","-\frac{5 \sqrt{a+\frac{b}{x^2}}}{2 b^3 x}+\frac{5}{3 b^2 x^3 \sqrt{a+\frac{b}{x^2}}}+\frac{5 a \tanh ^{-1}\left(\frac{\sqrt{b}}{x \sqrt{a+\frac{b}{x^2}}}\right)}{2 b^{7/2}}+\frac{1}{3 b x^5 \left(a+\frac{b}{x^2}\right)^{3/2}}",1,"1/(3*b*(a + b/x^2)^(3/2)*x^5) + 5/(3*b^2*Sqrt[a + b/x^2]*x^3) - (5*Sqrt[a + b/x^2])/(2*b^3*x) + (5*a*ArcTanh[Sqrt[b]/(Sqrt[a + b/x^2]*x)])/(2*b^(7/2))","A",6,5,15,0.3333,1,"{335, 288, 321, 217, 206}"
1957,1,13,0,0.0031485,"\int \frac{\sqrt[3]{1+\frac{1}{x^2}}}{x^3} \, dx","Int[(1 + x^(-2))^(1/3)/x^3,x]","-\frac{3}{8} \left(\frac{1}{x^2}+1\right)^{4/3}","-\frac{3}{8} \left(\frac{1}{x^2}+1\right)^{4/3}",1,"(-3*(1 + x^(-2))^(4/3))/8","A",1,1,13,0.07692,1,"{261}"
1958,1,13,0,0.0035764,"\int \frac{\left(1+\frac{1}{x^2}\right)^{5/3}}{x^3} \, dx","Int[(1 + x^(-2))^(5/3)/x^3,x]","-\frac{3}{16} \left(\frac{1}{x^2}+1\right)^{8/3}","-\frac{3}{16} \left(\frac{1}{x^2}+1\right)^{8/3}",1,"(-3*(1 + x^(-2))^(8/3))/16","A",1,1,13,0.07692,1,"{261}"
1959,1,44,0,0.0223979,"\int \left(1+\frac{b}{x^2}\right)^{3/2} (c x)^m \, dx","Int[(1 + b/x^2)^(3/2)*(c*x)^m,x]","\frac{(c x)^{m+1} \, _2F_1\left(-\frac{3}{2},\frac{1}{2} (-m-1);\frac{1-m}{2};-\frac{b}{x^2}\right)}{c (m+1)}","\frac{(c x)^{m+1} \, _2F_1\left(-\frac{3}{2},\frac{1}{2} (-m-1);\frac{1-m}{2};-\frac{b}{x^2}\right)}{c (m+1)}",1,"((c*x)^(1 + m)*Hypergeometric2F1[-3/2, (-1 - m)/2, (1 - m)/2, -(b/x^2)])/(c*(1 + m))","A",2,2,17,0.1176,1,"{339, 364}"
1960,1,44,0,0.0170517,"\int \sqrt{1+\frac{b}{x^2}} (c x)^m \, dx","Int[Sqrt[1 + b/x^2]*(c*x)^m,x]","\frac{(c x)^{m+1} \, _2F_1\left(-\frac{1}{2},\frac{1}{2} (-m-1);\frac{1-m}{2};-\frac{b}{x^2}\right)}{c (m+1)}","\frac{(c x)^{m+1} \, _2F_1\left(-\frac{1}{2},\frac{1}{2} (-m-1);\frac{1-m}{2};-\frac{b}{x^2}\right)}{c (m+1)}",1,"((c*x)^(1 + m)*Hypergeometric2F1[-1/2, (-1 - m)/2, (1 - m)/2, -(b/x^2)])/(c*(1 + m))","A",2,2,17,0.1176,1,"{339, 364}"
1961,1,44,0,0.0173229,"\int \frac{(c x)^m}{\sqrt{1+\frac{b}{x^2}}} \, dx","Int[(c*x)^m/Sqrt[1 + b/x^2],x]","\frac{(c x)^{m+1} \, _2F_1\left(\frac{1}{2},\frac{1}{2} (-m-1);\frac{1-m}{2};-\frac{b}{x^2}\right)}{c (m+1)}","\frac{(c x)^{m+1} \, _2F_1\left(\frac{1}{2},\frac{1}{2} (-m-1);\frac{1-m}{2};-\frac{b}{x^2}\right)}{c (m+1)}",1,"((c*x)^(1 + m)*Hypergeometric2F1[1/2, (-1 - m)/2, (1 - m)/2, -(b/x^2)])/(c*(1 + m))","A",2,2,17,0.1176,1,"{339, 364}"
1962,1,44,0,0.017609,"\int \frac{(c x)^m}{\left(1+\frac{b}{x^2}\right)^{3/2}} \, dx","Int[(c*x)^m/(1 + b/x^2)^(3/2),x]","\frac{(c x)^{m+1} \, _2F_1\left(\frac{3}{2},\frac{1}{2} (-m-1);\frac{1-m}{2};-\frac{b}{x^2}\right)}{c (m+1)}","\frac{(c x)^{m+1} \, _2F_1\left(\frac{3}{2},\frac{1}{2} (-m-1);\frac{1-m}{2};-\frac{b}{x^2}\right)}{c (m+1)}",1,"((c*x)^(1 + m)*Hypergeometric2F1[3/2, (-1 - m)/2, (1 - m)/2, -(b/x^2)])/(c*(1 + m))","A",2,2,17,0.1176,1,"{339, 364}"
1963,1,44,0,0.0169594,"\int \left(1+\frac{b}{x^2}\right)^p (c x)^m \, dx","Int[(1 + b/x^2)^p*(c*x)^m,x]","\frac{(c x)^{m+1} \, _2F_1\left(\frac{1}{2} (-m-1),-p;\frac{1-m}{2};-\frac{b}{x^2}\right)}{c (m+1)}","\frac{(c x)^{m+1} \, _2F_1\left(\frac{1}{2} (-m-1),-p;\frac{1-m}{2};-\frac{b}{x^2}\right)}{c (m+1)}",1,"((c*x)^(1 + m)*Hypergeometric2F1[(-1 - m)/2, -p, (1 - m)/2, -(b/x^2)])/(c*(1 + m))","A",2,2,15,0.1333,1,"{339, 364}"
1964,1,70,0,0.03036,"\int \left(a+\frac{b}{x^2}\right)^p (c x)^m \, dx","Int[(a + b/x^2)^p*(c*x)^m,x]","\frac{(c x)^{m+1} \left(a+\frac{b}{x^2}\right)^p \left(\frac{b}{a x^2}+1\right)^{-p} \, _2F_1\left(\frac{1}{2} (-m-1),-p;\frac{1-m}{2};-\frac{b}{a x^2}\right)}{c (m+1)}","\frac{(c x)^{m+1} \left(a+\frac{b}{x^2}\right)^p \left(\frac{b}{a x^2}+1\right)^{-p} \, _2F_1\left(\frac{1}{2} (-m-1),-p;\frac{1-m}{2};-\frac{b}{a x^2}\right)}{c (m+1)}",1,"((a + b/x^2)^p*(c*x)^(1 + m)*Hypergeometric2F1[(-1 - m)/2, -p, (1 - m)/2, -(b/(a*x^2))])/(c*(1 + m)*(1 + b/(a*x^2))^p)","A",3,3,15,0.2000,1,"{339, 365, 364}"
1965,1,40,0,0.0260559,"\int \frac{x^5}{a+\frac{b}{x^3}} \, dx","Int[x^5/(a + b/x^3),x]","\frac{b^2 \log \left(a x^3+b\right)}{3 a^3}-\frac{b x^3}{3 a^2}+\frac{x^6}{6 a}","\frac{b^2 \log \left(a x^3+b\right)}{3 a^3}-\frac{b x^3}{3 a^2}+\frac{x^6}{6 a}",1,"-(b*x^3)/(3*a^2) + x^6/(6*a) + (b^2*Log[b + a*x^3])/(3*a^3)","A",4,3,13,0.2308,1,"{263, 266, 43}"
1966,1,136,0,0.0954198,"\int \frac{x^4}{a+\frac{b}{x^3}} \, dx","Int[x^4/(a + b/x^3),x]","\frac{b^{5/3} \log \left(a^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3}\right)}{6 a^{8/3}}-\frac{b^{5/3} \log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{3 a^{8/3}}-\frac{b^{5/3} \tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a} x}{\sqrt{3} \sqrt[3]{b}}\right)}{\sqrt{3} a^{8/3}}-\frac{b x^2}{2 a^2}+\frac{x^5}{5 a}","\frac{b^{5/3} \log \left(a^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3}\right)}{6 a^{8/3}}-\frac{b^{5/3} \log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{3 a^{8/3}}-\frac{b^{5/3} \tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a} x}{\sqrt{3} \sqrt[3]{b}}\right)}{\sqrt{3} a^{8/3}}-\frac{b x^2}{2 a^2}+\frac{x^5}{5 a}",1,"-(b*x^2)/(2*a^2) + x^5/(5*a) - (b^(5/3)*ArcTan[(b^(1/3) - 2*a^(1/3)*x)/(Sqrt[3]*b^(1/3))])/(Sqrt[3]*a^(8/3)) - (b^(5/3)*Log[b^(1/3) + a^(1/3)*x])/(3*a^(8/3)) + (b^(5/3)*Log[b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2])/(6*a^(8/3))","A",9,8,13,0.6154,1,"{263, 302, 292, 31, 634, 617, 204, 628}"
1967,1,132,0,0.0818292,"\int \frac{x^3}{a+\frac{b}{x^3}} \, dx","Int[x^3/(a + b/x^3),x]","-\frac{b^{4/3} \log \left(a^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3}\right)}{6 a^{7/3}}+\frac{b^{4/3} \log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{3 a^{7/3}}-\frac{b^{4/3} \tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a} x}{\sqrt{3} \sqrt[3]{b}}\right)}{\sqrt{3} a^{7/3}}-\frac{b x}{a^2}+\frac{x^4}{4 a}","-\frac{b^{4/3} \log \left(a^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3}\right)}{6 a^{7/3}}+\frac{b^{4/3} \log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{3 a^{7/3}}-\frac{b^{4/3} \tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a} x}{\sqrt{3} \sqrt[3]{b}}\right)}{\sqrt{3} a^{7/3}}-\frac{b x}{a^2}+\frac{x^4}{4 a}",1,"-((b*x)/a^2) + x^4/(4*a) - (b^(4/3)*ArcTan[(b^(1/3) - 2*a^(1/3)*x)/(Sqrt[3]*b^(1/3))])/(Sqrt[3]*a^(7/3)) + (b^(4/3)*Log[b^(1/3) + a^(1/3)*x])/(3*a^(7/3)) - (b^(4/3)*Log[b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2])/(6*a^(7/3))","A",9,8,13,0.6154,1,"{263, 302, 200, 31, 634, 617, 204, 628}"
1968,1,27,0,0.0205104,"\int \frac{x^2}{a+\frac{b}{x^3}} \, dx","Int[x^2/(a + b/x^3),x]","\frac{x^3}{3 a}-\frac{b \log \left(a x^3+b\right)}{3 a^2}","\frac{x^3}{3 a}-\frac{b \log \left(a x^3+b\right)}{3 a^2}",1,"x^3/(3*a) - (b*Log[b + a*x^3])/(3*a^2)","A",4,3,13,0.2308,1,"{263, 266, 43}"
1969,1,124,0,0.0663078,"\int \frac{x}{a+\frac{b}{x^3}} \, dx","Int[x/(a + b/x^3),x]","-\frac{b^{2/3} \log \left(a^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3}\right)}{6 a^{5/3}}+\frac{b^{2/3} \log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{3 a^{5/3}}+\frac{b^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a} x}{\sqrt{3} \sqrt[3]{b}}\right)}{\sqrt{3} a^{5/3}}+\frac{x^2}{2 a}","-\frac{b^{2/3} \log \left(a^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3}\right)}{6 a^{5/3}}+\frac{b^{2/3} \log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{3 a^{5/3}}+\frac{b^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a} x}{\sqrt{3} \sqrt[3]{b}}\right)}{\sqrt{3} a^{5/3}}+\frac{x^2}{2 a}",1,"x^2/(2*a) + (b^(2/3)*ArcTan[(b^(1/3) - 2*a^(1/3)*x)/(Sqrt[3]*b^(1/3))])/(Sqrt[3]*a^(5/3)) + (b^(2/3)*Log[b^(1/3) + a^(1/3)*x])/(3*a^(5/3)) - (b^(2/3)*Log[b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2])/(6*a^(5/3))","A",8,8,11,0.7273,1,"{263, 321, 292, 31, 634, 617, 204, 628}"
1970,1,119,0,0.0660836,"\int \frac{1}{a+\frac{b}{x^3}} \, dx","Int[(a + b/x^3)^(-1),x]","\frac{\sqrt[3]{b} \log \left(a^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3}\right)}{6 a^{4/3}}-\frac{\sqrt[3]{b} \log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{3 a^{4/3}}+\frac{\sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a} x}{\sqrt{3} \sqrt[3]{b}}\right)}{\sqrt{3} a^{4/3}}+\frac{x}{a}","\frac{\sqrt[3]{b} \log \left(a^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3}\right)}{6 a^{4/3}}-\frac{\sqrt[3]{b} \log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{3 a^{4/3}}+\frac{\sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a} x}{\sqrt{3} \sqrt[3]{b}}\right)}{\sqrt{3} a^{4/3}}+\frac{x}{a}",1,"x/a + (b^(1/3)*ArcTan[(b^(1/3) - 2*a^(1/3)*x)/(Sqrt[3]*b^(1/3))])/(Sqrt[3]*a^(4/3)) - (b^(1/3)*Log[b^(1/3) + a^(1/3)*x])/(3*a^(4/3)) + (b^(1/3)*Log[b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2])/(6*a^(4/3))","A",8,8,9,0.8889,1,"{193, 321, 200, 31, 634, 617, 204, 628}"
1971,1,15,0,0.0058785,"\int \frac{1}{\left(a+\frac{b}{x^3}\right) x} \, dx","Int[1/((a + b/x^3)*x),x]","\frac{\log \left(a x^3+b\right)}{3 a}","\frac{\log \left(a x^3+b\right)}{3 a}",1,"Log[b + a*x^3]/(3*a)","A",2,2,13,0.1538,1,"{263, 260}"
1972,1,115,0,0.0512239,"\int \frac{1}{\left(a+\frac{b}{x^3}\right) x^2} \, dx","Int[1/((a + b/x^3)*x^2),x]","\frac{\log \left(a^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3}\right)}{6 a^{2/3} \sqrt[3]{b}}-\frac{\log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{3 a^{2/3} \sqrt[3]{b}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a} x}{\sqrt{3} \sqrt[3]{b}}\right)}{\sqrt{3} a^{2/3} \sqrt[3]{b}}","\frac{\log \left(a^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3}\right)}{6 a^{2/3} \sqrt[3]{b}}-\frac{\log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{3 a^{2/3} \sqrt[3]{b}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a} x}{\sqrt{3} \sqrt[3]{b}}\right)}{\sqrt{3} a^{2/3} \sqrt[3]{b}}",1,"-(ArcTan[(b^(1/3) - 2*a^(1/3)*x)/(Sqrt[3]*b^(1/3))]/(Sqrt[3]*a^(2/3)*b^(1/3))) - Log[b^(1/3) + a^(1/3)*x]/(3*a^(2/3)*b^(1/3)) + Log[b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2]/(6*a^(2/3)*b^(1/3))","A",7,7,13,0.5385,1,"{263, 292, 31, 634, 617, 204, 628}"
1973,1,115,0,0.0509691,"\int \frac{1}{\left(a+\frac{b}{x^3}\right) x^3} \, dx","Int[1/((a + b/x^3)*x^3),x]","-\frac{\log \left(a^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3}\right)}{6 \sqrt[3]{a} b^{2/3}}+\frac{\log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{3 \sqrt[3]{a} b^{2/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a} x}{\sqrt{3} \sqrt[3]{b}}\right)}{\sqrt{3} \sqrt[3]{a} b^{2/3}}","-\frac{\log \left(a^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3}\right)}{6 \sqrt[3]{a} b^{2/3}}+\frac{\log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{3 \sqrt[3]{a} b^{2/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a} x}{\sqrt{3} \sqrt[3]{b}}\right)}{\sqrt{3} \sqrt[3]{a} b^{2/3}}",1,"-(ArcTan[(b^(1/3) - 2*a^(1/3)*x)/(Sqrt[3]*b^(1/3))]/(Sqrt[3]*a^(1/3)*b^(2/3))) + Log[b^(1/3) + a^(1/3)*x]/(3*a^(1/3)*b^(2/3)) - Log[b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2]/(6*a^(1/3)*b^(2/3))","A",7,7,13,0.5385,1,"{263, 200, 31, 634, 617, 204, 628}"
1974,1,15,0,0.0041136,"\int \frac{1}{\left(a+\frac{b}{x^3}\right) x^4} \, dx","Int[1/((a + b/x^3)*x^4),x]","-\frac{\log \left(a+\frac{b}{x^3}\right)}{3 b}","-\frac{\log \left(a+\frac{b}{x^3}\right)}{3 b}",1,"-Log[a + b/x^3]/(3*b)","A",1,1,13,0.07692,1,"{260}"
1975,1,122,0,0.0646309,"\int \frac{1}{\left(a+\frac{b}{x^3}\right) x^5} \, dx","Int[1/((a + b/x^3)*x^5),x]","-\frac{\sqrt[3]{a} \log \left(a^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3}\right)}{6 b^{4/3}}+\frac{\sqrt[3]{a} \log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{3 b^{4/3}}+\frac{\sqrt[3]{a} \tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a} x}{\sqrt{3} \sqrt[3]{b}}\right)}{\sqrt{3} b^{4/3}}-\frac{1}{b x}","-\frac{\sqrt[3]{a} \log \left(a^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3}\right)}{6 b^{4/3}}+\frac{\sqrt[3]{a} \log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{3 b^{4/3}}+\frac{\sqrt[3]{a} \tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a} x}{\sqrt{3} \sqrt[3]{b}}\right)}{\sqrt{3} b^{4/3}}-\frac{1}{b x}",1,"-(1/(b*x)) + (a^(1/3)*ArcTan[(b^(1/3) - 2*a^(1/3)*x)/(Sqrt[3]*b^(1/3))])/(Sqrt[3]*b^(4/3)) + (a^(1/3)*Log[b^(1/3) + a^(1/3)*x])/(3*b^(4/3)) - (a^(1/3)*Log[b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2])/(6*b^(4/3))","A",8,8,13,0.6154,1,"{263, 325, 292, 31, 634, 617, 204, 628}"
1976,1,124,0,0.0647602,"\int \frac{1}{\left(a+\frac{b}{x^3}\right) x^6} \, dx","Int[1/((a + b/x^3)*x^6),x]","\frac{a^{2/3} \log \left(a^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3}\right)}{6 b^{5/3}}-\frac{a^{2/3} \log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{3 b^{5/3}}+\frac{a^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a} x}{\sqrt{3} \sqrt[3]{b}}\right)}{\sqrt{3} b^{5/3}}-\frac{1}{2 b x^2}","\frac{a^{2/3} \log \left(a^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3}\right)}{6 b^{5/3}}-\frac{a^{2/3} \log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{3 b^{5/3}}+\frac{a^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a} x}{\sqrt{3} \sqrt[3]{b}}\right)}{\sqrt{3} b^{5/3}}-\frac{1}{2 b x^2}",1,"-1/(2*b*x^2) + (a^(2/3)*ArcTan[(b^(1/3) - 2*a^(1/3)*x)/(Sqrt[3]*b^(1/3))])/(Sqrt[3]*b^(5/3)) - (a^(2/3)*Log[b^(1/3) + a^(1/3)*x])/(3*b^(5/3)) + (a^(2/3)*Log[b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2])/(6*b^(5/3))","A",8,8,13,0.6154,1,"{263, 325, 200, 31, 634, 617, 204, 628}"
1977,1,35,0,0.0231146,"\int \frac{1}{\left(a+\frac{b}{x^3}\right) x^7} \, dx","Int[1/((a + b/x^3)*x^7),x]","\frac{a \log \left(a x^3+b\right)}{3 b^2}-\frac{a \log (x)}{b^2}-\frac{1}{3 b x^3}","\frac{a \log \left(a x^3+b\right)}{3 b^2}-\frac{a \log (x)}{b^2}-\frac{1}{3 b x^3}",1,"-1/(3*b*x^3) - (a*Log[x])/b^2 + (a*Log[b + a*x^3])/(3*b^2)","A",4,3,13,0.2308,1,"{263, 266, 44}"
1978,1,56,0,0.0401671,"\int \frac{x^5}{\left(a+\frac{b}{x^3}\right)^2} \, dx","Int[x^5/(a + b/x^3)^2,x]","\frac{b^3}{3 a^4 \left(a x^3+b\right)}+\frac{b^2 \log \left(a x^3+b\right)}{a^4}-\frac{2 b x^3}{3 a^3}+\frac{x^6}{6 a^2}","\frac{b^3}{3 a^4 \left(a x^3+b\right)}+\frac{b^2 \log \left(a x^3+b\right)}{a^4}-\frac{2 b x^3}{3 a^3}+\frac{x^6}{6 a^2}",1,"(-2*b*x^3)/(3*a^3) + x^6/(6*a^2) + b^3/(3*a^4*(b + a*x^3)) + (b^2*Log[b + a*x^3])/a^4","A",4,3,13,0.2308,1,"{263, 266, 43}"
1979,1,157,0,0.0968901,"\int \frac{x^4}{\left(a+\frac{b}{x^3}\right)^2} \, dx","Int[x^4/(a + b/x^3)^2,x]","\frac{4 b^{5/3} \log \left(a^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3}\right)}{9 a^{11/3}}-\frac{8 b^{5/3} \log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{9 a^{11/3}}-\frac{8 b^{5/3} \tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a} x}{\sqrt{3} \sqrt[3]{b}}\right)}{3 \sqrt{3} a^{11/3}}-\frac{4 b x^2}{3 a^3}+\frac{8 x^5}{15 a^2}-\frac{x^8}{3 a \left(a x^3+b\right)}","\frac{4 b^{5/3} \log \left(a^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3}\right)}{9 a^{11/3}}-\frac{8 b^{5/3} \log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{9 a^{11/3}}-\frac{8 b^{5/3} \tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a} x}{\sqrt{3} \sqrt[3]{b}}\right)}{3 \sqrt{3} a^{11/3}}-\frac{4 b x^2}{3 a^3}+\frac{8 x^5}{15 a^2}-\frac{x^8}{3 a \left(a x^3+b\right)}",1,"(-4*b*x^2)/(3*a^3) + (8*x^5)/(15*a^2) - x^8/(3*a*(b + a*x^3)) - (8*b^(5/3)*ArcTan[(b^(1/3) - 2*a^(1/3)*x)/(Sqrt[3]*b^(1/3))])/(3*Sqrt[3]*a^(11/3)) - (8*b^(5/3)*Log[b^(1/3) + a^(1/3)*x])/(9*a^(11/3)) + (4*b^(5/3)*Log[b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2])/(9*a^(11/3))","A",10,9,13,0.6923,1,"{263, 288, 302, 292, 31, 634, 617, 204, 628}"
1980,1,155,0,0.0943547,"\int \frac{x^3}{\left(a+\frac{b}{x^3}\right)^2} \, dx","Int[x^3/(a + b/x^3)^2,x]","-\frac{7 b^{4/3} \log \left(a^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3}\right)}{18 a^{10/3}}+\frac{7 b^{4/3} \log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{9 a^{10/3}}-\frac{7 b^{4/3} \tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a} x}{\sqrt{3} \sqrt[3]{b}}\right)}{3 \sqrt{3} a^{10/3}}-\frac{7 b x}{3 a^3}+\frac{7 x^4}{12 a^2}-\frac{x^7}{3 a \left(a x^3+b\right)}","-\frac{7 b^{4/3} \log \left(a^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3}\right)}{18 a^{10/3}}+\frac{7 b^{4/3} \log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{9 a^{10/3}}-\frac{7 b^{4/3} \tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a} x}{\sqrt{3} \sqrt[3]{b}}\right)}{3 \sqrt{3} a^{10/3}}-\frac{7 b x}{3 a^3}+\frac{7 x^4}{12 a^2}-\frac{x^7}{3 a \left(a x^3+b\right)}",1,"(-7*b*x)/(3*a^3) + (7*x^4)/(12*a^2) - x^7/(3*a*(b + a*x^3)) - (7*b^(4/3)*ArcTan[(b^(1/3) - 2*a^(1/3)*x)/(Sqrt[3]*b^(1/3))])/(3*Sqrt[3]*a^(10/3)) + (7*b^(4/3)*Log[b^(1/3) + a^(1/3)*x])/(9*a^(10/3)) - (7*b^(4/3)*Log[b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2])/(18*a^(10/3))","A",10,9,13,0.6923,1,"{263, 288, 302, 200, 31, 634, 617, 204, 628}"
1981,1,46,0,0.0315299,"\int \frac{x^2}{\left(a+\frac{b}{x^3}\right)^2} \, dx","Int[x^2/(a + b/x^3)^2,x]","-\frac{b^2}{3 a^3 \left(a x^3+b\right)}-\frac{2 b \log \left(a x^3+b\right)}{3 a^3}+\frac{x^3}{3 a^2}","-\frac{b^2}{3 a^3 \left(a x^3+b\right)}-\frac{2 b \log \left(a x^3+b\right)}{3 a^3}+\frac{x^3}{3 a^2}",1,"x^3/(3*a^2) - b^2/(3*a^3*(b + a*x^3)) - (2*b*Log[b + a*x^3])/(3*a^3)","A",4,3,13,0.2308,1,"{263, 266, 43}"
1982,1,146,0,0.0758377,"\int \frac{x}{\left(a+\frac{b}{x^3}\right)^2} \, dx","Int[x/(a + b/x^3)^2,x]","-\frac{5 b^{2/3} \log \left(a^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3}\right)}{18 a^{8/3}}+\frac{5 b^{2/3} \log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{9 a^{8/3}}+\frac{5 b^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a} x}{\sqrt{3} \sqrt[3]{b}}\right)}{3 \sqrt{3} a^{8/3}}+\frac{5 x^2}{6 a^2}-\frac{x^5}{3 a \left(a x^3+b\right)}","-\frac{5 b^{2/3} \log \left(a^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3}\right)}{18 a^{8/3}}+\frac{5 b^{2/3} \log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{9 a^{8/3}}+\frac{5 b^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a} x}{\sqrt{3} \sqrt[3]{b}}\right)}{3 \sqrt{3} a^{8/3}}+\frac{5 x^2}{6 a^2}-\frac{x^5}{3 a \left(a x^3+b\right)}",1,"(5*x^2)/(6*a^2) - x^5/(3*a*(b + a*x^3)) + (5*b^(2/3)*ArcTan[(b^(1/3) - 2*a^(1/3)*x)/(Sqrt[3]*b^(1/3))])/(3*Sqrt[3]*a^(8/3)) + (5*b^(2/3)*Log[b^(1/3) + a^(1/3)*x])/(9*a^(8/3)) - (5*b^(2/3)*Log[b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2])/(18*a^(8/3))","A",9,9,11,0.8182,1,"{263, 288, 321, 292, 31, 634, 617, 204, 628}"
1983,1,144,0,0.0741316,"\int \frac{1}{\left(a+\frac{b}{x^3}\right)^2} \, dx","Int[(a + b/x^3)^(-2),x]","\frac{2 \sqrt[3]{b} \log \left(a^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3}\right)}{9 a^{7/3}}-\frac{4 \sqrt[3]{b} \log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{9 a^{7/3}}+\frac{4 \sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a} x}{\sqrt{3} \sqrt[3]{b}}\right)}{3 \sqrt{3} a^{7/3}}+\frac{4 x}{3 a^2}-\frac{x^4}{3 a \left(a x^3+b\right)}","\frac{2 \sqrt[3]{b} \log \left(a^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3}\right)}{9 a^{7/3}}-\frac{4 \sqrt[3]{b} \log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{9 a^{7/3}}+\frac{4 \sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a} x}{\sqrt{3} \sqrt[3]{b}}\right)}{3 \sqrt{3} a^{7/3}}+\frac{4 x}{3 a^2}-\frac{x^4}{3 a \left(a x^3+b\right)}",1,"(4*x)/(3*a^2) - x^4/(3*a*(b + a*x^3)) + (4*b^(1/3)*ArcTan[(b^(1/3) - 2*a^(1/3)*x)/(Sqrt[3]*b^(1/3))])/(3*Sqrt[3]*a^(7/3)) - (4*b^(1/3)*Log[b^(1/3) + a^(1/3)*x])/(9*a^(7/3)) + (2*b^(1/3)*Log[b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2])/(9*a^(7/3))","A",9,9,9,1.000,1,"{193, 288, 321, 200, 31, 634, 617, 204, 628}"
1984,1,33,0,0.0243806,"\int \frac{1}{\left(a+\frac{b}{x^3}\right)^2 x} \, dx","Int[1/((a + b/x^3)^2*x),x]","\frac{b}{3 a^2 \left(a x^3+b\right)}+\frac{\log \left(a x^3+b\right)}{3 a^2}","\frac{b}{3 a^2 \left(a x^3+b\right)}+\frac{\log \left(a x^3+b\right)}{3 a^2}",1,"b/(3*a^2*(b + a*x^3)) + Log[b + a*x^3]/(3*a^2)","A",4,3,13,0.2308,1,"{263, 266, 43}"
1985,1,136,0,0.0681602,"\int \frac{1}{\left(a+\frac{b}{x^3}\right)^2 x^2} \, dx","Int[1/((a + b/x^3)^2*x^2),x]","\frac{\log \left(a^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3}\right)}{9 a^{5/3} \sqrt[3]{b}}-\frac{2 \log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{9 a^{5/3} \sqrt[3]{b}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a} x}{\sqrt{3} \sqrt[3]{b}}\right)}{3 \sqrt{3} a^{5/3} \sqrt[3]{b}}-\frac{x^2}{3 a \left(a x^3+b\right)}","\frac{\log \left(a^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3}\right)}{9 a^{5/3} \sqrt[3]{b}}-\frac{2 \log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{9 a^{5/3} \sqrt[3]{b}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a} x}{\sqrt{3} \sqrt[3]{b}}\right)}{3 \sqrt{3} a^{5/3} \sqrt[3]{b}}-\frac{x^2}{3 a \left(a x^3+b\right)}",1,"-x^2/(3*a*(b + a*x^3)) - (2*ArcTan[(b^(1/3) - 2*a^(1/3)*x)/(Sqrt[3]*b^(1/3))])/(3*Sqrt[3]*a^(5/3)*b^(1/3)) - (2*Log[b^(1/3) + a^(1/3)*x])/(9*a^(5/3)*b^(1/3)) + Log[b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2]/(9*a^(5/3)*b^(1/3))","A",8,8,13,0.6154,1,"{263, 288, 292, 31, 634, 617, 204, 628}"
1986,1,134,0,0.0673843,"\int \frac{1}{\left(a+\frac{b}{x^3}\right)^2 x^3} \, dx","Int[1/((a + b/x^3)^2*x^3),x]","-\frac{\log \left(a^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3}\right)}{18 a^{4/3} b^{2/3}}+\frac{\log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{9 a^{4/3} b^{2/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a} x}{\sqrt{3} \sqrt[3]{b}}\right)}{3 \sqrt{3} a^{4/3} b^{2/3}}-\frac{x}{3 a \left(a x^3+b\right)}","-\frac{\log \left(a^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3}\right)}{18 a^{4/3} b^{2/3}}+\frac{\log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{9 a^{4/3} b^{2/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a} x}{\sqrt{3} \sqrt[3]{b}}\right)}{3 \sqrt{3} a^{4/3} b^{2/3}}-\frac{x}{3 a \left(a x^3+b\right)}",1,"-x/(3*a*(b + a*x^3)) - ArcTan[(b^(1/3) - 2*a^(1/3)*x)/(Sqrt[3]*b^(1/3))]/(3*Sqrt[3]*a^(4/3)*b^(2/3)) + Log[b^(1/3) + a^(1/3)*x]/(9*a^(4/3)*b^(2/3)) - Log[b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2]/(18*a^(4/3)*b^(2/3))","A",8,8,13,0.6154,1,"{263, 288, 200, 31, 634, 617, 204, 628}"
1987,1,16,0,0.004098,"\int \frac{1}{\left(a+\frac{b}{x^3}\right)^2 x^4} \, dx","Int[1/((a + b/x^3)^2*x^4),x]","\frac{1}{3 b \left(a+\frac{b}{x^3}\right)}","\frac{1}{3 b \left(a+\frac{b}{x^3}\right)}",1,"1/(3*b*(a + b/x^3))","A",1,1,13,0.07692,1,"{261}"
1988,1,136,0,0.0693039,"\int \frac{1}{\left(a+\frac{b}{x^3}\right)^2 x^5} \, dx","Int[1/((a + b/x^3)^2*x^5),x]","\frac{\log \left(a^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3}\right)}{18 a^{2/3} b^{4/3}}-\frac{\log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{9 a^{2/3} b^{4/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a} x}{\sqrt{3} \sqrt[3]{b}}\right)}{3 \sqrt{3} a^{2/3} b^{4/3}}+\frac{x^2}{3 b \left(a x^3+b\right)}","\frac{\log \left(a^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3}\right)}{18 a^{2/3} b^{4/3}}-\frac{\log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{9 a^{2/3} b^{4/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a} x}{\sqrt{3} \sqrt[3]{b}}\right)}{3 \sqrt{3} a^{2/3} b^{4/3}}+\frac{x^2}{3 b \left(a x^3+b\right)}",1,"x^2/(3*b*(b + a*x^3)) - ArcTan[(b^(1/3) - 2*a^(1/3)*x)/(Sqrt[3]*b^(1/3))]/(3*Sqrt[3]*a^(2/3)*b^(4/3)) - Log[b^(1/3) + a^(1/3)*x]/(9*a^(2/3)*b^(4/3)) + Log[b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2]/(18*a^(2/3)*b^(4/3))","A",8,8,13,0.6154,1,"{263, 290, 292, 31, 634, 617, 204, 628}"
1989,1,134,0,0.0625091,"\int \frac{1}{\left(a+\frac{b}{x^3}\right)^2 x^6} \, dx","Int[1/((a + b/x^3)^2*x^6),x]","-\frac{\log \left(a^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3}\right)}{9 \sqrt[3]{a} b^{5/3}}+\frac{2 \log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{9 \sqrt[3]{a} b^{5/3}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a} x}{\sqrt{3} \sqrt[3]{b}}\right)}{3 \sqrt{3} \sqrt[3]{a} b^{5/3}}+\frac{x}{3 b \left(a x^3+b\right)}","-\frac{\log \left(a^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3}\right)}{9 \sqrt[3]{a} b^{5/3}}+\frac{2 \log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{9 \sqrt[3]{a} b^{5/3}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a} x}{\sqrt{3} \sqrt[3]{b}}\right)}{3 \sqrt{3} \sqrt[3]{a} b^{5/3}}+\frac{x}{3 b \left(a x^3+b\right)}",1,"x/(3*b*(b + a*x^3)) - (2*ArcTan[(b^(1/3) - 2*a^(1/3)*x)/(Sqrt[3]*b^(1/3))])/(3*Sqrt[3]*a^(1/3)*b^(5/3)) + (2*Log[b^(1/3) + a^(1/3)*x])/(9*a^(1/3)*b^(5/3)) - Log[b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2]/(9*a^(1/3)*b^(5/3))","A",8,8,13,0.6154,1,"{263, 199, 200, 31, 634, 617, 204, 628}"
1990,1,38,0,0.0252161,"\int \frac{1}{\left(a+\frac{b}{x^3}\right)^2 x^7} \, dx","Int[1/((a + b/x^3)^2*x^7),x]","-\frac{\log \left(a x^3+b\right)}{3 b^2}+\frac{1}{3 b \left(a x^3+b\right)}+\frac{\log (x)}{b^2}","-\frac{\log \left(a x^3+b\right)}{3 b^2}+\frac{1}{3 b \left(a x^3+b\right)}+\frac{\log (x)}{b^2}",1,"1/(3*b*(b + a*x^3)) + Log[x]/b^2 - Log[b + a*x^3]/(3*b^2)","A",4,3,13,0.2308,1,"{263, 266, 44}"
1991,1,71,0,0.0360138,"\int \sqrt{a+\frac{b}{x^3}} x^5 \, dx","Int[Sqrt[a + b/x^3]*x^5,x]","-\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^3}}}{\sqrt{a}}\right)}{12 a^{3/2}}+\frac{1}{6} x^6 \sqrt{a+\frac{b}{x^3}}+\frac{b x^3 \sqrt{a+\frac{b}{x^3}}}{12 a}","-\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^3}}}{\sqrt{a}}\right)}{12 a^{3/2}}+\frac{1}{6} x^6 \sqrt{a+\frac{b}{x^3}}+\frac{b x^3 \sqrt{a+\frac{b}{x^3}}}{12 a}",1,"(b*Sqrt[a + b/x^3]*x^3)/(12*a) + (Sqrt[a + b/x^3]*x^6)/6 - (b^2*ArcTanh[Sqrt[a + b/x^3]/Sqrt[a]])/(12*a^(3/2))","A",5,5,15,0.3333,1,"{266, 47, 51, 63, 208}"
1992,1,47,0,0.0241335,"\int \sqrt{a+\frac{b}{x^3}} x^2 \, dx","Int[Sqrt[a + b/x^3]*x^2,x]","\frac{1}{3} x^3 \sqrt{a+\frac{b}{x^3}}+\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^3}}}{\sqrt{a}}\right)}{3 \sqrt{a}}","\frac{1}{3} x^3 \sqrt{a+\frac{b}{x^3}}+\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^3}}}{\sqrt{a}}\right)}{3 \sqrt{a}}",1,"(Sqrt[a + b/x^3]*x^3)/3 + (b*ArcTanh[Sqrt[a + b/x^3]/Sqrt[a]])/(3*Sqrt[a])","A",4,4,15,0.2667,1,"{266, 47, 63, 208}"
1993,1,43,0,0.0227685,"\int \frac{\sqrt{a+\frac{b}{x^3}}}{x} \, dx","Int[Sqrt[a + b/x^3]/x,x]","\frac{2}{3} \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^3}}}{\sqrt{a}}\right)-\frac{2}{3} \sqrt{a+\frac{b}{x^3}}","\frac{2}{3} \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^3}}}{\sqrt{a}}\right)-\frac{2}{3} \sqrt{a+\frac{b}{x^3}}",1,"(-2*Sqrt[a + b/x^3])/3 + (2*Sqrt[a]*ArcTanh[Sqrt[a + b/x^3]/Sqrt[a]])/3","A",4,4,15,0.2667,1,"{266, 50, 63, 208}"
1994,1,18,0,0.0059425,"\int \frac{\sqrt{a+\frac{b}{x^3}}}{x^4} \, dx","Int[Sqrt[a + b/x^3]/x^4,x]","-\frac{2 \left(a+\frac{b}{x^3}\right)^{3/2}}{9 b}","-\frac{2 \left(a+\frac{b}{x^3}\right)^{3/2}}{9 b}",1,"(-2*(a + b/x^3)^(3/2))/(9*b)","A",1,1,15,0.06667,1,"{261}"
1995,1,38,0,0.0210704,"\int \frac{\sqrt{a+\frac{b}{x^3}}}{x^7} \, dx","Int[Sqrt[a + b/x^3]/x^7,x]","\frac{2 a \left(a+\frac{b}{x^3}\right)^{3/2}}{9 b^2}-\frac{2 \left(a+\frac{b}{x^3}\right)^{5/2}}{15 b^2}","\frac{2 a \left(a+\frac{b}{x^3}\right)^{3/2}}{9 b^2}-\frac{2 \left(a+\frac{b}{x^3}\right)^{5/2}}{15 b^2}",1,"(2*a*(a + b/x^3)^(3/2))/(9*b^2) - (2*(a + b/x^3)^(5/2))/(15*b^2)","A",3,2,15,0.1333,1,"{266, 43}"
1996,1,59,0,0.0300644,"\int \frac{\sqrt{a+\frac{b}{x^3}}}{x^{10}} \, dx","Int[Sqrt[a + b/x^3]/x^10,x]","-\frac{2 a^2 \left(a+\frac{b}{x^3}\right)^{3/2}}{9 b^3}-\frac{2 \left(a+\frac{b}{x^3}\right)^{7/2}}{21 b^3}+\frac{4 a \left(a+\frac{b}{x^3}\right)^{5/2}}{15 b^3}","-\frac{2 a^2 \left(a+\frac{b}{x^3}\right)^{3/2}}{9 b^3}-\frac{2 \left(a+\frac{b}{x^3}\right)^{7/2}}{21 b^3}+\frac{4 a \left(a+\frac{b}{x^3}\right)^{5/2}}{15 b^3}",1,"(-2*a^2*(a + b/x^3)^(3/2))/(9*b^3) + (4*a*(a + b/x^3)^(5/2))/(15*b^3) - (2*(a + b/x^3)^(7/2))/(21*b^3)","A",3,2,15,0.1333,1,"{266, 43}"
1997,1,80,0,0.0413452,"\int \frac{\sqrt{a+\frac{b}{x^3}}}{x^{13}} \, dx","Int[Sqrt[a + b/x^3]/x^13,x]","-\frac{2 a^2 \left(a+\frac{b}{x^3}\right)^{5/2}}{5 b^4}+\frac{2 a^3 \left(a+\frac{b}{x^3}\right)^{3/2}}{9 b^4}-\frac{2 \left(a+\frac{b}{x^3}\right)^{9/2}}{27 b^4}+\frac{2 a \left(a+\frac{b}{x^3}\right)^{7/2}}{7 b^4}","-\frac{2 a^2 \left(a+\frac{b}{x^3}\right)^{5/2}}{5 b^4}+\frac{2 a^3 \left(a+\frac{b}{x^3}\right)^{3/2}}{9 b^4}-\frac{2 \left(a+\frac{b}{x^3}\right)^{9/2}}{27 b^4}+\frac{2 a \left(a+\frac{b}{x^3}\right)^{7/2}}{7 b^4}",1,"(2*a^3*(a + b/x^3)^(3/2))/(9*b^4) - (2*a^2*(a + b/x^3)^(5/2))/(5*b^4) + (2*a*(a + b/x^3)^(7/2))/(7*b^4) - (2*(a + b/x^3)^(9/2))/(27*b^4)","A",3,2,15,0.1333,1,"{266, 43}"
1998,1,291,0,0.1905272,"\int \sqrt{a+\frac{b}{x^3}} x^7 \, dx","Int[Sqrt[a + b/x^3]*x^7,x]","-\frac{21 b^2 x^2 \sqrt{a+\frac{b}{x^3}}}{320 a^2}-\frac{7\ 3^{3/4} \sqrt{2+\sqrt{3}} b^{8/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{320 a^2 \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{1}{8} x^8 \sqrt{a+\frac{b}{x^3}}+\frac{3 b x^5 \sqrt{a+\frac{b}{x^3}}}{80 a}","-\frac{21 b^2 x^2 \sqrt{a+\frac{b}{x^3}}}{320 a^2}-\frac{7\ 3^{3/4} \sqrt{2+\sqrt{3}} b^{8/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{320 a^2 \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{1}{8} x^8 \sqrt{a+\frac{b}{x^3}}+\frac{3 b x^5 \sqrt{a+\frac{b}{x^3}}}{80 a}",1,"(-21*b^2*Sqrt[a + b/x^3]*x^2)/(320*a^2) + (3*b*Sqrt[a + b/x^3]*x^5)/(80*a) + (Sqrt[a + b/x^3]*x^8)/8 - (7*3^(3/4)*Sqrt[2 + Sqrt[3]]*b^(8/3)*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(320*a^2*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2])","A",5,4,15,0.2667,1,"{335, 277, 325, 218}"
1999,1,267,0,0.1208255,"\int \sqrt{a+\frac{b}{x^3}} x^4 \, dx","Int[Sqrt[a + b/x^3]*x^4,x]","\frac{3^{3/4} \sqrt{2+\sqrt{3}} b^{5/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{20 a \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{1}{5} x^5 \sqrt{a+\frac{b}{x^3}}+\frac{3 b x^2 \sqrt{a+\frac{b}{x^3}}}{20 a}","\frac{3^{3/4} \sqrt{2+\sqrt{3}} b^{5/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{20 a \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{1}{5} x^5 \sqrt{a+\frac{b}{x^3}}+\frac{3 b x^2 \sqrt{a+\frac{b}{x^3}}}{20 a}",1,"(3*b*Sqrt[a + b/x^3]*x^2)/(20*a) + (Sqrt[a + b/x^3]*x^5)/5 + (3^(3/4)*Sqrt[2 + Sqrt[3]]*b^(5/3)*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(20*a*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2])","A",4,4,15,0.2667,1,"{335, 277, 325, 218}"
2000,1,242,0,0.0861561,"\int \sqrt{a+\frac{b}{x^3}} x \, dx","Int[Sqrt[a + b/x^3]*x,x]","\frac{1}{2} x^2 \sqrt{a+\frac{b}{x^3}}-\frac{3^{3/4} \sqrt{2+\sqrt{3}} b^{2/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}","\frac{1}{2} x^2 \sqrt{a+\frac{b}{x^3}}-\frac{3^{3/4} \sqrt{2+\sqrt{3}} b^{2/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}",1,"(Sqrt[a + b/x^3]*x^2)/2 - (3^(3/4)*Sqrt[2 + Sqrt[3]]*b^(2/3)*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(2*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2])","A",3,3,13,0.2308,1,"{335, 277, 218}"
2001,1,243,0,0.0882551,"\int \frac{\sqrt{a+\frac{b}{x^3}}}{x^2} \, dx","Int[Sqrt[a + b/x^3]/x^2,x]","-\frac{2\ 3^{3/4} \sqrt{2+\sqrt{3}} a \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{5 \sqrt[3]{b} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}-\frac{2 \sqrt{a+\frac{b}{x^3}}}{5 x}","-\frac{2\ 3^{3/4} \sqrt{2+\sqrt{3}} a \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{5 \sqrt[3]{b} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}-\frac{2 \sqrt{a+\frac{b}{x^3}}}{5 x}",1,"(-2*Sqrt[a + b/x^3])/(5*x) - (2*3^(3/4)*Sqrt[2 + Sqrt[3]]*a*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(5*b^(1/3)*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2])","A",3,3,15,0.2000,1,"{335, 195, 218}"
2002,1,267,0,0.123234,"\int \frac{\sqrt{a+\frac{b}{x^3}}}{x^5} \, dx","Int[Sqrt[a + b/x^3]/x^5,x]","\frac{4\ 3^{3/4} \sqrt{2+\sqrt{3}} a^2 \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{55 b^{4/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}-\frac{6 a \sqrt{a+\frac{b}{x^3}}}{55 b x}-\frac{2 \sqrt{a+\frac{b}{x^3}}}{11 x^4}","\frac{4\ 3^{3/4} \sqrt{2+\sqrt{3}} a^2 \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{55 b^{4/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}-\frac{6 a \sqrt{a+\frac{b}{x^3}}}{55 b x}-\frac{2 \sqrt{a+\frac{b}{x^3}}}{11 x^4}",1,"(-2*Sqrt[a + b/x^3])/(11*x^4) - (6*a*Sqrt[a + b/x^3])/(55*b*x) + (4*3^(3/4)*Sqrt[2 + Sqrt[3]]*a^2*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(55*b^(4/3)*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2])","A",4,4,15,0.2667,1,"{335, 279, 321, 218}"
2003,1,291,0,0.1553835,"\int \frac{\sqrt{a+\frac{b}{x^3}}}{x^8} \, dx","Int[Sqrt[a + b/x^3]/x^8,x]","\frac{48 a^2 \sqrt{a+\frac{b}{x^3}}}{935 b^2 x}-\frac{32\ 3^{3/4} \sqrt{2+\sqrt{3}} a^3 \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{935 b^{7/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}-\frac{6 a \sqrt{a+\frac{b}{x^3}}}{187 b x^4}-\frac{2 \sqrt{a+\frac{b}{x^3}}}{17 x^7}","\frac{48 a^2 \sqrt{a+\frac{b}{x^3}}}{935 b^2 x}-\frac{32\ 3^{3/4} \sqrt{2+\sqrt{3}} a^3 \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{935 b^{7/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}-\frac{6 a \sqrt{a+\frac{b}{x^3}}}{187 b x^4}-\frac{2 \sqrt{a+\frac{b}{x^3}}}{17 x^7}",1,"(-2*Sqrt[a + b/x^3])/(17*x^7) - (6*a*Sqrt[a + b/x^3])/(187*b*x^4) + (48*a^2*Sqrt[a + b/x^3])/(935*b^2*x) - (32*3^(3/4)*Sqrt[2 + Sqrt[3]]*a^3*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(935*b^(7/3)*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2])","A",5,4,15,0.2667,1,"{335, 279, 321, 218}"
2004,1,563,0,0.3885773,"\int \sqrt{a+\frac{b}{x^3}} x^6 \, dx","Int[Sqrt[a + b/x^3]*x^6,x]","-\frac{15 b^2 x \sqrt{a+\frac{b}{x^3}}}{112 a^2}+\frac{15 b^{7/3} \sqrt{a+\frac{b}{x^3}}}{112 a^2 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}+\frac{5\ 3^{3/4} b^{7/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{56 \sqrt{2} a^{5/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}-\frac{15 \sqrt[4]{3} \sqrt{2-\sqrt{3}} b^{7/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{224 a^{5/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{1}{7} x^7 \sqrt{a+\frac{b}{x^3}}+\frac{3 b x^4 \sqrt{a+\frac{b}{x^3}}}{56 a}","-\frac{15 b^2 x \sqrt{a+\frac{b}{x^3}}}{112 a^2}+\frac{15 b^{7/3} \sqrt{a+\frac{b}{x^3}}}{112 a^2 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}+\frac{5\ 3^{3/4} b^{7/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{56 \sqrt{2} a^{5/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}-\frac{15 \sqrt[4]{3} \sqrt{2-\sqrt{3}} b^{7/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{224 a^{5/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{1}{7} x^7 \sqrt{a+\frac{b}{x^3}}+\frac{3 b x^4 \sqrt{a+\frac{b}{x^3}}}{56 a}",1,"(15*b^(7/3)*Sqrt[a + b/x^3])/(112*a^2*((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)) - (15*b^2*Sqrt[a + b/x^3]*x)/(112*a^2) + (3*b*Sqrt[a + b/x^3]*x^4)/(56*a) + (Sqrt[a + b/x^3]*x^7)/7 - (15*3^(1/4)*Sqrt[2 - Sqrt[3]]*b^(7/3)*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(224*a^(5/3)*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]) + (5*3^(3/4)*b^(7/3)*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(56*Sqrt[2]*a^(5/3)*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2])","A",7,6,15,0.4000,1,"{335, 277, 325, 303, 218, 1877}"
2005,1,539,0,0.286306,"\int \sqrt{a+\frac{b}{x^3}} x^3 \, dx","Int[Sqrt[a + b/x^3]*x^3,x]","-\frac{3^{3/4} b^{4/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{4 \sqrt{2} a^{2/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} b^{4/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{16 a^{2/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}-\frac{3 b^{4/3} \sqrt{a+\frac{b}{x^3}}}{8 a \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}+\frac{1}{4} x^4 \sqrt{a+\frac{b}{x^3}}+\frac{3 b x \sqrt{a+\frac{b}{x^3}}}{8 a}","-\frac{3^{3/4} b^{4/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{4 \sqrt{2} a^{2/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} b^{4/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{16 a^{2/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}-\frac{3 b^{4/3} \sqrt{a+\frac{b}{x^3}}}{8 a \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}+\frac{1}{4} x^4 \sqrt{a+\frac{b}{x^3}}+\frac{3 b x \sqrt{a+\frac{b}{x^3}}}{8 a}",1,"(-3*b^(4/3)*Sqrt[a + b/x^3])/(8*a*((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)) + (3*b*Sqrt[a + b/x^3]*x)/(8*a) + (Sqrt[a + b/x^3]*x^4)/4 + (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*b^(4/3)*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(16*a^(2/3)*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]) - (3^(3/4)*b^(4/3)*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(4*Sqrt[2]*a^(2/3)*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2])","A",6,6,15,0.4000,1,"{335, 277, 325, 303, 218, 1877}"
2006,1,507,0,0.2330364,"\int \sqrt{a+\frac{b}{x^3}} \, dx","Int[Sqrt[a + b/x^3],x]","-\frac{\sqrt{2} 3^{3/4} \sqrt[3]{a} \sqrt[3]{b} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{\sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} \sqrt[3]{b} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+x \sqrt{a+\frac{b}{x^3}}-\frac{3 \sqrt[3]{b} \sqrt{a+\frac{b}{x^3}}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}","-\frac{\sqrt{2} 3^{3/4} \sqrt[3]{a} \sqrt[3]{b} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{\sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} \sqrt[3]{b} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+x \sqrt{a+\frac{b}{x^3}}-\frac{3 \sqrt[3]{b} \sqrt{a+\frac{b}{x^3}}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}",1,"(-3*b^(1/3)*Sqrt[a + b/x^3])/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x) + Sqrt[a + b/x^3]*x + (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(1/3)*b^(1/3)*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(2*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]) - (Sqrt[2]*3^(3/4)*a^(1/3)*b^(1/3)*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2])","A",5,5,11,0.4545,1,"{242, 277, 303, 218, 1877}"
2007,1,517,0,0.2446061,"\int \frac{\sqrt{a+\frac{b}{x^3}}}{x^3} \, dx","Int[Sqrt[a + b/x^3]/x^3,x]","-\frac{2 \sqrt{2} 3^{3/4} a^{4/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{7 b^{2/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{4/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{7 b^{2/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}-\frac{6 a \sqrt{a+\frac{b}{x^3}}}{7 b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}-\frac{2 \sqrt{a+\frac{b}{x^3}}}{7 x^2}","-\frac{2 \sqrt{2} 3^{3/4} a^{4/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{7 b^{2/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{4/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{7 b^{2/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}-\frac{6 a \sqrt{a+\frac{b}{x^3}}}{7 b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}-\frac{2 \sqrt{a+\frac{b}{x^3}}}{7 x^2}",1,"(-6*a*Sqrt[a + b/x^3])/(7*b^(2/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)) - (2*Sqrt[a + b/x^3])/(7*x^2) + (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(4/3)*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(7*b^(2/3)*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]) - (2*Sqrt[2]*3^(3/4)*a^(4/3)*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(7*b^(2/3)*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2])","A",5,5,15,0.3333,1,"{335, 279, 303, 218, 1877}"
2008,1,541,0,0.2987445,"\int \frac{\sqrt{a+\frac{b}{x^3}}}{x^6} \, dx","Int[Sqrt[a + b/x^3]/x^6,x]","\frac{24 a^2 \sqrt{a+\frac{b}{x^3}}}{91 b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}+\frac{8 \sqrt{2} 3^{3/4} a^{7/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{91 b^{5/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}-\frac{12 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{7/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{91 b^{5/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}-\frac{6 a \sqrt{a+\frac{b}{x^3}}}{91 b x^2}-\frac{2 \sqrt{a+\frac{b}{x^3}}}{13 x^5}","\frac{24 a^2 \sqrt{a+\frac{b}{x^3}}}{91 b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}+\frac{8 \sqrt{2} 3^{3/4} a^{7/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{91 b^{5/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}-\frac{12 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{7/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{91 b^{5/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}-\frac{6 a \sqrt{a+\frac{b}{x^3}}}{91 b x^2}-\frac{2 \sqrt{a+\frac{b}{x^3}}}{13 x^5}",1,"(24*a^2*Sqrt[a + b/x^3])/(91*b^(5/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)) - (2*Sqrt[a + b/x^3])/(13*x^5) - (6*a*Sqrt[a + b/x^3])/(91*b*x^2) - (12*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(7/3)*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(91*b^(5/3)*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]) + (8*Sqrt[2]*3^(3/4)*a^(7/3)*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(91*b^(5/3)*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2])","A",6,6,15,0.4000,1,"{335, 279, 321, 303, 218, 1877}"
2009,1,565,0,0.3561963,"\int \frac{\sqrt{a+\frac{b}{x^3}}}{x^9} \, dx","Int[Sqrt[a + b/x^3]/x^9,x]","-\frac{240 a^3 \sqrt{a+\frac{b}{x^3}}}{1729 b^{8/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}+\frac{60 a^2 \sqrt{a+\frac{b}{x^3}}}{1729 b^2 x^2}-\frac{80 \sqrt{2} 3^{3/4} a^{10/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{1729 b^{8/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{120 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{10/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{1729 b^{8/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}-\frac{6 a \sqrt{a+\frac{b}{x^3}}}{247 b x^5}-\frac{2 \sqrt{a+\frac{b}{x^3}}}{19 x^8}","-\frac{240 a^3 \sqrt{a+\frac{b}{x^3}}}{1729 b^{8/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}+\frac{60 a^2 \sqrt{a+\frac{b}{x^3}}}{1729 b^2 x^2}-\frac{80 \sqrt{2} 3^{3/4} a^{10/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{1729 b^{8/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{120 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{10/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{1729 b^{8/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}-\frac{6 a \sqrt{a+\frac{b}{x^3}}}{247 b x^5}-\frac{2 \sqrt{a+\frac{b}{x^3}}}{19 x^8}",1,"(-240*a^3*Sqrt[a + b/x^3])/(1729*b^(8/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)) - (2*Sqrt[a + b/x^3])/(19*x^8) - (6*a*Sqrt[a + b/x^3])/(247*b*x^5) + (60*a^2*Sqrt[a + b/x^3])/(1729*b^2*x^2) + (120*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(10/3)*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(1729*b^(8/3)*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]) - (80*Sqrt[2]*3^(3/4)*a^(10/3)*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(1729*b^(8/3)*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2])","A",7,6,15,0.4000,1,"{335, 279, 321, 303, 218, 1877}"
2010,1,68,0,0.0364547,"\int \left(a+\frac{b}{x^3}\right)^{3/2} x^5 \, dx","Int[(a + b/x^3)^(3/2)*x^5,x]","\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^3}}}{\sqrt{a}}\right)}{4 \sqrt{a}}+\frac{1}{6} x^6 \left(a+\frac{b}{x^3}\right)^{3/2}+\frac{1}{4} b x^3 \sqrt{a+\frac{b}{x^3}}","\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^3}}}{\sqrt{a}}\right)}{4 \sqrt{a}}+\frac{1}{6} x^6 \left(a+\frac{b}{x^3}\right)^{3/2}+\frac{1}{4} b x^3 \sqrt{a+\frac{b}{x^3}}",1,"(b*Sqrt[a + b/x^3]*x^3)/4 + ((a + b/x^3)^(3/2)*x^6)/6 + (b^2*ArcTanh[Sqrt[a + b/x^3]/Sqrt[a]])/(4*Sqrt[a])","A",5,4,15,0.2667,1,"{266, 47, 63, 208}"
2011,1,58,0,0.033664,"\int \left(a+\frac{b}{x^3}\right)^{3/2} x^2 \, dx","Int[(a + b/x^3)^(3/2)*x^2,x]","\frac{1}{3} x^3 \left(a+\frac{b}{x^3}\right)^{3/2}-b \sqrt{a+\frac{b}{x^3}}+\sqrt{a} b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^3}}}{\sqrt{a}}\right)","\frac{1}{3} x^3 \left(a+\frac{b}{x^3}\right)^{3/2}-b \sqrt{a+\frac{b}{x^3}}+\sqrt{a} b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^3}}}{\sqrt{a}}\right)",1,"-(b*Sqrt[a + b/x^3]) + ((a + b/x^3)^(3/2)*x^3)/3 + Sqrt[a]*b*ArcTanh[Sqrt[a + b/x^3]/Sqrt[a]]","A",5,5,15,0.3333,1,"{266, 47, 50, 63, 208}"
2012,1,59,0,0.0326469,"\int \frac{\left(a+\frac{b}{x^3}\right)^{3/2}}{x} \, dx","Int[(a + b/x^3)^(3/2)/x,x]","\frac{2}{3} a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^3}}}{\sqrt{a}}\right)-\frac{2}{3} a \sqrt{a+\frac{b}{x^3}}-\frac{2}{9} \left(a+\frac{b}{x^3}\right)^{3/2}","\frac{2}{3} a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^3}}}{\sqrt{a}}\right)-\frac{2}{3} a \sqrt{a+\frac{b}{x^3}}-\frac{2}{9} \left(a+\frac{b}{x^3}\right)^{3/2}",1,"(-2*a*Sqrt[a + b/x^3])/3 - (2*(a + b/x^3)^(3/2))/9 + (2*a^(3/2)*ArcTanh[Sqrt[a + b/x^3]/Sqrt[a]])/3","A",5,4,15,0.2667,1,"{266, 50, 63, 208}"
2013,1,18,0,0.0064478,"\int \frac{\left(a+\frac{b}{x^3}\right)^{3/2}}{x^4} \, dx","Int[(a + b/x^3)^(3/2)/x^4,x]","-\frac{2 \left(a+\frac{b}{x^3}\right)^{5/2}}{15 b}","-\frac{2 \left(a+\frac{b}{x^3}\right)^{5/2}}{15 b}",1,"(-2*(a + b/x^3)^(5/2))/(15*b)","A",1,1,15,0.06667,1,"{261}"
2014,1,38,0,0.0226198,"\int \frac{\left(a+\frac{b}{x^3}\right)^{3/2}}{x^7} \, dx","Int[(a + b/x^3)^(3/2)/x^7,x]","\frac{2 a \left(a+\frac{b}{x^3}\right)^{5/2}}{15 b^2}-\frac{2 \left(a+\frac{b}{x^3}\right)^{7/2}}{21 b^2}","\frac{2 a \left(a+\frac{b}{x^3}\right)^{5/2}}{15 b^2}-\frac{2 \left(a+\frac{b}{x^3}\right)^{7/2}}{21 b^2}",1,"(2*a*(a + b/x^3)^(5/2))/(15*b^2) - (2*(a + b/x^3)^(7/2))/(21*b^2)","A",3,2,15,0.1333,1,"{266, 43}"
2015,1,59,0,0.0316208,"\int \frac{\left(a+\frac{b}{x^3}\right)^{3/2}}{x^{10}} \, dx","Int[(a + b/x^3)^(3/2)/x^10,x]","-\frac{2 a^2 \left(a+\frac{b}{x^3}\right)^{5/2}}{15 b^3}-\frac{2 \left(a+\frac{b}{x^3}\right)^{9/2}}{27 b^3}+\frac{4 a \left(a+\frac{b}{x^3}\right)^{7/2}}{21 b^3}","-\frac{2 a^2 \left(a+\frac{b}{x^3}\right)^{5/2}}{15 b^3}-\frac{2 \left(a+\frac{b}{x^3}\right)^{9/2}}{27 b^3}+\frac{4 a \left(a+\frac{b}{x^3}\right)^{7/2}}{21 b^3}",1,"(-2*a^2*(a + b/x^3)^(5/2))/(15*b^3) + (4*a*(a + b/x^3)^(7/2))/(21*b^3) - (2*(a + b/x^3)^(9/2))/(27*b^3)","A",3,2,15,0.1333,1,"{266, 43}"
2016,1,80,0,0.0417916,"\int \frac{\left(a+\frac{b}{x^3}\right)^{3/2}}{x^{13}} \, dx","Int[(a + b/x^3)^(3/2)/x^13,x]","-\frac{2 a^2 \left(a+\frac{b}{x^3}\right)^{7/2}}{7 b^4}+\frac{2 a^3 \left(a+\frac{b}{x^3}\right)^{5/2}}{15 b^4}-\frac{2 \left(a+\frac{b}{x^3}\right)^{11/2}}{33 b^4}+\frac{2 a \left(a+\frac{b}{x^3}\right)^{9/2}}{9 b^4}","-\frac{2 a^2 \left(a+\frac{b}{x^3}\right)^{7/2}}{7 b^4}+\frac{2 a^3 \left(a+\frac{b}{x^3}\right)^{5/2}}{15 b^4}-\frac{2 \left(a+\frac{b}{x^3}\right)^{11/2}}{33 b^4}+\frac{2 a \left(a+\frac{b}{x^3}\right)^{9/2}}{9 b^4}",1,"(2*a^3*(a + b/x^3)^(5/2))/(15*b^4) - (2*a^2*(a + b/x^3)^(7/2))/(7*b^4) + (2*a*(a + b/x^3)^(9/2))/(9*b^4) - (2*(a + b/x^3)^(11/2))/(33*b^4)","A",3,2,15,0.1333,1,"{266, 43}"
2017,1,74,0,0.0374576,"\int \frac{x^5}{\sqrt{a+\frac{b}{x^3}}} \, dx","Int[x^5/Sqrt[a + b/x^3],x]","\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^3}}}{\sqrt{a}}\right)}{4 a^{5/2}}-\frac{b x^3 \sqrt{a+\frac{b}{x^3}}}{4 a^2}+\frac{x^6 \sqrt{a+\frac{b}{x^3}}}{6 a}","\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^3}}}{\sqrt{a}}\right)}{4 a^{5/2}}-\frac{b x^3 \sqrt{a+\frac{b}{x^3}}}{4 a^2}+\frac{x^6 \sqrt{a+\frac{b}{x^3}}}{6 a}",1,"-(b*Sqrt[a + b/x^3]*x^3)/(4*a^2) + (Sqrt[a + b/x^3]*x^6)/(6*a) + (b^2*ArcTanh[Sqrt[a + b/x^3]/Sqrt[a]])/(4*a^(5/2))","A",5,4,15,0.2667,1,"{266, 51, 63, 208}"
2018,1,50,0,0.0257762,"\int \frac{x^2}{\sqrt{a+\frac{b}{x^3}}} \, dx","Int[x^2/Sqrt[a + b/x^3],x]","\frac{x^3 \sqrt{a+\frac{b}{x^3}}}{3 a}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^3}}}{\sqrt{a}}\right)}{3 a^{3/2}}","\frac{x^3 \sqrt{a+\frac{b}{x^3}}}{3 a}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^3}}}{\sqrt{a}}\right)}{3 a^{3/2}}",1,"(Sqrt[a + b/x^3]*x^3)/(3*a) - (b*ArcTanh[Sqrt[a + b/x^3]/Sqrt[a]])/(3*a^(3/2))","A",4,4,15,0.2667,1,"{266, 51, 63, 208}"
2019,1,27,0,0.0176971,"\int \frac{1}{\sqrt{a+\frac{b}{x^3}} x} \, dx","Int[1/(Sqrt[a + b/x^3]*x),x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^3}}}{\sqrt{a}}\right)}{3 \sqrt{a}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^3}}}{\sqrt{a}}\right)}{3 \sqrt{a}}",1,"(2*ArcTanh[Sqrt[a + b/x^3]/Sqrt[a]])/(3*Sqrt[a])","A",3,3,15,0.2000,1,"{266, 63, 208}"
2020,1,18,0,0.0058873,"\int \frac{1}{\sqrt{a+\frac{b}{x^3}} x^4} \, dx","Int[1/(Sqrt[a + b/x^3]*x^4),x]","-\frac{2 \sqrt{a+\frac{b}{x^3}}}{3 b}","-\frac{2 \sqrt{a+\frac{b}{x^3}}}{3 b}",1,"(-2*Sqrt[a + b/x^3])/(3*b)","A",1,1,15,0.06667,1,"{261}"
2021,1,38,0,0.0204016,"\int \frac{1}{\sqrt{a+\frac{b}{x^3}} x^7} \, dx","Int[1/(Sqrt[a + b/x^3]*x^7),x]","\frac{2 a \sqrt{a+\frac{b}{x^3}}}{3 b^2}-\frac{2 \left(a+\frac{b}{x^3}\right)^{3/2}}{9 b^2}","\frac{2 a \sqrt{a+\frac{b}{x^3}}}{3 b^2}-\frac{2 \left(a+\frac{b}{x^3}\right)^{3/2}}{9 b^2}",1,"(2*a*Sqrt[a + b/x^3])/(3*b^2) - (2*(a + b/x^3)^(3/2))/(9*b^2)","A",3,2,15,0.1333,1,"{266, 43}"
2022,1,59,0,0.030736,"\int \frac{1}{\sqrt{a+\frac{b}{x^3}} x^{10}} \, dx","Int[1/(Sqrt[a + b/x^3]*x^10),x]","-\frac{2 a^2 \sqrt{a+\frac{b}{x^3}}}{3 b^3}-\frac{2 \left(a+\frac{b}{x^3}\right)^{5/2}}{15 b^3}+\frac{4 a \left(a+\frac{b}{x^3}\right)^{3/2}}{9 b^3}","-\frac{2 a^2 \sqrt{a+\frac{b}{x^3}}}{3 b^3}-\frac{2 \left(a+\frac{b}{x^3}\right)^{5/2}}{15 b^3}+\frac{4 a \left(a+\frac{b}{x^3}\right)^{3/2}}{9 b^3}",1,"(-2*a^2*Sqrt[a + b/x^3])/(3*b^3) + (4*a*(a + b/x^3)^(3/2))/(9*b^3) - (2*(a + b/x^3)^(5/2))/(15*b^3)","A",3,2,15,0.1333,1,"{266, 43}"
2023,1,80,0,0.039535,"\int \frac{1}{\sqrt{a+\frac{b}{x^3}} x^{13}} \, dx","Int[1/(Sqrt[a + b/x^3]*x^13),x]","-\frac{2 a^2 \left(a+\frac{b}{x^3}\right)^{3/2}}{3 b^4}+\frac{2 a^3 \sqrt{a+\frac{b}{x^3}}}{3 b^4}-\frac{2 \left(a+\frac{b}{x^3}\right)^{7/2}}{21 b^4}+\frac{2 a \left(a+\frac{b}{x^3}\right)^{5/2}}{5 b^4}","-\frac{2 a^2 \left(a+\frac{b}{x^3}\right)^{3/2}}{3 b^4}+\frac{2 a^3 \sqrt{a+\frac{b}{x^3}}}{3 b^4}-\frac{2 \left(a+\frac{b}{x^3}\right)^{7/2}}{21 b^4}+\frac{2 a \left(a+\frac{b}{x^3}\right)^{5/2}}{5 b^4}",1,"(2*a^3*Sqrt[a + b/x^3])/(3*b^4) - (2*a^2*(a + b/x^3)^(3/2))/(3*b^4) + (2*a*(a + b/x^3)^(5/2))/(5*b^4) - (2*(a + b/x^3)^(7/2))/(21*b^4)","A",3,2,15,0.1333,1,"{266, 43}"
2024,1,294,0,0.1498895,"\int \frac{x^7}{\sqrt{a+\frac{b}{x^3}}} \, dx","Int[x^7/Sqrt[a + b/x^3],x]","\frac{91 b^2 x^2 \sqrt{a+\frac{b}{x^3}}}{320 a^3}+\frac{91 \sqrt{2+\sqrt{3}} b^{8/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{320 \sqrt[4]{3} a^3 \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}-\frac{13 b x^5 \sqrt{a+\frac{b}{x^3}}}{80 a^2}+\frac{x^8 \sqrt{a+\frac{b}{x^3}}}{8 a}","\frac{91 b^2 x^2 \sqrt{a+\frac{b}{x^3}}}{320 a^3}+\frac{91 \sqrt{2+\sqrt{3}} b^{8/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{320 \sqrt[4]{3} a^3 \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}-\frac{13 b x^5 \sqrt{a+\frac{b}{x^3}}}{80 a^2}+\frac{x^8 \sqrt{a+\frac{b}{x^3}}}{8 a}",1,"(91*b^2*Sqrt[a + b/x^3]*x^2)/(320*a^3) - (13*b*Sqrt[a + b/x^3]*x^5)/(80*a^2) + (Sqrt[a + b/x^3]*x^8)/(8*a) + (91*Sqrt[2 + Sqrt[3]]*b^(8/3)*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(320*3^(1/4)*a^3*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2])","A",5,3,15,0.2000,1,"{335, 325, 218}"
2025,1,270,0,0.1192664,"\int \frac{x^4}{\sqrt{a+\frac{b}{x^3}}} \, dx","Int[x^4/Sqrt[a + b/x^3],x]","-\frac{7 \sqrt{2+\sqrt{3}} b^{5/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{20 \sqrt[4]{3} a^2 \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}-\frac{7 b x^2 \sqrt{a+\frac{b}{x^3}}}{20 a^2}+\frac{x^5 \sqrt{a+\frac{b}{x^3}}}{5 a}","-\frac{7 \sqrt{2+\sqrt{3}} b^{5/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{20 \sqrt[4]{3} a^2 \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}-\frac{7 b x^2 \sqrt{a+\frac{b}{x^3}}}{20 a^2}+\frac{x^5 \sqrt{a+\frac{b}{x^3}}}{5 a}",1,"(-7*b*Sqrt[a + b/x^3]*x^2)/(20*a^2) + (Sqrt[a + b/x^3]*x^5)/(5*a) - (7*Sqrt[2 + Sqrt[3]]*b^(5/3)*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(20*3^(1/4)*a^2*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2])","A",4,3,15,0.2000,1,"{335, 325, 218}"
2026,1,248,0,0.0883975,"\int \frac{x}{\sqrt{a+\frac{b}{x^3}}} \, dx","Int[x/Sqrt[a + b/x^3],x]","\frac{\sqrt{2+\sqrt{3}} b^{2/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt[4]{3} a \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{x^2 \sqrt{a+\frac{b}{x^3}}}{2 a}","\frac{\sqrt{2+\sqrt{3}} b^{2/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt[4]{3} a \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{x^2 \sqrt{a+\frac{b}{x^3}}}{2 a}",1,"(Sqrt[a + b/x^3]*x^2)/(2*a) + (Sqrt[2 + Sqrt[3]]*b^(2/3)*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(2*3^(1/4)*a*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2])","A",3,3,13,0.2308,1,"{335, 325, 218}"
2027,1,221,0,0.0624405,"\int \frac{1}{\sqrt{a+\frac{b}{x^3}} x^2} \, dx","Int[1/(Sqrt[a + b/x^3]*x^2),x]","-\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt[3]{b} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}","-\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt[3]{b} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}",1,"(-2*Sqrt[2 + Sqrt[3]]*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(3^(1/4)*b^(1/3)*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2])","A",2,2,15,0.1333,1,"{335, 218}"
2028,1,246,0,0.0903064,"\int \frac{1}{\sqrt{a+\frac{b}{x^3}} x^5} \, dx","Int[1/(Sqrt[a + b/x^3]*x^5),x]","\frac{4 \sqrt{2+\sqrt{3}} a \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{5 \sqrt[4]{3} b^{4/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}-\frac{2 \sqrt{a+\frac{b}{x^3}}}{5 b x}","\frac{4 \sqrt{2+\sqrt{3}} a \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{5 \sqrt[4]{3} b^{4/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}-\frac{2 \sqrt{a+\frac{b}{x^3}}}{5 b x}",1,"(-2*Sqrt[a + b/x^3])/(5*b*x) + (4*Sqrt[2 + Sqrt[3]]*a*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(5*3^(1/4)*b^(4/3)*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2])","A",3,3,15,0.2000,1,"{335, 321, 218}"
2029,1,270,0,0.11993,"\int \frac{1}{\sqrt{a+\frac{b}{x^3}} x^8} \, dx","Int[1/(Sqrt[a + b/x^3]*x^8),x]","-\frac{32 \sqrt{2+\sqrt{3}} a^2 \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{55 \sqrt[4]{3} b^{7/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{16 a \sqrt{a+\frac{b}{x^3}}}{55 b^2 x}-\frac{2 \sqrt{a+\frac{b}{x^3}}}{11 b x^4}","-\frac{32 \sqrt{2+\sqrt{3}} a^2 \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{55 \sqrt[4]{3} b^{7/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{16 a \sqrt{a+\frac{b}{x^3}}}{55 b^2 x}-\frac{2 \sqrt{a+\frac{b}{x^3}}}{11 b x^4}",1,"(-2*Sqrt[a + b/x^3])/(11*b*x^4) + (16*a*Sqrt[a + b/x^3])/(55*b^2*x) - (32*Sqrt[2 + Sqrt[3]]*a^2*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(55*3^(1/4)*b^(7/3)*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2])","A",4,3,15,0.2000,1,"{335, 321, 218}"
2030,1,566,0,0.3432893,"\int \frac{x^6}{\sqrt{a+\frac{b}{x^3}}} \, dx","Int[x^6/Sqrt[a + b/x^3],x]","\frac{55 b^2 x \sqrt{a+\frac{b}{x^3}}}{112 a^3}-\frac{55 b^{7/3} \sqrt{a+\frac{b}{x^3}}}{112 a^3 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}-\frac{55 b^{7/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{56 \sqrt{2} \sqrt[4]{3} a^{8/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{55 \sqrt[4]{3} \sqrt{2-\sqrt{3}} b^{7/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{224 a^{8/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}-\frac{11 b x^4 \sqrt{a+\frac{b}{x^3}}}{56 a^2}+\frac{x^7 \sqrt{a+\frac{b}{x^3}}}{7 a}","\frac{55 b^2 x \sqrt{a+\frac{b}{x^3}}}{112 a^3}-\frac{55 b^{7/3} \sqrt{a+\frac{b}{x^3}}}{112 a^3 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}-\frac{55 b^{7/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{56 \sqrt{2} \sqrt[4]{3} a^{8/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{55 \sqrt[4]{3} \sqrt{2-\sqrt{3}} b^{7/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{224 a^{8/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}-\frac{11 b x^4 \sqrt{a+\frac{b}{x^3}}}{56 a^2}+\frac{x^7 \sqrt{a+\frac{b}{x^3}}}{7 a}",1,"(-55*b^(7/3)*Sqrt[a + b/x^3])/(112*a^3*((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)) + (55*b^2*Sqrt[a + b/x^3]*x)/(112*a^3) - (11*b*Sqrt[a + b/x^3]*x^4)/(56*a^2) + (Sqrt[a + b/x^3]*x^7)/(7*a) + (55*3^(1/4)*Sqrt[2 - Sqrt[3]]*b^(7/3)*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(224*a^(8/3)*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]) - (55*b^(7/3)*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(56*Sqrt[2]*3^(1/4)*a^(8/3)*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2])","A",7,5,15,0.3333,1,"{335, 325, 303, 218, 1877}"
2031,1,542,0,0.2864485,"\int \frac{x^3}{\sqrt{a+\frac{b}{x^3}}} \, dx","Int[x^3/Sqrt[a + b/x^3],x]","\frac{5 b^{4/3} \sqrt{a+\frac{b}{x^3}}}{8 a^2 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}+\frac{5 b^{4/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{4 \sqrt{2} \sqrt[4]{3} a^{5/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}-\frac{5 \sqrt[4]{3} \sqrt{2-\sqrt{3}} b^{4/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{16 a^{5/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}-\frac{5 b x \sqrt{a+\frac{b}{x^3}}}{8 a^2}+\frac{x^4 \sqrt{a+\frac{b}{x^3}}}{4 a}","\frac{5 b^{4/3} \sqrt{a+\frac{b}{x^3}}}{8 a^2 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}+\frac{5 b^{4/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{4 \sqrt{2} \sqrt[4]{3} a^{5/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}-\frac{5 \sqrt[4]{3} \sqrt{2-\sqrt{3}} b^{4/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{16 a^{5/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}-\frac{5 b x \sqrt{a+\frac{b}{x^3}}}{8 a^2}+\frac{x^4 \sqrt{a+\frac{b}{x^3}}}{4 a}",1,"(5*b^(4/3)*Sqrt[a + b/x^3])/(8*a^2*((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)) - (5*b*Sqrt[a + b/x^3]*x)/(8*a^2) + (Sqrt[a + b/x^3]*x^4)/(4*a) - (5*3^(1/4)*Sqrt[2 - Sqrt[3]]*b^(4/3)*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(16*a^(5/3)*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]) + (5*b^(4/3)*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(4*Sqrt[2]*3^(1/4)*a^(5/3)*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2])","A",6,5,15,0.3333,1,"{335, 325, 303, 218, 1877}"
2032,1,513,0,0.227033,"\int \frac{1}{\sqrt{a+\frac{b}{x^3}}} \, dx","Int[1/Sqrt[a + b/x^3],x]","-\frac{\sqrt{2} \sqrt[3]{b} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} a^{2/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{b} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{2 a^{2/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{x \sqrt{a+\frac{b}{x^3}}}{a}-\frac{\sqrt[3]{b} \sqrt{a+\frac{b}{x^3}}}{a \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}","-\frac{\sqrt{2} \sqrt[3]{b} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} a^{2/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{b} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{2 a^{2/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{x \sqrt{a+\frac{b}{x^3}}}{a}-\frac{\sqrt[3]{b} \sqrt{a+\frac{b}{x^3}}}{a \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}",1,"-((b^(1/3)*Sqrt[a + b/x^3])/(a*((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x))) + (Sqrt[a + b/x^3]*x)/a + (3^(1/4)*Sqrt[2 - Sqrt[3]]*b^(1/3)*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(2*a^(2/3)*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]) - (Sqrt[2]*b^(1/3)*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(3^(1/4)*a^(2/3)*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2])","A",5,5,11,0.4545,1,"{242, 325, 303, 218, 1877}"
2033,1,491,0,0.1923574,"\int \frac{1}{\sqrt{a+\frac{b}{x^3}} x^3} \, dx","Int[1/(Sqrt[a + b/x^3]*x^3),x]","-\frac{2 \sqrt{2} \sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} b^{2/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{b^{2/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}-\frac{2 \sqrt{a+\frac{b}{x^3}}}{b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}","-\frac{2 \sqrt{2} \sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} b^{2/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{b^{2/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}-\frac{2 \sqrt{a+\frac{b}{x^3}}}{b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}",1,"(-2*Sqrt[a + b/x^3])/(b^(2/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)) + (3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(1/3)*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(b^(2/3)*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]) - (2*Sqrt[2]*a^(1/3)*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(3^(1/4)*b^(2/3)*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2])","A",4,4,15,0.2667,1,"{335, 303, 218, 1877}"
2034,1,520,0,0.2370672,"\int \frac{1}{\sqrt{a+\frac{b}{x^3}} x^6} \, dx","Int[1/(Sqrt[a + b/x^3]*x^6),x]","\frac{8 \sqrt{2} a^{4/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{7 \sqrt[4]{3} b^{5/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}-\frac{4 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{4/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{7 b^{5/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{8 a \sqrt{a+\frac{b}{x^3}}}{7 b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}-\frac{2 \sqrt{a+\frac{b}{x^3}}}{7 b x^2}","\frac{8 \sqrt{2} a^{4/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{7 \sqrt[4]{3} b^{5/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}-\frac{4 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{4/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{7 b^{5/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{8 a \sqrt{a+\frac{b}{x^3}}}{7 b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}-\frac{2 \sqrt{a+\frac{b}{x^3}}}{7 b x^2}",1,"(8*a*Sqrt[a + b/x^3])/(7*b^(5/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)) - (2*Sqrt[a + b/x^3])/(7*b*x^2) - (4*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(4/3)*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(7*b^(5/3)*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]) + (8*Sqrt[2]*a^(4/3)*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(7*3^(1/4)*b^(5/3)*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2])","A",5,5,15,0.3333,1,"{335, 321, 303, 218, 1877}"
2035,1,544,0,0.2950517,"\int \frac{1}{\sqrt{a+\frac{b}{x^3}} x^9} \, dx","Int[1/(Sqrt[a + b/x^3]*x^9),x]","-\frac{80 a^2 \sqrt{a+\frac{b}{x^3}}}{91 b^{8/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}-\frac{80 \sqrt{2} a^{7/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{91 \sqrt[4]{3} b^{8/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{40 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{7/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{91 b^{8/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{20 a \sqrt{a+\frac{b}{x^3}}}{91 b^2 x^2}-\frac{2 \sqrt{a+\frac{b}{x^3}}}{13 b x^5}","-\frac{80 a^2 \sqrt{a+\frac{b}{x^3}}}{91 b^{8/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}-\frac{80 \sqrt{2} a^{7/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{91 \sqrt[4]{3} b^{8/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{40 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{7/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{91 b^{8/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{20 a \sqrt{a+\frac{b}{x^3}}}{91 b^2 x^2}-\frac{2 \sqrt{a+\frac{b}{x^3}}}{13 b x^5}",1,"(-80*a^2*Sqrt[a + b/x^3])/(91*b^(8/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)) - (2*Sqrt[a + b/x^3])/(13*b*x^5) + (20*a*Sqrt[a + b/x^3])/(91*b^2*x^2) + (40*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(7/3)*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(91*b^(8/3)*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]) - (80*Sqrt[2]*a^(7/3)*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(91*3^(1/4)*b^(8/3)*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2])","A",6,5,15,0.3333,1,"{335, 321, 303, 218, 1877}"
2036,1,568,0,0.3485492,"\int \frac{1}{\sqrt{a+\frac{b}{x^3}} x^{12}} \, dx","Int[1/(Sqrt[a + b/x^3]*x^12),x]","\frac{1280 a^3 \sqrt{a+\frac{b}{x^3}}}{1729 b^{11/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}-\frac{320 a^2 \sqrt{a+\frac{b}{x^3}}}{1729 b^3 x^2}+\frac{1280 \sqrt{2} a^{10/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{1729 \sqrt[4]{3} b^{11/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}-\frac{640 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{10/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{1729 b^{11/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{32 a \sqrt{a+\frac{b}{x^3}}}{247 b^2 x^5}-\frac{2 \sqrt{a+\frac{b}{x^3}}}{19 b x^8}","\frac{1280 a^3 \sqrt{a+\frac{b}{x^3}}}{1729 b^{11/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}-\frac{320 a^2 \sqrt{a+\frac{b}{x^3}}}{1729 b^3 x^2}+\frac{1280 \sqrt{2} a^{10/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{1729 \sqrt[4]{3} b^{11/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}-\frac{640 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{10/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{1729 b^{11/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{32 a \sqrt{a+\frac{b}{x^3}}}{247 b^2 x^5}-\frac{2 \sqrt{a+\frac{b}{x^3}}}{19 b x^8}",1,"(1280*a^3*Sqrt[a + b/x^3])/(1729*b^(11/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)) - (2*Sqrt[a + b/x^3])/(19*b*x^8) + (32*a*Sqrt[a + b/x^3])/(247*b^2*x^5) - (320*a^2*Sqrt[a + b/x^3])/(1729*b^3*x^2) - (640*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(10/3)*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(1729*b^(11/3)*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]) + (1280*Sqrt[2]*a^(10/3)*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(1729*3^(1/4)*b^(11/3)*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2])","A",7,5,15,0.3333,1,"{335, 321, 303, 218, 1877}"
2037,1,95,0,0.046514,"\int \frac{x^5}{\left(a+\frac{b}{x^3}\right)^{3/2}} \, dx","Int[x^5/(a + b/x^3)^(3/2),x]","\frac{5 b^2 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^3}}}{\sqrt{a}}\right)}{4 a^{7/2}}+\frac{5 x^6 \sqrt{a+\frac{b}{x^3}}}{6 a^2}-\frac{5 b x^3 \sqrt{a+\frac{b}{x^3}}}{4 a^3}-\frac{2 x^6}{3 a \sqrt{a+\frac{b}{x^3}}}","-\frac{5 b^2}{4 a^3 \sqrt{a+\frac{b}{x^3}}}+\frac{5 b^2 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^3}}}{\sqrt{a}}\right)}{4 a^{7/2}}-\frac{5 b x^3}{12 a^2 \sqrt{a+\frac{b}{x^3}}}+\frac{x^6}{6 a \sqrt{a+\frac{b}{x^3}}}",1,"(-5*b*Sqrt[a + b/x^3]*x^3)/(4*a^3) - (2*x^6)/(3*a*Sqrt[a + b/x^3]) + (5*Sqrt[a + b/x^3]*x^6)/(6*a^2) + (5*b^2*ArcTanh[Sqrt[a + b/x^3]/Sqrt[a]])/(4*a^(7/2))","A",6,4,15,0.2667,1,"{266, 51, 63, 208}"
2038,1,66,0,0.0348064,"\int \frac{x^2}{\left(a+\frac{b}{x^3}\right)^{3/2}} \, dx","Int[x^2/(a + b/x^3)^(3/2),x]","\frac{x^3 \sqrt{a+\frac{b}{x^3}}}{a^2}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^3}}}{\sqrt{a}}\right)}{a^{5/2}}-\frac{2 x^3}{3 a \sqrt{a+\frac{b}{x^3}}}","\frac{b}{a^2 \sqrt{a+\frac{b}{x^3}}}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^3}}}{\sqrt{a}}\right)}{a^{5/2}}+\frac{x^3}{3 a \sqrt{a+\frac{b}{x^3}}}",1,"(-2*x^3)/(3*a*Sqrt[a + b/x^3]) + (Sqrt[a + b/x^3]*x^3)/a^2 - (b*ArcTanh[Sqrt[a + b/x^3]/Sqrt[a]])/a^(5/2)","A",5,4,15,0.2667,1,"{266, 51, 63, 208}"
2039,1,46,0,0.0245763,"\int \frac{1}{\left(a+\frac{b}{x^3}\right)^{3/2} x} \, dx","Int[1/((a + b/x^3)^(3/2)*x),x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^3}}}{\sqrt{a}}\right)}{3 a^{3/2}}-\frac{2}{3 a \sqrt{a+\frac{b}{x^3}}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^3}}}{\sqrt{a}}\right)}{3 a^{3/2}}-\frac{2}{3 a \sqrt{a+\frac{b}{x^3}}}",1,"-2/(3*a*Sqrt[a + b/x^3]) + (2*ArcTanh[Sqrt[a + b/x^3]/Sqrt[a]])/(3*a^(3/2))","A",4,4,15,0.2667,1,"{266, 51, 63, 208}"
2040,1,18,0,0.0063507,"\int \frac{1}{\left(a+\frac{b}{x^3}\right)^{3/2} x^4} \, dx","Int[1/((a + b/x^3)^(3/2)*x^4),x]","\frac{2}{3 b \sqrt{a+\frac{b}{x^3}}}","\frac{2}{3 b \sqrt{a+\frac{b}{x^3}}}",1,"2/(3*b*Sqrt[a + b/x^3])","A",1,1,15,0.06667,1,"{261}"
2041,1,38,0,0.0209723,"\int \frac{1}{\left(a+\frac{b}{x^3}\right)^{3/2} x^7} \, dx","Int[1/((a + b/x^3)^(3/2)*x^7),x]","-\frac{2 a}{3 b^2 \sqrt{a+\frac{b}{x^3}}}-\frac{2 \sqrt{a+\frac{b}{x^3}}}{3 b^2}","-\frac{2 a}{3 b^2 \sqrt{a+\frac{b}{x^3}}}-\frac{2 \sqrt{a+\frac{b}{x^3}}}{3 b^2}",1,"(-2*a)/(3*b^2*Sqrt[a + b/x^3]) - (2*Sqrt[a + b/x^3])/(3*b^2)","A",3,2,15,0.1333,1,"{266, 43}"
2042,1,59,0,0.0309743,"\int \frac{1}{\left(a+\frac{b}{x^3}\right)^{3/2} x^{10}} \, dx","Int[1/((a + b/x^3)^(3/2)*x^10),x]","\frac{2 a^2}{3 b^3 \sqrt{a+\frac{b}{x^3}}}+\frac{4 a \sqrt{a+\frac{b}{x^3}}}{3 b^3}-\frac{2 \left(a+\frac{b}{x^3}\right)^{3/2}}{9 b^3}","\frac{2 a^2}{3 b^3 \sqrt{a+\frac{b}{x^3}}}+\frac{4 a \sqrt{a+\frac{b}{x^3}}}{3 b^3}-\frac{2 \left(a+\frac{b}{x^3}\right)^{3/2}}{9 b^3}",1,"(2*a^2)/(3*b^3*Sqrt[a + b/x^3]) + (4*a*Sqrt[a + b/x^3])/(3*b^3) - (2*(a + b/x^3)^(3/2))/(9*b^3)","A",3,2,15,0.1333,1,"{266, 43}"
2043,1,78,0,0.0400413,"\int \frac{1}{\left(a+\frac{b}{x^3}\right)^{3/2} x^{13}} \, dx","Int[1/((a + b/x^3)^(3/2)*x^13),x]","-\frac{2 a^3}{3 b^4 \sqrt{a+\frac{b}{x^3}}}-\frac{2 a^2 \sqrt{a+\frac{b}{x^3}}}{b^4}+\frac{2 a \left(a+\frac{b}{x^3}\right)^{3/2}}{3 b^4}-\frac{2 \left(a+\frac{b}{x^3}\right)^{5/2}}{15 b^4}","-\frac{2 a^3}{3 b^4 \sqrt{a+\frac{b}{x^3}}}-\frac{2 a^2 \sqrt{a+\frac{b}{x^3}}}{b^4}+\frac{2 a \left(a+\frac{b}{x^3}\right)^{3/2}}{3 b^4}-\frac{2 \left(a+\frac{b}{x^3}\right)^{5/2}}{15 b^4}",1,"(-2*a^3)/(3*b^4*Sqrt[a + b/x^3]) - (2*a^2*Sqrt[a + b/x^3])/b^4 + (2*a*(a + b/x^3)^(3/2))/(3*b^4) - (2*(a + b/x^3)^(5/2))/(15*b^4)","A",3,2,15,0.1333,1,"{266, 43}"
2044,1,315,0,0.180317,"\int \frac{x^7}{\left(a+\frac{b}{x^3}\right)^{3/2}} \, dx","Int[x^7/(a + b/x^3)^(3/2),x]","\frac{1729 b^2 x^2 \sqrt{a+\frac{b}{x^3}}}{960 a^4}+\frac{1729 \sqrt{2+\sqrt{3}} b^{8/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{960 \sqrt[4]{3} a^4 \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{19 x^8 \sqrt{a+\frac{b}{x^3}}}{24 a^2}-\frac{247 b x^5 \sqrt{a+\frac{b}{x^3}}}{240 a^3}-\frac{2 x^8}{3 a \sqrt{a+\frac{b}{x^3}}}","\frac{1729 b^2 x^2 \sqrt{a+\frac{b}{x^3}}}{960 a^4}+\frac{1729 \sqrt{2+\sqrt{3}} b^{8/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{960 \sqrt[4]{3} a^4 \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{19 x^8 \sqrt{a+\frac{b}{x^3}}}{24 a^2}-\frac{247 b x^5 \sqrt{a+\frac{b}{x^3}}}{240 a^3}-\frac{2 x^8}{3 a \sqrt{a+\frac{b}{x^3}}}",1,"(1729*b^2*Sqrt[a + b/x^3]*x^2)/(960*a^4) - (247*b*Sqrt[a + b/x^3]*x^5)/(240*a^3) - (2*x^8)/(3*a*Sqrt[a + b/x^3]) + (19*Sqrt[a + b/x^3]*x^8)/(24*a^2) + (1729*Sqrt[2 + Sqrt[3]]*b^(8/3)*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(960*3^(1/4)*a^4*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2])","A",6,4,15,0.2667,1,"{335, 290, 325, 218}"
2045,1,291,0,0.1451559,"\int \frac{x^4}{\left(a+\frac{b}{x^3}\right)^{3/2}} \, dx","Int[x^4/(a + b/x^3)^(3/2),x]","-\frac{91 \sqrt{2+\sqrt{3}} b^{5/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{60 \sqrt[4]{3} a^3 \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{13 x^5 \sqrt{a+\frac{b}{x^3}}}{15 a^2}-\frac{91 b x^2 \sqrt{a+\frac{b}{x^3}}}{60 a^3}-\frac{2 x^5}{3 a \sqrt{a+\frac{b}{x^3}}}","-\frac{91 \sqrt{2+\sqrt{3}} b^{5/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{60 \sqrt[4]{3} a^3 \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{13 x^5 \sqrt{a+\frac{b}{x^3}}}{15 a^2}-\frac{91 b x^2 \sqrt{a+\frac{b}{x^3}}}{60 a^3}-\frac{2 x^5}{3 a \sqrt{a+\frac{b}{x^3}}}",1,"(-91*b*Sqrt[a + b/x^3]*x^2)/(60*a^3) - (2*x^5)/(3*a*Sqrt[a + b/x^3]) + (13*Sqrt[a + b/x^3]*x^5)/(15*a^2) - (91*Sqrt[2 + Sqrt[3]]*b^(5/3)*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(60*3^(1/4)*a^3*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2])","A",5,4,15,0.2667,1,"{335, 290, 325, 218}"
2046,1,269,0,0.1147129,"\int \frac{x}{\left(a+\frac{b}{x^3}\right)^{3/2}} \, dx","Int[x/(a + b/x^3)^(3/2),x]","\frac{7 \sqrt{2+\sqrt{3}} b^{2/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{6 \sqrt[4]{3} a^2 \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{7 x^2 \sqrt{a+\frac{b}{x^3}}}{6 a^2}-\frac{2 x^2}{3 a \sqrt{a+\frac{b}{x^3}}}","\frac{7 \sqrt{2+\sqrt{3}} b^{2/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{6 \sqrt[4]{3} a^2 \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{7 x^2 \sqrt{a+\frac{b}{x^3}}}{6 a^2}-\frac{2 x^2}{3 a \sqrt{a+\frac{b}{x^3}}}",1,"(-2*x^2)/(3*a*Sqrt[a + b/x^3]) + (7*Sqrt[a + b/x^3]*x^2)/(6*a^2) + (7*Sqrt[2 + Sqrt[3]]*b^(2/3)*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(6*3^(1/4)*a^2*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2])","A",4,4,13,0.3077,1,"{335, 290, 325, 218}"
2047,1,248,0,0.0880958,"\int \frac{1}{\left(a+\frac{b}{x^3}\right)^{3/2} x^2} \, dx","Int[1/((a + b/x^3)^(3/2)*x^2),x]","-\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} a \sqrt[3]{b} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}-\frac{2}{3 a x \sqrt{a+\frac{b}{x^3}}}","-\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} a \sqrt[3]{b} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}-\frac{2}{3 a x \sqrt{a+\frac{b}{x^3}}}",1,"-2/(3*a*Sqrt[a + b/x^3]*x) - (2*Sqrt[2 + Sqrt[3]]*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*a*b^(1/3)*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2])","A",3,3,15,0.2000,1,"{335, 199, 218}"
2048,1,245,0,0.0870381,"\int \frac{1}{\left(a+\frac{b}{x^3}\right)^{3/2} x^5} \, dx","Int[1/((a + b/x^3)^(3/2)*x^5),x]","\frac{2}{3 b x \sqrt{a+\frac{b}{x^3}}}-\frac{4 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} b^{4/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}","\frac{2}{3 b x \sqrt{a+\frac{b}{x^3}}}-\frac{4 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} b^{4/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}",1,"2/(3*b*Sqrt[a + b/x^3]*x) - (4*Sqrt[2 + Sqrt[3]]*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*b^(4/3)*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2])","A",3,3,15,0.2000,1,"{335, 288, 218}"
2049,1,267,0,0.1214717,"\int \frac{1}{\left(a+\frac{b}{x^3}\right)^{3/2} x^8} \, dx","Int[1/((a + b/x^3)^(3/2)*x^8),x]","\frac{32 \sqrt{2+\sqrt{3}} a \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{15 \sqrt[4]{3} b^{7/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}-\frac{16 \sqrt{a+\frac{b}{x^3}}}{15 b^2 x}+\frac{2}{3 b x^4 \sqrt{a+\frac{b}{x^3}}}","\frac{32 \sqrt{2+\sqrt{3}} a \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{15 \sqrt[4]{3} b^{7/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}-\frac{16 \sqrt{a+\frac{b}{x^3}}}{15 b^2 x}+\frac{2}{3 b x^4 \sqrt{a+\frac{b}{x^3}}}",1,"2/(3*b*Sqrt[a + b/x^3]*x^4) - (16*Sqrt[a + b/x^3])/(15*b^2*x) + (32*Sqrt[2 + Sqrt[3]]*a*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(15*3^(1/4)*b^(7/3)*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2])","A",4,4,15,0.2667,1,"{335, 288, 321, 218}"
2050,1,587,0,0.3935503,"\int \frac{x^6}{\left(a+\frac{b}{x^3}\right)^{3/2}} \, dx","Int[x^6/(a + b/x^3)^(3/2),x]","\frac{935 b^2 x \sqrt{a+\frac{b}{x^3}}}{336 a^4}-\frac{935 b^{7/3} \sqrt{a+\frac{b}{x^3}}}{336 a^4 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}-\frac{935 b^{7/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{168 \sqrt{2} \sqrt[4]{3} a^{11/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{935 \sqrt{2-\sqrt{3}} b^{7/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{224\ 3^{3/4} a^{11/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{17 x^7 \sqrt{a+\frac{b}{x^3}}}{21 a^2}-\frac{187 b x^4 \sqrt{a+\frac{b}{x^3}}}{168 a^3}-\frac{2 x^7}{3 a \sqrt{a+\frac{b}{x^3}}}","\frac{935 b^2 x \sqrt{a+\frac{b}{x^3}}}{336 a^4}-\frac{935 b^{7/3} \sqrt{a+\frac{b}{x^3}}}{336 a^4 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}-\frac{935 b^{7/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{168 \sqrt{2} \sqrt[4]{3} a^{11/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{935 \sqrt{2-\sqrt{3}} b^{7/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{224\ 3^{3/4} a^{11/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{17 x^7 \sqrt{a+\frac{b}{x^3}}}{21 a^2}-\frac{187 b x^4 \sqrt{a+\frac{b}{x^3}}}{168 a^3}-\frac{2 x^7}{3 a \sqrt{a+\frac{b}{x^3}}}",1,"(-935*b^(7/3)*Sqrt[a + b/x^3])/(336*a^4*((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)) + (935*b^2*Sqrt[a + b/x^3]*x)/(336*a^4) - (187*b*Sqrt[a + b/x^3]*x^4)/(168*a^3) - (2*x^7)/(3*a*Sqrt[a + b/x^3]) + (17*Sqrt[a + b/x^3]*x^7)/(21*a^2) + (935*Sqrt[2 - Sqrt[3]]*b^(7/3)*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(224*3^(3/4)*a^(11/3)*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]) - (935*b^(7/3)*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(168*Sqrt[2]*3^(1/4)*a^(11/3)*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2])","A",8,6,15,0.4000,1,"{335, 290, 325, 303, 218, 1877}"
2051,1,563,0,0.3365453,"\int \frac{x^3}{\left(a+\frac{b}{x^3}\right)^{3/2}} \, dx","Int[x^3/(a + b/x^3)^(3/2),x]","\frac{55 b^{4/3} \sqrt{a+\frac{b}{x^3}}}{24 a^3 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}+\frac{55 b^{4/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{12 \sqrt{2} \sqrt[4]{3} a^{8/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}-\frac{55 \sqrt{2-\sqrt{3}} b^{4/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{16\ 3^{3/4} a^{8/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{11 x^4 \sqrt{a+\frac{b}{x^3}}}{12 a^2}-\frac{55 b x \sqrt{a+\frac{b}{x^3}}}{24 a^3}-\frac{2 x^4}{3 a \sqrt{a+\frac{b}{x^3}}}","\frac{55 b^{4/3} \sqrt{a+\frac{b}{x^3}}}{24 a^3 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}+\frac{55 b^{4/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{12 \sqrt{2} \sqrt[4]{3} a^{8/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}-\frac{55 \sqrt{2-\sqrt{3}} b^{4/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{16\ 3^{3/4} a^{8/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{11 x^4 \sqrt{a+\frac{b}{x^3}}}{12 a^2}-\frac{55 b x \sqrt{a+\frac{b}{x^3}}}{24 a^3}-\frac{2 x^4}{3 a \sqrt{a+\frac{b}{x^3}}}",1,"(55*b^(4/3)*Sqrt[a + b/x^3])/(24*a^3*((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)) - (55*b*Sqrt[a + b/x^3]*x)/(24*a^3) - (2*x^4)/(3*a*Sqrt[a + b/x^3]) + (11*Sqrt[a + b/x^3]*x^4)/(12*a^2) - (55*Sqrt[2 - Sqrt[3]]*b^(4/3)*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(16*3^(3/4)*a^(8/3)*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]) + (55*b^(4/3)*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(12*Sqrt[2]*3^(1/4)*a^(8/3)*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2])","A",7,6,15,0.4000,1,"{335, 290, 325, 303, 218, 1877}"
2052,1,539,0,0.2830322,"\int \frac{1}{\left(a+\frac{b}{x^3}\right)^{3/2}} \, dx","Int[(a + b/x^3)^(-3/2),x]","-\frac{5 \sqrt{2} \sqrt[3]{b} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} a^{5/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{5 \sqrt{2-\sqrt{3}} \sqrt[3]{b} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{2\ 3^{3/4} a^{5/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{5 x \sqrt{a+\frac{b}{x^3}}}{3 a^2}-\frac{5 \sqrt[3]{b} \sqrt{a+\frac{b}{x^3}}}{3 a^2 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}-\frac{2 x}{3 a \sqrt{a+\frac{b}{x^3}}}","-\frac{5 \sqrt{2} \sqrt[3]{b} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} a^{5/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{5 \sqrt{2-\sqrt{3}} \sqrt[3]{b} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{2\ 3^{3/4} a^{5/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{5 x \sqrt{a+\frac{b}{x^3}}}{3 a^2}-\frac{5 \sqrt[3]{b} \sqrt{a+\frac{b}{x^3}}}{3 a^2 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}-\frac{2 x}{3 a \sqrt{a+\frac{b}{x^3}}}",1,"(-5*b^(1/3)*Sqrt[a + b/x^3])/(3*a^2*((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)) - (2*x)/(3*a*Sqrt[a + b/x^3]) + (5*Sqrt[a + b/x^3]*x)/(3*a^2) + (5*Sqrt[2 - Sqrt[3]]*b^(1/3)*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(2*3^(3/4)*a^(5/3)*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]) - (5*Sqrt[2]*b^(1/3)*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*a^(5/3)*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2])","A",6,6,11,0.5455,1,"{242, 290, 325, 303, 218, 1877}"
2053,1,520,0,0.2384761,"\int \frac{1}{\left(a+\frac{b}{x^3}\right)^{3/2} x^3} \, dx","Int[1/((a + b/x^3)^(3/2)*x^3),x]","\frac{2 \sqrt{2} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} a^{2/3} b^{2/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}-\frac{\sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{3^{3/4} a^{2/3} b^{2/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{2 \sqrt{a+\frac{b}{x^3}}}{3 a b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}-\frac{2}{3 a x^2 \sqrt{a+\frac{b}{x^3}}}","\frac{2 \sqrt{2} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} a^{2/3} b^{2/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}-\frac{\sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{3^{3/4} a^{2/3} b^{2/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{2 \sqrt{a+\frac{b}{x^3}}}{3 a b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}-\frac{2}{3 a x^2 \sqrt{a+\frac{b}{x^3}}}",1,"(2*Sqrt[a + b/x^3])/(3*a*b^(2/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)) - 2/(3*a*Sqrt[a + b/x^3]*x^2) - (Sqrt[2 - Sqrt[3]]*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(3^(3/4)*a^(2/3)*b^(2/3)*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]) + (2*Sqrt[2]*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*a^(2/3)*b^(2/3)*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2])","A",5,5,15,0.3333,1,"{335, 290, 303, 218, 1877}"
2054,1,517,0,0.2372021,"\int \frac{1}{\left(a+\frac{b}{x^3}\right)^{3/2} x^6} \, dx","Int[1/((a + b/x^3)^(3/2)*x^6),x]","-\frac{8 \sqrt{2} \sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} b^{5/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{4 \sqrt{2-\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{3^{3/4} b^{5/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}-\frac{8 \sqrt{a+\frac{b}{x^3}}}{3 b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}+\frac{2}{3 b x^2 \sqrt{a+\frac{b}{x^3}}}","-\frac{8 \sqrt{2} \sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} b^{5/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{4 \sqrt{2-\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{3^{3/4} b^{5/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}-\frac{8 \sqrt{a+\frac{b}{x^3}}}{3 b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}+\frac{2}{3 b x^2 \sqrt{a+\frac{b}{x^3}}}",1,"(-8*Sqrt[a + b/x^3])/(3*b^(5/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)) + 2/(3*b*Sqrt[a + b/x^3]*x^2) + (4*Sqrt[2 - Sqrt[3]]*a^(1/3)*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(3^(3/4)*b^(5/3)*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]) - (8*Sqrt[2]*a^(1/3)*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*b^(5/3)*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2])","A",5,5,15,0.3333,1,"{335, 288, 303, 218, 1877}"
2055,1,541,0,0.2939608,"\int \frac{1}{\left(a+\frac{b}{x^3}\right)^{3/2} x^9} \, dx","Int[1/((a + b/x^3)^(3/2)*x^9),x]","\frac{80 \sqrt{2} a^{4/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{21 \sqrt[4]{3} b^{8/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}-\frac{40 \sqrt{2-\sqrt{3}} a^{4/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{7\ 3^{3/4} b^{8/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{80 a \sqrt{a+\frac{b}{x^3}}}{21 b^{8/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}-\frac{20 \sqrt{a+\frac{b}{x^3}}}{21 b^2 x^2}+\frac{2}{3 b x^5 \sqrt{a+\frac{b}{x^3}}}","\frac{80 \sqrt{2} a^{4/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{21 \sqrt[4]{3} b^{8/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}-\frac{40 \sqrt{2-\sqrt{3}} a^{4/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{7\ 3^{3/4} b^{8/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{80 a \sqrt{a+\frac{b}{x^3}}}{21 b^{8/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}-\frac{20 \sqrt{a+\frac{b}{x^3}}}{21 b^2 x^2}+\frac{2}{3 b x^5 \sqrt{a+\frac{b}{x^3}}}",1,"(80*a*Sqrt[a + b/x^3])/(21*b^(8/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)) + 2/(3*b*Sqrt[a + b/x^3]*x^5) - (20*Sqrt[a + b/x^3])/(21*b^2*x^2) - (40*Sqrt[2 - Sqrt[3]]*a^(4/3)*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(7*3^(3/4)*b^(8/3)*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]) + (80*Sqrt[2]*a^(4/3)*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(21*3^(1/4)*b^(8/3)*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2])","A",6,6,15,0.4000,1,"{335, 288, 321, 303, 218, 1877}"
2056,1,565,0,0.3444792,"\int \frac{1}{\left(a+\frac{b}{x^3}\right)^{3/2} x^{12}} \, dx","Int[1/((a + b/x^3)^(3/2)*x^12),x]","-\frac{1280 a^2 \sqrt{a+\frac{b}{x^3}}}{273 b^{11/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}-\frac{1280 \sqrt{2} a^{7/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{273 \sqrt[4]{3} b^{11/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{640 \sqrt{2-\sqrt{3}} a^{7/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{91\ 3^{3/4} b^{11/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{320 a \sqrt{a+\frac{b}{x^3}}}{273 b^3 x^2}-\frac{32 \sqrt{a+\frac{b}{x^3}}}{39 b^2 x^5}+\frac{2}{3 b x^8 \sqrt{a+\frac{b}{x^3}}}","-\frac{1280 a^2 \sqrt{a+\frac{b}{x^3}}}{273 b^{11/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}-\frac{1280 \sqrt{2} a^{7/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{273 \sqrt[4]{3} b^{11/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{640 \sqrt{2-\sqrt{3}} a^{7/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b}}{x}+\frac{b^{2/3}}{x^2}}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}}\right)|-7-4 \sqrt{3}\right)}{91\ 3^{3/4} b^{11/3} \sqrt{a+\frac{b}{x^3}} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b}}{x}\right)^2}}}+\frac{320 a \sqrt{a+\frac{b}{x^3}}}{273 b^3 x^2}-\frac{32 \sqrt{a+\frac{b}{x^3}}}{39 b^2 x^5}+\frac{2}{3 b x^8 \sqrt{a+\frac{b}{x^3}}}",1,"(-1280*a^2*Sqrt[a + b/x^3])/(273*b^(11/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)) + 2/(3*b*Sqrt[a + b/x^3]*x^8) - (32*Sqrt[a + b/x^3])/(39*b^2*x^5) + (320*a*Sqrt[a + b/x^3])/(273*b^3*x^2) + (640*Sqrt[2 - Sqrt[3]]*a^(7/3)*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(91*3^(3/4)*b^(11/3)*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]) - (1280*Sqrt[2]*a^(7/3)*(a^(1/3) + b^(1/3)/x)*Sqrt[(a^(2/3) + b^(2/3)/x^2 - (a^(1/3)*b^(1/3))/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)/x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)], -7 - 4*Sqrt[3]])/(273*3^(1/4)*b^(11/3)*Sqrt[a + b/x^3]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)/x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)/x)^2])","A",7,6,15,0.4000,1,"{335, 288, 321, 303, 218, 1877}"
2057,1,190,0,0.1323123,"\int \frac{1}{a+\frac{b}{x^4}} \, dx","Int[(a + b/x^4)^(-1),x]","\frac{\sqrt[4]{b} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a} x^2+\sqrt{b}\right)}{4 \sqrt{2} a^{5/4}}-\frac{\sqrt[4]{b} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a} x^2+\sqrt{b}\right)}{4 \sqrt{2} a^{5/4}}+\frac{\sqrt[4]{b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a} x}{\sqrt[4]{b}}\right)}{2 \sqrt{2} a^{5/4}}-\frac{\sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} x}{\sqrt[4]{b}}+1\right)}{2 \sqrt{2} a^{5/4}}+\frac{x}{a}","\frac{\sqrt[4]{b} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a} x^2+\sqrt{b}\right)}{4 \sqrt{2} a^{5/4}}-\frac{\sqrt[4]{b} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a} x^2+\sqrt{b}\right)}{4 \sqrt{2} a^{5/4}}+\frac{\sqrt[4]{b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a} x}{\sqrt[4]{b}}\right)}{2 \sqrt{2} a^{5/4}}-\frac{\sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} x}{\sqrt[4]{b}}+1\right)}{2 \sqrt{2} a^{5/4}}+\frac{x}{a}",1,"x/a + (b^(1/4)*ArcTan[1 - (Sqrt[2]*a^(1/4)*x)/b^(1/4)])/(2*Sqrt[2]*a^(5/4)) - (b^(1/4)*ArcTan[1 + (Sqrt[2]*a^(1/4)*x)/b^(1/4)])/(2*Sqrt[2]*a^(5/4)) + (b^(1/4)*Log[Sqrt[b] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[a]*x^2])/(4*Sqrt[2]*a^(5/4)) - (b^(1/4)*Log[Sqrt[b] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[a]*x^2])/(4*Sqrt[2]*a^(5/4))","A",11,8,9,0.8889,1,"{193, 321, 211, 1165, 628, 1162, 617, 204}"
2058,1,47,0,0.0256478,"\int \sqrt{a+\frac{b}{x^4}} x^3 \, dx","Int[Sqrt[a + b/x^4]*x^3,x]","\frac{1}{4} x^4 \sqrt{a+\frac{b}{x^4}}+\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^4}}}{\sqrt{a}}\right)}{4 \sqrt{a}}","\frac{1}{4} x^4 \sqrt{a+\frac{b}{x^4}}+\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^4}}}{\sqrt{a}}\right)}{4 \sqrt{a}}",1,"(Sqrt[a + b/x^4]*x^4)/4 + (b*ArcTanh[Sqrt[a + b/x^4]/Sqrt[a]])/(4*Sqrt[a])","A",4,4,15,0.2667,1,"{266, 47, 63, 208}"
2059,1,49,0,0.0366982,"\int \sqrt{a+\frac{b}{x^4}} x \, dx","Int[Sqrt[a + b/x^4]*x,x]","\frac{1}{2} x^2 \sqrt{a+\frac{b}{x^4}}-\frac{1}{2} \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b}}{x^2 \sqrt{a+\frac{b}{x^4}}}\right)","\frac{1}{2} x^2 \sqrt{a+\frac{b}{x^4}}-\frac{1}{2} \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b}}{x^2 \sqrt{a+\frac{b}{x^4}}}\right)",1,"(Sqrt[a + b/x^4]*x^2)/2 - (Sqrt[b]*ArcTanh[Sqrt[b]/(Sqrt[a + b/x^4]*x^2)])/2","A",5,5,13,0.3846,1,"{335, 275, 277, 217, 206}"
2060,1,43,0,0.0237749,"\int \frac{\sqrt{a+\frac{b}{x^4}}}{x} \, dx","Int[Sqrt[a + b/x^4]/x,x]","\frac{1}{2} \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^4}}}{\sqrt{a}}\right)-\frac{1}{2} \sqrt{a+\frac{b}{x^4}}","\frac{1}{2} \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^4}}}{\sqrt{a}}\right)-\frac{1}{2} \sqrt{a+\frac{b}{x^4}}",1,"-Sqrt[a + b/x^4]/2 + (Sqrt[a]*ArcTanh[Sqrt[a + b/x^4]/Sqrt[a]])/2","A",4,4,15,0.2667,1,"{266, 50, 63, 208}"
2061,1,50,0,0.0360257,"\int \frac{\sqrt{a+\frac{b}{x^4}}}{x^3} \, dx","Int[Sqrt[a + b/x^4]/x^3,x]","-\frac{\sqrt{a+\frac{b}{x^4}}}{4 x^2}-\frac{a \tanh ^{-1}\left(\frac{\sqrt{b}}{x^2 \sqrt{a+\frac{b}{x^4}}}\right)}{4 \sqrt{b}}","-\frac{\sqrt{a+\frac{b}{x^4}}}{4 x^2}-\frac{a \tanh ^{-1}\left(\frac{\sqrt{b}}{x^2 \sqrt{a+\frac{b}{x^4}}}\right)}{4 \sqrt{b}}",1,"-Sqrt[a + b/x^4]/(4*x^2) - (a*ArcTanh[Sqrt[b]/(Sqrt[a + b/x^4]*x^2)])/(4*Sqrt[b])","A",5,5,15,0.3333,1,"{335, 275, 195, 217, 206}"
2062,1,107,0,0.0479689,"\int \sqrt{a+\frac{b}{x^4}} x^2 \, dx","Int[Sqrt[a + b/x^4]*x^2,x]","\frac{1}{3} x^3 \sqrt{a+\frac{b}{x^4}}-\frac{b^{3/4} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) F\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{3 \sqrt[4]{a} \sqrt{a+\frac{b}{x^4}}}","\frac{1}{3} x^3 \sqrt{a+\frac{b}{x^4}}-\frac{b^{3/4} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) F\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{3 \sqrt[4]{a} \sqrt{a+\frac{b}{x^4}}}",1,"(Sqrt[a + b/x^4]*x^3)/3 - (b^(3/4)*Sqrt[(a + b/x^4)/(Sqrt[a] + Sqrt[b]/x^2)^2]*(Sqrt[a] + Sqrt[b]/x^2)*EllipticF[2*ArcCot[(a^(1/4)*x)/b^(1/4)], 1/2])/(3*a^(1/4)*Sqrt[a + b/x^4])","A",3,3,15,0.2000,1,"{335, 277, 220}"
2063,1,224,0,0.1078176,"\int \sqrt{a+\frac{b}{x^4}} \, dx","Int[Sqrt[a + b/x^4],x]","x \sqrt{a+\frac{b}{x^4}}-\frac{2 \sqrt{b} \sqrt{a+\frac{b}{x^4}}}{x \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)}-\frac{\sqrt[4]{a} \sqrt[4]{b} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) F\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{\sqrt{a+\frac{b}{x^4}}}+\frac{2 \sqrt[4]{a} \sqrt[4]{b} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) E\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{\sqrt{a+\frac{b}{x^4}}}","x \sqrt{a+\frac{b}{x^4}}-\frac{2 \sqrt{b} \sqrt{a+\frac{b}{x^4}}}{x \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)}-\frac{\sqrt[4]{a} \sqrt[4]{b} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) F\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{\sqrt{a+\frac{b}{x^4}}}+\frac{2 \sqrt[4]{a} \sqrt[4]{b} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) E\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{\sqrt{a+\frac{b}{x^4}}}",1,"(-2*Sqrt[b]*Sqrt[a + b/x^4])/((Sqrt[a] + Sqrt[b]/x^2)*x) + Sqrt[a + b/x^4]*x + (2*a^(1/4)*b^(1/4)*Sqrt[(a + b/x^4)/(Sqrt[a] + Sqrt[b]/x^2)^2]*(Sqrt[a] + Sqrt[b]/x^2)*EllipticE[2*ArcCot[(a^(1/4)*x)/b^(1/4)], 1/2])/Sqrt[a + b/x^4] - (a^(1/4)*b^(1/4)*Sqrt[(a + b/x^4)/(Sqrt[a] + Sqrt[b]/x^2)^2]*(Sqrt[a] + Sqrt[b]/x^2)*EllipticF[2*ArcCot[(a^(1/4)*x)/b^(1/4)], 1/2])/Sqrt[a + b/x^4]","A",5,5,11,0.4545,1,"{242, 277, 305, 220, 1196}"
2064,1,107,0,0.042532,"\int \frac{\sqrt{a+\frac{b}{x^4}}}{x^2} \, dx","Int[Sqrt[a + b/x^4]/x^2,x]","-\frac{a^{3/4} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) F\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{3 \sqrt[4]{b} \sqrt{a+\frac{b}{x^4}}}-\frac{\sqrt{a+\frac{b}{x^4}}}{3 x}","-\frac{a^{3/4} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) F\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{3 \sqrt[4]{b} \sqrt{a+\frac{b}{x^4}}}-\frac{\sqrt{a+\frac{b}{x^4}}}{3 x}",1,"-Sqrt[a + b/x^4]/(3*x) - (a^(3/4)*Sqrt[(a + b/x^4)/(Sqrt[a] + Sqrt[b]/x^2)^2]*(Sqrt[a] + Sqrt[b]/x^2)*EllipticF[2*ArcCot[(a^(1/4)*x)/b^(1/4)], 1/2])/(3*b^(1/4)*Sqrt[a + b/x^4])","A",3,3,15,0.2000,1,"{335, 195, 220}"
2065,1,236,0,0.115039,"\int \frac{\sqrt{a+\frac{b}{x^4}}}{x^4} \, dx","Int[Sqrt[a + b/x^4]/x^4,x]","-\frac{a^{5/4} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) F\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 b^{3/4} \sqrt{a+\frac{b}{x^4}}}+\frac{2 a^{5/4} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) E\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 b^{3/4} \sqrt{a+\frac{b}{x^4}}}-\frac{2 a \sqrt{a+\frac{b}{x^4}}}{5 \sqrt{b} x \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)}-\frac{\sqrt{a+\frac{b}{x^4}}}{5 x^3}","-\frac{a^{5/4} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) F\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 b^{3/4} \sqrt{a+\frac{b}{x^4}}}+\frac{2 a^{5/4} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) E\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 b^{3/4} \sqrt{a+\frac{b}{x^4}}}-\frac{2 a \sqrt{a+\frac{b}{x^4}}}{5 \sqrt{b} x \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)}-\frac{\sqrt{a+\frac{b}{x^4}}}{5 x^3}",1,"-Sqrt[a + b/x^4]/(5*x^3) - (2*a*Sqrt[a + b/x^4])/(5*Sqrt[b]*(Sqrt[a] + Sqrt[b]/x^2)*x) + (2*a^(5/4)*Sqrt[(a + b/x^4)/(Sqrt[a] + Sqrt[b]/x^2)^2]*(Sqrt[a] + Sqrt[b]/x^2)*EllipticE[2*ArcCot[(a^(1/4)*x)/b^(1/4)], 1/2])/(5*b^(3/4)*Sqrt[a + b/x^4]) - (a^(5/4)*Sqrt[(a + b/x^4)/(Sqrt[a] + Sqrt[b]/x^2)^2]*(Sqrt[a] + Sqrt[b]/x^2)*EllipticF[2*ArcCot[(a^(1/4)*x)/b^(1/4)], 1/2])/(5*b^(3/4)*Sqrt[a + b/x^4])","A",5,5,15,0.3333,1,"{335, 279, 305, 220, 1196}"
2066,1,63,0,0.0342218,"\int \left(a+\frac{b}{x^4}\right)^{3/2} x^3 \, dx","Int[(a + b/x^4)^(3/2)*x^3,x]","\frac{1}{4} x^4 \left(a+\frac{b}{x^4}\right)^{3/2}-\frac{3}{4} b \sqrt{a+\frac{b}{x^4}}+\frac{3}{4} \sqrt{a} b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^4}}}{\sqrt{a}}\right)","\frac{1}{4} x^4 \left(a+\frac{b}{x^4}\right)^{3/2}-\frac{3}{4} b \sqrt{a+\frac{b}{x^4}}+\frac{3}{4} \sqrt{a} b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^4}}}{\sqrt{a}}\right)",1,"(-3*b*Sqrt[a + b/x^4])/4 + ((a + b/x^4)^(3/2)*x^4)/4 + (3*Sqrt[a]*b*ArcTanh[Sqrt[a + b/x^4]/Sqrt[a]])/4","A",5,5,15,0.3333,1,"{266, 47, 50, 63, 208}"
2067,1,69,0,0.0554472,"\int \left(a+\frac{b}{x^4}\right)^{3/2} x \, dx","Int[(a + b/x^4)^(3/2)*x,x]","\frac{1}{2} x^2 \left(a+\frac{b}{x^4}\right)^{3/2}-\frac{3 b \sqrt{a+\frac{b}{x^4}}}{4 x^2}-\frac{3}{4} a \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b}}{x^2 \sqrt{a+\frac{b}{x^4}}}\right)","\frac{1}{2} x^2 \left(a+\frac{b}{x^4}\right)^{3/2}-\frac{3 b \sqrt{a+\frac{b}{x^4}}}{4 x^2}-\frac{3}{4} a \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b}}{x^2 \sqrt{a+\frac{b}{x^4}}}\right)",1,"(-3*b*Sqrt[a + b/x^4])/(4*x^2) + ((a + b/x^4)^(3/2)*x^2)/2 - (3*a*Sqrt[b]*ArcTanh[Sqrt[b]/(Sqrt[a + b/x^4]*x^2)])/4","A",6,6,13,0.4615,1,"{335, 275, 277, 195, 217, 206}"
2068,1,59,0,0.0340354,"\int \frac{\left(a+\frac{b}{x^4}\right)^{3/2}}{x} \, dx","Int[(a + b/x^4)^(3/2)/x,x]","\frac{1}{2} a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^4}}}{\sqrt{a}}\right)-\frac{1}{2} a \sqrt{a+\frac{b}{x^4}}-\frac{1}{6} \left(a+\frac{b}{x^4}\right)^{3/2}","\frac{1}{2} a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^4}}}{\sqrt{a}}\right)-\frac{1}{2} a \sqrt{a+\frac{b}{x^4}}-\frac{1}{6} \left(a+\frac{b}{x^4}\right)^{3/2}",1,"-(a*Sqrt[a + b/x^4])/2 - (a + b/x^4)^(3/2)/6 + (a^(3/2)*ArcTanh[Sqrt[a + b/x^4]/Sqrt[a]])/2","A",5,4,15,0.2667,1,"{266, 50, 63, 208}"
2069,1,71,0,0.0520998,"\int \frac{\left(a+\frac{b}{x^4}\right)^{3/2}}{x^3} \, dx","Int[(a + b/x^4)^(3/2)/x^3,x]","-\frac{3 a^2 \tanh ^{-1}\left(\frac{\sqrt{b}}{x^2 \sqrt{a+\frac{b}{x^4}}}\right)}{16 \sqrt{b}}-\frac{3 a \sqrt{a+\frac{b}{x^4}}}{16 x^2}-\frac{\left(a+\frac{b}{x^4}\right)^{3/2}}{8 x^2}","-\frac{3 a^2 \tanh ^{-1}\left(\frac{\sqrt{b}}{x^2 \sqrt{a+\frac{b}{x^4}}}\right)}{16 \sqrt{b}}-\frac{3 a \sqrt{a+\frac{b}{x^4}}}{16 x^2}-\frac{\left(a+\frac{b}{x^4}\right)^{3/2}}{8 x^2}",1,"(-3*a*Sqrt[a + b/x^4])/(16*x^2) - (a + b/x^4)^(3/2)/(8*x^2) - (3*a^2*ArcTanh[Sqrt[b]/(Sqrt[a + b/x^4]*x^2)])/(16*Sqrt[b])","A",6,5,15,0.3333,1,"{335, 275, 195, 217, 206}"
2070,1,126,0,0.0590829,"\int \left(a+\frac{b}{x^4}\right)^{3/2} x^2 \, dx","Int[(a + b/x^4)^(3/2)*x^2,x]","-\frac{2 a^{3/4} b^{3/4} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) F\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{3 \sqrt{a+\frac{b}{x^4}}}+\frac{1}{3} x^3 \left(a+\frac{b}{x^4}\right)^{3/2}-\frac{2 b \sqrt{a+\frac{b}{x^4}}}{3 x}","-\frac{2 a^{3/4} b^{3/4} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) F\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{3 \sqrt{a+\frac{b}{x^4}}}+\frac{1}{3} x^3 \left(a+\frac{b}{x^4}\right)^{3/2}-\frac{2 b \sqrt{a+\frac{b}{x^4}}}{3 x}",1,"(-2*b*Sqrt[a + b/x^4])/(3*x) + ((a + b/x^4)^(3/2)*x^3)/3 - (2*a^(3/4)*b^(3/4)*Sqrt[(a + b/x^4)/(Sqrt[a] + Sqrt[b]/x^2)^2]*(Sqrt[a] + Sqrt[b]/x^2)*EllipticF[2*ArcCot[(a^(1/4)*x)/b^(1/4)], 1/2])/(3*Sqrt[a + b/x^4])","A",4,4,15,0.2667,1,"{335, 277, 195, 220}"
2071,1,250,0,0.1318872,"\int \left(a+\frac{b}{x^4}\right)^{3/2} \, dx","Int[(a + b/x^4)^(3/2),x]","-\frac{6 a^{5/4} \sqrt[4]{b} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) F\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 \sqrt{a+\frac{b}{x^4}}}+\frac{12 a^{5/4} \sqrt[4]{b} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) E\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 \sqrt{a+\frac{b}{x^4}}}+x \left(a+\frac{b}{x^4}\right)^{3/2}-\frac{12 a \sqrt{b} \sqrt{a+\frac{b}{x^4}}}{5 x \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)}-\frac{6 b \sqrt{a+\frac{b}{x^4}}}{5 x^3}","-\frac{6 a^{5/4} \sqrt[4]{b} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) F\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 \sqrt{a+\frac{b}{x^4}}}+\frac{12 a^{5/4} \sqrt[4]{b} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) E\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 \sqrt{a+\frac{b}{x^4}}}+x \left(a+\frac{b}{x^4}\right)^{3/2}-\frac{12 a \sqrt{b} \sqrt{a+\frac{b}{x^4}}}{5 x \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)}-\frac{6 b \sqrt{a+\frac{b}{x^4}}}{5 x^3}",1,"(-6*b*Sqrt[a + b/x^4])/(5*x^3) - (12*a*Sqrt[b]*Sqrt[a + b/x^4])/(5*(Sqrt[a] + Sqrt[b]/x^2)*x) + (a + b/x^4)^(3/2)*x + (12*a^(5/4)*b^(1/4)*Sqrt[(a + b/x^4)/(Sqrt[a] + Sqrt[b]/x^2)^2]*(Sqrt[a] + Sqrt[b]/x^2)*EllipticE[2*ArcCot[(a^(1/4)*x)/b^(1/4)], 1/2])/(5*Sqrt[a + b/x^4]) - (6*a^(5/4)*b^(1/4)*Sqrt[(a + b/x^4)/(Sqrt[a] + Sqrt[b]/x^2)^2]*(Sqrt[a] + Sqrt[b]/x^2)*EllipticF[2*ArcCot[(a^(1/4)*x)/b^(1/4)], 1/2])/(5*Sqrt[a + b/x^4])","A",6,6,11,0.5455,1,"{242, 277, 279, 305, 220, 1196}"
2072,1,126,0,0.0546435,"\int \frac{\left(a+\frac{b}{x^4}\right)^{3/2}}{x^2} \, dx","Int[(a + b/x^4)^(3/2)/x^2,x]","-\frac{2 a^{7/4} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) F\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{7 \sqrt[4]{b} \sqrt{a+\frac{b}{x^4}}}-\frac{2 a \sqrt{a+\frac{b}{x^4}}}{7 x}-\frac{\left(a+\frac{b}{x^4}\right)^{3/2}}{7 x}","-\frac{2 a^{7/4} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) F\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{7 \sqrt[4]{b} \sqrt{a+\frac{b}{x^4}}}-\frac{2 a \sqrt{a+\frac{b}{x^4}}}{7 x}-\frac{\left(a+\frac{b}{x^4}\right)^{3/2}}{7 x}",1,"(-2*a*Sqrt[a + b/x^4])/(7*x) - (a + b/x^4)^(3/2)/(7*x) - (2*a^(7/4)*Sqrt[(a + b/x^4)/(Sqrt[a] + Sqrt[b]/x^2)^2]*(Sqrt[a] + Sqrt[b]/x^2)*EllipticF[2*ArcCot[(a^(1/4)*x)/b^(1/4)], 1/2])/(7*b^(1/4)*Sqrt[a + b/x^4])","A",4,3,15,0.2000,1,"{335, 195, 220}"
2073,1,257,0,0.1356771,"\int \frac{\left(a+\frac{b}{x^4}\right)^{3/2}}{x^4} \, dx","Int[(a + b/x^4)^(3/2)/x^4,x]","-\frac{2 a^{9/4} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) F\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 b^{3/4} \sqrt{a+\frac{b}{x^4}}}+\frac{4 a^{9/4} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) E\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 b^{3/4} \sqrt{a+\frac{b}{x^4}}}-\frac{4 a^2 \sqrt{a+\frac{b}{x^4}}}{15 \sqrt{b} x \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)}-\frac{2 a \sqrt{a+\frac{b}{x^4}}}{15 x^3}-\frac{\left(a+\frac{b}{x^4}\right)^{3/2}}{9 x^3}","-\frac{2 a^{9/4} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) F\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 b^{3/4} \sqrt{a+\frac{b}{x^4}}}+\frac{4 a^{9/4} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) E\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 b^{3/4} \sqrt{a+\frac{b}{x^4}}}-\frac{4 a^2 \sqrt{a+\frac{b}{x^4}}}{15 \sqrt{b} x \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)}-\frac{2 a \sqrt{a+\frac{b}{x^4}}}{15 x^3}-\frac{\left(a+\frac{b}{x^4}\right)^{3/2}}{9 x^3}",1,"(-2*a*Sqrt[a + b/x^4])/(15*x^3) - (a + b/x^4)^(3/2)/(9*x^3) - (4*a^2*Sqrt[a + b/x^4])/(15*Sqrt[b]*(Sqrt[a] + Sqrt[b]/x^2)*x) + (4*a^(9/4)*Sqrt[(a + b/x^4)/(Sqrt[a] + Sqrt[b]/x^2)^2]*(Sqrt[a] + Sqrt[b]/x^2)*EllipticE[2*ArcCot[(a^(1/4)*x)/b^(1/4)], 1/2])/(15*b^(3/4)*Sqrt[a + b/x^4]) - (2*a^(9/4)*Sqrt[(a + b/x^4)/(Sqrt[a] + Sqrt[b]/x^2)^2]*(Sqrt[a] + Sqrt[b]/x^2)*EllipticF[2*ArcCot[(a^(1/4)*x)/b^(1/4)], 1/2])/(15*b^(3/4)*Sqrt[a + b/x^4])","A",6,5,15,0.3333,1,"{335, 279, 305, 220, 1196}"
2074,1,80,0,0.0437962,"\int \left(a+\frac{b}{x^4}\right)^{5/2} x^3 \, dx","Int[(a + b/x^4)^(5/2)*x^3,x]","\frac{5}{4} a^{3/2} b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^4}}}{\sqrt{a}}\right)+\frac{1}{4} x^4 \left(a+\frac{b}{x^4}\right)^{5/2}-\frac{5}{12} b \left(a+\frac{b}{x^4}\right)^{3/2}-\frac{5}{4} a b \sqrt{a+\frac{b}{x^4}}","\frac{5}{4} a^{3/2} b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^4}}}{\sqrt{a}}\right)+\frac{1}{4} x^4 \left(a+\frac{b}{x^4}\right)^{5/2}-\frac{5}{12} b \left(a+\frac{b}{x^4}\right)^{3/2}-\frac{5}{4} a b \sqrt{a+\frac{b}{x^4}}",1,"(-5*a*b*Sqrt[a + b/x^4])/4 - (5*b*(a + b/x^4)^(3/2))/12 + ((a + b/x^4)^(5/2)*x^4)/4 + (5*a^(3/2)*b*ArcTanh[Sqrt[a + b/x^4]/Sqrt[a]])/4","A",6,5,15,0.3333,1,"{266, 47, 50, 63, 208}"
2075,1,91,0,0.0733903,"\int \left(a+\frac{b}{x^4}\right)^{5/2} x \, dx","Int[(a + b/x^4)^(5/2)*x,x]","-\frac{15}{16} a^2 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b}}{x^2 \sqrt{a+\frac{b}{x^4}}}\right)+\frac{1}{2} x^2 \left(a+\frac{b}{x^4}\right)^{5/2}-\frac{5 b \left(a+\frac{b}{x^4}\right)^{3/2}}{8 x^2}-\frac{15 a b \sqrt{a+\frac{b}{x^4}}}{16 x^2}","-\frac{15}{16} a^2 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b}}{x^2 \sqrt{a+\frac{b}{x^4}}}\right)+\frac{1}{2} x^2 \left(a+\frac{b}{x^4}\right)^{5/2}-\frac{5 b \left(a+\frac{b}{x^4}\right)^{3/2}}{8 x^2}-\frac{15 a b \sqrt{a+\frac{b}{x^4}}}{16 x^2}",1,"(-15*a*b*Sqrt[a + b/x^4])/(16*x^2) - (5*b*(a + b/x^4)^(3/2))/(8*x^2) + ((a + b/x^4)^(5/2)*x^2)/2 - (15*a^2*Sqrt[b]*ArcTanh[Sqrt[b]/(Sqrt[a + b/x^4]*x^2)])/16","A",7,6,13,0.4615,1,"{335, 275, 277, 195, 217, 206}"
2076,1,77,0,0.0405486,"\int \frac{\left(a+\frac{b}{x^4}\right)^{5/2}}{x} \, dx","Int[(a + b/x^4)^(5/2)/x,x]","-\frac{1}{2} a^2 \sqrt{a+\frac{b}{x^4}}+\frac{1}{2} a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^4}}}{\sqrt{a}}\right)-\frac{1}{6} a \left(a+\frac{b}{x^4}\right)^{3/2}-\frac{1}{10} \left(a+\frac{b}{x^4}\right)^{5/2}","-\frac{1}{2} a^2 \sqrt{a+\frac{b}{x^4}}+\frac{1}{2} a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^4}}}{\sqrt{a}}\right)-\frac{1}{6} a \left(a+\frac{b}{x^4}\right)^{3/2}-\frac{1}{10} \left(a+\frac{b}{x^4}\right)^{5/2}",1,"-(a^2*Sqrt[a + b/x^4])/2 - (a*(a + b/x^4)^(3/2))/6 - (a + b/x^4)^(5/2)/10 + (a^(5/2)*ArcTanh[Sqrt[a + b/x^4]/Sqrt[a]])/2","A",6,4,15,0.2667,1,"{266, 50, 63, 208}"
2077,1,92,0,0.0671092,"\int \frac{\left(a+\frac{b}{x^4}\right)^{5/2}}{x^3} \, dx","Int[(a + b/x^4)^(5/2)/x^3,x]","-\frac{5 a^2 \sqrt{a+\frac{b}{x^4}}}{32 x^2}-\frac{5 a^3 \tanh ^{-1}\left(\frac{\sqrt{b}}{x^2 \sqrt{a+\frac{b}{x^4}}}\right)}{32 \sqrt{b}}-\frac{5 a \left(a+\frac{b}{x^4}\right)^{3/2}}{48 x^2}-\frac{\left(a+\frac{b}{x^4}\right)^{5/2}}{12 x^2}","-\frac{5 a^2 \sqrt{a+\frac{b}{x^4}}}{32 x^2}-\frac{5 a^3 \tanh ^{-1}\left(\frac{\sqrt{b}}{x^2 \sqrt{a+\frac{b}{x^4}}}\right)}{32 \sqrt{b}}-\frac{5 a \left(a+\frac{b}{x^4}\right)^{3/2}}{48 x^2}-\frac{\left(a+\frac{b}{x^4}\right)^{5/2}}{12 x^2}",1,"(-5*a^2*Sqrt[a + b/x^4])/(32*x^2) - (5*a*(a + b/x^4)^(3/2))/(48*x^2) - (a + b/x^4)^(5/2)/(12*x^2) - (5*a^3*ArcTanh[Sqrt[b]/(Sqrt[a + b/x^4]*x^2)])/(32*Sqrt[b])","A",7,5,15,0.3333,1,"{335, 275, 195, 217, 206}"
2078,1,146,0,0.0696952,"\int \left(a+\frac{b}{x^4}\right)^{5/2} x^2 \, dx","Int[(a + b/x^4)^(5/2)*x^2,x]","-\frac{20 a^{7/4} b^{3/4} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) F\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{21 \sqrt{a+\frac{b}{x^4}}}+\frac{1}{3} x^3 \left(a+\frac{b}{x^4}\right)^{5/2}-\frac{10 b \left(a+\frac{b}{x^4}\right)^{3/2}}{21 x}-\frac{20 a b \sqrt{a+\frac{b}{x^4}}}{21 x}","-\frac{20 a^{7/4} b^{3/4} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) F\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{21 \sqrt{a+\frac{b}{x^4}}}+\frac{1}{3} x^3 \left(a+\frac{b}{x^4}\right)^{5/2}-\frac{10 b \left(a+\frac{b}{x^4}\right)^{3/2}}{21 x}-\frac{20 a b \sqrt{a+\frac{b}{x^4}}}{21 x}",1,"(-20*a*b*Sqrt[a + b/x^4])/(21*x) - (10*b*(a + b/x^4)^(3/2))/(21*x) + ((a + b/x^4)^(5/2)*x^3)/3 - (20*a^(7/4)*b^(3/4)*Sqrt[(a + b/x^4)/(Sqrt[a] + Sqrt[b]/x^2)^2]*(Sqrt[a] + Sqrt[b]/x^2)*EllipticF[2*ArcCot[(a^(1/4)*x)/b^(1/4)], 1/2])/(21*Sqrt[a + b/x^4])","A",5,4,15,0.2667,1,"{335, 277, 195, 220}"
2079,1,272,0,0.1538635,"\int \left(a+\frac{b}{x^4}\right)^{5/2} \, dx","Int[(a + b/x^4)^(5/2),x]","-\frac{8 a^2 \sqrt{b} \sqrt{a+\frac{b}{x^4}}}{3 x \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)}-\frac{4 a^{9/4} \sqrt[4]{b} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) F\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{3 \sqrt{a+\frac{b}{x^4}}}+\frac{8 a^{9/4} \sqrt[4]{b} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) E\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{3 \sqrt{a+\frac{b}{x^4}}}+x \left(a+\frac{b}{x^4}\right)^{5/2}-\frac{10 b \left(a+\frac{b}{x^4}\right)^{3/2}}{9 x^3}-\frac{4 a b \sqrt{a+\frac{b}{x^4}}}{3 x^3}","-\frac{8 a^2 \sqrt{b} \sqrt{a+\frac{b}{x^4}}}{3 x \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)}-\frac{4 a^{9/4} \sqrt[4]{b} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) F\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{3 \sqrt{a+\frac{b}{x^4}}}+\frac{8 a^{9/4} \sqrt[4]{b} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) E\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{3 \sqrt{a+\frac{b}{x^4}}}+x \left(a+\frac{b}{x^4}\right)^{5/2}-\frac{10 b \left(a+\frac{b}{x^4}\right)^{3/2}}{9 x^3}-\frac{4 a b \sqrt{a+\frac{b}{x^4}}}{3 x^3}",1,"(-4*a*b*Sqrt[a + b/x^4])/(3*x^3) - (10*b*(a + b/x^4)^(3/2))/(9*x^3) - (8*a^2*Sqrt[b]*Sqrt[a + b/x^4])/(3*(Sqrt[a] + Sqrt[b]/x^2)*x) + (a + b/x^4)^(5/2)*x + (8*a^(9/4)*b^(1/4)*Sqrt[(a + b/x^4)/(Sqrt[a] + Sqrt[b]/x^2)^2]*(Sqrt[a] + Sqrt[b]/x^2)*EllipticE[2*ArcCot[(a^(1/4)*x)/b^(1/4)], 1/2])/(3*Sqrt[a + b/x^4]) - (4*a^(9/4)*b^(1/4)*Sqrt[(a + b/x^4)/(Sqrt[a] + Sqrt[b]/x^2)^2]*(Sqrt[a] + Sqrt[b]/x^2)*EllipticF[2*ArcCot[(a^(1/4)*x)/b^(1/4)], 1/2])/(3*Sqrt[a + b/x^4])","A",7,6,11,0.5455,1,"{242, 277, 279, 305, 220, 1196}"
2080,1,147,0,0.0698347,"\int \frac{\left(a+\frac{b}{x^4}\right)^{5/2}}{x^2} \, dx","Int[(a + b/x^4)^(5/2)/x^2,x]","-\frac{20 a^2 \sqrt{a+\frac{b}{x^4}}}{77 x}-\frac{20 a^{11/4} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) F\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{77 \sqrt[4]{b} \sqrt{a+\frac{b}{x^4}}}-\frac{10 a \left(a+\frac{b}{x^4}\right)^{3/2}}{77 x}-\frac{\left(a+\frac{b}{x^4}\right)^{5/2}}{11 x}","-\frac{20 a^2 \sqrt{a+\frac{b}{x^4}}}{77 x}-\frac{20 a^{11/4} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) F\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{77 \sqrt[4]{b} \sqrt{a+\frac{b}{x^4}}}-\frac{10 a \left(a+\frac{b}{x^4}\right)^{3/2}}{77 x}-\frac{\left(a+\frac{b}{x^4}\right)^{5/2}}{11 x}",1,"(-20*a^2*Sqrt[a + b/x^4])/(77*x) - (10*a*(a + b/x^4)^(3/2))/(77*x) - (a + b/x^4)^(5/2)/(11*x) - (20*a^(11/4)*Sqrt[(a + b/x^4)/(Sqrt[a] + Sqrt[b]/x^2)^2]*(Sqrt[a] + Sqrt[b]/x^2)*EllipticF[2*ArcCot[(a^(1/4)*x)/b^(1/4)], 1/2])/(77*b^(1/4)*Sqrt[a + b/x^4])","A",5,3,15,0.2000,1,"{335, 195, 220}"
2081,1,278,0,0.1637775,"\int \frac{\left(a+\frac{b}{x^4}\right)^{5/2}}{x^4} \, dx","Int[(a + b/x^4)^(5/2)/x^4,x]","-\frac{4 a^{13/4} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) F\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{39 b^{3/4} \sqrt{a+\frac{b}{x^4}}}+\frac{8 a^{13/4} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) E\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{39 b^{3/4} \sqrt{a+\frac{b}{x^4}}}-\frac{8 a^3 \sqrt{a+\frac{b}{x^4}}}{39 \sqrt{b} x \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)}-\frac{4 a^2 \sqrt{a+\frac{b}{x^4}}}{39 x^3}-\frac{10 a \left(a+\frac{b}{x^4}\right)^{3/2}}{117 x^3}-\frac{\left(a+\frac{b}{x^4}\right)^{5/2}}{13 x^3}","-\frac{4 a^{13/4} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) F\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{39 b^{3/4} \sqrt{a+\frac{b}{x^4}}}+\frac{8 a^{13/4} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) E\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{39 b^{3/4} \sqrt{a+\frac{b}{x^4}}}-\frac{8 a^3 \sqrt{a+\frac{b}{x^4}}}{39 \sqrt{b} x \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)}-\frac{4 a^2 \sqrt{a+\frac{b}{x^4}}}{39 x^3}-\frac{10 a \left(a+\frac{b}{x^4}\right)^{3/2}}{117 x^3}-\frac{\left(a+\frac{b}{x^4}\right)^{5/2}}{13 x^3}",1,"(-4*a^2*Sqrt[a + b/x^4])/(39*x^3) - (10*a*(a + b/x^4)^(3/2))/(117*x^3) - (a + b/x^4)^(5/2)/(13*x^3) - (8*a^3*Sqrt[a + b/x^4])/(39*Sqrt[b]*(Sqrt[a] + Sqrt[b]/x^2)*x) + (8*a^(13/4)*Sqrt[(a + b/x^4)/(Sqrt[a] + Sqrt[b]/x^2)^2]*(Sqrt[a] + Sqrt[b]/x^2)*EllipticE[2*ArcCot[(a^(1/4)*x)/b^(1/4)], 1/2])/(39*b^(3/4)*Sqrt[a + b/x^4]) - (4*a^(13/4)*Sqrt[(a + b/x^4)/(Sqrt[a] + Sqrt[b]/x^2)^2]*(Sqrt[a] + Sqrt[b]/x^2)*EllipticF[2*ArcCot[(a^(1/4)*x)/b^(1/4)], 1/2])/(39*b^(3/4)*Sqrt[a + b/x^4])","A",7,5,15,0.3333,1,"{335, 279, 305, 220, 1196}"
2082,1,50,0,0.0258321,"\int \frac{x^3}{\sqrt{a+\frac{b}{x^4}}} \, dx","Int[x^3/Sqrt[a + b/x^4],x]","\frac{x^4 \sqrt{a+\frac{b}{x^4}}}{4 a}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^4}}}{\sqrt{a}}\right)}{4 a^{3/2}}","\frac{x^4 \sqrt{a+\frac{b}{x^4}}}{4 a}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^4}}}{\sqrt{a}}\right)}{4 a^{3/2}}",1,"(Sqrt[a + b/x^4]*x^4)/(4*a) - (b*ArcTanh[Sqrt[a + b/x^4]/Sqrt[a]])/(4*a^(3/2))","A",4,4,15,0.2667,1,"{266, 51, 63, 208}"
2083,1,21,0,0.0046884,"\int \frac{x}{\sqrt{a+\frac{b}{x^4}}} \, dx","Int[x/Sqrt[a + b/x^4],x]","\frac{x^2 \sqrt{a+\frac{b}{x^4}}}{2 a}","\frac{x^2 \sqrt{a+\frac{b}{x^4}}}{2 a}",1,"(Sqrt[a + b/x^4]*x^2)/(2*a)","A",1,1,13,0.07692,1,"{264}"
2084,1,27,0,0.017586,"\int \frac{1}{\sqrt{a+\frac{b}{x^4}} x} \, dx","Int[1/(Sqrt[a + b/x^4]*x),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^4}}}{\sqrt{a}}\right)}{2 \sqrt{a}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^4}}}{\sqrt{a}}\right)}{2 \sqrt{a}}",1,"ArcTanh[Sqrt[a + b/x^4]/Sqrt[a]]/(2*Sqrt[a])","A",3,3,15,0.2000,1,"{266, 63, 208}"
2085,1,30,0,0.0244563,"\int \frac{1}{\sqrt{a+\frac{b}{x^4}} x^3} \, dx","Int[1/(Sqrt[a + b/x^4]*x^3),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{b}}{x^2 \sqrt{a+\frac{b}{x^4}}}\right)}{2 \sqrt{b}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{b}}{x^2 \sqrt{a+\frac{b}{x^4}}}\right)}{2 \sqrt{b}}",1,"-ArcTanh[Sqrt[b]/(Sqrt[a + b/x^4]*x^2)]/(2*Sqrt[b])","A",4,4,15,0.2667,1,"{335, 275, 217, 206}"
2086,1,110,0,0.0451209,"\int \frac{x^2}{\sqrt{a+\frac{b}{x^4}}} \, dx","Int[x^2/Sqrt[a + b/x^4],x]","\frac{b^{3/4} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) F\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{6 a^{5/4} \sqrt{a+\frac{b}{x^4}}}+\frac{x^3 \sqrt{a+\frac{b}{x^4}}}{3 a}","\frac{b^{3/4} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) F\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{6 a^{5/4} \sqrt{a+\frac{b}{x^4}}}+\frac{x^3 \sqrt{a+\frac{b}{x^4}}}{3 a}",1,"(Sqrt[a + b/x^4]*x^3)/(3*a) + (b^(3/4)*Sqrt[(a + b/x^4)/(Sqrt[a] + Sqrt[b]/x^2)^2]*(Sqrt[a] + Sqrt[b]/x^2)*EllipticF[2*ArcCot[(a^(1/4)*x)/b^(1/4)], 1/2])/(6*a^(5/4)*Sqrt[a + b/x^4])","A",3,3,15,0.2000,1,"{335, 325, 220}"
2087,1,231,0,0.1021092,"\int \frac{1}{\sqrt{a+\frac{b}{x^4}}} \, dx","Int[1/Sqrt[a + b/x^4],x]","-\frac{\sqrt[4]{b} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) F\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{2 a^{3/4} \sqrt{a+\frac{b}{x^4}}}+\frac{\sqrt[4]{b} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) E\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{a^{3/4} \sqrt{a+\frac{b}{x^4}}}+\frac{x \sqrt{a+\frac{b}{x^4}}}{a}-\frac{\sqrt{b} \sqrt{a+\frac{b}{x^4}}}{a x \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)}","-\frac{\sqrt[4]{b} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) F\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{2 a^{3/4} \sqrt{a+\frac{b}{x^4}}}+\frac{\sqrt[4]{b} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) E\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{a^{3/4} \sqrt{a+\frac{b}{x^4}}}+\frac{x \sqrt{a+\frac{b}{x^4}}}{a}-\frac{\sqrt{b} \sqrt{a+\frac{b}{x^4}}}{a x \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)}",1,"-((Sqrt[b]*Sqrt[a + b/x^4])/(a*(Sqrt[a] + Sqrt[b]/x^2)*x)) + (Sqrt[a + b/x^4]*x)/a + (b^(1/4)*Sqrt[(a + b/x^4)/(Sqrt[a] + Sqrt[b]/x^2)^2]*(Sqrt[a] + Sqrt[b]/x^2)*EllipticE[2*ArcCot[(a^(1/4)*x)/b^(1/4)], 1/2])/(a^(3/4)*Sqrt[a + b/x^4]) - (b^(1/4)*Sqrt[(a + b/x^4)/(Sqrt[a] + Sqrt[b]/x^2)^2]*(Sqrt[a] + Sqrt[b]/x^2)*EllipticF[2*ArcCot[(a^(1/4)*x)/b^(1/4)], 1/2])/(2*a^(3/4)*Sqrt[a + b/x^4])","A",5,5,11,0.4545,1,"{242, 325, 305, 220, 1196}"
2088,1,88,0,0.0282787,"\int \frac{1}{\sqrt{a+\frac{b}{x^4}} x^2} \, dx","Int[1/(Sqrt[a + b/x^4]*x^2),x]","-\frac{\sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) F\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a} \sqrt[4]{b} \sqrt{a+\frac{b}{x^4}}}","-\frac{\sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) F\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a} \sqrt[4]{b} \sqrt{a+\frac{b}{x^4}}}",1,"-(Sqrt[(a + b/x^4)/(Sqrt[a] + Sqrt[b]/x^2)^2]*(Sqrt[a] + Sqrt[b]/x^2)*EllipticF[2*ArcCot[(a^(1/4)*x)/b^(1/4)], 1/2])/(2*a^(1/4)*b^(1/4)*Sqrt[a + b/x^4])","A",2,2,15,0.1333,1,"{335, 220}"
2089,1,212,0,0.0843018,"\int \frac{1}{\sqrt{a+\frac{b}{x^4}} x^4} \, dx","Int[1/(Sqrt[a + b/x^4]*x^4),x]","-\frac{\sqrt[4]{a} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) F\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{2 b^{3/4} \sqrt{a+\frac{b}{x^4}}}+\frac{\sqrt[4]{a} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) E\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{b^{3/4} \sqrt{a+\frac{b}{x^4}}}-\frac{\sqrt{a+\frac{b}{x^4}}}{\sqrt{b} x \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)}","-\frac{\sqrt[4]{a} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) F\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{2 b^{3/4} \sqrt{a+\frac{b}{x^4}}}+\frac{\sqrt[4]{a} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) E\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{b^{3/4} \sqrt{a+\frac{b}{x^4}}}-\frac{\sqrt{a+\frac{b}{x^4}}}{\sqrt{b} x \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)}",1,"-(Sqrt[a + b/x^4]/(Sqrt[b]*(Sqrt[a] + Sqrt[b]/x^2)*x)) + (a^(1/4)*Sqrt[(a + b/x^4)/(Sqrt[a] + Sqrt[b]/x^2)^2]*(Sqrt[a] + Sqrt[b]/x^2)*EllipticE[2*ArcCot[(a^(1/4)*x)/b^(1/4)], 1/2])/(b^(3/4)*Sqrt[a + b/x^4]) - (a^(1/4)*Sqrt[(a + b/x^4)/(Sqrt[a] + Sqrt[b]/x^2)^2]*(Sqrt[a] + Sqrt[b]/x^2)*EllipticF[2*ArcCot[(a^(1/4)*x)/b^(1/4)], 1/2])/(2*b^(3/4)*Sqrt[a + b/x^4])","A",4,4,15,0.2667,1,"{335, 305, 220, 1196}"
2090,1,71,0,0.0355107,"\int \frac{x^3}{\left(a+\frac{b}{x^4}\right)^{3/2}} \, dx","Int[x^3/(a + b/x^4)^(3/2),x]","\frac{3 x^4 \sqrt{a+\frac{b}{x^4}}}{4 a^2}-\frac{3 b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^4}}}{\sqrt{a}}\right)}{4 a^{5/2}}-\frac{x^4}{2 a \sqrt{a+\frac{b}{x^4}}}","\frac{3 b}{4 a^2 \sqrt{a+\frac{b}{x^4}}}-\frac{3 b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^4}}}{\sqrt{a}}\right)}{4 a^{5/2}}+\frac{x^4}{4 a \sqrt{a+\frac{b}{x^4}}}",1,"-x^4/(2*a*Sqrt[a + b/x^4]) + (3*Sqrt[a + b/x^4]*x^4)/(4*a^2) - (3*b*ArcTanh[Sqrt[a + b/x^4]/Sqrt[a]])/(4*a^(5/2))","A",5,4,15,0.2667,1,"{266, 51, 63, 208}"
2091,1,40,0,0.0109285,"\int \frac{x}{\left(a+\frac{b}{x^4}\right)^{3/2}} \, dx","Int[x/(a + b/x^4)^(3/2),x]","\frac{x^2 \sqrt{a+\frac{b}{x^4}}}{a^2}-\frac{x^2}{2 a \sqrt{a+\frac{b}{x^4}}}","\frac{x^2 \sqrt{a+\frac{b}{x^4}}}{a^2}-\frac{x^2}{2 a \sqrt{a+\frac{b}{x^4}}}",1,"-x^2/(2*a*Sqrt[a + b/x^4]) + (Sqrt[a + b/x^4]*x^2)/a^2","A",2,2,13,0.1538,1,"{273, 264}"
2092,1,46,0,0.0252541,"\int \frac{1}{\left(a+\frac{b}{x^4}\right)^{3/2} x} \, dx","Int[1/((a + b/x^4)^(3/2)*x),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^4}}}{\sqrt{a}}\right)}{2 a^{3/2}}-\frac{1}{2 a \sqrt{a+\frac{b}{x^4}}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^4}}}{\sqrt{a}}\right)}{2 a^{3/2}}-\frac{1}{2 a \sqrt{a+\frac{b}{x^4}}}",1,"-1/(2*a*Sqrt[a + b/x^4]) + ArcTanh[Sqrt[a + b/x^4]/Sqrt[a]]/(2*a^(3/2))","A",4,4,15,0.2667,1,"{266, 51, 63, 208}"
2093,1,21,0,0.0066597,"\int \frac{1}{\left(a+\frac{b}{x^4}\right)^{3/2} x^3} \, dx","Int[1/((a + b/x^4)^(3/2)*x^3),x]","-\frac{1}{2 a x^2 \sqrt{a+\frac{b}{x^4}}}","-\frac{1}{2 a x^2 \sqrt{a+\frac{b}{x^4}}}",1,"-1/(2*a*Sqrt[a + b/x^4]*x^2)","A",1,1,15,0.06667,1,"{264}"
2094,1,131,0,0.0610674,"\int \frac{x^2}{\left(a+\frac{b}{x^4}\right)^{3/2}} \, dx","Int[x^2/(a + b/x^4)^(3/2),x]","\frac{5 b^{3/4} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) F\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{12 a^{9/4} \sqrt{a+\frac{b}{x^4}}}+\frac{5 x^3 \sqrt{a+\frac{b}{x^4}}}{6 a^2}-\frac{x^3}{2 a \sqrt{a+\frac{b}{x^4}}}","\frac{5 b^{3/4} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) F\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{12 a^{9/4} \sqrt{a+\frac{b}{x^4}}}+\frac{5 x^3 \sqrt{a+\frac{b}{x^4}}}{6 a^2}-\frac{x^3}{2 a \sqrt{a+\frac{b}{x^4}}}",1,"-x^3/(2*a*Sqrt[a + b/x^4]) + (5*Sqrt[a + b/x^4]*x^3)/(6*a^2) + (5*b^(3/4)*Sqrt[(a + b/x^4)/(Sqrt[a] + Sqrt[b]/x^2)^2]*(Sqrt[a] + Sqrt[b]/x^2)*EllipticF[2*ArcCot[(a^(1/4)*x)/b^(1/4)], 1/2])/(12*a^(9/4)*Sqrt[a + b/x^4])","A",4,4,15,0.2667,1,"{335, 290, 325, 220}"
2095,1,258,0,0.1297831,"\int \frac{1}{\left(a+\frac{b}{x^4}\right)^{3/2}} \, dx","Int[(a + b/x^4)^(-3/2),x]","\frac{3 x \sqrt{a+\frac{b}{x^4}}}{2 a^2}-\frac{3 \sqrt{b} \sqrt{a+\frac{b}{x^4}}}{2 a^2 x \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)}-\frac{3 \sqrt[4]{b} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) F\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{4 a^{7/4} \sqrt{a+\frac{b}{x^4}}}+\frac{3 \sqrt[4]{b} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) E\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{2 a^{7/4} \sqrt{a+\frac{b}{x^4}}}-\frac{x}{2 a \sqrt{a+\frac{b}{x^4}}}","\frac{3 x \sqrt{a+\frac{b}{x^4}}}{2 a^2}-\frac{3 \sqrt{b} \sqrt{a+\frac{b}{x^4}}}{2 a^2 x \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)}-\frac{3 \sqrt[4]{b} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) F\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{4 a^{7/4} \sqrt{a+\frac{b}{x^4}}}+\frac{3 \sqrt[4]{b} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) E\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{2 a^{7/4} \sqrt{a+\frac{b}{x^4}}}-\frac{x}{2 a \sqrt{a+\frac{b}{x^4}}}",1,"(-3*Sqrt[b]*Sqrt[a + b/x^4])/(2*a^2*(Sqrt[a] + Sqrt[b]/x^2)*x) - x/(2*a*Sqrt[a + b/x^4]) + (3*Sqrt[a + b/x^4]*x)/(2*a^2) + (3*b^(1/4)*Sqrt[(a + b/x^4)/(Sqrt[a] + Sqrt[b]/x^2)^2]*(Sqrt[a] + Sqrt[b]/x^2)*EllipticE[2*ArcCot[(a^(1/4)*x)/b^(1/4)], 1/2])/(2*a^(7/4)*Sqrt[a + b/x^4]) - (3*b^(1/4)*Sqrt[(a + b/x^4)/(Sqrt[a] + Sqrt[b]/x^2)^2]*(Sqrt[a] + Sqrt[b]/x^2)*EllipticF[2*ArcCot[(a^(1/4)*x)/b^(1/4)], 1/2])/(4*a^(7/4)*Sqrt[a + b/x^4])","A",6,6,11,0.5455,1,"{242, 290, 325, 305, 220, 1196}"
2096,1,110,0,0.0405668,"\int \frac{1}{\left(a+\frac{b}{x^4}\right)^{3/2} x^2} \, dx","Int[1/((a + b/x^4)^(3/2)*x^2),x]","-\frac{\sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) F\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{4 a^{5/4} \sqrt[4]{b} \sqrt{a+\frac{b}{x^4}}}-\frac{1}{2 a x \sqrt{a+\frac{b}{x^4}}}","-\frac{\sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) F\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{4 a^{5/4} \sqrt[4]{b} \sqrt{a+\frac{b}{x^4}}}-\frac{1}{2 a x \sqrt{a+\frac{b}{x^4}}}",1,"-1/(2*a*Sqrt[a + b/x^4]*x) - (Sqrt[(a + b/x^4)/(Sqrt[a] + Sqrt[b]/x^2)^2]*(Sqrt[a] + Sqrt[b]/x^2)*EllipticF[2*ArcCot[(a^(1/4)*x)/b^(1/4)], 1/2])/(4*a^(5/4)*b^(1/4)*Sqrt[a + b/x^4])","A",3,3,15,0.2000,1,"{335, 199, 220}"
2097,1,241,0,0.1092249,"\int \frac{1}{\left(a+\frac{b}{x^4}\right)^{3/2} x^4} \, dx","Int[1/((a + b/x^4)^(3/2)*x^4),x]","\frac{\sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) F\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{4 a^{3/4} b^{3/4} \sqrt{a+\frac{b}{x^4}}}-\frac{\sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) E\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{2 a^{3/4} b^{3/4} \sqrt{a+\frac{b}{x^4}}}+\frac{\sqrt{a+\frac{b}{x^4}}}{2 a \sqrt{b} x \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)}-\frac{1}{2 a x^3 \sqrt{a+\frac{b}{x^4}}}","\frac{\sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) F\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{4 a^{3/4} b^{3/4} \sqrt{a+\frac{b}{x^4}}}-\frac{\sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) E\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{2 a^{3/4} b^{3/4} \sqrt{a+\frac{b}{x^4}}}+\frac{\sqrt{a+\frac{b}{x^4}}}{2 a \sqrt{b} x \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)}-\frac{1}{2 a x^3 \sqrt{a+\frac{b}{x^4}}}",1,"-1/(2*a*Sqrt[a + b/x^4]*x^3) + Sqrt[a + b/x^4]/(2*a*Sqrt[b]*(Sqrt[a] + Sqrt[b]/x^2)*x) - (Sqrt[(a + b/x^4)/(Sqrt[a] + Sqrt[b]/x^2)^2]*(Sqrt[a] + Sqrt[b]/x^2)*EllipticE[2*ArcCot[(a^(1/4)*x)/b^(1/4)], 1/2])/(2*a^(3/4)*b^(3/4)*Sqrt[a + b/x^4]) + (Sqrt[(a + b/x^4)/(Sqrt[a] + Sqrt[b]/x^2)^2]*(Sqrt[a] + Sqrt[b]/x^2)*EllipticF[2*ArcCot[(a^(1/4)*x)/b^(1/4)], 1/2])/(4*a^(3/4)*b^(3/4)*Sqrt[a + b/x^4])","A",5,5,15,0.3333,1,"{335, 290, 305, 220, 1196}"
2098,1,92,0,0.0465678,"\int \frac{x^3}{\left(a+\frac{b}{x^4}\right)^{5/2}} \, dx","Int[x^3/(a + b/x^4)^(5/2),x]","\frac{5 x^4 \sqrt{a+\frac{b}{x^4}}}{4 a^3}-\frac{5 x^4}{6 a^2 \sqrt{a+\frac{b}{x^4}}}-\frac{5 b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^4}}}{\sqrt{a}}\right)}{4 a^{7/2}}-\frac{x^4}{6 a \left(a+\frac{b}{x^4}\right)^{3/2}}","\frac{5 b}{4 a^3 \sqrt{a+\frac{b}{x^4}}}+\frac{5 b}{12 a^2 \left(a+\frac{b}{x^4}\right)^{3/2}}-\frac{5 b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^4}}}{\sqrt{a}}\right)}{4 a^{7/2}}+\frac{x^4}{4 a \left(a+\frac{b}{x^4}\right)^{3/2}}",1,"-x^4/(6*a*(a + b/x^4)^(3/2)) - (5*x^4)/(6*a^2*Sqrt[a + b/x^4]) + (5*Sqrt[a + b/x^4]*x^4)/(4*a^3) - (5*b*ArcTanh[Sqrt[a + b/x^4]/Sqrt[a]])/(4*a^(7/2))","A",6,4,15,0.2667,1,"{266, 51, 63, 208}"
2099,1,64,0,0.019163,"\int \frac{x}{\left(a+\frac{b}{x^4}\right)^{5/2}} \, dx","Int[x/(a + b/x^4)^(5/2),x]","\frac{4 x^2 \sqrt{a+\frac{b}{x^4}}}{3 a^3}-\frac{2 x^2}{3 a^2 \sqrt{a+\frac{b}{x^4}}}-\frac{x^2}{6 a \left(a+\frac{b}{x^4}\right)^{3/2}}","\frac{4 x^2 \sqrt{a+\frac{b}{x^4}}}{3 a^3}-\frac{2 x^2}{3 a^2 \sqrt{a+\frac{b}{x^4}}}-\frac{x^2}{6 a \left(a+\frac{b}{x^4}\right)^{3/2}}",1,"-x^2/(6*a*(a + b/x^4)^(3/2)) - (2*x^2)/(3*a^2*Sqrt[a + b/x^4]) + (4*Sqrt[a + b/x^4]*x^2)/(3*a^3)","A",3,2,13,0.1538,1,"{273, 264}"
2100,1,64,0,0.0332934,"\int \frac{1}{\left(a+\frac{b}{x^4}\right)^{5/2} x} \, dx","Int[1/((a + b/x^4)^(5/2)*x),x]","-\frac{1}{2 a^2 \sqrt{a+\frac{b}{x^4}}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^4}}}{\sqrt{a}}\right)}{2 a^{5/2}}-\frac{1}{6 a \left(a+\frac{b}{x^4}\right)^{3/2}}","-\frac{1}{2 a^2 \sqrt{a+\frac{b}{x^4}}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^4}}}{\sqrt{a}}\right)}{2 a^{5/2}}-\frac{1}{6 a \left(a+\frac{b}{x^4}\right)^{3/2}}",1,"-1/(6*a*(a + b/x^4)^(3/2)) - 1/(2*a^2*Sqrt[a + b/x^4]) + ArcTanh[Sqrt[a + b/x^4]/Sqrt[a]]/(2*a^(5/2))","A",5,4,15,0.2667,1,"{266, 51, 63, 208}"
2101,1,44,0,0.0143726,"\int \frac{1}{\left(a+\frac{b}{x^4}\right)^{5/2} x^3} \, dx","Int[1/((a + b/x^4)^(5/2)*x^3),x]","-\frac{b}{3 a^2 x^6 \left(a+\frac{b}{x^4}\right)^{3/2}}-\frac{1}{2 a x^2 \left(a+\frac{b}{x^4}\right)^{3/2}}","-\frac{b}{3 a^2 x^6 \left(a+\frac{b}{x^4}\right)^{3/2}}-\frac{1}{2 a x^2 \left(a+\frac{b}{x^4}\right)^{3/2}}",1,"-b/(3*a^2*(a + b/x^4)^(3/2)*x^6) - 1/(2*a*(a + b/x^4)^(3/2)*x^2)","A",2,2,15,0.1333,1,"{271, 264}"
2102,1,152,0,0.0772644,"\int \frac{x^2}{\left(a+\frac{b}{x^4}\right)^{5/2}} \, dx","Int[x^2/(a + b/x^4)^(5/2),x]","\frac{5 b^{3/4} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) F\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{8 a^{13/4} \sqrt{a+\frac{b}{x^4}}}+\frac{5 x^3 \sqrt{a+\frac{b}{x^4}}}{4 a^3}-\frac{3 x^3}{4 a^2 \sqrt{a+\frac{b}{x^4}}}-\frac{x^3}{6 a \left(a+\frac{b}{x^4}\right)^{3/2}}","\frac{5 b^{3/4} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) F\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{8 a^{13/4} \sqrt{a+\frac{b}{x^4}}}+\frac{5 x^3 \sqrt{a+\frac{b}{x^4}}}{4 a^3}-\frac{3 x^3}{4 a^2 \sqrt{a+\frac{b}{x^4}}}-\frac{x^3}{6 a \left(a+\frac{b}{x^4}\right)^{3/2}}",1,"-x^3/(6*a*(a + b/x^4)^(3/2)) - (3*x^3)/(4*a^2*Sqrt[a + b/x^4]) + (5*Sqrt[a + b/x^4]*x^3)/(4*a^3) + (5*b^(3/4)*Sqrt[(a + b/x^4)/(Sqrt[a] + Sqrt[b]/x^2)^2]*(Sqrt[a] + Sqrt[b]/x^2)*EllipticF[2*ArcCot[(a^(1/4)*x)/b^(1/4)], 1/2])/(8*a^(13/4)*Sqrt[a + b/x^4])","A",5,4,15,0.2667,1,"{335, 290, 325, 220}"
2103,1,277,0,0.1597745,"\int \frac{1}{\left(a+\frac{b}{x^4}\right)^{5/2}} \, dx","Int[(a + b/x^4)^(-5/2),x]","\frac{7 x \sqrt{a+\frac{b}{x^4}}}{4 a^3}-\frac{7 x}{12 a^2 \sqrt{a+\frac{b}{x^4}}}-\frac{7 \sqrt{b} \sqrt{a+\frac{b}{x^4}}}{4 a^3 x \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)}-\frac{7 \sqrt[4]{b} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) F\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{8 a^{11/4} \sqrt{a+\frac{b}{x^4}}}+\frac{7 \sqrt[4]{b} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) E\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{4 a^{11/4} \sqrt{a+\frac{b}{x^4}}}-\frac{x}{6 a \left(a+\frac{b}{x^4}\right)^{3/2}}","\frac{7 x \sqrt{a+\frac{b}{x^4}}}{4 a^3}-\frac{7 x}{12 a^2 \sqrt{a+\frac{b}{x^4}}}-\frac{7 \sqrt{b} \sqrt{a+\frac{b}{x^4}}}{4 a^3 x \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)}-\frac{7 \sqrt[4]{b} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) F\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{8 a^{11/4} \sqrt{a+\frac{b}{x^4}}}+\frac{7 \sqrt[4]{b} \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) E\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{4 a^{11/4} \sqrt{a+\frac{b}{x^4}}}-\frac{x}{6 a \left(a+\frac{b}{x^4}\right)^{3/2}}",1,"(-7*Sqrt[b]*Sqrt[a + b/x^4])/(4*a^3*(Sqrt[a] + Sqrt[b]/x^2)*x) - x/(6*a*(a + b/x^4)^(3/2)) - (7*x)/(12*a^2*Sqrt[a + b/x^4]) + (7*Sqrt[a + b/x^4]*x)/(4*a^3) + (7*b^(1/4)*Sqrt[(a + b/x^4)/(Sqrt[a] + Sqrt[b]/x^2)^2]*(Sqrt[a] + Sqrt[b]/x^2)*EllipticE[2*ArcCot[(a^(1/4)*x)/b^(1/4)], 1/2])/(4*a^(11/4)*Sqrt[a + b/x^4]) - (7*b^(1/4)*Sqrt[(a + b/x^4)/(Sqrt[a] + Sqrt[b]/x^2)^2]*(Sqrt[a] + Sqrt[b]/x^2)*EllipticF[2*ArcCot[(a^(1/4)*x)/b^(1/4)], 1/2])/(8*a^(11/4)*Sqrt[a + b/x^4])","A",7,6,11,0.5455,1,"{242, 290, 325, 305, 220, 1196}"
2104,1,131,0,0.0555304,"\int \frac{1}{\left(a+\frac{b}{x^4}\right)^{5/2} x^2} \, dx","Int[1/((a + b/x^4)^(5/2)*x^2),x]","-\frac{5}{12 a^2 x \sqrt{a+\frac{b}{x^4}}}-\frac{5 \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) F\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{24 a^{9/4} \sqrt[4]{b} \sqrt{a+\frac{b}{x^4}}}-\frac{1}{6 a x \left(a+\frac{b}{x^4}\right)^{3/2}}","-\frac{5}{12 a^2 x \sqrt{a+\frac{b}{x^4}}}-\frac{5 \sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) F\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{24 a^{9/4} \sqrt[4]{b} \sqrt{a+\frac{b}{x^4}}}-\frac{1}{6 a x \left(a+\frac{b}{x^4}\right)^{3/2}}",1,"-1/(6*a*(a + b/x^4)^(3/2)*x) - 5/(12*a^2*Sqrt[a + b/x^4]*x) - (5*Sqrt[(a + b/x^4)/(Sqrt[a] + Sqrt[b]/x^2)^2]*(Sqrt[a] + Sqrt[b]/x^2)*EllipticF[2*ArcCot[(a^(1/4)*x)/b^(1/4)], 1/2])/(24*a^(9/4)*b^(1/4)*Sqrt[a + b/x^4])","A",4,3,15,0.2000,1,"{335, 199, 220}"
2105,1,262,0,0.1333278,"\int \frac{1}{\left(a+\frac{b}{x^4}\right)^{5/2} x^4} \, dx","Int[1/((a + b/x^4)^(5/2)*x^4),x]","\frac{\sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) F\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{8 a^{7/4} b^{3/4} \sqrt{a+\frac{b}{x^4}}}-\frac{\sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) E\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{4 a^{7/4} b^{3/4} \sqrt{a+\frac{b}{x^4}}}+\frac{\sqrt{a+\frac{b}{x^4}}}{4 a^2 \sqrt{b} x \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)}-\frac{1}{4 a^2 x^3 \sqrt{a+\frac{b}{x^4}}}-\frac{1}{6 a x^3 \left(a+\frac{b}{x^4}\right)^{3/2}}","\frac{\sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) F\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{8 a^{7/4} b^{3/4} \sqrt{a+\frac{b}{x^4}}}-\frac{\sqrt{\frac{a+\frac{b}{x^4}}{\left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)^2}} \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right) E\left(2 \cot ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{4 a^{7/4} b^{3/4} \sqrt{a+\frac{b}{x^4}}}+\frac{\sqrt{a+\frac{b}{x^4}}}{4 a^2 \sqrt{b} x \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)}-\frac{1}{4 a^2 x^3 \sqrt{a+\frac{b}{x^4}}}-\frac{1}{6 a x^3 \left(a+\frac{b}{x^4}\right)^{3/2}}",1,"-1/(6*a*(a + b/x^4)^(3/2)*x^3) - 1/(4*a^2*Sqrt[a + b/x^4]*x^3) + Sqrt[a + b/x^4]/(4*a^2*Sqrt[b]*(Sqrt[a] + Sqrt[b]/x^2)*x) - (Sqrt[(a + b/x^4)/(Sqrt[a] + Sqrt[b]/x^2)^2]*(Sqrt[a] + Sqrt[b]/x^2)*EllipticE[2*ArcCot[(a^(1/4)*x)/b^(1/4)], 1/2])/(4*a^(7/4)*b^(3/4)*Sqrt[a + b/x^4]) + (Sqrt[(a + b/x^4)/(Sqrt[a] + Sqrt[b]/x^2)^2]*(Sqrt[a] + Sqrt[b]/x^2)*EllipticF[2*ArcCot[(a^(1/4)*x)/b^(1/4)], 1/2])/(8*a^(7/4)*b^(3/4)*Sqrt[a + b/x^4])","A",6,5,15,0.3333,1,"{335, 290, 305, 220, 1196}"
2106,1,310,0,0.6575495,"\int \frac{1}{a+\frac{b}{x^5}} \, dx","Int[(a + b/x^5)^(-1),x]","\frac{\left(1-\sqrt{5}\right) \sqrt[5]{b} \log \left(a^{2/5} x^2-\frac{1}{2} \left(1-\sqrt{5}\right) \sqrt[5]{a} \sqrt[5]{b} x+b^{2/5}\right)}{20 a^{6/5}}+\frac{\left(1+\sqrt{5}\right) \sqrt[5]{b} \log \left(a^{2/5} x^2-\frac{1}{2} \left(1+\sqrt{5}\right) \sqrt[5]{a} \sqrt[5]{b} x+b^{2/5}\right)}{20 a^{6/5}}-\frac{\sqrt[5]{b} \log \left(\sqrt[5]{a} x+\sqrt[5]{b}\right)}{5 a^{6/5}}-\frac{\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} \sqrt[5]{b} \tan ^{-1}\left(\frac{2 \sqrt{\frac{2}{5+\sqrt{5}}} \sqrt[5]{a} x}{\sqrt[5]{b}}+\sqrt{\frac{1}{5} \left(5-2 \sqrt{5}\right)}\right)}{5 a^{6/5}}+\frac{\sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \sqrt[5]{b} \tan ^{-1}\left(\sqrt{\frac{1}{5} \left(5+2 \sqrt{5}\right)}-\frac{\sqrt{\frac{2}{5} \left(5+\sqrt{5}\right)} \sqrt[5]{a} x}{\sqrt[5]{b}}\right)}{5 a^{6/5}}+\frac{x}{a}","\frac{\left(1-\sqrt{5}\right) \sqrt[5]{b} \log \left(a^{2/5} x^2-\frac{1}{2} \left(1-\sqrt{5}\right) \sqrt[5]{a} \sqrt[5]{b} x+b^{2/5}\right)}{20 a^{6/5}}+\frac{\left(1+\sqrt{5}\right) \sqrt[5]{b} \log \left(a^{2/5} x^2-\frac{1}{2} \left(1+\sqrt{5}\right) \sqrt[5]{a} \sqrt[5]{b} x+b^{2/5}\right)}{20 a^{6/5}}-\frac{\sqrt[5]{b} \log \left(\sqrt[5]{a} x+\sqrt[5]{b}\right)}{5 a^{6/5}}-\frac{\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} \sqrt[5]{b} \tan ^{-1}\left(\frac{2 \sqrt{\frac{2}{5+\sqrt{5}}} \sqrt[5]{a} x}{\sqrt[5]{b}}+\sqrt{\frac{1}{5} \left(5-2 \sqrt{5}\right)}\right)}{5 a^{6/5}}+\frac{\sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \sqrt[5]{b} \tan ^{-1}\left(\sqrt{\frac{1}{5} \left(5+2 \sqrt{5}\right)}-\frac{\sqrt{\frac{2}{5} \left(5+\sqrt{5}\right)} \sqrt[5]{a} x}{\sqrt[5]{b}}\right)}{5 a^{6/5}}+\frac{x}{a}",1,"x/a - (Sqrt[(5 + Sqrt[5])/2]*b^(1/5)*ArcTan[Sqrt[(5 - 2*Sqrt[5])/5] + (2*Sqrt[2/(5 + Sqrt[5])]*a^(1/5)*x)/b^(1/5)])/(5*a^(6/5)) + (Sqrt[(5 - Sqrt[5])/2]*b^(1/5)*ArcTan[Sqrt[(5 + 2*Sqrt[5])/5] - (Sqrt[(2*(5 + Sqrt[5]))/5]*a^(1/5)*x)/b^(1/5)])/(5*a^(6/5)) - (b^(1/5)*Log[b^(1/5) + a^(1/5)*x])/(5*a^(6/5)) + ((1 - Sqrt[5])*b^(1/5)*Log[b^(2/5) - ((1 - Sqrt[5])*a^(1/5)*b^(1/5)*x)/2 + a^(2/5)*x^2])/(20*a^(6/5)) + ((1 + Sqrt[5])*b^(1/5)*Log[b^(2/5) - ((1 + Sqrt[5])*a^(1/5)*b^(1/5)*x)/2 + a^(2/5)*x^2])/(20*a^(6/5))","A",8,8,9,0.8889,1,"{193, 321, 201, 634, 618, 204, 628, 31}"
2107,1,27,0,0.0194627,"\int \frac{1}{\sqrt{a+\frac{b}{x^5}} x} \, dx","Int[1/(Sqrt[a + b/x^5]*x),x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^5}}}{\sqrt{a}}\right)}{5 \sqrt{a}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^5}}}{\sqrt{a}}\right)}{5 \sqrt{a}}",1,"(2*ArcTanh[Sqrt[a + b/x^5]/Sqrt[a]])/(5*Sqrt[a])","A",3,3,15,0.2000,1,"{266, 63, 208}"
2108,1,29,0,0.0196157,"\int \frac{1}{\sqrt{-a+\frac{b}{x^5}} x} \, dx","Int[1/(Sqrt[-a + b/x^5]*x),x]","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{\frac{b}{x^5}-a}}{\sqrt{a}}\right)}{5 \sqrt{a}}","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{\frac{b}{x^5}-a}}{\sqrt{a}}\right)}{5 \sqrt{a}}",1,"(-2*ArcTan[Sqrt[-a + b/x^5]/Sqrt[a]])/(5*Sqrt[a])","A",3,3,17,0.1765,1,"{266, 63, 205}"
2109,1,220,0,0.4362595,"\int \frac{1}{a+\frac{b}{x^6}} \, dx","Int[(a + b/x^6)^(-1),x]","\frac{\sqrt[6]{b} \log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a} x^2+\sqrt[3]{b}\right)}{4 \sqrt{3} a^{7/6}}-\frac{\sqrt[6]{b} \log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a} x^2+\sqrt[3]{b}\right)}{4 \sqrt{3} a^{7/6}}-\frac{\sqrt[6]{b} \tan ^{-1}\left(\frac{\sqrt[6]{a} x}{\sqrt[6]{b}}\right)}{3 a^{7/6}}+\frac{\sqrt[6]{b} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{b}-2 \sqrt[6]{a} x}{\sqrt[6]{b}}\right)}{6 a^{7/6}}-\frac{\sqrt[6]{b} \tan ^{-1}\left(\frac{2 \sqrt[6]{a} x+\sqrt{3} \sqrt[6]{b}}{\sqrt[6]{b}}\right)}{6 a^{7/6}}+\frac{x}{a}","\frac{\sqrt[6]{b} \log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a} x^2+\sqrt[3]{b}\right)}{4 \sqrt{3} a^{7/6}}-\frac{\sqrt[6]{b} \log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a} x^2+\sqrt[3]{b}\right)}{4 \sqrt{3} a^{7/6}}-\frac{\sqrt[6]{b} \tan ^{-1}\left(\frac{\sqrt[6]{a} x}{\sqrt[6]{b}}\right)}{3 a^{7/6}}+\frac{\sqrt[6]{b} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{b}-2 \sqrt[6]{a} x}{\sqrt[6]{b}}\right)}{6 a^{7/6}}-\frac{\sqrt[6]{b} \tan ^{-1}\left(\frac{2 \sqrt[6]{a} x+\sqrt{3} \sqrt[6]{b}}{\sqrt[6]{b}}\right)}{6 a^{7/6}}+\frac{x}{a}",1,"x/a - (b^(1/6)*ArcTan[(a^(1/6)*x)/b^(1/6)])/(3*a^(7/6)) + (b^(1/6)*ArcTan[(Sqrt[3]*b^(1/6) - 2*a^(1/6)*x)/b^(1/6)])/(6*a^(7/6)) - (b^(1/6)*ArcTan[(Sqrt[3]*b^(1/6) + 2*a^(1/6)*x)/b^(1/6)])/(6*a^(7/6)) + (b^(1/6)*Log[b^(1/3) - Sqrt[3]*a^(1/6)*b^(1/6)*x + a^(1/3)*x^2])/(4*Sqrt[3]*a^(7/6)) - (b^(1/6)*Log[b^(1/3) + Sqrt[3]*a^(1/6)*b^(1/6)*x + a^(1/3)*x^2])/(4*Sqrt[3]*a^(7/6))","A",12,8,9,0.8889,1,"{193, 321, 209, 634, 618, 204, 628, 205}"
2110,1,272,0,0.2706146,"\int \frac{1}{a+\frac{b}{x^8}} \, dx","Int[(a + b/x^8)^(-1),x]","-\frac{\sqrt[8]{b} \log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{b} x+\sqrt[4]{-a} x^2+\sqrt[4]{b}\right)}{8 \sqrt{2} (-a)^{9/8}}+\frac{\sqrt[8]{b} \log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{b} x+\sqrt[4]{-a} x^2+\sqrt[4]{b}\right)}{8 \sqrt{2} (-a)^{9/8}}+\frac{\sqrt[8]{b} \tan ^{-1}\left(\frac{\sqrt[8]{-a} x}{\sqrt[8]{b}}\right)}{4 (-a)^{9/8}}-\frac{\sqrt[8]{b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{-a} x}{\sqrt[8]{b}}\right)}{4 \sqrt{2} (-a)^{9/8}}+\frac{\sqrt[8]{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{-a} x}{\sqrt[8]{b}}+1\right)}{4 \sqrt{2} (-a)^{9/8}}+\frac{\sqrt[8]{b} \tanh ^{-1}\left(\frac{\sqrt[8]{-a} x}{\sqrt[8]{b}}\right)}{4 (-a)^{9/8}}+\frac{x}{a}","-\frac{\sqrt[8]{b} \log \left(-\sqrt{2} \sqrt[8]{-a} \sqrt[8]{b} x+\sqrt[4]{-a} x^2+\sqrt[4]{b}\right)}{8 \sqrt{2} (-a)^{9/8}}+\frac{\sqrt[8]{b} \log \left(\sqrt{2} \sqrt[8]{-a} \sqrt[8]{b} x+\sqrt[4]{-a} x^2+\sqrt[4]{b}\right)}{8 \sqrt{2} (-a)^{9/8}}+\frac{\sqrt[8]{b} \tan ^{-1}\left(\frac{\sqrt[8]{-a} x}{\sqrt[8]{b}}\right)}{4 (-a)^{9/8}}-\frac{\sqrt[8]{b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{-a} x}{\sqrt[8]{b}}\right)}{4 \sqrt{2} (-a)^{9/8}}+\frac{\sqrt[8]{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{-a} x}{\sqrt[8]{b}}+1\right)}{4 \sqrt{2} (-a)^{9/8}}+\frac{\sqrt[8]{b} \tanh ^{-1}\left(\frac{\sqrt[8]{-a} x}{\sqrt[8]{b}}\right)}{4 (-a)^{9/8}}+\frac{x}{a}",1,"x/a + (b^(1/8)*ArcTan[((-a)^(1/8)*x)/b^(1/8)])/(4*(-a)^(9/8)) - (b^(1/8)*ArcTan[1 - (Sqrt[2]*(-a)^(1/8)*x)/b^(1/8)])/(4*Sqrt[2]*(-a)^(9/8)) + (b^(1/8)*ArcTan[1 + (Sqrt[2]*(-a)^(1/8)*x)/b^(1/8)])/(4*Sqrt[2]*(-a)^(9/8)) + (b^(1/8)*ArcTanh[((-a)^(1/8)*x)/b^(1/8)])/(4*(-a)^(9/8)) - (b^(1/8)*Log[b^(1/4) - Sqrt[2]*(-a)^(1/8)*b^(1/8)*x + (-a)^(1/4)*x^2])/(8*Sqrt[2]*(-a)^(9/8)) + (b^(1/8)*Log[b^(1/4) + Sqrt[2]*(-a)^(1/8)*b^(1/8)*x + (-a)^(1/4)*x^2])/(8*Sqrt[2]*(-a)^(9/8))","A",15,12,9,1.333,1,"{193, 321, 214, 212, 208, 205, 211, 1165, 628, 1162, 617, 204}"
2111,1,19,0,0.0053891,"\int \left(a+b \sqrt{x}\right) x^4 \, dx","Int[(a + b*Sqrt[x])*x^4,x]","\frac{a x^5}{5}+\frac{2}{11} b x^{11/2}","\frac{a x^5}{5}+\frac{2}{11} b x^{11/2}",1,"(a*x^5)/5 + (2*b*x^(11/2))/11","A",2,1,13,0.07692,1,"{14}"
2112,1,19,0,0.0049615,"\int \left(a+b \sqrt{x}\right) x^3 \, dx","Int[(a + b*Sqrt[x])*x^3,x]","\frac{a x^4}{4}+\frac{2}{9} b x^{9/2}","\frac{a x^4}{4}+\frac{2}{9} b x^{9/2}",1,"(a*x^4)/4 + (2*b*x^(9/2))/9","A",2,1,13,0.07692,1,"{14}"
2113,1,19,0,0.0048315,"\int \left(a+b \sqrt{x}\right) x^2 \, dx","Int[(a + b*Sqrt[x])*x^2,x]","\frac{a x^3}{3}+\frac{2}{7} b x^{7/2}","\frac{a x^3}{3}+\frac{2}{7} b x^{7/2}",1,"(a*x^3)/3 + (2*b*x^(7/2))/7","A",2,1,13,0.07692,1,"{14}"
2114,1,19,0,0.0048254,"\int \left(a+b \sqrt{x}\right) x \, dx","Int[(a + b*Sqrt[x])*x,x]","\frac{a x^2}{2}+\frac{2}{5} b x^{5/2}","\frac{a x^2}{2}+\frac{2}{5} b x^{5/2}",1,"(a*x^2)/2 + (2*b*x^(5/2))/5","A",2,1,11,0.09091,1,"{14}"
2115,1,14,0,0.0022963,"\int \left(a+b \sqrt{x}\right) \, dx","Int[a + b*Sqrt[x],x]","a x+\frac{2}{3} b x^{3/2}","a x+\frac{2}{3} b x^{3/2}",1,"a*x + (2*b*x^(3/2))/3","A",1,0,9,0,1,"{}"
2116,1,13,0,0.0045222,"\int \frac{a+b \sqrt{x}}{x} \, dx","Int[(a + b*Sqrt[x])/x,x]","a \log (x)+2 b \sqrt{x}","a \log (x)+2 b \sqrt{x}",1,"2*b*Sqrt[x] + a*Log[x]","A",2,1,13,0.07692,1,"{14}"
2117,1,15,0,0.0047636,"\int \frac{a+b \sqrt{x}}{x^2} \, dx","Int[(a + b*Sqrt[x])/x^2,x]","-\frac{a}{x}-\frac{2 b}{\sqrt{x}}","-\frac{a}{x}-\frac{2 b}{\sqrt{x}}",1,"-(a/x) - (2*b)/Sqrt[x]","A",2,1,13,0.07692,1,"{14}"
2118,1,19,0,0.0051484,"\int \frac{a+b \sqrt{x}}{x^3} \, dx","Int[(a + b*Sqrt[x])/x^3,x]","-\frac{a}{2 x^2}-\frac{2 b}{3 x^{3/2}}","-\frac{a}{2 x^2}-\frac{2 b}{3 x^{3/2}}",1,"-a/(2*x^2) - (2*b)/(3*x^(3/2))","A",2,1,13,0.07692,1,"{14}"
2119,1,19,0,0.004937,"\int \frac{a+b \sqrt{x}}{x^4} \, dx","Int[(a + b*Sqrt[x])/x^4,x]","-\frac{a}{3 x^3}-\frac{2 b}{5 x^{5/2}}","-\frac{a}{3 x^3}-\frac{2 b}{5 x^{5/2}}",1,"-a/(3*x^3) - (2*b)/(5*x^(5/2))","A",2,1,13,0.07692,1,"{14}"
2120,1,32,0,0.0261072,"\int \left(a+b \sqrt{x}\right)^2 x^4 \, dx","Int[(a + b*Sqrt[x])^2*x^4,x]","\frac{a^2 x^5}{5}+\frac{4}{11} a b x^{11/2}+\frac{b^2 x^6}{6}","\frac{a^2 x^5}{5}+\frac{4}{11} a b x^{11/2}+\frac{b^2 x^6}{6}",1,"(a^2*x^5)/5 + (4*a*b*x^(11/2))/11 + (b^2*x^6)/6","A",3,2,15,0.1333,1,"{266, 43}"
2121,1,32,0,0.023469,"\int \left(a+b \sqrt{x}\right)^2 x^3 \, dx","Int[(a + b*Sqrt[x])^2*x^3,x]","\frac{a^2 x^4}{4}+\frac{4}{9} a b x^{9/2}+\frac{b^2 x^5}{5}","\frac{a^2 x^4}{4}+\frac{4}{9} a b x^{9/2}+\frac{b^2 x^5}{5}",1,"(a^2*x^4)/4 + (4*a*b*x^(9/2))/9 + (b^2*x^5)/5","A",3,2,15,0.1333,1,"{266, 43}"
2122,1,32,0,0.0214081,"\int \left(a+b \sqrt{x}\right)^2 x^2 \, dx","Int[(a + b*Sqrt[x])^2*x^2,x]","\frac{a^2 x^3}{3}+\frac{4}{7} a b x^{7/2}+\frac{b^2 x^4}{4}","\frac{a^2 x^3}{3}+\frac{4}{7} a b x^{7/2}+\frac{b^2 x^4}{4}",1,"(a^2*x^3)/3 + (4*a*b*x^(7/2))/7 + (b^2*x^4)/4","A",3,2,15,0.1333,1,"{266, 43}"
2123,1,32,0,0.0178599,"\int \left(a+b \sqrt{x}\right)^2 x \, dx","Int[(a + b*Sqrt[x])^2*x,x]","\frac{a^2 x^2}{2}+\frac{4}{5} a b x^{5/2}+\frac{b^2 x^3}{3}","\frac{a^2 x^2}{2}+\frac{4}{5} a b x^{5/2}+\frac{b^2 x^3}{3}",1,"(a^2*x^2)/2 + (4*a*b*x^(5/2))/5 + (b^2*x^3)/3","A",3,2,13,0.1538,1,"{266, 43}"
2124,1,27,0,0.0160736,"\int \left(a+b \sqrt{x}\right)^2 \, dx","Int[(a + b*Sqrt[x])^2,x]","a^2 x+\frac{4}{3} a b x^{3/2}+\frac{b^2 x^2}{2}","a^2 x+\frac{4}{3} a b x^{3/2}+\frac{b^2 x^2}{2}",1,"a^2*x + (4*a*b*x^(3/2))/3 + (b^2*x^2)/2","A",3,2,11,0.1818,1,"{190, 43}"
2125,1,21,0,0.0119502,"\int \frac{\left(a+b \sqrt{x}\right)^2}{x} \, dx","Int[(a + b*Sqrt[x])^2/x,x]","a^2 \log (x)+4 a b \sqrt{x}+b^2 x","a^2 \log (x)+4 a b \sqrt{x}+b^2 x",1,"4*a*b*Sqrt[x] + b^2*x + a^2*Log[x]","A",3,2,15,0.1333,1,"{266, 43}"
2126,1,24,0,0.0132717,"\int \frac{\left(a+b \sqrt{x}\right)^2}{x^2} \, dx","Int[(a + b*Sqrt[x])^2/x^2,x]","-\frac{a^2}{x}-\frac{4 a b}{\sqrt{x}}+b^2 \log (x)","-\frac{a^2}{x}-\frac{4 a b}{\sqrt{x}}+b^2 \log (x)",1,"-(a^2/x) - (4*a*b)/Sqrt[x] + b^2*Log[x]","A",3,2,15,0.1333,1,"{266, 43}"
2127,1,30,0,0.0137169,"\int \frac{\left(a+b \sqrt{x}\right)^2}{x^3} \, dx","Int[(a + b*Sqrt[x])^2/x^3,x]","-\frac{a^2}{2 x^2}-\frac{4 a b}{3 x^{3/2}}-\frac{b^2}{x}","-\frac{a^2}{2 x^2}-\frac{4 a b}{3 x^{3/2}}-\frac{b^2}{x}",1,"-a^2/(2*x^2) - (4*a*b)/(3*x^(3/2)) - b^2/x","A",3,2,15,0.1333,1,"{266, 43}"
2128,1,32,0,0.0136014,"\int \frac{\left(a+b \sqrt{x}\right)^2}{x^4} \, dx","Int[(a + b*Sqrt[x])^2/x^4,x]","-\frac{a^2}{3 x^3}-\frac{4 a b}{5 x^{5/2}}-\frac{b^2}{2 x^2}","-\frac{a^2}{3 x^3}-\frac{4 a b}{5 x^{5/2}}-\frac{b^2}{2 x^2}",1,"-a^2/(3*x^3) - (4*a*b)/(5*x^(5/2)) - b^2/(2*x^2)","A",3,2,15,0.1333,1,"{266, 43}"
2129,1,32,0,0.0142292,"\int \frac{\left(a+b \sqrt{x}\right)^2}{x^5} \, dx","Int[(a + b*Sqrt[x])^2/x^5,x]","-\frac{a^2}{4 x^4}-\frac{4 a b}{7 x^{7/2}}-\frac{b^2}{3 x^3}","-\frac{a^2}{4 x^4}-\frac{4 a b}{7 x^{7/2}}-\frac{b^2}{3 x^3}",1,"-a^2/(4*x^4) - (4*a*b)/(7*x^(7/2)) - b^2/(3*x^3)","A",3,2,15,0.1333,1,"{266, 43}"
2130,1,47,0,0.0301109,"\int \left(a+b \sqrt{x}\right)^3 x^4 \, dx","Int[(a + b*Sqrt[x])^3*x^4,x]","\frac{6}{11} a^2 b x^{11/2}+\frac{a^3 x^5}{5}+\frac{1}{2} a b^2 x^6+\frac{2}{13} b^3 x^{13/2}","\frac{6}{11} a^2 b x^{11/2}+\frac{a^3 x^5}{5}+\frac{1}{2} a b^2 x^6+\frac{2}{13} b^3 x^{13/2}",1,"(a^3*x^5)/5 + (6*a^2*b*x^(11/2))/11 + (a*b^2*x^6)/2 + (2*b^3*x^(13/2))/13","A",3,2,15,0.1333,1,"{266, 43}"
2131,1,47,0,0.0283058,"\int \left(a+b \sqrt{x}\right)^3 x^3 \, dx","Int[(a + b*Sqrt[x])^3*x^3,x]","\frac{2}{3} a^2 b x^{9/2}+\frac{a^3 x^4}{4}+\frac{3}{5} a b^2 x^5+\frac{2}{11} b^3 x^{11/2}","\frac{2}{3} a^2 b x^{9/2}+\frac{a^3 x^4}{4}+\frac{3}{5} a b^2 x^5+\frac{2}{11} b^3 x^{11/2}",1,"(a^3*x^4)/4 + (2*a^2*b*x^(9/2))/3 + (3*a*b^2*x^5)/5 + (2*b^3*x^(11/2))/11","A",3,2,15,0.1333,1,"{266, 43}"
2132,1,47,0,0.0277525,"\int \left(a+b \sqrt{x}\right)^3 x^2 \, dx","Int[(a + b*Sqrt[x])^3*x^2,x]","\frac{6}{7} a^2 b x^{7/2}+\frac{a^3 x^3}{3}+\frac{3}{4} a b^2 x^4+\frac{2}{9} b^3 x^{9/2}","\frac{6}{7} a^2 b x^{7/2}+\frac{a^3 x^3}{3}+\frac{3}{4} a b^2 x^4+\frac{2}{9} b^3 x^{9/2}",1,"(a^3*x^3)/3 + (6*a^2*b*x^(7/2))/7 + (3*a*b^2*x^4)/4 + (2*b^3*x^(9/2))/9","A",3,2,15,0.1333,1,"{266, 43}"
2133,1,44,0,0.0245843,"\int \left(a+b \sqrt{x}\right)^3 x \, dx","Int[(a + b*Sqrt[x])^3*x,x]","\frac{6}{5} a^2 b x^{5/2}+\frac{a^3 x^2}{2}+a b^2 x^3+\frac{2}{7} b^3 x^{7/2}","\frac{6}{5} a^2 b x^{5/2}+\frac{a^3 x^2}{2}+a b^2 x^3+\frac{2}{7} b^3 x^{7/2}",1,"(a^3*x^2)/2 + (6*a^2*b*x^(5/2))/5 + a*b^2*x^3 + (2*b^3*x^(7/2))/7","A",3,2,13,0.1538,1,"{266, 43}"
2134,1,38,0,0.01534,"\int \left(a+b \sqrt{x}\right)^3 \, dx","Int[(a + b*Sqrt[x])^3,x]","\frac{2 \left(a+b \sqrt{x}\right)^5}{5 b^2}-\frac{a \left(a+b \sqrt{x}\right)^4}{2 b^2}","\frac{2 \left(a+b \sqrt{x}\right)^5}{5 b^2}-\frac{a \left(a+b \sqrt{x}\right)^4}{2 b^2}",1,"-(a*(a + b*Sqrt[x])^4)/(2*b^2) + (2*(a + b*Sqrt[x])^5)/(5*b^2)","A",3,2,11,0.1818,1,"{190, 43}"
2135,1,37,0,0.0175741,"\int \frac{\left(a+b \sqrt{x}\right)^3}{x} \, dx","Int[(a + b*Sqrt[x])^3/x,x]","6 a^2 b \sqrt{x}+a^3 \log (x)+3 a b^2 x+\frac{2}{3} b^3 x^{3/2}","6 a^2 b \sqrt{x}+a^3 \log (x)+3 a b^2 x+\frac{2}{3} b^3 x^{3/2}",1,"6*a^2*b*Sqrt[x] + 3*a*b^2*x + (2*b^3*x^(3/2))/3 + a^3*Log[x]","A",3,2,15,0.1333,1,"{266, 43}"
2136,1,38,0,0.0195794,"\int \frac{\left(a+b \sqrt{x}\right)^3}{x^2} \, dx","Int[(a + b*Sqrt[x])^3/x^2,x]","-\frac{6 a^2 b}{\sqrt{x}}-\frac{a^3}{x}+3 a b^2 \log (x)+2 b^3 \sqrt{x}","-\frac{6 a^2 b}{\sqrt{x}}-\frac{a^3}{x}+3 a b^2 \log (x)+2 b^3 \sqrt{x}",1,"-(a^3/x) - (6*a^2*b)/Sqrt[x] + 2*b^3*Sqrt[x] + 3*a*b^2*Log[x]","A",3,2,15,0.1333,1,"{266, 43}"
2137,1,21,0,0.0033667,"\int \frac{\left(a+b \sqrt{x}\right)^3}{x^3} \, dx","Int[(a + b*Sqrt[x])^3/x^3,x]","-\frac{\left(a+b \sqrt{x}\right)^4}{2 a x^2}","-\frac{\left(a+b \sqrt{x}\right)^4}{2 a x^2}",1,"-(a + b*Sqrt[x])^4/(2*a*x^2)","A",1,1,15,0.06667,1,"{264}"
2138,1,47,0,0.0201946,"\int \frac{\left(a+b \sqrt{x}\right)^3}{x^4} \, dx","Int[(a + b*Sqrt[x])^3/x^4,x]","-\frac{6 a^2 b}{5 x^{5/2}}-\frac{a^3}{3 x^3}-\frac{3 a b^2}{2 x^2}-\frac{2 b^3}{3 x^{3/2}}","-\frac{6 a^2 b}{5 x^{5/2}}-\frac{a^3}{3 x^3}-\frac{3 a b^2}{2 x^2}-\frac{2 b^3}{3 x^{3/2}}",1,"-a^3/(3*x^3) - (6*a^2*b)/(5*x^(5/2)) - (3*a*b^2)/(2*x^2) - (2*b^3)/(3*x^(3/2))","A",3,2,15,0.1333,1,"{266, 43}"
2139,1,45,0,0.0203438,"\int \frac{\left(a+b \sqrt{x}\right)^3}{x^5} \, dx","Int[(a + b*Sqrt[x])^3/x^5,x]","-\frac{6 a^2 b}{7 x^{7/2}}-\frac{a^3}{4 x^4}-\frac{a b^2}{x^3}-\frac{2 b^3}{5 x^{5/2}}","-\frac{6 a^2 b}{7 x^{7/2}}-\frac{a^3}{4 x^4}-\frac{a b^2}{x^3}-\frac{2 b^3}{5 x^{5/2}}",1,"-a^3/(4*x^4) - (6*a^2*b)/(7*x^(7/2)) - (a*b^2)/x^3 - (2*b^3)/(5*x^(5/2))","A",3,2,15,0.1333,1,"{266, 43}"
2140,1,47,0,0.0197708,"\int \frac{\left(a+b \sqrt{x}\right)^3}{x^6} \, dx","Int[(a + b*Sqrt[x])^3/x^6,x]","-\frac{2 a^2 b}{3 x^{9/2}}-\frac{a^3}{5 x^5}-\frac{3 a b^2}{4 x^4}-\frac{2 b^3}{7 x^{7/2}}","-\frac{2 a^2 b}{3 x^{9/2}}-\frac{a^3}{5 x^5}-\frac{3 a b^2}{4 x^4}-\frac{2 b^3}{7 x^{7/2}}",1,"-a^3/(5*x^5) - (2*a^2*b)/(3*x^(9/2)) - (3*a*b^2)/(4*x^4) - (2*b^3)/(7*x^(7/2))","A",3,2,15,0.1333,1,"{266, 43}"
2141,1,75,0,0.0453066,"\int \left(a+b \sqrt{x}\right)^5 x^4 \, dx","Int[(a + b*Sqrt[x])^5*x^4,x]","\frac{20}{13} a^2 b^3 x^{13/2}+\frac{5}{3} a^3 b^2 x^6+\frac{10}{11} a^4 b x^{11/2}+\frac{a^5 x^5}{5}+\frac{5}{7} a b^4 x^7+\frac{2}{15} b^5 x^{15/2}","\frac{20}{13} a^2 b^3 x^{13/2}+\frac{5}{3} a^3 b^2 x^6+\frac{10}{11} a^4 b x^{11/2}+\frac{a^5 x^5}{5}+\frac{5}{7} a b^4 x^7+\frac{2}{15} b^5 x^{15/2}",1,"(a^5*x^5)/5 + (10*a^4*b*x^(11/2))/11 + (5*a^3*b^2*x^6)/3 + (20*a^2*b^3*x^(13/2))/13 + (5*a*b^4*x^7)/7 + (2*b^5*x^(15/2))/15","A",3,2,15,0.1333,1,"{266, 43}"
2142,1,73,0,0.0411744,"\int \left(a+b \sqrt{x}\right)^5 x^3 \, dx","Int[(a + b*Sqrt[x])^5*x^3,x]","\frac{20}{11} a^2 b^3 x^{11/2}+2 a^3 b^2 x^5+\frac{10}{9} a^4 b x^{9/2}+\frac{a^5 x^4}{4}+\frac{5}{6} a b^4 x^6+\frac{2}{13} b^5 x^{13/2}","\frac{20}{11} a^2 b^3 x^{11/2}+2 a^3 b^2 x^5+\frac{10}{9} a^4 b x^{9/2}+\frac{a^5 x^4}{4}+\frac{5}{6} a b^4 x^6+\frac{2}{13} b^5 x^{13/2}",1,"(a^5*x^4)/4 + (10*a^4*b*x^(9/2))/9 + 2*a^3*b^2*x^5 + (20*a^2*b^3*x^(11/2))/11 + (5*a*b^4*x^6)/6 + (2*b^5*x^(13/2))/13","A",3,2,15,0.1333,1,"{266, 43}"
2143,1,72,0,0.0402159,"\int \left(a+b \sqrt{x}\right)^5 x^2 \, dx","Int[(a + b*Sqrt[x])^5*x^2,x]","\frac{20}{9} a^2 b^3 x^{9/2}+\frac{5}{2} a^3 b^2 x^4+\frac{10}{7} a^4 b x^{7/2}+\frac{a^5 x^3}{3}+a b^4 x^5+\frac{2}{11} b^5 x^{11/2}","\frac{20}{9} a^2 b^3 x^{9/2}+\frac{5}{2} a^3 b^2 x^4+\frac{10}{7} a^4 b x^{7/2}+\frac{a^5 x^3}{3}+a b^4 x^5+\frac{2}{11} b^5 x^{11/2}",1,"(a^5*x^3)/3 + (10*a^4*b*x^(7/2))/7 + (5*a^3*b^2*x^4)/2 + (20*a^2*b^3*x^(9/2))/9 + a*b^4*x^5 + (2*b^5*x^(11/2))/11","A",3,2,15,0.1333,1,"{266, 43}"
2144,1,80,0,0.0370688,"\int \left(a+b \sqrt{x}\right)^5 x \, dx","Int[(a + b*Sqrt[x])^5*x,x]","\frac{6 a^2 \left(a+b \sqrt{x}\right)^7}{7 b^4}-\frac{a^3 \left(a+b \sqrt{x}\right)^6}{3 b^4}+\frac{2 \left(a+b \sqrt{x}\right)^9}{9 b^4}-\frac{3 a \left(a+b \sqrt{x}\right)^8}{4 b^4}","\frac{6 a^2 \left(a+b \sqrt{x}\right)^7}{7 b^4}-\frac{a^3 \left(a+b \sqrt{x}\right)^6}{3 b^4}+\frac{2 \left(a+b \sqrt{x}\right)^9}{9 b^4}-\frac{3 a \left(a+b \sqrt{x}\right)^8}{4 b^4}",1,"-(a^3*(a + b*Sqrt[x])^6)/(3*b^4) + (6*a^2*(a + b*Sqrt[x])^7)/(7*b^4) - (3*a*(a + b*Sqrt[x])^8)/(4*b^4) + (2*(a + b*Sqrt[x])^9)/(9*b^4)","A",3,2,13,0.1538,1,"{266, 43}"
2145,1,38,0,0.0133622,"\int \left(a+b \sqrt{x}\right)^5 \, dx","Int[(a + b*Sqrt[x])^5,x]","\frac{2 \left(a+b \sqrt{x}\right)^7}{7 b^2}-\frac{a \left(a+b \sqrt{x}\right)^6}{3 b^2}","\frac{2 \left(a+b \sqrt{x}\right)^7}{7 b^2}-\frac{a \left(a+b \sqrt{x}\right)^6}{3 b^2}",1,"-(a*(a + b*Sqrt[x])^6)/(3*b^2) + (2*(a + b*Sqrt[x])^7)/(7*b^2)","A",3,2,11,0.1818,1,"{190, 43}"
2146,1,65,0,0.0311541,"\int \frac{\left(a+b \sqrt{x}\right)^5}{x} \, dx","Int[(a + b*Sqrt[x])^5/x,x]","\frac{20}{3} a^2 b^3 x^{3/2}+10 a^3 b^2 x+10 a^4 b \sqrt{x}+a^5 \log (x)+\frac{5}{2} a b^4 x^2+\frac{2}{5} b^5 x^{5/2}","\frac{20}{3} a^2 b^3 x^{3/2}+10 a^3 b^2 x+10 a^4 b \sqrt{x}+a^5 \log (x)+\frac{5}{2} a b^4 x^2+\frac{2}{5} b^5 x^{5/2}",1,"10*a^4*b*Sqrt[x] + 10*a^3*b^2*x + (20*a^2*b^3*x^(3/2))/3 + (5*a*b^4*x^2)/2 + (2*b^5*x^(5/2))/5 + a^5*Log[x]","A",3,2,15,0.1333,1,"{266, 43}"
2147,1,62,0,0.033022,"\int \frac{\left(a+b \sqrt{x}\right)^5}{x^2} \, dx","Int[(a + b*Sqrt[x])^5/x^2,x]","20 a^2 b^3 \sqrt{x}+10 a^3 b^2 \log (x)-\frac{10 a^4 b}{\sqrt{x}}-\frac{a^5}{x}+5 a b^4 x+\frac{2}{3} b^5 x^{3/2}","20 a^2 b^3 \sqrt{x}+10 a^3 b^2 \log (x)-\frac{10 a^4 b}{\sqrt{x}}-\frac{a^5}{x}+5 a b^4 x+\frac{2}{3} b^5 x^{3/2}",1,"-(a^5/x) - (10*a^4*b)/Sqrt[x] + 20*a^2*b^3*Sqrt[x] + 5*a*b^4*x + (2*b^5*x^(3/2))/3 + 10*a^3*b^2*Log[x]","A",3,2,15,0.1333,1,"{266, 43}"
2148,1,66,0,0.0306667,"\int \frac{\left(a+b \sqrt{x}\right)^5}{x^3} \, dx","Int[(a + b*Sqrt[x])^5/x^3,x]","-\frac{10 a^3 b^2}{x}-\frac{20 a^2 b^3}{\sqrt{x}}-\frac{10 a^4 b}{3 x^{3/2}}-\frac{a^5}{2 x^2}+5 a b^4 \log (x)+2 b^5 \sqrt{x}","-\frac{10 a^3 b^2}{x}-\frac{20 a^2 b^3}{\sqrt{x}}-\frac{10 a^4 b}{3 x^{3/2}}-\frac{a^5}{2 x^2}+5 a b^4 \log (x)+2 b^5 \sqrt{x}",1,"-a^5/(2*x^2) - (10*a^4*b)/(3*x^(3/2)) - (10*a^3*b^2)/x - (20*a^2*b^3)/Sqrt[x] + 2*b^5*Sqrt[x] + 5*a*b^4*Log[x]","A",3,2,15,0.1333,1,"{266, 43}"
2149,1,21,0,0.0032821,"\int \frac{\left(a+b \sqrt{x}\right)^5}{x^4} \, dx","Int[(a + b*Sqrt[x])^5/x^4,x]","-\frac{\left(a+b \sqrt{x}\right)^6}{3 a x^3}","-\frac{\left(a+b \sqrt{x}\right)^6}{3 a x^3}",1,"-(a + b*Sqrt[x])^6/(3*a*x^3)","A",1,1,15,0.06667,1,"{264}"
2150,1,70,0,0.0217816,"\int \frac{\left(a+b \sqrt{x}\right)^5}{x^5} \, dx","Int[(a + b*Sqrt[x])^5/x^5,x]","-\frac{b^2 \left(a+b \sqrt{x}\right)^6}{84 a^3 x^3}+\frac{b \left(a+b \sqrt{x}\right)^6}{14 a^2 x^{7/2}}-\frac{\left(a+b \sqrt{x}\right)^6}{4 a x^4}","-\frac{b^2 \left(a+b \sqrt{x}\right)^6}{84 a^3 x^3}+\frac{b \left(a+b \sqrt{x}\right)^6}{14 a^2 x^{7/2}}-\frac{\left(a+b \sqrt{x}\right)^6}{4 a x^4}",1,"-(a + b*Sqrt[x])^6/(4*a*x^4) + (b*(a + b*Sqrt[x])^6)/(14*a^2*x^(7/2)) - (b^2*(a + b*Sqrt[x])^6)/(84*a^3*x^3)","A",4,3,15,0.2000,1,"{266, 45, 37}"
2151,1,75,0,0.0319221,"\int \frac{\left(a+b \sqrt{x}\right)^5}{x^6} \, dx","Int[(a + b*Sqrt[x])^5/x^6,x]","-\frac{5 a^3 b^2}{2 x^4}-\frac{20 a^2 b^3}{7 x^{7/2}}-\frac{10 a^4 b}{9 x^{9/2}}-\frac{a^5}{5 x^5}-\frac{5 a b^4}{3 x^3}-\frac{2 b^5}{5 x^{5/2}}","-\frac{5 a^3 b^2}{2 x^4}-\frac{20 a^2 b^3}{7 x^{7/2}}-\frac{10 a^4 b}{9 x^{9/2}}-\frac{a^5}{5 x^5}-\frac{5 a b^4}{3 x^3}-\frac{2 b^5}{5 x^{5/2}}",1,"-a^5/(5*x^5) - (10*a^4*b)/(9*x^(9/2)) - (5*a^3*b^2)/(2*x^4) - (20*a^2*b^3)/(7*x^(7/2)) - (5*a*b^4)/(3*x^3) - (2*b^5)/(5*x^(5/2))","A",3,2,15,0.1333,1,"{266, 43}"
2152,1,73,0,0.032088,"\int \frac{\left(a+b \sqrt{x}\right)^5}{x^7} \, dx","Int[(a + b*Sqrt[x])^5/x^7,x]","-\frac{2 a^3 b^2}{x^5}-\frac{20 a^2 b^3}{9 x^{9/2}}-\frac{10 a^4 b}{11 x^{11/2}}-\frac{a^5}{6 x^6}-\frac{5 a b^4}{4 x^4}-\frac{2 b^5}{7 x^{7/2}}","-\frac{2 a^3 b^2}{x^5}-\frac{20 a^2 b^3}{9 x^{9/2}}-\frac{10 a^4 b}{11 x^{11/2}}-\frac{a^5}{6 x^6}-\frac{5 a b^4}{4 x^4}-\frac{2 b^5}{7 x^{7/2}}",1,"-a^5/(6*x^6) - (10*a^4*b)/(11*x^(11/2)) - (2*a^3*b^2)/x^5 - (20*a^2*b^3)/(9*x^(9/2)) - (5*a*b^4)/(4*x^4) - (2*b^5)/(7*x^(7/2))","A",3,2,15,0.1333,1,"{266, 43}"
2153,1,140,0,0.0967475,"\int \left(a+b \sqrt{x}\right)^{10} x^4 \, dx","Int[(a + b*Sqrt[x])^10*x^4,x]","\frac{15}{2} a^8 b^2 x^6+\frac{240}{13} a^7 b^3 x^{13/2}+30 a^6 b^4 x^7+\frac{168}{5} a^5 b^5 x^{15/2}+\frac{105}{4} a^4 b^6 x^8+\frac{240}{17} a^3 b^7 x^{17/2}+5 a^2 b^8 x^9+\frac{20}{11} a^9 b x^{11/2}+\frac{a^{10} x^5}{5}+\frac{20}{19} a b^9 x^{19/2}+\frac{b^{10} x^{10}}{10}","\frac{15}{2} a^8 b^2 x^6+\frac{240}{13} a^7 b^3 x^{13/2}+30 a^6 b^4 x^7+\frac{168}{5} a^5 b^5 x^{15/2}+\frac{105}{4} a^4 b^6 x^8+\frac{240}{17} a^3 b^7 x^{17/2}+5 a^2 b^8 x^9+\frac{20}{11} a^9 b x^{11/2}+\frac{a^{10} x^5}{5}+\frac{20}{19} a b^9 x^{19/2}+\frac{b^{10} x^{10}}{10}",1,"(a^10*x^5)/5 + (20*a^9*b*x^(11/2))/11 + (15*a^8*b^2*x^6)/2 + (240*a^7*b^3*x^(13/2))/13 + 30*a^6*b^4*x^7 + (168*a^5*b^5*x^(15/2))/5 + (105*a^4*b^6*x^8)/4 + (240*a^3*b^7*x^(17/2))/17 + 5*a^2*b^8*x^9 + (20*a*b^9*x^(19/2))/19 + (b^10*x^10)/10","A",3,2,15,0.1333,1,"{266, 43}"
2154,1,162,0,0.0804328,"\int \left(a+b \sqrt{x}\right)^{10} x^3 \, dx","Int[(a + b*Sqrt[x])^10*x^3,x]","\frac{21 a^2 \left(a+b \sqrt{x}\right)^{16}}{8 b^8}-\frac{14 a^3 \left(a+b \sqrt{x}\right)^{15}}{3 b^8}+\frac{5 a^4 \left(a+b \sqrt{x}\right)^{14}}{b^8}-\frac{42 a^5 \left(a+b \sqrt{x}\right)^{13}}{13 b^8}+\frac{7 a^6 \left(a+b \sqrt{x}\right)^{12}}{6 b^8}-\frac{2 a^7 \left(a+b \sqrt{x}\right)^{11}}{11 b^8}+\frac{\left(a+b \sqrt{x}\right)^{18}}{9 b^8}-\frac{14 a \left(a+b \sqrt{x}\right)^{17}}{17 b^8}","\frac{21 a^2 \left(a+b \sqrt{x}\right)^{16}}{8 b^8}-\frac{14 a^3 \left(a+b \sqrt{x}\right)^{15}}{3 b^8}+\frac{5 a^4 \left(a+b \sqrt{x}\right)^{14}}{b^8}-\frac{42 a^5 \left(a+b \sqrt{x}\right)^{13}}{13 b^8}+\frac{7 a^6 \left(a+b \sqrt{x}\right)^{12}}{6 b^8}-\frac{2 a^7 \left(a+b \sqrt{x}\right)^{11}}{11 b^8}+\frac{\left(a+b \sqrt{x}\right)^{18}}{9 b^8}-\frac{14 a \left(a+b \sqrt{x}\right)^{17}}{17 b^8}",1,"(-2*a^7*(a + b*Sqrt[x])^11)/(11*b^8) + (7*a^6*(a + b*Sqrt[x])^12)/(6*b^8) - (42*a^5*(a + b*Sqrt[x])^13)/(13*b^8) + (5*a^4*(a + b*Sqrt[x])^14)/b^8 - (14*a^3*(a + b*Sqrt[x])^15)/(3*b^8) + (21*a^2*(a + b*Sqrt[x])^16)/(8*b^8) - (14*a*(a + b*Sqrt[x])^17)/(17*b^8) + (a + b*Sqrt[x])^18/(9*b^8)","A",3,2,15,0.1333,1,"{266, 43}"
2155,1,122,0,0.0642877,"\int \left(a+b \sqrt{x}\right)^{10} x^2 \, dx","Int[(a + b*Sqrt[x])^10*x^2,x]","\frac{10 a^2 \left(a+b \sqrt{x}\right)^{14}}{7 b^6}-\frac{20 a^3 \left(a+b \sqrt{x}\right)^{13}}{13 b^6}+\frac{5 a^4 \left(a+b \sqrt{x}\right)^{12}}{6 b^6}-\frac{2 a^5 \left(a+b \sqrt{x}\right)^{11}}{11 b^6}+\frac{\left(a+b \sqrt{x}\right)^{16}}{8 b^6}-\frac{2 a \left(a+b \sqrt{x}\right)^{15}}{3 b^6}","\frac{10 a^2 \left(a+b \sqrt{x}\right)^{14}}{7 b^6}-\frac{20 a^3 \left(a+b \sqrt{x}\right)^{13}}{13 b^6}+\frac{5 a^4 \left(a+b \sqrt{x}\right)^{12}}{6 b^6}-\frac{2 a^5 \left(a+b \sqrt{x}\right)^{11}}{11 b^6}+\frac{\left(a+b \sqrt{x}\right)^{16}}{8 b^6}-\frac{2 a \left(a+b \sqrt{x}\right)^{15}}{3 b^6}",1,"(-2*a^5*(a + b*Sqrt[x])^11)/(11*b^6) + (5*a^4*(a + b*Sqrt[x])^12)/(6*b^6) - (20*a^3*(a + b*Sqrt[x])^13)/(13*b^6) + (10*a^2*(a + b*Sqrt[x])^14)/(7*b^6) - (2*a*(a + b*Sqrt[x])^15)/(3*b^6) + (a + b*Sqrt[x])^16/(8*b^6)","A",3,2,15,0.1333,1,"{266, 43}"
2156,1,80,0,0.045463,"\int \left(a+b \sqrt{x}\right)^{10} x \, dx","Int[(a + b*Sqrt[x])^10*x,x]","\frac{a^2 \left(a+b \sqrt{x}\right)^{12}}{2 b^4}-\frac{2 a^3 \left(a+b \sqrt{x}\right)^{11}}{11 b^4}+\frac{\left(a+b \sqrt{x}\right)^{14}}{7 b^4}-\frac{6 a \left(a+b \sqrt{x}\right)^{13}}{13 b^4}","\frac{a^2 \left(a+b \sqrt{x}\right)^{12}}{2 b^4}-\frac{2 a^3 \left(a+b \sqrt{x}\right)^{11}}{11 b^4}+\frac{\left(a+b \sqrt{x}\right)^{14}}{7 b^4}-\frac{6 a \left(a+b \sqrt{x}\right)^{13}}{13 b^4}",1,"(-2*a^3*(a + b*Sqrt[x])^11)/(11*b^4) + (a^2*(a + b*Sqrt[x])^12)/(2*b^4) - (6*a*(a + b*Sqrt[x])^13)/(13*b^4) + (a + b*Sqrt[x])^14/(7*b^4)","A",3,2,13,0.1538,1,"{266, 43}"
2157,1,38,0,0.0146011,"\int \left(a+b \sqrt{x}\right)^{10} \, dx","Int[(a + b*Sqrt[x])^10,x]","\frac{\left(a+b \sqrt{x}\right)^{12}}{6 b^2}-\frac{2 a \left(a+b \sqrt{x}\right)^{11}}{11 b^2}","\frac{\left(a+b \sqrt{x}\right)^{12}}{6 b^2}-\frac{2 a \left(a+b \sqrt{x}\right)^{11}}{11 b^2}",1,"(-2*a*(a + b*Sqrt[x])^11)/(11*b^2) + (a + b*Sqrt[x])^12/(6*b^2)","A",3,2,11,0.1818,1,"{190, 43}"
2158,1,128,0,0.0656418,"\int \frac{\left(a+b \sqrt{x}\right)^{10}}{x} \, dx","Int[(a + b*Sqrt[x])^10/x,x]","80 a^7 b^3 x^{3/2}+105 a^6 b^4 x^2+\frac{504}{5} a^5 b^5 x^{5/2}+70 a^4 b^6 x^3+\frac{240}{7} a^3 b^7 x^{7/2}+\frac{45}{4} a^2 b^8 x^4+45 a^8 b^2 x+20 a^9 b \sqrt{x}+a^{10} \log (x)+\frac{20}{9} a b^9 x^{9/2}+\frac{b^{10} x^5}{5}","80 a^7 b^3 x^{3/2}+105 a^6 b^4 x^2+\frac{504}{5} a^5 b^5 x^{5/2}+70 a^4 b^6 x^3+\frac{240}{7} a^3 b^7 x^{7/2}+\frac{45}{4} a^2 b^8 x^4+45 a^8 b^2 x+20 a^9 b \sqrt{x}+a^{10} \log (x)+\frac{20}{9} a b^9 x^{9/2}+\frac{b^{10} x^5}{5}",1,"20*a^9*b*Sqrt[x] + 45*a^8*b^2*x + 80*a^7*b^3*x^(3/2) + 105*a^6*b^4*x^2 + (504*a^5*b^5*x^(5/2))/5 + 70*a^4*b^6*x^3 + (240*a^3*b^7*x^(7/2))/7 + (45*a^2*b^8*x^4)/4 + (20*a*b^9*x^(9/2))/9 + (b^10*x^5)/5 + a^10*Log[x]","A",3,2,15,0.1333,1,"{266, 43}"
2159,1,123,0,0.0691617,"\int \frac{\left(a+b \sqrt{x}\right)^{10}}{x^2} \, dx","Int[(a + b*Sqrt[x])^10/x^2,x]","168 a^5 b^5 x^{3/2}+105 a^4 b^6 x^2+48 a^3 b^7 x^{5/2}+15 a^2 b^8 x^3+240 a^7 b^3 \sqrt{x}+210 a^6 b^4 x+45 a^8 b^2 \log (x)-\frac{20 a^9 b}{\sqrt{x}}-\frac{a^{10}}{x}+\frac{20}{7} a b^9 x^{7/2}+\frac{b^{10} x^4}{4}","168 a^5 b^5 x^{3/2}+105 a^4 b^6 x^2+48 a^3 b^7 x^{5/2}+15 a^2 b^8 x^3+240 a^7 b^3 \sqrt{x}+210 a^6 b^4 x+45 a^8 b^2 \log (x)-\frac{20 a^9 b}{\sqrt{x}}-\frac{a^{10}}{x}+\frac{20}{7} a b^9 x^{7/2}+\frac{b^{10} x^4}{4}",1,"-(a^10/x) - (20*a^9*b)/Sqrt[x] + 240*a^7*b^3*Sqrt[x] + 210*a^6*b^4*x + 168*a^5*b^5*x^(3/2) + 105*a^4*b^6*x^2 + 48*a^3*b^7*x^(5/2) + 15*a^2*b^8*x^3 + (20*a*b^9*x^(7/2))/7 + (b^10*x^4)/4 + 45*a^8*b^2*Log[x]","A",3,2,15,0.1333,1,"{266, 43}"
2160,1,127,0,0.070199,"\int \frac{\left(a+b \sqrt{x}\right)^{10}}{x^3} \, dx","Int[(a + b*Sqrt[x])^10/x^3,x]","80 a^3 b^7 x^{3/2}+\frac{45}{2} a^2 b^8 x^2-\frac{45 a^8 b^2}{x}-\frac{240 a^7 b^3}{\sqrt{x}}+504 a^5 b^5 \sqrt{x}+210 a^4 b^6 x+210 a^6 b^4 \log (x)-\frac{20 a^9 b}{3 x^{3/2}}-\frac{a^{10}}{2 x^2}+4 a b^9 x^{5/2}+\frac{b^{10} x^3}{3}","80 a^3 b^7 x^{3/2}+\frac{45}{2} a^2 b^8 x^2-\frac{45 a^8 b^2}{x}-\frac{240 a^7 b^3}{\sqrt{x}}+504 a^5 b^5 \sqrt{x}+210 a^4 b^6 x+210 a^6 b^4 \log (x)-\frac{20 a^9 b}{3 x^{3/2}}-\frac{a^{10}}{2 x^2}+4 a b^9 x^{5/2}+\frac{b^{10} x^3}{3}",1,"-a^10/(2*x^2) - (20*a^9*b)/(3*x^(3/2)) - (45*a^8*b^2)/x - (240*a^7*b^3)/Sqrt[x] + 504*a^5*b^5*Sqrt[x] + 210*a^4*b^6*x + 80*a^3*b^7*x^(3/2) + (45*a^2*b^8*x^2)/2 + 4*a*b^9*x^(5/2) + (b^10*x^3)/3 + 210*a^6*b^4*Log[x]","A",3,2,15,0.1333,1,"{266, 43}"
2161,1,127,0,0.0689496,"\int \frac{\left(a+b \sqrt{x}\right)^{10}}{x^4} \, dx","Int[(a + b*Sqrt[x])^10/x^4,x]","-\frac{45 a^8 b^2}{2 x^2}-\frac{80 a^7 b^3}{x^{3/2}}-\frac{210 a^6 b^4}{x}-\frac{504 a^5 b^5}{\sqrt{x}}+240 a^3 b^7 \sqrt{x}+45 a^2 b^8 x+210 a^4 b^6 \log (x)-\frac{4 a^9 b}{x^{5/2}}-\frac{a^{10}}{3 x^3}+\frac{20}{3} a b^9 x^{3/2}+\frac{b^{10} x^2}{2}","-\frac{45 a^8 b^2}{2 x^2}-\frac{80 a^7 b^3}{x^{3/2}}-\frac{210 a^6 b^4}{x}-\frac{504 a^5 b^5}{\sqrt{x}}+240 a^3 b^7 \sqrt{x}+45 a^2 b^8 x+210 a^4 b^6 \log (x)-\frac{4 a^9 b}{x^{5/2}}-\frac{a^{10}}{3 x^3}+\frac{20}{3} a b^9 x^{3/2}+\frac{b^{10} x^2}{2}",1,"-a^10/(3*x^3) - (4*a^9*b)/x^(5/2) - (45*a^8*b^2)/(2*x^2) - (80*a^7*b^3)/x^(3/2) - (210*a^6*b^4)/x - (504*a^5*b^5)/Sqrt[x] + 240*a^3*b^7*Sqrt[x] + 45*a^2*b^8*x + (20*a*b^9*x^(3/2))/3 + (b^10*x^2)/2 + 210*a^4*b^6*Log[x]","A",3,2,15,0.1333,1,"{266, 43}"
2162,1,122,0,0.0674332,"\int \frac{\left(a+b \sqrt{x}\right)^{10}}{x^5} \, dx","Int[(a + b*Sqrt[x])^10/x^5,x]","-\frac{15 a^8 b^2}{x^3}-\frac{48 a^7 b^3}{x^{5/2}}-\frac{105 a^6 b^4}{x^2}-\frac{168 a^5 b^5}{x^{3/2}}-\frac{210 a^4 b^6}{x}-\frac{240 a^3 b^7}{\sqrt{x}}+45 a^2 b^8 \log (x)-\frac{20 a^9 b}{7 x^{7/2}}-\frac{a^{10}}{4 x^4}+20 a b^9 \sqrt{x}+b^{10} x","-\frac{15 a^8 b^2}{x^3}-\frac{48 a^7 b^3}{x^{5/2}}-\frac{105 a^6 b^4}{x^2}-\frac{168 a^5 b^5}{x^{3/2}}-\frac{210 a^4 b^6}{x}-\frac{240 a^3 b^7}{\sqrt{x}}+45 a^2 b^8 \log (x)-\frac{20 a^9 b}{7 x^{7/2}}-\frac{a^{10}}{4 x^4}+20 a b^9 \sqrt{x}+b^{10} x",1,"-a^10/(4*x^4) - (20*a^9*b)/(7*x^(7/2)) - (15*a^8*b^2)/x^3 - (48*a^7*b^3)/x^(5/2) - (105*a^6*b^4)/x^2 - (168*a^5*b^5)/x^(3/2) - (210*a^4*b^6)/x - (240*a^3*b^7)/Sqrt[x] + 20*a*b^9*Sqrt[x] + b^10*x + 45*a^2*b^8*Log[x]","A",3,2,15,0.1333,1,"{266, 43}"
2163,1,130,0,0.068445,"\int \frac{\left(a+b \sqrt{x}\right)^{10}}{x^6} \, dx","Int[(a + b*Sqrt[x])^10/x^6,x]","-\frac{45 a^8 b^2}{4 x^4}-\frac{240 a^7 b^3}{7 x^{7/2}}-\frac{70 a^6 b^4}{x^3}-\frac{504 a^5 b^5}{5 x^{5/2}}-\frac{105 a^4 b^6}{x^2}-\frac{80 a^3 b^7}{x^{3/2}}-\frac{45 a^2 b^8}{x}-\frac{20 a^9 b}{9 x^{9/2}}-\frac{a^{10}}{5 x^5}-\frac{20 a b^9}{\sqrt{x}}+b^{10} \log (x)","-\frac{45 a^8 b^2}{4 x^4}-\frac{240 a^7 b^3}{7 x^{7/2}}-\frac{70 a^6 b^4}{x^3}-\frac{504 a^5 b^5}{5 x^{5/2}}-\frac{105 a^4 b^6}{x^2}-\frac{80 a^3 b^7}{x^{3/2}}-\frac{45 a^2 b^8}{x}-\frac{20 a^9 b}{9 x^{9/2}}-\frac{a^{10}}{5 x^5}-\frac{20 a b^9}{\sqrt{x}}+b^{10} \log (x)",1,"-a^10/(5*x^5) - (20*a^9*b)/(9*x^(9/2)) - (45*a^8*b^2)/(4*x^4) - (240*a^7*b^3)/(7*x^(7/2)) - (70*a^6*b^4)/x^3 - (504*a^5*b^5)/(5*x^(5/2)) - (105*a^4*b^6)/x^2 - (80*a^3*b^7)/x^(3/2) - (45*a^2*b^8)/x - (20*a*b^9)/Sqrt[x] + b^10*Log[x]","A",3,2,15,0.1333,1,"{266, 43}"
2164,1,46,0,0.013311,"\int \frac{\left(a+b \sqrt{x}\right)^{10}}{x^7} \, dx","Int[(a + b*Sqrt[x])^10/x^7,x]","\frac{b \left(a+b \sqrt{x}\right)^{11}}{66 a^2 x^{11/2}}-\frac{\left(a+b \sqrt{x}\right)^{11}}{6 a x^6}","\frac{b \left(a+b \sqrt{x}\right)^{11}}{66 a^2 x^{11/2}}-\frac{\left(a+b \sqrt{x}\right)^{11}}{6 a x^6}",1,"-(a + b*Sqrt[x])^11/(6*a*x^6) + (b*(a + b*Sqrt[x])^11)/(66*a^2*x^(11/2))","A",3,3,15,0.2000,1,"{266, 45, 37}"
2165,1,96,0,0.0341753,"\int \frac{\left(a+b \sqrt{x}\right)^{10}}{x^8} \, dx","Int[(a + b*Sqrt[x])^10/x^8,x]","\frac{b^3 \left(a+b \sqrt{x}\right)^{11}}{2002 a^4 x^{11/2}}-\frac{b^2 \left(a+b \sqrt{x}\right)^{11}}{182 a^3 x^6}+\frac{3 b \left(a+b \sqrt{x}\right)^{11}}{91 a^2 x^{13/2}}-\frac{\left(a+b \sqrt{x}\right)^{11}}{7 a x^7}","\frac{b^3 \left(a+b \sqrt{x}\right)^{11}}{2002 a^4 x^{11/2}}-\frac{b^2 \left(a+b \sqrt{x}\right)^{11}}{182 a^3 x^6}+\frac{3 b \left(a+b \sqrt{x}\right)^{11}}{91 a^2 x^{13/2}}-\frac{\left(a+b \sqrt{x}\right)^{11}}{7 a x^7}",1,"-(a + b*Sqrt[x])^11/(7*a*x^7) + (3*b*(a + b*Sqrt[x])^11)/(91*a^2*x^(13/2)) - (b^2*(a + b*Sqrt[x])^11)/(182*a^3*x^6) + (b^3*(a + b*Sqrt[x])^11)/(2002*a^4*x^(11/2))","A",5,3,15,0.2000,1,"{266, 45, 37}"
2166,1,146,0,0.0572555,"\int \frac{\left(a+b \sqrt{x}\right)^{10}}{x^9} \, dx","Int[(a + b*Sqrt[x])^10/x^9,x]","\frac{b^5 \left(a+b \sqrt{x}\right)^{11}}{24024 a^6 x^{11/2}}-\frac{b^4 \left(a+b \sqrt{x}\right)^{11}}{2184 a^5 x^6}+\frac{b^3 \left(a+b \sqrt{x}\right)^{11}}{364 a^4 x^{13/2}}-\frac{b^2 \left(a+b \sqrt{x}\right)^{11}}{84 a^3 x^7}+\frac{b \left(a+b \sqrt{x}\right)^{11}}{24 a^2 x^{15/2}}-\frac{\left(a+b \sqrt{x}\right)^{11}}{8 a x^8}","\frac{b^5 \left(a+b \sqrt{x}\right)^{11}}{24024 a^6 x^{11/2}}-\frac{b^4 \left(a+b \sqrt{x}\right)^{11}}{2184 a^5 x^6}+\frac{b^3 \left(a+b \sqrt{x}\right)^{11}}{364 a^4 x^{13/2}}-\frac{b^2 \left(a+b \sqrt{x}\right)^{11}}{84 a^3 x^7}+\frac{b \left(a+b \sqrt{x}\right)^{11}}{24 a^2 x^{15/2}}-\frac{\left(a+b \sqrt{x}\right)^{11}}{8 a x^8}",1,"-(a + b*Sqrt[x])^11/(8*a*x^8) + (b*(a + b*Sqrt[x])^11)/(24*a^2*x^(15/2)) - (b^2*(a + b*Sqrt[x])^11)/(84*a^3*x^7) + (b^3*(a + b*Sqrt[x])^11)/(364*a^4*x^(13/2)) - (b^4*(a + b*Sqrt[x])^11)/(2184*a^5*x^6) + (b^5*(a + b*Sqrt[x])^11)/(24024*a^6*x^(11/2))","A",7,3,15,0.2000,1,"{266, 45, 37}"
2167,1,136,0,0.0676372,"\int \frac{\left(a+b \sqrt{x}\right)^{10}}{x^{10}} \, dx","Int[(a + b*Sqrt[x])^10/x^10,x]","-\frac{45 a^8 b^2}{8 x^8}-\frac{16 a^7 b^3}{x^{15/2}}-\frac{30 a^6 b^4}{x^7}-\frac{504 a^5 b^5}{13 x^{13/2}}-\frac{35 a^4 b^6}{x^6}-\frac{240 a^3 b^7}{11 x^{11/2}}-\frac{9 a^2 b^8}{x^5}-\frac{20 a^9 b}{17 x^{17/2}}-\frac{a^{10}}{9 x^9}-\frac{20 a b^9}{9 x^{9/2}}-\frac{b^{10}}{4 x^4}","-\frac{45 a^8 b^2}{8 x^8}-\frac{16 a^7 b^3}{x^{15/2}}-\frac{30 a^6 b^4}{x^7}-\frac{504 a^5 b^5}{13 x^{13/2}}-\frac{35 a^4 b^6}{x^6}-\frac{240 a^3 b^7}{11 x^{11/2}}-\frac{9 a^2 b^8}{x^5}-\frac{20 a^9 b}{17 x^{17/2}}-\frac{a^{10}}{9 x^9}-\frac{20 a b^9}{9 x^{9/2}}-\frac{b^{10}}{4 x^4}",1,"-a^10/(9*x^9) - (20*a^9*b)/(17*x^(17/2)) - (45*a^8*b^2)/(8*x^8) - (16*a^7*b^3)/x^(15/2) - (30*a^6*b^4)/x^7 - (504*a^5*b^5)/(13*x^(13/2)) - (35*a^4*b^6)/x^6 - (240*a^3*b^7)/(11*x^(11/2)) - (9*a^2*b^8)/x^5 - (20*a*b^9)/(9*x^(9/2)) - b^10/(4*x^4)","A",3,2,15,0.1333,1,"{266, 43}"
2168,1,140,0,0.0662356,"\int \frac{\left(a+b \sqrt{x}\right)^{10}}{x^{11}} \, dx","Int[(a + b*Sqrt[x])^10/x^11,x]","-\frac{5 a^8 b^2}{x^9}-\frac{240 a^7 b^3}{17 x^{17/2}}-\frac{105 a^6 b^4}{4 x^8}-\frac{168 a^5 b^5}{5 x^{15/2}}-\frac{30 a^4 b^6}{x^7}-\frac{240 a^3 b^7}{13 x^{13/2}}-\frac{15 a^2 b^8}{2 x^6}-\frac{20 a^9 b}{19 x^{19/2}}-\frac{a^{10}}{10 x^{10}}-\frac{20 a b^9}{11 x^{11/2}}-\frac{b^{10}}{5 x^5}","-\frac{5 a^8 b^2}{x^9}-\frac{240 a^7 b^3}{17 x^{17/2}}-\frac{105 a^6 b^4}{4 x^8}-\frac{168 a^5 b^5}{5 x^{15/2}}-\frac{30 a^4 b^6}{x^7}-\frac{240 a^3 b^7}{13 x^{13/2}}-\frac{15 a^2 b^8}{2 x^6}-\frac{20 a^9 b}{19 x^{19/2}}-\frac{a^{10}}{10 x^{10}}-\frac{20 a b^9}{11 x^{11/2}}-\frac{b^{10}}{5 x^5}",1,"-a^10/(10*x^10) - (20*a^9*b)/(19*x^(19/2)) - (5*a^8*b^2)/x^9 - (240*a^7*b^3)/(17*x^(17/2)) - (105*a^6*b^4)/(4*x^8) - (168*a^5*b^5)/(5*x^(15/2)) - (30*a^4*b^6)/x^7 - (240*a^3*b^7)/(13*x^(13/2)) - (15*a^2*b^8)/(2*x^6) - (20*a*b^9)/(11*x^(11/2)) - b^10/(5*x^5)","A",3,2,15,0.1333,1,"{266, 43}"
2169,1,242,0,0.1618661,"\int \left(a+b \sqrt{x}\right)^{15} x^5 \, dx","Int[(a + b*Sqrt[x])^15*x^5,x]","\frac{22 a^2 \left(a+b \sqrt{x}\right)^{25}}{5 b^{12}}-\frac{55 a^3 \left(a+b \sqrt{x}\right)^{24}}{4 b^{12}}+\frac{660 a^4 \left(a+b \sqrt{x}\right)^{23}}{23 b^{12}}-\frac{42 a^5 \left(a+b \sqrt{x}\right)^{22}}{b^{12}}+\frac{44 a^6 \left(a+b \sqrt{x}\right)^{21}}{b^{12}}-\frac{33 a^7 \left(a+b \sqrt{x}\right)^{20}}{b^{12}}+\frac{330 a^8 \left(a+b \sqrt{x}\right)^{19}}{19 b^{12}}-\frac{55 a^9 \left(a+b \sqrt{x}\right)^{18}}{9 b^{12}}+\frac{22 a^{10} \left(a+b \sqrt{x}\right)^{17}}{17 b^{12}}-\frac{a^{11} \left(a+b \sqrt{x}\right)^{16}}{8 b^{12}}+\frac{2 \left(a+b \sqrt{x}\right)^{27}}{27 b^{12}}-\frac{11 a \left(a+b \sqrt{x}\right)^{26}}{13 b^{12}}","\frac{22 a^2 \left(a+b \sqrt{x}\right)^{25}}{5 b^{12}}-\frac{55 a^3 \left(a+b \sqrt{x}\right)^{24}}{4 b^{12}}+\frac{660 a^4 \left(a+b \sqrt{x}\right)^{23}}{23 b^{12}}-\frac{42 a^5 \left(a+b \sqrt{x}\right)^{22}}{b^{12}}+\frac{44 a^6 \left(a+b \sqrt{x}\right)^{21}}{b^{12}}-\frac{33 a^7 \left(a+b \sqrt{x}\right)^{20}}{b^{12}}+\frac{330 a^8 \left(a+b \sqrt{x}\right)^{19}}{19 b^{12}}-\frac{55 a^9 \left(a+b \sqrt{x}\right)^{18}}{9 b^{12}}+\frac{22 a^{10} \left(a+b \sqrt{x}\right)^{17}}{17 b^{12}}-\frac{a^{11} \left(a+b \sqrt{x}\right)^{16}}{8 b^{12}}+\frac{2 \left(a+b \sqrt{x}\right)^{27}}{27 b^{12}}-\frac{11 a \left(a+b \sqrt{x}\right)^{26}}{13 b^{12}}",1,"-(a^11*(a + b*Sqrt[x])^16)/(8*b^12) + (22*a^10*(a + b*Sqrt[x])^17)/(17*b^12) - (55*a^9*(a + b*Sqrt[x])^18)/(9*b^12) + (330*a^8*(a + b*Sqrt[x])^19)/(19*b^12) - (33*a^7*(a + b*Sqrt[x])^20)/b^12 + (44*a^6*(a + b*Sqrt[x])^21)/b^12 - (42*a^5*(a + b*Sqrt[x])^22)/b^12 + (660*a^4*(a + b*Sqrt[x])^23)/(23*b^12) - (55*a^3*(a + b*Sqrt[x])^24)/(4*b^12) + (22*a^2*(a + b*Sqrt[x])^25)/(5*b^12) - (11*a*(a + b*Sqrt[x])^26)/(13*b^12) + (2*(a + b*Sqrt[x])^27)/(27*b^12)","A",3,2,15,0.1333,1,"{266, 43}"
2170,1,202,0,0.1117498,"\int \left(a+b \sqrt{x}\right)^{15} x^4 \, dx","Int[(a + b*Sqrt[x])^15*x^4,x]","\frac{72 a^2 \left(a+b \sqrt{x}\right)^{23}}{23 b^{10}}-\frac{84 a^3 \left(a+b \sqrt{x}\right)^{22}}{11 b^{10}}+\frac{12 a^4 \left(a+b \sqrt{x}\right)^{21}}{b^{10}}-\frac{63 a^5 \left(a+b \sqrt{x}\right)^{20}}{5 b^{10}}+\frac{168 a^6 \left(a+b \sqrt{x}\right)^{19}}{19 b^{10}}-\frac{4 a^7 \left(a+b \sqrt{x}\right)^{18}}{b^{10}}+\frac{18 a^8 \left(a+b \sqrt{x}\right)^{17}}{17 b^{10}}-\frac{a^9 \left(a+b \sqrt{x}\right)^{16}}{8 b^{10}}+\frac{2 \left(a+b \sqrt{x}\right)^{25}}{25 b^{10}}-\frac{3 a \left(a+b \sqrt{x}\right)^{24}}{4 b^{10}}","\frac{72 a^2 \left(a+b \sqrt{x}\right)^{23}}{23 b^{10}}-\frac{84 a^3 \left(a+b \sqrt{x}\right)^{22}}{11 b^{10}}+\frac{12 a^4 \left(a+b \sqrt{x}\right)^{21}}{b^{10}}-\frac{63 a^5 \left(a+b \sqrt{x}\right)^{20}}{5 b^{10}}+\frac{168 a^6 \left(a+b \sqrt{x}\right)^{19}}{19 b^{10}}-\frac{4 a^7 \left(a+b \sqrt{x}\right)^{18}}{b^{10}}+\frac{18 a^8 \left(a+b \sqrt{x}\right)^{17}}{17 b^{10}}-\frac{a^9 \left(a+b \sqrt{x}\right)^{16}}{8 b^{10}}+\frac{2 \left(a+b \sqrt{x}\right)^{25}}{25 b^{10}}-\frac{3 a \left(a+b \sqrt{x}\right)^{24}}{4 b^{10}}",1,"-(a^9*(a + b*Sqrt[x])^16)/(8*b^10) + (18*a^8*(a + b*Sqrt[x])^17)/(17*b^10) - (4*a^7*(a + b*Sqrt[x])^18)/b^10 + (168*a^6*(a + b*Sqrt[x])^19)/(19*b^10) - (63*a^5*(a + b*Sqrt[x])^20)/(5*b^10) + (12*a^4*(a + b*Sqrt[x])^21)/b^10 - (84*a^3*(a + b*Sqrt[x])^22)/(11*b^10) + (72*a^2*(a + b*Sqrt[x])^23)/(23*b^10) - (3*a*(a + b*Sqrt[x])^24)/(4*b^10) + (2*(a + b*Sqrt[x])^25)/(25*b^10)","A",3,2,15,0.1333,1,"{266, 43}"
2171,1,162,0,0.0918026,"\int \left(a+b \sqrt{x}\right)^{15} x^3 \, dx","Int[(a + b*Sqrt[x])^15*x^3,x]","\frac{2 a^2 \left(a+b \sqrt{x}\right)^{21}}{b^8}-\frac{7 a^3 \left(a+b \sqrt{x}\right)^{20}}{2 b^8}+\frac{70 a^4 \left(a+b \sqrt{x}\right)^{19}}{19 b^8}-\frac{7 a^5 \left(a+b \sqrt{x}\right)^{18}}{3 b^8}+\frac{14 a^6 \left(a+b \sqrt{x}\right)^{17}}{17 b^8}-\frac{a^7 \left(a+b \sqrt{x}\right)^{16}}{8 b^8}+\frac{2 \left(a+b \sqrt{x}\right)^{23}}{23 b^8}-\frac{7 a \left(a+b \sqrt{x}\right)^{22}}{11 b^8}","\frac{2 a^2 \left(a+b \sqrt{x}\right)^{21}}{b^8}-\frac{7 a^3 \left(a+b \sqrt{x}\right)^{20}}{2 b^8}+\frac{70 a^4 \left(a+b \sqrt{x}\right)^{19}}{19 b^8}-\frac{7 a^5 \left(a+b \sqrt{x}\right)^{18}}{3 b^8}+\frac{14 a^6 \left(a+b \sqrt{x}\right)^{17}}{17 b^8}-\frac{a^7 \left(a+b \sqrt{x}\right)^{16}}{8 b^8}+\frac{2 \left(a+b \sqrt{x}\right)^{23}}{23 b^8}-\frac{7 a \left(a+b \sqrt{x}\right)^{22}}{11 b^8}",1,"-(a^7*(a + b*Sqrt[x])^16)/(8*b^8) + (14*a^6*(a + b*Sqrt[x])^17)/(17*b^8) - (7*a^5*(a + b*Sqrt[x])^18)/(3*b^8) + (70*a^4*(a + b*Sqrt[x])^19)/(19*b^8) - (7*a^3*(a + b*Sqrt[x])^20)/(2*b^8) + (2*a^2*(a + b*Sqrt[x])^21)/b^8 - (7*a*(a + b*Sqrt[x])^22)/(11*b^8) + (2*(a + b*Sqrt[x])^23)/(23*b^8)","A",3,2,15,0.1333,1,"{266, 43}"
2172,1,122,0,0.0736079,"\int \left(a+b \sqrt{x}\right)^{15} x^2 \, dx","Int[(a + b*Sqrt[x])^15*x^2,x]","\frac{20 a^2 \left(a+b \sqrt{x}\right)^{19}}{19 b^6}-\frac{10 a^3 \left(a+b \sqrt{x}\right)^{18}}{9 b^6}+\frac{10 a^4 \left(a+b \sqrt{x}\right)^{17}}{17 b^6}-\frac{a^5 \left(a+b \sqrt{x}\right)^{16}}{8 b^6}+\frac{2 \left(a+b \sqrt{x}\right)^{21}}{21 b^6}-\frac{a \left(a+b \sqrt{x}\right)^{20}}{2 b^6}","\frac{20 a^2 \left(a+b \sqrt{x}\right)^{19}}{19 b^6}-\frac{10 a^3 \left(a+b \sqrt{x}\right)^{18}}{9 b^6}+\frac{10 a^4 \left(a+b \sqrt{x}\right)^{17}}{17 b^6}-\frac{a^5 \left(a+b \sqrt{x}\right)^{16}}{8 b^6}+\frac{2 \left(a+b \sqrt{x}\right)^{21}}{21 b^6}-\frac{a \left(a+b \sqrt{x}\right)^{20}}{2 b^6}",1,"-(a^5*(a + b*Sqrt[x])^16)/(8*b^6) + (10*a^4*(a + b*Sqrt[x])^17)/(17*b^6) - (10*a^3*(a + b*Sqrt[x])^18)/(9*b^6) + (20*a^2*(a + b*Sqrt[x])^19)/(19*b^6) - (a*(a + b*Sqrt[x])^20)/(2*b^6) + (2*(a + b*Sqrt[x])^21)/(21*b^6)","A",3,2,15,0.1333,1,"{266, 43}"
2173,1,80,0,0.0574581,"\int \left(a+b \sqrt{x}\right)^{15} x \, dx","Int[(a + b*Sqrt[x])^15*x,x]","\frac{6 a^2 \left(a+b \sqrt{x}\right)^{17}}{17 b^4}-\frac{a^3 \left(a+b \sqrt{x}\right)^{16}}{8 b^4}+\frac{2 \left(a+b \sqrt{x}\right)^{19}}{19 b^4}-\frac{a \left(a+b \sqrt{x}\right)^{18}}{3 b^4}","\frac{6 a^2 \left(a+b \sqrt{x}\right)^{17}}{17 b^4}-\frac{a^3 \left(a+b \sqrt{x}\right)^{16}}{8 b^4}+\frac{2 \left(a+b \sqrt{x}\right)^{19}}{19 b^4}-\frac{a \left(a+b \sqrt{x}\right)^{18}}{3 b^4}",1,"-(a^3*(a + b*Sqrt[x])^16)/(8*b^4) + (6*a^2*(a + b*Sqrt[x])^17)/(17*b^4) - (a*(a + b*Sqrt[x])^18)/(3*b^4) + (2*(a + b*Sqrt[x])^19)/(19*b^4)","A",3,2,13,0.1538,1,"{266, 43}"
2174,1,38,0,0.013963,"\int \left(a+b \sqrt{x}\right)^{15} \, dx","Int[(a + b*Sqrt[x])^15,x]","\frac{2 \left(a+b \sqrt{x}\right)^{17}}{17 b^2}-\frac{a \left(a+b \sqrt{x}\right)^{16}}{8 b^2}","\frac{2 \left(a+b \sqrt{x}\right)^{17}}{17 b^2}-\frac{a \left(a+b \sqrt{x}\right)^{16}}{8 b^2}",1,"-(a*(a + b*Sqrt[x])^16)/(8*b^2) + (2*(a + b*Sqrt[x])^17)/(17*b^2)","A",3,2,11,0.1818,1,"{190, 43}"
2175,1,205,0,0.1119913,"\int \frac{\left(a+b \sqrt{x}\right)^{15}}{x} \, dx","Int[(a + b*Sqrt[x])^15/x,x]","\frac{910}{3} a^{12} b^3 x^{3/2}+\frac{1365}{2} a^{11} b^4 x^2+\frac{6006}{5} a^{10} b^5 x^{5/2}+\frac{5005}{3} a^9 b^6 x^3+\frac{12870}{7} a^8 b^7 x^{7/2}+\frac{6435}{4} a^7 b^8 x^4+\frac{10010}{9} a^6 b^9 x^{9/2}+\frac{3003}{5} a^5 b^{10} x^5+\frac{2730}{11} a^4 b^{11} x^{11/2}+\frac{455}{6} a^3 b^{12} x^6+\frac{210}{13} a^2 b^{13} x^{13/2}+105 a^{13} b^2 x+30 a^{14} b \sqrt{x}+a^{15} \log (x)+\frac{15}{7} a b^{14} x^7+\frac{2}{15} b^{15} x^{15/2}","\frac{910}{3} a^{12} b^3 x^{3/2}+\frac{1365}{2} a^{11} b^4 x^2+\frac{6006}{5} a^{10} b^5 x^{5/2}+\frac{5005}{3} a^9 b^6 x^3+\frac{12870}{7} a^8 b^7 x^{7/2}+\frac{6435}{4} a^7 b^8 x^4+\frac{10010}{9} a^6 b^9 x^{9/2}+\frac{3003}{5} a^5 b^{10} x^5+\frac{2730}{11} a^4 b^{11} x^{11/2}+\frac{455}{6} a^3 b^{12} x^6+\frac{210}{13} a^2 b^{13} x^{13/2}+105 a^{13} b^2 x+30 a^{14} b \sqrt{x}+a^{15} \log (x)+\frac{15}{7} a b^{14} x^7+\frac{2}{15} b^{15} x^{15/2}",1,"30*a^14*b*Sqrt[x] + 105*a^13*b^2*x + (910*a^12*b^3*x^(3/2))/3 + (1365*a^11*b^4*x^2)/2 + (6006*a^10*b^5*x^(5/2))/5 + (5005*a^9*b^6*x^3)/3 + (12870*a^8*b^7*x^(7/2))/7 + (6435*a^7*b^8*x^4)/4 + (10010*a^6*b^9*x^(9/2))/9 + (3003*a^5*b^10*x^5)/5 + (2730*a^4*b^11*x^(11/2))/11 + (455*a^3*b^12*x^6)/6 + (210*a^2*b^13*x^(13/2))/13 + (15*a*b^14*x^7)/7 + (2*b^15*x^(15/2))/15 + a^15*Log[x]","A",3,2,15,0.1333,1,"{266, 43}"
2176,1,192,0,0.117044,"\int \frac{\left(a+b \sqrt{x}\right)^{15}}{x^2} \, dx","Int[(a + b*Sqrt[x])^15/x^2,x]","2002 a^{10} b^5 x^{3/2}+\frac{5005}{2} a^9 b^6 x^2+2574 a^8 b^7 x^{5/2}+2145 a^7 b^8 x^3+1430 a^6 b^9 x^{7/2}+\frac{3003}{4} a^5 b^{10} x^4+\frac{910}{3} a^4 b^{11} x^{9/2}+91 a^3 b^{12} x^5+\frac{210}{11} a^2 b^{13} x^{11/2}+910 a^{12} b^3 \sqrt{x}+1365 a^{11} b^4 x+105 a^{13} b^2 \log (x)-\frac{30 a^{14} b}{\sqrt{x}}-\frac{a^{15}}{x}+\frac{5}{2} a b^{14} x^6+\frac{2}{13} b^{15} x^{13/2}","2002 a^{10} b^5 x^{3/2}+\frac{5005}{2} a^9 b^6 x^2+2574 a^8 b^7 x^{5/2}+2145 a^7 b^8 x^3+1430 a^6 b^9 x^{7/2}+\frac{3003}{4} a^5 b^{10} x^4+\frac{910}{3} a^4 b^{11} x^{9/2}+91 a^3 b^{12} x^5+\frac{210}{11} a^2 b^{13} x^{11/2}+910 a^{12} b^3 \sqrt{x}+1365 a^{11} b^4 x+105 a^{13} b^2 \log (x)-\frac{30 a^{14} b}{\sqrt{x}}-\frac{a^{15}}{x}+\frac{5}{2} a b^{14} x^6+\frac{2}{13} b^{15} x^{13/2}",1,"-(a^15/x) - (30*a^14*b)/Sqrt[x] + 910*a^12*b^3*Sqrt[x] + 1365*a^11*b^4*x + 2002*a^10*b^5*x^(3/2) + (5005*a^9*b^6*x^2)/2 + 2574*a^8*b^7*x^(5/2) + 2145*a^7*b^8*x^3 + 1430*a^6*b^9*x^(7/2) + (3003*a^5*b^10*x^4)/4 + (910*a^4*b^11*x^(9/2))/3 + 91*a^3*b^12*x^5 + (210*a^2*b^13*x^(11/2))/11 + (5*a*b^14*x^6)/2 + (2*b^15*x^(13/2))/13 + 105*a^13*b^2*Log[x]","A",3,2,15,0.1333,1,"{266, 43}"
2177,1,190,0,0.1154179,"\int \frac{\left(a+b \sqrt{x}\right)^{15}}{x^3} \, dx","Int[(a + b*Sqrt[x])^15/x^3,x]","4290 a^8 b^7 x^{3/2}+\frac{6435}{2} a^7 b^8 x^2+2002 a^6 b^9 x^{5/2}+1001 a^5 b^{10} x^3+390 a^4 b^{11} x^{7/2}+\frac{455}{4} a^3 b^{12} x^4+\frac{70}{3} a^2 b^{13} x^{9/2}-\frac{105 a^{13} b^2}{x}-\frac{910 a^{12} b^3}{\sqrt{x}}+6006 a^{10} b^5 \sqrt{x}+5005 a^9 b^6 x+1365 a^{11} b^4 \log (x)-\frac{10 a^{14} b}{x^{3/2}}-\frac{a^{15}}{2 x^2}+3 a b^{14} x^5+\frac{2}{11} b^{15} x^{11/2}","4290 a^8 b^7 x^{3/2}+\frac{6435}{2} a^7 b^8 x^2+2002 a^6 b^9 x^{5/2}+1001 a^5 b^{10} x^3+390 a^4 b^{11} x^{7/2}+\frac{455}{4} a^3 b^{12} x^4+\frac{70}{3} a^2 b^{13} x^{9/2}-\frac{105 a^{13} b^2}{x}-\frac{910 a^{12} b^3}{\sqrt{x}}+6006 a^{10} b^5 \sqrt{x}+5005 a^9 b^6 x+1365 a^{11} b^4 \log (x)-\frac{10 a^{14} b}{x^{3/2}}-\frac{a^{15}}{2 x^2}+3 a b^{14} x^5+\frac{2}{11} b^{15} x^{11/2}",1,"-a^15/(2*x^2) - (10*a^14*b)/x^(3/2) - (105*a^13*b^2)/x - (910*a^12*b^3)/Sqrt[x] + 6006*a^10*b^5*Sqrt[x] + 5005*a^9*b^6*x + 4290*a^8*b^7*x^(3/2) + (6435*a^7*b^8*x^2)/2 + 2002*a^6*b^9*x^(5/2) + 1001*a^5*b^10*x^3 + 390*a^4*b^11*x^(7/2) + (455*a^3*b^12*x^4)/4 + (70*a^2*b^13*x^(9/2))/3 + 3*a*b^14*x^5 + (2*b^15*x^(11/2))/11 + 1365*a^11*b^4*Log[x]","A",3,2,15,0.1333,1,"{266, 43}"
2178,1,196,0,0.1159214,"\int \frac{\left(a+b \sqrt{x}\right)^{15}}{x^4} \, dx","Int[(a + b*Sqrt[x])^15/x^4,x]","-\frac{105 a^{13} b^2}{2 x^2}-\frac{910 a^{12} b^3}{3 x^{3/2}}+\frac{10010}{3} a^6 b^9 x^{3/2}+\frac{3003}{2} a^5 b^{10} x^2+546 a^4 b^{11} x^{5/2}+\frac{455}{3} a^3 b^{12} x^3+30 a^2 b^{13} x^{7/2}-\frac{1365 a^{11} b^4}{x}-\frac{6006 a^{10} b^5}{\sqrt{x}}+12870 a^8 b^7 \sqrt{x}+6435 a^7 b^8 x+5005 a^9 b^6 \log (x)-\frac{6 a^{14} b}{x^{5/2}}-\frac{a^{15}}{3 x^3}+\frac{15}{4} a b^{14} x^4+\frac{2}{9} b^{15} x^{9/2}","-\frac{105 a^{13} b^2}{2 x^2}-\frac{910 a^{12} b^3}{3 x^{3/2}}+\frac{10010}{3} a^6 b^9 x^{3/2}+\frac{3003}{2} a^5 b^{10} x^2+546 a^4 b^{11} x^{5/2}+\frac{455}{3} a^3 b^{12} x^3+30 a^2 b^{13} x^{7/2}-\frac{1365 a^{11} b^4}{x}-\frac{6006 a^{10} b^5}{\sqrt{x}}+12870 a^8 b^7 \sqrt{x}+6435 a^7 b^8 x+5005 a^9 b^6 \log (x)-\frac{6 a^{14} b}{x^{5/2}}-\frac{a^{15}}{3 x^3}+\frac{15}{4} a b^{14} x^4+\frac{2}{9} b^{15} x^{9/2}",1,"-a^15/(3*x^3) - (6*a^14*b)/x^(5/2) - (105*a^13*b^2)/(2*x^2) - (910*a^12*b^3)/(3*x^(3/2)) - (1365*a^11*b^4)/x - (6006*a^10*b^5)/Sqrt[x] + 12870*a^8*b^7*Sqrt[x] + 6435*a^7*b^8*x + (10010*a^6*b^9*x^(3/2))/3 + (3003*a^5*b^10*x^2)/2 + 546*a^4*b^11*x^(5/2) + (455*a^3*b^12*x^3)/3 + 30*a^2*b^13*x^(7/2) + (15*a*b^14*x^4)/4 + (2*b^15*x^(9/2))/9 + 5005*a^9*b^6*Log[x]","A",3,2,15,0.1333,1,"{266, 43}"
2179,1,194,0,0.1166998,"\int \frac{\left(a+b \sqrt{x}\right)^{15}}{x^6} \, dx","Int[(a + b*Sqrt[x])^15/x^6,x]","-\frac{105 a^{13} b^2}{4 x^4}-\frac{130 a^{12} b^3}{x^{7/2}}-\frac{455 a^{11} b^4}{x^3}-\frac{6006 a^{10} b^5}{5 x^{5/2}}-\frac{5005 a^9 b^6}{2 x^2}-\frac{4290 a^8 b^7}{x^{3/2}}+70 a^2 b^{13} x^{3/2}-\frac{6435 a^7 b^8}{x}-\frac{10010 a^6 b^9}{\sqrt{x}}+2730 a^4 b^{11} \sqrt{x}+455 a^3 b^{12} x+3003 a^5 b^{10} \log (x)-\frac{10 a^{14} b}{3 x^{9/2}}-\frac{a^{15}}{5 x^5}+\frac{15}{2} a b^{14} x^2+\frac{2}{5} b^{15} x^{5/2}","-\frac{105 a^{13} b^2}{4 x^4}-\frac{130 a^{12} b^3}{x^{7/2}}-\frac{455 a^{11} b^4}{x^3}-\frac{6006 a^{10} b^5}{5 x^{5/2}}-\frac{5005 a^9 b^6}{2 x^2}-\frac{4290 a^8 b^7}{x^{3/2}}+70 a^2 b^{13} x^{3/2}-\frac{6435 a^7 b^8}{x}-\frac{10010 a^6 b^9}{\sqrt{x}}+2730 a^4 b^{11} \sqrt{x}+455 a^3 b^{12} x+3003 a^5 b^{10} \log (x)-\frac{10 a^{14} b}{3 x^{9/2}}-\frac{a^{15}}{5 x^5}+\frac{15}{2} a b^{14} x^2+\frac{2}{5} b^{15} x^{5/2}",1,"-a^15/(5*x^5) - (10*a^14*b)/(3*x^(9/2)) - (105*a^13*b^2)/(4*x^4) - (130*a^12*b^3)/x^(7/2) - (455*a^11*b^4)/x^3 - (6006*a^10*b^5)/(5*x^(5/2)) - (5005*a^9*b^6)/(2*x^2) - (4290*a^8*b^7)/x^(3/2) - (6435*a^7*b^8)/x - (10010*a^6*b^9)/Sqrt[x] + 2730*a^4*b^11*Sqrt[x] + 455*a^3*b^12*x + 70*a^2*b^13*x^(3/2) + (15*a*b^14*x^2)/2 + (2*b^15*x^(5/2))/5 + 3003*a^5*b^10*Log[x]","A",3,2,15,0.1333,1,"{266, 43}"
2180,1,196,0,0.1137863,"\int \frac{\left(a+b \sqrt{x}\right)^{15}}{x^7} \, dx","Int[(a + b*Sqrt[x])^15/x^7,x]","-\frac{21 a^{13} b^2}{x^5}-\frac{910 a^{12} b^3}{9 x^{9/2}}-\frac{1365 a^{11} b^4}{4 x^4}-\frac{858 a^{10} b^5}{x^{7/2}}-\frac{5005 a^9 b^6}{3 x^3}-\frac{2574 a^8 b^7}{x^{5/2}}-\frac{6435 a^7 b^8}{2 x^2}-\frac{10010 a^6 b^9}{3 x^{3/2}}-\frac{3003 a^5 b^{10}}{x}-\frac{2730 a^4 b^{11}}{\sqrt{x}}+210 a^2 b^{13} \sqrt{x}+455 a^3 b^{12} \log (x)-\frac{30 a^{14} b}{11 x^{11/2}}-\frac{a^{15}}{6 x^6}+15 a b^{14} x+\frac{2}{3} b^{15} x^{3/2}","-\frac{21 a^{13} b^2}{x^5}-\frac{910 a^{12} b^3}{9 x^{9/2}}-\frac{1365 a^{11} b^4}{4 x^4}-\frac{858 a^{10} b^5}{x^{7/2}}-\frac{5005 a^9 b^6}{3 x^3}-\frac{2574 a^8 b^7}{x^{5/2}}-\frac{6435 a^7 b^8}{2 x^2}-\frac{10010 a^6 b^9}{3 x^{3/2}}-\frac{3003 a^5 b^{10}}{x}-\frac{2730 a^4 b^{11}}{\sqrt{x}}+210 a^2 b^{13} \sqrt{x}+455 a^3 b^{12} \log (x)-\frac{30 a^{14} b}{11 x^{11/2}}-\frac{a^{15}}{6 x^6}+15 a b^{14} x+\frac{2}{3} b^{15} x^{3/2}",1,"-a^15/(6*x^6) - (30*a^14*b)/(11*x^(11/2)) - (21*a^13*b^2)/x^5 - (910*a^12*b^3)/(9*x^(9/2)) - (1365*a^11*b^4)/(4*x^4) - (858*a^10*b^5)/x^(7/2) - (5005*a^9*b^6)/(3*x^3) - (2574*a^8*b^7)/x^(5/2) - (6435*a^7*b^8)/(2*x^2) - (10010*a^6*b^9)/(3*x^(3/2)) - (3003*a^5*b^10)/x - (2730*a^4*b^11)/Sqrt[x] + 210*a^2*b^13*Sqrt[x] + 15*a*b^14*x + (2*b^15*x^(3/2))/3 + 455*a^3*b^12*Log[x]","A",3,2,15,0.1333,1,"{266, 43}"
2181,1,198,0,0.1102184,"\int \frac{\left(a+b \sqrt{x}\right)^{15}}{x^8} \, dx","Int[(a + b*Sqrt[x])^15/x^8,x]","-\frac{35 a^{13} b^2}{2 x^6}-\frac{910 a^{12} b^3}{11 x^{11/2}}-\frac{273 a^{11} b^4}{x^5}-\frac{2002 a^{10} b^5}{3 x^{9/2}}-\frac{5005 a^9 b^6}{4 x^4}-\frac{12870 a^8 b^7}{7 x^{7/2}}-\frac{2145 a^7 b^8}{x^3}-\frac{2002 a^6 b^9}{x^{5/2}}-\frac{3003 a^5 b^{10}}{2 x^2}-\frac{910 a^4 b^{11}}{x^{3/2}}-\frac{455 a^3 b^{12}}{x}-\frac{210 a^2 b^{13}}{\sqrt{x}}-\frac{30 a^{14} b}{13 x^{13/2}}-\frac{a^{15}}{7 x^7}+15 a b^{14} \log (x)+2 b^{15} \sqrt{x}","-\frac{35 a^{13} b^2}{2 x^6}-\frac{910 a^{12} b^3}{11 x^{11/2}}-\frac{273 a^{11} b^4}{x^5}-\frac{2002 a^{10} b^5}{3 x^{9/2}}-\frac{5005 a^9 b^6}{4 x^4}-\frac{12870 a^8 b^7}{7 x^{7/2}}-\frac{2145 a^7 b^8}{x^3}-\frac{2002 a^6 b^9}{x^{5/2}}-\frac{3003 a^5 b^{10}}{2 x^2}-\frac{910 a^4 b^{11}}{x^{3/2}}-\frac{455 a^3 b^{12}}{x}-\frac{210 a^2 b^{13}}{\sqrt{x}}-\frac{30 a^{14} b}{13 x^{13/2}}-\frac{a^{15}}{7 x^7}+15 a b^{14} \log (x)+2 b^{15} \sqrt{x}",1,"-a^15/(7*x^7) - (30*a^14*b)/(13*x^(13/2)) - (35*a^13*b^2)/(2*x^6) - (910*a^12*b^3)/(11*x^(11/2)) - (273*a^11*b^4)/x^5 - (2002*a^10*b^5)/(3*x^(9/2)) - (5005*a^9*b^6)/(4*x^4) - (12870*a^8*b^7)/(7*x^(7/2)) - (2145*a^7*b^8)/x^3 - (2002*a^6*b^9)/x^(5/2) - (3003*a^5*b^10)/(2*x^2) - (910*a^4*b^11)/x^(3/2) - (455*a^3*b^12)/x - (210*a^2*b^13)/Sqrt[x] + 2*b^15*Sqrt[x] + 15*a*b^14*Log[x]","A",3,2,15,0.1333,1,"{266, 43}"
2182,1,21,0,0.0032669,"\int \frac{\left(a+b \sqrt{x}\right)^{15}}{x^9} \, dx","Int[(a + b*Sqrt[x])^15/x^9,x]","-\frac{\left(a+b \sqrt{x}\right)^{16}}{8 a x^8}","-\frac{\left(a+b \sqrt{x}\right)^{16}}{8 a x^8}",1,"-(a + b*Sqrt[x])^16/(8*a*x^8)","A",1,1,15,0.06667,1,"{264}"
2183,1,70,0,0.0236033,"\int \frac{\left(a+b \sqrt{x}\right)^{15}}{x^{10}} \, dx","Int[(a + b*Sqrt[x])^15/x^10,x]","-\frac{b^2 \left(a+b \sqrt{x}\right)^{16}}{1224 a^3 x^8}+\frac{2 b \left(a+b \sqrt{x}\right)^{16}}{153 a^2 x^{17/2}}-\frac{\left(a+b \sqrt{x}\right)^{16}}{9 a x^9}","-\frac{b^2 \left(a+b \sqrt{x}\right)^{16}}{1224 a^3 x^8}+\frac{2 b \left(a+b \sqrt{x}\right)^{16}}{153 a^2 x^{17/2}}-\frac{\left(a+b \sqrt{x}\right)^{16}}{9 a x^9}",1,"-(a + b*Sqrt[x])^16/(9*a*x^9) + (2*b*(a + b*Sqrt[x])^16)/(153*a^2*x^(17/2)) - (b^2*(a + b*Sqrt[x])^16)/(1224*a^3*x^8)","A",4,3,15,0.2000,1,"{266, 45, 37}"
2184,1,120,0,0.0452624,"\int \frac{\left(a+b \sqrt{x}\right)^{15}}{x^{11}} \, dx","Int[(a + b*Sqrt[x])^15/x^11,x]","-\frac{b^4 \left(a+b \sqrt{x}\right)^{16}}{38760 a^5 x^8}+\frac{2 b^3 \left(a+b \sqrt{x}\right)^{16}}{4845 a^4 x^{17/2}}-\frac{b^2 \left(a+b \sqrt{x}\right)^{16}}{285 a^3 x^9}+\frac{2 b \left(a+b \sqrt{x}\right)^{16}}{95 a^2 x^{19/2}}-\frac{\left(a+b \sqrt{x}\right)^{16}}{10 a x^{10}}","-\frac{b^4 \left(a+b \sqrt{x}\right)^{16}}{38760 a^5 x^8}+\frac{2 b^3 \left(a+b \sqrt{x}\right)^{16}}{4845 a^4 x^{17/2}}-\frac{b^2 \left(a+b \sqrt{x}\right)^{16}}{285 a^3 x^9}+\frac{2 b \left(a+b \sqrt{x}\right)^{16}}{95 a^2 x^{19/2}}-\frac{\left(a+b \sqrt{x}\right)^{16}}{10 a x^{10}}",1,"-(a + b*Sqrt[x])^16/(10*a*x^10) + (2*b*(a + b*Sqrt[x])^16)/(95*a^2*x^(19/2)) - (b^2*(a + b*Sqrt[x])^16)/(285*a^3*x^9) + (2*b^3*(a + b*Sqrt[x])^16)/(4845*a^4*x^(17/2)) - (b^4*(a + b*Sqrt[x])^16)/(38760*a^5*x^8)","A",6,3,15,0.2000,1,"{266, 45, 37}"
2185,1,170,0,0.0721561,"\int \frac{\left(a+b \sqrt{x}\right)^{15}}{x^{12}} \, dx","Int[(a + b*Sqrt[x])^15/x^12,x]","-\frac{b^6 \left(a+b \sqrt{x}\right)^{16}}{596904 a^7 x^8}+\frac{2 b^5 \left(a+b \sqrt{x}\right)^{16}}{74613 a^6 x^{17/2}}-\frac{b^4 \left(a+b \sqrt{x}\right)^{16}}{4389 a^5 x^9}+\frac{2 b^3 \left(a+b \sqrt{x}\right)^{16}}{1463 a^4 x^{19/2}}-\frac{b^2 \left(a+b \sqrt{x}\right)^{16}}{154 a^3 x^{10}}+\frac{2 b \left(a+b \sqrt{x}\right)^{16}}{77 a^2 x^{21/2}}-\frac{\left(a+b \sqrt{x}\right)^{16}}{11 a x^{11}}","-\frac{b^6 \left(a+b \sqrt{x}\right)^{16}}{596904 a^7 x^8}+\frac{2 b^5 \left(a+b \sqrt{x}\right)^{16}}{74613 a^6 x^{17/2}}-\frac{b^4 \left(a+b \sqrt{x}\right)^{16}}{4389 a^5 x^9}+\frac{2 b^3 \left(a+b \sqrt{x}\right)^{16}}{1463 a^4 x^{19/2}}-\frac{b^2 \left(a+b \sqrt{x}\right)^{16}}{154 a^3 x^{10}}+\frac{2 b \left(a+b \sqrt{x}\right)^{16}}{77 a^2 x^{21/2}}-\frac{\left(a+b \sqrt{x}\right)^{16}}{11 a x^{11}}",1,"-(a + b*Sqrt[x])^16/(11*a*x^11) + (2*b*(a + b*Sqrt[x])^16)/(77*a^2*x^(21/2)) - (b^2*(a + b*Sqrt[x])^16)/(154*a^3*x^10) + (2*b^3*(a + b*Sqrt[x])^16)/(1463*a^4*x^(19/2)) - (b^4*(a + b*Sqrt[x])^16)/(4389*a^5*x^9) + (2*b^5*(a + b*Sqrt[x])^16)/(74613*a^6*x^(17/2)) - (b^6*(a + b*Sqrt[x])^16)/(596904*a^7*x^8)","A",8,3,15,0.2000,1,"{266, 45, 37}"
2186,1,220,0,0.1079125,"\int \frac{\left(a+b \sqrt{x}\right)^{15}}{x^{13}} \, dx","Int[(a + b*Sqrt[x])^15/x^13,x]","-\frac{b^8 \left(a+b \sqrt{x}\right)^{16}}{5883768 a^9 x^8}+\frac{2 b^7 \left(a+b \sqrt{x}\right)^{16}}{735471 a^8 x^{17/2}}-\frac{b^6 \left(a+b \sqrt{x}\right)^{16}}{43263 a^7 x^9}+\frac{2 b^5 \left(a+b \sqrt{x}\right)^{16}}{14421 a^6 x^{19/2}}-\frac{b^4 \left(a+b \sqrt{x}\right)^{16}}{1518 a^5 x^{10}}+\frac{2 b^3 \left(a+b \sqrt{x}\right)^{16}}{759 a^4 x^{21/2}}-\frac{7 b^2 \left(a+b \sqrt{x}\right)^{16}}{759 a^3 x^{11}}+\frac{2 b \left(a+b \sqrt{x}\right)^{16}}{69 a^2 x^{23/2}}-\frac{\left(a+b \sqrt{x}\right)^{16}}{12 a x^{12}}","-\frac{b^8 \left(a+b \sqrt{x}\right)^{16}}{5883768 a^9 x^8}+\frac{2 b^7 \left(a+b \sqrt{x}\right)^{16}}{735471 a^8 x^{17/2}}-\frac{b^6 \left(a+b \sqrt{x}\right)^{16}}{43263 a^7 x^9}+\frac{2 b^5 \left(a+b \sqrt{x}\right)^{16}}{14421 a^6 x^{19/2}}-\frac{b^4 \left(a+b \sqrt{x}\right)^{16}}{1518 a^5 x^{10}}+\frac{2 b^3 \left(a+b \sqrt{x}\right)^{16}}{759 a^4 x^{21/2}}-\frac{7 b^2 \left(a+b \sqrt{x}\right)^{16}}{759 a^3 x^{11}}+\frac{2 b \left(a+b \sqrt{x}\right)^{16}}{69 a^2 x^{23/2}}-\frac{\left(a+b \sqrt{x}\right)^{16}}{12 a x^{12}}",1,"-(a + b*Sqrt[x])^16/(12*a*x^12) + (2*b*(a + b*Sqrt[x])^16)/(69*a^2*x^(23/2)) - (7*b^2*(a + b*Sqrt[x])^16)/(759*a^3*x^11) + (2*b^3*(a + b*Sqrt[x])^16)/(759*a^4*x^(21/2)) - (b^4*(a + b*Sqrt[x])^16)/(1518*a^5*x^10) + (2*b^5*(a + b*Sqrt[x])^16)/(14421*a^6*x^(19/2)) - (b^6*(a + b*Sqrt[x])^16)/(43263*a^7*x^9) + (2*b^7*(a + b*Sqrt[x])^16)/(735471*a^8*x^(17/2)) - (b^8*(a + b*Sqrt[x])^16)/(5883768*a^9*x^8)","A",10,3,15,0.2000,1,"{266, 45, 37}"
2187,1,270,0,0.1509931,"\int \frac{\left(a+b \sqrt{x}\right)^{15}}{x^{14}} \, dx","Int[(a + b*Sqrt[x])^15/x^14,x]","-\frac{b^{10} \left(a+b \sqrt{x}\right)^{16}}{42493880 a^{11} x^8}+\frac{2 b^9 \left(a+b \sqrt{x}\right)^{16}}{5311735 a^{10} x^{17/2}}-\frac{b^8 \left(a+b \sqrt{x}\right)^{16}}{312455 a^9 x^9}+\frac{6 b^7 \left(a+b \sqrt{x}\right)^{16}}{312455 a^8 x^{19/2}}-\frac{3 b^6 \left(a+b \sqrt{x}\right)^{16}}{32890 a^7 x^{10}}+\frac{6 b^5 \left(a+b \sqrt{x}\right)^{16}}{16445 a^6 x^{21/2}}-\frac{21 b^4 \left(a+b \sqrt{x}\right)^{16}}{16445 a^5 x^{11}}+\frac{6 b^3 \left(a+b \sqrt{x}\right)^{16}}{1495 a^4 x^{23/2}}-\frac{3 b^2 \left(a+b \sqrt{x}\right)^{16}}{260 a^3 x^{12}}+\frac{2 b \left(a+b \sqrt{x}\right)^{16}}{65 a^2 x^{25/2}}-\frac{\left(a+b \sqrt{x}\right)^{16}}{13 a x^{13}}","-\frac{b^{10} \left(a+b \sqrt{x}\right)^{16}}{42493880 a^{11} x^8}+\frac{2 b^9 \left(a+b \sqrt{x}\right)^{16}}{5311735 a^{10} x^{17/2}}-\frac{b^8 \left(a+b \sqrt{x}\right)^{16}}{312455 a^9 x^9}+\frac{6 b^7 \left(a+b \sqrt{x}\right)^{16}}{312455 a^8 x^{19/2}}-\frac{3 b^6 \left(a+b \sqrt{x}\right)^{16}}{32890 a^7 x^{10}}+\frac{6 b^5 \left(a+b \sqrt{x}\right)^{16}}{16445 a^6 x^{21/2}}-\frac{21 b^4 \left(a+b \sqrt{x}\right)^{16}}{16445 a^5 x^{11}}+\frac{6 b^3 \left(a+b \sqrt{x}\right)^{16}}{1495 a^4 x^{23/2}}-\frac{3 b^2 \left(a+b \sqrt{x}\right)^{16}}{260 a^3 x^{12}}+\frac{2 b \left(a+b \sqrt{x}\right)^{16}}{65 a^2 x^{25/2}}-\frac{\left(a+b \sqrt{x}\right)^{16}}{13 a x^{13}}",1,"-(a + b*Sqrt[x])^16/(13*a*x^13) + (2*b*(a + b*Sqrt[x])^16)/(65*a^2*x^(25/2)) - (3*b^2*(a + b*Sqrt[x])^16)/(260*a^3*x^12) + (6*b^3*(a + b*Sqrt[x])^16)/(1495*a^4*x^(23/2)) - (21*b^4*(a + b*Sqrt[x])^16)/(16445*a^5*x^11) + (6*b^5*(a + b*Sqrt[x])^16)/(16445*a^6*x^(21/2)) - (3*b^6*(a + b*Sqrt[x])^16)/(32890*a^7*x^10) + (6*b^7*(a + b*Sqrt[x])^16)/(312455*a^8*x^(19/2)) - (b^8*(a + b*Sqrt[x])^16)/(312455*a^9*x^9) + (2*b^9*(a + b*Sqrt[x])^16)/(5311735*a^10*x^(17/2)) - (b^10*(a + b*Sqrt[x])^16)/(42493880*a^11*x^8)","A",12,3,15,0.2000,1,"{266, 45, 37}"
2188,1,211,0,0.1163855,"\int \frac{\left(a+b \sqrt{x}\right)^{15}}{x^{15}} \, dx","Int[(a + b*Sqrt[x])^15/x^15,x]","-\frac{105 a^{13} b^2}{13 x^{13}}-\frac{182 a^{12} b^3}{5 x^{25/2}}-\frac{455 a^{11} b^4}{4 x^{12}}-\frac{6006 a^{10} b^5}{23 x^{23/2}}-\frac{455 a^9 b^6}{x^{11}}-\frac{4290 a^8 b^7}{7 x^{21/2}}-\frac{1287 a^7 b^8}{2 x^{10}}-\frac{10010 a^6 b^9}{19 x^{19/2}}-\frac{1001 a^5 b^{10}}{3 x^9}-\frac{2730 a^4 b^{11}}{17 x^{17/2}}-\frac{455 a^3 b^{12}}{8 x^8}-\frac{14 a^2 b^{13}}{x^{15/2}}-\frac{10 a^{14} b}{9 x^{27/2}}-\frac{a^{15}}{14 x^{14}}-\frac{15 a b^{14}}{7 x^7}-\frac{2 b^{15}}{13 x^{13/2}}","-\frac{105 a^{13} b^2}{13 x^{13}}-\frac{182 a^{12} b^3}{5 x^{25/2}}-\frac{455 a^{11} b^4}{4 x^{12}}-\frac{6006 a^{10} b^5}{23 x^{23/2}}-\frac{455 a^9 b^6}{x^{11}}-\frac{4290 a^8 b^7}{7 x^{21/2}}-\frac{1287 a^7 b^8}{2 x^{10}}-\frac{10010 a^6 b^9}{19 x^{19/2}}-\frac{1001 a^5 b^{10}}{3 x^9}-\frac{2730 a^4 b^{11}}{17 x^{17/2}}-\frac{455 a^3 b^{12}}{8 x^8}-\frac{14 a^2 b^{13}}{x^{15/2}}-\frac{10 a^{14} b}{9 x^{27/2}}-\frac{a^{15}}{14 x^{14}}-\frac{15 a b^{14}}{7 x^7}-\frac{2 b^{15}}{13 x^{13/2}}",1,"-a^15/(14*x^14) - (10*a^14*b)/(9*x^(27/2)) - (105*a^13*b^2)/(13*x^13) - (182*a^12*b^3)/(5*x^(25/2)) - (455*a^11*b^4)/(4*x^12) - (6006*a^10*b^5)/(23*x^(23/2)) - (455*a^9*b^6)/x^11 - (4290*a^8*b^7)/(7*x^(21/2)) - (1287*a^7*b^8)/(2*x^10) - (10010*a^6*b^9)/(19*x^(19/2)) - (1001*a^5*b^10)/(3*x^9) - (2730*a^4*b^11)/(17*x^(17/2)) - (455*a^3*b^12)/(8*x^8) - (14*a^2*b^13)/x^(15/2) - (15*a*b^14)/(7*x^7) - (2*b^15)/(13*x^(13/2))","A",3,2,15,0.1333,1,"{266, 43}"
2189,1,211,0,0.1129556,"\int \frac{\left(a+b \sqrt{x}\right)^{15}}{x^{16}} \, dx","Int[(a + b*Sqrt[x])^15/x^16,x]","-\frac{15 a^{13} b^2}{2 x^{14}}-\frac{910 a^{12} b^3}{27 x^{27/2}}-\frac{105 a^{11} b^4}{x^{13}}-\frac{6006 a^{10} b^5}{25 x^{25/2}}-\frac{5005 a^9 b^6}{12 x^{12}}-\frac{12870 a^8 b^7}{23 x^{23/2}}-\frac{585 a^7 b^8}{x^{11}}-\frac{1430 a^6 b^9}{3 x^{21/2}}-\frac{3003 a^5 b^{10}}{10 x^{10}}-\frac{2730 a^4 b^{11}}{19 x^{19/2}}-\frac{455 a^3 b^{12}}{9 x^9}-\frac{210 a^2 b^{13}}{17 x^{17/2}}-\frac{30 a^{14} b}{29 x^{29/2}}-\frac{a^{15}}{15 x^{15}}-\frac{15 a b^{14}}{8 x^8}-\frac{2 b^{15}}{15 x^{15/2}}","-\frac{15 a^{13} b^2}{2 x^{14}}-\frac{910 a^{12} b^3}{27 x^{27/2}}-\frac{105 a^{11} b^4}{x^{13}}-\frac{6006 a^{10} b^5}{25 x^{25/2}}-\frac{5005 a^9 b^6}{12 x^{12}}-\frac{12870 a^8 b^7}{23 x^{23/2}}-\frac{585 a^7 b^8}{x^{11}}-\frac{1430 a^6 b^9}{3 x^{21/2}}-\frac{3003 a^5 b^{10}}{10 x^{10}}-\frac{2730 a^4 b^{11}}{19 x^{19/2}}-\frac{455 a^3 b^{12}}{9 x^9}-\frac{210 a^2 b^{13}}{17 x^{17/2}}-\frac{30 a^{14} b}{29 x^{29/2}}-\frac{a^{15}}{15 x^{15}}-\frac{15 a b^{14}}{8 x^8}-\frac{2 b^{15}}{15 x^{15/2}}",1,"-a^15/(15*x^15) - (30*a^14*b)/(29*x^(29/2)) - (15*a^13*b^2)/(2*x^14) - (910*a^12*b^3)/(27*x^(27/2)) - (105*a^11*b^4)/x^13 - (6006*a^10*b^5)/(25*x^(25/2)) - (5005*a^9*b^6)/(12*x^12) - (12870*a^8*b^7)/(23*x^(23/2)) - (585*a^7*b^8)/x^11 - (1430*a^6*b^9)/(3*x^(21/2)) - (3003*a^5*b^10)/(10*x^10) - (2730*a^4*b^11)/(19*x^(19/2)) - (455*a^3*b^12)/(9*x^9) - (210*a^2*b^13)/(17*x^(17/2)) - (15*a*b^14)/(8*x^8) - (2*b^15)/(15*x^(15/2))","A",3,2,15,0.1333,1,"{266, 43}"
2190,1,207,0,0.1106302,"\int \frac{\left(a+b \sqrt{x}\right)^{15}}{x^{17}} \, dx","Int[(a + b*Sqrt[x])^15/x^17,x]","-\frac{7 a^{13} b^2}{x^{15}}-\frac{910 a^{12} b^3}{29 x^{29/2}}-\frac{195 a^{11} b^4}{2 x^{14}}-\frac{2002 a^{10} b^5}{9 x^{27/2}}-\frac{385 a^9 b^6}{x^{13}}-\frac{2574 a^8 b^7}{5 x^{25/2}}-\frac{2145 a^7 b^8}{4 x^{12}}-\frac{10010 a^6 b^9}{23 x^{23/2}}-\frac{273 a^5 b^{10}}{x^{11}}-\frac{130 a^4 b^{11}}{x^{21/2}}-\frac{91 a^3 b^{12}}{2 x^{10}}-\frac{210 a^2 b^{13}}{19 x^{19/2}}-\frac{30 a^{14} b}{31 x^{31/2}}-\frac{a^{15}}{16 x^{16}}-\frac{5 a b^{14}}{3 x^9}-\frac{2 b^{15}}{17 x^{17/2}}","-\frac{7 a^{13} b^2}{x^{15}}-\frac{910 a^{12} b^3}{29 x^{29/2}}-\frac{195 a^{11} b^4}{2 x^{14}}-\frac{2002 a^{10} b^5}{9 x^{27/2}}-\frac{385 a^9 b^6}{x^{13}}-\frac{2574 a^8 b^7}{5 x^{25/2}}-\frac{2145 a^7 b^8}{4 x^{12}}-\frac{10010 a^6 b^9}{23 x^{23/2}}-\frac{273 a^5 b^{10}}{x^{11}}-\frac{130 a^4 b^{11}}{x^{21/2}}-\frac{91 a^3 b^{12}}{2 x^{10}}-\frac{210 a^2 b^{13}}{19 x^{19/2}}-\frac{30 a^{14} b}{31 x^{31/2}}-\frac{a^{15}}{16 x^{16}}-\frac{5 a b^{14}}{3 x^9}-\frac{2 b^{15}}{17 x^{17/2}}",1,"-a^15/(16*x^16) - (30*a^14*b)/(31*x^(31/2)) - (7*a^13*b^2)/x^15 - (910*a^12*b^3)/(29*x^(29/2)) - (195*a^11*b^4)/(2*x^14) - (2002*a^10*b^5)/(9*x^(27/2)) - (385*a^9*b^6)/x^13 - (2574*a^8*b^7)/(5*x^(25/2)) - (2145*a^7*b^8)/(4*x^12) - (10010*a^6*b^9)/(23*x^(23/2)) - (273*a^5*b^10)/x^11 - (130*a^4*b^11)/x^(21/2) - (91*a^3*b^12)/(2*x^10) - (210*a^2*b^13)/(19*x^(19/2)) - (5*a*b^14)/(3*x^9) - (2*b^15)/(17*x^(17/2))","A",3,2,15,0.1333,1,"{266, 43}"
2191,1,107,0,0.0697978,"\int \frac{x^3}{a+b \sqrt{x}} \, dx","Int[x^3/(a + b*Sqrt[x]),x]","\frac{2 a^4 x^{3/2}}{3 b^5}-\frac{a^3 x^2}{2 b^4}+\frac{2 a^2 x^{5/2}}{5 b^3}+\frac{2 a^6 \sqrt{x}}{b^7}-\frac{a^5 x}{b^6}-\frac{2 a^7 \log \left(a+b \sqrt{x}\right)}{b^8}-\frac{a x^3}{3 b^2}+\frac{2 x^{7/2}}{7 b}","\frac{2 a^4 x^{3/2}}{3 b^5}-\frac{a^3 x^2}{2 b^4}+\frac{2 a^2 x^{5/2}}{5 b^3}+\frac{2 a^6 \sqrt{x}}{b^7}-\frac{a^5 x}{b^6}-\frac{2 a^7 \log \left(a+b \sqrt{x}\right)}{b^8}-\frac{a x^3}{3 b^2}+\frac{2 x^{7/2}}{7 b}",1,"(2*a^6*Sqrt[x])/b^7 - (a^5*x)/b^6 + (2*a^4*x^(3/2))/(3*b^5) - (a^3*x^2)/(2*b^4) + (2*a^2*x^(5/2))/(5*b^3) - (a*x^3)/(3*b^2) + (2*x^(7/2))/(7*b) - (2*a^7*Log[a + b*Sqrt[x]])/b^8","A",3,2,15,0.1333,1,"{266, 43}"
2192,1,79,0,0.0459683,"\int \frac{x^2}{a+b \sqrt{x}} \, dx","Int[x^2/(a + b*Sqrt[x]),x]","\frac{2 a^2 x^{3/2}}{3 b^3}+\frac{2 a^4 \sqrt{x}}{b^5}-\frac{a^3 x}{b^4}-\frac{2 a^5 \log \left(a+b \sqrt{x}\right)}{b^6}-\frac{a x^2}{2 b^2}+\frac{2 x^{5/2}}{5 b}","\frac{2 a^2 x^{3/2}}{3 b^3}+\frac{2 a^4 \sqrt{x}}{b^5}-\frac{a^3 x}{b^4}-\frac{2 a^5 \log \left(a+b \sqrt{x}\right)}{b^6}-\frac{a x^2}{2 b^2}+\frac{2 x^{5/2}}{5 b}",1,"(2*a^4*Sqrt[x])/b^5 - (a^3*x)/b^4 + (2*a^2*x^(3/2))/(3*b^3) - (a*x^2)/(2*b^2) + (2*x^(5/2))/(5*b) - (2*a^5*Log[a + b*Sqrt[x]])/b^6","A",3,2,15,0.1333,1,"{266, 43}"
2193,1,51,0,0.0279938,"\int \frac{x}{a+b \sqrt{x}} \, dx","Int[x/(a + b*Sqrt[x]),x]","\frac{2 a^2 \sqrt{x}}{b^3}-\frac{2 a^3 \log \left(a+b \sqrt{x}\right)}{b^4}-\frac{a x}{b^2}+\frac{2 x^{3/2}}{3 b}","\frac{2 a^2 \sqrt{x}}{b^3}-\frac{2 a^3 \log \left(a+b \sqrt{x}\right)}{b^4}-\frac{a x}{b^2}+\frac{2 x^{3/2}}{3 b}",1,"(2*a^2*Sqrt[x])/b^3 - (a*x)/b^2 + (2*x^(3/2))/(3*b) - (2*a^3*Log[a + b*Sqrt[x]])/b^4","A",3,2,13,0.1538,1,"{266, 43}"
2194,1,27,0,0.0135099,"\int \frac{1}{a+b \sqrt{x}} \, dx","Int[(a + b*Sqrt[x])^(-1),x]","\frac{2 \sqrt{x}}{b}-\frac{2 a \log \left(a+b \sqrt{x}\right)}{b^2}","\frac{2 \sqrt{x}}{b}-\frac{2 a \log \left(a+b \sqrt{x}\right)}{b^2}",1,"(2*Sqrt[x])/b - (2*a*Log[a + b*Sqrt[x]])/b^2","A",3,2,11,0.1818,1,"{190, 43}"
2195,1,22,0,0.0091657,"\int \frac{1}{\left(a+b \sqrt{x}\right) x} \, dx","Int[1/((a + b*Sqrt[x])*x),x]","\frac{\log (x)}{a}-\frac{2 \log \left(a+b \sqrt{x}\right)}{a}","\frac{\log (x)}{a}-\frac{2 \log \left(a+b \sqrt{x}\right)}{a}",1,"(-2*Log[a + b*Sqrt[x]])/a + Log[x]/a","A",4,4,15,0.2667,1,"{266, 36, 29, 31}"
2196,1,47,0,0.0288228,"\int \frac{1}{\left(a+b \sqrt{x}\right) x^2} \, dx","Int[1/((a + b*Sqrt[x])*x^2),x]","-\frac{2 b^2 \log \left(a+b \sqrt{x}\right)}{a^3}+\frac{b^2 \log (x)}{a^3}+\frac{2 b}{a^2 \sqrt{x}}-\frac{1}{a x}","-\frac{2 b^2 \log \left(a+b \sqrt{x}\right)}{a^3}+\frac{b^2 \log (x)}{a^3}+\frac{2 b}{a^2 \sqrt{x}}-\frac{1}{a x}",1,"-(1/(a*x)) + (2*b)/(a^2*Sqrt[x]) - (2*b^2*Log[a + b*Sqrt[x]])/a^3 + (b^2*Log[x])/a^3","A",3,2,15,0.1333,1,"{266, 44}"
2197,1,75,0,0.0383596,"\int \frac{1}{\left(a+b \sqrt{x}\right) x^3} \, dx","Int[1/((a + b*Sqrt[x])*x^3),x]","\frac{2 b^3}{a^4 \sqrt{x}}-\frac{b^2}{a^3 x}-\frac{2 b^4 \log \left(a+b \sqrt{x}\right)}{a^5}+\frac{b^4 \log (x)}{a^5}+\frac{2 b}{3 a^2 x^{3/2}}-\frac{1}{2 a x^2}","\frac{2 b^3}{a^4 \sqrt{x}}-\frac{b^2}{a^3 x}-\frac{2 b^4 \log \left(a+b \sqrt{x}\right)}{a^5}+\frac{b^4 \log (x)}{a^5}+\frac{2 b}{3 a^2 x^{3/2}}-\frac{1}{2 a x^2}",1,"-1/(2*a*x^2) + (2*b)/(3*a^2*x^(3/2)) - b^2/(a^3*x) + (2*b^3)/(a^4*Sqrt[x]) - (2*b^4*Log[a + b*Sqrt[x]])/a^5 + (b^4*Log[x])/a^5","A",3,2,15,0.1333,1,"{266, 44}"
2198,1,103,0,0.0515842,"\int \frac{1}{\left(a+b \sqrt{x}\right) x^4} \, dx","Int[1/((a + b*Sqrt[x])*x^4),x]","\frac{2 b^3}{3 a^4 x^{3/2}}-\frac{b^2}{2 a^3 x^2}+\frac{2 b^5}{a^6 \sqrt{x}}-\frac{b^4}{a^5 x}-\frac{2 b^6 \log \left(a+b \sqrt{x}\right)}{a^7}+\frac{b^6 \log (x)}{a^7}+\frac{2 b}{5 a^2 x^{5/2}}-\frac{1}{3 a x^3}","\frac{2 b^3}{3 a^4 x^{3/2}}-\frac{b^2}{2 a^3 x^2}+\frac{2 b^5}{a^6 \sqrt{x}}-\frac{b^4}{a^5 x}-\frac{2 b^6 \log \left(a+b \sqrt{x}\right)}{a^7}+\frac{b^6 \log (x)}{a^7}+\frac{2 b}{5 a^2 x^{5/2}}-\frac{1}{3 a x^3}",1,"-1/(3*a*x^3) + (2*b)/(5*a^2*x^(5/2)) - b^2/(2*a^3*x^2) + (2*b^3)/(3*a^4*x^(3/2)) - b^4/(a^5*x) + (2*b^5)/(a^6*Sqrt[x]) - (2*b^6*Log[a + b*Sqrt[x]])/a^7 + (b^6*Log[x])/a^7","A",3,2,15,0.1333,1,"{266, 44}"
2199,1,111,0,0.0827748,"\int \frac{x^3}{\left(a+b \sqrt{x}\right)^2} \, dx","Int[x^3/(a + b*Sqrt[x])^2,x]","-\frac{8 a^3 x^{3/2}}{3 b^5}+\frac{3 a^2 x^2}{2 b^4}+\frac{2 a^7}{b^8 \left(a+b \sqrt{x}\right)}-\frac{12 a^5 \sqrt{x}}{b^7}+\frac{5 a^4 x}{b^6}+\frac{14 a^6 \log \left(a+b \sqrt{x}\right)}{b^8}-\frac{4 a x^{5/2}}{5 b^3}+\frac{x^3}{3 b^2}","-\frac{8 a^3 x^{3/2}}{3 b^5}+\frac{3 a^2 x^2}{2 b^4}+\frac{2 a^7}{b^8 \left(a+b \sqrt{x}\right)}-\frac{12 a^5 \sqrt{x}}{b^7}+\frac{5 a^4 x}{b^6}+\frac{14 a^6 \log \left(a+b \sqrt{x}\right)}{b^8}-\frac{4 a x^{5/2}}{5 b^3}+\frac{x^3}{3 b^2}",1,"(2*a^7)/(b^8*(a + b*Sqrt[x])) - (12*a^5*Sqrt[x])/b^7 + (5*a^4*x)/b^6 - (8*a^3*x^(3/2))/(3*b^5) + (3*a^2*x^2)/(2*b^4) - (4*a*x^(5/2))/(5*b^3) + x^3/(3*b^2) + (14*a^6*Log[a + b*Sqrt[x]])/b^8","A",3,2,15,0.1333,1,"{266, 43}"
2200,1,83,0,0.0596308,"\int \frac{x^2}{\left(a+b \sqrt{x}\right)^2} \, dx","Int[x^2/(a + b*Sqrt[x])^2,x]","\frac{2 a^5}{b^6 \left(a+b \sqrt{x}\right)}-\frac{8 a^3 \sqrt{x}}{b^5}+\frac{3 a^2 x}{b^4}+\frac{10 a^4 \log \left(a+b \sqrt{x}\right)}{b^6}-\frac{4 a x^{3/2}}{3 b^3}+\frac{x^2}{2 b^2}","\frac{2 a^5}{b^6 \left(a+b \sqrt{x}\right)}-\frac{8 a^3 \sqrt{x}}{b^5}+\frac{3 a^2 x}{b^4}+\frac{10 a^4 \log \left(a+b \sqrt{x}\right)}{b^6}-\frac{4 a x^{3/2}}{3 b^3}+\frac{x^2}{2 b^2}",1,"(2*a^5)/(b^6*(a + b*Sqrt[x])) - (8*a^3*Sqrt[x])/b^5 + (3*a^2*x)/b^4 - (4*a*x^(3/2))/(3*b^3) + x^2/(2*b^2) + (10*a^4*Log[a + b*Sqrt[x]])/b^6","A",3,2,15,0.1333,1,"{266, 43}"
2201,1,54,0,0.0363245,"\int \frac{x}{\left(a+b \sqrt{x}\right)^2} \, dx","Int[x/(a + b*Sqrt[x])^2,x]","\frac{2 a^3}{b^4 \left(a+b \sqrt{x}\right)}+\frac{6 a^2 \log \left(a+b \sqrt{x}\right)}{b^4}-\frac{4 a \sqrt{x}}{b^3}+\frac{x}{b^2}","\frac{2 a^3}{b^4 \left(a+b \sqrt{x}\right)}+\frac{6 a^2 \log \left(a+b \sqrt{x}\right)}{b^4}-\frac{4 a \sqrt{x}}{b^3}+\frac{x}{b^2}",1,"(2*a^3)/(b^4*(a + b*Sqrt[x])) - (4*a*Sqrt[x])/b^3 + x/b^2 + (6*a^2*Log[a + b*Sqrt[x]])/b^4","A",3,2,13,0.1538,1,"{266, 43}"
2202,1,33,0,0.0178957,"\int \frac{1}{\left(a+b \sqrt{x}\right)^2} \, dx","Int[(a + b*Sqrt[x])^(-2),x]","\frac{2 a}{b^2 \left(a+b \sqrt{x}\right)}+\frac{2 \log \left(a+b \sqrt{x}\right)}{b^2}","\frac{2 a}{b^2 \left(a+b \sqrt{x}\right)}+\frac{2 \log \left(a+b \sqrt{x}\right)}{b^2}",1,"(2*a)/(b^2*(a + b*Sqrt[x])) + (2*Log[a + b*Sqrt[x]])/b^2","A",3,2,11,0.1818,1,"{190, 43}"
2203,1,38,0,0.0219209,"\int \frac{1}{\left(a+b \sqrt{x}\right)^2 x} \, dx","Int[1/((a + b*Sqrt[x])^2*x),x]","-\frac{2 \log \left(a+b \sqrt{x}\right)}{a^2}+\frac{\log (x)}{a^2}+\frac{2}{a \left(a+b \sqrt{x}\right)}","-\frac{2 \log \left(a+b \sqrt{x}\right)}{a^2}+\frac{\log (x)}{a^2}+\frac{2}{a \left(a+b \sqrt{x}\right)}",1,"2/(a*(a + b*Sqrt[x])) - (2*Log[a + b*Sqrt[x]])/a^2 + Log[x]/a^2","A",3,2,15,0.1333,1,"{266, 44}"
2204,1,67,0,0.0416603,"\int \frac{1}{\left(a+b \sqrt{x}\right)^2 x^2} \, dx","Int[1/((a + b*Sqrt[x])^2*x^2),x]","\frac{2 b^2}{a^3 \left(a+b \sqrt{x}\right)}-\frac{6 b^2 \log \left(a+b \sqrt{x}\right)}{a^4}+\frac{3 b^2 \log (x)}{a^4}+\frac{4 b}{a^3 \sqrt{x}}-\frac{1}{a^2 x}","\frac{2 b^2}{a^3 \left(a+b \sqrt{x}\right)}-\frac{6 b^2 \log \left(a+b \sqrt{x}\right)}{a^4}+\frac{3 b^2 \log (x)}{a^4}+\frac{4 b}{a^3 \sqrt{x}}-\frac{1}{a^2 x}",1,"(2*b^2)/(a^3*(a + b*Sqrt[x])) - 1/(a^2*x) + (4*b)/(a^3*Sqrt[x]) - (6*b^2*Log[a + b*Sqrt[x]])/a^4 + (3*b^2*Log[x])/a^4","A",3,2,15,0.1333,1,"{266, 44}"
2205,1,95,0,0.0611979,"\int \frac{1}{\left(a+b \sqrt{x}\right)^2 x^3} \, dx","Int[1/((a + b*Sqrt[x])^2*x^3),x]","\frac{2 b^4}{a^5 \left(a+b \sqrt{x}\right)}+\frac{8 b^3}{a^5 \sqrt{x}}-\frac{3 b^2}{a^4 x}-\frac{10 b^4 \log \left(a+b \sqrt{x}\right)}{a^6}+\frac{5 b^4 \log (x)}{a^6}+\frac{4 b}{3 a^3 x^{3/2}}-\frac{1}{2 a^2 x^2}","\frac{2 b^4}{a^5 \left(a+b \sqrt{x}\right)}+\frac{8 b^3}{a^5 \sqrt{x}}-\frac{3 b^2}{a^4 x}-\frac{10 b^4 \log \left(a+b \sqrt{x}\right)}{a^6}+\frac{5 b^4 \log (x)}{a^6}+\frac{4 b}{3 a^3 x^{3/2}}-\frac{1}{2 a^2 x^2}",1,"(2*b^4)/(a^5*(a + b*Sqrt[x])) - 1/(2*a^2*x^2) + (4*b)/(3*a^3*x^(3/2)) - (3*b^2)/(a^4*x) + (8*b^3)/(a^5*Sqrt[x]) - (10*b^4*Log[a + b*Sqrt[x]])/a^6 + (5*b^4*Log[x])/a^6","A",3,2,15,0.1333,1,"{266, 44}"
2206,1,123,0,0.0792728,"\int \frac{1}{\left(a+b \sqrt{x}\right)^2 x^4} \, dx","Int[1/((a + b*Sqrt[x])^2*x^4),x]","\frac{8 b^3}{3 a^5 x^{3/2}}-\frac{3 b^2}{2 a^4 x^2}+\frac{2 b^6}{a^7 \left(a+b \sqrt{x}\right)}+\frac{12 b^5}{a^7 \sqrt{x}}-\frac{5 b^4}{a^6 x}-\frac{14 b^6 \log \left(a+b \sqrt{x}\right)}{a^8}+\frac{7 b^6 \log (x)}{a^8}+\frac{4 b}{5 a^3 x^{5/2}}-\frac{1}{3 a^2 x^3}","\frac{8 b^3}{3 a^5 x^{3/2}}-\frac{3 b^2}{2 a^4 x^2}+\frac{2 b^6}{a^7 \left(a+b \sqrt{x}\right)}+\frac{12 b^5}{a^7 \sqrt{x}}-\frac{5 b^4}{a^6 x}-\frac{14 b^6 \log \left(a+b \sqrt{x}\right)}{a^8}+\frac{7 b^6 \log (x)}{a^8}+\frac{4 b}{5 a^3 x^{5/2}}-\frac{1}{3 a^2 x^3}",1,"(2*b^6)/(a^7*(a + b*Sqrt[x])) - 1/(3*a^2*x^3) + (4*b)/(5*a^3*x^(5/2)) - (3*b^2)/(2*a^4*x^2) + (8*b^3)/(3*a^5*x^(3/2)) - (5*b^4)/(a^6*x) + (12*b^5)/(a^7*Sqrt[x]) - (14*b^6*Log[a + b*Sqrt[x]])/a^8 + (7*b^6*Log[x])/a^8","A",3,2,15,0.1333,1,"{266, 44}"
2207,1,114,0,0.087194,"\int \frac{x^3}{\left(a+b \sqrt{x}\right)^3} \, dx","Int[x^3/(a + b*Sqrt[x])^3,x]","\frac{4 a^2 x^{3/2}}{b^5}+\frac{a^7}{b^8 \left(a+b \sqrt{x}\right)^2}-\frac{14 a^6}{b^8 \left(a+b \sqrt{x}\right)}+\frac{30 a^4 \sqrt{x}}{b^7}-\frac{10 a^3 x}{b^6}-\frac{42 a^5 \log \left(a+b \sqrt{x}\right)}{b^8}-\frac{3 a x^2}{2 b^4}+\frac{2 x^{5/2}}{5 b^3}","\frac{4 a^2 x^{3/2}}{b^5}+\frac{a^7}{b^8 \left(a+b \sqrt{x}\right)^2}-\frac{14 a^6}{b^8 \left(a+b \sqrt{x}\right)}+\frac{30 a^4 \sqrt{x}}{b^7}-\frac{10 a^3 x}{b^6}-\frac{42 a^5 \log \left(a+b \sqrt{x}\right)}{b^8}-\frac{3 a x^2}{2 b^4}+\frac{2 x^{5/2}}{5 b^3}",1,"a^7/(b^8*(a + b*Sqrt[x])^2) - (14*a^6)/(b^8*(a + b*Sqrt[x])) + (30*a^4*Sqrt[x])/b^7 - (10*a^3*x)/b^6 + (4*a^2*x^(3/2))/b^5 - (3*a*x^2)/(2*b^4) + (2*x^(5/2))/(5*b^3) - (42*a^5*Log[a + b*Sqrt[x]])/b^8","A",3,2,15,0.1333,1,"{266, 43}"
2208,1,88,0,0.0627423,"\int \frac{x^2}{\left(a+b \sqrt{x}\right)^3} \, dx","Int[x^2/(a + b*Sqrt[x])^3,x]","\frac{a^5}{b^6 \left(a+b \sqrt{x}\right)^2}-\frac{10 a^4}{b^6 \left(a+b \sqrt{x}\right)}+\frac{12 a^2 \sqrt{x}}{b^5}-\frac{20 a^3 \log \left(a+b \sqrt{x}\right)}{b^6}-\frac{3 a x}{b^4}+\frac{2 x^{3/2}}{3 b^3}","\frac{a^5}{b^6 \left(a+b \sqrt{x}\right)^2}-\frac{10 a^4}{b^6 \left(a+b \sqrt{x}\right)}+\frac{12 a^2 \sqrt{x}}{b^5}-\frac{20 a^3 \log \left(a+b \sqrt{x}\right)}{b^6}-\frac{3 a x}{b^4}+\frac{2 x^{3/2}}{3 b^3}",1,"a^5/(b^6*(a + b*Sqrt[x])^2) - (10*a^4)/(b^6*(a + b*Sqrt[x])) + (12*a^2*Sqrt[x])/b^5 - (3*a*x)/b^4 + (2*x^(3/2))/(3*b^3) - (20*a^3*Log[a + b*Sqrt[x]])/b^6","A",3,2,15,0.1333,1,"{266, 43}"
2209,1,64,0,0.0369614,"\int \frac{x}{\left(a+b \sqrt{x}\right)^3} \, dx","Int[x/(a + b*Sqrt[x])^3,x]","\frac{a^3}{b^4 \left(a+b \sqrt{x}\right)^2}-\frac{6 a^2}{b^4 \left(a+b \sqrt{x}\right)}-\frac{6 a \log \left(a+b \sqrt{x}\right)}{b^4}+\frac{2 \sqrt{x}}{b^3}","\frac{a^3}{b^4 \left(a+b \sqrt{x}\right)^2}-\frac{6 a^2}{b^4 \left(a+b \sqrt{x}\right)}-\frac{6 a \log \left(a+b \sqrt{x}\right)}{b^4}+\frac{2 \sqrt{x}}{b^3}",1,"a^3/(b^4*(a + b*Sqrt[x])^2) - (6*a^2)/(b^4*(a + b*Sqrt[x])) + (2*Sqrt[x])/b^3 - (6*a*Log[a + b*Sqrt[x]])/b^4","A",3,2,13,0.1538,1,"{266, 43}"
2210,1,16,0,0.0050682,"\int \frac{1}{\left(a+b \sqrt{x}\right)^3} \, dx","Int[(a + b*Sqrt[x])^(-3),x]","\frac{x}{a \left(a+b \sqrt{x}\right)^2}","\frac{x}{a \left(a+b \sqrt{x}\right)^2}",1,"x/(a*(a + b*Sqrt[x])^2)","A",2,2,11,0.1818,1,"{190, 37}"
2211,1,53,0,0.0307791,"\int \frac{1}{\left(a+b \sqrt{x}\right)^3 x} \, dx","Int[1/((a + b*Sqrt[x])^3*x),x]","\frac{2}{a^2 \left(a+b \sqrt{x}\right)}-\frac{2 \log \left(a+b \sqrt{x}\right)}{a^3}+\frac{\log (x)}{a^3}+\frac{1}{a \left(a+b \sqrt{x}\right)^2}","\frac{2}{a^2 \left(a+b \sqrt{x}\right)}-\frac{2 \log \left(a+b \sqrt{x}\right)}{a^3}+\frac{\log (x)}{a^3}+\frac{1}{a \left(a+b \sqrt{x}\right)^2}",1,"1/(a*(a + b*Sqrt[x])^2) + 2/(a^2*(a + b*Sqrt[x])) - (2*Log[a + b*Sqrt[x]])/a^3 + Log[x]/a^3","A",3,2,15,0.1333,1,"{266, 44}"
2212,1,85,0,0.0565994,"\int \frac{1}{\left(a+b \sqrt{x}\right)^3 x^2} \, dx","Int[1/((a + b*Sqrt[x])^3*x^2),x]","\frac{6 b^2}{a^4 \left(a+b \sqrt{x}\right)}+\frac{b^2}{a^3 \left(a+b \sqrt{x}\right)^2}-\frac{12 b^2 \log \left(a+b \sqrt{x}\right)}{a^5}+\frac{6 b^2 \log (x)}{a^5}+\frac{6 b}{a^4 \sqrt{x}}-\frac{1}{a^3 x}","\frac{6 b^2}{a^4 \left(a+b \sqrt{x}\right)}+\frac{b^2}{a^3 \left(a+b \sqrt{x}\right)^2}-\frac{12 b^2 \log \left(a+b \sqrt{x}\right)}{a^5}+\frac{6 b^2 \log (x)}{a^5}+\frac{6 b}{a^4 \sqrt{x}}-\frac{1}{a^3 x}",1,"b^2/(a^3*(a + b*Sqrt[x])^2) + (6*b^2)/(a^4*(a + b*Sqrt[x])) - 1/(a^3*x) + (6*b)/(a^4*Sqrt[x]) - (12*b^2*Log[a + b*Sqrt[x]])/a^5 + (6*b^2*Log[x])/a^5","A",3,2,15,0.1333,1,"{266, 44}"
2213,1,111,0,0.0714815,"\int \frac{1}{\left(a+b \sqrt{x}\right)^3 x^3} \, dx","Int[1/((a + b*Sqrt[x])^3*x^3),x]","\frac{10 b^4}{a^6 \left(a+b \sqrt{x}\right)}+\frac{b^4}{a^5 \left(a+b \sqrt{x}\right)^2}+\frac{20 b^3}{a^6 \sqrt{x}}-\frac{6 b^2}{a^5 x}-\frac{30 b^4 \log \left(a+b \sqrt{x}\right)}{a^7}+\frac{15 b^4 \log (x)}{a^7}+\frac{2 b}{a^4 x^{3/2}}-\frac{1}{2 a^3 x^2}","\frac{10 b^4}{a^6 \left(a+b \sqrt{x}\right)}+\frac{b^4}{a^5 \left(a+b \sqrt{x}\right)^2}+\frac{20 b^3}{a^6 \sqrt{x}}-\frac{6 b^2}{a^5 x}-\frac{30 b^4 \log \left(a+b \sqrt{x}\right)}{a^7}+\frac{15 b^4 \log (x)}{a^7}+\frac{2 b}{a^4 x^{3/2}}-\frac{1}{2 a^3 x^2}",1,"b^4/(a^5*(a + b*Sqrt[x])^2) + (10*b^4)/(a^6*(a + b*Sqrt[x])) - 1/(2*a^3*x^2) + (2*b)/(a^4*x^(3/2)) - (6*b^2)/(a^5*x) + (20*b^3)/(a^6*Sqrt[x]) - (30*b^4*Log[a + b*Sqrt[x]])/a^7 + (15*b^4*Log[x])/a^7","A",3,2,15,0.1333,1,"{266, 44}"
2214,1,139,0,0.0993551,"\int \frac{1}{\left(a+b \sqrt{x}\right)^3 x^4} \, dx","Int[1/((a + b*Sqrt[x])^3*x^4),x]","\frac{20 b^3}{3 a^6 x^{3/2}}-\frac{3 b^2}{a^5 x^2}+\frac{14 b^6}{a^8 \left(a+b \sqrt{x}\right)}+\frac{b^6}{a^7 \left(a+b \sqrt{x}\right)^2}+\frac{42 b^5}{a^8 \sqrt{x}}-\frac{15 b^4}{a^7 x}-\frac{56 b^6 \log \left(a+b \sqrt{x}\right)}{a^9}+\frac{28 b^6 \log (x)}{a^9}+\frac{6 b}{5 a^4 x^{5/2}}-\frac{1}{3 a^3 x^3}","\frac{20 b^3}{3 a^6 x^{3/2}}-\frac{3 b^2}{a^5 x^2}+\frac{14 b^6}{a^8 \left(a+b \sqrt{x}\right)}+\frac{b^6}{a^7 \left(a+b \sqrt{x}\right)^2}+\frac{42 b^5}{a^8 \sqrt{x}}-\frac{15 b^4}{a^7 x}-\frac{56 b^6 \log \left(a+b \sqrt{x}\right)}{a^9}+\frac{28 b^6 \log (x)}{a^9}+\frac{6 b}{5 a^4 x^{5/2}}-\frac{1}{3 a^3 x^3}",1,"b^6/(a^7*(a + b*Sqrt[x])^2) + (14*b^6)/(a^8*(a + b*Sqrt[x])) - 1/(3*a^3*x^3) + (6*b)/(5*a^4*x^(5/2)) - (3*b^2)/(a^5*x^2) + (20*b^3)/(3*a^6*x^(3/2)) - (15*b^4)/(a^7*x) + (42*b^5)/(a^8*Sqrt[x]) - (56*b^6*Log[a + b*Sqrt[x]])/a^9 + (28*b^6*Log[x])/a^9","A",3,2,15,0.1333,1,"{266, 44}"
2215,1,155,0,0.1398891,"\int \frac{x^4}{\left(a+b \sqrt{x}\right)^5} \, dx","Int[x^4/(a + b*Sqrt[x])^5,x]","\frac{10 a^2 x^{3/2}}{b^7}+\frac{a^9}{2 b^{10} \left(a+b \sqrt{x}\right)^4}-\frac{6 a^8}{b^{10} \left(a+b \sqrt{x}\right)^3}+\frac{36 a^7}{b^{10} \left(a+b \sqrt{x}\right)^2}-\frac{168 a^6}{b^{10} \left(a+b \sqrt{x}\right)}+\frac{140 a^4 \sqrt{x}}{b^9}-\frac{35 a^3 x}{b^8}-\frac{252 a^5 \log \left(a+b \sqrt{x}\right)}{b^{10}}-\frac{5 a x^2}{2 b^6}+\frac{2 x^{5/2}}{5 b^5}","\frac{10 a^2 x^{3/2}}{b^7}+\frac{a^9}{2 b^{10} \left(a+b \sqrt{x}\right)^4}-\frac{6 a^8}{b^{10} \left(a+b \sqrt{x}\right)^3}+\frac{36 a^7}{b^{10} \left(a+b \sqrt{x}\right)^2}-\frac{168 a^6}{b^{10} \left(a+b \sqrt{x}\right)}+\frac{140 a^4 \sqrt{x}}{b^9}-\frac{35 a^3 x}{b^8}-\frac{252 a^5 \log \left(a+b \sqrt{x}\right)}{b^{10}}-\frac{5 a x^2}{2 b^6}+\frac{2 x^{5/2}}{5 b^5}",1,"a^9/(2*b^10*(a + b*Sqrt[x])^4) - (6*a^8)/(b^10*(a + b*Sqrt[x])^3) + (36*a^7)/(b^10*(a + b*Sqrt[x])^2) - (168*a^6)/(b^10*(a + b*Sqrt[x])) + (140*a^4*Sqrt[x])/b^9 - (35*a^3*x)/b^8 + (10*a^2*x^(3/2))/b^7 - (5*a*x^2)/(2*b^6) + (2*x^(5/2))/(5*b^5) - (252*a^5*Log[a + b*Sqrt[x]])/b^10","A",3,2,15,0.1333,1,"{266, 43}"
2216,1,131,0,0.1047657,"\int \frac{x^3}{\left(a+b \sqrt{x}\right)^5} \, dx","Int[x^3/(a + b*Sqrt[x])^5,x]","\frac{a^7}{2 b^8 \left(a+b \sqrt{x}\right)^4}-\frac{14 a^6}{3 b^8 \left(a+b \sqrt{x}\right)^3}+\frac{21 a^5}{b^8 \left(a+b \sqrt{x}\right)^2}-\frac{70 a^4}{b^8 \left(a+b \sqrt{x}\right)}+\frac{30 a^2 \sqrt{x}}{b^7}-\frac{70 a^3 \log \left(a+b \sqrt{x}\right)}{b^8}-\frac{5 a x}{b^6}+\frac{2 x^{3/2}}{3 b^5}","\frac{a^7}{2 b^8 \left(a+b \sqrt{x}\right)^4}-\frac{14 a^6}{3 b^8 \left(a+b \sqrt{x}\right)^3}+\frac{21 a^5}{b^8 \left(a+b \sqrt{x}\right)^2}-\frac{70 a^4}{b^8 \left(a+b \sqrt{x}\right)}+\frac{30 a^2 \sqrt{x}}{b^7}-\frac{70 a^3 \log \left(a+b \sqrt{x}\right)}{b^8}-\frac{5 a x}{b^6}+\frac{2 x^{3/2}}{3 b^5}",1,"a^7/(2*b^8*(a + b*Sqrt[x])^4) - (14*a^6)/(3*b^8*(a + b*Sqrt[x])^3) + (21*a^5)/(b^8*(a + b*Sqrt[x])^2) - (70*a^4)/(b^8*(a + b*Sqrt[x])) + (30*a^2*Sqrt[x])/b^7 - (5*a*x)/b^6 + (2*x^(3/2))/(3*b^5) - (70*a^3*Log[a + b*Sqrt[x]])/b^8","A",3,2,15,0.1333,1,"{266, 43}"
2217,1,107,0,0.06793,"\int \frac{x^2}{\left(a+b \sqrt{x}\right)^5} \, dx","Int[x^2/(a + b*Sqrt[x])^5,x]","\frac{a^5}{2 b^6 \left(a+b \sqrt{x}\right)^4}-\frac{10 a^4}{3 b^6 \left(a+b \sqrt{x}\right)^3}+\frac{10 a^3}{b^6 \left(a+b \sqrt{x}\right)^2}-\frac{20 a^2}{b^6 \left(a+b \sqrt{x}\right)}-\frac{10 a \log \left(a+b \sqrt{x}\right)}{b^6}+\frac{2 \sqrt{x}}{b^5}","\frac{a^5}{2 b^6 \left(a+b \sqrt{x}\right)^4}-\frac{10 a^4}{3 b^6 \left(a+b \sqrt{x}\right)^3}+\frac{10 a^3}{b^6 \left(a+b \sqrt{x}\right)^2}-\frac{20 a^2}{b^6 \left(a+b \sqrt{x}\right)}-\frac{10 a \log \left(a+b \sqrt{x}\right)}{b^6}+\frac{2 \sqrt{x}}{b^5}",1,"a^5/(2*b^6*(a + b*Sqrt[x])^4) - (10*a^4)/(3*b^6*(a + b*Sqrt[x])^3) + (10*a^3)/(b^6*(a + b*Sqrt[x])^2) - (20*a^2)/(b^6*(a + b*Sqrt[x])) + (2*Sqrt[x])/b^5 - (10*a*Log[a + b*Sqrt[x]])/b^6","A",3,2,15,0.1333,1,"{266, 43}"
2218,1,21,0,0.002909,"\int \frac{x}{\left(a+b \sqrt{x}\right)^5} \, dx","Int[x/(a + b*Sqrt[x])^5,x]","\frac{x^2}{2 a \left(a+b \sqrt{x}\right)^4}","\frac{x^2}{2 a \left(a+b \sqrt{x}\right)^4}",1,"x^2/(2*a*(a + b*Sqrt[x])^4)","A",1,1,13,0.07692,1,"{264}"
2219,1,38,0,0.020523,"\int \frac{1}{\left(a+b \sqrt{x}\right)^5} \, dx","Int[(a + b*Sqrt[x])^(-5),x]","\frac{a}{2 b^2 \left(a+b \sqrt{x}\right)^4}-\frac{2}{3 b^2 \left(a+b \sqrt{x}\right)^3}","\frac{a}{2 b^2 \left(a+b \sqrt{x}\right)^4}-\frac{2}{3 b^2 \left(a+b \sqrt{x}\right)^3}",1,"a/(2*b^2*(a + b*Sqrt[x])^4) - 2/(3*b^2*(a + b*Sqrt[x])^3)","A",3,2,11,0.1818,1,"{190, 43}"
2220,1,89,0,0.0518065,"\int \frac{1}{\left(a+b \sqrt{x}\right)^5 x} \, dx","Int[1/((a + b*Sqrt[x])^5*x),x]","\frac{2}{a^4 \left(a+b \sqrt{x}\right)}+\frac{1}{a^3 \left(a+b \sqrt{x}\right)^2}+\frac{2}{3 a^2 \left(a+b \sqrt{x}\right)^3}-\frac{2 \log \left(a+b \sqrt{x}\right)}{a^5}+\frac{\log (x)}{a^5}+\frac{1}{2 a \left(a+b \sqrt{x}\right)^4}","\frac{2}{a^4 \left(a+b \sqrt{x}\right)}+\frac{1}{a^3 \left(a+b \sqrt{x}\right)^2}+\frac{2}{3 a^2 \left(a+b \sqrt{x}\right)^3}-\frac{2 \log \left(a+b \sqrt{x}\right)}{a^5}+\frac{\log (x)}{a^5}+\frac{1}{2 a \left(a+b \sqrt{x}\right)^4}",1,"1/(2*a*(a + b*Sqrt[x])^4) + 2/(3*a^2*(a + b*Sqrt[x])^3) + 1/(a^3*(a + b*Sqrt[x])^2) + 2/(a^4*(a + b*Sqrt[x])) - (2*Log[a + b*Sqrt[x]])/a^5 + Log[x]/a^5","A",3,2,15,0.1333,1,"{266, 44}"
2221,1,126,0,0.0853851,"\int \frac{1}{\left(a+b \sqrt{x}\right)^5 x^2} \, dx","Int[1/((a + b*Sqrt[x])^5*x^2),x]","\frac{20 b^2}{a^6 \left(a+b \sqrt{x}\right)}+\frac{6 b^2}{a^5 \left(a+b \sqrt{x}\right)^2}+\frac{2 b^2}{a^4 \left(a+b \sqrt{x}\right)^3}+\frac{b^2}{2 a^3 \left(a+b \sqrt{x}\right)^4}-\frac{30 b^2 \log \left(a+b \sqrt{x}\right)}{a^7}+\frac{15 b^2 \log (x)}{a^7}+\frac{10 b}{a^6 \sqrt{x}}-\frac{1}{a^5 x}","\frac{20 b^2}{a^6 \left(a+b \sqrt{x}\right)}+\frac{6 b^2}{a^5 \left(a+b \sqrt{x}\right)^2}+\frac{2 b^2}{a^4 \left(a+b \sqrt{x}\right)^3}+\frac{b^2}{2 a^3 \left(a+b \sqrt{x}\right)^4}-\frac{30 b^2 \log \left(a+b \sqrt{x}\right)}{a^7}+\frac{15 b^2 \log (x)}{a^7}+\frac{10 b}{a^6 \sqrt{x}}-\frac{1}{a^5 x}",1,"b^2/(2*a^3*(a + b*Sqrt[x])^4) + (2*b^2)/(a^4*(a + b*Sqrt[x])^3) + (6*b^2)/(a^5*(a + b*Sqrt[x])^2) + (20*b^2)/(a^6*(a + b*Sqrt[x])) - 1/(a^5*x) + (10*b)/(a^6*Sqrt[x]) - (30*b^2*Log[a + b*Sqrt[x]])/a^7 + (15*b^2*Log[x])/a^7","A",3,2,15,0.1333,1,"{266, 44}"
2222,1,156,0,0.1085704,"\int \frac{1}{\left(a+b \sqrt{x}\right)^5 x^3} \, dx","Int[1/((a + b*Sqrt[x])^5*x^3),x]","\frac{70 b^4}{a^8 \left(a+b \sqrt{x}\right)}+\frac{15 b^4}{a^7 \left(a+b \sqrt{x}\right)^2}+\frac{10 b^4}{3 a^6 \left(a+b \sqrt{x}\right)^3}+\frac{b^4}{2 a^5 \left(a+b \sqrt{x}\right)^4}+\frac{70 b^3}{a^8 \sqrt{x}}-\frac{15 b^2}{a^7 x}-\frac{140 b^4 \log \left(a+b \sqrt{x}\right)}{a^9}+\frac{70 b^4 \log (x)}{a^9}+\frac{10 b}{3 a^6 x^{3/2}}-\frac{1}{2 a^5 x^2}","\frac{70 b^4}{a^8 \left(a+b \sqrt{x}\right)}+\frac{15 b^4}{a^7 \left(a+b \sqrt{x}\right)^2}+\frac{10 b^4}{3 a^6 \left(a+b \sqrt{x}\right)^3}+\frac{b^4}{2 a^5 \left(a+b \sqrt{x}\right)^4}+\frac{70 b^3}{a^8 \sqrt{x}}-\frac{15 b^2}{a^7 x}-\frac{140 b^4 \log \left(a+b \sqrt{x}\right)}{a^9}+\frac{70 b^4 \log (x)}{a^9}+\frac{10 b}{3 a^6 x^{3/2}}-\frac{1}{2 a^5 x^2}",1,"b^4/(2*a^5*(a + b*Sqrt[x])^4) + (10*b^4)/(3*a^6*(a + b*Sqrt[x])^3) + (15*b^4)/(a^7*(a + b*Sqrt[x])^2) + (70*b^4)/(a^8*(a + b*Sqrt[x])) - 1/(2*a^5*x^2) + (10*b)/(3*a^6*x^(3/2)) - (15*b^2)/(a^7*x) + (70*b^3)/(a^8*Sqrt[x]) - (140*b^4*Log[a + b*Sqrt[x]])/a^9 + (70*b^4*Log[x])/a^9","A",3,2,15,0.1333,1,"{266, 44}"
2223,1,203,0,0.1986539,"\int \frac{x^5}{\left(a+b \sqrt{x}\right)^8} \, dx","Int[x^5/(a + b*Sqrt[x])^8,x]","\frac{2 a^{11}}{7 b^{12} \left(a+b \sqrt{x}\right)^7}-\frac{11 a^{10}}{3 b^{12} \left(a+b \sqrt{x}\right)^6}+\frac{22 a^9}{b^{12} \left(a+b \sqrt{x}\right)^5}-\frac{165 a^8}{2 b^{12} \left(a+b \sqrt{x}\right)^4}+\frac{220 a^7}{b^{12} \left(a+b \sqrt{x}\right)^3}-\frac{462 a^6}{b^{12} \left(a+b \sqrt{x}\right)^2}+\frac{924 a^5}{b^{12} \left(a+b \sqrt{x}\right)}-\frac{240 a^3 \sqrt{x}}{b^{11}}+\frac{36 a^2 x}{b^{10}}+\frac{660 a^4 \log \left(a+b \sqrt{x}\right)}{b^{12}}-\frac{16 a x^{3/2}}{3 b^9}+\frac{x^2}{2 b^8}","\frac{2 a^{11}}{7 b^{12} \left(a+b \sqrt{x}\right)^7}-\frac{11 a^{10}}{3 b^{12} \left(a+b \sqrt{x}\right)^6}+\frac{22 a^9}{b^{12} \left(a+b \sqrt{x}\right)^5}-\frac{165 a^8}{2 b^{12} \left(a+b \sqrt{x}\right)^4}+\frac{220 a^7}{b^{12} \left(a+b \sqrt{x}\right)^3}-\frac{462 a^6}{b^{12} \left(a+b \sqrt{x}\right)^2}+\frac{924 a^5}{b^{12} \left(a+b \sqrt{x}\right)}-\frac{240 a^3 \sqrt{x}}{b^{11}}+\frac{36 a^2 x}{b^{10}}+\frac{660 a^4 \log \left(a+b \sqrt{x}\right)}{b^{12}}-\frac{16 a x^{3/2}}{3 b^9}+\frac{x^2}{2 b^8}",1,"(2*a^11)/(7*b^12*(a + b*Sqrt[x])^7) - (11*a^10)/(3*b^12*(a + b*Sqrt[x])^6) + (22*a^9)/(b^12*(a + b*Sqrt[x])^5) - (165*a^8)/(2*b^12*(a + b*Sqrt[x])^4) + (220*a^7)/(b^12*(a + b*Sqrt[x])^3) - (462*a^6)/(b^12*(a + b*Sqrt[x])^2) + (924*a^5)/(b^12*(a + b*Sqrt[x])) - (240*a^3*Sqrt[x])/b^11 + (36*a^2*x)/b^10 - (16*a*x^(3/2))/(3*b^9) + x^2/(2*b^8) + (660*a^4*Log[a + b*Sqrt[x]])/b^12","A",3,2,15,0.1333,1,"{266, 43}"
2224,1,172,0,0.1573605,"\int \frac{x^4}{\left(a+b \sqrt{x}\right)^8} \, dx","Int[x^4/(a + b*Sqrt[x])^8,x]","\frac{2 a^9}{7 b^{10} \left(a+b \sqrt{x}\right)^7}-\frac{3 a^8}{b^{10} \left(a+b \sqrt{x}\right)^6}+\frac{72 a^7}{5 b^{10} \left(a+b \sqrt{x}\right)^5}-\frac{42 a^6}{b^{10} \left(a+b \sqrt{x}\right)^4}+\frac{84 a^5}{b^{10} \left(a+b \sqrt{x}\right)^3}-\frac{126 a^4}{b^{10} \left(a+b \sqrt{x}\right)^2}+\frac{168 a^3}{b^{10} \left(a+b \sqrt{x}\right)}+\frac{72 a^2 \log \left(a+b \sqrt{x}\right)}{b^{10}}-\frac{16 a \sqrt{x}}{b^9}+\frac{x}{b^8}","\frac{2 a^9}{7 b^{10} \left(a+b \sqrt{x}\right)^7}-\frac{3 a^8}{b^{10} \left(a+b \sqrt{x}\right)^6}+\frac{72 a^7}{5 b^{10} \left(a+b \sqrt{x}\right)^5}-\frac{42 a^6}{b^{10} \left(a+b \sqrt{x}\right)^4}+\frac{84 a^5}{b^{10} \left(a+b \sqrt{x}\right)^3}-\frac{126 a^4}{b^{10} \left(a+b \sqrt{x}\right)^2}+\frac{168 a^3}{b^{10} \left(a+b \sqrt{x}\right)}+\frac{72 a^2 \log \left(a+b \sqrt{x}\right)}{b^{10}}-\frac{16 a \sqrt{x}}{b^9}+\frac{x}{b^8}",1,"(2*a^9)/(7*b^10*(a + b*Sqrt[x])^7) - (3*a^8)/(b^10*(a + b*Sqrt[x])^6) + (72*a^7)/(5*b^10*(a + b*Sqrt[x])^5) - (42*a^6)/(b^10*(a + b*Sqrt[x])^4) + (84*a^5)/(b^10*(a + b*Sqrt[x])^3) - (126*a^4)/(b^10*(a + b*Sqrt[x])^2) + (168*a^3)/(b^10*(a + b*Sqrt[x])) - (16*a*Sqrt[x])/b^9 + x/b^8 + (72*a^2*Log[a + b*Sqrt[x]])/b^10","A",3,2,15,0.1333,1,"{266, 43}"
2225,1,157,0,0.1064991,"\int \frac{x^3}{\left(a+b \sqrt{x}\right)^8} \, dx","Int[x^3/(a + b*Sqrt[x])^8,x]","\frac{2 a^7}{7 b^8 \left(a+b \sqrt{x}\right)^7}-\frac{7 a^6}{3 b^8 \left(a+b \sqrt{x}\right)^6}+\frac{42 a^5}{5 b^8 \left(a+b \sqrt{x}\right)^5}-\frac{35 a^4}{2 b^8 \left(a+b \sqrt{x}\right)^4}+\frac{70 a^3}{3 b^8 \left(a+b \sqrt{x}\right)^3}-\frac{21 a^2}{b^8 \left(a+b \sqrt{x}\right)^2}+\frac{14 a}{b^8 \left(a+b \sqrt{x}\right)}+\frac{2 \log \left(a+b \sqrt{x}\right)}{b^8}","\frac{2 a^7}{7 b^8 \left(a+b \sqrt{x}\right)^7}-\frac{7 a^6}{3 b^8 \left(a+b \sqrt{x}\right)^6}+\frac{42 a^5}{5 b^8 \left(a+b \sqrt{x}\right)^5}-\frac{35 a^4}{2 b^8 \left(a+b \sqrt{x}\right)^4}+\frac{70 a^3}{3 b^8 \left(a+b \sqrt{x}\right)^3}-\frac{21 a^2}{b^8 \left(a+b \sqrt{x}\right)^2}+\frac{14 a}{b^8 \left(a+b \sqrt{x}\right)}+\frac{2 \log \left(a+b \sqrt{x}\right)}{b^8}",1,"(2*a^7)/(7*b^8*(a + b*Sqrt[x])^7) - (7*a^6)/(3*b^8*(a + b*Sqrt[x])^6) + (42*a^5)/(5*b^8*(a + b*Sqrt[x])^5) - (35*a^4)/(2*b^8*(a + b*Sqrt[x])^4) + (70*a^3)/(3*b^8*(a + b*Sqrt[x])^3) - (21*a^2)/(b^8*(a + b*Sqrt[x])^2) + (14*a)/(b^8*(a + b*Sqrt[x])) + (2*Log[a + b*Sqrt[x]])/b^8","A",3,2,15,0.1333,1,"{266, 43}"
2226,1,43,0,0.0141991,"\int \frac{x^2}{\left(a+b \sqrt{x}\right)^8} \, dx","Int[x^2/(a + b*Sqrt[x])^8,x]","\frac{x^3}{21 a^2 \left(a+b \sqrt{x}\right)^6}+\frac{2 x^3}{7 a \left(a+b \sqrt{x}\right)^7}","\frac{x^3}{21 a^2 \left(a+b \sqrt{x}\right)^6}+\frac{2 x^3}{7 a \left(a+b \sqrt{x}\right)^7}",1,"(2*x^3)/(7*a*(a + b*Sqrt[x])^7) + x^3/(21*a^2*(a + b*Sqrt[x])^6)","A",3,3,15,0.2000,1,"{266, 45, 37}"
2227,1,78,0,0.049026,"\int \frac{x}{\left(a+b \sqrt{x}\right)^8} \, dx","Int[x/(a + b*Sqrt[x])^8,x]","\frac{2 a^3}{7 b^4 \left(a+b \sqrt{x}\right)^7}-\frac{a^2}{b^4 \left(a+b \sqrt{x}\right)^6}+\frac{6 a}{5 b^4 \left(a+b \sqrt{x}\right)^5}-\frac{1}{2 b^4 \left(a+b \sqrt{x}\right)^4}","\frac{2 a^3}{7 b^4 \left(a+b \sqrt{x}\right)^7}-\frac{a^2}{b^4 \left(a+b \sqrt{x}\right)^6}+\frac{6 a}{5 b^4 \left(a+b \sqrt{x}\right)^5}-\frac{1}{2 b^4 \left(a+b \sqrt{x}\right)^4}",1,"(2*a^3)/(7*b^4*(a + b*Sqrt[x])^7) - a^2/(b^4*(a + b*Sqrt[x])^6) + (6*a)/(5*b^4*(a + b*Sqrt[x])^5) - 1/(2*b^4*(a + b*Sqrt[x])^4)","A",3,2,13,0.1538,1,"{266, 43}"
2228,1,38,0,0.0210688,"\int \frac{1}{\left(a+b \sqrt{x}\right)^8} \, dx","Int[(a + b*Sqrt[x])^(-8),x]","\frac{2 a}{7 b^2 \left(a+b \sqrt{x}\right)^7}-\frac{1}{3 b^2 \left(a+b \sqrt{x}\right)^6}","\frac{2 a}{7 b^2 \left(a+b \sqrt{x}\right)^7}-\frac{1}{3 b^2 \left(a+b \sqrt{x}\right)^6}",1,"(2*a)/(7*b^2*(a + b*Sqrt[x])^7) - 1/(3*b^2*(a + b*Sqrt[x])^6)","A",3,2,11,0.1818,1,"{190, 43}"
2229,1,143,0,0.088623,"\int \frac{1}{\left(a+b \sqrt{x}\right)^8 x} \, dx","Int[1/((a + b*Sqrt[x])^8*x),x]","\frac{2}{a^7 \left(a+b \sqrt{x}\right)}+\frac{1}{a^6 \left(a+b \sqrt{x}\right)^2}+\frac{2}{3 a^5 \left(a+b \sqrt{x}\right)^3}+\frac{1}{2 a^4 \left(a+b \sqrt{x}\right)^4}+\frac{2}{5 a^3 \left(a+b \sqrt{x}\right)^5}+\frac{1}{3 a^2 \left(a+b \sqrt{x}\right)^6}-\frac{2 \log \left(a+b \sqrt{x}\right)}{a^8}+\frac{\log (x)}{a^8}+\frac{2}{7 a \left(a+b \sqrt{x}\right)^7}","\frac{2}{a^7 \left(a+b \sqrt{x}\right)}+\frac{1}{a^6 \left(a+b \sqrt{x}\right)^2}+\frac{2}{3 a^5 \left(a+b \sqrt{x}\right)^3}+\frac{1}{2 a^4 \left(a+b \sqrt{x}\right)^4}+\frac{2}{5 a^3 \left(a+b \sqrt{x}\right)^5}+\frac{1}{3 a^2 \left(a+b \sqrt{x}\right)^6}-\frac{2 \log \left(a+b \sqrt{x}\right)}{a^8}+\frac{\log (x)}{a^8}+\frac{2}{7 a \left(a+b \sqrt{x}\right)^7}",1,"2/(7*a*(a + b*Sqrt[x])^7) + 1/(3*a^2*(a + b*Sqrt[x])^6) + 2/(5*a^3*(a + b*Sqrt[x])^5) + 1/(2*a^4*(a + b*Sqrt[x])^4) + 2/(3*a^5*(a + b*Sqrt[x])^3) + 1/(a^6*(a + b*Sqrt[x])^2) + 2/(a^7*(a + b*Sqrt[x])) - (2*Log[a + b*Sqrt[x]])/a^8 + Log[x]/a^8","A",3,2,15,0.1333,1,"{266, 44}"
2230,1,184,0,0.1581641,"\int \frac{1}{\left(a+b \sqrt{x}\right)^8 x^2} \, dx","Int[1/((a + b*Sqrt[x])^8*x^2),x]","\frac{56 b^2}{a^9 \left(a+b \sqrt{x}\right)}+\frac{21 b^2}{a^8 \left(a+b \sqrt{x}\right)^2}+\frac{10 b^2}{a^7 \left(a+b \sqrt{x}\right)^3}+\frac{5 b^2}{a^6 \left(a+b \sqrt{x}\right)^4}+\frac{12 b^2}{5 a^5 \left(a+b \sqrt{x}\right)^5}+\frac{b^2}{a^4 \left(a+b \sqrt{x}\right)^6}+\frac{2 b^2}{7 a^3 \left(a+b \sqrt{x}\right)^7}-\frac{72 b^2 \log \left(a+b \sqrt{x}\right)}{a^{10}}+\frac{36 b^2 \log (x)}{a^{10}}+\frac{16 b}{a^9 \sqrt{x}}-\frac{1}{a^8 x}","\frac{56 b^2}{a^9 \left(a+b \sqrt{x}\right)}+\frac{21 b^2}{a^8 \left(a+b \sqrt{x}\right)^2}+\frac{10 b^2}{a^7 \left(a+b \sqrt{x}\right)^3}+\frac{5 b^2}{a^6 \left(a+b \sqrt{x}\right)^4}+\frac{12 b^2}{5 a^5 \left(a+b \sqrt{x}\right)^5}+\frac{b^2}{a^4 \left(a+b \sqrt{x}\right)^6}+\frac{2 b^2}{7 a^3 \left(a+b \sqrt{x}\right)^7}-\frac{72 b^2 \log \left(a+b \sqrt{x}\right)}{a^{10}}+\frac{36 b^2 \log (x)}{a^{10}}+\frac{16 b}{a^9 \sqrt{x}}-\frac{1}{a^8 x}",1,"(2*b^2)/(7*a^3*(a + b*Sqrt[x])^7) + b^2/(a^4*(a + b*Sqrt[x])^6) + (12*b^2)/(5*a^5*(a + b*Sqrt[x])^5) + (5*b^2)/(a^6*(a + b*Sqrt[x])^4) + (10*b^2)/(a^7*(a + b*Sqrt[x])^3) + (21*b^2)/(a^8*(a + b*Sqrt[x])^2) + (56*b^2)/(a^9*(a + b*Sqrt[x])) - 1/(a^8*x) + (16*b)/(a^9*Sqrt[x]) - (72*b^2*Log[a + b*Sqrt[x]])/a^10 + (36*b^2*Log[x])/a^10","A",3,2,15,0.1333,1,"{266, 44}"
2231,1,217,0,0.1914097,"\int \frac{1}{\left(a+b \sqrt{x}\right)^8 x^3} \, dx","Int[1/((a + b*Sqrt[x])^8*x^3),x]","\frac{420 b^4}{a^{11} \left(a+b \sqrt{x}\right)}+\frac{126 b^4}{a^{10} \left(a+b \sqrt{x}\right)^2}+\frac{140 b^4}{3 a^9 \left(a+b \sqrt{x}\right)^3}+\frac{35 b^4}{2 a^8 \left(a+b \sqrt{x}\right)^4}+\frac{6 b^4}{a^7 \left(a+b \sqrt{x}\right)^5}+\frac{5 b^4}{3 a^6 \left(a+b \sqrt{x}\right)^6}+\frac{2 b^4}{7 a^5 \left(a+b \sqrt{x}\right)^7}+\frac{240 b^3}{a^{11} \sqrt{x}}-\frac{36 b^2}{a^{10} x}-\frac{660 b^4 \log \left(a+b \sqrt{x}\right)}{a^{12}}+\frac{330 b^4 \log (x)}{a^{12}}+\frac{16 b}{3 a^9 x^{3/2}}-\frac{1}{2 a^8 x^2}","\frac{420 b^4}{a^{11} \left(a+b \sqrt{x}\right)}+\frac{126 b^4}{a^{10} \left(a+b \sqrt{x}\right)^2}+\frac{140 b^4}{3 a^9 \left(a+b \sqrt{x}\right)^3}+\frac{35 b^4}{2 a^8 \left(a+b \sqrt{x}\right)^4}+\frac{6 b^4}{a^7 \left(a+b \sqrt{x}\right)^5}+\frac{5 b^4}{3 a^6 \left(a+b \sqrt{x}\right)^6}+\frac{2 b^4}{7 a^5 \left(a+b \sqrt{x}\right)^7}+\frac{240 b^3}{a^{11} \sqrt{x}}-\frac{36 b^2}{a^{10} x}-\frac{660 b^4 \log \left(a+b \sqrt{x}\right)}{a^{12}}+\frac{330 b^4 \log (x)}{a^{12}}+\frac{16 b}{3 a^9 x^{3/2}}-\frac{1}{2 a^8 x^2}",1,"(2*b^4)/(7*a^5*(a + b*Sqrt[x])^7) + (5*b^4)/(3*a^6*(a + b*Sqrt[x])^6) + (6*b^4)/(a^7*(a + b*Sqrt[x])^5) + (35*b^4)/(2*a^8*(a + b*Sqrt[x])^4) + (140*b^4)/(3*a^9*(a + b*Sqrt[x])^3) + (126*b^4)/(a^10*(a + b*Sqrt[x])^2) + (420*b^4)/(a^11*(a + b*Sqrt[x])) - 1/(2*a^8*x^2) + (16*b)/(3*a^9*x^(3/2)) - (36*b^2)/(a^10*x) + (240*b^3)/(a^11*Sqrt[x]) - (660*b^4*Log[a + b*Sqrt[x]])/a^12 + (330*b^4*Log[x])/a^12","A",3,2,15,0.1333,1,"{266, 44}"
2232,1,19,0,0.0082974,"\int \frac{1}{\left(2+b \sqrt{x}\right) x} \, dx","Int[1/((2 + b*Sqrt[x])*x),x]","\frac{\log (x)}{2}-\log \left(b \sqrt{x}+2\right)","\frac{\log (x)}{2}-\log \left(b \sqrt{x}+2\right)",1,"-Log[2 + b*Sqrt[x]] + Log[x]/2","A",4,4,15,0.2667,1,"{266, 36, 29, 31}"
2233,1,132,0,0.0618827,"\int \sqrt{a+b \sqrt{x}} x^2 \, dx","Int[Sqrt[a + b*Sqrt[x]]*x^2,x]","\frac{40 a^2 \left(a+b \sqrt{x}\right)^{9/2}}{9 b^6}-\frac{40 a^3 \left(a+b \sqrt{x}\right)^{7/2}}{7 b^6}+\frac{4 a^4 \left(a+b \sqrt{x}\right)^{5/2}}{b^6}-\frac{4 a^5 \left(a+b \sqrt{x}\right)^{3/2}}{3 b^6}+\frac{4 \left(a+b \sqrt{x}\right)^{13/2}}{13 b^6}-\frac{20 a \left(a+b \sqrt{x}\right)^{11/2}}{11 b^6}","\frac{40 a^2 \left(a+b \sqrt{x}\right)^{9/2}}{9 b^6}-\frac{40 a^3 \left(a+b \sqrt{x}\right)^{7/2}}{7 b^6}+\frac{4 a^4 \left(a+b \sqrt{x}\right)^{5/2}}{b^6}-\frac{4 a^5 \left(a+b \sqrt{x}\right)^{3/2}}{3 b^6}+\frac{4 \left(a+b \sqrt{x}\right)^{13/2}}{13 b^6}-\frac{20 a \left(a+b \sqrt{x}\right)^{11/2}}{11 b^6}",1,"(-4*a^5*(a + b*Sqrt[x])^(3/2))/(3*b^6) + (4*a^4*(a + b*Sqrt[x])^(5/2))/b^6 - (40*a^3*(a + b*Sqrt[x])^(7/2))/(7*b^6) + (40*a^2*(a + b*Sqrt[x])^(9/2))/(9*b^6) - (20*a*(a + b*Sqrt[x])^(11/2))/(11*b^6) + (4*(a + b*Sqrt[x])^(13/2))/(13*b^6)","A",3,2,17,0.1176,1,"{266, 43}"
2234,1,88,0,0.037432,"\int \sqrt{a+b \sqrt{x}} x \, dx","Int[Sqrt[a + b*Sqrt[x]]*x,x]","\frac{12 a^2 \left(a+b \sqrt{x}\right)^{5/2}}{5 b^4}-\frac{4 a^3 \left(a+b \sqrt{x}\right)^{3/2}}{3 b^4}+\frac{4 \left(a+b \sqrt{x}\right)^{9/2}}{9 b^4}-\frac{12 a \left(a+b \sqrt{x}\right)^{7/2}}{7 b^4}","\frac{12 a^2 \left(a+b \sqrt{x}\right)^{5/2}}{5 b^4}-\frac{4 a^3 \left(a+b \sqrt{x}\right)^{3/2}}{3 b^4}+\frac{4 \left(a+b \sqrt{x}\right)^{9/2}}{9 b^4}-\frac{12 a \left(a+b \sqrt{x}\right)^{7/2}}{7 b^4}",1,"(-4*a^3*(a + b*Sqrt[x])^(3/2))/(3*b^4) + (12*a^2*(a + b*Sqrt[x])^(5/2))/(5*b^4) - (12*a*(a + b*Sqrt[x])^(7/2))/(7*b^4) + (4*(a + b*Sqrt[x])^(9/2))/(9*b^4)","A",3,2,15,0.1333,1,"{266, 43}"
2235,1,42,0,0.0169726,"\int \sqrt{a+b \sqrt{x}} \, dx","Int[Sqrt[a + b*Sqrt[x]],x]","\frac{4 \left(a+b \sqrt{x}\right)^{5/2}}{5 b^2}-\frac{4 a \left(a+b \sqrt{x}\right)^{3/2}}{3 b^2}","\frac{4 \left(a+b \sqrt{x}\right)^{5/2}}{5 b^2}-\frac{4 a \left(a+b \sqrt{x}\right)^{3/2}}{3 b^2}",1,"(-4*a*(a + b*Sqrt[x])^(3/2))/(3*b^2) + (4*(a + b*Sqrt[x])^(5/2))/(5*b^2)","A",3,2,13,0.1538,1,"{190, 43}"
2236,1,43,0,0.0217346,"\int \frac{\sqrt{a+b \sqrt{x}}}{x} \, dx","Int[Sqrt[a + b*Sqrt[x]]/x,x]","4 \sqrt{a+b \sqrt{x}}-4 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{x}}}{\sqrt{a}}\right)","4 \sqrt{a+b \sqrt{x}}-4 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{x}}}{\sqrt{a}}\right)",1,"4*Sqrt[a + b*Sqrt[x]] - 4*Sqrt[a]*ArcTanh[Sqrt[a + b*Sqrt[x]]/Sqrt[a]]","A",4,4,17,0.2353,1,"{266, 50, 63, 208}"
2237,1,77,0,0.0336536,"\int \frac{\sqrt{a+b \sqrt{x}}}{x^2} \, dx","Int[Sqrt[a + b*Sqrt[x]]/x^2,x]","\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{x}}}{\sqrt{a}}\right)}{2 a^{3/2}}-\frac{b \sqrt{a+b \sqrt{x}}}{2 a \sqrt{x}}-\frac{\sqrt{a+b \sqrt{x}}}{x}","\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{x}}}{\sqrt{a}}\right)}{2 a^{3/2}}-\frac{b \sqrt{a+b \sqrt{x}}}{2 a \sqrt{x}}-\frac{\sqrt{a+b \sqrt{x}}}{x}",1,"-(Sqrt[a + b*Sqrt[x]]/x) - (b*Sqrt[a + b*Sqrt[x]])/(2*a*Sqrt[x]) + (b^2*ArcTanh[Sqrt[a + b*Sqrt[x]]/Sqrt[a]])/(2*a^(3/2))","A",5,5,17,0.2941,1,"{266, 47, 51, 63, 208}"
2238,1,133,0,0.0608528,"\int \frac{\sqrt{a+b \sqrt{x}}}{x^3} \, dx","Int[Sqrt[a + b*Sqrt[x]]/x^3,x]","-\frac{5 b^3 \sqrt{a+b \sqrt{x}}}{32 a^3 \sqrt{x}}+\frac{5 b^2 \sqrt{a+b \sqrt{x}}}{48 a^2 x}+\frac{5 b^4 \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{x}}}{\sqrt{a}}\right)}{32 a^{7/2}}-\frac{b \sqrt{a+b \sqrt{x}}}{12 a x^{3/2}}-\frac{\sqrt{a+b \sqrt{x}}}{2 x^2}","-\frac{5 b^3 \sqrt{a+b \sqrt{x}}}{32 a^3 \sqrt{x}}+\frac{5 b^2 \sqrt{a+b \sqrt{x}}}{48 a^2 x}+\frac{5 b^4 \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{x}}}{\sqrt{a}}\right)}{32 a^{7/2}}-\frac{b \sqrt{a+b \sqrt{x}}}{12 a x^{3/2}}-\frac{\sqrt{a+b \sqrt{x}}}{2 x^2}",1,"-Sqrt[a + b*Sqrt[x]]/(2*x^2) - (b*Sqrt[a + b*Sqrt[x]])/(12*a*x^(3/2)) + (5*b^2*Sqrt[a + b*Sqrt[x]])/(48*a^2*x) - (5*b^3*Sqrt[a + b*Sqrt[x]])/(32*a^3*Sqrt[x]) + (5*b^4*ArcTanh[Sqrt[a + b*Sqrt[x]]/Sqrt[a]])/(32*a^(7/2))","A",7,5,17,0.2941,1,"{266, 47, 51, 63, 208}"
2239,1,130,0,0.0585677,"\int \frac{x^2}{\sqrt{a+b \sqrt{x}}} \, dx","Int[x^2/Sqrt[a + b*Sqrt[x]],x]","\frac{40 a^2 \left(a+b \sqrt{x}\right)^{7/2}}{7 b^6}-\frac{8 a^3 \left(a+b \sqrt{x}\right)^{5/2}}{b^6}+\frac{20 a^4 \left(a+b \sqrt{x}\right)^{3/2}}{3 b^6}-\frac{4 a^5 \sqrt{a+b \sqrt{x}}}{b^6}+\frac{4 \left(a+b \sqrt{x}\right)^{11/2}}{11 b^6}-\frac{20 a \left(a+b \sqrt{x}\right)^{9/2}}{9 b^6}","\frac{40 a^2 \left(a+b \sqrt{x}\right)^{7/2}}{7 b^6}-\frac{8 a^3 \left(a+b \sqrt{x}\right)^{5/2}}{b^6}+\frac{20 a^4 \left(a+b \sqrt{x}\right)^{3/2}}{3 b^6}-\frac{4 a^5 \sqrt{a+b \sqrt{x}}}{b^6}+\frac{4 \left(a+b \sqrt{x}\right)^{11/2}}{11 b^6}-\frac{20 a \left(a+b \sqrt{x}\right)^{9/2}}{9 b^6}",1,"(-4*a^5*Sqrt[a + b*Sqrt[x]])/b^6 + (20*a^4*(a + b*Sqrt[x])^(3/2))/(3*b^6) - (8*a^3*(a + b*Sqrt[x])^(5/2))/b^6 + (40*a^2*(a + b*Sqrt[x])^(7/2))/(7*b^6) - (20*a*(a + b*Sqrt[x])^(9/2))/(9*b^6) + (4*(a + b*Sqrt[x])^(11/2))/(11*b^6)","A",3,2,17,0.1176,1,"{266, 43}"
2240,1,84,0,0.0382357,"\int \frac{x}{\sqrt{a+b \sqrt{x}}} \, dx","Int[x/Sqrt[a + b*Sqrt[x]],x]","\frac{4 a^2 \left(a+b \sqrt{x}\right)^{3/2}}{b^4}-\frac{4 a^3 \sqrt{a+b \sqrt{x}}}{b^4}+\frac{4 \left(a+b \sqrt{x}\right)^{7/2}}{7 b^4}-\frac{12 a \left(a+b \sqrt{x}\right)^{5/2}}{5 b^4}","\frac{4 a^2 \left(a+b \sqrt{x}\right)^{3/2}}{b^4}-\frac{4 a^3 \sqrt{a+b \sqrt{x}}}{b^4}+\frac{4 \left(a+b \sqrt{x}\right)^{7/2}}{7 b^4}-\frac{12 a \left(a+b \sqrt{x}\right)^{5/2}}{5 b^4}",1,"(-4*a^3*Sqrt[a + b*Sqrt[x]])/b^4 + (4*a^2*(a + b*Sqrt[x])^(3/2))/b^4 - (12*a*(a + b*Sqrt[x])^(5/2))/(5*b^4) + (4*(a + b*Sqrt[x])^(7/2))/(7*b^4)","A",3,2,15,0.1333,1,"{266, 43}"
2241,1,40,0,0.0170122,"\int \frac{1}{\sqrt{a+b \sqrt{x}}} \, dx","Int[1/Sqrt[a + b*Sqrt[x]],x]","\frac{4 \left(a+b \sqrt{x}\right)^{3/2}}{3 b^2}-\frac{4 a \sqrt{a+b \sqrt{x}}}{b^2}","\frac{4 \left(a+b \sqrt{x}\right)^{3/2}}{3 b^2}-\frac{4 a \sqrt{a+b \sqrt{x}}}{b^2}",1,"(-4*a*Sqrt[a + b*Sqrt[x]])/b^2 + (4*(a + b*Sqrt[x])^(3/2))/(3*b^2)","A",3,2,13,0.1538,1,"{190, 43}"
2242,1,27,0,0.0161422,"\int \frac{1}{\sqrt{a+b \sqrt{x}} x} \, dx","Int[1/(Sqrt[a + b*Sqrt[x]]*x),x]","-\frac{4 \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{x}}}{\sqrt{a}}\right)}{\sqrt{a}}","-\frac{4 \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{x}}}{\sqrt{a}}\right)}{\sqrt{a}}",1,"(-4*ArcTanh[Sqrt[a + b*Sqrt[x]]/Sqrt[a]])/Sqrt[a]","A",3,3,17,0.1765,1,"{266, 63, 208}"
2243,1,80,0,0.0351734,"\int \frac{1}{\sqrt{a+b \sqrt{x}} x^2} \, dx","Int[1/(Sqrt[a + b*Sqrt[x]]*x^2),x]","-\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{x}}}{\sqrt{a}}\right)}{2 a^{5/2}}+\frac{3 b \sqrt{a+b \sqrt{x}}}{2 a^2 \sqrt{x}}-\frac{\sqrt{a+b \sqrt{x}}}{a x}","-\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{x}}}{\sqrt{a}}\right)}{2 a^{5/2}}+\frac{3 b \sqrt{a+b \sqrt{x}}}{2 a^2 \sqrt{x}}-\frac{\sqrt{a+b \sqrt{x}}}{a x}",1,"-(Sqrt[a + b*Sqrt[x]]/(a*x)) + (3*b*Sqrt[a + b*Sqrt[x]])/(2*a^2*Sqrt[x]) - (3*b^2*ArcTanh[Sqrt[a + b*Sqrt[x]]/Sqrt[a]])/(2*a^(5/2))","A",5,4,17,0.2353,1,"{266, 51, 63, 208}"
2244,1,136,0,0.0589333,"\int \frac{1}{\sqrt{a+b \sqrt{x}} x^3} \, dx","Int[1/(Sqrt[a + b*Sqrt[x]]*x^3),x]","\frac{35 b^3 \sqrt{a+b \sqrt{x}}}{32 a^4 \sqrt{x}}-\frac{35 b^2 \sqrt{a+b \sqrt{x}}}{48 a^3 x}-\frac{35 b^4 \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{x}}}{\sqrt{a}}\right)}{32 a^{9/2}}+\frac{7 b \sqrt{a+b \sqrt{x}}}{12 a^2 x^{3/2}}-\frac{\sqrt{a+b \sqrt{x}}}{2 a x^2}","\frac{35 b^3 \sqrt{a+b \sqrt{x}}}{32 a^4 \sqrt{x}}-\frac{35 b^2 \sqrt{a+b \sqrt{x}}}{48 a^3 x}-\frac{35 b^4 \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{x}}}{\sqrt{a}}\right)}{32 a^{9/2}}+\frac{7 b \sqrt{a+b \sqrt{x}}}{12 a^2 x^{3/2}}-\frac{\sqrt{a+b \sqrt{x}}}{2 a x^2}",1,"-Sqrt[a + b*Sqrt[x]]/(2*a*x^2) + (7*b*Sqrt[a + b*Sqrt[x]])/(12*a^2*x^(3/2)) - (35*b^2*Sqrt[a + b*Sqrt[x]])/(48*a^3*x) + (35*b^3*Sqrt[a + b*Sqrt[x]])/(32*a^4*Sqrt[x]) - (35*b^4*ArcTanh[Sqrt[a + b*Sqrt[x]]/Sqrt[a]])/(32*a^(9/2))","A",7,4,17,0.2353,1,"{266, 51, 63, 208}"
2245,1,74,0,0.0403011,"\int \left(a+b \sqrt{x}\right)^n \sqrt{x} \, dx","Int[(a + b*Sqrt[x])^n*Sqrt[x],x]","\frac{2 a^2 \left(a+b \sqrt{x}\right)^{n+1}}{b^3 (n+1)}-\frac{4 a \left(a+b \sqrt{x}\right)^{n+2}}{b^3 (n+2)}+\frac{2 \left(a+b \sqrt{x}\right)^{n+3}}{b^3 (n+3)}","\frac{2 a^2 \left(a+b \sqrt{x}\right)^{n+1}}{b^3 (n+1)}-\frac{4 a \left(a+b \sqrt{x}\right)^{n+2}}{b^3 (n+2)}+\frac{2 \left(a+b \sqrt{x}\right)^{n+3}}{b^3 (n+3)}",1,"(2*a^2*(a + b*Sqrt[x])^(1 + n))/(b^3*(1 + n)) - (4*a*(a + b*Sqrt[x])^(2 + n))/(b^3*(2 + n)) + (2*(a + b*Sqrt[x])^(3 + n))/(b^3*(3 + n))","A",3,2,17,0.1176,1,"{266, 43}"
2246,1,23,0,0.0051468,"\int \frac{\left(a+b \sqrt{x}\right)^n}{\sqrt{x}} \, dx","Int[(a + b*Sqrt[x])^n/Sqrt[x],x]","\frac{2 \left(a+b \sqrt{x}\right)^{n+1}}{b (n+1)}","\frac{2 \left(a+b \sqrt{x}\right)^{n+1}}{b (n+1)}",1,"(2*(a + b*Sqrt[x])^(1 + n))/(b*(1 + n))","A",1,1,17,0.05882,1,"{261}"
2247,1,9,0,0.0025924,"\int \frac{1+\sqrt{x}}{\sqrt{x}} \, dx","Int[(1 + Sqrt[x])/Sqrt[x],x]","x+2 \sqrt{x}","x+2 \sqrt{x}",1,"2*Sqrt[x] + x","A",2,1,13,0.07692,1,"{14}"
2248,1,13,0,0.0020405,"\int \frac{\left(1+\sqrt{x}\right)^2}{\sqrt{x}} \, dx","Int[(1 + Sqrt[x])^2/Sqrt[x],x]","\frac{2}{3} \left(\sqrt{x}+1\right)^3","\frac{2}{3} \left(\sqrt{x}+1\right)^3",1,"(2*(1 + Sqrt[x])^3)/3","A",1,1,15,0.06667,1,"{261}"
2249,1,13,0,0.0022539,"\int \frac{\left(1+\sqrt{x}\right)^3}{\sqrt{x}} \, dx","Int[(1 + Sqrt[x])^3/Sqrt[x],x]","\frac{1}{2} \left(\sqrt{x}+1\right)^4","\frac{1}{2} \left(\sqrt{x}+1\right)^4",1,"(1 + Sqrt[x])^4/2","A",1,1,15,0.06667,1,"{261}"
2250,1,19,0,0.0107918,"\int \frac{\sqrt{x}}{1+\sqrt{x}} \, dx","Int[Sqrt[x]/(1 + Sqrt[x]),x]","x-2 \sqrt{x}+2 \log \left(\sqrt{x}+1\right)","x-2 \sqrt{x}+2 \log \left(\sqrt{x}+1\right)",1,"-2*Sqrt[x] + x + 2*Log[1 + Sqrt[x]]","A",3,2,15,0.1333,1,"{266, 43}"
2251,1,10,0,0.0021274,"\int \frac{1}{\left(1+\sqrt{x}\right) \sqrt{x}} \, dx","Int[1/((1 + Sqrt[x])*Sqrt[x]),x]","2 \log \left(\sqrt{x}+1\right)","2 \log \left(\sqrt{x}+1\right)",1,"2*Log[1 + Sqrt[x]]","A",1,1,15,0.06667,1,"{260}"
2252,1,11,0,0.0020008,"\int \frac{1}{\left(1+\sqrt{x}\right)^2 \sqrt{x}} \, dx","Int[1/((1 + Sqrt[x])^2*Sqrt[x]),x]","-\frac{2}{\sqrt{x}+1}","-\frac{2}{\sqrt{x}+1}",1,"-2/(1 + Sqrt[x])","A",1,1,15,0.06667,1,"{261}"
2253,1,11,0,0.0022699,"\int \frac{1}{\left(1+\sqrt{x}\right)^3 \sqrt{x}} \, dx","Int[1/((1 + Sqrt[x])^3*Sqrt[x]),x]","-\frac{1}{\left(\sqrt{x}+1\right)^2}","-\frac{1}{\left(\sqrt{x}+1\right)^2}",1,"-(1 + Sqrt[x])^(-2)","A",1,1,15,0.06667,1,"{261}"
2254,1,46,0,0.0120141,"\int \sqrt{1+\sqrt{x}} \sqrt{x} \, dx","Int[Sqrt[1 + Sqrt[x]]*Sqrt[x],x]","\frac{4}{7} \left(\sqrt{x}+1\right)^{7/2}-\frac{8}{5} \left(\sqrt{x}+1\right)^{5/2}+\frac{4}{3} \left(\sqrt{x}+1\right)^{3/2}","\frac{4}{7} \left(\sqrt{x}+1\right)^{7/2}-\frac{8}{5} \left(\sqrt{x}+1\right)^{5/2}+\frac{4}{3} \left(\sqrt{x}+1\right)^{3/2}",1,"(4*(1 + Sqrt[x])^(3/2))/3 - (8*(1 + Sqrt[x])^(5/2))/5 + (4*(1 + Sqrt[x])^(7/2))/7","A",3,2,17,0.1176,1,"{266, 43}"
2255,1,15,0,0.0023161,"\int \frac{\sqrt{1+\sqrt{x}}}{\sqrt{x}} \, dx","Int[Sqrt[1 + Sqrt[x]]/Sqrt[x],x]","\frac{4}{3} \left(\sqrt{x}+1\right)^{3/2}","\frac{4}{3} \left(\sqrt{x}+1\right)^{3/2}",1,"(4*(1 + Sqrt[x])^(3/2))/3","A",1,1,17,0.05882,1,"{261}"
2256,1,58,0,0.02957,"\int \frac{\sqrt[3]{x}}{1+\sqrt{x}} \, dx","Int[x^(1/3)/(1 + Sqrt[x]),x]","\frac{6 x^{5/6}}{5}-3 \sqrt[3]{x}-3 \log \left(\sqrt[6]{x}+1\right)+\log \left(\sqrt{x}+1\right)-2 \sqrt{3} \tan ^{-1}\left(\frac{1-2 \sqrt[6]{x}}{\sqrt{3}}\right)","\frac{6 x^{5/6}}{5}-3 \sqrt[3]{x}-3 \log \left(\sqrt[6]{x}+1\right)+\log \left(\sqrt{x}+1\right)-2 \sqrt{3} \tan ^{-1}\left(\frac{1-2 \sqrt[6]{x}}{\sqrt{3}}\right)",1,"-3*x^(1/3) + (6*x^(5/6))/5 - 2*Sqrt[3]*ArcTan[(1 - 2*x^(1/6))/Sqrt[3]] - 3*Log[1 + x^(1/6)] + Log[1 + Sqrt[x]]","A",7,6,15,0.4000,1,"{341, 50, 56, 618, 204, 31}"
2257,1,87,0,0.0428044,"\int \left(a+b \sqrt{x}\right)^4 x^m \, dx","Int[(a + b*Sqrt[x])^4*x^m,x]","\frac{6 a^2 b^2 x^{m+2}}{m+2}+\frac{8 a^3 b x^{m+\frac{3}{2}}}{2 m+3}+\frac{a^4 x^{m+1}}{m+1}+\frac{8 a b^3 x^{m+\frac{5}{2}}}{2 m+5}+\frac{b^4 x^{m+3}}{m+3}","\frac{6 a^2 b^2 x^{m+2}}{m+2}+\frac{8 a^3 b x^{m+\frac{3}{2}}}{2 m+3}+\frac{a^4 x^{m+1}}{m+1}+\frac{8 a b^3 x^{m+\frac{5}{2}}}{2 m+5}+\frac{b^4 x^{m+3}}{m+3}",1,"(a^4*x^(1 + m))/(1 + m) + (8*a^3*b*x^(3/2 + m))/(3 + 2*m) + (6*a^2*b^2*x^(2 + m))/(2 + m) + (8*a*b^3*x^(5/2 + m))/(5 + 2*m) + (b^4*x^(3 + m))/(3 + m)","A",2,1,15,0.06667,1,"{270}"
2258,1,70,0,0.0268059,"\int \left(a+b \sqrt{x}\right)^3 x^m \, dx","Int[(a + b*Sqrt[x])^3*x^m,x]","\frac{6 a^2 b x^{m+\frac{3}{2}}}{2 m+3}+\frac{a^3 x^{m+1}}{m+1}+\frac{3 a b^2 x^{m+2}}{m+2}+\frac{2 b^3 x^{m+\frac{5}{2}}}{2 m+5}","\frac{6 a^2 b x^{m+\frac{3}{2}}}{2 m+3}+\frac{a^3 x^{m+1}}{m+1}+\frac{3 a b^2 x^{m+2}}{m+2}+\frac{2 b^3 x^{m+\frac{5}{2}}}{2 m+5}",1,"(a^3*x^(1 + m))/(1 + m) + (6*a^2*b*x^(3/2 + m))/(3 + 2*m) + (3*a*b^2*x^(2 + m))/(2 + m) + (2*b^3*x^(5/2 + m))/(5 + 2*m)","A",2,1,15,0.06667,1,"{270}"
2259,1,47,0,0.0173857,"\int \left(a+b \sqrt{x}\right)^2 x^m \, dx","Int[(a + b*Sqrt[x])^2*x^m,x]","\frac{a^2 x^{m+1}}{m+1}+\frac{4 a b x^{m+\frac{3}{2}}}{2 m+3}+\frac{b^2 x^{m+2}}{m+2}","\frac{a^2 x^{m+1}}{m+1}+\frac{4 a b x^{m+\frac{3}{2}}}{2 m+3}+\frac{b^2 x^{m+2}}{m+2}",1,"(a^2*x^(1 + m))/(1 + m) + (4*a*b*x^(3/2 + m))/(3 + 2*m) + (b^2*x^(2 + m))/(2 + m)","A",2,1,15,0.06667,1,"{270}"
2260,1,30,0,0.0083188,"\int \left(a+b \sqrt{x}\right) x^m \, dx","Int[(a + b*Sqrt[x])*x^m,x]","\frac{a x^{m+1}}{m+1}+\frac{2 b x^{m+\frac{3}{2}}}{2 m+3}","\frac{a x^{m+1}}{m+1}+\frac{2 b x^{m+\frac{3}{2}}}{2 m+3}",1,"(a*x^(1 + m))/(1 + m) + (2*b*x^(3/2 + m))/(3 + 2*m)","A",2,1,13,0.07692,1,"{14}"
2261,1,37,0,0.0148449,"\int \frac{x^m}{a+b \sqrt{x}} \, dx","Int[x^m/(a + b*Sqrt[x]),x]","\frac{x^{m+1} \, _2F_1\left(1,2 (m+1);2 m+3;-\frac{b \sqrt{x}}{a}\right)}{a (m+1)}","\frac{x^{m+1} \, _2F_1\left(1,2 (m+1);2 m+3;-\frac{b \sqrt{x}}{a}\right)}{a (m+1)}",1,"(x^(1 + m)*Hypergeometric2F1[1, 2*(1 + m), 3 + 2*m, -((b*Sqrt[x])/a)])/(a*(1 + m))","A",2,2,15,0.1333,1,"{341, 64}"
2262,1,37,0,0.0142629,"\int \frac{x^m}{\left(a+b \sqrt{x}\right)^2} \, dx","Int[x^m/(a + b*Sqrt[x])^2,x]","\frac{x^{m+1} \, _2F_1\left(2,2 (m+1);2 m+3;-\frac{b \sqrt{x}}{a}\right)}{a^2 (m+1)}","\frac{x^{m+1} \, _2F_1\left(2,2 (m+1);2 m+3;-\frac{b \sqrt{x}}{a}\right)}{a^2 (m+1)}",1,"(x^(1 + m)*Hypergeometric2F1[2, 2*(1 + m), 3 + 2*m, -((b*Sqrt[x])/a)])/(a^2*(1 + m))","A",2,2,15,0.1333,1,"{341, 64}"
2263,1,63,0,0.0264015,"\int \left(a+b \sqrt{x}\right)^p x^m \, dx","Int[(a + b*Sqrt[x])^p*x^m,x]","\frac{x^{m+1} \left(a+b \sqrt{x}\right)^p \left(\frac{b \sqrt{x}}{a}+1\right)^{-p} \, _2F_1\left(2 (m+1),-p;2 m+3;-\frac{b \sqrt{x}}{a}\right)}{m+1}","-\frac{2 x^{m+1} \left(a+b \sqrt{x}\right)^{p+1} \, _2F_1\left(1,2 m+p+3;p+2;\frac{a+b \sqrt{x}}{a}\right)}{a (p+1)}",1,"((a + b*Sqrt[x])^p*x^(1 + m)*Hypergeometric2F1[2*(1 + m), -p, 3 + 2*m, -((b*Sqrt[x])/a)])/((1 + m)*(1 + (b*Sqrt[x])/a)^p)","A",3,3,15,0.2000,1,"{341, 66, 64}"
2264,1,204,0,0.1178156,"\int \left(a+b \sqrt{x}\right)^p x^3 \, dx","Int[(a + b*Sqrt[x])^p*x^3,x]","-\frac{2 a^7 \left(a+b \sqrt{x}\right)^{p+1}}{b^8 (p+1)}+\frac{14 a^6 \left(a+b \sqrt{x}\right)^{p+2}}{b^8 (p+2)}-\frac{42 a^5 \left(a+b \sqrt{x}\right)^{p+3}}{b^8 (p+3)}+\frac{70 a^4 \left(a+b \sqrt{x}\right)^{p+4}}{b^8 (p+4)}-\frac{70 a^3 \left(a+b \sqrt{x}\right)^{p+5}}{b^8 (p+5)}+\frac{42 a^2 \left(a+b \sqrt{x}\right)^{p+6}}{b^8 (p+6)}-\frac{14 a \left(a+b \sqrt{x}\right)^{p+7}}{b^8 (p+7)}+\frac{2 \left(a+b \sqrt{x}\right)^{p+8}}{b^8 (p+8)}","-\frac{2 a^7 \left(a+b \sqrt{x}\right)^{p+1}}{b^8 (p+1)}+\frac{14 a^6 \left(a+b \sqrt{x}\right)^{p+2}}{b^8 (p+2)}-\frac{42 a^5 \left(a+b \sqrt{x}\right)^{p+3}}{b^8 (p+3)}+\frac{70 a^4 \left(a+b \sqrt{x}\right)^{p+4}}{b^8 (p+4)}-\frac{70 a^3 \left(a+b \sqrt{x}\right)^{p+5}}{b^8 (p+5)}+\frac{42 a^2 \left(a+b \sqrt{x}\right)^{p+6}}{b^8 (p+6)}-\frac{14 a \left(a+b \sqrt{x}\right)^{p+7}}{b^8 (p+7)}+\frac{2 \left(a+b \sqrt{x}\right)^{p+8}}{b^8 (p+8)}",1,"(-2*a^7*(a + b*Sqrt[x])^(1 + p))/(b^8*(1 + p)) + (14*a^6*(a + b*Sqrt[x])^(2 + p))/(b^8*(2 + p)) - (42*a^5*(a + b*Sqrt[x])^(3 + p))/(b^8*(3 + p)) + (70*a^4*(a + b*Sqrt[x])^(4 + p))/(b^8*(4 + p)) - (70*a^3*(a + b*Sqrt[x])^(5 + p))/(b^8*(5 + p)) + (42*a^2*(a + b*Sqrt[x])^(6 + p))/(b^8*(6 + p)) - (14*a*(a + b*Sqrt[x])^(7 + p))/(b^8*(7 + p)) + (2*(a + b*Sqrt[x])^(8 + p))/(b^8*(8 + p))","A",3,2,15,0.1333,1,"{266, 43}"
2265,1,152,0,0.0812685,"\int \left(a+b \sqrt{x}\right)^p x^2 \, dx","Int[(a + b*Sqrt[x])^p*x^2,x]","-\frac{2 a^5 \left(a+b \sqrt{x}\right)^{p+1}}{b^6 (p+1)}+\frac{10 a^4 \left(a+b \sqrt{x}\right)^{p+2}}{b^6 (p+2)}-\frac{20 a^3 \left(a+b \sqrt{x}\right)^{p+3}}{b^6 (p+3)}+\frac{20 a^2 \left(a+b \sqrt{x}\right)^{p+4}}{b^6 (p+4)}-\frac{10 a \left(a+b \sqrt{x}\right)^{p+5}}{b^6 (p+5)}+\frac{2 \left(a+b \sqrt{x}\right)^{p+6}}{b^6 (p+6)}","-\frac{2 a^5 \left(a+b \sqrt{x}\right)^{p+1}}{b^6 (p+1)}+\frac{10 a^4 \left(a+b \sqrt{x}\right)^{p+2}}{b^6 (p+2)}-\frac{20 a^3 \left(a+b \sqrt{x}\right)^{p+3}}{b^6 (p+3)}+\frac{20 a^2 \left(a+b \sqrt{x}\right)^{p+4}}{b^6 (p+4)}-\frac{10 a \left(a+b \sqrt{x}\right)^{p+5}}{b^6 (p+5)}+\frac{2 \left(a+b \sqrt{x}\right)^{p+6}}{b^6 (p+6)}",1,"(-2*a^5*(a + b*Sqrt[x])^(1 + p))/(b^6*(1 + p)) + (10*a^4*(a + b*Sqrt[x])^(2 + p))/(b^6*(2 + p)) - (20*a^3*(a + b*Sqrt[x])^(3 + p))/(b^6*(3 + p)) + (20*a^2*(a + b*Sqrt[x])^(4 + p))/(b^6*(4 + p)) - (10*a*(a + b*Sqrt[x])^(5 + p))/(b^6*(5 + p)) + (2*(a + b*Sqrt[x])^(6 + p))/(b^6*(6 + p))","A",3,2,15,0.1333,1,"{266, 43}"
2266,1,100,0,0.0507882,"\int \left(a+b \sqrt{x}\right)^p x \, dx","Int[(a + b*Sqrt[x])^p*x,x]","-\frac{2 a^3 \left(a+b \sqrt{x}\right)^{p+1}}{b^4 (p+1)}+\frac{6 a^2 \left(a+b \sqrt{x}\right)^{p+2}}{b^4 (p+2)}-\frac{6 a \left(a+b \sqrt{x}\right)^{p+3}}{b^4 (p+3)}+\frac{2 \left(a+b \sqrt{x}\right)^{p+4}}{b^4 (p+4)}","-\frac{2 a^3 \left(a+b \sqrt{x}\right)^{p+1}}{b^4 (p+1)}+\frac{6 a^2 \left(a+b \sqrt{x}\right)^{p+2}}{b^4 (p+2)}-\frac{6 a \left(a+b \sqrt{x}\right)^{p+3}}{b^4 (p+3)}+\frac{2 \left(a+b \sqrt{x}\right)^{p+4}}{b^4 (p+4)}",1,"(-2*a^3*(a + b*Sqrt[x])^(1 + p))/(b^4*(1 + p)) + (6*a^2*(a + b*Sqrt[x])^(2 + p))/(b^4*(2 + p)) - (6*a*(a + b*Sqrt[x])^(3 + p))/(b^4*(3 + p)) + (2*(a + b*Sqrt[x])^(4 + p))/(b^4*(4 + p))","A",3,2,13,0.1538,1,"{266, 43}"
2267,1,48,0,0.0222112,"\int \left(a+b \sqrt{x}\right)^p \, dx","Int[(a + b*Sqrt[x])^p,x]","\frac{2 \left(a+b \sqrt{x}\right)^{p+2}}{b^2 (p+2)}-\frac{2 a \left(a+b \sqrt{x}\right)^{p+1}}{b^2 (p+1)}","\frac{2 \left(a+b \sqrt{x}\right)^{p+2}}{b^2 (p+2)}-\frac{2 a \left(a+b \sqrt{x}\right)^{p+1}}{b^2 (p+1)}",1,"(-2*a*(a + b*Sqrt[x])^(1 + p))/(b^2*(1 + p)) + (2*(a + b*Sqrt[x])^(2 + p))/(b^2*(2 + p))","A",3,2,11,0.1818,1,"{190, 43}"
2268,1,43,0,0.0160082,"\int \frac{\left(a+b \sqrt{x}\right)^p}{x} \, dx","Int[(a + b*Sqrt[x])^p/x,x]","-\frac{2 \left(a+b \sqrt{x}\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{\sqrt{x} b}{a}+1\right)}{a (p+1)}","-\frac{2 \left(a+b \sqrt{x}\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{\sqrt{x} b}{a}+1\right)}{a (p+1)}",1,"(-2*(a + b*Sqrt[x])^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, 1 + (b*Sqrt[x])/a])/(a*(1 + p))","A",2,2,15,0.1333,1,"{266, 65}"
2269,1,46,0,0.0188881,"\int \frac{\left(a+b \sqrt{x}\right)^p}{x^2} \, dx","Int[(a + b*Sqrt[x])^p/x^2,x]","-\frac{2 b^2 \left(a+b \sqrt{x}\right)^{p+1} \, _2F_1\left(3,p+1;p+2;\frac{\sqrt{x} b}{a}+1\right)}{a^3 (p+1)}","-\frac{2 b^2 \left(a+b \sqrt{x}\right)^{p+1} \, _2F_1\left(3,p+1;p+2;\frac{\sqrt{x} b}{a}+1\right)}{a^3 (p+1)}",1,"(-2*b^2*(a + b*Sqrt[x])^(1 + p)*Hypergeometric2F1[3, 1 + p, 2 + p, 1 + (b*Sqrt[x])/a])/(a^3*(1 + p))","A",2,2,15,0.1333,1,"{266, 65}"
2270,1,12,0,0.0025368,"\int \frac{\sqrt{x}}{1+x^{3/2}} \, dx","Int[Sqrt[x]/(1 + x^(3/2)),x]","\frac{2}{3} \log \left(x^{3/2}+1\right)","\frac{2}{3} \log \left(x^{3/2}+1\right)",1,"(2*Log[1 + x^(3/2)])/3","A",1,1,15,0.06667,1,"{260}"
2271,1,198,0,0.1621393,"\int \frac{x^3}{\left(a+b x^{3/2}\right)^{2/3}} \, dx","Int[x^3/(a + b*x^(3/2))^(2/3),x]","-\frac{10 a^2 \log \left(1-\frac{\sqrt[3]{b} \sqrt{x}}{\sqrt[3]{a+b x^{3/2}}}\right)}{27 b^{8/3}}+\frac{5 a^2 \log \left(\frac{b^{2/3} x}{\left(a+b x^{3/2}\right)^{2/3}}+\frac{\sqrt[3]{b} \sqrt{x}}{\sqrt[3]{a+b x^{3/2}}}+1\right)}{27 b^{8/3}}-\frac{10 a^2 \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} \sqrt{x}}{\sqrt[3]{a+b x^{3/2}}}+1}{\sqrt{3}}\right)}{9 \sqrt{3} b^{8/3}}-\frac{5 a x \sqrt[3]{a+b x^{3/2}}}{9 b^2}+\frac{x^{5/2} \sqrt[3]{a+b x^{3/2}}}{3 b}","-\frac{5 a^2 \log \left(\sqrt[3]{b} \sqrt{x}-\sqrt[3]{a+b x^{3/2}}\right)}{9 b^{8/3}}-\frac{10 a^2 \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} \sqrt{x}}{\sqrt[3]{a+b x^{3/2}}}+1}{\sqrt{3}}\right)}{9 \sqrt{3} b^{8/3}}-\frac{5 a x \sqrt[3]{a+b x^{3/2}}}{9 b^2}+\frac{x^{5/2} \sqrt[3]{a+b x^{3/2}}}{3 b}",1,"(-5*a*x*(a + b*x^(3/2))^(1/3))/(9*b^2) + (x^(5/2)*(a + b*x^(3/2))^(1/3))/(3*b) - (10*a^2*ArcTan[(1 + (2*b^(1/3)*Sqrt[x])/(a + b*x^(3/2))^(1/3))/Sqrt[3]])/(9*Sqrt[3]*b^(8/3)) - (10*a^2*Log[1 - (b^(1/3)*Sqrt[x])/(a + b*x^(3/2))^(1/3)])/(27*b^(8/3)) + (5*a^2*Log[1 + (b^(2/3)*x)/(a + b*x^(3/2))^(2/3) + (b^(1/3)*Sqrt[x])/(a + b*x^(3/2))^(1/3)])/(27*b^(8/3))","A",10,9,17,0.5294,1,"{341, 321, 331, 292, 31, 634, 617, 204, 628}"
2272,1,140,0,0.0946295,"\int \frac{1}{\left(a+b x^{3/2}\right)^{2/3}} \, dx","Int[(a + b*x^(3/2))^(-2/3),x]","-\frac{2 \log \left(1-\frac{\sqrt[3]{b} \sqrt{x}}{\sqrt[3]{a+b x^{3/2}}}\right)}{3 b^{2/3}}+\frac{\log \left(\frac{b^{2/3} x}{\left(a+b x^{3/2}\right)^{2/3}}+\frac{\sqrt[3]{b} \sqrt{x}}{\sqrt[3]{a+b x^{3/2}}}+1\right)}{3 b^{2/3}}-\frac{2 \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} \sqrt{x}}{\sqrt[3]{a+b x^{3/2}}}+1}{\sqrt{3}}\right)}{\sqrt{3} b^{2/3}}","-\frac{\log \left(\sqrt[3]{b} \sqrt{x}-\sqrt[3]{a+b x^{3/2}}\right)}{b^{2/3}}-\frac{2 \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} \sqrt{x}}{\sqrt[3]{a+b x^{3/2}}}+1}{\sqrt{3}}\right)}{\sqrt{3} b^{2/3}}",1,"(-2*ArcTan[(1 + (2*b^(1/3)*Sqrt[x])/(a + b*x^(3/2))^(1/3))/Sqrt[3]])/(Sqrt[3]*b^(2/3)) - (2*Log[1 - (b^(1/3)*Sqrt[x])/(a + b*x^(3/2))^(1/3)])/(3*b^(2/3)) + Log[1 + (b^(2/3)*x)/(a + b*x^(3/2))^(2/3) + (b^(1/3)*Sqrt[x])/(a + b*x^(3/2))^(1/3)]/(3*b^(2/3))","A",8,8,13,0.6154,1,"{243, 331, 292, 31, 634, 617, 204, 628}"
2273,1,50,0,0.012822,"\int \frac{1}{x^3 \left(a+b x^{3/2}\right)^{2/3}} \, dx","Int[1/(x^3*(a + b*x^(3/2))^(2/3)),x]","\frac{3 b \sqrt[3]{a+b x^{3/2}}}{2 a^2 \sqrt{x}}-\frac{\sqrt[3]{a+b x^{3/2}}}{2 a x^2}","\frac{3 b \sqrt[3]{a+b x^{3/2}}}{2 a^2 \sqrt{x}}-\frac{\sqrt[3]{a+b x^{3/2}}}{2 a x^2}",1,"-(a + b*x^(3/2))^(1/3)/(2*a*x^2) + (3*b*(a + b*x^(3/2))^(1/3))/(2*a^2*Sqrt[x])","A",2,2,17,0.1176,1,"{271, 264}"
2274,1,104,0,0.0330675,"\int \frac{1}{x^6 \left(a+b x^{3/2}\right)^{2/3}} \, dx","Int[1/(x^6*(a + b*x^(3/2))^(2/3)),x]","\frac{81 b^3 \sqrt[3]{a+b x^{3/2}}}{70 a^4 \sqrt{x}}-\frac{27 b^2 \sqrt[3]{a+b x^{3/2}}}{70 a^3 x^2}+\frac{9 b \sqrt[3]{a+b x^{3/2}}}{35 a^2 x^{7/2}}-\frac{\sqrt[3]{a+b x^{3/2}}}{5 a x^5}","\frac{81 b^3 \sqrt[3]{a+b x^{3/2}}}{70 a^4 \sqrt{x}}-\frac{27 b^2 \sqrt[3]{a+b x^{3/2}}}{70 a^3 x^2}+\frac{9 b \sqrt[3]{a+b x^{3/2}}}{35 a^2 x^{7/2}}-\frac{\sqrt[3]{a+b x^{3/2}}}{5 a x^5}",1,"-(a + b*x^(3/2))^(1/3)/(5*a*x^5) + (9*b*(a + b*x^(3/2))^(1/3))/(35*a^2*x^(7/2)) - (27*b^2*(a + b*x^(3/2))^(1/3))/(70*a^3*x^2) + (81*b^3*(a + b*x^(3/2))^(1/3))/(70*a^4*Sqrt[x])","A",4,2,17,0.1176,1,"{271, 264}"
2275,1,158,0,0.060664,"\int \frac{1}{x^9 \left(a+b x^{3/2}\right)^{2/3}} \, dx","Int[1/(x^9*(a + b*x^(3/2))^(2/3)),x]","\frac{729 b^5 \sqrt[3]{a+b x^{3/2}}}{728 a^6 \sqrt{x}}-\frac{243 b^4 \sqrt[3]{a+b x^{3/2}}}{728 a^5 x^2}+\frac{81 b^3 \sqrt[3]{a+b x^{3/2}}}{364 a^4 x^{7/2}}-\frac{9 b^2 \sqrt[3]{a+b x^{3/2}}}{52 a^3 x^5}+\frac{15 b \sqrt[3]{a+b x^{3/2}}}{104 a^2 x^{13/2}}-\frac{\sqrt[3]{a+b x^{3/2}}}{8 a x^8}","\frac{729 b^5 \sqrt[3]{a+b x^{3/2}}}{728 a^6 \sqrt{x}}-\frac{243 b^4 \sqrt[3]{a+b x^{3/2}}}{728 a^5 x^2}+\frac{81 b^3 \sqrt[3]{a+b x^{3/2}}}{364 a^4 x^{7/2}}-\frac{9 b^2 \sqrt[3]{a+b x^{3/2}}}{52 a^3 x^5}+\frac{15 b \sqrt[3]{a+b x^{3/2}}}{104 a^2 x^{13/2}}-\frac{\sqrt[3]{a+b x^{3/2}}}{8 a x^8}",1,"-(a + b*x^(3/2))^(1/3)/(8*a*x^8) + (15*b*(a + b*x^(3/2))^(1/3))/(104*a^2*x^(13/2)) - (9*b^2*(a + b*x^(3/2))^(1/3))/(52*a^3*x^5) + (81*b^3*(a + b*x^(3/2))^(1/3))/(364*a^4*x^(7/2)) - (243*b^4*(a + b*x^(3/2))^(1/3))/(728*a^5*x^2) + (729*b^5*(a + b*x^(3/2))^(1/3))/(728*a^6*Sqrt[x])","A",6,2,17,0.1176,1,"{271, 264}"
2276,1,130,0,0.0614772,"\int \frac{x^8}{\left(a+b x^{3/2}\right)^{2/3}} \, dx","Int[x^8/(a + b*x^(3/2))^(2/3),x]","\frac{2 a^2 \left(a+b x^{3/2}\right)^{10/3}}{b^6}-\frac{20 a^3 \left(a+b x^{3/2}\right)^{7/3}}{7 b^6}+\frac{5 a^4 \left(a+b x^{3/2}\right)^{4/3}}{2 b^6}-\frac{2 a^5 \sqrt[3]{a+b x^{3/2}}}{b^6}+\frac{\left(a+b x^{3/2}\right)^{16/3}}{8 b^6}-\frac{10 a \left(a+b x^{3/2}\right)^{13/3}}{13 b^6}","\frac{2 a^2 \left(a+b x^{3/2}\right)^{10/3}}{b^6}-\frac{20 a^3 \left(a+b x^{3/2}\right)^{7/3}}{7 b^6}+\frac{5 a^4 \left(a+b x^{3/2}\right)^{4/3}}{2 b^6}-\frac{2 a^5 \sqrt[3]{a+b x^{3/2}}}{b^6}+\frac{\left(a+b x^{3/2}\right)^{16/3}}{8 b^6}-\frac{10 a \left(a+b x^{3/2}\right)^{13/3}}{13 b^6}",1,"(-2*a^5*(a + b*x^(3/2))^(1/3))/b^6 + (5*a^4*(a + b*x^(3/2))^(4/3))/(2*b^6) - (20*a^3*(a + b*x^(3/2))^(7/3))/(7*b^6) + (2*a^2*(a + b*x^(3/2))^(10/3))/b^6 - (10*a*(a + b*x^(3/2))^(13/3))/(13*b^6) + (a + b*x^(3/2))^(16/3)/(8*b^6)","A",3,2,17,0.1176,1,"{266, 43}"
2277,1,86,0,0.0408598,"\int \frac{x^5}{\left(a+b x^{3/2}\right)^{2/3}} \, dx","Int[x^5/(a + b*x^(3/2))^(2/3),x]","\frac{3 a^2 \left(a+b x^{3/2}\right)^{4/3}}{2 b^4}-\frac{2 a^3 \sqrt[3]{a+b x^{3/2}}}{b^4}+\frac{\left(a+b x^{3/2}\right)^{10/3}}{5 b^4}-\frac{6 a \left(a+b x^{3/2}\right)^{7/3}}{7 b^4}","\frac{3 a^2 \left(a+b x^{3/2}\right)^{4/3}}{2 b^4}-\frac{2 a^3 \sqrt[3]{a+b x^{3/2}}}{b^4}+\frac{\left(a+b x^{3/2}\right)^{10/3}}{5 b^4}-\frac{6 a \left(a+b x^{3/2}\right)^{7/3}}{7 b^4}",1,"(-2*a^3*(a + b*x^(3/2))^(1/3))/b^4 + (3*a^2*(a + b*x^(3/2))^(4/3))/(2*b^4) - (6*a*(a + b*x^(3/2))^(7/3))/(7*b^4) + (a + b*x^(3/2))^(10/3)/(5*b^4)","A",3,2,17,0.1176,1,"{266, 43}"
2278,1,40,0,0.0205204,"\int \frac{x^2}{\left(a+b x^{3/2}\right)^{2/3}} \, dx","Int[x^2/(a + b*x^(3/2))^(2/3),x]","\frac{\left(a+b x^{3/2}\right)^{4/3}}{2 b^2}-\frac{2 a \sqrt[3]{a+b x^{3/2}}}{b^2}","\frac{\left(a+b x^{3/2}\right)^{4/3}}{2 b^2}-\frac{2 a \sqrt[3]{a+b x^{3/2}}}{b^2}",1,"(-2*a*(a + b*x^(3/2))^(1/3))/b^2 + (a + b*x^(3/2))^(4/3)/(2*b^2)","A",3,2,17,0.1176,1,"{266, 43}"
2279,1,85,0,0.0543483,"\int \frac{1}{x \left(a+b x^{3/2}\right)^{2/3}} \, dx","Int[1/(x*(a + b*x^(3/2))^(2/3)),x]","\frac{\log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^{3/2}}\right)}{a^{2/3}}-\frac{2 \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^{3/2}}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3}}-\frac{\log (x)}{2 a^{2/3}}","\frac{\log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^{3/2}}\right)}{a^{2/3}}-\frac{2 \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^{3/2}}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3}}-\frac{\log (x)}{2 a^{2/3}}",1,"(-2*ArcTan[(a^(1/3) + 2*(a + b*x^(3/2))^(1/3))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(2/3)) - Log[x]/(2*a^(2/3)) + Log[a^(1/3) - (a + b*x^(3/2))^(1/3)]/a^(2/3)","A",5,5,17,0.2941,1,"{266, 57, 617, 204, 31}"
2280,1,148,0,0.0878129,"\int \frac{1}{x^4 \left(a+b x^{3/2}\right)^{2/3}} \, dx","Int[1/(x^4*(a + b*x^(3/2))^(2/3)),x]","\frac{5 b^2 \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^{3/2}}\right)}{9 a^{8/3}}-\frac{10 b^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^{3/2}}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{8/3}}-\frac{5 b^2 \log (x)}{18 a^{8/3}}+\frac{5 b \sqrt[3]{a+b x^{3/2}}}{9 a^2 x^{3/2}}-\frac{\sqrt[3]{a+b x^{3/2}}}{3 a x^3}","\frac{5 b^2 \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^{3/2}}\right)}{9 a^{8/3}}-\frac{10 b^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^{3/2}}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{8/3}}-\frac{5 b^2 \log (x)}{18 a^{8/3}}+\frac{5 b \sqrt[3]{a+b x^{3/2}}}{9 a^2 x^{3/2}}-\frac{\sqrt[3]{a+b x^{3/2}}}{3 a x^3}",1,"-(a + b*x^(3/2))^(1/3)/(3*a*x^3) + (5*b*(a + b*x^(3/2))^(1/3))/(9*a^2*x^(3/2)) - (10*b^2*ArcTan[(a^(1/3) + 2*(a + b*x^(3/2))^(1/3))/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(8/3)) - (5*b^2*Log[x])/(18*a^(8/3)) + (5*b^2*Log[a^(1/3) - (a + b*x^(3/2))^(1/3)])/(9*a^(8/3))","A",7,6,17,0.3529,1,"{266, 51, 57, 617, 204, 31}"
2281,1,57,0,0.0343892,"\int \frac{x^4}{\left(a+b x^{3/2}\right)^{2/3}} \, dx","Int[x^4/(a + b*x^(3/2))^(2/3),x]","\frac{x^5 \left(\frac{b x^{3/2}}{a}+1\right)^{2/3} \, _2F_1\left(\frac{2}{3},\frac{10}{3};\frac{13}{3};-\frac{b x^{3/2}}{a}\right)}{5 \left(a+b x^{3/2}\right)^{2/3}}","\frac{x^5 \sqrt[3]{a+b x^{3/2}} \, _2F_1\left(1,\frac{11}{3};\frac{13}{3};-\frac{b x^{3/2}}{a}\right)}{5 a}",1,"(x^5*(1 + (b*x^(3/2))/a)^(2/3)*Hypergeometric2F1[2/3, 10/3, 13/3, -((b*x^(3/2))/a)])/(5*(a + b*x^(3/2))^(2/3))","A",3,3,17,0.1765,1,"{341, 365, 364}"
2282,1,57,0,0.0299314,"\int \frac{x}{\left(a+b x^{3/2}\right)^{2/3}} \, dx","Int[x/(a + b*x^(3/2))^(2/3),x]","\frac{x^2 \left(\frac{b x^{3/2}}{a}+1\right)^{2/3} \, _2F_1\left(\frac{2}{3},\frac{4}{3};\frac{7}{3};-\frac{b x^{3/2}}{a}\right)}{2 \left(a+b x^{3/2}\right)^{2/3}}","\frac{x^2 \sqrt[3]{a+b x^{3/2}} \, _2F_1\left(1,\frac{5}{3};\frac{7}{3};-\frac{b x^{3/2}}{a}\right)}{2 a}",1,"(x^2*(1 + (b*x^(3/2))/a)^(2/3)*Hypergeometric2F1[2/3, 4/3, 7/3, -((b*x^(3/2))/a)])/(2*(a + b*x^(3/2))^(2/3))","A",3,3,15,0.2000,1,"{341, 365, 364}"
2283,1,55,0,0.0330628,"\int \frac{1}{x^2 \left(a+b x^{3/2}\right)^{2/3}} \, dx","Int[1/(x^2*(a + b*x^(3/2))^(2/3)),x]","-\frac{\left(\frac{b x^{3/2}}{a}+1\right)^{2/3} \, _2F_1\left(-\frac{2}{3},\frac{2}{3};\frac{1}{3};-\frac{b x^{3/2}}{a}\right)}{x \left(a+b x^{3/2}\right)^{2/3}}","-\frac{\sqrt[3]{a+b x^{3/2}} \, _2F_1\left(-\frac{1}{3},1;\frac{1}{3};-\frac{b x^{3/2}}{a}\right)}{a x}",1,"-(((1 + (b*x^(3/2))/a)^(2/3)*Hypergeometric2F1[-2/3, 2/3, 1/3, -((b*x^(3/2))/a)])/(x*(a + b*x^(3/2))^(2/3)))","A",3,3,17,0.1765,1,"{341, 365, 364}"
2284,1,57,0,0.0326803,"\int \frac{1}{x^5 \left(a+b x^{3/2}\right)^{2/3}} \, dx","Int[1/(x^5*(a + b*x^(3/2))^(2/3)),x]","-\frac{\left(\frac{b x^{3/2}}{a}+1\right)^{2/3} \, _2F_1\left(-\frac{8}{3},\frac{2}{3};-\frac{5}{3};-\frac{b x^{3/2}}{a}\right)}{4 x^4 \left(a+b x^{3/2}\right)^{2/3}}","-\frac{\left(\frac{b x^{3/2}}{a}+1\right)^{2/3} \, _2F_1\left(-\frac{8}{3},\frac{2}{3};-\frac{5}{3};-\frac{b x^{3/2}}{a}\right)}{4 x^4 \left(a+b x^{3/2}\right)^{2/3}}",1,"-((1 + (b*x^(3/2))/a)^(2/3)*Hypergeometric2F1[-8/3, 2/3, -5/3, -((b*x^(3/2))/a)])/(4*x^4*(a + b*x^(3/2))^(2/3))","A",3,3,17,0.1765,1,"{341, 365, 364}"
2285,1,19,0,0.0052233,"\int \left(a+b \sqrt[3]{x}\right) x^4 \, dx","Int[(a + b*x^(1/3))*x^4,x]","\frac{a x^5}{5}+\frac{3}{16} b x^{16/3}","\frac{a x^5}{5}+\frac{3}{16} b x^{16/3}",1,"(a*x^5)/5 + (3*b*x^(16/3))/16","A",2,1,13,0.07692,1,"{14}"
2286,1,19,0,0.0047911,"\int \left(a+b \sqrt[3]{x}\right) x^3 \, dx","Int[(a + b*x^(1/3))*x^3,x]","\frac{a x^4}{4}+\frac{3}{13} b x^{13/3}","\frac{a x^4}{4}+\frac{3}{13} b x^{13/3}",1,"(a*x^4)/4 + (3*b*x^(13/3))/13","A",2,1,13,0.07692,1,"{14}"
2287,1,19,0,0.0046951,"\int \left(a+b \sqrt[3]{x}\right) x^2 \, dx","Int[(a + b*x^(1/3))*x^2,x]","\frac{a x^3}{3}+\frac{3}{10} b x^{10/3}","\frac{a x^3}{3}+\frac{3}{10} b x^{10/3}",1,"(a*x^3)/3 + (3*b*x^(10/3))/10","A",2,1,13,0.07692,1,"{14}"
2288,1,19,0,0.0050783,"\int \left(a+b \sqrt[3]{x}\right) x \, dx","Int[(a + b*x^(1/3))*x,x]","\frac{a x^2}{2}+\frac{3}{7} b x^{7/3}","\frac{a x^2}{2}+\frac{3}{7} b x^{7/3}",1,"(a*x^2)/2 + (3*b*x^(7/3))/7","A",2,1,11,0.09091,1,"{14}"
2289,1,14,0,0.002333,"\int \left(a+b \sqrt[3]{x}\right) \, dx","Int[a + b*x^(1/3),x]","a x+\frac{3}{4} b x^{4/3}","a x+\frac{3}{4} b x^{4/3}",1,"a*x + (3*b*x^(4/3))/4","A",1,0,9,0,1,"{}"
2290,1,13,0,0.0049706,"\int \frac{a+b \sqrt[3]{x}}{x} \, dx","Int[(a + b*x^(1/3))/x,x]","a \log (x)+3 b \sqrt[3]{x}","a \log (x)+3 b \sqrt[3]{x}",1,"3*b*x^(1/3) + a*Log[x]","A",2,1,13,0.07692,1,"{14}"
2291,1,17,0,0.0050521,"\int \frac{a+b \sqrt[3]{x}}{x^2} \, dx","Int[(a + b*x^(1/3))/x^2,x]","-\frac{a}{x}-\frac{3 b}{2 x^{2/3}}","-\frac{a}{x}-\frac{3 b}{2 x^{2/3}}",1,"-(a/x) - (3*b)/(2*x^(2/3))","A",2,1,13,0.07692,1,"{14}"
2292,1,19,0,0.0050065,"\int \frac{a+b \sqrt[3]{x}}{x^3} \, dx","Int[(a + b*x^(1/3))/x^3,x]","-\frac{a}{2 x^2}-\frac{3 b}{5 x^{5/3}}","-\frac{a}{2 x^2}-\frac{3 b}{5 x^{5/3}}",1,"-a/(2*x^2) - (3*b)/(5*x^(5/3))","A",2,1,13,0.07692,1,"{14}"
2293,1,19,0,0.0052725,"\int \frac{a+b \sqrt[3]{x}}{x^4} \, dx","Int[(a + b*x^(1/3))/x^4,x]","-\frac{a}{3 x^3}-\frac{3 b}{8 x^{8/3}}","-\frac{a}{3 x^3}-\frac{3 b}{8 x^{8/3}}",1,"-a/(3*x^3) - (3*b)/(8*x^(8/3))","A",2,1,13,0.07692,1,"{14}"
2294,1,34,0,0.0301086,"\int \left(a+b \sqrt[3]{x}\right)^2 x^4 \, dx","Int[(a + b*x^(1/3))^2*x^4,x]","\frac{a^2 x^5}{5}+\frac{3}{8} a b x^{16/3}+\frac{3}{17} b^2 x^{17/3}","\frac{a^2 x^5}{5}+\frac{3}{8} a b x^{16/3}+\frac{3}{17} b^2 x^{17/3}",1,"(a^2*x^5)/5 + (3*a*b*x^(16/3))/8 + (3*b^2*x^(17/3))/17","A",3,2,15,0.1333,1,"{266, 43}"
2295,1,34,0,0.0291076,"\int \left(a+b \sqrt[3]{x}\right)^2 x^3 \, dx","Int[(a + b*x^(1/3))^2*x^3,x]","\frac{a^2 x^4}{4}+\frac{6}{13} a b x^{13/3}+\frac{3}{14} b^2 x^{14/3}","\frac{a^2 x^4}{4}+\frac{6}{13} a b x^{13/3}+\frac{3}{14} b^2 x^{14/3}",1,"(a^2*x^4)/4 + (6*a*b*x^(13/3))/13 + (3*b^2*x^(14/3))/14","A",3,2,15,0.1333,1,"{266, 43}"
2296,1,34,0,0.024967,"\int \left(a+b \sqrt[3]{x}\right)^2 x^2 \, dx","Int[(a + b*x^(1/3))^2*x^2,x]","\frac{a^2 x^3}{3}+\frac{3}{5} a b x^{10/3}+\frac{3}{11} b^2 x^{11/3}","\frac{a^2 x^3}{3}+\frac{3}{5} a b x^{10/3}+\frac{3}{11} b^2 x^{11/3}",1,"(a^2*x^3)/3 + (3*a*b*x^(10/3))/5 + (3*b^2*x^(11/3))/11","A",3,2,15,0.1333,1,"{266, 43}"
2297,1,34,0,0.0202066,"\int \left(a+b \sqrt[3]{x}\right)^2 x \, dx","Int[(a + b*x^(1/3))^2*x,x]","\frac{a^2 x^2}{2}+\frac{6}{7} a b x^{7/3}+\frac{3}{8} b^2 x^{8/3}","\frac{a^2 x^2}{2}+\frac{6}{7} a b x^{7/3}+\frac{3}{8} b^2 x^{8/3}",1,"(a^2*x^2)/2 + (6*a*b*x^(7/3))/7 + (3*b^2*x^(8/3))/8","A",3,2,13,0.1538,1,"{266, 43}"
2298,1,29,0,0.0155383,"\int \left(a+b \sqrt[3]{x}\right)^2 \, dx","Int[(a + b*x^(1/3))^2,x]","a^2 x+\frac{3}{2} a b x^{4/3}+\frac{3}{5} b^2 x^{5/3}","a^2 x+\frac{3}{2} a b x^{4/3}+\frac{3}{5} b^2 x^{5/3}",1,"a^2*x + (3*a*b*x^(4/3))/2 + (3*b^2*x^(5/3))/5","A",3,2,11,0.1818,1,"{190, 43}"
2299,1,28,0,0.0112806,"\int \frac{\left(a+b \sqrt[3]{x}\right)^2}{x} \, dx","Int[(a + b*x^(1/3))^2/x,x]","a^2 \log (x)+6 a b \sqrt[3]{x}+\frac{3}{2} b^2 x^{2/3}","a^2 \log (x)+6 a b \sqrt[3]{x}+\frac{3}{2} b^2 x^{2/3}",1,"6*a*b*x^(1/3) + (3*b^2*x^(2/3))/2 + a^2*Log[x]","A",3,2,15,0.1333,1,"{266, 43}"
2300,1,19,0,0.003261,"\int \frac{\left(a+b \sqrt[3]{x}\right)^2}{x^2} \, dx","Int[(a + b*x^(1/3))^2/x^2,x]","-\frac{\left(a+b \sqrt[3]{x}\right)^3}{a x}","-\frac{\left(a+b \sqrt[3]{x}\right)^3}{a x}",1,"-((a + b*x^(1/3))^3/(a*x))","A",1,1,15,0.06667,1,"{264}"
2301,1,34,0,0.014822,"\int \frac{\left(a+b \sqrt[3]{x}\right)^2}{x^3} \, dx","Int[(a + b*x^(1/3))^2/x^3,x]","-\frac{a^2}{2 x^2}-\frac{6 a b}{5 x^{5/3}}-\frac{3 b^2}{4 x^{4/3}}","-\frac{a^2}{2 x^2}-\frac{6 a b}{5 x^{5/3}}-\frac{3 b^2}{4 x^{4/3}}",1,"-a^2/(2*x^2) - (6*a*b)/(5*x^(5/3)) - (3*b^2)/(4*x^(4/3))","A",3,2,15,0.1333,1,"{266, 43}"
2302,1,34,0,0.0139323,"\int \frac{\left(a+b \sqrt[3]{x}\right)^2}{x^4} \, dx","Int[(a + b*x^(1/3))^2/x^4,x]","-\frac{a^2}{3 x^3}-\frac{3 a b}{4 x^{8/3}}-\frac{3 b^2}{7 x^{7/3}}","-\frac{a^2}{3 x^3}-\frac{3 a b}{4 x^{8/3}}-\frac{3 b^2}{7 x^{7/3}}",1,"-a^2/(3*x^3) - (3*a*b)/(4*x^(8/3)) - (3*b^2)/(7*x^(7/3))","A",3,2,15,0.1333,1,"{266, 43}"
2303,1,47,0,0.0353205,"\int \left(a+b \sqrt[3]{x}\right)^3 x^4 \, dx","Int[(a + b*x^(1/3))^3*x^4,x]","\frac{9}{16} a^2 b x^{16/3}+\frac{a^3 x^5}{5}+\frac{9}{17} a b^2 x^{17/3}+\frac{b^3 x^6}{6}","\frac{9}{16} a^2 b x^{16/3}+\frac{a^3 x^5}{5}+\frac{9}{17} a b^2 x^{17/3}+\frac{b^3 x^6}{6}",1,"(a^3*x^5)/5 + (9*a^2*b*x^(16/3))/16 + (9*a*b^2*x^(17/3))/17 + (b^3*x^6)/6","A",3,2,15,0.1333,1,"{266, 43}"
2304,1,47,0,0.0329955,"\int \left(a+b \sqrt[3]{x}\right)^3 x^3 \, dx","Int[(a + b*x^(1/3))^3*x^3,x]","\frac{9}{13} a^2 b x^{13/3}+\frac{a^3 x^4}{4}+\frac{9}{14} a b^2 x^{14/3}+\frac{b^3 x^5}{5}","\frac{9}{13} a^2 b x^{13/3}+\frac{a^3 x^4}{4}+\frac{9}{14} a b^2 x^{14/3}+\frac{b^3 x^5}{5}",1,"(a^3*x^4)/4 + (9*a^2*b*x^(13/3))/13 + (9*a*b^2*x^(14/3))/14 + (b^3*x^5)/5","A",3,2,15,0.1333,1,"{266, 43}"
2305,1,47,0,0.0300415,"\int \left(a+b \sqrt[3]{x}\right)^3 x^2 \, dx","Int[(a + b*x^(1/3))^3*x^2,x]","\frac{9}{10} a^2 b x^{10/3}+\frac{a^3 x^3}{3}+\frac{9}{11} a b^2 x^{11/3}+\frac{b^3 x^4}{4}","\frac{9}{10} a^2 b x^{10/3}+\frac{a^3 x^3}{3}+\frac{9}{11} a b^2 x^{11/3}+\frac{b^3 x^4}{4}",1,"(a^3*x^3)/3 + (9*a^2*b*x^(10/3))/10 + (9*a*b^2*x^(11/3))/11 + (b^3*x^4)/4","A",3,2,15,0.1333,1,"{266, 43}"
2306,1,47,0,0.0255488,"\int \left(a+b \sqrt[3]{x}\right)^3 x \, dx","Int[(a + b*x^(1/3))^3*x,x]","\frac{9}{7} a^2 b x^{7/3}+\frac{a^3 x^2}{2}+\frac{9}{8} a b^2 x^{8/3}+\frac{b^3 x^3}{3}","\frac{9}{7} a^2 b x^{7/3}+\frac{a^3 x^2}{2}+\frac{9}{8} a b^2 x^{8/3}+\frac{b^3 x^3}{3}",1,"(a^3*x^2)/2 + (9*a^2*b*x^(7/3))/7 + (9*a*b^2*x^(8/3))/8 + (b^3*x^3)/3","A",3,2,13,0.1538,1,"{266, 43}"
2307,1,42,0,0.0219194,"\int \left(a+b \sqrt[3]{x}\right)^3 \, dx","Int[(a + b*x^(1/3))^3,x]","\frac{9}{4} a^2 b x^{4/3}+a^3 x+\frac{9}{5} a b^2 x^{5/3}+\frac{b^3 x^2}{2}","\frac{9}{4} a^2 b x^{4/3}+a^3 x+\frac{9}{5} a b^2 x^{5/3}+\frac{b^3 x^2}{2}",1,"a^3*x + (9*a^2*b*x^(4/3))/4 + (9*a*b^2*x^(5/3))/5 + (b^3*x^2)/2","A",3,2,11,0.1818,1,"{190, 43}"
2308,1,36,0,0.0167985,"\int \frac{\left(a+b \sqrt[3]{x}\right)^3}{x} \, dx","Int[(a + b*x^(1/3))^3/x,x]","9 a^2 b \sqrt[3]{x}+a^3 \log (x)+\frac{9}{2} a b^2 x^{2/3}+b^3 x","9 a^2 b \sqrt[3]{x}+a^3 \log (x)+\frac{9}{2} a b^2 x^{2/3}+b^3 x",1,"9*a^2*b*x^(1/3) + (9*a*b^2*x^(2/3))/2 + b^3*x + a^3*Log[x]","A",3,2,15,0.1333,1,"{266, 43}"
2309,1,39,0,0.0190188,"\int \frac{\left(a+b \sqrt[3]{x}\right)^3}{x^2} \, dx","Int[(a + b*x^(1/3))^3/x^2,x]","-\frac{9 a^2 b}{2 x^{2/3}}-\frac{a^3}{x}-\frac{9 a b^2}{\sqrt[3]{x}}+b^3 \log (x)","-\frac{9 a^2 b}{2 x^{2/3}}-\frac{a^3}{x}-\frac{9 a b^2}{\sqrt[3]{x}}+b^3 \log (x)",1,"-(a^3/x) - (9*a^2*b)/(2*x^(2/3)) - (9*a*b^2)/x^(1/3) + b^3*Log[x]","A",3,2,15,0.1333,1,"{266, 43}"
2310,1,45,0,0.0191243,"\int \frac{\left(a+b \sqrt[3]{x}\right)^3}{x^3} \, dx","Int[(a + b*x^(1/3))^3/x^3,x]","-\frac{9 a^2 b}{5 x^{5/3}}-\frac{a^3}{2 x^2}-\frac{9 a b^2}{4 x^{4/3}}-\frac{b^3}{x}","-\frac{9 a^2 b}{5 x^{5/3}}-\frac{a^3}{2 x^2}-\frac{9 a b^2}{4 x^{4/3}}-\frac{b^3}{x}",1,"-a^3/(2*x^2) - (9*a^2*b)/(5*x^(5/3)) - (9*a*b^2)/(4*x^(4/3)) - b^3/x","A",3,2,15,0.1333,1,"{266, 43}"
2311,1,47,0,0.0207683,"\int \frac{\left(a+b \sqrt[3]{x}\right)^3}{x^4} \, dx","Int[(a + b*x^(1/3))^3/x^4,x]","-\frac{9 a^2 b}{8 x^{8/3}}-\frac{a^3}{3 x^3}-\frac{9 a b^2}{7 x^{7/3}}-\frac{b^3}{2 x^2}","-\frac{9 a^2 b}{8 x^{8/3}}-\frac{a^3}{3 x^3}-\frac{9 a b^2}{7 x^{7/3}}-\frac{b^3}{2 x^2}",1,"-a^3/(3*x^3) - (9*a^2*b)/(8*x^(8/3)) - (9*a*b^2)/(7*x^(7/3)) - b^3/(2*x^2)","A",3,2,15,0.1333,1,"{266, 43}"
2312,1,77,0,0.0506198,"\int \left(a+b \sqrt[3]{x}\right)^5 x^4 \, dx","Int[(a + b*x^(1/3))^5*x^4,x]","\frac{5}{3} a^2 b^3 x^6+\frac{30}{17} a^3 b^2 x^{17/3}+\frac{15}{16} a^4 b x^{16/3}+\frac{a^5 x^5}{5}+\frac{15}{19} a b^4 x^{19/3}+\frac{3}{20} b^5 x^{20/3}","\frac{5}{3} a^2 b^3 x^6+\frac{30}{17} a^3 b^2 x^{17/3}+\frac{15}{16} a^4 b x^{16/3}+\frac{a^5 x^5}{5}+\frac{15}{19} a b^4 x^{19/3}+\frac{3}{20} b^5 x^{20/3}",1,"(a^5*x^5)/5 + (15*a^4*b*x^(16/3))/16 + (30*a^3*b^2*x^(17/3))/17 + (5*a^2*b^3*x^6)/3 + (15*a*b^4*x^(19/3))/19 + (3*b^5*x^(20/3))/20","A",3,2,15,0.1333,1,"{266, 43}"
2313,1,75,0,0.0453484,"\int \left(a+b \sqrt[3]{x}\right)^5 x^3 \, dx","Int[(a + b*x^(1/3))^5*x^3,x]","2 a^2 b^3 x^5+\frac{15}{7} a^3 b^2 x^{14/3}+\frac{15}{13} a^4 b x^{13/3}+\frac{a^5 x^4}{4}+\frac{15}{16} a b^4 x^{16/3}+\frac{3}{17} b^5 x^{17/3}","2 a^2 b^3 x^5+\frac{15}{7} a^3 b^2 x^{14/3}+\frac{15}{13} a^4 b x^{13/3}+\frac{a^5 x^4}{4}+\frac{15}{16} a b^4 x^{16/3}+\frac{3}{17} b^5 x^{17/3}",1,"(a^5*x^4)/4 + (15*a^4*b*x^(13/3))/13 + (15*a^3*b^2*x^(14/3))/7 + 2*a^2*b^3*x^5 + (15*a*b^4*x^(16/3))/16 + (3*b^5*x^(17/3))/17","A",3,2,15,0.1333,1,"{266, 43}"
2314,1,77,0,0.0447806,"\int \left(a+b \sqrt[3]{x}\right)^5 x^2 \, dx","Int[(a + b*x^(1/3))^5*x^2,x]","\frac{30}{11} a^3 b^2 x^{11/3}+\frac{5}{2} a^2 b^3 x^4+\frac{3}{2} a^4 b x^{10/3}+\frac{a^5 x^3}{3}+\frac{15}{13} a b^4 x^{13/3}+\frac{3}{14} b^5 x^{14/3}","\frac{30}{11} a^3 b^2 x^{11/3}+\frac{5}{2} a^2 b^3 x^4+\frac{3}{2} a^4 b x^{10/3}+\frac{a^5 x^3}{3}+\frac{15}{13} a b^4 x^{13/3}+\frac{3}{14} b^5 x^{14/3}",1,"(a^5*x^3)/3 + (3*a^4*b*x^(10/3))/2 + (30*a^3*b^2*x^(11/3))/11 + (5*a^2*b^3*x^4)/2 + (15*a*b^4*x^(13/3))/13 + (3*b^5*x^(14/3))/14","A",3,2,15,0.1333,1,"{266, 43}"
2315,1,77,0,0.0408262,"\int \left(a+b \sqrt[3]{x}\right)^5 x \, dx","Int[(a + b*x^(1/3))^5*x,x]","\frac{15}{4} a^3 b^2 x^{8/3}+\frac{10}{3} a^2 b^3 x^3+\frac{15}{7} a^4 b x^{7/3}+\frac{a^5 x^2}{2}+\frac{3}{2} a b^4 x^{10/3}+\frac{3}{11} b^5 x^{11/3}","\frac{15}{4} a^3 b^2 x^{8/3}+\frac{10}{3} a^2 b^3 x^3+\frac{15}{7} a^4 b x^{7/3}+\frac{a^5 x^2}{2}+\frac{3}{2} a b^4 x^{10/3}+\frac{3}{11} b^5 x^{11/3}",1,"(a^5*x^2)/2 + (15*a^4*b*x^(7/3))/7 + (15*a^3*b^2*x^(8/3))/4 + (10*a^2*b^3*x^3)/3 + (3*a*b^4*x^(10/3))/2 + (3*b^5*x^(11/3))/11","A",3,2,13,0.1538,1,"{266, 43}"
2316,1,59,0,0.0392421,"\int \left(a+b \sqrt[3]{x}\right)^5 \, dx","Int[(a + b*x^(1/3))^5,x]","\frac{a^2 \left(a+b \sqrt[3]{x}\right)^6}{2 b^3}+\frac{3 \left(a+b \sqrt[3]{x}\right)^8}{8 b^3}-\frac{6 a \left(a+b \sqrt[3]{x}\right)^7}{7 b^3}","\frac{a^2 \left(a+b \sqrt[3]{x}\right)^6}{2 b^3}+\frac{3 \left(a+b \sqrt[3]{x}\right)^8}{8 b^3}-\frac{6 a \left(a+b \sqrt[3]{x}\right)^7}{7 b^3}",1,"(a^2*(a + b*x^(1/3))^6)/(2*b^3) - (6*a*(a + b*x^(1/3))^7)/(7*b^3) + (3*(a + b*x^(1/3))^8)/(8*b^3)","A",3,2,11,0.1818,1,"{190, 43}"
2317,1,65,0,0.0287267,"\int \frac{\left(a+b \sqrt[3]{x}\right)^5}{x} \, dx","Int[(a + b*x^(1/3))^5/x,x]","15 a^3 b^2 x^{2/3}+10 a^2 b^3 x+15 a^4 b \sqrt[3]{x}+a^5 \log (x)+\frac{15}{4} a b^4 x^{4/3}+\frac{3}{5} b^5 x^{5/3}","15 a^3 b^2 x^{2/3}+10 a^2 b^3 x+15 a^4 b \sqrt[3]{x}+a^5 \log (x)+\frac{15}{4} a b^4 x^{4/3}+\frac{3}{5} b^5 x^{5/3}",1,"15*a^4*b*x^(1/3) + 15*a^3*b^2*x^(2/3) + 10*a^2*b^3*x + (15*a*b^4*x^(4/3))/4 + (3*b^5*x^(5/3))/5 + a^5*Log[x]","A",3,2,15,0.1333,1,"{266, 43}"
2318,1,68,0,0.0319101,"\int \frac{\left(a+b \sqrt[3]{x}\right)^5}{x^2} \, dx","Int[(a + b*x^(1/3))^5/x^2,x]","-\frac{30 a^3 b^2}{\sqrt[3]{x}}+10 a^2 b^3 \log (x)-\frac{15 a^4 b}{2 x^{2/3}}-\frac{a^5}{x}+15 a b^4 \sqrt[3]{x}+\frac{3}{2} b^5 x^{2/3}","-\frac{30 a^3 b^2}{\sqrt[3]{x}}+10 a^2 b^3 \log (x)-\frac{15 a^4 b}{2 x^{2/3}}-\frac{a^5}{x}+15 a b^4 \sqrt[3]{x}+\frac{3}{2} b^5 x^{2/3}",1,"-(a^5/x) - (15*a^4*b)/(2*x^(2/3)) - (30*a^3*b^2)/x^(1/3) + 15*a*b^4*x^(1/3) + (3*b^5*x^(2/3))/2 + 10*a^2*b^3*Log[x]","A",3,2,15,0.1333,1,"{266, 43}"
2319,1,21,0,0.0033234,"\int \frac{\left(a+b \sqrt[3]{x}\right)^5}{x^3} \, dx","Int[(a + b*x^(1/3))^5/x^3,x]","-\frac{\left(a+b \sqrt[3]{x}\right)^6}{2 a x^2}","-\frac{\left(a+b \sqrt[3]{x}\right)^6}{2 a x^2}",1,"-(a + b*x^(1/3))^6/(2*a*x^2)","A",1,1,15,0.06667,1,"{264}"
2320,1,73,0,0.0332598,"\int \frac{\left(a+b \sqrt[3]{x}\right)^5}{x^4} \, dx","Int[(a + b*x^(1/3))^5/x^4,x]","-\frac{30 a^3 b^2}{7 x^{7/3}}-\frac{5 a^2 b^3}{x^2}-\frac{15 a^4 b}{8 x^{8/3}}-\frac{a^5}{3 x^3}-\frac{3 a b^4}{x^{5/3}}-\frac{3 b^5}{4 x^{4/3}}","-\frac{30 a^3 b^2}{7 x^{7/3}}-\frac{5 a^2 b^3}{x^2}-\frac{15 a^4 b}{8 x^{8/3}}-\frac{a^5}{3 x^3}-\frac{3 a b^4}{x^{5/3}}-\frac{3 b^5}{4 x^{4/3}}",1,"-a^5/(3*x^3) - (15*a^4*b)/(8*x^(8/3)) - (30*a^3*b^2)/(7*x^(7/3)) - (5*a^2*b^3)/x^2 - (3*a*b^4)/x^(5/3) - (3*b^5)/(4*x^(4/3))","A",3,2,15,0.1333,1,"{266, 43}"
2321,1,75,0,0.0334341,"\int \frac{\left(a+b \sqrt[3]{x}\right)^5}{x^5} \, dx","Int[(a + b*x^(1/3))^5/x^5,x]","-\frac{3 a^3 b^2}{x^{10/3}}-\frac{10 a^2 b^3}{3 x^3}-\frac{15 a^4 b}{11 x^{11/3}}-\frac{a^5}{4 x^4}-\frac{15 a b^4}{8 x^{8/3}}-\frac{3 b^5}{7 x^{7/3}}","-\frac{3 a^3 b^2}{x^{10/3}}-\frac{10 a^2 b^3}{3 x^3}-\frac{15 a^4 b}{11 x^{11/3}}-\frac{a^5}{4 x^4}-\frac{15 a b^4}{8 x^{8/3}}-\frac{3 b^5}{7 x^{7/3}}",1,"-a^5/(4*x^4) - (15*a^4*b)/(11*x^(11/3)) - (3*a^3*b^2)/x^(10/3) - (10*a^2*b^3)/(3*x^3) - (15*a*b^4)/(8*x^(8/3)) - (3*b^5)/(7*x^(7/3))","A",3,2,15,0.1333,1,"{266, 43}"
2322,1,77,0,0.0337491,"\int \frac{\left(a+b \sqrt[3]{x}\right)^5}{x^6} \, dx","Int[(a + b*x^(1/3))^5/x^6,x]","-\frac{30 a^3 b^2}{13 x^{13/3}}-\frac{5 a^2 b^3}{2 x^4}-\frac{15 a^4 b}{14 x^{14/3}}-\frac{a^5}{5 x^5}-\frac{15 a b^4}{11 x^{11/3}}-\frac{3 b^5}{10 x^{10/3}}","-\frac{30 a^3 b^2}{13 x^{13/3}}-\frac{5 a^2 b^3}{2 x^4}-\frac{15 a^4 b}{14 x^{14/3}}-\frac{a^5}{5 x^5}-\frac{15 a b^4}{11 x^{11/3}}-\frac{3 b^5}{10 x^{10/3}}",1,"-a^5/(5*x^5) - (15*a^4*b)/(14*x^(14/3)) - (30*a^3*b^2)/(13*x^(13/3)) - (5*a^2*b^3)/(2*x^4) - (15*a*b^4)/(11*x^(11/3)) - (3*b^5)/(10*x^(10/3))","A",3,2,15,0.1333,1,"{266, 43}"
2323,1,75,0,0.0352752,"\int \frac{\left(a+b \sqrt[3]{x}\right)^5}{x^7} \, dx","Int[(a + b*x^(1/3))^5/x^7,x]","-\frac{15 a^3 b^2}{8 x^{16/3}}-\frac{2 a^2 b^3}{x^5}-\frac{15 a^4 b}{17 x^{17/3}}-\frac{a^5}{6 x^6}-\frac{15 a b^4}{14 x^{14/3}}-\frac{3 b^5}{13 x^{13/3}}","-\frac{15 a^3 b^2}{8 x^{16/3}}-\frac{2 a^2 b^3}{x^5}-\frac{15 a^4 b}{17 x^{17/3}}-\frac{a^5}{6 x^6}-\frac{15 a b^4}{14 x^{14/3}}-\frac{3 b^5}{13 x^{13/3}}",1,"-a^5/(6*x^6) - (15*a^4*b)/(17*x^(17/3)) - (15*a^3*b^2)/(8*x^(16/3)) - (2*a^2*b^3)/x^5 - (15*a*b^4)/(14*x^(14/3)) - (3*b^5)/(13*x^(13/3))","A",3,2,15,0.1333,1,"{266, 43}"
2324,1,144,0,0.0952417,"\int \left(a+b \sqrt[3]{x}\right)^{10} x^4 \, dx","Int[(a + b*x^(1/3))^10*x^4,x]","\frac{135}{17} a^8 b^2 x^{17/3}+20 a^7 b^3 x^6+\frac{630}{19} a^6 b^4 x^{19/3}+\frac{189}{5} a^5 b^5 x^{20/3}+30 a^4 b^6 x^7+\frac{180}{11} a^3 b^7 x^{22/3}+\frac{135}{23} a^2 b^8 x^{23/3}+\frac{15}{8} a^9 b x^{16/3}+\frac{a^{10} x^5}{5}+\frac{5}{4} a b^9 x^8+\frac{3}{25} b^{10} x^{25/3}","\frac{135}{17} a^8 b^2 x^{17/3}+20 a^7 b^3 x^6+\frac{630}{19} a^6 b^4 x^{19/3}+\frac{189}{5} a^5 b^5 x^{20/3}+30 a^4 b^6 x^7+\frac{180}{11} a^3 b^7 x^{22/3}+\frac{135}{23} a^2 b^8 x^{23/3}+\frac{15}{8} a^9 b x^{16/3}+\frac{a^{10} x^5}{5}+\frac{5}{4} a b^9 x^8+\frac{3}{25} b^{10} x^{25/3}",1,"(a^10*x^5)/5 + (15*a^9*b*x^(16/3))/8 + (135*a^8*b^2*x^(17/3))/17 + 20*a^7*b^3*x^6 + (630*a^6*b^4*x^(19/3))/19 + (189*a^5*b^5*x^(20/3))/5 + 30*a^4*b^6*x^7 + (180*a^3*b^7*x^(22/3))/11 + (135*a^2*b^8*x^(23/3))/23 + (5*a*b^9*x^8)/4 + (3*b^10*x^(25/3))/25","A",3,2,15,0.1333,1,"{266, 43}"
2325,1,144,0,0.0852495,"\int \left(a+b \sqrt[3]{x}\right)^{10} x^3 \, dx","Int[(a + b*x^(1/3))^10*x^3,x]","\frac{135}{14} a^8 b^2 x^{14/3}+24 a^7 b^3 x^5+\frac{315}{8} a^6 b^4 x^{16/3}+\frac{756}{17} a^5 b^5 x^{17/3}+35 a^4 b^6 x^6+\frac{360}{19} a^3 b^7 x^{19/3}+\frac{27}{4} a^2 b^8 x^{20/3}+\frac{30}{13} a^9 b x^{13/3}+\frac{a^{10} x^4}{4}+\frac{10}{7} a b^9 x^7+\frac{3}{22} b^{10} x^{22/3}","\frac{135}{14} a^8 b^2 x^{14/3}+24 a^7 b^3 x^5+\frac{315}{8} a^6 b^4 x^{16/3}+\frac{756}{17} a^5 b^5 x^{17/3}+35 a^4 b^6 x^6+\frac{360}{19} a^3 b^7 x^{19/3}+\frac{27}{4} a^2 b^8 x^{20/3}+\frac{30}{13} a^9 b x^{13/3}+\frac{a^{10} x^4}{4}+\frac{10}{7} a b^9 x^7+\frac{3}{22} b^{10} x^{22/3}",1,"(a^10*x^4)/4 + (30*a^9*b*x^(13/3))/13 + (135*a^8*b^2*x^(14/3))/14 + 24*a^7*b^3*x^5 + (315*a^6*b^4*x^(16/3))/8 + (756*a^5*b^5*x^(17/3))/17 + 35*a^4*b^6*x^6 + (360*a^3*b^7*x^(19/3))/19 + (27*a^2*b^8*x^(20/3))/4 + (10*a*b^9*x^7)/7 + (3*b^10*x^(22/3))/22","A",3,2,15,0.1333,1,"{266, 43}"
2326,1,179,0,0.0919547,"\int \left(a+b \sqrt[3]{x}\right)^{10} x^2 \, dx","Int[(a + b*x^(1/3))^10*x^2,x]","\frac{84 a^2 \left(a+b \sqrt[3]{x}\right)^{17}}{17 b^9}-\frac{21 a^3 \left(a+b \sqrt[3]{x}\right)^{16}}{2 b^9}+\frac{14 a^4 \left(a+b \sqrt[3]{x}\right)^{15}}{b^9}-\frac{12 a^5 \left(a+b \sqrt[3]{x}\right)^{14}}{b^9}+\frac{84 a^6 \left(a+b \sqrt[3]{x}\right)^{13}}{13 b^9}-\frac{2 a^7 \left(a+b \sqrt[3]{x}\right)^{12}}{b^9}+\frac{3 a^8 \left(a+b \sqrt[3]{x}\right)^{11}}{11 b^9}+\frac{3 \left(a+b \sqrt[3]{x}\right)^{19}}{19 b^9}-\frac{4 a \left(a+b \sqrt[3]{x}\right)^{18}}{3 b^9}","\frac{84 a^2 \left(a+b \sqrt[3]{x}\right)^{17}}{17 b^9}-\frac{21 a^3 \left(a+b \sqrt[3]{x}\right)^{16}}{2 b^9}+\frac{14 a^4 \left(a+b \sqrt[3]{x}\right)^{15}}{b^9}-\frac{12 a^5 \left(a+b \sqrt[3]{x}\right)^{14}}{b^9}+\frac{84 a^6 \left(a+b \sqrt[3]{x}\right)^{13}}{13 b^9}-\frac{2 a^7 \left(a+b \sqrt[3]{x}\right)^{12}}{b^9}+\frac{3 a^8 \left(a+b \sqrt[3]{x}\right)^{11}}{11 b^9}+\frac{3 \left(a+b \sqrt[3]{x}\right)^{19}}{19 b^9}-\frac{4 a \left(a+b \sqrt[3]{x}\right)^{18}}{3 b^9}",1,"(3*a^8*(a + b*x^(1/3))^11)/(11*b^9) - (2*a^7*(a + b*x^(1/3))^12)/b^9 + (84*a^6*(a + b*x^(1/3))^13)/(13*b^9) - (12*a^5*(a + b*x^(1/3))^14)/b^9 + (14*a^4*(a + b*x^(1/3))^15)/b^9 - (21*a^3*(a + b*x^(1/3))^16)/(2*b^9) + (84*a^2*(a + b*x^(1/3))^17)/(17*b^9) - (4*a*(a + b*x^(1/3))^18)/(3*b^9) + (3*(a + b*x^(1/3))^19)/(19*b^9)","A",3,2,15,0.1333,1,"{266, 43}"
2327,1,120,0,0.065163,"\int \left(a+b \sqrt[3]{x}\right)^{10} x \, dx","Int[(a + b*x^(1/3))^10*x,x]","\frac{15 a^2 \left(a+b \sqrt[3]{x}\right)^{14}}{7 b^6}-\frac{30 a^3 \left(a+b \sqrt[3]{x}\right)^{13}}{13 b^6}+\frac{5 a^4 \left(a+b \sqrt[3]{x}\right)^{12}}{4 b^6}-\frac{3 a^5 \left(a+b \sqrt[3]{x}\right)^{11}}{11 b^6}+\frac{3 \left(a+b \sqrt[3]{x}\right)^{16}}{16 b^6}-\frac{a \left(a+b \sqrt[3]{x}\right)^{15}}{b^6}","\frac{15 a^2 \left(a+b \sqrt[3]{x}\right)^{14}}{7 b^6}-\frac{30 a^3 \left(a+b \sqrt[3]{x}\right)^{13}}{13 b^6}+\frac{5 a^4 \left(a+b \sqrt[3]{x}\right)^{12}}{4 b^6}-\frac{3 a^5 \left(a+b \sqrt[3]{x}\right)^{11}}{11 b^6}+\frac{3 \left(a+b \sqrt[3]{x}\right)^{16}}{16 b^6}-\frac{a \left(a+b \sqrt[3]{x}\right)^{15}}{b^6}",1,"(-3*a^5*(a + b*x^(1/3))^11)/(11*b^6) + (5*a^4*(a + b*x^(1/3))^12)/(4*b^6) - (30*a^3*(a + b*x^(1/3))^13)/(13*b^6) + (15*a^2*(a + b*x^(1/3))^14)/(7*b^6) - (a*(a + b*x^(1/3))^15)/b^6 + (3*(a + b*x^(1/3))^16)/(16*b^6)","A",3,2,13,0.1538,1,"{266, 43}"
2328,1,59,0,0.0376548,"\int \left(a+b \sqrt[3]{x}\right)^{10} \, dx","Int[(a + b*x^(1/3))^10,x]","\frac{3 a^2 \left(a+b \sqrt[3]{x}\right)^{11}}{11 b^3}+\frac{3 \left(a+b \sqrt[3]{x}\right)^{13}}{13 b^3}-\frac{a \left(a+b \sqrt[3]{x}\right)^{12}}{2 b^3}","\frac{3 a^2 \left(a+b \sqrt[3]{x}\right)^{11}}{11 b^3}+\frac{3 \left(a+b \sqrt[3]{x}\right)^{13}}{13 b^3}-\frac{a \left(a+b \sqrt[3]{x}\right)^{12}}{2 b^3}",1,"(3*a^2*(a + b*x^(1/3))^11)/(11*b^3) - (a*(a + b*x^(1/3))^12)/(2*b^3) + (3*(a + b*x^(1/3))^13)/(13*b^3)","A",3,2,11,0.1818,1,"{190, 43}"
2329,1,136,0,0.0655307,"\int \frac{\left(a+b \sqrt[3]{x}\right)^{10}}{x} \, dx","Int[(a + b*x^(1/3))^10/x,x]","\frac{135}{2} a^8 b^2 x^{2/3}+\frac{315}{2} a^6 b^4 x^{4/3}+\frac{756}{5} a^5 b^5 x^{5/3}+105 a^4 b^6 x^2+\frac{360}{7} a^3 b^7 x^{7/3}+\frac{135}{8} a^2 b^8 x^{8/3}+120 a^7 b^3 x+30 a^9 b \sqrt[3]{x}+a^{10} \log (x)+\frac{10}{3} a b^9 x^3+\frac{3}{10} b^{10} x^{10/3}","\frac{135}{2} a^8 b^2 x^{2/3}+\frac{315}{2} a^6 b^4 x^{4/3}+\frac{756}{5} a^5 b^5 x^{5/3}+105 a^4 b^6 x^2+\frac{360}{7} a^3 b^7 x^{7/3}+\frac{135}{8} a^2 b^8 x^{8/3}+120 a^7 b^3 x+30 a^9 b \sqrt[3]{x}+a^{10} \log (x)+\frac{10}{3} a b^9 x^3+\frac{3}{10} b^{10} x^{10/3}",1,"30*a^9*b*x^(1/3) + (135*a^8*b^2*x^(2/3))/2 + 120*a^7*b^3*x + (315*a^6*b^4*x^(4/3))/2 + (756*a^5*b^5*x^(5/3))/5 + 105*a^4*b^6*x^2 + (360*a^3*b^7*x^(7/3))/7 + (135*a^2*b^8*x^(8/3))/8 + (10*a*b^9*x^3)/3 + (3*b^10*x^(10/3))/10 + a^10*Log[x]","A",3,2,15,0.1333,1,"{266, 43}"
2330,1,125,0,0.0706347,"\int \frac{\left(a+b \sqrt[3]{x}\right)^{10}}{x^2} \, dx","Int[(a + b*x^(1/3))^10/x^2,x]","378 a^5 b^5 x^{2/3}+90 a^3 b^7 x^{4/3}+27 a^2 b^8 x^{5/3}-\frac{135 a^8 b^2}{\sqrt[3]{x}}+630 a^6 b^4 \sqrt[3]{x}+210 a^4 b^6 x+120 a^7 b^3 \log (x)-\frac{15 a^9 b}{x^{2/3}}-\frac{a^{10}}{x}+5 a b^9 x^2+\frac{3}{7} b^{10} x^{7/3}","378 a^5 b^5 x^{2/3}+90 a^3 b^7 x^{4/3}+27 a^2 b^8 x^{5/3}-\frac{135 a^8 b^2}{\sqrt[3]{x}}+630 a^6 b^4 \sqrt[3]{x}+210 a^4 b^6 x+120 a^7 b^3 \log (x)-\frac{15 a^9 b}{x^{2/3}}-\frac{a^{10}}{x}+5 a b^9 x^2+\frac{3}{7} b^{10} x^{7/3}",1,"-(a^10/x) - (15*a^9*b)/x^(2/3) - (135*a^8*b^2)/x^(1/3) + 630*a^6*b^4*x^(1/3) + 378*a^5*b^5*x^(2/3) + 210*a^4*b^6*x + 90*a^3*b^7*x^(4/3) + 27*a^2*b^8*x^(5/3) + 5*a*b^9*x^2 + (3*b^10*x^(7/3))/7 + 120*a^7*b^3*Log[x]","A",3,2,15,0.1333,1,"{266, 43}"
2331,1,131,0,0.0722625,"\int \frac{\left(a+b \sqrt[3]{x}\right)^{10}}{x^3} \, dx","Int[(a + b*x^(1/3))^10/x^3,x]","-\frac{135 a^8 b^2}{4 x^{4/3}}-\frac{315 a^6 b^4}{x^{2/3}}+\frac{135}{2} a^2 b^8 x^{2/3}-\frac{120 a^7 b^3}{x}-\frac{756 a^5 b^5}{\sqrt[3]{x}}+360 a^3 b^7 \sqrt[3]{x}+210 a^4 b^6 \log (x)-\frac{6 a^9 b}{x^{5/3}}-\frac{a^{10}}{2 x^2}+10 a b^9 x+\frac{3}{4} b^{10} x^{4/3}","-\frac{135 a^8 b^2}{4 x^{4/3}}-\frac{315 a^6 b^4}{x^{2/3}}+\frac{135}{2} a^2 b^8 x^{2/3}-\frac{120 a^7 b^3}{x}-\frac{756 a^5 b^5}{\sqrt[3]{x}}+360 a^3 b^7 \sqrt[3]{x}+210 a^4 b^6 \log (x)-\frac{6 a^9 b}{x^{5/3}}-\frac{a^{10}}{2 x^2}+10 a b^9 x+\frac{3}{4} b^{10} x^{4/3}",1,"-a^10/(2*x^2) - (6*a^9*b)/x^(5/3) - (135*a^8*b^2)/(4*x^(4/3)) - (120*a^7*b^3)/x - (315*a^6*b^4)/x^(2/3) - (756*a^5*b^5)/x^(1/3) + 360*a^3*b^7*x^(1/3) + (135*a^2*b^8*x^(2/3))/2 + 10*a*b^9*x + (3*b^10*x^(4/3))/4 + 210*a^4*b^6*Log[x]","A",3,2,15,0.1333,1,"{266, 43}"
2332,1,131,0,0.0714533,"\int \frac{\left(a+b \sqrt[3]{x}\right)^{10}}{x^4} \, dx","Int[(a + b*x^(1/3))^10/x^4,x]","-\frac{135 a^8 b^2}{7 x^{7/3}}-\frac{60 a^7 b^3}{x^2}-\frac{126 a^6 b^4}{x^{5/3}}-\frac{189 a^5 b^5}{x^{4/3}}-\frac{180 a^3 b^7}{x^{2/3}}-\frac{210 a^4 b^6}{x}-\frac{135 a^2 b^8}{\sqrt[3]{x}}-\frac{15 a^9 b}{4 x^{8/3}}-\frac{a^{10}}{3 x^3}+10 a b^9 \log (x)+3 b^{10} \sqrt[3]{x}","-\frac{135 a^8 b^2}{7 x^{7/3}}-\frac{60 a^7 b^3}{x^2}-\frac{126 a^6 b^4}{x^{5/3}}-\frac{189 a^5 b^5}{x^{4/3}}-\frac{180 a^3 b^7}{x^{2/3}}-\frac{210 a^4 b^6}{x}-\frac{135 a^2 b^8}{\sqrt[3]{x}}-\frac{15 a^9 b}{4 x^{8/3}}-\frac{a^{10}}{3 x^3}+10 a b^9 \log (x)+3 b^{10} \sqrt[3]{x}",1,"-a^10/(3*x^3) - (15*a^9*b)/(4*x^(8/3)) - (135*a^8*b^2)/(7*x^(7/3)) - (60*a^7*b^3)/x^2 - (126*a^6*b^4)/x^(5/3) - (189*a^5*b^5)/x^(4/3) - (210*a^4*b^6)/x - (180*a^3*b^7)/x^(2/3) - (135*a^2*b^8)/x^(1/3) + 3*b^10*x^(1/3) + 10*a*b^9*Log[x]","A",3,2,15,0.1333,1,"{266, 43}"
2333,1,46,0,0.0136786,"\int \frac{\left(a+b \sqrt[3]{x}\right)^{10}}{x^5} \, dx","Int[(a + b*x^(1/3))^10/x^5,x]","\frac{b \left(a+b \sqrt[3]{x}\right)^{11}}{44 a^2 x^{11/3}}-\frac{\left(a+b \sqrt[3]{x}\right)^{11}}{4 a x^4}","\frac{b \left(a+b \sqrt[3]{x}\right)^{11}}{44 a^2 x^{11/3}}-\frac{\left(a+b \sqrt[3]{x}\right)^{11}}{4 a x^4}",1,"-(a + b*x^(1/3))^11/(4*a*x^4) + (b*(a + b*x^(1/3))^11)/(44*a^2*x^(11/3))","A",3,3,15,0.2000,1,"{266, 45, 37}"
2334,1,122,0,0.0465489,"\int \frac{\left(a+b \sqrt[3]{x}\right)^{10}}{x^6} \, dx","Int[(a + b*x^(1/3))^10/x^6,x]","-\frac{b^4 \left(a+b \sqrt[3]{x}\right)^{11}}{5005 a^5 x^{11/3}}+\frac{b^3 \left(a+b \sqrt[3]{x}\right)^{11}}{455 a^4 x^4}-\frac{6 b^2 \left(a+b \sqrt[3]{x}\right)^{11}}{455 a^3 x^{13/3}}+\frac{2 b \left(a+b \sqrt[3]{x}\right)^{11}}{35 a^2 x^{14/3}}-\frac{\left(a+b \sqrt[3]{x}\right)^{11}}{5 a x^5}","-\frac{b^4 \left(a+b \sqrt[3]{x}\right)^{11}}{5005 a^5 x^{11/3}}+\frac{b^3 \left(a+b \sqrt[3]{x}\right)^{11}}{455 a^4 x^4}-\frac{6 b^2 \left(a+b \sqrt[3]{x}\right)^{11}}{455 a^3 x^{13/3}}+\frac{2 b \left(a+b \sqrt[3]{x}\right)^{11}}{35 a^2 x^{14/3}}-\frac{\left(a+b \sqrt[3]{x}\right)^{11}}{5 a x^5}",1,"-(a + b*x^(1/3))^11/(5*a*x^5) + (2*b*(a + b*x^(1/3))^11)/(35*a^2*x^(14/3)) - (6*b^2*(a + b*x^(1/3))^11)/(455*a^3*x^(13/3)) + (b^3*(a + b*x^(1/3))^11)/(455*a^4*x^4) - (b^4*(a + b*x^(1/3))^11)/(5005*a^5*x^(11/3))","A",6,3,15,0.2000,1,"{266, 45, 37}"
2335,1,144,0,0.073725,"\int \frac{\left(a+b \sqrt[3]{x}\right)^{10}}{x^7} \, dx","Int[(a + b*x^(1/3))^10/x^7,x]","-\frac{135 a^8 b^2}{16 x^{16/3}}-\frac{24 a^7 b^3}{x^5}-\frac{45 a^6 b^4}{x^{14/3}}-\frac{756 a^5 b^5}{13 x^{13/3}}-\frac{105 a^4 b^6}{2 x^4}-\frac{360 a^3 b^7}{11 x^{11/3}}-\frac{27 a^2 b^8}{2 x^{10/3}}-\frac{30 a^9 b}{17 x^{17/3}}-\frac{a^{10}}{6 x^6}-\frac{10 a b^9}{3 x^3}-\frac{3 b^{10}}{8 x^{8/3}}","-\frac{135 a^8 b^2}{16 x^{16/3}}-\frac{24 a^7 b^3}{x^5}-\frac{45 a^6 b^4}{x^{14/3}}-\frac{756 a^5 b^5}{13 x^{13/3}}-\frac{105 a^4 b^6}{2 x^4}-\frac{360 a^3 b^7}{11 x^{11/3}}-\frac{27 a^2 b^8}{2 x^{10/3}}-\frac{30 a^9 b}{17 x^{17/3}}-\frac{a^{10}}{6 x^6}-\frac{10 a b^9}{3 x^3}-\frac{3 b^{10}}{8 x^{8/3}}",1,"-a^10/(6*x^6) - (30*a^9*b)/(17*x^(17/3)) - (135*a^8*b^2)/(16*x^(16/3)) - (24*a^7*b^3)/x^5 - (45*a^6*b^4)/x^(14/3) - (756*a^5*b^5)/(13*x^(13/3)) - (105*a^4*b^6)/(2*x^4) - (360*a^3*b^7)/(11*x^(11/3)) - (27*a^2*b^8)/(2*x^(10/3)) - (10*a*b^9)/(3*x^3) - (3*b^10)/(8*x^(8/3))","A",3,2,15,0.1333,1,"{266, 43}"
2336,1,144,0,0.0675585,"\int \frac{\left(a+b \sqrt[3]{x}\right)^{10}}{x^8} \, dx","Int[(a + b*x^(1/3))^10/x^8,x]","-\frac{135 a^8 b^2}{19 x^{19/3}}-\frac{20 a^7 b^3}{x^6}-\frac{630 a^6 b^4}{17 x^{17/3}}-\frac{189 a^5 b^5}{4 x^{16/3}}-\frac{42 a^4 b^6}{x^5}-\frac{180 a^3 b^7}{7 x^{14/3}}-\frac{135 a^2 b^8}{13 x^{13/3}}-\frac{3 a^9 b}{2 x^{20/3}}-\frac{a^{10}}{7 x^7}-\frac{5 a b^9}{2 x^4}-\frac{3 b^{10}}{11 x^{11/3}}","-\frac{135 a^8 b^2}{19 x^{19/3}}-\frac{20 a^7 b^3}{x^6}-\frac{630 a^6 b^4}{17 x^{17/3}}-\frac{189 a^5 b^5}{4 x^{16/3}}-\frac{42 a^4 b^6}{x^5}-\frac{180 a^3 b^7}{7 x^{14/3}}-\frac{135 a^2 b^8}{13 x^{13/3}}-\frac{3 a^9 b}{2 x^{20/3}}-\frac{a^{10}}{7 x^7}-\frac{5 a b^9}{2 x^4}-\frac{3 b^{10}}{11 x^{11/3}}",1,"-a^10/(7*x^7) - (3*a^9*b)/(2*x^(20/3)) - (135*a^8*b^2)/(19*x^(19/3)) - (20*a^7*b^3)/x^6 - (630*a^6*b^4)/(17*x^(17/3)) - (189*a^5*b^5)/(4*x^(16/3)) - (42*a^4*b^6)/x^5 - (180*a^3*b^7)/(7*x^(14/3)) - (135*a^2*b^8)/(13*x^(13/3)) - (5*a*b^9)/(2*x^4) - (3*b^10)/(11*x^(11/3))","A",3,2,15,0.1333,1,"{266, 43}"
2337,1,144,0,0.0706039,"\int \frac{\left(a+b \sqrt[3]{x}\right)^{10}}{x^9} \, dx","Int[(a + b*x^(1/3))^10/x^9,x]","-\frac{135 a^8 b^2}{22 x^{22/3}}-\frac{120 a^7 b^3}{7 x^7}-\frac{63 a^6 b^4}{2 x^{20/3}}-\frac{756 a^5 b^5}{19 x^{19/3}}-\frac{35 a^4 b^6}{x^6}-\frac{360 a^3 b^7}{17 x^{17/3}}-\frac{135 a^2 b^8}{16 x^{16/3}}-\frac{30 a^9 b}{23 x^{23/3}}-\frac{a^{10}}{8 x^8}-\frac{2 a b^9}{x^5}-\frac{3 b^{10}}{14 x^{14/3}}","-\frac{135 a^8 b^2}{22 x^{22/3}}-\frac{120 a^7 b^3}{7 x^7}-\frac{63 a^6 b^4}{2 x^{20/3}}-\frac{756 a^5 b^5}{19 x^{19/3}}-\frac{35 a^4 b^6}{x^6}-\frac{360 a^3 b^7}{17 x^{17/3}}-\frac{135 a^2 b^8}{16 x^{16/3}}-\frac{30 a^9 b}{23 x^{23/3}}-\frac{a^{10}}{8 x^8}-\frac{2 a b^9}{x^5}-\frac{3 b^{10}}{14 x^{14/3}}",1,"-a^10/(8*x^8) - (30*a^9*b)/(23*x^(23/3)) - (135*a^8*b^2)/(22*x^(22/3)) - (120*a^7*b^3)/(7*x^7) - (63*a^6*b^4)/(2*x^(20/3)) - (756*a^5*b^5)/(19*x^(19/3)) - (35*a^4*b^6)/x^6 - (360*a^3*b^7)/(17*x^(17/3)) - (135*a^2*b^8)/(16*x^(16/3)) - (2*a*b^9)/x^5 - (3*b^10)/(14*x^(14/3))","A",3,2,15,0.1333,1,"{266, 43}"
2338,1,142,0,0.0693011,"\int \frac{\left(a+b \sqrt[3]{x}\right)^{10}}{x^{10}} \, dx","Int[(a + b*x^(1/3))^10/x^10,x]","-\frac{27 a^8 b^2}{5 x^{25/3}}-\frac{15 a^7 b^3}{x^8}-\frac{630 a^6 b^4}{23 x^{23/3}}-\frac{378 a^5 b^5}{11 x^{22/3}}-\frac{30 a^4 b^6}{x^7}-\frac{18 a^3 b^7}{x^{20/3}}-\frac{135 a^2 b^8}{19 x^{19/3}}-\frac{15 a^9 b}{13 x^{26/3}}-\frac{a^{10}}{9 x^9}-\frac{5 a b^9}{3 x^6}-\frac{3 b^{10}}{17 x^{17/3}}","-\frac{27 a^8 b^2}{5 x^{25/3}}-\frac{15 a^7 b^3}{x^8}-\frac{630 a^6 b^4}{23 x^{23/3}}-\frac{378 a^5 b^5}{11 x^{22/3}}-\frac{30 a^4 b^6}{x^7}-\frac{18 a^3 b^7}{x^{20/3}}-\frac{135 a^2 b^8}{19 x^{19/3}}-\frac{15 a^9 b}{13 x^{26/3}}-\frac{a^{10}}{9 x^9}-\frac{5 a b^9}{3 x^6}-\frac{3 b^{10}}{17 x^{17/3}}",1,"-a^10/(9*x^9) - (15*a^9*b)/(13*x^(26/3)) - (27*a^8*b^2)/(5*x^(25/3)) - (15*a^7*b^3)/x^8 - (630*a^6*b^4)/(23*x^(23/3)) - (378*a^5*b^5)/(11*x^(22/3)) - (30*a^4*b^6)/x^7 - (18*a^3*b^7)/x^(20/3) - (135*a^2*b^8)/(19*x^(19/3)) - (5*a*b^9)/(3*x^6) - (3*b^10)/(17*x^(17/3))","A",3,2,15,0.1333,1,"{266, 43}"
2339,1,217,0,0.1715536,"\int \left(a+b \sqrt[3]{x}\right)^{15} x^5 \, dx","Int[(a + b*x^(1/3))^15*x^5,x]","\frac{63}{4} a^{13} b^2 x^{20/3}+65 a^{12} b^3 x^7+\frac{4095}{22} a^{11} b^4 x^{22/3}+\frac{9009}{23} a^{10} b^5 x^{23/3}+\frac{5005}{8} a^9 b^6 x^8+\frac{3861}{5} a^8 b^7 x^{25/3}+\frac{1485}{2} a^7 b^8 x^{26/3}+\frac{5005}{9} a^6 b^9 x^9+\frac{1287}{4} a^5 b^{10} x^{28/3}+\frac{4095}{29} a^4 b^{11} x^{29/3}+\frac{91}{2} a^3 b^{12} x^{10}+\frac{315}{31} a^2 b^{13} x^{31/3}+\frac{45}{19} a^{14} b x^{19/3}+\frac{a^{15} x^6}{6}+\frac{45}{32} a b^{14} x^{32/3}+\frac{b^{15} x^{11}}{11}","\frac{63}{4} a^{13} b^2 x^{20/3}+65 a^{12} b^3 x^7+\frac{4095}{22} a^{11} b^4 x^{22/3}+\frac{9009}{23} a^{10} b^5 x^{23/3}+\frac{5005}{8} a^9 b^6 x^8+\frac{3861}{5} a^8 b^7 x^{25/3}+\frac{1485}{2} a^7 b^8 x^{26/3}+\frac{5005}{9} a^6 b^9 x^9+\frac{1287}{4} a^5 b^{10} x^{28/3}+\frac{4095}{29} a^4 b^{11} x^{29/3}+\frac{91}{2} a^3 b^{12} x^{10}+\frac{315}{31} a^2 b^{13} x^{31/3}+\frac{45}{19} a^{14} b x^{19/3}+\frac{a^{15} x^6}{6}+\frac{45}{32} a b^{14} x^{32/3}+\frac{b^{15} x^{11}}{11}",1,"(a^15*x^6)/6 + (45*a^14*b*x^(19/3))/19 + (63*a^13*b^2*x^(20/3))/4 + 65*a^12*b^3*x^7 + (4095*a^11*b^4*x^(22/3))/22 + (9009*a^10*b^5*x^(23/3))/23 + (5005*a^9*b^6*x^8)/8 + (3861*a^8*b^7*x^(25/3))/5 + (1485*a^7*b^8*x^(26/3))/2 + (5005*a^6*b^9*x^9)/9 + (1287*a^5*b^10*x^(28/3))/4 + (4095*a^4*b^11*x^(29/3))/29 + (91*a^3*b^12*x^10)/2 + (315*a^2*b^13*x^(31/3))/31 + (45*a*b^14*x^(32/3))/32 + (b^15*x^11)/11","A",3,2,15,0.1333,1,"{266, 43}"
2340,1,217,0,0.1334119,"\int \left(a+b \sqrt[3]{x}\right)^{15} x^4 \, dx","Int[(a + b*x^(1/3))^15*x^4,x]","\frac{315}{17} a^{13} b^2 x^{17/3}+\frac{455}{6} a^{12} b^3 x^6+\frac{4095}{19} a^{11} b^4 x^{19/3}+\frac{9009}{20} a^{10} b^5 x^{20/3}+715 a^9 b^6 x^7+\frac{1755}{2} a^8 b^7 x^{22/3}+\frac{19305}{23} a^7 b^8 x^{23/3}+\frac{5005}{8} a^6 b^9 x^8+\frac{9009}{25} a^5 b^{10} x^{25/3}+\frac{315}{2} a^4 b^{11} x^{26/3}+\frac{455}{9} a^3 b^{12} x^9+\frac{45}{4} a^2 b^{13} x^{28/3}+\frac{45}{16} a^{14} b x^{16/3}+\frac{a^{15} x^5}{5}+\frac{45}{29} a b^{14} x^{29/3}+\frac{b^{15} x^{10}}{10}","\frac{315}{17} a^{13} b^2 x^{17/3}+\frac{455}{6} a^{12} b^3 x^6+\frac{4095}{19} a^{11} b^4 x^{19/3}+\frac{9009}{20} a^{10} b^5 x^{20/3}+715 a^9 b^6 x^7+\frac{1755}{2} a^8 b^7 x^{22/3}+\frac{19305}{23} a^7 b^8 x^{23/3}+\frac{5005}{8} a^6 b^9 x^8+\frac{9009}{25} a^5 b^{10} x^{25/3}+\frac{315}{2} a^4 b^{11} x^{26/3}+\frac{455}{9} a^3 b^{12} x^9+\frac{45}{4} a^2 b^{13} x^{28/3}+\frac{45}{16} a^{14} b x^{16/3}+\frac{a^{15} x^5}{5}+\frac{45}{29} a b^{14} x^{29/3}+\frac{b^{15} x^{10}}{10}",1,"(a^15*x^5)/5 + (45*a^14*b*x^(16/3))/16 + (315*a^13*b^2*x^(17/3))/17 + (455*a^12*b^3*x^6)/6 + (4095*a^11*b^4*x^(19/3))/19 + (9009*a^10*b^5*x^(20/3))/20 + 715*a^9*b^6*x^7 + (1755*a^8*b^7*x^(22/3))/2 + (19305*a^7*b^8*x^(23/3))/23 + (5005*a^6*b^9*x^8)/8 + (9009*a^5*b^10*x^(25/3))/25 + (315*a^4*b^11*x^(26/3))/2 + (455*a^3*b^12*x^9)/9 + (45*a^2*b^13*x^(28/3))/4 + (45*a*b^14*x^(29/3))/29 + (b^15*x^10)/10","A",3,2,15,0.1333,1,"{266, 43}"
2341,1,244,0,0.1356675,"\int \left(a+b \sqrt[3]{x}\right)^{15} x^3 \, dx","Int[(a + b*x^(1/3))^15*x^3,x]","\frac{33 a^2 \left(a+b \sqrt[3]{x}\right)^{25}}{5 b^{12}}-\frac{165 a^3 \left(a+b \sqrt[3]{x}\right)^{24}}{8 b^{12}}+\frac{990 a^4 \left(a+b \sqrt[3]{x}\right)^{23}}{23 b^{12}}-\frac{63 a^5 \left(a+b \sqrt[3]{x}\right)^{22}}{b^{12}}+\frac{66 a^6 \left(a+b \sqrt[3]{x}\right)^{21}}{b^{12}}-\frac{99 a^7 \left(a+b \sqrt[3]{x}\right)^{20}}{2 b^{12}}+\frac{495 a^8 \left(a+b \sqrt[3]{x}\right)^{19}}{19 b^{12}}-\frac{55 a^9 \left(a+b \sqrt[3]{x}\right)^{18}}{6 b^{12}}+\frac{33 a^{10} \left(a+b \sqrt[3]{x}\right)^{17}}{17 b^{12}}-\frac{3 a^{11} \left(a+b \sqrt[3]{x}\right)^{16}}{16 b^{12}}+\frac{\left(a+b \sqrt[3]{x}\right)^{27}}{9 b^{12}}-\frac{33 a \left(a+b \sqrt[3]{x}\right)^{26}}{26 b^{12}}","\frac{33 a^2 \left(a+b \sqrt[3]{x}\right)^{25}}{5 b^{12}}-\frac{165 a^3 \left(a+b \sqrt[3]{x}\right)^{24}}{8 b^{12}}+\frac{990 a^4 \left(a+b \sqrt[3]{x}\right)^{23}}{23 b^{12}}-\frac{63 a^5 \left(a+b \sqrt[3]{x}\right)^{22}}{b^{12}}+\frac{66 a^6 \left(a+b \sqrt[3]{x}\right)^{21}}{b^{12}}-\frac{99 a^7 \left(a+b \sqrt[3]{x}\right)^{20}}{2 b^{12}}+\frac{495 a^8 \left(a+b \sqrt[3]{x}\right)^{19}}{19 b^{12}}-\frac{55 a^9 \left(a+b \sqrt[3]{x}\right)^{18}}{6 b^{12}}+\frac{33 a^{10} \left(a+b \sqrt[3]{x}\right)^{17}}{17 b^{12}}-\frac{3 a^{11} \left(a+b \sqrt[3]{x}\right)^{16}}{16 b^{12}}+\frac{\left(a+b \sqrt[3]{x}\right)^{27}}{9 b^{12}}-\frac{33 a \left(a+b \sqrt[3]{x}\right)^{26}}{26 b^{12}}",1,"(-3*a^11*(a + b*x^(1/3))^16)/(16*b^12) + (33*a^10*(a + b*x^(1/3))^17)/(17*b^12) - (55*a^9*(a + b*x^(1/3))^18)/(6*b^12) + (495*a^8*(a + b*x^(1/3))^19)/(19*b^12) - (99*a^7*(a + b*x^(1/3))^20)/(2*b^12) + (66*a^6*(a + b*x^(1/3))^21)/b^12 - (63*a^5*(a + b*x^(1/3))^22)/b^12 + (990*a^4*(a + b*x^(1/3))^23)/(23*b^12) - (165*a^3*(a + b*x^(1/3))^24)/(8*b^12) + (33*a^2*(a + b*x^(1/3))^25)/(5*b^12) - (33*a*(a + b*x^(1/3))^26)/(26*b^12) + (a + b*x^(1/3))^27/(9*b^12)","A",3,2,15,0.1333,1,"{266, 43}"
2342,1,183,0,0.1007914,"\int \left(a+b \sqrt[3]{x}\right)^{15} x^2 \, dx","Int[(a + b*x^(1/3))^15*x^2,x]","\frac{42 a^2 \left(a+b \sqrt[3]{x}\right)^{22}}{11 b^9}-\frac{8 a^3 \left(a+b \sqrt[3]{x}\right)^{21}}{b^9}+\frac{21 a^4 \left(a+b \sqrt[3]{x}\right)^{20}}{2 b^9}-\frac{168 a^5 \left(a+b \sqrt[3]{x}\right)^{19}}{19 b^9}+\frac{14 a^6 \left(a+b \sqrt[3]{x}\right)^{18}}{3 b^9}-\frac{24 a^7 \left(a+b \sqrt[3]{x}\right)^{17}}{17 b^9}+\frac{3 a^8 \left(a+b \sqrt[3]{x}\right)^{16}}{16 b^9}+\frac{\left(a+b \sqrt[3]{x}\right)^{24}}{8 b^9}-\frac{24 a \left(a+b \sqrt[3]{x}\right)^{23}}{23 b^9}","\frac{42 a^2 \left(a+b \sqrt[3]{x}\right)^{22}}{11 b^9}-\frac{8 a^3 \left(a+b \sqrt[3]{x}\right)^{21}}{b^9}+\frac{21 a^4 \left(a+b \sqrt[3]{x}\right)^{20}}{2 b^9}-\frac{168 a^5 \left(a+b \sqrt[3]{x}\right)^{19}}{19 b^9}+\frac{14 a^6 \left(a+b \sqrt[3]{x}\right)^{18}}{3 b^9}-\frac{24 a^7 \left(a+b \sqrt[3]{x}\right)^{17}}{17 b^9}+\frac{3 a^8 \left(a+b \sqrt[3]{x}\right)^{16}}{16 b^9}+\frac{\left(a+b \sqrt[3]{x}\right)^{24}}{8 b^9}-\frac{24 a \left(a+b \sqrt[3]{x}\right)^{23}}{23 b^9}",1,"(3*a^8*(a + b*x^(1/3))^16)/(16*b^9) - (24*a^7*(a + b*x^(1/3))^17)/(17*b^9) + (14*a^6*(a + b*x^(1/3))^18)/(3*b^9) - (168*a^5*(a + b*x^(1/3))^19)/(19*b^9) + (21*a^4*(a + b*x^(1/3))^20)/(2*b^9) - (8*a^3*(a + b*x^(1/3))^21)/b^9 + (42*a^2*(a + b*x^(1/3))^22)/(11*b^9) - (24*a*(a + b*x^(1/3))^23)/(23*b^9) + (a + b*x^(1/3))^24/(8*b^9)","A",3,2,15,0.1333,1,"{266, 43}"
2343,1,122,0,0.075441,"\int \left(a+b \sqrt[3]{x}\right)^{15} x \, dx","Int[(a + b*x^(1/3))^15*x,x]","\frac{30 a^2 \left(a+b \sqrt[3]{x}\right)^{19}}{19 b^6}-\frac{5 a^3 \left(a+b \sqrt[3]{x}\right)^{18}}{3 b^6}+\frac{15 a^4 \left(a+b \sqrt[3]{x}\right)^{17}}{17 b^6}-\frac{3 a^5 \left(a+b \sqrt[3]{x}\right)^{16}}{16 b^6}+\frac{\left(a+b \sqrt[3]{x}\right)^{21}}{7 b^6}-\frac{3 a \left(a+b \sqrt[3]{x}\right)^{20}}{4 b^6}","\frac{30 a^2 \left(a+b \sqrt[3]{x}\right)^{19}}{19 b^6}-\frac{5 a^3 \left(a+b \sqrt[3]{x}\right)^{18}}{3 b^6}+\frac{15 a^4 \left(a+b \sqrt[3]{x}\right)^{17}}{17 b^6}-\frac{3 a^5 \left(a+b \sqrt[3]{x}\right)^{16}}{16 b^6}+\frac{\left(a+b \sqrt[3]{x}\right)^{21}}{7 b^6}-\frac{3 a \left(a+b \sqrt[3]{x}\right)^{20}}{4 b^6}",1,"(-3*a^5*(a + b*x^(1/3))^16)/(16*b^6) + (15*a^4*(a + b*x^(1/3))^17)/(17*b^6) - (5*a^3*(a + b*x^(1/3))^18)/(3*b^6) + (30*a^2*(a + b*x^(1/3))^19)/(19*b^6) - (3*a*(a + b*x^(1/3))^20)/(4*b^6) + (a + b*x^(1/3))^21/(7*b^6)","A",3,2,13,0.1538,1,"{266, 43}"
2344,1,59,0,0.0473349,"\int \left(a+b \sqrt[3]{x}\right)^{15} \, dx","Int[(a + b*x^(1/3))^15,x]","\frac{3 a^2 \left(a+b \sqrt[3]{x}\right)^{16}}{16 b^3}+\frac{\left(a+b \sqrt[3]{x}\right)^{18}}{6 b^3}-\frac{6 a \left(a+b \sqrt[3]{x}\right)^{17}}{17 b^3}","\frac{3 a^2 \left(a+b \sqrt[3]{x}\right)^{16}}{16 b^3}+\frac{\left(a+b \sqrt[3]{x}\right)^{18}}{6 b^3}-\frac{6 a \left(a+b \sqrt[3]{x}\right)^{17}}{17 b^3}",1,"(3*a^2*(a + b*x^(1/3))^16)/(16*b^3) - (6*a*(a + b*x^(1/3))^17)/(17*b^3) + (a + b*x^(1/3))^18/(6*b^3)","A",3,2,11,0.1818,1,"{190, 43}"
2345,1,209,0,0.1052162,"\int \frac{\left(a+b \sqrt[3]{x}\right)^{15}}{x} \, dx","Int[(a + b*x^(1/3))^15/x,x]","\frac{315}{2} a^{13} b^2 x^{2/3}+\frac{4095}{4} a^{11} b^4 x^{4/3}+\frac{9009}{5} a^{10} b^5 x^{5/3}+\frac{5005}{2} a^9 b^6 x^2+\frac{19305}{7} a^8 b^7 x^{7/3}+\frac{19305}{8} a^7 b^8 x^{8/3}+\frac{5005}{3} a^6 b^9 x^3+\frac{9009}{10} a^5 b^{10} x^{10/3}+\frac{4095}{11} a^4 b^{11} x^{11/3}+\frac{455}{4} a^3 b^{12} x^4+\frac{315}{13} a^2 b^{13} x^{13/3}+455 a^{12} b^3 x+45 a^{14} b \sqrt[3]{x}+a^{15} \log (x)+\frac{45}{14} a b^{14} x^{14/3}+\frac{b^{15} x^5}{5}","\frac{315}{2} a^{13} b^2 x^{2/3}+\frac{4095}{4} a^{11} b^4 x^{4/3}+\frac{9009}{5} a^{10} b^5 x^{5/3}+\frac{5005}{2} a^9 b^6 x^2+\frac{19305}{7} a^8 b^7 x^{7/3}+\frac{19305}{8} a^7 b^8 x^{8/3}+\frac{5005}{3} a^6 b^9 x^3+\frac{9009}{10} a^5 b^{10} x^{10/3}+\frac{4095}{11} a^4 b^{11} x^{11/3}+\frac{455}{4} a^3 b^{12} x^4+\frac{315}{13} a^2 b^{13} x^{13/3}+455 a^{12} b^3 x+45 a^{14} b \sqrt[3]{x}+a^{15} \log (x)+\frac{45}{14} a b^{14} x^{14/3}+\frac{b^{15} x^5}{5}",1,"45*a^14*b*x^(1/3) + (315*a^13*b^2*x^(2/3))/2 + 455*a^12*b^3*x + (4095*a^11*b^4*x^(4/3))/4 + (9009*a^10*b^5*x^(5/3))/5 + (5005*a^9*b^6*x^2)/2 + (19305*a^8*b^7*x^(7/3))/7 + (19305*a^7*b^8*x^(8/3))/8 + (5005*a^6*b^9*x^3)/3 + (9009*a^5*b^10*x^(10/3))/10 + (4095*a^4*b^11*x^(11/3))/11 + (455*a^3*b^12*x^4)/4 + (315*a^2*b^13*x^(13/3))/13 + (45*a*b^14*x^(14/3))/14 + (b^15*x^5)/5 + a^15*Log[x]","A",3,2,15,0.1333,1,"{266, 43}"
2346,1,202,0,0.1180233,"\int \frac{\left(a+b \sqrt[3]{x}\right)^{15}}{x^2} \, dx","Int[(a + b*x^(1/3))^15/x^2,x]","\frac{9009}{2} a^{10} b^5 x^{2/3}+\frac{19305}{4} a^8 b^7 x^{4/3}+3861 a^7 b^8 x^{5/3}+\frac{5005}{2} a^6 b^9 x^2+1287 a^5 b^{10} x^{7/3}+\frac{4095}{8} a^4 b^{11} x^{8/3}+\frac{455}{3} a^3 b^{12} x^3+\frac{63}{2} a^2 b^{13} x^{10/3}-\frac{315 a^{13} b^2}{\sqrt[3]{x}}+4095 a^{11} b^4 \sqrt[3]{x}+5005 a^9 b^6 x+455 a^{12} b^3 \log (x)-\frac{45 a^{14} b}{2 x^{2/3}}-\frac{a^{15}}{x}+\frac{45}{11} a b^{14} x^{11/3}+\frac{b^{15} x^4}{4}","\frac{9009}{2} a^{10} b^5 x^{2/3}+\frac{19305}{4} a^8 b^7 x^{4/3}+3861 a^7 b^8 x^{5/3}+\frac{5005}{2} a^6 b^9 x^2+1287 a^5 b^{10} x^{7/3}+\frac{4095}{8} a^4 b^{11} x^{8/3}+\frac{455}{3} a^3 b^{12} x^3+\frac{63}{2} a^2 b^{13} x^{10/3}-\frac{315 a^{13} b^2}{\sqrt[3]{x}}+4095 a^{11} b^4 \sqrt[3]{x}+5005 a^9 b^6 x+455 a^{12} b^3 \log (x)-\frac{45 a^{14} b}{2 x^{2/3}}-\frac{a^{15}}{x}+\frac{45}{11} a b^{14} x^{11/3}+\frac{b^{15} x^4}{4}",1,"-(a^15/x) - (45*a^14*b)/(2*x^(2/3)) - (315*a^13*b^2)/x^(1/3) + 4095*a^11*b^4*x^(1/3) + (9009*a^10*b^5*x^(2/3))/2 + 5005*a^9*b^6*x + (19305*a^8*b^7*x^(4/3))/4 + 3861*a^7*b^8*x^(5/3) + (5005*a^6*b^9*x^2)/2 + 1287*a^5*b^10*x^(7/3) + (4095*a^4*b^11*x^(8/3))/8 + (455*a^3*b^12*x^3)/3 + (63*a^2*b^13*x^(10/3))/2 + (45*a*b^14*x^(11/3))/11 + (b^15*x^4)/4 + 455*a^12*b^3*Log[x]","A",3,2,15,0.1333,1,"{266, 43}"
2347,1,200,0,0.1156211,"\int \frac{\left(a+b \sqrt[3]{x}\right)^{15}}{x^3} \, dx","Int[(a + b*x^(1/3))^15/x^3,x]","-\frac{315 a^{13} b^2}{4 x^{4/3}}-\frac{4095 a^{11} b^4}{2 x^{2/3}}+\frac{19305}{2} a^7 b^8 x^{2/3}+\frac{9009}{4} a^5 b^{10} x^{4/3}+819 a^4 b^{11} x^{5/3}+\frac{455}{2} a^3 b^{12} x^2+45 a^2 b^{13} x^{7/3}-\frac{455 a^{12} b^3}{x}-\frac{9009 a^{10} b^5}{\sqrt[3]{x}}+19305 a^8 b^7 \sqrt[3]{x}+5005 a^6 b^9 x+5005 a^9 b^6 \log (x)-\frac{9 a^{14} b}{x^{5/3}}-\frac{a^{15}}{2 x^2}+\frac{45}{8} a b^{14} x^{8/3}+\frac{b^{15} x^3}{3}","-\frac{315 a^{13} b^2}{4 x^{4/3}}-\frac{4095 a^{11} b^4}{2 x^{2/3}}+\frac{19305}{2} a^7 b^8 x^{2/3}+\frac{9009}{4} a^5 b^{10} x^{4/3}+819 a^4 b^{11} x^{5/3}+\frac{455}{2} a^3 b^{12} x^2+45 a^2 b^{13} x^{7/3}-\frac{455 a^{12} b^3}{x}-\frac{9009 a^{10} b^5}{\sqrt[3]{x}}+19305 a^8 b^7 \sqrt[3]{x}+5005 a^6 b^9 x+5005 a^9 b^6 \log (x)-\frac{9 a^{14} b}{x^{5/3}}-\frac{a^{15}}{2 x^2}+\frac{45}{8} a b^{14} x^{8/3}+\frac{b^{15} x^3}{3}",1,"-a^15/(2*x^2) - (9*a^14*b)/x^(5/3) - (315*a^13*b^2)/(4*x^(4/3)) - (455*a^12*b^3)/x - (4095*a^11*b^4)/(2*x^(2/3)) - (9009*a^10*b^5)/x^(1/3) + 19305*a^8*b^7*x^(1/3) + (19305*a^7*b^8*x^(2/3))/2 + 5005*a^6*b^9*x + (9009*a^5*b^10*x^(4/3))/4 + 819*a^4*b^11*x^(5/3) + (455*a^3*b^12*x^2)/2 + 45*a^2*b^13*x^(7/3) + (45*a*b^14*x^(8/3))/8 + (b^15*x^3)/3 + 5005*a^9*b^6*Log[x]","A",3,2,15,0.1333,1,"{266, 43}"
2348,1,200,0,0.1216911,"\int \frac{\left(a+b \sqrt[3]{x}\right)^{15}}{x^4} \, dx","Int[(a + b*x^(1/3))^15/x^4,x]","-\frac{45 a^{13} b^2}{x^{7/3}}-\frac{455 a^{12} b^3}{2 x^2}-\frac{819 a^{11} b^4}{x^{5/3}}-\frac{9009 a^{10} b^5}{4 x^{4/3}}-\frac{19305 a^8 b^7}{2 x^{2/3}}+\frac{4095}{2} a^4 b^{11} x^{2/3}+\frac{315}{4} a^2 b^{13} x^{4/3}-\frac{5005 a^9 b^6}{x}-\frac{19305 a^7 b^8}{\sqrt[3]{x}}+9009 a^5 b^{10} \sqrt[3]{x}+455 a^3 b^{12} x+5005 a^6 b^9 \log (x)-\frac{45 a^{14} b}{8 x^{8/3}}-\frac{a^{15}}{3 x^3}+9 a b^{14} x^{5/3}+\frac{b^{15} x^2}{2}","-\frac{45 a^{13} b^2}{x^{7/3}}-\frac{455 a^{12} b^3}{2 x^2}-\frac{819 a^{11} b^4}{x^{5/3}}-\frac{9009 a^{10} b^5}{4 x^{4/3}}-\frac{19305 a^8 b^7}{2 x^{2/3}}+\frac{4095}{2} a^4 b^{11} x^{2/3}+\frac{315}{4} a^2 b^{13} x^{4/3}-\frac{5005 a^9 b^6}{x}-\frac{19305 a^7 b^8}{\sqrt[3]{x}}+9009 a^5 b^{10} \sqrt[3]{x}+455 a^3 b^{12} x+5005 a^6 b^9 \log (x)-\frac{45 a^{14} b}{8 x^{8/3}}-\frac{a^{15}}{3 x^3}+9 a b^{14} x^{5/3}+\frac{b^{15} x^2}{2}",1,"-a^15/(3*x^3) - (45*a^14*b)/(8*x^(8/3)) - (45*a^13*b^2)/x^(7/3) - (455*a^12*b^3)/(2*x^2) - (819*a^11*b^4)/x^(5/3) - (9009*a^10*b^5)/(4*x^(4/3)) - (5005*a^9*b^6)/x - (19305*a^8*b^7)/(2*x^(2/3)) - (19305*a^7*b^8)/x^(1/3) + 9009*a^5*b^10*x^(1/3) + (4095*a^4*b^11*x^(2/3))/2 + 455*a^3*b^12*x + (315*a^2*b^13*x^(4/3))/4 + 9*a*b^14*x^(5/3) + (b^15*x^2)/2 + 5005*a^6*b^9*Log[x]","A",3,2,15,0.1333,1,"{266, 43}"
2349,1,211,0,0.116477,"\int \frac{\left(a+b \sqrt[3]{x}\right)^{15}}{x^6} \, dx","Int[(a + b*x^(1/3))^15/x^6,x]","-\frac{315 a^{13} b^2}{13 x^{13/3}}-\frac{455 a^{12} b^3}{4 x^4}-\frac{4095 a^{11} b^4}{11 x^{11/3}}-\frac{9009 a^{10} b^5}{10 x^{10/3}}-\frac{5005 a^9 b^6}{3 x^3}-\frac{19305 a^8 b^7}{8 x^{8/3}}-\frac{19305 a^7 b^8}{7 x^{7/3}}-\frac{5005 a^6 b^9}{2 x^2}-\frac{9009 a^5 b^{10}}{5 x^{5/3}}-\frac{4095 a^4 b^{11}}{4 x^{4/3}}-\frac{315 a^2 b^{13}}{2 x^{2/3}}-\frac{455 a^3 b^{12}}{x}-\frac{45 a^{14} b}{14 x^{14/3}}-\frac{a^{15}}{5 x^5}-\frac{45 a b^{14}}{\sqrt[3]{x}}+b^{15} \log (x)","-\frac{315 a^{13} b^2}{13 x^{13/3}}-\frac{455 a^{12} b^3}{4 x^4}-\frac{4095 a^{11} b^4}{11 x^{11/3}}-\frac{9009 a^{10} b^5}{10 x^{10/3}}-\frac{5005 a^9 b^6}{3 x^3}-\frac{19305 a^8 b^7}{8 x^{8/3}}-\frac{19305 a^7 b^8}{7 x^{7/3}}-\frac{5005 a^6 b^9}{2 x^2}-\frac{9009 a^5 b^{10}}{5 x^{5/3}}-\frac{4095 a^4 b^{11}}{4 x^{4/3}}-\frac{315 a^2 b^{13}}{2 x^{2/3}}-\frac{455 a^3 b^{12}}{x}-\frac{45 a^{14} b}{14 x^{14/3}}-\frac{a^{15}}{5 x^5}-\frac{45 a b^{14}}{\sqrt[3]{x}}+b^{15} \log (x)",1,"-a^15/(5*x^5) - (45*a^14*b)/(14*x^(14/3)) - (315*a^13*b^2)/(13*x^(13/3)) - (455*a^12*b^3)/(4*x^4) - (4095*a^11*b^4)/(11*x^(11/3)) - (9009*a^10*b^5)/(10*x^(10/3)) - (5005*a^9*b^6)/(3*x^3) - (19305*a^8*b^7)/(8*x^(8/3)) - (19305*a^7*b^8)/(7*x^(7/3)) - (5005*a^6*b^9)/(2*x^2) - (9009*a^5*b^10)/(5*x^(5/3)) - (4095*a^4*b^11)/(4*x^(4/3)) - (455*a^3*b^12)/x - (315*a^2*b^13)/(2*x^(2/3)) - (45*a*b^14)/x^(1/3) + b^15*Log[x]","A",3,2,15,0.1333,1,"{266, 43}"
2350,1,72,0,0.0232657,"\int \frac{\left(a+b \sqrt[3]{x}\right)^{15}}{x^7} \, dx","Int[(a + b*x^(1/3))^15/x^7,x]","-\frac{b^2 \left(a+b \sqrt[3]{x}\right)^{16}}{816 a^3 x^{16/3}}+\frac{b \left(a+b \sqrt[3]{x}\right)^{16}}{51 a^2 x^{17/3}}-\frac{\left(a+b \sqrt[3]{x}\right)^{16}}{6 a x^6}","-\frac{b^2 \left(a+b \sqrt[3]{x}\right)^{16}}{816 a^3 x^{16/3}}+\frac{b \left(a+b \sqrt[3]{x}\right)^{16}}{51 a^2 x^{17/3}}-\frac{\left(a+b \sqrt[3]{x}\right)^{16}}{6 a x^6}",1,"-(a + b*x^(1/3))^16/(6*a*x^6) + (b*(a + b*x^(1/3))^16)/(51*a^2*x^(17/3)) - (b^2*(a + b*x^(1/3))^16)/(816*a^3*x^(16/3))","A",4,3,15,0.2000,1,"{266, 45, 37}"
2351,1,148,0,0.0610956,"\int \frac{\left(a+b \sqrt[3]{x}\right)^{15}}{x^8} \, dx","Int[(a + b*x^(1/3))^15/x^8,x]","\frac{b^5 \left(a+b \sqrt[3]{x}\right)^{16}}{108528 a^6 x^{16/3}}-\frac{b^4 \left(a+b \sqrt[3]{x}\right)^{16}}{6783 a^5 x^{17/3}}+\frac{b^3 \left(a+b \sqrt[3]{x}\right)^{16}}{798 a^4 x^6}-\frac{b^2 \left(a+b \sqrt[3]{x}\right)^{16}}{133 a^3 x^{19/3}}+\frac{b \left(a+b \sqrt[3]{x}\right)^{16}}{28 a^2 x^{20/3}}-\frac{\left(a+b \sqrt[3]{x}\right)^{16}}{7 a x^7}","\frac{b^5 \left(a+b \sqrt[3]{x}\right)^{16}}{108528 a^6 x^{16/3}}-\frac{b^4 \left(a+b \sqrt[3]{x}\right)^{16}}{6783 a^5 x^{17/3}}+\frac{b^3 \left(a+b \sqrt[3]{x}\right)^{16}}{798 a^4 x^6}-\frac{b^2 \left(a+b \sqrt[3]{x}\right)^{16}}{133 a^3 x^{19/3}}+\frac{b \left(a+b \sqrt[3]{x}\right)^{16}}{28 a^2 x^{20/3}}-\frac{\left(a+b \sqrt[3]{x}\right)^{16}}{7 a x^7}",1,"-(a + b*x^(1/3))^16/(7*a*x^7) + (b*(a + b*x^(1/3))^16)/(28*a^2*x^(20/3)) - (b^2*(a + b*x^(1/3))^16)/(133*a^3*x^(19/3)) + (b^3*(a + b*x^(1/3))^16)/(798*a^4*x^6) - (b^4*(a + b*x^(1/3))^16)/(6783*a^5*x^(17/3)) + (b^5*(a + b*x^(1/3))^16)/(108528*a^6*x^(16/3))","A",7,3,15,0.2000,1,"{266, 45, 37}"
2352,1,224,0,0.1105311,"\int \frac{\left(a+b \sqrt[3]{x}\right)^{15}}{x^9} \, dx","Int[(a + b*x^(1/3))^15/x^9,x]","-\frac{b^8 \left(a+b \sqrt[3]{x}\right)^{16}}{3922512 a^9 x^{16/3}}+\frac{b^7 \left(a+b \sqrt[3]{x}\right)^{16}}{245157 a^8 x^{17/3}}-\frac{b^6 \left(a+b \sqrt[3]{x}\right)^{16}}{28842 a^7 x^6}+\frac{b^5 \left(a+b \sqrt[3]{x}\right)^{16}}{4807 a^6 x^{19/3}}-\frac{b^4 \left(a+b \sqrt[3]{x}\right)^{16}}{1012 a^5 x^{20/3}}+\frac{b^3 \left(a+b \sqrt[3]{x}\right)^{16}}{253 a^4 x^7}-\frac{7 b^2 \left(a+b \sqrt[3]{x}\right)^{16}}{506 a^3 x^{22/3}}+\frac{b \left(a+b \sqrt[3]{x}\right)^{16}}{23 a^2 x^{23/3}}-\frac{\left(a+b \sqrt[3]{x}\right)^{16}}{8 a x^8}","-\frac{b^8 \left(a+b \sqrt[3]{x}\right)^{16}}{3922512 a^9 x^{16/3}}+\frac{b^7 \left(a+b \sqrt[3]{x}\right)^{16}}{245157 a^8 x^{17/3}}-\frac{b^6 \left(a+b \sqrt[3]{x}\right)^{16}}{28842 a^7 x^6}+\frac{b^5 \left(a+b \sqrt[3]{x}\right)^{16}}{4807 a^6 x^{19/3}}-\frac{b^4 \left(a+b \sqrt[3]{x}\right)^{16}}{1012 a^5 x^{20/3}}+\frac{b^3 \left(a+b \sqrt[3]{x}\right)^{16}}{253 a^4 x^7}-\frac{7 b^2 \left(a+b \sqrt[3]{x}\right)^{16}}{506 a^3 x^{22/3}}+\frac{b \left(a+b \sqrt[3]{x}\right)^{16}}{23 a^2 x^{23/3}}-\frac{\left(a+b \sqrt[3]{x}\right)^{16}}{8 a x^8}",1,"-(a + b*x^(1/3))^16/(8*a*x^8) + (b*(a + b*x^(1/3))^16)/(23*a^2*x^(23/3)) - (7*b^2*(a + b*x^(1/3))^16)/(506*a^3*x^(22/3)) + (b^3*(a + b*x^(1/3))^16)/(253*a^4*x^7) - (b^4*(a + b*x^(1/3))^16)/(1012*a^5*x^(20/3)) + (b^5*(a + b*x^(1/3))^16)/(4807*a^6*x^(19/3)) - (b^6*(a + b*x^(1/3))^16)/(28842*a^7*x^6) + (b^7*(a + b*x^(1/3))^16)/(245157*a^8*x^(17/3)) - (b^8*(a + b*x^(1/3))^16)/(3922512*a^9*x^(16/3))","A",10,3,15,0.2000,1,"{266, 45, 37}"
2353,1,215,0,0.1126838,"\int \frac{\left(a+b \sqrt[3]{x}\right)^{15}}{x^{10}} \, dx","Int[(a + b*x^(1/3))^15/x^10,x]","-\frac{63 a^{13} b^2}{5 x^{25/3}}-\frac{455 a^{12} b^3}{8 x^8}-\frac{4095 a^{11} b^4}{23 x^{23/3}}-\frac{819 a^{10} b^5}{2 x^{22/3}}-\frac{715 a^9 b^6}{x^7}-\frac{3861 a^8 b^7}{4 x^{20/3}}-\frac{19305 a^7 b^8}{19 x^{19/3}}-\frac{5005 a^6 b^9}{6 x^6}-\frac{9009 a^5 b^{10}}{17 x^{17/3}}-\frac{4095 a^4 b^{11}}{16 x^{16/3}}-\frac{91 a^3 b^{12}}{x^5}-\frac{45 a^2 b^{13}}{2 x^{14/3}}-\frac{45 a^{14} b}{26 x^{26/3}}-\frac{a^{15}}{9 x^9}-\frac{45 a b^{14}}{13 x^{13/3}}-\frac{b^{15}}{4 x^4}","-\frac{63 a^{13} b^2}{5 x^{25/3}}-\frac{455 a^{12} b^3}{8 x^8}-\frac{4095 a^{11} b^4}{23 x^{23/3}}-\frac{819 a^{10} b^5}{2 x^{22/3}}-\frac{715 a^9 b^6}{x^7}-\frac{3861 a^8 b^7}{4 x^{20/3}}-\frac{19305 a^7 b^8}{19 x^{19/3}}-\frac{5005 a^6 b^9}{6 x^6}-\frac{9009 a^5 b^{10}}{17 x^{17/3}}-\frac{4095 a^4 b^{11}}{16 x^{16/3}}-\frac{91 a^3 b^{12}}{x^5}-\frac{45 a^2 b^{13}}{2 x^{14/3}}-\frac{45 a^{14} b}{26 x^{26/3}}-\frac{a^{15}}{9 x^9}-\frac{45 a b^{14}}{13 x^{13/3}}-\frac{b^{15}}{4 x^4}",1,"-a^15/(9*x^9) - (45*a^14*b)/(26*x^(26/3)) - (63*a^13*b^2)/(5*x^(25/3)) - (455*a^12*b^3)/(8*x^8) - (4095*a^11*b^4)/(23*x^(23/3)) - (819*a^10*b^5)/(2*x^(22/3)) - (715*a^9*b^6)/x^7 - (3861*a^8*b^7)/(4*x^(20/3)) - (19305*a^7*b^8)/(19*x^(19/3)) - (5005*a^6*b^9)/(6*x^6) - (9009*a^5*b^10)/(17*x^(17/3)) - (4095*a^4*b^11)/(16*x^(16/3)) - (91*a^3*b^12)/x^5 - (45*a^2*b^13)/(2*x^(14/3)) - (45*a*b^14)/(13*x^(13/3)) - b^15/(4*x^4)","A",3,2,15,0.1333,1,"{266, 43}"
2354,1,217,0,0.11242,"\int \frac{\left(a+b \sqrt[3]{x}\right)^{15}}{x^{11}} \, dx","Int[(a + b*x^(1/3))^15/x^11,x]","-\frac{45 a^{13} b^2}{4 x^{28/3}}-\frac{455 a^{12} b^3}{9 x^9}-\frac{315 a^{11} b^4}{2 x^{26/3}}-\frac{9009 a^{10} b^5}{25 x^{25/3}}-\frac{5005 a^9 b^6}{8 x^8}-\frac{19305 a^8 b^7}{23 x^{23/3}}-\frac{1755 a^7 b^8}{2 x^{22/3}}-\frac{715 a^6 b^9}{x^7}-\frac{9009 a^5 b^{10}}{20 x^{20/3}}-\frac{4095 a^4 b^{11}}{19 x^{19/3}}-\frac{455 a^3 b^{12}}{6 x^6}-\frac{315 a^2 b^{13}}{17 x^{17/3}}-\frac{45 a^{14} b}{29 x^{29/3}}-\frac{a^{15}}{10 x^{10}}-\frac{45 a b^{14}}{16 x^{16/3}}-\frac{b^{15}}{5 x^5}","-\frac{45 a^{13} b^2}{4 x^{28/3}}-\frac{455 a^{12} b^3}{9 x^9}-\frac{315 a^{11} b^4}{2 x^{26/3}}-\frac{9009 a^{10} b^5}{25 x^{25/3}}-\frac{5005 a^9 b^6}{8 x^8}-\frac{19305 a^8 b^7}{23 x^{23/3}}-\frac{1755 a^7 b^8}{2 x^{22/3}}-\frac{715 a^6 b^9}{x^7}-\frac{9009 a^5 b^{10}}{20 x^{20/3}}-\frac{4095 a^4 b^{11}}{19 x^{19/3}}-\frac{455 a^3 b^{12}}{6 x^6}-\frac{315 a^2 b^{13}}{17 x^{17/3}}-\frac{45 a^{14} b}{29 x^{29/3}}-\frac{a^{15}}{10 x^{10}}-\frac{45 a b^{14}}{16 x^{16/3}}-\frac{b^{15}}{5 x^5}",1,"-a^15/(10*x^10) - (45*a^14*b)/(29*x^(29/3)) - (45*a^13*b^2)/(4*x^(28/3)) - (455*a^12*b^3)/(9*x^9) - (315*a^11*b^4)/(2*x^(26/3)) - (9009*a^10*b^5)/(25*x^(25/3)) - (5005*a^9*b^6)/(8*x^8) - (19305*a^8*b^7)/(23*x^(23/3)) - (1755*a^7*b^8)/(2*x^(22/3)) - (715*a^6*b^9)/x^7 - (9009*a^5*b^10)/(20*x^(20/3)) - (4095*a^4*b^11)/(19*x^(19/3)) - (455*a^3*b^12)/(6*x^6) - (315*a^2*b^13)/(17*x^(17/3)) - (45*a*b^14)/(16*x^(16/3)) - b^15/(5*x^5)","A",3,2,15,0.1333,1,"{266, 43}"
2355,1,217,0,0.1180267,"\int \frac{\left(a+b \sqrt[3]{x}\right)^{15}}{x^{12}} \, dx","Int[(a + b*x^(1/3))^15/x^12,x]","-\frac{315 a^{13} b^2}{31 x^{31/3}}-\frac{91 a^{12} b^3}{2 x^{10}}-\frac{4095 a^{11} b^4}{29 x^{29/3}}-\frac{1287 a^{10} b^5}{4 x^{28/3}}-\frac{5005 a^9 b^6}{9 x^9}-\frac{1485 a^8 b^7}{2 x^{26/3}}-\frac{3861 a^7 b^8}{5 x^{25/3}}-\frac{5005 a^6 b^9}{8 x^8}-\frac{9009 a^5 b^{10}}{23 x^{23/3}}-\frac{4095 a^4 b^{11}}{22 x^{22/3}}-\frac{65 a^3 b^{12}}{x^7}-\frac{63 a^2 b^{13}}{4 x^{20/3}}-\frac{45 a^{14} b}{32 x^{32/3}}-\frac{a^{15}}{11 x^{11}}-\frac{45 a b^{14}}{19 x^{19/3}}-\frac{b^{15}}{6 x^6}","-\frac{315 a^{13} b^2}{31 x^{31/3}}-\frac{91 a^{12} b^3}{2 x^{10}}-\frac{4095 a^{11} b^4}{29 x^{29/3}}-\frac{1287 a^{10} b^5}{4 x^{28/3}}-\frac{5005 a^9 b^6}{9 x^9}-\frac{1485 a^8 b^7}{2 x^{26/3}}-\frac{3861 a^7 b^8}{5 x^{25/3}}-\frac{5005 a^6 b^9}{8 x^8}-\frac{9009 a^5 b^{10}}{23 x^{23/3}}-\frac{4095 a^4 b^{11}}{22 x^{22/3}}-\frac{65 a^3 b^{12}}{x^7}-\frac{63 a^2 b^{13}}{4 x^{20/3}}-\frac{45 a^{14} b}{32 x^{32/3}}-\frac{a^{15}}{11 x^{11}}-\frac{45 a b^{14}}{19 x^{19/3}}-\frac{b^{15}}{6 x^6}",1,"-a^15/(11*x^11) - (45*a^14*b)/(32*x^(32/3)) - (315*a^13*b^2)/(31*x^(31/3)) - (91*a^12*b^3)/(2*x^10) - (4095*a^11*b^4)/(29*x^(29/3)) - (1287*a^10*b^5)/(4*x^(28/3)) - (5005*a^9*b^6)/(9*x^9) - (1485*a^8*b^7)/(2*x^(26/3)) - (3861*a^7*b^8)/(5*x^(25/3)) - (5005*a^6*b^9)/(8*x^8) - (9009*a^5*b^10)/(23*x^(23/3)) - (4095*a^4*b^11)/(22*x^(22/3)) - (65*a^3*b^12)/x^7 - (63*a^2*b^13)/(4*x^(20/3)) - (45*a*b^14)/(19*x^(19/3)) - b^15/(6*x^6)","A",3,2,15,0.1333,1,"{266, 43}"
2356,1,166,0,0.1088254,"\int \frac{x^3}{a+b \sqrt[3]{x}} \, dx","Int[x^3/(a + b*x^(1/3)),x]","-\frac{3 a^9 x^{2/3}}{2 b^{10}}-\frac{3 a^7 x^{4/3}}{4 b^8}+\frac{3 a^6 x^{5/3}}{5 b^7}-\frac{a^5 x^2}{2 b^6}+\frac{3 a^4 x^{7/3}}{7 b^5}-\frac{3 a^3 x^{8/3}}{8 b^4}+\frac{a^2 x^3}{3 b^3}+\frac{3 a^{10} \sqrt[3]{x}}{b^{11}}+\frac{a^8 x}{b^9}-\frac{3 a^{11} \log \left(a+b \sqrt[3]{x}\right)}{b^{12}}-\frac{3 a x^{10/3}}{10 b^2}+\frac{3 x^{11/3}}{11 b}","-\frac{3 a^9 x^{2/3}}{2 b^{10}}-\frac{3 a^7 x^{4/3}}{4 b^8}+\frac{3 a^6 x^{5/3}}{5 b^7}-\frac{a^5 x^2}{2 b^6}+\frac{3 a^4 x^{7/3}}{7 b^5}-\frac{3 a^3 x^{8/3}}{8 b^4}+\frac{a^2 x^3}{3 b^3}+\frac{3 a^{10} \sqrt[3]{x}}{b^{11}}+\frac{a^8 x}{b^9}-\frac{3 a^{11} \log \left(a+b \sqrt[3]{x}\right)}{b^{12}}-\frac{3 a x^{10/3}}{10 b^2}+\frac{3 x^{11/3}}{11 b}",1,"(3*a^10*x^(1/3))/b^11 - (3*a^9*x^(2/3))/(2*b^10) + (a^8*x)/b^9 - (3*a^7*x^(4/3))/(4*b^8) + (3*a^6*x^(5/3))/(5*b^7) - (a^5*x^2)/(2*b^6) + (3*a^4*x^(7/3))/(7*b^5) - (3*a^3*x^(8/3))/(8*b^4) + (a^2*x^3)/(3*b^3) - (3*a*x^(10/3))/(10*b^2) + (3*x^(11/3))/(11*b) - (3*a^11*Log[a + b*x^(1/3)])/b^12","A",3,2,15,0.1333,1,"{266, 43}"
2357,1,124,0,0.0704568,"\int \frac{x^2}{a+b \sqrt[3]{x}} \, dx","Int[x^2/(a + b*x^(1/3)),x]","\frac{3 a^6 x^{2/3}}{2 b^7}+\frac{3 a^4 x^{4/3}}{4 b^5}-\frac{3 a^3 x^{5/3}}{5 b^4}+\frac{a^2 x^2}{2 b^3}-\frac{3 a^7 \sqrt[3]{x}}{b^8}-\frac{a^5 x}{b^6}+\frac{3 a^8 \log \left(a+b \sqrt[3]{x}\right)}{b^9}-\frac{3 a x^{7/3}}{7 b^2}+\frac{3 x^{8/3}}{8 b}","\frac{3 a^6 x^{2/3}}{2 b^7}+\frac{3 a^4 x^{4/3}}{4 b^5}-\frac{3 a^3 x^{5/3}}{5 b^4}+\frac{a^2 x^2}{2 b^3}-\frac{3 a^7 \sqrt[3]{x}}{b^8}-\frac{a^5 x}{b^6}+\frac{3 a^8 \log \left(a+b \sqrt[3]{x}\right)}{b^9}-\frac{3 a x^{7/3}}{7 b^2}+\frac{3 x^{8/3}}{8 b}",1,"(-3*a^7*x^(1/3))/b^8 + (3*a^6*x^(2/3))/(2*b^7) - (a^5*x)/b^6 + (3*a^4*x^(4/3))/(4*b^5) - (3*a^3*x^(5/3))/(5*b^4) + (a^2*x^2)/(2*b^3) - (3*a*x^(7/3))/(7*b^2) + (3*x^(8/3))/(8*b) + (3*a^8*Log[a + b*x^(1/3)])/b^9","A",3,2,15,0.1333,1,"{266, 43}"
2358,1,80,0,0.0460705,"\int \frac{x}{a+b \sqrt[3]{x}} \, dx","Int[x/(a + b*x^(1/3)),x]","-\frac{3 a^3 x^{2/3}}{2 b^4}+\frac{3 a^4 \sqrt[3]{x}}{b^5}+\frac{a^2 x}{b^3}-\frac{3 a^5 \log \left(a+b \sqrt[3]{x}\right)}{b^6}-\frac{3 a x^{4/3}}{4 b^2}+\frac{3 x^{5/3}}{5 b}","-\frac{3 a^3 x^{2/3}}{2 b^4}+\frac{3 a^4 \sqrt[3]{x}}{b^5}+\frac{a^2 x}{b^3}-\frac{3 a^5 \log \left(a+b \sqrt[3]{x}\right)}{b^6}-\frac{3 a x^{4/3}}{4 b^2}+\frac{3 x^{5/3}}{5 b}",1,"(3*a^4*x^(1/3))/b^5 - (3*a^3*x^(2/3))/(2*b^4) + (a^2*x)/b^3 - (3*a*x^(4/3))/(4*b^2) + (3*x^(5/3))/(5*b) - (3*a^5*Log[a + b*x^(1/3)])/b^6","A",3,2,13,0.1538,1,"{266, 43}"
2359,1,42,0,0.021423,"\int \frac{1}{a+b \sqrt[3]{x}} \, dx","Int[(a + b*x^(1/3))^(-1),x]","\frac{3 a^2 \log \left(a+b \sqrt[3]{x}\right)}{b^3}-\frac{3 a \sqrt[3]{x}}{b^2}+\frac{3 x^{2/3}}{2 b}","\frac{3 a^2 \log \left(a+b \sqrt[3]{x}\right)}{b^3}-\frac{3 a \sqrt[3]{x}}{b^2}+\frac{3 x^{2/3}}{2 b}",1,"(-3*a*x^(1/3))/b^2 + (3*x^(2/3))/(2*b) + (3*a^2*Log[a + b*x^(1/3)])/b^3","A",3,2,11,0.1818,1,"{190, 43}"
2360,1,22,0,0.0092022,"\int \frac{1}{\left(a+b \sqrt[3]{x}\right) x} \, dx","Int[1/((a + b*x^(1/3))*x),x]","\frac{\log (x)}{a}-\frac{3 \log \left(a+b \sqrt[3]{x}\right)}{a}","\frac{\log (x)}{a}-\frac{3 \log \left(a+b \sqrt[3]{x}\right)}{a}",1,"(-3*Log[a + b*x^(1/3)])/a + Log[x]/a","A",4,4,15,0.2667,1,"{266, 36, 29, 31}"
2361,1,63,0,0.0344333,"\int \frac{1}{\left(a+b \sqrt[3]{x}\right) x^2} \, dx","Int[1/((a + b*x^(1/3))*x^2),x]","-\frac{3 b^2}{a^3 \sqrt[3]{x}}+\frac{3 b^3 \log \left(a+b \sqrt[3]{x}\right)}{a^4}-\frac{b^3 \log (x)}{a^4}+\frac{3 b}{2 a^2 x^{2/3}}-\frac{1}{a x}","-\frac{3 b^2}{a^3 \sqrt[3]{x}}+\frac{3 b^3 \log \left(a+b \sqrt[3]{x}\right)}{a^4}-\frac{b^3 \log (x)}{a^4}+\frac{3 b}{2 a^2 x^{2/3}}-\frac{1}{a x}",1,"-(1/(a*x)) + (3*b)/(2*a^2*x^(2/3)) - (3*b^2)/(a^3*x^(1/3)) + (3*b^3*Log[a + b*x^(1/3)])/a^4 - (b^3*Log[x])/a^4","A",3,2,15,0.1333,1,"{266, 44}"
2362,1,104,0,0.0537924,"\int \frac{1}{\left(a+b \sqrt[3]{x}\right) x^3} \, dx","Int[1/((a + b*x^(1/3))*x^3),x]","-\frac{3 b^4}{2 a^5 x^{2/3}}-\frac{3 b^2}{4 a^3 x^{4/3}}+\frac{3 b^5}{a^6 \sqrt[3]{x}}+\frac{b^3}{a^4 x}-\frac{3 b^6 \log \left(a+b \sqrt[3]{x}\right)}{a^7}+\frac{b^6 \log (x)}{a^7}+\frac{3 b}{5 a^2 x^{5/3}}-\frac{1}{2 a x^2}","-\frac{3 b^4}{2 a^5 x^{2/3}}-\frac{3 b^2}{4 a^3 x^{4/3}}+\frac{3 b^5}{a^6 \sqrt[3]{x}}+\frac{b^3}{a^4 x}-\frac{3 b^6 \log \left(a+b \sqrt[3]{x}\right)}{a^7}+\frac{b^6 \log (x)}{a^7}+\frac{3 b}{5 a^2 x^{5/3}}-\frac{1}{2 a x^2}",1,"-1/(2*a*x^2) + (3*b)/(5*a^2*x^(5/3)) - (3*b^2)/(4*a^3*x^(4/3)) + b^3/(a^4*x) - (3*b^4)/(2*a^5*x^(2/3)) + (3*b^5)/(a^6*x^(1/3)) - (3*b^6*Log[a + b*x^(1/3)])/a^7 + (b^6*Log[x])/a^7","A",3,2,15,0.1333,1,"{266, 44}"
2363,1,149,0,0.0785077,"\int \frac{1}{\left(a+b \sqrt[3]{x}\right) x^4} \, dx","Int[1/((a + b*x^(1/3))*x^4),x]","\frac{3 b^7}{2 a^8 x^{2/3}}+\frac{3 b^5}{4 a^6 x^{4/3}}-\frac{3 b^4}{5 a^5 x^{5/3}}+\frac{b^3}{2 a^4 x^2}-\frac{3 b^2}{7 a^3 x^{7/3}}-\frac{3 b^8}{a^9 \sqrt[3]{x}}-\frac{b^6}{a^7 x}+\frac{3 b^9 \log \left(a+b \sqrt[3]{x}\right)}{a^{10}}-\frac{b^9 \log (x)}{a^{10}}+\frac{3 b}{8 a^2 x^{8/3}}-\frac{1}{3 a x^3}","\frac{3 b^7}{2 a^8 x^{2/3}}+\frac{3 b^5}{4 a^6 x^{4/3}}-\frac{3 b^4}{5 a^5 x^{5/3}}+\frac{b^3}{2 a^4 x^2}-\frac{3 b^2}{7 a^3 x^{7/3}}-\frac{3 b^8}{a^9 \sqrt[3]{x}}-\frac{b^6}{a^7 x}+\frac{3 b^9 \log \left(a+b \sqrt[3]{x}\right)}{a^{10}}-\frac{b^9 \log (x)}{a^{10}}+\frac{3 b}{8 a^2 x^{8/3}}-\frac{1}{3 a x^3}",1,"-1/(3*a*x^3) + (3*b)/(8*a^2*x^(8/3)) - (3*b^2)/(7*a^3*x^(7/3)) + b^3/(2*a^4*x^2) - (3*b^4)/(5*a^5*x^(5/3)) + (3*b^5)/(4*a^6*x^(4/3)) - b^6/(a^7*x) + (3*b^7)/(2*a^8*x^(2/3)) - (3*b^8)/(a^9*x^(1/3)) + (3*b^9*Log[a + b*x^(1/3)])/a^10 - (b^9*Log[x])/a^10","A",3,2,15,0.1333,1,"{266, 44}"
2364,1,21,0,0.0077708,"\int \frac{1}{\left(2+b \sqrt[3]{x}\right) x} \, dx","Int[1/((2 + b*x^(1/3))*x),x]","\frac{\log (x)}{2}-\frac{3}{2} \log \left(b \sqrt[3]{x}+2\right)","\frac{\log (x)}{2}-\frac{3}{2} \log \left(b \sqrt[3]{x}+2\right)",1,"(-3*Log[2 + b*x^(1/3)])/2 + Log[x]/2","A",4,4,15,0.2667,1,"{266, 36, 29, 31}"
2365,1,171,0,0.1350193,"\int \frac{x^3}{\left(a+b \sqrt[3]{x}\right)^2} \, dx","Int[x^3/(a + b*x^(1/3))^2,x]","\frac{27 a^8 x^{2/3}}{2 b^{10}}+\frac{21 a^6 x^{4/3}}{4 b^8}-\frac{18 a^5 x^{5/3}}{5 b^7}+\frac{5 a^4 x^2}{2 b^6}-\frac{12 a^3 x^{7/3}}{7 b^5}+\frac{9 a^2 x^{8/3}}{8 b^4}+\frac{3 a^{11}}{b^{12} \left(a+b \sqrt[3]{x}\right)}-\frac{30 a^9 \sqrt[3]{x}}{b^{11}}-\frac{8 a^7 x}{b^9}+\frac{33 a^{10} \log \left(a+b \sqrt[3]{x}\right)}{b^{12}}-\frac{2 a x^3}{3 b^3}+\frac{3 x^{10/3}}{10 b^2}","\frac{27 a^8 x^{2/3}}{2 b^{10}}+\frac{21 a^6 x^{4/3}}{4 b^8}-\frac{18 a^5 x^{5/3}}{5 b^7}+\frac{5 a^4 x^2}{2 b^6}-\frac{12 a^3 x^{7/3}}{7 b^5}+\frac{9 a^2 x^{8/3}}{8 b^4}+\frac{3 a^{11}}{b^{12} \left(a+b \sqrt[3]{x}\right)}-\frac{30 a^9 \sqrt[3]{x}}{b^{11}}-\frac{8 a^7 x}{b^9}+\frac{33 a^{10} \log \left(a+b \sqrt[3]{x}\right)}{b^{12}}-\frac{2 a x^3}{3 b^3}+\frac{3 x^{10/3}}{10 b^2}",1,"(3*a^11)/(b^12*(a + b*x^(1/3))) - (30*a^9*x^(1/3))/b^11 + (27*a^8*x^(2/3))/(2*b^10) - (8*a^7*x)/b^9 + (21*a^6*x^(4/3))/(4*b^8) - (18*a^5*x^(5/3))/(5*b^7) + (5*a^4*x^2)/(2*b^6) - (12*a^3*x^(7/3))/(7*b^5) + (9*a^2*x^(8/3))/(8*b^4) - (2*a*x^3)/(3*b^3) + (3*x^(10/3))/(10*b^2) + (33*a^10*Log[a + b*x^(1/3)])/b^12","A",3,2,15,0.1333,1,"{266, 43}"
2366,1,122,0,0.0885099,"\int \frac{x^2}{\left(a+b \sqrt[3]{x}\right)^2} \, dx","Int[x^2/(a + b*x^(1/3))^2,x]","-\frac{9 a^5 x^{2/3}}{b^7}-\frac{3 a^3 x^{4/3}}{b^5}+\frac{9 a^2 x^{5/3}}{5 b^4}-\frac{3 a^8}{b^9 \left(a+b \sqrt[3]{x}\right)}+\frac{21 a^6 \sqrt[3]{x}}{b^8}+\frac{5 a^4 x}{b^6}-\frac{24 a^7 \log \left(a+b \sqrt[3]{x}\right)}{b^9}-\frac{a x^2}{b^3}+\frac{3 x^{7/3}}{7 b^2}","-\frac{9 a^5 x^{2/3}}{b^7}-\frac{3 a^3 x^{4/3}}{b^5}+\frac{9 a^2 x^{5/3}}{5 b^4}-\frac{3 a^8}{b^9 \left(a+b \sqrt[3]{x}\right)}+\frac{21 a^6 \sqrt[3]{x}}{b^8}+\frac{5 a^4 x}{b^6}-\frac{24 a^7 \log \left(a+b \sqrt[3]{x}\right)}{b^9}-\frac{a x^2}{b^3}+\frac{3 x^{7/3}}{7 b^2}",1,"(-3*a^8)/(b^9*(a + b*x^(1/3))) + (21*a^6*x^(1/3))/b^8 - (9*a^5*x^(2/3))/b^7 + (5*a^4*x)/b^6 - (3*a^3*x^(4/3))/b^5 + (9*a^2*x^(5/3))/(5*b^4) - (a*x^2)/b^3 + (3*x^(7/3))/(7*b^2) - (24*a^7*Log[a + b*x^(1/3)])/b^9","A",3,2,15,0.1333,1,"{266, 43}"
2367,1,85,0,0.0554201,"\int \frac{x}{\left(a+b \sqrt[3]{x}\right)^2} \, dx","Int[x/(a + b*x^(1/3))^2,x]","\frac{9 a^2 x^{2/3}}{2 b^4}+\frac{3 a^5}{b^6 \left(a+b \sqrt[3]{x}\right)}-\frac{12 a^3 \sqrt[3]{x}}{b^5}+\frac{15 a^4 \log \left(a+b \sqrt[3]{x}\right)}{b^6}-\frac{2 a x}{b^3}+\frac{3 x^{4/3}}{4 b^2}","\frac{9 a^2 x^{2/3}}{2 b^4}+\frac{3 a^5}{b^6 \left(a+b \sqrt[3]{x}\right)}-\frac{12 a^3 \sqrt[3]{x}}{b^5}+\frac{15 a^4 \log \left(a+b \sqrt[3]{x}\right)}{b^6}-\frac{2 a x}{b^3}+\frac{3 x^{4/3}}{4 b^2}",1,"(3*a^5)/(b^6*(a + b*x^(1/3))) - (12*a^3*x^(1/3))/b^5 + (9*a^2*x^(2/3))/(2*b^4) - (2*a*x)/b^3 + (3*x^(4/3))/(4*b^2) + (15*a^4*Log[a + b*x^(1/3)])/b^6","A",3,2,13,0.1538,1,"{266, 43}"
2368,1,46,0,0.0259325,"\int \frac{1}{\left(a+b \sqrt[3]{x}\right)^2} \, dx","Int[(a + b*x^(1/3))^(-2),x]","-\frac{3 a^2}{b^3 \left(a+b \sqrt[3]{x}\right)}-\frac{6 a \log \left(a+b \sqrt[3]{x}\right)}{b^3}+\frac{3 \sqrt[3]{x}}{b^2}","-\frac{3 a^2}{b^3 \left(a+b \sqrt[3]{x}\right)}-\frac{6 a \log \left(a+b \sqrt[3]{x}\right)}{b^3}+\frac{3 \sqrt[3]{x}}{b^2}",1,"(-3*a^2)/(b^3*(a + b*x^(1/3))) + (3*x^(1/3))/b^2 - (6*a*Log[a + b*x^(1/3)])/b^3","A",3,2,11,0.1818,1,"{190, 43}"
2369,1,38,0,0.0220806,"\int \frac{1}{\left(a+b \sqrt[3]{x}\right)^2 x} \, dx","Int[1/((a + b*x^(1/3))^2*x),x]","-\frac{3 \log \left(a+b \sqrt[3]{x}\right)}{a^2}+\frac{\log (x)}{a^2}+\frac{3}{a \left(a+b \sqrt[3]{x}\right)}","-\frac{3 \log \left(a+b \sqrt[3]{x}\right)}{a^2}+\frac{\log (x)}{a^2}+\frac{3}{a \left(a+b \sqrt[3]{x}\right)}",1,"3/(a*(a + b*x^(1/3))) - (3*Log[a + b*x^(1/3)])/a^2 + Log[x]/a^2","A",3,2,15,0.1333,1,"{266, 44}"
2370,1,80,0,0.0508855,"\int \frac{1}{\left(a+b \sqrt[3]{x}\right)^2 x^2} \, dx","Int[1/((a + b*x^(1/3))^2*x^2),x]","-\frac{3 b^3}{a^4 \left(a+b \sqrt[3]{x}\right)}-\frac{9 b^2}{a^4 \sqrt[3]{x}}+\frac{12 b^3 \log \left(a+b \sqrt[3]{x}\right)}{a^5}-\frac{4 b^3 \log (x)}{a^5}+\frac{3 b}{a^3 x^{2/3}}-\frac{1}{a^2 x}","-\frac{3 b^3}{a^4 \left(a+b \sqrt[3]{x}\right)}-\frac{9 b^2}{a^4 \sqrt[3]{x}}+\frac{12 b^3 \log \left(a+b \sqrt[3]{x}\right)}{a^5}-\frac{4 b^3 \log (x)}{a^5}+\frac{3 b}{a^3 x^{2/3}}-\frac{1}{a^2 x}",1,"(-3*b^3)/(a^4*(a + b*x^(1/3))) - 1/(a^2*x) + (3*b)/(a^3*x^(2/3)) - (9*b^2)/(a^4*x^(1/3)) + (12*b^3*Log[a + b*x^(1/3)])/a^5 - (4*b^3*Log[x])/a^5","A",3,2,15,0.1333,1,"{266, 44}"
2371,1,125,0,0.0837684,"\int \frac{1}{\left(a+b \sqrt[3]{x}\right)^2 x^3} \, dx","Int[1/((a + b*x^(1/3))^2*x^3),x]","-\frac{15 b^4}{2 a^6 x^{2/3}}-\frac{9 b^2}{4 a^4 x^{4/3}}+\frac{3 b^6}{a^7 \left(a+b \sqrt[3]{x}\right)}+\frac{18 b^5}{a^7 \sqrt[3]{x}}+\frac{4 b^3}{a^5 x}-\frac{21 b^6 \log \left(a+b \sqrt[3]{x}\right)}{a^8}+\frac{7 b^6 \log (x)}{a^8}+\frac{6 b}{5 a^3 x^{5/3}}-\frac{1}{2 a^2 x^2}","-\frac{15 b^4}{2 a^6 x^{2/3}}-\frac{9 b^2}{4 a^4 x^{4/3}}+\frac{3 b^6}{a^7 \left(a+b \sqrt[3]{x}\right)}+\frac{18 b^5}{a^7 \sqrt[3]{x}}+\frac{4 b^3}{a^5 x}-\frac{21 b^6 \log \left(a+b \sqrt[3]{x}\right)}{a^8}+\frac{7 b^6 \log (x)}{a^8}+\frac{6 b}{5 a^3 x^{5/3}}-\frac{1}{2 a^2 x^2}",1,"(3*b^6)/(a^7*(a + b*x^(1/3))) - 1/(2*a^2*x^2) + (6*b)/(5*a^3*x^(5/3)) - (9*b^2)/(4*a^4*x^(4/3)) + (4*b^3)/(a^5*x) - (15*b^4)/(2*a^6*x^(2/3)) + (18*b^5)/(a^7*x^(1/3)) - (21*b^6*Log[a + b*x^(1/3)])/a^8 + (7*b^6*Log[x])/a^8","A",3,2,15,0.1333,1,"{266, 44}"
2372,1,162,0,0.1149861,"\int \frac{1}{\left(a+b \sqrt[3]{x}\right)^2 x^4} \, dx","Int[1/((a + b*x^(1/3))^2*x^4),x]","\frac{12 b^7}{a^9 x^{2/3}}+\frac{9 b^5}{2 a^7 x^{4/3}}-\frac{3 b^4}{a^6 x^{5/3}}+\frac{2 b^3}{a^5 x^2}-\frac{9 b^2}{7 a^4 x^{7/3}}-\frac{3 b^9}{a^{10} \left(a+b \sqrt[3]{x}\right)}-\frac{27 b^8}{a^{10} \sqrt[3]{x}}-\frac{7 b^6}{a^8 x}+\frac{30 b^9 \log \left(a+b \sqrt[3]{x}\right)}{a^{11}}-\frac{10 b^9 \log (x)}{a^{11}}+\frac{3 b}{4 a^3 x^{8/3}}-\frac{1}{3 a^2 x^3}","\frac{12 b^7}{a^9 x^{2/3}}+\frac{9 b^5}{2 a^7 x^{4/3}}-\frac{3 b^4}{a^6 x^{5/3}}+\frac{2 b^3}{a^5 x^2}-\frac{9 b^2}{7 a^4 x^{7/3}}-\frac{3 b^9}{a^{10} \left(a+b \sqrt[3]{x}\right)}-\frac{27 b^8}{a^{10} \sqrt[3]{x}}-\frac{7 b^6}{a^8 x}+\frac{30 b^9 \log \left(a+b \sqrt[3]{x}\right)}{a^{11}}-\frac{10 b^9 \log (x)}{a^{11}}+\frac{3 b}{4 a^3 x^{8/3}}-\frac{1}{3 a^2 x^3}",1,"(-3*b^9)/(a^10*(a + b*x^(1/3))) - 1/(3*a^2*x^3) + (3*b)/(4*a^3*x^(8/3)) - (9*b^2)/(7*a^4*x^(7/3)) + (2*b^3)/(a^5*x^2) - (3*b^4)/(a^6*x^(5/3)) + (9*b^5)/(2*a^7*x^(4/3)) - (7*b^6)/(a^8*x) + (12*b^7)/(a^9*x^(2/3)) - (27*b^8)/(a^10*x^(1/3)) + (30*b^9*Log[a + b*x^(1/3)])/a^11 - (10*b^9*Log[x])/a^11","A",3,2,15,0.1333,1,"{266, 44}"
2373,1,171,0,0.1480633,"\int \frac{x^3}{\left(a+b \sqrt[3]{x}\right)^3} \, dx","Int[x^3/(a + b*x^(1/3))^3,x]","-\frac{54 a^7 x^{2/3}}{b^{10}}-\frac{63 a^5 x^{4/3}}{4 b^8}+\frac{9 a^4 x^{5/3}}{b^7}-\frac{5 a^3 x^2}{b^6}+\frac{18 a^2 x^{7/3}}{7 b^5}+\frac{3 a^{11}}{2 b^{12} \left(a+b \sqrt[3]{x}\right)^2}-\frac{33 a^{10}}{b^{12} \left(a+b \sqrt[3]{x}\right)}+\frac{135 a^8 \sqrt[3]{x}}{b^{11}}+\frac{28 a^6 x}{b^9}-\frac{165 a^9 \log \left(a+b \sqrt[3]{x}\right)}{b^{12}}-\frac{9 a x^{8/3}}{8 b^4}+\frac{x^3}{3 b^3}","-\frac{54 a^7 x^{2/3}}{b^{10}}-\frac{63 a^5 x^{4/3}}{4 b^8}+\frac{9 a^4 x^{5/3}}{b^7}-\frac{5 a^3 x^2}{b^6}+\frac{18 a^2 x^{7/3}}{7 b^5}+\frac{3 a^{11}}{2 b^{12} \left(a+b \sqrt[3]{x}\right)^2}-\frac{33 a^{10}}{b^{12} \left(a+b \sqrt[3]{x}\right)}+\frac{135 a^8 \sqrt[3]{x}}{b^{11}}+\frac{28 a^6 x}{b^9}-\frac{165 a^9 \log \left(a+b \sqrt[3]{x}\right)}{b^{12}}-\frac{9 a x^{8/3}}{8 b^4}+\frac{x^3}{3 b^3}",1,"(3*a^11)/(2*b^12*(a + b*x^(1/3))^2) - (33*a^10)/(b^12*(a + b*x^(1/3))) + (135*a^8*x^(1/3))/b^11 - (54*a^7*x^(2/3))/b^10 + (28*a^6*x)/b^9 - (63*a^5*x^(4/3))/(4*b^8) + (9*a^4*x^(5/3))/b^7 - (5*a^3*x^2)/b^6 + (18*a^2*x^(7/3))/(7*b^5) - (9*a*x^(8/3))/(8*b^4) + x^3/(3*b^3) - (165*a^9*Log[a + b*x^(1/3)])/b^12","A",3,2,15,0.1333,1,"{266, 43}"
2374,1,134,0,0.1002821,"\int \frac{x^2}{\left(a+b \sqrt[3]{x}\right)^3} \, dx","Int[x^2/(a + b*x^(1/3))^3,x]","\frac{45 a^4 x^{2/3}}{2 b^7}+\frac{9 a^2 x^{4/3}}{2 b^5}-\frac{3 a^8}{2 b^9 \left(a+b \sqrt[3]{x}\right)^2}+\frac{24 a^7}{b^9 \left(a+b \sqrt[3]{x}\right)}-\frac{63 a^5 \sqrt[3]{x}}{b^8}-\frac{10 a^3 x}{b^6}+\frac{84 a^6 \log \left(a+b \sqrt[3]{x}\right)}{b^9}-\frac{9 a x^{5/3}}{5 b^4}+\frac{x^2}{2 b^3}","\frac{45 a^4 x^{2/3}}{2 b^7}+\frac{9 a^2 x^{4/3}}{2 b^5}-\frac{3 a^8}{2 b^9 \left(a+b \sqrt[3]{x}\right)^2}+\frac{24 a^7}{b^9 \left(a+b \sqrt[3]{x}\right)}-\frac{63 a^5 \sqrt[3]{x}}{b^8}-\frac{10 a^3 x}{b^6}+\frac{84 a^6 \log \left(a+b \sqrt[3]{x}\right)}{b^9}-\frac{9 a x^{5/3}}{5 b^4}+\frac{x^2}{2 b^3}",1,"(-3*a^8)/(2*b^9*(a + b*x^(1/3))^2) + (24*a^7)/(b^9*(a + b*x^(1/3))) - (63*a^5*x^(1/3))/b^8 + (45*a^4*x^(2/3))/(2*b^7) - (10*a^3*x)/b^6 + (9*a^2*x^(4/3))/(2*b^5) - (9*a*x^(5/3))/(5*b^4) + x^2/(2*b^3) + (84*a^6*Log[a + b*x^(1/3)])/b^9","A",3,2,15,0.1333,1,"{266, 43}"
2375,1,90,0,0.0611164,"\int \frac{x}{\left(a+b \sqrt[3]{x}\right)^3} \, dx","Int[x/(a + b*x^(1/3))^3,x]","\frac{3 a^5}{2 b^6 \left(a+b \sqrt[3]{x}\right)^2}-\frac{15 a^4}{b^6 \left(a+b \sqrt[3]{x}\right)}+\frac{18 a^2 \sqrt[3]{x}}{b^5}-\frac{30 a^3 \log \left(a+b \sqrt[3]{x}\right)}{b^6}-\frac{9 a x^{2/3}}{2 b^4}+\frac{x}{b^3}","\frac{3 a^5}{2 b^6 \left(a+b \sqrt[3]{x}\right)^2}-\frac{15 a^4}{b^6 \left(a+b \sqrt[3]{x}\right)}+\frac{18 a^2 \sqrt[3]{x}}{b^5}-\frac{30 a^3 \log \left(a+b \sqrt[3]{x}\right)}{b^6}-\frac{9 a x^{2/3}}{2 b^4}+\frac{x}{b^3}",1,"(3*a^5)/(2*b^6*(a + b*x^(1/3))^2) - (15*a^4)/(b^6*(a + b*x^(1/3))) + (18*a^2*x^(1/3))/b^5 - (9*a*x^(2/3))/(2*b^4) + x/b^3 - (30*a^3*Log[a + b*x^(1/3)])/b^6","A",3,2,13,0.1538,1,"{266, 43}"
2376,1,54,0,0.0299247,"\int \frac{1}{\left(a+b \sqrt[3]{x}\right)^3} \, dx","Int[(a + b*x^(1/3))^(-3),x]","-\frac{3 a^2}{2 b^3 \left(a+b \sqrt[3]{x}\right)^2}+\frac{6 a}{b^3 \left(a+b \sqrt[3]{x}\right)}+\frac{3 \log \left(a+b \sqrt[3]{x}\right)}{b^3}","-\frac{3 a^2}{2 b^3 \left(a+b \sqrt[3]{x}\right)^2}+\frac{6 a}{b^3 \left(a+b \sqrt[3]{x}\right)}+\frac{3 \log \left(a+b \sqrt[3]{x}\right)}{b^3}",1,"(-3*a^2)/(2*b^3*(a + b*x^(1/3))^2) + (6*a)/(b^3*(a + b*x^(1/3))) + (3*Log[a + b*x^(1/3)])/b^3","A",3,2,11,0.1818,1,"{190, 43}"
2377,1,56,0,0.0320444,"\int \frac{1}{\left(a+b \sqrt[3]{x}\right)^3 x} \, dx","Int[1/((a + b*x^(1/3))^3*x),x]","\frac{3}{a^2 \left(a+b \sqrt[3]{x}\right)}-\frac{3 \log \left(a+b \sqrt[3]{x}\right)}{a^3}+\frac{\log (x)}{a^3}+\frac{3}{2 a \left(a+b \sqrt[3]{x}\right)^2}","\frac{3}{a^2 \left(a+b \sqrt[3]{x}\right)}-\frac{3 \log \left(a+b \sqrt[3]{x}\right)}{a^3}+\frac{\log (x)}{a^3}+\frac{3}{2 a \left(a+b \sqrt[3]{x}\right)^2}",1,"3/(2*a*(a + b*x^(1/3))^2) + 3/(a^2*(a + b*x^(1/3))) - (3*Log[a + b*x^(1/3)])/a^3 + Log[x]/a^3","A",3,2,15,0.1333,1,"{266, 44}"
2378,1,103,0,0.065565,"\int \frac{1}{\left(a+b \sqrt[3]{x}\right)^3 x^2} \, dx","Int[1/((a + b*x^(1/3))^3*x^2),x]","-\frac{12 b^3}{a^5 \left(a+b \sqrt[3]{x}\right)}-\frac{3 b^3}{2 a^4 \left(a+b \sqrt[3]{x}\right)^2}-\frac{18 b^2}{a^5 \sqrt[3]{x}}+\frac{30 b^3 \log \left(a+b \sqrt[3]{x}\right)}{a^6}-\frac{10 b^3 \log (x)}{a^6}+\frac{9 b}{2 a^4 x^{2/3}}-\frac{1}{a^3 x}","-\frac{12 b^3}{a^5 \left(a+b \sqrt[3]{x}\right)}-\frac{3 b^3}{2 a^4 \left(a+b \sqrt[3]{x}\right)^2}-\frac{18 b^2}{a^5 \sqrt[3]{x}}+\frac{30 b^3 \log \left(a+b \sqrt[3]{x}\right)}{a^6}-\frac{10 b^3 \log (x)}{a^6}+\frac{9 b}{2 a^4 x^{2/3}}-\frac{1}{a^3 x}",1,"(-3*b^3)/(2*a^4*(a + b*x^(1/3))^2) - (12*b^3)/(a^5*(a + b*x^(1/3))) - 1/(a^3*x) + (9*b)/(2*a^4*x^(2/3)) - (18*b^2)/(a^5*x^(1/3)) + (30*b^3*Log[a + b*x^(1/3)])/a^6 - (10*b^3*Log[x])/a^6","A",3,2,15,0.1333,1,"{266, 44}"
2379,1,146,0,0.0995701,"\int \frac{1}{\left(a+b \sqrt[3]{x}\right)^3 x^3} \, dx","Int[1/((a + b*x^(1/3))^3*x^3),x]","-\frac{45 b^4}{2 a^7 x^{2/3}}-\frac{9 b^2}{2 a^5 x^{4/3}}+\frac{21 b^6}{a^8 \left(a+b \sqrt[3]{x}\right)}+\frac{3 b^6}{2 a^7 \left(a+b \sqrt[3]{x}\right)^2}+\frac{63 b^5}{a^8 \sqrt[3]{x}}+\frac{10 b^3}{a^6 x}-\frac{84 b^6 \log \left(a+b \sqrt[3]{x}\right)}{a^9}+\frac{28 b^6 \log (x)}{a^9}+\frac{9 b}{5 a^4 x^{5/3}}-\frac{1}{2 a^3 x^2}","-\frac{45 b^4}{2 a^7 x^{2/3}}-\frac{9 b^2}{2 a^5 x^{4/3}}+\frac{21 b^6}{a^8 \left(a+b \sqrt[3]{x}\right)}+\frac{3 b^6}{2 a^7 \left(a+b \sqrt[3]{x}\right)^2}+\frac{63 b^5}{a^8 \sqrt[3]{x}}+\frac{10 b^3}{a^6 x}-\frac{84 b^6 \log \left(a+b \sqrt[3]{x}\right)}{a^9}+\frac{28 b^6 \log (x)}{a^9}+\frac{9 b}{5 a^4 x^{5/3}}-\frac{1}{2 a^3 x^2}",1,"(3*b^6)/(2*a^7*(a + b*x^(1/3))^2) + (21*b^6)/(a^8*(a + b*x^(1/3))) - 1/(2*a^3*x^2) + (9*b)/(5*a^4*x^(5/3)) - (9*b^2)/(2*a^5*x^(4/3)) + (10*b^3)/(a^6*x) - (45*b^4)/(2*a^7*x^(2/3)) + (63*b^5)/(a^8*x^(1/3)) - (84*b^6*Log[a + b*x^(1/3)])/a^9 + (28*b^6*Log[x])/a^9","A",3,2,15,0.1333,1,"{266, 44}"
2380,1,183,0,0.1398357,"\int \frac{1}{\left(a+b \sqrt[3]{x}\right)^3 x^4} \, dx","Int[1/((a + b*x^(1/3))^3*x^4),x]","\frac{54 b^7}{a^{10} x^{2/3}}+\frac{63 b^5}{4 a^8 x^{4/3}}-\frac{9 b^4}{a^7 x^{5/3}}+\frac{5 b^3}{a^6 x^2}-\frac{18 b^2}{7 a^5 x^{7/3}}-\frac{30 b^9}{a^{11} \left(a+b \sqrt[3]{x}\right)}-\frac{3 b^9}{2 a^{10} \left(a+b \sqrt[3]{x}\right)^2}-\frac{135 b^8}{a^{11} \sqrt[3]{x}}-\frac{28 b^6}{a^9 x}+\frac{165 b^9 \log \left(a+b \sqrt[3]{x}\right)}{a^{12}}-\frac{55 b^9 \log (x)}{a^{12}}+\frac{9 b}{8 a^4 x^{8/3}}-\frac{1}{3 a^3 x^3}","\frac{54 b^7}{a^{10} x^{2/3}}+\frac{63 b^5}{4 a^8 x^{4/3}}-\frac{9 b^4}{a^7 x^{5/3}}+\frac{5 b^3}{a^6 x^2}-\frac{18 b^2}{7 a^5 x^{7/3}}-\frac{30 b^9}{a^{11} \left(a+b \sqrt[3]{x}\right)}-\frac{3 b^9}{2 a^{10} \left(a+b \sqrt[3]{x}\right)^2}-\frac{135 b^8}{a^{11} \sqrt[3]{x}}-\frac{28 b^6}{a^9 x}+\frac{165 b^9 \log \left(a+b \sqrt[3]{x}\right)}{a^{12}}-\frac{55 b^9 \log (x)}{a^{12}}+\frac{9 b}{8 a^4 x^{8/3}}-\frac{1}{3 a^3 x^3}",1,"(-3*b^9)/(2*a^10*(a + b*x^(1/3))^2) - (30*b^9)/(a^11*(a + b*x^(1/3))) - 1/(3*a^3*x^3) + (9*b)/(8*a^4*x^(8/3)) - (18*b^2)/(7*a^5*x^(7/3)) + (5*b^3)/(a^6*x^2) - (9*b^4)/(a^7*x^(5/3)) + (63*b^5)/(4*a^8*x^(4/3)) - (28*b^6)/(a^9*x) + (54*b^7)/(a^10*x^(2/3)) - (135*b^8)/(a^11*x^(1/3)) + (165*b^9*Log[a + b*x^(1/3)])/a^12 - (55*b^9*Log[x])/a^12","A",3,2,15,0.1333,1,"{266, 44}"
2381,1,42,0,0.0106895,"\int \frac{1}{\sqrt{1+\sqrt[3]{x}}} \, dx","Int[1/Sqrt[1 + x^(1/3)],x]","\frac{6}{5} \left(\sqrt[3]{x}+1\right)^{5/2}-4 \left(\sqrt[3]{x}+1\right)^{3/2}+6 \sqrt{\sqrt[3]{x}+1}","\frac{6}{5} \left(\sqrt[3]{x}+1\right)^{5/2}-4 \left(\sqrt[3]{x}+1\right)^{3/2}+6 \sqrt{\sqrt[3]{x}+1}",1,"6*Sqrt[1 + x^(1/3)] - 4*(1 + x^(1/3))^(3/2) + (6*(1 + x^(1/3))^(5/2))/5","A",3,2,11,0.1818,1,"{190, 43}"
2382,1,23,0,0.0081758,"\int \frac{1}{\left(1+\sqrt[3]{x}\right) x^{3/2}} \, dx","Int[1/((1 + x^(1/3))*x^(3/2)),x]","\frac{6}{\sqrt[6]{x}}-\frac{2}{\sqrt{x}}+6 \tan ^{-1}\left(\sqrt[6]{x}\right)","\frac{6}{\sqrt[6]{x}}-\frac{2}{\sqrt{x}}+6 \tan ^{-1}\left(\sqrt[6]{x}\right)",1,"-2/Sqrt[x] + 6/x^(1/6) + 6*ArcTan[x^(1/6)]","A",5,4,15,0.2667,1,"{341, 51, 63, 203}"
2383,1,39,0,0.0155377,"\int \frac{x^{2/3}}{1+\sqrt[3]{x}} \, dx","Int[x^(2/3)/(1 + x^(1/3)),x]","\frac{3 x^{4/3}}{4}+\frac{3 x^{2/3}}{2}-x-3 \sqrt[3]{x}+3 \log \left(\sqrt[3]{x}+1\right)","\frac{3 x^{4/3}}{4}+\frac{3 x^{2/3}}{2}-x-3 \sqrt[3]{x}+3 \log \left(\sqrt[3]{x}+1\right)",1,"-3*x^(1/3) + (3*x^(2/3))/2 - x + (3*x^(4/3))/4 + 3*Log[1 + x^(1/3)]","A",3,2,15,0.1333,1,"{266, 43}"
2384,1,16,0,0.0053561,"\int \frac{1}{1+x^{2/3}} \, dx","Int[(1 + x^(2/3))^(-1),x]","3 \sqrt[3]{x}-3 \tan ^{-1}\left(\sqrt[3]{x}\right)","3 \sqrt[3]{x}-3 \tan ^{-1}\left(\sqrt[3]{x}\right)",1,"3*x^(1/3) - 3*ArcTan[x^(1/3)]","A",3,3,9,0.3333,1,"{243, 321, 203}"
2385,1,12,0,0.0027598,"\int \frac{1}{\left(1+x^{2/3}\right) \sqrt[3]{x}} \, dx","Int[1/((1 + x^(2/3))*x^(1/3)),x]","\frac{3}{2} \log \left(x^{2/3}+1\right)","\frac{3}{2} \log \left(x^{2/3}+1\right)",1,"(3*Log[1 + x^(2/3)])/2","A",1,1,15,0.06667,1,"{260}"
2386,1,8,0,0.0038923,"\int \frac{1}{\left(1+x^{2/3}\right) x^{2/3}} \, dx","Int[1/((1 + x^(2/3))*x^(2/3)),x]","3 \tan ^{-1}\left(\sqrt[3]{x}\right)","3 \tan ^{-1}\left(\sqrt[3]{x}\right)",1,"3*ArcTan[x^(1/3)]","A",2,2,15,0.1333,1,"{341, 203}"
2387,1,11,0,0.002669,"\int \frac{\sqrt{-1+x^{2/3}}}{\sqrt[3]{x}} \, dx","Int[Sqrt[-1 + x^(2/3)]/x^(1/3),x]","\left(x^{2/3}-1\right)^{3/2}","\left(x^{2/3}-1\right)^{3/2}",1,"(-1 + x^(2/3))^(3/2)","A",1,1,17,0.05882,1,"{261}"
2388,1,15,0,0.0030703,"\int \frac{\left(1+x^{2/3}\right)^{3/2}}{\sqrt[3]{x}} \, dx","Int[(1 + x^(2/3))^(3/2)/x^(1/3),x]","\frac{3}{5} \left(x^{2/3}+1\right)^{5/2}","\frac{3}{5} \left(x^{2/3}+1\right)^{5/2}",1,"(3*(1 + x^(2/3))^(5/2))/5","A",1,1,17,0.05882,1,"{261}"
2389,1,117,0,0.0771903,"\int \frac{\sqrt{x}}{1+x^{2/3}} \, dx","Int[Sqrt[x]/(1 + x^(2/3)),x]","\frac{6 x^{5/6}}{5}-6 \sqrt[6]{x}-\frac{3 \log \left(\sqrt[3]{x}-\sqrt{2} \sqrt[6]{x}+1\right)}{2 \sqrt{2}}+\frac{3 \log \left(\sqrt[3]{x}+\sqrt{2} \sqrt[6]{x}+1\right)}{2 \sqrt{2}}-\frac{3 \tan ^{-1}\left(1-\sqrt{2} \sqrt[6]{x}\right)}{\sqrt{2}}+\frac{3 \tan ^{-1}\left(\sqrt{2} \sqrt[6]{x}+1\right)}{\sqrt{2}}","\frac{6 x^{5/6}}{5}-6 \sqrt[6]{x}-\frac{3 \log \left(\sqrt[3]{x}-\sqrt{2} \sqrt[6]{x}+1\right)}{2 \sqrt{2}}+\frac{3 \log \left(\sqrt[3]{x}+\sqrt{2} \sqrt[6]{x}+1\right)}{2 \sqrt{2}}-\frac{3 \tan ^{-1}\left(1-\sqrt{2} \sqrt[6]{x}\right)}{\sqrt{2}}+\frac{3 \tan ^{-1}\left(\sqrt{2} \sqrt[6]{x}+1\right)}{\sqrt{2}}",1,"-6*x^(1/6) + (6*x^(5/6))/5 - (3*ArcTan[1 - Sqrt[2]*x^(1/6)])/Sqrt[2] + (3*ArcTan[1 + Sqrt[2]*x^(1/6)])/Sqrt[2] - (3*Log[1 - Sqrt[2]*x^(1/6) + x^(1/3)])/(2*Sqrt[2]) + (3*Log[1 + Sqrt[2]*x^(1/6) + x^(1/3)])/(2*Sqrt[2])","A",13,9,15,0.6000,1,"{341, 321, 329, 211, 1165, 628, 1162, 617, 204}"
2390,1,200,0,0.3511433,"\int \frac{\sqrt[3]{x}}{-1+x^{5/6}} \, dx","Int[x^(1/3)/(-1 + x^(5/6)),x]","2 \sqrt{x}+\frac{6}{5} \log \left(1-\sqrt[6]{x}\right)-\frac{3}{10} \left(1+\sqrt{5}\right) \log \left(2 \sqrt[3]{x}-\sqrt{5} \sqrt[6]{x}+\sqrt[6]{x}+2\right)-\frac{3}{10} \left(1-\sqrt{5}\right) \log \left(2 \sqrt[3]{x}+\sqrt{5} \sqrt[6]{x}+\sqrt[6]{x}+2\right)+\frac{3}{5} \sqrt{2 \left(5-\sqrt{5}\right)} \tan ^{-1}\left(\frac{4 \sqrt[6]{x}-\sqrt{5}+1}{\sqrt{2 \left(5+\sqrt{5}\right)}}\right)-\frac{3}{5} \sqrt{2 \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\frac{1}{2} \sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} \left(4 \sqrt[6]{x}+\sqrt{5}+1\right)\right)","2 \sqrt{x}+\frac{6}{5} \log \left(1-\sqrt[6]{x}\right)-\frac{3}{10} \left(1+\sqrt{5}\right) \log \left(2 \sqrt[3]{x}+\left(1-\sqrt{5}\right) \sqrt[6]{x}+2\right)-\frac{3}{10} \left(1-\sqrt{5}\right) \log \left(2 \sqrt[3]{x}+\left(1+\sqrt{5}\right) \sqrt[6]{x}+2\right)+\frac{3}{5} \sqrt{10-2 \sqrt{5}} \tan ^{-1}\left(\frac{4 \sqrt[6]{x}-\sqrt{5}+1}{\sqrt{10+2 \sqrt{5}}}\right)-\frac{3}{5} \sqrt{10+2 \sqrt{5}} \tan ^{-1}\left(\frac{4 \sqrt[6]{x}+\sqrt{5}+1}{\sqrt{10-2 \sqrt{5}}}\right)",1,"2*Sqrt[x] + (3*Sqrt[2*(5 - Sqrt[5])]*ArcTan[(1 - Sqrt[5] + 4*x^(1/6))/Sqrt[2*(5 + Sqrt[5])]])/5 - (3*Sqrt[2*(5 + Sqrt[5])]*ArcTan[(Sqrt[(5 + Sqrt[5])/10]*(1 + Sqrt[5] + 4*x^(1/6)))/2])/5 + (6*Log[1 - x^(1/6)])/5 - (3*(1 + Sqrt[5])*Log[2 + x^(1/6) - Sqrt[5]*x^(1/6) + 2*x^(1/3)])/10 - (3*(1 - Sqrt[5])*Log[2 + x^(1/6) + Sqrt[5]*x^(1/6) + 2*x^(1/3)])/10","A",8,8,15,0.5333,1,"{341, 321, 294, 634, 618, 204, 628, 31}"
2391,1,67,0,0.0248713,"\int \sqrt{3-\frac{1}{\sqrt{x}}} \, dx","Int[Sqrt[3 - 1/Sqrt[x]],x]","\sqrt{3-\frac{1}{\sqrt{x}}} x-\frac{1}{6} \sqrt{3-\frac{1}{\sqrt{x}}} \sqrt{x}-\frac{\tanh ^{-1}\left(\frac{\sqrt{3-\frac{1}{\sqrt{x}}}}{\sqrt{3}}\right)}{6 \sqrt{3}}","\sqrt{3-\frac{1}{\sqrt{x}}} x-\frac{1}{6} \sqrt{3-\frac{1}{\sqrt{x}}} \sqrt{x}-\frac{\tanh ^{-1}\left(\frac{\sqrt{3-\frac{1}{\sqrt{x}}}}{\sqrt{3}}\right)}{6 \sqrt{3}}",1,"-(Sqrt[3 - 1/Sqrt[x]]*Sqrt[x])/6 + Sqrt[3 - 1/Sqrt[x]]*x - ArcTanh[Sqrt[3 - 1/Sqrt[x]]/Sqrt[3]]/(6*Sqrt[3])","A",5,5,13,0.3846,1,"{190, 47, 51, 63, 206}"
2392,1,50,0,0.0146517,"\int \frac{1}{\sqrt{1+\frac{1}{\sqrt{x}}}} \, dx","Int[1/Sqrt[1 + 1/Sqrt[x]],x]","\sqrt{\frac{1}{\sqrt{x}}+1} x-\frac{3}{2} \sqrt{\frac{1}{\sqrt{x}}+1} \sqrt{x}+\frac{3}{2} \tanh ^{-1}\left(\sqrt{\frac{1}{\sqrt{x}}+1}\right)","\sqrt{\frac{1}{\sqrt{x}}+1} x-\frac{3}{2} \sqrt{\frac{1}{\sqrt{x}}+1} \sqrt{x}+\frac{3}{2} \tanh ^{-1}\left(\sqrt{\frac{1}{\sqrt{x}}+1}\right)",1,"(-3*Sqrt[1 + 1/Sqrt[x]]*Sqrt[x])/2 + Sqrt[1 + 1/Sqrt[x]]*x + (3*ArcTanh[Sqrt[1 + 1/Sqrt[x]]])/2","A",5,4,11,0.3636,1,"{190, 51, 63, 207}"
2393,1,95,0,0.0901612,"\int \left(a+\frac{b}{x^{3/2}}\right)^{2/3} \, dx","Int[(a + b/x^(3/2))^(2/3),x]","b^{2/3} \log \left(\sqrt[3]{a+\frac{b}{x^{3/2}}}-\frac{\sqrt[3]{b}}{\sqrt{x}}\right)-\frac{2 b^{2/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b}}{\sqrt{x} \sqrt[3]{a+\frac{b}{x^{3/2}}}}+1}{\sqrt{3}}\right)}{\sqrt{3}}+x \left(a+\frac{b}{x^{3/2}}\right)^{2/3}","b^{2/3} \log \left(\sqrt[3]{a+\frac{b}{x^{3/2}}}-\frac{\sqrt[3]{b}}{\sqrt{x}}\right)-\frac{2 b^{2/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b}}{\sqrt{x} \sqrt[3]{a+\frac{b}{x^{3/2}}}}+1}{\sqrt{3}}\right)}{\sqrt{3}}+x \left(a+\frac{b}{x^{3/2}}\right)^{2/3}",1,"(a + b/x^(3/2))^(2/3)*x - (2*b^(2/3)*ArcTan[(1 + (2*b^(1/3))/((a + b/x^(3/2))^(1/3)*Sqrt[x]))/Sqrt[3]])/Sqrt[3] + b^(2/3)*Log[(a + b/x^(3/2))^(1/3) - b^(1/3)/Sqrt[x]]","A",4,4,13,0.3077,1,"{243, 335, 277, 239}"
2394,1,19,0,0.0060266,"\int \left(a+\frac{b}{\sqrt[3]{x}}\right) x^4 \, dx","Int[(a + b/x^(1/3))*x^4,x]","\frac{a x^5}{5}+\frac{3}{14} b x^{14/3}","\frac{a x^5}{5}+\frac{3}{14} b x^{14/3}",1,"(3*b*x^(14/3))/14 + (a*x^5)/5","A",2,1,13,0.07692,1,"{14}"
2395,1,19,0,0.0051967,"\int \left(a+\frac{b}{\sqrt[3]{x}}\right) x^3 \, dx","Int[(a + b/x^(1/3))*x^3,x]","\frac{a x^4}{4}+\frac{3}{11} b x^{11/3}","\frac{a x^4}{4}+\frac{3}{11} b x^{11/3}",1,"(3*b*x^(11/3))/11 + (a*x^4)/4","A",2,1,13,0.07692,1,"{14}"
2396,1,19,0,0.0049467,"\int \left(a+\frac{b}{\sqrt[3]{x}}\right) x^2 \, dx","Int[(a + b/x^(1/3))*x^2,x]","\frac{a x^3}{3}+\frac{3}{8} b x^{8/3}","\frac{a x^3}{3}+\frac{3}{8} b x^{8/3}",1,"(3*b*x^(8/3))/8 + (a*x^3)/3","A",2,1,13,0.07692,1,"{14}"
2397,1,19,0,0.0048784,"\int \left(a+\frac{b}{\sqrt[3]{x}}\right) x \, dx","Int[(a + b/x^(1/3))*x,x]","\frac{a x^2}{2}+\frac{3}{5} b x^{5/3}","\frac{a x^2}{2}+\frac{3}{5} b x^{5/3}",1,"(3*b*x^(5/3))/5 + (a*x^2)/2","A",2,1,11,0.09091,1,"{14}"
2398,1,14,0,0.0024813,"\int \left(a+\frac{b}{\sqrt[3]{x}}\right) \, dx","Int[a + b/x^(1/3),x]","a x+\frac{3}{2} b x^{2/3}","a x+\frac{3}{2} b x^{2/3}",1,"(3*b*x^(2/3))/2 + a*x","A",1,0,9,0,1,"{}"
2399,1,13,0,0.0053345,"\int \frac{a+\frac{b}{\sqrt[3]{x}}}{x} \, dx","Int[(a + b/x^(1/3))/x,x]","a \log (x)-\frac{3 b}{\sqrt[3]{x}}","a \log (x)-\frac{3 b}{\sqrt[3]{x}}",1,"(-3*b)/x^(1/3) + a*Log[x]","A",2,1,13,0.07692,1,"{14}"
2400,1,17,0,0.0049935,"\int \frac{a+\frac{b}{\sqrt[3]{x}}}{x^2} \, dx","Int[(a + b/x^(1/3))/x^2,x]","-\frac{a}{x}-\frac{3 b}{4 x^{4/3}}","-\frac{a}{x}-\frac{3 b}{4 x^{4/3}}",1,"(-3*b)/(4*x^(4/3)) - a/x","A",2,1,13,0.07692,1,"{14}"
2401,1,19,0,0.0050827,"\int \frac{a+\frac{b}{\sqrt[3]{x}}}{x^3} \, dx","Int[(a + b/x^(1/3))/x^3,x]","-\frac{a}{2 x^2}-\frac{3 b}{7 x^{7/3}}","-\frac{a}{2 x^2}-\frac{3 b}{7 x^{7/3}}",1,"(-3*b)/(7*x^(7/3)) - a/(2*x^2)","A",2,1,13,0.07692,1,"{14}"
2402,1,19,0,0.0048825,"\int \frac{a+\frac{b}{\sqrt[3]{x}}}{x^4} \, dx","Int[(a + b/x^(1/3))/x^4,x]","-\frac{a}{3 x^3}-\frac{3 b}{10 x^{10/3}}","-\frac{a}{3 x^3}-\frac{3 b}{10 x^{10/3}}",1,"(-3*b)/(10*x^(10/3)) - a/(3*x^3)","A",2,1,13,0.07692,1,"{14}"
2403,1,34,0,0.0307636,"\int \left(a+\frac{b}{\sqrt[3]{x}}\right)^2 x^4 \, dx","Int[(a + b/x^(1/3))^2*x^4,x]","\frac{a^2 x^5}{5}+\frac{3}{7} a b x^{14/3}+\frac{3}{13} b^2 x^{13/3}","\frac{a^2 x^5}{5}+\frac{3}{7} a b x^{14/3}+\frac{3}{13} b^2 x^{13/3}",1,"(3*b^2*x^(13/3))/13 + (3*a*b*x^(14/3))/7 + (a^2*x^5)/5","A",4,3,15,0.2000,1,"{263, 266, 43}"
2404,1,34,0,0.027699,"\int \left(a+\frac{b}{\sqrt[3]{x}}\right)^2 x^3 \, dx","Int[(a + b/x^(1/3))^2*x^3,x]","\frac{a^2 x^4}{4}+\frac{6}{11} a b x^{11/3}+\frac{3}{10} b^2 x^{10/3}","\frac{a^2 x^4}{4}+\frac{6}{11} a b x^{11/3}+\frac{3}{10} b^2 x^{10/3}",1,"(3*b^2*x^(10/3))/10 + (6*a*b*x^(11/3))/11 + (a^2*x^4)/4","A",4,3,15,0.2000,1,"{263, 266, 43}"
2405,1,34,0,0.0235163,"\int \left(a+\frac{b}{\sqrt[3]{x}}\right)^2 x^2 \, dx","Int[(a + b/x^(1/3))^2*x^2,x]","\frac{a^2 x^3}{3}+\frac{3}{4} a b x^{8/3}+\frac{3}{7} b^2 x^{7/3}","\frac{a^2 x^3}{3}+\frac{3}{4} a b x^{8/3}+\frac{3}{7} b^2 x^{7/3}",1,"(3*b^2*x^(7/3))/7 + (3*a*b*x^(8/3))/4 + (a^2*x^3)/3","A",4,3,15,0.2000,1,"{263, 266, 43}"
2406,1,34,0,0.0195002,"\int \left(a+\frac{b}{\sqrt[3]{x}}\right)^2 x \, dx","Int[(a + b/x^(1/3))^2*x,x]","\frac{a^2 x^2}{2}+\frac{6}{5} a b x^{5/3}+\frac{3}{4} b^2 x^{4/3}","\frac{a^2 x^2}{2}+\frac{6}{5} a b x^{5/3}+\frac{3}{4} b^2 x^{4/3}",1,"(3*b^2*x^(4/3))/4 + (6*a*b*x^(5/3))/5 + (a^2*x^2)/2","A",4,3,13,0.2308,1,"{263, 266, 43}"
2407,1,16,0,0.0069336,"\int \left(a+\frac{b}{\sqrt[3]{x}}\right)^2 \, dx","Int[(a + b/x^(1/3))^2,x]","\frac{x \left(a+\frac{b}{\sqrt[3]{x}}\right)^3}{a}","\frac{x \left(a+\frac{b}{\sqrt[3]{x}}\right)^3}{a}",1,"((a + b/x^(1/3))^3*x)/a","A",2,2,11,0.1818,1,"{190, 37}"
2408,1,28,0,0.0154615,"\int \frac{\left(a+\frac{b}{\sqrt[3]{x}}\right)^2}{x} \, dx","Int[(a + b/x^(1/3))^2/x,x]","a^2 \log (x)-\frac{6 a b}{\sqrt[3]{x}}-\frac{3 b^2}{2 x^{2/3}}","a^2 \log (x)-\frac{6 a b}{\sqrt[3]{x}}-\frac{3 b^2}{2 x^{2/3}}",1,"(-3*b^2)/(2*x^(2/3)) - (6*a*b)/x^(1/3) + a^2*Log[x]","A",4,3,15,0.2000,1,"{263, 266, 43}"
2409,1,32,0,0.0163252,"\int \frac{\left(a+\frac{b}{\sqrt[3]{x}}\right)^2}{x^2} \, dx","Int[(a + b/x^(1/3))^2/x^2,x]","-\frac{a^2}{x}-\frac{3 a b}{2 x^{4/3}}-\frac{3 b^2}{5 x^{5/3}}","-\frac{a^2}{x}-\frac{3 a b}{2 x^{4/3}}-\frac{3 b^2}{5 x^{5/3}}",1,"(-3*b^2)/(5*x^(5/3)) - (3*a*b)/(2*x^(4/3)) - a^2/x","A",4,3,15,0.2000,1,"{263, 266, 43}"
2410,1,34,0,0.0173652,"\int \frac{\left(a+\frac{b}{\sqrt[3]{x}}\right)^2}{x^3} \, dx","Int[(a + b/x^(1/3))^2/x^3,x]","-\frac{a^2}{2 x^2}-\frac{6 a b}{7 x^{7/3}}-\frac{3 b^2}{8 x^{8/3}}","-\frac{a^2}{2 x^2}-\frac{6 a b}{7 x^{7/3}}-\frac{3 b^2}{8 x^{8/3}}",1,"(-3*b^2)/(8*x^(8/3)) - (6*a*b)/(7*x^(7/3)) - a^2/(2*x^2)","A",4,3,15,0.2000,1,"{263, 266, 43}"
2411,1,34,0,0.0159659,"\int \frac{\left(a+\frac{b}{\sqrt[3]{x}}\right)^2}{x^4} \, dx","Int[(a + b/x^(1/3))^2/x^4,x]","-\frac{a^2}{3 x^3}-\frac{3 a b}{5 x^{10/3}}-\frac{3 b^2}{11 x^{11/3}}","-\frac{a^2}{3 x^3}-\frac{3 a b}{5 x^{10/3}}-\frac{3 b^2}{11 x^{11/3}}",1,"(-3*b^2)/(11*x^(11/3)) - (3*a*b)/(5*x^(10/3)) - a^2/(3*x^3)","A",4,3,15,0.2000,1,"{263, 266, 43}"
2412,1,47,0,0.0371428,"\int \left(a+\frac{b}{\sqrt[3]{x}}\right)^3 x^4 \, dx","Int[(a + b/x^(1/3))^3*x^4,x]","\frac{9}{14} a^2 b x^{14/3}+\frac{a^3 x^5}{5}+\frac{9}{13} a b^2 x^{13/3}+\frac{b^3 x^4}{4}","\frac{9}{14} a^2 b x^{14/3}+\frac{a^3 x^5}{5}+\frac{9}{13} a b^2 x^{13/3}+\frac{b^3 x^4}{4}",1,"(b^3*x^4)/4 + (9*a*b^2*x^(13/3))/13 + (9*a^2*b*x^(14/3))/14 + (a^3*x^5)/5","A",4,3,15,0.2000,1,"{263, 266, 43}"
2413,1,47,0,0.0343602,"\int \left(a+\frac{b}{\sqrt[3]{x}}\right)^3 x^3 \, dx","Int[(a + b/x^(1/3))^3*x^3,x]","\frac{9}{11} a^2 b x^{11/3}+\frac{a^3 x^4}{4}+\frac{9}{10} a b^2 x^{10/3}+\frac{b^3 x^3}{3}","\frac{9}{11} a^2 b x^{11/3}+\frac{a^3 x^4}{4}+\frac{9}{10} a b^2 x^{10/3}+\frac{b^3 x^3}{3}",1,"(b^3*x^3)/3 + (9*a*b^2*x^(10/3))/10 + (9*a^2*b*x^(11/3))/11 + (a^3*x^4)/4","A",4,3,15,0.2000,1,"{263, 266, 43}"
2414,1,47,0,0.0300391,"\int \left(a+\frac{b}{\sqrt[3]{x}}\right)^3 x^2 \, dx","Int[(a + b/x^(1/3))^3*x^2,x]","\frac{9}{8} a^2 b x^{8/3}+\frac{a^3 x^3}{3}+\frac{9}{7} a b^2 x^{7/3}+\frac{b^3 x^2}{2}","\frac{9}{8} a^2 b x^{8/3}+\frac{a^3 x^3}{3}+\frac{9}{7} a b^2 x^{7/3}+\frac{b^3 x^2}{2}",1,"(b^3*x^2)/2 + (9*a*b^2*x^(7/3))/7 + (9*a^2*b*x^(8/3))/8 + (a^3*x^3)/3","A",4,3,15,0.2000,1,"{263, 266, 43}"
2415,1,42,0,0.0235856,"\int \left(a+\frac{b}{\sqrt[3]{x}}\right)^3 x \, dx","Int[(a + b/x^(1/3))^3*x,x]","\frac{9}{5} a^2 b x^{5/3}+\frac{a^3 x^2}{2}+\frac{9}{4} a b^2 x^{4/3}+b^3 x","\frac{9}{5} a^2 b x^{5/3}+\frac{a^3 x^2}{2}+\frac{9}{4} a b^2 x^{4/3}+b^3 x",1,"b^3*x + (9*a*b^2*x^(4/3))/4 + (9*a^2*b*x^(5/3))/5 + (a^3*x^2)/2","A",4,3,13,0.2308,1,"{263, 190, 43}"
2416,1,36,0,0.019956,"\int \left(a+\frac{b}{\sqrt[3]{x}}\right)^3 \, dx","Int[(a + b/x^(1/3))^3,x]","\frac{9}{2} a^2 b x^{2/3}+a^3 x+9 a b^2 \sqrt[3]{x}+b^3 \log (x)","\frac{9}{2} a^2 b x^{2/3}+a^3 x+9 a b^2 \sqrt[3]{x}+b^3 \log (x)",1,"9*a*b^2*x^(1/3) + (9*a^2*b*x^(2/3))/2 + a^3*x + b^3*Log[x]","A",3,2,11,0.1818,1,"{190, 43}"
2417,1,39,0,0.0231502,"\int \frac{\left(a+\frac{b}{\sqrt[3]{x}}\right)^3}{x} \, dx","Int[(a + b/x^(1/3))^3/x,x]","-\frac{9 a^2 b}{\sqrt[3]{x}}+a^3 \log (x)-\frac{9 a b^2}{2 x^{2/3}}-\frac{b^3}{x}","-\frac{9 a^2 b}{\sqrt[3]{x}}+a^3 \log (x)-\frac{9 a b^2}{2 x^{2/3}}-\frac{b^3}{x}",1,"-(b^3/x) - (9*a*b^2)/(2*x^(2/3)) - (9*a^2*b)/x^(1/3) + a^3*Log[x]","A",4,3,15,0.2000,1,"{263, 266, 43}"
2418,1,45,0,0.0220165,"\int \frac{\left(a+\frac{b}{\sqrt[3]{x}}\right)^3}{x^2} \, dx","Int[(a + b/x^(1/3))^3/x^2,x]","-\frac{9 a^2 b}{4 x^{4/3}}-\frac{a^3}{x}-\frac{9 a b^2}{5 x^{5/3}}-\frac{b^3}{2 x^2}","-\frac{9 a^2 b}{4 x^{4/3}}-\frac{a^3}{x}-\frac{9 a b^2}{5 x^{5/3}}-\frac{b^3}{2 x^2}",1,"-b^3/(2*x^2) - (9*a*b^2)/(5*x^(5/3)) - (9*a^2*b)/(4*x^(4/3)) - a^3/x","A",4,3,15,0.2000,1,"{263, 266, 43}"
2419,1,47,0,0.0218488,"\int \frac{\left(a+\frac{b}{\sqrt[3]{x}}\right)^3}{x^3} \, dx","Int[(a + b/x^(1/3))^3/x^3,x]","-\frac{9 a^2 b}{7 x^{7/3}}-\frac{a^3}{2 x^2}-\frac{9 a b^2}{8 x^{8/3}}-\frac{b^3}{3 x^3}","-\frac{9 a^2 b}{7 x^{7/3}}-\frac{a^3}{2 x^2}-\frac{9 a b^2}{8 x^{8/3}}-\frac{b^3}{3 x^3}",1,"-b^3/(3*x^3) - (9*a*b^2)/(8*x^(8/3)) - (9*a^2*b)/(7*x^(7/3)) - a^3/(2*x^2)","A",4,3,15,0.2000,1,"{263, 266, 43}"
2420,1,47,0,0.0214049,"\int \frac{\left(a+\frac{b}{\sqrt[3]{x}}\right)^3}{x^4} \, dx","Int[(a + b/x^(1/3))^3/x^4,x]","-\frac{9 a^2 b}{10 x^{10/3}}-\frac{a^3}{3 x^3}-\frac{9 a b^2}{11 x^{11/3}}-\frac{b^3}{4 x^4}","-\frac{9 a^2 b}{10 x^{10/3}}-\frac{a^3}{3 x^3}-\frac{9 a b^2}{11 x^{11/3}}-\frac{b^3}{4 x^4}",1,"-b^3/(4*x^4) - (9*a*b^2)/(11*x^(11/3)) - (9*a^2*b)/(10*x^(10/3)) - a^3/(3*x^3)","A",4,3,15,0.2000,1,"{263, 266, 43}"
2421,1,136,0,0.0892607,"\int \frac{x^2}{a+\frac{b}{\sqrt[3]{x}}} \, dx","Int[x^2/(a + b/x^(1/3)),x]","-\frac{3 b^7 x^{2/3}}{2 a^8}-\frac{3 b^5 x^{4/3}}{4 a^6}+\frac{3 b^4 x^{5/3}}{5 a^5}-\frac{b^3 x^2}{2 a^4}+\frac{3 b^2 x^{7/3}}{7 a^3}+\frac{3 b^8 \sqrt[3]{x}}{a^9}+\frac{b^6 x}{a^7}-\frac{3 b^9 \log \left(a \sqrt[3]{x}+b\right)}{a^{10}}-\frac{3 b x^{8/3}}{8 a^2}+\frac{x^3}{3 a}","-\frac{3 b^7 x^{2/3}}{2 a^8}-\frac{3 b^5 x^{4/3}}{4 a^6}+\frac{3 b^4 x^{5/3}}{5 a^5}-\frac{b^3 x^2}{2 a^4}+\frac{3 b^2 x^{7/3}}{7 a^3}+\frac{3 b^8 \sqrt[3]{x}}{a^9}+\frac{b^6 x}{a^7}-\frac{3 b^9 \log \left(a \sqrt[3]{x}+b\right)}{a^{10}}-\frac{3 b x^{8/3}}{8 a^2}+\frac{x^3}{3 a}",1,"(3*b^8*x^(1/3))/a^9 - (3*b^7*x^(2/3))/(2*a^8) + (b^6*x)/a^7 - (3*b^5*x^(4/3))/(4*a^6) + (3*b^4*x^(5/3))/(5*a^5) - (b^3*x^2)/(2*a^4) + (3*b^2*x^(7/3))/(7*a^3) - (3*b*x^(8/3))/(8*a^2) + x^3/(3*a) - (3*b^9*Log[b + a*x^(1/3)])/a^10","A",4,3,15,0.2000,1,"{263, 266, 43}"
2422,1,94,0,0.0535049,"\int \frac{x}{a+\frac{b}{\sqrt[3]{x}}} \, dx","Int[x/(a + b/x^(1/3)),x]","\frac{3 b^4 x^{2/3}}{2 a^5}+\frac{3 b^2 x^{4/3}}{4 a^3}-\frac{3 b^5 \sqrt[3]{x}}{a^6}-\frac{b^3 x}{a^4}+\frac{3 b^6 \log \left(a \sqrt[3]{x}+b\right)}{a^7}-\frac{3 b x^{5/3}}{5 a^2}+\frac{x^2}{2 a}","\frac{3 b^4 x^{2/3}}{2 a^5}+\frac{3 b^2 x^{4/3}}{4 a^3}-\frac{3 b^5 \sqrt[3]{x}}{a^6}-\frac{b^3 x}{a^4}+\frac{3 b^6 \log \left(a \sqrt[3]{x}+b\right)}{a^7}-\frac{3 b x^{5/3}}{5 a^2}+\frac{x^2}{2 a}",1,"(-3*b^5*x^(1/3))/a^6 + (3*b^4*x^(2/3))/(2*a^5) - (b^3*x)/a^4 + (3*b^2*x^(4/3))/(4*a^3) - (3*b*x^(5/3))/(5*a^2) + x^2/(2*a) + (3*b^6*Log[b + a*x^(1/3)])/a^7","A",4,3,13,0.2308,1,"{263, 266, 43}"
2423,1,60,0,0.0366103,"\int \frac{1}{a+\frac{b}{\sqrt[3]{x}}} \, dx","Int[(a + b/x^(1/3))^(-1),x]","\frac{3 b^2 \sqrt[3]{x}}{a^3}-\frac{3 b^3 \log \left(a+\frac{b}{\sqrt[3]{x}}\right)}{a^4}-\frac{b^3 \log (x)}{a^4}-\frac{3 b x^{2/3}}{2 a^2}+\frac{x}{a}","\frac{3 b^2 \sqrt[3]{x}}{a^3}-\frac{3 b^3 \log \left(a+\frac{b}{\sqrt[3]{x}}\right)}{a^4}-\frac{b^3 \log (x)}{a^4}-\frac{3 b x^{2/3}}{2 a^2}+\frac{x}{a}",1,"(3*b^2*x^(1/3))/a^3 - (3*b*x^(2/3))/(2*a^2) + x/a - (3*b^3*Log[a + b/x^(1/3)])/a^4 - (b^3*Log[x])/a^4","A",3,2,11,0.1818,1,"{190, 44}"
2424,1,15,0,0.0059596,"\int \frac{1}{\left(a+\frac{b}{\sqrt[3]{x}}\right) x} \, dx","Int[1/((a + b/x^(1/3))*x),x]","\frac{3 \log \left(a \sqrt[3]{x}+b\right)}{a}","\frac{3 \log \left(a \sqrt[3]{x}+b\right)}{a}",1,"(3*Log[b + a*x^(1/3)])/a","A",2,2,15,0.1333,1,"{263, 260}"
2425,1,51,0,0.0309035,"\int \frac{1}{\left(a+\frac{b}{\sqrt[3]{x}}\right) x^2} \, dx","Int[1/((a + b/x^(1/3))*x^2),x]","-\frac{3 a^2 \log \left(a \sqrt[3]{x}+b\right)}{b^3}+\frac{a^2 \log (x)}{b^3}+\frac{3 a}{b^2 \sqrt[3]{x}}-\frac{3}{2 b x^{2/3}}","-\frac{3 a^2 \log \left(a \sqrt[3]{x}+b\right)}{b^3}+\frac{a^2 \log (x)}{b^3}+\frac{3 a}{b^2 \sqrt[3]{x}}-\frac{3}{2 b x^{2/3}}",1,"-3/(2*b*x^(2/3)) + (3*a)/(b^2*x^(1/3)) - (3*a^2*Log[b + a*x^(1/3)])/b^3 + (a^2*Log[x])/b^3","A",4,3,15,0.2000,1,"{263, 266, 44}"
2426,1,93,0,0.0514041,"\int \frac{1}{\left(a+\frac{b}{\sqrt[3]{x}}\right) x^3} \, dx","Int[1/((a + b/x^(1/3))*x^3),x]","\frac{3 a^3}{2 b^4 x^{2/3}}-\frac{3 a^4}{b^5 \sqrt[3]{x}}-\frac{a^2}{b^3 x}+\frac{3 a^5 \log \left(a \sqrt[3]{x}+b\right)}{b^6}-\frac{a^5 \log (x)}{b^6}+\frac{3 a}{4 b^2 x^{4/3}}-\frac{3}{5 b x^{5/3}}","\frac{3 a^3}{2 b^4 x^{2/3}}-\frac{3 a^4}{b^5 \sqrt[3]{x}}-\frac{a^2}{b^3 x}+\frac{3 a^5 \log \left(a \sqrt[3]{x}+b\right)}{b^6}-\frac{a^5 \log (x)}{b^6}+\frac{3 a}{4 b^2 x^{4/3}}-\frac{3}{5 b x^{5/3}}",1,"-3/(5*b*x^(5/3)) + (3*a)/(4*b^2*x^(4/3)) - a^2/(b^3*x) + (3*a^3)/(2*b^4*x^(2/3)) - (3*a^4)/(b^5*x^(1/3)) + (3*a^5*Log[b + a*x^(1/3)])/b^6 - (a^5*Log[x])/b^6","A",4,3,15,0.2000,1,"{263, 266, 44}"
2427,1,134,0,0.0756118,"\int \frac{1}{\left(a+\frac{b}{\sqrt[3]{x}}\right) x^4} \, dx","Int[1/((a + b/x^(1/3))*x^4),x]","-\frac{3 a^6}{2 b^7 x^{2/3}}-\frac{3 a^4}{4 b^5 x^{4/3}}+\frac{3 a^3}{5 b^4 x^{5/3}}-\frac{a^2}{2 b^3 x^2}+\frac{3 a^7}{b^8 \sqrt[3]{x}}+\frac{a^5}{b^6 x}-\frac{3 a^8 \log \left(a \sqrt[3]{x}+b\right)}{b^9}+\frac{a^8 \log (x)}{b^9}+\frac{3 a}{7 b^2 x^{7/3}}-\frac{3}{8 b x^{8/3}}","-\frac{3 a^6}{2 b^7 x^{2/3}}-\frac{3 a^4}{4 b^5 x^{4/3}}+\frac{3 a^3}{5 b^4 x^{5/3}}-\frac{a^2}{2 b^3 x^2}+\frac{3 a^7}{b^8 \sqrt[3]{x}}+\frac{a^5}{b^6 x}-\frac{3 a^8 \log \left(a \sqrt[3]{x}+b\right)}{b^9}+\frac{a^8 \log (x)}{b^9}+\frac{3 a}{7 b^2 x^{7/3}}-\frac{3}{8 b x^{8/3}}",1,"-3/(8*b*x^(8/3)) + (3*a)/(7*b^2*x^(7/3)) - a^2/(2*b^3*x^2) + (3*a^3)/(5*b^4*x^(5/3)) - (3*a^4)/(4*b^5*x^(4/3)) + a^5/(b^6*x) - (3*a^6)/(2*b^7*x^(2/3)) + (3*a^7)/(b^8*x^(1/3)) - (3*a^8*Log[b + a*x^(1/3)])/b^9 + (a^8*Log[x])/b^9","A",4,3,15,0.2000,1,"{263, 266, 44}"
2428,1,179,0,0.0939117,"\int \frac{1}{\left(a+\frac{b}{\sqrt[3]{x}}\right) x^5} \, dx","Int[1/((a + b/x^(1/3))*x^5),x]","\frac{3 a^9}{2 b^{10} x^{2/3}}+\frac{3 a^7}{4 b^8 x^{4/3}}-\frac{3 a^6}{5 b^7 x^{5/3}}+\frac{a^5}{2 b^6 x^2}-\frac{3 a^4}{7 b^5 x^{7/3}}+\frac{3 a^3}{8 b^4 x^{8/3}}-\frac{a^2}{3 b^3 x^3}-\frac{3 a^{10}}{b^{11} \sqrt[3]{x}}-\frac{a^8}{b^9 x}+\frac{3 a^{11} \log \left(a \sqrt[3]{x}+b\right)}{b^{12}}-\frac{a^{11} \log (x)}{b^{12}}+\frac{3 a}{10 b^2 x^{10/3}}-\frac{3}{11 b x^{11/3}}","\frac{3 a^9}{2 b^{10} x^{2/3}}+\frac{3 a^7}{4 b^8 x^{4/3}}-\frac{3 a^6}{5 b^7 x^{5/3}}+\frac{a^5}{2 b^6 x^2}-\frac{3 a^4}{7 b^5 x^{7/3}}+\frac{3 a^3}{8 b^4 x^{8/3}}-\frac{a^2}{3 b^3 x^3}-\frac{3 a^{10}}{b^{11} \sqrt[3]{x}}-\frac{a^8}{b^9 x}+\frac{3 a^{11} \log \left(a \sqrt[3]{x}+b\right)}{b^{12}}-\frac{a^{11} \log (x)}{b^{12}}+\frac{3 a}{10 b^2 x^{10/3}}-\frac{3}{11 b x^{11/3}}",1,"-3/(11*b*x^(11/3)) + (3*a)/(10*b^2*x^(10/3)) - a^2/(3*b^3*x^3) + (3*a^3)/(8*b^4*x^(8/3)) - (3*a^4)/(7*b^5*x^(7/3)) + a^5/(2*b^6*x^2) - (3*a^6)/(5*b^7*x^(5/3)) + (3*a^7)/(4*b^8*x^(4/3)) - a^8/(b^9*x) + (3*a^9)/(2*b^10*x^(2/3)) - (3*a^10)/(b^11*x^(1/3)) + (3*a^11*Log[b + a*x^(1/3)])/b^12 - (a^11*Log[x])/b^12","A",4,3,15,0.2000,1,"{263, 266, 44}"
2429,1,150,0,0.1317662,"\int \frac{x^2}{\left(a+\frac{b}{\sqrt[3]{x}}\right)^2} \, dx","Int[x^2/(a + b/x^(1/3))^2,x]","-\frac{12 b^7 x^{2/3}}{a^9}-\frac{9 b^5 x^{4/3}}{2 a^7}+\frac{3 b^4 x^{5/3}}{a^6}-\frac{2 b^3 x^2}{a^5}+\frac{9 b^2 x^{7/3}}{7 a^4}-\frac{3 b^{10}}{a^{11} \left(a \sqrt[3]{x}+b\right)}+\frac{27 b^8 \sqrt[3]{x}}{a^{10}}+\frac{7 b^6 x}{a^8}-\frac{30 b^9 \log \left(a \sqrt[3]{x}+b\right)}{a^{11}}-\frac{3 b x^{8/3}}{4 a^3}+\frac{x^3}{3 a^2}","-\frac{12 b^7 x^{2/3}}{a^9}-\frac{9 b^5 x^{4/3}}{2 a^7}+\frac{3 b^4 x^{5/3}}{a^6}-\frac{2 b^3 x^2}{a^5}+\frac{9 b^2 x^{7/3}}{7 a^4}-\frac{3 b^{10}}{a^{11} \left(a \sqrt[3]{x}+b\right)}+\frac{27 b^8 \sqrt[3]{x}}{a^{10}}+\frac{7 b^6 x}{a^8}-\frac{30 b^9 \log \left(a \sqrt[3]{x}+b\right)}{a^{11}}-\frac{3 b x^{8/3}}{4 a^3}+\frac{x^3}{3 a^2}",1,"(-3*b^10)/(a^11*(b + a*x^(1/3))) + (27*b^8*x^(1/3))/a^10 - (12*b^7*x^(2/3))/a^9 + (7*b^6*x)/a^8 - (9*b^5*x^(4/3))/(2*a^7) + (3*b^4*x^(5/3))/a^6 - (2*b^3*x^2)/a^5 + (9*b^2*x^(7/3))/(7*a^4) - (3*b*x^(8/3))/(4*a^3) + x^3/(3*a^2) - (30*b^9*Log[b + a*x^(1/3)])/a^11","A",4,3,15,0.2000,1,"{263, 266, 43}"
2430,1,113,0,0.085341,"\int \frac{x}{\left(a+\frac{b}{\sqrt[3]{x}}\right)^2} \, dx","Int[x/(a + b/x^(1/3))^2,x]","\frac{15 b^4 x^{2/3}}{2 a^6}+\frac{9 b^2 x^{4/3}}{4 a^4}+\frac{3 b^7}{a^8 \left(a \sqrt[3]{x}+b\right)}-\frac{18 b^5 \sqrt[3]{x}}{a^7}-\frac{4 b^3 x}{a^5}+\frac{21 b^6 \log \left(a \sqrt[3]{x}+b\right)}{a^8}-\frac{6 b x^{5/3}}{5 a^3}+\frac{x^2}{2 a^2}","\frac{15 b^4 x^{2/3}}{2 a^6}+\frac{9 b^2 x^{4/3}}{4 a^4}+\frac{3 b^7}{a^8 \left(a \sqrt[3]{x}+b\right)}-\frac{18 b^5 \sqrt[3]{x}}{a^7}-\frac{4 b^3 x}{a^5}+\frac{21 b^6 \log \left(a \sqrt[3]{x}+b\right)}{a^8}-\frac{6 b x^{5/3}}{5 a^3}+\frac{x^2}{2 a^2}",1,"(3*b^7)/(a^8*(b + a*x^(1/3))) - (18*b^5*x^(1/3))/a^7 + (15*b^4*x^(2/3))/(2*a^6) - (4*b^3*x)/a^5 + (9*b^2*x^(4/3))/(4*a^4) - (6*b*x^(5/3))/(5*a^3) + x^2/(2*a^2) + (21*b^6*Log[b + a*x^(1/3)])/a^8","A",4,3,13,0.2308,1,"{263, 266, 43}"
2431,1,77,0,0.0515696,"\int \frac{1}{\left(a+\frac{b}{\sqrt[3]{x}}\right)^2} \, dx","Int[(a + b/x^(1/3))^(-2),x]","\frac{3 b^3}{a^4 \left(a+\frac{b}{\sqrt[3]{x}}\right)}+\frac{9 b^2 \sqrt[3]{x}}{a^4}-\frac{12 b^3 \log \left(a+\frac{b}{\sqrt[3]{x}}\right)}{a^5}-\frac{4 b^3 \log (x)}{a^5}-\frac{3 b x^{2/3}}{a^3}+\frac{x}{a^2}","\frac{3 b^3}{a^4 \left(a+\frac{b}{\sqrt[3]{x}}\right)}+\frac{9 b^2 \sqrt[3]{x}}{a^4}-\frac{12 b^3 \log \left(a+\frac{b}{\sqrt[3]{x}}\right)}{a^5}-\frac{4 b^3 \log (x)}{a^5}-\frac{3 b x^{2/3}}{a^3}+\frac{x}{a^2}",1,"(3*b^3)/(a^4*(a + b/x^(1/3))) + (9*b^2*x^(1/3))/a^4 - (3*b*x^(2/3))/a^3 + x/a^2 - (12*b^3*Log[a + b/x^(1/3)])/a^5 - (4*b^3*Log[x])/a^5","A",3,2,11,0.1818,1,"{190, 44}"
2432,1,33,0,0.0214783,"\int \frac{1}{\left(a+\frac{b}{\sqrt[3]{x}}\right)^2 x} \, dx","Int[1/((a + b/x^(1/3))^2*x),x]","\frac{3 b}{a^2 \left(a \sqrt[3]{x}+b\right)}+\frac{3 \log \left(a \sqrt[3]{x}+b\right)}{a^2}","\frac{3 b}{a^2 \left(a \sqrt[3]{x}+b\right)}+\frac{3 \log \left(a \sqrt[3]{x}+b\right)}{a^2}",1,"(3*b)/(a^2*(b + a*x^(1/3))) + (3*Log[b + a*x^(1/3)])/a^2","A",4,3,15,0.2000,1,"{263, 266, 43}"
2433,1,52,0,0.0349992,"\int \frac{1}{\left(a+\frac{b}{\sqrt[3]{x}}\right)^2 x^2} \, dx","Int[1/((a + b/x^(1/3))^2*x^2),x]","-\frac{3 a}{b^2 \left(a \sqrt[3]{x}+b\right)}+\frac{6 a \log \left(a \sqrt[3]{x}+b\right)}{b^3}-\frac{2 a \log (x)}{b^3}-\frac{3}{b^2 \sqrt[3]{x}}","-\frac{3 a}{b^2 \left(a \sqrt[3]{x}+b\right)}+\frac{6 a \log \left(a \sqrt[3]{x}+b\right)}{b^3}-\frac{2 a \log (x)}{b^3}-\frac{3}{b^2 \sqrt[3]{x}}",1,"(-3*a)/(b^2*(b + a*x^(1/3))) - 3/(b^2*x^(1/3)) + (6*a*Log[b + a*x^(1/3)])/b^3 - (2*a*Log[x])/b^3","A",4,3,15,0.2000,1,"{263, 266, 44}"
2434,1,97,0,0.0647476,"\int \frac{1}{\left(a+\frac{b}{\sqrt[3]{x}}\right)^2 x^3} \, dx","Int[1/((a + b/x^(1/3))^2*x^3),x]","-\frac{9 a^2}{2 b^4 x^{2/3}}+\frac{3 a^4}{b^5 \left(a \sqrt[3]{x}+b\right)}+\frac{12 a^3}{b^5 \sqrt[3]{x}}-\frac{15 a^4 \log \left(a \sqrt[3]{x}+b\right)}{b^6}+\frac{5 a^4 \log (x)}{b^6}+\frac{2 a}{b^3 x}-\frac{3}{4 b^2 x^{4/3}}","-\frac{9 a^2}{2 b^4 x^{2/3}}+\frac{3 a^4}{b^5 \left(a \sqrt[3]{x}+b\right)}+\frac{12 a^3}{b^5 \sqrt[3]{x}}-\frac{15 a^4 \log \left(a \sqrt[3]{x}+b\right)}{b^6}+\frac{5 a^4 \log (x)}{b^6}+\frac{2 a}{b^3 x}-\frac{3}{4 b^2 x^{4/3}}",1,"(3*a^4)/(b^5*(b + a*x^(1/3))) - 3/(4*b^2*x^(4/3)) + (2*a)/(b^3*x) - (9*a^2)/(2*b^4*x^(2/3)) + (12*a^3)/(b^5*x^(1/3)) - (15*a^4*Log[b + a*x^(1/3)])/b^6 + (5*a^4*Log[x])/b^6","A",4,3,15,0.2000,1,"{263, 266, 44}"
2435,1,133,0,0.1032386,"\int \frac{1}{\left(a+\frac{b}{\sqrt[3]{x}}\right)^2 x^4} \, dx","Int[1/((a + b/x^(1/3))^2*x^4),x]","\frac{9 a^5}{b^7 x^{2/3}}+\frac{3 a^3}{b^5 x^{4/3}}-\frac{9 a^2}{5 b^4 x^{5/3}}-\frac{3 a^7}{b^8 \left(a \sqrt[3]{x}+b\right)}-\frac{21 a^6}{b^8 \sqrt[3]{x}}-\frac{5 a^4}{b^6 x}+\frac{24 a^7 \log \left(a \sqrt[3]{x}+b\right)}{b^9}-\frac{8 a^7 \log (x)}{b^9}+\frac{a}{b^3 x^2}-\frac{3}{7 b^2 x^{7/3}}","\frac{9 a^5}{b^7 x^{2/3}}+\frac{3 a^3}{b^5 x^{4/3}}-\frac{9 a^2}{5 b^4 x^{5/3}}-\frac{3 a^7}{b^8 \left(a \sqrt[3]{x}+b\right)}-\frac{21 a^6}{b^8 \sqrt[3]{x}}-\frac{5 a^4}{b^6 x}+\frac{24 a^7 \log \left(a \sqrt[3]{x}+b\right)}{b^9}-\frac{8 a^7 \log (x)}{b^9}+\frac{a}{b^3 x^2}-\frac{3}{7 b^2 x^{7/3}}",1,"(-3*a^7)/(b^8*(b + a*x^(1/3))) - 3/(7*b^2*x^(7/3)) + a/(b^3*x^2) - (9*a^2)/(5*b^4*x^(5/3)) + (3*a^3)/(b^5*x^(4/3)) - (5*a^4)/(b^6*x) + (9*a^5)/(b^7*x^(2/3)) - (21*a^6)/(b^8*x^(1/3)) + (24*a^7*Log[b + a*x^(1/3)])/b^9 - (8*a^7*Log[x])/b^9","A",4,3,15,0.2000,1,"{263, 266, 44}"
2436,1,183,0,0.1316647,"\int \frac{1}{\left(a+\frac{b}{\sqrt[3]{x}}\right)^2 x^5} \, dx","Int[1/((a + b/x^(1/3))^2*x^5),x]","-\frac{27 a^8}{2 b^{10} x^{2/3}}-\frac{21 a^6}{4 b^8 x^{4/3}}+\frac{18 a^5}{5 b^7 x^{5/3}}-\frac{5 a^4}{2 b^6 x^2}+\frac{12 a^3}{7 b^5 x^{7/3}}-\frac{9 a^2}{8 b^4 x^{8/3}}+\frac{3 a^{10}}{b^{11} \left(a \sqrt[3]{x}+b\right)}+\frac{30 a^9}{b^{11} \sqrt[3]{x}}+\frac{8 a^7}{b^9 x}-\frac{33 a^{10} \log \left(a \sqrt[3]{x}+b\right)}{b^{12}}+\frac{11 a^{10} \log (x)}{b^{12}}+\frac{2 a}{3 b^3 x^3}-\frac{3}{10 b^2 x^{10/3}}","-\frac{27 a^8}{2 b^{10} x^{2/3}}-\frac{21 a^6}{4 b^8 x^{4/3}}+\frac{18 a^5}{5 b^7 x^{5/3}}-\frac{5 a^4}{2 b^6 x^2}+\frac{12 a^3}{7 b^5 x^{7/3}}-\frac{9 a^2}{8 b^4 x^{8/3}}+\frac{3 a^{10}}{b^{11} \left(a \sqrt[3]{x}+b\right)}+\frac{30 a^9}{b^{11} \sqrt[3]{x}}+\frac{8 a^7}{b^9 x}-\frac{33 a^{10} \log \left(a \sqrt[3]{x}+b\right)}{b^{12}}+\frac{11 a^{10} \log (x)}{b^{12}}+\frac{2 a}{3 b^3 x^3}-\frac{3}{10 b^2 x^{10/3}}",1,"(3*a^10)/(b^11*(b + a*x^(1/3))) - 3/(10*b^2*x^(10/3)) + (2*a)/(3*b^3*x^3) - (9*a^2)/(8*b^4*x^(8/3)) + (12*a^3)/(7*b^5*x^(7/3)) - (5*a^4)/(2*b^6*x^2) + (18*a^5)/(5*b^7*x^(5/3)) - (21*a^6)/(4*b^8*x^(4/3)) + (8*a^7)/(b^9*x) - (27*a^8)/(2*b^10*x^(2/3)) + (30*a^9)/(b^11*x^(1/3)) - (33*a^10*Log[b + a*x^(1/3)])/b^12 + (11*a^10*Log[x])/b^12","A",4,3,15,0.2000,1,"{263, 266, 44}"
2437,1,171,0,0.1518026,"\int \frac{x^2}{\left(a+\frac{b}{\sqrt[3]{x}}\right)^3} \, dx","Int[x^2/(a + b/x^(1/3))^3,x]","-\frac{54 b^7 x^{2/3}}{a^{10}}-\frac{63 b^5 x^{4/3}}{4 a^8}+\frac{9 b^4 x^{5/3}}{a^7}-\frac{5 b^3 x^2}{a^6}+\frac{18 b^2 x^{7/3}}{7 a^5}+\frac{3 b^{11}}{2 a^{12} \left(a \sqrt[3]{x}+b\right)^2}-\frac{33 b^{10}}{a^{12} \left(a \sqrt[3]{x}+b\right)}+\frac{135 b^8 \sqrt[3]{x}}{a^{11}}+\frac{28 b^6 x}{a^9}-\frac{165 b^9 \log \left(a \sqrt[3]{x}+b\right)}{a^{12}}-\frac{9 b x^{8/3}}{8 a^4}+\frac{x^3}{3 a^3}","-\frac{54 b^7 x^{2/3}}{a^{10}}-\frac{63 b^5 x^{4/3}}{4 a^8}+\frac{9 b^4 x^{5/3}}{a^7}-\frac{5 b^3 x^2}{a^6}+\frac{18 b^2 x^{7/3}}{7 a^5}+\frac{3 b^{11}}{2 a^{12} \left(a \sqrt[3]{x}+b\right)^2}-\frac{33 b^{10}}{a^{12} \left(a \sqrt[3]{x}+b\right)}+\frac{135 b^8 \sqrt[3]{x}}{a^{11}}+\frac{28 b^6 x}{a^9}-\frac{165 b^9 \log \left(a \sqrt[3]{x}+b\right)}{a^{12}}-\frac{9 b x^{8/3}}{8 a^4}+\frac{x^3}{3 a^3}",1,"(3*b^11)/(2*a^12*(b + a*x^(1/3))^2) - (33*b^10)/(a^12*(b + a*x^(1/3))) + (135*b^8*x^(1/3))/a^11 - (54*b^7*x^(2/3))/a^10 + (28*b^6*x)/a^9 - (63*b^5*x^(4/3))/(4*a^8) + (9*b^4*x^(5/3))/a^7 - (5*b^3*x^2)/a^6 + (18*b^2*x^(7/3))/(7*a^5) - (9*b*x^(8/3))/(8*a^4) + x^3/(3*a^3) - (165*b^9*Log[b + a*x^(1/3)])/a^12","A",4,3,15,0.2000,1,"{263, 266, 43}"
2438,1,134,0,0.1055566,"\int \frac{x}{\left(a+\frac{b}{\sqrt[3]{x}}\right)^3} \, dx","Int[x/(a + b/x^(1/3))^3,x]","\frac{45 b^4 x^{2/3}}{2 a^7}+\frac{9 b^2 x^{4/3}}{2 a^5}-\frac{3 b^8}{2 a^9 \left(a \sqrt[3]{x}+b\right)^2}+\frac{24 b^7}{a^9 \left(a \sqrt[3]{x}+b\right)}-\frac{63 b^5 \sqrt[3]{x}}{a^8}-\frac{10 b^3 x}{a^6}+\frac{84 b^6 \log \left(a \sqrt[3]{x}+b\right)}{a^9}-\frac{9 b x^{5/3}}{5 a^4}+\frac{x^2}{2 a^3}","\frac{45 b^4 x^{2/3}}{2 a^7}+\frac{9 b^2 x^{4/3}}{2 a^5}-\frac{3 b^8}{2 a^9 \left(a \sqrt[3]{x}+b\right)^2}+\frac{24 b^7}{a^9 \left(a \sqrt[3]{x}+b\right)}-\frac{63 b^5 \sqrt[3]{x}}{a^8}-\frac{10 b^3 x}{a^6}+\frac{84 b^6 \log \left(a \sqrt[3]{x}+b\right)}{a^9}-\frac{9 b x^{5/3}}{5 a^4}+\frac{x^2}{2 a^3}",1,"(-3*b^8)/(2*a^9*(b + a*x^(1/3))^2) + (24*b^7)/(a^9*(b + a*x^(1/3))) - (63*b^5*x^(1/3))/a^8 + (45*b^4*x^(2/3))/(2*a^7) - (10*b^3*x)/a^6 + (9*b^2*x^(4/3))/(2*a^5) - (9*b*x^(5/3))/(5*a^4) + x^2/(2*a^3) + (84*b^6*Log[b + a*x^(1/3)])/a^9","A",4,3,13,0.2308,1,"{263, 266, 43}"
2439,1,100,0,0.0683635,"\int \frac{1}{\left(a+\frac{b}{\sqrt[3]{x}}\right)^3} \, dx","Int[(a + b/x^(1/3))^(-3),x]","\frac{12 b^3}{a^5 \left(a+\frac{b}{\sqrt[3]{x}}\right)}+\frac{3 b^3}{2 a^4 \left(a+\frac{b}{\sqrt[3]{x}}\right)^2}+\frac{18 b^2 \sqrt[3]{x}}{a^5}-\frac{30 b^3 \log \left(a+\frac{b}{\sqrt[3]{x}}\right)}{a^6}-\frac{10 b^3 \log (x)}{a^6}-\frac{9 b x^{2/3}}{2 a^4}+\frac{x}{a^3}","\frac{12 b^3}{a^5 \left(a+\frac{b}{\sqrt[3]{x}}\right)}+\frac{3 b^3}{2 a^4 \left(a+\frac{b}{\sqrt[3]{x}}\right)^2}+\frac{18 b^2 \sqrt[3]{x}}{a^5}-\frac{30 b^3 \log \left(a+\frac{b}{\sqrt[3]{x}}\right)}{a^6}-\frac{10 b^3 \log (x)}{a^6}-\frac{9 b x^{2/3}}{2 a^4}+\frac{x}{a^3}",1,"(3*b^3)/(2*a^4*(a + b/x^(1/3))^2) + (12*b^3)/(a^5*(a + b/x^(1/3))) + (18*b^2*x^(1/3))/a^5 - (9*b*x^(2/3))/(2*a^4) + x/a^3 - (30*b^3*Log[a + b/x^(1/3)])/a^6 - (10*b^3*Log[x])/a^6","A",3,2,11,0.1818,1,"{190, 44}"
2440,1,54,0,0.0321558,"\int \frac{1}{\left(a+\frac{b}{\sqrt[3]{x}}\right)^3 x} \, dx","Int[1/((a + b/x^(1/3))^3*x),x]","-\frac{3 b^2}{2 a^3 \left(a \sqrt[3]{x}+b\right)^2}+\frac{6 b}{a^3 \left(a \sqrt[3]{x}+b\right)}+\frac{3 \log \left(a \sqrt[3]{x}+b\right)}{a^3}","-\frac{3 b^2}{2 a^3 \left(a \sqrt[3]{x}+b\right)^2}+\frac{6 b}{a^3 \left(a \sqrt[3]{x}+b\right)}+\frac{3 \log \left(a \sqrt[3]{x}+b\right)}{a^3}",1,"(-3*b^2)/(2*a^3*(b + a*x^(1/3))^2) + (6*b)/(a^3*(b + a*x^(1/3))) + (3*Log[b + a*x^(1/3)])/a^3","A",4,3,15,0.2000,1,"{263, 190, 43}"
2441,1,56,0,0.0340394,"\int \frac{1}{\left(a+\frac{b}{\sqrt[3]{x}}\right)^3 x^2} \, dx","Int[1/((a + b/x^(1/3))^3*x^2),x]","\frac{3}{b^2 \left(a \sqrt[3]{x}+b\right)}-\frac{3 \log \left(a \sqrt[3]{x}+b\right)}{b^3}+\frac{3}{2 b \left(a \sqrt[3]{x}+b\right)^2}+\frac{\log (x)}{b^3}","\frac{3}{b^2 \left(a \sqrt[3]{x}+b\right)}-\frac{3 \log \left(a \sqrt[3]{x}+b\right)}{b^3}+\frac{3}{2 b \left(a \sqrt[3]{x}+b\right)^2}+\frac{\log (x)}{b^3}",1,"3/(2*b*(b + a*x^(1/3))^2) + 3/(b^2*(b + a*x^(1/3))) - (3*Log[b + a*x^(1/3)])/b^3 + Log[x]/b^3","A",4,3,15,0.2000,1,"{263, 266, 44}"
2442,1,103,0,0.0684681,"\int \frac{1}{\left(a+\frac{b}{\sqrt[3]{x}}\right)^3 x^3} \, dx","Int[1/((a + b/x^(1/3))^3*x^3),x]","-\frac{12 a^3}{b^5 \left(a \sqrt[3]{x}+b\right)}-\frac{3 a^3}{2 b^4 \left(a \sqrt[3]{x}+b\right)^2}-\frac{18 a^2}{b^5 \sqrt[3]{x}}+\frac{30 a^3 \log \left(a \sqrt[3]{x}+b\right)}{b^6}-\frac{10 a^3 \log (x)}{b^6}+\frac{9 a}{2 b^4 x^{2/3}}-\frac{1}{b^3 x}","-\frac{12 a^3}{b^5 \left(a \sqrt[3]{x}+b\right)}-\frac{3 a^3}{2 b^4 \left(a \sqrt[3]{x}+b\right)^2}-\frac{18 a^2}{b^5 \sqrt[3]{x}}+\frac{30 a^3 \log \left(a \sqrt[3]{x}+b\right)}{b^6}-\frac{10 a^3 \log (x)}{b^6}+\frac{9 a}{2 b^4 x^{2/3}}-\frac{1}{b^3 x}",1,"(-3*a^3)/(2*b^4*(b + a*x^(1/3))^2) - (12*a^3)/(b^5*(b + a*x^(1/3))) - 1/(b^3*x) + (9*a)/(2*b^4*x^(2/3)) - (18*a^2)/(b^5*x^(1/3)) + (30*a^3*Log[b + a*x^(1/3)])/b^6 - (10*a^3*Log[x])/b^6","A",4,3,15,0.2000,1,"{263, 266, 44}"
2443,1,146,0,0.1061494,"\int \frac{1}{\left(a+\frac{b}{\sqrt[3]{x}}\right)^3 x^4} \, dx","Int[1/((a + b/x^(1/3))^3*x^4),x]","-\frac{45 a^4}{2 b^7 x^{2/3}}-\frac{9 a^2}{2 b^5 x^{4/3}}+\frac{21 a^6}{b^8 \left(a \sqrt[3]{x}+b\right)}+\frac{3 a^6}{2 b^7 \left(a \sqrt[3]{x}+b\right)^2}+\frac{63 a^5}{b^8 \sqrt[3]{x}}+\frac{10 a^3}{b^6 x}-\frac{84 a^6 \log \left(a \sqrt[3]{x}+b\right)}{b^9}+\frac{28 a^6 \log (x)}{b^9}+\frac{9 a}{5 b^4 x^{5/3}}-\frac{1}{2 b^3 x^2}","-\frac{45 a^4}{2 b^7 x^{2/3}}-\frac{9 a^2}{2 b^5 x^{4/3}}+\frac{21 a^6}{b^8 \left(a \sqrt[3]{x}+b\right)}+\frac{3 a^6}{2 b^7 \left(a \sqrt[3]{x}+b\right)^2}+\frac{63 a^5}{b^8 \sqrt[3]{x}}+\frac{10 a^3}{b^6 x}-\frac{84 a^6 \log \left(a \sqrt[3]{x}+b\right)}{b^9}+\frac{28 a^6 \log (x)}{b^9}+\frac{9 a}{5 b^4 x^{5/3}}-\frac{1}{2 b^3 x^2}",1,"(3*a^6)/(2*b^7*(b + a*x^(1/3))^2) + (21*a^6)/(b^8*(b + a*x^(1/3))) - 1/(2*b^3*x^2) + (9*a)/(5*b^4*x^(5/3)) - (9*a^2)/(2*b^5*x^(4/3)) + (10*a^3)/(b^6*x) - (45*a^4)/(2*b^7*x^(2/3)) + (63*a^5)/(b^8*x^(1/3)) - (84*a^6*Log[b + a*x^(1/3)])/b^9 + (28*a^6*Log[x])/b^9","A",4,3,15,0.2000,1,"{263, 266, 44}"
2444,1,183,0,0.143918,"\int \frac{1}{\left(a+\frac{b}{\sqrt[3]{x}}\right)^3 x^5} \, dx","Int[1/((a + b/x^(1/3))^3*x^5),x]","\frac{54 a^7}{b^{10} x^{2/3}}+\frac{63 a^5}{4 b^8 x^{4/3}}-\frac{9 a^4}{b^7 x^{5/3}}+\frac{5 a^3}{b^6 x^2}-\frac{18 a^2}{7 b^5 x^{7/3}}-\frac{30 a^9}{b^{11} \left(a \sqrt[3]{x}+b\right)}-\frac{3 a^9}{2 b^{10} \left(a \sqrt[3]{x}+b\right)^2}-\frac{135 a^8}{b^{11} \sqrt[3]{x}}-\frac{28 a^6}{b^9 x}+\frac{165 a^9 \log \left(a \sqrt[3]{x}+b\right)}{b^{12}}-\frac{55 a^9 \log (x)}{b^{12}}+\frac{9 a}{8 b^4 x^{8/3}}-\frac{1}{3 b^3 x^3}","\frac{54 a^7}{b^{10} x^{2/3}}+\frac{63 a^5}{4 b^8 x^{4/3}}-\frac{9 a^4}{b^7 x^{5/3}}+\frac{5 a^3}{b^6 x^2}-\frac{18 a^2}{7 b^5 x^{7/3}}-\frac{30 a^9}{b^{11} \left(a \sqrt[3]{x}+b\right)}-\frac{3 a^9}{2 b^{10} \left(a \sqrt[3]{x}+b\right)^2}-\frac{135 a^8}{b^{11} \sqrt[3]{x}}-\frac{28 a^6}{b^9 x}+\frac{165 a^9 \log \left(a \sqrt[3]{x}+b\right)}{b^{12}}-\frac{55 a^9 \log (x)}{b^{12}}+\frac{9 a}{8 b^4 x^{8/3}}-\frac{1}{3 b^3 x^3}",1,"(-3*a^9)/(2*b^10*(b + a*x^(1/3))^2) - (30*a^9)/(b^11*(b + a*x^(1/3))) - 1/(3*b^3*x^3) + (9*a)/(8*b^4*x^(8/3)) - (18*a^2)/(7*b^5*x^(7/3)) + (5*a^3)/(b^6*x^2) - (9*a^4)/(b^7*x^(5/3)) + (63*a^5)/(4*b^8*x^(4/3)) - (28*a^6)/(b^9*x) + (54*a^7)/(b^10*x^(2/3)) - (135*a^8)/(b^11*x^(1/3)) + (165*a^9*Log[b + a*x^(1/3)])/b^12 - (55*a^9*Log[x])/b^12","A",4,3,15,0.2000,1,"{263, 266, 44}"
2445,1,44,0,0.0238145,"\int \frac{1}{1+\frac{b}{\sqrt[3]{x}}} \, dx","Int[(1 + b/x^(1/3))^(-1),x]","3 b^2 \sqrt[3]{x}-3 b^3 \log \left(\frac{b}{\sqrt[3]{x}}+1\right)-b^3 \log (x)-\frac{3}{2} b x^{2/3}+x","3 b^2 \sqrt[3]{x}-3 b^3 \log \left(\frac{b}{\sqrt[3]{x}}+1\right)-b^3 \log (x)-\frac{3}{2} b x^{2/3}+x",1,"3*b^2*x^(1/3) - (3*b*x^(2/3))/2 + x - 3*b^3*Log[1 + b/x^(1/3)] - b^3*Log[x]","A",3,2,11,0.1818,1,"{190, 44}"
2446,1,15,0,0.0031098,"\int x^{2/3} \left(1+x^{5/3}\right)^{2/3} \, dx","Int[x^(2/3)*(1 + x^(5/3))^(2/3),x]","\frac{9}{25} \left(x^{5/3}+1\right)^{5/3}","\frac{9}{25} \left(x^{5/3}+1\right)^{5/3}",1,"(9*(1 + x^(5/3))^(5/3))/25","A",1,1,17,0.05882,1,"{261}"
2447,1,21,0,0.0044601,"\int x^{7/3} \left(a^{10/3}-x^{10/3}\right)^{19/7} \, dx","Int[x^(7/3)*(a^(10/3) - x^(10/3))^(19/7),x]","-\frac{21}{260} \left(a^{10/3}-x^{10/3}\right)^{26/7}","-\frac{21}{260} \left(a^{10/3}-x^{10/3}\right)^{26/7}",1,"(-21*(a^(10/3) - x^(10/3))^(26/7))/260","A",1,1,23,0.04348,1,"{261}"
2448,1,45,0,0.0147312,"\int \frac{1}{1+\sqrt[5]{x}} \, dx","Int[(1 + x^(1/5))^(-1),x]","\frac{5 x^{4/5}}{4}-\frac{5 x^{3/5}}{3}+\frac{5 x^{2/5}}{2}-5 \sqrt[5]{x}+5 \log \left(\sqrt[5]{x}+1\right)","\frac{5 x^{4/5}}{4}-\frac{5 x^{3/5}}{3}+\frac{5 x^{2/5}}{2}-5 \sqrt[5]{x}+5 \log \left(\sqrt[5]{x}+1\right)",1,"-5*x^(1/5) + (5*x^(2/5))/2 - (5*x^(3/5))/3 + (5*x^(4/5))/4 + 5*Log[1 + x^(1/5)]","A",3,2,9,0.2222,1,"{190, 43}"
2449,1,15,0,0.0030842,"\int \frac{1}{\sqrt{1+x^{4/5}} \sqrt[5]{x}} \, dx","Int[1/(Sqrt[1 + x^(4/5)]*x^(1/5)),x]","\frac{5}{2} \sqrt{x^{4/5}+1}","\frac{5}{2} \sqrt{x^{4/5}+1}",1,"(5*Sqrt[1 + x^(4/5)])/2","A",1,1,17,0.05882,1,"{261}"
2450,1,18,0,0.0025717,"\int \left(a+\frac{b}{x^{3/5}}\right)^{2/3} \, dx","Int[(a + b/x^(3/5))^(2/3),x]","\frac{x \left(a+\frac{b}{x^{3/5}}\right)^{5/3}}{a}","\frac{x \left(a+\frac{b}{x^{3/5}}\right)^{5/3}}{a}",1,"((a + b/x^(3/5))^(5/3)*x)/a","A",1,1,13,0.07692,1,"{191}"
2451,1,21,0,0.0090356,"\int x^3 \left(a+b x^n\right) \, dx","Int[x^3*(a + b*x^n),x]","\frac{a x^4}{4}+\frac{b x^{n+4}}{n+4}","\frac{a x^4}{4}+\frac{b x^{n+4}}{n+4}",1,"(a*x^4)/4 + (b*x^(4 + n))/(4 + n)","A",2,1,11,0.09091,1,"{14}"
2452,1,21,0,0.0081223,"\int x^2 \left(a+b x^n\right) \, dx","Int[x^2*(a + b*x^n),x]","\frac{a x^3}{3}+\frac{b x^{n+3}}{n+3}","\frac{a x^3}{3}+\frac{b x^{n+3}}{n+3}",1,"(a*x^3)/3 + (b*x^(3 + n))/(3 + n)","A",2,1,11,0.09091,1,"{14}"
2453,1,21,0,0.0071917,"\int x \left(a+b x^n\right) \, dx","Int[x*(a + b*x^n),x]","\frac{a x^2}{2}+\frac{b x^{n+2}}{n+2}","\frac{a x^2}{2}+\frac{b x^{n+2}}{n+2}",1,"(a*x^2)/2 + (b*x^(2 + n))/(2 + n)","A",2,1,9,0.1111,1,"{14}"
2454,1,16,0,0.0035536,"\int \left(a+b x^n\right) \, dx","Int[a + b*x^n,x]","a x+\frac{b x^{n+1}}{n+1}","a x+\frac{b x^{n+1}}{n+1}",1,"a*x + (b*x^(1 + n))/(1 + n)","A",1,0,7,0,1,"{}"
2455,1,13,0,0.0064869,"\int \frac{a+b x^n}{x} \, dx","Int[(a + b*x^n)/x,x]","a \log (x)+\frac{b x^n}{n}","a \log (x)+\frac{b x^n}{n}",1,"(b*x^n)/n + a*Log[x]","A",2,1,11,0.09091,1,"{14}"
2456,1,22,0,0.0087256,"\int \frac{a+b x^n}{x^2} \, dx","Int[(a + b*x^n)/x^2,x]","-\frac{a}{x}-\frac{b x^{n-1}}{1-n}","-\frac{a}{x}-\frac{b x^{n-1}}{1-n}",1,"-(a/x) - (b*x^(-1 + n))/(1 - n)","A",2,1,11,0.09091,1,"{14}"
2457,1,24,0,0.0087493,"\int \frac{a+b x^n}{x^3} \, dx","Int[(a + b*x^n)/x^3,x]","-\frac{a}{2 x^2}-\frac{b x^{n-2}}{2-n}","-\frac{a}{2 x^2}-\frac{b x^{n-2}}{2-n}",1,"-a/(2*x^2) - (b*x^(-2 + n))/(2 - n)","A",2,1,11,0.09091,1,"{14}"
2458,1,44,0,0.0178456,"\int x^3 \left(a+b x^n\right)^2 \, dx","Int[x^3*(a + b*x^n)^2,x]","\frac{a^2 x^4}{4}+\frac{2 a b x^{n+4}}{n+4}+\frac{b^2 x^{2 (n+2)}}{2 (n+2)}","\frac{a^2 x^4}{4}+\frac{2 a b x^{n+4}}{n+4}+\frac{b^2 x^{2 (n+2)}}{2 (n+2)}",1,"(a^2*x^4)/4 + (b^2*x^(2*(2 + n)))/(2*(2 + n)) + (2*a*b*x^(4 + n))/(4 + n)","A",2,1,13,0.07692,1,"{270}"
2459,1,43,0,0.0199481,"\int x^2 \left(a+b x^n\right)^2 \, dx","Int[x^2*(a + b*x^n)^2,x]","\frac{a^2 x^3}{3}+\frac{2 a b x^{n+3}}{n+3}+\frac{b^2 x^{2 n+3}}{2 n+3}","\frac{a^2 x^3}{3}+\frac{2 a b x^{n+3}}{n+3}+\frac{b^2 x^{2 n+3}}{2 n+3}",1,"(a^2*x^3)/3 + (2*a*b*x^(3 + n))/(3 + n) + (b^2*x^(3 + 2*n))/(3 + 2*n)","A",2,1,13,0.07692,1,"{270}"
2460,1,44,0,0.0162416,"\int x \left(a+b x^n\right)^2 \, dx","Int[x*(a + b*x^n)^2,x]","\frac{a^2 x^2}{2}+\frac{2 a b x^{n+2}}{n+2}+\frac{b^2 x^{2 (n+1)}}{2 (n+1)}","\frac{a^2 x^2}{2}+\frac{2 a b x^{n+2}}{n+2}+\frac{b^2 x^{2 (n+1)}}{2 (n+1)}",1,"(a^2*x^2)/2 + (b^2*x^(2*(1 + n)))/(2*(1 + n)) + (2*a*b*x^(2 + n))/(2 + n)","A",2,1,11,0.09091,1,"{270}"
2461,1,38,0,0.0147325,"\int \left(a+b x^n\right)^2 \, dx","Int[(a + b*x^n)^2,x]","a^2 x+\frac{2 a b x^{n+1}}{n+1}+\frac{b^2 x^{2 n+1}}{2 n+1}","a^2 x+\frac{2 a b x^{n+1}}{n+1}+\frac{b^2 x^{2 n+1}}{2 n+1}",1,"a^2*x + (2*a*b*x^(1 + n))/(1 + n) + (b^2*x^(1 + 2*n))/(1 + 2*n)","A",2,1,9,0.1111,1,"{244}"
2462,1,32,0,0.0140607,"\int \frac{\left(a+b x^n\right)^2}{x} \, dx","Int[(a + b*x^n)^2/x,x]","a^2 \log (x)+\frac{2 a b x^n}{n}+\frac{b^2 x^{2 n}}{2 n}","a^2 \log (x)+\frac{2 a b x^n}{n}+\frac{b^2 x^{2 n}}{2 n}",1,"(2*a*b*x^n)/n + (b^2*x^(2*n))/(2*n) + a^2*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
2463,1,44,0,0.0218228,"\int \frac{\left(a+b x^n\right)^2}{x^2} \, dx","Int[(a + b*x^n)^2/x^2,x]","-\frac{a^2}{x}-\frac{2 a b x^{n-1}}{1-n}-\frac{b^2 x^{2 n-1}}{1-2 n}","-\frac{a^2}{x}-\frac{2 a b x^{n-1}}{1-n}-\frac{b^2 x^{2 n-1}}{1-2 n}",1,"-(a^2/x) - (2*a*b*x^(-1 + n))/(1 - n) - (b^2*x^(-1 + 2*n))/(1 - 2*n)","A",2,1,13,0.07692,1,"{270}"
2464,1,50,0,0.0209923,"\int \frac{\left(a+b x^n\right)^2}{x^3} \, dx","Int[(a + b*x^n)^2/x^3,x]","-\frac{a^2}{2 x^2}-\frac{2 a b x^{n-2}}{2-n}-\frac{b^2 x^{-2 (1-n)}}{2 (1-n)}","-\frac{a^2}{2 x^2}-\frac{2 a b x^{n-2}}{2-n}-\frac{b^2 x^{-2 (1-n)}}{2 (1-n)}",1,"-a^2/(2*x^2) - b^2/(2*(1 - n)*x^(2*(1 - n))) - (2*a*b*x^(-2 + n))/(2 - n)","A",2,1,13,0.07692,1,"{270}"
2465,1,65,0,0.0315563,"\int x^3 \left(a+b x^n\right)^3 \, dx","Int[x^3*(a + b*x^n)^3,x]","\frac{3 a^2 b x^{n+4}}{n+4}+\frac{a^3 x^4}{4}+\frac{3 a b^2 x^{2 (n+2)}}{2 (n+2)}+\frac{b^3 x^{3 n+4}}{3 n+4}","\frac{3 a^2 b x^{n+4}}{n+4}+\frac{a^3 x^4}{4}+\frac{3 a b^2 x^{2 (n+2)}}{2 (n+2)}+\frac{b^3 x^{3 n+4}}{3 n+4}",1,"(a^3*x^4)/4 + (3*a*b^2*x^(2*(2 + n)))/(2*(2 + n)) + (3*a^2*b*x^(4 + n))/(4 + n) + (b^3*x^(4 + 3*n))/(4 + 3*n)","A",2,1,13,0.07692,1,"{270}"
2466,1,66,0,0.0265586,"\int x^2 \left(a+b x^n\right)^3 \, dx","Int[x^2*(a + b*x^n)^3,x]","\frac{3 a^2 b x^{n+3}}{n+3}+\frac{a^3 x^3}{3}+\frac{3 a b^2 x^{2 n+3}}{2 n+3}+\frac{b^3 x^{3 (n+1)}}{3 (n+1)}","\frac{3 a^2 b x^{n+3}}{n+3}+\frac{a^3 x^3}{3}+\frac{3 a b^2 x^{2 n+3}}{2 n+3}+\frac{b^3 x^{3 (n+1)}}{3 (n+1)}",1,"(a^3*x^3)/3 + (b^3*x^(3*(1 + n)))/(3*(1 + n)) + (3*a^2*b*x^(3 + n))/(3 + n) + (3*a*b^2*x^(3 + 2*n))/(3 + 2*n)","A",2,1,13,0.07692,1,"{270}"
2467,1,65,0,0.0256181,"\int x \left(a+b x^n\right)^3 \, dx","Int[x*(a + b*x^n)^3,x]","\frac{3 a^2 b x^{n+2}}{n+2}+\frac{a^3 x^2}{2}+\frac{3 a b^2 x^{2 (n+1)}}{2 (n+1)}+\frac{b^3 x^{3 n+2}}{3 n+2}","\frac{3 a^2 b x^{n+2}}{n+2}+\frac{a^3 x^2}{2}+\frac{3 a b^2 x^{2 (n+1)}}{2 (n+1)}+\frac{b^3 x^{3 n+2}}{3 n+2}",1,"(a^3*x^2)/2 + (3*a*b^2*x^(2*(1 + n)))/(2*(1 + n)) + (3*a^2*b*x^(2 + n))/(2 + n) + (b^3*x^(2 + 3*n))/(2 + 3*n)","A",2,1,11,0.09091,1,"{270}"
2468,1,60,0,0.021777,"\int \left(a+b x^n\right)^3 \, dx","Int[(a + b*x^n)^3,x]","\frac{3 a^2 b x^{n+1}}{n+1}+a^3 x+\frac{3 a b^2 x^{2 n+1}}{2 n+1}+\frac{b^3 x^{3 n+1}}{3 n+1}","\frac{3 a^2 b x^{n+1}}{n+1}+a^3 x+\frac{3 a b^2 x^{2 n+1}}{2 n+1}+\frac{b^3 x^{3 n+1}}{3 n+1}",1,"a^3*x + (3*a^2*b*x^(1 + n))/(1 + n) + (3*a*b^2*x^(1 + 2*n))/(1 + 2*n) + (b^3*x^(1 + 3*n))/(1 + 3*n)","A",2,1,9,0.1111,1,"{244}"
2469,1,50,0,0.0194838,"\int \frac{\left(a+b x^n\right)^3}{x} \, dx","Int[(a + b*x^n)^3/x,x]","\frac{3 a^2 b x^n}{n}+a^3 \log (x)+\frac{3 a b^2 x^{2 n}}{2 n}+\frac{b^3 x^{3 n}}{3 n}","\frac{3 a^2 b x^n}{n}+a^3 \log (x)+\frac{3 a b^2 x^{2 n}}{2 n}+\frac{b^3 x^{3 n}}{3 n}",1,"(3*a^2*b*x^n)/n + (3*a*b^2*x^(2*n))/(2*n) + (b^3*x^(3*n))/(3*n) + a^3*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
2470,1,66,0,0.0319257,"\int \frac{\left(a+b x^n\right)^3}{x^2} \, dx","Int[(a + b*x^n)^3/x^2,x]","-\frac{3 a^2 b x^{n-1}}{1-n}-\frac{a^3}{x}-\frac{3 a b^2 x^{2 n-1}}{1-2 n}-\frac{b^3 x^{3 n-1}}{1-3 n}","-\frac{3 a^2 b x^{n-1}}{1-n}-\frac{a^3}{x}-\frac{3 a b^2 x^{2 n-1}}{1-2 n}-\frac{b^3 x^{3 n-1}}{1-3 n}",1,"-(a^3/x) - (3*a^2*b*x^(-1 + n))/(1 - n) - (3*a*b^2*x^(-1 + 2*n))/(1 - 2*n) - (b^3*x^(-1 + 3*n))/(1 - 3*n)","A",2,1,13,0.07692,1,"{270}"
2471,1,72,0,0.033153,"\int \frac{\left(a+b x^n\right)^3}{x^3} \, dx","Int[(a + b*x^n)^3/x^3,x]","-\frac{3 a^2 b x^{n-2}}{2-n}-\frac{a^3}{2 x^2}-\frac{3 a b^2 x^{-2 (1-n)}}{2 (1-n)}-\frac{b^3 x^{3 n-2}}{2-3 n}","-\frac{3 a^2 b x^{n-2}}{2-n}-\frac{a^3}{2 x^2}-\frac{3 a b^2 x^{-2 (1-n)}}{2 (1-n)}-\frac{b^3 x^{3 n-2}}{2-3 n}",1,"-a^3/(2*x^2) - (3*a*b^2)/(2*(1 - n)*x^(2*(1 - n))) - (3*a^2*b*x^(-2 + n))/(2 - n) - (b^3*x^(-2 + 3*n))/(2 - 3*n)","A",2,1,13,0.07692,1,"{270}"
2472,1,33,0,0.0077799,"\int \frac{x}{a+b x^n} \, dx","Int[x/(a + b*x^n),x]","\frac{x^2 \, _2F_1\left(1,\frac{2}{n};\frac{n+2}{n};-\frac{b x^n}{a}\right)}{2 a}","\frac{x^2 \, _2F_1\left(1,\frac{2}{n};\frac{n+2}{n};-\frac{b x^n}{a}\right)}{2 a}",1,"(x^2*Hypergeometric2F1[1, 2/n, (2 + n)/n, -((b*x^n)/a)])/(2*a)","A",1,1,11,0.09091,1,"{364}"
2473,1,24,0,0.0051298,"\int \frac{1}{a+b x^n} \, dx","Int[(a + b*x^n)^(-1),x]","\frac{x \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a}","\frac{x \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a}",1,"(x*Hypergeometric2F1[1, n^(-1), 1 + n^(-1), -((b*x^n)/a)])/a","A",1,1,9,0.1111,1,"{245}"
2474,1,23,0,0.0105708,"\int \frac{1}{x \left(a+b x^n\right)} \, dx","Int[1/(x*(a + b*x^n)),x]","\frac{\log (x)}{a}-\frac{\log \left(a+b x^n\right)}{a n}","\frac{\log (x)}{a}-\frac{\log \left(a+b x^n\right)}{a n}",1,"Log[x]/a - Log[a + b*x^n]/(a*n)","A",4,4,13,0.3077,1,"{266, 36, 29, 31}"
2475,1,34,0,0.007369,"\int \frac{1}{x^2 \left(a+b x^n\right)} \, dx","Int[1/(x^2*(a + b*x^n)),x]","-\frac{\, _2F_1\left(1,-\frac{1}{n};-\frac{1-n}{n};-\frac{b x^n}{a}\right)}{a x}","-\frac{\, _2F_1\left(1,-\frac{1}{n};-\frac{1-n}{n};-\frac{b x^n}{a}\right)}{a x}",1,"-(Hypergeometric2F1[1, -n^(-1), -((1 - n)/n), -((b*x^n)/a)]/(a*x))","A",1,1,13,0.07692,1,"{364}"
2476,1,36,0,0.0073568,"\int \frac{1}{x^3 \left(a+b x^n\right)} \, dx","Int[1/(x^3*(a + b*x^n)),x]","-\frac{\, _2F_1\left(1,-\frac{2}{n};-\frac{2-n}{n};-\frac{b x^n}{a}\right)}{2 a x^2}","-\frac{\, _2F_1\left(1,-\frac{2}{n};-\frac{2-n}{n};-\frac{b x^n}{a}\right)}{2 a x^2}",1,"-Hypergeometric2F1[1, -2/n, -((2 - n)/n), -((b*x^n)/a)]/(2*a*x^2)","A",1,1,13,0.07692,1,"{364}"
2477,1,33,0,0.0060406,"\int \frac{x}{\left(a+b x^n\right)^2} \, dx","Int[x/(a + b*x^n)^2,x]","\frac{x^2 \, _2F_1\left(2,\frac{2}{n};\frac{n+2}{n};-\frac{b x^n}{a}\right)}{2 a^2}","\frac{x^2 \, _2F_1\left(2,\frac{2}{n};\frac{n+2}{n};-\frac{b x^n}{a}\right)}{2 a^2}",1,"(x^2*Hypergeometric2F1[2, 2/n, (2 + n)/n, -((b*x^n)/a)])/(2*a^2)","A",1,1,11,0.09091,1,"{364}"
2478,1,24,0,0.0053188,"\int \frac{1}{\left(a+b x^n\right)^2} \, dx","Int[(a + b*x^n)^(-2),x]","\frac{x \, _2F_1\left(2,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a^2}","\frac{x \, _2F_1\left(2,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a^2}",1,"(x*Hypergeometric2F1[2, n^(-1), 1 + n^(-1), -((b*x^n)/a)])/a^2","A",1,1,9,0.1111,1,"{245}"
2479,1,39,0,0.0228375,"\int \frac{1}{x \left(a+b x^n\right)^2} \, dx","Int[1/(x*(a + b*x^n)^2),x]","-\frac{\log \left(a+b x^n\right)}{a^2 n}+\frac{\log (x)}{a^2}+\frac{1}{a n \left(a+b x^n\right)}","-\frac{\log \left(a+b x^n\right)}{a^2 n}+\frac{\log (x)}{a^2}+\frac{1}{a n \left(a+b x^n\right)}",1,"1/(a*n*(a + b*x^n)) + Log[x]/a^2 - Log[a + b*x^n]/(a^2*n)","A",3,2,13,0.1538,1,"{266, 44}"
2480,1,34,0,0.0070304,"\int \frac{1}{x^2 \left(a+b x^n\right)^2} \, dx","Int[1/(x^2*(a + b*x^n)^2),x]","-\frac{\, _2F_1\left(2,-\frac{1}{n};-\frac{1-n}{n};-\frac{b x^n}{a}\right)}{a^2 x}","-\frac{\, _2F_1\left(2,-\frac{1}{n};-\frac{1-n}{n};-\frac{b x^n}{a}\right)}{a^2 x}",1,"-(Hypergeometric2F1[2, -n^(-1), -((1 - n)/n), -((b*x^n)/a)]/(a^2*x))","A",1,1,13,0.07692,1,"{364}"
2481,1,36,0,0.0071335,"\int \frac{1}{x^3 \left(a+b x^n\right)^2} \, dx","Int[1/(x^3*(a + b*x^n)^2),x]","-\frac{\, _2F_1\left(2,-\frac{2}{n};-\frac{2-n}{n};-\frac{b x^n}{a}\right)}{2 a^2 x^2}","-\frac{\, _2F_1\left(2,-\frac{2}{n};-\frac{2-n}{n};-\frac{b x^n}{a}\right)}{2 a^2 x^2}",1,"-Hypergeometric2F1[2, -2/n, -((2 - n)/n), -((b*x^n)/a)]/(2*a^2*x^2)","A",1,1,13,0.07692,1,"{364}"
2482,1,33,0,0.0060812,"\int \frac{x}{\left(a+b x^n\right)^3} \, dx","Int[x/(a + b*x^n)^3,x]","\frac{x^2 \, _2F_1\left(3,\frac{2}{n};\frac{n+2}{n};-\frac{b x^n}{a}\right)}{2 a^3}","\frac{x^2 \, _2F_1\left(3,\frac{2}{n};\frac{n+2}{n};-\frac{b x^n}{a}\right)}{2 a^3}",1,"(x^2*Hypergeometric2F1[3, 2/n, (2 + n)/n, -((b*x^n)/a)])/(2*a^3)","A",1,1,11,0.09091,1,"{364}"
2483,1,24,0,0.0045994,"\int \frac{1}{\left(a+b x^n\right)^3} \, dx","Int[(a + b*x^n)^(-3),x]","\frac{x \, _2F_1\left(3,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a^3}","\frac{x \, _2F_1\left(3,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a^3}",1,"(x*Hypergeometric2F1[3, n^(-1), 1 + n^(-1), -((b*x^n)/a)])/a^3","A",1,1,9,0.1111,1,"{245}"
2484,1,58,0,0.0316219,"\int \frac{1}{x \left(a+b x^n\right)^3} \, dx","Int[1/(x*(a + b*x^n)^3),x]","\frac{1}{a^2 n \left(a+b x^n\right)}-\frac{\log \left(a+b x^n\right)}{a^3 n}+\frac{\log (x)}{a^3}+\frac{1}{2 a n \left(a+b x^n\right)^2}","\frac{1}{a^2 n \left(a+b x^n\right)}-\frac{\log \left(a+b x^n\right)}{a^3 n}+\frac{\log (x)}{a^3}+\frac{1}{2 a n \left(a+b x^n\right)^2}",1,"1/(2*a*n*(a + b*x^n)^2) + 1/(a^2*n*(a + b*x^n)) + Log[x]/a^3 - Log[a + b*x^n]/(a^3*n)","A",3,2,13,0.1538,1,"{266, 44}"
2485,1,34,0,0.0071909,"\int \frac{1}{x^2 \left(a+b x^n\right)^3} \, dx","Int[1/(x^2*(a + b*x^n)^3),x]","-\frac{\, _2F_1\left(3,-\frac{1}{n};-\frac{1-n}{n};-\frac{b x^n}{a}\right)}{a^3 x}","-\frac{\, _2F_1\left(3,-\frac{1}{n};-\frac{1-n}{n};-\frac{b x^n}{a}\right)}{a^3 x}",1,"-(Hypergeometric2F1[3, -n^(-1), -((1 - n)/n), -((b*x^n)/a)]/(a^3*x))","A",1,1,13,0.07692,1,"{364}"
2486,1,36,0,0.0070326,"\int \frac{1}{x^3 \left(a+b x^n\right)^3} \, dx","Int[1/(x^3*(a + b*x^n)^3),x]","-\frac{\, _2F_1\left(3,-\frac{2}{n};-\frac{2-n}{n};-\frac{b x^n}{a}\right)}{2 a^3 x^2}","-\frac{\, _2F_1\left(3,-\frac{2}{n};-\frac{2-n}{n};-\frac{b x^n}{a}\right)}{2 a^3 x^2}",1,"-Hypergeometric2F1[3, -2/n, -((2 - n)/n), -((b*x^n)/a)]/(2*a^3*x^2)","A",1,1,13,0.07692,1,"{364}"
2487,1,57,0,0.0144223,"\int x \sqrt{a+b x^n} \, dx","Int[x*Sqrt[a + b*x^n],x]","\frac{x^2 \sqrt{a+b x^n} \, _2F_1\left(-\frac{1}{2},\frac{2}{n};\frac{n+2}{n};-\frac{b x^n}{a}\right)}{2 \sqrt{\frac{b x^n}{a}+1}}","\frac{x^2 \left(a+b x^n\right)^{3/2} \, _2F_1\left(1,\frac{3}{2}+\frac{2}{n};\frac{n+2}{n};-\frac{b x^n}{a}\right)}{2 a}",1,"(x^2*Sqrt[a + b*x^n]*Hypergeometric2F1[-1/2, 2/n, (2 + n)/n, -((b*x^n)/a)])/(2*Sqrt[1 + (b*x^n)/a])","A",2,2,13,0.1538,1,"{365, 364}"
2488,1,48,0,0.0119397,"\int \sqrt{a+b x^n} \, dx","Int[Sqrt[a + b*x^n],x]","\frac{x \sqrt{a+b x^n} \, _2F_1\left(-\frac{1}{2},\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{\sqrt{\frac{b x^n}{a}+1}}","\frac{x \left(a+b x^n\right)^{3/2} \, _2F_1\left(1,\frac{3}{2}+\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a}",1,"(x*Sqrt[a + b*x^n]*Hypergeometric2F1[-1/2, n^(-1), 1 + n^(-1), -((b*x^n)/a)])/Sqrt[1 + (b*x^n)/a]","A",2,2,11,0.1818,1,"{246, 245}"
2489,1,45,0,0.0233814,"\int \frac{\sqrt{a+b x^n}}{x} \, dx","Int[Sqrt[a + b*x^n]/x,x]","\frac{2 \sqrt{a+b x^n}}{n}-\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b x^n}}{\sqrt{a}}\right)}{n}","\frac{2 \sqrt{a+b x^n}}{n}-\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b x^n}}{\sqrt{a}}\right)}{n}",1,"(2*Sqrt[a + b*x^n])/n - (2*Sqrt[a]*ArcTanh[Sqrt[a + b*x^n]/Sqrt[a]])/n","A",4,4,15,0.2667,1,"{266, 50, 63, 208}"
2490,1,58,0,0.0185204,"\int \frac{\sqrt{a+b x^n}}{x^2} \, dx","Int[Sqrt[a + b*x^n]/x^2,x]","-\frac{\sqrt{a+b x^n} \, _2F_1\left(-\frac{1}{2},-\frac{1}{n};-\frac{1-n}{n};-\frac{b x^n}{a}\right)}{x \sqrt{\frac{b x^n}{a}+1}}","-\frac{\left(a+b x^n\right)^{3/2} \, _2F_1\left(1,\frac{3}{2}-\frac{1}{n};-\frac{1-n}{n};-\frac{b x^n}{a}\right)}{a x}",1,"-((Sqrt[a + b*x^n]*Hypergeometric2F1[-1/2, -n^(-1), -((1 - n)/n), -((b*x^n)/a)])/(x*Sqrt[1 + (b*x^n)/a]))","A",2,2,15,0.1333,1,"{365, 364}"
2491,1,60,0,0.018756,"\int \frac{\sqrt{a+b x^n}}{x^3} \, dx","Int[Sqrt[a + b*x^n]/x^3,x]","-\frac{\sqrt{a+b x^n} \, _2F_1\left(-\frac{1}{2},-\frac{2}{n};-\frac{2-n}{n};-\frac{b x^n}{a}\right)}{2 x^2 \sqrt{\frac{b x^n}{a}+1}}","-\frac{\left(a+b x^n\right)^{3/2} \, _2F_1\left(1,\frac{3}{2}-\frac{2}{n};-\frac{2-n}{n};-\frac{b x^n}{a}\right)}{2 a x^2}",1,"-(Sqrt[a + b*x^n]*Hypergeometric2F1[-1/2, -2/n, -((2 - n)/n), -((b*x^n)/a)])/(2*x^2*Sqrt[1 + (b*x^n)/a])","A",2,2,15,0.1333,1,"{365, 364}"
2492,1,58,0,0.0152103,"\int x \left(a+b x^n\right)^{3/2} \, dx","Int[x*(a + b*x^n)^(3/2),x]","\frac{a x^2 \sqrt{a+b x^n} \, _2F_1\left(-\frac{3}{2},\frac{2}{n};\frac{n+2}{n};-\frac{b x^n}{a}\right)}{2 \sqrt{\frac{b x^n}{a}+1}}","\frac{x^2 \left(a+b x^n\right)^{5/2} \, _2F_1\left(1,\frac{5}{2}+\frac{2}{n};\frac{n+2}{n};-\frac{b x^n}{a}\right)}{2 a}",1,"(a*x^2*Sqrt[a + b*x^n]*Hypergeometric2F1[-3/2, 2/n, (2 + n)/n, -((b*x^n)/a)])/(2*Sqrt[1 + (b*x^n)/a])","A",2,2,13,0.1538,1,"{365, 364}"
2493,1,49,0,0.0115191,"\int \left(a+b x^n\right)^{3/2} \, dx","Int[(a + b*x^n)^(3/2),x]","\frac{a x \sqrt{a+b x^n} \, _2F_1\left(-\frac{3}{2},\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{\sqrt{\frac{b x^n}{a}+1}}","\frac{x \left(a+b x^n\right)^{5/2} \, _2F_1\left(1,\frac{5}{2}+\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a}",1,"(a*x*Sqrt[a + b*x^n]*Hypergeometric2F1[-3/2, n^(-1), 1 + n^(-1), -((b*x^n)/a)])/Sqrt[1 + (b*x^n)/a]","A",2,2,11,0.1818,1,"{246, 245}"
2494,1,64,0,0.03055,"\int \frac{\left(a+b x^n\right)^{3/2}}{x} \, dx","Int[(a + b*x^n)^(3/2)/x,x]","-\frac{2 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b x^n}}{\sqrt{a}}\right)}{n}+\frac{2 a \sqrt{a+b x^n}}{n}+\frac{2 \left(a+b x^n\right)^{3/2}}{3 n}","-\frac{2 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b x^n}}{\sqrt{a}}\right)}{n}+\frac{2 a \sqrt{a+b x^n}}{n}+\frac{2 \left(a+b x^n\right)^{3/2}}{3 n}",1,"(2*a*Sqrt[a + b*x^n])/n + (2*(a + b*x^n)^(3/2))/(3*n) - (2*a^(3/2)*ArcTanh[Sqrt[a + b*x^n]/Sqrt[a]])/n","A",5,4,15,0.2667,1,"{266, 50, 63, 208}"
2495,1,59,0,0.0187181,"\int \frac{\left(a+b x^n\right)^{3/2}}{x^2} \, dx","Int[(a + b*x^n)^(3/2)/x^2,x]","-\frac{a \sqrt{a+b x^n} \, _2F_1\left(-\frac{3}{2},-\frac{1}{n};-\frac{1-n}{n};-\frac{b x^n}{a}\right)}{x \sqrt{\frac{b x^n}{a}+1}}","-\frac{\left(a+b x^n\right)^{5/2} \, _2F_1\left(1,\frac{5}{2}-\frac{1}{n};-\frac{1-n}{n};-\frac{b x^n}{a}\right)}{a x}",1,"-((a*Sqrt[a + b*x^n]*Hypergeometric2F1[-3/2, -n^(-1), -((1 - n)/n), -((b*x^n)/a)])/(x*Sqrt[1 + (b*x^n)/a]))","A",2,2,15,0.1333,1,"{365, 364}"
2496,1,61,0,0.0203248,"\int \frac{\left(a+b x^n\right)^{3/2}}{x^3} \, dx","Int[(a + b*x^n)^(3/2)/x^3,x]","-\frac{a \sqrt{a+b x^n} \, _2F_1\left(-\frac{3}{2},-\frac{2}{n};-\frac{2-n}{n};-\frac{b x^n}{a}\right)}{2 x^2 \sqrt{\frac{b x^n}{a}+1}}","-\frac{\left(a+b x^n\right)^{5/2} \, _2F_1\left(1,\frac{5}{2}-\frac{2}{n};-\frac{2-n}{n};-\frac{b x^n}{a}\right)}{2 a x^2}",1,"-(a*Sqrt[a + b*x^n]*Hypergeometric2F1[-3/2, -2/n, -((2 - n)/n), -((b*x^n)/a)])/(2*x^2*Sqrt[1 + (b*x^n)/a])","A",2,2,15,0.1333,1,"{365, 364}"
2497,1,60,0,0.0158963,"\int x \left(a+b x^n\right)^{5/2} \, dx","Int[x*(a + b*x^n)^(5/2),x]","\frac{a^2 x^2 \sqrt{a+b x^n} \, _2F_1\left(-\frac{5}{2},\frac{2}{n};\frac{n+2}{n};-\frac{b x^n}{a}\right)}{2 \sqrt{\frac{b x^n}{a}+1}}","\frac{x^2 \left(a+b x^n\right)^{7/2} \, _2F_1\left(1,\frac{7}{2}+\frac{2}{n};\frac{n+2}{n};-\frac{b x^n}{a}\right)}{2 a}",1,"(a^2*x^2*Sqrt[a + b*x^n]*Hypergeometric2F1[-5/2, 2/n, (2 + n)/n, -((b*x^n)/a)])/(2*Sqrt[1 + (b*x^n)/a])","A",2,2,13,0.1538,1,"{365, 364}"
2498,1,51,0,0.0109987,"\int \left(a+b x^n\right)^{5/2} \, dx","Int[(a + b*x^n)^(5/2),x]","\frac{a^2 x \sqrt{a+b x^n} \, _2F_1\left(-\frac{5}{2},\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{\sqrt{\frac{b x^n}{a}+1}}","\frac{x \left(a+b x^n\right)^{7/2} \, _2F_1\left(1,\frac{7}{2}+\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a}",1,"(a^2*x*Sqrt[a + b*x^n]*Hypergeometric2F1[-5/2, n^(-1), 1 + n^(-1), -((b*x^n)/a)])/Sqrt[1 + (b*x^n)/a]","A",2,2,11,0.1818,1,"{246, 245}"
2499,1,85,0,0.0414165,"\int \frac{\left(a+b x^n\right)^{5/2}}{x} \, dx","Int[(a + b*x^n)^(5/2)/x,x]","\frac{2 a^2 \sqrt{a+b x^n}}{n}-\frac{2 a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+b x^n}}{\sqrt{a}}\right)}{n}+\frac{2 a \left(a+b x^n\right)^{3/2}}{3 n}+\frac{2 \left(a+b x^n\right)^{5/2}}{5 n}","\frac{2 a^2 \sqrt{a+b x^n}}{n}-\frac{2 a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+b x^n}}{\sqrt{a}}\right)}{n}+\frac{2 a \left(a+b x^n\right)^{3/2}}{3 n}+\frac{2 \left(a+b x^n\right)^{5/2}}{5 n}",1,"(2*a^2*Sqrt[a + b*x^n])/n + (2*a*(a + b*x^n)^(3/2))/(3*n) + (2*(a + b*x^n)^(5/2))/(5*n) - (2*a^(5/2)*ArcTanh[Sqrt[a + b*x^n]/Sqrt[a]])/n","A",6,4,15,0.2667,1,"{266, 50, 63, 208}"
2500,1,61,0,0.020951,"\int \frac{\left(a+b x^n\right)^{5/2}}{x^2} \, dx","Int[(a + b*x^n)^(5/2)/x^2,x]","-\frac{a^2 \sqrt{a+b x^n} \, _2F_1\left(-\frac{5}{2},-\frac{1}{n};-\frac{1-n}{n};-\frac{b x^n}{a}\right)}{x \sqrt{\frac{b x^n}{a}+1}}","-\frac{\left(a+b x^n\right)^{7/2} \, _2F_1\left(1,\frac{7}{2}-\frac{1}{n};-\frac{1-n}{n};-\frac{b x^n}{a}\right)}{a x}",1,"-((a^2*Sqrt[a + b*x^n]*Hypergeometric2F1[-5/2, -n^(-1), -((1 - n)/n), -((b*x^n)/a)])/(x*Sqrt[1 + (b*x^n)/a]))","A",2,2,15,0.1333,1,"{365, 364}"
2501,1,63,0,0.0192186,"\int \frac{\left(a+b x^n\right)^{5/2}}{x^3} \, dx","Int[(a + b*x^n)^(5/2)/x^3,x]","-\frac{a^2 \sqrt{a+b x^n} \, _2F_1\left(-\frac{5}{2},-\frac{2}{n};-\frac{2-n}{n};-\frac{b x^n}{a}\right)}{2 x^2 \sqrt{\frac{b x^n}{a}+1}}","-\frac{\left(a+b x^n\right)^{7/2} \, _2F_1\left(1,\frac{7}{2}-\frac{2}{n};-\frac{2-n}{n};-\frac{b x^n}{a}\right)}{2 a x^2}",1,"-(a^2*Sqrt[a + b*x^n]*Hypergeometric2F1[-5/2, -2/n, -((2 - n)/n), -((b*x^n)/a)])/(2*x^2*Sqrt[1 + (b*x^n)/a])","A",2,2,15,0.1333,1,"{365, 364}"
2502,1,57,0,0.0153886,"\int \frac{x}{\sqrt{a+b x^n}} \, dx","Int[x/Sqrt[a + b*x^n],x]","\frac{x^2 \sqrt{\frac{b x^n}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{2}{n};\frac{n+2}{n};-\frac{b x^n}{a}\right)}{2 \sqrt{a+b x^n}}","\frac{x^2 \sqrt{a+b x^n} \, _2F_1\left(1,\frac{1}{2}+\frac{2}{n};\frac{n+2}{n};-\frac{b x^n}{a}\right)}{2 a}",1,"(x^2*Sqrt[1 + (b*x^n)/a]*Hypergeometric2F1[1/2, 2/n, (2 + n)/n, -((b*x^n)/a)])/(2*Sqrt[a + b*x^n])","A",2,2,13,0.1538,1,"{365, 364}"
2503,1,48,0,0.0108998,"\int \frac{1}{\sqrt{a+b x^n}} \, dx","Int[1/Sqrt[a + b*x^n],x]","\frac{x \sqrt{\frac{b x^n}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{\sqrt{a+b x^n}}","\frac{x \sqrt{a+b x^n} \, _2F_1\left(1,\frac{1}{2}+\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a}",1,"(x*Sqrt[1 + (b*x^n)/a]*Hypergeometric2F1[1/2, n^(-1), 1 + n^(-1), -((b*x^n)/a)])/Sqrt[a + b*x^n]","A",2,2,11,0.1818,1,"{246, 245}"
2504,1,28,0,0.0191689,"\int \frac{1}{x \sqrt{a+b x^n}} \, dx","Int[1/(x*Sqrt[a + b*x^n]),x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b x^n}}{\sqrt{a}}\right)}{\sqrt{a} n}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b x^n}}{\sqrt{a}}\right)}{\sqrt{a} n}",1,"(-2*ArcTanh[Sqrt[a + b*x^n]/Sqrt[a]])/(Sqrt[a]*n)","A",3,3,15,0.2000,1,"{266, 63, 208}"
2505,1,58,0,0.0185416,"\int \frac{1}{x^2 \sqrt{a+b x^n}} \, dx","Int[1/(x^2*Sqrt[a + b*x^n]),x]","-\frac{\sqrt{\frac{b x^n}{a}+1} \, _2F_1\left(\frac{1}{2},-\frac{1}{n};-\frac{1-n}{n};-\frac{b x^n}{a}\right)}{x \sqrt{a+b x^n}}","-\frac{\sqrt{a+b x^n} \, _2F_1\left(1,\frac{1}{2}-\frac{1}{n};-\frac{1-n}{n};-\frac{b x^n}{a}\right)}{a x}",1,"-((Sqrt[1 + (b*x^n)/a]*Hypergeometric2F1[1/2, -n^(-1), -((1 - n)/n), -((b*x^n)/a)])/(x*Sqrt[a + b*x^n]))","A",2,2,15,0.1333,1,"{365, 364}"
2506,1,60,0,0.018222,"\int \frac{1}{x^3 \sqrt{a+b x^n}} \, dx","Int[1/(x^3*Sqrt[a + b*x^n]),x]","-\frac{\sqrt{\frac{b x^n}{a}+1} \, _2F_1\left(\frac{1}{2},-\frac{2}{n};-\frac{2-n}{n};-\frac{b x^n}{a}\right)}{2 x^2 \sqrt{a+b x^n}}","-\frac{\sqrt{a+b x^n} \, _2F_1\left(1,\frac{1}{2}-\frac{2}{n};-\frac{2-n}{n};-\frac{b x^n}{a}\right)}{2 a x^2}",1,"-(Sqrt[1 + (b*x^n)/a]*Hypergeometric2F1[1/2, -2/n, -((2 - n)/n), -((b*x^n)/a)])/(2*x^2*Sqrt[a + b*x^n])","A",2,2,15,0.1333,1,"{365, 364}"
2507,1,60,0,0.0168044,"\int \frac{x}{\left(a+b x^n\right)^{3/2}} \, dx","Int[x/(a + b*x^n)^(3/2),x]","\frac{x^2 \sqrt{\frac{b x^n}{a}+1} \, _2F_1\left(\frac{3}{2},\frac{2}{n};\frac{n+2}{n};-\frac{b x^n}{a}\right)}{2 a \sqrt{a+b x^n}}","\frac{x^2 \, _2F_1\left(1,\frac{2}{n}-\frac{1}{2};\frac{n+2}{n};-\frac{b x^n}{a}\right)}{2 a \sqrt{a+b x^n}}",1,"(x^2*Sqrt[1 + (b*x^n)/a]*Hypergeometric2F1[3/2, 2/n, (2 + n)/n, -((b*x^n)/a)])/(2*a*Sqrt[a + b*x^n])","A",2,2,13,0.1538,1,"{365, 364}"
2508,1,51,0,0.0114792,"\int \frac{1}{\left(a+b x^n\right)^{3/2}} \, dx","Int[(a + b*x^n)^(-3/2),x]","\frac{x \sqrt{\frac{b x^n}{a}+1} \, _2F_1\left(\frac{3}{2},\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a \sqrt{a+b x^n}}","\frac{x \, _2F_1\left(1,\frac{1}{n}-\frac{1}{2};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a \sqrt{a+b x^n}}",1,"(x*Sqrt[1 + (b*x^n)/a]*Hypergeometric2F1[3/2, n^(-1), 1 + n^(-1), -((b*x^n)/a)])/(a*Sqrt[a + b*x^n])","A",2,2,11,0.1818,1,"{246, 245}"
2509,1,48,0,0.026104,"\int \frac{1}{x \left(a+b x^n\right)^{3/2}} \, dx","Int[1/(x*(a + b*x^n)^(3/2)),x]","\frac{2}{a n \sqrt{a+b x^n}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b x^n}}{\sqrt{a}}\right)}{a^{3/2} n}","\frac{2}{a n \sqrt{a+b x^n}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b x^n}}{\sqrt{a}}\right)}{a^{3/2} n}",1,"2/(a*n*Sqrt[a + b*x^n]) - (2*ArcTanh[Sqrt[a + b*x^n]/Sqrt[a]])/(a^(3/2)*n)","A",4,4,15,0.2667,1,"{266, 51, 63, 208}"
2510,1,61,0,0.0195183,"\int \frac{1}{x^2 \left(a+b x^n\right)^{3/2}} \, dx","Int[1/(x^2*(a + b*x^n)^(3/2)),x]","-\frac{\sqrt{\frac{b x^n}{a}+1} \, _2F_1\left(\frac{3}{2},-\frac{1}{n};-\frac{1-n}{n};-\frac{b x^n}{a}\right)}{a x \sqrt{a+b x^n}}","-\frac{\, _2F_1\left(1,-\frac{1}{2}-\frac{1}{n};-\frac{1-n}{n};-\frac{b x^n}{a}\right)}{a x \sqrt{a+b x^n}}",1,"-((Sqrt[1 + (b*x^n)/a]*Hypergeometric2F1[3/2, -n^(-1), -((1 - n)/n), -((b*x^n)/a)])/(a*x*Sqrt[a + b*x^n]))","A",2,2,15,0.1333,1,"{365, 364}"
2511,1,63,0,0.0193079,"\int \frac{1}{x^3 \left(a+b x^n\right)^{3/2}} \, dx","Int[1/(x^3*(a + b*x^n)^(3/2)),x]","-\frac{\sqrt{\frac{b x^n}{a}+1} \, _2F_1\left(\frac{3}{2},-\frac{2}{n};-\frac{2-n}{n};-\frac{b x^n}{a}\right)}{2 a x^2 \sqrt{a+b x^n}}","-\frac{\, _2F_1\left(1,-\frac{1}{2}-\frac{2}{n};-\frac{2-n}{n};-\frac{b x^n}{a}\right)}{2 a x^2 \sqrt{a+b x^n}}",1,"-(Sqrt[1 + (b*x^n)/a]*Hypergeometric2F1[3/2, -2/n, -((2 - n)/n), -((b*x^n)/a)])/(2*a*x^2*Sqrt[a + b*x^n])","A",2,2,15,0.1333,1,"{365, 364}"
2512,1,60,0,0.0170939,"\int \frac{x}{\left(a+b x^n\right)^{5/2}} \, dx","Int[x/(a + b*x^n)^(5/2),x]","\frac{x^2 \sqrt{\frac{b x^n}{a}+1} \, _2F_1\left(\frac{5}{2},\frac{2}{n};\frac{n+2}{n};-\frac{b x^n}{a}\right)}{2 a^2 \sqrt{a+b x^n}}","\frac{x^2 \, _2F_1\left(1,\frac{2}{n}-\frac{3}{2};\frac{n+2}{n};-\frac{b x^n}{a}\right)}{2 a \left(a+b x^n\right)^{3/2}}",1,"(x^2*Sqrt[1 + (b*x^n)/a]*Hypergeometric2F1[5/2, 2/n, (2 + n)/n, -((b*x^n)/a)])/(2*a^2*Sqrt[a + b*x^n])","A",2,2,13,0.1538,1,"{365, 364}"
2513,1,51,0,0.0111834,"\int \frac{1}{\left(a+b x^n\right)^{5/2}} \, dx","Int[(a + b*x^n)^(-5/2),x]","\frac{x \sqrt{\frac{b x^n}{a}+1} \, _2F_1\left(\frac{5}{2},\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a^2 \sqrt{a+b x^n}}","\frac{x \, _2F_1\left(1,\frac{1}{n}-\frac{3}{2};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a \left(a+b x^n\right)^{3/2}}",1,"(x*Sqrt[1 + (b*x^n)/a]*Hypergeometric2F1[5/2, n^(-1), 1 + n^(-1), -((b*x^n)/a)])/(a^2*Sqrt[a + b*x^n])","A",2,2,11,0.1818,1,"{246, 245}"
2514,1,69,0,0.0362646,"\int \frac{1}{x \left(a+b x^n\right)^{5/2}} \, dx","Int[1/(x*(a + b*x^n)^(5/2)),x]","\frac{2}{a^2 n \sqrt{a+b x^n}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b x^n}}{\sqrt{a}}\right)}{a^{5/2} n}+\frac{2}{3 a n \left(a+b x^n\right)^{3/2}}","\frac{2}{a^2 n \sqrt{a+b x^n}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b x^n}}{\sqrt{a}}\right)}{a^{5/2} n}+\frac{2}{3 a n \left(a+b x^n\right)^{3/2}}",1,"2/(3*a*n*(a + b*x^n)^(3/2)) + 2/(a^2*n*Sqrt[a + b*x^n]) - (2*ArcTanh[Sqrt[a + b*x^n]/Sqrt[a]])/(a^(5/2)*n)","A",5,4,15,0.2667,1,"{266, 51, 63, 208}"
2515,1,61,0,0.0196507,"\int \frac{1}{x^2 \left(a+b x^n\right)^{5/2}} \, dx","Int[1/(x^2*(a + b*x^n)^(5/2)),x]","-\frac{\sqrt{\frac{b x^n}{a}+1} \, _2F_1\left(\frac{5}{2},-\frac{1}{n};-\frac{1-n}{n};-\frac{b x^n}{a}\right)}{a^2 x \sqrt{a+b x^n}}","-\frac{\, _2F_1\left(1,-\frac{3}{2}-\frac{1}{n};-\frac{1-n}{n};-\frac{b x^n}{a}\right)}{a x \left(a+b x^n\right)^{3/2}}",1,"-((Sqrt[1 + (b*x^n)/a]*Hypergeometric2F1[5/2, -n^(-1), -((1 - n)/n), -((b*x^n)/a)])/(a^2*x*Sqrt[a + b*x^n]))","A",2,2,15,0.1333,1,"{365, 364}"
2516,1,63,0,0.0196486,"\int \frac{1}{x^3 \left(a+b x^n\right)^{5/2}} \, dx","Int[1/(x^3*(a + b*x^n)^(5/2)),x]","-\frac{\sqrt{\frac{b x^n}{a}+1} \, _2F_1\left(\frac{5}{2},-\frac{2}{n};-\frac{2-n}{n};-\frac{b x^n}{a}\right)}{2 a^2 x^2 \sqrt{a+b x^n}}","-\frac{\, _2F_1\left(1,-\frac{3}{2}-\frac{2}{n};-\frac{2-n}{n};-\frac{b x^n}{a}\right)}{2 a x^2 \left(a+b x^n\right)^{3/2}}",1,"-(Sqrt[1 + (b*x^n)/a]*Hypergeometric2F1[5/2, -2/n, -((2 - n)/n), -((b*x^n)/a)])/(2*a^2*x^2*Sqrt[a + b*x^n])","A",2,2,15,0.1333,1,"{365, 364}"
2517,1,106,0,0.0673738,"\int \frac{\sqrt[3]{a+b x^n}}{x} \, dx","Int[(a + b*x^n)^(1/3)/x,x]","\frac{3 \sqrt[3]{a+b x^n}}{n}+\frac{3 \sqrt[3]{a} \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^n}\right)}{2 n}-\frac{\sqrt{3} \sqrt[3]{a} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^n}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{n}-\frac{1}{2} \sqrt[3]{a} \log (x)","\frac{3 \sqrt[3]{a+b x^n}}{n}+\frac{3 \sqrt[3]{a} \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^n}\right)}{2 n}-\frac{\sqrt{3} \sqrt[3]{a} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^n}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{n}-\frac{1}{2} \sqrt[3]{a} \log (x)",1,"(3*(a + b*x^n)^(1/3))/n - (Sqrt[3]*a^(1/3)*ArcTan[(a^(1/3) + 2*(a + b*x^n)^(1/3))/(Sqrt[3]*a^(1/3))])/n - (a^(1/3)*Log[x])/2 + (3*a^(1/3)*Log[a^(1/3) - (a + b*x^n)^(1/3)])/(2*n)","A",6,6,15,0.4000,1,"{266, 50, 57, 617, 204, 31}"
2518,1,27,0,0.0075547,"\int x^{-1+4 n} \left(a+b x^n\right) \, dx","Int[x^(-1 + 4*n)*(a + b*x^n),x]","\frac{a x^{4 n}}{4 n}+\frac{b x^{5 n}}{5 n}","\frac{a x^{4 n}}{4 n}+\frac{b x^{5 n}}{5 n}",1,"(a*x^(4*n))/(4*n) + (b*x^(5*n))/(5*n)","A",2,1,15,0.06667,1,"{14}"
2519,1,27,0,0.0073678,"\int x^{-1+3 n} \left(a+b x^n\right) \, dx","Int[x^(-1 + 3*n)*(a + b*x^n),x]","\frac{a x^{3 n}}{3 n}+\frac{b x^{4 n}}{4 n}","\frac{a x^{3 n}}{3 n}+\frac{b x^{4 n}}{4 n}",1,"(a*x^(3*n))/(3*n) + (b*x^(4*n))/(4*n)","A",2,1,15,0.06667,1,"{14}"
2520,1,27,0,0.0070684,"\int x^{-1+2 n} \left(a+b x^n\right) \, dx","Int[x^(-1 + 2*n)*(a + b*x^n),x]","\frac{a x^{2 n}}{2 n}+\frac{b x^{3 n}}{3 n}","\frac{a x^{2 n}}{2 n}+\frac{b x^{3 n}}{3 n}",1,"(a*x^(2*n))/(2*n) + (b*x^(3*n))/(3*n)","A",2,1,15,0.06667,1,"{14}"
2521,1,22,0,0.0064788,"\int x^{-1+n} \left(a+b x^n\right) \, dx","Int[x^(-1 + n)*(a + b*x^n),x]","\frac{a x^n}{n}+\frac{b x^{2 n}}{2 n}","\frac{a x^n}{n}+\frac{b x^{2 n}}{2 n}",1,"(a*x^n)/n + (b*x^(2*n))/(2*n)","A",2,1,13,0.07692,1,"{14}"
2522,1,13,0,0.0064349,"\int \frac{a+b x^n}{x} \, dx","Int[(a + b*x^n)/x,x]","a \log (x)+\frac{b x^n}{n}","a \log (x)+\frac{b x^n}{n}",1,"(b*x^n)/n + a*Log[x]","A",2,1,11,0.09091,1,"{14}"
2523,1,16,0,0.0055173,"\int x^{-1-n} \left(a+b x^n\right) \, dx","Int[x^(-1 - n)*(a + b*x^n),x]","b \log (x)-\frac{a x^{-n}}{n}","b \log (x)-\frac{a x^{-n}}{n}",1,"-(a/(n*x^n)) + b*Log[x]","A",2,1,15,0.06667,1,"{14}"
2524,1,25,0,0.0072845,"\int x^{-1-2 n} \left(a+b x^n\right) \, dx","Int[x^(-1 - 2*n)*(a + b*x^n),x]","-\frac{a x^{-2 n}}{2 n}-\frac{b x^{-n}}{n}","-\frac{a x^{-2 n}}{2 n}-\frac{b x^{-n}}{n}",1,"-a/(2*n*x^(2*n)) - b/(n*x^n)","A",2,1,15,0.06667,1,"{14}"
2525,1,27,0,0.0068886,"\int x^{-1-3 n} \left(a+b x^n\right) \, dx","Int[x^(-1 - 3*n)*(a + b*x^n),x]","-\frac{a x^{-3 n}}{3 n}-\frac{b x^{-2 n}}{2 n}","-\frac{a x^{-3 n}}{3 n}-\frac{b x^{-2 n}}{2 n}",1,"-a/(3*n*x^(3*n)) - b/(2*n*x^(2*n))","A",2,1,15,0.06667,1,"{14}"
2526,1,27,0,0.0072164,"\int x^{-1-4 n} \left(a+b x^n\right) \, dx","Int[x^(-1 - 4*n)*(a + b*x^n),x]","-\frac{a x^{-4 n}}{4 n}-\frac{b x^{-3 n}}{3 n}","-\frac{a x^{-4 n}}{4 n}-\frac{b x^{-3 n}}{3 n}",1,"-a/(4*n*x^(4*n)) - b/(3*n*x^(3*n))","A",2,1,15,0.06667,1,"{14}"
2527,1,27,0,0.0077876,"\int x^{-1-5 n} \left(a+b x^n\right) \, dx","Int[x^(-1 - 5*n)*(a + b*x^n),x]","-\frac{a x^{-5 n}}{5 n}-\frac{b x^{-4 n}}{4 n}","-\frac{a x^{-5 n}}{5 n}-\frac{b x^{-4 n}}{4 n}",1,"-a/(5*n*x^(5*n)) - b/(4*n*x^(4*n))","A",2,1,15,0.06667,1,"{14}"
2528,1,45,0,0.019128,"\int x^{-1+4 n} \left(a+b x^n\right)^2 \, dx","Int[x^(-1 + 4*n)*(a + b*x^n)^2,x]","\frac{a^2 x^{4 n}}{4 n}+\frac{2 a b x^{5 n}}{5 n}+\frac{b^2 x^{6 n}}{6 n}","\frac{a^2 x^{4 n}}{4 n}+\frac{2 a b x^{5 n}}{5 n}+\frac{b^2 x^{6 n}}{6 n}",1,"(a^2*x^(4*n))/(4*n) + (2*a*b*x^(5*n))/(5*n) + (b^2*x^(6*n))/(6*n)","A",3,2,17,0.1176,1,"{266, 43}"
2529,1,45,0,0.0170564,"\int x^{-1+3 n} \left(a+b x^n\right)^2 \, dx","Int[x^(-1 + 3*n)*(a + b*x^n)^2,x]","\frac{a^2 x^{3 n}}{3 n}+\frac{a b x^{4 n}}{2 n}+\frac{b^2 x^{5 n}}{5 n}","\frac{a^2 x^{3 n}}{3 n}+\frac{a b x^{4 n}}{2 n}+\frac{b^2 x^{5 n}}{5 n}",1,"(a^2*x^(3*n))/(3*n) + (a*b*x^(4*n))/(2*n) + (b^2*x^(5*n))/(5*n)","A",3,2,17,0.1176,1,"{266, 43}"
2530,1,45,0,0.0173006,"\int x^{-1+2 n} \left(a+b x^n\right)^2 \, dx","Int[x^(-1 + 2*n)*(a + b*x^n)^2,x]","\frac{a^2 x^{2 n}}{2 n}+\frac{2 a b x^{3 n}}{3 n}+\frac{b^2 x^{4 n}}{4 n}","\frac{a^2 x^{2 n}}{2 n}+\frac{2 a b x^{3 n}}{3 n}+\frac{b^2 x^{4 n}}{4 n}",1,"(a^2*x^(2*n))/(2*n) + (2*a*b*x^(3*n))/(3*n) + (b^2*x^(4*n))/(4*n)","A",3,2,17,0.1176,1,"{266, 43}"
2531,1,19,0,0.0044414,"\int x^{-1+n} \left(a+b x^n\right)^2 \, dx","Int[x^(-1 + n)*(a + b*x^n)^2,x]","\frac{\left(a+b x^n\right)^3}{3 b n}","\frac{\left(a+b x^n\right)^3}{3 b n}",1,"(a + b*x^n)^3/(3*b*n)","A",1,1,15,0.06667,1,"{261}"
2532,1,32,0,0.0126149,"\int \frac{\left(a+b x^n\right)^2}{x} \, dx","Int[(a + b*x^n)^2/x,x]","a^2 \log (x)+\frac{2 a b x^n}{n}+\frac{b^2 x^{2 n}}{2 n}","a^2 \log (x)+\frac{2 a b x^n}{n}+\frac{b^2 x^{2 n}}{2 n}",1,"(2*a*b*x^n)/n + (b^2*x^(2*n))/(2*n) + a^2*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
2533,1,30,0,0.0152437,"\int x^{-1-n} \left(a+b x^n\right)^2 \, dx","Int[x^(-1 - n)*(a + b*x^n)^2,x]","-\frac{a^2 x^{-n}}{n}+2 a b \log (x)+\frac{b^2 x^n}{n}","-\frac{a^2 x^{-n}}{n}+2 a b \log (x)+\frac{b^2 x^n}{n}",1,"-(a^2/(n*x^n)) + (b^2*x^n)/n + 2*a*b*Log[x]","A",3,2,17,0.1176,1,"{266, 43}"
2534,1,34,0,0.0159883,"\int x^{-1-2 n} \left(a+b x^n\right)^2 \, dx","Int[x^(-1 - 2*n)*(a + b*x^n)^2,x]","-\frac{a^2 x^{-2 n}}{2 n}-\frac{2 a b x^{-n}}{n}+b^2 \log (x)","-\frac{a^2 x^{-2 n}}{2 n}-\frac{2 a b x^{-n}}{n}+b^2 \log (x)",1,"-a^2/(2*n*x^(2*n)) - (2*a*b)/(n*x^n) + b^2*Log[x]","A",3,2,17,0.1176,1,"{266, 43}"
2535,1,24,0,0.0048236,"\int x^{-1-3 n} \left(a+b x^n\right)^2 \, dx","Int[x^(-1 - 3*n)*(a + b*x^n)^2,x]","-\frac{x^{-3 n} \left(a+b x^n\right)^3}{3 a n}","-\frac{x^{-3 n} \left(a+b x^n\right)^3}{3 a n}",1,"-(a + b*x^n)^3/(3*a*n*x^(3*n))","A",1,1,17,0.05882,1,"{264}"
2536,1,45,0,0.0166628,"\int x^{-1-4 n} \left(a+b x^n\right)^2 \, dx","Int[x^(-1 - 4*n)*(a + b*x^n)^2,x]","-\frac{a^2 x^{-4 n}}{4 n}-\frac{2 a b x^{-3 n}}{3 n}-\frac{b^2 x^{-2 n}}{2 n}","-\frac{a^2 x^{-4 n}}{4 n}-\frac{2 a b x^{-3 n}}{3 n}-\frac{b^2 x^{-2 n}}{2 n}",1,"-a^2/(4*n*x^(4*n)) - (2*a*b)/(3*n*x^(3*n)) - b^2/(2*n*x^(2*n))","A",3,2,17,0.1176,1,"{266, 43}"
2537,1,45,0,0.0180822,"\int x^{-1-5 n} \left(a+b x^n\right)^2 \, dx","Int[x^(-1 - 5*n)*(a + b*x^n)^2,x]","-\frac{a^2 x^{-5 n}}{5 n}-\frac{a b x^{-4 n}}{2 n}-\frac{b^2 x^{-3 n}}{3 n}","-\frac{a^2 x^{-5 n}}{5 n}-\frac{a b x^{-4 n}}{2 n}-\frac{b^2 x^{-3 n}}{3 n}",1,"-a^2/(5*n*x^(5*n)) - (a*b)/(2*n*x^(4*n)) - b^2/(3*n*x^(3*n))","A",3,2,17,0.1176,1,"{266, 43}"
2538,1,45,0,0.0170153,"\int x^{-1-6 n} \left(a+b x^n\right)^2 \, dx","Int[x^(-1 - 6*n)*(a + b*x^n)^2,x]","-\frac{a^2 x^{-6 n}}{6 n}-\frac{2 a b x^{-5 n}}{5 n}-\frac{b^2 x^{-4 n}}{4 n}","-\frac{a^2 x^{-6 n}}{6 n}-\frac{2 a b x^{-5 n}}{5 n}-\frac{b^2 x^{-4 n}}{4 n}",1,"-a^2/(6*n*x^(6*n)) - (2*a*b)/(5*n*x^(5*n)) - b^2/(4*n*x^(4*n))","A",3,2,17,0.1176,1,"{266, 43}"
2539,1,63,0,0.0271848,"\int x^{-1+4 n} \left(a+b x^n\right)^3 \, dx","Int[x^(-1 + 4*n)*(a + b*x^n)^3,x]","\frac{3 a^2 b x^{5 n}}{5 n}+\frac{a^3 x^{4 n}}{4 n}+\frac{a b^2 x^{6 n}}{2 n}+\frac{b^3 x^{7 n}}{7 n}","\frac{3 a^2 b x^{5 n}}{5 n}+\frac{a^3 x^{4 n}}{4 n}+\frac{a b^2 x^{6 n}}{2 n}+\frac{b^3 x^{7 n}}{7 n}",1,"(a^3*x^(4*n))/(4*n) + (3*a^2*b*x^(5*n))/(5*n) + (a*b^2*x^(6*n))/(2*n) + (b^3*x^(7*n))/(7*n)","A",3,2,17,0.1176,1,"{266, 43}"
2540,1,63,0,0.0261481,"\int x^{-1+3 n} \left(a+b x^n\right)^3 \, dx","Int[x^(-1 + 3*n)*(a + b*x^n)^3,x]","\frac{3 a^2 b x^{4 n}}{4 n}+\frac{a^3 x^{3 n}}{3 n}+\frac{3 a b^2 x^{5 n}}{5 n}+\frac{b^3 x^{6 n}}{6 n}","\frac{3 a^2 b x^{4 n}}{4 n}+\frac{a^3 x^{3 n}}{3 n}+\frac{3 a b^2 x^{5 n}}{5 n}+\frac{b^3 x^{6 n}}{6 n}",1,"(a^3*x^(3*n))/(3*n) + (3*a^2*b*x^(4*n))/(4*n) + (3*a*b^2*x^(5*n))/(5*n) + (b^3*x^(6*n))/(6*n)","A",3,2,17,0.1176,1,"{266, 43}"
2541,1,40,0,0.0184661,"\int x^{-1+2 n} \left(a+b x^n\right)^3 \, dx","Int[x^(-1 + 2*n)*(a + b*x^n)^3,x]","\frac{\left(a+b x^n\right)^5}{5 b^2 n}-\frac{a \left(a+b x^n\right)^4}{4 b^2 n}","\frac{\left(a+b x^n\right)^5}{5 b^2 n}-\frac{a \left(a+b x^n\right)^4}{4 b^2 n}",1,"-(a*(a + b*x^n)^4)/(4*b^2*n) + (a + b*x^n)^5/(5*b^2*n)","A",3,2,17,0.1176,1,"{266, 43}"
2542,1,19,0,0.0045087,"\int x^{-1+n} \left(a+b x^n\right)^3 \, dx","Int[x^(-1 + n)*(a + b*x^n)^3,x]","\frac{\left(a+b x^n\right)^4}{4 b n}","\frac{\left(a+b x^n\right)^4}{4 b n}",1,"(a + b*x^n)^4/(4*b*n)","A",1,1,15,0.06667,1,"{261}"
2543,1,50,0,0.0201271,"\int \frac{\left(a+b x^n\right)^3}{x} \, dx","Int[(a + b*x^n)^3/x,x]","\frac{3 a^2 b x^n}{n}+a^3 \log (x)+\frac{3 a b^2 x^{2 n}}{2 n}+\frac{b^3 x^{3 n}}{3 n}","\frac{3 a^2 b x^n}{n}+a^3 \log (x)+\frac{3 a b^2 x^{2 n}}{2 n}+\frac{b^3 x^{3 n}}{3 n}",1,"(3*a^2*b*x^n)/n + (3*a*b^2*x^(2*n))/(2*n) + (b^3*x^(3*n))/(3*n) + a^3*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
2544,1,49,0,0.0222159,"\int x^{-1-n} \left(a+b x^n\right)^3 \, dx","Int[x^(-1 - n)*(a + b*x^n)^3,x]","3 a^2 b \log (x)-\frac{a^3 x^{-n}}{n}+\frac{3 a b^2 x^n}{n}+\frac{b^3 x^{2 n}}{2 n}","3 a^2 b \log (x)-\frac{a^3 x^{-n}}{n}+\frac{3 a b^2 x^n}{n}+\frac{b^3 x^{2 n}}{2 n}",1,"-(a^3/(n*x^n)) + (3*a*b^2*x^n)/n + (b^3*x^(2*n))/(2*n) + 3*a^2*b*Log[x]","A",3,2,17,0.1176,1,"{266, 43}"
2545,1,48,0,0.0214762,"\int x^{-1-2 n} \left(a+b x^n\right)^3 \, dx","Int[x^(-1 - 2*n)*(a + b*x^n)^3,x]","-\frac{3 a^2 b x^{-n}}{n}-\frac{a^3 x^{-2 n}}{2 n}+3 a b^2 \log (x)+\frac{b^3 x^n}{n}","-\frac{3 a^2 b x^{-n}}{n}-\frac{a^3 x^{-2 n}}{2 n}+3 a b^2 \log (x)+\frac{b^3 x^n}{n}",1,"-a^3/(2*n*x^(2*n)) - (3*a^2*b)/(n*x^n) + (b^3*x^n)/n + 3*a*b^2*Log[x]","A",3,2,17,0.1176,1,"{266, 43}"
2546,1,52,0,0.0217421,"\int x^{-1-3 n} \left(a+b x^n\right)^3 \, dx","Int[x^(-1 - 3*n)*(a + b*x^n)^3,x]","-\frac{3 a^2 b x^{-2 n}}{2 n}-\frac{a^3 x^{-3 n}}{3 n}-\frac{3 a b^2 x^{-n}}{n}+b^3 \log (x)","-\frac{3 a^2 b x^{-2 n}}{2 n}-\frac{a^3 x^{-3 n}}{3 n}-\frac{3 a b^2 x^{-n}}{n}+b^3 \log (x)",1,"-a^3/(3*n*x^(3*n)) - (3*a^2*b)/(2*n*x^(2*n)) - (3*a*b^2)/(n*x^n) + b^3*Log[x]","A",3,2,17,0.1176,1,"{266, 43}"
2547,1,24,0,0.0049612,"\int x^{-1-4 n} \left(a+b x^n\right)^3 \, dx","Int[x^(-1 - 4*n)*(a + b*x^n)^3,x]","-\frac{x^{-4 n} \left(a+b x^n\right)^4}{4 a n}","-\frac{x^{-4 n} \left(a+b x^n\right)^4}{4 a n}",1,"-(a + b*x^n)^4/(4*a*n*x^(4*n))","A",1,1,17,0.05882,1,"{264}"
2548,1,50,0,0.0162479,"\int x^{-1-5 n} \left(a+b x^n\right)^3 \, dx","Int[x^(-1 - 5*n)*(a + b*x^n)^3,x]","\frac{b x^{-4 n} \left(a+b x^n\right)^4}{20 a^2 n}-\frac{x^{-5 n} \left(a+b x^n\right)^4}{5 a n}","\frac{b x^{-4 n} \left(a+b x^n\right)^4}{20 a^2 n}-\frac{x^{-5 n} \left(a+b x^n\right)^4}{5 a n}",1,"-(a + b*x^n)^4/(5*a*n*x^(5*n)) + (b*(a + b*x^n)^4)/(20*a^2*n*x^(4*n))","A",3,3,17,0.1765,1,"{266, 45, 37}"
2549,1,63,0,0.0225921,"\int x^{-1-6 n} \left(a+b x^n\right)^3 \, dx","Int[x^(-1 - 6*n)*(a + b*x^n)^3,x]","-\frac{3 a^2 b x^{-5 n}}{5 n}-\frac{a^3 x^{-6 n}}{6 n}-\frac{3 a b^2 x^{-4 n}}{4 n}-\frac{b^3 x^{-3 n}}{3 n}","-\frac{3 a^2 b x^{-5 n}}{5 n}-\frac{a^3 x^{-6 n}}{6 n}-\frac{3 a b^2 x^{-4 n}}{4 n}-\frac{b^3 x^{-3 n}}{3 n}",1,"-a^3/(6*n*x^(6*n)) - (3*a^2*b)/(5*n*x^(5*n)) - (3*a*b^2)/(4*n*x^(4*n)) - b^3/(3*n*x^(3*n))","A",3,2,17,0.1176,1,"{266, 43}"
2550,1,63,0,0.0235806,"\int x^{-1-7 n} \left(a+b x^n\right)^3 \, dx","Int[x^(-1 - 7*n)*(a + b*x^n)^3,x]","-\frac{a^2 b x^{-6 n}}{2 n}-\frac{a^3 x^{-7 n}}{7 n}-\frac{3 a b^2 x^{-5 n}}{5 n}-\frac{b^3 x^{-4 n}}{4 n}","-\frac{a^2 b x^{-6 n}}{2 n}-\frac{a^3 x^{-7 n}}{7 n}-\frac{3 a b^2 x^{-5 n}}{5 n}-\frac{b^3 x^{-4 n}}{4 n}",1,"-a^3/(7*n*x^(7*n)) - (a^2*b)/(2*n*x^(6*n)) - (3*a*b^2)/(5*n*x^(5*n)) - b^3/(4*n*x^(4*n))","A",3,2,17,0.1176,1,"{266, 43}"
2551,1,84,0,0.0466852,"\int x^{-1+4 n} \left(a+b x^n\right)^5 \, dx","Int[x^(-1 + 4*n)*(a + b*x^n)^5,x]","\frac{3 a^2 \left(a+b x^n\right)^7}{7 b^4 n}-\frac{a^3 \left(a+b x^n\right)^6}{6 b^4 n}+\frac{\left(a+b x^n\right)^9}{9 b^4 n}-\frac{3 a \left(a+b x^n\right)^8}{8 b^4 n}","\frac{3 a^2 \left(a+b x^n\right)^7}{7 b^4 n}-\frac{a^3 \left(a+b x^n\right)^6}{6 b^4 n}+\frac{\left(a+b x^n\right)^9}{9 b^4 n}-\frac{3 a \left(a+b x^n\right)^8}{8 b^4 n}",1,"-(a^3*(a + b*x^n)^6)/(6*b^4*n) + (3*a^2*(a + b*x^n)^7)/(7*b^4*n) - (3*a*(a + b*x^n)^8)/(8*b^4*n) + (a + b*x^n)^9/(9*b^4*n)","A",3,2,17,0.1176,1,"{266, 43}"
2552,1,62,0,0.0351237,"\int x^{-1+3 n} \left(a+b x^n\right)^5 \, dx","Int[x^(-1 + 3*n)*(a + b*x^n)^5,x]","\frac{a^2 \left(a+b x^n\right)^6}{6 b^3 n}+\frac{\left(a+b x^n\right)^8}{8 b^3 n}-\frac{2 a \left(a+b x^n\right)^7}{7 b^3 n}","\frac{a^2 \left(a+b x^n\right)^6}{6 b^3 n}+\frac{\left(a+b x^n\right)^8}{8 b^3 n}-\frac{2 a \left(a+b x^n\right)^7}{7 b^3 n}",1,"(a^2*(a + b*x^n)^6)/(6*b^3*n) - (2*a*(a + b*x^n)^7)/(7*b^3*n) + (a + b*x^n)^8/(8*b^3*n)","A",3,2,17,0.1176,1,"{266, 43}"
2553,1,40,0,0.0193388,"\int x^{-1+2 n} \left(a+b x^n\right)^5 \, dx","Int[x^(-1 + 2*n)*(a + b*x^n)^5,x]","\frac{\left(a+b x^n\right)^7}{7 b^2 n}-\frac{a \left(a+b x^n\right)^6}{6 b^2 n}","\frac{\left(a+b x^n\right)^7}{7 b^2 n}-\frac{a \left(a+b x^n\right)^6}{6 b^2 n}",1,"-(a*(a + b*x^n)^6)/(6*b^2*n) + (a + b*x^n)^7/(7*b^2*n)","A",3,2,17,0.1176,1,"{266, 43}"
2554,1,19,0,0.0050139,"\int x^{-1+n} \left(a+b x^n\right)^5 \, dx","Int[x^(-1 + n)*(a + b*x^n)^5,x]","\frac{\left(a+b x^n\right)^6}{6 b n}","\frac{\left(a+b x^n\right)^6}{6 b n}",1,"(a + b*x^n)^6/(6*b*n)","A",1,1,15,0.06667,1,"{261}"
2555,1,84,0,0.0352064,"\int \frac{\left(a+b x^n\right)^5}{x} \, dx","Int[(a + b*x^n)^5/x,x]","\frac{5 a^3 b^2 x^{2 n}}{n}+\frac{10 a^2 b^3 x^{3 n}}{3 n}+\frac{5 a^4 b x^n}{n}+a^5 \log (x)+\frac{5 a b^4 x^{4 n}}{4 n}+\frac{b^5 x^{5 n}}{5 n}","\frac{5 a^3 b^2 x^{2 n}}{n}+\frac{10 a^2 b^3 x^{3 n}}{3 n}+\frac{5 a^4 b x^n}{n}+a^5 \log (x)+\frac{5 a b^4 x^{4 n}}{4 n}+\frac{b^5 x^{5 n}}{5 n}",1,"(5*a^4*b*x^n)/n + (5*a^3*b^2*x^(2*n))/n + (10*a^2*b^3*x^(3*n))/(3*n) + (5*a*b^4*x^(4*n))/(4*n) + (b^5*x^(5*n))/(5*n) + a^5*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
2556,1,83,0,0.0369853,"\int x^{-1-n} \left(a+b x^n\right)^5 \, dx","Int[x^(-1 - n)*(a + b*x^n)^5,x]","\frac{10 a^3 b^2 x^n}{n}+\frac{5 a^2 b^3 x^{2 n}}{n}+5 a^4 b \log (x)-\frac{a^5 x^{-n}}{n}+\frac{5 a b^4 x^{3 n}}{3 n}+\frac{b^5 x^{4 n}}{4 n}","\frac{10 a^3 b^2 x^n}{n}+\frac{5 a^2 b^3 x^{2 n}}{n}+5 a^4 b \log (x)-\frac{a^5 x^{-n}}{n}+\frac{5 a b^4 x^{3 n}}{3 n}+\frac{b^5 x^{4 n}}{4 n}",1,"-(a^5/(n*x^n)) + (10*a^3*b^2*x^n)/n + (5*a^2*b^3*x^(2*n))/n + (5*a*b^4*x^(3*n))/(3*n) + (b^5*x^(4*n))/(4*n) + 5*a^4*b*Log[x]","A",3,2,17,0.1176,1,"{266, 43}"
2557,1,85,0,0.0370283,"\int x^{-1-2 n} \left(a+b x^n\right)^5 \, dx","Int[x^(-1 - 2*n)*(a + b*x^n)^5,x]","\frac{10 a^2 b^3 x^n}{n}+10 a^3 b^2 \log (x)-\frac{5 a^4 b x^{-n}}{n}-\frac{a^5 x^{-2 n}}{2 n}+\frac{5 a b^4 x^{2 n}}{2 n}+\frac{b^5 x^{3 n}}{3 n}","\frac{10 a^2 b^3 x^n}{n}+10 a^3 b^2 \log (x)-\frac{5 a^4 b x^{-n}}{n}-\frac{a^5 x^{-2 n}}{2 n}+\frac{5 a b^4 x^{2 n}}{2 n}+\frac{b^5 x^{3 n}}{3 n}",1,"-a^5/(2*n*x^(2*n)) - (5*a^4*b)/(n*x^n) + (10*a^2*b^3*x^n)/n + (5*a*b^4*x^(2*n))/(2*n) + (b^5*x^(3*n))/(3*n) + 10*a^3*b^2*Log[x]","A",3,2,17,0.1176,1,"{266, 43}"
2558,1,85,0,0.036219,"\int x^{-1-3 n} \left(a+b x^n\right)^5 \, dx","Int[x^(-1 - 3*n)*(a + b*x^n)^5,x]","-\frac{10 a^3 b^2 x^{-n}}{n}+10 a^2 b^3 \log (x)-\frac{5 a^4 b x^{-2 n}}{2 n}-\frac{a^5 x^{-3 n}}{3 n}+\frac{5 a b^4 x^n}{n}+\frac{b^5 x^{2 n}}{2 n}","-\frac{10 a^3 b^2 x^{-n}}{n}+10 a^2 b^3 \log (x)-\frac{5 a^4 b x^{-2 n}}{2 n}-\frac{a^5 x^{-3 n}}{3 n}+\frac{5 a b^4 x^n}{n}+\frac{b^5 x^{2 n}}{2 n}",1,"-a^5/(3*n*x^(3*n)) - (5*a^4*b)/(2*n*x^(2*n)) - (10*a^3*b^2)/(n*x^n) + (5*a*b^4*x^n)/n + (b^5*x^(2*n))/(2*n) + 10*a^2*b^3*Log[x]","A",3,2,17,0.1176,1,"{266, 43}"
2559,1,82,0,0.0350119,"\int x^{-1-4 n} \left(a+b x^n\right)^5 \, dx","Int[x^(-1 - 4*n)*(a + b*x^n)^5,x]","-\frac{5 a^3 b^2 x^{-2 n}}{n}-\frac{10 a^2 b^3 x^{-n}}{n}-\frac{5 a^4 b x^{-3 n}}{3 n}-\frac{a^5 x^{-4 n}}{4 n}+5 a b^4 \log (x)+\frac{b^5 x^n}{n}","-\frac{5 a^3 b^2 x^{-2 n}}{n}-\frac{10 a^2 b^3 x^{-n}}{n}-\frac{5 a^4 b x^{-3 n}}{3 n}-\frac{a^5 x^{-4 n}}{4 n}+5 a b^4 \log (x)+\frac{b^5 x^n}{n}",1,"-a^5/(4*n*x^(4*n)) - (5*a^4*b)/(3*n*x^(3*n)) - (5*a^3*b^2)/(n*x^(2*n)) - (10*a^2*b^3)/(n*x^n) + (b^5*x^n)/n + 5*a*b^4*Log[x]","A",3,2,17,0.1176,1,"{266, 43}"
2560,1,86,0,0.0372315,"\int x^{-1-5 n} \left(a+b x^n\right)^5 \, dx","Int[x^(-1 - 5*n)*(a + b*x^n)^5,x]","-\frac{10 a^3 b^2 x^{-3 n}}{3 n}-\frac{5 a^2 b^3 x^{-2 n}}{n}-\frac{5 a^4 b x^{-4 n}}{4 n}-\frac{a^5 x^{-5 n}}{5 n}-\frac{5 a b^4 x^{-n}}{n}+b^5 \log (x)","-\frac{10 a^3 b^2 x^{-3 n}}{3 n}-\frac{5 a^2 b^3 x^{-2 n}}{n}-\frac{5 a^4 b x^{-4 n}}{4 n}-\frac{a^5 x^{-5 n}}{5 n}-\frac{5 a b^4 x^{-n}}{n}+b^5 \log (x)",1,"-a^5/(5*n*x^(5*n)) - (5*a^4*b)/(4*n*x^(4*n)) - (10*a^3*b^2)/(3*n*x^(3*n)) - (5*a^2*b^3)/(n*x^(2*n)) - (5*a*b^4)/(n*x^n) + b^5*Log[x]","A",3,2,17,0.1176,1,"{266, 43}"
2561,1,24,0,0.004856,"\int x^{-1-6 n} \left(a+b x^n\right)^5 \, dx","Int[x^(-1 - 6*n)*(a + b*x^n)^5,x]","-\frac{x^{-6 n} \left(a+b x^n\right)^6}{6 a n}","-\frac{x^{-6 n} \left(a+b x^n\right)^6}{6 a n}",1,"-(a + b*x^n)^6/(6*a*n*x^(6*n))","A",1,1,17,0.05882,1,"{264}"
2562,1,50,0,0.0166591,"\int x^{-1-7 n} \left(a+b x^n\right)^5 \, dx","Int[x^(-1 - 7*n)*(a + b*x^n)^5,x]","\frac{b x^{-6 n} \left(a+b x^n\right)^6}{42 a^2 n}-\frac{x^{-7 n} \left(a+b x^n\right)^6}{7 a n}","\frac{b x^{-6 n} \left(a+b x^n\right)^6}{42 a^2 n}-\frac{x^{-7 n} \left(a+b x^n\right)^6}{7 a n}",1,"-(a + b*x^n)^6/(7*a*n*x^(7*n)) + (b*(a + b*x^n)^6)/(42*a^2*n*x^(6*n))","A",3,3,17,0.1765,1,"{266, 45, 37}"
2563,1,77,0,0.027085,"\int x^{-1-8 n} \left(a+b x^n\right)^5 \, dx","Int[x^(-1 - 8*n)*(a + b*x^n)^5,x]","-\frac{b^2 x^{-6 n} \left(a+b x^n\right)^6}{168 a^3 n}+\frac{b x^{-7 n} \left(a+b x^n\right)^6}{28 a^2 n}-\frac{x^{-8 n} \left(a+b x^n\right)^6}{8 a n}","-\frac{b^2 x^{-6 n} \left(a+b x^n\right)^6}{168 a^3 n}+\frac{b x^{-7 n} \left(a+b x^n\right)^6}{28 a^2 n}-\frac{x^{-8 n} \left(a+b x^n\right)^6}{8 a n}",1,"-(a + b*x^n)^6/(8*a*n*x^(8*n)) + (b*(a + b*x^n)^6)/(28*a^2*n*x^(7*n)) - (b^2*(a + b*x^n)^6)/(168*a^3*n*x^(6*n))","A",4,3,17,0.1765,1,"{266, 45, 37}"
2564,1,97,0,0.0385956,"\int x^{-1-9 n} \left(a+b x^n\right)^5 \, dx","Int[x^(-1 - 9*n)*(a + b*x^n)^5,x]","-\frac{10 a^3 b^2 x^{-7 n}}{7 n}-\frac{5 a^2 b^3 x^{-6 n}}{3 n}-\frac{5 a^4 b x^{-8 n}}{8 n}-\frac{a^5 x^{-9 n}}{9 n}-\frac{a b^4 x^{-5 n}}{n}-\frac{b^5 x^{-4 n}}{4 n}","-\frac{10 a^3 b^2 x^{-7 n}}{7 n}-\frac{5 a^2 b^3 x^{-6 n}}{3 n}-\frac{5 a^4 b x^{-8 n}}{8 n}-\frac{a^5 x^{-9 n}}{9 n}-\frac{a b^4 x^{-5 n}}{n}-\frac{b^5 x^{-4 n}}{4 n}",1,"-a^5/(9*n*x^(9*n)) - (5*a^4*b)/(8*n*x^(8*n)) - (10*a^3*b^2)/(7*n*x^(7*n)) - (5*a^2*b^3)/(3*n*x^(6*n)) - (a*b^4)/(n*x^(5*n)) - b^5/(4*n*x^(4*n))","A",3,2,17,0.1176,1,"{266, 43}"
2565,1,99,0,0.040428,"\int x^{-1-10 n} \left(a+b x^n\right)^5 \, dx","Int[x^(-1 - 10*n)*(a + b*x^n)^5,x]","-\frac{5 a^3 b^2 x^{-8 n}}{4 n}-\frac{10 a^2 b^3 x^{-7 n}}{7 n}-\frac{5 a^4 b x^{-9 n}}{9 n}-\frac{a^5 x^{-10 n}}{10 n}-\frac{5 a b^4 x^{-6 n}}{6 n}-\frac{b^5 x^{-5 n}}{5 n}","-\frac{5 a^3 b^2 x^{-8 n}}{4 n}-\frac{10 a^2 b^3 x^{-7 n}}{7 n}-\frac{5 a^4 b x^{-9 n}}{9 n}-\frac{a^5 x^{-10 n}}{10 n}-\frac{5 a b^4 x^{-6 n}}{6 n}-\frac{b^5 x^{-5 n}}{5 n}",1,"-a^5/(10*n*x^(10*n)) - (5*a^4*b)/(9*n*x^(9*n)) - (5*a^3*b^2)/(4*n*x^(8*n)) - (10*a^2*b^3)/(7*n*x^(7*n)) - (5*a*b^4)/(6*n*x^(6*n)) - b^5/(5*n*x^(5*n))","A",3,2,17,0.1176,1,"{266, 43}"
2566,1,151,0,0.0783979,"\int x^{-1+9 n} \left(a+b x^n\right)^8 \, dx","Int[x^(-1 + 9*n)*(a + b*x^n)^8,x]","\frac{28 a^6 b^2 x^{11 n}}{11 n}+\frac{14 a^5 b^3 x^{12 n}}{3 n}+\frac{70 a^4 b^4 x^{13 n}}{13 n}+\frac{4 a^3 b^5 x^{14 n}}{n}+\frac{28 a^2 b^6 x^{15 n}}{15 n}+\frac{4 a^7 b x^{10 n}}{5 n}+\frac{a^8 x^{9 n}}{9 n}+\frac{a b^7 x^{16 n}}{2 n}+\frac{b^8 x^{17 n}}{17 n}","\frac{28 a^6 b^2 x^{11 n}}{11 n}+\frac{14 a^5 b^3 x^{12 n}}{3 n}+\frac{70 a^4 b^4 x^{13 n}}{13 n}+\frac{4 a^3 b^5 x^{14 n}}{n}+\frac{28 a^2 b^6 x^{15 n}}{15 n}+\frac{4 a^7 b x^{10 n}}{5 n}+\frac{a^8 x^{9 n}}{9 n}+\frac{a b^7 x^{16 n}}{2 n}+\frac{b^8 x^{17 n}}{17 n}",1,"(a^8*x^(9*n))/(9*n) + (4*a^7*b*x^(10*n))/(5*n) + (28*a^6*b^2*x^(11*n))/(11*n) + (14*a^5*b^3*x^(12*n))/(3*n) + (70*a^4*b^4*x^(13*n))/(13*n) + (4*a^3*b^5*x^(14*n))/n + (28*a^2*b^6*x^(15*n))/(15*n) + (a*b^7*x^(16*n))/(2*n) + (b^8*x^(17*n))/(17*n)","A",3,2,17,0.1176,1,"{266, 43}"
2567,1,151,0,0.0721068,"\int x^{-1+8 n} \left(a+b x^n\right)^8 \, dx","Int[x^(-1 + 8*n)*(a + b*x^n)^8,x]","\frac{14 a^6 b^2 x^{10 n}}{5 n}+\frac{56 a^5 b^3 x^{11 n}}{11 n}+\frac{35 a^4 b^4 x^{12 n}}{6 n}+\frac{56 a^3 b^5 x^{13 n}}{13 n}+\frac{2 a^2 b^6 x^{14 n}}{n}+\frac{8 a^7 b x^{9 n}}{9 n}+\frac{a^8 x^{8 n}}{8 n}+\frac{8 a b^7 x^{15 n}}{15 n}+\frac{b^8 x^{16 n}}{16 n}","\frac{14 a^6 b^2 x^{10 n}}{5 n}+\frac{56 a^5 b^3 x^{11 n}}{11 n}+\frac{35 a^4 b^4 x^{12 n}}{6 n}+\frac{56 a^3 b^5 x^{13 n}}{13 n}+\frac{2 a^2 b^6 x^{14 n}}{n}+\frac{8 a^7 b x^{9 n}}{9 n}+\frac{a^8 x^{8 n}}{8 n}+\frac{8 a b^7 x^{15 n}}{15 n}+\frac{b^8 x^{16 n}}{16 n}",1,"(a^8*x^(8*n))/(8*n) + (8*a^7*b*x^(9*n))/(9*n) + (14*a^6*b^2*x^(10*n))/(5*n) + (56*a^5*b^3*x^(11*n))/(11*n) + (35*a^4*b^4*x^(12*n))/(6*n) + (56*a^3*b^5*x^(13*n))/(13*n) + (2*a^2*b^6*x^(14*n))/n + (8*a*b^7*x^(15*n))/(15*n) + (b^8*x^(16*n))/(16*n)","A",3,2,17,0.1176,1,"{266, 43}"
2568,1,150,0,0.0780009,"\int x^{-1+7 n} \left(a+b x^n\right)^8 \, dx","Int[x^(-1 + 7*n)*(a + b*x^n)^8,x]","\frac{15 a^2 \left(a+b x^n\right)^{13}}{13 b^7 n}-\frac{5 a^3 \left(a+b x^n\right)^{12}}{3 b^7 n}+\frac{15 a^4 \left(a+b x^n\right)^{11}}{11 b^7 n}-\frac{3 a^5 \left(a+b x^n\right)^{10}}{5 b^7 n}+\frac{a^6 \left(a+b x^n\right)^9}{9 b^7 n}+\frac{\left(a+b x^n\right)^{15}}{15 b^7 n}-\frac{3 a \left(a+b x^n\right)^{14}}{7 b^7 n}","\frac{15 a^2 \left(a+b x^n\right)^{13}}{13 b^7 n}-\frac{5 a^3 \left(a+b x^n\right)^{12}}{3 b^7 n}+\frac{15 a^4 \left(a+b x^n\right)^{11}}{11 b^7 n}-\frac{3 a^5 \left(a+b x^n\right)^{10}}{5 b^7 n}+\frac{a^6 \left(a+b x^n\right)^9}{9 b^7 n}+\frac{\left(a+b x^n\right)^{15}}{15 b^7 n}-\frac{3 a \left(a+b x^n\right)^{14}}{7 b^7 n}",1,"(a^6*(a + b*x^n)^9)/(9*b^7*n) - (3*a^5*(a + b*x^n)^10)/(5*b^7*n) + (15*a^4*(a + b*x^n)^11)/(11*b^7*n) - (5*a^3*(a + b*x^n)^12)/(3*b^7*n) + (15*a^2*(a + b*x^n)^13)/(13*b^7*n) - (3*a*(a + b*x^n)^14)/(7*b^7*n) + (a + b*x^n)^15/(15*b^7*n)","A",3,2,17,0.1176,1,"{266, 43}"
2569,1,128,0,0.0676856,"\int x^{-1+6 n} \left(a+b x^n\right)^8 \, dx","Int[x^(-1 + 6*n)*(a + b*x^n)^8,x]","\frac{5 a^2 \left(a+b x^n\right)^{12}}{6 b^6 n}-\frac{10 a^3 \left(a+b x^n\right)^{11}}{11 b^6 n}+\frac{a^4 \left(a+b x^n\right)^{10}}{2 b^6 n}-\frac{a^5 \left(a+b x^n\right)^9}{9 b^6 n}+\frac{\left(a+b x^n\right)^{14}}{14 b^6 n}-\frac{5 a \left(a+b x^n\right)^{13}}{13 b^6 n}","\frac{5 a^2 \left(a+b x^n\right)^{12}}{6 b^6 n}-\frac{10 a^3 \left(a+b x^n\right)^{11}}{11 b^6 n}+\frac{a^4 \left(a+b x^n\right)^{10}}{2 b^6 n}-\frac{a^5 \left(a+b x^n\right)^9}{9 b^6 n}+\frac{\left(a+b x^n\right)^{14}}{14 b^6 n}-\frac{5 a \left(a+b x^n\right)^{13}}{13 b^6 n}",1,"-(a^5*(a + b*x^n)^9)/(9*b^6*n) + (a^4*(a + b*x^n)^10)/(2*b^6*n) - (10*a^3*(a + b*x^n)^11)/(11*b^6*n) + (5*a^2*(a + b*x^n)^12)/(6*b^6*n) - (5*a*(a + b*x^n)^13)/(13*b^6*n) + (a + b*x^n)^14/(14*b^6*n)","A",3,2,17,0.1176,1,"{266, 43}"
2570,1,106,0,0.0583547,"\int x^{-1+5 n} \left(a+b x^n\right)^8 \, dx","Int[x^(-1 + 5*n)*(a + b*x^n)^8,x]","\frac{6 a^2 \left(a+b x^n\right)^{11}}{11 b^5 n}-\frac{2 a^3 \left(a+b x^n\right)^{10}}{5 b^5 n}+\frac{a^4 \left(a+b x^n\right)^9}{9 b^5 n}+\frac{\left(a+b x^n\right)^{13}}{13 b^5 n}-\frac{a \left(a+b x^n\right)^{12}}{3 b^5 n}","\frac{6 a^2 \left(a+b x^n\right)^{11}}{11 b^5 n}-\frac{2 a^3 \left(a+b x^n\right)^{10}}{5 b^5 n}+\frac{a^4 \left(a+b x^n\right)^9}{9 b^5 n}+\frac{\left(a+b x^n\right)^{13}}{13 b^5 n}-\frac{a \left(a+b x^n\right)^{12}}{3 b^5 n}",1,"(a^4*(a + b*x^n)^9)/(9*b^5*n) - (2*a^3*(a + b*x^n)^10)/(5*b^5*n) + (6*a^2*(a + b*x^n)^11)/(11*b^5*n) - (a*(a + b*x^n)^12)/(3*b^5*n) + (a + b*x^n)^13/(13*b^5*n)","A",3,2,17,0.1176,1,"{266, 43}"
2571,1,84,0,0.0497295,"\int x^{-1+4 n} \left(a+b x^n\right)^8 \, dx","Int[x^(-1 + 4*n)*(a + b*x^n)^8,x]","\frac{3 a^2 \left(a+b x^n\right)^{10}}{10 b^4 n}-\frac{a^3 \left(a+b x^n\right)^9}{9 b^4 n}+\frac{\left(a+b x^n\right)^{12}}{12 b^4 n}-\frac{3 a \left(a+b x^n\right)^{11}}{11 b^4 n}","\frac{3 a^2 \left(a+b x^n\right)^{10}}{10 b^4 n}-\frac{a^3 \left(a+b x^n\right)^9}{9 b^4 n}+\frac{\left(a+b x^n\right)^{12}}{12 b^4 n}-\frac{3 a \left(a+b x^n\right)^{11}}{11 b^4 n}",1,"-(a^3*(a + b*x^n)^9)/(9*b^4*n) + (3*a^2*(a + b*x^n)^10)/(10*b^4*n) - (3*a*(a + b*x^n)^11)/(11*b^4*n) + (a + b*x^n)^12/(12*b^4*n)","A",3,2,17,0.1176,1,"{266, 43}"
2572,1,62,0,0.0388772,"\int x^{-1+3 n} \left(a+b x^n\right)^8 \, dx","Int[x^(-1 + 3*n)*(a + b*x^n)^8,x]","\frac{a^2 \left(a+b x^n\right)^9}{9 b^3 n}+\frac{\left(a+b x^n\right)^{11}}{11 b^3 n}-\frac{a \left(a+b x^n\right)^{10}}{5 b^3 n}","\frac{a^2 \left(a+b x^n\right)^9}{9 b^3 n}+\frac{\left(a+b x^n\right)^{11}}{11 b^3 n}-\frac{a \left(a+b x^n\right)^{10}}{5 b^3 n}",1,"(a^2*(a + b*x^n)^9)/(9*b^3*n) - (a*(a + b*x^n)^10)/(5*b^3*n) + (a + b*x^n)^11/(11*b^3*n)","A",3,2,17,0.1176,1,"{266, 43}"
2573,1,40,0,0.0185763,"\int x^{-1+2 n} \left(a+b x^n\right)^8 \, dx","Int[x^(-1 + 2*n)*(a + b*x^n)^8,x]","\frac{\left(a+b x^n\right)^{10}}{10 b^2 n}-\frac{a \left(a+b x^n\right)^9}{9 b^2 n}","\frac{\left(a+b x^n\right)^{10}}{10 b^2 n}-\frac{a \left(a+b x^n\right)^9}{9 b^2 n}",1,"-(a*(a + b*x^n)^9)/(9*b^2*n) + (a + b*x^n)^10/(10*b^2*n)","A",3,2,17,0.1176,1,"{266, 43}"
2574,1,19,0,0.0045803,"\int x^{-1+n} \left(a+b x^n\right)^8 \, dx","Int[x^(-1 + n)*(a + b*x^n)^8,x]","\frac{\left(a+b x^n\right)^9}{9 b n}","\frac{\left(a+b x^n\right)^9}{9 b n}",1,"(a + b*x^n)^9/(9*b*n)","A",1,1,15,0.06667,1,"{261}"
2575,1,138,0,0.0545366,"\int \frac{\left(a+b x^n\right)^8}{x} \, dx","Int[(a + b*x^n)^8/x,x]","\frac{14 a^6 b^2 x^{2 n}}{n}+\frac{56 a^5 b^3 x^{3 n}}{3 n}+\frac{35 a^4 b^4 x^{4 n}}{2 n}+\frac{56 a^3 b^5 x^{5 n}}{5 n}+\frac{14 a^2 b^6 x^{6 n}}{3 n}+\frac{8 a^7 b x^n}{n}+a^8 \log (x)+\frac{8 a b^7 x^{7 n}}{7 n}+\frac{b^8 x^{8 n}}{8 n}","\frac{14 a^6 b^2 x^{2 n}}{n}+\frac{56 a^5 b^3 x^{3 n}}{3 n}+\frac{35 a^4 b^4 x^{4 n}}{2 n}+\frac{56 a^3 b^5 x^{5 n}}{5 n}+\frac{14 a^2 b^6 x^{6 n}}{3 n}+\frac{8 a^7 b x^n}{n}+a^8 \log (x)+\frac{8 a b^7 x^{7 n}}{7 n}+\frac{b^8 x^{8 n}}{8 n}",1,"(8*a^7*b*x^n)/n + (14*a^6*b^2*x^(2*n))/n + (56*a^5*b^3*x^(3*n))/(3*n) + (35*a^4*b^4*x^(4*n))/(2*n) + (56*a^3*b^5*x^(5*n))/(5*n) + (14*a^2*b^6*x^(6*n))/(3*n) + (8*a*b^7*x^(7*n))/(7*n) + (b^8*x^(8*n))/(8*n) + a^8*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
2576,1,135,0,0.0573147,"\int x^{-1-n} \left(a+b x^n\right)^8 \, dx","Int[x^(-1 - n)*(a + b*x^n)^8,x]","\frac{28 a^6 b^2 x^n}{n}+\frac{28 a^5 b^3 x^{2 n}}{n}+\frac{70 a^4 b^4 x^{3 n}}{3 n}+\frac{14 a^3 b^5 x^{4 n}}{n}+\frac{28 a^2 b^6 x^{5 n}}{5 n}+8 a^7 b \log (x)-\frac{a^8 x^{-n}}{n}+\frac{4 a b^7 x^{6 n}}{3 n}+\frac{b^8 x^{7 n}}{7 n}","\frac{28 a^6 b^2 x^n}{n}+\frac{28 a^5 b^3 x^{2 n}}{n}+\frac{70 a^4 b^4 x^{3 n}}{3 n}+\frac{14 a^3 b^5 x^{4 n}}{n}+\frac{28 a^2 b^6 x^{5 n}}{5 n}+8 a^7 b \log (x)-\frac{a^8 x^{-n}}{n}+\frac{4 a b^7 x^{6 n}}{3 n}+\frac{b^8 x^{7 n}}{7 n}",1,"-(a^8/(n*x^n)) + (28*a^6*b^2*x^n)/n + (28*a^5*b^3*x^(2*n))/n + (70*a^4*b^4*x^(3*n))/(3*n) + (14*a^3*b^5*x^(4*n))/n + (28*a^2*b^6*x^(5*n))/(5*n) + (4*a*b^7*x^(6*n))/(3*n) + (b^8*x^(7*n))/(7*n) + 8*a^7*b*Log[x]","A",3,2,17,0.1176,1,"{266, 43}"
2577,1,135,0,0.0572692,"\int x^{-1-2 n} \left(a+b x^n\right)^8 \, dx","Int[x^(-1 - 2*n)*(a + b*x^n)^8,x]","\frac{56 a^5 b^3 x^n}{n}+\frac{35 a^4 b^4 x^{2 n}}{n}+\frac{56 a^3 b^5 x^{3 n}}{3 n}+\frac{7 a^2 b^6 x^{4 n}}{n}+28 a^6 b^2 \log (x)-\frac{8 a^7 b x^{-n}}{n}-\frac{a^8 x^{-2 n}}{2 n}+\frac{8 a b^7 x^{5 n}}{5 n}+\frac{b^8 x^{6 n}}{6 n}","\frac{56 a^5 b^3 x^n}{n}+\frac{35 a^4 b^4 x^{2 n}}{n}+\frac{56 a^3 b^5 x^{3 n}}{3 n}+\frac{7 a^2 b^6 x^{4 n}}{n}+28 a^6 b^2 \log (x)-\frac{8 a^7 b x^{-n}}{n}-\frac{a^8 x^{-2 n}}{2 n}+\frac{8 a b^7 x^{5 n}}{5 n}+\frac{b^8 x^{6 n}}{6 n}",1,"-a^8/(2*n*x^(2*n)) - (8*a^7*b)/(n*x^n) + (56*a^5*b^3*x^n)/n + (35*a^4*b^4*x^(2*n))/n + (56*a^3*b^5*x^(3*n))/(3*n) + (7*a^2*b^6*x^(4*n))/n + (8*a*b^7*x^(5*n))/(5*n) + (b^8*x^(6*n))/(6*n) + 28*a^6*b^2*Log[x]","A",3,2,17,0.1176,1,"{266, 43}"
2578,1,133,0,0.0584728,"\int x^{-1-3 n} \left(a+b x^n\right)^8 \, dx","Int[x^(-1 - 3*n)*(a + b*x^n)^8,x]","-\frac{28 a^6 b^2 x^{-n}}{n}+\frac{70 a^4 b^4 x^n}{n}+\frac{28 a^3 b^5 x^{2 n}}{n}+\frac{28 a^2 b^6 x^{3 n}}{3 n}+56 a^5 b^3 \log (x)-\frac{4 a^7 b x^{-2 n}}{n}-\frac{a^8 x^{-3 n}}{3 n}+\frac{2 a b^7 x^{4 n}}{n}+\frac{b^8 x^{5 n}}{5 n}","-\frac{28 a^6 b^2 x^{-n}}{n}+\frac{70 a^4 b^4 x^n}{n}+\frac{28 a^3 b^5 x^{2 n}}{n}+\frac{28 a^2 b^6 x^{3 n}}{3 n}+56 a^5 b^3 \log (x)-\frac{4 a^7 b x^{-2 n}}{n}-\frac{a^8 x^{-3 n}}{3 n}+\frac{2 a b^7 x^{4 n}}{n}+\frac{b^8 x^{5 n}}{5 n}",1,"-a^8/(3*n*x^(3*n)) - (4*a^7*b)/(n*x^(2*n)) - (28*a^6*b^2)/(n*x^n) + (70*a^4*b^4*x^n)/n + (28*a^3*b^5*x^(2*n))/n + (28*a^2*b^6*x^(3*n))/(3*n) + (2*a*b^7*x^(4*n))/n + (b^8*x^(5*n))/(5*n) + 56*a^5*b^3*Log[x]","A",3,2,17,0.1176,1,"{266, 43}"
2579,1,135,0,0.059085,"\int x^{-1-4 n} \left(a+b x^n\right)^8 \, dx","Int[x^(-1 - 4*n)*(a + b*x^n)^8,x]","-\frac{14 a^6 b^2 x^{-2 n}}{n}-\frac{56 a^5 b^3 x^{-n}}{n}+\frac{56 a^3 b^5 x^n}{n}+\frac{14 a^2 b^6 x^{2 n}}{n}+70 a^4 b^4 \log (x)-\frac{8 a^7 b x^{-3 n}}{3 n}-\frac{a^8 x^{-4 n}}{4 n}+\frac{8 a b^7 x^{3 n}}{3 n}+\frac{b^8 x^{4 n}}{4 n}","-\frac{14 a^6 b^2 x^{-2 n}}{n}-\frac{56 a^5 b^3 x^{-n}}{n}+\frac{56 a^3 b^5 x^n}{n}+\frac{14 a^2 b^6 x^{2 n}}{n}+70 a^4 b^4 \log (x)-\frac{8 a^7 b x^{-3 n}}{3 n}-\frac{a^8 x^{-4 n}}{4 n}+\frac{8 a b^7 x^{3 n}}{3 n}+\frac{b^8 x^{4 n}}{4 n}",1,"-a^8/(4*n*x^(4*n)) - (8*a^7*b)/(3*n*x^(3*n)) - (14*a^6*b^2)/(n*x^(2*n)) - (56*a^5*b^3)/(n*x^n) + (56*a^3*b^5*x^n)/n + (14*a^2*b^6*x^(2*n))/n + (8*a*b^7*x^(3*n))/(3*n) + (b^8*x^(4*n))/(4*n) + 70*a^4*b^4*Log[x]","A",3,2,17,0.1176,1,"{266, 43}"
2580,1,133,0,0.0583786,"\int x^{-1-5 n} \left(a+b x^n\right)^8 \, dx","Int[x^(-1 - 5*n)*(a + b*x^n)^8,x]","-\frac{28 a^6 b^2 x^{-3 n}}{3 n}-\frac{28 a^5 b^3 x^{-2 n}}{n}-\frac{70 a^4 b^4 x^{-n}}{n}+\frac{28 a^2 b^6 x^n}{n}+56 a^3 b^5 \log (x)-\frac{2 a^7 b x^{-4 n}}{n}-\frac{a^8 x^{-5 n}}{5 n}+\frac{4 a b^7 x^{2 n}}{n}+\frac{b^8 x^{3 n}}{3 n}","-\frac{28 a^6 b^2 x^{-3 n}}{3 n}-\frac{28 a^5 b^3 x^{-2 n}}{n}-\frac{70 a^4 b^4 x^{-n}}{n}+\frac{28 a^2 b^6 x^n}{n}+56 a^3 b^5 \log (x)-\frac{2 a^7 b x^{-4 n}}{n}-\frac{a^8 x^{-5 n}}{5 n}+\frac{4 a b^7 x^{2 n}}{n}+\frac{b^8 x^{3 n}}{3 n}",1,"-a^8/(5*n*x^(5*n)) - (2*a^7*b)/(n*x^(4*n)) - (28*a^6*b^2)/(3*n*x^(3*n)) - (28*a^5*b^3)/(n*x^(2*n)) - (70*a^4*b^4)/(n*x^n) + (28*a^2*b^6*x^n)/n + (4*a*b^7*x^(2*n))/n + (b^8*x^(3*n))/(3*n) + 56*a^3*b^5*Log[x]","A",3,2,17,0.1176,1,"{266, 43}"
2581,1,135,0,0.0609833,"\int x^{-1-6 n} \left(a+b x^n\right)^8 \, dx","Int[x^(-1 - 6*n)*(a + b*x^n)^8,x]","-\frac{7 a^6 b^2 x^{-4 n}}{n}-\frac{56 a^5 b^3 x^{-3 n}}{3 n}-\frac{35 a^4 b^4 x^{-2 n}}{n}-\frac{56 a^3 b^5 x^{-n}}{n}+28 a^2 b^6 \log (x)-\frac{8 a^7 b x^{-5 n}}{5 n}-\frac{a^8 x^{-6 n}}{6 n}+\frac{8 a b^7 x^n}{n}+\frac{b^8 x^{2 n}}{2 n}","-\frac{7 a^6 b^2 x^{-4 n}}{n}-\frac{56 a^5 b^3 x^{-3 n}}{3 n}-\frac{35 a^4 b^4 x^{-2 n}}{n}-\frac{56 a^3 b^5 x^{-n}}{n}+28 a^2 b^6 \log (x)-\frac{8 a^7 b x^{-5 n}}{5 n}-\frac{a^8 x^{-6 n}}{6 n}+\frac{8 a b^7 x^n}{n}+\frac{b^8 x^{2 n}}{2 n}",1,"-a^8/(6*n*x^(6*n)) - (8*a^7*b)/(5*n*x^(5*n)) - (7*a^6*b^2)/(n*x^(4*n)) - (56*a^5*b^3)/(3*n*x^(3*n)) - (35*a^4*b^4)/(n*x^(2*n)) - (56*a^3*b^5)/(n*x^n) + (8*a*b^7*x^n)/n + (b^8*x^(2*n))/(2*n) + 28*a^2*b^6*Log[x]","A",3,2,17,0.1176,1,"{266, 43}"
2582,1,134,0,0.0614759,"\int x^{-1-7 n} \left(a+b x^n\right)^8 \, dx","Int[x^(-1 - 7*n)*(a + b*x^n)^8,x]","-\frac{28 a^6 b^2 x^{-5 n}}{5 n}-\frac{14 a^5 b^3 x^{-4 n}}{n}-\frac{70 a^4 b^4 x^{-3 n}}{3 n}-\frac{28 a^3 b^5 x^{-2 n}}{n}-\frac{28 a^2 b^6 x^{-n}}{n}-\frac{4 a^7 b x^{-6 n}}{3 n}-\frac{a^8 x^{-7 n}}{7 n}+8 a b^7 \log (x)+\frac{b^8 x^n}{n}","-\frac{28 a^6 b^2 x^{-5 n}}{5 n}-\frac{14 a^5 b^3 x^{-4 n}}{n}-\frac{70 a^4 b^4 x^{-3 n}}{3 n}-\frac{28 a^3 b^5 x^{-2 n}}{n}-\frac{28 a^2 b^6 x^{-n}}{n}-\frac{4 a^7 b x^{-6 n}}{3 n}-\frac{a^8 x^{-7 n}}{7 n}+8 a b^7 \log (x)+\frac{b^8 x^n}{n}",1,"-a^8/(7*n*x^(7*n)) - (4*a^7*b)/(3*n*x^(6*n)) - (28*a^6*b^2)/(5*n*x^(5*n)) - (14*a^5*b^3)/(n*x^(4*n)) - (70*a^4*b^4)/(3*n*x^(3*n)) - (28*a^3*b^5)/(n*x^(2*n)) - (28*a^2*b^6)/(n*x^n) + (b^8*x^n)/n + 8*a*b^7*Log[x]","A",3,2,17,0.1176,1,"{266, 43}"
2583,1,140,0,0.0588352,"\int x^{-1-8 n} \left(a+b x^n\right)^8 \, dx","Int[x^(-1 - 8*n)*(a + b*x^n)^8,x]","-\frac{14 a^6 b^2 x^{-6 n}}{3 n}-\frac{56 a^5 b^3 x^{-5 n}}{5 n}-\frac{35 a^4 b^4 x^{-4 n}}{2 n}-\frac{56 a^3 b^5 x^{-3 n}}{3 n}-\frac{14 a^2 b^6 x^{-2 n}}{n}-\frac{8 a^7 b x^{-7 n}}{7 n}-\frac{a^8 x^{-8 n}}{8 n}-\frac{8 a b^7 x^{-n}}{n}+b^8 \log (x)","-\frac{14 a^6 b^2 x^{-6 n}}{3 n}-\frac{56 a^5 b^3 x^{-5 n}}{5 n}-\frac{35 a^4 b^4 x^{-4 n}}{2 n}-\frac{56 a^3 b^5 x^{-3 n}}{3 n}-\frac{14 a^2 b^6 x^{-2 n}}{n}-\frac{8 a^7 b x^{-7 n}}{7 n}-\frac{a^8 x^{-8 n}}{8 n}-\frac{8 a b^7 x^{-n}}{n}+b^8 \log (x)",1,"-a^8/(8*n*x^(8*n)) - (8*a^7*b)/(7*n*x^(7*n)) - (14*a^6*b^2)/(3*n*x^(6*n)) - (56*a^5*b^3)/(5*n*x^(5*n)) - (35*a^4*b^4)/(2*n*x^(4*n)) - (56*a^3*b^5)/(3*n*x^(3*n)) - (14*a^2*b^6)/(n*x^(2*n)) - (8*a*b^7)/(n*x^n) + b^8*Log[x]","A",3,2,17,0.1176,1,"{266, 43}"
2584,1,24,0,0.0058193,"\int x^{-1-9 n} \left(a+b x^n\right)^8 \, dx","Int[x^(-1 - 9*n)*(a + b*x^n)^8,x]","-\frac{x^{-9 n} \left(a+b x^n\right)^9}{9 a n}","-\frac{x^{-9 n} \left(a+b x^n\right)^9}{9 a n}",1,"-(a + b*x^n)^9/(9*a*n*x^(9*n))","A",1,1,17,0.05882,1,"{264}"
2585,1,50,0,0.0191083,"\int x^{-1-10 n} \left(a+b x^n\right)^8 \, dx","Int[x^(-1 - 10*n)*(a + b*x^n)^8,x]","\frac{b x^{-9 n} \left(a+b x^n\right)^9}{90 a^2 n}-\frac{x^{-10 n} \left(a+b x^n\right)^9}{10 a n}","\frac{b x^{-9 n} \left(a+b x^n\right)^9}{90 a^2 n}-\frac{x^{-10 n} \left(a+b x^n\right)^9}{10 a n}",1,"-(a + b*x^n)^9/(10*a*n*x^(10*n)) + (b*(a + b*x^n)^9)/(90*a^2*n*x^(9*n))","A",3,3,17,0.1765,1,"{266, 45, 37}"
2586,1,77,0,0.0290084,"\int x^{-1-11 n} \left(a+b x^n\right)^8 \, dx","Int[x^(-1 - 11*n)*(a + b*x^n)^8,x]","-\frac{b^2 x^{-9 n} \left(a+b x^n\right)^9}{495 a^3 n}+\frac{b x^{-10 n} \left(a+b x^n\right)^9}{55 a^2 n}-\frac{x^{-11 n} \left(a+b x^n\right)^9}{11 a n}","-\frac{b^2 x^{-9 n} \left(a+b x^n\right)^9}{495 a^3 n}+\frac{b x^{-10 n} \left(a+b x^n\right)^9}{55 a^2 n}-\frac{x^{-11 n} \left(a+b x^n\right)^9}{11 a n}",1,"-(a + b*x^n)^9/(11*a*n*x^(11*n)) + (b*(a + b*x^n)^9)/(55*a^2*n*x^(10*n)) - (b^2*(a + b*x^n)^9)/(495*a^3*n*x^(9*n))","A",4,3,17,0.1765,1,"{266, 45, 37}"
2587,1,104,0,0.0395928,"\int x^{-1-12 n} \left(a+b x^n\right)^8 \, dx","Int[x^(-1 - 12*n)*(a + b*x^n)^8,x]","-\frac{b^2 x^{-10 n} \left(a+b x^n\right)^9}{220 a^3 n}+\frac{b^3 x^{-9 n} \left(a+b x^n\right)^9}{1980 a^4 n}+\frac{b x^{-11 n} \left(a+b x^n\right)^9}{44 a^2 n}-\frac{x^{-12 n} \left(a+b x^n\right)^9}{12 a n}","-\frac{b^2 x^{-10 n} \left(a+b x^n\right)^9}{220 a^3 n}+\frac{b^3 x^{-9 n} \left(a+b x^n\right)^9}{1980 a^4 n}+\frac{b x^{-11 n} \left(a+b x^n\right)^9}{44 a^2 n}-\frac{x^{-12 n} \left(a+b x^n\right)^9}{12 a n}",1,"-(a + b*x^n)^9/(12*a*n*x^(12*n)) + (b*(a + b*x^n)^9)/(44*a^2*n*x^(11*n)) - (b^2*(a + b*x^n)^9)/(220*a^3*n*x^(10*n)) + (b^3*(a + b*x^n)^9)/(1980*a^4*n*x^(9*n))","A",5,3,17,0.1765,1,"{266, 45, 37}"
2588,1,131,0,0.0538214,"\int x^{-1-13 n} \left(a+b x^n\right)^8 \, dx","Int[x^(-1 - 13*n)*(a + b*x^n)^8,x]","-\frac{b^2 x^{-11 n} \left(a+b x^n\right)^9}{143 a^3 n}+\frac{b^3 x^{-10 n} \left(a+b x^n\right)^9}{715 a^4 n}-\frac{b^4 x^{-9 n} \left(a+b x^n\right)^9}{6435 a^5 n}+\frac{b x^{-12 n} \left(a+b x^n\right)^9}{39 a^2 n}-\frac{x^{-13 n} \left(a+b x^n\right)^9}{13 a n}","-\frac{b^2 x^{-11 n} \left(a+b x^n\right)^9}{143 a^3 n}+\frac{b^3 x^{-10 n} \left(a+b x^n\right)^9}{715 a^4 n}-\frac{b^4 x^{-9 n} \left(a+b x^n\right)^9}{6435 a^5 n}+\frac{b x^{-12 n} \left(a+b x^n\right)^9}{39 a^2 n}-\frac{x^{-13 n} \left(a+b x^n\right)^9}{13 a n}",1,"-(a + b*x^n)^9/(13*a*n*x^(13*n)) + (b*(a + b*x^n)^9)/(39*a^2*n*x^(12*n)) - (b^2*(a + b*x^n)^9)/(143*a^3*n*x^(11*n)) + (b^3*(a + b*x^n)^9)/(715*a^4*n*x^(10*n)) - (b^4*(a + b*x^n)^9)/(6435*a^5*n*x^(9*n))","A",6,3,17,0.1765,1,"{266, 45, 37}"
2589,1,151,0,0.061078,"\int x^{-1-14 n} \left(a+b x^n\right)^8 \, dx","Int[x^(-1 - 14*n)*(a + b*x^n)^8,x]","-\frac{7 a^6 b^2 x^{-12 n}}{3 n}-\frac{56 a^5 b^3 x^{-11 n}}{11 n}-\frac{7 a^4 b^4 x^{-10 n}}{n}-\frac{56 a^3 b^5 x^{-9 n}}{9 n}-\frac{7 a^2 b^6 x^{-8 n}}{2 n}-\frac{8 a^7 b x^{-13 n}}{13 n}-\frac{a^8 x^{-14 n}}{14 n}-\frac{8 a b^7 x^{-7 n}}{7 n}-\frac{b^8 x^{-6 n}}{6 n}","-\frac{7 a^6 b^2 x^{-12 n}}{3 n}-\frac{56 a^5 b^3 x^{-11 n}}{11 n}-\frac{7 a^4 b^4 x^{-10 n}}{n}-\frac{56 a^3 b^5 x^{-9 n}}{9 n}-\frac{7 a^2 b^6 x^{-8 n}}{2 n}-\frac{8 a^7 b x^{-13 n}}{13 n}-\frac{a^8 x^{-14 n}}{14 n}-\frac{8 a b^7 x^{-7 n}}{7 n}-\frac{b^8 x^{-6 n}}{6 n}",1,"-a^8/(14*n*x^(14*n)) - (8*a^7*b)/(13*n*x^(13*n)) - (7*a^6*b^2)/(3*n*x^(12*n)) - (56*a^5*b^3)/(11*n*x^(11*n)) - (7*a^4*b^4)/(n*x^(10*n)) - (56*a^3*b^5)/(9*n*x^(9*n)) - (7*a^2*b^6)/(2*n*x^(8*n)) - (8*a*b^7)/(7*n*x^(7*n)) - b^8/(6*n*x^(6*n))","A",3,2,17,0.1176,1,"{266, 43}"
2590,1,151,0,0.0608719,"\int x^{-1-15 n} \left(a+b x^n\right)^8 \, dx","Int[x^(-1 - 15*n)*(a + b*x^n)^8,x]","-\frac{28 a^6 b^2 x^{-13 n}}{13 n}-\frac{14 a^5 b^3 x^{-12 n}}{3 n}-\frac{70 a^4 b^4 x^{-11 n}}{11 n}-\frac{28 a^3 b^5 x^{-10 n}}{5 n}-\frac{28 a^2 b^6 x^{-9 n}}{9 n}-\frac{4 a^7 b x^{-14 n}}{7 n}-\frac{a^8 x^{-15 n}}{15 n}-\frac{a b^7 x^{-8 n}}{n}-\frac{b^8 x^{-7 n}}{7 n}","-\frac{28 a^6 b^2 x^{-13 n}}{13 n}-\frac{14 a^5 b^3 x^{-12 n}}{3 n}-\frac{70 a^4 b^4 x^{-11 n}}{11 n}-\frac{28 a^3 b^5 x^{-10 n}}{5 n}-\frac{28 a^2 b^6 x^{-9 n}}{9 n}-\frac{4 a^7 b x^{-14 n}}{7 n}-\frac{a^8 x^{-15 n}}{15 n}-\frac{a b^7 x^{-8 n}}{n}-\frac{b^8 x^{-7 n}}{7 n}",1,"-a^8/(15*n*x^(15*n)) - (4*a^7*b)/(7*n*x^(14*n)) - (28*a^6*b^2)/(13*n*x^(13*n)) - (14*a^5*b^3)/(3*n*x^(12*n)) - (70*a^4*b^4)/(11*n*x^(11*n)) - (28*a^3*b^5)/(5*n*x^(10*n)) - (28*a^2*b^6)/(9*n*x^(9*n)) - (a*b^7)/(n*x^(8*n)) - b^8/(7*n*x^(7*n))","A",3,2,17,0.1176,1,"{266, 43}"
2591,1,19,0,0.0044505,"\int x^{-1+n} \left(a+b x^n\right)^{16} \, dx","Int[x^(-1 + n)*(a + b*x^n)^16,x]","\frac{\left(a+b x^n\right)^{17}}{17 b n}","\frac{\left(a+b x^n\right)^{17}}{17 b n}",1,"(a + b*x^n)^17/(17*b*n)","A",1,1,15,0.06667,1,"{261}"
2592,1,16,0,0.0031126,"\int x^{12} \left(a+b x^{13}\right)^{12} \, dx","Int[x^12*(a + b*x^13)^12,x]","\frac{\left(a+b x^{13}\right)^{13}}{169 b}","\frac{\left(a+b x^{13}\right)^{13}}{169 b}",1,"(a + b*x^13)^13/(169*b)","A",1,1,13,0.07692,1,"{261}"
2593,1,16,0,0.0028365,"\int x^{24} \left(a+b x^{25}\right)^{12} \, dx","Int[x^24*(a + b*x^25)^12,x]","\frac{\left(a+b x^{25}\right)^{13}}{325 b}","\frac{\left(a+b x^{25}\right)^{13}}{325 b}",1,"(a + b*x^25)^13/(325*b)","A",1,1,13,0.07692,1,"{261}"
2594,1,16,0,0.0028098,"\int x^{36} \left(a+b x^{37}\right)^{12} \, dx","Int[x^36*(a + b*x^37)^12,x]","\frac{\left(a+b x^{37}\right)^{13}}{481 b}","\frac{\left(a+b x^{37}\right)^{13}}{481 b}",1,"(a + b*x^37)^13/(481*b)","A",1,1,13,0.07692,1,"{261}"
2595,1,27,0,0.0073397,"\int x^{12 m} \left(a+b x^{1+12 m}\right)^{12} \, dx","Int[x^(12*m)*(a + b*x^(1 + 12*m))^12,x]","\frac{\left(a+b x^{12 m+1}\right)^{13}}{13 b (12 m+1)}","\frac{\left(a+b x^{12 m+1}\right)^{13}}{13 b (12 m+1)}",1,"(a + b*x^(1 + 12*m))^13/(13*b*(1 + 12*m))","A",1,1,19,0.05263,1,"{261}"
2596,1,27,0,0.0063404,"\int x^{12+12 (-1+m)} \left(a+b x^{1+12 m}\right)^{12} \, dx","Int[x^(12 + 12*(-1 + m))*(a + b*x^(1 + 12*m))^12,x]","\frac{\left(a+b x^{12 m+1}\right)^{13}}{13 b (12 m+1)}","\frac{\left(a+b x^{12 m+1}\right)^{13}}{13 b (12 m+1)}",1,"(a + b*x^(1 + 12*m))^13/(13*b*(1 + 12*m))","A",1,1,23,0.04348,1,"{261}"
2597,1,82,0,0.0451149,"\int \frac{x^{-1+5 n}}{a+b x^n} \, dx","Int[x^(-1 + 5*n)/(a + b*x^n),x]","-\frac{a^3 x^n}{b^4 n}+\frac{a^2 x^{2 n}}{2 b^3 n}+\frac{a^4 \log \left(a+b x^n\right)}{b^5 n}-\frac{a x^{3 n}}{3 b^2 n}+\frac{x^{4 n}}{4 b n}","-\frac{a^3 x^n}{b^4 n}+\frac{a^2 x^{2 n}}{2 b^3 n}+\frac{a^4 \log \left(a+b x^n\right)}{b^5 n}-\frac{a x^{3 n}}{3 b^2 n}+\frac{x^{4 n}}{4 b n}",1,"-((a^3*x^n)/(b^4*n)) + (a^2*x^(2*n))/(2*b^3*n) - (a*x^(3*n))/(3*b^2*n) + x^(4*n)/(4*b*n) + (a^4*Log[a + b*x^n])/(b^5*n)","A",3,2,17,0.1176,1,"{266, 43}"
2598,1,64,0,0.0337004,"\int \frac{x^{-1+4 n}}{a+b x^n} \, dx","Int[x^(-1 + 4*n)/(a + b*x^n),x]","\frac{a^2 x^n}{b^3 n}-\frac{a^3 \log \left(a+b x^n\right)}{b^4 n}-\frac{a x^{2 n}}{2 b^2 n}+\frac{x^{3 n}}{3 b n}","\frac{a^2 x^n}{b^3 n}-\frac{a^3 \log \left(a+b x^n\right)}{b^4 n}-\frac{a x^{2 n}}{2 b^2 n}+\frac{x^{3 n}}{3 b n}",1,"(a^2*x^n)/(b^3*n) - (a*x^(2*n))/(2*b^2*n) + x^(3*n)/(3*b*n) - (a^3*Log[a + b*x^n])/(b^4*n)","A",3,2,17,0.1176,1,"{266, 43}"
2599,1,46,0,0.025152,"\int \frac{x^{-1+3 n}}{a+b x^n} \, dx","Int[x^(-1 + 3*n)/(a + b*x^n),x]","\frac{a^2 \log \left(a+b x^n\right)}{b^3 n}-\frac{a x^n}{b^2 n}+\frac{x^{2 n}}{2 b n}","\frac{a^2 \log \left(a+b x^n\right)}{b^3 n}-\frac{a x^n}{b^2 n}+\frac{x^{2 n}}{2 b n}",1,"-((a*x^n)/(b^2*n)) + x^(2*n)/(2*b*n) + (a^2*Log[a + b*x^n])/(b^3*n)","A",3,2,17,0.1176,1,"{266, 43}"
2600,1,28,0,0.0172597,"\int \frac{x^{-1+2 n}}{a+b x^n} \, dx","Int[x^(-1 + 2*n)/(a + b*x^n),x]","\frac{x^n}{b n}-\frac{a \log \left(a+b x^n\right)}{b^2 n}","\frac{x^n}{b n}-\frac{a \log \left(a+b x^n\right)}{b^2 n}",1,"x^n/(b*n) - (a*Log[a + b*x^n])/(b^2*n)","A",3,2,17,0.1176,1,"{266, 43}"
2601,1,15,0,0.0043788,"\int \frac{x^{-1+n}}{a+b x^n} \, dx","Int[x^(-1 + n)/(a + b*x^n),x]","\frac{\log \left(a+b x^n\right)}{b n}","\frac{\log \left(a+b x^n\right)}{b n}",1,"Log[a + b*x^n]/(b*n)","A",1,1,15,0.06667,1,"{260}"
2602,1,23,0,0.0096308,"\int \frac{1}{x \left(a+b x^n\right)} \, dx","Int[1/(x*(a + b*x^n)),x]","\frac{\log (x)}{a}-\frac{\log \left(a+b x^n\right)}{a n}","\frac{\log (x)}{a}-\frac{\log \left(a+b x^n\right)}{a n}",1,"Log[x]/a - Log[a + b*x^n]/(a*n)","A",4,4,13,0.3077,1,"{266, 36, 29, 31}"
2603,1,38,0,0.0215037,"\int \frac{x^{-1-n}}{a+b x^n} \, dx","Int[x^(-1 - n)/(a + b*x^n),x]","\frac{b \log \left(a+b x^n\right)}{a^2 n}-\frac{b \log (x)}{a^2}-\frac{x^{-n}}{a n}","\frac{b \log \left(a+b x^n\right)}{a^2 n}-\frac{b \log (x)}{a^2}-\frac{x^{-n}}{a n}",1,"-(1/(a*n*x^n)) - (b*Log[x])/a^2 + (b*Log[a + b*x^n])/(a^2*n)","A",3,2,17,0.1176,1,"{266, 44}"
2604,1,57,0,0.0293391,"\int \frac{x^{-1-2 n}}{a+b x^n} \, dx","Int[x^(-1 - 2*n)/(a + b*x^n),x]","-\frac{b^2 \log \left(a+b x^n\right)}{a^3 n}+\frac{b^2 \log (x)}{a^3}+\frac{b x^{-n}}{a^2 n}-\frac{x^{-2 n}}{2 a n}","-\frac{b^2 \log \left(a+b x^n\right)}{a^3 n}+\frac{b^2 \log (x)}{a^3}+\frac{b x^{-n}}{a^2 n}-\frac{x^{-2 n}}{2 a n}",1,"-1/(2*a*n*x^(2*n)) + b/(a^2*n*x^n) + (b^2*Log[x])/a^3 - (b^2*Log[a + b*x^n])/(a^3*n)","A",3,2,17,0.1176,1,"{266, 44}"
2605,1,76,0,0.0360553,"\int \frac{x^{-1-3 n}}{a+b x^n} \, dx","Int[x^(-1 - 3*n)/(a + b*x^n),x]","-\frac{b^2 x^{-n}}{a^3 n}+\frac{b^3 \log \left(a+b x^n\right)}{a^4 n}-\frac{b^3 \log (x)}{a^4}+\frac{b x^{-2 n}}{2 a^2 n}-\frac{x^{-3 n}}{3 a n}","-\frac{b^2 x^{-n}}{a^3 n}+\frac{b^3 \log \left(a+b x^n\right)}{a^4 n}-\frac{b^3 \log (x)}{a^4}+\frac{b x^{-2 n}}{2 a^2 n}-\frac{x^{-3 n}}{3 a n}",1,"-1/(3*a*n*x^(3*n)) + b/(2*a^2*n*x^(2*n)) - b^2/(a^3*n*x^n) - (b^3*Log[x])/a^4 + (b^3*Log[a + b*x^n])/(a^4*n)","A",3,2,17,0.1176,1,"{266, 44}"
2606,1,82,0,0.0398073,"\int \frac{x^{4+5 (-1+n)}}{a+b x^n} \, dx","Int[x^(4 + 5*(-1 + n))/(a + b*x^n),x]","-\frac{a^3 x^n}{b^4 n}+\frac{a^2 x^{2 n}}{2 b^3 n}+\frac{a^4 \log \left(a+b x^n\right)}{b^5 n}-\frac{a x^{3 n}}{3 b^2 n}+\frac{x^{4 n}}{4 b n}","-\frac{a^3 x^n}{b^4 n}+\frac{a^2 x^{2 n}}{2 b^3 n}+\frac{a^4 \log \left(a+b x^n\right)}{b^5 n}-\frac{a x^{3 n}}{3 b^2 n}+\frac{x^{4 n}}{4 b n}",1,"-((a^3*x^n)/(b^4*n)) + (a^2*x^(2*n))/(2*b^3*n) - (a*x^(3*n))/(3*b^2*n) + x^(4*n)/(4*b*n) + (a^4*Log[a + b*x^n])/(b^5*n)","A",3,2,19,0.1053,1,"{266, 43}"
2607,1,64,0,0.0310129,"\int \frac{x^{3+4 (-1+n)}}{a+b x^n} \, dx","Int[x^(3 + 4*(-1 + n))/(a + b*x^n),x]","\frac{a^2 x^n}{b^3 n}-\frac{a^3 \log \left(a+b x^n\right)}{b^4 n}-\frac{a x^{2 n}}{2 b^2 n}+\frac{x^{3 n}}{3 b n}","\frac{a^2 x^n}{b^3 n}-\frac{a^3 \log \left(a+b x^n\right)}{b^4 n}-\frac{a x^{2 n}}{2 b^2 n}+\frac{x^{3 n}}{3 b n}",1,"(a^2*x^n)/(b^3*n) - (a*x^(2*n))/(2*b^2*n) + x^(3*n)/(3*b*n) - (a^3*Log[a + b*x^n])/(b^4*n)","A",3,2,19,0.1053,1,"{266, 43}"
2608,1,46,0,0.0242214,"\int \frac{x^{2+3 (-1+n)}}{a+b x^n} \, dx","Int[x^(2 + 3*(-1 + n))/(a + b*x^n),x]","\frac{a^2 \log \left(a+b x^n\right)}{b^3 n}-\frac{a x^n}{b^2 n}+\frac{x^{2 n}}{2 b n}","\frac{a^2 \log \left(a+b x^n\right)}{b^3 n}-\frac{a x^n}{b^2 n}+\frac{x^{2 n}}{2 b n}",1,"-((a*x^n)/(b^2*n)) + x^(2*n)/(2*b*n) + (a^2*Log[a + b*x^n])/(b^3*n)","A",3,2,19,0.1053,1,"{266, 43}"
2609,1,28,0,0.0168601,"\int \frac{x^{1+2 (-1+n)}}{a+b x^n} \, dx","Int[x^(1 + 2*(-1 + n))/(a + b*x^n),x]","\frac{x^n}{b n}-\frac{a \log \left(a+b x^n\right)}{b^2 n}","\frac{x^n}{b n}-\frac{a \log \left(a+b x^n\right)}{b^2 n}",1,"x^n/(b*n) - (a*Log[a + b*x^n])/(b^2*n)","A",3,2,19,0.1053,1,"{266, 43}"
2610,1,15,0,0.0050448,"\int \frac{x^{-1+n}}{a+b x^n} \, dx","Int[x^(-1 + n)/(a + b*x^n),x]","\frac{\log \left(a+b x^n\right)}{b n}","\frac{\log \left(a+b x^n\right)}{b n}",1,"Log[a + b*x^n]/(b*n)","A",1,1,15,0.06667,1,"{260}"
2611,1,23,0,0.0097021,"\int \frac{1}{x \left(a+b x^n\right)} \, dx","Int[1/(x*(a + b*x^n)),x]","\frac{\log (x)}{a}-\frac{\log \left(a+b x^n\right)}{a n}","\frac{\log (x)}{a}-\frac{\log \left(a+b x^n\right)}{a n}",1,"Log[x]/a - Log[a + b*x^n]/(a*n)","A",4,4,13,0.3077,1,"{266, 36, 29, 31}"
2612,1,38,0,0.0204866,"\int \frac{x^{-1-n}}{a+b x^n} \, dx","Int[x^(-1 - n)/(a + b*x^n),x]","\frac{b \log \left(a+b x^n\right)}{a^2 n}-\frac{b \log (x)}{a^2}-\frac{x^{-n}}{a n}","\frac{b \log \left(a+b x^n\right)}{a^2 n}-\frac{b \log (x)}{a^2}-\frac{x^{-n}}{a n}",1,"-(1/(a*n*x^n)) - (b*Log[x])/a^2 + (b*Log[a + b*x^n])/(a^2*n)","A",3,2,17,0.1176,1,"{266, 44}"
2613,1,57,0,0.0280814,"\int \frac{x^{-3-2 (-1+n)}}{a+b x^n} \, dx","Int[x^(-3 - 2*(-1 + n))/(a + b*x^n),x]","-\frac{b^2 \log \left(a+b x^n\right)}{a^3 n}+\frac{b^2 \log (x)}{a^3}+\frac{b x^{-n}}{a^2 n}-\frac{x^{-2 n}}{2 a n}","-\frac{b^2 \log \left(a+b x^n\right)}{a^3 n}+\frac{b^2 \log (x)}{a^3}+\frac{b x^{-n}}{a^2 n}-\frac{x^{-2 n}}{2 a n}",1,"-1/(2*a*n*x^(2*n)) + b/(a^2*n*x^n) + (b^2*Log[x])/a^3 - (b^2*Log[a + b*x^n])/(a^3*n)","A",3,2,19,0.1053,1,"{266, 44}"
2614,1,76,0,0.0336892,"\int \frac{x^{-4-3 (-1+n)}}{a+b x^n} \, dx","Int[x^(-4 - 3*(-1 + n))/(a + b*x^n),x]","-\frac{b^2 x^{-n}}{a^3 n}+\frac{b^3 \log \left(a+b x^n\right)}{a^4 n}-\frac{b^3 \log (x)}{a^4}+\frac{b x^{-2 n}}{2 a^2 n}-\frac{x^{-3 n}}{3 a n}","-\frac{b^2 x^{-n}}{a^3 n}+\frac{b^3 \log \left(a+b x^n\right)}{a^4 n}-\frac{b^3 \log (x)}{a^4}+\frac{b x^{-2 n}}{2 a^2 n}-\frac{x^{-3 n}}{3 a n}",1,"-1/(3*a*n*x^(3*n)) + b/(2*a^2*n*x^(2*n)) - b^2/(a^3*n*x^n) - (b^3*Log[x])/a^4 + (b^3*Log[a + b*x^n])/(a^4*n)","A",3,2,19,0.1053,1,"{266, 44}"
2615,1,71,0,0.0342742,"\int \frac{x^{-1+5 n}}{2+b x^n} \, dx","Int[x^(-1 + 5*n)/(2 + b*x^n),x]","-\frac{8 x^n}{b^4 n}+\frac{2 x^{2 n}}{b^3 n}-\frac{2 x^{3 n}}{3 b^2 n}+\frac{16 \log \left(b x^n+2\right)}{b^5 n}+\frac{x^{4 n}}{4 b n}","-\frac{8 x^n}{b^4 n}+\frac{2 x^{2 n}}{b^3 n}-\frac{2 x^{3 n}}{3 b^2 n}+\frac{16 \log \left(b x^n+2\right)}{b^5 n}+\frac{x^{4 n}}{4 b n}",1,"(-8*x^n)/(b^4*n) + (2*x^(2*n))/(b^3*n) - (2*x^(3*n))/(3*b^2*n) + x^(4*n)/(4*b*n) + (16*Log[2 + b*x^n])/(b^5*n)","A",3,2,17,0.1176,1,"{266, 43}"
2616,1,56,0,0.0264837,"\int \frac{x^{-1+4 n}}{2+b x^n} \, dx","Int[x^(-1 + 4*n)/(2 + b*x^n),x]","\frac{4 x^n}{b^3 n}-\frac{x^{2 n}}{b^2 n}-\frac{8 \log \left(b x^n+2\right)}{b^4 n}+\frac{x^{3 n}}{3 b n}","\frac{4 x^n}{b^3 n}-\frac{x^{2 n}}{b^2 n}-\frac{8 \log \left(b x^n+2\right)}{b^4 n}+\frac{x^{3 n}}{3 b n}",1,"(4*x^n)/(b^3*n) - x^(2*n)/(b^2*n) + x^(3*n)/(3*b*n) - (8*Log[2 + b*x^n])/(b^4*n)","A",3,2,17,0.1176,1,"{266, 43}"
2617,1,43,0,0.0214277,"\int \frac{x^{-1+3 n}}{2+b x^n} \, dx","Int[x^(-1 + 3*n)/(2 + b*x^n),x]","-\frac{2 x^n}{b^2 n}+\frac{4 \log \left(b x^n+2\right)}{b^3 n}+\frac{x^{2 n}}{2 b n}","-\frac{2 x^n}{b^2 n}+\frac{4 \log \left(b x^n+2\right)}{b^3 n}+\frac{x^{2 n}}{2 b n}",1,"(-2*x^n)/(b^2*n) + x^(2*n)/(2*b*n) + (4*Log[2 + b*x^n])/(b^3*n)","A",3,2,17,0.1176,1,"{266, 43}"
2618,1,27,0,0.0155853,"\int \frac{x^{-1+2 n}}{2+b x^n} \, dx","Int[x^(-1 + 2*n)/(2 + b*x^n),x]","\frac{x^n}{b n}-\frac{2 \log \left(b x^n+2\right)}{b^2 n}","\frac{x^n}{b n}-\frac{2 \log \left(b x^n+2\right)}{b^2 n}",1,"x^n/(b*n) - (2*Log[2 + b*x^n])/(b^2*n)","A",3,2,17,0.1176,1,"{266, 43}"
2619,1,15,0,0.0049866,"\int \frac{x^{-1+n}}{2+b x^n} \, dx","Int[x^(-1 + n)/(2 + b*x^n),x]","\frac{\log \left(b x^n+2\right)}{b n}","\frac{\log \left(b x^n+2\right)}{b n}",1,"Log[2 + b*x^n]/(b*n)","A",1,1,15,0.06667,1,"{260}"
2620,1,22,0,0.00948,"\int \frac{1}{x \left(2+b x^n\right)} \, dx","Int[1/(x*(2 + b*x^n)),x]","\frac{\log (x)}{2}-\frac{\log \left(b x^n+2\right)}{2 n}","\frac{\log (x)}{2}-\frac{\log \left(b x^n+2\right)}{2 n}",1,"Log[x]/2 - Log[2 + b*x^n]/(2*n)","A",4,4,13,0.3077,1,"{266, 36, 29, 31}"
2621,1,36,0,0.0190837,"\int \frac{x^{-1-n}}{2+b x^n} \, dx","Int[x^(-1 - n)/(2 + b*x^n),x]","\frac{b \log \left(b x^n+2\right)}{4 n}-\frac{1}{4} b \log (x)-\frac{x^{-n}}{2 n}","\frac{b \log \left(b x^n+2\right)}{4 n}-\frac{1}{4} b \log (x)-\frac{x^{-n}}{2 n}",1,"-1/(2*n*x^n) - (b*Log[x])/4 + (b*Log[2 + b*x^n])/(4*n)","A",3,2,17,0.1176,1,"{266, 44}"
2622,1,53,0,0.0233912,"\int \frac{x^{-1-2 n}}{2+b x^n} \, dx","Int[x^(-1 - 2*n)/(2 + b*x^n),x]","-\frac{b^2 \log \left(b x^n+2\right)}{8 n}+\frac{1}{8} b^2 \log (x)+\frac{b x^{-n}}{4 n}-\frac{x^{-2 n}}{4 n}","-\frac{b^2 \log \left(b x^n+2\right)}{8 n}+\frac{1}{8} b^2 \log (x)+\frac{b x^{-n}}{4 n}-\frac{x^{-2 n}}{4 n}",1,"-1/(4*n*x^(2*n)) + b/(4*n*x^n) + (b^2*Log[x])/8 - (b^2*Log[2 + b*x^n])/(8*n)","A",3,2,17,0.1176,1,"{266, 44}"
2623,1,68,0,0.0297424,"\int \frac{x^{-1-3 n}}{2+b x^n} \, dx","Int[x^(-1 - 3*n)/(2 + b*x^n),x]","-\frac{b^2 x^{-n}}{8 n}+\frac{b^3 \log \left(b x^n+2\right)}{16 n}-\frac{1}{16} b^3 \log (x)+\frac{b x^{-2 n}}{8 n}-\frac{x^{-3 n}}{6 n}","-\frac{b^2 x^{-n}}{8 n}+\frac{b^3 \log \left(b x^n+2\right)}{16 n}-\frac{1}{16} b^3 \log (x)+\frac{b x^{-2 n}}{8 n}-\frac{x^{-3 n}}{6 n}",1,"-1/(6*n*x^(3*n)) + b/(8*n*x^(2*n)) - b^2/(8*n*x^n) - (b^3*Log[x])/16 + (b^3*Log[2 + b*x^n])/(16*n)","A",3,2,17,0.1176,1,"{266, 44}"
2624,1,66,0,0.0406642,"\int \frac{x^{-1+4 n}}{\left(a+b x^n\right)^2} \, dx","Int[x^(-1 + 4*n)/(a + b*x^n)^2,x]","\frac{a^3}{b^4 n \left(a+b x^n\right)}+\frac{3 a^2 \log \left(a+b x^n\right)}{b^4 n}-\frac{2 a x^n}{b^3 n}+\frac{x^{2 n}}{2 b^2 n}","\frac{a^3}{b^4 n \left(a+b x^n\right)}+\frac{3 a^2 \log \left(a+b x^n\right)}{b^4 n}-\frac{2 a x^n}{b^3 n}+\frac{x^{2 n}}{2 b^2 n}",1,"(-2*a*x^n)/(b^3*n) + x^(2*n)/(2*b^2*n) + a^3/(b^4*n*(a + b*x^n)) + (3*a^2*Log[a + b*x^n])/(b^4*n)","A",3,2,17,0.1176,1,"{266, 43}"
2625,1,48,0,0.0315231,"\int \frac{x^{-1+3 n}}{\left(a+b x^n\right)^2} \, dx","Int[x^(-1 + 3*n)/(a + b*x^n)^2,x]","-\frac{a^2}{b^3 n \left(a+b x^n\right)}-\frac{2 a \log \left(a+b x^n\right)}{b^3 n}+\frac{x^n}{b^2 n}","-\frac{a^2}{b^3 n \left(a+b x^n\right)}-\frac{2 a \log \left(a+b x^n\right)}{b^3 n}+\frac{x^n}{b^2 n}",1,"x^n/(b^2*n) - a^2/(b^3*n*(a + b*x^n)) - (2*a*Log[a + b*x^n])/(b^3*n)","A",3,2,17,0.1176,1,"{266, 43}"
2626,1,33,0,0.0230451,"\int \frac{x^{-1+2 n}}{\left(a+b x^n\right)^2} \, dx","Int[x^(-1 + 2*n)/(a + b*x^n)^2,x]","\frac{a}{b^2 n \left(a+b x^n\right)}+\frac{\log \left(a+b x^n\right)}{b^2 n}","\frac{a}{b^2 n \left(a+b x^n\right)}+\frac{\log \left(a+b x^n\right)}{b^2 n}",1,"a/(b^2*n*(a + b*x^n)) + Log[a + b*x^n]/(b^2*n)","A",3,2,17,0.1176,1,"{266, 43}"
2627,1,17,0,0.0045928,"\int \frac{x^{-1+n}}{\left(a+b x^n\right)^2} \, dx","Int[x^(-1 + n)/(a + b*x^n)^2,x]","-\frac{1}{b n \left(a+b x^n\right)}","-\frac{1}{b n \left(a+b x^n\right)}",1,"-(1/(b*n*(a + b*x^n)))","A",1,1,15,0.06667,1,"{261}"
2628,1,39,0,0.0236343,"\int \frac{1}{x \left(a+b x^n\right)^2} \, dx","Int[1/(x*(a + b*x^n)^2),x]","-\frac{\log \left(a+b x^n\right)}{a^2 n}+\frac{\log (x)}{a^2}+\frac{1}{a n \left(a+b x^n\right)}","-\frac{\log \left(a+b x^n\right)}{a^2 n}+\frac{\log (x)}{a^2}+\frac{1}{a n \left(a+b x^n\right)}",1,"1/(a*n*(a + b*x^n)) + Log[x]/a^2 - Log[a + b*x^n]/(a^2*n)","A",3,2,13,0.1538,1,"{266, 44}"
2629,1,57,0,0.0330685,"\int \frac{x^{-1-n}}{\left(a+b x^n\right)^2} \, dx","Int[x^(-1 - n)/(a + b*x^n)^2,x]","-\frac{b}{a^2 n \left(a+b x^n\right)}+\frac{2 b \log \left(a+b x^n\right)}{a^3 n}-\frac{2 b \log (x)}{a^3}-\frac{x^{-n}}{a^2 n}","-\frac{b}{a^2 n \left(a+b x^n\right)}+\frac{2 b \log \left(a+b x^n\right)}{a^3 n}-\frac{2 b \log (x)}{a^3}-\frac{x^{-n}}{a^2 n}",1,"-(1/(a^2*n*x^n)) - b/(a^2*n*(a + b*x^n)) - (2*b*Log[x])/a^3 + (2*b*Log[a + b*x^n])/(a^3*n)","A",3,2,17,0.1176,1,"{266, 44}"
2630,1,78,0,0.0443638,"\int \frac{x^{-1-2 n}}{\left(a+b x^n\right)^2} \, dx","Int[x^(-1 - 2*n)/(a + b*x^n)^2,x]","\frac{b^2}{a^3 n \left(a+b x^n\right)}-\frac{3 b^2 \log \left(a+b x^n\right)}{a^4 n}+\frac{3 b^2 \log (x)}{a^4}+\frac{2 b x^{-n}}{a^3 n}-\frac{x^{-2 n}}{2 a^2 n}","\frac{b^2}{a^3 n \left(a+b x^n\right)}-\frac{3 b^2 \log \left(a+b x^n\right)}{a^4 n}+\frac{3 b^2 \log (x)}{a^4}+\frac{2 b x^{-n}}{a^3 n}-\frac{x^{-2 n}}{2 a^2 n}",1,"-1/(2*a^2*n*x^(2*n)) + (2*b)/(a^3*n*x^n) + b^2/(a^3*n*(a + b*x^n)) + (3*b^2*Log[x])/a^4 - (3*b^2*Log[a + b*x^n])/(a^4*n)","A",3,2,17,0.1176,1,"{266, 44}"
2631,1,94,0,0.0560242,"\int \frac{x^{-1-3 n}}{\left(a+b x^n\right)^2} \, dx","Int[x^(-1 - 3*n)/(a + b*x^n)^2,x]","-\frac{3 b^2 x^{-n}}{a^4 n}-\frac{b^3}{a^4 n \left(a+b x^n\right)}+\frac{4 b^3 \log \left(a+b x^n\right)}{a^5 n}-\frac{4 b^3 \log (x)}{a^5}+\frac{b x^{-2 n}}{a^3 n}-\frac{x^{-3 n}}{3 a^2 n}","-\frac{3 b^2 x^{-n}}{a^4 n}-\frac{b^3}{a^4 n \left(a+b x^n\right)}+\frac{4 b^3 \log \left(a+b x^n\right)}{a^5 n}-\frac{4 b^3 \log (x)}{a^5}+\frac{b x^{-2 n}}{a^3 n}-\frac{x^{-3 n}}{3 a^2 n}",1,"-1/(3*a^2*n*x^(3*n)) + b/(a^3*n*x^(2*n)) - (3*b^2)/(a^4*n*x^n) - b^3/(a^4*n*(a + b*x^n)) - (4*b^3*Log[x])/a^5 + (4*b^3*Log[a + b*x^n])/(a^5*n)","A",3,2,17,0.1176,1,"{266, 44}"
2632,1,70,0,0.043986,"\int \frac{x^{-1+4 n}}{\left(a+b x^n\right)^3} \, dx","Int[x^(-1 + 4*n)/(a + b*x^n)^3,x]","-\frac{3 a^2}{b^4 n \left(a+b x^n\right)}+\frac{a^3}{2 b^4 n \left(a+b x^n\right)^2}-\frac{3 a \log \left(a+b x^n\right)}{b^4 n}+\frac{x^n}{b^3 n}","-\frac{3 a^2}{b^4 n \left(a+b x^n\right)}+\frac{a^3}{2 b^4 n \left(a+b x^n\right)^2}-\frac{3 a \log \left(a+b x^n\right)}{b^4 n}+\frac{x^n}{b^3 n}",1,"x^n/(b^3*n) + a^3/(2*b^4*n*(a + b*x^n)^2) - (3*a^2)/(b^4*n*(a + b*x^n)) - (3*a*Log[a + b*x^n])/(b^4*n)","A",3,2,17,0.1176,1,"{266, 43}"
2633,1,56,0,0.0330859,"\int \frac{x^{-1+3 n}}{\left(a+b x^n\right)^3} \, dx","Int[x^(-1 + 3*n)/(a + b*x^n)^3,x]","-\frac{a^2}{2 b^3 n \left(a+b x^n\right)^2}+\frac{2 a}{b^3 n \left(a+b x^n\right)}+\frac{\log \left(a+b x^n\right)}{b^3 n}","-\frac{a^2}{2 b^3 n \left(a+b x^n\right)^2}+\frac{2 a}{b^3 n \left(a+b x^n\right)}+\frac{\log \left(a+b x^n\right)}{b^3 n}",1,"-a^2/(2*b^3*n*(a + b*x^n)^2) + (2*a)/(b^3*n*(a + b*x^n)) + Log[a + b*x^n]/(b^3*n)","A",3,2,17,0.1176,1,"{266, 43}"
2634,1,24,0,0.0051769,"\int \frac{x^{-1+2 n}}{\left(a+b x^n\right)^3} \, dx","Int[x^(-1 + 2*n)/(a + b*x^n)^3,x]","\frac{x^{2 n}}{2 a n \left(a+b x^n\right)^2}","\frac{x^{2 n}}{2 a n \left(a+b x^n\right)^2}",1,"x^(2*n)/(2*a*n*(a + b*x^n)^2)","A",1,1,17,0.05882,1,"{264}"
2635,1,19,0,0.0045467,"\int \frac{x^{-1+n}}{\left(a+b x^n\right)^3} \, dx","Int[x^(-1 + n)/(a + b*x^n)^3,x]","-\frac{1}{2 b n \left(a+b x^n\right)^2}","-\frac{1}{2 b n \left(a+b x^n\right)^2}",1,"-1/(2*b*n*(a + b*x^n)^2)","A",1,1,15,0.06667,1,"{261}"
2636,1,58,0,0.0309098,"\int \frac{1}{x \left(a+b x^n\right)^3} \, dx","Int[1/(x*(a + b*x^n)^3),x]","\frac{1}{a^2 n \left(a+b x^n\right)}-\frac{\log \left(a+b x^n\right)}{a^3 n}+\frac{\log (x)}{a^3}+\frac{1}{2 a n \left(a+b x^n\right)^2}","\frac{1}{a^2 n \left(a+b x^n\right)}-\frac{\log \left(a+b x^n\right)}{a^3 n}+\frac{\log (x)}{a^3}+\frac{1}{2 a n \left(a+b x^n\right)^2}",1,"1/(2*a*n*(a + b*x^n)^2) + 1/(a^2*n*(a + b*x^n)) + Log[x]/a^3 - Log[a + b*x^n]/(a^3*n)","A",3,2,13,0.1538,1,"{266, 44}"
2637,1,77,0,0.0473548,"\int \frac{x^{-1-n}}{\left(a+b x^n\right)^3} \, dx","Int[x^(-1 - n)/(a + b*x^n)^3,x]","-\frac{2 b}{a^3 n \left(a+b x^n\right)}-\frac{b}{2 a^2 n \left(a+b x^n\right)^2}+\frac{3 b \log \left(a+b x^n\right)}{a^4 n}-\frac{3 b \log (x)}{a^4}-\frac{x^{-n}}{a^3 n}","-\frac{2 b}{a^3 n \left(a+b x^n\right)}-\frac{b}{2 a^2 n \left(a+b x^n\right)^2}+\frac{3 b \log \left(a+b x^n\right)}{a^4 n}-\frac{3 b \log (x)}{a^4}-\frac{x^{-n}}{a^3 n}",1,"-(1/(a^3*n*x^n)) - b/(2*a^2*n*(a + b*x^n)^2) - (2*b)/(a^3*n*(a + b*x^n)) - (3*b*Log[x])/a^4 + (3*b*Log[a + b*x^n])/(a^4*n)","A",3,2,17,0.1176,1,"{266, 44}"
2638,1,101,0,0.0586034,"\int \frac{x^{-1-2 n}}{\left(a+b x^n\right)^3} \, dx","Int[x^(-1 - 2*n)/(a + b*x^n)^3,x]","\frac{3 b^2}{a^4 n \left(a+b x^n\right)}+\frac{b^2}{2 a^3 n \left(a+b x^n\right)^2}-\frac{6 b^2 \log \left(a+b x^n\right)}{a^5 n}+\frac{6 b^2 \log (x)}{a^5}+\frac{3 b x^{-n}}{a^4 n}-\frac{x^{-2 n}}{2 a^3 n}","\frac{3 b^2}{a^4 n \left(a+b x^n\right)}+\frac{b^2}{2 a^3 n \left(a+b x^n\right)^2}-\frac{6 b^2 \log \left(a+b x^n\right)}{a^5 n}+\frac{6 b^2 \log (x)}{a^5}+\frac{3 b x^{-n}}{a^4 n}-\frac{x^{-2 n}}{2 a^3 n}",1,"-1/(2*a^3*n*x^(2*n)) + (3*b)/(a^4*n*x^n) + b^2/(2*a^3*n*(a + b*x^n)^2) + (3*b^2)/(a^4*n*(a + b*x^n)) + (6*b^2*Log[x])/a^5 - (6*b^2*Log[a + b*x^n])/(a^5*n)","A",3,2,17,0.1176,1,"{266, 44}"
2639,1,50,0,0.0249862,"\int \frac{x^{-1-\frac{n}{2}}}{a+b x^n} \, dx","Int[x^(-1 - n/2)/(a + b*x^n),x]","\frac{2 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a} x^{-n/2}}{\sqrt{b}}\right)}{a^{3/2} n}-\frac{2 x^{-n/2}}{a n}","\frac{2 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a} x^{-n/2}}{\sqrt{b}}\right)}{a^{3/2} n}-\frac{2 x^{-n/2}}{a n}",1,"-2/(a*n*x^(n/2)) + (2*Sqrt[b]*ArcTan[Sqrt[a]/(Sqrt[b]*x^(n/2))])/(a^(3/2)*n)","A",4,4,19,0.2105,1,"{345, 193, 321, 205}"
2640,1,160,0,0.1143047,"\int \frac{x^{-1-\frac{2 n}{3}}}{a+b x^n} \, dx","Int[x^(-1 - (2*n)/3)/(a + b*x^n),x]","-\frac{b^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x^{n/3}\right)}{a^{5/3} n}+\frac{b^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x^{n/3}+b^{2/3} x^{2 n/3}\right)}{2 a^{5/3} n}+\frac{\sqrt{3} b^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x^{n/3}}{\sqrt{3} \sqrt[3]{a}}\right)}{a^{5/3} n}-\frac{3 x^{-2 n/3}}{2 a n}","-\frac{b^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x^{n/3}\right)}{a^{5/3} n}+\frac{b^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x^{n/3}+b^{2/3} x^{2 n/3}\right)}{2 a^{5/3} n}+\frac{\sqrt{3} b^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x^{n/3}}{\sqrt{3} \sqrt[3]{a}}\right)}{a^{5/3} n}-\frac{3 x^{-2 n/3}}{2 a n}",1,"-3/(2*a*n*x^((2*n)/3)) + (Sqrt[3]*b^(2/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x^(n/3))/(Sqrt[3]*a^(1/3))])/(a^(5/3)*n) - (b^(2/3)*Log[a^(1/3) + b^(1/3)*x^(n/3)])/(a^(5/3)*n) + (b^(2/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x^(n/3) + b^(2/3)*x^((2*n)/3)])/(2*a^(5/3)*n)","A",8,8,19,0.4211,1,"{362, 345, 200, 31, 634, 617, 204, 628}"
2641,1,236,0,0.1997405,"\int \frac{x^{-1-\frac{3 n}{4}}}{a+b x^n} \, dx","Int[x^(-1 - (3*n)/4)/(a + b*x^n),x]","\frac{b^{3/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x^{n/4}+\sqrt{a}+\sqrt{b} x^{n/2}\right)}{\sqrt{2} a^{7/4} n}-\frac{b^{3/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x^{n/4}+\sqrt{a}+\sqrt{b} x^{n/2}\right)}{\sqrt{2} a^{7/4} n}+\frac{\sqrt{2} b^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x^{n/4}}{\sqrt[4]{a}}\right)}{a^{7/4} n}-\frac{\sqrt{2} b^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x^{n/4}}{\sqrt[4]{a}}+1\right)}{a^{7/4} n}-\frac{4 x^{-3 n/4}}{3 a n}","\frac{b^{3/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x^{n/4}+\sqrt{a}+\sqrt{b} x^{n/2}\right)}{\sqrt{2} a^{7/4} n}-\frac{b^{3/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x^{n/4}+\sqrt{a}+\sqrt{b} x^{n/2}\right)}{\sqrt{2} a^{7/4} n}+\frac{\sqrt{2} b^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x^{n/4}}{\sqrt[4]{a}}\right)}{a^{7/4} n}-\frac{\sqrt{2} b^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x^{n/4}}{\sqrt[4]{a}}+1\right)}{a^{7/4} n}-\frac{4 x^{-3 n/4}}{3 a n}",1,"-4/(3*a*n*x^((3*n)/4)) + (Sqrt[2]*b^(3/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*x^(n/4))/a^(1/4)])/(a^(7/4)*n) - (Sqrt[2]*b^(3/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*x^(n/4))/a^(1/4)])/(a^(7/4)*n) + (b^(3/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x^(n/4) + Sqrt[b]*x^(n/2)])/(Sqrt[2]*a^(7/4)*n) - (b^(3/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x^(n/4) + Sqrt[b]*x^(n/2)])/(Sqrt[2]*a^(7/4)*n)","A",11,8,19,0.4211,1,"{362, 345, 211, 1165, 628, 1162, 617, 204}"
2642,1,38,0,0.0206152,"\int \frac{x^{-1-n}}{a+b x^n} \, dx","Int[x^(-1 - n)/(a + b*x^n),x]","\frac{b \log \left(a+b x^n\right)}{a^2 n}-\frac{b \log (x)}{a^2}-\frac{x^{-n}}{a n}","\frac{b \log \left(a+b x^n\right)}{a^2 n}-\frac{b \log (x)}{a^2}-\frac{x^{-n}}{a n}",1,"-(1/(a*n*x^n)) - (b*Log[x])/a^2 + (b*Log[a + b*x^n])/(a^2*n)","A",3,2,17,0.1176,1,"{266, 44}"
2643,1,50,0,0.0226298,"\int \frac{x^{-1-\frac{n}{2}}}{a+b x^n} \, dx","Int[x^(-1 - n/2)/(a + b*x^n),x]","\frac{2 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a} x^{-n/2}}{\sqrt{b}}\right)}{a^{3/2} n}-\frac{2 x^{-n/2}}{a n}","\frac{2 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a} x^{-n/2}}{\sqrt{b}}\right)}{a^{3/2} n}-\frac{2 x^{-n/2}}{a n}",1,"-2/(a*n*x^(n/2)) + (2*Sqrt[b]*ArcTan[Sqrt[a]/(Sqrt[b]*x^(n/2))])/(a^(3/2)*n)","A",4,4,19,0.2105,1,"{345, 193, 321, 205}"
2644,1,158,0,0.1081812,"\int \frac{x^{-1-\frac{n}{3}}}{a+b x^n} \, dx","Int[x^(-1 - n/3)/(a + b*x^n),x]","-\frac{\sqrt[3]{b} \log \left(a^{2/3} x^{-2 n/3}-\sqrt[3]{a} \sqrt[3]{b} x^{-n/3}+b^{2/3}\right)}{2 a^{4/3} n}+\frac{\sqrt[3]{b} \log \left(\sqrt[3]{a} x^{-n/3}+\sqrt[3]{b}\right)}{a^{4/3} n}-\frac{\sqrt{3} \sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a} x^{-n/3}}{\sqrt{3} \sqrt[3]{b}}\right)}{a^{4/3} n}-\frac{3 x^{-n/3}}{a n}","-\frac{\sqrt[3]{b} \log \left(a^{2/3} x^{-2 n/3}-\sqrt[3]{a} \sqrt[3]{b} x^{-n/3}+b^{2/3}\right)}{2 a^{4/3} n}+\frac{\sqrt[3]{b} \log \left(\sqrt[3]{a} x^{-n/3}+\sqrt[3]{b}\right)}{a^{4/3} n}-\frac{\sqrt{3} \sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a} x^{-n/3}}{\sqrt{3} \sqrt[3]{b}}\right)}{a^{4/3} n}-\frac{3 x^{-n/3}}{a n}",1,"-3/(a*n*x^(n/3)) - (Sqrt[3]*b^(1/3)*ArcTan[(b^(1/3) - (2*a^(1/3))/x^(n/3))/(Sqrt[3]*b^(1/3))])/(a^(4/3)*n) + (b^(1/3)*Log[b^(1/3) + a^(1/3)/x^(n/3)])/(a^(4/3)*n) - (b^(1/3)*Log[b^(2/3) + a^(2/3)/x^((2*n)/3) - (a^(1/3)*b^(1/3))/x^(n/3)])/(2*a^(4/3)*n)","A",9,9,19,0.4737,1,"{345, 193, 321, 200, 31, 634, 617, 204, 628}"
2645,1,234,0,0.184002,"\int \frac{x^{-1-\frac{n}{4}}}{a+b x^n} \, dx","Int[x^(-1 - n/4)/(a + b*x^n),x]","-\frac{\sqrt[4]{b} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x^{-n/4}+\sqrt{a} x^{-n/2}+\sqrt{b}\right)}{\sqrt{2} a^{5/4} n}+\frac{\sqrt[4]{b} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x^{-n/4}+\sqrt{a} x^{-n/2}+\sqrt{b}\right)}{\sqrt{2} a^{5/4} n}-\frac{\sqrt{2} \sqrt[4]{b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a} x^{-n/4}}{\sqrt[4]{b}}\right)}{a^{5/4} n}+\frac{\sqrt{2} \sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} x^{-n/4}}{\sqrt[4]{b}}+1\right)}{a^{5/4} n}-\frac{4 x^{-n/4}}{a n}","-\frac{\sqrt[4]{b} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x^{-n/4}+\sqrt{a} x^{-n/2}+\sqrt{b}\right)}{\sqrt{2} a^{5/4} n}+\frac{\sqrt[4]{b} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x^{-n/4}+\sqrt{a} x^{-n/2}+\sqrt{b}\right)}{\sqrt{2} a^{5/4} n}-\frac{\sqrt{2} \sqrt[4]{b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a} x^{-n/4}}{\sqrt[4]{b}}\right)}{a^{5/4} n}+\frac{\sqrt{2} \sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} x^{-n/4}}{\sqrt[4]{b}}+1\right)}{a^{5/4} n}-\frac{4 x^{-n/4}}{a n}",1,"-4/(a*n*x^(n/4)) - (Sqrt[2]*b^(1/4)*ArcTan[1 - (Sqrt[2]*a^(1/4))/(b^(1/4)*x^(n/4))])/(a^(5/4)*n) + (Sqrt[2]*b^(1/4)*ArcTan[1 + (Sqrt[2]*a^(1/4))/(b^(1/4)*x^(n/4))])/(a^(5/4)*n) - (b^(1/4)*Log[Sqrt[b] + Sqrt[a]/x^(n/2) - (Sqrt[2]*a^(1/4)*b^(1/4))/x^(n/4)])/(Sqrt[2]*a^(5/4)*n) + (b^(1/4)*Log[Sqrt[b] + Sqrt[a]/x^(n/2) + (Sqrt[2]*a^(1/4)*b^(1/4))/x^(n/4)])/(Sqrt[2]*a^(5/4)*n)","A",12,9,19,0.4737,1,"{345, 193, 321, 211, 1165, 628, 1162, 617, 204}"
2646,1,68,0,0.0360525,"\int \frac{x^{-1-\frac{3 n}{2}}}{a+b x^n} \, dx","Int[x^(-1 - (3*n)/2)/(a + b*x^n),x]","-\frac{2 b^{3/2} \tan ^{-1}\left(\frac{\sqrt{a} x^{-n/2}}{\sqrt{b}}\right)}{a^{5/2} n}+\frac{2 b x^{-n/2}}{a^2 n}-\frac{2 x^{-3 n/2}}{3 a n}","-\frac{2 b^{3/2} \tan ^{-1}\left(\frac{\sqrt{a} x^{-n/2}}{\sqrt{b}}\right)}{a^{5/2} n}+\frac{2 b x^{-n/2}}{a^2 n}-\frac{2 x^{-3 n/2}}{3 a n}",1,"-2/(3*a*n*x^((3*n)/2)) + (2*b)/(a^2*n*x^(n/2)) - (2*b^(3/2)*ArcTan[Sqrt[a]/(Sqrt[b]*x^(n/2))])/(a^(5/2)*n)","A",5,5,19,0.2632,1,"{362, 345, 193, 321, 205}"
2647,1,176,0,0.1117566,"\int \frac{x^{-1-\frac{4 n}{3}}}{a+b x^n} \, dx","Int[x^(-1 - (4*n)/3)/(a + b*x^n),x]","-\frac{b^{4/3} \log \left(\sqrt[3]{a} x^{-n/3}+\sqrt[3]{b}\right)}{a^{7/3} n}+\frac{b^{4/3} \log \left(a^{2/3} x^{-2 n/3}-\sqrt[3]{a} \sqrt[3]{b} x^{-n/3}+b^{2/3}\right)}{2 a^{7/3} n}+\frac{\sqrt{3} b^{4/3} \tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a} x^{-n/3}}{\sqrt{3} \sqrt[3]{b}}\right)}{a^{7/3} n}+\frac{3 b x^{-n/3}}{a^2 n}-\frac{3 x^{-4 n/3}}{4 a n}","-\frac{b^{4/3} \log \left(\sqrt[3]{a} x^{-n/3}+\sqrt[3]{b}\right)}{a^{7/3} n}+\frac{b^{4/3} \log \left(a^{2/3} x^{-2 n/3}-\sqrt[3]{a} \sqrt[3]{b} x^{-n/3}+b^{2/3}\right)}{2 a^{7/3} n}+\frac{\sqrt{3} b^{4/3} \tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a} x^{-n/3}}{\sqrt{3} \sqrt[3]{b}}\right)}{a^{7/3} n}+\frac{3 b x^{-n/3}}{a^2 n}-\frac{3 x^{-4 n/3}}{4 a n}",1,"-3/(4*a*n*x^((4*n)/3)) + (3*b)/(a^2*n*x^(n/3)) + (Sqrt[3]*b^(4/3)*ArcTan[(b^(1/3) - (2*a^(1/3))/x^(n/3))/(Sqrt[3]*b^(1/3))])/(a^(7/3)*n) - (b^(4/3)*Log[b^(1/3) + a^(1/3)/x^(n/3)])/(a^(7/3)*n) + (b^(4/3)*Log[b^(2/3) + a^(2/3)/x^((2*n)/3) - (a^(1/3)*b^(1/3))/x^(n/3)])/(2*a^(7/3)*n)","A",10,10,19,0.5263,1,"{362, 345, 193, 321, 200, 31, 634, 617, 204, 628}"
2648,1,252,0,0.1973323,"\int \frac{x^{-1-\frac{5 n}{4}}}{a+b x^n} \, dx","Int[x^(-1 - (5*n)/4)/(a + b*x^n),x]","\frac{b^{5/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x^{-n/4}+\sqrt{a} x^{-n/2}+\sqrt{b}\right)}{\sqrt{2} a^{9/4} n}-\frac{b^{5/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x^{-n/4}+\sqrt{a} x^{-n/2}+\sqrt{b}\right)}{\sqrt{2} a^{9/4} n}+\frac{\sqrt{2} b^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a} x^{-n/4}}{\sqrt[4]{b}}\right)}{a^{9/4} n}-\frac{\sqrt{2} b^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} x^{-n/4}}{\sqrt[4]{b}}+1\right)}{a^{9/4} n}+\frac{4 b x^{-n/4}}{a^2 n}-\frac{4 x^{-5 n/4}}{5 a n}","\frac{b^{5/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x^{-n/4}+\sqrt{a} x^{-n/2}+\sqrt{b}\right)}{\sqrt{2} a^{9/4} n}-\frac{b^{5/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x^{-n/4}+\sqrt{a} x^{-n/2}+\sqrt{b}\right)}{\sqrt{2} a^{9/4} n}+\frac{\sqrt{2} b^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a} x^{-n/4}}{\sqrt[4]{b}}\right)}{a^{9/4} n}-\frac{\sqrt{2} b^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} x^{-n/4}}{\sqrt[4]{b}}+1\right)}{a^{9/4} n}+\frac{4 b x^{-n/4}}{a^2 n}-\frac{4 x^{-5 n/4}}{5 a n}",1,"-4/(5*a*n*x^((5*n)/4)) + (4*b)/(a^2*n*x^(n/4)) + (Sqrt[2]*b^(5/4)*ArcTan[1 - (Sqrt[2]*a^(1/4))/(b^(1/4)*x^(n/4))])/(a^(9/4)*n) - (Sqrt[2]*b^(5/4)*ArcTan[1 + (Sqrt[2]*a^(1/4))/(b^(1/4)*x^(n/4))])/(a^(9/4)*n) + (b^(5/4)*Log[Sqrt[b] + Sqrt[a]/x^(n/2) - (Sqrt[2]*a^(1/4)*b^(1/4))/x^(n/4)])/(Sqrt[2]*a^(9/4)*n) - (b^(5/4)*Log[Sqrt[b] + Sqrt[a]/x^(n/2) + (Sqrt[2]*a^(1/4)*b^(1/4))/x^(n/4)])/(Sqrt[2]*a^(9/4)*n)","A",13,10,19,0.5263,1,"{362, 345, 193, 321, 211, 1165, 628, 1162, 617, 204}"
2649,1,92,0,0.0430168,"\int x^{-1+4 n} \sqrt{a+b x^n} \, dx","Int[x^(-1 + 4*n)*Sqrt[a + b*x^n],x]","\frac{6 a^2 \left(a+b x^n\right)^{5/2}}{5 b^4 n}-\frac{2 a^3 \left(a+b x^n\right)^{3/2}}{3 b^4 n}+\frac{2 \left(a+b x^n\right)^{9/2}}{9 b^4 n}-\frac{6 a \left(a+b x^n\right)^{7/2}}{7 b^4 n}","\frac{6 a^2 \left(a+b x^n\right)^{5/2}}{5 b^4 n}-\frac{2 a^3 \left(a+b x^n\right)^{3/2}}{3 b^4 n}+\frac{2 \left(a+b x^n\right)^{9/2}}{9 b^4 n}-\frac{6 a \left(a+b x^n\right)^{7/2}}{7 b^4 n}",1,"(-2*a^3*(a + b*x^n)^(3/2))/(3*b^4*n) + (6*a^2*(a + b*x^n)^(5/2))/(5*b^4*n) - (6*a*(a + b*x^n)^(7/2))/(7*b^4*n) + (2*(a + b*x^n)^(9/2))/(9*b^4*n)","A",3,2,19,0.1053,1,"{266, 43}"
2650,1,68,0,0.032652,"\int x^{-1+3 n} \sqrt{a+b x^n} \, dx","Int[x^(-1 + 3*n)*Sqrt[a + b*x^n],x]","\frac{2 a^2 \left(a+b x^n\right)^{3/2}}{3 b^3 n}+\frac{2 \left(a+b x^n\right)^{7/2}}{7 b^3 n}-\frac{4 a \left(a+b x^n\right)^{5/2}}{5 b^3 n}","\frac{2 a^2 \left(a+b x^n\right)^{3/2}}{3 b^3 n}+\frac{2 \left(a+b x^n\right)^{7/2}}{7 b^3 n}-\frac{4 a \left(a+b x^n\right)^{5/2}}{5 b^3 n}",1,"(2*a^2*(a + b*x^n)^(3/2))/(3*b^3*n) - (4*a*(a + b*x^n)^(5/2))/(5*b^3*n) + (2*(a + b*x^n)^(7/2))/(7*b^3*n)","A",3,2,19,0.1053,1,"{266, 43}"
2651,1,44,0,0.0218498,"\int x^{-1+2 n} \sqrt{a+b x^n} \, dx","Int[x^(-1 + 2*n)*Sqrt[a + b*x^n],x]","\frac{2 \left(a+b x^n\right)^{5/2}}{5 b^2 n}-\frac{2 a \left(a+b x^n\right)^{3/2}}{3 b^2 n}","\frac{2 \left(a+b x^n\right)^{5/2}}{5 b^2 n}-\frac{2 a \left(a+b x^n\right)^{3/2}}{3 b^2 n}",1,"(-2*a*(a + b*x^n)^(3/2))/(3*b^2*n) + (2*(a + b*x^n)^(5/2))/(5*b^2*n)","A",3,2,19,0.1053,1,"{266, 43}"
2652,1,21,0,0.0055118,"\int x^{-1+n} \sqrt{a+b x^n} \, dx","Int[x^(-1 + n)*Sqrt[a + b*x^n],x]","\frac{2 \left(a+b x^n\right)^{3/2}}{3 b n}","\frac{2 \left(a+b x^n\right)^{3/2}}{3 b n}",1,"(2*(a + b*x^n)^(3/2))/(3*b*n)","A",1,1,17,0.05882,1,"{261}"
2653,1,45,0,0.0239282,"\int \frac{\sqrt{a+b x^n}}{x} \, dx","Int[Sqrt[a + b*x^n]/x,x]","\frac{2 \sqrt{a+b x^n}}{n}-\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b x^n}}{\sqrt{a}}\right)}{n}","\frac{2 \sqrt{a+b x^n}}{n}-\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b x^n}}{\sqrt{a}}\right)}{n}",1,"(2*Sqrt[a + b*x^n])/n - (2*Sqrt[a]*ArcTanh[Sqrt[a + b*x^n]/Sqrt[a]])/n","A",4,4,15,0.2667,1,"{266, 50, 63, 208}"
2654,1,51,0,0.0244006,"\int x^{-1-n} \sqrt{a+b x^n} \, dx","Int[x^(-1 - n)*Sqrt[a + b*x^n],x]","-\frac{x^{-n} \sqrt{a+b x^n}}{n}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+b x^n}}{\sqrt{a}}\right)}{\sqrt{a} n}","-\frac{x^{-n} \sqrt{a+b x^n}}{n}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+b x^n}}{\sqrt{a}}\right)}{\sqrt{a} n}",1,"-(Sqrt[a + b*x^n]/(n*x^n)) - (b*ArcTanh[Sqrt[a + b*x^n]/Sqrt[a]])/(Sqrt[a]*n)","A",4,4,19,0.2105,1,"{266, 47, 63, 208}"
2655,1,84,0,0.0368521,"\int x^{-1-2 n} \sqrt{a+b x^n} \, dx","Int[x^(-1 - 2*n)*Sqrt[a + b*x^n],x]","\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x^n}}{\sqrt{a}}\right)}{4 a^{3/2} n}-\frac{x^{-2 n} \sqrt{a+b x^n}}{2 n}-\frac{b x^{-n} \sqrt{a+b x^n}}{4 a n}","\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x^n}}{\sqrt{a}}\right)}{4 a^{3/2} n}-\frac{x^{-2 n} \sqrt{a+b x^n}}{2 n}-\frac{b x^{-n} \sqrt{a+b x^n}}{4 a n}",1,"-Sqrt[a + b*x^n]/(2*n*x^(2*n)) - (b*Sqrt[a + b*x^n])/(4*a*n*x^n) + (b^2*ArcTanh[Sqrt[a + b*x^n]/Sqrt[a]])/(4*a^(3/2)*n)","A",5,5,19,0.2632,1,"{266, 47, 51, 63, 208}"
2656,1,113,0,0.0507471,"\int x^{-1-3 n} \sqrt{a+b x^n} \, dx","Int[x^(-1 - 3*n)*Sqrt[a + b*x^n],x]","\frac{b^2 x^{-n} \sqrt{a+b x^n}}{8 a^2 n}-\frac{b^3 \tanh ^{-1}\left(\frac{\sqrt{a+b x^n}}{\sqrt{a}}\right)}{8 a^{5/2} n}-\frac{x^{-3 n} \sqrt{a+b x^n}}{3 n}-\frac{b x^{-2 n} \sqrt{a+b x^n}}{12 a n}","\frac{b^2 x^{-n} \sqrt{a+b x^n}}{8 a^2 n}-\frac{b^3 \tanh ^{-1}\left(\frac{\sqrt{a+b x^n}}{\sqrt{a}}\right)}{8 a^{5/2} n}-\frac{x^{-3 n} \sqrt{a+b x^n}}{3 n}-\frac{b x^{-2 n} \sqrt{a+b x^n}}{12 a n}",1,"-Sqrt[a + b*x^n]/(3*n*x^(3*n)) - (b*Sqrt[a + b*x^n])/(12*a*n*x^(2*n)) + (b^2*Sqrt[a + b*x^n])/(8*a^2*n*x^n) - (b^3*ArcTanh[Sqrt[a + b*x^n]/Sqrt[a]])/(8*a^(5/2)*n)","A",6,5,19,0.2632,1,"{266, 47, 51, 63, 208}"
2657,1,142,0,0.0666474,"\int x^{-1-4 n} \sqrt{a+b x^n} \, dx","Int[x^(-1 - 4*n)*Sqrt[a + b*x^n],x]","\frac{5 b^2 x^{-2 n} \sqrt{a+b x^n}}{96 a^2 n}-\frac{5 b^3 x^{-n} \sqrt{a+b x^n}}{64 a^3 n}+\frac{5 b^4 \tanh ^{-1}\left(\frac{\sqrt{a+b x^n}}{\sqrt{a}}\right)}{64 a^{7/2} n}-\frac{x^{-4 n} \sqrt{a+b x^n}}{4 n}-\frac{b x^{-3 n} \sqrt{a+b x^n}}{24 a n}","\frac{5 b^2 x^{-2 n} \sqrt{a+b x^n}}{96 a^2 n}-\frac{5 b^3 x^{-n} \sqrt{a+b x^n}}{64 a^3 n}+\frac{5 b^4 \tanh ^{-1}\left(\frac{\sqrt{a+b x^n}}{\sqrt{a}}\right)}{64 a^{7/2} n}-\frac{x^{-4 n} \sqrt{a+b x^n}}{4 n}-\frac{b x^{-3 n} \sqrt{a+b x^n}}{24 a n}",1,"-Sqrt[a + b*x^n]/(4*n*x^(4*n)) - (b*Sqrt[a + b*x^n])/(24*a*n*x^(3*n)) + (5*b^2*Sqrt[a + b*x^n])/(96*a^2*n*x^(2*n)) - (5*b^3*Sqrt[a + b*x^n])/(64*a^3*n*x^n) + (5*b^4*ArcTanh[Sqrt[a + b*x^n]/Sqrt[a]])/(64*a^(7/2)*n)","A",7,5,19,0.2632,1,"{266, 47, 51, 63, 208}"
2658,1,88,0,0.0410302,"\int \frac{x^{-1+4 n}}{\sqrt{a+b x^n}} \, dx","Int[x^(-1 + 4*n)/Sqrt[a + b*x^n],x]","\frac{2 a^2 \left(a+b x^n\right)^{3/2}}{b^4 n}-\frac{2 a^3 \sqrt{a+b x^n}}{b^4 n}+\frac{2 \left(a+b x^n\right)^{7/2}}{7 b^4 n}-\frac{6 a \left(a+b x^n\right)^{5/2}}{5 b^4 n}","\frac{2 a^2 \left(a+b x^n\right)^{3/2}}{b^4 n}-\frac{2 a^3 \sqrt{a+b x^n}}{b^4 n}+\frac{2 \left(a+b x^n\right)^{7/2}}{7 b^4 n}-\frac{6 a \left(a+b x^n\right)^{5/2}}{5 b^4 n}",1,"(-2*a^3*Sqrt[a + b*x^n])/(b^4*n) + (2*a^2*(a + b*x^n)^(3/2))/(b^4*n) - (6*a*(a + b*x^n)^(5/2))/(5*b^4*n) + (2*(a + b*x^n)^(7/2))/(7*b^4*n)","A",3,2,19,0.1053,1,"{266, 43}"
2659,1,66,0,0.0298117,"\int \frac{x^{-1+3 n}}{\sqrt{a+b x^n}} \, dx","Int[x^(-1 + 3*n)/Sqrt[a + b*x^n],x]","\frac{2 a^2 \sqrt{a+b x^n}}{b^3 n}+\frac{2 \left(a+b x^n\right)^{5/2}}{5 b^3 n}-\frac{4 a \left(a+b x^n\right)^{3/2}}{3 b^3 n}","\frac{2 a^2 \sqrt{a+b x^n}}{b^3 n}+\frac{2 \left(a+b x^n\right)^{5/2}}{5 b^3 n}-\frac{4 a \left(a+b x^n\right)^{3/2}}{3 b^3 n}",1,"(2*a^2*Sqrt[a + b*x^n])/(b^3*n) - (4*a*(a + b*x^n)^(3/2))/(3*b^3*n) + (2*(a + b*x^n)^(5/2))/(5*b^3*n)","A",3,2,19,0.1053,1,"{266, 43}"
2660,1,42,0,0.0202429,"\int \frac{x^{-1+2 n}}{\sqrt{a+b x^n}} \, dx","Int[x^(-1 + 2*n)/Sqrt[a + b*x^n],x]","\frac{2 \left(a+b x^n\right)^{3/2}}{3 b^2 n}-\frac{2 a \sqrt{a+b x^n}}{b^2 n}","\frac{2 \left(a+b x^n\right)^{3/2}}{3 b^2 n}-\frac{2 a \sqrt{a+b x^n}}{b^2 n}",1,"(-2*a*Sqrt[a + b*x^n])/(b^2*n) + (2*(a + b*x^n)^(3/2))/(3*b^2*n)","A",3,2,19,0.1053,1,"{266, 43}"
2661,1,19,0,0.0058899,"\int \frac{x^{-1+n}}{\sqrt{a+b x^n}} \, dx","Int[x^(-1 + n)/Sqrt[a + b*x^n],x]","\frac{2 \sqrt{a+b x^n}}{b n}","\frac{2 \sqrt{a+b x^n}}{b n}",1,"(2*Sqrt[a + b*x^n])/(b*n)","A",1,1,17,0.05882,1,"{261}"
2662,1,28,0,0.0164945,"\int \frac{1}{x \sqrt{a+b x^n}} \, dx","Int[1/(x*Sqrt[a + b*x^n]),x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b x^n}}{\sqrt{a}}\right)}{\sqrt{a} n}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b x^n}}{\sqrt{a}}\right)}{\sqrt{a} n}",1,"(-2*ArcTanh[Sqrt[a + b*x^n]/Sqrt[a]])/(Sqrt[a]*n)","A",3,3,15,0.2000,1,"{266, 63, 208}"
2663,1,53,0,0.0253995,"\int \frac{x^{-1-n}}{\sqrt{a+b x^n}} \, dx","Int[x^(-1 - n)/Sqrt[a + b*x^n],x]","\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+b x^n}}{\sqrt{a}}\right)}{a^{3/2} n}-\frac{x^{-n} \sqrt{a+b x^n}}{a n}","\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+b x^n}}{\sqrt{a}}\right)}{a^{3/2} n}-\frac{x^{-n} \sqrt{a+b x^n}}{a n}",1,"-(Sqrt[a + b*x^n]/(a*n*x^n)) + (b*ArcTanh[Sqrt[a + b*x^n]/Sqrt[a]])/(a^(3/2)*n)","A",4,4,19,0.2105,1,"{266, 51, 63, 208}"
2664,1,87,0,0.0357873,"\int \frac{x^{-1-2 n}}{\sqrt{a+b x^n}} \, dx","Int[x^(-1 - 2*n)/Sqrt[a + b*x^n],x]","-\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x^n}}{\sqrt{a}}\right)}{4 a^{5/2} n}+\frac{3 b x^{-n} \sqrt{a+b x^n}}{4 a^2 n}-\frac{x^{-2 n} \sqrt{a+b x^n}}{2 a n}","-\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x^n}}{\sqrt{a}}\right)}{4 a^{5/2} n}+\frac{3 b x^{-n} \sqrt{a+b x^n}}{4 a^2 n}-\frac{x^{-2 n} \sqrt{a+b x^n}}{2 a n}",1,"-Sqrt[a + b*x^n]/(2*a*n*x^(2*n)) + (3*b*Sqrt[a + b*x^n])/(4*a^2*n*x^n) - (3*b^2*ArcTanh[Sqrt[a + b*x^n]/Sqrt[a]])/(4*a^(5/2)*n)","A",5,4,19,0.2105,1,"{266, 51, 63, 208}"
2665,1,116,0,0.0483145,"\int \frac{x^{-1-3 n}}{\sqrt{a+b x^n}} \, dx","Int[x^(-1 - 3*n)/Sqrt[a + b*x^n],x]","-\frac{5 b^2 x^{-n} \sqrt{a+b x^n}}{8 a^3 n}+\frac{5 b^3 \tanh ^{-1}\left(\frac{\sqrt{a+b x^n}}{\sqrt{a}}\right)}{8 a^{7/2} n}+\frac{5 b x^{-2 n} \sqrt{a+b x^n}}{12 a^2 n}-\frac{x^{-3 n} \sqrt{a+b x^n}}{3 a n}","-\frac{5 b^2 x^{-n} \sqrt{a+b x^n}}{8 a^3 n}+\frac{5 b^3 \tanh ^{-1}\left(\frac{\sqrt{a+b x^n}}{\sqrt{a}}\right)}{8 a^{7/2} n}+\frac{5 b x^{-2 n} \sqrt{a+b x^n}}{12 a^2 n}-\frac{x^{-3 n} \sqrt{a+b x^n}}{3 a n}",1,"-Sqrt[a + b*x^n]/(3*a*n*x^(3*n)) + (5*b*Sqrt[a + b*x^n])/(12*a^2*n*x^(2*n)) - (5*b^2*Sqrt[a + b*x^n])/(8*a^3*n*x^n) + (5*b^3*ArcTanh[Sqrt[a + b*x^n]/Sqrt[a]])/(8*a^(7/2)*n)","A",6,4,19,0.2105,1,"{266, 51, 63, 208}"
2666,1,145,0,0.0656875,"\int \frac{x^{-1-4 n}}{\sqrt{a+b x^n}} \, dx","Int[x^(-1 - 4*n)/Sqrt[a + b*x^n],x]","-\frac{35 b^2 x^{-2 n} \sqrt{a+b x^n}}{96 a^3 n}+\frac{35 b^3 x^{-n} \sqrt{a+b x^n}}{64 a^4 n}-\frac{35 b^4 \tanh ^{-1}\left(\frac{\sqrt{a+b x^n}}{\sqrt{a}}\right)}{64 a^{9/2} n}+\frac{7 b x^{-3 n} \sqrt{a+b x^n}}{24 a^2 n}-\frac{x^{-4 n} \sqrt{a+b x^n}}{4 a n}","-\frac{35 b^2 x^{-2 n} \sqrt{a+b x^n}}{96 a^3 n}+\frac{35 b^3 x^{-n} \sqrt{a+b x^n}}{64 a^4 n}-\frac{35 b^4 \tanh ^{-1}\left(\frac{\sqrt{a+b x^n}}{\sqrt{a}}\right)}{64 a^{9/2} n}+\frac{7 b x^{-3 n} \sqrt{a+b x^n}}{24 a^2 n}-\frac{x^{-4 n} \sqrt{a+b x^n}}{4 a n}",1,"-Sqrt[a + b*x^n]/(4*a*n*x^(4*n)) + (7*b*Sqrt[a + b*x^n])/(24*a^2*n*x^(3*n)) - (35*b^2*Sqrt[a + b*x^n])/(96*a^3*n*x^(2*n)) + (35*b^3*Sqrt[a + b*x^n])/(64*a^4*n*x^n) - (35*b^4*ArcTanh[Sqrt[a + b*x^n]/Sqrt[a]])/(64*a^(9/2)*n)","A",7,4,19,0.2105,1,"{266, 51, 63, 208}"
2667,1,75,0,0.0340715,"\int x^m \left(a+b x^n\right)^3 \, dx","Int[x^m*(a + b*x^n)^3,x]","\frac{3 a^2 b x^{m+n+1}}{m+n+1}+\frac{a^3 x^{m+1}}{m+1}+\frac{3 a b^2 x^{m+2 n+1}}{m+2 n+1}+\frac{b^3 x^{m+3 n+1}}{m+3 n+1}","\frac{3 a^2 b x^{m+n+1}}{m+n+1}+\frac{a^3 x^{m+1}}{m+1}+\frac{3 a b^2 x^{m+2 n+1}}{m+2 n+1}+\frac{b^3 x^{m+3 n+1}}{m+3 n+1}",1,"(a^3*x^(1 + m))/(1 + m) + (3*a^2*b*x^(1 + m + n))/(1 + m + n) + (3*a*b^2*x^(1 + m + 2*n))/(1 + m + 2*n) + (b^3*x^(1 + m + 3*n))/(1 + m + 3*n)","A",2,1,13,0.07692,1,"{270}"
2668,1,51,0,0.0182556,"\int x^m \left(a+b x^n\right)^2 \, dx","Int[x^m*(a + b*x^n)^2,x]","\frac{a^2 x^{m+1}}{m+1}+\frac{2 a b x^{m+n+1}}{m+n+1}+\frac{b^2 x^{m+2 n+1}}{m+2 n+1}","\frac{a^2 x^{m+1}}{m+1}+\frac{2 a b x^{m+n+1}}{m+n+1}+\frac{b^2 x^{m+2 n+1}}{m+2 n+1}",1,"(a^2*x^(1 + m))/(1 + m) + (2*a*b*x^(1 + m + n))/(1 + m + n) + (b^2*x^(1 + m + 2*n))/(1 + m + 2*n)","A",2,1,13,0.07692,1,"{270}"
2669,1,27,0,0.0079004,"\int x^m \left(a+b x^n\right) \, dx","Int[x^m*(a + b*x^n),x]","\frac{a x^{m+1}}{m+1}+\frac{b x^{m+n+1}}{m+n+1}","\frac{a x^{m+1}}{m+1}+\frac{b x^{m+n+1}}{m+n+1}",1,"(a*x^(1 + m))/(1 + m) + (b*x^(1 + m + n))/(1 + m + n)","A",2,1,11,0.09091,1,"{14}"
2670,1,40,0,0.0096072,"\int \frac{x^m}{a+b x^n} \, dx","Int[x^m/(a + b*x^n),x]","\frac{x^{m+1} \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right)}{a (m+1)}","\frac{x^{m+1} \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right)}{a (m+1)}",1,"(x^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)])/(a*(1 + m))","A",1,1,13,0.07692,1,"{364}"
2671,1,40,0,0.0100506,"\int \frac{x^m}{\left(a+b x^n\right)^2} \, dx","Int[x^m/(a + b*x^n)^2,x]","\frac{x^{m+1} \, _2F_1\left(2,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right)}{a^2 (m+1)}","\frac{x^{m+1} \, _2F_1\left(2,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right)}{a^2 (m+1)}",1,"(x^(1 + m)*Hypergeometric2F1[2, (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)])/(a^2*(1 + m))","A",1,1,13,0.07692,1,"{364}"
2672,1,40,0,0.0094211,"\int \frac{x^m}{\left(a+b x^n\right)^3} \, dx","Int[x^m/(a + b*x^n)^3,x]","\frac{x^{m+1} \, _2F_1\left(3,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right)}{a^3 (m+1)}","\frac{x^{m+1} \, _2F_1\left(3,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right)}{a^3 (m+1)}",1,"(x^(1 + m)*Hypergeometric2F1[3, (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)])/(a^3*(1 + m))","A",1,1,13,0.07692,1,"{364}"
2673,1,65,0,0.0227152,"\int x^m \left(a+b x^n\right)^{3/2} \, dx","Int[x^m*(a + b*x^n)^(3/2),x]","\frac{a x^{m+1} \sqrt{a+b x^n} \, _2F_1\left(-\frac{3}{2},\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right)}{(m+1) \sqrt{\frac{b x^n}{a}+1}}","\frac{x^{m+1} \left(a+b x^n\right)^{5/2} \, _2F_1\left(1,\frac{m+1}{n}+\frac{5}{2};\frac{m+n+1}{n};-\frac{b x^n}{a}\right)}{a (m+1)}",1,"(a*x^(1 + m)*Sqrt[a + b*x^n]*Hypergeometric2F1[-3/2, (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)])/((1 + m)*Sqrt[1 + (b*x^n)/a])","A",2,2,15,0.1333,1,"{365, 364}"
2674,1,64,0,0.020358,"\int x^m \sqrt{a+b x^n} \, dx","Int[x^m*Sqrt[a + b*x^n],x]","\frac{x^{m+1} \sqrt{a+b x^n} \, _2F_1\left(-\frac{1}{2},\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right)}{(m+1) \sqrt{\frac{b x^n}{a}+1}}","\frac{x^{m+1} \left(a+b x^n\right)^{3/2} \, _2F_1\left(1,\frac{m+1}{n}+\frac{3}{2};\frac{m+n+1}{n};-\frac{b x^n}{a}\right)}{a (m+1)}",1,"(x^(1 + m)*Sqrt[a + b*x^n]*Hypergeometric2F1[-1/2, (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)])/((1 + m)*Sqrt[1 + (b*x^n)/a])","A",2,2,15,0.1333,1,"{365, 364}"
2675,1,64,0,0.0202928,"\int \frac{x^m}{\sqrt{a+b x^n}} \, dx","Int[x^m/Sqrt[a + b*x^n],x]","\frac{x^{m+1} \sqrt{\frac{b x^n}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right)}{(m+1) \sqrt{a+b x^n}}","\frac{x^{m+1} \sqrt{a+b x^n} \, _2F_1\left(1,\frac{m+1}{n}+\frac{1}{2};\frac{m+n+1}{n};-\frac{b x^n}{a}\right)}{a (m+1)}",1,"(x^(1 + m)*Sqrt[1 + (b*x^n)/a]*Hypergeometric2F1[1/2, (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)])/((1 + m)*Sqrt[a + b*x^n])","A",2,2,15,0.1333,1,"{365, 364}"
2676,1,67,0,0.0217171,"\int \frac{x^m}{\left(a+b x^n\right)^{3/2}} \, dx","Int[x^m/(a + b*x^n)^(3/2),x]","\frac{x^{m+1} \sqrt{\frac{b x^n}{a}+1} \, _2F_1\left(\frac{3}{2},\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right)}{a (m+1) \sqrt{a+b x^n}}","\frac{x^{m+1} \, _2F_1\left(1,\frac{m+1}{n}-\frac{1}{2};\frac{m+n+1}{n};-\frac{b x^n}{a}\right)}{a (m+1) \sqrt{a+b x^n}}",1,"(x^(1 + m)*Sqrt[1 + (b*x^n)/a]*Hypergeometric2F1[3/2, (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)])/(a*(1 + m)*Sqrt[a + b*x^n])","A",2,2,15,0.1333,1,"{365, 364}"
2677,1,67,0,0.0236711,"\int \frac{x^m}{\left(a+b x^n\right)^{5/2}} \, dx","Int[x^m/(a + b*x^n)^(5/2),x]","\frac{x^{m+1} \sqrt{\frac{b x^n}{a}+1} \, _2F_1\left(\frac{5}{2},\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right)}{a^2 (m+1) \sqrt{a+b x^n}}","\frac{x^{m+1} \, _2F_1\left(1,\frac{m+1}{n}-\frac{3}{2};\frac{m+n+1}{n};-\frac{b x^n}{a}\right)}{a (m+1) \left(a+b x^n\right)^{3/2}}",1,"(x^(1 + m)*Sqrt[1 + (b*x^n)/a]*Hypergeometric2F1[5/2, (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)])/(a^2*(1 + m)*Sqrt[a + b*x^n])","A",2,2,15,0.1333,1,"{365, 364}"
2678,1,70,0,0.0241425,"\int \frac{x^{3+2 n}}{\sqrt{a+b x^n}} \, dx","Int[x^(3 + 2*n)/Sqrt[a + b*x^n],x]","\frac{x^{2 (n+2)} \sqrt{\frac{b x^n}{a}+1} \, _2F_1\left(\frac{1}{2},2 \left(1+\frac{2}{n}\right);3+\frac{4}{n};-\frac{b x^n}{a}\right)}{2 (n+2) \sqrt{a+b x^n}}","\frac{x^{2 (n+2)} \sqrt{a+b x^n} \, _2F_1\left(1,\frac{1}{2} \left(5+\frac{8}{n}\right);3+\frac{4}{n};-\frac{b x^n}{a}\right)}{2 a (n+2)}",1,"(x^(2*(2 + n))*Sqrt[1 + (b*x^n)/a]*Hypergeometric2F1[1/2, 2*(1 + 2/n), 3 + 4/n, -((b*x^n)/a)])/(2*(2 + n)*Sqrt[a + b*x^n])","A",2,2,19,0.1053,1,"{365, 364}"
2679,1,65,0,0.0224352,"\int \frac{x^{3+n}}{\sqrt{a+b x^n}} \, dx","Int[x^(3 + n)/Sqrt[a + b*x^n],x]","\frac{x^{n+4} \sqrt{\frac{b x^n}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{n+4}{n};2 \left(1+\frac{2}{n}\right);-\frac{b x^n}{a}\right)}{(n+4) \sqrt{a+b x^n}}","\frac{x^{n+4} \sqrt{a+b x^n} \, _2F_1\left(1,\frac{1}{2} \left(3+\frac{8}{n}\right);2 \left(1+\frac{2}{n}\right);-\frac{b x^n}{a}\right)}{a (n+4)}",1,"(x^(4 + n)*Sqrt[1 + (b*x^n)/a]*Hypergeometric2F1[1/2, (4 + n)/n, 2*(1 + 2/n), -((b*x^n)/a)])/((4 + n)*Sqrt[a + b*x^n])","A",2,2,17,0.1176,1,"{365, 364}"
2680,1,65,0,0.023815,"\int \frac{x^{3-n}}{\sqrt{a+b x^n}} \, dx","Int[x^(3 - n)/Sqrt[a + b*x^n],x]","\frac{x^{4-n} \sqrt{\frac{b x^n}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{4}{n}-1;\frac{4}{n};-\frac{b x^n}{a}\right)}{(4-n) \sqrt{a+b x^n}}","\frac{x^{4-n} \sqrt{a+b x^n} \, _2F_1\left(1,\frac{1}{2} \left(\frac{8}{n}-1\right);\frac{4}{n};-\frac{b x^n}{a}\right)}{a (4-n)}",1,"(x^(4 - n)*Sqrt[1 + (b*x^n)/a]*Hypergeometric2F1[1/2, -1 + 4/n, 4/n, -((b*x^n)/a)])/((4 - n)*Sqrt[a + b*x^n])","A",2,2,19,0.1053,1,"{365, 364}"
2681,1,72,0,0.0263921,"\int \frac{x^{3-2 n}}{\sqrt{a+b x^n}} \, dx","Int[x^(3 - 2*n)/Sqrt[a + b*x^n],x]","\frac{x^{4-2 n} \sqrt{\frac{b x^n}{a}+1} \, _2F_1\left(\frac{1}{2},-2 \left(1-\frac{2}{n}\right);\frac{4}{n}-1;-\frac{b x^n}{a}\right)}{2 (2-n) \sqrt{a+b x^n}}","\frac{x^{4-2 n} \sqrt{a+b x^n} \, _2F_1\left(1,\frac{1}{2} \left(\frac{8}{n}-3\right);\frac{4}{n}-1;-\frac{b x^n}{a}\right)}{2 a (2-n)}",1,"(x^(4 - 2*n)*Sqrt[1 + (b*x^n)/a]*Hypergeometric2F1[1/2, -2*(1 - 2/n), -1 + 4/n, -((b*x^n)/a)])/(2*(2 - n)*Sqrt[a + b*x^n])","A",2,2,19,0.1053,1,"{365, 364}"
2682,1,75,0,0.0262065,"\int \frac{x^{m+2 n}}{\sqrt{a+b x^n}} \, dx","Int[x^(m + 2*n)/Sqrt[a + b*x^n],x]","\frac{x^{m+2 n+1} \sqrt{\frac{b x^n}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{m+2 n+1}{n};\frac{m+3 n+1}{n};-\frac{b x^n}{a}\right)}{(m+2 n+1) \sqrt{a+b x^n}}","\frac{x^{m+2 n+1} \sqrt{a+b x^n} \, _2F_1\left(1,\frac{1}{2} \left(\frac{2 (m+1)}{n}+5\right);\frac{m+3 n+1}{n};-\frac{b x^n}{a}\right)}{a (m+2 n+1)}",1,"(x^(1 + m + 2*n)*Sqrt[1 + (b*x^n)/a]*Hypergeometric2F1[1/2, (1 + m + 2*n)/n, (1 + m + 3*n)/n, -((b*x^n)/a)])/((1 + m + 2*n)*Sqrt[a + b*x^n])","A",2,2,19,0.1053,1,"{365, 364}"
2683,1,69,0,0.0248149,"\int \frac{x^{m+n}}{\sqrt{a+b x^n}} \, dx","Int[x^(m + n)/Sqrt[a + b*x^n],x]","\frac{x^{m+n+1} \sqrt{\frac{b x^n}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{m+n+1}{n};\frac{m+2 n+1}{n};-\frac{b x^n}{a}\right)}{(m+n+1) \sqrt{a+b x^n}}","\frac{x^{m+n+1} \sqrt{a+b x^n} \, _2F_1\left(1,\frac{m+n+1}{n}+\frac{1}{2};\frac{m+2 n+1}{n};-\frac{b x^n}{a}\right)}{a (m+n+1)}",1,"(x^(1 + m + n)*Sqrt[1 + (b*x^n)/a]*Hypergeometric2F1[1/2, (1 + m + n)/n, (1 + m + 2*n)/n, -((b*x^n)/a)])/((1 + m + n)*Sqrt[a + b*x^n])","A",2,2,17,0.1176,1,"{365, 364}"
2684,1,72,0,0.0269554,"\int \frac{x^{m-n}}{\sqrt{a+b x^n}} \, dx","Int[x^(m - n)/Sqrt[a + b*x^n],x]","\frac{x^{m-n+1} \sqrt{\frac{b x^n}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{m-n+1}{n};\frac{m+1}{n};-\frac{b x^n}{a}\right)}{(m-n+1) \sqrt{a+b x^n}}","\frac{x^{m-n+1} \sqrt{a+b x^n} \, _2F_1\left(1,\frac{1}{2} \left(\frac{2 (m+1)}{n}-1\right);\frac{m+1}{n};-\frac{b x^n}{a}\right)}{a (m-n+1)}",1,"(x^(1 + m - n)*Sqrt[1 + (b*x^n)/a]*Hypergeometric2F1[1/2, (1 + m - n)/n, (1 + m)/n, -((b*x^n)/a)])/((1 + m - n)*Sqrt[a + b*x^n])","A",2,2,19,0.1053,1,"{365, 364}"
2685,1,75,0,0.0269902,"\int \frac{x^{m-2 n}}{\sqrt{a+b x^n}} \, dx","Int[x^(m - 2*n)/Sqrt[a + b*x^n],x]","\frac{x^{m-2 n+1} \sqrt{\frac{b x^n}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{m-2 n+1}{n};\frac{m-n+1}{n};-\frac{b x^n}{a}\right)}{(m-2 n+1) \sqrt{a+b x^n}}","\frac{x^{m-2 n+1} \sqrt{a+b x^n} \, _2F_1\left(1,\frac{1}{2} \left(\frac{2 (m+1)}{n}-3\right);\frac{m-n+1}{n};-\frac{b x^n}{a}\right)}{a (m-2 n+1)}",1,"(x^(1 + m - 2*n)*Sqrt[1 + (b*x^n)/a]*Hypergeometric2F1[1/2, (1 + m - 2*n)/n, (1 + m - n)/n, -((b*x^n)/a)])/((1 + m - 2*n)*Sqrt[a + b*x^n])","A",2,2,19,0.1053,1,"{365, 364}"
2686,1,126,0,0.0776162,"\int \left(-\frac{b n x^{-1+m+n}}{2 \left(a+b x^n\right)^{3/2}}+\frac{m x^{-1+m}}{\sqrt{a+b x^n}}\right) \, dx","Int[-(b*n*x^(-1 + m + n))/(2*(a + b*x^n)^(3/2)) + (m*x^(-1 + m))/Sqrt[a + b*x^n],x]","\frac{x^m \sqrt{\frac{b x^n}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{m}{n};\frac{m+n}{n};-\frac{b x^n}{a}\right)}{\sqrt{a+b x^n}}-\frac{b n x^{m+n} \sqrt{\frac{b x^n}{a}+1} \, _2F_1\left(\frac{3}{2},\frac{m+n}{n};\frac{m}{n}+2;-\frac{b x^n}{a}\right)}{2 a (m+n) \sqrt{a+b x^n}}","\frac{x^m}{\sqrt{a+b x^n}}",1,"(x^m*Sqrt[1 + (b*x^n)/a]*Hypergeometric2F1[1/2, m/n, (m + n)/n, -((b*x^n)/a)])/Sqrt[a + b*x^n] - (b*n*x^(m + n)*Sqrt[1 + (b*x^n)/a]*Hypergeometric2F1[3/2, (m + n)/n, 2 + m/n, -((b*x^n)/a)])/(2*a*(m + n)*Sqrt[a + b*x^n])","C",5,2,42,0.04762,1,"{365, 364}"
2687,1,129,0,0.0590889,"\int \frac{x^{-1+\frac{7 n}{2}}}{\sqrt{a+b x^n}} \, dx","Int[x^(-1 + (7*n)/2)/Sqrt[a + b*x^n],x]","\frac{5 a^2 x^{n/2} \sqrt{a+b x^n}}{8 b^3 n}-\frac{5 a^3 \tanh ^{-1}\left(\frac{\sqrt{b} x^{n/2}}{\sqrt{a+b x^n}}\right)}{8 b^{7/2} n}-\frac{5 a x^{3 n/2} \sqrt{a+b x^n}}{12 b^2 n}+\frac{x^{5 n/2} \sqrt{a+b x^n}}{3 b n}","\frac{5 a^2 x^{n/2} \sqrt{a+b x^n}}{8 b^3 n}-\frac{5 a^3 \tanh ^{-1}\left(\frac{\sqrt{b} x^{n/2}}{\sqrt{a+b x^n}}\right)}{8 b^{7/2} n}-\frac{5 a x^{3 n/2} \sqrt{a+b x^n}}{12 b^2 n}+\frac{x^{5 n/2} \sqrt{a+b x^n}}{3 b n}",1,"(5*a^2*x^(n/2)*Sqrt[a + b*x^n])/(8*b^3*n) - (5*a*x^((3*n)/2)*Sqrt[a + b*x^n])/(12*b^2*n) + (x^((5*n)/2)*Sqrt[a + b*x^n])/(3*b*n) - (5*a^3*ArcTanh[(Sqrt[b]*x^(n/2))/Sqrt[a + b*x^n]])/(8*b^(7/2)*n)","A",5,3,21,0.1429,1,"{355, 288, 206}"
2688,1,98,0,0.0415703,"\int \frac{x^{-1+\frac{5 n}{2}}}{\sqrt{a+b x^n}} \, dx","Int[x^(-1 + (5*n)/2)/Sqrt[a + b*x^n],x]","\frac{3 a^2 \tanh ^{-1}\left(\frac{\sqrt{b} x^{n/2}}{\sqrt{a+b x^n}}\right)}{4 b^{5/2} n}-\frac{3 a x^{n/2} \sqrt{a+b x^n}}{4 b^2 n}+\frac{x^{3 n/2} \sqrt{a+b x^n}}{2 b n}","\frac{3 a^2 \tanh ^{-1}\left(\frac{\sqrt{b} x^{n/2}}{\sqrt{a+b x^n}}\right)}{4 b^{5/2} n}-\frac{3 a x^{n/2} \sqrt{a+b x^n}}{4 b^2 n}+\frac{x^{3 n/2} \sqrt{a+b x^n}}{2 b n}",1,"(-3*a*x^(n/2)*Sqrt[a + b*x^n])/(4*b^2*n) + (x^((3*n)/2)*Sqrt[a + b*x^n])/(2*b*n) + (3*a^2*ArcTanh[(Sqrt[b]*x^(n/2))/Sqrt[a + b*x^n]])/(4*b^(5/2)*n)","A",4,3,21,0.1429,1,"{355, 288, 206}"
2689,1,62,0,0.0265925,"\int \frac{x^{-1+\frac{3 n}{2}}}{\sqrt{a+b x^n}} \, dx","Int[x^(-1 + (3*n)/2)/Sqrt[a + b*x^n],x]","\frac{x^{n/2} \sqrt{a+b x^n}}{b n}-\frac{a \tanh ^{-1}\left(\frac{\sqrt{b} x^{n/2}}{\sqrt{a+b x^n}}\right)}{b^{3/2} n}","\frac{x^{n/2} \sqrt{a+b x^n}}{b n}-\frac{a \tanh ^{-1}\left(\frac{\sqrt{b} x^{n/2}}{\sqrt{a+b x^n}}\right)}{b^{3/2} n}",1,"(x^(n/2)*Sqrt[a + b*x^n])/(b*n) - (a*ArcTanh[(Sqrt[b]*x^(n/2))/Sqrt[a + b*x^n]])/(b^(3/2)*n)","A",3,3,21,0.1429,1,"{355, 288, 206}"
2690,1,35,0,0.0186138,"\int \frac{x^{-1+\frac{n}{2}}}{\sqrt{a+b x^n}} \, dx","Int[x^(-1 + n/2)/Sqrt[a + b*x^n],x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} x^{n/2}}{\sqrt{a+b x^n}}\right)}{\sqrt{b} n}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} x^{n/2}}{\sqrt{a+b x^n}}\right)}{\sqrt{b} n}",1,"(2*ArcTanh[(Sqrt[b]*x^(n/2))/Sqrt[a + b*x^n]])/(Sqrt[b]*n)","A",3,3,21,0.1429,1,"{345, 217, 206}"
2691,1,26,0,0.00625,"\int \frac{x^{-1-\frac{n}{2}}}{\sqrt{a+b x^n}} \, dx","Int[x^(-1 - n/2)/Sqrt[a + b*x^n],x]","-\frac{2 x^{-n/2} \sqrt{a+b x^n}}{a n}","-\frac{2 x^{-n/2} \sqrt{a+b x^n}}{a n}",1,"(-2*Sqrt[a + b*x^n])/(a*n*x^(n/2))","A",1,1,21,0.04762,1,"{264}"
2692,1,58,0,0.0146927,"\int \frac{x^{-1-\frac{3 n}{2}}}{\sqrt{a+b x^n}} \, dx","Int[x^(-1 - (3*n)/2)/Sqrt[a + b*x^n],x]","\frac{4 b x^{-n/2} \sqrt{a+b x^n}}{3 a^2 n}-\frac{2 x^{-3 n/2} \sqrt{a+b x^n}}{3 a n}","\frac{4 b x^{-n/2} \sqrt{a+b x^n}}{3 a^2 n}-\frac{2 x^{-3 n/2} \sqrt{a+b x^n}}{3 a n}",1,"(-2*Sqrt[a + b*x^n])/(3*a*n*x^((3*n)/2)) + (4*b*Sqrt[a + b*x^n])/(3*a^2*n*x^(n/2))","A",2,2,21,0.09524,1,"{271, 264}"
2693,1,89,0,0.0265203,"\int \frac{x^{-1-\frac{5 n}{2}}}{\sqrt{a+b x^n}} \, dx","Int[x^(-1 - (5*n)/2)/Sqrt[a + b*x^n],x]","-\frac{16 b^2 x^{-n/2} \sqrt{a+b x^n}}{15 a^3 n}+\frac{8 b x^{-3 n/2} \sqrt{a+b x^n}}{15 a^2 n}-\frac{2 x^{-5 n/2} \sqrt{a+b x^n}}{5 a n}","-\frac{16 b^2 x^{-n/2} \sqrt{a+b x^n}}{15 a^3 n}+\frac{8 b x^{-3 n/2} \sqrt{a+b x^n}}{15 a^2 n}-\frac{2 x^{-5 n/2} \sqrt{a+b x^n}}{5 a n}",1,"(-2*Sqrt[a + b*x^n])/(5*a*n*x^((5*n)/2)) + (8*b*Sqrt[a + b*x^n])/(15*a^2*n*x^((3*n)/2)) - (16*b^2*Sqrt[a + b*x^n])/(15*a^3*n*x^(n/2))","A",3,2,21,0.09524,1,"{271, 264}"
2694,1,120,0,0.0391954,"\int \frac{x^{-1-\frac{7 n}{2}}}{\sqrt{a+b x^n}} \, dx","Int[x^(-1 - (7*n)/2)/Sqrt[a + b*x^n],x]","-\frac{16 b^2 x^{-3 n/2} \sqrt{a+b x^n}}{35 a^3 n}+\frac{32 b^3 x^{-n/2} \sqrt{a+b x^n}}{35 a^4 n}+\frac{12 b x^{-5 n/2} \sqrt{a+b x^n}}{35 a^2 n}-\frac{2 x^{-7 n/2} \sqrt{a+b x^n}}{7 a n}","-\frac{16 b^2 x^{-3 n/2} \sqrt{a+b x^n}}{35 a^3 n}+\frac{32 b^3 x^{-n/2} \sqrt{a+b x^n}}{35 a^4 n}+\frac{12 b x^{-5 n/2} \sqrt{a+b x^n}}{35 a^2 n}-\frac{2 x^{-7 n/2} \sqrt{a+b x^n}}{7 a n}",1,"(-2*Sqrt[a + b*x^n])/(7*a*n*x^((7*n)/2)) + (12*b*Sqrt[a + b*x^n])/(35*a^2*n*x^((5*n)/2)) - (16*b^2*Sqrt[a + b*x^n])/(35*a^3*n*x^((3*n)/2)) + (32*b^3*Sqrt[a + b*x^n])/(35*a^4*n*x^(n/2))","A",4,2,21,0.09524,1,"{271, 264}"
2695,1,80,0,0.0318297,"\int \frac{x^m}{\sqrt{a+b x^{-2+m}}} \, dx","Int[x^m/Sqrt[a + b*x^(-2 + m)],x]","\frac{x^{m+1} \sqrt{\frac{b x^{m-2}}{a}+1} \, _2F_1\left(\frac{1}{2},-\frac{m+1}{2-m};\frac{1-2 m}{2-m};-\frac{b x^{m-2}}{a}\right)}{(m+1) \sqrt{a+b x^{m-2}}}","\frac{x^{m+1} \sqrt{a+b x^{m-2}} \, _2F_1\left(1,-\frac{3 m}{2 (2-m)};\frac{1-2 m}{2-m};-\frac{b x^{m-2}}{a}\right)}{a (m+1)}",1,"(x^(1 + m)*Sqrt[1 + (b*x^(-2 + m))/a]*Hypergeometric2F1[1/2, -((1 + m)/(2 - m)), (1 - 2*m)/(2 - m), -((b*x^(-2 + m))/a)])/((1 + m)*Sqrt[a + b*x^(-2 + m)])","A",2,2,17,0.1176,1,"{365, 364}"
2696,1,81,0,0.0341092,"\int \frac{x^m}{\sqrt{a+b x^{2-m}}} \, dx","Int[x^m/Sqrt[a + b*x^(2 - m)],x]","\frac{x^{m+1} \sqrt{\frac{b x^{2-m}}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2-m};\frac{3}{2-m};-\frac{b x^{2-m}}{a}\right)}{(m+1) \sqrt{a+b x^{2-m}}}","\frac{x^{m+1} \sqrt{a+b x^{2-m}} \, _2F_1\left(1,\frac{m+4}{2 (2-m)};\frac{3}{2-m};-\frac{b x^{2-m}}{a}\right)}{a (m+1)}",1,"(x^(1 + m)*Sqrt[1 + (b*x^(2 - m))/a]*Hypergeometric2F1[1/2, (1 + m)/(2 - m), 3/(2 - m), -((b*x^(2 - m))/a)])/((1 + m)*Sqrt[a + b*x^(2 - m)])","A",2,2,19,0.1053,1,"{365, 364}"
2697,1,160,0,0.0855866,"\int \left(\frac{6 a x^2}{b (4+m) \sqrt{a+b x^{-2+m}}}+\frac{x^m}{\sqrt{a+b x^{-2+m}}}\right) \, dx","Int[(6*a*x^2)/(b*(4 + m)*Sqrt[a + b*x^(-2 + m)]) + x^m/Sqrt[a + b*x^(-2 + m)],x]","\frac{x^{m+1} \sqrt{\frac{b x^{m-2}}{a}+1} \, _2F_1\left(\frac{1}{2},-\frac{m+1}{2-m};\frac{1-2 m}{2-m};-\frac{b x^{m-2}}{a}\right)}{(m+1) \sqrt{a+b x^{m-2}}}+\frac{2 a x^3 \sqrt{\frac{b x^{m-2}}{a}+1} \, _2F_1\left(\frac{1}{2},-\frac{3}{2-m};-\frac{m+1}{2-m};-\frac{b x^{m-2}}{a}\right)}{b (m+4) \sqrt{a+b x^{m-2}}}","\frac{2 x^3 \sqrt{a+b x^{m-2}}}{b (m+4)}",1,"(2*a*x^3*Sqrt[1 + (b*x^(-2 + m))/a]*Hypergeometric2F1[1/2, -3/(2 - m), -((1 + m)/(2 - m)), -((b*x^(-2 + m))/a)])/(b*(4 + m)*Sqrt[a + b*x^(-2 + m)]) + (x^(1 + m)*Sqrt[1 + (b*x^(-2 + m))/a]*Hypergeometric2F1[1/2, -((1 + m)/(2 - m)), (1 - 2*m)/(2 - m), -((b*x^(-2 + m))/a)])/((1 + m)*Sqrt[a + b*x^(-2 + m)])","C",5,2,45,0.04444,1,"{365, 364}"
2698,1,15,0,0.0182856,"\int \frac{x^{-1+m} \left(2 a m+b (2 m-n) x^n\right)}{2 \left(a+b x^n\right)^{3/2}} \, dx","Int[(x^(-1 + m)*(2*a*m + b*(2*m - n)*x^n))/(2*(a + b*x^n)^(3/2)),x]","\frac{x^m}{\sqrt{a+b x^n}}","\frac{x^m}{\sqrt{a+b x^n}}",1,"x^m/Sqrt[a + b*x^n]","A",2,2,37,0.05405,1,"{12, 449}"
2699,1,126,0,0.0724515,"\int \left(-\frac{b n x^{-1+m+n}}{2 \left(a+b x^n\right)^{3/2}}+\frac{m x^{-1+m}}{\sqrt{a+b x^n}}\right) \, dx","Int[-(b*n*x^(-1 + m + n))/(2*(a + b*x^n)^(3/2)) + (m*x^(-1 + m))/Sqrt[a + b*x^n],x]","\frac{x^m \sqrt{\frac{b x^n}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{m}{n};\frac{m+n}{n};-\frac{b x^n}{a}\right)}{\sqrt{a+b x^n}}-\frac{b n x^{m+n} \sqrt{\frac{b x^n}{a}+1} \, _2F_1\left(\frac{3}{2},\frac{m+n}{n};\frac{m}{n}+2;-\frac{b x^n}{a}\right)}{2 a (m+n) \sqrt{a+b x^n}}","\frac{x^m}{\sqrt{a+b x^n}}",1,"(x^m*Sqrt[1 + (b*x^n)/a]*Hypergeometric2F1[1/2, m/n, (m + n)/n, -((b*x^n)/a)])/Sqrt[a + b*x^n] - (b*n*x^(m + n)*Sqrt[1 + (b*x^n)/a]*Hypergeometric2F1[3/2, (m + n)/n, 2 + m/n, -((b*x^n)/a)])/(2*a*(m + n)*Sqrt[a + b*x^n])","C",5,2,42,0.04762,1,"{365, 364}"
2700,1,97,0,0.0473381,"\int \frac{x^m}{\sqrt[3]{a+b x^{3 (1+m)}}} \, dx","Int[x^m/(a + b*x^(3*(1 + m)))^(1/3),x]","\frac{\tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x^{m+1}}{\sqrt[3]{a+b x^{3 (m+1)}}}+1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{b} (m+1)}-\frac{\log \left(\sqrt[3]{b} x^{m+1}-\sqrt[3]{a+b x^{3 (m+1)}}\right)}{2 \sqrt[3]{b} (m+1)}","\frac{\tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x^{m+1}}{\sqrt[3]{a+b x^{3 (m+1)}}}+1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{b} (m+1)}-\frac{\log \left(\sqrt[3]{b} x^{m+1}-\sqrt[3]{a+b x^{3 (m+1)}}\right)}{2 \sqrt[3]{b} (m+1)}",1,"ArcTan[(1 + (2*b^(1/3)*x^(1 + m))/(a + b*x^(3*(1 + m)))^(1/3))/Sqrt[3]]/(Sqrt[3]*b^(1/3)*(1 + m)) - Log[b^(1/3)*x^(1 + m) - (a + b*x^(3*(1 + m)))^(1/3)]/(2*b^(1/3)*(1 + m))","A",2,2,19,0.1053,1,"{345, 239}"
2701,1,139,0,0.1147498,"\int x^m \left(a+b x^{-\frac{3}{2} (1+m)}\right)^{2/3} \, dx","Int[x^m*(a + b/x^((3*(1 + m))/2))^(2/3),x]","\frac{b^{2/3} \log \left(\sqrt[3]{b} x^{\frac{1}{2} (-m-1)}-\sqrt[3]{a+b x^{-\frac{3}{2} (m+1)}}\right)}{m+1}-\frac{2 b^{2/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x^{\frac{1}{2} (-m-1)}}{\sqrt[3]{a+b x^{-\frac{3}{2} (m+1)}}}+1}{\sqrt{3}}\right)}{\sqrt{3} (m+1)}+\frac{x^{m+1} \left(a+b x^{-\frac{3}{2} (m+1)}\right)^{2/3}}{m+1}","\frac{b^{2/3} \log \left(\sqrt[3]{b} x^{\frac{1}{2} (-m-1)}-\sqrt[3]{a+b x^{-\frac{3}{2} (m+1)}}\right)}{m+1}-\frac{2 b^{2/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x^{\frac{1}{2} (-m-1)}}{\sqrt[3]{a+b x^{-\frac{3}{2} (m+1)}}}+1}{\sqrt{3}}\right)}{\sqrt{3} (m+1)}+\frac{x^{m+1} \left(a+b x^{-\frac{3}{2} (m+1)}\right)^{2/3}}{m+1}",1,"(x^(1 + m)*(a + b/x^((3*(1 + m))/2))^(2/3))/(1 + m) - (2*b^(2/3)*ArcTan[(1 + (2*b^(1/3)*x^((-1 - m)/2))/(a + b/x^((3*(1 + m))/2))^(1/3))/Sqrt[3]])/(Sqrt[3]*(1 + m)) + (b^(2/3)*Log[b^(1/3)*x^((-1 - m)/2) - (a + b/x^((3*(1 + m))/2))^(1/3)])/(1 + m)","A",3,3,21,0.1429,1,"{349, 345, 239}"
2702,1,89,0,0.0401447,"\int \frac{x^{-1+\frac{n}{3}}}{\sqrt[3]{a+b x^n}} \, dx","Int[x^(-1 + n/3)/(a + b*x^n)^(1/3),x]","\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x^{n/3}}{\sqrt[3]{a+b x^n}}+1}{\sqrt{3}}\right)}{\sqrt[3]{b} n}-\frac{3 \log \left(\sqrt[3]{b} x^{n/3}-\sqrt[3]{a+b x^n}\right)}{2 \sqrt[3]{b} n}","\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x^{n/3}}{\sqrt[3]{a+b x^n}}+1}{\sqrt{3}}\right)}{\sqrt[3]{b} n}-\frac{3 \log \left(\sqrt[3]{b} x^{n/3}-\sqrt[3]{a+b x^n}\right)}{2 \sqrt[3]{b} n}",1,"(Sqrt[3]*ArcTan[(1 + (2*b^(1/3)*x^(n/3))/(a + b*x^n)^(1/3))/Sqrt[3]])/(b^(1/3)*n) - (3*Log[b^(1/3)*x^(n/3) - (a + b*x^n)^(1/3)])/(2*b^(1/3)*n)","A",2,2,21,0.09524,1,"{345, 239}"
2703,1,114,0,0.0541963,"\int x^{-1-\frac{2 n}{3}} \left(a+b x^n\right)^{2/3} \, dx","Int[x^(-1 - (2*n)/3)*(a + b*x^n)^(2/3),x]","-\frac{3 b^{2/3} \log \left(\sqrt[3]{b} x^{n/3}-\sqrt[3]{a+b x^n}\right)}{2 n}+\frac{\sqrt{3} b^{2/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x^{n/3}}{\sqrt[3]{a+b x^n}}+1}{\sqrt{3}}\right)}{n}-\frac{3 x^{-2 n/3} \left(a+b x^n\right)^{2/3}}{2 n}","-\frac{3 b^{2/3} \log \left(\sqrt[3]{b} x^{n/3}-\sqrt[3]{a+b x^n}\right)}{2 n}+\frac{\sqrt{3} b^{2/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x^{n/3}}{\sqrt[3]{a+b x^n}}+1}{\sqrt{3}}\right)}{n}-\frac{3 x^{-2 n/3} \left(a+b x^n\right)^{2/3}}{2 n}",1,"(-3*(a + b*x^n)^(2/3))/(2*n*x^((2*n)/3)) + (Sqrt[3]*b^(2/3)*ArcTan[(1 + (2*b^(1/3)*x^(n/3))/(a + b*x^n)^(1/3))/Sqrt[3]])/n - (3*b^(2/3)*Log[b^(1/3)*x^(n/3) - (a + b*x^n)^(1/3)])/(2*n)","A",3,3,21,0.1429,1,"{349, 345, 239}"
2704,1,62,0,0.018242,"\int x^m \left(a+b x^n\right)^p \, dx","Int[x^m*(a + b*x^n)^p,x]","\frac{x^{m+1} \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+1}{n},-p;\frac{m+n+1}{n};-\frac{b x^n}{a}\right)}{m+1}","\frac{x^{m+1} \left(a+b x^n\right)^{p+1} \, _2F_1\left(1,\frac{m+1}{n}+p+1;\frac{m+n+1}{n};-\frac{b x^n}{a}\right)}{a (m+1)}",1,"(x^(1 + m)*(a + b*x^n)^p*Hypergeometric2F1[(1 + m)/n, -p, (1 + m + n)/n, -((b*x^n)/a)])/((1 + m)*(1 + (b*x^n)/a)^p)","A",2,2,13,0.1538,1,"{365, 364}"
2705,1,146,0,0.0884908,"\int \left(a+b x^n\right)^{-4-\frac{1}{n}} \, dx","Int[(a + b*x^n)^(-4 - n^(-1)),x]","\frac{3 n x \left(a+b x^n\right)^{-\frac{1}{n}-2}}{a^2 \left(6 n^2+5 n+1\right)}+\frac{6 n^2 x \left(a+b x^n\right)^{-\frac{1}{n}-1}}{a^3 (n+1) (2 n+1) (3 n+1)}+\frac{6 n^3 x \left(a+b x^n\right)^{-1/n}}{a^4 (n+1) (2 n+1) (3 n+1)}+\frac{x \left(a+b x^n\right)^{-\frac{1}{n}-3}}{a (3 n+1)}","\frac{3 n x \left(a+b x^n\right)^{-\frac{1}{n}-2}}{a^2 \left(6 n^2+5 n+1\right)}+\frac{6 n^2 x \left(a+b x^n\right)^{-\frac{1}{n}-1}}{a^3 (n+1) (2 n+1) (3 n+1)}+\frac{6 n^3 x \left(a+b x^n\right)^{-1/n}}{a^4 (n+1) (2 n+1) (3 n+1)}+\frac{x \left(a+b x^n\right)^{-\frac{1}{n}-3}}{a (3 n+1)}",1,"(x*(a + b*x^n)^(-3 - n^(-1)))/(a*(1 + 3*n)) + (3*n*x*(a + b*x^n)^(-2 - n^(-1)))/(a^2*(1 + 5*n + 6*n^2)) + (6*n^2*x*(a + b*x^n)^(-1 - n^(-1)))/(a^3*(1 + n)*(1 + 2*n)*(1 + 3*n)) + (6*n^3*x)/(a^4*(1 + n)*(1 + 2*n)*(1 + 3*n)*(a + b*x^n)^n^(-1))","A",4,2,15,0.1333,1,"{192, 191}"
2706,1,96,0,0.0334893,"\int \left(a+b x^n\right)^{-3-\frac{1}{n}} \, dx","Int[(a + b*x^n)^(-3 - n^(-1)),x]","\frac{2 n^2 x \left(a+b x^n\right)^{-1/n}}{a^3 (n+1) (2 n+1)}+\frac{2 n x \left(a+b x^n\right)^{-\frac{1}{n}-1}}{a^2 (n+1) (2 n+1)}+\frac{x \left(a+b x^n\right)^{-\frac{1}{n}-2}}{a (2 n+1)}","\frac{2 n^2 x \left(a+b x^n\right)^{-1/n}}{a^3 (n+1) (2 n+1)}+\frac{2 n x \left(a+b x^n\right)^{-\frac{1}{n}-1}}{a^2 (n+1) (2 n+1)}+\frac{x \left(a+b x^n\right)^{-\frac{1}{n}-2}}{a (2 n+1)}",1,"(x*(a + b*x^n)^(-2 - n^(-1)))/(a*(1 + 2*n)) + (2*n*x*(a + b*x^n)^(-1 - n^(-1)))/(a^2*(1 + n)*(1 + 2*n)) + (2*n^2*x)/(a^3*(1 + n)*(1 + 2*n)*(a + b*x^n)^n^(-1))","A",3,2,15,0.1333,1,"{192, 191}"
2707,1,50,0,0.0121668,"\int \left(a+b x^n\right)^{-2-\frac{1}{n}} \, dx","Int[(a + b*x^n)^(-2 - n^(-1)),x]","\frac{n x \left(a+b x^n\right)^{-1/n}}{a^2 (n+1)}+\frac{x \left(a+b x^n\right)^{-\frac{1}{n}-1}}{a (n+1)}","\frac{n x \left(a+b x^n\right)^{-1/n}}{a^2 (n+1)}+\frac{x \left(a+b x^n\right)^{-\frac{1}{n}-1}}{a (n+1)}",1,"(x*(a + b*x^n)^(-1 - n^(-1)))/(a*(1 + n)) + (n*x)/(a^2*(1 + n)*(a + b*x^n)^n^(-1))","A",2,2,15,0.1333,1,"{192, 191}"
2708,1,18,0,0.002757,"\int \left(a+b x^n\right)^{-1-\frac{1}{n}} \, dx","Int[(a + b*x^n)^(-1 - n^(-1)),x]","\frac{x \left(a+b x^n\right)^{-1/n}}{a}","\frac{x \left(a+b x^n\right)^{-1/n}}{a}",1,"x/(a*(a + b*x^n)^n^(-1))","A",1,1,15,0.06667,1,"{191}"
2709,1,50,0,0.0125115,"\int \left(a+b x^n\right)^{-1/n} \, dx","Int[(a + b*x^n)^(-n^(-1)),x]","x \left(a+b x^n\right)^{-1/n} \left(\frac{b x^n}{a}+1\right)^{\frac{1}{n}} \, _2F_1\left(\frac{1}{n},\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)","x \left(a+b x^n\right)^{-1/n} \left(\frac{b x^n}{a}+1\right)^{\frac{1}{n}} \, _2F_1\left(\frac{1}{n},\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)",1,"(x*(1 + (b*x^n)/a)^n^(-1)*Hypergeometric2F1[n^(-1), n^(-1), 1 + n^(-1), -((b*x^n)/a)])/(a + b*x^n)^n^(-1)","A",2,2,13,0.1538,1,"{246, 245}"
2710,1,53,0,0.0111911,"\int \left(a+b x^n\right)^{1-\frac{1}{n}} \, dx","Int[(a + b*x^n)^(1 - n^(-1)),x]","a x \left(a+b x^n\right)^{-1/n} \left(\frac{b x^n}{a}+1\right)^{\frac{1}{n}} \, _2F_1\left(\frac{1}{n}-1,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)","a x \left(a+b x^n\right)^{-1/n} \left(\frac{b x^n}{a}+1\right)^{\frac{1}{n}} \, _2F_1\left(\frac{1}{n}-1,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)",1,"(a*x*(1 + (b*x^n)/a)^n^(-1)*Hypergeometric2F1[-1 + n^(-1), n^(-1), 1 + n^(-1), -((b*x^n)/a)])/(a + b*x^n)^n^(-1)","A",2,2,15,0.1333,1,"{246, 245}"
2711,1,55,0,0.01257,"\int \left(a+b x^n\right)^{2-\frac{1}{n}} \, dx","Int[(a + b*x^n)^(2 - n^(-1)),x]","a^2 x \left(a+b x^n\right)^{-1/n} \left(\frac{b x^n}{a}+1\right)^{\frac{1}{n}} \, _2F_1\left(\frac{1}{n}-2,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)","a^2 x \left(a+b x^n\right)^{-1/n} \left(\frac{b x^n}{a}+1\right)^{\frac{1}{n}} \, _2F_1\left(\frac{1}{n}-2,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)",1,"(a^2*x*(1 + (b*x^n)/a)^n^(-1)*Hypergeometric2F1[-2 + n^(-1), n^(-1), 1 + n^(-1), -((b*x^n)/a)])/(a + b*x^n)^n^(-1)","A",2,2,15,0.1333,1,"{246, 245}"
2712,1,21,0,0.0062687,"\int x^m \left(b x^n\right)^p \, dx","Int[x^m*(b*x^n)^p,x]","\frac{x^{m+1} \left(b x^n\right)^p}{m+n p+1}","\frac{x^{m+1} \left(b x^n\right)^p}{m+n p+1}",1,"(x^(1 + m)*(b*x^n)^p)/(1 + m + n*p)","A",2,2,11,0.1818,1,"{15, 30}"
2713,1,18,0,0.0060111,"\int x^2 \left(b x^n\right)^p \, dx","Int[x^2*(b*x^n)^p,x]","\frac{x^3 \left(b x^n\right)^p}{n p+3}","\frac{x^3 \left(b x^n\right)^p}{n p+3}",1,"(x^3*(b*x^n)^p)/(3 + n*p)","A",2,2,11,0.1818,1,"{15, 30}"
2714,1,18,0,0.005121,"\int x \left(b x^n\right)^p \, dx","Int[x*(b*x^n)^p,x]","\frac{x^2 \left(b x^n\right)^p}{n p+2}","\frac{x^2 \left(b x^n\right)^p}{n p+2}",1,"(x^2*(b*x^n)^p)/(2 + n*p)","A",2,2,9,0.2222,1,"{15, 30}"
2715,1,16,0,0.0050465,"\int \left(b x^n\right)^p \, dx","Int[(b*x^n)^p,x]","\frac{x \left(b x^n\right)^p}{n p+1}","\frac{x \left(b x^n\right)^p}{n p+1}",1,"(x*(b*x^n)^p)/(1 + n*p)","A",2,2,7,0.2857,1,"{15, 30}"
2716,1,14,0,0.0038183,"\int \frac{\left(b x^n\right)^p}{x} \, dx","Int[(b*x^n)^p/x,x]","\frac{\left(b x^n\right)^p}{n p}","\frac{\left(b x^n\right)^p}{n p}",1,"(b*x^n)^p/(n*p)","A",2,2,11,0.1818,1,"{15, 30}"
2717,1,20,0,0.0076785,"\int \frac{\left(b x^n\right)^p}{x^2} \, dx","Int[(b*x^n)^p/x^2,x]","-\frac{\left(b x^n\right)^p}{x (1-n p)}","-\frac{\left(b x^n\right)^p}{x (1-n p)}",1,"-((b*x^n)^p/((1 - n*p)*x))","A",2,2,11,0.1818,1,"{15, 30}"
2718,1,20,0,0.0073232,"\int \frac{\left(b x^n\right)^p}{x^3} \, dx","Int[(b*x^n)^p/x^3,x]","-\frac{\left(b x^n\right)^p}{x^2 (2-n p)}","-\frac{\left(b x^n\right)^p}{x^2 (2-n p)}",1,"-((b*x^n)^p/((2 - n*p)*x^2))","A",2,2,11,0.1818,1,"{15, 30}"
2719,1,20,0,0.0065255,"\int \frac{\left(b x^n\right)^p}{x^4} \, dx","Int[(b*x^n)^p/x^4,x]","-\frac{\left(b x^n\right)^p}{x^3 (3-n p)}","-\frac{\left(b x^n\right)^p}{x^3 (3-n p)}",1,"-((b*x^n)^p/((3 - n*p)*x^3))","A",2,2,11,0.1818,1,"{15, 30}"
2720,1,23,0,0.0083898,"\int x^{-1+n} \left(a+b x^n\right)^p \, dx","Int[x^(-1 + n)*(a + b*x^n)^p,x]","\frac{\left(a+b x^n\right)^{p+1}}{b n (p+1)}","\frac{\left(a+b x^n\right)^{p+1}}{b n (p+1)}",1,"(a + b*x^n)^(1 + p)/(b*n*(1 + p))","A",1,1,15,0.06667,1,"{261}"
2721,1,49,0,0.0316899,"\int x^{-1+2 n} \left(a+b x^n\right)^p \, dx","Int[x^(-1 + 2*n)*(a + b*x^n)^p,x]","\frac{\left(a+b x^n\right)^{p+2}}{b^2 n (p+2)}-\frac{a \left(a+b x^n\right)^{p+1}}{b^2 n (p+1)}","\frac{\left(a+b x^n\right)^{p+2}}{b^2 n (p+2)}-\frac{a \left(a+b x^n\right)^{p+1}}{b^2 n (p+1)}",1,"-((a*(a + b*x^n)^(1 + p))/(b^2*n*(1 + p))) + (a + b*x^n)^(2 + p)/(b^2*n*(2 + p))","A",3,2,17,0.1176,1,"{266, 43}"
2722,1,75,0,0.0448444,"\int x^{-1+3 n} \left(a+b x^n\right)^p \, dx","Int[x^(-1 + 3*n)*(a + b*x^n)^p,x]","\frac{a^2 \left(a+b x^n\right)^{p+1}}{b^3 n (p+1)}-\frac{2 a \left(a+b x^n\right)^{p+2}}{b^3 n (p+2)}+\frac{\left(a+b x^n\right)^{p+3}}{b^3 n (p+3)}","\frac{a^2 \left(a+b x^n\right)^{p+1}}{b^3 n (p+1)}-\frac{2 a \left(a+b x^n\right)^{p+2}}{b^3 n (p+2)}+\frac{\left(a+b x^n\right)^{p+3}}{b^3 n (p+3)}",1,"(a^2*(a + b*x^n)^(1 + p))/(b^3*n*(1 + p)) - (2*a*(a + b*x^n)^(2 + p))/(b^3*n*(2 + p)) + (a + b*x^n)^(3 + p)/(b^3*n*(3 + p))","A",3,2,17,0.1176,1,"{266, 43}"
2723,1,103,0,0.0607738,"\int x^{-1+4 n} \left(a+b x^n\right)^p \, dx","Int[x^(-1 + 4*n)*(a + b*x^n)^p,x]","-\frac{a^3 \left(a+b x^n\right)^{p+1}}{b^4 n (p+1)}+\frac{3 a^2 \left(a+b x^n\right)^{p+2}}{b^4 n (p+2)}-\frac{3 a \left(a+b x^n\right)^{p+3}}{b^4 n (p+3)}+\frac{\left(a+b x^n\right)^{p+4}}{b^4 n (p+4)}","-\frac{a^3 \left(a+b x^n\right)^{p+1}}{b^4 n (p+1)}+\frac{3 a^2 \left(a+b x^n\right)^{p+2}}{b^4 n (p+2)}-\frac{3 a \left(a+b x^n\right)^{p+3}}{b^4 n (p+3)}+\frac{\left(a+b x^n\right)^{p+4}}{b^4 n (p+4)}",1,"-((a^3*(a + b*x^n)^(1 + p))/(b^4*n*(1 + p))) + (3*a^2*(a + b*x^n)^(2 + p))/(b^4*n*(2 + p)) - (3*a*(a + b*x^n)^(3 + p))/(b^4*n*(3 + p)) + (a + b*x^n)^(4 + p)/(b^4*n*(4 + p))","A",3,2,17,0.1176,1,"{266, 43}"
2724,1,32,0,0.0092007,"\int x^{-1-n-n p} \left(a+b x^n\right)^p \, dx","Int[x^(-1 - n - n*p)*(a + b*x^n)^p,x]","-\frac{x^{-n (p+1)} \left(a+b x^n\right)^{p+1}}{a n (p+1)}","-\frac{x^{-n (p+1)} \left(a+b x^n\right)^{p+1}}{a n (p+1)}",1,"-((a + b*x^n)^(1 + p)/(a*n*(1 + p)*x^(n*(1 + p))))","A",1,1,21,0.04762,1,"{264}"
2725,1,24,0,0.005459,"\int x^{-1-9 n} \left(a+b x^n\right)^8 \, dx","Int[x^(-1 - 9*n)*(a + b*x^n)^8,x]","-\frac{x^{-9 n} \left(a+b x^n\right)^9}{9 a n}","-\frac{x^{-9 n} \left(a+b x^n\right)^9}{9 a n}",1,"-(a + b*x^n)^9/(9*a*n*x^(9*n))","A",1,1,17,0.05882,1,"{264}"
2726,1,30,0,0.0076007,"\int x^{-4-3 p} \left(a+b x^3\right)^p \, dx","Int[x^(-4 - 3*p)*(a + b*x^3)^p,x]","-\frac{x^{-3 (p+1)} \left(a+b x^3\right)^{p+1}}{3 a (p+1)}","-\frac{x^{-3 (p+1)} \left(a+b x^3\right)^{p+1}}{3 a (p+1)}",1,"-(a + b*x^3)^(1 + p)/(3*a*(1 + p)*x^(3*(1 + p)))","A",1,1,17,0.05882,1,"{264}"
2727,1,19,0,0.0031853,"\int \frac{\left(a+b x^3\right)^8}{x^{28}} \, dx","Int[(a + b*x^3)^8/x^28,x]","-\frac{\left(a+b x^3\right)^9}{27 a x^{27}}","-\frac{\left(a+b x^3\right)^9}{27 a x^{27}}",1,"-(a + b*x^3)^9/(27*a*x^27)","A",1,1,13,0.07692,1,"{264}"
2728,1,23,0,0.0104905,"\int \frac{1}{x \left(a+b x^n\right)} \, dx","Int[1/(x*(a + b*x^n)),x]","\frac{\log (x)}{a}-\frac{\log \left(a+b x^n\right)}{a n}","\frac{\log (x)}{a}-\frac{\log \left(a+b x^n\right)}{a n}",1,"Log[x]/a - Log[a + b*x^n]/(a*n)","A",4,4,13,0.3077,1,"{266, 36, 29, 31}"
2729,1,22,0,0.0118628,"\int \frac{1}{x \left(a+b x^3\right)} \, dx","Int[1/(x*(a + b*x^3)),x]","\frac{\log (x)}{a}-\frac{\log \left(a+b x^3\right)}{3 a}","\frac{\log (x)}{a}-\frac{\log \left(a+b x^3\right)}{3 a}",1,"Log[x]/a - Log[a + b*x^3]/(3*a)","A",4,4,13,0.3077,1,"{266, 36, 29, 31}"
2730,1,147,0,0.1028603,"\int \left(a+b x^n\right)^{-\frac{1+4 n}{n}} \, dx","Int[(a + b*x^n)^(-((1 + 4*n)/n)),x]","\frac{3 n x \left(a+b x^n\right)^{-\frac{1}{n}-2}}{a^2 \left(6 n^2+5 n+1\right)}+\frac{6 n^3 x \left(a+b x^n\right)^{-1/n}}{a^4 (n+1) (2 n+1) (3 n+1)}+\frac{6 n^2 x \left(a+b x^n\right)^{-\frac{n+1}{n}}}{a^3 (n+1) (2 n+1) (3 n+1)}+\frac{x \left(a+b x^n\right)^{-\frac{1}{n}-3}}{a (3 n+1)}","\frac{3 n x \left(a+b x^n\right)^{-\frac{1}{n}-2}}{a^2 \left(6 n^2+5 n+1\right)}+\frac{6 n^3 x \left(a+b x^n\right)^{-1/n}}{a^4 (n+1) (2 n+1) (3 n+1)}+\frac{6 n^2 x \left(a+b x^n\right)^{-\frac{n+1}{n}}}{a^3 (n+1) (2 n+1) (3 n+1)}+\frac{x \left(a+b x^n\right)^{-\frac{1}{n}-3}}{a (3 n+1)}",1,"(x*(a + b*x^n)^(-3 - n^(-1)))/(a*(1 + 3*n)) + (3*n*x*(a + b*x^n)^(-2 - n^(-1)))/(a^2*(1 + 5*n + 6*n^2)) + (6*n^3*x)/(a^4*(1 + n)*(1 + 2*n)*(1 + 3*n)*(a + b*x^n)^n^(-1)) + (6*n^2*x)/(a^3*(1 + n)*(1 + 2*n)*(1 + 3*n)*(a + b*x^n)^((1 + n)/n))","A",4,2,18,0.1111,1,"{192, 191}"
2731,1,97,0,0.0527182,"\int \left(a+b x^n\right)^{-\frac{1+3 n}{n}} \, dx","Int[(a + b*x^n)^(-((1 + 3*n)/n)),x]","\frac{2 n^2 x \left(a+b x^n\right)^{-1/n}}{a^3 (n+1) (2 n+1)}+\frac{2 n x \left(a+b x^n\right)^{-\frac{n+1}{n}}}{a^2 (n+1) (2 n+1)}+\frac{x \left(a+b x^n\right)^{-\frac{1}{n}-2}}{a (2 n+1)}","\frac{2 n^2 x \left(a+b x^n\right)^{-1/n}}{a^3 (n+1) (2 n+1)}+\frac{2 n x \left(a+b x^n\right)^{-\frac{n+1}{n}}}{a^2 (n+1) (2 n+1)}+\frac{x \left(a+b x^n\right)^{-\frac{1}{n}-2}}{a (2 n+1)}",1,"(x*(a + b*x^n)^(-2 - n^(-1)))/(a*(1 + 2*n)) + (2*n^2*x)/(a^3*(1 + n)*(1 + 2*n)*(a + b*x^n)^n^(-1)) + (2*n*x)/(a^2*(1 + n)*(1 + 2*n)*(a + b*x^n)^((1 + n)/n))","A",3,2,18,0.1111,1,"{192, 191}"
2732,1,51,0,0.0193038,"\int \left(a+b x^n\right)^{-\frac{1+2 n}{n}} \, dx","Int[(a + b*x^n)^(-((1 + 2*n)/n)),x]","\frac{n x \left(a+b x^n\right)^{-1/n}}{a^2 (n+1)}+\frac{x \left(a+b x^n\right)^{-\frac{n+1}{n}}}{a (n+1)}","\frac{n x \left(a+b x^n\right)^{-1/n}}{a^2 (n+1)}+\frac{x \left(a+b x^n\right)^{-\frac{n+1}{n}}}{a (n+1)}",1,"(n*x)/(a^2*(1 + n)*(a + b*x^n)^n^(-1)) + x/(a*(1 + n)*(a + b*x^n)^((1 + n)/n))","A",2,2,18,0.1111,1,"{192, 191}"
2733,1,18,0,0.0029852,"\int \left(a+b x^n\right)^{-\frac{1+n}{n}} \, dx","Int[(a + b*x^n)^(-((1 + n)/n)),x]","\frac{x \left(a+b x^n\right)^{-1/n}}{a}","\frac{x \left(a+b x^n\right)^{-1/n}}{a}",1,"x/(a*(a + b*x^n)^n^(-1))","A",1,1,16,0.06250,1,"{191}"
2734,1,50,0,0.0107844,"\int \left(a+b x^n\right)^{-1/n} \, dx","Int[(a + b*x^n)^(-n^(-1)),x]","x \left(a+b x^n\right)^{-1/n} \left(\frac{b x^n}{a}+1\right)^{\frac{1}{n}} \, _2F_1\left(\frac{1}{n},\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)","x \left(a+b x^n\right)^{-1/n} \left(\frac{b x^n}{a}+1\right)^{\frac{1}{n}} \, _2F_1\left(\frac{1}{n},\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)",1,"(x*(1 + (b*x^n)/a)^n^(-1)*Hypergeometric2F1[n^(-1), n^(-1), 1 + n^(-1), -((b*x^n)/a)])/(a + b*x^n)^n^(-1)","A",2,2,13,0.1538,1,"{246, 245}"
2735,1,59,0,0.0125478,"\int \left(a+b x^n\right)^{-\frac{1-n}{n}} \, dx","Int[(a + b*x^n)^(-((1 - n)/n)),x]","x \left(a+b x^n\right)^{-\frac{1-n}{n}} \left(\frac{b x^n}{a}+1\right)^{\frac{1}{n}-1} \, _2F_1\left(\frac{1}{n}-1,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)","x \left(a+b x^n\right)^{-\frac{1-n}{n}} \left(\frac{b x^n}{a}+1\right)^{\frac{1}{n}-1} \, _2F_1\left(\frac{1}{n}-1,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)",1,"(x*(1 + (b*x^n)/a)^(-1 + n^(-1))*Hypergeometric2F1[-1 + n^(-1), n^(-1), 1 + n^(-1), -((b*x^n)/a)])/(a + b*x^n)^((1 - n)/n)","A",2,2,18,0.1111,1,"{246, 245}"
2736,1,56,0,0.0130124,"\int \left(a+b x^n\right)^{-\frac{1-2 n}{n}} \, dx","Int[(a + b*x^n)^(-((1 - 2*n)/n)),x]","x \left(a+b x^n\right)^{2-\frac{1}{n}} \left(\frac{b x^n}{a}+1\right)^{\frac{1}{n}-2} \, _2F_1\left(\frac{1}{n}-2,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)","x \left(a+b x^n\right)^{2-\frac{1}{n}} \left(\frac{b x^n}{a}+1\right)^{\frac{1}{n}-2} \, _2F_1\left(\frac{1}{n}-2,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)",1,"x*(a + b*x^n)^(2 - n^(-1))*(1 + (b*x^n)/a)^(-2 + n^(-1))*Hypergeometric2F1[-2 + n^(-1), n^(-1), 1 + n^(-1), -((b*x^n)/a)]","A",2,2,18,0.1111,1,"{246, 245}"
2737,1,15,0,0.0077497,"\int \frac{1}{x \left(a+b x^{-n}\right)} \, dx","Int[1/(x*(a + b/x^n)),x]","\frac{\log \left(a x^n+b\right)}{a n}","\frac{\log \left(a x^n+b\right)}{a n}",1,"Log[b + a*x^n]/(a*n)","A",2,2,15,0.1333,1,"{263, 260}"
2738,1,19,0,0.0051135,"\int \frac{x^m}{a+b x^{1+m}} \, dx","Int[x^m/(a + b*x^(1 + m)),x]","\frac{\log \left(a+b x^{m+1}\right)}{b (m+1)}","\frac{\log \left(a+b x^{m+1}\right)}{b (m+1)}",1,"Log[a + b*x^(1 + m)]/(b*(1 + m))","A",1,1,15,0.06667,1,"{260}"
2739,1,27,0,0.0096207,"\int x^m \left(a+b x^{1+m}\right)^n \, dx","Int[x^m*(a + b*x^(1 + m))^n,x]","\frac{\left(a+b x^{m+1}\right)^{n+1}}{b (m+1) (n+1)}","\frac{\left(a+b x^{m+1}\right)^{n+1}}{b (m+1) (n+1)}",1,"(a + b*x^(1 + m))^(1 + n)/(b*(1 + m)*(1 + n))","A",1,1,15,0.06667,1,"{261}"
2740,1,71,0,0.0361272,"\int x^m \left(a+b x^{2+2 m}\right)^3 \, dx","Int[x^m*(a + b*x^(2 + 2*m))^3,x]","\frac{a^2 b x^{3 (m+1)}}{m+1}+\frac{a^3 x^{m+1}}{m+1}+\frac{3 a b^2 x^{5 (m+1)}}{5 (m+1)}+\frac{b^3 x^{7 (m+1)}}{7 (m+1)}","\frac{a^2 b x^{3 (m+1)}}{m+1}+\frac{a^3 x^{m+1}}{m+1}+\frac{3 a b^2 x^{5 (m+1)}}{5 (m+1)}+\frac{b^3 x^{7 (m+1)}}{7 (m+1)}",1,"(a^3*x^(1 + m))/(1 + m) + (a^2*b*x^(3*(1 + m)))/(1 + m) + (3*a*b^2*x^(5*(1 + m)))/(5*(1 + m)) + (b^3*x^(7*(1 + m)))/(7*(1 + m))","A",2,1,17,0.05882,1,"{270}"
2741,1,52,0,0.021432,"\int x^m \left(a+b x^{2+2 m}\right)^2 \, dx","Int[x^m*(a + b*x^(2 + 2*m))^2,x]","\frac{a^2 x^{m+1}}{m+1}+\frac{2 a b x^{3 (m+1)}}{3 (m+1)}+\frac{b^2 x^{5 (m+1)}}{5 (m+1)}","\frac{a^2 x^{m+1}}{m+1}+\frac{2 a b x^{3 (m+1)}}{3 (m+1)}+\frac{b^2 x^{5 (m+1)}}{5 (m+1)}",1,"(a^2*x^(1 + m))/(1 + m) + (2*a*b*x^(3*(1 + m)))/(3*(1 + m)) + (b^2*x^(5*(1 + m)))/(5*(1 + m))","A",2,1,17,0.05882,1,"{270}"
2742,1,30,0,0.0082643,"\int x^m \left(a+b x^{2+2 m}\right) \, dx","Int[x^m*(a + b*x^(2 + 2*m)),x]","\frac{a x^{m+1}}{m+1}+\frac{b x^{3 (m+1)}}{3 (m+1)}","\frac{a x^{m+1}}{m+1}+\frac{b x^{3 (m+1)}}{3 (m+1)}",1,"(a*x^(1 + m))/(1 + m) + (b*x^(3*(1 + m)))/(3*(1 + m))","A",2,1,15,0.06667,1,"{14}"
2743,1,33,0,0.0172386,"\int \frac{x^m}{a+b x^{2+2 m}} \, dx","Int[x^m/(a + b*x^(2 + 2*m)),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x^{m+1}}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} (m+1)}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x^{m+1}}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} (m+1)}",1,"ArcTan[(Sqrt[b]*x^(1 + m))/Sqrt[a]]/(Sqrt[a]*Sqrt[b]*(1 + m))","A",2,2,17,0.1176,1,"{345, 205}"
2744,1,67,0,0.0255506,"\int \frac{x^m}{\left(a+b x^{2+2 m}\right)^2} \, dx","Int[x^m/(a + b*x^(2 + 2*m))^2,x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x^{m+1}}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} (m+1)}+\frac{x^{m+1}}{2 a (m+1) \left(a+b x^{2 (m+1)}\right)}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x^{m+1}}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} (m+1)}+\frac{x^{m+1}}{2 a (m+1) \left(a+b x^{2 (m+1)}\right)}",1,"x^(1 + m)/(2*a*(1 + m)*(a + b*x^(2*(1 + m)))) + ArcTan[(Sqrt[b]*x^(1 + m))/Sqrt[a]]/(2*a^(3/2)*Sqrt[b]*(1 + m))","A",3,3,17,0.1765,1,"{345, 199, 205}"
2745,1,97,0,0.0380523,"\int \frac{x^m}{\left(a+b x^{2+2 m}\right)^3} \, dx","Int[x^m/(a + b*x^(2 + 2*m))^3,x]","\frac{3 x^{m+1}}{8 a^2 (m+1) \left(a+b x^{2 (m+1)}\right)}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{b} x^{m+1}}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{b} (m+1)}+\frac{x^{m+1}}{4 a (m+1) \left(a+b x^{2 (m+1)}\right)^2}","\frac{3 x^{m+1}}{8 a^2 (m+1) \left(a+b x^{2 (m+1)}\right)}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{b} x^{m+1}}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{b} (m+1)}+\frac{x^{m+1}}{4 a (m+1) \left(a+b x^{2 (m+1)}\right)^2}",1,"x^(1 + m)/(4*a*(1 + m)*(a + b*x^(2*(1 + m)))^2) + (3*x^(1 + m))/(8*a^2*(1 + m)*(a + b*x^(2*(1 + m)))) + (3*ArcTan[(Sqrt[b]*x^(1 + m))/Sqrt[a]])/(8*a^(5/2)*Sqrt[b]*(1 + m))","A",4,3,17,0.1765,1,"{345, 199, 205}"
2746,1,136,0,0.0539171,"\int x^m \left(a+b x^{2+2 m}\right)^{5/2} \, dx","Int[x^m*(a + b*x^(2 + 2*m))^(5/2),x]","\frac{5 a^2 x^{m+1} \sqrt{a+b x^{2 (m+1)}}}{16 (m+1)}+\frac{5 a^3 \tanh ^{-1}\left(\frac{\sqrt{b} x^{m+1}}{\sqrt{a+b x^{2 (m+1)}}}\right)}{16 \sqrt{b} (m+1)}+\frac{x^{m+1} \left(a+b x^{2 (m+1)}\right)^{5/2}}{6 (m+1)}+\frac{5 a x^{m+1} \left(a+b x^{2 (m+1)}\right)^{3/2}}{24 (m+1)}","\frac{5 a^2 x^{m+1} \sqrt{a+b x^{2 (m+1)}}}{16 (m+1)}+\frac{5 a^3 \tanh ^{-1}\left(\frac{\sqrt{b} x^{m+1}}{\sqrt{a+b x^{2 (m+1)}}}\right)}{16 \sqrt{b} (m+1)}+\frac{x^{m+1} \left(a+b x^{2 (m+1)}\right)^{5/2}}{6 (m+1)}+\frac{5 a x^{m+1} \left(a+b x^{2 (m+1)}\right)^{3/2}}{24 (m+1)}",1,"(5*a^2*x^(1 + m)*Sqrt[a + b*x^(2*(1 + m))])/(16*(1 + m)) + (5*a*x^(1 + m)*(a + b*x^(2*(1 + m)))^(3/2))/(24*(1 + m)) + (x^(1 + m)*(a + b*x^(2*(1 + m)))^(5/2))/(6*(1 + m)) + (5*a^3*ArcTanh[(Sqrt[b]*x^(1 + m))/Sqrt[a + b*x^(2*(1 + m))]])/(16*Sqrt[b]*(1 + m))","A",6,4,19,0.2105,1,"{345, 195, 217, 206}"
2747,1,104,0,0.03923,"\int x^m \left(a+b x^{2+2 m}\right)^{3/2} \, dx","Int[x^m*(a + b*x^(2 + 2*m))^(3/2),x]","\frac{3 a^2 \tanh ^{-1}\left(\frac{\sqrt{b} x^{m+1}}{\sqrt{a+b x^{2 (m+1)}}}\right)}{8 \sqrt{b} (m+1)}+\frac{x^{m+1} \left(a+b x^{2 (m+1)}\right)^{3/2}}{4 (m+1)}+\frac{3 a x^{m+1} \sqrt{a+b x^{2 (m+1)}}}{8 (m+1)}","\frac{3 a^2 \tanh ^{-1}\left(\frac{\sqrt{b} x^{m+1}}{\sqrt{a+b x^{2 (m+1)}}}\right)}{8 \sqrt{b} (m+1)}+\frac{x^{m+1} \left(a+b x^{2 (m+1)}\right)^{3/2}}{4 (m+1)}+\frac{3 a x^{m+1} \sqrt{a+b x^{2 (m+1)}}}{8 (m+1)}",1,"(3*a*x^(1 + m)*Sqrt[a + b*x^(2*(1 + m))])/(8*(1 + m)) + (x^(1 + m)*(a + b*x^(2*(1 + m)))^(3/2))/(4*(1 + m)) + (3*a^2*ArcTanh[(Sqrt[b]*x^(1 + m))/Sqrt[a + b*x^(2*(1 + m))]])/(8*Sqrt[b]*(1 + m))","A",5,4,19,0.2105,1,"{345, 195, 217, 206}"
2748,1,72,0,0.028386,"\int x^m \sqrt{a+b x^{2+2 m}} \, dx","Int[x^m*Sqrt[a + b*x^(2 + 2*m)],x]","\frac{x^{m+1} \sqrt{a+b x^{2 (m+1)}}}{2 (m+1)}+\frac{a \tanh ^{-1}\left(\frac{\sqrt{b} x^{m+1}}{\sqrt{a+b x^{2 (m+1)}}}\right)}{2 \sqrt{b} (m+1)}","\frac{x^{m+1} \sqrt{a+b x^{2 (m+1)}}}{2 (m+1)}+\frac{a \tanh ^{-1}\left(\frac{\sqrt{b} x^{m+1}}{\sqrt{a+b x^{2 (m+1)}}}\right)}{2 \sqrt{b} (m+1)}",1,"(x^(1 + m)*Sqrt[a + b*x^(2*(1 + m))])/(2*(1 + m)) + (a*ArcTanh[(Sqrt[b]*x^(1 + m))/Sqrt[a + b*x^(2*(1 + m))]])/(2*Sqrt[b]*(1 + m))","A",4,4,19,0.2105,1,"{345, 195, 217, 206}"
2749,1,38,0,0.0199075,"\int \frac{x^m}{\sqrt{a+b x^{2+2 m}}} \, dx","Int[x^m/Sqrt[a + b*x^(2 + 2*m)],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x^{m+1}}{\sqrt{a+b x^{2 (m+1)}}}\right)}{\sqrt{b} (m+1)}","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x^{m+1}}{\sqrt{a+b x^{2 (m+1)}}}\right)}{\sqrt{b} (m+1)}",1,"ArcTanh[(Sqrt[b]*x^(1 + m))/Sqrt[a + b*x^(2*(1 + m))]]/(Sqrt[b]*(1 + m))","A",3,3,19,0.1579,1,"{345, 217, 206}"
2750,1,29,0,0.0081341,"\int \frac{x^m}{\left(a+b x^{2+2 m}\right)^{3/2}} \, dx","Int[x^m/(a + b*x^(2 + 2*m))^(3/2),x]","\frac{x^{m+1}}{a (m+1) \sqrt{a+b x^{2 (m+1)}}}","\frac{x^{m+1}}{a (m+1) \sqrt{a+b x^{2 (m+1)}}}",1,"x^(1 + m)/(a*(1 + m)*Sqrt[a + b*x^(2*(1 + m))])","A",1,1,19,0.05263,1,"{264}"
2751,1,65,0,0.0254742,"\int \frac{x^m}{\left(a+b x^{2+2 m}\right)^{5/2}} \, dx","Int[x^m/(a + b*x^(2 + 2*m))^(5/2),x]","\frac{2 b x^{3 (m+1)}}{3 a^2 (m+1) \left(a+b x^{2 (m+1)}\right)^{3/2}}+\frac{x^{m+1}}{a (m+1) \left(a+b x^{2 (m+1)}\right)^{3/2}}","\frac{2 b x^{3 (m+1)}}{3 a^2 (m+1) \left(a+b x^{2 (m+1)}\right)^{3/2}}+\frac{x^{m+1}}{a (m+1) \left(a+b x^{2 (m+1)}\right)^{3/2}}",1,"x^(1 + m)/(a*(1 + m)*(a + b*x^(2*(1 + m)))^(3/2)) + (2*b*x^(3*(1 + m)))/(3*a^2*(1 + m)*(a + b*x^(2*(1 + m)))^(3/2))","A",2,2,19,0.1053,1,"{271, 264}"
2752,1,102,0,0.0537406,"\int \frac{x^m}{\left(a+b x^{2+2 m}\right)^{7/2}} \, dx","Int[x^m/(a + b*x^(2 + 2*m))^(7/2),x]","\frac{8 b^2 x^{5 (m+1)}}{15 a^3 (m+1) \left(a+b x^{2 (m+1)}\right)^{5/2}}+\frac{4 b x^{3 (m+1)}}{3 a^2 (m+1) \left(a+b x^{2 (m+1)}\right)^{5/2}}+\frac{x^{m+1}}{a (m+1) \left(a+b x^{2 (m+1)}\right)^{5/2}}","\frac{8 b^2 x^{5 (m+1)}}{15 a^3 (m+1) \left(a+b x^{2 (m+1)}\right)^{5/2}}+\frac{4 b x^{3 (m+1)}}{3 a^2 (m+1) \left(a+b x^{2 (m+1)}\right)^{5/2}}+\frac{x^{m+1}}{a (m+1) \left(a+b x^{2 (m+1)}\right)^{5/2}}",1,"x^(1 + m)/(a*(1 + m)*(a + b*x^(2*(1 + m)))^(5/2)) + (4*b*x^(3*(1 + m)))/(3*a^2*(1 + m)*(a + b*x^(2*(1 + m)))^(5/2)) + (8*b^2*x^(5*(1 + m)))/(15*a^3*(1 + m)*(a + b*x^(2*(1 + m)))^(5/2))","A",3,2,19,0.1053,1,"{271, 264}"
2753,1,20,0,0.0047202,"\int x^n \sqrt{1+x^{1+n}} \, dx","Int[x^n*Sqrt[1 + x^(1 + n)],x]","\frac{2 \left(x^{n+1}+1\right)^{3/2}}{3 (n+1)}","\frac{2 \left(x^{n+1}+1\right)^{3/2}}{3 (n+1)}",1,"(2*(1 + x^(1 + n))^(3/2))/(3*(1 + n))","A",1,1,15,0.06667,1,"{261}"
2754,1,22,0,0.0049375,"\int x^n \sqrt{a^2+x^{1+n}} \, dx","Int[x^n*Sqrt[a^2 + x^(1 + n)],x]","\frac{2 \left(a^2+x^{n+1}\right)^{3/2}}{3 (n+1)}","\frac{2 \left(a^2+x^{n+1}\right)^{3/2}}{3 (n+1)}",1,"(2*(a^2 + x^(1 + n))^(3/2))/(3*(1 + n))","A",1,1,17,0.05882,1,"{261}"
2755,1,64,0,0.0334044,"\int (c x)^m \left(a+b x^n\right)^2 \, dx","Int[(c*x)^m*(a + b*x^n)^2,x]","\frac{a^2 (c x)^{m+1}}{c (m+1)}+\frac{2 a b x^{n+1} (c x)^m}{m+n+1}+\frac{b^2 x^{2 n+1} (c x)^m}{m+2 n+1}","\frac{a^2 (c x)^{m+1}}{c (m+1)}+\frac{2 a b x^{n+1} (c x)^m}{m+n+1}+\frac{b^2 x^{2 n+1} (c x)^m}{m+2 n+1}",1,"(2*a*b*x^(1 + n)*(c*x)^m)/(1 + m + n) + (b^2*x^(1 + 2*n)*(c*x)^m)/(1 + m + 2*n) + (a^2*(c*x)^(1 + m))/(c*(1 + m))","A",6,3,15,0.2000,1,"{270, 20, 30}"
2756,1,58,0,0.0298515,"\int (c x)^m \left(a+b x^3\right)^2 \, dx","Int[(c*x)^m*(a + b*x^3)^2,x]","\frac{a^2 (c x)^{m+1}}{c (m+1)}+\frac{2 a b (c x)^{m+4}}{c^4 (m+4)}+\frac{b^2 (c x)^{m+7}}{c^7 (m+7)}","\frac{a^2 (c x)^{m+1}}{c (m+1)}+\frac{2 a b (c x)^{m+4}}{c^4 (m+4)}+\frac{b^2 (c x)^{m+7}}{c^7 (m+7)}",1,"(a^2*(c*x)^(1 + m))/(c*(1 + m)) + (2*a*b*(c*x)^(4 + m))/(c^4*(4 + m)) + (b^2*(c*x)^(7 + m))/(c^7*(7 + m))","A",2,1,15,0.06667,1,"{270}"
2757,1,58,0,0.0266718,"\int (c x)^m \left(a+b x^2\right)^2 \, dx","Int[(c*x)^m*(a + b*x^2)^2,x]","\frac{a^2 (c x)^{m+1}}{c (m+1)}+\frac{2 a b (c x)^{m+3}}{c^3 (m+3)}+\frac{b^2 (c x)^{m+5}}{c^5 (m+5)}","\frac{a^2 (c x)^{m+1}}{c (m+1)}+\frac{2 a b (c x)^{m+3}}{c^3 (m+3)}+\frac{b^2 (c x)^{m+5}}{c^5 (m+5)}",1,"(a^2*(c*x)^(1 + m))/(c*(1 + m)) + (2*a*b*(c*x)^(3 + m))/(c^3*(3 + m)) + (b^2*(c*x)^(5 + m))/(c^5*(5 + m))","A",2,1,15,0.06667,1,"{270}"
2758,1,58,0,0.0230505,"\int (c x)^m (a+b x)^2 \, dx","Int[(c*x)^m*(a + b*x)^2,x]","\frac{a^2 (c x)^{m+1}}{c (m+1)}+\frac{2 a b (c x)^{m+2}}{c^2 (m+2)}+\frac{b^2 (c x)^{m+3}}{c^3 (m+3)}","\frac{a^2 (c x)^{m+1}}{c (m+1)}+\frac{2 a b (c x)^{m+2}}{c^2 (m+2)}+\frac{b^2 (c x)^{m+3}}{c^3 (m+3)}",1,"(a^2*(c*x)^(1 + m))/(c*(1 + m)) + (2*a*b*(c*x)^(2 + m))/(c^2*(2 + m)) + (b^2*(c*x)^(3 + m))/(c^3*(3 + m))","A",2,1,13,0.07692,1,"{43}"
2759,1,52,0,0.0220231,"\int \left(a+\frac{b}{x}\right)^2 (c x)^m \, dx","Int[(a + b/x)^2*(c*x)^m,x]","\frac{a^2 (c x)^{m+1}}{c (m+1)}+\frac{2 a b (c x)^m}{m}-\frac{b^2 c (c x)^{m-1}}{1-m}","\frac{a^2 (c x)^{m+1}}{c (m+1)}+\frac{2 a b (c x)^m}{m}-\frac{b^2 c (c x)^{m-1}}{1-m}",1,"-((b^2*c*(c*x)^(-1 + m))/(1 - m)) + (2*a*b*(c*x)^m)/m + (a^2*(c*x)^(1 + m))/(c*(1 + m))","A",2,1,15,0.06667,1,"{270}"
2760,1,61,0,0.0287716,"\int \left(a+\frac{b}{x^2}\right)^2 (c x)^m \, dx","Int[(a + b/x^2)^2*(c*x)^m,x]","\frac{a^2 (c x)^{m+1}}{c (m+1)}-\frac{2 a b c (c x)^{m-1}}{1-m}-\frac{b^2 c^3 (c x)^{m-3}}{3-m}","\frac{a^2 (c x)^{m+1}}{c (m+1)}-\frac{2 a b c (c x)^{m-1}}{1-m}-\frac{b^2 c^3 (c x)^{m-3}}{3-m}",1,"-((b^2*c^3*(c*x)^(-3 + m))/(3 - m)) - (2*a*b*c*(c*x)^(-1 + m))/(1 - m) + (a^2*(c*x)^(1 + m))/(c*(1 + m))","A",2,1,15,0.06667,1,"{270}"
2761,1,63,0,0.0288464,"\int \left(a+\frac{b}{x^3}\right)^2 (c x)^m \, dx","Int[(a + b/x^3)^2*(c*x)^m,x]","\frac{a^2 (c x)^{m+1}}{c (m+1)}-\frac{2 a b c^2 (c x)^{m-2}}{2-m}-\frac{b^2 c^5 (c x)^{m-5}}{5-m}","\frac{a^2 (c x)^{m+1}}{c (m+1)}-\frac{2 a b c^2 (c x)^{m-2}}{2-m}-\frac{b^2 c^5 (c x)^{m-5}}{5-m}",1,"-((b^2*c^5*(c*x)^(-5 + m))/(5 - m)) - (2*a*b*c^2*(c*x)^(-2 + m))/(2 - m) + (a^2*(c*x)^(1 + m))/(c*(1 + m))","A",2,1,15,0.06667,1,"{270}"
2762,1,74,0,0.0365788,"\int \frac{(c x)^{-1-\frac{n}{2}}}{a+b x^n} \, dx","Int[(c*x)^(-1 - n/2)/(a + b*x^n),x]","\frac{2 \sqrt{b} x^{n/2} (c x)^{-n/2} \tan ^{-1}\left(\frac{\sqrt{a} x^{-n/2}}{\sqrt{b}}\right)}{a^{3/2} c n}-\frac{2 (c x)^{-n/2}}{a c n}","\frac{2 \sqrt{b} x^{n/2} (c x)^{-n/2} \tan ^{-1}\left(\frac{\sqrt{a} x^{-n/2}}{\sqrt{b}}\right)}{a^{3/2} c n}-\frac{2 (c x)^{-n/2}}{a c n}",1,"-2/(a*c*n*(c*x)^(n/2)) + (2*Sqrt[b]*x^(n/2)*ArcTan[Sqrt[a]/(Sqrt[b]*x^(n/2))])/(a^(3/2)*c*n*(c*x)^(n/2))","A",5,5,21,0.2381,1,"{347, 345, 193, 321, 205}"
2763,1,222,0,0.1381058,"\int \frac{(c x)^{-1-\frac{2 n}{3}}}{a+b x^n} \, dx","Int[(c*x)^(-1 - (2*n)/3)/(a + b*x^n),x]","-\frac{b^{2/3} x^{2 n/3} (c x)^{-2 n/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x^{n/3}\right)}{a^{5/3} c n}+\frac{b^{2/3} x^{2 n/3} (c x)^{-2 n/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x^{n/3}+b^{2/3} x^{2 n/3}\right)}{2 a^{5/3} c n}+\frac{\sqrt{3} b^{2/3} x^{2 n/3} (c x)^{-2 n/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x^{n/3}}{\sqrt{3} \sqrt[3]{a}}\right)}{a^{5/3} c n}-\frac{3 (c x)^{-2 n/3}}{2 a c n}","-\frac{b^{2/3} x^{2 n/3} (c x)^{-2 n/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x^{n/3}\right)}{a^{5/3} c n}+\frac{b^{2/3} x^{2 n/3} (c x)^{-2 n/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x^{n/3}+b^{2/3} x^{2 n/3}\right)}{2 a^{5/3} c n}+\frac{\sqrt{3} b^{2/3} x^{2 n/3} (c x)^{-2 n/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x^{n/3}}{\sqrt{3} \sqrt[3]{a}}\right)}{a^{5/3} c n}-\frac{3 (c x)^{-2 n/3}}{2 a c n}",1,"-3/(2*a*c*n*(c*x)^((2*n)/3)) + (Sqrt[3]*b^(2/3)*x^((2*n)/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x^(n/3))/(Sqrt[3]*a^(1/3))])/(a^(5/3)*c*n*(c*x)^((2*n)/3)) - (b^(2/3)*x^((2*n)/3)*Log[a^(1/3) + b^(1/3)*x^(n/3)])/(a^(5/3)*c*n*(c*x)^((2*n)/3)) + (b^(2/3)*x^((2*n)/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x^(n/3) + b^(2/3)*x^((2*n)/3)])/(2*a^(5/3)*c*n*(c*x)^((2*n)/3))","A",9,9,21,0.4286,1,"{363, 362, 345, 200, 31, 634, 617, 204, 628}"
2764,1,317,0,0.242825,"\int \frac{(c x)^{-1-\frac{3 n}{4}}}{a+b x^n} \, dx","Int[(c*x)^(-1 - (3*n)/4)/(a + b*x^n),x]","\frac{b^{3/4} x^{3 n/4} (c x)^{-3 n/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x^{n/4}+\sqrt{a}+\sqrt{b} x^{n/2}\right)}{\sqrt{2} a^{7/4} c n}-\frac{b^{3/4} x^{3 n/4} (c x)^{-3 n/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x^{n/4}+\sqrt{a}+\sqrt{b} x^{n/2}\right)}{\sqrt{2} a^{7/4} c n}+\frac{\sqrt{2} b^{3/4} x^{3 n/4} (c x)^{-3 n/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x^{n/4}}{\sqrt[4]{a}}\right)}{a^{7/4} c n}-\frac{\sqrt{2} b^{3/4} x^{3 n/4} (c x)^{-3 n/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x^{n/4}}{\sqrt[4]{a}}+1\right)}{a^{7/4} c n}-\frac{4 (c x)^{-3 n/4}}{3 a c n}","\frac{b^{3/4} x^{3 n/4} (c x)^{-3 n/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x^{n/4}+\sqrt{a}+\sqrt{b} x^{n/2}\right)}{\sqrt{2} a^{7/4} c n}-\frac{b^{3/4} x^{3 n/4} (c x)^{-3 n/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x^{n/4}+\sqrt{a}+\sqrt{b} x^{n/2}\right)}{\sqrt{2} a^{7/4} c n}+\frac{\sqrt{2} b^{3/4} x^{3 n/4} (c x)^{-3 n/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x^{n/4}}{\sqrt[4]{a}}\right)}{a^{7/4} c n}-\frac{\sqrt{2} b^{3/4} x^{3 n/4} (c x)^{-3 n/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x^{n/4}}{\sqrt[4]{a}}+1\right)}{a^{7/4} c n}-\frac{4 (c x)^{-3 n/4}}{3 a c n}",1,"-4/(3*a*c*n*(c*x)^((3*n)/4)) + (Sqrt[2]*b^(3/4)*x^((3*n)/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*x^(n/4))/a^(1/4)])/(a^(7/4)*c*n*(c*x)^((3*n)/4)) - (Sqrt[2]*b^(3/4)*x^((3*n)/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*x^(n/4))/a^(1/4)])/(a^(7/4)*c*n*(c*x)^((3*n)/4)) + (b^(3/4)*x^((3*n)/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x^(n/4) + Sqrt[b]*x^(n/2)])/(Sqrt[2]*a^(7/4)*c*n*(c*x)^((3*n)/4)) - (b^(3/4)*x^((3*n)/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x^(n/4) + Sqrt[b]*x^(n/2)])/(Sqrt[2]*a^(7/4)*c*n*(c*x)^((3*n)/4))","A",12,9,21,0.4286,1,"{363, 362, 345, 211, 1165, 628, 1162, 617, 204}"
2765,1,69,0,0.037959,"\int \frac{(c x)^{-1-n}}{a+b x^n} \, dx","Int[(c*x)^(-1 - n)/(a + b*x^n),x]","-\frac{b x^n \log (x) (c x)^{-n}}{a^2 c}+\frac{b x^n (c x)^{-n} \log \left(a+b x^n\right)}{a^2 c n}-\frac{(c x)^{-n}}{a c n}","-\frac{b x^n \log (x) (c x)^{-n}}{a^2 c}+\frac{b x^n (c x)^{-n} \log \left(a+b x^n\right)}{a^2 c n}-\frac{(c x)^{-n}}{a c n}",1,"-(1/(a*c*n*(c*x)^n)) - (b*x^n*Log[x])/(a^2*c*(c*x)^n) + (b*x^n*Log[a + b*x^n])/(a^2*c*n*(c*x)^n)","A",4,3,19,0.1579,1,"{268, 266, 44}"
2766,1,74,0,0.0363829,"\int \frac{(c x)^{-1-\frac{n}{2}}}{a+b x^n} \, dx","Int[(c*x)^(-1 - n/2)/(a + b*x^n),x]","\frac{2 \sqrt{b} x^{n/2} (c x)^{-n/2} \tan ^{-1}\left(\frac{\sqrt{a} x^{-n/2}}{\sqrt{b}}\right)}{a^{3/2} c n}-\frac{2 (c x)^{-n/2}}{a c n}","\frac{2 \sqrt{b} x^{n/2} (c x)^{-n/2} \tan ^{-1}\left(\frac{\sqrt{a} x^{-n/2}}{\sqrt{b}}\right)}{a^{3/2} c n}-\frac{2 (c x)^{-n/2}}{a c n}",1,"-2/(a*c*n*(c*x)^(n/2)) + (2*Sqrt[b]*x^(n/2)*ArcTan[Sqrt[a]/(Sqrt[b]*x^(n/2))])/(a^(3/2)*c*n*(c*x)^(n/2))","A",5,5,21,0.2381,1,"{347, 345, 193, 321, 205}"
2767,1,220,0,0.1374705,"\int \frac{(c x)^{-1-\frac{n}{3}}}{a+b x^n} \, dx","Int[(c*x)^(-1 - n/3)/(a + b*x^n),x]","-\frac{\sqrt[3]{b} x^{n/3} (c x)^{-n/3} \log \left(a^{2/3} x^{-2 n/3}-\sqrt[3]{a} \sqrt[3]{b} x^{-n/3}+b^{2/3}\right)}{2 a^{4/3} c n}+\frac{\sqrt[3]{b} x^{n/3} (c x)^{-n/3} \log \left(\sqrt[3]{a} x^{-n/3}+\sqrt[3]{b}\right)}{a^{4/3} c n}-\frac{\sqrt{3} \sqrt[3]{b} x^{n/3} (c x)^{-n/3} \tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a} x^{-n/3}}{\sqrt{3} \sqrt[3]{b}}\right)}{a^{4/3} c n}-\frac{3 (c x)^{-n/3}}{a c n}","-\frac{\sqrt[3]{b} x^{n/3} (c x)^{-n/3} \log \left(a^{2/3} x^{-2 n/3}-\sqrt[3]{a} \sqrt[3]{b} x^{-n/3}+b^{2/3}\right)}{2 a^{4/3} c n}+\frac{\sqrt[3]{b} x^{n/3} (c x)^{-n/3} \log \left(\sqrt[3]{a} x^{-n/3}+\sqrt[3]{b}\right)}{a^{4/3} c n}-\frac{\sqrt{3} \sqrt[3]{b} x^{n/3} (c x)^{-n/3} \tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a} x^{-n/3}}{\sqrt{3} \sqrt[3]{b}}\right)}{a^{4/3} c n}-\frac{3 (c x)^{-n/3}}{a c n}",1,"-3/(a*c*n*(c*x)^(n/3)) - (Sqrt[3]*b^(1/3)*x^(n/3)*ArcTan[(b^(1/3) - (2*a^(1/3))/x^(n/3))/(Sqrt[3]*b^(1/3))])/(a^(4/3)*c*n*(c*x)^(n/3)) + (b^(1/3)*x^(n/3)*Log[b^(1/3) + a^(1/3)/x^(n/3)])/(a^(4/3)*c*n*(c*x)^(n/3)) - (b^(1/3)*x^(n/3)*Log[b^(2/3) + a^(2/3)/x^((2*n)/3) - (a^(1/3)*b^(1/3))/x^(n/3)])/(2*a^(4/3)*c*n*(c*x)^(n/3))","A",10,10,21,0.4762,1,"{347, 345, 193, 321, 200, 31, 634, 617, 204, 628}"
2768,1,315,0,0.2280679,"\int \frac{(c x)^{-1-\frac{n}{4}}}{a+b x^n} \, dx","Int[(c*x)^(-1 - n/4)/(a + b*x^n),x]","-\frac{\sqrt[4]{b} x^{n/4} (c x)^{-n/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x^{-n/4}+\sqrt{a} x^{-n/2}+\sqrt{b}\right)}{\sqrt{2} a^{5/4} c n}+\frac{\sqrt[4]{b} x^{n/4} (c x)^{-n/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x^{-n/4}+\sqrt{a} x^{-n/2}+\sqrt{b}\right)}{\sqrt{2} a^{5/4} c n}-\frac{\sqrt{2} \sqrt[4]{b} x^{n/4} (c x)^{-n/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a} x^{-n/4}}{\sqrt[4]{b}}\right)}{a^{5/4} c n}+\frac{\sqrt{2} \sqrt[4]{b} x^{n/4} (c x)^{-n/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} x^{-n/4}}{\sqrt[4]{b}}+1\right)}{a^{5/4} c n}-\frac{4 (c x)^{-n/4}}{a c n}","-\frac{\sqrt[4]{b} x^{n/4} (c x)^{-n/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x^{-n/4}+\sqrt{a} x^{-n/2}+\sqrt{b}\right)}{\sqrt{2} a^{5/4} c n}+\frac{\sqrt[4]{b} x^{n/4} (c x)^{-n/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x^{-n/4}+\sqrt{a} x^{-n/2}+\sqrt{b}\right)}{\sqrt{2} a^{5/4} c n}-\frac{\sqrt{2} \sqrt[4]{b} x^{n/4} (c x)^{-n/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a} x^{-n/4}}{\sqrt[4]{b}}\right)}{a^{5/4} c n}+\frac{\sqrt{2} \sqrt[4]{b} x^{n/4} (c x)^{-n/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} x^{-n/4}}{\sqrt[4]{b}}+1\right)}{a^{5/4} c n}-\frac{4 (c x)^{-n/4}}{a c n}",1,"-4/(a*c*n*(c*x)^(n/4)) - (Sqrt[2]*b^(1/4)*x^(n/4)*ArcTan[1 - (Sqrt[2]*a^(1/4))/(b^(1/4)*x^(n/4))])/(a^(5/4)*c*n*(c*x)^(n/4)) + (Sqrt[2]*b^(1/4)*x^(n/4)*ArcTan[1 + (Sqrt[2]*a^(1/4))/(b^(1/4)*x^(n/4))])/(a^(5/4)*c*n*(c*x)^(n/4)) - (b^(1/4)*x^(n/4)*Log[Sqrt[b] + Sqrt[a]/x^(n/2) - (Sqrt[2]*a^(1/4)*b^(1/4))/x^(n/4)])/(Sqrt[2]*a^(5/4)*c*n*(c*x)^(n/4)) + (b^(1/4)*x^(n/4)*Log[Sqrt[b] + Sqrt[a]/x^(n/2) + (Sqrt[2]*a^(1/4)*b^(1/4))/x^(n/4)])/(Sqrt[2]*a^(5/4)*c*n*(c*x)^(n/4))","A",13,10,21,0.4762,1,"{347, 345, 193, 321, 211, 1165, 628, 1162, 617, 204}"
2769,1,100,0,0.0522623,"\int \frac{(c x)^{-1-\frac{3 n}{2}}}{a+b x^n} \, dx","Int[(c*x)^(-1 - (3*n)/2)/(a + b*x^n),x]","-\frac{2 b^{3/2} x^{3 n/2} (c x)^{-3 n/2} \tan ^{-1}\left(\frac{\sqrt{a} x^{-n/2}}{\sqrt{b}}\right)}{a^{5/2} c n}+\frac{2 b x^n (c x)^{-3 n/2}}{a^2 c n}-\frac{2 (c x)^{-3 n/2}}{3 a c n}","-\frac{2 b^{3/2} x^{3 n/2} (c x)^{-3 n/2} \tan ^{-1}\left(\frac{\sqrt{a} x^{-n/2}}{\sqrt{b}}\right)}{a^{5/2} c n}+\frac{2 b x^n (c x)^{-3 n/2}}{a^2 c n}-\frac{2 (c x)^{-3 n/2}}{3 a c n}",1,"-2/(3*a*c*n*(c*x)^((3*n)/2)) + (2*b*x^n)/(a^2*c*n*(c*x)^((3*n)/2)) - (2*b^(3/2)*x^((3*n)/2)*ArcTan[Sqrt[a]/(Sqrt[b]*x^(n/2))])/(a^(5/2)*c*n*(c*x)^((3*n)/2))","A",6,6,21,0.2857,1,"{363, 362, 345, 193, 321, 205}"
2770,1,246,0,0.1508597,"\int \frac{(c x)^{-1-\frac{4 n}{3}}}{a+b x^n} \, dx","Int[(c*x)^(-1 - (4*n)/3)/(a + b*x^n),x]","-\frac{b^{4/3} x^{4 n/3} (c x)^{-4 n/3} \log \left(\sqrt[3]{a} x^{-n/3}+\sqrt[3]{b}\right)}{a^{7/3} c n}+\frac{b^{4/3} x^{4 n/3} (c x)^{-4 n/3} \log \left(a^{2/3} x^{-2 n/3}-\sqrt[3]{a} \sqrt[3]{b} x^{-n/3}+b^{2/3}\right)}{2 a^{7/3} c n}+\frac{\sqrt{3} b^{4/3} x^{4 n/3} (c x)^{-4 n/3} \tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a} x^{-n/3}}{\sqrt{3} \sqrt[3]{b}}\right)}{a^{7/3} c n}+\frac{3 b x^n (c x)^{-4 n/3}}{a^2 c n}-\frac{3 (c x)^{-4 n/3}}{4 a c n}","-\frac{b^{4/3} x^{4 n/3} (c x)^{-4 n/3} \log \left(\sqrt[3]{a} x^{-n/3}+\sqrt[3]{b}\right)}{a^{7/3} c n}+\frac{b^{4/3} x^{4 n/3} (c x)^{-4 n/3} \log \left(a^{2/3} x^{-2 n/3}-\sqrt[3]{a} \sqrt[3]{b} x^{-n/3}+b^{2/3}\right)}{2 a^{7/3} c n}+\frac{\sqrt{3} b^{4/3} x^{4 n/3} (c x)^{-4 n/3} \tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a} x^{-n/3}}{\sqrt{3} \sqrt[3]{b}}\right)}{a^{7/3} c n}+\frac{3 b x^n (c x)^{-4 n/3}}{a^2 c n}-\frac{3 (c x)^{-4 n/3}}{4 a c n}",1,"-3/(4*a*c*n*(c*x)^((4*n)/3)) + (3*b*x^n)/(a^2*c*n*(c*x)^((4*n)/3)) + (Sqrt[3]*b^(4/3)*x^((4*n)/3)*ArcTan[(b^(1/3) - (2*a^(1/3))/x^(n/3))/(Sqrt[3]*b^(1/3))])/(a^(7/3)*c*n*(c*x)^((4*n)/3)) - (b^(4/3)*x^((4*n)/3)*Log[b^(1/3) + a^(1/3)/x^(n/3)])/(a^(7/3)*c*n*(c*x)^((4*n)/3)) + (b^(4/3)*x^((4*n)/3)*Log[b^(2/3) + a^(2/3)/x^((2*n)/3) - (a^(1/3)*b^(1/3))/x^(n/3)])/(2*a^(7/3)*c*n*(c*x)^((4*n)/3))","A",11,11,21,0.5238,1,"{363, 362, 345, 193, 321, 200, 31, 634, 617, 204, 628}"
2771,1,341,0,0.236374,"\int \frac{(c x)^{-1-\frac{5 n}{4}}}{a+b x^n} \, dx","Int[(c*x)^(-1 - (5*n)/4)/(a + b*x^n),x]","\frac{b^{5/4} x^{5 n/4} (c x)^{-5 n/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x^{-n/4}+\sqrt{a} x^{-n/2}+\sqrt{b}\right)}{\sqrt{2} a^{9/4} c n}-\frac{b^{5/4} x^{5 n/4} (c x)^{-5 n/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x^{-n/4}+\sqrt{a} x^{-n/2}+\sqrt{b}\right)}{\sqrt{2} a^{9/4} c n}+\frac{\sqrt{2} b^{5/4} x^{5 n/4} (c x)^{-5 n/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a} x^{-n/4}}{\sqrt[4]{b}}\right)}{a^{9/4} c n}-\frac{\sqrt{2} b^{5/4} x^{5 n/4} (c x)^{-5 n/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} x^{-n/4}}{\sqrt[4]{b}}+1\right)}{a^{9/4} c n}+\frac{4 b x^n (c x)^{-5 n/4}}{a^2 c n}-\frac{4 (c x)^{-5 n/4}}{5 a c n}","\frac{b^{5/4} x^{5 n/4} (c x)^{-5 n/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x^{-n/4}+\sqrt{a} x^{-n/2}+\sqrt{b}\right)}{\sqrt{2} a^{9/4} c n}-\frac{b^{5/4} x^{5 n/4} (c x)^{-5 n/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x^{-n/4}+\sqrt{a} x^{-n/2}+\sqrt{b}\right)}{\sqrt{2} a^{9/4} c n}+\frac{\sqrt{2} b^{5/4} x^{5 n/4} (c x)^{-5 n/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a} x^{-n/4}}{\sqrt[4]{b}}\right)}{a^{9/4} c n}-\frac{\sqrt{2} b^{5/4} x^{5 n/4} (c x)^{-5 n/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} x^{-n/4}}{\sqrt[4]{b}}+1\right)}{a^{9/4} c n}+\frac{4 b x^n (c x)^{-5 n/4}}{a^2 c n}-\frac{4 (c x)^{-5 n/4}}{5 a c n}",1,"-4/(5*a*c*n*(c*x)^((5*n)/4)) + (4*b*x^n)/(a^2*c*n*(c*x)^((5*n)/4)) + (Sqrt[2]*b^(5/4)*x^((5*n)/4)*ArcTan[1 - (Sqrt[2]*a^(1/4))/(b^(1/4)*x^(n/4))])/(a^(9/4)*c*n*(c*x)^((5*n)/4)) - (Sqrt[2]*b^(5/4)*x^((5*n)/4)*ArcTan[1 + (Sqrt[2]*a^(1/4))/(b^(1/4)*x^(n/4))])/(a^(9/4)*c*n*(c*x)^((5*n)/4)) + (b^(5/4)*x^((5*n)/4)*Log[Sqrt[b] + Sqrt[a]/x^(n/2) - (Sqrt[2]*a^(1/4)*b^(1/4))/x^(n/4)])/(Sqrt[2]*a^(9/4)*c*n*(c*x)^((5*n)/4)) - (b^(5/4)*x^((5*n)/4)*Log[Sqrt[b] + Sqrt[a]/x^(n/2) + (Sqrt[2]*a^(1/4)*b^(1/4))/x^(n/4)])/(Sqrt[2]*a^(9/4)*c*n*(c*x)^((5*n)/4))","A",14,11,21,0.5238,1,"{363, 362, 345, 193, 321, 211, 1165, 628, 1162, 617, 204}"
2772,1,44,0,0.0176047,"\int \frac{(c x)^{4+n}}{a+b x^n} \, dx","Int[(c*x)^(4 + n)/(a + b*x^n),x]","\frac{(c x)^{n+5} \, _2F_1\left(1,\frac{n+5}{n};2+\frac{5}{n};-\frac{b x^n}{a}\right)}{a c (n+5)}","\frac{(c x)^{n+5} \, _2F_1\left(1,\frac{n+5}{n};2+\frac{5}{n};-\frac{b x^n}{a}\right)}{a c (n+5)}",1,"((c*x)^(5 + n)*Hypergeometric2F1[1, (5 + n)/n, 2 + 5/n, -((b*x^n)/a)])/(a*c*(5 + n))","A",1,1,17,0.05882,1,"{364}"
2773,1,46,0,0.0130571,"\int \frac{(c x)^{3+n}}{a+b x^n} \, dx","Int[(c*x)^(3 + n)/(a + b*x^n),x]","\frac{(c x)^{n+4} \, _2F_1\left(1,\frac{n+4}{n};2 \left(1+\frac{2}{n}\right);-\frac{b x^n}{a}\right)}{a c (n+4)}","\frac{(c x)^{n+4} \, _2F_1\left(1,\frac{n+4}{n};2 \left(1+\frac{2}{n}\right);-\frac{b x^n}{a}\right)}{a c (n+4)}",1,"((c*x)^(4 + n)*Hypergeometric2F1[1, (4 + n)/n, 2*(1 + 2/n), -((b*x^n)/a)])/(a*c*(4 + n))","A",1,1,17,0.05882,1,"{364}"
2774,1,44,0,0.0132325,"\int \frac{(c x)^{2+n}}{a+b x^n} \, dx","Int[(c*x)^(2 + n)/(a + b*x^n),x]","\frac{(c x)^{n+3} \, _2F_1\left(1,\frac{n+3}{n};2+\frac{3}{n};-\frac{b x^n}{a}\right)}{a c (n+3)}","\frac{(c x)^{n+3} \, _2F_1\left(1,\frac{n+3}{n};2+\frac{3}{n};-\frac{b x^n}{a}\right)}{a c (n+3)}",1,"((c*x)^(3 + n)*Hypergeometric2F1[1, (3 + n)/n, 2 + 3/n, -((b*x^n)/a)])/(a*c*(3 + n))","A",1,1,17,0.05882,1,"{364}"
2775,1,44,0,0.0130062,"\int \frac{(c x)^{1+n}}{a+b x^n} \, dx","Int[(c*x)^(1 + n)/(a + b*x^n),x]","\frac{(c x)^{n+2} \, _2F_1\left(1,\frac{n+2}{n};2 \left(1+\frac{1}{n}\right);-\frac{b x^n}{a}\right)}{a c (n+2)}","\frac{(c x)^{n+2} \, _2F_1\left(1,\frac{n+2}{n};2 \left(1+\frac{1}{n}\right);-\frac{b x^n}{a}\right)}{a c (n+2)}",1,"((c*x)^(2 + n)*Hypergeometric2F1[1, (2 + n)/n, 2*(1 + n^(-1)), -((b*x^n)/a)])/(a*c*(2 + n))","A",1,1,17,0.05882,1,"{364}"
2776,1,40,0,0.012494,"\int \frac{(c x)^n}{a+b x^n} \, dx","Int[(c*x)^n/(a + b*x^n),x]","\frac{(c x)^{n+1} \, _2F_1\left(1,1+\frac{1}{n};2+\frac{1}{n};-\frac{b x^n}{a}\right)}{a c (n+1)}","\frac{(c x)^{n+1} \, _2F_1\left(1,1+\frac{1}{n};2+\frac{1}{n};-\frac{b x^n}{a}\right)}{a c (n+1)}",1,"((c*x)^(1 + n)*Hypergeometric2F1[1, 1 + n^(-1), 2 + n^(-1), -((b*x^n)/a)])/(a*c*(1 + n))","A",1,1,15,0.06667,1,"{364}"
2777,1,28,0,0.0109541,"\int \frac{(c x)^{-1+n}}{a+b x^n} \, dx","Int[(c*x)^(-1 + n)/(a + b*x^n),x]","\frac{x^{-n} (c x)^n \log \left(a+b x^n\right)}{b c n}","\frac{x^{-n} (c x)^n \log \left(a+b x^n\right)}{b c n}",1,"((c*x)^n*Log[a + b*x^n])/(b*c*n*x^n)","A",2,2,17,0.1176,1,"{268, 260}"
2778,1,50,0,0.0127508,"\int \frac{(c x)^{-2+n}}{a+b x^n} \, dx","Int[(c*x)^(-2 + n)/(a + b*x^n),x]","-\frac{(c x)^{n-1} \, _2F_1\left(1,-\frac{1-n}{n};2-\frac{1}{n};-\frac{b x^n}{a}\right)}{a c (1-n)}","-\frac{(c x)^{n-1} \, _2F_1\left(1,-\frac{1-n}{n};2-\frac{1}{n};-\frac{b x^n}{a}\right)}{a c (1-n)}",1,"-(((c*x)^(-1 + n)*Hypergeometric2F1[1, -((1 - n)/n), 2 - n^(-1), -((b*x^n)/a)])/(a*c*(1 - n)))","A",1,1,17,0.05882,1,"{364}"
2779,1,52,0,0.0126807,"\int \frac{(c x)^{-3+n}}{a+b x^n} \, dx","Int[(c*x)^(-3 + n)/(a + b*x^n),x]","-\frac{(c x)^{n-2} \, _2F_1\left(1,-\frac{2-n}{n};2 \left(1-\frac{1}{n}\right);-\frac{b x^n}{a}\right)}{a c (2-n)}","-\frac{(c x)^{n-2} \, _2F_1\left(1,-\frac{2-n}{n};2 \left(1-\frac{1}{n}\right);-\frac{b x^n}{a}\right)}{a c (2-n)}",1,"-(((c*x)^(-2 + n)*Hypergeometric2F1[1, -((2 - n)/n), 2*(1 - n^(-1)), -((b*x^n)/a)])/(a*c*(2 - n)))","A",1,1,17,0.05882,1,"{364}"
2780,1,24,0,0.0056073,"\int \frac{(c x)^{-1+n}}{\left(a+b x^n\right)^2} \, dx","Int[(c*x)^(-1 + n)/(a + b*x^n)^2,x]","\frac{(c x)^n}{a c n \left(a+b x^n\right)}","\frac{(c x)^n}{a c n \left(a+b x^n\right)}",1,"(c*x)^n/(a*c*n*(a + b*x^n))","A",1,1,17,0.05882,1,"{264}"
2781,1,178,0,0.0815932,"\int \frac{(c x)^{-1+\frac{7 n}{2}}}{\sqrt{a+b x^n}} \, dx","Int[(c*x)^(-1 + (7*n)/2)/Sqrt[a + b*x^n],x]","\frac{5 a^2 x^{-3 n} (c x)^{7 n/2} \sqrt{a+b x^n}}{8 b^3 c n}-\frac{5 a^3 x^{-7 n/2} (c x)^{7 n/2} \tanh ^{-1}\left(\frac{\sqrt{b} x^{n/2}}{\sqrt{a+b x^n}}\right)}{8 b^{7/2} c n}-\frac{5 a x^{-2 n} (c x)^{7 n/2} \sqrt{a+b x^n}}{12 b^2 c n}+\frac{x^{-n} (c x)^{7 n/2} \sqrt{a+b x^n}}{3 b c n}","\frac{5 a^2 x^{-3 n} (c x)^{7 n/2} \sqrt{a+b x^n}}{8 b^3 c n}-\frac{5 a^3 x^{-7 n/2} (c x)^{7 n/2} \tanh ^{-1}\left(\frac{\sqrt{b} x^{n/2}}{\sqrt{a+b x^n}}\right)}{8 b^{7/2} c n}-\frac{5 a x^{-2 n} (c x)^{7 n/2} \sqrt{a+b x^n}}{12 b^2 c n}+\frac{x^{-n} (c x)^{7 n/2} \sqrt{a+b x^n}}{3 b c n}",1,"(5*a^2*(c*x)^((7*n)/2)*Sqrt[a + b*x^n])/(8*b^3*c*n*x^(3*n)) - (5*a*(c*x)^((7*n)/2)*Sqrt[a + b*x^n])/(12*b^2*c*n*x^(2*n)) + ((c*x)^((7*n)/2)*Sqrt[a + b*x^n])/(3*b*c*n*x^n) - (5*a^3*(c*x)^((7*n)/2)*ArcTanh[(Sqrt[b]*x^(n/2))/Sqrt[a + b*x^n]])/(8*b^(7/2)*c*n*x^((7*n)/2))","A",6,4,23,0.1739,1,"{357, 355, 288, 206}"
2782,1,137,0,0.0570214,"\int \frac{(c x)^{-1+\frac{5 n}{2}}}{\sqrt{a+b x^n}} \, dx","Int[(c*x)^(-1 + (5*n)/2)/Sqrt[a + b*x^n],x]","\frac{3 a^2 x^{-5 n/2} (c x)^{5 n/2} \tanh ^{-1}\left(\frac{\sqrt{b} x^{n/2}}{\sqrt{a+b x^n}}\right)}{4 b^{5/2} c n}-\frac{3 a x^{-2 n} (c x)^{5 n/2} \sqrt{a+b x^n}}{4 b^2 c n}+\frac{x^{-n} (c x)^{5 n/2} \sqrt{a+b x^n}}{2 b c n}","\frac{3 a^2 x^{-5 n/2} (c x)^{5 n/2} \tanh ^{-1}\left(\frac{\sqrt{b} x^{n/2}}{\sqrt{a+b x^n}}\right)}{4 b^{5/2} c n}-\frac{3 a x^{-2 n} (c x)^{5 n/2} \sqrt{a+b x^n}}{4 b^2 c n}+\frac{x^{-n} (c x)^{5 n/2} \sqrt{a+b x^n}}{2 b c n}",1,"(-3*a*(c*x)^((5*n)/2)*Sqrt[a + b*x^n])/(4*b^2*c*n*x^(2*n)) + ((c*x)^((5*n)/2)*Sqrt[a + b*x^n])/(2*b*c*n*x^n) + (3*a^2*(c*x)^((5*n)/2)*ArcTanh[(Sqrt[b]*x^(n/2))/Sqrt[a + b*x^n]])/(4*b^(5/2)*c*n*x^((5*n)/2))","A",5,4,23,0.1739,1,"{357, 355, 288, 206}"
2783,1,91,0,0.0399805,"\int \frac{(c x)^{-1+\frac{3 n}{2}}}{\sqrt{a+b x^n}} \, dx","Int[(c*x)^(-1 + (3*n)/2)/Sqrt[a + b*x^n],x]","\frac{x^{-n} (c x)^{3 n/2} \sqrt{a+b x^n}}{b c n}-\frac{a x^{-3 n/2} (c x)^{3 n/2} \tanh ^{-1}\left(\frac{\sqrt{b} x^{n/2}}{\sqrt{a+b x^n}}\right)}{b^{3/2} c n}","\frac{x^{-n} (c x)^{3 n/2} \sqrt{a+b x^n}}{b c n}-\frac{a x^{-3 n/2} (c x)^{3 n/2} \tanh ^{-1}\left(\frac{\sqrt{b} x^{n/2}}{\sqrt{a+b x^n}}\right)}{b^{3/2} c n}",1,"((c*x)^((3*n)/2)*Sqrt[a + b*x^n])/(b*c*n*x^n) - (a*(c*x)^((3*n)/2)*ArcTanh[(Sqrt[b]*x^(n/2))/Sqrt[a + b*x^n]])/(b^(3/2)*c*n*x^((3*n)/2))","A",4,4,23,0.1739,1,"{357, 355, 288, 206}"
2784,1,54,0,0.0300451,"\int \frac{(c x)^{-1+\frac{n}{2}}}{\sqrt{a+b x^n}} \, dx","Int[(c*x)^(-1 + n/2)/Sqrt[a + b*x^n],x]","\frac{2 x^{-n/2} (c x)^{n/2} \tanh ^{-1}\left(\frac{\sqrt{b} x^{n/2}}{\sqrt{a+b x^n}}\right)}{\sqrt{b} c n}","\frac{2 x^{-n/2} (c x)^{n/2} \tanh ^{-1}\left(\frac{\sqrt{b} x^{n/2}}{\sqrt{a+b x^n}}\right)}{\sqrt{b} c n}",1,"(2*(c*x)^(n/2)*ArcTanh[(Sqrt[b]*x^(n/2))/Sqrt[a + b*x^n]])/(Sqrt[b]*c*n*x^(n/2))","A",4,4,23,0.1739,1,"{347, 345, 217, 206}"
2785,1,31,0,0.0086017,"\int \frac{(c x)^{-1-\frac{n}{2}}}{\sqrt{a+b x^n}} \, dx","Int[(c*x)^(-1 - n/2)/Sqrt[a + b*x^n],x]","-\frac{2 (c x)^{-n/2} \sqrt{a+b x^n}}{a c n}","-\frac{2 (c x)^{-n/2} \sqrt{a+b x^n}}{a c n}",1,"(-2*Sqrt[a + b*x^n])/(a*c*n*(c*x)^(n/2))","A",1,1,23,0.04348,1,"{264}"
2786,1,65,0,0.0174776,"\int \frac{(c x)^{-1-\frac{3 n}{2}}}{\sqrt{a+b x^n}} \, dx","Int[(c*x)^(-1 - (3*n)/2)/Sqrt[a + b*x^n],x]","\frac{4 (c x)^{-3 n/2} \left(a+b x^n\right)^{3/2}}{3 a^2 c n}-\frac{2 (c x)^{-3 n/2} \sqrt{a+b x^n}}{a c n}","\frac{4 (c x)^{-3 n/2} \left(a+b x^n\right)^{3/2}}{3 a^2 c n}-\frac{2 (c x)^{-3 n/2} \sqrt{a+b x^n}}{a c n}",1,"(-2*Sqrt[a + b*x^n])/(a*c*n*(c*x)^((3*n)/2)) + (4*(a + b*x^n)^(3/2))/(3*a^2*c*n*(c*x)^((3*n)/2))","A",2,2,23,0.08696,1,"{273, 264}"
2787,1,98,0,0.0305248,"\int \frac{(c x)^{-1-\frac{5 n}{2}}}{\sqrt{a+b x^n}} \, dx","Int[(c*x)^(-1 - (5*n)/2)/Sqrt[a + b*x^n],x]","-\frac{16 (c x)^{-5 n/2} \left(a+b x^n\right)^{5/2}}{15 a^3 c n}+\frac{8 (c x)^{-5 n/2} \left(a+b x^n\right)^{3/2}}{3 a^2 c n}-\frac{2 (c x)^{-5 n/2} \sqrt{a+b x^n}}{a c n}","-\frac{16 (c x)^{-5 n/2} \left(a+b x^n\right)^{5/2}}{15 a^3 c n}+\frac{8 (c x)^{-5 n/2} \left(a+b x^n\right)^{3/2}}{3 a^2 c n}-\frac{2 (c x)^{-5 n/2} \sqrt{a+b x^n}}{a c n}",1,"(-2*Sqrt[a + b*x^n])/(a*c*n*(c*x)^((5*n)/2)) + (8*(a + b*x^n)^(3/2))/(3*a^2*c*n*(c*x)^((5*n)/2)) - (16*(a + b*x^n)^(5/2))/(15*a^3*c*n*(c*x)^((5*n)/2))","A",3,2,23,0.08696,1,"{273, 264}"
2788,1,129,0,0.0502062,"\int \frac{(c x)^{-1-\frac{7 n}{2}}}{\sqrt{a+b x^n}} \, dx","Int[(c*x)^(-1 - (7*n)/2)/Sqrt[a + b*x^n],x]","\frac{32 (c x)^{-7 n/2} \left(a+b x^n\right)^{7/2}}{35 a^4 c n}-\frac{16 (c x)^{-7 n/2} \left(a+b x^n\right)^{5/2}}{5 a^3 c n}+\frac{4 (c x)^{-7 n/2} \left(a+b x^n\right)^{3/2}}{a^2 c n}-\frac{2 (c x)^{-7 n/2} \sqrt{a+b x^n}}{a c n}","\frac{32 (c x)^{-7 n/2} \left(a+b x^n\right)^{7/2}}{35 a^4 c n}-\frac{16 (c x)^{-7 n/2} \left(a+b x^n\right)^{5/2}}{5 a^3 c n}+\frac{4 (c x)^{-7 n/2} \left(a+b x^n\right)^{3/2}}{a^2 c n}-\frac{2 (c x)^{-7 n/2} \sqrt{a+b x^n}}{a c n}",1,"(-2*Sqrt[a + b*x^n])/(a*c*n*(c*x)^((7*n)/2)) + (4*(a + b*x^n)^(3/2))/(a^2*c*n*(c*x)^((7*n)/2)) - (16*(a + b*x^n)^(5/2))/(5*a^3*c*n*(c*x)^((7*n)/2)) + (32*(a + b*x^n)^(7/2))/(35*a^4*c*n*(c*x)^((7*n)/2))","A",4,2,23,0.08696,1,"{273, 264}"
2789,1,67,0,0.0234132,"\int (c x)^m \left(a+b x^n\right)^p \, dx","Int[(c*x)^m*(a + b*x^n)^p,x]","\frac{(c x)^{m+1} \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+1}{n},-p;\frac{m+n+1}{n};-\frac{b x^n}{a}\right)}{c (m+1)}","\frac{(c x)^{m+1} \left(a+b x^n\right)^{p+1} \, _2F_1\left(1,\frac{m+1}{n}+p+1;\frac{m+n+1}{n};-\frac{b x^n}{a}\right)}{a c (m+1)}",1,"((c*x)^(1 + m)*(a + b*x^n)^p*Hypergeometric2F1[(1 + m)/n, -p, (1 + m + n)/n, -((b*x^n)/a)])/(c*(1 + m)*(1 + (b*x^n)/a)^p)","A",2,2,15,0.1333,1,"{365, 364}"
2790,1,66,0,0.0247784,"\int (c x)^{3 n} \left(a+b x^n\right)^p \, dx","Int[(c*x)^(3*n)*(a + b*x^n)^p,x]","\frac{(c x)^{3 n+1} \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} \, _2F_1\left(3+\frac{1}{n},-p;4+\frac{1}{n};-\frac{b x^n}{a}\right)}{c (3 n+1)}","\frac{(c x)^{3 n+1} \left(a+b x^n\right)^{p+1} \, _2F_1\left(1,p+\frac{1}{n}+4;4+\frac{1}{n};-\frac{b x^n}{a}\right)}{a c (3 n+1)}",1,"((c*x)^(1 + 3*n)*(a + b*x^n)^p*Hypergeometric2F1[3 + n^(-1), -p, 4 + n^(-1), -((b*x^n)/a)])/(c*(1 + 3*n)*(1 + (b*x^n)/a)^p)","A",2,2,17,0.1176,1,"{365, 364}"
2791,1,66,0,0.0220576,"\int (c x)^{2 n} \left(a+b x^n\right)^p \, dx","Int[(c*x)^(2*n)*(a + b*x^n)^p,x]","\frac{(c x)^{2 n+1} \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} \, _2F_1\left(2+\frac{1}{n},-p;3+\frac{1}{n};-\frac{b x^n}{a}\right)}{c (2 n+1)}","\frac{(c x)^{2 n+1} \left(a+b x^n\right)^{p+1} \, _2F_1\left(1,p+\frac{1}{n}+3;3+\frac{1}{n};-\frac{b x^n}{a}\right)}{a c (2 n+1)}",1,"((c*x)^(1 + 2*n)*(a + b*x^n)^p*Hypergeometric2F1[2 + n^(-1), -p, 3 + n^(-1), -((b*x^n)/a)])/(c*(1 + 2*n)*(1 + (b*x^n)/a)^p)","A",2,2,17,0.1176,1,"{365, 364}"
2792,1,62,0,0.0211233,"\int (c x)^n \left(a+b x^n\right)^p \, dx","Int[(c*x)^n*(a + b*x^n)^p,x]","\frac{(c x)^{n+1} \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} \, _2F_1\left(1+\frac{1}{n},-p;2+\frac{1}{n};-\frac{b x^n}{a}\right)}{c (n+1)}","\frac{(c x)^{n+1} \left(a+b x^n\right)^{p+1} \, _2F_1\left(1,p+\frac{1}{n}+2;2+\frac{1}{n};-\frac{b x^n}{a}\right)}{a c (n+1)}",1,"((c*x)^(1 + n)*(a + b*x^n)^p*Hypergeometric2F1[1 + n^(-1), -p, 2 + n^(-1), -((b*x^n)/a)])/(c*(1 + n)*(1 + (b*x^n)/a)^p)","A",2,2,15,0.1333,1,"{365, 364}"
2793,1,46,0,0.0111188,"\int \left(a+b x^n\right)^p \, dx","Int[(a + b*x^n)^p,x]","x \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} \, _2F_1\left(\frac{1}{n},-p;1+\frac{1}{n};-\frac{b x^n}{a}\right)","\frac{x \left(a+b x^n\right)^{p+1} \, _2F_1\left(1,p+\frac{1}{n}+1;1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a}",1,"(x*(a + b*x^n)^p*Hypergeometric2F1[n^(-1), -p, 1 + n^(-1), -((b*x^n)/a)])/(1 + (b*x^n)/a)^p","A",2,2,9,0.2222,1,"{246, 245}"
2794,1,64,0,0.0229762,"\int (c x)^{-n} \left(a+b x^n\right)^p \, dx","Int[(a + b*x^n)^p/(c*x)^n,x]","\frac{(c x)^{1-n} \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} \, _2F_1\left(\frac{1}{n}-1,-p;\frac{1}{n};-\frac{b x^n}{a}\right)}{c (1-n)}","\frac{(c x)^{1-n} \left(a+b x^n\right)^{p+1} \, _2F_1\left(1,p+\frac{1}{n};\frac{1}{n};-\frac{b x^n}{a}\right)}{a c (1-n)}",1,"((c*x)^(1 - n)*(a + b*x^n)^p*Hypergeometric2F1[-1 + n^(-1), -p, n^(-1), -((b*x^n)/a)])/(c*(1 - n)*(1 + (b*x^n)/a)^p)","A",2,2,17,0.1176,1,"{365, 364}"
2795,1,66,0,0.0241345,"\int (c x)^{-2 n} \left(a+b x^n\right)^p \, dx","Int[(a + b*x^n)^p/(c*x)^(2*n),x]","\frac{(c x)^{1-2 n} \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} \, _2F_1\left(\frac{1}{n}-2,-p;\frac{1}{n}-1;-\frac{b x^n}{a}\right)}{c (1-2 n)}","\frac{(c x)^{1-2 n} \left(a+b x^n\right)^{p+1} \, _2F_1\left(1,p+\frac{1}{n}-1;\frac{1}{n}-1;-\frac{b x^n}{a}\right)}{a c (1-2 n)}",1,"((c*x)^(1 - 2*n)*(a + b*x^n)^p*Hypergeometric2F1[-2 + n^(-1), -p, -1 + n^(-1), -((b*x^n)/a)])/(c*(1 - 2*n)*(1 + (b*x^n)/a)^p)","A",2,2,17,0.1176,1,"{365, 364}"
2796,1,66,0,0.0251569,"\int (c x)^{-3 n} \left(a+b x^n\right)^p \, dx","Int[(a + b*x^n)^p/(c*x)^(3*n),x]","\frac{(c x)^{1-3 n} \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} \, _2F_1\left(\frac{1}{n}-3,-p;\frac{1}{n}-2;-\frac{b x^n}{a}\right)}{c (1-3 n)}","\frac{(c x)^{1-3 n} \left(a+b x^n\right)^{p+1} \, _2F_1\left(1,p+\frac{1}{n}-2;\frac{1}{n}-2;-\frac{b x^n}{a}\right)}{a c (1-3 n)}",1,"((c*x)^(1 - 3*n)*(a + b*x^n)^p*Hypergeometric2F1[-3 + n^(-1), -p, -2 + n^(-1), -((b*x^n)/a)])/(c*(1 - 3*n)*(1 + (b*x^n)/a)^p)","A",2,2,17,0.1176,1,"{365, 364}"
2797,1,63,0,0.0241856,"\int (c x)^{-1-n p} \left(a+b x^n\right)^p \, dx","Int[(c*x)^(-1 - n*p)*(a + b*x^n)^p,x]","-\frac{(c x)^{-n p} \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} \, _2F_1\left(-p,-p;1-p;-\frac{b x^n}{a}\right)}{c n p}","-\frac{(c x)^{-n p} \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} \, _2F_1\left(-p,-p;1-p;-\frac{b x^n}{a}\right)}{c n p}",1,"-(((a + b*x^n)^p*Hypergeometric2F1[-p, -p, 1 - p, -((b*x^n)/a)])/(c*n*p*(c*x)^(n*p)*(1 + (b*x^n)/a)^p))","A",2,2,20,0.1000,1,"{365, 364}"
2798,1,37,0,0.0123034,"\int (c x)^{-1-n-n p} \left(a+b x^n\right)^p \, dx","Int[(c*x)^(-1 - n - n*p)*(a + b*x^n)^p,x]","-\frac{(c x)^{-n (p+1)} \left(a+b x^n\right)^{p+1}}{a c n (p+1)}","-\frac{(c x)^{-n (p+1)} \left(a+b x^n\right)^{p+1}}{a c n (p+1)}",1,"-((a + b*x^n)^(1 + p)/(a*c*n*(1 + p)*(c*x)^(n*(1 + p))))","A",1,1,23,0.04348,1,"{264}"
2799,1,79,0,0.0393983,"\int (c x)^{-1-2 n-n p} \left(a+b x^n\right)^p \, dx","Int[(c*x)^(-1 - 2*n - n*p)*(a + b*x^n)^p,x]","\frac{(c x)^{-n (p+2)} \left(a+b x^n\right)^{p+2}}{a^2 c n (p+1) (p+2)}-\frac{(c x)^{-n (p+2)} \left(a+b x^n\right)^{p+1}}{a c n (p+1)}","\frac{(c x)^{-n (p+2)} \left(a+b x^n\right)^{p+2}}{a^2 c n (p+1) (p+2)}-\frac{(c x)^{-n (p+2)} \left(a+b x^n\right)^{p+1}}{a c n (p+1)}",1,"-((a + b*x^n)^(1 + p)/(a*c*n*(1 + p)*(c*x)^(n*(2 + p)))) + (a + b*x^n)^(2 + p)/(a^2*c*n*(1 + p)*(2 + p)*(c*x)^(n*(2 + p)))","A",2,2,23,0.08696,1,"{273, 264}"
2800,1,127,0,0.073555,"\int (c x)^{-1-3 n-n p} \left(a+b x^n\right)^p \, dx","Int[(c*x)^(-1 - 3*n - n*p)*(a + b*x^n)^p,x]","\frac{2 (c x)^{-n (p+3)} \left(a+b x^n\right)^{p+2}}{a^2 c n (p+1) (p+2)}-\frac{2 (c x)^{-n (p+3)} \left(a+b x^n\right)^{p+3}}{a^3 c n (p+1) (p+2) (p+3)}-\frac{(c x)^{-n (p+3)} \left(a+b x^n\right)^{p+1}}{a c n (p+1)}","\frac{2 (c x)^{-n (p+3)} \left(a+b x^n\right)^{p+2}}{a^2 c n (p+1) (p+2)}-\frac{2 (c x)^{-n (p+3)} \left(a+b x^n\right)^{p+3}}{a^3 c n (p+1) (p+2) (p+3)}-\frac{(c x)^{-n (p+3)} \left(a+b x^n\right)^{p+1}}{a c n (p+1)}",1,"-((a + b*x^n)^(1 + p)/(a*c*n*(1 + p)*(c*x)^(n*(3 + p)))) + (2*(a + b*x^n)^(2 + p))/(a^2*c*n*(1 + p)*(2 + p)*(c*x)^(n*(3 + p))) - (2*(a + b*x^n)^(3 + p))/(a^3*c*n*(1 + p)*(2 + p)*(3 + p)*(c*x)^(n*(3 + p)))","A",3,2,23,0.08696,1,"{273, 264}"
2801,1,179,0,0.1298754,"\int (c x)^{-1-4 n-n p} \left(a+b x^n\right)^p \, dx","Int[(c*x)^(-1 - 4*n - n*p)*(a + b*x^n)^p,x]","\frac{3 (c x)^{-n (p+4)} \left(a+b x^n\right)^{p+2}}{a^2 c n (p+1) (p+2)}-\frac{6 (c x)^{-n (p+4)} \left(a+b x^n\right)^{p+3}}{a^3 c n (p+1) (p+2) (p+3)}+\frac{6 (c x)^{-n (p+4)} \left(a+b x^n\right)^{p+4}}{a^4 c n (p+1) (p+2) (p+3) (p+4)}-\frac{(c x)^{-n (p+4)} \left(a+b x^n\right)^{p+1}}{a c n (p+1)}","\frac{3 (c x)^{-n (p+4)} \left(a+b x^n\right)^{p+2}}{a^2 c n (p+1) (p+2)}-\frac{6 (c x)^{-n (p+4)} \left(a+b x^n\right)^{p+3}}{a^3 c n (p+1) (p+2) (p+3)}+\frac{6 (c x)^{-n (p+4)} \left(a+b x^n\right)^{p+4}}{a^4 c n (p+1) (p+2) (p+3) (p+4)}-\frac{(c x)^{-n (p+4)} \left(a+b x^n\right)^{p+1}}{a c n (p+1)}",1,"-((a + b*x^n)^(1 + p)/(a*c*n*(1 + p)*(c*x)^(n*(4 + p)))) + (3*(a + b*x^n)^(2 + p))/(a^2*c*n*(1 + p)*(2 + p)*(c*x)^(n*(4 + p))) - (6*(a + b*x^n)^(3 + p))/(a^3*c*n*(1 + p)*(2 + p)*(3 + p)*(c*x)^(n*(4 + p))) + (6*(a + b*x^n)^(4 + p))/(a^4*c*n*(1 + p)*(2 + p)*(3 + p)*(4 + p)*(c*x)^(n*(4 + p)))","A",4,2,23,0.08696,1,"{273, 264}"
2802,1,30,0,0.0111322,"\int \left(c (a+b x)^2\right)^{5/2} \, dx","Int[(c*(a + b*x)^2)^(5/2),x]","\frac{c^2 (a+b x)^5 \sqrt{c (a+b x)^2}}{6 b}","\frac{c^2 (a+b x)^5 \sqrt{c (a+b x)^2}}{6 b}",1,"(c^2*(a + b*x)^5*Sqrt[c*(a + b*x)^2])/(6*b)","A",3,3,13,0.2308,1,"{247, 15, 30}"
2803,1,28,0,0.0106663,"\int \left(c (a+b x)^2\right)^{3/2} \, dx","Int[(c*(a + b*x)^2)^(3/2),x]","\frac{c (a+b x)^3 \sqrt{c (a+b x)^2}}{4 b}","\frac{c (a+b x)^3 \sqrt{c (a+b x)^2}}{4 b}",1,"(c*(a + b*x)^3*Sqrt[c*(a + b*x)^2])/(4*b)","A",3,3,13,0.2308,1,"{247, 15, 30}"
2804,1,25,0,0.010434,"\int \sqrt{c (a+b x)^2} \, dx","Int[Sqrt[c*(a + b*x)^2],x]","\frac{(a+b x) \sqrt{c (a+b x)^2}}{2 b}","\frac{(a+b x) \sqrt{c (a+b x)^2}}{2 b}",1,"((a + b*x)*Sqrt[c*(a + b*x)^2])/(2*b)","A",3,3,13,0.2308,1,"{247, 15, 30}"
2805,1,28,0,0.0123486,"\int \frac{1}{\sqrt{c (a+b x)^2}} \, dx","Int[1/Sqrt[c*(a + b*x)^2],x]","\frac{(a+b x) \log (a+b x)}{b \sqrt{c (a+b x)^2}}","\frac{(a+b x) \log (a+b x)}{b \sqrt{c (a+b x)^2}}",1,"((a + b*x)*Log[a + b*x])/(b*Sqrt[c*(a + b*x)^2])","A",3,3,13,0.2308,1,"{247, 15, 29}"
2806,1,30,0,0.0112982,"\int \frac{1}{\left(c (a+b x)^2\right)^{3/2}} \, dx","Int[(c*(a + b*x)^2)^(-3/2),x]","-\frac{1}{2 b c (a+b x) \sqrt{c (a+b x)^2}}","-\frac{1}{2 b c (a+b x) \sqrt{c (a+b x)^2}}",1,"-1/(2*b*c*(a + b*x)*Sqrt[c*(a + b*x)^2])","A",3,3,13,0.2308,1,"{247, 15, 30}"
2807,1,30,0,0.0125872,"\int \frac{1}{\left(c (a+b x)^2\right)^{5/2}} \, dx","Int[(c*(a + b*x)^2)^(-5/2),x]","-\frac{1}{4 b c^2 (a+b x)^3 \sqrt{c (a+b x)^2}}","-\frac{1}{4 b c^2 (a+b x)^3 \sqrt{c (a+b x)^2}}",1,"-1/(4*b*c^2*(a + b*x)^3*Sqrt[c*(a + b*x)^2])","A",3,3,13,0.2308,1,"{247, 15, 30}"
2808,1,20,0,0.0048126,"\int \sqrt{(3+5 x)^2} \, dx","Int[Sqrt[(3 + 5*x)^2],x]","\frac{1}{10} (5 x+3) \sqrt{(5 x+3)^2}","\frac{1}{10} (5 x+3) \sqrt{(5 x+3)^2}",1,"((3 + 5*x)*Sqrt[(3 + 5*x)^2])/10","A",3,3,11,0.2727,1,"{247, 15, 30}"
2809,1,20,0,0.0045488,"\int \sqrt{(6+10 x)^2} \, dx","Int[Sqrt[(6 + 10*x)^2],x]","\frac{1}{5} (5 x+3) \sqrt{(5 x+3)^2}","\frac{1}{5} (5 x+3) \sqrt{(5 x+3)^2}",1,"((3 + 5*x)*Sqrt[(3 + 5*x)^2])/5","A",3,3,11,0.2727,1,"{247, 15, 30}"
2810,1,26,0,0.0048987,"\int \frac{1}{\sqrt{(3+5 x)^2}} \, dx","Int[1/Sqrt[(3 + 5*x)^2],x]","\frac{(5 x+3) \log (5 x+3)}{5 \sqrt{(5 x+3)^2}}","\frac{(5 x+3) \log (5 x+3)}{5 \sqrt{(5 x+3)^2}}",1,"((3 + 5*x)*Log[3 + 5*x])/(5*Sqrt[(3 + 5*x)^2])","A",3,3,11,0.2727,1,"{247, 15, 29}"
2811,1,26,0,0.0050095,"\int \frac{1}{\sqrt{(6+10 x)^2}} \, dx","Int[1/Sqrt[(6 + 10*x)^2],x]","\frac{(5 x+3) \log (10 x+6)}{10 \sqrt{(5 x+3)^2}}","\frac{(5 x+3) \log (5 x+3)}{10 \sqrt{(5 x+3)^2}}",1,"((3 + 5*x)*Log[6 + 10*x])/(10*Sqrt[(3 + 5*x)^2])","A",3,3,11,0.2727,1,"{247, 15, 29}"
2812,1,28,0,0.008147,"\int \frac{1}{\sqrt{-(2+3 x)^2}} \, dx","Int[1/Sqrt[-(2 + 3*x)^2],x]","\frac{(3 x+2) \log (3 x+2)}{3 \sqrt{-(3 x+2)^2}}","\frac{(3 x+2) \log (3 x+2)}{3 \sqrt{-(3 x+2)^2}}",1,"((2 + 3*x)*Log[2 + 3*x])/(3*Sqrt[-(2 + 3*x)^2])","A",3,3,13,0.2308,1,"{247, 15, 29}"
2813,1,30,0,0.0152229,"\int \left(c (a+b x)^3\right)^{5/2} \, dx","Int[(c*(a + b*x)^3)^(5/2),x]","\frac{2 c^2 (a+b x)^7 \sqrt{c (a+b x)^3}}{17 b}","\frac{2 c^2 (a+b x)^7 \sqrt{c (a+b x)^3}}{17 b}",1,"(2*c^2*(a + b*x)^7*Sqrt[c*(a + b*x)^3])/(17*b)","A",3,3,13,0.2308,1,"{247, 15, 30}"
2814,1,28,0,0.0116544,"\int \left(c (a+b x)^3\right)^{3/2} \, dx","Int[(c*(a + b*x)^3)^(3/2),x]","\frac{2 c (a+b x)^4 \sqrt{c (a+b x)^3}}{11 b}","\frac{2 c (a+b x)^4 \sqrt{c (a+b x)^3}}{11 b}",1,"(2*c*(a + b*x)^4*Sqrt[c*(a + b*x)^3])/(11*b)","A",3,3,13,0.2308,1,"{247, 15, 30}"
2815,1,25,0,0.0112732,"\int \sqrt{c (a+b x)^3} \, dx","Int[Sqrt[c*(a + b*x)^3],x]","\frac{2 (a+b x) \sqrt{c (a+b x)^3}}{5 b}","\frac{2 (a+b x) \sqrt{c (a+b x)^3}}{5 b}",1,"(2*(a + b*x)*Sqrt[c*(a + b*x)^3])/(5*b)","A",3,3,13,0.2308,1,"{247, 15, 30}"
2816,1,23,0,0.0110628,"\int \frac{1}{\sqrt{c (a+b x)^3}} \, dx","Int[1/Sqrt[c*(a + b*x)^3],x]","-\frac{2 (a+b x)}{b \sqrt{c (a+b x)^3}}","-\frac{2 (a+b x)}{b \sqrt{c (a+b x)^3}}",1,"(-2*(a + b*x))/(b*Sqrt[c*(a + b*x)^3])","A",3,3,13,0.2308,1,"{247, 15, 30}"
2817,1,30,0,0.0126426,"\int \frac{1}{\left(c (a+b x)^3\right)^{3/2}} \, dx","Int[(c*(a + b*x)^3)^(-3/2),x]","-\frac{2}{7 b c (a+b x)^2 \sqrt{c (a+b x)^3}}","-\frac{2}{7 b c (a+b x)^2 \sqrt{c (a+b x)^3}}",1,"-2/(7*b*c*(a + b*x)^2*Sqrt[c*(a + b*x)^3])","A",3,3,13,0.2308,1,"{247, 15, 30}"
2818,1,30,0,0.0128352,"\int \frac{1}{\left(c (a+b x)^3\right)^{5/2}} \, dx","Int[(c*(a + b*x)^3)^(-5/2),x]","-\frac{2}{13 b c^2 (a+b x)^5 \sqrt{c (a+b x)^3}}","-\frac{2}{13 b c^2 (a+b x)^5 \sqrt{c (a+b x)^3}}",1,"-2/(13*b*c^2*(a + b*x)^5*Sqrt[c*(a + b*x)^3])","A",3,3,13,0.2308,1,"{247, 15, 30}"
2819,1,30,0,0.0079889,"\int \left(\frac{c}{a+b x}\right)^{5/2} \, dx","Int[(c/(a + b*x))^(5/2),x]","-\frac{2 c^2 \sqrt{\frac{c}{a+b x}}}{3 b (a+b x)}","-\frac{2 c^2 \sqrt{\frac{c}{a+b x}}}{3 b (a+b x)}",1,"(-2*c^2*Sqrt[c/(a + b*x)])/(3*b*(a + b*x))","A",3,3,13,0.2308,1,"{247, 15, 30}"
2820,1,19,0,0.0060305,"\int \left(\frac{c}{a+b x}\right)^{3/2} \, dx","Int[(c/(a + b*x))^(3/2),x]","-\frac{2 c \sqrt{\frac{c}{a+b x}}}{b}","-\frac{2 c \sqrt{\frac{c}{a+b x}}}{b}",1,"(-2*c*Sqrt[c/(a + b*x)])/b","A",3,3,13,0.2308,1,"{247, 15, 30}"
2821,1,23,0,0.0063936,"\int \sqrt{\frac{c}{a+b x}} \, dx","Int[Sqrt[c/(a + b*x)],x]","\frac{2 (a+b x) \sqrt{\frac{c}{a+b x}}}{b}","\frac{2 (a+b x) \sqrt{\frac{c}{a+b x}}}{b}",1,"(2*Sqrt[c/(a + b*x)]*(a + b*x))/b","A",3,3,13,0.2308,1,"{247, 15, 30}"
2822,1,25,0,0.006398,"\int \frac{1}{\sqrt{\frac{c}{a+b x}}} \, dx","Int[1/Sqrt[c/(a + b*x)],x]","\frac{2 (a+b x)}{3 b \sqrt{\frac{c}{a+b x}}}","\frac{2 (a+b x)}{3 b \sqrt{\frac{c}{a+b x}}}",1,"(2*(a + b*x))/(3*b*Sqrt[c/(a + b*x)])","A",3,3,13,0.2308,1,"{247, 15, 30}"
2823,1,30,0,0.008121,"\int \frac{1}{\left(\frac{c}{a+b x}\right)^{3/2}} \, dx","Int[(c/(a + b*x))^(-3/2),x]","\frac{2 (a+b x)^2}{5 b c \sqrt{\frac{c}{a+b x}}}","\frac{2 (a+b x)^2}{5 b c \sqrt{\frac{c}{a+b x}}}",1,"(2*(a + b*x)^2)/(5*b*c*Sqrt[c/(a + b*x)])","A",3,3,13,0.2308,1,"{247, 15, 30}"
2824,1,30,0,0.0087011,"\int \frac{1}{\left(\frac{c}{a+b x}\right)^{5/2}} \, dx","Int[(c/(a + b*x))^(-5/2),x]","\frac{2 (a+b x)^3}{7 b c^2 \sqrt{\frac{c}{a+b x}}}","\frac{2 (a+b x)^3}{7 b c^2 \sqrt{\frac{c}{a+b x}}}",1,"(2*(a + b*x)^3)/(7*b*c^2*Sqrt[c/(a + b*x)])","A",3,3,13,0.2308,1,"{247, 15, 30}"
2825,1,30,0,0.0087175,"\int \left(\frac{c}{(a+b x)^2}\right)^{5/2} \, dx","Int[(c/(a + b*x)^2)^(5/2),x]","-\frac{c^2 \sqrt{\frac{c}{(a+b x)^2}}}{4 b (a+b x)^3}","-\frac{c^2 \sqrt{\frac{c}{(a+b x)^2}}}{4 b (a+b x)^3}",1,"-(c^2*Sqrt[c/(a + b*x)^2])/(4*b*(a + b*x)^3)","A",3,3,13,0.2308,1,"{247, 15, 30}"
2826,1,28,0,0.0078393,"\int \left(\frac{c}{(a+b x)^2}\right)^{3/2} \, dx","Int[(c/(a + b*x)^2)^(3/2),x]","-\frac{c \sqrt{\frac{c}{(a+b x)^2}}}{2 b (a+b x)}","-\frac{c \sqrt{\frac{c}{(a+b x)^2}}}{2 b (a+b x)}",1,"-(c*Sqrt[c/(a + b*x)^2])/(2*b*(a + b*x))","A",3,3,13,0.2308,1,"{247, 15, 30}"
2827,1,28,0,0.0096413,"\int \sqrt{\frac{c}{(a+b x)^2}} \, dx","Int[Sqrt[c/(a + b*x)^2],x]","\frac{(a+b x) \sqrt{\frac{c}{(a+b x)^2}} \log (a+b x)}{b}","\frac{(a+b x) \sqrt{\frac{c}{(a+b x)^2}} \log (a+b x)}{b}",1,"(Sqrt[c/(a + b*x)^2]*(a + b*x)*Log[a + b*x])/b","A",3,3,13,0.2308,1,"{247, 15, 29}"
2828,1,25,0,0.0073814,"\int \frac{1}{\sqrt{\frac{c}{(a+b x)^2}}} \, dx","Int[1/Sqrt[c/(a + b*x)^2],x]","\frac{a+b x}{2 b \sqrt{\frac{c}{(a+b x)^2}}}","\frac{a+b x}{2 b \sqrt{\frac{c}{(a+b x)^2}}}",1,"(a + b*x)/(2*b*Sqrt[c/(a + b*x)^2])","A",3,3,13,0.2308,1,"{247, 15, 30}"
2829,1,30,0,0.0084612,"\int \frac{1}{\left(\frac{c}{(a+b x)^2}\right)^{3/2}} \, dx","Int[(c/(a + b*x)^2)^(-3/2),x]","\frac{(a+b x)^3}{4 b c \sqrt{\frac{c}{(a+b x)^2}}}","\frac{(a+b x)^3}{4 b c \sqrt{\frac{c}{(a+b x)^2}}}",1,"(a + b*x)^3/(4*b*c*Sqrt[c/(a + b*x)^2])","A",3,3,13,0.2308,1,"{247, 15, 30}"
2830,1,30,0,0.0090109,"\int \frac{1}{\left(\frac{c}{(a+b x)^2}\right)^{5/2}} \, dx","Int[(c/(a + b*x)^2)^(-5/2),x]","\frac{(a+b x)^5}{6 b c^2 \sqrt{\frac{c}{(a+b x)^2}}}","\frac{(a+b x)^5}{6 b c^2 \sqrt{\frac{c}{(a+b x)^2}}}",1,"(a + b*x)^5/(6*b*c^2*Sqrt[c/(a + b*x)^2])","A",3,3,13,0.2308,1,"{247, 15, 30}"
2831,1,30,0,0.0092784,"\int \left(\frac{c}{(a+b x)^3}\right)^{5/2} \, dx","Int[(c/(a + b*x)^3)^(5/2),x]","-\frac{2 c^2 \sqrt{\frac{c}{(a+b x)^3}}}{13 b (a+b x)^5}","-\frac{2 c^2 \sqrt{\frac{c}{(a+b x)^3}}}{13 b (a+b x)^5}",1,"(-2*c^2*Sqrt[c/(a + b*x)^3])/(13*b*(a + b*x)^5)","A",3,3,13,0.2308,1,"{247, 15, 30}"
2832,1,28,0,0.0087339,"\int \left(\frac{c}{(a+b x)^3}\right)^{3/2} \, dx","Int[(c/(a + b*x)^3)^(3/2),x]","-\frac{2 c \sqrt{\frac{c}{(a+b x)^3}}}{7 b (a+b x)^2}","-\frac{2 c \sqrt{\frac{c}{(a+b x)^3}}}{7 b (a+b x)^2}",1,"(-2*c*Sqrt[c/(a + b*x)^3])/(7*b*(a + b*x)^2)","A",3,3,13,0.2308,1,"{247, 15, 30}"
2833,1,23,0,0.0076797,"\int \sqrt{\frac{c}{(a+b x)^3}} \, dx","Int[Sqrt[c/(a + b*x)^3],x]","-\frac{2 (a+b x) \sqrt{\frac{c}{(a+b x)^3}}}{b}","-\frac{2 (a+b x) \sqrt{\frac{c}{(a+b x)^3}}}{b}",1,"(-2*Sqrt[c/(a + b*x)^3]*(a + b*x))/b","A",3,3,13,0.2308,1,"{247, 15, 30}"
2834,1,25,0,0.0082432,"\int \frac{1}{\sqrt{\frac{c}{(a+b x)^3}}} \, dx","Int[1/Sqrt[c/(a + b*x)^3],x]","\frac{2 (a+b x)}{5 b \sqrt{\frac{c}{(a+b x)^3}}}","\frac{2 (a+b x)}{5 b \sqrt{\frac{c}{(a+b x)^3}}}",1,"(2*(a + b*x))/(5*b*Sqrt[c/(a + b*x)^3])","A",3,3,13,0.2308,1,"{247, 15, 30}"
2835,1,30,0,0.0088129,"\int \frac{1}{\left(\frac{c}{(a+b x)^3}\right)^{3/2}} \, dx","Int[(c/(a + b*x)^3)^(-3/2),x]","\frac{2 (a+b x)^4}{11 b c \sqrt{\frac{c}{(a+b x)^3}}}","\frac{2 (a+b x)^4}{11 b c \sqrt{\frac{c}{(a+b x)^3}}}",1,"(2*(a + b*x)^4)/(11*b*c*Sqrt[c/(a + b*x)^3])","A",3,3,13,0.2308,1,"{247, 15, 30}"
2836,1,30,0,0.0095543,"\int \frac{1}{\left(\frac{c}{(a+b x)^3}\right)^{5/2}} \, dx","Int[(c/(a + b*x)^3)^(-5/2),x]","\frac{2 (a+b x)^7}{17 b c^2 \sqrt{\frac{c}{(a+b x)^3}}}","\frac{2 (a+b x)^7}{17 b c^2 \sqrt{\frac{c}{(a+b x)^3}}}",1,"(2*(a + b*x)^7)/(17*b*c^2*Sqrt[c/(a + b*x)^3])","A",3,3,13,0.2308,1,"{247, 15, 30}"
2837,1,27,0,0.0095091,"\int \left(c (a+b x)^{3/2}\right)^{2/3} \, dx","Int[(c*(a + b*x)^(3/2))^(2/3),x]","\frac{(a+b x) \left(c (a+b x)^{3/2}\right)^{2/3}}{2 b}","\frac{(a+b x) \left(c (a+b x)^{3/2}\right)^{2/3}}{2 b}",1,"((a + b*x)*(c*(a + b*x)^(3/2))^(2/3))/(2*b)","A",3,3,15,0.2000,1,"{247, 15, 30}"
2838,1,32,0,0.0097607,"\int \left(c (a+b x)^{2/3}\right)^{3/2} \, dx","Int[(c*(a + b*x)^(2/3))^(3/2),x]","\frac{c (a+b x)^{5/3} \sqrt{c (a+b x)^{2/3}}}{2 b}","\frac{c (a+b x)^{5/3} \sqrt{c (a+b x)^{2/3}}}{2 b}",1,"(c*Sqrt[c*(a + b*x)^(2/3)]*(a + b*x)^(5/3))/(2*b)","A",3,3,15,0.2000,1,"{247, 15, 30}"
2839,1,27,0,0.0101676,"\int \frac{1}{\left(\frac{c}{(a+b x)^{3/2}}\right)^{2/3}} \, dx","Int[(c/(a + b*x)^(3/2))^(-2/3),x]","\frac{a+b x}{2 b \left(\frac{c}{(a+b x)^{3/2}}\right)^{2/3}}","\frac{a+b x}{2 b \left(\frac{c}{(a+b x)^{3/2}}\right)^{2/3}}",1,"(a + b*x)/(2*b*(c/(a + b*x)^(3/2))^(2/3))","A",3,3,15,0.2000,1,"{247, 15, 30}"
2840,1,34,0,0.0114691,"\int \frac{1}{\left(\frac{c}{(a+b x)^{2/3}}\right)^{3/2}} \, dx","Int[(c/(a + b*x)^(2/3))^(-3/2),x]","\frac{(a+b x)^{5/3}}{2 b c \sqrt{\frac{c}{(a+b x)^{2/3}}}}","\frac{(a+b x)^{5/3}}{2 b c \sqrt{\frac{c}{(a+b x)^{2/3}}}}",1,"(a + b*x)^(5/3)/(2*b*c*Sqrt[c/(a + b*x)^(2/3)])","A",3,3,15,0.2000,1,"{247, 15, 30}"
2841,1,31,0,0.0256384,"\int (c+d x)^3 \left(a+b (c+d x)^2\right) \, dx","Int[(c + d*x)^3*(a + b*(c + d*x)^2),x]","\frac{a (c+d x)^4}{4 d}+\frac{b (c+d x)^6}{6 d}","\frac{a (c+d x)^4}{4 d}+\frac{b (c+d x)^6}{6 d}",1,"(a*(c + d*x)^4)/(4*d) + (b*(c + d*x)^6)/(6*d)","A",3,2,19,0.1053,1,"{372, 14}"
2842,1,51,0,0.0673907,"\int (c+d x)^3 \left(a+b (c+d x)^2\right)^2 \, dx","Int[(c + d*x)^3*(a + b*(c + d*x)^2)^2,x]","\frac{a^2 (c+d x)^4}{4 d}+\frac{a b (c+d x)^6}{3 d}+\frac{b^2 (c+d x)^8}{8 d}","\frac{a^2 (c+d x)^4}{4 d}+\frac{a b (c+d x)^6}{3 d}+\frac{b^2 (c+d x)^8}{8 d}",1,"(a^2*(c + d*x)^4)/(4*d) + (a*b*(c + d*x)^6)/(3*d) + (b^2*(c + d*x)^8)/(8*d)","A",4,3,21,0.1429,1,"{372, 266, 43}"
2843,1,48,0,0.2177871,"\int (c+d x)^3 \left(a+b (c+d x)^2\right)^3 \, dx","Int[(c + d*x)^3*(a + b*(c + d*x)^2)^3,x]","\frac{\left(a+b (c+d x)^2\right)^5}{10 b^2 d}-\frac{a \left(a+b (c+d x)^2\right)^4}{8 b^2 d}","\frac{\left(a+b (c+d x)^2\right)^5}{10 b^2 d}-\frac{a \left(a+b (c+d x)^2\right)^4}{8 b^2 d}",1,"-(a*(a + b*(c + d*x)^2)^4)/(8*b^2*d) + (a + b*(c + d*x)^2)^5/(10*b^2*d)","A",4,3,21,0.1429,1,"{372, 266, 43}"
2844,1,12,0,0.0057401,"\int \frac{2+x}{1+(2+x)^2} \, dx","Int[(2 + x)/(1 + (2 + x)^2),x]","\frac{1}{2} \log \left((x+2)^2+1\right)","\frac{1}{2} \log \left((x+2)^2+1\right)",1,"Log[1 + (2 + x)^2]/2","A",2,2,13,0.1538,1,"{372, 260}"
2845,1,13,0,0.0051081,"\int \frac{2+x}{\left(1+(2+x)^2\right)^2} \, dx","Int[(2 + x)/(1 + (2 + x)^2)^2,x]","-\frac{1}{2 \left((x+2)^2+1\right)}","-\frac{1}{2 \left((x+2)^2+1\right)}",1,"-1/(2*(1 + (2 + x)^2))","A",2,2,13,0.1538,1,"{372, 261}"
2846,1,13,0,0.005537,"\int \frac{2+x}{\left(1+(2+x)^2\right)^3} \, dx","Int[(2 + x)/(1 + (2 + x)^2)^3,x]","-\frac{1}{4 \left((x+2)^2+1\right)^2}","-\frac{1}{4 \left((x+2)^2+1\right)^2}",1,"-1/(4*(1 + (2 + x)^2)^2)","A",2,2,13,0.1538,1,"{372, 261}"
2847,1,93,0,0.0950768,"\int (c+d x)^5 \left(a+b (c+d x)^2\right)^p \, dx","Int[(c + d*x)^5*(a + b*(c + d*x)^2)^p,x]","\frac{a^2 \left(a+b (c+d x)^2\right)^{p+1}}{2 b^3 d (p+1)}-\frac{a \left(a+b (c+d x)^2\right)^{p+2}}{b^3 d (p+2)}+\frac{\left(a+b (c+d x)^2\right)^{p+3}}{2 b^3 d (p+3)}","\frac{a^2 \left(a+b (c+d x)^2\right)^{p+1}}{2 b^3 d (p+1)}-\frac{a \left(a+b (c+d x)^2\right)^{p+2}}{b^3 d (p+2)}+\frac{\left(a+b (c+d x)^2\right)^{p+3}}{2 b^3 d (p+3)}",1,"(a^2*(a + b*(c + d*x)^2)^(1 + p))/(2*b^3*d*(1 + p)) - (a*(a + b*(c + d*x)^2)^(2 + p))/(b^3*d*(2 + p)) + (a + b*(c + d*x)^2)^(3 + p)/(2*b^3*d*(3 + p))","A",4,3,21,0.1429,1,"{372, 266, 43}"
2848,1,68,0,0.0524839,"\int (c+d x)^4 \left(a+b (c+d x)^2\right)^p \, dx","Int[(c + d*x)^4*(a + b*(c + d*x)^2)^p,x]","\frac{(c+d x)^5 \left(a+b (c+d x)^2\right)^p \left(\frac{b (c+d x)^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{5}{2},-p;\frac{7}{2};-\frac{b (c+d x)^2}{a}\right)}{5 d}","\frac{(c+d x)^5 \left(a+b (c+d x)^2\right)^{p+1} \, _2F_1\left(1,p+\frac{7}{2};\frac{7}{2};-\frac{b (c+d x)^2}{a}\right)}{5 a d}",1,"((c + d*x)^5*(a + b*(c + d*x)^2)^p*Hypergeometric2F1[5/2, -p, 7/2, -((b*(c + d*x)^2)/a)])/(5*d*(1 + (b*(c + d*x)^2)/a)^p)","A",3,3,21,0.1429,1,"{372, 365, 364}"
2849,1,62,0,0.0590412,"\int (c+d x)^3 \left(a+b (c+d x)^2\right)^p \, dx","Int[(c + d*x)^3*(a + b*(c + d*x)^2)^p,x]","\frac{\left(a+b (c+d x)^2\right)^{p+2}}{2 b^2 d (p+2)}-\frac{a \left(a+b (c+d x)^2\right)^{p+1}}{2 b^2 d (p+1)}","\frac{\left(a+b (c+d x)^2\right)^{p+2}}{2 b^2 d (p+2)}-\frac{a \left(a+b (c+d x)^2\right)^{p+1}}{2 b^2 d (p+1)}",1,"-(a*(a + b*(c + d*x)^2)^(1 + p))/(2*b^2*d*(1 + p)) + (a + b*(c + d*x)^2)^(2 + p)/(2*b^2*d*(2 + p))","A",4,3,21,0.1429,1,"{372, 266, 43}"
2850,1,68,0,0.0470593,"\int (c+d x)^2 \left(a+b (c+d x)^2\right)^p \, dx","Int[(c + d*x)^2*(a + b*(c + d*x)^2)^p,x]","\frac{(c+d x)^3 \left(a+b (c+d x)^2\right)^p \left(\frac{b (c+d x)^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{3}{2},-p;\frac{5}{2};-\frac{b (c+d x)^2}{a}\right)}{3 d}","\frac{(c+d x)^3 \left(a+b (c+d x)^2\right)^{p+1} \, _2F_1\left(1,p+\frac{5}{2};\frac{5}{2};-\frac{b (c+d x)^2}{a}\right)}{3 a d}",1,"((c + d*x)^3*(a + b*(c + d*x)^2)^p*Hypergeometric2F1[3/2, -p, 5/2, -((b*(c + d*x)^2)/a)])/(3*d*(1 + (b*(c + d*x)^2)/a)^p)","A",3,3,21,0.1429,1,"{372, 365, 364}"
2851,1,30,0,0.0212933,"\int (c+d x) \left(a+b (c+d x)^2\right)^p \, dx","Int[(c + d*x)*(a + b*(c + d*x)^2)^p,x]","\frac{\left(a+b (c+d x)^2\right)^{p+1}}{2 b d (p+1)}","\frac{\left(a+b (c+d x)^2\right)^{p+1}}{2 b d (p+1)}",1,"(a + b*(c + d*x)^2)^(1 + p)/(2*b*d*(1 + p))","A",2,2,19,0.1053,1,"{372, 261}"
2852,1,52,0,0.0532383,"\int \frac{\left(a+b (c+d x)^2\right)^p}{c+d x} \, dx","Int[(a + b*(c + d*x)^2)^p/(c + d*x),x]","-\frac{\left(a+b (c+d x)^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{b (c+d x)^2}{a}+1\right)}{2 a d (p+1)}","-\frac{\left(a+b (c+d x)^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{b (c+d x)^2}{a}+1\right)}{2 a d (p+1)}",1,"-((a + b*(c + d*x)^2)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, 1 + (b*(c + d*x)^2)/a])/(2*a*d*(1 + p))","A",3,3,21,0.1429,1,"{372, 266, 65}"
2853,1,31,0,0.029149,"\int (c+d x)^3 \left(a+b (c+d x)^3\right) \, dx","Int[(c + d*x)^3*(a + b*(c + d*x)^3),x]","\frac{a (c+d x)^4}{4 d}+\frac{b (c+d x)^7}{7 d}","\frac{a (c+d x)^4}{4 d}+\frac{b (c+d x)^7}{7 d}",1,"(a*(c + d*x)^4)/(4*d) + (b*(c + d*x)^7)/(7*d)","A",3,2,19,0.1053,1,"{372, 14}"
2854,1,51,0,0.0632952,"\int (c+d x)^3 \left(a+b (c+d x)^3\right)^2 \, dx","Int[(c + d*x)^3*(a + b*(c + d*x)^3)^2,x]","\frac{a^2 (c+d x)^4}{4 d}+\frac{2 a b (c+d x)^7}{7 d}+\frac{b^2 (c+d x)^{10}}{10 d}","\frac{a^2 (c+d x)^4}{4 d}+\frac{2 a b (c+d x)^7}{7 d}+\frac{b^2 (c+d x)^{10}}{10 d}",1,"(a^2*(c + d*x)^4)/(4*d) + (2*a*b*(c + d*x)^7)/(7*d) + (b^2*(c + d*x)^10)/(10*d)","A",3,2,21,0.09524,1,"{372, 270}"
2855,1,71,0,0.1082585,"\int (c+d x)^3 \left(a+b (c+d x)^3\right)^3 \, dx","Int[(c + d*x)^3*(a + b*(c + d*x)^3)^3,x]","\frac{3 a^2 b (c+d x)^7}{7 d}+\frac{a^3 (c+d x)^4}{4 d}+\frac{3 a b^2 (c+d x)^{10}}{10 d}+\frac{b^3 (c+d x)^{13}}{13 d}","\frac{3 a^2 b (c+d x)^7}{7 d}+\frac{a^3 (c+d x)^4}{4 d}+\frac{3 a b^2 (c+d x)^{10}}{10 d}+\frac{b^3 (c+d x)^{13}}{13 d}",1,"(a^3*(c + d*x)^4)/(4*d) + (3*a^2*b*(c + d*x)^7)/(7*d) + (3*a*b^2*(c + d*x)^10)/(10*d) + (b^3*(c + d*x)^13)/(13*d)","A",3,2,21,0.09524,1,"{372, 270}"
2856,1,37,0,0.0291845,"\int (c e+d e x)^3 \left(a+b (c+d x)^3\right) \, dx","Int[(c*e + d*e*x)^3*(a + b*(c + d*x)^3),x]","\frac{a e^3 (c+d x)^4}{4 d}+\frac{b e^3 (c+d x)^7}{7 d}","\frac{a e^3 (c+d x)^4}{4 d}+\frac{b e^3 (c+d x)^7}{7 d}",1,"(a*e^3*(c + d*x)^4)/(4*d) + (b*e^3*(c + d*x)^7)/(7*d)","A",3,2,22,0.09091,1,"{372, 14}"
2857,1,60,0,0.0623818,"\int (c e+d e x)^3 \left(a+b (c+d x)^3\right)^2 \, dx","Int[(c*e + d*e*x)^3*(a + b*(c + d*x)^3)^2,x]","\frac{a^2 e^3 (c+d x)^4}{4 d}+\frac{2 a b e^3 (c+d x)^7}{7 d}+\frac{b^2 e^3 (c+d x)^{10}}{10 d}","\frac{a^2 e^3 (c+d x)^4}{4 d}+\frac{2 a b e^3 (c+d x)^7}{7 d}+\frac{b^2 e^3 (c+d x)^{10}}{10 d}",1,"(a^2*e^3*(c + d*x)^4)/(4*d) + (2*a*b*e^3*(c + d*x)^7)/(7*d) + (b^2*e^3*(c + d*x)^10)/(10*d)","A",3,2,24,0.08333,1,"{372, 270}"
2858,1,83,0,0.0987832,"\int (c e+d e x)^3 \left(a+b (c+d x)^3\right)^3 \, dx","Int[(c*e + d*e*x)^3*(a + b*(c + d*x)^3)^3,x]","\frac{3 a^2 b e^3 (c+d x)^7}{7 d}+\frac{a^3 e^3 (c+d x)^4}{4 d}+\frac{3 a b^2 e^3 (c+d x)^{10}}{10 d}+\frac{b^3 e^3 (c+d x)^{13}}{13 d}","\frac{3 a^2 b e^3 (c+d x)^7}{7 d}+\frac{a^3 e^3 (c+d x)^4}{4 d}+\frac{3 a b^2 e^3 (c+d x)^{10}}{10 d}+\frac{b^3 e^3 (c+d x)^{13}}{13 d}",1,"(a^3*e^3*(c + d*x)^4)/(4*d) + (3*a^2*b*e^3*(c + d*x)^7)/(7*d) + (3*a*b^2*e^3*(c + d*x)^10)/(10*d) + (b^3*e^3*(c + d*x)^13)/(13*d)","A",3,2,24,0.08333,1,"{372, 270}"
2859,1,156,0,0.1666879,"\int \frac{(c+d x)^4}{a+b (c+d x)^3} \, dx","Int[(c + d*x)^4/(a + b*(c + d*x)^3),x]","\frac{a^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{3 b^{5/3} d}-\frac{a^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{6 b^{5/3} d}+\frac{a^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^{5/3} d}+\frac{(c+d x)^2}{2 b d}","\frac{a^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{3 b^{5/3} d}-\frac{a^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{6 b^{5/3} d}+\frac{a^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^{5/3} d}+\frac{(c+d x)^2}{2 b d}",1,"(c + d*x)^2/(2*b*d) + (a^(2/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*b^(5/3)*d) + (a^(2/3)*Log[a^(1/3) + b^(1/3)*(c + d*x)])/(3*b^(5/3)*d) - (a^(2/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2])/(6*b^(5/3)*d)","A",8,8,21,0.3810,1,"{372, 321, 292, 31, 634, 617, 204, 628}"
2860,1,144,0,0.1348335,"\int \frac{(c+d x)^3}{a+b (c+d x)^3} \, dx","Int[(c + d*x)^3/(a + b*(c + d*x)^3),x]","\frac{\sqrt[3]{a} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{6 b^{4/3} d}-\frac{\sqrt[3]{a} \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{3 b^{4/3} d}+\frac{\sqrt[3]{a} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^{4/3} d}+\frac{x}{b}","\frac{\sqrt[3]{a} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{6 b^{4/3} d}-\frac{\sqrt[3]{a} \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{3 b^{4/3} d}+\frac{\sqrt[3]{a} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^{4/3} d}+\frac{x}{b}",1,"x/b + (a^(1/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*b^(4/3)*d) - (a^(1/3)*Log[a^(1/3) + b^(1/3)*(c + d*x)])/(3*b^(4/3)*d) + (a^(1/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2])/(6*b^(4/3)*d)","A",8,8,21,0.3810,1,"{372, 321, 200, 31, 634, 617, 204, 628}"
2861,1,22,0,0.0213417,"\int \frac{(c+d x)^2}{a+b (c+d x)^3} \, dx","Int[(c + d*x)^2/(a + b*(c + d*x)^3),x]","\frac{\log \left(a+b (c+d x)^3\right)}{3 b d}","\frac{\log \left(a+b (c+d x)^3\right)}{3 b d}",1,"Log[a + b*(c + d*x)^3]/(3*b*d)","A",2,2,21,0.09524,1,"{372, 260}"
2862,1,140,0,0.1139133,"\int \frac{c+d x}{a+b (c+d x)^3} \, dx","Int[(c + d*x)/(a + b*(c + d*x)^3),x]","\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{6 \sqrt[3]{a} b^{2/3} d}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{3 \sqrt[3]{a} b^{2/3} d}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} \sqrt[3]{a} b^{2/3} d}","\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{6 \sqrt[3]{a} b^{2/3} d}-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{3 \sqrt[3]{a} b^{2/3} d}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} \sqrt[3]{a} b^{2/3} d}",1,"-(ArcTan[(a^(1/3) - 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))]/(Sqrt[3]*a^(1/3)*b^(2/3)*d)) - Log[a^(1/3) + b^(1/3)*(c + d*x)]/(3*a^(1/3)*b^(2/3)*d) + Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2]/(6*a^(1/3)*b^(2/3)*d)","A",7,7,19,0.3684,1,"{372, 292, 31, 634, 617, 204, 628}"
2863,1,140,0,0.1096636,"\int \frac{1}{a+b (c+d x)^3} \, dx","Int[(a + b*(c + d*x)^3)^(-1),x]","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{6 a^{2/3} \sqrt[3]{b} d}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{3 a^{2/3} \sqrt[3]{b} d}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} \sqrt[3]{b} d}","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{6 a^{2/3} \sqrt[3]{b} d}+\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{3 a^{2/3} \sqrt[3]{b} d}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} \sqrt[3]{b} d}",1,"-(ArcTan[(a^(1/3) - 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))]/(Sqrt[3]*a^(2/3)*b^(1/3)*d)) + Log[a^(1/3) + b^(1/3)*(c + d*x)]/(3*a^(2/3)*b^(1/3)*d) - Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2]/(6*a^(2/3)*b^(1/3)*d)","A",7,7,13,0.5385,1,"{247, 200, 31, 634, 617, 204, 628}"
2864,1,36,0,0.0277494,"\int \frac{1}{(c+d x) \left(a+b (c+d x)^3\right)} \, dx","Int[1/((c + d*x)*(a + b*(c + d*x)^3)),x]","\frac{\log (c+d x)}{a d}-\frac{\log \left(a+b (c+d x)^3\right)}{3 a d}","\frac{\log (c+d x)}{a d}-\frac{\log \left(a+b (c+d x)^3\right)}{3 a d}",1,"Log[c + d*x]/(a*d) - Log[a + b*(c + d*x)^3]/(3*a*d)","A",5,5,21,0.2381,1,"{372, 266, 36, 29, 31}"
2865,1,154,0,0.1253818,"\int \frac{1}{(c+d x)^2 \left(a+b (c+d x)^3\right)} \, dx","Int[1/((c + d*x)^2*(a + b*(c + d*x)^3)),x]","-\frac{\sqrt[3]{b} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{6 a^{4/3} d}+\frac{\sqrt[3]{b} \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{3 a^{4/3} d}+\frac{\sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{4/3} d}-\frac{1}{a d (c+d x)}","-\frac{\sqrt[3]{b} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{6 a^{4/3} d}+\frac{\sqrt[3]{b} \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{3 a^{4/3} d}+\frac{\sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{4/3} d}-\frac{1}{a d (c+d x)}",1,"-(1/(a*d*(c + d*x))) + (b^(1/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(4/3)*d) + (b^(1/3)*Log[a^(1/3) + b^(1/3)*(c + d*x)])/(3*a^(4/3)*d) - (b^(1/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2])/(6*a^(4/3)*d)","A",8,8,21,0.3810,1,"{372, 325, 292, 31, 634, 617, 204, 628}"
2866,1,156,0,0.1233228,"\int \frac{1}{(c+d x)^3 \left(a+b (c+d x)^3\right)} \, dx","Int[1/((c + d*x)^3*(a + b*(c + d*x)^3)),x]","-\frac{b^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{3 a^{5/3} d}+\frac{b^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{6 a^{5/3} d}+\frac{b^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{5/3} d}-\frac{1}{2 a d (c+d x)^2}","-\frac{b^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{3 a^{5/3} d}+\frac{b^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{6 a^{5/3} d}+\frac{b^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{5/3} d}-\frac{1}{2 a d (c+d x)^2}",1,"-1/(2*a*d*(c + d*x)^2) + (b^(2/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(5/3)*d) - (b^(2/3)*Log[a^(1/3) + b^(1/3)*(c + d*x)])/(3*a^(5/3)*d) + (b^(2/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2])/(6*a^(5/3)*d)","A",8,8,21,0.3810,1,"{372, 325, 200, 31, 634, 617, 204, 628}"
2867,1,56,0,0.0414471,"\int \frac{1}{(c+d x)^4 \left(a+b (c+d x)^3\right)} \, dx","Int[1/((c + d*x)^4*(a + b*(c + d*x)^3)),x]","-\frac{b \log (c+d x)}{a^2 d}+\frac{b \log \left(a+b (c+d x)^3\right)}{3 a^2 d}-\frac{1}{3 a d (c+d x)^3}","-\frac{b \log (c+d x)}{a^2 d}+\frac{b \log \left(a+b (c+d x)^3\right)}{3 a^2 d}-\frac{1}{3 a d (c+d x)^3}",1,"-1/(3*a*d*(c + d*x)^3) - (b*Log[c + d*x])/(a^2*d) + (b*Log[a + b*(c + d*x)^3])/(3*a^2*d)","A",4,3,21,0.1429,1,"{372, 266, 44}"
2868,1,172,0,0.1364115,"\int \frac{(c+d x)^4}{\left(a+b (c+d x)^3\right)^2} \, dx","Int[(c + d*x)^4/(a + b*(c + d*x)^3)^2,x]","\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{9 \sqrt[3]{a} b^{5/3} d}-\frac{2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{9 \sqrt[3]{a} b^{5/3} d}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} \sqrt[3]{a} b^{5/3} d}-\frac{(c+d x)^2}{3 b d \left(a+b (c+d x)^3\right)}","\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{9 \sqrt[3]{a} b^{5/3} d}-\frac{2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{9 \sqrt[3]{a} b^{5/3} d}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} \sqrt[3]{a} b^{5/3} d}-\frac{(c+d x)^2}{3 b d \left(a+b (c+d x)^3\right)}",1,"-(c + d*x)^2/(3*b*d*(a + b*(c + d*x)^3)) - (2*ArcTan[(a^(1/3) - 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(1/3)*b^(5/3)*d) - (2*Log[a^(1/3) + b^(1/3)*(c + d*x)])/(9*a^(1/3)*b^(5/3)*d) + Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2]/(9*a^(1/3)*b^(5/3)*d)","A",8,8,21,0.3810,1,"{372, 288, 292, 31, 634, 617, 204, 628}"
2869,1,170,0,0.14064,"\int \frac{(c+d x)^3}{\left(a+b (c+d x)^3\right)^2} \, dx","Int[(c + d*x)^3/(a + b*(c + d*x)^3)^2,x]","\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{9 a^{2/3} b^{4/3} d}-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{18 a^{2/3} b^{4/3} d}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{2/3} b^{4/3} d}-\frac{c+d x}{3 b d \left(a+b (c+d x)^3\right)}","\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{9 a^{2/3} b^{4/3} d}-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{18 a^{2/3} b^{4/3} d}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{2/3} b^{4/3} d}-\frac{c+d x}{3 b d \left(a+b (c+d x)^3\right)}",1,"-(c + d*x)/(3*b*d*(a + b*(c + d*x)^3)) - ArcTan[(a^(1/3) - 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))]/(3*Sqrt[3]*a^(2/3)*b^(4/3)*d) + Log[a^(1/3) + b^(1/3)*(c + d*x)]/(9*a^(2/3)*b^(4/3)*d) - Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2]/(18*a^(2/3)*b^(4/3)*d)","A",8,8,21,0.3810,1,"{372, 288, 200, 31, 634, 617, 204, 628}"
2870,1,23,0,0.0188829,"\int \frac{(c+d x)^2}{\left(a+b (c+d x)^3\right)^2} \, dx","Int[(c + d*x)^2/(a + b*(c + d*x)^3)^2,x]","-\frac{1}{3 b d \left(a+b (c+d x)^3\right)}","-\frac{1}{3 b d \left(a+b (c+d x)^3\right)}",1,"-1/(3*b*d*(a + b*(c + d*x)^3))","A",2,2,21,0.09524,1,"{372, 261}"
2871,1,172,0,0.1356915,"\int \frac{c+d x}{\left(a+b (c+d x)^3\right)^2} \, dx","Int[(c + d*x)/(a + b*(c + d*x)^3)^2,x]","-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{9 a^{4/3} b^{2/3} d}+\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{18 a^{4/3} b^{2/3} d}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{4/3} b^{2/3} d}+\frac{(c+d x)^2}{3 a d \left(a+b (c+d x)^3\right)}","-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{9 a^{4/3} b^{2/3} d}+\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{18 a^{4/3} b^{2/3} d}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{4/3} b^{2/3} d}+\frac{(c+d x)^2}{3 a d \left(a+b (c+d x)^3\right)}",1,"(c + d*x)^2/(3*a*d*(a + b*(c + d*x)^3)) - ArcTan[(a^(1/3) - 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))]/(3*Sqrt[3]*a^(4/3)*b^(2/3)*d) - Log[a^(1/3) + b^(1/3)*(c + d*x)]/(9*a^(4/3)*b^(2/3)*d) + Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2]/(18*a^(4/3)*b^(2/3)*d)","A",8,8,19,0.4211,1,"{372, 290, 292, 31, 634, 617, 204, 628}"
2872,1,170,0,0.133399,"\int \frac{1}{\left(a+b (c+d x)^3\right)^2} \, dx","Int[(a + b*(c + d*x)^3)^(-2),x]","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{9 a^{5/3} \sqrt[3]{b} d}+\frac{2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{9 a^{5/3} \sqrt[3]{b} d}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{5/3} \sqrt[3]{b} d}+\frac{c+d x}{3 a d \left(a+b (c+d x)^3\right)}","-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{9 a^{5/3} \sqrt[3]{b} d}+\frac{2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{9 a^{5/3} \sqrt[3]{b} d}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{5/3} \sqrt[3]{b} d}+\frac{c+d x}{3 a d \left(a+b (c+d x)^3\right)}",1,"(c + d*x)/(3*a*d*(a + b*(c + d*x)^3)) - (2*ArcTan[(a^(1/3) - 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(5/3)*b^(1/3)*d) + (2*Log[a^(1/3) + b^(1/3)*(c + d*x)])/(9*a^(5/3)*b^(1/3)*d) - Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2]/(9*a^(5/3)*b^(1/3)*d)","A",8,8,13,0.6154,1,"{247, 199, 200, 31, 634, 617, 204, 628}"
2873,1,59,0,0.0571008,"\int \frac{1}{(c+d x) \left(a+b (c+d x)^3\right)^2} \, dx","Int[1/((c + d*x)*(a + b*(c + d*x)^3)^2),x]","-\frac{\log \left(a+b (c+d x)^3\right)}{3 a^2 d}+\frac{\log (c+d x)}{a^2 d}+\frac{1}{3 a d \left(a+b (c+d x)^3\right)}","-\frac{\log \left(a+b (c+d x)^3\right)}{3 a^2 d}+\frac{\log (c+d x)}{a^2 d}+\frac{1}{3 a d \left(a+b (c+d x)^3\right)}",1,"1/(3*a*d*(a + b*(c + d*x)^3)) + Log[c + d*x]/(a^2*d) - Log[a + b*(c + d*x)^3]/(3*a^2*d)","A",4,3,21,0.1429,1,"{372, 266, 44}"
2874,1,189,0,0.1598279,"\int \frac{1}{(c+d x)^2 \left(a+b (c+d x)^3\right)^2} \, dx","Int[1/((c + d*x)^2*(a + b*(c + d*x)^3)^2),x]","-\frac{2 \sqrt[3]{b} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{9 a^{7/3} d}+\frac{4 \sqrt[3]{b} \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{9 a^{7/3} d}+\frac{4 \sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{7/3} d}-\frac{4}{3 a^2 d (c+d x)}+\frac{1}{3 a d (c+d x) \left(a+b (c+d x)^3\right)}","-\frac{2 \sqrt[3]{b} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{9 a^{7/3} d}+\frac{4 \sqrt[3]{b} \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{9 a^{7/3} d}+\frac{4 \sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{7/3} d}-\frac{4}{3 a^2 d (c+d x)}+\frac{1}{3 a d (c+d x) \left(a+b (c+d x)^3\right)}",1,"-4/(3*a^2*d*(c + d*x)) + 1/(3*a*d*(c + d*x)*(a + b*(c + d*x)^3)) + (4*b^(1/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(7/3)*d) + (4*b^(1/3)*Log[a^(1/3) + b^(1/3)*(c + d*x)])/(9*a^(7/3)*d) - (2*b^(1/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2])/(9*a^(7/3)*d)","A",9,9,21,0.4286,1,"{372, 290, 325, 292, 31, 634, 617, 204, 628}"
2875,1,189,0,0.1528195,"\int \frac{1}{(c+d x)^3 \left(a+b (c+d x)^3\right)^2} \, dx","Int[1/((c + d*x)^3*(a + b*(c + d*x)^3)^2),x]","-\frac{5 b^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{9 a^{8/3} d}+\frac{5 b^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{18 a^{8/3} d}+\frac{5 b^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{8/3} d}-\frac{5}{6 a^2 d (c+d x)^2}+\frac{1}{3 a d (c+d x)^2 \left(a+b (c+d x)^3\right)}","-\frac{5 b^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{9 a^{8/3} d}+\frac{5 b^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{18 a^{8/3} d}+\frac{5 b^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{8/3} d}-\frac{5}{6 a^2 d (c+d x)^2}+\frac{1}{3 a d (c+d x)^2 \left(a+b (c+d x)^3\right)}",1,"-5/(6*a^2*d*(c + d*x)^2) + 1/(3*a*d*(c + d*x)^2*(a + b*(c + d*x)^3)) + (5*b^(2/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(8/3)*d) - (5*b^(2/3)*Log[a^(1/3) + b^(1/3)*(c + d*x)])/(9*a^(8/3)*d) + (5*b^(2/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2])/(18*a^(8/3)*d)","A",9,9,21,0.4286,1,"{372, 290, 325, 200, 31, 634, 617, 204, 628}"
2876,1,80,0,0.0701192,"\int \frac{1}{(c+d x)^4 \left(a+b (c+d x)^3\right)^2} \, dx","Int[1/((c + d*x)^4*(a + b*(c + d*x)^3)^2),x]","-\frac{b}{3 a^2 d \left(a+b (c+d x)^3\right)}-\frac{2 b \log (c+d x)}{a^3 d}+\frac{2 b \log \left(a+b (c+d x)^3\right)}{3 a^3 d}-\frac{1}{3 a^2 d (c+d x)^3}","-\frac{b}{3 a^2 d \left(a+b (c+d x)^3\right)}-\frac{2 b \log (c+d x)}{a^3 d}+\frac{2 b \log \left(a+b (c+d x)^3\right)}{3 a^3 d}-\frac{1}{3 a^2 d (c+d x)^3}",1,"-1/(3*a^2*d*(c + d*x)^3) - b/(3*a^2*d*(a + b*(c + d*x)^3)) - (2*b*Log[c + d*x])/(a^3*d) + (2*b*Log[a + b*(c + d*x)^3])/(3*a^3*d)","A",4,3,21,0.1429,1,"{372, 266, 44}"
2877,1,205,0,0.1695581,"\int \frac{(c+d x)^4}{\left(a+b (c+d x)^3\right)^3} \, dx","Int[(c + d*x)^4/(a + b*(c + d*x)^3)^3,x]","-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{27 a^{4/3} b^{5/3} d}+\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{54 a^{4/3} b^{5/3} d}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{4/3} b^{5/3} d}+\frac{(c+d x)^2}{9 a b d \left(a+b (c+d x)^3\right)}-\frac{(c+d x)^2}{6 b d \left(a+b (c+d x)^3\right)^2}","-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{27 a^{4/3} b^{5/3} d}+\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{54 a^{4/3} b^{5/3} d}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{4/3} b^{5/3} d}+\frac{(c+d x)^2}{9 a b d \left(a+b (c+d x)^3\right)}-\frac{(c+d x)^2}{6 b d \left(a+b (c+d x)^3\right)^2}",1,"-(c + d*x)^2/(6*b*d*(a + b*(c + d*x)^3)^2) + (c + d*x)^2/(9*a*b*d*(a + b*(c + d*x)^3)) - ArcTan[(a^(1/3) - 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))]/(9*Sqrt[3]*a^(4/3)*b^(5/3)*d) - Log[a^(1/3) + b^(1/3)*(c + d*x)]/(27*a^(4/3)*b^(5/3)*d) + Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2]/(54*a^(4/3)*b^(5/3)*d)","A",9,9,21,0.4286,1,"{372, 288, 290, 292, 31, 634, 617, 204, 628}"
2878,1,201,0,0.1637436,"\int \frac{(c+d x)^3}{\left(a+b (c+d x)^3\right)^3} \, dx","Int[(c + d*x)^3/(a + b*(c + d*x)^3)^3,x]","\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{27 a^{5/3} b^{4/3} d}-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{54 a^{5/3} b^{4/3} d}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{5/3} b^{4/3} d}+\frac{c+d x}{18 a b d \left(a+b (c+d x)^3\right)}-\frac{c+d x}{6 b d \left(a+b (c+d x)^3\right)^2}","\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{27 a^{5/3} b^{4/3} d}-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{54 a^{5/3} b^{4/3} d}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{5/3} b^{4/3} d}+\frac{c+d x}{18 a b d \left(a+b (c+d x)^3\right)}-\frac{c+d x}{6 b d \left(a+b (c+d x)^3\right)^2}",1,"-(c + d*x)/(6*b*d*(a + b*(c + d*x)^3)^2) + (c + d*x)/(18*a*b*d*(a + b*(c + d*x)^3)) - ArcTan[(a^(1/3) - 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))]/(9*Sqrt[3]*a^(5/3)*b^(4/3)*d) + Log[a^(1/3) + b^(1/3)*(c + d*x)]/(27*a^(5/3)*b^(4/3)*d) - Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2]/(54*a^(5/3)*b^(4/3)*d)","A",9,9,21,0.4286,1,"{372, 288, 199, 200, 31, 634, 617, 204, 628}"
2879,1,23,0,0.0193356,"\int \frac{(c+d x)^2}{\left(a+b (c+d x)^3\right)^3} \, dx","Int[(c + d*x)^2/(a + b*(c + d*x)^3)^3,x]","-\frac{1}{6 b d \left(a+b (c+d x)^3\right)^2}","-\frac{1}{6 b d \left(a+b (c+d x)^3\right)^2}",1,"-1/(6*b*d*(a + b*(c + d*x)^3)^2)","A",2,2,21,0.09524,1,"{372, 261}"
2880,1,202,0,0.166015,"\int \frac{c+d x}{\left(a+b (c+d x)^3\right)^3} \, dx","Int[(c + d*x)/(a + b*(c + d*x)^3)^3,x]","-\frac{2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{27 a^{7/3} b^{2/3} d}+\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{27 a^{7/3} b^{2/3} d}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{7/3} b^{2/3} d}+\frac{2 (c+d x)^2}{9 a^2 d \left(a+b (c+d x)^3\right)}+\frac{(c+d x)^2}{6 a d \left(a+b (c+d x)^3\right)^2}","-\frac{2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{27 a^{7/3} b^{2/3} d}+\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{27 a^{7/3} b^{2/3} d}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{7/3} b^{2/3} d}+\frac{2 (c+d x)^2}{9 a^2 d \left(a+b (c+d x)^3\right)}+\frac{(c+d x)^2}{6 a d \left(a+b (c+d x)^3\right)^2}",1,"(c + d*x)^2/(6*a*d*(a + b*(c + d*x)^3)^2) + (2*(c + d*x)^2)/(9*a^2*d*(a + b*(c + d*x)^3)) - (2*ArcTan[(a^(1/3) - 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(7/3)*b^(2/3)*d) - (2*Log[a^(1/3) + b^(1/3)*(c + d*x)])/(27*a^(7/3)*b^(2/3)*d) + Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2]/(27*a^(7/3)*b^(2/3)*d)","A",9,8,19,0.4211,1,"{372, 290, 292, 31, 634, 617, 204, 628}"
2881,1,198,0,0.1561014,"\int \frac{1}{\left(a+b (c+d x)^3\right)^3} \, dx","Int[(a + b*(c + d*x)^3)^(-3),x]","-\frac{5 \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{54 a^{8/3} \sqrt[3]{b} d}+\frac{5 (c+d x)}{18 a^2 d \left(a+b (c+d x)^3\right)}+\frac{5 \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{27 a^{8/3} \sqrt[3]{b} d}-\frac{5 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{8/3} \sqrt[3]{b} d}+\frac{c+d x}{6 a d \left(a+b (c+d x)^3\right)^2}","-\frac{5 \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{54 a^{8/3} \sqrt[3]{b} d}+\frac{5 (c+d x)}{18 a^2 d \left(a+b (c+d x)^3\right)}+\frac{5 \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{27 a^{8/3} \sqrt[3]{b} d}-\frac{5 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{8/3} \sqrt[3]{b} d}+\frac{c+d x}{6 a d \left(a+b (c+d x)^3\right)^2}",1,"(c + d*x)/(6*a*d*(a + b*(c + d*x)^3)^2) + (5*(c + d*x))/(18*a^2*d*(a + b*(c + d*x)^3)) - (5*ArcTan[(a^(1/3) - 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(8/3)*b^(1/3)*d) + (5*Log[a^(1/3) + b^(1/3)*(c + d*x)])/(27*a^(8/3)*b^(1/3)*d) - (5*Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2])/(54*a^(8/3)*b^(1/3)*d)","A",9,8,13,0.6154,1,"{247, 199, 200, 31, 634, 617, 204, 628}"
2882,1,82,0,0.0754286,"\int \frac{1}{(c+d x) \left(a+b (c+d x)^3\right)^3} \, dx","Int[1/((c + d*x)*(a + b*(c + d*x)^3)^3),x]","\frac{1}{3 a^2 d \left(a+b (c+d x)^3\right)}-\frac{\log \left(a+b (c+d x)^3\right)}{3 a^3 d}+\frac{\log (c+d x)}{a^3 d}+\frac{1}{6 a d \left(a+b (c+d x)^3\right)^2}","\frac{1}{3 a^2 d \left(a+b (c+d x)^3\right)}-\frac{\log \left(a+b (c+d x)^3\right)}{3 a^3 d}+\frac{\log (c+d x)}{a^3 d}+\frac{1}{6 a d \left(a+b (c+d x)^3\right)^2}",1,"1/(6*a*d*(a + b*(c + d*x)^3)^2) + 1/(3*a^2*d*(a + b*(c + d*x)^3)) + Log[c + d*x]/(a^3*d) - Log[a + b*(c + d*x)^3]/(3*a^3*d)","A",4,3,21,0.1429,1,"{372, 266, 44}"
2883,1,219,0,0.1874791,"\int \frac{1}{(c+d x)^2 \left(a+b (c+d x)^3\right)^3} \, dx","Int[1/((c + d*x)^2*(a + b*(c + d*x)^3)^3),x]","-\frac{7 \sqrt[3]{b} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{27 a^{10/3} d}+\frac{7}{18 a^2 d (c+d x) \left(a+b (c+d x)^3\right)}+\frac{14 \sqrt[3]{b} \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{27 a^{10/3} d}+\frac{14 \sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{10/3} d}-\frac{14}{9 a^3 d (c+d x)}+\frac{1}{6 a d (c+d x) \left(a+b (c+d x)^3\right)^2}","-\frac{7 \sqrt[3]{b} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{27 a^{10/3} d}+\frac{7}{18 a^2 d (c+d x) \left(a+b (c+d x)^3\right)}+\frac{14 \sqrt[3]{b} \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{27 a^{10/3} d}+\frac{14 \sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{10/3} d}-\frac{14}{9 a^3 d (c+d x)}+\frac{1}{6 a d (c+d x) \left(a+b (c+d x)^3\right)^2}",1,"-14/(9*a^3*d*(c + d*x)) + 1/(6*a*d*(c + d*x)*(a + b*(c + d*x)^3)^2) + 7/(18*a^2*d*(c + d*x)*(a + b*(c + d*x)^3)) + (14*b^(1/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(10/3)*d) + (14*b^(1/3)*Log[a^(1/3) + b^(1/3)*(c + d*x)])/(27*a^(10/3)*d) - (7*b^(1/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2])/(27*a^(10/3)*d)","A",10,9,21,0.4286,1,"{372, 290, 325, 292, 31, 634, 617, 204, 628}"
2884,1,219,0,0.1791399,"\int \frac{1}{(c+d x)^3 \left(a+b (c+d x)^3\right)^3} \, dx","Int[1/((c + d*x)^3*(a + b*(c + d*x)^3)^3),x]","-\frac{20 b^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{27 a^{11/3} d}+\frac{10 b^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{27 a^{11/3} d}+\frac{20 b^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{11/3} d}+\frac{4}{9 a^2 d (c+d x)^2 \left(a+b (c+d x)^3\right)}-\frac{10}{9 a^3 d (c+d x)^2}+\frac{1}{6 a d (c+d x)^2 \left(a+b (c+d x)^3\right)^2}","-\frac{20 b^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{27 a^{11/3} d}+\frac{10 b^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{27 a^{11/3} d}+\frac{20 b^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{11/3} d}+\frac{4}{9 a^2 d (c+d x)^2 \left(a+b (c+d x)^3\right)}-\frac{10}{9 a^3 d (c+d x)^2}+\frac{1}{6 a d (c+d x)^2 \left(a+b (c+d x)^3\right)^2}",1,"-10/(9*a^3*d*(c + d*x)^2) + 1/(6*a*d*(c + d*x)^2*(a + b*(c + d*x)^3)^2) + 4/(9*a^2*d*(c + d*x)^2*(a + b*(c + d*x)^3)) + (20*b^(2/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(11/3)*d) - (20*b^(2/3)*Log[a^(1/3) + b^(1/3)*(c + d*x)])/(27*a^(11/3)*d) + (10*b^(2/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2])/(27*a^(11/3)*d)","A",10,9,21,0.4286,1,"{372, 290, 325, 200, 31, 634, 617, 204, 628}"
2885,1,101,0,0.0951593,"\int \frac{1}{(c+d x)^4 \left(a+b (c+d x)^3\right)^3} \, dx","Int[1/((c + d*x)^4*(a + b*(c + d*x)^3)^3),x]","-\frac{2 b}{3 a^3 d \left(a+b (c+d x)^3\right)}-\frac{b}{6 a^2 d \left(a+b (c+d x)^3\right)^2}-\frac{3 b \log (c+d x)}{a^4 d}+\frac{b \log \left(a+b (c+d x)^3\right)}{a^4 d}-\frac{1}{3 a^3 d (c+d x)^3}","-\frac{2 b}{3 a^3 d \left(a+b (c+d x)^3\right)}-\frac{b}{6 a^2 d \left(a+b (c+d x)^3\right)^2}-\frac{3 b \log (c+d x)}{a^4 d}+\frac{b \log \left(a+b (c+d x)^3\right)}{a^4 d}-\frac{1}{3 a^3 d (c+d x)^3}",1,"-1/(3*a^3*d*(c + d*x)^3) - b/(6*a^2*d*(a + b*(c + d*x)^3)^2) - (2*b)/(3*a^3*d*(a + b*(c + d*x)^3)) - (3*b*Log[c + d*x])/(a^4*d) + (b*Log[a + b*(c + d*x)^3])/(a^4*d)","A",4,3,21,0.1429,1,"{372, 266, 44}"
2886,1,168,0,0.1343112,"\int \frac{(c e+d e x)^4}{a+b (c+d x)^3} \, dx","Int[(c*e + d*e*x)^4/(a + b*(c + d*x)^3),x]","\frac{a^{2/3} e^4 \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{3 b^{5/3} d}-\frac{a^{2/3} e^4 \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{6 b^{5/3} d}+\frac{a^{2/3} e^4 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^{5/3} d}+\frac{e^4 (c+d x)^2}{2 b d}","\frac{a^{2/3} e^4 \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{3 b^{5/3} d}-\frac{a^{2/3} e^4 \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{6 b^{5/3} d}+\frac{a^{2/3} e^4 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^{5/3} d}+\frac{e^4 (c+d x)^2}{2 b d}",1,"(e^4*(c + d*x)^2)/(2*b*d) + (a^(2/3)*e^4*ArcTan[(a^(1/3) - 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*b^(5/3)*d) + (a^(2/3)*e^4*Log[a^(1/3) + b^(1/3)*(c + d*x)])/(3*b^(5/3)*d) - (a^(2/3)*e^4*Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2])/(6*b^(5/3)*d)","A",8,8,24,0.3333,1,"{372, 321, 292, 31, 634, 617, 204, 628}"
2887,1,156,0,0.1294917,"\int \frac{(c e+d e x)^3}{a+b (c+d x)^3} \, dx","Int[(c*e + d*e*x)^3/(a + b*(c + d*x)^3),x]","\frac{\sqrt[3]{a} e^3 \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{6 b^{4/3} d}-\frac{\sqrt[3]{a} e^3 \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{3 b^{4/3} d}+\frac{\sqrt[3]{a} e^3 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^{4/3} d}+\frac{e^3 x}{b}","\frac{\sqrt[3]{a} e^3 \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{6 b^{4/3} d}-\frac{\sqrt[3]{a} e^3 \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{3 b^{4/3} d}+\frac{\sqrt[3]{a} e^3 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^{4/3} d}+\frac{e^3 x}{b}",1,"(e^3*x)/b + (a^(1/3)*e^3*ArcTan[(a^(1/3) - 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*b^(4/3)*d) - (a^(1/3)*e^3*Log[a^(1/3) + b^(1/3)*(c + d*x)])/(3*b^(4/3)*d) + (a^(1/3)*e^3*Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2])/(6*b^(4/3)*d)","A",8,8,24,0.3333,1,"{372, 321, 200, 31, 634, 617, 204, 628}"
2888,1,25,0,0.0201235,"\int \frac{(c e+d e x)^2}{a+b (c+d x)^3} \, dx","Int[(c*e + d*e*x)^2/(a + b*(c + d*x)^3),x]","\frac{e^2 \log \left(a+b (c+d x)^3\right)}{3 b d}","\frac{e^2 \log \left(a+b (c+d x)^3\right)}{3 b d}",1,"(e^2*Log[a + b*(c + d*x)^3])/(3*b*d)","A",2,2,24,0.08333,1,"{372, 260}"
2889,1,143,0,0.1190654,"\int \frac{c e+d e x}{a+b (c+d x)^3} \, dx","Int[(c*e + d*e*x)/(a + b*(c + d*x)^3),x]","\frac{e \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{6 \sqrt[3]{a} b^{2/3} d}-\frac{e \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{3 \sqrt[3]{a} b^{2/3} d}-\frac{e \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} \sqrt[3]{a} b^{2/3} d}","\frac{e \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{6 \sqrt[3]{a} b^{2/3} d}-\frac{e \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{3 \sqrt[3]{a} b^{2/3} d}-\frac{e \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} \sqrt[3]{a} b^{2/3} d}",1,"-((e*ArcTan[(a^(1/3) - 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(1/3)*b^(2/3)*d)) - (e*Log[a^(1/3) + b^(1/3)*(c + d*x)])/(3*a^(1/3)*b^(2/3)*d) + (e*Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2])/(6*a^(1/3)*b^(2/3)*d)","A",7,7,22,0.3182,1,"{372, 292, 31, 634, 617, 204, 628}"
2890,1,42,0,0.033349,"\int \frac{1}{(c e+d e x) \left(a+b (c+d x)^3\right)} \, dx","Int[1/((c*e + d*e*x)*(a + b*(c + d*x)^3)),x]","\frac{\log (c+d x)}{a d e}-\frac{\log \left(a+b (c+d x)^3\right)}{3 a d e}","\frac{\log (c+d x)}{a d e}-\frac{\log \left(a+b (c+d x)^3\right)}{3 a d e}",1,"Log[c + d*x]/(a*d*e) - Log[a + b*(c + d*x)^3]/(3*a*d*e)","A",5,5,24,0.2083,1,"{372, 266, 36, 29, 31}"
2891,1,166,0,0.1303279,"\int \frac{1}{(c e+d e x)^2 \left(a+b (c+d x)^3\right)} \, dx","Int[1/((c*e + d*e*x)^2*(a + b*(c + d*x)^3)),x]","-\frac{\sqrt[3]{b} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{6 a^{4/3} d e^2}+\frac{\sqrt[3]{b} \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{3 a^{4/3} d e^2}+\frac{\sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{4/3} d e^2}-\frac{1}{a d e^2 (c+d x)}","-\frac{\sqrt[3]{b} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{6 a^{4/3} d e^2}+\frac{\sqrt[3]{b} \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{3 a^{4/3} d e^2}+\frac{\sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{4/3} d e^2}-\frac{1}{a d e^2 (c+d x)}",1,"-(1/(a*d*e^2*(c + d*x))) + (b^(1/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(4/3)*d*e^2) + (b^(1/3)*Log[a^(1/3) + b^(1/3)*(c + d*x)])/(3*a^(4/3)*d*e^2) - (b^(1/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2])/(6*a^(4/3)*d*e^2)","A",8,8,24,0.3333,1,"{372, 325, 292, 31, 634, 617, 204, 628}"
2892,1,168,0,0.126265,"\int \frac{1}{(c e+d e x)^3 \left(a+b (c+d x)^3\right)} \, dx","Int[1/((c*e + d*e*x)^3*(a + b*(c + d*x)^3)),x]","-\frac{b^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{3 a^{5/3} d e^3}+\frac{b^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{6 a^{5/3} d e^3}+\frac{b^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{5/3} d e^3}-\frac{1}{2 a d e^3 (c+d x)^2}","-\frac{b^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{3 a^{5/3} d e^3}+\frac{b^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{6 a^{5/3} d e^3}+\frac{b^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{5/3} d e^3}-\frac{1}{2 a d e^3 (c+d x)^2}",1,"-1/(2*a*d*e^3*(c + d*x)^2) + (b^(2/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(5/3)*d*e^3) - (b^(2/3)*Log[a^(1/3) + b^(1/3)*(c + d*x)])/(3*a^(5/3)*d*e^3) + (b^(2/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2])/(6*a^(5/3)*d*e^3)","A",8,8,24,0.3333,1,"{372, 325, 200, 31, 634, 617, 204, 628}"
2893,1,65,0,0.0452679,"\int \frac{1}{(c e+d e x)^4 \left(a+b (c+d x)^3\right)} \, dx","Int[1/((c*e + d*e*x)^4*(a + b*(c + d*x)^3)),x]","-\frac{b \log (c+d x)}{a^2 d e^4}+\frac{b \log \left(a+b (c+d x)^3\right)}{3 a^2 d e^4}-\frac{1}{3 a d e^4 (c+d x)^3}","-\frac{b \log (c+d x)}{a^2 d e^4}+\frac{b \log \left(a+b (c+d x)^3\right)}{3 a^2 d e^4}-\frac{1}{3 a d e^4 (c+d x)^3}",1,"-1/(3*a*d*e^4*(c + d*x)^3) - (b*Log[c + d*x])/(a^2*d*e^4) + (b*Log[a + b*(c + d*x)^3])/(3*a^2*d*e^4)","A",4,3,24,0.1250,1,"{372, 266, 44}"
2894,1,184,0,0.142301,"\int \frac{(c e+d e x)^4}{\left(a+b (c+d x)^3\right)^2} \, dx","Int[(c*e + d*e*x)^4/(a + b*(c + d*x)^3)^2,x]","\frac{e^4 \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{9 \sqrt[3]{a} b^{5/3} d}-\frac{2 e^4 \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{9 \sqrt[3]{a} b^{5/3} d}-\frac{2 e^4 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} \sqrt[3]{a} b^{5/3} d}-\frac{e^4 (c+d x)^2}{3 b d \left(a+b (c+d x)^3\right)}","\frac{e^4 \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{9 \sqrt[3]{a} b^{5/3} d}-\frac{2 e^4 \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{9 \sqrt[3]{a} b^{5/3} d}-\frac{2 e^4 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} \sqrt[3]{a} b^{5/3} d}-\frac{e^4 (c+d x)^2}{3 b d \left(a+b (c+d x)^3\right)}",1,"-(e^4*(c + d*x)^2)/(3*b*d*(a + b*(c + d*x)^3)) - (2*e^4*ArcTan[(a^(1/3) - 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(1/3)*b^(5/3)*d) - (2*e^4*Log[a^(1/3) + b^(1/3)*(c + d*x)])/(9*a^(1/3)*b^(5/3)*d) + (e^4*Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2])/(9*a^(1/3)*b^(5/3)*d)","A",8,8,24,0.3333,1,"{372, 288, 292, 31, 634, 617, 204, 628}"
2895,1,182,0,0.1402133,"\int \frac{(c e+d e x)^3}{\left(a+b (c+d x)^3\right)^2} \, dx","Int[(c*e + d*e*x)^3/(a + b*(c + d*x)^3)^2,x]","\frac{e^3 \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{9 a^{2/3} b^{4/3} d}-\frac{e^3 \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{18 a^{2/3} b^{4/3} d}-\frac{e^3 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{2/3} b^{4/3} d}-\frac{e^3 (c+d x)}{3 b d \left(a+b (c+d x)^3\right)}","\frac{e^3 \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{9 a^{2/3} b^{4/3} d}-\frac{e^3 \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{18 a^{2/3} b^{4/3} d}-\frac{e^3 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{2/3} b^{4/3} d}-\frac{e^3 (c+d x)}{3 b d \left(a+b (c+d x)^3\right)}",1,"-(e^3*(c + d*x))/(3*b*d*(a + b*(c + d*x)^3)) - (e^3*ArcTan[(a^(1/3) - 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(2/3)*b^(4/3)*d) + (e^3*Log[a^(1/3) + b^(1/3)*(c + d*x)])/(9*a^(2/3)*b^(4/3)*d) - (e^3*Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2])/(18*a^(2/3)*b^(4/3)*d)","A",8,8,24,0.3333,1,"{372, 288, 200, 31, 634, 617, 204, 628}"
2896,1,26,0,0.0218556,"\int \frac{(c e+d e x)^2}{\left(a+b (c+d x)^3\right)^2} \, dx","Int[(c*e + d*e*x)^2/(a + b*(c + d*x)^3)^2,x]","-\frac{e^2}{3 b d \left(a+b (c+d x)^3\right)}","-\frac{e^2}{3 b d \left(a+b (c+d x)^3\right)}",1,"-e^2/(3*b*d*(a + b*(c + d*x)^3))","A",2,2,24,0.08333,1,"{372, 261}"
2897,1,176,0,0.1448194,"\int \frac{c e+d e x}{\left(a+b (c+d x)^3\right)^2} \, dx","Int[(c*e + d*e*x)/(a + b*(c + d*x)^3)^2,x]","-\frac{e \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{9 a^{4/3} b^{2/3} d}+\frac{e \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{18 a^{4/3} b^{2/3} d}-\frac{e \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{4/3} b^{2/3} d}+\frac{e (c+d x)^2}{3 a d \left(a+b (c+d x)^3\right)}","-\frac{e \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{9 a^{4/3} b^{2/3} d}+\frac{e \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{18 a^{4/3} b^{2/3} d}-\frac{e \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{4/3} b^{2/3} d}+\frac{e (c+d x)^2}{3 a d \left(a+b (c+d x)^3\right)}",1,"(e*(c + d*x)^2)/(3*a*d*(a + b*(c + d*x)^3)) - (e*ArcTan[(a^(1/3) - 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(4/3)*b^(2/3)*d) - (e*Log[a^(1/3) + b^(1/3)*(c + d*x)])/(9*a^(4/3)*b^(2/3)*d) + (e*Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2])/(18*a^(4/3)*b^(2/3)*d)","A",8,8,22,0.3636,1,"{372, 290, 292, 31, 634, 617, 204, 628}"
2898,1,68,0,0.0581019,"\int \frac{1}{(c e+d e x) \left(a+b (c+d x)^3\right)^2} \, dx","Int[1/((c*e + d*e*x)*(a + b*(c + d*x)^3)^2),x]","-\frac{\log \left(a+b (c+d x)^3\right)}{3 a^2 d e}+\frac{\log (c+d x)}{a^2 d e}+\frac{1}{3 a d e \left(a+b (c+d x)^3\right)}","-\frac{\log \left(a+b (c+d x)^3\right)}{3 a^2 d e}+\frac{\log (c+d x)}{a^2 d e}+\frac{1}{3 a d e \left(a+b (c+d x)^3\right)}",1,"1/(3*a*d*e*(a + b*(c + d*x)^3)) + Log[c + d*x]/(a^2*d*e) - Log[a + b*(c + d*x)^3]/(3*a^2*d*e)","A",4,3,24,0.1250,1,"{372, 266, 44}"
2899,1,204,0,0.1512367,"\int \frac{1}{(c e+d e x)^2 \left(a+b (c+d x)^3\right)^2} \, dx","Int[1/((c*e + d*e*x)^2*(a + b*(c + d*x)^3)^2),x]","-\frac{2 \sqrt[3]{b} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{9 a^{7/3} d e^2}+\frac{4 \sqrt[3]{b} \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{9 a^{7/3} d e^2}+\frac{4 \sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{7/3} d e^2}-\frac{4}{3 a^2 d e^2 (c+d x)}+\frac{1}{3 a d e^2 (c+d x) \left(a+b (c+d x)^3\right)}","-\frac{2 \sqrt[3]{b} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{9 a^{7/3} d e^2}+\frac{4 \sqrt[3]{b} \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{9 a^{7/3} d e^2}+\frac{4 \sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{7/3} d e^2}-\frac{4}{3 a^2 d e^2 (c+d x)}+\frac{1}{3 a d e^2 (c+d x) \left(a+b (c+d x)^3\right)}",1,"-4/(3*a^2*d*e^2*(c + d*x)) + 1/(3*a*d*e^2*(c + d*x)*(a + b*(c + d*x)^3)) + (4*b^(1/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(7/3)*d*e^2) + (4*b^(1/3)*Log[a^(1/3) + b^(1/3)*(c + d*x)])/(9*a^(7/3)*d*e^2) - (2*b^(1/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2])/(9*a^(7/3)*d*e^2)","A",9,9,24,0.3750,1,"{372, 290, 325, 292, 31, 634, 617, 204, 628}"
2900,1,204,0,0.1504364,"\int \frac{1}{(c e+d e x)^3 \left(a+b (c+d x)^3\right)^2} \, dx","Int[1/((c*e + d*e*x)^3*(a + b*(c + d*x)^3)^2),x]","-\frac{5 b^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{9 a^{8/3} d e^3}+\frac{5 b^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{18 a^{8/3} d e^3}+\frac{5 b^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{8/3} d e^3}-\frac{5}{6 a^2 d e^3 (c+d x)^2}+\frac{1}{3 a d e^3 (c+d x)^2 \left(a+b (c+d x)^3\right)}","-\frac{5 b^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{9 a^{8/3} d e^3}+\frac{5 b^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{18 a^{8/3} d e^3}+\frac{5 b^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{8/3} d e^3}-\frac{5}{6 a^2 d e^3 (c+d x)^2}+\frac{1}{3 a d e^3 (c+d x)^2 \left(a+b (c+d x)^3\right)}",1,"-5/(6*a^2*d*e^3*(c + d*x)^2) + 1/(3*a*d*e^3*(c + d*x)^2*(a + b*(c + d*x)^3)) + (5*b^(2/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(8/3)*d*e^3) - (5*b^(2/3)*Log[a^(1/3) + b^(1/3)*(c + d*x)])/(9*a^(8/3)*d*e^3) + (5*b^(2/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2])/(18*a^(8/3)*d*e^3)","A",9,9,24,0.3750,1,"{372, 290, 325, 200, 31, 634, 617, 204, 628}"
2901,1,92,0,0.0673652,"\int \frac{1}{(c e+d e x)^4 \left(a+b (c+d x)^3\right)^2} \, dx","Int[1/((c*e + d*e*x)^4*(a + b*(c + d*x)^3)^2),x]","-\frac{b}{3 a^2 d e^4 \left(a+b (c+d x)^3\right)}-\frac{2 b \log (c+d x)}{a^3 d e^4}+\frac{2 b \log \left(a+b (c+d x)^3\right)}{3 a^3 d e^4}-\frac{1}{3 a^2 d e^4 (c+d x)^3}","-\frac{b}{3 a^2 d e^4 \left(a+b (c+d x)^3\right)}-\frac{2 b \log (c+d x)}{a^3 d e^4}+\frac{2 b \log \left(a+b (c+d x)^3\right)}{3 a^3 d e^4}-\frac{1}{3 a^2 d e^4 (c+d x)^3}",1,"-1/(3*a^2*d*e^4*(c + d*x)^3) - b/(3*a^2*d*e^4*(a + b*(c + d*x)^3)) - (2*b*Log[c + d*x])/(a^3*d*e^4) + (2*b*Log[a + b*(c + d*x)^3])/(3*a^3*d*e^4)","A",4,3,24,0.1250,1,"{372, 266, 44}"
2902,1,220,0,0.1597118,"\int \frac{(c e+d e x)^4}{\left(a+b (c+d x)^3\right)^3} \, dx","Int[(c*e + d*e*x)^4/(a + b*(c + d*x)^3)^3,x]","-\frac{e^4 \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{27 a^{4/3} b^{5/3} d}+\frac{e^4 \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{54 a^{4/3} b^{5/3} d}-\frac{e^4 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{4/3} b^{5/3} d}+\frac{e^4 (c+d x)^2}{9 a b d \left(a+b (c+d x)^3\right)}-\frac{e^4 (c+d x)^2}{6 b d \left(a+b (c+d x)^3\right)^2}","-\frac{e^4 \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{27 a^{4/3} b^{5/3} d}+\frac{e^4 \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{54 a^{4/3} b^{5/3} d}-\frac{e^4 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{4/3} b^{5/3} d}+\frac{e^4 (c+d x)^2}{9 a b d \left(a+b (c+d x)^3\right)}-\frac{e^4 (c+d x)^2}{6 b d \left(a+b (c+d x)^3\right)^2}",1,"-(e^4*(c + d*x)^2)/(6*b*d*(a + b*(c + d*x)^3)^2) + (e^4*(c + d*x)^2)/(9*a*b*d*(a + b*(c + d*x)^3)) - (e^4*ArcTan[(a^(1/3) - 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(4/3)*b^(5/3)*d) - (e^4*Log[a^(1/3) + b^(1/3)*(c + d*x)])/(27*a^(4/3)*b^(5/3)*d) + (e^4*Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2])/(54*a^(4/3)*b^(5/3)*d)","A",9,9,24,0.3750,1,"{372, 288, 290, 292, 31, 634, 617, 204, 628}"
2903,1,216,0,0.1648382,"\int \frac{(c e+d e x)^3}{\left(a+b (c+d x)^3\right)^3} \, dx","Int[(c*e + d*e*x)^3/(a + b*(c + d*x)^3)^3,x]","\frac{e^3 \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{27 a^{5/3} b^{4/3} d}-\frac{e^3 \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{54 a^{5/3} b^{4/3} d}-\frac{e^3 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{5/3} b^{4/3} d}+\frac{e^3 (c+d x)}{18 a b d \left(a+b (c+d x)^3\right)}-\frac{e^3 (c+d x)}{6 b d \left(a+b (c+d x)^3\right)^2}","\frac{e^3 \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{27 a^{5/3} b^{4/3} d}-\frac{e^3 \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{54 a^{5/3} b^{4/3} d}-\frac{e^3 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{5/3} b^{4/3} d}+\frac{e^3 (c+d x)}{18 a b d \left(a+b (c+d x)^3\right)}-\frac{e^3 (c+d x)}{6 b d \left(a+b (c+d x)^3\right)^2}",1,"-(e^3*(c + d*x))/(6*b*d*(a + b*(c + d*x)^3)^2) + (e^3*(c + d*x))/(18*a*b*d*(a + b*(c + d*x)^3)) - (e^3*ArcTan[(a^(1/3) - 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(5/3)*b^(4/3)*d) + (e^3*Log[a^(1/3) + b^(1/3)*(c + d*x)])/(27*a^(5/3)*b^(4/3)*d) - (e^3*Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2])/(54*a^(5/3)*b^(4/3)*d)","A",9,9,24,0.3750,1,"{372, 288, 199, 200, 31, 634, 617, 204, 628}"
2904,1,26,0,0.0205789,"\int \frac{(c e+d e x)^2}{\left(a+b (c+d x)^3\right)^3} \, dx","Int[(c*e + d*e*x)^2/(a + b*(c + d*x)^3)^3,x]","-\frac{e^2}{6 b d \left(a+b (c+d x)^3\right)^2}","-\frac{e^2}{6 b d \left(a+b (c+d x)^3\right)^2}",1,"-e^2/(6*b*d*(a + b*(c + d*x)^3)^2)","A",2,2,24,0.08333,1,"{372, 261}"
2905,1,207,0,0.1744874,"\int \frac{c e+d e x}{\left(a+b (c+d x)^3\right)^3} \, dx","Int[(c*e + d*e*x)/(a + b*(c + d*x)^3)^3,x]","-\frac{2 e \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{27 a^{7/3} b^{2/3} d}+\frac{e \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{27 a^{7/3} b^{2/3} d}-\frac{2 e \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{7/3} b^{2/3} d}+\frac{2 e (c+d x)^2}{9 a^2 d \left(a+b (c+d x)^3\right)}+\frac{e (c+d x)^2}{6 a d \left(a+b (c+d x)^3\right)^2}","-\frac{2 e \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{27 a^{7/3} b^{2/3} d}+\frac{e \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{27 a^{7/3} b^{2/3} d}-\frac{2 e \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{7/3} b^{2/3} d}+\frac{2 e (c+d x)^2}{9 a^2 d \left(a+b (c+d x)^3\right)}+\frac{e (c+d x)^2}{6 a d \left(a+b (c+d x)^3\right)^2}",1,"(e*(c + d*x)^2)/(6*a*d*(a + b*(c + d*x)^3)^2) + (2*e*(c + d*x)^2)/(9*a^2*d*(a + b*(c + d*x)^3)) - (2*e*ArcTan[(a^(1/3) - 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(7/3)*b^(2/3)*d) - (2*e*Log[a^(1/3) + b^(1/3)*(c + d*x)])/(27*a^(7/3)*b^(2/3)*d) + (e*Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2])/(27*a^(7/3)*b^(2/3)*d)","A",9,8,22,0.3636,1,"{372, 290, 292, 31, 634, 617, 204, 628}"
2906,1,94,0,0.0825657,"\int \frac{1}{(c e+d e x) \left(a+b (c+d x)^3\right)^3} \, dx","Int[1/((c*e + d*e*x)*(a + b*(c + d*x)^3)^3),x]","\frac{1}{3 a^2 d e \left(a+b (c+d x)^3\right)}-\frac{\log \left(a+b (c+d x)^3\right)}{3 a^3 d e}+\frac{\log (c+d x)}{a^3 d e}+\frac{1}{6 a d e \left(a+b (c+d x)^3\right)^2}","\frac{1}{3 a^2 d e \left(a+b (c+d x)^3\right)}-\frac{\log \left(a+b (c+d x)^3\right)}{3 a^3 d e}+\frac{\log (c+d x)}{a^3 d e}+\frac{1}{6 a d e \left(a+b (c+d x)^3\right)^2}",1,"1/(6*a*d*e*(a + b*(c + d*x)^3)^2) + 1/(3*a^2*d*e*(a + b*(c + d*x)^3)) + Log[c + d*x]/(a^3*d*e) - Log[a + b*(c + d*x)^3]/(3*a^3*d*e)","A",4,3,24,0.1250,1,"{372, 266, 44}"
2907,1,237,0,0.1808758,"\int \frac{1}{(c e+d e x)^2 \left(a+b (c+d x)^3\right)^3} \, dx","Int[1/((c*e + d*e*x)^2*(a + b*(c + d*x)^3)^3),x]","-\frac{7 \sqrt[3]{b} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{27 a^{10/3} d e^2}+\frac{7}{18 a^2 d e^2 (c+d x) \left(a+b (c+d x)^3\right)}+\frac{14 \sqrt[3]{b} \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{27 a^{10/3} d e^2}+\frac{14 \sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{10/3} d e^2}-\frac{14}{9 a^3 d e^2 (c+d x)}+\frac{1}{6 a d e^2 (c+d x) \left(a+b (c+d x)^3\right)^2}","-\frac{7 \sqrt[3]{b} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{27 a^{10/3} d e^2}+\frac{7}{18 a^2 d e^2 (c+d x) \left(a+b (c+d x)^3\right)}+\frac{14 \sqrt[3]{b} \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{27 a^{10/3} d e^2}+\frac{14 \sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{10/3} d e^2}-\frac{14}{9 a^3 d e^2 (c+d x)}+\frac{1}{6 a d e^2 (c+d x) \left(a+b (c+d x)^3\right)^2}",1,"-14/(9*a^3*d*e^2*(c + d*x)) + 1/(6*a*d*e^2*(c + d*x)*(a + b*(c + d*x)^3)^2) + 7/(18*a^2*d*e^2*(c + d*x)*(a + b*(c + d*x)^3)) + (14*b^(1/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(10/3)*d*e^2) + (14*b^(1/3)*Log[a^(1/3) + b^(1/3)*(c + d*x)])/(27*a^(10/3)*d*e^2) - (7*b^(1/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2])/(27*a^(10/3)*d*e^2)","A",10,9,24,0.3750,1,"{372, 290, 325, 292, 31, 634, 617, 204, 628}"
2908,1,237,0,0.1836309,"\int \frac{1}{(c e+d e x)^3 \left(a+b (c+d x)^3\right)^3} \, dx","Int[1/((c*e + d*e*x)^3*(a + b*(c + d*x)^3)^3),x]","-\frac{20 b^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{27 a^{11/3} d e^3}+\frac{10 b^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{27 a^{11/3} d e^3}+\frac{20 b^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{11/3} d e^3}+\frac{4}{9 a^2 d e^3 (c+d x)^2 \left(a+b (c+d x)^3\right)}-\frac{10}{9 a^3 d e^3 (c+d x)^2}+\frac{1}{6 a d e^3 (c+d x)^2 \left(a+b (c+d x)^3\right)^2}","-\frac{20 b^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{27 a^{11/3} d e^3}+\frac{10 b^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{27 a^{11/3} d e^3}+\frac{20 b^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{11/3} d e^3}+\frac{4}{9 a^2 d e^3 (c+d x)^2 \left(a+b (c+d x)^3\right)}-\frac{10}{9 a^3 d e^3 (c+d x)^2}+\frac{1}{6 a d e^3 (c+d x)^2 \left(a+b (c+d x)^3\right)^2}",1,"-10/(9*a^3*d*e^3*(c + d*x)^2) + 1/(6*a*d*e^3*(c + d*x)^2*(a + b*(c + d*x)^3)^2) + 4/(9*a^2*d*e^3*(c + d*x)^2*(a + b*(c + d*x)^3)) + (20*b^(2/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(11/3)*d*e^3) - (20*b^(2/3)*Log[a^(1/3) + b^(1/3)*(c + d*x)])/(27*a^(11/3)*d*e^3) + (10*b^(2/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2])/(27*a^(11/3)*d*e^3)","A",10,9,24,0.3750,1,"{372, 290, 325, 200, 31, 634, 617, 204, 628}"
2909,1,116,0,0.0892053,"\int \frac{1}{(c e+d e x)^4 \left(a+b (c+d x)^3\right)^3} \, dx","Int[1/((c*e + d*e*x)^4*(a + b*(c + d*x)^3)^3),x]","-\frac{2 b}{3 a^3 d e^4 \left(a+b (c+d x)^3\right)}-\frac{b}{6 a^2 d e^4 \left(a+b (c+d x)^3\right)^2}-\frac{3 b \log (c+d x)}{a^4 d e^4}+\frac{b \log \left(a+b (c+d x)^3\right)}{a^4 d e^4}-\frac{1}{3 a^3 d e^4 (c+d x)^3}","-\frac{2 b}{3 a^3 d e^4 \left(a+b (c+d x)^3\right)}-\frac{b}{6 a^2 d e^4 \left(a+b (c+d x)^3\right)^2}-\frac{3 b \log (c+d x)}{a^4 d e^4}+\frac{b \log \left(a+b (c+d x)^3\right)}{a^4 d e^4}-\frac{1}{3 a^3 d e^4 (c+d x)^3}",1,"-1/(3*a^3*d*e^4*(c + d*x)^3) - b/(6*a^2*d*e^4*(a + b*(c + d*x)^3)^2) - (2*b)/(3*a^3*d*e^4*(a + b*(c + d*x)^3)) - (3*b*Log[c + d*x])/(a^4*d*e^4) + (b*Log[a + b*(c + d*x)^3])/(a^4*d*e^4)","A",4,3,24,0.1250,1,"{372, 266, 44}"
2910,1,30,0,0.0301744,"\int (c+d x)^3 \left(a+b (c+d x)^4\right)^p \, dx","Int[(c + d*x)^3*(a + b*(c + d*x)^4)^p,x]","\frac{\left(a+b (c+d x)^4\right)^{p+1}}{4 b d (p+1)}","\frac{\left(a+b (c+d x)^4\right)^{p+1}}{4 b d (p+1)}",1,"(a + b*(c + d*x)^4)^(1 + p)/(4*b*d*(1 + p))","A",2,2,21,0.09524,1,"{372, 261}"
2911,1,31,0,0.030693,"\int (c+d x)^3 \left(a+b (c+d x)^4\right) \, dx","Int[(c + d*x)^3*(a + b*(c + d*x)^4),x]","\frac{a (c+d x)^4}{4 d}+\frac{b (c+d x)^8}{8 d}","\frac{\left(a+b (c+d x)^4\right)^2}{8 b d}",1,"(a*(c + d*x)^4)/(4*d) + (b*(c + d*x)^8)/(8*d)","A",3,2,19,0.1053,1,"{372, 14}"
2912,1,23,0,0.0931545,"\int (c+d x)^3 \left(a+b (c+d x)^4\right)^2 \, dx","Int[(c + d*x)^3*(a + b*(c + d*x)^4)^2,x]","\frac{\left(a+b (c+d x)^4\right)^3}{12 b d}","\frac{\left(a+b (c+d x)^4\right)^3}{12 b d}",1,"(a + b*(c + d*x)^4)^3/(12*b*d)","A",2,2,21,0.09524,1,"{372, 261}"
2913,1,23,0,0.1657999,"\int (c+d x)^3 \left(a+b (c+d x)^4\right)^3 \, dx","Int[(c + d*x)^3*(a + b*(c + d*x)^4)^3,x]","\frac{\left(a+b (c+d x)^4\right)^4}{16 b d}","\frac{\left(a+b (c+d x)^4\right)^4}{16 b d}",1,"(a + b*(c + d*x)^4)^4/(16*b*d)","A",2,2,21,0.09524,1,"{372, 261}"
2914,1,22,0,0.0242018,"\int \frac{(c+d x)^3}{a+b (c+d x)^4} \, dx","Int[(c + d*x)^3/(a + b*(c + d*x)^4),x]","\frac{\log \left(a+b (c+d x)^4\right)}{4 b d}","\frac{\log \left(a+b (c+d x)^4\right)}{4 b d}",1,"Log[a + b*(c + d*x)^4]/(4*b*d)","A",2,2,21,0.09524,1,"{372, 260}"
2915,1,23,0,0.0255701,"\int \frac{(c+d x)^3}{\left(a+b (c+d x)^4\right)^2} \, dx","Int[(c + d*x)^3/(a + b*(c + d*x)^4)^2,x]","-\frac{1}{4 b d \left(a+b (c+d x)^4\right)}","-\frac{1}{4 b d \left(a+b (c+d x)^4\right)}",1,"-1/(4*b*d*(a + b*(c + d*x)^4))","A",2,2,21,0.09524,1,"{372, 261}"
2916,1,23,0,0.0261986,"\int \frac{(c+d x)^3}{\left(a+b (c+d x)^4\right)^3} \, dx","Int[(c + d*x)^3/(a + b*(c + d*x)^4)^3,x]","-\frac{1}{8 b d \left(a+b (c+d x)^4\right)^2}","-\frac{1}{8 b d \left(a+b (c+d x)^4\right)^2}",1,"-1/(8*b*d*(a + b*(c + d*x)^4)^2)","A",2,2,21,0.09524,1,"{372, 261}"
2917,1,111,0,0.1011648,"\int \frac{1}{\sqrt{a+b (c+d x)^4}} \, dx","Int[1/Sqrt[a + b*(c + d*x)^4],x]","\frac{\left(\sqrt{a}+\sqrt{b} (c+d x)^2\right) \sqrt{\frac{a+b (c+d x)^4}{\left(\sqrt{a}+\sqrt{b} (c+d x)^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a} \sqrt[4]{b} d \sqrt{a+b (c+d x)^4}}","\frac{\left(\sqrt{a}+\sqrt{b} (c+d x)^2\right) \sqrt{\frac{a+b (c+d x)^4}{\left(\sqrt{a}+\sqrt{b} (c+d x)^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a} \sqrt[4]{b} d \sqrt{a+b (c+d x)^4}}",1,"((Sqrt[a] + Sqrt[b]*(c + d*x)^2)*Sqrt[(a + b*(c + d*x)^4)/(Sqrt[a] + Sqrt[b]*(c + d*x)^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*(c + d*x))/a^(1/4)], 1/2])/(2*a^(1/4)*b^(1/4)*d*Sqrt[a + b*(c + d*x)^4])","A",2,2,15,0.1333,1,"{247, 220}"
2918,1,154,0,0.1688295,"\int \frac{x}{\sqrt{a+b (c+d x)^4}} \, dx","Int[x/Sqrt[a + b*(c + d*x)^4],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} (c+d x)^2}{\sqrt{a+b (c+d x)^4}}\right)}{2 \sqrt{b} d^2}-\frac{c \left(\sqrt{a}+\sqrt{b} (c+d x)^2\right) \sqrt{\frac{a+b (c+d x)^4}{\left(\sqrt{a}+\sqrt{b} (c+d x)^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a} \sqrt[4]{b} d^2 \sqrt{a+b (c+d x)^4}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} (c+d x)^2}{\sqrt{a+b (c+d x)^4}}\right)}{2 \sqrt{b} d^2}-\frac{c \left(\sqrt{a}+\sqrt{b} (c+d x)^2\right) \sqrt{\frac{a+b (c+d x)^4}{\left(\sqrt{a}+\sqrt{b} (c+d x)^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a} \sqrt[4]{b} d^2 \sqrt{a+b (c+d x)^4}}",1,"ArcTanh[(Sqrt[b]*(c + d*x)^2)/Sqrt[a + b*(c + d*x)^4]]/(2*Sqrt[b]*d^2) - (c*(Sqrt[a] + Sqrt[b]*(c + d*x)^2)*Sqrt[(a + b*(c + d*x)^4)/(Sqrt[a] + Sqrt[b]*(c + d*x)^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*(c + d*x))/a^(1/4)], 1/2])/(2*a^(1/4)*b^(1/4)*d^2*Sqrt[a + b*(c + d*x)^4])","A",7,6,17,0.3529,1,"{371, 1885, 220, 275, 217, 206}"
2919,1,78,0,0.0827579,"\int (d x)^m \sqrt{a+b (c x)^{3/2}} \, dx","Int[(d*x)^m*Sqrt[a + b*(c*x)^(3/2)],x]","\frac{x (d x)^m \sqrt{a+b (c x)^{3/2}} \, _2F_1\left(-\frac{1}{2},\frac{2 (m+1)}{3};\frac{1}{3} (2 m+5);-\frac{b (c x)^{3/2}}{a}\right)}{(m+1) \sqrt{\frac{b (c x)^{3/2}}{a}+1}}","\frac{x (d x)^m \sqrt{a+b (c x)^{3/2}} \, _2F_1\left(-\frac{1}{2},\frac{2 (m+1)}{3};\frac{1}{3} (2 m+5);-\frac{b (c x)^{3/2}}{a}\right)}{(m+1) \sqrt{\frac{b (c x)^{3/2}}{a}+1}}",1,"(x*(d*x)^m*Sqrt[a + b*(c*x)^(3/2)]*Hypergeometric2F1[-1/2, (2*(1 + m))/3, (5 + 2*m)/3, -((b*(c*x)^(3/2))/a)])/((1 + m)*Sqrt[1 + (b*(c*x)^(3/2))/a])","A",5,5,21,0.2381,1,"{367, 343, 341, 365, 364}"
2920,1,74,0,0.0660279,"\int (d x)^m \sqrt{a+b \sqrt{c x}} \, dx","Int[(d*x)^m*Sqrt[a + b*Sqrt[c*x]],x]","-\frac{4 a (d x)^m \left(a+b \sqrt{c x}\right)^{3/2} \left(-\frac{b \sqrt{c x}}{a}\right)^{-2 m} \, _2F_1\left(\frac{3}{2},-2 m-1;\frac{5}{2};\frac{\sqrt{c x} b}{a}+1\right)}{3 b^2 c}","-\frac{4 a (d x)^m \left(a+b \sqrt{c x}\right)^{3/2} \left(-\frac{b \sqrt{c x}}{a}\right)^{-2 m} \, _2F_1\left(\frac{3}{2},-2 m-1;\frac{5}{2};\frac{\sqrt{c x} b}{a}+1\right)}{3 b^2 c}",1,"(-4*a*(d*x)^m*(a + b*Sqrt[c*x])^(3/2)*Hypergeometric2F1[3/2, -1 - 2*m, 5/2, 1 + (b*Sqrt[c*x])/a])/(3*b^2*c*(-((b*Sqrt[c*x])/a))^(2*m))","A",5,5,21,0.2381,1,"{367, 343, 341, 67, 65}"
2921,1,76,0,0.0928944,"\int (d x)^m \sqrt{a+\frac{b}{\sqrt{c x}}} \, dx","Int[(d*x)^m*Sqrt[a + b/Sqrt[c*x]],x]","\frac{4 b^2 (d x)^m \left(a+\frac{b}{\sqrt{c x}}\right)^{3/2} \left(-\frac{b}{a \sqrt{c x}}\right)^{2 m} \, _2F_1\left(\frac{3}{2},2 m+3;\frac{5}{2};\frac{b}{a \sqrt{c x}}+1\right)}{3 a^3 c}","\frac{4 b^2 (d x)^m \left(a+\frac{b}{\sqrt{c x}}\right)^{3/2} \left(-\frac{b}{a \sqrt{c x}}\right)^{2 m} \, _2F_1\left(\frac{3}{2},2 m+3;\frac{5}{2};\frac{b}{a \sqrt{c x}}+1\right)}{3 a^3 c}",1,"(4*b^2*(d*x)^m*(-(b/(a*Sqrt[c*x])))^(2*m)*(a + b/Sqrt[c*x])^(3/2)*Hypergeometric2F1[3/2, 3 + 2*m, 5/2, 1 + b/(a*Sqrt[c*x])])/(3*a^3*c)","A",6,6,21,0.2857,1,"{367, 343, 341, 339, 67, 65}"
2922,1,78,0,0.1088365,"\int (d x)^m \sqrt{a+\frac{b}{(c x)^{3/2}}} \, dx","Int[(d*x)^m*Sqrt[a + b/(c*x)^(3/2)],x]","\frac{x (d x)^m \sqrt{a+\frac{b}{(c x)^{3/2}}} \, _2F_1\left(-\frac{1}{2},-\frac{2}{3} (m+1);\frac{1}{3} (1-2 m);-\frac{b}{a (c x)^{3/2}}\right)}{(m+1) \sqrt{\frac{b}{a (c x)^{3/2}}+1}}","\frac{x (d x)^m \sqrt{a+\frac{b}{(c x)^{3/2}}} \, _2F_1\left(-\frac{1}{2},-\frac{2}{3} (m+1);\frac{1}{3} (1-2 m);-\frac{b}{a (c x)^{3/2}}\right)}{(m+1) \sqrt{\frac{b}{a (c x)^{3/2}}+1}}",1,"(x*(d*x)^m*Sqrt[a + b/(c*x)^(3/2)]*Hypergeometric2F1[-1/2, (-2*(1 + m))/3, (1 - 2*m)/3, -(b/(a*(c*x)^(3/2)))])/((1 + m)*Sqrt[1 + b/(a*(c*x)^(3/2))])","A",6,6,21,0.2857,1,"{367, 343, 341, 339, 365, 364}"
2923,1,73,0,0.0443885,"\int (d x)^m \left(a+b (c x)^n\right)^p \, dx","Int[(d*x)^m*(a + b*(c*x)^n)^p,x]","\frac{(d x)^{m+1} \left(a+b (c x)^n\right)^p \left(\frac{b (c x)^n}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+1}{n},-p;\frac{m+n+1}{n};-\frac{b (c x)^n}{a}\right)}{d (m+1)}","\frac{(d x)^{m+1} \left(a+b (c x)^n\right)^p \left(\frac{b (c x)^n}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+1}{n},-p;\frac{m+n+1}{n};-\frac{b (c x)^n}{a}\right)}{d (m+1)}",1,"((d*x)^(1 + m)*(a + b*(c*x)^n)^p*Hypergeometric2F1[(1 + m)/n, -p, (1 + m + n)/n, -((b*(c*x)^n)/a)])/(d*(1 + m)*(1 + (b*(c*x)^n)/a)^p)","A",3,3,17,0.1765,1,"{367, 365, 364}"
2924,1,61,0,0.0364421,"\int x^2 \left(a+b (c x)^n\right)^p \, dx","Int[x^2*(a + b*(c*x)^n)^p,x]","\frac{1}{3} x^3 \left(a+b (c x)^n\right)^p \left(\frac{b (c x)^n}{a}+1\right)^{-p} \, _2F_1\left(\frac{3}{n},-p;\frac{n+3}{n};-\frac{b (c x)^n}{a}\right)","\frac{1}{3} x^3 \left(a+b (c x)^n\right)^p \left(\frac{b (c x)^n}{a}+1\right)^{-p} \, _2F_1\left(\frac{3}{n},-p;\frac{n+3}{n};-\frac{b (c x)^n}{a}\right)",1,"(x^3*(a + b*(c*x)^n)^p*Hypergeometric2F1[3/n, -p, (3 + n)/n, -((b*(c*x)^n)/a)])/(3*(1 + (b*(c*x)^n)/a)^p)","A",4,4,15,0.2667,1,"{367, 12, 365, 364}"
2925,1,61,0,0.0326114,"\int x \left(a+b (c x)^n\right)^p \, dx","Int[x*(a + b*(c*x)^n)^p,x]","\frac{1}{2} x^2 \left(a+b (c x)^n\right)^p \left(\frac{b (c x)^n}{a}+1\right)^{-p} \, _2F_1\left(\frac{2}{n},-p;\frac{n+2}{n};-\frac{b (c x)^n}{a}\right)","\frac{1}{2} x^2 \left(a+b (c x)^n\right)^p \left(\frac{b (c x)^n}{a}+1\right)^{-p} \, _2F_1\left(\frac{2}{n},-p;\frac{n+2}{n};-\frac{b (c x)^n}{a}\right)",1,"(x^2*(a + b*(c*x)^n)^p*Hypergeometric2F1[2/n, -p, (2 + n)/n, -((b*(c*x)^n)/a)])/(2*(1 + (b*(c*x)^n)/a)^p)","A",4,4,13,0.3077,1,"{367, 12, 365, 364}"
2926,1,52,0,0.0256385,"\int \left(a+b (c x)^n\right)^p \, dx","Int[(a + b*(c*x)^n)^p,x]","x \left(a+b (c x)^n\right)^p \left(\frac{b (c x)^n}{a}+1\right)^{-p} \, _2F_1\left(\frac{1}{n},-p;1+\frac{1}{n};-\frac{b (c x)^n}{a}\right)","x \left(a+b (c x)^n\right)^p \left(\frac{b (c x)^n}{a}+1\right)^{-p} \, _2F_1\left(\frac{1}{n},-p;1+\frac{1}{n};-\frac{b (c x)^n}{a}\right)",1,"(x*(a + b*(c*x)^n)^p*Hypergeometric2F1[n^(-1), -p, 1 + n^(-1), -((b*(c*x)^n)/a)])/(1 + (b*(c*x)^n)/a)^p","A",3,3,11,0.2727,1,"{247, 246, 245}"
2927,1,46,0,0.0406841,"\int \frac{\left(a+b (c x)^n\right)^p}{x} \, dx","Int[(a + b*(c*x)^n)^p/x,x]","-\frac{\left(a+b (c x)^n\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{b (c x)^n}{a}+1\right)}{a n (p+1)}","-\frac{\left(a+b (c x)^n\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{b (c x)^n}{a}+1\right)}{a n (p+1)}",1,"-(((a + b*(c*x)^n)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, 1 + (b*(c*x)^n)/a])/(a*n*(1 + p)))","A",4,4,15,0.2667,1,"{367, 12, 266, 65}"
2928,1,62,0,0.0350772,"\int \frac{\left(a+b (c x)^n\right)^p}{x^2} \, dx","Int[(a + b*(c*x)^n)^p/x^2,x]","-\frac{\left(a+b (c x)^n\right)^p \left(\frac{b (c x)^n}{a}+1\right)^{-p} \, _2F_1\left(-\frac{1}{n},-p;-\frac{1-n}{n};-\frac{b (c x)^n}{a}\right)}{x}","-\frac{\left(a+b (c x)^n\right)^p \left(\frac{b (c x)^n}{a}+1\right)^{-p} \, _2F_1\left(-\frac{1}{n},-p;-\frac{1-n}{n};-\frac{b (c x)^n}{a}\right)}{x}",1,"-(((a + b*(c*x)^n)^p*Hypergeometric2F1[-n^(-1), -p, -((1 - n)/n), -((b*(c*x)^n)/a)])/(x*(1 + (b*(c*x)^n)/a)^p))","A",4,4,15,0.2667,1,"{367, 12, 365, 364}"
2929,1,83,0,0.0385793,"\int \frac{1}{1+\left(x^2\right)^{3/2}} \, dx","Int[(1 + (x^2)^(3/2))^(-1),x]","-\frac{x \log \left(x^2-\sqrt{x^2}+1\right)}{6 \sqrt{x^2}}+\frac{x \log \left(\sqrt{x^2}+1\right)}{3 \sqrt{x^2}}-\frac{x \tan ^{-1}\left(\frac{1-2 \sqrt{x^2}}{\sqrt{3}}\right)}{\sqrt{3} \sqrt{x^2}}","-\frac{x \log \left(x^2-\sqrt{x^2}+1\right)}{6 \sqrt{x^2}}+\frac{x \log \left(\sqrt{x^2}+1\right)}{3 \sqrt{x^2}}-\frac{x \tan ^{-1}\left(\frac{1-2 \sqrt{x^2}}{\sqrt{3}}\right)}{\sqrt{3} \sqrt{x^2}}",1,"-((x*ArcTan[(1 - 2*Sqrt[x^2])/Sqrt[3]])/(Sqrt[3]*Sqrt[x^2])) - (x*Log[1 + x^2 - Sqrt[x^2]])/(6*Sqrt[x^2]) + (x*Log[1 + Sqrt[x^2]])/(3*Sqrt[x^2])","A",7,7,11,0.6364,1,"{254, 200, 31, 634, 618, 204, 628}"
2930,1,174,0,0.080875,"\int x^5 \sqrt{a+b \sqrt{c x^2}} \, dx","Int[x^5*Sqrt[a + b*Sqrt[c*x^2]],x]","\frac{20 a^2 \left(a+b \sqrt{c x^2}\right)^{9/2}}{9 b^6 c^3}-\frac{20 a^3 \left(a+b \sqrt{c x^2}\right)^{7/2}}{7 b^6 c^3}+\frac{2 a^4 \left(a+b \sqrt{c x^2}\right)^{5/2}}{b^6 c^3}-\frac{2 a^5 \left(a+b \sqrt{c x^2}\right)^{3/2}}{3 b^6 c^3}+\frac{2 \left(a+b \sqrt{c x^2}\right)^{13/2}}{13 b^6 c^3}-\frac{10 a \left(a+b \sqrt{c x^2}\right)^{11/2}}{11 b^6 c^3}","\frac{20 a^2 \left(a+b \sqrt{c x^2}\right)^{9/2}}{9 b^6 c^3}-\frac{20 a^3 \left(a+b \sqrt{c x^2}\right)^{7/2}}{7 b^6 c^3}+\frac{2 a^4 \left(a+b \sqrt{c x^2}\right)^{5/2}}{b^6 c^3}-\frac{2 a^5 \left(a+b \sqrt{c x^2}\right)^{3/2}}{3 b^6 c^3}+\frac{2 \left(a+b \sqrt{c x^2}\right)^{13/2}}{13 b^6 c^3}-\frac{10 a \left(a+b \sqrt{c x^2}\right)^{11/2}}{11 b^6 c^3}",1,"(-2*a^5*(a + b*Sqrt[c*x^2])^(3/2))/(3*b^6*c^3) + (2*a^4*(a + b*Sqrt[c*x^2])^(5/2))/(b^6*c^3) - (20*a^3*(a + b*Sqrt[c*x^2])^(7/2))/(7*b^6*c^3) + (20*a^2*(a + b*Sqrt[c*x^2])^(9/2))/(9*b^6*c^3) - (10*a*(a + b*Sqrt[c*x^2])^(11/2))/(11*b^6*c^3) + (2*(a + b*Sqrt[c*x^2])^(13/2))/(13*b^6*c^3)","A",3,2,21,0.09524,1,"{368, 43}"
2931,1,116,0,0.0524936,"\int x^3 \sqrt{a+b \sqrt{c x^2}} \, dx","Int[x^3*Sqrt[a + b*Sqrt[c*x^2]],x]","\frac{6 a^2 \left(a+b \sqrt{c x^2}\right)^{5/2}}{5 b^4 c^2}-\frac{2 a^3 \left(a+b \sqrt{c x^2}\right)^{3/2}}{3 b^4 c^2}+\frac{2 \left(a+b \sqrt{c x^2}\right)^{9/2}}{9 b^4 c^2}-\frac{6 a \left(a+b \sqrt{c x^2}\right)^{7/2}}{7 b^4 c^2}","\frac{6 a^2 \left(a+b \sqrt{c x^2}\right)^{5/2}}{5 b^4 c^2}-\frac{2 a^3 \left(a+b \sqrt{c x^2}\right)^{3/2}}{3 b^4 c^2}+\frac{2 \left(a+b \sqrt{c x^2}\right)^{9/2}}{9 b^4 c^2}-\frac{6 a \left(a+b \sqrt{c x^2}\right)^{7/2}}{7 b^4 c^2}",1,"(-2*a^3*(a + b*Sqrt[c*x^2])^(3/2))/(3*b^4*c^2) + (6*a^2*(a + b*Sqrt[c*x^2])^(5/2))/(5*b^4*c^2) - (6*a*(a + b*Sqrt[c*x^2])^(7/2))/(7*b^4*c^2) + (2*(a + b*Sqrt[c*x^2])^(9/2))/(9*b^4*c^2)","A",3,2,21,0.09524,1,"{368, 43}"
2932,1,56,0,0.0250762,"\int x \sqrt{a+b \sqrt{c x^2}} \, dx","Int[x*Sqrt[a + b*Sqrt[c*x^2]],x]","\frac{2 \left(a+b \sqrt{c x^2}\right)^{5/2}}{5 b^2 c}-\frac{2 a \left(a+b \sqrt{c x^2}\right)^{3/2}}{3 b^2 c}","\frac{2 \left(a+b \sqrt{c x^2}\right)^{5/2}}{5 b^2 c}-\frac{2 a \left(a+b \sqrt{c x^2}\right)^{3/2}}{3 b^2 c}",1,"(-2*a*(a + b*Sqrt[c*x^2])^(3/2))/(3*b^2*c) + (2*(a + b*Sqrt[c*x^2])^(5/2))/(5*b^2*c)","A",3,2,19,0.1053,1,"{368, 43}"
2933,1,51,0,0.0239181,"\int \frac{\sqrt{a+b \sqrt{c x^2}}}{x} \, dx","Int[Sqrt[a + b*Sqrt[c*x^2]]/x,x]","2 \sqrt{a+b \sqrt{c x^2}}-2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{c x^2}}}{\sqrt{a}}\right)","2 \sqrt{a+b \sqrt{c x^2}}-2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{c x^2}}}{\sqrt{a}}\right)",1,"2*Sqrt[a + b*Sqrt[c*x^2]] - 2*Sqrt[a]*ArcTanh[Sqrt[a + b*Sqrt[c*x^2]]/Sqrt[a]]","A",4,4,21,0.1905,1,"{368, 50, 63, 208}"
2934,1,97,0,0.0427247,"\int \frac{\sqrt{a+b \sqrt{c x^2}}}{x^3} \, dx","Int[Sqrt[a + b*Sqrt[c*x^2]]/x^3,x]","\frac{b^2 c \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{c x^2}}}{\sqrt{a}}\right)}{4 a^{3/2}}-\frac{b c \sqrt{a+b \sqrt{c x^2}}}{4 a \sqrt{c x^2}}-\frac{\sqrt{a+b \sqrt{c x^2}}}{2 x^2}","\frac{b^2 c \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{c x^2}}}{\sqrt{a}}\right)}{4 a^{3/2}}-\frac{b c \sqrt{a+b \sqrt{c x^2}}}{4 a \sqrt{c x^2}}-\frac{\sqrt{a+b \sqrt{c x^2}}}{2 x^2}",1,"-Sqrt[a + b*Sqrt[c*x^2]]/(2*x^2) - (b*c*Sqrt[a + b*Sqrt[c*x^2]])/(4*a*Sqrt[c*x^2]) + (b^2*c*ArcTanh[Sqrt[a + b*Sqrt[c*x^2]]/Sqrt[a]])/(4*a^(3/2))","A",5,5,21,0.2381,1,"{368, 47, 51, 63, 208}"
2935,1,171,0,0.0781574,"\int \frac{\sqrt{a+b \sqrt{c x^2}}}{x^5} \, dx","Int[Sqrt[a + b*Sqrt[c*x^2]]/x^5,x]","-\frac{5 b^3 c^2 \sqrt{a+b \sqrt{c x^2}}}{64 a^3 \sqrt{c x^2}}+\frac{5 b^4 c^2 \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{c x^2}}}{\sqrt{a}}\right)}{64 a^{7/2}}+\frac{5 b^2 c \sqrt{a+b \sqrt{c x^2}}}{96 a^2 x^2}-\frac{b c^2 \sqrt{a+b \sqrt{c x^2}}}{24 a \left(c x^2\right)^{3/2}}-\frac{\sqrt{a+b \sqrt{c x^2}}}{4 x^4}","-\frac{5 b^3 c^2 \sqrt{a+b \sqrt{c x^2}}}{64 a^3 \sqrt{c x^2}}+\frac{5 b^4 c^2 \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{c x^2}}}{\sqrt{a}}\right)}{64 a^{7/2}}+\frac{5 b^2 c \sqrt{a+b \sqrt{c x^2}}}{96 a^2 x^2}-\frac{b c^2 \sqrt{a+b \sqrt{c x^2}}}{24 a \left(c x^2\right)^{3/2}}-\frac{\sqrt{a+b \sqrt{c x^2}}}{4 x^4}",1,"-Sqrt[a + b*Sqrt[c*x^2]]/(4*x^4) + (5*b^2*c*Sqrt[a + b*Sqrt[c*x^2]])/(96*a^2*x^2) - (b*c^2*Sqrt[a + b*Sqrt[c*x^2]])/(24*a*(c*x^2)^(3/2)) - (5*b^3*c^2*Sqrt[a + b*Sqrt[c*x^2]])/(64*a^3*Sqrt[c*x^2]) + (5*b^4*c^2*ArcTanh[Sqrt[a + b*Sqrt[c*x^2]]/Sqrt[a]])/(64*a^(7/2))","A",7,5,21,0.2381,1,"{368, 47, 51, 63, 208}"
2936,1,191,0,0.0680984,"\int x^4 \sqrt{a+b \sqrt{c x^2}} \, dx","Int[x^4*Sqrt[a + b*Sqrt[c*x^2]],x]","\frac{12 a^2 x^5 \left(a+b \sqrt{c x^2}\right)^{7/2}}{7 b^5 \left(c x^2\right)^{5/2}}-\frac{8 a^3 x^5 \left(a+b \sqrt{c x^2}\right)^{5/2}}{5 b^5 \left(c x^2\right)^{5/2}}+\frac{2 a^4 x^5 \left(a+b \sqrt{c x^2}\right)^{3/2}}{3 b^5 \left(c x^2\right)^{5/2}}+\frac{2 x^5 \left(a+b \sqrt{c x^2}\right)^{11/2}}{11 b^5 \left(c x^2\right)^{5/2}}-\frac{8 a x^5 \left(a+b \sqrt{c x^2}\right)^{9/2}}{9 b^5 \left(c x^2\right)^{5/2}}","\frac{12 a^2 x^5 \left(a+b \sqrt{c x^2}\right)^{7/2}}{7 b^5 \left(c x^2\right)^{5/2}}-\frac{8 a^3 x^5 \left(a+b \sqrt{c x^2}\right)^{5/2}}{5 b^5 \left(c x^2\right)^{5/2}}+\frac{2 a^4 x^5 \left(a+b \sqrt{c x^2}\right)^{3/2}}{3 b^5 \left(c x^2\right)^{5/2}}+\frac{2 x^5 \left(a+b \sqrt{c x^2}\right)^{11/2}}{11 b^5 \left(c x^2\right)^{5/2}}-\frac{8 a x^5 \left(a+b \sqrt{c x^2}\right)^{9/2}}{9 b^5 \left(c x^2\right)^{5/2}}",1,"(2*a^4*x^5*(a + b*Sqrt[c*x^2])^(3/2))/(3*b^5*(c*x^2)^(5/2)) - (8*a^3*x^5*(a + b*Sqrt[c*x^2])^(5/2))/(5*b^5*(c*x^2)^(5/2)) + (12*a^2*x^5*(a + b*Sqrt[c*x^2])^(7/2))/(7*b^5*(c*x^2)^(5/2)) - (8*a*x^5*(a + b*Sqrt[c*x^2])^(9/2))/(9*b^5*(c*x^2)^(5/2)) + (2*x^5*(a + b*Sqrt[c*x^2])^(11/2))/(11*b^5*(c*x^2)^(5/2))","A",3,2,21,0.09524,1,"{368, 43}"
2937,1,113,0,0.0397586,"\int x^2 \sqrt{a+b \sqrt{c x^2}} \, dx","Int[x^2*Sqrt[a + b*Sqrt[c*x^2]],x]","\frac{2 a^2 x^3 \left(a+b \sqrt{c x^2}\right)^{3/2}}{3 b^3 \left(c x^2\right)^{3/2}}+\frac{2 x^3 \left(a+b \sqrt{c x^2}\right)^{7/2}}{7 b^3 \left(c x^2\right)^{3/2}}-\frac{4 a x^3 \left(a+b \sqrt{c x^2}\right)^{5/2}}{5 b^3 \left(c x^2\right)^{3/2}}","\frac{2 a^2 x^3 \left(a+b \sqrt{c x^2}\right)^{3/2}}{3 b^3 \left(c x^2\right)^{3/2}}+\frac{2 x^3 \left(a+b \sqrt{c x^2}\right)^{7/2}}{7 b^3 \left(c x^2\right)^{3/2}}-\frac{4 a x^3 \left(a+b \sqrt{c x^2}\right)^{5/2}}{5 b^3 \left(c x^2\right)^{3/2}}",1,"(2*a^2*x^3*(a + b*Sqrt[c*x^2])^(3/2))/(3*b^3*(c*x^2)^(3/2)) - (4*a*x^3*(a + b*Sqrt[c*x^2])^(5/2))/(5*b^3*(c*x^2)^(3/2)) + (2*x^3*(a + b*Sqrt[c*x^2])^(7/2))/(7*b^3*(c*x^2)^(3/2))","A",3,2,21,0.09524,1,"{368, 43}"
2938,1,34,0,0.0105151,"\int \sqrt{a+b \sqrt{c x^2}} \, dx","Int[Sqrt[a + b*Sqrt[c*x^2]],x]","\frac{2 x \left(a+b \sqrt{c x^2}\right)^{3/2}}{3 b \sqrt{c x^2}}","\frac{2 x \left(a+b \sqrt{c x^2}\right)^{3/2}}{3 b \sqrt{c x^2}}",1,"(2*x*(a + b*Sqrt[c*x^2])^(3/2))/(3*b*Sqrt[c*x^2])","A",2,2,17,0.1176,1,"{254, 32}"
2939,1,67,0,0.0289001,"\int \frac{\sqrt{a+b \sqrt{c x^2}}}{x^2} \, dx","Int[Sqrt[a + b*Sqrt[c*x^2]]/x^2,x]","-\frac{\sqrt{a+b \sqrt{c x^2}}}{x}-\frac{b \sqrt{c x^2} \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{c x^2}}}{\sqrt{a}}\right)}{\sqrt{a} x}","-\frac{\sqrt{a+b \sqrt{c x^2}}}{x}-\frac{b \sqrt{c x^2} \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{c x^2}}}{\sqrt{a}}\right)}{\sqrt{a} x}",1,"-(Sqrt[a + b*Sqrt[c*x^2]]/x) - (b*Sqrt[c*x^2]*ArcTanh[Sqrt[a + b*Sqrt[c*x^2]]/Sqrt[a]])/(Sqrt[a]*x)","A",4,4,21,0.1905,1,"{368, 47, 63, 208}"
2940,1,144,0,0.0592248,"\int \frac{\sqrt{a+b \sqrt{c x^2}}}{x^4} \, dx","Int[Sqrt[a + b*Sqrt[c*x^2]]/x^4,x]","\frac{b^2 c \sqrt{a+b \sqrt{c x^2}}}{8 a^2 x}-\frac{b^3 \left(c x^2\right)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{c x^2}}}{\sqrt{a}}\right)}{8 a^{5/2} x^3}-\frac{b \left(c x^2\right)^{3/2} \sqrt{a+b \sqrt{c x^2}}}{12 a c x^5}-\frac{\sqrt{a+b \sqrt{c x^2}}}{3 x^3}","\frac{b^2 c \sqrt{a+b \sqrt{c x^2}}}{8 a^2 x}-\frac{b^3 \left(c x^2\right)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{c x^2}}}{\sqrt{a}}\right)}{8 a^{5/2} x^3}-\frac{b \left(c x^2\right)^{3/2} \sqrt{a+b \sqrt{c x^2}}}{12 a c x^5}-\frac{\sqrt{a+b \sqrt{c x^2}}}{3 x^3}",1,"-Sqrt[a + b*Sqrt[c*x^2]]/(3*x^3) + (b^2*c*Sqrt[a + b*Sqrt[c*x^2]])/(8*a^2*x) - (b*(c*x^2)^(3/2)*Sqrt[a + b*Sqrt[c*x^2]])/(12*a*c*x^5) - (b^3*(c*x^2)^(3/2)*ArcTanh[Sqrt[a + b*Sqrt[c*x^2]]/Sqrt[a]])/(8*a^(5/2)*x^3)","A",6,5,21,0.2381,1,"{368, 47, 51, 63, 208}"
2941,1,219,0,0.0939607,"\int \frac{\sqrt{a+b \sqrt{c x^2}}}{x^6} \, dx","Int[Sqrt[a + b*Sqrt[c*x^2]]/x^6,x]","\frac{7 b^4 c^2 \sqrt{a+b \sqrt{c x^2}}}{128 a^4 x}-\frac{7 b^3 \left(c x^2\right)^{5/2} \sqrt{a+b \sqrt{c x^2}}}{192 a^3 c x^7}+\frac{7 b^2 c \sqrt{a+b \sqrt{c x^2}}}{240 a^2 x^3}-\frac{7 b^5 \left(c x^2\right)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{c x^2}}}{\sqrt{a}}\right)}{128 a^{9/2} x^5}-\frac{b \left(c x^2\right)^{5/2} \sqrt{a+b \sqrt{c x^2}}}{40 a c^2 x^9}-\frac{\sqrt{a+b \sqrt{c x^2}}}{5 x^5}","\frac{7 b^4 c^2 \sqrt{a+b \sqrt{c x^2}}}{128 a^4 x}-\frac{7 b^3 \left(c x^2\right)^{5/2} \sqrt{a+b \sqrt{c x^2}}}{192 a^3 c x^7}+\frac{7 b^2 c \sqrt{a+b \sqrt{c x^2}}}{240 a^2 x^3}-\frac{7 b^5 \left(c x^2\right)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{c x^2}}}{\sqrt{a}}\right)}{128 a^{9/2} x^5}-\frac{b \left(c x^2\right)^{5/2} \sqrt{a+b \sqrt{c x^2}}}{40 a c^2 x^9}-\frac{\sqrt{a+b \sqrt{c x^2}}}{5 x^5}",1,"-Sqrt[a + b*Sqrt[c*x^2]]/(5*x^5) + (7*b^2*c*Sqrt[a + b*Sqrt[c*x^2]])/(240*a^2*x^3) + (7*b^4*c^2*Sqrt[a + b*Sqrt[c*x^2]])/(128*a^4*x) - (b*(c*x^2)^(5/2)*Sqrt[a + b*Sqrt[c*x^2]])/(40*a*c^2*x^9) - (7*b^3*(c*x^2)^(5/2)*Sqrt[a + b*Sqrt[c*x^2]])/(192*a^3*c*x^7) - (7*b^5*(c*x^2)^(5/2)*ArcTanh[Sqrt[a + b*Sqrt[c*x^2]]/Sqrt[a]])/(128*a^(9/2)*x^5)","A",8,5,21,0.2381,1,"{368, 47, 51, 63, 208}"
2942,1,113,0,0.0669988,"\int x^8 \sqrt{a+b \left(c x^2\right)^{3/2}} \, dx","Int[x^8*Sqrt[a + b*(c*x^2)^(3/2)],x]","\frac{2 a^2 x^9 \left(a+b \left(c x^2\right)^{3/2}\right)^{3/2}}{9 b^3 \left(c x^2\right)^{9/2}}+\frac{2 x^9 \left(a+b \left(c x^2\right)^{3/2}\right)^{7/2}}{21 b^3 \left(c x^2\right)^{9/2}}-\frac{4 a x^9 \left(a+b \left(c x^2\right)^{3/2}\right)^{5/2}}{15 b^3 \left(c x^2\right)^{9/2}}","\frac{2 a^2 x^9 \left(a+b \left(c x^2\right)^{3/2}\right)^{3/2}}{9 b^3 \left(c x^2\right)^{9/2}}+\frac{2 x^9 \left(a+b \left(c x^2\right)^{3/2}\right)^{7/2}}{21 b^3 \left(c x^2\right)^{9/2}}-\frac{4 a x^9 \left(a+b \left(c x^2\right)^{3/2}\right)^{5/2}}{15 b^3 \left(c x^2\right)^{9/2}}",1,"(2*a^2*x^9*(a + b*(c*x^2)^(3/2))^(3/2))/(9*b^3*(c*x^2)^(9/2)) - (4*a*x^9*(a + b*(c*x^2)^(3/2))^(5/2))/(15*b^3*(c*x^2)^(9/2)) + (2*x^9*(a + b*(c*x^2)^(3/2))^(7/2))/(21*b^3*(c*x^2)^(9/2))","A",4,3,21,0.1429,1,"{368, 266, 43}"
2943,1,56,0,0.0448986,"\int x^5 \sqrt{a+b \left(c x^2\right)^{3/2}} \, dx","Int[x^5*Sqrt[a + b*(c*x^2)^(3/2)],x]","\frac{2 \left(a+b \left(c x^2\right)^{3/2}\right)^{5/2}}{15 b^2 c^3}-\frac{2 a \left(a+b \left(c x^2\right)^{3/2}\right)^{3/2}}{9 b^2 c^3}","\frac{2 \left(a+b \left(c x^2\right)^{3/2}\right)^{5/2}}{15 b^2 c^3}-\frac{2 a \left(a+b \left(c x^2\right)^{3/2}\right)^{3/2}}{9 b^2 c^3}",1,"(-2*a*(a + b*(c*x^2)^(3/2))^(3/2))/(9*b^2*c^3) + (2*(a + b*(c*x^2)^(3/2))^(5/2))/(15*b^2*c^3)","A",4,3,21,0.1429,1,"{368, 266, 43}"
2944,1,36,0,0.0173357,"\int x^2 \sqrt{a+b \left(c x^2\right)^{3/2}} \, dx","Int[x^2*Sqrt[a + b*(c*x^2)^(3/2)],x]","\frac{2 x^3 \left(a+b \left(c x^2\right)^{3/2}\right)^{3/2}}{9 b \left(c x^2\right)^{3/2}}","\frac{2 x^3 \left(a+b \left(c x^2\right)^{3/2}\right)^{3/2}}{9 b \left(c x^2\right)^{3/2}}",1,"(2*x^3*(a + b*(c*x^2)^(3/2))^(3/2))/(9*b*(c*x^2)^(3/2))","A",2,2,21,0.09524,1,"{368, 261}"
2945,1,55,0,0.0429101,"\int \frac{\sqrt{a+b \left(c x^2\right)^{3/2}}}{x} \, dx","Int[Sqrt[a + b*(c*x^2)^(3/2)]/x,x]","\frac{2}{3} \sqrt{a+b \left(c x^2\right)^{3/2}}-\frac{2}{3} \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \left(c x^2\right)^{3/2}}}{\sqrt{a}}\right)","\frac{2}{3} \sqrt{a+b \left(c x^2\right)^{3/2}}-\frac{2}{3} \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \left(c x^2\right)^{3/2}}}{\sqrt{a}}\right)",1,"(2*Sqrt[a + b*(c*x^2)^(3/2)])/3 - (2*Sqrt[a]*ArcTanh[Sqrt[a + b*(c*x^2)^(3/2)]/Sqrt[a]])/3","A",5,5,21,0.2381,1,"{368, 266, 50, 63, 208}"
2946,1,71,0,0.0641282,"\int \frac{\sqrt{a+b \left(c x^2\right)^{3/2}}}{x^4} \, dx","Int[Sqrt[a + b*(c*x^2)^(3/2)]/x^4,x]","-\frac{\sqrt{a+b \left(c x^2\right)^{3/2}}}{3 x^3}-\frac{b \left(c x^2\right)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \left(c x^2\right)^{3/2}}}{\sqrt{a}}\right)}{3 \sqrt{a} x^3}","-\frac{\sqrt{a+b \left(c x^2\right)^{3/2}}}{3 x^3}-\frac{b \left(c x^2\right)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \left(c x^2\right)^{3/2}}}{\sqrt{a}}\right)}{3 \sqrt{a} x^3}",1,"-Sqrt[a + b*(c*x^2)^(3/2)]/(3*x^3) - (b*(c*x^2)^(3/2)*ArcTanh[Sqrt[a + b*(c*x^2)^(3/2)]/Sqrt[a]])/(3*Sqrt[a]*x^3)","A",5,5,21,0.2381,1,"{368, 266, 47, 63, 208}"
2947,1,340,0,0.2471563,"\int x^3 \sqrt{a+b \left(c x^2\right)^{3/2}} \, dx","Int[x^3*Sqrt[a + b*(c*x^2)^(3/2)],x]","-\frac{4\ 3^{3/4} \sqrt{2+\sqrt{3}} a^2 \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt{c x^2}+b^{2/3} c x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} \sqrt{c x^2}+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} \sqrt{c x^2}+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{55 b^{4/3} c^2 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)^2}} \sqrt{a+b \left(c x^2\right)^{3/2}}}+\frac{6 a \sqrt{c x^2} \sqrt{a+b \left(c x^2\right)^{3/2}}}{55 b c^2}+\frac{2}{11} x^4 \sqrt{a+b \left(c x^2\right)^{3/2}}","-\frac{4\ 3^{3/4} \sqrt{2+\sqrt{3}} a^2 \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt{c x^2}+b^{2/3} c x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} \sqrt{c x^2}+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} \sqrt{c x^2}+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{55 b^{4/3} c^2 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)^2}} \sqrt{a+b \left(c x^2\right)^{3/2}}}+\frac{6 a \sqrt{c x^2} \sqrt{a+b \left(c x^2\right)^{3/2}}}{55 b c^2}+\frac{2}{11} x^4 \sqrt{a+b \left(c x^2\right)^{3/2}}",1,"(2*x^4*Sqrt[a + b*(c*x^2)^(3/2)])/11 + (6*a*Sqrt[c*x^2]*Sqrt[a + b*(c*x^2)^(3/2)])/(55*b*c^2) - (4*3^(3/4)*Sqrt[2 + Sqrt[3]]*a^2*(a^(1/3) + b^(1/3)*Sqrt[c*x^2])*Sqrt[(a^(2/3) + b^(2/3)*c*x^2 - a^(1/3)*b^(1/3)*Sqrt[c*x^2])/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^2])^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^2])/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^2])], -7 - 4*Sqrt[3]])/(55*b^(4/3)*c^2*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*Sqrt[c*x^2]))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^2])^2]*Sqrt[a + b*(c*x^2)^(3/2)])","A",4,4,21,0.1905,1,"{368, 279, 321, 218}"
2948,1,306,0,0.1431255,"\int \sqrt{a+b \left(c x^2\right)^{3/2}} \, dx","Int[Sqrt[a + b*(c*x^2)^(3/2)],x]","\frac{2\ 3^{3/4} \sqrt{2+\sqrt{3}} a x \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt{c x^2}+b^{2/3} c x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} \sqrt{c x^2}+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} \sqrt{c x^2}+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{5 \sqrt[3]{b} \sqrt{c x^2} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)^2}} \sqrt{a+b \left(c x^2\right)^{3/2}}}+\frac{2}{5} x \sqrt{a+b \left(c x^2\right)^{3/2}}","\frac{2\ 3^{3/4} \sqrt{2+\sqrt{3}} a x \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt{c x^2}+b^{2/3} c x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} \sqrt{c x^2}+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} \sqrt{c x^2}+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{5 \sqrt[3]{b} \sqrt{c x^2} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)^2}} \sqrt{a+b \left(c x^2\right)^{3/2}}}+\frac{2}{5} x \sqrt{a+b \left(c x^2\right)^{3/2}}",1,"(2*x*Sqrt[a + b*(c*x^2)^(3/2)])/5 + (2*3^(3/4)*Sqrt[2 + Sqrt[3]]*a*x*(a^(1/3) + b^(1/3)*Sqrt[c*x^2])*Sqrt[(a^(2/3) + b^(2/3)*c*x^2 - a^(1/3)*b^(1/3)*Sqrt[c*x^2])/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^2])^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^2])/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^2])], -7 - 4*Sqrt[3]])/(5*b^(1/3)*Sqrt[c*x^2]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*Sqrt[c*x^2]))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^2])^2]*Sqrt[a + b*(c*x^2)^(3/2)])","A",3,3,17,0.1765,1,"{254, 195, 218}"
2949,1,298,0,0.1426042,"\int \frac{\sqrt{a+b \left(c x^2\right)^{3/2}}}{x^3} \, dx","Int[Sqrt[a + b*(c*x^2)^(3/2)]/x^3,x]","\frac{3^{3/4} \sqrt{2+\sqrt{3}} b^{2/3} c \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt{c x^2}+b^{2/3} c x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} \sqrt{c x^2}+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} \sqrt{c x^2}+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)^2}} \sqrt{a+b \left(c x^2\right)^{3/2}}}-\frac{\sqrt{a+b \left(c x^2\right)^{3/2}}}{2 x^2}","\frac{3^{3/4} \sqrt{2+\sqrt{3}} b^{2/3} c \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt{c x^2}+b^{2/3} c x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} \sqrt{c x^2}+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} \sqrt{c x^2}+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)^2}} \sqrt{a+b \left(c x^2\right)^{3/2}}}-\frac{\sqrt{a+b \left(c x^2\right)^{3/2}}}{2 x^2}",1,"-Sqrt[a + b*(c*x^2)^(3/2)]/(2*x^2) + (3^(3/4)*Sqrt[2 + Sqrt[3]]*b^(2/3)*c*(a^(1/3) + b^(1/3)*Sqrt[c*x^2])*Sqrt[(a^(2/3) + b^(2/3)*c*x^2 - a^(1/3)*b^(1/3)*Sqrt[c*x^2])/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^2])^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^2])/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^2])], -7 - 4*Sqrt[3]])/(2*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*Sqrt[c*x^2]))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^2])^2]*Sqrt[a + b*(c*x^2)^(3/2)])","A",3,3,21,0.1429,1,"{368, 277, 218}"
2950,1,352,0,0.1856788,"\int \frac{\sqrt{a+b \left(c x^2\right)^{3/2}}}{x^6} \, dx","Int[Sqrt[a + b*(c*x^2)^(3/2)]/x^6,x]","-\frac{3^{3/4} \sqrt{2+\sqrt{3}} b^{5/3} \left(c x^2\right)^{5/2} \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt{c x^2}+b^{2/3} c x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} \sqrt{c x^2}+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} \sqrt{c x^2}+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{20 a x^5 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)^2}} \sqrt{a+b \left(c x^2\right)^{3/2}}}-\frac{3 b \left(c x^2\right)^{5/2} \sqrt{a+b \left(c x^2\right)^{3/2}}}{20 a c x^7}-\frac{\sqrt{a+b \left(c x^2\right)^{3/2}}}{5 x^5}","-\frac{3^{3/4} \sqrt{2+\sqrt{3}} b^{5/3} \left(c x^2\right)^{5/2} \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt{c x^2}+b^{2/3} c x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} \sqrt{c x^2}+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} \sqrt{c x^2}+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{20 a x^5 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)^2}} \sqrt{a+b \left(c x^2\right)^{3/2}}}-\frac{3 b \left(c x^2\right)^{5/2} \sqrt{a+b \left(c x^2\right)^{3/2}}}{20 a c x^7}-\frac{\sqrt{a+b \left(c x^2\right)^{3/2}}}{5 x^5}",1,"-Sqrt[a + b*(c*x^2)^(3/2)]/(5*x^5) - (3*b*(c*x^2)^(5/2)*Sqrt[a + b*(c*x^2)^(3/2)])/(20*a*c*x^7) - (3^(3/4)*Sqrt[2 + Sqrt[3]]*b^(5/3)*(c*x^2)^(5/2)*(a^(1/3) + b^(1/3)*Sqrt[c*x^2])*Sqrt[(a^(2/3) + b^(2/3)*c*x^2 - a^(1/3)*b^(1/3)*Sqrt[c*x^2])/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^2])^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^2])/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^2])], -7 - 4*Sqrt[3]])/(20*a*x^5*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*Sqrt[c*x^2]))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^2])^2]*Sqrt[a + b*(c*x^2)^(3/2)])","A",4,4,21,0.1905,1,"{368, 277, 325, 218}"
2951,1,709,0,0.4900391,"\int x^4 \sqrt{a+b \left(c x^2\right)^{3/2}} \, dx","Int[x^4*Sqrt[a + b*(c*x^2)^(3/2)],x]","-\frac{24 a^2 x^5 \sqrt{a+b \left(c x^2\right)^{3/2}}}{91 b^{5/3} \left(c x^2\right)^{5/2} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)}-\frac{8 \sqrt{2} 3^{3/4} a^{7/3} x^5 \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt{c x^2}+b^{2/3} c x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} \sqrt{c x^2}+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} \sqrt{c x^2}+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{91 b^{5/3} \left(c x^2\right)^{5/2} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)^2}} \sqrt{a+b \left(c x^2\right)^{3/2}}}+\frac{12 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{7/3} x^5 \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt{c x^2}+b^{2/3} c x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} \sqrt{c x^2}+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} \sqrt{c x^2}+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{91 b^{5/3} \left(c x^2\right)^{5/2} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)^2}} \sqrt{a+b \left(c x^2\right)^{3/2}}}+\frac{6 a c x^7 \sqrt{a+b \left(c x^2\right)^{3/2}}}{91 b \left(c x^2\right)^{5/2}}+\frac{2}{13} x^5 \sqrt{a+b \left(c x^2\right)^{3/2}}","-\frac{24 a^2 x^5 \sqrt{a+b \left(c x^2\right)^{3/2}}}{91 b^{5/3} \left(c x^2\right)^{5/2} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)}-\frac{8 \sqrt{2} 3^{3/4} a^{7/3} x^5 \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt{c x^2}+b^{2/3} c x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} \sqrt{c x^2}+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} \sqrt{c x^2}+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{91 b^{5/3} \left(c x^2\right)^{5/2} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)^2}} \sqrt{a+b \left(c x^2\right)^{3/2}}}+\frac{12 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{7/3} x^5 \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt{c x^2}+b^{2/3} c x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} \sqrt{c x^2}+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} \sqrt{c x^2}+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{91 b^{5/3} \left(c x^2\right)^{5/2} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)^2}} \sqrt{a+b \left(c x^2\right)^{3/2}}}+\frac{6 a c x^7 \sqrt{a+b \left(c x^2\right)^{3/2}}}{91 b \left(c x^2\right)^{5/2}}+\frac{2}{13} x^5 \sqrt{a+b \left(c x^2\right)^{3/2}}",1,"(2*x^5*Sqrt[a + b*(c*x^2)^(3/2)])/13 + (6*a*c*x^7*Sqrt[a + b*(c*x^2)^(3/2)])/(91*b*(c*x^2)^(5/2)) - (24*a^2*x^5*Sqrt[a + b*(c*x^2)^(3/2)])/(91*b^(5/3)*(c*x^2)^(5/2)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^2])) + (12*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(7/3)*x^5*(a^(1/3) + b^(1/3)*Sqrt[c*x^2])*Sqrt[(a^(2/3) + b^(2/3)*c*x^2 - a^(1/3)*b^(1/3)*Sqrt[c*x^2])/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^2])^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^2])/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^2])], -7 - 4*Sqrt[3]])/(91*b^(5/3)*(c*x^2)^(5/2)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*Sqrt[c*x^2]))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^2])^2]*Sqrt[a + b*(c*x^2)^(3/2)]) - (8*Sqrt[2]*3^(3/4)*a^(7/3)*x^5*(a^(1/3) + b^(1/3)*Sqrt[c*x^2])*Sqrt[(a^(2/3) + b^(2/3)*c*x^2 - a^(1/3)*b^(1/3)*Sqrt[c*x^2])/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^2])^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^2])/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^2])], -7 - 4*Sqrt[3]])/(91*b^(5/3)*(c*x^2)^(5/2)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*Sqrt[c*x^2]))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^2])^2]*Sqrt[a + b*(c*x^2)^(3/2)])","A",6,6,21,0.2857,1,"{368, 279, 321, 303, 218, 1877}"
2952,1,642,0,0.3613916,"\int x \sqrt{a+b \left(c x^2\right)^{3/2}} \, dx","Int[x*Sqrt[a + b*(c*x^2)^(3/2)],x]","\frac{2 \sqrt{2} 3^{3/4} a^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt{c x^2}+b^{2/3} c x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} \sqrt{c x^2}+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} \sqrt{c x^2}+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{7 b^{2/3} c \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)^2}} \sqrt{a+b \left(c x^2\right)^{3/2}}}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt{c x^2}+b^{2/3} c x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} \sqrt{c x^2}+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} \sqrt{c x^2}+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{7 b^{2/3} c \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)^2}} \sqrt{a+b \left(c x^2\right)^{3/2}}}+\frac{6 a \sqrt{a+b \left(c x^2\right)^{3/2}}}{7 b^{2/3} c \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)}+\frac{2}{7} x^2 \sqrt{a+b \left(c x^2\right)^{3/2}}","\frac{2 \sqrt{2} 3^{3/4} a^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt{c x^2}+b^{2/3} c x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} \sqrt{c x^2}+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} \sqrt{c x^2}+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{7 b^{2/3} c \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)^2}} \sqrt{a+b \left(c x^2\right)^{3/2}}}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt{c x^2}+b^{2/3} c x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} \sqrt{c x^2}+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} \sqrt{c x^2}+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{7 b^{2/3} c \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)^2}} \sqrt{a+b \left(c x^2\right)^{3/2}}}+\frac{6 a \sqrt{a+b \left(c x^2\right)^{3/2}}}{7 b^{2/3} c \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)}+\frac{2}{7} x^2 \sqrt{a+b \left(c x^2\right)^{3/2}}",1,"(2*x^2*Sqrt[a + b*(c*x^2)^(3/2)])/7 + (6*a*Sqrt[a + b*(c*x^2)^(3/2)])/(7*b^(2/3)*c*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^2])) - (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(4/3)*(a^(1/3) + b^(1/3)*Sqrt[c*x^2])*Sqrt[(a^(2/3) + b^(2/3)*c*x^2 - a^(1/3)*b^(1/3)*Sqrt[c*x^2])/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^2])^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^2])/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^2])], -7 - 4*Sqrt[3]])/(7*b^(2/3)*c*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*Sqrt[c*x^2]))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^2])^2]*Sqrt[a + b*(c*x^2)^(3/2)]) + (2*Sqrt[2]*3^(3/4)*a^(4/3)*(a^(1/3) + b^(1/3)*Sqrt[c*x^2])*Sqrt[(a^(2/3) + b^(2/3)*c*x^2 - a^(1/3)*b^(1/3)*Sqrt[c*x^2])/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^2])^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^2])/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^2])], -7 - 4*Sqrt[3]])/(7*b^(2/3)*c*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*Sqrt[c*x^2]))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^2])^2]*Sqrt[a + b*(c*x^2)^(3/2)])","A",5,5,19,0.2632,1,"{368, 279, 303, 218, 1877}"
2953,1,661,0,0.346997,"\int \frac{\sqrt{a+b \left(c x^2\right)^{3/2}}}{x^2} \, dx","Int[Sqrt[a + b*(c*x^2)^(3/2)]/x^2,x]","\frac{\sqrt{2} 3^{3/4} \sqrt[3]{a} \sqrt[3]{b} \sqrt{c x^2} \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt{c x^2}+b^{2/3} c x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} \sqrt{c x^2}+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} \sqrt{c x^2}+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{x \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)^2}} \sqrt{a+b \left(c x^2\right)^{3/2}}}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} \sqrt[3]{b} \sqrt{c x^2} \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt{c x^2}+b^{2/3} c x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} \sqrt{c x^2}+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} \sqrt{c x^2}+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{2 x \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)^2}} \sqrt{a+b \left(c x^2\right)^{3/2}}}-\frac{\sqrt{a+b \left(c x^2\right)^{3/2}}}{x}+\frac{3 \sqrt[3]{b} \sqrt{c x^2} \sqrt{a+b \left(c x^2\right)^{3/2}}}{x \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)}","\frac{\sqrt{2} 3^{3/4} \sqrt[3]{a} \sqrt[3]{b} \sqrt{c x^2} \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt{c x^2}+b^{2/3} c x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} \sqrt{c x^2}+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} \sqrt{c x^2}+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{x \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)^2}} \sqrt{a+b \left(c x^2\right)^{3/2}}}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} \sqrt[3]{b} \sqrt{c x^2} \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt{c x^2}+b^{2/3} c x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} \sqrt{c x^2}+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} \sqrt{c x^2}+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{2 x \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)^2}} \sqrt{a+b \left(c x^2\right)^{3/2}}}-\frac{\sqrt{a+b \left(c x^2\right)^{3/2}}}{x}+\frac{3 \sqrt[3]{b} \sqrt{c x^2} \sqrt{a+b \left(c x^2\right)^{3/2}}}{x \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)}",1,"-(Sqrt[a + b*(c*x^2)^(3/2)]/x) + (3*b^(1/3)*Sqrt[c*x^2]*Sqrt[a + b*(c*x^2)^(3/2)])/(x*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^2])) - (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(1/3)*b^(1/3)*Sqrt[c*x^2]*(a^(1/3) + b^(1/3)*Sqrt[c*x^2])*Sqrt[(a^(2/3) + b^(2/3)*c*x^2 - a^(1/3)*b^(1/3)*Sqrt[c*x^2])/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^2])^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^2])/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^2])], -7 - 4*Sqrt[3]])/(2*x*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*Sqrt[c*x^2]))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^2])^2]*Sqrt[a + b*(c*x^2)^(3/2)]) + (Sqrt[2]*3^(3/4)*a^(1/3)*b^(1/3)*Sqrt[c*x^2]*(a^(1/3) + b^(1/3)*Sqrt[c*x^2])*Sqrt[(a^(2/3) + b^(2/3)*c*x^2 - a^(1/3)*b^(1/3)*Sqrt[c*x^2])/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^2])^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^2])/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^2])], -7 - 4*Sqrt[3]])/(x*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*Sqrt[c*x^2]))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^2])^2]*Sqrt[a + b*(c*x^2)^(3/2)])","A",5,5,21,0.2381,1,"{368, 277, 303, 218, 1877}"
2954,1,681,0,0.4172068,"\int \frac{\sqrt{a+b \left(c x^2\right)^{3/2}}}{x^5} \, dx","Int[Sqrt[a + b*(c*x^2)^(3/2)]/x^5,x]","\frac{3^{3/4} b^{4/3} c^2 \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt{c x^2}+b^{2/3} c x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} \sqrt{c x^2}+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} \sqrt{c x^2}+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{4 \sqrt{2} a^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)^2}} \sqrt{a+b \left(c x^2\right)^{3/2}}}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} b^{4/3} c^2 \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt{c x^2}+b^{2/3} c x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} \sqrt{c x^2}+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} \sqrt{c x^2}+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{16 a^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)^2}} \sqrt{a+b \left(c x^2\right)^{3/2}}}+\frac{3 b^{4/3} c^2 \sqrt{a+b \left(c x^2\right)^{3/2}}}{8 a \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)}-\frac{3 b c^2 \sqrt{a+b \left(c x^2\right)^{3/2}}}{8 a \sqrt{c x^2}}-\frac{\sqrt{a+b \left(c x^2\right)^{3/2}}}{4 x^4}","\frac{3^{3/4} b^{4/3} c^2 \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt{c x^2}+b^{2/3} c x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} \sqrt{c x^2}+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} \sqrt{c x^2}+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{4 \sqrt{2} a^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)^2}} \sqrt{a+b \left(c x^2\right)^{3/2}}}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} b^{4/3} c^2 \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt{c x^2}+b^{2/3} c x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} \sqrt{c x^2}+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} \sqrt{c x^2}+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{16 a^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)^2}} \sqrt{a+b \left(c x^2\right)^{3/2}}}+\frac{3 b^{4/3} c^2 \sqrt{a+b \left(c x^2\right)^{3/2}}}{8 a \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^2}\right)}-\frac{3 b c^2 \sqrt{a+b \left(c x^2\right)^{3/2}}}{8 a \sqrt{c x^2}}-\frac{\sqrt{a+b \left(c x^2\right)^{3/2}}}{4 x^4}",1,"-Sqrt[a + b*(c*x^2)^(3/2)]/(4*x^4) - (3*b*c^2*Sqrt[a + b*(c*x^2)^(3/2)])/(8*a*Sqrt[c*x^2]) + (3*b^(4/3)*c^2*Sqrt[a + b*(c*x^2)^(3/2)])/(8*a*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^2])) - (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*b^(4/3)*c^2*(a^(1/3) + b^(1/3)*Sqrt[c*x^2])*Sqrt[(a^(2/3) + b^(2/3)*c*x^2 - a^(1/3)*b^(1/3)*Sqrt[c*x^2])/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^2])^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^2])/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^2])], -7 - 4*Sqrt[3]])/(16*a^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*Sqrt[c*x^2]))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^2])^2]*Sqrt[a + b*(c*x^2)^(3/2)]) + (3^(3/4)*b^(4/3)*c^2*(a^(1/3) + b^(1/3)*Sqrt[c*x^2])*Sqrt[(a^(2/3) + b^(2/3)*c*x^2 - a^(1/3)*b^(1/3)*Sqrt[c*x^2])/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^2])^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^2])/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^2])], -7 - 4*Sqrt[3]])/(4*Sqrt[2]*a^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*Sqrt[c*x^2]))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^2])^2]*Sqrt[a + b*(c*x^2)^(3/2)])","A",6,6,21,0.2857,1,"{368, 277, 325, 303, 218, 1877}"
2955,1,86,0,0.0556542,"\int (d x)^m \sqrt{a+b \left(c x^2\right)^{3/2}} \, dx","Int[(d*x)^m*Sqrt[a + b*(c*x^2)^(3/2)],x]","\frac{(d x)^{m+1} \sqrt{a+b \left(c x^2\right)^{3/2}} \, _2F_1\left(-\frac{1}{2},\frac{m+1}{3};\frac{m+4}{3};-\frac{b \left(c x^2\right)^{3/2}}{a}\right)}{d (m+1) \sqrt{\frac{b \left(c x^2\right)^{3/2}}{a}+1}}","\frac{(d x)^{m+1} \sqrt{a+b \left(c x^2\right)^{3/2}} \, _2F_1\left(-\frac{1}{2},\frac{m+1}{3};\frac{m+4}{3};-\frac{b \left(c x^2\right)^{3/2}}{a}\right)}{d (m+1) \sqrt{\frac{b \left(c x^2\right)^{3/2}}{a}+1}}",1,"((d*x)^(1 + m)*Sqrt[a + b*(c*x^2)^(3/2)]*Hypergeometric2F1[-1/2, (1 + m)/3, (4 + m)/3, -((b*(c*x^2)^(3/2))/a)])/(d*(1 + m)*Sqrt[1 + (b*(c*x^2)^(3/2))/a])","A",3,3,23,0.1304,1,"{368, 365, 364}"
2956,1,88,0,0.0369729,"\int (d x)^m \sqrt{a+b \sqrt{c x^2}} \, dx","Int[(d*x)^m*Sqrt[a + b*Sqrt[c*x^2]],x]","\frac{2 (d x)^{m+1} \left(a+b \sqrt{c x^2}\right)^{3/2} \left(-\frac{b \sqrt{c x^2}}{a}\right)^{-m} \, _2F_1\left(\frac{3}{2},-m;\frac{5}{2};\frac{\sqrt{c x^2} b}{a}+1\right)}{3 b d \sqrt{c x^2}}","\frac{2 (d x)^{m+1} \left(a+b \sqrt{c x^2}\right)^{3/2} \left(-\frac{b \sqrt{c x^2}}{a}\right)^{-m} \, _2F_1\left(\frac{3}{2},-m;\frac{5}{2};\frac{\sqrt{c x^2} b}{a}+1\right)}{3 b d \sqrt{c x^2}}",1,"(2*(d*x)^(1 + m)*(a + b*Sqrt[c*x^2])^(3/2)*Hypergeometric2F1[3/2, -m, 5/2, 1 + (b*Sqrt[c*x^2])/a])/(3*b*d*Sqrt[c*x^2]*(-((b*Sqrt[c*x^2])/a))^m)","A",3,3,23,0.1304,1,"{368, 67, 65}"
2957,1,87,0,0.0666992,"\int (d x)^m \sqrt{a+\frac{b}{\sqrt{c x^2}}} \, dx","Int[(d*x)^m*Sqrt[a + b/Sqrt[c*x^2]],x]","-\frac{2 b (d x)^{m+1} \left(a+\frac{b}{\sqrt{c x^2}}\right)^{3/2} \left(-\frac{b}{a \sqrt{c x^2}}\right)^m \, _2F_1\left(\frac{3}{2},m+2;\frac{5}{2};\frac{b}{a \sqrt{c x^2}}+1\right)}{3 a^2 d \sqrt{c x^2}}","-\frac{2 b (d x)^{m+1} \left(a+\frac{b}{\sqrt{c x^2}}\right)^{3/2} \left(-\frac{b}{a \sqrt{c x^2}}\right)^m \, _2F_1\left(\frac{3}{2},m+2;\frac{5}{2};\frac{b}{a \sqrt{c x^2}}+1\right)}{3 a^2 d \sqrt{c x^2}}",1,"(-2*b*(d*x)^(1 + m)*(-(b/(a*Sqrt[c*x^2])))^m*(a + b/Sqrt[c*x^2])^(3/2)*Hypergeometric2F1[3/2, 2 + m, 5/2, 1 + b/(a*Sqrt[c*x^2])])/(3*a^2*d*Sqrt[c*x^2])","A",4,4,23,0.1739,1,"{368, 339, 67, 65}"
2958,1,90,0,0.0836774,"\int (d x)^m \sqrt{a+\frac{b}{\left(c x^2\right)^{3/2}}} \, dx","Int[(d*x)^m*Sqrt[a + b/(c*x^2)^(3/2)],x]","\frac{(d x)^{m+1} \sqrt{a+\frac{b}{\left(c x^2\right)^{3/2}}} \, _2F_1\left(-\frac{1}{2},\frac{1}{3} (-m-1);\frac{2-m}{3};-\frac{b}{a \left(c x^2\right)^{3/2}}\right)}{d (m+1) \sqrt{\frac{b}{a \left(c x^2\right)^{3/2}}+1}}","\frac{(d x)^{m+1} \sqrt{a+\frac{b}{\left(c x^2\right)^{3/2}}} \, _2F_1\left(-\frac{1}{2},\frac{1}{3} (-m-1);\frac{2-m}{3};-\frac{b}{a \left(c x^2\right)^{3/2}}\right)}{d (m+1) \sqrt{\frac{b}{a \left(c x^2\right)^{3/2}}+1}}",1,"((d*x)^(1 + m)*Sqrt[a + b/(c*x^2)^(3/2)]*Hypergeometric2F1[-1/2, (-1 - m)/3, (2 - m)/3, -(b/(a*(c*x^2)^(3/2)))])/(d*(1 + m)*Sqrt[1 + b/(a*(c*x^2)^(3/2))])","A",4,4,23,0.1739,1,"{368, 339, 365, 364}"
2959,1,17,0,0.0049069,"\int \frac{1}{1+\left(x^3\right)^{2/3}} \, dx","Int[(1 + (x^3)^(2/3))^(-1),x]","\frac{x \tan ^{-1}\left(\sqrt[3]{x^3}\right)}{\sqrt[3]{x^3}}","\frac{x \tan ^{-1}\left(\sqrt[3]{x^3}\right)}{\sqrt[3]{x^3}}",1,"(x*ArcTan[(x^3)^(1/3)])/(x^3)^(1/3)","A",2,2,11,0.1818,1,"{254, 203}"
2960,1,116,0,0.0686541,"\int x^5 \sqrt{a+b \sqrt{c x^3}} \, dx","Int[x^5*Sqrt[a + b*Sqrt[c*x^3]],x]","\frac{4 a^2 \left(a+b \sqrt{c x^3}\right)^{5/2}}{5 b^4 c^2}-\frac{4 a^3 \left(a+b \sqrt{c x^3}\right)^{3/2}}{9 b^4 c^2}+\frac{4 \left(a+b \sqrt{c x^3}\right)^{9/2}}{27 b^4 c^2}-\frac{4 a \left(a+b \sqrt{c x^3}\right)^{7/2}}{7 b^4 c^2}","\frac{4 a^2 \left(a+b \sqrt{c x^3}\right)^{5/2}}{5 b^4 c^2}-\frac{4 a^3 \left(a+b \sqrt{c x^3}\right)^{3/2}}{9 b^4 c^2}+\frac{4 \left(a+b \sqrt{c x^3}\right)^{9/2}}{27 b^4 c^2}-\frac{4 a \left(a+b \sqrt{c x^3}\right)^{7/2}}{7 b^4 c^2}",1,"(-4*a^3*(a + b*Sqrt[c*x^3])^(3/2))/(9*b^4*c^2) + (4*a^2*(a + b*Sqrt[c*x^3])^(5/2))/(5*b^4*c^2) - (4*a*(a + b*Sqrt[c*x^3])^(7/2))/(7*b^4*c^2) + (4*(a + b*Sqrt[c*x^3])^(9/2))/(27*b^4*c^2)","A",4,3,21,0.1429,1,"{369, 266, 43}"
2961,1,56,0,0.0352788,"\int x^2 \sqrt{a+b \sqrt{c x^3}} \, dx","Int[x^2*Sqrt[a + b*Sqrt[c*x^3]],x]","\frac{4 \left(a+b \sqrt{c x^3}\right)^{5/2}}{15 b^2 c}-\frac{4 a \left(a+b \sqrt{c x^3}\right)^{3/2}}{9 b^2 c}","\frac{4 \left(a+b \sqrt{c x^3}\right)^{5/2}}{15 b^2 c}-\frac{4 a \left(a+b \sqrt{c x^3}\right)^{3/2}}{9 b^2 c}",1,"(-4*a*(a + b*Sqrt[c*x^3])^(3/2))/(9*b^2*c) + (4*(a + b*Sqrt[c*x^3])^(5/2))/(15*b^2*c)","A",4,3,21,0.1429,1,"{369, 266, 43}"
2962,1,55,0,0.0347186,"\int \frac{\sqrt{a+b \sqrt{c x^3}}}{x} \, dx","Int[Sqrt[a + b*Sqrt[c*x^3]]/x,x]","\frac{4}{3} \sqrt{a+b \sqrt{c x^3}}-\frac{4}{3} \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{c x^3}}}{\sqrt{a}}\right)","\frac{4}{3} \sqrt{a+b \sqrt{c x^3}}-\frac{4}{3} \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{c x^3}}}{\sqrt{a}}\right)",1,"(4*Sqrt[a + b*Sqrt[c*x^3]])/3 - (4*Sqrt[a]*ArcTanh[Sqrt[a + b*Sqrt[c*x^3]]/Sqrt[a]])/3","A",5,5,21,0.2381,1,"{369, 266, 50, 63, 208}"
2963,1,97,0,0.0548172,"\int \frac{\sqrt{a+b \sqrt{c x^3}}}{x^4} \, dx","Int[Sqrt[a + b*Sqrt[c*x^3]]/x^4,x]","\frac{b^2 c \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{c x^3}}}{\sqrt{a}}\right)}{6 a^{3/2}}-\frac{b c \sqrt{a+b \sqrt{c x^3}}}{6 a \sqrt{c x^3}}-\frac{\sqrt{a+b \sqrt{c x^3}}}{3 x^3}","\frac{b^2 c \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{c x^3}}}{\sqrt{a}}\right)}{6 a^{3/2}}-\frac{b c \sqrt{a+b \sqrt{c x^3}}}{6 a \sqrt{c x^3}}-\frac{\sqrt{a+b \sqrt{c x^3}}}{3 x^3}",1,"-Sqrt[a + b*Sqrt[c*x^3]]/(3*x^3) - (b*c*Sqrt[a + b*Sqrt[c*x^3]])/(6*a*Sqrt[c*x^3]) + (b^2*c*ArcTanh[Sqrt[a + b*Sqrt[c*x^3]]/Sqrt[a]])/(6*a^(3/2))","A",6,6,21,0.2857,1,"{369, 266, 47, 51, 63, 208}"
2964,1,400,0,0.2482808,"\int x \sqrt{a+b \sqrt{c x^3}} \, dx","Int[x*Sqrt[a + b*Sqrt[c*x^3]],x]","-\frac{8\ 3^{3/4} \sqrt{2+\sqrt{3}} a^2 \left(\sqrt[3]{a}+\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+b^{2/3} \sqrt[3]{c} x}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}\right)^2}} F\left(\sin ^{-1}\left(\frac{\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{55 b^{4/3} c^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}\right)^2}} \sqrt{a+b \sqrt{c x^3}}}+\frac{12 a x^2 \sqrt{a+b \sqrt{c x^3}}}{55 b \sqrt{c x^3}}+\frac{4}{11} x^2 \sqrt{a+b \sqrt{c x^3}}","-\frac{8\ 3^{3/4} \sqrt{2+\sqrt{3}} a^2 \left(\sqrt[3]{a}+\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+b^{2/3} \sqrt[3]{c} x}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}\right)^2}} F\left(\sin ^{-1}\left(\frac{\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{55 b^{4/3} c^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}\right)^2}} \sqrt{a+b \sqrt{c x^3}}}+\frac{12 a x^2 \sqrt{a+b \sqrt{c x^3}}}{55 b \sqrt{c x^3}}+\frac{4}{11} x^2 \sqrt{a+b \sqrt{c x^3}}",1,"(4*x^2*Sqrt[a + b*Sqrt[c*x^3]])/11 + (12*a*x^2*Sqrt[a + b*Sqrt[c*x^3]])/(55*b*Sqrt[c*x^3]) - (8*3^(3/4)*Sqrt[2 + Sqrt[3]]*a^2*(a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])*Sqrt[(a^(2/3) + b^(2/3)*c^(1/3)*x - (a^(1/3)*b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])/((1 + Sqrt[3])*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])/((1 + Sqrt[3])*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])], -7 - 4*Sqrt[3]])/(55*b^(4/3)*c^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3]))/((1 + Sqrt[3])*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])^2]*Sqrt[a + b*Sqrt[c*x^3]])","A",5,5,19,0.2632,1,"{369, 341, 279, 321, 218}"
2965,1,355,0,0.1487772,"\int \frac{\sqrt{a+b \sqrt{c x^3}}}{x^2} \, dx","Int[Sqrt[a + b*Sqrt[c*x^3]]/x^2,x]","\frac{3^{3/4} \sqrt{2+\sqrt{3}} b^{2/3} \sqrt[3]{c} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+b^{2/3} \sqrt[3]{c} x}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}\right)^2}} F\left(\sin ^{-1}\left(\frac{\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{\sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}\right)^2}} \sqrt{a+b \sqrt{c x^3}}}-\frac{\sqrt{a+b \sqrt{c x^3}}}{x}","\frac{3^{3/4} \sqrt{2+\sqrt{3}} b^{2/3} \sqrt[3]{c} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+b^{2/3} \sqrt[3]{c} x}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}\right)^2}} F\left(\sin ^{-1}\left(\frac{\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{\sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}\right)^2}} \sqrt{a+b \sqrt{c x^3}}}-\frac{\sqrt{a+b \sqrt{c x^3}}}{x}",1,"-(Sqrt[a + b*Sqrt[c*x^3]]/x) + (3^(3/4)*Sqrt[2 + Sqrt[3]]*b^(2/3)*c^(1/3)*(a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])*Sqrt[(a^(2/3) + b^(2/3)*c^(1/3)*x - (a^(1/3)*b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])/((1 + Sqrt[3])*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])/((1 + Sqrt[3])*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])], -7 - 4*Sqrt[3]])/(Sqrt[(a^(1/3)*(a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3]))/((1 + Sqrt[3])*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])^2]*Sqrt[a + b*Sqrt[c*x^3]])","A",4,4,21,0.1905,1,"{369, 341, 277, 218}"
2966,1,434,0,0.2676194,"\int \frac{\sqrt{a+b \sqrt{c x^3}}}{x^5} \, dx","Int[Sqrt[a + b*Sqrt[c*x^3]]/x^5,x]","\frac{7\ 3^{3/4} \sqrt{2+\sqrt{3}} b^{8/3} c^{4/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+b^{2/3} \sqrt[3]{c} x}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}\right)^2}} F\left(\sin ^{-1}\left(\frac{\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{160 a^2 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}\right)^2}} \sqrt{a+b \sqrt{c x^3}}}+\frac{21 b^2 c \sqrt{a+b \sqrt{c x^3}}}{160 a^2 x}-\frac{3 b c^3 x^5 \sqrt{a+b \sqrt{c x^3}}}{40 a \left(c x^3\right)^{5/2}}-\frac{\sqrt{a+b \sqrt{c x^3}}}{4 x^4}","\frac{7\ 3^{3/4} \sqrt{2+\sqrt{3}} b^{8/3} c^{4/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+b^{2/3} \sqrt[3]{c} x}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}\right)^2}} F\left(\sin ^{-1}\left(\frac{\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{160 a^2 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}\right)^2}} \sqrt{a+b \sqrt{c x^3}}}+\frac{21 b^2 c \sqrt{a+b \sqrt{c x^3}}}{160 a^2 x}-\frac{3 b c^3 x^5 \sqrt{a+b \sqrt{c x^3}}}{40 a \left(c x^3\right)^{5/2}}-\frac{\sqrt{a+b \sqrt{c x^3}}}{4 x^4}",1,"-Sqrt[a + b*Sqrt[c*x^3]]/(4*x^4) + (21*b^2*c*Sqrt[a + b*Sqrt[c*x^3]])/(160*a^2*x) - (3*b*c^3*x^5*Sqrt[a + b*Sqrt[c*x^3]])/(40*a*(c*x^3)^(5/2)) + (7*3^(3/4)*Sqrt[2 + Sqrt[3]]*b^(8/3)*c^(4/3)*(a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])*Sqrt[(a^(2/3) + b^(2/3)*c^(1/3)*x - (a^(1/3)*b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])/((1 + Sqrt[3])*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])/((1 + Sqrt[3])*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])], -7 - 4*Sqrt[3]])/(160*a^2*Sqrt[(a^(1/3)*(a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3]))/((1 + Sqrt[3])*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])^2]*Sqrt[a + b*Sqrt[c*x^3]])","A",6,5,21,0.2381,1,"{369, 341, 277, 325, 218}"
2967,1,843,0,0.6363429,"\int x^3 \sqrt{a+b \sqrt{c x^3}} \, dx","Int[x^3*Sqrt[a + b*Sqrt[c*x^3]],x]","\frac{4}{19} \sqrt{a+b \sqrt{c x^3}} x^4+\frac{12 a \sqrt{c x^3} \sqrt{a+b \sqrt{c x^3}} x}{247 b c}-\frac{120 a^2 \sqrt{a+b \sqrt{c x^3}} x}{1729 b^2 c}-\frac{240 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{10/3} \left(\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\sqrt[3]{a}\right) \sqrt{\frac{-\frac{\sqrt[3]{a} \sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+b^{2/3} \sqrt[3]{c} x+a^{2/3}}{\left(\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1+\sqrt{3}\right) \sqrt[3]{a}\right)^2}} E\left(\sin ^{-1}\left(\frac{\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{1729 b^{8/3} c^{4/3} \sqrt{\frac{\sqrt[3]{a} \left(\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\sqrt[3]{a}\right)}{\left(\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1+\sqrt{3}\right) \sqrt[3]{a}\right)^2}} \sqrt{a+b \sqrt{c x^3}}}+\frac{160 \sqrt{2} 3^{3/4} a^{10/3} \left(\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\sqrt[3]{a}\right) \sqrt{\frac{-\frac{\sqrt[3]{a} \sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+b^{2/3} \sqrt[3]{c} x+a^{2/3}}{\left(\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1+\sqrt{3}\right) \sqrt[3]{a}\right)^2}} F\left(\sin ^{-1}\left(\frac{\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{1729 b^{8/3} c^{4/3} \sqrt{\frac{\sqrt[3]{a} \left(\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\sqrt[3]{a}\right)}{\left(\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1+\sqrt{3}\right) \sqrt[3]{a}\right)^2}} \sqrt{a+b \sqrt{c x^3}}}+\frac{480 a^3 \sqrt{a+b \sqrt{c x^3}}}{1729 b^{8/3} c^{4/3} \left(\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1+\sqrt{3}\right) \sqrt[3]{a}\right)}","\frac{4}{19} \sqrt{a+b \sqrt{c x^3}} x^4+\frac{12 a \sqrt{c x^3} \sqrt{a+b \sqrt{c x^3}} x}{247 b c}-\frac{120 a^2 \sqrt{a+b \sqrt{c x^3}} x}{1729 b^2 c}-\frac{240 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{10/3} \left(\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\sqrt[3]{a}\right) \sqrt{\frac{-\frac{\sqrt[3]{a} \sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+b^{2/3} \sqrt[3]{c} x+a^{2/3}}{\left(\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1+\sqrt{3}\right) \sqrt[3]{a}\right)^2}} E\left(\sin ^{-1}\left(\frac{\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{1729 b^{8/3} c^{4/3} \sqrt{\frac{\sqrt[3]{a} \left(\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\sqrt[3]{a}\right)}{\left(\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1+\sqrt{3}\right) \sqrt[3]{a}\right)^2}} \sqrt{a+b \sqrt{c x^3}}}+\frac{160 \sqrt{2} 3^{3/4} a^{10/3} \left(\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\sqrt[3]{a}\right) \sqrt{\frac{-\frac{\sqrt[3]{a} \sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+b^{2/3} \sqrt[3]{c} x+a^{2/3}}{\left(\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1+\sqrt{3}\right) \sqrt[3]{a}\right)^2}} F\left(\sin ^{-1}\left(\frac{\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{1729 b^{8/3} c^{4/3} \sqrt{\frac{\sqrt[3]{a} \left(\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\sqrt[3]{a}\right)}{\left(\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1+\sqrt{3}\right) \sqrt[3]{a}\right)^2}} \sqrt{a+b \sqrt{c x^3}}}+\frac{480 a^3 \sqrt{a+b \sqrt{c x^3}}}{1729 b^{8/3} c^{4/3} \left(\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1+\sqrt{3}\right) \sqrt[3]{a}\right)}",1,"(-120*a^2*x*Sqrt[a + b*Sqrt[c*x^3]])/(1729*b^2*c) + (4*x^4*Sqrt[a + b*Sqrt[c*x^3]])/19 + (12*a*x*Sqrt[c*x^3]*Sqrt[a + b*Sqrt[c*x^3]])/(247*b*c) + (480*a^3*Sqrt[a + b*Sqrt[c*x^3]])/(1729*b^(8/3)*c^(4/3)*((1 + Sqrt[3])*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])) - (240*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(10/3)*(a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])*Sqrt[(a^(2/3) + b^(2/3)*c^(1/3)*x - (a^(1/3)*b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])/((1 + Sqrt[3])*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])/((1 + Sqrt[3])*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])], -7 - 4*Sqrt[3]])/(1729*b^(8/3)*c^(4/3)*Sqrt[(a^(1/3)*(a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3]))/((1 + Sqrt[3])*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])^2]*Sqrt[a + b*Sqrt[c*x^3]]) + (160*Sqrt[2]*3^(3/4)*a^(10/3)*(a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])*Sqrt[(a^(2/3) + b^(2/3)*c^(1/3)*x - (a^(1/3)*b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])/((1 + Sqrt[3])*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])/((1 + Sqrt[3])*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])], -7 - 4*Sqrt[3]])/(1729*b^(8/3)*c^(4/3)*Sqrt[(a^(1/3)*(a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3]))/((1 + Sqrt[3])*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])^2]*Sqrt[a + b*Sqrt[c*x^3]])","A",8,7,21,0.3333,1,"{369, 341, 279, 321, 303, 218, 1877}"
2968,1,770,0,0.3942965,"\int \sqrt{a+b \sqrt{c x^3}} \, dx","Int[Sqrt[a + b*Sqrt[c*x^3]],x]","\frac{4 \sqrt{2} 3^{3/4} a^{4/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+b^{2/3} \sqrt[3]{c} x}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}\right)^2}} F\left(\sin ^{-1}\left(\frac{\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{7 b^{2/3} \sqrt[3]{c} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}\right)^2}} \sqrt{a+b \sqrt{c x^3}}}-\frac{6 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{4/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+b^{2/3} \sqrt[3]{c} x}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}\right)^2}} E\left(\sin ^{-1}\left(\frac{\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{7 b^{2/3} \sqrt[3]{c} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}\right)^2}} \sqrt{a+b \sqrt{c x^3}}}+\frac{12 a \sqrt{a+b \sqrt{c x^3}}}{7 b^{2/3} \sqrt[3]{c} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}\right)}+\frac{4}{7} x \sqrt{a+b \sqrt{c x^3}}","\frac{4 \sqrt{2} 3^{3/4} a^{4/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+b^{2/3} \sqrt[3]{c} x}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}\right)^2}} F\left(\sin ^{-1}\left(\frac{\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{7 b^{2/3} \sqrt[3]{c} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}\right)^2}} \sqrt{a+b \sqrt{c x^3}}}-\frac{6 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{4/3} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}\right) \sqrt{\frac{a^{2/3}-\frac{\sqrt[3]{a} \sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+b^{2/3} \sqrt[3]{c} x}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}\right)^2}} E\left(\sin ^{-1}\left(\frac{\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{7 b^{2/3} \sqrt[3]{c} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}\right)^2}} \sqrt{a+b \sqrt{c x^3}}}+\frac{12 a \sqrt{a+b \sqrt{c x^3}}}{7 b^{2/3} \sqrt[3]{c} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}\right)}+\frac{4}{7} x \sqrt{a+b \sqrt{c x^3}}",1,"(4*x*Sqrt[a + b*Sqrt[c*x^3]])/7 + (12*a*Sqrt[a + b*Sqrt[c*x^3]])/(7*b^(2/3)*c^(1/3)*((1 + Sqrt[3])*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])) - (6*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(4/3)*(a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])*Sqrt[(a^(2/3) + b^(2/3)*c^(1/3)*x - (a^(1/3)*b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])/((1 + Sqrt[3])*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])/((1 + Sqrt[3])*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])], -7 - 4*Sqrt[3]])/(7*b^(2/3)*c^(1/3)*Sqrt[(a^(1/3)*(a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3]))/((1 + Sqrt[3])*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])^2]*Sqrt[a + b*Sqrt[c*x^3]]) + (4*Sqrt[2]*3^(3/4)*a^(4/3)*(a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])*Sqrt[(a^(2/3) + b^(2/3)*c^(1/3)*x - (a^(1/3)*b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])/((1 + Sqrt[3])*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])/((1 + Sqrt[3])*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])], -7 - 4*Sqrt[3]])/(7*b^(2/3)*c^(1/3)*Sqrt[(a^(1/3)*(a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3]))/((1 + Sqrt[3])*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])^2]*Sqrt[a + b*Sqrt[c*x^3]])","A",6,6,17,0.3529,1,"{255, 243, 279, 303, 218, 1877}"
2969,1,810,0,0.4587662,"\int \frac{\sqrt{a+b \sqrt{c x^3}}}{x^3} \, dx","Int[Sqrt[a + b*Sqrt[c*x^3]]/x^3,x]","-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} c^{2/3} \left(\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\sqrt[3]{a}\right) \sqrt{\frac{-\frac{\sqrt[3]{a} \sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+b^{2/3} \sqrt[3]{c} x+a^{2/3}}{\left(\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1+\sqrt{3}\right) \sqrt[3]{a}\right)^2}} E\left(\sin ^{-1}\left(\frac{\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right) b^{4/3}}{8 a^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\sqrt[3]{a}\right)}{\left(\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1+\sqrt{3}\right) \sqrt[3]{a}\right)^2}} \sqrt{a+b \sqrt{c x^3}}}+\frac{3^{3/4} c^{2/3} \left(\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\sqrt[3]{a}\right) \sqrt{\frac{-\frac{\sqrt[3]{a} \sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+b^{2/3} \sqrt[3]{c} x+a^{2/3}}{\left(\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1+\sqrt{3}\right) \sqrt[3]{a}\right)^2}} F\left(\sin ^{-1}\left(\frac{\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right) b^{4/3}}{2 \sqrt{2} a^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\sqrt[3]{a}\right)}{\left(\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1+\sqrt{3}\right) \sqrt[3]{a}\right)^2}} \sqrt{a+b \sqrt{c x^3}}}+\frac{3 c^{2/3} \sqrt{a+b \sqrt{c x^3}} b^{4/3}}{4 a \left(\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1+\sqrt{3}\right) \sqrt[3]{a}\right)}-\frac{3 c x \sqrt{a+b \sqrt{c x^3}} b}{4 a \sqrt{c x^3}}-\frac{\sqrt{a+b \sqrt{c x^3}}}{2 x^2}","-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} c^{2/3} \left(\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\sqrt[3]{a}\right) \sqrt{\frac{-\frac{\sqrt[3]{a} \sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+b^{2/3} \sqrt[3]{c} x+a^{2/3}}{\left(\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1+\sqrt{3}\right) \sqrt[3]{a}\right)^2}} E\left(\sin ^{-1}\left(\frac{\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right) b^{4/3}}{8 a^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\sqrt[3]{a}\right)}{\left(\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1+\sqrt{3}\right) \sqrt[3]{a}\right)^2}} \sqrt{a+b \sqrt{c x^3}}}+\frac{3^{3/4} c^{2/3} \left(\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\sqrt[3]{a}\right) \sqrt{\frac{-\frac{\sqrt[3]{a} \sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+b^{2/3} \sqrt[3]{c} x+a^{2/3}}{\left(\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1+\sqrt{3}\right) \sqrt[3]{a}\right)^2}} F\left(\sin ^{-1}\left(\frac{\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right) b^{4/3}}{2 \sqrt{2} a^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\sqrt[3]{a}\right)}{\left(\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1+\sqrt{3}\right) \sqrt[3]{a}\right)^2}} \sqrt{a+b \sqrt{c x^3}}}+\frac{3 c^{2/3} \sqrt{a+b \sqrt{c x^3}} b^{4/3}}{4 a \left(\frac{\sqrt[3]{b} c^{2/3} x^2}{\sqrt{c x^3}}+\left(1+\sqrt{3}\right) \sqrt[3]{a}\right)}-\frac{3 c x \sqrt{a+b \sqrt{c x^3}} b}{4 a \sqrt{c x^3}}-\frac{\sqrt{a+b \sqrt{c x^3}}}{2 x^2}",1,"-Sqrt[a + b*Sqrt[c*x^3]]/(2*x^2) - (3*b*c*x*Sqrt[a + b*Sqrt[c*x^3]])/(4*a*Sqrt[c*x^3]) + (3*b^(4/3)*c^(2/3)*Sqrt[a + b*Sqrt[c*x^3]])/(4*a*((1 + Sqrt[3])*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])) - (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*b^(4/3)*c^(2/3)*(a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])*Sqrt[(a^(2/3) + b^(2/3)*c^(1/3)*x - (a^(1/3)*b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])/((1 + Sqrt[3])*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])/((1 + Sqrt[3])*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])], -7 - 4*Sqrt[3]])/(8*a^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3]))/((1 + Sqrt[3])*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])^2]*Sqrt[a + b*Sqrt[c*x^3]]) + (3^(3/4)*b^(4/3)*c^(2/3)*(a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])*Sqrt[(a^(2/3) + b^(2/3)*c^(1/3)*x - (a^(1/3)*b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])/((1 + Sqrt[3])*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])/((1 + Sqrt[3])*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])], -7 - 4*Sqrt[3]])/(2*Sqrt[2]*a^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3]))/((1 + Sqrt[3])*a^(1/3) + (b^(1/3)*c^(2/3)*x^2)/Sqrt[c*x^3])^2]*Sqrt[a + b*Sqrt[c*x^3]])","A",7,7,21,0.3333,1,"{369, 341, 277, 325, 303, 218, 1877}"
2970,1,116,0,0.0764661,"\int x^{17} \sqrt{a+b \left(c x^3\right)^{3/2}} \, dx","Int[x^17*Sqrt[a + b*(c*x^3)^(3/2)],x]","\frac{4 a^2 \left(a+b \left(c x^3\right)^{3/2}\right)^{5/2}}{15 b^4 c^6}-\frac{4 a^3 \left(a+b \left(c x^3\right)^{3/2}\right)^{3/2}}{27 b^4 c^6}+\frac{4 \left(a+b \left(c x^3\right)^{3/2}\right)^{9/2}}{81 b^4 c^6}-\frac{4 a \left(a+b \left(c x^3\right)^{3/2}\right)^{7/2}}{21 b^4 c^6}","\frac{4 a^2 \left(a+b \left(c x^3\right)^{3/2}\right)^{5/2}}{15 b^4 c^6}-\frac{4 a^3 \left(a+b \left(c x^3\right)^{3/2}\right)^{3/2}}{27 b^4 c^6}+\frac{4 \left(a+b \left(c x^3\right)^{3/2}\right)^{9/2}}{81 b^4 c^6}-\frac{4 a \left(a+b \left(c x^3\right)^{3/2}\right)^{7/2}}{21 b^4 c^6}",1,"(-4*a^3*(a + b*(c*x^3)^(3/2))^(3/2))/(27*b^4*c^6) + (4*a^2*(a + b*(c*x^3)^(3/2))^(5/2))/(15*b^4*c^6) - (4*a*(a + b*(c*x^3)^(3/2))^(7/2))/(21*b^4*c^6) + (4*(a + b*(c*x^3)^(3/2))^(9/2))/(81*b^4*c^6)","A",4,3,21,0.1429,1,"{369, 266, 43}"
2971,1,56,0,0.0367072,"\int x^8 \sqrt{a+b \left(c x^3\right)^{3/2}} \, dx","Int[x^8*Sqrt[a + b*(c*x^3)^(3/2)],x]","\frac{4 \left(a+b \left(c x^3\right)^{3/2}\right)^{5/2}}{45 b^2 c^3}-\frac{4 a \left(a+b \left(c x^3\right)^{3/2}\right)^{3/2}}{27 b^2 c^3}","\frac{4 \left(a+b \left(c x^3\right)^{3/2}\right)^{5/2}}{45 b^2 c^3}-\frac{4 a \left(a+b \left(c x^3\right)^{3/2}\right)^{3/2}}{27 b^2 c^3}",1,"(-4*a*(a + b*(c*x^3)^(3/2))^(3/2))/(27*b^2*c^3) + (4*(a + b*(c*x^3)^(3/2))^(5/2))/(45*b^2*c^3)","A",4,3,21,0.1429,1,"{369, 266, 43}"
2972,1,55,0,0.0575646,"\int \frac{\sqrt{a+b \left(c x^3\right)^{3/2}}}{x} \, dx","Int[Sqrt[a + b*(c*x^3)^(3/2)]/x,x]","\frac{4}{9} \sqrt{a+b \left(c x^3\right)^{3/2}}-\frac{4}{9} \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \left(c x^3\right)^{3/2}}}{\sqrt{a}}\right)","\frac{4}{9} \sqrt{a+b \left(c x^3\right)^{3/2}}-\frac{4}{9} \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \left(c x^3\right)^{3/2}}}{\sqrt{a}}\right)",1,"(4*Sqrt[a + b*(c*x^3)^(3/2)])/9 - (4*Sqrt[a]*ArcTanh[Sqrt[a + b*(c*x^3)^(3/2)]/Sqrt[a]])/9","A",5,5,21,0.2381,1,"{369, 266, 50, 63, 208}"
2973,1,104,0,0.065108,"\int \frac{\sqrt{a+b \left(c x^3\right)^{3/2}}}{x^{10}} \, dx","Int[Sqrt[a + b*(c*x^3)^(3/2)]/x^10,x]","\frac{b^2 c^3 \tanh ^{-1}\left(\frac{\sqrt{a+b \left(c x^3\right)^{3/2}}}{\sqrt{a}}\right)}{18 a^{3/2}}-\frac{b c^6 x^9 \sqrt{a+b \left(c x^3\right)^{3/2}}}{18 a \left(c x^3\right)^{9/2}}-\frac{\sqrt{a+b \left(c x^3\right)^{3/2}}}{9 x^9}","\frac{b^2 c^3 \tanh ^{-1}\left(\frac{\sqrt{a+b \left(c x^3\right)^{3/2}}}{\sqrt{a}}\right)}{18 a^{3/2}}-\frac{b c^3 \sqrt{a+b \left(c x^3\right)^{3/2}}}{18 a \left(c x^3\right)^{3/2}}-\frac{\sqrt{a+b \left(c x^3\right)^{3/2}}}{9 x^9}",1,"-Sqrt[a + b*(c*x^3)^(3/2)]/(9*x^9) - (b*c^6*x^9*Sqrt[a + b*(c*x^3)^(3/2)])/(18*a*(c*x^3)^(9/2)) + (b^2*c^3*ArcTanh[Sqrt[a + b*(c*x^3)^(3/2)]/Sqrt[a]])/(18*a^(3/2))","A",6,6,21,0.2857,1,"{369, 266, 47, 51, 63, 208}"
2974,1,642,0,0.7348256,"\int x^2 \sqrt{a+b \left(c x^3\right)^{3/2}} \, dx","Int[x^2*Sqrt[a + b*(c*x^3)^(3/2)],x]","\frac{4 \sqrt{2} a^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^3}\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt{c x^3}+b^{2/3} c x^3}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^3}\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} \sqrt{c x^3}+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} \sqrt{c x^3}+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{7 \sqrt[4]{3} b^{2/3} c \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^3}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^3}\right)^2}} \sqrt{a+b \left(c x^3\right)^{3/2}}}-\frac{2 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^3}\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt{c x^3}+b^{2/3} c x^3}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^3}\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} \sqrt{c x^3}+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} \sqrt{c x^3}+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{7 b^{2/3} c \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^3}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^3}\right)^2}} \sqrt{a+b \left(c x^3\right)^{3/2}}}+\frac{4 a \sqrt{a+b \left(c x^3\right)^{3/2}}}{7 b^{2/3} c \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^3}\right)}+\frac{4}{21} x^3 \sqrt{a+b \left(c x^3\right)^{3/2}}","\frac{4 \sqrt{2} a^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^3}\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt{c x^3}+b^{2/3} c x^3}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^3}\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} \sqrt{c x^3}+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} \sqrt{c x^3}+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{7 \sqrt[4]{3} b^{2/3} c \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^3}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^3}\right)^2}} \sqrt{a+b \left(c x^3\right)^{3/2}}}-\frac{2 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^3}\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sqrt{c x^3}+b^{2/3} c x^3}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^3}\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} \sqrt{c x^3}+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} \sqrt{c x^3}+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{7 b^{2/3} c \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^3}\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^3}\right)^2}} \sqrt{a+b \left(c x^3\right)^{3/2}}}+\frac{4 a \sqrt{a+b \left(c x^3\right)^{3/2}}}{7 b^{2/3} c \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} \sqrt{c x^3}\right)}+\frac{4}{21} x^3 \sqrt{a+b \left(c x^3\right)^{3/2}}",1,"(4*x^3*Sqrt[a + b*(c*x^3)^(3/2)])/21 + (4*a*Sqrt[a + b*(c*x^3)^(3/2)])/(7*b^(2/3)*c*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^3])) - (2*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(4/3)*(a^(1/3) + b^(1/3)*Sqrt[c*x^3])*Sqrt[(a^(2/3) + b^(2/3)*c*x^3 - a^(1/3)*b^(1/3)*Sqrt[c*x^3])/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^3])^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^3])/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^3])], -7 - 4*Sqrt[3]])/(7*b^(2/3)*c*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*Sqrt[c*x^3]))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^3])^2]*Sqrt[a + b*(c*x^3)^(3/2)]) + (4*Sqrt[2]*a^(4/3)*(a^(1/3) + b^(1/3)*Sqrt[c*x^3])*Sqrt[(a^(2/3) + b^(2/3)*c*x^3 - a^(1/3)*b^(1/3)*Sqrt[c*x^3])/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^3])^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^3])/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^3])], -7 - 4*Sqrt[3]])/(7*3^(1/4)*b^(2/3)*c*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*Sqrt[c*x^3]))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*Sqrt[c*x^3])^2]*Sqrt[a + b*(c*x^3)^(3/2)])","A",7,7,21,0.3333,1,"{369, 341, 275, 279, 303, 218, 1877}"
2975,1,170,0,0.1281016,"\int x^9 \sqrt{a+b \left(c x^3\right)^{3/2}} \, dx","Int[x^9*Sqrt[a + b*(c*x^3)^(3/2)],x]","\frac{792 a^3 x \sqrt{\frac{b \left(c x^3\right)^{3/2}}{a}+1} \, _2F_1\left(\frac{2}{9},\frac{1}{2};\frac{11}{9};-\frac{b \left(c x^3\right)^{3/2}}{a}\right)}{19747 b^2 c^3 \sqrt{a+b \left(c x^3\right)^{3/2}}}-\frac{792 a^2 x \sqrt{a+b \left(c x^3\right)^{3/2}}}{19747 b^2 c^3}+\frac{36 a x \left(c x^3\right)^{3/2} \sqrt{a+b \left(c x^3\right)^{3/2}}}{1519 b c^3}+\frac{4}{49} x^{10} \sqrt{a+b \left(c x^3\right)^{3/2}}","\frac{792 a^3 x \sqrt{\frac{b \left(c x^3\right)^{3/2}}{a}+1} \, _2F_1\left(\frac{2}{9},\frac{1}{2};\frac{11}{9};-\frac{b \left(c x^3\right)^{3/2}}{a}\right)}{19747 b^2 c^3 \sqrt{a+b \left(c x^3\right)^{3/2}}}-\frac{792 a^2 x \sqrt{a+b \left(c x^3\right)^{3/2}}}{19747 b^2 c^3}+\frac{36 a x \left(c x^3\right)^{3/2} \sqrt{a+b \left(c x^3\right)^{3/2}}}{1519 b c^3}+\frac{4}{49} x^{10} \sqrt{a+b \left(c x^3\right)^{3/2}}",1,"(-792*a^2*x*Sqrt[a + b*(c*x^3)^(3/2)])/(19747*b^2*c^3) + (4*x^10*Sqrt[a + b*(c*x^3)^(3/2)])/49 + (36*a*x*(c*x^3)^(3/2)*Sqrt[a + b*(c*x^3)^(3/2)])/(1519*b*c^3) + (792*a^3*x*Sqrt[1 + (b*(c*x^3)^(3/2))/a]*Hypergeometric2F1[2/9, 1/2, 11/9, -((b*(c*x^3)^(3/2))/a)])/(19747*b^2*c^3*Sqrt[a + b*(c*x^3)^(3/2)])","A",7,6,21,0.2857,1,"{369, 341, 279, 321, 365, 364}"
2976,1,91,0,0.0522511,"\int \sqrt{a+b \left(c x^3\right)^{3/2}} \, dx","Int[Sqrt[a + b*(c*x^3)^(3/2)],x]","\frac{9 a x \sqrt{\frac{b \left(c x^3\right)^{3/2}}{a}+1} \, _2F_1\left(\frac{2}{9},\frac{1}{2};\frac{11}{9};-\frac{b \left(c x^3\right)^{3/2}}{a}\right)}{13 \sqrt{a+b \left(c x^3\right)^{3/2}}}+\frac{4}{13} x \sqrt{a+b \left(c x^3\right)^{3/2}}","\frac{9 a x \sqrt{\frac{b \left(c x^3\right)^{3/2}}{a}+1} \, _2F_1\left(\frac{2}{9},\frac{1}{2};\frac{11}{9};-\frac{b \left(c x^3\right)^{3/2}}{a}\right)}{13 \sqrt{a+b \left(c x^3\right)^{3/2}}}+\frac{4}{13} x \sqrt{a+b \left(c x^3\right)^{3/2}}",1,"(4*x*Sqrt[a + b*(c*x^3)^(3/2)])/13 + (9*a*x*Sqrt[1 + (b*(c*x^3)^(3/2))/a]*Hypergeometric2F1[2/9, 1/2, 11/9, -((b*(c*x^3)^(3/2))/a)])/(13*Sqrt[a + b*(c*x^3)^(3/2)])","A",5,5,17,0.2941,1,"{255, 243, 279, 365, 364}"
2977,1,141,0,0.0916807,"\int \frac{\sqrt{a+b \left(c x^3\right)^{3/2}}}{x^9} \, dx","Int[Sqrt[a + b*(c*x^3)^(3/2)]/x^9,x]","-\frac{45 b^2 c^3 x \sqrt{\frac{b \left(c x^3\right)^{3/2}}{a}+1} \, _2F_1\left(\frac{2}{9},\frac{1}{2};\frac{11}{9};-\frac{b \left(c x^3\right)^{3/2}}{a}\right)}{448 a \sqrt{a+b \left(c x^3\right)^{3/2}}}-\frac{9 b c^5 x^7 \sqrt{a+b \left(c x^3\right)^{3/2}}}{112 a \left(c x^3\right)^{7/2}}-\frac{\sqrt{a+b \left(c x^3\right)^{3/2}}}{8 x^8}","-\frac{45 b^2 c^3 x \sqrt{\frac{b \left(c x^3\right)^{3/2}}{a}+1} \, _2F_1\left(\frac{2}{9},\frac{1}{2};\frac{11}{9};-\frac{b \left(c x^3\right)^{3/2}}{a}\right)}{448 a \sqrt{a+b \left(c x^3\right)^{3/2}}}-\frac{9 b c^3 x \sqrt{a+b \left(c x^3\right)^{3/2}}}{112 a \left(c x^3\right)^{3/2}}-\frac{\sqrt{a+b \left(c x^3\right)^{3/2}}}{8 x^8}",1,"-Sqrt[a + b*(c*x^3)^(3/2)]/(8*x^8) - (9*b*c^5*x^7*Sqrt[a + b*(c*x^3)^(3/2)])/(112*a*(c*x^3)^(7/2)) - (45*b^2*c^3*x*Sqrt[1 + (b*(c*x^3)^(3/2))/a]*Hypergeometric2F1[2/9, 1/2, 11/9, -((b*(c*x^3)^(3/2))/a)])/(448*a*Sqrt[a + b*(c*x^3)^(3/2)])","A",6,6,21,0.2857,1,"{369, 341, 277, 325, 365, 364}"
2978,1,84,0,0.0667372,"\int (d x)^m \sqrt{a+b \left(c x^3\right)^{3/2}} \, dx","Int[(d*x)^m*Sqrt[a + b*(c*x^3)^(3/2)],x]","\frac{x (d x)^m \sqrt{a+b \left(c x^3\right)^{3/2}} \, _2F_1\left(-\frac{1}{2},\frac{2 (m+1)}{9};\frac{2 (m+1)}{9}+1;-\frac{b \left(c x^3\right)^{3/2}}{a}\right)}{(m+1) \sqrt{\frac{b \left(c x^3\right)^{3/2}}{a}+1}}","\frac{x (d x)^m \sqrt{a+b \left(c x^3\right)^{3/2}} \, _2F_1\left(-\frac{1}{2},\frac{2 (m+1)}{9};\frac{2 (m+1)}{9}+1;-\frac{b \left(c x^3\right)^{3/2}}{a}\right)}{(m+1) \sqrt{\frac{b \left(c x^3\right)^{3/2}}{a}+1}}",1,"(x*(d*x)^m*Sqrt[a + b*(c*x^3)^(3/2)]*Hypergeometric2F1[-1/2, (2*(1 + m))/9, 1 + (2*(1 + m))/9, -((b*(c*x^3)^(3/2))/a)])/((1 + m)*Sqrt[1 + (b*(c*x^3)^(3/2))/a])","A",5,5,23,0.2174,1,"{369, 343, 341, 365, 364}"
2979,1,84,0,0.0702241,"\int (d x)^m \sqrt{a+b \sqrt{c x^3}} \, dx","Int[(d*x)^m*Sqrt[a + b*Sqrt[c*x^3]],x]","\frac{x (d x)^m \sqrt{a+b \sqrt{c x^3}} \, _2F_1\left(-\frac{1}{2},\frac{2 (m+1)}{3};\frac{1}{3} (2 m+5);-\frac{b \sqrt{c x^3}}{a}\right)}{(m+1) \sqrt{\frac{b \sqrt{c x^3}}{a}+1}}","\frac{x (d x)^m \sqrt{a+b \sqrt{c x^3}} \, _2F_1\left(-\frac{1}{2},\frac{2 (m+1)}{3};\frac{1}{3} (2 m+5);-\frac{b \sqrt{c x^3}}{a}\right)}{(m+1) \sqrt{\frac{b \sqrt{c x^3}}{a}+1}}",1,"(x*(d*x)^m*Sqrt[a + b*Sqrt[c*x^3]]*Hypergeometric2F1[-1/2, (2*(1 + m))/3, (5 + 2*m)/3, -((b*Sqrt[c*x^3])/a)])/((1 + m)*Sqrt[1 + (b*Sqrt[c*x^3])/a])","A",5,5,23,0.2174,1,"{369, 343, 341, 365, 364}"
2980,1,84,0,0.1191832,"\int (d x)^m \sqrt{a+\frac{b}{\sqrt{c x^3}}} \, dx","Int[(d*x)^m*Sqrt[a + b/Sqrt[c*x^3]],x]","\frac{x (d x)^m \sqrt{a+\frac{b}{\sqrt{c x^3}}} \, _2F_1\left(-\frac{1}{2},-\frac{2}{3} (m+1);\frac{1}{3} (1-2 m);-\frac{b}{a \sqrt{c x^3}}\right)}{(m+1) \sqrt{\frac{b}{a \sqrt{c x^3}}+1}}","\frac{x (d x)^m \sqrt{a+\frac{b}{\sqrt{c x^3}}} \, _2F_1\left(-\frac{1}{2},-\frac{2}{3} (m+1);\frac{1}{3} (1-2 m);-\frac{b}{a \sqrt{c x^3}}\right)}{(m+1) \sqrt{\frac{b}{a \sqrt{c x^3}}+1}}",1,"(x*(d*x)^m*Sqrt[a + b/Sqrt[c*x^3]]*Hypergeometric2F1[-1/2, (-2*(1 + m))/3, (1 - 2*m)/3, -(b/(a*Sqrt[c*x^3]))])/((1 + m)*Sqrt[1 + b/(a*Sqrt[c*x^3])])","A",6,6,23,0.2609,1,"{369, 343, 341, 339, 365, 364}"
2981,1,102,0,0.1226161,"\int (d x)^m \sqrt{a+\frac{b}{\left(c x^3\right)^{3/2}}} \, dx","Int[(d*x)^m*Sqrt[a + b/(c*x^3)^(3/2)],x]","\frac{x (d x)^m \sqrt{a+\frac{b c^3 x^9}{\left(c x^3\right)^{9/2}}} \, _2F_1\left(-\frac{1}{2},-\frac{2}{9} (m+1);\frac{1}{9} (7-2 m);-\frac{b c^3 x^9}{a \left(c x^3\right)^{9/2}}\right)}{(m+1) \sqrt{\frac{b c^3 x^9}{a \left(c x^3\right)^{9/2}}+1}}","\frac{x (d x)^m \sqrt{a+\frac{b c^3 x^9}{\left(c x^3\right)^{9/2}}} \, _2F_1\left(-\frac{1}{2},-\frac{2}{9} (m+1);\frac{1}{9} (7-2 m);-\frac{b c^3 x^9}{a \left(c x^3\right)^{9/2}}\right)}{(m+1) \sqrt{\frac{b c^3 x^9}{a \left(c x^3\right)^{9/2}}+1}}",1,"(x*(d*x)^m*Sqrt[a + (b*c^3*x^9)/(c*x^3)^(9/2)]*Hypergeometric2F1[-1/2, (-2*(1 + m))/9, (7 - 2*m)/9, -((b*c^3*x^9)/(a*(c*x^3)^(9/2)))])/((1 + m)*Sqrt[1 + (b*c^3*x^9)/(a*(c*x^3)^(9/2))])","A",6,6,23,0.2609,1,"{369, 343, 341, 339, 365, 364}"
2982,1,172,0,0.101512,"\int \sqrt{a+b \sqrt{\frac{c}{x}}} x \, dx","Int[Sqrt[a + b*Sqrt[c/x]]*x,x]","\frac{5 b^3 c^2 \sqrt{a+b \sqrt{\frac{c}{x}}}}{32 a^3 \sqrt{\frac{c}{x}}}-\frac{5 b^4 c^2 \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{\frac{c}{x}}}}{\sqrt{a}}\right)}{32 a^{7/2}}-\frac{5 b^2 c x \sqrt{a+b \sqrt{\frac{c}{x}}}}{48 a^2}+\frac{b x^3 \left(\frac{c}{x}\right)^{3/2} \sqrt{a+b \sqrt{\frac{c}{x}}}}{12 a c}+\frac{1}{2} x^2 \sqrt{a+b \sqrt{\frac{c}{x}}}","\frac{5 b^3 c^2 \sqrt{a+b \sqrt{\frac{c}{x}}}}{32 a^3 \sqrt{\frac{c}{x}}}-\frac{5 b^4 c^2 \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{\frac{c}{x}}}}{\sqrt{a}}\right)}{32 a^{7/2}}-\frac{5 b^2 c x \sqrt{a+b \sqrt{\frac{c}{x}}}}{48 a^2}+\frac{b c^2 \sqrt{a+b \sqrt{\frac{c}{x}}}}{12 a \left(\frac{c}{x}\right)^{3/2}}+\frac{1}{2} x^2 \sqrt{a+b \sqrt{\frac{c}{x}}}",1,"(5*b^3*c^2*Sqrt[a + b*Sqrt[c/x]])/(32*a^3*Sqrt[c/x]) - (5*b^2*c*Sqrt[a + b*Sqrt[c/x]]*x)/(48*a^2) + (Sqrt[a + b*Sqrt[c/x]]*x^2)/2 + (b*Sqrt[a + b*Sqrt[c/x]]*(c/x)^(3/2)*x^3)/(12*a*c) - (5*b^4*c^2*ArcTanh[Sqrt[a + b*Sqrt[c/x]]/Sqrt[a]])/(32*a^(7/2))","A",8,6,19,0.3158,1,"{369, 266, 47, 51, 63, 208}"
2983,1,92,0,0.0486613,"\int \sqrt{a+b \sqrt{\frac{c}{x}}} \, dx","Int[Sqrt[a + b*Sqrt[c/x]],x]","-\frac{b^2 c \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{\frac{c}{x}}}}{\sqrt{a}}\right)}{2 a^{3/2}}+\frac{b c \sqrt{a+b \sqrt{\frac{c}{x}}}}{2 a \sqrt{\frac{c}{x}}}+x \sqrt{a+b \sqrt{\frac{c}{x}}}","-\frac{b^2 c \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{\frac{c}{x}}}}{\sqrt{a}}\right)}{2 a^{3/2}}+\frac{b c \sqrt{a+b \sqrt{\frac{c}{x}}}}{2 a \sqrt{\frac{c}{x}}}+x \sqrt{a+b \sqrt{\frac{c}{x}}}",1,"(b*c*Sqrt[a + b*Sqrt[c/x]])/(2*a*Sqrt[c/x]) + Sqrt[a + b*Sqrt[c/x]]*x - (b^2*c*ArcTanh[Sqrt[a + b*Sqrt[c/x]]/Sqrt[a]])/(2*a^(3/2))","A",6,6,17,0.3529,1,"{255, 190, 47, 51, 63, 208}"
2984,1,51,0,0.0349198,"\int \frac{\sqrt{a+b \sqrt{\frac{c}{x}}}}{x} \, dx","Int[Sqrt[a + b*Sqrt[c/x]]/x,x]","4 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{\frac{c}{x}}}}{\sqrt{a}}\right)-4 \sqrt{a+b \sqrt{\frac{c}{x}}}","4 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{\frac{c}{x}}}}{\sqrt{a}}\right)-4 \sqrt{a+b \sqrt{\frac{c}{x}}}",1,"-4*Sqrt[a + b*Sqrt[c/x]] + 4*Sqrt[a]*ArcTanh[Sqrt[a + b*Sqrt[c/x]]/Sqrt[a]]","A",5,5,21,0.2381,1,"{369, 266, 50, 63, 208}"
2985,1,56,0,0.0380851,"\int \frac{\sqrt{a+b \sqrt{\frac{c}{x}}}}{x^2} \, dx","Int[Sqrt[a + b*Sqrt[c/x]]/x^2,x]","\frac{4 a \left(a+b \sqrt{\frac{c}{x}}\right)^{3/2}}{3 b^2 c}-\frac{4 \left(a+b \sqrt{\frac{c}{x}}\right)^{5/2}}{5 b^2 c}","\frac{4 a \left(a+b \sqrt{\frac{c}{x}}\right)^{3/2}}{3 b^2 c}-\frac{4 \left(a+b \sqrt{\frac{c}{x}}\right)^{5/2}}{5 b^2 c}",1,"(4*a*(a + b*Sqrt[c/x])^(3/2))/(3*b^2*c) - (4*(a + b*Sqrt[c/x])^(5/2))/(5*b^2*c)","A",4,3,21,0.1429,1,"{369, 266, 43}"
2986,1,116,0,0.0686195,"\int \frac{\sqrt{a+b \sqrt{\frac{c}{x}}}}{x^3} \, dx","Int[Sqrt[a + b*Sqrt[c/x]]/x^3,x]","-\frac{12 a^2 \left(a+b \sqrt{\frac{c}{x}}\right)^{5/2}}{5 b^4 c^2}+\frac{4 a^3 \left(a+b \sqrt{\frac{c}{x}}\right)^{3/2}}{3 b^4 c^2}-\frac{4 \left(a+b \sqrt{\frac{c}{x}}\right)^{9/2}}{9 b^4 c^2}+\frac{12 a \left(a+b \sqrt{\frac{c}{x}}\right)^{7/2}}{7 b^4 c^2}","-\frac{12 a^2 \left(a+b \sqrt{\frac{c}{x}}\right)^{5/2}}{5 b^4 c^2}+\frac{4 a^3 \left(a+b \sqrt{\frac{c}{x}}\right)^{3/2}}{3 b^4 c^2}-\frac{4 \left(a+b \sqrt{\frac{c}{x}}\right)^{9/2}}{9 b^4 c^2}+\frac{12 a \left(a+b \sqrt{\frac{c}{x}}\right)^{7/2}}{7 b^4 c^2}",1,"(4*a^3*(a + b*Sqrt[c/x])^(3/2))/(3*b^4*c^2) - (12*a^2*(a + b*Sqrt[c/x])^(5/2))/(5*b^4*c^2) + (12*a*(a + b*Sqrt[c/x])^(7/2))/(7*b^4*c^2) - (4*(a + b*Sqrt[c/x])^(9/2))/(9*b^4*c^2)","A",4,3,21,0.1429,1,"{369, 266, 43}"
2987,1,174,0,0.1084465,"\int \frac{\sqrt{a+b \sqrt{\frac{c}{x}}}}{x^4} \, dx","Int[Sqrt[a + b*Sqrt[c/x]]/x^4,x]","-\frac{40 a^2 \left(a+b \sqrt{\frac{c}{x}}\right)^{9/2}}{9 b^6 c^3}+\frac{40 a^3 \left(a+b \sqrt{\frac{c}{x}}\right)^{7/2}}{7 b^6 c^3}-\frac{4 a^4 \left(a+b \sqrt{\frac{c}{x}}\right)^{5/2}}{b^6 c^3}+\frac{4 a^5 \left(a+b \sqrt{\frac{c}{x}}\right)^{3/2}}{3 b^6 c^3}-\frac{4 \left(a+b \sqrt{\frac{c}{x}}\right)^{13/2}}{13 b^6 c^3}+\frac{20 a \left(a+b \sqrt{\frac{c}{x}}\right)^{11/2}}{11 b^6 c^3}","-\frac{40 a^2 \left(a+b \sqrt{\frac{c}{x}}\right)^{9/2}}{9 b^6 c^3}+\frac{40 a^3 \left(a+b \sqrt{\frac{c}{x}}\right)^{7/2}}{7 b^6 c^3}-\frac{4 a^4 \left(a+b \sqrt{\frac{c}{x}}\right)^{5/2}}{b^6 c^3}+\frac{4 a^5 \left(a+b \sqrt{\frac{c}{x}}\right)^{3/2}}{3 b^6 c^3}-\frac{4 \left(a+b \sqrt{\frac{c}{x}}\right)^{13/2}}{13 b^6 c^3}+\frac{20 a \left(a+b \sqrt{\frac{c}{x}}\right)^{11/2}}{11 b^6 c^3}",1,"(4*a^5*(a + b*Sqrt[c/x])^(3/2))/(3*b^6*c^3) - (4*a^4*(a + b*Sqrt[c/x])^(5/2))/(b^6*c^3) + (40*a^3*(a + b*Sqrt[c/x])^(7/2))/(7*b^6*c^3) - (40*a^2*(a + b*Sqrt[c/x])^(9/2))/(9*b^6*c^3) + (20*a*(a + b*Sqrt[c/x])^(11/2))/(11*b^6*c^3) - (4*(a + b*Sqrt[c/x])^(13/2))/(13*b^6*c^3)","A",4,3,21,0.1429,1,"{369, 266, 43}"
2988,1,175,0,0.1214228,"\int \frac{x}{\sqrt{a+b \sqrt{\frac{c}{x}}}} \, dx","Int[x/Sqrt[a + b*Sqrt[c/x]],x]","-\frac{35 b^3 c^2 \sqrt{a+b \sqrt{\frac{c}{x}}}}{32 a^4 \sqrt{\frac{c}{x}}}+\frac{35 b^4 c^2 \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{\frac{c}{x}}}}{\sqrt{a}}\right)}{32 a^{9/2}}+\frac{35 b^2 c x \sqrt{a+b \sqrt{\frac{c}{x}}}}{48 a^3}-\frac{7 b x^3 \left(\frac{c}{x}\right)^{3/2} \sqrt{a+b \sqrt{\frac{c}{x}}}}{12 a^2 c}+\frac{x^2 \sqrt{a+b \sqrt{\frac{c}{x}}}}{2 a}","-\frac{35 b^3 c^2 \sqrt{a+b \sqrt{\frac{c}{x}}}}{32 a^4 \sqrt{\frac{c}{x}}}+\frac{35 b^4 c^2 \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{\frac{c}{x}}}}{\sqrt{a}}\right)}{32 a^{9/2}}+\frac{35 b^2 c x \sqrt{a+b \sqrt{\frac{c}{x}}}}{48 a^3}-\frac{7 b c^2 \sqrt{a+b \sqrt{\frac{c}{x}}}}{12 a^2 \left(\frac{c}{x}\right)^{3/2}}+\frac{x^2 \sqrt{a+b \sqrt{\frac{c}{x}}}}{2 a}",1,"(-35*b^3*c^2*Sqrt[a + b*Sqrt[c/x]])/(32*a^4*Sqrt[c/x]) + (35*b^2*c*Sqrt[a + b*Sqrt[c/x]]*x)/(48*a^3) + (Sqrt[a + b*Sqrt[c/x]]*x^2)/(2*a) - (7*b*Sqrt[a + b*Sqrt[c/x]]*(c/x)^(3/2)*x^3)/(12*a^2*c) + (35*b^4*c^2*ArcTanh[Sqrt[a + b*Sqrt[c/x]]/Sqrt[a]])/(32*a^(9/2))","A",8,5,19,0.2632,1,"{369, 266, 51, 63, 208}"
2989,1,95,0,0.0516822,"\int \frac{1}{\sqrt{a+b \sqrt{\frac{c}{x}}}} \, dx","Int[1/Sqrt[a + b*Sqrt[c/x]],x]","\frac{3 b^2 c \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{\frac{c}{x}}}}{\sqrt{a}}\right)}{2 a^{5/2}}-\frac{3 b c \sqrt{a+b \sqrt{\frac{c}{x}}}}{2 a^2 \sqrt{\frac{c}{x}}}+\frac{x \sqrt{a+b \sqrt{\frac{c}{x}}}}{a}","\frac{3 b^2 c \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{\frac{c}{x}}}}{\sqrt{a}}\right)}{2 a^{5/2}}-\frac{3 b c \sqrt{a+b \sqrt{\frac{c}{x}}}}{2 a^2 \sqrt{\frac{c}{x}}}+\frac{x \sqrt{a+b \sqrt{\frac{c}{x}}}}{a}",1,"(-3*b*c*Sqrt[a + b*Sqrt[c/x]])/(2*a^2*Sqrt[c/x]) + (Sqrt[a + b*Sqrt[c/x]]*x)/a + (3*b^2*c*ArcTanh[Sqrt[a + b*Sqrt[c/x]]/Sqrt[a]])/(2*a^(5/2))","A",6,5,17,0.2941,1,"{255, 190, 51, 63, 208}"
2990,1,31,0,0.0326503,"\int \frac{1}{\sqrt{a+b \sqrt{\frac{c}{x}}} x} \, dx","Int[1/(Sqrt[a + b*Sqrt[c/x]]*x),x]","\frac{4 \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{\frac{c}{x}}}}{\sqrt{a}}\right)}{\sqrt{a}}","\frac{4 \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{\frac{c}{x}}}}{\sqrt{a}}\right)}{\sqrt{a}}",1,"(4*ArcTanh[Sqrt[a + b*Sqrt[c/x]]/Sqrt[a]])/Sqrt[a]","A",4,4,21,0.1905,1,"{369, 266, 63, 208}"
2991,1,54,0,0.0441508,"\int \frac{1}{\sqrt{a+b \sqrt{\frac{c}{x}}} x^2} \, dx","Int[1/(Sqrt[a + b*Sqrt[c/x]]*x^2),x]","\frac{4 a \sqrt{a+b \sqrt{\frac{c}{x}}}}{b^2 c}-\frac{4 \left(a+b \sqrt{\frac{c}{x}}\right)^{3/2}}{3 b^2 c}","\frac{4 a \sqrt{a+b \sqrt{\frac{c}{x}}}}{b^2 c}-\frac{4 \left(a+b \sqrt{\frac{c}{x}}\right)^{3/2}}{3 b^2 c}",1,"(4*a*Sqrt[a + b*Sqrt[c/x]])/(b^2*c) - (4*(a + b*Sqrt[c/x])^(3/2))/(3*b^2*c)","A",4,3,21,0.1429,1,"{369, 266, 43}"
2992,1,112,0,0.0705248,"\int \frac{1}{\sqrt{a+b \sqrt{\frac{c}{x}}} x^3} \, dx","Int[1/(Sqrt[a + b*Sqrt[c/x]]*x^3),x]","-\frac{4 a^2 \left(a+b \sqrt{\frac{c}{x}}\right)^{3/2}}{b^4 c^2}+\frac{4 a^3 \sqrt{a+b \sqrt{\frac{c}{x}}}}{b^4 c^2}-\frac{4 \left(a+b \sqrt{\frac{c}{x}}\right)^{7/2}}{7 b^4 c^2}+\frac{12 a \left(a+b \sqrt{\frac{c}{x}}\right)^{5/2}}{5 b^4 c^2}","-\frac{4 a^2 \left(a+b \sqrt{\frac{c}{x}}\right)^{3/2}}{b^4 c^2}+\frac{4 a^3 \sqrt{a+b \sqrt{\frac{c}{x}}}}{b^4 c^2}-\frac{4 \left(a+b \sqrt{\frac{c}{x}}\right)^{7/2}}{7 b^4 c^2}+\frac{12 a \left(a+b \sqrt{\frac{c}{x}}\right)^{5/2}}{5 b^4 c^2}",1,"(4*a^3*Sqrt[a + b*Sqrt[c/x]])/(b^4*c^2) - (4*a^2*(a + b*Sqrt[c/x])^(3/2))/(b^4*c^2) + (12*a*(a + b*Sqrt[c/x])^(5/2))/(5*b^4*c^2) - (4*(a + b*Sqrt[c/x])^(7/2))/(7*b^4*c^2)","A",4,3,21,0.1429,1,"{369, 266, 43}"
2993,1,172,0,0.1030328,"\int \frac{1}{\sqrt{a+b \sqrt{\frac{c}{x}}} x^4} \, dx","Int[1/(Sqrt[a + b*Sqrt[c/x]]*x^4),x]","-\frac{40 a^2 \left(a+b \sqrt{\frac{c}{x}}\right)^{7/2}}{7 b^6 c^3}+\frac{8 a^3 \left(a+b \sqrt{\frac{c}{x}}\right)^{5/2}}{b^6 c^3}-\frac{20 a^4 \left(a+b \sqrt{\frac{c}{x}}\right)^{3/2}}{3 b^6 c^3}+\frac{4 a^5 \sqrt{a+b \sqrt{\frac{c}{x}}}}{b^6 c^3}-\frac{4 \left(a+b \sqrt{\frac{c}{x}}\right)^{11/2}}{11 b^6 c^3}+\frac{20 a \left(a+b \sqrt{\frac{c}{x}}\right)^{9/2}}{9 b^6 c^3}","-\frac{40 a^2 \left(a+b \sqrt{\frac{c}{x}}\right)^{7/2}}{7 b^6 c^3}+\frac{8 a^3 \left(a+b \sqrt{\frac{c}{x}}\right)^{5/2}}{b^6 c^3}-\frac{20 a^4 \left(a+b \sqrt{\frac{c}{x}}\right)^{3/2}}{3 b^6 c^3}+\frac{4 a^5 \sqrt{a+b \sqrt{\frac{c}{x}}}}{b^6 c^3}-\frac{4 \left(a+b \sqrt{\frac{c}{x}}\right)^{11/2}}{11 b^6 c^3}+\frac{20 a \left(a+b \sqrt{\frac{c}{x}}\right)^{9/2}}{9 b^6 c^3}",1,"(4*a^5*Sqrt[a + b*Sqrt[c/x]])/(b^6*c^3) - (20*a^4*(a + b*Sqrt[c/x])^(3/2))/(3*b^6*c^3) + (8*a^3*(a + b*Sqrt[c/x])^(5/2))/(b^6*c^3) - (40*a^2*(a + b*Sqrt[c/x])^(7/2))/(7*b^6*c^3) + (20*a*(a + b*Sqrt[c/x])^(9/2))/(9*b^6*c^3) - (4*(a + b*Sqrt[c/x])^(11/2))/(11*b^6*c^3)","A",4,3,21,0.1429,1,"{369, 266, 43}"
2994,1,58,0,0.0158496,"\int \frac{1}{\sqrt{1+\sqrt{\frac{1}{x}}}} \, dx","Int[1/Sqrt[1 + Sqrt[x^(-1)]],x]","\sqrt{\sqrt{\frac{1}{x}}+1} x-\frac{3 \sqrt{\sqrt{\frac{1}{x}}+1}}{2 \sqrt{\frac{1}{x}}}+\frac{3}{2} \tanh ^{-1}\left(\sqrt{\sqrt{\frac{1}{x}}+1}\right)","\sqrt{\sqrt{\frac{1}{x}}+1} x-\frac{3 \sqrt{\sqrt{\frac{1}{x}}+1}}{2 \sqrt{\frac{1}{x}}}+\frac{3}{2} \tanh ^{-1}\left(\sqrt{\sqrt{\frac{1}{x}}+1}\right)",1,"(-3*Sqrt[1 + Sqrt[x^(-1)]])/(2*Sqrt[x^(-1)]) + Sqrt[1 + Sqrt[x^(-1)]]*x + (3*ArcTanh[Sqrt[1 + Sqrt[x^(-1)]]])/2","A",6,5,13,0.3846,1,"{255, 190, 51, 63, 207}"
2995,1,102,0,0.1052561,"\int \sqrt{a+b \left(\frac{c}{x}\right)^{3/2}} (d x)^m \, dx","Int[Sqrt[a + b*(c/x)^(3/2)]*(d*x)^m,x]","\frac{x (d x)^m \sqrt{a+\frac{b c^3}{x^3 \left(\frac{c}{x}\right)^{3/2}}} \, _2F_1\left(-\frac{1}{2},-\frac{2}{3} (m+1);\frac{1}{3} (1-2 m);-\frac{b c^3}{a \left(\frac{c}{x}\right)^{3/2} x^3}\right)}{(m+1) \sqrt{\frac{b c^3}{a x^3 \left(\frac{c}{x}\right)^{3/2}}+1}}","\frac{x (d x)^m \sqrt{a+\frac{b c^3}{x^3 \left(\frac{c}{x}\right)^{3/2}}} \, _2F_1\left(-\frac{1}{2},-\frac{2}{3} (m+1);\frac{1}{3} (1-2 m);-\frac{b c^3}{a \left(\frac{c}{x}\right)^{3/2} x^3}\right)}{(m+1) \sqrt{\frac{b c^3}{a x^3 \left(\frac{c}{x}\right)^{3/2}}+1}}",1,"(Sqrt[a + (b*c^3)/((c/x)^(3/2)*x^3)]*x*(d*x)^m*Hypergeometric2F1[-1/2, (-2*(1 + m))/3, (1 - 2*m)/3, -((b*c^3)/(a*(c/x)^(3/2)*x^3))])/((1 + m)*Sqrt[1 + (b*c^3)/(a*(c/x)^(3/2)*x^3)])","A",6,6,23,0.2609,1,"{369, 343, 341, 339, 365, 364}"
2996,1,80,0,0.0904063,"\int \sqrt{a+b \sqrt{\frac{c}{x}}} (d x)^m \, dx","Int[Sqrt[a + b*Sqrt[c/x]]*(d*x)^m,x]","\frac{4 b^2 c (d x)^m \left(a+b \sqrt{\frac{c}{x}}\right)^{3/2} \left(-\frac{b \sqrt{\frac{c}{x}}}{a}\right)^{2 m} \, _2F_1\left(\frac{3}{2},2 m+3;\frac{5}{2};\frac{\sqrt{\frac{c}{x}} b}{a}+1\right)}{3 a^3}","\frac{4 x^{m+1} \left(a+b \sqrt{\frac{c}{x}}\right)^{3/2} \, _2F_1\left(1,\frac{1}{2} (-4 m-1);\frac{5}{2};\frac{a+b \sqrt{\frac{c}{x}}}{a}\right)}{3 a}",1,"(4*b^2*c*(a + b*Sqrt[c/x])^(3/2)*(-((b*Sqrt[c/x])/a))^(2*m)*(d*x)^m*Hypergeometric2F1[3/2, 3 + 2*m, 5/2, 1 + (b*Sqrt[c/x])/a])/(3*a^3)","A",6,6,23,0.2609,1,"{369, 343, 341, 339, 67, 65}"
2997,1,78,0,0.0760735,"\int \sqrt{a+\frac{b}{\sqrt{\frac{c}{x}}}} (d x)^m \, dx","Int[Sqrt[a + b/Sqrt[c/x]]*(d*x)^m,x]","-\frac{4 a c (d x)^m \left(a+\frac{b}{\sqrt{\frac{c}{x}}}\right)^{3/2} \left(-\frac{b}{a \sqrt{\frac{c}{x}}}\right)^{-2 m} \, _2F_1\left(\frac{3}{2},-2 m-1;\frac{5}{2};\frac{b}{a \sqrt{\frac{c}{x}}}+1\right)}{3 b^2}","-\frac{4 a c (d x)^m \left(a+\frac{b}{\sqrt{\frac{c}{x}}}\right)^{3/2} \left(-\frac{b}{a \sqrt{\frac{c}{x}}}\right)^{-2 m} \, _2F_1\left(\frac{3}{2},-2 m-1;\frac{5}{2};\frac{b}{a \sqrt{\frac{c}{x}}}+1\right)}{3 b^2}",1,"(-4*a*c*(a + b/Sqrt[c/x])^(3/2)*(d*x)^m*Hypergeometric2F1[3/2, -1 - 2*m, 5/2, 1 + b/(a*Sqrt[c/x])])/(3*b^2*(-(b/(a*Sqrt[c/x])))^(2*m))","A",5,5,23,0.2174,1,"{369, 343, 341, 67, 65}"
2998,1,102,0,0.0874423,"\int \sqrt{a+\frac{b}{\left(\frac{c}{x}\right)^{3/2}}} (d x)^m \, dx","Int[Sqrt[a + b/(c/x)^(3/2)]*(d*x)^m,x]","\frac{x (d x)^m \sqrt{a+\frac{b x^3 \left(\frac{c}{x}\right)^{3/2}}{c^3}} \, _2F_1\left(-\frac{1}{2},\frac{2 (m+1)}{3};\frac{1}{3} (2 m+5);-\frac{b \left(\frac{c}{x}\right)^{3/2} x^3}{a c^3}\right)}{(m+1) \sqrt{\frac{b x^3 \left(\frac{c}{x}\right)^{3/2}}{a c^3}+1}}","\frac{x (d x)^m \sqrt{a+\frac{b x^3 \left(\frac{c}{x}\right)^{3/2}}{c^3}} \, _2F_1\left(-\frac{1}{2},\frac{2 (m+1)}{3};\frac{1}{3} (2 m+5);-\frac{b \left(\frac{c}{x}\right)^{3/2} x^3}{a c^3}\right)}{(m+1) \sqrt{\frac{b x^3 \left(\frac{c}{x}\right)^{3/2}}{a c^3}+1}}",1,"(x*(d*x)^m*Sqrt[a + (b*(c/x)^(3/2)*x^3)/c^3]*Hypergeometric2F1[-1/2, (2*(1 + m))/3, (5 + 2*m)/3, -((b*(c/x)^(3/2)*x^3)/(a*c^3))])/((1 + m)*Sqrt[1 + (b*(c/x)^(3/2)*x^3)/(a*c^3)])","A",5,5,23,0.2174,1,"{369, 343, 341, 365, 364}"
2999,1,102,0,0.0968887,"\int \frac{(d x)^m}{\sqrt{a+b \left(\frac{c}{x}\right)^{3/2}}} \, dx","Int[(d*x)^m/Sqrt[a + b*(c/x)^(3/2)],x]","\frac{x (d x)^m \sqrt{\frac{b c^3}{a x^3 \left(\frac{c}{x}\right)^{3/2}}+1} \, _2F_1\left(\frac{1}{2},-\frac{2}{3} (m+1);\frac{1}{3} (1-2 m);-\frac{b c^3}{a \left(\frac{c}{x}\right)^{3/2} x^3}\right)}{(m+1) \sqrt{a+\frac{b c^3}{x^3 \left(\frac{c}{x}\right)^{3/2}}}}","\frac{x (d x)^m \sqrt{\frac{b c^3}{a x^3 \left(\frac{c}{x}\right)^{3/2}}+1} \, _2F_1\left(\frac{1}{2},-\frac{2}{3} (m+1);\frac{1}{3} (1-2 m);-\frac{b c^3}{a \left(\frac{c}{x}\right)^{3/2} x^3}\right)}{(m+1) \sqrt{a+\frac{b c^3}{x^3 \left(\frac{c}{x}\right)^{3/2}}}}",1,"(Sqrt[1 + (b*c^3)/(a*(c/x)^(3/2)*x^3)]*x*(d*x)^m*Hypergeometric2F1[1/2, (-2*(1 + m))/3, (1 - 2*m)/3, -((b*c^3)/(a*(c/x)^(3/2)*x^3))])/((1 + m)*Sqrt[a + (b*c^3)/((c/x)^(3/2)*x^3)])","A",6,6,23,0.2609,1,"{369, 343, 341, 339, 365, 364}"
3000,1,78,0,0.0876514,"\int \frac{(d x)^m}{\sqrt{a+b \sqrt{\frac{c}{x}}}} \, dx","Int[(d*x)^m/Sqrt[a + b*Sqrt[c/x]],x]","\frac{4 b^2 c (d x)^m \sqrt{a+b \sqrt{\frac{c}{x}}} \left(-\frac{b \sqrt{\frac{c}{x}}}{a}\right)^{2 m} \, _2F_1\left(\frac{1}{2},2 m+3;\frac{3}{2};\frac{\sqrt{\frac{c}{x}} b}{a}+1\right)}{a^3}","\frac{4 x^{m+1} \sqrt{a+b \sqrt{\frac{c}{x}}} \, _2F_1\left(1,\frac{1}{2} (-4 m-3);\frac{3}{2};\frac{a+b \sqrt{\frac{c}{x}}}{a}\right)}{a}",1,"(4*b^2*c*Sqrt[a + b*Sqrt[c/x]]*(-((b*Sqrt[c/x])/a))^(2*m)*(d*x)^m*Hypergeometric2F1[1/2, 3 + 2*m, 3/2, 1 + (b*Sqrt[c/x])/a])/a^3","A",6,6,23,0.2609,1,"{369, 343, 341, 339, 67, 65}"
3001,1,76,0,0.0667351,"\int \frac{(d x)^m}{\sqrt{a+\frac{b}{\sqrt{\frac{c}{x}}}}} \, dx","Int[(d*x)^m/Sqrt[a + b/Sqrt[c/x]],x]","-\frac{4 a c (d x)^m \sqrt{a+\frac{b}{\sqrt{\frac{c}{x}}}} \left(-\frac{b}{a \sqrt{\frac{c}{x}}}\right)^{-2 m} \, _2F_1\left(\frac{1}{2},-2 m-1;\frac{3}{2};\frac{b}{a \sqrt{\frac{c}{x}}}+1\right)}{b^2}","-\frac{4 a c (d x)^m \sqrt{a+\frac{b}{\sqrt{\frac{c}{x}}}} \left(-\frac{b}{a \sqrt{\frac{c}{x}}}\right)^{-2 m} \, _2F_1\left(\frac{1}{2},-2 m-1;\frac{3}{2};\frac{b}{a \sqrt{\frac{c}{x}}}+1\right)}{b^2}",1,"(-4*a*c*Sqrt[a + b/Sqrt[c/x]]*(d*x)^m*Hypergeometric2F1[1/2, -1 - 2*m, 3/2, 1 + b/(a*Sqrt[c/x])])/(b^2*(-(b/(a*Sqrt[c/x])))^(2*m))","A",5,5,23,0.2174,1,"{369, 343, 341, 67, 65}"
3002,1,102,0,0.0797451,"\int \frac{(d x)^m}{\sqrt{a+\frac{b}{\left(\frac{c}{x}\right)^{3/2}}}} \, dx","Int[(d*x)^m/Sqrt[a + b/(c/x)^(3/2)],x]","\frac{x (d x)^m \sqrt{\frac{b x^3 \left(\frac{c}{x}\right)^{3/2}}{a c^3}+1} \, _2F_1\left(\frac{1}{2},\frac{2 (m+1)}{3};\frac{1}{3} (2 m+5);-\frac{b \left(\frac{c}{x}\right)^{3/2} x^3}{a c^3}\right)}{(m+1) \sqrt{a+\frac{b x^3 \left(\frac{c}{x}\right)^{3/2}}{c^3}}}","\frac{x (d x)^m \sqrt{\frac{b x^3 \left(\frac{c}{x}\right)^{3/2}}{a c^3}+1} \, _2F_1\left(\frac{1}{2},\frac{2 (m+1)}{3};\frac{1}{3} (2 m+5);-\frac{b \left(\frac{c}{x}\right)^{3/2} x^3}{a c^3}\right)}{(m+1) \sqrt{a+\frac{b x^3 \left(\frac{c}{x}\right)^{3/2}}{c^3}}}",1,"(x*(d*x)^m*Sqrt[1 + (b*(c/x)^(3/2)*x^3)/(a*c^3)]*Hypergeometric2F1[1/2, (2*(1 + m))/3, (5 + 2*m)/3, -((b*(c/x)^(3/2)*x^3)/(a*c^3))])/((1 + m)*Sqrt[a + (b*(c/x)^(3/2)*x^3)/c^3])","A",5,5,23,0.2174,1,"{369, 343, 341, 365, 364}"
3003,1,19,0,0.0051805,"\int \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right) \, dx","Int[a + b*(c*x^n)^n^(-1),x]","a x+\frac{1}{2} b x \left(c x^n\right)^{\frac{1}{n}}","a x+\frac{1}{2} b x \left(c x^n\right)^{\frac{1}{n}}",1,"a*x + (b*x*(c*x^n)^n^(-1))/2","A",3,2,13,0.1538,1,"{15, 30}"
3004,1,34,0,0.0087369,"\int \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^2 \, dx","Int[(a + b*(c*x^n)^n^(-1))^2,x]","\frac{x \left(c x^n\right)^{-1/n} \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^3}{3 b}","\frac{x \left(c x^n\right)^{-1/n} \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^3}{3 b}",1,"(x*(a + b*(c*x^n)^n^(-1))^3)/(3*b*(c*x^n)^n^(-1))","A",2,2,15,0.1333,1,"{254, 32}"
3005,1,34,0,0.0077302,"\int \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^3 \, dx","Int[(a + b*(c*x^n)^n^(-1))^3,x]","\frac{x \left(c x^n\right)^{-1/n} \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^4}{4 b}","\frac{x \left(c x^n\right)^{-1/n} \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^4}{4 b}",1,"(x*(a + b*(c*x^n)^n^(-1))^4)/(4*b*(c*x^n)^n^(-1))","A",2,2,15,0.1333,1,"{254, 32}"
3006,1,101,0,0.0370195,"\int \frac{x^3}{a+b \left(c x^n\right)^{\frac{1}{n}}} \, dx","Int[x^3/(a + b*(c*x^n)^n^(-1)),x]","\frac{a^2 x^4 \left(c x^n\right)^{-3/n}}{b^3}-\frac{a^3 x^4 \left(c x^n\right)^{-4/n} \log \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)}{b^4}-\frac{a x^4 \left(c x^n\right)^{-2/n}}{2 b^2}+\frac{x^4 \left(c x^n\right)^{-1/n}}{3 b}","\frac{a^2 x^4 \left(c x^n\right)^{-3/n}}{b^3}-\frac{a^3 x^4 \left(c x^n\right)^{-4/n} \log \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)}{b^4}-\frac{a x^4 \left(c x^n\right)^{-2/n}}{2 b^2}+\frac{x^4 \left(c x^n\right)^{-1/n}}{3 b}",1,"(a^2*x^4)/(b^3*(c*x^n)^(3/n)) - (a*x^4)/(2*b^2*(c*x^n)^(2/n)) + x^4/(3*b*(c*x^n)^n^(-1)) - (a^3*x^4*Log[a + b*(c*x^n)^n^(-1)])/(b^4*(c*x^n)^(4/n))","A",3,2,19,0.1053,1,"{368, 43}"
3007,1,77,0,0.0269364,"\int \frac{x^2}{a+b \left(c x^n\right)^{\frac{1}{n}}} \, dx","Int[x^2/(a + b*(c*x^n)^n^(-1)),x]","\frac{a^2 x^3 \left(c x^n\right)^{-3/n} \log \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)}{b^3}-\frac{a x^3 \left(c x^n\right)^{-2/n}}{b^2}+\frac{x^3 \left(c x^n\right)^{-1/n}}{2 b}","\frac{a^2 x^3 \left(c x^n\right)^{-3/n} \log \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)}{b^3}-\frac{a x^3 \left(c x^n\right)^{-2/n}}{b^2}+\frac{x^3 \left(c x^n\right)^{-1/n}}{2 b}",1,"-((a*x^3)/(b^2*(c*x^n)^(2/n))) + x^3/(2*b*(c*x^n)^n^(-1)) + (a^2*x^3*Log[a + b*(c*x^n)^n^(-1)])/(b^3*(c*x^n)^(3/n))","A",3,2,19,0.1053,1,"{368, 43}"
3008,1,53,0,0.0178758,"\int \frac{x}{a+b \left(c x^n\right)^{\frac{1}{n}}} \, dx","Int[x/(a + b*(c*x^n)^n^(-1)),x]","\frac{x^2 \left(c x^n\right)^{-1/n}}{b}-\frac{a x^2 \left(c x^n\right)^{-2/n} \log \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)}{b^2}","\frac{x^2 \left(c x^n\right)^{-1/n}}{b}-\frac{a x^2 \left(c x^n\right)^{-2/n} \log \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)}{b^2}",1,"x^2/(b*(c*x^n)^n^(-1)) - (a*x^2*Log[a + b*(c*x^n)^n^(-1)])/(b^2*(c*x^n)^(2/n))","A",3,2,17,0.1176,1,"{368, 43}"
3009,1,30,0,0.007532,"\int \frac{1}{a+b \left(c x^n\right)^{\frac{1}{n}}} \, dx","Int[(a + b*(c*x^n)^n^(-1))^(-1),x]","\frac{x \left(c x^n\right)^{-1/n} \log \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)}{b}","\frac{x \left(c x^n\right)^{-1/n} \log \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)}{b}",1,"(x*Log[a + b*(c*x^n)^n^(-1)])/(b*(c*x^n)^n^(-1))","A",2,2,15,0.1333,1,"{254, 31}"
3010,1,26,0,0.0089402,"\int \frac{1}{x \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)} \, dx","Int[1/(x*(a + b*(c*x^n)^n^(-1))),x]","\frac{\log (x)}{a}-\frac{\log \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)}{a}","\frac{\log (x)}{a}-\frac{\log \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)}{a}",1,"Log[x]/a - Log[a + b*(c*x^n)^n^(-1)]/a","A",4,4,19,0.2105,1,"{368, 36, 29, 31}"
3011,1,60,0,0.0232409,"\int \frac{1}{x^2 \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)} \, dx","Int[1/(x^2*(a + b*(c*x^n)^n^(-1))),x]","-\frac{b \log (x) \left(c x^n\right)^{\frac{1}{n}}}{a^2 x}+\frac{b \left(c x^n\right)^{\frac{1}{n}} \log \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)}{a^2 x}-\frac{1}{a x}","-\frac{b \log (x) \left(c x^n\right)^{\frac{1}{n}}}{a^2 x}+\frac{b \left(c x^n\right)^{\frac{1}{n}} \log \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)}{a^2 x}-\frac{1}{a x}",1,"-(1/(a*x)) - (b*(c*x^n)^n^(-1)*Log[x])/(a^2*x) + (b*(c*x^n)^n^(-1)*Log[a + b*(c*x^n)^n^(-1)])/(a^2*x)","A",3,2,19,0.1053,1,"{368, 44}"
3012,1,87,0,0.0321322,"\int \frac{1}{x^3 \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)} \, dx","Int[1/(x^3*(a + b*(c*x^n)^n^(-1))),x]","\frac{b^2 \log (x) \left(c x^n\right)^{2/n}}{a^3 x^2}-\frac{b^2 \left(c x^n\right)^{2/n} \log \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)}{a^3 x^2}+\frac{b \left(c x^n\right)^{\frac{1}{n}}}{a^2 x^2}-\frac{1}{2 a x^2}","\frac{b^2 \log (x) \left(c x^n\right)^{2/n}}{a^3 x^2}-\frac{b^2 \left(c x^n\right)^{2/n} \log \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)}{a^3 x^2}+\frac{b \left(c x^n\right)^{\frac{1}{n}}}{a^2 x^2}-\frac{1}{2 a x^2}",1,"-1/(2*a*x^2) + (b*(c*x^n)^n^(-1))/(a^2*x^2) + (b^2*(c*x^n)^(2/n)*Log[x])/(a^3*x^2) - (b^2*(c*x^n)^(2/n)*Log[a + b*(c*x^n)^n^(-1)])/(a^3*x^2)","A",3,2,19,0.1053,1,"{368, 44}"
3013,1,114,0,0.0437005,"\int \frac{x^3}{\left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^2} \, dx","Int[x^3/(a + b*(c*x^n)^n^(-1))^2,x]","\frac{a^3 x^4 \left(c x^n\right)^{-4/n}}{b^4 \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)}+\frac{3 a^2 x^4 \left(c x^n\right)^{-4/n} \log \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)}{b^4}-\frac{2 a x^4 \left(c x^n\right)^{-3/n}}{b^3}+\frac{x^4 \left(c x^n\right)^{-2/n}}{2 b^2}","\frac{a^3 x^4 \left(c x^n\right)^{-4/n}}{b^4 \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)}+\frac{3 a^2 x^4 \left(c x^n\right)^{-4/n} \log \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)}{b^4}-\frac{2 a x^4 \left(c x^n\right)^{-3/n}}{b^3}+\frac{x^4 \left(c x^n\right)^{-2/n}}{2 b^2}",1,"(-2*a*x^4)/(b^3*(c*x^n)^(3/n)) + x^4/(2*b^2*(c*x^n)^(2/n)) + (a^3*x^4)/(b^4*(c*x^n)^(4/n)*(a + b*(c*x^n)^n^(-1))) + (3*a^2*x^4*Log[a + b*(c*x^n)^n^(-1)])/(b^4*(c*x^n)^(4/n))","A",3,2,19,0.1053,1,"{368, 43}"
3014,1,90,0,0.0328159,"\int \frac{x^2}{\left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^2} \, dx","Int[x^2/(a + b*(c*x^n)^n^(-1))^2,x]","-\frac{a^2 x^3 \left(c x^n\right)^{-3/n}}{b^3 \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)}-\frac{2 a x^3 \left(c x^n\right)^{-3/n} \log \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)}{b^3}+\frac{x^3 \left(c x^n\right)^{-2/n}}{b^2}","-\frac{a^2 x^3 \left(c x^n\right)^{-3/n}}{b^3 \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)}-\frac{2 a x^3 \left(c x^n\right)^{-3/n} \log \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)}{b^3}+\frac{x^3 \left(c x^n\right)^{-2/n}}{b^2}",1,"x^3/(b^2*(c*x^n)^(2/n)) - (a^2*x^3)/(b^3*(c*x^n)^(3/n)*(a + b*(c*x^n)^n^(-1))) - (2*a*x^3*Log[a + b*(c*x^n)^n^(-1)])/(b^3*(c*x^n)^(3/n))","A",3,2,19,0.1053,1,"{368, 43}"
3015,1,67,0,0.0257055,"\int \frac{x}{\left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^2} \, dx","Int[x/(a + b*(c*x^n)^n^(-1))^2,x]","\frac{a x^2 \left(c x^n\right)^{-2/n}}{b^2 \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)}+\frac{x^2 \left(c x^n\right)^{-2/n} \log \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)}{b^2}","\frac{a x^2 \left(c x^n\right)^{-2/n}}{b^2 \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)}+\frac{x^2 \left(c x^n\right)^{-2/n} \log \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)}{b^2}",1,"(a*x^2)/(b^2*(c*x^n)^(2/n)*(a + b*(c*x^n)^n^(-1))) + (x^2*Log[a + b*(c*x^n)^n^(-1)])/(b^2*(c*x^n)^(2/n))","A",3,2,17,0.1176,1,"{368, 43}"
3016,1,32,0,0.0083064,"\int \frac{1}{\left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^2} \, dx","Int[(a + b*(c*x^n)^n^(-1))^(-2),x]","-\frac{x \left(c x^n\right)^{-1/n}}{b \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)}","\frac{x}{a^2+a b \left(c x^n\right)^{\frac{1}{n}}}",1,"-(x/(b*(c*x^n)^n^(-1)*(a + b*(c*x^n)^n^(-1))))","A",2,2,15,0.1333,1,"{254, 32}"
3017,1,45,0,0.0202457,"\int \frac{1}{x \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^2} \, dx","Int[1/(x*(a + b*(c*x^n)^n^(-1))^2),x]","-\frac{\log \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)}{a^2}+\frac{\log (x)}{a^2}+\frac{1}{a \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)}","-\frac{\log \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)}{a^2}+\frac{\log (x)}{a^2}+\frac{1}{a \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)}",1,"1/(a*(a + b*(c*x^n)^n^(-1))) + Log[x]/a^2 - Log[a + b*(c*x^n)^n^(-1)]/a^2","A",3,2,19,0.1053,1,"{368, 44}"
3018,1,94,0,0.0376218,"\int \frac{1}{x^2 \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^2} \, dx","Int[1/(x^2*(a + b*(c*x^n)^n^(-1))^2),x]","-\frac{b \left(c x^n\right)^{\frac{1}{n}}}{a^2 x \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)}-\frac{2 b \log (x) \left(c x^n\right)^{\frac{1}{n}}}{a^3 x}+\frac{2 b \left(c x^n\right)^{\frac{1}{n}} \log \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)}{a^3 x}-\frac{1}{a^2 x}","-\frac{b \left(c x^n\right)^{\frac{1}{n}}}{a^2 x \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)}-\frac{2 b \log (x) \left(c x^n\right)^{\frac{1}{n}}}{a^3 x}+\frac{2 b \left(c x^n\right)^{\frac{1}{n}} \log \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)}{a^3 x}-\frac{1}{a^2 x}",1,"-(1/(a^2*x)) - (b*(c*x^n)^n^(-1))/(a^2*x*(a + b*(c*x^n)^n^(-1))) - (2*b*(c*x^n)^n^(-1)*Log[x])/(a^3*x) + (2*b*(c*x^n)^n^(-1)*Log[a + b*(c*x^n)^n^(-1)])/(a^3*x)","A",3,2,19,0.1053,1,"{368, 44}"
3019,1,125,0,0.0501029,"\int \frac{1}{x^3 \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^2} \, dx","Int[1/(x^3*(a + b*(c*x^n)^n^(-1))^2),x]","\frac{b^2 \left(c x^n\right)^{2/n}}{a^3 x^2 \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)}+\frac{3 b^2 \log (x) \left(c x^n\right)^{2/n}}{a^4 x^2}-\frac{3 b^2 \left(c x^n\right)^{2/n} \log \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)}{a^4 x^2}+\frac{2 b \left(c x^n\right)^{\frac{1}{n}}}{a^3 x^2}-\frac{1}{2 a^2 x^2}","\frac{b^2 \left(c x^n\right)^{2/n}}{a^3 x^2 \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)}+\frac{3 b^2 \log (x) \left(c x^n\right)^{2/n}}{a^4 x^2}-\frac{3 b^2 \left(c x^n\right)^{2/n} \log \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)}{a^4 x^2}+\frac{2 b \left(c x^n\right)^{\frac{1}{n}}}{a^3 x^2}-\frac{1}{2 a^2 x^2}",1,"-1/(2*a^2*x^2) + (2*b*(c*x^n)^n^(-1))/(a^3*x^2) + (b^2*(c*x^n)^(2/n))/(a^3*x^2*(a + b*(c*x^n)^n^(-1))) + (3*b^2*(c*x^n)^(2/n)*Log[x])/(a^4*x^2) - (3*b^2*(c*x^n)^(2/n)*Log[a + b*(c*x^n)^n^(-1)])/(a^4*x^2)","A",3,2,19,0.1053,1,"{368, 44}"
3020,1,34,0,0.0081762,"\int \frac{1}{\left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^3} \, dx","Int[(a + b*(c*x^n)^n^(-1))^(-3),x]","-\frac{x \left(c x^n\right)^{-1/n}}{2 b \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^2}","-\frac{x \left(c x^n\right)^{-1/n}}{2 b \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^2}",1,"-x/(2*b*(c*x^n)^n^(-1)*(a + b*(c*x^n)^n^(-1))^2)","A",2,2,15,0.1333,1,"{254, 32}"
3021,1,48,0,0.0113031,"\int \frac{x}{\left(1+\left(x^n\right)^{\frac{1}{n}}\right)^2} \, dx","Int[x/(1 + (x^n)^n^(-1))^2,x]","\frac{x^2 \left(x^n\right)^{-2/n}}{\left(x^n\right)^{\frac{1}{n}}+1}+x^2 \left(x^n\right)^{-2/n} \log \left(\left(x^n\right)^{\frac{1}{n}}+1\right)","\frac{x^2 \left(x^n\right)^{-2/n}}{\left(x^n\right)^{\frac{1}{n}}+1}+x^2 \left(x^n\right)^{-2/n} \log \left(\left(x^n\right)^{\frac{1}{n}}+1\right)",1,"x^2/((x^n)^(2/n)*(1 + (x^n)^n^(-1))) + (x^2*Log[1 + (x^n)^n^(-1)])/(x^n)^(2/n)","A",3,2,13,0.1538,1,"{368, 43}"
3022,1,171,0,0.063625,"\int x^3 \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^p \, dx","Int[x^3*(a + b*(c*x^n)^n^(-1))^p,x]","-\frac{a^3 x^4 \left(c x^n\right)^{-4/n} \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^{p+1}}{b^4 (p+1)}+\frac{3 a^2 x^4 \left(c x^n\right)^{-4/n} \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^{p+2}}{b^4 (p+2)}-\frac{3 a x^4 \left(c x^n\right)^{-4/n} \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^{p+3}}{b^4 (p+3)}+\frac{x^4 \left(c x^n\right)^{-4/n} \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^{p+4}}{b^4 (p+4)}","-\frac{a^3 x^4 \left(c x^n\right)^{-4/n} \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^{p+1}}{b^4 (p+1)}+\frac{3 a^2 x^4 \left(c x^n\right)^{-4/n} \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^{p+2}}{b^4 (p+2)}-\frac{3 a x^4 \left(c x^n\right)^{-4/n} \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^{p+3}}{b^4 (p+3)}+\frac{x^4 \left(c x^n\right)^{-4/n} \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^{p+4}}{b^4 (p+4)}",1,"-((a^3*x^4*(a + b*(c*x^n)^n^(-1))^(1 + p))/(b^4*(1 + p)*(c*x^n)^(4/n))) + (3*a^2*x^4*(a + b*(c*x^n)^n^(-1))^(2 + p))/(b^4*(2 + p)*(c*x^n)^(4/n)) - (3*a*x^4*(a + b*(c*x^n)^n^(-1))^(3 + p))/(b^4*(3 + p)*(c*x^n)^(4/n)) + (x^4*(a + b*(c*x^n)^n^(-1))^(4 + p))/(b^4*(4 + p)*(c*x^n)^(4/n))","A",3,2,19,0.1053,1,"{368, 43}"
3023,1,126,0,0.0453388,"\int x^2 \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^p \, dx","Int[x^2*(a + b*(c*x^n)^n^(-1))^p,x]","\frac{a^2 x^3 \left(c x^n\right)^{-3/n} \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^{p+1}}{b^3 (p+1)}-\frac{2 a x^3 \left(c x^n\right)^{-3/n} \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^{p+2}}{b^3 (p+2)}+\frac{x^3 \left(c x^n\right)^{-3/n} \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^{p+3}}{b^3 (p+3)}","\frac{a^2 x^3 \left(c x^n\right)^{-3/n} \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^{p+1}}{b^3 (p+1)}-\frac{2 a x^3 \left(c x^n\right)^{-3/n} \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^{p+2}}{b^3 (p+2)}+\frac{x^3 \left(c x^n\right)^{-3/n} \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^{p+3}}{b^3 (p+3)}",1,"(a^2*x^3*(a + b*(c*x^n)^n^(-1))^(1 + p))/(b^3*(1 + p)*(c*x^n)^(3/n)) - (2*a*x^3*(a + b*(c*x^n)^n^(-1))^(2 + p))/(b^3*(2 + p)*(c*x^n)^(3/n)) + (x^3*(a + b*(c*x^n)^n^(-1))^(3 + p))/(b^3*(3 + p)*(c*x^n)^(3/n))","A",3,2,19,0.1053,1,"{368, 43}"
3024,1,83,0,0.0303635,"\int x \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^p \, dx","Int[x*(a + b*(c*x^n)^n^(-1))^p,x]","\frac{x^2 \left(c x^n\right)^{-2/n} \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^{p+2}}{b^2 (p+2)}-\frac{a x^2 \left(c x^n\right)^{-2/n} \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^{p+1}}{b^2 (p+1)}","\frac{x^2 \left(c x^n\right)^{-2/n} \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^{p+2}}{b^2 (p+2)}-\frac{a x^2 \left(c x^n\right)^{-2/n} \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^{p+1}}{b^2 (p+1)}",1,"-((a*x^2*(a + b*(c*x^n)^n^(-1))^(1 + p))/(b^2*(1 + p)*(c*x^n)^(2/n))) + (x^2*(a + b*(c*x^n)^n^(-1))^(2 + p))/(b^2*(2 + p)*(c*x^n)^(2/n))","A",3,2,17,0.1176,1,"{368, 43}"
3025,1,38,0,0.0120628,"\int \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^p \, dx","Int[(a + b*(c*x^n)^n^(-1))^p,x]","\frac{x \left(c x^n\right)^{-1/n} \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^{p+1}}{b (p+1)}","\frac{x \left(c x^n\right)^{-1/n} \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^{p+1}}{b (p+1)}",1,"(x*(a + b*(c*x^n)^n^(-1))^(1 + p))/(b*(1 + p)*(c*x^n)^n^(-1))","A",2,2,15,0.1333,1,"{254, 32}"
3026,1,51,0,0.0164345,"\int \frac{\left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^p}{x} \, dx","Int[(a + b*(c*x^n)^n^(-1))^p/x,x]","-\frac{\left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{b \left(c x^n\right)^{\frac{1}{n}}}{a}+1\right)}{a (p+1)}","-\frac{\left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{b \left(c x^n\right)^{\frac{1}{n}}}{a}+1\right)}{a (p+1)}",1,"-(((a + b*(c*x^n)^n^(-1))^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, 1 + (b*(c*x^n)^n^(-1))/a])/(a*(1 + p)))","A",2,2,19,0.1053,1,"{368, 65}"
3027,1,63,0,0.0248413,"\int \frac{\left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^p}{x^2} \, dx","Int[(a + b*(c*x^n)^n^(-1))^p/x^2,x]","\frac{b \left(c x^n\right)^{\frac{1}{n}} \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^{p+1} \, _2F_1\left(2,p+1;p+2;\frac{b \left(c x^n\right)^{\frac{1}{n}}}{a}+1\right)}{a^2 (p+1) x}","\frac{b \left(c x^n\right)^{\frac{1}{n}} \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^{p+1} \, _2F_1\left(2,p+1;p+2;\frac{b \left(c x^n\right)^{\frac{1}{n}}}{a}+1\right)}{a^2 (p+1) x}",1,"(b*(c*x^n)^n^(-1)*(a + b*(c*x^n)^n^(-1))^(1 + p)*Hypergeometric2F1[2, 1 + p, 2 + p, 1 + (b*(c*x^n)^n^(-1))/a])/(a^2*(1 + p)*x)","A",2,2,19,0.1053,1,"{368, 65}"
3028,1,62,0,0.0232592,"\int \left(a+b \left(c x^n\right)^{2/n}\right)^3 \, dx","Int[(a + b*(c*x^n)^(2/n))^3,x]","a^2 b x \left(c x^n\right)^{2/n}+a^3 x+\frac{3}{5} a b^2 x \left(c x^n\right)^{4/n}+\frac{1}{7} b^3 x \left(c x^n\right)^{6/n}","a^2 b x \left(c x^n\right)^{2/n}+a^3 x+\frac{3}{5} a b^2 x \left(c x^n\right)^{4/n}+\frac{1}{7} b^3 x \left(c x^n\right)^{6/n}",1,"a^3*x + a^2*b*x*(c*x^n)^(2/n) + (3*a*b^2*x*(c*x^n)^(4/n))/5 + (b^3*x*(c*x^n)^(6/n))/7","A",3,2,17,0.1176,1,"{254, 194}"
3029,1,43,0,0.0171888,"\int \left(a+b \left(c x^n\right)^{2/n}\right)^2 \, dx","Int[(a + b*(c*x^n)^(2/n))^2,x]","a^2 x+\frac{2}{3} a b x \left(c x^n\right)^{2/n}+\frac{1}{5} b^2 x \left(c x^n\right)^{4/n}","a^2 x+\frac{2}{3} a b x \left(c x^n\right)^{2/n}+\frac{1}{5} b^2 x \left(c x^n\right)^{4/n}",1,"a^2*x + (2*a*b*x*(c*x^n)^(2/n))/3 + (b^2*x*(c*x^n)^(4/n))/5","A",3,2,17,0.1176,1,"{254, 194}"
3030,1,21,0,0.0056403,"\int \left(a+b \left(c x^n\right)^{2/n}\right) \, dx","Int[a + b*(c*x^n)^(2/n),x]","a x+\frac{1}{3} b x \left(c x^n\right)^{2/n}","a x+\frac{1}{3} b x \left(c x^n\right)^{2/n}",1,"a*x + (b*x*(c*x^n)^(2/n))/3","A",3,2,15,0.1333,1,"{15, 30}"
3031,1,44,0,0.0123477,"\int \frac{1}{a+b \left(c x^n\right)^{2/n}} \, dx","Int[(a + b*(c*x^n)^(2/n))^(-1),x]","\frac{x \left(c x^n\right)^{-1/n} \tan ^{-1}\left(\frac{\sqrt{b} \left(c x^n\right)^{\frac{1}{n}}}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b}}","\frac{x \left(c x^n\right)^{-1/n} \tan ^{-1}\left(\frac{\sqrt{b} \left(c x^n\right)^{\frac{1}{n}}}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b}}",1,"(x*ArcTan[(Sqrt[b]*(c*x^n)^n^(-1))/Sqrt[a]])/(Sqrt[a]*Sqrt[b]*(c*x^n)^n^(-1))","A",2,2,17,0.1176,1,"{254, 205}"
3032,1,73,0,0.0240274,"\int \frac{1}{\left(a+b \left(c x^n\right)^{2/n}\right)^2} \, dx","Int[(a + b*(c*x^n)^(2/n))^(-2),x]","\frac{x \left(c x^n\right)^{-1/n} \tan ^{-1}\left(\frac{\sqrt{b} \left(c x^n\right)^{\frac{1}{n}}}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b}}+\frac{x}{2 a \left(a+b \left(c x^n\right)^{2/n}\right)}","\frac{x \left(c x^n\right)^{-1/n} \tan ^{-1}\left(\frac{\sqrt{b} \left(c x^n\right)^{\frac{1}{n}}}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b}}+\frac{x}{2 a \left(a+b \left(c x^n\right)^{2/n}\right)}",1,"x/(2*a*(a + b*(c*x^n)^(2/n))) + (x*ArcTan[(Sqrt[b]*(c*x^n)^n^(-1))/Sqrt[a]])/(2*a^(3/2)*Sqrt[b]*(c*x^n)^n^(-1))","A",3,3,17,0.1765,1,"{254, 199, 205}"
3033,1,98,0,0.0343084,"\int \frac{1}{\left(a+b \left(c x^n\right)^{2/n}\right)^3} \, dx","Int[(a + b*(c*x^n)^(2/n))^(-3),x]","\frac{3 x}{8 a^2 \left(a+b \left(c x^n\right)^{2/n}\right)}+\frac{3 x \left(c x^n\right)^{-1/n} \tan ^{-1}\left(\frac{\sqrt{b} \left(c x^n\right)^{\frac{1}{n}}}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{b}}+\frac{x}{4 a \left(a+b \left(c x^n\right)^{2/n}\right)^2}","\frac{3 x}{8 a^2 \left(a+b \left(c x^n\right)^{2/n}\right)}+\frac{3 x \left(c x^n\right)^{-1/n} \tan ^{-1}\left(\frac{\sqrt{b} \left(c x^n\right)^{\frac{1}{n}}}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{b}}+\frac{x}{4 a \left(a+b \left(c x^n\right)^{2/n}\right)^2}",1,"x/(4*a*(a + b*(c*x^n)^(2/n))^2) + (3*x)/(8*a^2*(a + b*(c*x^n)^(2/n))) + (3*x*ArcTan[(Sqrt[b]*(c*x^n)^n^(-1))/Sqrt[a]])/(8*a^(5/2)*Sqrt[b]*(c*x^n)^n^(-1))","A",4,3,17,0.1765,1,"{254, 199, 205}"
3034,1,22,0,0.0060316,"\int \frac{1}{1+4 \sqrt{x^4}} \, dx","Int[(1 + 4*Sqrt[x^4])^(-1),x]","\frac{x \tan ^{-1}\left(2 \sqrt[4]{x^4}\right)}{2 \sqrt[4]{x^4}}","\frac{x \tan ^{-1}\left(2 \sqrt[4]{x^4}\right)}{2 \sqrt[4]{x^4}}",1,"(x*ArcTan[2*(x^4)^(1/4)])/(2*(x^4)^(1/4))","A",2,2,13,0.1538,1,"{254, 203}"
3035,1,22,0,0.004652,"\int \frac{1}{1-4 \sqrt{x^4}} \, dx","Int[(1 - 4*Sqrt[x^4])^(-1),x]","\frac{x \tanh ^{-1}\left(2 \sqrt[4]{x^4}\right)}{2 \sqrt[4]{x^4}}","\frac{x \tanh ^{-1}\left(2 \sqrt[4]{x^4}\right)}{2 \sqrt[4]{x^4}}",1,"(x*ArcTanh[2*(x^4)^(1/4)])/(2*(x^4)^(1/4))","A",2,2,13,0.1538,1,"{254, 206}"
3036,1,22,0,0.0061772,"\int \frac{1}{1+4 \sqrt[3]{x^6}} \, dx","Int[(1 + 4*(x^6)^(1/3))^(-1),x]","\frac{x \tan ^{-1}\left(2 \sqrt[6]{x^6}\right)}{2 \sqrt[6]{x^6}}","\frac{x \tan ^{-1}\left(2 \sqrt[6]{x^6}\right)}{2 \sqrt[6]{x^6}}",1,"(x*ArcTan[2*(x^6)^(1/6)])/(2*(x^6)^(1/6))","A",2,2,13,0.1538,1,"{254, 203}"
3037,1,22,0,0.0047655,"\int \frac{1}{1-4 \sqrt[3]{x^6}} \, dx","Int[(1 - 4*(x^6)^(1/3))^(-1),x]","\frac{x \tanh ^{-1}\left(2 \sqrt[6]{x^6}\right)}{2 \sqrt[6]{x^6}}","\frac{x \tanh ^{-1}\left(2 \sqrt[6]{x^6}\right)}{2 \sqrt[6]{x^6}}",1,"(x*ArcTanh[2*(x^6)^(1/6)])/(2*(x^6)^(1/6))","A",2,2,13,0.1538,1,"{254, 206}"
3038,1,34,0,0.006593,"\int \frac{1}{1+4 \left(x^{2 n}\right)^{\frac{1}{n}}} \, dx","Int[(1 + 4*(x^(2*n))^n^(-1))^(-1),x]","\frac{1}{2} x \left(x^{2 n}\right)^{\left.-\frac{1}{2}\right/n} \tan ^{-1}\left(2 \left(x^{2 n}\right)^{\left.\frac{1}{2}\right/n}\right)","\frac{1}{2} x \left(x^{2 n}\right)^{\left.-\frac{1}{2}\right/n} \tan ^{-1}\left(2 \left(x^{2 n}\right)^{\left.\frac{1}{2}\right/n}\right)",1,"(x*ArcTan[2*(x^(2*n))^(1/(2*n))])/(2*(x^(2*n))^(1/(2*n)))","A",2,2,15,0.1333,1,"{254, 203}"
3039,1,34,0,0.0056382,"\int \frac{1}{1-4 \left(x^{2 n}\right)^{\frac{1}{n}}} \, dx","Int[(1 - 4*(x^(2*n))^n^(-1))^(-1),x]","\frac{1}{2} x \left(x^{2 n}\right)^{\left.-\frac{1}{2}\right/n} \tanh ^{-1}\left(2 \left(x^{2 n}\right)^{\left.\frac{1}{2}\right/n}\right)","\frac{1}{2} x \left(x^{2 n}\right)^{\left.-\frac{1}{2}\right/n} \tanh ^{-1}\left(2 \left(x^{2 n}\right)^{\left.\frac{1}{2}\right/n}\right)",1,"(x*ArcTanh[2*(x^(2*n))^(1/(2*n))])/(2*(x^(2*n))^(1/(2*n)))","A",2,2,15,0.1333,1,"{254, 206}"
3040,1,65,0,0.0227796,"\int \left(a+b \left(c x^n\right)^{3/n}\right)^3 \, dx","Int[(a + b*(c*x^n)^(3/n))^3,x]","\frac{3}{4} a^2 b x \left(c x^n\right)^{3/n}+a^3 x+\frac{3}{7} a b^2 x \left(c x^n\right)^{6/n}+\frac{1}{10} b^3 x \left(c x^n\right)^{9/n}","\frac{3}{4} a^2 b x \left(c x^n\right)^{3/n}+a^3 x+\frac{3}{7} a b^2 x \left(c x^n\right)^{6/n}+\frac{1}{10} b^3 x \left(c x^n\right)^{9/n}",1,"a^3*x + (3*a^2*b*x*(c*x^n)^(3/n))/4 + (3*a*b^2*x*(c*x^n)^(6/n))/7 + (b^3*x*(c*x^n)^(9/n))/10","A",3,2,17,0.1176,1,"{254, 194}"
3041,1,43,0,0.0147318,"\int \left(a+b \left(c x^n\right)^{3/n}\right)^2 \, dx","Int[(a + b*(c*x^n)^(3/n))^2,x]","a^2 x+\frac{1}{2} a b x \left(c x^n\right)^{3/n}+\frac{1}{7} b^2 x \left(c x^n\right)^{6/n}","a^2 x+\frac{1}{2} a b x \left(c x^n\right)^{3/n}+\frac{1}{7} b^2 x \left(c x^n\right)^{6/n}",1,"a^2*x + (a*b*x*(c*x^n)^(3/n))/2 + (b^2*x*(c*x^n)^(6/n))/7","A",3,2,17,0.1176,1,"{254, 194}"
3042,1,21,0,0.0063415,"\int \left(a+b \left(c x^n\right)^{3/n}\right) \, dx","Int[a + b*(c*x^n)^(3/n),x]","a x+\frac{1}{4} b x \left(c x^n\right)^{3/n}","a x+\frac{1}{4} b x \left(c x^n\right)^{3/n}",1,"a*x + (b*x*(c*x^n)^(3/n))/4","A",3,2,15,0.1333,1,"{15, 30}"
3043,1,183,0,0.0769335,"\int \frac{1}{a+b \left(c x^n\right)^{3/n}} \, dx","Int[(a + b*(c*x^n)^(3/n))^(-1),x]","-\frac{x \left(c x^n\right)^{-1/n} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \left(c x^n\right)^{\frac{1}{n}}+b^{2/3} \left(c x^n\right)^{2/n}\right)}{6 a^{2/3} \sqrt[3]{b}}+\frac{x \left(c x^n\right)^{-1/n} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \left(c x^n\right)^{\frac{1}{n}}\right)}{3 a^{2/3} \sqrt[3]{b}}-\frac{x \left(c x^n\right)^{-1/n} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \left(c x^n\right)^{\frac{1}{n}}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} \sqrt[3]{b}}","-\frac{x \left(c x^n\right)^{-1/n} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \left(c x^n\right)^{\frac{1}{n}}+b^{2/3} \left(c x^n\right)^{2/n}\right)}{6 a^{2/3} \sqrt[3]{b}}+\frac{x \left(c x^n\right)^{-1/n} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \left(c x^n\right)^{\frac{1}{n}}\right)}{3 a^{2/3} \sqrt[3]{b}}-\frac{x \left(c x^n\right)^{-1/n} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \left(c x^n\right)^{\frac{1}{n}}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} \sqrt[3]{b}}",1,"-((x*ArcTan[(a^(1/3) - 2*b^(1/3)*(c*x^n)^n^(-1))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(2/3)*b^(1/3)*(c*x^n)^n^(-1))) + (x*Log[a^(1/3) + b^(1/3)*(c*x^n)^n^(-1)])/(3*a^(2/3)*b^(1/3)*(c*x^n)^n^(-1)) - (x*Log[a^(2/3) - a^(1/3)*b^(1/3)*(c*x^n)^n^(-1) + b^(2/3)*(c*x^n)^(2/n)])/(6*a^(2/3)*b^(1/3)*(c*x^n)^n^(-1))","A",7,7,17,0.4118,1,"{254, 200, 31, 634, 617, 204, 628}"
3044,1,210,0,0.0948812,"\int \frac{1}{\left(a+b \left(c x^n\right)^{3/n}\right)^2} \, dx","Int[(a + b*(c*x^n)^(3/n))^(-2),x]","-\frac{x \left(c x^n\right)^{-1/n} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \left(c x^n\right)^{\frac{1}{n}}+b^{2/3} \left(c x^n\right)^{2/n}\right)}{9 a^{5/3} \sqrt[3]{b}}+\frac{2 x \left(c x^n\right)^{-1/n} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \left(c x^n\right)^{\frac{1}{n}}\right)}{9 a^{5/3} \sqrt[3]{b}}-\frac{2 x \left(c x^n\right)^{-1/n} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \left(c x^n\right)^{\frac{1}{n}}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{5/3} \sqrt[3]{b}}+\frac{x}{3 a \left(a+b \left(c x^n\right)^{3/n}\right)}","-\frac{x \left(c x^n\right)^{-1/n} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \left(c x^n\right)^{\frac{1}{n}}+b^{2/3} \left(c x^n\right)^{2/n}\right)}{9 a^{5/3} \sqrt[3]{b}}+\frac{2 x \left(c x^n\right)^{-1/n} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \left(c x^n\right)^{\frac{1}{n}}\right)}{9 a^{5/3} \sqrt[3]{b}}-\frac{2 x \left(c x^n\right)^{-1/n} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \left(c x^n\right)^{\frac{1}{n}}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{5/3} \sqrt[3]{b}}+\frac{x}{3 a \left(a+b \left(c x^n\right)^{3/n}\right)}",1,"x/(3*a*(a + b*(c*x^n)^(3/n))) - (2*x*ArcTan[(a^(1/3) - 2*b^(1/3)*(c*x^n)^n^(-1))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(5/3)*b^(1/3)*(c*x^n)^n^(-1)) + (2*x*Log[a^(1/3) + b^(1/3)*(c*x^n)^n^(-1)])/(9*a^(5/3)*b^(1/3)*(c*x^n)^n^(-1)) - (x*Log[a^(2/3) - a^(1/3)*b^(1/3)*(c*x^n)^n^(-1) + b^(2/3)*(c*x^n)^(2/n)])/(9*a^(5/3)*b^(1/3)*(c*x^n)^n^(-1))","A",8,8,17,0.4706,1,"{254, 199, 200, 31, 634, 617, 204, 628}"
3045,1,235,0,0.1157084,"\int \frac{1}{\left(a+b \left(c x^n\right)^{3/n}\right)^3} \, dx","Int[(a + b*(c*x^n)^(3/n))^(-3),x]","-\frac{5 x \left(c x^n\right)^{-1/n} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \left(c x^n\right)^{\frac{1}{n}}+b^{2/3} \left(c x^n\right)^{2/n}\right)}{54 a^{8/3} \sqrt[3]{b}}+\frac{5 x}{18 a^2 \left(a+b \left(c x^n\right)^{3/n}\right)}+\frac{5 x \left(c x^n\right)^{-1/n} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \left(c x^n\right)^{\frac{1}{n}}\right)}{27 a^{8/3} \sqrt[3]{b}}-\frac{5 x \left(c x^n\right)^{-1/n} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \left(c x^n\right)^{\frac{1}{n}}}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{8/3} \sqrt[3]{b}}+\frac{x}{6 a \left(a+b \left(c x^n\right)^{3/n}\right)^2}","-\frac{5 x \left(c x^n\right)^{-1/n} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \left(c x^n\right)^{\frac{1}{n}}+b^{2/3} \left(c x^n\right)^{2/n}\right)}{54 a^{8/3} \sqrt[3]{b}}+\frac{5 x}{18 a^2 \left(a+b \left(c x^n\right)^{3/n}\right)}+\frac{5 x \left(c x^n\right)^{-1/n} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \left(c x^n\right)^{\frac{1}{n}}\right)}{27 a^{8/3} \sqrt[3]{b}}-\frac{5 x \left(c x^n\right)^{-1/n} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \left(c x^n\right)^{\frac{1}{n}}}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{8/3} \sqrt[3]{b}}+\frac{x}{6 a \left(a+b \left(c x^n\right)^{3/n}\right)^2}",1,"x/(6*a*(a + b*(c*x^n)^(3/n))^2) + (5*x)/(18*a^2*(a + b*(c*x^n)^(3/n))) - (5*x*ArcTan[(a^(1/3) - 2*b^(1/3)*(c*x^n)^n^(-1))/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(8/3)*b^(1/3)*(c*x^n)^n^(-1)) + (5*x*Log[a^(1/3) + b^(1/3)*(c*x^n)^n^(-1)])/(27*a^(8/3)*b^(1/3)*(c*x^n)^n^(-1)) - (5*x*Log[a^(2/3) - a^(1/3)*b^(1/3)*(c*x^n)^n^(-1) + b^(2/3)*(c*x^n)^(2/n)])/(54*a^(8/3)*b^(1/3)*(c*x^n)^n^(-1))","A",9,8,17,0.4706,1,"{254, 199, 200, 31, 634, 617, 204, 628}"
3046,1,86,0,0.0437766,"\int (d x)^m \left(a+b \left(c x^q\right)^n\right)^p \, dx","Int[(d*x)^m*(a + b*(c*x^q)^n)^p,x]","\frac{(d x)^{m+1} \left(a+b \left(c x^q\right)^n\right)^p \left(\frac{b \left(c x^q\right)^n}{a}+1\right)^{-p} \, _2F_1\left(-p,\frac{m+1}{n q};\frac{m+1}{n q}+1;-\frac{b \left(c x^q\right)^n}{a}\right)}{d (m+1)}","\frac{(d x)^{m+1} \left(a+b \left(c x^q\right)^n\right)^p \left(\frac{b \left(c x^q\right)^n}{a}+1\right)^{-p} \, _2F_1\left(-p,\frac{m+1}{n q};\frac{m+1}{n q}+1;-\frac{b \left(c x^q\right)^n}{a}\right)}{d (m+1)}",1,"((d*x)^(1 + m)*(a + b*(c*x^q)^n)^p*Hypergeometric2F1[-p, (1 + m)/(n*q), 1 + (1 + m)/(n*q), -((b*(c*x^q)^n)/a)])/(d*(1 + m)*(1 + (b*(c*x^q)^n)/a)^p)","A",3,3,19,0.1579,1,"{370, 365, 364}"
3047,1,73,0,0.0293813,"\int x^2 \left(a+b \left(c x^q\right)^n\right)^p \, dx","Int[x^2*(a + b*(c*x^q)^n)^p,x]","\frac{1}{3} x^3 \left(a+b \left(c x^q\right)^n\right)^p \left(\frac{b \left(c x^q\right)^n}{a}+1\right)^{-p} \, _2F_1\left(-p,\frac{3}{n q};1+\frac{3}{n q};-\frac{b \left(c x^q\right)^n}{a}\right)","\frac{1}{3} x^3 \left(a+b \left(c x^q\right)^n\right)^p \left(\frac{b \left(c x^q\right)^n}{a}+1\right)^{-p} \, _2F_1\left(-p,\frac{3}{n q};1+\frac{3}{n q};-\frac{b \left(c x^q\right)^n}{a}\right)",1,"(x^3*(a + b*(c*x^q)^n)^p*Hypergeometric2F1[-p, 3/(n*q), 1 + 3/(n*q), -((b*(c*x^q)^n)/a)])/(3*(1 + (b*(c*x^q)^n)/a)^p)","A",3,3,17,0.1765,1,"{370, 365, 364}"
3048,1,73,0,0.0239907,"\int x \left(a+b \left(c x^q\right)^n\right)^p \, dx","Int[x*(a + b*(c*x^q)^n)^p,x]","\frac{1}{2} x^2 \left(a+b \left(c x^q\right)^n\right)^p \left(\frac{b \left(c x^q\right)^n}{a}+1\right)^{-p} \, _2F_1\left(-p,\frac{2}{n q};1+\frac{2}{n q};-\frac{b \left(c x^q\right)^n}{a}\right)","\frac{1}{2} x^2 \left(a+b \left(c x^q\right)^n\right)^p \left(\frac{b \left(c x^q\right)^n}{a}+1\right)^{-p} \, _2F_1\left(-p,\frac{2}{n q};1+\frac{2}{n q};-\frac{b \left(c x^q\right)^n}{a}\right)",1,"(x^2*(a + b*(c*x^q)^n)^p*Hypergeometric2F1[-p, 2/(n*q), 1 + 2/(n*q), -((b*(c*x^q)^n)/a)])/(2*(1 + (b*(c*x^q)^n)/a)^p)","A",3,3,15,0.2000,1,"{370, 365, 364}"
3049,1,66,0,0.026935,"\int \left(a+b \left(c x^q\right)^n\right)^p \, dx","Int[(a + b*(c*x^q)^n)^p,x]","x \left(a+b \left(c x^q\right)^n\right)^p \left(\frac{b \left(c x^q\right)^n}{a}+1\right)^{-p} \, _2F_1\left(-p,\frac{1}{n q};1+\frac{1}{n q};-\frac{b \left(c x^q\right)^n}{a}\right)","x \left(a+b \left(c x^q\right)^n\right)^p \left(\frac{b \left(c x^q\right)^n}{a}+1\right)^{-p} \, _2F_1\left(-p,\frac{1}{n q};1+\frac{1}{n q};-\frac{b \left(c x^q\right)^n}{a}\right)",1,"(x*(a + b*(c*x^q)^n)^p*Hypergeometric2F1[-p, 1/(n*q), 1 + 1/(n*q), -((b*(c*x^q)^n)/a)])/(1 + (b*(c*x^q)^n)/a)^p","A",3,3,13,0.2308,1,"{256, 246, 245}"
3050,1,53,0,0.0335463,"\int \frac{\left(a+b \left(c x^q\right)^n\right)^p}{x} \, dx","Int[(a + b*(c*x^q)^n)^p/x,x]","-\frac{\left(a+b \left(c x^q\right)^n\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{b \left(c x^q\right)^n}{a}+1\right)}{a n (p+1) q}","-\frac{\left(a+b \left(c x^q\right)^n\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{b \left(c x^q\right)^n}{a}+1\right)}{a n (p+1) q}",1,"-(((a + b*(c*x^q)^n)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, 1 + (b*(c*x^q)^n)/a])/(a*n*(1 + p)*q))","A",3,3,17,0.1765,1,"{370, 266, 65}"
3051,1,71,0,0.0290384,"\int \frac{\left(a+b \left(c x^q\right)^n\right)^p}{x^2} \, dx","Int[(a + b*(c*x^q)^n)^p/x^2,x]","-\frac{\left(a+b \left(c x^q\right)^n\right)^p \left(\frac{b \left(c x^q\right)^n}{a}+1\right)^{-p} \, _2F_1\left(-p,-\frac{1}{n q};1-\frac{1}{n q};-\frac{b \left(c x^q\right)^n}{a}\right)}{x}","-\frac{\left(a+b \left(c x^q\right)^n\right)^p \left(\frac{b \left(c x^q\right)^n}{a}+1\right)^{-p} \, _2F_1\left(-p,-\frac{1}{n q};1-\frac{1}{n q};-\frac{b \left(c x^q\right)^n}{a}\right)}{x}",1,"-(((a + b*(c*x^q)^n)^p*Hypergeometric2F1[-p, -(1/(n*q)), 1 - 1/(n*q), -((b*(c*x^q)^n)/a)])/(x*(1 + (b*(c*x^q)^n)/a)^p))","A",3,3,17,0.1765,1,"{370, 365, 364}"
3052,1,230,0,0.7194734,"\int \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}} x^m \, dx","Int[Sqrt[a + b*Sqrt[d/x] + c/x]*x^m,x]","\frac{x^{m+1} \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}} F_1\left(-2 (m+1);-\frac{1}{2},-\frac{1}{2};-2 m-1;-\frac{2 c \sqrt{\frac{d}{x}}}{\sqrt{d} \left(b \sqrt{d}-\sqrt{b^2 d-4 a c}\right)},-\frac{2 c \sqrt{\frac{d}{x}}}{\sqrt{d} \left(\sqrt{d} b+\sqrt{b^2 d-4 a c}\right)}\right)}{(m+1) \sqrt{\frac{2 c \sqrt{\frac{d}{x}}}{\sqrt{d} \left(b \sqrt{d}-\sqrt{b^2 d-4 a c}\right)}+1} \sqrt{\frac{2 c \sqrt{\frac{d}{x}}}{\sqrt{d} \left(\sqrt{b^2 d-4 a c}+b \sqrt{d}\right)}+1}}","\frac{x^{m+1} \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}} F_1\left(-2 (m+1);-\frac{1}{2},-\frac{1}{2};-2 m-1;-\frac{2 c \sqrt{\frac{d}{x}}}{\sqrt{d} \left(b \sqrt{d}-\sqrt{b^2 d-4 a c}\right)},-\frac{2 c \sqrt{\frac{d}{x}}}{\sqrt{d} \left(\sqrt{d} b+\sqrt{b^2 d-4 a c}\right)}\right)}{(m+1) \sqrt{\frac{2 c \sqrt{\frac{d}{x}}}{\sqrt{d} \left(b \sqrt{d}-\sqrt{b^2 d-4 a c}\right)}+1} \sqrt{\frac{2 c \sqrt{\frac{d}{x}}}{\sqrt{d} \left(\sqrt{b^2 d-4 a c}+b \sqrt{d}\right)}+1}}",1,"(Sqrt[a + b*Sqrt[d/x] + c/x]*x^(1 + m)*AppellF1[-2*(1 + m), -1/2, -1/2, -1 - 2*m, (-2*c*Sqrt[d/x])/(Sqrt[d]*(b*Sqrt[d] - Sqrt[-4*a*c + b^2*d])), (-2*c*Sqrt[d/x])/(Sqrt[d]*(b*Sqrt[d] + Sqrt[-4*a*c + b^2*d]))])/((1 + m)*Sqrt[1 + (2*c*Sqrt[d/x])/(Sqrt[d]*(b*Sqrt[d] - Sqrt[-4*a*c + b^2*d]))]*Sqrt[1 + (2*c*Sqrt[d/x])/(Sqrt[d]*(b*Sqrt[d] + Sqrt[-4*a*c + b^2*d]))])","A",4,4,26,0.1538,1,"{1971, 1379, 759, 133}"
3053,1,333,0,0.5997703,"\int \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}} x^2 \, dx","Int[Sqrt[a + b*Sqrt[d/x] + c/x]*x^2,x]","\frac{x \left(16 a^2 c^2-56 a b^2 c d+21 b^4 d^2\right) \left(2 a+b \sqrt{\frac{d}{x}}\right) \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{256 a^5}+\frac{\left(4 a c-b^2 d\right) \left(16 a^2 c^2-56 a b^2 c d+21 b^4 d^2\right) \tanh ^{-1}\left(\frac{2 a+b \sqrt{\frac{d}{x}}}{2 \sqrt{a} \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}\right)}{512 a^{11/2}}+\frac{7 b d^2 \left(28 a c-15 b^2 d\right) \left(a+b \sqrt{\frac{d}{x}}+\frac{c}{x}\right)^{3/2}}{480 a^4 \left(\frac{d}{x}\right)^{3/2}}-\frac{x^2 \left(20 a c-21 b^2 d\right) \left(a+b \sqrt{\frac{d}{x}}+\frac{c}{x}\right)^{3/2}}{80 a^3}-\frac{3 b d^3 \left(a+b \sqrt{\frac{d}{x}}+\frac{c}{x}\right)^{3/2}}{10 a^2 \left(\frac{d}{x}\right)^{5/2}}+\frac{x^3 \left(a+b \sqrt{\frac{d}{x}}+\frac{c}{x}\right)^{3/2}}{3 a}","\frac{x \left(16 a^2 c^2-56 a b^2 c d+21 b^4 d^2\right) \left(2 a+b \sqrt{\frac{d}{x}}\right) \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{256 a^5}+\frac{\left(4 a c-b^2 d\right) \left(16 a^2 c^2-56 a b^2 c d+21 b^4 d^2\right) \tanh ^{-1}\left(\frac{2 a+b \sqrt{\frac{d}{x}}}{2 \sqrt{a} \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}\right)}{512 a^{11/2}}+\frac{7 b d^2 \left(28 a c-15 b^2 d\right) \left(a+b \sqrt{\frac{d}{x}}+\frac{c}{x}\right)^{3/2}}{480 a^4 \left(\frac{d}{x}\right)^{3/2}}-\frac{x^2 \left(20 a c-21 b^2 d\right) \left(a+b \sqrt{\frac{d}{x}}+\frac{c}{x}\right)^{3/2}}{80 a^3}-\frac{3 b d^3 \left(a+b \sqrt{\frac{d}{x}}+\frac{c}{x}\right)^{3/2}}{10 a^2 \left(\frac{d}{x}\right)^{5/2}}+\frac{x^3 \left(a+b \sqrt{\frac{d}{x}}+\frac{c}{x}\right)^{3/2}}{3 a}",1,"(-3*b*d^3*(a + b*Sqrt[d/x] + c/x)^(3/2))/(10*a^2*(d/x)^(5/2)) + (7*b*d^2*(28*a*c - 15*b^2*d)*(a + b*Sqrt[d/x] + c/x)^(3/2))/(480*a^4*(d/x)^(3/2)) + ((16*a^2*c^2 - 56*a*b^2*c*d + 21*b^4*d^2)*(2*a + b*Sqrt[d/x])*Sqrt[a + b*Sqrt[d/x] + c/x]*x)/(256*a^5) - ((20*a*c - 21*b^2*d)*(a + b*Sqrt[d/x] + c/x)^(3/2)*x^2)/(80*a^3) + ((a + b*Sqrt[d/x] + c/x)^(3/2)*x^3)/(3*a) + ((4*a*c - b^2*d)*(16*a^2*c^2 - 56*a*b^2*c*d + 21*b^4*d^2)*ArcTanh[(2*a + b*Sqrt[d/x])/(2*Sqrt[a]*Sqrt[a + b*Sqrt[d/x] + c/x])])/(512*a^(11/2))","A",9,8,26,0.3077,1,"{1970, 1357, 744, 834, 806, 720, 724, 206}"
3054,1,209,0,0.2842135,"\int \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}} x \, dx","Int[Sqrt[a + b*Sqrt[d/x] + c/x]*x,x]","-\frac{x \left(4 a c-5 b^2 d\right) \left(2 a+b \sqrt{\frac{d}{x}}\right) \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{32 a^3}-\frac{\left(4 a c-5 b^2 d\right) \left(4 a c-b^2 d\right) \tanh ^{-1}\left(\frac{2 a+b \sqrt{\frac{d}{x}}}{2 \sqrt{a} \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}\right)}{64 a^{7/2}}-\frac{5 b d^2 \left(a+b \sqrt{\frac{d}{x}}+\frac{c}{x}\right)^{3/2}}{12 a^2 \left(\frac{d}{x}\right)^{3/2}}+\frac{x^2 \left(a+b \sqrt{\frac{d}{x}}+\frac{c}{x}\right)^{3/2}}{2 a}","-\frac{x \left(4 a c-5 b^2 d\right) \left(2 a+b \sqrt{\frac{d}{x}}\right) \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{32 a^3}-\frac{\left(4 a c-5 b^2 d\right) \left(4 a c-b^2 d\right) \tanh ^{-1}\left(\frac{2 a+b \sqrt{\frac{d}{x}}}{2 \sqrt{a} \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}\right)}{64 a^{7/2}}-\frac{5 b d^2 \left(a+b \sqrt{\frac{d}{x}}+\frac{c}{x}\right)^{3/2}}{12 a^2 \left(\frac{d}{x}\right)^{3/2}}+\frac{x^2 \left(a+b \sqrt{\frac{d}{x}}+\frac{c}{x}\right)^{3/2}}{2 a}",1,"(-5*b*d^2*(a + b*Sqrt[d/x] + c/x)^(3/2))/(12*a^2*(d/x)^(3/2)) - ((4*a*c - 5*b^2*d)*(2*a + b*Sqrt[d/x])*Sqrt[a + b*Sqrt[d/x] + c/x]*x)/(32*a^3) + ((a + b*Sqrt[d/x] + c/x)^(3/2)*x^2)/(2*a) - ((4*a*c - 5*b^2*d)*(4*a*c - b^2*d)*ArcTanh[(2*a + b*Sqrt[d/x])/(2*Sqrt[a]*Sqrt[a + b*Sqrt[d/x] + c/x])])/(64*a^(7/2))","A",7,7,24,0.2917,1,"{1970, 1357, 744, 806, 720, 724, 206}"
3055,1,113,0,0.1177508,"\int \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}} \, dx","Int[Sqrt[a + b*Sqrt[d/x] + c/x],x]","\frac{\left(4 a c-b^2 d\right) \tanh ^{-1}\left(\frac{2 a+b \sqrt{\frac{d}{x}}}{2 \sqrt{a} \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}\right)}{4 a^{3/2}}+\frac{x \left(2 a+b \sqrt{\frac{d}{x}}\right) \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{2 a}","\frac{\left(4 a c-b^2 d\right) \tanh ^{-1}\left(\frac{2 a+b \sqrt{\frac{d}{x}}}{2 \sqrt{a} \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}\right)}{4 a^{3/2}}+\frac{x \left(2 a+b \sqrt{\frac{d}{x}}\right) \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{2 a}",1,"((2*a + b*Sqrt[d/x])*Sqrt[a + b*Sqrt[d/x] + c/x]*x)/(2*a) + ((4*a*c - b^2*d)*ArcTanh[(2*a + b*Sqrt[d/x])/(2*Sqrt[a]*Sqrt[a + b*Sqrt[d/x] + c/x])])/(4*a^(3/2))","A",5,5,22,0.2273,1,"{1969, 1357, 720, 724, 206}"
3056,1,145,0,0.2075946,"\int \frac{\sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{x} \, dx","Int[Sqrt[a + b*Sqrt[d/x] + c/x]/x,x]","-2 \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}+2 \sqrt{a} \tanh ^{-1}\left(\frac{2 a+b \sqrt{\frac{d}{x}}}{2 \sqrt{a} \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}\right)-\frac{b \sqrt{d} \tanh ^{-1}\left(\frac{b d+2 c \sqrt{\frac{d}{x}}}{2 \sqrt{c} \sqrt{d} \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}\right)}{\sqrt{c}}","-2 \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}+2 \sqrt{a} \tanh ^{-1}\left(\frac{2 a+b \sqrt{\frac{d}{x}}}{2 \sqrt{a} \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}\right)-\frac{b \sqrt{d} \tanh ^{-1}\left(\frac{b d+2 c \sqrt{\frac{d}{x}}}{2 \sqrt{c} \sqrt{d} \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}\right)}{\sqrt{c}}",1,"-2*Sqrt[a + b*Sqrt[d/x] + c/x] + 2*Sqrt[a]*ArcTanh[(2*a + b*Sqrt[d/x])/(2*Sqrt[a]*Sqrt[a + b*Sqrt[d/x] + c/x])] - (b*Sqrt[d]*ArcTanh[(b*d + 2*c*Sqrt[d/x])/(2*Sqrt[c]*Sqrt[d]*Sqrt[a + b*Sqrt[d/x] + c/x])])/Sqrt[c]","A",8,7,26,0.2692,1,"{1970, 1357, 734, 843, 621, 206, 724}"
3057,1,155,0,0.1836112,"\int \frac{\sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{x^2} \, dx","Int[Sqrt[a + b*Sqrt[d/x] + c/x]/x^2,x]","\frac{b \sqrt{d} \left(4 a c-b^2 d\right) \tanh ^{-1}\left(\frac{b d+2 c \sqrt{\frac{d}{x}}}{2 \sqrt{c} \sqrt{d} \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}\right)}{8 c^{5/2}}+\frac{b \left(b d+2 c \sqrt{\frac{d}{x}}\right) \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{4 c^2}-\frac{2 \left(a+b \sqrt{\frac{d}{x}}+\frac{c}{x}\right)^{3/2}}{3 c}","\frac{b \sqrt{d} \left(4 a c-b^2 d\right) \tanh ^{-1}\left(\frac{b d+2 c \sqrt{\frac{d}{x}}}{2 \sqrt{c} \sqrt{d} \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}\right)}{8 c^{5/2}}+\frac{b \left(b d+2 c \sqrt{\frac{d}{x}}\right) \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{4 c^2}-\frac{2 \left(a+b \sqrt{\frac{d}{x}}+\frac{c}{x}\right)^{3/2}}{3 c}",1,"(b*(b*d + 2*c*Sqrt[d/x])*Sqrt[a + b*Sqrt[d/x] + c/x])/(4*c^2) - (2*(a + b*Sqrt[d/x] + c/x)^(3/2))/(3*c) + (b*Sqrt[d]*(4*a*c - b^2*d)*ArcTanh[(b*d + 2*c*Sqrt[d/x])/(2*Sqrt[c]*Sqrt[d]*Sqrt[a + b*Sqrt[d/x] + c/x])])/(8*c^(5/2))","A",6,6,26,0.2308,1,"{1970, 1341, 640, 612, 621, 206}"
3058,1,233,0,0.3076959,"\int \frac{\sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{x^3} \, dx","Int[Sqrt[a + b*Sqrt[d/x] + c/x]/x^3,x]","\frac{\left(32 a c-35 b^2 d+42 b c \sqrt{\frac{d}{x}}\right) \left(a+b \sqrt{\frac{d}{x}}+\frac{c}{x}\right)^{3/2}}{120 c^3}-\frac{b \left(12 a c-7 b^2 d\right) \left(b d+2 c \sqrt{\frac{d}{x}}\right) \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{64 c^4}-\frac{b \sqrt{d} \left(12 a c-7 b^2 d\right) \left(4 a c-b^2 d\right) \tanh ^{-1}\left(\frac{b d+2 c \sqrt{\frac{d}{x}}}{2 \sqrt{c} \sqrt{d} \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}\right)}{128 c^{9/2}}-\frac{2 \left(a+b \sqrt{\frac{d}{x}}+\frac{c}{x}\right)^{3/2}}{5 c x}","\frac{\left(32 a c-35 b^2 d+42 b c \sqrt{\frac{d}{x}}\right) \left(a+b \sqrt{\frac{d}{x}}+\frac{c}{x}\right)^{3/2}}{120 c^3}-\frac{b \left(12 a c-7 b^2 d\right) \left(b d+2 c \sqrt{\frac{d}{x}}\right) \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{64 c^4}-\frac{b \sqrt{d} \left(12 a c-7 b^2 d\right) \left(4 a c-b^2 d\right) \tanh ^{-1}\left(\frac{b d+2 c \sqrt{\frac{d}{x}}}{2 \sqrt{c} \sqrt{d} \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}\right)}{128 c^{9/2}}-\frac{2 \left(a+b \sqrt{\frac{d}{x}}+\frac{c}{x}\right)^{3/2}}{5 c x}",1,"-(b*(12*a*c - 7*b^2*d)*(b*d + 2*c*Sqrt[d/x])*Sqrt[a + b*Sqrt[d/x] + c/x])/(64*c^4) + ((32*a*c - 35*b^2*d + 42*b*c*Sqrt[d/x])*(a + b*Sqrt[d/x] + c/x)^(3/2))/(120*c^3) - (2*(a + b*Sqrt[d/x] + c/x)^(3/2))/(5*c*x) - (b*Sqrt[d]*(12*a*c - 7*b^2*d)*(4*a*c - b^2*d)*ArcTanh[(b*d + 2*c*Sqrt[d/x])/(2*Sqrt[c]*Sqrt[d]*Sqrt[a + b*Sqrt[d/x] + c/x])])/(128*c^(9/2))","A",7,7,26,0.2692,1,"{1970, 1357, 742, 779, 612, 621, 206}"
3059,1,371,0,0.6648564,"\int \frac{\sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{x^4} \, dx","Int[Sqrt[a + b*Sqrt[d/x] + c/x]/x^4,x]","-\frac{\left(1024 a^2 c^2+18 b c \sqrt{\frac{d}{x}} \left(148 a c-77 b^2 d\right)-3276 a b^2 c d+1155 b^4 d^2\right) \left(a+b \sqrt{\frac{d}{x}}+\frac{c}{x}\right)^{3/2}}{6720 c^5}+\frac{b \left(80 a^2 c^2-120 a b^2 c d+33 b^4 d^2\right) \left(b d+2 c \sqrt{\frac{d}{x}}\right) \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{512 c^6}+\frac{b \sqrt{d} \left(4 a c-b^2 d\right) \left(80 a^2 c^2-120 a b^2 c d+33 b^4 d^2\right) \tanh ^{-1}\left(\frac{b d+2 c \sqrt{\frac{d}{x}}}{2 \sqrt{c} \sqrt{d} \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}\right)}{1024 c^{13/2}}+\frac{\left(32 a c-33 b^2 d\right) \left(a+b \sqrt{\frac{d}{x}}+\frac{c}{x}\right)^{3/2}}{140 c^3 x}+\frac{11 b \left(\frac{d}{x}\right)^{3/2} \left(a+b \sqrt{\frac{d}{x}}+\frac{c}{x}\right)^{3/2}}{42 c^2 d}-\frac{2 \left(a+b \sqrt{\frac{d}{x}}+\frac{c}{x}\right)^{3/2}}{7 c x^2}","-\frac{\left(1024 a^2 c^2+18 b c \sqrt{\frac{d}{x}} \left(148 a c-77 b^2 d\right)-3276 a b^2 c d+1155 b^4 d^2\right) \left(a+b \sqrt{\frac{d}{x}}+\frac{c}{x}\right)^{3/2}}{6720 c^5}+\frac{b \left(80 a^2 c^2-120 a b^2 c d+33 b^4 d^2\right) \left(b d+2 c \sqrt{\frac{d}{x}}\right) \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{512 c^6}+\frac{b \sqrt{d} \left(4 a c-b^2 d\right) \left(80 a^2 c^2-120 a b^2 c d+33 b^4 d^2\right) \tanh ^{-1}\left(\frac{b d+2 c \sqrt{\frac{d}{x}}}{2 \sqrt{c} \sqrt{d} \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}\right)}{1024 c^{13/2}}+\frac{\left(32 a c-33 b^2 d\right) \left(a+b \sqrt{\frac{d}{x}}+\frac{c}{x}\right)^{3/2}}{140 c^3 x}+\frac{11 b \left(\frac{d}{x}\right)^{3/2} \left(a+b \sqrt{\frac{d}{x}}+\frac{c}{x}\right)^{3/2}}{42 c^2 d}-\frac{2 \left(a+b \sqrt{\frac{d}{x}}+\frac{c}{x}\right)^{3/2}}{7 c x^2}",1,"(b*(80*a^2*c^2 - 120*a*b^2*c*d + 33*b^4*d^2)*(b*d + 2*c*Sqrt[d/x])*Sqrt[a + b*Sqrt[d/x] + c/x])/(512*c^6) - ((1024*a^2*c^2 - 3276*a*b^2*c*d + 1155*b^4*d^2 + 18*b*c*(148*a*c - 77*b^2*d)*Sqrt[d/x])*(a + b*Sqrt[d/x] + c/x)^(3/2))/(6720*c^5) + (11*b*(a + b*Sqrt[d/x] + c/x)^(3/2)*(d/x)^(3/2))/(42*c^2*d) - (2*(a + b*Sqrt[d/x] + c/x)^(3/2))/(7*c*x^2) + ((32*a*c - 33*b^2*d)*(a + b*Sqrt[d/x] + c/x)^(3/2))/(140*c^3*x) + (b*Sqrt[d]*(4*a*c - b^2*d)*(80*a^2*c^2 - 120*a*b^2*c*d + 33*b^4*d^2)*ArcTanh[(b*d + 2*c*Sqrt[d/x])/(2*Sqrt[c]*Sqrt[d]*Sqrt[a + b*Sqrt[d/x] + c/x])])/(1024*c^(13/2))","A",9,8,26,0.3077,1,"{1970, 1357, 742, 832, 779, 612, 621, 206}"
3060,1,230,0,0.4747192,"\int \frac{x^m}{\sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}} \, dx","Int[x^m/Sqrt[a + b*Sqrt[d/x] + c/x],x]","\frac{x^{m+1} \sqrt{\frac{2 c \sqrt{\frac{d}{x}}}{\sqrt{d} \left(b \sqrt{d}-\sqrt{b^2 d-4 a c}\right)}+1} \sqrt{\frac{2 c \sqrt{\frac{d}{x}}}{\sqrt{d} \left(\sqrt{b^2 d-4 a c}+b \sqrt{d}\right)}+1} F_1\left(-2 (m+1);\frac{1}{2},\frac{1}{2};-2 m-1;-\frac{2 c \sqrt{\frac{d}{x}}}{\sqrt{d} \left(b \sqrt{d}-\sqrt{b^2 d-4 a c}\right)},-\frac{2 c \sqrt{\frac{d}{x}}}{\sqrt{d} \left(\sqrt{d} b+\sqrt{b^2 d-4 a c}\right)}\right)}{(m+1) \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}","\frac{x^{m+1} \sqrt{\frac{2 c \sqrt{\frac{d}{x}}}{\sqrt{d} \left(b \sqrt{d}-\sqrt{b^2 d-4 a c}\right)}+1} \sqrt{\frac{2 c \sqrt{\frac{d}{x}}}{\sqrt{d} \left(\sqrt{b^2 d-4 a c}+b \sqrt{d}\right)}+1} F_1\left(-2 (m+1);\frac{1}{2},\frac{1}{2};-2 m-1;-\frac{2 c \sqrt{\frac{d}{x}}}{\sqrt{d} \left(b \sqrt{d}-\sqrt{b^2 d-4 a c}\right)},-\frac{2 c \sqrt{\frac{d}{x}}}{\sqrt{d} \left(\sqrt{d} b+\sqrt{b^2 d-4 a c}\right)}\right)}{(m+1) \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}",1,"(Sqrt[1 + (2*c*Sqrt[d/x])/(Sqrt[d]*(b*Sqrt[d] - Sqrt[-4*a*c + b^2*d]))]*Sqrt[1 + (2*c*Sqrt[d/x])/(Sqrt[d]*(b*Sqrt[d] + Sqrt[-4*a*c + b^2*d]))]*x^(1 + m)*AppellF1[-2*(1 + m), 1/2, 1/2, -1 - 2*m, (-2*c*Sqrt[d/x])/(Sqrt[d]*(b*Sqrt[d] - Sqrt[-4*a*c + b^2*d])), (-2*c*Sqrt[d/x])/(Sqrt[d]*(b*Sqrt[d] + Sqrt[-4*a*c + b^2*d]))])/((1 + m)*Sqrt[a + b*Sqrt[d/x] + c/x])","A",4,4,26,0.1538,1,"{1971, 1379, 759, 133}"
3061,1,386,0,0.7288653,"\int \frac{x^2}{\sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}} \, dx","Int[x^2/Sqrt[a + b*Sqrt[d/x] + c/x],x]","-\frac{7 b d \left(528 a^2 c^2-680 a b^2 c d+165 b^4 d^2\right) \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{1280 a^6 \sqrt{\frac{d}{x}}}+\frac{x \left(400 a^2 c^2-1176 a b^2 c d+385 b^4 d^2\right) \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{640 a^5}-\frac{\left(-1680 a^2 b^2 c^2 d+320 a^3 c^3+1260 a b^4 c d^2-231 b^6 d^3\right) \tanh ^{-1}\left(\frac{2 a+b \sqrt{\frac{d}{x}}}{2 \sqrt{a} \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}\right)}{512 a^{13/2}}+\frac{b d^2 \left(156 a c-77 b^2 d\right) \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{160 a^4 \left(\frac{d}{x}\right)^{3/2}}-\frac{x^2 \left(100 a c-99 b^2 d\right) \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{240 a^3}-\frac{11 b d^3 \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{30 a^2 \left(\frac{d}{x}\right)^{5/2}}+\frac{x^3 \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{3 a}","-\frac{7 b d \left(528 a^2 c^2-680 a b^2 c d+165 b^4 d^2\right) \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{1280 a^6 \sqrt{\frac{d}{x}}}+\frac{x \left(400 a^2 c^2-1176 a b^2 c d+385 b^4 d^2\right) \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{640 a^5}-\frac{\left(-1680 a^2 b^2 c^2 d+320 a^3 c^3+1260 a b^4 c d^2-231 b^6 d^3\right) \tanh ^{-1}\left(\frac{2 a+b \sqrt{\frac{d}{x}}}{2 \sqrt{a} \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}\right)}{512 a^{13/2}}+\frac{b d^2 \left(156 a c-77 b^2 d\right) \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{160 a^4 \left(\frac{d}{x}\right)^{3/2}}-\frac{x^2 \left(100 a c-99 b^2 d\right) \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{240 a^3}-\frac{11 b d^3 \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{30 a^2 \left(\frac{d}{x}\right)^{5/2}}+\frac{x^3 \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{3 a}",1,"(-11*b*d^3*Sqrt[a + b*Sqrt[d/x] + c/x])/(30*a^2*(d/x)^(5/2)) + (b*d^2*(156*a*c - 77*b^2*d)*Sqrt[a + b*Sqrt[d/x] + c/x])/(160*a^4*(d/x)^(3/2)) - (7*b*d*(528*a^2*c^2 - 680*a*b^2*c*d + 165*b^4*d^2)*Sqrt[a + b*Sqrt[d/x] + c/x])/(1280*a^6*Sqrt[d/x]) + ((400*a^2*c^2 - 1176*a*b^2*c*d + 385*b^4*d^2)*Sqrt[a + b*Sqrt[d/x] + c/x]*x)/(640*a^5) - ((100*a*c - 99*b^2*d)*Sqrt[a + b*Sqrt[d/x] + c/x]*x^2)/(240*a^3) + (Sqrt[a + b*Sqrt[d/x] + c/x]*x^3)/(3*a) - ((320*a^3*c^3 - 1680*a^2*b^2*c^2*d + 1260*a*b^4*c*d^2 - 231*b^6*d^3)*ArcTanh[(2*a + b*Sqrt[d/x])/(2*Sqrt[a]*Sqrt[a + b*Sqrt[d/x] + c/x])])/(512*a^(13/2))","A",10,7,26,0.2692,1,"{1970, 1357, 744, 834, 806, 724, 206}"
3062,1,248,0,0.4304925,"\int \frac{x}{\sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}} \, dx","Int[x/Sqrt[a + b*Sqrt[d/x] + c/x],x]","\frac{\left(48 a^2 c^2-120 a b^2 c d+35 b^4 d^2\right) \tanh ^{-1}\left(\frac{2 a+b \sqrt{\frac{d}{x}}}{2 \sqrt{a} \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}\right)}{64 a^{9/2}}+\frac{5 b d \left(44 a c-21 b^2 d\right) \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{96 a^4 \sqrt{\frac{d}{x}}}-\frac{x \left(36 a c-35 b^2 d\right) \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{48 a^3}-\frac{7 b d^2 \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{12 a^2 \left(\frac{d}{x}\right)^{3/2}}+\frac{x^2 \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{2 a}","\frac{\left(48 a^2 c^2-120 a b^2 c d+35 b^4 d^2\right) \tanh ^{-1}\left(\frac{2 a+b \sqrt{\frac{d}{x}}}{2 \sqrt{a} \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}\right)}{64 a^{9/2}}+\frac{5 b d \left(44 a c-21 b^2 d\right) \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{96 a^4 \sqrt{\frac{d}{x}}}-\frac{x \left(36 a c-35 b^2 d\right) \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{48 a^3}-\frac{7 b d^2 \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{12 a^2 \left(\frac{d}{x}\right)^{3/2}}+\frac{x^2 \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{2 a}",1,"(-7*b*d^2*Sqrt[a + b*Sqrt[d/x] + c/x])/(12*a^2*(d/x)^(3/2)) + (5*b*d*(44*a*c - 21*b^2*d)*Sqrt[a + b*Sqrt[d/x] + c/x])/(96*a^4*Sqrt[d/x]) - ((36*a*c - 35*b^2*d)*Sqrt[a + b*Sqrt[d/x] + c/x]*x)/(48*a^3) + (Sqrt[a + b*Sqrt[d/x] + c/x]*x^2)/(2*a) + ((48*a^2*c^2 - 120*a*b^2*c*d + 35*b^4*d^2)*ArcTanh[(2*a + b*Sqrt[d/x])/(2*Sqrt[a]*Sqrt[a + b*Sqrt[d/x] + c/x])])/(64*a^(9/2))","A",8,7,24,0.2917,1,"{1970, 1357, 744, 834, 806, 724, 206}"
3063,1,135,0,0.1800833,"\int \frac{1}{\sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}} \, dx","Int[1/Sqrt[a + b*Sqrt[d/x] + c/x],x]","-\frac{\left(4 a c-3 b^2 d\right) \tanh ^{-1}\left(\frac{2 a+b \sqrt{\frac{d}{x}}}{2 \sqrt{a} \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}\right)}{4 a^{5/2}}-\frac{3 b d \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{2 a^2 \sqrt{\frac{d}{x}}}+\frac{x \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{a}","-\frac{\left(4 a c-3 b^2 d\right) \tanh ^{-1}\left(\frac{2 a+b \sqrt{\frac{d}{x}}}{2 \sqrt{a} \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}\right)}{4 a^{5/2}}-\frac{3 b d \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{2 a^2 \sqrt{\frac{d}{x}}}+\frac{x \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{a}",1,"(-3*b*d*Sqrt[a + b*Sqrt[d/x] + c/x])/(2*a^2*Sqrt[d/x]) + (Sqrt[a + b*Sqrt[d/x] + c/x]*x)/a - ((4*a*c - 3*b^2*d)*ArcTanh[(2*a + b*Sqrt[d/x])/(2*Sqrt[a]*Sqrt[a + b*Sqrt[d/x] + c/x])])/(4*a^(5/2))","A",6,6,22,0.2727,1,"{1969, 1357, 744, 806, 724, 206}"
3064,1,54,0,0.0975098,"\int \frac{1}{\sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}} x} \, dx","Int[1/(Sqrt[a + b*Sqrt[d/x] + c/x]*x),x]","\frac{2 \tanh ^{-1}\left(\frac{2 a+b \sqrt{\frac{d}{x}}}{2 \sqrt{a} \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}\right)}{\sqrt{a}}","\frac{2 \tanh ^{-1}\left(\frac{2 a+b \sqrt{\frac{d}{x}}}{2 \sqrt{a} \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}\right)}{\sqrt{a}}",1,"(2*ArcTanh[(2*a + b*Sqrt[d/x])/(2*Sqrt[a]*Sqrt[a + b*Sqrt[d/x] + c/x])])/Sqrt[a]","A",4,4,26,0.1538,1,"{1970, 1357, 724, 206}"
3065,1,93,0,0.1220884,"\int \frac{1}{\sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}} x^2} \, dx","Int[1/(Sqrt[a + b*Sqrt[d/x] + c/x]*x^2),x]","\frac{b \sqrt{d} \tanh ^{-1}\left(\frac{b d+2 c \sqrt{\frac{d}{x}}}{2 \sqrt{c} \sqrt{d} \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}\right)}{c^{3/2}}-\frac{2 \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{c}","\frac{b \sqrt{d} \tanh ^{-1}\left(\frac{b d+2 c \sqrt{\frac{d}{x}}}{2 \sqrt{c} \sqrt{d} \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}\right)}{c^{3/2}}-\frac{2 \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{c}",1,"(-2*Sqrt[a + b*Sqrt[d/x] + c/x])/c + (b*Sqrt[d]*ArcTanh[(b*d + 2*c*Sqrt[d/x])/(2*Sqrt[c]*Sqrt[d]*Sqrt[a + b*Sqrt[d/x] + c/x])])/c^(3/2)","A",5,5,26,0.1923,1,"{1970, 1341, 640, 621, 206}"
3066,1,165,0,0.2279703,"\int \frac{1}{\sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}} x^3} \, dx","Int[1/(Sqrt[a + b*Sqrt[d/x] + c/x]*x^3),x]","\frac{\sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}} \left(16 a c-15 b^2 d+10 b c \sqrt{\frac{d}{x}}\right)}{12 c^3}-\frac{b \sqrt{d} \left(12 a c-5 b^2 d\right) \tanh ^{-1}\left(\frac{b d+2 c \sqrt{\frac{d}{x}}}{2 \sqrt{c} \sqrt{d} \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}\right)}{8 c^{7/2}}-\frac{2 \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{3 c x}","\frac{\sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}} \left(16 a c-15 b^2 d+10 b c \sqrt{\frac{d}{x}}\right)}{12 c^3}-\frac{b \sqrt{d} \left(12 a c-5 b^2 d\right) \tanh ^{-1}\left(\frac{b d+2 c \sqrt{\frac{d}{x}}}{2 \sqrt{c} \sqrt{d} \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}\right)}{8 c^{7/2}}-\frac{2 \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{3 c x}",1,"((16*a*c - 15*b^2*d + 10*b*c*Sqrt[d/x])*Sqrt[a + b*Sqrt[d/x] + c/x])/(12*c^3) - (2*Sqrt[a + b*Sqrt[d/x] + c/x])/(3*c*x) - (b*Sqrt[d]*(12*a*c - 5*b^2*d)*ArcTanh[(b*d + 2*c*Sqrt[d/x])/(2*Sqrt[c]*Sqrt[d]*Sqrt[a + b*Sqrt[d/x] + c/x])])/(8*c^(7/2))","A",6,6,26,0.2308,1,"{1970, 1357, 742, 779, 621, 206}"
3067,1,289,0,0.5391238,"\int \frac{1}{\sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}} x^4} \, dx","Int[1/(Sqrt[a + b*Sqrt[d/x] + c/x]*x^4),x]","-\frac{\left(1024 a^2 c^2+14 b c \sqrt{\frac{d}{x}} \left(92 a c-45 b^2 d\right)-2940 a b^2 c d+945 b^4 d^2\right) \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{960 c^5}+\frac{b \sqrt{d} \left(240 a^2 c^2-280 a b^2 c d+63 b^4 d^2\right) \tanh ^{-1}\left(\frac{b d+2 c \sqrt{\frac{d}{x}}}{2 \sqrt{c} \sqrt{d} \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}\right)}{128 c^{11/2}}+\frac{\left(64 a c-63 b^2 d\right) \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{120 c^3 x}+\frac{9 b \left(\frac{d}{x}\right)^{3/2} \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{20 c^2 d}-\frac{2 \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{5 c x^2}","-\frac{\left(1024 a^2 c^2+14 b c \sqrt{\frac{d}{x}} \left(92 a c-45 b^2 d\right)-2940 a b^2 c d+945 b^4 d^2\right) \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{960 c^5}+\frac{b \sqrt{d} \left(240 a^2 c^2-280 a b^2 c d+63 b^4 d^2\right) \tanh ^{-1}\left(\frac{b d+2 c \sqrt{\frac{d}{x}}}{2 \sqrt{c} \sqrt{d} \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}\right)}{128 c^{11/2}}+\frac{\left(64 a c-63 b^2 d\right) \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{120 c^3 x}+\frac{9 b \left(\frac{d}{x}\right)^{3/2} \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{20 c^2 d}-\frac{2 \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{5 c x^2}",1,"-((1024*a^2*c^2 - 2940*a*b^2*c*d + 945*b^4*d^2 + 14*b*c*(92*a*c - 45*b^2*d)*Sqrt[d/x])*Sqrt[a + b*Sqrt[d/x] + c/x])/(960*c^5) + (9*b*Sqrt[a + b*Sqrt[d/x] + c/x]*(d/x)^(3/2))/(20*c^2*d) - (2*Sqrt[a + b*Sqrt[d/x] + c/x])/(5*c*x^2) + ((64*a*c - 63*b^2*d)*Sqrt[a + b*Sqrt[d/x] + c/x])/(120*c^3*x) + (b*Sqrt[d]*(240*a^2*c^2 - 280*a*b^2*c*d + 63*b^4*d^2)*ArcTanh[(b*d + 2*c*Sqrt[d/x])/(2*Sqrt[c]*Sqrt[d]*Sqrt[a + b*Sqrt[d/x] + c/x])])/(128*c^(11/2))","A",8,7,26,0.2692,1,"{1970, 1357, 742, 832, 779, 621, 206}"
3068,1,26,0,0.0259805,"\int \sqrt{\sqrt{\frac{1}{x}}+\frac{1}{x}} \, dx","Int[Sqrt[Sqrt[x^(-1)] + x^(-1)],x]","\frac{4 \left(\sqrt{\frac{1}{x}}+\frac{1}{x}\right)^{3/2}}{3 \left(\frac{1}{x}\right)^{3/2}}","\frac{4 \left(\sqrt{\frac{1}{x}}+\frac{1}{x}\right)^{3/2}}{3 \left(\frac{1}{x}\right)^{3/2}}",1,"(4*(Sqrt[x^(-1)] + x^(-1))^(3/2))/(3*(x^(-1))^(3/2))","A",2,2,15,0.1333,1,"{1966, 2014}"
3069,1,75,0,0.0420452,"\int \sqrt{2+\sqrt{\frac{1}{x}}+\frac{1}{x}} \, dx","Int[Sqrt[2 + Sqrt[x^(-1)] + x^(-1)],x]","\frac{1}{4} \left(\sqrt{\frac{1}{x}}+4\right) \sqrt{\sqrt{\frac{1}{x}}+\frac{1}{x}+2} x+\frac{7 \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{x}}+4}{2 \sqrt{2} \sqrt{\sqrt{\frac{1}{x}}+\frac{1}{x}+2}}\right)}{8 \sqrt{2}}","\frac{1}{4} \left(\sqrt{\frac{1}{x}}+4\right) \sqrt{\sqrt{\frac{1}{x}}+\frac{1}{x}+2} x+\frac{7 \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{x}}+4}{2 \sqrt{2} \sqrt{\sqrt{\frac{1}{x}}+\frac{1}{x}+2}}\right)}{8 \sqrt{2}}",1,"((4 + Sqrt[x^(-1)])*Sqrt[2 + Sqrt[x^(-1)] + x^(-1)]*x)/4 + (7*ArcTanh[(4 + Sqrt[x^(-1)])/(2*Sqrt[2]*Sqrt[2 + Sqrt[x^(-1)] + x^(-1)])])/(8*Sqrt[2])","A",5,5,16,0.3125,1,"{1966, 1357, 720, 724, 206}"
3070,1,79,0,0.0407553,"\int \left(c x^n\right)^{\frac{1}{n}} \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^p \, dx","Int[(c*x^n)^n^(-1)*(a + b*(c*x^n)^n^(-1))^p,x]","\frac{x \left(c x^n\right)^{-1/n} \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^{p+2}}{b^2 (p+2)}-\frac{a x \left(c x^n\right)^{-1/n} \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^{p+1}}{b^2 (p+1)}","\frac{x \left(c x^n\right)^{-1/n} \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^{p+2}}{b^2 (p+2)}-\frac{a x \left(c x^n\right)^{-1/n} \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^{p+1}}{b^2 (p+1)}",1,"-((a*x*(a + b*(c*x^n)^n^(-1))^(1 + p))/(b^2*(1 + p)*(c*x^n)^n^(-1))) + (x*(a + b*(c*x^n)^n^(-1))^(2 + p))/(b^2*(2 + p)*(c*x^n)^n^(-1))","A",4,3,25,0.1200,1,"{15, 368, 43}"
3071,1,70,0,0.0306298,"\int \left(c x^n\right)^{\frac{1}{n}} \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^3 \, dx","Int[(c*x^n)^n^(-1)*(a + b*(c*x^n)^n^(-1))^3,x]","\frac{x \left(c x^n\right)^{-1/n} \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^5}{5 b^2}-\frac{a x \left(c x^n\right)^{-1/n} \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^4}{4 b^2}","\frac{x \left(c x^n\right)^{-1/n} \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^5}{5 b^2}-\frac{a x \left(c x^n\right)^{-1/n} \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^4}{4 b^2}",1,"-(a*x*(a + b*(c*x^n)^n^(-1))^4)/(4*b^2*(c*x^n)^n^(-1)) + (x*(a + b*(c*x^n)^n^(-1))^5)/(5*b^2*(c*x^n)^n^(-1))","A",4,3,25,0.1200,1,"{15, 368, 43}"
3072,1,55,0,0.0252137,"\int \left(c x^n\right)^{\frac{1}{n}} \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^2 \, dx","Int[(c*x^n)^n^(-1)*(a + b*(c*x^n)^n^(-1))^2,x]","\frac{1}{2} a^2 x \left(c x^n\right)^{\frac{1}{n}}+\frac{2}{3} a b x \left(c x^n\right)^{2/n}+\frac{1}{4} b^2 x \left(c x^n\right)^{3/n}","\frac{1}{2} a^2 x \left(c x^n\right)^{\frac{1}{n}}+\frac{2}{3} a b x \left(c x^n\right)^{2/n}+\frac{1}{4} b^2 x \left(c x^n\right)^{3/n}",1,"(a^2*x*(c*x^n)^n^(-1))/2 + (2*a*b*x*(c*x^n)^(2/n))/3 + (b^2*x*(c*x^n)^(3/n))/4","A",4,3,25,0.1200,1,"{15, 368, 43}"
3073,1,33,0,0.0141981,"\int \left(c x^n\right)^{\frac{1}{n}} \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right) \, dx","Int[(c*x^n)^n^(-1)*(a + b*(c*x^n)^n^(-1)),x]","\frac{1}{2} a x \left(c x^n\right)^{\frac{1}{n}}+\frac{1}{3} b x \left(c x^n\right)^{2/n}","\frac{1}{2} a x \left(c x^n\right)^{\frac{1}{n}}+\frac{1}{3} b x \left(c x^n\right)^{2/n}",1,"(a*x*(c*x^n)^n^(-1))/2 + (b*x*(c*x^n)^(2/n))/3","A",5,3,23,0.1304,1,"{15, 14, 30}"
3074,1,38,0,0.0244707,"\int \frac{\left(c x^n\right)^{\frac{1}{n}}}{a+b \left(c x^n\right)^{\frac{1}{n}}} \, dx","Int[(c*x^n)^n^(-1)/(a + b*(c*x^n)^n^(-1)),x]","\frac{x}{b}-\frac{a x \left(c x^n\right)^{-1/n} \log \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)}{b^2}","\frac{x}{b}-\frac{a x \left(c x^n\right)^{-1/n} \log \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)}{b^2}",1,"x/b - (a*x*Log[a + b*(c*x^n)^n^(-1)])/(b^2*(c*x^n)^n^(-1))","A",4,3,25,0.1200,1,"{15, 368, 43}"
3075,1,63,0,0.0316528,"\int \frac{\left(c x^n\right)^{\frac{1}{n}}}{\left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^2} \, dx","Int[(c*x^n)^n^(-1)/(a + b*(c*x^n)^n^(-1))^2,x]","\frac{a x \left(c x^n\right)^{-1/n}}{b^2 \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)}+\frac{x \left(c x^n\right)^{-1/n} \log \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)}{b^2}","\frac{a x \left(c x^n\right)^{-1/n}}{b^2 \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)}+\frac{x \left(c x^n\right)^{-1/n} \log \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)}{b^2}",1,"(a*x)/(b^2*(c*x^n)^n^(-1)*(a + b*(c*x^n)^n^(-1))) + (x*Log[a + b*(c*x^n)^n^(-1)])/(b^2*(c*x^n)^n^(-1))","A",4,3,25,0.1200,1,"{15, 368, 43}"
3076,1,32,0,0.0129269,"\int \frac{\left(c x^n\right)^{\frac{1}{n}}}{\left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^3} \, dx","Int[(c*x^n)^n^(-1)/(a + b*(c*x^n)^n^(-1))^3,x]","\frac{x \left(c x^n\right)^{\frac{1}{n}}}{2 a \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^2}","\frac{x \left(c x^n\right)^{\frac{1}{n}}}{2 a \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^2}",1,"(x*(c*x^n)^n^(-1))/(2*a*(a + b*(c*x^n)^n^(-1))^2)","A",3,3,25,0.1200,1,"{15, 368, 37}"
3077,1,70,0,0.0347402,"\int \frac{\left(c x^n\right)^{\frac{1}{n}}}{\left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^4} \, dx","Int[(c*x^n)^n^(-1)/(a + b*(c*x^n)^n^(-1))^4,x]","\frac{a x \left(c x^n\right)^{-1/n}}{3 b^2 \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^3}-\frac{x \left(c x^n\right)^{-1/n}}{2 b^2 \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^2}","\frac{a x \left(c x^n\right)^{-1/n}}{3 b^2 \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^3}-\frac{x \left(c x^n\right)^{-1/n}}{2 b^2 \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^2}",1,"(a*x)/(3*b^2*(c*x^n)^n^(-1)*(a + b*(c*x^n)^n^(-1))^3) - x/(2*b^2*(c*x^n)^n^(-1)*(a + b*(c*x^n)^n^(-1))^2)","A",4,3,25,0.1200,1,"{15, 368, 43}"
3078,1,70,0,0.034735,"\int \frac{\left(c x^n\right)^{\frac{1}{n}}}{\left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^5} \, dx","Int[(c*x^n)^n^(-1)/(a + b*(c*x^n)^n^(-1))^5,x]","\frac{a x \left(c x^n\right)^{-1/n}}{4 b^2 \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^4}-\frac{x \left(c x^n\right)^{-1/n}}{3 b^2 \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^3}","\frac{a x \left(c x^n\right)^{-1/n}}{4 b^2 \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^4}-\frac{x \left(c x^n\right)^{-1/n}}{3 b^2 \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^3}",1,"(a*x)/(4*b^2*(c*x^n)^n^(-1)*(a + b*(c*x^n)^n^(-1))^4) - x/(3*b^2*(c*x^n)^n^(-1)*(a + b*(c*x^n)^n^(-1))^3)","A",4,3,25,0.1200,1,"{15, 368, 43}"