1,1,18,22,0.004142,"\int (b x)^p (c x)^m \, dx","Integrate[(b*x)^p*(c*x)^m,x]","\frac{x (b x)^p (c x)^m}{m+p+1}","\frac{(b x)^{p+1} (c x)^m}{b (m+p+1)}",1,"(x*(b*x)^p*(c*x)^m)/(1 + m + p)","A",1
2,1,16,16,0.0018823,"\int x^3 \sqrt{b x^2} \, dx","Integrate[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",1
3,1,16,16,0.001225,"\int x^2 \sqrt{b x^2} \, dx","Integrate[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",1
4,1,16,16,0.0011044,"\int x \sqrt{b x^2} \, dx","Integrate[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",1
5,1,14,14,0.0008098,"\int \sqrt{b x^2} \, dx","Integrate[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",1
6,1,14,9,0.001875,"\int \frac{\sqrt{b x^2}}{x} \, dx","Integrate[Sqrt[b*x^2]/x,x]","\frac{b x^2}{\sqrt{b x^2}}","\sqrt{b x^2}",1,"(b*x^2)/Sqrt[b*x^2]","A",1
7,1,14,15,0.001431,"\int \frac{\sqrt{b x^2}}{x^2} \, dx","Integrate[Sqrt[b*x^2]/x^2,x]","\frac{b x \log (x)}{\sqrt{b x^2}}","\frac{\sqrt{b x^2} \log (x)}{x}",1,"(b*x*Log[x])/Sqrt[b*x^2]","A",1
8,1,14,14,0.0020802,"\int \frac{\sqrt{b x^2}}{x^3} \, dx","Integrate[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",1
9,1,16,16,0.0011965,"\int \frac{\sqrt{b x^2}}{x^4} \, dx","Integrate[Sqrt[b*x^2]/x^4,x]","-\frac{\sqrt{b x^2}}{2 x^3}","-\frac{\sqrt{b x^2}}{2 x^3}",1,"-1/2*Sqrt[b*x^2]/x^3","A",1
10,1,16,16,0.0011868,"\int \frac{\sqrt{b x^2}}{x^5} \, dx","Integrate[Sqrt[b*x^2]/x^5,x]","-\frac{\sqrt{b x^2}}{3 x^4}","-\frac{\sqrt{b x^2}}{3 x^4}",1,"-1/3*Sqrt[b*x^2]/x^4","A",1
11,1,12,14,0.0041138,"\int \left(x^2\right)^{3/2} \, dx","Integrate[(x^2)^(3/2),x]","\frac{1}{4} x \left(x^2\right)^{3/2}","\frac{1}{4} x^3 \sqrt{x^2}",1,"(x*(x^2)^(3/2))/4","A",1
12,1,16,17,0.0018302,"\int x^2 \left(b x^2\right)^{3/2} \, dx","Integrate[x^2*(b*x^2)^(3/2),x]","\frac{1}{6} x^3 \left(b x^2\right)^{3/2}","\frac{1}{6} b x^5 \sqrt{b x^2}",1,"(x^3*(b*x^2)^(3/2))/6","A",1
13,1,16,17,0.0013554,"\int x \left(b x^2\right)^{3/2} \, dx","Integrate[x*(b*x^2)^(3/2),x]","\frac{1}{5} x^2 \left(b x^2\right)^{3/2}","\frac{1}{5} b x^4 \sqrt{b x^2}",1,"(x^2*(b*x^2)^(3/2))/5","A",1
14,1,14,17,0.0007016,"\int \left(b x^2\right)^{3/2} \, dx","Integrate[(b*x^2)^(3/2),x]","\frac{1}{4} x \left(b x^2\right)^{3/2}","\frac{1}{4} b x^3 \sqrt{b x^2}",1,"(x*(b*x^2)^(3/2))/4","A",1
15,1,17,17,0.0010768,"\int \frac{\left(b x^2\right)^{3/2}}{x} \, dx","Integrate[(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",1
16,1,15,15,0.0011187,"\int \frac{\left(b x^2\right)^{3/2}}{x^2} \, dx","Integrate[(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",1
17,1,13,11,0.0011656,"\int \frac{\left(b x^2\right)^{3/2}}{x^3} \, dx","Integrate[(b*x^2)^(3/2)/x^3,x]","\frac{\left(b x^2\right)^{3/2}}{x^2}","b \sqrt{b x^2}",1,"(b*x^2)^(3/2)/x^2","A",1
18,1,15,16,0.001953,"\int \frac{\left(b x^2\right)^{3/2}}{x^4} \, dx","Integrate[(b*x^2)^(3/2)/x^4,x]","\frac{\left(b x^2\right)^{3/2} \log (x)}{x^3}","\frac{b \sqrt{b x^2} \log (x)}{x}",1,"((b*x^2)^(3/2)*Log[x])/x^3","A",1
19,1,14,15,0.001746,"\int \frac{\left(b x^2\right)^{3/2}}{x^5} \, dx","Integrate[(b*x^2)^(3/2)/x^5,x]","-\frac{\left(b x^2\right)^{3/2}}{x^4}","-\frac{b \sqrt{b x^2}}{x^2}",1,"-((b*x^2)^(3/2)/x^4)","A",1
20,1,16,17,0.0014209,"\int \frac{\left(b x^2\right)^{3/2}}{x^6} \, dx","Integrate[(b*x^2)^(3/2)/x^6,x]","-\frac{\left(b x^2\right)^{3/2}}{2 x^5}","-\frac{b \sqrt{b x^2}}{2 x^3}",1,"-1/2*(b*x^2)^(3/2)/x^5","A",1
21,1,16,17,0.0013169,"\int \frac{\left(b x^2\right)^{3/2}}{x^7} \, dx","Integrate[(b*x^2)^(3/2)/x^7,x]","-\frac{\left(b x^2\right)^{3/2}}{3 x^6}","-\frac{b \sqrt{b x^2}}{3 x^4}",1,"-1/3*(b*x^2)^(3/2)/x^6","A",1
22,1,12,14,0.0035002,"\int \left(x^2\right)^{5/2} \, dx","Integrate[(x^2)^(5/2),x]","\frac{1}{6} x \left(x^2\right)^{5/2}","\frac{1}{6} x^5 \sqrt{x^2}",1,"(x*(x^2)^(5/2))/6","A",1
23,1,16,19,0.0021669,"\int x \left(b x^2\right)^{5/2} \, dx","Integrate[x*(b*x^2)^(5/2),x]","\frac{1}{7} x^2 \left(b x^2\right)^{5/2}","\frac{1}{7} b^2 x^6 \sqrt{b x^2}",1,"(x^2*(b*x^2)^(5/2))/7","A",1
24,1,14,19,0.0008864,"\int \left(b x^2\right)^{5/2} \, dx","Integrate[(b*x^2)^(5/2),x]","\frac{1}{6} x \left(b x^2\right)^{5/2}","\frac{1}{6} b^2 x^5 \sqrt{b x^2}",1,"(x*(b*x^2)^(5/2))/6","A",1
25,1,17,19,0.0015082,"\int \frac{\left(b x^2\right)^{5/2}}{x} \, dx","Integrate[(b*x^2)^(5/2)/x,x]","\frac{1}{5} b x^2 \left(b x^2\right)^{3/2}","\frac{1}{5} b^2 x^4 \sqrt{b x^2}",1,"(b*x^2*(b*x^2)^(3/2))/5","A",1
26,1,15,19,0.0009931,"\int \frac{\left(b x^2\right)^{5/2}}{x^2} \, dx","Integrate[(b*x^2)^(5/2)/x^2,x]","\frac{1}{4} b x \left(b x^2\right)^{3/2}","\frac{1}{4} b^2 x^3 \sqrt{b x^2}",1,"(b*x*(b*x^2)^(3/2))/4","A",1
27,1,16,19,0.0017918,"\int \frac{\left(b x^2\right)^{5/2}}{x^3} \, dx","Integrate[(b*x^2)^(5/2)/x^3,x]","\frac{\left(b x^2\right)^{5/2}}{3 x^2}","\frac{1}{3} b^2 x^2 \sqrt{b x^2}",1,"(b*x^2)^(5/2)/(3*x^2)","A",1
28,1,17,17,0.001753,"\int \frac{\left(b x^2\right)^{5/2}}{x^4} \, dx","Integrate[(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",1
29,1,13,13,0.00137,"\int \frac{\left(b x^2\right)^{5/2}}{x^5} \, dx","Integrate[(b*x^2)^(5/2)/x^5,x]","\frac{\left(b x^2\right)^{5/2}}{x^4}","b^2 \sqrt{b x^2}",1,"(b*x^2)^(5/2)/x^4","A",1
30,1,15,18,0.0022171,"\int \frac{\left(b x^2\right)^{5/2}}{x^6} \, dx","Integrate[(b*x^2)^(5/2)/x^6,x]","\frac{\left(b x^2\right)^{5/2} \log (x)}{x^5}","\frac{b^2 \sqrt{b x^2} \log (x)}{x}",1,"((b*x^2)^(5/2)*Log[x])/x^5","A",1
31,1,14,17,0.0023186,"\int \frac{\left(b x^2\right)^{5/2}}{x^7} \, dx","Integrate[(b*x^2)^(5/2)/x^7,x]","-\frac{\left(b x^2\right)^{5/2}}{x^6}","-\frac{b^2 \sqrt{b x^2}}{x^2}",1,"-((b*x^2)^(5/2)/x^6)","A",1
32,1,16,19,0.0014422,"\int \frac{\left(b x^2\right)^{5/2}}{x^8} \, dx","Integrate[(b*x^2)^(5/2)/x^8,x]","-\frac{\left(b x^2\right)^{5/2}}{2 x^7}","-\frac{b^2 \sqrt{b x^2}}{2 x^3}",1,"-1/2*(b*x^2)^(5/2)/x^7","A",1
33,1,16,19,0.0013928,"\int \frac{\left(b x^2\right)^{5/2}}{x^9} \, dx","Integrate[(b*x^2)^(5/2)/x^9,x]","-\frac{\left(b x^2\right)^{5/2}}{3 x^8}","-\frac{b^2 \sqrt{b x^2}}{3 x^4}",1,"-1/3*(b*x^2)^(5/2)/x^8","A",1
34,1,12,14,0.0033551,"\int \left(x^2\right)^{7/2} \, dx","Integrate[(x^2)^(7/2),x]","\frac{1}{8} x \left(x^2\right)^{7/2}","\frac{1}{8} x^7 \sqrt{x^2}",1,"(x*(x^2)^(7/2))/8","A",1
35,1,16,16,0.0017324,"\int \frac{x^3}{\sqrt{b x^2}} \, dx","Integrate[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",1
36,1,13,13,0.0008245,"\int \frac{x}{\sqrt{b x^2}} \, dx","Integrate[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",1
37,1,15,11,0.0023119,"\int \frac{1}{x \sqrt{b x^2}} \, dx","Integrate[1/(x*Sqrt[b*x^2]),x]","-\frac{b x^2}{\left(b x^2\right)^{3/2}}","-\frac{1}{\sqrt{b x^2}}",1,"-((b*x^2)/(b*x^2)^(3/2))","A",1
38,1,16,16,0.0023482,"\int \frac{1}{x^3 \sqrt{b x^2}} \, dx","Integrate[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*1/(x^2*Sqrt[b*x^2])","A",1
39,1,16,16,0.001501,"\int \frac{x^2}{\sqrt{b x^2}} \, dx","Integrate[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",1
40,1,13,13,0.0002235,"\int \frac{1}{\sqrt{b x^2}} \, dx","Integrate[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",1
41,1,15,16,0.0018565,"\int \frac{1}{x^2 \sqrt{b x^2}} \, dx","Integrate[1/(x^2*Sqrt[b*x^2]),x]","-\frac{b x}{2 \left(b x^2\right)^{3/2}}","-\frac{1}{2 x \sqrt{b x^2}}",1,"-1/2*(b*x)/(b*x^2)^(3/2)","A",1
42,1,16,19,0.0012075,"\int \frac{x^5}{\left(b x^2\right)^{3/2}} \, dx","Integrate[x^5/(b*x^2)^(3/2),x]","\frac{x^6}{3 \left(b x^2\right)^{3/2}}","\frac{x^4}{3 b \sqrt{b x^2}}",1,"x^6/(3*(b*x^2)^(3/2))","A",1
43,1,13,16,0.0012411,"\int \frac{x^3}{\left(b x^2\right)^{3/2}} \, dx","Integrate[x^3/(b*x^2)^(3/2),x]","\frac{x^4}{\left(b x^2\right)^{3/2}}","\frac{x^2}{b \sqrt{b x^2}}",1,"x^4/(b*x^2)^(3/2)","A",1
44,1,14,14,0.0007681,"\int \frac{x}{\left(b x^2\right)^{3/2}} \, dx","Integrate[x/(b*x^2)^(3/2),x]","-\frac{x^2}{\left(b x^2\right)^{3/2}}","-\frac{1}{b \sqrt{b x^2}}",1,"-(x^2/(b*x^2)^(3/2))","A",1
45,1,17,19,0.0026228,"\int \frac{1}{x \left(b x^2\right)^{3/2}} \, dx","Integrate[1/(x*(b*x^2)^(3/2)),x]","-\frac{b x^2}{3 \left(b x^2\right)^{5/2}}","-\frac{1}{3 b x^2 \sqrt{b x^2}}",1,"-1/3*(b*x^2)/(b*x^2)^(5/2)","A",1
46,1,16,19,0.0025442,"\int \frac{1}{x^3 \left(b x^2\right)^{3/2}} \, dx","Integrate[1/(x^3*(b*x^2)^(3/2)),x]","-\frac{1}{5 x^2 \left(b x^2\right)^{3/2}}","-\frac{1}{5 b x^4 \sqrt{b x^2}}",1,"-1/5*1/(x^2*(b*x^2)^(3/2))","A",1
47,1,16,19,0.0016021,"\int \frac{x^6}{\left(b x^2\right)^{3/2}} \, dx","Integrate[x^6/(b*x^2)^(3/2),x]","\frac{x^7}{4 \left(b x^2\right)^{3/2}}","\frac{x^5}{4 b \sqrt{b x^2}}",1,"x^7/(4*(b*x^2)^(3/2))","A",1
48,1,16,19,0.0015287,"\int \frac{x^4}{\left(b x^2\right)^{3/2}} \, dx","Integrate[x^4/(b*x^2)^(3/2),x]","\frac{x^5}{2 \left(b x^2\right)^{3/2}}","\frac{x^3}{2 b \sqrt{b x^2}}",1,"x^5/(2*(b*x^2)^(3/2))","A",1
49,1,15,16,0.0014637,"\int \frac{x^2}{\left(b x^2\right)^{3/2}} \, dx","Integrate[x^2/(b*x^2)^(3/2),x]","\frac{x^3 \log (x)}{\left(b x^2\right)^{3/2}}","\frac{x \log (x)}{b \sqrt{b x^2}}",1,"(x^3*Log[x])/(b*x^2)^(3/2)","A",1
50,1,14,19,0.0002388,"\int \frac{1}{\left(b x^2\right)^{3/2}} \, dx","Integrate[(b*x^2)^(-3/2),x]","-\frac{x}{2 \left(b x^2\right)^{3/2}}","-\frac{1}{2 b x \sqrt{b x^2}}",1,"-1/2*x/(b*x^2)^(3/2)","A",1
51,1,15,19,0.0022086,"\int \frac{1}{x^2 \left(b x^2\right)^{3/2}} \, dx","Integrate[1/(x^2*(b*x^2)^(3/2)),x]","-\frac{b x}{4 \left(b x^2\right)^{5/2}}","-\frac{1}{4 b x^3 \sqrt{b x^2}}",1,"-1/4*(b*x)/(b*x^2)^(5/2)","A",1
52,1,16,19,0.0013347,"\int \frac{x^7}{\left(b x^2\right)^{5/2}} \, dx","Integrate[x^7/(b*x^2)^(5/2),x]","\frac{x^8}{3 \left(b x^2\right)^{5/2}}","\frac{x^4}{3 b^2 \sqrt{b x^2}}",1,"x^8/(3*(b*x^2)^(5/2))","A",1
53,1,13,16,0.0015076,"\int \frac{x^5}{\left(b x^2\right)^{5/2}} \, dx","Integrate[x^5/(b*x^2)^(5/2),x]","\frac{x^6}{\left(b x^2\right)^{5/2}}","\frac{x^2}{b^2 \sqrt{b x^2}}",1,"x^6/(b*x^2)^(5/2)","A",1
54,1,14,14,0.002696,"\int \frac{x^3}{\left(b x^2\right)^{5/2}} \, dx","Integrate[x^3/(b*x^2)^(5/2),x]","-\frac{x^4}{\left(b x^2\right)^{5/2}}","-\frac{1}{b^2 \sqrt{b x^2}}",1,"-(x^4/(b*x^2)^(5/2))","A",1
55,1,16,19,0.0008176,"\int \frac{x}{\left(b x^2\right)^{5/2}} \, dx","Integrate[x/(b*x^2)^(5/2),x]","-\frac{x^2}{3 \left(b x^2\right)^{5/2}}","-\frac{1}{3 b^2 x^2 \sqrt{b x^2}}",1,"-1/3*x^2/(b*x^2)^(5/2)","A",1
56,1,17,19,0.0036414,"\int \frac{1}{x \left(b x^2\right)^{5/2}} \, dx","Integrate[1/(x*(b*x^2)^(5/2)),x]","-\frac{b x^2}{5 \left(b x^2\right)^{7/2}}","-\frac{1}{5 b^2 x^4 \sqrt{b x^2}}",1,"-1/5*(b*x^2)/(b*x^2)^(7/2)","A",1
57,1,16,19,0.0018248,"\int \frac{x^6}{\left(b x^2\right)^{5/2}} \, dx","Integrate[x^6/(b*x^2)^(5/2),x]","\frac{x^7}{2 \left(b x^2\right)^{5/2}}","\frac{x^3}{2 b^2 \sqrt{b x^2}}",1,"x^7/(2*(b*x^2)^(5/2))","A",1
58,1,15,16,0.0013884,"\int \frac{x^4}{\left(b x^2\right)^{5/2}} \, dx","Integrate[x^4/(b*x^2)^(5/2),x]","\frac{x^5 \log (x)}{\left(b x^2\right)^{5/2}}","\frac{x \log (x)}{b^2 \sqrt{b x^2}}",1,"(x^5*Log[x])/(b*x^2)^(5/2)","A",1
59,1,16,19,0.0013447,"\int \frac{x^2}{\left(b x^2\right)^{5/2}} \, dx","Integrate[x^2/(b*x^2)^(5/2),x]","-\frac{x^3}{2 \left(b x^2\right)^{5/2}}","-\frac{1}{2 b^2 x \sqrt{b x^2}}",1,"-1/2*x^3/(b*x^2)^(5/2)","A",1
60,1,14,19,0.0002799,"\int \frac{1}{\left(b x^2\right)^{5/2}} \, dx","Integrate[(b*x^2)^(-5/2),x]","-\frac{x}{4 \left(b x^2\right)^{5/2}}","-\frac{1}{4 b^2 x^3 \sqrt{b x^2}}",1,"-1/4*x/(b*x^2)^(5/2)","A",1
61,1,15,19,0.0020682,"\int \frac{1}{x^2 \left(b x^2\right)^{5/2}} \, dx","Integrate[1/(x^2*(b*x^2)^(5/2)),x]","-\frac{b x}{6 \left(b x^2\right)^{7/2}}","-\frac{1}{6 b^2 x^5 \sqrt{b x^2}}",1,"-1/6*(b*x)/(b*x^2)^(7/2)","A",1
62,1,21,29,0.0049521,"\int (c x)^m \left(b x^2\right)^{3/2} \, dx","Integrate[(c*x)^m*(b*x^2)^(3/2),x]","\frac{x \left(b x^2\right)^{3/2} (c x)^m}{m+4}","\frac{b \sqrt{b x^2} (c x)^{m+4}}{c^4 (m+4) x}",1,"(x*(c*x)^m*(b*x^2)^(3/2))/(4 + m)","A",1
63,1,21,28,0.0037006,"\int (c x)^m \sqrt{b x^2} \, dx","Integrate[(c*x)^m*Sqrt[b*x^2],x]","\frac{x \sqrt{b x^2} (c x)^m}{m+2}","\frac{\sqrt{b x^2} (c x)^{m+2}}{c^2 (m+2) x}",1,"(x*(c*x)^m*Sqrt[b*x^2])/(2 + m)","A",1
64,1,19,19,0.0027801,"\int \frac{(c x)^m}{\sqrt{b x^2}} \, dx","Integrate[(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",1
65,1,21,32,0.0050729,"\int \frac{(c x)^m}{\left(b x^2\right)^{3/2}} \, dx","Integrate[(c*x)^m/(b*x^2)^(3/2),x]","\frac{x (c x)^m}{(m-2) \left(b x^2\right)^{3/2}}","-\frac{c^2 x (c x)^{m-2}}{b (2-m) \sqrt{b x^2}}",1,"(x*(c*x)^m)/((-2 + m)*(b*x^2)^(3/2))","A",1
66,1,21,21,0.003697,"\int x^m \left(b x^2\right)^p \, dx","Integrate[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",1
67,1,22,22,0.0032526,"\int (c x)^m \left(b x^2\right)^p \, dx","Integrate[(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",1
68,1,13,13,0.0064491,"\int x^{-1-2 p} \left(x^2\right)^p \, dx","Integrate[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",1
69,1,18,19,0.002546,"\int x^3 \left(b x^2\right)^p \, dx","Integrate[x^3*(b*x^2)^p,x]","\frac{x^4 \left(b x^2\right)^p}{2 p+4}","\frac{x^4 \left(b x^2\right)^p}{2 (p+2)}",1,"(x^4*(b*x^2)^p)/(4 + 2*p)","A",1
70,1,18,18,0.0024497,"\int x^2 \left(b x^2\right)^p \, dx","Integrate[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",1
71,1,18,19,0.0025116,"\int x \left(b x^2\right)^p \, dx","Integrate[x*(b*x^2)^p,x]","\frac{x^2 \left(b x^2\right)^p}{2 p+2}","\frac{x^2 \left(b x^2\right)^p}{2 (p+1)}",1,"(x^2*(b*x^2)^p)/(2 + 2*p)","A",1
72,1,16,16,0.001727,"\int \left(b x^2\right)^p \, dx","Integrate[(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",1
73,1,14,14,0.0012666,"\int \frac{\left(b x^2\right)^p}{x} \, dx","Integrate[(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",1
74,1,18,19,0.0037076,"\int \frac{\left(b x^2\right)^p}{x^2} \, dx","Integrate[(b*x^2)^p/x^2,x]","\frac{\left(b x^2\right)^p}{(2 p-1) x}","-\frac{\left(b x^2\right)^p}{(1-2 p) x}",1,"(b*x^2)^p/((-1 + 2*p)*x)","A",1
75,1,18,21,0.0026317,"\int \frac{\left(b x^2\right)^p}{x^3} \, dx","Integrate[(b*x^2)^p/x^3,x]","\frac{\left(b x^2\right)^p}{(2 p-2) x^2}","-\frac{\left(b x^2\right)^p}{2 (1-p) x^2}",1,"(b*x^2)^p/((-2 + 2*p)*x^2)","A",1
76,1,18,19,0.0022254,"\int \frac{\left(b x^2\right)^p}{x^4} \, dx","Integrate[(b*x^2)^p/x^4,x]","\frac{\left(b x^2\right)^p}{(2 p-3) 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",1
77,1,14,14,0.0014107,"\int \sqrt{b x^3} \, dx","Integrate[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",1
78,1,14,14,0.0008869,"\int \sqrt{b x^2} \, dx","Integrate[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",1
79,1,12,14,0.0010351,"\int \sqrt{b x} \, dx","Integrate[Sqrt[b*x],x]","\frac{2}{3} x \sqrt{b x}","\frac{2 (b x)^{3/2}}{3 b}",1,"(2*x*Sqrt[b*x])/3","A",1
80,1,12,12,0.0013267,"\int \sqrt{\frac{b}{x}} \, dx","Integrate[Sqrt[b/x],x]","2 x \sqrt{\frac{b}{x}}","2 x \sqrt{\frac{b}{x}}",1,"2*Sqrt[b/x]*x","A",1
81,1,13,13,0.0016507,"\int \sqrt{\frac{b}{x^2}} \, dx","Integrate[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",1
82,1,12,12,0.0014173,"\int \sqrt{\frac{b}{x^3}} \, dx","Integrate[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",1
83,1,14,17,0.0013682,"\int \left(b x^3\right)^{3/2} \, dx","Integrate[(b*x^3)^(3/2),x]","\frac{2}{11} x \left(b x^3\right)^{3/2}","\frac{2}{11} b x^4 \sqrt{b x^3}",1,"(2*x*(b*x^3)^(3/2))/11","A",1
84,1,14,17,0.0002474,"\int \left(b x^2\right)^{3/2} \, dx","Integrate[(b*x^2)^(3/2),x]","\frac{1}{4} x \left(b x^2\right)^{3/2}","\frac{1}{4} b x^3 \sqrt{b x^2}",1,"(x*(b*x^2)^(3/2))/4","A",1
85,1,12,14,0.0014952,"\int (b x)^{3/2} \, dx","Integrate[(b*x)^(3/2),x]","\frac{2}{5} x (b x)^{3/2}","\frac{2 (b x)^{5/2}}{5 b}",1,"(2*x*(b*x)^(3/2))/5","A",1
86,1,12,12,0.0012889,"\int \left(\frac{b}{x}\right)^{3/2} \, dx","Integrate[(b/x)^(3/2),x]","-2 x \left(\frac{b}{x}\right)^{3/2}","-2 b \sqrt{\frac{b}{x}}",1,"-2*(b/x)^(3/2)*x","A",1
87,1,14,17,0.0013441,"\int \left(\frac{b}{x^2}\right)^{3/2} \, dx","Integrate[(b/x^2)^(3/2),x]","-\frac{1}{2} x \left(\frac{b}{x^2}\right)^{3/2}","-\frac{b \sqrt{\frac{b}{x^2}}}{2 x}",1,"-1/2*((b/x^2)^(3/2)*x)","A",1
88,1,14,17,0.001412,"\int \left(\frac{b}{x^3}\right)^{3/2} \, dx","Integrate[(b/x^3)^(3/2),x]","-\frac{2}{7} x \left(\frac{b}{x^3}\right)^{3/2}","-\frac{2 b \sqrt{\frac{b}{x^3}}}{7 x^2}",1,"(-2*(b/x^3)^(3/2)*x)/7","A",1
89,1,12,12,0.001736,"\int \frac{1}{\sqrt{b x^3}} \, dx","Integrate[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",1
90,1,13,13,0.0006014,"\int \frac{1}{\sqrt{b x^2}} \, dx","Integrate[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",1
91,1,10,12,0.0012194,"\int \frac{1}{\sqrt{b x}} \, dx","Integrate[1/Sqrt[b*x],x]","\frac{2 x}{\sqrt{b x}}","\frac{2 \sqrt{b x}}{b}",1,"(2*x)/Sqrt[b*x]","A",1
92,1,14,14,0.0016743,"\int \frac{1}{\sqrt{\frac{b}{x}}} \, dx","Integrate[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",1
93,1,14,14,0.0018266,"\int \frac{1}{\sqrt{\frac{b}{x^2}}} \, dx","Integrate[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",1
94,1,14,14,0.0018121,"\int \frac{1}{\sqrt{\frac{b}{x^3}}} \, dx","Integrate[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",1
95,1,14,19,0.00202,"\int \frac{1}{\left(b x^3\right)^{3/2}} \, dx","Integrate[(b*x^3)^(-3/2),x]","-\frac{2 x}{7 \left(b x^3\right)^{3/2}}","-\frac{2}{7 b x^2 \sqrt{b x^3}}",1,"(-2*x)/(7*(b*x^3)^(3/2))","A",1
96,1,14,19,0.0011916,"\int \frac{1}{\left(b x^2\right)^{3/2}} \, dx","Integrate[(b*x^2)^(-3/2),x]","-\frac{x}{2 \left(b x^2\right)^{3/2}}","-\frac{1}{2 b x \sqrt{b x^2}}",1,"-1/2*x/(b*x^2)^(3/2)","A",1
97,1,10,12,0.0012689,"\int \frac{1}{(b x)^{3/2}} \, dx","Integrate[(b*x)^(-3/2),x]","-\frac{2 x}{(b x)^{3/2}}","-\frac{2}{b \sqrt{b x}}",1,"(-2*x)/(b*x)^(3/2)","A",1
98,1,14,19,0.0018073,"\int \frac{1}{\left(\frac{b}{x}\right)^{3/2}} \, dx","Integrate[(b/x)^(-3/2),x]","\frac{2 x}{5 \left(\frac{b}{x}\right)^{3/2}}","\frac{2 x^2}{5 b \sqrt{\frac{b}{x}}}",1,"(2*x)/(5*(b/x)^(3/2))","A",1
99,1,14,19,0.0018387,"\int \frac{1}{\left(\frac{b}{x^2}\right)^{3/2}} \, dx","Integrate[(b/x^2)^(-3/2),x]","\frac{x}{4 \left(\frac{b}{x^2}\right)^{3/2}}","\frac{x^3}{4 b \sqrt{\frac{b}{x^2}}}",1,"x/(4*(b/x^2)^(3/2))","A",1
100,1,14,19,0.0019724,"\int \frac{1}{\left(\frac{b}{x^3}\right)^{3/2}} \, dx","Integrate[(b/x^3)^(-3/2),x]","\frac{2 x}{11 \left(\frac{b}{x^3}\right)^{3/2}}","\frac{2 x^4}{11 b \sqrt{\frac{b}{x^3}}}",1,"(2*x)/(11*(b/x^3)^(3/2))","A",1
101,1,17,17,0.0026571,"\int \sqrt[3]{b x^n} \, dx","Integrate[(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",1
102,1,14,14,0.0013424,"\int \sqrt[3]{b x^3} \, dx","Integrate[(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",1
103,1,14,14,0.0010988,"\int \sqrt[3]{b x^2} \, dx","Integrate[(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",1
104,1,12,14,0.0010218,"\int \sqrt[3]{b x} \, dx","Integrate[(b*x)^(1/3),x]","\frac{3}{4} x \sqrt[3]{b x}","\frac{3 (b x)^{4/3}}{4 b}",1,"(3*x*(b*x)^(1/3))/4","A",1
105,1,14,14,0.0011019,"\int \sqrt[3]{\frac{b}{x}} \, dx","Integrate[(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",1
106,1,12,12,0.0011367,"\int \sqrt[3]{\frac{b}{x^2}} \, dx","Integrate[(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",1
107,1,13,13,0.0012196,"\int \sqrt[3]{\frac{b}{x^3}} \, dx","Integrate[(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",1
108,1,12,12,0.0084739,"\int \sqrt[3]{\frac{b}{x^4}} \, dx","Integrate[(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",1
109,1,20,19,0.0029125,"\int \left(b x^n\right)^{2/3} \, dx","Integrate[(b*x^n)^(2/3),x]","\frac{x \left(b x^n\right)^{2/3}}{\frac{2 n}{3}+1}","\frac{3 x \left(b x^n\right)^{2/3}}{2 n+3}",1,"(x*(b*x^n)^(2/3))/(1 + (2*n)/3)","A",1
110,1,14,14,0.001316,"\int \left(b x^2\right)^{2/3} \, dx","Integrate[(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",1
111,1,12,14,0.0012423,"\int (b x)^{2/3} \, dx","Integrate[(b*x)^(2/3),x]","\frac{3}{5} x (b x)^{2/3}","\frac{3 (b x)^{5/3}}{5 b}",1,"(3*x*(b*x)^(2/3))/5","A",1
112,1,12,12,0.0017859,"\int \left(\frac{b}{x}\right)^{2/3} \, dx","Integrate[(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",1
113,1,12,12,0.0054923,"\int \left(\frac{b}{x^2}\right)^{2/3} \, dx","Integrate[(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",1
114,1,12,12,0.0012906,"\int \left(\frac{b}{x^3}\right)^{2/3} \, dx","Integrate[(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",1
115,1,14,14,0.0013022,"\int \left(\frac{b}{x^4}\right)^{2/3} \, dx","Integrate[(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",1
116,1,17,19,0.0051995,"\int \frac{1}{\sqrt[3]{b x^n}} \, dx","Integrate[(b*x^n)^(-1/3),x]","-\frac{3 x}{(n-3) \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",1
117,1,12,12,0.0018168,"\int \frac{1}{\sqrt[3]{b x^4}} \, dx","Integrate[(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",1
118,1,13,13,0.0017194,"\int \frac{1}{\sqrt[3]{b x^3}} \, dx","Integrate[(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",1
119,1,12,12,0.0017243,"\int \frac{1}{\sqrt[3]{b x^2}} \, dx","Integrate[(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",1
120,1,12,14,0.0016968,"\int \frac{1}{\sqrt[3]{b x}} \, dx","Integrate[(b*x)^(-1/3),x]","\frac{3 x}{2 \sqrt[3]{b x}}","\frac{3 (b x)^{2/3}}{2 b}",1,"(3*x)/(2*(b*x)^(1/3))","A",1
121,1,14,14,0.0017325,"\int \frac{1}{\sqrt[3]{\frac{b}{x}}} \, dx","Integrate[(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",1
122,1,14,14,0.0018036,"\int \frac{1}{\sqrt[3]{\frac{b}{x^2}}} \, dx","Integrate[(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",1
123,1,14,14,0.0018555,"\int \frac{1}{\sqrt[3]{\frac{b}{x^3}}} \, dx","Integrate[(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",1
124,1,20,19,0.0059366,"\int \frac{1}{\left(b x^n\right)^{2/3}} \, dx","Integrate[(b*x^n)^(-2/3),x]","\frac{x}{\left(1-\frac{2 n}{3}\right) \left(b x^n\right)^{2/3}}","\frac{3 x}{(3-2 n) \left(b x^n\right)^{2/3}}",1,"x/((1 - (2*n)/3)*(b*x^n)^(2/3))","A",1
125,1,12,12,0.0018855,"\int \frac{1}{\left(b x^3\right)^{2/3}} \, dx","Integrate[(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",1
126,1,12,12,0.0018162,"\int \frac{1}{\left(b x^2\right)^{2/3}} \, dx","Integrate[(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",1
127,1,10,12,0.0014921,"\int \frac{1}{(b x)^{2/3}} \, dx","Integrate[(b*x)^(-2/3),x]","\frac{3 x}{(b x)^{2/3}}","\frac{3 \sqrt[3]{b x}}{b}",1,"(3*x)/(b*x)^(2/3)","A",1
128,1,14,14,0.001865,"\int \frac{1}{\left(\frac{b}{x}\right)^{2/3}} \, dx","Integrate[(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",1
129,1,14,14,0.0018651,"\int \frac{1}{\left(\frac{b}{x^2}\right)^{2/3}} \, dx","Integrate[(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",1
130,1,14,14,0.0017693,"\int \frac{1}{\left(\frac{b}{x^3}\right)^{2/3}} \, dx","Integrate[(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",1
131,1,19,19,0.0036982,"\int x^2 \sqrt{b x^n} \, dx","Integrate[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",1
132,1,19,19,0.0183579,"\int x \sqrt{b x^n} \, dx","Integrate[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",1
133,1,17,17,0.0017045,"\int \sqrt{b x^n} \, dx","Integrate[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",1
134,1,14,14,0.0016886,"\int \frac{\sqrt{b x^n}}{x} \, dx","Integrate[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",1
135,1,19,21,0.0021475,"\int \frac{\sqrt{b x^n}}{x^2} \, dx","Integrate[Sqrt[b*x^n]/x^2,x]","\frac{2 \sqrt{b x^n}}{(n-2) x}","-\frac{2 \sqrt{b x^n}}{(2-n) x}",1,"(2*Sqrt[b*x^n])/((-2 + n)*x)","A",1
136,1,19,21,0.0092073,"\int \frac{\sqrt{b x^n}}{x^3} \, dx","Integrate[Sqrt[b*x^n]/x^3,x]","\frac{2 \sqrt{b x^n}}{(n-4) x^2}","-\frac{2 \sqrt{b x^n}}{(4-n) x^2}",1,"(2*Sqrt[b*x^n])/((-4 + n)*x^2)","A",1
137,1,22,24,0.0056162,"\int x \left(b x^n\right)^{3/2} \, dx","Integrate[x*(b*x^n)^(3/2),x]","\frac{x^2 \left(b x^n\right)^{3/2}}{\frac{3 n}{2}+2}","\frac{2 b x^{n+2} \sqrt{b x^n}}{3 n+4}",1,"(x^2*(b*x^n)^(3/2))/(2 + (3*n)/2)","A",1
138,1,20,24,0.0038481,"\int \left(b x^n\right)^{3/2} \, dx","Integrate[(b*x^n)^(3/2),x]","\frac{x \left(b x^n\right)^{3/2}}{\frac{3 n}{2}+1}","\frac{2 b x^{n+1} \sqrt{b x^n}}{3 n+2}",1,"(x*(b*x^n)^(3/2))/(1 + (3*n)/2)","A",1
139,1,16,20,0.0023265,"\int \frac{\left(b x^n\right)^{3/2}}{x} \, dx","Integrate[(b*x^n)^(3/2)/x,x]","\frac{2 \left(b x^n\right)^{3/2}}{3 n}","\frac{2 b x^n \sqrt{b x^n}}{3 n}",1,"(2*(b*x^n)^(3/2))/(3*n)","A",1
140,1,22,24,0.007296,"\int \frac{\left(b x^n\right)^{3/2}}{x^2} \, dx","Integrate[(b*x^n)^(3/2)/x^2,x]","\frac{\left(b x^n\right)^{3/2}}{\left(\frac{3 n}{2}-1\right) x}","-\frac{2 b x^{n-1} \sqrt{b x^n}}{2-3 n}",1,"(b*x^n)^(3/2)/((-1 + (3*n)/2)*x)","A",1
141,1,22,24,0.0060811,"\int \frac{\left(b x^n\right)^{3/2}}{x^3} \, dx","Integrate[(b*x^n)^(3/2)/x^3,x]","\frac{\left(b x^n\right)^{3/2}}{\left(\frac{3 n}{2}-2\right) x^2}","-\frac{2 b x^{n-2} \sqrt{b x^n}}{4-3 n}",1,"(b*x^n)^(3/2)/((-2 + (3*n)/2)*x^2)","A",1
142,1,22,26,0.0057438,"\int \frac{\left(b x^n\right)^{3/2}}{x^4} \, dx","Integrate[(b*x^n)^(3/2)/x^4,x]","\frac{\left(b x^n\right)^{3/2}}{\left(\frac{3 n}{2}-3\right) x^3}","-\frac{2 b x^{n-3} \sqrt{b x^n}}{3 (2-n)}",1,"(b*x^n)^(3/2)/((-3 + (3*n)/2)*x^3)","A",1
143,1,19,21,0.0052318,"\int \frac{x^2}{\sqrt{b x^n}} \, dx","Integrate[x^2/Sqrt[b*x^n],x]","-\frac{2 x^3}{(n-6) \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",1
144,1,19,21,0.0039422,"\int \frac{x}{\sqrt{b x^n}} \, dx","Integrate[x/Sqrt[b*x^n],x]","-\frac{2 x^2}{(n-4) \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",1
145,1,17,19,0.0027573,"\int \frac{1}{\sqrt{b x^n}} \, dx","Integrate[1/Sqrt[b*x^n],x]","-\frac{2 x}{(n-2) \sqrt{b x^n}}","\frac{2 x}{(2-n) \sqrt{b x^n}}",1,"(-2*x)/((-2 + n)*Sqrt[b*x^n])","A",1
146,1,14,14,0.0023463,"\int \frac{1}{x \sqrt{b x^n}} \, dx","Integrate[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",1
147,1,19,19,0.0209002,"\int \frac{1}{x^2 \sqrt{b x^n}} \, dx","Integrate[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",1
148,1,19,19,0.0043829,"\int \frac{1}{x^3 \sqrt{b x^n}} \, dx","Integrate[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",1
149,1,22,30,0.0078277,"\int \frac{x^2}{\left(b x^n\right)^{3/2}} \, dx","Integrate[x^2/(b*x^n)^(3/2),x]","\frac{x^3}{\left(3-\frac{3 n}{2}\right) \left(b x^n\right)^{3/2}}","\frac{2 x^{3-n}}{3 b (2-n) \sqrt{b x^n}}",1,"x^3/((3 - (3*n)/2)*(b*x^n)^(3/2))","A",1
150,1,22,28,0.0066358,"\int \frac{x}{\left(b x^n\right)^{3/2}} \, dx","Integrate[x/(b*x^n)^(3/2),x]","\frac{x^2}{\left(2-\frac{3 n}{2}\right) \left(b x^n\right)^{3/2}}","\frac{2 x^{2-n}}{b (4-3 n) \sqrt{b x^n}}",1,"x^2/((2 - (3*n)/2)*(b*x^n)^(3/2))","A",1
151,1,20,28,0.0051815,"\int \frac{1}{\left(b x^n\right)^{3/2}} \, dx","Integrate[(b*x^n)^(-3/2),x]","\frac{x}{\left(1-\frac{3 n}{2}\right) \left(b x^n\right)^{3/2}}","\frac{2 x^{1-n}}{b (2-3 n) \sqrt{b x^n}}",1,"x/((1 - (3*n)/2)*(b*x^n)^(3/2))","A",1
152,1,16,24,0.0032972,"\int \frac{1}{x \left(b x^n\right)^{3/2}} \, dx","Integrate[1/(x*(b*x^n)^(3/2)),x]","-\frac{2}{3 n \left(b x^n\right)^{3/2}}","-\frac{2 x^{-n}}{3 b n \sqrt{b x^n}}",1,"-2/(3*n*(b*x^n)^(3/2))","A",1
153,1,22,28,0.0070733,"\int \frac{1}{x^2 \left(b x^n\right)^{3/2}} \, dx","Integrate[1/(x^2*(b*x^n)^(3/2)),x]","\frac{1}{\left(-\frac{3 n}{2}-1\right) x \left(b x^n\right)^{3/2}}","-\frac{2 x^{-n-1}}{b (3 n+2) \sqrt{b x^n}}",1,"1/((-1 - (3*n)/2)*x*(b*x^n)^(3/2))","A",1
154,1,22,28,0.007039,"\int \frac{1}{x^3 \left(b x^n\right)^{3/2}} \, dx","Integrate[1/(x^3*(b*x^n)^(3/2)),x]","\frac{1}{\left(-\frac{3 n}{2}-2\right) x^2 \left(b x^n\right)^{3/2}}","-\frac{2 x^{-n-2}}{b (3 n+4) \sqrt{b x^n}}",1,"1/((-2 - (3*n)/2)*x^2*(b*x^n)^(3/2))","A",1
155,1,22,28,0.007857,"\int \frac{1}{x^4 \left(b x^n\right)^{3/2}} \, dx","Integrate[1/(x^4*(b*x^n)^(3/2)),x]","\frac{1}{\left(-\frac{3 n}{2}-3\right) x^3 \left(b x^n\right)^{3/2}}","-\frac{2 x^{-n-3}}{3 b (n+2) \sqrt{b x^n}}",1,"1/((-3 - (3*n)/2)*x^3*(b*x^n)^(3/2))","A",1
156,1,25,32,0.0097167,"\int \frac{x^m}{\left(a x^n\right)^{3/2}} \, dx","Integrate[x^m/(a*x^n)^(3/2),x]","\frac{x^{m+1}}{\left(m-\frac{3 n}{2}+1\right) \left(a x^n\right)^{3/2}}","\frac{2 x^{m-n+1}}{a (2 m-3 n+2) \sqrt{a x^n}}",1,"x^(1 + m)/((1 + m - (3*n)/2)*(a*x^n)^(3/2))","A",1
157,1,26,36,0.0061992,"\int \frac{(c x)^m}{\left(a x^n\right)^{3/2}} \, dx","Integrate[(c*x)^m/(a*x^n)^(3/2),x]","\frac{x (c x)^m}{\left(m-\frac{3 n}{2}+1\right) \left(a x^n\right)^{3/2}}","\frac{2 x^{1-n} (c x)^m}{a (2 m-3 n+2) \sqrt{a x^n}}",1,"(x*(c*x)^m)/((1 + m - (3*n)/2)*(a*x^n)^(3/2))","A",1
158,1,25,28,0.0193902,"\int x^m \left(b x^n\right)^{3/2} \, dx","Integrate[x^m*(b*x^n)^(3/2),x]","\frac{x^{m+1} \left(b x^n\right)^{3/2}}{m+\frac{3 n}{2}+1}","\frac{2 b \sqrt{b x^n} x^{m+n+1}}{2 m+3 n+2}",1,"(x^(1 + m)*(b*x^n)^(3/2))/(1 + m + (3*n)/2)","A",1
159,1,25,24,0.0043659,"\int x^m \sqrt{b x^n} \, dx","Integrate[x^m*Sqrt[b*x^n],x]","\frac{x^{m+1} \sqrt{b x^n}}{m+\frac{n}{2}+1}","\frac{2 x^{m+1} \sqrt{b x^n}}{2 m+n+2}",1,"(x^(1 + m)*Sqrt[b*x^n])/(1 + m + n/2)","A",1
160,1,25,26,0.0060827,"\int \frac{x^m}{\sqrt{b x^n}} \, dx","Integrate[x^m/Sqrt[b*x^n],x]","\frac{x^{m+1}}{\left(m-\frac{n}{2}+1\right) \sqrt{b x^n}}","\frac{2 x^{m+1}}{(2 m-n+2) \sqrt{b x^n}}",1,"x^(1 + m)/((1 + m - n/2)*Sqrt[b*x^n])","A",1
161,1,25,32,0.0060118,"\int \frac{x^m}{\left(b x^n\right)^{3/2}} \, dx","Integrate[x^m/(b*x^n)^(3/2),x]","\frac{x^{m+1}}{\left(m-\frac{3 n}{2}+1\right) \left(b x^n\right)^{3/2}}","\frac{2 x^{m-n+1}}{b (2 m-3 n+2) \sqrt{b x^n}}",1,"x^(1 + m)/((1 + m - (3*n)/2)*(b*x^n)^(3/2))","A",1
162,1,26,31,0.0099926,"\int (c x)^m \left(b x^n\right)^{5/2} \, dx","Integrate[(c*x)^m*(b*x^n)^(5/2),x]","\frac{x \left(b x^n\right)^{5/2} (c x)^m}{m+\frac{5 n}{2}+1}","\frac{2 \left(b x^n\right)^{5/2} (c x)^{m+1}}{c (2 m+5 n+2)}",1,"(x*(c*x)^m*(b*x^n)^(5/2))/(1 + m + (5*n)/2)","A",1
163,1,26,32,0.0058857,"\int (c x)^m \left(b x^n\right)^{3/2} \, dx","Integrate[(c*x)^m*(b*x^n)^(3/2),x]","\frac{x \left(b x^n\right)^{3/2} (c x)^m}{m+\frac{3 n}{2}+1}","\frac{2 b x^{n+1} \sqrt{b x^n} (c x)^m}{2 m+3 n+2}",1,"(x*(c*x)^m*(b*x^n)^(3/2))/(1 + m + (3*n)/2)","A",1
164,1,26,29,0.0046119,"\int (c x)^m \sqrt{b x^n} \, dx","Integrate[(c*x)^m*Sqrt[b*x^n],x]","\frac{x \sqrt{b x^n} (c x)^m}{m+\frac{n}{2}+1}","\frac{2 \sqrt{b x^n} (c x)^{m+1}}{c (2 m+n+2)}",1,"(x*(c*x)^m*Sqrt[b*x^n])/(1 + m + n/2)","A",1
165,1,26,27,0.0051712,"\int \frac{(c x)^m}{\sqrt{b x^n}} \, dx","Integrate[(c*x)^m/Sqrt[b*x^n],x]","\frac{x (c x)^m}{\left(m-\frac{n}{2}+1\right) \sqrt{b x^n}}","\frac{2 x (c x)^m}{(2 m-n+2) \sqrt{b x^n}}",1,"(x*(c*x)^m)/((1 + m - n/2)*Sqrt[b*x^n])","A",1
166,1,26,36,0.0051071,"\int \frac{(c x)^m}{\left(b x^n\right)^{3/2}} \, dx","Integrate[(c*x)^m/(b*x^n)^(3/2),x]","\frac{x (c x)^m}{\left(m-\frac{3 n}{2}+1\right) \left(b x^n\right)^{3/2}}","\frac{2 x^{1-n} (c x)^m}{b (2 m-3 n+2) \sqrt{b x^n}}",1,"(x*(c*x)^m)/((1 + m - (3*n)/2)*(b*x^n)^(3/2))","A",1
167,1,26,36,0.0190737,"\int \frac{(c x)^m}{\left(b x^n\right)^{5/2}} \, dx","Integrate[(c*x)^m/(b*x^n)^(5/2),x]","\frac{x (c x)^m}{\left(m-\frac{5 n}{2}+1\right) \left(b x^n\right)^{5/2}}","\frac{2 x^{1-2 n} (c x)^m}{b^2 (2 m-5 n+2) \sqrt{b x^n}}",1,"(x*(c*x)^m)/((1 + m - (5*n)/2)*(b*x^n)^(5/2))","A",1
168,1,19,20,0.0046579,"\int x^{-1-\frac{3 n}{2}} \left(b x^n\right)^{3/2} \, dx","Integrate[x^(-1 - (3*n)/2)*(b*x^n)^(3/2),x]","x^{-3 n/2} \log (x) \left(b x^n\right)^{3/2}","b x^{-n/2} \log (x) \sqrt{b x^n}",1,"((b*x^n)^(3/2)*Log[x])/x^((3*n)/2)","A",1
169,1,19,19,0.0042424,"\int x^{-1-\frac{n}{2}} \sqrt{b x^n} \, dx","Integrate[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",1
170,1,19,19,0.0030455,"\int \frac{x^{-1+\frac{n}{2}}}{\sqrt{b x^n}} \, dx","Integrate[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",1
171,1,19,22,0.0033484,"\int \frac{x^{-1+\frac{3 n}{2}}}{\left(b x^n\right)^{3/2}} \, dx","Integrate[x^(-1 + (3*n)/2)/(b*x^n)^(3/2),x]","\frac{x^{3 n/2} \log (x)}{\left(b x^n\right)^{3/2}}","\frac{x^{n/2} \log (x)}{b \sqrt{b x^n}}",1,"(x^((3*n)/2)*Log[x])/(b*x^n)^(3/2)","A",1
172,1,21,21,0.0045504,"\int x^m \left(b x^n\right)^p \, dx","Integrate[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",1
173,1,22,26,0.0036542,"\int (c x)^m \left(b x^n\right)^p \, dx","Integrate[(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",1
174,1,18,18,0.0028203,"\int x^2 \left(b x^n\right)^p \, dx","Integrate[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",1
175,1,18,18,0.009471,"\int x \left(b x^n\right)^p \, dx","Integrate[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",1
176,1,16,16,0.0018871,"\int \left(b x^n\right)^p \, dx","Integrate[(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",1
177,1,14,14,0.0015145,"\int \frac{\left(b x^n\right)^p}{x} \, dx","Integrate[(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",1
178,1,18,20,0.0034623,"\int \frac{\left(b x^n\right)^p}{x^2} \, dx","Integrate[(b*x^n)^p/x^2,x]","\frac{\left(b x^n\right)^p}{x (n p-1)}","-\frac{\left(b x^n\right)^p}{x (1-n p)}",1,"(b*x^n)^p/((-1 + n*p)*x)","A",1
179,1,18,20,0.002662,"\int \frac{\left(b x^n\right)^p}{x^3} \, dx","Integrate[(b*x^n)^p/x^3,x]","\frac{\left(b x^n\right)^p}{x^2 (n p-2)}","-\frac{\left(b x^n\right)^p}{x^2 (2-n p)}",1,"(b*x^n)^p/((-2 + n*p)*x^2)","A",1
180,1,20,20,0.0042465,"\int x^m \left(a x^n\right)^{-1/n} \, dx","Integrate[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",1
181,1,21,21,0.0024802,"\int (c x)^m \left(a x^n\right)^{-1/n} \, dx","Integrate[(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",1
182,1,18,18,0.0021484,"\int x^2 \left(a x^n\right)^{-1/n} \, dx","Integrate[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",1
183,1,15,15,0.0013842,"\int x \left(a x^n\right)^{-1/n} \, dx","Integrate[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",1
184,1,15,15,0.0010503,"\int \left(a x^n\right)^{-1/n} \, dx","Integrate[(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",1
185,1,13,13,0.0012657,"\int \frac{\left(a x^n\right)^{-1/n}}{x} \, dx","Integrate[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",1
186,1,18,18,0.0019181,"\int \frac{\left(a x^n\right)^{-1/n}}{x^2} \, dx","Integrate[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*1/(x*(a*x^n)^n^(-1))","A",1
187,1,22,22,0.0080719,"\int x^m \left(a x^n\right)^{-\frac{1+m}{n}} \, dx","Integrate[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",1
188,1,16,16,0.0100622,"\int x^{-1-n p} \left(a x^n\right)^p \, dx","Integrate[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",1
189,1,26,26,0.008021,"\int x^m \left(a \left(b x^n\right)^p\right)^q \, dx","Integrate[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",1
190,1,23,23,0.0048854,"\int x^2 \left(a \left(b x^n\right)^p\right)^q \, dx","Integrate[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",1
191,1,23,23,0.0047085,"\int x \left(a \left(b x^n\right)^p\right)^q \, dx","Integrate[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",1
192,1,21,21,0.0030597,"\int \left(a \left(b x^n\right)^p\right)^q \, dx","Integrate[(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",1
193,1,21,21,0.0024241,"\int \frac{\left(a \left(b x^n\right)^p\right)^q}{x} \, dx","Integrate[(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",1
194,1,23,25,0.0055616,"\int \frac{\left(a \left(b x^n\right)^p\right)^q}{x^2} \, dx","Integrate[(a*(b*x^n)^p)^q/x^2,x]","\frac{\left(a \left(b x^n\right)^p\right)^q}{x (n p q-1)}","-\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",1
195,1,23,25,0.0042874,"\int \frac{\left(a \left(b x^n\right)^p\right)^q}{x^3} \, dx","Integrate[(a*(b*x^n)^p)^q/x^3,x]","\frac{\left(a \left(b x^n\right)^p\right)^q}{x^2 (n p q-2)}","-\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",1
196,1,25,25,0.0100973,"\int x^2 \left(a \left(b x^m\right)^n\right)^{-\frac{1}{m n}} \, dx","Integrate[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",1
197,1,22,22,0.0023536,"\int x \left(a \left(b x^m\right)^n\right)^{-\frac{1}{m n}} \, dx","Integrate[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",1
198,1,22,22,0.0019715,"\int \left(a \left(b x^m\right)^n\right)^{-\frac{1}{m n}} \, dx","Integrate[(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",1
199,1,20,20,0.0022687,"\int \frac{\left(a \left(b x^m\right)^n\right)^{-\frac{1}{m n}}}{x} \, dx","Integrate[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",1
200,1,25,25,0.0034209,"\int \frac{\left(a \left(b x^m\right)^n\right)^{-\frac{1}{m n}}}{x^2} \, dx","Integrate[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*1/(x*(a*(b*x^m)^n)^(1/(m*n)))","A",1
201,1,24,24,0.0104261,"\int x^{2-n p q} \left(a \left(b x^n\right)^p\right)^q \, dx","Integrate[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",1
202,1,24,24,0.0043789,"\int x^{1-n p q} \left(a \left(b x^n\right)^p\right)^q \, dx","Integrate[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",1
203,1,21,21,0.0084547,"\int x^{-n p q} \left(a \left(b x^n\right)^p\right)^q \, dx","Integrate[(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",1
204,1,21,21,0.0057346,"\int x^{-1-n p q} \left(a \left(b x^n\right)^p\right)^q \, dx","Integrate[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",1
205,1,22,22,0.0058414,"\int x^{-2-n p q} \left(a \left(b x^n\right)^p\right)^q \, dx","Integrate[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",1
206,1,17,17,0.0014909,"\int x^3 \left(a+b x^3\right) \, dx","Integrate[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",1
207,1,17,17,0.0011452,"\int x^2 \left(a+b x^3\right) \, dx","Integrate[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",1
208,1,17,17,0.0010774,"\int x \left(a+b x^3\right) \, dx","Integrate[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",1
209,1,12,12,0.0000826,"\int \left(a+b x^3\right) \, dx","Integrate[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
210,1,13,13,0.0020151,"\int \frac{a+b x^3}{x} \, dx","Integrate[(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",1
211,1,15,15,0.0011696,"\int \frac{a+b x^3}{x^2} \, dx","Integrate[(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",1
212,1,12,12,0.0008312,"\int \frac{a+b x^3}{x^3} \, dx","Integrate[(a + b*x^3)/x^3,x]","b x-\frac{a}{2 x^2}","b x-\frac{a}{2 x^2}",1,"-1/2*a/x^2 + b*x","A",1
213,1,13,13,0.0022568,"\int \frac{a+b x^3}{x^4} \, dx","Integrate[(a + b*x^3)/x^4,x]","b \log (x)-\frac{a}{3 x^3}","b \log (x)-\frac{a}{3 x^3}",1,"-1/3*a/x^3 + b*Log[x]","A",1
214,1,15,15,0.0020582,"\int \frac{a+b x^3}{x^5} \, dx","Integrate[(a + b*x^3)/x^5,x]","-\frac{a}{4 x^4}-\frac{b}{x}","-\frac{a}{4 x^4}-\frac{b}{x}",1,"-1/4*a/x^4 - b/x","A",1
215,1,17,17,0.0020179,"\int \frac{a+b x^3}{x^6} \, dx","Integrate[(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,"-1/5*a/x^5 - b/(2*x^2)","A",1
216,1,17,17,0.0021158,"\int \frac{a+b x^3}{x^7} \, dx","Integrate[(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,"-1/6*a/x^6 - b/(3*x^3)","A",1
217,1,17,17,0.0021192,"\int \frac{a+b x^3}{x^8} \, dx","Integrate[(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,"-1/7*a/x^7 - b/(4*x^4)","A",1
218,1,30,30,0.0011011,"\int x^4 \left(a+b x^3\right)^2 \, dx","Integrate[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",1
219,1,30,30,0.0007781,"\int x^3 \left(a+b x^3\right)^2 \, dx","Integrate[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",1
220,1,30,16,0.0008066,"\int x^2 \left(a+b x^3\right)^2 \, dx","Integrate[x^2*(a + b*x^3)^2,x]","\frac{a^2 x^3}{3}+\frac{1}{3} a b x^6+\frac{b^2 x^9}{9}","\frac{\left(a+b x^3\right)^3}{9 b}",1,"(a^2*x^3)/3 + (a*b*x^6)/3 + (b^2*x^9)/9","A",1
221,1,30,30,0.0014116,"\int x \left(a+b x^3\right)^2 \, dx","Integrate[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",1
222,1,25,25,0.0008796,"\int \left(a+b x^3\right)^2 \, dx","Integrate[(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",1
223,1,26,26,0.0007171,"\int \frac{\left(a+b x^3\right)^2}{x} \, dx","Integrate[(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",1
224,1,25,25,0.0009069,"\int \frac{\left(a+b x^3\right)^2}{x^2} \, dx","Integrate[(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",1
225,1,26,26,0.000756,"\int \frac{\left(a+b x^3\right)^2}{x^3} \, dx","Integrate[(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,"-1/2*a^2/x^2 + 2*a*b*x + (b^2*x^4)/4","A",1
226,1,27,27,0.0007765,"\int \frac{\left(a+b x^3\right)^2}{x^4} \, dx","Integrate[(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,"-1/3*a^2/x^3 + (b^2*x^3)/3 + 2*a*b*Log[x]","A",1
227,1,28,28,0.0009281,"\int \frac{\left(a+b x^3\right)^2}{x^5} \, dx","Integrate[(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,"-1/4*a^2/x^4 - (2*a*b)/x + (b^2*x^2)/2","A",1
228,1,23,23,0.000845,"\int \frac{\left(a+b x^3\right)^2}{x^6} \, dx","Integrate[(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,"-1/5*a^2/x^5 - (a*b)/x^2 + b^2*x","A",1
229,1,26,26,0.0010065,"\int \frac{\left(a+b x^3\right)^2}{x^7} \, dx","Integrate[(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,"-1/6*a^2/x^6 - (2*a*b)/(3*x^3) + b^2*Log[x]","A",1
230,1,28,28,0.000948,"\int \frac{\left(a+b x^3\right)^2}{x^8} \, dx","Integrate[(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,"-1/7*a^2/x^7 - (a*b)/(2*x^4) - b^2/x","A",1
231,1,30,30,0.0008673,"\int \frac{\left(a+b x^3\right)^2}{x^9} \, dx","Integrate[(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,"-1/8*a^2/x^8 - (2*a*b)/(5*x^5) - b^2/(2*x^2)","A",1
232,1,30,19,0.0009144,"\int \frac{\left(a+b x^3\right)^2}{x^{10}} \, dx","Integrate[(a + b*x^3)^2/x^10,x]","-\frac{a^2}{9 x^9}-\frac{a b}{3 x^6}-\frac{b^2}{3 x^3}","-\frac{\left(a+b x^3\right)^3}{9 a x^9}",1,"-1/9*a^2/x^9 - (a*b)/(3*x^6) - b^2/(3*x^3)","A",1
233,1,30,30,0.0008428,"\int \frac{\left(a+b x^3\right)^2}{x^{11}} \, dx","Integrate[(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,"-1/10*a^2/x^10 - (2*a*b)/(7*x^7) - b^2/(4*x^4)","A",1
234,1,30,30,0.000882,"\int \frac{\left(a+b x^3\right)^2}{x^{12}} \, dx","Integrate[(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,"-1/11*a^2/x^11 - (a*b)/(4*x^8) - b^2/(5*x^5)","A",1
235,1,30,30,0.0008871,"\int \frac{\left(a+b x^3\right)^2}{x^{13}} \, dx","Integrate[(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,"-1/12*a^2/x^12 - (2*a*b)/(9*x^9) - b^2/(6*x^6)","A",1
236,1,43,43,0.0022502,"\int x^{14} \left(a+b x^3\right)^3 \, dx","Integrate[x^14*(a + b*x^3)^3,x]","\frac{a^3 x^{15}}{15}+\frac{1}{6} a^2 b x^{18}+\frac{1}{7} a b^2 x^{21}+\frac{b^3 x^{24}}{24}","\frac{a^3 x^{15}}{15}+\frac{1}{6} a^2 b x^{18}+\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",1
237,1,43,43,0.001962,"\int x^{11} \left(a+b x^3\right)^3 \, dx","Integrate[x^11*(a + b*x^3)^3,x]","\frac{a^3 x^{12}}{12}+\frac{1}{5} a^2 b x^{15}+\frac{1}{6} a b^2 x^{18}+\frac{b^3 x^{21}}{21}","\frac{a^3 x^{12}}{12}+\frac{1}{5} a^2 b x^{15}+\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",1
238,1,43,43,0.002261,"\int x^8 \left(a+b x^3\right)^3 \, dx","Integrate[x^8*(a + b*x^3)^3,x]","\frac{a^3 x^9}{9}+\frac{1}{4} a^2 b x^{12}+\frac{1}{5} a b^2 x^{15}+\frac{b^3 x^{18}}{18}","\frac{a^3 x^9}{9}+\frac{1}{4} a^2 b x^{12}+\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",1
239,1,43,34,0.0018538,"\int x^5 \left(a+b x^3\right)^3 \, dx","Integrate[x^5*(a + b*x^3)^3,x]","\frac{a^3 x^6}{6}+\frac{1}{3} a^2 b x^9+\frac{1}{4} a b^2 x^{12}+\frac{b^3 x^{15}}{15}","\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^3*x^6)/6 + (a^2*b*x^9)/3 + (a*b^2*x^12)/4 + (b^3*x^15)/15","A",1
240,1,43,16,0.0020083,"\int x^2 \left(a+b x^3\right)^3 \, dx","Integrate[x^2*(a + b*x^3)^3,x]","\frac{a^3 x^3}{3}+\frac{1}{2} a^2 b x^6+\frac{1}{3} a b^2 x^9+\frac{b^3 x^{12}}{12}","\frac{\left(a+b x^3\right)^4}{12 b}",1,"(a^3*x^3)/3 + (a^2*b*x^6)/2 + (a*b^2*x^9)/3 + (b^3*x^12)/12","B",1
241,1,36,36,0.0069104,"\int \frac{\left(a+b x^3\right)^3}{x} \, dx","Integrate[(a + b*x^3)^3/x,x]","a^3 \log (x)+a^2 b x^3+\frac{1}{2} a b^2 x^6+\frac{b^3 x^9}{9}","a^3 \log (x)+a^2 b x^3+\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",1
242,1,37,37,0.0046353,"\int \frac{\left(a+b x^3\right)^3}{x^4} \, dx","Integrate[(a + b*x^3)^3/x^4,x]","-\frac{a^3}{3 x^3}+3 a^2 b \log (x)+a b^2 x^3+\frac{b^3 x^6}{6}","-\frac{a^3}{3 x^3}+3 a^2 b \log (x)+a b^2 x^3+\frac{b^3 x^6}{6}",1,"-1/3*a^3/x^3 + a*b^2*x^3 + (b^3*x^6)/6 + 3*a^2*b*Log[x]","A",1
243,1,38,38,0.0045791,"\int \frac{\left(a+b x^3\right)^3}{x^7} \, dx","Integrate[(a + b*x^3)^3/x^7,x]","-\frac{a^3}{6 x^6}-\frac{a^2 b}{x^3}+3 a b^2 \log (x)+\frac{b^3 x^3}{3}","-\frac{a^3}{6 x^6}-\frac{a^2 b}{x^3}+3 a b^2 \log (x)+\frac{b^3 x^3}{3}",1,"-1/6*a^3/x^6 - (a^2*b)/x^3 + (b^3*x^3)/3 + 3*a*b^2*Log[x]","A",1
244,1,37,37,0.0044256,"\int \frac{\left(a+b x^3\right)^3}{x^{10}} \, dx","Integrate[(a + b*x^3)^3/x^10,x]","-\frac{a^3}{9 x^9}-\frac{a^2 b}{2 x^6}-\frac{a b^2}{x^3}+b^3 \log (x)","-\frac{a^3}{9 x^9}-\frac{a^2 b}{2 x^6}-\frac{a b^2}{x^3}+b^3 \log (x)",1,"-1/9*a^3/x^9 - (a^2*b)/(2*x^6) - (a*b^2)/x^3 + b^3*Log[x]","A",1
245,1,43,19,0.0052629,"\int \frac{\left(a+b x^3\right)^3}{x^{13}} \, dx","Integrate[(a + b*x^3)^3/x^13,x]","-\frac{a^3}{12 x^{12}}-\frac{a^2 b}{3 x^9}-\frac{a b^2}{2 x^6}-\frac{b^3}{3 x^3}","-\frac{\left(a+b x^3\right)^4}{12 a x^{12}}",1,"-1/12*a^3/x^12 - (a^2*b)/(3*x^9) - (a*b^2)/(2*x^6) - b^3/(3*x^3)","B",1
246,1,43,40,0.004247,"\int \frac{\left(a+b x^3\right)^3}{x^{16}} \, dx","Integrate[(a + b*x^3)^3/x^16,x]","-\frac{a^3}{15 x^{15}}-\frac{a^2 b}{4 x^{12}}-\frac{a b^2}{3 x^9}-\frac{b^3}{6 x^6}","\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,"-1/15*a^3/x^15 - (a^2*b)/(4*x^12) - (a*b^2)/(3*x^9) - b^3/(6*x^6)","A",1
247,1,43,43,0.0039631,"\int \frac{\left(a+b x^3\right)^3}{x^{19}} \, dx","Integrate[(a + b*x^3)^3/x^19,x]","-\frac{a^3}{18 x^{18}}-\frac{a^2 b}{5 x^{15}}-\frac{a b^2}{4 x^{12}}-\frac{b^3}{9 x^9}","-\frac{a^3}{18 x^{18}}-\frac{a^2 b}{5 x^{15}}-\frac{a b^2}{4 x^{12}}-\frac{b^3}{9 x^9}",1,"-1/18*a^3/x^18 - (a^2*b)/(5*x^15) - (a*b^2)/(4*x^12) - b^3/(9*x^9)","A",1
248,1,43,43,0.0041718,"\int \frac{\left(a+b x^3\right)^3}{x^{22}} \, dx","Integrate[(a + b*x^3)^3/x^22,x]","-\frac{a^3}{21 x^{21}}-\frac{a^2 b}{6 x^{18}}-\frac{a b^2}{5 x^{15}}-\frac{b^3}{12 x^{12}}","-\frac{a^3}{21 x^{21}}-\frac{a^2 b}{6 x^{18}}-\frac{a b^2}{5 x^{15}}-\frac{b^3}{12 x^{12}}",1,"-1/21*a^3/x^21 - (a^2*b)/(6*x^18) - (a*b^2)/(5*x^15) - b^3/(12*x^12)","A",1
249,1,43,43,0.0019084,"\int x^4 \left(a+b x^3\right)^3 \, dx","Integrate[x^4*(a + b*x^3)^3,x]","\frac{a^3 x^5}{5}+\frac{3}{8} a^2 b x^8+\frac{3}{11} a b^2 x^{11}+\frac{b^3 x^{14}}{14}","\frac{a^3 x^5}{5}+\frac{3}{8} a^2 b x^8+\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",1
250,1,43,43,0.0018696,"\int x^3 \left(a+b x^3\right)^3 \, dx","Integrate[x^3*(a + b*x^3)^3,x]","\frac{a^3 x^4}{4}+\frac{3}{7} a^2 b x^7+\frac{3}{10} a b^2 x^{10}+\frac{b^3 x^{13}}{13}","\frac{a^3 x^4}{4}+\frac{3}{7} a^2 b x^7+\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",1
251,1,43,43,0.0016625,"\int x \left(a+b x^3\right)^3 \, dx","Integrate[x*(a + b*x^3)^3,x]","\frac{a^3 x^2}{2}+\frac{3}{5} a^2 b x^5+\frac{3}{8} a b^2 x^8+\frac{b^3 x^{11}}{11}","\frac{a^3 x^2}{2}+\frac{3}{5} a^2 b x^5+\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",1
252,1,38,38,0.0009433,"\int \left(a+b x^3\right)^3 \, dx","Integrate[(a + b*x^3)^3,x]","a^3 x+\frac{3}{4} a^2 b x^4+\frac{3}{7} a b^2 x^7+\frac{b^3 x^{10}}{10}","a^3 x+\frac{3}{4} a^2 b x^4+\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",1
253,1,41,41,0.0081963,"\int \frac{\left(a+b x^3\right)^3}{x^2} \, dx","Integrate[(a + b*x^3)^3/x^2,x]","-\frac{a^3}{x}+\frac{3}{2} a^2 b x^2+\frac{3}{5} a b^2 x^5+\frac{b^3 x^8}{8}","-\frac{a^3}{x}+\frac{3}{2} a^2 b x^2+\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",1
254,1,39,39,0.0064934,"\int \frac{\left(a+b x^3\right)^3}{x^3} \, dx","Integrate[(a + b*x^3)^3/x^3,x]","-\frac{a^3}{2 x^2}+3 a^2 b x+\frac{3}{4} a b^2 x^4+\frac{b^3 x^7}{7}","-\frac{a^3}{2 x^2}+3 a^2 b x+\frac{3}{4} a b^2 x^4+\frac{b^3 x^7}{7}",1,"-1/2*a^3/x^2 + 3*a^2*b*x + (3*a*b^2*x^4)/4 + (b^3*x^7)/7","A",1
255,1,41,41,0.0040032,"\int \frac{\left(a+b x^3\right)^3}{x^5} \, dx","Integrate[(a + b*x^3)^3/x^5,x]","-\frac{a^3}{4 x^4}-\frac{3 a^2 b}{x}+\frac{3}{2} a b^2 x^2+\frac{b^3 x^5}{5}","-\frac{a^3}{4 x^4}-\frac{3 a^2 b}{x}+\frac{3}{2} a b^2 x^2+\frac{b^3 x^5}{5}",1,"-1/4*a^3/x^4 - (3*a^2*b)/x + (3*a*b^2*x^2)/2 + (b^3*x^5)/5","A",1
256,1,39,39,0.0062357,"\int \frac{\left(a+b x^3\right)^3}{x^6} \, dx","Integrate[(a + b*x^3)^3/x^6,x]","-\frac{a^3}{5 x^5}-\frac{3 a^2 b}{2 x^2}+3 a b^2 x+\frac{b^3 x^4}{4}","-\frac{a^3}{5 x^5}-\frac{3 a^2 b}{2 x^2}+3 a b^2 x+\frac{b^3 x^4}{4}",1,"-1/5*a^3/x^5 - (3*a^2*b)/(2*x^2) + 3*a*b^2*x + (b^3*x^4)/4","A",1
257,1,41,41,0.0040375,"\int \frac{\left(a+b x^3\right)^3}{x^8} \, dx","Integrate[(a + b*x^3)^3/x^8,x]","-\frac{a^3}{7 x^7}-\frac{3 a^2 b}{4 x^4}-\frac{3 a b^2}{x}+\frac{b^3 x^2}{2}","-\frac{a^3}{7 x^7}-\frac{3 a^2 b}{4 x^4}-\frac{3 a b^2}{x}+\frac{b^3 x^2}{2}",1,"-1/7*a^3/x^7 - (3*a^2*b)/(4*x^4) - (3*a*b^2)/x + (b^3*x^2)/2","A",1
258,1,69,69,0.0030952,"\int x^{17} \left(a+b x^3\right)^5 \, dx","Integrate[x^17*(a + b*x^3)^5,x]","\frac{a^5 x^{18}}{18}+\frac{5}{21} a^4 b x^{21}+\frac{5}{12} a^3 b^2 x^{24}+\frac{10}{27} a^2 b^3 x^{27}+\frac{1}{6} a b^4 x^{30}+\frac{b^5 x^{33}}{33}","\frac{a^5 x^{18}}{18}+\frac{5}{21} a^4 b x^{21}+\frac{5}{12} a^3 b^2 x^{24}+\frac{10}{27} a^2 b^3 x^{27}+\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",1
259,1,69,69,0.0025397,"\int x^{14} \left(a+b x^3\right)^5 \, dx","Integrate[x^14*(a + b*x^3)^5,x]","\frac{a^5 x^{15}}{15}+\frac{5}{18} a^4 b x^{18}+\frac{10}{21} a^3 b^2 x^{21}+\frac{5}{12} a^2 b^3 x^{24}+\frac{5}{27} a b^4 x^{27}+\frac{b^5 x^{30}}{30}","\frac{a^5 x^{15}}{15}+\frac{5}{18} a^4 b x^{18}+\frac{10}{21} a^3 b^2 x^{21}+\frac{5}{12} a^2 b^3 x^{24}+\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",1
260,1,69,72,0.0024966,"\int x^{11} \left(a+b x^3\right)^5 \, dx","Integrate[x^11*(a + b*x^3)^5,x]","\frac{a^5 x^{12}}{12}+\frac{1}{3} a^4 b x^{15}+\frac{5}{9} a^3 b^2 x^{18}+\frac{10}{21} a^2 b^3 x^{21}+\frac{5}{24} a b^4 x^{24}+\frac{b^5 x^{27}}{27}","-\frac{a^3 \left(a+b x^3\right)^6}{18 b^4}+\frac{a^2 \left(a+b x^3\right)^7}{7 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^5*x^12)/12 + (a^4*b*x^15)/3 + (5*a^3*b^2*x^18)/9 + (10*a^2*b^3*x^21)/21 + (5*a*b^4*x^24)/24 + (b^5*x^27)/27","A",1
261,1,69,53,0.0024378,"\int x^8 \left(a+b x^3\right)^5 \, dx","Integrate[x^8*(a + b*x^3)^5,x]","\frac{a^5 x^9}{9}+\frac{5}{12} a^4 b x^{12}+\frac{2}{3} a^3 b^2 x^{15}+\frac{5}{9} a^2 b^3 x^{18}+\frac{5}{21} a b^4 x^{21}+\frac{b^5 x^{24}}{24}","\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^5*x^9)/9 + (5*a^4*b*x^12)/12 + (2*a^3*b^2*x^15)/3 + (5*a^2*b^3*x^18)/9 + (5*a*b^4*x^21)/21 + (b^5*x^24)/24","A",1
262,1,69,34,0.002288,"\int x^5 \left(a+b x^3\right)^5 \, dx","Integrate[x^5*(a + b*x^3)^5,x]","\frac{a^5 x^6}{6}+\frac{5}{9} a^4 b x^9+\frac{5}{6} a^3 b^2 x^{12}+\frac{2}{3} a^2 b^3 x^{15}+\frac{5}{18} a b^4 x^{18}+\frac{b^5 x^{21}}{21}","\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^5*x^6)/6 + (5*a^4*b*x^9)/9 + (5*a^3*b^2*x^12)/6 + (2*a^2*b^3*x^15)/3 + (5*a*b^4*x^18)/18 + (b^5*x^21)/21","B",1
263,1,69,16,0.0023997,"\int x^2 \left(a+b x^3\right)^5 \, dx","Integrate[x^2*(a + b*x^3)^5,x]","\frac{a^5 x^3}{3}+\frac{5}{6} a^4 b x^6+\frac{10}{9} a^3 b^2 x^9+\frac{5}{6} a^2 b^3 x^{12}+\frac{1}{3} a b^4 x^{15}+\frac{b^5 x^{18}}{18}","\frac{\left(a+b x^3\right)^6}{18 b}",1,"(a^5*x^3)/3 + (5*a^4*b*x^6)/6 + (10*a^3*b^2*x^9)/9 + (5*a^2*b^3*x^12)/6 + (a*b^4*x^15)/3 + (b^5*x^18)/18","B",1
264,1,65,65,0.004481,"\int \frac{\left(a+b x^3\right)^5}{x} \, dx","Integrate[(a + b*x^3)^5/x,x]","a^5 \log (x)+\frac{5}{3} a^4 b x^3+\frac{5}{3} a^3 b^2 x^6+\frac{10}{9} a^2 b^3 x^9+\frac{5}{12} a b^4 x^{12}+\frac{b^5 x^{15}}{15}","a^5 \log (x)+\frac{5}{3} a^4 b x^3+\frac{5}{3} a^3 b^2 x^6+\frac{10}{9} a^2 b^3 x^9+\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",1
265,1,66,66,0.0047625,"\int \frac{\left(a+b x^3\right)^5}{x^4} \, dx","Integrate[(a + b*x^3)^5/x^4,x]","-\frac{a^5}{3 x^3}+5 a^4 b \log (x)+\frac{10}{3} a^3 b^2 x^3+\frac{5}{3} a^2 b^3 x^6+\frac{5}{9} a b^4 x^9+\frac{b^5 x^{12}}{12}","-\frac{a^5}{3 x^3}+5 a^4 b \log (x)+\frac{10}{3} a^3 b^2 x^3+\frac{5}{3} a^2 b^3 x^6+\frac{5}{9} a b^4 x^9+\frac{b^5 x^{12}}{12}",1,"-1/3*a^5/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",1
266,1,66,66,0.0047738,"\int \frac{\left(a+b x^3\right)^5}{x^7} \, dx","Integrate[(a + b*x^3)^5/x^7,x]","-\frac{a^5}{6 x^6}-\frac{5 a^4 b}{3 x^3}+10 a^3 b^2 \log (x)+\frac{10}{3} a^2 b^3 x^3+\frac{5}{6} a b^4 x^6+\frac{b^5 x^9}{9}","-\frac{a^5}{6 x^6}-\frac{5 a^4 b}{3 x^3}+10 a^3 b^2 \log (x)+\frac{10}{3} a^2 b^3 x^3+\frac{5}{6} a b^4 x^6+\frac{b^5 x^9}{9}",1,"-1/6*a^5/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",1
267,1,66,66,0.0066982,"\int \frac{\left(a+b x^3\right)^5}{x^{10}} \, dx","Integrate[(a + b*x^3)^5/x^10,x]","-\frac{a^5}{9 x^9}-\frac{5 a^4 b}{6 x^6}-\frac{10 a^3 b^2}{3 x^3}+10 a^2 b^3 \log (x)+\frac{5}{3} a b^4 x^3+\frac{b^5 x^6}{6}","-\frac{a^5}{9 x^9}-\frac{5 a^4 b}{6 x^6}-\frac{10 a^3 b^2}{3 x^3}+10 a^2 b^3 \log (x)+\frac{5}{3} a b^4 x^3+\frac{b^5 x^6}{6}",1,"-1/9*a^5/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",1
268,1,66,66,0.0049322,"\int \frac{\left(a+b x^3\right)^5}{x^{13}} \, dx","Integrate[(a + b*x^3)^5/x^13,x]","-\frac{a^5}{12 x^{12}}-\frac{5 a^4 b}{9 x^9}-\frac{5 a^3 b^2}{3 x^6}-\frac{10 a^2 b^3}{3 x^3}+5 a b^4 \log (x)+\frac{b^5 x^3}{3}","-\frac{a^5}{12 x^{12}}-\frac{5 a^4 b}{9 x^9}-\frac{5 a^3 b^2}{3 x^6}-\frac{10 a^2 b^3}{3 x^3}+5 a b^4 \log (x)+\frac{b^5 x^3}{3}",1,"-1/12*a^5/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",1
269,1,65,65,0.0047748,"\int \frac{\left(a+b x^3\right)^5}{x^{16}} \, dx","Integrate[(a + b*x^3)^5/x^16,x]","-\frac{a^5}{15 x^{15}}-\frac{5 a^4 b}{12 x^{12}}-\frac{10 a^3 b^2}{9 x^9}-\frac{5 a^2 b^3}{3 x^6}-\frac{5 a b^4}{3 x^3}+b^5 \log (x)","-\frac{a^5}{15 x^{15}}-\frac{5 a^4 b}{12 x^{12}}-\frac{10 a^3 b^2}{9 x^9}-\frac{5 a^2 b^3}{3 x^6}-\frac{5 a b^4}{3 x^3}+b^5 \log (x)",1,"-1/15*a^5/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",1
270,1,69,19,0.0044105,"\int \frac{\left(a+b x^3\right)^5}{x^{19}} \, dx","Integrate[(a + b*x^3)^5/x^19,x]","-\frac{a^5}{18 x^{18}}-\frac{a^4 b}{3 x^{15}}-\frac{5 a^3 b^2}{6 x^{12}}-\frac{10 a^2 b^3}{9 x^9}-\frac{5 a b^4}{6 x^6}-\frac{b^5}{3 x^3}","-\frac{\left(a+b x^3\right)^6}{18 a x^{18}}",1,"-1/18*a^5/x^18 - (a^4*b)/(3*x^15) - (5*a^3*b^2)/(6*x^12) - (10*a^2*b^3)/(9*x^9) - (5*a*b^4)/(6*x^6) - b^5/(3*x^3)","B",1
271,1,69,40,0.0209706,"\int \frac{\left(a+b x^3\right)^5}{x^{22}} \, dx","Integrate[(a + b*x^3)^5/x^22,x]","-\frac{a^5}{21 x^{21}}-\frac{5 a^4 b}{18 x^{18}}-\frac{2 a^3 b^2}{3 x^{15}}-\frac{5 a^2 b^3}{6 x^{12}}-\frac{5 a b^4}{9 x^9}-\frac{b^5}{6 x^6}","\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,"-1/21*a^5/x^21 - (5*a^4*b)/(18*x^18) - (2*a^3*b^2)/(3*x^15) - (5*a^2*b^3)/(6*x^12) - (5*a*b^4)/(9*x^9) - b^5/(6*x^6)","A",1
272,1,69,62,0.0071455,"\int \frac{\left(a+b x^3\right)^5}{x^{25}} \, dx","Integrate[(a + b*x^3)^5/x^25,x]","-\frac{a^5}{24 x^{24}}-\frac{5 a^4 b}{21 x^{21}}-\frac{5 a^3 b^2}{9 x^{18}}-\frac{2 a^2 b^3}{3 x^{15}}-\frac{5 a b^4}{12 x^{12}}-\frac{b^5}{9 x^9}","-\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,"-1/24*a^5/x^24 - (5*a^4*b)/(21*x^21) - (5*a^3*b^2)/(9*x^18) - (2*a^2*b^3)/(3*x^15) - (5*a*b^4)/(12*x^12) - b^5/(9*x^9)","A",1
273,1,69,69,0.0047739,"\int \frac{\left(a+b x^3\right)^5}{x^{28}} \, dx","Integrate[(a + b*x^3)^5/x^28,x]","-\frac{a^5}{27 x^{27}}-\frac{5 a^4 b}{24 x^{24}}-\frac{10 a^3 b^2}{21 x^{21}}-\frac{5 a^2 b^3}{9 x^{18}}-\frac{a b^4}{3 x^{15}}-\frac{b^5}{12 x^{12}}","-\frac{a^5}{27 x^{27}}-\frac{5 a^4 b}{24 x^{24}}-\frac{10 a^3 b^2}{21 x^{21}}-\frac{5 a^2 b^3}{9 x^{18}}-\frac{a b^4}{3 x^{15}}-\frac{b^5}{12 x^{12}}",1,"-1/27*a^5/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",1
274,1,69,69,0.0075146,"\int \frac{\left(a+b x^3\right)^5}{x^{31}} \, dx","Integrate[(a + b*x^3)^5/x^31,x]","-\frac{a^5}{30 x^{30}}-\frac{5 a^4 b}{27 x^{27}}-\frac{5 a^3 b^2}{12 x^{24}}-\frac{10 a^2 b^3}{21 x^{21}}-\frac{5 a b^4}{18 x^{18}}-\frac{b^5}{15 x^{15}}","-\frac{a^5}{30 x^{30}}-\frac{5 a^4 b}{27 x^{27}}-\frac{5 a^3 b^2}{12 x^{24}}-\frac{10 a^2 b^3}{21 x^{21}}-\frac{5 a b^4}{18 x^{18}}-\frac{b^5}{15 x^{15}}",1,"-1/30*a^5/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",1
275,1,69,69,0.0022152,"\int x^4 \left(a+b x^3\right)^5 \, dx","Integrate[x^4*(a + b*x^3)^5,x]","\frac{a^5 x^5}{5}+\frac{5}{8} a^4 b x^8+\frac{10}{11} a^3 b^2 x^{11}+\frac{5}{7} a^2 b^3 x^{14}+\frac{5}{17} a b^4 x^{17}+\frac{b^5 x^{20}}{20}","\frac{a^5 x^5}{5}+\frac{5}{8} a^4 b x^8+\frac{10}{11} a^3 b^2 x^{11}+\frac{5}{7} a^2 b^3 x^{14}+\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",1
276,1,66,66,0.0024963,"\int x^3 \left(a+b x^3\right)^5 \, dx","Integrate[x^3*(a + b*x^3)^5,x]","\frac{a^5 x^4}{4}+\frac{5}{7} a^4 b x^7+a^3 b^2 x^{10}+\frac{10}{13} a^2 b^3 x^{13}+\frac{5}{16} a b^4 x^{16}+\frac{b^5 x^{19}}{19}","\frac{a^5 x^4}{4}+\frac{5}{7} a^4 b x^7+a^3 b^2 x^{10}+\frac{10}{13} a^2 b^3 x^{13}+\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",1
277,1,66,66,0.0021033,"\int x \left(a+b x^3\right)^5 \, dx","Integrate[x*(a + b*x^3)^5,x]","\frac{a^5 x^2}{2}+a^4 b x^5+\frac{5}{4} a^3 b^2 x^8+\frac{10}{11} a^2 b^3 x^{11}+\frac{5}{14} a b^4 x^{14}+\frac{b^5 x^{17}}{17}","\frac{a^5 x^2}{2}+a^4 b x^5+\frac{5}{4} a^3 b^2 x^8+\frac{10}{11} a^2 b^3 x^{11}+\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",1
278,1,61,61,0.0011521,"\int \left(a+b x^3\right)^5 \, dx","Integrate[(a + b*x^3)^5,x]","a^5 x+\frac{5}{4} a^4 b x^4+\frac{10}{7} a^3 b^2 x^7+a^2 b^3 x^{10}+\frac{5}{13} a b^4 x^{13}+\frac{b^5 x^{16}}{16}","a^5 x+\frac{5}{4} a^4 b x^4+\frac{10}{7} a^3 b^2 x^7+a^2 b^3 x^{10}+\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",1
279,1,65,65,0.0042222,"\int \frac{\left(a+b x^3\right)^5}{x^2} \, dx","Integrate[(a + b*x^3)^5/x^2,x]","-\frac{a^5}{x}+\frac{5}{2} a^4 b x^2+2 a^3 b^2 x^5+\frac{5}{4} a^2 b^3 x^8+\frac{5}{11} a b^4 x^{11}+\frac{b^5 x^{14}}{14}","-\frac{a^5}{x}+\frac{5}{2} a^4 b x^2+2 a^3 b^2 x^5+\frac{5}{4} a^2 b^3 x^8+\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",1
280,1,65,65,0.0039964,"\int \frac{\left(a+b x^3\right)^5}{x^3} \, dx","Integrate[(a + b*x^3)^5/x^3,x]","-\frac{a^5}{2 x^2}+5 a^4 b x+\frac{5}{2} a^3 b^2 x^4+\frac{10}{7} a^2 b^3 x^7+\frac{1}{2} a b^4 x^{10}+\frac{b^5 x^{13}}{13}","-\frac{a^5}{2 x^2}+5 a^4 b x+\frac{5}{2} a^3 b^2 x^4+\frac{10}{7} a^2 b^3 x^7+\frac{1}{2} a b^4 x^{10}+\frac{b^5 x^{13}}{13}",1,"-1/2*a^5/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",1
281,1,63,63,0.0065355,"\int \frac{\left(a+b x^3\right)^5}{x^5} \, dx","Integrate[(a + b*x^3)^5/x^5,x]","-\frac{a^5}{4 x^4}-\frac{5 a^4 b}{x}+5 a^3 b^2 x^2+2 a^2 b^3 x^5+\frac{5}{8} a b^4 x^8+\frac{b^5 x^{11}}{11}","-\frac{a^5}{4 x^4}-\frac{5 a^4 b}{x}+5 a^3 b^2 x^2+2 a^2 b^3 x^5+\frac{5}{8} a b^4 x^8+\frac{b^5 x^{11}}{11}",1,"-1/4*a^5/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",1
282,1,65,65,0.0040643,"\int \frac{\left(a+b x^3\right)^5}{x^6} \, dx","Integrate[(a + b*x^3)^5/x^6,x]","-\frac{a^5}{5 x^5}-\frac{5 a^4 b}{2 x^2}+10 a^3 b^2 x+\frac{5}{2} a^2 b^3 x^4+\frac{5}{7} a b^4 x^7+\frac{b^5 x^{10}}{10}","-\frac{a^5}{5 x^5}-\frac{5 a^4 b}{2 x^2}+10 a^3 b^2 x+\frac{5}{2} a^2 b^3 x^4+\frac{5}{7} a b^4 x^7+\frac{b^5 x^{10}}{10}",1,"-1/5*a^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",1
283,1,62,62,0.0170777,"\int \frac{\left(a+b x^3\right)^5}{x^8} \, dx","Integrate[(a + b*x^3)^5/x^8,x]","-\frac{a^5}{7 x^7}-\frac{5 a^4 b}{4 x^4}-\frac{10 a^3 b^2}{x}+5 a^2 b^3 x^2+a b^4 x^5+\frac{b^5 x^8}{8}","-\frac{a^5}{7 x^7}-\frac{5 a^4 b}{4 x^4}-\frac{10 a^3 b^2}{x}+5 a^2 b^3 x^2+a b^4 x^5+\frac{b^5 x^8}{8}",1,"-1/7*a^5/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",1
284,1,61,61,0.0041253,"\int \frac{\left(a+b x^3\right)^5}{x^9} \, dx","Integrate[(a + b*x^3)^5/x^9,x]","-\frac{a^5}{8 x^8}-\frac{a^4 b}{x^5}-\frac{5 a^3 b^2}{x^2}+10 a^2 b^3 x+\frac{5}{4} a b^4 x^4+\frac{b^5 x^7}{7}","-\frac{a^5}{8 x^8}-\frac{a^4 b}{x^5}-\frac{5 a^3 b^2}{x^2}+10 a^2 b^3 x+\frac{5}{4} a b^4 x^4+\frac{b^5 x^7}{7}",1,"-1/8*a^5/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",1
285,1,108,129,0.0040872,"\int x^{20} \left(a+b x^3\right)^8 \, dx","Integrate[x^20*(a + b*x^3)^8,x]","\frac{a^8 x^{21}}{21}+\frac{1}{3} a^7 b x^{24}+\frac{28}{27} a^6 b^2 x^{27}+\frac{28}{15} a^5 b^3 x^{30}+\frac{70}{33} a^4 b^4 x^{33}+\frac{14}{9} a^3 b^5 x^{36}+\frac{28}{39} a^2 b^6 x^{39}+\frac{4}{21} a b^7 x^{42}+\frac{b^8 x^{45}}{45}","\frac{a^6 \left(a+b x^3\right)^9}{27 b^7}-\frac{a^5 \left(a+b x^3\right)^{10}}{5 b^7}+\frac{5 a^4 \left(a+b x^3\right)^{11}}{11 b^7}-\frac{5 a^3 \left(a+b x^3\right)^{12}}{9 b^7}+\frac{5 a^2 \left(a+b x^3\right)^{13}}{13 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^8*x^21)/21 + (a^7*b*x^24)/3 + (28*a^6*b^2*x^27)/27 + (28*a^5*b^3*x^30)/15 + (70*a^4*b^4*x^33)/33 + (14*a^3*b^5*x^36)/9 + (28*a^2*b^6*x^39)/39 + (4*a*b^7*x^42)/21 + (b^8*x^45)/45","A",1
286,1,108,110,0.0031759,"\int x^{17} \left(a+b x^3\right)^8 \, dx","Integrate[x^17*(a + b*x^3)^8,x]","\frac{a^8 x^{18}}{18}+\frac{8}{21} a^7 b x^{21}+\frac{7}{6} a^6 b^2 x^{24}+\frac{56}{27} a^5 b^3 x^{27}+\frac{7}{3} a^4 b^4 x^{30}+\frac{56}{33} a^3 b^5 x^{33}+\frac{7}{9} a^2 b^6 x^{36}+\frac{8}{39} a b^7 x^{39}+\frac{b^8 x^{42}}{42}","-\frac{a^5 \left(a+b x^3\right)^9}{27 b^6}+\frac{a^4 \left(a+b x^3\right)^{10}}{6 b^6}-\frac{10 a^3 \left(a+b x^3\right)^{11}}{33 b^6}+\frac{5 a^2 \left(a+b x^3\right)^{12}}{18 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^8*x^18)/18 + (8*a^7*b*x^21)/21 + (7*a^6*b^2*x^24)/6 + (56*a^5*b^3*x^27)/27 + (7*a^4*b^4*x^30)/3 + (56*a^3*b^5*x^33)/33 + (7*a^2*b^6*x^36)/9 + (8*a*b^7*x^39)/39 + (b^8*x^42)/42","A",1
287,1,108,91,0.0032087,"\int x^{14} \left(a+b x^3\right)^8 \, dx","Integrate[x^14*(a + b*x^3)^8,x]","\frac{a^8 x^{15}}{15}+\frac{4}{9} a^7 b x^{18}+\frac{4}{3} a^6 b^2 x^{21}+\frac{7}{3} a^5 b^3 x^{24}+\frac{70}{27} a^4 b^4 x^{27}+\frac{28}{15} a^3 b^5 x^{30}+\frac{28}{33} a^2 b^6 x^{33}+\frac{2}{9} a b^7 x^{36}+\frac{b^8 x^{39}}{39}","\frac{a^4 \left(a+b x^3\right)^9}{27 b^5}-\frac{2 a^3 \left(a+b x^3\right)^{10}}{15 b^5}+\frac{2 a^2 \left(a+b x^3\right)^{11}}{11 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^8*x^15)/15 + (4*a^7*b*x^18)/9 + (4*a^6*b^2*x^21)/3 + (7*a^5*b^3*x^24)/3 + (70*a^4*b^4*x^27)/27 + (28*a^3*b^5*x^30)/15 + (28*a^2*b^6*x^33)/33 + (2*a*b^7*x^36)/9 + (b^8*x^39)/39","A",1
288,1,108,72,0.0241413,"\int x^{11} \left(a+b x^3\right)^8 \, dx","Integrate[x^11*(a + b*x^3)^8,x]","\frac{a^8 x^{12}}{12}+\frac{8}{15} a^7 b x^{15}+\frac{14}{9} a^6 b^2 x^{18}+\frac{8}{3} a^5 b^3 x^{21}+\frac{35}{12} a^4 b^4 x^{24}+\frac{56}{27} a^3 b^5 x^{27}+\frac{14}{15} a^2 b^6 x^{30}+\frac{8}{33} a b^7 x^{33}+\frac{b^8 x^{36}}{36}","-\frac{a^3 \left(a+b x^3\right)^9}{27 b^4}+\frac{a^2 \left(a+b x^3\right)^{10}}{10 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^8*x^12)/12 + (8*a^7*b*x^15)/15 + (14*a^6*b^2*x^18)/9 + (8*a^5*b^3*x^21)/3 + (35*a^4*b^4*x^24)/12 + (56*a^3*b^5*x^27)/27 + (14*a^2*b^6*x^30)/15 + (8*a*b^7*x^33)/33 + (b^8*x^36)/36","A",1
289,1,108,53,0.0034474,"\int x^8 \left(a+b x^3\right)^8 \, dx","Integrate[x^8*(a + b*x^3)^8,x]","\frac{a^8 x^9}{9}+\frac{2}{3} a^7 b x^{12}+\frac{28}{15} a^6 b^2 x^{15}+\frac{28}{9} a^5 b^3 x^{18}+\frac{10}{3} a^4 b^4 x^{21}+\frac{7}{3} a^3 b^5 x^{24}+\frac{28}{27} a^2 b^6 x^{27}+\frac{4}{15} a b^7 x^{30}+\frac{b^8 x^{33}}{33}","\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^8*x^9)/9 + (2*a^7*b*x^12)/3 + (28*a^6*b^2*x^15)/15 + (28*a^5*b^3*x^18)/9 + (10*a^4*b^4*x^21)/3 + (7*a^3*b^5*x^24)/3 + (28*a^2*b^6*x^27)/27 + (4*a*b^7*x^30)/15 + (b^8*x^33)/33","B",1
290,1,108,34,0.0030604,"\int x^5 \left(a+b x^3\right)^8 \, dx","Integrate[x^5*(a + b*x^3)^8,x]","\frac{a^8 x^6}{6}+\frac{8}{9} a^7 b x^9+\frac{7}{3} a^6 b^2 x^{12}+\frac{56}{15} a^5 b^3 x^{15}+\frac{35}{9} a^4 b^4 x^{18}+\frac{8}{3} a^3 b^5 x^{21}+\frac{7}{6} a^2 b^6 x^{24}+\frac{8}{27} a b^7 x^{27}+\frac{b^8 x^{30}}{30}","\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^8*x^6)/6 + (8*a^7*b*x^9)/9 + (7*a^6*b^2*x^12)/3 + (56*a^5*b^3*x^15)/15 + (35*a^4*b^4*x^18)/9 + (8*a^3*b^5*x^21)/3 + (7*a^2*b^6*x^24)/6 + (8*a*b^7*x^27)/27 + (b^8*x^30)/30","B",1
291,1,108,16,0.0030069,"\int x^2 \left(a+b x^3\right)^8 \, dx","Integrate[x^2*(a + b*x^3)^8,x]","\frac{a^8 x^3}{3}+\frac{4}{3} a^7 b x^6+\frac{28}{9} a^6 b^2 x^9+\frac{14}{3} a^5 b^3 x^{12}+\frac{14}{3} a^4 b^4 x^{15}+\frac{28}{9} a^3 b^5 x^{18}+\frac{4}{3} a^2 b^6 x^{21}+\frac{1}{3} a b^7 x^{24}+\frac{b^8 x^{27}}{27}","\frac{\left(a+b x^3\right)^9}{27 b}",1,"(a^8*x^3)/3 + (4*a^7*b*x^6)/3 + (28*a^6*b^2*x^9)/9 + (14*a^5*b^3*x^12)/3 + (14*a^4*b^4*x^15)/3 + (28*a^3*b^5*x^18)/9 + (4*a^2*b^6*x^21)/3 + (a*b^7*x^24)/3 + (b^8*x^27)/27","B",1
292,1,104,104,0.0050279,"\int \frac{\left(a+b x^3\right)^8}{x} \, dx","Integrate[(a + b*x^3)^8/x,x]","a^8 \log (x)+\frac{8}{3} a^7 b x^3+\frac{14}{3} a^6 b^2 x^6+\frac{56}{9} a^5 b^3 x^9+\frac{35}{6} a^4 b^4 x^{12}+\frac{56}{15} a^3 b^5 x^{15}+\frac{14}{9} a^2 b^6 x^{18}+\frac{8}{21} a b^7 x^{21}+\frac{b^8 x^{24}}{24}","a^8 \log (x)+\frac{8}{3} a^7 b x^3+\frac{14}{3} a^6 b^2 x^6+\frac{56}{9} a^5 b^3 x^9+\frac{35}{6} a^4 b^4 x^{12}+\frac{56}{15} a^3 b^5 x^{15}+\frac{14}{9} a^2 b^6 x^{18}+\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",1
293,1,105,105,0.0099759,"\int \frac{\left(a+b x^3\right)^8}{x^4} \, dx","Integrate[(a + b*x^3)^8/x^4,x]","-\frac{a^8}{3 x^3}+8 a^7 b \log (x)+\frac{28}{3} a^6 b^2 x^3+\frac{28}{3} a^5 b^3 x^6+\frac{70}{9} a^4 b^4 x^9+\frac{14}{3} a^3 b^5 x^{12}+\frac{28}{15} a^2 b^6 x^{15}+\frac{4}{9} a b^7 x^{18}+\frac{b^8 x^{21}}{21}","-\frac{a^8}{3 x^3}+8 a^7 b \log (x)+\frac{28}{3} a^6 b^2 x^3+\frac{28}{3} a^5 b^3 x^6+\frac{70}{9} a^4 b^4 x^9+\frac{14}{3} a^3 b^5 x^{12}+\frac{28}{15} a^2 b^6 x^{15}+\frac{4}{9} a b^7 x^{18}+\frac{b^8 x^{21}}{21}",1,"-1/3*a^8/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",1
294,1,105,105,0.0054542,"\int \frac{\left(a+b x^3\right)^8}{x^7} \, dx","Integrate[(a + b*x^3)^8/x^7,x]","-\frac{a^8}{6 x^6}-\frac{8 a^7 b}{3 x^3}+28 a^6 b^2 \log (x)+\frac{56}{3} a^5 b^3 x^3+\frac{35}{3} a^4 b^4 x^6+\frac{56}{9} a^3 b^5 x^9+\frac{7}{3} a^2 b^6 x^{12}+\frac{8}{15} a b^7 x^{15}+\frac{b^8 x^{18}}{18}","-\frac{a^8}{6 x^6}-\frac{8 a^7 b}{3 x^3}+28 a^6 b^2 \log (x)+\frac{56}{3} a^5 b^3 x^3+\frac{35}{3} a^4 b^4 x^6+\frac{56}{9} a^3 b^5 x^9+\frac{7}{3} a^2 b^6 x^{12}+\frac{8}{15} a b^7 x^{15}+\frac{b^8 x^{18}}{18}",1,"-1/6*a^8/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",1
295,1,105,105,0.0108523,"\int \frac{\left(a+b x^3\right)^8}{x^{10}} \, dx","Integrate[(a + b*x^3)^8/x^10,x]","-\frac{a^8}{9 x^9}-\frac{4 a^7 b}{3 x^6}-\frac{28 a^6 b^2}{3 x^3}+56 a^5 b^3 \log (x)+\frac{70}{3} a^4 b^4 x^3+\frac{28}{3} a^3 b^5 x^6+\frac{28}{9} a^2 b^6 x^9+\frac{2}{3} a b^7 x^{12}+\frac{b^8 x^{15}}{15}","-\frac{a^8}{9 x^9}-\frac{4 a^7 b}{3 x^6}-\frac{28 a^6 b^2}{3 x^3}+56 a^5 b^3 \log (x)+\frac{70}{3} a^4 b^4 x^3+\frac{28}{3} a^3 b^5 x^6+\frac{28}{9} a^2 b^6 x^9+\frac{2}{3} a b^7 x^{12}+\frac{b^8 x^{15}}{15}",1,"-1/9*a^8/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",1
296,1,105,105,0.0054713,"\int \frac{\left(a+b x^3\right)^8}{x^{13}} \, dx","Integrate[(a + b*x^3)^8/x^13,x]","-\frac{a^8}{12 x^{12}}-\frac{8 a^7 b}{9 x^9}-\frac{14 a^6 b^2}{3 x^6}-\frac{56 a^5 b^3}{3 x^3}+70 a^4 b^4 \log (x)+\frac{56}{3} a^3 b^5 x^3+\frac{14}{3} a^2 b^6 x^6+\frac{8}{9} a b^7 x^9+\frac{b^8 x^{12}}{12}","-\frac{a^8}{12 x^{12}}-\frac{8 a^7 b}{9 x^9}-\frac{14 a^6 b^2}{3 x^6}-\frac{56 a^5 b^3}{3 x^3}+70 a^4 b^4 \log (x)+\frac{56}{3} a^3 b^5 x^3+\frac{14}{3} a^2 b^6 x^6+\frac{8}{9} a b^7 x^9+\frac{b^8 x^{12}}{12}",1,"-1/12*a^8/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",1
297,1,105,105,0.0075927,"\int \frac{\left(a+b x^3\right)^8}{x^{16}} \, dx","Integrate[(a + b*x^3)^8/x^16,x]","-\frac{a^8}{15 x^{15}}-\frac{2 a^7 b}{3 x^{12}}-\frac{28 a^6 b^2}{9 x^9}-\frac{28 a^5 b^3}{3 x^6}-\frac{70 a^4 b^4}{3 x^3}+56 a^3 b^5 \log (x)+\frac{28}{3} a^2 b^6 x^3+\frac{4}{3} a b^7 x^6+\frac{b^8 x^9}{9}","-\frac{a^8}{15 x^{15}}-\frac{2 a^7 b}{3 x^{12}}-\frac{28 a^6 b^2}{9 x^9}-\frac{28 a^5 b^3}{3 x^6}-\frac{70 a^4 b^4}{3 x^3}+56 a^3 b^5 \log (x)+\frac{28}{3} a^2 b^6 x^3+\frac{4}{3} a b^7 x^6+\frac{b^8 x^9}{9}",1,"-1/15*a^8/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",1
298,1,105,105,0.005534,"\int \frac{\left(a+b x^3\right)^8}{x^{19}} \, dx","Integrate[(a + b*x^3)^8/x^19,x]","-\frac{a^8}{18 x^{18}}-\frac{8 a^7 b}{15 x^{15}}-\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}{3} a b^7 x^3+\frac{b^8 x^6}{6}","-\frac{a^8}{18 x^{18}}-\frac{8 a^7 b}{15 x^{15}}-\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}{3} a b^7 x^3+\frac{b^8 x^6}{6}",1,"-1/18*a^8/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",1
299,1,105,105,0.0111532,"\int \frac{\left(a+b x^3\right)^8}{x^{22}} \, dx","Integrate[(a + b*x^3)^8/x^22,x]","-\frac{a^8}{21 x^{21}}-\frac{4 a^7 b}{9 x^{18}}-\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}+8 a b^7 \log (x)+\frac{b^8 x^3}{3}","-\frac{a^8}{21 x^{21}}-\frac{4 a^7 b}{9 x^{18}}-\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}+8 a b^7 \log (x)+\frac{b^8 x^3}{3}",1,"-1/21*a^8/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",1
300,1,104,104,0.005299,"\int \frac{\left(a+b x^3\right)^8}{x^{25}} \, dx","Integrate[(a + b*x^3)^8/x^25,x]","-\frac{a^8}{24 x^{24}}-\frac{8 a^7 b}{21 x^{21}}-\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 b^7}{3 x^3}+b^8 \log (x)","-\frac{a^8}{24 x^{24}}-\frac{8 a^7 b}{21 x^{21}}-\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 b^7}{3 x^3}+b^8 \log (x)",1,"-1/24*a^8/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",1
301,1,108,19,0.0094071,"\int \frac{\left(a+b x^3\right)^8}{x^{28}} \, dx","Integrate[(a + b*x^3)^8/x^28,x]","-\frac{a^8}{27 x^{27}}-\frac{a^7 b}{3 x^{24}}-\frac{4 a^6 b^2}{3 x^{21}}-\frac{28 a^5 b^3}{9 x^{18}}-\frac{14 a^4 b^4}{3 x^{15}}-\frac{14 a^3 b^5}{3 x^{12}}-\frac{28 a^2 b^6}{9 x^9}-\frac{4 a b^7}{3 x^6}-\frac{b^8}{3 x^3}","-\frac{\left(a+b x^3\right)^9}{27 a x^{27}}",1,"-1/27*a^8/x^27 - (a^7*b)/(3*x^24) - (4*a^6*b^2)/(3*x^21) - (28*a^5*b^3)/(9*x^18) - (14*a^4*b^4)/(3*x^15) - (14*a^3*b^5)/(3*x^12) - (28*a^2*b^6)/(9*x^9) - (4*a*b^7)/(3*x^6) - b^8/(3*x^3)","B",1
302,1,108,40,0.0047193,"\int \frac{\left(a+b x^3\right)^8}{x^{31}} \, dx","Integrate[(a + b*x^3)^8/x^31,x]","-\frac{a^8}{30 x^{30}}-\frac{8 a^7 b}{27 x^{27}}-\frac{7 a^6 b^2}{6 x^{24}}-\frac{8 a^5 b^3}{3 x^{21}}-\frac{35 a^4 b^4}{9 x^{18}}-\frac{56 a^3 b^5}{15 x^{15}}-\frac{7 a^2 b^6}{3 x^{12}}-\frac{8 a b^7}{9 x^9}-\frac{b^8}{6 x^6}","\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,"-1/30*a^8/x^30 - (8*a^7*b)/(27*x^27) - (7*a^6*b^2)/(6*x^24) - (8*a^5*b^3)/(3*x^21) - (35*a^4*b^4)/(9*x^18) - (56*a^3*b^5)/(15*x^15) - (7*a^2*b^6)/(3*x^12) - (8*a*b^7)/(9*x^9) - b^8/(6*x^6)","B",1
303,1,108,62,0.0104772,"\int \frac{\left(a+b x^3\right)^8}{x^{34}} \, dx","Integrate[(a + b*x^3)^8/x^34,x]","-\frac{a^8}{33 x^{33}}-\frac{4 a^7 b}{15 x^{30}}-\frac{28 a^6 b^2}{27 x^{27}}-\frac{7 a^5 b^3}{3 x^{24}}-\frac{10 a^4 b^4}{3 x^{21}}-\frac{28 a^3 b^5}{9 x^{18}}-\frac{28 a^2 b^6}{15 x^{15}}-\frac{2 a b^7}{3 x^{12}}-\frac{b^8}{9 x^9}","-\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,"-1/33*a^8/x^33 - (4*a^7*b)/(15*x^30) - (28*a^6*b^2)/(27*x^27) - (7*a^5*b^3)/(3*x^24) - (10*a^4*b^4)/(3*x^21) - (28*a^3*b^5)/(9*x^18) - (28*a^2*b^6)/(15*x^15) - (2*a*b^7)/(3*x^12) - b^8/(9*x^9)","A",1
304,1,108,84,0.005087,"\int \frac{\left(a+b x^3\right)^8}{x^{37}} \, dx","Integrate[(a + b*x^3)^8/x^37,x]","-\frac{a^8}{36 x^{36}}-\frac{8 a^7 b}{33 x^{33}}-\frac{14 a^6 b^2}{15 x^{30}}-\frac{56 a^5 b^3}{27 x^{27}}-\frac{35 a^4 b^4}{12 x^{24}}-\frac{8 a^3 b^5}{3 x^{21}}-\frac{14 a^2 b^6}{9 x^{18}}-\frac{8 a b^7}{15 x^{15}}-\frac{b^8}{12 x^{12}}","\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,"-1/36*a^8/x^36 - (8*a^7*b)/(33*x^33) - (14*a^6*b^2)/(15*x^30) - (56*a^5*b^3)/(27*x^27) - (35*a^4*b^4)/(12*x^24) - (8*a^3*b^5)/(3*x^21) - (14*a^2*b^6)/(9*x^18) - (8*a*b^7)/(15*x^15) - b^8/(12*x^12)","A",1
305,1,108,106,0.0073752,"\int \frac{\left(a+b x^3\right)^8}{x^{40}} \, dx","Integrate[(a + b*x^3)^8/x^40,x]","-\frac{a^8}{39 x^{39}}-\frac{2 a^7 b}{9 x^{36}}-\frac{28 a^6 b^2}{33 x^{33}}-\frac{28 a^5 b^3}{15 x^{30}}-\frac{70 a^4 b^4}{27 x^{27}}-\frac{7 a^3 b^5}{3 x^{24}}-\frac{4 a^2 b^6}{3 x^{21}}-\frac{4 a b^7}{9 x^{18}}-\frac{b^8}{15 x^{15}}","-\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,"-1/39*a^8/x^39 - (2*a^7*b)/(9*x^36) - (28*a^6*b^2)/(33*x^33) - (28*a^5*b^3)/(15*x^30) - (70*a^4*b^4)/(27*x^27) - (7*a^3*b^5)/(3*x^24) - (4*a^2*b^6)/(3*x^21) - (4*a*b^7)/(9*x^18) - b^8/(15*x^15)","A",1
306,1,108,108,0.0050758,"\int \frac{\left(a+b x^3\right)^8}{x^{43}} \, dx","Integrate[(a + b*x^3)^8/x^43,x]","-\frac{a^8}{42 x^{42}}-\frac{8 a^7 b}{39 x^{39}}-\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 b^7}{21 x^{21}}-\frac{b^8}{18 x^{18}}","-\frac{a^8}{42 x^{42}}-\frac{8 a^7 b}{39 x^{39}}-\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 b^7}{21 x^{21}}-\frac{b^8}{18 x^{18}}",1,"-1/42*a^8/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",1
307,1,108,108,0.0102339,"\int \frac{\left(a+b x^3\right)^8}{x^{46}} \, dx","Integrate[(a + b*x^3)^8/x^46,x]","-\frac{a^8}{45 x^{45}}-\frac{4 a^7 b}{21 x^{42}}-\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{a b^7}{3 x^{24}}-\frac{b^8}{21 x^{21}}","-\frac{a^8}{45 x^{45}}-\frac{4 a^7 b}{21 x^{42}}-\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{a b^7}{3 x^{24}}-\frac{b^8}{21 x^{21}}",1,"-1/45*a^8/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",1
308,1,103,103,0.003086,"\int x^4 \left(a+b x^3\right)^8 \, dx","Integrate[x^4*(a + b*x^3)^8,x]","\frac{a^8 x^5}{5}+a^7 b x^8+\frac{28}{11} a^6 b^2 x^{11}+4 a^5 b^3 x^{14}+\frac{70}{17} a^4 b^4 x^{17}+\frac{14}{5} a^3 b^5 x^{20}+\frac{28}{23} a^2 b^6 x^{23}+\frac{4}{13} a b^7 x^{26}+\frac{b^8 x^{29}}{29}","\frac{a^8 x^5}{5}+a^7 b x^8+\frac{28}{11} a^6 b^2 x^{11}+4 a^5 b^3 x^{14}+\frac{70}{17} a^4 b^4 x^{17}+\frac{14}{5} a^3 b^5 x^{20}+\frac{28}{23} a^2 b^6 x^{23}+\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",1
309,1,108,108,0.0030194,"\int x^3 \left(a+b x^3\right)^8 \, dx","Integrate[x^3*(a + b*x^3)^8,x]","\frac{a^8 x^4}{4}+\frac{8}{7} a^7 b x^7+\frac{14}{5} a^6 b^2 x^{10}+\frac{56}{13} a^5 b^3 x^{13}+\frac{35}{8} a^4 b^4 x^{16}+\frac{56}{19} a^3 b^5 x^{19}+\frac{14}{11} a^2 b^6 x^{22}+\frac{8}{25} a b^7 x^{25}+\frac{b^8 x^{28}}{28}","\frac{a^8 x^4}{4}+\frac{8}{7} a^7 b x^7+\frac{14}{5} a^6 b^2 x^{10}+\frac{56}{13} a^5 b^3 x^{13}+\frac{35}{8} a^4 b^4 x^{16}+\frac{56}{19} a^3 b^5 x^{19}+\frac{14}{11} a^2 b^6 x^{22}+\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",1
310,1,106,106,0.0027516,"\int x \left(a+b x^3\right)^8 \, dx","Integrate[x*(a + b*x^3)^8,x]","\frac{a^8 x^2}{2}+\frac{8}{5} a^7 b x^5+\frac{7}{2} a^6 b^2 x^8+\frac{56}{11} a^5 b^3 x^{11}+5 a^4 b^4 x^{14}+\frac{56}{17} a^3 b^5 x^{17}+\frac{7}{5} a^2 b^6 x^{20}+\frac{8}{23} a b^7 x^{23}+\frac{b^8 x^{26}}{26}","\frac{a^8 x^2}{2}+\frac{8}{5} a^7 b x^5+\frac{7}{2} a^6 b^2 x^8+\frac{56}{11} a^5 b^3 x^{11}+5 a^4 b^4 x^{14}+\frac{56}{17} a^3 b^5 x^{17}+\frac{7}{5} a^2 b^6 x^{20}+\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",1
311,1,99,99,0.0016639,"\int \left(a+b x^3\right)^8 \, dx","Integrate[(a + b*x^3)^8,x]","a^8 x+2 a^7 b x^4+4 a^6 b^2 x^7+\frac{28}{5} a^5 b^3 x^{10}+\frac{70}{13} a^4 b^4 x^{13}+\frac{7}{2} a^3 b^5 x^{16}+\frac{28}{19} a^2 b^6 x^{19}+\frac{4}{11} a b^7 x^{22}+\frac{b^8 x^{25}}{25}","a^8 x+2 a^7 b x^4+4 a^6 b^2 x^7+\frac{28}{5} a^5 b^3 x^{10}+\frac{70}{13} a^4 b^4 x^{13}+\frac{7}{2} a^3 b^5 x^{16}+\frac{28}{19} a^2 b^6 x^{19}+\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",1
312,1,100,100,0.0102168,"\int \frac{\left(a+b x^3\right)^8}{x^2} \, dx","Integrate[(a + b*x^3)^8/x^2,x]","-\frac{a^8}{x}+4 a^7 b x^2+\frac{28}{5} a^6 b^2 x^5+7 a^5 b^3 x^8+\frac{70}{11} a^4 b^4 x^{11}+4 a^3 b^5 x^{14}+\frac{28}{17} a^2 b^6 x^{17}+\frac{2}{5} a b^7 x^{20}+\frac{b^8 x^{23}}{23}","-\frac{a^8}{x}+4 a^7 b x^2+\frac{28}{5} a^6 b^2 x^5+7 a^5 b^3 x^8+\frac{70}{11} a^4 b^4 x^{11}+4 a^3 b^5 x^{14}+\frac{28}{17} a^2 b^6 x^{17}+\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",1
313,1,98,98,0.0051034,"\int \frac{\left(a+b x^3\right)^8}{x^3} \, dx","Integrate[(a + b*x^3)^8/x^3,x]","-\frac{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}+\frac{56}{13} a^3 b^5 x^{13}+\frac{7}{4} a^2 b^6 x^{16}+\frac{8}{19} a b^7 x^{19}+\frac{b^8 x^{22}}{22}","-\frac{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}+\frac{56}{13} a^3 b^5 x^{13}+\frac{7}{4} a^2 b^6 x^{16}+\frac{8}{19} a b^7 x^{19}+\frac{b^8 x^{22}}{22}",1,"-1/2*a^8/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",1
314,1,102,102,0.0052198,"\int \frac{\left(a+b x^3\right)^8}{x^5} \, dx","Integrate[(a + b*x^3)^8/x^5,x]","-\frac{a^8}{4 x^4}-\frac{8 a^7 b}{x}+14 a^6 b^2 x^2+\frac{56}{5} a^5 b^3 x^5+\frac{35}{4} a^4 b^4 x^8+\frac{56}{11} a^3 b^5 x^{11}+2 a^2 b^6 x^{14}+\frac{8}{17} a b^7 x^{17}+\frac{b^8 x^{20}}{20}","-\frac{a^8}{4 x^4}-\frac{8 a^7 b}{x}+14 a^6 b^2 x^2+\frac{56}{5} a^5 b^3 x^5+\frac{35}{4} a^4 b^4 x^8+\frac{56}{11} a^3 b^5 x^{11}+2 a^2 b^6 x^{14}+\frac{8}{17} a b^7 x^{17}+\frac{b^8 x^{20}}{20}",1,"-1/4*a^8/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",1
315,1,98,98,0.0099852,"\int \frac{\left(a+b x^3\right)^8}{x^6} \, dx","Integrate[(a + b*x^3)^8/x^6,x]","-\frac{a^8}{5 x^5}-\frac{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+\frac{28}{5} a^3 b^5 x^{10}+\frac{28}{13} a^2 b^6 x^{13}+\frac{1}{2} a b^7 x^{16}+\frac{b^8 x^{19}}{19}","-\frac{a^8}{5 x^5}-\frac{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+\frac{28}{5} a^3 b^5 x^{10}+\frac{28}{13} a^2 b^6 x^{13}+\frac{1}{2} a b^7 x^{16}+\frac{b^8 x^{19}}{19}",1,"-1/5*a^8/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",1
316,1,98,98,0.0070145,"\int \frac{\left(a+b x^3\right)^8}{x^8} \, dx","Integrate[(a + b*x^3)^8/x^8,x]","-\frac{a^8}{7 x^7}-\frac{2 a^7 b}{x^4}-\frac{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+\frac{28}{11} a^2 b^6 x^{11}+\frac{4}{7} a b^7 x^{14}+\frac{b^8 x^{17}}{17}","-\frac{a^8}{7 x^7}-\frac{2 a^7 b}{x^4}-\frac{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+\frac{28}{11} a^2 b^6 x^{11}+\frac{4}{7} a b^7 x^{14}+\frac{b^8 x^{17}}{17}",1,"-1/7*a^8/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",1
317,1,100,100,0.0048722,"\int \frac{\left(a+b x^3\right)^8}{x^9} \, dx","Integrate[(a + b*x^3)^8/x^9,x]","-\frac{a^8}{8 x^8}-\frac{8 a^7 b}{5 x^5}-\frac{14 a^6 b^2}{x^2}+56 a^5 b^3 x+\frac{35}{2} a^4 b^4 x^4+8 a^3 b^5 x^7+\frac{14}{5} a^2 b^6 x^{10}+\frac{8}{13} a b^7 x^{13}+\frac{b^8 x^{16}}{16}","-\frac{a^8}{8 x^8}-\frac{8 a^7 b}{5 x^5}-\frac{14 a^6 b^2}{x^2}+56 a^5 b^3 x+\frac{35}{2} a^4 b^4 x^4+8 a^3 b^5 x^7+\frac{14}{5} a^2 b^6 x^{10}+\frac{8}{13} a b^7 x^{13}+\frac{b^8 x^{16}}{16}",1,"-1/8*a^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",1
318,1,40,40,0.0062852,"\int \frac{x^8}{a+b x^3} \, dx","Integrate[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,"-1/3*(a*x^3)/b^2 + x^6/(6*b) + (a^2*Log[a + b*x^3])/(3*b^3)","A",1
319,1,27,27,0.0044895,"\int \frac{x^5}{a+b x^3} \, dx","Integrate[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",1
320,1,15,15,0.0028609,"\int \frac{x^2}{a+b x^3} \, dx","Integrate[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
321,1,22,22,0.005328,"\int \frac{1}{x \left(a+b x^3\right)} \, dx","Integrate[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",1
322,1,35,35,0.0069267,"\int \frac{1}{x^4 \left(a+b x^3\right)} \, dx","Integrate[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*1/(a*x^3) - (b*Log[x])/a^2 + (b*Log[a + b*x^3])/(3*a^2)","A",1
323,1,111,124,0.0607814,"\int \frac{x^4}{a+b x^3} \, dx","Integrate[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)+2 a^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)+2 \sqrt{3} a^{2/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a}}}{\sqrt{3}}\right)+3 b^{2/3} x^2}{6 b^{5/3}}","-\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,"(3*b^(2/3)*x^2 + 2*Sqrt[3]*a^(2/3)*ArcTan[(1 - (2*b^(1/3)*x)/a^(1/3))/Sqrt[3]] + 2*a^(2/3)*Log[a^(1/3) + b^(1/3)*x] - a^(2/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*b^(5/3))","A",1
324,1,108,119,0.0163757,"\int \frac{x^3}{a+b x^3} \, dx","Integrate[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)-2 \sqrt[3]{a} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)+2 \sqrt{3} \sqrt[3]{a} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a}}}{\sqrt{3}}\right)+6 \sqrt[3]{b} x}{6 b^{4/3}}","\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,"(6*b^(1/3)*x + 2*Sqrt[3]*a^(1/3)*ArcTan[(1 - (2*b^(1/3)*x)/a^(1/3))/Sqrt[3]] - 2*a^(1/3)*Log[a^(1/3) + b^(1/3)*x] + a^(1/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*b^(4/3))","A",1
325,1,89,115,0.0109128,"\int \frac{x}{a+b x^3} \, dx","Integrate[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)-2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)-2 \sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a}}}{\sqrt{3}}\right)}{6 \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,"(-2*Sqrt[3]*ArcTan[(1 - (2*b^(1/3)*x)/a^(1/3))/Sqrt[3]] - 2*Log[a^(1/3) + b^(1/3)*x] + Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(1/3)*b^(2/3))","A",1
326,1,89,115,0.0122521,"\int \frac{1}{a+b x^3} \, dx","Integrate[(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)-2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a}}}{\sqrt{3}}\right)}{6 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,"-1/6*(2*Sqrt[3]*ArcTan[(1 - (2*b^(1/3)*x)/a^(1/3))/Sqrt[3]] - 2*Log[a^(1/3) + b^(1/3)*x] + Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(a^(2/3)*b^(1/3))","A",1
327,1,114,122,0.0188172,"\int \frac{1}{x^2 \left(a+b x^3\right)} \, dx","Integrate[1/(x^2*(a + b*x^3)),x]","\frac{-\sqrt[3]{b} x \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)+2 \sqrt[3]{b} x \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)+2 \sqrt{3} \sqrt[3]{b} x \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a}}}{\sqrt{3}}\right)-6 \sqrt[3]{a}}{6 a^{4/3} 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}",1,"(-6*a^(1/3) + 2*Sqrt[3]*b^(1/3)*x*ArcTan[(1 - (2*b^(1/3)*x)/a^(1/3))/Sqrt[3]] + 2*b^(1/3)*x*Log[a^(1/3) + b^(1/3)*x] - b^(1/3)*x*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(4/3)*x)","A",1
328,1,119,124,0.0210699,"\int \frac{1}{x^3 \left(a+b x^3\right)} \, dx","Integrate[1/(x^3*(a + b*x^3)),x]","\frac{b^{2/3} x^2 \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)-3 a^{2/3}-2 b^{2/3} x^2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)+2 \sqrt{3} b^{2/3} x^2 \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a}}}{\sqrt{3}}\right)}{6 a^{5/3} 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,"(-3*a^(2/3) + 2*Sqrt[3]*b^(2/3)*x^2*ArcTan[(1 - (2*b^(1/3)*x)/a^(1/3))/Sqrt[3]] - 2*b^(2/3)*x^2*Log[a^(1/3) + b^(1/3)*x] + b^(2/3)*x^2*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(5/3)*x^2)","A",1
329,1,38,46,0.0179835,"\int \frac{x^8}{\left(a+b x^3\right)^2} \, dx","Integrate[x^8/(a + b*x^3)^2,x]","\frac{-\frac{a^2}{a+b x^3}-2 a \log \left(a+b x^3\right)+b x^3}{3 b^3}","-\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,"(b*x^3 - a^2/(a + b*x^3) - 2*a*Log[a + b*x^3])/(3*b^3)","A",1
330,1,27,33,0.0088014,"\int \frac{x^5}{\left(a+b x^3\right)^2} \, dx","Integrate[x^5/(a + b*x^3)^2,x]","\frac{\frac{a}{a+b x^3}+\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/(a + b*x^3) + Log[a + b*x^3])/(3*b^2)","A",1
331,1,16,16,0.0049909,"\int \frac{x^2}{\left(a+b x^3\right)^2} \, dx","Integrate[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*1/(b*(a + b*x^3))","A",1
332,1,33,38,0.0158938,"\int \frac{1}{x \left(a+b x^3\right)^2} \, dx","Integrate[1/(x*(a + b*x^3)^2),x]","\frac{\frac{a}{a+b x^3}-\log \left(a+b x^3\right)+3 \log (x)}{3 a^2}","-\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,"(a/(a + b*x^3) + 3*Log[x] - Log[a + b*x^3])/(3*a^2)","A",1
333,1,41,52,0.0417875,"\int \frac{1}{x^4 \left(a+b x^3\right)^2} \, dx","Integrate[1/(x^4*(a + b*x^3)^2),x]","-\frac{a \left(\frac{b}{a+b x^3}+\frac{1}{x^3}\right)-2 b \log \left(a+b x^3\right)+6 b \log (x)}{3 a^3}","\frac{2 b \log \left(a+b x^3\right)}{3 a^3}-\frac{2 b \log (x)}{a^3}-\frac{b}{3 a^2 \left(a+b x^3\right)}-\frac{1}{3 a^2 x^3}",1,"-1/3*(a*(x^(-3) + b/(a + b*x^3)) + 6*b*Log[x] - 2*b*Log[a + b*x^3])/a^3","A",1
334,1,119,136,0.0803753,"\int \frac{x^4}{\left(a+b x^3\right)^2} \, dx","Integrate[x^4/(a + b*x^3)^2,x]","\frac{\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{\sqrt[3]{a}}-\frac{3 b^{2/3} x^2}{a+b x^3}-\frac{2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a}}-\frac{2 \sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a}}}{\sqrt{3}}\right)}{\sqrt[3]{a}}}{9 b^{5/3}}","\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,"((-3*b^(2/3)*x^2)/(a + b*x^3) - (2*Sqrt[3]*ArcTan[(1 - (2*b^(1/3)*x)/a^(1/3))/Sqrt[3]])/a^(1/3) - (2*Log[a^(1/3) + b^(1/3)*x])/a^(1/3) + Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2]/a^(1/3))/(9*b^(5/3))","A",1
335,1,118,134,0.0646718,"\int \frac{x^3}{\left(a+b x^3\right)^2} \, dx","Integrate[x^3/(a + b*x^3)^2,x]","\frac{-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{a^{2/3}}+\frac{2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{a^{2/3}}-\frac{2 \sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a}}}{\sqrt{3}}\right)}{a^{2/3}}-\frac{6 \sqrt[3]{b} x}{a+b x^3}}{18 b^{4/3}}","-\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,"((-6*b^(1/3)*x)/(a + b*x^3) - (2*Sqrt[3]*ArcTan[(1 - (2*b^(1/3)*x)/a^(1/3))/Sqrt[3]])/a^(2/3) + (2*Log[a^(1/3) + b^(1/3)*x])/a^(2/3) - Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2]/a^(2/3))/(18*b^(4/3))","A",1
336,1,119,136,0.0620092,"\int \frac{x}{\left(a+b x^3\right)^2} \, dx","Integrate[x/(a + b*x^3)^2,x]","\frac{\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{b^{2/3}}-\frac{2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{b^{2/3}}-\frac{2 \sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a}}}{\sqrt{3}}\right)}{b^{2/3}}+\frac{6 \sqrt[3]{a} x^2}{a+b x^3}}{18 a^{4/3}}","\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,"((6*a^(1/3)*x^2)/(a + b*x^3) - (2*Sqrt[3]*ArcTan[(1 - (2*b^(1/3)*x)/a^(1/3))/Sqrt[3]])/b^(2/3) - (2*Log[a^(1/3) + b^(1/3)*x])/b^(2/3) + Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2]/b^(2/3))/(18*a^(4/3))","A",1
337,1,118,134,0.0604462,"\int \frac{1}{\left(a+b x^3\right)^2} \, dx","Integrate[(a + b*x^3)^(-2),x]","\frac{-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{\sqrt[3]{b}}+\frac{3 a^{2/3} x}{a+b x^3}+\frac{2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b}}-\frac{2 \sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a}}}{\sqrt{3}}\right)}{\sqrt[3]{b}}}{9 a^{5/3}}","-\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,"((3*a^(2/3)*x)/(a + b*x^3) - (2*Sqrt[3]*ArcTan[(1 - (2*b^(1/3)*x)/a^(1/3))/Sqrt[3]])/b^(1/3) + (2*Log[a^(1/3) + b^(1/3)*x])/b^(1/3) - Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2]/b^(1/3))/(9*a^(5/3))","A",1
338,1,131,146,0.0890005,"\int \frac{1}{x^2 \left(a+b x^3\right)^2} \, dx","Integrate[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)-\frac{3 \sqrt[3]{a} b x^2}{a+b x^3}+4 \sqrt[3]{b} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)+4 \sqrt{3} \sqrt[3]{b} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a}}}{\sqrt{3}}\right)-\frac{9 \sqrt[3]{a}}{x}}{9 a^{7/3}}","-\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,"((-9*a^(1/3))/x - (3*a^(1/3)*b*x^2)/(a + b*x^3) + 4*Sqrt[3]*b^(1/3)*ArcTan[(1 - (2*b^(1/3)*x)/a^(1/3))/Sqrt[3]] + 4*b^(1/3)*Log[a^(1/3) + b^(1/3)*x] - 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",1
339,1,129,146,0.0906073,"\int \frac{1}{x^3 \left(a+b x^3\right)^2} \, dx","Integrate[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)-\frac{6 a^{2/3} b x}{a+b x^3}-\frac{9 a^{2/3}}{x^2}-10 b^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)+10 \sqrt{3} b^{2/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a}}}{\sqrt{3}}\right)}{18 a^{8/3}}","\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,"((-9*a^(2/3))/x^2 - (6*a^(2/3)*b*x)/(a + b*x^3) + 10*Sqrt[3]*b^(2/3)*ArcTan[(1 - (2*b^(1/3)*x)/a^(1/3))/Sqrt[3]] - 10*b^(2/3)*Log[a^(1/3) + b^(1/3)*x] + 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",1
340,1,48,61,0.0577966,"\int \frac{x^{11}}{\left(a+b x^3\right)^3} \, dx","Integrate[x^11/(a + b*x^3)^3,x]","-\frac{\frac{a^2 \left(5 a+6 b x^3\right)}{\left(a+b x^3\right)^2}+6 a \log \left(a+b x^3\right)-2 b x^3}{6 b^4}","\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,"-1/6*(-2*b*x^3 + (a^2*(5*a + 6*b*x^3))/(a + b*x^3)^2 + 6*a*Log[a + b*x^3])/b^4","A",1
341,1,39,52,0.0157855,"\int \frac{x^8}{\left(a+b x^3\right)^3} \, dx","Integrate[x^8/(a + b*x^3)^3,x]","\frac{\frac{a \left(3 a+4 b x^3\right)}{\left(a+b x^3\right)^2}+2 \log \left(a+b x^3\right)}{6 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*(3*a + 4*b*x^3))/(a + b*x^3)^2 + 2*Log[a + b*x^3])/(6*b^3)","A",1
342,1,24,19,0.0069854,"\int \frac{x^5}{\left(a+b x^3\right)^3} \, dx","Integrate[x^5/(a + b*x^3)^3,x]","-\frac{a+2 b x^3}{6 b^2 \left(a+b x^3\right)^2}","\frac{x^6}{6 a \left(a+b x^3\right)^2}",1,"-1/6*(a + 2*b*x^3)/(b^2*(a + b*x^3)^2)","A",1
343,1,16,16,0.0046666,"\int \frac{x^2}{\left(a+b x^3\right)^3} \, dx","Integrate[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*1/(b*(a + b*x^3)^2)","A",1
344,1,43,54,0.0324284,"\int \frac{1}{x \left(a+b x^3\right)^3} \, dx","Integrate[1/(x*(a + b*x^3)^3),x]","\frac{\frac{a \left(3 a+2 b x^3\right)}{\left(a+b x^3\right)^2}-2 \log \left(a+b x^3\right)+6 \log (x)}{6 a^3}","-\frac{\log \left(a+b x^3\right)}{3 a^3}+\frac{\log (x)}{a^3}+\frac{1}{3 a^2 \left(a+b x^3\right)}+\frac{1}{6 a \left(a+b x^3\right)^2}",1,"((a*(3*a + 2*b*x^3))/(a + b*x^3)^2 + 6*Log[x] - 2*Log[a + b*x^3])/(6*a^3)","A",1
345,1,59,66,0.063519,"\int \frac{1}{x^4 \left(a+b x^3\right)^3} \, dx","Integrate[1/(x^4*(a + b*x^3)^3),x]","-\frac{\frac{a \left(2 a^2+9 a b x^3+6 b^2 x^6\right)}{x^3 \left(a+b x^3\right)^2}-6 b \log \left(a+b x^3\right)+18 b \log (x)}{6 a^4}","\frac{b \log \left(a+b x^3\right)}{a^4}-\frac{3 b \log (x)}{a^4}-\frac{2 b}{3 a^3 \left(a+b x^3\right)}-\frac{1}{3 a^3 x^3}-\frac{b}{6 a^2 \left(a+b x^3\right)^2}",1,"-1/6*((a*(2*a^2 + 9*a*b*x^3 + 6*b^2*x^6))/(x^3*(a + b*x^3)^2) + 18*b*Log[x] - 6*b*Log[a + b*x^3])/a^4","A",1
346,1,140,155,0.0744241,"\int \frac{x^7}{\left(a+b x^3\right)^3} \, dx","Integrate[x^7/(a + b*x^3)^3,x]","\frac{\frac{5 \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{\sqrt[3]{a}}-\frac{24 b^{2/3} x^2}{a+b x^3}+\frac{9 a b^{2/3} x^2}{\left(a+b x^3\right)^2}-\frac{10 \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a}}-\frac{10 \sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a}}}{\sqrt{3}}\right)}{\sqrt[3]{a}}}{54 b^{8/3}}","\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 \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{5 x^2}{18 b^2 \left(a+b x^3\right)}-\frac{x^5}{6 b \left(a+b x^3\right)^2}",1,"((9*a*b^(2/3)*x^2)/(a + b*x^3)^2 - (24*b^(2/3)*x^2)/(a + b*x^3) - (10*Sqrt[3]*ArcTan[(1 - (2*b^(1/3)*x)/a^(1/3))/Sqrt[3]])/a^(1/3) - (10*Log[a^(1/3) + b^(1/3)*x])/a^(1/3) + (5*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/a^(1/3))/(54*b^(8/3))","A",1
347,1,136,153,0.07246,"\int \frac{x^6}{\left(a+b x^3\right)^3} \, dx","Integrate[x^6/(a + b*x^3)^3,x]","\frac{-\frac{2 \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{a^{2/3}}+\frac{4 \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{a^{2/3}}-\frac{4 \sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a}}}{\sqrt{3}}\right)}{a^{2/3}}-\frac{21 \sqrt[3]{b} x}{a+b x^3}+\frac{9 a \sqrt[3]{b} x}{\left(a+b x^3\right)^2}}{54 b^{7/3}}","-\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,"((9*a*b^(1/3)*x)/(a + b*x^3)^2 - (21*b^(1/3)*x)/(a + b*x^3) - (4*Sqrt[3]*ArcTan[(1 - (2*b^(1/3)*x)/a^(1/3))/Sqrt[3]])/a^(2/3) + (4*Log[a^(1/3) + b^(1/3)*x])/a^(2/3) - (2*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/a^(2/3))/(54*b^(7/3))","A",1
348,1,141,158,0.1058413,"\int \frac{x^4}{\left(a+b x^3\right)^3} \, dx","Integrate[x^4/(a + b*x^3)^3,x]","\frac{\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{a^{4/3}}-\frac{2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{a^{4/3}}-\frac{2 \sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a}}}{\sqrt{3}}\right)}{a^{4/3}}+\frac{6 b^{2/3} x^2}{a^2+a b x^3}-\frac{9 b^{2/3} x^2}{\left(a+b x^3\right)^2}}{54 b^{5/3}}","\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,"((-9*b^(2/3)*x^2)/(a + b*x^3)^2 + (6*b^(2/3)*x^2)/(a^2 + a*b*x^3) - (2*Sqrt[3]*ArcTan[(1 - (2*b^(1/3)*x)/a^(1/3))/Sqrt[3]])/a^(4/3) - (2*Log[a^(1/3) + b^(1/3)*x])/a^(4/3) + Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2]/a^(4/3))/(54*b^(5/3))","A",1
349,1,138,154,0.0771406,"\int \frac{x^3}{\left(a+b x^3\right)^3} \, dx","Integrate[x^3/(a + b*x^3)^3,x]","\frac{-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{a^{5/3}}+\frac{2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{a^{5/3}}-\frac{2 \sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a}}}{\sqrt{3}}\right)}{a^{5/3}}+\frac{3 \sqrt[3]{b} x}{a^2+a b x^3}-\frac{9 \sqrt[3]{b} x}{\left(a+b x^3\right)^2}}{54 b^{4/3}}","-\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,"((-9*b^(1/3)*x)/(a + b*x^3)^2 + (3*b^(1/3)*x)/(a^2 + a*b*x^3) - (2*Sqrt[3]*ArcTan[(1 - (2*b^(1/3)*x)/a^(1/3))/Sqrt[3]])/a^(5/3) + (2*Log[a^(1/3) + b^(1/3)*x])/a^(5/3) - Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2]/a^(5/3))/(54*b^(4/3))","A",1
350,1,139,155,0.0735467,"\int \frac{x}{\left(a+b x^3\right)^3} \, dx","Integrate[x/(a + b*x^3)^3,x]","\frac{\frac{2 \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{b^{2/3}}+\frac{9 a^{4/3} x^2}{\left(a+b x^3\right)^2}-\frac{4 \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{b^{2/3}}-\frac{4 \sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a}}}{\sqrt{3}}\right)}{b^{2/3}}+\frac{12 \sqrt[3]{a} x^2}{a+b x^3}}{54 a^{7/3}}","\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,"((9*a^(4/3)*x^2)/(a + b*x^3)^2 + (12*a^(1/3)*x^2)/(a + b*x^3) - (4*Sqrt[3]*ArcTan[(1 - (2*b^(1/3)*x)/a^(1/3))/Sqrt[3]])/b^(2/3) - (4*Log[a^(1/3) + b^(1/3)*x])/b^(2/3) + (2*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/b^(2/3))/(54*a^(7/3))","A",1
351,1,135,151,0.0704391,"\int \frac{1}{\left(a+b x^3\right)^3} \, dx","Integrate[(a + b*x^3)^(-3),x]","\frac{-\frac{5 \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{\sqrt[3]{b}}+\frac{9 a^{5/3} x}{\left(a+b x^3\right)^2}+\frac{15 a^{2/3} x}{a+b x^3}+\frac{10 \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b}}-\frac{10 \sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a}}}{\sqrt{3}}\right)}{\sqrt[3]{b}}}{54 a^{8/3}}","-\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 \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{5 x}{18 a^2 \left(a+b x^3\right)}+\frac{x}{6 a \left(a+b x^3\right)^2}",1,"((9*a^(5/3)*x)/(a + b*x^3)^2 + (15*a^(2/3)*x)/(a + b*x^3) - (10*Sqrt[3]*ArcTan[(1 - (2*b^(1/3)*x)/a^(1/3))/Sqrt[3]])/b^(1/3) + (10*Log[a^(1/3) + b^(1/3)*x])/b^(1/3) - (5*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/b^(1/3))/(54*a^(8/3))","A",1
352,1,41,41,0.0078404,"\int \frac{x^8}{a-b x^3} \, dx","Integrate[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,"-1/3*(a*x^3)/b^2 - x^6/(6*b) - (a^2*Log[a - b*x^3])/(3*b^3)","A",1
353,1,28,28,0.0050271,"\int \frac{x^5}{a-b x^3} \, dx","Integrate[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,"-1/3*x^3/b - (a*Log[a - b*x^3])/(3*b^2)","A",1
354,1,16,16,0.0031143,"\int \frac{x^2}{a-b x^3} \, dx","Integrate[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,"-1/3*Log[a - b*x^3]/b","A",1
355,1,23,23,0.0067314,"\int \frac{1}{x \left(a-b x^3\right)} \, dx","Integrate[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",1
356,1,35,35,0.009191,"\int \frac{1}{x^4 \left(a-b x^3\right)} \, dx","Integrate[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*1/(a*x^3) + (b*Log[x])/a^2 - (b*Log[a - b*x^3])/(3*a^2)","A",1
357,1,111,125,0.038619,"\int \frac{x^4}{a-b x^3} \, dx","Integrate[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)+2 a^{2/3} \log \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)+2 \sqrt{3} a^{2/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a}}+1}{\sqrt{3}}\right)+3 b^{2/3} x^2}{6 b^{5/3}}","\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,"-1/6*(3*b^(2/3)*x^2 + 2*Sqrt[3]*a^(2/3)*ArcTan[(1 + (2*b^(1/3)*x)/a^(1/3))/Sqrt[3]] + 2*a^(2/3)*Log[a^(1/3) - b^(1/3)*x] - a^(2/3)*Log[a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/b^(5/3)","A",1
358,1,108,120,0.0165841,"\int \frac{x^3}{a-b x^3} \, dx","Integrate[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)-2 \sqrt[3]{a} \log \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)+2 \sqrt{3} \sqrt[3]{a} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a}}+1}{\sqrt{3}}\right)-6 \sqrt[3]{b} x}{6 b^{4/3}}","\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,"(-6*b^(1/3)*x + 2*Sqrt[3]*a^(1/3)*ArcTan[(1 + (2*b^(1/3)*x)/a^(1/3))/Sqrt[3]] - 2*a^(1/3)*Log[a^(1/3) - b^(1/3)*x] + a^(1/3)*Log[a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*b^(4/3))","A",1
359,1,89,115,0.0110256,"\int \frac{x}{a-b x^3} \, dx","Integrate[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)-2 \log \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)-2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a}}+1}{\sqrt{3}}\right)}{6 \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,"(-2*Sqrt[3]*ArcTan[(1 + (2*b^(1/3)*x)/a^(1/3))/Sqrt[3]] - 2*Log[a^(1/3) - b^(1/3)*x] + Log[a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(1/3)*b^(2/3))","A",1
360,1,89,114,0.0105265,"\int \frac{1}{a-b x^3} \, dx","Integrate[(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)-2 \log \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a}}+1}{\sqrt{3}}\right)}{6 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,"(2*Sqrt[3]*ArcTan[(1 + (2*b^(1/3)*x)/a^(1/3))/Sqrt[3]] - 2*Log[a^(1/3) - b^(1/3)*x] + Log[a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(2/3)*b^(1/3))","A",1
361,1,114,123,0.0439908,"\int \frac{1}{x^2 \left(a-b x^3\right)} \, dx","Integrate[1/(x^2*(a - b*x^3)),x]","-\frac{-\sqrt[3]{b} x \log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)+2 \sqrt[3]{b} x \log \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)+2 \sqrt{3} \sqrt[3]{b} x \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a}}+1}{\sqrt{3}}\right)+6 \sqrt[3]{a}}{6 a^{4/3} 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}",1,"-1/6*(6*a^(1/3) + 2*Sqrt[3]*b^(1/3)*x*ArcTan[(1 + (2*b^(1/3)*x)/a^(1/3))/Sqrt[3]] + 2*b^(1/3)*x*Log[a^(1/3) - b^(1/3)*x] - b^(1/3)*x*Log[a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(a^(4/3)*x)","A",1
362,1,119,124,0.0316165,"\int \frac{1}{x^3 \left(a-b x^3\right)} \, dx","Integrate[1/(x^3*(a - b*x^3)),x]","\frac{b^{2/3} x^2 \log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)-3 a^{2/3}-2 b^{2/3} x^2 \log \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)+2 \sqrt{3} b^{2/3} x^2 \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a}}+1}{\sqrt{3}}\right)}{6 a^{5/3} 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,"(-3*a^(2/3) + 2*Sqrt[3]*b^(2/3)*x^2*ArcTan[(1 + (2*b^(1/3)*x)/a^(1/3))/Sqrt[3]] - 2*b^(2/3)*x^2*Log[a^(1/3) - b^(1/3)*x] + b^(2/3)*x^2*Log[a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(5/3)*x^2)","A",1
363,1,101,125,0.0543678,"\int \frac{1}{1+a+b x^3} \, dx","Integrate[(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)+2 \log \left(\sqrt[3]{a+1}+\sqrt[3]{b} x\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+1}}-1}{\sqrt{3}}\right)}{6 (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,"(2*Sqrt[3]*ArcTan[(-1 + (2*b^(1/3)*x)/(1 + a)^(1/3))/Sqrt[3]] + 2*Log[(1 + a)^(1/3) + b^(1/3)*x] - 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",1
364,1,124,124,0.0873668,"\int \frac{1}{1+a-b x^3} \, dx","Integrate[(1 + a - b*x^3)^(-1),x]","\frac{(-1)^{2/3} \left(\log \left(-\sqrt[3]{-1} \sqrt[3]{a+1} \sqrt[3]{b} x+(a+1)^{2/3}+(-1)^{2/3} b^{2/3} x^2\right)-2 \log \left(\sqrt[3]{a+1}+\sqrt[3]{-1} \sqrt[3]{b} x\right)-2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{-1} \sqrt[3]{b} x}{\sqrt[3]{a+1}}-1}{\sqrt{3}}\right)\right)}{6 (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,"((-1)^(2/3)*(-2*Sqrt[3]*ArcTan[(-1 + (2*(-1)^(1/3)*b^(1/3)*x)/(1 + a)^(1/3))/Sqrt[3]] - 2*Log[(1 + a)^(1/3) + (-1)^(1/3)*b^(1/3)*x] + Log[(1 + a)^(2/3) - (-1)^(1/3)*(1 + a)^(1/3)*b^(1/3)*x + (-1)^(2/3)*b^(2/3)*x^2]))/(6*(1 + a)^(2/3)*b^(1/3))","A",1
365,1,101,139,0.0356446,"\int \frac{1}{-1+a+b x^3} \, dx","Integrate[(-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)+2 \log \left(\sqrt[3]{a-1}+\sqrt[3]{b} x\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a-1}}-1}{\sqrt{3}}\right)}{6 (a-1)^{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,"(2*Sqrt[3]*ArcTan[(-1 + (2*b^(1/3)*x)/(-1 + a)^(1/3))/Sqrt[3]] + 2*Log[(-1 + a)^(1/3) + b^(1/3)*x] - 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",1
366,1,124,138,0.0876514,"\int \frac{1}{-1+a-b x^3} \, dx","Integrate[(-1 + a - b*x^3)^(-1),x]","\frac{(-1)^{2/3} \left(\log \left(-\sqrt[3]{-1} \sqrt[3]{a-1} \sqrt[3]{b} x+(a-1)^{2/3}+(-1)^{2/3} b^{2/3} x^2\right)-2 \log \left(\sqrt[3]{a-1}+\sqrt[3]{-1} \sqrt[3]{b} x\right)-2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{-1} \sqrt[3]{b} x}{\sqrt[3]{a-1}}-1}{\sqrt{3}}\right)\right)}{6 (a-1)^{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,"((-1)^(2/3)*(-2*Sqrt[3]*ArcTan[(-1 + (2*(-1)^(1/3)*b^(1/3)*x)/(-1 + a)^(1/3))/Sqrt[3]] - 2*Log[(-1 + a)^(1/3) + (-1)^(1/3)*b^(1/3)*x] + Log[(-1 + a)^(2/3) - (-1)^(1/3)*(-1 + a)^(1/3)*b^(1/3)*x + (-1)^(2/3)*b^(2/3)*x^2]))/(6*(-1 + a)^(2/3)*b^(1/3))","A",1
367,1,10,10,0.0026529,"\int \frac{\sqrt{x}}{1+x^3} \, dx","Integrate[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",1
368,1,50,80,0.0524188,"\int x^{11} \sqrt{a+b x^3} \, dx","Integrate[x^11*Sqrt[a + b*x^3],x]","\frac{2 \left(a+b x^3\right)^{3/2} \left(-16 a^3+24 a^2 b x^3-30 a b^2 x^6+35 b^3 x^9\right)}{945 b^4}","-\frac{2 a^3 \left(a+b x^3\right)^{3/2}}{9 b^4}+\frac{2 a^2 \left(a+b x^3\right)^{5/2}}{5 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 + b*x^3)^(3/2)*(-16*a^3 + 24*a^2*b*x^3 - 30*a*b^2*x^6 + 35*b^3*x^9))/(945*b^4)","A",1
369,1,39,59,0.0188936,"\int x^8 \sqrt{a+b x^3} \, dx","Integrate[x^8*Sqrt[a + b*x^3],x]","\frac{2 \left(a+b x^3\right)^{3/2} \left(8 a^2-12 a b x^3+15 b^2 x^6\right)}{315 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 + b*x^3)^(3/2)*(8*a^2 - 12*a*b*x^3 + 15*b^2*x^6))/(315*b^3)","A",1
370,1,28,38,0.0137356,"\int x^5 \sqrt{a+b x^3} \, dx","Integrate[x^5*Sqrt[a + b*x^3],x]","\frac{2 \left(a+b x^3\right)^{3/2} \left(3 b x^3-2 a\right)}{45 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 + b*x^3)^(3/2)*(-2*a + 3*b*x^3))/(45*b^2)","A",1
371,1,18,18,0.0205282,"\int x^2 \sqrt{a+b x^3} \, dx","Integrate[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
372,1,43,43,0.0097386,"\int \frac{\sqrt{a+b x^3}}{x} \, dx","Integrate[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",1
373,1,59,47,0.0483536,"\int \frac{\sqrt{a+b x^3}}{x^4} \, dx","Integrate[Sqrt[a + b*x^3]/x^4,x]","-\frac{b x^3 \sqrt{\frac{b x^3}{a}+1} \tanh ^{-1}\left(\sqrt{\frac{b x^3}{a}+1}\right)+a+b x^3}{3 x^3 \sqrt{a+b x^3}}","-\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,"-1/3*(a + b*x^3 + b*x^3*Sqrt[1 + (b*x^3)/a]*ArcTanh[Sqrt[1 + (b*x^3)/a]])/(x^3*Sqrt[a + b*x^3])","A",1
374,1,39,71,0.0093181,"\int \frac{\sqrt{a+b x^3}}{x^7} \, dx","Integrate[Sqrt[a + b*x^3]/x^7,x]","-\frac{2 b^2 \left(a+b x^3\right)^{3/2} \, _2F_1\left(\frac{3}{2},3;\frac{5}{2};\frac{b x^3}{a}+1\right)}{9 a^3}","\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,"(-2*b^2*(a + b*x^3)^(3/2)*Hypergeometric2F1[3/2, 3, 5/2, 1 + (b*x^3)/a])/(9*a^3)","C",1
375,1,39,95,0.0306757,"\int \frac{\sqrt{a+b x^3}}{x^{10}} \, dx","Integrate[Sqrt[a + b*x^3]/x^10,x]","\frac{2 b^3 \left(a+b x^3\right)^{3/2} \, _2F_1\left(\frac{3}{2},4;\frac{5}{2};\frac{b x^3}{a}+1\right)}{9 a^4}","-\frac{b^3 \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{24 a^{5/2}}+\frac{b^2 \sqrt{a+b x^3}}{24 a^2 x^3}-\frac{\sqrt{a+b x^3}}{9 x^9}-\frac{b \sqrt{a+b x^3}}{36 a x^6}",1,"(2*b^3*(a + b*x^3)^(3/2)*Hypergeometric2F1[3/2, 4, 5/2, 1 + (b*x^3)/a])/(9*a^4)","C",1
376,1,94,275,0.0744051,"\int x^6 \sqrt{a+b x^3} \, dx","Integrate[x^6*Sqrt[a + b*x^3],x]","\frac{2 x \sqrt{a+b x^3} \left(\sqrt{\frac{b x^3}{a}+1} \left(-8 a^2+3 a b x^3+11 b^2 x^6\right)+8 a^2 \, _2F_1\left(-\frac{1}{2},\frac{1}{3};\frac{4}{3};-\frac{b x^3}{a}\right)\right)}{187 b^2 \sqrt{\frac{b x^3}{a}+1}}","-\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,"(2*x*Sqrt[a + b*x^3]*(Sqrt[1 + (b*x^3)/a]*(-8*a^2 + 3*a*b*x^3 + 11*b^2*x^6) + 8*a^2*Hypergeometric2F1[-1/2, 1/3, 4/3, -((b*x^3)/a)]))/(187*b^2*Sqrt[1 + (b*x^3)/a])","C",1
377,1,62,251,0.0609587,"\int x^3 \sqrt{a+b x^3} \, dx","Integrate[x^3*Sqrt[a + b*x^3],x]","\frac{2 x \sqrt{a+b x^3} \left(-\frac{a \, _2F_1\left(-\frac{1}{2},\frac{1}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{\sqrt{\frac{b x^3}{a}+1}}+a+b x^3\right)}{11 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{6 a x \sqrt{a+b x^3}}{55 b}+\frac{2}{11} x^4 \sqrt{a+b x^3}",1,"(2*x*Sqrt[a + b*x^3]*(a + b*x^3 - (a*Hypergeometric2F1[-1/2, 1/3, 4/3, -((b*x^3)/a)])/Sqrt[1 + (b*x^3)/a]))/(11*b)","C",1
378,1,46,227,0.0048296,"\int \sqrt{a+b x^3} \, dx","Integrate[Sqrt[a + b*x^3],x]","\frac{x \sqrt{a+b x^3} \, _2F_1\left(-\frac{1}{2},\frac{1}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{\sqrt{\frac{b x^3}{a}+1}}","\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,"(x*Sqrt[a + b*x^3]*Hypergeometric2F1[-1/2, 1/3, 4/3, -((b*x^3)/a)])/Sqrt[1 + (b*x^3)/a]","C",1
379,1,51,228,0.009001,"\int \frac{\sqrt{a+b x^3}}{x^3} \, dx","Integrate[Sqrt[a + b*x^3]/x^3,x]","-\frac{\sqrt{a+b x^3} \, _2F_1\left(-\frac{2}{3},-\frac{1}{2};\frac{1}{3};-\frac{b x^3}{a}\right)}{2 x^2 \sqrt{\frac{b x^3}{a}+1}}","\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,"-1/2*(Sqrt[a + b*x^3]*Hypergeometric2F1[-2/3, -1/2, 1/3, -((b*x^3)/a)])/(x^2*Sqrt[1 + (b*x^3)/a])","C",1
380,1,51,253,0.0094349,"\int \frac{\sqrt{a+b x^3}}{x^6} \, dx","Integrate[Sqrt[a + b*x^3]/x^6,x]","-\frac{\sqrt{a+b x^3} \, _2F_1\left(-\frac{5}{3},-\frac{1}{2};-\frac{2}{3};-\frac{b x^3}{a}\right)}{5 x^5 \sqrt{\frac{b x^3}{a}+1}}","-\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{\sqrt{a+b x^3}}{5 x^5}-\frac{3 b \sqrt{a+b x^3}}{20 a x^2}",1,"-1/5*(Sqrt[a + b*x^3]*Hypergeometric2F1[-5/3, -1/2, -2/3, -((b*x^3)/a)])/(x^5*Sqrt[1 + (b*x^3)/a])","C",1
381,1,51,277,0.0092182,"\int \frac{\sqrt{a+b x^3}}{x^9} \, dx","Integrate[Sqrt[a + b*x^3]/x^9,x]","-\frac{\sqrt{a+b x^3} \, _2F_1\left(-\frac{8}{3},-\frac{1}{2};-\frac{5}{3};-\frac{b x^3}{a}\right)}{8 x^8 \sqrt{\frac{b x^3}{a}+1}}","\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{\sqrt{a+b x^3}}{8 x^8}-\frac{3 b \sqrt{a+b x^3}}{80 a x^5}",1,"-1/8*(Sqrt[a + b*x^3]*Hypergeometric2F1[-8/3, -1/2, -5/3, -((b*x^3)/a)])/(x^8*Sqrt[1 + (b*x^3)/a])","C",1
382,1,96,535,0.0789084,"\int x^7 \sqrt{a+b x^3} \, dx","Integrate[x^7*Sqrt[a + b*x^3],x]","\frac{2 x^2 \sqrt{a+b x^3} \left(\sqrt{\frac{b x^3}{a}+1} \left(-10 a^2+3 a b x^3+13 b^2 x^6\right)+10 a^2 \, _2F_1\left(-\frac{1}{2},\frac{2}{3};\frac{5}{3};-\frac{b x^3}{a}\right)\right)}{247 b^2 \sqrt{\frac{b x^3}{a}+1}}","\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{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{60 a^2 x^2 \sqrt{a+b x^3}}{1729 b^2}+\frac{2}{19} x^8 \sqrt{a+b x^3}+\frac{6 a x^5 \sqrt{a+b x^3}}{247 b}",1,"(2*x^2*Sqrt[a + b*x^3]*(Sqrt[1 + (b*x^3)/a]*(-10*a^2 + 3*a*b*x^3 + 13*b^2*x^6) + 10*a^2*Hypergeometric2F1[-1/2, 2/3, 5/3, -((b*x^3)/a)]))/(247*b^2*Sqrt[1 + (b*x^3)/a])","C",1
383,1,64,511,0.0768345,"\int x^4 \sqrt{a+b x^3} \, dx","Integrate[x^4*Sqrt[a + b*x^3],x]","\frac{2 x^2 \sqrt{a+b x^3} \left(-\frac{a \, _2F_1\left(-\frac{1}{2},\frac{2}{3};\frac{5}{3};-\frac{b x^3}{a}\right)}{\sqrt{\frac{b x^3}{a}+1}}+a+b x^3\right)}{13 b}","-\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{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{2}{13} x^5 \sqrt{a+b x^3}+\frac{6 a x^2 \sqrt{a+b x^3}}{91 b}",1,"(2*x^2*Sqrt[a + b*x^3]*(a + b*x^3 - (a*Hypergeometric2F1[-1/2, 2/3, 5/3, -((b*x^3)/a)])/Sqrt[1 + (b*x^3)/a]))/(13*b)","C",1
384,1,51,487,0.0076017,"\int x \sqrt{a+b x^3} \, dx","Integrate[x*Sqrt[a + b*x^3],x]","\frac{x^2 \sqrt{a+b x^3} \, _2F_1\left(-\frac{1}{2},\frac{2}{3};\frac{5}{3};-\frac{b x^3}{a}\right)}{2 \sqrt{\frac{b x^3}{a}+1}}","\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,"(x^2*Sqrt[a + b*x^3]*Hypergeometric2F1[-1/2, 2/3, 5/3, -((b*x^3)/a)])/(2*Sqrt[1 + (b*x^3)/a])","C",1
385,1,49,479,0.0082791,"\int \frac{\sqrt{a+b x^3}}{x^2} \, dx","Integrate[Sqrt[a + b*x^3]/x^2,x]","-\frac{\sqrt{a+b x^3} \, _2F_1\left(-\frac{1}{2},-\frac{1}{3};\frac{2}{3};-\frac{b x^3}{a}\right)}{x \sqrt{\frac{b x^3}{a}+1}}","\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]*Hypergeometric2F1[-1/2, -1/3, 2/3, -((b*x^3)/a)])/(x*Sqrt[1 + (b*x^3)/a]))","C",1
386,1,51,511,0.0093526,"\int \frac{\sqrt{a+b x^3}}{x^5} \, dx","Integrate[Sqrt[a + b*x^3]/x^5,x]","-\frac{\sqrt{a+b x^3} \, _2F_1\left(-\frac{4}{3},-\frac{1}{2};-\frac{1}{3};-\frac{b x^3}{a}\right)}{4 x^4 \sqrt{\frac{b x^3}{a}+1}}","\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,"-1/4*(Sqrt[a + b*x^3]*Hypergeometric2F1[-4/3, -1/2, -1/3, -((b*x^3)/a)])/(x^4*Sqrt[1 + (b*x^3)/a])","C",1
387,1,50,80,0.0299168,"\int x^{11} \left(a+b x^3\right)^{3/2} \, dx","Integrate[x^11*(a + b*x^3)^(3/2),x]","\frac{2 \left(a+b x^3\right)^{5/2} \left(-16 a^3+40 a^2 b x^3-70 a b^2 x^6+105 b^3 x^9\right)}{3465 b^4}","-\frac{2 a^3 \left(a+b x^3\right)^{5/2}}{15 b^4}+\frac{2 a^2 \left(a+b x^3\right)^{7/2}}{7 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 + b*x^3)^(5/2)*(-16*a^3 + 40*a^2*b*x^3 - 70*a*b^2*x^6 + 105*b^3*x^9))/(3465*b^4)","A",1
388,1,39,59,0.0202267,"\int x^8 \left(a+b x^3\right)^{3/2} \, dx","Integrate[x^8*(a + b*x^3)^(3/2),x]","\frac{2 \left(a+b x^3\right)^{5/2} \left(8 a^2-20 a b x^3+35 b^2 x^6\right)}{945 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 + b*x^3)^(5/2)*(8*a^2 - 20*a*b*x^3 + 35*b^2*x^6))/(945*b^3)","A",1
389,1,28,38,0.0159679,"\int x^5 \left(a+b x^3\right)^{3/2} \, dx","Integrate[x^5*(a + b*x^3)^(3/2),x]","\frac{2 \left(a+b x^3\right)^{5/2} \left(5 b x^3-2 a\right)}{105 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 + b*x^3)^(5/2)*(-2*a + 5*b*x^3))/(105*b^2)","A",1
390,1,18,18,0.0062558,"\int x^2 \left(a+b x^3\right)^{3/2} \, dx","Integrate[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
391,1,51,59,0.0317766,"\int \frac{\left(a+b x^3\right)^{3/2}}{x} \, dx","Integrate[(a + b*x^3)^(3/2)/x,x]","\frac{2}{9} \left(\sqrt{a+b x^3} \left(4 a+b x^3\right)-3 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)\right)","-\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*(Sqrt[a + b*x^3]*(4*a + b*x^3) - 3*a^(3/2)*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]]))/9","A",1
392,1,37,58,0.0089055,"\int \frac{\left(a+b x^3\right)^{3/2}}{x^4} \, dx","Integrate[(a + b*x^3)^(3/2)/x^4,x]","\frac{2 b \left(a+b x^3\right)^{5/2} \, _2F_1\left(2,\frac{5}{2};\frac{7}{2};\frac{b x^3}{a}+1\right)}{15 a^2}","-\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,"(2*b*(a + b*x^3)^(5/2)*Hypergeometric2F1[2, 5/2, 7/2, 1 + (b*x^3)/a])/(15*a^2)","C",1
393,1,76,68,0.0414384,"\int \frac{\left(a+b x^3\right)^{3/2}}{x^7} \, dx","Integrate[(a + b*x^3)^(3/2)/x^7,x]","-\frac{2 a^2+3 b^2 x^6 \sqrt{\frac{b x^3}{a}+1} \tanh ^{-1}\left(\sqrt{\frac{b x^3}{a}+1}\right)+7 a b x^3+5 b^2 x^6}{12 x^6 \sqrt{a+b x^3}}","-\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,"-1/12*(2*a^2 + 7*a*b*x^3 + 5*b^2*x^6 + 3*b^2*x^6*Sqrt[1 + (b*x^3)/a]*ArcTanh[Sqrt[1 + (b*x^3)/a]])/(x^6*Sqrt[a + b*x^3])","A",1
394,1,79,296,0.076393,"\int x^6 \left(a+b x^3\right)^{3/2} \, dx","Integrate[x^6*(a + b*x^3)^(3/2),x]","\frac{2 x \sqrt{a+b x^3} \left(\frac{8 a^3 \, _2F_1\left(-\frac{3}{2},\frac{1}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{\sqrt{\frac{b x^3}{a}+1}}-\left(8 a-17 b x^3\right) \left(a+b x^3\right)^2\right)}{391 b^2}","-\frac{432 a^3 x \sqrt{a+b x^3}}{21505 b^2}+\frac{54 a^2 x^4 \sqrt{a+b x^3}}{4301 b}+\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{2}{23} x^7 \left(a+b x^3\right)^{3/2}+\frac{18}{391} a x^7 \sqrt{a+b x^3}",1,"(2*x*Sqrt[a + b*x^3]*(-((8*a - 17*b*x^3)*(a + b*x^3)^2) + (8*a^3*Hypergeometric2F1[-3/2, 1/3, 4/3, -((b*x^3)/a)])/Sqrt[1 + (b*x^3)/a]))/(391*b^2)","C",1
395,1,67,272,0.0566187,"\int x^3 \left(a+b x^3\right)^{3/2} \, dx","Integrate[x^3*(a + b*x^3)^(3/2),x]","\frac{2 x \sqrt{a+b x^3} \left(\left(a+b x^3\right)^2-\frac{a^2 \, _2F_1\left(-\frac{3}{2},\frac{1}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{\sqrt{\frac{b x^3}{a}+1}}\right)}{17 b}","\frac{54 a^2 x \sqrt{a+b x^3}}{935 b}-\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{2}{17} x^4 \left(a+b x^3\right)^{3/2}+\frac{18}{187} a x^4 \sqrt{a+b x^3}",1,"(2*x*Sqrt[a + b*x^3]*((a + b*x^3)^2 - (a^2*Hypergeometric2F1[-3/2, 1/3, 4/3, -((b*x^3)/a)])/Sqrt[1 + (b*x^3)/a]))/(17*b)","C",1
396,1,47,246,0.0050924,"\int \left(a+b x^3\right)^{3/2} \, dx","Integrate[(a + b*x^3)^(3/2),x]","\frac{a x \sqrt{a+b x^3} \, _2F_1\left(-\frac{3}{2},\frac{1}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{\sqrt{\frac{b x^3}{a}+1}}","\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,"(a*x*Sqrt[a + b*x^3]*Hypergeometric2F1[-3/2, 1/3, 4/3, -((b*x^3)/a)])/Sqrt[1 + (b*x^3)/a]","C",1
397,1,52,246,0.0171542,"\int \frac{\left(a+b x^3\right)^{3/2}}{x^3} \, dx","Integrate[(a + b*x^3)^(3/2)/x^3,x]","-\frac{a \sqrt{a+b x^3} \, _2F_1\left(-\frac{3}{2},-\frac{2}{3};\frac{1}{3};-\frac{b x^3}{a}\right)}{2 x^2 \sqrt{\frac{b x^3}{a}+1}}","\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{9}{10} b x \sqrt{a+b x^3}-\frac{\left(a+b x^3\right)^{3/2}}{2 x^2}",1,"-1/2*(a*Sqrt[a + b*x^3]*Hypergeometric2F1[-3/2, -2/3, 1/3, -((b*x^3)/a)])/(x^2*Sqrt[1 + (b*x^3)/a])","C",1
398,1,52,247,0.010035,"\int \frac{\left(a+b x^3\right)^{3/2}}{x^6} \, dx","Integrate[(a + b*x^3)^(3/2)/x^6,x]","-\frac{a \sqrt{a+b x^3} \, _2F_1\left(-\frac{5}{3},-\frac{3}{2};-\frac{2}{3};-\frac{b x^3}{a}\right)}{5 x^5 \sqrt{\frac{b x^3}{a}+1}}","\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{\left(a+b x^3\right)^{3/2}}{5 x^5}-\frac{9 b \sqrt{a+b x^3}}{20 x^2}",1,"-1/5*(a*Sqrt[a + b*x^3]*Hypergeometric2F1[-5/3, -3/2, -2/3, -((b*x^3)/a)])/(x^5*Sqrt[1 + (b*x^3)/a])","C",1
399,1,81,556,0.1133575,"\int x^7 \left(a+b x^3\right)^{3/2} \, dx","Integrate[x^7*(a + b*x^3)^(3/2),x]","\frac{2 x^2 \sqrt{a+b x^3} \left(\frac{10 a^3 \, _2F_1\left(-\frac{3}{2},\frac{2}{3};\frac{5}{3};-\frac{b x^3}{a}\right)}{\sqrt{\frac{b x^3}{a}+1}}-\left(10 a-19 b x^3\right) \left(a+b x^3\right)^2\right)}{475 b^2}","\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{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{108 a^3 x^2 \sqrt{a+b x^3}}{8645 b^2}+\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,"(2*x^2*Sqrt[a + b*x^3]*(-((10*a - 19*b*x^3)*(a + b*x^3)^2) + (10*a^3*Hypergeometric2F1[-3/2, 2/3, 5/3, -((b*x^3)/a)])/Sqrt[1 + (b*x^3)/a]))/(475*b^2)","C",1
400,1,69,532,0.0783325,"\int x^4 \left(a+b x^3\right)^{3/2} \, dx","Integrate[x^4*(a + b*x^3)^(3/2),x]","\frac{2 x^2 \sqrt{a+b x^3} \left(\left(a+b x^3\right)^2-\frac{a^2 \, _2F_1\left(-\frac{3}{2},\frac{2}{3};\frac{5}{3};-\frac{b x^3}{a}\right)}{\sqrt{\frac{b x^3}{a}+1}}\right)}{19 b}","-\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{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{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,"(2*x^2*Sqrt[a + b*x^3]*((a + b*x^3)^2 - (a^2*Hypergeometric2F1[-3/2, 2/3, 5/3, -((b*x^3)/a)])/Sqrt[1 + (b*x^3)/a]))/(19*b)","C",1
401,1,52,508,0.0084573,"\int x \left(a+b x^3\right)^{3/2} \, dx","Integrate[x*(a + b*x^3)^(3/2),x]","\frac{a x^2 \sqrt{a+b x^3} \, _2F_1\left(-\frac{3}{2},\frac{2}{3};\frac{5}{3};-\frac{b x^3}{a}\right)}{2 \sqrt{\frac{b x^3}{a}+1}}","\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{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}{91} a x^2 \sqrt{a+b x^3}+\frac{2}{13} x^2 \left(a+b x^3\right)^{3/2}",1,"(a*x^2*Sqrt[a + b*x^3]*Hypergeometric2F1[-3/2, 2/3, 5/3, -((b*x^3)/a)])/(2*Sqrt[1 + (b*x^3)/a])","C",1
402,1,50,504,0.0094476,"\int \frac{\left(a+b x^3\right)^{3/2}}{x^2} \, dx","Integrate[(a + b*x^3)^(3/2)/x^2,x]","-\frac{a \sqrt{a+b x^3} \, _2F_1\left(-\frac{3}{2},-\frac{1}{3};\frac{2}{3};-\frac{b x^3}{a}\right)}{x \sqrt{\frac{b x^3}{a}+1}}","\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{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}{7} b x^2 \sqrt{a+b x^3}",1,"-((a*Sqrt[a + b*x^3]*Hypergeometric2F1[-3/2, -1/3, 2/3, -((b*x^3)/a)])/(x*Sqrt[1 + (b*x^3)/a]))","C",1
403,1,52,505,0.0097837,"\int \frac{\left(a+b x^3\right)^{3/2}}{x^5} \, dx","Integrate[(a + b*x^3)^(3/2)/x^5,x]","-\frac{a \sqrt{a+b x^3} \, _2F_1\left(-\frac{3}{2},-\frac{4}{3};-\frac{1}{3};-\frac{b x^3}{a}\right)}{4 x^4 \sqrt{\frac{b x^3}{a}+1}}","\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{9 b \sqrt{a+b x^3}}{8 x}-\frac{\left(a+b x^3\right)^{3/2}}{4 x^4}",1,"-1/4*(a*Sqrt[a + b*x^3]*Hypergeometric2F1[-3/2, -4/3, -1/3, -((b*x^3)/a)])/(x^4*Sqrt[1 + (b*x^3)/a])","C",1
404,1,50,80,0.0287796,"\int \frac{x^{11}}{\sqrt{a+b x^3}} \, dx","Integrate[x^11/Sqrt[a + b*x^3],x]","\frac{2 \sqrt{a+b x^3} \left(-16 a^3+8 a^2 b x^3-6 a b^2 x^6+5 b^3 x^9\right)}{105 b^4}","-\frac{2 a^3 \sqrt{a+b x^3}}{3 b^4}+\frac{2 a^2 \left(a+b x^3\right)^{3/2}}{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*Sqrt[a + b*x^3]*(-16*a^3 + 8*a^2*b*x^3 - 6*a*b^2*x^6 + 5*b^3*x^9))/(105*b^4)","A",1
405,1,39,59,0.0239518,"\int \frac{x^8}{\sqrt{a+b x^3}} \, dx","Integrate[x^8/Sqrt[a + b*x^3],x]","\frac{2 \sqrt{a+b x^3} \left(8 a^2-4 a b x^3+3 b^2 x^6\right)}{45 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*Sqrt[a + b*x^3]*(8*a^2 - 4*a*b*x^3 + 3*b^2*x^6))/(45*b^3)","A",1
406,1,27,38,0.014473,"\int \frac{x^5}{\sqrt{a+b x^3}} \, dx","Integrate[x^5/Sqrt[a + b*x^3],x]","\frac{2 \left(b x^3-2 a\right) \sqrt{a+b x^3}}{9 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*(-2*a + b*x^3)*Sqrt[a + b*x^3])/(9*b^2)","A",1
407,1,18,18,0.0037001,"\int \frac{x^2}{\sqrt{a+b x^3}} \, dx","Integrate[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
408,1,27,27,0.0046511,"\int \frac{1}{x \sqrt{a+b x^3}} \, dx","Integrate[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",1
409,1,64,50,0.0507629,"\int \frac{1}{x^4 \sqrt{a+b x^3}} \, dx","Integrate[1/(x^4*Sqrt[a + b*x^3]),x]","\frac{2 b \sqrt{a+b x^3} \left(\frac{\tanh ^{-1}\left(\sqrt{\frac{b x^3}{a}+1}\right)}{2 \sqrt{\frac{b x^3}{a}+1}}-\frac{a}{2 b x^3}\right)}{3 a^2}","\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,"(2*b*Sqrt[a + b*x^3]*(-1/2*a/(b*x^3) + ArcTanh[Sqrt[1 + (b*x^3)/a]]/(2*Sqrt[1 + (b*x^3)/a])))/(3*a^2)","A",1
410,1,39,74,0.0080955,"\int \frac{1}{x^7 \sqrt{a+b x^3}} \, dx","Integrate[1/(x^7*Sqrt[a + b*x^3]),x]","-\frac{2 b^2 \sqrt{a+b x^3} \, _2F_1\left(\frac{1}{2},3;\frac{3}{2};\frac{b x^3}{a}+1\right)}{3 a^3}","-\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,"(-2*b^2*Sqrt[a + b*x^3]*Hypergeometric2F1[1/2, 3, 3/2, 1 + (b*x^3)/a])/(3*a^3)","C",1
411,1,79,254,0.0391102,"\int \frac{x^6}{\sqrt{a+b x^3}} \, dx","Integrate[x^6/Sqrt[a + b*x^3],x]","\frac{2 \left(8 a^2 x \sqrt{\frac{b x^3}{a}+1} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};-\frac{b x^3}{a}\right)-8 a^2 x-3 a b x^4+5 b^2 x^7\right)}{55 b^2 \sqrt{a+b x^3}}","\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,"(2*(-8*a^2*x - 3*a*b*x^4 + 5*b^2*x^7 + 8*a^2*x*Sqrt[1 + (b*x^3)/a]*Hypergeometric2F1[1/3, 1/2, 4/3, -((b*x^3)/a)]))/(55*b^2*Sqrt[a + b*x^3])","C",1
412,1,62,230,0.018561,"\int \frac{x^3}{\sqrt{a+b x^3}} \, dx","Integrate[x^3/Sqrt[a + b*x^3],x]","\frac{2 x \left(-a \sqrt{\frac{b x^3}{a}+1} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};-\frac{b x^3}{a}\right)+a+b x^3\right)}{5 b \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*(a + b*x^3 - a*Sqrt[1 + (b*x^3)/a]*Hypergeometric2F1[1/3, 1/2, 4/3, -((b*x^3)/a)]))/(5*b*Sqrt[a + b*x^3])","C",1
413,1,46,207,0.0076432,"\int \frac{1}{\sqrt{a+b x^3}} \, dx","Integrate[1/Sqrt[a + b*x^3],x]","\frac{x \sqrt{\frac{b x^3}{a}+1} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};-\frac{b x^3}{a}\right)}{\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,"(x*Sqrt[1 + (b*x^3)/a]*Hypergeometric2F1[1/3, 1/2, 4/3, -((b*x^3)/a)])/Sqrt[a + b*x^3]","C",1
414,1,51,234,0.0090344,"\int \frac{1}{x^3 \sqrt{a+b x^3}} \, dx","Integrate[1/(x^3*Sqrt[a + b*x^3]),x]","-\frac{\sqrt{\frac{b x^3}{a}+1} \, _2F_1\left(-\frac{2}{3},\frac{1}{2};\frac{1}{3};-\frac{b x^3}{a}\right)}{2 x^2 \sqrt{a+b x^3}}","-\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,"-1/2*(Sqrt[1 + (b*x^3)/a]*Hypergeometric2F1[-2/3, 1/2, 1/3, -((b*x^3)/a)])/(x^2*Sqrt[a + b*x^3])","C",1
415,1,51,256,0.0092572,"\int \frac{1}{x^6 \sqrt{a+b x^3}} \, dx","Integrate[1/(x^6*Sqrt[a + b*x^3]),x]","-\frac{\sqrt{\frac{b x^3}{a}+1} \, _2F_1\left(-\frac{5}{3},\frac{1}{2};-\frac{2}{3};-\frac{b x^3}{a}\right)}{5 x^5 \sqrt{a+b x^3}}","\frac{7 b \sqrt{a+b x^3}}{20 a^2 x^2}+\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{\sqrt{a+b x^3}}{5 a x^5}",1,"-1/5*(Sqrt[1 + (b*x^3)/a]*Hypergeometric2F1[-5/3, 1/2, -2/3, -((b*x^3)/a)])/(x^5*Sqrt[a + b*x^3])","C",1
416,1,80,514,0.0309855,"\int \frac{x^7}{\sqrt{a+b x^3}} \, dx","Integrate[x^7/Sqrt[a + b*x^3],x]","\frac{2 x^2 \left(10 a^2 \sqrt{\frac{b x^3}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};-\frac{b x^3}{a}\right)-10 a^2-3 a b x^3+7 b^2 x^6\right)}{91 b^2 \sqrt{a+b x^3}}","\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{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{20 a x^2 \sqrt{a+b x^3}}{91 b^2}+\frac{2 x^5 \sqrt{a+b x^3}}{13 b}",1,"(2*x^2*(-10*a^2 - 3*a*b*x^3 + 7*b^2*x^6 + 10*a^2*Sqrt[1 + (b*x^3)/a]*Hypergeometric2F1[1/2, 2/3, 5/3, -((b*x^3)/a)]))/(91*b^2*Sqrt[a + b*x^3])","C",1
417,1,64,490,0.0232874,"\int \frac{x^4}{\sqrt{a+b x^3}} \, dx","Integrate[x^4/Sqrt[a + b*x^3],x]","\frac{2 x^2 \left(-a \sqrt{\frac{b x^3}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};-\frac{b x^3}{a}\right)+a+b x^3\right)}{7 b \sqrt{a+b x^3}}","-\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*(a + b*x^3 - a*Sqrt[1 + (b*x^3)/a]*Hypergeometric2F1[1/2, 2/3, 5/3, -((b*x^3)/a)]))/(7*b*Sqrt[a + b*x^3])","C",1
418,1,51,462,0.0081023,"\int \frac{x}{\sqrt{a+b x^3}} \, dx","Integrate[x/Sqrt[a + b*x^3],x]","\frac{x^2 \sqrt{\frac{b x^3}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};-\frac{b x^3}{a}\right)}{2 \sqrt{a+b x^3}}","\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,"(x^2*Sqrt[1 + (b*x^3)/a]*Hypergeometric2F1[1/2, 2/3, 5/3, -((b*x^3)/a)])/(2*Sqrt[a + b*x^3])","C",1
419,1,49,484,0.0099885,"\int \frac{1}{x^2 \sqrt{a+b x^3}} \, dx","Integrate[1/(x^2*Sqrt[a + b*x^3]),x]","-\frac{\sqrt{\frac{b x^3}{a}+1} \, _2F_1\left(-\frac{1}{3},\frac{1}{2};\frac{2}{3};-\frac{b x^3}{a}\right)}{x \sqrt{a+b x^3}}","\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[1 + (b*x^3)/a]*Hypergeometric2F1[-1/3, 1/2, 2/3, -((b*x^3)/a)])/(x*Sqrt[a + b*x^3]))","C",1
420,1,51,514,0.0093788,"\int \frac{1}{x^5 \sqrt{a+b x^3}} \, dx","Integrate[1/(x^5*Sqrt[a + b*x^3]),x]","-\frac{\sqrt{\frac{b x^3}{a}+1} \, _2F_1\left(-\frac{4}{3},\frac{1}{2};-\frac{1}{3};-\frac{b x^3}{a}\right)}{4 x^4 \sqrt{a+b x^3}}","-\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^{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 \sqrt{a+b x^3}}{8 a^2 x}-\frac{\sqrt{a+b x^3}}{4 a x^4}",1,"-1/4*(Sqrt[1 + (b*x^3)/a]*Hypergeometric2F1[-4/3, 1/2, -1/3, -((b*x^3)/a)])/(x^4*Sqrt[a + b*x^3])","C",1
421,1,49,78,0.0342586,"\int \frac{x^{11}}{\left(a+b x^3\right)^{3/2}} \, dx","Integrate[x^11/(a + b*x^3)^(3/2),x]","\frac{2 \left(16 a^3+8 a^2 b x^3-2 a b^2 x^6+b^3 x^9\right)}{15 b^4 \sqrt{a+b x^3}}","\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*(16*a^3 + 8*a^2*b*x^3 - 2*a*b^2*x^6 + b^3*x^9))/(15*b^4*Sqrt[a + b*x^3])","A",1
422,1,38,59,0.0390501,"\int \frac{x^8}{\left(a+b x^3\right)^{3/2}} \, dx","Integrate[x^8/(a + b*x^3)^(3/2),x]","\frac{2 \left(-8 a^2-4 a b x^3+b^2 x^6\right)}{9 b^3 \sqrt{a+b x^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*(-8*a^2 - 4*a*b*x^3 + b^2*x^6))/(9*b^3*Sqrt[a + b*x^3])","A",1
423,1,27,38,0.0136402,"\int \frac{x^5}{\left(a+b x^3\right)^{3/2}} \, dx","Integrate[x^5/(a + b*x^3)^(3/2),x]","\frac{2 \left(2 a+b x^3\right)}{3 b^2 \sqrt{a+b x^3}}","\frac{2 a}{3 b^2 \sqrt{a+b x^3}}+\frac{2 \sqrt{a+b x^3}}{3 b^2}",1,"(2*(2*a + b*x^3))/(3*b^2*Sqrt[a + b*x^3])","A",1
424,1,18,18,0.0043858,"\int \frac{x^2}{\left(a+b x^3\right)^{3/2}} \, dx","Integrate[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
425,1,36,46,0.007004,"\int \frac{1}{x \left(a+b x^3\right)^{3/2}} \, dx","Integrate[1/(x*(a + b*x^3)^(3/2)),x]","\frac{2 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{b x^3}{a}+1\right)}{3 a \sqrt{a+b x^3}}","\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*Hypergeometric2F1[-1/2, 1, 1/2, 1 + (b*x^3)/a])/(3*a*Sqrt[a + b*x^3])","C",1
426,1,37,64,0.0075964,"\int \frac{1}{x^4 \left(a+b x^3\right)^{3/2}} \, dx","Integrate[1/(x^4*(a + b*x^3)^(3/2)),x]","-\frac{2 b \, _2F_1\left(-\frac{1}{2},2;\frac{1}{2};\frac{b x^3}{a}+1\right)}{3 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{b}{a^2 \sqrt{a+b x^3}}-\frac{1}{3 a x^3 \sqrt{a+b x^3}}",1,"(-2*b*Hypergeometric2F1[-1/2, 2, 1/2, 1 + (b*x^3)/a])/(3*a^2*Sqrt[a + b*x^3])","C",1
427,1,39,95,0.025834,"\int \frac{1}{x^7 \left(a+b x^3\right)^{3/2}} \, dx","Integrate[1/(x^7*(a + b*x^3)^(3/2)),x]","\frac{2 b^2 \, _2F_1\left(-\frac{1}{2},3;\frac{1}{2};\frac{b x^3}{a}+1\right)}{3 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^2}{4 a^3 \sqrt{a+b x^3}}+\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*b^2*Hypergeometric2F1[-1/2, 3, 1/2, 1 + (b*x^3)/a])/(3*a^3*Sqrt[a + b*x^3])","C",1
428,1,65,251,0.0504171,"\int \frac{x^6}{\left(a+b x^3\right)^{3/2}} \, dx","Integrate[x^6/(a + b*x^3)^(3/2),x]","\frac{2 x \left(-8 a \sqrt{\frac{b x^3}{a}+1} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};-\frac{b x^3}{a}\right)+8 a+3 b x^3\right)}{15 b^2 \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*(8*a + 3*b*x^3 - 8*a*Sqrt[1 + (b*x^3)/a]*Hypergeometric2F1[1/3, 1/2, 4/3, -((b*x^3)/a)]))/(15*b^2*Sqrt[a + b*x^3])","C",1
429,1,55,229,0.0175866,"\int \frac{x^3}{\left(a+b x^3\right)^{3/2}} \, dx","Integrate[x^3/(a + b*x^3)^(3/2),x]","\frac{2 x \left(\sqrt{\frac{b x^3}{a}+1} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};-\frac{b x^3}{a}\right)-1\right)}{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*(-1 + Sqrt[1 + (b*x^3)/a]*Hypergeometric2F1[1/3, 1/2, 4/3, -((b*x^3)/a)]))/(3*b*Sqrt[a + b*x^3])","C",1
430,1,55,232,0.0125733,"\int \frac{1}{\left(a+b x^3\right)^{3/2}} \, dx","Integrate[(a + b*x^3)^(-3/2),x]","\frac{x \left(\sqrt{\frac{b x^3}{a}+1} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};-\frac{b x^3}{a}\right)+2\right)}{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,"(x*(2 + Sqrt[1 + (b*x^3)/a]*Hypergeometric2F1[1/3, 1/2, 4/3, -((b*x^3)/a)]))/(3*a*Sqrt[a + b*x^3])","C",1
431,1,54,255,0.0091883,"\int \frac{1}{x^3 \left(a+b x^3\right)^{3/2}} \, dx","Integrate[1/(x^3*(a + b*x^3)^(3/2)),x]","-\frac{\sqrt{\frac{b x^3}{a}+1} \, _2F_1\left(-\frac{2}{3},\frac{3}{2};\frac{1}{3};-\frac{b x^3}{a}\right)}{2 a x^2 \sqrt{a+b x^3}}","-\frac{7 \sqrt{a+b x^3}}{6 a^2 x^2}-\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{2}{3 a x^2 \sqrt{a+b x^3}}",1,"-1/2*(Sqrt[1 + (b*x^3)/a]*Hypergeometric2F1[-2/3, 3/2, 1/3, -((b*x^3)/a)])/(a*x^2*Sqrt[a + b*x^3])","C",1
432,1,54,277,0.0097658,"\int \frac{1}{x^6 \left(a+b x^3\right)^{3/2}} \, dx","Integrate[1/(x^6*(a + b*x^3)^(3/2)),x]","-\frac{\sqrt{\frac{b x^3}{a}+1} \, _2F_1\left(-\frac{5}{3},\frac{3}{2};-\frac{2}{3};-\frac{b x^3}{a}\right)}{5 a x^5 \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{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{2}{3 a x^5 \sqrt{a+b x^3}}",1,"-1/5*(Sqrt[1 + (b*x^3)/a]*Hypergeometric2F1[-5/3, 3/2, -2/3, -((b*x^3)/a)])/(a*x^5*Sqrt[a + b*x^3])","C",1
433,1,66,511,0.0318922,"\int \frac{x^7}{\left(a+b x^3\right)^{3/2}} \, dx","Integrate[x^7/(a + b*x^3)^(3/2),x]","\frac{2 x^2 \left(10 a \sqrt{\frac{b x^3}{a}+1} \, _2F_1\left(\frac{2}{3},\frac{3}{2};\frac{5}{3};-\frac{b x^3}{a}\right)-10 a+b x^3\right)}{7 b^2 \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{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{20 x^2 \sqrt{a+b x^3}}{21 b^2}-\frac{2 x^5}{3 b \sqrt{a+b x^3}}",1,"(2*x^2*(-10*a + b*x^3 + 10*a*Sqrt[1 + (b*x^3)/a]*Hypergeometric2F1[2/3, 3/2, 5/3, -((b*x^3)/a)]))/(7*b^2*Sqrt[a + b*x^3])","C",1
434,1,55,487,0.0198502,"\int \frac{x^4}{\left(a+b x^3\right)^{3/2}} \, dx","Integrate[x^4/(a + b*x^3)^(3/2),x]","-\frac{2 x^2 \left(\sqrt{\frac{b x^3}{a}+1} \, _2F_1\left(\frac{2}{3},\frac{3}{2};\frac{5}{3};-\frac{b x^3}{a}\right)-1\right)}{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*(-1 + Sqrt[1 + (b*x^3)/a]*Hypergeometric2F1[2/3, 3/2, 5/3, -((b*x^3)/a)]))/(b*Sqrt[a + b*x^3])","C",1
435,1,54,489,0.0088606,"\int \frac{x}{\left(a+b x^3\right)^{3/2}} \, dx","Integrate[x/(a + b*x^3)^(3/2),x]","\frac{x^2 \sqrt{\frac{b x^3}{a}+1} \, _2F_1\left(\frac{2}{3},\frac{3}{2};\frac{5}{3};-\frac{b x^3}{a}\right)}{2 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,"(x^2*Sqrt[1 + (b*x^3)/a]*Hypergeometric2F1[2/3, 3/2, 5/3, -((b*x^3)/a)])/(2*a*Sqrt[a + b*x^3])","C",1
436,1,52,513,0.010062,"\int \frac{1}{x^2 \left(a+b x^3\right)^{3/2}} \, dx","Integrate[1/(x^2*(a + b*x^3)^(3/2)),x]","-\frac{\sqrt{\frac{b x^3}{a}+1} \, _2F_1\left(-\frac{1}{3},\frac{3}{2};\frac{2}{3};-\frac{b x^3}{a}\right)}{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,"-((Sqrt[1 + (b*x^3)/a]*Hypergeometric2F1[-1/3, 3/2, 2/3, -((b*x^3)/a)])/(a*x*Sqrt[a + b*x^3]))","C",1
437,1,54,535,0.0105605,"\int \frac{1}{x^5 \left(a+b x^3\right)^{3/2}} \, dx","Integrate[1/(x^5*(a + b*x^3)^(3/2)),x]","-\frac{\sqrt{\frac{b x^3}{a}+1} \, _2F_1\left(-\frac{4}{3},\frac{3}{2};-\frac{1}{3};-\frac{b x^3}{a}\right)}{4 a x^4 \sqrt{a+b x^3}}","-\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^{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 \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,"-1/4*(Sqrt[1 + (b*x^3)/a]*Hypergeometric2F1[-4/3, 3/2, -1/3, -((b*x^3)/a)])/(a*x^4*Sqrt[a + b*x^3])","C",1
438,1,30,53,0.0095212,"\int \frac{x^{11}}{\sqrt{1+x^3}} \, dx","Integrate[x^11/Sqrt[1 + x^3],x]","\frac{2}{105} \sqrt{x^3+1} \left(5 x^9-6 x^6+8 x^3-16\right)","\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]*(-16 + 8*x^3 - 6*x^6 + 5*x^9))/105","A",1
439,1,25,40,0.0073103,"\int \frac{x^8}{\sqrt{1+x^3}} \, dx","Integrate[x^8/Sqrt[1 + x^3],x]","\frac{2}{45} \sqrt{x^3+1} \left(3 x^6-4 x^3+8\right)","\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]*(8 - 4*x^3 + 3*x^6))/45","A",1
440,1,18,27,0.0054227,"\int \frac{x^5}{\sqrt{1+x^3}} \, dx","Integrate[x^5/Sqrt[1 + x^3],x]","\frac{2}{9} \left(x^3-2\right) \sqrt{x^3+1}","\frac{2}{9} \left(x^3+1\right)^{3/2}-\frac{2 \sqrt{x^3+1}}{3}",1,"(2*(-2 + x^3)*Sqrt[1 + x^3])/9","A",1
441,1,13,13,0.0020792,"\int \frac{x^2}{\sqrt{1+x^3}} \, dx","Integrate[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
442,1,14,14,0.0024958,"\int \frac{1}{x \sqrt{1+x^3}} \, dx","Integrate[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",1
443,1,31,31,0.0078356,"\int \frac{1}{x^4 \sqrt{1+x^3}} \, dx","Integrate[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,"-1/3*Sqrt[1 + x^3]/x^3 + ArcTanh[Sqrt[1 + x^3]]/3","A",1
444,1,26,47,0.005015,"\int \frac{1}{x^7 \sqrt{1+x^3}} \, dx","Integrate[1/(x^7*Sqrt[1 + x^3]),x]","-\frac{2}{3} \sqrt{x^3+1} \, _2F_1\left(\frac{1}{2},3;\frac{3}{2};x^3+1\right)","\frac{\sqrt{x^3+1}}{4 x^3}-\frac{1}{4} \tanh ^{-1}\left(\sqrt{x^3+1}\right)-\frac{\sqrt{x^3+1}}{6 x^6}",1,"(-2*Sqrt[1 + x^3]*Hypergeometric2F1[1/2, 3, 3/2, 1 + x^3])/3","C",1
445,1,26,63,0.0049045,"\int \frac{1}{x^{10} \sqrt{1+x^3}} \, dx","Integrate[1/(x^10*Sqrt[1 + x^3]),x]","\frac{2}{3} \sqrt{x^3+1} \, _2F_1\left(\frac{1}{2},4;\frac{3}{2};x^3+1\right)","-\frac{5 \sqrt{x^3+1}}{24 x^3}+\frac{5}{24} \tanh ^{-1}\left(\sqrt{x^3+1}\right)-\frac{\sqrt{x^3+1}}{9 x^9}+\frac{5 \sqrt{x^3+1}}{36 x^6}",1,"(2*Sqrt[1 + x^3]*Hypergeometric2F1[1/2, 4, 3/2, 1 + x^3])/3","C",1
446,1,40,136,0.0119207,"\int \frac{x^6}{\sqrt{1+x^3}} \, dx","Integrate[x^6/Sqrt[1 + x^3],x]","\frac{2}{55} x \left(8 \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};-x^3\right)+\sqrt{x^3+1} \left(5 x^3-8\right)\right)","-\frac{16}{55} \sqrt{x^3+1} x+\frac{2}{11} \sqrt{x^3+1} x^4+\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,"(2*x*(Sqrt[1 + x^3]*(-8 + 5*x^3) + 8*Hypergeometric2F1[1/3, 1/2, 4/3, -x^3]))/55","C",1
447,1,32,120,0.0063431,"\int \frac{x^3}{\sqrt{1+x^3}} \, dx","Integrate[x^3/Sqrt[1 + x^3],x]","\frac{2}{5} x \left(\sqrt{x^3+1}-\, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};-x^3\right)\right)","\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] - Hypergeometric2F1[1/3, 1/2, 4/3, -x^3]))/5","C",1
448,1,17,103,0.0018361,"\int \frac{1}{\sqrt{1+x^3}} \, dx","Integrate[1/Sqrt[1 + x^3],x]","x \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};-x^3\right)","\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,"x*Hypergeometric2F1[1/3, 1/2, 4/3, -x^3]","C",1
449,1,22,122,0.0028271,"\int \frac{1}{x^3 \sqrt{1+x^3}} \, dx","Integrate[1/(x^3*Sqrt[1 + x^3]),x]","-\frac{\, _2F_1\left(-\frac{2}{3},\frac{1}{2};\frac{1}{3};-x^3\right)}{2 x^2}","-\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,"-1/2*Hypergeometric2F1[-2/3, 1/2, 1/3, -x^3]/x^2","C",1
450,1,22,138,0.0029568,"\int \frac{1}{x^6 \sqrt{1+x^3}} \, dx","Integrate[1/(x^6*Sqrt[1 + x^3]),x]","-\frac{\, _2F_1\left(-\frac{5}{3},\frac{1}{2};-\frac{2}{3};-x^3\right)}{5 x^5}","-\frac{\sqrt{x^3+1}}{5 x^5}+\frac{7 \sqrt{x^3+1}}{20 x^2}+\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,"-1/5*Hypergeometric2F1[-5/3, 1/2, -2/3, -x^3]/x^5","C",1
451,1,42,262,0.0133591,"\int \frac{x^7}{\sqrt{1+x^3}} \, dx","Integrate[x^7/Sqrt[1 + x^3],x]","\frac{2}{91} x^2 \left(10 \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};-x^3\right)+\sqrt{x^3+1} \left(7 x^3-10\right)\right)","\frac{80 \sqrt{x^3+1}}{91 \left(x+\sqrt{3}+1\right)}+\frac{2}{13} \sqrt{x^3+1} x^5-\frac{20}{91} \sqrt{x^3+1} x^2+\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,"(2*x^2*(Sqrt[1 + x^3]*(-10 + 7*x^3) + 10*Hypergeometric2F1[1/2, 2/3, 5/3, -x^3]))/91","C",1
452,1,34,246,0.0053128,"\int \frac{x^4}{\sqrt{1+x^3}} \, dx","Integrate[x^4/Sqrt[1 + x^3],x]","\frac{2}{7} x^2 \left(\sqrt{x^3+1}-\, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};-x^3\right)\right)","-\frac{8 \sqrt{x^3+1}}{7 \left(x+\sqrt{3}+1\right)}+\frac{2}{7} \sqrt{x^3+1} x^2-\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] - Hypergeometric2F1[1/2, 2/3, 5/3, -x^3]))/7","C",1
453,1,22,224,0.0023321,"\int \frac{x}{\sqrt{1+x^3}} \, dx","Integrate[x/Sqrt[1 + x^3],x]","\frac{1}{2} x^2 \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};-x^3\right)","\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,"(x^2*Hypergeometric2F1[1/2, 2/3, 5/3, -x^3])/2","C",1
454,1,20,238,0.0027631,"\int \frac{1}{x^2 \sqrt{1+x^3}} \, dx","Integrate[1/(x^2*Sqrt[1 + x^3]),x]","-\frac{\, _2F_1\left(-\frac{1}{3},\frac{1}{2};\frac{2}{3};-x^3\right)}{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}}",1,"-(Hypergeometric2F1[-1/3, 1/2, 2/3, -x^3]/x)","C",1
455,1,22,262,0.0138241,"\int \frac{1}{x^5 \sqrt{1+x^3}} \, dx","Integrate[1/(x^5*Sqrt[1 + x^3]),x]","-\frac{\, _2F_1\left(-\frac{4}{3},\frac{1}{2};-\frac{1}{3};-x^3\right)}{4 x^4}","\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,"-1/4*Hypergeometric2F1[-4/3, 1/2, -1/3, -x^3]/x^4","C",1
456,1,32,61,0.0111444,"\int \frac{x^{11}}{\sqrt{1-x^3}} \, dx","Integrate[x^11/Sqrt[1 - x^3],x]","-\frac{2}{105} \sqrt{1-x^3} \left(5 x^9+6 x^6+8 x^3+16\right)","\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]*(16 + 8*x^3 + 6*x^6 + 5*x^9))/105","A",1
457,1,27,46,0.008525,"\int \frac{x^8}{\sqrt{1-x^3}} \, dx","Integrate[x^8/Sqrt[1 - x^3],x]","-\frac{2}{45} \sqrt{1-x^3} \left(3 x^6+4 x^3+8\right)","-\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]*(8 + 4*x^3 + 3*x^6))/45","A",1
458,1,20,31,0.0063229,"\int \frac{x^5}{\sqrt{1-x^3}} \, dx","Integrate[x^5/Sqrt[1 - x^3],x]","-\frac{2}{9} \sqrt{1-x^3} \left(x^3+2\right)","\frac{2}{9} \left(1-x^3\right)^{3/2}-\frac{2 \sqrt{1-x^3}}{3}",1,"(-2*Sqrt[1 - x^3]*(2 + x^3))/9","A",1
459,1,15,15,0.005203,"\int \frac{x^2}{\sqrt{1-x^3}} \, dx","Integrate[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
460,1,16,16,0.00285,"\int \frac{1}{x \sqrt{1-x^3}} \, dx","Integrate[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",1
461,1,35,35,0.0112876,"\int \frac{1}{x^4 \sqrt{1-x^3}} \, dx","Integrate[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,"-1/3*Sqrt[1 - x^3]/x^3 - ArcTanh[Sqrt[1 - x^3]]/3","A",1
462,1,30,53,0.0052326,"\int \frac{1}{x^7 \sqrt{1-x^3}} \, dx","Integrate[1/(x^7*Sqrt[1 - x^3]),x]","-\frac{2}{3} \sqrt{1-x^3} \, _2F_1\left(\frac{1}{2},3;\frac{3}{2};1-x^3\right)","-\frac{\sqrt{1-x^3}}{4 x^3}-\frac{1}{4} \tanh ^{-1}\left(\sqrt{1-x^3}\right)-\frac{\sqrt{1-x^3}}{6 x^6}",1,"(-2*Sqrt[1 - x^3]*Hypergeometric2F1[1/2, 3, 3/2, 1 - x^3])/3","C",1
463,1,30,71,0.0055381,"\int \frac{1}{x^{10} \sqrt{1-x^3}} \, dx","Integrate[1/(x^10*Sqrt[1 - x^3]),x]","-\frac{2}{3} \sqrt{1-x^3} \, _2F_1\left(\frac{1}{2},4;\frac{3}{2};1-x^3\right)","-\frac{5 \sqrt{1-x^3}}{24 x^3}-\frac{5}{24} \tanh ^{-1}\left(\sqrt{1-x^3}\right)-\frac{\sqrt{1-x^3}}{9 x^9}-\frac{5 \sqrt{1-x^3}}{36 x^6}",1,"(-2*Sqrt[1 - x^3]*Hypergeometric2F1[1/2, 4, 3/2, 1 - x^3])/3","C",1
464,1,40,152,0.0326991,"\int \frac{x^6}{\sqrt{1-x^3}} \, dx","Integrate[x^6/Sqrt[1 - x^3],x]","-\frac{2}{55} x \left(\sqrt{1-x^3} \left(5 x^3+8\right)-8 \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};x^3\right)\right)","-\frac{16}{55} \sqrt{1-x^3} x-\frac{2}{11} \sqrt{1-x^3} x^4-\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,"(-2*x*(Sqrt[1 - x^3]*(8 + 5*x^3) - 8*Hypergeometric2F1[1/3, 1/2, 4/3, x^3]))/55","C",1
465,1,32,134,0.0058509,"\int \frac{x^3}{\sqrt{1-x^3}} \, dx","Integrate[x^3/Sqrt[1 - x^3],x]","\frac{2}{5} x \left(\, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};x^3\right)-\sqrt{1-x^3}\right)","-\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] + Hypergeometric2F1[1/3, 1/2, 4/3, x^3]))/5","C",1
466,1,15,115,0.0019653,"\int \frac{1}{\sqrt{1-x^3}} \, dx","Integrate[1/Sqrt[1 - x^3],x]","x \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};x^3\right)","-\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,"x*Hypergeometric2F1[1/3, 1/2, 4/3, x^3]","C",1
467,1,20,136,0.0031002,"\int \frac{1}{x^3 \sqrt{1-x^3}} \, dx","Integrate[1/(x^3*Sqrt[1 - x^3]),x]","-\frac{\, _2F_1\left(-\frac{2}{3},\frac{1}{2};\frac{1}{3};x^3\right)}{2 x^2}","-\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,"-1/2*Hypergeometric2F1[-2/3, 1/2, 1/3, x^3]/x^2","C",1
468,1,20,154,0.0031728,"\int \frac{1}{x^6 \sqrt{1-x^3}} \, dx","Integrate[1/(x^6*Sqrt[1 - x^3]),x]","-\frac{\, _2F_1\left(-\frac{5}{3},\frac{1}{2};-\frac{2}{3};x^3\right)}{5 x^5}","-\frac{\sqrt{1-x^3}}{5 x^5}-\frac{7 \sqrt{1-x^3}}{20 x^2}-\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,"-1/5*Hypergeometric2F1[-5/3, 1/2, -2/3, x^3]/x^5","C",1
469,1,42,294,0.0183108,"\int \frac{x^7}{\sqrt{1-x^3}} \, dx","Integrate[x^7/Sqrt[1 - x^3],x]","-\frac{2}{91} x^2 \left(\sqrt{1-x^3} \left(7 x^3+10\right)-10 \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};x^3\right)\right)","\frac{80 \sqrt{1-x^3}}{91 \left(-x+\sqrt{3}+1\right)}-\frac{2}{13} \sqrt{1-x^3} x^5-\frac{20}{91} \sqrt{1-x^3} x^2+\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,"(-2*x^2*(Sqrt[1 - x^3]*(10 + 7*x^3) - 10*Hypergeometric2F1[1/2, 2/3, 5/3, x^3]))/91","C",1
470,1,34,276,0.0062291,"\int \frac{x^4}{\sqrt{1-x^3}} \, dx","Integrate[x^4/Sqrt[1 - x^3],x]","\frac{2}{7} x^2 \left(\, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};x^3\right)-\sqrt{1-x^3}\right)","\frac{8 \sqrt{1-x^3}}{7 \left(-x+\sqrt{3}+1\right)}-\frac{2}{7} \sqrt{1-x^3} x^2+\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,"(2*x^2*(-Sqrt[1 - x^3] + Hypergeometric2F1[1/2, 2/3, 5/3, x^3]))/7","C",1
471,1,20,252,0.0026732,"\int \frac{x}{\sqrt{1-x^3}} \, dx","Integrate[x/Sqrt[1 - x^3],x]","\frac{1}{2} x^2 \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};x^3\right)","\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,"(x^2*Hypergeometric2F1[1/2, 2/3, 5/3, x^3])/2","C",1
472,1,18,270,0.0031355,"\int \frac{1}{x^2 \sqrt{1-x^3}} \, dx","Integrate[1/(x^2*Sqrt[1 - x^3]),x]","-\frac{\, _2F_1\left(-\frac{1}{3},\frac{1}{2};\frac{2}{3};x^3\right)}{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}}",1,"-(Hypergeometric2F1[-1/3, 1/2, 2/3, x^3]/x)","C",1
473,1,20,294,0.0029719,"\int \frac{1}{x^5 \sqrt{1-x^3}} \, dx","Integrate[1/(x^5*Sqrt[1 - x^3]),x]","-\frac{\, _2F_1\left(-\frac{4}{3},\frac{1}{2};-\frac{1}{3};x^3\right)}{4 x^4}","-\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,"-1/4*Hypergeometric2F1[-4/3, 1/2, -1/3, x^3]/x^4","C",1
474,1,30,53,0.0132402,"\int \frac{x^{11}}{\sqrt{-1+x^3}} \, dx","Integrate[x^11/Sqrt[-1 + x^3],x]","\frac{2}{105} \sqrt{x^3-1} \left(5 x^9+6 x^6+8 x^3+16\right)","\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]*(16 + 8*x^3 + 6*x^6 + 5*x^9))/105","A",1
475,1,25,40,0.007306,"\int \frac{x^8}{\sqrt{-1+x^3}} \, dx","Integrate[x^8/Sqrt[-1 + x^3],x]","\frac{2}{45} \sqrt{x^3-1} \left(3 x^6+4 x^3+8\right)","\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]*(8 + 4*x^3 + 3*x^6))/45","A",1
476,1,18,27,0.0055714,"\int \frac{x^5}{\sqrt{-1+x^3}} \, dx","Integrate[x^5/Sqrt[-1 + x^3],x]","\frac{2}{9} \sqrt{x^3-1} \left(x^3+2\right)","\frac{2}{9} \left(x^3-1\right)^{3/2}+\frac{2 \sqrt{x^3-1}}{3}",1,"(2*Sqrt[-1 + x^3]*(2 + x^3))/9","A",1
477,1,13,13,0.0020755,"\int \frac{x^2}{\sqrt{-1+x^3}} \, dx","Integrate[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
478,1,14,14,0.0025679,"\int \frac{1}{x \sqrt{-1+x^3}} \, dx","Integrate[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",1
479,1,41,31,0.0339121,"\int \frac{1}{x^4 \sqrt{-1+x^3}} \, dx","Integrate[1/(x^4*Sqrt[-1 + x^3]),x]","\frac{1}{3} \sqrt{x^3-1} \left(\frac{1}{x^3}+\frac{\tanh ^{-1}\left(\sqrt{1-x^3}\right)}{\sqrt{1-x^3}}\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]*(x^(-3) + ArcTanh[Sqrt[1 - x^3]]/Sqrt[1 - x^3]))/3","A",1
480,1,28,47,0.0042357,"\int \frac{1}{x^7 \sqrt{-1+x^3}} \, dx","Integrate[1/(x^7*Sqrt[-1 + x^3]),x]","\frac{2}{3} \sqrt{x^3-1} \, _2F_1\left(\frac{1}{2},3;\frac{3}{2};1-x^3\right)","\frac{\sqrt{x^3-1}}{4 x^3}+\frac{1}{4} \tan ^{-1}\left(\sqrt{x^3-1}\right)+\frac{\sqrt{x^3-1}}{6 x^6}",1,"(2*Sqrt[-1 + x^3]*Hypergeometric2F1[1/2, 3, 3/2, 1 - x^3])/3","C",1
481,1,28,63,0.0152517,"\int \frac{1}{x^{10} \sqrt{-1+x^3}} \, dx","Integrate[1/(x^10*Sqrt[-1 + x^3]),x]","\frac{2}{3} \sqrt{x^3-1} \, _2F_1\left(\frac{1}{2},4;\frac{3}{2};1-x^3\right)","\frac{5 \sqrt{x^3-1}}{24 x^3}+\frac{5}{24} \tan ^{-1}\left(\sqrt{x^3-1}\right)+\frac{\sqrt{x^3-1}}{9 x^9}+\frac{5 \sqrt{x^3-1}}{36 x^6}",1,"(2*Sqrt[-1 + x^3]*Hypergeometric2F1[1/2, 4, 3/2, 1 - x^3])/3","C",1
482,1,52,153,0.0129823,"\int \frac{x^6}{\sqrt{-1+x^3}} \, dx","Integrate[x^6/Sqrt[-1 + x^3],x]","\frac{2 x \left(8 \sqrt{1-x^3} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};x^3\right)+5 x^6+3 x^3-8\right)}{55 \sqrt{x^3-1}}","\frac{16}{55} \sqrt{x^3-1} x+\frac{2}{11} \sqrt{x^3-1} x^4-\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,"(2*x*(-8 + 3*x^3 + 5*x^6 + 8*Sqrt[1 - x^3]*Hypergeometric2F1[1/3, 1/2, 4/3, x^3]))/(55*Sqrt[-1 + x^3])","C",1
483,1,44,137,0.0091524,"\int \frac{x^3}{\sqrt{-1+x^3}} \, dx","Integrate[x^3/Sqrt[-1 + x^3],x]","\frac{2 x \left(\sqrt{1-x^3} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};x^3\right)+x^3-1\right)}{5 \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*(-1 + x^3 + Sqrt[1 - x^3]*Hypergeometric2F1[1/3, 1/2, 4/3, x^3]))/(5*Sqrt[-1 + x^3])","C",1
484,1,35,120,0.0032068,"\int \frac{1}{\sqrt{-1+x^3}} \, dx","Integrate[1/Sqrt[-1 + x^3],x]","\frac{x \sqrt{1-x^3} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};x^3\right)}{\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,"(x*Sqrt[1 - x^3]*Hypergeometric2F1[1/3, 1/2, 4/3, x^3])/Sqrt[-1 + x^3]","C",1
485,1,40,139,0.0058279,"\int \frac{1}{x^3 \sqrt{-1+x^3}} \, dx","Integrate[1/(x^3*Sqrt[-1 + x^3]),x]","-\frac{\sqrt{1-x^3} \, _2F_1\left(-\frac{2}{3},\frac{1}{2};\frac{1}{3};x^3\right)}{2 x^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,"-1/2*(Sqrt[1 - x^3]*Hypergeometric2F1[-2/3, 1/2, 1/3, x^3])/(x^2*Sqrt[-1 + x^3])","C",1
486,1,40,155,0.0057708,"\int \frac{1}{x^6 \sqrt{-1+x^3}} \, dx","Integrate[1/(x^6*Sqrt[-1 + x^3]),x]","-\frac{\sqrt{1-x^3} \, _2F_1\left(-\frac{5}{3},\frac{1}{2};-\frac{2}{3};x^3\right)}{5 x^5 \sqrt{x^3-1}}","\frac{\sqrt{x^3-1}}{5 x^5}+\frac{7 \sqrt{x^3-1}}{20 x^2}-\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,"-1/5*(Sqrt[1 - x^3]*Hypergeometric2F1[-5/3, 1/2, -2/3, x^3])/(x^5*Sqrt[-1 + x^3])","C",1
487,1,54,294,0.0106361,"\int \frac{x^7}{\sqrt{-1+x^3}} \, dx","Integrate[x^7/Sqrt[-1 + x^3],x]","\frac{2 x^2 \left(10 \sqrt{1-x^3} \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};x^3\right)+7 x^6+3 x^3-10\right)}{91 \sqrt{x^3-1}}","-\frac{80 \sqrt{x^3-1}}{91 \left(-x-\sqrt{3}+1\right)}+\frac{2}{13} \sqrt{x^3-1} x^5+\frac{20}{91} \sqrt{x^3-1} x^2-\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,"(2*x^2*(-10 + 3*x^3 + 7*x^6 + 10*Sqrt[1 - x^3]*Hypergeometric2F1[1/2, 2/3, 5/3, x^3]))/(91*Sqrt[-1 + x^3])","C",1
488,1,46,278,0.0103087,"\int \frac{x^4}{\sqrt{-1+x^3}} \, dx","Integrate[x^4/Sqrt[-1 + x^3],x]","\frac{2 x^2 \left(\sqrt{1-x^3} \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};x^3\right)+x^3-1\right)}{7 \sqrt{x^3-1}}","-\frac{8 \sqrt{x^3-1}}{7 \left(-x-\sqrt{3}+1\right)}+\frac{2}{7} \sqrt{x^3-1} x^2-\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,"(2*x^2*(-1 + x^3 + Sqrt[1 - x^3]*Hypergeometric2F1[1/2, 2/3, 5/3, x^3]))/(7*Sqrt[-1 + x^3])","C",1
489,1,40,255,0.0040178,"\int \frac{x}{\sqrt{-1+x^3}} \, dx","Integrate[x/Sqrt[-1 + x^3],x]","\frac{x^2 \sqrt{1-x^3} \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};x^3\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,"(x^2*Sqrt[1 - x^3]*Hypergeometric2F1[1/2, 2/3, 5/3, x^3])/(2*Sqrt[-1 + x^3])","C",1
490,1,38,269,0.0060043,"\int \frac{1}{x^2 \sqrt{-1+x^3}} \, dx","Integrate[1/(x^2*Sqrt[-1 + x^3]),x]","-\frac{\sqrt{1-x^3} \, _2F_1\left(-\frac{1}{3},\frac{1}{2};\frac{2}{3};x^3\right)}{x \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]*Hypergeometric2F1[-1/3, 1/2, 2/3, x^3])/(x*Sqrt[-1 + x^3]))","C",1
491,1,40,294,0.0061379,"\int \frac{1}{x^5 \sqrt{-1+x^3}} \, dx","Integrate[1/(x^5*Sqrt[-1 + x^3]),x]","-\frac{\sqrt{1-x^3} \, _2F_1\left(-\frac{4}{3},\frac{1}{2};-\frac{1}{3};x^3\right)}{4 x^4 \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,"-1/4*(Sqrt[1 - x^3]*Hypergeometric2F1[-4/3, 1/2, -1/3, x^3])/(x^4*Sqrt[-1 + x^3])","C",1
492,1,32,61,0.0110834,"\int \frac{x^{11}}{\sqrt{-1-x^3}} \, dx","Integrate[x^11/Sqrt[-1 - x^3],x]","-\frac{2}{105} \sqrt{-x^3-1} \left(5 x^9-6 x^6+8 x^3-16\right)","\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]*(-16 + 8*x^3 - 6*x^6 + 5*x^9))/105","A",1
493,1,27,46,0.0085443,"\int \frac{x^8}{\sqrt{-1-x^3}} \, dx","Integrate[x^8/Sqrt[-1 - x^3],x]","-\frac{2}{45} \sqrt{-x^3-1} \left(3 x^6-4 x^3+8\right)","-\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]*(8 - 4*x^3 + 3*x^6))/45","A",1
494,1,20,31,0.0064191,"\int \frac{x^5}{\sqrt{-1-x^3}} \, dx","Integrate[x^5/Sqrt[-1 - x^3],x]","-\frac{2}{9} \sqrt{-x^3-1} \left(x^3-2\right)","\frac{2}{9} \left(-x^3-1\right)^{3/2}+\frac{2}{3} \sqrt{-x^3-1}",1,"(-2*Sqrt[-1 - x^3]*(-2 + x^3))/9","A",1
495,1,15,15,0.0022989,"\int \frac{x^2}{\sqrt{-1-x^3}} \, dx","Integrate[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
496,1,16,16,0.0028618,"\int \frac{1}{x \sqrt{-1-x^3}} \, dx","Integrate[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",1
497,1,40,35,0.0241593,"\int \frac{1}{x^4 \sqrt{-1-x^3}} \, dx","Integrate[1/(x^4*Sqrt[-1 - x^3]),x]","\frac{1}{3} \sqrt{-x^3-1} \left(\frac{1}{x^3}-\frac{\tanh ^{-1}\left(\sqrt{x^3+1}\right)}{\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]*(x^(-3) - ArcTanh[Sqrt[1 + x^3]]/Sqrt[1 + x^3]))/3","A",1
498,1,28,53,0.0053486,"\int \frac{1}{x^7 \sqrt{-1-x^3}} \, dx","Integrate[1/(x^7*Sqrt[-1 - x^3]),x]","\frac{2}{3} \sqrt{-x^3-1} \, _2F_1\left(\frac{1}{2},3;\frac{3}{2};x^3+1\right)","-\frac{\sqrt{-x^3-1}}{4 x^3}+\frac{1}{4} \tan ^{-1}\left(\sqrt{-x^3-1}\right)+\frac{\sqrt{-x^3-1}}{6 x^6}",1,"(2*Sqrt[-1 - x^3]*Hypergeometric2F1[1/2, 3, 3/2, 1 + x^3])/3","C",1
499,1,28,71,0.0062039,"\int \frac{1}{x^{10} \sqrt{-1-x^3}} \, dx","Integrate[1/(x^10*Sqrt[-1 - x^3]),x]","-\frac{2}{3} \sqrt{-x^3-1} \, _2F_1\left(\frac{1}{2},4;\frac{3}{2};x^3+1\right)","\frac{5 \sqrt{-x^3-1}}{24 x^3}-\frac{5}{24} \tan ^{-1}\left(\sqrt{-x^3-1}\right)+\frac{\sqrt{-x^3-1}}{9 x^9}-\frac{5 \sqrt{-x^3-1}}{36 x^6}",1,"(-2*Sqrt[-1 - x^3]*Hypergeometric2F1[1/2, 4, 3/2, 1 + x^3])/3","C",1
500,1,54,149,0.0132774,"\int \frac{x^6}{\sqrt{-1-x^3}} \, dx","Integrate[x^6/Sqrt[-1 - x^3],x]","\frac{2 x \left(8 \sqrt{x^3+1} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};-x^3\right)+5 x^6-3 x^3-8\right)}{55 \sqrt{-x^3-1}}","\frac{16}{55} \sqrt{-x^3-1} x-\frac{2}{11} \sqrt{-x^3-1} x^4+\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,"(2*x*(-8 - 3*x^3 + 5*x^6 + 8*Sqrt[1 + x^3]*Hypergeometric2F1[1/3, 1/2, 4/3, -x^3]))/(55*Sqrt[-1 - x^3])","C",1
501,1,47,131,0.0193842,"\int \frac{x^3}{\sqrt{-1-x^3}} \, dx","Integrate[x^3/Sqrt[-1 - x^3],x]","\frac{2 \left(-\sqrt{x^3+1} x \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};-x^3\right)+x^4+x\right)}{5 \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 + x^4 - x*Sqrt[1 + x^3]*Hypergeometric2F1[1/3, 1/2, 4/3, -x^3]))/(5*Sqrt[-1 - x^3])","C",1
502,1,37,112,0.0036011,"\int \frac{1}{\sqrt{-1-x^3}} \, dx","Integrate[1/Sqrt[-1 - x^3],x]","\frac{x \sqrt{x^3+1} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};-x^3\right)}{\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,"(x*Sqrt[1 + x^3]*Hypergeometric2F1[1/3, 1/2, 4/3, -x^3])/Sqrt[-1 - x^3]","C",1
503,1,42,133,0.0052717,"\int \frac{1}{x^3 \sqrt{-1-x^3}} \, dx","Integrate[1/(x^3*Sqrt[-1 - x^3]),x]","-\frac{\sqrt{x^3+1} \, _2F_1\left(-\frac{2}{3},\frac{1}{2};\frac{1}{3};-x^3\right)}{2 x^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,"-1/2*(Sqrt[1 + x^3]*Hypergeometric2F1[-2/3, 1/2, 1/3, -x^3])/(x^2*Sqrt[-1 - x^3])","C",1
504,1,42,151,0.0286667,"\int \frac{1}{x^6 \sqrt{-1-x^3}} \, dx","Integrate[1/(x^6*Sqrt[-1 - x^3]),x]","-\frac{\sqrt{x^3+1} \, _2F_1\left(-\frac{5}{3},\frac{1}{2};-\frac{2}{3};-x^3\right)}{5 x^5 \sqrt{-x^3-1}}","\frac{\sqrt{-x^3-1}}{5 x^5}-\frac{7 \sqrt{-x^3-1}}{20 x^2}+\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,"-1/5*(Sqrt[1 + x^3]*Hypergeometric2F1[-5/3, 1/2, -2/3, -x^3])/(x^5*Sqrt[-1 - x^3])","C",1
505,1,56,282,0.0137124,"\int \frac{x^7}{\sqrt{-1-x^3}} \, dx","Integrate[x^7/Sqrt[-1 - x^3],x]","\frac{2 x^2 \left(10 \sqrt{x^3+1} \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};-x^3\right)+7 x^6-3 x^3-10\right)}{91 \sqrt{-x^3-1}}","-\frac{80 \sqrt{-x^3-1}}{91 \left(x-\sqrt{3}+1\right)}-\frac{2}{13} \sqrt{-x^3-1} x^5+\frac{20}{91} \sqrt{-x^3-1} x^2-\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,"(2*x^2*(-10 - 3*x^3 + 7*x^6 + 10*Sqrt[1 + x^3]*Hypergeometric2F1[1/2, 2/3, 5/3, -x^3]))/(91*Sqrt[-1 - x^3])","C",1
506,1,49,264,0.0111632,"\int \frac{x^4}{\sqrt{-1-x^3}} \, dx","Integrate[x^4/Sqrt[-1 - x^3],x]","\frac{2 x^2 \left(-\sqrt{x^3+1} \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};-x^3\right)+x^3+1\right)}{7 \sqrt{-x^3-1}}","\frac{8 \sqrt{-x^3-1}}{7 \left(x-\sqrt{3}+1\right)}-\frac{2}{7} \sqrt{-x^3-1} x^2+\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*(1 + x^3 - Sqrt[1 + x^3]*Hypergeometric2F1[1/2, 2/3, 5/3, -x^3]))/(7*Sqrt[-1 - x^3])","C",1
507,1,42,239,0.004756,"\int \frac{x}{\sqrt{-1-x^3}} \, dx","Integrate[x/Sqrt[-1 - x^3],x]","\frac{x^2 \sqrt{x^3+1} \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};-x^3\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,"(x^2*Sqrt[1 + x^3]*Hypergeometric2F1[1/2, 2/3, 5/3, -x^3])/(2*Sqrt[-1 - x^3])","C",1
508,1,40,257,0.0059741,"\int \frac{1}{x^2 \sqrt{-1-x^3}} \, dx","Integrate[1/(x^2*Sqrt[-1 - x^3]),x]","-\frac{\sqrt{x^3+1} \, _2F_1\left(-\frac{1}{3},\frac{1}{2};\frac{2}{3};-x^3\right)}{x \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]*Hypergeometric2F1[-1/3, 1/2, 2/3, -x^3])/(x*Sqrt[-1 - x^3]))","C",1
509,1,42,282,0.0062362,"\int \frac{1}{x^5 \sqrt{-1-x^3}} \, dx","Integrate[1/(x^5*Sqrt[-1 - x^3]),x]","-\frac{\sqrt{x^3+1} \, _2F_1\left(-\frac{4}{3},\frac{1}{2};-\frac{1}{3};-x^3\right)}{4 x^4 \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,"-1/4*(Sqrt[1 + x^3]*Hypergeometric2F1[-4/3, 1/2, -1/3, -x^3])/(x^4*Sqrt[-1 - x^3])","C",1
510,1,50,80,0.0397738,"\int x^{11} \sqrt[3]{a+b x^3} \, dx","Integrate[x^11*(a + b*x^3)^(1/3),x]","\frac{\left(a+b x^3\right)^{4/3} \left(-81 a^3+108 a^2 b x^3-126 a b^2 x^6+140 b^3 x^9\right)}{1820 b^4}","-\frac{a^3 \left(a+b x^3\right)^{4/3}}{4 b^4}+\frac{3 a^2 \left(a+b x^3\right)^{7/3}}{7 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 + b*x^3)^(4/3)*(-81*a^3 + 108*a^2*b*x^3 - 126*a*b^2*x^6 + 140*b^3*x^9))/(1820*b^4)","A",1
511,1,39,59,0.0319304,"\int x^8 \sqrt[3]{a+b x^3} \, dx","Integrate[x^8*(a + b*x^3)^(1/3),x]","\frac{\left(a+b x^3\right)^{4/3} \left(9 a^2-12 a b x^3+14 b^2 x^6\right)}{140 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 + b*x^3)^(4/3)*(9*a^2 - 12*a*b*x^3 + 14*b^2*x^6))/(140*b^3)","A",1
512,1,28,38,0.0190692,"\int x^5 \sqrt[3]{a+b x^3} \, dx","Integrate[x^5*(a + b*x^3)^(1/3),x]","\frac{\left(a+b x^3\right)^{4/3} \left(4 b x^3-3 a\right)}{28 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 + b*x^3)^(4/3)*(-3*a + 4*b*x^3))/(28*b^2)","A",1
513,1,18,18,0.0037931,"\int x^2 \sqrt[3]{a+b x^3} \, dx","Integrate[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
514,1,124,95,0.067373,"\int \frac{\sqrt[3]{a+b x^3}}{x} \, dx","Integrate[(a + b*x^3)^(1/3)/x,x]","-\frac{1}{6} \sqrt[3]{a} \log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^3}+\left(a+b x^3\right)^{2/3}\right)+\sqrt[3]{a+b x^3}+\frac{1}{3} \sqrt[3]{a} \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)-\frac{\sqrt[3]{a} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{a+b x^3}}{\sqrt[3]{a}}+1}{\sqrt{3}}\right)}{\sqrt{3}}","\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[(1 + (2*(a + b*x^3)^(1/3))/a^(1/3))/Sqrt[3]])/Sqrt[3] + (a^(1/3)*Log[a^(1/3) - (a + b*x^3)^(1/3)])/3 - (a^(1/3)*Log[a^(2/3) + a^(1/3)*(a + b*x^3)^(1/3) + (a + b*x^3)^(2/3)])/6","A",1
515,1,37,107,0.0087298,"\int \frac{\sqrt[3]{a+b x^3}}{x^4} \, dx","Integrate[(a + b*x^3)^(1/3)/x^4,x]","\frac{b \left(a+b x^3\right)^{4/3} \, _2F_1\left(\frac{4}{3},2;\frac{7}{3};\frac{b x^3}{a}+1\right)}{4 a^2}","\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,"(b*(a + b*x^3)^(4/3)*Hypergeometric2F1[4/3, 2, 7/3, 1 + (b*x^3)/a])/(4*a^2)","C",1
516,1,64,120,0.0876909,"\int x^4 \sqrt[3]{a+b x^3} \, dx","Integrate[x^4*(a + b*x^3)^(1/3),x]","\frac{x^2 \sqrt[3]{a+b x^3} \left(-\frac{a \, _2F_1\left(-\frac{1}{3},\frac{2}{3};\frac{5}{3};-\frac{b x^3}{a}\right)}{\sqrt[3]{\frac{b x^3}{a}+1}}+a+b x^3\right)}{6 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,"(x^2*(a + b*x^3)^(1/3)*(a + b*x^3 - (a*Hypergeometric2F1[-1/3, 2/3, 5/3, -((b*x^3)/a)])/(1 + (b*x^3)/a)^(1/3)))/(6*b)","C",1
517,1,51,94,0.0120456,"\int x \sqrt[3]{a+b x^3} \, dx","Integrate[x*(a + b*x^3)^(1/3),x]","\frac{x^2 \sqrt[3]{a+b x^3} \, _2F_1\left(-\frac{1}{3},\frac{2}{3};\frac{5}{3};-\frac{b x^3}{a}\right)}{2 \sqrt[3]{\frac{b x^3}{a}+1}}","-\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)*Hypergeometric2F1[-1/3, 2/3, 5/3, -((b*x^3)/a)])/(2*(1 + (b*x^3)/a)^(1/3))","C",1
518,1,49,88,0.0089932,"\int \frac{\sqrt[3]{a+b x^3}}{x^2} \, dx","Integrate[(a + b*x^3)^(1/3)/x^2,x]","-\frac{\sqrt[3]{a+b x^3} \, _2F_1\left(-\frac{1}{3},-\frac{1}{3};\frac{2}{3};-\frac{b x^3}{a}\right)}{x \sqrt[3]{\frac{b x^3}{a}+1}}","-\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)*Hypergeometric2F1[-1/3, -1/3, 2/3, -((b*x^3)/a)])/(x*(1 + (b*x^3)/a)^(1/3)))","C",1
519,1,21,21,0.0045114,"\int \frac{\sqrt[3]{a+b x^3}}{x^5} \, dx","Integrate[(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,"-1/4*(a + b*x^3)^(4/3)/(a*x^4)","A",1
520,1,31,44,0.0091605,"\int \frac{\sqrt[3]{a+b x^3}}{x^8} \, dx","Integrate[(a + b*x^3)^(1/3)/x^8,x]","\frac{\left(a+b x^3\right)^{4/3} \left(3 b x^3-4 a\right)}{28 a^2 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)*(-4*a + 3*b*x^3))/(28*a^2*x^7)","A",1
521,1,42,68,0.0180608,"\int \frac{\sqrt[3]{a+b x^3}}{x^{11}} \, dx","Integrate[(a + b*x^3)^(1/3)/x^11,x]","-\frac{\left(a+b x^3\right)^{4/3} \left(14 a^2-12 a b x^3+9 b^2 x^6\right)}{140 a^3 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,"-1/140*((a + b*x^3)^(4/3)*(14*a^2 - 12*a*b*x^3 + 9*b^2*x^6))/(a^3*x^10)","A",1
522,1,53,92,0.0368016,"\int \frac{\sqrt[3]{a+b x^3}}{x^{14}} \, dx","Integrate[(a + b*x^3)^(1/3)/x^14,x]","\frac{\left(a+b x^3\right)^{4/3} \left(-140 a^3+126 a^2 b x^3-108 a b^2 x^6+81 b^3 x^9\right)}{1820 a^4 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)*(-140*a^3 + 126*a^2*b*x^3 - 108*a*b^2*x^6 + 81*b^3*x^9))/(1820*a^4*x^13)","A",1
523,1,51,38,0.0115238,"\int x^3 \sqrt[3]{a+b x^3} \, dx","Integrate[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",1
524,1,196,33,0.2490544,"\int \sqrt[3]{a+b x^3} \, dx","Integrate[(a + b*x^3)^(1/3),x]","\frac{3 \left((-1)^{2/3} \sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt[3]{a+b x^3} F_1\left(\frac{4}{3};-\frac{1}{3},-\frac{1}{3};\frac{7}{3};-\frac{i \left(\sqrt[3]{b} x+(-1)^{2/3} \sqrt[3]{a}\right)}{\sqrt{3} \sqrt[3]{a}},\frac{-\frac{2 i \sqrt[3]{b} x}{\sqrt[3]{a}}+\sqrt{3}+i}{3 i+\sqrt{3}}\right)}{4 \sqrt[3]{2} \sqrt[3]{b} \sqrt[3]{\frac{\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b} x}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{a}}} \sqrt[3]{\frac{i \left(\frac{\sqrt[3]{b} x}{\sqrt[3]{a}}+1\right)}{\sqrt{3}+3 i}}}","\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,"(3*((-1)^(2/3)*a^(1/3) + b^(1/3)*x)*(a + b*x^3)^(1/3)*AppellF1[4/3, -1/3, -1/3, 7/3, ((-I)*((-1)^(2/3)*a^(1/3) + b^(1/3)*x))/(Sqrt[3]*a^(1/3)), (I + Sqrt[3] - ((2*I)*b^(1/3)*x)/a^(1/3))/(3*I + Sqrt[3])])/(4*2^(1/3)*b^(1/3)*((a^(1/3) + (-1)^(2/3)*b^(1/3)*x)/((1 + (-1)^(1/3))*a^(1/3)))^(1/3)*((I*(1 + (b^(1/3)*x)/a^(1/3)))/(3*I + Sqrt[3]))^(1/3))","C",0
525,1,51,38,0.0099513,"\int \frac{\sqrt[3]{a+b x^3}}{x^3} \, dx","Integrate[(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,"-1/2*((a + b*x^3)^(1/3)*Hypergeometric2F1[-2/3, -1/3, 1/3, -((b*x^3)/a)])/(x^2*(1 + (b*x^3)/a)^(1/3))","A",1
526,1,51,38,0.0097558,"\int \frac{\sqrt[3]{a+b x^3}}{x^6} \, dx","Integrate[(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,"-1/5*((a + b*x^3)^(1/3)*Hypergeometric2F1[-5/3, -1/3, -2/3, -((b*x^3)/a)])/(x^5*(1 + (b*x^3)/a)^(1/3))","A",1
527,1,50,80,0.0260121,"\int x^{11} \left(a+b x^3\right)^{2/3} \, dx","Integrate[x^11*(a + b*x^3)^(2/3),x]","\frac{\left(a+b x^3\right)^{5/3} \left(-81 a^3+135 a^2 b x^3-180 a b^2 x^6+220 b^3 x^9\right)}{3080 b^4}","-\frac{a^3 \left(a+b x^3\right)^{5/3}}{5 b^4}+\frac{3 a^2 \left(a+b x^3\right)^{8/3}}{8 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 + b*x^3)^(5/3)*(-81*a^3 + 135*a^2*b*x^3 - 180*a*b^2*x^6 + 220*b^3*x^9))/(3080*b^4)","A",1
528,1,39,59,0.041835,"\int x^8 \left(a+b x^3\right)^{2/3} \, dx","Integrate[x^8*(a + b*x^3)^(2/3),x]","\frac{\left(a+b x^3\right)^{5/3} \left(9 a^2-15 a b x^3+20 b^2 x^6\right)}{220 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 + b*x^3)^(5/3)*(9*a^2 - 15*a*b*x^3 + 20*b^2*x^6))/(220*b^3)","A",1
529,1,28,38,0.0165558,"\int x^5 \left(a+b x^3\right)^{2/3} \, dx","Integrate[x^5*(a + b*x^3)^(2/3),x]","\frac{\left(a+b x^3\right)^{5/3} \left(5 b x^3-3 a\right)}{40 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 + b*x^3)^(5/3)*(-3*a + 5*b*x^3))/(40*b^2)","A",1
530,1,18,18,0.0038796,"\int x^2 \left(a+b x^3\right)^{2/3} \, dx","Integrate[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
531,1,90,98,0.0833541,"\int \frac{\left(a+b x^3\right)^{2/3}}{x} \, dx","Integrate[(a + b*x^3)^(2/3)/x,x]","\frac{1}{2} \left(a^{2/3} \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)-a^{2/3} \log (x)+\left(a+b x^3\right)^{2/3}\right)+\frac{a^{2/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{a+b x^3}}{\sqrt[3]{a}}+1}{\sqrt{3}}\right)}{\sqrt{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^(2/3)*ArcTan[(1 + (2*(a + b*x^3)^(1/3))/a^(1/3))/Sqrt[3]])/Sqrt[3] + ((a + b*x^3)^(2/3) - a^(2/3)*Log[x] + a^(2/3)*Log[a^(1/3) - (a + b*x^3)^(1/3)])/2","A",1
532,1,37,107,0.0082305,"\int \frac{\left(a+b x^3\right)^{2/3}}{x^4} \, dx","Integrate[(a + b*x^3)^(2/3)/x^4,x]","\frac{b \left(a+b x^3\right)^{5/3} \, _2F_1\left(\frac{5}{3},2;\frac{8}{3};\frac{b x^3}{a}+1\right)}{5 a^2}","-\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,"(b*(a + b*x^3)^(5/3)*Hypergeometric2F1[5/3, 2, 8/3, 1 + (b*x^3)/a])/(5*a^2)","C",1
533,1,51,38,0.0130611,"\int x^4 \left(a+b x^3\right)^{2/3} \, dx","Integrate[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",1
534,1,51,38,0.0094783,"\int x \left(a+b x^3\right)^{2/3} \, dx","Integrate[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",1
535,1,49,36,0.0184342,"\int \frac{\left(a+b x^3\right)^{2/3}}{x^2} \, dx","Integrate[(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",1
536,1,51,38,0.0098589,"\int \frac{\left(a+b x^3\right)^{2/3}}{x^5} \, dx","Integrate[(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,"-1/4*((a + b*x^3)^(2/3)*Hypergeometric2F1[-4/3, -2/3, -1/3, -((b*x^3)/a)])/(x^4*(1 + (b*x^3)/a)^(2/3))","A",1
537,1,62,117,0.0567645,"\int x^3 \left(a+b x^3\right)^{2/3} \, dx","Integrate[x^3*(a + b*x^3)^(2/3),x]","\frac{x \left(a+b x^3\right)^{2/3} \left(-\frac{a \, _2F_1\left(-\frac{2}{3},\frac{1}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{\left(\frac{b x^3}{a}+1\right)^{2/3}}+a+b x^3\right)}{6 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{a x \left(a+b x^3\right)^{2/3}}{9 b}+\frac{1}{6} x^4 \left(a+b x^3\right)^{2/3}",1,"(x*(a + b*x^3)^(2/3)*(a + b*x^3 - (a*Hypergeometric2F1[-2/3, 1/3, 4/3, -((b*x^3)/a)])/(1 + (b*x^3)/a)^(2/3)))/(6*b)","C",1
538,1,196,91,0.2206477,"\int \left(a+b x^3\right)^{2/3} \, dx","Integrate[(a + b*x^3)^(2/3),x]","\frac{3 \left((-1)^{2/3} \sqrt[3]{a}+\sqrt[3]{b} x\right) \left(a+b x^3\right)^{2/3} F_1\left(\frac{5}{3};-\frac{2}{3},-\frac{2}{3};\frac{8}{3};-\frac{i \left(\sqrt[3]{b} x+(-1)^{2/3} \sqrt[3]{a}\right)}{\sqrt{3} \sqrt[3]{a}},\frac{-\frac{2 i \sqrt[3]{b} x}{\sqrt[3]{a}}+\sqrt{3}+i}{3 i+\sqrt{3}}\right)}{5\ 2^{2/3} \sqrt[3]{b} \left(\frac{\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b} x}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{a}}\right)^{2/3} \left(\frac{i \left(\frac{\sqrt[3]{b} x}{\sqrt[3]{a}}+1\right)}{\sqrt{3}+3 i}\right)^{2/3}}","\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,"(3*((-1)^(2/3)*a^(1/3) + b^(1/3)*x)*(a + b*x^3)^(2/3)*AppellF1[5/3, -2/3, -2/3, 8/3, ((-I)*((-1)^(2/3)*a^(1/3) + b^(1/3)*x))/(Sqrt[3]*a^(1/3)), (I + Sqrt[3] - ((2*I)*b^(1/3)*x)/a^(1/3))/(3*I + Sqrt[3])])/(5*2^(2/3)*b^(1/3)*((a^(1/3) + (-1)^(2/3)*b^(1/3)*x)/((1 + (-1)^(1/3))*a^(1/3)))^(2/3)*((I*(1 + (b^(1/3)*x)/a^(1/3)))/(3*I + Sqrt[3]))^(2/3))","C",0
539,1,51,88,0.012471,"\int \frac{\left(a+b x^3\right)^{2/3}}{x^3} \, dx","Integrate[(a + b*x^3)^(2/3)/x^3,x]","-\frac{\left(a+b x^3\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(\frac{b x^3}{a}+1\right)^{2/3}}","-\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,"-1/2*((a + b*x^3)^(2/3)*Hypergeometric2F1[-2/3, -2/3, 1/3, -((b*x^3)/a)])/(x^2*(1 + (b*x^3)/a)^(2/3))","C",1
540,1,21,21,0.0050123,"\int \frac{\left(a+b x^3\right)^{2/3}}{x^6} \, dx","Integrate[(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,"-1/5*(a + b*x^3)^(5/3)/(a*x^5)","A",1
541,1,31,44,0.0100128,"\int \frac{\left(a+b x^3\right)^{2/3}}{x^9} \, dx","Integrate[(a + b*x^3)^(2/3)/x^9,x]","\frac{\left(a+b x^3\right)^{5/3} \left(3 b x^3-5 a\right)}{40 a^2 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)*(-5*a + 3*b*x^3))/(40*a^2*x^8)","A",1
542,1,42,68,0.0122262,"\int \frac{\left(a+b x^3\right)^{2/3}}{x^{12}} \, dx","Integrate[(a + b*x^3)^(2/3)/x^12,x]","-\frac{\left(a+b x^3\right)^{5/3} \left(20 a^2-15 a b x^3+9 b^2 x^6\right)}{220 a^3 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,"-1/220*((a + b*x^3)^(5/3)*(20*a^2 - 15*a*b*x^3 + 9*b^2*x^6))/(a^3*x^11)","A",1
543,1,27,46,0.0145167,"\int x^8 \left(1-x^3\right)^{6/5} \, dx","Integrate[x^8*(1 - x^3)^(6/5),x]","-\frac{5 \left(1-x^3\right)^{11/5} \left(88 x^6+55 x^3+25\right)}{5544}","-\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)*(25 + 55*x^3 + 88*x^6))/5544","A",1
544,1,50,80,0.0248803,"\int \frac{x^{11}}{\sqrt[3]{a+b x^3}} \, dx","Integrate[x^11/(a + b*x^3)^(1/3),x]","\frac{\left(a+b x^3\right)^{2/3} \left(-81 a^3+54 a^2 b x^3-45 a b^2 x^6+40 b^3 x^9\right)}{440 b^4}","-\frac{a^3 \left(a+b x^3\right)^{2/3}}{2 b^4}+\frac{3 a^2 \left(a+b x^3\right)^{5/3}}{5 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 + b*x^3)^(2/3)*(-81*a^3 + 54*a^2*b*x^3 - 45*a*b^2*x^6 + 40*b^3*x^9))/(440*b^4)","A",1
545,1,39,59,0.0193302,"\int \frac{x^8}{\sqrt[3]{a+b x^3}} \, dx","Integrate[x^8/(a + b*x^3)^(1/3),x]","\frac{\left(a+b x^3\right)^{2/3} \left(9 a^2-6 a b x^3+5 b^2 x^6\right)}{40 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 + b*x^3)^(2/3)*(9*a^2 - 6*a*b*x^3 + 5*b^2*x^6))/(40*b^3)","A",1
546,1,28,38,0.0121075,"\int \frac{x^5}{\sqrt[3]{a+b x^3}} \, dx","Integrate[x^5/(a + b*x^3)^(1/3),x]","\frac{\left(a+b x^3\right)^{2/3} \left(2 b x^3-3 a\right)}{10 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 + b*x^3)^(2/3)*(-3*a + 2*b*x^3))/(10*b^2)","A",1
547,1,18,18,0.0033147,"\int \frac{x^2}{\sqrt[3]{a+b x^3}} \, dx","Integrate[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
548,1,70,83,0.0203206,"\int \frac{1}{x \sqrt[3]{a+b x^3}} \, dx","Integrate[1/(x*(a + b*x^3)^(1/3)),x]","\frac{3 \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{a+b x^3}}{\sqrt[3]{a}}+1}{\sqrt{3}}\right)-3 \log (x)}{6 \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,"(2*Sqrt[3]*ArcTan[(1 + (2*(a + b*x^3)^(1/3))/a^(1/3))/Sqrt[3]] - 3*Log[x] + 3*Log[a^(1/3) - (a + b*x^3)^(1/3)])/(6*a^(1/3))","A",1
549,1,37,110,0.0072824,"\int \frac{1}{x^4 \sqrt[3]{a+b x^3}} \, dx","Integrate[1/(x^4*(a + b*x^3)^(1/3)),x]","\frac{b \left(a+b x^3\right)^{2/3} \, _2F_1\left(\frac{2}{3},2;\frac{5}{3};\frac{b x^3}{a}+1\right)}{2 a^2}","-\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,"(b*(a + b*x^3)^(2/3)*Hypergeometric2F1[2/3, 2, 5/3, 1 + (b*x^3)/a])/(2*a^2)","C",1
550,1,51,38,0.0104049,"\int \frac{x^7}{\sqrt[3]{a+b x^3}} \, dx","Integrate[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",1
551,1,51,38,0.009252,"\int \frac{x^4}{\sqrt[3]{a+b x^3}} \, dx","Integrate[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",1
552,1,51,38,0.0082984,"\int \frac{x}{\sqrt[3]{a+b x^3}} \, dx","Integrate[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",1
553,1,49,36,0.0092234,"\int \frac{1}{x^2 \sqrt[3]{a+b x^3}} \, dx","Integrate[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",1
554,1,51,38,0.0094763,"\int \frac{1}{x^5 \sqrt[3]{a+b x^3}} \, dx","Integrate[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,"-1/4*((1 + (b*x^3)/a)^(1/3)*Hypergeometric2F1[-4/3, 1/3, -1/3, -((b*x^3)/a)])/(x^4*(a + b*x^3)^(1/3))","A",1
555,1,134,94,0.1067307,"\int \frac{x^3}{\sqrt[3]{a+b x^3}} \, dx","Integrate[x^3/(a + b*x^3)^(1/3),x]","\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)+6 \sqrt[3]{b} x \left(a+b x^3\right)^{2/3}+2 a \log \left(1-\frac{\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}\right)-2 \sqrt{3} a \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{18 b^{4/3}}","\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,"(6*b^(1/3)*x*(a + b*x^3)^(2/3) - 2*Sqrt[3]*a*ArcTan[(1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/Sqrt[3]] + 2*a*Log[1 - (b^(1/3)*x)/(a + b*x^3)^(1/3)] - 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^(4/3))","A",1
556,1,110,70,0.0215067,"\int \frac{1}{\sqrt[3]{a+b x^3}} \, dx","Integrate[(a + b*x^3)^(-1/3),x]","\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)-2 \log \left(1-\frac{\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{6 \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,"(2*Sqrt[3]*ArcTan[(1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/Sqrt[3]] - 2*Log[1 - (b^(1/3)*x)/(a + b*x^3)^(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*b^(1/3))","A",1
557,1,21,21,0.0041089,"\int \frac{1}{x^3 \sqrt[3]{a+b x^3}} \, dx","Integrate[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,"-1/2*(a + b*x^3)^(2/3)/(a*x^2)","A",1
558,1,31,44,0.011708,"\int \frac{1}{x^6 \sqrt[3]{a+b x^3}} \, dx","Integrate[1/(x^6*(a + b*x^3)^(1/3)),x]","\frac{\left(a+b x^3\right)^{2/3} \left(3 b x^3-2 a\right)}{10 a^2 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)*(-2*a + 3*b*x^3))/(10*a^2*x^5)","A",1
559,1,42,68,0.0330697,"\int \frac{1}{x^9 \sqrt[3]{a+b x^3}} \, dx","Integrate[1/(x^9*(a + b*x^3)^(1/3)),x]","-\frac{\left(a+b x^3\right)^{2/3} \left(5 a^2-6 a b x^3+9 b^2 x^6\right)}{40 a^3 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,"-1/40*((a + b*x^3)^(2/3)*(5*a^2 - 6*a*b*x^3 + 9*b^2*x^6))/(a^3*x^8)","A",1
560,1,53,92,0.0244816,"\int \frac{1}{x^{12} \sqrt[3]{a+b x^3}} \, dx","Integrate[1/(x^12*(a + b*x^3)^(1/3)),x]","\frac{\left(a+b x^3\right)^{2/3} \left(-40 a^3+45 a^2 b x^3-54 a b^2 x^6+81 b^3 x^9\right)}{440 a^4 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)*(-40*a^3 + 45*a^2*b*x^3 - 54*a*b^2*x^6 + 81*b^3*x^9))/(440*a^4*x^11)","A",1
561,1,50,78,0.0345279,"\int \frac{x^{11}}{\left(a+b x^3\right)^{2/3}} \, dx","Integrate[x^11/(a + b*x^3)^(2/3),x]","\frac{\sqrt[3]{a+b x^3} \left(-81 a^3+27 a^2 b x^3-18 a b^2 x^6+14 b^3 x^9\right)}{140 b^4}","-\frac{a^3 \sqrt[3]{a+b x^3}}{b^4}+\frac{3 a^2 \left(a+b x^3\right)^{4/3}}{4 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 + b*x^3)^(1/3)*(-81*a^3 + 27*a^2*b*x^3 - 18*a*b^2*x^6 + 14*b^3*x^9))/(140*b^4)","A",1
562,1,39,56,0.0219314,"\int \frac{x^8}{\left(a+b x^3\right)^{2/3}} \, dx","Integrate[x^8/(a + b*x^3)^(2/3),x]","\frac{\sqrt[3]{a+b x^3} \left(9 a^2-3 a b x^3+2 b^2 x^6\right)}{14 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 + b*x^3)^(1/3)*(9*a^2 - 3*a*b*x^3 + 2*b^2*x^6))/(14*b^3)","A",1
563,1,27,36,0.0328151,"\int \frac{x^5}{\left(a+b x^3\right)^{2/3}} \, dx","Integrate[x^5/(a + b*x^3)^(2/3),x]","\frac{\left(b x^3-3 a\right) \sqrt[3]{a+b x^3}}{4 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,"((-3*a + b*x^3)*(a + b*x^3)^(1/3))/(4*b^2)","A",1
564,1,15,15,0.0031199,"\int \frac{x^2}{\left(a+b x^3\right)^{2/3}} \, dx","Integrate[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
565,1,101,84,0.0455357,"\int \frac{1}{x \left(a+b x^3\right)^{2/3}} \, dx","Integrate[1/(x*(a + b*x^3)^(2/3)),x]","-\frac{\log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^3}+\left(a+b x^3\right)^{2/3}\right)-2 \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{a+b x^3}}{\sqrt[3]{a}}+1}{\sqrt{3}}\right)}{6 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,"-1/6*(2*Sqrt[3]*ArcTan[(1 + (2*(a + b*x^3)^(1/3))/a^(1/3))/Sqrt[3]] - 2*Log[a^(1/3) - (a + b*x^3)^(1/3)] + Log[a^(2/3) + a^(1/3)*(a + b*x^3)^(1/3) + (a + b*x^3)^(2/3)])/a^(2/3)","A",1
566,1,34,110,0.0067543,"\int \frac{1}{x^4 \left(a+b x^3\right)^{2/3}} \, dx","Integrate[1/(x^4*(a + b*x^3)^(2/3)),x]","\frac{b \sqrt[3]{a+b x^3} \, _2F_1\left(\frac{1}{3},2;\frac{4}{3};\frac{b x^3}{a}+1\right)}{a^2}","-\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,"(b*(a + b*x^3)^(1/3)*Hypergeometric2F1[1/3, 2, 4/3, 1 + (b*x^3)/a])/a^2","C",1
567,1,69,123,0.0204655,"\int \frac{x^7}{\left(a+b x^3\right)^{2/3}} \, dx","Integrate[x^7/(a + b*x^3)^(2/3),x]","\frac{x^2 \left(5 a^2 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{b x^3}{b x^3+a}\right)-5 a^2-2 a b x^3+3 b^2 x^6\right)}{18 b^2 \left(a+b x^3\right)^{2/3}}","-\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,"(x^2*(-5*a^2 - 2*a*b*x^3 + 3*b^2*x^6 + 5*a^2*Hypergeometric2F1[2/3, 1, 5/3, (b*x^3)/(a + b*x^3)]))/(18*b^2*(a + b*x^3)^(2/3))","C",1
568,1,53,97,0.010727,"\int \frac{x^4}{\left(a+b x^3\right)^{2/3}} \, dx","Integrate[x^4/(a + b*x^3)^(2/3),x]","\frac{x^2 \left(-a \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{b x^3}{b x^3+a}\right)+a+b x^3\right)}{3 b \left(a+b x^3\right)^{2/3}}","\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 - a*Hypergeometric2F1[2/3, 1, 5/3, (b*x^3)/(a + b*x^3)]))/(3*b*(a + b*x^3)^(2/3))","C",1
569,1,40,72,0.0064736,"\int \frac{x}{\left(a+b x^3\right)^{2/3}} \, dx","Integrate[x/(a + b*x^3)^(2/3),x]","\frac{x^2 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{b x^3}{b x^3+a}\right)}{2 \left(a+b x^3\right)^{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,"(x^2*Hypergeometric2F1[2/3, 1, 5/3, (b*x^3)/(a + b*x^3)])/(2*(a + b*x^3)^(2/3))","C",1
570,1,19,19,0.0225243,"\int \frac{1}{x^2 \left(a+b x^3\right)^{2/3}} \, dx","Integrate[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
571,1,29,44,0.0121064,"\int \frac{1}{x^5 \left(a+b x^3\right)^{2/3}} \, dx","Integrate[1/(x^5*(a + b*x^3)^(2/3)),x]","-\frac{\left(a-3 b x^3\right) \sqrt[3]{a+b x^3}}{4 a^2 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,"-1/4*((a - 3*b*x^3)*(a + b*x^3)^(1/3))/(a^2*x^4)","A",1
572,1,42,68,0.0227373,"\int \frac{1}{x^8 \left(a+b x^3\right)^{2/3}} \, dx","Integrate[1/(x^8*(a + b*x^3)^(2/3)),x]","-\frac{\sqrt[3]{a+b x^3} \left(2 a^2-3 a b x^3+9 b^2 x^6\right)}{14 a^3 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,"-1/14*((a + b*x^3)^(1/3)*(2*a^2 - 3*a*b*x^3 + 9*b^2*x^6))/(a^3*x^7)","A",1
573,1,53,92,0.0253641,"\int \frac{1}{x^{11} \left(a+b x^3\right)^{2/3}} \, dx","Integrate[1/(x^11*(a + b*x^3)^(2/3)),x]","\frac{\sqrt[3]{a+b x^3} \left(-14 a^3+18 a^2 b x^3-27 a b^2 x^6+81 b^3 x^9\right)}{140 a^4 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)*(-14*a^3 + 18*a^2*b*x^3 - 27*a*b^2*x^6 + 81*b^3*x^9))/(140*a^4*x^10)","A",1
574,1,51,38,0.0093158,"\int \frac{x^6}{\left(a+b x^3\right)^{2/3}} \, dx","Integrate[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",1
575,1,51,38,0.0148357,"\int \frac{x^3}{\left(a+b x^3\right)^{2/3}} \, dx","Integrate[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",1
576,1,177,33,0.2209916,"\int \frac{1}{\left(a+b x^3\right)^{2/3}} \, dx","Integrate[(a + b*x^3)^(-2/3),x]","\frac{3 \sqrt[3]{2} \left((-1)^{2/3} \sqrt[3]{a}+\sqrt[3]{b} x\right) \left(\frac{\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b} x}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{a}}\right)^{2/3} \sqrt[3]{\frac{i \left(\frac{\sqrt[3]{b} x}{\sqrt[3]{a}}+1\right)}{\sqrt{3}+3 i}} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};\frac{\left(1-i \sqrt{3}\right) \sqrt[3]{b} x+\left(1+i \sqrt{3}\right) \sqrt[3]{a}}{2 \left(\sqrt[3]{b} x+\sqrt[3]{a}\right)}\right)}{\sqrt[3]{b} \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,"(3*2^(1/3)*((-1)^(2/3)*a^(1/3) + b^(1/3)*x)*((a^(1/3) + (-1)^(2/3)*b^(1/3)*x)/((1 + (-1)^(1/3))*a^(1/3)))^(2/3)*((I*(1 + (b^(1/3)*x)/a^(1/3)))/(3*I + Sqrt[3]))^(1/3)*Hypergeometric2F1[1/3, 2/3, 4/3, ((1 + I*Sqrt[3])*a^(1/3) + (1 - I*Sqrt[3])*b^(1/3)*x)/(2*(a^(1/3) + b^(1/3)*x))])/(b^(1/3)*(a + b*x^3)^(2/3))","C",0
577,1,51,38,0.0103831,"\int \frac{1}{x^3 \left(a+b x^3\right)^{2/3}} \, dx","Integrate[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,"-1/2*((1 + (b*x^3)/a)^(2/3)*Hypergeometric2F1[-2/3, 2/3, 1/3, -((b*x^3)/a)])/(x^2*(a + b*x^3)^(2/3))","A",1
578,1,51,38,0.00975,"\int \frac{1}{x^6 \left(a+b x^3\right)^{2/3}} \, dx","Integrate[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,"-1/5*((1 + (b*x^3)/a)^(2/3)*Hypergeometric2F1[-5/3, 2/3, -2/3, -((b*x^3)/a)])/(x^5*(a + b*x^3)^(2/3))","A",1
579,1,116,72,0.1116833,"\int \frac{1}{\sqrt[3]{a-b x^3}} \, dx","Integrate[(a - b*x^3)^(-1/3),x]","\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)+2 \log \left(\frac{\sqrt[3]{b} x}{\sqrt[3]{a-b x^3}}+1\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a-b x^3}}-1}{\sqrt{3}}\right)}{6 \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,"(2*Sqrt[3]*ArcTan[(-1 + (2*b^(1/3)*x)/(a - b*x^3)^(1/3))/Sqrt[3]] - Log[1 + (b^(2/3)*x^2)/(a - b*x^3)^(2/3) - (b^(1/3)*x)/(a - b*x^3)^(1/3)] + 2*Log[1 + (b^(1/3)*x)/(a - b*x^3)^(1/3)])/(6*b^(1/3))","A",1
580,1,78,46,0.0523115,"\int \frac{1}{\sqrt[3]{2+x^3}} \, dx","Integrate[(2 + x^3)^(-1/3),x]","-\frac{1}{3} \log \left(1-\frac{x}{\sqrt[3]{x^3+2}}\right)+\frac{\tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3+2}}+1}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{1}{6} \log \left(\frac{x}{\sqrt[3]{x^3+2}}+\frac{x^2}{\left(x^3+2\right)^{2/3}}+1\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[1 - x/(2 + x^3)^(1/3)]/3 + Log[1 + x^2/(2 + x^3)^(2/3) + x/(2 + x^3)^(1/3)]/6","A",1
581,1,37,53,0.0093115,"\int \frac{x}{\left(1-x^3\right)^{2/3}} \, dx","Integrate[x/(1 - x^3)^(2/3),x]","\frac{x^2 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{x^3}{x^3-1}\right)}{2 \left(1-x^3\right)^{2/3}}","-\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,"(x^2*Hypergeometric2F1[2/3, 1, 5/3, x^3/(-1 + x^3)])/(2*(1 - x^3)^(2/3))","C",1
582,1,13,13,0.0027205,"\int \frac{x^2}{\sqrt[4]{2+x^3}} \, dx","Integrate[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
583,1,136,151,0.1061798,"\int x^m \left(a+b x^3\right)^8 \, dx","Integrate[x^m*(a + b*x^3)^8,x]","x^{m+1} \left(\frac{a^8}{m+1}+\frac{8 a^7 b x^3}{m+4}+\frac{28 a^6 b^2 x^6}{m+7}+\frac{56 a^5 b^3 x^9}{m+10}+\frac{70 a^4 b^4 x^{12}}{m+13}+\frac{56 a^3 b^5 x^{15}}{m+16}+\frac{28 a^2 b^6 x^{18}}{m+19}+\frac{8 a b^7 x^{21}}{m+22}+\frac{b^8 x^{24}}{m+25}\right)","\frac{a^8 x^{m+1}}{m+1}+\frac{8 a^7 b x^{m+4}}{m+4}+\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 b^7 x^{m+22}}{m+22}+\frac{b^8 x^{m+25}}{m+25}",1,"x^(1 + m)*(a^8/(1 + m) + (8*a^7*b*x^3)/(4 + m) + (28*a^6*b^2*x^6)/(7 + m) + (56*a^5*b^3*x^9)/(10 + m) + (70*a^4*b^4*x^12)/(13 + m) + (56*a^3*b^5*x^15)/(16 + m) + (28*a^2*b^6*x^18)/(19 + m) + (8*a*b^7*x^21)/(22 + m) + (b^8*x^24)/(25 + m))","A",1
584,1,88,97,0.0525362,"\int x^m \left(a+b x^3\right)^5 \, dx","Integrate[x^m*(a + b*x^3)^5,x]","x^{m+1} \left(\frac{a^5}{m+1}+\frac{5 a^4 b x^3}{m+4}+\frac{10 a^3 b^2 x^6}{m+7}+\frac{10 a^2 b^3 x^9}{m+10}+\frac{5 a b^4 x^{12}}{m+13}+\frac{b^5 x^{15}}{m+16}\right)","\frac{a^5 x^{m+1}}{m+1}+\frac{5 a^4 b x^{m+4}}{m+4}+\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 b^4 x^{m+13}}{m+13}+\frac{b^5 x^{m+16}}{m+16}",1,"x^(1 + m)*(a^5/(1 + m) + (5*a^4*b*x^3)/(4 + m) + (10*a^3*b^2*x^6)/(7 + m) + (10*a^2*b^3*x^9)/(10 + m) + (5*a*b^4*x^12)/(13 + m) + (b^5*x^15)/(16 + m))","A",1
585,1,56,61,0.0348754,"\int x^m \left(a+b x^3\right)^3 \, dx","Integrate[x^m*(a + b*x^3)^3,x]","x^{m+1} \left(\frac{a^3}{m+1}+\frac{3 a^2 b x^3}{m+4}+\frac{3 a b^2 x^6}{m+7}+\frac{b^3 x^9}{m+10}\right)","\frac{a^3 x^{m+1}}{m+1}+\frac{3 a^2 b x^{m+4}}{m+4}+\frac{3 a b^2 x^{m+7}}{m+7}+\frac{b^3 x^{m+10}}{m+10}",1,"x^(1 + m)*(a^3/(1 + m) + (3*a^2*b*x^3)/(4 + m) + (3*a*b^2*x^6)/(7 + m) + (b^3*x^9)/(10 + m))","A",1
586,1,40,43,0.0230595,"\int x^m \left(a+b x^3\right)^2 \, dx","Integrate[x^m*(a + b*x^3)^2,x]","x^{m+1} \left(\frac{a^2}{m+1}+\frac{2 a b x^3}{m+4}+\frac{b^2 x^6}{m+7}\right)","\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,"x^(1 + m)*(a^2/(1 + m) + (2*a*b*x^3)/(4 + m) + (b^2*x^6)/(7 + m))","A",1
587,1,25,25,0.0139469,"\int x^m \left(a+b x^3\right) \, dx","Integrate[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",1
588,1,41,39,0.0117267,"\int \frac{x^m}{a+b x^3} \, dx","Integrate[x^m/(a + b*x^3),x]","\frac{x^{m+1} \, _2F_1\left(1,\frac{m+1}{3};\frac{m+1}{3}+1;-\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, 1 + (1 + m)/3, -((b*x^3)/a)])/(a*(1 + m))","A",1
589,1,41,39,0.0074419,"\int \frac{x^m}{\left(a+b x^3\right)^2} \, dx","Integrate[x^m/(a + b*x^3)^2,x]","\frac{x^{m+1} \, _2F_1\left(2,\frac{m+1}{3};\frac{m+1}{3}+1;-\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, 1 + (1 + m)/3, -((b*x^3)/a)])/(a^2*(1 + m))","A",1
590,1,41,39,0.0073423,"\int \frac{x^m}{\left(a+b x^3\right)^3} \, dx","Integrate[x^m/(a + b*x^3)^3,x]","\frac{x^{m+1} \, _2F_1\left(3,\frac{m+1}{3};\frac{m+1}{3}+1;-\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, 1 + (1 + m)/3, -((b*x^3)/a)])/(a^3*(1 + m))","A",1
591,1,66,64,0.026487,"\int x^m \left(a+b x^3\right)^{3/2} \, dx","Integrate[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+1}{3}+1;-\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, 1 + (1 + m)/3, -((b*x^3)/a)])/((1 + m)*Sqrt[1 + (b*x^3)/a])","A",1
592,1,65,63,0.0141066,"\int x^m \sqrt{a+b x^3} \, dx","Integrate[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+1}{3}+1;-\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, 1 + (1 + m)/3, -((b*x^3)/a)])/((1 + m)*Sqrt[1 + (b*x^3)/a])","A",1
593,1,65,52,0.0171927,"\int \frac{x^m}{\sqrt{a+b x^3}} \, dx","Integrate[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+1}{3}+1;-\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, 1 + (1 + m)/3, -((b*x^3)/a)])/((1 + m)*Sqrt[a + b*x^3])","A",1
594,1,68,66,0.0175681,"\int \frac{x^m}{\left(a+b x^3\right)^{3/2}} \, dx","Integrate[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+1}{3}+1;-\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, 1 + (1 + m)/3, -((b*x^3)/a)])/(a*(1 + m)*Sqrt[a + b*x^3])","A",1
595,1,67,69,0.023295,"\int (c x)^m \left(a+b x^3\right)^{4/3} \, dx","Integrate[(c*x)^m*(a + b*x^3)^(4/3),x]","\frac{a x \sqrt[3]{a+b x^3} (c x)^m \, _2F_1\left(-\frac{4}{3},\frac{m+1}{3};\frac{m+1}{3}+1;-\frac{b x^3}{a}\right)}{(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*x*(c*x)^m*(a + b*x^3)^(1/3)*Hypergeometric2F1[-4/3, (1 + m)/3, 1 + (1 + m)/3, -((b*x^3)/a)])/((1 + m)*(1 + (b*x^3)/a)^(1/3))","A",1
596,1,66,61,0.0202084,"\int (c x)^m \left(a+b x^3\right)^{2/3} \, dx","Integrate[(c*x)^m*(a + b*x^3)^(2/3),x]","\frac{x \left(a+b x^3\right)^{2/3} (c x)^m \, _2F_1\left(-\frac{2}{3},\frac{m+1}{3};\frac{m+1}{3}+1;-\frac{b x^3}{a}\right)}{(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,"(x*(c*x)^m*(a + b*x^3)^(2/3)*Hypergeometric2F1[-2/3, (1 + m)/3, 1 + (1 + m)/3, -((b*x^3)/a)])/((1 + m)*(1 + (b*x^3)/a)^(2/3))","A",1
597,1,66,61,0.0293187,"\int (c x)^m \sqrt[3]{a+b x^3} \, dx","Integrate[(c*x)^m*(a + b*x^3)^(1/3),x]","\frac{x \sqrt[3]{a+b x^3} (c x)^m \, _2F_1\left(-\frac{1}{3},\frac{m+1}{3};\frac{m+1}{3}+1;-\frac{b x^3}{a}\right)}{(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,"(x*(c*x)^m*(a + b*x^3)^(1/3)*Hypergeometric2F1[-1/3, (1 + m)/3, 1 + (1 + m)/3, -((b*x^3)/a)])/((1 + m)*(1 + (b*x^3)/a)^(1/3))","A",1
598,1,64,66,0.0143442,"\int (c x)^m \left(a+b x^3\right)^p \, dx","Integrate[(c*x)^m*(a + b*x^3)^p,x]","\frac{x (c x)^m \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+1}{3}+1;-\frac{b x^3}{a}\right)}{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,"(x*(c*x)^m*(a + b*x^3)^p*Hypergeometric2F1[(1 + m)/3, -p, 1 + (1 + m)/3, -((b*x^3)/a)])/((1 + m)*(1 + (b*x^3)/a)^p)","A",1
599,1,23,23,0.0060428,"\int x^2 \left(a+b x^3\right)^p \, dx","Integrate[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
600,1,40,48,0.0308127,"\int x^5 \left(a+b x^3\right)^p \, dx","Integrate[x^5*(a + b*x^3)^p,x]","\frac{\left(a+b x^3\right)^{p+1} \left(b (p+1) x^3-a\right)}{3 b^2 (p+1) (p+2)}","\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 + b*x^3)^(1 + p)*(-a + b*(1 + p)*x^3))/(3*b^2*(1 + p)*(2 + p))","A",1
601,1,64,74,0.0380653,"\int x^8 \left(a+b x^3\right)^p \, dx","Integrate[x^8*(a + b*x^3)^p,x]","\frac{\left(a+b x^3\right)^{p+1} \left(2 a^2-2 a b (p+1) x^3+b^2 \left(p^2+3 p+2\right) x^6\right)}{3 b^3 (p+1) (p+2) (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 + b*x^3)^(1 + p)*(2*a^2 - 2*a*b*(1 + p)*x^3 + b^2*(2 + 3*p + p^2)*x^6))/(3*b^3*(1 + p)*(2 + p)*(3 + p))","A",1
602,1,95,95,0.0474848,"\int x^{11} \left(a+b x^3\right)^p \, dx","Integrate[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,"-1/3*(a^3*(a + b*x^3)^(1 + p))/(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",1
603,1,25,25,0.013577,"\int x^m \left(a+b x^4\right) \, dx","Integrate[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",1
604,1,17,17,0.0011711,"\int x^5 \left(a+b x^4\right) \, dx","Integrate[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",1
605,1,17,17,0.0012422,"\int x^4 \left(a+b x^4\right) \, dx","Integrate[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",1
606,1,17,17,0.001208,"\int x^3 \left(a+b x^4\right) \, dx","Integrate[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",1
607,1,17,17,0.0011065,"\int x^2 \left(a+b x^4\right) \, dx","Integrate[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",1
608,1,17,17,0.0010523,"\int x \left(a+b x^4\right) \, dx","Integrate[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",1
609,1,12,12,0.000078,"\int \left(a+b x^4\right) \, dx","Integrate[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
610,1,13,13,0.0022921,"\int \frac{a+b x^4}{x} \, dx","Integrate[(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",1
611,1,15,15,0.0020192,"\int \frac{a+b x^4}{x^2} \, dx","Integrate[(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",1
612,1,17,17,0.0012205,"\int \frac{a+b x^4}{x^3} \, dx","Integrate[(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,"-1/2*a/x^2 + (b*x^2)/2","A",1
613,1,12,12,0.0011328,"\int \frac{a+b x^4}{x^4} \, dx","Integrate[(a + b*x^4)/x^4,x]","b x-\frac{a}{3 x^3}","b x-\frac{a}{3 x^3}",1,"-1/3*a/x^3 + b*x","A",1
614,1,13,13,0.0025393,"\int \frac{a+b x^4}{x^5} \, dx","Integrate[(a + b*x^4)/x^5,x]","b \log (x)-\frac{a}{4 x^4}","b \log (x)-\frac{a}{4 x^4}",1,"-1/4*a/x^4 + b*Log[x]","A",1
615,1,15,15,0.0021427,"\int \frac{a+b x^4}{x^6} \, dx","Integrate[(a + b*x^4)/x^6,x]","-\frac{a}{5 x^5}-\frac{b}{x}","-\frac{a}{5 x^5}-\frac{b}{x}",1,"-1/5*a/x^5 - b/x","A",1
616,1,17,17,0.002229,"\int \frac{a+b x^4}{x^7} \, dx","Integrate[(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,"-1/6*a/x^6 - b/(2*x^2)","A",1
617,1,17,17,0.0020916,"\int \frac{a+b x^4}{x^8} \, dx","Integrate[(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,"-1/7*a/x^7 - b/(3*x^3)","A",1
618,1,17,17,0.0024659,"\int \frac{a+b x^4}{x^9} \, dx","Integrate[(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,"-1/8*a/x^8 - b/(4*x^4)","A",1
619,1,17,17,0.0022429,"\int \frac{a+b x^4}{x^{10}} \, dx","Integrate[(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,"-1/9*a/x^9 - b/(5*x^5)","A",1
620,1,40,43,0.0250155,"\int x^m \left(a+b x^4\right)^2 \, dx","Integrate[x^m*(a + b*x^4)^2,x]","x^{m+1} \left(\frac{a^2}{m+1}+\frac{2 a b x^4}{m+5}+\frac{b^2 x^8}{m+9}\right)","\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,"x^(1 + m)*(a^2/(1 + m) + (2*a*b*x^4)/(5 + m) + (b^2*x^8)/(9 + m))","A",1
621,1,30,30,0.0008307,"\int x^5 \left(a+b x^4\right)^2 \, dx","Integrate[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",1
622,1,30,30,0.0011514,"\int x^4 \left(a+b x^4\right)^2 \, dx","Integrate[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",1
623,1,30,16,0.0008632,"\int x^3 \left(a+b x^4\right)^2 \, dx","Integrate[x^3*(a + b*x^4)^2,x]","\frac{a^2 x^4}{4}+\frac{1}{4} a b x^8+\frac{b^2 x^{12}}{12}","\frac{\left(a+b x^4\right)^3}{12 b}",1,"(a^2*x^4)/4 + (a*b*x^8)/4 + (b^2*x^12)/12","A",1
624,1,30,30,0.0007724,"\int x^2 \left(a+b x^4\right)^2 \, dx","Integrate[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",1
625,1,30,30,0.0015244,"\int x \left(a+b x^4\right)^2 \, dx","Integrate[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",1
626,1,25,25,0.0009334,"\int \left(a+b x^4\right)^2 \, dx","Integrate[(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",1
627,1,26,26,0.0009715,"\int \frac{\left(a+b x^4\right)^2}{x} \, dx","Integrate[(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",1
628,1,28,28,0.0008487,"\int \frac{\left(a+b x^4\right)^2}{x^2} \, dx","Integrate[(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",1
629,1,27,27,0.000962,"\int \frac{\left(a+b x^4\right)^2}{x^3} \, dx","Integrate[(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,"-1/2*a^2/x^2 + a*b*x^2 + (b^2*x^6)/6","A",1
630,1,26,26,0.0007511,"\int \frac{\left(a+b x^4\right)^2}{x^4} \, dx","Integrate[(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,"-1/3*a^2/x^3 + 2*a*b*x + (b^2*x^5)/5","A",1
631,1,27,27,0.0007946,"\int \frac{\left(a+b x^4\right)^2}{x^5} \, dx","Integrate[(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,"-1/4*a^2/x^4 + (b^2*x^4)/4 + 2*a*b*Log[x]","A",1
632,1,56,61,0.031404,"\int x^m \left(a+b x^4\right)^3 \, dx","Integrate[x^m*(a + b*x^4)^3,x]","x^{m+1} \left(\frac{a^3}{m+1}+\frac{3 a^2 b x^4}{m+5}+\frac{3 a b^2 x^8}{m+9}+\frac{b^3 x^{12}}{m+13}\right)","\frac{a^3 x^{m+1}}{m+1}+\frac{3 a^2 b x^{m+5}}{m+5}+\frac{3 a b^2 x^{m+9}}{m+9}+\frac{b^3 x^{m+13}}{m+13}",1,"x^(1 + m)*(a^3/(1 + m) + (3*a^2*b*x^4)/(5 + m) + (3*a*b^2*x^8)/(9 + m) + (b^3*x^12)/(13 + m))","A",1
633,1,43,43,0.0020402,"\int x^5 \left(a+b x^4\right)^3 \, dx","Integrate[x^5*(a + b*x^4)^3,x]","\frac{a^3 x^6}{6}+\frac{3}{10} a^2 b x^{10}+\frac{3}{14} a b^2 x^{14}+\frac{b^3 x^{18}}{18}","\frac{a^3 x^6}{6}+\frac{3}{10} a^2 b x^{10}+\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",1
634,1,43,43,0.0019511,"\int x^4 \left(a+b x^4\right)^3 \, dx","Integrate[x^4*(a + b*x^4)^3,x]","\frac{a^3 x^5}{5}+\frac{1}{3} a^2 b x^9+\frac{3}{13} a b^2 x^{13}+\frac{b^3 x^{17}}{17}","\frac{a^3 x^5}{5}+\frac{1}{3} a^2 b x^9+\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",1
635,1,43,16,0.0021726,"\int x^3 \left(a+b x^4\right)^3 \, dx","Integrate[x^3*(a + b*x^4)^3,x]","\frac{a^3 x^4}{4}+\frac{3}{8} a^2 b x^8+\frac{1}{4} a b^2 x^{12}+\frac{b^3 x^{16}}{16}","\frac{\left(a+b x^4\right)^4}{16 b}",1,"(a^3*x^4)/4 + (3*a^2*b*x^8)/8 + (a*b^2*x^12)/4 + (b^3*x^16)/16","B",1
636,1,43,43,0.0017734,"\int x^2 \left(a+b x^4\right)^3 \, dx","Integrate[x^2*(a + b*x^4)^3,x]","\frac{a^3 x^3}{3}+\frac{3}{7} a^2 b x^7+\frac{3}{11} a b^2 x^{11}+\frac{b^3 x^{15}}{15}","\frac{a^3 x^3}{3}+\frac{3}{7} a^2 b x^7+\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",1
637,1,43,43,0.0017883,"\int x \left(a+b x^4\right)^3 \, dx","Integrate[x*(a + b*x^4)^3,x]","\frac{a^3 x^2}{2}+\frac{1}{2} a^2 b x^6+\frac{3}{10} a b^2 x^{10}+\frac{b^3 x^{14}}{14}","\frac{a^3 x^2}{2}+\frac{1}{2} a^2 b x^6+\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",1
638,1,38,38,0.0010077,"\int \left(a+b x^4\right)^3 \, dx","Integrate[(a + b*x^4)^3,x]","a^3 x+\frac{3}{5} a^2 b x^5+\frac{1}{3} a b^2 x^9+\frac{b^3 x^{13}}{13}","a^3 x+\frac{3}{5} a^2 b x^5+\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",1
639,1,39,39,0.0041975,"\int \frac{\left(a+b x^4\right)^3}{x} \, dx","Integrate[(a + b*x^4)^3/x,x]","a^3 \log (x)+\frac{3}{4} a^2 b x^4+\frac{3}{8} a b^2 x^8+\frac{b^3 x^{12}}{12}","a^3 \log (x)+\frac{3}{4} a^2 b x^4+\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",1
640,1,38,38,0.0040042,"\int \frac{\left(a+b x^4\right)^3}{x^2} \, dx","Integrate[(a + b*x^4)^3/x^2,x]","-\frac{a^3}{x}+a^2 b x^3+\frac{3}{7} a b^2 x^7+\frac{b^3 x^{11}}{11}","-\frac{a^3}{x}+a^2 b x^3+\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",1
641,1,43,43,0.0064525,"\int \frac{\left(a+b x^4\right)^3}{x^3} \, dx","Integrate[(a + b*x^4)^3/x^3,x]","-\frac{a^3}{2 x^2}+\frac{3}{2} a^2 b x^2+\frac{1}{2} a b^2 x^6+\frac{b^3 x^{10}}{10}","-\frac{a^3}{2 x^2}+\frac{3}{2} a^2 b x^2+\frac{1}{2} a b^2 x^6+\frac{b^3 x^{10}}{10}",1,"-1/2*a^3/x^2 + (3*a^2*b*x^2)/2 + (a*b^2*x^6)/2 + (b^3*x^10)/10","A",1
642,1,39,39,0.0044449,"\int \frac{\left(a+b x^4\right)^3}{x^4} \, dx","Integrate[(a + b*x^4)^3/x^4,x]","-\frac{a^3}{3 x^3}+3 a^2 b x+\frac{3}{5} a b^2 x^5+\frac{b^3 x^9}{9}","-\frac{a^3}{3 x^3}+3 a^2 b x+\frac{3}{5} a b^2 x^5+\frac{b^3 x^9}{9}",1,"-1/3*a^3/x^3 + 3*a^2*b*x + (3*a*b^2*x^5)/5 + (b^3*x^9)/9","A",1
643,1,40,40,0.0050655,"\int \frac{\left(a+b x^4\right)^3}{x^5} \, dx","Integrate[(a + b*x^4)^3/x^5,x]","-\frac{a^3}{4 x^4}+3 a^2 b \log (x)+\frac{3}{4} a b^2 x^4+\frac{b^3 x^8}{8}","-\frac{a^3}{4 x^4}+3 a^2 b \log (x)+\frac{3}{4} a b^2 x^4+\frac{b^3 x^8}{8}",1,"-1/4*a^3/x^4 + (3*a*b^2*x^4)/4 + (b^3*x^8)/8 + 3*a^2*b*Log[x]","A",1
644,1,48,51,0.0317789,"\int \frac{x^9}{a+c x^4} \, dx","Integrate[x^9/(a + c*x^4),x]","\frac{1}{6} \left(\frac{3 a^{3/2} \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{c^{5/2}}+\frac{c x^6-3 a x^2}{c^2}\right)","\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,"((-3*a*x^2 + c*x^6)/c^2 + (3*a^(3/2)*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/c^(5/2))/6","A",1
645,1,27,27,0.0063624,"\int \frac{x^7}{a+c x^4} \, dx","Integrate[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",1
646,1,40,40,0.0129848,"\int \frac{x^5}{a+c x^4} \, dx","Integrate[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",1
647,1,15,15,0.0038819,"\int \frac{x^3}{a+c x^4} \, dx","Integrate[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
648,1,29,29,0.006123,"\int \frac{x}{a+c x^4} \, dx","Integrate[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",1
649,1,22,22,0.0062132,"\int \frac{1}{x \left(a+c x^4\right)} \, dx","Integrate[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",1
650,1,79,40,0.0343731,"\int \frac{1}{x^3 \left(a+c x^4\right)} \, dx","Integrate[1/(x^3*(a + c*x^4)),x]","\frac{\sqrt{c} x^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)+\sqrt{c} x^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)-\sqrt{a}}{2 a^{3/2} 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,"(-Sqrt[a] + Sqrt[c]*x^2*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)] + Sqrt[c]*x^2*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*a^(3/2)*x^2)","A",1
651,1,35,35,0.0075963,"\int \frac{1}{x^5 \left(a+c x^4\right)} \, dx","Integrate[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*1/(a*x^4) - (c*Log[x])/a^2 + (c*Log[a + c*x^4])/(4*a^2)","A",1
652,1,88,51,0.0391441,"\int \frac{1}{x^7 \left(a+c x^4\right)} \, dx","Integrate[1/(x^7*(a + c*x^4)),x]","-\frac{3 c^{3/2} x^6 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)+3 c^{3/2} x^6 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)+\sqrt{a} \left(a-3 c x^4\right)}{6 a^{5/2} 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*(Sqrt[a]*(a - 3*c*x^4) + 3*c^(3/2)*x^6*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)] + 3*c^(3/2)*x^6*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(a^(5/2)*x^6)","A",1
653,1,173,190,0.0331503,"\int \frac{x^4}{a+c x^4} \, dx","Integrate[x^4/(a + c*x^4),x]","\frac{\sqrt{2} \sqrt[4]{a} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)-\sqrt{2} \sqrt[4]{a} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)+2 \sqrt{2} \sqrt[4]{a} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)-2 \sqrt{2} \sqrt[4]{a} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)+8 \sqrt[4]{c} x}{8 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} \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,"(8*c^(1/4)*x + 2*Sqrt[2]*a^(1/4)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)] - 2*Sqrt[2]*a^(1/4)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)] + Sqrt[2]*a^(1/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2] - Sqrt[2]*a^(1/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(8*c^(5/4))","A",1
654,1,134,185,0.0210485,"\int \frac{x^2}{a+c x^4} \, dx","Integrate[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)-\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)-2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)+2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\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{\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,"(-2*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)] + 2*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)] + Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2] - 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",1
655,1,134,185,0.0179776,"\int \frac{1}{a+c x^4} \, dx","Integrate[(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)+\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)-2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)+2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\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{\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,"(-2*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)] + 2*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)] - Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2] + 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",1
656,1,179,193,0.0280196,"\int \frac{1}{x^2 \left(a+c x^4\right)} \, dx","Integrate[1/(x^2*(a + c*x^4)),x]","\frac{-\sqrt{2} \sqrt[4]{c} x \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)+\sqrt{2} \sqrt[4]{c} x \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)+2 \sqrt{2} \sqrt[4]{c} x \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)-2 \sqrt{2} \sqrt[4]{c} x \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)-8 \sqrt[4]{a}}{8 a^{5/4} 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}",1,"(-8*a^(1/4) + 2*Sqrt[2]*c^(1/4)*x*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)] - 2*Sqrt[2]*c^(1/4)*x*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)] - Sqrt[2]*c^(1/4)*x*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2] + Sqrt[2]*c^(1/4)*x*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(8*a^(5/4)*x)","A",1
657,1,188,195,0.031808,"\int \frac{1}{x^4 \left(a+c x^4\right)} \, dx","Integrate[1/(x^4*(a + c*x^4)),x]","\frac{-8 a^{3/4}+6 \sqrt{2} c^{3/4} x^3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)-6 \sqrt{2} c^{3/4} x^3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)+3 \sqrt{2} c^{3/4} x^3 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)-3 \sqrt{2} c^{3/4} x^3 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{24 a^{7/4} 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,"(-8*a^(3/4) + 6*Sqrt[2]*c^(3/4)*x^3*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)] - 6*Sqrt[2]*c^(3/4)*x^3*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)] + 3*Sqrt[2]*c^(3/4)*x^3*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2] - 3*Sqrt[2]*c^(3/4)*x^3*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(24*a^(7/4)*x^3)","A",1
658,1,38,46,0.0199382,"\int \frac{x^{11}}{\left(a+c x^4\right)^2} \, dx","Integrate[x^11/(a + c*x^4)^2,x]","\frac{-\frac{a^2}{a+c x^4}-2 a \log \left(a+c x^4\right)+c x^4}{4 c^3}","-\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,"(c*x^4 - a^2/(a + c*x^4) - 2*a*Log[a + c*x^4])/(4*c^3)","A",1
659,1,60,59,0.0463863,"\int \frac{x^9}{\left(a+c x^4\right)^2} \, dx","Integrate[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{a x^2}{4 c^2 \left(a+c x^4\right)}+\frac{x^2}{2 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,"x^2/(2*c^2) + (a*x^2)/(4*c^2*(a + c*x^4)) - (3*Sqrt[a]*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(4*c^(5/2))","A",1
660,1,27,33,0.0103838,"\int \frac{x^7}{\left(a+c x^4\right)^2} \, dx","Integrate[x^7/(a + c*x^4)^2,x]","\frac{\frac{a}{a+c x^4}+\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/(a + c*x^4) + Log[a + c*x^4])/(4*c^2)","A",1
661,1,49,49,0.0231512,"\int \frac{x^5}{\left(a+c x^4\right)^2} \, dx","Integrate[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,"-1/4*x^2/(c*(a + c*x^4)) + ArcTan[(Sqrt[c]*x^2)/Sqrt[a]]/(4*Sqrt[a]*c^(3/2))","A",1
662,1,16,16,0.0038482,"\int \frac{x^3}{\left(a+c x^4\right)^2} \, dx","Integrate[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*1/(c*(a + c*x^4))","A",1
663,1,49,49,0.0259955,"\int \frac{x}{\left(a+c x^4\right)^2} \, dx","Integrate[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",1
664,1,33,38,0.016096,"\int \frac{1}{x \left(a+c x^4\right)^2} \, dx","Integrate[1/(x*(a + c*x^4)^2),x]","\frac{\frac{a}{a+c x^4}-\log \left(a+c x^4\right)+4 \log (x)}{4 a^2}","-\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,"(a/(a + c*x^4) + 4*Log[x] - Log[a + c*x^4])/(4*a^2)","A",1
665,1,94,59,0.0540419,"\int \frac{1}{x^3 \left(a+c x^4\right)^2} \, dx","Integrate[1/(x^3*(a + c*x^4)^2),x]","\frac{-\frac{\sqrt{a} \left(2 a+3 c x^4\right)}{x^2 \left(a+c x^4\right)}+3 \sqrt{c} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)+3 \sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{4 a^{5/2}}","-\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,"(-((Sqrt[a]*(2*a + 3*c*x^4))/(x^2*(a + c*x^4))) + 3*Sqrt[c]*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)] + 3*Sqrt[c]*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(4*a^(5/2))","A",1
666,1,185,204,0.1160534,"\int \frac{x^6}{\left(a+c x^4\right)^2} \, dx","Integrate[x^6/(a + c*x^4)^2,x]","\frac{-\frac{8 c^{3/4} x^3}{a+c x^4}+\frac{3 \sqrt{2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{\sqrt[4]{a}}-\frac{3 \sqrt{2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{\sqrt[4]{a}}-\frac{6 \sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{\sqrt[4]{a}}+\frac{6 \sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{\sqrt[4]{a}}}{32 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 \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,"((-8*c^(3/4)*x^3)/(a + c*x^4) - (6*Sqrt[2]*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/a^(1/4) + (6*Sqrt[2]*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/a^(1/4) + (3*Sqrt[2]*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/a^(1/4) - (3*Sqrt[2]*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/a^(1/4))/(32*c^(7/4))","A",1
667,1,182,202,0.1154151,"\int \frac{x^4}{\left(a+c x^4\right)^2} \, dx","Integrate[x^4/(a + c*x^4)^2,x]","\frac{-\frac{\sqrt{2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{a^{3/4}}+\frac{\sqrt{2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{a^{3/4}}-\frac{2 \sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{a^{3/4}}+\frac{2 \sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{a^{3/4}}-\frac{8 \sqrt[4]{c} x}{a+c x^4}}{32 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{\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,"((-8*c^(1/4)*x)/(a + c*x^4) - (2*Sqrt[2]*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/a^(3/4) + (2*Sqrt[2]*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/a^(3/4) - (Sqrt[2]*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/a^(3/4) + (Sqrt[2]*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/a^(3/4))/(32*c^(5/4))","A",1
668,1,184,204,0.1062919,"\int \frac{x^2}{\left(a+c x^4\right)^2} \, dx","Integrate[x^2/(a + c*x^4)^2,x]","\frac{\frac{\sqrt{2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{c^{3/4}}-\frac{\sqrt{2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{c^{3/4}}-\frac{2 \sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{c^{3/4}}+\frac{2 \sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{c^{3/4}}+\frac{8 \sqrt[4]{a} x^3}{a+c x^4}}{32 a^{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^{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,"((8*a^(1/4)*x^3)/(a + c*x^4) - (2*Sqrt[2]*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/c^(3/4) + (2*Sqrt[2]*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/c^(3/4) + (Sqrt[2]*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/c^(3/4) - (Sqrt[2]*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/c^(3/4))/(32*a^(5/4))","A",1
669,1,183,202,0.0999267,"\int \frac{1}{\left(a+c x^4\right)^2} \, dx","Integrate[(a + c*x^4)^(-2),x]","\frac{\frac{8 a^{3/4} x}{a+c x^4}-\frac{3 \sqrt{2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{\sqrt[4]{c}}+\frac{3 \sqrt{2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{\sqrt[4]{c}}-\frac{6 \sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{\sqrt[4]{c}}+\frac{6 \sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{\sqrt[4]{c}}}{32 a^{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} 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,"((8*a^(3/4)*x)/(a + c*x^4) - (6*Sqrt[2]*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/c^(1/4) + (6*Sqrt[2]*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/c^(1/4) - (3*Sqrt[2]*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/c^(1/4) + (3*Sqrt[2]*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/c^(1/4))/(32*a^(7/4))","A",1
670,1,196,214,0.1330657,"\int \frac{1}{x^2 \left(a+c x^4\right)^2} \, dx","Integrate[1/(x^2*(a + c*x^4)^2),x]","\frac{-5 \sqrt{2} \sqrt[4]{c} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)+5 \sqrt{2} \sqrt[4]{c} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)-\frac{8 \sqrt[4]{a} c x^3}{a+c x^4}+10 \sqrt{2} \sqrt[4]{c} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)-10 \sqrt{2} \sqrt[4]{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)-\frac{32 \sqrt[4]{a}}{x}}{32 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} \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,"((-32*a^(1/4))/x - (8*a^(1/4)*c*x^3)/(a + c*x^4) + 10*Sqrt[2]*c^(1/4)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)] - 10*Sqrt[2]*c^(1/4)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)] - 5*Sqrt[2]*c^(1/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2] + 5*Sqrt[2]*c^(1/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(32*a^(9/4))","A",1
671,1,194,214,0.1378763,"\int \frac{1}{x^4 \left(a+c x^4\right)^2} \, dx","Integrate[1/(x^4*(a + c*x^4)^2),x]","\frac{-\frac{24 a^{3/4} c x}{a+c x^4}-\frac{32 a^{3/4}}{x^3}+21 \sqrt{2} c^{3/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)-21 \sqrt{2} c^{3/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)+42 \sqrt{2} c^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)-42 \sqrt{2} c^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{96 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} \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,"((-32*a^(3/4))/x^3 - (24*a^(3/4)*c*x)/(a + c*x^4) + 42*Sqrt[2]*c^(3/4)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)] - 42*Sqrt[2]*c^(3/4)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)] + 21*Sqrt[2]*c^(3/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2] - 21*Sqrt[2]*c^(3/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(96*a^(11/4))","A",1
672,1,39,52,0.0190694,"\int \frac{x^{11}}{\left(a+c x^4\right)^3} \, dx","Integrate[x^11/(a + c*x^4)^3,x]","\frac{\frac{a \left(3 a+4 c x^4\right)}{\left(a+c x^4\right)^2}+2 \log \left(a+c x^4\right)}{8 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*(3*a + 4*c*x^4))/(a + c*x^4)^2 + 2*Log[a + c*x^4])/(8*c^3)","A",1
673,1,58,68,0.0507244,"\int \frac{x^9}{\left(a+c x^4\right)^3} \, dx","Integrate[x^9/(a + c*x^4)^3,x]","\frac{1}{16} \left(\frac{3 \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{\sqrt{a} c^{5/2}}+\frac{-3 a x^2-5 c x^6}{c^2 \left(a+c x^4\right)^2}\right)","\frac{3 \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{16 \sqrt{a} c^{5/2}}-\frac{3 x^2}{16 c^2 \left(a+c x^4\right)}-\frac{x^6}{8 c \left(a+c x^4\right)^2}",1,"((-3*a*x^2 - 5*c*x^6)/(c^2*(a + c*x^4)^2) + (3*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(Sqrt[a]*c^(5/2)))/16","A",1
674,1,24,19,0.0097232,"\int \frac{x^7}{\left(a+c x^4\right)^3} \, dx","Integrate[x^7/(a + c*x^4)^3,x]","-\frac{a+2 c x^4}{8 c^2 \left(a+c x^4\right)^2}","\frac{x^8}{8 a \left(a+c x^4\right)^2}",1,"-1/8*(a + 2*c*x^4)/(c^2*(a + c*x^4)^2)","A",1
675,1,62,71,0.0345321,"\int \frac{x^5}{\left(a+c x^4\right)^3} \, dx","Integrate[x^5/(a + c*x^4)^3,x]","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)+\frac{\sqrt{a} \sqrt{c} x^2 \left(c x^4-a\right)}{\left(a+c x^4\right)^2}}{16 a^{3/2} c^{3/2}}","\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,"((Sqrt[a]*Sqrt[c]*x^2*(-a + c*x^4))/(a + c*x^4)^2 + ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(16*a^(3/2)*c^(3/2))","A",1
676,1,16,16,0.0040928,"\int \frac{x^3}{\left(a+c x^4\right)^3} \, dx","Integrate[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*1/(c*(a + c*x^4)^2)","A",1
677,1,58,68,0.0486889,"\int \frac{x}{\left(a+c x^4\right)^3} \, dx","Integrate[x/(a + c*x^4)^3,x]","\frac{1}{16} \left(\frac{3 \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{a^{5/2} \sqrt{c}}+\frac{5 a x^2+3 c x^6}{a^2 \left(a+c x^4\right)^2}\right)","\frac{3 \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{16 a^{5/2} \sqrt{c}}+\frac{3 x^2}{16 a^2 \left(a+c x^4\right)}+\frac{x^2}{8 a \left(a+c x^4\right)^2}",1,"((5*a*x^2 + 3*c*x^6)/(a^2*(a + c*x^4)^2) + (3*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(a^(5/2)*Sqrt[c]))/16","A",1
678,1,43,54,0.0428846,"\int \frac{1}{x \left(a+c x^4\right)^3} \, dx","Integrate[1/(x*(a + c*x^4)^3),x]","\frac{\frac{a \left(3 a+2 c x^4\right)}{\left(a+c x^4\right)^2}-2 \log \left(a+c x^4\right)+8 \log (x)}{8 a^3}","-\frac{\log \left(a+c x^4\right)}{4 a^3}+\frac{\log (x)}{a^3}+\frac{1}{4 a^2 \left(a+c x^4\right)}+\frac{1}{8 a \left(a+c x^4\right)^2}",1,"((a*(3*a + 2*c*x^4))/(a + c*x^4)^2 + 8*Log[x] - 2*Log[a + c*x^4])/(8*a^3)","A",1
679,1,105,78,0.0907,"\int \frac{1}{x^3 \left(a+c x^4\right)^3} \, dx","Integrate[1/(x^3*(a + c*x^4)^3),x]","\frac{-\frac{\sqrt{a} \left(8 a^2+25 a c x^4+15 c^2 x^8\right)}{x^2 \left(a+c x^4\right)^2}+15 \sqrt{c} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)+15 \sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{16 a^{7/2}}","-\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{5}{16 a^2 x^2 \left(a+c x^4\right)}+\frac{1}{8 a x^2 \left(a+c x^4\right)^2}",1,"(-((Sqrt[a]*(8*a^2 + 25*a*c*x^4 + 15*c^2*x^8))/(x^2*(a + c*x^4)^2)) + 15*Sqrt[c]*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)] + 15*Sqrt[c]*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(16*a^(7/2))","A",1
680,1,205,223,0.0975679,"\int \frac{x^{10}}{\left(a+c x^4\right)^3} \, dx","Integrate[x^10/(a + c*x^4)^3,x]","\frac{-\frac{88 c^{3/4} x^3}{a+c x^4}+\frac{32 a c^{3/4} x^3}{\left(a+c x^4\right)^2}+\frac{21 \sqrt{2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{\sqrt[4]{a}}-\frac{21 \sqrt{2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{\sqrt[4]{a}}-\frac{42 \sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{\sqrt[4]{a}}+\frac{42 \sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{\sqrt[4]{a}}}{256 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 \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{7 x^3}{32 c^2 \left(a+c x^4\right)}-\frac{x^7}{8 c \left(a+c x^4\right)^2}",1,"((32*a*c^(3/4)*x^3)/(a + c*x^4)^2 - (88*c^(3/4)*x^3)/(a + c*x^4) - (42*Sqrt[2]*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/a^(1/4) + (42*Sqrt[2]*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/a^(1/4) + (21*Sqrt[2]*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/a^(1/4) - (21*Sqrt[2]*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/a^(1/4))/(256*c^(11/4))","A",1
681,1,201,221,0.0977452,"\int \frac{x^8}{\left(a+c x^4\right)^3} \, dx","Integrate[x^8/(a + c*x^4)^3,x]","\frac{-\frac{5 \sqrt{2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{a^{3/4}}+\frac{5 \sqrt{2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{a^{3/4}}-\frac{10 \sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{a^{3/4}}+\frac{10 \sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{a^{3/4}}-\frac{72 \sqrt[4]{c} x}{a+c x^4}+\frac{32 a \sqrt[4]{c} x}{\left(a+c x^4\right)^2}}{256 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 \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,"((32*a*c^(1/4)*x)/(a + c*x^4)^2 - (72*c^(1/4)*x)/(a + c*x^4) - (10*Sqrt[2]*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/a^(3/4) + (10*Sqrt[2]*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/a^(3/4) - (5*Sqrt[2]*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/a^(3/4) + (5*Sqrt[2]*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/a^(3/4))/(256*c^(9/4))","A",1
682,1,207,226,0.1075933,"\int \frac{x^6}{\left(a+c x^4\right)^3} \, dx","Integrate[x^6/(a + c*x^4)^3,x]","\frac{\frac{3 \sqrt{2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{a^{5/4}}-\frac{3 \sqrt{2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{a^{5/4}}-\frac{6 \sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{a^{5/4}}+\frac{6 \sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{a^{5/4}}+\frac{24 c^{3/4} x^3}{a^2+a c x^4}-\frac{32 c^{3/4} x^3}{\left(a+c x^4\right)^2}}{256 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 \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,"((-32*c^(3/4)*x^3)/(a + c*x^4)^2 + (24*c^(3/4)*x^3)/(a^2 + a*c*x^4) - (6*Sqrt[2]*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/a^(5/4) + (6*Sqrt[2]*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/a^(5/4) + (3*Sqrt[2]*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/a^(5/4) - (3*Sqrt[2]*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/a^(5/4))/(256*c^(7/4))","A",1
683,1,203,222,0.0961961,"\int \frac{x^4}{\left(a+c x^4\right)^3} \, dx","Integrate[x^4/(a + c*x^4)^3,x]","\frac{-\frac{3 \sqrt{2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{a^{7/4}}+\frac{3 \sqrt{2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{a^{7/4}}-\frac{6 \sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{a^{7/4}}+\frac{6 \sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{a^{7/4}}+\frac{8 \sqrt[4]{c} x}{a^2+a c x^4}-\frac{32 \sqrt[4]{c} x}{\left(a+c x^4\right)^2}}{256 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 \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,"((-32*c^(1/4)*x)/(a + c*x^4)^2 + (8*c^(1/4)*x)/(a^2 + a*c*x^4) - (6*Sqrt[2]*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/a^(7/4) + (6*Sqrt[2]*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/a^(7/4) - (3*Sqrt[2]*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/a^(7/4) + (3*Sqrt[2]*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/a^(7/4))/(256*c^(5/4))","A",1
684,1,204,223,0.0941715,"\int \frac{x^2}{\left(a+c x^4\right)^3} \, dx","Integrate[x^2/(a + c*x^4)^3,x]","\frac{\frac{32 a^{5/4} x^3}{\left(a+c x^4\right)^2}+\frac{5 \sqrt{2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{c^{3/4}}-\frac{5 \sqrt{2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{c^{3/4}}-\frac{10 \sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{c^{3/4}}+\frac{10 \sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{c^{3/4}}+\frac{40 \sqrt[4]{a} x^3}{a+c x^4}}{256 a^{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^{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,"((32*a^(5/4)*x^3)/(a + c*x^4)^2 + (40*a^(1/4)*x^3)/(a + c*x^4) - (10*Sqrt[2]*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/c^(3/4) + (10*Sqrt[2]*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/c^(3/4) + (5*Sqrt[2]*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/c^(3/4) - (5*Sqrt[2]*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/c^(3/4))/(256*a^(9/4))","A",1
685,1,200,219,0.0898826,"\int \frac{1}{\left(a+c x^4\right)^3} \, dx","Integrate[(a + c*x^4)^(-3),x]","\frac{\frac{32 a^{7/4} x}{\left(a+c x^4\right)^2}+\frac{56 a^{3/4} x}{a+c x^4}-\frac{21 \sqrt{2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{\sqrt[4]{c}}+\frac{21 \sqrt{2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{\sqrt[4]{c}}-\frac{42 \sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{\sqrt[4]{c}}+\frac{42 \sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{\sqrt[4]{c}}}{256 a^{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} 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{7 x}{32 a^2 \left(a+c x^4\right)}+\frac{x}{8 a \left(a+c x^4\right)^2}",1,"((32*a^(7/4)*x)/(a + c*x^4)^2 + (56*a^(3/4)*x)/(a + c*x^4) - (42*Sqrt[2]*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/c^(1/4) + (42*Sqrt[2]*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/c^(1/4) - (21*Sqrt[2]*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/c^(1/4) + (21*Sqrt[2]*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/c^(1/4))/(256*a^(11/4))","A",1
686,1,216,233,0.1042852,"\int \frac{1}{x^2 \left(a+c x^4\right)^3} \, dx","Integrate[1/(x^2*(a + c*x^4)^3),x]","\frac{-\frac{32 a^{5/4} c x^3}{\left(a+c x^4\right)^2}-45 \sqrt{2} \sqrt[4]{c} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)+45 \sqrt{2} \sqrt[4]{c} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)-\frac{104 \sqrt[4]{a} c x^3}{a+c x^4}+90 \sqrt{2} \sqrt[4]{c} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)-90 \sqrt{2} \sqrt[4]{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)-\frac{256 \sqrt[4]{a}}{x}}{256 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} \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{9}{32 a^2 x \left(a+c x^4\right)}+\frac{1}{8 a x \left(a+c x^4\right)^2}",1,"((-256*a^(1/4))/x - (32*a^(5/4)*c*x^3)/(a + c*x^4)^2 - (104*a^(1/4)*c*x^3)/(a + c*x^4) + 90*Sqrt[2]*c^(1/4)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)] - 90*Sqrt[2]*c^(1/4)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)] - 45*Sqrt[2]*c^(1/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2] + 45*Sqrt[2]*c^(1/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(256*a^(13/4))","A",1
687,1,34,38,0.0158909,"\int \frac{x^9}{2+3 x^4} \, dx","Integrate[x^9/(2 + 3*x^4),x]","\frac{1}{54} \left(3 x^6-6 x^2+2 \sqrt{6} \tan ^{-1}\left(\sqrt{\frac{3}{2}} x^2\right)\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,"(-6*x^2 + 3*x^6 + 2*Sqrt[6]*ArcTan[Sqrt[3/2]*x^2])/54","A",1
688,1,21,20,0.0049377,"\int \frac{x^7}{2+3 x^4} \, dx","Integrate[x^7/(2 + 3*x^4),x]","\frac{1}{36} \left(3 x^4-2 \log \left(3 x^4+2\right)+2\right)","\frac{x^4}{12}-\frac{1}{18} \log \left(3 x^4+2\right)",1,"(2 + 3*x^4 - 2*Log[2 + 3*x^4])/36","A",1
689,1,29,29,0.0099694,"\int \frac{x^5}{2+3 x^4} \, dx","Integrate[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",1
690,1,12,12,0.0028206,"\int \frac{x^3}{2+3 x^4} \, dx","Integrate[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
691,1,21,21,0.0144392,"\int \frac{x}{2+3 x^4} \, dx","Integrate[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",1
692,1,19,19,0.0033935,"\int \frac{1}{x \left(2+3 x^4\right)} \, dx","Integrate[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",1
693,1,48,31,0.0226045,"\int \frac{1}{x^3 \left(2+3 x^4\right)} \, dx","Integrate[1/(x^3*(2 + 3*x^4)),x]","\frac{\sqrt{6} x^2 \tan ^{-1}\left(1-\sqrt[4]{6} x\right)+\sqrt{6} x^2 \tan ^{-1}\left(\sqrt[4]{6} x+1\right)-2}{8 x^2}","-\frac{1}{4 x^2}-\frac{1}{4} \sqrt{\frac{3}{2}} \tan ^{-1}\left(\sqrt{\frac{3}{2}} x^2\right)",1,"(-2 + Sqrt[6]*x^2*ArcTan[1 - 6^(1/4)*x] + Sqrt[6]*x^2*ArcTan[1 + 6^(1/4)*x])/(8*x^2)","A",1
694,1,98,104,0.0267204,"\int \frac{x^6}{2+3 x^4} \, dx","Integrate[x^6/(2 + 3*x^4),x]","\frac{1}{36} \left(4 x^3-\sqrt[4]{6} \log \left(\sqrt{6} x^2-2 \sqrt[4]{6} x+2\right)+\sqrt[4]{6} \log \left(\sqrt{6} x^2+2 \sqrt[4]{6} x+2\right)+2 \sqrt[4]{6} \tan ^{-1}\left(1-\sqrt[4]{6} x\right)-2 \sqrt[4]{6} \tan ^{-1}\left(\sqrt[4]{6} x+1\right)\right)","\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,"(4*x^3 + 2*6^(1/4)*ArcTan[1 - 6^(1/4)*x] - 2*6^(1/4)*ArcTan[1 + 6^(1/4)*x] - 6^(1/4)*Log[2 - 2*6^(1/4)*x + Sqrt[6]*x^2] + 6^(1/4)*Log[2 + 2*6^(1/4)*x + Sqrt[6]*x^2])/36","A",1
695,1,96,102,0.0248253,"\int \frac{x^4}{2+3 x^4} \, dx","Integrate[x^4/(2 + 3*x^4),x]","\frac{1}{72} \left(6^{3/4} \log \left(\sqrt{6} x^2-2 \sqrt[4]{6} x+2\right)-6^{3/4} \log \left(\sqrt{6} x^2+2 \sqrt[4]{6} x+2\right)+24 x+2\ 6^{3/4} \tan ^{-1}\left(1-\sqrt[4]{6} x\right)-2\ 6^{3/4} \tan ^{-1}\left(\sqrt[4]{6} x+1\right)\right)","\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,"(24*x + 2*6^(3/4)*ArcTan[1 - 6^(1/4)*x] - 2*6^(3/4)*ArcTan[1 + 6^(1/4)*x] + 6^(3/4)*Log[2 - 2*6^(1/4)*x + Sqrt[6]*x^2] - 6^(3/4)*Log[2 + 2*6^(1/4)*x + Sqrt[6]*x^2])/72","A",1
696,1,77,97,0.0147365,"\int \frac{x^2}{2+3 x^4} \, dx","Integrate[x^2/(2 + 3*x^4),x]","\frac{\log \left(\sqrt{6} x^2-2 \sqrt[4]{6} x+2\right)-\log \left(\sqrt{6} x^2+2 \sqrt[4]{6} x+2\right)-2 \tan ^{-1}\left(1-\sqrt[4]{6} x\right)+2 \tan ^{-1}\left(\sqrt[4]{6} x+1\right)}{4\ 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,"(-2*ArcTan[1 - 6^(1/4)*x] + 2*ArcTan[1 + 6^(1/4)*x] + Log[2 - 2*6^(1/4)*x + Sqrt[6]*x^2] - Log[2 + 2*6^(1/4)*x + Sqrt[6]*x^2])/(4*6^(3/4))","A",1
697,1,77,97,0.0152561,"\int \frac{1}{2+3 x^4} \, dx","Integrate[(2 + 3*x^4)^(-1),x]","\frac{-\log \left(\sqrt{6} x^2-2 \sqrt[4]{6} x+2\right)+\log \left(\sqrt{6} x^2+2 \sqrt[4]{6} x+2\right)-2 \tan ^{-1}\left(1-\sqrt[4]{6} x\right)+2 \tan ^{-1}\left(\sqrt[4]{6} x+1\right)}{8 \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,"(-2*ArcTan[1 - 6^(1/4)*x] + 2*ArcTan[1 + 6^(1/4)*x] - Log[2 - 2*6^(1/4)*x + Sqrt[6]*x^2] + Log[2 + 2*6^(1/4)*x + Sqrt[6]*x^2])/(8*6^(1/4))","A",1
698,1,101,124,0.0277971,"\int \frac{1}{x^2 \left(2+3 x^4\right)} \, dx","Integrate[1/(x^2*(2 + 3*x^4)),x]","-\frac{\sqrt[4]{6} x \log \left(\sqrt{6} x^2-2 \sqrt[4]{6} x+2\right)-\sqrt[4]{6} x \log \left(\sqrt{6} x^2+2 \sqrt[4]{6} x+2\right)-2 \sqrt[4]{6} x \tan ^{-1}\left(1-\sqrt[4]{6} x\right)+2 \sqrt[4]{6} x \tan ^{-1}\left(\sqrt[4]{6} x+1\right)+8}{16 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}}",1,"-1/16*(8 - 2*6^(1/4)*x*ArcTan[1 - 6^(1/4)*x] + 2*6^(1/4)*x*ArcTan[1 + 6^(1/4)*x] + 6^(1/4)*x*Log[2 - 2*6^(1/4)*x + Sqrt[6]*x^2] - 6^(1/4)*x*Log[2 + 2*6^(1/4)*x + Sqrt[6]*x^2])/x","A",1
699,1,13,13,0.0032435,"\int \frac{x^3}{\left(2+3 x^4\right)^2} \, dx","Integrate[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*1/(2 + 3*x^4)","A",1
700,1,38,38,0.0170482,"\int \frac{x}{\left(2+3 x^4\right)^2} \, dx","Integrate[x/(2 + 3*x^4)^2,x]","\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}}+\frac{x^2}{8 \left(3 x^4+2\right)}",1,"x^2/(8*(2 + 3*x^4)) + ArcTan[Sqrt[3/2]*x^2]/(8*Sqrt[6])","A",1
701,1,32,32,0.0099532,"\int \frac{1}{x \left(2+3 x^4\right)^2} \, dx","Integrate[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",1
702,1,59,47,0.0469453,"\int \frac{1}{x^3 \left(2+3 x^4\right)^2} \, dx","Integrate[1/(x^3*(2 + 3*x^4)^2),x]","\frac{1}{32} \left(-\frac{4}{x^2}-\frac{6 x^2}{3 x^4+2}+3 \sqrt{6} \tan ^{-1}\left(1-\sqrt[4]{6} x\right)+3 \sqrt{6} \tan ^{-1}\left(\sqrt[4]{6} x+1\right)\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)}",1,"(-4/x^2 - (6*x^2)/(2 + 3*x^4) + 3*Sqrt[6]*ArcTan[1 - 6^(1/4)*x] + 3*Sqrt[6]*ArcTan[1 + 6^(1/4)*x])/32","A",1
703,1,105,111,0.1168529,"\int \frac{x^4}{\left(2+3 x^4\right)^2} \, dx","Integrate[x^4/(2 + 3*x^4)^2,x]","\frac{1}{576} \left(-\frac{48 x}{3 x^4+2}-6^{3/4} \log \left(\sqrt{6} x^2-2 \sqrt[4]{6} x+2\right)+6^{3/4} \log \left(\sqrt{6} x^2+2 \sqrt[4]{6} x+2\right)-2\ 6^{3/4} \tan ^{-1}\left(1-\sqrt[4]{6} x\right)+2\ 6^{3/4} \tan ^{-1}\left(\sqrt[4]{6} x+1\right)\right)","-\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,"((-48*x)/(2 + 3*x^4) - 2*6^(3/4)*ArcTan[1 - 6^(1/4)*x] + 2*6^(3/4)*ArcTan[1 + 6^(1/4)*x] - 6^(3/4)*Log[2 - 2*6^(1/4)*x + Sqrt[6]*x^2] + 6^(3/4)*Log[2 + 2*6^(1/4)*x + Sqrt[6]*x^2])/576","A",1
704,1,107,113,0.0943845,"\int \frac{x^2}{\left(2+3 x^4\right)^2} \, dx","Integrate[x^2/(2 + 3*x^4)^2,x]","\frac{1}{192} \left(\sqrt[4]{6} \log \left(\sqrt{6} x^2-2 \sqrt[4]{6} x+2\right)-\sqrt[4]{6} \log \left(\sqrt{6} x^2+2 \sqrt[4]{6} x+2\right)+\frac{24 x^3}{3 x^4+2}-2 \sqrt[4]{6} \tan ^{-1}\left(1-\sqrt[4]{6} x\right)+2 \sqrt[4]{6} \tan ^{-1}\left(\sqrt[4]{6} x+1\right)\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{x^3}{8 \left(3 x^4+2\right)}-\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,"((24*x^3)/(2 + 3*x^4) - 2*6^(1/4)*ArcTan[1 - 6^(1/4)*x] + 2*6^(1/4)*ArcTan[1 + 6^(1/4)*x] + 6^(1/4)*Log[2 - 2*6^(1/4)*x + Sqrt[6]*x^2] - 6^(1/4)*Log[2 + 2*6^(1/4)*x + Sqrt[6]*x^2])/192","A",1
705,1,105,131,0.0787877,"\int \frac{1}{\left(2+3 x^4\right)^2} \, dx","Integrate[(2 + 3*x^4)^(-2),x]","\frac{1}{128} \left(\frac{16 x}{3 x^4+2}-6^{3/4} \log \left(\sqrt{6} x^2-2 \sqrt[4]{6} x+2\right)+6^{3/4} \log \left(\sqrt{6} x^2+2 \sqrt[4]{6} x+2\right)-2\ 6^{3/4} \tan ^{-1}\left(1-\sqrt[4]{6} x\right)+2\ 6^{3/4} \tan ^{-1}\left(\sqrt[4]{6} x+1\right)\right)","\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,"((16*x)/(2 + 3*x^4) - 2*6^(3/4)*ArcTan[1 - 6^(1/4)*x] + 2*6^(3/4)*ArcTan[1 + 6^(1/4)*x] - 6^(3/4)*Log[2 - 2*6^(1/4)*x + Sqrt[6]*x^2] + 6^(3/4)*Log[2 + 2*6^(1/4)*x + Sqrt[6]*x^2])/128","A",1
706,1,113,140,0.1185227,"\int \frac{1}{x^2 \left(2+3 x^4\right)^2} \, dx","Integrate[1/(x^2*(2 + 3*x^4)^2),x]","\frac{1}{128} \left(-5 \sqrt[4]{6} \log \left(\sqrt{6} x^2-2 \sqrt[4]{6} x+2\right)+5 \sqrt[4]{6} \log \left(\sqrt{6} x^2+2 \sqrt[4]{6} x+2\right)-\frac{24 x^3}{3 x^4+2}-\frac{32}{x}+10 \sqrt[4]{6} \tan ^{-1}\left(1-\sqrt[4]{6} x\right)-10 \sqrt[4]{6} \tan ^{-1}\left(\sqrt[4]{6} x+1\right)\right)","\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,"(-32/x - (24*x^3)/(2 + 3*x^4) + 10*6^(1/4)*ArcTan[1 - 6^(1/4)*x] - 10*6^(1/4)*ArcTan[1 + 6^(1/4)*x] - 5*6^(1/4)*Log[2 - 2*6^(1/4)*x + Sqrt[6]*x^2] + 5*6^(1/4)*Log[2 + 2*6^(1/4)*x + Sqrt[6]*x^2])/128","A",1
707,1,101,133,0.0493368,"\int \frac{x^2}{3+x^4} \, dx","Integrate[x^2/(3 + x^4),x]","\frac{\log \left(\sqrt{3} x^2-\sqrt{2} 3^{3/4} x+3\right)-\log \left(\sqrt{3} x^2+\sqrt{2} 3^{3/4} x+3\right)-2 \tan ^{-1}\left(1-\frac{\sqrt{2} x}{\sqrt[4]{3}}\right)+2 \tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt[4]{3}}+1\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{\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,"(-2*ArcTan[1 - (Sqrt[2]*x)/3^(1/4)] + 2*ArcTan[1 + (Sqrt[2]*x)/3^(1/4)] + Log[3 - Sqrt[2]*3^(3/4)*x + Sqrt[3]*x^2] - Log[3 + Sqrt[2]*3^(3/4)*x + Sqrt[3]*x^2])/(4*Sqrt[2]*3^(1/4))","A",1
708,1,160,83,0.081145,"\int \frac{1}{1+a+(-1+a) x^4} \, dx","Integrate[(1 + a + (-1 + a)*x^4)^(-1),x]","\frac{-\log \left(\sqrt{a-1} x^2-\sqrt{2} \sqrt[4]{a-1} \sqrt[4]{a+1} x+\sqrt{a+1}\right)+\log \left(\sqrt{a-1} x^2+\sqrt{2} \sqrt[4]{a-1} \sqrt[4]{a+1} x+\sqrt{a+1}\right)-2 \tan ^{-1}\left(1-\sqrt{2} \sqrt[4]{\frac{a-1}{a+1}} x\right)+2 \tan ^{-1}\left(\sqrt{2} \sqrt[4]{\frac{a-1}{a+1}} x+1\right)}{4 \sqrt{2} \sqrt[4]{a-1} (a+1)^{3/4}}","\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,"(-2*ArcTan[1 - Sqrt[2]*((-1 + a)/(1 + a))^(1/4)*x] + 2*ArcTan[1 + Sqrt[2]*((-1 + a)/(1 + a))^(1/4)*x] - Log[Sqrt[1 + a] - Sqrt[2]*(-1 + a)^(1/4)*(1 + a)^(1/4)*x + Sqrt[-1 + a]*x^2] + Log[Sqrt[1 + a] + Sqrt[2]*(-1 + a)^(1/4)*(1 + a)^(1/4)*x + Sqrt[-1 + a]*x^2])/(4*Sqrt[2]*(-1 + a)^(1/4)*(1 + a)^(3/4))","A",0
709,1,128,79,0.0994208,"\int \frac{1}{2 a+2 b+x^4} \, dx","Integrate[(2*a + 2*b + x^4)^(-1),x]","\frac{-\log \left(-2 \sqrt[4]{2} x \sqrt[4]{a+b}+2 \sqrt{a+b}+\sqrt{2} x^2\right)+\log \left(2 \sqrt[4]{2} x \sqrt[4]{a+b}+2 \sqrt{a+b}+\sqrt{2} x^2\right)-2 \tan ^{-1}\left(1-\frac{\sqrt[4]{2} x}{\sqrt[4]{a+b}}\right)+2 \tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{a+b}}+1\right)}{8 \sqrt[4]{2} (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,"(-2*ArcTan[1 - (2^(1/4)*x)/(a + b)^(1/4)] + 2*ArcTan[1 + (2^(1/4)*x)/(a + b)^(1/4)] - Log[2*Sqrt[a + b] - 2*2^(1/4)*(a + b)^(1/4)*x + Sqrt[2]*x^2] + Log[2*Sqrt[a + b] + 2*2^(1/4)*(a + b)^(1/4)*x + Sqrt[2]*x^2])/(8*2^(1/4)*(a + b)^(3/4))","A",1
710,1,128,79,0.0181106,"\int \frac{1}{2 (a+b)+x^4} \, dx","Integrate[(2*(a + b) + x^4)^(-1),x]","\frac{-\log \left(-2 \sqrt[4]{2} x \sqrt[4]{a+b}+2 \sqrt{a+b}+\sqrt{2} x^2\right)+\log \left(2 \sqrt[4]{2} x \sqrt[4]{a+b}+2 \sqrt{a+b}+\sqrt{2} x^2\right)-2 \tan ^{-1}\left(1-\frac{\sqrt[4]{2} x}{\sqrt[4]{a+b}}\right)+2 \tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{a+b}}+1\right)}{8 \sqrt[4]{2} (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,"(-2*ArcTan[1 - (2^(1/4)*x)/(a + b)^(1/4)] + 2*ArcTan[1 + (2^(1/4)*x)/(a + b)^(1/4)] - Log[2*Sqrt[a + b] - 2*2^(1/4)*(a + b)^(1/4)*x + Sqrt[2]*x^2] + Log[2*Sqrt[a + b] + 2*2^(1/4)*(a + b)^(1/4)*x + Sqrt[2]*x^2])/(8*2^(1/4)*(a + b)^(3/4))","A",1
711,1,33,33,0.0086658,"\int \frac{x}{2 a+2 b+x^4} \, dx","Integrate[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",1
712,1,33,33,0.0055308,"\int \frac{x}{2 (a+b)+x^4} \, dx","Integrate[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",1
713,1,128,79,0.0331392,"\int \frac{x^2}{2 a+2 b+x^4} \, dx","Integrate[x^2/(2*a + 2*b + x^4),x]","\frac{\log \left(-2 \sqrt[4]{2} x \sqrt[4]{a+b}+2 \sqrt{a+b}+\sqrt{2} x^2\right)-\log \left(2 \sqrt[4]{2} x \sqrt[4]{a+b}+2 \sqrt{a+b}+\sqrt{2} x^2\right)-2 \tan ^{-1}\left(1-\frac{\sqrt[4]{2} x}{\sqrt[4]{a+b}}\right)+2 \tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{a+b}}+1\right)}{4\ 2^{3/4} \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,"(-2*ArcTan[1 - (2^(1/4)*x)/(a + b)^(1/4)] + 2*ArcTan[1 + (2^(1/4)*x)/(a + b)^(1/4)] + Log[2*Sqrt[a + b] - 2*2^(1/4)*(a + b)^(1/4)*x + Sqrt[2]*x^2] - Log[2*Sqrt[a + b] + 2*2^(1/4)*(a + b)^(1/4)*x + Sqrt[2]*x^2])/(4*2^(3/4)*(a + b)^(1/4))","A",1
714,1,128,79,0.0119716,"\int \frac{x^2}{2 (a+b)+x^4} \, dx","Integrate[x^2/(2*(a + b) + x^4),x]","\frac{\log \left(-2 \sqrt[4]{2} x \sqrt[4]{a+b}+2 \sqrt{a+b}+\sqrt{2} x^2\right)-\log \left(2 \sqrt[4]{2} x \sqrt[4]{a+b}+2 \sqrt{a+b}+\sqrt{2} x^2\right)-2 \tan ^{-1}\left(1-\frac{\sqrt[4]{2} x}{\sqrt[4]{a+b}}\right)+2 \tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{a+b}}+1\right)}{4\ 2^{3/4} \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,"(-2*ArcTan[1 - (2^(1/4)*x)/(a + b)^(1/4)] + 2*ArcTan[1 + (2^(1/4)*x)/(a + b)^(1/4)] + Log[2*Sqrt[a + b] - 2*2^(1/4)*(a + b)^(1/4)*x + Sqrt[2]*x^2] - Log[2*Sqrt[a + b] + 2*2^(1/4)*(a + b)^(1/4)*x + Sqrt[2]*x^2])/(4*2^(3/4)*(a + b)^(1/4))","A",1
715,1,15,14,0.0042099,"\int \frac{x^3}{2 a+2 b+x^4} \, dx","Integrate[x^3/(2*a + 2*b + x^4),x]","\frac{1}{4} \log \left(2 a+2 b+x^4\right)","\frac{1}{4} \log \left(2 (a+b)+x^4\right)",1,"Log[2*a + 2*b + x^4]/4","A",1
716,1,15,14,0.0041111,"\int \frac{x^3}{2 (a+b)+x^4} \, dx","Integrate[x^3/(2*(a + b) + x^4),x]","\frac{1}{4} \log \left(2 a+2 b+x^4\right)","\frac{1}{4} \log \left(2 (a+b)+x^4\right)",1,"Log[2*a + 2*b + x^4]/4","A",1
717,1,21,21,0.0050708,"\int x^{5/2} \left(a+c x^4\right) \, dx","Integrate[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",1
718,1,21,21,0.0047331,"\int x^{3/2} \left(a+c x^4\right) \, dx","Integrate[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",1
719,1,21,21,0.0126666,"\int \sqrt{x} \left(a+c x^4\right) \, dx","Integrate[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",1
720,1,19,19,0.0045138,"\int \frac{a+c x^4}{\sqrt{x}} \, dx","Integrate[(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",1
721,1,19,19,0.0051891,"\int \frac{a+c x^4}{x^{3/2}} \, dx","Integrate[(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",1
722,1,21,21,0.0296605,"\int \frac{a+c x^4}{x^{5/2}} \, dx","Integrate[(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",1
723,1,21,21,0.0056297,"\int \frac{a+c x^4}{x^{7/2}} \, dx","Integrate[(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",1
724,1,30,36,0.014961,"\int x^{5/2} \left(a+c x^4\right)^2 \, dx","Integrate[x^(5/2)*(a + c*x^4)^2,x]","\frac{2 x^{7/2} \left(345 a^2+322 a c x^4+105 c^2 x^8\right)}{2415}","\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*x^(7/2)*(345*a^2 + 322*a*c*x^4 + 105*c^2*x^8))/2415","A",1
725,1,30,36,0.0079029,"\int x^{3/2} \left(a+c x^4\right)^2 \, dx","Integrate[x^(3/2)*(a + c*x^4)^2,x]","\frac{2 x^{5/2} \left(273 a^2+210 a c x^4+65 c^2 x^8\right)}{1365}","\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*x^(5/2)*(273*a^2 + 210*a*c*x^4 + 65*c^2*x^8))/1365","A",1
726,1,30,36,0.015984,"\int \sqrt{x} \left(a+c x^4\right)^2 \, dx","Integrate[Sqrt[x]*(a + c*x^4)^2,x]","\frac{2}{627} x^{3/2} \left(209 a^2+114 a c x^4+33 c^2 x^8\right)","\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*x^(3/2)*(209*a^2 + 114*a*c*x^4 + 33*c^2*x^8))/627","A",1
727,1,30,34,0.0082189,"\int \frac{\left(a+c x^4\right)^2}{\sqrt{x}} \, dx","Integrate[(a + c*x^4)^2/Sqrt[x],x]","\frac{2}{153} \sqrt{x} \left(153 a^2+34 a c x^4+9 c^2 x^8\right)","2 a^2 \sqrt{x}+\frac{4}{9} a c x^{9/2}+\frac{2}{17} c^2 x^{17/2}",1,"(2*Sqrt[x]*(153*a^2 + 34*a*c*x^4 + 9*c^2*x^8))/153","A",1
728,1,30,34,0.0310753,"\int \frac{\left(a+c x^4\right)^2}{x^{3/2}} \, dx","Integrate[(a + c*x^4)^2/x^(3/2),x]","\frac{2 \left(-105 a^2+30 a c x^4+7 c^2 x^8\right)}{105 \sqrt{x}}","-\frac{2 a^2}{\sqrt{x}}+\frac{4}{7} a c x^{7/2}+\frac{2}{15} c^2 x^{15/2}",1,"(2*(-105*a^2 + 30*a*c*x^4 + 7*c^2*x^8))/(105*Sqrt[x])","A",1
729,1,30,36,0.0086872,"\int \frac{\left(a+c x^4\right)^2}{x^{5/2}} \, dx","Integrate[(a + c*x^4)^2/x^(5/2),x]","\frac{2 \left(-65 a^2+78 a c x^4+15 c^2 x^8\right)}{195 x^{3/2}}","-\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*(-65*a^2 + 78*a*c*x^4 + 15*c^2*x^8))/(195*x^(3/2))","A",1
730,1,30,36,0.0094484,"\int \frac{\left(a+c x^4\right)^2}{x^{7/2}} \, dx","Integrate[(a + c*x^4)^2/x^(7/2),x]","\frac{2 \left(-33 a^2+110 a c x^4+15 c^2 x^8\right)}{165 x^{5/2}}","-\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*(-33*a^2 + 110*a*c*x^4 + 15*c^2*x^8))/(165*x^(5/2))","A",1
731,1,51,51,0.0210677,"\int x^{5/2} \left(a+c x^4\right)^3 \, dx","Integrate[x^(5/2)*(a + c*x^4)^3,x]","\frac{2}{7} a^3 x^{7/2}+\frac{2}{5} a^2 c x^{15/2}+\frac{6}{23} a c^2 x^{23/2}+\frac{2}{31} c^3 x^{31/2}","\frac{2}{7} a^3 x^{7/2}+\frac{2}{5} a^2 c x^{15/2}+\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",1
732,1,51,51,0.0124637,"\int x^{3/2} \left(a+c x^4\right)^3 \, dx","Integrate[x^(3/2)*(a + c*x^4)^3,x]","\frac{2}{5} a^3 x^{5/2}+\frac{6}{13} a^2 c x^{13/2}+\frac{2}{7} a c^2 x^{21/2}+\frac{2}{29} c^3 x^{29/2}","\frac{2}{5} a^3 x^{5/2}+\frac{6}{13} a^2 c x^{13/2}+\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",1
733,1,41,51,0.0101692,"\int \sqrt{x} \left(a+c x^4\right)^3 \, dx","Integrate[Sqrt[x]*(a + c*x^4)^3,x]","\frac{2 x^{3/2} \left(1881 a^3+1539 a^2 c x^4+891 a c^2 x^8+209 c^3 x^{12}\right)}{5643}","\frac{2}{3} a^3 x^{3/2}+\frac{6}{11} a^2 c x^{11/2}+\frac{6}{19} a c^2 x^{19/2}+\frac{2}{27} c^3 x^{27/2}",1,"(2*x^(3/2)*(1881*a^3 + 1539*a^2*c*x^4 + 891*a*c^2*x^8 + 209*c^3*x^12))/5643","A",1
734,1,41,49,0.0122143,"\int \frac{\left(a+c x^4\right)^3}{\sqrt{x}} \, dx","Integrate[(a + c*x^4)^3/Sqrt[x],x]","\frac{2 \sqrt{x} \left(1275 a^3+425 a^2 c x^4+225 a c^2 x^8+51 c^3 x^{12}\right)}{1275}","2 a^3 \sqrt{x}+\frac{2}{3} a^2 c x^{9/2}+\frac{6}{17} a c^2 x^{17/2}+\frac{2}{25} c^3 x^{25/2}",1,"(2*Sqrt[x]*(1275*a^3 + 425*a^2*c*x^4 + 225*a*c^2*x^8 + 51*c^3*x^12))/1275","A",1
735,1,41,49,0.0202723,"\int \frac{\left(a+c x^4\right)^3}{x^{3/2}} \, dx","Integrate[(a + c*x^4)^3/x^(3/2),x]","\frac{2 \left(-805 a^3+345 a^2 c x^4+161 a c^2 x^8+35 c^3 x^{12}\right)}{805 \sqrt{x}}","-\frac{2 a^3}{\sqrt{x}}+\frac{6}{7} a^2 c x^{7/2}+\frac{2}{5} a c^2 x^{15/2}+\frac{2}{23} c^3 x^{23/2}",1,"(2*(-805*a^3 + 345*a^2*c*x^4 + 161*a*c^2*x^8 + 35*c^3*x^12))/(805*Sqrt[x])","A",1
736,1,41,51,0.0116296,"\int \frac{\left(a+c x^4\right)^3}{x^{5/2}} \, dx","Integrate[(a + c*x^4)^3/x^(5/2),x]","\frac{2 \left(-455 a^3+819 a^2 c x^4+315 a c^2 x^8+65 c^3 x^{12}\right)}{1365 x^{3/2}}","-\frac{2 a^3}{3 x^{3/2}}+\frac{6}{5} a^2 c x^{5/2}+\frac{6}{13} a c^2 x^{13/2}+\frac{2}{21} c^3 x^{21/2}",1,"(2*(-455*a^3 + 819*a^2*c*x^4 + 315*a*c^2*x^8 + 65*c^3*x^12))/(1365*x^(3/2))","A",1
737,1,41,49,0.0130458,"\int \frac{\left(a+c x^4\right)^3}{x^{7/2}} \, dx","Integrate[(a + c*x^4)^3/x^(7/2),x]","\frac{2 \left(-209 a^3+1045 a^2 c x^4+285 a c^2 x^8+55 c^3 x^{12}\right)}{1045 x^{5/2}}","-\frac{2 a^3}{5 x^{5/2}}+2 a^2 c x^{3/2}+\frac{6}{11} a c^2 x^{11/2}+\frac{2}{19} c^3 x^{19/2}",1,"(2*(-209*a^3 + 1045*a^2*c*x^4 + 285*a*c^2*x^8 + 55*c^3*x^12))/(1045*x^(5/2))","A",1
738,1,31,299,0.0082073,"\int \frac{x^{9/2}}{a+c x^4} \, dx","Integrate[x^(9/2)/(a + c*x^4),x]","-\frac{2 x^{3/2} \left(\, _2F_1\left(\frac{3}{8},1;\frac{11}{8};-\frac{c x^4}{a}\right)-1\right)}{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)*(-1 + Hypergeometric2F1[3/8, 1, 11/8, -((c*x^4)/a)]))/(3*c)","C",1
739,1,29,297,0.019602,"\int \frac{x^{7/2}}{a+c x^4} \, dx","Integrate[x^(7/2)/(a + c*x^4),x]","-\frac{2 \sqrt{x} \left(\, _2F_1\left(\frac{1}{8},1;\frac{9}{8};-\frac{c x^4}{a}\right)-1\right)}{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]*(-1 + Hypergeometric2F1[1/8, 1, 9/8, -((c*x^4)/a)]))/c","C",1
740,1,29,287,0.006781,"\int \frac{x^{5/2}}{a+c x^4} \, dx","Integrate[x^(5/2)/(a + c*x^4),x]","\frac{2 x^{7/2} \, _2F_1\left(\frac{7}{8},1;\frac{15}{8};-\frac{c x^4}{a}\right)}{7 a}","\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,"(2*x^(7/2)*Hypergeometric2F1[7/8, 1, 15/8, -((c*x^4)/a)])/(7*a)","C",1
741,1,29,287,0.0065306,"\int \frac{x^{3/2}}{a+c x^4} \, dx","Integrate[x^(3/2)/(a + c*x^4),x]","\frac{2 x^{5/2} \, _2F_1\left(\frac{5}{8},1;\frac{13}{8};-\frac{c x^4}{a}\right)}{5 a}","-\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,"(2*x^(5/2)*Hypergeometric2F1[5/8, 1, 13/8, -((c*x^4)/a)])/(5*a)","C",1
742,1,29,287,0.0061994,"\int \frac{\sqrt{x}}{a+c x^4} \, dx","Integrate[Sqrt[x]/(a + c*x^4),x]","\frac{2 x^{3/2} \, _2F_1\left(\frac{3}{8},1;\frac{11}{8};-\frac{c x^4}{a}\right)}{3 a}","-\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,"(2*x^(3/2)*Hypergeometric2F1[3/8, 1, 11/8, -((c*x^4)/a)])/(3*a)","C",1
743,1,27,287,0.0059141,"\int \frac{1}{\sqrt{x} \left(a+c x^4\right)} \, dx","Integrate[1/(Sqrt[x]*(a + c*x^4)),x]","\frac{2 \sqrt{x} \, _2F_1\left(\frac{1}{8},1;\frac{9}{8};-\frac{c x^4}{a}\right)}{a}","\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,"(2*Sqrt[x]*Hypergeometric2F1[1/8, 1, 9/8, -((c*x^4)/a)])/a","C",1
744,1,27,297,0.0060093,"\int \frac{1}{x^{3/2} \left(a+c x^4\right)} \, dx","Integrate[1/(x^(3/2)*(a + c*x^4)),x]","-\frac{2 \, _2F_1\left(-\frac{1}{8},1;\frac{7}{8};-\frac{c x^4}{a}\right)}{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*Hypergeometric2F1[-1/8, 1, 7/8, -((c*x^4)/a)])/(a*Sqrt[x])","C",1
745,1,29,299,0.0090136,"\int \frac{1}{x^{5/2} \left(a+c x^4\right)} \, dx","Integrate[1/(x^(5/2)*(a + c*x^4)),x]","-\frac{2 \, _2F_1\left(-\frac{3}{8},1;\frac{5}{8};-\frac{c x^4}{a}\right)}{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*Hypergeometric2F1[-3/8, 1, 5/8, -((c*x^4)/a)])/(3*a*x^(3/2))","C",1
746,1,43,308,0.0398786,"\int \frac{x^{13/2}}{\left(a+c x^4\right)^2} \, dx","Integrate[x^(13/2)/(a + c*x^4)^2,x]","\frac{2 x^{7/2} \left(\frac{\, _2F_1\left(\frac{7}{8},2;\frac{15}{8};-\frac{c x^4}{a}\right)}{a}-\frac{1}{a+c x^4}\right)}{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} \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,"(2*x^(7/2)*(-(a + c*x^4)^(-1) + Hypergeometric2F1[7/8, 2, 15/8, -((c*x^4)/a)]/a))/c","C",1
747,1,54,308,0.0122669,"\int \frac{x^{11/2}}{\left(a+c x^4\right)^2} \, dx","Integrate[x^(11/2)/(a + c*x^4)^2,x]","\frac{2 x^{5/2} \, _2F_1\left(\frac{5}{8},2;\frac{13}{8};-\frac{c x^4}{a}\right)}{3 a c}-\frac{2 x^{5/2}}{3 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,"(-2*x^(5/2))/(3*c*(a + c*x^4)) + (2*x^(5/2)*Hypergeometric2F1[5/8, 2, 13/8, -((c*x^4)/a)])/(3*a*c)","C",1
748,1,54,308,0.0129243,"\int \frac{x^{9/2}}{\left(a+c x^4\right)^2} \, dx","Integrate[x^(9/2)/(a + c*x^4)^2,x]","\frac{2 x^{3/2} \, _2F_1\left(\frac{3}{8},2;\frac{11}{8};-\frac{c x^4}{a}\right)}{5 a c}-\frac{2 x^{3/2}}{5 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,"(-2*x^(3/2))/(5*c*(a + c*x^4)) + (2*x^(3/2)*Hypergeometric2F1[3/8, 2, 11/8, -((c*x^4)/a)])/(5*a*c)","C",1
749,1,54,308,0.0138322,"\int \frac{x^{7/2}}{\left(a+c x^4\right)^2} \, dx","Integrate[x^(7/2)/(a + c*x^4)^2,x]","\frac{\sqrt{x} \, _2F_1\left(\frac{1}{8},1;\frac{9}{8};-\frac{c x^4}{a}\right)}{4 a c}-\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,"-1/4*Sqrt[x]/(c*(a + c*x^4)) + (Sqrt[x]*Hypergeometric2F1[1/8, 1, 9/8, -((c*x^4)/a)])/(4*a*c)","C",1
750,1,29,308,0.0059214,"\int \frac{x^{5/2}}{\left(a+c x^4\right)^2} \, dx","Integrate[x^(5/2)/(a + c*x^4)^2,x]","\frac{2 x^{7/2} \, _2F_1\left(\frac{7}{8},2;\frac{15}{8};-\frac{c x^4}{a}\right)}{7 a^2}","-\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,"(2*x^(7/2)*Hypergeometric2F1[7/8, 2, 15/8, -((c*x^4)/a)])/(7*a^2)","C",1
751,1,29,308,0.0054754,"\int \frac{x^{3/2}}{\left(a+c x^4\right)^2} \, dx","Integrate[x^(3/2)/(a + c*x^4)^2,x]","\frac{2 x^{5/2} \, _2F_1\left(\frac{5}{8},2;\frac{13}{8};-\frac{c x^4}{a}\right)}{5 a^2}","\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,"(2*x^(5/2)*Hypergeometric2F1[5/8, 2, 13/8, -((c*x^4)/a)])/(5*a^2)","C",1
752,1,29,308,0.0063229,"\int \frac{\sqrt{x}}{\left(a+c x^4\right)^2} \, dx","Integrate[Sqrt[x]/(a + c*x^4)^2,x]","\frac{2 x^{3/2} \, _2F_1\left(\frac{3}{8},2;\frac{11}{8};-\frac{c x^4}{a}\right)}{3 a^2}","\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,"(2*x^(3/2)*Hypergeometric2F1[3/8, 2, 11/8, -((c*x^4)/a)])/(3*a^2)","C",1
753,1,51,308,0.0128505,"\int \frac{1}{\sqrt{x} \left(a+c x^4\right)^2} \, dx","Integrate[1/(Sqrt[x]*(a + c*x^4)^2),x]","\frac{7 \sqrt{x} \, _2F_1\left(\frac{1}{8},1;\frac{9}{8};-\frac{c x^4}{a}\right)}{4 a^2}+\frac{\sqrt{x}}{4 a \left(a+c x^4\right)}","\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*Sqrt[x]*Hypergeometric2F1[1/8, 1, 9/8, -((c*x^4)/a)])/(4*a^2)","C",1
754,1,27,320,0.0056451,"\int \frac{1}{x^{3/2} \left(a+c x^4\right)^2} \, dx","Integrate[1/(x^(3/2)*(a + c*x^4)^2),x]","-\frac{2 \, _2F_1\left(-\frac{1}{8},2;\frac{7}{8};-\frac{c x^4}{a}\right)}{a^2 \sqrt{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}}",1,"(-2*Hypergeometric2F1[-1/8, 2, 7/8, -((c*x^4)/a)])/(a^2*Sqrt[x])","C",1
755,1,66,329,0.0199978,"\int \frac{x^{15/2}}{\left(a+c x^4\right)^3} \, dx","Integrate[x^(15/2)/(a + c*x^4)^3,x]","\frac{\sqrt{x} \left(9 \left(a+c x^4\right)^2 \, _2F_1\left(\frac{1}{8},1;\frac{9}{8};-\frac{c x^4}{a}\right)-a \left(9 a+17 c x^4\right)\right)}{64 a c^2 \left(a+c x^4\right)^2}","\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{9 \sqrt{x}}{64 c^2 \left(a+c x^4\right)}-\frac{x^{9/2}}{8 c \left(a+c x^4\right)^2}",1,"(Sqrt[x]*(-(a*(9*a + 17*c*x^4)) + 9*(a + c*x^4)^2*Hypergeometric2F1[1/8, 1, 9/8, -((c*x^4)/a)]))/(64*a*c^2*(a + c*x^4)^2)","C",1
756,1,45,332,0.0179365,"\int \frac{x^{13/2}}{\left(a+c x^4\right)^3} \, dx","Integrate[x^(13/2)/(a + c*x^4)^3,x]","\frac{2 x^{7/2} \left(\frac{\, _2F_1\left(\frac{7}{8},3;\frac{15}{8};-\frac{c x^4}{a}\right)}{a^2}-\frac{1}{\left(a+c x^4\right)^2}\right)}{9 c}","-\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,"(2*x^(7/2)*(-(a + c*x^4)^(-2) + Hypergeometric2F1[7/8, 3, 15/8, -((c*x^4)/a)]/a^2))/(9*c)","C",1
757,1,45,332,0.0241239,"\int \frac{x^{11/2}}{\left(a+c x^4\right)^3} \, dx","Integrate[x^(11/2)/(a + c*x^4)^3,x]","\frac{2 x^{5/2} \left(\frac{\, _2F_1\left(\frac{5}{8},3;\frac{13}{8};-\frac{c x^4}{a}\right)}{a^2}-\frac{1}{\left(a+c x^4\right)^2}\right)}{11 c}","\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,"(2*x^(5/2)*(-(a + c*x^4)^(-2) + Hypergeometric2F1[5/8, 3, 13/8, -((c*x^4)/a)]/a^2))/(11*c)","C",1
758,1,45,332,0.0161191,"\int \frac{x^{9/2}}{\left(a+c x^4\right)^3} \, dx","Integrate[x^(9/2)/(a + c*x^4)^3,x]","\frac{2 x^{3/2} \left(\frac{\, _2F_1\left(\frac{3}{8},3;\frac{11}{8};-\frac{c x^4}{a}\right)}{a^2}-\frac{1}{\left(a+c x^4\right)^2}\right)}{13 c}","\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,"(2*x^(3/2)*(-(a + c*x^4)^(-2) + Hypergeometric2F1[3/8, 3, 11/8, -((c*x^4)/a)]/a^2))/(13*c)","C",1
759,1,64,332,0.0175271,"\int \frac{x^{7/2}}{\left(a+c x^4\right)^3} \, dx","Integrate[x^(7/2)/(a + c*x^4)^3,x]","\frac{\sqrt{x} \left(7 \left(a+c x^4\right)^2 \, _2F_1\left(\frac{1}{8},1;\frac{9}{8};-\frac{c x^4}{a}\right)+a \left(c x^4-7 a\right)\right)}{64 a^2 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]*(a*(-7*a + c*x^4) + 7*(a + c*x^4)^2*Hypergeometric2F1[1/8, 1, 9/8, -((c*x^4)/a)]))/(64*a^2*c*(a + c*x^4)^2)","C",1
760,1,29,329,0.0054508,"\int \frac{x^{5/2}}{\left(a+c x^4\right)^3} \, dx","Integrate[x^(5/2)/(a + c*x^4)^3,x]","\frac{2 x^{7/2} \, _2F_1\left(\frac{7}{8},3;\frac{15}{8};-\frac{c x^4}{a}\right)}{7 a^3}","\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,"(2*x^(7/2)*Hypergeometric2F1[7/8, 3, 15/8, -((c*x^4)/a)])/(7*a^3)","C",1
761,1,29,329,0.0060395,"\int \frac{x^{3/2}}{\left(a+c x^4\right)^3} \, dx","Integrate[x^(3/2)/(a + c*x^4)^3,x]","\frac{2 x^{5/2} \, _2F_1\left(\frac{5}{8},3;\frac{13}{8};-\frac{c x^4}{a}\right)}{5 a^3}","\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,"(2*x^(5/2)*Hypergeometric2F1[5/8, 3, 13/8, -((c*x^4)/a)])/(5*a^3)","C",1
762,1,29,329,0.005987,"\int \frac{\sqrt{x}}{\left(a+c x^4\right)^3} \, dx","Integrate[Sqrt[x]/(a + c*x^4)^3,x]","\frac{2 x^{3/2} \, _2F_1\left(\frac{3}{8},3;\frac{11}{8};-\frac{c x^4}{a}\right)}{3 a^3}","\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,"(2*x^(3/2)*Hypergeometric2F1[3/8, 3, 11/8, -((c*x^4)/a)])/(3*a^3)","C",1
763,1,62,329,0.0164316,"\int \frac{1}{\sqrt{x} \left(a+c x^4\right)^3} \, dx","Integrate[1/(Sqrt[x]*(a + c*x^4)^3),x]","\frac{\sqrt{x} \left(105 \left(a+c x^4\right)^2 \, _2F_1\left(\frac{1}{8},1;\frac{9}{8};-\frac{c x^4}{a}\right)+a \left(23 a+15 c x^4\right)\right)}{64 a^3 \left(a+c x^4\right)^2}","\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]*(a*(23*a + 15*c*x^4) + 105*(a + c*x^4)^2*Hypergeometric2F1[1/8, 1, 9/8, -((c*x^4)/a)]))/(64*a^3*(a + c*x^4)^2)","C",1
764,1,39,59,0.0356971,"\int x^{11} \sqrt{a+c x^4} \, dx","Integrate[x^11*Sqrt[a + c*x^4],x]","\frac{\left(a+c x^4\right)^{3/2} \left(8 a^2-12 a c x^4+15 c^2 x^8\right)}{210 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 + c*x^4)^(3/2)*(8*a^2 - 12*a*c*x^4 + 15*c^2*x^8))/(210*c^3)","A",1
765,1,28,38,0.0260571,"\int x^7 \sqrt{a+c x^4} \, dx","Integrate[x^7*Sqrt[a + c*x^4],x]","\frac{\left(a+c x^4\right)^{3/2} \left(3 c x^4-2 a\right)}{30 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 + c*x^4)^(3/2)*(-2*a + 3*c*x^4))/(30*c^2)","A",1
766,1,18,18,0.0034733,"\int x^3 \sqrt{a+c x^4} \, dx","Integrate[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
767,1,43,43,0.0101466,"\int \frac{\sqrt{a+c x^4}}{x} \, dx","Integrate[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",1
768,1,59,47,0.0348574,"\int \frac{\sqrt{a+c x^4}}{x^5} \, dx","Integrate[Sqrt[a + c*x^4]/x^5,x]","-\frac{c x^4 \sqrt{\frac{c x^4}{a}+1} \tanh ^{-1}\left(\sqrt{\frac{c x^4}{a}+1}\right)+a+c x^4}{4 x^4 \sqrt{a+c x^4}}","-\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,"-1/4*(a + c*x^4 + c*x^4*Sqrt[1 + (c*x^4)/a]*ArcTanh[Sqrt[1 + (c*x^4)/a]])/(x^4*Sqrt[a + c*x^4])","A",1
769,1,39,71,0.0094478,"\int \frac{\sqrt{a+c x^4}}{x^9} \, dx","Integrate[Sqrt[a + c*x^4]/x^9,x]","-\frac{c^2 \left(a+c x^4\right)^{3/2} \, _2F_1\left(\frac{3}{2},3;\frac{5}{2};\frac{c x^4}{a}+1\right)}{6 a^3}","\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,"-1/6*(c^2*(a + c*x^4)^(3/2)*Hypergeometric2F1[3/2, 3, 5/2, 1 + (c*x^4)/a])/a^3","C",1
770,1,74,74,0.1438831,"\int x^5 \sqrt{a+c x^4} \, dx","Integrate[x^5*Sqrt[a + c*x^4],x]","\frac{\sqrt{a+c x^4} \left(\sqrt{c} x^2 \left(a+2 c x^4\right)-\frac{a^{3/2} \sinh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{\sqrt{\frac{c x^4}{a}+1}}\right)}{16 c^{3/2}}","-\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,"(Sqrt[a + c*x^4]*(Sqrt[c]*x^2*(a + 2*c*x^4) - (a^(3/2)*ArcSinh[(Sqrt[c]*x^2)/Sqrt[a]])/Sqrt[1 + (c*x^4)/a]))/(16*c^(3/2))","A",1
771,1,72,50,0.0683835,"\int x \sqrt{a+c x^4} \, dx","Integrate[x*Sqrt[a + c*x^4],x]","\frac{a^{3/2} \sqrt{\frac{c x^4}{a}+1} \sinh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)+\sqrt{c} x^2 \left(a+c x^4\right)}{4 \sqrt{c} \sqrt{a+c x^4}}","\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,"(Sqrt[c]*x^2*(a + c*x^4) + a^(3/2)*Sqrt[1 + (c*x^4)/a]*ArcSinh[(Sqrt[c]*x^2)/Sqrt[a]])/(4*Sqrt[c]*Sqrt[a + c*x^4])","A",1
772,1,69,49,0.1106251,"\int \frac{\sqrt{a+c x^4}}{x^3} \, dx","Integrate[Sqrt[a + c*x^4]/x^3,x]","-\frac{-\sqrt{a} \sqrt{c} x^2 \sqrt{\frac{c x^4}{a}+1} \sinh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)+a+c x^4}{2 x^2 \sqrt{a+c x^4}}","\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,"-1/2*(a + c*x^4 - Sqrt[a]*Sqrt[c]*x^2*Sqrt[1 + (c*x^4)/a]*ArcSinh[(Sqrt[c]*x^2)/Sqrt[a]])/(x^2*Sqrt[a + c*x^4])","A",1
773,1,21,21,0.0047864,"\int \frac{\sqrt{a+c x^4}}{x^7} \, dx","Integrate[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,"-1/6*(a + c*x^4)^(3/2)/(a*x^6)","A",1
774,1,31,44,0.0105526,"\int \frac{\sqrt{a+c x^4}}{x^{11}} \, dx","Integrate[Sqrt[a + c*x^4]/x^11,x]","\frac{\left(a+c x^4\right)^{3/2} \left(2 c x^4-3 a\right)}{30 a^2 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)*(-3*a + 2*c*x^4))/(30*a^2*x^10)","A",1
775,1,42,68,0.0113757,"\int \frac{\sqrt{a+c x^4}}{x^{15}} \, dx","Integrate[Sqrt[a + c*x^4]/x^15,x]","-\frac{\left(a+c x^4\right)^{3/2} \left(15 a^2-12 a c x^4+8 c^2 x^8\right)}{210 a^3 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,"-1/210*((a + c*x^4)^(3/2)*(15*a^2 - 12*a*c*x^4 + 8*c^2*x^8))/(a^3*x^14)","A",1
776,1,62,127,0.060652,"\int x^4 \sqrt{a+c x^4} \, dx","Integrate[x^4*Sqrt[a + c*x^4],x]","\frac{x \sqrt{a+c x^4} \left(-\frac{a \, _2F_1\left(-\frac{1}{2},\frac{1}{4};\frac{5}{4};-\frac{c x^4}{a}\right)}{\sqrt{\frac{c x^4}{a}+1}}+a+c x^4\right)}{7 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{2 a x \sqrt{a+c x^4}}{21 c}+\frac{1}{7} x^5 \sqrt{a+c x^4}",1,"(x*Sqrt[a + c*x^4]*(a + c*x^4 - (a*Hypergeometric2F1[-1/2, 1/4, 5/4, -((c*x^4)/a)])/Sqrt[1 + (c*x^4)/a]))/(7*c)","C",1
777,1,89,105,0.157812,"\int \sqrt{a+c x^4} \, dx","Integrate[Sqrt[a + c*x^4],x]","\frac{x \left(a+c x^4\right)-\frac{2 i a \sqrt{\frac{c x^4}{a}+1} F\left(\left.i \sinh ^{-1}\left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}} x\right)\right|-1\right)}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}}}{3 \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*(a + c*x^4) - ((2*I)*a*Sqrt[1 + (c*x^4)/a]*EllipticF[I*ArcSinh[Sqrt[(I*Sqrt[c])/Sqrt[a]]*x], -1])/Sqrt[(I*Sqrt[c])/Sqrt[a]])/(3*Sqrt[a + c*x^4])","C",1
778,1,51,107,0.009708,"\int \frac{\sqrt{a+c x^4}}{x^4} \, dx","Integrate[Sqrt[a + c*x^4]/x^4,x]","-\frac{\sqrt{a+c x^4} \, _2F_1\left(-\frac{3}{4},-\frac{1}{2};\frac{1}{4};-\frac{c x^4}{a}\right)}{3 x^3 \sqrt{\frac{c x^4}{a}+1}}","\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,"-1/3*(Sqrt[a + c*x^4]*Hypergeometric2F1[-3/4, -1/2, 1/4, -((c*x^4)/a)])/(x^3*Sqrt[1 + (c*x^4)/a])","C",1
779,1,51,129,0.021509,"\int \frac{\sqrt{a+c x^4}}{x^8} \, dx","Integrate[Sqrt[a + c*x^4]/x^8,x]","-\frac{\sqrt{a+c x^4} \, _2F_1\left(-\frac{7}{4},-\frac{1}{2};-\frac{3}{4};-\frac{c x^4}{a}\right)}{7 x^7 \sqrt{\frac{c x^4}{a}+1}}","-\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{\sqrt{a+c x^4}}{7 x^7}-\frac{2 c \sqrt{a+c x^4}}{21 a x^3}",1,"-1/7*(Sqrt[a + c*x^4]*Hypergeometric2F1[-7/4, -1/2, -3/4, -((c*x^4)/a)])/(x^7*Sqrt[1 + (c*x^4)/a])","C",1
780,1,51,234,0.0096006,"\int x^2 \sqrt{a+c x^4} \, dx","Integrate[x^2*Sqrt[a + c*x^4],x]","\frac{x^3 \sqrt{a+c x^4} \, _2F_1\left(-\frac{1}{2},\frac{3}{4};\frac{7}{4};-\frac{c x^4}{a}\right)}{3 \sqrt{\frac{c x^4}{a}+1}}","\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]*Hypergeometric2F1[-1/2, 3/4, 7/4, -((c*x^4)/a)])/(3*Sqrt[1 + (c*x^4)/a])","C",1
781,1,49,224,0.0097808,"\int \frac{\sqrt{a+c x^4}}{x^2} \, dx","Integrate[Sqrt[a + c*x^4]/x^2,x]","-\frac{\sqrt{a+c x^4} \, _2F_1\left(-\frac{1}{2},-\frac{1}{4};\frac{3}{4};-\frac{c x^4}{a}\right)}{x \sqrt{\frac{c x^4}{a}+1}}","-\frac{\sqrt{a+c x^4}}{x}+\frac{2 \sqrt{c} x \sqrt{a+c x^4}}{\sqrt{a}+\sqrt{c} x^2}+\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]*Hypergeometric2F1[-1/2, -1/4, 3/4, -((c*x^4)/a)])/(x*Sqrt[1 + (c*x^4)/a]))","C",1
782,1,51,258,0.0094581,"\int \frac{\sqrt{a+c x^4}}{x^6} \, dx","Integrate[Sqrt[a + c*x^4]/x^6,x]","-\frac{\sqrt{a+c x^4} \, _2F_1\left(-\frac{5}{4},-\frac{1}{2};-\frac{1}{4};-\frac{c x^4}{a}\right)}{5 x^5 \sqrt{\frac{c x^4}{a}+1}}","\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,"-1/5*(Sqrt[a + c*x^4]*Hypergeometric2F1[-5/4, -1/2, -1/4, -((c*x^4)/a)])/(x^5*Sqrt[1 + (c*x^4)/a])","C",1
783,1,39,59,0.0261113,"\int x^{11} \left(a+c x^4\right)^{3/2} \, dx","Integrate[x^11*(a + c*x^4)^(3/2),x]","\frac{\left(a+c x^4\right)^{5/2} \left(8 a^2-20 a c x^4+35 c^2 x^8\right)}{630 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 + c*x^4)^(5/2)*(8*a^2 - 20*a*c*x^4 + 35*c^2*x^8))/(630*c^3)","A",1
784,1,28,38,0.0164161,"\int x^7 \left(a+c x^4\right)^{3/2} \, dx","Integrate[x^7*(a + c*x^4)^(3/2),x]","\frac{\left(a+c x^4\right)^{5/2} \left(5 c x^4-2 a\right)}{70 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 + c*x^4)^(5/2)*(-2*a + 5*c*x^4))/(70*c^2)","A",1
785,1,18,18,0.0081218,"\int x^3 \left(a+c x^4\right)^{3/2} \, dx","Integrate[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
786,1,51,59,0.0223644,"\int \frac{\left(a+c x^4\right)^{3/2}}{x} \, dx","Integrate[(a + c*x^4)^(3/2)/x,x]","\frac{1}{6} \left(\sqrt{a+c x^4} \left(4 a+c x^4\right)-3 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+c x^4}}{\sqrt{a}}\right)\right)","-\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,"(Sqrt[a + c*x^4]*(4*a + c*x^4) - 3*a^(3/2)*ArcTanh[Sqrt[a + c*x^4]/Sqrt[a]])/6","A",1
787,1,37,63,0.0097447,"\int \frac{\left(a+c x^4\right)^{3/2}}{x^5} \, dx","Integrate[(a + c*x^4)^(3/2)/x^5,x]","\frac{c \left(a+c x^4\right)^{5/2} \, _2F_1\left(2,\frac{5}{2};\frac{7}{2};\frac{c x^4}{a}+1\right)}{10 a^2}","-\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,"(c*(a + c*x^4)^(5/2)*Hypergeometric2F1[2, 5/2, 7/2, 1 + (c*x^4)/a])/(10*a^2)","C",1
788,1,76,68,0.0471157,"\int \frac{\left(a+c x^4\right)^{3/2}}{x^9} \, dx","Integrate[(a + c*x^4)^(3/2)/x^9,x]","-\frac{2 a^2+3 c^2 x^8 \sqrt{\frac{c x^4}{a}+1} \tanh ^{-1}\left(\sqrt{\frac{c x^4}{a}+1}\right)+7 a c x^4+5 c^2 x^8}{16 x^8 \sqrt{a+c x^4}}","-\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,"-1/16*(2*a^2 + 7*a*c*x^4 + 5*c^2*x^8 + 3*c^2*x^8*Sqrt[1 + (c*x^4)/a]*ArcTanh[Sqrt[1 + (c*x^4)/a]])/(x^8*Sqrt[a + c*x^4])","A",1
789,1,87,95,0.1372345,"\int x^5 \left(a+c x^4\right)^{3/2} \, dx","Integrate[x^5*(a + c*x^4)^(3/2),x]","\frac{\sqrt{a+c x^4} \left(\sqrt{c} x^2 \left(3 a^2+14 a c x^4+8 c^2 x^8\right)-\frac{3 a^{5/2} \sinh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{\sqrt{\frac{c x^4}{a}+1}}\right)}{96 c^{3/2}}","-\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,"(Sqrt[a + c*x^4]*(Sqrt[c]*x^2*(3*a^2 + 14*a*c*x^4 + 8*c^2*x^8) - (3*a^(5/2)*ArcSinh[(Sqrt[c]*x^2)/Sqrt[a]])/Sqrt[1 + (c*x^4)/a]))/(96*c^(3/2))","A",1
790,1,69,71,0.1202471,"\int x \left(a+c x^4\right)^{3/2} \, dx","Integrate[x*(a + c*x^4)^(3/2),x]","\frac{1}{16} \sqrt{a+c x^4} \left(\frac{3 a^{3/2} \sinh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{\sqrt{c} \sqrt{\frac{c x^4}{a}+1}}+5 a x^2+2 c x^6\right)","\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,"(Sqrt[a + c*x^4]*(5*a*x^2 + 2*c*x^6 + (3*a^(3/2)*ArcSinh[(Sqrt[c]*x^2)/Sqrt[a]])/(Sqrt[c]*Sqrt[1 + (c*x^4)/a])))/16","A",1
791,1,52,69,0.0123907,"\int \frac{\left(a+c x^4\right)^{3/2}}{x^3} \, dx","Integrate[(a + c*x^4)^(3/2)/x^3,x]","-\frac{a \sqrt{a+c x^4} \, _2F_1\left(-\frac{3}{2},-\frac{1}{2};\frac{1}{2};-\frac{c x^4}{a}\right)}{2 x^2 \sqrt{\frac{c x^4}{a}+1}}","\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,"-1/2*(a*Sqrt[a + c*x^4]*Hypergeometric2F1[-3/2, -1/2, 1/2, -((c*x^4)/a)])/(x^2*Sqrt[1 + (c*x^4)/a])","C",1
792,1,52,68,0.0121014,"\int \frac{\left(a+c x^4\right)^{3/2}}{x^7} \, dx","Integrate[(a + c*x^4)^(3/2)/x^7,x]","-\frac{a \sqrt{a+c x^4} \, _2F_1\left(-\frac{3}{2},-\frac{3}{2};-\frac{1}{2};-\frac{c x^4}{a}\right)}{6 x^6 \sqrt{\frac{c x^4}{a}+1}}","\frac{1}{2} c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a+c x^4}}\right)-\frac{\left(a+c x^4\right)^{3/2}}{6 x^6}-\frac{c \sqrt{a+c x^4}}{2 x^2}",1,"-1/6*(a*Sqrt[a + c*x^4]*Hypergeometric2F1[-3/2, -3/2, -1/2, -((c*x^4)/a)])/(x^6*Sqrt[1 + (c*x^4)/a])","C",1
793,1,21,21,0.0062592,"\int \frac{\left(a+c x^4\right)^{3/2}}{x^{11}} \, dx","Integrate[(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,"-1/10*(a + c*x^4)^(5/2)/(a*x^10)","A",1
794,1,31,44,0.0207882,"\int \frac{\left(a+c x^4\right)^{3/2}}{x^{15}} \, dx","Integrate[(a + c*x^4)^(3/2)/x^15,x]","\frac{\left(a+c x^4\right)^{5/2} \left(2 c x^4-5 a\right)}{70 a^2 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)*(-5*a + 2*c*x^4))/(70*a^2*x^14)","A",1
795,1,42,68,0.0126654,"\int \frac{\left(a+c x^4\right)^{3/2}}{x^{19}} \, dx","Integrate[(a + c*x^4)^(3/2)/x^19,x]","-\frac{\left(a+c x^4\right)^{5/2} \left(35 a^2-20 a c x^4+8 c^2 x^8\right)}{630 a^3 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,"-1/630*((a + c*x^4)^(5/2)*(35*a^2 - 20*a*c*x^4 + 8*c^2*x^8))/(a^3*x^18)","A",1
796,1,67,148,0.0986576,"\int x^4 \left(a+c x^4\right)^{3/2} \, dx","Integrate[x^4*(a + c*x^4)^(3/2),x]","\frac{x \sqrt{a+c x^4} \left(\left(a+c x^4\right)^2-\frac{a^2 \, _2F_1\left(-\frac{3}{2},\frac{1}{4};\frac{5}{4};-\frac{c x^4}{a}\right)}{\sqrt{\frac{c x^4}{a}+1}}\right)}{11 c}","-\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,"(x*Sqrt[a + c*x^4]*((a + c*x^4)^2 - (a^2*Hypergeometric2F1[-3/2, 1/4, 5/4, -((c*x^4)/a)])/Sqrt[1 + (c*x^4)/a]))/(11*c)","C",1
797,1,47,122,0.0222506,"\int \left(a+c x^4\right)^{3/2} \, dx","Integrate[(a + c*x^4)^(3/2),x]","\frac{a x \sqrt{a+c x^4} \, _2F_1\left(-\frac{3}{2},\frac{1}{4};\frac{5}{4};-\frac{c x^4}{a}\right)}{\sqrt{\frac{c x^4}{a}+1}}","\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,"(a*x*Sqrt[a + c*x^4]*Hypergeometric2F1[-3/2, 1/4, 5/4, -((c*x^4)/a)])/Sqrt[1 + (c*x^4)/a]","C",1
798,1,52,124,0.0098309,"\int \frac{\left(a+c x^4\right)^{3/2}}{x^4} \, dx","Integrate[(a + c*x^4)^(3/2)/x^4,x]","-\frac{a \sqrt{a+c x^4} \, _2F_1\left(-\frac{3}{2},-\frac{3}{4};\frac{1}{4};-\frac{c x^4}{a}\right)}{3 x^3 \sqrt{\frac{c x^4}{a}+1}}","\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{2}{3} c x \sqrt{a+c x^4}-\frac{\left(a+c x^4\right)^{3/2}}{3 x^3}",1,"-1/3*(a*Sqrt[a + c*x^4]*Hypergeometric2F1[-3/2, -3/4, 1/4, -((c*x^4)/a)])/(x^3*Sqrt[1 + (c*x^4)/a])","C",1
799,1,52,126,0.0103871,"\int \frac{\left(a+c x^4\right)^{3/2}}{x^8} \, dx","Integrate[(a + c*x^4)^(3/2)/x^8,x]","-\frac{a \sqrt{a+c x^4} \, _2F_1\left(-\frac{7}{4},-\frac{3}{2};-\frac{3}{4};-\frac{c x^4}{a}\right)}{7 x^7 \sqrt{\frac{c x^4}{a}+1}}","\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{\left(a+c x^4\right)^{3/2}}{7 x^7}-\frac{2 c \sqrt{a+c x^4}}{7 x^3}",1,"-1/7*(a*Sqrt[a + c*x^4]*Hypergeometric2F1[-7/4, -3/2, -3/4, -((c*x^4)/a)])/(x^7*Sqrt[1 + (c*x^4)/a])","C",1
800,1,52,255,0.0112335,"\int x^2 \left(a+c x^4\right)^{3/2} \, dx","Integrate[x^2*(a + c*x^4)^(3/2),x]","\frac{a x^3 \sqrt{a+c x^4} \, _2F_1\left(-\frac{3}{2},\frac{3}{4};\frac{7}{4};-\frac{c x^4}{a}\right)}{3 \sqrt{\frac{c x^4}{a}+1}}","\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,"(a*x^3*Sqrt[a + c*x^4]*Hypergeometric2F1[-3/2, 3/4, 7/4, -((c*x^4)/a)])/(3*Sqrt[1 + (c*x^4)/a])","C",1
801,1,50,251,0.0103292,"\int \frac{\left(a+c x^4\right)^{3/2}}{x^2} \, dx","Integrate[(a + c*x^4)^(3/2)/x^2,x]","-\frac{a \sqrt{a+c x^4} \, _2F_1\left(-\frac{3}{2},-\frac{1}{4};\frac{3}{4};-\frac{c x^4}{a}\right)}{x \sqrt{\frac{c x^4}{a}+1}}","\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{\left(a+c x^4\right)^{3/2}}{x}+\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)}",1,"-((a*Sqrt[a + c*x^4]*Hypergeometric2F1[-3/2, -1/4, 3/4, -((c*x^4)/a)])/(x*Sqrt[1 + (c*x^4)/a]))","C",1
802,1,52,252,0.0166317,"\int \frac{\left(a+c x^4\right)^{3/2}}{x^6} \, dx","Integrate[(a + c*x^4)^(3/2)/x^6,x]","-\frac{a \sqrt{a+c x^4} \, _2F_1\left(-\frac{3}{2},-\frac{5}{4};-\frac{1}{4};-\frac{c x^4}{a}\right)}{5 x^5 \sqrt{\frac{c x^4}{a}+1}}","\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,"-1/5*(a*Sqrt[a + c*x^4]*Hypergeometric2F1[-3/2, -5/4, -1/4, -((c*x^4)/a)])/(x^5*Sqrt[1 + (c*x^4)/a])","C",1
803,1,17,72,0.0022363,"\int \left(1+x^4\right)^{3/2} \, dx","Integrate[(1 + x^4)^(3/2),x]","x \, _2F_1\left(-\frac{3}{2},\frac{1}{4};\frac{5}{4};-x^4\right)","\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,"x*Hypergeometric2F1[-3/2, 1/4, 5/4, -x^4]","C",1
804,1,15,41,0.0026901,"\int \left(1-x^4\right)^{3/2} \, dx","Integrate[(1 - x^4)^(3/2),x]","x \, _2F_1\left(-\frac{3}{2},\frac{1}{4};\frac{5}{4};x^4\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,"x*Hypergeometric2F1[-3/2, 1/4, 5/4, x^4]","C",1
805,1,22,31,0.0082372,"\int x^7 \sqrt{5+3 x^4} \, dx","Integrate[x^7*Sqrt[5 + 3*x^4],x]","\frac{1}{270} \left(3 x^4+5\right)^{3/2} \left(9 x^4-10\right)","\frac{1}{90} \left(3 x^4+5\right)^{5/2}-\frac{5}{54} \left(3 x^4+5\right)^{3/2}",1,"((5 + 3*x^4)^(3/2)*(-10 + 9*x^4))/270","A",1
806,1,13,13,0.0032666,"\int x^3 \sqrt{5+x^4} \, dx","Integrate[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
807,1,40,40,0.0310718,"\int x \sqrt{3+2 x^4} \, dx","Integrate[x*Sqrt[3 + 2*x^4],x]","\frac{1}{8} \left(3 \sqrt{2} \sinh ^{-1}\left(\sqrt{\frac{2}{3}} x^2\right)+2 \sqrt{2 x^4+3} x^2\right)","\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",1,"(2*x^2*Sqrt[3 + 2*x^4] + 3*Sqrt[2]*ArcSinh[Sqrt[2/3]*x^2])/8","A",1
808,1,50,35,0.0299534,"\int x \sqrt{-2+x^4} \, dx","Integrate[x*Sqrt[-2 + x^4],x]","\frac{\left(x^4-2\right) \left(2 \sin ^{-1}\left(\frac{x^2}{\sqrt{2}}\right)+\sqrt{2-x^4} x^2\right)}{4 \sqrt{-\left(x^4-2\right)^2}}","\frac{1}{4} x^2 \sqrt{x^4-2}-\frac{1}{2} \tanh ^{-1}\left(\frac{x^2}{\sqrt{x^4-2}}\right)",1,"((-2 + x^4)*(x^2*Sqrt[2 - x^4] + 2*ArcSin[x^2/Sqrt[2]]))/(4*Sqrt[-(-2 + x^4)^2])","A",1
809,1,48,58,0.0284809,"\int \sqrt{1+x^4} \, dx","Integrate[Sqrt[1 + x^4],x]","\frac{x^5-2 \sqrt[4]{-1} \sqrt{x^4+1} F\left(\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-1\right)+x}{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 + x^5 - 2*(-1)^(1/4)*Sqrt[1 + x^4]*EllipticF[I*ArcSinh[(-1)^(1/4)*x], -1])/(3*Sqrt[1 + x^4])","C",1
810,1,39,25,0.0191649,"\int \sqrt{1-x^4} \, dx","Integrate[Sqrt[1 - x^4],x]","\frac{-x^5+2 \sqrt{1-x^4} F\left(\left.\sin ^{-1}(x)\right|-1\right)+x}{3 \sqrt{1-x^4}}","\frac{1}{3} \sqrt{1-x^4} x+\frac{2}{3} F\left(\left.\sin ^{-1}(x)\right|-1\right)",1,"(x - x^5 + 2*Sqrt[1 - x^4]*EllipticF[ArcSin[x], -1])/(3*Sqrt[1 - x^4])","A",1
811,1,39,59,0.0217247,"\int \frac{x^{11}}{\sqrt{a+b x^4}} \, dx","Integrate[x^11/Sqrt[a + b*x^4],x]","\frac{\sqrt{a+b x^4} \left(8 a^2-4 a b x^4+3 b^2 x^8\right)}{30 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,"(Sqrt[a + b*x^4]*(8*a^2 - 4*a*b*x^4 + 3*b^2*x^8))/(30*b^3)","A",1
812,1,27,38,0.0131509,"\int \frac{x^7}{\sqrt{a+b x^4}} \, dx","Integrate[x^7/Sqrt[a + b*x^4],x]","\frac{\left(b x^4-2 a\right) \sqrt{a+b x^4}}{6 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,"((-2*a + b*x^4)*Sqrt[a + b*x^4])/(6*b^2)","A",1
813,1,18,18,0.0177306,"\int \frac{x^3}{\sqrt{a+b x^4}} \, dx","Integrate[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
814,1,27,27,0.0056914,"\int \frac{1}{x \sqrt{a+b x^4}} \, dx","Integrate[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,"-1/2*ArcTanh[Sqrt[a + b*x^4]/Sqrt[a]]/Sqrt[a]","A",1
815,1,64,50,0.0905622,"\int \frac{1}{x^5 \sqrt{a+b x^4}} \, dx","Integrate[1/(x^5*Sqrt[a + b*x^4]),x]","\frac{b \sqrt{a+b x^4} \left(\frac{\tanh ^{-1}\left(\sqrt{\frac{b x^4}{a}+1}\right)}{2 \sqrt{\frac{b x^4}{a}+1}}-\frac{a}{2 b x^4}\right)}{2 a^2}","\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,"(b*Sqrt[a + b*x^4]*(-1/2*a/(b*x^4) + ArcTanh[Sqrt[1 + (b*x^4)/a]]/(2*Sqrt[1 + (b*x^4)/a])))/(2*a^2)","A",1
816,1,53,53,0.0353496,"\int \frac{x^5}{\sqrt{a+b x^4}} \, dx","Integrate[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",1
817,1,30,30,0.0045515,"\int \frac{x}{\sqrt{a+b x^4}} \, dx","Integrate[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",1
818,1,21,21,0.0041841,"\int \frac{1}{x^3 \sqrt{a+b x^4}} \, dx","Integrate[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,"-1/2*Sqrt[a + b*x^4]/(a*x^2)","A",1
819,1,29,44,0.0071923,"\int \frac{1}{x^7 \sqrt{a+b x^4}} \, dx","Integrate[1/(x^7*Sqrt[a + b*x^4]),x]","-\frac{\left(a-2 b x^4\right) \sqrt{a+b x^4}}{6 a^2 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,"-1/6*((a - 2*b*x^4)*Sqrt[a + b*x^4])/(a^2*x^6)","A",1
820,1,42,68,0.0215181,"\int \frac{1}{x^{11} \sqrt{a+b x^4}} \, dx","Integrate[1/(x^11*Sqrt[a + b*x^4]),x]","-\frac{\sqrt{a+b x^4} \left(3 a^2-4 a b x^4+8 b^2 x^8\right)}{30 a^3 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,"-1/30*(Sqrt[a + b*x^4]*(3*a^2 - 4*a*b*x^4 + 8*b^2*x^8))/(a^3*x^10)","A",1
821,1,79,130,0.0213317,"\int \frac{x^8}{\sqrt{a+b x^4}} \, dx","Integrate[x^8/Sqrt[a + b*x^4],x]","\frac{5 a^2 x \sqrt{\frac{b x^4}{a}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\frac{b x^4}{a}\right)-5 a^2 x-2 a b x^5+3 b^2 x^9}{21 b^2 \sqrt{a+b x^4}}","\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^2*x - 2*a*b*x^5 + 3*b^2*x^9 + 5*a^2*x*Sqrt[1 + (b*x^4)/a]*Hypergeometric2F1[1/4, 1/2, 5/4, -((b*x^4)/a)])/(21*b^2*Sqrt[a + b*x^4])","C",1
822,1,62,108,0.0498251,"\int \frac{x^4}{\sqrt{a+b x^4}} \, dx","Integrate[x^4/Sqrt[a + b*x^4],x]","\frac{x \left(-a \sqrt{\frac{b x^4}{a}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\frac{b x^4}{a}\right)+a+b x^4\right)}{3 b \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*(a + b*x^4 - a*Sqrt[1 + (b*x^4)/a]*Hypergeometric2F1[1/4, 1/2, 5/4, -((b*x^4)/a)]))/(3*b*Sqrt[a + b*x^4])","C",1
823,1,74,88,0.0345612,"\int \frac{1}{\sqrt{a+b x^4}} \, dx","Integrate[1/Sqrt[a + b*x^4],x]","-\frac{i \sqrt{\frac{b x^4}{a}+1} F\left(\left.i \sinh ^{-1}\left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}} x\right)\right|-1\right)}{\sqrt{\frac{i \sqrt{b}}{\sqrt{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)}{2 \sqrt[4]{a} \sqrt[4]{b} \sqrt{a+b x^4}}",1,"((-I)*Sqrt[1 + (b*x^4)/a]*EllipticF[I*ArcSinh[Sqrt[(I*Sqrt[b])/Sqrt[a]]*x], -1])/(Sqrt[(I*Sqrt[b])/Sqrt[a]]*Sqrt[a + b*x^4])","C",1
824,1,51,110,0.0096499,"\int \frac{1}{x^4 \sqrt{a+b x^4}} \, dx","Integrate[1/(x^4*Sqrt[a + b*x^4]),x]","-\frac{\sqrt{\frac{b x^4}{a}+1} \, _2F_1\left(-\frac{3}{4},\frac{1}{2};\frac{1}{4};-\frac{b x^4}{a}\right)}{3 x^3 \sqrt{a+b x^4}}","-\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,"-1/3*(Sqrt[1 + (b*x^4)/a]*Hypergeometric2F1[-3/4, 1/2, 1/4, -((b*x^4)/a)])/(x^3*Sqrt[a + b*x^4])","C",1
825,1,51,132,0.0410627,"\int \frac{1}{x^8 \sqrt{a+b x^4}} \, dx","Integrate[1/(x^8*Sqrt[a + b*x^4]),x]","-\frac{\sqrt{\frac{b x^4}{a}+1} \, _2F_1\left(-\frac{7}{4},\frac{1}{2};-\frac{3}{4};-\frac{b x^4}{a}\right)}{7 x^7 \sqrt{a+b x^4}}","\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,"-1/7*(Sqrt[1 + (b*x^4)/a]*Hypergeometric2F1[-7/4, 1/2, -3/4, -((b*x^4)/a)])/(x^7*Sqrt[a + b*x^4])","C",1
826,1,80,261,0.031052,"\int \frac{x^{10}}{\sqrt{a+b x^4}} \, dx","Integrate[x^10/Sqrt[a + b*x^4],x]","\frac{x^3 \left(7 a^2 \sqrt{\frac{b x^4}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};-\frac{b x^4}{a}\right)-7 a^2-2 a b x^4+5 b^2 x^8\right)}{45 b^2 \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}} 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^2 x \sqrt{a+b x^4}}{15 b^{5/2} \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{7 a x^3 \sqrt{a+b x^4}}{45 b^2}+\frac{x^7 \sqrt{a+b x^4}}{9 b}",1,"(x^3*(-7*a^2 - 2*a*b*x^4 + 5*b^2*x^8 + 7*a^2*Sqrt[1 + (b*x^4)/a]*Hypergeometric2F1[1/2, 3/4, 7/4, -((b*x^4)/a)]))/(45*b^2*Sqrt[a + b*x^4])","C",1
827,1,64,237,0.0198549,"\int \frac{x^6}{\sqrt{a+b x^4}} \, dx","Integrate[x^6/Sqrt[a + b*x^4],x]","\frac{x^3 \left(-a \sqrt{\frac{b x^4}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};-\frac{b x^4}{a}\right)+a+b x^4\right)}{5 b \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}} 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*(a + b*x^4 - a*Sqrt[1 + (b*x^4)/a]*Hypergeometric2F1[1/2, 3/4, 7/4, -((b*x^4)/a)]))/(5*b*Sqrt[a + b*x^4])","C",1
828,1,51,210,0.0085903,"\int \frac{x^2}{\sqrt{a+b x^4}} \, dx","Integrate[x^2/Sqrt[a + b*x^4],x]","\frac{x^3 \sqrt{\frac{b x^4}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};-\frac{b x^4}{a}\right)}{3 \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}} 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^3*Sqrt[1 + (b*x^4)/a]*Hypergeometric2F1[1/2, 3/4, 7/4, -((b*x^4)/a)])/(3*Sqrt[a + b*x^4])","C",1
829,1,49,232,0.0097528,"\int \frac{1}{x^2 \sqrt{a+b x^4}} \, dx","Integrate[1/(x^2*Sqrt[a + b*x^4]),x]","-\frac{\sqrt{\frac{b x^4}{a}+1} \, _2F_1\left(-\frac{1}{4},\frac{1}{2};\frac{3}{4};-\frac{b x^4}{a}\right)}{x \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}} 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{a+b x^4}}{a x}+\frac{\sqrt{b} x \sqrt{a+b x^4}}{a \left(\sqrt{a}+\sqrt{b} x^2\right)}",1,"-((Sqrt[1 + (b*x^4)/a]*Hypergeometric2F1[-1/4, 1/2, 3/4, -((b*x^4)/a)])/(x*Sqrt[a + b*x^4]))","C",1
830,1,51,261,0.0091488,"\int \frac{1}{x^6 \sqrt{a+b x^4}} \, dx","Integrate[1/(x^6*Sqrt[a + b*x^4]),x]","-\frac{\sqrt{\frac{b x^4}{a}+1} \, _2F_1\left(-\frac{5}{4},\frac{1}{2};-\frac{1}{4};-\frac{b x^4}{a}\right)}{5 x^5 \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}} 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^{3/2} x \sqrt{a+b x^4}}{5 a^2 \left(\sqrt{a}+\sqrt{b} x^2\right)}+\frac{3 b \sqrt{a+b x^4}}{5 a^2 x}-\frac{\sqrt{a+b x^4}}{5 a x^5}",1,"-1/5*(Sqrt[1 + (b*x^4)/a]*Hypergeometric2F1[-5/4, 1/2, -1/4, -((b*x^4)/a)])/(x^5*Sqrt[a + b*x^4])","C",1
831,1,40,62,0.0240546,"\int \frac{x^{11}}{\sqrt{a-b x^4}} \, dx","Integrate[x^11/Sqrt[a - b*x^4],x]","-\frac{\sqrt{a-b x^4} \left(8 a^2+4 a b x^4+3 b^2 x^8\right)}{30 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,"-1/30*(Sqrt[a - b*x^4]*(8*a^2 + 4*a*b*x^4 + 3*b^2*x^8))/b^3","A",1
832,1,28,40,0.0148713,"\int \frac{x^7}{\sqrt{a-b x^4}} \, dx","Integrate[x^7/Sqrt[a - b*x^4],x]","-\frac{\sqrt{a-b x^4} \left(2 a+b x^4\right)}{6 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,"-1/6*(Sqrt[a - b*x^4]*(2*a + b*x^4))/b^2","A",1
833,1,19,19,0.0045856,"\int \frac{x^3}{\sqrt{a-b x^4}} \, dx","Integrate[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,"-1/2*Sqrt[a - b*x^4]/b","A",1
834,1,28,28,0.0064923,"\int \frac{1}{x \sqrt{a-b x^4}} \, dx","Integrate[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,"-1/2*ArcTanh[Sqrt[a - b*x^4]/Sqrt[a]]/Sqrt[a]","A",1
835,1,61,52,0.0761233,"\int \frac{1}{x^5 \sqrt{a-b x^4}} \, dx","Integrate[1/(x^5*Sqrt[a - b*x^4]),x]","-\frac{b \sqrt{a-b x^4} \left(\frac{a}{b x^4}+\frac{\tanh ^{-1}\left(\sqrt{1-\frac{b x^4}{a}}\right)}{\sqrt{1-\frac{b x^4}{a}}}\right)}{4 a^2}","-\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,"-1/4*(b*Sqrt[a - b*x^4]*(a/(b*x^4) + ArcTanh[Sqrt[1 - (b*x^4)/a]]/Sqrt[1 - (b*x^4)/a]))/a^2","A",1
836,1,55,55,0.0254675,"\int \frac{x^5}{\sqrt{a-b x^4}} \, dx","Integrate[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,"-1/4*(x^2*Sqrt[a - b*x^4])/b + (a*ArcTan[(Sqrt[b]*x^2)/Sqrt[a - b*x^4]])/(4*b^(3/2))","A",1
837,1,31,31,0.004732,"\int \frac{x}{\sqrt{a-b x^4}} \, dx","Integrate[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",1
838,1,22,22,0.00398,"\int \frac{1}{x^3 \sqrt{a-b x^4}} \, dx","Integrate[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,"-1/2*Sqrt[a - b*x^4]/(a*x^2)","A",1
839,1,30,46,0.0082534,"\int \frac{1}{x^7 \sqrt{a-b x^4}} \, dx","Integrate[1/(x^7*Sqrt[a - b*x^4]),x]","-\frac{\sqrt{a-b x^4} \left(a+2 b x^4\right)}{6 a^2 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,"-1/6*(Sqrt[a - b*x^4]*(a + 2*b*x^4))/(a^2*x^6)","A",1
840,1,43,71,0.0099949,"\int \frac{1}{x^{11} \sqrt{a-b x^4}} \, dx","Integrate[1/(x^11*Sqrt[a - b*x^4]),x]","-\frac{\sqrt{a-b x^4} \left(3 a^2+4 a b x^4+8 b^2 x^8\right)}{30 a^3 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,"-1/30*(Sqrt[a - b*x^4]*(3*a^2 + 4*a*b*x^4 + 8*b^2*x^8))/(a^3*x^10)","A",1
841,1,80,100,0.02134,"\int \frac{x^8}{\sqrt{a-b x^4}} \, dx","Integrate[x^8/Sqrt[a - b*x^4],x]","\frac{5 a^2 x \sqrt{1-\frac{b x^4}{a}} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};\frac{b x^4}{a}\right)-5 a^2 x+2 a b x^5+3 b^2 x^9}{21 b^2 \sqrt{a-b x^4}}","\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^2*x + 2*a*b*x^5 + 3*b^2*x^9 + 5*a^2*x*Sqrt[1 - (b*x^4)/a]*Hypergeometric2F1[1/4, 1/2, 5/4, (b*x^4)/a])/(21*b^2*Sqrt[a - b*x^4])","C",1
842,1,64,77,0.0227053,"\int \frac{x^4}{\sqrt{a-b x^4}} \, dx","Integrate[x^4/Sqrt[a - b*x^4],x]","\frac{x \left(a \sqrt{1-\frac{b x^4}{a}} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};\frac{b x^4}{a}\right)-a+b x^4\right)}{3 b \sqrt{a-b x^4}}","\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*(-a + b*x^4 + a*Sqrt[1 - (b*x^4)/a]*Hypergeometric2F1[1/4, 1/2, 5/4, (b*x^4)/a]))/(3*b*Sqrt[a - b*x^4])","C",1
843,1,72,53,0.0446139,"\int \frac{1}{\sqrt{a-b x^4}} \, dx","Integrate[1/Sqrt[a - b*x^4],x]","-\frac{i \sqrt{1-\frac{b x^4}{a}} F\left(\left.i \sinh ^{-1}\left(\sqrt{-\frac{\sqrt{b}}{\sqrt{a}}} x\right)\right|-1\right)}{\sqrt{-\frac{\sqrt{b}}{\sqrt{a}}} \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,"((-I)*Sqrt[1 - (b*x^4)/a]*EllipticF[I*ArcSinh[Sqrt[-(Sqrt[b]/Sqrt[a])]*x], -1])/(Sqrt[-(Sqrt[b]/Sqrt[a])]*Sqrt[a - b*x^4])","C",1
844,1,52,79,0.025258,"\int \frac{1}{x^4 \sqrt{a-b x^4}} \, dx","Integrate[1/(x^4*Sqrt[a - b*x^4]),x]","-\frac{\sqrt{1-\frac{b x^4}{a}} \, _2F_1\left(-\frac{3}{4},\frac{1}{2};\frac{1}{4};\frac{b x^4}{a}\right)}{3 x^3 \sqrt{a-b x^4}}","\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,"-1/3*(Sqrt[1 - (b*x^4)/a]*Hypergeometric2F1[-3/4, 1/2, 1/4, (b*x^4)/a])/(x^3*Sqrt[a - b*x^4])","C",1
845,1,52,102,0.0109494,"\int \frac{1}{x^8 \sqrt{a-b x^4}} \, dx","Integrate[1/(x^8*Sqrt[a - b*x^4]),x]","-\frac{\sqrt{1-\frac{b x^4}{a}} \, _2F_1\left(-\frac{7}{4},\frac{1}{2};-\frac{3}{4};\frac{b x^4}{a}\right)}{7 x^7 \sqrt{a-b x^4}}","\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,"-1/7*(Sqrt[1 - (b*x^4)/a]*Hypergeometric2F1[-7/4, 1/2, -3/4, (b*x^4)/a])/(x^7*Sqrt[a - b*x^4])","C",1
846,1,81,158,0.0407673,"\int \frac{x^{10}}{\sqrt{a-b x^4}} \, dx","Integrate[x^10/Sqrt[a - b*x^4],x]","\frac{x^3 \left(7 a^2 \sqrt{1-\frac{b x^4}{a}} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};\frac{b x^4}{a}\right)-7 a^2+2 a b x^4+5 b^2 x^8\right)}{45 b^2 \sqrt{a-b x^4}}","-\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,"(x^3*(-7*a^2 + 2*a*b*x^4 + 5*b^2*x^8 + 7*a^2*Sqrt[1 - (b*x^4)/a]*Hypergeometric2F1[1/2, 3/4, 7/4, (b*x^4)/a]))/(45*b^2*Sqrt[a - b*x^4])","C",1
847,1,66,135,0.0253196,"\int \frac{x^6}{\sqrt{a-b x^4}} \, dx","Integrate[x^6/Sqrt[a - b*x^4],x]","\frac{x^3 \left(a \sqrt{1-\frac{b x^4}{a}} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};\frac{b x^4}{a}\right)-a+b x^4\right)}{5 b \sqrt{a-b x^4}}","-\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*(-a + b*x^4 + a*Sqrt[1 - (b*x^4)/a]*Hypergeometric2F1[1/2, 3/4, 7/4, (b*x^4)/a]))/(5*b*Sqrt[a - b*x^4])","C",1
848,1,52,108,0.0091523,"\int \frac{x^2}{\sqrt{a-b x^4}} \, dx","Integrate[x^2/Sqrt[a - b*x^4],x]","\frac{x^3 \sqrt{1-\frac{b x^4}{a}} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};\frac{b x^4}{a}\right)}{3 \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,"(x^3*Sqrt[1 - (b*x^4)/a]*Hypergeometric2F1[1/2, 3/4, 7/4, (b*x^4)/a])/(3*Sqrt[a - b*x^4])","C",1
849,1,50,128,0.010317,"\int \frac{1}{x^2 \sqrt{a-b x^4}} \, dx","Integrate[1/(x^2*Sqrt[a - b*x^4]),x]","-\frac{\sqrt{1-\frac{b x^4}{a}} \, _2F_1\left(-\frac{1}{4},\frac{1}{2};\frac{3}{4};\frac{b x^4}{a}\right)}{x \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[1 - (b*x^4)/a]*Hypergeometric2F1[-1/4, 1/2, 3/4, (b*x^4)/a])/(x*Sqrt[a - b*x^4]))","C",1
850,1,52,158,0.0108815,"\int \frac{1}{x^6 \sqrt{a-b x^4}} \, dx","Integrate[1/(x^6*Sqrt[a - b*x^4]),x]","-\frac{\sqrt{1-\frac{b x^4}{a}} \, _2F_1\left(-\frac{5}{4},\frac{1}{2};-\frac{1}{4};\frac{b x^4}{a}\right)}{5 x^5 \sqrt{a-b x^4}}","\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,"-1/5*(Sqrt[1 - (b*x^4)/a]*Hypergeometric2F1[-5/4, 1/2, -1/4, (b*x^4)/a])/(x^5*Sqrt[a - b*x^4])","C",1
851,1,38,57,0.0374299,"\int \frac{x^{11}}{\left(a+b x^4\right)^{3/2}} \, dx","Integrate[x^11/(a + b*x^4)^(3/2),x]","\frac{-8 a^2-4 a b x^4+b^2 x^8}{6 b^3 \sqrt{a+b x^4}}","-\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,"(-8*a^2 - 4*a*b*x^4 + b^2*x^8)/(6*b^3*Sqrt[a + b*x^4])","A",1
852,1,27,38,0.0168498,"\int \frac{x^7}{\left(a+b x^4\right)^{3/2}} \, dx","Integrate[x^7/(a + b*x^4)^(3/2),x]","\frac{2 a+b x^4}{2 b^2 \sqrt{a+b x^4}}","\frac{a}{2 b^2 \sqrt{a+b x^4}}+\frac{\sqrt{a+b x^4}}{2 b^2}",1,"(2*a + b*x^4)/(2*b^2*Sqrt[a + b*x^4])","A",1
853,1,18,18,0.0047059,"\int \frac{x^3}{\left(a+b x^4\right)^{3/2}} \, dx","Integrate[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*1/(b*Sqrt[a + b*x^4])","A",1
854,1,36,46,0.0146354,"\int \frac{1}{x \left(a+b x^4\right)^{3/2}} \, dx","Integrate[1/(x*(a + b*x^4)^(3/2)),x]","\frac{\, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{b x^4}{a}+1\right)}{2 a \sqrt{a+b x^4}}","\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,"Hypergeometric2F1[-1/2, 1, 1/2, 1 + (b*x^4)/a]/(2*a*Sqrt[a + b*x^4])","C",1
855,1,37,69,0.0090837,"\int \frac{1}{x^5 \left(a+b x^4\right)^{3/2}} \, dx","Integrate[1/(x^5*(a + b*x^4)^(3/2)),x]","-\frac{b \, _2F_1\left(-\frac{1}{2},2;\frac{1}{2};\frac{b x^4}{a}+1\right)}{2 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{3 b}{4 a^2 \sqrt{a+b x^4}}-\frac{1}{4 a x^4 \sqrt{a+b x^4}}",1,"-1/2*(b*Hypergeometric2F1[-1/2, 2, 1/2, 1 + (b*x^4)/a])/(a^2*Sqrt[a + b*x^4])","C",1
856,1,75,74,0.0651067,"\int \frac{x^9}{\left(a+b x^4\right)^{3/2}} \, dx","Integrate[x^9/(a + b*x^4)^(3/2),x]","\frac{\sqrt{b} x^2 \left(3 a+b x^4\right)-3 a^{3/2} \sqrt{\frac{b x^4}{a}+1} \sinh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{4 b^{5/2} \sqrt{a+b x^4}}","-\frac{3 a \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{4 b^{5/2}}+\frac{3 x^2 \sqrt{a+b x^4}}{4 b^2}-\frac{x^6}{2 b \sqrt{a+b x^4}}",1,"(Sqrt[b]*x^2*(3*a + b*x^4) - 3*a^(3/2)*Sqrt[1 + (b*x^4)/a]*ArcSinh[(Sqrt[b]*x^2)/Sqrt[a]])/(4*b^(5/2)*Sqrt[a + b*x^4])","A",1
857,1,66,52,0.0892005,"\int \frac{x^5}{\left(a+b x^4\right)^{3/2}} \, dx","Integrate[x^5/(a + b*x^4)^(3/2),x]","\frac{\sqrt{a} \sqrt{\frac{b x^4}{a}+1} \sinh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)-\sqrt{b} x^2}{2 b^{3/2} \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,"(-(Sqrt[b]*x^2) + Sqrt[a]*Sqrt[1 + (b*x^4)/a]*ArcSinh[(Sqrt[b]*x^2)/Sqrt[a]])/(2*b^(3/2)*Sqrt[a + b*x^4])","A",1
858,1,21,21,0.019498,"\int \frac{x}{\left(a+b x^4\right)^{3/2}} \, dx","Integrate[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
859,1,29,42,0.0075378,"\int \frac{1}{x^3 \left(a+b x^4\right)^{3/2}} \, dx","Integrate[1/(x^3*(a + b*x^4)^(3/2)),x]","-\frac{a+2 b x^4}{2 a^2 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 + 2*b*x^4)/(a^2*x^2*Sqrt[a + b*x^4])","A",1
860,1,40,68,0.0108485,"\int \frac{1}{x^7 \left(a+b x^4\right)^{3/2}} \, dx","Integrate[1/(x^7*(a + b*x^4)^(3/2)),x]","-\frac{a^2-4 a b x^4-8 b^2 x^8}{6 a^3 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^2 - 4*a*b*x^4 - 8*b^2*x^8)/(a^3*x^6*Sqrt[a + b*x^4])","A",1
861,1,79,151,0.0387341,"\int \frac{x^{12}}{\left(a+b x^4\right)^{3/2}} \, dx","Integrate[x^12/(a + b*x^4)^(3/2),x]","\frac{15 a^2 x \sqrt{\frac{b x^4}{a}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\frac{b x^4}{a}\right)-15 a^2 x-6 a b x^5+2 b^2 x^9}{14 b^3 \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{15 a x \sqrt{a+b x^4}}{14 b^3}+\frac{9 x^5 \sqrt{a+b x^4}}{14 b^2}-\frac{x^9}{2 b \sqrt{a+b x^4}}",1,"(-15*a^2*x - 6*a*b*x^5 + 2*b^2*x^9 + 15*a^2*x*Sqrt[1 + (b*x^4)/a]*Hypergeometric2F1[1/4, 1/2, 5/4, -((b*x^4)/a)])/(14*b^3*Sqrt[a + b*x^4])","C",1
862,1,66,129,0.04413,"\int \frac{x^8}{\left(a+b x^4\right)^{3/2}} \, dx","Integrate[x^8/(a + b*x^4)^(3/2),x]","\frac{-5 a x \sqrt{\frac{b x^4}{a}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\frac{b x^4}{a}\right)+5 a x+2 b x^5}{6 b^2 \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,"(5*a*x + 2*b*x^5 - 5*a*x*Sqrt[1 + (b*x^4)/a]*Hypergeometric2F1[1/4, 1/2, 5/4, -((b*x^4)/a)])/(6*b^2*Sqrt[a + b*x^4])","C",1
863,1,55,108,0.0241848,"\int \frac{x^4}{\left(a+b x^4\right)^{3/2}} \, dx","Integrate[x^4/(a + b*x^4)^(3/2),x]","\frac{x \left(\sqrt{\frac{b x^4}{a}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\frac{b x^4}{a}\right)-1\right)}{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*(-1 + Sqrt[1 + (b*x^4)/a]*Hypergeometric2F1[1/4, 1/2, 5/4, -((b*x^4)/a)]))/(2*b*Sqrt[a + b*x^4])","C",1
864,1,55,108,0.0184965,"\int \frac{1}{\left(a+b x^4\right)^{3/2}} \, dx","Integrate[(a + b*x^4)^(-3/2),x]","\frac{x \sqrt{\frac{b x^4}{a}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\frac{b x^4}{a}\right)+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 + x*Sqrt[1 + (b*x^4)/a]*Hypergeometric2F1[1/4, 1/2, 5/4, -((b*x^4)/a)])/(2*a*Sqrt[a + b*x^4])","C",1
865,1,54,131,0.0095426,"\int \frac{1}{x^4 \left(a+b x^4\right)^{3/2}} \, dx","Integrate[1/(x^4*(a + b*x^4)^(3/2)),x]","-\frac{\sqrt{\frac{b x^4}{a}+1} \, _2F_1\left(-\frac{3}{4},\frac{3}{2};\frac{1}{4};-\frac{b x^4}{a}\right)}{3 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,"-1/3*(Sqrt[1 + (b*x^4)/a]*Hypergeometric2F1[-3/4, 3/2, 1/4, -((b*x^4)/a)])/(a*x^3*Sqrt[a + b*x^4])","C",1
866,1,54,153,0.0096939,"\int \frac{1}{x^8 \left(a+b x^4\right)^{3/2}} \, dx","Integrate[1/(x^8*(a + b*x^4)^(3/2)),x]","-\frac{\sqrt{\frac{b x^4}{a}+1} \, _2F_1\left(-\frac{7}{4},\frac{3}{2};-\frac{3}{4};-\frac{b x^4}{a}\right)}{7 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,"-1/7*(Sqrt[1 + (b*x^4)/a]*Hypergeometric2F1[-7/4, 3/2, -3/4, -((b*x^4)/a)])/(a*x^7*Sqrt[a + b*x^4])","C",1
867,1,80,282,0.0308673,"\int \frac{x^{14}}{\left(a+b x^4\right)^{3/2}} \, dx","Integrate[x^14/(a + b*x^4)^(3/2),x]","\frac{x^3 \left(-77 a^2 \sqrt{\frac{b x^4}{a}+1} \, _2F_1\left(\frac{3}{4},\frac{3}{2};\frac{7}{4};-\frac{b x^4}{a}\right)+77 a^2-11 a b x^4+5 b^2 x^8\right)}{45 b^3 \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}} 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{77 a^2 x \sqrt{a+b x^4}}{30 b^{7/2} \left(\sqrt{a}+\sqrt{b} x^2\right)}-\frac{77 a x^3 \sqrt{a+b x^4}}{90 b^3}+\frac{11 x^7 \sqrt{a+b x^4}}{18 b^2}-\frac{x^{11}}{2 b \sqrt{a+b x^4}}",1,"(x^3*(77*a^2 - 11*a*b*x^4 + 5*b^2*x^8 - 77*a^2*Sqrt[1 + (b*x^4)/a]*Hypergeometric2F1[3/4, 3/2, 7/4, -((b*x^4)/a)]))/(45*b^3*Sqrt[a + b*x^4])","C",1
868,1,66,258,0.0281521,"\int \frac{x^{10}}{\left(a+b x^4\right)^{3/2}} \, dx","Integrate[x^10/(a + b*x^4)^(3/2),x]","\frac{x^3 \left(7 a \sqrt{\frac{b x^4}{a}+1} \, _2F_1\left(\frac{3}{4},\frac{3}{2};\frac{7}{4};-\frac{b x^4}{a}\right)-7 a+b x^4\right)}{5 b^2 \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{21 a x \sqrt{a+b x^4}}{10 b^{5/2} \left(\sqrt{a}+\sqrt{b} x^2\right)}+\frac{7 x^3 \sqrt{a+b x^4}}{10 b^2}-\frac{x^7}{2 b \sqrt{a+b x^4}}",1,"(x^3*(-7*a + b*x^4 + 7*a*Sqrt[1 + (b*x^4)/a]*Hypergeometric2F1[3/4, 3/2, 7/4, -((b*x^4)/a)]))/(5*b^2*Sqrt[a + b*x^4])","C",1
869,1,57,236,0.0169249,"\int \frac{x^6}{\left(a+b x^4\right)^{3/2}} \, dx","Integrate[x^6/(a + b*x^4)^(3/2),x]","\frac{x^3-x^3 \sqrt{\frac{b x^4}{a}+1} \, _2F_1\left(\frac{3}{4},\frac{3}{2};\frac{7}{4};-\frac{b x^4}{a}\right)}{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 - x^3*Sqrt[1 + (b*x^4)/a]*Hypergeometric2F1[3/4, 3/2, 7/4, -((b*x^4)/a)])/(b*Sqrt[a + b*x^4])","C",1
870,1,54,239,0.0093732,"\int \frac{x^2}{\left(a+b x^4\right)^{3/2}} \, dx","Integrate[x^2/(a + b*x^4)^(3/2),x]","\frac{x^3 \sqrt{\frac{b x^4}{a}+1} \, _2F_1\left(\frac{3}{4},\frac{3}{2};\frac{7}{4};-\frac{b x^4}{a}\right)}{3 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^{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*Sqrt[1 + (b*x^4)/a]*Hypergeometric2F1[3/4, 3/2, 7/4, -((b*x^4)/a)])/(3*a*Sqrt[a + b*x^4])","C",1
871,1,52,260,0.0094058,"\int \frac{1}{x^2 \left(a+b x^4\right)^{3/2}} \, dx","Integrate[1/(x^2*(a + b*x^4)^(3/2)),x]","-\frac{\sqrt{\frac{b x^4}{a}+1} \, _2F_1\left(-\frac{1}{4},\frac{3}{2};\frac{3}{4};-\frac{b x^4}{a}\right)}{a x \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}} 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{3 \sqrt{a+b x^4}}{2 a^2 x}+\frac{3 \sqrt{b} x \sqrt{a+b x^4}}{2 a^2 \left(\sqrt{a}+\sqrt{b} x^2\right)}+\frac{1}{2 a x \sqrt{a+b x^4}}",1,"-((Sqrt[1 + (b*x^4)/a]*Hypergeometric2F1[-1/4, 3/2, 3/4, -((b*x^4)/a)])/(a*x*Sqrt[a + b*x^4]))","C",1
872,1,54,282,0.0094265,"\int \frac{1}{x^6 \left(a+b x^4\right)^{3/2}} \, dx","Integrate[1/(x^6*(a + b*x^4)^(3/2)),x]","-\frac{\sqrt{\frac{b x^4}{a}+1} \, _2F_1\left(-\frac{5}{4},\frac{3}{2};-\frac{1}{4};-\frac{b x^4}{a}\right)}{5 a x^5 \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}} 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^{3/2} x \sqrt{a+b x^4}}{10 a^3 \left(\sqrt{a}+\sqrt{b} x^2\right)}+\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,"-1/5*(Sqrt[1 + (b*x^4)/a]*Hypergeometric2F1[-5/4, 3/2, -1/4, -((b*x^4)/a)])/(a*x^5*Sqrt[a + b*x^4])","C",1
873,1,72,127,0.0375152,"\int \frac{1}{\left(a+b x^4\right)^{5/2}} \, dx","Integrate[(a + b*x^4)^(-5/2),x]","\frac{5 x \left(a+b x^4\right) \sqrt{\frac{b x^4}{a}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\frac{b x^4}{a}\right)+7 a x+5 b x^5}{12 a^2 \left(a+b x^4\right)^{3/2}}","\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{5 x}{12 a^2 \sqrt{a+b x^4}}+\frac{x}{6 a \left(a+b x^4\right)^{3/2}}",1,"(7*a*x + 5*b*x^5 + 5*x*(a + b*x^4)*Sqrt[1 + (b*x^4)/a]*Hypergeometric2F1[1/4, 1/2, 5/4, -((b*x^4)/a)])/(12*a^2*(a + b*x^4)^(3/2))","C",1
874,1,27,46,0.0092979,"\int \frac{x^{11}}{\sqrt{1-x^4}} \, dx","Integrate[x^11/Sqrt[1 - x^4],x]","-\frac{1}{30} \sqrt{1-x^4} \left(3 x^8+4 x^4+8\right)","-\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,"-1/30*(Sqrt[1 - x^4]*(8 + 4*x^4 + 3*x^8))","A",1
875,1,20,31,0.0064933,"\int \frac{x^7}{\sqrt{1-x^4}} \, dx","Integrate[x^7/Sqrt[1 - x^4],x]","-\frac{1}{6} \sqrt{1-x^4} \left(x^4+2\right)","\frac{1}{6} \left(1-x^4\right)^{3/2}-\frac{\sqrt{1-x^4}}{2}",1,"-1/6*(Sqrt[1 - x^4]*(2 + x^4))","A",1
876,1,15,15,0.0022633,"\int \frac{x^3}{\sqrt{1-x^4}} \, dx","Integrate[x^3/Sqrt[1 - x^4],x]","-\frac{1}{2} \sqrt{1-x^4}","-\frac{1}{2} \sqrt{1-x^4}",1,"-1/2*Sqrt[1 - x^4]","A",1
877,1,16,16,0.0027605,"\int \frac{1}{x \sqrt{1-x^4}} \, dx","Integrate[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,"-1/2*ArcTanh[Sqrt[1 - x^4]]","A",1
878,1,35,35,0.0087821,"\int \frac{1}{x^5 \sqrt{1-x^4}} \, dx","Integrate[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,"-1/4*Sqrt[1 - x^4]/x^4 - ArcTanh[Sqrt[1 - x^4]]/4","A",1
879,1,27,27,0.0068421,"\int \frac{x^5}{\sqrt{1-x^4}} \, dx","Integrate[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,"-1/4*(x^2*Sqrt[1 - x^4]) + ArcSin[x^2]/4","A",1
880,1,8,8,0.0026997,"\int \frac{x}{\sqrt{1-x^4}} \, dx","Integrate[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",1
881,1,18,18,0.0028772,"\int \frac{1}{x^3 \sqrt{1-x^4}} \, dx","Integrate[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,"-1/2*Sqrt[1 - x^4]/x^2","A",1
882,1,25,37,0.0050665,"\int \frac{1}{x^7 \sqrt{1-x^4}} \, dx","Integrate[1/(x^7*Sqrt[1 - x^4]),x]","-\frac{\sqrt{1-x^4} \left(2 x^4+1\right)}{6 x^6}","-\frac{\sqrt{1-x^4}}{6 x^6}-\frac{\sqrt{1-x^4}}{3 x^2}",1,"-1/6*(Sqrt[1 - x^4]*(1 + 2*x^4))/x^6","A",1
883,1,30,55,0.0078695,"\int \frac{1}{x^{11} \sqrt{1-x^4}} \, dx","Integrate[1/(x^11*Sqrt[1 - x^4]),x]","-\frac{\sqrt{1-x^4} \left(8 x^8+4 x^4+3\right)}{30 x^{10}}","-\frac{\sqrt{1-x^4}}{10 x^{10}}-\frac{2 \sqrt{1-x^4}}{15 x^6}-\frac{4 \sqrt{1-x^4}}{15 x^2}",1,"-1/30*(Sqrt[1 - x^4]*(3 + 4*x^4 + 8*x^8))/x^10","A",1
884,1,42,43,0.0138294,"\int \frac{x^8}{\sqrt{1-x^4}} \, dx","Integrate[x^8/Sqrt[1 - x^4],x]","\frac{1}{21} \left(5 x \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};x^4\right)-x \sqrt{1-x^4} \left(3 x^4+5\right)\right)","-\frac{5}{21} \sqrt{1-x^4} x-\frac{1}{7} \sqrt{1-x^4} x^5+\frac{5}{21} F\left(\left.\sin ^{-1}(x)\right|-1\right)",1,"(-(x*Sqrt[1 - x^4]*(5 + 3*x^4)) + 5*x*Hypergeometric2F1[1/4, 1/2, 5/4, x^4])/21","C",1
885,1,32,25,0.0073216,"\int \frac{x^4}{\sqrt{1-x^4}} \, dx","Integrate[x^4/Sqrt[1 - x^4],x]","\frac{1}{3} x \left(\, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};x^4\right)-\sqrt{1-x^4}\right)","\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] + Hypergeometric2F1[1/4, 1/2, 5/4, x^4]))/3","C",1
886,1,4,4,0.0124387,"\int \frac{1}{\sqrt{1-x^4}} \, dx","Integrate[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
887,1,20,27,0.0031264,"\int \frac{1}{x^4 \sqrt{1-x^4}} \, dx","Integrate[1/(x^4*Sqrt[1 - x^4]),x]","-\frac{\, _2F_1\left(-\frac{3}{4},\frac{1}{2};\frac{1}{4};x^4\right)}{3 x^3}","\frac{1}{3} F\left(\left.\sin ^{-1}(x)\right|-1\right)-\frac{\sqrt{1-x^4}}{3 x^3}",1,"-1/3*Hypergeometric2F1[-3/4, 1/2, 1/4, x^4]/x^3","C",1
888,1,20,45,0.0033242,"\int \frac{1}{x^8 \sqrt{1-x^4}} \, dx","Integrate[1/(x^8*Sqrt[1 - x^4]),x]","-\frac{\, _2F_1\left(-\frac{7}{4},\frac{1}{2};-\frac{3}{4};x^4\right)}{7 x^7}","-\frac{\sqrt{1-x^4}}{7 x^7}-\frac{5 \sqrt{1-x^4}}{21 x^3}+\frac{5}{21} F\left(\left.\sin ^{-1}(x)\right|-1\right)",1,"-1/7*Hypergeometric2F1[-7/4, 1/2, -3/4, x^4]/x^7","C",1
889,1,43,53,0.0304165,"\int \frac{x^{10}}{\sqrt{1-x^4}} \, dx","Integrate[x^10/Sqrt[1 - x^4],x]","\frac{1}{45} x^3 \left(7 \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};x^4\right)-\sqrt{1-x^4} \left(5 x^4+7\right)\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,"(x^3*(-(Sqrt[1 - x^4]*(7 + 5*x^4)) + 7*Hypergeometric2F1[1/2, 3/4, 7/4, x^4]))/45","C",1
890,1,34,35,0.0066693,"\int \frac{x^6}{\sqrt{1-x^4}} \, dx","Integrate[x^6/Sqrt[1 - x^4],x]","\frac{1}{5} x^3 \left(\, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};x^4\right)-\sqrt{1-x^4}\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] + Hypergeometric2F1[1/2, 3/4, 7/4, x^4]))/5","C",1
891,1,20,11,0.0026542,"\int \frac{x^2}{\sqrt{1-x^4}} \, dx","Integrate[x^2/Sqrt[1 - x^4],x]","\frac{1}{3} x^3 \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};x^4\right)","E\left(\left.\sin ^{-1}(x)\right|-1\right)-F\left(\left.\sin ^{-1}(x)\right|-1\right)",1,"(x^3*Hypergeometric2F1[1/2, 3/4, 7/4, x^4])/3","C",1
892,1,18,27,0.0030792,"\int \frac{1}{x^2 \sqrt{1-x^4}} \, dx","Integrate[1/(x^2*Sqrt[1 - x^4]),x]","-\frac{\, _2F_1\left(-\frac{1}{4},\frac{1}{2};\frac{3}{4};x^4\right)}{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)",1,"-(Hypergeometric2F1[-1/4, 1/2, 3/4, x^4]/x)","C",1
893,1,20,53,0.003122,"\int \frac{1}{x^6 \sqrt{1-x^4}} \, dx","Integrate[1/(x^6*Sqrt[1 - x^4]),x]","-\frac{\, _2F_1\left(-\frac{5}{4},\frac{1}{2};-\frac{1}{4};x^4\right)}{5 x^5}","-\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,"-1/5*Hypergeometric2F1[-5/4, 1/2, -1/4, x^4]/x^5","C",1
894,1,27,42,0.0094608,"\int \frac{x^{11}}{\left(1-x^4\right)^{3/2}} \, dx","Integrate[x^11/(1 - x^4)^(3/2),x]","\frac{-x^8-4 x^4+8}{6 \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,"(8 - 4*x^4 - x^8)/(6*Sqrt[1 - x^4])","A",1
895,1,22,31,0.0072708,"\int \frac{x^7}{\left(1-x^4\right)^{3/2}} \, dx","Integrate[x^7/(1 - x^4)^(3/2),x]","\frac{2-x^4}{2 \sqrt{1-x^4}}","\frac{\sqrt{1-x^4}}{2}+\frac{1}{2 \sqrt{1-x^4}}",1,"(2 - x^4)/(2*Sqrt[1 - x^4])","A",1
896,1,15,15,0.0025752,"\int \frac{x^3}{\left(1-x^4\right)^{3/2}} \, dx","Integrate[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
897,1,30,32,0.0064958,"\int \frac{1}{x \left(1-x^4\right)^{3/2}} \, dx","Integrate[1/(x*(1 - x^4)^(3/2)),x]","\frac{\, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};1-x^4\right)}{2 \sqrt{1-x^4}}","\frac{1}{2 \sqrt{1-x^4}}-\frac{1}{2} \tanh ^{-1}\left(\sqrt{1-x^4}\right)",1,"Hypergeometric2F1[-1/2, 1, 1/2, 1 - x^4]/(2*Sqrt[1 - x^4])","C",1
898,1,30,50,0.0052284,"\int \frac{1}{x^5 \left(1-x^4\right)^{3/2}} \, dx","Integrate[1/(x^5*(1 - x^4)^(3/2)),x]","\frac{\, _2F_1\left(-\frac{1}{2},2;\frac{1}{2};1-x^4\right)}{2 \sqrt{1-x^4}}","-\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,"Hypergeometric2F1[-1/2, 2, 1/2, 1 - x^4]/(2*Sqrt[1 - x^4])","C",1
899,1,41,45,0.0215407,"\int \frac{x^9}{\left(1-x^4\right)^{3/2}} \, dx","Integrate[x^9/(1 - x^4)^(3/2),x]","-\frac{x^6-3 x^2+3 \sqrt{1-x^4} \sin ^{-1}\left(x^2\right)}{4 \sqrt{1-x^4}}","-\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",1,"-1/4*(-3*x^2 + x^6 + 3*Sqrt[1 - x^4]*ArcSin[x^2])/Sqrt[1 - x^4]","A",1
900,1,26,27,0.0235913,"\int \frac{x^5}{\left(1-x^4\right)^{3/2}} \, dx","Integrate[x^5/(1 - x^4)^(3/2),x]","\frac{1}{2} \left(\frac{x^2}{\sqrt{1-x^4}}-\sin ^{-1}\left(x^2\right)\right)","\frac{x^2}{2 \sqrt{1-x^4}}-\frac{1}{2} \sin ^{-1}\left(x^2\right)",1,"(x^2/Sqrt[1 - x^4] - ArcSin[x^2])/2","A",1
901,1,18,18,0.0027198,"\int \frac{x}{\left(1-x^4\right)^{3/2}} \, dx","Integrate[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
902,1,25,34,0.0053957,"\int \frac{1}{x^3 \left(1-x^4\right)^{3/2}} \, dx","Integrate[1/(x^3*(1 - x^4)^(3/2)),x]","-\frac{1-2 x^4}{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*(1 - 2*x^4)/(x^2*Sqrt[1 - x^4])","A",1
903,1,30,55,0.0062108,"\int \frac{1}{x^7 \left(1-x^4\right)^{3/2}} \, dx","Integrate[1/(x^7*(1 - x^4)^(3/2)),x]","-\frac{-8 x^8+4 x^4+1}{6 x^6 \sqrt{1-x^4}}","-\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}",1,"-1/6*(1 + 4*x^4 - 8*x^8)/(x^6*Sqrt[1 - x^4])","A",1
904,1,54,61,0.0114366,"\int \frac{x^{12}}{\left(1-x^4\right)^{3/2}} \, dx","Integrate[x^12/(1 - x^4)^(3/2),x]","-\frac{x \left(15 \sqrt{1-x^4} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};x^4\right)+2 x^8+6 x^4-15\right)}{14 \sqrt{1-x^4}}","\frac{15}{14} \sqrt{1-x^4} x+\frac{x^9}{2 \sqrt{1-x^4}}+\frac{9}{14} \sqrt{1-x^4} x^5-\frac{15}{14} F\left(\left.\sin ^{-1}(x)\right|-1\right)",1,"-1/14*(x*(-15 + 6*x^4 + 2*x^8 + 15*Sqrt[1 - x^4]*Hypergeometric2F1[1/4, 1/2, 5/4, x^4]))/Sqrt[1 - x^4]","C",1
905,1,49,43,0.0116214,"\int \frac{x^8}{\left(1-x^4\right)^{3/2}} \, dx","Integrate[x^8/(1 - x^4)^(3/2),x]","-\frac{x \left(5 \sqrt{1-x^4} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};x^4\right)+2 x^4-5\right)}{6 \sqrt{1-x^4}}","\frac{5}{6} \sqrt{1-x^4} x+\frac{x^5}{2 \sqrt{1-x^4}}-\frac{5}{6} F\left(\left.\sin ^{-1}(x)\right|-1\right)",1,"-1/6*(x*(-5 + 2*x^4 + 5*Sqrt[1 - x^4]*Hypergeometric2F1[1/4, 1/2, 5/4, x^4]))/Sqrt[1 - x^4]","C",1
906,1,32,25,0.0094237,"\int \frac{x^4}{\left(1-x^4\right)^{3/2}} \, dx","Integrate[x^4/(1 - x^4)^(3/2),x]","\frac{1}{2} x \left(\frac{1}{\sqrt{1-x^4}}-\, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};x^4\right)\right)","\frac{x}{2 \sqrt{1-x^4}}-\frac{1}{2} F\left(\left.\sin ^{-1}(x)\right|-1\right)",1,"(x*(1/Sqrt[1 - x^4] - Hypergeometric2F1[1/4, 1/2, 5/4, x^4]))/2","C",1
907,1,30,25,0.0184461,"\int \frac{1}{\left(1-x^4\right)^{3/2}} \, dx","Integrate[(1 - x^4)^(-3/2),x]","\frac{1}{2} x \left(\, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};x^4\right)+\frac{1}{\sqrt{1-x^4}}\right)","\frac{x}{2 \sqrt{1-x^4}}+\frac{1}{2} F\left(\left.\sin ^{-1}(x)\right|-1\right)",1,"(x*(1/Sqrt[1 - x^4] + Hypergeometric2F1[1/4, 1/2, 5/4, x^4]))/2","C",1
908,1,20,45,0.0030122,"\int \frac{1}{x^4 \left(1-x^4\right)^{3/2}} \, dx","Integrate[1/(x^4*(1 - x^4)^(3/2)),x]","-\frac{\, _2F_1\left(-\frac{3}{4},\frac{3}{2};\frac{1}{4};x^4\right)}{3 x^3}","-\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,"-1/3*Hypergeometric2F1[-3/4, 3/2, 1/4, x^4]/x^3","C",1
909,1,20,63,0.0032857,"\int \frac{1}{x^8 \left(1-x^4\right)^{3/2}} \, dx","Integrate[1/(x^8*(1 - x^4)^(3/2)),x]","-\frac{\, _2F_1\left(-\frac{7}{4},\frac{3}{2};-\frac{3}{4};x^4\right)}{7 x^7}","-\frac{9 \sqrt{1-x^4}}{14 x^7}+\frac{1}{2 x^7 \sqrt{1-x^4}}-\frac{15 \sqrt{1-x^4}}{14 x^3}+\frac{15}{14} F\left(\left.\sin ^{-1}(x)\right|-1\right)",1,"-1/7*Hypergeometric2F1[-7/4, 3/2, -3/4, x^4]/x^7","C",1
910,1,56,71,0.0215085,"\int \frac{x^{14}}{\left(1-x^4\right)^{3/2}} \, dx","Integrate[x^14/(1 - x^4)^(3/2),x]","-\frac{x^3 \left(-77 \sqrt{1-x^4} \, _2F_1\left(\frac{3}{4},\frac{3}{2};\frac{7}{4};x^4\right)+5 x^8+11 x^4+77\right)}{45 \sqrt{1-x^4}}","\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,"-1/45*(x^3*(77 + 11*x^4 + 5*x^8 - 77*Sqrt[1 - x^4]*Hypergeometric2F1[3/4, 3/2, 7/4, x^4]))/Sqrt[1 - x^4]","C",1
911,1,49,53,0.0269419,"\int \frac{x^{10}}{\left(1-x^4\right)^{3/2}} \, dx","Integrate[x^10/(1 - x^4)^(3/2),x]","-\frac{x^3 \left(-7 \sqrt{1-x^4} \, _2F_1\left(\frac{3}{4},\frac{3}{2};\frac{7}{4};x^4\right)+x^4+7\right)}{5 \sqrt{1-x^4}}","\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,"-1/5*(x^3*(7 + x^4 - 7*Sqrt[1 - x^4]*Hypergeometric2F1[3/4, 3/2, 7/4, x^4]))/Sqrt[1 - x^4]","C",1
912,1,31,35,0.00936,"\int \frac{x^6}{\left(1-x^4\right)^{3/2}} \, dx","Integrate[x^6/(1 - x^4)^(3/2),x]","x^3 \left(\, _2F_1\left(\frac{3}{4},\frac{3}{2};\frac{7}{4};x^4\right)-\frac{1}{\sqrt{1-x^4}}\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*(-(1/Sqrt[1 - x^4]) + Hypergeometric2F1[3/4, 3/2, 7/4, x^4])","C",1
913,1,20,35,0.0031158,"\int \frac{x^2}{\left(1-x^4\right)^{3/2}} \, dx","Integrate[x^2/(1 - x^4)^(3/2),x]","\frac{1}{3} x^3 \, _2F_1\left(\frac{3}{4},\frac{3}{2};\frac{7}{4};x^4\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*Hypergeometric2F1[3/4, 3/2, 7/4, x^4])/3","C",1
914,1,18,53,0.0032174,"\int \frac{1}{x^2 \left(1-x^4\right)^{3/2}} \, dx","Integrate[1/(x^2*(1 - x^4)^(3/2)),x]","-\frac{\, _2F_1\left(-\frac{1}{4},\frac{3}{2};\frac{3}{4};x^4\right)}{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)",1,"-(Hypergeometric2F1[-1/4, 3/2, 3/4, x^4]/x)","C",1
915,1,20,71,0.0067854,"\int \frac{1}{x^6 \left(1-x^4\right)^{3/2}} \, dx","Integrate[1/(x^6*(1 - x^4)^(3/2)),x]","-\frac{\, _2F_1\left(-\frac{5}{4},\frac{3}{2};-\frac{1}{4};x^4\right)}{5 x^5}","-\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,"-1/5*Hypergeometric2F1[-5/4, 3/2, -1/4, x^4]/x^5","C",1
916,1,51,41,0.0176273,"\int \frac{1}{\left(1-x^4\right)^{5/2}} \, dx","Integrate[(1 - x^4)^(-5/2),x]","\frac{5}{12} x \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};x^4\right)+\frac{5 x}{12 \sqrt{1-x^4}}+\frac{x}{6 \left(1-x^4\right)^{3/2}}","\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*x*Hypergeometric2F1[1/4, 1/2, 5/4, x^4])/12","C",1
917,1,25,40,0.0078229,"\int \frac{x^{11}}{\sqrt{1+x^4}} \, dx","Integrate[x^11/Sqrt[1 + x^4],x]","\frac{1}{30} \sqrt{x^4+1} \left(3 x^8-4 x^4+8\right)","\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]*(8 - 4*x^4 + 3*x^8))/30","A",1
918,1,18,27,0.005636,"\int \frac{x^7}{\sqrt{1+x^4}} \, dx","Integrate[x^7/Sqrt[1 + x^4],x]","\frac{1}{6} \left(x^4-2\right) \sqrt{x^4+1}","\frac{1}{6} \left(x^4+1\right)^{3/2}-\frac{\sqrt{x^4+1}}{2}",1,"((-2 + x^4)*Sqrt[1 + x^4])/6","A",1
919,1,13,13,0.0021252,"\int \frac{x^3}{\sqrt{1+x^4}} \, dx","Integrate[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
920,1,14,14,0.002504,"\int \frac{1}{x \sqrt{1+x^4}} \, dx","Integrate[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,"-1/2*ArcTanh[Sqrt[1 + x^4]]","A",1
921,1,31,31,0.0163268,"\int \frac{1}{x^5 \sqrt{1+x^4}} \, dx","Integrate[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,"-1/4*Sqrt[1 + x^4]/x^4 + ArcTanh[Sqrt[1 + x^4]]/4","A",1
922,1,25,25,0.0055439,"\int \frac{x^5}{\sqrt{1+x^4}} \, dx","Integrate[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",1
923,1,8,8,0.0021602,"\int \frac{x}{\sqrt{1+x^4}} \, dx","Integrate[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",1
924,1,16,16,0.0260646,"\int \frac{1}{x^3 \sqrt{1+x^4}} \, dx","Integrate[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,"-1/2*Sqrt[1 + x^4]/x^2","A",1
925,1,23,33,0.0045306,"\int \frac{1}{x^7 \sqrt{1+x^4}} \, dx","Integrate[1/(x^7*Sqrt[1 + x^4]),x]","-\frac{\left(1-2 x^4\right) \sqrt{x^4+1}}{6 x^6}","\frac{\sqrt{x^4+1}}{3 x^2}-\frac{\sqrt{x^4+1}}{6 x^6}",1,"-1/6*((1 - 2*x^4)*Sqrt[1 + x^4])/x^6","A",1
926,1,28,49,0.0055793,"\int \frac{1}{x^{11} \sqrt{1+x^4}} \, dx","Integrate[1/(x^11*Sqrt[1 + x^4]),x]","-\frac{\sqrt{x^4+1} \left(8 x^8-4 x^4+3\right)}{30 x^{10}}","-\frac{\sqrt{x^4+1}}{10 x^{10}}+\frac{2 \sqrt{x^4+1}}{15 x^6}-\frac{4 \sqrt{x^4+1}}{15 x^2}",1,"-1/30*(Sqrt[1 + x^4]*(3 - 4*x^4 + 8*x^8))/x^10","A",1
927,1,40,74,0.0121673,"\int \frac{x^8}{\sqrt{1+x^4}} \, dx","Integrate[x^8/Sqrt[1 + x^4],x]","\frac{1}{21} x \left(5 \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-x^4\right)+\sqrt{x^4+1} \left(3 x^4-5\right)\right)","-\frac{5}{21} \sqrt{x^4+1} x+\frac{1}{7} \sqrt{x^4+1} x^5+\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,"(x*(Sqrt[1 + x^4]*(-5 + 3*x^4) + 5*Hypergeometric2F1[1/4, 1/2, 5/4, -x^4]))/21","C",1
928,1,32,58,0.0061108,"\int \frac{x^4}{\sqrt{1+x^4}} \, dx","Integrate[x^4/Sqrt[1 + x^4],x]","\frac{1}{3} x \left(\sqrt{x^4+1}-\, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-x^4\right)\right)","\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] - Hypergeometric2F1[1/4, 1/2, 5/4, -x^4]))/3","C",1
929,1,21,43,0.0246615,"\int \frac{1}{\sqrt{1+x^4}} \, dx","Integrate[1/Sqrt[1 + x^4],x]","-\sqrt[4]{-1} F\left(\left.i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)\right|-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)}{2 \sqrt{x^4+1}}",1,"-((-1)^(1/4)*EllipticF[I*ArcSinh[(-1)^(1/4)*x], -1])","C",1
930,1,22,60,0.0029836,"\int \frac{1}{x^4 \sqrt{1+x^4}} \, dx","Integrate[1/(x^4*Sqrt[1 + x^4]),x]","-\frac{\, _2F_1\left(-\frac{3}{4},\frac{1}{2};\frac{1}{4};-x^4\right)}{3 x^3}","-\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,"-1/3*Hypergeometric2F1[-3/4, 1/2, 1/4, -x^4]/x^3","C",1
931,1,22,76,0.0031751,"\int \frac{1}{x^8 \sqrt{1+x^4}} \, dx","Integrate[1/(x^8*Sqrt[1 + x^4]),x]","-\frac{\, _2F_1\left(-\frac{7}{4},\frac{1}{2};-\frac{3}{4};-x^4\right)}{7 x^7}","-\frac{\sqrt{x^4+1}}{7 x^7}+\frac{5 \sqrt{x^4+1}}{21 x^3}+\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,"-1/7*Hypergeometric2F1[-7/4, 1/2, -3/4, -x^4]/x^7","C",1
932,1,42,140,0.0231533,"\int \frac{x^{10}}{\sqrt{1+x^4}} \, dx","Integrate[x^10/Sqrt[1 + x^4],x]","\frac{1}{45} x^3 \left(7 \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};-x^4\right)+\sqrt{x^4+1} \left(5 x^4-7\right)\right)","\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,"(x^3*(Sqrt[1 + x^4]*(-7 + 5*x^4) + 7*Hypergeometric2F1[1/2, 3/4, 7/4, -x^4]))/45","C",1
933,1,34,124,0.0074297,"\int \frac{x^6}{\sqrt{1+x^4}} \, dx","Integrate[x^6/Sqrt[1 + x^4],x]","\frac{1}{5} x^3 \left(\sqrt{x^4+1}-\, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};-x^4\right)\right)","\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] - Hypergeometric2F1[1/2, 3/4, 7/4, -x^4]))/5","C",1
934,1,22,103,0.0025048,"\int \frac{x^2}{\sqrt{1+x^4}} \, dx","Integrate[x^2/Sqrt[1 + x^4],x]","\frac{1}{3} x^3 \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};-x^4\right)","\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^3*Hypergeometric2F1[1/2, 3/4, 7/4, -x^4])/3","C",1
935,1,20,117,0.0079174,"\int \frac{1}{x^2 \sqrt{1+x^4}} \, dx","Integrate[1/(x^2*Sqrt[1 + x^4]),x]","-\frac{\, _2F_1\left(-\frac{1}{4},\frac{1}{2};\frac{3}{4};-x^4\right)}{x}","-\frac{\sqrt{x^4+1}}{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}}",1,"-(Hypergeometric2F1[-1/4, 1/2, 3/4, -x^4]/x)","C",1
936,1,22,140,0.0030387,"\int \frac{1}{x^6 \sqrt{1+x^4}} \, dx","Integrate[1/(x^6*Sqrt[1 + x^4]),x]","-\frac{\, _2F_1\left(-\frac{5}{4},\frac{1}{2};-\frac{1}{4};-x^4\right)}{5 x^5}","\frac{3 \sqrt{x^4+1}}{5 x}-\frac{\sqrt{x^4+1}}{5 x^5}-\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,"-1/5*Hypergeometric2F1[-5/4, 1/2, -1/4, -x^4]/x^5","C",1
937,1,23,38,0.0241565,"\int \frac{x^{11}}{\left(1+x^4\right)^{3/2}} \, dx","Integrate[x^11/(1 + x^4)^(3/2),x]","\frac{x^8-4 x^4-8}{6 \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,"(-8 - 4*x^4 + x^8)/(6*Sqrt[1 + x^4])","A",1
938,1,18,27,0.0060934,"\int \frac{x^7}{\left(1+x^4\right)^{3/2}} \, dx","Integrate[x^7/(1 + x^4)^(3/2),x]","\frac{x^4+2}{2 \sqrt{x^4+1}}","\frac{\sqrt{x^4+1}}{2}+\frac{1}{2 \sqrt{x^4+1}}",1,"(2 + x^4)/(2*Sqrt[1 + x^4])","A",1
939,1,13,13,0.0023287,"\int \frac{x^3}{\left(1+x^4\right)^{3/2}} \, dx","Integrate[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*1/Sqrt[1 + x^4]","A",1
940,1,26,28,0.005289,"\int \frac{1}{x \left(1+x^4\right)^{3/2}} \, dx","Integrate[1/(x*(1 + x^4)^(3/2)),x]","\frac{\, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};x^4+1\right)}{2 \sqrt{x^4+1}}","\frac{1}{2 \sqrt{x^4+1}}-\frac{1}{2} \tanh ^{-1}\left(\sqrt{x^4+1}\right)",1,"Hypergeometric2F1[-1/2, 1, 1/2, 1 + x^4]/(2*Sqrt[1 + x^4])","C",1
941,1,26,44,0.0053781,"\int \frac{1}{x^5 \left(1+x^4\right)^{3/2}} \, dx","Integrate[1/(x^5*(1 + x^4)^(3/2)),x]","-\frac{\, _2F_1\left(-\frac{1}{2},2;\frac{1}{2};x^4+1\right)}{2 \sqrt{x^4+1}}","-\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*Hypergeometric2F1[-1/2, 2, 1/2, 1 + x^4]/Sqrt[1 + x^4]","C",1
942,1,37,41,0.0107452,"\int \frac{x^9}{\left(1+x^4\right)^{3/2}} \, dx","Integrate[x^9/(1 + x^4)^(3/2),x]","\frac{x^6+3 x^2-3 \sqrt{x^4+1} \sinh ^{-1}\left(x^2\right)}{4 \sqrt{x^4+1}}","-\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",1,"(3*x^2 + x^6 - 3*Sqrt[1 + x^4]*ArcSinh[x^2])/(4*Sqrt[1 + x^4])","A",1
943,1,23,25,0.020416,"\int \frac{x^5}{\left(1+x^4\right)^{3/2}} \, dx","Integrate[x^5/(1 + x^4)^(3/2),x]","\frac{1}{2} \left(\sinh ^{-1}\left(x^2\right)-\frac{x^2}{\sqrt{x^4+1}}\right)","\frac{1}{2} \sinh ^{-1}\left(x^2\right)-\frac{x^2}{2 \sqrt{x^4+1}}",1,"(-(x^2/Sqrt[1 + x^4]) + ArcSinh[x^2])/2","A",1
944,1,16,16,0.0026379,"\int \frac{x}{\left(1+x^4\right)^{3/2}} \, dx","Integrate[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
945,1,23,31,0.004865,"\int \frac{1}{x^3 \left(1+x^4\right)^{3/2}} \, dx","Integrate[1/(x^3*(1 + x^4)^(3/2)),x]","-\frac{2 x^4+1}{2 x^2 \sqrt{x^4+1}}","-\frac{x^2}{\sqrt{x^4+1}}-\frac{1}{2 \sqrt{x^4+1} x^2}",1,"-1/2*(1 + 2*x^4)/(x^2*Sqrt[1 + x^4])","A",1
946,1,28,49,0.0055481,"\int \frac{1}{x^7 \left(1+x^4\right)^{3/2}} \, dx","Integrate[1/(x^7*(1 + x^4)^(3/2)),x]","-\frac{-8 x^8-4 x^4+1}{6 x^6 \sqrt{x^4+1}}","-\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}",1,"-1/6*(1 - 4*x^4 - 8*x^8)/(x^6*Sqrt[1 + x^4])","A",1
947,1,52,90,0.0217935,"\int \frac{x^{12}}{\left(1+x^4\right)^{3/2}} \, dx","Integrate[x^12/(1 + x^4)^(3/2),x]","\frac{x \left(15 \sqrt{x^4+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-x^4\right)+2 x^8-6 x^4-15\right)}{14 \sqrt{x^4+1}}","-\frac{15}{14} \sqrt{x^4+1} x-\frac{x^9}{2 \sqrt{x^4+1}}+\frac{9}{14} \sqrt{x^4+1} x^5+\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*(-15 - 6*x^4 + 2*x^8 + 15*Sqrt[1 + x^4]*Hypergeometric2F1[1/4, 1/2, 5/4, -x^4]))/(14*Sqrt[1 + x^4])","C",1
948,1,47,74,0.0087554,"\int \frac{x^8}{\left(1+x^4\right)^{3/2}} \, dx","Integrate[x^8/(1 + x^4)^(3/2),x]","\frac{x \left(-5 \sqrt{x^4+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-x^4\right)+2 x^4+5\right)}{6 \sqrt{x^4+1}}","\frac{5}{6} \sqrt{x^4+1} x-\frac{x^5}{2 \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,"(x*(5 + 2*x^4 - 5*Sqrt[1 + x^4]*Hypergeometric2F1[1/4, 1/2, 5/4, -x^4]))/(6*Sqrt[1 + x^4])","C",1
949,1,32,58,0.0197718,"\int \frac{x^4}{\left(1+x^4\right)^{3/2}} \, dx","Integrate[x^4/(1 + x^4)^(3/2),x]","\frac{1}{2} x \left(\, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-x^4\right)-\frac{1}{\sqrt{x^4+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{x}{2 \sqrt{x^4+1}}",1,"(x*(-(1/Sqrt[1 + x^4]) + Hypergeometric2F1[1/4, 1/2, 5/4, -x^4]))/2","C",1
950,1,30,58,0.0227582,"\int \frac{1}{\left(1+x^4\right)^{3/2}} \, dx","Integrate[(1 + x^4)^(-3/2),x]","\frac{1}{2} x \left(\, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-x^4\right)+\frac{1}{\sqrt{x^4+1}}\right)","\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*(1/Sqrt[1 + x^4] + Hypergeometric2F1[1/4, 1/2, 5/4, -x^4]))/2","C",1
951,1,22,76,0.0029662,"\int \frac{1}{x^4 \left(1+x^4\right)^{3/2}} \, dx","Integrate[1/(x^4*(1 + x^4)^(3/2)),x]","-\frac{\, _2F_1\left(-\frac{3}{4},\frac{3}{2};\frac{1}{4};-x^4\right)}{3 x^3}","-\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,"-1/3*Hypergeometric2F1[-3/4, 3/2, 1/4, -x^4]/x^3","C",1
952,1,22,92,0.0033029,"\int \frac{1}{x^8 \left(1+x^4\right)^{3/2}} \, dx","Integrate[1/(x^8*(1 + x^4)^(3/2)),x]","-\frac{\, _2F_1\left(-\frac{7}{4},\frac{3}{2};-\frac{3}{4};-x^4\right)}{7 x^7}","-\frac{9 \sqrt{x^4+1}}{14 x^7}+\frac{1}{2 x^7 \sqrt{x^4+1}}+\frac{15 \sqrt{x^4+1}}{14 x^3}+\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,"-1/7*Hypergeometric2F1[-7/4, 3/2, -3/4, -x^4]/x^7","C",1
953,1,54,156,0.0152624,"\int \frac{x^{14}}{\left(1+x^4\right)^{3/2}} \, dx","Integrate[x^14/(1 + x^4)^(3/2),x]","\frac{x^3 \left(-77 \sqrt{x^4+1} \, _2F_1\left(\frac{3}{4},\frac{3}{2};\frac{7}{4};-x^4\right)+5 x^8-11 x^4+77\right)}{45 \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^3*(77 - 11*x^4 + 5*x^8 - 77*Sqrt[1 + x^4]*Hypergeometric2F1[3/4, 3/2, 7/4, -x^4]))/(45*Sqrt[1 + x^4])","C",1
954,1,47,140,0.0181887,"\int \frac{x^{10}}{\left(1+x^4\right)^{3/2}} \, dx","Integrate[x^10/(1 + x^4)^(3/2),x]","\frac{x^3 \left(7 \sqrt{x^4+1} \, _2F_1\left(\frac{3}{4},\frac{3}{2};\frac{7}{4};-x^4\right)+x^4-7\right)}{5 \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^3*(-7 + x^4 + 7*Sqrt[1 + x^4]*Hypergeometric2F1[3/4, 3/2, 7/4, -x^4]))/(5*Sqrt[1 + x^4])","C",1
955,1,31,124,0.0092504,"\int \frac{x^6}{\left(1+x^4\right)^{3/2}} \, dx","Integrate[x^6/(1 + x^4)^(3/2),x]","x^3 \left(\frac{1}{\sqrt{x^4+1}}-\, _2F_1\left(\frac{3}{4},\frac{3}{2};\frac{7}{4};-x^4\right)\right)","-\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*(1/Sqrt[1 + x^4] - Hypergeometric2F1[3/4, 3/2, 7/4, -x^4])","C",1
956,1,22,124,0.003197,"\int \frac{x^2}{\left(1+x^4\right)^{3/2}} \, dx","Integrate[x^2/(1 + x^4)^(3/2),x]","\frac{1}{3} x^3 \, _2F_1\left(\frac{3}{4},\frac{3}{2};\frac{7}{4};-x^4\right)","\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*Hypergeometric2F1[3/4, 3/2, 7/4, -x^4])/3","C",1
957,1,20,140,0.0032511,"\int \frac{1}{x^2 \left(1+x^4\right)^{3/2}} \, dx","Integrate[1/(x^2*(1 + x^4)^(3/2)),x]","-\frac{\, _2F_1\left(-\frac{1}{4},\frac{3}{2};\frac{3}{4};-x^4\right)}{x}","-\frac{3 \sqrt{x^4+1}}{2 x}+\frac{1}{2 \sqrt{x^4+1} x}+\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,"-(Hypergeometric2F1[-1/4, 3/2, 3/4, -x^4]/x)","C",1
958,1,22,156,0.0032677,"\int \frac{1}{x^6 \left(1+x^4\right)^{3/2}} \, dx","Integrate[1/(x^6*(1 + x^4)^(3/2)),x]","-\frac{\, _2F_1\left(-\frac{5}{4},\frac{3}{2};-\frac{1}{4};-x^4\right)}{5 x^5}","\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 \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,"-1/5*Hypergeometric2F1[-5/4, 3/2, -1/4, -x^4]/x^5","C",1
959,1,49,72,0.018608,"\int \frac{1}{\left(1+x^4\right)^{5/2}} \, dx","Integrate[(1 + x^4)^(-5/2),x]","\frac{5}{12} x \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-x^4\right)+\frac{5 x}{12 \sqrt{x^4+1}}+\frac{x}{6 \left(x^4+1\right)^{3/2}}","\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*x*Hypergeometric2F1[1/4, 1/2, 5/4, -x^4])/12","C",1
960,1,20,29,0.0076799,"\int \frac{x^7}{\sqrt{16-x^4}} \, dx","Integrate[x^7/Sqrt[16 - x^4],x]","-\frac{1}{6} \sqrt{16-x^4} \left(x^4+32\right)","\frac{1}{6} \left(16-x^4\right)^{3/2}-8 \sqrt{16-x^4}",1,"-1/6*(Sqrt[16 - x^4]*(32 + x^4))","A",1
961,1,29,29,0.0281185,"\int \frac{x^5}{\sqrt{16-x^4}} \, dx","Integrate[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,"-1/4*(x^2*Sqrt[16 - x^4]) + 4*ArcSin[x^2/4]","A",1
962,1,15,15,0.0025523,"\int \frac{x^3}{\sqrt{16-x^4}} \, dx","Integrate[x^3/Sqrt[16 - x^4],x]","-\frac{1}{2} \sqrt{16-x^4}","-\frac{1}{2} \sqrt{16-x^4}",1,"-1/2*Sqrt[16 - x^4]","A",1
963,1,12,12,0.0024594,"\int \frac{x}{\sqrt{16-x^4}} \, dx","Integrate[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",1
964,1,20,20,0.0029503,"\int \frac{1}{x \sqrt{16-x^4}} \, dx","Integrate[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,"-1/8*ArcTanh[Sqrt[16 - x^4]/4]","A",1
965,1,18,18,0.008249,"\int \frac{1}{x^3 \sqrt{16-x^4}} \, dx","Integrate[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,"-1/32*Sqrt[16 - x^4]/x^2","A",1
966,1,37,39,0.0113006,"\int \frac{1}{x^5 \sqrt{16-x^4}} \, dx","Integrate[1/(x^5*Sqrt[16 - x^4]),x]","\frac{1}{256} \left(-\frac{4 \sqrt{16-x^4}}{x^4}-\tanh ^{-1}\left(\sqrt{1-\frac{x^4}{16}}\right)\right)","-\frac{\sqrt{16-x^4}}{64 x^4}-\frac{1}{256} \tanh ^{-1}\left(\frac{\sqrt{16-x^4}}{4}\right)",1,"((-4*Sqrt[16 - x^4])/x^4 - ArcTanh[Sqrt[1 - x^4/16]])/256","A",1
967,1,25,37,0.0113579,"\int \frac{1}{x^7 \sqrt{16-x^4}} \, dx","Integrate[1/(x^7*Sqrt[16 - x^4]),x]","-\frac{\sqrt{1-\frac{x^4}{16}} \left(x^4+8\right)}{192 x^6}","-\frac{\sqrt{16-x^4}}{96 x^6}-\frac{\sqrt{16-x^4}}{768 x^2}",1,"-1/192*(Sqrt[1 - x^4/16]*(8 + x^4))/x^6","A",1
968,1,38,43,0.0059524,"\int \frac{x^6}{\sqrt{16-x^4}} \, dx","Integrate[x^6/Sqrt[16 - x^4],x]","-\frac{1}{5} x^3 \left(\sqrt{16-x^4}-4 \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};\frac{x^4}{16}\right)\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,"-1/5*(x^3*(Sqrt[16 - x^4] - 4*Hypergeometric2F1[1/2, 3/4, 7/4, x^4/16]))","C",1
969,1,36,29,0.0062332,"\int \frac{x^4}{\sqrt{16-x^4}} \, dx","Integrate[x^4/Sqrt[16 - x^4],x]","-\frac{1}{3} x \left(\sqrt{16-x^4}-4 \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};\frac{x^4}{16}\right)\right)","\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,"-1/3*(x*(Sqrt[16 - x^4] - 4*Hypergeometric2F1[1/4, 1/2, 5/4, x^4/16]))","C",1
970,1,24,21,0.0029722,"\int \frac{x^2}{\sqrt{16-x^4}} \, dx","Integrate[x^2/Sqrt[16 - x^4],x]","\frac{1}{12} x^3 \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};\frac{x^4}{16}\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,"(x^3*Hypergeometric2F1[1/2, 3/4, 7/4, x^4/16])/12","C",1
971,1,12,12,0.0137012,"\int \frac{1}{\sqrt{16-x^4}} \, dx","Integrate[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
972,1,24,43,0.0030987,"\int \frac{1}{x^2 \sqrt{16-x^4}} \, dx","Integrate[1/(x^2*Sqrt[16 - x^4]),x]","-\frac{\, _2F_1\left(-\frac{1}{4},\frac{1}{2};\frac{3}{4};\frac{x^4}{16}\right)}{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)",1,"-1/4*Hypergeometric2F1[-1/4, 1/2, 3/4, x^4/16]/x","C",1
973,1,24,31,0.0030108,"\int \frac{1}{x^4 \sqrt{16-x^4}} \, dx","Integrate[1/(x^4*Sqrt[16 - x^4]),x]","-\frac{\, _2F_1\left(-\frac{3}{4},\frac{1}{2};\frac{1}{4};\frac{x^4}{16}\right)}{12 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,"-1/12*Hypergeometric2F1[-3/4, 1/2, 1/4, x^4/16]/x^3","C",1
974,1,18,18,0.0029457,"\int \frac{x}{\sqrt{-4+x^4}} \, dx","Integrate[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",1
975,1,12,12,0.0026094,"\int \frac{x}{\sqrt{4+x^4}} \, dx","Integrate[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",1
976,1,14,14,0.002968,"\int \frac{1}{x \sqrt{-1+x^4}} \, dx","Integrate[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",1
977,1,44,72,0.0088185,"\int \frac{x^4}{\sqrt{-1+x^4}} \, dx","Integrate[x^4/Sqrt[-1 + x^4],x]","\frac{x \left(\sqrt{1-x^4} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};x^4\right)+x^4-1\right)}{3 \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*(-1 + x^4 + Sqrt[1 - x^4]*Hypergeometric2F1[1/4, 1/2, 5/4, x^4]))/(3*Sqrt[-1 + x^4])","C",1
978,1,25,54,0.0267746,"\int \frac{1}{\sqrt{-1+x^4}} \, dx","Integrate[1/Sqrt[-1 + x^4],x]","\frac{\sqrt{1-x^4} F\left(\left.\sin ^{-1}(x)\right|-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}}",1,"(Sqrt[1 - x^4]*EllipticF[ArcSin[x], -1])/Sqrt[-1 + x^4]","A",1
979,1,40,74,0.0058902,"\int \frac{1}{x^4 \sqrt{-1+x^4}} \, dx","Integrate[1/(x^4*Sqrt[-1 + x^4]),x]","-\frac{\sqrt{1-x^4} \, _2F_1\left(-\frac{3}{4},\frac{1}{2};\frac{1}{4};x^4\right)}{3 x^3 \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,"-1/3*(Sqrt[1 - x^4]*Hypergeometric2F1[-3/4, 1/2, 1/4, x^4])/(x^3*Sqrt[-1 + x^4])","C",1
980,1,46,150,0.0363276,"\int \frac{x^6}{\sqrt{-1+x^4}} \, dx","Integrate[x^6/Sqrt[-1 + x^4],x]","\frac{x^3 \left(\sqrt{1-x^4} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};x^4\right)+x^4-1\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,"(x^3*(-1 + x^4 + Sqrt[1 - x^4]*Hypergeometric2F1[1/2, 3/4, 7/4, x^4]))/(5*Sqrt[-1 + x^4])","C",1
981,1,40,126,0.0045295,"\int \frac{x^2}{\sqrt{-1+x^4}} \, dx","Integrate[x^2/Sqrt[-1 + x^4],x]","\frac{x^3 \sqrt{1-x^4} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};x^4\right)}{3 \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^3*Sqrt[1 - x^4]*Hypergeometric2F1[1/2, 3/4, 7/4, x^4])/(3*Sqrt[-1 + x^4])","C",1
982,1,38,140,0.0056821,"\int \frac{1}{x^2 \sqrt{-1+x^4}} \, dx","Integrate[1/(x^2*Sqrt[-1 + x^4]),x]","-\frac{\sqrt{1-x^4} \, _2F_1\left(-\frac{1}{4},\frac{1}{2};\frac{3}{4};x^4\right)}{x \sqrt{x^4-1}}","\frac{\sqrt{x^4-1}}{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}}",1,"-((Sqrt[1 - x^4]*Hypergeometric2F1[-1/4, 1/2, 3/4, x^4])/(x*Sqrt[-1 + x^4]))","C",1
983,1,29,48,0.0093608,"\int \frac{x^2}{\sqrt{3-2 x^4}} \, dx","Integrate[x^2/Sqrt[3 - 2*x^4],x]","\frac{x^3 \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};\frac{2 x^4}{3}\right)}{3 \sqrt{3}}","\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,"(x^3*Hypergeometric2F1[1/2, 3/4, 7/4, (2*x^4)/3])/(3*Sqrt[3])","C",1
984,1,30,54,0.00661,"\int \frac{x^2}{\sqrt{3-b x^4}} \, dx","Integrate[x^2/Sqrt[3 - b*x^4],x]","\frac{x^3 \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};\frac{b x^4}{3}\right)}{3 \sqrt{3}}","\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,"(x^3*Hypergeometric2F1[1/2, 3/4, 7/4, (b*x^4)/3])/(3*Sqrt[3])","C",1
985,1,20,27,0.0064157,"\int x^7 \sqrt[3]{1+x^4} \, dx","Integrate[x^7*(1 + x^4)^(1/3),x]","\frac{3}{112} \left(x^4+1\right)^{4/3} \left(4 x^4-3\right)","\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)*(-3 + 4*x^4))/112","A",1
986,1,13,13,0.0029628,"\int \frac{x^3}{\left(1+x^4\right)^{4/3}} \, dx","Integrate[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
987,1,13,13,0.0166166,"\int \frac{x^3}{\sqrt[3]{1+x^4}} \, dx","Integrate[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
988,1,61,101,0.0343773,"\int x^{19} \sqrt[4]{a+b x^4} \, dx","Integrate[x^19*(a + b*x^4)^(1/4),x]","\frac{\left(a+b x^4\right)^{5/4} \left(2048 a^4-2560 a^3 b x^4+2880 a^2 b^2 x^8-3120 a b^3 x^{12}+3315 b^4 x^{16}\right)}{69615 b^5}","\frac{a^4 \left(a+b x^4\right)^{5/4}}{5 b^5}-\frac{4 a^3 \left(a+b x^4\right)^{9/4}}{9 b^5}+\frac{6 a^2 \left(a+b x^4\right)^{13/4}}{13 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 + b*x^4)^(5/4)*(2048*a^4 - 2560*a^3*b*x^4 + 2880*a^2*b^2*x^8 - 3120*a*b^3*x^12 + 3315*b^4*x^16))/(69615*b^5)","A",1
989,1,50,80,0.0439012,"\int x^{15} \sqrt[4]{a+b x^4} \, dx","Integrate[x^15*(a + b*x^4)^(1/4),x]","\frac{\left(a+b x^4\right)^{5/4} \left(-128 a^3+160 a^2 b x^4-180 a b^2 x^8+195 b^3 x^{12}\right)}{3315 b^4}","-\frac{a^3 \left(a+b x^4\right)^{5/4}}{5 b^4}+\frac{a^2 \left(a+b x^4\right)^{9/4}}{3 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 + b*x^4)^(5/4)*(-128*a^3 + 160*a^2*b*x^4 - 180*a*b^2*x^8 + 195*b^3*x^12))/(3315*b^4)","A",1
990,1,39,59,0.0202654,"\int x^{11} \sqrt[4]{a+b x^4} \, dx","Integrate[x^11*(a + b*x^4)^(1/4),x]","\frac{\left(a+b x^4\right)^{5/4} \left(32 a^2-40 a b x^4+45 b^2 x^8\right)}{585 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 + b*x^4)^(5/4)*(32*a^2 - 40*a*b*x^4 + 45*b^2*x^8))/(585*b^3)","A",1
991,1,28,38,0.0153207,"\int x^7 \sqrt[4]{a+b x^4} \, dx","Integrate[x^7*(a + b*x^4)^(1/4),x]","\frac{\left(a+b x^4\right)^{5/4} \left(5 b x^4-4 a\right)}{45 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 + b*x^4)^(5/4)*(-4*a + 5*b*x^4))/(45*b^2)","A",1
992,1,18,18,0.0038263,"\int x^3 \sqrt[4]{a+b x^4} \, dx","Integrate[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
993,1,66,66,0.0332164,"\int \frac{\sqrt[4]{a+b x^4}}{x} \, dx","Integrate[(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",1
994,1,37,75,0.0245266,"\int \frac{\sqrt[4]{a+b x^4}}{x^5} \, dx","Integrate[(a + b*x^4)^(1/4)/x^5,x]","\frac{b \left(a+b x^4\right)^{5/4} \, _2F_1\left(\frac{5}{4},2;\frac{9}{4};\frac{b x^4}{a}+1\right)}{5 a^2}","-\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,"(b*(a + b*x^4)^(5/4)*Hypergeometric2F1[5/4, 2, 9/4, 1 + (b*x^4)/a])/(5*a^2)","C",1
995,1,39,101,0.0096137,"\int \frac{\sqrt[4]{a+b x^4}}{x^9} \, dx","Integrate[(a + b*x^4)^(1/4)/x^9,x]","-\frac{b^2 \left(a+b x^4\right)^{5/4} \, _2F_1\left(\frac{5}{4},3;\frac{9}{4};\frac{b x^4}{a}+1\right)}{5 a^3}","\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,"-1/5*(b^2*(a + b*x^4)^(5/4)*Hypergeometric2F1[5/4, 3, 9/4, 1 + (b*x^4)/a])/a^3","C",1
996,1,95,125,0.0849054,"\int x^9 \sqrt[4]{a+b x^4} \, dx","Integrate[x^9*(a + b*x^4)^(1/4),x]","\frac{x^2 \sqrt[4]{a+b x^4} \left(\sqrt[4]{\frac{b x^4}{a}+1} \left(-6 a^2+a b x^4+7 b^2 x^8\right)+6 a^2 \, _2F_1\left(-\frac{1}{4},\frac{1}{2};\frac{3}{2};-\frac{b x^4}{a}\right)\right)}{77 b^2 \sqrt[4]{\frac{b x^4}{a}+1}}","\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{2 a^2 x^2 \sqrt[4]{a+b x^4}}{77 b^2}+\frac{1}{11} x^{10} \sqrt[4]{a+b x^4}+\frac{a x^6 \sqrt[4]{a+b x^4}}{77 b}",1,"(x^2*(a + b*x^4)^(1/4)*((1 + (b*x^4)/a)^(1/4)*(-6*a^2 + a*b*x^4 + 7*b^2*x^8) + 6*a^2*Hypergeometric2F1[-1/4, 1/2, 3/2, -((b*x^4)/a)]))/(77*b^2*(1 + (b*x^4)/a)^(1/4))","C",1
997,1,64,101,0.0919666,"\int x^5 \sqrt[4]{a+b x^4} \, dx","Integrate[x^5*(a + b*x^4)^(1/4),x]","\frac{x^2 \sqrt[4]{a+b x^4} \left(-\frac{a \, _2F_1\left(-\frac{1}{4},\frac{1}{2};\frac{3}{2};-\frac{b x^4}{a}\right)}{\sqrt[4]{\frac{b x^4}{a}+1}}+a+b x^4\right)}{7 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,"(x^2*(a + b*x^4)^(1/4)*(a + b*x^4 - (a*Hypergeometric2F1[-1/4, 1/2, 3/2, -((b*x^4)/a)])/(1 + (b*x^4)/a)^(1/4)))/(7*b)","C",1
998,1,51,79,0.0198987,"\int x \sqrt[4]{a+b x^4} \, dx","Integrate[x*(a + b*x^4)^(1/4),x]","\frac{x^2 \sqrt[4]{a+b x^4} \, _2F_1\left(-\frac{1}{4},\frac{1}{2};\frac{3}{2};-\frac{b x^4}{a}\right)}{2 \sqrt[4]{\frac{b x^4}{a}+1}}","\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)*Hypergeometric2F1[-1/4, 1/2, 3/2, -((b*x^4)/a)])/(2*(1 + (b*x^4)/a)^(1/4))","C",1
999,1,51,79,0.0191413,"\int \frac{\sqrt[4]{a+b x^4}}{x^3} \, dx","Integrate[(a + b*x^4)^(1/4)/x^3,x]","-\frac{\sqrt[4]{a+b x^4} \, _2F_1\left(-\frac{1}{2},-\frac{1}{4};\frac{1}{2};-\frac{b x^4}{a}\right)}{2 x^2 \sqrt[4]{\frac{b x^4}{a}+1}}","\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,"-1/2*((a + b*x^4)^(1/4)*Hypergeometric2F1[-1/2, -1/4, 1/2, -((b*x^4)/a)])/(x^2*(1 + (b*x^4)/a)^(1/4))","C",1
1000,1,51,101,0.0293071,"\int \frac{\sqrt[4]{a+b x^4}}{x^7} \, dx","Integrate[(a + b*x^4)^(1/4)/x^7,x]","-\frac{\sqrt[4]{a+b x^4} \, _2F_1\left(-\frac{3}{2},-\frac{1}{4};-\frac{1}{2};-\frac{b x^4}{a}\right)}{6 x^6 \sqrt[4]{\frac{b x^4}{a}+1}}","-\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{\sqrt[4]{a+b x^4}}{6 x^6}-\frac{b \sqrt[4]{a+b x^4}}{12 a x^2}",1,"-1/6*((a + b*x^4)^(1/4)*Hypergeometric2F1[-3/2, -1/4, -1/2, -((b*x^4)/a)])/(x^6*(1 + (b*x^4)/a)^(1/4))","C",1
1001,1,51,125,0.0324595,"\int \frac{\sqrt[4]{a+b x^4}}{x^{11}} \, dx","Integrate[(a + b*x^4)^(1/4)/x^11,x]","-\frac{\sqrt[4]{a+b x^4} \, _2F_1\left(-\frac{5}{2},-\frac{1}{4};-\frac{3}{2};-\frac{b x^4}{a}\right)}{10 x^{10} \sqrt[4]{\frac{b x^4}{a}+1}}","\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^2 \sqrt[4]{a+b x^4}}{24 a^2 x^2}-\frac{\sqrt[4]{a+b x^4}}{10 x^{10}}-\frac{b \sqrt[4]{a+b x^4}}{60 a x^6}",1,"-1/10*((a + b*x^4)^(1/4)*Hypergeometric2F1[-5/2, -1/4, -3/2, -((b*x^4)/a)])/(x^10*(1 + (b*x^4)/a)^(1/4))","C",1
1002,1,64,103,0.0613172,"\int x^6 \sqrt[4]{a+b x^4} \, dx","Integrate[x^6*(a + b*x^4)^(1/4),x]","\frac{x^3 \sqrt[4]{a+b x^4} \left(-\frac{a \, _2F_1\left(-\frac{1}{4},\frac{3}{4};\frac{7}{4};-\frac{b x^4}{a}\right)}{\sqrt[4]{\frac{b x^4}{a}+1}}+a+b x^4\right)}{8 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,"(x^3*(a + b*x^4)^(1/4)*(a + b*x^4 - (a*Hypergeometric2F1[-1/4, 3/4, 7/4, -((b*x^4)/a)])/(1 + (b*x^4)/a)^(1/4)))/(8*b)","C",1
1003,1,51,77,0.052328,"\int x^2 \sqrt[4]{a+b x^4} \, dx","Integrate[x^2*(a + b*x^4)^(1/4),x]","\frac{x^3 \sqrt[4]{a+b x^4} \, _2F_1\left(-\frac{1}{4},\frac{3}{4};\frac{7}{4};-\frac{b x^4}{a}\right)}{3 \sqrt[4]{\frac{b x^4}{a}+1}}","-\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)*Hypergeometric2F1[-1/4, 3/4, 7/4, -((b*x^4)/a)])/(3*(1 + (b*x^4)/a)^(1/4))","C",1
1004,1,49,73,0.008911,"\int \frac{\sqrt[4]{a+b x^4}}{x^2} \, dx","Integrate[(a + b*x^4)^(1/4)/x^2,x]","-\frac{\sqrt[4]{a+b x^4} \, _2F_1\left(-\frac{1}{4},-\frac{1}{4};\frac{3}{4};-\frac{b x^4}{a}\right)}{x \sqrt[4]{\frac{b x^4}{a}+1}}","-\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)*Hypergeometric2F1[-1/4, -1/4, 3/4, -((b*x^4)/a)])/(x*(1 + (b*x^4)/a)^(1/4)))","C",1
1005,1,21,21,0.0048533,"\int \frac{\sqrt[4]{a+b x^4}}{x^6} \, dx","Integrate[(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,"-1/5*(a + b*x^4)^(5/4)/(a*x^5)","A",1
1006,1,31,44,0.0096084,"\int \frac{\sqrt[4]{a+b x^4}}{x^{10}} \, dx","Integrate[(a + b*x^4)^(1/4)/x^10,x]","\frac{\left(a+b x^4\right)^{5/4} \left(4 b x^4-5 a\right)}{45 a^2 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)*(-5*a + 4*b*x^4))/(45*a^2*x^9)","A",1
1007,1,42,68,0.0111665,"\int \frac{\sqrt[4]{a+b x^4}}{x^{14}} \, dx","Integrate[(a + b*x^4)^(1/4)/x^14,x]","-\frac{\left(a+b x^4\right)^{5/4} \left(45 a^2-40 a b x^4+32 b^2 x^8\right)}{585 a^3 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,"-1/585*((a + b*x^4)^(5/4)*(45*a^2 - 40*a*b*x^4 + 32*b^2*x^8))/(a^3*x^13)","A",1
1008,1,53,92,0.0142352,"\int \frac{\sqrt[4]{a+b x^4}}{x^{18}} \, dx","Integrate[(a + b*x^4)^(1/4)/x^18,x]","\frac{\left(a+b x^4\right)^{5/4} \left(-195 a^3+180 a^2 b x^4-160 a b^2 x^8+128 b^3 x^{12}\right)}{3315 a^4 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)*(-195*a^3 + 180*a^2*b*x^4 - 160*a*b^2*x^8 + 128*b^3*x^12))/(3315*a^4*x^17)","A",1
1009,1,105,150,0.0780984,"\int x^{12} \sqrt[4]{a+b x^4} \, dx","Integrate[x^12*(a + b*x^4)^(1/4),x]","\frac{x \sqrt[4]{a+b x^4} \left(\sqrt[4]{\frac{b x^4}{a}+1} \left(15 a^3-3 a^2 b x^4+2 a b^2 x^8+20 b^3 x^{12}\right)-15 a^3 \, _2F_1\left(-\frac{1}{4},\frac{1}{4};\frac{5}{4};-\frac{b x^4}{a}\right)\right)}{280 b^3 \sqrt[4]{\frac{b x^4}{a}+1}}","\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{3 a^3 x \sqrt[4]{a+b x^4}}{112 b^3}-\frac{3 a^2 x^5 \sqrt[4]{a+b x^4}}{280 b^2}+\frac{1}{14} x^{13} \sqrt[4]{a+b x^4}+\frac{a x^9 \sqrt[4]{a+b x^4}}{140 b}",1,"(x*(a + b*x^4)^(1/4)*((1 + (b*x^4)/a)^(1/4)*(15*a^3 - 3*a^2*b*x^4 + 2*a*b^2*x^8 + 20*b^3*x^12) - 15*a^3*Hypergeometric2F1[-1/4, 1/4, 5/4, -((b*x^4)/a)]))/(280*b^3*(1 + (b*x^4)/a)^(1/4))","C",1
1010,1,93,126,0.0558988,"\int x^8 \sqrt[4]{a+b x^4} \, dx","Integrate[x^8*(a + b*x^4)^(1/4),x]","\frac{x \sqrt[4]{a+b x^4} \left(\sqrt[4]{\frac{b x^4}{a}+1} \left(-5 a^2+a b x^4+6 b^2 x^8\right)+5 a^2 \, _2F_1\left(-\frac{1}{4},\frac{1}{4};\frac{5}{4};-\frac{b x^4}{a}\right)\right)}{60 b^2 \sqrt[4]{\frac{b x^4}{a}+1}}","-\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{a^2 x \sqrt[4]{a+b x^4}}{24 b^2}+\frac{1}{10} x^9 \sqrt[4]{a+b x^4}+\frac{a x^5 \sqrt[4]{a+b x^4}}{60 b}",1,"(x*(a + b*x^4)^(1/4)*((1 + (b*x^4)/a)^(1/4)*(-5*a^2 + a*b*x^4 + 6*b^2*x^8) + 5*a^2*Hypergeometric2F1[-1/4, 1/4, 5/4, -((b*x^4)/a)]))/(60*b^2*(1 + (b*x^4)/a)^(1/4))","C",1
1011,1,62,102,0.0739224,"\int x^4 \sqrt[4]{a+b x^4} \, dx","Integrate[x^4*(a + b*x^4)^(1/4),x]","\frac{x \sqrt[4]{a+b x^4} \left(-\frac{a \, _2F_1\left(-\frac{1}{4},\frac{1}{4};\frac{5}{4};-\frac{b x^4}{a}\right)}{\sqrt[4]{\frac{b x^4}{a}+1}}+a+b x^4\right)}{6 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{a x \sqrt[4]{a+b x^4}}{12 b}+\frac{1}{6} x^5 \sqrt[4]{a+b x^4}",1,"(x*(a + b*x^4)^(1/4)*(a + b*x^4 - (a*Hypergeometric2F1[-1/4, 1/4, 5/4, -((b*x^4)/a)])/(1 + (b*x^4)/a)^(1/4)))/(6*b)","C",1
1012,1,46,80,0.0059017,"\int \sqrt[4]{a+b x^4} \, dx","Integrate[(a + b*x^4)^(1/4),x]","\frac{x \sqrt[4]{a+b x^4} \, _2F_1\left(-\frac{1}{4},\frac{1}{4};\frac{5}{4};-\frac{b x^4}{a}\right)}{\sqrt[4]{\frac{b x^4}{a}+1}}","\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)*Hypergeometric2F1[-1/4, 1/4, 5/4, -((b*x^4)/a)])/(1 + (b*x^4)/a)^(1/4)","C",1
1013,1,51,82,0.0093021,"\int \frac{\sqrt[4]{a+b x^4}}{x^4} \, dx","Integrate[(a + b*x^4)^(1/4)/x^4,x]","-\frac{\sqrt[4]{a+b x^4} \, _2F_1\left(-\frac{3}{4},-\frac{1}{4};\frac{1}{4};-\frac{b x^4}{a}\right)}{3 x^3 \sqrt[4]{\frac{b x^4}{a}+1}}","-\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,"-1/3*((a + b*x^4)^(1/4)*Hypergeometric2F1[-3/4, -1/4, 1/4, -((b*x^4)/a)])/(x^3*(1 + (b*x^4)/a)^(1/4))","C",1
1014,1,51,104,0.0104269,"\int \frac{\sqrt[4]{a+b x^4}}{x^8} \, dx","Integrate[(a + b*x^4)^(1/4)/x^8,x]","-\frac{\sqrt[4]{a+b x^4} \, _2F_1\left(-\frac{7}{4},-\frac{1}{4};-\frac{3}{4};-\frac{b x^4}{a}\right)}{7 x^7 \sqrt[4]{\frac{b x^4}{a}+1}}","\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{\sqrt[4]{a+b x^4}}{7 x^7}-\frac{b \sqrt[4]{a+b x^4}}{21 a x^3}",1,"-1/7*((a + b*x^4)^(1/4)*Hypergeometric2F1[-7/4, -1/4, -3/4, -((b*x^4)/a)])/(x^7*(1 + (b*x^4)/a)^(1/4))","C",1
1015,1,51,128,0.0098704,"\int \frac{\sqrt[4]{a+b x^4}}{x^{12}} \, dx","Integrate[(a + b*x^4)^(1/4)/x^12,x]","-\frac{\sqrt[4]{a+b x^4} \, _2F_1\left(-\frac{11}{4},-\frac{1}{4};-\frac{7}{4};-\frac{b x^4}{a}\right)}{11 x^{11} \sqrt[4]{\frac{b x^4}{a}+1}}","-\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{2 b^2 \sqrt[4]{a+b x^4}}{77 a^2 x^3}-\frac{\sqrt[4]{a+b x^4}}{11 x^{11}}-\frac{b \sqrt[4]{a+b x^4}}{77 a x^7}",1,"-1/11*((a + b*x^4)^(1/4)*Hypergeometric2F1[-11/4, -1/4, -7/4, -((b*x^4)/a)])/(x^11*(1 + (b*x^4)/a)^(1/4))","C",1
1016,1,51,152,0.0117091,"\int \frac{\sqrt[4]{a+b x^4}}{x^{16}} \, dx","Integrate[(a + b*x^4)^(1/4)/x^16,x]","-\frac{\sqrt[4]{a+b x^4} \, _2F_1\left(-\frac{15}{4},-\frac{1}{4};-\frac{11}{4};-\frac{b x^4}{a}\right)}{15 x^{15} \sqrt[4]{\frac{b x^4}{a}+1}}","\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{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{\sqrt[4]{a+b x^4}}{15 x^{15}}-\frac{b \sqrt[4]{a+b x^4}}{165 a x^{11}}",1,"-1/15*((a + b*x^4)^(1/4)*Hypergeometric2F1[-15/4, -1/4, -11/4, -((b*x^4)/a)])/(x^15*(1 + (b*x^4)/a)^(1/4))","C",1
1017,1,61,101,0.0469828,"\int x^{19} \left(a+b x^4\right)^{3/4} \, dx","Integrate[x^19*(a + b*x^4)^(3/4),x]","\frac{\left(a+b x^4\right)^{7/4} \left(2048 a^4-3584 a^3 b x^4+4928 a^2 b^2 x^8-6160 a b^3 x^{12}+7315 b^4 x^{16}\right)}{168245 b^5}","\frac{a^4 \left(a+b x^4\right)^{7/4}}{7 b^5}-\frac{4 a^3 \left(a+b x^4\right)^{11/4}}{11 b^5}+\frac{2 a^2 \left(a+b x^4\right)^{15/4}}{5 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 + b*x^4)^(7/4)*(2048*a^4 - 3584*a^3*b*x^4 + 4928*a^2*b^2*x^8 - 6160*a*b^3*x^12 + 7315*b^4*x^16))/(168245*b^5)","A",1
1018,1,50,80,0.0253438,"\int x^{15} \left(a+b x^4\right)^{3/4} \, dx","Integrate[x^15*(a + b*x^4)^(3/4),x]","\frac{\left(a+b x^4\right)^{7/4} \left(-128 a^3+224 a^2 b x^4-308 a b^2 x^8+385 b^3 x^{12}\right)}{7315 b^4}","-\frac{a^3 \left(a+b x^4\right)^{7/4}}{7 b^4}+\frac{3 a^2 \left(a+b x^4\right)^{11/4}}{11 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 + b*x^4)^(7/4)*(-128*a^3 + 224*a^2*b*x^4 - 308*a*b^2*x^8 + 385*b^3*x^12))/(7315*b^4)","A",1
1019,1,39,59,0.0349145,"\int x^{11} \left(a+b x^4\right)^{3/4} \, dx","Integrate[x^11*(a + b*x^4)^(3/4),x]","\frac{\left(a+b x^4\right)^{7/4} \left(32 a^2-56 a b x^4+77 b^2 x^8\right)}{1155 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 + b*x^4)^(7/4)*(32*a^2 - 56*a*b*x^4 + 77*b^2*x^8))/(1155*b^3)","A",1
1020,1,28,38,0.0229351,"\int x^7 \left(a+b x^4\right)^{3/4} \, dx","Integrate[x^7*(a + b*x^4)^(3/4),x]","\frac{\left(a+b x^4\right)^{7/4} \left(7 b x^4-4 a\right)}{77 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 + b*x^4)^(7/4)*(-4*a + 7*b*x^4))/(77*b^2)","A",1
1021,1,18,18,0.0040693,"\int x^3 \left(a+b x^4\right)^{3/4} \, dx","Integrate[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
1022,1,70,70,0.0251793,"\int \frac{\left(a+b x^4\right)^{3/4}}{x} \, dx","Integrate[(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",1
1023,1,37,75,0.0268751,"\int \frac{\left(a+b x^4\right)^{3/4}}{x^5} \, dx","Integrate[(a + b*x^4)^(3/4)/x^5,x]","\frac{b \left(a+b x^4\right)^{7/4} \, _2F_1\left(\frac{7}{4},2;\frac{11}{4};\frac{b x^4}{a}+1\right)}{7 a^2}","-\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,"(b*(a + b*x^4)^(7/4)*Hypergeometric2F1[7/4, 2, 11/4, 1 + (b*x^4)/a])/(7*a^2)","C",1
1024,1,39,101,0.0095365,"\int \frac{\left(a+b x^4\right)^{3/4}}{x^9} \, dx","Integrate[(a + b*x^4)^(3/4)/x^9,x]","-\frac{b^2 \left(a+b x^4\right)^{7/4} \, _2F_1\left(\frac{7}{4},3;\frac{11}{4};\frac{b x^4}{a}+1\right)}{7 a^3}","-\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,"-1/7*(b^2*(a + b*x^4)^(7/4)*Hypergeometric2F1[7/4, 3, 11/4, 1 + (b*x^4)/a])/a^3","C",1
1025,1,95,149,0.0883533,"\int x^9 \left(a+b x^4\right)^{3/4} \, dx","Integrate[x^9*(a + b*x^4)^(3/4),x]","\frac{x^2 \left(a+b x^4\right)^{3/4} \left(\left(\frac{b x^4}{a}+1\right)^{3/4} \left(-2 a^2+a b x^4+3 b^2 x^8\right)+2 a^2 \, _2F_1\left(-\frac{3}{4},\frac{1}{2};\frac{3}{2};-\frac{b x^4}{a}\right)\right)}{39 b^2 \left(\frac{b x^4}{a}+1\right)^{3/4}}","-\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{4 a^3 x^2}{65 b^2 \sqrt[4]{a+b x^4}}-\frac{2 a^2 x^2 \left(a+b x^4\right)^{3/4}}{65 b^2}+\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,"(x^2*(a + b*x^4)^(3/4)*((1 + (b*x^4)/a)^(3/4)*(-2*a^2 + a*b*x^4 + 3*b^2*x^8) + 2*a^2*Hypergeometric2F1[-3/4, 1/2, 3/2, -((b*x^4)/a)]))/(39*b^2*(1 + (b*x^4)/a)^(3/4))","C",1
1026,1,64,125,0.0870352,"\int x^5 \left(a+b x^4\right)^{3/4} \, dx","Integrate[x^5*(a + b*x^4)^(3/4),x]","\frac{x^2 \left(a+b x^4\right)^{3/4} \left(-\frac{a \, _2F_1\left(-\frac{3}{4},\frac{1}{2};\frac{3}{2};-\frac{b x^4}{a}\right)}{\left(\frac{b x^4}{a}+1\right)^{3/4}}+a+b x^4\right)}{9 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,"(x^2*(a + b*x^4)^(3/4)*(a + b*x^4 - (a*Hypergeometric2F1[-3/4, 1/2, 3/2, -((b*x^4)/a)])/(1 + (b*x^4)/a)^(3/4)))/(9*b)","C",1
1027,1,51,98,0.0089931,"\int x \left(a+b x^4\right)^{3/4} \, dx","Integrate[x*(a + b*x^4)^(3/4),x]","\frac{x^2 \left(a+b x^4\right)^{3/4} \, _2F_1\left(-\frac{3}{4},\frac{1}{2};\frac{3}{2};-\frac{b x^4}{a}\right)}{2 \left(\frac{b x^4}{a}+1\right)^{3/4}}","-\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,"(x^2*(a + b*x^4)^(3/4)*Hypergeometric2F1[-3/4, 1/2, 3/2, -((b*x^4)/a)])/(2*(1 + (b*x^4)/a)^(3/4))","C",1
1028,1,51,98,0.0106815,"\int \frac{\left(a+b x^4\right)^{3/4}}{x^3} \, dx","Integrate[(a + b*x^4)^(3/4)/x^3,x]","-\frac{\left(a+b x^4\right)^{3/4} \, _2F_1\left(-\frac{3}{4},-\frac{1}{2};\frac{1}{2};-\frac{b x^4}{a}\right)}{2 x^2 \left(\frac{b x^4}{a}+1\right)^{3/4}}","\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,"-1/2*((a + b*x^4)^(3/4)*Hypergeometric2F1[-3/4, -1/2, 1/2, -((b*x^4)/a)])/(x^2*(1 + (b*x^4)/a)^(3/4))","C",1
1029,1,51,125,0.0157872,"\int \frac{\left(a+b x^4\right)^{3/4}}{x^7} \, dx","Integrate[(a + b*x^4)^(3/4)/x^7,x]","-\frac{\left(a+b x^4\right)^{3/4} \, _2F_1\left(-\frac{3}{2},-\frac{3}{4};-\frac{1}{2};-\frac{b x^4}{a}\right)}{6 x^6 \left(\frac{b x^4}{a}+1\right)^{3/4}}","-\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^2 x^2}{4 a \sqrt[4]{a+b x^4}}-\frac{\left(a+b x^4\right)^{3/4}}{6 x^6}-\frac{b \left(a+b x^4\right)^{3/4}}{4 a x^2}",1,"-1/6*((a + b*x^4)^(3/4)*Hypergeometric2F1[-3/2, -3/4, -1/2, -((b*x^4)/a)])/(x^6*(1 + (b*x^4)/a)^(3/4))","C",1
1030,1,51,149,0.0120472,"\int \frac{\left(a+b x^4\right)^{3/4}}{x^{11}} \, dx","Integrate[(a + b*x^4)^(3/4)/x^11,x]","-\frac{\left(a+b x^4\right)^{3/4} \, _2F_1\left(-\frac{5}{2},-\frac{3}{4};-\frac{3}{2};-\frac{b x^4}{a}\right)}{10 x^{10} \left(\frac{b x^4}{a}+1\right)^{3/4}}","\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{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{\left(a+b x^4\right)^{3/4}}{10 x^{10}}-\frac{b \left(a+b x^4\right)^{3/4}}{20 a x^6}",1,"-1/10*((a + b*x^4)^(3/4)*Hypergeometric2F1[-5/2, -3/4, -3/2, -((b*x^4)/a)])/(x^10*(1 + (b*x^4)/a)^(3/4))","C",1
1031,1,105,149,0.1015965,"\int x^{12} \left(a+b x^4\right)^{3/4} \, dx","Integrate[x^12*(a + b*x^4)^(3/4),x]","\frac{x \left(a+b x^4\right)^{3/4} \left(\left(\frac{b x^4}{a}+1\right)^{3/4} \left(15 a^3-9 a^2 b x^4+8 a b^2 x^8+32 b^3 x^{12}\right)-15 a^3 \, _2F_1\left(-\frac{3}{4},\frac{1}{4};\frac{5}{4};-\frac{b x^4}{a}\right)\right)}{512 b^3 \left(\frac{b x^4}{a}+1\right)^{3/4}}","-\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{45 a^3 x \left(a+b x^4\right)^{3/4}}{2048 b^3}-\frac{9 a^2 x^5 \left(a+b x^4\right)^{3/4}}{512 b^2}+\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,"(x*(a + b*x^4)^(3/4)*((1 + (b*x^4)/a)^(3/4)*(15*a^3 - 9*a^2*b*x^4 + 8*a*b^2*x^8 + 32*b^3*x^12) - 15*a^3*Hypergeometric2F1[-3/4, 1/4, 5/4, -((b*x^4)/a)]))/(512*b^3*(1 + (b*x^4)/a)^(3/4))","C",1
1032,1,94,125,0.0525029,"\int x^8 \left(a+b x^4\right)^{3/4} \, dx","Integrate[x^8*(a + b*x^4)^(3/4),x]","\frac{x \left(a+b x^4\right)^{3/4} \left(\left(\frac{b x^4}{a}+1\right)^{3/4} \left(-5 a^2+3 a b x^4+8 b^2 x^8\right)+5 a^2 \, _2F_1\left(-\frac{3}{4},\frac{1}{4};\frac{5}{4};-\frac{b x^4}{a}\right)\right)}{96 b^2 \left(\frac{b x^4}{a}+1\right)^{3/4}}","\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{5 a^2 x \left(a+b x^4\right)^{3/4}}{128 b^2}+\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,"(x*(a + b*x^4)^(3/4)*((1 + (b*x^4)/a)^(3/4)*(-5*a^2 + 3*a*b*x^4 + 8*b^2*x^8) + 5*a^2*Hypergeometric2F1[-3/4, 1/4, 5/4, -((b*x^4)/a)]))/(96*b^2*(1 + (b*x^4)/a)^(3/4))","C",1
1033,1,62,101,0.068709,"\int x^4 \left(a+b x^4\right)^{3/4} \, dx","Integrate[x^4*(a + b*x^4)^(3/4),x]","\frac{x \left(a+b x^4\right)^{3/4} \left(-\frac{a \, _2F_1\left(-\frac{3}{4},\frac{1}{4};\frac{5}{4};-\frac{b x^4}{a}\right)}{\left(\frac{b x^4}{a}+1\right)^{3/4}}+a+b x^4\right)}{8 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{3 a x \left(a+b x^4\right)^{3/4}}{32 b}+\frac{1}{8} x^5 \left(a+b x^4\right)^{3/4}",1,"(x*(a + b*x^4)^(3/4)*(a + b*x^4 - (a*Hypergeometric2F1[-3/4, 1/4, 5/4, -((b*x^4)/a)])/(1 + (b*x^4)/a)^(3/4)))/(8*b)","C",1
1034,1,46,75,0.0059591,"\int \left(a+b x^4\right)^{3/4} \, dx","Integrate[(a + b*x^4)^(3/4),x]","\frac{x \left(a+b x^4\right)^{3/4} \, _2F_1\left(-\frac{3}{4},\frac{1}{4};\frac{5}{4};-\frac{b x^4}{a}\right)}{\left(\frac{b x^4}{a}+1\right)^{3/4}}","\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)*Hypergeometric2F1[-3/4, 1/4, 5/4, -((b*x^4)/a)])/(1 + (b*x^4)/a)^(3/4)","C",1
1035,1,51,75,0.0096418,"\int \frac{\left(a+b x^4\right)^{3/4}}{x^4} \, dx","Integrate[(a + b*x^4)^(3/4)/x^4,x]","-\frac{\left(a+b x^4\right)^{3/4} \, _2F_1\left(-\frac{3}{4},-\frac{3}{4};\frac{1}{4};-\frac{b x^4}{a}\right)}{3 x^3 \left(\frac{b x^4}{a}+1\right)^{3/4}}","\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,"-1/3*((a + b*x^4)^(3/4)*Hypergeometric2F1[-3/4, -3/4, 1/4, -((b*x^4)/a)])/(x^3*(1 + (b*x^4)/a)^(3/4))","C",1
1036,1,21,21,0.0052944,"\int \frac{\left(a+b x^4\right)^{3/4}}{x^8} \, dx","Integrate[(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,"-1/7*(a + b*x^4)^(7/4)/(a*x^7)","A",1
1037,1,31,44,0.0095031,"\int \frac{\left(a+b x^4\right)^{3/4}}{x^{12}} \, dx","Integrate[(a + b*x^4)^(3/4)/x^12,x]","\frac{\left(a+b x^4\right)^{7/4} \left(4 b x^4-7 a\right)}{77 a^2 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)*(-7*a + 4*b*x^4))/(77*a^2*x^11)","A",1
1038,1,42,68,0.0112283,"\int \frac{\left(a+b x^4\right)^{3/4}}{x^{16}} \, dx","Integrate[(a + b*x^4)^(3/4)/x^16,x]","-\frac{\left(a+b x^4\right)^{7/4} \left(77 a^2-56 a b x^4+32 b^2 x^8\right)}{1155 a^3 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,"-1/1155*((a + b*x^4)^(7/4)*(77*a^2 - 56*a*b*x^4 + 32*b^2*x^8))/(a^3*x^15)","A",1
1039,1,53,92,0.0143196,"\int \frac{\left(a+b x^4\right)^{3/4}}{x^{20}} \, dx","Integrate[(a + b*x^4)^(3/4)/x^20,x]","\frac{\left(a+b x^4\right)^{7/4} \left(-385 a^3+308 a^2 b x^4-224 a b^2 x^8+128 b^3 x^{12}\right)}{7315 a^4 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)*(-385*a^3 + 308*a^2*b*x^4 - 224*a*b^2*x^8 + 128*b^3*x^12))/(7315*a^4*x^19)","A",1
1040,1,96,150,0.0659143,"\int x^{10} \left(a+b x^4\right)^{3/4} \, dx","Integrate[x^10*(a + b*x^4)^(3/4),x]","\frac{x^3 \left(a+b x^4\right)^{3/4} \left(\left(\frac{b x^4}{a}+1\right)^{3/4} \left(-7 a^2+3 a b x^4+10 b^2 x^8\right)+7 a^2 \, _2F_1\left(-\frac{3}{4},\frac{3}{4};\frac{7}{4};-\frac{b x^4}{a}\right)\right)}{140 b^2 \left(\frac{b x^4}{a}+1\right)^{3/4}}","\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{3 a^3 x^3}{80 b^2 \sqrt[4]{a+b x^4}}-\frac{a^2 x^3 \left(a+b x^4\right)^{3/4}}{40 b^2}+\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,"(x^3*(a + b*x^4)^(3/4)*((1 + (b*x^4)/a)^(3/4)*(-7*a^2 + 3*a*b*x^4 + 10*b^2*x^8) + 7*a^2*Hypergeometric2F1[-3/4, 3/4, 7/4, -((b*x^4)/a)]))/(140*b^2*(1 + (b*x^4)/a)^(3/4))","C",1
1041,1,64,126,0.0591556,"\int x^6 \left(a+b x^4\right)^{3/4} \, dx","Integrate[x^6*(a + b*x^4)^(3/4),x]","\frac{x^3 \left(a+b x^4\right)^{3/4} \left(-\frac{a \, _2F_1\left(-\frac{3}{4},\frac{3}{4};\frac{7}{4};-\frac{b x^4}{a}\right)}{\left(\frac{b x^4}{a}+1\right)^{3/4}}+a+b x^4\right)}{10 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,"(x^3*(a + b*x^4)^(3/4)*(a + b*x^4 - (a*Hypergeometric2F1[-3/4, 3/4, 7/4, -((b*x^4)/a)])/(1 + (b*x^4)/a)^(3/4)))/(10*b)","C",1
1042,1,51,99,0.0103696,"\int x^2 \left(a+b x^4\right)^{3/4} \, dx","Integrate[x^2*(a + b*x^4)^(3/4),x]","\frac{x^3 \left(a+b x^4\right)^{3/4} \, _2F_1\left(-\frac{3}{4},\frac{3}{4};\frac{7}{4};-\frac{b x^4}{a}\right)}{3 \left(\frac{b x^4}{a}+1\right)^{3/4}}","\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,"(x^3*(a + b*x^4)^(3/4)*Hypergeometric2F1[-3/4, 3/4, 7/4, -((b*x^4)/a)])/(3*(1 + (b*x^4)/a)^(3/4))","C",1
1043,1,49,97,0.010643,"\int \frac{\left(a+b x^4\right)^{3/4}}{x^2} \, dx","Integrate[(a + b*x^4)^(3/4)/x^2,x]","-\frac{\left(a+b x^4\right)^{3/4} \, _2F_1\left(-\frac{3}{4},-\frac{1}{4};\frac{3}{4};-\frac{b x^4}{a}\right)}{x \left(\frac{b x^4}{a}+1\right)^{3/4}}","-\frac{\left(a+b x^4\right)^{3/4}}{x}+\frac{3 b x^3}{2 \sqrt[4]{a+b x^4}}+\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,"-(((a + b*x^4)^(3/4)*Hypergeometric2F1[-3/4, -1/4, 3/4, -((b*x^4)/a)])/(x*(1 + (b*x^4)/a)^(3/4)))","C",1
1044,1,51,99,0.0103552,"\int \frac{\left(a+b x^4\right)^{3/4}}{x^6} \, dx","Integrate[(a + b*x^4)^(3/4)/x^6,x]","-\frac{\left(a+b x^4\right)^{3/4} \, _2F_1\left(-\frac{5}{4},-\frac{3}{4};-\frac{1}{4};-\frac{b x^4}{a}\right)}{5 x^5 \left(\frac{b x^4}{a}+1\right)^{3/4}}","\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,"-1/5*((a + b*x^4)^(3/4)*Hypergeometric2F1[-5/4, -3/4, -1/4, -((b*x^4)/a)])/(x^5*(1 + (b*x^4)/a)^(3/4))","C",1
1045,1,51,126,0.0096095,"\int \frac{\left(a+b x^4\right)^{3/4}}{x^{10}} \, dx","Integrate[(a + b*x^4)^(3/4)/x^10,x]","-\frac{\left(a+b x^4\right)^{3/4} \, _2F_1\left(-\frac{9}{4},-\frac{3}{4};-\frac{5}{4};-\frac{b x^4}{a}\right)}{9 x^9 \left(\frac{b x^4}{a}+1\right)^{3/4}}","-\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{\left(a+b x^4\right)^{3/4}}{9 x^9}-\frac{b \left(a+b x^4\right)^{3/4}}{15 a x^5}",1,"-1/9*((a + b*x^4)^(3/4)*Hypergeometric2F1[-9/4, -3/4, -5/4, -((b*x^4)/a)])/(x^9*(1 + (b*x^4)/a)^(3/4))","C",1
1046,1,51,150,0.0106537,"\int \frac{\left(a+b x^4\right)^{3/4}}{x^{14}} \, dx","Integrate[(a + b*x^4)^(3/4)/x^14,x]","-\frac{\left(a+b x^4\right)^{3/4} \, _2F_1\left(-\frac{13}{4},-\frac{3}{4};-\frac{9}{4};-\frac{b x^4}{a}\right)}{13 x^{13} \left(\frac{b x^4}{a}+1\right)^{3/4}}","\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{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{\left(a+b x^4\right)^{3/4}}{13 x^{13}}-\frac{b \left(a+b x^4\right)^{3/4}}{39 a x^9}",1,"-1/13*((a + b*x^4)^(3/4)*Hypergeometric2F1[-13/4, -3/4, -9/4, -((b*x^4)/a)])/(x^13*(1 + (b*x^4)/a)^(3/4))","C",1
1047,1,61,101,0.0388846,"\int x^{19} \left(a+b x^4\right)^{5/4} \, dx","Integrate[x^19*(a + b*x^4)^(5/4),x]","\frac{\left(a+b x^4\right)^{9/4} \left(2048 a^4-4608 a^3 b x^4+7488 a^2 b^2 x^8-10608 a b^3 x^{12}+13923 b^4 x^{16}\right)}{348075 b^5}","\frac{a^4 \left(a+b x^4\right)^{9/4}}{9 b^5}-\frac{4 a^3 \left(a+b x^4\right)^{13/4}}{13 b^5}+\frac{6 a^2 \left(a+b x^4\right)^{17/4}}{17 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 + b*x^4)^(9/4)*(2048*a^4 - 4608*a^3*b*x^4 + 7488*a^2*b^2*x^8 - 10608*a*b^3*x^12 + 13923*b^4*x^16))/(348075*b^5)","A",1
1048,1,50,80,0.0297311,"\int x^{15} \left(a+b x^4\right)^{5/4} \, dx","Integrate[x^15*(a + b*x^4)^(5/4),x]","\frac{\left(a+b x^4\right)^{9/4} \left(-128 a^3+288 a^2 b x^4-468 a b^2 x^8+663 b^3 x^{12}\right)}{13923 b^4}","-\frac{a^3 \left(a+b x^4\right)^{9/4}}{9 b^4}+\frac{3 a^2 \left(a+b x^4\right)^{13/4}}{13 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 + b*x^4)^(9/4)*(-128*a^3 + 288*a^2*b*x^4 - 468*a*b^2*x^8 + 663*b^3*x^12))/(13923*b^4)","A",1
1049,1,39,59,0.0201308,"\int x^{11} \left(a+b x^4\right)^{5/4} \, dx","Integrate[x^11*(a + b*x^4)^(5/4),x]","\frac{\left(a+b x^4\right)^{9/4} \left(32 a^2-72 a b x^4+117 b^2 x^8\right)}{1989 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 + b*x^4)^(9/4)*(32*a^2 - 72*a*b*x^4 + 117*b^2*x^8))/(1989*b^3)","A",1
1050,1,28,38,0.0151969,"\int x^7 \left(a+b x^4\right)^{5/4} \, dx","Integrate[x^7*(a + b*x^4)^(5/4),x]","\frac{\left(a+b x^4\right)^{9/4} \left(9 b x^4-4 a\right)}{117 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 + b*x^4)^(9/4)*(-4*a + 9*b*x^4))/(117*b^2)","A",1
1051,1,18,18,0.0066819,"\int x^3 \left(a+b x^4\right)^{5/4} \, dx","Integrate[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
1052,1,77,83,0.0431202,"\int \frac{\left(a+b x^4\right)^{5/4}}{x} \, dx","Integrate[(a + b*x^4)^(5/4)/x,x]","\frac{1}{10} \left(-5 a^{5/4} \tan ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)-5 a^{5/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)+2 \sqrt[4]{a+b x^4} \left(6 a+b x^4\right)\right)","-\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,"(2*(a + b*x^4)^(1/4)*(6*a + b*x^4) - 5*a^(5/4)*ArcTan[(a + b*x^4)^(1/4)/a^(1/4)] - 5*a^(5/4)*ArcTanh[(a + b*x^4)^(1/4)/a^(1/4)])/10","A",1
1053,1,37,91,0.0090925,"\int \frac{\left(a+b x^4\right)^{5/4}}{x^5} \, dx","Integrate[(a + b*x^4)^(5/4)/x^5,x]","\frac{b \left(a+b x^4\right)^{9/4} \, _2F_1\left(2,\frac{9}{4};\frac{13}{4};\frac{b x^4}{a}+1\right)}{9 a^2}","-\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,"(b*(a + b*x^4)^(9/4)*Hypergeometric2F1[2, 9/4, 13/4, 1 + (b*x^4)/a])/(9*a^2)","C",1
1054,1,39,98,0.0104726,"\int \frac{\left(a+b x^4\right)^{5/4}}{x^9} \, dx","Integrate[(a + b*x^4)^(5/4)/x^9,x]","-\frac{b^2 \left(a+b x^4\right)^{9/4} \, _2F_1\left(\frac{9}{4},3;\frac{13}{4};\frac{b x^4}{a}+1\right)}{9 a^3}","-\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,"-1/9*(b^2*(a + b*x^4)^(9/4)*Hypergeometric2F1[9/4, 3, 13/4, 1 + (b*x^4)/a])/a^3","C",1
1055,1,81,146,0.1049692,"\int x^9 \left(a+b x^4\right)^{5/4} \, dx","Integrate[x^9*(a + b*x^4)^(5/4),x]","\frac{x^2 \sqrt[4]{a+b x^4} \left(\frac{6 a^3 \, _2F_1\left(-\frac{5}{4},\frac{1}{2};\frac{3}{2};-\frac{b x^4}{a}\right)}{\sqrt[4]{\frac{b x^4}{a}+1}}-\left(6 a-11 b x^4\right) \left(a+b x^4\right)^2\right)}{165 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{2 a^3 x^2 \sqrt[4]{a+b x^4}}{231 b^2}+\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,"(x^2*(a + b*x^4)^(1/4)*(-((6*a - 11*b*x^4)*(a + b*x^4)^2) + (6*a^3*Hypergeometric2F1[-5/4, 1/2, 3/2, -((b*x^4)/a)])/(1 + (b*x^4)/a)^(1/4)))/(165*b^2)","C",1
1056,1,69,122,0.0986768,"\int x^5 \left(a+b x^4\right)^{5/4} \, dx","Integrate[x^5*(a + b*x^4)^(5/4),x]","\frac{x^2 \sqrt[4]{a+b x^4} \left(\left(a+b x^4\right)^2-\frac{a^2 \, _2F_1\left(-\frac{5}{4},\frac{1}{2};\frac{3}{2};-\frac{b x^4}{a}\right)}{\sqrt[4]{\frac{b x^4}{a}+1}}\right)}{11 b}","-\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,"(x^2*(a + b*x^4)^(1/4)*((a + b*x^4)^2 - (a^2*Hypergeometric2F1[-5/4, 1/2, 3/2, -((b*x^4)/a)])/(1 + (b*x^4)/a)^(1/4)))/(11*b)","C",1
1057,1,52,98,0.0097547,"\int x \left(a+b x^4\right)^{5/4} \, dx","Integrate[x*(a + b*x^4)^(5/4),x]","\frac{a x^2 \sqrt[4]{a+b x^4} \, _2F_1\left(-\frac{5}{4},\frac{1}{2};\frac{3}{2};-\frac{b x^4}{a}\right)}{2 \sqrt[4]{\frac{b x^4}{a}+1}}","\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,"(a*x^2*(a + b*x^4)^(1/4)*Hypergeometric2F1[-5/4, 1/2, 3/2, -((b*x^4)/a)])/(2*(1 + (b*x^4)/a)^(1/4))","C",1
1058,1,52,98,0.0390938,"\int \frac{\left(a+b x^4\right)^{5/4}}{x^3} \, dx","Integrate[(a + b*x^4)^(5/4)/x^3,x]","-\frac{a \sqrt[4]{a+b x^4} \, _2F_1\left(-\frac{5}{4},-\frac{1}{2};\frac{1}{2};-\frac{b x^4}{a}\right)}{2 x^2 \sqrt[4]{\frac{b x^4}{a}+1}}","\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,"-1/2*(a*(a + b*x^4)^(1/4)*Hypergeometric2F1[-5/4, -1/2, 1/2, -((b*x^4)/a)])/(x^2*(1 + (b*x^4)/a)^(1/4))","C",1
1059,1,52,98,0.0119327,"\int \frac{\left(a+b x^4\right)^{5/4}}{x^7} \, dx","Integrate[(a + b*x^4)^(5/4)/x^7,x]","-\frac{a \sqrt[4]{a+b x^4} \, _2F_1\left(-\frac{3}{2},-\frac{5}{4};-\frac{1}{2};-\frac{b x^4}{a}\right)}{6 x^6 \sqrt[4]{\frac{b x^4}{a}+1}}","\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{\left(a+b x^4\right)^{5/4}}{6 x^6}-\frac{5 b \sqrt[4]{a+b x^4}}{12 x^2}",1,"-1/6*(a*(a + b*x^4)^(1/4)*Hypergeometric2F1[-3/2, -5/4, -1/2, -((b*x^4)/a)])/(x^6*(1 + (b*x^4)/a)^(1/4))","C",1
1060,1,52,122,0.0124208,"\int \frac{\left(a+b x^4\right)^{5/4}}{x^{11}} \, dx","Integrate[(a + b*x^4)^(5/4)/x^11,x]","-\frac{a \sqrt[4]{a+b x^4} \, _2F_1\left(-\frac{5}{2},-\frac{5}{4};-\frac{3}{2};-\frac{b x^4}{a}\right)}{10 x^{10} \sqrt[4]{\frac{b x^4}{a}+1}}","-\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^2 \sqrt[4]{a+b x^4}}{24 a x^2}-\frac{\left(a+b x^4\right)^{5/4}}{10 x^{10}}-\frac{b \sqrt[4]{a+b x^4}}{12 x^6}",1,"-1/10*(a*(a + b*x^4)^(1/4)*Hypergeometric2F1[-5/2, -5/4, -3/2, -((b*x^4)/a)])/(x^10*(1 + (b*x^4)/a)^(1/4))","C",1
1061,1,52,146,0.0146101,"\int \frac{\left(a+b x^4\right)^{5/4}}{x^{15}} \, dx","Integrate[(a + b*x^4)^(5/4)/x^15,x]","-\frac{a \sqrt[4]{a+b x^4} \, _2F_1\left(-\frac{7}{2},-\frac{5}{4};-\frac{5}{2};-\frac{b x^4}{a}\right)}{14 x^{14} \sqrt[4]{\frac{b x^4}{a}+1}}","\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{5 b^3 \sqrt[4]{a+b x^4}}{336 a^2 x^2}-\frac{b^2 \sqrt[4]{a+b x^4}}{168 a x^6}-\frac{\left(a+b x^4\right)^{5/4}}{14 x^{14}}-\frac{b \sqrt[4]{a+b x^4}}{28 x^{10}}",1,"-1/14*(a*(a + b*x^4)^(1/4)*Hypergeometric2F1[-7/2, -5/4, -5/2, -((b*x^4)/a)])/(x^14*(1 + (b*x^4)/a)^(1/4))","C",1
1062,1,81,148,0.1066492,"\int x^{10} \left(a+b x^4\right)^{5/4} \, dx","Integrate[x^10*(a + b*x^4)^(5/4),x]","\frac{x^3 \sqrt[4]{a+b x^4} \left(\frac{7 a^3 \, _2F_1\left(-\frac{5}{4},\frac{3}{4};\frac{7}{4};-\frac{b x^4}{a}\right)}{\sqrt[4]{\frac{b x^4}{a}+1}}-\left(7 a-12 b x^4\right) \left(a+b x^4\right)^2\right)}{192 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{35 a^3 x^3 \sqrt[4]{a+b x^4}}{6144 b^2}+\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,"(x^3*(a + b*x^4)^(1/4)*(-((7*a - 12*b*x^4)*(a + b*x^4)^2) + (7*a^3*Hypergeometric2F1[-5/4, 3/4, 7/4, -((b*x^4)/a)])/(1 + (b*x^4)/a)^(1/4)))/(192*b^2)","C",1
1063,1,69,124,0.0818424,"\int x^6 \left(a+b x^4\right)^{5/4} \, dx","Integrate[x^6*(a + b*x^4)^(5/4),x]","\frac{x^3 \sqrt[4]{a+b x^4} \left(\left(a+b x^4\right)^2-\frac{a^2 \, _2F_1\left(-\frac{5}{4},\frac{3}{4};\frac{7}{4};-\frac{b x^4}{a}\right)}{\sqrt[4]{\frac{b x^4}{a}+1}}\right)}{12 b}","\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,"(x^3*(a + b*x^4)^(1/4)*((a + b*x^4)^2 - (a^2*Hypergeometric2F1[-5/4, 3/4, 7/4, -((b*x^4)/a)])/(1 + (b*x^4)/a)^(1/4)))/(12*b)","C",1
1064,1,52,100,0.0089656,"\int x^2 \left(a+b x^4\right)^{5/4} \, dx","Integrate[x^2*(a + b*x^4)^(5/4),x]","\frac{a x^3 \sqrt[4]{a+b x^4} \, _2F_1\left(-\frac{5}{4},\frac{3}{4};\frac{7}{4};-\frac{b x^4}{a}\right)}{3 \sqrt[4]{\frac{b x^4}{a}+1}}","-\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,"(a*x^3*(a + b*x^4)^(1/4)*Hypergeometric2F1[-5/4, 3/4, 7/4, -((b*x^4)/a)])/(3*(1 + (b*x^4)/a)^(1/4))","C",1
1065,1,50,94,0.0096293,"\int \frac{\left(a+b x^4\right)^{5/4}}{x^2} \, dx","Integrate[(a + b*x^4)^(5/4)/x^2,x]","-\frac{a \sqrt[4]{a+b x^4} \, _2F_1\left(-\frac{5}{4},-\frac{1}{4};\frac{3}{4};-\frac{b x^4}{a}\right)}{x \sqrt[4]{\frac{b x^4}{a}+1}}","-\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}",1,"-((a*(a + b*x^4)^(1/4)*Hypergeometric2F1[-5/4, -1/4, 3/4, -((b*x^4)/a)])/(x*(1 + (b*x^4)/a)^(1/4)))","C",1
1066,1,52,92,0.010025,"\int \frac{\left(a+b x^4\right)^{5/4}}{x^6} \, dx","Integrate[(a + b*x^4)^(5/4)/x^6,x]","-\frac{a \sqrt[4]{a+b x^4} \, _2F_1\left(-\frac{5}{4},-\frac{5}{4};-\frac{1}{4};-\frac{b x^4}{a}\right)}{5 x^5 \sqrt[4]{\frac{b x^4}{a}+1}}","-\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,"-1/5*(a*(a + b*x^4)^(1/4)*Hypergeometric2F1[-5/4, -5/4, -1/4, -((b*x^4)/a)])/(x^5*(1 + (b*x^4)/a)^(1/4))","C",1
1067,1,21,21,0.0142121,"\int \frac{\left(a+b x^4\right)^{5/4}}{x^{10}} \, dx","Integrate[(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,"-1/9*(a + b*x^4)^(9/4)/(a*x^9)","A",1
1068,1,31,44,0.0109231,"\int \frac{\left(a+b x^4\right)^{5/4}}{x^{14}} \, dx","Integrate[(a + b*x^4)^(5/4)/x^14,x]","\frac{\left(a+b x^4\right)^{9/4} \left(4 b x^4-9 a\right)}{117 a^2 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)*(-9*a + 4*b*x^4))/(117*a^2*x^13)","A",1
1069,1,42,68,0.0115194,"\int \frac{\left(a+b x^4\right)^{5/4}}{x^{18}} \, dx","Integrate[(a + b*x^4)^(5/4)/x^18,x]","-\frac{\left(a+b x^4\right)^{9/4} \left(117 a^2-72 a b x^4+32 b^2 x^8\right)}{1989 a^3 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,"-1/1989*((a + b*x^4)^(9/4)*(117*a^2 - 72*a*b*x^4 + 32*b^2*x^8))/(a^3*x^17)","A",1
1070,1,53,92,0.0147653,"\int \frac{\left(a+b x^4\right)^{5/4}}{x^{22}} \, dx","Integrate[(a + b*x^4)^(5/4)/x^22,x]","\frac{\left(a+b x^4\right)^{9/4} \left(-663 a^3+468 a^2 b x^4-288 a b^2 x^8+128 b^3 x^{12}\right)}{13923 a^4 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)*(-663*a^3 + 468*a^2*b*x^4 - 288*a*b^2*x^8 + 128*b^3*x^12))/(13923*a^4*x^21)","A",1
1071,1,89,171,0.1310957,"\int x^{12} \left(a+b x^4\right)^{5/4} \, dx","Integrate[x^12*(a + b*x^4)^(5/4),x]","\frac{x \sqrt[4]{a+b x^4} \left(\left(a+b x^4\right)^2 \left(9 a^2-18 a b x^4+28 b^2 x^8\right)-\frac{9 a^4 \, _2F_1\left(-\frac{5}{4},\frac{1}{4};\frac{5}{4};-\frac{b x^4}{a}\right)}{\sqrt[4]{\frac{b x^4}{a}+1}}\right)}{504 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{5 a^4 x \sqrt[4]{a+b x^4}}{672 b^3}-\frac{a^3 x^5 \sqrt[4]{a+b x^4}}{336 b^2}+\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,"(x*(a + b*x^4)^(1/4)*((a + b*x^4)^2*(9*a^2 - 18*a*b*x^4 + 28*b^2*x^8) - (9*a^4*Hypergeometric2F1[-5/4, 1/4, 5/4, -((b*x^4)/a)])/(1 + (b*x^4)/a)^(1/4)))/(504*b^3)","C",1
1072,1,76,147,0.1157468,"\int x^8 \left(a+b x^4\right)^{5/4} \, dx","Integrate[x^8*(a + b*x^4)^(5/4),x]","\frac{x \sqrt[4]{a+b x^4} \left(\frac{a^3 \, _2F_1\left(-\frac{5}{4},\frac{1}{4};\frac{5}{4};-\frac{b x^4}{a}\right)}{\sqrt[4]{\frac{b x^4}{a}+1}}-\left(a-2 b x^4\right) \left(a+b x^4\right)^2\right)}{28 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{5 a^3 x \sqrt[4]{a+b x^4}}{336 b^2}+\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,"(x*(a + b*x^4)^(1/4)*(-((a - 2*b*x^4)*(a + b*x^4)^2) + (a^3*Hypergeometric2F1[-5/4, 1/4, 5/4, -((b*x^4)/a)])/(1 + (b*x^4)/a)^(1/4)))/(28*b^2)","C",1
1073,1,67,123,0.0868799,"\int x^4 \left(a+b x^4\right)^{5/4} \, dx","Integrate[x^4*(a + b*x^4)^(5/4),x]","\frac{x \sqrt[4]{a+b x^4} \left(\left(a+b x^4\right)^2-\frac{a^2 \, _2F_1\left(-\frac{5}{4},\frac{1}{4};\frac{5}{4};-\frac{b x^4}{a}\right)}{\sqrt[4]{\frac{b x^4}{a}+1}}\right)}{10 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{a^2 x \sqrt[4]{a+b x^4}}{24 b}+\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,"(x*(a + b*x^4)^(1/4)*((a + b*x^4)^2 - (a^2*Hypergeometric2F1[-5/4, 1/4, 5/4, -((b*x^4)/a)])/(1 + (b*x^4)/a)^(1/4)))/(10*b)","C",1
1074,1,47,97,0.0053294,"\int \left(a+b x^4\right)^{5/4} \, dx","Integrate[(a + b*x^4)^(5/4),x]","\frac{a x \sqrt[4]{a+b x^4} \, _2F_1\left(-\frac{5}{4},\frac{1}{4};\frac{5}{4};-\frac{b x^4}{a}\right)}{\sqrt[4]{\frac{b x^4}{a}+1}}","-\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,"(a*x*(a + b*x^4)^(1/4)*Hypergeometric2F1[-5/4, 1/4, 5/4, -((b*x^4)/a)])/(1 + (b*x^4)/a)^(1/4)","C",1
1075,1,52,99,0.0327701,"\int \frac{\left(a+b x^4\right)^{5/4}}{x^4} \, dx","Integrate[(a + b*x^4)^(5/4)/x^4,x]","-\frac{a \sqrt[4]{a+b x^4} \, _2F_1\left(-\frac{5}{4},-\frac{3}{4};\frac{1}{4};-\frac{b x^4}{a}\right)}{3 x^3 \sqrt[4]{\frac{b x^4}{a}+1}}","-\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,"-1/3*(a*(a + b*x^4)^(1/4)*Hypergeometric2F1[-5/4, -3/4, 1/4, -((b*x^4)/a)])/(x^3*(1 + (b*x^4)/a)^(1/4))","C",1
1076,1,52,101,0.0121261,"\int \frac{\left(a+b x^4\right)^{5/4}}{x^8} \, dx","Integrate[(a + b*x^4)^(5/4)/x^8,x]","-\frac{a \sqrt[4]{a+b x^4} \, _2F_1\left(-\frac{7}{4},-\frac{5}{4};-\frac{3}{4};-\frac{b x^4}{a}\right)}{7 x^7 \sqrt[4]{\frac{b x^4}{a}+1}}","-\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{\left(a+b x^4\right)^{5/4}}{7 x^7}-\frac{5 b \sqrt[4]{a+b x^4}}{21 x^3}",1,"-1/7*(a*(a + b*x^4)^(1/4)*Hypergeometric2F1[-7/4, -5/4, -3/4, -((b*x^4)/a)])/(x^7*(1 + (b*x^4)/a)^(1/4))","C",1
1077,1,52,125,0.0103452,"\int \frac{\left(a+b x^4\right)^{5/4}}{x^{12}} \, dx","Integrate[(a + b*x^4)^(5/4)/x^12,x]","-\frac{a \sqrt[4]{a+b x^4} \, _2F_1\left(-\frac{11}{4},-\frac{5}{4};-\frac{7}{4};-\frac{b x^4}{a}\right)}{11 x^{11} \sqrt[4]{\frac{b x^4}{a}+1}}","\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{\left(a+b x^4\right)^{5/4}}{11 x^{11}}-\frac{5 b \sqrt[4]{a+b x^4}}{77 x^7}",1,"-1/11*(a*(a + b*x^4)^(1/4)*Hypergeometric2F1[-11/4, -5/4, -7/4, -((b*x^4)/a)])/(x^11*(1 + (b*x^4)/a)^(1/4))","C",1
1078,1,52,149,0.0112928,"\int \frac{\left(a+b x^4\right)^{5/4}}{x^{16}} \, dx","Integrate[(a + b*x^4)^(5/4)/x^16,x]","-\frac{a \sqrt[4]{a+b x^4} \, _2F_1\left(-\frac{15}{4},-\frac{5}{4};-\frac{11}{4};-\frac{b x^4}{a}\right)}{15 x^{15} \sqrt[4]{\frac{b x^4}{a}+1}}","-\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{2 b^3 \sqrt[4]{a+b x^4}}{231 a^2 x^3}-\frac{b^2 \sqrt[4]{a+b x^4}}{231 a x^7}-\frac{\left(a+b x^4\right)^{5/4}}{15 x^{15}}-\frac{b \sqrt[4]{a+b x^4}}{33 x^{11}}",1,"-1/15*(a*(a + b*x^4)^(1/4)*Hypergeometric2F1[-15/4, -5/4, -11/4, -((b*x^4)/a)])/(x^15*(1 + (b*x^4)/a)^(1/4))","C",1
1079,1,47,96,0.0103661,"\int \left(a+b x^4\right)^{7/4} \, dx","Integrate[(a + b*x^4)^(7/4),x]","\frac{a x \left(a+b x^4\right)^{3/4} \, _2F_1\left(-\frac{7}{4},\frac{1}{4};\frac{5}{4};-\frac{b x^4}{a}\right)}{\left(\frac{b x^4}{a}+1\right)^{3/4}}","\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,"(a*x*(a + b*x^4)^(3/4)*Hypergeometric2F1[-7/4, 1/4, 5/4, -((b*x^4)/a)])/(1 + (b*x^4)/a)^(3/4)","C",1
1080,1,61,101,0.0467909,"\int \frac{x^{19}}{\sqrt[4]{a+b x^4}} \, dx","Integrate[x^19/(a + b*x^4)^(1/4),x]","\frac{\left(a+b x^4\right)^{3/4} \left(2048 a^4-1536 a^3 b x^4+1344 a^2 b^2 x^8-1232 a b^3 x^{12}+1155 b^4 x^{16}\right)}{21945 b^5}","\frac{a^4 \left(a+b x^4\right)^{3/4}}{3 b^5}-\frac{4 a^3 \left(a+b x^4\right)^{7/4}}{7 b^5}+\frac{6 a^2 \left(a+b x^4\right)^{11/4}}{11 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 + b*x^4)^(3/4)*(2048*a^4 - 1536*a^3*b*x^4 + 1344*a^2*b^2*x^8 - 1232*a*b^3*x^12 + 1155*b^4*x^16))/(21945*b^5)","A",1
1081,1,50,80,0.0253232,"\int \frac{x^{15}}{\sqrt[4]{a+b x^4}} \, dx","Integrate[x^15/(a + b*x^4)^(1/4),x]","\frac{\left(a+b x^4\right)^{3/4} \left(-128 a^3+96 a^2 b x^4-84 a b^2 x^8+77 b^3 x^{12}\right)}{1155 b^4}","-\frac{a^3 \left(a+b x^4\right)^{3/4}}{3 b^4}+\frac{3 a^2 \left(a+b x^4\right)^{7/4}}{7 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 + b*x^4)^(3/4)*(-128*a^3 + 96*a^2*b*x^4 - 84*a*b^2*x^8 + 77*b^3*x^12))/(1155*b^4)","A",1
1082,1,39,59,0.0294088,"\int \frac{x^{11}}{\sqrt[4]{a+b x^4}} \, dx","Integrate[x^11/(a + b*x^4)^(1/4),x]","\frac{\left(a+b x^4\right)^{3/4} \left(32 a^2-24 a b x^4+21 b^2 x^8\right)}{231 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 + b*x^4)^(3/4)*(32*a^2 - 24*a*b*x^4 + 21*b^2*x^8))/(231*b^3)","A",1
1083,1,28,38,0.0182096,"\int \frac{x^7}{\sqrt[4]{a+b x^4}} \, dx","Integrate[x^7/(a + b*x^4)^(1/4),x]","\frac{\left(a+b x^4\right)^{3/4} \left(3 b x^4-4 a\right)}{21 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 + b*x^4)^(3/4)*(-4*a + 3*b*x^4))/(21*b^2)","A",1
1084,1,18,18,0.0035487,"\int \frac{x^3}{\sqrt[4]{a+b x^4}} \, dx","Integrate[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
1085,1,48,55,0.0285135,"\int \frac{1}{x \sqrt[4]{a+b x^4}} \, dx","Integrate[1/(x*(a + b*x^4)^(1/4)),x]","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)-\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)] - ArcTanh[(a + b*x^4)^(1/4)/a^(1/4)])/(2*a^(1/4))","A",1
1086,1,37,78,0.0080375,"\int \frac{1}{x^5 \sqrt[4]{a+b x^4}} \, dx","Integrate[1/(x^5*(a + b*x^4)^(1/4)),x]","\frac{b \left(a+b x^4\right)^{3/4} \, _2F_1\left(\frac{3}{4},2;\frac{7}{4};\frac{b x^4}{a}+1\right)}{3 a^2}","-\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,"(b*(a + b*x^4)^(3/4)*Hypergeometric2F1[3/4, 2, 7/4, 1 + (b*x^4)/a])/(3*a^2)","C",1
1087,1,39,104,0.0078381,"\int \frac{1}{x^9 \sqrt[4]{a+b x^4}} \, dx","Integrate[1/(x^9*(a + b*x^4)^(1/4)),x]","-\frac{b^2 \left(a+b x^4\right)^{3/4} \, _2F_1\left(\frac{3}{4},3;\frac{7}{4};\frac{b x^4}{a}+1\right)}{3 a^3}","\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,"-1/3*(b^2*(a + b*x^4)^(3/4)*Hypergeometric2F1[3/4, 3, 7/4, 1 + (b*x^4)/a])/a^3","C",1
1088,1,91,152,0.0374651,"\int \frac{x^{13}}{\sqrt[4]{a+b x^4}} \, dx","Integrate[x^13/(a + b*x^4)^(1/4),x]","\frac{x^2 \left(-12 a^3 \sqrt[4]{\frac{b x^4}{a}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{3}{2};-\frac{b x^4}{a}\right)+12 a^3+2 a^2 b x^4-a b^2 x^8+9 b^3 x^{12}\right)}{117 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{8 a^3 x^2}{39 b^3 \sqrt[4]{a+b x^4}}+\frac{4 a^2 x^2 \left(a+b x^4\right)^{3/4}}{39 b^3}-\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,"(x^2*(12*a^3 + 2*a^2*b*x^4 - a*b^2*x^8 + 9*b^3*x^12 - 12*a^3*(1 + (b*x^4)/a)^(1/4)*Hypergeometric2F1[1/4, 1/2, 3/2, -((b*x^4)/a)]))/(117*b^3*(a + b*x^4)^(1/4))","C",1
1089,1,80,128,0.0317849,"\int \frac{x^9}{\sqrt[4]{a+b x^4}} \, dx","Integrate[x^9/(a + b*x^4)^(1/4),x]","\frac{x^2 \left(6 a^2 \sqrt[4]{\frac{b x^4}{a}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{3}{2};-\frac{b x^4}{a}\right)-6 a^2-a b x^4+5 b^2 x^8\right)}{45 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{4 a^2 x^2}{15 b^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,"(x^2*(-6*a^2 - a*b*x^4 + 5*b^2*x^8 + 6*a^2*(1 + (b*x^4)/a)^(1/4)*Hypergeometric2F1[1/4, 1/2, 3/2, -((b*x^4)/a)]))/(45*b^2*(a + b*x^4)^(1/4))","C",1
1090,1,64,104,0.0195743,"\int \frac{x^5}{\sqrt[4]{a+b x^4}} \, dx","Integrate[x^5/(a + b*x^4)^(1/4),x]","\frac{x^2 \left(-a \sqrt[4]{\frac{b x^4}{a}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{3}{2};-\frac{b x^4}{a}\right)+a+b x^4\right)}{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,"(x^2*(a + b*x^4 - a*(1 + (b*x^4)/a)^(1/4)*Hypergeometric2F1[1/4, 1/2, 3/2, -((b*x^4)/a)]))/(5*b*(a + b*x^4)^(1/4))","C",1
1091,1,51,74,0.0094686,"\int \frac{x}{\sqrt[4]{a+b x^4}} \, dx","Integrate[x/(a + b*x^4)^(1/4),x]","\frac{x^2 \sqrt[4]{\frac{b x^4}{a}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{3}{2};-\frac{b x^4}{a}\right)}{2 \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*(1 + (b*x^4)/a)^(1/4)*Hypergeometric2F1[1/4, 1/2, 3/2, -((b*x^4)/a)])/(2*(a + b*x^4)^(1/4))","C",1
1092,1,51,104,0.0118433,"\int \frac{1}{x^3 \sqrt[4]{a+b x^4}} \, dx","Integrate[1/(x^3*(a + b*x^4)^(1/4)),x]","-\frac{\sqrt[4]{\frac{b x^4}{a}+1} \, _2F_1\left(-\frac{1}{2},\frac{1}{4};\frac{1}{2};-\frac{b x^4}{a}\right)}{2 x^2 \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,"-1/2*((1 + (b*x^4)/a)^(1/4)*Hypergeometric2F1[-1/2, 1/4, 1/2, -((b*x^4)/a)])/(x^2*(a + b*x^4)^(1/4))","C",1
1093,1,51,128,0.0113672,"\int \frac{1}{x^7 \sqrt[4]{a+b x^4}} \, dx","Integrate[1/(x^7*(a + b*x^4)^(1/4)),x]","-\frac{\sqrt[4]{\frac{b x^4}{a}+1} \, _2F_1\left(-\frac{3}{2},\frac{1}{4};-\frac{1}{2};-\frac{b x^4}{a}\right)}{6 x^6 \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^2 x^2}{4 a^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,"-1/6*((1 + (b*x^4)/a)^(1/4)*Hypergeometric2F1[-3/2, 1/4, -1/2, -((b*x^4)/a)])/(x^6*(a + b*x^4)^(1/4))","C",1
1094,1,51,152,0.0116127,"\int \frac{1}{x^{11} \sqrt[4]{a+b x^4}} \, dx","Integrate[1/(x^11*(a + b*x^4)^(1/4)),x]","-\frac{\sqrt[4]{\frac{b x^4}{a}+1} \, _2F_1\left(-\frac{5}{2},\frac{1}{4};-\frac{3}{2};-\frac{b x^4}{a}\right)}{10 x^{10} \sqrt[4]{a+b x^4}}","-\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^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 \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,"-1/10*((1 + (b*x^4)/a)^(1/4)*Hypergeometric2F1[-5/2, 1/4, -3/2, -((b*x^4)/a)])/(x^10*(a + b*x^4)^(1/4))","C",1
1095,1,87,104,0.0588159,"\int \frac{x^8}{\sqrt[4]{a+b x^4}} \, dx","Integrate[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)+5 a^2 \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)+2 \sqrt[4]{b} x \left(a+b x^4\right)^{3/4} \left(4 b x^4-5 a\right)}{64 b^{9/4}}","\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,"(2*b^(1/4)*x*(a + b*x^4)^(3/4)*(-5*a + 4*b*x^4) + 5*a^2*ArcTan[(b^(1/4)*x)/(a + b*x^4)^(1/4)] + 5*a^2*ArcTanh[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/(64*b^(9/4))","A",1
1096,1,73,78,0.0350653,"\int \frac{x^4}{\sqrt[4]{a+b x^4}} \, dx","Integrate[x^4/(a + b*x^4)^(1/4),x]","\frac{2 \sqrt[4]{b} x \left(a+b x^4\right)^{3/4}-a \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)-a \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{8 b^{5/4}}","-\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,"(2*b^(1/4)*x*(a + b*x^4)^(3/4) - a*ArcTan[(b^(1/4)*x)/(a + b*x^4)^(1/4)] - a*ArcTanh[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/(8*b^(5/4))","A",1
1097,1,76,57,0.0306162,"\int \frac{1}{\sqrt[4]{a+b x^4}} \, dx","Integrate[(a + b*x^4)^(-1/4),x]","\frac{-\log \left(1-\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)+\log \left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}+1\right)+2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{4 \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,"(2*ArcTan[(b^(1/4)*x)/(a + b*x^4)^(1/4)] - Log[1 - (b^(1/4)*x)/(a + b*x^4)^(1/4)] + Log[1 + (b^(1/4)*x)/(a + b*x^4)^(1/4)])/(4*b^(1/4))","A",1
1098,1,21,21,0.0040228,"\int \frac{1}{x^4 \sqrt[4]{a+b x^4}} \, dx","Integrate[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,"-1/3*(a + b*x^4)^(3/4)/(a*x^3)","A",1
1099,1,31,44,0.0115131,"\int \frac{1}{x^8 \sqrt[4]{a+b x^4}} \, dx","Integrate[1/(x^8*(a + b*x^4)^(1/4)),x]","\frac{\left(a+b x^4\right)^{3/4} \left(4 b x^4-3 a\right)}{21 a^2 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)*(-3*a + 4*b*x^4))/(21*a^2*x^7)","A",1
1100,1,42,68,0.0192981,"\int \frac{1}{x^{12} \sqrt[4]{a+b x^4}} \, dx","Integrate[1/(x^12*(a + b*x^4)^(1/4)),x]","-\frac{\left(a+b x^4\right)^{3/4} \left(21 a^2-24 a b x^4+32 b^2 x^8\right)}{231 a^3 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,"-1/231*((a + b*x^4)^(3/4)*(21*a^2 - 24*a*b*x^4 + 32*b^2*x^8))/(a^3*x^11)","A",1
1101,1,53,92,0.032816,"\int \frac{1}{x^{16} \sqrt[4]{a+b x^4}} \, dx","Integrate[1/(x^16*(a + b*x^4)^(1/4)),x]","\frac{\left(a+b x^4\right)^{3/4} \left(-77 a^3+84 a^2 b x^4-96 a b^2 x^8+128 b^3 x^{12}\right)}{1155 a^4 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)*(-77*a^3 + 84*a^2*b*x^4 - 96*a*b^2*x^8 + 128*b^3*x^12))/(1155*a^4*x^15)","A",1
1102,1,64,116,0.0494552,"\int \frac{1}{x^{20} \sqrt[4]{a+b x^4}} \, dx","Integrate[1/(x^20*(a + b*x^4)^(1/4)),x]","-\frac{\left(a+b x^4\right)^{3/4} \left(1155 a^4-1232 a^3 b x^4+1344 a^2 b^2 x^8-1536 a b^3 x^{12}+2048 b^4 x^{16}\right)}{21945 a^5 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,"-1/21945*((a + b*x^4)^(3/4)*(1155*a^4 - 1232*a^3*b*x^4 + 1344*a^2*b^2*x^8 - 1536*a*b^3*x^12 + 2048*b^4*x^16))/(a^5*x^19)","A",1
1103,1,80,129,0.0375005,"\int \frac{x^{10}}{\sqrt[4]{a+b x^4}} \, dx","Integrate[x^10/(a + b*x^4)^(1/4),x]","\frac{x^3 \left(7 a^2 \sqrt[4]{\frac{b x^4}{a}+1} \, _2F_1\left(\frac{1}{4},\frac{3}{4};\frac{7}{4};-\frac{b x^4}{a}\right)-7 a^2-a b x^4+6 b^2 x^8\right)}{60 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^2 x^3}{40 b^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,"(x^3*(-7*a^2 - a*b*x^4 + 6*b^2*x^8 + 7*a^2*(1 + (b*x^4)/a)^(1/4)*Hypergeometric2F1[1/4, 3/4, 7/4, -((b*x^4)/a)]))/(60*b^2*(a + b*x^4)^(1/4))","C",1
1104,1,64,105,0.0181002,"\int \frac{x^6}{\sqrt[4]{a+b x^4}} \, dx","Integrate[x^6/(a + b*x^4)^(1/4),x]","\frac{x^3 \left(-a \sqrt[4]{\frac{b x^4}{a}+1} \, _2F_1\left(\frac{1}{4},\frac{3}{4};\frac{7}{4};-\frac{b x^4}{a}\right)+a+b x^4\right)}{6 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,"(x^3*(a + b*x^4 - a*(1 + (b*x^4)/a)^(1/4)*Hypergeometric2F1[1/4, 3/4, 7/4, -((b*x^4)/a)]))/(6*b*(a + b*x^4)^(1/4))","C",1
1105,1,51,80,0.0085892,"\int \frac{x^2}{\sqrt[4]{a+b x^4}} \, dx","Integrate[x^2/(a + b*x^4)^(1/4),x]","\frac{x^3 \sqrt[4]{\frac{b x^4}{a}+1} \, _2F_1\left(\frac{1}{4},\frac{3}{4};\frac{7}{4};-\frac{b x^4}{a}\right)}{3 \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*(1 + (b*x^4)/a)^(1/4)*Hypergeometric2F1[1/4, 3/4, 7/4, -((b*x^4)/a)])/(3*(a + b*x^4)^(1/4))","C",1
1106,1,49,75,0.0096812,"\int \frac{1}{x^2 \sqrt[4]{a+b x^4}} \, dx","Integrate[1/(x^2*(a + b*x^4)^(1/4)),x]","-\frac{\sqrt[4]{\frac{b x^4}{a}+1} \, _2F_1\left(-\frac{1}{4},\frac{1}{4};\frac{3}{4};-\frac{b x^4}{a}\right)}{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 + (b*x^4)/a)^(1/4)*Hypergeometric2F1[-1/4, 1/4, 3/4, -((b*x^4)/a)])/(x*(a + b*x^4)^(1/4)))","C",1
1107,1,51,105,0.0102554,"\int \frac{1}{x^6 \sqrt[4]{a+b x^4}} \, dx","Integrate[1/(x^6*(a + b*x^4)^(1/4)),x]","-\frac{\sqrt[4]{\frac{b x^4}{a}+1} \, _2F_1\left(-\frac{5}{4},\frac{1}{4};-\frac{1}{4};-\frac{b x^4}{a}\right)}{5 x^5 \sqrt[4]{a+b x^4}}","-\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,"-1/5*((1 + (b*x^4)/a)^(1/4)*Hypergeometric2F1[-5/4, 1/4, -1/4, -((b*x^4)/a)])/(x^5*(a + b*x^4)^(1/4))","C",1
1108,1,51,129,0.0100302,"\int \frac{1}{x^{10} \sqrt[4]{a+b x^4}} \, dx","Integrate[1/(x^10*(a + b*x^4)^(1/4)),x]","-\frac{\sqrt[4]{\frac{b x^4}{a}+1} \, _2F_1\left(-\frac{9}{4},\frac{1}{4};-\frac{5}{4};-\frac{b x^4}{a}\right)}{9 x^9 \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{4 b^2}{15 a^2 x \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,"-1/9*((1 + (b*x^4)/a)^(1/4)*Hypergeometric2F1[-9/4, 1/4, -5/4, -((b*x^4)/a)])/(x^9*(a + b*x^4)^(1/4))","C",1
1109,1,51,153,0.0100932,"\int \frac{1}{x^{14} \sqrt[4]{a+b x^4}} \, dx","Integrate[1/(x^14*(a + b*x^4)^(1/4)),x]","-\frac{\sqrt[4]{\frac{b x^4}{a}+1} \, _2F_1\left(-\frac{13}{4},\frac{1}{4};-\frac{9}{4};-\frac{b x^4}{a}\right)}{13 x^{13} \sqrt[4]{a+b x^4}}","-\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{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{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,"-1/13*((1 + (b*x^4)/a)^(1/4)*Hypergeometric2F1[-13/4, 1/4, -9/4, -((b*x^4)/a)])/(x^13*(a + b*x^4)^(1/4))","C",1
1110,1,61,98,0.0377121,"\int \frac{x^{19}}{\left(a+b x^4\right)^{3/4}} \, dx","Integrate[x^19/(a + b*x^4)^(3/4),x]","\frac{\sqrt[4]{a+b x^4} \left(2048 a^4-512 a^3 b x^4+320 a^2 b^2 x^8-240 a b^3 x^{12}+195 b^4 x^{16}\right)}{3315 b^5}","\frac{a^4 \sqrt[4]{a+b x^4}}{b^5}-\frac{4 a^3 \left(a+b x^4\right)^{5/4}}{5 b^5}+\frac{2 a^2 \left(a+b x^4\right)^{9/4}}{3 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 + b*x^4)^(1/4)*(2048*a^4 - 512*a^3*b*x^4 + 320*a^2*b^2*x^8 - 240*a*b^3*x^12 + 195*b^4*x^16))/(3315*b^5)","A",1
1111,1,50,78,0.0236635,"\int \frac{x^{15}}{\left(a+b x^4\right)^{3/4}} \, dx","Integrate[x^15/(a + b*x^4)^(3/4),x]","\frac{\sqrt[4]{a+b x^4} \left(-128 a^3+32 a^2 b x^4-20 a b^2 x^8+15 b^3 x^{12}\right)}{195 b^4}","-\frac{a^3 \sqrt[4]{a+b x^4}}{b^4}+\frac{3 a^2 \left(a+b x^4\right)^{5/4}}{5 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 + b*x^4)^(1/4)*(-128*a^3 + 32*a^2*b*x^4 - 20*a*b^2*x^8 + 15*b^3*x^12))/(195*b^4)","A",1
1112,1,39,56,0.0441069,"\int \frac{x^{11}}{\left(a+b x^4\right)^{3/4}} \, dx","Integrate[x^11/(a + b*x^4)^(3/4),x]","\frac{\sqrt[4]{a+b x^4} \left(32 a^2-8 a b x^4+5 b^2 x^8\right)}{45 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 + b*x^4)^(1/4)*(32*a^2 - 8*a*b*x^4 + 5*b^2*x^8))/(45*b^3)","A",1
1113,1,27,36,0.0127717,"\int \frac{x^7}{\left(a+b x^4\right)^{3/4}} \, dx","Integrate[x^7/(a + b*x^4)^(3/4),x]","\frac{\left(b x^4-4 a\right) \sqrt[4]{a+b x^4}}{5 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,"((-4*a + b*x^4)*(a + b*x^4)^(1/4))/(5*b^2)","A",1
1114,1,15,15,0.0033934,"\int \frac{x^3}{\left(a+b x^4\right)^{3/4}} \, dx","Integrate[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
1115,1,46,55,0.0103233,"\int \frac{1}{x \left(a+b x^4\right)^{3/4}} \, dx","Integrate[1/(x*(a + b*x^4)^(3/4)),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a+b x^4}}{\sqrt[4]{a}}\right)+\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,"-1/2*(ArcTan[(a + b*x^4)^(1/4)/a^(1/4)] + ArcTanh[(a + b*x^4)^(1/4)/a^(1/4)])/a^(3/4)","A",1
1116,1,34,78,0.0071862,"\int \frac{1}{x^5 \left(a+b x^4\right)^{3/4}} \, dx","Integrate[1/(x^5*(a + b*x^4)^(3/4)),x]","\frac{b \sqrt[4]{a+b x^4} \, _2F_1\left(\frac{1}{4},2;\frac{5}{4};\frac{b x^4}{a}+1\right)}{a^2}","\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,"(b*(a + b*x^4)^(1/4)*Hypergeometric2F1[1/4, 2, 5/4, 1 + (b*x^4)/a])/a^2","C",1
1117,1,37,104,0.0073459,"\int \frac{1}{x^9 \left(a+b x^4\right)^{3/4}} \, dx","Integrate[1/(x^9*(a + b*x^4)^(3/4)),x]","-\frac{b^2 \sqrt[4]{a+b x^4} \, _2F_1\left(\frac{1}{4},3;\frac{5}{4};\frac{b x^4}{a}+1\right)}{a^3}","-\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,"-((b^2*(a + b*x^4)^(1/4)*Hypergeometric2F1[1/4, 3, 5/4, 1 + (b*x^4)/a])/a^3)","C",1
1118,1,91,128,0.0460761,"\int \frac{x^{13}}{\left(a+b x^4\right)^{3/4}} \, dx","Integrate[x^13/(a + b*x^4)^(3/4),x]","\frac{x^2 \left(-20 a^3 \left(\frac{b x^4}{a}+1\right)^{3/4} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{3}{2};-\frac{b x^4}{a}\right)+20 a^3+10 a^2 b x^4-3 a b^2 x^8+7 b^3 x^{12}\right)}{77 b^3 \left(a+b x^4\right)^{3/4}}","-\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{20 a^2 x^2 \sqrt[4]{a+b x^4}}{77 b^3}-\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,"(x^2*(20*a^3 + 10*a^2*b*x^4 - 3*a*b^2*x^8 + 7*b^3*x^12 - 20*a^3*(1 + (b*x^4)/a)^(3/4)*Hypergeometric2F1[1/2, 3/4, 3/2, -((b*x^4)/a)]))/(77*b^3*(a + b*x^4)^(3/4))","C",1
1119,1,79,104,0.0460337,"\int \frac{x^9}{\left(a+b x^4\right)^{3/4}} \, dx","Integrate[x^9/(a + b*x^4)^(3/4),x]","\frac{x^2 \left(2 a^2 \left(\frac{b x^4}{a}+1\right)^{3/4} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{3}{2};-\frac{b x^4}{a}\right)-2 a^2-a b x^4+b^2 x^8\right)}{7 b^2 \left(a+b x^4\right)^{3/4}}","\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,"(x^2*(-2*a^2 - a*b*x^4 + b^2*x^8 + 2*a^2*(1 + (b*x^4)/a)^(3/4)*Hypergeometric2F1[1/2, 3/4, 3/2, -((b*x^4)/a)]))/(7*b^2*(a + b*x^4)^(3/4))","C",1
1120,1,64,82,0.0218733,"\int \frac{x^5}{\left(a+b x^4\right)^{3/4}} \, dx","Integrate[x^5/(a + b*x^4)^(3/4),x]","\frac{x^2 \left(-a \left(\frac{b x^4}{a}+1\right)^{3/4} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{3}{2};-\frac{b x^4}{a}\right)+a+b x^4\right)}{3 b \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 - a*(1 + (b*x^4)/a)^(3/4)*Hypergeometric2F1[1/2, 3/4, 3/2, -((b*x^4)/a)]))/(3*b*(a + b*x^4)^(3/4))","C",1
1121,1,51,57,0.0098473,"\int \frac{x}{\left(a+b x^4\right)^{3/4}} \, dx","Integrate[x/(a + b*x^4)^(3/4),x]","\frac{x^2 \left(\frac{b x^4}{a}+1\right)^{3/4} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{3}{2};-\frac{b x^4}{a}\right)}{2 \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,"(x^2*(1 + (b*x^4)/a)^(3/4)*Hypergeometric2F1[1/2, 3/4, 3/2, -((b*x^4)/a)])/(2*(a + b*x^4)^(3/4))","C",1
1122,1,51,82,0.0116117,"\int \frac{1}{x^3 \left(a+b x^4\right)^{3/4}} \, dx","Integrate[1/(x^3*(a + b*x^4)^(3/4)),x]","-\frac{\left(\frac{b x^4}{a}+1\right)^{3/4} \, _2F_1\left(-\frac{1}{2},\frac{3}{4};\frac{1}{2};-\frac{b x^4}{a}\right)}{2 x^2 \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,"-1/2*((1 + (b*x^4)/a)^(3/4)*Hypergeometric2F1[-1/2, 3/4, 1/2, -((b*x^4)/a)])/(x^2*(a + b*x^4)^(3/4))","C",1
1123,1,51,104,0.0116745,"\int \frac{1}{x^7 \left(a+b x^4\right)^{3/4}} \, dx","Integrate[1/(x^7*(a + b*x^4)^(3/4)),x]","-\frac{\left(\frac{b x^4}{a}+1\right)^{3/4} \, _2F_1\left(-\frac{3}{2},\frac{3}{4};-\frac{1}{2};-\frac{b x^4}{a}\right)}{6 x^6 \left(a+b x^4\right)^{3/4}}","\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,"-1/6*((1 + (b*x^4)/a)^(3/4)*Hypergeometric2F1[-3/2, 3/4, -1/2, -((b*x^4)/a)])/(x^6*(a + b*x^4)^(3/4))","C",1
1124,1,51,128,0.0115112,"\int \frac{1}{x^{11} \left(a+b x^4\right)^{3/4}} \, dx","Integrate[1/(x^11*(a + b*x^4)^(3/4)),x]","-\frac{\left(\frac{b x^4}{a}+1\right)^{3/4} \, _2F_1\left(-\frac{5}{2},\frac{3}{4};-\frac{3}{2};-\frac{b x^4}{a}\right)}{10 x^{10} \left(a+b x^4\right)^{3/4}}","-\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^2 \sqrt[4]{a+b x^4}}{8 a^3 x^2}+\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,"-1/10*((1 + (b*x^4)/a)^(3/4)*Hypergeometric2F1[-5/2, 3/4, -3/2, -((b*x^4)/a)])/(x^10*(a + b*x^4)^(3/4))","C",1
1125,1,89,106,0.0441727,"\int \frac{x^{10}}{\left(a+b x^4\right)^{3/4}} \, dx","Integrate[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)+21 a^2 \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)+2 b^{3/4} x^3 \sqrt[4]{a+b x^4} \left(4 b x^4-7 a\right)}{64 b^{11/4}}","-\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,"(2*b^(3/4)*x^3*(a + b*x^4)^(1/4)*(-7*a + 4*b*x^4) - 21*a^2*ArcTan[(b^(1/4)*x)/(a + b*x^4)^(1/4)] + 21*a^2*ArcTanh[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/(64*b^(11/4))","A",1
1126,1,75,80,0.0153026,"\int \frac{x^6}{\left(a+b x^4\right)^{3/4}} \, dx","Integrate[x^6/(a + b*x^4)^(3/4),x]","\frac{2 b^{3/4} x^3 \sqrt[4]{a+b x^4}+3 a \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)-3 a \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a+b x^4}}\right)}{8 b^{7/4}}","\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,"(2*b^(3/4)*x^3*(a + b*x^4)^(1/4) + 3*a*ArcTan[(b^(1/4)*x)/(a + b*x^4)^(1/4)] - 3*a*ArcTanh[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/(8*b^(7/4))","A",1
1127,1,50,57,0.007074,"\int \frac{x^2}{\left(a+b x^4\right)^{3/4}} \, dx","Integrate[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)-\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)] + ArcTanh[(b^(1/4)*x)/(a + b*x^4)^(1/4)])/(2*b^(3/4))","A",1
1128,1,19,19,0.0159698,"\int \frac{1}{x^2 \left(a+b x^4\right)^{3/4}} \, dx","Integrate[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
1129,1,29,44,0.0104358,"\int \frac{1}{x^6 \left(a+b x^4\right)^{3/4}} \, dx","Integrate[1/(x^6*(a + b*x^4)^(3/4)),x]","-\frac{\left(a-4 b x^4\right) \sqrt[4]{a+b x^4}}{5 a^2 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,"-1/5*((a - 4*b*x^4)*(a + b*x^4)^(1/4))/(a^2*x^5)","A",1
1130,1,42,68,0.0281621,"\int \frac{1}{x^{10} \left(a+b x^4\right)^{3/4}} \, dx","Integrate[1/(x^10*(a + b*x^4)^(3/4)),x]","-\frac{\sqrt[4]{a+b x^4} \left(5 a^2-8 a b x^4+32 b^2 x^8\right)}{45 a^3 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,"-1/45*((a + b*x^4)^(1/4)*(5*a^2 - 8*a*b*x^4 + 32*b^2*x^8))/(a^3*x^9)","A",1
1131,1,53,92,0.0312225,"\int \frac{1}{x^{14} \left(a+b x^4\right)^{3/4}} \, dx","Integrate[1/(x^14*(a + b*x^4)^(3/4)),x]","\frac{\sqrt[4]{a+b x^4} \left(-15 a^3+20 a^2 b x^4-32 a b^2 x^8+128 b^3 x^{12}\right)}{195 a^4 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)*(-15*a^3 + 20*a^2*b*x^4 - 32*a*b^2*x^8 + 128*b^3*x^12))/(195*a^4*x^13)","A",1
1132,1,90,129,0.0251137,"\int \frac{x^{12}}{\left(a+b x^4\right)^{3/4}} \, dx","Integrate[x^12/(a + b*x^4)^(3/4),x]","\frac{-15 a^3 x \left(\frac{b x^4}{a}+1\right)^{3/4} \, _2F_1\left(\frac{1}{4},\frac{3}{4};\frac{5}{4};-\frac{b x^4}{a}\right)+15 a^3 x+9 a^2 b x^5-2 a b^2 x^9+4 b^3 x^{13}}{40 b^3 \left(a+b x^4\right)^{3/4}}","\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^2 x \sqrt[4]{a+b x^4}}{8 b^3}-\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,"(15*a^3*x + 9*a^2*b*x^5 - 2*a*b^2*x^9 + 4*b^3*x^13 - 15*a^3*x*(1 + (b*x^4)/a)^(3/4)*Hypergeometric2F1[1/4, 3/4, 5/4, -((b*x^4)/a)])/(40*b^3*(a + b*x^4)^(3/4))","C",1
1133,1,79,105,0.0201351,"\int \frac{x^8}{\left(a+b x^4\right)^{3/4}} \, dx","Integrate[x^8/(a + b*x^4)^(3/4),x]","\frac{5 a^2 x \left(\frac{b x^4}{a}+1\right)^{3/4} \, _2F_1\left(\frac{1}{4},\frac{3}{4};\frac{5}{4};-\frac{b x^4}{a}\right)-5 a^2 x-3 a b x^5+2 b^2 x^9}{12 b^2 \left(a+b x^4\right)^{3/4}}","-\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^2*x - 3*a*b*x^5 + 2*b^2*x^9 + 5*a^2*x*(1 + (b*x^4)/a)^(3/4)*Hypergeometric2F1[1/4, 3/4, 5/4, -((b*x^4)/a)])/(12*b^2*(a + b*x^4)^(3/4))","C",1
1134,1,62,83,0.0178942,"\int \frac{x^4}{\left(a+b x^4\right)^{3/4}} \, dx","Integrate[x^4/(a + b*x^4)^(3/4),x]","\frac{x \left(-a \left(\frac{b x^4}{a}+1\right)^{3/4} \, _2F_1\left(\frac{1}{4},\frac{3}{4};\frac{5}{4};-\frac{b x^4}{a}\right)+a+b x^4\right)}{2 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 - a*(1 + (b*x^4)/a)^(3/4)*Hypergeometric2F1[1/4, 3/4, 5/4, -((b*x^4)/a)]))/(2*b*(a + b*x^4)^(3/4))","C",1
1135,1,46,61,0.0074701,"\int \frac{1}{\left(a+b x^4\right)^{3/4}} \, dx","Integrate[(a + b*x^4)^(-3/4),x]","\frac{x \left(\frac{b x^4}{a}+1\right)^{3/4} \, _2F_1\left(\frac{1}{4},\frac{3}{4};\frac{5}{4};-\frac{b x^4}{a}\right)}{\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,"(x*(1 + (b*x^4)/a)^(3/4)*Hypergeometric2F1[1/4, 3/4, 5/4, -((b*x^4)/a)])/(a + b*x^4)^(3/4)","C",1
1136,1,51,85,0.0098168,"\int \frac{1}{x^4 \left(a+b x^4\right)^{3/4}} \, dx","Integrate[1/(x^4*(a + b*x^4)^(3/4)),x]","-\frac{\left(\frac{b x^4}{a}+1\right)^{3/4} \, _2F_1\left(-\frac{3}{4},\frac{3}{4};\frac{1}{4};-\frac{b x^4}{a}\right)}{3 x^3 \left(a+b x^4\right)^{3/4}}","\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,"-1/3*((1 + (b*x^4)/a)^(3/4)*Hypergeometric2F1[-3/4, 3/4, 1/4, -((b*x^4)/a)])/(x^3*(a + b*x^4)^(3/4))","C",1
1137,1,51,107,0.0099486,"\int \frac{1}{x^8 \left(a+b x^4\right)^{3/4}} \, dx","Integrate[1/(x^8*(a + b*x^4)^(3/4)),x]","-\frac{\left(\frac{b x^4}{a}+1\right)^{3/4} \, _2F_1\left(-\frac{7}{4},\frac{3}{4};-\frac{3}{4};-\frac{b x^4}{a}\right)}{7 x^7 \left(a+b x^4\right)^{3/4}}","-\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,"-1/7*((1 + (b*x^4)/a)^(3/4)*Hypergeometric2F1[-7/4, 3/4, -3/4, -((b*x^4)/a)])/(x^7*(a + b*x^4)^(3/4))","C",1
1138,1,51,131,0.0106057,"\int \frac{1}{x^{12} \left(a+b x^4\right)^{3/4}} \, dx","Integrate[1/(x^12*(a + b*x^4)^(3/4)),x]","-\frac{\left(\frac{b x^4}{a}+1\right)^{3/4} \, _2F_1\left(-\frac{11}{4},\frac{3}{4};-\frac{7}{4};-\frac{b x^4}{a}\right)}{11 x^{11} \left(a+b x^4\right)^{3/4}}","\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{20 b^2 \sqrt[4]{a+b x^4}}{77 a^3 x^3}+\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,"-1/11*((1 + (b*x^4)/a)^(3/4)*Hypergeometric2F1[-11/4, 3/4, -7/4, -((b*x^4)/a)])/(x^11*(a + b*x^4)^(3/4))","C",1
1139,1,61,99,0.0472188,"\int \frac{x^{19}}{\left(a+b x^4\right)^{5/4}} \, dx","Integrate[x^19/(a + b*x^4)^(5/4),x]","\frac{-2048 a^4-512 a^3 b x^4+192 a^2 b^2 x^8-112 a b^3 x^{12}+77 b^4 x^{16}}{1155 b^5 \sqrt[4]{a+b x^4}}","-\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,"(-2048*a^4 - 512*a^3*b*x^4 + 192*a^2*b^2*x^8 - 112*a*b^3*x^12 + 77*b^4*x^16)/(1155*b^5*(a + b*x^4)^(1/4))","A",1
1140,1,50,74,0.0221771,"\int \frac{x^{15}}{\left(a+b x^4\right)^{5/4}} \, dx","Integrate[x^15/(a + b*x^4)^(5/4),x]","\frac{128 a^3+32 a^2 b x^4-12 a b^2 x^8+7 b^3 x^{12}}{77 b^4 \sqrt[4]{a+b x^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,"(128*a^3 + 32*a^2*b*x^4 - 12*a*b^2*x^8 + 7*b^3*x^12)/(77*b^4*(a + b*x^4)^(1/4))","A",1
1141,1,39,57,0.0170054,"\int \frac{x^{11}}{\left(a+b x^4\right)^{5/4}} \, dx","Integrate[x^11/(a + b*x^4)^(5/4),x]","\frac{-32 a^2-8 a b x^4+3 b^2 x^8}{21 b^3 \sqrt[4]{a+b x^4}}","-\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,"(-32*a^2 - 8*a*b*x^4 + 3*b^2*x^8)/(21*b^3*(a + b*x^4)^(1/4))","A",1
1142,1,27,35,0.0116506,"\int \frac{x^7}{\left(a+b x^4\right)^{5/4}} \, dx","Integrate[x^7/(a + b*x^4)^(5/4),x]","\frac{4 a+b x^4}{3 b^2 \sqrt[4]{a+b x^4}}","\frac{a}{b^2 \sqrt[4]{a+b x^4}}+\frac{\left(a+b x^4\right)^{3/4}}{3 b^2}",1,"(4*a + b*x^4)/(3*b^2*(a + b*x^4)^(1/4))","A",1
1143,1,16,16,0.0043003,"\int \frac{x^3}{\left(a+b x^4\right)^{5/4}} \, dx","Integrate[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
1144,1,33,70,0.0072842,"\int \frac{1}{x \left(a+b x^4\right)^{5/4}} \, dx","Integrate[1/(x*(a + b*x^4)^(5/4)),x]","\frac{\, _2F_1\left(-\frac{1}{4},1;\frac{3}{4};\frac{b x^4}{a}+1\right)}{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,"Hypergeometric2F1[-1/4, 1, 3/4, 1 + (b*x^4)/a]/(a*(a + b*x^4)^(1/4))","C",1
1145,1,35,97,0.0088493,"\int \frac{1}{x^5 \left(a+b x^4\right)^{5/4}} \, dx","Integrate[1/(x^5*(a + b*x^4)^(5/4)),x]","-\frac{b \, _2F_1\left(-\frac{1}{4},2;\frac{3}{4};\frac{b x^4}{a}+1\right)}{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{5 b}{4 a^2 \sqrt[4]{a+b x^4}}-\frac{1}{4 a x^4 \sqrt[4]{a+b x^4}}",1,"-((b*Hypergeometric2F1[-1/4, 2, 3/4, 1 + (b*x^4)/a])/(a^2*(a + b*x^4)^(1/4)))","C",1
1146,1,36,125,0.0086907,"\int \frac{1}{x^9 \left(a+b x^4\right)^{5/4}} \, dx","Integrate[1/(x^9*(a + b*x^4)^(5/4)),x]","\frac{b^2 \, _2F_1\left(-\frac{1}{4},3;\frac{3}{4};\frac{b x^4}{a}+1\right)}{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{45 b^2}{32 a^3 \sqrt[4]{a+b x^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,"(b^2*Hypergeometric2F1[-1/4, 3, 3/4, 1 + (b*x^4)/a])/(a^3*(a + b*x^4)^(1/4))","C",1
1147,1,79,128,0.0451569,"\int \frac{x^{13}}{\left(a+b x^4\right)^{5/4}} \, dx","Integrate[x^13/(a + b*x^4)^(5/4),x]","\frac{x^2 \left(12 a^2 \sqrt[4]{\frac{b x^4}{a}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{3}{2};-\frac{b x^4}{a}\right)-12 a^2-2 a b x^4+b^2 x^8\right)}{9 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{4 a^2 x^2}{3 b^3 \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,"(x^2*(-12*a^2 - 2*a*b*x^4 + b^2*x^8 + 12*a^2*(1 + (b*x^4)/a)^(1/4)*Hypergeometric2F1[1/4, 1/2, 3/2, -((b*x^4)/a)]))/(9*b^3*(a + b*x^4)^(1/4))","C",1
1148,1,66,104,0.0241494,"\int \frac{x^9}{\left(a+b x^4\right)^{5/4}} \, dx","Integrate[x^9/(a + b*x^4)^(5/4),x]","\frac{x^2 \left(-6 a \sqrt[4]{\frac{b x^4}{a}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{3}{2};-\frac{b x^4}{a}\right)+6 a+b x^4\right)}{5 b^2 \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,"(x^2*(6*a + b*x^4 - 6*a*(1 + (b*x^4)/a)^(1/4)*Hypergeometric2F1[1/4, 1/2, 3/2, -((b*x^4)/a)]))/(5*b^2*(a + b*x^4)^(1/4))","C",1
1149,1,54,77,0.020647,"\int \frac{x^5}{\left(a+b x^4\right)^{5/4}} \, dx","Integrate[x^5/(a + b*x^4)^(5/4),x]","\frac{x^2 \left(\sqrt[4]{\frac{b x^4}{a}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{3}{2};-\frac{b x^4}{a}\right)-1\right)}{b \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*(-1 + (1 + (b*x^4)/a)^(1/4)*Hypergeometric2F1[1/4, 1/2, 3/2, -((b*x^4)/a)]))/(b*(a + b*x^4)^(1/4))","C",1
1150,1,57,57,0.0152741,"\int \frac{x}{\left(a+b x^4\right)^{5/4}} \, dx","Integrate[x/(a + b*x^4)^(5/4),x]","-\frac{x^2 \left(\sqrt[4]{\frac{b x^4}{a}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{3}{2};-\frac{b x^4}{a}\right)-2\right)}{2 a \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,"-1/2*(x^2*(-2 + (1 + (b*x^4)/a)^(1/4)*Hypergeometric2F1[1/4, 1/2, 3/2, -((b*x^4)/a)]))/(a*(a + b*x^4)^(1/4))","C",1
1151,1,54,82,0.0111121,"\int \frac{1}{x^3 \left(a+b x^4\right)^{5/4}} \, dx","Integrate[1/(x^3*(a + b*x^4)^(5/4)),x]","-\frac{\sqrt[4]{\frac{b x^4}{a}+1} \, _2F_1\left(-\frac{1}{2},\frac{5}{4};\frac{1}{2};-\frac{b x^4}{a}\right)}{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*((1 + (b*x^4)/a)^(1/4)*Hypergeometric2F1[-1/2, 5/4, 1/2, -((b*x^4)/a)])/(a*x^2*(a + b*x^4)^(1/4))","C",1
1152,1,54,104,0.0114613,"\int \frac{1}{x^7 \left(a+b x^4\right)^{5/4}} \, dx","Integrate[1/(x^7*(a + b*x^4)^(5/4)),x]","-\frac{\sqrt[4]{\frac{b x^4}{a}+1} \, _2F_1\left(-\frac{3}{2},\frac{5}{4};-\frac{1}{2};-\frac{b x^4}{a}\right)}{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*((1 + (b*x^4)/a)^(1/4)*Hypergeometric2F1[-3/2, 5/4, -1/2, -((b*x^4)/a)])/(a*x^6*(a + b*x^4)^(1/4))","C",1
1153,1,54,128,0.0115684,"\int \frac{1}{x^{11} \left(a+b x^4\right)^{5/4}} \, dx","Integrate[1/(x^11*(a + b*x^4)^(5/4)),x]","-\frac{\sqrt[4]{\frac{b x^4}{a}+1} \, _2F_1\left(-\frac{5}{2},\frac{5}{4};-\frac{3}{2};-\frac{b x^4}{a}\right)}{10 a x^{10} \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{77 b^2}{120 a^3 x^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*((1 + (b*x^4)/a)^(1/4)*Hypergeometric2F1[-5/2, 5/4, -3/2, -((b*x^4)/a)])/(a*x^10*(a + b*x^4)^(1/4))","C",1
1154,1,67,123,0.0256449,"\int \frac{x^{12}}{\left(a+b x^4\right)^{5/4}} \, dx","Integrate[x^12/(a + b*x^4)^(5/4),x]","\frac{x^5 \left(9 a \sqrt[4]{\frac{b x^4}{a}+1} \, _2F_1\left(\frac{5}{4},\frac{5}{4};\frac{9}{4};-\frac{b x^4}{a}\right)-9 a+4 b x^4\right)}{32 b^2 \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{45 a x \left(a+b x^4\right)^{3/4}}{32 b^3}+\frac{9 x^5 \left(a+b x^4\right)^{3/4}}{8 b^2}-\frac{x^9}{b \sqrt[4]{a+b x^4}}",1,"(x^5*(-9*a + 4*b*x^4 + 9*a*(1 + (b*x^4)/a)^(1/4)*Hypergeometric2F1[5/4, 5/4, 9/4, -((b*x^4)/a)]))/(32*b^2*(a + b*x^4)^(1/4))","C",1
1155,1,60,97,0.0162719,"\int \frac{x^8}{\left(a+b x^4\right)^{5/4}} \, dx","Integrate[x^8/(a + b*x^4)^(5/4),x]","\frac{x^5-x^5 \sqrt[4]{\frac{b x^4}{a}+1} \, _2F_1\left(\frac{5}{4},\frac{5}{4};\frac{9}{4};-\frac{b x^4}{a}\right)}{4 b \sqrt[4]{a+b x^4}}","-\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{5 x \left(a+b x^4\right)^{3/4}}{4 b^2}-\frac{x^5}{b \sqrt[4]{a+b x^4}}",1,"(x^5 - x^5*(1 + (b*x^4)/a)^(1/4)*Hypergeometric2F1[5/4, 5/4, 9/4, -((b*x^4)/a)])/(4*b*(a + b*x^4)^(1/4))","C",1
1156,1,54,74,0.0110763,"\int \frac{x^4}{\left(a+b x^4\right)^{5/4}} \, dx","Integrate[x^4/(a + b*x^4)^(5/4),x]","\frac{x^5 \sqrt[4]{\frac{b x^4}{a}+1} \, _2F_1\left(\frac{5}{4},\frac{5}{4};\frac{9}{4};-\frac{b x^4}{a}\right)}{5 a \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^5*(1 + (b*x^4)/a)^(1/4)*Hypergeometric2F1[5/4, 5/4, 9/4, -((b*x^4)/a)])/(5*a*(a + b*x^4)^(1/4))","C",1
1157,1,16,16,0.0057932,"\int \frac{1}{\left(a+b x^4\right)^{5/4}} \, dx","Integrate[(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
1158,1,29,42,0.0134656,"\int \frac{1}{x^4 \left(a+b x^4\right)^{5/4}} \, dx","Integrate[1/(x^4*(a + b*x^4)^(5/4)),x]","-\frac{a+4 b x^4}{3 a^2 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 + 4*b*x^4)/(a^2*x^3*(a + b*x^4)^(1/4))","A",1
1159,1,42,66,0.0081251,"\int \frac{1}{x^8 \left(a+b x^4\right)^{5/4}} \, dx","Integrate[1/(x^8*(a + b*x^4)^(5/4)),x]","-\frac{3 a^2-8 a b x^4-32 b^2 x^8}{21 a^3 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,"-1/21*(3*a^2 - 8*a*b*x^4 - 32*b^2*x^8)/(a^3*x^7*(a + b*x^4)^(1/4))","A",1
1160,1,53,90,0.0097463,"\int \frac{1}{x^{12} \left(a+b x^4\right)^{5/4}} \, dx","Integrate[1/(x^12*(a + b*x^4)^(5/4)),x]","-\frac{7 a^3-12 a^2 b x^4+32 a b^2 x^8+128 b^3 x^{12}}{77 a^4 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,"-1/77*(7*a^3 - 12*a^2*b*x^4 + 32*a*b^2*x^8 + 128*b^3*x^12)/(a^4*x^11*(a + b*x^4)^(1/4))","A",1
1161,1,64,114,0.0104501,"\int \frac{1}{x^{16} \left(a+b x^4\right)^{5/4}} \, dx","Integrate[1/(x^16*(a + b*x^4)^(5/4)),x]","-\frac{77 a^4-112 a^3 b x^4+192 a^2 b^2 x^8-512 a b^3 x^{12}-2048 b^4 x^{16}}{1155 a^5 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,"-1/1155*(77*a^4 - 112*a^3*b*x^4 + 192*a^2*b^2*x^8 - 512*a*b^3*x^12 - 2048*b^4*x^16)/(a^5*x^15*(a + b*x^4)^(1/4))","A",1
1162,1,80,129,0.0363464,"\int \frac{x^{14}}{\left(a+b x^4\right)^{5/4}} \, dx","Integrate[x^14/(a + b*x^4)^(5/4),x]","\frac{x^3 \left(-77 a^2 \sqrt[4]{\frac{b x^4}{a}+1} \, _2F_1\left(\frac{3}{4},\frac{5}{4};\frac{7}{4};-\frac{b x^4}{a}\right)+77 a^2-22 a b x^4+12 b^2 x^8\right)}{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{77 a^2 x^3}{120 b^3 \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,"(x^3*(77*a^2 - 22*a*b*x^4 + 12*b^2*x^8 - 77*a^2*(1 + (b*x^4)/a)^(1/4)*Hypergeometric2F1[3/4, 5/4, 7/4, -((b*x^4)/a)]))/(120*b^3*(a + b*x^4)^(1/4))","C",1
1163,1,67,105,0.0222522,"\int \frac{x^{10}}{\left(a+b x^4\right)^{5/4}} \, dx","Integrate[x^10/(a + b*x^4)^(5/4),x]","\frac{x^3 \left(7 a \sqrt[4]{\frac{b x^4}{a}+1} \, _2F_1\left(\frac{3}{4},\frac{5}{4};\frac{7}{4};-\frac{b x^4}{a}\right)-7 a+2 b x^4\right)}{12 b^2 \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,"(x^3*(-7*a + 2*b*x^4 + 7*a*(1 + (b*x^4)/a)^(1/4)*Hypergeometric2F1[3/4, 5/4, 7/4, -((b*x^4)/a)]))/(12*b^2*(a + b*x^4)^(1/4))","C",1
1164,1,60,83,0.0155101,"\int \frac{x^6}{\left(a+b x^4\right)^{5/4}} \, dx","Integrate[x^6/(a + b*x^4)^(5/4),x]","\frac{x^3-x^3 \sqrt[4]{\frac{b x^4}{a}+1} \, _2F_1\left(\frac{3}{4},\frac{5}{4};\frac{7}{4};-\frac{b x^4}{a}\right)}{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 - x^3*(1 + (b*x^4)/a)^(1/4)*Hypergeometric2F1[3/4, 5/4, 7/4, -((b*x^4)/a)])/(2*b*(a + b*x^4)^(1/4))","C",1
1165,1,54,59,0.0092862,"\int \frac{x^2}{\left(a+b x^4\right)^{5/4}} \, dx","Integrate[x^2/(a + b*x^4)^(5/4),x]","\frac{x^3 \sqrt[4]{\frac{b x^4}{a}+1} \, _2F_1\left(\frac{3}{4},\frac{5}{4};\frac{7}{4};-\frac{b x^4}{a}\right)}{3 a \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,"(x^3*(1 + (b*x^4)/a)^(1/4)*Hypergeometric2F1[3/4, 5/4, 7/4, -((b*x^4)/a)])/(3*a*(a + b*x^4)^(1/4))","C",1
1166,1,52,79,0.0097005,"\int \frac{1}{x^2 \left(a+b x^4\right)^{5/4}} \, dx","Integrate[1/(x^2*(a + b*x^4)^(5/4)),x]","-\frac{\sqrt[4]{\frac{b x^4}{a}+1} \, _2F_1\left(-\frac{1}{4},\frac{5}{4};\frac{3}{4};-\frac{b x^4}{a}\right)}{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 + (b*x^4)/a)^(1/4)*Hypergeometric2F1[-1/4, 5/4, 3/4, -((b*x^4)/a)])/(a*x*(a + b*x^4)^(1/4)))","C",1
1167,1,54,105,0.0173672,"\int \frac{1}{x^6 \left(a+b x^4\right)^{5/4}} \, dx","Integrate[1/(x^6*(a + b*x^4)^(5/4)),x]","-\frac{\sqrt[4]{\frac{b x^4}{a}+1} \, _2F_1\left(-\frac{5}{4},\frac{5}{4};-\frac{1}{4};-\frac{b x^4}{a}\right)}{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*((1 + (b*x^4)/a)^(1/4)*Hypergeometric2F1[-5/4, 5/4, -1/4, -((b*x^4)/a)])/(a*x^5*(a + b*x^4)^(1/4))","C",1
1168,1,54,129,0.0164273,"\int \frac{1}{x^{10} \left(a+b x^4\right)^{5/4}} \, dx","Integrate[1/(x^10*(a + b*x^4)^(5/4)),x]","-\frac{\sqrt[4]{\frac{b x^4}{a}+1} \, _2F_1\left(-\frac{9}{4},\frac{5}{4};-\frac{5}{4};-\frac{b x^4}{a}\right)}{9 a x^9 \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{4 b^2}{3 a^3 x \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*((1 + (b*x^4)/a)^(1/4)*Hypergeometric2F1[-9/4, 5/4, -5/4, -((b*x^4)/a)])/(a*x^9*(a + b*x^4)^(1/4))","C",1
1169,1,54,153,0.0158421,"\int \frac{1}{x^{14} \left(a+b x^4\right)^{5/4}} \, dx","Integrate[1/(x^14*(a + b*x^4)^(5/4)),x]","-\frac{\sqrt[4]{\frac{b x^4}{a}+1} \, _2F_1\left(-\frac{13}{4},\frac{5}{4};-\frac{9}{4};-\frac{b x^4}{a}\right)}{13 a x^{13} \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{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{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*((1 + (b*x^4)/a)^(1/4)*Hypergeometric2F1[-13/4, 5/4, -9/4, -((b*x^4)/a)])/(a*x^13*(a + b*x^4)^(1/4))","C",1
1170,1,56,83,0.0384414,"\int \frac{1}{\left(a+b x^4\right)^{7/4}} \, dx","Integrate[(a + b*x^4)^(-7/4),x]","\frac{2 x \left(\frac{b x^4}{a}+1\right)^{3/4} \, _2F_1\left(\frac{1}{4},\frac{3}{4};\frac{5}{4};-\frac{b x^4}{a}\right)+x}{3 a \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 + 2*x*(1 + (b*x^4)/a)^(3/4)*Hypergeometric2F1[1/4, 3/4, 5/4, -((b*x^4)/a)])/(3*a*(a + b*x^4)^(3/4))","C",1
1171,1,29,39,0.0110686,"\int \frac{1}{\left(a+b x^4\right)^{9/4}} \, dx","Integrate[(a + b*x^4)^(-9/4),x]","\frac{x \left(5 a+4 b x^4\right)}{5 a^2 \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 + 4*b*x^4))/(5*a^2*(a + b*x^4)^(5/4))","A",1
1172,1,72,102,0.05143,"\int \frac{1}{\left(a+b x^4\right)^{11/4}} \, dx","Integrate[(a + b*x^4)^(-11/4),x]","\frac{4 x \left(a+b x^4\right) \left(\frac{b x^4}{a}+1\right)^{3/4} \, _2F_1\left(\frac{1}{4},\frac{3}{4};\frac{5}{4};-\frac{b x^4}{a}\right)+3 a x+2 b x^5}{7 a^2 \left(a+b x^4\right)^{7/4}}","-\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{2 x}{7 a^2 \left(a+b x^4\right)^{3/4}}+\frac{x}{7 a \left(a+b x^4\right)^{7/4}}",1,"(3*a*x + 2*b*x^5 + 4*x*(a + b*x^4)*(1 + (b*x^4)/a)^(3/4)*Hypergeometric2F1[1/4, 3/4, 5/4, -((b*x^4)/a)])/(7*a^2*(a + b*x^4)^(7/4))","C",1
1173,1,40,58,0.0138436,"\int \frac{1}{\left(a+b x^4\right)^{13/4}} \, dx","Integrate[(a + b*x^4)^(-13/4),x]","\frac{x \left(45 a^2+72 a b x^4+32 b^2 x^8\right)}{45 a^3 \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*(45*a^2 + 72*a*b*x^4 + 32*b^2*x^8))/(45*a^3*(a + b*x^4)^(9/4))","A",1
1174,1,51,77,0.0166778,"\int \frac{1}{\left(a+b x^4\right)^{17/4}} \, dx","Integrate[(a + b*x^4)^(-17/4),x]","\frac{x \left(195 a^3+468 a^2 b x^4+416 a b^2 x^8+128 b^3 x^{12}\right)}{195 a^4 \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*(195*a^3 + 468*a^2*b*x^4 + 416*a*b^2*x^8 + 128*b^3*x^12))/(195*a^4*(a + b*x^4)^(13/4))","A",1
1175,1,62,106,0.0499017,"\int x^{19} \sqrt[4]{a-b x^4} \, dx","Integrate[x^19*(a - b*x^4)^(1/4),x]","-\frac{\left(a-b x^4\right)^{5/4} \left(2048 a^4+2560 a^3 b x^4+2880 a^2 b^2 x^8+3120 a b^3 x^{12}+3315 b^4 x^{16}\right)}{69615 b^5}","-\frac{a^4 \left(a-b x^4\right)^{5/4}}{5 b^5}+\frac{4 a^3 \left(a-b x^4\right)^{9/4}}{9 b^5}-\frac{6 a^2 \left(a-b x^4\right)^{13/4}}{13 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,"-1/69615*((a - b*x^4)^(5/4)*(2048*a^4 + 2560*a^3*b*x^4 + 2880*a^2*b^2*x^8 + 3120*a*b^3*x^12 + 3315*b^4*x^16))/b^5","A",1
1176,1,51,84,0.024679,"\int x^{15} \sqrt[4]{a-b x^4} \, dx","Integrate[x^15*(a - b*x^4)^(1/4),x]","-\frac{\left(a-b x^4\right)^{5/4} \left(128 a^3+160 a^2 b x^4+180 a b^2 x^8+195 b^3 x^{12}\right)}{3315 b^4}","-\frac{a^3 \left(a-b x^4\right)^{5/4}}{5 b^4}+\frac{a^2 \left(a-b x^4\right)^{9/4}}{3 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,"-1/3315*((a - b*x^4)^(5/4)*(128*a^3 + 160*a^2*b*x^4 + 180*a*b^2*x^8 + 195*b^3*x^12))/b^4","A",1
1177,1,40,62,0.0216047,"\int x^{11} \sqrt[4]{a-b x^4} \, dx","Integrate[x^11*(a - b*x^4)^(1/4),x]","-\frac{\left(a-b x^4\right)^{5/4} \left(32 a^2+40 a b x^4+45 b^2 x^8\right)}{585 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,"-1/585*((a - b*x^4)^(5/4)*(32*a^2 + 40*a*b*x^4 + 45*b^2*x^8))/b^3","A",1
1178,1,29,40,0.0268892,"\int x^7 \sqrt[4]{a-b x^4} \, dx","Integrate[x^7*(a - b*x^4)^(1/4),x]","-\frac{\left(a-b x^4\right)^{5/4} \left(4 a+5 b x^4\right)}{45 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,"-1/45*((a - b*x^4)^(5/4)*(4*a + 5*b*x^4))/b^2","A",1
1179,1,19,19,0.0046718,"\int x^3 \sqrt[4]{a-b x^4} \, dx","Integrate[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,"-1/5*(a - b*x^4)^(5/4)/b","A",1
1180,1,69,69,0.0358665,"\int \frac{\sqrt[4]{a-b x^4}}{x} \, dx","Integrate[(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",1
1181,1,39,78,0.0106633,"\int \frac{\sqrt[4]{a-b x^4}}{x^5} \, dx","Integrate[(a - b*x^4)^(1/4)/x^5,x]","-\frac{b \left(a-b x^4\right)^{5/4} \, _2F_1\left(\frac{5}{4},2;\frac{9}{4};1-\frac{b x^4}{a}\right)}{5 a^2}","\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,"-1/5*(b*(a - b*x^4)^(5/4)*Hypergeometric2F1[5/4, 2, 9/4, 1 - (b*x^4)/a])/a^2","C",1
1182,1,41,105,0.0098617,"\int \frac{\sqrt[4]{a-b x^4}}{x^9} \, dx","Integrate[(a - b*x^4)^(1/4)/x^9,x]","-\frac{b^2 \left(a-b x^4\right)^{5/4} \, _2F_1\left(\frac{5}{4},3;\frac{9}{4};1-\frac{b x^4}{a}\right)}{5 a^3}","\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,"-1/5*(b^2*(a - b*x^4)^(5/4)*Hypergeometric2F1[5/4, 3, 9/4, 1 - (b*x^4)/a])/a^3","C",1
1183,1,98,130,0.0893102,"\int x^9 \sqrt[4]{a-b x^4} \, dx","Integrate[x^9*(a - b*x^4)^(1/4),x]","\frac{x^2 \sqrt[4]{a-b x^4} \left(6 a^2 \, _2F_1\left(-\frac{1}{4},\frac{1}{2};\frac{3}{2};\frac{b x^4}{a}\right)-\sqrt[4]{1-\frac{b x^4}{a}} \left(6 a^2+a b x^4-7 b^2 x^8\right)\right)}{77 b^2 \sqrt[4]{1-\frac{b x^4}{a}}}","\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{2 a^2 x^2 \sqrt[4]{a-b x^4}}{77 b^2}+\frac{1}{11} x^{10} \sqrt[4]{a-b x^4}-\frac{a x^6 \sqrt[4]{a-b x^4}}{77 b}",1,"(x^2*(a - b*x^4)^(1/4)*(-((1 - (b*x^4)/a)^(1/4)*(6*a^2 + a*b*x^4 - 7*b^2*x^8)) + 6*a^2*Hypergeometric2F1[-1/4, 1/2, 3/2, (b*x^4)/a]))/(77*b^2*(1 - (b*x^4)/a)^(1/4))","C",1
1184,1,66,105,0.1109326,"\int x^5 \sqrt[4]{a-b x^4} \, dx","Integrate[x^5*(a - b*x^4)^(1/4),x]","\frac{x^2 \sqrt[4]{a-b x^4} \left(\frac{a \, _2F_1\left(-\frac{1}{4},\frac{1}{2};\frac{3}{2};\frac{b x^4}{a}\right)}{\sqrt[4]{1-\frac{b x^4}{a}}}-a+b x^4\right)}{7 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,"(x^2*(a - b*x^4)^(1/4)*(-a + b*x^4 + (a*Hypergeometric2F1[-1/4, 1/2, 3/2, (b*x^4)/a])/(1 - (b*x^4)/a)^(1/4)))/(7*b)","C",1
1185,1,52,82,0.0103545,"\int x \sqrt[4]{a-b x^4} \, dx","Integrate[x*(a - b*x^4)^(1/4),x]","\frac{x^2 \sqrt[4]{a-b x^4} \, _2F_1\left(-\frac{1}{4},\frac{1}{2};\frac{3}{2};\frac{b x^4}{a}\right)}{2 \sqrt[4]{1-\frac{b x^4}{a}}}","\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)*Hypergeometric2F1[-1/4, 1/2, 3/2, (b*x^4)/a])/(2*(1 - (b*x^4)/a)^(1/4))","C",1
1186,1,52,82,0.0107168,"\int \frac{\sqrt[4]{a-b x^4}}{x^3} \, dx","Integrate[(a - b*x^4)^(1/4)/x^3,x]","-\frac{\sqrt[4]{a-b x^4} \, _2F_1\left(-\frac{1}{2},-\frac{1}{4};\frac{1}{2};\frac{b x^4}{a}\right)}{2 x^2 \sqrt[4]{1-\frac{b x^4}{a}}}","-\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,"-1/2*((a - b*x^4)^(1/4)*Hypergeometric2F1[-1/2, -1/4, 1/2, (b*x^4)/a])/(x^2*(1 - (b*x^4)/a)^(1/4))","C",1
1187,1,52,105,0.0115914,"\int \frac{\sqrt[4]{a-b x^4}}{x^7} \, dx","Integrate[(a - b*x^4)^(1/4)/x^7,x]","-\frac{\sqrt[4]{a-b x^4} \, _2F_1\left(-\frac{3}{2},-\frac{1}{4};-\frac{1}{2};\frac{b x^4}{a}\right)}{6 x^6 \sqrt[4]{1-\frac{b x^4}{a}}}","-\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{\sqrt[4]{a-b x^4}}{6 x^6}+\frac{b \sqrt[4]{a-b x^4}}{12 a x^2}",1,"-1/6*((a - b*x^4)^(1/4)*Hypergeometric2F1[-3/2, -1/4, -1/2, (b*x^4)/a])/(x^6*(1 - (b*x^4)/a)^(1/4))","C",1
1188,1,52,130,0.0278676,"\int \frac{\sqrt[4]{a-b x^4}}{x^{11}} \, dx","Integrate[(a - b*x^4)^(1/4)/x^11,x]","-\frac{\sqrt[4]{a-b x^4} \, _2F_1\left(-\frac{5}{2},-\frac{1}{4};-\frac{3}{2};\frac{b x^4}{a}\right)}{10 x^{10} \sqrt[4]{1-\frac{b x^4}{a}}}","-\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^2 \sqrt[4]{a-b x^4}}{24 a^2 x^2}-\frac{\sqrt[4]{a-b x^4}}{10 x^{10}}+\frac{b \sqrt[4]{a-b x^4}}{60 a x^6}",1,"-1/10*((a - b*x^4)^(1/4)*Hypergeometric2F1[-5/2, -1/4, -3/2, (b*x^4)/a])/(x^10*(1 - (b*x^4)/a)^(1/4))","C",1
1189,1,66,263,0.0783851,"\int x^6 \sqrt[4]{a-b x^4} \, dx","Integrate[x^6*(a - b*x^4)^(1/4),x]","\frac{x^3 \sqrt[4]{a-b x^4} \left(\frac{a \, _2F_1\left(-\frac{1}{4},\frac{3}{4};\frac{7}{4};\frac{b x^4}{a}\right)}{\sqrt[4]{1-\frac{b x^4}{a}}}-a+b x^4\right)}{8 b}","-\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{3 a^2 \log \left(-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}+1\right)}{128 \sqrt{2} b^{7/4}}-\frac{3 a^2 \log \left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}+1\right)}{128 \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,"(x^3*(a - b*x^4)^(1/4)*(-a + b*x^4 + (a*Hypergeometric2F1[-1/4, 3/4, 7/4, (b*x^4)/a])/(1 - (b*x^4)/a)^(1/4)))/(8*b)","C",1
1190,1,52,232,0.0126814,"\int x^2 \sqrt[4]{a-b x^4} \, dx","Integrate[x^2*(a - b*x^4)^(1/4),x]","\frac{x^3 \sqrt[4]{a-b x^4} \, _2F_1\left(-\frac{1}{4},\frac{3}{4};\frac{7}{4};\frac{b x^4}{a}\right)}{3 \sqrt[4]{1-\frac{b x^4}{a}}}","-\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{a \log \left(-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}+1\right)}{16 \sqrt{2} b^{3/4}}-\frac{a \log \left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}+1\right)}{16 \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)*Hypergeometric2F1[-1/4, 3/4, 7/4, (b*x^4)/a])/(3*(1 - (b*x^4)/a)^(1/4))","C",1
1191,1,50,226,0.0304536,"\int \frac{\sqrt[4]{a-b x^4}}{x^2} \, dx","Integrate[(a - b*x^4)^(1/4)/x^2,x]","-\frac{\sqrt[4]{a-b x^4} \, _2F_1\left(-\frac{1}{4},-\frac{1}{4};\frac{3}{4};\frac{b x^4}{a}\right)}{x \sqrt[4]{1-\frac{b x^4}{a}}}","-\frac{\sqrt[4]{a-b x^4}}{x}+\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]{b} \log \left(-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}+1\right)}{4 \sqrt{2}}+\frac{\sqrt[4]{b} \log \left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}+1\right)}{4 \sqrt{2}}",1,"-(((a - b*x^4)^(1/4)*Hypergeometric2F1[-1/4, -1/4, 3/4, (b*x^4)/a])/(x*(1 - (b*x^4)/a)^(1/4)))","C",1
1192,1,22,22,0.0248105,"\int \frac{\sqrt[4]{a-b x^4}}{x^6} \, dx","Integrate[(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,"-1/5*(a - b*x^4)^(5/4)/(a*x^5)","A",1
1193,1,32,46,0.008224,"\int \frac{\sqrt[4]{a-b x^4}}{x^{10}} \, dx","Integrate[(a - b*x^4)^(1/4)/x^10,x]","-\frac{\left(a-b x^4\right)^{5/4} \left(5 a+4 b x^4\right)}{45 a^2 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,"-1/45*((a - b*x^4)^(5/4)*(5*a + 4*b*x^4))/(a^2*x^9)","A",1
1194,1,43,71,0.0113273,"\int \frac{\sqrt[4]{a-b x^4}}{x^{14}} \, dx","Integrate[(a - b*x^4)^(1/4)/x^14,x]","-\frac{\left(a-b x^4\right)^{5/4} \left(45 a^2+40 a b x^4+32 b^2 x^8\right)}{585 a^3 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,"-1/585*((a - b*x^4)^(5/4)*(45*a^2 + 40*a*b*x^4 + 32*b^2*x^8))/(a^3*x^13)","A",1
1195,1,54,96,0.0225425,"\int \frac{\sqrt[4]{a-b x^4}}{x^{18}} \, dx","Integrate[(a - b*x^4)^(1/4)/x^18,x]","-\frac{\left(a-b x^4\right)^{5/4} \left(195 a^3+180 a^2 b x^4+160 a b^2 x^8+128 b^3 x^{12}\right)}{3315 a^4 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,"-1/3315*((a - b*x^4)^(5/4)*(195*a^3 + 180*a^2*b*x^4 + 160*a*b^2*x^8 + 128*b^3*x^12))/(a^4*x^17)","A",1
1196,1,108,156,0.0872009,"\int x^{12} \sqrt[4]{a-b x^4} \, dx","Integrate[x^12*(a - b*x^4)^(1/4),x]","\frac{x \sqrt[4]{a-b x^4} \left(15 a^3 \, _2F_1\left(-\frac{1}{4},\frac{1}{4};\frac{5}{4};\frac{b x^4}{a}\right)-\sqrt[4]{1-\frac{b x^4}{a}} \left(15 a^3+3 a^2 b x^4+2 a b^2 x^8-20 b^3 x^{12}\right)\right)}{280 b^3 \sqrt[4]{1-\frac{b x^4}{a}}}","-\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{3 a^3 x \sqrt[4]{a-b x^4}}{112 b^3}-\frac{3 a^2 x^5 \sqrt[4]{a-b x^4}}{280 b^2}+\frac{1}{14} x^{13} \sqrt[4]{a-b x^4}-\frac{a x^9 \sqrt[4]{a-b x^4}}{140 b}",1,"(x*(a - b*x^4)^(1/4)*(-((1 - (b*x^4)/a)^(1/4)*(15*a^3 + 3*a^2*b*x^4 + 2*a*b^2*x^8 - 20*b^3*x^12)) + 15*a^3*Hypergeometric2F1[-1/4, 1/4, 5/4, (b*x^4)/a]))/(280*b^3*(1 - (b*x^4)/a)^(1/4))","C",1
1197,1,96,131,0.0729667,"\int x^8 \sqrt[4]{a-b x^4} \, dx","Integrate[x^8*(a - b*x^4)^(1/4),x]","\frac{x \sqrt[4]{a-b x^4} \left(5 a^2 \, _2F_1\left(-\frac{1}{4},\frac{1}{4};\frac{5}{4};\frac{b x^4}{a}\right)-\sqrt[4]{1-\frac{b x^4}{a}} \left(5 a^2+a b x^4-6 b^2 x^8\right)\right)}{60 b^2 \sqrt[4]{1-\frac{b x^4}{a}}}","-\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{a^2 x \sqrt[4]{a-b x^4}}{24 b^2}+\frac{1}{10} x^9 \sqrt[4]{a-b x^4}-\frac{a x^5 \sqrt[4]{a-b x^4}}{60 b}",1,"(x*(a - b*x^4)^(1/4)*(-((1 - (b*x^4)/a)^(1/4)*(5*a^2 + a*b*x^4 - 6*b^2*x^8)) + 5*a^2*Hypergeometric2F1[-1/4, 1/4, 5/4, (b*x^4)/a]))/(60*b^2*(1 - (b*x^4)/a)^(1/4))","C",1
1198,1,64,106,0.052167,"\int x^4 \sqrt[4]{a-b x^4} \, dx","Integrate[x^4*(a - b*x^4)^(1/4),x]","\frac{x \sqrt[4]{a-b x^4} \left(\frac{a \, _2F_1\left(-\frac{1}{4},\frac{1}{4};\frac{5}{4};\frac{b x^4}{a}\right)}{\sqrt[4]{1-\frac{b x^4}{a}}}-a+b x^4\right)}{6 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{a x \sqrt[4]{a-b x^4}}{12 b}+\frac{1}{6} x^5 \sqrt[4]{a-b x^4}",1,"(x*(a - b*x^4)^(1/4)*(-a + b*x^4 + (a*Hypergeometric2F1[-1/4, 1/4, 5/4, (b*x^4)/a])/(1 - (b*x^4)/a)^(1/4)))/(6*b)","C",1
1199,1,47,83,0.0059654,"\int \sqrt[4]{a-b x^4} \, dx","Integrate[(a - b*x^4)^(1/4),x]","\frac{x \sqrt[4]{a-b x^4} \, _2F_1\left(-\frac{1}{4},\frac{1}{4};\frac{5}{4};\frac{b x^4}{a}\right)}{\sqrt[4]{1-\frac{b x^4}{a}}}","\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)*Hypergeometric2F1[-1/4, 1/4, 5/4, (b*x^4)/a])/(1 - (b*x^4)/a)^(1/4)","C",1
1200,1,52,85,0.0093977,"\int \frac{\sqrt[4]{a-b x^4}}{x^4} \, dx","Integrate[(a - b*x^4)^(1/4)/x^4,x]","-\frac{\sqrt[4]{a-b x^4} \, _2F_1\left(-\frac{3}{4},-\frac{1}{4};\frac{1}{4};\frac{b x^4}{a}\right)}{3 x^3 \sqrt[4]{1-\frac{b x^4}{a}}}","\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,"-1/3*((a - b*x^4)^(1/4)*Hypergeometric2F1[-3/4, -1/4, 1/4, (b*x^4)/a])/(x^3*(1 - (b*x^4)/a)^(1/4))","C",1
1201,1,52,108,0.0101712,"\int \frac{\sqrt[4]{a-b x^4}}{x^8} \, dx","Integrate[(a - b*x^4)^(1/4)/x^8,x]","-\frac{\sqrt[4]{a-b x^4} \, _2F_1\left(-\frac{7}{4},-\frac{1}{4};-\frac{3}{4};\frac{b x^4}{a}\right)}{7 x^7 \sqrt[4]{1-\frac{b x^4}{a}}}","\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{\sqrt[4]{a-b x^4}}{7 x^7}+\frac{b \sqrt[4]{a-b x^4}}{21 a x^3}",1,"-1/7*((a - b*x^4)^(1/4)*Hypergeometric2F1[-7/4, -1/4, -3/4, (b*x^4)/a])/(x^7*(1 - (b*x^4)/a)^(1/4))","C",1
1202,1,52,133,0.011212,"\int \frac{\sqrt[4]{a-b x^4}}{x^{12}} \, dx","Integrate[(a - b*x^4)^(1/4)/x^12,x]","-\frac{\sqrt[4]{a-b x^4} \, _2F_1\left(-\frac{11}{4},-\frac{1}{4};-\frac{7}{4};\frac{b x^4}{a}\right)}{11 x^{11} \sqrt[4]{1-\frac{b x^4}{a}}}","\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{2 b^2 \sqrt[4]{a-b x^4}}{77 a^2 x^3}-\frac{\sqrt[4]{a-b x^4}}{11 x^{11}}+\frac{b \sqrt[4]{a-b x^4}}{77 a x^7}",1,"-1/11*((a - b*x^4)^(1/4)*Hypergeometric2F1[-11/4, -1/4, -7/4, (b*x^4)/a])/(x^11*(1 - (b*x^4)/a)^(1/4))","C",1
1203,1,52,158,0.0095891,"\int \frac{\sqrt[4]{a-b x^4}}{x^{16}} \, dx","Integrate[(a - b*x^4)^(1/4)/x^16,x]","-\frac{\sqrt[4]{a-b x^4} \, _2F_1\left(-\frac{15}{4},-\frac{1}{4};-\frac{11}{4};\frac{b x^4}{a}\right)}{15 x^{15} \sqrt[4]{1-\frac{b x^4}{a}}}","\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{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{\sqrt[4]{a-b x^4}}{15 x^{15}}+\frac{b \sqrt[4]{a-b x^4}}{165 a x^{11}}",1,"-1/15*((a - b*x^4)^(1/4)*Hypergeometric2F1[-15/4, -1/4, -11/4, (b*x^4)/a])/(x^15*(1 - (b*x^4)/a)^(1/4))","C",1
1204,1,62,106,0.0342276,"\int \frac{x^{19}}{\sqrt[4]{a-b x^4}} \, dx","Integrate[x^19/(a - b*x^4)^(1/4),x]","-\frac{\left(a-b x^4\right)^{3/4} \left(2048 a^4+1536 a^3 b x^4+1344 a^2 b^2 x^8+1232 a b^3 x^{12}+1155 b^4 x^{16}\right)}{21945 b^5}","-\frac{a^4 \left(a-b x^4\right)^{3/4}}{3 b^5}+\frac{4 a^3 \left(a-b x^4\right)^{7/4}}{7 b^5}-\frac{6 a^2 \left(a-b x^4\right)^{11/4}}{11 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,"-1/21945*((a - b*x^4)^(3/4)*(2048*a^4 + 1536*a^3*b*x^4 + 1344*a^2*b^2*x^8 + 1232*a*b^3*x^12 + 1155*b^4*x^16))/b^5","A",1
1205,1,51,84,0.026745,"\int \frac{x^{15}}{\sqrt[4]{a-b x^4}} \, dx","Integrate[x^15/(a - b*x^4)^(1/4),x]","-\frac{\left(a-b x^4\right)^{3/4} \left(128 a^3+96 a^2 b x^4+84 a b^2 x^8+77 b^3 x^{12}\right)}{1155 b^4}","-\frac{a^3 \left(a-b x^4\right)^{3/4}}{3 b^4}+\frac{3 a^2 \left(a-b x^4\right)^{7/4}}{7 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,"-1/1155*((a - b*x^4)^(3/4)*(128*a^3 + 96*a^2*b*x^4 + 84*a*b^2*x^8 + 77*b^3*x^12))/b^4","A",1
1206,1,40,62,0.0201999,"\int \frac{x^{11}}{\sqrt[4]{a-b x^4}} \, dx","Integrate[x^11/(a - b*x^4)^(1/4),x]","-\frac{\left(a-b x^4\right)^{3/4} \left(32 a^2+24 a b x^4+21 b^2 x^8\right)}{231 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,"-1/231*((a - b*x^4)^(3/4)*(32*a^2 + 24*a*b*x^4 + 21*b^2*x^8))/b^3","A",1
1207,1,29,40,0.0125751,"\int \frac{x^7}{\sqrt[4]{a-b x^4}} \, dx","Integrate[x^7/(a - b*x^4)^(1/4),x]","-\frac{\left(a-b x^4\right)^{3/4} \left(4 a+3 b x^4\right)}{21 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,"-1/21*((a - b*x^4)^(3/4)*(4*a + 3*b*x^4))/b^2","A",1
1208,1,19,19,0.0042375,"\int \frac{x^3}{\sqrt[4]{a-b x^4}} \, dx","Integrate[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,"-1/3*(a - b*x^4)^(3/4)/b","A",1
1209,1,50,57,0.0094287,"\int \frac{1}{x \sqrt[4]{a-b x^4}} \, dx","Integrate[1/(x*(a - b*x^4)^(1/4)),x]","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a-b x^4}}{\sqrt[4]{a}}\right)-\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)] - ArcTanh[(a - b*x^4)^(1/4)/a^(1/4)])/(2*a^(1/4))","A",1
1210,1,39,81,0.0076933,"\int \frac{1}{x^5 \sqrt[4]{a-b x^4}} \, dx","Integrate[1/(x^5*(a - b*x^4)^(1/4)),x]","-\frac{b \left(a-b x^4\right)^{3/4} \, _2F_1\left(\frac{3}{4},2;\frac{7}{4};1-\frac{b x^4}{a}\right)}{3 a^2}","\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,"-1/3*(b*(a - b*x^4)^(3/4)*Hypergeometric2F1[3/4, 2, 7/4, 1 - (b*x^4)/a])/a^2","C",1
1211,1,41,108,0.0086273,"\int \frac{1}{x^9 \sqrt[4]{a-b x^4}} \, dx","Integrate[1/(x^9*(a - b*x^4)^(1/4)),x]","-\frac{b^2 \left(a-b x^4\right)^{3/4} \, _2F_1\left(\frac{3}{4},3;\frac{7}{4};1-\frac{b x^4}{a}\right)}{3 a^3}","\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,"-1/3*(b^2*(a - b*x^4)^(3/4)*Hypergeometric2F1[3/4, 3, 7/4, 1 - (b*x^4)/a])/a^3","C",1
1212,1,91,133,0.0666304,"\int \frac{x^{13}}{\sqrt[4]{a-b x^4}} \, dx","Integrate[x^13/(a - b*x^4)^(1/4),x]","\frac{x^2 \left(12 a^3 \sqrt[4]{1-\frac{b x^4}{a}} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{3}{2};\frac{b x^4}{a}\right)-12 a^3+2 a^2 b x^4+a b^2 x^8+9 b^3 x^{12}\right)}{117 b^3 \sqrt[4]{a-b x^4}}","\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{4 a^2 x^2 \left(a-b x^4\right)^{3/4}}{39 b^3}-\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,"(x^2*(-12*a^3 + 2*a^2*b*x^4 + a*b^2*x^8 + 9*b^3*x^12 + 12*a^3*(1 - (b*x^4)/a)^(1/4)*Hypergeometric2F1[1/4, 1/2, 3/2, (b*x^4)/a]))/(117*b^3*(a - b*x^4)^(1/4))","C",1
1213,1,80,108,0.0352785,"\int \frac{x^9}{\sqrt[4]{a-b x^4}} \, dx","Integrate[x^9/(a - b*x^4)^(1/4),x]","\frac{x^2 \left(6 a^2 \sqrt[4]{1-\frac{b x^4}{a}} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{3}{2};\frac{b x^4}{a}\right)-6 a^2+a b x^4+5 b^2 x^8\right)}{45 b^2 \sqrt[4]{a-b x^4}}","\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,"(x^2*(-6*a^2 + a*b*x^4 + 5*b^2*x^8 + 6*a^2*(1 - (b*x^4)/a)^(1/4)*Hypergeometric2F1[1/4, 1/2, 3/2, (b*x^4)/a]))/(45*b^2*(a - b*x^4)^(1/4))","C",1
1214,1,66,85,0.0210013,"\int \frac{x^5}{\sqrt[4]{a-b x^4}} \, dx","Integrate[x^5/(a - b*x^4)^(1/4),x]","\frac{x^2 \left(a \sqrt[4]{1-\frac{b x^4}{a}} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{3}{2};\frac{b x^4}{a}\right)-a+b x^4\right)}{5 b \sqrt[4]{a-b x^4}}","\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 + a*(1 - (b*x^4)/a)^(1/4)*Hypergeometric2F1[1/4, 1/2, 3/2, (b*x^4)/a]))/(5*b*(a - b*x^4)^(1/4))","C",1
1215,1,52,59,0.0108936,"\int \frac{x}{\sqrt[4]{a-b x^4}} \, dx","Integrate[x/(a - b*x^4)^(1/4),x]","\frac{x^2 \sqrt[4]{1-\frac{b x^4}{a}} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{3}{2};\frac{b x^4}{a}\right)}{2 \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,"(x^2*(1 - (b*x^4)/a)^(1/4)*Hypergeometric2F1[1/4, 1/2, 3/2, (b*x^4)/a])/(2*(a - b*x^4)^(1/4))","C",1
1216,1,52,85,0.0123802,"\int \frac{1}{x^3 \sqrt[4]{a-b x^4}} \, dx","Integrate[1/(x^3*(a - b*x^4)^(1/4)),x]","-\frac{\sqrt[4]{1-\frac{b x^4}{a}} \, _2F_1\left(-\frac{1}{2},\frac{1}{4};\frac{1}{2};\frac{b x^4}{a}\right)}{2 x^2 \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,"-1/2*((1 - (b*x^4)/a)^(1/4)*Hypergeometric2F1[-1/2, 1/4, 1/2, (b*x^4)/a])/(x^2*(a - b*x^4)^(1/4))","C",1
1217,1,52,108,0.0268092,"\int \frac{1}{x^7 \sqrt[4]{a-b x^4}} \, dx","Integrate[1/(x^7*(a - b*x^4)^(1/4)),x]","-\frac{\sqrt[4]{1-\frac{b x^4}{a}} \, _2F_1\left(-\frac{3}{2},\frac{1}{4};-\frac{1}{2};\frac{b x^4}{a}\right)}{6 x^6 \sqrt[4]{a-b x^4}}","-\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,"-1/6*((1 - (b*x^4)/a)^(1/4)*Hypergeometric2F1[-3/2, 1/4, -1/2, (b*x^4)/a])/(x^6*(a - b*x^4)^(1/4))","C",1
1218,1,52,133,0.0133461,"\int \frac{1}{x^{11} \sqrt[4]{a-b x^4}} \, dx","Integrate[1/(x^11*(a - b*x^4)^(1/4)),x]","-\frac{\sqrt[4]{1-\frac{b x^4}{a}} \, _2F_1\left(-\frac{5}{2},\frac{1}{4};-\frac{3}{2};\frac{b x^4}{a}\right)}{10 x^{10} \sqrt[4]{a-b x^4}}","-\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^2 \left(a-b x^4\right)^{3/4}}{40 a^3 x^2}-\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,"-1/10*((1 - (b*x^4)/a)^(1/4)*Hypergeometric2F1[-5/2, 1/4, -3/2, (b*x^4)/a])/(x^10*(a - b*x^4)^(1/4))","C",1
1219,1,245,264,0.1774316,"\int \frac{x^8}{\sqrt[4]{a-b x^4}} \, dx","Integrate[x^8/(a - b*x^4)^(1/4),x]","-\frac{10 \sqrt{2} a^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}\right)-10 \sqrt{2} a^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)+5 \sqrt{2} a^2 \log \left(-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}+1\right)-5 \sqrt{2} a^2 \log \left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}+1\right)+32 b^{5/4} x^5 \left(a-b x^4\right)^{3/4}+40 a \sqrt[4]{b} x \left(a-b x^4\right)^{3/4}}{256 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^2 \log \left(-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}+1\right)}{128 \sqrt{2} b^{9/4}}+\frac{5 a^2 \log \left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}+1\right)}{128 \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,"-1/256*(40*a*b^(1/4)*x*(a - b*x^4)^(3/4) + 32*b^(5/4)*x^5*(a - b*x^4)^(3/4) + 10*Sqrt[2]*a^2*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/(a - b*x^4)^(1/4)] - 10*Sqrt[2]*a^2*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/(a - b*x^4)^(1/4)] + 5*Sqrt[2]*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)] - 5*Sqrt[2]*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)])/b^(9/4)","A",1
1220,1,213,233,0.0854177,"\int \frac{x^4}{\sqrt[4]{a-b x^4}} \, dx","Integrate[x^4/(a - b*x^4)^(1/4),x]","-\frac{8 \sqrt[4]{b} x \left(a-b x^4\right)^{3/4}+2 \sqrt{2} a \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}\right)-2 \sqrt{2} a \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)+\sqrt{2} a \log \left(-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}+1\right)-\sqrt{2} a \log \left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}+1\right)}{32 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{a \log \left(-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}+1\right)}{16 \sqrt{2} b^{5/4}}+\frac{a \log \left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}+1\right)}{16 \sqrt{2} b^{5/4}}-\frac{x \left(a-b x^4\right)^{3/4}}{4 b}",1,"-1/32*(8*b^(1/4)*x*(a - b*x^4)^(3/4) + 2*Sqrt[2]*a*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/(a - b*x^4)^(1/4)] - 2*Sqrt[2]*a*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/(a - b*x^4)^(1/4)] + Sqrt[2]*a*Log[1 + (Sqrt[b]*x^2)/Sqrt[a - b*x^4] - (Sqrt[2]*b^(1/4)*x)/(a - b*x^4)^(1/4)] - Sqrt[2]*a*Log[1 + (Sqrt[b]*x^2)/Sqrt[a - b*x^4] + (Sqrt[2]*b^(1/4)*x)/(a - b*x^4)^(1/4)])/b^(5/4)","A",1
1221,1,173,209,0.0346822,"\int \frac{1}{\sqrt[4]{a-b x^4}} \, dx","Integrate[(a - b*x^4)^(-1/4),x]","\frac{-2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}\right)+2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+1\right)-\log \left(-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}+1\right)+\log \left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+\frac{\sqrt{b} x^2}{\sqrt{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{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}+1\right)}{4 \sqrt{2} \sqrt[4]{b}}+\frac{\log \left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}+1\right)}{4 \sqrt{2} \sqrt[4]{b}}",1,"(-2*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/(a - b*x^4)^(1/4)] + 2*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/(a - b*x^4)^(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)] + 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",1
1222,1,22,22,0.0043134,"\int \frac{1}{x^4 \sqrt[4]{a-b x^4}} \, dx","Integrate[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,"-1/3*(a - b*x^4)^(3/4)/(a*x^3)","A",1
1223,1,32,46,0.0202177,"\int \frac{1}{x^8 \sqrt[4]{a-b x^4}} \, dx","Integrate[1/(x^8*(a - b*x^4)^(1/4)),x]","-\frac{\left(a-b x^4\right)^{3/4} \left(3 a+4 b x^4\right)}{21 a^2 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,"-1/21*((a - b*x^4)^(3/4)*(3*a + 4*b*x^4))/(a^2*x^7)","A",1
1224,1,43,71,0.0401957,"\int \frac{1}{x^{12} \sqrt[4]{a-b x^4}} \, dx","Integrate[1/(x^12*(a - b*x^4)^(1/4)),x]","-\frac{\left(a-b x^4\right)^{3/4} \left(21 a^2+24 a b x^4+32 b^2 x^8\right)}{231 a^3 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,"-1/231*((a - b*x^4)^(3/4)*(21*a^2 + 24*a*b*x^4 + 32*b^2*x^8))/(a^3*x^11)","A",1
1225,1,54,96,0.0204086,"\int \frac{1}{x^{16} \sqrt[4]{a-b x^4}} \, dx","Integrate[1/(x^16*(a - b*x^4)^(1/4)),x]","-\frac{\left(a-b x^4\right)^{3/4} \left(77 a^3+84 a^2 b x^4+96 a b^2 x^8+128 b^3 x^{12}\right)}{1155 a^4 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,"-1/1155*((a - b*x^4)^(3/4)*(77*a^3 + 84*a^2*b*x^4 + 96*a*b^2*x^8 + 128*b^3*x^12))/(a^4*x^15)","A",1
1226,1,65,121,0.0251953,"\int \frac{1}{x^{20} \sqrt[4]{a-b x^4}} \, dx","Integrate[1/(x^20*(a - b*x^4)^(1/4)),x]","-\frac{\left(a-b x^4\right)^{3/4} \left(1155 a^4+1232 a^3 b x^4+1344 a^2 b^2 x^8+1536 a b^3 x^{12}+2048 b^4 x^{16}\right)}{21945 a^5 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,"-1/21945*((a - b*x^4)^(3/4)*(1155*a^4 + 1232*a^3*b*x^4 + 1344*a^2*b^2*x^8 + 1536*a*b^3*x^12 + 2048*b^4*x^16))/(a^5*x^19)","A",1
1227,1,80,134,0.0302418,"\int \frac{x^{10}}{\sqrt[4]{a-b x^4}} \, dx","Integrate[x^10/(a - b*x^4)^(1/4),x]","\frac{x^3 \left(7 a^2 \sqrt[4]{1-\frac{b x^4}{a}} \, _2F_1\left(\frac{1}{4},\frac{3}{4};\frac{7}{4};\frac{b x^4}{a}\right)-7 a^2+a b x^4+6 b^2 x^8\right)}{60 b^2 \sqrt[4]{a-b x^4}}","\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^2 \left(a-b x^4\right)^{3/4}}{40 b^3 x}-\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,"(x^3*(-7*a^2 + a*b*x^4 + 6*b^2*x^8 + 7*a^2*(1 - (b*x^4)/a)^(1/4)*Hypergeometric2F1[1/4, 3/4, 7/4, (b*x^4)/a]))/(60*b^2*(a - b*x^4)^(1/4))","C",1
1228,1,66,109,0.0198508,"\int \frac{x^6}{\sqrt[4]{a-b x^4}} \, dx","Integrate[x^6/(a - b*x^4)^(1/4),x]","\frac{x^3 \left(a \sqrt[4]{1-\frac{b x^4}{a}} \, _2F_1\left(\frac{1}{4},\frac{3}{4};\frac{7}{4};\frac{b x^4}{a}\right)-a+b x^4\right)}{6 b \sqrt[4]{a-b x^4}}","\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,"(x^3*(-a + b*x^4 + a*(1 - (b*x^4)/a)^(1/4)*Hypergeometric2F1[1/4, 3/4, 7/4, (b*x^4)/a]))/(6*b*(a - b*x^4)^(1/4))","C",1
1229,1,52,86,0.0699609,"\int \frac{x^2}{\sqrt[4]{a-b x^4}} \, dx","Integrate[x^2/(a - b*x^4)^(1/4),x]","\frac{x^3 \sqrt[4]{1-\frac{b x^4}{a}} \, _2F_1\left(\frac{1}{4},\frac{3}{4};\frac{7}{4};\frac{b x^4}{a}\right)}{3 \sqrt[4]{a-b x^4}}","\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,"(x^3*(1 - (b*x^4)/a)^(1/4)*Hypergeometric2F1[1/4, 3/4, 7/4, (b*x^4)/a])/(3*(a - b*x^4)^(1/4))","C",1
1230,1,50,61,0.009794,"\int \frac{1}{x^2 \sqrt[4]{a-b x^4}} \, dx","Integrate[1/(x^2*(a - b*x^4)^(1/4)),x]","-\frac{\sqrt[4]{1-\frac{b x^4}{a}} \, _2F_1\left(-\frac{1}{4},\frac{1}{4};\frac{3}{4};\frac{b x^4}{a}\right)}{x \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,"-(((1 - (b*x^4)/a)^(1/4)*Hypergeometric2F1[-1/4, 1/4, 3/4, (b*x^4)/a])/(x*(a - b*x^4)^(1/4)))","C",1
1231,1,52,86,0.0105039,"\int \frac{1}{x^6 \sqrt[4]{a-b x^4}} \, dx","Integrate[1/(x^6*(a - b*x^4)^(1/4)),x]","-\frac{\sqrt[4]{1-\frac{b x^4}{a}} \, _2F_1\left(-\frac{5}{4},\frac{1}{4};-\frac{1}{4};\frac{b x^4}{a}\right)}{5 x^5 \sqrt[4]{a-b x^4}}","-\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,"-1/5*((1 - (b*x^4)/a)^(1/4)*Hypergeometric2F1[-5/4, 1/4, -1/4, (b*x^4)/a])/(x^5*(a - b*x^4)^(1/4))","C",1
1232,1,52,109,0.0132966,"\int \frac{1}{x^{10} \sqrt[4]{a-b x^4}} \, dx","Integrate[1/(x^10*(a - b*x^4)^(1/4)),x]","-\frac{\sqrt[4]{1-\frac{b x^4}{a}} \, _2F_1\left(-\frac{9}{4},\frac{1}{4};-\frac{5}{4};\frac{b x^4}{a}\right)}{9 x^9 \sqrt[4]{a-b x^4}}","-\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,"-1/9*((1 - (b*x^4)/a)^(1/4)*Hypergeometric2F1[-9/4, 1/4, -5/4, (b*x^4)/a])/(x^9*(a - b*x^4)^(1/4))","C",1
1233,1,52,134,0.0096816,"\int \frac{1}{x^{14} \sqrt[4]{a-b x^4}} \, dx","Integrate[1/(x^14*(a - b*x^4)^(1/4)),x]","-\frac{\sqrt[4]{1-\frac{b x^4}{a}} \, _2F_1\left(-\frac{13}{4},\frac{1}{4};-\frac{9}{4};\frac{b x^4}{a}\right)}{13 x^{13} \sqrt[4]{a-b x^4}}","-\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{4 b^2 \left(a-b x^4\right)^{3/4}}{39 a^3 x^5}-\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,"-1/13*((1 - (b*x^4)/a)^(1/4)*Hypergeometric2F1[-13/4, 1/4, -9/4, (b*x^4)/a])/(x^13*(a - b*x^4)^(1/4))","C",1
1234,1,62,104,0.0323266,"\int \frac{x^{19}}{\left(a-b x^4\right)^{3/4}} \, dx","Integrate[x^19/(a - b*x^4)^(3/4),x]","-\frac{\sqrt[4]{a-b x^4} \left(2048 a^4+512 a^3 b x^4+320 a^2 b^2 x^8+240 a b^3 x^{12}+195 b^4 x^{16}\right)}{3315 b^5}","-\frac{a^4 \sqrt[4]{a-b x^4}}{b^5}+\frac{4 a^3 \left(a-b x^4\right)^{5/4}}{5 b^5}-\frac{2 a^2 \left(a-b x^4\right)^{9/4}}{3 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,"-1/3315*((a - b*x^4)^(1/4)*(2048*a^4 + 512*a^3*b*x^4 + 320*a^2*b^2*x^8 + 240*a*b^3*x^12 + 195*b^4*x^16))/b^5","A",1
1235,1,51,82,0.0432295,"\int \frac{x^{15}}{\left(a-b x^4\right)^{3/4}} \, dx","Integrate[x^15/(a - b*x^4)^(3/4),x]","-\frac{\sqrt[4]{a-b x^4} \left(128 a^3+32 a^2 b x^4+20 a b^2 x^8+15 b^3 x^{12}\right)}{195 b^4}","-\frac{a^3 \sqrt[4]{a-b x^4}}{b^4}+\frac{3 a^2 \left(a-b x^4\right)^{5/4}}{5 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,"-1/195*((a - b*x^4)^(1/4)*(128*a^3 + 32*a^2*b*x^4 + 20*a*b^2*x^8 + 15*b^3*x^12))/b^4","A",1
1236,1,40,60,0.0192453,"\int \frac{x^{11}}{\left(a-b x^4\right)^{3/4}} \, dx","Integrate[x^11/(a - b*x^4)^(3/4),x]","-\frac{\sqrt[4]{a-b x^4} \left(32 a^2+8 a b x^4+5 b^2 x^8\right)}{45 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,"-1/45*((a - b*x^4)^(1/4)*(32*a^2 + 8*a*b*x^4 + 5*b^2*x^8))/b^3","A",1
1237,1,28,38,0.0142158,"\int \frac{x^7}{\left(a-b x^4\right)^{3/4}} \, dx","Integrate[x^7/(a - b*x^4)^(3/4),x]","-\frac{\sqrt[4]{a-b x^4} \left(4 a+b x^4\right)}{5 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,"-1/5*((a - b*x^4)^(1/4)*(4*a + b*x^4))/b^2","A",1
1238,1,17,17,0.0042145,"\int \frac{x^3}{\left(a-b x^4\right)^{3/4}} \, dx","Integrate[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
1239,1,48,57,0.009354,"\int \frac{1}{x \left(a-b x^4\right)^{3/4}} \, dx","Integrate[1/(x*(a - b*x^4)^(3/4)),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a-b x^4}}{\sqrt[4]{a}}\right)+\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,"-1/2*(ArcTan[(a - b*x^4)^(1/4)/a^(1/4)] + ArcTanh[(a - b*x^4)^(1/4)/a^(1/4)])/a^(3/4)","A",1
1240,1,37,81,0.0075574,"\int \frac{1}{x^5 \left(a-b x^4\right)^{3/4}} \, dx","Integrate[1/(x^5*(a - b*x^4)^(3/4)),x]","-\frac{b \sqrt[4]{a-b x^4} \, _2F_1\left(\frac{1}{4},2;\frac{5}{4};1-\frac{b x^4}{a}\right)}{a^2}","-\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,"-((b*(a - b*x^4)^(1/4)*Hypergeometric2F1[1/4, 2, 5/4, 1 - (b*x^4)/a])/a^2)","C",1
1241,1,39,108,0.0174592,"\int \frac{1}{x^9 \left(a-b x^4\right)^{3/4}} \, dx","Integrate[1/(x^9*(a - b*x^4)^(3/4)),x]","-\frac{b^2 \sqrt[4]{a-b x^4} \, _2F_1\left(\frac{1}{4},3;\frac{5}{4};1-\frac{b x^4}{a}\right)}{a^3}","-\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,"-((b^2*(a - b*x^4)^(1/4)*Hypergeometric2F1[1/4, 3, 5/4, 1 - (b*x^4)/a])/a^3)","C",1
1242,1,92,133,0.0367777,"\int \frac{x^{13}}{\left(a-b x^4\right)^{3/4}} \, dx","Integrate[x^13/(a - b*x^4)^(3/4),x]","\frac{x^2 \left(20 a^3 \left(1-\frac{b x^4}{a}\right)^{3/4} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{3}{2};\frac{b x^4}{a}\right)-20 a^3+10 a^2 b x^4+3 a b^2 x^8+7 b^3 x^{12}\right)}{77 b^3 \left(a-b x^4\right)^{3/4}}","\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{20 a^2 x^2 \sqrt[4]{a-b x^4}}{77 b^3}-\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,"(x^2*(-20*a^3 + 10*a^2*b*x^4 + 3*a*b^2*x^8 + 7*b^3*x^12 + 20*a^3*(1 - (b*x^4)/a)^(3/4)*Hypergeometric2F1[1/2, 3/4, 3/2, (b*x^4)/a]))/(77*b^3*(a - b*x^4)^(3/4))","C",1
1243,1,79,108,0.0323426,"\int \frac{x^9}{\left(a-b x^4\right)^{3/4}} \, dx","Integrate[x^9/(a - b*x^4)^(3/4),x]","\frac{x^2 \left(2 a^2 \left(1-\frac{b x^4}{a}\right)^{3/4} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{3}{2};\frac{b x^4}{a}\right)-2 a^2+a b x^4+b^2 x^8\right)}{7 b^2 \left(a-b x^4\right)^{3/4}}","\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,"(x^2*(-2*a^2 + a*b*x^4 + b^2*x^8 + 2*a^2*(1 - (b*x^4)/a)^(3/4)*Hypergeometric2F1[1/2, 3/4, 3/2, (b*x^4)/a]))/(7*b^2*(a - b*x^4)^(3/4))","C",1
1244,1,66,85,0.0212583,"\int \frac{x^5}{\left(a-b x^4\right)^{3/4}} \, dx","Integrate[x^5/(a - b*x^4)^(3/4),x]","\frac{x^2 \left(a \left(1-\frac{b x^4}{a}\right)^{3/4} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{3}{2};\frac{b x^4}{a}\right)-a+b x^4\right)}{3 b \left(a-b x^4\right)^{3/4}}","\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 + a*(1 - (b*x^4)/a)^(3/4)*Hypergeometric2F1[1/2, 3/4, 3/2, (b*x^4)/a]))/(3*b*(a - b*x^4)^(3/4))","C",1
1245,1,52,59,0.0114334,"\int \frac{x}{\left(a-b x^4\right)^{3/4}} \, dx","Integrate[x/(a - b*x^4)^(3/4),x]","\frac{x^2 \left(1-\frac{b x^4}{a}\right)^{3/4} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{3}{2};\frac{b x^4}{a}\right)}{2 \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,"(x^2*(1 - (b*x^4)/a)^(3/4)*Hypergeometric2F1[1/2, 3/4, 3/2, (b*x^4)/a])/(2*(a - b*x^4)^(3/4))","C",1
1246,1,52,85,0.0122029,"\int \frac{1}{x^3 \left(a-b x^4\right)^{3/4}} \, dx","Integrate[1/(x^3*(a - b*x^4)^(3/4)),x]","-\frac{\left(1-\frac{b x^4}{a}\right)^{3/4} \, _2F_1\left(-\frac{1}{2},\frac{3}{4};\frac{1}{2};\frac{b x^4}{a}\right)}{2 x^2 \left(a-b x^4\right)^{3/4}}","\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,"-1/2*((1 - (b*x^4)/a)^(3/4)*Hypergeometric2F1[-1/2, 3/4, 1/2, (b*x^4)/a])/(x^2*(a - b*x^4)^(3/4))","C",1
1247,1,52,108,0.0126651,"\int \frac{1}{x^7 \left(a-b x^4\right)^{3/4}} \, dx","Integrate[1/(x^7*(a - b*x^4)^(3/4)),x]","-\frac{\left(1-\frac{b x^4}{a}\right)^{3/4} \, _2F_1\left(-\frac{3}{2},\frac{3}{4};-\frac{1}{2};\frac{b x^4}{a}\right)}{6 x^6 \left(a-b x^4\right)^{3/4}}","\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,"-1/6*((1 - (b*x^4)/a)^(3/4)*Hypergeometric2F1[-3/2, 3/4, -1/2, (b*x^4)/a])/(x^6*(a - b*x^4)^(3/4))","C",1
1248,1,52,133,0.0122528,"\int \frac{1}{x^{11} \left(a-b x^4\right)^{3/4}} \, dx","Integrate[1/(x^11*(a - b*x^4)^(3/4)),x]","-\frac{\left(1-\frac{b x^4}{a}\right)^{3/4} \, _2F_1\left(-\frac{5}{2},\frac{3}{4};-\frac{3}{2};\frac{b x^4}{a}\right)}{10 x^{10} \left(a-b x^4\right)^{3/4}}","\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^2 \sqrt[4]{a-b x^4}}{8 a^3 x^2}-\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,"-1/10*((1 - (b*x^4)/a)^(3/4)*Hypergeometric2F1[-5/2, 3/4, -3/2, (b*x^4)/a])/(x^10*(a - b*x^4)^(3/4))","C",1
1249,1,104,266,0.0514489,"\int \frac{x^{10}}{\left(a-b x^4\right)^{3/4}} \, dx","Integrate[x^10/(a - b*x^4)^(3/4),x]","\frac{21 a^2 \sqrt[4]{-b} \tan ^{-1}\left(\frac{\sqrt[4]{-b} x}{\sqrt[4]{a-b x^4}}\right)-21 a^2 \sqrt[4]{-b} \tanh ^{-1}\left(\frac{\sqrt[4]{-b} x}{\sqrt[4]{a-b x^4}}\right)-2 b x^3 \sqrt[4]{a-b x^4} \left(7 a+4 b x^4\right)}{64 b^3}","-\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{21 a^2 \log \left(-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}+1\right)}{128 \sqrt{2} b^{11/4}}-\frac{21 a^2 \log \left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}+1\right)}{128 \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,"(-2*b*x^3*(a - b*x^4)^(1/4)*(7*a + 4*b*x^4) + 21*a^2*(-b)^(1/4)*ArcTan[((-b)^(1/4)*x)/(a - b*x^4)^(1/4)] - 21*a^2*(-b)^(1/4)*ArcTanh[((-b)^(1/4)*x)/(a - b*x^4)^(1/4)])/(64*b^3)","A",1
1250,1,90,235,0.034113,"\int \frac{x^6}{\left(a-b x^4\right)^{3/4}} \, dx","Integrate[x^6/(a - b*x^4)^(3/4),x]","-\frac{-3 a \sqrt[4]{-b} \tan ^{-1}\left(\frac{\sqrt[4]{-b} x}{\sqrt[4]{a-b x^4}}\right)+3 a \sqrt[4]{-b} \tanh ^{-1}\left(\frac{\sqrt[4]{-b} x}{\sqrt[4]{a-b x^4}}\right)+2 b x^3 \sqrt[4]{a-b x^4}}{8 b^2}","-\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{3 a \log \left(-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}+1\right)}{16 \sqrt{2} b^{7/4}}-\frac{3 a \log \left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}+1\right)}{16 \sqrt{2} b^{7/4}}-\frac{x^3 \sqrt[4]{a-b x^4}}{4 b}",1,"-1/8*(2*b*x^3*(a - b*x^4)^(1/4) - 3*a*(-b)^(1/4)*ArcTan[((-b)^(1/4)*x)/(a - b*x^4)^(1/4)] + 3*a*(-b)^(1/4)*ArcTanh[((-b)^(1/4)*x)/(a - b*x^4)^(1/4)])/b^2","A",1
1251,1,58,209,0.0267212,"\int \frac{x^2}{\left(a-b x^4\right)^{3/4}} \, dx","Integrate[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)-\tan ^{-1}\left(\frac{\sqrt[4]{-b} x}{\sqrt[4]{a-b x^4}}\right)}{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{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}+1\right)}{4 \sqrt{2} b^{3/4}}-\frac{\log \left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a-b x^4}}+\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}+1\right)}{4 \sqrt{2} b^{3/4}}",1,"(-ArcTan[((-b)^(1/4)*x)/(a - b*x^4)^(1/4)] + ArcTanh[((-b)^(1/4)*x)/(a - b*x^4)^(1/4)])/(2*(-b)^(3/4))","A",1
1252,1,20,20,0.006153,"\int \frac{1}{x^2 \left(a-b x^4\right)^{3/4}} \, dx","Integrate[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
1253,1,30,46,0.0127468,"\int \frac{1}{x^6 \left(a-b x^4\right)^{3/4}} \, dx","Integrate[1/(x^6*(a - b*x^4)^(3/4)),x]","-\frac{\sqrt[4]{a-b x^4} \left(a+4 b x^4\right)}{5 a^2 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,"-1/5*((a - b*x^4)^(1/4)*(a + 4*b*x^4))/(a^2*x^5)","A",1
1254,1,43,71,0.0157785,"\int \frac{1}{x^{10} \left(a-b x^4\right)^{3/4}} \, dx","Integrate[1/(x^10*(a - b*x^4)^(3/4)),x]","-\frac{\sqrt[4]{a-b x^4} \left(5 a^2+8 a b x^4+32 b^2 x^8\right)}{45 a^3 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,"-1/45*((a - b*x^4)^(1/4)*(5*a^2 + 8*a*b*x^4 + 32*b^2*x^8))/(a^3*x^9)","A",1
1255,1,54,96,0.0322755,"\int \frac{1}{x^{14} \left(a-b x^4\right)^{3/4}} \, dx","Integrate[1/(x^14*(a - b*x^4)^(3/4)),x]","-\frac{\sqrt[4]{a-b x^4} \left(15 a^3+20 a^2 b x^4+32 a b^2 x^8+128 b^3 x^{12}\right)}{195 a^4 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,"-1/195*((a - b*x^4)^(1/4)*(15*a^3 + 20*a^2*b*x^4 + 32*a*b^2*x^8 + 128*b^3*x^12))/(a^4*x^13)","A",1
1256,1,91,134,0.0276413,"\int \frac{x^{12}}{\left(a-b x^4\right)^{3/4}} \, dx","Integrate[x^12/(a - b*x^4)^(3/4),x]","\frac{15 a^3 x \left(1-\frac{b x^4}{a}\right)^{3/4} \, _2F_1\left(\frac{1}{4},\frac{3}{4};\frac{5}{4};\frac{b x^4}{a}\right)-15 a^3 x+9 a^2 b x^5+2 a b^2 x^9+4 b^3 x^{13}}{40 b^3 \left(a-b x^4\right)^{3/4}}","-\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^2 x \sqrt[4]{a-b x^4}}{8 b^3}-\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,"(-15*a^3*x + 9*a^2*b*x^5 + 2*a*b^2*x^9 + 4*b^3*x^13 + 15*a^3*x*(1 - (b*x^4)/a)^(3/4)*Hypergeometric2F1[1/4, 3/4, 5/4, (b*x^4)/a])/(40*b^3*(a - b*x^4)^(3/4))","C",1
1257,1,80,109,0.0216457,"\int \frac{x^8}{\left(a-b x^4\right)^{3/4}} \, dx","Integrate[x^8/(a - b*x^4)^(3/4),x]","\frac{5 a^2 x \left(1-\frac{b x^4}{a}\right)^{3/4} \, _2F_1\left(\frac{1}{4},\frac{3}{4};\frac{5}{4};\frac{b x^4}{a}\right)-5 a^2 x+3 a b x^5+2 b^2 x^9}{12 b^2 \left(a-b x^4\right)^{3/4}}","-\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^2*x + 3*a*b*x^5 + 2*b^2*x^9 + 5*a^2*x*(1 - (b*x^4)/a)^(3/4)*Hypergeometric2F1[1/4, 3/4, 5/4, (b*x^4)/a])/(12*b^2*(a - b*x^4)^(3/4))","C",1
1258,1,64,86,0.0305191,"\int \frac{x^4}{\left(a-b x^4\right)^{3/4}} \, dx","Integrate[x^4/(a - b*x^4)^(3/4),x]","\frac{x \left(a \left(1-\frac{b x^4}{a}\right)^{3/4} \, _2F_1\left(\frac{1}{4},\frac{3}{4};\frac{5}{4};\frac{b x^4}{a}\right)-a+b x^4\right)}{2 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 + a*(1 - (b*x^4)/a)^(3/4)*Hypergeometric2F1[1/4, 3/4, 5/4, (b*x^4)/a]))/(2*b*(a - b*x^4)^(3/4))","C",1
1259,1,47,63,0.0074418,"\int \frac{1}{\left(a-b x^4\right)^{3/4}} \, dx","Integrate[(a - b*x^4)^(-3/4),x]","\frac{x \left(1-\frac{b x^4}{a}\right)^{3/4} \, _2F_1\left(\frac{1}{4},\frac{3}{4};\frac{5}{4};\frac{b x^4}{a}\right)}{\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,"(x*(1 - (b*x^4)/a)^(3/4)*Hypergeometric2F1[1/4, 3/4, 5/4, (b*x^4)/a])/(a - b*x^4)^(3/4)","C",1
1260,1,52,88,0.0108647,"\int \frac{1}{x^4 \left(a-b x^4\right)^{3/4}} \, dx","Integrate[1/(x^4*(a - b*x^4)^(3/4)),x]","-\frac{\left(1-\frac{b x^4}{a}\right)^{3/4} \, _2F_1\left(-\frac{3}{4},\frac{3}{4};\frac{1}{4};\frac{b x^4}{a}\right)}{3 x^3 \left(a-b x^4\right)^{3/4}}","-\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,"-1/3*((1 - (b*x^4)/a)^(3/4)*Hypergeometric2F1[-3/4, 3/4, 1/4, (b*x^4)/a])/(x^3*(a - b*x^4)^(3/4))","C",1
1261,1,52,111,0.0113219,"\int \frac{1}{x^8 \left(a-b x^4\right)^{3/4}} \, dx","Integrate[1/(x^8*(a - b*x^4)^(3/4)),x]","-\frac{\left(1-\frac{b x^4}{a}\right)^{3/4} \, _2F_1\left(-\frac{7}{4},\frac{3}{4};-\frac{3}{4};\frac{b x^4}{a}\right)}{7 x^7 \left(a-b x^4\right)^{3/4}}","-\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,"-1/7*((1 - (b*x^4)/a)^(3/4)*Hypergeometric2F1[-7/4, 3/4, -3/4, (b*x^4)/a])/(x^7*(a - b*x^4)^(3/4))","C",1
1262,1,52,136,0.0110679,"\int \frac{1}{x^{12} \left(a-b x^4\right)^{3/4}} \, dx","Integrate[1/(x^12*(a - b*x^4)^(3/4)),x]","-\frac{\left(1-\frac{b x^4}{a}\right)^{3/4} \, _2F_1\left(-\frac{11}{4},\frac{3}{4};-\frac{7}{4};\frac{b x^4}{a}\right)}{11 x^{11} \left(a-b x^4\right)^{3/4}}","-\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{20 b^2 \sqrt[4]{a-b x^4}}{77 a^3 x^3}-\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,"-1/11*((1 - (b*x^4)/a)^(3/4)*Hypergeometric2F1[-11/4, 3/4, -7/4, (b*x^4)/a])/(x^11*(a - b*x^4)^(3/4))","C",1
1263,1,55,81,0.0409289,"\int \frac{x^2}{\left(a-b x^4\right)^{5/4}} \, dx","Integrate[x^2/(a - b*x^4)^(5/4),x]","\frac{x^3 \sqrt[4]{1-\frac{b x^4}{a}} \, _2F_1\left(\frac{3}{4},\frac{5}{4};\frac{7}{4};\frac{b x^4}{a}\right)}{3 a \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,"(x^3*(1 - (b*x^4)/a)^(1/4)*Hypergeometric2F1[3/4, 5/4, 7/4, (b*x^4)/a])/(3*a*(a - b*x^4)^(1/4))","C",1
1264,1,40,48,0.0213306,"\int x^7 \left(a+b x^4\right)^p \, dx","Integrate[x^7*(a + b*x^4)^p,x]","\frac{\left(a+b x^4\right)^{p+1} \left(b (p+1) x^4-a\right)}{4 b^2 (p+1) (p+2)}","\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 + b*x^4)^(1 + p)*(-a + b*(1 + p)*x^4))/(4*b^2*(1 + p)*(2 + p))","A",1
1265,1,23,23,0.0050054,"\int x^3 \left(a+b x^4\right)^p \, dx","Integrate[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
1266,1,41,41,0.0203706,"\int \frac{\left(a+b x^4\right)^p}{x} \, dx","Integrate[(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,"-1/4*((a + b*x^4)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, 1 + (b*x^4)/a])/(a*(1 + p))","A",1
1267,1,66,66,0.007585,"\int \frac{x^{24}}{a+b x^5} \, dx","Integrate[x^24/(a + b*x^5),x]","\frac{a^4 \log \left(a+b x^5\right)}{5 b^5}-\frac{a^3 x^5}{5 b^4}+\frac{a^2 x^{10}}{10 b^3}-\frac{a x^{15}}{15 b^2}+\frac{x^{20}}{20 b}","\frac{a^4 \log \left(a+b x^5\right)}{5 b^5}-\frac{a^3 x^5}{5 b^4}+\frac{a^2 x^{10}}{10 b^3}-\frac{a x^{15}}{15 b^2}+\frac{x^{20}}{20 b}",1,"-1/5*(a^3*x^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",1
1268,1,53,53,0.0057523,"\int \frac{x^{19}}{a+b x^5} \, dx","Integrate[x^19/(a + b*x^5),x]","-\frac{a^3 \log \left(a+b x^5\right)}{5 b^4}+\frac{a^2 x^5}{5 b^3}-\frac{a x^{10}}{10 b^2}+\frac{x^{15}}{15 b}","-\frac{a^3 \log \left(a+b x^5\right)}{5 b^4}+\frac{a^2 x^5}{5 b^3}-\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",1
1269,1,40,40,0.0060863,"\int \frac{x^{14}}{a+b x^5} \, dx","Integrate[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,"-1/5*(a*x^5)/b^2 + x^10/(10*b) + (a^2*Log[a + b*x^5])/(5*b^3)","A",1
1270,1,27,27,0.0046082,"\int \frac{x^9}{a+b x^5} \, dx","Integrate[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",1
1271,1,15,15,0.0028738,"\int \frac{x^4}{a+b x^5} \, dx","Integrate[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
1272,1,22,22,0.0053481,"\int \frac{1}{x \left(a+b x^5\right)} \, dx","Integrate[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",1
1273,1,35,35,0.0065296,"\int \frac{1}{x^6 \left(a+b x^5\right)} \, dx","Integrate[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*1/(a*x^5) - (b*Log[x])/a^2 + (b*Log[a + b*x^5])/(5*a^2)","A",1
1274,1,49,49,0.0068947,"\int \frac{1}{x^{11} \left(a+b x^5\right)} \, dx","Integrate[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*1/(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",1
1275,1,63,63,0.0073393,"\int \frac{1}{x^{16} \left(a+b x^5\right)} \, dx","Integrate[1/(x^16*(a + b*x^5)),x]","\frac{b^3 \log \left(a+b x^5\right)}{5 a^4}-\frac{b^3 \log (x)}{a^4}-\frac{b^2}{5 a^3 x^5}+\frac{b}{10 a^2 x^{10}}-\frac{1}{15 a x^{15}}","\frac{b^3 \log \left(a+b x^5\right)}{5 a^4}-\frac{b^3 \log (x)}{a^4}-\frac{b^2}{5 a^3 x^5}+\frac{b}{10 a^2 x^{10}}-\frac{1}{15 a x^{15}}",1,"-1/15*1/(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",1
1276,1,311,301,0.2282051,"\int \frac{1}{a+b x^5} \, dx","Integrate[(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{2 \sqrt{\frac{5}{8}+\frac{\sqrt{5}}{8}} \tan ^{-1}\left(\frac{\sqrt[5]{b} x-\frac{1}{4} \left(1-\sqrt{5}\right) \sqrt[5]{a}}{\sqrt{\frac{5}{8}+\frac{\sqrt{5}}{8}} \sqrt[5]{a}}\right)}{5 a^{4/5} \sqrt[5]{b}}+\frac{2 \sqrt{\frac{5}{8}-\frac{\sqrt{5}}{8}} \tan ^{-1}\left(\frac{\sqrt[5]{b} x-\frac{1}{4} \left(1+\sqrt{5}\right) \sqrt[5]{a}}{\sqrt{\frac{5}{8}-\frac{\sqrt{5}}{8}} \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,"(2*Sqrt[5/8 + Sqrt[5]/8]*ArcTan[(-1/4*((1 - Sqrt[5])*a^(1/5)) + b^(1/5)*x)/(Sqrt[5/8 + Sqrt[5]/8]*a^(1/5))])/(5*a^(4/5)*b^(1/5)) + (2*Sqrt[5/8 - Sqrt[5]/8]*ArcTan[(-1/4*((1 + Sqrt[5])*a^(1/5)) + b^(1/5)*x)/(Sqrt[5/8 - Sqrt[5]/8]*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",1
1277,1,60,72,0.0280422,"\int \frac{x^{24}}{\left(a+b x^5\right)^2} \, dx","Integrate[x^24/(a + b*x^5)^2,x]","\frac{-\frac{3 a^4}{a+b x^5}-12 a^3 \log \left(a+b x^5\right)+9 a^2 b x^5-3 a b^2 x^{10}+b^3 x^{15}}{15 b^5}","-\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{3 a^2 x^5}{5 b^4}-\frac{a x^{10}}{5 b^3}+\frac{x^{15}}{15 b^2}",1,"(9*a^2*b*x^5 - 3*a*b^2*x^10 + b^3*x^15 - (3*a^4)/(a + b*x^5) - 12*a^3*Log[a + b*x^5])/(15*b^5)","A",1
1278,1,49,59,0.0303956,"\int \frac{x^{19}}{\left(a+b x^5\right)^2} \, dx","Integrate[x^19/(a + b*x^5)^2,x]","\frac{\frac{2 a^3}{a+b x^5}+6 a^2 \log \left(a+b x^5\right)-4 a b x^5+b^2 x^{10}}{10 b^4}","\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,"(-4*a*b*x^5 + b^2*x^10 + (2*a^3)/(a + b*x^5) + 6*a^2*Log[a + b*x^5])/(10*b^4)","A",1
1279,1,38,46,0.0316321,"\int \frac{x^{14}}{\left(a+b x^5\right)^2} \, dx","Integrate[x^14/(a + b*x^5)^2,x]","\frac{-\frac{a^2}{a+b x^5}-2 a \log \left(a+b x^5\right)+b x^5}{5 b^3}","-\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,"(b*x^5 - a^2/(a + b*x^5) - 2*a*Log[a + b*x^5])/(5*b^3)","A",1
1280,1,27,33,0.0119694,"\int \frac{x^9}{\left(a+b x^5\right)^2} \, dx","Integrate[x^9/(a + b*x^5)^2,x]","\frac{\frac{a}{a+b x^5}+\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/(a + b*x^5) + Log[a + b*x^5])/(5*b^2)","A",1
1281,1,16,16,0.0048152,"\int \frac{x^4}{\left(a+b x^5\right)^2} \, dx","Integrate[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*1/(b*(a + b*x^5))","A",1
1282,1,33,38,0.0304015,"\int \frac{1}{x \left(a+b x^5\right)^2} \, dx","Integrate[1/(x*(a + b*x^5)^2),x]","\frac{\frac{a}{a+b x^5}-\log \left(a+b x^5\right)+5 \log (x)}{5 a^2}","-\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,"(a/(a + b*x^5) + 5*Log[x] - Log[a + b*x^5])/(5*a^2)","A",1
1283,1,41,52,0.0578923,"\int \frac{1}{x^6 \left(a+b x^5\right)^2} \, dx","Integrate[1/(x^6*(a + b*x^5)^2),x]","-\frac{a \left(\frac{b}{a+b x^5}+\frac{1}{x^5}\right)-2 b \log \left(a+b x^5\right)+10 b \log (x)}{5 a^3}","\frac{2 b \log \left(a+b x^5\right)}{5 a^3}-\frac{2 b \log (x)}{a^3}-\frac{b}{5 a^2 \left(a+b x^5\right)}-\frac{1}{5 a^2 x^5}",1,"-1/5*(a*(x^(-5) + b/(a + b*x^5)) + 10*b*Log[x] - 2*b*Log[a + b*x^5])/a^3","A",1
1284,1,57,69,0.0837801,"\int \frac{1}{x^{11} \left(a+b x^5\right)^2} \, dx","Integrate[1/(x^11*(a + b*x^5)^2),x]","\frac{-6 b^2 \log \left(a+b x^5\right)+a \left(\frac{2 b^2}{a+b x^5}-\frac{a}{x^{10}}+\frac{4 b}{x^5}\right)+30 b^2 \log (x)}{10 a^4}","-\frac{3 b^2 \log \left(a+b x^5\right)}{5 a^4}+\frac{3 b^2 \log (x)}{a^4}+\frac{b^2}{5 a^3 \left(a+b x^5\right)}+\frac{2 b}{5 a^3 x^5}-\frac{1}{10 a^2 x^{10}}",1,"(a*(-(a/x^10) + (4*b)/x^5 + (2*b^2)/(a + b*x^5)) + 30*b^2*Log[x] - 6*b^2*Log[a + b*x^5])/(10*a^4)","A",1
1285,1,25,34,0.0111144,"\int \frac{x^{14}}{2 b+b x^5} \, dx","Integrate[x^14/(2*b + b*x^5),x]","\frac{x^{10}-4 x^5+8 \log \left(x^5+2\right)-12}{10 b}","\frac{x^{10}}{10 b}-\frac{2 x^5}{5 b}+\frac{4 \log \left(x^5+2\right)}{5 b}",1,"(-12 - 4*x^5 + x^10 + 8*Log[2 + x^5])/(10*b)","A",1
1286,1,24,24,0.003777,"\int \frac{x^9}{2 b+b x^5} \, dx","Integrate[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",1
1287,1,17,13,0.00312,"\int \frac{x^4}{2 b+b x^5} \, dx","Integrate[x^4/(2*b + b*x^5),x]","\frac{\log \left(b x^5+2 b\right)}{5 b}","\frac{\log \left(x^5+2\right)}{5 b}",1,"Log[2*b + b*x^5]/(5*b)","A",1
1288,1,23,23,0.0062024,"\int \frac{1}{x \left(2 b+b x^5\right)} \, dx","Integrate[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",1
1289,1,33,33,0.0043156,"\int \frac{1}{x^6 \left(2 b+b x^5\right)} \, dx","Integrate[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*1/(b*x^5) - Log[x]/(4*b) + Log[2 + x^5]/(20*b)","A",1
1290,1,36,36,0.0199802,"\int \frac{x^{14}}{3+b x^5} \, dx","Integrate[x^14/(3 + b*x^5),x]","\frac{9 \log \left(b x^5+3\right)}{5 b^3}-\frac{3 x^5}{5 b^2}+\frac{x^{10}}{10 b}","\frac{9 \log \left(b x^5+3\right)}{5 b^3}-\frac{3 x^5}{5 b^2}+\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",1
1291,1,26,26,0.0043826,"\int \frac{x^9}{3+b x^5} \, dx","Integrate[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",1
1292,1,15,15,0.0027371,"\int \frac{x^4}{3+b x^5} \, dx","Integrate[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
1293,1,19,19,0.0040549,"\int \frac{1}{x \left(3+b x^5\right)} \, dx","Integrate[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",1
1294,1,28,28,0.0050528,"\int \frac{1}{x^6 \left(3+b x^5\right)} \, dx","Integrate[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*1/x^5 - (b*Log[x])/9 + (b*Log[3 + b*x^5])/45","A",1
1295,1,22,25,0.0051042,"\int \frac{x^{14}}{1+x^5} \, dx","Integrate[x^14/(1 + x^5),x]","\frac{1}{10} \left(x^{10}-2 x^5+2 \log \left(x^5+1\right)-3\right)","\frac{x^{10}}{10}-\frac{x^5}{5}+\frac{1}{5} \log \left(x^5+1\right)",1,"(-3 - 2*x^5 + x^10 + 2*Log[1 + x^5])/10","A",1
1296,1,18,18,0.0025714,"\int \frac{x^9}{1+x^5} \, dx","Integrate[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",1
1297,1,10,10,0.0020684,"\int \frac{x^4}{1+x^5} \, dx","Integrate[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
1298,1,13,13,0.0030311,"\int \frac{1}{x \left(1+x^5\right)} \, dx","Integrate[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",1
1299,1,22,22,0.0040157,"\int \frac{1}{x^6 \left(1+x^5\right)} \, dx","Integrate[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*1/x^5 - Log[x] + Log[1 + x^5]/5","A",1
1300,1,147,186,0.1415525,"\int \frac{x^5}{1+x^5} \, dx","Integrate[x^5/(1 + x^5),x]","\frac{1}{20} \left(-\left(\sqrt{5}-1\right) \log \left(x^2+\frac{1}{2} \left(\sqrt{5}-1\right) x+1\right)+\left(1+\sqrt{5}\right) \log \left(x^2-\frac{1}{2} \left(1+\sqrt{5}\right) x+1\right)+20 x-4 \log (x+1)+2 \sqrt{10-2 \sqrt{5}} \tan ^{-1}\left(\frac{-4 x+\sqrt{5}+1}{\sqrt{10-2 \sqrt{5}}}\right)-2 \sqrt{2 \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\frac{4 x+\sqrt{5}-1}{\sqrt{2 \left(5+\sqrt{5}\right)}}\right)\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,"(20*x + 2*Sqrt[10 - 2*Sqrt[5]]*ArcTan[(1 + Sqrt[5] - 4*x)/Sqrt[10 - 2*Sqrt[5]]] - 2*Sqrt[2*(5 + Sqrt[5])]*ArcTan[(-1 + Sqrt[5] + 4*x)/Sqrt[2*(5 + Sqrt[5])]] - 4*Log[1 + x] - (-1 + Sqrt[5])*Log[1 + ((-1 + Sqrt[5])*x)/2 + x^2] + (1 + Sqrt[5])*Log[1 - ((1 + Sqrt[5])*x)/2 + x^2])/20","A",1
1301,1,144,185,0.0992385,"\int \frac{x^3}{1+x^5} \, dx","Integrate[x^3/(1 + x^5),x]","\frac{1}{20} \left(-\left(\sqrt{5}-1\right) \log \left(x^2+\frac{1}{2} \left(\sqrt{5}-1\right) x+1\right)+\left(1+\sqrt{5}\right) \log \left(x^2-\frac{1}{2} \left(1+\sqrt{5}\right) x+1\right)-4 \log (x+1)-2 \sqrt{10-2 \sqrt{5}} \tan ^{-1}\left(\frac{-4 x+\sqrt{5}+1}{\sqrt{10-2 \sqrt{5}}}\right)+2 \sqrt{2 \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\frac{4 x+\sqrt{5}-1}{\sqrt{2 \left(5+\sqrt{5}\right)}}\right)\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,"(-2*Sqrt[10 - 2*Sqrt[5]]*ArcTan[(1 + Sqrt[5] - 4*x)/Sqrt[10 - 2*Sqrt[5]]] + 2*Sqrt[2*(5 + Sqrt[5])]*ArcTan[(-1 + Sqrt[5] + 4*x)/Sqrt[2*(5 + Sqrt[5])]] - 4*Log[1 + x] - (-1 + Sqrt[5])*Log[1 + ((-1 + Sqrt[5])*x)/2 + x^2] + (1 + Sqrt[5])*Log[1 - ((1 + Sqrt[5])*x)/2 + x^2])/20","A",1
1302,1,144,185,0.1021168,"\int \frac{x^2}{1+x^5} \, dx","Integrate[x^2/(1 + x^5),x]","\frac{1}{20} \left(-\left(1+\sqrt{5}\right) \log \left(x^2+\frac{1}{2} \left(\sqrt{5}-1\right) x+1\right)+\left(\sqrt{5}-1\right) \log \left(x^2-\frac{1}{2} \left(1+\sqrt{5}\right) x+1\right)+4 \log (x+1)-2 \sqrt{2 \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\frac{-4 x+\sqrt{5}+1}{\sqrt{10-2 \sqrt{5}}}\right)-2 \sqrt{10-2 \sqrt{5}} \tan ^{-1}\left(\frac{4 x+\sqrt{5}-1}{\sqrt{2 \left(5+\sqrt{5}\right)}}\right)\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,"(-2*Sqrt[2*(5 + Sqrt[5])]*ArcTan[(1 + Sqrt[5] - 4*x)/Sqrt[10 - 2*Sqrt[5]]] - 2*Sqrt[10 - 2*Sqrt[5]]*ArcTan[(-1 + Sqrt[5] + 4*x)/Sqrt[2*(5 + Sqrt[5])]] + 4*Log[1 + x] - (1 + Sqrt[5])*Log[1 + ((-1 + Sqrt[5])*x)/2 + x^2] + (-1 + Sqrt[5])*Log[1 - ((1 + Sqrt[5])*x)/2 + x^2])/20","A",0
1303,1,144,185,0.0694823,"\int \frac{x}{1+x^5} \, dx","Integrate[x/(1 + x^5),x]","\frac{1}{20} \left(\left(1+\sqrt{5}\right) \log \left(x^2+\frac{1}{2} \left(\sqrt{5}-1\right) x+1\right)-\left(\sqrt{5}-1\right) \log \left(x^2-\frac{1}{2} \left(1+\sqrt{5}\right) x+1\right)-4 \log (x+1)-2 \sqrt{2 \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\frac{-4 x+\sqrt{5}+1}{\sqrt{10-2 \sqrt{5}}}\right)-2 \sqrt{10-2 \sqrt{5}} \tan ^{-1}\left(\frac{4 x+\sqrt{5}-1}{\sqrt{2 \left(5+\sqrt{5}\right)}}\right)\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,"(-2*Sqrt[2*(5 + Sqrt[5])]*ArcTan[(1 + Sqrt[5] - 4*x)/Sqrt[10 - 2*Sqrt[5]]] - 2*Sqrt[10 - 2*Sqrt[5]]*ArcTan[(-1 + Sqrt[5] + 4*x)/Sqrt[2*(5 + Sqrt[5])]] - 4*Log[1 + x] + (1 + Sqrt[5])*Log[1 + ((-1 + Sqrt[5])*x)/2 + x^2] - (-1 + Sqrt[5])*Log[1 - ((1 + Sqrt[5])*x)/2 + x^2])/20","A",0
1304,1,144,168,0.0706939,"\int \frac{1}{1+x^5} \, dx","Integrate[(1 + x^5)^(-1),x]","\frac{1}{20} \left(\left(\sqrt{5}-1\right) \log \left(x^2+\frac{1}{2} \left(\sqrt{5}-1\right) x+1\right)-\left(1+\sqrt{5}\right) \log \left(x^2-\frac{1}{2} \left(1+\sqrt{5}\right) x+1\right)+4 \log (x+1)-2 \sqrt{10-2 \sqrt{5}} \tan ^{-1}\left(\frac{-4 x+\sqrt{5}+1}{\sqrt{10-2 \sqrt{5}}}\right)+2 \sqrt{2 \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\frac{4 x+\sqrt{5}-1}{\sqrt{2 \left(5+\sqrt{5}\right)}}\right)\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,"(-2*Sqrt[10 - 2*Sqrt[5]]*ArcTan[(1 + Sqrt[5] - 4*x)/Sqrt[10 - 2*Sqrt[5]]] + 2*Sqrt[2*(5 + Sqrt[5])]*ArcTan[(-1 + Sqrt[5] + 4*x)/Sqrt[2*(5 + Sqrt[5])]] + 4*Log[1 + x] + (-1 + Sqrt[5])*Log[1 + ((-1 + Sqrt[5])*x)/2 + x^2] - (1 + Sqrt[5])*Log[1 - ((1 + Sqrt[5])*x)/2 + x^2])/20","A",1
1305,1,149,190,0.1033534,"\int \frac{1}{x^2 \left(1+x^5\right)} \, dx","Integrate[1/(x^2*(1 + x^5)),x]","\frac{1}{20} \left(\left(\sqrt{5}-1\right) \log \left(x^2+\frac{1}{2} \left(\sqrt{5}-1\right) x+1\right)-\left(1+\sqrt{5}\right) \log \left(x^2-\frac{1}{2} \left(1+\sqrt{5}\right) x+1\right)-\frac{20}{x}+4 \log (x+1)+2 \sqrt{10-2 \sqrt{5}} \tan ^{-1}\left(\frac{-4 x+\sqrt{5}+1}{\sqrt{10-2 \sqrt{5}}}\right)-2 \sqrt{2 \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\frac{4 x+\sqrt{5}-1}{\sqrt{2 \left(5+\sqrt{5}\right)}}\right)\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,"(-20/x + 2*Sqrt[10 - 2*Sqrt[5]]*ArcTan[(1 + Sqrt[5] - 4*x)/Sqrt[10 - 2*Sqrt[5]]] - 2*Sqrt[2*(5 + Sqrt[5])]*ArcTan[(-1 + Sqrt[5] + 4*x)/Sqrt[2*(5 + Sqrt[5])]] + 4*Log[1 + x] + (-1 + Sqrt[5])*Log[1 + ((-1 + Sqrt[5])*x)/2 + x^2] - (1 + Sqrt[5])*Log[1 - ((1 + Sqrt[5])*x)/2 + x^2])/20","A",1
1306,1,149,192,0.1187066,"\int \frac{1}{x^3 \left(1+x^5\right)} \, dx","Integrate[1/(x^3*(1 + x^5)),x]","\frac{1}{20} \left(-\frac{10}{x^2}+\left(1+\sqrt{5}\right) \log \left(x^2+\frac{1}{2} \left(\sqrt{5}-1\right) x+1\right)-\left(\sqrt{5}-1\right) \log \left(x^2-\frac{1}{2} \left(1+\sqrt{5}\right) x+1\right)-4 \log (x+1)+2 \sqrt{2 \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\frac{-4 x+\sqrt{5}+1}{\sqrt{10-2 \sqrt{5}}}\right)+2 \sqrt{10-2 \sqrt{5}} \tan ^{-1}\left(\frac{4 x+\sqrt{5}-1}{\sqrt{2 \left(5+\sqrt{5}\right)}}\right)\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,"(-10/x^2 + 2*Sqrt[2*(5 + Sqrt[5])]*ArcTan[(1 + Sqrt[5] - 4*x)/Sqrt[10 - 2*Sqrt[5]]] + 2*Sqrt[10 - 2*Sqrt[5]]*ArcTan[(-1 + Sqrt[5] + 4*x)/Sqrt[2*(5 + Sqrt[5])]] - 4*Log[1 + x] + (1 + Sqrt[5])*Log[1 + ((-1 + Sqrt[5])*x)/2 + x^2] - (-1 + Sqrt[5])*Log[1 - ((1 + Sqrt[5])*x)/2 + x^2])/20","A",0
1307,1,150,192,0.1426698,"\int \frac{1}{x^4 \left(1+x^5\right)} \, dx","Integrate[1/(x^4*(1 + x^5)),x]","\frac{1}{60} \left(-\frac{20}{x^3}-3 \left(1+\sqrt{5}\right) \log \left(x^2+\frac{1}{2} \left(\sqrt{5}-1\right) x+1\right)+3 \left(\sqrt{5}-1\right) \log \left(x^2-\frac{1}{2} \left(1+\sqrt{5}\right) x+1\right)+12 \log (x+1)+6 \sqrt{2 \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\frac{-4 x+\sqrt{5}+1}{\sqrt{10-2 \sqrt{5}}}\right)+6 \sqrt{10-2 \sqrt{5}} \tan ^{-1}\left(\frac{4 x+\sqrt{5}-1}{\sqrt{2 \left(5+\sqrt{5}\right)}}\right)\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,"(-20/x^3 + 6*Sqrt[2*(5 + Sqrt[5])]*ArcTan[(1 + Sqrt[5] - 4*x)/Sqrt[10 - 2*Sqrt[5]]] + 6*Sqrt[10 - 2*Sqrt[5]]*ArcTan[(-1 + Sqrt[5] + 4*x)/Sqrt[2*(5 + Sqrt[5])]] + 12*Log[1 + x] - 3*(1 + Sqrt[5])*Log[1 + ((-1 + Sqrt[5])*x)/2 + x^2] + 3*(-1 + Sqrt[5])*Log[1 - ((1 + Sqrt[5])*x)/2 + x^2])/60","A",0
1308,1,70,83,0.0326919,"\int \frac{x^{23/2}}{\sqrt{a+b x^5}} \, dx","Integrate[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)+\sqrt{b} x^{5/2} \sqrt{a+b x^5} \left(2 b x^5-3 a\right)}{20 b^{5/2}}","\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,"(Sqrt[b]*x^(5/2)*Sqrt[a + b*x^5]*(-3*a + 2*b*x^5) + 3*a^2*ArcTanh[(Sqrt[b]*x^(5/2))/Sqrt[a + b*x^5]])/(20*b^(5/2))","A",1
1309,1,57,57,0.0225375,"\int \frac{x^{13/2}}{\sqrt{a+b x^5}} \, dx","Integrate[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",1
1310,1,32,32,0.005709,"\int \frac{x^{3/2}}{\sqrt{a+b x^5}} \, dx","Integrate[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",1
1311,1,23,23,0.0050385,"\int \frac{1}{x^{7/2} \sqrt{a+b x^5}} \, dx","Integrate[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
1312,1,31,48,0.0099549,"\int \frac{1}{x^{17/2} \sqrt{a+b x^5}} \, dx","Integrate[1/(x^(17/2)*Sqrt[a + b*x^5]),x]","-\frac{2 \left(a-2 b x^5\right) \sqrt{a+b x^5}}{15 a^2 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*(a - 2*b*x^5)*Sqrt[a + b*x^5])/(15*a^2*x^(15/2))","A",1
1313,1,35,47,0.0138571,"\int \frac{x^{23/2}}{\sqrt{1+x^5}} \, dx","Integrate[x^(23/2)/Sqrt[1 + x^5],x]","\frac{1}{20} \left(3 \sinh ^{-1}\left(x^{5/2}\right)+\sqrt{x^5+1} \left(2 x^5-3\right) x^{5/2}\right)","\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}",1,"(x^(5/2)*Sqrt[1 + x^5]*(-3 + 2*x^5) + 3*ArcSinh[x^(5/2)])/20","A",1
1314,1,29,29,0.0062153,"\int \frac{x^{13/2}}{\sqrt{1+x^5}} \, dx","Integrate[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",1
1315,1,10,10,0.0030887,"\int \frac{x^{3/2}}{\sqrt{1+x^5}} \, dx","Integrate[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",1
1316,1,18,18,0.0037429,"\int \frac{1}{x^{7/2} \sqrt{1+x^5}} \, dx","Integrate[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
1317,1,25,37,0.0062628,"\int \frac{1}{x^{17/2} \sqrt{1+x^5}} \, dx","Integrate[1/(x^(17/2)*Sqrt[1 + x^5]),x]","-\frac{2 \left(1-2 x^5\right) \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*(1 - 2*x^5)*Sqrt[1 + x^5])/(15*x^(15/2))","A",1
1318,1,40,40,0.0151506,"\int \frac{x^8}{a+b x^6} \, dx","Integrate[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",1
1319,1,186,133,0.0552357,"\int \frac{x^7}{a+b x^6} \, dx","Integrate[x^7/(a + b*x^6),x]","\frac{-2 \sqrt[3]{a} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x^2\right)+\sqrt[3]{a} \log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)+\sqrt[3]{a} \log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)+2 \sqrt{3} \sqrt[3]{a} \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{b} x}{\sqrt[6]{a}}\right)+2 \sqrt{3} \sqrt[3]{a} \tan ^{-1}\left(\frac{2 \sqrt[6]{b} x}{\sqrt[6]{a}}+\sqrt{3}\right)+6 \sqrt[3]{b} x^2}{12 b^{4/3}}","\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,"(6*b^(1/3)*x^2 + 2*Sqrt[3]*a^(1/3)*ArcTan[Sqrt[3] - (2*b^(1/6)*x)/a^(1/6)] + 2*Sqrt[3]*a^(1/3)*ArcTan[Sqrt[3] + (2*b^(1/6)*x)/a^(1/6)] - 2*a^(1/3)*Log[a^(1/3) + b^(1/3)*x^2] + a^(1/3)*Log[a^(1/3) - Sqrt[3]*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2] + a^(1/3)*Log[a^(1/3) + Sqrt[3]*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2])/(12*b^(4/3))","A",1
1320,1,182,220,0.0360315,"\int \frac{x^6}{a+b x^6} \, dx","Integrate[x^6/(a + b*x^6),x]","\frac{\sqrt{3} \sqrt[6]{a} \log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)-\sqrt{3} \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[6]{a} \tan ^{-1}\left(\frac{\sqrt[6]{b} x}{\sqrt[6]{a}}\right)+2 \sqrt[6]{a} \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{b} x}{\sqrt[6]{a}}\right)-2 \sqrt[6]{a} \tan ^{-1}\left(\frac{2 \sqrt[6]{b} x}{\sqrt[6]{a}}+\sqrt{3}\right)+12 \sqrt[6]{b} x}{12 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} \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,"(12*b^(1/6)*x - 4*a^(1/6)*ArcTan[(b^(1/6)*x)/a^(1/6)] + 2*a^(1/6)*ArcTan[Sqrt[3] - (2*b^(1/6)*x)/a^(1/6)] - 2*a^(1/6)*ArcTan[Sqrt[3] + (2*b^(1/6)*x)/a^(1/6)] + Sqrt[3]*a^(1/6)*Log[a^(1/3) - Sqrt[3]*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2] - Sqrt[3]*a^(1/6)*Log[a^(1/3) + Sqrt[3]*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2])/(12*b^(7/6))","A",1
1321,1,15,15,0.0040188,"\int \frac{x^5}{a+b x^6} \, dx","Integrate[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
1322,1,154,215,0.0208403,"\int \frac{x^4}{a+b x^6} \, dx","Integrate[x^4/(a + b*x^6),x]","\frac{\sqrt{3} \log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)-\sqrt{3} \log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)+4 \tan ^{-1}\left(\frac{\sqrt[6]{b} x}{\sqrt[6]{a}}\right)-2 \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{b} x}{\sqrt[6]{a}}\right)+2 \tan ^{-1}\left(\frac{2 \sqrt[6]{b} x}{\sqrt[6]{a}}+\sqrt{3}\right)}{12 \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,"(4*ArcTan[(b^(1/6)*x)/a^(1/6)] - 2*ArcTan[Sqrt[3] - (2*b^(1/6)*x)/a^(1/6)] + 2*ArcTan[Sqrt[3] + (2*b^(1/6)*x)/a^(1/6)] + Sqrt[3]*Log[a^(1/3) - Sqrt[3]*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2] - Sqrt[3]*Log[a^(1/3) + Sqrt[3]*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2])/(12*a^(1/6)*b^(5/6))","A",1
1323,1,154,123,0.0196075,"\int \frac{x^3}{a+b x^6} \, dx","Integrate[x^3/(a + b*x^6),x]","\frac{-2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} x^2\right)+\log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)+\log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)-2 \sqrt{3} \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{b} x}{\sqrt[6]{a}}\right)-2 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[6]{b} x}{\sqrt[6]{a}}+\sqrt{3}\right)}{12 \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,"(-2*Sqrt[3]*ArcTan[Sqrt[3] - (2*b^(1/6)*x)/a^(1/6)] - 2*Sqrt[3]*ArcTan[Sqrt[3] + (2*b^(1/6)*x)/a^(1/6)] - 2*Log[a^(1/3) + b^(1/3)*x^2] + Log[a^(1/3) - Sqrt[3]*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2] + Log[a^(1/3) + Sqrt[3]*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2])/(12*a^(1/3)*b^(2/3))","A",1
1324,1,29,29,0.0058641,"\int \frac{x^2}{a+b x^6} \, dx","Integrate[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",1
1325,1,154,123,0.023166,"\int \frac{x}{a+b x^6} \, dx","Integrate[x/(a + b*x^6),x]","-\frac{-2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} x^2\right)+\log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)+\log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)+2 \sqrt{3} \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{b} x}{\sqrt[6]{a}}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[6]{b} x}{\sqrt[6]{a}}+\sqrt{3}\right)}{12 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,"-1/12*(2*Sqrt[3]*ArcTan[Sqrt[3] - (2*b^(1/6)*x)/a^(1/6)] + 2*Sqrt[3]*ArcTan[Sqrt[3] + (2*b^(1/6)*x)/a^(1/6)] - 2*Log[a^(1/3) + b^(1/3)*x^2] + Log[a^(1/3) - Sqrt[3]*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2] + Log[a^(1/3) + Sqrt[3]*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2])/(a^(2/3)*b^(1/3))","A",1
1326,1,154,215,0.0199383,"\int \frac{1}{a+b x^6} \, dx","Integrate[(a + b*x^6)^(-1),x]","\frac{-\sqrt{3} \log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)+\sqrt{3} \log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)+4 \tan ^{-1}\left(\frac{\sqrt[6]{b} x}{\sqrt[6]{a}}\right)-2 \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{b} x}{\sqrt[6]{a}}\right)+2 \tan ^{-1}\left(\frac{2 \sqrt[6]{b} x}{\sqrt[6]{a}}+\sqrt{3}\right)}{12 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,"(4*ArcTan[(b^(1/6)*x)/a^(1/6)] - 2*ArcTan[Sqrt[3] - (2*b^(1/6)*x)/a^(1/6)] + 2*ArcTan[Sqrt[3] + (2*b^(1/6)*x)/a^(1/6)] - Sqrt[3]*Log[a^(1/3) - Sqrt[3]*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2] + Sqrt[3]*Log[a^(1/3) + Sqrt[3]*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2])/(12*a^(5/6)*b^(1/6))","A",1
1327,1,22,22,0.0062009,"\int \frac{1}{x \left(a+b x^6\right)} \, dx","Integrate[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",1
1328,1,189,223,0.0458039,"\int \frac{1}{x^2 \left(a+b x^6\right)} \, dx","Integrate[1/(x^2*(a + b*x^6)),x]","-\frac{\sqrt{3} \sqrt[6]{b} x \log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)-\sqrt{3} \sqrt[6]{b} x \log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)+4 \sqrt[6]{b} x \tan ^{-1}\left(\frac{\sqrt[6]{b} x}{\sqrt[6]{a}}\right)-2 \sqrt[6]{b} x \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{b} x}{\sqrt[6]{a}}\right)+2 \sqrt[6]{b} x \tan ^{-1}\left(\frac{2 \sqrt[6]{b} x}{\sqrt[6]{a}}+\sqrt{3}\right)+12 \sqrt[6]{a}}{12 a^{7/6} 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}",1,"-1/12*(12*a^(1/6) + 4*b^(1/6)*x*ArcTan[(b^(1/6)*x)/a^(1/6)] - 2*b^(1/6)*x*ArcTan[Sqrt[3] - (2*b^(1/6)*x)/a^(1/6)] + 2*b^(1/6)*x*ArcTan[Sqrt[3] + (2*b^(1/6)*x)/a^(1/6)] + Sqrt[3]*b^(1/6)*x*Log[a^(1/3) - Sqrt[3]*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2] - Sqrt[3]*b^(1/6)*x*Log[a^(1/3) + Sqrt[3]*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2])/(a^(7/6)*x)","A",1
1329,1,203,133,0.0312204,"\int \frac{1}{x^3 \left(a+b x^6\right)} \, dx","Integrate[1/(x^3*(a + b*x^6)),x]","\frac{2 \sqrt[3]{b} x^2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} x^2\right)-\sqrt[3]{b} x^2 \log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)-\sqrt[3]{b} x^2 \log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)+2 \sqrt{3} \sqrt[3]{b} x^2 \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{b} x}{\sqrt[6]{a}}\right)+2 \sqrt{3} \sqrt[3]{b} x^2 \tan ^{-1}\left(\frac{2 \sqrt[6]{b} x}{\sqrt[6]{a}}+\sqrt{3}\right)-6 \sqrt[3]{a}}{12 a^{4/3} 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,"(-6*a^(1/3) + 2*Sqrt[3]*b^(1/3)*x^2*ArcTan[Sqrt[3] - (2*b^(1/6)*x)/a^(1/6)] + 2*Sqrt[3]*b^(1/3)*x^2*ArcTan[Sqrt[3] + (2*b^(1/6)*x)/a^(1/6)] + 2*b^(1/3)*x^2*Log[a^(1/3) + b^(1/3)*x^2] - b^(1/3)*x^2*Log[a^(1/3) - Sqrt[3]*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2] - b^(1/3)*x^2*Log[a^(1/3) + Sqrt[3]*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2])/(12*a^(4/3)*x^2)","A",1
1330,1,101,40,0.0205991,"\int \frac{1}{x^4 \left(a+b x^6\right)} \, dx","Integrate[1/(x^4*(a + b*x^6)),x]","\frac{\sqrt{b} x^3 \tan ^{-1}\left(\frac{\sqrt[6]{b} x}{\sqrt[6]{a}}\right)+\sqrt{b} x^3 \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{b} x}{\sqrt[6]{a}}\right)-\sqrt{b} x^3 \tan ^{-1}\left(\frac{2 \sqrt[6]{b} x}{\sqrt[6]{a}}+\sqrt{3}\right)-\sqrt{a}}{3 a^{3/2} 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,"(-Sqrt[a] + Sqrt[b]*x^3*ArcTan[(b^(1/6)*x)/a^(1/6)] + Sqrt[b]*x^3*ArcTan[Sqrt[3] - (2*b^(1/6)*x)/a^(1/6)] - Sqrt[b]*x^3*ArcTan[Sqrt[3] + (2*b^(1/6)*x)/a^(1/6)])/(3*a^(3/2)*x^3)","B",1
1331,1,49,49,0.0263615,"\int \frac{x^8}{\left(a+b x^6\right)^2} \, dx","Integrate[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,"-1/6*x^3/(b*(a + b*x^6)) + ArcTan[(Sqrt[b]*x^3)/Sqrt[a]]/(6*Sqrt[a]*b^(3/2))","A",1
1332,1,197,142,0.1282984,"\int \frac{x^7}{\left(a+b x^6\right)^2} \, dx","Integrate[x^7/(a + b*x^6)^2,x]","\frac{\frac{2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{a^{2/3}}-\frac{\log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{a^{2/3}}-\frac{\log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{a^{2/3}}-\frac{2 \sqrt{3} \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{a^{2/3}}-\frac{2 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[6]{b} x}{\sqrt[6]{a}}+\sqrt{3}\right)}{a^{2/3}}-\frac{6 \sqrt[3]{b} x^2}{a+b x^6}}{36 b^{4/3}}","\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{18 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{\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{x^2}{6 b \left(a+b x^6\right)}",1,"((-6*b^(1/3)*x^2)/(a + b*x^6) - (2*Sqrt[3]*ArcTan[Sqrt[3] - (2*b^(1/6)*x)/a^(1/6)])/a^(2/3) - (2*Sqrt[3]*ArcTan[Sqrt[3] + (2*b^(1/6)*x)/a^(1/6)])/a^(2/3) + (2*Log[a^(1/3) + b^(1/3)*x^2])/a^(2/3) - Log[a^(1/3) - Sqrt[3]*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2]/a^(2/3) - Log[a^(1/3) + Sqrt[3]*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2]/a^(2/3))/(36*b^(4/3))","A",1
1333,1,191,232,0.1240857,"\int \frac{x^6}{\left(a+b x^6\right)^2} \, dx","Integrate[x^6/(a + b*x^6)^2,x]","\frac{-\frac{\sqrt{3} \log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{a^{5/6}}+\frac{\sqrt{3} \log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{a^{5/6}}+\frac{4 \tan ^{-1}\left(\frac{\sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{a^{5/6}}-\frac{2 \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{a^{5/6}}+\frac{2 \tan ^{-1}\left(\frac{2 \sqrt[6]{b} x}{\sqrt[6]{a}}+\sqrt{3}\right)}{a^{5/6}}-\frac{12 \sqrt[6]{b} x}{a+b x^6}}{72 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{\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,"((-12*b^(1/6)*x)/(a + b*x^6) + (4*ArcTan[(b^(1/6)*x)/a^(1/6)])/a^(5/6) - (2*ArcTan[Sqrt[3] - (2*b^(1/6)*x)/a^(1/6)])/a^(5/6) + (2*ArcTan[Sqrt[3] + (2*b^(1/6)*x)/a^(1/6)])/a^(5/6) - (Sqrt[3]*Log[a^(1/3) - Sqrt[3]*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2])/a^(5/6) + (Sqrt[3]*Log[a^(1/3) + Sqrt[3]*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2])/a^(5/6))/(72*b^(7/6))","A",1
1334,1,16,16,0.0039679,"\int \frac{x^5}{\left(a+b x^6\right)^2} \, dx","Integrate[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*1/(b*(a + b*x^6))","A",1
1335,1,193,234,0.1138123,"\int \frac{x^4}{\left(a+b x^6\right)^2} \, dx","Integrate[x^4/(a + b*x^6)^2,x]","\frac{\frac{\sqrt{3} \log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{b^{5/6}}-\frac{\sqrt{3} \log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{b^{5/6}}+\frac{4 \tan ^{-1}\left(\frac{\sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{b^{5/6}}-\frac{2 \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{b^{5/6}}+\frac{2 \tan ^{-1}\left(\frac{2 \sqrt[6]{b} x}{\sqrt[6]{a}}+\sqrt{3}\right)}{b^{5/6}}+\frac{12 \sqrt[6]{a} x^5}{a+b x^6}}{72 a^{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^{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,"((12*a^(1/6)*x^5)/(a + b*x^6) + (4*ArcTan[(b^(1/6)*x)/a^(1/6)])/b^(5/6) - (2*ArcTan[Sqrt[3] - (2*b^(1/6)*x)/a^(1/6)])/b^(5/6) + (2*ArcTan[Sqrt[3] + (2*b^(1/6)*x)/a^(1/6)])/b^(5/6) + (Sqrt[3]*Log[a^(1/3) - Sqrt[3]*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2])/b^(5/6) - (Sqrt[3]*Log[a^(1/3) + Sqrt[3]*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2])/b^(5/6))/(72*a^(7/6))","A",1
1336,1,195,142,0.1104864,"\int \frac{x^3}{\left(a+b x^6\right)^2} \, dx","Integrate[x^3/(a + b*x^6)^2,x]","\frac{-\frac{2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{b^{2/3}}+\frac{\log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{b^{2/3}}+\frac{\log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{b^{2/3}}-\frac{2 \sqrt{3} \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{b^{2/3}}-\frac{2 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[6]{b} x}{\sqrt[6]{a}}+\sqrt{3}\right)}{b^{2/3}}+\frac{6 \sqrt[3]{a} x^4}{a+b x^6}}{36 a^{4/3}}","-\frac{\log \left(\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{18 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{\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{x^4}{6 a \left(a+b x^6\right)}",1,"((6*a^(1/3)*x^4)/(a + b*x^6) - (2*Sqrt[3]*ArcTan[Sqrt[3] - (2*b^(1/6)*x)/a^(1/6)])/b^(2/3) - (2*Sqrt[3]*ArcTan[Sqrt[3] + (2*b^(1/6)*x)/a^(1/6)])/b^(2/3) - (2*Log[a^(1/3) + b^(1/3)*x^2])/b^(2/3) + Log[a^(1/3) - Sqrt[3]*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2]/b^(2/3) + Log[a^(1/3) + Sqrt[3]*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2]/b^(2/3))/(36*a^(4/3))","A",1
1337,1,49,49,0.0274298,"\int \frac{x^2}{\left(a+b x^6\right)^2} \, dx","Integrate[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",1
1338,1,197,142,0.1160605,"\int \frac{x}{\left(a+b x^6\right)^2} \, dx","Integrate[x/(a + b*x^6)^2,x]","\frac{\frac{3 a^{2/3} x^2}{a+b x^6}+\frac{2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{\sqrt[3]{b}}-\frac{\log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{\sqrt[3]{b}}-\frac{\log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{\sqrt[3]{b}}-\frac{2 \sqrt{3} \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{\sqrt[3]{b}}-\frac{2 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[6]{b} x}{\sqrt[6]{a}}+\sqrt{3}\right)}{\sqrt[3]{b}}}{18 a^{5/3}}","-\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,"((3*a^(2/3)*x^2)/(a + b*x^6) - (2*Sqrt[3]*ArcTan[Sqrt[3] - (2*b^(1/6)*x)/a^(1/6)])/b^(1/3) - (2*Sqrt[3]*ArcTan[Sqrt[3] + (2*b^(1/6)*x)/a^(1/6)])/b^(1/3) + (2*Log[a^(1/3) + b^(1/3)*x^2])/b^(1/3) - Log[a^(1/3) - Sqrt[3]*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2]/b^(1/3) - Log[a^(1/3) + Sqrt[3]*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2]/b^(1/3))/(18*a^(5/3))","A",1
1339,1,192,232,0.1188703,"\int \frac{1}{\left(a+b x^6\right)^2} \, dx","Integrate[(a + b*x^6)^(-2),x]","\frac{\frac{12 a^{5/6} x}{a+b x^6}-\frac{5 \sqrt{3} \log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{\sqrt[6]{b}}+\frac{5 \sqrt{3} \log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)}{\sqrt[6]{b}}+\frac{20 \tan ^{-1}\left(\frac{\sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{\sqrt[6]{b}}-\frac{10 \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{b} x}{\sqrt[6]{a}}\right)}{\sqrt[6]{b}}+\frac{10 \tan ^{-1}\left(\frac{2 \sqrt[6]{b} x}{\sqrt[6]{a}}+\sqrt{3}\right)}{\sqrt[6]{b}}}{72 a^{11/6}}","-\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,"((12*a^(5/6)*x)/(a + b*x^6) + (20*ArcTan[(b^(1/6)*x)/a^(1/6)])/b^(1/6) - (10*ArcTan[Sqrt[3] - (2*b^(1/6)*x)/a^(1/6)])/b^(1/6) + (10*ArcTan[Sqrt[3] + (2*b^(1/6)*x)/a^(1/6)])/b^(1/6) - (5*Sqrt[3]*Log[a^(1/3) - Sqrt[3]*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2])/b^(1/6) + (5*Sqrt[3]*Log[a^(1/3) + Sqrt[3]*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2])/b^(1/6))/(72*a^(11/6))","A",1
1340,1,33,38,0.0183218,"\int \frac{1}{x \left(a+b x^6\right)^2} \, dx","Integrate[1/(x*(a + b*x^6)^2),x]","\frac{\frac{a}{a+b x^6}-\log \left(a+b x^6\right)+6 \log (x)}{6 a^2}","-\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,"(a/(a + b*x^6) + 6*Log[x] - Log[a + b*x^6])/(6*a^2)","A",1
1341,1,205,244,0.1446327,"\int \frac{1}{x^2 \left(a+b x^6\right)^2} \, dx","Integrate[1/(x^2*(a + b*x^6)^2),x]","\frac{-7 \sqrt{3} \sqrt[6]{b} \log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)+7 \sqrt{3} \sqrt[6]{b} \log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)-\frac{12 \sqrt[6]{a} b x^5}{a+b x^6}-28 \sqrt[6]{b} \tan ^{-1}\left(\frac{\sqrt[6]{b} x}{\sqrt[6]{a}}\right)+14 \sqrt[6]{b} \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{b} x}{\sqrt[6]{a}}\right)-14 \sqrt[6]{b} \tan ^{-1}\left(\frac{2 \sqrt[6]{b} x}{\sqrt[6]{a}}+\sqrt{3}\right)-\frac{72 \sqrt[6]{a}}{x}}{72 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} \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,"((-72*a^(1/6))/x - (12*a^(1/6)*b*x^5)/(a + b*x^6) - 28*b^(1/6)*ArcTan[(b^(1/6)*x)/a^(1/6)] + 14*b^(1/6)*ArcTan[Sqrt[3] - (2*b^(1/6)*x)/a^(1/6)] - 14*b^(1/6)*ArcTan[Sqrt[3] + (2*b^(1/6)*x)/a^(1/6)] - 7*Sqrt[3]*b^(1/6)*Log[a^(1/3) - Sqrt[3]*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2] + 7*Sqrt[3]*b^(1/6)*Log[a^(1/3) + Sqrt[3]*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2])/(72*a^(13/6))","A",1
1342,1,208,152,0.1384449,"\int \frac{1}{x^3 \left(a+b x^6\right)^2} \, dx","Integrate[1/(x^3*(a + b*x^6)^2),x]","\frac{4 \sqrt[3]{b} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x^2\right)-2 \sqrt[3]{b} \log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)-2 \sqrt[3]{b} \log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a}+\sqrt[3]{b} x^2\right)-\frac{3 \sqrt[3]{a} b x^4}{a+b x^6}+4 \sqrt{3} \sqrt[3]{b} \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{b} x}{\sqrt[6]{a}}\right)+4 \sqrt{3} \sqrt[3]{b} \tan ^{-1}\left(\frac{2 \sqrt[6]{b} x}{\sqrt[6]{a}}+\sqrt{3}\right)-\frac{9 \sqrt[3]{a}}{x^2}}{18 a^{7/3}}","-\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,"((-9*a^(1/3))/x^2 - (3*a^(1/3)*b*x^4)/(a + b*x^6) + 4*Sqrt[3]*b^(1/3)*ArcTan[Sqrt[3] - (2*b^(1/6)*x)/a^(1/6)] + 4*Sqrt[3]*b^(1/3)*ArcTan[Sqrt[3] + (2*b^(1/6)*x)/a^(1/6)] + 4*b^(1/3)*Log[a^(1/3) + b^(1/3)*x^2] - 2*b^(1/3)*Log[a^(1/3) - Sqrt[3]*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2] - 2*b^(1/3)*Log[a^(1/3) + Sqrt[3]*a^(1/6)*b^(1/6)*x + b^(1/3)*x^2])/(18*a^(7/3))","A",1
1343,1,114,59,0.0895329,"\int \frac{1}{x^4 \left(a+b x^6\right)^2} \, dx","Integrate[1/(x^4*(a + b*x^6)^2),x]","\frac{-\frac{\sqrt{a} b x^3}{a+b x^6}+3 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt[6]{b} x}{\sqrt[6]{a}}\right)+3 \sqrt{b} \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{b} x}{\sqrt[6]{a}}\right)-3 \sqrt{b} \tan ^{-1}\left(\frac{2 \sqrt[6]{b} x}{\sqrt[6]{a}}+\sqrt{3}\right)-\frac{2 \sqrt{a}}{x^3}}{6 a^{5/2}}","-\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,"((-2*Sqrt[a])/x^3 - (Sqrt[a]*b*x^3)/(a + b*x^6) + 3*Sqrt[b]*ArcTan[(b^(1/6)*x)/a^(1/6)] + 3*Sqrt[b]*ArcTan[Sqrt[3] - (2*b^(1/6)*x)/a^(1/6)] - 3*Sqrt[b]*ArcTan[Sqrt[3] + (2*b^(1/6)*x)/a^(1/6)])/(6*a^(5/2))","A",1
1344,1,30,16,0.0049259,"\int \frac{x^8}{1-x^6} \, dx","Integrate[x^8/(1 - x^6),x]","-\frac{x^3}{3}-\frac{1}{6} \log \left(1-x^3\right)+\frac{1}{6} \log \left(x^3+1\right)","\frac{1}{3} \tanh ^{-1}\left(x^3\right)-\frac{x^3}{3}",1,"-1/3*x^3 - Log[1 - x^3]/6 + Log[1 + x^3]/6","A",1
1345,1,78,56,0.0211865,"\int \frac{x^7}{1-x^6} \, dx","Integrate[x^7/(1 - x^6),x]","\frac{1}{12} \left(-6 x^2+\log \left(x^2-x+1\right)+\log \left(x^2+x+1\right)-2 \log (1-x)-2 \log (x+1)+2 \sqrt{3} \tan ^{-1}\left(\frac{2 x-1}{\sqrt{3}}\right)-2 \sqrt{3} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)\right)","-\frac{x^2}{2}-\frac{1}{6} \log \left(1-x^2\right)+\frac{\tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{1}{12} \log \left(x^4+x^2+1\right)",1,"(-6*x^2 + 2*Sqrt[3]*ArcTan[(-1 + 2*x)/Sqrt[3]] - 2*Sqrt[3]*ArcTan[(1 + 2*x)/Sqrt[3]] - 2*Log[1 - x] - 2*Log[1 + x] + Log[1 - x + x^2] + Log[1 + x + x^2])/12","A",1
1346,1,78,50,0.0126404,"\int \frac{x^6}{1-x^6} \, dx","Integrate[x^6/(1 - x^6),x]","\frac{1}{12} \left(-\log \left(x^2-x+1\right)+\log \left(x^2+x+1\right)-12 x-2 \log (1-x)+2 \log (x+1)+2 \sqrt{3} \tan ^{-1}\left(\frac{2 x-1}{\sqrt{3}}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)\right)","\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,"(-12*x + 2*Sqrt[3]*ArcTan[(-1 + 2*x)/Sqrt[3]] + 2*Sqrt[3]*ArcTan[(1 + 2*x)/Sqrt[3]] - 2*Log[1 - x] + 2*Log[1 + x] - Log[1 - x + x^2] + Log[1 + x + x^2])/12","A",1
1347,1,12,12,0.0031859,"\int \frac{x^5}{1-x^6} \, dx","Integrate[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,"-1/6*Log[1 - x^6]","A",1
1348,1,75,47,0.0124049,"\int \frac{x^4}{1-x^6} \, dx","Integrate[x^4/(1 - x^6),x]","\frac{1}{12} \left(-\log \left(x^2-x+1\right)+\log \left(x^2+x+1\right)-2 \log (1-x)+2 \log (x+1)-2 \sqrt{3} \tan ^{-1}\left(\frac{2 x-1}{\sqrt{3}}\right)-2 \sqrt{3} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)\right)","-\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,"(-2*Sqrt[3]*ArcTan[(-1 + 2*x)/Sqrt[3]] - 2*Sqrt[3]*ArcTan[(1 + 2*x)/Sqrt[3]] - 2*Log[1 - x] + 2*Log[1 + x] - Log[1 - x + x^2] + Log[1 + x + x^2])/12","A",1
1349,1,73,49,0.0094105,"\int \frac{x^3}{1-x^6} \, dx","Integrate[x^3/(1 - x^6),x]","\frac{1}{12} \left(\log \left(x^2-x+1\right)+\log \left(x^2+x+1\right)-2 \log (1-x)-2 \log (x+1)-2 \sqrt{3} \tan ^{-1}\left(\frac{2 x-1}{\sqrt{3}}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)\right)","-\frac{1}{6} \log \left(1-x^2\right)-\frac{\tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{1}{12} \log \left(x^4+x^2+1\right)",1,"(-2*Sqrt[3]*ArcTan[(-1 + 2*x)/Sqrt[3]] + 2*Sqrt[3]*ArcTan[(1 + 2*x)/Sqrt[3]] - 2*Log[1 - x] - 2*Log[1 + x] + Log[1 - x + x^2] + Log[1 + x + x^2])/12","A",1
1350,1,23,8,0.0036138,"\int \frac{x^2}{1-x^6} \, dx","Integrate[x^2/(1 - x^6),x]","\frac{1}{6} \log \left(x^3+1\right)-\frac{1}{6} \log \left(1-x^3\right)","\frac{1}{3} \tanh ^{-1}\left(x^3\right)",1,"-1/6*Log[1 - x^3] + Log[1 + x^3]/6","B",1
1351,1,73,49,0.0095271,"\int \frac{x}{1-x^6} \, dx","Integrate[x/(1 - x^6),x]","\frac{1}{12} \left(\log \left(x^2-x+1\right)+\log \left(x^2+x+1\right)-2 \log (1-x)-2 \log (x+1)+2 \sqrt{3} \tan ^{-1}\left(\frac{2 x-1}{\sqrt{3}}\right)-2 \sqrt{3} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)\right)","-\frac{1}{6} \log \left(1-x^2\right)+\frac{\tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{1}{12} \log \left(x^4+x^2+1\right)",1,"(2*Sqrt[3]*ArcTan[(-1 + 2*x)/Sqrt[3]] - 2*Sqrt[3]*ArcTan[(1 + 2*x)/Sqrt[3]] - 2*Log[1 - x] - 2*Log[1 + x] + Log[1 - x + x^2] + Log[1 + x + x^2])/12","A",1
1352,1,75,47,0.0104212,"\int \frac{1}{1-x^6} \, dx","Integrate[(1 - x^6)^(-1),x]","\frac{1}{12} \left(-\log \left(x^2-x+1\right)+\log \left(x^2+x+1\right)-2 \log (1-x)+2 \log (x+1)+2 \sqrt{3} \tan ^{-1}\left(\frac{2 x-1}{\sqrt{3}}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)\right)","\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,"(2*Sqrt[3]*ArcTan[(-1 + 2*x)/Sqrt[3]] + 2*Sqrt[3]*ArcTan[(1 + 2*x)/Sqrt[3]] - 2*Log[1 - x] + 2*Log[1 + x] - Log[1 - x + x^2] + Log[1 + x + x^2])/12","A",1
1353,1,15,15,0.0036393,"\int \frac{1}{x \left(1-x^6\right)} \, dx","Integrate[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",1
1354,1,86,52,0.0218028,"\int \frac{1}{x^2 \left(1-x^6\right)} \, dx","Integrate[1/(x^2*(1 - x^6)),x]","-\frac{x \log \left(x^2-x+1\right)-x \log \left(x^2+x+1\right)+2 x \log (1-x)-2 x \log (x+1)+2 \sqrt{3} x \tan ^{-1}\left(\frac{2 x-1}{\sqrt{3}}\right)+2 \sqrt{3} x \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)+12}{12 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,"-1/12*(12 + 2*Sqrt[3]*x*ArcTan[(-1 + 2*x)/Sqrt[3]] + 2*Sqrt[3]*x*ArcTan[(1 + 2*x)/Sqrt[3]] + 2*x*Log[1 - x] - 2*x*Log[1 + x] + x*Log[1 - x + x^2] - x*Log[1 + x + x^2])/x","A",1
1355,1,78,56,0.0239813,"\int \frac{1}{x^3 \left(1-x^6\right)} \, dx","Integrate[1/(x^3*(1 - x^6)),x]","\frac{1}{12} \left(-\frac{6}{x^2}+\log \left(x^2-x+1\right)+\log \left(x^2+x+1\right)-2 \log (1-x)-2 \log (x+1)-2 \sqrt{3} \tan ^{-1}\left(\frac{2 x-1}{\sqrt{3}}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)\right)","-\frac{1}{2 x^2}-\frac{1}{6} \log \left(1-x^2\right)-\frac{\tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{1}{12} \log \left(x^4+x^2+1\right)",1,"(-6/x^2 - 2*Sqrt[3]*ArcTan[(-1 + 2*x)/Sqrt[3]] + 2*Sqrt[3]*ArcTan[(1 + 2*x)/Sqrt[3]] - 2*Log[1 - x] - 2*Log[1 + x] + Log[1 - x + x^2] + Log[1 + x + x^2])/12","A",1
1356,1,30,16,0.0042445,"\int \frac{1}{x^4 \left(1-x^6\right)} \, dx","Integrate[1/(x^4*(1 - x^6)),x]","-\frac{1}{3 x^3}-\frac{1}{6} \log \left(1-x^3\right)+\frac{1}{6} \log \left(x^3+1\right)","\frac{1}{3} \tanh ^{-1}\left(x^3\right)-\frac{1}{3 x^3}",1,"-1/3*1/x^3 - Log[1 - x^3]/6 + Log[1 + x^3]/6","A",1
1357,1,78,56,0.0260334,"\int \frac{1}{x^5 \left(1-x^6\right)} \, dx","Integrate[1/(x^5*(1 - x^6)),x]","\frac{1}{12} \left(-\frac{3}{x^4}+\log \left(x^2-x+1\right)+\log \left(x^2+x+1\right)-2 \log (1-x)-2 \log (x+1)+2 \sqrt{3} \tan ^{-1}\left(\frac{2 x-1}{\sqrt{3}}\right)-2 \sqrt{3} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)\right)","-\frac{1}{4 x^4}-\frac{1}{6} \log \left(1-x^2\right)+\frac{\tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{1}{12} \log \left(x^4+x^2+1\right)",1,"(-3/x^4 + 2*Sqrt[3]*ArcTan[(-1 + 2*x)/Sqrt[3]] - 2*Sqrt[3]*ArcTan[(1 + 2*x)/Sqrt[3]] - 2*Log[1 - x] - 2*Log[1 + x] + Log[1 - x + x^2] + Log[1 + x + x^2])/12","A",1
1358,1,82,80,0.0264316,"\int \frac{1}{x^6 \left(1-x^6\right)} \, dx","Integrate[1/(x^6*(1 - x^6)),x]","\frac{1}{60} \left(-\frac{12}{x^5}-5 \log \left(x^2-x+1\right)+5 \log \left(x^2+x+1\right)-10 \log (1-x)+10 \log (x+1)+10 \sqrt{3} \tan ^{-1}\left(\frac{2 x-1}{\sqrt{3}}\right)+10 \sqrt{3} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)\right)","-\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,"(-12/x^5 + 10*Sqrt[3]*ArcTan[(-1 + 2*x)/Sqrt[3]] + 10*Sqrt[3]*ArcTan[(1 + 2*x)/Sqrt[3]] - 10*Log[1 - x] + 10*Log[1 + x] - 5*Log[1 - x + x^2] + 5*Log[1 + x + x^2])/60","A",1
1359,1,22,22,0.004064,"\int \frac{1}{x^7 \left(1-x^6\right)} \, dx","Integrate[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*1/x^6 + Log[x] - Log[1 - x^6]/6","A",1
1360,1,87,85,0.0288834,"\int \frac{1}{x^8 \left(1-x^6\right)} \, dx","Integrate[1/(x^8*(1 - x^6)),x]","\frac{1}{84} \left(-\frac{12}{x^7}-7 \log \left(x^2-x+1\right)+7 \log \left(x^2+x+1\right)-\frac{84}{x}-14 \log (1-x)+14 \log (x+1)-14 \sqrt{3} \tan ^{-1}\left(\frac{2 x-1}{\sqrt{3}}\right)-14 \sqrt{3} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)\right)","-\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,"(-12/x^7 - 84/x - 14*Sqrt[3]*ArcTan[(-1 + 2*x)/Sqrt[3]] - 14*Sqrt[3]*ArcTan[(1 + 2*x)/Sqrt[3]] - 14*Log[1 - x] + 14*Log[1 + x] - 7*Log[1 - x + x^2] + 7*Log[1 + x + x^2])/84","A",1
1361,1,16,16,0.0058872,"\int \frac{x^8}{1+x^6} \, dx","Integrate[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",1
1362,1,79,56,0.0172157,"\int \frac{x^7}{1+x^6} \, dx","Integrate[x^7/(1 + x^6),x]","\frac{1}{12} \left(6 x^2-2 \log \left(x^2+1\right)+\log \left(x^2-\sqrt{3} x+1\right)+\log \left(x^2+\sqrt{3} x+1\right)+2 \sqrt{3} \tan ^{-1}\left(\sqrt{3}-2 x\right)+2 \sqrt{3} \tan ^{-1}\left(2 x+\sqrt{3}\right)\right)","\frac{x^2}{2}-\frac{1}{6} \log \left(x^2+1\right)+\frac{\tan ^{-1}\left(\frac{1-2 x^2}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{1}{12} \log \left(x^4-x^2+1\right)",1,"(6*x^2 + 2*Sqrt[3]*ArcTan[Sqrt[3] - 2*x] + 2*Sqrt[3]*ArcTan[Sqrt[3] + 2*x] - 2*Log[1 + x^2] + Log[1 - Sqrt[3]*x + x^2] + Log[1 + Sqrt[3]*x + x^2])/12","A",1
1363,1,76,81,0.0187222,"\int \frac{x^6}{1+x^6} \, dx","Integrate[x^6/(1 + x^6),x]","\frac{1}{12} \left(\sqrt{3} \log \left(x^2-\sqrt{3} x+1\right)-\sqrt{3} \log \left(x^2+\sqrt{3} x+1\right)+12 x+2 \tan ^{-1}\left(\sqrt{3}-2 x\right)-4 \tan ^{-1}(x)-2 \tan ^{-1}\left(2 x+\sqrt{3}\right)\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,"(12*x + 2*ArcTan[Sqrt[3] - 2*x] - 4*ArcTan[x] - 2*ArcTan[Sqrt[3] + 2*x] + Sqrt[3]*Log[1 - Sqrt[3]*x + x^2] - Sqrt[3]*Log[1 + Sqrt[3]*x + x^2])/12","A",1
1364,1,10,10,0.0029122,"\int \frac{x^5}{1+x^6} \, dx","Integrate[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
1365,1,73,80,0.0353436,"\int \frac{x^4}{1+x^6} \, dx","Integrate[x^4/(1 + x^6),x]","\frac{1}{12} \left(\sqrt{3} \log \left(x^2-\sqrt{3} x+1\right)-\sqrt{3} \log \left(x^2+\sqrt{3} x+1\right)-2 \tan ^{-1}\left(\sqrt{3}-2 x\right)+4 \tan ^{-1}(x)+2 \tan ^{-1}\left(2 x+\sqrt{3}\right)\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,"(-2*ArcTan[Sqrt[3] - 2*x] + 4*ArcTan[x] + 2*ArcTan[Sqrt[3] + 2*x] + Sqrt[3]*Log[1 - Sqrt[3]*x + x^2] - Sqrt[3]*Log[1 + Sqrt[3]*x + x^2])/12","A",1
1366,1,74,49,0.0104506,"\int \frac{x^3}{1+x^6} \, dx","Integrate[x^3/(1 + x^6),x]","\frac{1}{12} \left(-2 \log \left(x^2+1\right)+\log \left(x^2-\sqrt{3} x+1\right)+\log \left(x^2+\sqrt{3} x+1\right)-2 \sqrt{3} \tan ^{-1}\left(\sqrt{3}-2 x\right)-2 \sqrt{3} \tan ^{-1}\left(2 x+\sqrt{3}\right)\right)","-\frac{1}{6} \log \left(x^2+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 x^2}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{1}{12} \log \left(x^4-x^2+1\right)",1,"(-2*Sqrt[3]*ArcTan[Sqrt[3] - 2*x] - 2*Sqrt[3]*ArcTan[Sqrt[3] + 2*x] - 2*Log[1 + x^2] + Log[1 - Sqrt[3]*x + x^2] + Log[1 + Sqrt[3]*x + x^2])/12","A",1
1367,1,8,8,0.0043374,"\int \frac{x^2}{1+x^6} \, dx","Integrate[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",1
1368,1,78,49,0.0098287,"\int \frac{x}{1+x^6} \, dx","Integrate[x/(1 + x^6),x]","\frac{1}{12} \left(2 \log \left(x^2+1\right)-\log \left(x^2-\sqrt{3} x+1\right)-\log \left(x^2+\sqrt{3} x+1\right)-2 \sqrt{3} \tan ^{-1}\left(\sqrt{3}-2 x\right)-2 \sqrt{3} \tan ^{-1}\left(2 x+\sqrt{3}\right)\right)","\frac{1}{6} \log \left(x^2+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 x^2}{\sqrt{3}}\right)}{2 \sqrt{3}}-\frac{1}{12} \log \left(x^4-x^2+1\right)",1,"(-2*Sqrt[3]*ArcTan[Sqrt[3] - 2*x] - 2*Sqrt[3]*ArcTan[Sqrt[3] + 2*x] + 2*Log[1 + x^2] - Log[1 - Sqrt[3]*x + x^2] - Log[1 + Sqrt[3]*x + x^2])/12","A",1
1369,1,73,80,0.0117064,"\int \frac{1}{1+x^6} \, dx","Integrate[(1 + x^6)^(-1),x]","\frac{1}{12} \left(-\sqrt{3} \log \left(x^2-\sqrt{3} x+1\right)+\sqrt{3} \log \left(x^2+\sqrt{3} x+1\right)-2 \tan ^{-1}\left(\sqrt{3}-2 x\right)+4 \tan ^{-1}(x)+2 \tan ^{-1}\left(2 x+\sqrt{3}\right)\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,"(-2*ArcTan[Sqrt[3] - 2*x] + 4*ArcTan[x] + 2*ArcTan[Sqrt[3] + 2*x] - Sqrt[3]*Log[1 - Sqrt[3]*x + x^2] + Sqrt[3]*Log[1 + Sqrt[3]*x + x^2])/12","A",1
1370,1,13,13,0.0033706,"\int \frac{1}{x \left(1+x^6\right)} \, dx","Integrate[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",1
1371,1,82,85,0.0405249,"\int \frac{1}{x^2 \left(1+x^6\right)} \, dx","Integrate[1/(x^2*(1 + x^6)),x]","-\frac{\sqrt{3} x \log \left(x^2-\sqrt{3} x+1\right)-\sqrt{3} x \log \left(x^2+\sqrt{3} x+1\right)-2 x \tan ^{-1}\left(\sqrt{3}-2 x\right)+4 x \tan ^{-1}(x)+2 x \tan ^{-1}\left(2 x+\sqrt{3}\right)+12}{12 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)",1,"-1/12*(12 - 2*x*ArcTan[Sqrt[3] - 2*x] + 4*x*ArcTan[x] + 2*x*ArcTan[Sqrt[3] + 2*x] + Sqrt[3]*x*Log[1 - Sqrt[3]*x + x^2] - Sqrt[3]*x*Log[1 + Sqrt[3]*x + x^2])/x","A",1
1372,1,83,56,0.0756678,"\int \frac{1}{x^3 \left(1+x^6\right)} \, dx","Integrate[1/(x^3*(1 + x^6)),x]","\frac{1}{12} \left(-\frac{6}{x^2}+2 \log \left(x^2+1\right)-\log \left(x^2-\sqrt{3} x+1\right)-\log \left(x^2+\sqrt{3} x+1\right)+2 \sqrt{3} \tan ^{-1}\left(\sqrt{3}-2 x\right)+2 \sqrt{3} \tan ^{-1}\left(2 x+\sqrt{3}\right)\right)","-\frac{1}{2 x^2}+\frac{1}{6} \log \left(x^2+1\right)+\frac{\tan ^{-1}\left(\frac{1-2 x^2}{\sqrt{3}}\right)}{2 \sqrt{3}}-\frac{1}{12} \log \left(x^4-x^2+1\right)",1,"(-6/x^2 + 2*Sqrt[3]*ArcTan[Sqrt[3] - 2*x] + 2*Sqrt[3]*ArcTan[Sqrt[3] + 2*x] + 2*Log[1 + x^2] - Log[1 - Sqrt[3]*x + x^2] - Log[1 + Sqrt[3]*x + x^2])/12","A",1
1373,1,16,16,0.0056879,"\int \frac{1}{x^4 \left(1+x^6\right)} \, dx","Integrate[1/(x^4*(1 + x^6)),x]","\frac{1}{3} \tan ^{-1}\left(\frac{1}{x^3}\right)-\frac{1}{3 x^3}","-\frac{1}{3 x^3}-\frac{1}{3} \tan ^{-1}\left(x^3\right)",1,"-1/3*1/x^3 + ArcTan[x^(-3)]/3","A",1
1374,1,79,56,0.0217573,"\int \frac{1}{x^5 \left(1+x^6\right)} \, dx","Integrate[1/(x^5*(1 + x^6)),x]","\frac{1}{12} \left(-\frac{3}{x^4}-2 \log \left(x^2+1\right)+\log \left(x^2-\sqrt{3} x+1\right)+\log \left(x^2+\sqrt{3} x+1\right)+2 \sqrt{3} \tan ^{-1}\left(\sqrt{3}-2 x\right)+2 \sqrt{3} \tan ^{-1}\left(2 x+\sqrt{3}\right)\right)","-\frac{1}{4 x^4}-\frac{1}{6} \log \left(x^2+1\right)+\frac{\tan ^{-1}\left(\frac{1-2 x^2}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{1}{12} \log \left(x^4-x^2+1\right)",1,"(-3/x^4 + 2*Sqrt[3]*ArcTan[Sqrt[3] - 2*x] + 2*Sqrt[3]*ArcTan[Sqrt[3] + 2*x] - 2*Log[1 + x^2] + Log[1 - Sqrt[3]*x + x^2] + Log[1 + Sqrt[3]*x + x^2])/12","A",1
1375,1,79,87,0.0285302,"\int \frac{1}{x^6 \left(1+x^6\right)} \, dx","Integrate[1/(x^6*(1 + x^6)),x]","\frac{1}{60} \left(-\frac{12}{x^5}+5 \sqrt{3} \log \left(x^2-\sqrt{3} x+1\right)-5 \sqrt{3} \log \left(x^2+\sqrt{3} x+1\right)+10 \tan ^{-1}\left(\sqrt{3}-2 x\right)-20 \tan ^{-1}(x)-10 \tan ^{-1}\left(2 x+\sqrt{3}\right)\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,"(-12/x^5 + 10*ArcTan[Sqrt[3] - 2*x] - 20*ArcTan[x] - 10*ArcTan[Sqrt[3] + 2*x] + 5*Sqrt[3]*Log[1 - Sqrt[3]*x + x^2] - 5*Sqrt[3]*Log[1 + Sqrt[3]*x + x^2])/60","A",1
1376,1,22,22,0.0037872,"\int \frac{1}{x^7 \left(1+x^6\right)} \, dx","Integrate[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*1/x^6 - Log[x] + Log[1 + x^6]/6","A",1
1377,1,84,90,0.0322773,"\int \frac{1}{x^8 \left(1+x^6\right)} \, dx","Integrate[1/(x^8*(1 + x^6)),x]","\frac{1}{84} \left(-\frac{12}{x^7}+7 \sqrt{3} \log \left(x^2-\sqrt{3} x+1\right)-7 \sqrt{3} \log \left(x^2+\sqrt{3} x+1\right)+\frac{84}{x}-14 \tan ^{-1}\left(\sqrt{3}-2 x\right)+28 \tan ^{-1}(x)+14 \tan ^{-1}\left(2 x+\sqrt{3}\right)\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,"(-12/x^7 + 84/x - 14*ArcTan[Sqrt[3] - 2*x] + 28*ArcTan[x] + 14*ArcTan[Sqrt[3] + 2*x] + 7*Sqrt[3]*Log[1 - Sqrt[3]*x + x^2] - 7*Sqrt[3]*Log[1 + Sqrt[3]*x + x^2])/84","A",1
1378,1,162,180,0.0751018,"\int \frac{1}{2-3 x^6} \, dx","Integrate[(2 - 3*x^6)^(-1),x]","\frac{\sqrt{3} \left(-\log \left(2^{2/3} \sqrt[3]{3} x^2-2^{5/6} \sqrt[6]{3} x+2\right)+\log \left(2^{2/3} \sqrt[3]{3} x^2+2^{5/6} \sqrt[6]{3} x+2\right)-2 \log \left(2-2^{5/6} \sqrt[6]{3} x\right)+2 \log \left(2^{5/6} \sqrt[6]{3} x+2\right)\right)+6 \tan ^{-1}\left(\frac{2^{5/6} x}{\sqrt[3]{3}}+\frac{1}{\sqrt{3}}\right)+6 \tan ^{-1}\left(\frac{2^{5/6} \sqrt[6]{3} x-1}{\sqrt{3}}\right)}{12\ 2^{5/6} 3^{2/3}}","-\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,"(6*ArcTan[1/Sqrt[3] + (2^(5/6)*x)/3^(1/3)] + 6*ArcTan[(-1 + 2^(5/6)*3^(1/6)*x)/Sqrt[3]] + Sqrt[3]*(-2*Log[2 - 2^(5/6)*3^(1/6)*x] + 2*Log[2 + 2^(5/6)*3^(1/6)*x] - Log[2 - 2^(5/6)*3^(1/6)*x + 2^(2/3)*3^(1/3)*x^2] + Log[2 + 2^(5/6)*3^(1/6)*x + 2^(2/3)*3^(1/3)*x^2]))/(12*2^(5/6)*3^(2/3))","A",1
1379,1,20,244,0.0068914,"\int \frac{\sqrt[3]{x}}{1-x^6} \, dx","Integrate[x^(1/3)/(1 - x^6),x]","\frac{3}{4} x^{4/3} \, _2F_1\left(\frac{2}{9},1;\frac{11}{9};x^6\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,"(3*x^(4/3)*Hypergeometric2F1[2/9, 1, 11/9, x^6])/4","C",1
1380,1,56,58,0.0302594,"\int x^8 \sqrt{-1+4 x^6} \, dx","Integrate[x^8*Sqrt[-1 + 4*x^6],x]","\frac{\left(4 x^6-1\right) \left(\sin ^{-1}\left(2 x^3\right)+2 \sqrt{1-4 x^6} \left(8 x^6-1\right) x^3\right)}{192 \sqrt{-\left(1-4 x^6\right)^2}}","\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,"((-1 + 4*x^6)*(2*x^3*Sqrt[1 - 4*x^6]*(-1 + 8*x^6) + ArcSin[2*x^3]))/(192*Sqrt[-(1 - 4*x^6)^2])","A",1
1381,1,17,17,0.0054692,"\int x^5 \sqrt{a^6-x^6} \, dx","Integrate[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,"-1/9*(a^6 - x^6)^(3/2)","A",1
1382,1,50,35,0.0202008,"\int x^2 \sqrt{-2+x^6} \, dx","Integrate[x^2*Sqrt[-2 + x^6],x]","\frac{\left(x^6-2\right) \left(2 \sin ^{-1}\left(\frac{x^3}{\sqrt{2}}\right)+\sqrt{2-x^6} x^3\right)}{6 \sqrt{-\left(x^6-2\right)^2}}","\frac{1}{6} x^3 \sqrt{x^6-2}-\frac{1}{3} \tanh ^{-1}\left(\frac{x^3}{\sqrt{x^6-2}}\right)",1,"((-2 + x^6)*(x^3*Sqrt[2 - x^6] + 2*ArcSin[x^3/Sqrt[2]]))/(6*Sqrt[-(-2 + x^6)^2])","A",1
1383,1,30,53,0.011468,"\int \frac{x^{23}}{\sqrt{2+x^6}} \, dx","Integrate[x^23/Sqrt[2 + x^6],x]","\frac{1}{105} \sqrt{x^6+2} \left(5 x^{18}-12 x^{12}+32 x^6-128\right)","\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,"(Sqrt[2 + x^6]*(-128 + 32*x^6 - 12*x^12 + 5*x^18))/105","A",1
1384,1,25,40,0.0080433,"\int \frac{x^{17}}{\sqrt{2+x^6}} \, dx","Integrate[x^17/Sqrt[2 + x^6],x]","\frac{1}{45} \sqrt{x^6+2} \left(3 x^{12}-8 x^6+32\right)","\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,"(Sqrt[2 + x^6]*(32 - 8*x^6 + 3*x^12))/45","A",1
1385,1,18,27,0.0053306,"\int \frac{x^{11}}{\sqrt{2+x^6}} \, dx","Integrate[x^11/Sqrt[2 + x^6],x]","\frac{1}{9} \left(x^6-4\right) \sqrt{x^6+2}","\frac{1}{9} \left(x^6+2\right)^{3/2}-\frac{2 \sqrt{x^6+2}}{3}",1,"((-4 + x^6)*Sqrt[2 + x^6])/9","A",1
1386,1,13,13,0.0020299,"\int \frac{x^5}{\sqrt{2+x^6}} \, dx","Integrate[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
1387,1,25,25,0.0060408,"\int \frac{1}{x \sqrt{2+x^6}} \, dx","Integrate[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,"-1/3*ArcTanh[Sqrt[2 + x^6]/Sqrt[2]]/Sqrt[2]","A",1
1388,1,42,42,0.0080558,"\int \frac{1}{x^7 \sqrt{2+x^6}} \, dx","Integrate[1/(x^7*Sqrt[2 + x^6]),x]","\frac{\sqrt{2} x^6 \tanh ^{-1}\left(\sqrt{\frac{x^6}{2}+1}\right)-2 \sqrt{x^6+2}}{24 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,"(-2*Sqrt[2 + x^6] + Sqrt[2]*x^6*ArcTanh[Sqrt[1 + x^6/2]])/(24*x^6)","A",1
1389,1,30,58,0.0073178,"\int \frac{1}{x^{13} \sqrt{2+x^6}} \, dx","Integrate[1/(x^13*Sqrt[2 + x^6]),x]","-\frac{1}{24} \sqrt{x^6+2} \, _2F_1\left(\frac{1}{2},3;\frac{3}{2};\frac{x^6}{2}+1\right)","\frac{\sqrt{x^6+2}}{32 x^6}-\frac{\tanh ^{-1}\left(\frac{\sqrt{x^6+2}}{\sqrt{2}}\right)}{32 \sqrt{2}}-\frac{\sqrt{x^6+2}}{24 x^{12}}",1,"-1/24*(Sqrt[2 + x^6]*Hypergeometric2F1[1/2, 3, 3/2, 1 + x^6/2])","C",1
1390,1,35,47,0.0123309,"\int \frac{x^{14}}{\sqrt{2+x^6}} \, dx","Integrate[x^14/Sqrt[2 + x^6],x]","\frac{1}{12} \left(6 \sinh ^{-1}\left(\frac{x^3}{\sqrt{2}}\right)+\left(x^6-3\right) \sqrt{x^6+2} x^3\right)","\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",1,"(x^3*(-3 + x^6)*Sqrt[2 + x^6] + 6*ArcSinh[x^3/Sqrt[2]])/12","A",1
1391,1,31,31,0.0068464,"\int \frac{x^8}{\sqrt{2+x^6}} \, dx","Integrate[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",1
1392,1,14,14,0.0024152,"\int \frac{x^2}{\sqrt{2+x^6}} \, dx","Integrate[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",1
1393,1,16,16,0.0026485,"\int \frac{1}{x^4 \sqrt{2+x^6}} \, dx","Integrate[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,"-1/6*Sqrt[2 + x^6]/x^3","A",1
1394,1,21,33,0.0048063,"\int \frac{1}{x^{10} \sqrt{2+x^6}} \, dx","Integrate[1/(x^10*Sqrt[2 + x^6]),x]","\frac{\left(x^6-1\right) \sqrt{x^6+2}}{18 x^9}","\frac{\sqrt{x^6+2}}{18 x^3}-\frac{\sqrt{x^6+2}}{18 x^9}",1,"((-1 + x^6)*Sqrt[2 + x^6])/(18*x^9)","A",1
1395,1,28,49,0.0068575,"\int \frac{1}{x^{16} \sqrt{2+x^6}} \, dx","Integrate[1/(x^16*Sqrt[2 + x^6]),x]","-\frac{\sqrt{x^6+2} \left(2 x^{12}-2 x^6+3\right)}{90 x^{15}}","-\frac{\sqrt{x^6+2}}{30 x^{15}}+\frac{\sqrt{x^6+2}}{45 x^9}-\frac{\sqrt{x^6+2}}{45 x^3}",1,"-1/90*(Sqrt[2 + x^6]*(3 - 2*x^6 + 2*x^12))/x^15","A",1
1396,1,41,186,0.0087694,"\int \frac{x^7}{\sqrt{2+x^6}} \, dx","Integrate[x^7/Sqrt[2 + x^6],x]","\frac{1}{5} x^2 \left(\sqrt{x^6+2}-\sqrt{2} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};-\frac{x^6}{2}\right)\right)","\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] - Sqrt[2]*Hypergeometric2F1[1/3, 1/2, 4/3, -1/2*x^6]))/5","C",1
1397,1,29,166,0.0053189,"\int \frac{x}{\sqrt{2+x^6}} \, dx","Integrate[x/Sqrt[2 + x^6],x]","\frac{x^2 \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};-\frac{x^6}{2}\right)}{2 \sqrt{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,"(x^2*Hypergeometric2F1[1/3, 1/2, 4/3, -1/2*x^6])/(2*Sqrt[2])","C",1
1398,1,29,186,0.0055427,"\int \frac{1}{x^5 \sqrt{2+x^6}} \, dx","Integrate[1/(x^5*Sqrt[2 + x^6]),x]","-\frac{\, _2F_1\left(-\frac{2}{3},\frac{1}{2};\frac{1}{3};-\frac{x^6}{2}\right)}{4 \sqrt{2} x^4}","-\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,"-1/4*Hypergeometric2F1[-2/3, 1/2, 1/3, -1/2*x^6]/(Sqrt[2]*x^4)","C",1
1399,1,39,179,0.008077,"\int \frac{x^6}{\sqrt{2+x^6}} \, dx","Integrate[x^6/Sqrt[2 + x^6],x]","\frac{1}{4} x \left(\sqrt{x^6+2}-\sqrt{2} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};-\frac{x^6}{2}\right)\right)","\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] - Sqrt[2]*Hypergeometric2F1[1/6, 1/2, 7/6, -1/2*x^6]))/4","C",1
1400,1,24,164,0.0027131,"\int \frac{1}{\sqrt{2+x^6}} \, dx","Integrate[1/Sqrt[2 + x^6],x]","\frac{x \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};-\frac{x^6}{2}\right)}{\sqrt{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*Hypergeometric2F1[1/6, 1/2, 7/6, -1/2*x^6])/Sqrt[2]","C",1
1401,1,29,181,0.0048745,"\int \frac{1}{x^6 \sqrt{2+x^6}} \, dx","Integrate[1/(x^6*Sqrt[2 + x^6]),x]","-\frac{\, _2F_1\left(-\frac{5}{6},\frac{1}{2};\frac{1}{6};-\frac{x^6}{2}\right)}{5 \sqrt{2} x^5}","-\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,"-1/5*Hypergeometric2F1[-5/6, 1/2, 1/6, -1/2*x^6]/(Sqrt[2]*x^5)","C",1
1402,1,41,378,0.0274574,"\int \frac{x^9}{\sqrt{2+x^6}} \, dx","Integrate[x^9/Sqrt[2 + x^6],x]","\frac{1}{7} x^4 \left(\sqrt{x^6+2}-\sqrt{2} \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};-\frac{x^6}{2}\right)\right)","\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] - Sqrt[2]*Hypergeometric2F1[1/2, 2/3, 5/3, -1/2*x^6]))/7","C",1
1403,1,29,354,0.0052476,"\int \frac{x^3}{\sqrt{2+x^6}} \, dx","Integrate[x^3/Sqrt[2 + x^6],x]","\frac{x^4 \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};-\frac{x^6}{2}\right)}{4 \sqrt{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,"(x^4*Hypergeometric2F1[1/2, 2/3, 5/3, -1/2*x^6])/(4*Sqrt[2])","C",1
1404,1,29,378,0.0062151,"\int \frac{1}{x^3 \sqrt{2+x^6}} \, dx","Integrate[1/(x^3*Sqrt[2 + x^6]),x]","-\frac{\, _2F_1\left(-\frac{1}{3},\frac{1}{2};\frac{2}{3};-\frac{x^6}{2}\right)}{2 \sqrt{2} x^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,"-1/2*Hypergeometric2F1[-1/3, 1/2, 2/3, -1/2*x^6]/(Sqrt[2]*x^2)","C",1
1405,1,41,394,0.0194641,"\int \frac{x^{10}}{\sqrt{2+x^6}} \, dx","Integrate[x^10/Sqrt[2 + x^6],x]","\frac{1}{8} x^5 \left(\sqrt{x^6+2}-\sqrt{2} \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};-\frac{x^6}{2}\right)\right)","\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] - Sqrt[2]*Hypergeometric2F1[1/2, 5/6, 11/6, -1/2*x^6]))/8","C",1
1406,1,29,376,0.0046807,"\int \frac{x^4}{\sqrt{2+x^6}} \, dx","Integrate[x^4/Sqrt[2 + x^6],x]","\frac{x^5 \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};-\frac{x^6}{2}\right)}{5 \sqrt{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,"(x^5*Hypergeometric2F1[1/2, 5/6, 11/6, -1/2*x^6])/(5*Sqrt[2])","C",1
1407,1,27,392,0.0046366,"\int \frac{1}{x^2 \sqrt{2+x^6}} \, dx","Integrate[1/(x^2*Sqrt[2 + x^6]),x]","-\frac{\, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{5}{6};-\frac{x^6}{2}\right)}{\sqrt{2} x}","-\frac{\sqrt{x^6+2}}{2 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}}",1,"-(Hypergeometric2F1[-1/6, 1/2, 5/6, -1/2*x^6]/(Sqrt[2]*x))","C",1
1408,1,28,51,0.0105104,"\int \frac{x^{23}}{\left(2+x^6\right)^{3/2}} \, dx","Integrate[x^23/(2 + x^6)^(3/2),x]","\frac{x^{18}-4 x^{12}+32 x^6+128}{15 \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,"(128 + 32*x^6 - 4*x^12 + x^18)/(15*Sqrt[2 + x^6])","A",1
1409,1,23,40,0.0097669,"\int \frac{x^{17}}{\left(2+x^6\right)^{3/2}} \, dx","Integrate[x^17/(2 + x^6)^(3/2),x]","\frac{x^{12}-8 x^6-32}{9 \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,"(-32 - 8*x^6 + x^12)/(9*Sqrt[2 + x^6])","A",1
1410,1,18,27,0.0065348,"\int \frac{x^{11}}{\left(2+x^6\right)^{3/2}} \, dx","Integrate[x^11/(2 + x^6)^(3/2),x]","\frac{x^6+4}{3 \sqrt{x^6+2}}","\frac{\sqrt{x^6+2}}{3}+\frac{2}{3 \sqrt{x^6+2}}",1,"(4 + x^6)/(3*Sqrt[2 + x^6])","A",1
1411,1,13,13,0.0024803,"\int \frac{x^5}{\left(2+x^6\right)^{3/2}} \, dx","Integrate[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*1/Sqrt[2 + x^6]","A",1
1412,1,30,39,0.0063554,"\int \frac{1}{x \left(2+x^6\right)^{3/2}} \, dx","Integrate[1/(x*(2 + x^6)^(3/2)),x]","\frac{\, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{x^6}{2}+1\right)}{6 \sqrt{x^6+2}}","\frac{1}{6 \sqrt{x^6+2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{x^6+2}}{\sqrt{2}}\right)}{6 \sqrt{2}}",1,"Hypergeometric2F1[-1/2, 1, 1/2, 1 + x^6/2]/(6*Sqrt[2 + x^6])","C",1
1413,1,30,55,0.0063953,"\int \frac{1}{x^7 \left(2+x^6\right)^{3/2}} \, dx","Integrate[1/(x^7*(2 + x^6)^(3/2)),x]","-\frac{\, _2F_1\left(-\frac{1}{2},2;\frac{1}{2};\frac{x^6}{2}+1\right)}{12 \sqrt{x^6+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,"-1/12*Hypergeometric2F1[-1/2, 2, 1/2, 1 + x^6/2]/Sqrt[2 + x^6]","C",1
1414,1,30,71,0.0065681,"\int \frac{1}{x^{13} \left(2+x^6\right)^{3/2}} \, dx","Integrate[1/(x^13*(2 + x^6)^(3/2)),x]","\frac{\, _2F_1\left(-\frac{1}{2},3;\frac{1}{2};\frac{x^6}{2}+1\right)}{24 \sqrt{x^6+2}}","\frac{5}{96 x^6 \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}}-\frac{1}{24 x^{12} \sqrt{x^6+2}}",1,"Hypergeometric2F1[-1/2, 3, 1/2, 1 + x^6/2]/(24*Sqrt[2 + x^6])","C",1
1415,1,43,45,0.0197542,"\int \frac{x^{14}}{\left(2+x^6\right)^{3/2}} \, dx","Integrate[x^14/(2 + x^6)^(3/2),x]","\frac{x^9+6 x^3-6 \sqrt{x^6+2} \sinh ^{-1}\left(\frac{x^3}{\sqrt{2}}\right)}{6 \sqrt{x^6+2}}","-\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",1,"(6*x^3 + x^9 - 6*Sqrt[2 + x^6]*ArcSinh[x^3/Sqrt[2]])/(6*Sqrt[2 + x^6])","A",1
1416,1,29,31,0.0166437,"\int \frac{x^8}{\left(2+x^6\right)^{3/2}} \, dx","Integrate[x^8/(2 + x^6)^(3/2),x]","\frac{1}{3} \left(\sinh ^{-1}\left(\frac{x^3}{\sqrt{2}}\right)-\frac{x^3}{\sqrt{x^6+2}}\right)","\frac{1}{3} \sinh ^{-1}\left(\frac{x^3}{\sqrt{2}}\right)-\frac{x^3}{3 \sqrt{x^6+2}}",1,"(-(x^3/Sqrt[2 + x^6]) + ArcSinh[x^3/Sqrt[2]])/3","A",1
1417,1,16,16,0.0025561,"\int \frac{x^2}{\left(2+x^6\right)^{3/2}} \, dx","Integrate[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
1418,1,23,33,0.0054247,"\int \frac{1}{x^4 \left(2+x^6\right)^{3/2}} \, dx","Integrate[1/(x^4*(2 + x^6)^(3/2)),x]","\frac{-x^6-1}{6 x^3 \sqrt{x^6+2}}","-\frac{x^3}{6 \sqrt{x^6+2}}-\frac{1}{6 \sqrt{x^6+2} x^3}",1,"(-1 - x^6)/(6*x^3*Sqrt[2 + x^6])","A",1
1419,1,28,49,0.005841,"\int \frac{1}{x^{10} \left(2+x^6\right)^{3/2}} \, dx","Integrate[1/(x^10*(2 + x^6)^(3/2)),x]","\frac{2 x^{12}+2 x^6-1}{18 x^9 \sqrt{x^6+2}}","-\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}",1,"(-1 + 2*x^6 + 2*x^12)/(18*x^9*Sqrt[2 + x^6])","A",1
1420,1,56,202,0.0138983,"\int \frac{x^{13}}{\left(2+x^6\right)^{3/2}} \, dx","Integrate[x^13/(2 + x^6)^(3/2),x]","\frac{x^2 \left(-8 \sqrt{2} \sqrt{x^6+2} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};-\frac{x^6}{2}\right)+3 x^6+16\right)}{15 \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^2*(16 + 3*x^6 - 8*Sqrt[2]*Sqrt[2 + x^6]*Hypergeometric2F1[1/3, 1/2, 4/3, -1/2*x^6]))/(15*Sqrt[2 + x^6])","C",1
1421,1,42,186,0.0125109,"\int \frac{x^7}{\left(2+x^6\right)^{3/2}} \, dx","Integrate[x^7/(2 + x^6)^(3/2),x]","\frac{1}{6} x^2 \left(\sqrt{2} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};-\frac{x^6}{2}\right)-\frac{2}{\sqrt{x^6+2}}\right)","\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*(-2/Sqrt[2 + x^6] + Sqrt[2]*Hypergeometric2F1[1/3, 1/2, 4/3, -1/2*x^6]))/6","C",1
1422,1,42,186,0.0096906,"\int \frac{x}{\left(2+x^6\right)^{3/2}} \, dx","Integrate[x/(2 + x^6)^(3/2),x]","\frac{1}{24} x^2 \left(\sqrt{2} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};-\frac{x^6}{2}\right)+\frac{4}{\sqrt{x^6+2}}\right)","\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*(4/Sqrt[2 + x^6] + Sqrt[2]*Hypergeometric2F1[1/3, 1/2, 4/3, -1/2*x^6]))/24","C",1
1423,1,29,202,0.0061313,"\int \frac{1}{x^5 \left(2+x^6\right)^{3/2}} \, dx","Integrate[1/(x^5*(2 + x^6)^(3/2)),x]","-\frac{\, _2F_1\left(-\frac{2}{3},\frac{3}{2};\frac{1}{3};-\frac{x^6}{2}\right)}{8 \sqrt{2} x^4}","-\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,"-1/8*Hypergeometric2F1[-2/3, 3/2, 1/3, -1/2*x^6]/(Sqrt[2]*x^4)","C",1
1424,1,54,195,0.0135012,"\int \frac{x^{12}}{\left(2+x^6\right)^{3/2}} \, dx","Integrate[x^12/(2 + x^6)^(3/2),x]","\frac{x \left(-7 \sqrt{2} \sqrt{x^6+2} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};-\frac{x^6}{2}\right)+3 x^6+14\right)}{12 \sqrt{x^6+2}}","\frac{7}{12} \sqrt{x^6+2} x-\frac{x^7}{3 \sqrt{x^6+2}}-\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*(14 + 3*x^6 - 7*Sqrt[2]*Sqrt[2 + x^6]*Hypergeometric2F1[1/6, 1/2, 7/6, -1/2*x^6]))/(12*Sqrt[2 + x^6])","C",1
1425,1,42,179,0.0107552,"\int \frac{x^6}{\left(2+x^6\right)^{3/2}} \, dx","Integrate[x^6/(2 + x^6)^(3/2),x]","\frac{x \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};-\frac{x^6}{2}\right)}{3 \sqrt{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,"-1/3*x/Sqrt[2 + x^6] + (x*Hypergeometric2F1[1/6, 1/2, 7/6, -1/2*x^6])/(3*Sqrt[2])","C",1
1426,1,38,179,0.0182223,"\int \frac{1}{\left(2+x^6\right)^{3/2}} \, dx","Integrate[(2 + x^6)^(-3/2),x]","\frac{1}{6} x \left(\sqrt{2} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};-\frac{x^6}{2}\right)+\frac{1}{\sqrt{x^6+2}}\right)","\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*(1/Sqrt[2 + x^6] + Sqrt[2]*Hypergeometric2F1[1/6, 1/2, 7/6, -1/2*x^6]))/6","C",1
1427,1,29,197,0.0049825,"\int \frac{1}{x^6 \left(2+x^6\right)^{3/2}} \, dx","Integrate[1/(x^6*(2 + x^6)^(3/2)),x]","-\frac{\, _2F_1\left(-\frac{5}{6},\frac{3}{2};\frac{1}{6};-\frac{x^6}{2}\right)}{10 \sqrt{2} x^5}","-\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,"-1/10*Hypergeometric2F1[-5/6, 3/2, 1/6, -1/2*x^6]/(Sqrt[2]*x^5)","C",1
1428,1,54,394,0.0126868,"\int \frac{x^{15}}{\left(2+x^6\right)^{3/2}} \, dx","Integrate[x^15/(2 + x^6)^(3/2),x]","\frac{x^4 \left(10 \sqrt{2} \sqrt{x^6+2} \, _2F_1\left(\frac{2}{3},\frac{3}{2};\frac{5}{3};-\frac{x^6}{2}\right)+x^6-20\right)}{7 \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^4*(-20 + x^6 + 10*Sqrt[2]*Sqrt[2 + x^6]*Hypergeometric2F1[2/3, 3/2, 5/3, -1/2*x^6]))/(7*Sqrt[2 + x^6])","C",1
1429,1,41,376,0.0129895,"\int \frac{x^9}{\left(2+x^6\right)^{3/2}} \, dx","Integrate[x^9/(2 + x^6)^(3/2),x]","\frac{x^4}{\sqrt{x^6+2}}-\frac{x^4 \, _2F_1\left(\frac{2}{3},\frac{3}{2};\frac{5}{3};-\frac{x^6}{2}\right)}{\sqrt{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/Sqrt[2 + x^6] - (x^4*Hypergeometric2F1[2/3, 3/2, 5/3, -1/2*x^6])/Sqrt[2]","C",1
1430,1,29,378,0.0058869,"\int \frac{x^3}{\left(2+x^6\right)^{3/2}} \, dx","Integrate[x^3/(2 + x^6)^(3/2),x]","\frac{x^4 \, _2F_1\left(\frac{2}{3},\frac{3}{2};\frac{5}{3};-\frac{x^6}{2}\right)}{8 \sqrt{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*Hypergeometric2F1[2/3, 3/2, 5/3, -1/2*x^6])/(8*Sqrt[2])","C",1
1431,1,29,394,0.0293978,"\int \frac{1}{x^3 \left(2+x^6\right)^{3/2}} \, dx","Integrate[1/(x^3*(2 + x^6)^(3/2)),x]","-\frac{\, _2F_1\left(-\frac{1}{3},\frac{3}{2};\frac{2}{3};-\frac{x^6}{2}\right)}{4 \sqrt{2} x^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,"-1/4*Hypergeometric2F1[-1/3, 3/2, 2/3, -1/2*x^6]/(Sqrt[2]*x^2)","C",1
1432,1,43,392,0.0154134,"\int \frac{x^{10}}{\left(2+x^6\right)^{3/2}} \, dx","Integrate[x^10/(2 + x^6)^(3/2),x]","\frac{1}{4} x^5 \left(\frac{2}{\sqrt{x^6+2}}-\sqrt{2} \, _2F_1\left(\frac{5}{6},\frac{3}{2};\frac{11}{6};-\frac{x^6}{2}\right)\right)","-\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*(2/Sqrt[2 + x^6] - Sqrt[2]*Hypergeometric2F1[5/6, 3/2, 11/6, -1/2*x^6]))/4","C",1
1433,1,29,391,0.0049687,"\int \frac{x^4}{\left(2+x^6\right)^{3/2}} \, dx","Integrate[x^4/(2 + x^6)^(3/2),x]","\frac{x^5 \, _2F_1\left(\frac{5}{6},\frac{3}{2};\frac{11}{6};-\frac{x^6}{2}\right)}{10 \sqrt{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*Hypergeometric2F1[5/6, 3/2, 11/6, -1/2*x^6])/(10*Sqrt[2])","C",1
1434,1,29,408,0.0048038,"\int \frac{1}{x^2 \left(2+x^6\right)^{3/2}} \, dx","Integrate[1/(x^2*(2 + x^6)^(3/2)),x]","-\frac{\, _2F_1\left(-\frac{1}{6},\frac{3}{2};\frac{5}{6};-\frac{x^6}{2}\right)}{2 \sqrt{2} x}","-\frac{\sqrt{x^6+2}}{3 x}+\frac{1}{6 \sqrt{x^6+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{\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,"-1/2*Hypergeometric2F1[-1/6, 3/2, 5/6, -1/2*x^6]/(Sqrt[2]*x)","C",1
1435,1,25,25,0.0194685,"\int x^m \left(a+b x^7\right) \, dx","Integrate[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",1
1436,1,17,17,0.001282,"\int x^8 \left(a+b x^7\right) \, dx","Integrate[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",1
1437,1,13,13,0.0029843,"\int \frac{a+b x^7}{x^8} \, dx","Integrate[(a + b*x^7)/x^8,x]","b \log (x)-\frac{a}{7 x^7}","b \log (x)-\frac{a}{7 x^7}",1,"-1/7*a/x^7 + b*Log[x]","A",1
1438,1,40,43,0.0301377,"\int x^m \left(a+b x^7\right)^2 \, dx","Integrate[x^m*(a + b*x^7)^2,x]","x^{m+1} \left(\frac{a^2}{m+1}+\frac{2 a b x^7}{m+8}+\frac{b^2 x^{14}}{m+15}\right)","\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,"x^(1 + m)*(a^2/(1 + m) + (2*a*b*x^7)/(8 + m) + (b^2*x^14)/(15 + m))","A",1
1439,1,30,30,0.0012167,"\int x^8 \left(a+b x^7\right)^2 \, dx","Integrate[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",1
1440,1,27,27,0.0008288,"\int \frac{\left(a+b x^7\right)^2}{x^8} \, dx","Integrate[(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,"-1/7*a^2/x^7 + (b^2*x^7)/7 + 2*a*b*Log[x]","A",1
1441,1,41,39,0.0099373,"\int \frac{x^m}{a+b x^7} \, dx","Integrate[x^m/(a + b*x^7),x]","\frac{x^{m+1} \, _2F_1\left(1,\frac{m+1}{7};\frac{m+1}{7}+1;-\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, 1 + (1 + m)/7, -((b*x^7)/a)])/(a*(1 + m))","A",1
1442,1,15,15,0.0028967,"\int \frac{x^6}{a+b x^7} \, dx","Integrate[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
1443,1,262,335,0.3890534,"\int \frac{1}{a+b x^7} \, dx","Integrate[(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)-\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)-\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)+\log \left(\sqrt[7]{a}+\sqrt[7]{b} x\right)+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)+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)-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] + 2*ArcTan[(b^(1/7)*x*Sec[(3*Pi)/14])/a^(1/7) + Tan[(3*Pi)/14]]*Cos[(3*Pi)/14] + Log[a^(1/7) + b^(1/7)*x] - Cos[Pi/7]*Log[a^(2/7) + b^(2/7)*x^2 - 2*a^(1/7)*b^(1/7)*x*Cos[Pi/7]] - Log[a^(2/7) + b^(2/7)*x^2 - 2*a^(1/7)*b^(1/7)*x*Sin[Pi/14]]*Sin[Pi/14] - 2*ArcTan[Cot[Pi/7] - (b^(1/7)*x*Csc[Pi/7])/a^(1/7)]*Sin[Pi/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",1
1444,1,22,22,0.0056171,"\int \frac{1}{x \left(a+b x^7\right)} \, dx","Integrate[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",1
1445,1,40,38,0.0084669,"\int \frac{x^m}{a-b x^7} \, dx","Integrate[x^m/(a - b*x^7),x]","\frac{x^{m+1} \, _2F_1\left(1,\frac{m+1}{7};\frac{m+1}{7}+1;\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, 1 + (1 + m)/7, (b*x^7)/a])/(a*(1 + m))","A",1
1446,1,16,16,0.0032465,"\int \frac{x^6}{a-b x^7} \, dx","Integrate[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,"-1/7*Log[a - b*x^7]/b","A",1
1447,1,263,335,0.2979594,"\int \frac{1}{a-b x^7} \, dx","Integrate[(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)+\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)+\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)-\log \left(\sqrt[7]{a}-\sqrt[7]{b} x\right)+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)+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)+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] + 2*ArcTan[(b^(1/7)*x*Sec[(3*Pi)/14])/a^(1/7) - Tan[(3*Pi)/14]]*Cos[(3*Pi)/14] - Log[a^(1/7) - b^(1/7)*x] + Cos[Pi/7]*Log[a^(2/7) + b^(2/7)*x^2 + 2*a^(1/7)*b^(1/7)*x*Cos[Pi/7]] + Log[a^(2/7) + b^(2/7)*x^2 + 2*a^(1/7)*b^(1/7)*x*Sin[Pi/14]]*Sin[Pi/14] + 2*ArcTan[Cot[Pi/7] + (b^(1/7)*x*Csc[Pi/7])/a^(1/7)]*Sin[Pi/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",1
1448,1,23,23,0.006898,"\int \frac{1}{x \left(a-b x^7\right)} \, dx","Integrate[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",1
1449,1,166,166,0.0046938,"\int \frac{1}{1-x^7} \, dx","Integrate[(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",1
1450,1,166,165,0.0044191,"\int \frac{1}{1+x^7} \, dx","Integrate[(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} \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 (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[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",1
1451,1,361,203,0.3271941,"\int \frac{x^9}{a+b x^8} \, dx","Integrate[x^9/(a + b*x^8),x]","\frac{-\sqrt{2} \sqrt[4]{a} \log \left(-2 \sqrt[8]{a} \sqrt[8]{b} x \sin \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)-\sqrt{2} \sqrt[4]{a} \log \left(2 \sqrt[8]{a} \sqrt[8]{b} x \sin \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)+\sqrt{2} \sqrt[4]{a} \log \left(-2 \sqrt[8]{a} \sqrt[8]{b} x \cos \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)+\sqrt{2} \sqrt[4]{a} \log \left(2 \sqrt[8]{a} \sqrt[8]{b} x \cos \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)-2 \sqrt{2} \sqrt[4]{a} \tan ^{-1}\left(\frac{\sqrt[8]{b} x \sec \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}-\tan \left(\frac{\pi }{8}\right)\right)+2 \sqrt{2} \sqrt[4]{a} \tan ^{-1}\left(\frac{\sqrt[8]{b} x \sec \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}+\tan \left(\frac{\pi }{8}\right)\right)+2 \sqrt{2} \sqrt[4]{a} \tan ^{-1}\left(\cot \left(\frac{\pi }{8}\right)-\frac{\sqrt[8]{b} x \csc \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}\right)+2 \sqrt{2} \sqrt[4]{a} \tan ^{-1}\left(\frac{\sqrt[8]{b} x \csc \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}+\cot \left(\frac{\pi }{8}\right)\right)+8 \sqrt[4]{b} x^2}{16 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{\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{x^2}{2 b}",1,"(8*b^(1/4)*x^2 + 2*Sqrt[2]*a^(1/4)*ArcTan[Cot[Pi/8] - (b^(1/8)*x*Csc[Pi/8])/a^(1/8)] + 2*Sqrt[2]*a^(1/4)*ArcTan[Cot[Pi/8] + (b^(1/8)*x*Csc[Pi/8])/a^(1/8)] - 2*Sqrt[2]*a^(1/4)*ArcTan[(b^(1/8)*x*Sec[Pi/8])/a^(1/8) - Tan[Pi/8]] + 2*Sqrt[2]*a^(1/4)*ArcTan[(b^(1/8)*x*Sec[Pi/8])/a^(1/8) + Tan[Pi/8]] + Sqrt[2]*a^(1/4)*Log[a^(1/4) + b^(1/4)*x^2 - 2*a^(1/8)*b^(1/8)*x*Cos[Pi/8]] + Sqrt[2]*a^(1/4)*Log[a^(1/4) + b^(1/4)*x^2 + 2*a^(1/8)*b^(1/8)*x*Cos[Pi/8]] - Sqrt[2]*a^(1/4)*Log[a^(1/4) + b^(1/4)*x^2 - 2*a^(1/8)*b^(1/8)*x*Sin[Pi/8]] - Sqrt[2]*a^(1/4)*Log[a^(1/4) + b^(1/4)*x^2 + 2*a^(1/8)*b^(1/8)*x*Sin[Pi/8]])/(16*b^(5/4))","A",1
1452,1,15,15,0.0042865,"\int \frac{x^7}{a+b x^8} \, dx","Integrate[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
1453,1,279,193,0.074093,"\int \frac{x^5}{a+b x^8} \, dx","Integrate[x^5/(a + b*x^8),x]","-\frac{\log \left(-2 \sqrt[8]{a} \sqrt[8]{b} x \sin \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)+\log \left(2 \sqrt[8]{a} \sqrt[8]{b} x \sin \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)-\log \left(-2 \sqrt[8]{a} \sqrt[8]{b} x \cos \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)-\log \left(2 \sqrt[8]{a} \sqrt[8]{b} x \cos \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)-2 \tan ^{-1}\left(\frac{\sqrt[8]{b} x \sec \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}-\tan \left(\frac{\pi }{8}\right)\right)+2 \tan ^{-1}\left(\frac{\sqrt[8]{b} x \sec \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}+\tan \left(\frac{\pi }{8}\right)\right)+2 \tan ^{-1}\left(\cot \left(\frac{\pi }{8}\right)-\frac{\sqrt[8]{b} x \csc \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}\right)+2 \tan ^{-1}\left(\frac{\sqrt[8]{b} x \csc \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}+\cot \left(\frac{\pi }{8}\right)\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}}",1,"-1/8*(2*ArcTan[Cot[Pi/8] - (b^(1/8)*x*Csc[Pi/8])/a^(1/8)] + 2*ArcTan[Cot[Pi/8] + (b^(1/8)*x*Csc[Pi/8])/a^(1/8)] - 2*ArcTan[(b^(1/8)*x*Sec[Pi/8])/a^(1/8) - Tan[Pi/8]] + 2*ArcTan[(b^(1/8)*x*Sec[Pi/8])/a^(1/8) + Tan[Pi/8]] - Log[a^(1/4) + b^(1/4)*x^2 - 2*a^(1/8)*b^(1/8)*x*Cos[Pi/8]] - Log[a^(1/4) + b^(1/4)*x^2 + 2*a^(1/8)*b^(1/8)*x*Cos[Pi/8]] + Log[a^(1/4) + b^(1/4)*x^2 - 2*a^(1/8)*b^(1/8)*x*Sin[Pi/8]] + Log[a^(1/4) + b^(1/4)*x^2 + 2*a^(1/8)*b^(1/8)*x*Sin[Pi/8]])/(Sqrt[2]*a^(1/4)*b^(3/4))","A",1
1454,1,29,29,0.0067023,"\int \frac{x^3}{a+b x^8} \, dx","Integrate[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",1
1455,1,279,193,0.0425199,"\int \frac{x}{a+b x^8} \, dx","Integrate[x/(a + b*x^8),x]","-\frac{-\log \left(-2 \sqrt[8]{a} \sqrt[8]{b} x \sin \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)-\log \left(2 \sqrt[8]{a} \sqrt[8]{b} x \sin \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)+\log \left(-2 \sqrt[8]{a} \sqrt[8]{b} x \cos \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)+\log \left(2 \sqrt[8]{a} \sqrt[8]{b} x \cos \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)-2 \tan ^{-1}\left(\frac{\sqrt[8]{b} x \sec \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}-\tan \left(\frac{\pi }{8}\right)\right)+2 \tan ^{-1}\left(\frac{\sqrt[8]{b} x \sec \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}+\tan \left(\frac{\pi }{8}\right)\right)+2 \tan ^{-1}\left(\cot \left(\frac{\pi }{8}\right)-\frac{\sqrt[8]{b} x \csc \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}\right)+2 \tan ^{-1}\left(\frac{\sqrt[8]{b} x \csc \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}+\cot \left(\frac{\pi }{8}\right)\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}}",1,"-1/8*(2*ArcTan[Cot[Pi/8] - (b^(1/8)*x*Csc[Pi/8])/a^(1/8)] + 2*ArcTan[Cot[Pi/8] + (b^(1/8)*x*Csc[Pi/8])/a^(1/8)] - 2*ArcTan[(b^(1/8)*x*Sec[Pi/8])/a^(1/8) - Tan[Pi/8]] + 2*ArcTan[(b^(1/8)*x*Sec[Pi/8])/a^(1/8) + Tan[Pi/8]] + Log[a^(1/4) + b^(1/4)*x^2 - 2*a^(1/8)*b^(1/8)*x*Cos[Pi/8]] + Log[a^(1/4) + b^(1/4)*x^2 + 2*a^(1/8)*b^(1/8)*x*Cos[Pi/8]] - Log[a^(1/4) + b^(1/4)*x^2 - 2*a^(1/8)*b^(1/8)*x*Sin[Pi/8]] - Log[a^(1/4) + b^(1/4)*x^2 + 2*a^(1/8)*b^(1/8)*x*Sin[Pi/8]])/(Sqrt[2]*a^(3/4)*b^(1/4))","A",1
1456,1,22,22,0.006259,"\int \frac{1}{x \left(a+b x^8\right)} \, dx","Integrate[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",1
1457,1,385,203,0.0792008,"\int \frac{1}{x^3 \left(a+b x^8\right)} \, dx","Integrate[1/(x^3*(a + b*x^8)),x]","\frac{\sqrt{2} \sqrt[4]{b} x^2 \log \left(-2 \sqrt[8]{a} \sqrt[8]{b} x \sin \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)+\sqrt{2} \sqrt[4]{b} x^2 \log \left(2 \sqrt[8]{a} \sqrt[8]{b} x \sin \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)-\sqrt{2} \sqrt[4]{b} x^2 \log \left(-2 \sqrt[8]{a} \sqrt[8]{b} x \cos \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)-\sqrt{2} \sqrt[4]{b} x^2 \log \left(2 \sqrt[8]{a} \sqrt[8]{b} x \cos \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)-2 \sqrt{2} \sqrt[4]{b} x^2 \tan ^{-1}\left(\frac{\sqrt[8]{b} x \sec \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}-\tan \left(\frac{\pi }{8}\right)\right)+2 \sqrt{2} \sqrt[4]{b} x^2 \tan ^{-1}\left(\frac{\sqrt[8]{b} x \sec \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}+\tan \left(\frac{\pi }{8}\right)\right)+2 \sqrt{2} \sqrt[4]{b} x^2 \tan ^{-1}\left(\cot \left(\frac{\pi }{8}\right)-\frac{\sqrt[8]{b} x \csc \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}\right)+2 \sqrt{2} \sqrt[4]{b} x^2 \tan ^{-1}\left(\frac{\sqrt[8]{b} x \csc \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}+\cot \left(\frac{\pi }{8}\right)\right)-8 \sqrt[4]{a}}{16 a^{5/4} x^2}","\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{\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{1}{2 a x^2}",1,"(-8*a^(1/4) + 2*Sqrt[2]*b^(1/4)*x^2*ArcTan[Cot[Pi/8] - (b^(1/8)*x*Csc[Pi/8])/a^(1/8)] + 2*Sqrt[2]*b^(1/4)*x^2*ArcTan[Cot[Pi/8] + (b^(1/8)*x*Csc[Pi/8])/a^(1/8)] - 2*Sqrt[2]*b^(1/4)*x^2*ArcTan[(b^(1/8)*x*Sec[Pi/8])/a^(1/8) - Tan[Pi/8]] + 2*Sqrt[2]*b^(1/4)*x^2*ArcTan[(b^(1/8)*x*Sec[Pi/8])/a^(1/8) + Tan[Pi/8]] - Sqrt[2]*b^(1/4)*x^2*Log[a^(1/4) + b^(1/4)*x^2 - 2*a^(1/8)*b^(1/8)*x*Cos[Pi/8]] - Sqrt[2]*b^(1/4)*x^2*Log[a^(1/4) + b^(1/4)*x^2 + 2*a^(1/8)*b^(1/8)*x*Cos[Pi/8]] + Sqrt[2]*b^(1/4)*x^2*Log[a^(1/4) + b^(1/4)*x^2 - 2*a^(1/8)*b^(1/8)*x*Sin[Pi/8]] + Sqrt[2]*b^(1/4)*x^2*Log[a^(1/4) + b^(1/4)*x^2 + 2*a^(1/8)*b^(1/8)*x*Sin[Pi/8]])/(16*a^(5/4)*x^2)","A",1
1458,1,164,40,0.0496746,"\int \frac{1}{x^5 \left(a+b x^8\right)} \, dx","Integrate[1/(x^5*(a + b*x^8)),x]","\frac{\sqrt{b} x^4 \tan ^{-1}\left(\frac{\sqrt[8]{b} x \sec \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}-\tan \left(\frac{\pi }{8}\right)\right)-\sqrt{b} x^4 \tan ^{-1}\left(\frac{\sqrt[8]{b} x \sec \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}+\tan \left(\frac{\pi }{8}\right)\right)+\sqrt{b} x^4 \tan ^{-1}\left(\cot \left(\frac{\pi }{8}\right)-\frac{\sqrt[8]{b} x \csc \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}\right)+\sqrt{b} x^4 \tan ^{-1}\left(\frac{\sqrt[8]{b} x \csc \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}+\cot \left(\frac{\pi }{8}\right)\right)-\sqrt{a}}{4 a^{3/2} 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,"(-Sqrt[a] + Sqrt[b]*x^4*ArcTan[Cot[Pi/8] - (b^(1/8)*x*Csc[Pi/8])/a^(1/8)] + Sqrt[b]*x^4*ArcTan[Cot[Pi/8] + (b^(1/8)*x*Csc[Pi/8])/a^(1/8)] + Sqrt[b]*x^4*ArcTan[(b^(1/8)*x*Sec[Pi/8])/a^(1/8) - Tan[Pi/8]] - Sqrt[b]*x^4*ArcTan[(b^(1/8)*x*Sec[Pi/8])/a^(1/8) + Tan[Pi/8]])/(4*a^(3/2)*x^4)","B",1
1459,1,387,203,0.1005497,"\int \frac{1}{x^7 \left(a+b x^8\right)} \, dx","Integrate[1/(x^7*(a + b*x^8)),x]","\frac{-8 a^{3/4}-6 \sqrt{2} b^{3/4} x^6 \tan ^{-1}\left(\frac{\sqrt[8]{b} x \sec \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}-\tan \left(\frac{\pi }{8}\right)\right)+6 \sqrt{2} b^{3/4} x^6 \tan ^{-1}\left(\frac{\sqrt[8]{b} x \sec \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}+\tan \left(\frac{\pi }{8}\right)\right)+6 \sqrt{2} b^{3/4} x^6 \tan ^{-1}\left(\cot \left(\frac{\pi }{8}\right)-\frac{\sqrt[8]{b} x \csc \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}\right)+6 \sqrt{2} b^{3/4} x^6 \tan ^{-1}\left(\frac{\sqrt[8]{b} x \csc \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}+\cot \left(\frac{\pi }{8}\right)\right)-3 \sqrt{2} b^{3/4} x^6 \log \left(-2 \sqrt[8]{a} \sqrt[8]{b} x \sin \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)-3 \sqrt{2} b^{3/4} x^6 \log \left(2 \sqrt[8]{a} \sqrt[8]{b} x \sin \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)+3 \sqrt{2} b^{3/4} x^6 \log \left(-2 \sqrt[8]{a} \sqrt[8]{b} x \cos \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)+3 \sqrt{2} b^{3/4} x^6 \log \left(2 \sqrt[8]{a} \sqrt[8]{b} x \cos \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)}{48 a^{7/4} x^6}","\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{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{1}{6 a x^6}",1,"(-8*a^(3/4) + 6*Sqrt[2]*b^(3/4)*x^6*ArcTan[Cot[Pi/8] - (b^(1/8)*x*Csc[Pi/8])/a^(1/8)] + 6*Sqrt[2]*b^(3/4)*x^6*ArcTan[Cot[Pi/8] + (b^(1/8)*x*Csc[Pi/8])/a^(1/8)] - 6*Sqrt[2]*b^(3/4)*x^6*ArcTan[(b^(1/8)*x*Sec[Pi/8])/a^(1/8) - Tan[Pi/8]] + 6*Sqrt[2]*b^(3/4)*x^6*ArcTan[(b^(1/8)*x*Sec[Pi/8])/a^(1/8) + Tan[Pi/8]] + 3*Sqrt[2]*b^(3/4)*x^6*Log[a^(1/4) + b^(1/4)*x^2 - 2*a^(1/8)*b^(1/8)*x*Cos[Pi/8]] + 3*Sqrt[2]*b^(3/4)*x^6*Log[a^(1/4) + b^(1/4)*x^2 + 2*a^(1/8)*b^(1/8)*x*Cos[Pi/8]] - 3*Sqrt[2]*b^(3/4)*x^6*Log[a^(1/4) + b^(1/4)*x^2 - 2*a^(1/8)*b^(1/8)*x*Sin[Pi/8]] - 3*Sqrt[2]*b^(3/4)*x^6*Log[a^(1/4) + b^(1/4)*x^2 + 2*a^(1/8)*b^(1/8)*x*Sin[Pi/8]])/(48*a^(7/4)*x^6)","A",1
1460,1,35,35,0.0074844,"\int \frac{1}{x^9 \left(a+b x^8\right)} \, dx","Integrate[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*1/(a*x^8) - (b*Log[x])/a^2 + (b*Log[a + b*x^8])/(8*a^2)","A",1
1461,1,367,272,0.0967024,"\int \frac{x^8}{a+b x^8} \, dx","Integrate[x^8/(a + b*x^8),x]","\frac{\sqrt[8]{a} \sin \left(\frac{\pi }{8}\right) \log \left(-2 \sqrt[8]{a} \sqrt[8]{b} x \sin \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)-\sqrt[8]{a} \sin \left(\frac{\pi }{8}\right) \log \left(2 \sqrt[8]{a} \sqrt[8]{b} x \sin \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)+\sqrt[8]{a} \cos \left(\frac{\pi }{8}\right) \log \left(-2 \sqrt[8]{a} \sqrt[8]{b} x \cos \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)-\sqrt[8]{a} \cos \left(\frac{\pi }{8}\right) \log \left(2 \sqrt[8]{a} \sqrt[8]{b} x \cos \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)-2 \sqrt[8]{a} \cos \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\frac{\sqrt[8]{b} x \sec \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}-\tan \left(\frac{\pi }{8}\right)\right)-2 \sqrt[8]{a} \cos \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\frac{\sqrt[8]{b} x \sec \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}+\tan \left(\frac{\pi }{8}\right)\right)+2 \sqrt[8]{a} \sin \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\cot \left(\frac{\pi }{8}\right)-\frac{\sqrt[8]{b} x \csc \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}\right)-2 \sqrt[8]{a} \sin \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\frac{\sqrt[8]{b} x \csc \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}+\cot \left(\frac{\pi }{8}\right)\right)+8 \sqrt[8]{b} x}{8 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} \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,"(8*b^(1/8)*x - 2*a^(1/8)*ArcTan[(b^(1/8)*x*Sec[Pi/8])/a^(1/8) - Tan[Pi/8]]*Cos[Pi/8] - 2*a^(1/8)*ArcTan[(b^(1/8)*x*Sec[Pi/8])/a^(1/8) + Tan[Pi/8]]*Cos[Pi/8] + a^(1/8)*Cos[Pi/8]*Log[a^(1/4) + b^(1/4)*x^2 - 2*a^(1/8)*b^(1/8)*x*Cos[Pi/8]] - a^(1/8)*Cos[Pi/8]*Log[a^(1/4) + b^(1/4)*x^2 + 2*a^(1/8)*b^(1/8)*x*Cos[Pi/8]] + 2*a^(1/8)*ArcTan[Cot[Pi/8] - (b^(1/8)*x*Csc[Pi/8])/a^(1/8)]*Sin[Pi/8] - 2*a^(1/8)*ArcTan[Cot[Pi/8] + (b^(1/8)*x*Csc[Pi/8])/a^(1/8)]*Sin[Pi/8] + a^(1/8)*Log[a^(1/4) + b^(1/4)*x^2 - 2*a^(1/8)*b^(1/8)*x*Sin[Pi/8]]*Sin[Pi/8] - a^(1/8)*Log[a^(1/4) + b^(1/4)*x^2 + 2*a^(1/8)*b^(1/8)*x*Sin[Pi/8]]*Sin[Pi/8])/(8*b^(9/8))","A",1
1462,1,324,267,0.0749459,"\int \frac{x^6}{a+b x^8} \, dx","Integrate[x^6/(a + b*x^8),x]","\frac{\sin \left(\frac{\pi }{8}\right) \log \left(-2 \sqrt[8]{a} \sqrt[8]{b} x \sin \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)-\sin \left(\frac{\pi }{8}\right) \log \left(2 \sqrt[8]{a} \sqrt[8]{b} x \sin \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)+\cos \left(\frac{\pi }{8}\right) \log \left(-2 \sqrt[8]{a} \sqrt[8]{b} x \cos \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)-\cos \left(\frac{\pi }{8}\right) \log \left(2 \sqrt[8]{a} \sqrt[8]{b} x \cos \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)+2 \cos \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\frac{\sqrt[8]{b} x \sec \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}-\tan \left(\frac{\pi }{8}\right)\right)+2 \cos \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\frac{\sqrt[8]{b} x \sec \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}+\tan \left(\frac{\pi }{8}\right)\right)-2 \sin \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\cot \left(\frac{\pi }{8}\right)-\frac{\sqrt[8]{b} x \csc \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}\right)+2 \sin \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\frac{\sqrt[8]{b} x \csc \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}+\cot \left(\frac{\pi }{8}\right)\right)}{8 \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,"(2*ArcTan[(b^(1/8)*x*Sec[Pi/8])/a^(1/8) - Tan[Pi/8]]*Cos[Pi/8] + 2*ArcTan[(b^(1/8)*x*Sec[Pi/8])/a^(1/8) + Tan[Pi/8]]*Cos[Pi/8] + Cos[Pi/8]*Log[a^(1/4) + b^(1/4)*x^2 - 2*a^(1/8)*b^(1/8)*x*Cos[Pi/8]] - Cos[Pi/8]*Log[a^(1/4) + b^(1/4)*x^2 + 2*a^(1/8)*b^(1/8)*x*Cos[Pi/8]] - 2*ArcTan[Cot[Pi/8] - (b^(1/8)*x*Csc[Pi/8])/a^(1/8)]*Sin[Pi/8] + 2*ArcTan[Cot[Pi/8] + (b^(1/8)*x*Csc[Pi/8])/a^(1/8)]*Sin[Pi/8] + Log[a^(1/4) + b^(1/4)*x^2 - 2*a^(1/8)*b^(1/8)*x*Sin[Pi/8]]*Sin[Pi/8] - Log[a^(1/4) + b^(1/4)*x^2 + 2*a^(1/8)*b^(1/8)*x*Sin[Pi/8]]*Sin[Pi/8])/(8*a^(1/8)*b^(7/8))","A",1
1463,1,324,267,0.0994175,"\int \frac{x^4}{a+b x^8} \, dx","Integrate[x^4/(a + b*x^8),x]","-\frac{\cos \left(\frac{\pi }{8}\right) \log \left(-2 \sqrt[8]{a} \sqrt[8]{b} x \sin \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)-\cos \left(\frac{\pi }{8}\right) \log \left(2 \sqrt[8]{a} \sqrt[8]{b} x \sin \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)-\sin \left(\frac{\pi }{8}\right) \log \left(-2 \sqrt[8]{a} \sqrt[8]{b} x \cos \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)+\sin \left(\frac{\pi }{8}\right) \log \left(2 \sqrt[8]{a} \sqrt[8]{b} x \cos \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)+2 \sin \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\frac{\sqrt[8]{b} x \sec \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}-\tan \left(\frac{\pi }{8}\right)\right)+2 \sin \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\frac{\sqrt[8]{b} x \sec \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}+\tan \left(\frac{\pi }{8}\right)\right)+2 \cos \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\cot \left(\frac{\pi }{8}\right)-\frac{\sqrt[8]{b} x \csc \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}\right)-2 \cos \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\frac{\sqrt[8]{b} x \csc \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}+\cot \left(\frac{\pi }{8}\right)\right)}{8 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,"-1/8*(2*ArcTan[Cot[Pi/8] - (b^(1/8)*x*Csc[Pi/8])/a^(1/8)]*Cos[Pi/8] - 2*ArcTan[Cot[Pi/8] + (b^(1/8)*x*Csc[Pi/8])/a^(1/8)]*Cos[Pi/8] + Cos[Pi/8]*Log[a^(1/4) + b^(1/4)*x^2 - 2*a^(1/8)*b^(1/8)*x*Sin[Pi/8]] - Cos[Pi/8]*Log[a^(1/4) + b^(1/4)*x^2 + 2*a^(1/8)*b^(1/8)*x*Sin[Pi/8]] + 2*ArcTan[(b^(1/8)*x*Sec[Pi/8])/a^(1/8) - Tan[Pi/8]]*Sin[Pi/8] + 2*ArcTan[(b^(1/8)*x*Sec[Pi/8])/a^(1/8) + Tan[Pi/8]]*Sin[Pi/8] - Log[a^(1/4) + b^(1/4)*x^2 - 2*a^(1/8)*b^(1/8)*x*Cos[Pi/8]]*Sin[Pi/8] + Log[a^(1/4) + b^(1/4)*x^2 + 2*a^(1/8)*b^(1/8)*x*Cos[Pi/8]]*Sin[Pi/8])/(a^(3/8)*b^(5/8))","A",1
1464,1,324,267,0.087417,"\int \frac{x^2}{a+b x^8} \, dx","Integrate[x^2/(a + b*x^8),x]","-\frac{-\cos \left(\frac{\pi }{8}\right) \log \left(-2 \sqrt[8]{a} \sqrt[8]{b} x \sin \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)+\cos \left(\frac{\pi }{8}\right) \log \left(2 \sqrt[8]{a} \sqrt[8]{b} x \sin \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)+\sin \left(\frac{\pi }{8}\right) \log \left(-2 \sqrt[8]{a} \sqrt[8]{b} x \cos \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)-\sin \left(\frac{\pi }{8}\right) \log \left(2 \sqrt[8]{a} \sqrt[8]{b} x \cos \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)+2 \sin \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\frac{\sqrt[8]{b} x \sec \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}-\tan \left(\frac{\pi }{8}\right)\right)+2 \sin \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\frac{\sqrt[8]{b} x \sec \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}+\tan \left(\frac{\pi }{8}\right)\right)+2 \cos \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\cot \left(\frac{\pi }{8}\right)-\frac{\sqrt[8]{b} x \csc \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}\right)-2 \cos \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\frac{\sqrt[8]{b} x \csc \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}+\cot \left(\frac{\pi }{8}\right)\right)}{8 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,"-1/8*(2*ArcTan[Cot[Pi/8] - (b^(1/8)*x*Csc[Pi/8])/a^(1/8)]*Cos[Pi/8] - 2*ArcTan[Cot[Pi/8] + (b^(1/8)*x*Csc[Pi/8])/a^(1/8)]*Cos[Pi/8] - Cos[Pi/8]*Log[a^(1/4) + b^(1/4)*x^2 - 2*a^(1/8)*b^(1/8)*x*Sin[Pi/8]] + Cos[Pi/8]*Log[a^(1/4) + b^(1/4)*x^2 + 2*a^(1/8)*b^(1/8)*x*Sin[Pi/8]] + 2*ArcTan[(b^(1/8)*x*Sec[Pi/8])/a^(1/8) - Tan[Pi/8]]*Sin[Pi/8] + 2*ArcTan[(b^(1/8)*x*Sec[Pi/8])/a^(1/8) + Tan[Pi/8]]*Sin[Pi/8] + Log[a^(1/4) + b^(1/4)*x^2 - 2*a^(1/8)*b^(1/8)*x*Cos[Pi/8]]*Sin[Pi/8] - Log[a^(1/4) + b^(1/4)*x^2 + 2*a^(1/8)*b^(1/8)*x*Cos[Pi/8]]*Sin[Pi/8])/(a^(5/8)*b^(3/8))","A",1
1465,1,324,267,0.1037226,"\int \frac{1}{a+b x^8} \, dx","Integrate[(a + b*x^8)^(-1),x]","\frac{-\sin \left(\frac{\pi }{8}\right) \log \left(-2 \sqrt[8]{a} \sqrt[8]{b} x \sin \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)+\sin \left(\frac{\pi }{8}\right) \log \left(2 \sqrt[8]{a} \sqrt[8]{b} x \sin \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)-\cos \left(\frac{\pi }{8}\right) \log \left(-2 \sqrt[8]{a} \sqrt[8]{b} x \cos \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)+\cos \left(\frac{\pi }{8}\right) \log \left(2 \sqrt[8]{a} \sqrt[8]{b} x \cos \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)+2 \cos \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\frac{\sqrt[8]{b} x \sec \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}-\tan \left(\frac{\pi }{8}\right)\right)+2 \cos \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\frac{\sqrt[8]{b} x \sec \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}+\tan \left(\frac{\pi }{8}\right)\right)-2 \sin \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\cot \left(\frac{\pi }{8}\right)-\frac{\sqrt[8]{b} x \csc \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}\right)+2 \sin \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\frac{\sqrt[8]{b} x \csc \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}+\cot \left(\frac{\pi }{8}\right)\right)}{8 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,"(2*ArcTan[(b^(1/8)*x*Sec[Pi/8])/a^(1/8) - Tan[Pi/8]]*Cos[Pi/8] + 2*ArcTan[(b^(1/8)*x*Sec[Pi/8])/a^(1/8) + Tan[Pi/8]]*Cos[Pi/8] - Cos[Pi/8]*Log[a^(1/4) + b^(1/4)*x^2 - 2*a^(1/8)*b^(1/8)*x*Cos[Pi/8]] + Cos[Pi/8]*Log[a^(1/4) + b^(1/4)*x^2 + 2*a^(1/8)*b^(1/8)*x*Cos[Pi/8]] - 2*ArcTan[Cot[Pi/8] - (b^(1/8)*x*Csc[Pi/8])/a^(1/8)]*Sin[Pi/8] + 2*ArcTan[Cot[Pi/8] + (b^(1/8)*x*Csc[Pi/8])/a^(1/8)]*Sin[Pi/8] - Log[a^(1/4) + b^(1/4)*x^2 - 2*a^(1/8)*b^(1/8)*x*Sin[Pi/8]]*Sin[Pi/8] + Log[a^(1/4) + b^(1/4)*x^2 + 2*a^(1/8)*b^(1/8)*x*Sin[Pi/8]]*Sin[Pi/8])/(8*a^(7/8)*b^(1/8))","A",1
1466,1,377,275,0.1317327,"\int \frac{1}{x^2 \left(a+b x^8\right)} \, dx","Integrate[1/(x^2*(a + b*x^8)),x]","-\frac{\sqrt[8]{b} x \sin \left(\frac{\pi }{8}\right) \log \left(-2 \sqrt[8]{a} \sqrt[8]{b} x \sin \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)-\sqrt[8]{b} x \sin \left(\frac{\pi }{8}\right) \log \left(2 \sqrt[8]{a} \sqrt[8]{b} x \sin \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)+\sqrt[8]{b} x \cos \left(\frac{\pi }{8}\right) \log \left(-2 \sqrt[8]{a} \sqrt[8]{b} x \cos \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)-\sqrt[8]{b} x \cos \left(\frac{\pi }{8}\right) \log \left(2 \sqrt[8]{a} \sqrt[8]{b} x \cos \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)+2 \sqrt[8]{b} x \cos \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\frac{\sqrt[8]{b} x \sec \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}-\tan \left(\frac{\pi }{8}\right)\right)+2 \sqrt[8]{b} x \cos \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\frac{\sqrt[8]{b} x \sec \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}+\tan \left(\frac{\pi }{8}\right)\right)-2 \sqrt[8]{b} x \sin \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\cot \left(\frac{\pi }{8}\right)-\frac{\sqrt[8]{b} x \csc \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}\right)+2 \sqrt[8]{b} x \sin \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\frac{\sqrt[8]{b} x \csc \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}+\cot \left(\frac{\pi }{8}\right)\right)+8 \sqrt[8]{a}}{8 a^{9/8} 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}",1,"-1/8*(8*a^(1/8) + 2*b^(1/8)*x*ArcTan[(b^(1/8)*x*Sec[Pi/8])/a^(1/8) - Tan[Pi/8]]*Cos[Pi/8] + 2*b^(1/8)*x*ArcTan[(b^(1/8)*x*Sec[Pi/8])/a^(1/8) + Tan[Pi/8]]*Cos[Pi/8] + b^(1/8)*x*Cos[Pi/8]*Log[a^(1/4) + b^(1/4)*x^2 - 2*a^(1/8)*b^(1/8)*x*Cos[Pi/8]] - b^(1/8)*x*Cos[Pi/8]*Log[a^(1/4) + b^(1/4)*x^2 + 2*a^(1/8)*b^(1/8)*x*Cos[Pi/8]] - 2*b^(1/8)*x*ArcTan[Cot[Pi/8] - (b^(1/8)*x*Csc[Pi/8])/a^(1/8)]*Sin[Pi/8] + 2*b^(1/8)*x*ArcTan[Cot[Pi/8] + (b^(1/8)*x*Csc[Pi/8])/a^(1/8)]*Sin[Pi/8] + b^(1/8)*x*Log[a^(1/4) + b^(1/4)*x^2 - 2*a^(1/8)*b^(1/8)*x*Sin[Pi/8]]*Sin[Pi/8] - b^(1/8)*x*Log[a^(1/4) + b^(1/4)*x^2 + 2*a^(1/8)*b^(1/8)*x*Sin[Pi/8]]*Sin[Pi/8])/(a^(9/8)*x)","A",1
1467,1,395,277,0.092458,"\int \frac{1}{x^4 \left(a+b x^8\right)} \, dx","Integrate[1/(x^4*(a + b*x^8)),x]","\frac{-8 a^{3/8}+6 b^{3/8} x^3 \sin \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\frac{\sqrt[8]{b} x \sec \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}-\tan \left(\frac{\pi }{8}\right)\right)+6 b^{3/8} x^3 \sin \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\frac{\sqrt[8]{b} x \sec \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}+\tan \left(\frac{\pi }{8}\right)\right)+6 b^{3/8} x^3 \cos \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\cot \left(\frac{\pi }{8}\right)-\frac{\sqrt[8]{b} x \csc \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}\right)-6 b^{3/8} x^3 \cos \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\frac{\sqrt[8]{b} x \csc \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}+\cot \left(\frac{\pi }{8}\right)\right)+3 b^{3/8} x^3 \cos \left(\frac{\pi }{8}\right) \log \left(-2 \sqrt[8]{a} \sqrt[8]{b} x \sin \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)-3 b^{3/8} x^3 \cos \left(\frac{\pi }{8}\right) \log \left(2 \sqrt[8]{a} \sqrt[8]{b} x \sin \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)-3 b^{3/8} x^3 \sin \left(\frac{\pi }{8}\right) \log \left(-2 \sqrt[8]{a} \sqrt[8]{b} x \cos \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)+3 b^{3/8} x^3 \sin \left(\frac{\pi }{8}\right) \log \left(2 \sqrt[8]{a} \sqrt[8]{b} x \cos \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)}{24 a^{11/8} 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,"(-8*a^(3/8) + 6*b^(3/8)*x^3*ArcTan[Cot[Pi/8] - (b^(1/8)*x*Csc[Pi/8])/a^(1/8)]*Cos[Pi/8] - 6*b^(3/8)*x^3*ArcTan[Cot[Pi/8] + (b^(1/8)*x*Csc[Pi/8])/a^(1/8)]*Cos[Pi/8] + 3*b^(3/8)*x^3*Cos[Pi/8]*Log[a^(1/4) + b^(1/4)*x^2 - 2*a^(1/8)*b^(1/8)*x*Sin[Pi/8]] - 3*b^(3/8)*x^3*Cos[Pi/8]*Log[a^(1/4) + b^(1/4)*x^2 + 2*a^(1/8)*b^(1/8)*x*Sin[Pi/8]] + 6*b^(3/8)*x^3*ArcTan[(b^(1/8)*x*Sec[Pi/8])/a^(1/8) - Tan[Pi/8]]*Sin[Pi/8] + 6*b^(3/8)*x^3*ArcTan[(b^(1/8)*x*Sec[Pi/8])/a^(1/8) + Tan[Pi/8]]*Sin[Pi/8] - 3*b^(3/8)*x^3*Log[a^(1/4) + b^(1/4)*x^2 - 2*a^(1/8)*b^(1/8)*x*Cos[Pi/8]]*Sin[Pi/8] + 3*b^(3/8)*x^3*Log[a^(1/4) + b^(1/4)*x^2 + 2*a^(1/8)*b^(1/8)*x*Cos[Pi/8]]*Sin[Pi/8])/(24*a^(11/8)*x^3)","A",1
1468,1,395,277,0.0996637,"\int \frac{1}{x^6 \left(a+b x^8\right)} \, dx","Integrate[1/(x^6*(a + b*x^8)),x]","\frac{-8 a^{5/8}+10 b^{5/8} x^5 \sin \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\frac{\sqrt[8]{b} x \sec \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}-\tan \left(\frac{\pi }{8}\right)\right)+10 b^{5/8} x^5 \sin \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\frac{\sqrt[8]{b} x \sec \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}+\tan \left(\frac{\pi }{8}\right)\right)+10 b^{5/8} x^5 \cos \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\cot \left(\frac{\pi }{8}\right)-\frac{\sqrt[8]{b} x \csc \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}\right)-10 b^{5/8} x^5 \cos \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\frac{\sqrt[8]{b} x \csc \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}+\cot \left(\frac{\pi }{8}\right)\right)-5 b^{5/8} x^5 \cos \left(\frac{\pi }{8}\right) \log \left(-2 \sqrt[8]{a} \sqrt[8]{b} x \sin \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)+5 b^{5/8} x^5 \cos \left(\frac{\pi }{8}\right) \log \left(2 \sqrt[8]{a} \sqrt[8]{b} x \sin \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)+5 b^{5/8} x^5 \sin \left(\frac{\pi }{8}\right) \log \left(-2 \sqrt[8]{a} \sqrt[8]{b} x \cos \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)-5 b^{5/8} x^5 \sin \left(\frac{\pi }{8}\right) \log \left(2 \sqrt[8]{a} \sqrt[8]{b} x \cos \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)}{40 a^{13/8} 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,"(-8*a^(5/8) + 10*b^(5/8)*x^5*ArcTan[Cot[Pi/8] - (b^(1/8)*x*Csc[Pi/8])/a^(1/8)]*Cos[Pi/8] - 10*b^(5/8)*x^5*ArcTan[Cot[Pi/8] + (b^(1/8)*x*Csc[Pi/8])/a^(1/8)]*Cos[Pi/8] - 5*b^(5/8)*x^5*Cos[Pi/8]*Log[a^(1/4) + b^(1/4)*x^2 - 2*a^(1/8)*b^(1/8)*x*Sin[Pi/8]] + 5*b^(5/8)*x^5*Cos[Pi/8]*Log[a^(1/4) + b^(1/4)*x^2 + 2*a^(1/8)*b^(1/8)*x*Sin[Pi/8]] + 10*b^(5/8)*x^5*ArcTan[(b^(1/8)*x*Sec[Pi/8])/a^(1/8) - Tan[Pi/8]]*Sin[Pi/8] + 10*b^(5/8)*x^5*ArcTan[(b^(1/8)*x*Sec[Pi/8])/a^(1/8) + Tan[Pi/8]]*Sin[Pi/8] + 5*b^(5/8)*x^5*Log[a^(1/4) + b^(1/4)*x^2 - 2*a^(1/8)*b^(1/8)*x*Cos[Pi/8]]*Sin[Pi/8] - 5*b^(5/8)*x^5*Log[a^(1/4) + b^(1/4)*x^2 + 2*a^(1/8)*b^(1/8)*x*Cos[Pi/8]]*Sin[Pi/8])/(40*a^(13/8)*x^5)","A",1
1469,1,395,277,0.2126239,"\int \frac{1}{x^8 \left(a+b x^8\right)} \, dx","Integrate[1/(x^8*(a + b*x^8)),x]","-\frac{8 a^{7/8}+14 b^{7/8} x^7 \cos \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\frac{\sqrt[8]{b} x \sec \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}-\tan \left(\frac{\pi }{8}\right)\right)+14 b^{7/8} x^7 \cos \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\frac{\sqrt[8]{b} x \sec \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}+\tan \left(\frac{\pi }{8}\right)\right)-14 b^{7/8} x^7 \sin \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\cot \left(\frac{\pi }{8}\right)-\frac{\sqrt[8]{b} x \csc \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}\right)+14 b^{7/8} x^7 \sin \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\frac{\sqrt[8]{b} x \csc \left(\frac{\pi }{8}\right)}{\sqrt[8]{a}}+\cot \left(\frac{\pi }{8}\right)\right)-7 b^{7/8} x^7 \sin \left(\frac{\pi }{8}\right) \log \left(-2 \sqrt[8]{a} \sqrt[8]{b} x \sin \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)+7 b^{7/8} x^7 \sin \left(\frac{\pi }{8}\right) \log \left(2 \sqrt[8]{a} \sqrt[8]{b} x \sin \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)-7 b^{7/8} x^7 \cos \left(\frac{\pi }{8}\right) \log \left(-2 \sqrt[8]{a} \sqrt[8]{b} x \cos \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)+7 b^{7/8} x^7 \cos \left(\frac{\pi }{8}\right) \log \left(2 \sqrt[8]{a} \sqrt[8]{b} x \cos \left(\frac{\pi }{8}\right)+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)}{56 a^{15/8} 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,"-1/56*(8*a^(7/8) + 14*b^(7/8)*x^7*ArcTan[(b^(1/8)*x*Sec[Pi/8])/a^(1/8) - Tan[Pi/8]]*Cos[Pi/8] + 14*b^(7/8)*x^7*ArcTan[(b^(1/8)*x*Sec[Pi/8])/a^(1/8) + Tan[Pi/8]]*Cos[Pi/8] - 7*b^(7/8)*x^7*Cos[Pi/8]*Log[a^(1/4) + b^(1/4)*x^2 - 2*a^(1/8)*b^(1/8)*x*Cos[Pi/8]] + 7*b^(7/8)*x^7*Cos[Pi/8]*Log[a^(1/4) + b^(1/4)*x^2 + 2*a^(1/8)*b^(1/8)*x*Cos[Pi/8]] - 14*b^(7/8)*x^7*ArcTan[Cot[Pi/8] - (b^(1/8)*x*Csc[Pi/8])/a^(1/8)]*Sin[Pi/8] + 14*b^(7/8)*x^7*ArcTan[Cot[Pi/8] + (b^(1/8)*x*Csc[Pi/8])/a^(1/8)]*Sin[Pi/8] - 7*b^(7/8)*x^7*Log[a^(1/4) + b^(1/4)*x^2 - 2*a^(1/8)*b^(1/8)*x*Sin[Pi/8]]*Sin[Pi/8] + 7*b^(7/8)*x^7*Log[a^(1/4) + b^(1/4)*x^2 + 2*a^(1/8)*b^(1/8)*x*Sin[Pi/8]]*Sin[Pi/8])/(a^(15/8)*x^7)","A",1
1470,1,198,239,0.0761427,"\int \frac{1}{a-b x^8} \, dx","Integrate[(a - b*x^8)^(-1),x]","\frac{-\sqrt{2} \log \left(-\sqrt{2} \sqrt[8]{a} \sqrt[8]{b} x+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)+\sqrt{2} \log \left(\sqrt{2} \sqrt[8]{a} \sqrt[8]{b} x+\sqrt[4]{a}+\sqrt[4]{b} x^2\right)-2 \log \left(\sqrt[8]{a}-\sqrt[8]{b} x\right)+2 \log \left(\sqrt[8]{a}+\sqrt[8]{b} x\right)+4 \tan ^{-1}\left(\frac{\sqrt[8]{b} x}{\sqrt[8]{a}}\right)-2 \sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{b} x}{\sqrt[8]{a}}\right)+2 \sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{b} x}{\sqrt[8]{a}}+1\right)}{16 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,"(4*ArcTan[(b^(1/8)*x)/a^(1/8)] - 2*Sqrt[2]*ArcTan[1 - (Sqrt[2]*b^(1/8)*x)/a^(1/8)] + 2*Sqrt[2]*ArcTan[1 + (Sqrt[2]*b^(1/8)*x)/a^(1/8)] - 2*Log[a^(1/8) - b^(1/8)*x] + 2*Log[a^(1/8) + b^(1/8)*x] - Sqrt[2]*Log[a^(1/4) - Sqrt[2]*a^(1/8)*b^(1/8)*x + b^(1/4)*x^2] + Sqrt[2]*Log[a^(1/4) + Sqrt[2]*a^(1/8)*b^(1/8)*x + b^(1/4)*x^2])/(16*a^(7/8)*b^(1/8))","A",1
1471,1,38,24,0.0087265,"\int \frac{x^9}{1-x^8} \, dx","Integrate[x^9/(1 - x^8),x]","-\frac{x^2}{2}-\frac{1}{8} \log \left(1-x^2\right)+\frac{1}{8} \log \left(x^2+1\right)-\frac{1}{4} \tan ^{-1}\left(\frac{1}{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,"-1/2*x^2 - ArcTan[x^(-2)]/4 - Log[1 - x^2]/8 + Log[1 + x^2]/8","A",1
1472,1,12,12,0.0031373,"\int \frac{x^7}{1-x^8} \, dx","Integrate[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,"-1/8*Log[1 - x^8]","A",1
1473,1,31,17,0.0077155,"\int \frac{x^5}{1-x^8} \, dx","Integrate[x^5/(1 - x^8),x]","-\frac{1}{8} \log \left(1-x^2\right)+\frac{1}{8} \log \left(x^2+1\right)+\frac{1}{4} \tan ^{-1}\left(\frac{1}{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 - Log[1 - x^2]/8 + Log[1 + x^2]/8","A",1
1474,1,23,8,0.0048349,"\int \frac{x^3}{1-x^8} \, dx","Integrate[x^3/(1 - x^8),x]","\frac{1}{8} \log \left(x^4+1\right)-\frac{1}{8} \log \left(1-x^4\right)","\frac{1}{4} \tanh ^{-1}\left(x^4\right)",1,"-1/8*Log[1 - x^4] + Log[1 + x^4]/8","B",1
1475,1,31,17,0.0050016,"\int \frac{x}{1-x^8} \, dx","Integrate[x/(1 - x^8),x]","-\frac{1}{8} \log \left(1-x^2\right)+\frac{1}{8} \log \left(x^2+1\right)-\frac{1}{4} \tan ^{-1}\left(\frac{1}{x^2}\right)","\frac{1}{4} \tan ^{-1}\left(x^2\right)+\frac{1}{4} \tanh ^{-1}\left(x^2\right)",1,"-1/4*ArcTan[x^(-2)] - Log[1 - x^2]/8 + Log[1 + x^2]/8","A",1
1476,1,15,15,0.0034643,"\int \frac{1}{x \left(1-x^8\right)} \, dx","Integrate[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",1
1477,1,38,24,0.0054575,"\int \frac{1}{x^3 \left(1-x^8\right)} \, dx","Integrate[1/(x^3*(1 - x^8)),x]","-\frac{1}{2 x^2}-\frac{1}{8} \log \left(1-x^2\right)+\frac{1}{8} \log \left(x^2+1\right)+\frac{1}{4} \tan ^{-1}\left(\frac{1}{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*1/x^2 + ArcTan[x^(-2)]/4 - Log[1 - x^2]/8 + Log[1 + x^2]/8","A",1
1478,1,30,16,0.0043186,"\int \frac{1}{x^5 \left(1-x^8\right)} \, dx","Integrate[1/(x^5*(1 - x^8)),x]","-\frac{1}{4 x^4}-\frac{1}{8} \log \left(1-x^4\right)+\frac{1}{8} \log \left(x^4+1\right)","\frac{1}{4} \tanh ^{-1}\left(x^4\right)-\frac{1}{4 x^4}",1,"-1/4*1/x^4 - Log[1 - x^4]/8 + Log[1 + x^4]/8","A",1
1479,1,38,24,0.0064154,"\int \frac{1}{x^7 \left(1-x^8\right)} \, dx","Integrate[1/(x^7*(1 - x^8)),x]","-\frac{1}{6 x^6}-\frac{1}{8} \log \left(1-x^2\right)+\frac{1}{8} \log \left(x^2+1\right)-\frac{1}{4} \tan ^{-1}\left(\frac{1}{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*1/x^6 - ArcTan[x^(-2)]/4 - Log[1 - x^2]/8 + Log[1 + x^2]/8","A",1
1480,1,22,22,0.0039556,"\int \frac{1}{x^9 \left(1-x^8\right)} \, dx","Integrate[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*1/x^8 + Log[x] - Log[1 - x^8]/8","A",1
1481,1,101,100,0.0383642,"\int \frac{x^8}{1-x^8} \, dx","Integrate[x^8/(1 - x^8),x]","\frac{1}{16} \left(-\sqrt{2} \log \left(x^2-\sqrt{2} x+1\right)+\sqrt{2} \log \left(x^2+\sqrt{2} x+1\right)-16 x-2 \log (1-x)+2 \log (x+1)+4 \tan ^{-1}(x)-2 \sqrt{2} \tan ^{-1}\left(1-\sqrt{2} x\right)+2 \sqrt{2} \tan ^{-1}\left(\sqrt{2} x+1\right)\right)","-\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,"(-16*x + 4*ArcTan[x] - 2*Sqrt[2]*ArcTan[1 - Sqrt[2]*x] + 2*Sqrt[2]*ArcTan[1 + Sqrt[2]*x] - 2*Log[1 - x] + 2*Log[1 + x] - Sqrt[2]*Log[1 - Sqrt[2]*x + x^2] + Sqrt[2]*Log[1 + Sqrt[2]*x + x^2])/16","A",1
1482,1,98,97,0.0194842,"\int \frac{x^6}{1-x^8} \, dx","Integrate[x^6/(1 - x^8),x]","\frac{1}{16} \left(-\sqrt{2} \log \left(x^2-\sqrt{2} x+1\right)+\sqrt{2} \log \left(x^2+\sqrt{2} x+1\right)-2 \log (1-x)+2 \log (x+1)-4 \tan ^{-1}(x)+2 \sqrt{2} \tan ^{-1}\left(1-\sqrt{2} x\right)-2 \sqrt{2} \tan ^{-1}\left(\sqrt{2} x+1\right)\right)","-\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,"(-4*ArcTan[x] + 2*Sqrt[2]*ArcTan[1 - Sqrt[2]*x] - 2*Sqrt[2]*ArcTan[1 + Sqrt[2]*x] - 2*Log[1 - x] + 2*Log[1 + x] - Sqrt[2]*Log[1 - Sqrt[2]*x + x^2] + Sqrt[2]*Log[1 + Sqrt[2]*x + x^2])/16","A",1
1483,1,98,97,0.027327,"\int \frac{x^4}{1-x^8} \, dx","Integrate[x^4/(1 - x^8),x]","\frac{1}{16} \left(\sqrt{2} \log \left(x^2-\sqrt{2} x+1\right)-\sqrt{2} \log \left(x^2+\sqrt{2} x+1\right)-2 \log (1-x)+2 \log (x+1)+4 \tan ^{-1}(x)+2 \sqrt{2} \tan ^{-1}\left(1-\sqrt{2} x\right)-2 \sqrt{2} \tan ^{-1}\left(\sqrt{2} x+1\right)\right)","\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,"(4*ArcTan[x] + 2*Sqrt[2]*ArcTan[1 - Sqrt[2]*x] - 2*Sqrt[2]*ArcTan[1 + Sqrt[2]*x] - 2*Log[1 - x] + 2*Log[1 + x] + Sqrt[2]*Log[1 - Sqrt[2]*x + x^2] - Sqrt[2]*Log[1 + Sqrt[2]*x + x^2])/16","A",1
1484,1,98,97,0.0164224,"\int \frac{x^2}{1-x^8} \, dx","Integrate[x^2/(1 - x^8),x]","\frac{1}{16} \left(\sqrt{2} \log \left(x^2-\sqrt{2} x+1\right)-\sqrt{2} \log \left(x^2+\sqrt{2} x+1\right)-2 \log (1-x)+2 \log (x+1)-4 \tan ^{-1}(x)-2 \sqrt{2} \tan ^{-1}\left(1-\sqrt{2} x\right)+2 \sqrt{2} \tan ^{-1}\left(\sqrt{2} x+1\right)\right)","\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,"(-4*ArcTan[x] - 2*Sqrt[2]*ArcTan[1 - Sqrt[2]*x] + 2*Sqrt[2]*ArcTan[1 + Sqrt[2]*x] - 2*Log[1 - x] + 2*Log[1 + x] + Sqrt[2]*Log[1 - Sqrt[2]*x + x^2] - Sqrt[2]*Log[1 + Sqrt[2]*x + x^2])/16","A",1
1485,1,98,97,0.0275112,"\int \frac{1}{1-x^8} \, dx","Integrate[(1 - x^8)^(-1),x]","\frac{1}{16} \left(-\sqrt{2} \log \left(x^2-\sqrt{2} x+1\right)+\sqrt{2} \log \left(x^2+\sqrt{2} x+1\right)-2 \log (1-x)+2 \log (x+1)+4 \tan ^{-1}(x)-2 \sqrt{2} \tan ^{-1}\left(1-\sqrt{2} x\right)+2 \sqrt{2} \tan ^{-1}\left(\sqrt{2} x+1\right)\right)","-\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,"(4*ArcTan[x] - 2*Sqrt[2]*ArcTan[1 - Sqrt[2]*x] + 2*Sqrt[2]*ArcTan[1 + Sqrt[2]*x] - 2*Log[1 - x] + 2*Log[1 + x] - Sqrt[2]*Log[1 - Sqrt[2]*x + x^2] + Sqrt[2]*Log[1 + Sqrt[2]*x + x^2])/16","A",1
1486,1,109,102,0.0431213,"\int \frac{1}{x^2 \left(1-x^8\right)} \, dx","Integrate[1/(x^2*(1 - x^8)),x]","-\frac{\sqrt{2} x \log \left(x^2-\sqrt{2} x+1\right)-\sqrt{2} x \log \left(x^2+\sqrt{2} x+1\right)+2 x \log (1-x)-2 x \log (x+1)+4 x \tan ^{-1}(x)-2 \sqrt{2} x \tan ^{-1}\left(1-\sqrt{2} x\right)+2 \sqrt{2} x \tan ^{-1}\left(\sqrt{2} x+1\right)+16}{16 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,"-1/16*(16 + 4*x*ArcTan[x] - 2*Sqrt[2]*x*ArcTan[1 - Sqrt[2]*x] + 2*Sqrt[2]*x*ArcTan[1 + Sqrt[2]*x] + 2*x*Log[1 - x] - 2*x*Log[1 + x] + Sqrt[2]*x*Log[1 - Sqrt[2]*x + x^2] - Sqrt[2]*x*Log[1 + Sqrt[2]*x + x^2])/x","A",1
1487,1,104,104,0.0507845,"\int \frac{1}{x^4 \left(1-x^8\right)} \, dx","Integrate[1/(x^4*(1 - x^8)),x]","\frac{1}{48} \left(-\frac{16}{x^3}+3 \sqrt{2} \log \left(x^2-\sqrt{2} x+1\right)-3 \sqrt{2} \log \left(x^2+\sqrt{2} x+1\right)-6 \log (1-x)+6 \log (x+1)+12 \tan ^{-1}(x)+6 \sqrt{2} \tan ^{-1}\left(1-\sqrt{2} x\right)-6 \sqrt{2} \tan ^{-1}\left(\sqrt{2} x+1\right)\right)","-\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,"(-16/x^3 + 12*ArcTan[x] + 6*Sqrt[2]*ArcTan[1 - Sqrt[2]*x] - 6*Sqrt[2]*ArcTan[1 + Sqrt[2]*x] - 6*Log[1 - x] + 6*Log[1 + x] + 3*Sqrt[2]*Log[1 - Sqrt[2]*x + x^2] - 3*Sqrt[2]*Log[1 + Sqrt[2]*x + x^2])/48","A",1
1488,1,104,104,0.0505453,"\int \frac{1}{x^6 \left(1-x^8\right)} \, dx","Integrate[1/(x^6*(1 - x^8)),x]","\frac{1}{80} \left(-\frac{16}{x^5}+5 \sqrt{2} \log \left(x^2-\sqrt{2} x+1\right)-5 \sqrt{2} \log \left(x^2+\sqrt{2} x+1\right)-10 \log (1-x)+10 \log (x+1)-20 \tan ^{-1}(x)-10 \sqrt{2} \tan ^{-1}\left(1-\sqrt{2} x\right)+10 \sqrt{2} \tan ^{-1}\left(\sqrt{2} x+1\right)\right)","-\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,"(-16/x^5 - 20*ArcTan[x] - 10*Sqrt[2]*ArcTan[1 - Sqrt[2]*x] + 10*Sqrt[2]*ArcTan[1 + Sqrt[2]*x] - 10*Log[1 - x] + 10*Log[1 + x] + 5*Sqrt[2]*Log[1 - Sqrt[2]*x + x^2] - 5*Sqrt[2]*Log[1 + Sqrt[2]*x + x^2])/80","A",1
1489,1,104,104,0.0609069,"\int \frac{1}{x^8 \left(1-x^8\right)} \, dx","Integrate[1/(x^8*(1 - x^8)),x]","\frac{1}{112} \left(-\frac{16}{x^7}-7 \sqrt{2} \log \left(x^2-\sqrt{2} x+1\right)+7 \sqrt{2} \log \left(x^2+\sqrt{2} x+1\right)-14 \log (1-x)+14 \log (x+1)+28 \tan ^{-1}(x)-14 \sqrt{2} \tan ^{-1}\left(1-\sqrt{2} x\right)+14 \sqrt{2} \tan ^{-1}\left(\sqrt{2} x+1\right)\right)","-\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,"(-16/x^7 + 28*ArcTan[x] - 14*Sqrt[2]*ArcTan[1 - Sqrt[2]*x] + 14*Sqrt[2]*ArcTan[1 + Sqrt[2]*x] - 14*Log[1 - x] + 14*Log[1 + x] - 7*Sqrt[2]*Log[1 - Sqrt[2]*x + x^2] + 7*Sqrt[2]*Log[1 + Sqrt[2]*x + x^2])/112","A",1
1490,1,191,100,0.1162195,"\int \frac{x^9}{1+x^8} \, dx","Integrate[x^9/(1 + x^8),x]","\frac{1}{16} \left(8 x^2-\sqrt{2} \log \left(x^2-2 x \sin \left(\frac{\pi }{8}\right)+1\right)-\sqrt{2} \log \left(x^2+2 x \sin \left(\frac{\pi }{8}\right)+1\right)+\sqrt{2} \log \left(x^2-2 x \cos \left(\frac{\pi }{8}\right)+1\right)+\sqrt{2} \log \left(x^2+2 x \cos \left(\frac{\pi }{8}\right)+1\right)-2 \sqrt{2} \tan ^{-1}\left(x \sec \left(\frac{\pi }{8}\right)-\tan \left(\frac{\pi }{8}\right)\right)+2 \sqrt{2} \tan ^{-1}\left(\csc \left(\frac{\pi }{8}\right) \left(x+\cos \left(\frac{\pi }{8}\right)\right)\right)+2 \sqrt{2} \tan ^{-1}\left(\cot \left(\frac{\pi }{8}\right)-x \csc \left(\frac{\pi }{8}\right)\right)+2 \sqrt{2} \tan ^{-1}\left(\sec \left(\frac{\pi }{8}\right) \left(x+\sin \left(\frac{\pi }{8}\right)\right)\right)\right)","\frac{x^2}{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}}",1,"(8*x^2 + 2*Sqrt[2]*ArcTan[(x + Cos[Pi/8])*Csc[Pi/8]] + 2*Sqrt[2]*ArcTan[Cot[Pi/8] - x*Csc[Pi/8]] + 2*Sqrt[2]*ArcTan[Sec[Pi/8]*(x + Sin[Pi/8])] - 2*Sqrt[2]*ArcTan[x*Sec[Pi/8] - Tan[Pi/8]] + Sqrt[2]*Log[1 + x^2 - 2*x*Cos[Pi/8]] + Sqrt[2]*Log[1 + x^2 + 2*x*Cos[Pi/8]] - Sqrt[2]*Log[1 + x^2 - 2*x*Sin[Pi/8]] - Sqrt[2]*Log[1 + x^2 + 2*x*Sin[Pi/8]])/16","A",1
1491,1,10,10,0.0025532,"\int \frac{x^7}{1+x^8} \, dx","Integrate[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
1492,1,149,93,0.0524259,"\int \frac{x^5}{1+x^8} \, dx","Integrate[x^5/(1 + x^8),x]","-\frac{\log \left(x^2-2 x \sin \left(\frac{\pi }{8}\right)+1\right)+\log \left(x^2+2 x \sin \left(\frac{\pi }{8}\right)+1\right)-\log \left(x^2-2 x \cos \left(\frac{\pi }{8}\right)+1\right)-\log \left(x^2+2 x \cos \left(\frac{\pi }{8}\right)+1\right)-2 \tan ^{-1}\left(x \sec \left(\frac{\pi }{8}\right)-\tan \left(\frac{\pi }{8}\right)\right)+2 \tan ^{-1}\left(\csc \left(\frac{\pi }{8}\right) \left(x+\cos \left(\frac{\pi }{8}\right)\right)\right)+2 \tan ^{-1}\left(\cot \left(\frac{\pi }{8}\right)-x \csc \left(\frac{\pi }{8}\right)\right)+2 \tan ^{-1}\left(\sec \left(\frac{\pi }{8}\right) \left(x+\sin \left(\frac{\pi }{8}\right)\right)\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}}",1,"-1/8*(2*ArcTan[(x + Cos[Pi/8])*Csc[Pi/8]] + 2*ArcTan[Cot[Pi/8] - x*Csc[Pi/8]] + 2*ArcTan[Sec[Pi/8]*(x + Sin[Pi/8])] - 2*ArcTan[x*Sec[Pi/8] - Tan[Pi/8]] - Log[1 + x^2 - 2*x*Cos[Pi/8]] - Log[1 + x^2 + 2*x*Cos[Pi/8]] + Log[1 + x^2 - 2*x*Sin[Pi/8]] + Log[1 + x^2 + 2*x*Sin[Pi/8]])/Sqrt[2]","A",1
1493,1,8,8,0.0048778,"\int \frac{x^3}{1+x^8} \, dx","Integrate[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",1
1494,1,149,93,0.0386163,"\int \frac{x}{1+x^8} \, dx","Integrate[x/(1 + x^8),x]","-\frac{-\log \left(x^2-2 x \sin \left(\frac{\pi }{8}\right)+1\right)-\log \left(x^2+2 x \sin \left(\frac{\pi }{8}\right)+1\right)+\log \left(x^2-2 x \cos \left(\frac{\pi }{8}\right)+1\right)+\log \left(x^2+2 x \cos \left(\frac{\pi }{8}\right)+1\right)-2 \tan ^{-1}\left(x \sec \left(\frac{\pi }{8}\right)-\tan \left(\frac{\pi }{8}\right)\right)+2 \tan ^{-1}\left(\csc \left(\frac{\pi }{8}\right) \left(x+\cos \left(\frac{\pi }{8}\right)\right)\right)+2 \tan ^{-1}\left(\cot \left(\frac{\pi }{8}\right)-x \csc \left(\frac{\pi }{8}\right)\right)+2 \tan ^{-1}\left(\sec \left(\frac{\pi }{8}\right) \left(x+\sin \left(\frac{\pi }{8}\right)\right)\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}}",1,"-1/8*(2*ArcTan[(x + Cos[Pi/8])*Csc[Pi/8]] + 2*ArcTan[Cot[Pi/8] - x*Csc[Pi/8]] + 2*ArcTan[Sec[Pi/8]*(x + Sin[Pi/8])] - 2*ArcTan[x*Sec[Pi/8] - Tan[Pi/8]] + Log[1 + x^2 - 2*x*Cos[Pi/8]] + Log[1 + x^2 + 2*x*Cos[Pi/8]] - Log[1 + x^2 - 2*x*Sin[Pi/8]] - Log[1 + x^2 + 2*x*Sin[Pi/8]])/Sqrt[2]","A",1
1495,1,13,13,0.003327,"\int \frac{1}{x \left(1+x^8\right)} \, dx","Integrate[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",1
1496,1,208,100,0.0379247,"\int \frac{1}{x^3 \left(1+x^8\right)} \, dx","Integrate[1/(x^3*(1 + x^8)),x]","-\frac{1}{2 x^2}+\frac{\log \left(x^2-2 x \sin \left(\frac{\pi }{8}\right)+1\right)}{8 \sqrt{2}}+\frac{\log \left(x^2+2 x \sin \left(\frac{\pi }{8}\right)+1\right)}{8 \sqrt{2}}-\frac{\log \left(x^2-2 x \cos \left(\frac{\pi }{8}\right)+1\right)}{8 \sqrt{2}}-\frac{\log \left(x^2+2 x \cos \left(\frac{\pi }{8}\right)+1\right)}{8 \sqrt{2}}-\frac{\tan ^{-1}\left(\csc \left(\frac{\pi }{8}\right) \left(x-\cos \left(\frac{\pi }{8}\right)\right)\right)}{4 \sqrt{2}}+\frac{\tan ^{-1}\left(\csc \left(\frac{\pi }{8}\right) \left(x+\cos \left(\frac{\pi }{8}\right)\right)\right)}{4 \sqrt{2}}-\frac{\tan ^{-1}\left(\sec \left(\frac{\pi }{8}\right) \left(x-\sin \left(\frac{\pi }{8}\right)\right)\right)}{4 \sqrt{2}}+\frac{\tan ^{-1}\left(\sec \left(\frac{\pi }{8}\right) \left(x+\sin \left(\frac{\pi }{8}\right)\right)\right)}{4 \sqrt{2}}","-\frac{1}{2 x^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}}",1,"-1/2*1/x^2 - ArcTan[(x - Cos[Pi/8])*Csc[Pi/8]]/(4*Sqrt[2]) + ArcTan[(x + Cos[Pi/8])*Csc[Pi/8]]/(4*Sqrt[2]) - ArcTan[Sec[Pi/8]*(x - Sin[Pi/8])]/(4*Sqrt[2]) + ArcTan[Sec[Pi/8]*(x + Sin[Pi/8])]/(4*Sqrt[2]) - Log[1 + x^2 - 2*x*Cos[Pi/8]]/(8*Sqrt[2]) - Log[1 + x^2 + 2*x*Cos[Pi/8]]/(8*Sqrt[2]) + Log[1 + x^2 - 2*x*Sin[Pi/8]]/(8*Sqrt[2]) + Log[1 + x^2 + 2*x*Sin[Pi/8]]/(8*Sqrt[2])","B",1
1497,1,16,16,0.0063014,"\int \frac{1}{x^5 \left(1+x^8\right)} \, dx","Integrate[1/(x^5*(1 + x^8)),x]","\frac{1}{4} \tan ^{-1}\left(\frac{1}{x^4}\right)-\frac{1}{4 x^4}","-\frac{1}{4 x^4}-\frac{1}{4} \tan ^{-1}\left(x^4\right)",1,"-1/4*1/x^4 + ArcTan[x^(-4)]/4","A",1
1498,1,193,100,0.0824481,"\int \frac{1}{x^7 \left(1+x^8\right)} \, dx","Integrate[1/(x^7*(1 + x^8)),x]","\frac{1}{48} \left(-\frac{8}{x^6}-3 \sqrt{2} \log \left(x^2-2 x \sin \left(\frac{\pi }{8}\right)+1\right)-3 \sqrt{2} \log \left(x^2+2 x \sin \left(\frac{\pi }{8}\right)+1\right)+3 \sqrt{2} \log \left(x^2-2 x \cos \left(\frac{\pi }{8}\right)+1\right)+3 \sqrt{2} \log \left(x^2+2 x \cos \left(\frac{\pi }{8}\right)+1\right)-6 \sqrt{2} \tan ^{-1}\left(x \sec \left(\frac{\pi }{8}\right)-\tan \left(\frac{\pi }{8}\right)\right)+6 \sqrt{2} \tan ^{-1}\left(\csc \left(\frac{\pi }{8}\right) \left(x+\cos \left(\frac{\pi }{8}\right)\right)\right)+6 \sqrt{2} \tan ^{-1}\left(\cot \left(\frac{\pi }{8}\right)-x \csc \left(\frac{\pi }{8}\right)\right)+6 \sqrt{2} \tan ^{-1}\left(\sec \left(\frac{\pi }{8}\right) \left(x+\sin \left(\frac{\pi }{8}\right)\right)\right)\right)","-\frac{1}{6 x^6}+\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}}",1,"(-8/x^6 + 6*Sqrt[2]*ArcTan[(x + Cos[Pi/8])*Csc[Pi/8]] + 6*Sqrt[2]*ArcTan[Cot[Pi/8] - x*Csc[Pi/8]] + 6*Sqrt[2]*ArcTan[Sec[Pi/8]*(x + Sin[Pi/8])] - 6*Sqrt[2]*ArcTan[x*Sec[Pi/8] - Tan[Pi/8]] + 3*Sqrt[2]*Log[1 + x^2 - 2*x*Cos[Pi/8]] + 3*Sqrt[2]*Log[1 + x^2 + 2*x*Cos[Pi/8]] - 3*Sqrt[2]*Log[1 + x^2 - 2*x*Sin[Pi/8]] - 3*Sqrt[2]*Log[1 + x^2 + 2*x*Sin[Pi/8]])/48","A",1
1499,1,22,22,0.0039477,"\int \frac{1}{x^9 \left(1+x^8\right)} \, dx","Integrate[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*1/x^8 - Log[x] + Log[1 + x^8]/8","A",1
1500,1,210,340,0.0071105,"\int \frac{x^8}{1+x^8} \, dx","Integrate[x^8/(1 + x^8),x]","\frac{1}{8} \sin \left(\frac{\pi }{8}\right) \log \left(x^2-2 x \sin \left(\frac{\pi }{8}\right)+1\right)-\frac{1}{8} \sin \left(\frac{\pi }{8}\right) \log \left(x^2+2 x \sin \left(\frac{\pi }{8}\right)+1\right)+\frac{1}{8} \cos \left(\frac{\pi }{8}\right) \log \left(x^2-2 x \cos \left(\frac{\pi }{8}\right)+1\right)-\frac{1}{8} \cos \left(\frac{\pi }{8}\right) \log \left(x^2+2 x \cos \left(\frac{\pi }{8}\right)+1\right)+x-\frac{1}{4} \sin \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\csc \left(\frac{\pi }{8}\right) \left(x-\cos \left(\frac{\pi }{8}\right)\right)\right)-\frac{1}{4} \sin \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\csc \left(\frac{\pi }{8}\right) \left(x+\cos \left(\frac{\pi }{8}\right)\right)\right)-\frac{1}{4} \cos \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\sec \left(\frac{\pi }{8}\right) \left(x-\sin \left(\frac{\pi }{8}\right)\right)\right)-\frac{1}{4} \cos \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\sec \left(\frac{\pi }{8}\right) \left(x+\sin \left(\frac{\pi }{8}\right)\right)\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[Sec[Pi/8]*(x - Sin[Pi/8])]*Cos[Pi/8])/4 - (ArcTan[Sec[Pi/8]*(x + Sin[Pi/8])]*Cos[Pi/8])/4 + (Cos[Pi/8]*Log[1 + x^2 - 2*x*Cos[Pi/8]])/8 - (Cos[Pi/8]*Log[1 + x^2 + 2*x*Cos[Pi/8]])/8 - (ArcTan[(x - Cos[Pi/8])*Csc[Pi/8]]*Sin[Pi/8])/4 - (ArcTan[(x + Cos[Pi/8])*Csc[Pi/8]]*Sin[Pi/8])/4 + (Log[1 + x^2 - 2*x*Sin[Pi/8]]*Sin[Pi/8])/8 - (Log[1 + x^2 + 2*x*Sin[Pi/8]]*Sin[Pi/8])/8","A",1
1501,1,209,339,0.0066691,"\int \frac{x^6}{1+x^8} \, dx","Integrate[x^6/(1 + x^8),x]","\frac{1}{8} \sin \left(\frac{\pi }{8}\right) \log \left(x^2-2 x \sin \left(\frac{\pi }{8}\right)+1\right)-\frac{1}{8} \sin \left(\frac{\pi }{8}\right) \log \left(x^2+2 x \sin \left(\frac{\pi }{8}\right)+1\right)+\frac{1}{8} \cos \left(\frac{\pi }{8}\right) \log \left(x^2-2 x \cos \left(\frac{\pi }{8}\right)+1\right)-\frac{1}{8} \cos \left(\frac{\pi }{8}\right) \log \left(x^2+2 x \cos \left(\frac{\pi }{8}\right)+1\right)+\frac{1}{4} \sin \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\csc \left(\frac{\pi }{8}\right) \left(x-\cos \left(\frac{\pi }{8}\right)\right)\right)+\frac{1}{4} \sin \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\csc \left(\frac{\pi }{8}\right) \left(x+\cos \left(\frac{\pi }{8}\right)\right)\right)+\frac{1}{4} \cos \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\sec \left(\frac{\pi }{8}\right) \left(x-\sin \left(\frac{\pi }{8}\right)\right)\right)+\frac{1}{4} \cos \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\sec \left(\frac{\pi }{8}\right) \left(x+\sin \left(\frac{\pi }{8}\right)\right)\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[Sec[Pi/8]*(x - Sin[Pi/8])]*Cos[Pi/8])/4 + (ArcTan[Sec[Pi/8]*(x + Sin[Pi/8])]*Cos[Pi/8])/4 + (Cos[Pi/8]*Log[1 + x^2 - 2*x*Cos[Pi/8]])/8 - (Cos[Pi/8]*Log[1 + x^2 + 2*x*Cos[Pi/8]])/8 + (ArcTan[(x - Cos[Pi/8])*Csc[Pi/8]]*Sin[Pi/8])/4 + (ArcTan[(x + Cos[Pi/8])*Csc[Pi/8]]*Sin[Pi/8])/4 + (Log[1 + x^2 - 2*x*Sin[Pi/8]]*Sin[Pi/8])/8 - (Log[1 + x^2 + 2*x*Sin[Pi/8]]*Sin[Pi/8])/8","A",1
1502,1,209,347,0.0073381,"\int \frac{x^4}{1+x^8} \, dx","Integrate[x^4/(1 + x^8),x]","-\frac{1}{8} \cos \left(\frac{\pi }{8}\right) \log \left(x^2-2 x \sin \left(\frac{\pi }{8}\right)+1\right)+\frac{1}{8} \cos \left(\frac{\pi }{8}\right) \log \left(x^2+2 x \sin \left(\frac{\pi }{8}\right)+1\right)+\frac{1}{8} \sin \left(\frac{\pi }{8}\right) \log \left(x^2-2 x \cos \left(\frac{\pi }{8}\right)+1\right)-\frac{1}{8} \sin \left(\frac{\pi }{8}\right) \log \left(x^2+2 x \cos \left(\frac{\pi }{8}\right)+1\right)+\frac{1}{4} \cos \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\csc \left(\frac{\pi }{8}\right) \left(x-\cos \left(\frac{\pi }{8}\right)\right)\right)+\frac{1}{4} \cos \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\csc \left(\frac{\pi }{8}\right) \left(x+\cos \left(\frac{\pi }{8}\right)\right)\right)-\frac{1}{4} \sin \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\sec \left(\frac{\pi }{8}\right) \left(x-\sin \left(\frac{\pi }{8}\right)\right)\right)-\frac{1}{4} \sin \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\sec \left(\frac{\pi }{8}\right) \left(x+\sin \left(\frac{\pi }{8}\right)\right)\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[(x - Cos[Pi/8])*Csc[Pi/8]]*Cos[Pi/8])/4 + (ArcTan[(x + Cos[Pi/8])*Csc[Pi/8]]*Cos[Pi/8])/4 - (Cos[Pi/8]*Log[1 + x^2 - 2*x*Sin[Pi/8]])/8 + (Cos[Pi/8]*Log[1 + x^2 + 2*x*Sin[Pi/8]])/8 - (ArcTan[Sec[Pi/8]*(x - Sin[Pi/8])]*Sin[Pi/8])/4 - (ArcTan[Sec[Pi/8]*(x + Sin[Pi/8])]*Sin[Pi/8])/4 + (Log[1 + x^2 - 2*x*Cos[Pi/8]]*Sin[Pi/8])/8 - (Log[1 + x^2 + 2*x*Cos[Pi/8]]*Sin[Pi/8])/8","A",1
1503,1,209,339,0.0066943,"\int \frac{x^2}{1+x^8} \, dx","Integrate[x^2/(1 + x^8),x]","\frac{1}{8} \cos \left(\frac{\pi }{8}\right) \log \left(x^2-2 x \sin \left(\frac{\pi }{8}\right)+1\right)-\frac{1}{8} \cos \left(\frac{\pi }{8}\right) \log \left(x^2+2 x \sin \left(\frac{\pi }{8}\right)+1\right)-\frac{1}{8} \sin \left(\frac{\pi }{8}\right) \log \left(x^2-2 x \cos \left(\frac{\pi }{8}\right)+1\right)+\frac{1}{8} \sin \left(\frac{\pi }{8}\right) \log \left(x^2+2 x \cos \left(\frac{\pi }{8}\right)+1\right)+\frac{1}{4} \cos \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\csc \left(\frac{\pi }{8}\right) \left(x-\cos \left(\frac{\pi }{8}\right)\right)\right)+\frac{1}{4} \cos \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\csc \left(\frac{\pi }{8}\right) \left(x+\cos \left(\frac{\pi }{8}\right)\right)\right)-\frac{1}{4} \sin \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\sec \left(\frac{\pi }{8}\right) \left(x-\sin \left(\frac{\pi }{8}\right)\right)\right)-\frac{1}{4} \sin \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\sec \left(\frac{\pi }{8}\right) \left(x+\sin \left(\frac{\pi }{8}\right)\right)\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,"(ArcTan[(x - Cos[Pi/8])*Csc[Pi/8]]*Cos[Pi/8])/4 + (ArcTan[(x + Cos[Pi/8])*Csc[Pi/8]]*Cos[Pi/8])/4 + (Cos[Pi/8]*Log[1 + x^2 - 2*x*Sin[Pi/8]])/8 - (Cos[Pi/8]*Log[1 + x^2 + 2*x*Sin[Pi/8]])/8 - (ArcTan[Sec[Pi/8]*(x - Sin[Pi/8])]*Sin[Pi/8])/4 - (ArcTan[Sec[Pi/8]*(x + Sin[Pi/8])]*Sin[Pi/8])/4 - (Log[1 + x^2 - 2*x*Cos[Pi/8]]*Sin[Pi/8])/8 + (Log[1 + x^2 + 2*x*Cos[Pi/8]]*Sin[Pi/8])/8","A",1
1504,1,209,339,0.0074756,"\int \frac{1}{1+x^8} \, dx","Integrate[(1 + x^8)^(-1),x]","-\frac{1}{8} \sin \left(\frac{\pi }{8}\right) \log \left(x^2-2 x \sin \left(\frac{\pi }{8}\right)+1\right)+\frac{1}{8} \sin \left(\frac{\pi }{8}\right) \log \left(x^2+2 x \sin \left(\frac{\pi }{8}\right)+1\right)-\frac{1}{8} \cos \left(\frac{\pi }{8}\right) \log \left(x^2-2 x \cos \left(\frac{\pi }{8}\right)+1\right)+\frac{1}{8} \cos \left(\frac{\pi }{8}\right) \log \left(x^2+2 x \cos \left(\frac{\pi }{8}\right)+1\right)+\frac{1}{4} \sin \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\csc \left(\frac{\pi }{8}\right) \left(x-\cos \left(\frac{\pi }{8}\right)\right)\right)+\frac{1}{4} \sin \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\csc \left(\frac{\pi }{8}\right) \left(x+\cos \left(\frac{\pi }{8}\right)\right)\right)+\frac{1}{4} \cos \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\sec \left(\frac{\pi }{8}\right) \left(x-\sin \left(\frac{\pi }{8}\right)\right)\right)+\frac{1}{4} \cos \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\sec \left(\frac{\pi }{8}\right) \left(x+\sin \left(\frac{\pi }{8}\right)\right)\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[Sec[Pi/8]*(x - Sin[Pi/8])]*Cos[Pi/8])/4 + (ArcTan[Sec[Pi/8]*(x + Sin[Pi/8])]*Cos[Pi/8])/4 - (Cos[Pi/8]*Log[1 + x^2 - 2*x*Cos[Pi/8]])/8 + (Cos[Pi/8]*Log[1 + x^2 + 2*x*Cos[Pi/8]])/8 + (ArcTan[(x - Cos[Pi/8])*Csc[Pi/8]]*Sin[Pi/8])/4 + (ArcTan[(x + Cos[Pi/8])*Csc[Pi/8]]*Sin[Pi/8])/4 - (Log[1 + x^2 - 2*x*Sin[Pi/8]]*Sin[Pi/8])/8 + (Log[1 + x^2 + 2*x*Sin[Pi/8]]*Sin[Pi/8])/8","A",1
1505,1,214,344,0.0077645,"\int \frac{1}{x^2 \left(1+x^8\right)} \, dx","Integrate[1/(x^2*(1 + x^8)),x]","-\frac{1}{8} \sin \left(\frac{\pi }{8}\right) \log \left(x^2-2 x \sin \left(\frac{\pi }{8}\right)+1\right)+\frac{1}{8} \sin \left(\frac{\pi }{8}\right) \log \left(x^2+2 x \sin \left(\frac{\pi }{8}\right)+1\right)-\frac{1}{8} \cos \left(\frac{\pi }{8}\right) \log \left(x^2-2 x \cos \left(\frac{\pi }{8}\right)+1\right)+\frac{1}{8} \cos \left(\frac{\pi }{8}\right) \log \left(x^2+2 x \cos \left(\frac{\pi }{8}\right)+1\right)-\frac{1}{x}-\frac{1}{4} \sin \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\csc \left(\frac{\pi }{8}\right) \left(x-\cos \left(\frac{\pi }{8}\right)\right)\right)-\frac{1}{4} \sin \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\csc \left(\frac{\pi }{8}\right) \left(x+\cos \left(\frac{\pi }{8}\right)\right)\right)-\frac{1}{4} \cos \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\sec \left(\frac{\pi }{8}\right) \left(x-\sin \left(\frac{\pi }{8}\right)\right)\right)-\frac{1}{4} \cos \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\sec \left(\frac{\pi }{8}\right) \left(x+\sin \left(\frac{\pi }{8}\right)\right)\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[Sec[Pi/8]*(x - Sin[Pi/8])]*Cos[Pi/8])/4 - (ArcTan[Sec[Pi/8]*(x + Sin[Pi/8])]*Cos[Pi/8])/4 - (Cos[Pi/8]*Log[1 + x^2 - 2*x*Cos[Pi/8]])/8 + (Cos[Pi/8]*Log[1 + x^2 + 2*x*Cos[Pi/8]])/8 - (ArcTan[(x - Cos[Pi/8])*Csc[Pi/8]]*Sin[Pi/8])/4 - (ArcTan[(x + Cos[Pi/8])*Csc[Pi/8]]*Sin[Pi/8])/4 - (Log[1 + x^2 - 2*x*Sin[Pi/8]]*Sin[Pi/8])/8 + (Log[1 + x^2 + 2*x*Sin[Pi/8]]*Sin[Pi/8])/8","A",1
1506,1,216,354,0.00844,"\int \frac{1}{x^4 \left(1+x^8\right)} \, dx","Integrate[1/(x^4*(1 + x^8)),x]","-\frac{1}{3 x^3}+\frac{1}{8} \cos \left(\frac{\pi }{8}\right) \log \left(x^2-2 x \sin \left(\frac{\pi }{8}\right)+1\right)-\frac{1}{8} \cos \left(\frac{\pi }{8}\right) \log \left(x^2+2 x \sin \left(\frac{\pi }{8}\right)+1\right)-\frac{1}{8} \sin \left(\frac{\pi }{8}\right) \log \left(x^2-2 x \cos \left(\frac{\pi }{8}\right)+1\right)+\frac{1}{8} \sin \left(\frac{\pi }{8}\right) \log \left(x^2+2 x \cos \left(\frac{\pi }{8}\right)+1\right)-\frac{1}{4} \cos \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\csc \left(\frac{\pi }{8}\right) \left(x-\cos \left(\frac{\pi }{8}\right)\right)\right)-\frac{1}{4} \cos \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\csc \left(\frac{\pi }{8}\right) \left(x+\cos \left(\frac{\pi }{8}\right)\right)\right)+\frac{1}{4} \sin \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\sec \left(\frac{\pi }{8}\right) \left(x-\sin \left(\frac{\pi }{8}\right)\right)\right)+\frac{1}{4} \sin \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\sec \left(\frac{\pi }{8}\right) \left(x+\sin \left(\frac{\pi }{8}\right)\right)\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*1/x^3 - (ArcTan[(x - Cos[Pi/8])*Csc[Pi/8]]*Cos[Pi/8])/4 - (ArcTan[(x + Cos[Pi/8])*Csc[Pi/8]]*Cos[Pi/8])/4 + (Cos[Pi/8]*Log[1 + x^2 - 2*x*Sin[Pi/8]])/8 - (Cos[Pi/8]*Log[1 + x^2 + 2*x*Sin[Pi/8]])/8 + (ArcTan[Sec[Pi/8]*(x - Sin[Pi/8])]*Sin[Pi/8])/4 + (ArcTan[Sec[Pi/8]*(x + Sin[Pi/8])]*Sin[Pi/8])/4 - (Log[1 + x^2 - 2*x*Cos[Pi/8]]*Sin[Pi/8])/8 + (Log[1 + x^2 + 2*x*Cos[Pi/8]]*Sin[Pi/8])/8","A",1
1507,1,216,346,0.010575,"\int \frac{1}{x^6 \left(1+x^8\right)} \, dx","Integrate[1/(x^6*(1 + x^8)),x]","-\frac{1}{5 x^5}-\frac{1}{8} \cos \left(\frac{\pi }{8}\right) \log \left(x^2-2 x \sin \left(\frac{\pi }{8}\right)+1\right)+\frac{1}{8} \cos \left(\frac{\pi }{8}\right) \log \left(x^2+2 x \sin \left(\frac{\pi }{8}\right)+1\right)+\frac{1}{8} \sin \left(\frac{\pi }{8}\right) \log \left(x^2-2 x \cos \left(\frac{\pi }{8}\right)+1\right)-\frac{1}{8} \sin \left(\frac{\pi }{8}\right) \log \left(x^2+2 x \cos \left(\frac{\pi }{8}\right)+1\right)-\frac{1}{4} \cos \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\csc \left(\frac{\pi }{8}\right) \left(x-\cos \left(\frac{\pi }{8}\right)\right)\right)-\frac{1}{4} \cos \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\csc \left(\frac{\pi }{8}\right) \left(x+\cos \left(\frac{\pi }{8}\right)\right)\right)+\frac{1}{4} \sin \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\sec \left(\frac{\pi }{8}\right) \left(x-\sin \left(\frac{\pi }{8}\right)\right)\right)+\frac{1}{4} \sin \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\sec \left(\frac{\pi }{8}\right) \left(x+\sin \left(\frac{\pi }{8}\right)\right)\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*1/x^5 - (ArcTan[(x - Cos[Pi/8])*Csc[Pi/8]]*Cos[Pi/8])/4 - (ArcTan[(x + Cos[Pi/8])*Csc[Pi/8]]*Cos[Pi/8])/4 - (Cos[Pi/8]*Log[1 + x^2 - 2*x*Sin[Pi/8]])/8 + (Cos[Pi/8]*Log[1 + x^2 + 2*x*Sin[Pi/8]])/8 + (ArcTan[Sec[Pi/8]*(x - Sin[Pi/8])]*Sin[Pi/8])/4 + (ArcTan[Sec[Pi/8]*(x + Sin[Pi/8])]*Sin[Pi/8])/4 + (Log[1 + x^2 - 2*x*Cos[Pi/8]]*Sin[Pi/8])/8 - (Log[1 + x^2 + 2*x*Cos[Pi/8]]*Sin[Pi/8])/8","A",1
1508,1,216,346,0.0080839,"\int \frac{1}{x^8 \left(1+x^8\right)} \, dx","Integrate[1/(x^8*(1 + x^8)),x]","-\frac{1}{7 x^7}+\frac{1}{8} \sin \left(\frac{\pi }{8}\right) \log \left(x^2-2 x \sin \left(\frac{\pi }{8}\right)+1\right)-\frac{1}{8} \sin \left(\frac{\pi }{8}\right) \log \left(x^2+2 x \sin \left(\frac{\pi }{8}\right)+1\right)+\frac{1}{8} \cos \left(\frac{\pi }{8}\right) \log \left(x^2-2 x \cos \left(\frac{\pi }{8}\right)+1\right)-\frac{1}{8} \cos \left(\frac{\pi }{8}\right) \log \left(x^2+2 x \cos \left(\frac{\pi }{8}\right)+1\right)-\frac{1}{4} \sin \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\csc \left(\frac{\pi }{8}\right) \left(x-\cos \left(\frac{\pi }{8}\right)\right)\right)-\frac{1}{4} \sin \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\csc \left(\frac{\pi }{8}\right) \left(x+\cos \left(\frac{\pi }{8}\right)\right)\right)-\frac{1}{4} \cos \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\sec \left(\frac{\pi }{8}\right) \left(x-\sin \left(\frac{\pi }{8}\right)\right)\right)-\frac{1}{4} \cos \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\sec \left(\frac{\pi }{8}\right) \left(x+\sin \left(\frac{\pi }{8}\right)\right)\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*1/x^7 - (ArcTan[Sec[Pi/8]*(x - Sin[Pi/8])]*Cos[Pi/8])/4 - (ArcTan[Sec[Pi/8]*(x + Sin[Pi/8])]*Cos[Pi/8])/4 + (Cos[Pi/8]*Log[1 + x^2 - 2*x*Cos[Pi/8]])/8 - (Cos[Pi/8]*Log[1 + x^2 + 2*x*Cos[Pi/8]])/8 - (ArcTan[(x - Cos[Pi/8])*Csc[Pi/8]]*Sin[Pi/8])/4 - (ArcTan[(x + Cos[Pi/8])*Csc[Pi/8]]*Sin[Pi/8])/4 + (Log[1 + x^2 - 2*x*Sin[Pi/8]]*Sin[Pi/8])/8 - (Log[1 + x^2 + 2*x*Sin[Pi/8]]*Sin[Pi/8])/8","A",1
1509,1,22,25,0.0069506,"\int x^3 \sqrt{1+x^8} \, dx","Integrate[x^3*Sqrt[1 + x^8],x]","\frac{1}{8} \left(\sinh ^{-1}\left(x^4\right)+\sqrt{x^8+1} x^4\right)","\frac{1}{8} \sinh ^{-1}\left(x^4\right)+\frac{1}{8} \sqrt{x^8+1} x^4",1,"(x^4*Sqrt[1 + x^8] + ArcSinh[x^4])/8","A",1
1510,1,22,62,0.0027558,"\int x \sqrt{1+x^8} \, dx","Integrate[x*Sqrt[1 + x^8],x]","\frac{1}{2} x^2 \, _2F_1\left(-\frac{1}{2},\frac{1}{4};\frac{5}{4};-x^8\right)","\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*Hypergeometric2F1[-1/2, 1/4, 5/4, -x^8])/2","C",1
1511,1,28,28,0.0043835,"\int \frac{\sqrt{1+x^8}}{x} \, dx","Integrate[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",1
1512,1,22,125,0.0033485,"\int \frac{\sqrt{1+x^8}}{x^3} \, dx","Integrate[Sqrt[1 + x^8]/x^3,x]","-\frac{\, _2F_1\left(-\frac{1}{2},-\frac{1}{4};\frac{3}{4};-x^8\right)}{2 x^2}","-\frac{\sqrt{x^8+1}}{2 x^2}+\frac{\sqrt{x^8+1} x^2}{x^4+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)}{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,"-1/2*Hypergeometric2F1[-1/2, -1/4, 3/4, -x^8]/x^2","C",1
1513,1,50,35,0.0363377,"\int x^3 \sqrt{-2+x^8} \, dx","Integrate[x^3*Sqrt[-2 + x^8],x]","\frac{\left(x^8-2\right) \left(2 \sin ^{-1}\left(\frac{x^4}{\sqrt{2}}\right)+\sqrt{2-x^8} x^4\right)}{8 \sqrt{-\left(x^8-2\right)^2}}","\frac{1}{8} x^4 \sqrt{x^8-2}-\frac{1}{4} \tanh ^{-1}\left(\frac{x^4}{\sqrt{x^8-2}}\right)",1,"((-2 + x^8)*(x^4*Sqrt[2 - x^8] + 2*ArcSin[x^4/Sqrt[2]]))/(8*Sqrt[-(-2 + x^8)^2])","A",1
1514,1,31,41,0.0115581,"\int \frac{x^{19}}{\sqrt{1+x^8}} \, dx","Integrate[x^19/Sqrt[1 + x^8],x]","\frac{1}{32} \left(3 \sinh ^{-1}\left(x^4\right)+\sqrt{x^8+1} \left(2 x^8-3\right) x^4\right)","\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",1,"(x^4*Sqrt[1 + x^8]*(-3 + 2*x^8) + 3*ArcSinh[x^4])/32","A",1
1515,1,18,27,0.0051936,"\int \frac{x^{15}}{\sqrt{1+x^8}} \, dx","Integrate[x^15/Sqrt[1 + x^8],x]","\frac{1}{12} \left(x^8-2\right) \sqrt{x^8+1}","\frac{1}{12} \left(x^8+1\right)^{3/2}-\frac{\sqrt{x^8+1}}{4}",1,"((-2 + x^8)*Sqrt[1 + x^8])/12","A",1
1516,1,25,25,0.0052588,"\int \frac{x^{11}}{\sqrt{1+x^8}} \, dx","Integrate[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",1
1517,1,13,13,0.0020719,"\int \frac{x^7}{\sqrt{1+x^8}} \, dx","Integrate[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
1518,1,8,8,0.0022753,"\int \frac{x^3}{\sqrt{1+x^8}} \, dx","Integrate[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",1
1519,1,14,14,0.0022849,"\int \frac{1}{x \sqrt{1+x^8}} \, dx","Integrate[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,"-1/4*ArcTanh[Sqrt[1 + x^8]]","A",1
1520,1,16,16,0.0027105,"\int \frac{1}{x^5 \sqrt{1+x^8}} \, dx","Integrate[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,"-1/4*Sqrt[1 + x^8]/x^4","A",1
1521,1,31,31,0.0163529,"\int \frac{1}{x^9 \sqrt{1+x^8}} \, dx","Integrate[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,"-1/8*Sqrt[1 + x^8]/x^8 + ArcTanh[Sqrt[1 + x^8]]/8","A",1
1522,1,23,33,0.0044667,"\int \frac{1}{x^{13} \sqrt{1+x^8}} \, dx","Integrate[1/(x^13*Sqrt[1 + x^8]),x]","-\frac{\left(1-2 x^8\right) \sqrt{x^8+1}}{12 x^{12}}","\frac{\sqrt{x^8+1}}{6 x^4}-\frac{\sqrt{x^8+1}}{12 x^{12}}",1,"-1/12*((1 - 2*x^8)*Sqrt[1 + x^8])/x^12","A",1
1523,1,26,47,0.005118,"\int \frac{1}{x^{17} \sqrt{1+x^8}} \, dx","Integrate[1/(x^17*Sqrt[1 + x^8]),x]","-\frac{1}{4} \sqrt{x^8+1} \, _2F_1\left(\frac{1}{2},3;\frac{3}{2};x^8+1\right)","\frac{3 \sqrt{x^8+1}}{32 x^8}-\frac{3}{32} \tanh ^{-1}\left(\sqrt{x^8+1}\right)-\frac{\sqrt{x^8+1}}{16 x^{16}}",1,"-1/4*(Sqrt[1 + x^8]*Hypergeometric2F1[1/2, 3, 3/2, 1 + x^8])","C",1
1524,1,34,130,0.0065059,"\int \frac{x^{13}}{\sqrt{1+x^8}} \, dx","Integrate[x^13/Sqrt[1 + x^8],x]","\frac{1}{10} x^6 \left(\sqrt{x^8+1}-\, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};-x^8\right)\right)","\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] - Hypergeometric2F1[1/2, 3/4, 7/4, -x^8]))/10","C",1
1525,1,34,62,0.0084765,"\int \frac{x^9}{\sqrt{1+x^8}} \, dx","Integrate[x^9/Sqrt[1 + x^8],x]","\frac{1}{6} x^2 \left(\sqrt{x^8+1}-\, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-x^8\right)\right)","\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] - Hypergeometric2F1[1/4, 1/2, 5/4, -x^8]))/6","C",1
1526,1,22,114,0.0036079,"\int \frac{x^5}{\sqrt{1+x^8}} \, dx","Integrate[x^5/Sqrt[1 + x^8],x]","\frac{1}{6} x^6 \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};-x^8\right)","\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^6*Hypergeometric2F1[1/2, 3/4, 7/4, -x^8])/6","C",1
1527,1,22,45,0.003323,"\int \frac{x}{\sqrt{1+x^8}} \, dx","Integrate[x/Sqrt[1 + x^8],x]","\frac{1}{2} x^2 \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-x^8\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}}",1,"(x^2*Hypergeometric2F1[1/4, 1/2, 5/4, -x^8])/2","C",1
1528,1,22,130,0.0039887,"\int \frac{1}{x^3 \sqrt{1+x^8}} \, dx","Integrate[1/(x^3*Sqrt[1 + x^8]),x]","-\frac{\, _2F_1\left(-\frac{1}{4},\frac{1}{2};\frac{3}{4};-x^8\right)}{2 x^2}","-\frac{\sqrt{x^8+1}}{2 x^2}+\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,"-1/2*Hypergeometric2F1[-1/4, 1/2, 3/4, -x^8]/x^2","C",1
1529,1,22,62,0.0118748,"\int \frac{1}{x^7 \sqrt{1+x^8}} \, dx","Integrate[1/(x^7*Sqrt[1 + x^8]),x]","-\frac{\, _2F_1\left(-\frac{3}{4},\frac{1}{2};\frac{1}{4};-x^8\right)}{6 x^6}","-\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,"-1/6*Hypergeometric2F1[-3/4, 1/2, 1/4, -x^8]/x^6","C",1
1530,1,34,239,0.0077296,"\int \frac{x^{10}}{\sqrt{1+x^8}} \, dx","Integrate[x^10/Sqrt[1 + x^8],x]","\frac{1}{7} x^3 \left(\sqrt{x^8+1}-\, _2F_1\left(\frac{3}{8},\frac{1}{2};\frac{11}{8};-x^8\right)\right)","\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] - Hypergeometric2F1[3/8, 1/2, 11/8, -x^8]))/7","C",1
1531,1,32,237,0.0070476,"\int \frac{x^8}{\sqrt{1+x^8}} \, dx","Integrate[x^8/Sqrt[1 + x^8],x]","\frac{1}{5} x \left(\sqrt{x^8+1}-\, _2F_1\left(\frac{1}{8},\frac{1}{2};\frac{9}{8};-x^8\right)\right)","\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] - Hypergeometric2F1[1/8, 1/2, 9/8, -x^8]))/5","C",1
1532,1,22,22,0.0031521,"\int \frac{x^6}{\sqrt{1+x^8}} \, dx","Integrate[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
1533,1,22,22,0.0025607,"\int \frac{x^4}{\sqrt{1+x^8}} \, dx","Integrate[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
1534,1,22,223,0.0028765,"\int \frac{x^2}{\sqrt{1+x^8}} \, dx","Integrate[x^2/Sqrt[1 + x^8],x]","\frac{1}{3} x^3 \, _2F_1\left(\frac{3}{8},\frac{1}{2};\frac{11}{8};-x^8\right)","-\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*Hypergeometric2F1[3/8, 1/2, 11/8, -x^8])/3","C",1
1535,1,17,223,0.0019012,"\int \frac{1}{\sqrt{1+x^8}} \, dx","Integrate[1/Sqrt[1 + x^8],x]","x \, _2F_1\left(\frac{1}{8},\frac{1}{2};\frac{9}{8};-x^8\right)","\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*Hypergeometric2F1[1/8, 1/2, 9/8, -x^8]","C",1
1536,1,20,37,0.0029336,"\int \frac{1}{x^2 \sqrt{1+x^8}} \, dx","Integrate[1/(x^2*Sqrt[1 + x^8]),x]","-\frac{\, _2F_1\left(-\frac{1}{8},\frac{1}{2};\frac{7}{8};-x^8\right)}{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,"-(Hypergeometric2F1[-1/8, 1/2, 7/8, -x^8]/x)","A",1
1537,1,22,39,0.0030049,"\int \frac{1}{x^4 \sqrt{1+x^8}} \, dx","Integrate[1/(x^4*Sqrt[1 + x^8]),x]","-\frac{\, _2F_1\left(-\frac{3}{8},\frac{1}{2};\frac{5}{8};-x^8\right)}{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,"-1/3*Hypergeometric2F1[-3/8, 1/2, 5/8, -x^8]/x^3","A",1
1538,1,22,239,0.0032496,"\int \frac{1}{x^6 \sqrt{1+x^8}} \, dx","Integrate[1/(x^6*Sqrt[1 + x^8]),x]","-\frac{\, _2F_1\left(-\frac{5}{8},\frac{1}{2};\frac{3}{8};-x^8\right)}{5 x^5}","-\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,"-1/5*Hypergeometric2F1[-5/8, 1/2, 3/8, -x^8]/x^5","C",1
1539,1,22,239,0.0030279,"\int \frac{1}{x^8 \sqrt{1+x^8}} \, dx","Integrate[1/(x^8*Sqrt[1 + x^8]),x]","-\frac{\, _2F_1\left(-\frac{7}{8},\frac{1}{2};\frac{1}{8};-x^8\right)}{7 x^7}","-\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,"-1/7*Hypergeometric2F1[-7/8, 1/2, 1/8, -x^8]/x^7","C",1
1540,1,289,163,0.2553534,"\int \frac{1}{1-x^{10}} \, dx","Integrate[(1 - x^10)^(-1),x]","\frac{1}{40} \left(-\left(\sqrt{5}-1\right) \log \left(x^2-\frac{1}{2} \left(\sqrt{5}-1\right) x+1\right)+\left(\sqrt{5}-1\right) \log \left(x^2+\frac{1}{2} \left(\sqrt{5}-1\right) x+1\right)-\left(1+\sqrt{5}\right) \log \left(x^2-\frac{1}{2} \left(1+\sqrt{5}\right) x+1\right)+\left(1+\sqrt{5}\right) \log \left(\frac{1}{2} \left(2 x^2+\sqrt{5} x+x+2\right)\right)-4 \log (1-x)+4 \log (x+1)-2 \sqrt{10-2 \sqrt{5}} \tan ^{-1}\left(\frac{-4 x+\sqrt{5}+1}{\sqrt{10-2 \sqrt{5}}}\right)+2 \sqrt{2 \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\frac{4 x-\sqrt{5}+1}{\sqrt{2 \left(5+\sqrt{5}\right)}}\right)+2 \sqrt{2 \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\frac{4 x+\sqrt{5}-1}{\sqrt{2 \left(5+\sqrt{5}\right)}}\right)+2 \sqrt{10-2 \sqrt{5}} \tan ^{-1}\left(\frac{4 x+\sqrt{5}+1}{\sqrt{10-2 \sqrt{5}}}\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} \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,"(-2*Sqrt[10 - 2*Sqrt[5]]*ArcTan[(1 + Sqrt[5] - 4*x)/Sqrt[10 - 2*Sqrt[5]]] + 2*Sqrt[2*(5 + Sqrt[5])]*ArcTan[(1 - Sqrt[5] + 4*x)/Sqrt[2*(5 + Sqrt[5])]] + 2*Sqrt[2*(5 + Sqrt[5])]*ArcTan[(-1 + Sqrt[5] + 4*x)/Sqrt[2*(5 + Sqrt[5])]] + 2*Sqrt[10 - 2*Sqrt[5]]*ArcTan[(1 + Sqrt[5] + 4*x)/Sqrt[10 - 2*Sqrt[5]]] - 4*Log[1 - x] + 4*Log[1 + x] - (-1 + Sqrt[5])*Log[1 - ((-1 + Sqrt[5])*x)/2 + x^2] + (-1 + Sqrt[5])*Log[1 + ((-1 + Sqrt[5])*x)/2 + x^2] - (1 + Sqrt[5])*Log[1 - ((1 + Sqrt[5])*x)/2 + x^2] + (1 + Sqrt[5])*Log[(2 + x + Sqrt[5]*x + 2*x^2)/2])/40","A",1
1541,1,8,8,0.0032512,"\int \frac{x^4}{\sqrt{1-x^{10}}} \, dx","Integrate[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",1
1542,1,18,18,0.0031729,"\int \frac{x^4}{\sqrt{-2+x^{10}}} \, dx","Integrate[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",1
1543,1,12,12,0.0053498,"\int \frac{x^5}{9+x^{12}} \, dx","Integrate[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",1
1544,1,23,12,0.0038626,"\int \frac{x^5}{9-x^{12}} \, dx","Integrate[x^5/(9 - x^12),x]","\frac{1}{36} \log \left(x^6+3\right)-\frac{1}{36} \log \left(3-x^6\right)","\frac{1}{18} \tanh ^{-1}\left(\frac{x^6}{3}\right)",1,"-1/36*Log[3 - x^6] + Log[3 + x^6]/36","A",1
1545,1,28,29,0.0073387,"\int x^5 \sqrt{9+x^{12}} \, dx","Integrate[x^5*Sqrt[9 + x^12],x]","\frac{1}{12} \left(9 \sinh ^{-1}\left(\frac{x^6}{3}\right)+\sqrt{x^{12}+9} x^6\right)","\frac{3}{4} \sinh ^{-1}\left(\frac{x^6}{3}\right)+\frac{1}{12} \sqrt{x^{12}+9} x^6",1,"(x^6*Sqrt[9 + x^12] + 9*ArcSinh[x^6/3])/12","A",1
1546,1,17,17,0.0016156,"\int \left(a+\frac{b}{x}\right) x^6 \, dx","Integrate[(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",1
1547,1,17,17,0.0012309,"\int \left(a+\frac{b}{x}\right) x^5 \, dx","Integrate[(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",1
1548,1,17,17,0.0012339,"\int \left(a+\frac{b}{x}\right) x^4 \, dx","Integrate[(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",1
1549,1,17,17,0.0011979,"\int \left(a+\frac{b}{x}\right) x^3 \, dx","Integrate[(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",1
1550,1,17,17,0.0010709,"\int \left(a+\frac{b}{x}\right) x^2 \, dx","Integrate[(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",1
1551,1,12,12,0.00058,"\int \left(a+\frac{b}{x}\right) x \, dx","Integrate[(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",1
1552,1,8,8,0.0007874,"\int \left(a+\frac{b}{x}\right) \, dx","Integrate[a + b/x,x]","a x+b \log (x)","a x+b \log (x)",1,"a*x + b*Log[x]","A",1
1553,1,11,11,0.0018641,"\int \frac{a+\frac{b}{x}}{x} \, dx","Integrate[(a + b/x)/x,x]","a \log (x)-\frac{b}{x}","a \log (x)-\frac{b}{x}",1,"-(b/x) + a*Log[x]","A",1
1554,1,15,15,0.0016739,"\int \frac{a+\frac{b}{x}}{x^2} \, dx","Integrate[(a + b/x)/x^2,x]","-\frac{a}{x}-\frac{b}{2 x^2}","-\frac{a}{x}-\frac{b}{2 x^2}",1,"-1/2*b/x^2 - a/x","A",1
1555,1,17,17,0.0020803,"\int \frac{a+\frac{b}{x}}{x^3} \, dx","Integrate[(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,"-1/3*b/x^3 - a/(2*x^2)","A",1
1556,1,17,17,0.0016204,"\int \frac{a+\frac{b}{x}}{x^4} \, dx","Integrate[(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,"-1/4*b/x^4 - a/(3*x^3)","A",1
1557,1,17,17,0.002015,"\int \frac{a+\frac{b}{x}}{x^5} \, dx","Integrate[(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,"-1/5*b/x^5 - a/(4*x^4)","A",1
1558,1,17,17,0.0017432,"\int \frac{a+\frac{b}{x}}{x^6} \, dx","Integrate[(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,"-1/6*b/x^6 - a/(5*x^5)","A",1
1559,1,30,30,0.0021072,"\int \left(a+\frac{b}{x}\right)^2 x^5 \, dx","Integrate[(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",1
1560,1,30,30,0.0019912,"\int \left(a+\frac{b}{x}\right)^2 x^4 \, dx","Integrate[(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",1
1561,1,30,30,0.0014706,"\int \left(a+\frac{b}{x}\right)^2 x^3 \, dx","Integrate[(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",1
1562,1,14,14,0.0016839,"\int \left(a+\frac{b}{x}\right)^2 x^2 \, dx","Integrate[(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",1
1563,1,22,22,0.0011378,"\int \left(a+\frac{b}{x}\right)^2 x \, dx","Integrate[(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",1
1564,1,20,20,0.0035046,"\int \left(a+\frac{b}{x}\right)^2 \, dx","Integrate[(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",1
1565,1,24,24,0.0037894,"\int \frac{\left(a+\frac{b}{x}\right)^2}{x} \, dx","Integrate[(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,"-1/2*b^2/x^2 - (2*a*b)/x + a^2*Log[x]","A",1
1566,1,26,16,0.0070139,"\int \frac{\left(a+\frac{b}{x}\right)^2}{x^2} \, dx","Integrate[(a + b/x)^2/x^2,x]","-\frac{a^2}{x}-\frac{a b}{x^2}-\frac{b^2}{3 x^3}","-\frac{\left(a+\frac{b}{x}\right)^3}{3 b}",1,"-1/3*b^2/x^3 - (a*b)/x^2 - a^2/x","A",1
1567,1,30,30,0.0035241,"\int \frac{\left(a+\frac{b}{x}\right)^2}{x^3} \, dx","Integrate[(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,"-1/4*b^2/x^4 - (2*a*b)/(3*x^3) - a^2/(2*x^2)","A",1
1568,1,30,30,0.0071645,"\int \frac{\left(a+\frac{b}{x}\right)^2}{x^4} \, dx","Integrate[(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,"-1/5*b^2/x^5 - (a*b)/(2*x^4) - a^2/(3*x^3)","A",1
1569,1,30,30,0.0036205,"\int \frac{\left(a+\frac{b}{x}\right)^2}{x^5} \, dx","Integrate[(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,"-1/6*b^2/x^6 - (2*a*b)/(5*x^5) - a^2/(4*x^4)","A",1
1570,1,43,43,0.0021804,"\int \left(a+\frac{b}{x}\right)^3 x^6 \, dx","Integrate[(a + b/x)^3*x^6,x]","\frac{a^3 x^7}{7}+\frac{1}{2} a^2 b x^6+\frac{3}{5} a b^2 x^5+\frac{b^3 x^4}{4}","\frac{a^3 x^7}{7}+\frac{1}{2} a^2 b x^6+\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",1
1571,1,43,43,0.0019519,"\int \left(a+\frac{b}{x}\right)^3 x^5 \, dx","Integrate[(a + b/x)^3*x^5,x]","\frac{a^3 x^6}{6}+\frac{3}{5} a^2 b x^5+\frac{3}{4} a b^2 x^4+\frac{b^3 x^3}{3}","\frac{a^3 x^6}{6}+\frac{3}{5} a^2 b x^5+\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",1
1572,1,40,30,0.0016995,"\int \left(a+\frac{b}{x}\right)^3 x^4 \, dx","Integrate[(a + b/x)^3*x^4,x]","\frac{a^3 x^5}{5}+\frac{3}{4} a^2 b x^4+a b^2 x^3+\frac{b^3 x^2}{2}","\frac{(a x+b)^5}{5 a^2}-\frac{b (a x+b)^4}{4 a^2}",1,"(b^3*x^2)/2 + a*b^2*x^3 + (3*a^2*b*x^4)/4 + (a^3*x^5)/5","A",1
1573,1,14,14,0.0016877,"\int \left(a+\frac{b}{x}\right)^3 x^3 \, dx","Integrate[(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",1
1574,1,35,35,0.0032138,"\int \left(a+\frac{b}{x}\right)^3 x^2 \, dx","Integrate[(a + b/x)^3*x^2,x]","\frac{a^3 x^3}{3}+\frac{3}{2} a^2 b x^2+3 a b^2 x+b^3 \log (x)","\frac{a^3 x^3}{3}+\frac{3}{2} a^2 b x^2+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",1
1575,1,34,34,0.0047029,"\int \left(a+\frac{b}{x}\right)^3 x \, dx","Integrate[(a + b/x)^3*x,x]","\frac{a^3 x^2}{2}+3 a^2 b x+3 a b^2 \log (x)-\frac{b^3}{x}","\frac{a^3 x^2}{2}+3 a^2 b x+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",1
1576,1,33,33,0.0042618,"\int \left(a+\frac{b}{x}\right)^3 \, dx","Integrate[(a + b/x)^3,x]","a^3 x+3 a^2 b \log (x)-\frac{3 a b^2}{x}-\frac{b^3}{2 x^2}","a^3 x+3 a^2 b \log (x)-\frac{3 a b^2}{x}-\frac{b^3}{2 x^2}",1,"-1/2*b^3/x^2 - (3*a*b^2)/x + a^3*x + 3*a^2*b*Log[x]","A",1
1577,1,37,37,0.0038614,"\int \frac{\left(a+\frac{b}{x}\right)^3}{x} \, dx","Integrate[(a + b/x)^3/x,x]","a^3 \log (x)-\frac{3 a^2 b}{x}-\frac{3 a b^2}{2 x^2}-\frac{b^3}{3 x^3}","a^3 \log (x)-\frac{3 a^2 b}{x}-\frac{3 a b^2}{2 x^2}-\frac{b^3}{3 x^3}",1,"-1/3*b^3/x^3 - (3*a*b^2)/(2*x^2) - (3*a^2*b)/x + a^3*Log[x]","A",1
1578,1,39,16,0.0100077,"\int \frac{\left(a+\frac{b}{x}\right)^3}{x^2} \, dx","Integrate[(a + b/x)^3/x^2,x]","-\frac{a^3}{x}-\frac{3 a^2 b}{2 x^2}-\frac{a b^2}{x^3}-\frac{b^3}{4 x^4}","-\frac{\left(a+\frac{b}{x}\right)^4}{4 b}",1,"-1/4*b^3/x^4 - (a*b^2)/x^3 - (3*a^2*b)/(2*x^2) - a^3/x","B",1
1579,1,41,36,0.0063559,"\int \frac{\left(a+\frac{b}{x}\right)^3}{x^3} \, dx","Integrate[(a + b/x)^3/x^3,x]","-\frac{a^3}{2 x^2}-\frac{a^2 b}{x^3}-\frac{3 a b^2}{4 x^4}-\frac{b^3}{5 x^5}","\frac{a (a x+b)^4}{20 b^2 x^4}-\frac{(a x+b)^4}{5 b x^5}",1,"-1/5*b^3/x^5 - (3*a*b^2)/(4*x^4) - (a^2*b)/x^3 - a^3/(2*x^2)","A",1
1580,1,43,43,0.0036443,"\int \frac{\left(a+\frac{b}{x}\right)^3}{x^4} \, dx","Integrate[(a + b/x)^3/x^4,x]","-\frac{a^3}{3 x^3}-\frac{3 a^2 b}{4 x^4}-\frac{3 a b^2}{5 x^5}-\frac{b^3}{6 x^6}","-\frac{a^3}{3 x^3}-\frac{3 a^2 b}{4 x^4}-\frac{3 a b^2}{5 x^5}-\frac{b^3}{6 x^6}",1,"-1/6*b^3/x^6 - (3*a*b^2)/(5*x^5) - (3*a^2*b)/(4*x^4) - a^3/(3*x^3)","A",1
1581,1,43,43,0.0040499,"\int \frac{\left(a+\frac{b}{x}\right)^3}{x^5} \, dx","Integrate[(a + b/x)^3/x^5,x]","-\frac{a^3}{4 x^4}-\frac{3 a^2 b}{5 x^5}-\frac{a b^2}{2 x^6}-\frac{b^3}{7 x^7}","-\frac{a^3}{4 x^4}-\frac{3 a^2 b}{5 x^5}-\frac{a b^2}{2 x^6}-\frac{b^3}{7 x^7}",1,"-1/7*b^3/x^7 - (a*b^2)/(2*x^6) - (3*a^2*b)/(5*x^5) - a^3/(4*x^4)","A",1
1582,1,43,43,0.0064999,"\int \frac{\left(a+\frac{b}{x}\right)^3}{x^6} \, dx","Integrate[(a + b/x)^3/x^6,x]","-\frac{a^3}{5 x^5}-\frac{a^2 b}{2 x^6}-\frac{3 a b^2}{7 x^7}-\frac{b^3}{8 x^8}","-\frac{a^3}{5 x^5}-\frac{a^2 b}{2 x^6}-\frac{3 a b^2}{7 x^7}-\frac{b^3}{8 x^8}",1,"-1/8*b^3/x^8 - (3*a*b^2)/(7*x^7) - (a^2*b)/(2*x^6) - a^3/(5*x^5)","A",1
1583,1,106,106,0.0031874,"\int \left(a+\frac{b}{x}\right)^8 x^{16} \, dx","Integrate[(a + b/x)^8*x^16,x]","\frac{a^8 x^{17}}{17}+\frac{1}{2} a^7 b x^{16}+\frac{28}{15} a^6 b^2 x^{15}+4 a^5 b^3 x^{14}+\frac{70}{13} a^4 b^4 x^{13}+\frac{14}{3} a^3 b^5 x^{12}+\frac{28}{11} a^2 b^6 x^{11}+\frac{4}{5} a b^7 x^{10}+\frac{b^8 x^9}{9}","\frac{a^8 x^{17}}{17}+\frac{1}{2} a^7 b x^{16}+\frac{28}{15} a^6 b^2 x^{15}+4 a^5 b^3 x^{14}+\frac{70}{13} a^4 b^4 x^{13}+\frac{14}{3} a^3 b^5 x^{12}+\frac{28}{11} a^2 b^6 x^{11}+\frac{4}{5} a b^7 x^{10}+\frac{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",1
1584,1,106,106,0.0029147,"\int \left(a+\frac{b}{x}\right)^8 x^{15} \, dx","Integrate[(a + b/x)^8*x^15,x]","\frac{a^8 x^{16}}{16}+\frac{8}{15} a^7 b x^{15}+2 a^6 b^2 x^{14}+\frac{56}{13} a^5 b^3 x^{13}+\frac{35}{6} a^4 b^4 x^{12}+\frac{56}{11} a^3 b^5 x^{11}+\frac{14}{5} a^2 b^6 x^{10}+\frac{8}{9} a b^7 x^9+\frac{b^8 x^8}{8}","\frac{a^8 x^{16}}{16}+\frac{8}{15} a^7 b x^{15}+2 a^6 b^2 x^{14}+\frac{56}{13} a^5 b^3 x^{13}+\frac{35}{6} a^4 b^4 x^{12}+\frac{56}{11} a^3 b^5 x^{11}+\frac{14}{5} a^2 b^6 x^{10}+\frac{8}{9} a b^7 x^9+\frac{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",1
1585,1,106,98,0.0028329,"\int \left(a+\frac{b}{x}\right)^8 x^{13} \, dx","Integrate[(a + b/x)^8*x^13,x]","\frac{a^8 x^{14}}{14}+\frac{8}{13} a^7 b x^{13}+\frac{7}{3} a^6 b^2 x^{12}+\frac{56}{11} a^5 b^3 x^{11}+7 a^4 b^4 x^{10}+\frac{56}{9} a^3 b^5 x^9+\frac{7}{2} a^2 b^6 x^8+\frac{8}{7} a b^7 x^7+\frac{b^8 x^6}{6}","-\frac{b^5 (a x+b)^9}{9 a^6}+\frac{b^4 (a x+b)^{10}}{2 a^6}-\frac{10 b^3 (a x+b)^{11}}{11 a^6}+\frac{5 b^2 (a x+b)^{12}}{6 a^6}+\frac{(a x+b)^{14}}{14 a^6}-\frac{5 b (a x+b)^{13}}{13 a^6}",1,"(b^8*x^6)/6 + (8*a*b^7*x^7)/7 + (7*a^2*b^6*x^8)/2 + (56*a^3*b^5*x^9)/9 + 7*a^4*b^4*x^10 + (56*a^5*b^3*x^11)/11 + (7*a^6*b^2*x^12)/3 + (8*a^7*b*x^13)/13 + (a^8*x^14)/14","A",1
1586,1,104,81,0.0028753,"\int \left(a+\frac{b}{x}\right)^8 x^{12} \, dx","Integrate[(a + b/x)^8*x^12,x]","\frac{a^8 x^{13}}{13}+\frac{2}{3} a^7 b x^{12}+\frac{28}{11} a^6 b^2 x^{11}+\frac{28}{5} a^5 b^3 x^{10}+\frac{70}{9} a^4 b^4 x^9+7 a^3 b^5 x^8+4 a^2 b^6 x^7+\frac{4}{3} a b^7 x^6+\frac{b^8 x^5}{5}","\frac{b^4 (a x+b)^9}{9 a^5}-\frac{2 b^3 (a x+b)^{10}}{5 a^5}+\frac{6 b^2 (a x+b)^{11}}{11 a^5}+\frac{(a x+b)^{13}}{13 a^5}-\frac{b (a x+b)^{12}}{3 a^5}",1,"(b^8*x^5)/5 + (4*a*b^7*x^6)/3 + 4*a^2*b^6*x^7 + 7*a^3*b^5*x^8 + (70*a^4*b^4*x^9)/9 + (28*a^5*b^3*x^10)/5 + (28*a^6*b^2*x^11)/11 + (2*a^7*b*x^12)/3 + (a^8*x^13)/13","A",1
1587,1,106,64,0.0027956,"\int \left(a+\frac{b}{x}\right)^8 x^{11} \, dx","Integrate[(a + b/x)^8*x^11,x]","\frac{a^8 x^{12}}{12}+\frac{8}{11} a^7 b x^{11}+\frac{14}{5} a^6 b^2 x^{10}+\frac{56}{9} a^5 b^3 x^9+\frac{35}{4} a^4 b^4 x^8+8 a^3 b^5 x^7+\frac{14}{3} a^2 b^6 x^6+\frac{8}{5} a b^7 x^5+\frac{b^8 x^4}{4}","-\frac{b^3 (a x+b)^9}{9 a^4}+\frac{3 b^2 (a x+b)^{10}}{10 a^4}+\frac{(a x+b)^{12}}{12 a^4}-\frac{3 b (a x+b)^{11}}{11 a^4}",1,"(b^8*x^4)/4 + (8*a*b^7*x^5)/5 + (14*a^2*b^6*x^6)/3 + 8*a^3*b^5*x^7 + (35*a^4*b^4*x^8)/4 + (56*a^5*b^3*x^9)/9 + (14*a^6*b^2*x^10)/5 + (8*a^7*b*x^11)/11 + (a^8*x^12)/12","A",1
1588,1,102,47,0.0030486,"\int \left(a+\frac{b}{x}\right)^8 x^{10} \, dx","Integrate[(a + b/x)^8*x^10,x]","\frac{a^8 x^{11}}{11}+\frac{4}{5} a^7 b x^{10}+\frac{28}{9} a^6 b^2 x^9+7 a^5 b^3 x^8+10 a^4 b^4 x^7+\frac{28}{3} a^3 b^5 x^6+\frac{28}{5} a^2 b^6 x^5+2 a b^7 x^4+\frac{b^8 x^3}{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^8*x^3)/3 + 2*a*b^7*x^4 + (28*a^2*b^6*x^5)/5 + (28*a^3*b^5*x^6)/3 + 10*a^4*b^4*x^7 + 7*a^5*b^3*x^8 + (28*a^6*b^2*x^9)/9 + (4*a^7*b*x^10)/5 + (a^8*x^11)/11","B",1
1589,1,104,30,0.0025172,"\int \left(a+\frac{b}{x}\right)^8 x^9 \, dx","Integrate[(a + b/x)^8*x^9,x]","\frac{a^8 x^{10}}{10}+\frac{8}{9} a^7 b x^9+\frac{7}{2} a^6 b^2 x^8+8 a^5 b^3 x^7+\frac{35}{3} a^4 b^4 x^6+\frac{56}{5} a^3 b^5 x^5+7 a^2 b^6 x^4+\frac{8}{3} a b^7 x^3+\frac{b^8 x^2}{2}","\frac{(a x+b)^{10}}{10 a^2}-\frac{b (a x+b)^9}{9 a^2}",1,"(b^8*x^2)/2 + (8*a*b^7*x^3)/3 + 7*a^2*b^6*x^4 + (56*a^3*b^5*x^5)/5 + (35*a^4*b^4*x^6)/3 + 8*a^5*b^3*x^7 + (7*a^6*b^2*x^8)/2 + (8*a^7*b*x^9)/9 + (a^8*x^10)/10","B",1
1590,1,14,14,0.0011887,"\int \left(a+\frac{b}{x}\right)^8 x^8 \, dx","Integrate[(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",1
1591,1,98,98,0.0051427,"\int \left(a+\frac{b}{x}\right)^8 x^7 \, dx","Integrate[(a + b/x)^8*x^7,x]","\frac{a^8 x^8}{8}+\frac{8}{7} a^7 b x^7+\frac{14}{3} a^6 b^2 x^6+\frac{56}{5} a^5 b^3 x^5+\frac{35}{2} a^4 b^4 x^4+\frac{56}{3} a^3 b^5 x^3+14 a^2 b^6 x^2+8 a b^7 x+b^8 \log (x)","\frac{a^8 x^8}{8}+\frac{8}{7} a^7 b x^7+\frac{14}{3} a^6 b^2 x^6+\frac{56}{5} a^5 b^3 x^5+\frac{35}{2} a^4 b^4 x^4+\frac{56}{3} a^3 b^5 x^3+14 a^2 b^6 x^2+8 a b^7 x+b^8 \log (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",1
1592,1,95,95,0.0092154,"\int \left(a+\frac{b}{x}\right)^8 x^6 \, dx","Integrate[(a + b/x)^8*x^6,x]","\frac{a^8 x^7}{7}+\frac{4}{3} a^7 b x^6+\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+8 a b^7 \log (x)-\frac{b^8}{x}","\frac{a^8 x^7}{7}+\frac{4}{3} a^7 b x^6+\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+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",1
1593,1,95,95,0.0051061,"\int \left(a+\frac{b}{x}\right)^8 x^5 \, dx","Integrate[(a + b/x)^8*x^5,x]","\frac{a^8 x^6}{6}+\frac{8}{5} a^7 b x^5+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 a b^7}{x}-\frac{b^8}{2 x^2}","\frac{a^8 x^6}{6}+\frac{8}{5} a^7 b x^5+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 a b^7}{x}-\frac{b^8}{2 x^2}",1,"-1/2*b^8/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",1
1594,1,93,93,0.0086655,"\int \left(a+\frac{b}{x}\right)^8 x^4 \, dx","Integrate[(a + b/x)^8*x^4,x]","\frac{a^8 x^5}{5}+2 a^7 b x^4+\frac{28}{3} a^6 b^2 x^3+28 a^5 b^3 x^2+70 a^4 b^4 x+56 a^3 b^5 \log (x)-\frac{28 a^2 b^6}{x}-\frac{4 a b^7}{x^2}-\frac{b^8}{3 x^3}","\frac{a^8 x^5}{5}+2 a^7 b x^4+\frac{28}{3} a^6 b^2 x^3+28 a^5 b^3 x^2+70 a^4 b^4 x+56 a^3 b^5 \log (x)-\frac{28 a^2 b^6}{x}-\frac{4 a b^7}{x^2}-\frac{b^8}{3 x^3}",1,"-1/3*b^8/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",1
1595,1,95,95,0.0048656,"\int \left(a+\frac{b}{x}\right)^8 x^3 \, dx","Integrate[(a + b/x)^8*x^3,x]","\frac{a^8 x^4}{4}+\frac{8}{3} a^7 b x^3+14 a^6 b^2 x^2+56 a^5 b^3 x+70 a^4 b^4 \log (x)-\frac{56 a^3 b^5}{x}-\frac{14 a^2 b^6}{x^2}-\frac{8 a b^7}{3 x^3}-\frac{b^8}{4 x^4}","\frac{a^8 x^4}{4}+\frac{8}{3} a^7 b x^3+14 a^6 b^2 x^2+56 a^5 b^3 x+70 a^4 b^4 \log (x)-\frac{56 a^3 b^5}{x}-\frac{14 a^2 b^6}{x^2}-\frac{8 a b^7}{3 x^3}-\frac{b^8}{4 x^4}",1,"-1/4*b^8/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",1
1596,1,93,93,0.0095372,"\int \left(a+\frac{b}{x}\right)^8 x^2 \, dx","Integrate[(a + b/x)^8*x^2,x]","\frac{a^8 x^3}{3}+4 a^7 b x^2+28 a^6 b^2 x+56 a^5 b^3 \log (x)-\frac{70 a^4 b^4}{x}-\frac{28 a^3 b^5}{x^2}-\frac{28 a^2 b^6}{3 x^3}-\frac{2 a b^7}{x^4}-\frac{b^8}{5 x^5}","\frac{a^8 x^3}{3}+4 a^7 b x^2+28 a^6 b^2 x+56 a^5 b^3 \log (x)-\frac{70 a^4 b^4}{x}-\frac{28 a^3 b^5}{x^2}-\frac{28 a^2 b^6}{3 x^3}-\frac{2 a b^7}{x^4}-\frac{b^8}{5 x^5}",1,"-1/5*b^8/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",1
1597,1,95,95,0.0058507,"\int \left(a+\frac{b}{x}\right)^8 x \, dx","Integrate[(a + b/x)^8*x,x]","\frac{a^8 x^2}{2}+8 a^7 b x+28 a^6 b^2 \log (x)-\frac{56 a^5 b^3}{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{8 a b^7}{5 x^5}-\frac{b^8}{6 x^6}","\frac{a^8 x^2}{2}+8 a^7 b x+28 a^6 b^2 \log (x)-\frac{56 a^5 b^3}{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{8 a b^7}{5 x^5}-\frac{b^8}{6 x^6}",1,"-1/6*b^8/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",1
1598,1,94,94,0.0048146,"\int \left(a+\frac{b}{x}\right)^8 \, dx","Integrate[(a + b/x)^8,x]","a^8 x+8 a^7 b \log (x)-\frac{28 a^6 b^2}{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{4 a b^7}{3 x^6}-\frac{b^8}{7 x^7}","a^8 x+8 a^7 b \log (x)-\frac{28 a^6 b^2}{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{4 a b^7}{3 x^6}-\frac{b^8}{7 x^7}",1,"-1/7*b^8/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",1
1599,1,100,100,0.0048022,"\int \frac{\left(a+\frac{b}{x}\right)^8}{x} \, dx","Integrate[(a + b/x)^8/x,x]","a^8 \log (x)-\frac{8 a^7 b}{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 b^7}{7 x^7}-\frac{b^8}{8 x^8}","a^8 \log (x)-\frac{8 a^7 b}{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 b^7}{7 x^7}-\frac{b^8}{8 x^8}",1,"-1/8*b^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",1
1600,1,96,16,0.0101454,"\int \frac{\left(a+\frac{b}{x}\right)^8}{x^2} \, dx","Integrate[(a + b/x)^8/x^2,x]","-\frac{a^8}{x}-\frac{4 a^7 b}{x^2}-\frac{28 a^6 b^2}{3 x^3}-\frac{14 a^5 b^3}{x^4}-\frac{14 a^4 b^4}{x^5}-\frac{28 a^3 b^5}{3 x^6}-\frac{4 a^2 b^6}{x^7}-\frac{a b^7}{x^8}-\frac{b^8}{9 x^9}","-\frac{\left(a+\frac{b}{x}\right)^9}{9 b}",1,"-1/9*b^8/x^9 - (a*b^7)/x^8 - (4*a^2*b^6)/x^7 - (28*a^3*b^5)/(3*x^6) - (14*a^4*b^4)/x^5 - (14*a^5*b^3)/x^4 - (28*a^6*b^2)/(3*x^3) - (4*a^7*b)/x^2 - a^8/x","B",1
1601,1,104,36,0.0043764,"\int \frac{\left(a+\frac{b}{x}\right)^8}{x^3} \, dx","Integrate[(a + b/x)^8/x^3,x]","-\frac{a^8}{2 x^2}-\frac{8 a^7 b}{3 x^3}-\frac{7 a^6 b^2}{x^4}-\frac{56 a^5 b^3}{5 x^5}-\frac{35 a^4 b^4}{3 x^6}-\frac{8 a^3 b^5}{x^7}-\frac{7 a^2 b^6}{2 x^8}-\frac{8 a b^7}{9 x^9}-\frac{b^8}{10 x^{10}}","\frac{a (a x+b)^9}{90 b^2 x^9}-\frac{(a x+b)^9}{10 b x^{10}}",1,"-1/10*b^8/x^10 - (8*a*b^7)/(9*x^9) - (7*a^2*b^6)/(2*x^8) - (8*a^3*b^5)/x^7 - (35*a^4*b^4)/(3*x^6) - (56*a^5*b^3)/(5*x^5) - (7*a^6*b^2)/x^4 - (8*a^7*b)/(3*x^3) - a^8/(2*x^2)","B",1
1602,1,102,56,0.0090271,"\int \frac{\left(a+\frac{b}{x}\right)^8}{x^4} \, dx","Integrate[(a + b/x)^8/x^4,x]","-\frac{a^8}{3 x^3}-\frac{2 a^7 b}{x^4}-\frac{28 a^6 b^2}{5 x^5}-\frac{28 a^5 b^3}{3 x^6}-\frac{10 a^4 b^4}{x^7}-\frac{7 a^3 b^5}{x^8}-\frac{28 a^2 b^6}{9 x^9}-\frac{4 a b^7}{5 x^{10}}-\frac{b^8}{11 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,"-1/11*b^8/x^11 - (4*a*b^7)/(5*x^10) - (28*a^2*b^6)/(9*x^9) - (7*a^3*b^5)/x^8 - (10*a^4*b^4)/x^7 - (28*a^5*b^3)/(3*x^6) - (28*a^6*b^2)/(5*x^5) - (2*a^7*b)/x^4 - a^8/(3*x^3)","A",1
1603,1,106,76,0.0046311,"\int \frac{\left(a+\frac{b}{x}\right)^8}{x^5} \, dx","Integrate[(a + b/x)^8/x^5,x]","-\frac{a^8}{4 x^4}-\frac{8 a^7 b}{5 x^5}-\frac{14 a^6 b^2}{3 x^6}-\frac{8 a^5 b^3}{x^7}-\frac{35 a^4 b^4}{4 x^8}-\frac{56 a^3 b^5}{9 x^9}-\frac{14 a^2 b^6}{5 x^{10}}-\frac{8 a b^7}{11 x^{11}}-\frac{b^8}{12 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,"-1/12*b^8/x^12 - (8*a*b^7)/(11*x^11) - (14*a^2*b^6)/(5*x^10) - (56*a^3*b^5)/(9*x^9) - (35*a^4*b^4)/(4*x^8) - (8*a^5*b^3)/x^7 - (14*a^6*b^2)/(3*x^6) - (8*a^7*b)/(5*x^5) - a^8/(4*x^4)","A",1
1604,1,104,96,0.024415,"\int \frac{\left(a+\frac{b}{x}\right)^8}{x^6} \, dx","Integrate[(a + b/x)^8/x^6,x]","-\frac{a^8}{5 x^5}-\frac{4 a^7 b}{3 x^6}-\frac{4 a^6 b^2}{x^7}-\frac{7 a^5 b^3}{x^8}-\frac{70 a^4 b^4}{9 x^9}-\frac{28 a^3 b^5}{5 x^{10}}-\frac{28 a^2 b^6}{11 x^{11}}-\frac{2 a b^7}{3 x^{12}}-\frac{b^8}{13 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,"-1/13*b^8/x^13 - (2*a*b^7)/(3*x^12) - (28*a^2*b^6)/(11*x^11) - (28*a^3*b^5)/(5*x^10) - (70*a^4*b^4)/(9*x^9) - (7*a^5*b^3)/x^8 - (4*a^6*b^2)/x^7 - (4*a^7*b)/(3*x^6) - a^8/(5*x^5)","A",1
1605,1,106,106,0.0128692,"\int \frac{\left(a+\frac{b}{x}\right)^8}{x^7} \, dx","Integrate[(a + b/x)^8/x^7,x]","-\frac{a^8}{6 x^6}-\frac{8 a^7 b}{7 x^7}-\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 b^7}{13 x^{13}}-\frac{b^8}{14 x^{14}}","-\frac{a^8}{6 x^6}-\frac{8 a^7 b}{7 x^7}-\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 b^7}{13 x^{13}}-\frac{b^8}{14 x^{14}}",1,"-1/14*b^8/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",1
1606,1,106,106,0.0122884,"\int \frac{\left(a+\frac{b}{x}\right)^8}{x^8} \, dx","Integrate[(a + b/x)^8/x^8,x]","-\frac{a^8}{7 x^7}-\frac{a^7 b}{x^8}-\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{4 a b^7}{7 x^{14}}-\frac{b^8}{15 x^{15}}","-\frac{a^8}{7 x^7}-\frac{a^7 b}{x^8}-\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{4 a b^7}{7 x^{14}}-\frac{b^8}{15 x^{15}}",1,"-1/15*b^8/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",1
1607,1,70,70,0.0053179,"\int \frac{x^4}{a+\frac{b}{x}} \, dx","Integrate[x^4/(a + b/x),x]","-\frac{b^5 \log (a x+b)}{a^6}+\frac{b^4 x}{a^5}-\frac{b^3 x^2}{2 a^4}+\frac{b^2 x^3}{3 a^3}-\frac{b x^4}{4 a^2}+\frac{x^5}{5 a}","-\frac{b^5 \log (a x+b)}{a^6}+\frac{b^4 x}{a^5}-\frac{b^3 x^2}{2 a^4}+\frac{b^2 x^3}{3 a^3}-\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",1
1608,1,57,57,0.0052924,"\int \frac{x^3}{a+\frac{b}{x}} \, dx","Integrate[x^3/(a + b/x),x]","\frac{b^4 \log (a x+b)}{a^5}-\frac{b^3 x}{a^4}+\frac{b^2 x^2}{2 a^3}-\frac{b x^3}{3 a^2}+\frac{x^4}{4 a}","\frac{b^4 \log (a x+b)}{a^5}-\frac{b^3 x}{a^4}+\frac{b^2 x^2}{2 a^3}-\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",1
1609,1,44,44,0.0045295,"\int \frac{x^2}{a+\frac{b}{x}} \, dx","Integrate[x^2/(a + b/x),x]","-\frac{b^3 \log (a x+b)}{a^4}+\frac{b^2 x}{a^3}-\frac{b x^2}{2 a^2}+\frac{x^3}{3 a}","-\frac{b^3 \log (a x+b)}{a^4}+\frac{b^2 x}{a^3}-\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",1
1610,1,31,31,0.0036358,"\int \frac{x}{a+\frac{b}{x}} \, dx","Integrate[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",1
1611,1,18,18,0.0030329,"\int \frac{1}{a+\frac{b}{x}} \, dx","Integrate[(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",1
1612,1,10,10,0.0011837,"\int \frac{1}{\left(a+\frac{b}{x}\right) x} \, dx","Integrate[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",1
1613,1,18,13,0.0039047,"\int \frac{1}{\left(a+\frac{b}{x}\right) x^2} \, dx","Integrate[1/((a + b/x)*x^2),x]","\frac{\log (x)}{b}-\frac{\log (a x+b)}{b}","-\frac{\log \left(a+\frac{b}{x}\right)}{b}",1,"Log[x]/b - Log[b + a*x]/b","A",1
1614,1,28,28,0.0057019,"\int \frac{1}{\left(a+\frac{b}{x}\right) x^3} \, dx","Integrate[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",1
1615,1,42,42,0.0048652,"\int \frac{1}{\left(a+\frac{b}{x}\right) x^4} \, dx","Integrate[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*1/(b*x^2) + a/(b^2*x) + (a^2*Log[x])/b^3 - (a^2*Log[b + a*x])/b^3","A",1
1616,1,56,56,0.0060253,"\int \frac{1}{\left(a+\frac{b}{x}\right) x^5} \, dx","Integrate[1/((a + b/x)*x^5),x]","-\frac{a^3 \log (x)}{b^4}+\frac{a^3 \log (a x+b)}{b^4}-\frac{a^2}{b^3 x}+\frac{a}{2 b^2 x^2}-\frac{1}{3 b x^3}","-\frac{a^3 \log (x)}{b^4}+\frac{a^3 \log (a x+b)}{b^4}-\frac{a^2}{b^3 x}+\frac{a}{2 b^2 x^2}-\frac{1}{3 b x^3}",1,"-1/3*1/(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",1
1617,1,68,68,0.0059841,"\int \frac{1}{\left(a+\frac{b}{x}\right) x^6} \, dx","Integrate[1/((a + b/x)*x^6),x]","\frac{a^4 \log (x)}{b^5}-\frac{a^4 \log (a x+b)}{b^5}+\frac{a^3}{b^4 x}-\frac{a^2}{2 b^3 x^2}+\frac{a}{3 b^2 x^3}-\frac{1}{4 b x^4}","\frac{a^4 \log (x)}{b^5}-\frac{a^4 \log (a x+b)}{b^5}+\frac{a^3}{b^4 x}-\frac{a^2}{2 b^3 x^2}+\frac{a}{3 b^2 x^3}-\frac{1}{4 b x^4}",1,"-1/4*1/(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",1
1618,1,82,82,0.007544,"\int \frac{1}{\left(a+\frac{b}{x}\right) x^7} \, dx","Integrate[1/((a + b/x)*x^7),x]","-\frac{a^5 \log (x)}{b^6}+\frac{a^5 \log (a x+b)}{b^6}-\frac{a^4}{b^5 x}+\frac{a^3}{2 b^4 x^2}-\frac{a^2}{3 b^3 x^3}+\frac{a}{4 b^2 x^4}-\frac{1}{5 b x^5}","-\frac{a^5 \log (x)}{b^6}+\frac{a^5 \log (a x+b)}{b^6}-\frac{a^4}{b^5 x}+\frac{a^3}{2 b^4 x^2}-\frac{a^2}{3 b^3 x^3}+\frac{a}{4 b^2 x^4}-\frac{1}{5 b x^5}",1,"-1/5*1/(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",1
1619,1,88,98,0.0228924,"\int \frac{x^5}{\left(a+\frac{b}{x}\right)^2} \, dx","Integrate[x^5/(a + b/x)^2,x]","\frac{10 a^6 x^6-24 a^5 b x^5+45 a^4 b^2 x^4-80 a^3 b^3 x^3+150 a^2 b^4 x^2+\frac{60 b^7}{a x+b}+420 b^6 \log (a x+b)-360 a b^5 x}{60 a^8}","\frac{b^7}{a^8 (a x+b)}+\frac{7 b^6 \log (a x+b)}{a^8}-\frac{6 b^5 x}{a^7}+\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{2 b x^5}{5 a^3}+\frac{x^6}{6 a^2}",1,"(-360*a*b^5*x + 150*a^2*b^4*x^2 - 80*a^3*b^3*x^3 + 45*a^4*b^2*x^4 - 24*a^5*b*x^5 + 10*a^6*x^6 + (60*b^7)/(b + a*x) + 420*b^6*Log[b + a*x])/(60*a^8)","A",1
1620,1,77,81,0.025346,"\int \frac{x^4}{\left(a+\frac{b}{x}\right)^2} \, dx","Integrate[x^4/(a + b/x)^2,x]","\frac{2 a^5 x^5-5 a^4 b x^4+10 a^3 b^2 x^3-20 a^2 b^3 x^2-\frac{10 b^6}{a x+b}-60 b^5 \log (a x+b)+50 a b^4 x}{10 a^7}","-\frac{b^6}{a^7 (a x+b)}-\frac{6 b^5 \log (a x+b)}{a^7}+\frac{5 b^4 x}{a^6}-\frac{2 b^3 x^2}{a^5}+\frac{b^2 x^3}{a^4}-\frac{b x^4}{2 a^3}+\frac{x^5}{5 a^2}",1,"(50*a*b^4*x - 20*a^2*b^3*x^2 + 10*a^3*b^2*x^3 - 5*a^4*b*x^4 + 2*a^5*x^5 - (10*b^6)/(b + a*x) - 60*b^5*Log[b + a*x])/(10*a^7)","A",1
1621,1,66,72,0.0175282,"\int \frac{x^3}{\left(a+\frac{b}{x}\right)^2} \, dx","Integrate[x^3/(a + b/x)^2,x]","\frac{3 a^4 x^4-8 a^3 b x^3+18 a^2 b^2 x^2+\frac{12 b^5}{a x+b}+60 b^4 \log (a x+b)-48 a b^3 x}{12 a^6}","\frac{b^5}{a^6 (a x+b)}+\frac{5 b^4 \log (a x+b)}{a^6}-\frac{4 b^3 x}{a^5}+\frac{3 b^2 x^2}{2 a^4}-\frac{2 b x^3}{3 a^3}+\frac{x^4}{4 a^2}",1,"(-48*a*b^3*x + 18*a^2*b^2*x^2 - 8*a^3*b*x^3 + 3*a^4*x^4 + (12*b^5)/(b + a*x) + 60*b^4*Log[b + a*x])/(12*a^6)","A",1
1622,1,54,58,0.0268492,"\int \frac{x^2}{\left(a+\frac{b}{x}\right)^2} \, dx","Integrate[x^2/(a + b/x)^2,x]","\frac{a^3 x^3-3 a^2 b x^2-\frac{3 b^4}{a x+b}-12 b^3 \log (a x+b)+9 a b^2 x}{3 a^5}","-\frac{b^4}{a^5 (a x+b)}-\frac{4 b^3 \log (a x+b)}{a^5}+\frac{3 b^2 x}{a^4}-\frac{b x^2}{a^3}+\frac{x^3}{3 a^2}",1,"(9*a*b^2*x - 3*a^2*b*x^2 + a^3*x^3 - (3*b^4)/(b + a*x) - 12*b^3*Log[b + a*x])/(3*a^5)","A",1
1623,1,43,46,0.0149683,"\int \frac{x}{\left(a+\frac{b}{x}\right)^2} \, dx","Integrate[x/(a + b/x)^2,x]","\frac{a^2 x^2+\frac{2 b^3}{a x+b}+6 b^2 \log (a x+b)-4 a b x}{2 a^4}","\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,"(-4*a*b*x + a^2*x^2 + (2*b^3)/(b + a*x) + 6*b^2*Log[b + a*x])/(2*a^4)","A",1
1624,1,29,34,0.0117445,"\int \frac{1}{\left(a+\frac{b}{x}\right)^2} \, dx","Integrate[(a + b/x)^(-2),x]","\frac{-\frac{b^2}{a x+b}-2 b \log (a x+b)+a x}{a^3}","-\frac{2 b \log (a x+b)}{a^3}+\frac{2 x}{a^2}-\frac{x}{a \left(a+\frac{b}{x}\right)}",1,"(a*x - b^2/(b + a*x) - 2*b*Log[b + a*x])/a^3","A",1
1625,1,20,23,0.0071588,"\int \frac{1}{\left(a+\frac{b}{x}\right)^2 x} \, dx","Integrate[1/((a + b/x)^2*x),x]","\frac{\frac{b}{a x+b}+\log (a x+b)}{a^2}","\frac{b}{a^2 (a x+b)}+\frac{\log (a x+b)}{a^2}",1,"(b/(b + a*x) + Log[b + a*x])/a^2","A",1
1626,1,12,13,0.0032057,"\int \frac{1}{\left(a+\frac{b}{x}\right)^2 x^2} \, dx","Integrate[1/((a + b/x)^2*x^2),x]","-\frac{1}{a (a x+b)}","\frac{1}{b \left(a+\frac{b}{x}\right)}",1,"-(1/(a*(b + a*x)))","A",1
1627,1,24,29,0.0126127,"\int \frac{1}{\left(a+\frac{b}{x}\right)^2 x^3} \, dx","Integrate[1/((a + b/x)^2*x^3),x]","\frac{\frac{b}{a x+b}-\log (a x+b)+\log (x)}{b^2}","-\frac{\log (a x+b)}{b^2}+\frac{1}{b (a x+b)}+\frac{\log (x)}{b^2}",1,"(b/(b + a*x) + Log[x] - Log[b + a*x])/b^2","A",1
1628,1,35,42,0.0409883,"\int \frac{1}{\left(a+\frac{b}{x}\right)^2 x^4} \, dx","Integrate[1/((a + b/x)^2*x^4),x]","-\frac{b \left(\frac{a}{a x+b}+\frac{1}{x}\right)-2 a \log (a x+b)+2 a \log (x)}{b^3}","-\frac{2 a \log (x)}{b^3}+\frac{2 a \log (a x+b)}{b^3}-\frac{a}{b^2 (a x+b)}-\frac{1}{b^2 x}",1,"-((b*(x^(-1) + a/(b + a*x)) + 2*a*Log[x] - 2*a*Log[b + a*x])/b^3)","A",1
1629,1,53,58,0.0554169,"\int \frac{1}{\left(a+\frac{b}{x}\right)^2 x^5} \, dx","Integrate[1/((a + b/x)^2*x^5),x]","\frac{b \left(\frac{2 a^2}{a x+b}+\frac{4 a}{x}-\frac{b}{x^2}\right)-6 a^2 \log (a x+b)+6 a^2 \log (x)}{2 b^4}","\frac{3 a^2 \log (x)}{b^4}-\frac{3 a^2 \log (a x+b)}{b^4}+\frac{a^2}{b^3 (a x+b)}+\frac{2 a}{b^3 x}-\frac{1}{2 b^2 x^2}",1,"(b*(-(b/x^2) + (4*a)/x + (2*a^2)/(b + a*x)) + 6*a^2*Log[x] - 6*a^2*Log[b + a*x])/(2*b^4)","A",1
1630,1,66,69,0.0616893,"\int \frac{1}{\left(a+\frac{b}{x}\right)^2 x^6} \, dx","Integrate[1/((a + b/x)^2*x^6),x]","-\frac{-12 a^3 \log (a x+b)+12 a^3 \log (x)+\frac{b \left(12 a^3 x^3+6 a^2 b x^2-2 a b^2 x+b^3\right)}{x^3 (a x+b)}}{3 b^5}","-\frac{4 a^3 \log (x)}{b^5}+\frac{4 a^3 \log (a x+b)}{b^5}-\frac{a^3}{b^4 (a x+b)}-\frac{3 a^2}{b^4 x}+\frac{a}{b^3 x^2}-\frac{1}{3 b^2 x^3}",1,"-1/3*((b*(b^3 - 2*a*b^2*x + 6*a^2*b*x^2 + 12*a^3*x^3))/(x^3*(b + a*x)) + 12*a^3*Log[x] - 12*a^3*Log[b + a*x])/b^5","A",1
1631,1,79,84,0.044963,"\int \frac{1}{\left(a+\frac{b}{x}\right)^2 x^7} \, dx","Integrate[1/((a + b/x)^2*x^7),x]","\frac{-60 a^4 \log (a x+b)+60 a^4 \log (x)+\frac{b \left(60 a^4 x^4+30 a^3 b x^3-10 a^2 b^2 x^2+5 a b^3 x-3 b^4\right)}{x^4 (a x+b)}}{12 b^6}","\frac{5 a^4 \log (x)}{b^6}-\frac{5 a^4 \log (a x+b)}{b^6}+\frac{a^4}{b^5 (a x+b)}+\frac{4 a^3}{b^5 x}-\frac{3 a^2}{2 b^4 x^2}+\frac{2 a}{3 b^3 x^3}-\frac{1}{4 b^2 x^4}",1,"((b*(-3*b^4 + 5*a*b^3*x - 10*a^2*b^2*x^2 + 30*a^3*b*x^3 + 60*a^4*x^4))/(x^4*(b + a*x)) + 60*a^4*Log[x] - 60*a^4*Log[b + a*x])/(12*b^6)","A",1
1632,1,90,94,0.0737797,"\int \frac{1}{\left(a+\frac{b}{x}\right)^2 x^8} \, dx","Integrate[1/((a + b/x)^2*x^8),x]","-\frac{-60 a^5 \log (a x+b)+60 a^5 \log (x)+\frac{b \left(60 a^5 x^5+30 a^4 b x^4-10 a^3 b^2 x^3+5 a^2 b^3 x^2-3 a b^4 x+2 b^5\right)}{x^5 (a x+b)}}{10 b^7}","-\frac{6 a^5 \log (x)}{b^7}+\frac{6 a^5 \log (a x+b)}{b^7}-\frac{a^5}{b^6 (a x+b)}-\frac{5 a^4}{b^6 x}+\frac{2 a^3}{b^5 x^2}-\frac{a^2}{b^4 x^3}+\frac{a}{2 b^3 x^4}-\frac{1}{5 b^2 x^5}",1,"-1/10*((b*(2*b^5 - 3*a*b^4*x + 5*a^2*b^3*x^2 - 10*a^3*b^2*x^3 + 30*a^4*b*x^4 + 60*a^5*x^5))/(x^5*(b + a*x)) + 60*a^5*Log[x] - 60*a^5*Log[b + a*x])/b^7","A",1
1633,1,85,99,0.0604949,"\int \frac{x^4}{\left(a+\frac{b}{x}\right)^3} \, dx","Integrate[x^4/(a + b/x)^3,x]","\frac{4 a^5 x^5-15 a^4 b x^4+40 a^3 b^2 x^3-100 a^2 b^3 x^2-\frac{10 b^6 (14 a x+13 b)}{(a x+b)^2}-420 b^5 \log (a x+b)+300 a b^4 x}{20 a^8}","\frac{b^7}{2 a^8 (a x+b)^2}-\frac{7 b^6}{a^8 (a x+b)}-\frac{21 b^5 \log (a x+b)}{a^8}+\frac{15 b^4 x}{a^7}-\frac{5 b^3 x^2}{a^6}+\frac{2 b^2 x^3}{a^5}-\frac{3 b x^4}{4 a^4}+\frac{x^5}{5 a^3}",1,"(300*a*b^4*x - 100*a^2*b^3*x^2 + 40*a^3*b^2*x^3 - 15*a^4*b*x^4 + 4*a^5*x^5 - (10*b^6*(13*b + 14*a*x))/(b + a*x)^2 - 420*b^5*Log[b + a*x])/(20*a^8)","A",1
1634,1,73,86,0.0579109,"\int \frac{x^3}{\left(a+\frac{b}{x}\right)^3} \, dx","Integrate[x^3/(a + b/x)^3,x]","\frac{a^4 x^4-4 a^3 b x^3+12 a^2 b^2 x^2+\frac{2 b^5 (12 a x+11 b)}{(a x+b)^2}+60 b^4 \log (a x+b)-40 a b^3 x}{4 a^7}","-\frac{b^6}{2 a^7 (a x+b)^2}+\frac{6 b^5}{a^7 (a x+b)}+\frac{15 b^4 \log (a x+b)}{a^7}-\frac{10 b^3 x}{a^6}+\frac{3 b^2 x^2}{a^5}-\frac{b x^3}{a^4}+\frac{x^4}{4 a^3}",1,"(-40*a*b^3*x + 12*a^2*b^2*x^2 - 4*a^3*b*x^3 + a^4*x^4 + (2*b^5*(11*b + 12*a*x))/(b + a*x)^2 + 60*b^4*Log[b + a*x])/(4*a^7)","A",1
1635,1,63,77,0.0631643,"\int \frac{x^2}{\left(a+\frac{b}{x}\right)^3} \, dx","Integrate[x^2/(a + b/x)^3,x]","\frac{2 a^3 x^3-9 a^2 b x^2-\frac{3 b^4 (10 a x+9 b)}{(a x+b)^2}-60 b^3 \log (a x+b)+36 a b^2 x}{6 a^6}","\frac{b^5}{2 a^6 (a x+b)^2}-\frac{5 b^4}{a^6 (a x+b)}-\frac{10 b^3 \log (a x+b)}{a^6}+\frac{6 b^2 x}{a^5}-\frac{3 b x^2}{2 a^4}+\frac{x^3}{3 a^3}",1,"(36*a*b^2*x - 9*a^2*b*x^2 + 2*a^3*x^3 - (3*b^4*(9*b + 10*a*x))/(b + a*x)^2 - 60*b^3*Log[b + a*x])/(6*a^6)","A",1
1636,1,50,64,0.0361915,"\int \frac{x}{\left(a+\frac{b}{x}\right)^3} \, dx","Integrate[x/(a + b/x)^3,x]","\frac{a^2 x^2+\frac{b^3 (8 a x+7 b)}{(a x+b)^2}+12 b^2 \log (a x+b)-6 a b x}{2 a^5}","-\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,"(-6*a*b*x + a^2*x^2 + (b^3*(7*b + 8*a*x))/(b + a*x)^2 + 12*b^2*Log[b + a*x])/(2*a^5)","A",1
1637,1,40,53,0.0419758,"\int \frac{1}{\left(a+\frac{b}{x}\right)^3} \, dx","Integrate[(a + b/x)^(-3),x]","-\frac{\frac{b^2 (6 a x+5 b)}{(a x+b)^2}+6 b \log (a x+b)-2 a x}{2 a^4}","-\frac{3 b \log (a x+b)}{a^4}+\frac{3 x}{a^3}-\frac{3 x}{2 a^2 \left(a+\frac{b}{x}\right)}-\frac{x}{2 a \left(a+\frac{b}{x}\right)^2}",1,"-1/2*(-2*a*x + (b^2*(5*b + 6*a*x))/(b + a*x)^2 + 6*b*Log[b + a*x])/a^4","A",1
1638,1,33,41,0.0138405,"\int \frac{1}{\left(a+\frac{b}{x}\right)^3 x} \, dx","Integrate[1/((a + b/x)^3*x),x]","\frac{\frac{b (4 a x+3 b)}{(a x+b)^2}+2 \log (a x+b)}{2 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*(3*b + 4*a*x))/(b + a*x)^2 + 2*Log[b + a*x])/(2*a^3)","A",1
1639,1,20,16,0.0055,"\int \frac{1}{\left(a+\frac{b}{x}\right)^3 x^2} \, dx","Integrate[1/((a + b/x)^3*x^2),x]","-\frac{2 a x+b}{2 a^2 (a x+b)^2}","\frac{1}{2 b \left(a+\frac{b}{x}\right)^2}",1,"-1/2*(b + 2*a*x)/(a^2*(b + a*x)^2)","A",1
1640,1,14,14,0.0030823,"\int \frac{1}{\left(a+\frac{b}{x}\right)^3 x^3} \, dx","Integrate[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*1/(a*(b + a*x)^2)","A",1
1641,1,37,43,0.0328193,"\int \frac{1}{\left(a+\frac{b}{x}\right)^3 x^4} \, dx","Integrate[1/((a + b/x)^3*x^4),x]","\frac{\frac{b (2 a x+3 b)}{(a x+b)^2}-2 \log (a x+b)+2 \log (x)}{2 b^3}","-\frac{\log (a x+b)}{b^3}+\frac{1}{b^2 (a x+b)}+\frac{1}{2 b (a x+b)^2}+\frac{\log (x)}{b^3}",1,"((b*(3*b + 2*a*x))/(b + a*x)^2 + 2*Log[x] - 2*Log[b + a*x])/(2*b^3)","A",1
1642,1,53,57,0.0529947,"\int \frac{1}{\left(a+\frac{b}{x}\right)^3 x^5} \, dx","Integrate[1/((a + b/x)^3*x^5),x]","-\frac{\frac{b \left(6 a^2 x^2+9 a b x+2 b^2\right)}{x (a x+b)^2}-6 a \log (a x+b)+6 a \log (x)}{2 b^4}","-\frac{3 a \log (x)}{b^4}+\frac{3 a \log (a x+b)}{b^4}-\frac{2 a}{b^3 (a x+b)}-\frac{a}{2 b^2 (a x+b)^2}-\frac{1}{b^3 x}",1,"-1/2*((b*(2*b^2 + 9*a*b*x + 6*a^2*x^2))/(x*(b + a*x)^2) + 6*a*Log[x] - 6*a*Log[b + a*x])/b^4","A",1
1643,1,68,76,0.0521925,"\int \frac{1}{\left(a+\frac{b}{x}\right)^3 x^6} \, dx","Integrate[1/((a + b/x)^3*x^6),x]","\frac{-12 a^2 \log (a x+b)+12 a^2 \log (x)+\frac{b \left(12 a^3 x^3+18 a^2 b x^2+4 a b^2 x-b^3\right)}{x^2 (a x+b)^2}}{2 b^5}","\frac{6 a^2 \log (x)}{b^5}-\frac{6 a^2 \log (a x+b)}{b^5}+\frac{3 a^2}{b^4 (a x+b)}+\frac{a^2}{2 b^3 (a x+b)^2}+\frac{3 a}{b^4 x}-\frac{1}{2 b^3 x^2}",1,"((b*(-b^3 + 4*a*b^2*x + 18*a^2*b*x^2 + 12*a^3*x^3))/(x^2*(b + a*x)^2) + 12*a^2*Log[x] - 12*a^2*Log[b + a*x])/(2*b^5)","A",1
1644,1,79,89,0.0781953,"\int \frac{1}{\left(a+\frac{b}{x}\right)^3 x^7} \, dx","Integrate[1/((a + b/x)^3*x^7),x]","-\frac{-60 a^3 \log (a x+b)+60 a^3 \log (x)+\frac{b \left(60 a^4 x^4+90 a^3 b x^3+20 a^2 b^2 x^2-5 a b^3 x+2 b^4\right)}{x^3 (a x+b)^2}}{6 b^6}","-\frac{10 a^3 \log (x)}{b^6}+\frac{10 a^3 \log (a x+b)}{b^6}-\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{3 a}{2 b^4 x^2}-\frac{1}{3 b^3 x^3}",1,"-1/6*((b*(2*b^4 - 5*a*b^3*x + 20*a^2*b^2*x^2 + 90*a^3*b*x^3 + 60*a^4*x^4))/(x^3*(b + a*x)^2) + 60*a^3*Log[x] - 60*a^3*Log[b + a*x])/b^6","A",1
1645,1,90,97,0.058444,"\int \frac{1}{\left(a+\frac{b}{x}\right)^3 x^8} \, dx","Integrate[1/((a + b/x)^3*x^8),x]","\frac{-60 a^4 \log (a x+b)+60 a^4 \log (x)+\frac{b \left(60 a^5 x^5+90 a^4 b x^4+20 a^3 b^2 x^3-5 a^2 b^3 x^2+2 a b^4 x-b^5\right)}{x^4 (a x+b)^2}}{4 b^7}","\frac{15 a^4 \log (x)}{b^7}-\frac{15 a^4 \log (a x+b)}{b^7}+\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{3 a^2}{b^5 x^2}+\frac{a}{b^4 x^3}-\frac{1}{4 b^3 x^4}",1,"((b*(-b^5 + 2*a*b^4*x - 5*a^2*b^3*x^2 + 20*a^3*b^2*x^3 + 90*a^4*b*x^4 + 60*a^5*x^5))/(x^4*(b + a*x)^2) + 60*a^4*Log[x] - 60*a^4*Log[b + a*x])/(4*b^7)","A",1
1646,1,101,111,0.09525,"\int \frac{1}{\left(a+\frac{b}{x}\right)^3 x^9} \, dx","Integrate[1/((a + b/x)^3*x^9),x]","-\frac{-420 a^5 \log (a x+b)+420 a^5 \log (x)+\frac{b \left(420 a^6 x^6+630 a^5 b x^5+140 a^4 b^2 x^4-35 a^3 b^3 x^3+14 a^2 b^4 x^2-7 a b^5 x+4 b^6\right)}{x^5 (a x+b)^2}}{20 b^8}","-\frac{21 a^5 \log (x)}{b^8}+\frac{21 a^5 \log (a x+b)}{b^8}-\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{5 a^3}{b^6 x^2}-\frac{2 a^2}{b^5 x^3}+\frac{3 a}{4 b^4 x^4}-\frac{1}{5 b^3 x^5}",1,"-1/20*((b*(4*b^6 - 7*a*b^5*x + 14*a^2*b^4*x^2 - 35*a^3*b^3*x^3 + 140*a^4*b^2*x^4 + 630*a^5*b*x^5 + 420*a^6*x^6))/(x^5*(b + a*x)^2) + 420*a^5*Log[x] - 420*a^5*Log[b + a*x])/b^8","A",1
1647,1,17,21,0.0048699,"\int \left(a+\frac{b}{x}\right) x^{5/2} \, dx","Integrate[(a + b/x)*x^(5/2),x]","\frac{2}{35} x^{5/2} (5 a x+7 b)","\frac{2}{7} a x^{7/2}+\frac{2}{5} b x^{5/2}",1,"(2*x^(5/2)*(7*b + 5*a*x))/35","A",1
1648,1,17,21,0.0059509,"\int \left(a+\frac{b}{x}\right) x^{3/2} \, dx","Integrate[(a + b/x)*x^(3/2),x]","\frac{2}{15} x^{3/2} (3 a x+5 b)","\frac{2}{5} a x^{5/2}+\frac{2}{3} b x^{3/2}",1,"(2*x^(3/2)*(5*b + 3*a*x))/15","A",1
1649,1,16,19,0.0048818,"\int \left(a+\frac{b}{x}\right) \sqrt{x} \, dx","Integrate[(a + b/x)*Sqrt[x],x]","\frac{2}{3} \sqrt{x} (a x+3 b)","\frac{2}{3} a x^{3/2}+2 b \sqrt{x}",1,"(2*Sqrt[x]*(3*b + a*x))/3","A",1
1650,1,14,17,0.0050355,"\int \frac{a+\frac{b}{x}}{\sqrt{x}} \, dx","Integrate[(a + b/x)/Sqrt[x],x]","\frac{2 (a x-b)}{\sqrt{x}}","2 a \sqrt{x}-\frac{2 b}{\sqrt{x}}",1,"(2*(-b + a*x))/Sqrt[x]","A",1
1651,1,15,19,0.0054693,"\int \frac{a+\frac{b}{x}}{x^{3/2}} \, dx","Integrate[(a + b/x)/x^(3/2),x]","-\frac{2 (3 a x+b)}{3 x^{3/2}}","-\frac{2 a}{\sqrt{x}}-\frac{2 b}{3 x^{3/2}}",1,"(-2*(b + 3*a*x))/(3*x^(3/2))","A",1
1652,1,17,21,0.0053709,"\int \frac{a+\frac{b}{x}}{x^{5/2}} \, dx","Integrate[(a + b/x)/x^(5/2),x]","-\frac{2 (5 a x+3 b)}{15 x^{5/2}}","-\frac{2 a}{3 x^{3/2}}-\frac{2 b}{5 x^{5/2}}",1,"(-2*(3*b + 5*a*x))/(15*x^(5/2))","A",1
1653,1,28,36,0.0082123,"\int \left(a+\frac{b}{x}\right)^2 x^{5/2} \, dx","Integrate[(a + b/x)^2*x^(5/2),x]","\frac{2}{105} x^{3/2} \left(15 a^2 x^2+42 a b x+35 b^2\right)","\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*x^(3/2)*(35*b^2 + 42*a*b*x + 15*a^2*x^2))/105","A",1
1654,1,28,34,0.008434,"\int \left(a+\frac{b}{x}\right)^2 x^{3/2} \, dx","Integrate[(a + b/x)^2*x^(3/2),x]","\frac{2}{15} \sqrt{x} \left(3 a^2 x^2+10 a b x+15 b^2\right)","\frac{2}{5} a^2 x^{5/2}+\frac{4}{3} a b x^{3/2}+2 b^2 \sqrt{x}",1,"(2*Sqrt[x]*(15*b^2 + 10*a*b*x + 3*a^2*x^2))/15","A",1
1655,1,27,32,0.0090253,"\int \left(a+\frac{b}{x}\right)^2 \sqrt{x} \, dx","Integrate[(a + b/x)^2*Sqrt[x],x]","\frac{2 \left(a^2 x^2+6 a b x-3 b^2\right)}{3 \sqrt{x}}","\frac{2}{3} a^2 x^{3/2}+4 a b \sqrt{x}-\frac{2 b^2}{\sqrt{x}}",1,"(2*(-3*b^2 + 6*a*b*x + a^2*x^2))/(3*Sqrt[x])","A",1
1656,1,26,32,0.0086799,"\int \frac{\left(a+\frac{b}{x}\right)^2}{\sqrt{x}} \, dx","Integrate[(a + b/x)^2/Sqrt[x],x]","-\frac{2 \left(-3 a^2 x^2+6 a b x+b^2\right)}{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 + 6*a*b*x - 3*a^2*x^2))/(3*x^(3/2))","A",1
1657,1,28,34,0.0082288,"\int \frac{\left(a+\frac{b}{x}\right)^2}{x^{3/2}} \, dx","Integrate[(a + b/x)^2/x^(3/2),x]","-\frac{2 \left(15 a^2 x^2+10 a b x+3 b^2\right)}{15 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*(3*b^2 + 10*a*b*x + 15*a^2*x^2))/(15*x^(5/2))","A",1
1658,1,28,36,0.0092617,"\int \frac{\left(a+\frac{b}{x}\right)^2}{x^{5/2}} \, dx","Integrate[(a + b/x)^2/x^(5/2),x]","-\frac{2 \left(35 a^2 x^2+42 a b x+15 b^2\right)}{105 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*(15*b^2 + 42*a*b*x + 35*a^2*x^2))/(105*x^(7/2))","A",1
1659,1,39,47,0.0108904,"\int \left(a+\frac{b}{x}\right)^3 x^{5/2} \, dx","Integrate[(a + b/x)^3*x^(5/2),x]","\frac{2}{35} \sqrt{x} \left(5 a^3 x^3+21 a^2 b x^2+35 a b^2 x+35 b^3\right)","\frac{2}{7} a^3 x^{7/2}+\frac{6}{5} a^2 b x^{5/2}+2 a b^2 x^{3/2}+2 b^3 \sqrt{x}",1,"(2*Sqrt[x]*(35*b^3 + 35*a*b^2*x + 21*a^2*b*x^2 + 5*a^3*x^3))/35","A",1
1660,1,38,45,0.0202635,"\int \left(a+\frac{b}{x}\right)^3 x^{3/2} \, dx","Integrate[(a + b/x)^3*x^(3/2),x]","\frac{2 \left(a^3 x^3+5 a^2 b x^2+15 a b^2 x-5 b^3\right)}{5 \sqrt{x}}","\frac{2}{5} a^3 x^{5/2}+2 a^2 b x^{3/2}+6 a b^2 \sqrt{x}-\frac{2 b^3}{\sqrt{x}}",1,"(2*(-5*b^3 + 15*a*b^2*x + 5*a^2*b*x^2 + a^3*x^3))/(5*Sqrt[x])","A",1
1661,1,38,47,0.011331,"\int \left(a+\frac{b}{x}\right)^3 \sqrt{x} \, dx","Integrate[(a + b/x)^3*Sqrt[x],x]","\frac{2 \left(a^3 x^3+9 a^2 b x^2-9 a b^2 x-b^3\right)}{3 x^{3/2}}","\frac{2}{3} a^3 x^{3/2}+6 a^2 b \sqrt{x}-\frac{6 a b^2}{\sqrt{x}}-\frac{2 b^3}{3 x^{3/2}}",1,"(2*(-b^3 - 9*a*b^2*x + 9*a^2*b*x^2 + a^3*x^3))/(3*x^(3/2))","A",1
1662,1,39,45,0.0106773,"\int \frac{\left(a+\frac{b}{x}\right)^3}{\sqrt{x}} \, dx","Integrate[(a + b/x)^3/Sqrt[x],x]","\frac{2 \left(5 a^3 x^3-15 a^2 b x^2-5 a b^2 x-b^3\right)}{5 x^{5/2}}","2 a^3 \sqrt{x}-\frac{6 a^2 b}{\sqrt{x}}-\frac{2 a b^2}{x^{3/2}}-\frac{2 b^3}{5 x^{5/2}}",1,"(2*(-b^3 - 5*a*b^2*x - 15*a^2*b*x^2 + 5*a^3*x^3))/(5*x^(5/2))","A",1
1663,1,39,47,0.0209854,"\int \frac{\left(a+\frac{b}{x}\right)^3}{x^{3/2}} \, dx","Integrate[(a + b/x)^3/x^(3/2),x]","-\frac{2 \left(35 a^3 x^3+35 a^2 b x^2+21 a b^2 x+5 b^3\right)}{35 x^{7/2}}","-\frac{2 a^3}{\sqrt{x}}-\frac{2 a^2 b}{x^{3/2}}-\frac{6 a b^2}{5 x^{5/2}}-\frac{2 b^3}{7 x^{7/2}}",1,"(-2*(5*b^3 + 21*a*b^2*x + 35*a^2*b*x^2 + 35*a^3*x^3))/(35*x^(7/2))","A",1
1664,1,39,51,0.0119149,"\int \frac{\left(a+\frac{b}{x}\right)^3}{x^{5/2}} \, dx","Integrate[(a + b/x)^3/x^(5/2),x]","-\frac{2 \left(105 a^3 x^3+189 a^2 b x^2+135 a b^2 x+35 b^3\right)}{315 x^{9/2}}","-\frac{2 a^3}{3 x^{3/2}}-\frac{6 a^2 b}{5 x^{5/2}}-\frac{6 a b^2}{7 x^{7/2}}-\frac{2 b^3}{9 x^{9/2}}",1,"(-2*(35*b^3 + 135*a*b^2*x + 189*a^2*b*x^2 + 105*a^3*x^3))/(315*x^(9/2))","A",1
1665,1,72,83,0.043697,"\int \frac{x^{5/2}}{a+\frac{b}{x}} \, dx","Integrate[x^(5/2)/(a + b/x),x]","\frac{2 b^{7/2} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{a^{9/2}}+\frac{2 \sqrt{x} \left(15 a^3 x^3-21 a^2 b x^2+35 a b^2 x-105 b^3\right)}{105 a^4}","\frac{2 b^{7/2} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{a^{9/2}}-\frac{2 b^3 \sqrt{x}}{a^4}+\frac{2 b^2 x^{3/2}}{3 a^3}-\frac{2 b x^{5/2}}{5 a^2}+\frac{2 x^{7/2}}{7 a}",1,"(2*Sqrt[x]*(-105*b^3 + 35*a*b^2*x - 21*a^2*b*x^2 + 15*a^3*x^3))/(105*a^4) + (2*b^(7/2)*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]])/a^(9/2)","A",1
1666,1,61,68,0.0317241,"\int \frac{x^{3/2}}{a+\frac{b}{x}} \, dx","Integrate[x^(3/2)/(a + b/x),x]","\frac{2 \sqrt{x} \left(3 a^2 x^2-5 a b x+15 b^2\right)}{15 a^3}-\frac{2 b^{5/2} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{a^{7/2}}","-\frac{2 b^{5/2} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{a^{7/2}}+\frac{2 b^2 \sqrt{x}}{a^3}-\frac{2 b x^{3/2}}{3 a^2}+\frac{2 x^{5/2}}{5 a}",1,"(2*Sqrt[x]*(15*b^2 - 5*a*b*x + 3*a^2*x^2))/(15*a^3) - (2*b^(5/2)*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]])/a^(7/2)","A",1
1667,1,49,53,0.0187887,"\int \frac{\sqrt{x}}{a+\frac{b}{x}} \, dx","Integrate[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 \sqrt{x} (a x-3 b)}{3 a^2}","\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*Sqrt[x]*(-3*b + a*x))/(3*a^2) + (2*b^(3/2)*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]])/a^(5/2)","A",1
1668,1,40,40,0.0100057,"\int \frac{1}{\left(a+\frac{b}{x}\right) \sqrt{x}} \, dx","Integrate[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",1
1669,1,29,29,0.0053515,"\int \frac{1}{\left(a+\frac{b}{x}\right) x^{3/2}} \, dx","Integrate[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",1
1670,1,25,40,0.0124455,"\int \frac{1}{\left(a+\frac{b}{x}\right) x^{5/2}} \, dx","Integrate[1/((a + b/x)*x^(5/2)),x]","-\frac{2 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};-\frac{a x}{b}\right)}{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*Hypergeometric2F1[-1/2, 1, 1/2, -((a*x)/b)])/(b*Sqrt[x])","C",1
1671,1,27,53,0.005316,"\int \frac{1}{\left(a+\frac{b}{x}\right) x^{7/2}} \, dx","Integrate[1/((a + b/x)*x^(7/2)),x]","-\frac{2 \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};-\frac{a x}{b}\right)}{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*Hypergeometric2F1[-3/2, 1, -1/2, -((a*x)/b)])/(3*b*x^(3/2))","C",1
1672,1,27,68,0.0056591,"\int \frac{1}{\left(a+\frac{b}{x}\right) x^{9/2}} \, dx","Integrate[1/((a + b/x)*x^(9/2)),x]","-\frac{2 \, _2F_1\left(-\frac{5}{2},1;-\frac{3}{2};-\frac{a x}{b}\right)}{5 b x^{5/2}}","-\frac{2 a^{5/2} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{b^{7/2}}-\frac{2 a^2}{b^3 \sqrt{x}}+\frac{2 a}{3 b^2 x^{3/2}}-\frac{2}{5 b x^{5/2}}",1,"(-2*Hypergeometric2F1[-5/2, 1, -3/2, -((a*x)/b)])/(5*b*x^(5/2))","C",1
1673,1,27,98,0.0051776,"\int \frac{x^{5/2}}{\left(a+\frac{b}{x}\right)^2} \, dx","Integrate[x^(5/2)/(a + b/x)^2,x]","\frac{2 x^{11/2} \, _2F_1\left(2,\frac{11}{2};\frac{13}{2};-\frac{a x}{b}\right)}{11 b^2}","\frac{9 b^{7/2} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{a^{11/2}}-\frac{9 b^3 \sqrt{x}}{a^5}+\frac{3 b^2 x^{3/2}}{a^4}-\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,"(2*x^(11/2)*Hypergeometric2F1[2, 11/2, 13/2, -((a*x)/b)])/(11*b^2)","C",1
1674,1,27,85,0.0046933,"\int \frac{x^{3/2}}{\left(a+\frac{b}{x}\right)^2} \, dx","Integrate[x^(3/2)/(a + b/x)^2,x]","\frac{2 x^{9/2} \, _2F_1\left(2,\frac{9}{2};\frac{11}{2};-\frac{a x}{b}\right)}{9 b^2}","-\frac{7 b^{5/2} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{a^{9/2}}+\frac{7 b^2 \sqrt{x}}{a^4}-\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,"(2*x^(9/2)*Hypergeometric2F1[2, 9/2, 11/2, -((a*x)/b)])/(9*b^2)","C",1
1675,1,27,70,0.0046724,"\int \frac{\sqrt{x}}{\left(a+\frac{b}{x}\right)^2} \, dx","Integrate[Sqrt[x]/(a + b/x)^2,x]","\frac{2 x^{7/2} \, _2F_1\left(2,\frac{7}{2};\frac{9}{2};-\frac{a x}{b}\right)}{7 b^2}","\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,"(2*x^(7/2)*Hypergeometric2F1[2, 7/2, 9/2, -((a*x)/b)])/(7*b^2)","C",1
1676,1,27,57,0.0040599,"\int \frac{1}{\left(a+\frac{b}{x}\right)^2 \sqrt{x}} \, dx","Integrate[1/((a + b/x)^2*Sqrt[x]),x]","\frac{2 x^{5/2} \, _2F_1\left(2,\frac{5}{2};\frac{7}{2};-\frac{a x}{b}\right)}{5 b^2}","-\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,"(2*x^(5/2)*Hypergeometric2F1[2, 5/2, 7/2, -((a*x)/b)])/(5*b^2)","C",1
1677,1,46,46,0.0301081,"\int \frac{1}{\left(a+\frac{b}{x}\right)^2 x^{3/2}} \, dx","Integrate[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",1
1678,1,45,45,0.0324306,"\int \frac{1}{\left(a+\frac{b}{x}\right)^2 x^{5/2}} \, dx","Integrate[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}}{a b x+b^2}","\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^2 + a*b*x) + ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]]/(Sqrt[a]*b^(3/2))","A",1
1679,1,25,56,0.0045666,"\int \frac{1}{\left(a+\frac{b}{x}\right)^2 x^{7/2}} \, dx","Integrate[1/((a + b/x)^2*x^(7/2)),x]","-\frac{2 \, _2F_1\left(-\frac{1}{2},2;\frac{1}{2};-\frac{a x}{b}\right)}{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,"(-2*Hypergeometric2F1[-1/2, 2, 1/2, -((a*x)/b)])/(b^2*Sqrt[x])","C",1
1680,1,27,69,0.0050802,"\int \frac{1}{\left(a+\frac{b}{x}\right)^2 x^{9/2}} \, dx","Integrate[1/((a + b/x)^2*x^(9/2)),x]","-\frac{2 \, _2F_1\left(-\frac{3}{2},2;-\frac{1}{2};-\frac{a x}{b}\right)}{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,"(-2*Hypergeometric2F1[-3/2, 2, -1/2, -((a*x)/b)])/(3*b^2*x^(3/2))","C",1
1681,1,27,84,0.0060565,"\int \frac{1}{\left(a+\frac{b}{x}\right)^2 x^{11/2}} \, dx","Integrate[1/((a + b/x)^2*x^(11/2)),x]","-\frac{2 \, _2F_1\left(-\frac{5}{2},2;-\frac{3}{2};-\frac{a x}{b}\right)}{5 b^2 x^{5/2}}","-\frac{7 a^{5/2} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{b^{9/2}}-\frac{7 a^2}{b^4 \sqrt{x}}+\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,"(-2*Hypergeometric2F1[-5/2, 2, -3/2, -((a*x)/b)])/(5*b^2*x^(5/2))","C",1
1682,1,27,110,0.0118133,"\int \frac{x^{3/2}}{\left(a+\frac{b}{x}\right)^3} \, dx","Integrate[x^(3/2)/(a + b/x)^3,x]","\frac{2 x^{11/2} \, _2F_1\left(3,\frac{11}{2};\frac{13}{2};-\frac{a x}{b}\right)}{11 b^3}","-\frac{63 b^{5/2} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{4 a^{11/2}}+\frac{63 b^2 \sqrt{x}}{4 a^5}-\frac{21 b x^{3/2}}{4 a^4}+\frac{63 x^{5/2}}{20 a^3}-\frac{9 x^{7/2}}{4 a^2 (a x+b)}-\frac{x^{9/2}}{2 a (a x+b)^2}",1,"(2*x^(11/2)*Hypergeometric2F1[3, 11/2, 13/2, -((a*x)/b)])/(11*b^3)","C",1
1683,1,27,95,0.0048758,"\int \frac{\sqrt{x}}{\left(a+\frac{b}{x}\right)^3} \, dx","Integrate[Sqrt[x]/(a + b/x)^3,x]","\frac{2 x^{9/2} \, _2F_1\left(3,\frac{9}{2};\frac{11}{2};-\frac{a x}{b}\right)}{9 b^3}","\frac{35 b^{3/2} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{4 a^{9/2}}-\frac{35 b \sqrt{x}}{4 a^4}+\frac{35 x^{3/2}}{12 a^3}-\frac{7 x^{5/2}}{4 a^2 (a x+b)}-\frac{x^{7/2}}{2 a (a x+b)^2}",1,"(2*x^(9/2)*Hypergeometric2F1[3, 9/2, 11/2, -((a*x)/b)])/(9*b^3)","C",1
1684,1,27,82,0.0051547,"\int \frac{1}{\left(a+\frac{b}{x}\right)^3 \sqrt{x}} \, dx","Integrate[1/((a + b/x)^3*Sqrt[x]),x]","\frac{2 x^{7/2} \, _2F_1\left(3,\frac{7}{2};\frac{9}{2};-\frac{a x}{b}\right)}{7 b^3}","-\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{5 x^{3/2}}{4 a^2 (a x+b)}-\frac{x^{5/2}}{2 a (a x+b)^2}",1,"(2*x^(7/2)*Hypergeometric2F1[3, 7/2, 9/2, -((a*x)/b)])/(7*b^3)","C",1
1685,1,59,70,0.0476075,"\int \frac{1}{\left(a+\frac{b}{x}\right)^3 x^{3/2}} \, dx","Integrate[1/((a + b/x)^3*x^(3/2)),x]","\frac{3 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{4 a^{5/2} \sqrt{b}}-\frac{\sqrt{x} (5 a x+3 b)}{4 a^2 (a x+b)^2}","\frac{3 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{4 a^{5/2} \sqrt{b}}-\frac{3 \sqrt{x}}{4 a^2 (a x+b)}-\frac{x^{3/2}}{2 a (a x+b)^2}",1,"-1/4*(Sqrt[x]*(3*b + 5*a*x))/(a^2*(b + a*x)^2) + (3*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]])/(4*a^(5/2)*Sqrt[b])","A",1
1686,1,27,73,0.0147552,"\int \frac{1}{\left(a+\frac{b}{x}\right)^3 x^{5/2}} \, dx","Integrate[1/((a + b/x)^3*x^(5/2)),x]","\frac{2 x^{3/2} \, _2F_1\left(\frac{3}{2},3;\frac{5}{2};-\frac{a x}{b}\right)}{3 b^3}","\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,"(2*x^(3/2)*Hypergeometric2F1[3/2, 3, 5/2, -((a*x)/b)])/(3*b^3)","C",1
1687,1,25,70,0.0049693,"\int \frac{1}{\left(a+\frac{b}{x}\right)^3 x^{7/2}} \, dx","Integrate[1/((a + b/x)^3*x^(7/2)),x]","\frac{2 \sqrt{x} \, _2F_1\left(\frac{1}{2},3;\frac{3}{2};-\frac{a x}{b}\right)}{b^3}","\frac{3 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{4 \sqrt{a} b^{5/2}}+\frac{3 \sqrt{x}}{4 b^2 (a x+b)}+\frac{\sqrt{x}}{2 b (a x+b)^2}",1,"(2*Sqrt[x]*Hypergeometric2F1[1/2, 3, 3/2, -((a*x)/b)])/b^3","C",1
1688,1,25,82,0.0045381,"\int \frac{1}{\left(a+\frac{b}{x}\right)^3 x^{9/2}} \, dx","Integrate[1/((a + b/x)^3*x^(9/2)),x]","-\frac{2 \, _2F_1\left(-\frac{1}{2},3;\frac{1}{2};-\frac{a x}{b}\right)}{b^3 \sqrt{x}}","-\frac{15 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{4 b^{7/2}}+\frac{5}{4 b^2 \sqrt{x} (a x+b)}+\frac{1}{2 b \sqrt{x} (a x+b)^2}-\frac{15}{4 b^3 \sqrt{x}}",1,"(-2*Hypergeometric2F1[-1/2, 3, 1/2, -((a*x)/b)])/(b^3*Sqrt[x])","C",1
1689,1,27,95,0.0053895,"\int \frac{1}{\left(a+\frac{b}{x}\right)^3 x^{11/2}} \, dx","Integrate[1/((a + b/x)^3*x^(11/2)),x]","-\frac{2 \, _2F_1\left(-\frac{3}{2},3;-\frac{1}{2};-\frac{a x}{b}\right)}{3 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{35 a}{4 b^4 \sqrt{x}}+\frac{7}{4 b^2 x^{3/2} (a x+b)}+\frac{1}{2 b x^{3/2} (a x+b)^2}-\frac{35}{12 b^3 x^{3/2}}",1,"(-2*Hypergeometric2F1[-3/2, 3, -1/2, -((a*x)/b)])/(3*b^3*x^(3/2))","C",1
1690,1,27,110,0.0055392,"\int \frac{1}{\left(a+\frac{b}{x}\right)^3 x^{13/2}} \, dx","Integrate[1/((a + b/x)^3*x^(13/2)),x]","-\frac{2 \, _2F_1\left(-\frac{5}{2},3;-\frac{3}{2};-\frac{a x}{b}\right)}{5 b^3 x^{5/2}}","-\frac{63 a^{5/2} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)}{4 b^{11/2}}-\frac{63 a^2}{4 b^5 \sqrt{x}}+\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,"(-2*Hypergeometric2F1[-5/2, 3, -3/2, -((a*x)/b)])/(5*b^3*x^(5/2))","C",1
1691,1,39,117,0.0156792,"\int \sqrt{a+\frac{b}{x}} x^3 \, dx","Integrate[Sqrt[a + b/x]*x^3,x]","\frac{2 b^4 \left(a+\frac{b}{x}\right)^{3/2} \, _2F_1\left(\frac{3}{2},5;\frac{5}{2};\frac{b}{a x}+1\right)}{3 a^5}","-\frac{5 b^4 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{64 a^{7/2}}+\frac{5 b^3 x \sqrt{a+\frac{b}{x}}}{64 a^3}-\frac{5 b^2 x^2 \sqrt{a+\frac{b}{x}}}{96 a^2}+\frac{1}{4} x^4 \sqrt{a+\frac{b}{x}}+\frac{b x^3 \sqrt{a+\frac{b}{x}}}{24 a}",1,"(2*b^4*(a + b/x)^(3/2)*Hypergeometric2F1[3/2, 5, 5/2, 1 + b/(a*x)])/(3*a^5)","C",1
1692,1,39,93,0.014905,"\int \sqrt{a+\frac{b}{x}} x^2 \, dx","Integrate[Sqrt[a + b/x]*x^2,x]","-\frac{2 b^3 \left(a+\frac{b}{x}\right)^{3/2} \, _2F_1\left(\frac{3}{2},4;\frac{5}{2};\frac{b}{a x}+1\right)}{3 a^4}","\frac{b^3 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{8 a^{5/2}}-\frac{b^2 x \sqrt{a+\frac{b}{x}}}{8 a^2}+\frac{1}{3} x^3 \sqrt{a+\frac{b}{x}}+\frac{b x^2 \sqrt{a+\frac{b}{x}}}{12 a}",1,"(-2*b^3*(a + b/x)^(3/2)*Hypergeometric2F1[3/2, 4, 5/2, 1 + b/(a*x)])/(3*a^4)","C",1
1693,1,39,69,0.0135752,"\int \sqrt{a+\frac{b}{x}} x \, dx","Integrate[Sqrt[a + b/x]*x,x]","\frac{2 b^2 \left(a+\frac{b}{x}\right)^{3/2} \, _2F_1\left(\frac{3}{2},3;\frac{5}{2};\frac{b}{a x}+1\right)}{3 a^3}","-\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,"(2*b^2*(a + b/x)^(3/2)*Hypergeometric2F1[3/2, 3, 5/2, 1 + b/(a*x)])/(3*a^3)","C",1
1694,1,39,39,0.024005,"\int \sqrt{a+\frac{b}{x}} \, dx","Integrate[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",1
1695,1,39,39,0.0112435,"\int \frac{\sqrt{a+\frac{b}{x}}}{x} \, dx","Integrate[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",1
1696,1,18,18,0.0069715,"\int \frac{\sqrt{a+\frac{b}{x}}}{x^2} \, dx","Integrate[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
1697,1,34,38,0.0155972,"\int \frac{\sqrt{a+\frac{b}{x}}}{x^3} \, dx","Integrate[Sqrt[a + b/x]/x^3,x]","\frac{2 \sqrt{a+\frac{b}{x}} (a x+b) (2 a x-3 b)}{15 b^2 x^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*Sqrt[a + b/x]*(b + a*x)*(-3*b + 2*a*x))/(15*b^2*x^2)","A",1
1698,1,45,59,0.0208111,"\int \frac{\sqrt{a+\frac{b}{x}}}{x^4} \, dx","Integrate[Sqrt[a + b/x]/x^4,x]","-\frac{2 \sqrt{a+\frac{b}{x}} (a x+b) \left(8 a^2 x^2-12 a b x+15 b^2\right)}{105 b^3 x^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*Sqrt[a + b/x]*(b + a*x)*(15*b^2 - 12*a*b*x + 8*a^2*x^2))/(105*b^3*x^3)","A",1
1699,1,56,80,0.0294436,"\int \frac{\sqrt{a+\frac{b}{x}}}{x^5} \, dx","Integrate[Sqrt[a + b/x]/x^5,x]","\frac{2 \sqrt{a+\frac{b}{x}} (a x+b) \left(16 a^3 x^3-24 a^2 b x^2+30 a b^2 x-35 b^3\right)}{315 b^4 x^4}","\frac{2 a^3 \left(a+\frac{b}{x}\right)^{3/2}}{3 b^4}-\frac{6 a^2 \left(a+\frac{b}{x}\right)^{5/2}}{5 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*Sqrt[a + b/x]*(b + a*x)*(-35*b^3 + 30*a*b^2*x - 24*a^2*b*x^2 + 16*a^3*x^3))/(315*b^4*x^4)","A",1
1700,1,67,101,0.0631021,"\int \frac{\sqrt{a+\frac{b}{x}}}{x^6} \, dx","Integrate[Sqrt[a + b/x]/x^6,x]","-\frac{2 \sqrt{a+\frac{b}{x}} (a x+b) \left(128 a^4 x^4-192 a^3 b x^3+240 a^2 b^2 x^2-280 a b^3 x+315 b^4\right)}{3465 b^5 x^5}","-\frac{2 a^4 \left(a+\frac{b}{x}\right)^{3/2}}{3 b^5}+\frac{8 a^3 \left(a+\frac{b}{x}\right)^{5/2}}{5 b^5}-\frac{12 a^2 \left(a+\frac{b}{x}\right)^{7/2}}{7 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*Sqrt[a + b/x]*(b + a*x)*(315*b^4 - 280*a*b^3*x + 240*a^2*b^2*x^2 - 192*a^3*b*x^3 + 128*a^4*x^4))/(3465*b^5*x^5)","A",1
1701,1,39,114,0.0167514,"\int \left(a+\frac{b}{x}\right)^{3/2} x^3 \, dx","Integrate[(a + b/x)^(3/2)*x^3,x]","\frac{2 b^4 \left(a+\frac{b}{x}\right)^{5/2} \, _2F_1\left(\frac{5}{2},5;\frac{7}{2};\frac{b}{a x}+1\right)}{5 a^5}","\frac{3 b^4 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{64 a^{5/2}}-\frac{3 b^3 x \sqrt{a+\frac{b}{x}}}{64 a^2}+\frac{b^2 x^2 \sqrt{a+\frac{b}{x}}}{32 a}+\frac{1}{4} x^4 \left(a+\frac{b}{x}\right)^{3/2}+\frac{1}{8} b x^3 \sqrt{a+\frac{b}{x}}",1,"(2*b^4*(a + b/x)^(5/2)*Hypergeometric2F1[5/2, 5, 7/2, 1 + b/(a*x)])/(5*a^5)","C",1
1702,1,39,90,0.0141398,"\int \left(a+\frac{b}{x}\right)^{3/2} x^2 \, dx","Integrate[(a + b/x)^(3/2)*x^2,x]","-\frac{2 b^3 \left(a+\frac{b}{x}\right)^{5/2} \, _2F_1\left(\frac{5}{2},4;\frac{7}{2};\frac{b}{a x}+1\right)}{5 a^4}","-\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}{3} x^3 \left(a+\frac{b}{x}\right)^{3/2}+\frac{1}{4} b x^2 \sqrt{a+\frac{b}{x}}",1,"(-2*b^3*(a + b/x)^(5/2)*Hypergeometric2F1[5/2, 4, 7/2, 1 + b/(a*x)])/(5*a^4)","C",1
1703,1,76,66,0.0554997,"\int \left(a+\frac{b}{x}\right)^{3/2} x \, dx","Integrate[(a + b/x)^(3/2)*x,x]","\frac{x \sqrt{a+\frac{b}{x}} \left(2 a^2 x^2+3 b^2 \sqrt{\frac{b}{a x}+1} \tanh ^{-1}\left(\sqrt{\frac{b}{a x}+1}\right)+7 a b x+5 b^2\right)}{4 (a x+b)}","\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,"(Sqrt[a + b/x]*x*(5*b^2 + 7*a*b*x + 2*a^2*x^2 + 3*b^2*Sqrt[1 + b/(a*x)]*ArcTanh[Sqrt[1 + b/(a*x)]]))/(4*(b + a*x))","A",1
1704,1,46,54,0.0328856,"\int \left(a+\frac{b}{x}\right)^{3/2} \, dx","Integrate[(a + b/x)^(3/2),x]","\sqrt{a+\frac{b}{x}} (a x-2 b)+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,"Sqrt[a + b/x]*(-2*b + a*x) + 3*Sqrt[a]*b*ArcTanh[Sqrt[a + b/x]/Sqrt[a]]","A",1
1705,1,50,55,0.055519,"\int \frac{\left(a+\frac{b}{x}\right)^{3/2}}{x} \, dx","Integrate[(a + b/x)^(3/2)/x,x]","2 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)-\frac{2 \sqrt{a+\frac{b}{x}} (4 a x+b)}{3 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}",1,"(-2*Sqrt[a + b/x]*(b + 4*a*x))/(3*x) + 2*a^(3/2)*ArcTanh[Sqrt[a + b/x]/Sqrt[a]]","A",1
1706,1,18,18,0.0091434,"\int \frac{\left(a+\frac{b}{x}\right)^{3/2}}{x^2} \, dx","Integrate[(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
1707,1,38,38,0.0285903,"\int \frac{\left(a+\frac{b}{x}\right)^{3/2}}{x^3} \, dx","Integrate[(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",1
1708,1,47,59,0.039574,"\int \frac{\left(a+\frac{b}{x}\right)^{3/2}}{x^4} \, dx","Integrate[(a + b/x)^(3/2)/x^4,x]","-\frac{2 \sqrt{a+\frac{b}{x}} (a x+b)^2 \left(8 a^2 x^2-20 a b x+35 b^2\right)}{315 b^3 x^4}","-\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*Sqrt[a + b/x]*(b + a*x)^2*(35*b^2 - 20*a*b*x + 8*a^2*x^2))/(315*b^3*x^4)","A",1
1709,1,58,80,0.0308913,"\int \frac{\left(a+\frac{b}{x}\right)^{3/2}}{x^5} \, dx","Integrate[(a + b/x)^(3/2)/x^5,x]","\frac{2 \sqrt{a+\frac{b}{x}} (a x+b)^2 \left(16 a^3 x^3-40 a^2 b x^2+70 a b^2 x-105 b^3\right)}{1155 b^4 x^5}","\frac{2 a^3 \left(a+\frac{b}{x}\right)^{5/2}}{5 b^4}-\frac{6 a^2 \left(a+\frac{b}{x}\right)^{7/2}}{7 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*Sqrt[a + b/x]*(b + a*x)^2*(-105*b^3 + 70*a*b^2*x - 40*a^2*b*x^2 + 16*a^3*x^3))/(1155*b^4*x^5)","A",1
1710,1,69,101,0.0470811,"\int \frac{\left(a+\frac{b}{x}\right)^{3/2}}{x^6} \, dx","Integrate[(a + b/x)^(3/2)/x^6,x]","-\frac{2 \sqrt{a+\frac{b}{x}} (a x+b)^2 \left(128 a^4 x^4-320 a^3 b x^3+560 a^2 b^2 x^2-840 a b^3 x+1155 b^4\right)}{15015 b^5 x^6}","-\frac{2 a^4 \left(a+\frac{b}{x}\right)^{5/2}}{5 b^5}+\frac{8 a^3 \left(a+\frac{b}{x}\right)^{7/2}}{7 b^5}-\frac{4 a^2 \left(a+\frac{b}{x}\right)^{9/2}}{3 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*Sqrt[a + b/x]*(b + a*x)^2*(1155*b^4 - 840*a*b^3*x + 560*a^2*b^2*x^2 - 320*a^3*b*x^3 + 128*a^4*x^4))/(15015*b^5*x^6)","A",1
1711,1,80,122,0.0532171,"\int \frac{\left(a+\frac{b}{x}\right)^{3/2}}{x^7} \, dx","Integrate[(a + b/x)^(3/2)/x^7,x]","\frac{2 \sqrt{a+\frac{b}{x}} (a x+b)^2 \left(256 a^5 x^5-640 a^4 b x^4+1120 a^3 b^2 x^3-1680 a^2 b^3 x^2+2310 a b^4 x-3003 b^5\right)}{45045 b^6 x^7}","\frac{2 a^5 \left(a+\frac{b}{x}\right)^{5/2}}{5 b^6}-\frac{10 a^4 \left(a+\frac{b}{x}\right)^{7/2}}{7 b^6}+\frac{20 a^3 \left(a+\frac{b}{x}\right)^{9/2}}{9 b^6}-\frac{20 a^2 \left(a+\frac{b}{x}\right)^{11/2}}{11 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*Sqrt[a + b/x]*(b + a*x)^2*(-3003*b^5 + 2310*a*b^4*x - 1680*a^2*b^3*x^2 + 1120*a^3*b^2*x^3 - 640*a^4*b*x^4 + 256*a^5*x^5))/(45045*b^6*x^7)","A",1
1712,1,39,111,0.019189,"\int \left(a+\frac{b}{x}\right)^{5/2} x^3 \, dx","Integrate[(a + b/x)^(5/2)*x^3,x]","\frac{2 b^4 \left(a+\frac{b}{x}\right)^{7/2} \, _2F_1\left(\frac{7}{2},5;\frac{9}{2};\frac{b}{a x}+1\right)}{7 a^5}","-\frac{5 b^4 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{64 a^{3/2}}+\frac{5 b^3 x \sqrt{a+\frac{b}{x}}}{64 a}+\frac{5}{32} b^2 x^2 \sqrt{a+\frac{b}{x}}+\frac{1}{4} x^4 \left(a+\frac{b}{x}\right)^{5/2}+\frac{5}{24} b x^3 \left(a+\frac{b}{x}\right)^{3/2}",1,"(2*b^4*(a + b/x)^(7/2)*Hypergeometric2F1[7/2, 5, 9/2, 1 + b/(a*x)])/(7*a^5)","C",1
1713,1,87,87,0.0435207,"\int \left(a+\frac{b}{x}\right)^{5/2} x^2 \, dx","Integrate[(a + b/x)^(5/2)*x^2,x]","\frac{x \sqrt{a+\frac{b}{x}} \left(8 a^3 x^3+34 a^2 b x^2+15 b^3 \sqrt{\frac{b}{a x}+1} \tanh ^{-1}\left(\sqrt{\frac{b}{a x}+1}\right)+59 a b^2 x+33 b^3\right)}{24 (a x+b)}","\frac{5 b^3 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{8 \sqrt{a}}+\frac{5}{8} b^2 x \sqrt{a+\frac{b}{x}}+\frac{1}{3} x^3 \left(a+\frac{b}{x}\right)^{5/2}+\frac{5}{12} b x^2 \left(a+\frac{b}{x}\right)^{3/2}",1,"(Sqrt[a + b/x]*x*(33*b^3 + 59*a*b^2*x + 34*a^2*b*x^2 + 8*a^3*x^3 + 15*b^3*Sqrt[1 + b/(a*x)]*ArcTanh[Sqrt[1 + b/(a*x)]]))/(24*(b + a*x))","A",1
1714,1,39,84,0.0361329,"\int \left(a+\frac{b}{x}\right)^{5/2} x \, dx","Integrate[(a + b/x)^(5/2)*x,x]","\frac{2 b^2 \left(a+\frac{b}{x}\right)^{7/2} \, _2F_1\left(3,\frac{7}{2};\frac{9}{2};\frac{b}{a x}+1\right)}{7 a^3}","-\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,"(2*b^2*(a + b/x)^(7/2)*Hypergeometric2F1[3, 7/2, 9/2, 1 + b/(a*x)])/(7*a^3)","C",1
1715,1,64,71,0.0660243,"\int \left(a+\frac{b}{x}\right)^{5/2} \, dx","Integrate[(a + b/x)^(5/2),x]","5 a^{3/2} b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)+\frac{\sqrt{a+\frac{b}{x}} \left(3 a^2 x^2-14 a b x-2 b^2\right)}{3 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,"(Sqrt[a + b/x]*(-2*b^2 - 14*a*b*x + 3*a^2*x^2))/(3*x) + 5*a^(3/2)*b*ArcTanh[Sqrt[a + b/x]/Sqrt[a]]","A",1
1716,1,63,73,0.0770245,"\int \frac{\left(a+\frac{b}{x}\right)^{5/2}}{x} \, dx","Integrate[(a + b/x)^(5/2)/x,x]","2 a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)-\frac{2 \sqrt{a+\frac{b}{x}} \left(23 a^2 x^2+11 a b x+3 b^2\right)}{15 x^2}","2 a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)-2 a^2 \sqrt{a+\frac{b}{x}}-\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*Sqrt[a + b/x]*(3*b^2 + 11*a*b*x + 23*a^2*x^2))/(15*x^2) + 2*a^(5/2)*ArcTanh[Sqrt[a + b/x]/Sqrt[a]]","A",1
1717,1,18,18,0.0119693,"\int \frac{\left(a+\frac{b}{x}\right)^{5/2}}{x^2} \, dx","Integrate[(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
1718,1,38,38,0.0393973,"\int \frac{\left(a+\frac{b}{x}\right)^{5/2}}{x^3} \, dx","Integrate[(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",1
1719,1,47,59,0.0295441,"\int \frac{\left(a+\frac{b}{x}\right)^{5/2}}{x^4} \, dx","Integrate[(a + b/x)^(5/2)/x^4,x]","-\frac{2 \sqrt{a+\frac{b}{x}} (a x+b)^3 \left(8 a^2 x^2-28 a b x+63 b^2\right)}{693 b^3 x^5}","-\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*Sqrt[a + b/x]*(b + a*x)^3*(63*b^2 - 28*a*b*x + 8*a^2*x^2))/(693*b^3*x^5)","A",1
1720,1,58,80,0.0420154,"\int \frac{\left(a+\frac{b}{x}\right)^{5/2}}{x^5} \, dx","Integrate[(a + b/x)^(5/2)/x^5,x]","\frac{2 \sqrt{a+\frac{b}{x}} (a x+b)^3 \left(16 a^3 x^3-56 a^2 b x^2+126 a b^2 x-231 b^3\right)}{3003 b^4 x^6}","\frac{2 a^3 \left(a+\frac{b}{x}\right)^{7/2}}{7 b^4}-\frac{2 a^2 \left(a+\frac{b}{x}\right)^{9/2}}{3 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*Sqrt[a + b/x]*(b + a*x)^3*(-231*b^3 + 126*a*b^2*x - 56*a^2*b*x^2 + 16*a^3*x^3))/(3003*b^4*x^6)","A",1
1721,1,69,101,0.0427753,"\int \frac{\left(a+\frac{b}{x}\right)^{5/2}}{x^6} \, dx","Integrate[(a + b/x)^(5/2)/x^6,x]","-\frac{2 \sqrt{a+\frac{b}{x}} (a x+b)^3 \left(128 a^4 x^4-448 a^3 b x^3+1008 a^2 b^2 x^2-1848 a b^3 x+3003 b^4\right)}{45045 b^5 x^7}","-\frac{2 a^4 \left(a+\frac{b}{x}\right)^{7/2}}{7 b^5}+\frac{8 a^3 \left(a+\frac{b}{x}\right)^{9/2}}{9 b^5}-\frac{12 a^2 \left(a+\frac{b}{x}\right)^{11/2}}{11 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*Sqrt[a + b/x]*(b + a*x)^3*(3003*b^4 - 1848*a*b^3*x + 1008*a^2*b^2*x^2 - 448*a^3*b*x^3 + 128*a^4*x^4))/(45045*b^5*x^7)","A",1
1722,1,37,120,0.0116044,"\int \frac{x^3}{\sqrt{a+\frac{b}{x}}} \, dx","Integrate[x^3/Sqrt[a + b/x],x]","\frac{2 b^4 \sqrt{a+\frac{b}{x}} \, _2F_1\left(\frac{1}{2},5;\frac{3}{2};\frac{b}{a x}+1\right)}{a^5}","\frac{35 b^4 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{64 a^{9/2}}-\frac{35 b^3 x \sqrt{a+\frac{b}{x}}}{64 a^4}+\frac{35 b^2 x^2 \sqrt{a+\frac{b}{x}}}{96 a^3}-\frac{7 b x^3 \sqrt{a+\frac{b}{x}}}{24 a^2}+\frac{x^4 \sqrt{a+\frac{b}{x}}}{4 a}",1,"(2*b^4*Sqrt[a + b/x]*Hypergeometric2F1[1/2, 5, 3/2, 1 + b/(a*x)])/a^5","C",1
1723,1,37,96,0.0121895,"\int \frac{x^2}{\sqrt{a+\frac{b}{x}}} \, dx","Integrate[x^2/Sqrt[a + b/x],x]","-\frac{2 b^3 \sqrt{a+\frac{b}{x}} \, _2F_1\left(\frac{1}{2},4;\frac{3}{2};\frac{b}{a x}+1\right)}{a^4}","-\frac{5 b^3 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{8 a^{7/2}}+\frac{5 b^2 x \sqrt{a+\frac{b}{x}}}{8 a^3}-\frac{5 b x^2 \sqrt{a+\frac{b}{x}}}{12 a^2}+\frac{x^3 \sqrt{a+\frac{b}{x}}}{3 a}",1,"(-2*b^3*Sqrt[a + b/x]*Hypergeometric2F1[1/2, 4, 3/2, 1 + b/(a*x)])/a^4","C",1
1724,1,37,72,0.0367694,"\int \frac{x}{\sqrt{a+\frac{b}{x}}} \, dx","Integrate[x/Sqrt[a + b/x],x]","\frac{2 b^2 \sqrt{a+\frac{b}{x}} \, _2F_1\left(\frac{1}{2},3;\frac{3}{2};\frac{b}{a x}+1\right)}{a^3}","\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,"(2*b^2*Sqrt[a + b/x]*Hypergeometric2F1[1/2, 3, 3/2, 1 + b/(a*x)])/a^3","C",1
1725,1,43,43,0.0209369,"\int \frac{1}{\sqrt{a+\frac{b}{x}}} \, dx","Integrate[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",1
1726,1,25,25,0.0076862,"\int \frac{1}{\sqrt{a+\frac{b}{x}} x} \, dx","Integrate[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",1
1727,1,16,16,0.0066326,"\int \frac{1}{\sqrt{a+\frac{b}{x}} x^2} \, dx","Integrate[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
1728,1,29,36,0.0356755,"\int \frac{1}{\sqrt{a+\frac{b}{x}} x^3} \, dx","Integrate[1/(Sqrt[a + b/x]*x^3),x]","\frac{2 \sqrt{a+\frac{b}{x}} (2 a x-b)}{3 b^2 x}","\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*Sqrt[a + b/x]*(-b + 2*a*x))/(3*b^2*x)","A",1
1729,1,40,57,0.0362748,"\int \frac{1}{\sqrt{a+\frac{b}{x}} x^4} \, dx","Integrate[1/(Sqrt[a + b/x]*x^4),x]","-\frac{2 \sqrt{a+\frac{b}{x}} \left(8 a^2 x^2-4 a b x+3 b^2\right)}{15 b^3 x^2}","-\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*Sqrt[a + b/x]*(3*b^2 - 4*a*b*x + 8*a^2*x^2))/(15*b^3*x^2)","A",1
1730,1,51,76,0.0414552,"\int \frac{1}{\sqrt{a+\frac{b}{x}} x^5} \, dx","Integrate[1/(Sqrt[a + b/x]*x^5),x]","\frac{2 \sqrt{a+\frac{b}{x}} \left(16 a^3 x^3-8 a^2 b x^2+6 a b^2 x-5 b^3\right)}{35 b^4 x^3}","\frac{2 a^3 \sqrt{a+\frac{b}{x}}}{b^4}-\frac{2 a^2 \left(a+\frac{b}{x}\right)^{3/2}}{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*Sqrt[a + b/x]*(-5*b^3 + 6*a*b^2*x - 8*a^2*b*x^2 + 16*a^3*x^3))/(35*b^4*x^3)","A",1
1731,1,62,99,0.0489808,"\int \frac{1}{\sqrt{a+\frac{b}{x}} x^6} \, dx","Integrate[1/(Sqrt[a + b/x]*x^6),x]","-\frac{2 \sqrt{a+\frac{b}{x}} \left(128 a^4 x^4-64 a^3 b x^3+48 a^2 b^2 x^2-40 a b^3 x+35 b^4\right)}{315 b^5 x^4}","-\frac{2 a^4 \sqrt{a+\frac{b}{x}}}{b^5}+\frac{8 a^3 \left(a+\frac{b}{x}\right)^{3/2}}{3 b^5}-\frac{12 a^2 \left(a+\frac{b}{x}\right)^{5/2}}{5 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*Sqrt[a + b/x]*(35*b^4 - 40*a*b^3*x + 48*a^2*b^2*x^2 - 64*a^3*b*x^3 + 128*a^4*x^4))/(315*b^5*x^4)","A",1
1732,1,37,117,0.0123924,"\int \frac{x^2}{\left(a+\frac{b}{x}\right)^{3/2}} \, dx","Integrate[x^2/(a + b/x)^(3/2),x]","\frac{2 b^3 \, _2F_1\left(-\frac{1}{2},4;\frac{1}{2};\frac{b}{a x}+1\right)}{a^4 \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{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{7 b x^2}{12 a^2 \sqrt{a+\frac{b}{x}}}+\frac{x^3}{3 a \sqrt{a+\frac{b}{x}}}",1,"(2*b^3*Hypergeometric2F1[-1/2, 4, 1/2, 1 + b/(a*x)])/(a^4*Sqrt[a + b/x])","C",1
1733,1,37,93,0.0106572,"\int \frac{x}{\left(a+\frac{b}{x}\right)^{3/2}} \, dx","Integrate[x/(a + b/x)^(3/2),x]","-\frac{2 b^2 \, _2F_1\left(-\frac{1}{2},3;\frac{1}{2};\frac{b}{a x}+1\right)}{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{15 b^2}{4 a^3 \sqrt{a+\frac{b}{x}}}-\frac{5 b x}{4 a^2 \sqrt{a+\frac{b}{x}}}+\frac{x^2}{2 a \sqrt{a+\frac{b}{x}}}",1,"(-2*b^2*Hypergeometric2F1[-1/2, 3, 1/2, 1 + b/(a*x)])/(a^3*Sqrt[a + b/x])","C",1
1734,1,36,60,0.0377815,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{3/2}} \, dx","Integrate[(a + b/x)^(-3/2),x]","\frac{2 b \, _2F_1\left(-\frac{1}{2},2;\frac{1}{2};\frac{a+\frac{b}{x}}{a}\right)}{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{3 b}{a^2 \sqrt{a+\frac{b}{x}}}+\frac{x}{a \sqrt{a+\frac{b}{x}}}",1,"(2*b*Hypergeometric2F1[-1/2, 2, 1/2, (a + b/x)/a])/(a^2*Sqrt[a + b/x])","C",1
1735,1,34,42,0.0167752,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{3/2} x} \, dx","Integrate[1/((a + b/x)^(3/2)*x),x]","-\frac{2 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{b}{a x}+1\right)}{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*Hypergeometric2F1[-1/2, 1, 1/2, 1 + b/(a*x)])/(a*Sqrt[a + b/x])","C",1
1736,1,16,16,0.0078258,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{3/2} x^2} \, dx","Integrate[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
1737,1,25,34,0.043221,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{3/2} x^3} \, dx","Integrate[1/((a + b/x)^(3/2)*x^3),x]","-\frac{2 (2 a x+b)}{b^2 x \sqrt{a+\frac{b}{x}}}","-\frac{2 a}{b^2 \sqrt{a+\frac{b}{x}}}-\frac{2 \sqrt{a+\frac{b}{x}}}{b^2}",1,"(-2*(b + 2*a*x))/(b^2*Sqrt[a + b/x]*x)","A",1
1738,1,40,55,0.0249239,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{3/2} x^4} \, dx","Integrate[1/((a + b/x)^(3/2)*x^4),x]","\frac{16 a^2 x^2+8 a b x-2 b^2}{3 b^3 x^2 \sqrt{a+\frac{b}{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}",1,"(-2*b^2 + 8*a*b*x + 16*a^2*x^2)/(3*b^3*Sqrt[a + b/x]*x^2)","A",1
1739,1,49,74,0.0436337,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{3/2} x^5} \, dx","Integrate[1/((a + b/x)^(3/2)*x^5),x]","-\frac{2 \left(16 a^3 x^3+8 a^2 b x^2-2 a b^2 x+b^3\right)}{5 b^4 x^3 \sqrt{a+\frac{b}{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}",1,"(-2*(b^3 - 2*a*b^2*x + 8*a^2*b*x^2 + 16*a^3*x^3))/(5*b^4*Sqrt[a + b/x]*x^3)","A",1
1740,1,62,95,0.0373679,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{3/2} x^6} \, dx","Integrate[1/((a + b/x)^(3/2)*x^6),x]","\frac{2 \left(128 a^4 x^4+64 a^3 b x^3-16 a^2 b^2 x^2+8 a b^3 x-5 b^4\right)}{35 b^5 x^4 \sqrt{a+\frac{b}{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}",1,"(2*(-5*b^4 + 8*a*b^3*x - 16*a^2*b^2*x^2 + 64*a^3*b*x^3 + 128*a^4*x^4))/(35*b^5*Sqrt[a + b/x]*x^4)","A",1
1741,1,73,116,0.0762417,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{3/2} x^7} \, dx","Integrate[1/((a + b/x)^(3/2)*x^7),x]","-\frac{2 \left(256 a^5 x^5+128 a^4 b x^4-32 a^3 b^2 x^3+16 a^2 b^3 x^2-10 a b^4 x+7 b^5\right)}{63 b^6 x^5 \sqrt{a+\frac{b}{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}",1,"(-2*(7*b^5 - 10*a*b^4*x + 16*a^2*b^3*x^2 - 32*a^3*b^2*x^3 + 128*a^4*b*x^4 + 256*a^5*x^5))/(63*b^6*Sqrt[a + b/x]*x^5)","A",1
1742,1,39,138,0.0169075,"\int \frac{x^2}{\left(a+\frac{b}{x}\right)^{5/2}} \, dx","Integrate[x^2/(a + b/x)^(5/2),x]","\frac{2 b^3 \, _2F_1\left(-\frac{3}{2},4;-\frac{1}{2};\frac{b}{a x}+1\right)}{3 a^4 \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{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{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,"(2*b^3*Hypergeometric2F1[-3/2, 4, -1/2, 1 + b/(a*x)])/(3*a^4*(a + b/x)^(3/2))","C",1
1743,1,39,114,0.0114542,"\int \frac{x}{\left(a+\frac{b}{x}\right)^{5/2}} \, dx","Integrate[x/(a + b/x)^(5/2),x]","-\frac{2 b^2 \, _2F_1\left(-\frac{3}{2},3;-\frac{1}{2};\frac{b}{a x}+1\right)}{3 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{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{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,"(-2*b^2*Hypergeometric2F1[-3/2, 3, -1/2, 1 + b/(a*x)])/(3*a^3*(a + b/x)^(3/2))","C",1
1744,1,38,79,0.0187393,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{5/2}} \, dx","Integrate[(a + b/x)^(-5/2),x]","\frac{2 b \, _2F_1\left(-\frac{3}{2},2;-\frac{1}{2};\frac{a+\frac{b}{x}}{a}\right)}{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{5 b}{a^3 \sqrt{a+\frac{b}{x}}}+\frac{5 b}{3 a^2 \left(a+\frac{b}{x}\right)^{3/2}}+\frac{x}{a \left(a+\frac{b}{x}\right)^{3/2}}",1,"(2*b*Hypergeometric2F1[-3/2, 2, -1/2, (a + b/x)/a])/(3*a^2*(a + b/x)^(3/2))","C",1
1745,1,36,60,0.0291727,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{5/2} x} \, dx","Integrate[1/((a + b/x)^(5/2)*x),x]","-\frac{2 \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{b}{a x}+1\right)}{3 a \left(a+\frac{b}{x}\right)^{3/2}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{5/2}}-\frac{2}{a^2 \sqrt{a+\frac{b}{x}}}-\frac{2}{3 a \left(a+\frac{b}{x}\right)^{3/2}}",1,"(-2*Hypergeometric2F1[-3/2, 1, -1/2, 1 + b/(a*x)])/(3*a*(a + b/x)^(3/2))","C",1
1746,1,18,18,0.0100994,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{5/2} x^2} \, dx","Integrate[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
1747,1,33,36,0.026002,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{5/2} x^3} \, dx","Integrate[1/((a + b/x)^(5/2)*x^3),x]","\frac{4 a x+6 b}{3 b^2 \sqrt{a+\frac{b}{x}} (a x+b)}","\frac{2}{b^2 \sqrt{a+\frac{b}{x}}}-\frac{2 a}{3 b^2 \left(a+\frac{b}{x}\right)^{3/2}}",1,"(6*b + 4*a*x)/(3*b^2*Sqrt[a + b/x]*(b + a*x))","A",1
1748,1,44,55,0.037834,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{5/2} x^4} \, dx","Integrate[1/((a + b/x)^(5/2)*x^4),x]","-\frac{2 \sqrt{a+\frac{b}{x}} \left(8 a^2 x^2+12 a b x+3 b^2\right)}{3 b^3 (a x+b)^2}","\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*Sqrt[a + b/x]*(3*b^2 + 12*a*b*x + 8*a^2*x^2))/(3*b^3*(b + a*x)^2)","A",1
1749,1,58,76,0.0416296,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{5/2} x^5} \, dx","Integrate[1/((a + b/x)^(5/2)*x^5),x]","\frac{32 a^3 x^3+48 a^2 b x^2+12 a b^2 x-2 b^3}{3 b^4 x^2 \sqrt{a+\frac{b}{x}} (a x+b)}","-\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*b^3 + 12*a*b^2*x + 48*a^2*b*x^2 + 32*a^3*x^3)/(3*b^4*Sqrt[a + b/x]*x^2*(b + a*x))","A",1
1750,1,69,97,0.059037,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{5/2} x^6} \, dx","Integrate[1/((a + b/x)^(5/2)*x^6),x]","-\frac{2 \left(128 a^4 x^4+192 a^3 b x^3+48 a^2 b^2 x^2-8 a b^3 x+3 b^4\right)}{15 b^5 x^3 \sqrt{a+\frac{b}{x}} (a x+b)}","\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*(3*b^4 - 8*a*b^3*x + 48*a^2*b^2*x^2 + 192*a^3*b*x^3 + 128*a^4*x^4))/(15*b^5*Sqrt[a + b/x]*x^3*(b + a*x))","A",1
1751,1,80,116,0.0756191,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{5/2} x^7} \, dx","Integrate[1/((a + b/x)^(5/2)*x^7),x]","\frac{2 \left(256 a^5 x^5+384 a^4 b x^4+96 a^3 b^2 x^3-16 a^2 b^3 x^2+6 a b^4 x-3 b^5\right)}{21 b^6 x^4 \sqrt{a+\frac{b}{x}} (a x+b)}","-\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*(-3*b^5 + 6*a*b^4*x - 16*a^2*b^3*x^2 + 96*a^3*b^2*x^3 + 384*a^4*b*x^4 + 256*a^5*x^5))/(21*b^6*Sqrt[a + b/x]*x^4*(b + a*x))","A",1
1752,1,58,100,0.0174347,"\int \sqrt{a+\frac{b}{x}} x^{7/2} \, dx","Integrate[Sqrt[a + b/x]*x^(7/2),x]","\frac{2 \sqrt{x} \sqrt{a+\frac{b}{x}} (a x+b) \left(35 a^3 x^3-30 a^2 b x^2+24 a b^2 x-16 b^3\right)}{315 a^4}","-\frac{32 b^3 x^{3/2} \left(a+\frac{b}{x}\right)^{3/2}}{315 a^4}+\frac{16 b^2 x^{5/2} \left(a+\frac{b}{x}\right)^{3/2}}{105 a^3}-\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,"(2*Sqrt[a + b/x]*Sqrt[x]*(b + a*x)*(-16*b^3 + 24*a*b^2*x - 30*a^2*b*x^2 + 35*a^3*x^3))/(315*a^4)","A",1
1753,1,47,74,0.0161023,"\int \sqrt{a+\frac{b}{x}} x^{5/2} \, dx","Integrate[Sqrt[a + b/x]*x^(5/2),x]","\frac{2 \sqrt{x} \sqrt{a+\frac{b}{x}} (a x+b) \left(15 a^2 x^2-12 a b x+8 b^2\right)}{105 a^3}","\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,"(2*Sqrt[a + b/x]*Sqrt[x]*(b + a*x)*(8*b^2 - 12*a*b*x + 15*a^2*x^2))/(105*a^3)","A",1
1754,1,36,48,0.0390538,"\int \sqrt{a+\frac{b}{x}} x^{3/2} \, dx","Integrate[Sqrt[a + b/x]*x^(3/2),x]","\frac{2 \sqrt{x} \sqrt{a+\frac{b}{x}} (a x+b) (3 a x-2 b)}{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,"(2*Sqrt[a + b/x]*Sqrt[x]*(b + a*x)*(-2*b + 3*a*x))/(15*a^2)","A",1
1755,1,23,23,0.0113427,"\int \sqrt{a+\frac{b}{x}} \sqrt{x} \, dx","Integrate[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
1756,1,78,49,0.1239666,"\int \frac{\sqrt{a+\frac{b}{x}}}{\sqrt{x}} \, dx","Integrate[Sqrt[a + b/x]/Sqrt[x],x]","\frac{2 \sqrt{x} \sqrt{a+\frac{b}{x}} \left(-\sqrt{a} \sqrt{b} \sqrt{x} \sqrt{\frac{b}{a x}+1} \sinh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{a} \sqrt{x}}\right)+a x+b\right)}{a x+b}","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]*(b + a*x - Sqrt[a]*Sqrt[b]*Sqrt[1 + b/(a*x)]*Sqrt[x]*ArcSinh[Sqrt[b]/(Sqrt[a]*Sqrt[x])]))/(b + a*x)","A",1
1757,1,74,50,0.2294901,"\int \frac{\sqrt{a+\frac{b}{x}}}{x^{3/2}} \, dx","Integrate[Sqrt[a + b/x]/x^(3/2),x]","\frac{\sqrt{a+\frac{b}{x}} \left(-\frac{a^{3/2} x^{3/2} \sqrt{\frac{b}{a x}+1} \sinh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{a} \sqrt{x}}\right)}{\sqrt{b} (a x+b)}-1\right)}{\sqrt{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}}",1,"(Sqrt[a + b/x]*(-1 - (a^(3/2)*Sqrt[1 + b/(a*x)]*x^(3/2)*ArcSinh[Sqrt[b]/(Sqrt[a]*Sqrt[x])])/(Sqrt[b]*(b + a*x))))/Sqrt[x]","A",1
1758,1,77,80,0.1714095,"\int \frac{\sqrt{a+\frac{b}{x}}}{x^{5/2}} \, dx","Integrate[Sqrt[a + b/x]/x^(5/2),x]","\frac{\sqrt{a+\frac{b}{x}} \left(\frac{a^{3/2} \sinh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{a} \sqrt{x}}\right)}{\sqrt{\frac{b}{a x}+1}}-\frac{\sqrt{b} (a x+2 b)}{x^{3/2}}\right)}{4 b^{3/2}}","\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]*(-((Sqrt[b]*(2*b + a*x))/x^(3/2)) + (a^(3/2)*ArcSinh[Sqrt[b]/(Sqrt[a]*Sqrt[x])])/Sqrt[1 + b/(a*x)]))/(4*b^(3/2))","A",1
1759,1,89,106,0.2715079,"\int \frac{\sqrt{a+\frac{b}{x}}}{x^{7/2}} \, dx","Integrate[Sqrt[a + b/x]/x^(7/2),x]","\frac{\sqrt{a+\frac{b}{x}} \left(\frac{\sqrt{b} \left(3 a^2 x^2-2 a b x-8 b^2\right)}{x^{5/2}}-\frac{3 a^{5/2} \sinh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{a} \sqrt{x}}\right)}{\sqrt{\frac{b}{a x}+1}}\right)}{24 b^{5/2}}","-\frac{a^3 \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)}{8 b^{5/2}}+\frac{a^2 \sqrt{a+\frac{b}{x}}}{8 b^2 \sqrt{x}}-\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]*((Sqrt[b]*(-8*b^2 - 2*a*b*x + 3*a^2*x^2))/x^(5/2) - (3*a^(5/2)*ArcSinh[Sqrt[b]/(Sqrt[a]*Sqrt[x])])/Sqrt[1 + b/(a*x)]))/(24*b^(5/2))","A",1
1760,1,60,100,0.02517,"\int \left(a+\frac{b}{x}\right)^{3/2} x^{9/2} \, dx","Integrate[(a + b/x)^(3/2)*x^(9/2),x]","\frac{2 \sqrt{x} \sqrt{a+\frac{b}{x}} (a x+b)^2 \left(105 a^3 x^3-70 a^2 b x^2+40 a b^2 x-16 b^3\right)}{1155 a^4}","-\frac{32 b^3 x^{5/2} \left(a+\frac{b}{x}\right)^{5/2}}{1155 a^4}+\frac{16 b^2 x^{7/2} \left(a+\frac{b}{x}\right)^{5/2}}{231 a^3}-\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,"(2*Sqrt[a + b/x]*Sqrt[x]*(b + a*x)^2*(-16*b^3 + 40*a*b^2*x - 70*a^2*b*x^2 + 105*a^3*x^3))/(1155*a^4)","A",1
1761,1,49,74,0.0175815,"\int \left(a+\frac{b}{x}\right)^{3/2} x^{7/2} \, dx","Integrate[(a + b/x)^(3/2)*x^(7/2),x]","\frac{2 \sqrt{x} \sqrt{a+\frac{b}{x}} (a x+b)^2 \left(35 a^2 x^2-20 a b x+8 b^2\right)}{315 a^3}","\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,"(2*Sqrt[a + b/x]*Sqrt[x]*(b + a*x)^2*(8*b^2 - 20*a*b*x + 35*a^2*x^2))/(315*a^3)","A",1
1762,1,40,48,0.0162941,"\int \left(a+\frac{b}{x}\right)^{3/2} x^{5/2} \, dx","Integrate[(a + b/x)^(3/2)*x^(5/2),x]","\frac{2}{35} x^{5/2} \sqrt{a+\frac{b}{x}} \left(\frac{b}{a x}+1\right)^2 (5 a x-2 b)","\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,"(2*Sqrt[a + b/x]*(1 + b/(a*x))^2*x^(5/2)*(-2*b + 5*a*x))/35","A",1
1763,1,23,23,0.0159512,"\int \left(a+\frac{b}{x}\right)^{3/2} x^{3/2} \, dx","Integrate[(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
1764,1,54,70,0.0128896,"\int \left(a+\frac{b}{x}\right)^{3/2} \sqrt{x} \, dx","Integrate[(a + b/x)^(3/2)*Sqrt[x],x]","\frac{2 a x^{3/2} \sqrt{a+\frac{b}{x}} \, _2F_1\left(-\frac{3}{2},-\frac{3}{2};-\frac{1}{2};-\frac{b}{a x}\right)}{3 \sqrt{\frac{b}{a x}+1}}","-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*a*Sqrt[a + b/x]*x^(3/2)*Hypergeometric2F1[-3/2, -3/2, -1/2, -(b/(a*x))])/(3*Sqrt[1 + b/(a*x)])","C",1
1765,1,52,69,0.0145966,"\int \frac{\left(a+\frac{b}{x}\right)^{3/2}}{\sqrt{x}} \, dx","Integrate[(a + b/x)^(3/2)/Sqrt[x],x]","\frac{2 a \sqrt{x} \sqrt{a+\frac{b}{x}} \, _2F_1\left(-\frac{3}{2},-\frac{1}{2};\frac{1}{2};-\frac{b}{a x}\right)}{\sqrt{\frac{b}{a x}+1}}","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,"(2*a*Sqrt[a + b/x]*Sqrt[x]*Hypergeometric2F1[-3/2, -1/2, 1/2, -(b/(a*x))])/Sqrt[1 + b/(a*x)]","C",1
1766,1,73,77,0.1917712,"\int \frac{\left(a+\frac{b}{x}\right)^{3/2}}{x^{3/2}} \, dx","Integrate[(a + b/x)^(3/2)/x^(3/2),x]","\frac{1}{4} \sqrt{a+\frac{b}{x}} \left(\frac{-5 a x-2 b}{x^{3/2}}-\frac{3 a^{3/2} \sinh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{a} \sqrt{x}}\right)}{\sqrt{b} \sqrt{\frac{b}{a x}+1}}\right)","-\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,"(Sqrt[a + b/x]*((-2*b - 5*a*x)/x^(3/2) - (3*a^(3/2)*ArcSinh[Sqrt[b]/(Sqrt[a]*Sqrt[x])])/(Sqrt[b]*Sqrt[1 + b/(a*x)])))/4","A",1
1767,1,90,103,0.1860361,"\int \frac{\left(a+\frac{b}{x}\right)^{3/2}}{x^{5/2}} \, dx","Integrate[(a + b/x)^(3/2)/x^(5/2),x]","\frac{\sqrt{a+\frac{b}{x}} \left(\frac{3 a^{5/2} \sinh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{a} \sqrt{x}}\right)}{\sqrt{\frac{b}{a x}+1}}-\frac{\sqrt{b} \left(3 a^2 x^2+14 a b x+8 b^2\right)}{x^{5/2}}\right)}{24 b^{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,"(Sqrt[a + b/x]*(-((Sqrt[b]*(8*b^2 + 14*a*b*x + 3*a^2*x^2))/x^(5/2)) + (3*a^(5/2)*ArcSinh[Sqrt[b]/(Sqrt[a]*Sqrt[x])])/Sqrt[1 + b/(a*x)]))/(24*b^(3/2))","A",1
1768,1,60,100,0.0211105,"\int \left(a+\frac{b}{x}\right)^{5/2} x^{11/2} \, dx","Integrate[(a + b/x)^(5/2)*x^(11/2),x]","\frac{2 \sqrt{x} \sqrt{a+\frac{b}{x}} (a x+b)^3 \left(231 a^3 x^3-126 a^2 b x^2+56 a b^2 x-16 b^3\right)}{3003 a^4}","-\frac{32 b^3 x^{7/2} \left(a+\frac{b}{x}\right)^{7/2}}{3003 a^4}+\frac{16 b^2 x^{9/2} \left(a+\frac{b}{x}\right)^{7/2}}{429 a^3}-\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,"(2*Sqrt[a + b/x]*Sqrt[x]*(b + a*x)^3*(-16*b^3 + 56*a*b^2*x - 126*a^2*b*x^2 + 231*a^3*x^3))/(3003*a^4)","A",1
1769,1,51,74,0.0367427,"\int \left(a+\frac{b}{x}\right)^{5/2} x^{9/2} \, dx","Integrate[(a + b/x)^(5/2)*x^(9/2),x]","\frac{2}{693} x^{7/2} \sqrt{a+\frac{b}{x}} \left(\frac{b}{a x}+1\right)^3 \left(63 a^2 x^2-28 a b x+8 b^2\right)","\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,"(2*Sqrt[a + b/x]*(1 + b/(a*x))^3*x^(7/2)*(8*b^2 - 28*a*b*x + 63*a^2*x^2))/693","A",1
1770,1,38,48,0.0288223,"\int \left(a+\frac{b}{x}\right)^{5/2} x^{7/2} \, dx","Integrate[(a + b/x)^(5/2)*x^(7/2),x]","\frac{2 \sqrt{x} \sqrt{a+\frac{b}{x}} (a x+b)^3 (7 a x-2 b)}{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,"(2*Sqrt[a + b/x]*Sqrt[x]*(b + a*x)^3*(-2*b + 7*a*x))/(63*a^2)","A",1
1771,1,23,23,0.0267371,"\int \left(a+\frac{b}{x}\right)^{5/2} x^{5/2} \, dx","Integrate[(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
1772,1,56,93,0.0164587,"\int \left(a+\frac{b}{x}\right)^{5/2} x^{3/2} \, dx","Integrate[(a + b/x)^(5/2)*x^(3/2),x]","\frac{2 a^2 x^{5/2} \sqrt{a+\frac{b}{x}} \, _2F_1\left(-\frac{5}{2},-\frac{5}{2};-\frac{3}{2};-\frac{b}{a x}\right)}{5 \sqrt{\frac{b}{a x}+1}}","-2 b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)+2 b^2 \sqrt{x} \sqrt{a+\frac{b}{x}}+\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*a^2*Sqrt[a + b/x]*x^(5/2)*Hypergeometric2F1[-5/2, -5/2, -3/2, -(b/(a*x))])/(5*Sqrt[1 + b/(a*x)])","C",1
1773,1,56,94,0.0317099,"\int \left(a+\frac{b}{x}\right)^{5/2} \sqrt{x} \, dx","Integrate[(a + b/x)^(5/2)*Sqrt[x],x]","\frac{2 a^2 x^{3/2} \sqrt{a+\frac{b}{x}} \, _2F_1\left(-\frac{5}{2},-\frac{3}{2};-\frac{1}{2};-\frac{b}{a x}\right)}{3 \sqrt{\frac{b}{a x}+1}}","-5 a b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)-\frac{5 b^2 \sqrt{a+\frac{b}{x}}}{\sqrt{x}}+\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,"(2*a^2*Sqrt[a + b/x]*x^(3/2)*Hypergeometric2F1[-5/2, -3/2, -1/2, -(b/(a*x))])/(3*Sqrt[1 + b/(a*x)])","C",1
1774,1,54,97,0.0270782,"\int \frac{\left(a+\frac{b}{x}\right)^{5/2}}{\sqrt{x}} \, dx","Integrate[(a + b/x)^(5/2)/Sqrt[x],x]","\frac{2 a^2 \sqrt{x} \sqrt{a+\frac{b}{x}} \, _2F_1\left(-\frac{5}{2},-\frac{1}{2};\frac{1}{2};-\frac{b}{a x}\right)}{\sqrt{\frac{b}{a x}+1}}","-\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,"(2*a^2*Sqrt[a + b/x]*Sqrt[x]*Hypergeometric2F1[-5/2, -1/2, 1/2, -(b/(a*x))])/Sqrt[1 + b/(a*x)]","C",1
1775,1,85,100,0.2237787,"\int \frac{\left(a+\frac{b}{x}\right)^{5/2}}{x^{3/2}} \, dx","Integrate[(a + b/x)^(5/2)/x^(3/2),x]","\frac{1}{24} \sqrt{a+\frac{b}{x}} \left(-\frac{15 a^{5/2} \sinh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{a} \sqrt{x}}\right)}{\sqrt{b} \sqrt{\frac{b}{a x}+1}}-\frac{33 a^2 x^2+26 a b x+8 b^2}{x^{5/2}}\right)","-\frac{5 a^3 \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)}{8 \sqrt{b}}-\frac{5 a^2 \sqrt{a+\frac{b}{x}}}{8 \sqrt{x}}-\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,"(Sqrt[a + b/x]*(-((8*b^2 + 26*a*b*x + 33*a^2*x^2)/x^(5/2)) - (15*a^(5/2)*ArcSinh[Sqrt[b]/(Sqrt[a]*Sqrt[x])])/(Sqrt[b]*Sqrt[1 + b/(a*x)])))/24","A",1
1776,1,101,126,0.2176263,"\int \frac{\left(a+\frac{b}{x}\right)^{5/2}}{x^{5/2}} \, dx","Integrate[(a + b/x)^(5/2)/x^(5/2),x]","\frac{\sqrt{a+\frac{b}{x}} \left(\frac{15 a^{7/2} \sinh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{a} \sqrt{x}}\right)}{\sqrt{\frac{b}{a x}+1}}-\frac{\sqrt{b} \left(15 a^3 x^3+118 a^2 b x^2+136 a b^2 x+48 b^3\right)}{x^{7/2}}\right)}{192 b^{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^3 \sqrt{a+\frac{b}{x}}}{64 b \sqrt{x}}-\frac{5 a^2 \sqrt{a+\frac{b}{x}}}{32 x^{3/2}}-\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,"(Sqrt[a + b/x]*(-((Sqrt[b]*(48*b^3 + 136*a*b^2*x + 118*a^2*b*x^2 + 15*a^3*x^3))/x^(7/2)) + (15*a^(7/2)*ArcSinh[Sqrt[b]/(Sqrt[a]*Sqrt[x])])/Sqrt[1 + b/(a*x)]))/(192*b^(3/2))","A",1
1777,1,64,126,0.0413666,"\int \frac{x^{7/2}}{\sqrt{a+\frac{b}{x}}} \, dx","Integrate[x^(7/2)/Sqrt[a + b/x],x]","\frac{2 \sqrt{x} \sqrt{a+\frac{b}{x}} \left(35 a^4 x^4-40 a^3 b x^3+48 a^2 b^2 x^2-64 a b^3 x+128 b^4\right)}{315 a^5}","\frac{256 b^4 \sqrt{x} \sqrt{a+\frac{b}{x}}}{315 a^5}-\frac{128 b^3 x^{3/2} \sqrt{a+\frac{b}{x}}}{315 a^4}+\frac{32 b^2 x^{5/2} \sqrt{a+\frac{b}{x}}}{105 a^3}-\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,"(2*Sqrt[a + b/x]*Sqrt[x]*(128*b^4 - 64*a*b^3*x + 48*a^2*b^2*x^2 - 40*a^3*b*x^3 + 35*a^4*x^4))/(315*a^5)","A",1
1778,1,53,100,0.0222713,"\int \frac{x^{5/2}}{\sqrt{a+\frac{b}{x}}} \, dx","Integrate[x^(5/2)/Sqrt[a + b/x],x]","\frac{2 \sqrt{x} \sqrt{a+\frac{b}{x}} \left(5 a^3 x^3-6 a^2 b x^2+8 a b^2 x-16 b^3\right)}{35 a^4}","-\frac{32 b^3 \sqrt{x} \sqrt{a+\frac{b}{x}}}{35 a^4}+\frac{16 b^2 x^{3/2} \sqrt{a+\frac{b}{x}}}{35 a^3}-\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,"(2*Sqrt[a + b/x]*Sqrt[x]*(-16*b^3 + 8*a*b^2*x - 6*a^2*b*x^2 + 5*a^3*x^3))/(35*a^4)","A",1
1779,1,42,74,0.0185418,"\int \frac{x^{3/2}}{\sqrt{a+\frac{b}{x}}} \, dx","Integrate[x^(3/2)/Sqrt[a + b/x],x]","\frac{2 \sqrt{x} \sqrt{a+\frac{b}{x}} \left(3 a^2 x^2-4 a b x+8 b^2\right)}{15 a^3}","\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,"(2*Sqrt[a + b/x]*Sqrt[x]*(8*b^2 - 4*a*b*x + 3*a^2*x^2))/(15*a^3)","A",1
1780,1,30,48,0.017209,"\int \frac{\sqrt{x}}{\sqrt{a+\frac{b}{x}}} \, dx","Integrate[Sqrt[x]/Sqrt[a + b/x],x]","\frac{2 \sqrt{x} \sqrt{a+\frac{b}{x}} (a x-2 b)}{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,"(2*Sqrt[a + b/x]*Sqrt[x]*(-2*b + a*x))/(3*a^2)","A",1
1781,1,21,21,0.0095117,"\int \frac{1}{\sqrt{a+\frac{b}{x}} \sqrt{x}} \, dx","Integrate[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
1782,1,54,30,0.019374,"\int \frac{1}{\sqrt{a+\frac{b}{x}} x^{3/2}} \, dx","Integrate[1/(Sqrt[a + b/x]*x^(3/2)),x]","-\frac{2 \sqrt{a} \sqrt{\frac{b}{a x}+1} \sinh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{a} \sqrt{x}}\right)}{\sqrt{b} \sqrt{a+\frac{b}{x}}}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)}{\sqrt{b}}",1,"(-2*Sqrt[a]*Sqrt[1 + b/(a*x)]*ArcSinh[Sqrt[b]/(Sqrt[a]*Sqrt[x])])/(Sqrt[b]*Sqrt[a + b/x])","A",1
1783,1,77,52,0.0607993,"\int \frac{1}{\sqrt{a+\frac{b}{x}} x^{5/2}} \, dx","Integrate[1/(Sqrt[a + b/x]*x^(5/2)),x]","\frac{a^{3/2} x^{3/2} \sqrt{\frac{b}{a x}+1} \sinh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{a} \sqrt{x}}\right)-\sqrt{b} (a x+b)}{b^{3/2} x^{3/2} \sqrt{a+\frac{b}{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[b]*(b + a*x)) + a^(3/2)*Sqrt[1 + b/(a*x)]*x^(3/2)*ArcSinh[Sqrt[b]/(Sqrt[a]*Sqrt[x])])/(b^(3/2)*Sqrt[a + b/x]*x^(3/2))","A",1
1784,1,93,83,0.0717426,"\int \frac{1}{\sqrt{a+\frac{b}{x}} x^{7/2}} \, dx","Integrate[1/(Sqrt[a + b/x]*x^(7/2)),x]","\frac{\sqrt{b} \left(3 a^2 x^2+a b x-2 b^2\right)-3 a^{5/2} x^{5/2} \sqrt{\frac{b}{a x}+1} \sinh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{a} \sqrt{x}}\right)}{4 b^{5/2} x^{5/2} \sqrt{a+\frac{b}{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}}",1,"(Sqrt[b]*(-2*b^2 + a*b*x + 3*a^2*x^2) - 3*a^(5/2)*Sqrt[1 + b/(a*x)]*x^(5/2)*ArcSinh[Sqrt[b]/(Sqrt[a]*Sqrt[x])])/(4*b^(5/2)*Sqrt[a + b/x]*x^(5/2))","A",1
1785,1,106,109,0.0820272,"\int \frac{1}{\sqrt{a+\frac{b}{x}} x^{9/2}} \, dx","Integrate[1/(Sqrt[a + b/x]*x^(9/2)),x]","\frac{15 a^{7/2} x^{7/2} \sqrt{\frac{b}{a x}+1} \sinh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{a} \sqrt{x}}\right)-\sqrt{b} \left(15 a^3 x^3+5 a^2 b x^2-2 a b^2 x+8 b^3\right)}{24 b^{7/2} x^{7/2} \sqrt{a+\frac{b}{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^2 \sqrt{a+\frac{b}{x}}}{8 b^3 \sqrt{x}}+\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[b]*(8*b^3 - 2*a*b^2*x + 5*a^2*b*x^2 + 15*a^3*x^3)) + 15*a^(7/2)*Sqrt[1 + b/(a*x)]*x^(7/2)*ArcSinh[Sqrt[b]/(Sqrt[a]*Sqrt[x])])/(24*b^(7/2)*Sqrt[a + b/x]*x^(7/2))","A",1
1786,1,64,126,0.0162568,"\int \frac{x^{5/2}}{\left(a+\frac{b}{x}\right)^{3/2}} \, dx","Integrate[x^(5/2)/(a + b/x)^(3/2),x]","\frac{2 \left(5 a^4 x^4-8 a^3 b x^3+16 a^2 b^2 x^2-64 a b^3 x-128 b^4\right)}{35 a^5 \sqrt{x} \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{32 b^2 x^{3/2}}{35 a^3 \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,"(2*(-128*b^4 - 64*a*b^3*x + 16*a^2*b^2*x^2 - 8*a^3*b*x^3 + 5*a^4*x^4))/(35*a^5*Sqrt[a + b/x]*Sqrt[x])","A",1
1787,1,52,100,0.0137905,"\int \frac{x^{3/2}}{\left(a+\frac{b}{x}\right)^{3/2}} \, dx","Integrate[x^(3/2)/(a + b/x)^(3/2),x]","\frac{2 \left(a^3 x^3-2 a^2 b x^2+8 a b^2 x+16 b^3\right)}{5 a^4 \sqrt{x} \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,"(2*(16*b^3 + 8*a*b^2*x - 2*a^2*b*x^2 + a^3*x^3))/(5*a^4*Sqrt[a + b/x]*Sqrt[x])","A",1
1788,1,41,74,0.011887,"\int \frac{\sqrt{x}}{\left(a+\frac{b}{x}\right)^{3/2}} \, dx","Integrate[Sqrt[x]/(a + b/x)^(3/2),x]","\frac{2 \left(a^2 x^2-4 a b x-8 b^2\right)}{3 a^3 \sqrt{x} \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,"(2*(-8*b^2 - 4*a*b*x + a^2*x^2))/(3*a^3*Sqrt[a + b/x]*Sqrt[x])","A",1
1789,1,28,44,0.0124814,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{3/2} \sqrt{x}} \, dx","Integrate[1/((a + b/x)^(3/2)*Sqrt[x]),x]","\frac{2 (a x+2 b)}{a^2 \sqrt{x} \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,"(2*(2*b + a*x))/(a^2*Sqrt[a + b/x]*Sqrt[x])","A",1
1790,1,21,21,0.0123626,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{3/2} x^{3/2}} \, dx","Integrate[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
1791,1,73,52,0.0861317,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{3/2} x^{5/2}} \, dx","Integrate[1/((a + b/x)^(3/2)*x^(5/2)),x]","\frac{2 \sqrt{b}-2 \sqrt{a} \sqrt{x} \sqrt{\frac{b}{a x}+1} \sinh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{a} \sqrt{x}}\right)}{b^{3/2} \sqrt{x} \sqrt{a+\frac{b}{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}}",1,"(2*Sqrt[b] - 2*Sqrt[a]*Sqrt[1 + b/(a*x)]*Sqrt[x]*ArcSinh[Sqrt[b]/(Sqrt[a]*Sqrt[x])])/(b^(3/2)*Sqrt[a + b/x]*Sqrt[x])","A",1
1792,1,56,74,0.0169844,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{3/2} x^{7/2}} \, dx","Integrate[1/((a + b/x)^(3/2)*x^(7/2)),x]","-\frac{2 \sqrt{\frac{b}{a x}+1} \, _2F_1\left(\frac{3}{2},\frac{5}{2};\frac{7}{2};-\frac{b}{a x}\right)}{5 a x^{5/2} \sqrt{a+\frac{b}{x}}}","\frac{3 a \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)}{b^{5/2}}-\frac{3 \sqrt{a+\frac{b}{x}}}{b^2 \sqrt{x}}+\frac{2}{b x^{3/2} \sqrt{a+\frac{b}{x}}}",1,"(-2*Sqrt[1 + b/(a*x)]*Hypergeometric2F1[3/2, 5/2, 7/2, -(b/(a*x))])/(5*a*Sqrt[a + b/x]*x^(5/2))","C",1
1793,1,56,104,0.0173069,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{3/2} x^{9/2}} \, dx","Integrate[1/((a + b/x)^(3/2)*x^(9/2)),x]","-\frac{2 \sqrt{\frac{b}{a x}+1} \, _2F_1\left(\frac{3}{2},\frac{7}{2};\frac{9}{2};-\frac{b}{a x}\right)}{7 a x^{7/2} \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{15 a \sqrt{a+\frac{b}{x}}}{4 b^3 \sqrt{x}}-\frac{5 \sqrt{a+\frac{b}{x}}}{2 b^2 x^{3/2}}+\frac{2}{b x^{5/2} \sqrt{a+\frac{b}{x}}}",1,"(-2*Sqrt[1 + b/(a*x)]*Hypergeometric2F1[3/2, 7/2, 9/2, -(b/(a*x))])/(7*a*Sqrt[a + b/x]*x^(7/2))","C",1
1794,1,56,130,0.0242246,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{3/2} x^{11/2}} \, dx","Integrate[1/((a + b/x)^(3/2)*x^(11/2)),x]","-\frac{2 \sqrt{\frac{b}{a x}+1} \, _2F_1\left(\frac{3}{2},\frac{9}{2};\frac{11}{2};-\frac{b}{a x}\right)}{9 a x^{9/2} \sqrt{a+\frac{b}{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^2 \sqrt{a+\frac{b}{x}}}{8 b^4 \sqrt{x}}+\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*Sqrt[1 + b/(a*x)]*Hypergeometric2F1[3/2, 9/2, 11/2, -(b/(a*x))])/(9*a*Sqrt[a + b/x]*x^(9/2))","C",1
1795,1,82,152,0.0222893,"\int \frac{x^{5/2}}{\left(a+\frac{b}{x}\right)^{5/2}} \, dx","Integrate[x^(5/2)/(a + b/x)^(5/2),x]","\frac{2 \left(3 a^5 x^5-6 a^4 b x^4+16 a^3 b^2 x^3-96 a^2 b^3 x^2-384 a b^4 x-256 b^5\right)}{21 a^6 \sqrt{x} \sqrt{a+\frac{b}{x}} (a x+b)}","-\frac{512 b^5}{21 a^6 x^{3/2} \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{32 b^2 x^{3/2}}{21 a^3 \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,"(2*(-256*b^5 - 384*a*b^4*x - 96*a^2*b^3*x^2 + 16*a^3*b^2*x^3 - 6*a^4*b*x^4 + 3*a^5*x^5))/(21*a^6*Sqrt[a + b/x]*Sqrt[x]*(b + a*x))","A",1
1796,1,71,126,0.0289168,"\int \frac{x^{3/2}}{\left(a+\frac{b}{x}\right)^{5/2}} \, dx","Integrate[x^(3/2)/(a + b/x)^(5/2),x]","\frac{2 \sqrt{x} \sqrt{a+\frac{b}{x}} \left(3 a^4 x^4-8 a^3 b x^3+48 a^2 b^2 x^2+192 a b^3 x+128 b^4\right)}{15 a^5 (a x+b)^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,"(2*Sqrt[a + b/x]*Sqrt[x]*(128*b^4 + 192*a*b^3*x + 48*a^2*b^2*x^2 - 8*a^3*b*x^3 + 3*a^4*x^4))/(15*a^5*(b + a*x)^2)","A",1
1797,1,59,96,0.017611,"\int \frac{\sqrt{x}}{\left(a+\frac{b}{x}\right)^{5/2}} \, dx","Integrate[Sqrt[x]/(a + b/x)^(5/2),x]","\frac{2 \left(a^3 x^3-6 a^2 b x^2-24 a b^2 x-16 b^3\right)}{3 a^4 \sqrt{x} \sqrt{a+\frac{b}{x}} (a x+b)}","-\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,"(2*(-16*b^3 - 24*a*b^2*x - 6*a^2*b*x^2 + a^3*x^3))/(3*a^4*Sqrt[a + b/x]*Sqrt[x]*(b + a*x))","A",1
1798,1,49,70,0.0285096,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{5/2} \sqrt{x}} \, dx","Integrate[1/((a + b/x)^(5/2)*Sqrt[x]),x]","\frac{2 \sqrt{x} \sqrt{a+\frac{b}{x}} \left(3 a^2 x^2+12 a b x+8 b^2\right)}{3 a^3 (a x+b)^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,"(2*Sqrt[a + b/x]*Sqrt[x]*(8*b^2 + 12*a*b*x + 3*a^2*x^2))/(3*a^3*(b + a*x)^2)","A",1
1799,1,38,46,0.0259462,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{5/2} x^{3/2}} \, dx","Integrate[1/((a + b/x)^(5/2)*x^(3/2)),x]","-\frac{2 \sqrt{x} \sqrt{a+\frac{b}{x}} (3 a x+2 b)}{3 a^2 (a x+b)^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,"(-2*Sqrt[a + b/x]*Sqrt[x]*(2*b + 3*a*x))/(3*a^2*(b + a*x)^2)","A",1
1800,1,23,23,0.0166292,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{5/2} x^{5/2}} \, dx","Integrate[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
1801,1,94,75,0.1790182,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{5/2} x^{7/2}} \, dx","Integrate[1/((a + b/x)^(5/2)*x^(7/2)),x]","\frac{2 \left(\sqrt{b} \sqrt{x} (3 a x+4 b)-3 \sqrt{a} x \sqrt{\frac{b}{a x}+1} (a x+b) \sinh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{a} \sqrt{x}}\right)\right)}{3 b^{5/2} x \sqrt{a+\frac{b}{x}} (a x+b)}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)}{b^{5/2}}+\frac{2}{b^2 \sqrt{x} \sqrt{a+\frac{b}{x}}}+\frac{2}{3 b x^{3/2} \left(a+\frac{b}{x}\right)^{3/2}}",1,"(2*(Sqrt[b]*Sqrt[x]*(4*b + 3*a*x) - 3*Sqrt[a]*Sqrt[1 + b/(a*x)]*x*(b + a*x)*ArcSinh[Sqrt[b]/(Sqrt[a]*Sqrt[x])]))/(3*b^(5/2)*Sqrt[a + b/x]*x*(b + a*x))","A",1
1802,1,56,99,0.0186477,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{5/2} x^{9/2}} \, dx","Integrate[1/((a + b/x)^(5/2)*x^(9/2)),x]","-\frac{2 \sqrt{\frac{b}{a x}+1} \, _2F_1\left(\frac{5}{2},\frac{7}{2};\frac{9}{2};-\frac{b}{a x}\right)}{7 a^2 x^{7/2} \sqrt{a+\frac{b}{x}}}","\frac{5 a \tanh ^{-1}\left(\frac{\sqrt{b}}{\sqrt{x} \sqrt{a+\frac{b}{x}}}\right)}{b^{7/2}}-\frac{5 \sqrt{a+\frac{b}{x}}}{b^3 \sqrt{x}}+\frac{10}{3 b^2 x^{3/2} \sqrt{a+\frac{b}{x}}}+\frac{2}{3 b x^{5/2} \left(a+\frac{b}{x}\right)^{3/2}}",1,"(-2*Sqrt[1 + b/(a*x)]*Hypergeometric2F1[5/2, 7/2, 9/2, -(b/(a*x))])/(7*a^2*Sqrt[a + b/x]*x^(7/2))","C",1
1803,1,56,129,0.0180441,"\int \frac{1}{\left(a+\frac{b}{x}\right)^{5/2} x^{11/2}} \, dx","Integrate[1/((a + b/x)^(5/2)*x^(11/2)),x]","-\frac{2 \sqrt{\frac{b}{a x}+1} \, _2F_1\left(\frac{5}{2},\frac{9}{2};\frac{11}{2};-\frac{b}{a x}\right)}{9 a^2 x^{9/2} \sqrt{a+\frac{b}{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 a \sqrt{a+\frac{b}{x}}}{4 b^4 \sqrt{x}}-\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{2}{3 b x^{7/2} \left(a+\frac{b}{x}\right)^{3/2}}",1,"(-2*Sqrt[1 + b/(a*x)]*Hypergeometric2F1[5/2, 9/2, 11/2, -(b/(a*x))])/(9*a^2*Sqrt[a + b/x]*x^(9/2))","C",1
1804,1,17,17,0.001533,"\int \left(a+\frac{b}{x^2}\right) x^6 \, dx","Integrate[(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",1
1805,1,17,17,0.0012288,"\int \left(a+\frac{b}{x^2}\right) x^5 \, dx","Integrate[(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",1
1806,1,17,17,0.0011937,"\int \left(a+\frac{b}{x^2}\right) x^4 \, dx","Integrate[(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",1
1807,1,17,17,0.0011199,"\int \left(a+\frac{b}{x^2}\right) x^3 \, dx","Integrate[(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",1
1808,1,12,12,0.0004958,"\int \left(a+\frac{b}{x^2}\right) x^2 \, dx","Integrate[(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",1
1809,1,13,13,0.0028083,"\int \left(a+\frac{b}{x^2}\right) x \, dx","Integrate[(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",1
1810,1,10,10,0.000234,"\int \left(a+\frac{b}{x^2}\right) \, dx","Integrate[a + b/x^2,x]","a x-\frac{b}{x}","a x-\frac{b}{x}",1,"-(b/x) + a*x","A",1
1811,1,13,13,0.0024087,"\int \frac{a+\frac{b}{x^2}}{x} \, dx","Integrate[(a + b/x^2)/x,x]","a \log (x)-\frac{b}{2 x^2}","a \log (x)-\frac{b}{2 x^2}",1,"-1/2*b/x^2 + a*Log[x]","A",1
1812,1,15,15,0.0020463,"\int \frac{a+\frac{b}{x^2}}{x^2} \, dx","Integrate[(a + b/x^2)/x^2,x]","-\frac{a}{x}-\frac{b}{3 x^3}","-\frac{a}{x}-\frac{b}{3 x^3}",1,"-1/3*b/x^3 - a/x","A",1
1813,1,17,17,0.0020615,"\int \frac{a+\frac{b}{x^2}}{x^3} \, dx","Integrate[(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,"-1/4*b/x^4 - a/(2*x^2)","A",1
1814,1,17,17,0.002091,"\int \frac{a+\frac{b}{x^2}}{x^4} \, dx","Integrate[(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,"-1/5*b/x^5 - a/(3*x^3)","A",1
1815,1,17,17,0.0021055,"\int \frac{a+\frac{b}{x^2}}{x^5} \, dx","Integrate[(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,"-1/6*b/x^6 - a/(4*x^4)","A",1
1816,1,17,17,0.0021917,"\int \frac{a+\frac{b}{x^2}}{x^6} \, dx","Integrate[(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,"-1/7*b/x^7 - a/(5*x^5)","A",1
1817,1,30,30,0.0012475,"\int \left(a+\frac{b}{x^2}\right)^2 x^6 \, dx","Integrate[(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",1
1818,1,16,16,0.0019869,"\int \left(a+\frac{b}{x^2}\right)^2 x^5 \, dx","Integrate[(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",1
1819,1,25,25,0.0011345,"\int \left(a+\frac{b}{x^2}\right)^2 x^4 \, dx","Integrate[(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",1
1820,1,23,23,0.001193,"\int \left(a+\frac{b}{x^2}\right)^2 x^3 \, dx","Integrate[(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",1
1821,1,24,24,0.0010301,"\int \left(a+\frac{b}{x^2}\right)^2 x^2 \, dx","Integrate[(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",1
1822,1,27,27,0.0047208,"\int \left(a+\frac{b}{x^2}\right)^2 x \, dx","Integrate[(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,"-1/2*b^2/x^2 + (a^2*x^2)/2 + 2*a*b*Log[x]","A",1
1823,1,23,23,0.0047662,"\int \left(a+\frac{b}{x^2}\right)^2 \, dx","Integrate[(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,"-1/3*b^2/x^3 - (2*a*b)/x + a^2*x","A",1
1824,1,24,24,0.0009287,"\int \frac{\left(a+\frac{b}{x^2}\right)^2}{x} \, dx","Integrate[(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,"-1/4*b^2/x^4 - (a*b)/x^2 + a^2*Log[x]","A",1
1825,1,28,28,0.0008604,"\int \frac{\left(a+\frac{b}{x^2}\right)^2}{x^2} \, dx","Integrate[(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,"-1/5*b^2/x^5 - (2*a*b)/(3*x^3) - a^2/x","A",1
1826,1,30,16,0.0009137,"\int \frac{\left(a+\frac{b}{x^2}\right)^2}{x^3} \, dx","Integrate[(a + b/x^2)^2/x^3,x]","-\frac{a^2}{2 x^2}-\frac{a b}{2 x^4}-\frac{b^2}{6 x^6}","-\frac{\left(a+\frac{b}{x^2}\right)^3}{6 b}",1,"-1/6*b^2/x^6 - (a*b)/(2*x^4) - a^2/(2*x^2)","A",1
1827,1,30,30,0.0009205,"\int \frac{\left(a+\frac{b}{x^2}\right)^2}{x^4} \, dx","Integrate[(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,"-1/7*b^2/x^7 - (2*a*b)/(5*x^5) - a^2/(3*x^3)","A",1
1828,1,30,30,0.0009267,"\int \frac{\left(a+\frac{b}{x^2}\right)^2}{x^5} \, dx","Integrate[(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,"-1/8*b^2/x^8 - (a*b)/(3*x^6) - a^2/(4*x^4)","A",1
1829,1,30,30,0.0011213,"\int \frac{\left(a+\frac{b}{x^2}\right)^2}{x^6} \, dx","Integrate[(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,"-1/9*b^2/x^9 - (2*a*b)/(7*x^7) - a^2/(5*x^5)","A",1
1830,1,35,35,0.0011663,"\int \left(a+\frac{b}{x^2}\right)^3 x^6 \, dx","Integrate[(a + b/x^2)^3*x^6,x]","\frac{a^3 x^7}{7}+\frac{3}{5} a^2 b x^5+a b^2 x^3+b^3 x","\frac{a^3 x^7}{7}+\frac{3}{5} a^2 b x^5+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",1
1831,1,39,39,0.0044169,"\int \left(a+\frac{b}{x^2}\right)^3 x^5 \, dx","Integrate[(a + b/x^2)^3*x^5,x]","\frac{a^3 x^6}{6}+\frac{3}{4} a^2 b x^4+\frac{3}{2} a b^2 x^2+b^3 \log (x)","\frac{a^3 x^6}{6}+\frac{3}{4} a^2 b x^4+\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",1
1832,1,34,34,0.0039934,"\int \left(a+\frac{b}{x^2}\right)^3 x^4 \, dx","Integrate[(a + b/x^2)^3*x^4,x]","\frac{a^3 x^5}{5}+a^2 b x^3+3 a b^2 x-\frac{b^3}{x}","\frac{a^3 x^5}{5}+a^2 b x^3+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",1
1833,1,40,40,0.0074216,"\int \left(a+\frac{b}{x^2}\right)^3 x^3 \, dx","Integrate[(a + b/x^2)^3*x^3,x]","\frac{a^3 x^4}{4}+\frac{3}{2} a^2 b x^2+3 a b^2 \log (x)-\frac{b^3}{2 x^2}","\frac{a^3 x^4}{4}+\frac{3}{2} a^2 b x^2+3 a b^2 \log (x)-\frac{b^3}{2 x^2}",1,"-1/2*b^3/x^2 + (3*a^2*b*x^2)/2 + (a^3*x^4)/4 + 3*a*b^2*Log[x]","A",1
1834,1,37,37,0.0043555,"\int \left(a+\frac{b}{x^2}\right)^3 x^2 \, dx","Integrate[(a + b/x^2)^3*x^2,x]","\frac{a^3 x^3}{3}+3 a^2 b x-\frac{3 a b^2}{x}-\frac{b^3}{3 x^3}","\frac{a^3 x^3}{3}+3 a^2 b x-\frac{3 a b^2}{x}-\frac{b^3}{3 x^3}",1,"-1/3*b^3/x^3 - (3*a*b^2)/x + 3*a^2*b*x + (a^3*x^3)/3","A",1
1835,1,40,40,0.0051475,"\int \left(a+\frac{b}{x^2}\right)^3 x \, dx","Integrate[(a + b/x^2)^3*x,x]","\frac{a^3 x^2}{2}+3 a^2 b \log (x)-\frac{3 a b^2}{2 x^2}-\frac{b^3}{4 x^4}","\frac{a^3 x^2}{2}+3 a^2 b \log (x)-\frac{3 a b^2}{2 x^2}-\frac{b^3}{4 x^4}",1,"-1/4*b^3/x^4 - (3*a*b^2)/(2*x^2) + (a^3*x^2)/2 + 3*a^2*b*Log[x]","A",1
1836,1,34,34,0.0052596,"\int \left(a+\frac{b}{x^2}\right)^3 \, dx","Integrate[(a + b/x^2)^3,x]","a^3 x-\frac{3 a^2 b}{x}-\frac{a b^2}{x^3}-\frac{b^3}{5 x^5}","a^3 x-\frac{3 a^2 b}{x}-\frac{a b^2}{x^3}-\frac{b^3}{5 x^5}",1,"-1/5*b^3/x^5 - (a*b^2)/x^3 - (3*a^2*b)/x + a^3*x","A",1
1837,1,39,39,0.0044099,"\int \frac{\left(a+\frac{b}{x^2}\right)^3}{x} \, dx","Integrate[(a + b/x^2)^3/x,x]","a^3 \log (x)-\frac{3 a^2 b}{2 x^2}-\frac{3 a b^2}{4 x^4}-\frac{b^3}{6 x^6}","a^3 \log (x)-\frac{3 a^2 b}{2 x^2}-\frac{3 a b^2}{4 x^4}-\frac{b^3}{6 x^6}",1,"-1/6*b^3/x^6 - (3*a*b^2)/(4*x^4) - (3*a^2*b)/(2*x^2) + a^3*Log[x]","A",1
1838,1,39,39,0.0041408,"\int \frac{\left(a+\frac{b}{x^2}\right)^3}{x^2} \, dx","Integrate[(a + b/x^2)^3/x^2,x]","-\frac{a^3}{x}-\frac{a^2 b}{x^3}-\frac{3 a b^2}{5 x^5}-\frac{b^3}{7 x^7}","-\frac{a^3}{x}-\frac{a^2 b}{x^3}-\frac{3 a b^2}{5 x^5}-\frac{b^3}{7 x^7}",1,"-1/7*b^3/x^7 - (3*a*b^2)/(5*x^5) - (a^2*b)/x^3 - a^3/x","A",1
1839,1,43,16,0.0068522,"\int \frac{\left(a+\frac{b}{x^2}\right)^3}{x^3} \, dx","Integrate[(a + b/x^2)^3/x^3,x]","-\frac{a^3}{2 x^2}-\frac{3 a^2 b}{4 x^4}-\frac{a b^2}{2 x^6}-\frac{b^3}{8 x^8}","-\frac{\left(a+\frac{b}{x^2}\right)^4}{8 b}",1,"-1/8*b^3/x^8 - (a*b^2)/(2*x^6) - (3*a^2*b)/(4*x^4) - a^3/(2*x^2)","B",1
1840,1,43,43,0.0043581,"\int \frac{\left(a+\frac{b}{x^2}\right)^3}{x^4} \, dx","Integrate[(a + b/x^2)^3/x^4,x]","-\frac{a^3}{3 x^3}-\frac{3 a^2 b}{5 x^5}-\frac{3 a b^2}{7 x^7}-\frac{b^3}{9 x^9}","-\frac{a^3}{3 x^3}-\frac{3 a^2 b}{5 x^5}-\frac{3 a b^2}{7 x^7}-\frac{b^3}{9 x^9}",1,"-1/9*b^3/x^9 - (3*a*b^2)/(7*x^7) - (3*a^2*b)/(5*x^5) - a^3/(3*x^3)","A",1
1841,1,43,40,0.004745,"\int \frac{\left(a+\frac{b}{x^2}\right)^3}{x^5} \, dx","Integrate[(a + b/x^2)^3/x^5,x]","-\frac{a^3}{4 x^4}-\frac{a^2 b}{2 x^6}-\frac{3 a b^2}{8 x^8}-\frac{b^3}{10 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,"-1/10*b^3/x^10 - (3*a*b^2)/(8*x^8) - (a^2*b)/(2*x^6) - a^3/(4*x^4)","A",1
1842,1,43,43,0.0075242,"\int \frac{\left(a+\frac{b}{x^2}\right)^3}{x^6} \, dx","Integrate[(a + b/x^2)^3/x^6,x]","-\frac{a^3}{5 x^5}-\frac{3 a^2 b}{7 x^7}-\frac{a b^2}{3 x^9}-\frac{b^3}{11 x^{11}}","-\frac{a^3}{5 x^5}-\frac{3 a^2 b}{7 x^7}-\frac{a b^2}{3 x^9}-\frac{b^3}{11 x^{11}}",1,"-1/11*b^3/x^11 - (a*b^2)/(3*x^9) - (3*a^2*b)/(7*x^7) - a^3/(5*x^5)","A",1
1843,1,68,68,0.0277524,"\int \frac{x^6}{a+\frac{b}{x^2}} \, dx","Integrate[x^6/(a + b/x^2),x]","\frac{b^{7/2} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{a^{9/2}}-\frac{b^3 x}{a^4}+\frac{b^2 x^3}{3 a^3}-\frac{b x^5}{5 a^2}+\frac{x^7}{7 a}","\frac{b^{7/2} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{a^{9/2}}-\frac{b^3 x}{a^4}+\frac{b^2 x^3}{3 a^3}-\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",1
1844,1,53,53,0.0058252,"\int \frac{x^5}{a+\frac{b}{x^2}} \, dx","Integrate[x^5/(a + b/x^2),x]","-\frac{b^3 \log \left(a x^2+b\right)}{2 a^4}+\frac{b^2 x^2}{2 a^3}-\frac{b x^4}{4 a^2}+\frac{x^6}{6 a}","-\frac{b^3 \log \left(a x^2+b\right)}{2 a^4}+\frac{b^2 x^2}{2 a^3}-\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",1
1845,1,55,55,0.0252403,"\int \frac{x^4}{a+\frac{b}{x^2}} \, dx","Integrate[x^4/(a + b/x^2),x]","-\frac{b^{5/2} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{a^{7/2}}+\frac{b^2 x}{a^3}-\frac{b x^3}{3 a^2}+\frac{x^5}{5 a}","-\frac{b^{5/2} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{a^{7/2}}+\frac{b^2 x}{a^3}-\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",1
1846,1,40,40,0.005866,"\int \frac{x^3}{a+\frac{b}{x^2}} \, dx","Integrate[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,"-1/2*(b*x^2)/a^2 + x^4/(4*a) + (b^2*Log[b + a*x^2])/(2*a^3)","A",1
1847,1,42,42,0.0218394,"\int \frac{x^2}{a+\frac{b}{x^2}} \, dx","Integrate[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",1
1848,1,27,27,0.0051293,"\int \frac{x}{a+\frac{b}{x^2}} \, dx","Integrate[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",1
1849,1,31,31,0.0087061,"\int \frac{1}{a+\frac{b}{x^2}} \, dx","Integrate[(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",1
1850,1,15,15,0.0026962,"\int \frac{1}{\left(a+\frac{b}{x^2}\right) x} \, dx","Integrate[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",1
1851,1,24,24,0.0046648,"\int \frac{1}{\left(a+\frac{b}{x^2}\right) x^2} \, dx","Integrate[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",1
1852,1,22,15,0.0057669,"\int \frac{1}{\left(a+\frac{b}{x^2}\right) x^3} \, dx","Integrate[1/((a + b/x^2)*x^3),x]","\frac{\log (x)}{b}-\frac{\log \left(a x^2+b\right)}{2 b}","-\frac{\log \left(a+\frac{b}{x^2}\right)}{2 b}",1,"Log[x]/b - Log[b + a*x^2]/(2*b)","A",1
1853,1,34,34,0.0134745,"\int \frac{1}{\left(a+\frac{b}{x^2}\right) x^4} \, dx","Integrate[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",1
1854,1,35,35,0.0072112,"\int \frac{1}{\left(a+\frac{b}{x^2}\right) x^5} \, dx","Integrate[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*1/(b*x^2) - (a*Log[x])/b^2 + (a*Log[b + a*x^2])/(2*b^2)","A",1
1855,1,43,43,0.0230459,"\int \frac{1}{\left(a+\frac{b}{x^2}\right) x^6} \, dx","Integrate[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*1/(b*x^3) + a/(b^2*x) + (a^(3/2)*ArcTan[(Sqrt[a]*x)/Sqrt[b]])/b^(5/2)","A",1
1856,1,49,49,0.0078658,"\int \frac{1}{\left(a+\frac{b}{x^2}\right) x^7} \, dx","Integrate[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*1/(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",1
1857,1,58,58,0.0271178,"\int \frac{1}{\left(a+\frac{b}{x^2}\right) x^8} \, dx","Integrate[1/((a + b/x^2)*x^8),x]","-\frac{a^{5/2} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{b^{7/2}}-\frac{a^2}{b^3 x}+\frac{a}{3 b^2 x^3}-\frac{1}{5 b x^5}","-\frac{a^{5/2} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{b^{7/2}}-\frac{a^2}{b^3 x}+\frac{a}{3 b^2 x^3}-\frac{1}{5 b x^5}",1,"-1/5*1/(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",1
1858,1,82,92,0.0581262,"\int \frac{x^6}{\left(a+\frac{b}{x^2}\right)^2} \, dx","Integrate[x^6/(a + b/x^2)^2,x]","\frac{9 b^{7/2} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{2 a^{11/2}}+\frac{x \left(10 a^3 x^6-28 a^2 b x^4-\frac{35 b^4}{a x^2+b}+70 a b^2 x^2-280 b^3\right)}{70 a^5}","\frac{9 b^{7/2} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{2 a^{11/2}}-\frac{9 b^3 x}{2 a^5}+\frac{3 b^2 x^3}{2 a^4}-\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,"(x*(-280*b^3 + 70*a*b^2*x^2 - 28*a^2*b*x^4 + 10*a^3*x^6 - (35*b^4)/(b + a*x^2)))/(70*a^5) + (9*b^(7/2)*ArcTan[(Sqrt[a]*x)/Sqrt[b]])/(2*a^(11/2))","A",1
1859,1,60,70,0.0226318,"\int \frac{x^5}{\left(a+\frac{b}{x^2}\right)^2} \, dx","Integrate[x^5/(a + b/x^2)^2,x]","\frac{a^3 x^6-3 a^2 b x^4-\frac{3 b^4}{a x^2+b}-12 b^3 \log \left(a x^2+b\right)+9 a b^2 x^2}{6 a^5}","-\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{3 b^2 x^2}{2 a^4}-\frac{b x^4}{2 a^3}+\frac{x^6}{6 a^2}",1,"(9*a*b^2*x^2 - 3*a^2*b*x^4 + a^3*x^6 - (3*b^4)/(b + a*x^2) - 12*b^3*Log[b + a*x^2])/(6*a^5)","A",1
1860,1,71,79,0.0515683,"\int \frac{x^4}{\left(a+\frac{b}{x^2}\right)^2} \, dx","Integrate[x^4/(a + b/x^2)^2,x]","\frac{x \left(6 a^2 x^4+\frac{15 b^3}{a x^2+b}-20 a b x^2+90 b^2\right)}{30 a^4}-\frac{7 b^{5/2} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{2 a^{9/2}}","-\frac{7 b^{5/2} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{2 a^{9/2}}+\frac{7 b^2 x}{2 a^4}-\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,"(x*(90*b^2 - 20*a*b*x^2 + 6*a^2*x^4 + (15*b^3)/(b + a*x^2)))/(30*a^4) - (7*b^(5/2)*ArcTan[(Sqrt[a]*x)/Sqrt[b]])/(2*a^(9/2))","A",1
1861,1,49,57,0.0171348,"\int \frac{x^3}{\left(a+\frac{b}{x^2}\right)^2} \, dx","Integrate[x^3/(a + b/x^2)^2,x]","\frac{a^2 x^4+\frac{2 b^3}{a x^2+b}+6 b^2 \log \left(a x^2+b\right)-4 a b x^2}{4 a^4}","\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,"(-4*a*b*x^2 + a^2*x^4 + (2*b^3)/(b + a*x^2) + 6*b^2*Log[b + a*x^2])/(4*a^4)","A",1
1862,1,60,66,0.0461564,"\int \frac{x^2}{\left(a+\frac{b}{x^2}\right)^2} \, dx","Integrate[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{x \left(-\frac{3 b^2}{a x^2+b}+2 a x^2-12 b\right)}{6 a^3}","\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,"(x*(-12*b + 2*a*x^2 - (3*b^2)/(b + a*x^2)))/(6*a^3) + (5*b^(3/2)*ArcTan[(Sqrt[a]*x)/Sqrt[b]])/(2*a^(7/2))","A",1
1863,1,38,44,0.0190142,"\int \frac{x}{\left(a+\frac{b}{x^2}\right)^2} \, dx","Integrate[x/(a + b/x^2)^2,x]","\frac{-\frac{b^2}{a x^2+b}-2 b \log \left(a x^2+b\right)+a x^2}{2 a^3}","-\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,"(a*x^2 - b^2/(b + a*x^2) - 2*b*Log[b + a*x^2])/(2*a^3)","A",1
1864,1,51,55,0.0340318,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^2} \, dx","Integrate[(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{b x}{2 a^2 \left(a x^2+b\right)}+\frac{x}{a^2}","-\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,"x/a^2 + (b*x)/(2*a^2*(b + a*x^2)) - (3*Sqrt[b]*ArcTan[(Sqrt[a]*x)/Sqrt[b]])/(2*a^(5/2))","A",1
1865,1,27,33,0.00856,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^2 x} \, dx","Integrate[1/((a + b/x^2)^2*x),x]","\frac{\frac{b}{a x^2+b}+\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/(b + a*x^2) + Log[b + a*x^2])/(2*a^2)","A",1
1866,1,45,45,0.0230883,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^2 x^2} \, dx","Integrate[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,"-1/2*x/(a*(b + a*x^2)) + ArcTan[(Sqrt[a]*x)/Sqrt[b]]/(2*a^(3/2)*Sqrt[b])","A",1
1867,1,16,16,0.0024866,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^2 x^3} \, dx","Integrate[1/((a + b/x^2)^2*x^3),x]","-\frac{1}{2 a \left(a x^2+b\right)}","\frac{1}{2 b \left(a+\frac{b}{x^2}\right)}",1,"-1/2*1/(a*(b + a*x^2))","A",1
1868,1,45,45,0.0270134,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^2 x^4} \, dx","Integrate[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",1
1869,1,33,38,0.0168727,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^2 x^5} \, dx","Integrate[1/((a + b/x^2)^2*x^5),x]","\frac{\frac{b}{a x^2+b}-\log \left(a x^2+b\right)+2 \log (x)}{2 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,"(b/(b + a*x^2) + 2*Log[x] - Log[b + a*x^2])/(2*b^2)","A",1
1870,1,54,57,0.0449977,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^2 x^6} \, dx","Integrate[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{a x}{2 b^2 \left(a x^2+b\right)}-\frac{1}{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,"-(1/(b^2*x)) - (a*x)/(2*b^2*(b + a*x^2)) - (3*Sqrt[a]*ArcTan[(Sqrt[a]*x)/Sqrt[b]])/(2*b^(5/2))","A",1
1871,1,41,49,0.0426854,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^2 x^7} \, dx","Integrate[1/((a + b/x^2)^2*x^7),x]","-\frac{b \left(\frac{a}{a x^2+b}+\frac{1}{x^2}\right)-2 a \log \left(a x^2+b\right)+4 a \log (x)}{2 b^3}","\frac{a \log \left(a x^2+b\right)}{b^3}-\frac{2 a \log (x)}{b^3}-\frac{a}{2 b^2 \left(a x^2+b\right)}-\frac{1}{2 b^2 x^2}",1,"-1/2*(b*(x^(-2) + a/(b + a*x^2)) + 4*a*Log[x] - 2*a*Log[b + a*x^2])/b^3","A",1
1872,1,67,68,0.05443,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^2 x^8} \, dx","Integrate[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{a^2 x}{2 b^3 \left(a x^2+b\right)}+\frac{2 a}{b^3 x}-\frac{1}{3 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,"-1/3*1/(b^2*x^3) + (2*a)/(b^3*x) + (a^2*x)/(2*b^3*(b + a*x^2)) + (5*a^(3/2)*ArcTan[(Sqrt[a]*x)/Sqrt[b]])/(2*b^(7/2))","A",1
1873,1,57,66,0.0587987,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^2 x^9} \, dx","Integrate[1/((a + b/x^2)^2*x^9),x]","\frac{-6 a^2 \log \left(a x^2+b\right)+b \left(\frac{2 a^2}{a x^2+b}+\frac{4 a}{x^2}-\frac{b}{x^4}\right)+12 a^2 \log (x)}{4 b^4}","-\frac{3 a^2 \log \left(a x^2+b\right)}{2 b^4}+\frac{3 a^2 \log (x)}{b^4}+\frac{a^2}{2 b^3 \left(a x^2+b\right)}+\frac{a}{b^3 x^2}-\frac{1}{4 b^2 x^4}",1,"(b*(-(b/x^4) + (4*a)/x^2 + (2*a^2)/(b + a*x^2)) + 12*a^2*Log[x] - 6*a^2*Log[b + a*x^2])/(4*b^4)","A",1
1874,1,71,87,0.0743037,"\int \frac{x^5}{\left(a+\frac{b}{x^2}\right)^3} \, dx","Integrate[x^5/(a + b/x^2)^3,x]","\frac{2 a^3 x^6-9 a^2 b x^4-\frac{3 b^4 \left(10 a x^2+9 b\right)}{\left(a x^2+b\right)^2}-60 b^3 \log \left(a x^2+b\right)+36 a b^2 x^2}{12 a^6}","\frac{b^5}{4 a^6 \left(a x^2+b\right)^2}-\frac{5 b^4}{2 a^6 \left(a x^2+b\right)}-\frac{5 b^3 \log \left(a x^2+b\right)}{a^6}+\frac{3 b^2 x^2}{a^5}-\frac{3 b x^4}{4 a^4}+\frac{x^6}{6 a^3}",1,"(36*a*b^2*x^2 - 9*a^2*b*x^4 + 2*a^3*x^6 - (3*b^4*(9*b + 10*a*x^2))/(b + a*x^2)^2 - 60*b^3*Log[b + a*x^2])/(12*a^6)","A",1
1875,1,88,98,0.0509198,"\int \frac{x^4}{\left(a+\frac{b}{x^2}\right)^3} \, dx","Integrate[x^4/(a + b/x^2)^3,x]","\frac{8 a^4 x^9-24 a^3 b x^7+168 a^2 b^2 x^5+525 a b^3 x^3+315 b^4 x}{40 a^5 \left(a x^2+b\right)^2}-\frac{63 b^{5/2} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{8 a^{11/2}}","-\frac{63 b^{5/2} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{8 a^{11/2}}+\frac{63 b^2 x}{8 a^5}-\frac{21 b x^3}{8 a^4}+\frac{63 x^5}{40 a^3}-\frac{9 x^7}{8 a^2 \left(a x^2+b\right)}-\frac{x^9}{4 a \left(a x^2+b\right)^2}",1,"(315*b^4*x + 525*a*b^3*x^3 + 168*a^2*b^2*x^5 - 24*a^3*b*x^7 + 8*a^4*x^9)/(40*a^5*(b + a*x^2)^2) - (63*b^(5/2)*ArcTan[(Sqrt[a]*x)/Sqrt[b]])/(8*a^(11/2))","A",1
1876,1,58,74,0.0457857,"\int \frac{x^3}{\left(a+\frac{b}{x^2}\right)^3} \, dx","Integrate[x^3/(a + b/x^2)^3,x]","\frac{a^2 x^4+\frac{b^3 \left(8 a x^2+7 b\right)}{\left(a x^2+b\right)^2}+12 b^2 \log \left(a x^2+b\right)-6 a b x^2}{4 a^5}","-\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,"(-6*a*b*x^2 + a^2*x^4 + (b^3*(7*b + 8*a*x^2))/(b + a*x^2)^2 + 12*b^2*Log[b + a*x^2])/(4*a^5)","A",1
1877,1,77,85,0.0474802,"\int \frac{x^2}{\left(a+\frac{b}{x^2}\right)^3} \, dx","Integrate[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{-8 a^3 x^7+56 a^2 b x^5+175 a b^2 x^3+105 b^3 x}{24 a^4 \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{35 b x}{8 a^4}+\frac{35 x^3}{24 a^3}-\frac{7 x^5}{8 a^2 \left(a x^2+b\right)}-\frac{x^7}{4 a \left(a x^2+b\right)^2}",1,"-1/24*(105*b^3*x + 175*a*b^2*x^3 + 56*a^2*b*x^5 - 8*a^3*x^7)/(a^4*(b + a*x^2)^2) + (35*b^(3/2)*ArcTan[(Sqrt[a]*x)/Sqrt[b]])/(8*a^(9/2))","A",1
1878,1,48,65,0.0667064,"\int \frac{x}{\left(a+\frac{b}{x^2}\right)^3} \, dx","Integrate[x/(a + b/x^2)^3,x]","-\frac{\frac{b^2 \left(6 a x^2+5 b\right)}{\left(a x^2+b\right)^2}+6 b \log \left(a x^2+b\right)-2 a x^2}{4 a^4}","\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,"-1/4*(-2*a*x^2 + (b^2*(5*b + 6*a*x^2))/(b + a*x^2)^2 + 6*b*Log[b + a*x^2])/a^4","A",1
1879,1,66,74,0.0467609,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^3} \, dx","Integrate[(a + b/x^2)^(-3),x]","\frac{8 a^2 x^5+25 a b x^3+15 b^2 x}{8 a^3 \left(a x^2+b\right)^2}-\frac{15 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{8 a^{7/2}}","-\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{5 x^3}{8 a^2 \left(a x^2+b\right)}-\frac{x^5}{4 a \left(a x^2+b\right)^2}",1,"(15*b^2*x + 25*a*b*x^3 + 8*a^2*x^5)/(8*a^3*(b + a*x^2)^2) - (15*Sqrt[b]*ArcTan[(Sqrt[a]*x)/Sqrt[b]])/(8*a^(7/2))","A",1
1880,1,39,49,0.0161449,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^3 x} \, dx","Integrate[1/((a + b/x^2)^3*x),x]","\frac{\frac{b \left(4 a x^2+3 b\right)}{\left(a x^2+b\right)^2}+2 \log \left(a x^2+b\right)}{4 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*(3*b + 4*a*x^2))/(b + a*x^2)^2 + 2*Log[b + a*x^2])/(4*a^3)","A",1
1881,1,55,64,0.0431556,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^3 x^2} \, dx","Integrate[1/((a + b/x^2)^3*x^2),x]","\frac{3 \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{8 a^{5/2} \sqrt{b}}-\frac{5 a x^3+3 b x}{8 a^2 \left(a x^2+b\right)^2}","\frac{3 \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{8 a^{5/2} \sqrt{b}}-\frac{3 x}{8 a^2 \left(a x^2+b\right)}-\frac{x^3}{4 a \left(a x^2+b\right)^2}",1,"-1/8*(3*b*x + 5*a*x^3)/(a^2*(b + a*x^2)^2) + (3*ArcTan[(Sqrt[a]*x)/Sqrt[b]])/(8*a^(5/2)*Sqrt[b])","A",1
1882,1,24,16,0.0065226,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^3 x^3} \, dx","Integrate[1/((a + b/x^2)^3*x^3),x]","-\frac{2 a x^2+b}{4 a^2 \left(a x^2+b\right)^2}","\frac{1}{4 b \left(a+\frac{b}{x^2}\right)^2}",1,"-1/4*(b + 2*a*x^2)/(a^2*(b + a*x^2)^2)","A",1
1883,1,58,65,0.0308866,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^3 x^4} \, dx","Integrate[1/((a + b/x^2)^3*x^4),x]","\frac{\frac{\sqrt{a} \sqrt{b} x \left(a x^2-b\right)}{\left(a x^2+b\right)^2}+\tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{8 a^{3/2} b^{3/2}}","\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,"((Sqrt[a]*Sqrt[b]*x*(-b + a*x^2))/(b + a*x^2)^2 + ArcTan[(Sqrt[a]*x)/Sqrt[b]])/(8*a^(3/2)*b^(3/2))","A",1
1884,1,16,16,0.002399,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^3 x^5} \, dx","Integrate[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*1/(a*(b + a*x^2)^2)","A",1
1885,1,55,62,0.0478399,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^3 x^6} \, dx","Integrate[1/((a + b/x^2)^3*x^6),x]","\frac{3 \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{8 \sqrt{a} b^{5/2}}+\frac{3 a x^3+5 b x}{8 b^2 \left(a x^2+b\right)^2}","\frac{3 \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{8 \sqrt{a} b^{5/2}}+\frac{3 x}{8 b^2 \left(a x^2+b\right)}+\frac{x}{4 b \left(a x^2+b\right)^2}",1,"(5*b*x + 3*a*x^3)/(8*b^2*(b + a*x^2)^2) + (3*ArcTan[(Sqrt[a]*x)/Sqrt[b]])/(8*Sqrt[a]*b^(5/2))","A",1
1886,1,43,54,0.0359722,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^3 x^7} \, dx","Integrate[1/((a + b/x^2)^3*x^7),x]","\frac{\frac{b \left(2 a x^2+3 b\right)}{\left(a x^2+b\right)^2}-2 \log \left(a x^2+b\right)+4 \log (x)}{4 b^3}","-\frac{\log \left(a x^2+b\right)}{2 b^3}+\frac{1}{2 b^2 \left(a x^2+b\right)}+\frac{1}{4 b \left(a x^2+b\right)^2}+\frac{\log (x)}{b^3}",1,"((b*(3*b + 2*a*x^2))/(b + a*x^2)^2 + 4*Log[x] - 2*Log[b + a*x^2])/(4*b^3)","A",1
1887,1,68,76,0.0430282,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^3 x^8} \, dx","Integrate[1/((a + b/x^2)^3*x^8),x]","-\frac{15 a^2 x^4+25 a b x^2+8 b^2}{8 b^3 x \left(a x^2+b\right)^2}-\frac{15 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{8 b^{7/2}}","-\frac{15 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{8 b^{7/2}}+\frac{5}{8 b^2 x \left(a x^2+b\right)}+\frac{1}{4 b x \left(a x^2+b\right)^2}-\frac{15}{8 b^3 x}",1,"-1/8*(8*b^2 + 25*a*b*x^2 + 15*a^2*x^4)/(b^3*x*(b + a*x^2)^2) - (15*Sqrt[a]*ArcTan[(Sqrt[a]*x)/Sqrt[b]])/(8*b^(7/2))","A",1
1888,1,59,67,0.0596577,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^3 x^9} \, dx","Integrate[1/((a + b/x^2)^3*x^9),x]","-\frac{\frac{b \left(6 a^2 x^4+9 a b x^2+2 b^2\right)}{x^2 \left(a x^2+b\right)^2}-6 a \log \left(a x^2+b\right)+12 a \log (x)}{4 b^4}","\frac{3 a \log \left(a x^2+b\right)}{2 b^4}-\frac{3 a \log (x)}{b^4}-\frac{a}{b^3 \left(a x^2+b\right)}-\frac{a}{4 b^2 \left(a x^2+b\right)^2}-\frac{1}{2 b^3 x^2}",1,"-1/4*((b*(2*b^2 + 9*a*b*x^2 + 6*a^2*x^4))/(x^2*(b + a*x^2)^2) + 12*a*Log[x] - 6*a*Log[b + a*x^2])/b^4","A",1
1889,1,79,87,0.0451017,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^3 x^{10}} \, dx","Integrate[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{105 a^3 x^6+175 a^2 b x^4+56 a b^2 x^2-8 b^3}{24 b^4 x^3 \left(a x^2+b\right)^2}","\frac{35 a^{3/2} \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{8 b^{9/2}}+\frac{35 a}{8 b^4 x}+\frac{7}{8 b^2 x^3 \left(a x^2+b\right)}+\frac{1}{4 b x^3 \left(a x^2+b\right)^2}-\frac{35}{24 b^3 x^3}",1,"(-8*b^3 + 56*a*b^2*x^2 + 175*a^2*b*x^4 + 105*a^3*x^6)/(24*b^4*x^3*(b + a*x^2)^2) + (35*a^(3/2)*ArcTan[(Sqrt[a]*x)/Sqrt[b]])/(8*b^(9/2))","A",1
1890,1,74,86,0.0496839,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^3 x^{11}} \, dx","Integrate[1/((a + b/x^2)^3*x^11),x]","\frac{-12 a^2 \log \left(a x^2+b\right)+24 a^2 \log (x)+\frac{b \left(12 a^3 x^6+18 a^2 b x^4+4 a b^2 x^2-b^3\right)}{x^4 \left(a x^2+b\right)^2}}{4 b^5}","-\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}{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 b^4 x^2}-\frac{1}{4 b^3 x^4}",1,"((b*(-b^3 + 4*a*b^2*x^2 + 18*a^2*b*x^4 + 12*a^3*x^6))/(x^4*(b + a*x^2)^2) + 24*a^2*Log[x] - 12*a^2*Log[b + a*x^2])/(4*b^5)","A",1
1891,1,88,71,0.0418277,"\int \sqrt{a+\frac{b}{x^2}} x^3 \, dx","Integrate[Sqrt[a + b/x^2]*x^3,x]","x \sqrt{a+\frac{b}{x^2}} \left(\frac{b x}{8 a}+\frac{x^3}{4}\right)-\frac{b^2 x \sqrt{a+\frac{b}{x^2}} \log \left(\sqrt{a} \sqrt{a x^2+b}+a x\right)}{8 a^{3/2} \sqrt{a x^2+b}}","-\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^2}}}{\sqrt{a}}\right)}{8 a^{3/2}}+\frac{b x^2 \sqrt{a+\frac{b}{x^2}}}{8 a}+\frac{1}{4} x^4 \sqrt{a+\frac{b}{x^2}}",1,"Sqrt[a + b/x^2]*x*((b*x)/(8*a) + x^3/4) - (b^2*Sqrt[a + b/x^2]*x*Log[a*x + Sqrt[a]*Sqrt[b + a*x^2]])/(8*a^(3/2)*Sqrt[b + a*x^2])","A",1
1892,1,26,21,0.0054486,"\int \sqrt{a+\frac{b}{x^2}} x^2 \, dx","Integrate[Sqrt[a + b/x^2]*x^2,x]","\frac{x \sqrt{a+\frac{b}{x^2}} \left(a x^2+b\right)}{3 a}","\frac{x^3 \left(a+\frac{b}{x^2}\right)^{3/2}}{3 a}",1,"(Sqrt[a + b/x^2]*x*(b + a*x^2))/(3*a)","A",1
1893,1,58,47,0.0291508,"\int \sqrt{a+\frac{b}{x^2}} x \, dx","Integrate[Sqrt[a + b/x^2]*x,x]","\frac{1}{2} x \sqrt{a+\frac{b}{x^2}} \left(\frac{b \log \left(\sqrt{a} \sqrt{a x^2+b}+a x\right)}{\sqrt{a} \sqrt{a x^2+b}}+x\right)","\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*(x + (b*Log[a*x + Sqrt[a]*Sqrt[b + a*x^2]])/(Sqrt[a]*Sqrt[b + a*x^2])))/2","A",1
1894,1,62,42,0.0253649,"\int \sqrt{a+\frac{b}{x^2}} \, dx","Integrate[Sqrt[a + b/x^2],x]","x \sqrt{a+\frac{b}{x^2}}-\frac{\sqrt{b} x \sqrt{a+\frac{b}{x^2}} \tanh ^{-1}\left(\frac{\sqrt{a x^2+b}}{\sqrt{b}}\right)}{\sqrt{a x^2+b}}","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]*Sqrt[a + b/x^2]*x*ArcTanh[Sqrt[b + a*x^2]/Sqrt[b]])/Sqrt[b + a*x^2]","A",1
1895,1,69,38,0.0718473,"\int \frac{\sqrt{a+\frac{b}{x^2}}}{x} \, dx","Integrate[Sqrt[a + b/x^2]/x,x]","-\frac{\sqrt{a+\frac{b}{x^2}} \left(-\sqrt{a} \sqrt{b} x \sqrt{\frac{a x^2}{b}+1} \sinh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)+a x^2+b\right)}{a x^2+b}","\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]*(b + a*x^2 - Sqrt[a]*Sqrt[b]*x*Sqrt[1 + (a*x^2)/b]*ArcSinh[(Sqrt[a]*x)/Sqrt[b]]))/(b + a*x^2))","A",1
1896,1,68,50,0.0302456,"\int \frac{\sqrt{a+\frac{b}{x^2}}}{x^2} \, dx","Integrate[Sqrt[a + b/x^2]/x^2,x]","-\frac{\sqrt{a+\frac{b}{x^2}} \left(a x^2 \sqrt{\frac{a x^2}{b}+1} \tanh ^{-1}\left(\sqrt{\frac{a x^2}{b}+1}\right)+a x^2+b\right)}{2 x \left(a x^2+b\right)}","-\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,"-1/2*(Sqrt[a + b/x^2]*(b + a*x^2 + a*x^2*Sqrt[1 + (a*x^2)/b]*ArcTanh[Sqrt[1 + (a*x^2)/b]]))/(x*(b + a*x^2))","A",1
1897,1,18,18,0.0116238,"\int \frac{\sqrt{a+\frac{b}{x^2}}}{x^3} \, dx","Integrate[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,"-1/3*(a + b/x^2)^(3/2)/b","A",1
1898,1,47,74,0.0113232,"\int \frac{\sqrt{a+\frac{b}{x^2}}}{x^4} \, dx","Integrate[Sqrt[a + b/x^2]/x^4,x]","-\frac{a^2 x \sqrt{a+\frac{b}{x^2}} \left(a x^2+b\right) \, _2F_1\left(\frac{3}{2},3;\frac{5}{2};\frac{a x^2}{b}+1\right)}{3 b^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,"-1/3*(a^2*Sqrt[a + b/x^2]*x*(b + a*x^2)*Hypergeometric2F1[3/2, 3, 5/2, 1 + (a*x^2)/b])/b^3","C",1
1899,1,66,68,0.1549923,"\int \left(a+\frac{b}{x^2}\right)^{3/2} x^3 \, dx","Integrate[(a + b/x^2)^(3/2)*x^3,x]","\frac{1}{8} x \sqrt{a+\frac{b}{x^2}} \left(\frac{3 b^{3/2} \sinh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{\sqrt{a} \sqrt{\frac{a x^2}{b}+1}}+2 a x^3+5 b x\right)","\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^2}}}{\sqrt{a}}\right)}{8 \sqrt{a}}+\frac{3}{8} b x^2 \sqrt{a+\frac{b}{x^2}}+\frac{1}{4} x^4 \left(a+\frac{b}{x^2}\right)^{3/2}",1,"(Sqrt[a + b/x^2]*x*(5*b*x + 2*a*x^3 + (3*b^(3/2)*ArcSinh[(Sqrt[a]*x)/Sqrt[b]])/(Sqrt[a]*Sqrt[1 + (a*x^2)/b])))/8","A",1
1900,1,74,61,0.0585522,"\int \left(a+\frac{b}{x^2}\right)^{3/2} x^2 \, dx","Integrate[(a + b/x^2)^(3/2)*x^2,x]","\frac{x \sqrt{a+\frac{b}{x^2}} \left(\sqrt{a x^2+b} \left(a x^2+4 b\right)-3 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a x^2+b}}{\sqrt{b}}\right)\right)}{3 \sqrt{a x^2+b}}","-b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b}}{x \sqrt{a+\frac{b}{x^2}}}\right)+b x \sqrt{a+\frac{b}{x^2}}+\frac{1}{3} x^3 \left(a+\frac{b}{x^2}\right)^{3/2}",1,"(Sqrt[a + b/x^2]*x*(Sqrt[b + a*x^2]*(4*b + a*x^2) - 3*b^(3/2)*ArcTanh[Sqrt[b + a*x^2]/Sqrt[b]]))/(3*Sqrt[b + a*x^2])","A",1
1901,1,47,63,0.0130929,"\int \left(a+\frac{b}{x^2}\right)^{3/2} x \, dx","Integrate[(a + b/x^2)^(3/2)*x,x]","-\frac{b \sqrt{a+\frac{b}{x^2}} \, _2F_1\left(-\frac{3}{2},-\frac{1}{2};\frac{1}{2};-\frac{a x^2}{b}\right)}{\sqrt{\frac{a x^2}{b}+1}}","\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,"-((b*Sqrt[a + b/x^2]*Hypergeometric2F1[-3/2, -1/2, 1/2, -((a*x^2)/b)])/Sqrt[1 + (a*x^2)/b])","C",1
1902,1,47,64,0.0122927,"\int \left(a+\frac{b}{x^2}\right)^{3/2} \, dx","Integrate[(a + b/x^2)^(3/2),x]","\frac{a x^3 \left(a+\frac{b}{x^2}\right)^{3/2} \left(a x^2+b\right) \, _2F_1\left(2,\frac{5}{2};\frac{7}{2};\frac{a x^2}{b}+1\right)}{5 b^2}","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,"(a*(a + b/x^2)^(3/2)*x^3*(b + a*x^2)*Hypergeometric2F1[2, 5/2, 7/2, 1 + (a*x^2)/b])/(5*b^2)","C",1
1903,1,52,54,0.0296624,"\int \frac{\left(a+\frac{b}{x^2}\right)^{3/2}}{x} \, dx","Integrate[(a + b/x^2)^(3/2)/x,x]","-\frac{b \sqrt{a+\frac{b}{x^2}} \, _2F_1\left(-\frac{3}{2},-\frac{3}{2};-\frac{1}{2};-\frac{a x^2}{b}\right)}{3 x^2 \sqrt{\frac{a x^2}{b}+1}}","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,"-1/3*(b*Sqrt[a + b/x^2]*Hypergeometric2F1[-3/2, -3/2, -1/2, -((a*x^2)/b)])/(x^2*Sqrt[1 + (a*x^2)/b])","C",1
1904,1,85,71,0.0486448,"\int \frac{\left(a+\frac{b}{x^2}\right)^{3/2}}{x^2} \, dx","Integrate[(a + b/x^2)^(3/2)/x^2,x]","-\frac{\sqrt{a+\frac{b}{x^2}} \left(3 a^2 x^4 \sqrt{\frac{a x^2}{b}+1} \tanh ^{-1}\left(\sqrt{\frac{a x^2}{b}+1}\right)+5 a^2 x^4+7 a b x^2+2 b^2\right)}{8 x^3 \left(a x^2+b\right)}","-\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,"-1/8*(Sqrt[a + b/x^2]*(2*b^2 + 7*a*b*x^2 + 5*a^2*x^4 + 3*a^2*x^4*Sqrt[1 + (a*x^2)/b]*ArcTanh[Sqrt[1 + (a*x^2)/b]]))/(x^3*(b + a*x^2))","A",1
1905,1,28,18,0.0254981,"\int \frac{\left(a+\frac{b}{x^2}\right)^{3/2}}{x^3} \, dx","Integrate[(a + b/x^2)^(3/2)/x^3,x]","-\frac{\left(a+\frac{b}{x^2}\right)^{3/2} \left(a x^2+b\right)}{5 b x^2}","-\frac{\left(a+\frac{b}{x^2}\right)^{5/2}}{5 b}",1,"-1/5*((a + b/x^2)^(3/2)*(b + a*x^2))/(b*x^2)","A",1
1906,1,49,95,0.0140255,"\int \frac{\left(a+\frac{b}{x^2}\right)^{3/2}}{x^4} \, dx","Integrate[(a + b/x^2)^(3/2)/x^4,x]","\frac{a^3 x^3 \left(a+\frac{b}{x^2}\right)^{3/2} \left(a x^2+b\right) \, _2F_1\left(\frac{5}{2},4;\frac{7}{2};\frac{a x^2}{b}+1\right)}{5 b^4}","\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^3*(a + b/x^2)^(3/2)*x^3*(b + a*x^2)*Hypergeometric2F1[5/2, 4, 7/2, 1 + (a*x^2)/b])/(5*b^4)","C",1
1907,1,49,86,0.0143476,"\int \left(a+\frac{b}{x^2}\right)^{5/2} x^3 \, dx","Integrate[(a + b/x^2)^(5/2)*x^3,x]","-\frac{b^2 \sqrt{a+\frac{b}{x^2}} \, _2F_1\left(-\frac{5}{2},-\frac{1}{2};\frac{1}{2};-\frac{a x^2}{b}\right)}{\sqrt{\frac{a x^2}{b}+1}}","-\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{5}{8} b x^2 \left(a+\frac{b}{x^2}\right)^{3/2}+\frac{1}{4} x^4 \left(a+\frac{b}{x^2}\right)^{5/2}",1,"-((b^2*Sqrt[a + b/x^2]*Hypergeometric2F1[-5/2, -1/2, 1/2, -((a*x^2)/b)])/Sqrt[1 + (a*x^2)/b])","C",1
1908,1,47,88,0.0149709,"\int \left(a+\frac{b}{x^2}\right)^{5/2} x^2 \, dx","Integrate[(a + b/x^2)^(5/2)*x^2,x]","\frac{a x^5 \left(a+\frac{b}{x^2}\right)^{5/2} \left(a x^2+b\right) \, _2F_1\left(2,\frac{7}{2};\frac{9}{2};\frac{a x^2}{b}+1\right)}{7 b^2}","-\frac{5}{2} a b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b}}{x \sqrt{a+\frac{b}{x^2}}}\right)-\frac{5 b^2 \sqrt{a+\frac{b}{x^2}}}{2 x}+\frac{5}{3} b x \left(a+\frac{b}{x^2}\right)^{3/2}+\frac{1}{3} x^3 \left(a+\frac{b}{x^2}\right)^{5/2}",1,"(a*(a + b/x^2)^(5/2)*x^5*(b + a*x^2)*Hypergeometric2F1[2, 7/2, 9/2, 1 + (a*x^2)/b])/(7*b^2)","C",1
1909,1,54,80,0.0131299,"\int \left(a+\frac{b}{x^2}\right)^{5/2} x \, dx","Integrate[(a + b/x^2)^(5/2)*x,x]","-\frac{b^2 \sqrt{a+\frac{b}{x^2}} \, _2F_1\left(-\frac{5}{2},-\frac{3}{2};-\frac{1}{2};-\frac{a x^2}{b}\right)}{3 x^2 \sqrt{\frac{a x^2}{b}+1}}","\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,"-1/3*(b^2*Sqrt[a + b/x^2]*Hypergeometric2F1[-5/2, -3/2, -1/2, -((a*x^2)/b)])/(x^2*Sqrt[1 + (a*x^2)/b])","C",1
1910,1,49,86,0.0148804,"\int \left(a+\frac{b}{x^2}\right)^{5/2} \, dx","Integrate[(a + b/x^2)^(5/2),x]","-\frac{a^2 x^5 \left(a+\frac{b}{x^2}\right)^{5/2} \left(a x^2+b\right) \, _2F_1\left(3,\frac{7}{2};\frac{9}{2};\frac{a x^2}{b}+1\right)}{7 b^3}","-\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,"-1/7*(a^2*(a + b/x^2)^(5/2)*x^5*(b + a*x^2)*Hypergeometric2F1[3, 7/2, 9/2, 1 + (a*x^2)/b])/b^3","C",1
1911,1,54,72,0.0142577,"\int \frac{\left(a+\frac{b}{x^2}\right)^{5/2}}{x} \, dx","Integrate[(a + b/x^2)^(5/2)/x,x]","-\frac{b^2 \sqrt{a+\frac{b}{x^2}} \, _2F_1\left(-\frac{5}{2},-\frac{5}{2};-\frac{3}{2};-\frac{a x^2}{b}\right)}{5 x^4 \sqrt{\frac{a x^2}{b}+1}}","a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^2}}}{\sqrt{a}}\right)-a^2 \sqrt{a+\frac{b}{x^2}}-\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,"-1/5*(b^2*Sqrt[a + b/x^2]*Hypergeometric2F1[-5/2, -5/2, -3/2, -((a*x^2)/b)])/(x^4*Sqrt[1 + (a*x^2)/b])","C",1
1912,1,96,92,0.0416561,"\int \frac{\left(a+\frac{b}{x^2}\right)^{5/2}}{x^2} \, dx","Integrate[(a + b/x^2)^(5/2)/x^2,x]","-\frac{\sqrt{a+\frac{b}{x^2}} \left(15 a^3 x^6 \sqrt{\frac{a x^2}{b}+1} \tanh ^{-1}\left(\sqrt{\frac{a x^2}{b}+1}\right)+33 a^3 x^6+59 a^2 b x^4+34 a b^2 x^2+8 b^3\right)}{48 x^5 \left(a x^2+b\right)}","-\frac{5 a^3 \tanh ^{-1}\left(\frac{\sqrt{b}}{x \sqrt{a+\frac{b}{x^2}}}\right)}{16 \sqrt{b}}-\frac{5 a^2 \sqrt{a+\frac{b}{x^2}}}{16 x}-\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,"-1/48*(Sqrt[a + b/x^2]*(8*b^3 + 34*a*b^2*x^2 + 59*a^2*b*x^4 + 33*a^3*x^6 + 15*a^3*x^6*Sqrt[1 + (a*x^2)/b]*ArcTanh[Sqrt[1 + (a*x^2)/b]]))/(x^5*(b + a*x^2))","A",1
1913,1,28,18,0.0113225,"\int \frac{\left(a+\frac{b}{x^2}\right)^{5/2}}{x^3} \, dx","Integrate[(a + b/x^2)^(5/2)/x^3,x]","-\frac{\left(a+\frac{b}{x^2}\right)^{5/2} \left(a x^2+b\right)}{7 b x^2}","-\frac{\left(a+\frac{b}{x^2}\right)^{7/2}}{7 b}",1,"-1/7*((a + b/x^2)^(5/2)*(b + a*x^2))/(b*x^2)","A",1
1914,1,49,116,0.0159876,"\int \frac{\left(a+\frac{b}{x^2}\right)^{5/2}}{x^4} \, dx","Integrate[(a + b/x^2)^(5/2)/x^4,x]","-\frac{a^4 x^5 \left(a+\frac{b}{x^2}\right)^{5/2} \left(a x^2+b\right) \, _2F_1\left(\frac{7}{2},5;\frac{9}{2};\frac{a x^2}{b}+1\right)}{7 b^5}","\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,"-1/7*(a^4*(a + b/x^2)^(5/2)*x^5*(b + a*x^2)*Hypergeometric2F1[7/2, 5, 9/2, 1 + (a*x^2)/b])/b^5","C",1
1915,1,87,74,0.033343,"\int \frac{x^3}{\sqrt{a+\frac{b}{x^2}}} \, dx","Integrate[x^3/Sqrt[a + b/x^2],x]","\frac{\sqrt{a} x \left(2 a^2 x^4-a b x^2-3 b^2\right)+3 b^2 \sqrt{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b}}\right)}{8 a^{5/2} x \sqrt{a+\frac{b}{x^2}}}","\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,"(Sqrt[a]*x*(-3*b^2 - a*b*x^2 + 2*a^2*x^4) + 3*b^2*Sqrt[b + a*x^2]*ArcTanh[(Sqrt[a]*x)/Sqrt[b + a*x^2]])/(8*a^(5/2)*Sqrt[a + b/x^2]*x)","A",1
1916,1,71,50,0.023814,"\int \frac{x}{\sqrt{a+\frac{b}{x^2}}} \, dx","Integrate[x/Sqrt[a + b/x^2],x]","\frac{\sqrt{a} x \left(a x^2+b\right)-b \sqrt{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b}}\right)}{2 a^{3/2} x \sqrt{a+\frac{b}{x^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]*x*(b + a*x^2) - b*Sqrt[b + a*x^2]*ArcTanh[(Sqrt[a]*x)/Sqrt[b + a*x^2]])/(2*a^(3/2)*Sqrt[a + b/x^2]*x)","A",1
1917,1,50,24,0.0153489,"\int \frac{1}{\sqrt{a+\frac{b}{x^2}} x} \, dx","Integrate[1/(Sqrt[a + b/x^2]*x),x]","\frac{\sqrt{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b}}\right)}{\sqrt{a} x \sqrt{a+\frac{b}{x^2}}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^2}}}{\sqrt{a}}\right)}{\sqrt{a}}",1,"(Sqrt[b + a*x^2]*ArcTanh[(Sqrt[a]*x)/Sqrt[b + a*x^2]])/(Sqrt[a]*Sqrt[a + b/x^2]*x)","B",1
1918,1,16,16,0.0100035,"\int \frac{1}{\sqrt{a+\frac{b}{x^2}} x^3} \, dx","Integrate[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
1919,1,31,35,0.0153115,"\int \frac{1}{\sqrt{a+\frac{b}{x^2}} x^5} \, dx","Integrate[1/(Sqrt[a + b/x^2]*x^5),x]","\frac{\sqrt{a+\frac{b}{x^2}} \left(2 a x^2-b\right)}{3 b^2 x^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,"(Sqrt[a + b/x^2]*(-b + 2*a*x^2))/(3*b^2*x^2)","A",1
1920,1,42,57,0.0203683,"\int \frac{1}{\sqrt{a+\frac{b}{x^2}} x^7} \, dx","Integrate[1/(Sqrt[a + b/x^2]*x^7),x]","-\frac{\sqrt{a+\frac{b}{x^2}} \left(8 a^2 x^4-4 a b x^2+3 b^2\right)}{15 b^3 x^4}","-\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,"-1/15*(Sqrt[a + b/x^2]*(3*b^2 - 4*a*b*x^2 + 8*a^2*x^4))/(b^3*x^4)","A",1
1921,1,53,75,0.0182538,"\int \frac{1}{\sqrt{a+\frac{b}{x^2}} x^9} \, dx","Integrate[1/(Sqrt[a + b/x^2]*x^9),x]","\frac{\sqrt{a+\frac{b}{x^2}} \left(16 a^3 x^6-8 a^2 b x^4+6 a b^2 x^2-5 b^3\right)}{35 b^4 x^6}","\frac{a^3 \sqrt{a+\frac{b}{x^2}}}{b^4}-\frac{a^2 \left(a+\frac{b}{x^2}\right)^{3/2}}{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,"(Sqrt[a + b/x^2]*(-5*b^3 + 6*a*b^2*x^2 - 8*a^2*b*x^4 + 16*a^3*x^6))/(35*b^4*x^6)","A",1
1922,1,40,66,0.0266792,"\int \frac{x^4}{\sqrt{a+\frac{b}{x^2}}} \, dx","Integrate[x^4/Sqrt[a + b/x^2],x]","\frac{x \sqrt{a+\frac{b}{x^2}} \left(3 a^2 x^4-4 a b x^2+8 b^2\right)}{15 a^3}","\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,"(Sqrt[a + b/x^2]*x*(8*b^2 - 4*a*b*x^2 + 3*a^2*x^4))/(15*a^3)","A",1
1923,1,28,42,0.0217261,"\int \frac{x^2}{\sqrt{a+\frac{b}{x^2}}} \, dx","Integrate[x^2/Sqrt[a + b/x^2],x]","\frac{x \sqrt{a+\frac{b}{x^2}} \left(a x^2-2 b\right)}{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,"(Sqrt[a + b/x^2]*x*(-2*b + a*x^2))/(3*a^2)","A",1
1924,1,16,16,0.0064292,"\int \frac{1}{\sqrt{a+\frac{b}{x^2}}} \, dx","Integrate[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
1925,1,50,28,0.0158706,"\int \frac{1}{\sqrt{a+\frac{b}{x^2}} x^2} \, dx","Integrate[1/(Sqrt[a + b/x^2]*x^2),x]","-\frac{\sqrt{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt{a x^2+b}}{\sqrt{b}}\right)}{\sqrt{b} x \sqrt{a+\frac{b}{x^2}}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{b}}{x \sqrt{a+\frac{b}{x^2}}}\right)}{\sqrt{b}}",1,"-((Sqrt[b + a*x^2]*ArcTanh[Sqrt[b + a*x^2]/Sqrt[b]])/(Sqrt[b]*Sqrt[a + b/x^2]*x))","A",1
1926,1,71,53,0.0506944,"\int \frac{1}{\sqrt{a+\frac{b}{x^2}} x^4} \, dx","Integrate[1/(Sqrt[a + b/x^2]*x^4),x]","\frac{a \left(a x^2+b\right) \left(\frac{\tanh ^{-1}\left(\sqrt{\frac{a x^2}{b}+1}\right)}{2 \sqrt{\frac{a x^2}{b}+1}}-\frac{b}{2 a x^2}\right)}{b^2 x \sqrt{a+\frac{b}{x^2}}}","\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,"(a*(b + a*x^2)*(-1/2*b/(a*x^2) + ArcTanh[Sqrt[1 + (a*x^2)/b]]/(2*Sqrt[1 + (a*x^2)/b])))/(b^2*Sqrt[a + b/x^2]*x)","A",1
1927,1,56,27,0.0364964,"\int \frac{1}{\sqrt{-a+\frac{b}{x^2}} x} \, dx","Integrate[1/(Sqrt[-a + b/x^2]*x),x]","\frac{\sqrt{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2-b}}\right)}{\sqrt{a} x \sqrt{\frac{b}{x^2}-a}}","-\frac{\tan ^{-1}\left(\frac{\sqrt{\frac{b}{x^2}-a}}{\sqrt{a}}\right)}{\sqrt{a}}",1,"(Sqrt[-b + a*x^2]*ArcTanh[(Sqrt[a]*x)/Sqrt[-b + a*x^2]])/(Sqrt[a]*Sqrt[-a + b/x^2]*x)","B",1
1928,1,50,20,0.0175255,"\int \frac{1}{\sqrt{2+\frac{b}{x^2}} x^2} \, dx","Integrate[1/(Sqrt[2 + b/x^2]*x^2),x]","-\frac{\sqrt{b+2 x^2} \tanh ^{-1}\left(\frac{\sqrt{b+2 x^2}}{\sqrt{b}}\right)}{\sqrt{b} x \sqrt{\frac{b}{x^2}+2}}","-\frac{\text{csch}^{-1}\left(\frac{\sqrt{2} x}{\sqrt{b}}\right)}{\sqrt{b}}",1,"-((Sqrt[b + 2*x^2]*ArcTanh[Sqrt[b + 2*x^2]/Sqrt[b]])/(Sqrt[b]*Sqrt[2 + b/x^2]*x))","B",1
1929,1,54,20,0.0188747,"\int \frac{1}{\sqrt{2-\frac{b}{x^2}} x^2} \, dx","Integrate[1/(Sqrt[2 - b/x^2]*x^2),x]","\frac{\sqrt{2 x^2-b} \tan ^{-1}\left(\frac{\sqrt{2 x^2-b}}{\sqrt{b}}\right)}{\sqrt{b} x \sqrt{2-\frac{b}{x^2}}}","-\frac{\csc ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{b}}\right)}{\sqrt{b}}",1,"(Sqrt[-b + 2*x^2]*ArcTan[Sqrt[-b + 2*x^2]/Sqrt[b]])/(Sqrt[b]*Sqrt[2 - b/x^2]*x)","B",1
1930,1,86,95,0.0571592,"\int \frac{x^3}{\left(a+\frac{b}{x^2}\right)^{3/2}} \, dx","Integrate[x^3/(a + b/x^2)^(3/2),x]","\frac{\sqrt{a} x \left(2 a^2 x^4-5 a b x^2-15 b^2\right)+15 b^{5/2} \sqrt{\frac{a x^2}{b}+1} \sinh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{8 a^{7/2} x \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{15 b^2}{8 a^3 \sqrt{a+\frac{b}{x^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,"(Sqrt[a]*x*(-15*b^2 - 5*a*b*x^2 + 2*a^2*x^4) + 15*b^(5/2)*Sqrt[1 + (a*x^2)/b]*ArcSinh[(Sqrt[a]*x)/Sqrt[b]])/(8*a^(7/2)*Sqrt[a + b/x^2]*x)","A",1
1931,1,74,69,0.039862,"\int \frac{x}{\left(a+\frac{b}{x^2}\right)^{3/2}} \, dx","Integrate[x/(a + b/x^2)^(3/2),x]","\frac{\sqrt{a} x \left(a x^2+3 b\right)-3 b^{3/2} \sqrt{\frac{a x^2}{b}+1} \sinh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{2 a^{5/2} x \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{3 b}{2 a^2 \sqrt{a+\frac{b}{x^2}}}+\frac{x^2}{2 a \sqrt{a+\frac{b}{x^2}}}",1,"(Sqrt[a]*x*(3*b + a*x^2) - 3*b^(3/2)*Sqrt[1 + (a*x^2)/b]*ArcSinh[(Sqrt[a]*x)/Sqrt[b]])/(2*a^(5/2)*Sqrt[a + b/x^2]*x)","A",1
1932,1,62,41,0.0585742,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^{3/2} x} \, dx","Integrate[1/((a + b/x^2)^(3/2)*x),x]","\frac{\sqrt{b} \sqrt{\frac{a x^2}{b}+1} \sinh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)-\sqrt{a} x}{a^{3/2} x \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,"(-(Sqrt[a]*x) + Sqrt[b]*Sqrt[1 + (a*x^2)/b]*ArcSinh[(Sqrt[a]*x)/Sqrt[b]])/(a^(3/2)*Sqrt[a + b/x^2]*x)","A",1
1933,1,15,15,0.0067929,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^{3/2} x^3} \, dx","Integrate[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
1934,1,28,34,0.0092897,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^{3/2} x^5} \, dx","Integrate[1/((a + b/x^2)^(3/2)*x^5),x]","\frac{-2 a x^2-b}{b^2 x^2 \sqrt{a+\frac{b}{x^2}}}","-\frac{a}{b^2 \sqrt{a+\frac{b}{x^2}}}-\frac{\sqrt{a+\frac{b}{x^2}}}{b^2}",1,"(-b - 2*a*x^2)/(b^2*Sqrt[a + b/x^2]*x^2)","A",1
1935,1,42,54,0.0102932,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^{3/2} x^7} \, dx","Integrate[1/((a + b/x^2)^(3/2)*x^7),x]","\frac{8 a^2 x^4+4 a b x^2-b^2}{3 b^3 x^4 \sqrt{a+\frac{b}{x^2}}}","\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,"(-b^2 + 4*a*b*x^2 + 8*a^2*x^4)/(3*b^3*Sqrt[a + b/x^2]*x^4)","A",1
1936,1,53,73,0.012522,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^{3/2} x^9} \, dx","Integrate[1/((a + b/x^2)^(3/2)*x^9),x]","\frac{-16 a^3 x^6-8 a^2 b x^4+2 a b^2 x^2-b^3}{5 b^4 x^6 \sqrt{a+\frac{b}{x^2}}}","-\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,"(-b^3 + 2*a*b^2*x^2 - 8*a^2*b*x^4 - 16*a^3*x^6)/(5*b^4*Sqrt[a + b/x^2]*x^6)","A",1
1937,1,52,88,0.0256904,"\int \frac{x^4}{\left(a+\frac{b}{x^2}\right)^{3/2}} \, dx","Integrate[x^4/(a + b/x^2)^(3/2),x]","\frac{a^3 x^6-2 a^2 b x^4+8 a b^2 x^2+16 b^3}{5 a^4 x \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,"(16*b^3 + 8*a*b^2*x^2 - 2*a^2*b*x^4 + a^3*x^6)/(5*a^4*Sqrt[a + b/x^2]*x)","A",1
1938,1,41,62,0.0193227,"\int \frac{x^2}{\left(a+\frac{b}{x^2}\right)^{3/2}} \, dx","Integrate[x^2/(a + b/x^2)^(3/2),x]","\frac{a^2 x^4-4 a b x^2-8 b^2}{3 a^3 x \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,"(-8*b^2 - 4*a*b*x^2 + a^2*x^4)/(3*a^3*Sqrt[a + b/x^2]*x)","A",1
1939,1,27,35,0.0127136,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^{3/2}} \, dx","Integrate[(a + b/x^2)^(-3/2),x]","\frac{a x^2+2 b}{a^2 x \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,"(2*b + a*x^2)/(a^2*Sqrt[a + b/x^2]*x)","A",1
1940,1,19,19,0.0054746,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^{3/2} x^2} \, dx","Integrate[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
1941,1,36,47,0.0102545,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^{3/2} x^4} \, dx","Integrate[1/((a + b/x^2)^(3/2)*x^4),x]","\frac{\, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{a x^2}{b}+1\right)}{b x \sqrt{a+\frac{b}{x^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,"Hypergeometric2F1[-1/2, 1, 1/2, 1 + (a*x^2)/b]/(b*Sqrt[a + b/x^2]*x)","C",1
1942,1,38,71,0.0110128,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^{3/2} x^6} \, dx","Integrate[1/((a + b/x^2)^(3/2)*x^6),x]","-\frac{a \, _2F_1\left(-\frac{1}{2},2;\frac{1}{2};\frac{a x^2}{b}+1\right)}{b^2 x \sqrt{a+\frac{b}{x^2}}}","\frac{3 a \tanh ^{-1}\left(\frac{\sqrt{b}}{x \sqrt{a+\frac{b}{x^2}}}\right)}{2 b^{5/2}}-\frac{3 \sqrt{a+\frac{b}{x^2}}}{2 b^2 x}+\frac{1}{b x^3 \sqrt{a+\frac{b}{x^2}}}",1,"-((a*Hypergeometric2F1[-1/2, 2, 1/2, 1 + (a*x^2)/b])/(b^2*Sqrt[a + b/x^2]*x))","C",1
1943,1,39,95,0.011316,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^{3/2} x^8} \, dx","Integrate[1/((a + b/x^2)^(3/2)*x^8),x]","\frac{a^2 \, _2F_1\left(-\frac{1}{2},3;\frac{1}{2};\frac{a x^2}{b}+1\right)}{b^3 x \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,"(a^2*Hypergeometric2F1[-1/2, 3, 1/2, 1 + (a*x^2)/b])/(b^3*Sqrt[a + b/x^2]*x)","C",1
1944,1,112,116,0.2255001,"\int \frac{x^3}{\left(a+\frac{b}{x^2}\right)^{5/2}} \, dx","Integrate[x^3/(a + b/x^2)^(5/2),x]","\frac{\sqrt{a} \left(6 a^3 x^6-21 a^2 b x^4-140 a b^2 x^2-105 b^3\right)+\frac{105 b^{5/2} \left(a x^2+b\right) \sqrt{\frac{a x^2}{b}+1} \sinh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{x}}{24 a^{9/2} \sqrt{a+\frac{b}{x^2}} \left(a x^2+b\right)}","\frac{35 b^2 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^2}}}{\sqrt{a}}\right)}{8 a^{9/2}}-\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{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,"(Sqrt[a]*(-105*b^3 - 140*a*b^2*x^2 - 21*a^2*b*x^4 + 6*a^3*x^6) + (105*b^(5/2)*(b + a*x^2)*Sqrt[1 + (a*x^2)/b]*ArcSinh[(Sqrt[a]*x)/Sqrt[b]])/x)/(24*a^(9/2)*Sqrt[a + b/x^2]*(b + a*x^2))","A",1
1945,1,101,88,0.1678931,"\int \frac{x}{\left(a+\frac{b}{x^2}\right)^{5/2}} \, dx","Integrate[x/(a + b/x^2)^(5/2),x]","\frac{\sqrt{a} \left(3 a^2 x^4+20 a b x^2+15 b^2\right)-\frac{15 b^{3/2} \left(a x^2+b\right) \sqrt{\frac{a x^2}{b}+1} \sinh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{x}}{6 a^{7/2} \sqrt{a+\frac{b}{x^2}} \left(a x^2+b\right)}","-\frac{5 b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^2}}}{\sqrt{a}}\right)}{2 a^{7/2}}+\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{x^2}{2 a \left(a+\frac{b}{x^2}\right)^{3/2}}",1,"(Sqrt[a]*(15*b^2 + 20*a*b*x^2 + 3*a^2*x^4) - (15*b^(3/2)*(b + a*x^2)*Sqrt[1 + (a*x^2)/b]*ArcSinh[(Sqrt[a]*x)/Sqrt[b]])/x)/(6*a^(7/2)*Sqrt[a + b/x^2]*(b + a*x^2))","A",1
1946,1,91,59,0.1753754,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^{5/2} x} \, dx","Integrate[1/((a + b/x^2)^(5/2)*x),x]","\frac{\frac{3 \sqrt{b} \left(a x^2+b\right) \sqrt{\frac{a x^2}{b}+1} \sinh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{x}-\sqrt{a} \left(4 a x^2+3 b\right)}{3 a^{5/2} \sqrt{a+\frac{b}{x^2}} \left(a x^2+b\right)}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^2}}}{\sqrt{a}}\right)}{a^{5/2}}-\frac{1}{a^2 \sqrt{a+\frac{b}{x^2}}}-\frac{1}{3 a \left(a+\frac{b}{x^2}\right)^{3/2}}",1,"(-(Sqrt[a]*(3*b + 4*a*x^2)) + (3*Sqrt[b]*(b + a*x^2)*Sqrt[1 + (a*x^2)/b]*ArcSinh[(Sqrt[a]*x)/Sqrt[b]])/x)/(3*a^(5/2)*Sqrt[a + b/x^2]*(b + a*x^2))","A",1
1947,1,28,18,0.0094624,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^{5/2} x^3} \, dx","Integrate[1/((a + b/x^2)^(5/2)*x^3),x]","\frac{a x^2+b}{3 b x^2 \left(a+\frac{b}{x^2}\right)^{5/2}}","\frac{1}{3 b \left(a+\frac{b}{x^2}\right)^{3/2}}",1,"(b + a*x^2)/(3*b*(a + b/x^2)^(5/2)*x^2)","A",1
1948,1,37,35,0.0195365,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^{5/2} x^5} \, dx","Integrate[1/((a + b/x^2)^(5/2)*x^5),x]","\frac{2 a x^2+3 b}{3 b^2 \sqrt{a+\frac{b}{x^2}} \left(a x^2+b\right)}","\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,"(3*b + 2*a*x^2)/(3*b^2*Sqrt[a + b/x^2]*(b + a*x^2))","A",1
1949,1,48,55,0.021476,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^{5/2} x^7} \, dx","Integrate[1/((a + b/x^2)^(5/2)*x^7),x]","-\frac{\sqrt{a+\frac{b}{x^2}} \left(8 a^2 x^4+12 a b x^2+3 b^2\right)}{3 b^3 \left(a x^2+b\right)^2}","\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,"-1/3*(Sqrt[a + b/x^2]*(3*b^2 + 12*a*b*x^2 + 8*a^2*x^4))/(b^3*(b + a*x^2)^2)","A",1
1950,1,62,76,0.0137809,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^{5/2} x^9} \, dx","Integrate[1/((a + b/x^2)^(5/2)*x^9),x]","\frac{16 a^3 x^6+24 a^2 b x^4+6 a b^2 x^2-b^3}{3 b^4 x^4 \sqrt{a+\frac{b}{x^2}} \left(a x^2+b\right)}","-\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,"(-b^3 + 6*a*b^2*x^2 + 24*a^2*b*x^4 + 16*a^3*x^6)/(3*b^4*Sqrt[a + b/x^2]*x^4*(b + a*x^2))","A",1
1951,1,61,82,0.0296146,"\int \frac{x^2}{\left(a+\frac{b}{x^2}\right)^{5/2}} \, dx","Integrate[x^2/(a + b/x^2)^(5/2),x]","\frac{a^3 x^6-6 a^2 b x^4-24 a b^2 x^2-16 b^3}{3 a^4 x \sqrt{a+\frac{b}{x^2}} \left(a x^2+b\right)}","-\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,"(-16*b^3 - 24*a*b^2*x^2 - 6*a^2*b*x^4 + a^3*x^6)/(3*a^4*Sqrt[a + b/x^2]*x*(b + a*x^2))","A",1
1952,1,51,58,0.0280492,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^{5/2}} \, dx","Integrate[(a + b/x^2)^(-5/2),x]","\frac{3 a^2 x^4+12 a b x^2+8 b^2}{3 a^3 x \sqrt{a+\frac{b}{x^2}} \left(a x^2+b\right)}","\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,"(8*b^2 + 12*a*b*x^2 + 3*a^2*x^4)/(3*a^3*Sqrt[a + b/x^2]*x*(b + a*x^2))","A",1
1953,1,38,42,0.023766,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^{5/2} x^2} \, dx","Integrate[1/((a + b/x^2)^(5/2)*x^2),x]","-\frac{x \sqrt{a+\frac{b}{x^2}} \left(3 a x^2+2 b\right)}{3 a^2 \left(a x^2+b\right)^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,"-1/3*(Sqrt[a + b/x^2]*x*(2*b + 3*a*x^2))/(a^2*(b + a*x^2)^2)","A",1
1954,1,28,21,0.0077284,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^{5/2} x^4} \, dx","Integrate[1/((a + b/x^2)^(5/2)*x^4),x]","-\frac{a x^2+b}{3 a x^5 \left(a+\frac{b}{x^2}\right)^{5/2}}","-\frac{1}{3 a x^3 \left(a+\frac{b}{x^2}\right)^{3/2}}",1,"-1/3*(b + a*x^2)/(a*(a + b/x^2)^(5/2)*x^5)","A",1
1955,1,46,68,0.0112171,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^{5/2} x^6} \, dx","Integrate[1/((a + b/x^2)^(5/2)*x^6),x]","\frac{\left(a x^2+b\right) \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{a x^2}{b}+1\right)}{3 b x^5 \left(a+\frac{b}{x^2}\right)^{5/2}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{b}}{x \sqrt{a+\frac{b}{x^2}}}\right)}{b^{5/2}}+\frac{1}{b^2 x \sqrt{a+\frac{b}{x^2}}}+\frac{1}{3 b x^3 \left(a+\frac{b}{x^2}\right)^{3/2}}",1,"((b + a*x^2)*Hypergeometric2F1[-3/2, 1, -1/2, 1 + (a*x^2)/b])/(3*b*(a + b/x^2)^(5/2)*x^5)","C",1
1956,1,47,95,0.0124381,"\int \frac{1}{\left(a+\frac{b}{x^2}\right)^{5/2} x^8} \, dx","Integrate[1/((a + b/x^2)^(5/2)*x^8),x]","-\frac{a \left(a x^2+b\right) \, _2F_1\left(-\frac{3}{2},2;-\frac{1}{2};\frac{a x^2}{b}+1\right)}{3 b^2 x^5 \left(a+\frac{b}{x^2}\right)^{5/2}}","\frac{5 a \tanh ^{-1}\left(\frac{\sqrt{b}}{x \sqrt{a+\frac{b}{x^2}}}\right)}{2 b^{7/2}}-\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{1}{3 b x^5 \left(a+\frac{b}{x^2}\right)^{3/2}}",1,"-1/3*(a*(b + a*x^2)*Hypergeometric2F1[-3/2, 2, -1/2, 1 + (a*x^2)/b])/(b^2*(a + b/x^2)^(5/2)*x^5)","C",1
1957,1,13,13,0.0068598,"\int \frac{\sqrt[3]{1+\frac{1}{x^2}}}{x^3} \, dx","Integrate[(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
1958,1,21,13,0.0078584,"\int \frac{\left(1+\frac{1}{x^2}\right)^{5/3}}{x^3} \, dx","Integrate[(1 + x^(-2))^(5/3)/x^3,x]","-\frac{3 \left(\frac{1}{x^2}+1\right)^{5/3} \left(x^2+1\right)}{16 x^2}","-\frac{3}{16} \left(\frac{1}{x^2}+1\right)^{8/3}",1,"(-3*(1 + x^(-2))^(5/3)*(1 + x^2))/(16*x^2)","A",1
1959,1,63,44,0.0319058,"\int \left(1+\frac{b}{x^2}\right)^{3/2} (c x)^m \, dx","Integrate[(1 + b/x^2)^(3/2)*(c*x)^m,x]","\frac{b \sqrt{\frac{b}{x^2}+1} (c x)^m \, _2F_1\left(-\frac{3}{2},\frac{m}{2}-1;\frac{m}{2};-\frac{x^2}{b}\right)}{(m-2) x \sqrt{\frac{b+x^2}{b}}}","\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,"(b*Sqrt[1 + b/x^2]*(c*x)^m*Hypergeometric2F1[-3/2, -1 + m/2, m/2, -(x^2/b)])/((-2 + m)*x*Sqrt[(b + x^2)/b])","A",1
1960,1,58,44,0.0167467,"\int \sqrt{1+\frac{b}{x^2}} (c x)^m \, dx","Integrate[Sqrt[1 + b/x^2]*(c*x)^m,x]","\frac{x \sqrt{\frac{b}{x^2}+1} (c x)^m \, _2F_1\left(-\frac{1}{2},\frac{m}{2};\frac{m}{2}+1;-\frac{x^2}{b}\right)}{m \sqrt{\frac{x^2}{b}+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,"(Sqrt[1 + b/x^2]*x*(c*x)^m*Hypergeometric2F1[-1/2, m/2, 1 + m/2, -(x^2/b)])/(m*Sqrt[1 + x^2/b])","A",1
1961,1,64,44,0.0226714,"\int \frac{(c x)^m}{\sqrt{1+\frac{b}{x^2}}} \, dx","Integrate[(c*x)^m/Sqrt[1 + b/x^2],x]","\frac{x \sqrt{\frac{x^2}{b}+1} (c x)^m \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+2}{2}+1;-\frac{x^2}{b}\right)}{(m+2) \sqrt{\frac{b}{x^2}+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,"(x*(c*x)^m*Sqrt[1 + x^2/b]*Hypergeometric2F1[1/2, (2 + m)/2, 1 + (2 + m)/2, -(x^2/b)])/((2 + m)*Sqrt[1 + b/x^2])","A",1
1962,1,67,44,0.0400956,"\int \frac{(c x)^m}{\left(1+\frac{b}{x^2}\right)^{3/2}} \, dx","Integrate[(c*x)^m/(1 + b/x^2)^(3/2),x]","\frac{x^3 \sqrt{\frac{b+x^2}{b}} (c x)^m \, _2F_1\left(\frac{3}{2},\frac{m}{2}+2;\frac{m}{2}+3;-\frac{x^2}{b}\right)}{b (m+4) \sqrt{\frac{b}{x^2}+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,"(x^3*(c*x)^m*Sqrt[(b + x^2)/b]*Hypergeometric2F1[3/2, 2 + m/2, 3 + m/2, -(x^2/b)])/(b*(4 + m)*Sqrt[1 + b/x^2])","A",1
1963,1,71,44,0.0198406,"\int \left(1+\frac{b}{x^2}\right)^p (c x)^m \, dx","Integrate[(1 + b/x^2)^p*(c*x)^m,x]","\frac{x \left(\frac{b}{x^2}+1\right)^p \left(\frac{x^2}{b}+1\right)^{-p} (c x)^m \, _2F_1\left(\frac{1}{2} (m-2 p+1),-p;\frac{1}{2} (m-2 p+1)+1;-\frac{x^2}{b}\right)}{m-2 p+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,"((1 + b/x^2)^p*x*(c*x)^m*Hypergeometric2F1[(1 + m - 2*p)/2, -p, 1 + (1 + m - 2*p)/2, -(x^2/b)])/((1 + m - 2*p)*(1 + x^2/b)^p)","A",1
1964,1,73,70,0.0197106,"\int \left(a+\frac{b}{x^2}\right)^p (c x)^m \, dx","Integrate[(a + b/x^2)^p*(c*x)^m,x]","\frac{x (c x)^m \left(a+\frac{b}{x^2}\right)^p \left(\frac{a x^2}{b}+1\right)^{-p} \, _2F_1\left(\frac{1}{2} (m-2 p+1),-p;\frac{1}{2} (m-2 p+1)+1;-\frac{a x^2}{b}\right)}{m-2 p+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*x*(c*x)^m*Hypergeometric2F1[(1 + m - 2*p)/2, -p, 1 + (1 + m - 2*p)/2, -((a*x^2)/b)])/((1 + m - 2*p)*(1 + (a*x^2)/b)^p)","A",1
1965,1,40,40,0.0069075,"\int \frac{x^5}{a+\frac{b}{x^3}} \, dx","Integrate[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,"-1/3*(b*x^3)/a^2 + x^6/(6*a) + (b^2*Log[b + a*x^3])/(3*a^3)","A",1
1966,1,122,136,0.0592894,"\int \frac{x^4}{a+\frac{b}{x^3}} \, dx","Integrate[x^4/(a + b/x^3),x]","\frac{5 b^{5/3} \log \left(a^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3}\right)-15 a^{2/3} b x^2+6 a^{5/3} x^5-10 b^{5/3} \log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)-10 \sqrt{3} b^{5/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{a} x}{\sqrt[3]{b}}}{\sqrt{3}}\right)}{30 a^{8/3}}","\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,"(-15*a^(2/3)*b*x^2 + 6*a^(5/3)*x^5 - 10*Sqrt[3]*b^(5/3)*ArcTan[(1 - (2*a^(1/3)*x)/b^(1/3))/Sqrt[3]] - 10*b^(5/3)*Log[b^(1/3) + a^(1/3)*x] + 5*b^(5/3)*Log[b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2])/(30*a^(8/3))","A",1
1967,1,120,132,0.0521007,"\int \frac{x^3}{a+\frac{b}{x^3}} \, dx","Integrate[x^3/(a + b/x^3),x]","\frac{-2 b^{4/3} \log \left(a^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3}\right)+3 a^{4/3} x^4+4 b^{4/3} \log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)-4 \sqrt{3} b^{4/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{a} x}{\sqrt[3]{b}}}{\sqrt{3}}\right)-12 \sqrt[3]{a} b x}{12 a^{7/3}}","-\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,"(-12*a^(1/3)*b*x + 3*a^(4/3)*x^4 - 4*Sqrt[3]*b^(4/3)*ArcTan[(1 - (2*a^(1/3)*x)/b^(1/3))/Sqrt[3]] + 4*b^(4/3)*Log[b^(1/3) + a^(1/3)*x] - 2*b^(4/3)*Log[b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2])/(12*a^(7/3))","A",1
1968,1,27,27,0.0049424,"\int \frac{x^2}{a+\frac{b}{x^3}} \, dx","Integrate[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",1
1969,1,111,124,0.0560547,"\int \frac{x}{a+\frac{b}{x^3}} \, dx","Integrate[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)+3 a^{2/3} x^2+2 b^{2/3} \log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)+2 \sqrt{3} b^{2/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{a} x}{\sqrt[3]{b}}}{\sqrt{3}}\right)}{6 a^{5/3}}","-\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,"(3*a^(2/3)*x^2 + 2*Sqrt[3]*b^(2/3)*ArcTan[(1 - (2*a^(1/3)*x)/b^(1/3))/Sqrt[3]] + 2*b^(2/3)*Log[b^(1/3) + a^(1/3)*x] - b^(2/3)*Log[b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2])/(6*a^(5/3))","A",1
1970,1,108,119,0.0213658,"\int \frac{1}{a+\frac{b}{x^3}} \, dx","Integrate[(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)-2 \sqrt[3]{b} \log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)+2 \sqrt{3} \sqrt[3]{b} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{a} x}{\sqrt[3]{b}}}{\sqrt{3}}\right)+6 \sqrt[3]{a} x}{6 a^{4/3}}","\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,"(6*a^(1/3)*x + 2*Sqrt[3]*b^(1/3)*ArcTan[(1 - (2*a^(1/3)*x)/b^(1/3))/Sqrt[3]] - 2*b^(1/3)*Log[b^(1/3) + a^(1/3)*x] + b^(1/3)*Log[b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2])/(6*a^(4/3))","A",1
1971,1,15,15,0.0037274,"\int \frac{1}{\left(a+\frac{b}{x^3}\right) x} \, dx","Integrate[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",1
1972,1,89,115,0.0143818,"\int \frac{1}{\left(a+\frac{b}{x^3}\right) x^2} \, dx","Integrate[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)-2 \log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)-2 \sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{a} x}{\sqrt[3]{b}}}{\sqrt{3}}\right)}{6 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,"(-2*Sqrt[3]*ArcTan[(1 - (2*a^(1/3)*x)/b^(1/3))/Sqrt[3]] - 2*Log[b^(1/3) + a^(1/3)*x] + Log[b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2])/(6*a^(2/3)*b^(1/3))","A",1
1973,1,89,115,0.0142933,"\int \frac{1}{\left(a+\frac{b}{x^3}\right) x^3} \, dx","Integrate[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)-2 \log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{a} x}{\sqrt[3]{b}}}{\sqrt{3}}\right)}{6 \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,"-1/6*(2*Sqrt[3]*ArcTan[(1 - (2*a^(1/3)*x)/b^(1/3))/Sqrt[3]] - 2*Log[b^(1/3) + a^(1/3)*x] + Log[b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2])/(a^(1/3)*b^(2/3))","A",1
1974,1,22,15,0.0136354,"\int \frac{1}{\left(a+\frac{b}{x^3}\right) x^4} \, dx","Integrate[1/((a + b/x^3)*x^4),x]","\frac{\log (x)}{b}-\frac{\log \left(a x^3+b\right)}{3 b}","-\frac{\log \left(a+\frac{b}{x^3}\right)}{3 b}",1,"Log[x]/b - Log[b + a*x^3]/(3*b)","A",1
1975,1,114,122,0.0213373,"\int \frac{1}{\left(a+\frac{b}{x^3}\right) x^5} \, dx","Integrate[1/((a + b/x^3)*x^5),x]","\frac{-\sqrt[3]{a} x \log \left(a^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3}\right)+2 \sqrt[3]{a} x \log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)+2 \sqrt{3} \sqrt[3]{a} x \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{a} x}{\sqrt[3]{b}}}{\sqrt{3}}\right)-6 \sqrt[3]{b}}{6 b^{4/3} 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,"(-6*b^(1/3) + 2*Sqrt[3]*a^(1/3)*x*ArcTan[(1 - (2*a^(1/3)*x)/b^(1/3))/Sqrt[3]] + 2*a^(1/3)*x*Log[b^(1/3) + a^(1/3)*x] - a^(1/3)*x*Log[b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2])/(6*b^(4/3)*x)","A",1
1976,1,119,124,0.0285971,"\int \frac{1}{\left(a+\frac{b}{x^3}\right) x^6} \, dx","Integrate[1/((a + b/x^3)*x^6),x]","\frac{a^{2/3} x^2 \log \left(a^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3}\right)-2 a^{2/3} x^2 \log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)+2 \sqrt{3} a^{2/3} x^2 \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{a} x}{\sqrt[3]{b}}}{\sqrt{3}}\right)-3 b^{2/3}}{6 b^{5/3} 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,"(-3*b^(2/3) + 2*Sqrt[3]*a^(2/3)*x^2*ArcTan[(1 - (2*a^(1/3)*x)/b^(1/3))/Sqrt[3]] - 2*a^(2/3)*x^2*Log[b^(1/3) + a^(1/3)*x] + a^(2/3)*x^2*Log[b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2])/(6*b^(5/3)*x^2)","A",1
1977,1,35,35,0.0077117,"\int \frac{1}{\left(a+\frac{b}{x^3}\right) x^7} \, dx","Integrate[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*1/(b*x^3) - (a*Log[x])/b^2 + (a*Log[b + a*x^3])/(3*b^2)","A",1
1978,1,49,56,0.0192406,"\int \frac{x^5}{\left(a+\frac{b}{x^3}\right)^2} \, dx","Integrate[x^5/(a + b/x^3)^2,x]","\frac{a^2 x^6+\frac{2 b^3}{a x^3+b}+6 b^2 \log \left(a x^3+b\right)-4 a b x^3}{6 a^4}","\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,"(-4*a*b*x^3 + a^2*x^6 + (2*b^3)/(b + a*x^3) + 6*b^2*Log[b + a*x^3])/(6*a^4)","A",1
1979,1,144,157,0.1094327,"\int \frac{x^4}{\left(a+\frac{b}{x^3}\right)^2} \, dx","Integrate[x^4/(a + b/x^3)^2,x]","\frac{20 b^{5/3} \log \left(a^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3}\right)-\frac{15 a^{2/3} b^2 x^2}{a x^3+b}-45 a^{2/3} b x^2+9 a^{5/3} x^5-40 b^{5/3} \log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)-40 \sqrt{3} b^{5/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{a} x}{\sqrt[3]{b}}}{\sqrt{3}}\right)}{45 a^{11/3}}","\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,"(-45*a^(2/3)*b*x^2 + 9*a^(5/3)*x^5 - (15*a^(2/3)*b^2*x^2)/(b + a*x^3) - 40*Sqrt[3]*b^(5/3)*ArcTan[(1 - (2*a^(1/3)*x)/b^(1/3))/Sqrt[3]] - 40*b^(5/3)*Log[b^(1/3) + a^(1/3)*x] + 20*b^(5/3)*Log[b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2])/(45*a^(11/3))","A",1
1980,1,140,155,0.1055231,"\int \frac{x^3}{\left(a+\frac{b}{x^3}\right)^2} \, dx","Integrate[x^3/(a + b/x^3)^2,x]","\frac{-14 b^{4/3} \log \left(a^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3}\right)+9 a^{4/3} x^4+28 b^{4/3} \log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)-28 \sqrt{3} b^{4/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{a} x}{\sqrt[3]{b}}}{\sqrt{3}}\right)-\frac{12 \sqrt[3]{a} b^2 x}{a x^3+b}-72 \sqrt[3]{a} b x}{36 a^{10/3}}","-\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,"(-72*a^(1/3)*b*x + 9*a^(4/3)*x^4 - (12*a^(1/3)*b^2*x)/(b + a*x^3) - 28*Sqrt[3]*b^(4/3)*ArcTan[(1 - (2*a^(1/3)*x)/b^(1/3))/Sqrt[3]] + 28*b^(4/3)*Log[b^(1/3) + a^(1/3)*x] - 14*b^(4/3)*Log[b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2])/(36*a^(10/3))","A",1
1981,1,38,46,0.0234373,"\int \frac{x^2}{\left(a+\frac{b}{x^3}\right)^2} \, dx","Integrate[x^2/(a + b/x^3)^2,x]","\frac{-\frac{b^2}{a x^3+b}-2 b \log \left(a x^3+b\right)+a x^3}{3 a^3}","-\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,"(a*x^3 - b^2/(b + a*x^3) - 2*b*Log[b + a*x^3])/(3*a^3)","A",1
1982,1,131,146,0.093243,"\int \frac{x}{\left(a+\frac{b}{x^3}\right)^2} \, dx","Integrate[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)+\frac{6 a^{2/3} b x^2}{a x^3+b}+9 a^{2/3} x^2+10 b^{2/3} \log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)+10 \sqrt{3} b^{2/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{a} x}{\sqrt[3]{b}}}{\sqrt{3}}\right)}{18 a^{8/3}}","-\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,"(9*a^(2/3)*x^2 + (6*a^(2/3)*b*x^2)/(b + a*x^3) + 10*Sqrt[3]*b^(2/3)*ArcTan[(1 - (2*a^(1/3)*x)/b^(1/3))/Sqrt[3]] + 10*b^(2/3)*Log[b^(1/3) + a^(1/3)*x] - 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",1
1983,1,127,144,0.1153892,"\int \frac{1}{\left(a+\frac{b}{x^3}\right)^2} \, dx","Integrate[(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)+\frac{3 \sqrt[3]{a} b x}{a x^3+b}-4 \sqrt[3]{b} \log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)+4 \sqrt{3} \sqrt[3]{b} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{a} x}{\sqrt[3]{b}}}{\sqrt{3}}\right)+9 \sqrt[3]{a} x}{9 a^{7/3}}","\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,"(9*a^(1/3)*x + (3*a^(1/3)*b*x)/(b + a*x^3) + 4*Sqrt[3]*b^(1/3)*ArcTan[(1 - (2*a^(1/3)*x)/b^(1/3))/Sqrt[3]] - 4*b^(1/3)*Log[b^(1/3) + a^(1/3)*x] + 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",1
1984,1,27,33,0.0102402,"\int \frac{1}{\left(a+\frac{b}{x^3}\right)^2 x} \, dx","Integrate[1/((a + b/x^3)^2*x),x]","\frac{\frac{b}{a x^3+b}+\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/(b + a*x^3) + Log[b + a*x^3])/(3*a^2)","A",1
1985,1,119,136,0.0769165,"\int \frac{1}{\left(a+\frac{b}{x^3}\right)^2 x^2} \, dx","Integrate[1/((a + b/x^3)^2*x^2),x]","\frac{\frac{\log \left(a^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3}\right)}{\sqrt[3]{b}}-\frac{3 a^{2/3} x^2}{a x^3+b}-\frac{2 \log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{\sqrt[3]{b}}-\frac{2 \sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{a} x}{\sqrt[3]{b}}}{\sqrt{3}}\right)}{\sqrt[3]{b}}}{9 a^{5/3}}","\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,"((-3*a^(2/3)*x^2)/(b + a*x^3) - (2*Sqrt[3]*ArcTan[(1 - (2*a^(1/3)*x)/b^(1/3))/Sqrt[3]])/b^(1/3) - (2*Log[b^(1/3) + a^(1/3)*x])/b^(1/3) + Log[b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2]/b^(1/3))/(9*a^(5/3))","A",1
1986,1,118,134,0.0689575,"\int \frac{1}{\left(a+\frac{b}{x^3}\right)^2 x^3} \, dx","Integrate[1/((a + b/x^3)^2*x^3),x]","\frac{-\frac{\log \left(a^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3}\right)}{b^{2/3}}+\frac{2 \log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{b^{2/3}}-\frac{2 \sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{a} x}{\sqrt[3]{b}}}{\sqrt{3}}\right)}{b^{2/3}}-\frac{6 \sqrt[3]{a} x}{a x^3+b}}{18 a^{4/3}}","-\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,"((-6*a^(1/3)*x)/(b + a*x^3) - (2*Sqrt[3]*ArcTan[(1 - (2*a^(1/3)*x)/b^(1/3))/Sqrt[3]])/b^(2/3) + (2*Log[b^(1/3) + a^(1/3)*x])/b^(2/3) - Log[b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2]/b^(2/3))/(18*a^(4/3))","A",1
1987,1,16,16,0.0054627,"\int \frac{1}{\left(a+\frac{b}{x^3}\right)^2 x^4} \, dx","Integrate[1/((a + b/x^3)^2*x^4),x]","-\frac{1}{3 a \left(a x^3+b\right)}","\frac{1}{3 b \left(a+\frac{b}{x^3}\right)}",1,"-1/3*1/(a*(b + a*x^3))","A",1
1988,1,119,136,0.0685684,"\int \frac{1}{\left(a+\frac{b}{x^3}\right)^2 x^5} \, dx","Integrate[1/((a + b/x^3)^2*x^5),x]","\frac{\frac{\log \left(a^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3}\right)}{a^{2/3}}-\frac{2 \log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{a^{2/3}}-\frac{2 \sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{a} x}{\sqrt[3]{b}}}{\sqrt{3}}\right)}{a^{2/3}}+\frac{6 \sqrt[3]{b} x^2}{a x^3+b}}{18 b^{4/3}}","\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,"((6*b^(1/3)*x^2)/(b + a*x^3) - (2*Sqrt[3]*ArcTan[(1 - (2*a^(1/3)*x)/b^(1/3))/Sqrt[3]])/a^(2/3) - (2*Log[b^(1/3) + a^(1/3)*x])/a^(2/3) + Log[b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2]/a^(2/3))/(18*b^(4/3))","A",1
1989,1,118,134,0.0666619,"\int \frac{1}{\left(a+\frac{b}{x^3}\right)^2 x^6} \, dx","Integrate[1/((a + b/x^3)^2*x^6),x]","\frac{-\frac{\log \left(a^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3}\right)}{\sqrt[3]{a}}+\frac{3 b^{2/3} x}{a x^3+b}+\frac{2 \log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{\sqrt[3]{a}}-\frac{2 \sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{a} x}{\sqrt[3]{b}}}{\sqrt{3}}\right)}{\sqrt[3]{a}}}{9 b^{5/3}}","-\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,"((3*b^(2/3)*x)/(b + a*x^3) - (2*Sqrt[3]*ArcTan[(1 - (2*a^(1/3)*x)/b^(1/3))/Sqrt[3]])/a^(1/3) + (2*Log[b^(1/3) + a^(1/3)*x])/a^(1/3) - Log[b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2]/a^(1/3))/(9*b^(5/3))","A",1
1990,1,33,38,0.0186365,"\int \frac{1}{\left(a+\frac{b}{x^3}\right)^2 x^7} \, dx","Integrate[1/((a + b/x^3)^2*x^7),x]","\frac{\frac{b}{a x^3+b}-\log \left(a x^3+b\right)+3 \log (x)}{3 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,"(b/(b + a*x^3) + 3*Log[x] - Log[b + a*x^3])/(3*b^2)","A",1
1991,1,83,71,0.166961,"\int \sqrt{a+\frac{b}{x^3}} x^5 \, dx","Integrate[Sqrt[a + b/x^3]*x^5,x]","\frac{x^{3/2} \sqrt{a+\frac{b}{x^3}} \left(\sqrt{a} x^{3/2} \left(2 a x^3+b\right)-\frac{b^{3/2} \sinh ^{-1}\left(\frac{\sqrt{a} x^{3/2}}{\sqrt{b}}\right)}{\sqrt{\frac{a x^3}{b}+1}}\right)}{12 a^{3/2}}","-\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^3}}}{\sqrt{a}}\right)}{12 a^{3/2}}+\frac{b x^3 \sqrt{a+\frac{b}{x^3}}}{12 a}+\frac{1}{6} x^6 \sqrt{a+\frac{b}{x^3}}",1,"(Sqrt[a + b/x^3]*x^(3/2)*(Sqrt[a]*x^(3/2)*(b + 2*a*x^3) - (b^(3/2)*ArcSinh[(Sqrt[a]*x^(3/2))/Sqrt[b]])/Sqrt[1 + (a*x^3)/b]))/(12*a^(3/2))","A",1
1992,1,68,47,0.1143613,"\int \sqrt{a+\frac{b}{x^3}} x^2 \, dx","Integrate[Sqrt[a + b/x^3]*x^2,x]","\frac{1}{3} x^{3/2} \sqrt{a+\frac{b}{x^3}} \left(\frac{\sqrt{b} \sinh ^{-1}\left(\frac{\sqrt{a} x^{3/2}}{\sqrt{b}}\right)}{\sqrt{a} \sqrt{\frac{a x^3}{b}+1}}+x^{3/2}\right)","\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^(3/2)*(x^(3/2) + (Sqrt[b]*ArcSinh[(Sqrt[a]*x^(3/2))/Sqrt[b]])/(Sqrt[a]*Sqrt[1 + (a*x^3)/b])))/3","A",1
1993,1,64,43,0.0959951,"\int \frac{\sqrt{a+\frac{b}{x^3}}}{x} \, dx","Integrate[Sqrt[a + b/x^3]/x,x]","\frac{2}{3} \sqrt{a+\frac{b}{x^3}} \left(\frac{\sqrt{a} x^{3/2} \sinh ^{-1}\left(\frac{\sqrt{a} x^{3/2}}{\sqrt{b}}\right)}{\sqrt{b} \sqrt{\frac{a x^3}{b}+1}}-1\right)","\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]*(-1 + (Sqrt[a]*x^(3/2)*ArcSinh[(Sqrt[a]*x^(3/2))/Sqrt[b]])/(Sqrt[b]*Sqrt[1 + (a*x^3)/b])))/3","A",1
1994,1,18,18,0.0116651,"\int \frac{\sqrt{a+\frac{b}{x^3}}}{x^4} \, dx","Integrate[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
1995,1,38,38,0.0110098,"\int \frac{\sqrt{a+\frac{b}{x^3}}}{x^7} \, dx","Integrate[Sqrt[a + b/x^3]/x^7,x]","\frac{2 \sqrt{a+\frac{b}{x^3}} \left(a x^3+b\right) \left(2 a x^3-3 b\right)}{45 b^2 x^6}","\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*Sqrt[a + b/x^3]*(b + a*x^3)*(-3*b + 2*a*x^3))/(45*b^2*x^6)","A",1
1996,1,49,59,0.0126585,"\int \frac{\sqrt{a+\frac{b}{x^3}}}{x^{10}} \, dx","Integrate[Sqrt[a + b/x^3]/x^10,x]","-\frac{2 \sqrt{a+\frac{b}{x^3}} \left(a x^3+b\right) \left(8 a^2 x^6-12 a b x^3+15 b^2\right)}{315 b^3 x^9}","-\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*Sqrt[a + b/x^3]*(b + a*x^3)*(15*b^2 - 12*a*b*x^3 + 8*a^2*x^6))/(315*b^3*x^9)","A",1
1997,1,60,80,0.0138676,"\int \frac{\sqrt{a+\frac{b}{x^3}}}{x^{13}} \, dx","Integrate[Sqrt[a + b/x^3]/x^13,x]","\frac{2 \sqrt{a+\frac{b}{x^3}} \left(a x^3+b\right) \left(16 a^3 x^9-24 a^2 b x^6+30 a b^2 x^3-35 b^3\right)}{945 b^4 x^{12}}","\frac{2 a^3 \left(a+\frac{b}{x^3}\right)^{3/2}}{9 b^4}-\frac{2 a^2 \left(a+\frac{b}{x^3}\right)^{5/2}}{5 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*Sqrt[a + b/x^3]*(b + a*x^3)*(-35*b^3 + 30*a*b^2*x^3 - 24*a^2*b*x^6 + 16*a^3*x^9))/(945*b^4*x^12)","A",1
1998,1,96,291,0.0761971,"\int \sqrt{a+\frac{b}{x^3}} x^7 \, dx","Integrate[Sqrt[a + b/x^3]*x^7,x]","\frac{x^2 \sqrt{a+\frac{b}{x^3}} \left(\sqrt{\frac{a x^3}{b}+1} \left(10 a^2 x^6+3 a b x^3-7 b^2\right)+7 b^2 \, _2F_1\left(-\frac{1}{2},\frac{1}{6};\frac{7}{6};-\frac{a x^3}{b}\right)\right)}{80 a^2 \sqrt{\frac{a x^3}{b}+1}}","-\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,"(Sqrt[a + b/x^3]*x^2*(Sqrt[1 + (a*x^3)/b]*(-7*b^2 + 3*a*b*x^3 + 10*a^2*x^6) + 7*b^2*Hypergeometric2F1[-1/2, 1/6, 7/6, -((a*x^3)/b)]))/(80*a^2*Sqrt[1 + (a*x^3)/b])","C",1
1999,1,80,267,0.0575389,"\int \sqrt{a+\frac{b}{x^3}} x^4 \, dx","Integrate[Sqrt[a + b/x^3]*x^4,x]","\frac{x^2 \sqrt{a+\frac{b}{x^3}} \left(\left(a x^3+b\right) \sqrt{\frac{a x^3}{b}+1}-b \, _2F_1\left(-\frac{1}{2},\frac{1}{6};\frac{7}{6};-\frac{a x^3}{b}\right)\right)}{5 a \sqrt{\frac{a x^3}{b}+1}}","\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,"(Sqrt[a + b/x^3]*x^2*((b + a*x^3)*Sqrt[1 + (a*x^3)/b] - b*Hypergeometric2F1[-1/2, 1/6, 7/6, -((a*x^3)/b)]))/(5*a*Sqrt[1 + (a*x^3)/b])","C",1
2000,1,49,242,0.0098405,"\int \sqrt{a+\frac{b}{x^3}} x \, dx","Integrate[Sqrt[a + b/x^3]*x,x]","\frac{2 x^2 \sqrt{a+\frac{b}{x^3}} \, _2F_1\left(-\frac{1}{2},\frac{1}{6};\frac{7}{6};-\frac{a x^3}{b}\right)}{\sqrt{\frac{a x^3}{b}+1}}","\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,"(2*Sqrt[a + b/x^3]*x^2*Hypergeometric2F1[-1/2, 1/6, 7/6, -((a*x^3)/b)])/Sqrt[1 + (a*x^3)/b]","C",1
2001,1,51,243,0.013249,"\int \frac{\sqrt{a+\frac{b}{x^3}}}{x^2} \, dx","Integrate[Sqrt[a + b/x^3]/x^2,x]","-\frac{2 \sqrt{a+\frac{b}{x^3}} \, _2F_1\left(-\frac{5}{6},-\frac{1}{2};\frac{1}{6};-\frac{a x^3}{b}\right)}{5 x \sqrt{\frac{a x^3}{b}+1}}","-\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]*Hypergeometric2F1[-5/6, -1/2, 1/6, -((a*x^3)/b)])/(5*x*Sqrt[1 + (a*x^3)/b])","C",1
2002,1,51,267,0.0182961,"\int \frac{\sqrt{a+\frac{b}{x^3}}}{x^5} \, dx","Integrate[Sqrt[a + b/x^3]/x^5,x]","-\frac{2 \sqrt{a+\frac{b}{x^3}} \, _2F_1\left(-\frac{11}{6},-\frac{1}{2};-\frac{5}{6};-\frac{a x^3}{b}\right)}{11 x^4 \sqrt{\frac{a x^3}{b}+1}}","\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]*Hypergeometric2F1[-11/6, -1/2, -5/6, -((a*x^3)/b)])/(11*x^4*Sqrt[1 + (a*x^3)/b])","C",1
2003,1,51,291,0.0142204,"\int \frac{\sqrt{a+\frac{b}{x^3}}}{x^8} \, dx","Integrate[Sqrt[a + b/x^3]/x^8,x]","-\frac{2 \sqrt{a+\frac{b}{x^3}} \, _2F_1\left(-\frac{17}{6},-\frac{1}{2};-\frac{11}{6};-\frac{a x^3}{b}\right)}{17 x^7 \sqrt{\frac{a x^3}{b}+1}}","\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{2 \sqrt{a+\frac{b}{x^3}}}{17 x^7}-\frac{6 a \sqrt{a+\frac{b}{x^3}}}{187 b x^4}",1,"(-2*Sqrt[a + b/x^3]*Hypergeometric2F1[-17/6, -1/2, -11/6, -((a*x^3)/b)])/(17*x^7*Sqrt[1 + (a*x^3)/b])","C",1
2004,1,80,563,0.0497677,"\int \sqrt{a+\frac{b}{x^3}} x^6 \, dx","Integrate[Sqrt[a + b/x^3]*x^6,x]","\frac{x^4 \sqrt{a+\frac{b}{x^3}} \left(\left(a x^3+b\right) \sqrt{\frac{a x^3}{b}+1}-b \, _2F_1\left(-\frac{1}{2},\frac{5}{6};\frac{11}{6};-\frac{a x^3}{b}\right)\right)}{7 a \sqrt{\frac{a x^3}{b}+1}}","\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{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{15 b^2 x \sqrt{a+\frac{b}{x^3}}}{112 a^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,"(Sqrt[a + b/x^3]*x^4*((b + a*x^3)*Sqrt[1 + (a*x^3)/b] - b*Hypergeometric2F1[-1/2, 5/6, 11/6, -((a*x^3)/b)]))/(7*a*Sqrt[1 + (a*x^3)/b])","C",1
2005,1,51,539,0.0120063,"\int \sqrt{a+\frac{b}{x^3}} x^3 \, dx","Integrate[Sqrt[a + b/x^3]*x^3,x]","\frac{2 x^4 \sqrt{a+\frac{b}{x^3}} \, _2F_1\left(-\frac{1}{2},\frac{5}{6};\frac{11}{6};-\frac{a x^3}{b}\right)}{5 \sqrt{\frac{a x^3}{b}+1}}","-\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{3 b x \sqrt{a+\frac{b}{x^3}}}{8 a}+\frac{1}{4} x^4 \sqrt{a+\frac{b}{x^3}}",1,"(2*Sqrt[a + b/x^3]*x^4*Hypergeometric2F1[-1/2, 5/6, 11/6, -((a*x^3)/b)])/(5*Sqrt[1 + (a*x^3)/b])","C",1
2006,1,47,507,0.0110424,"\int \sqrt{a+\frac{b}{x^3}} \, dx","Integrate[Sqrt[a + b/x^3],x]","-\frac{2 x \sqrt{a+\frac{b}{x^3}} \, _2F_1\left(-\frac{1}{2},-\frac{1}{6};\frac{5}{6};-\frac{a x^3}{b}\right)}{\sqrt{\frac{a x^3}{b}+1}}","-\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,"(-2*Sqrt[a + b/x^3]*x*Hypergeometric2F1[-1/2, -1/6, 5/6, -((a*x^3)/b)])/Sqrt[1 + (a*x^3)/b]","C",1
2007,1,51,517,0.0140508,"\int \frac{\sqrt{a+\frac{b}{x^3}}}{x^3} \, dx","Integrate[Sqrt[a + b/x^3]/x^3,x]","-\frac{2 \sqrt{a+\frac{b}{x^3}} \, _2F_1\left(-\frac{7}{6},-\frac{1}{2};-\frac{1}{6};-\frac{a x^3}{b}\right)}{7 x^2 \sqrt{\frac{a x^3}{b}+1}}","-\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,"(-2*Sqrt[a + b/x^3]*Hypergeometric2F1[-7/6, -1/2, -1/6, -((a*x^3)/b)])/(7*x^2*Sqrt[1 + (a*x^3)/b])","C",1
2008,1,51,541,0.014166,"\int \frac{\sqrt{a+\frac{b}{x^3}}}{x^6} \, dx","Integrate[Sqrt[a + b/x^3]/x^6,x]","-\frac{2 \sqrt{a+\frac{b}{x^3}} \, _2F_1\left(-\frac{13}{6},-\frac{1}{2};-\frac{7}{6};-\frac{a x^3}{b}\right)}{13 x^5 \sqrt{\frac{a x^3}{b}+1}}","\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{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{2 \sqrt{a+\frac{b}{x^3}}}{13 x^5}-\frac{6 a \sqrt{a+\frac{b}{x^3}}}{91 b x^2}",1,"(-2*Sqrt[a + b/x^3]*Hypergeometric2F1[-13/6, -1/2, -7/6, -((a*x^3)/b)])/(13*x^5*Sqrt[1 + (a*x^3)/b])","C",1
2009,1,51,565,0.0141125,"\int \frac{\sqrt{a+\frac{b}{x^3}}}{x^9} \, dx","Integrate[Sqrt[a + b/x^3]/x^9,x]","-\frac{2 \sqrt{a+\frac{b}{x^3}} \, _2F_1\left(-\frac{19}{6},-\frac{1}{2};-\frac{13}{6};-\frac{a x^3}{b}\right)}{19 x^8 \sqrt{\frac{a x^3}{b}+1}}","-\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{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{2 \sqrt{a+\frac{b}{x^3}}}{19 x^8}-\frac{6 a \sqrt{a+\frac{b}{x^3}}}{247 b x^5}",1,"(-2*Sqrt[a + b/x^3]*Hypergeometric2F1[-19/6, -1/2, -13/6, -((a*x^3)/b)])/(19*x^8*Sqrt[1 + (a*x^3)/b])","C",1
2010,1,80,68,0.1884045,"\int \left(a+\frac{b}{x^3}\right)^{3/2} x^5 \, dx","Integrate[(a + b/x^3)^(3/2)*x^5,x]","\frac{1}{12} x^{3/2} \sqrt{a+\frac{b}{x^3}} \left(\frac{3 b^{3/2} \sinh ^{-1}\left(\frac{\sqrt{a} x^{3/2}}{\sqrt{b}}\right)}{\sqrt{a} \sqrt{\frac{a x^3}{b}+1}}+x^{3/2} \left(2 a x^3+5 b\right)\right)","\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^3}}}{\sqrt{a}}\right)}{4 \sqrt{a}}+\frac{1}{4} b x^3 \sqrt{a+\frac{b}{x^3}}+\frac{1}{6} x^6 \left(a+\frac{b}{x^3}\right)^{3/2}",1,"(Sqrt[a + b/x^3]*x^(3/2)*(x^(3/2)*(5*b + 2*a*x^3) + (3*b^(3/2)*ArcSinh[(Sqrt[a]*x^(3/2))/Sqrt[b]])/(Sqrt[a]*Sqrt[1 + (a*x^3)/b])))/12","A",1
2011,1,49,58,0.0183394,"\int \left(a+\frac{b}{x^3}\right)^{3/2} x^2 \, dx","Integrate[(a + b/x^3)^(3/2)*x^2,x]","-\frac{2 b \sqrt{a+\frac{b}{x^3}} \, _2F_1\left(-\frac{3}{2},-\frac{1}{2};\frac{1}{2};-\frac{a x^3}{b}\right)}{3 \sqrt{\frac{a x^3}{b}+1}}","\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,"(-2*b*Sqrt[a + b/x^3]*Hypergeometric2F1[-3/2, -1/2, 1/2, -((a*x^3)/b)])/(3*Sqrt[1 + (a*x^3)/b])","C",1
2012,1,52,59,0.0229287,"\int \frac{\left(a+\frac{b}{x^3}\right)^{3/2}}{x} \, dx","Integrate[(a + b/x^3)^(3/2)/x,x]","-\frac{2 b \sqrt{a+\frac{b}{x^3}} \, _2F_1\left(-\frac{3}{2},-\frac{3}{2};-\frac{1}{2};-\frac{a x^3}{b}\right)}{9 x^3 \sqrt{\frac{a x^3}{b}+1}}","\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*b*Sqrt[a + b/x^3]*Hypergeometric2F1[-3/2, -3/2, -1/2, -((a*x^3)/b)])/(9*x^3*Sqrt[1 + (a*x^3)/b])","C",1
2013,1,28,18,0.0101389,"\int \frac{\left(a+\frac{b}{x^3}\right)^{3/2}}{x^4} \, dx","Integrate[(a + b/x^3)^(3/2)/x^4,x]","-\frac{2 \left(a+\frac{b}{x^3}\right)^{3/2} \left(a x^3+b\right)}{15 b x^3}","-\frac{2 \left(a+\frac{b}{x^3}\right)^{5/2}}{15 b}",1,"(-2*(a + b/x^3)^(3/2)*(b + a*x^3))/(15*b*x^3)","A",1
2014,1,40,38,0.0122721,"\int \frac{\left(a+\frac{b}{x^3}\right)^{3/2}}{x^7} \, dx","Integrate[(a + b/x^3)^(3/2)/x^7,x]","\frac{2 \sqrt{a+\frac{b}{x^3}} \left(a x^3+b\right)^2 \left(2 a x^3-5 b\right)}{105 b^2 x^9}","\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*Sqrt[a + b/x^3]*(b + a*x^3)^2*(-5*b + 2*a*x^3))/(105*b^2*x^9)","A",1
2015,1,51,59,0.0141933,"\int \frac{\left(a+\frac{b}{x^3}\right)^{3/2}}{x^{10}} \, dx","Integrate[(a + b/x^3)^(3/2)/x^10,x]","-\frac{2 \sqrt{a+\frac{b}{x^3}} \left(a x^3+b\right)^2 \left(8 a^2 x^6-20 a b x^3+35 b^2\right)}{945 b^3 x^{12}}","-\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*Sqrt[a + b/x^3]*(b + a*x^3)^2*(35*b^2 - 20*a*b*x^3 + 8*a^2*x^6))/(945*b^3*x^12)","A",1
2016,1,62,80,0.0160082,"\int \frac{\left(a+\frac{b}{x^3}\right)^{3/2}}{x^{13}} \, dx","Integrate[(a + b/x^3)^(3/2)/x^13,x]","\frac{2 \sqrt{a+\frac{b}{x^3}} \left(a x^3+b\right)^2 \left(16 a^3 x^9-40 a^2 b x^6+70 a b^2 x^3-105 b^3\right)}{3465 b^4 x^{15}}","\frac{2 a^3 \left(a+\frac{b}{x^3}\right)^{5/2}}{15 b^4}-\frac{2 a^2 \left(a+\frac{b}{x^3}\right)^{7/2}}{7 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*Sqrt[a + b/x^3]*(b + a*x^3)^2*(-105*b^3 + 70*a*b^2*x^3 - 40*a^2*b*x^6 + 16*a^3*x^9))/(3465*b^4*x^15)","A",1
2017,1,97,74,0.0428589,"\int \frac{x^5}{\sqrt{a+\frac{b}{x^3}}} \, dx","Integrate[x^5/Sqrt[a + b/x^3],x]","\frac{\sqrt{a} x^{3/2} \left(2 a^2 x^6-a b x^3-3 b^2\right)+3 b^2 \sqrt{a x^3+b} \tanh ^{-1}\left(\frac{\sqrt{a} x^{3/2}}{\sqrt{a x^3+b}}\right)}{12 a^{5/2} x^{3/2} \sqrt{a+\frac{b}{x^3}}}","\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,"(Sqrt[a]*x^(3/2)*(-3*b^2 - a*b*x^3 + 2*a^2*x^6) + 3*b^2*Sqrt[b + a*x^3]*ArcTanh[(Sqrt[a]*x^(3/2))/Sqrt[b + a*x^3]])/(12*a^(5/2)*Sqrt[a + b/x^3]*x^(3/2))","A",1
2018,1,81,50,0.0272052,"\int \frac{x^2}{\sqrt{a+\frac{b}{x^3}}} \, dx","Integrate[x^2/Sqrt[a + b/x^3],x]","\frac{\sqrt{a} x^{3/2} \left(a x^3+b\right)-b \sqrt{a x^3+b} \tanh ^{-1}\left(\frac{\sqrt{a} x^{3/2}}{\sqrt{a x^3+b}}\right)}{3 a^{3/2} x^{3/2} \sqrt{a+\frac{b}{x^3}}}","\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]*x^(3/2)*(b + a*x^3) - b*Sqrt[b + a*x^3]*ArcTanh[(Sqrt[a]*x^(3/2))/Sqrt[b + a*x^3]])/(3*a^(3/2)*Sqrt[a + b/x^3]*x^(3/2))","A",1
2019,1,59,27,0.0163621,"\int \frac{1}{\sqrt{a+\frac{b}{x^3}} x} \, dx","Integrate[1/(Sqrt[a + b/x^3]*x),x]","\frac{2 \sqrt{a x^3+b} \tanh ^{-1}\left(\frac{\sqrt{a} x^{3/2}}{\sqrt{a x^3+b}}\right)}{3 \sqrt{a} x^{3/2} \sqrt{a+\frac{b}{x^3}}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^3}}}{\sqrt{a}}\right)}{3 \sqrt{a}}",1,"(2*Sqrt[b + a*x^3]*ArcTanh[(Sqrt[a]*x^(3/2))/Sqrt[b + a*x^3]])/(3*Sqrt[a]*Sqrt[a + b/x^3]*x^(3/2))","B",1
2020,1,18,18,0.0082543,"\int \frac{1}{\sqrt{a+\frac{b}{x^3}} x^4} \, dx","Integrate[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
2021,1,31,38,0.0161706,"\int \frac{1}{\sqrt{a+\frac{b}{x^3}} x^7} \, dx","Integrate[1/(Sqrt[a + b/x^3]*x^7),x]","\frac{2 \sqrt{a+\frac{b}{x^3}} \left(2 a x^3-b\right)}{9 b^2 x^3}","\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*Sqrt[a + b/x^3]*(-b + 2*a*x^3))/(9*b^2*x^3)","A",1
2022,1,42,59,0.0175731,"\int \frac{1}{\sqrt{a+\frac{b}{x^3}} x^{10}} \, dx","Integrate[1/(Sqrt[a + b/x^3]*x^10),x]","-\frac{2 \sqrt{a+\frac{b}{x^3}} \left(8 a^2 x^6-4 a b x^3+3 b^2\right)}{45 b^3 x^6}","-\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*Sqrt[a + b/x^3]*(3*b^2 - 4*a*b*x^3 + 8*a^2*x^6))/(45*b^3*x^6)","A",1
2023,1,53,80,0.0196841,"\int \frac{1}{\sqrt{a+\frac{b}{x^3}} x^{13}} \, dx","Integrate[1/(Sqrt[a + b/x^3]*x^13),x]","\frac{2 \sqrt{a+\frac{b}{x^3}} \left(16 a^3 x^9-8 a^2 b x^6+6 a b^2 x^3-5 b^3\right)}{105 b^4 x^9}","\frac{2 a^3 \sqrt{a+\frac{b}{x^3}}}{3 b^4}-\frac{2 a^2 \left(a+\frac{b}{x^3}\right)^{3/2}}{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*Sqrt[a + b/x^3]*(-5*b^3 + 6*a*b^2*x^3 - 8*a^2*b*x^6 + 16*a^3*x^9))/(105*b^4*x^9)","A",1
2024,1,91,294,0.0289303,"\int \frac{x^7}{\sqrt{a+\frac{b}{x^3}}} \, dx","Integrate[x^7/Sqrt[a + b/x^3],x]","\frac{40 a^3 x^9-12 a^2 b x^6-91 b^3 \sqrt{\frac{a x^3}{b}+1} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};-\frac{a x^3}{b}\right)+39 a b^2 x^3+91 b^3}{320 a^3 x \sqrt{a+\frac{b}{x^3}}}","\frac{91 b^2 x^2 \sqrt{a+\frac{b}{x^3}}}{320 a^3}-\frac{13 b x^5 \sqrt{a+\frac{b}{x^3}}}{80 a^2}+\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{x^8 \sqrt{a+\frac{b}{x^3}}}{8 a}",1,"(91*b^3 + 39*a*b^2*x^3 - 12*a^2*b*x^6 + 40*a^3*x^9 - 91*b^3*Sqrt[1 + (a*x^3)/b]*Hypergeometric2F1[1/6, 1/2, 7/6, -((a*x^3)/b)])/(320*a^3*Sqrt[a + b/x^3]*x)","C",1
2025,1,80,270,0.0256406,"\int \frac{x^4}{\sqrt{a+\frac{b}{x^3}}} \, dx","Integrate[x^4/Sqrt[a + b/x^3],x]","\frac{4 a^2 x^6+7 b^2 \sqrt{\frac{a x^3}{b}+1} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};-\frac{a x^3}{b}\right)-3 a b x^3-7 b^2}{20 a^2 x \sqrt{a+\frac{b}{x^3}}}","-\frac{7 b x^2 \sqrt{a+\frac{b}{x^3}}}{20 a^2}-\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{x^5 \sqrt{a+\frac{b}{x^3}}}{5 a}",1,"(-7*b^2 - 3*a*b*x^3 + 4*a^2*x^6 + 7*b^2*Sqrt[1 + (a*x^3)/b]*Hypergeometric2F1[1/6, 1/2, 7/6, -((a*x^3)/b)])/(20*a^2*Sqrt[a + b/x^3]*x)","C",1
2026,1,64,248,0.0212546,"\int \frac{x}{\sqrt{a+\frac{b}{x^3}}} \, dx","Integrate[x/Sqrt[a + b/x^3],x]","\frac{-b \sqrt{\frac{a x^3}{b}+1} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};-\frac{a x^3}{b}\right)+a x^3+b}{2 a x \sqrt{a+\frac{b}{x^3}}}","\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,"(b + a*x^3 - b*Sqrt[1 + (a*x^3)/b]*Hypergeometric2F1[1/6, 1/2, 7/6, -((a*x^3)/b)])/(2*a*Sqrt[a + b/x^3]*x)","C",1
2027,1,49,221,0.0119579,"\int \frac{1}{\sqrt{a+\frac{b}{x^3}} x^2} \, dx","Integrate[1/(Sqrt[a + b/x^3]*x^2),x]","\frac{2 \sqrt{\frac{a x^3}{b}+1} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};-\frac{a x^3}{b}\right)}{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)}{\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[1 + (a*x^3)/b]*Hypergeometric2F1[1/6, 1/2, 7/6, -((a*x^3)/b)])/(Sqrt[a + b/x^3]*x)","C",1
2028,1,51,246,0.0138922,"\int \frac{1}{\sqrt{a+\frac{b}{x^3}} x^5} \, dx","Integrate[1/(Sqrt[a + b/x^3]*x^5),x]","-\frac{2 \sqrt{\frac{a x^3}{b}+1} \, _2F_1\left(-\frac{5}{6},\frac{1}{2};\frac{1}{6};-\frac{a x^3}{b}\right)}{5 x^4 \sqrt{a+\frac{b}{x^3}}}","\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[1 + (a*x^3)/b]*Hypergeometric2F1[-5/6, 1/2, 1/6, -((a*x^3)/b)])/(5*Sqrt[a + b/x^3]*x^4)","C",1
2029,1,51,270,0.0128495,"\int \frac{1}{\sqrt{a+\frac{b}{x^3}} x^8} \, dx","Integrate[1/(Sqrt[a + b/x^3]*x^8),x]","-\frac{2 \sqrt{\frac{a x^3}{b}+1} \, _2F_1\left(-\frac{11}{6},\frac{1}{2};-\frac{5}{6};-\frac{a x^3}{b}\right)}{11 x^7 \sqrt{a+\frac{b}{x^3}}}","-\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[1 + (a*x^3)/b]*Hypergeometric2F1[-11/6, 1/2, -5/6, -((a*x^3)/b)])/(11*Sqrt[a + b/x^3]*x^7)","C",1
2030,1,79,566,0.0255946,"\int \frac{x^6}{\sqrt{a+\frac{b}{x^3}}} \, dx","Integrate[x^6/Sqrt[a + b/x^3],x]","\frac{8 a^2 x^7+11 b^2 x \sqrt{\frac{a x^3}{b}+1} \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};-\frac{a x^3}{b}\right)-3 a b x^4-11 b^2 x}{56 a^2 \sqrt{a+\frac{b}{x^3}}}","-\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{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^2 x \sqrt{a+\frac{b}{x^3}}}{112 a^3}-\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,"(-11*b^2*x - 3*a*b*x^4 + 8*a^2*x^7 + 11*b^2*x*Sqrt[1 + (a*x^3)/b]*Hypergeometric2F1[1/2, 5/6, 11/6, -((a*x^3)/b)])/(56*a^2*Sqrt[a + b/x^3])","C",1
2031,1,62,542,0.0239472,"\int \frac{x^3}{\sqrt{a+\frac{b}{x^3}}} \, dx","Integrate[x^3/Sqrt[a + b/x^3],x]","\frac{x \left(-b \sqrt{\frac{a x^3}{b}+1} \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};-\frac{a x^3}{b}\right)+a x^3+b\right)}{4 a \sqrt{a+\frac{b}{x^3}}}","\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^{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 x \sqrt{a+\frac{b}{x^3}}}{8 a^2}+\frac{x^4 \sqrt{a+\frac{b}{x^3}}}{4 a}",1,"(x*(b + a*x^3 - b*Sqrt[1 + (a*x^3)/b]*Hypergeometric2F1[1/2, 5/6, 11/6, -((a*x^3)/b)]))/(4*a*Sqrt[a + b/x^3])","C",1
2032,1,49,513,0.0116084,"\int \frac{1}{\sqrt{a+\frac{b}{x^3}}} \, dx","Integrate[1/Sqrt[a + b/x^3],x]","\frac{2 x \sqrt{\frac{a x^3}{b}+1} \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};-\frac{a x^3}{b}\right)}{5 \sqrt{a+\frac{b}{x^3}}}","-\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,"(2*x*Sqrt[1 + (a*x^3)/b]*Hypergeometric2F1[1/2, 5/6, 11/6, -((a*x^3)/b)])/(5*Sqrt[a + b/x^3])","C",1
2033,1,49,491,0.013646,"\int \frac{1}{\sqrt{a+\frac{b}{x^3}} x^3} \, dx","Integrate[1/(Sqrt[a + b/x^3]*x^3),x]","-\frac{2 \sqrt{\frac{a x^3}{b}+1} \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{5}{6};-\frac{a x^3}{b}\right)}{x^2 \sqrt{a+\frac{b}{x^3}}}","-\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[1 + (a*x^3)/b]*Hypergeometric2F1[-1/6, 1/2, 5/6, -((a*x^3)/b)])/(Sqrt[a + b/x^3]*x^2)","C",1
2034,1,51,520,0.0143231,"\int \frac{1}{\sqrt{a+\frac{b}{x^3}} x^6} \, dx","Integrate[1/(Sqrt[a + b/x^3]*x^6),x]","-\frac{2 \sqrt{\frac{a x^3}{b}+1} \, _2F_1\left(-\frac{7}{6},\frac{1}{2};-\frac{1}{6};-\frac{a x^3}{b}\right)}{7 x^5 \sqrt{a+\frac{b}{x^3}}}","\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,"(-2*Sqrt[1 + (a*x^3)/b]*Hypergeometric2F1[-7/6, 1/2, -1/6, -((a*x^3)/b)])/(7*Sqrt[a + b/x^3]*x^5)","C",1
2035,1,51,544,0.021447,"\int \frac{1}{\sqrt{a+\frac{b}{x^3}} x^9} \, dx","Integrate[1/(Sqrt[a + b/x^3]*x^9),x]","-\frac{2 \sqrt{\frac{a x^3}{b}+1} \, _2F_1\left(-\frac{13}{6},\frac{1}{2};-\frac{7}{6};-\frac{a x^3}{b}\right)}{13 x^8 \sqrt{a+\frac{b}{x^3}}}","-\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{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{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,"(-2*Sqrt[1 + (a*x^3)/b]*Hypergeometric2F1[-13/6, 1/2, -7/6, -((a*x^3)/b)])/(13*Sqrt[a + b/x^3]*x^8)","C",1
2036,1,51,568,0.0151953,"\int \frac{1}{\sqrt{a+\frac{b}{x^3}} x^{12}} \, dx","Integrate[1/(Sqrt[a + b/x^3]*x^12),x]","-\frac{2 \sqrt{\frac{a x^3}{b}+1} \, _2F_1\left(-\frac{19}{6},\frac{1}{2};-\frac{13}{6};-\frac{a x^3}{b}\right)}{19 x^{11} \sqrt{a+\frac{b}{x^3}}}","\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{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{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,"(-2*Sqrt[1 + (a*x^3)/b]*Hypergeometric2F1[-19/6, 1/2, -13/6, -((a*x^3)/b)])/(19*Sqrt[a + b/x^3]*x^11)","C",1
2037,1,96,95,0.0553848,"\int \frac{x^5}{\left(a+\frac{b}{x^3}\right)^{3/2}} \, dx","Integrate[x^5/(a + b/x^3)^(3/2),x]","\frac{\sqrt{a} x^{3/2} \left(2 a^2 x^6-5 a b x^3-15 b^2\right)+15 b^{5/2} \sqrt{\frac{a x^3}{b}+1} \sinh ^{-1}\left(\frac{\sqrt{a} x^{3/2}}{\sqrt{b}}\right)}{12 a^{7/2} x^{3/2} \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^2}{4 a^3 \sqrt{a+\frac{b}{x^3}}}-\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,"(Sqrt[a]*x^(3/2)*(-15*b^2 - 5*a*b*x^3 + 2*a^2*x^6) + 15*b^(5/2)*Sqrt[1 + (a*x^3)/b]*ArcSinh[(Sqrt[a]*x^(3/2))/Sqrt[b]])/(12*a^(7/2)*Sqrt[a + b/x^3]*x^(3/2))","A",1
2038,1,84,64,0.0448773,"\int \frac{x^2}{\left(a+\frac{b}{x^3}\right)^{3/2}} \, dx","Integrate[x^2/(a + b/x^3)^(3/2),x]","\frac{\sqrt{a} x^{3/2} \left(a x^3+3 b\right)-3 b^{3/2} \sqrt{\frac{a x^3}{b}+1} \sinh ^{-1}\left(\frac{\sqrt{a} x^{3/2}}{\sqrt{b}}\right)}{3 a^{5/2} x^{3/2} \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{b}{a^2 \sqrt{a+\frac{b}{x^3}}}+\frac{x^3}{3 a \sqrt{a+\frac{b}{x^3}}}",1,"(Sqrt[a]*x^(3/2)*(3*b + a*x^3) - 3*b^(3/2)*Sqrt[1 + (a*x^3)/b]*ArcSinh[(Sqrt[a]*x^(3/2))/Sqrt[b]])/(3*a^(5/2)*Sqrt[a + b/x^3]*x^(3/2))","A",1
2039,1,75,46,0.0761896,"\int \frac{1}{\left(a+\frac{b}{x^3}\right)^{3/2} x} \, dx","Integrate[1/((a + b/x^3)^(3/2)*x),x]","\frac{2 \left(\sqrt{b} \sqrt{\frac{a x^3}{b}+1} \sinh ^{-1}\left(\frac{\sqrt{a} x^{3/2}}{\sqrt{b}}\right)-\sqrt{a} x^{3/2}\right)}{3 a^{3/2} x^{3/2} \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*(-(Sqrt[a]*x^(3/2)) + Sqrt[b]*Sqrt[1 + (a*x^3)/b]*ArcSinh[(Sqrt[a]*x^(3/2))/Sqrt[b]]))/(3*a^(3/2)*Sqrt[a + b/x^3]*x^(3/2))","A",1
2040,1,18,18,0.007254,"\int \frac{1}{\left(a+\frac{b}{x^3}\right)^{3/2} x^4} \, dx","Integrate[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
2041,1,29,38,0.0110441,"\int \frac{1}{\left(a+\frac{b}{x^3}\right)^{3/2} x^7} \, dx","Integrate[1/((a + b/x^3)^(3/2)*x^7),x]","-\frac{2 \left(2 a x^3+b\right)}{3 b^2 x^3 \sqrt{a+\frac{b}{x^3}}}","-\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*(b + 2*a*x^3))/(3*b^2*Sqrt[a + b/x^3]*x^3)","A",1
2042,1,42,59,0.0149302,"\int \frac{1}{\left(a+\frac{b}{x^3}\right)^{3/2} x^{10}} \, dx","Integrate[1/((a + b/x^3)^(3/2)*x^10),x]","\frac{2 \left(8 a^2 x^6+4 a b x^3-b^2\right)}{9 b^3 x^6 \sqrt{a+\frac{b}{x^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*(-b^2 + 4*a*b*x^3 + 8*a^2*x^6))/(9*b^3*Sqrt[a + b/x^3]*x^6)","A",1
2043,1,51,78,0.0157087,"\int \frac{1}{\left(a+\frac{b}{x^3}\right)^{3/2} x^{13}} \, dx","Integrate[1/((a + b/x^3)^(3/2)*x^13),x]","-\frac{2 \left(16 a^3 x^9+8 a^2 b x^6-2 a b^2 x^3+b^3\right)}{15 b^4 x^9 \sqrt{a+\frac{b}{x^3}}}","-\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*(b^3 - 2*a*b^2*x^3 + 8*a^2*b*x^6 + 16*a^3*x^9))/(15*b^4*Sqrt[a + b/x^3]*x^9)","A",1
2044,1,91,315,0.0321689,"\int \frac{x^7}{\left(a+\frac{b}{x^3}\right)^{3/2}} \, dx","Integrate[x^7/(a + b/x^3)^(3/2),x]","\frac{120 a^3 x^9-228 a^2 b x^6-1729 b^3 \sqrt{\frac{a x^3}{b}+1} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};-\frac{a x^3}{b}\right)+741 a b^2 x^3+1729 b^3}{960 a^4 x \sqrt{a+\frac{b}{x^3}}}","\frac{1729 b^2 x^2 \sqrt{a+\frac{b}{x^3}}}{960 a^4}-\frac{247 b x^5 \sqrt{a+\frac{b}{x^3}}}{240 a^3}+\frac{19 x^8 \sqrt{a+\frac{b}{x^3}}}{24 a^2}+\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{2 x^8}{3 a \sqrt{a+\frac{b}{x^3}}}",1,"(1729*b^3 + 741*a*b^2*x^3 - 228*a^2*b*x^6 + 120*a^3*x^9 - 1729*b^3*Sqrt[1 + (a*x^3)/b]*Hypergeometric2F1[1/6, 1/2, 7/6, -((a*x^3)/b)])/(960*a^4*Sqrt[a + b/x^3]*x)","C",1
2045,1,80,291,0.0359942,"\int \frac{x^4}{\left(a+\frac{b}{x^3}\right)^{3/2}} \, dx","Integrate[x^4/(a + b/x^3)^(3/2),x]","\frac{12 a^2 x^6+91 b^2 \sqrt{\frac{a x^3}{b}+1} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};-\frac{a x^3}{b}\right)-39 a b x^3-91 b^2}{60 a^3 x \sqrt{a+\frac{b}{x^3}}}","-\frac{91 b x^2 \sqrt{a+\frac{b}{x^3}}}{60 a^3}+\frac{13 x^5 \sqrt{a+\frac{b}{x^3}}}{15 a^2}-\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{2 x^5}{3 a \sqrt{a+\frac{b}{x^3}}}",1,"(-91*b^2 - 39*a*b*x^3 + 12*a^2*x^6 + 91*b^2*Sqrt[1 + (a*x^3)/b]*Hypergeometric2F1[1/6, 1/2, 7/6, -((a*x^3)/b)])/(60*a^3*Sqrt[a + b/x^3]*x)","C",1
2046,1,67,269,0.0368121,"\int \frac{x}{\left(a+\frac{b}{x^3}\right)^{3/2}} \, dx","Integrate[x/(a + b/x^3)^(3/2),x]","\frac{-7 b \sqrt{\frac{a x^3}{b}+1} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};-\frac{a x^3}{b}\right)+3 a x^3+7 b}{6 a^2 x \sqrt{a+\frac{b}{x^3}}}","\frac{7 x^2 \sqrt{a+\frac{b}{x^3}}}{6 a^2}+\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{2 x^2}{3 a \sqrt{a+\frac{b}{x^3}}}",1,"(7*b + 3*a*x^3 - 7*b*Sqrt[1 + (a*x^3)/b]*Hypergeometric2F1[1/6, 1/2, 7/6, -((a*x^3)/b)])/(6*a^2*Sqrt[a + b/x^3]*x)","C",1
2047,1,57,248,0.0243359,"\int \frac{1}{\left(a+\frac{b}{x^3}\right)^{3/2} x^2} \, dx","Integrate[1/((a + b/x^3)^(3/2)*x^2),x]","\frac{2 \left(\sqrt{\frac{a x^3}{b}+1} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};-\frac{a x^3}{b}\right)-1\right)}{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*(-1 + Sqrt[1 + (a*x^3)/b]*Hypergeometric2F1[1/6, 1/2, 7/6, -((a*x^3)/b)]))/(3*a*Sqrt[a + b/x^3]*x)","C",1
2048,1,58,245,0.0442416,"\int \frac{1}{\left(a+\frac{b}{x^3}\right)^{3/2} x^5} \, dx","Integrate[1/((a + b/x^3)^(3/2)*x^5),x]","\frac{4 \sqrt{\frac{a x^3}{b}+1} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};-\frac{a x^3}{b}\right)+2}{3 b x \sqrt{a+\frac{b}{x^3}}}","\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 + 4*Sqrt[1 + (a*x^3)/b]*Hypergeometric2F1[1/6, 1/2, 7/6, -((a*x^3)/b)])/(3*b*Sqrt[a + b/x^3]*x)","C",1
2049,1,54,267,0.015826,"\int \frac{1}{\left(a+\frac{b}{x^3}\right)^{3/2} x^8} \, dx","Integrate[1/((a + b/x^3)^(3/2)*x^8),x]","-\frac{2 \sqrt{\frac{a x^3}{b}+1} \, _2F_1\left(-\frac{5}{6},\frac{3}{2};\frac{1}{6};-\frac{a x^3}{b}\right)}{5 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*Sqrt[1 + (a*x^3)/b]*Hypergeometric2F1[-5/6, 3/2, 1/6, -((a*x^3)/b)])/(5*b*Sqrt[a + b/x^3]*x^4)","C",1
2050,1,78,587,0.051591,"\int \frac{x^6}{\left(a+\frac{b}{x^3}\right)^{3/2}} \, dx","Integrate[x^6/(a + b/x^3)^(3/2),x]","\frac{x \left(16 a^2 x^6-187 b^2 \sqrt{\frac{a x^3}{b}+1} \, _2F_1\left(\frac{5}{6},\frac{3}{2};\frac{11}{6};-\frac{a x^3}{b}\right)-34 a b x^3+187 b^2\right)}{112 a^3 \sqrt{a+\frac{b}{x^3}}}","-\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{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^2 x \sqrt{a+\frac{b}{x^3}}}{336 a^4}-\frac{187 b x^4 \sqrt{a+\frac{b}{x^3}}}{168 a^3}+\frac{17 x^7 \sqrt{a+\frac{b}{x^3}}}{21 a^2}-\frac{2 x^7}{3 a \sqrt{a+\frac{b}{x^3}}}",1,"(x*(187*b^2 - 34*a*b*x^3 + 16*a^2*x^6 - 187*b^2*Sqrt[1 + (a*x^3)/b]*Hypergeometric2F1[5/6, 3/2, 11/6, -((a*x^3)/b)]))/(112*a^3*Sqrt[a + b/x^3])","C",1
2051,1,65,563,0.028375,"\int \frac{x^3}{\left(a+\frac{b}{x^3}\right)^{3/2}} \, dx","Integrate[x^3/(a + b/x^3)^(3/2),x]","\frac{x \left(11 b \sqrt{\frac{a x^3}{b}+1} \, _2F_1\left(\frac{5}{6},\frac{3}{2};\frac{11}{6};-\frac{a x^3}{b}\right)+2 a x^3-11 b\right)}{8 a^2 \sqrt{a+\frac{b}{x^3}}}","\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{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 x \sqrt{a+\frac{b}{x^3}}}{24 a^3}+\frac{11 x^4 \sqrt{a+\frac{b}{x^3}}}{12 a^2}-\frac{2 x^4}{3 a \sqrt{a+\frac{b}{x^3}}}",1,"(x*(-11*b + 2*a*x^3 + 11*b*Sqrt[1 + (a*x^3)/b]*Hypergeometric2F1[5/6, 3/2, 11/6, -((a*x^3)/b)]))/(8*a^2*Sqrt[a + b/x^3])","C",1
2052,1,53,539,0.0305401,"\int \frac{1}{\left(a+\frac{b}{x^3}\right)^{3/2}} \, dx","Integrate[(a + b/x^3)^(-3/2),x]","\frac{x-x \sqrt{\frac{a x^3}{b}+1} \, _2F_1\left(\frac{5}{6},\frac{3}{2};\frac{11}{6};-\frac{a x^3}{b}\right)}{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,"(x - x*Sqrt[1 + (a*x^3)/b]*Hypergeometric2F1[5/6, 3/2, 11/6, -((a*x^3)/b)])/(a*Sqrt[a + b/x^3])","C",1
2053,1,52,520,0.0142327,"\int \frac{1}{\left(a+\frac{b}{x^3}\right)^{3/2} x^3} \, dx","Integrate[1/((a + b/x^3)^(3/2)*x^3),x]","\frac{2 x \sqrt{\frac{a x^3}{b}+1} \, _2F_1\left(\frac{5}{6},\frac{3}{2};\frac{11}{6};-\frac{a x^3}{b}\right)}{5 b \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*x*Sqrt[1 + (a*x^3)/b]*Hypergeometric2F1[5/6, 3/2, 11/6, -((a*x^3)/b)])/(5*b*Sqrt[a + b/x^3])","C",1
2054,1,52,517,0.0287793,"\int \frac{1}{\left(a+\frac{b}{x^3}\right)^{3/2} x^6} \, dx","Integrate[1/((a + b/x^3)^(3/2)*x^6),x]","-\frac{2 \sqrt{\frac{a x^3}{b}+1} \, _2F_1\left(-\frac{1}{6},\frac{3}{2};\frac{5}{6};-\frac{a x^3}{b}\right)}{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,"(-2*Sqrt[1 + (a*x^3)/b]*Hypergeometric2F1[-1/6, 3/2, 5/6, -((a*x^3)/b)])/(b*Sqrt[a + b/x^3]*x^2)","C",1
2055,1,54,541,0.0164893,"\int \frac{1}{\left(a+\frac{b}{x^3}\right)^{3/2} x^9} \, dx","Integrate[1/((a + b/x^3)^(3/2)*x^9),x]","-\frac{2 \sqrt{\frac{a x^3}{b}+1} \, _2F_1\left(-\frac{7}{6},\frac{3}{2};-\frac{1}{6};-\frac{a x^3}{b}\right)}{7 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,"(-2*Sqrt[1 + (a*x^3)/b]*Hypergeometric2F1[-7/6, 3/2, -1/6, -((a*x^3)/b)])/(7*b*Sqrt[a + b/x^3]*x^5)","C",1
2056,1,54,565,0.021206,"\int \frac{1}{\left(a+\frac{b}{x^3}\right)^{3/2} x^{12}} \, dx","Integrate[1/((a + b/x^3)^(3/2)*x^12),x]","-\frac{2 \sqrt{\frac{a x^3}{b}+1} \, _2F_1\left(-\frac{13}{6},\frac{3}{2};-\frac{7}{6};-\frac{a x^3}{b}\right)}{13 b x^8 \sqrt{a+\frac{b}{x^3}}}","-\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{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{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,"(-2*Sqrt[1 + (a*x^3)/b]*Hypergeometric2F1[-13/6, 3/2, -7/6, -((a*x^3)/b)])/(13*b*Sqrt[a + b/x^3]*x^8)","C",1
2057,1,173,190,0.0612017,"\int \frac{1}{a+\frac{b}{x^4}} \, dx","Integrate[(a + b/x^4)^(-1),x]","\frac{\sqrt{2} \sqrt[4]{b} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a} x^2+\sqrt{b}\right)-\sqrt{2} \sqrt[4]{b} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a} x^2+\sqrt{b}\right)+2 \sqrt{2} \sqrt[4]{b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a} x}{\sqrt[4]{b}}\right)-2 \sqrt{2} \sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} x}{\sqrt[4]{b}}+1\right)+8 \sqrt[4]{a} x}{8 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} \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,"(8*a^(1/4)*x + 2*Sqrt[2]*b^(1/4)*ArcTan[1 - (Sqrt[2]*a^(1/4)*x)/b^(1/4)] - 2*Sqrt[2]*b^(1/4)*ArcTan[1 + (Sqrt[2]*a^(1/4)*x)/b^(1/4)] + Sqrt[2]*b^(1/4)*Log[Sqrt[b] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[a]*x^2] - Sqrt[2]*b^(1/4)*Log[Sqrt[b] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[a]*x^2])/(8*a^(5/4))","A",1
2058,1,62,47,0.1444387,"\int \sqrt{a+\frac{b}{x^4}} x^3 \, dx","Integrate[Sqrt[a + b/x^4]*x^3,x]","\frac{1}{4} x^2 \sqrt{a+\frac{b}{x^4}} \left(\frac{\sqrt{b} \sinh ^{-1}\left(\frac{\sqrt{a} x^2}{\sqrt{b}}\right)}{\sqrt{a} \sqrt{\frac{a x^4}{b}+1}}+x^2\right)","\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^2*(x^2 + (Sqrt[b]*ArcSinh[(Sqrt[a]*x^2)/Sqrt[b]])/(Sqrt[a]*Sqrt[1 + (a*x^4)/b])))/4","A",1
2059,1,66,49,0.0568369,"\int \sqrt{a+\frac{b}{x^4}} x \, dx","Integrate[Sqrt[a + b/x^4]*x,x]","\frac{x^2 \sqrt{a+\frac{b}{x^4}} \left(\sqrt{a x^4+b}-\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{a x^4+b}}{\sqrt{b}}\right)\right)}{2 \sqrt{a x^4+b}}","\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*(Sqrt[b + a*x^4] - Sqrt[b]*ArcTanh[Sqrt[b + a*x^4]/Sqrt[b]]))/(2*Sqrt[b + a*x^4])","A",1
2060,1,60,43,0.1231928,"\int \frac{\sqrt{a+\frac{b}{x^4}}}{x} \, dx","Integrate[Sqrt[a + b/x^4]/x,x]","\frac{1}{2} \sqrt{a+\frac{b}{x^4}} \left(\frac{\sqrt{a} x^2 \sinh ^{-1}\left(\frac{\sqrt{a} x^2}{\sqrt{b}}\right)}{\sqrt{b} \sqrt{\frac{a x^4}{b}+1}}-1\right)","\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]*(-1 + (Sqrt[a]*x^2*ArcSinh[(Sqrt[a]*x^2)/Sqrt[b]])/(Sqrt[b]*Sqrt[1 + (a*x^4)/b])))/2","A",1
2061,1,68,50,0.0344864,"\int \frac{\sqrt{a+\frac{b}{x^4}}}{x^3} \, dx","Integrate[Sqrt[a + b/x^4]/x^3,x]","-\frac{\sqrt{a+\frac{b}{x^4}} \left(a x^4 \sqrt{\frac{a x^4}{b}+1} \tanh ^{-1}\left(\sqrt{\frac{a x^4}{b}+1}\right)+a x^4+b\right)}{4 x^2 \left(a x^4+b\right)}","-\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,"-1/4*(Sqrt[a + b/x^4]*(b + a*x^4 + a*x^4*Sqrt[1 + (a*x^4)/b]*ArcTanh[Sqrt[1 + (a*x^4)/b]]))/(x^2*(b + a*x^4))","A",1
2062,1,93,107,0.2459617,"\int \sqrt{a+\frac{b}{x^4}} x^2 \, dx","Integrate[Sqrt[a + b/x^4]*x^2,x]","\frac{1}{3} x^2 \sqrt{a+\frac{b}{x^4}} \left(x-\frac{2 i b \sqrt{\frac{a x^4}{b}+1} F\left(\left.i \sinh ^{-1}\left(\sqrt{\frac{i \sqrt{a}}{\sqrt{b}}} x\right)\right|-1\right)}{\sqrt{\frac{i \sqrt{a}}{\sqrt{b}}} \left(a x^4+b\right)}\right)","\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^2*(x - ((2*I)*b*Sqrt[1 + (a*x^4)/b]*EllipticF[I*ArcSinh[Sqrt[(I*Sqrt[a])/Sqrt[b]]*x], -1])/(Sqrt[(I*Sqrt[a])/Sqrt[b]]*(b + a*x^4))))/3","C",1
2063,1,47,224,0.0091887,"\int \sqrt{a+\frac{b}{x^4}} \, dx","Integrate[Sqrt[a + b/x^4],x]","-\frac{x \sqrt{a+\frac{b}{x^4}} \, _2F_1\left(-\frac{1}{2},-\frac{1}{4};\frac{3}{4};-\frac{a x^4}{b}\right)}{\sqrt{\frac{a x^4}{b}+1}}","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,"-((Sqrt[a + b/x^4]*x*Hypergeometric2F1[-1/2, -1/4, 3/4, -((a*x^4)/b)])/Sqrt[1 + (a*x^4)/b])","C",1
2064,1,51,107,0.0101612,"\int \frac{\sqrt{a+\frac{b}{x^4}}}{x^2} \, dx","Integrate[Sqrt[a + b/x^4]/x^2,x]","-\frac{\sqrt{a+\frac{b}{x^4}} \, _2F_1\left(-\frac{3}{4},-\frac{1}{2};\frac{1}{4};-\frac{a x^4}{b}\right)}{3 x \sqrt{\frac{a x^4}{b}+1}}","-\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,"-1/3*(Sqrt[a + b/x^4]*Hypergeometric2F1[-3/4, -1/2, 1/4, -((a*x^4)/b)])/(x*Sqrt[1 + (a*x^4)/b])","C",1
2065,1,51,236,0.0104867,"\int \frac{\sqrt{a+\frac{b}{x^4}}}{x^4} \, dx","Integrate[Sqrt[a + b/x^4]/x^4,x]","-\frac{\sqrt{a+\frac{b}{x^4}} \, _2F_1\left(-\frac{5}{4},-\frac{1}{2};-\frac{1}{4};-\frac{a x^4}{b}\right)}{5 x^3 \sqrt{\frac{a x^4}{b}+1}}","-\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{\sqrt{a+\frac{b}{x^4}}}{5 x^3}-\frac{2 a \sqrt{a+\frac{b}{x^4}}}{5 \sqrt{b} x \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)}",1,"-1/5*(Sqrt[a + b/x^4]*Hypergeometric2F1[-5/4, -1/2, -1/4, -((a*x^4)/b)])/(x^3*Sqrt[1 + (a*x^4)/b])","C",1
2066,1,49,63,0.0152569,"\int \left(a+\frac{b}{x^4}\right)^{3/2} x^3 \, dx","Integrate[(a + b/x^4)^(3/2)*x^3,x]","-\frac{b \sqrt{a+\frac{b}{x^4}} \, _2F_1\left(-\frac{3}{2},-\frac{1}{2};\frac{1}{2};-\frac{a x^4}{b}\right)}{2 \sqrt{\frac{a x^4}{b}+1}}","\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,"-1/2*(b*Sqrt[a + b/x^4]*Hypergeometric2F1[-3/2, -1/2, 1/2, -((a*x^4)/b)])/Sqrt[1 + (a*x^4)/b]","C",1
2067,1,47,69,0.0143347,"\int \left(a+\frac{b}{x^4}\right)^{3/2} x \, dx","Integrate[(a + b/x^4)^(3/2)*x,x]","\frac{a x^6 \left(a+\frac{b}{x^4}\right)^{3/2} \left(a x^4+b\right) \, _2F_1\left(2,\frac{5}{2};\frac{7}{2};\frac{a x^4}{b}+1\right)}{10 b^2}","\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,"(a*(a + b/x^4)^(3/2)*x^6*(b + a*x^4)*Hypergeometric2F1[2, 5/2, 7/2, 1 + (a*x^4)/b])/(10*b^2)","C",1
2068,1,52,59,0.0150658,"\int \frac{\left(a+\frac{b}{x^4}\right)^{3/2}}{x} \, dx","Integrate[(a + b/x^4)^(3/2)/x,x]","-\frac{b \sqrt{a+\frac{b}{x^4}} \, _2F_1\left(-\frac{3}{2},-\frac{3}{2};-\frac{1}{2};-\frac{a x^4}{b}\right)}{6 x^4 \sqrt{\frac{a x^4}{b}+1}}","\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,"-1/6*(b*Sqrt[a + b/x^4]*Hypergeometric2F1[-3/2, -3/2, -1/2, -((a*x^4)/b)])/(x^4*Sqrt[1 + (a*x^4)/b])","C",1
2069,1,85,71,0.0518422,"\int \frac{\left(a+\frac{b}{x^4}\right)^{3/2}}{x^3} \, dx","Integrate[(a + b/x^4)^(3/2)/x^3,x]","-\frac{\sqrt{a+\frac{b}{x^4}} \left(3 a^2 x^8 \sqrt{\frac{a x^4}{b}+1} \tanh ^{-1}\left(\sqrt{\frac{a x^4}{b}+1}\right)+5 a^2 x^8+7 a b x^4+2 b^2\right)}{16 x^6 \left(a x^4+b\right)}","-\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,"-1/16*(Sqrt[a + b/x^4]*(2*b^2 + 7*a*b*x^4 + 5*a^2*x^8 + 3*a^2*x^8*Sqrt[1 + (a*x^4)/b]*ArcTanh[Sqrt[1 + (a*x^4)/b]]))/(x^6*(b + a*x^4))","A",1
2070,1,52,126,0.0133358,"\int \left(a+\frac{b}{x^4}\right)^{3/2} x^2 \, dx","Integrate[(a + b/x^4)^(3/2)*x^2,x]","-\frac{b \sqrt{a+\frac{b}{x^4}} \, _2F_1\left(-\frac{3}{2},-\frac{3}{4};\frac{1}{4};-\frac{a x^4}{b}\right)}{3 x \sqrt{\frac{a x^4}{b}+1}}","-\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{2 b \sqrt{a+\frac{b}{x^4}}}{3 x}+\frac{1}{3} x^3 \left(a+\frac{b}{x^4}\right)^{3/2}",1,"-1/3*(b*Sqrt[a + b/x^4]*Hypergeometric2F1[-3/2, -3/4, 1/4, -((a*x^4)/b)])/(x*Sqrt[1 + (a*x^4)/b])","C",1
2071,1,52,250,0.0093841,"\int \left(a+\frac{b}{x^4}\right)^{3/2} \, dx","Integrate[(a + b/x^4)^(3/2),x]","-\frac{b \sqrt{a+\frac{b}{x^4}} \, _2F_1\left(-\frac{3}{2},-\frac{5}{4};-\frac{1}{4};-\frac{a x^4}{b}\right)}{5 x^3 \sqrt{\frac{a x^4}{b}+1}}","-\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{6 b \sqrt{a+\frac{b}{x^4}}}{5 x^3}-\frac{12 a \sqrt{b} \sqrt{a+\frac{b}{x^4}}}{5 x \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)}",1,"-1/5*(b*Sqrt[a + b/x^4]*Hypergeometric2F1[-3/2, -5/4, -1/4, -((a*x^4)/b)])/(x^3*Sqrt[1 + (a*x^4)/b])","C",1
2072,1,52,126,0.0284421,"\int \frac{\left(a+\frac{b}{x^4}\right)^{3/2}}{x^2} \, dx","Integrate[(a + b/x^4)^(3/2)/x^2,x]","-\frac{b \sqrt{a+\frac{b}{x^4}} \, _2F_1\left(-\frac{7}{4},-\frac{3}{2};-\frac{3}{4};-\frac{a x^4}{b}\right)}{7 x^5 \sqrt{\frac{a x^4}{b}+1}}","-\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,"-1/7*(b*Sqrt[a + b/x^4]*Hypergeometric2F1[-7/4, -3/2, -3/4, -((a*x^4)/b)])/(x^5*Sqrt[1 + (a*x^4)/b])","C",1
2073,1,52,257,0.0301799,"\int \frac{\left(a+\frac{b}{x^4}\right)^{3/2}}{x^4} \, dx","Integrate[(a + b/x^4)^(3/2)/x^4,x]","-\frac{b \sqrt{a+\frac{b}{x^4}} \, _2F_1\left(-\frac{9}{4},-\frac{3}{2};-\frac{5}{4};-\frac{a x^4}{b}\right)}{9 x^7 \sqrt{\frac{a x^4}{b}+1}}","-\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,"-1/9*(b*Sqrt[a + b/x^4]*Hypergeometric2F1[-9/4, -3/2, -5/4, -((a*x^4)/b)])/(x^7*Sqrt[1 + (a*x^4)/b])","C",1
2074,1,54,80,0.015663,"\int \left(a+\frac{b}{x^4}\right)^{5/2} x^3 \, dx","Integrate[(a + b/x^4)^(5/2)*x^3,x]","-\frac{b^2 \sqrt{a+\frac{b}{x^4}} \, _2F_1\left(-\frac{5}{2},-\frac{3}{2};-\frac{1}{2};-\frac{a x^4}{b}\right)}{6 x^4 \sqrt{\frac{a x^4}{b}+1}}","\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,"-1/6*(b^2*Sqrt[a + b/x^4]*Hypergeometric2F1[-5/2, -3/2, -1/2, -((a*x^4)/b)])/(x^4*Sqrt[1 + (a*x^4)/b])","C",1
2075,1,49,91,0.01637,"\int \left(a+\frac{b}{x^4}\right)^{5/2} x \, dx","Integrate[(a + b/x^4)^(5/2)*x,x]","-\frac{a^2 x^{10} \left(a+\frac{b}{x^4}\right)^{5/2} \left(a x^4+b\right) \, _2F_1\left(3,\frac{7}{2};\frac{9}{2};\frac{a x^4}{b}+1\right)}{14 b^3}","-\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,"-1/14*(a^2*(a + b/x^4)^(5/2)*x^10*(b + a*x^4)*Hypergeometric2F1[3, 7/2, 9/2, 1 + (a*x^4)/b])/b^3","C",1
2076,1,54,77,0.0355397,"\int \frac{\left(a+\frac{b}{x^4}\right)^{5/2}}{x} \, dx","Integrate[(a + b/x^4)^(5/2)/x,x]","-\frac{b^2 \sqrt{a+\frac{b}{x^4}} \, _2F_1\left(-\frac{5}{2},-\frac{5}{2};-\frac{3}{2};-\frac{a x^4}{b}\right)}{10 x^8 \sqrt{\frac{a x^4}{b}+1}}","\frac{1}{2} a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^4}}}{\sqrt{a}}\right)-\frac{1}{2} a^2 \sqrt{a+\frac{b}{x^4}}-\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,"-1/10*(b^2*Sqrt[a + b/x^4]*Hypergeometric2F1[-5/2, -5/2, -3/2, -((a*x^4)/b)])/(x^8*Sqrt[1 + (a*x^4)/b])","C",1
2077,1,96,92,0.0528219,"\int \frac{\left(a+\frac{b}{x^4}\right)^{5/2}}{x^3} \, dx","Integrate[(a + b/x^4)^(5/2)/x^3,x]","-\frac{\sqrt{a+\frac{b}{x^4}} \left(15 a^3 x^{12} \sqrt{\frac{a x^4}{b}+1} \tanh ^{-1}\left(\sqrt{\frac{a x^4}{b}+1}\right)+33 a^3 x^{12}+59 a^2 b x^8+34 a b^2 x^4+8 b^3\right)}{96 x^{10} \left(a x^4+b\right)}","-\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^2 \sqrt{a+\frac{b}{x^4}}}{32 x^2}-\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,"-1/96*(Sqrt[a + b/x^4]*(8*b^3 + 34*a*b^2*x^4 + 59*a^2*b*x^8 + 33*a^3*x^12 + 15*a^3*x^12*Sqrt[1 + (a*x^4)/b]*ArcTanh[Sqrt[1 + (a*x^4)/b]]))/(x^10*(b + a*x^4))","A",1
2078,1,54,146,0.034381,"\int \left(a+\frac{b}{x^4}\right)^{5/2} x^2 \, dx","Integrate[(a + b/x^4)^(5/2)*x^2,x]","-\frac{b^2 \sqrt{a+\frac{b}{x^4}} \, _2F_1\left(-\frac{5}{2},-\frac{7}{4};-\frac{3}{4};-\frac{a x^4}{b}\right)}{7 x^5 \sqrt{\frac{a x^4}{b}+1}}","-\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{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{1}{3} x^3 \left(a+\frac{b}{x^4}\right)^{5/2}",1,"-1/7*(b^2*Sqrt[a + b/x^4]*Hypergeometric2F1[-5/2, -7/4, -3/4, -((a*x^4)/b)])/(x^5*Sqrt[1 + (a*x^4)/b])","C",1
2079,1,54,272,0.0143154,"\int \left(a+\frac{b}{x^4}\right)^{5/2} \, dx","Integrate[(a + b/x^4)^(5/2),x]","-\frac{b^2 \sqrt{a+\frac{b}{x^4}} \, _2F_1\left(-\frac{5}{2},-\frac{9}{4};-\frac{5}{4};-\frac{a x^4}{b}\right)}{9 x^7 \sqrt{\frac{a x^4}{b}+1}}","-\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}}}-\frac{8 a^2 \sqrt{b} \sqrt{a+\frac{b}{x^4}}}{3 x \left(\sqrt{a}+\frac{\sqrt{b}}{x^2}\right)}+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,"-1/9*(b^2*Sqrt[a + b/x^4]*Hypergeometric2F1[-5/2, -9/4, -5/4, -((a*x^4)/b)])/(x^7*Sqrt[1 + (a*x^4)/b])","C",1
2080,1,54,147,0.0148671,"\int \frac{\left(a+\frac{b}{x^4}\right)^{5/2}}{x^2} \, dx","Integrate[(a + b/x^4)^(5/2)/x^2,x]","-\frac{b^2 \sqrt{a+\frac{b}{x^4}} \, _2F_1\left(-\frac{11}{4},-\frac{5}{2};-\frac{7}{4};-\frac{a x^4}{b}\right)}{11 x^9 \sqrt{\frac{a x^4}{b}+1}}","-\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{20 a^2 \sqrt{a+\frac{b}{x^4}}}{77 x}-\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,"-1/11*(b^2*Sqrt[a + b/x^4]*Hypergeometric2F1[-11/4, -5/2, -7/4, -((a*x^4)/b)])/(x^9*Sqrt[1 + (a*x^4)/b])","C",1
2081,1,54,278,0.014056,"\int \frac{\left(a+\frac{b}{x^4}\right)^{5/2}}{x^4} \, dx","Integrate[(a + b/x^4)^(5/2)/x^4,x]","-\frac{b^2 \sqrt{a+\frac{b}{x^4}} \, _2F_1\left(-\frac{13}{4},-\frac{5}{2};-\frac{9}{4};-\frac{a x^4}{b}\right)}{13 x^{11} \sqrt{\frac{a x^4}{b}+1}}","-\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,"-1/13*(b^2*Sqrt[a + b/x^4]*Hypergeometric2F1[-13/4, -5/2, -9/4, -((a*x^4)/b)])/(x^11*Sqrt[1 + (a*x^4)/b])","C",1
2082,1,75,50,0.0434736,"\int \frac{x^3}{\sqrt{a+\frac{b}{x^4}}} \, dx","Integrate[x^3/Sqrt[a + b/x^4],x]","\frac{\sqrt{a} x^2 \left(a x^4+b\right)-b \sqrt{a x^4+b} \tanh ^{-1}\left(\frac{\sqrt{a} x^2}{\sqrt{a x^4+b}}\right)}{4 a^{3/2} x^2 \sqrt{a+\frac{b}{x^4}}}","\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]*x^2*(b + a*x^4) - b*Sqrt[b + a*x^4]*ArcTanh[(Sqrt[a]*x^2)/Sqrt[b + a*x^4]])/(4*a^(3/2)*Sqrt[a + b/x^4]*x^2)","A",1
2083,1,21,21,0.0098892,"\int \frac{x}{\sqrt{a+\frac{b}{x^4}}} \, dx","Integrate[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
2084,1,55,27,0.0289484,"\int \frac{1}{\sqrt{a+\frac{b}{x^4}} x} \, dx","Integrate[1/(Sqrt[a + b/x^4]*x),x]","\frac{\sqrt{a x^4+b} \tanh ^{-1}\left(\frac{\sqrt{a} x^2}{\sqrt{a x^4+b}}\right)}{2 \sqrt{a} x^2 \sqrt{a+\frac{b}{x^4}}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^4}}}{\sqrt{a}}\right)}{2 \sqrt{a}}",1,"(Sqrt[b + a*x^4]*ArcTanh[(Sqrt[a]*x^2)/Sqrt[b + a*x^4]])/(2*Sqrt[a]*Sqrt[a + b/x^4]*x^2)","B",1
2085,1,52,30,0.0299342,"\int \frac{1}{\sqrt{a+\frac{b}{x^4}} x^3} \, dx","Integrate[1/(Sqrt[a + b/x^4]*x^3),x]","-\frac{\sqrt{a x^4+b} \tanh ^{-1}\left(\frac{\sqrt{a x^4+b}}{\sqrt{b}}\right)}{2 \sqrt{b} x^2 \sqrt{a+\frac{b}{x^4}}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{b}}{x^2 \sqrt{a+\frac{b}{x^4}}}\right)}{2 \sqrt{b}}",1,"-1/2*(Sqrt[b + a*x^4]*ArcTanh[Sqrt[b + a*x^4]/Sqrt[b]])/(Sqrt[b]*Sqrt[a + b/x^4]*x^2)","A",1
2086,1,64,110,0.0202429,"\int \frac{x^2}{\sqrt{a+\frac{b}{x^4}}} \, dx","Integrate[x^2/Sqrt[a + b/x^4],x]","\frac{-b \sqrt{\frac{a x^4}{b}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\frac{a x^4}{b}\right)+a x^4+b}{3 a x \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)}{6 a^{5/4} \sqrt{a+\frac{b}{x^4}}}+\frac{x^3 \sqrt{a+\frac{b}{x^4}}}{3 a}",1,"(b + a*x^4 - b*Sqrt[1 + (a*x^4)/b]*Hypergeometric2F1[1/4, 1/2, 5/4, -((a*x^4)/b)])/(3*a*Sqrt[a + b/x^4]*x)","C",1
2087,1,49,231,0.0098935,"\int \frac{1}{\sqrt{a+\frac{b}{x^4}}} \, dx","Integrate[1/Sqrt[a + b/x^4],x]","\frac{x \sqrt{\frac{a x^4}{b}+1} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};-\frac{a x^4}{b}\right)}{3 \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) 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,"(x*Sqrt[1 + (a*x^4)/b]*Hypergeometric2F1[1/2, 3/4, 7/4, -((a*x^4)/b)])/(3*Sqrt[a + b/x^4])","C",1
2088,1,77,88,0.059158,"\int \frac{1}{\sqrt{a+\frac{b}{x^4}} x^2} \, dx","Integrate[1/(Sqrt[a + b/x^4]*x^2),x]","-\frac{i \sqrt{\frac{a x^4}{b}+1} F\left(\left.i \sinh ^{-1}\left(\sqrt{\frac{i \sqrt{a}}{\sqrt{b}}} x\right)\right|-1\right)}{x^2 \sqrt{\frac{i \sqrt{a}}{\sqrt{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,"((-I)*Sqrt[1 + (a*x^4)/b]*EllipticF[I*ArcSinh[Sqrt[(I*Sqrt[a])/Sqrt[b]]*x], -1])/(Sqrt[(I*Sqrt[a])/Sqrt[b]]*Sqrt[a + b/x^4]*x^2)","C",1
2089,1,49,212,0.010298,"\int \frac{1}{\sqrt{a+\frac{b}{x^4}} x^4} \, dx","Integrate[1/(Sqrt[a + b/x^4]*x^4),x]","-\frac{\sqrt{\frac{a x^4}{b}+1} \, _2F_1\left(-\frac{1}{4},\frac{1}{2};\frac{3}{4};-\frac{a x^4}{b}\right)}{x^3 \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) 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[1 + (a*x^4)/b]*Hypergeometric2F1[-1/4, 1/2, 3/4, -((a*x^4)/b)])/(Sqrt[a + b/x^4]*x^3))","C",1
2090,1,78,69,0.0554512,"\int \frac{x^3}{\left(a+\frac{b}{x^4}\right)^{3/2}} \, dx","Integrate[x^3/(a + b/x^4)^(3/2),x]","\frac{\sqrt{a} x^2 \left(a x^4+3 b\right)-3 b^{3/2} \sqrt{\frac{a x^4}{b}+1} \sinh ^{-1}\left(\frac{\sqrt{a} x^2}{\sqrt{b}}\right)}{4 a^{5/2} x^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{3 b}{4 a^2 \sqrt{a+\frac{b}{x^4}}}+\frac{x^4}{4 a \sqrt{a+\frac{b}{x^4}}}",1,"(Sqrt[a]*x^2*(3*b + a*x^4) - 3*b^(3/2)*Sqrt[1 + (a*x^4)/b]*ArcSinh[(Sqrt[a]*x^2)/Sqrt[b]])/(4*a^(5/2)*Sqrt[a + b/x^4]*x^2)","A",1
2091,1,30,40,0.0203033,"\int \frac{x}{\left(a+\frac{b}{x^4}\right)^{3/2}} \, dx","Integrate[x/(a + b/x^4)^(3/2),x]","\frac{a x^4+2 b}{2 a^2 x^2 \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,"(2*b + a*x^4)/(2*a^2*Sqrt[a + b/x^4]*x^2)","A",1
2092,1,69,46,0.0898866,"\int \frac{1}{\left(a+\frac{b}{x^4}\right)^{3/2} x} \, dx","Integrate[1/((a + b/x^4)^(3/2)*x),x]","\frac{\sqrt{b} \sqrt{\frac{a x^4}{b}+1} \sinh ^{-1}\left(\frac{\sqrt{a} x^2}{\sqrt{b}}\right)-\sqrt{a} x^2}{2 a^{3/2} x^2 \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,"(-(Sqrt[a]*x^2) + Sqrt[b]*Sqrt[1 + (a*x^4)/b]*ArcSinh[(Sqrt[a]*x^2)/Sqrt[b]])/(2*a^(3/2)*Sqrt[a + b/x^4]*x^2)","A",1
2093,1,21,21,0.0134605,"\int \frac{1}{\left(a+\frac{b}{x^4}\right)^{3/2} x^3} \, dx","Integrate[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*1/(a*Sqrt[a + b/x^4]*x^2)","A",1
2094,1,67,131,0.0208464,"\int \frac{x^2}{\left(a+\frac{b}{x^4}\right)^{3/2}} \, dx","Integrate[x^2/(a + b/x^4)^(3/2),x]","\frac{-5 b \sqrt{\frac{a x^4}{b}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\frac{a x^4}{b}\right)+2 a x^4+5 b}{6 a^2 x \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,"(5*b + 2*a*x^4 - 5*b*Sqrt[1 + (a*x^4)/b]*Hypergeometric2F1[1/4, 1/2, 5/4, -((a*x^4)/b)])/(6*a^2*Sqrt[a + b/x^4]*x)","C",1
2095,1,53,258,0.0329185,"\int \frac{1}{\left(a+\frac{b}{x^4}\right)^{3/2}} \, dx","Integrate[(a + b/x^4)^(-3/2),x]","\frac{x-x \sqrt{\frac{a x^4}{b}+1} \, _2F_1\left(\frac{3}{4},\frac{3}{2};\frac{7}{4};-\frac{a x^4}{b}\right)}{a \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) 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{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{x}{2 a \sqrt{a+\frac{b}{x^4}}}",1,"(x - x*Sqrt[1 + (a*x^4)/b]*Hypergeometric2F1[3/4, 3/2, 7/4, -((a*x^4)/b)])/(a*Sqrt[a + b/x^4])","C",1
2096,1,57,110,0.019237,"\int \frac{1}{\left(a+\frac{b}{x^4}\right)^{3/2} x^2} \, dx","Integrate[1/((a + b/x^4)^(3/2)*x^2),x]","\frac{\sqrt{\frac{a x^4}{b}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\frac{a x^4}{b}\right)-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 + Sqrt[1 + (a*x^4)/b]*Hypergeometric2F1[1/4, 1/2, 5/4, -((a*x^4)/b)])/(2*a*Sqrt[a + b/x^4]*x)","C",1
2097,1,52,241,0.0255627,"\int \frac{1}{\left(a+\frac{b}{x^4}\right)^{3/2} x^4} \, dx","Integrate[1/((a + b/x^4)^(3/2)*x^4),x]","\frac{x \sqrt{\frac{a x^4}{b}+1} \, _2F_1\left(\frac{3}{4},\frac{3}{2};\frac{7}{4};-\frac{a x^4}{b}\right)}{3 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)}{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{1}{2 a x^3 \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)}",1,"(x*Sqrt[1 + (a*x^4)/b]*Hypergeometric2F1[3/4, 3/2, 7/4, -((a*x^4)/b)])/(3*b*Sqrt[a + b/x^4])","C",1
2098,1,103,88,0.2299144,"\int \frac{x^3}{\left(a+\frac{b}{x^4}\right)^{5/2}} \, dx","Integrate[x^3/(a + b/x^4)^(5/2),x]","\frac{\sqrt{a} \left(3 a^2 x^8+20 a b x^4+15 b^2\right)-\frac{15 b^{3/2} \left(a x^4+b\right) \sqrt{\frac{a x^4}{b}+1} \sinh ^{-1}\left(\frac{\sqrt{a} x^2}{\sqrt{b}}\right)}{x^2}}{12 a^{7/2} \sqrt{a+\frac{b}{x^4}} \left(a x^4+b\right)}","-\frac{5 b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^4}}}{\sqrt{a}}\right)}{4 a^{7/2}}+\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{x^4}{4 a \left(a+\frac{b}{x^4}\right)^{3/2}}",1,"(Sqrt[a]*(15*b^2 + 20*a*b*x^4 + 3*a^2*x^8) - (15*b^(3/2)*(b + a*x^4)*Sqrt[1 + (a*x^4)/b]*ArcSinh[(Sqrt[a]*x^2)/Sqrt[b]])/x^2)/(12*a^(7/2)*Sqrt[a + b/x^4]*(b + a*x^4))","A",1
2099,1,51,64,0.0244109,"\int \frac{x}{\left(a+\frac{b}{x^4}\right)^{5/2}} \, dx","Integrate[x/(a + b/x^4)^(5/2),x]","\frac{3 a^2 x^8+12 a b x^4+8 b^2}{6 a^3 x^2 \sqrt{a+\frac{b}{x^4}} \left(a x^4+b\right)}","\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,"(8*b^2 + 12*a*b*x^4 + 3*a^2*x^8)/(6*a^3*Sqrt[a + b/x^4]*x^2*(b + a*x^4))","A",1
2100,1,93,64,0.2433362,"\int \frac{1}{\left(a+\frac{b}{x^4}\right)^{5/2} x} \, dx","Integrate[1/((a + b/x^4)^(5/2)*x),x]","\frac{\frac{3 \sqrt{b} \left(a x^4+b\right) \sqrt{\frac{a x^4}{b}+1} \sinh ^{-1}\left(\frac{\sqrt{a} x^2}{\sqrt{b}}\right)}{x^2}-\sqrt{a} \left(4 a x^4+3 b\right)}{6 a^{5/2} \sqrt{a+\frac{b}{x^4}} \left(a x^4+b\right)}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^4}}}{\sqrt{a}}\right)}{2 a^{5/2}}-\frac{1}{2 a^2 \sqrt{a+\frac{b}{x^4}}}-\frac{1}{6 a \left(a+\frac{b}{x^4}\right)^{3/2}}",1,"(-(Sqrt[a]*(3*b + 4*a*x^4)) + (3*Sqrt[b]*(b + a*x^4)*Sqrt[1 + (a*x^4)/b]*ArcSinh[(Sqrt[a]*x^2)/Sqrt[b]])/x^2)/(6*a^(5/2)*Sqrt[a + b/x^4]*(b + a*x^4))","A",1
2101,1,40,44,0.018872,"\int \frac{1}{\left(a+\frac{b}{x^4}\right)^{5/2} x^3} \, dx","Integrate[1/((a + b/x^4)^(5/2)*x^3),x]","\frac{-3 a x^4-2 b}{6 a^2 x^2 \sqrt{a+\frac{b}{x^4}} \left(a x^4+b\right)}","-\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,"(-2*b - 3*a*x^4)/(6*a^2*Sqrt[a + b/x^4]*x^2*(b + a*x^4))","A",1
2102,1,94,152,0.0652378,"\int \frac{x^2}{\left(a+\frac{b}{x^4}\right)^{5/2}} \, dx","Integrate[x^2/(a + b/x^4)^(5/2),x]","\frac{4 a^2 x^8-15 b \left(a x^4+b\right) \sqrt{\frac{a x^4}{b}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\frac{a x^4}{b}\right)+21 a b x^4+15 b^2}{12 a^3 x \sqrt{a+\frac{b}{x^4}} \left(a x^4+b\right)}","\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,"(15*b^2 + 21*a*b*x^4 + 4*a^2*x^8 - 15*b*(b + a*x^4)*Sqrt[1 + (a*x^4)/b]*Hypergeometric2F1[1/4, 1/2, 5/4, -((a*x^4)/b)])/(12*a^3*Sqrt[a + b/x^4]*x*(b + a*x^4))","C",1
2103,1,81,277,0.0467205,"\int \frac{1}{\left(a+\frac{b}{x^4}\right)^{5/2}} \, dx","Integrate[(a + b/x^4)^(-5/2),x]","\frac{-7 x \left(a x^4+b\right) \sqrt{\frac{a x^4}{b}+1} \, _2F_1\left(\frac{3}{4},\frac{5}{2};\frac{7}{4};-\frac{a x^4}{b}\right)+3 a x^5+7 b x}{3 a^2 \sqrt{a+\frac{b}{x^4}} \left(a x^4+b\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{7 x \sqrt{a+\frac{b}{x^4}}}{4 a^3}-\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 x}{12 a^2 \sqrt{a+\frac{b}{x^4}}}-\frac{x}{6 a \left(a+\frac{b}{x^4}\right)^{3/2}}",1,"(7*b*x + 3*a*x^5 - 7*x*(b + a*x^4)*Sqrt[1 + (a*x^4)/b]*Hypergeometric2F1[3/4, 5/2, 7/4, -((a*x^4)/b)])/(3*a^2*Sqrt[a + b/x^4]*(b + a*x^4))","C",1
2104,1,82,131,0.059592,"\int \frac{1}{\left(a+\frac{b}{x^4}\right)^{5/2} x^2} \, dx","Integrate[1/((a + b/x^4)^(5/2)*x^2),x]","\frac{5 \left(a x^4+b\right) \sqrt{\frac{a x^4}{b}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\frac{a x^4}{b}\right)-7 a x^4-5 b}{12 a^2 x \sqrt{a+\frac{b}{x^4}} \left(a x^4+b\right)}","-\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{5}{12 a^2 x \sqrt{a+\frac{b}{x^4}}}-\frac{1}{6 a x \left(a+\frac{b}{x^4}\right)^{3/2}}",1,"(-5*b - 7*a*x^4 + 5*(b + a*x^4)*Sqrt[1 + (a*x^4)/b]*Hypergeometric2F1[1/4, 1/2, 5/4, -((a*x^4)/b)])/(12*a^2*Sqrt[a + b/x^4]*x*(b + a*x^4))","C",1
2105,1,77,262,0.0569059,"\int \frac{1}{\left(a+\frac{b}{x^4}\right)^{5/2} x^4} \, dx","Integrate[1/((a + b/x^4)^(5/2)*x^4),x]","\frac{x \left(a x^4+b\right) \sqrt{\frac{a x^4}{b}+1} \, _2F_1\left(\frac{3}{4},\frac{5}{2};\frac{7}{4};-\frac{a x^4}{b}\right)-b x}{3 a b \sqrt{a+\frac{b}{x^4}} \left(a x^4+b\right)}","\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{1}{4 a^2 x^3 \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}{6 a x^3 \left(a+\frac{b}{x^4}\right)^{3/2}}",1,"(-(b*x) + x*(b + a*x^4)*Sqrt[1 + (a*x^4)/b]*Hypergeometric2F1[3/4, 5/2, 7/4, -((a*x^4)/b)])/(3*a*b*Sqrt[a + b/x^4]*(b + a*x^4))","C",1
2106,1,267,310,0.2910912,"\int \frac{1}{a+\frac{b}{x^5}} \, dx","Integrate[(a + b/x^5)^(-1),x]","\frac{-\left(\sqrt{5}-1\right) \sqrt[5]{b} \log \left(a^{2/5} x^2+\frac{1}{2} \left(\sqrt{5}-1\right) \sqrt[5]{a} \sqrt[5]{b} x+b^{2/5}\right)+\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)-4 \sqrt[5]{b} \log \left(\sqrt[5]{a} x+\sqrt[5]{b}\right)-2 \sqrt{2 \left(5+\sqrt{5}\right)} \sqrt[5]{b} \tan ^{-1}\left(\frac{4 \sqrt[5]{a} x+\left(\sqrt{5}-1\right) \sqrt[5]{b}}{\sqrt{2 \left(5+\sqrt{5}\right)} \sqrt[5]{b}}\right)-2 \sqrt{10-2 \sqrt{5}} \sqrt[5]{b} \tan ^{-1}\left(\frac{4 \sqrt[5]{a} x-\left(1+\sqrt{5}\right) \sqrt[5]{b}}{\sqrt{10-2 \sqrt{5}} \sqrt[5]{b}}\right)+20 \sqrt[5]{a} x}{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{\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,"(20*a^(1/5)*x - 2*Sqrt[2*(5 + Sqrt[5])]*b^(1/5)*ArcTan[((-1 + Sqrt[5])*b^(1/5) + 4*a^(1/5)*x)/(Sqrt[2*(5 + Sqrt[5])]*b^(1/5))] - 2*Sqrt[10 - 2*Sqrt[5]]*b^(1/5)*ArcTan[(-((1 + Sqrt[5])*b^(1/5)) + 4*a^(1/5)*x)/(Sqrt[10 - 2*Sqrt[5]]*b^(1/5))] - 4*b^(1/5)*Log[b^(1/5) + a^(1/5)*x] - (-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] + (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",1
2107,1,59,27,0.0223193,"\int \frac{1}{\sqrt{a+\frac{b}{x^5}} x} \, dx","Integrate[1/(Sqrt[a + b/x^5]*x),x]","\frac{2 \sqrt{a x^5+b} \tanh ^{-1}\left(\frac{\sqrt{a} x^{5/2}}{\sqrt{a x^5+b}}\right)}{5 \sqrt{a} x^{5/2} \sqrt{a+\frac{b}{x^5}}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{x^5}}}{\sqrt{a}}\right)}{5 \sqrt{a}}",1,"(2*Sqrt[b + a*x^5]*ArcTanh[(Sqrt[a]*x^(5/2))/Sqrt[b + a*x^5]])/(5*Sqrt[a]*Sqrt[a + b/x^5]*x^(5/2))","B",1
2108,1,65,29,0.0371755,"\int \frac{1}{\sqrt{-a+\frac{b}{x^5}} x} \, dx","Integrate[1/(Sqrt[-a + b/x^5]*x),x]","\frac{2 \sqrt{a x^5-b} \tanh ^{-1}\left(\frac{\sqrt{a} x^{5/2}}{\sqrt{a x^5-b}}\right)}{5 \sqrt{a} x^{5/2} \sqrt{\frac{b}{x^5}-a}}","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{\frac{b}{x^5}-a}}{\sqrt{a}}\right)}{5 \sqrt{a}}",1,"(2*Sqrt[-b + a*x^5]*ArcTanh[(Sqrt[a]*x^(5/2))/Sqrt[-b + a*x^5]])/(5*Sqrt[a]*Sqrt[-a + b/x^5]*x^(5/2))","B",1
2109,1,182,220,0.0796973,"\int \frac{1}{a+\frac{b}{x^6}} \, dx","Integrate[(a + b/x^6)^(-1),x]","\frac{\sqrt{3} \sqrt[6]{b} \log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} x+\sqrt[3]{a} x^2+\sqrt[3]{b}\right)-\sqrt{3} \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[6]{b} \tan ^{-1}\left(\frac{\sqrt[6]{a} x}{\sqrt[6]{b}}\right)+2 \sqrt[6]{b} \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{a} x}{\sqrt[6]{b}}\right)-2 \sqrt[6]{b} \tan ^{-1}\left(\frac{2 \sqrt[6]{a} x}{\sqrt[6]{b}}+\sqrt{3}\right)+12 \sqrt[6]{a} x}{12 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} \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,"(12*a^(1/6)*x - 4*b^(1/6)*ArcTan[(a^(1/6)*x)/b^(1/6)] + 2*b^(1/6)*ArcTan[Sqrt[3] - (2*a^(1/6)*x)/b^(1/6)] - 2*b^(1/6)*ArcTan[Sqrt[3] + (2*a^(1/6)*x)/b^(1/6)] + Sqrt[3]*b^(1/6)*Log[b^(1/3) - Sqrt[3]*a^(1/6)*b^(1/6)*x + a^(1/3)*x^2] - Sqrt[3]*b^(1/6)*Log[b^(1/3) + Sqrt[3]*a^(1/6)*b^(1/6)*x + a^(1/3)*x^2])/(12*a^(7/6))","A",1
2110,1,367,272,0.3422013,"\int \frac{1}{a+\frac{b}{x^8}} \, dx","Integrate[(a + b/x^8)^(-1),x]","\frac{\sqrt[8]{b} \sin \left(\frac{\pi }{8}\right) \log \left(-2 \sqrt[8]{a} \sqrt[8]{b} x \sin \left(\frac{\pi }{8}\right)+\sqrt[4]{a} x^2+\sqrt[4]{b}\right)-\sqrt[8]{b} \sin \left(\frac{\pi }{8}\right) \log \left(2 \sqrt[8]{a} \sqrt[8]{b} x \sin \left(\frac{\pi }{8}\right)+\sqrt[4]{a} x^2+\sqrt[4]{b}\right)+\sqrt[8]{b} \cos \left(\frac{\pi }{8}\right) \log \left(-2 \sqrt[8]{a} \sqrt[8]{b} x \cos \left(\frac{\pi }{8}\right)+\sqrt[4]{a} x^2+\sqrt[4]{b}\right)-\sqrt[8]{b} \cos \left(\frac{\pi }{8}\right) \log \left(2 \sqrt[8]{a} \sqrt[8]{b} x \cos \left(\frac{\pi }{8}\right)+\sqrt[4]{a} x^2+\sqrt[4]{b}\right)-2 \sqrt[8]{b} \cos \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\frac{\sqrt[8]{a} x \sec \left(\frac{\pi }{8}\right)}{\sqrt[8]{b}}-\tan \left(\frac{\pi }{8}\right)\right)-2 \sqrt[8]{b} \cos \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\frac{\sqrt[8]{a} x \sec \left(\frac{\pi }{8}\right)}{\sqrt[8]{b}}+\tan \left(\frac{\pi }{8}\right)\right)+2 \sqrt[8]{b} \sin \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\cot \left(\frac{\pi }{8}\right)-\frac{\sqrt[8]{a} x \csc \left(\frac{\pi }{8}\right)}{\sqrt[8]{b}}\right)-2 \sqrt[8]{b} \sin \left(\frac{\pi }{8}\right) \tan ^{-1}\left(\frac{\sqrt[8]{a} x \csc \left(\frac{\pi }{8}\right)}{\sqrt[8]{b}}+\cot \left(\frac{\pi }{8}\right)\right)+8 \sqrt[8]{a} x}{8 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} \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,"(8*a^(1/8)*x - 2*b^(1/8)*ArcTan[(a^(1/8)*x*Sec[Pi/8])/b^(1/8) - Tan[Pi/8]]*Cos[Pi/8] - 2*b^(1/8)*ArcTan[(a^(1/8)*x*Sec[Pi/8])/b^(1/8) + Tan[Pi/8]]*Cos[Pi/8] + b^(1/8)*Cos[Pi/8]*Log[b^(1/4) + a^(1/4)*x^2 - 2*a^(1/8)*b^(1/8)*x*Cos[Pi/8]] - b^(1/8)*Cos[Pi/8]*Log[b^(1/4) + a^(1/4)*x^2 + 2*a^(1/8)*b^(1/8)*x*Cos[Pi/8]] + 2*b^(1/8)*ArcTan[Cot[Pi/8] - (a^(1/8)*x*Csc[Pi/8])/b^(1/8)]*Sin[Pi/8] - 2*b^(1/8)*ArcTan[Cot[Pi/8] + (a^(1/8)*x*Csc[Pi/8])/b^(1/8)]*Sin[Pi/8] + b^(1/8)*Log[b^(1/4) + a^(1/4)*x^2 - 2*a^(1/8)*b^(1/8)*x*Sin[Pi/8]]*Sin[Pi/8] - b^(1/8)*Log[b^(1/4) + a^(1/4)*x^2 + 2*a^(1/8)*b^(1/8)*x*Sin[Pi/8]]*Sin[Pi/8])/(8*a^(9/8))","A",1
2111,1,19,19,0.0071337,"\int \left(a+b \sqrt{x}\right) x^4 \, dx","Integrate[(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",1
2112,1,19,19,0.0057804,"\int \left(a+b \sqrt{x}\right) x^3 \, dx","Integrate[(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",1
2113,1,19,19,0.0059957,"\int \left(a+b \sqrt{x}\right) x^2 \, dx","Integrate[(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",1
2114,1,19,19,0.0055526,"\int \left(a+b \sqrt{x}\right) x \, dx","Integrate[(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",1
2115,1,14,14,0.0013558,"\int \left(a+b \sqrt{x}\right) \, dx","Integrate[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
2116,1,13,13,0.0054812,"\int \frac{a+b \sqrt{x}}{x} \, dx","Integrate[(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",1
2117,1,15,15,0.0061222,"\int \frac{a+b \sqrt{x}}{x^2} \, dx","Integrate[(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",1
2118,1,19,19,0.0073704,"\int \frac{a+b \sqrt{x}}{x^3} \, dx","Integrate[(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,"-1/2*a/x^2 - (2*b)/(3*x^(3/2))","A",1
2119,1,19,19,0.0074437,"\int \frac{a+b \sqrt{x}}{x^4} \, dx","Integrate[(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,"-1/3*a/x^3 - (2*b)/(5*x^(5/2))","A",1
2120,1,28,32,0.0222504,"\int \left(a+b \sqrt{x}\right)^2 x^4 \, dx","Integrate[(a + b*Sqrt[x])^2*x^4,x]","\frac{1}{330} x^5 \left(66 a^2+120 a b \sqrt{x}+55 b^2 x\right)","\frac{a^2 x^5}{5}+\frac{4}{11} a b x^{11/2}+\frac{b^2 x^6}{6}",1,"(x^5*(66*a^2 + 120*a*b*Sqrt[x] + 55*b^2*x))/330","A",1
2121,1,32,32,0.0177015,"\int \left(a+b \sqrt{x}\right)^2 x^3 \, dx","Integrate[(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",1
2122,1,28,32,0.0169157,"\int \left(a+b \sqrt{x}\right)^2 x^2 \, dx","Integrate[(a + b*Sqrt[x])^2*x^2,x]","\frac{1}{84} x^3 \left(28 a^2+48 a b \sqrt{x}+21 b^2 x\right)","\frac{a^2 x^3}{3}+\frac{4}{7} a b x^{7/2}+\frac{b^2 x^4}{4}",1,"(x^3*(28*a^2 + 48*a*b*Sqrt[x] + 21*b^2*x))/84","A",1
2123,1,28,32,0.0144611,"\int \left(a+b \sqrt{x}\right)^2 x \, dx","Integrate[(a + b*Sqrt[x])^2*x,x]","\frac{1}{30} x^2 \left(15 a^2+24 a b \sqrt{x}+10 b^2 x\right)","\frac{a^2 x^2}{2}+\frac{4}{5} a b x^{5/2}+\frac{b^2 x^3}{3}",1,"(x^2*(15*a^2 + 24*a*b*Sqrt[x] + 10*b^2*x))/30","A",1
2124,1,27,27,0.0129592,"\int \left(a+b \sqrt{x}\right)^2 \, dx","Integrate[(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",1
2125,1,21,21,0.0354123,"\int \frac{\left(a+b \sqrt{x}\right)^2}{x} \, dx","Integrate[(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",1
2126,1,24,24,0.0172786,"\int \frac{\left(a+b \sqrt{x}\right)^2}{x^2} \, dx","Integrate[(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",1
2127,1,30,30,0.0136372,"\int \frac{\left(a+b \sqrt{x}\right)^2}{x^3} \, dx","Integrate[(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,"-1/2*a^2/x^2 - (4*a*b)/(3*x^(3/2)) - b^2/x","A",1
2128,1,28,32,0.0139785,"\int \frac{\left(a+b \sqrt{x}\right)^2}{x^4} \, dx","Integrate[(a + b*Sqrt[x])^2/x^4,x]","-\frac{10 a^2+24 a b \sqrt{x}+15 b^2 x}{30 x^3}","-\frac{a^2}{3 x^3}-\frac{4 a b}{5 x^{5/2}}-\frac{b^2}{2 x^2}",1,"-1/30*(10*a^2 + 24*a*b*Sqrt[x] + 15*b^2*x)/x^3","A",1
2129,1,28,32,0.0388313,"\int \frac{\left(a+b \sqrt{x}\right)^2}{x^5} \, dx","Integrate[(a + b*Sqrt[x])^2/x^5,x]","-\frac{21 a^2+48 a b \sqrt{x}+28 b^2 x}{84 x^4}","-\frac{a^2}{4 x^4}-\frac{4 a b}{7 x^{7/2}}-\frac{b^2}{3 x^3}",1,"-1/84*(21*a^2 + 48*a*b*Sqrt[x] + 28*b^2*x)/x^4","A",1
2130,1,47,47,0.0489441,"\int \left(a+b \sqrt{x}\right)^3 x^4 \, dx","Integrate[(a + b*Sqrt[x])^3*x^4,x]","\frac{a^3 x^5}{5}+\frac{6}{11} a^2 b x^{11/2}+\frac{1}{2} a b^2 x^6+\frac{2}{13} b^3 x^{13/2}","\frac{a^3 x^5}{5}+\frac{6}{11} a^2 b x^{11/2}+\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",1
2131,1,47,47,0.0290117,"\int \left(a+b \sqrt{x}\right)^3 x^3 \, dx","Integrate[(a + b*Sqrt[x])^3*x^3,x]","\frac{a^3 x^4}{4}+\frac{2}{3} a^2 b x^{9/2}+\frac{3}{5} a b^2 x^5+\frac{2}{11} b^3 x^{11/2}","\frac{a^3 x^4}{4}+\frac{2}{3} a^2 b x^{9/2}+\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",1
2132,1,47,47,0.019454,"\int \left(a+b \sqrt{x}\right)^3 x^2 \, dx","Integrate[(a + b*Sqrt[x])^3*x^2,x]","\frac{a^3 x^3}{3}+\frac{6}{7} a^2 b x^{7/2}+\frac{3}{4} a b^2 x^4+\frac{2}{9} b^3 x^{9/2}","\frac{a^3 x^3}{3}+\frac{6}{7} a^2 b x^{7/2}+\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",1
2133,1,44,44,0.018063,"\int \left(a+b \sqrt{x}\right)^3 x \, dx","Integrate[(a + b*Sqrt[x])^3*x,x]","\frac{a^3 x^2}{2}+\frac{6}{5} a^2 b x^{5/2}+a b^2 x^3+\frac{2}{7} b^3 x^{7/2}","\frac{a^3 x^2}{2}+\frac{6}{5} a^2 b x^{5/2}+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",1
2134,1,28,38,0.018145,"\int \left(a+b \sqrt{x}\right)^3 \, dx","Integrate[(a + b*Sqrt[x])^3,x]","-\frac{\left(a-4 b \sqrt{x}\right) \left(a+b \sqrt{x}\right)^4}{10 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,"-1/10*((a - 4*b*Sqrt[x])*(a + b*Sqrt[x])^4)/b^2","A",1
2135,1,37,37,0.0140948,"\int \frac{\left(a+b \sqrt{x}\right)^3}{x} \, dx","Integrate[(a + b*Sqrt[x])^3/x,x]","a^3 \log (x)+6 a^2 b \sqrt{x}+3 a b^2 x+\frac{2}{3} b^3 x^{3/2}","a^3 \log (x)+6 a^2 b \sqrt{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",1
2136,1,38,38,0.0240152,"\int \frac{\left(a+b \sqrt{x}\right)^3}{x^2} \, dx","Integrate[(a + b*Sqrt[x])^3/x^2,x]","-\frac{a^3}{x}-\frac{6 a^2 b}{\sqrt{x}}+3 a b^2 \log (x)+2 b^3 \sqrt{x}","-\frac{a^3}{x}-\frac{6 a^2 b}{\sqrt{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",1
2137,1,21,21,0.003612,"\int \frac{\left(a+b \sqrt{x}\right)^3}{x^3} \, dx","Integrate[(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,"-1/2*(a + b*Sqrt[x])^4/(a*x^2)","A",1
2138,1,41,47,0.0180998,"\int \frac{\left(a+b \sqrt{x}\right)^3}{x^4} \, dx","Integrate[(a + b*Sqrt[x])^3/x^4,x]","-\frac{10 a^3+36 a^2 b \sqrt{x}+45 a b^2 x+20 b^3 x^{3/2}}{30 x^3}","-\frac{a^3}{3 x^3}-\frac{6 a^2 b}{5 x^{5/2}}-\frac{3 a b^2}{2 x^2}-\frac{2 b^3}{3 x^{3/2}}",1,"-1/30*(10*a^3 + 36*a^2*b*Sqrt[x] + 45*a*b^2*x + 20*b^3*x^(3/2))/x^3","A",1
2139,1,41,45,0.0180212,"\int \frac{\left(a+b \sqrt{x}\right)^3}{x^5} \, dx","Integrate[(a + b*Sqrt[x])^3/x^5,x]","-\frac{35 a^3+120 a^2 b \sqrt{x}+140 a b^2 x+56 b^3 x^{3/2}}{140 x^4}","-\frac{a^3}{4 x^4}-\frac{6 a^2 b}{7 x^{7/2}}-\frac{a b^2}{x^3}-\frac{2 b^3}{5 x^{5/2}}",1,"-1/140*(35*a^3 + 120*a^2*b*Sqrt[x] + 140*a*b^2*x + 56*b^3*x^(3/2))/x^4","A",1
2140,1,41,47,0.0186575,"\int \frac{\left(a+b \sqrt{x}\right)^3}{x^6} \, dx","Integrate[(a + b*Sqrt[x])^3/x^6,x]","-\frac{84 a^3+280 a^2 b \sqrt{x}+315 a b^2 x+120 b^3 x^{3/2}}{420 x^5}","-\frac{a^3}{5 x^5}-\frac{2 a^2 b}{3 x^{9/2}}-\frac{3 a b^2}{4 x^4}-\frac{2 b^3}{7 x^{7/2}}",1,"-1/420*(84*a^3 + 280*a^2*b*Sqrt[x] + 315*a*b^2*x + 120*b^3*x^(3/2))/x^5","A",1
2141,1,75,75,0.0342196,"\int \left(a+b \sqrt{x}\right)^5 x^4 \, dx","Integrate[(a + b*Sqrt[x])^5*x^4,x]","\frac{a^5 x^5}{5}+\frac{10}{11} a^4 b x^{11/2}+\frac{5}{3} a^3 b^2 x^6+\frac{20}{13} a^2 b^3 x^{13/2}+\frac{5}{7} a b^4 x^7+\frac{2}{15} b^5 x^{15/2}","\frac{a^5 x^5}{5}+\frac{10}{11} a^4 b x^{11/2}+\frac{5}{3} a^3 b^2 x^6+\frac{20}{13} a^2 b^3 x^{13/2}+\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",1
2142,1,73,73,0.029643,"\int \left(a+b \sqrt{x}\right)^5 x^3 \, dx","Integrate[(a + b*Sqrt[x])^5*x^3,x]","\frac{a^5 x^4}{4}+\frac{10}{9} a^4 b x^{9/2}+2 a^3 b^2 x^5+\frac{20}{11} a^2 b^3 x^{11/2}+\frac{5}{6} a b^4 x^6+\frac{2}{13} b^5 x^{13/2}","\frac{a^5 x^4}{4}+\frac{10}{9} a^4 b x^{9/2}+2 a^3 b^2 x^5+\frac{20}{11} a^2 b^3 x^{11/2}+\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",1
2143,1,72,72,0.0263359,"\int \left(a+b \sqrt{x}\right)^5 x^2 \, dx","Integrate[(a + b*Sqrt[x])^5*x^2,x]","\frac{a^5 x^3}{3}+\frac{10}{7} a^4 b x^{7/2}+\frac{5}{2} a^3 b^2 x^4+\frac{20}{9} a^2 b^3 x^{9/2}+a b^4 x^5+\frac{2}{11} b^5 x^{11/2}","\frac{a^5 x^3}{3}+\frac{10}{7} a^4 b x^{7/2}+\frac{5}{2} a^3 b^2 x^4+\frac{20}{9} a^2 b^3 x^{9/2}+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",1
2144,1,73,80,0.0245437,"\int \left(a+b \sqrt{x}\right)^5 x \, dx","Integrate[(a + b*Sqrt[x])^5*x,x]","\frac{a^5 x^2}{2}+2 a^4 b x^{5/2}+\frac{10}{3} a^3 b^2 x^3+\frac{20}{7} a^2 b^3 x^{7/2}+\frac{5}{4} a b^4 x^4+\frac{2}{9} b^5 x^{9/2}","-\frac{a^3 \left(a+b \sqrt{x}\right)^6}{3 b^4}+\frac{6 a^2 \left(a+b \sqrt{x}\right)^7}{7 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^5*x^2)/2 + 2*a^4*b*x^(5/2) + (10*a^3*b^2*x^3)/3 + (20*a^2*b^3*x^(7/2))/7 + (5*a*b^4*x^4)/4 + (2*b^5*x^(9/2))/9","A",1
2145,1,28,38,0.0208132,"\int \left(a+b \sqrt{x}\right)^5 \, dx","Integrate[(a + b*Sqrt[x])^5,x]","-\frac{\left(a-6 b \sqrt{x}\right) \left(a+b \sqrt{x}\right)^6}{21 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,"-1/21*((a - 6*b*Sqrt[x])*(a + b*Sqrt[x])^6)/b^2","A",1
2146,1,65,65,0.0210978,"\int \frac{\left(a+b \sqrt{x}\right)^5}{x} \, dx","Integrate[(a + b*Sqrt[x])^5/x,x]","a^5 \log (x)+10 a^4 b \sqrt{x}+10 a^3 b^2 x+\frac{20}{3} a^2 b^3 x^{3/2}+\frac{5}{2} a b^4 x^2+\frac{2}{5} b^5 x^{5/2}","a^5 \log (x)+10 a^4 b \sqrt{x}+10 a^3 b^2 x+\frac{20}{3} a^2 b^3 x^{3/2}+\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",1
2147,1,62,62,0.0308563,"\int \frac{\left(a+b \sqrt{x}\right)^5}{x^2} \, dx","Integrate[(a + b*Sqrt[x])^5/x^2,x]","-\frac{a^5}{x}-\frac{10 a^4 b}{\sqrt{x}}+10 a^3 b^2 \log (x)+20 a^2 b^3 \sqrt{x}+5 a b^4 x+\frac{2}{3} b^5 x^{3/2}","-\frac{a^5}{x}-\frac{10 a^4 b}{\sqrt{x}}+10 a^3 b^2 \log (x)+20 a^2 b^3 \sqrt{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",1
2148,1,66,66,0.0344094,"\int \frac{\left(a+b \sqrt{x}\right)^5}{x^3} \, dx","Integrate[(a + b*Sqrt[x])^5/x^3,x]","-\frac{a^5}{2 x^2}-\frac{10 a^4 b}{3 x^{3/2}}-\frac{10 a^3 b^2}{x}-\frac{20 a^2 b^3}{\sqrt{x}}+5 a b^4 \log (x)+2 b^5 \sqrt{x}","-\frac{a^5}{2 x^2}-\frac{10 a^4 b}{3 x^{3/2}}-\frac{10 a^3 b^2}{x}-\frac{20 a^2 b^3}{\sqrt{x}}+5 a b^4 \log (x)+2 b^5 \sqrt{x}",1,"-1/2*a^5/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",1
2149,1,21,21,0.0039313,"\int \frac{\left(a+b \sqrt{x}\right)^5}{x^4} \, dx","Integrate[(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,"-1/3*(a + b*Sqrt[x])^6/(a*x^3)","A",1
2150,1,65,70,0.0262394,"\int \frac{\left(a+b \sqrt{x}\right)^5}{x^5} \, dx","Integrate[(a + b*Sqrt[x])^5/x^5,x]","-\frac{21 a^5+120 a^4 b \sqrt{x}+280 a^3 b^2 x+336 a^2 b^3 x^{3/2}+210 a b^4 x^2+56 b^5 x^{5/2}}{84 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,"-1/84*(21*a^5 + 120*a^4*b*Sqrt[x] + 280*a^3*b^2*x + 336*a^2*b^3*x^(3/2) + 210*a*b^4*x^2 + 56*b^5*x^(5/2))/x^4","A",1
2151,1,65,75,0.0274058,"\int \frac{\left(a+b \sqrt{x}\right)^5}{x^6} \, dx","Integrate[(a + b*Sqrt[x])^5/x^6,x]","-\frac{126 a^5+700 a^4 b \sqrt{x}+1575 a^3 b^2 x+1800 a^2 b^3 x^{3/2}+1050 a b^4 x^2+252 b^5 x^{5/2}}{630 x^5}","-\frac{a^5}{5 x^5}-\frac{10 a^4 b}{9 x^{9/2}}-\frac{5 a^3 b^2}{2 x^4}-\frac{20 a^2 b^3}{7 x^{7/2}}-\frac{5 a b^4}{3 x^3}-\frac{2 b^5}{5 x^{5/2}}",1,"-1/630*(126*a^5 + 700*a^4*b*Sqrt[x] + 1575*a^3*b^2*x + 1800*a^2*b^3*x^(3/2) + 1050*a*b^4*x^2 + 252*b^5*x^(5/2))/x^5","A",1
2152,1,65,73,0.0278409,"\int \frac{\left(a+b \sqrt{x}\right)^5}{x^7} \, dx","Integrate[(a + b*Sqrt[x])^5/x^7,x]","-\frac{462 a^5+2520 a^4 b \sqrt{x}+5544 a^3 b^2 x+6160 a^2 b^3 x^{3/2}+3465 a b^4 x^2+792 b^5 x^{5/2}}{2772 x^6}","-\frac{a^5}{6 x^6}-\frac{10 a^4 b}{11 x^{11/2}}-\frac{2 a^3 b^2}{x^5}-\frac{20 a^2 b^3}{9 x^{9/2}}-\frac{5 a b^4}{4 x^4}-\frac{2 b^5}{7 x^{7/2}}",1,"-1/2772*(462*a^5 + 2520*a^4*b*Sqrt[x] + 5544*a^3*b^2*x + 6160*a^2*b^3*x^(3/2) + 3465*a*b^4*x^2 + 792*b^5*x^(5/2))/x^6","A",1
2153,1,140,140,0.07025,"\int \left(a+b \sqrt{x}\right)^{10} x^4 \, dx","Integrate[(a + b*Sqrt[x])^10*x^4,x]","\frac{a^{10} x^5}{5}+\frac{20}{11} a^9 b x^{11/2}+\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}{19} a b^9 x^{19/2}+\frac{b^{10} x^{10}}{10}","\frac{a^{10} x^5}{5}+\frac{20}{11} a^9 b x^{11/2}+\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}{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",1
2154,1,136,162,0.0550058,"\int \left(a+b \sqrt{x}\right)^{10} x^3 \, dx","Integrate[(a + b*Sqrt[x])^10*x^3,x]","\frac{a^{10} x^4}{4}+\frac{20}{9} a^9 b x^{9/2}+9 a^8 b^2 x^5+\frac{240}{11} a^7 b^3 x^{11/2}+35 a^6 b^4 x^6+\frac{504}{13} a^5 b^5 x^{13/2}+30 a^4 b^6 x^7+16 a^3 b^7 x^{15/2}+\frac{45}{8} a^2 b^8 x^8+\frac{20}{17} a b^9 x^{17/2}+\frac{b^{10} x^9}{9}","-\frac{2 a^7 \left(a+b \sqrt{x}\right)^{11}}{11 b^8}+\frac{7 a^6 \left(a+b \sqrt{x}\right)^{12}}{6 b^8}-\frac{42 a^5 \left(a+b \sqrt{x}\right)^{13}}{13 b^8}+\frac{5 a^4 \left(a+b \sqrt{x}\right)^{14}}{b^8}-\frac{14 a^3 \left(a+b \sqrt{x}\right)^{15}}{3 b^8}+\frac{21 a^2 \left(a+b \sqrt{x}\right)^{16}}{8 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,"(a^10*x^4)/4 + (20*a^9*b*x^(9/2))/9 + 9*a^8*b^2*x^5 + (240*a^7*b^3*x^(11/2))/11 + 35*a^6*b^4*x^6 + (504*a^5*b^5*x^(13/2))/13 + 30*a^4*b^6*x^7 + 16*a^3*b^7*x^(15/2) + (45*a^2*b^8*x^8)/8 + (20*a*b^9*x^(17/2))/17 + (b^10*x^9)/9","A",1
2155,1,74,122,0.0519543,"\int \left(a+b \sqrt{x}\right)^{10} x^2 \, dx","Integrate[(a + b*Sqrt[x])^10*x^2,x]","-\frac{\left(a+b \sqrt{x}\right)^{11} \left(a^5-11 a^4 b \sqrt{x}+66 a^3 b^2 x-286 a^2 b^3 x^{3/2}+1001 a b^4 x^2-3003 b^5 x^{5/2}\right)}{24024 b^6}","-\frac{2 a^5 \left(a+b \sqrt{x}\right)^{11}}{11 b^6}+\frac{5 a^4 \left(a+b \sqrt{x}\right)^{12}}{6 b^6}-\frac{20 a^3 \left(a+b \sqrt{x}\right)^{13}}{13 b^6}+\frac{10 a^2 \left(a+b \sqrt{x}\right)^{14}}{7 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,"-1/24024*((a + b*Sqrt[x])^11*(a^5 - 11*a^4*b*Sqrt[x] + 66*a^3*b^2*x - 286*a^2*b^3*x^(3/2) + 1001*a*b^4*x^2 - 3003*b^5*x^(5/2)))/b^6","A",1
2156,1,50,80,0.0390967,"\int \left(a+b \sqrt{x}\right)^{10} x \, dx","Integrate[(a + b*Sqrt[x])^10*x,x]","-\frac{\left(a+b \sqrt{x}\right)^{11} \left(a^3-11 a^2 b \sqrt{x}+66 a b^2 x-286 b^3 x^{3/2}\right)}{2002 b^4}","-\frac{2 a^3 \left(a+b \sqrt{x}\right)^{11}}{11 b^4}+\frac{a^2 \left(a+b \sqrt{x}\right)^{12}}{2 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,"-1/2002*((a + b*Sqrt[x])^11*(a^3 - 11*a^2*b*Sqrt[x] + 66*a*b^2*x - 286*b^3*x^(3/2)))/b^4","A",1
2157,1,28,38,0.0285231,"\int \left(a+b \sqrt{x}\right)^{10} \, dx","Integrate[(a + b*Sqrt[x])^10,x]","-\frac{\left(a-11 b \sqrt{x}\right) \left(a+b \sqrt{x}\right)^{11}}{66 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,"-1/66*((a - 11*b*Sqrt[x])*(a + b*Sqrt[x])^11)/b^2","A",1
2158,1,128,128,0.043868,"\int \frac{\left(a+b \sqrt{x}\right)^{10}}{x} \, dx","Integrate[(a + b*Sqrt[x])^10/x,x]","a^{10} \log (x)+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+\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+\frac{20}{9} a b^9 x^{9/2}+\frac{b^{10} x^5}{5}","a^{10} \log (x)+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+\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+\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",1
2159,1,123,123,0.0647551,"\int \frac{\left(a+b \sqrt{x}\right)^{10}}{x^2} \, dx","Integrate[(a + b*Sqrt[x])^10/x^2,x]","-\frac{a^{10}}{x}-\frac{20 a^9 b}{\sqrt{x}}+45 a^8 b^2 \log (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+\frac{20}{7} a b^9 x^{7/2}+\frac{b^{10} x^4}{4}","-\frac{a^{10}}{x}-\frac{20 a^9 b}{\sqrt{x}}+45 a^8 b^2 \log (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+\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",1
2160,1,127,127,0.0622883,"\int \frac{\left(a+b \sqrt{x}\right)^{10}}{x^3} \, dx","Integrate[(a + b*Sqrt[x])^10/x^3,x]","-\frac{a^{10}}{2 x^2}-\frac{20 a^9 b}{3 x^{3/2}}-\frac{45 a^8 b^2}{x}-\frac{240 a^7 b^3}{\sqrt{x}}+210 a^6 b^4 \log (x)+504 a^5 b^5 \sqrt{x}+210 a^4 b^6 x+80 a^3 b^7 x^{3/2}+\frac{45}{2} a^2 b^8 x^2+4 a b^9 x^{5/2}+\frac{b^{10} x^3}{3}","-\frac{a^{10}}{2 x^2}-\frac{20 a^9 b}{3 x^{3/2}}-\frac{45 a^8 b^2}{x}-\frac{240 a^7 b^3}{\sqrt{x}}+210 a^6 b^4 \log (x)+504 a^5 b^5 \sqrt{x}+210 a^4 b^6 x+80 a^3 b^7 x^{3/2}+\frac{45}{2} a^2 b^8 x^2+4 a b^9 x^{5/2}+\frac{b^{10} x^3}{3}",1,"-1/2*a^10/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",1
2161,1,124,127,0.0740701,"\int \frac{\left(a+b \sqrt{x}\right)^{10}}{x^4} \, dx","Integrate[(a + b*Sqrt[x])^10/x^4,x]","210 a^4 b^6 \log (x)-\frac{2 a^{10}+24 a^9 b \sqrt{x}+135 a^8 b^2 x+480 a^7 b^3 x^{3/2}+1260 a^6 b^4 x^2+3024 a^5 b^5 x^{5/2}-1440 a^3 b^7 x^{7/2}-270 a^2 b^8 x^4-40 a b^9 x^{9/2}-3 b^{10} x^5}{6 x^3}","-\frac{a^{10}}{3 x^3}-\frac{4 a^9 b}{x^{5/2}}-\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}}+210 a^4 b^6 \log (x)+240 a^3 b^7 \sqrt{x}+45 a^2 b^8 x+\frac{20}{3} a b^9 x^{3/2}+\frac{b^{10} x^2}{2}",1,"-1/6*(2*a^10 + 24*a^9*b*Sqrt[x] + 135*a^8*b^2*x + 480*a^7*b^3*x^(3/2) + 1260*a^6*b^4*x^2 + 3024*a^5*b^5*x^(5/2) - 1440*a^3*b^7*x^(7/2) - 270*a^2*b^8*x^4 - 40*a*b^9*x^(9/2) - 3*b^10*x^5)/x^3 + 210*a^4*b^6*Log[x]","A",1
2162,1,122,122,0.0869285,"\int \frac{\left(a+b \sqrt{x}\right)^{10}}{x^5} \, dx","Integrate[(a + b*Sqrt[x])^10/x^5,x]","-\frac{a^{10}}{4 x^4}-\frac{20 a^9 b}{7 x^{7/2}}-\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)+20 a b^9 \sqrt{x}+b^{10} x","-\frac{a^{10}}{4 x^4}-\frac{20 a^9 b}{7 x^{7/2}}-\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)+20 a b^9 \sqrt{x}+b^{10} x",1,"-1/4*a^10/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",1
2163,1,130,130,0.0811282,"\int \frac{\left(a+b \sqrt{x}\right)^{10}}{x^6} \, dx","Integrate[(a + b*Sqrt[x])^10/x^6,x]","-\frac{a^{10}}{5 x^5}-\frac{20 a^9 b}{9 x^{9/2}}-\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 b^9}{\sqrt{x}}+b^{10} \log (x)","-\frac{a^{10}}{5 x^5}-\frac{20 a^9 b}{9 x^{9/2}}-\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 b^9}{\sqrt{x}}+b^{10} \log (x)",1,"-1/5*a^10/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",1
2164,1,32,46,0.0083247,"\int \frac{\left(a+b \sqrt{x}\right)^{10}}{x^7} \, dx","Integrate[(a + b*Sqrt[x])^10/x^7,x]","\frac{\left(b \sqrt{x}-11 a\right) \left(a+b \sqrt{x}\right)^{11}}{66 a^2 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,"((-11*a + b*Sqrt[x])*(a + b*Sqrt[x])^11)/(66*a^2*x^6)","A",1
2165,1,54,96,0.0122289,"\int \frac{\left(a+b \sqrt{x}\right)^{10}}{x^8} \, dx","Integrate[(a + b*Sqrt[x])^10/x^8,x]","\frac{\left(a+b \sqrt{x}\right)^{11} \left(-286 a^3+66 a^2 b \sqrt{x}-11 a b^2 x+b^3 x^{3/2}\right)}{2002 a^4 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*(-286*a^3 + 66*a^2*b*Sqrt[x] - 11*a*b^2*x + b^3*x^(3/2)))/(2002*a^4*x^7)","A",1
2166,1,140,146,0.0298209,"\int \frac{\left(a+b \sqrt{x}\right)^{10}}{x^9} \, dx","Integrate[(a + b*Sqrt[x])^10/x^9,x]","-\frac{a^{10}}{8 x^8}-\frac{4 a^9 b}{3 x^{15/2}}-\frac{45 a^8 b^2}{7 x^7}-\frac{240 a^7 b^3}{13 x^{13/2}}-\frac{35 a^6 b^4}{x^6}-\frac{504 a^5 b^5}{11 x^{11/2}}-\frac{42 a^4 b^6}{x^5}-\frac{80 a^3 b^7}{3 x^{9/2}}-\frac{45 a^2 b^8}{4 x^4}-\frac{20 a b^9}{7 x^{7/2}}-\frac{b^{10}}{3 x^3}","\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,"-1/8*a^10/x^8 - (4*a^9*b)/(3*x^(15/2)) - (45*a^8*b^2)/(7*x^7) - (240*a^7*b^3)/(13*x^(13/2)) - (35*a^6*b^4)/x^6 - (504*a^5*b^5)/(11*x^(11/2)) - (42*a^4*b^6)/x^5 - (80*a^3*b^7)/(3*x^(9/2)) - (45*a^2*b^8)/(4*x^4) - (20*a*b^9)/(7*x^(7/2)) - b^10/(3*x^3)","A",1
2167,1,136,136,0.0642716,"\int \frac{\left(a+b \sqrt{x}\right)^{10}}{x^{10}} \, dx","Integrate[(a + b*Sqrt[x])^10/x^10,x]","-\frac{a^{10}}{9 x^9}-\frac{20 a^9 b}{17 x^{17/2}}-\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 b^9}{9 x^{9/2}}-\frac{b^{10}}{4 x^4}","-\frac{a^{10}}{9 x^9}-\frac{20 a^9 b}{17 x^{17/2}}-\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 b^9}{9 x^{9/2}}-\frac{b^{10}}{4 x^4}",1,"-1/9*a^10/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",1
2168,1,140,140,0.060557,"\int \frac{\left(a+b \sqrt{x}\right)^{10}}{x^{11}} \, dx","Integrate[(a + b*Sqrt[x])^10/x^11,x]","-\frac{a^{10}}{10 x^{10}}-\frac{20 a^9 b}{19 x^{19/2}}-\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 b^9}{11 x^{11/2}}-\frac{b^{10}}{5 x^5}","-\frac{a^{10}}{10 x^{10}}-\frac{20 a^9 b}{19 x^{19/2}}-\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 b^9}{11 x^{11/2}}-\frac{b^{10}}{5 x^5}",1,"-1/10*a^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",1
2169,1,211,242,0.1232026,"\int \left(a+b \sqrt{x}\right)^{15} x^5 \, dx","Integrate[(a + b*Sqrt[x])^15*x^5,x]","\frac{a^{15} x^6}{6}+\frac{30}{13} a^{14} b x^{13/2}+15 a^{13} b^2 x^7+\frac{182}{3} a^{12} b^3 x^{15/2}+\frac{1365}{8} a^{11} b^4 x^8+\frac{6006}{17} a^{10} b^5 x^{17/2}+\frac{5005}{9} a^9 b^6 x^9+\frac{12870}{19} a^8 b^7 x^{19/2}+\frac{1287}{2} a^7 b^8 x^{10}+\frac{1430}{3} a^6 b^9 x^{21/2}+273 a^5 b^{10} x^{11}+\frac{2730}{23} a^4 b^{11} x^{23/2}+\frac{455}{12} a^3 b^{12} x^{12}+\frac{42}{5} a^2 b^{13} x^{25/2}+\frac{15}{13} a b^{14} x^{13}+\frac{2}{27} b^{15} x^{27/2}","-\frac{a^{11} \left(a+b \sqrt{x}\right)^{16}}{8 b^{12}}+\frac{22 a^{10} \left(a+b \sqrt{x}\right)^{17}}{17 b^{12}}-\frac{55 a^9 \left(a+b \sqrt{x}\right)^{18}}{9 b^{12}}+\frac{330 a^8 \left(a+b \sqrt{x}\right)^{19}}{19 b^{12}}-\frac{33 a^7 \left(a+b \sqrt{x}\right)^{20}}{b^{12}}+\frac{44 a^6 \left(a+b \sqrt{x}\right)^{21}}{b^{12}}-\frac{42 a^5 \left(a+b \sqrt{x}\right)^{22}}{b^{12}}+\frac{660 a^4 \left(a+b \sqrt{x}\right)^{23}}{23 b^{12}}-\frac{55 a^3 \left(a+b \sqrt{x}\right)^{24}}{4 b^{12}}+\frac{22 a^2 \left(a+b \sqrt{x}\right)^{25}}{5 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^15*x^6)/6 + (30*a^14*b*x^(13/2))/13 + 15*a^13*b^2*x^7 + (182*a^12*b^3*x^(15/2))/3 + (1365*a^11*b^4*x^8)/8 + (6006*a^10*b^5*x^(17/2))/17 + (5005*a^9*b^6*x^9)/9 + (12870*a^8*b^7*x^(19/2))/19 + (1287*a^7*b^8*x^10)/2 + (1430*a^6*b^9*x^(21/2))/3 + 273*a^5*b^10*x^11 + (2730*a^4*b^11*x^(23/2))/23 + (455*a^3*b^12*x^12)/12 + (42*a^2*b^13*x^(25/2))/5 + (15*a*b^14*x^13)/13 + (2*b^15*x^(27/2))/27","A",1
2170,1,122,202,0.0978968,"\int \left(a+b \sqrt{x}\right)^{15} x^4 \, dx","Integrate[(a + b*Sqrt[x])^15*x^4,x]","-\frac{\left(a+b \sqrt{x}\right)^{16} \left(a^9-16 a^8 b \sqrt{x}+136 a^7 b^2 x-816 a^6 b^3 x^{3/2}+3876 a^5 b^4 x^2-15504 a^4 b^5 x^{5/2}+54264 a^3 b^6 x^3-170544 a^2 b^7 x^{7/2}+490314 a b^8 x^4-1307504 b^9 x^{9/2}\right)}{16343800 b^{10}}","-\frac{a^9 \left(a+b \sqrt{x}\right)^{16}}{8 b^{10}}+\frac{18 a^8 \left(a+b \sqrt{x}\right)^{17}}{17 b^{10}}-\frac{4 a^7 \left(a+b \sqrt{x}\right)^{18}}{b^{10}}+\frac{168 a^6 \left(a+b \sqrt{x}\right)^{19}}{19 b^{10}}-\frac{63 a^5 \left(a+b \sqrt{x}\right)^{20}}{5 b^{10}}+\frac{12 a^4 \left(a+b \sqrt{x}\right)^{21}}{b^{10}}-\frac{84 a^3 \left(a+b \sqrt{x}\right)^{22}}{11 b^{10}}+\frac{72 a^2 \left(a+b \sqrt{x}\right)^{23}}{23 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,"-1/16343800*((a + b*Sqrt[x])^16*(a^9 - 16*a^8*b*Sqrt[x] + 136*a^7*b^2*x - 816*a^6*b^3*x^(3/2) + 3876*a^5*b^4*x^2 - 15504*a^4*b^5*x^(5/2) + 54264*a^3*b^6*x^3 - 170544*a^2*b^7*x^(7/2) + 490314*a*b^8*x^4 - 1307504*b^9*x^(9/2)))/b^10","A",1
2171,1,98,162,0.0765133,"\int \left(a+b \sqrt{x}\right)^{15} x^3 \, dx","Integrate[(a + b*Sqrt[x])^15*x^3,x]","-\frac{\left(a+b \sqrt{x}\right)^{16} \left(a^7-16 a^6 b \sqrt{x}+136 a^5 b^2 x-816 a^4 b^3 x^{3/2}+3876 a^3 b^4 x^2-15504 a^2 b^5 x^{5/2}+54264 a b^6 x^3-170544 b^7 x^{7/2}\right)}{1961256 b^8}","-\frac{a^7 \left(a+b \sqrt{x}\right)^{16}}{8 b^8}+\frac{14 a^6 \left(a+b \sqrt{x}\right)^{17}}{17 b^8}-\frac{7 a^5 \left(a+b \sqrt{x}\right)^{18}}{3 b^8}+\frac{70 a^4 \left(a+b \sqrt{x}\right)^{19}}{19 b^8}-\frac{7 a^3 \left(a+b \sqrt{x}\right)^{20}}{2 b^8}+\frac{2 a^2 \left(a+b \sqrt{x}\right)^{21}}{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,"-1/1961256*((a + b*Sqrt[x])^16*(a^7 - 16*a^6*b*Sqrt[x] + 136*a^5*b^2*x - 816*a^4*b^3*x^(3/2) + 3876*a^3*b^4*x^2 - 15504*a^2*b^5*x^(5/2) + 54264*a*b^6*x^3 - 170544*b^7*x^(7/2)))/b^8","A",1
2172,1,74,122,0.0674622,"\int \left(a+b \sqrt{x}\right)^{15} x^2 \, dx","Integrate[(a + b*Sqrt[x])^15*x^2,x]","-\frac{\left(a+b \sqrt{x}\right)^{16} \left(a^5-16 a^4 b \sqrt{x}+136 a^3 b^2 x-816 a^2 b^3 x^{3/2}+3876 a b^4 x^2-15504 b^5 x^{5/2}\right)}{162792 b^6}","-\frac{a^5 \left(a+b \sqrt{x}\right)^{16}}{8 b^6}+\frac{10 a^4 \left(a+b \sqrt{x}\right)^{17}}{17 b^6}-\frac{10 a^3 \left(a+b \sqrt{x}\right)^{18}}{9 b^6}+\frac{20 a^2 \left(a+b \sqrt{x}\right)^{19}}{19 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,"-1/162792*((a + b*Sqrt[x])^16*(a^5 - 16*a^4*b*Sqrt[x] + 136*a^3*b^2*x - 816*a^2*b^3*x^(3/2) + 3876*a*b^4*x^2 - 15504*b^5*x^(5/2)))/b^6","A",1
2173,1,50,80,0.0568989,"\int \left(a+b \sqrt{x}\right)^{15} x \, dx","Integrate[(a + b*Sqrt[x])^15*x,x]","-\frac{\left(a+b \sqrt{x}\right)^{16} \left(a^3-16 a^2 b \sqrt{x}+136 a b^2 x-816 b^3 x^{3/2}\right)}{7752 b^4}","-\frac{a^3 \left(a+b \sqrt{x}\right)^{16}}{8 b^4}+\frac{6 a^2 \left(a+b \sqrt{x}\right)^{17}}{17 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,"-1/7752*((a + b*Sqrt[x])^16*(a^3 - 16*a^2*b*Sqrt[x] + 136*a*b^2*x - 816*b^3*x^(3/2)))/b^4","A",1
2174,1,28,38,0.0437958,"\int \left(a+b \sqrt{x}\right)^{15} \, dx","Integrate[(a + b*Sqrt[x])^15,x]","-\frac{\left(a-16 b \sqrt{x}\right) \left(a+b \sqrt{x}\right)^{16}}{136 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,"-1/136*((a - 16*b*Sqrt[x])*(a + b*Sqrt[x])^16)/b^2","A",1
2175,1,205,205,0.1055361,"\int \frac{\left(a+b \sqrt{x}\right)^{15}}{x} \, dx","Integrate[(a + b*Sqrt[x])^15/x,x]","a^{15} \log (x)+30 a^{14} b \sqrt{x}+105 a^{13} b^2 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}+\frac{15}{7} a b^{14} x^7+\frac{2}{15} b^{15} x^{15/2}","a^{15} \log (x)+30 a^{14} b \sqrt{x}+105 a^{13} b^2 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}+\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",1
2176,1,192,192,0.1307664,"\int \frac{\left(a+b \sqrt{x}\right)^{15}}{x^2} \, dx","Integrate[(a + b*Sqrt[x])^15/x^2,x]","-\frac{a^{15}}{x}-\frac{30 a^{14} b}{\sqrt{x}}+105 a^{13} b^2 \log (x)+910 a^{12} b^3 \sqrt{x}+1365 a^{11} b^4 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}+\frac{5}{2} a b^{14} x^6+\frac{2}{13} b^{15} x^{13/2}","-\frac{a^{15}}{x}-\frac{30 a^{14} b}{\sqrt{x}}+105 a^{13} b^2 \log (x)+910 a^{12} b^3 \sqrt{x}+1365 a^{11} b^4 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}+\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",1
2177,1,190,190,0.1389565,"\int \frac{\left(a+b \sqrt{x}\right)^{15}}{x^3} \, dx","Integrate[(a + b*Sqrt[x])^15/x^3,x]","-\frac{a^{15}}{2 x^2}-\frac{10 a^{14} b}{x^{3/2}}-\frac{105 a^{13} b^2}{x}-\frac{910 a^{12} b^3}{\sqrt{x}}+1365 a^{11} b^4 \log (x)+6006 a^{10} b^5 \sqrt{x}+5005 a^9 b^6 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}+3 a b^{14} x^5+\frac{2}{11} b^{15} x^{11/2}","-\frac{a^{15}}{2 x^2}-\frac{10 a^{14} b}{x^{3/2}}-\frac{105 a^{13} b^2}{x}-\frac{910 a^{12} b^3}{\sqrt{x}}+1365 a^{11} b^4 \log (x)+6006 a^{10} b^5 \sqrt{x}+5005 a^9 b^6 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}+3 a b^{14} x^5+\frac{2}{11} b^{15} x^{11/2}",1,"-1/2*a^15/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",1
2178,1,196,196,0.1443755,"\int \frac{\left(a+b \sqrt{x}\right)^{15}}{x^4} \, dx","Integrate[(a + b*Sqrt[x])^15/x^4,x]","-\frac{a^{15}}{3 x^3}-\frac{6 a^{14} b}{x^{5/2}}-\frac{105 a^{13} b^2}{2 x^2}-\frac{910 a^{12} b^3}{3 x^{3/2}}-\frac{1365 a^{11} b^4}{x}-\frac{6006 a^{10} b^5}{\sqrt{x}}+5005 a^9 b^6 \log (x)+12870 a^8 b^7 \sqrt{x}+6435 a^7 b^8 x+\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{15}{4} a b^{14} x^4+\frac{2}{9} b^{15} x^{9/2}","-\frac{a^{15}}{3 x^3}-\frac{6 a^{14} b}{x^{5/2}}-\frac{105 a^{13} b^2}{2 x^2}-\frac{910 a^{12} b^3}{3 x^{3/2}}-\frac{1365 a^{11} b^4}{x}-\frac{6006 a^{10} b^5}{\sqrt{x}}+5005 a^9 b^6 \log (x)+12870 a^8 b^7 \sqrt{x}+6435 a^7 b^8 x+\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{15}{4} a b^{14} x^4+\frac{2}{9} b^{15} x^{9/2}",1,"-1/3*a^15/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",1
2179,1,194,194,0.1513239,"\int \frac{\left(a+b \sqrt{x}\right)^{15}}{x^6} \, dx","Integrate[(a + b*Sqrt[x])^15/x^6,x]","-\frac{a^{15}}{5 x^5}-\frac{10 a^{14} b}{3 x^{9/2}}-\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}}-\frac{6435 a^7 b^8}{x}-\frac{10010 a^6 b^9}{\sqrt{x}}+3003 a^5 b^{10} \log (x)+2730 a^4 b^{11} \sqrt{x}+455 a^3 b^{12} x+70 a^2 b^{13} x^{3/2}+\frac{15}{2} a b^{14} x^2+\frac{2}{5} b^{15} x^{5/2}","-\frac{a^{15}}{5 x^5}-\frac{10 a^{14} b}{3 x^{9/2}}-\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}}-\frac{6435 a^7 b^8}{x}-\frac{10010 a^6 b^9}{\sqrt{x}}+3003 a^5 b^{10} \log (x)+2730 a^4 b^{11} \sqrt{x}+455 a^3 b^{12} x+70 a^2 b^{13} x^{3/2}+\frac{15}{2} a b^{14} x^2+\frac{2}{5} b^{15} x^{5/2}",1,"-1/5*a^15/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",1
2180,1,196,196,0.1586877,"\int \frac{\left(a+b \sqrt{x}\right)^{15}}{x^7} \, dx","Integrate[(a + b*Sqrt[x])^15/x^7,x]","-\frac{a^{15}}{6 x^6}-\frac{30 a^{14} b}{11 x^{11/2}}-\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}}+455 a^3 b^{12} \log (x)+210 a^2 b^{13} \sqrt{x}+15 a b^{14} x+\frac{2}{3} b^{15} x^{3/2}","-\frac{a^{15}}{6 x^6}-\frac{30 a^{14} b}{11 x^{11/2}}-\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}}+455 a^3 b^{12} \log (x)+210 a^2 b^{13} \sqrt{x}+15 a b^{14} x+\frac{2}{3} b^{15} x^{3/2}",1,"-1/6*a^15/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",1
2181,1,198,198,0.1805406,"\int \frac{\left(a+b \sqrt{x}\right)^{15}}{x^8} \, dx","Integrate[(a + b*Sqrt[x])^15/x^8,x]","-\frac{a^{15}}{7 x^7}-\frac{30 a^{14} b}{13 x^{13/2}}-\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}}+15 a b^{14} \log (x)+2 b^{15} \sqrt{x}","-\frac{a^{15}}{7 x^7}-\frac{30 a^{14} b}{13 x^{13/2}}-\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}}+15 a b^{14} \log (x)+2 b^{15} \sqrt{x}",1,"-1/7*a^15/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",1
2182,1,21,21,0.0070229,"\int \frac{\left(a+b \sqrt{x}\right)^{15}}{x^9} \, dx","Integrate[(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,"-1/8*(a + b*Sqrt[x])^16/(a*x^8)","A",1
2183,1,41,70,0.0110197,"\int \frac{\left(a+b \sqrt{x}\right)^{15}}{x^{10}} \, dx","Integrate[(a + b*Sqrt[x])^15/x^10,x]","-\frac{\left(a+b \sqrt{x}\right)^{16} \left(136 a^2-16 a b \sqrt{x}+b^2 x\right)}{1224 a^3 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,"-1/1224*((a + b*Sqrt[x])^16*(136*a^2 - 16*a*b*Sqrt[x] + b^2*x))/(a^3*x^9)","A",1
2184,1,65,120,0.0419248,"\int \frac{\left(a+b \sqrt{x}\right)^{15}}{x^{11}} \, dx","Integrate[(a + b*Sqrt[x])^15/x^11,x]","-\frac{\left(a+b \sqrt{x}\right)^{16} \left(3876 a^4-816 a^3 b \sqrt{x}+136 a^2 b^2 x-16 a b^3 x^{3/2}+b^4 x^2\right)}{38760 a^5 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,"-1/38760*((a + b*Sqrt[x])^16*(3876*a^4 - 816*a^3*b*Sqrt[x] + 136*a^2*b^2*x - 16*a*b^3*x^(3/2) + b^4*x^2))/(a^5*x^10)","A",1
2185,1,89,170,0.0190863,"\int \frac{\left(a+b \sqrt{x}\right)^{15}}{x^{12}} \, dx","Integrate[(a + b*Sqrt[x])^15/x^12,x]","-\frac{\left(a+b \sqrt{x}\right)^{16} \left(54264 a^6-15504 a^5 b \sqrt{x}+3876 a^4 b^2 x-816 a^3 b^3 x^{3/2}+136 a^2 b^4 x^2-16 a b^5 x^{5/2}+b^6 x^3\right)}{596904 a^7 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,"-1/596904*((a + b*Sqrt[x])^16*(54264*a^6 - 15504*a^5*b*Sqrt[x] + 3876*a^4*b^2*x - 816*a^3*b^3*x^(3/2) + 136*a^2*b^4*x^2 - 16*a*b^5*x^(5/2) + b^6*x^3))/(a^7*x^11)","A",1
2186,1,209,220,0.0648779,"\int \frac{\left(a+b \sqrt{x}\right)^{15}}{x^{13}} \, dx","Integrate[(a + b*Sqrt[x])^15/x^13,x]","-\frac{a^{15}}{12 x^{12}}-\frac{30 a^{14} b}{23 x^{23/2}}-\frac{105 a^{13} b^2}{11 x^{11}}-\frac{130 a^{12} b^3}{3 x^{21/2}}-\frac{273 a^{11} b^4}{2 x^{10}}-\frac{6006 a^{10} b^5}{19 x^{19/2}}-\frac{5005 a^9 b^6}{9 x^9}-\frac{12870 a^8 b^7}{17 x^{17/2}}-\frac{6435 a^7 b^8}{8 x^8}-\frac{2002 a^6 b^9}{3 x^{15/2}}-\frac{429 a^5 b^{10}}{x^7}-\frac{210 a^4 b^{11}}{x^{13/2}}-\frac{455 a^3 b^{12}}{6 x^6}-\frac{210 a^2 b^{13}}{11 x^{11/2}}-\frac{3 a b^{14}}{x^5}-\frac{2 b^{15}}{9 x^{9/2}}","-\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,"-1/12*a^15/x^12 - (30*a^14*b)/(23*x^(23/2)) - (105*a^13*b^2)/(11*x^11) - (130*a^12*b^3)/(3*x^(21/2)) - (273*a^11*b^4)/(2*x^10) - (6006*a^10*b^5)/(19*x^(19/2)) - (5005*a^9*b^6)/(9*x^9) - (12870*a^8*b^7)/(17*x^(17/2)) - (6435*a^7*b^8)/(8*x^8) - (2002*a^6*b^9)/(3*x^(15/2)) - (429*a^5*b^10)/x^7 - (210*a^4*b^11)/x^(13/2) - (455*a^3*b^12)/(6*x^6) - (210*a^2*b^13)/(11*x^(11/2)) - (3*a*b^14)/x^5 - (2*b^15)/(9*x^(9/2))","A",1
2187,1,207,270,0.1487175,"\int \frac{\left(a+b \sqrt{x}\right)^{15}}{x^{14}} \, dx","Integrate[(a + b*Sqrt[x])^15/x^14,x]","-\frac{a^{15}}{13 x^{13}}-\frac{6 a^{14} b}{5 x^{25/2}}-\frac{35 a^{13} b^2}{4 x^{12}}-\frac{910 a^{12} b^3}{23 x^{23/2}}-\frac{1365 a^{11} b^4}{11 x^{11}}-\frac{286 a^{10} b^5}{x^{21/2}}-\frac{1001 a^9 b^6}{2 x^{10}}-\frac{12870 a^8 b^7}{19 x^{19/2}}-\frac{715 a^7 b^8}{x^9}-\frac{10010 a^6 b^9}{17 x^{17/2}}-\frac{3003 a^5 b^{10}}{8 x^8}-\frac{182 a^4 b^{11}}{x^{15/2}}-\frac{65 a^3 b^{12}}{x^7}-\frac{210 a^2 b^{13}}{13 x^{13/2}}-\frac{5 a b^{14}}{2 x^6}-\frac{2 b^{15}}{11 x^{11/2}}","-\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,"-1/13*a^15/x^13 - (6*a^14*b)/(5*x^(25/2)) - (35*a^13*b^2)/(4*x^12) - (910*a^12*b^3)/(23*x^(23/2)) - (1365*a^11*b^4)/(11*x^11) - (286*a^10*b^5)/x^(21/2) - (1001*a^9*b^6)/(2*x^10) - (12870*a^8*b^7)/(19*x^(19/2)) - (715*a^7*b^8)/x^9 - (10010*a^6*b^9)/(17*x^(17/2)) - (3003*a^5*b^10)/(8*x^8) - (182*a^4*b^11)/x^(15/2) - (65*a^3*b^12)/x^7 - (210*a^2*b^13)/(13*x^(13/2)) - (5*a*b^14)/(2*x^6) - (2*b^15)/(11*x^(11/2))","A",1
2188,1,211,211,0.1343344,"\int \frac{\left(a+b \sqrt{x}\right)^{15}}{x^{15}} \, dx","Integrate[(a + b*Sqrt[x])^15/x^15,x]","-\frac{a^{15}}{14 x^{14}}-\frac{10 a^{14} b}{9 x^{27/2}}-\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{15 a b^{14}}{7 x^7}-\frac{2 b^{15}}{13 x^{13/2}}","-\frac{a^{15}}{14 x^{14}}-\frac{10 a^{14} b}{9 x^{27/2}}-\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{15 a b^{14}}{7 x^7}-\frac{2 b^{15}}{13 x^{13/2}}",1,"-1/14*a^15/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",1
2189,1,211,211,0.1402635,"\int \frac{\left(a+b \sqrt{x}\right)^{15}}{x^{16}} \, dx","Integrate[(a + b*Sqrt[x])^15/x^16,x]","-\frac{a^{15}}{15 x^{15}}-\frac{30 a^{14} b}{29 x^{29/2}}-\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{15 a b^{14}}{8 x^8}-\frac{2 b^{15}}{15 x^{15/2}}","-\frac{a^{15}}{15 x^{15}}-\frac{30 a^{14} b}{29 x^{29/2}}-\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{15 a b^{14}}{8 x^8}-\frac{2 b^{15}}{15 x^{15/2}}",1,"-1/15*a^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",1
2190,1,207,207,0.1386243,"\int \frac{\left(a+b \sqrt{x}\right)^{15}}{x^{17}} \, dx","Integrate[(a + b*Sqrt[x])^15/x^17,x]","-\frac{a^{15}}{16 x^{16}}-\frac{30 a^{14} b}{31 x^{31/2}}-\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{5 a b^{14}}{3 x^9}-\frac{2 b^{15}}{17 x^{17/2}}","-\frac{a^{15}}{16 x^{16}}-\frac{30 a^{14} b}{31 x^{31/2}}-\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{5 a b^{14}}{3 x^9}-\frac{2 b^{15}}{17 x^{17/2}}",1,"-1/16*a^15/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",1
2191,1,99,107,0.0955451,"\int \frac{x^3}{a+b \sqrt{x}} \, dx","Integrate[x^3/(a + b*Sqrt[x]),x]","\frac{-420 a^7 \log \left(a+b \sqrt{x}\right)+420 a^6 b \sqrt{x}-210 a^5 b^2 x+140 a^4 b^3 x^{3/2}-105 a^3 b^4 x^2+84 a^2 b^5 x^{5/2}-70 a b^6 x^3+60 b^7 x^{7/2}}{210 b^8}","-\frac{2 a^7 \log \left(a+b \sqrt{x}\right)}{b^8}+\frac{2 a^6 \sqrt{x}}{b^7}-\frac{a^5 x}{b^6}+\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{a x^3}{3 b^2}+\frac{2 x^{7/2}}{7 b}",1,"(420*a^6*b*Sqrt[x] - 210*a^5*b^2*x + 140*a^4*b^3*x^(3/2) - 105*a^3*b^4*x^2 + 84*a^2*b^5*x^(5/2) - 70*a*b^6*x^3 + 60*b^7*x^(7/2) - 420*a^7*Log[a + b*Sqrt[x]])/(210*b^8)","A",1
2192,1,75,79,0.0658702,"\int \frac{x^2}{a+b \sqrt{x}} \, dx","Integrate[x^2/(a + b*Sqrt[x]),x]","\frac{-60 a^5 \log \left(a+b \sqrt{x}\right)+60 a^4 b \sqrt{x}-30 a^3 b^2 x+20 a^2 b^3 x^{3/2}-15 a b^4 x^2+12 b^5 x^{5/2}}{30 b^6}","-\frac{2 a^5 \log \left(a+b \sqrt{x}\right)}{b^6}+\frac{2 a^4 \sqrt{x}}{b^5}-\frac{a^3 x}{b^4}+\frac{2 a^2 x^{3/2}}{3 b^3}-\frac{a x^2}{2 b^2}+\frac{2 x^{5/2}}{5 b}",1,"(60*a^4*b*Sqrt[x] - 30*a^3*b^2*x + 20*a^2*b^3*x^(3/2) - 15*a*b^4*x^2 + 12*b^5*x^(5/2) - 60*a^5*Log[a + b*Sqrt[x]])/(30*b^6)","A",1
2193,1,51,51,0.0295177,"\int \frac{x}{a+b \sqrt{x}} \, dx","Integrate[x/(a + b*Sqrt[x]),x]","-\frac{2 a^3 \log \left(a+b \sqrt{x}\right)}{b^4}+\frac{2 a^2 \sqrt{x}}{b^3}-\frac{a x}{b^2}+\frac{2 x^{3/2}}{3 b}","-\frac{2 a^3 \log \left(a+b \sqrt{x}\right)}{b^4}+\frac{2 a^2 \sqrt{x}}{b^3}-\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",1
2194,1,27,27,0.0345256,"\int \frac{1}{a+b \sqrt{x}} \, dx","Integrate[(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",1
2195,1,22,22,0.0041176,"\int \frac{1}{\left(a+b \sqrt{x}\right) x} \, dx","Integrate[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",1
2196,1,44,47,0.0324121,"\int \frac{1}{\left(a+b \sqrt{x}\right) x^2} \, dx","Integrate[1/((a + b*Sqrt[x])*x^2),x]","\frac{-2 b^2 x \log \left(a+b \sqrt{x}\right)-a \left(a-2 b \sqrt{x}\right)+b^2 x \log (x)}{a^3 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,"(-(a*(a - 2*b*Sqrt[x])) - 2*b^2*x*Log[a + b*Sqrt[x]] + b^2*x*Log[x])/(a^3*x)","A",1
2197,1,69,75,0.0749062,"\int \frac{1}{\left(a+b \sqrt{x}\right) x^3} \, dx","Integrate[1/((a + b*Sqrt[x])*x^3),x]","\frac{\frac{a \left(-3 a^3+4 a^2 b \sqrt{x}-6 a b^2 x+12 b^3 x^{3/2}\right)}{x^2}-12 b^4 \log \left(a+b \sqrt{x}\right)+6 b^4 \log (x)}{6 a^5}","-\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^4 \sqrt{x}}-\frac{b^2}{a^3 x}+\frac{2 b}{3 a^2 x^{3/2}}-\frac{1}{2 a x^2}",1,"((a*(-3*a^3 + 4*a^2*b*Sqrt[x] - 6*a*b^2*x + 12*b^3*x^(3/2)))/x^2 - 12*b^4*Log[a + b*Sqrt[x]] + 6*b^4*Log[x])/(6*a^5)","A",1
2198,1,93,103,0.0882463,"\int \frac{1}{\left(a+b \sqrt{x}\right) x^4} \, dx","Integrate[1/((a + b*Sqrt[x])*x^4),x]","\frac{\frac{a \left(-10 a^5+12 a^4 b \sqrt{x}-15 a^3 b^2 x+20 a^2 b^3 x^{3/2}-30 a b^4 x^2+60 b^5 x^{5/2}\right)}{x^3}-60 b^6 \log \left(a+b \sqrt{x}\right)+30 b^6 \log (x)}{30 a^7}","-\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^6 \sqrt{x}}-\frac{b^4}{a^5 x}+\frac{2 b^3}{3 a^4 x^{3/2}}-\frac{b^2}{2 a^3 x^2}+\frac{2 b}{5 a^2 x^{5/2}}-\frac{1}{3 a x^3}",1,"((a*(-10*a^5 + 12*a^4*b*Sqrt[x] - 15*a^3*b^2*x + 20*a^2*b^3*x^(3/2) - 30*a*b^4*x^2 + 60*b^5*x^(5/2)))/x^3 - 60*b^6*Log[a + b*Sqrt[x]] + 30*b^6*Log[x])/(30*a^7)","A",1
2199,1,102,111,0.108111,"\int \frac{x^3}{\left(a+b \sqrt{x}\right)^2} \, dx","Integrate[x^3/(a + b*Sqrt[x])^2,x]","\frac{\frac{60 a^7}{a+b \sqrt{x}}+420 a^6 \log \left(a+b \sqrt{x}\right)-360 a^5 b \sqrt{x}+150 a^4 b^2 x-80 a^3 b^3 x^{3/2}+45 a^2 b^4 x^2-24 a b^5 x^{5/2}+10 b^6 x^3}{30 b^8}","\frac{2 a^7}{b^8 \left(a+b \sqrt{x}\right)}+\frac{14 a^6 \log \left(a+b \sqrt{x}\right)}{b^8}-\frac{12 a^5 \sqrt{x}}{b^7}+\frac{5 a^4 x}{b^6}-\frac{8 a^3 x^{3/2}}{3 b^5}+\frac{3 a^2 x^2}{2 b^4}-\frac{4 a x^{5/2}}{5 b^3}+\frac{x^3}{3 b^2}",1,"((60*a^7)/(a + b*Sqrt[x]) - 360*a^5*b*Sqrt[x] + 150*a^4*b^2*x - 80*a^3*b^3*x^(3/2) + 45*a^2*b^4*x^2 - 24*a*b^5*x^(5/2) + 10*b^6*x^3 + 420*a^6*Log[a + b*Sqrt[x]])/(30*b^8)","A",1
2200,1,78,83,0.0628819,"\int \frac{x^2}{\left(a+b \sqrt{x}\right)^2} \, dx","Integrate[x^2/(a + b*Sqrt[x])^2,x]","\frac{\frac{12 a^5}{a+b \sqrt{x}}+60 a^4 \log \left(a+b \sqrt{x}\right)-48 a^3 b \sqrt{x}+18 a^2 b^2 x-8 a b^3 x^{3/2}+3 b^4 x^2}{6 b^6}","\frac{2 a^5}{b^6 \left(a+b \sqrt{x}\right)}+\frac{10 a^4 \log \left(a+b \sqrt{x}\right)}{b^6}-\frac{8 a^3 \sqrt{x}}{b^5}+\frac{3 a^2 x}{b^4}-\frac{4 a x^{3/2}}{3 b^3}+\frac{x^2}{2 b^2}",1,"((12*a^5)/(a + b*Sqrt[x]) - 48*a^3*b*Sqrt[x] + 18*a^2*b^2*x - 8*a*b^3*x^(3/2) + 3*b^4*x^2 + 60*a^4*Log[a + b*Sqrt[x]])/(6*b^6)","A",1
2201,1,50,54,0.0528233,"\int \frac{x}{\left(a+b \sqrt{x}\right)^2} \, dx","Integrate[x/(a + b*Sqrt[x])^2,x]","\frac{\frac{2 a^3}{a+b \sqrt{x}}+6 a^2 \log \left(a+b \sqrt{x}\right)-4 a b \sqrt{x}+b^2 x}{b^4}","\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)/(a + b*Sqrt[x]) - 4*a*b*Sqrt[x] + b^2*x + 6*a^2*Log[a + b*Sqrt[x]])/b^4","A",1
2202,1,29,33,0.0211249,"\int \frac{1}{\left(a+b \sqrt{x}\right)^2} \, dx","Integrate[(a + b*Sqrt[x])^(-2),x]","\frac{2 \left(\frac{a}{a+b \sqrt{x}}+\log \left(a+b \sqrt{x}\right)\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/(a + b*Sqrt[x]) + Log[a + b*Sqrt[x]]))/b^2","A",1
2203,1,33,38,0.0445892,"\int \frac{1}{\left(a+b \sqrt{x}\right)^2 x} \, dx","Integrate[1/((a + b*Sqrt[x])^2*x),x]","\frac{\frac{2 a}{a+b \sqrt{x}}-2 \log \left(a+b \sqrt{x}\right)+\log (x)}{a^2}","-\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]] + Log[x])/a^2","A",1
2204,1,60,67,0.1271787,"\int \frac{1}{\left(a+b \sqrt{x}\right)^2 x^2} \, dx","Integrate[1/((a + b*Sqrt[x])^2*x^2),x]","\frac{a \left(\frac{2 b^2}{a+b \sqrt{x}}-\frac{a}{x}+\frac{4 b}{\sqrt{x}}\right)-6 b^2 \log \left(a+b \sqrt{x}\right)+3 b^2 \log (x)}{a^4}","-\frac{6 b^2 \log \left(a+b \sqrt{x}\right)}{a^4}+\frac{3 b^2 \log (x)}{a^4}+\frac{2 b^2}{a^3 \left(a+b \sqrt{x}\right)}+\frac{4 b}{a^3 \sqrt{x}}-\frac{1}{a^2 x}",1,"(a*((2*b^2)/(a + b*Sqrt[x]) - a/x + (4*b)/Sqrt[x]) - 6*b^2*Log[a + b*Sqrt[x]] + 3*b^2*Log[x])/a^4","A",1
2205,1,91,95,0.1357077,"\int \frac{1}{\left(a+b \sqrt{x}\right)^2 x^3} \, dx","Integrate[1/((a + b*Sqrt[x])^2*x^3),x]","\frac{\frac{a \left(-3 a^4+5 a^3 b \sqrt{x}-10 a^2 b^2 x+30 a b^3 x^{3/2}+60 b^4 x^2\right)}{x^2 \left(a+b \sqrt{x}\right)}-60 b^4 \log \left(a+b \sqrt{x}\right)+30 b^4 \log (x)}{6 a^6}","-\frac{10 b^4 \log \left(a+b \sqrt{x}\right)}{a^6}+\frac{5 b^4 \log (x)}{a^6}+\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{4 b}{3 a^3 x^{3/2}}-\frac{1}{2 a^2 x^2}",1,"((a*(-3*a^4 + 5*a^3*b*Sqrt[x] - 10*a^2*b^2*x + 30*a*b^3*x^(3/2) + 60*b^4*x^2))/((a + b*Sqrt[x])*x^2) - 60*b^4*Log[a + b*Sqrt[x]] + 30*b^4*Log[x])/(6*a^6)","A",1
2206,1,115,123,0.1792458,"\int \frac{1}{\left(a+b \sqrt{x}\right)^2 x^4} \, dx","Integrate[1/((a + b*Sqrt[x])^2*x^4),x]","\frac{\frac{a \left(-10 a^6+14 a^5 b \sqrt{x}-21 a^4 b^2 x+35 a^3 b^3 x^{3/2}-70 a^2 b^4 x^2+210 a b^5 x^{5/2}+420 b^6 x^3\right)}{x^3 \left(a+b \sqrt{x}\right)}-420 b^6 \log \left(a+b \sqrt{x}\right)+210 b^6 \log (x)}{30 a^8}","-\frac{14 b^6 \log \left(a+b \sqrt{x}\right)}{a^8}+\frac{7 b^6 \log (x)}{a^8}+\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{8 b^3}{3 a^5 x^{3/2}}-\frac{3 b^2}{2 a^4 x^2}+\frac{4 b}{5 a^3 x^{5/2}}-\frac{1}{3 a^2 x^3}",1,"((a*(-10*a^6 + 14*a^5*b*Sqrt[x] - 21*a^4*b^2*x + 35*a^3*b^3*x^(3/2) - 70*a^2*b^4*x^2 + 210*a*b^5*x^(5/2) + 420*b^6*x^3))/((a + b*Sqrt[x])*x^3) - 420*b^6*Log[a + b*Sqrt[x]] + 210*b^6*Log[x])/(30*a^8)","A",1
2207,1,107,114,0.1332757,"\int \frac{x^3}{\left(a+b \sqrt{x}\right)^3} \, dx","Integrate[x^3/(a + b*Sqrt[x])^3,x]","\frac{\frac{10 a^7}{\left(a+b \sqrt{x}\right)^2}-\frac{140 a^6}{a+b \sqrt{x}}-420 a^5 \log \left(a+b \sqrt{x}\right)+300 a^4 b \sqrt{x}-100 a^3 b^2 x+40 a^2 b^3 x^{3/2}-15 a b^4 x^2+4 b^5 x^{5/2}}{10 b^8}","\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{42 a^5 \log \left(a+b \sqrt{x}\right)}{b^8}+\frac{30 a^4 \sqrt{x}}{b^7}-\frac{10 a^3 x}{b^6}+\frac{4 a^2 x^{3/2}}{b^5}-\frac{3 a x^2}{2 b^4}+\frac{2 x^{5/2}}{5 b^3}",1,"((10*a^7)/(a + b*Sqrt[x])^2 - (140*a^6)/(a + b*Sqrt[x]) + 300*a^4*b*Sqrt[x] - 100*a^3*b^2*x + 40*a^2*b^3*x^(3/2) - 15*a*b^4*x^2 + 4*b^5*x^(5/2) - 420*a^5*Log[a + b*Sqrt[x]])/(10*b^8)","A",1
2208,1,83,88,0.0832534,"\int \frac{x^2}{\left(a+b \sqrt{x}\right)^3} \, dx","Integrate[x^2/(a + b*Sqrt[x])^3,x]","\frac{\frac{3 a^5}{\left(a+b \sqrt{x}\right)^2}-\frac{30 a^4}{a+b \sqrt{x}}-60 a^3 \log \left(a+b \sqrt{x}\right)+36 a^2 b \sqrt{x}-9 a b^2 x+2 b^3 x^{3/2}}{3 b^6}","\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{20 a^3 \log \left(a+b \sqrt{x}\right)}{b^6}+\frac{12 a^2 \sqrt{x}}{b^5}-\frac{3 a x}{b^4}+\frac{2 x^{3/2}}{3 b^3}",1,"((3*a^5)/(a + b*Sqrt[x])^2 - (30*a^4)/(a + b*Sqrt[x]) + 36*a^2*b*Sqrt[x] - 9*a*b^2*x + 2*b^3*x^(3/2) - 60*a^3*Log[a + b*Sqrt[x]])/(3*b^6)","A",1
2209,1,57,64,0.0771394,"\int \frac{x}{\left(a+b \sqrt{x}\right)^3} \, dx","Integrate[x/(a + b*Sqrt[x])^3,x]","\frac{\frac{a^3}{\left(a+b \sqrt{x}\right)^2}-\frac{6 a^2}{a+b \sqrt{x}}-6 a \log \left(a+b \sqrt{x}\right)+2 b \sqrt{x}}{b^4}","\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/(a + b*Sqrt[x])^2 - (6*a^2)/(a + b*Sqrt[x]) + 2*b*Sqrt[x] - 6*a*Log[a + b*Sqrt[x]])/b^4","A",1
2210,1,16,16,0.0245239,"\int \frac{1}{\left(a+b \sqrt{x}\right)^3} \, dx","Integrate[(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",1
2211,1,44,53,0.0638474,"\int \frac{1}{\left(a+b \sqrt{x}\right)^3 x} \, dx","Integrate[1/((a + b*Sqrt[x])^3*x),x]","\frac{\frac{a \left(3 a+2 b \sqrt{x}\right)}{\left(a+b \sqrt{x}\right)^2}-2 \log \left(a+b \sqrt{x}\right)+\log (x)}{a^3}","-\frac{2 \log \left(a+b \sqrt{x}\right)}{a^3}+\frac{\log (x)}{a^3}+\frac{2}{a^2 \left(a+b \sqrt{x}\right)}+\frac{1}{a \left(a+b \sqrt{x}\right)^2}",1,"((a*(3*a + 2*b*Sqrt[x]))/(a + b*Sqrt[x])^2 - 2*Log[a + b*Sqrt[x]] + Log[x])/a^3","A",1
2212,1,77,85,0.1369093,"\int \frac{1}{\left(a+b \sqrt{x}\right)^3 x^2} \, dx","Integrate[1/((a + b*Sqrt[x])^3*x^2),x]","\frac{\frac{a \left(-a^3+4 a^2 b \sqrt{x}+18 a b^2 x+12 b^3 x^{3/2}\right)}{x \left(a+b \sqrt{x}\right)^2}-12 b^2 \log \left(a+b \sqrt{x}\right)+6 b^2 \log (x)}{a^5}","-\frac{12 b^2 \log \left(a+b \sqrt{x}\right)}{a^5}+\frac{6 b^2 \log (x)}{a^5}+\frac{6 b^2}{a^4 \left(a+b \sqrt{x}\right)}+\frac{6 b}{a^4 \sqrt{x}}+\frac{b^2}{a^3 \left(a+b \sqrt{x}\right)^2}-\frac{1}{a^3 x}",1,"((a*(-a^3 + 4*a^2*b*Sqrt[x] + 18*a*b^2*x + 12*b^3*x^(3/2)))/((a + b*Sqrt[x])^2*x) - 12*b^2*Log[a + b*Sqrt[x]] + 6*b^2*Log[x])/a^5","A",1
2213,1,104,111,0.1848403,"\int \frac{1}{\left(a+b \sqrt{x}\right)^3 x^3} \, dx","Integrate[1/((a + b*Sqrt[x])^3*x^3),x]","\frac{\frac{a \left(-a^5+2 a^4 b \sqrt{x}-5 a^3 b^2 x+20 a^2 b^3 x^{3/2}+90 a b^4 x^2+60 b^5 x^{5/2}\right)}{x^2 \left(a+b \sqrt{x}\right)^2}-60 b^4 \log \left(a+b \sqrt{x}\right)+30 b^4 \log (x)}{2 a^7}","-\frac{30 b^4 \log \left(a+b \sqrt{x}\right)}{a^7}+\frac{15 b^4 \log (x)}{a^7}+\frac{10 b^4}{a^6 \left(a+b \sqrt{x}\right)}+\frac{20 b^3}{a^6 \sqrt{x}}+\frac{b^4}{a^5 \left(a+b \sqrt{x}\right)^2}-\frac{6 b^2}{a^5 x}+\frac{2 b}{a^4 x^{3/2}}-\frac{1}{2 a^3 x^2}",1,"((a*(-a^5 + 2*a^4*b*Sqrt[x] - 5*a^3*b^2*x + 20*a^2*b^3*x^(3/2) + 90*a*b^4*x^2 + 60*b^5*x^(5/2)))/((a + b*Sqrt[x])^2*x^2) - 60*b^4*Log[a + b*Sqrt[x]] + 30*b^4*Log[x])/(2*a^7)","A",1
2214,1,128,139,0.2200205,"\int \frac{1}{\left(a+b \sqrt{x}\right)^3 x^4} \, dx","Integrate[1/((a + b*Sqrt[x])^3*x^4),x]","\frac{\frac{a \left(-5 a^7+8 a^6 b \sqrt{x}-14 a^5 b^2 x+28 a^4 b^3 x^{3/2}-70 a^3 b^4 x^2+280 a^2 b^5 x^{5/2}+1260 a b^6 x^3+840 b^7 x^{7/2}\right)}{x^3 \left(a+b \sqrt{x}\right)^2}-840 b^6 \log \left(a+b \sqrt{x}\right)+420 b^6 \log (x)}{15 a^9}","-\frac{56 b^6 \log \left(a+b \sqrt{x}\right)}{a^9}+\frac{28 b^6 \log (x)}{a^9}+\frac{14 b^6}{a^8 \left(a+b \sqrt{x}\right)}+\frac{42 b^5}{a^8 \sqrt{x}}+\frac{b^6}{a^7 \left(a+b \sqrt{x}\right)^2}-\frac{15 b^4}{a^7 x}+\frac{20 b^3}{3 a^6 x^{3/2}}-\frac{3 b^2}{a^5 x^2}+\frac{6 b}{5 a^4 x^{5/2}}-\frac{1}{3 a^3 x^3}",1,"((a*(-5*a^7 + 8*a^6*b*Sqrt[x] - 14*a^5*b^2*x + 28*a^4*b^3*x^(3/2) - 70*a^3*b^4*x^2 + 280*a^2*b^5*x^(5/2) + 1260*a*b^6*x^3 + 840*b^7*x^(7/2)))/((a + b*Sqrt[x])^2*x^3) - 840*b^6*Log[a + b*Sqrt[x]] + 420*b^6*Log[x])/(15*a^9)","A",1
2215,1,150,155,0.1924591,"\int \frac{x^4}{\left(a+b \sqrt{x}\right)^5} \, dx","Integrate[x^4/(a + b*Sqrt[x])^5,x]","\frac{-1375 a^9-2980 a^8 b \sqrt{x}+570 a^7 b^2 x+5420 a^6 b^3 x^{3/2}+3875 a^5 b^4 x^2-2520 a^5 \left(a+b \sqrt{x}\right)^4 \log \left(a+b \sqrt{x}\right)+504 a^4 b^5 x^{5/2}-84 a^3 b^6 x^3+24 a^2 b^7 x^{7/2}-9 a b^8 x^4+4 b^9 x^{9/2}}{10 b^{10} \left(a+b \sqrt{x}\right)^4}","\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{252 a^5 \log \left(a+b \sqrt{x}\right)}{b^{10}}+\frac{140 a^4 \sqrt{x}}{b^9}-\frac{35 a^3 x}{b^8}+\frac{10 a^2 x^{3/2}}{b^7}-\frac{5 a x^2}{2 b^6}+\frac{2 x^{5/2}}{5 b^5}",1,"(-1375*a^9 - 2980*a^8*b*Sqrt[x] + 570*a^7*b^2*x + 5420*a^6*b^3*x^(3/2) + 3875*a^5*b^4*x^2 + 504*a^4*b^5*x^(5/2) - 84*a^3*b^6*x^3 + 24*a^2*b^7*x^(7/2) - 9*a*b^8*x^4 + 4*b^9*x^(9/2) - 2520*a^5*(a + b*Sqrt[x])^4*Log[a + b*Sqrt[x]])/(10*b^10*(a + b*Sqrt[x])^4)","A",1
2216,1,126,131,0.1193773,"\int \frac{x^3}{\left(a+b \sqrt{x}\right)^5} \, dx","Integrate[x^3/(a + b*Sqrt[x])^5,x]","\frac{-319 a^7-856 a^6 b \sqrt{x}-444 a^5 b^2 x+544 a^4 b^3 x^{3/2}+556 a^3 b^4 x^2-420 a^3 \left(a+b \sqrt{x}\right)^4 \log \left(a+b \sqrt{x}\right)+84 a^2 b^5 x^{5/2}-14 a b^6 x^3+4 b^7 x^{7/2}}{6 b^8 \left(a+b \sqrt{x}\right)^4}","\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{70 a^3 \log \left(a+b \sqrt{x}\right)}{b^8}+\frac{30 a^2 \sqrt{x}}{b^7}-\frac{5 a x}{b^6}+\frac{2 x^{3/2}}{3 b^5}",1,"(-319*a^7 - 856*a^6*b*Sqrt[x] - 444*a^5*b^2*x + 544*a^4*b^3*x^(3/2) + 556*a^3*b^4*x^2 + 84*a^2*b^5*x^(5/2) - 14*a*b^6*x^3 + 4*b^7*x^(7/2) - 420*a^3*(a + b*Sqrt[x])^4*Log[a + b*Sqrt[x]])/(6*b^8*(a + b*Sqrt[x])^4)","A",1
2217,1,100,107,0.0901285,"\int \frac{x^2}{\left(a+b \sqrt{x}\right)^5} \, dx","Integrate[x^2/(a + b*Sqrt[x])^5,x]","-\frac{77 a^5+248 a^4 b \sqrt{x}+252 a^3 b^2 x+48 a^2 b^3 x^{3/2}-48 a b^4 x^2+60 a \left(a+b \sqrt{x}\right)^4 \log \left(a+b \sqrt{x}\right)-12 b^5 x^{5/2}}{6 b^6 \left(a+b \sqrt{x}\right)^4}","\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,"-1/6*(77*a^5 + 248*a^4*b*Sqrt[x] + 252*a^3*b^2*x + 48*a^2*b^3*x^(3/2) - 48*a*b^4*x^2 - 12*b^5*x^(5/2) + 60*a*(a + b*Sqrt[x])^4*Log[a + b*Sqrt[x]])/(b^6*(a + b*Sqrt[x])^4)","A",1
2218,1,21,21,0.0042862,"\int \frac{x}{\left(a+b \sqrt{x}\right)^5} \, dx","Integrate[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
2219,1,28,38,0.0193379,"\int \frac{1}{\left(a+b \sqrt{x}\right)^5} \, dx","Integrate[(a + b*Sqrt[x])^(-5),x]","-\frac{a+4 b \sqrt{x}}{6 b^2 \left(a+b \sqrt{x}\right)^4}","\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,"-1/6*(a + 4*b*Sqrt[x])/(b^2*(a + b*Sqrt[x])^4)","A",1
2220,1,71,89,0.1184535,"\int \frac{1}{\left(a+b \sqrt{x}\right)^5 x} \, dx","Integrate[1/((a + b*Sqrt[x])^5*x),x]","\frac{\frac{a \left(25 a^3+52 a^2 b \sqrt{x}+42 a b^2 x+12 b^3 x^{3/2}\right)}{\left(a+b \sqrt{x}\right)^4}-12 \log \left(a+b \sqrt{x}\right)+6 \log (x)}{6 a^5}","-\frac{2 \log \left(a+b \sqrt{x}\right)}{a^5}+\frac{\log (x)}{a^5}+\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{1}{2 a \left(a+b \sqrt{x}\right)^4}",1,"((a*(25*a^3 + 52*a^2*b*Sqrt[x] + 42*a*b^2*x + 12*b^3*x^(3/2)))/(a + b*Sqrt[x])^4 - 12*Log[a + b*Sqrt[x]] + 6*Log[x])/(6*a^5)","A",1
2221,1,104,126,0.1754974,"\int \frac{1}{\left(a+b \sqrt{x}\right)^5 x^2} \, dx","Integrate[1/((a + b*Sqrt[x])^5*x^2),x]","\frac{\frac{a \left(-2 a^5+12 a^4 b \sqrt{x}+125 a^3 b^2 x+260 a^2 b^3 x^{3/2}+210 a b^4 x^2+60 b^5 x^{5/2}\right)}{x \left(a+b \sqrt{x}\right)^4}-60 b^2 \log \left(a+b \sqrt{x}\right)+30 b^2 \log (x)}{2 a^7}","-\frac{30 b^2 \log \left(a+b \sqrt{x}\right)}{a^7}+\frac{15 b^2 \log (x)}{a^7}+\frac{20 b^2}{a^6 \left(a+b \sqrt{x}\right)}+\frac{10 b}{a^6 \sqrt{x}}+\frac{6 b^2}{a^5 \left(a+b \sqrt{x}\right)^2}-\frac{1}{a^5 x}+\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}",1,"((a*(-2*a^5 + 12*a^4*b*Sqrt[x] + 125*a^3*b^2*x + 260*a^2*b^3*x^(3/2) + 210*a*b^4*x^2 + 60*b^5*x^(5/2)))/((a + b*Sqrt[x])^4*x) - 60*b^2*Log[a + b*Sqrt[x]] + 30*b^2*Log[x])/(2*a^7)","A",1
2222,1,128,156,0.2099229,"\int \frac{1}{\left(a+b \sqrt{x}\right)^5 x^3} \, dx","Integrate[1/((a + b*Sqrt[x])^5*x^3),x]","\frac{\frac{a \left(-3 a^7+8 a^6 b \sqrt{x}-28 a^5 b^2 x+168 a^4 b^3 x^{3/2}+1750 a^3 b^4 x^2+3640 a^2 b^5 x^{5/2}+2940 a b^6 x^3+840 b^7 x^{7/2}\right)}{x^2 \left(a+b \sqrt{x}\right)^4}-840 b^4 \log \left(a+b \sqrt{x}\right)+420 b^4 \log (x)}{6 a^9}","-\frac{140 b^4 \log \left(a+b \sqrt{x}\right)}{a^9}+\frac{70 b^4 \log (x)}{a^9}+\frac{70 b^4}{a^8 \left(a+b \sqrt{x}\right)}+\frac{70 b^3}{a^8 \sqrt{x}}+\frac{15 b^4}{a^7 \left(a+b \sqrt{x}\right)^2}-\frac{15 b^2}{a^7 x}+\frac{10 b^4}{3 a^6 \left(a+b \sqrt{x}\right)^3}+\frac{10 b}{3 a^6 x^{3/2}}+\frac{b^4}{2 a^5 \left(a+b \sqrt{x}\right)^4}-\frac{1}{2 a^5 x^2}",1,"((a*(-3*a^7 + 8*a^6*b*Sqrt[x] - 28*a^5*b^2*x + 168*a^4*b^3*x^(3/2) + 1750*a^3*b^4*x^2 + 3640*a^2*b^5*x^(5/2) + 2940*a*b^6*x^3 + 840*b^7*x^(7/2)))/((a + b*Sqrt[x])^4*x^2) - 840*b^4*Log[a + b*Sqrt[x]] + 420*b^4*Log[x])/(6*a^9)","A",1
2223,1,174,203,0.2671806,"\int \frac{x^5}{\left(a+b \sqrt{x}\right)^8} \, dx","Integrate[x^5/(a + b*Sqrt[x])^8,x]","\frac{25961 a^{11}+154007 a^{10} b \sqrt{x}+365001 a^9 b^2 x+414295 a^8 b^3 x^{3/2}+171745 a^7 b^4 x^2-90993 a^6 b^5 x^{5/2}-127351 a^5 b^6 x^3-45913 a^4 b^7 x^{7/2}+27720 a^4 \left(a+b \sqrt{x}\right)^7 \log \left(a+b \sqrt{x}\right)-3465 a^3 b^8 x^4+385 a^2 b^9 x^{9/2}-77 a b^{10} x^5+21 b^{11} x^{11/2}}{42 b^{12} \left(a+b \sqrt{x}\right)^7}","\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{660 a^4 \log \left(a+b \sqrt{x}\right)}{b^{12}}-\frac{240 a^3 \sqrt{x}}{b^{11}}+\frac{36 a^2 x}{b^{10}}-\frac{16 a x^{3/2}}{3 b^9}+\frac{x^2}{2 b^8}",1,"(25961*a^11 + 154007*a^10*b*Sqrt[x] + 365001*a^9*b^2*x + 414295*a^8*b^3*x^(3/2) + 171745*a^7*b^4*x^2 - 90993*a^6*b^5*x^(5/2) - 127351*a^5*b^6*x^3 - 45913*a^4*b^7*x^(7/2) - 3465*a^3*b^8*x^4 + 385*a^2*b^9*x^(9/2) - 77*a*b^10*x^5 + 21*b^11*x^(11/2) + 27720*a^4*(a + b*Sqrt[x])^7*Log[a + b*Sqrt[x]])/(42*b^12*(a + b*Sqrt[x])^7)","A",1
2224,1,150,172,0.1778033,"\int \frac{x^4}{\left(a+b \sqrt{x}\right)^8} \, dx","Integrate[x^4/(a + b*Sqrt[x])^8,x]","\frac{3349 a^9+20923 a^8 b \sqrt{x}+53949 a^7 b^2 x+72275 a^6 b^3 x^{3/2}+50225 a^5 b^4 x^2+12495 a^4 b^5 x^{5/2}-4655 a^3 b^6 x^3-3185 a^2 b^7 x^{7/2}+2520 a^2 \left(a+b \sqrt{x}\right)^7 \log \left(a+b \sqrt{x}\right)-315 a b^8 x^4+35 b^9 x^{9/2}}{35 b^{10} \left(a+b \sqrt{x}\right)^7}","\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,"(3349*a^9 + 20923*a^8*b*Sqrt[x] + 53949*a^7*b^2*x + 72275*a^6*b^3*x^(3/2) + 50225*a^5*b^4*x^2 + 12495*a^4*b^5*x^(5/2) - 4655*a^3*b^6*x^3 - 3185*a^2*b^7*x^(7/2) - 315*a*b^8*x^4 + 35*b^9*x^(9/2) + 2520*a^2*(a + b*Sqrt[x])^7*Log[a + b*Sqrt[x]])/(35*b^10*(a + b*Sqrt[x])^7)","A",1
2225,1,102,157,0.1412572,"\int \frac{x^3}{\left(a+b \sqrt{x}\right)^8} \, dx","Integrate[x^3/(a + b*Sqrt[x])^8,x]","\frac{\frac{a \left(1089 a^6+7203 a^5 b \sqrt{x}+20139 a^4 b^2 x+30625 a^3 b^3 x^{3/2}+26950 a^2 b^4 x^2+13230 a b^5 x^{5/2}+2940 b^6 x^3\right)}{\left(a+b \sqrt{x}\right)^7}+420 \log \left(a+b \sqrt{x}\right)}{210 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,"((a*(1089*a^6 + 7203*a^5*b*Sqrt[x] + 20139*a^4*b^2*x + 30625*a^3*b^3*x^(3/2) + 26950*a^2*b^4*x^2 + 13230*a*b^5*x^(5/2) + 2940*b^6*x^3))/(a + b*Sqrt[x])^7 + 420*Log[a + b*Sqrt[x]])/(210*b^8)","A",1
2226,1,32,43,0.0085417,"\int \frac{x^2}{\left(a+b \sqrt{x}\right)^8} \, dx","Integrate[x^2/(a + b*Sqrt[x])^8,x]","\frac{x^3 \left(7 a+b \sqrt{x}\right)}{21 a^2 \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,"((7*a + b*Sqrt[x])*x^3)/(21*a^2*(a + b*Sqrt[x])^7)","A",1
2227,1,50,78,0.0519693,"\int \frac{x}{\left(a+b \sqrt{x}\right)^8} \, dx","Integrate[x/(a + b*Sqrt[x])^8,x]","-\frac{a^3+7 a^2 b \sqrt{x}+21 a b^2 x+35 b^3 x^{3/2}}{70 b^4 \left(a+b \sqrt{x}\right)^7}","\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,"-1/70*(a^3 + 7*a^2*b*Sqrt[x] + 21*a*b^2*x + 35*b^3*x^(3/2))/(b^4*(a + b*Sqrt[x])^7)","A",1
2228,1,28,38,0.0213747,"\int \frac{1}{\left(a+b \sqrt{x}\right)^8} \, dx","Integrate[(a + b*Sqrt[x])^(-8),x]","-\frac{a+7 b \sqrt{x}}{21 b^2 \left(a+b \sqrt{x}\right)^7}","\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,"-1/21*(a + 7*b*Sqrt[x])/(b^2*(a + b*Sqrt[x])^7)","A",1
2229,1,106,143,0.1812378,"\int \frac{1}{\left(a+b \sqrt{x}\right)^8 x} \, dx","Integrate[1/((a + b*Sqrt[x])^8*x),x]","\frac{\frac{a \left(1089 a^6+4683 a^5 b \sqrt{x}+9639 a^4 b^2 x+11165 a^3 b^3 x^{3/2}+7490 a^2 b^4 x^2+2730 a b^5 x^{5/2}+420 b^6 x^3\right)}{\left(a+b \sqrt{x}\right)^7}-420 \log \left(a+b \sqrt{x}\right)+210 \log (x)}{210 a^8}","-\frac{2 \log \left(a+b \sqrt{x}\right)}{a^8}+\frac{\log (x)}{a^8}+\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}{7 a \left(a+b \sqrt{x}\right)^7}",1,"((a*(1089*a^6 + 4683*a^5*b*Sqrt[x] + 9639*a^4*b^2*x + 11165*a^3*b^3*x^(3/2) + 7490*a^2*b^4*x^2 + 2730*a*b^5*x^(5/2) + 420*b^6*x^3))/(a + b*Sqrt[x])^7 - 420*Log[a + b*Sqrt[x]] + 210*Log[x])/(210*a^8)","A",1
2230,1,139,184,0.2695535,"\int \frac{1}{\left(a+b \sqrt{x}\right)^8 x^2} \, dx","Integrate[1/((a + b*Sqrt[x])^8*x^2),x]","\frac{\frac{a \left(-35 a^8+315 a^7 b \sqrt{x}+6534 a^6 b^2 x+28098 a^5 b^3 x^{3/2}+57834 a^4 b^4 x^2+66990 a^3 b^5 x^{5/2}+44940 a^2 b^6 x^3+16380 a b^7 x^{7/2}+2520 b^8 x^4\right)}{x \left(a+b \sqrt{x}\right)^7}-2520 b^2 \log \left(a+b \sqrt{x}\right)+1260 b^2 \log (x)}{35 a^{10}}","-\frac{72 b^2 \log \left(a+b \sqrt{x}\right)}{a^{10}}+\frac{36 b^2 \log (x)}{a^{10}}+\frac{56 b^2}{a^9 \left(a+b \sqrt{x}\right)}+\frac{16 b}{a^9 \sqrt{x}}+\frac{21 b^2}{a^8 \left(a+b \sqrt{x}\right)^2}-\frac{1}{a^8 x}+\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}",1,"((a*(-35*a^8 + 315*a^7*b*Sqrt[x] + 6534*a^6*b^2*x + 28098*a^5*b^3*x^(3/2) + 57834*a^4*b^4*x^2 + 66990*a^3*b^5*x^(5/2) + 44940*a^2*b^6*x^3 + 16380*a*b^7*x^(7/2) + 2520*b^8*x^4))/((a + b*Sqrt[x])^7*x) - 2520*b^2*Log[a + b*Sqrt[x]] + 1260*b^2*Log[x])/(35*a^10)","A",1
2231,1,163,217,0.3637797,"\int \frac{1}{\left(a+b \sqrt{x}\right)^8 x^3} \, dx","Integrate[1/((a + b*Sqrt[x])^8*x^3),x]","\frac{\frac{a \left(-21 a^{10}+77 a^9 b \sqrt{x}-385 a^8 b^2 x+3465 a^7 b^3 x^{3/2}+71874 a^6 b^4 x^2+309078 a^5 b^5 x^{5/2}+636174 a^4 b^6 x^3+736890 a^3 b^7 x^{7/2}+494340 a^2 b^8 x^4+180180 a b^9 x^{9/2}+27720 b^{10} x^5\right)}{x^2 \left(a+b \sqrt{x}\right)^7}-27720 b^4 \log \left(a+b \sqrt{x}\right)+13860 b^4 \log (x)}{42 a^{12}}","-\frac{660 b^4 \log \left(a+b \sqrt{x}\right)}{a^{12}}+\frac{330 b^4 \log (x)}{a^{12}}+\frac{420 b^4}{a^{11} \left(a+b \sqrt{x}\right)}+\frac{240 b^3}{a^{11} \sqrt{x}}+\frac{126 b^4}{a^{10} \left(a+b \sqrt{x}\right)^2}-\frac{36 b^2}{a^{10} x}+\frac{140 b^4}{3 a^9 \left(a+b \sqrt{x}\right)^3}+\frac{16 b}{3 a^9 x^{3/2}}+\frac{35 b^4}{2 a^8 \left(a+b \sqrt{x}\right)^4}-\frac{1}{2 a^8 x^2}+\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}",1,"((a*(-21*a^10 + 77*a^9*b*Sqrt[x] - 385*a^8*b^2*x + 3465*a^7*b^3*x^(3/2) + 71874*a^6*b^4*x^2 + 309078*a^5*b^5*x^(5/2) + 636174*a^4*b^6*x^3 + 736890*a^3*b^7*x^(7/2) + 494340*a^2*b^8*x^4 + 180180*a*b^9*x^(9/2) + 27720*b^10*x^5))/((a + b*Sqrt[x])^7*x^2) - 27720*b^4*Log[a + b*Sqrt[x]] + 13860*b^4*Log[x])/(42*a^12)","A",1
2232,1,19,19,0.005554,"\int \frac{1}{\left(2+b \sqrt{x}\right) x} \, dx","Integrate[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",1
2233,1,78,132,0.0700936,"\int \sqrt{a+b \sqrt{x}} x^2 \, dx","Integrate[Sqrt[a + b*Sqrt[x]]*x^2,x]","\frac{4 \left(a+b \sqrt{x}\right)^{3/2} \left(-256 a^5+384 a^4 b \sqrt{x}-480 a^3 b^2 x+560 a^2 b^3 x^{3/2}-630 a b^4 x^2+693 b^5 x^{5/2}\right)}{9009 b^6}","-\frac{4 a^5 \left(a+b \sqrt{x}\right)^{3/2}}{3 b^6}+\frac{4 a^4 \left(a+b \sqrt{x}\right)^{5/2}}{b^6}-\frac{40 a^3 \left(a+b \sqrt{x}\right)^{7/2}}{7 b^6}+\frac{40 a^2 \left(a+b \sqrt{x}\right)^{9/2}}{9 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 + b*Sqrt[x])^(3/2)*(-256*a^5 + 384*a^4*b*Sqrt[x] - 480*a^3*b^2*x + 560*a^2*b^3*x^(3/2) - 630*a*b^4*x^2 + 693*b^5*x^(5/2)))/(9009*b^6)","A",1
2234,1,54,88,0.0276105,"\int \sqrt{a+b \sqrt{x}} x \, dx","Integrate[Sqrt[a + b*Sqrt[x]]*x,x]","\frac{4 \left(a+b \sqrt{x}\right)^{3/2} \left(-16 a^3+24 a^2 b \sqrt{x}-30 a b^2 x+35 b^3 x^{3/2}\right)}{315 b^4}","-\frac{4 a^3 \left(a+b \sqrt{x}\right)^{3/2}}{3 b^4}+\frac{12 a^2 \left(a+b \sqrt{x}\right)^{5/2}}{5 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 + b*Sqrt[x])^(3/2)*(-16*a^3 + 24*a^2*b*Sqrt[x] - 30*a*b^2*x + 35*b^3*x^(3/2)))/(315*b^4)","A",1
2235,1,32,42,0.0179513,"\int \sqrt{a+b \sqrt{x}} \, dx","Integrate[Sqrt[a + b*Sqrt[x]],x]","\frac{4 \left(a+b \sqrt{x}\right)^{3/2} \left(3 b \sqrt{x}-2 a\right)}{15 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 + b*Sqrt[x])^(3/2)*(-2*a + 3*b*Sqrt[x]))/(15*b^2)","A",1
2236,1,43,43,0.0113273,"\int \frac{\sqrt{a+b \sqrt{x}}}{x} \, dx","Integrate[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",1
2237,1,43,77,0.0101473,"\int \frac{\sqrt{a+b \sqrt{x}}}{x^2} \, dx","Integrate[Sqrt[a + b*Sqrt[x]]/x^2,x]","-\frac{4 b^2 \left(a+b \sqrt{x}\right)^{3/2} \, _2F_1\left(\frac{3}{2},3;\frac{5}{2};\frac{\sqrt{x} b}{a}+1\right)}{3 a^3}","\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,"(-4*b^2*(a + b*Sqrt[x])^(3/2)*Hypergeometric2F1[3/2, 3, 5/2, 1 + (b*Sqrt[x])/a])/(3*a^3)","C",1
2238,1,43,133,0.0090127,"\int \frac{\sqrt{a+b \sqrt{x}}}{x^3} \, dx","Integrate[Sqrt[a + b*Sqrt[x]]/x^3,x]","-\frac{4 b^4 \left(a+b \sqrt{x}\right)^{3/2} \, _2F_1\left(\frac{3}{2},5;\frac{5}{2};\frac{\sqrt{x} b}{a}+1\right)}{3 a^5}","\frac{5 b^4 \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{x}}}{\sqrt{a}}\right)}{32 a^{7/2}}-\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{b \sqrt{a+b \sqrt{x}}}{12 a x^{3/2}}-\frac{\sqrt{a+b \sqrt{x}}}{2 x^2}",1,"(-4*b^4*(a + b*Sqrt[x])^(3/2)*Hypergeometric2F1[3/2, 5, 5/2, 1 + (b*Sqrt[x])/a])/(3*a^5)","C",1
2239,1,78,130,0.0564351,"\int \frac{x^2}{\sqrt{a+b \sqrt{x}}} \, dx","Integrate[x^2/Sqrt[a + b*Sqrt[x]],x]","\frac{4 \sqrt{a+b \sqrt{x}} \left(-256 a^5+128 a^4 b \sqrt{x}-96 a^3 b^2 x+80 a^2 b^3 x^{3/2}-70 a b^4 x^2+63 b^5 x^{5/2}\right)}{693 b^6}","-\frac{4 a^5 \sqrt{a+b \sqrt{x}}}{b^6}+\frac{20 a^4 \left(a+b \sqrt{x}\right)^{3/2}}{3 b^6}-\frac{8 a^3 \left(a+b \sqrt{x}\right)^{5/2}}{b^6}+\frac{40 a^2 \left(a+b \sqrt{x}\right)^{7/2}}{7 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*Sqrt[a + b*Sqrt[x]]*(-256*a^5 + 128*a^4*b*Sqrt[x] - 96*a^3*b^2*x + 80*a^2*b^3*x^(3/2) - 70*a*b^4*x^2 + 63*b^5*x^(5/2)))/(693*b^6)","A",1
2240,1,54,84,0.038252,"\int \frac{x}{\sqrt{a+b \sqrt{x}}} \, dx","Integrate[x/Sqrt[a + b*Sqrt[x]],x]","\frac{4 \sqrt{a+b \sqrt{x}} \left(-16 a^3+8 a^2 b \sqrt{x}-6 a b^2 x+5 b^3 x^{3/2}\right)}{35 b^4}","-\frac{4 a^3 \sqrt{a+b \sqrt{x}}}{b^4}+\frac{4 a^2 \left(a+b \sqrt{x}\right)^{3/2}}{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*Sqrt[a + b*Sqrt[x]]*(-16*a^3 + 8*a^2*b*Sqrt[x] - 6*a*b^2*x + 5*b^3*x^(3/2)))/(35*b^4)","A",1
2241,1,31,40,0.0287243,"\int \frac{1}{\sqrt{a+b \sqrt{x}}} \, dx","Integrate[1/Sqrt[a + b*Sqrt[x]],x]","\frac{4 \left(b \sqrt{x}-2 a\right) \sqrt{a+b \sqrt{x}}}{3 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*(-2*a + b*Sqrt[x])*Sqrt[a + b*Sqrt[x]])/(3*b^2)","A",1
2242,1,27,27,0.0044431,"\int \frac{1}{\sqrt{a+b \sqrt{x}} x} \, dx","Integrate[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",1
2243,1,41,80,0.0077061,"\int \frac{1}{\sqrt{a+b \sqrt{x}} x^2} \, dx","Integrate[1/(Sqrt[a + b*Sqrt[x]]*x^2),x]","-\frac{4 b^2 \sqrt{a+b \sqrt{x}} \, _2F_1\left(\frac{1}{2},3;\frac{3}{2};\frac{\sqrt{x} b}{a}+1\right)}{a^3}","-\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,"(-4*b^2*Sqrt[a + b*Sqrt[x]]*Hypergeometric2F1[1/2, 3, 3/2, 1 + (b*Sqrt[x])/a])/a^3","C",1
2244,1,41,136,0.0124287,"\int \frac{1}{\sqrt{a+b \sqrt{x}} x^3} \, dx","Integrate[1/(Sqrt[a + b*Sqrt[x]]*x^3),x]","-\frac{4 b^4 \sqrt{a+b \sqrt{x}} \, _2F_1\left(\frac{1}{2},5;\frac{3}{2};\frac{\sqrt{x} b}{a}+1\right)}{a^5}","-\frac{35 b^4 \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{x}}}{\sqrt{a}}\right)}{32 a^{9/2}}+\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{7 b \sqrt{a+b \sqrt{x}}}{12 a^2 x^{3/2}}-\frac{\sqrt{a+b \sqrt{x}}}{2 a x^2}",1,"(-4*b^4*Sqrt[a + b*Sqrt[x]]*Hypergeometric2F1[1/2, 5, 3/2, 1 + (b*Sqrt[x])/a])/a^5","C",1
2245,1,64,74,0.0626493,"\int \left(a+b \sqrt{x}\right)^n \sqrt{x} \, dx","Integrate[(a + b*Sqrt[x])^n*Sqrt[x],x]","\frac{2 \left(a+b \sqrt{x}\right)^{n+1} \left(2 a^2-2 a b (n+1) \sqrt{x}+b^2 \left(n^2+3 n+2\right) x\right)}{b^3 (n+1) (n+2) (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 + b*Sqrt[x])^(1 + n)*(2*a^2 - 2*a*b*(1 + n)*Sqrt[x] + b^2*(2 + 3*n + n^2)*x))/(b^3*(1 + n)*(2 + n)*(3 + n))","A",1
2246,1,23,23,0.0050704,"\int \frac{\left(a+b \sqrt{x}\right)^n}{\sqrt{x}} \, dx","Integrate[(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
2247,1,9,9,0.0016292,"\int \frac{1+\sqrt{x}}{\sqrt{x}} \, dx","Integrate[(1 + Sqrt[x])/Sqrt[x],x]","x+2 \sqrt{x}","x+2 \sqrt{x}",1,"2*Sqrt[x] + x","A",1
2248,1,20,13,0.0024642,"\int \frac{\left(1+\sqrt{x}\right)^2}{\sqrt{x}} \, dx","Integrate[(1 + Sqrt[x])^2/Sqrt[x],x]","\frac{2 x^{3/2}}{3}+2 x+2 \sqrt{x}","\frac{2}{3} \left(\sqrt{x}+1\right)^3",1,"2*Sqrt[x] + 2*x + (2*x^(3/2))/3","A",1
2249,1,13,13,0.0029957,"\int \frac{\left(1+\sqrt{x}\right)^3}{\sqrt{x}} \, dx","Integrate[(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
2250,1,19,19,0.0085969,"\int \frac{\sqrt{x}}{1+\sqrt{x}} \, dx","Integrate[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",1
2251,1,10,10,0.0014505,"\int \frac{1}{\left(1+\sqrt{x}\right) \sqrt{x}} \, dx","Integrate[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
2252,1,11,11,0.0082706,"\int \frac{1}{\left(1+\sqrt{x}\right)^2 \sqrt{x}} \, dx","Integrate[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
2253,1,11,11,0.0023016,"\int \frac{1}{\left(1+\sqrt{x}\right)^3 \sqrt{x}} \, dx","Integrate[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
2254,1,27,46,0.0093031,"\int \sqrt{1+\sqrt{x}} \sqrt{x} \, dx","Integrate[Sqrt[1 + Sqrt[x]]*Sqrt[x],x]","\frac{4}{105} \left(\sqrt{x}+1\right)^{3/2} \left(15 x-12 \sqrt{x}+8\right)","\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)*(8 - 12*Sqrt[x] + 15*x))/105","A",1
2255,1,15,15,0.0027565,"\int \frac{\sqrt{1+\sqrt{x}}}{\sqrt{x}} \, dx","Integrate[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
2256,1,35,58,0.0080737,"\int \frac{\sqrt[3]{x}}{1+\sqrt{x}} \, dx","Integrate[x^(1/3)/(1 + Sqrt[x]),x]","\frac{3}{5} \sqrt[3]{x} \left(5 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};-\sqrt{x}\right)+2 \sqrt{x}-5\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)*(-5 + 2*Sqrt[x] + 5*Hypergeometric2F1[2/3, 1, 5/3, -Sqrt[x]]))/5","C",1
2257,1,78,87,0.1003928,"\int \left(a+b \sqrt{x}\right)^4 x^m \, dx","Integrate[(a + b*Sqrt[x])^4*x^m,x]","x^{m+1} \left(\frac{a^4}{m+1}+\frac{8 a^3 b \sqrt{x}}{2 m+3}+\frac{6 a^2 b^2 x}{m+2}+\frac{8 a b^3 x^{3/2}}{2 m+5}+\frac{b^4 x^2}{m+3}\right)","\frac{a^4 x^{m+1}}{m+1}+\frac{8 a^3 b x^{m+\frac{3}{2}}}{2 m+3}+\frac{6 a^2 b^2 x^{m+2}}{m+2}+\frac{8 a b^3 x^{m+\frac{5}{2}}}{2 m+5}+\frac{b^4 x^{m+3}}{m+3}",1,"x^(1 + m)*(a^4/(1 + m) + (8*a^3*b*Sqrt[x])/(3 + 2*m) + (6*a^2*b^2*x)/(2 + m) + (8*a*b^3*x^(3/2))/(5 + 2*m) + (b^4*x^2)/(3 + m))","A",1
2258,1,63,70,0.0798901,"\int \left(a+b \sqrt{x}\right)^3 x^m \, dx","Integrate[(a + b*Sqrt[x])^3*x^m,x]","x^{m+1} \left(\frac{a^3}{m+1}+\frac{6 a^2 b \sqrt{x}}{2 m+3}+\frac{3 a b^2 x}{m+2}+\frac{2 b^3 x^{3/2}}{2 m+5}\right)","\frac{a^3 x^{m+1}}{m+1}+\frac{6 a^2 b x^{m+\frac{3}{2}}}{2 m+3}+\frac{3 a b^2 x^{m+2}}{m+2}+\frac{2 b^3 x^{m+\frac{5}{2}}}{2 m+5}",1,"x^(1 + m)*(a^3/(1 + m) + (6*a^2*b*Sqrt[x])/(3 + 2*m) + (3*a*b^2*x)/(2 + m) + (2*b^3*x^(3/2))/(5 + 2*m))","A",1
2259,1,42,47,0.0620591,"\int \left(a+b \sqrt{x}\right)^2 x^m \, dx","Integrate[(a + b*Sqrt[x])^2*x^m,x]","x^{m+1} \left(\frac{a^2}{m+1}+\frac{4 a b \sqrt{x}}{2 m+3}+\frac{b^2 x}{m+2}\right)","\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,"x^(1 + m)*(a^2/(1 + m) + (4*a*b*Sqrt[x])/(3 + 2*m) + (b^2*x)/(2 + m))","A",1
2260,1,30,30,0.0229715,"\int \left(a+b \sqrt{x}\right) x^m \, dx","Integrate[(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",1
2261,1,36,37,0.0124376,"\int \frac{x^m}{a+b \sqrt{x}} \, dx","Integrate[x^m/(a + b*Sqrt[x]),x]","\frac{x^{m+1} \, _2F_1\left(1,2 m+2;2 m+3;-\frac{b \sqrt{x}}{a}\right)}{a m+a}","\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 + 2*m, 3 + 2*m, -((b*Sqrt[x])/a)])/(a + a*m)","A",1
2262,1,39,37,0.0214906,"\int \frac{x^m}{\left(a+b \sqrt{x}\right)^2} \, dx","Integrate[x^m/(a + b*Sqrt[x])^2,x]","\frac{x^{m+1} \, _2F_1\left(2,2 (m+1);2 (m+1)+1;-\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), 1 + 2*(1 + m), -((b*Sqrt[x])/a)])/(a^2*(1 + m))","A",1
2263,1,65,52,0.0302083,"\int \left(a+b \sqrt{x}\right)^p x^m \, dx","Integrate[(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+1)+1;-\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, 1 + 2*(1 + m), -((b*Sqrt[x])/a)])/((1 + m)*(1 + (b*Sqrt[x])/a)^p)","A",1
2264,1,168,204,0.2220762,"\int \left(a+b \sqrt{x}\right)^p x^3 \, dx","Integrate[(a + b*Sqrt[x])^p*x^3,x]","\frac{2 \left(-\frac{a^7}{p+1}+\frac{7 a^6 \left(a+b \sqrt{x}\right)}{p+2}-\frac{21 a^5 \left(a+b \sqrt{x}\right)^2}{p+3}+\frac{35 a^4 \left(a+b \sqrt{x}\right)^3}{p+4}-\frac{35 a^3 \left(a+b \sqrt{x}\right)^4}{p+5}+\frac{21 a^2 \left(a+b \sqrt{x}\right)^5}{p+6}-\frac{7 a \left(a+b \sqrt{x}\right)^6}{p+7}+\frac{\left(a+b \sqrt{x}\right)^7}{p+8}\right) \left(a+b \sqrt{x}\right)^{p+1}}{b^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/(1 + p)) + (7*a^6*(a + b*Sqrt[x]))/(2 + p) - (21*a^5*(a + b*Sqrt[x])^2)/(3 + p) + (35*a^4*(a + b*Sqrt[x])^3)/(4 + p) - (35*a^3*(a + b*Sqrt[x])^4)/(5 + p) + (21*a^2*(a + b*Sqrt[x])^5)/(6 + p) - (7*a*(a + b*Sqrt[x])^6)/(7 + p) + (a + b*Sqrt[x])^7/(8 + p))*(a + b*Sqrt[x])^(1 + p))/b^8","A",1
2265,1,126,152,0.130794,"\int \left(a+b \sqrt{x}\right)^p x^2 \, dx","Integrate[(a + b*Sqrt[x])^p*x^2,x]","\frac{2 \left(-\frac{a^5}{p+1}+\frac{5 a^4 \left(a+b \sqrt{x}\right)}{p+2}-\frac{10 a^3 \left(a+b \sqrt{x}\right)^2}{p+3}+\frac{10 a^2 \left(a+b \sqrt{x}\right)^3}{p+4}-\frac{5 a \left(a+b \sqrt{x}\right)^4}{p+5}+\frac{\left(a+b \sqrt{x}\right)^5}{p+6}\right) \left(a+b \sqrt{x}\right)^{p+1}}{b^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/(1 + p)) + (5*a^4*(a + b*Sqrt[x]))/(2 + p) - (10*a^3*(a + b*Sqrt[x])^2)/(3 + p) + (10*a^2*(a + b*Sqrt[x])^3)/(4 + p) - (5*a*(a + b*Sqrt[x])^4)/(5 + p) + (a + b*Sqrt[x])^5/(6 + p))*(a + b*Sqrt[x])^(1 + p))/b^6","A",1
2266,1,95,100,0.0790167,"\int \left(a+b \sqrt{x}\right)^p x \, dx","Integrate[(a + b*Sqrt[x])^p*x,x]","\frac{2 \left(a+b \sqrt{x}\right)^{p+1} \left(-6 a^3+6 a^2 b (p+1) \sqrt{x}-3 a b^2 \left(p^2+3 p+2\right) x+b^3 \left(p^3+6 p^2+11 p+6\right) x^{3/2}\right)}{b^4 (p+1) (p+2) (p+3) (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 + b*Sqrt[x])^(1 + p)*(-6*a^3 + 6*a^2*b*(1 + p)*Sqrt[x] - 3*a*b^2*(2 + 3*p + p^2)*x + b^3*(6 + 11*p + 6*p^2 + p^3)*x^(3/2)))/(b^4*(1 + p)*(2 + p)*(3 + p)*(4 + p))","A",1
2267,1,42,48,0.0241621,"\int \left(a+b \sqrt{x}\right)^p \, dx","Integrate[(a + b*Sqrt[x])^p,x]","\frac{2 \left(a+b \sqrt{x}\right)^{p+1} \left(b (p+1) \sqrt{x}-a\right)}{b^2 (p+1) (p+2)}","\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 + b*Sqrt[x])^(1 + p)*(-a + b*(1 + p)*Sqrt[x]))/(b^2*(1 + p)*(2 + p))","A",1
2268,1,43,43,0.008603,"\int \frac{\left(a+b \sqrt{x}\right)^p}{x} \, dx","Integrate[(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",1
2269,1,46,46,0.0108969,"\int \frac{\left(a+b \sqrt{x}\right)^p}{x^2} \, dx","Integrate[(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",1
2270,1,12,12,0.0019033,"\int \frac{\sqrt{x}}{1+x^{3/2}} \, dx","Integrate[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
2271,1,75,139,0.0307479,"\int \frac{x^3}{\left(a+b x^{3/2}\right)^{2/3}} \, dx","Integrate[x^3/(a + b*x^(3/2))^(2/3),x]","\frac{x \left(5 a^2 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{b x^{3/2}}{b x^{3/2}+a}\right)-5 a^2-2 a b x^{3/2}+3 b^2 x^3\right)}{9 b^2 \left(a+b x^{3/2}\right)^{2/3}}","-\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,"(x*(-5*a^2 - 2*a*b*x^(3/2) + 3*b^2*x^3 + 5*a^2*Hypergeometric2F1[2/3, 1, 5/3, (b*x^(3/2))/(a + b*x^(3/2))]))/(9*b^2*(a + b*x^(3/2))^(2/3))","C",1
2272,1,52,82,0.0100351,"\int \frac{1}{\left(a+b x^{3/2}\right)^{2/3}} \, dx","Integrate[(a + b*x^(3/2))^(-2/3),x]","\frac{x \left(\frac{b x^{3/2}}{a}+1\right)^{2/3} \, _2F_1\left(\frac{2}{3},\frac{2}{3};\frac{5}{3};-\frac{b x^{3/2}}{a}\right)}{\left(a+b x^{3/2}\right)^{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,"(x*(1 + (b*x^(3/2))/a)^(2/3)*Hypergeometric2F1[2/3, 2/3, 5/3, -((b*x^(3/2))/a)])/(a + b*x^(3/2))^(2/3)","C",1
2273,1,33,50,0.0194576,"\int \frac{1}{x^3 \left(a+b x^{3/2}\right)^{2/3}} \, dx","Integrate[1/(x^3*(a + b*x^(3/2))^(2/3)),x]","-\frac{\left(a-3 b x^{3/2}\right) \sqrt[3]{a+b x^{3/2}}}{2 a^2 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,"-1/2*((a - 3*b*x^(3/2))*(a + b*x^(3/2))^(1/3))/(a^2*x^2)","A",1
2274,1,59,104,0.0529242,"\int \frac{1}{x^6 \left(a+b x^{3/2}\right)^{2/3}} \, dx","Integrate[1/(x^6*(a + b*x^(3/2))^(2/3)),x]","\frac{\sqrt[3]{a+b x^{3/2}} \left(-14 a^3+18 a^2 b x^{3/2}-27 a b^2 x^3+81 b^3 x^{9/2}\right)}{70 a^4 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)*(-14*a^3 + 18*a^2*b*x^(3/2) - 27*a*b^2*x^3 + 81*b^3*x^(9/2)))/(70*a^4*x^5)","A",1
2275,1,83,158,0.0446789,"\int \frac{1}{x^9 \left(a+b x^{3/2}\right)^{2/3}} \, dx","Integrate[1/(x^9*(a + b*x^(3/2))^(2/3)),x]","\frac{\sqrt[3]{a+b x^{3/2}} \left(-91 a^5+105 a^4 b x^{3/2}-126 a^3 b^2 x^3+162 a^2 b^3 x^{9/2}-243 a b^4 x^6+729 b^5 x^{15/2}\right)}{728 a^6 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)*(-91*a^5 + 105*a^4*b*x^(3/2) - 126*a^3*b^2*x^3 + 162*a^2*b^3*x^(9/2) - 243*a*b^4*x^6 + 729*b^5*x^(15/2)))/(728*a^6*x^8)","A",1
2276,1,80,130,0.0619516,"\int \frac{x^8}{\left(a+b x^{3/2}\right)^{2/3}} \, dx","Integrate[x^8/(a + b*x^(3/2))^(2/3),x]","\frac{\sqrt[3]{a+b x^{3/2}} \left(-729 a^5+243 a^4 b x^{3/2}-162 a^3 b^2 x^3+126 a^2 b^3 x^{9/2}-105 a b^4 x^6+91 b^5 x^{15/2}\right)}{728 b^6}","-\frac{2 a^5 \sqrt[3]{a+b x^{3/2}}}{b^6}+\frac{5 a^4 \left(a+b x^{3/2}\right)^{4/3}}{2 b^6}-\frac{20 a^3 \left(a+b x^{3/2}\right)^{7/3}}{7 b^6}+\frac{2 a^2 \left(a+b x^{3/2}\right)^{10/3}}{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,"((a + b*x^(3/2))^(1/3)*(-729*a^5 + 243*a^4*b*x^(3/2) - 162*a^3*b^2*x^3 + 126*a^2*b^3*x^(9/2) - 105*a*b^4*x^6 + 91*b^5*x^(15/2)))/(728*b^6)","A",1
2277,1,56,86,0.0275017,"\int \frac{x^5}{\left(a+b x^{3/2}\right)^{2/3}} \, dx","Integrate[x^5/(a + b*x^(3/2))^(2/3),x]","\frac{\sqrt[3]{a+b x^{3/2}} \left(-81 a^3+27 a^2 b x^{3/2}-18 a b^2 x^3+14 b^3 x^{9/2}\right)}{70 b^4}","-\frac{2 a^3 \sqrt[3]{a+b x^{3/2}}}{b^4}+\frac{3 a^2 \left(a+b x^{3/2}\right)^{4/3}}{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,"((a + b*x^(3/2))^(1/3)*(-81*a^3 + 27*a^2*b*x^(3/2) - 18*a*b^2*x^3 + 14*b^3*x^(9/2)))/(70*b^4)","A",1
2278,1,31,40,0.0149039,"\int \frac{x^2}{\left(a+b x^{3/2}\right)^{2/3}} \, dx","Integrate[x^2/(a + b*x^(3/2))^(2/3),x]","\frac{\left(b x^{3/2}-3 a\right) \sqrt[3]{a+b x^{3/2}}}{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,"((-3*a + b*x^(3/2))*(a + b*x^(3/2))^(1/3))/(2*b^2)","A",1
2279,1,109,85,0.0857402,"\int \frac{1}{x \left(a+b x^{3/2}\right)^{2/3}} \, dx","Integrate[1/(x*(a + b*x^(3/2))^(2/3)),x]","-\frac{\log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^{3/2}}+\left(a+b x^{3/2}\right)^{2/3}\right)-2 \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^{3/2}}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{a+b x^{3/2}}}{\sqrt[3]{a}}+1}{\sqrt{3}}\right)}{3 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,"-1/3*(2*Sqrt[3]*ArcTan[(1 + (2*(a + b*x^(3/2))^(1/3))/a^(1/3))/Sqrt[3]] - 2*Log[a^(1/3) - (a + b*x^(3/2))^(1/3)] + Log[a^(2/3) + a^(1/3)*(a + b*x^(3/2))^(1/3) + (a + b*x^(3/2))^(2/3)])/a^(2/3)","A",1
2280,1,41,148,0.0103736,"\int \frac{1}{x^4 \left(a+b x^{3/2}\right)^{2/3}} \, dx","Integrate[1/(x^4*(a + b*x^(3/2))^(2/3)),x]","-\frac{2 b^2 \sqrt[3]{a+b x^{3/2}} \, _2F_1\left(\frac{1}{3},3;\frac{4}{3};\frac{b x^{3/2}}{a}+1\right)}{a^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,"(-2*b^2*(a + b*x^(3/2))^(1/3)*Hypergeometric2F1[1/3, 3, 4/3, 1 + (b*x^(3/2))/a])/a^3","C",1
2281,1,57,42,0.0131783,"\int \frac{x^4}{\left(a+b x^{3/2}\right)^{2/3}} \, dx","Integrate[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",1
2282,1,57,42,0.0119672,"\int \frac{x}{\left(a+b x^{3/2}\right)^{2/3}} \, dx","Integrate[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",1
2283,1,55,40,0.0123254,"\int \frac{1}{x^2 \left(a+b x^{3/2}\right)^{2/3}} \, dx","Integrate[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",1
2284,1,57,57,0.0122601,"\int \frac{1}{x^5 \left(a+b x^{3/2}\right)^{2/3}} \, dx","Integrate[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,"-1/4*((1 + (b*x^(3/2))/a)^(2/3)*Hypergeometric2F1[-8/3, 2/3, -5/3, -((b*x^(3/2))/a)])/(x^4*(a + b*x^(3/2))^(2/3))","A",1
2285,1,19,19,0.0071265,"\int \left(a+b \sqrt[3]{x}\right) x^4 \, dx","Integrate[(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",1
2286,1,19,19,0.0059214,"\int \left(a+b \sqrt[3]{x}\right) x^3 \, dx","Integrate[(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",1
2287,1,19,19,0.0070122,"\int \left(a+b \sqrt[3]{x}\right) x^2 \, dx","Integrate[(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",1
2288,1,19,19,0.0058307,"\int \left(a+b \sqrt[3]{x}\right) x \, dx","Integrate[(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",1
2289,1,14,14,0.0016571,"\int \left(a+b \sqrt[3]{x}\right) \, dx","Integrate[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
2290,1,13,13,0.0054179,"\int \frac{a+b \sqrt[3]{x}}{x} \, dx","Integrate[(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",1
2291,1,17,17,0.0072145,"\int \frac{a+b \sqrt[3]{x}}{x^2} \, dx","Integrate[(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",1
2292,1,19,19,0.022183,"\int \frac{a+b \sqrt[3]{x}}{x^3} \, dx","Integrate[(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,"-1/2*a/x^2 - (3*b)/(5*x^(5/3))","A",1
2293,1,19,19,0.0068107,"\int \frac{a+b \sqrt[3]{x}}{x^4} \, dx","Integrate[(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,"-1/3*a/x^3 - (3*b)/(8*x^(8/3))","A",1
2294,1,34,34,0.0362323,"\int \left(a+b \sqrt[3]{x}\right)^2 x^4 \, dx","Integrate[(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",1
2295,1,34,34,0.0338465,"\int \left(a+b \sqrt[3]{x}\right)^2 x^3 \, dx","Integrate[(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",1
2296,1,34,34,0.0354611,"\int \left(a+b \sqrt[3]{x}\right)^2 x^2 \, dx","Integrate[(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",1
2297,1,34,34,0.0313045,"\int \left(a+b \sqrt[3]{x}\right)^2 x \, dx","Integrate[(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",1
2298,1,29,29,0.0181841,"\int \left(a+b \sqrt[3]{x}\right)^2 \, dx","Integrate[(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",1
2299,1,28,28,0.0113014,"\int \frac{\left(a+b \sqrt[3]{x}\right)^2}{x} \, dx","Integrate[(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",1
2300,1,19,19,0.0039833,"\int \frac{\left(a+b \sqrt[3]{x}\right)^2}{x^2} \, dx","Integrate[(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
2301,1,34,34,0.0131228,"\int \frac{\left(a+b \sqrt[3]{x}\right)^2}{x^3} \, dx","Integrate[(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,"-1/2*a^2/x^2 - (6*a*b)/(5*x^(5/3)) - (3*b^2)/(4*x^(4/3))","A",1
2302,1,34,34,0.0140343,"\int \frac{\left(a+b \sqrt[3]{x}\right)^2}{x^4} \, dx","Integrate[(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,"-1/3*a^2/x^3 - (3*a*b)/(4*x^(8/3)) - (3*b^2)/(7*x^(7/3))","A",1
2303,1,47,47,0.032137,"\int \left(a+b \sqrt[3]{x}\right)^3 x^4 \, dx","Integrate[(a + b*x^(1/3))^3*x^4,x]","\frac{a^3 x^5}{5}+\frac{9}{16} a^2 b x^{16/3}+\frac{9}{17} a b^2 x^{17/3}+\frac{b^3 x^6}{6}","\frac{a^3 x^5}{5}+\frac{9}{16} a^2 b x^{16/3}+\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",1
2304,1,47,47,0.0242993,"\int \left(a+b \sqrt[3]{x}\right)^3 x^3 \, dx","Integrate[(a + b*x^(1/3))^3*x^3,x]","\frac{a^3 x^4}{4}+\frac{9}{13} a^2 b x^{13/3}+\frac{9}{14} a b^2 x^{14/3}+\frac{b^3 x^5}{5}","\frac{a^3 x^4}{4}+\frac{9}{13} a^2 b x^{13/3}+\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",1
2305,1,41,47,0.0246539,"\int \left(a+b \sqrt[3]{x}\right)^3 x^2 \, dx","Integrate[(a + b*x^(1/3))^3*x^2,x]","\frac{1}{660} x^3 \left(220 a^3+594 a^2 b \sqrt[3]{x}+540 a b^2 x^{2/3}+165 b^3 x\right)","\frac{a^3 x^3}{3}+\frac{9}{10} a^2 b x^{10/3}+\frac{9}{11} a b^2 x^{11/3}+\frac{b^3 x^4}{4}",1,"(x^3*(220*a^3 + 594*a^2*b*x^(1/3) + 540*a*b^2*x^(2/3) + 165*b^3*x))/660","A",1
2306,1,47,47,0.019815,"\int \left(a+b \sqrt[3]{x}\right)^3 x \, dx","Integrate[(a + b*x^(1/3))^3*x,x]","\frac{a^3 x^2}{2}+\frac{9}{7} a^2 b x^{7/3}+\frac{9}{8} a b^2 x^{8/3}+\frac{b^3 x^3}{3}","\frac{a^3 x^2}{2}+\frac{9}{7} a^2 b x^{7/3}+\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",1
2307,1,42,42,0.017582,"\int \left(a+b \sqrt[3]{x}\right)^3 \, dx","Integrate[(a + b*x^(1/3))^3,x]","a^3 x+\frac{9}{4} a^2 b x^{4/3}+\frac{9}{5} a b^2 x^{5/3}+\frac{b^3 x^2}{2}","a^3 x+\frac{9}{4} a^2 b x^{4/3}+\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",1
2308,1,36,36,0.013445,"\int \frac{\left(a+b \sqrt[3]{x}\right)^3}{x} \, dx","Integrate[(a + b*x^(1/3))^3/x,x]","a^3 \log (x)+9 a^2 b \sqrt[3]{x}+\frac{9}{2} a b^2 x^{2/3}+b^3 x","a^3 \log (x)+9 a^2 b \sqrt[3]{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",1
2309,1,39,39,0.0258885,"\int \frac{\left(a+b \sqrt[3]{x}\right)^3}{x^2} \, dx","Integrate[(a + b*x^(1/3))^3/x^2,x]","-\frac{a^3}{x}-\frac{9 a^2 b}{2 x^{2/3}}-\frac{9 a b^2}{\sqrt[3]{x}}+b^3 \log (x)","-\frac{a^3}{x}-\frac{9 a^2 b}{2 x^{2/3}}-\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",1
2310,1,41,45,0.0171095,"\int \frac{\left(a+b \sqrt[3]{x}\right)^3}{x^3} \, dx","Integrate[(a + b*x^(1/3))^3/x^3,x]","-\frac{10 a^3+36 a^2 b \sqrt[3]{x}+45 a b^2 x^{2/3}+20 b^3 x}{20 x^2}","-\frac{a^3}{2 x^2}-\frac{9 a^2 b}{5 x^{5/3}}-\frac{9 a b^2}{4 x^{4/3}}-\frac{b^3}{x}",1,"-1/20*(10*a^3 + 36*a^2*b*x^(1/3) + 45*a*b^2*x^(2/3) + 20*b^3*x)/x^2","A",1
2311,1,41,47,0.018022,"\int \frac{\left(a+b \sqrt[3]{x}\right)^3}{x^4} \, dx","Integrate[(a + b*x^(1/3))^3/x^4,x]","-\frac{56 a^3+189 a^2 b \sqrt[3]{x}+216 a b^2 x^{2/3}+84 b^3 x}{168 x^3}","-\frac{a^3}{3 x^3}-\frac{9 a^2 b}{8 x^{8/3}}-\frac{9 a b^2}{7 x^{7/3}}-\frac{b^3}{2 x^2}",1,"-1/168*(56*a^3 + 189*a^2*b*x^(1/3) + 216*a*b^2*x^(2/3) + 84*b^3*x)/x^3","A",1
2312,1,77,77,0.0555526,"\int \left(a+b \sqrt[3]{x}\right)^5 x^4 \, dx","Integrate[(a + b*x^(1/3))^5*x^4,x]","\frac{a^5 x^5}{5}+\frac{15}{16} a^4 b x^{16/3}+\frac{30}{17} a^3 b^2 x^{17/3}+\frac{5}{3} a^2 b^3 x^6+\frac{15}{19} a b^4 x^{19/3}+\frac{3}{20} b^5 x^{20/3}","\frac{a^5 x^5}{5}+\frac{15}{16} a^4 b x^{16/3}+\frac{30}{17} a^3 b^2 x^{17/3}+\frac{5}{3} a^2 b^3 x^6+\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",1
2313,1,75,75,0.052462,"\int \left(a+b \sqrt[3]{x}\right)^5 x^3 \, dx","Integrate[(a + b*x^(1/3))^5*x^3,x]","\frac{a^5 x^4}{4}+\frac{15}{13} a^4 b x^{13/3}+\frac{15}{7} a^3 b^2 x^{14/3}+2 a^2 b^3 x^5+\frac{15}{16} a b^4 x^{16/3}+\frac{3}{17} b^5 x^{17/3}","\frac{a^5 x^4}{4}+\frac{15}{13} a^4 b x^{13/3}+\frac{15}{7} a^3 b^2 x^{14/3}+2 a^2 b^3 x^5+\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",1
2314,1,77,77,0.046278,"\int \left(a+b \sqrt[3]{x}\right)^5 x^2 \, dx","Integrate[(a + b*x^(1/3))^5*x^2,x]","\frac{a^5 x^3}{3}+\frac{3}{2} a^4 b x^{10/3}+\frac{30}{11} a^3 b^2 x^{11/3}+\frac{5}{2} a^2 b^3 x^4+\frac{15}{13} a b^4 x^{13/3}+\frac{3}{14} b^5 x^{14/3}","\frac{a^5 x^3}{3}+\frac{3}{2} a^4 b x^{10/3}+\frac{30}{11} a^3 b^2 x^{11/3}+\frac{5}{2} a^2 b^3 x^4+\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",1
2315,1,77,77,0.0435118,"\int \left(a+b \sqrt[3]{x}\right)^5 x \, dx","Integrate[(a + b*x^(1/3))^5*x,x]","\frac{a^5 x^2}{2}+\frac{15}{7} a^4 b x^{7/3}+\frac{15}{4} a^3 b^2 x^{8/3}+\frac{10}{3} a^2 b^3 x^3+\frac{3}{2} a b^4 x^{10/3}+\frac{3}{11} b^5 x^{11/3}","\frac{a^5 x^2}{2}+\frac{15}{7} a^4 b x^{7/3}+\frac{15}{4} a^3 b^2 x^{8/3}+\frac{10}{3} a^2 b^3 x^3+\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",1
2316,1,41,59,0.0243593,"\int \left(a+b \sqrt[3]{x}\right)^5 \, dx","Integrate[(a + b*x^(1/3))^5,x]","\frac{\left(a+b \sqrt[3]{x}\right)^6 \left(a^2-6 a b \sqrt[3]{x}+21 b^2 x^{2/3}\right)}{56 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 + b*x^(1/3))^6*(a^2 - 6*a*b*x^(1/3) + 21*b^2*x^(2/3)))/(56*b^3)","A",1
2317,1,65,65,0.0466375,"\int \frac{\left(a+b \sqrt[3]{x}\right)^5}{x} \, dx","Integrate[(a + b*x^(1/3))^5/x,x]","a^5 \log (x)+15 a^4 b \sqrt[3]{x}+15 a^3 b^2 x^{2/3}+10 a^2 b^3 x+\frac{15}{4} a b^4 x^{4/3}+\frac{3}{5} b^5 x^{5/3}","a^5 \log (x)+15 a^4 b \sqrt[3]{x}+15 a^3 b^2 x^{2/3}+10 a^2 b^3 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",1
2318,1,68,68,0.0265791,"\int \frac{\left(a+b \sqrt[3]{x}\right)^5}{x^2} \, dx","Integrate[(a + b*x^(1/3))^5/x^2,x]","-\frac{a^5}{x}-\frac{15 a^4 b}{2 x^{2/3}}-\frac{30 a^3 b^2}{\sqrt[3]{x}}+10 a^2 b^3 \log (x)+15 a b^4 \sqrt[3]{x}+\frac{3}{2} b^5 x^{2/3}","-\frac{a^5}{x}-\frac{15 a^4 b}{2 x^{2/3}}-\frac{30 a^3 b^2}{\sqrt[3]{x}}+10 a^2 b^3 \log (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",1
2319,1,21,21,0.0040868,"\int \frac{\left(a+b \sqrt[3]{x}\right)^5}{x^3} \, dx","Integrate[(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,"-1/2*(a + b*x^(1/3))^6/(a*x^2)","A",1
2320,1,67,73,0.0268104,"\int \frac{\left(a+b \sqrt[3]{x}\right)^5}{x^4} \, dx","Integrate[(a + b*x^(1/3))^5/x^4,x]","-\frac{56 a^5+315 a^4 b \sqrt[3]{x}+720 a^3 b^2 x^{2/3}+840 a^2 b^3 x+504 a b^4 x^{4/3}+126 b^5 x^{5/3}}{168 x^3}","-\frac{a^5}{3 x^3}-\frac{15 a^4 b}{8 x^{8/3}}-\frac{30 a^3 b^2}{7 x^{7/3}}-\frac{5 a^2 b^3}{x^2}-\frac{3 a b^4}{x^{5/3}}-\frac{3 b^5}{4 x^{4/3}}",1,"-1/168*(56*a^5 + 315*a^4*b*x^(1/3) + 720*a^3*b^2*x^(2/3) + 840*a^2*b^3*x + 504*a*b^4*x^(4/3) + 126*b^5*x^(5/3))/x^3","A",1
2321,1,67,75,0.03075,"\int \frac{\left(a+b \sqrt[3]{x}\right)^5}{x^5} \, dx","Integrate[(a + b*x^(1/3))^5/x^5,x]","-\frac{462 a^5+2520 a^4 b \sqrt[3]{x}+5544 a^3 b^2 x^{2/3}+6160 a^2 b^3 x+3465 a b^4 x^{4/3}+792 b^5 x^{5/3}}{1848 x^4}","-\frac{a^5}{4 x^4}-\frac{15 a^4 b}{11 x^{11/3}}-\frac{3 a^3 b^2}{x^{10/3}}-\frac{10 a^2 b^3}{3 x^3}-\frac{15 a b^4}{8 x^{8/3}}-\frac{3 b^5}{7 x^{7/3}}",1,"-1/1848*(462*a^5 + 2520*a^4*b*x^(1/3) + 5544*a^3*b^2*x^(2/3) + 6160*a^2*b^3*x + 3465*a*b^4*x^(4/3) + 792*b^5*x^(5/3))/x^4","A",1
2322,1,67,77,0.0335333,"\int \frac{\left(a+b \sqrt[3]{x}\right)^5}{x^6} \, dx","Integrate[(a + b*x^(1/3))^5/x^6,x]","-\frac{2002 a^5+10725 a^4 b \sqrt[3]{x}+23100 a^3 b^2 x^{2/3}+25025 a^2 b^3 x+13650 a b^4 x^{4/3}+3003 b^5 x^{5/3}}{10010 x^5}","-\frac{a^5}{5 x^5}-\frac{15 a^4 b}{14 x^{14/3}}-\frac{30 a^3 b^2}{13 x^{13/3}}-\frac{5 a^2 b^3}{2 x^4}-\frac{15 a b^4}{11 x^{11/3}}-\frac{3 b^5}{10 x^{10/3}}",1,"-1/10010*(2002*a^5 + 10725*a^4*b*x^(1/3) + 23100*a^3*b^2*x^(2/3) + 25025*a^2*b^3*x + 13650*a*b^4*x^(4/3) + 3003*b^5*x^(5/3))/x^5","A",1
2323,1,67,75,0.0302431,"\int \frac{\left(a+b \sqrt[3]{x}\right)^5}{x^7} \, dx","Integrate[(a + b*x^(1/3))^5/x^7,x]","-\frac{6188 a^5+32760 a^4 b \sqrt[3]{x}+69615 a^3 b^2 x^{2/3}+74256 a^2 b^3 x+39780 a b^4 x^{4/3}+8568 b^5 x^{5/3}}{37128 x^6}","-\frac{a^5}{6 x^6}-\frac{15 a^4 b}{17 x^{17/3}}-\frac{15 a^3 b^2}{8 x^{16/3}}-\frac{2 a^2 b^3}{x^5}-\frac{15 a b^4}{14 x^{14/3}}-\frac{3 b^5}{13 x^{13/3}}",1,"-1/37128*(6188*a^5 + 32760*a^4*b*x^(1/3) + 69615*a^3*b^2*x^(2/3) + 74256*a^2*b^3*x + 39780*a*b^4*x^(4/3) + 8568*b^5*x^(5/3))/x^6","A",1
2324,1,144,144,0.1070905,"\int \left(a+b \sqrt[3]{x}\right)^{10} x^4 \, dx","Integrate[(a + b*x^(1/3))^10*x^4,x]","\frac{a^{10} x^5}{5}+\frac{15}{8} a^9 b x^{16/3}+\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{5}{4} a b^9 x^8+\frac{3}{25} b^{10} x^{25/3}","\frac{a^{10} x^5}{5}+\frac{15}{8} a^9 b x^{16/3}+\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{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",1
2325,1,144,144,0.0812564,"\int \left(a+b \sqrt[3]{x}\right)^{10} x^3 \, dx","Integrate[(a + b*x^(1/3))^10*x^3,x]","\frac{a^{10} x^4}{4}+\frac{30}{13} a^9 b x^{13/3}+\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{10}{7} a b^9 x^7+\frac{3}{22} b^{10} x^{22/3}","\frac{a^{10} x^4}{4}+\frac{30}{13} a^9 b x^{13/3}+\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{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",1
2326,1,140,179,0.0858563,"\int \left(a+b \sqrt[3]{x}\right)^{10} x^2 \, dx","Integrate[(a + b*x^(1/3))^10*x^2,x]","\frac{a^{10} x^3}{3}+3 a^9 b x^{10/3}+\frac{135}{11} a^8 b^2 x^{11/3}+30 a^7 b^3 x^4+\frac{630}{13} a^6 b^4 x^{13/3}+54 a^5 b^5 x^{14/3}+42 a^4 b^6 x^5+\frac{45}{2} a^3 b^7 x^{16/3}+\frac{135}{17} a^2 b^8 x^{17/3}+\frac{5}{3} a b^9 x^6+\frac{3}{19} b^{10} x^{19/3}","\frac{3 a^8 \left(a+b \sqrt[3]{x}\right)^{11}}{11 b^9}-\frac{2 a^7 \left(a+b \sqrt[3]{x}\right)^{12}}{b^9}+\frac{84 a^6 \left(a+b \sqrt[3]{x}\right)^{13}}{13 b^9}-\frac{12 a^5 \left(a+b \sqrt[3]{x}\right)^{14}}{b^9}+\frac{14 a^4 \left(a+b \sqrt[3]{x}\right)^{15}}{b^9}-\frac{21 a^3 \left(a+b \sqrt[3]{x}\right)^{16}}{2 b^9}+\frac{84 a^2 \left(a+b \sqrt[3]{x}\right)^{17}}{17 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,"(a^10*x^3)/3 + 3*a^9*b*x^(10/3) + (135*a^8*b^2*x^(11/3))/11 + 30*a^7*b^3*x^4 + (630*a^6*b^4*x^(13/3))/13 + 54*a^5*b^5*x^(14/3) + 42*a^4*b^6*x^5 + (45*a^3*b^7*x^(16/3))/2 + (135*a^2*b^8*x^(17/3))/17 + (5*a*b^9*x^6)/3 + (3*b^10*x^(19/3))/19","A",1
2327,1,76,120,0.0851039,"\int \left(a+b \sqrt[3]{x}\right)^{10} x \, dx","Integrate[(a + b*x^(1/3))^10*x,x]","-\frac{\left(a+b \sqrt[3]{x}\right)^{11} \left(a^5-11 a^4 b \sqrt[3]{x}+66 a^3 b^2 x^{2/3}-286 a^2 b^3 x+1001 a b^4 x^{4/3}-3003 b^5 x^{5/3}\right)}{16016 b^6}","-\frac{3 a^5 \left(a+b \sqrt[3]{x}\right)^{11}}{11 b^6}+\frac{5 a^4 \left(a+b \sqrt[3]{x}\right)^{12}}{4 b^6}-\frac{30 a^3 \left(a+b \sqrt[3]{x}\right)^{13}}{13 b^6}+\frac{15 a^2 \left(a+b \sqrt[3]{x}\right)^{14}}{7 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,"-1/16016*((a + b*x^(1/3))^11*(a^5 - 11*a^4*b*x^(1/3) + 66*a^3*b^2*x^(2/3) - 286*a^2*b^3*x + 1001*a*b^4*x^(4/3) - 3003*b^5*x^(5/3)))/b^6","A",1
2328,1,41,59,0.0640829,"\int \left(a+b \sqrt[3]{x}\right)^{10} \, dx","Integrate[(a + b*x^(1/3))^10,x]","\frac{\left(a+b \sqrt[3]{x}\right)^{11} \left(a^2-11 a b \sqrt[3]{x}+66 b^2 x^{2/3}\right)}{286 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,"((a + b*x^(1/3))^11*(a^2 - 11*a*b*x^(1/3) + 66*b^2*x^(2/3)))/(286*b^3)","A",1
2329,1,136,136,0.0833927,"\int \frac{\left(a+b \sqrt[3]{x}\right)^{10}}{x} \, dx","Integrate[(a + b*x^(1/3))^10/x,x]","a^{10} \log (x)+30 a^9 b \sqrt[3]{x}+\frac{135}{2} a^8 b^2 x^{2/3}+120 a^7 b^3 x+\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}+\frac{10}{3} a b^9 x^3+\frac{3}{10} b^{10} x^{10/3}","a^{10} \log (x)+30 a^9 b \sqrt[3]{x}+\frac{135}{2} a^8 b^2 x^{2/3}+120 a^7 b^3 x+\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}+\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",1
2330,1,125,125,0.0773748,"\int \frac{\left(a+b \sqrt[3]{x}\right)^{10}}{x^2} \, dx","Integrate[(a + b*x^(1/3))^10/x^2,x]","-\frac{a^{10}}{x}-\frac{15 a^9 b}{x^{2/3}}-\frac{135 a^8 b^2}{\sqrt[3]{x}}+120 a^7 b^3 \log (x)+630 a^6 b^4 \sqrt[3]{x}+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+\frac{3}{7} b^{10} x^{7/3}","-\frac{a^{10}}{x}-\frac{15 a^9 b}{x^{2/3}}-\frac{135 a^8 b^2}{\sqrt[3]{x}}+120 a^7 b^3 \log (x)+630 a^6 b^4 \sqrt[3]{x}+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+\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",1
2331,1,131,131,0.0601077,"\int \frac{\left(a+b \sqrt[3]{x}\right)^{10}}{x^3} \, dx","Integrate[(a + b*x^(1/3))^10/x^3,x]","-\frac{a^{10}}{2 x^2}-\frac{6 a^9 b}{x^{5/3}}-\frac{135 a^8 b^2}{4 x^{4/3}}-\frac{120 a^7 b^3}{x}-\frac{315 a^6 b^4}{x^{2/3}}-\frac{756 a^5 b^5}{\sqrt[3]{x}}+210 a^4 b^6 \log (x)+360 a^3 b^7 \sqrt[3]{x}+\frac{135}{2} a^2 b^8 x^{2/3}+10 a b^9 x+\frac{3}{4} b^{10} x^{4/3}","-\frac{a^{10}}{2 x^2}-\frac{6 a^9 b}{x^{5/3}}-\frac{135 a^8 b^2}{4 x^{4/3}}-\frac{120 a^7 b^3}{x}-\frac{315 a^6 b^4}{x^{2/3}}-\frac{756 a^5 b^5}{\sqrt[3]{x}}+210 a^4 b^6 \log (x)+360 a^3 b^7 \sqrt[3]{x}+\frac{135}{2} a^2 b^8 x^{2/3}+10 a b^9 x+\frac{3}{4} b^{10} x^{4/3}",1,"-1/2*a^10/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",1
2332,1,131,131,0.0822675,"\int \frac{\left(a+b \sqrt[3]{x}\right)^{10}}{x^4} \, dx","Integrate[(a + b*x^(1/3))^10/x^4,x]","-\frac{a^{10}}{3 x^3}-\frac{15 a^9 b}{4 x^{8/3}}-\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{210 a^4 b^6}{x}-\frac{180 a^3 b^7}{x^{2/3}}-\frac{135 a^2 b^8}{\sqrt[3]{x}}+10 a b^9 \log (x)+3 b^{10} \sqrt[3]{x}","-\frac{a^{10}}{3 x^3}-\frac{15 a^9 b}{4 x^{8/3}}-\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{210 a^4 b^6}{x}-\frac{180 a^3 b^7}{x^{2/3}}-\frac{135 a^2 b^8}{\sqrt[3]{x}}+10 a b^9 \log (x)+3 b^{10} \sqrt[3]{x}",1,"-1/3*a^10/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",1
2333,1,32,46,0.0089415,"\int \frac{\left(a+b \sqrt[3]{x}\right)^{10}}{x^5} \, dx","Integrate[(a + b*x^(1/3))^10/x^5,x]","\frac{\left(b \sqrt[3]{x}-11 a\right) \left(a+b \sqrt[3]{x}\right)^{11}}{44 a^2 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,"((-11*a + b*x^(1/3))*(a + b*x^(1/3))^11)/(44*a^2*x^4)","A",1
2334,1,67,122,0.0140307,"\int \frac{\left(a+b \sqrt[3]{x}\right)^{10}}{x^6} \, dx","Integrate[(a + b*x^(1/3))^10/x^6,x]","-\frac{\left(a+b \sqrt[3]{x}\right)^{11} \left(1001 a^4-286 a^3 b \sqrt[3]{x}+66 a^2 b^2 x^{2/3}-11 a b^3 x+b^4 x^{4/3}\right)}{5005 a^5 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,"-1/5005*((a + b*x^(1/3))^11*(1001*a^4 - 286*a^3*b*x^(1/3) + 66*a^2*b^2*x^(2/3) - 11*a*b^3*x + b^4*x^(4/3)))/(a^5*x^5)","A",1
2335,1,144,144,0.0683709,"\int \frac{\left(a+b \sqrt[3]{x}\right)^{10}}{x^7} \, dx","Integrate[(a + b*x^(1/3))^10/x^7,x]","-\frac{a^{10}}{6 x^6}-\frac{30 a^9 b}{17 x^{17/3}}-\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{10 a b^9}{3 x^3}-\frac{3 b^{10}}{8 x^{8/3}}","-\frac{a^{10}}{6 x^6}-\frac{30 a^9 b}{17 x^{17/3}}-\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{10 a b^9}{3 x^3}-\frac{3 b^{10}}{8 x^{8/3}}",1,"-1/6*a^10/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",1
2336,1,144,144,0.0666234,"\int \frac{\left(a+b \sqrt[3]{x}\right)^{10}}{x^8} \, dx","Integrate[(a + b*x^(1/3))^10/x^8,x]","-\frac{a^{10}}{7 x^7}-\frac{3 a^9 b}{2 x^{20/3}}-\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{5 a b^9}{2 x^4}-\frac{3 b^{10}}{11 x^{11/3}}","-\frac{a^{10}}{7 x^7}-\frac{3 a^9 b}{2 x^{20/3}}-\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{5 a b^9}{2 x^4}-\frac{3 b^{10}}{11 x^{11/3}}",1,"-1/7*a^10/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",1
2337,1,144,144,0.0644268,"\int \frac{\left(a+b \sqrt[3]{x}\right)^{10}}{x^9} \, dx","Integrate[(a + b*x^(1/3))^10/x^9,x]","-\frac{a^{10}}{8 x^8}-\frac{30 a^9 b}{23 x^{23/3}}-\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{2 a b^9}{x^5}-\frac{3 b^{10}}{14 x^{14/3}}","-\frac{a^{10}}{8 x^8}-\frac{30 a^9 b}{23 x^{23/3}}-\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{2 a b^9}{x^5}-\frac{3 b^{10}}{14 x^{14/3}}",1,"-1/8*a^10/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",1
2338,1,142,142,0.06438,"\int \frac{\left(a+b \sqrt[3]{x}\right)^{10}}{x^{10}} \, dx","Integrate[(a + b*x^(1/3))^10/x^10,x]","-\frac{a^{10}}{9 x^9}-\frac{15 a^9 b}{13 x^{26/3}}-\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{5 a b^9}{3 x^6}-\frac{3 b^{10}}{17 x^{17/3}}","-\frac{a^{10}}{9 x^9}-\frac{15 a^9 b}{13 x^{26/3}}-\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{5 a b^9}{3 x^6}-\frac{3 b^{10}}{17 x^{17/3}}",1,"-1/9*a^10/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",1
2339,1,217,217,0.1256548,"\int \left(a+b \sqrt[3]{x}\right)^{15} x^5 \, dx","Integrate[(a + b*x^(1/3))^15*x^5,x]","\frac{a^{15} x^6}{6}+\frac{45}{19} a^{14} b x^{19/3}+\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}{32} a b^{14} x^{32/3}+\frac{b^{15} x^{11}}{11}","\frac{a^{15} x^6}{6}+\frac{45}{19} a^{14} b x^{19/3}+\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}{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",1
2340,1,217,217,0.1041243,"\int \left(a+b \sqrt[3]{x}\right)^{15} x^4 \, dx","Integrate[(a + b*x^(1/3))^15*x^4,x]","\frac{a^{15} x^5}{5}+\frac{45}{16} a^{14} b x^{16/3}+\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}{29} a b^{14} x^{29/3}+\frac{b^{15} x^{10}}{10}","\frac{a^{15} x^5}{5}+\frac{45}{16} a^{14} b x^{16/3}+\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}{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",1
2341,1,215,244,0.0914901,"\int \left(a+b \sqrt[3]{x}\right)^{15} x^3 \, dx","Integrate[(a + b*x^(1/3))^15*x^3,x]","\frac{a^{15} x^4}{4}+\frac{45}{13} a^{14} b x^{13/3}+\frac{45}{2} a^{13} b^2 x^{14/3}+91 a^{12} b^3 x^5+\frac{4095}{16} a^{11} b^4 x^{16/3}+\frac{9009}{17} a^{10} b^5 x^{17/3}+\frac{5005}{6} a^9 b^6 x^6+\frac{19305}{19} a^8 b^7 x^{19/3}+\frac{3861}{4} a^7 b^8 x^{20/3}+715 a^6 b^9 x^7+\frac{819}{2} a^5 b^{10} x^{22/3}+\frac{4095}{23} a^4 b^{11} x^{23/3}+\frac{455}{8} a^3 b^{12} x^8+\frac{63}{5} a^2 b^{13} x^{25/3}+\frac{45}{26} a b^{14} x^{26/3}+\frac{b^{15} x^9}{9}","-\frac{3 a^{11} \left(a+b \sqrt[3]{x}\right)^{16}}{16 b^{12}}+\frac{33 a^{10} \left(a+b \sqrt[3]{x}\right)^{17}}{17 b^{12}}-\frac{55 a^9 \left(a+b \sqrt[3]{x}\right)^{18}}{6 b^{12}}+\frac{495 a^8 \left(a+b \sqrt[3]{x}\right)^{19}}{19 b^{12}}-\frac{99 a^7 \left(a+b \sqrt[3]{x}\right)^{20}}{2 b^{12}}+\frac{66 a^6 \left(a+b \sqrt[3]{x}\right)^{21}}{b^{12}}-\frac{63 a^5 \left(a+b \sqrt[3]{x}\right)^{22}}{b^{12}}+\frac{990 a^4 \left(a+b \sqrt[3]{x}\right)^{23}}{23 b^{12}}-\frac{165 a^3 \left(a+b \sqrt[3]{x}\right)^{24}}{8 b^{12}}+\frac{33 a^2 \left(a+b \sqrt[3]{x}\right)^{25}}{5 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,"(a^15*x^4)/4 + (45*a^14*b*x^(13/3))/13 + (45*a^13*b^2*x^(14/3))/2 + 91*a^12*b^3*x^5 + (4095*a^11*b^4*x^(16/3))/16 + (9009*a^10*b^5*x^(17/3))/17 + (5005*a^9*b^6*x^6)/6 + (19305*a^8*b^7*x^(19/3))/19 + (3861*a^7*b^8*x^(20/3))/4 + 715*a^6*b^9*x^7 + (819*a^5*b^10*x^(22/3))/2 + (4095*a^4*b^11*x^(23/3))/23 + (455*a^3*b^12*x^8)/8 + (63*a^2*b^13*x^(25/3))/5 + (45*a*b^14*x^(26/3))/26 + (b^15*x^9)/9","A",1
2342,1,113,183,0.0795161,"\int \left(a+b \sqrt[3]{x}\right)^{15} x^2 \, dx","Integrate[(a + b*x^(1/3))^15*x^2,x]","\frac{\left(a+b \sqrt[3]{x}\right)^{16} \left(a^8-16 a^7 b \sqrt[3]{x}+136 a^6 b^2 x^{2/3}-816 a^5 b^3 x+3876 a^4 b^4 x^{4/3}-15504 a^3 b^5 x^{5/3}+54264 a^2 b^6 x^2-170544 a b^7 x^{7/3}+490314 b^8 x^{8/3}\right)}{3922512 b^9}","\frac{3 a^8 \left(a+b \sqrt[3]{x}\right)^{16}}{16 b^9}-\frac{24 a^7 \left(a+b \sqrt[3]{x}\right)^{17}}{17 b^9}+\frac{14 a^6 \left(a+b \sqrt[3]{x}\right)^{18}}{3 b^9}-\frac{168 a^5 \left(a+b \sqrt[3]{x}\right)^{19}}{19 b^9}+\frac{21 a^4 \left(a+b \sqrt[3]{x}\right)^{20}}{2 b^9}-\frac{8 a^3 \left(a+b \sqrt[3]{x}\right)^{21}}{b^9}+\frac{42 a^2 \left(a+b \sqrt[3]{x}\right)^{22}}{11 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,"((a + b*x^(1/3))^16*(a^8 - 16*a^7*b*x^(1/3) + 136*a^6*b^2*x^(2/3) - 816*a^5*b^3*x + 3876*a^4*b^4*x^(4/3) - 15504*a^3*b^5*x^(5/3) + 54264*a^2*b^6*x^2 - 170544*a*b^7*x^(7/3) + 490314*b^8*x^(8/3)))/(3922512*b^9)","A",1
2343,1,76,122,0.0646246,"\int \left(a+b \sqrt[3]{x}\right)^{15} x \, dx","Integrate[(a + b*x^(1/3))^15*x,x]","-\frac{\left(a+b \sqrt[3]{x}\right)^{16} \left(a^5-16 a^4 b \sqrt[3]{x}+136 a^3 b^2 x^{2/3}-816 a^2 b^3 x+3876 a b^4 x^{4/3}-15504 b^5 x^{5/3}\right)}{108528 b^6}","-\frac{3 a^5 \left(a+b \sqrt[3]{x}\right)^{16}}{16 b^6}+\frac{15 a^4 \left(a+b \sqrt[3]{x}\right)^{17}}{17 b^6}-\frac{5 a^3 \left(a+b \sqrt[3]{x}\right)^{18}}{3 b^6}+\frac{30 a^2 \left(a+b \sqrt[3]{x}\right)^{19}}{19 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,"-1/108528*((a + b*x^(1/3))^16*(a^5 - 16*a^4*b*x^(1/3) + 136*a^3*b^2*x^(2/3) - 816*a^2*b^3*x + 3876*a*b^4*x^(4/3) - 15504*b^5*x^(5/3)))/b^6","A",1
2344,1,41,59,0.0454395,"\int \left(a+b \sqrt[3]{x}\right)^{15} \, dx","Integrate[(a + b*x^(1/3))^15,x]","\frac{\left(a+b \sqrt[3]{x}\right)^{16} \left(a^2-16 a b \sqrt[3]{x}+136 b^2 x^{2/3}\right)}{816 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,"((a + b*x^(1/3))^16*(a^2 - 16*a*b*x^(1/3) + 136*b^2*x^(2/3)))/(816*b^3)","A",1
2345,1,209,209,0.0727637,"\int \frac{\left(a+b \sqrt[3]{x}\right)^{15}}{x} \, dx","Integrate[(a + b*x^(1/3))^15/x,x]","a^{15} \log (x)+45 a^{14} b \sqrt[3]{x}+\frac{315}{2} a^{13} b^2 x^{2/3}+455 a^{12} b^3 x+\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}+\frac{45}{14} a b^{14} x^{14/3}+\frac{b^{15} x^5}{5}","a^{15} \log (x)+45 a^{14} b \sqrt[3]{x}+\frac{315}{2} a^{13} b^2 x^{2/3}+455 a^{12} b^3 x+\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}+\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",1
2346,1,202,202,0.1035258,"\int \frac{\left(a+b \sqrt[3]{x}\right)^{15}}{x^2} \, dx","Integrate[(a + b*x^(1/3))^15/x^2,x]","-\frac{a^{15}}{x}-\frac{45 a^{14} b}{2 x^{2/3}}-\frac{315 a^{13} b^2}{\sqrt[3]{x}}+455 a^{12} b^3 \log (x)+4095 a^{11} b^4 \sqrt[3]{x}+\frac{9009}{2} a^{10} b^5 x^{2/3}+5005 a^9 b^6 x+\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{45}{11} a b^{14} x^{11/3}+\frac{b^{15} x^4}{4}","-\frac{a^{15}}{x}-\frac{45 a^{14} b}{2 x^{2/3}}-\frac{315 a^{13} b^2}{\sqrt[3]{x}}+455 a^{12} b^3 \log (x)+4095 a^{11} b^4 \sqrt[3]{x}+\frac{9009}{2} a^{10} b^5 x^{2/3}+5005 a^9 b^6 x+\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{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",1
2347,1,200,200,0.1094921,"\int \frac{\left(a+b \sqrt[3]{x}\right)^{15}}{x^3} \, dx","Integrate[(a + b*x^(1/3))^15/x^3,x]","-\frac{a^{15}}{2 x^2}-\frac{9 a^{14} b}{x^{5/3}}-\frac{315 a^{13} b^2}{4 x^{4/3}}-\frac{455 a^{12} b^3}{x}-\frac{4095 a^{11} b^4}{2 x^{2/3}}-\frac{9009 a^{10} b^5}{\sqrt[3]{x}}+5005 a^9 b^6 \log (x)+19305 a^8 b^7 \sqrt[3]{x}+\frac{19305}{2} a^7 b^8 x^{2/3}+5005 a^6 b^9 x+\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{45}{8} a b^{14} x^{8/3}+\frac{b^{15} x^3}{3}","-\frac{a^{15}}{2 x^2}-\frac{9 a^{14} b}{x^{5/3}}-\frac{315 a^{13} b^2}{4 x^{4/3}}-\frac{455 a^{12} b^3}{x}-\frac{4095 a^{11} b^4}{2 x^{2/3}}-\frac{9009 a^{10} b^5}{\sqrt[3]{x}}+5005 a^9 b^6 \log (x)+19305 a^8 b^7 \sqrt[3]{x}+\frac{19305}{2} a^7 b^8 x^{2/3}+5005 a^6 b^9 x+\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{45}{8} a b^{14} x^{8/3}+\frac{b^{15} x^3}{3}",1,"-1/2*a^15/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",1
2348,1,200,200,0.1144616,"\int \frac{\left(a+b \sqrt[3]{x}\right)^{15}}{x^4} \, dx","Integrate[(a + b*x^(1/3))^15/x^4,x]","-\frac{a^{15}}{3 x^3}-\frac{45 a^{14} b}{8 x^{8/3}}-\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{5005 a^9 b^6}{x}-\frac{19305 a^8 b^7}{2 x^{2/3}}-\frac{19305 a^7 b^8}{\sqrt[3]{x}}+5005 a^6 b^9 \log (x)+9009 a^5 b^{10} \sqrt[3]{x}+\frac{4095}{2} a^4 b^{11} x^{2/3}+455 a^3 b^{12} x+\frac{315}{4} a^2 b^{13} x^{4/3}+9 a b^{14} x^{5/3}+\frac{b^{15} x^2}{2}","-\frac{a^{15}}{3 x^3}-\frac{45 a^{14} b}{8 x^{8/3}}-\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{5005 a^9 b^6}{x}-\frac{19305 a^8 b^7}{2 x^{2/3}}-\frac{19305 a^7 b^8}{\sqrt[3]{x}}+5005 a^6 b^9 \log (x)+9009 a^5 b^{10} \sqrt[3]{x}+\frac{4095}{2} a^4 b^{11} x^{2/3}+455 a^3 b^{12} x+\frac{315}{4} a^2 b^{13} x^{4/3}+9 a b^{14} x^{5/3}+\frac{b^{15} x^2}{2}",1,"-1/3*a^15/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",1
2349,1,211,211,0.1383291,"\int \frac{\left(a+b \sqrt[3]{x}\right)^{15}}{x^6} \, dx","Integrate[(a + b*x^(1/3))^15/x^6,x]","-\frac{a^{15}}{5 x^5}-\frac{45 a^{14} b}{14 x^{14/3}}-\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{455 a^3 b^{12}}{x}-\frac{315 a^2 b^{13}}{2 x^{2/3}}-\frac{45 a b^{14}}{\sqrt[3]{x}}+b^{15} \log (x)","-\frac{a^{15}}{5 x^5}-\frac{45 a^{14} b}{14 x^{14/3}}-\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{455 a^3 b^{12}}{x}-\frac{315 a^2 b^{13}}{2 x^{2/3}}-\frac{45 a b^{14}}{\sqrt[3]{x}}+b^{15} \log (x)",1,"-1/5*a^15/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",1
2350,1,45,72,0.0111057,"\int \frac{\left(a+b \sqrt[3]{x}\right)^{15}}{x^7} \, dx","Integrate[(a + b*x^(1/3))^15/x^7,x]","-\frac{\left(a+b \sqrt[3]{x}\right)^{16} \left(136 a^2-16 a b \sqrt[3]{x}+b^2 x^{2/3}\right)}{816 a^3 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,"-1/816*((a + b*x^(1/3))^16*(136*a^2 - 16*a*b*x^(1/3) + b^2*x^(2/3)))/(a^3*x^6)","A",1
2351,1,80,148,0.0173507,"\int \frac{\left(a+b \sqrt[3]{x}\right)^{15}}{x^8} \, dx","Integrate[(a + b*x^(1/3))^15/x^8,x]","\frac{\left(a+b \sqrt[3]{x}\right)^{16} \left(-15504 a^5+3876 a^4 b \sqrt[3]{x}-816 a^3 b^2 x^{2/3}+136 a^2 b^3 x-16 a b^4 x^{4/3}+b^5 x^{5/3}\right)}{108528 a^6 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*(-15504*a^5 + 3876*a^4*b*x^(1/3) - 816*a^3*b^2*x^(2/3) + 136*a^2*b^3*x - 16*a*b^4*x^(4/3) + b^5*x^(5/3)))/(108528*a^6*x^7)","A",1
2352,1,213,224,0.0461986,"\int \frac{\left(a+b \sqrt[3]{x}\right)^{15}}{x^9} \, dx","Integrate[(a + b*x^(1/3))^15/x^9,x]","-\frac{a^{15}}{8 x^8}-\frac{45 a^{14} b}{23 x^{23/3}}-\frac{315 a^{13} b^2}{22 x^{22/3}}-\frac{65 a^{12} b^3}{x^7}-\frac{819 a^{11} b^4}{4 x^{20/3}}-\frac{9009 a^{10} b^5}{19 x^{19/3}}-\frac{5005 a^9 b^6}{6 x^6}-\frac{19305 a^8 b^7}{17 x^{17/3}}-\frac{19305 a^7 b^8}{16 x^{16/3}}-\frac{1001 a^6 b^9}{x^5}-\frac{1287 a^5 b^{10}}{2 x^{14/3}}-\frac{315 a^4 b^{11}}{x^{13/3}}-\frac{455 a^3 b^{12}}{4 x^4}-\frac{315 a^2 b^{13}}{11 x^{11/3}}-\frac{9 a b^{14}}{2 x^{10/3}}-\frac{b^{15}}{3 x^3}","-\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,"-1/8*a^15/x^8 - (45*a^14*b)/(23*x^(23/3)) - (315*a^13*b^2)/(22*x^(22/3)) - (65*a^12*b^3)/x^7 - (819*a^11*b^4)/(4*x^(20/3)) - (9009*a^10*b^5)/(19*x^(19/3)) - (5005*a^9*b^6)/(6*x^6) - (19305*a^8*b^7)/(17*x^(17/3)) - (19305*a^7*b^8)/(16*x^(16/3)) - (1001*a^6*b^9)/x^5 - (1287*a^5*b^10)/(2*x^(14/3)) - (315*a^4*b^11)/x^(13/3) - (455*a^3*b^12)/(4*x^4) - (315*a^2*b^13)/(11*x^(11/3)) - (9*a*b^14)/(2*x^(10/3)) - b^15/(3*x^3)","A",1
2353,1,215,215,0.1133393,"\int \frac{\left(a+b \sqrt[3]{x}\right)^{15}}{x^{10}} \, dx","Integrate[(a + b*x^(1/3))^15/x^10,x]","-\frac{a^{15}}{9 x^9}-\frac{45 a^{14} b}{26 x^{26/3}}-\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 b^{14}}{13 x^{13/3}}-\frac{b^{15}}{4 x^4}","-\frac{a^{15}}{9 x^9}-\frac{45 a^{14} b}{26 x^{26/3}}-\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 b^{14}}{13 x^{13/3}}-\frac{b^{15}}{4 x^4}",1,"-1/9*a^15/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",1
2354,1,217,217,0.1034815,"\int \frac{\left(a+b \sqrt[3]{x}\right)^{15}}{x^{11}} \, dx","Integrate[(a + b*x^(1/3))^15/x^11,x]","-\frac{a^{15}}{10 x^{10}}-\frac{45 a^{14} b}{29 x^{29/3}}-\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 b^{14}}{16 x^{16/3}}-\frac{b^{15}}{5 x^5}","-\frac{a^{15}}{10 x^{10}}-\frac{45 a^{14} b}{29 x^{29/3}}-\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 b^{14}}{16 x^{16/3}}-\frac{b^{15}}{5 x^5}",1,"-1/10*a^15/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",1
2355,1,217,217,0.1037789,"\int \frac{\left(a+b \sqrt[3]{x}\right)^{15}}{x^{12}} \, dx","Integrate[(a + b*x^(1/3))^15/x^12,x]","-\frac{a^{15}}{11 x^{11}}-\frac{45 a^{14} b}{32 x^{32/3}}-\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 b^{14}}{19 x^{19/3}}-\frac{b^{15}}{6 x^6}","-\frac{a^{15}}{11 x^{11}}-\frac{45 a^{14} b}{32 x^{32/3}}-\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 b^{14}}{19 x^{19/3}}-\frac{b^{15}}{6 x^6}",1,"-1/11*a^15/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",1
2356,1,166,166,0.1369301,"\int \frac{x^3}{a+b \sqrt[3]{x}} \, dx","Integrate[x^3/(a + b*x^(1/3)),x]","-\frac{3 a^{11} \log \left(a+b \sqrt[3]{x}\right)}{b^{12}}+\frac{3 a^{10} \sqrt[3]{x}}{b^{11}}-\frac{3 a^9 x^{2/3}}{2 b^{10}}+\frac{a^8 x}{b^9}-\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 x^{10/3}}{10 b^2}+\frac{3 x^{11/3}}{11 b}","-\frac{3 a^{11} \log \left(a+b \sqrt[3]{x}\right)}{b^{12}}+\frac{3 a^{10} \sqrt[3]{x}}{b^{11}}-\frac{3 a^9 x^{2/3}}{2 b^{10}}+\frac{a^8 x}{b^9}-\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 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",1
2357,1,124,124,0.0798047,"\int \frac{x^2}{a+b \sqrt[3]{x}} \, dx","Integrate[x^2/(a + b*x^(1/3)),x]","\frac{3 a^8 \log \left(a+b \sqrt[3]{x}\right)}{b^9}-\frac{3 a^7 \sqrt[3]{x}}{b^8}+\frac{3 a^6 x^{2/3}}{2 b^7}-\frac{a^5 x}{b^6}+\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 x^{7/3}}{7 b^2}+\frac{3 x^{8/3}}{8 b}","\frac{3 a^8 \log \left(a+b \sqrt[3]{x}\right)}{b^9}-\frac{3 a^7 \sqrt[3]{x}}{b^8}+\frac{3 a^6 x^{2/3}}{2 b^7}-\frac{a^5 x}{b^6}+\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 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",1
2358,1,77,80,0.0378059,"\int \frac{x}{a+b \sqrt[3]{x}} \, dx","Integrate[x/(a + b*x^(1/3)),x]","\frac{-60 a^5 \log \left(a+b \sqrt[3]{x}\right)+60 a^4 b \sqrt[3]{x}-30 a^3 b^2 x^{2/3}+20 a^2 b^3 x-15 a b^4 x^{4/3}+12 b^5 x^{5/3}}{20 b^6}","-\frac{3 a^5 \log \left(a+b \sqrt[3]{x}\right)}{b^6}+\frac{3 a^4 \sqrt[3]{x}}{b^5}-\frac{3 a^3 x^{2/3}}{2 b^4}+\frac{a^2 x}{b^3}-\frac{3 a x^{4/3}}{4 b^2}+\frac{3 x^{5/3}}{5 b}",1,"(60*a^4*b*x^(1/3) - 30*a^3*b^2*x^(2/3) + 20*a^2*b^3*x - 15*a*b^4*x^(4/3) + 12*b^5*x^(5/3) - 60*a^5*Log[a + b*x^(1/3)])/(20*b^6)","A",1
2359,1,42,42,0.0230745,"\int \frac{1}{a+b \sqrt[3]{x}} \, dx","Integrate[(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",1
2360,1,22,22,0.00402,"\int \frac{1}{\left(a+b \sqrt[3]{x}\right) x} \, dx","Integrate[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",1
2361,1,63,63,0.031093,"\int \frac{1}{\left(a+b \sqrt[3]{x}\right) x^2} \, dx","Integrate[1/((a + b*x^(1/3))*x^2),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^3 \sqrt[3]{x}}+\frac{3 b}{2 a^2 x^{2/3}}-\frac{1}{a 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^3 \sqrt[3]{x}}+\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",1
2362,1,95,104,0.0673953,"\int \frac{1}{\left(a+b \sqrt[3]{x}\right) x^3} \, dx","Integrate[1/((a + b*x^(1/3))*x^3),x]","\frac{\frac{a \left(-10 a^5+12 a^4 b \sqrt[3]{x}-15 a^3 b^2 x^{2/3}+20 a^2 b^3 x-30 a b^4 x^{4/3}+60 b^5 x^{5/3}\right)}{x^2}-60 b^6 \log \left(a+b \sqrt[3]{x}\right)+20 b^6 \log (x)}{20 a^7}","-\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^6 \sqrt[3]{x}}-\frac{3 b^4}{2 a^5 x^{2/3}}+\frac{b^3}{a^4 x}-\frac{3 b^2}{4 a^3 x^{4/3}}+\frac{3 b}{5 a^2 x^{5/3}}-\frac{1}{2 a x^2}",1,"((a*(-10*a^5 + 12*a^4*b*x^(1/3) - 15*a^3*b^2*x^(2/3) + 20*a^2*b^3*x - 30*a*b^4*x^(4/3) + 60*b^5*x^(5/3)))/x^2 - 60*b^6*Log[a + b*x^(1/3)] + 20*b^6*Log[x])/(20*a^7)","A",1
2363,1,138,149,0.0664971,"\int \frac{1}{\left(a+b \sqrt[3]{x}\right) x^4} \, dx","Integrate[1/((a + b*x^(1/3))*x^4),x]","-\frac{280 a^9-315 a^8 b \sqrt[3]{x}+360 a^7 b^2 x^{2/3}-420 a^6 b^3 x+504 a^5 b^4 x^{4/3}-630 a^4 b^5 x^{5/3}+840 a^3 b^6 x^2-1260 a^2 b^7 x^{7/3}-2520 b^9 x^3 \log \left(a+b \sqrt[3]{x}\right)+2520 a b^8 x^{8/3}+840 b^9 x^3 \log (x)}{840 a^{10} x^3}","\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^9 \sqrt[3]{x}}+\frac{3 b^7}{2 a^8 x^{2/3}}-\frac{b^6}{a^7 x}+\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^2 x^{8/3}}-\frac{1}{3 a x^3}",1,"-1/840*(280*a^9 - 315*a^8*b*x^(1/3) + 360*a^7*b^2*x^(2/3) - 420*a^6*b^3*x + 504*a^5*b^4*x^(4/3) - 630*a^4*b^5*x^(5/3) + 840*a^3*b^6*x^2 - 1260*a^2*b^7*x^(7/3) + 2520*a*b^8*x^(8/3) - 2520*b^9*x^3*Log[a + b*x^(1/3)] + 840*b^9*x^3*Log[x])/(a^10*x^3)","A",1
2364,1,21,21,0.0048586,"\int \frac{1}{\left(2+b \sqrt[3]{x}\right) x} \, dx","Integrate[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",1
2365,1,171,171,0.1600496,"\int \frac{x^3}{\left(a+b \sqrt[3]{x}\right)^2} \, dx","Integrate[x^3/(a + b*x^(1/3))^2,x]","\frac{3 a^{11}}{b^{12} \left(a+b \sqrt[3]{x}\right)}+\frac{33 a^{10} \log \left(a+b \sqrt[3]{x}\right)}{b^{12}}-\frac{30 a^9 \sqrt[3]{x}}{b^{11}}+\frac{27 a^8 x^{2/3}}{2 b^{10}}-\frac{8 a^7 x}{b^9}+\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{2 a x^3}{3 b^3}+\frac{3 x^{10/3}}{10 b^2}","\frac{3 a^{11}}{b^{12} \left(a+b \sqrt[3]{x}\right)}+\frac{33 a^{10} \log \left(a+b \sqrt[3]{x}\right)}{b^{12}}-\frac{30 a^9 \sqrt[3]{x}}{b^{11}}+\frac{27 a^8 x^{2/3}}{2 b^{10}}-\frac{8 a^7 x}{b^9}+\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{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",1
2366,1,122,122,0.1076284,"\int \frac{x^2}{\left(a+b \sqrt[3]{x}\right)^2} \, dx","Integrate[x^2/(a + b*x^(1/3))^2,x]","-\frac{3 a^8}{b^9 \left(a+b \sqrt[3]{x}\right)}-\frac{24 a^7 \log \left(a+b \sqrt[3]{x}\right)}{b^9}+\frac{21 a^6 \sqrt[3]{x}}{b^8}-\frac{9 a^5 x^{2/3}}{b^7}+\frac{5 a^4 x}{b^6}-\frac{3 a^3 x^{4/3}}{b^5}+\frac{9 a^2 x^{5/3}}{5 b^4}-\frac{a x^2}{b^3}+\frac{3 x^{7/3}}{7 b^2}","-\frac{3 a^8}{b^9 \left(a+b \sqrt[3]{x}\right)}-\frac{24 a^7 \log \left(a+b \sqrt[3]{x}\right)}{b^9}+\frac{21 a^6 \sqrt[3]{x}}{b^8}-\frac{9 a^5 x^{2/3}}{b^7}+\frac{5 a^4 x}{b^6}-\frac{3 a^3 x^{4/3}}{b^5}+\frac{9 a^2 x^{5/3}}{5 b^4}-\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",1
2367,1,80,85,0.0611048,"\int \frac{x}{\left(a+b \sqrt[3]{x}\right)^2} \, dx","Integrate[x/(a + b*x^(1/3))^2,x]","\frac{\frac{12 a^5}{a+b \sqrt[3]{x}}+60 a^4 \log \left(a+b \sqrt[3]{x}\right)-48 a^3 b \sqrt[3]{x}+18 a^2 b^2 x^{2/3}-8 a b^3 x+3 b^4 x^{4/3}}{4 b^6}","\frac{3 a^5}{b^6 \left(a+b \sqrt[3]{x}\right)}+\frac{15 a^4 \log \left(a+b \sqrt[3]{x}\right)}{b^6}-\frac{12 a^3 \sqrt[3]{x}}{b^5}+\frac{9 a^2 x^{2/3}}{2 b^4}-\frac{2 a x}{b^3}+\frac{3 x^{4/3}}{4 b^2}",1,"((12*a^5)/(a + b*x^(1/3)) - 48*a^3*b*x^(1/3) + 18*a^2*b^2*x^(2/3) - 8*a*b^3*x + 3*b^4*x^(4/3) + 60*a^4*Log[a + b*x^(1/3)])/(4*b^6)","A",1
2368,1,42,46,0.0389821,"\int \frac{1}{\left(a+b \sqrt[3]{x}\right)^2} \, dx","Integrate[(a + b*x^(1/3))^(-2),x]","\frac{3 \left(-\frac{a^2}{a+b \sqrt[3]{x}}-2 a \log \left(a+b \sqrt[3]{x}\right)+b \sqrt[3]{x}\right)}{b^3}","-\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/(a + b*x^(1/3))) + b*x^(1/3) - 2*a*Log[a + b*x^(1/3)]))/b^3","A",1
2369,1,33,38,0.0274735,"\int \frac{1}{\left(a+b \sqrt[3]{x}\right)^2 x} \, dx","Integrate[1/((a + b*x^(1/3))^2*x),x]","\frac{\frac{3 a}{a+b \sqrt[3]{x}}-3 \log \left(a+b \sqrt[3]{x}\right)+\log (x)}{a^2}","-\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)] + Log[x])/a^2","A",1
2370,1,77,80,0.1034681,"\int \frac{1}{\left(a+b \sqrt[3]{x}\right)^2 x^2} \, dx","Integrate[1/((a + b*x^(1/3))^2*x^2),x]","\frac{-\frac{a^4-2 a^3 b \sqrt[3]{x}+6 a^2 b^2 x^{2/3}+12 a b^3 x}{a x+b x^{4/3}}+12 b^3 \log \left(a+b \sqrt[3]{x}\right)-4 b^3 \log (x)}{a^5}","\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^3}{a^4 \left(a+b \sqrt[3]{x}\right)}-\frac{9 b^2}{a^4 \sqrt[3]{x}}+\frac{3 b}{a^3 x^{2/3}}-\frac{1}{a^2 x}",1,"(-((a^4 - 2*a^3*b*x^(1/3) + 6*a^2*b^2*x^(2/3) + 12*a*b^3*x)/(a*x + b*x^(4/3))) + 12*b^3*Log[a + b*x^(1/3)] - 4*b^3*Log[x])/a^5","A",1
2371,1,117,125,0.1371241,"\int \frac{1}{\left(a+b \sqrt[3]{x}\right)^2 x^3} \, dx","Integrate[1/((a + b*x^(1/3))^2*x^3),x]","\frac{\frac{a \left(-10 a^6+14 a^5 b \sqrt[3]{x}-21 a^4 b^2 x^{2/3}+35 a^3 b^3 x-70 a^2 b^4 x^{4/3}+210 a b^5 x^{5/3}+420 b^6 x^2\right)}{x^2 \left(a+b \sqrt[3]{x}\right)}-420 b^6 \log \left(a+b \sqrt[3]{x}\right)+140 b^6 \log (x)}{20 a^8}","-\frac{21 b^6 \log \left(a+b \sqrt[3]{x}\right)}{a^8}+\frac{7 b^6 \log (x)}{a^8}+\frac{3 b^6}{a^7 \left(a+b \sqrt[3]{x}\right)}+\frac{18 b^5}{a^7 \sqrt[3]{x}}-\frac{15 b^4}{2 a^6 x^{2/3}}+\frac{4 b^3}{a^5 x}-\frac{9 b^2}{4 a^4 x^{4/3}}+\frac{6 b}{5 a^3 x^{5/3}}-\frac{1}{2 a^2 x^2}",1,"((a*(-10*a^6 + 14*a^5*b*x^(1/3) - 21*a^4*b^2*x^(2/3) + 35*a^3*b^3*x - 70*a^2*b^4*x^(4/3) + 210*a*b^5*x^(5/3) + 420*b^6*x^2))/((a + b*x^(1/3))*x^2) - 420*b^6*Log[a + b*x^(1/3)] + 140*b^6*Log[x])/(20*a^8)","A",1
2372,1,154,162,0.2302674,"\int \frac{1}{\left(a+b \sqrt[3]{x}\right)^2 x^4} \, dx","Integrate[1/((a + b*x^(1/3))^2*x^4),x]","-\frac{\frac{a \left(28 a^9-35 a^8 b \sqrt[3]{x}+45 a^7 b^2 x^{2/3}-60 a^6 b^3 x+84 a^5 b^4 x^{4/3}-126 a^4 b^5 x^{5/3}+210 a^3 b^6 x^2-420 a^2 b^7 x^{7/3}+1260 a b^8 x^{8/3}+2520 b^9 x^3\right)}{x^3 \left(a+b \sqrt[3]{x}\right)}-2520 b^9 \log \left(a+b \sqrt[3]{x}\right)+840 b^9 \log (x)}{84 a^{11}}","\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^9}{a^{10} \left(a+b \sqrt[3]{x}\right)}-\frac{27 b^8}{a^{10} \sqrt[3]{x}}+\frac{12 b^7}{a^9 x^{2/3}}-\frac{7 b^6}{a^8 x}+\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}{4 a^3 x^{8/3}}-\frac{1}{3 a^2 x^3}",1,"-1/84*((a*(28*a^9 - 35*a^8*b*x^(1/3) + 45*a^7*b^2*x^(2/3) - 60*a^6*b^3*x + 84*a^5*b^4*x^(4/3) - 126*a^4*b^5*x^(5/3) + 210*a^3*b^6*x^2 - 420*a^2*b^7*x^(7/3) + 1260*a*b^8*x^(8/3) + 2520*b^9*x^3))/((a + b*x^(1/3))*x^3) - 2520*b^9*Log[a + b*x^(1/3)] + 840*b^9*Log[x])/a^11","A",1
2373,1,157,171,0.1689877,"\int \frac{x^3}{\left(a+b \sqrt[3]{x}\right)^3} \, dx","Integrate[x^3/(a + b*x^(1/3))^3,x]","\frac{\frac{252 a^{11}}{\left(a+b \sqrt[3]{x}\right)^2}-\frac{5544 a^{10}}{a+b \sqrt[3]{x}}-27720 a^9 \log \left(a+b \sqrt[3]{x}\right)+22680 a^8 b \sqrt[3]{x}-9072 a^7 b^2 x^{2/3}+4704 a^6 b^3 x-2646 a^5 b^4 x^{4/3}+1512 a^4 b^5 x^{5/3}-840 a^3 b^6 x^2+432 a^2 b^7 x^{7/3}-189 a b^8 x^{8/3}+56 b^9 x^3}{168 b^{12}}","\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{165 a^9 \log \left(a+b \sqrt[3]{x}\right)}{b^{12}}+\frac{135 a^8 \sqrt[3]{x}}{b^{11}}-\frac{54 a^7 x^{2/3}}{b^{10}}+\frac{28 a^6 x}{b^9}-\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{9 a x^{8/3}}{8 b^4}+\frac{x^3}{3 b^3}",1,"((252*a^11)/(a + b*x^(1/3))^2 - (5544*a^10)/(a + b*x^(1/3)) + 22680*a^8*b*x^(1/3) - 9072*a^7*b^2*x^(2/3) + 4704*a^6*b^3*x - 2646*a^5*b^4*x^(4/3) + 1512*a^4*b^5*x^(5/3) - 840*a^3*b^6*x^2 + 432*a^2*b^7*x^(7/3) - 189*a*b^8*x^(8/3) + 56*b^9*x^3 - 27720*a^9*Log[a + b*x^(1/3)])/(168*b^12)","A",1
2374,1,120,134,0.1088992,"\int \frac{x^2}{\left(a+b \sqrt[3]{x}\right)^3} \, dx","Integrate[x^2/(a + b*x^(1/3))^3,x]","\frac{-\frac{15 a^8}{\left(a+b \sqrt[3]{x}\right)^2}+\frac{240 a^7}{a+b \sqrt[3]{x}}+840 a^6 \log \left(a+b \sqrt[3]{x}\right)-630 a^5 b \sqrt[3]{x}+225 a^4 b^2 x^{2/3}-100 a^3 b^3 x+45 a^2 b^4 x^{4/3}-18 a b^5 x^{5/3}+5 b^6 x^2}{10 b^9}","-\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{84 a^6 \log \left(a+b \sqrt[3]{x}\right)}{b^9}-\frac{63 a^5 \sqrt[3]{x}}{b^8}+\frac{45 a^4 x^{2/3}}{2 b^7}-\frac{10 a^3 x}{b^6}+\frac{9 a^2 x^{4/3}}{2 b^5}-\frac{9 a x^{5/3}}{5 b^4}+\frac{x^2}{2 b^3}",1,"((-15*a^8)/(a + b*x^(1/3))^2 + (240*a^7)/(a + b*x^(1/3)) - 630*a^5*b*x^(1/3) + 225*a^4*b^2*x^(2/3) - 100*a^3*b^3*x + 45*a^2*b^4*x^(4/3) - 18*a*b^5*x^(5/3) + 5*b^6*x^2 + 840*a^6*Log[a + b*x^(1/3)])/(10*b^9)","A",1
2375,1,83,90,0.0705856,"\int \frac{x}{\left(a+b \sqrt[3]{x}\right)^3} \, dx","Integrate[x/(a + b*x^(1/3))^3,x]","\frac{\frac{3 a^5}{\left(a+b \sqrt[3]{x}\right)^2}-\frac{30 a^4}{a+b \sqrt[3]{x}}-60 a^3 \log \left(a+b \sqrt[3]{x}\right)+36 a^2 b \sqrt[3]{x}-9 a b^2 x^{2/3}+2 b^3 x}{2 b^6}","\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{30 a^3 \log \left(a+b \sqrt[3]{x}\right)}{b^6}+\frac{18 a^2 \sqrt[3]{x}}{b^5}-\frac{9 a x^{2/3}}{2 b^4}+\frac{x}{b^3}",1,"((3*a^5)/(a + b*x^(1/3))^2 - (30*a^4)/(a + b*x^(1/3)) + 36*a^2*b*x^(1/3) - 9*a*b^2*x^(2/3) + 2*b^3*x - 60*a^3*Log[a + b*x^(1/3)])/(2*b^6)","A",1
2376,1,45,54,0.0400348,"\int \frac{1}{\left(a+b \sqrt[3]{x}\right)^3} \, dx","Integrate[(a + b*x^(1/3))^(-3),x]","\frac{3 \left(\frac{a \left(3 a+4 b \sqrt[3]{x}\right)}{\left(a+b \sqrt[3]{x}\right)^2}+2 \log \left(a+b \sqrt[3]{x}\right)\right)}{2 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*(3*a + 4*b*x^(1/3)))/(a + b*x^(1/3))^2 + 2*Log[a + b*x^(1/3)]))/(2*b^3)","A",1
2377,1,50,56,0.0577943,"\int \frac{1}{\left(a+b \sqrt[3]{x}\right)^3 x} \, dx","Integrate[1/((a + b*x^(1/3))^3*x),x]","\frac{\frac{3 a \left(3 a+2 b \sqrt[3]{x}\right)}{\left(a+b \sqrt[3]{x}\right)^2}-6 \log \left(a+b \sqrt[3]{x}\right)+2 \log (x)}{2 a^3}","-\frac{3 \log \left(a+b \sqrt[3]{x}\right)}{a^3}+\frac{\log (x)}{a^3}+\frac{3}{a^2 \left(a+b \sqrt[3]{x}\right)}+\frac{3}{2 a \left(a+b \sqrt[3]{x}\right)^2}",1,"((3*a*(3*a + 2*b*x^(1/3)))/(a + b*x^(1/3))^2 - 6*Log[a + b*x^(1/3)] + 2*Log[x])/(2*a^3)","A",1
2378,1,93,103,0.1489657,"\int \frac{1}{\left(a+b \sqrt[3]{x}\right)^3 x^2} \, dx","Integrate[1/((a + b*x^(1/3))^3*x^2),x]","-\frac{\frac{a \left(2 a^4-5 a^3 b \sqrt[3]{x}+20 a^2 b^2 x^{2/3}+90 a b^3 x+60 b^4 x^{4/3}\right)}{x \left(a+b \sqrt[3]{x}\right)^2}-60 b^3 \log \left(a+b \sqrt[3]{x}\right)+20 b^3 \log (x)}{2 a^6}","\frac{30 b^3 \log \left(a+b \sqrt[3]{x}\right)}{a^6}-\frac{10 b^3 \log (x)}{a^6}-\frac{12 b^3}{a^5 \left(a+b \sqrt[3]{x}\right)}-\frac{18 b^2}{a^5 \sqrt[3]{x}}-\frac{3 b^3}{2 a^4 \left(a+b \sqrt[3]{x}\right)^2}+\frac{9 b}{2 a^4 x^{2/3}}-\frac{1}{a^3 x}",1,"-1/2*((a*(2*a^4 - 5*a^3*b*x^(1/3) + 20*a^2*b^2*x^(2/3) + 90*a*b^3*x + 60*b^4*x^(4/3)))/((a + b*x^(1/3))^2*x) - 60*b^3*Log[a + b*x^(1/3)] + 20*b^3*Log[x])/a^6","A",1
2379,1,130,146,0.1753573,"\int \frac{1}{\left(a+b \sqrt[3]{x}\right)^3 x^3} \, dx","Integrate[1/((a + b*x^(1/3))^3*x^3),x]","\frac{\frac{a \left(-5 a^7+8 a^6 b \sqrt[3]{x}-14 a^5 b^2 x^{2/3}+28 a^4 b^3 x-70 a^3 b^4 x^{4/3}+280 a^2 b^5 x^{5/3}+1260 a b^6 x^2+840 b^7 x^{7/3}\right)}{x^2 \left(a+b \sqrt[3]{x}\right)^2}-840 b^6 \log \left(a+b \sqrt[3]{x}\right)+280 b^6 \log (x)}{10 a^9}","-\frac{84 b^6 \log \left(a+b \sqrt[3]{x}\right)}{a^9}+\frac{28 b^6 \log (x)}{a^9}+\frac{21 b^6}{a^8 \left(a+b \sqrt[3]{x}\right)}+\frac{63 b^5}{a^8 \sqrt[3]{x}}+\frac{3 b^6}{2 a^7 \left(a+b \sqrt[3]{x}\right)^2}-\frac{45 b^4}{2 a^7 x^{2/3}}+\frac{10 b^3}{a^6 x}-\frac{9 b^2}{2 a^5 x^{4/3}}+\frac{9 b}{5 a^4 x^{5/3}}-\frac{1}{2 a^3 x^2}",1,"((a*(-5*a^7 + 8*a^6*b*x^(1/3) - 14*a^5*b^2*x^(2/3) + 28*a^4*b^3*x - 70*a^3*b^4*x^(4/3) + 280*a^2*b^5*x^(5/3) + 1260*a*b^6*x^2 + 840*b^7*x^(7/3)))/((a + b*x^(1/3))^2*x^2) - 840*b^6*Log[a + b*x^(1/3)] + 280*b^6*Log[x])/(10*a^9)","A",1
2380,1,167,183,0.2837198,"\int \frac{1}{\left(a+b \sqrt[3]{x}\right)^3 x^4} \, dx","Integrate[1/((a + b*x^(1/3))^3*x^4),x]","-\frac{\frac{a \left(56 a^{10}-77 a^9 b \sqrt[3]{x}+110 a^8 b^2 x^{2/3}-165 a^7 b^3 x+264 a^6 b^4 x^{4/3}-462 a^5 b^5 x^{5/3}+924 a^4 b^6 x^2-2310 a^3 b^7 x^{7/3}+9240 a^2 b^8 x^{8/3}+41580 a b^9 x^3+27720 b^{10} x^{10/3}\right)}{x^3 \left(a+b \sqrt[3]{x}\right)^2}-27720 b^9 \log \left(a+b \sqrt[3]{x}\right)+9240 b^9 \log (x)}{168 a^{12}}","\frac{165 b^9 \log \left(a+b \sqrt[3]{x}\right)}{a^{12}}-\frac{55 b^9 \log (x)}{a^{12}}-\frac{30 b^9}{a^{11} \left(a+b \sqrt[3]{x}\right)}-\frac{135 b^8}{a^{11} \sqrt[3]{x}}-\frac{3 b^9}{2 a^{10} \left(a+b \sqrt[3]{x}\right)^2}+\frac{54 b^7}{a^{10} x^{2/3}}-\frac{28 b^6}{a^9 x}+\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{9 b}{8 a^4 x^{8/3}}-\frac{1}{3 a^3 x^3}",1,"-1/168*((a*(56*a^10 - 77*a^9*b*x^(1/3) + 110*a^8*b^2*x^(2/3) - 165*a^7*b^3*x + 264*a^6*b^4*x^(4/3) - 462*a^5*b^5*x^(5/3) + 924*a^4*b^6*x^2 - 2310*a^3*b^7*x^(7/3) + 9240*a^2*b^8*x^(8/3) + 41580*a*b^9*x^3 + 27720*b^10*x^(10/3)))/((a + b*x^(1/3))^2*x^3) - 27720*b^9*Log[a + b*x^(1/3)] + 9240*b^9*Log[x])/a^12","A",1
2381,1,31,42,0.01121,"\int \frac{1}{\sqrt{1+\sqrt[3]{x}}} \, dx","Integrate[1/Sqrt[1 + x^(1/3)],x]","\frac{2}{5} \sqrt{\sqrt[3]{x}+1} \left(3 x^{2/3}-4 \sqrt[3]{x}+8\right)","\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,"(2*Sqrt[1 + x^(1/3)]*(8 - 4*x^(1/3) + 3*x^(2/3)))/5","A",1
2382,1,22,23,0.005095,"\int \frac{1}{\left(1+\sqrt[3]{x}\right) x^{3/2}} \, dx","Integrate[1/((1 + x^(1/3))*x^(3/2)),x]","-\frac{2 \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};-\sqrt[3]{x}\right)}{\sqrt{x}}","\frac{6}{\sqrt[6]{x}}-\frac{2}{\sqrt{x}}+6 \tan ^{-1}\left(\sqrt[6]{x}\right)",1,"(-2*Hypergeometric2F1[-3/2, 1, -1/2, -x^(1/3)])/Sqrt[x]","C",1
2383,1,39,39,0.0139133,"\int \frac{x^{2/3}}{1+\sqrt[3]{x}} \, dx","Integrate[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",1
2384,1,16,16,0.0037001,"\int \frac{1}{1+x^{2/3}} \, dx","Integrate[(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",1
2385,1,12,12,0.0017236,"\int \frac{1}{\left(1+x^{2/3}\right) \sqrt[3]{x}} \, dx","Integrate[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
2386,1,8,8,0.0022467,"\int \frac{1}{\left(1+x^{2/3}\right) x^{2/3}} \, dx","Integrate[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",1
2387,1,11,11,0.0031063,"\int \frac{\sqrt{-1+x^{2/3}}}{\sqrt[3]{x}} \, dx","Integrate[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
2388,1,15,15,0.0218485,"\int \frac{\left(1+x^{2/3}\right)^{3/2}}{\sqrt[3]{x}} \, dx","Integrate[(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
2389,1,117,117,0.041685,"\int \frac{\sqrt{x}}{1+x^{2/3}} \, dx","Integrate[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",1
2390,1,22,188,0.0074179,"\int \frac{\sqrt[3]{x}}{-1+x^{5/6}} \, dx","Integrate[x^(1/3)/(-1 + x^(5/6)),x]","-2 \sqrt{x} \left(\, _2F_1\left(\frac{3}{5},1;\frac{8}{5};x^{5/6}\right)-1\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]*(-1 + Hypergeometric2F1[3/5, 1, 8/5, x^(5/6)])","C",1
2391,1,36,67,0.0319565,"\int \sqrt{3-\frac{1}{\sqrt{x}}} \, dx","Integrate[Sqrt[3 - 1/Sqrt[x]],x]","\frac{4}{81} \left(3-\frac{1}{\sqrt{x}}\right)^{3/2} \, _2F_1\left(\frac{3}{2},3;\frac{5}{2};1-\frac{1}{3 \sqrt{x}}\right)","\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,"(4*(3 - 1/Sqrt[x])^(3/2)*Hypergeometric2F1[3/2, 3, 5/2, 1 - 1/(3*Sqrt[x])])/81","C",1
2392,1,28,50,0.0105928,"\int \frac{1}{\sqrt{1+\frac{1}{\sqrt{x}}}} \, dx","Integrate[1/Sqrt[1 + 1/Sqrt[x]],x]","4 \sqrt{\frac{1}{\sqrt{x}}+1} \, _2F_1\left(\frac{1}{2},3;\frac{3}{2};1+\frac{1}{\sqrt{x}}\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,"4*Sqrt[1 + 1/Sqrt[x]]*Hypergeometric2F1[1/2, 3, 3/2, 1 + 1/Sqrt[x]]","C",1
2393,1,52,95,0.0292517,"\int \left(a+\frac{b}{x^{3/2}}\right)^{2/3} \, dx","Integrate[(a + b/x^(3/2))^(2/3),x]","\frac{x \left(a+\frac{b}{x^{3/2}}\right)^{2/3} \, _2F_1\left(-\frac{2}{3},-\frac{2}{3};\frac{1}{3};-\frac{b}{a x^{3/2}}\right)}{\left(\frac{b}{a x^{3/2}}+1\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*Hypergeometric2F1[-2/3, -2/3, 1/3, -(b/(a*x^(3/2)))])/(1 + b/(a*x^(3/2)))^(2/3)","C",1
2394,1,19,19,0.0088474,"\int \left(a+\frac{b}{\sqrt[3]{x}}\right) x^4 \, dx","Integrate[(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",1
2395,1,19,19,0.0027949,"\int \left(a+\frac{b}{\sqrt[3]{x}}\right) x^3 \, dx","Integrate[(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",1
2396,1,19,19,0.0200298,"\int \left(a+\frac{b}{\sqrt[3]{x}}\right) x^2 \, dx","Integrate[(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",1
2397,1,19,19,0.0032092,"\int \left(a+\frac{b}{\sqrt[3]{x}}\right) x \, dx","Integrate[(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",1
2398,1,14,14,0.0016506,"\int \left(a+\frac{b}{\sqrt[3]{x}}\right) \, dx","Integrate[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
2399,1,13,13,0.013032,"\int \frac{a+\frac{b}{\sqrt[3]{x}}}{x} \, dx","Integrate[(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",1
2400,1,17,17,0.0082099,"\int \frac{a+\frac{b}{\sqrt[3]{x}}}{x^2} \, dx","Integrate[(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",1
2401,1,19,19,0.0083866,"\int \frac{a+\frac{b}{\sqrt[3]{x}}}{x^3} \, dx","Integrate[(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",1
2402,1,19,19,0.0087696,"\int \frac{a+\frac{b}{\sqrt[3]{x}}}{x^4} \, dx","Integrate[(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",1
2403,1,34,34,0.0296305,"\int \left(a+\frac{b}{\sqrt[3]{x}}\right)^2 x^4 \, dx","Integrate[(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",1
2404,1,34,34,0.0115582,"\int \left(a+\frac{b}{\sqrt[3]{x}}\right)^2 x^3 \, dx","Integrate[(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",1
2405,1,34,34,0.0237823,"\int \left(a+\frac{b}{\sqrt[3]{x}}\right)^2 x^2 \, dx","Integrate[(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",1
2406,1,34,34,0.0240314,"\int \left(a+\frac{b}{\sqrt[3]{x}}\right)^2 x \, dx","Integrate[(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",1
2407,1,25,16,0.0121477,"\int \left(a+\frac{b}{\sqrt[3]{x}}\right)^2 \, dx","Integrate[(a + b/x^(1/3))^2,x]","a^2 x+3 a b x^{2/3}+3 b^2 \sqrt[3]{x}","\frac{x \left(a+\frac{b}{\sqrt[3]{x}}\right)^3}{a}",1,"3*b^2*x^(1/3) + 3*a*b*x^(2/3) + a^2*x","A",1
2408,1,28,28,0.0188727,"\int \frac{\left(a+\frac{b}{\sqrt[3]{x}}\right)^2}{x} \, dx","Integrate[(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",1
2409,1,32,32,0.0226966,"\int \frac{\left(a+\frac{b}{\sqrt[3]{x}}\right)^2}{x^2} \, dx","Integrate[(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",1
2410,1,34,34,0.0353227,"\int \frac{\left(a+\frac{b}{\sqrt[3]{x}}\right)^2}{x^3} \, dx","Integrate[(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",1
2411,1,34,34,0.0397483,"\int \frac{\left(a+\frac{b}{\sqrt[3]{x}}\right)^2}{x^4} \, dx","Integrate[(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",1
2412,1,47,47,0.0321865,"\int \left(a+\frac{b}{\sqrt[3]{x}}\right)^3 x^4 \, dx","Integrate[(a + b/x^(1/3))^3*x^4,x]","\frac{a^3 x^5}{5}+\frac{9}{14} a^2 b x^{14/3}+\frac{9}{13} a b^2 x^{13/3}+\frac{b^3 x^4}{4}","\frac{a^3 x^5}{5}+\frac{9}{14} a^2 b x^{14/3}+\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",1
2413,1,41,47,0.024715,"\int \left(a+\frac{b}{\sqrt[3]{x}}\right)^3 x^3 \, dx","Integrate[(a + b/x^(1/3))^3*x^3,x]","\frac{1}{660} x^3 \left(165 a^3 x+540 a^2 b x^{2/3}+594 a b^2 \sqrt[3]{x}+220 b^3\right)","\frac{a^3 x^4}{4}+\frac{9}{11} a^2 b x^{11/3}+\frac{9}{10} a b^2 x^{10/3}+\frac{b^3 x^3}{3}",1,"(x^3*(220*b^3 + 594*a*b^2*x^(1/3) + 540*a^2*b*x^(2/3) + 165*a^3*x))/660","A",1
2414,1,47,47,0.0196254,"\int \left(a+\frac{b}{\sqrt[3]{x}}\right)^3 x^2 \, dx","Integrate[(a + b/x^(1/3))^3*x^2,x]","\frac{a^3 x^3}{3}+\frac{9}{8} a^2 b x^{8/3}+\frac{9}{7} a b^2 x^{7/3}+\frac{b^3 x^2}{2}","\frac{a^3 x^3}{3}+\frac{9}{8} a^2 b x^{8/3}+\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",1
2415,1,42,42,0.0170331,"\int \left(a+\frac{b}{\sqrt[3]{x}}\right)^3 x \, dx","Integrate[(a + b/x^(1/3))^3*x,x]","\frac{a^3 x^2}{2}+\frac{9}{5} a^2 b x^{5/3}+\frac{9}{4} a b^2 x^{4/3}+b^3 x","\frac{a^3 x^2}{2}+\frac{9}{5} a^2 b x^{5/3}+\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",1
2416,1,36,36,0.0294083,"\int \left(a+\frac{b}{\sqrt[3]{x}}\right)^3 \, dx","Integrate[(a + b/x^(1/3))^3,x]","a^3 x+\frac{9}{2} a^2 b x^{2/3}+9 a b^2 \sqrt[3]{x}+b^3 \log (x)","a^3 x+\frac{9}{2} a^2 b x^{2/3}+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",1
2417,1,39,39,0.04069,"\int \frac{\left(a+\frac{b}{\sqrt[3]{x}}\right)^3}{x} \, dx","Integrate[(a + b/x^(1/3))^3/x,x]","a^3 \log (x)-\frac{9 a^2 b}{\sqrt[3]{x}}-\frac{9 a b^2}{2 x^{2/3}}-\frac{b^3}{x}","a^3 \log (x)-\frac{9 a^2 b}{\sqrt[3]{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",1
2418,1,41,45,0.024469,"\int \frac{\left(a+\frac{b}{\sqrt[3]{x}}\right)^3}{x^2} \, dx","Integrate[(a + b/x^(1/3))^3/x^2,x]","-\frac{20 a^3 x+45 a^2 b x^{2/3}+36 a b^2 \sqrt[3]{x}+10 b^3}{20 x^2}","-\frac{a^3}{x}-\frac{9 a^2 b}{4 x^{4/3}}-\frac{9 a b^2}{5 x^{5/3}}-\frac{b^3}{2 x^2}",1,"-1/20*(10*b^3 + 36*a*b^2*x^(1/3) + 45*a^2*b*x^(2/3) + 20*a^3*x)/x^2","A",1
2419,1,41,47,0.0275312,"\int \frac{\left(a+\frac{b}{\sqrt[3]{x}}\right)^3}{x^3} \, dx","Integrate[(a + b/x^(1/3))^3/x^3,x]","-\frac{84 a^3 x+216 a^2 b x^{2/3}+189 a b^2 \sqrt[3]{x}+56 b^3}{168 x^3}","-\frac{a^3}{2 x^2}-\frac{9 a^2 b}{7 x^{7/3}}-\frac{9 a b^2}{8 x^{8/3}}-\frac{b^3}{3 x^3}",1,"-1/168*(56*b^3 + 189*a*b^2*x^(1/3) + 216*a^2*b*x^(2/3) + 84*a^3*x)/x^3","A",1
2420,1,41,47,0.034292,"\int \frac{\left(a+\frac{b}{\sqrt[3]{x}}\right)^3}{x^4} \, dx","Integrate[(a + b/x^(1/3))^3/x^4,x]","-\frac{220 a^3 x+594 a^2 b x^{2/3}+540 a b^2 \sqrt[3]{x}+165 b^3}{660 x^4}","-\frac{a^3}{3 x^3}-\frac{9 a^2 b}{10 x^{10/3}}-\frac{9 a b^2}{11 x^{11/3}}-\frac{b^3}{4 x^4}",1,"-1/660*(165*b^3 + 540*a*b^2*x^(1/3) + 594*a^2*b*x^(2/3) + 220*a^3*x)/x^4","A",1
2421,1,146,136,0.1394679,"\int \frac{x^2}{a+\frac{b}{\sqrt[3]{x}}} \, dx","Integrate[x^2/(a + b/x^(1/3)),x]","-\frac{3 b^9 \log \left(a+\frac{b}{\sqrt[3]{x}}\right)}{a^{10}}-\frac{b^9 \log (x)}{a^{10}}+\frac{3 b^8 \sqrt[3]{x}}{a^9}-\frac{3 b^7 x^{2/3}}{2 a^8}+\frac{b^6 x}{a^7}-\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 x^{8/3}}{8 a^2}+\frac{x^3}{3 a}","-\frac{3 b^9 \log \left(a \sqrt[3]{x}+b\right)}{a^{10}}+\frac{3 b^8 \sqrt[3]{x}}{a^9}-\frac{3 b^7 x^{2/3}}{2 a^8}+\frac{b^6 x}{a^7}-\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 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[a + b/x^(1/3)])/a^10 - (b^9*Log[x])/a^10","A",1
2422,1,95,94,0.0420267,"\int \frac{x}{a+\frac{b}{\sqrt[3]{x}}} \, dx","Integrate[x/(a + b/x^(1/3)),x]","\frac{10 a^6 x^2-12 a^5 b x^{5/3}+15 a^4 b^2 x^{4/3}-20 a^3 b^3 x+30 a^2 b^4 x^{2/3}+60 b^6 \log \left(a+\frac{b}{\sqrt[3]{x}}\right)-60 a b^5 \sqrt[3]{x}+20 b^6 \log (x)}{20 a^7}","\frac{3 b^6 \log \left(a \sqrt[3]{x}+b\right)}{a^7}-\frac{3 b^5 \sqrt[3]{x}}{a^6}+\frac{3 b^4 x^{2/3}}{2 a^5}-\frac{b^3 x}{a^4}+\frac{3 b^2 x^{4/3}}{4 a^3}-\frac{3 b x^{5/3}}{5 a^2}+\frac{x^2}{2 a}",1,"(-60*a*b^5*x^(1/3) + 30*a^2*b^4*x^(2/3) - 20*a^3*b^3*x + 15*a^4*b^2*x^(4/3) - 12*a^5*b*x^(5/3) + 10*a^6*x^2 + 60*b^6*Log[a + b/x^(1/3)] + 20*b^6*Log[x])/(20*a^7)","A",1
2423,1,50,60,0.0268381,"\int \frac{1}{a+\frac{b}{\sqrt[3]{x}}} \, dx","Integrate[(a + b/x^(1/3))^(-1),x]","-\frac{3 b^3 \log \left(a \sqrt[3]{x}+b\right)}{a^4}+\frac{3 b^2 \sqrt[3]{x}}{a^3}-\frac{3 b x^{2/3}}{2 a^2}+\frac{x}{a}","-\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^2 \sqrt[3]{x}}{a^3}-\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[b + a*x^(1/3)])/a^4","A",1
2424,1,15,15,0.0033794,"\int \frac{1}{\left(a+\frac{b}{\sqrt[3]{x}}\right) x} \, dx","Integrate[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",1
2425,1,48,51,0.0413508,"\int \frac{1}{\left(a+\frac{b}{\sqrt[3]{x}}\right) x^2} \, dx","Integrate[1/((a + b/x^(1/3))*x^2),x]","\frac{-6 a^2 \log \left(a \sqrt[3]{x}+b\right)+2 a^2 \log (x)-\frac{3 b \left(b-2 a \sqrt[3]{x}\right)}{x^{2/3}}}{2 b^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*b*(b - 2*a*x^(1/3)))/x^(2/3) - 6*a^2*Log[b + a*x^(1/3)] + 2*a^2*Log[x])/(2*b^3)","A",1
2426,1,84,93,0.0851967,"\int \frac{1}{\left(a+\frac{b}{\sqrt[3]{x}}\right) x^3} \, dx","Integrate[1/((a + b/x^(1/3))*x^3),x]","-\frac{-60 a^5 \log \left(a \sqrt[3]{x}+b\right)+20 a^5 \log (x)+\frac{b \left(60 a^4 x^{4/3}-30 a^3 b x+20 a^2 b^2 x^{2/3}-15 a b^3 \sqrt[3]{x}+12 b^4\right)}{x^{5/3}}}{20 b^6}","\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^5 \sqrt[3]{x}}+\frac{3 a^3}{2 b^4 x^{2/3}}-\frac{a^2}{b^3 x}+\frac{3 a}{4 b^2 x^{4/3}}-\frac{3}{5 b x^{5/3}}",1,"-1/20*((b*(12*b^4 - 15*a*b^3*x^(1/3) + 20*a^2*b^2*x^(2/3) - 30*a^3*b*x + 60*a^4*x^(4/3)))/x^(5/3) - 60*a^5*Log[b + a*x^(1/3)] + 20*a^5*Log[x])/b^6","A",1
2427,1,121,134,0.1197297,"\int \frac{1}{\left(a+\frac{b}{\sqrt[3]{x}}\right) x^4} \, dx","Integrate[1/((a + b/x^(1/3))*x^4),x]","\frac{-840 a^8 \log \left(a \sqrt[3]{x}+b\right)+280 a^8 \log (x)+\frac{b \left(840 a^7 x^{7/3}-420 a^6 b x^2+280 a^5 b^2 x^{5/3}-210 a^4 b^3 x^{4/3}+168 a^3 b^4 x-140 a^2 b^5 x^{2/3}+120 a b^6 \sqrt[3]{x}-105 b^7\right)}{x^{8/3}}}{280 b^9}","-\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^8 \sqrt[3]{x}}-\frac{3 a^6}{2 b^7 x^{2/3}}+\frac{a^5}{b^6 x}-\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^2 x^{7/3}}-\frac{3}{8 b x^{8/3}}",1,"((b*(-105*b^7 + 120*a*b^6*x^(1/3) - 140*a^2*b^5*x^(2/3) + 168*a^3*b^4*x - 210*a^4*b^3*x^(4/3) + 280*a^5*b^2*x^(5/3) - 420*a^6*b*x^2 + 840*a^7*x^(7/3)))/x^(8/3) - 840*a^8*Log[b + a*x^(1/3)] + 280*a^8*Log[x])/(280*b^9)","A",1
2428,1,158,179,0.1960418,"\int \frac{1}{\left(a+\frac{b}{\sqrt[3]{x}}\right) x^5} \, dx","Integrate[1/((a + b/x^(1/3))*x^5),x]","\frac{27720 a^{11} \log \left(a \sqrt[3]{x}+b\right)-9240 a^{11} \log (x)+\frac{b \left(-27720 a^{10} x^{10/3}+13860 a^9 b x^3-9240 a^8 b^2 x^{8/3}+6930 a^7 b^3 x^{7/3}-5544 a^6 b^4 x^2+4620 a^5 b^5 x^{5/3}-3960 a^4 b^6 x^{4/3}+3465 a^3 b^7 x-3080 a^2 b^8 x^{2/3}+2772 a b^9 \sqrt[3]{x}-2520 b^{10}\right)}{x^{11/3}}}{9240 b^{12}}","\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^{11} \sqrt[3]{x}}+\frac{3 a^9}{2 b^{10} x^{2/3}}-\frac{a^8}{b^9 x}+\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^2 x^{10/3}}-\frac{3}{11 b x^{11/3}}",1,"((b*(-2520*b^10 + 2772*a*b^9*x^(1/3) - 3080*a^2*b^8*x^(2/3) + 3465*a^3*b^7*x - 3960*a^4*b^6*x^(4/3) + 4620*a^5*b^5*x^(5/3) - 5544*a^6*b^4*x^2 + 6930*a^7*b^3*x^(7/3) - 9240*a^8*b^2*x^(8/3) + 13860*a^9*b*x^3 - 27720*a^10*x^(10/3)))/x^(11/3) + 27720*a^11*Log[b + a*x^(1/3)] - 9240*a^11*Log[x])/(9240*b^12)","A",1
2429,1,148,150,0.1972111,"\int \frac{x^2}{\left(a+\frac{b}{\sqrt[3]{x}}\right)^2} \, dx","Integrate[x^2/(a + b/x^(1/3))^2,x]","\frac{a \left(28 a^8 x^3-63 a^7 b x^{8/3}+108 a^6 b^2 x^{7/3}-168 a^5 b^3 x^2+252 a^4 b^4 x^{5/3}-378 a^3 b^5 x^{4/3}+588 a^2 b^6 x+\frac{252 b^9}{a+\frac{b}{\sqrt[3]{x}}}-1008 a b^7 x^{2/3}+2268 b^8 \sqrt[3]{x}\right)-2520 b^9 \log \left(a+\frac{b}{\sqrt[3]{x}}\right)-840 b^9 \log (x)}{84 a^{11}}","-\frac{3 b^{10}}{a^{11} \left(a \sqrt[3]{x}+b\right)}-\frac{30 b^9 \log \left(a \sqrt[3]{x}+b\right)}{a^{11}}+\frac{27 b^8 \sqrt[3]{x}}{a^{10}}-\frac{12 b^7 x^{2/3}}{a^9}+\frac{7 b^6 x}{a^8}-\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 x^{8/3}}{4 a^3}+\frac{x^3}{3 a^2}",1,"(a*((252*b^9)/(a + b/x^(1/3)) + 2268*b^8*x^(1/3) - 1008*a*b^7*x^(2/3) + 588*a^2*b^6*x - 378*a^3*b^5*x^(4/3) + 252*a^4*b^4*x^(5/3) - 168*a^5*b^3*x^2 + 108*a^6*b^2*x^(7/3) - 63*a^7*b*x^(8/3) + 28*a^8*x^3) - 2520*b^9*Log[a + b/x^(1/3)] - 840*b^9*Log[x])/(84*a^11)","A",1
2430,1,111,113,0.1408125,"\int \frac{x}{\left(a+\frac{b}{\sqrt[3]{x}}\right)^2} \, dx","Integrate[x/(a + b/x^(1/3))^2,x]","\frac{a \left(10 a^5 x^2-24 a^4 b x^{5/3}+45 a^3 b^2 x^{4/3}-80 a^2 b^3 x-\frac{60 b^6}{a+\frac{b}{\sqrt[3]{x}}}+150 a b^4 x^{2/3}-360 b^5 \sqrt[3]{x}\right)+420 b^6 \log \left(a+\frac{b}{\sqrt[3]{x}}\right)+140 b^6 \log (x)}{20 a^8}","\frac{3 b^7}{a^8 \left(a \sqrt[3]{x}+b\right)}+\frac{21 b^6 \log \left(a \sqrt[3]{x}+b\right)}{a^8}-\frac{18 b^5 \sqrt[3]{x}}{a^7}+\frac{15 b^4 x^{2/3}}{2 a^6}-\frac{4 b^3 x}{a^5}+\frac{9 b^2 x^{4/3}}{4 a^4}-\frac{6 b x^{5/3}}{5 a^3}+\frac{x^2}{2 a^2}",1,"(a*((-60*b^6)/(a + b/x^(1/3)) - 360*b^5*x^(1/3) + 150*a*b^4*x^(2/3) - 80*a^2*b^3*x + 45*a^3*b^2*x^(4/3) - 24*a^4*b*x^(5/3) + 10*a^5*x^2) + 420*b^6*Log[a + b/x^(1/3)] + 140*b^6*Log[x])/(20*a^8)","A",1
2431,1,63,77,0.0547656,"\int \frac{1}{\left(a+\frac{b}{\sqrt[3]{x}}\right)^2} \, dx","Integrate[(a + b/x^(1/3))^(-2),x]","\frac{a^3 x-3 a^2 b x^{2/3}-\frac{3 b^4}{a \sqrt[3]{x}+b}-12 b^3 \log \left(a \sqrt[3]{x}+b\right)+9 a b^2 \sqrt[3]{x}}{a^5}","-\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^3}{a^4 \left(a+\frac{b}{\sqrt[3]{x}}\right)}+\frac{9 b^2 \sqrt[3]{x}}{a^4}-\frac{3 b x^{2/3}}{a^3}+\frac{x}{a^2}",1,"((-3*b^4)/(b + a*x^(1/3)) + 9*a*b^2*x^(1/3) - 3*a^2*b*x^(2/3) + a^3*x - 12*b^3*Log[b + a*x^(1/3)])/a^5","A",1
2432,1,33,33,0.0318261,"\int \frac{1}{\left(a+\frac{b}{\sqrt[3]{x}}\right)^2 x} \, dx","Integrate[1/((a + b/x^(1/3))^2*x),x]","\frac{-\frac{3 a}{a+\frac{b}{\sqrt[3]{x}}}+3 \log \left(a+\frac{b}{\sqrt[3]{x}}\right)+\log (x)}{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*a)/(a + b/x^(1/3)) + 3*Log[a + b/x^(1/3)] + Log[x])/a^2","A",1
2433,1,46,52,0.0508252,"\int \frac{1}{\left(a+\frac{b}{\sqrt[3]{x}}\right)^2 x^2} \, dx","Integrate[1/((a + b/x^(1/3))^2*x^2),x]","\frac{-\frac{3 a b}{a \sqrt[3]{x}+b}+6 a \log \left(a \sqrt[3]{x}+b\right)-2 a \log (x)-\frac{3 b}{\sqrt[3]{x}}}{b^3}","\frac{6 a \log \left(a \sqrt[3]{x}+b\right)}{b^3}-\frac{2 a \log (x)}{b^3}-\frac{3 a}{b^2 \left(a \sqrt[3]{x}+b\right)}-\frac{3}{b^2 \sqrt[3]{x}}",1,"((-3*a*b)/(b + a*x^(1/3)) - (3*b)/x^(1/3) + 6*a*Log[b + a*x^(1/3)] - 2*a*Log[x])/b^3","A",1
2434,1,82,97,0.1017129,"\int \frac{1}{\left(a+\frac{b}{\sqrt[3]{x}}\right)^2 x^3} \, dx","Integrate[1/((a + b/x^(1/3))^2*x^3),x]","-\frac{\frac{12 a^5}{a+\frac{b}{\sqrt[3]{x}}}+60 a^4 \log \left(a+\frac{b}{\sqrt[3]{x}}\right)-\frac{48 a^3 b}{\sqrt[3]{x}}+\frac{18 a^2 b^2}{x^{2/3}}-\frac{8 a b^3}{x}+\frac{3 b^4}{x^{4/3}}}{4 b^6}","-\frac{15 a^4 \log \left(a \sqrt[3]{x}+b\right)}{b^6}+\frac{5 a^4 \log (x)}{b^6}+\frac{3 a^4}{b^5 \left(a \sqrt[3]{x}+b\right)}+\frac{12 a^3}{b^5 \sqrt[3]{x}}-\frac{9 a^2}{2 b^4 x^{2/3}}+\frac{2 a}{b^3 x}-\frac{3}{4 b^2 x^{4/3}}",1,"-1/4*((12*a^5)/(a + b/x^(1/3)) + (3*b^4)/x^(4/3) - (8*a*b^3)/x + (18*a^2*b^2)/x^(2/3) - (48*a^3*b)/x^(1/3) + 60*a^4*Log[a + b/x^(1/3)])/b^6","A",1
2435,1,123,133,0.1272715,"\int \frac{1}{\left(a+\frac{b}{\sqrt[3]{x}}\right)^2 x^4} \, dx","Integrate[1/((a + b/x^(1/3))^2*x^4),x]","\frac{3 a^8}{b^9 \left(a+\frac{b}{\sqrt[3]{x}}\right)}+\frac{24 a^7 \log \left(a+\frac{b}{\sqrt[3]{x}}\right)}{b^9}-\frac{21 a^6}{b^8 \sqrt[3]{x}}+\frac{9 a^5}{b^7 x^{2/3}}-\frac{5 a^4}{b^6 x}+\frac{3 a^3}{b^5 x^{4/3}}-\frac{9 a^2}{5 b^4 x^{5/3}}+\frac{a}{b^3 x^2}-\frac{3}{7 b^2 x^{7/3}}","\frac{24 a^7 \log \left(a \sqrt[3]{x}+b\right)}{b^9}-\frac{8 a^7 \log (x)}{b^9}-\frac{3 a^7}{b^8 \left(a \sqrt[3]{x}+b\right)}-\frac{21 a^6}{b^8 \sqrt[3]{x}}+\frac{9 a^5}{b^7 x^{2/3}}-\frac{5 a^4}{b^6 x}+\frac{3 a^3}{b^5 x^{4/3}}-\frac{9 a^2}{5 b^4 x^{5/3}}+\frac{a}{b^3 x^2}-\frac{3}{7 b^2 x^{7/3}}",1,"(3*a^8)/(b^9*(a + b/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[a + b/x^(1/3)])/b^9","A",1
2436,1,173,183,0.1641748,"\int \frac{1}{\left(a+\frac{b}{\sqrt[3]{x}}\right)^2 x^5} \, dx","Integrate[1/((a + b/x^(1/3))^2*x^5),x]","-\frac{3 a^{11}}{b^{12} \left(a+\frac{b}{\sqrt[3]{x}}\right)}-\frac{33 a^{10} \log \left(a+\frac{b}{\sqrt[3]{x}}\right)}{b^{12}}+\frac{30 a^9}{b^{11} \sqrt[3]{x}}-\frac{27 a^8}{2 b^{10} x^{2/3}}+\frac{8 a^7}{b^9 x}-\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{2 a}{3 b^3 x^3}-\frac{3}{10 b^2 x^{10/3}}","-\frac{33 a^{10} \log \left(a \sqrt[3]{x}+b\right)}{b^{12}}+\frac{11 a^{10} \log (x)}{b^{12}}+\frac{3 a^{10}}{b^{11} \left(a \sqrt[3]{x}+b\right)}+\frac{30 a^9}{b^{11} \sqrt[3]{x}}-\frac{27 a^8}{2 b^{10} x^{2/3}}+\frac{8 a^7}{b^9 x}-\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{2 a}{3 b^3 x^3}-\frac{3}{10 b^2 x^{10/3}}",1,"(-3*a^11)/(b^12*(a + b/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[a + b/x^(1/3)])/b^12","A",1
2437,1,157,171,0.1642995,"\int \frac{x^2}{\left(a+\frac{b}{\sqrt[3]{x}}\right)^3} \, dx","Integrate[x^2/(a + b/x^(1/3))^3,x]","\frac{56 a^9 x^3-189 a^8 b x^{8/3}+432 a^7 b^2 x^{7/3}-840 a^6 b^3 x^2+1512 a^5 b^4 x^{5/3}-2646 a^4 b^5 x^{4/3}+4704 a^3 b^6 x-9072 a^2 b^7 x^{2/3}+\frac{252 b^{11}}{\left(a \sqrt[3]{x}+b\right)^2}-\frac{5544 b^{10}}{a \sqrt[3]{x}+b}-27720 b^9 \log \left(a \sqrt[3]{x}+b\right)+22680 a b^8 \sqrt[3]{x}}{168 a^{12}}","\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{165 b^9 \log \left(a \sqrt[3]{x}+b\right)}{a^{12}}+\frac{135 b^8 \sqrt[3]{x}}{a^{11}}-\frac{54 b^7 x^{2/3}}{a^{10}}+\frac{28 b^6 x}{a^9}-\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{9 b x^{8/3}}{8 a^4}+\frac{x^3}{3 a^3}",1,"((252*b^11)/(b + a*x^(1/3))^2 - (5544*b^10)/(b + a*x^(1/3)) + 22680*a*b^8*x^(1/3) - 9072*a^2*b^7*x^(2/3) + 4704*a^3*b^6*x - 2646*a^4*b^5*x^(4/3) + 1512*a^5*b^4*x^(5/3) - 840*a^6*b^3*x^2 + 432*a^7*b^2*x^(7/3) - 189*a^8*b*x^(8/3) + 56*a^9*x^3 - 27720*b^9*Log[b + a*x^(1/3)])/(168*a^12)","A",1
2438,1,132,134,0.1564251,"\int \frac{x}{\left(a+\frac{b}{\sqrt[3]{x}}\right)^3} \, dx","Integrate[x/(a + b/x^(1/3))^3,x]","\frac{\frac{a \sqrt[3]{x} \left(5 a^7 x^{7/3}-8 a^6 b x^2+14 a^5 b^2 x^{5/3}-28 a^4 b^3 x^{4/3}+70 a^3 b^4 x-280 a^2 b^5 x^{2/3}-1260 a b^6 \sqrt[3]{x}-840 b^7\right)}{\left(a \sqrt[3]{x}+b\right)^2}+840 b^6 \log \left(a+\frac{b}{\sqrt[3]{x}}\right)+280 b^6 \log (x)}{10 a^9}","-\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{84 b^6 \log \left(a \sqrt[3]{x}+b\right)}{a^9}-\frac{63 b^5 \sqrt[3]{x}}{a^8}+\frac{45 b^4 x^{2/3}}{2 a^7}-\frac{10 b^3 x}{a^6}+\frac{9 b^2 x^{4/3}}{2 a^5}-\frac{9 b x^{5/3}}{5 a^4}+\frac{x^2}{2 a^3}",1,"((a*x^(1/3)*(-840*b^7 - 1260*a*b^6*x^(1/3) - 280*a^2*b^5*x^(2/3) + 70*a^3*b^4*x - 28*a^4*b^3*x^(4/3) + 14*a^5*b^2*x^(5/3) - 8*a^6*b*x^2 + 5*a^7*x^(7/3)))/(b + a*x^(1/3))^2 + 840*b^6*Log[a + b/x^(1/3)] + 280*b^6*Log[x])/(10*a^9)","A",1
2439,1,83,100,0.0817957,"\int \frac{1}{\left(a+\frac{b}{\sqrt[3]{x}}\right)^3} \, dx","Integrate[(a + b/x^(1/3))^(-3),x]","\frac{2 a^3 x-9 a^2 b x^{2/3}+\frac{3 b^5}{\left(a \sqrt[3]{x}+b\right)^2}-\frac{30 b^4}{a \sqrt[3]{x}+b}-60 b^3 \log \left(a \sqrt[3]{x}+b\right)+36 a b^2 \sqrt[3]{x}}{2 a^6}","-\frac{30 b^3 \log \left(a+\frac{b}{\sqrt[3]{x}}\right)}{a^6}-\frac{10 b^3 \log (x)}{a^6}+\frac{12 b^3}{a^5 \left(a+\frac{b}{\sqrt[3]{x}}\right)}+\frac{18 b^2 \sqrt[3]{x}}{a^5}+\frac{3 b^3}{2 a^4 \left(a+\frac{b}{\sqrt[3]{x}}\right)^2}-\frac{9 b x^{2/3}}{2 a^4}+\frac{x}{a^3}",1,"((3*b^5)/(b + a*x^(1/3))^2 - (30*b^4)/(b + a*x^(1/3)) + 36*a*b^2*x^(1/3) - 9*a^2*b*x^(2/3) + 2*a^3*x - 60*b^3*Log[b + a*x^(1/3)])/(2*a^6)","A",1
2440,1,45,54,0.0407745,"\int \frac{1}{\left(a+\frac{b}{\sqrt[3]{x}}\right)^3 x} \, dx","Integrate[1/((a + b/x^(1/3))^3*x),x]","\frac{3 \left(\frac{b \left(4 a \sqrt[3]{x}+3 b\right)}{\left(a \sqrt[3]{x}+b\right)^2}+2 \log \left(a \sqrt[3]{x}+b\right)\right)}{2 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*(3*b + 4*a*x^(1/3)))/(b + a*x^(1/3))^2 + 2*Log[b + a*x^(1/3)]))/(2*a^3)","A",1
2441,1,50,56,0.060874,"\int \frac{1}{\left(a+\frac{b}{\sqrt[3]{x}}\right)^3 x^2} \, dx","Integrate[1/((a + b/x^(1/3))^3*x^2),x]","\frac{\frac{3 b \left(2 a \sqrt[3]{x}+3 b\right)}{\left(a \sqrt[3]{x}+b\right)^2}-6 \log \left(a \sqrt[3]{x}+b\right)+2 \log (x)}{2 b^3}","-\frac{3 \log \left(a \sqrt[3]{x}+b\right)}{b^3}+\frac{3}{b^2 \left(a \sqrt[3]{x}+b\right)}+\frac{3}{2 b \left(a \sqrt[3]{x}+b\right)^2}+\frac{\log (x)}{b^3}",1,"((3*b*(3*b + 2*a*x^(1/3)))/(b + a*x^(1/3))^2 - 6*Log[b + a*x^(1/3)] + 2*Log[x])/(2*b^3)","A",1
2442,1,93,103,0.155562,"\int \frac{1}{\left(a+\frac{b}{\sqrt[3]{x}}\right)^3 x^3} \, dx","Integrate[1/((a + b/x^(1/3))^3*x^3),x]","-\frac{-60 a^3 \log \left(a \sqrt[3]{x}+b\right)+20 a^3 \log (x)+\frac{b \left(60 a^4 x^{4/3}+90 a^3 b x+20 a^2 b^2 x^{2/3}-5 a b^3 \sqrt[3]{x}+2 b^4\right)}{x \left(a \sqrt[3]{x}+b\right)^2}}{2 b^6}","\frac{30 a^3 \log \left(a \sqrt[3]{x}+b\right)}{b^6}-\frac{10 a^3 \log (x)}{b^6}-\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{9 a}{2 b^4 x^{2/3}}-\frac{1}{b^3 x}",1,"-1/2*((b*(2*b^4 - 5*a*b^3*x^(1/3) + 20*a^2*b^2*x^(2/3) + 90*a^3*b*x + 60*a^4*x^(4/3)))/((b + a*x^(1/3))^2*x) - 60*a^3*Log[b + a*x^(1/3)] + 20*a^3*Log[x])/b^6","A",1
2443,1,130,146,0.1718498,"\int \frac{1}{\left(a+\frac{b}{\sqrt[3]{x}}\right)^3 x^4} \, dx","Integrate[1/((a + b/x^(1/3))^3*x^4),x]","\frac{-840 a^6 \log \left(a \sqrt[3]{x}+b\right)+280 a^6 \log (x)+\frac{b \left(840 a^7 x^{7/3}+1260 a^6 b x^2+280 a^5 b^2 x^{5/3}-70 a^4 b^3 x^{4/3}+28 a^3 b^4 x-14 a^2 b^5 x^{2/3}+8 a b^6 \sqrt[3]{x}-5 b^7\right)}{x^2 \left(a \sqrt[3]{x}+b\right)^2}}{10 b^9}","-\frac{84 a^6 \log \left(a \sqrt[3]{x}+b\right)}{b^9}+\frac{28 a^6 \log (x)}{b^9}+\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{45 a^4}{2 b^7 x^{2/3}}+\frac{10 a^3}{b^6 x}-\frac{9 a^2}{2 b^5 x^{4/3}}+\frac{9 a}{5 b^4 x^{5/3}}-\frac{1}{2 b^3 x^2}",1,"((b*(-5*b^7 + 8*a*b^6*x^(1/3) - 14*a^2*b^5*x^(2/3) + 28*a^3*b^4*x - 70*a^4*b^3*x^(4/3) + 280*a^5*b^2*x^(5/3) + 1260*a^6*b*x^2 + 840*a^7*x^(7/3)))/((b + a*x^(1/3))^2*x^2) - 840*a^6*Log[b + a*x^(1/3)] + 280*a^6*Log[x])/(10*b^9)","A",1
2444,1,167,183,0.2824753,"\int \frac{1}{\left(a+\frac{b}{\sqrt[3]{x}}\right)^3 x^5} \, dx","Integrate[1/((a + b/x^(1/3))^3*x^5),x]","-\frac{-27720 a^9 \log \left(a \sqrt[3]{x}+b\right)+9240 a^9 \log (x)+\frac{b \left(27720 a^{10} x^{10/3}+41580 a^9 b x^3+9240 a^8 b^2 x^{8/3}-2310 a^7 b^3 x^{7/3}+924 a^6 b^4 x^2-462 a^5 b^5 x^{5/3}+264 a^4 b^6 x^{4/3}-165 a^3 b^7 x+110 a^2 b^8 x^{2/3}-77 a b^9 \sqrt[3]{x}+56 b^{10}\right)}{x^3 \left(a \sqrt[3]{x}+b\right)^2}}{168 b^{12}}","\frac{165 a^9 \log \left(a \sqrt[3]{x}+b\right)}{b^{12}}-\frac{55 a^9 \log (x)}{b^{12}}-\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{54 a^7}{b^{10} x^{2/3}}-\frac{28 a^6}{b^9 x}+\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{9 a}{8 b^4 x^{8/3}}-\frac{1}{3 b^3 x^3}",1,"-1/168*((b*(56*b^10 - 77*a*b^9*x^(1/3) + 110*a^2*b^8*x^(2/3) - 165*a^3*b^7*x + 264*a^4*b^6*x^(4/3) - 462*a^5*b^5*x^(5/3) + 924*a^6*b^4*x^2 - 2310*a^7*b^3*x^(7/3) + 9240*a^8*b^2*x^(8/3) + 41580*a^9*b*x^3 + 27720*a^10*x^(10/3)))/((b + a*x^(1/3))^2*x^3) - 27720*a^9*Log[b + a*x^(1/3)] + 9240*a^9*Log[x])/b^12","A",1
2445,1,35,44,0.0196306,"\int \frac{1}{1+\frac{b}{\sqrt[3]{x}}} \, dx","Integrate[(1 + b/x^(1/3))^(-1),x]","-3 b^3 \log \left(b+\sqrt[3]{x}\right)+3 b^2 \sqrt[3]{x}-\frac{3}{2} b x^{2/3}+x","-3 b^3 \log \left(\frac{b}{\sqrt[3]{x}}+1\right)-b^3 \log (x)+3 b^2 \sqrt[3]{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[b + x^(1/3)]","A",1
2446,1,15,15,0.0049753,"\int x^{2/3} \left(1+x^{5/3}\right)^{2/3} \, dx","Integrate[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
2447,1,21,21,0.0125127,"\int x^{7/3} \left(a^{10/3}-x^{10/3}\right)^{19/7} \, dx","Integrate[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
2448,1,45,45,0.0188127,"\int \frac{1}{1+\sqrt[5]{x}} \, dx","Integrate[(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",1
2449,1,15,15,0.0042707,"\int \frac{1}{\sqrt{1+x^{4/5}} \sqrt[5]{x}} \, dx","Integrate[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
2450,1,18,18,0.0192145,"\int \left(a+\frac{b}{x^{3/5}}\right)^{2/3} \, dx","Integrate[(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
2451,1,21,21,0.0168378,"\int x^3 \left(a+b x^n\right) \, dx","Integrate[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",1
2452,1,21,21,0.014929,"\int x^2 \left(a+b x^n\right) \, dx","Integrate[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",1
2453,1,21,21,0.015208,"\int x \left(a+b x^n\right) \, dx","Integrate[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",1
2454,1,16,16,0.0060347,"\int \left(a+b x^n\right) \, dx","Integrate[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
2455,1,13,13,0.0096491,"\int \frac{a+b x^n}{x} \, dx","Integrate[(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",1
2456,1,22,22,0.0105506,"\int \frac{a+b x^n}{x^2} \, dx","Integrate[(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",1
2457,1,20,24,0.0229403,"\int \frac{a+b x^n}{x^3} \, dx","Integrate[(a + b*x^n)/x^3,x]","-\frac{a-\frac{2 b x^n}{n-2}}{2 x^2}","-\frac{a}{2 x^2}-\frac{b x^{n-2}}{2-n}",1,"-1/2*(a - (2*b*x^n)/(-2 + n))/x^2","A",1
2458,1,38,44,0.0387752,"\int x^3 \left(a+b x^n\right)^2 \, dx","Integrate[x^3*(a + b*x^n)^2,x]","\frac{1}{4} x^4 \left(a^2+\frac{8 a b x^n}{n+4}+\frac{2 b^2 x^{2 n}}{n+2}\right)","\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,"(x^4*(a^2 + (8*a*b*x^n)/(4 + n) + (2*b^2*x^(2*n))/(2 + n)))/4","A",1
2459,1,40,43,0.0380764,"\int x^2 \left(a+b x^n\right)^2 \, dx","Integrate[x^2*(a + b*x^n)^2,x]","\frac{1}{3} x^3 \left(a^2+\frac{6 a b x^n}{n+3}+\frac{3 b^2 x^{2 n}}{2 n+3}\right)","\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,"(x^3*(a^2 + (6*a*b*x^n)/(3 + n) + (3*b^2*x^(2*n))/(3 + 2*n)))/3","A",1
2460,1,37,44,0.0340544,"\int x \left(a+b x^n\right)^2 \, dx","Integrate[x*(a + b*x^n)^2,x]","\frac{1}{2} x^2 \left(a^2+\frac{4 a b x^n}{n+2}+\frac{b^2 x^{2 n}}{n+1}\right)","\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,"(x^2*(a^2 + (4*a*b*x^n)/(2 + n) + (b^2*x^(2*n))/(1 + n)))/2","A",1
2461,1,34,38,0.0330265,"\int \left(a+b x^n\right)^2 \, dx","Integrate[(a + b*x^n)^2,x]","x \left(a^2+\frac{2 a b x^n}{n+1}+\frac{b^2 x^{2 n}}{2 n+1}\right)","a^2 x+\frac{2 a b x^{n+1}}{n+1}+\frac{b^2 x^{2 n+1}}{2 n+1}",1,"x*(a^2 + (2*a*b*x^n)/(1 + n) + (b^2*x^(2*n))/(1 + 2*n))","A",1
2462,1,27,32,0.0187315,"\int \frac{\left(a+b x^n\right)^2}{x} \, dx","Integrate[(a + b*x^n)^2/x,x]","a^2 \log (x)+\frac{b x^n \left(4 a+b x^n\right)}{2 n}","a^2 \log (x)+\frac{2 a b x^n}{n}+\frac{b^2 x^{2 n}}{2 n}",1,"(b*x^n*(4*a + b*x^n))/(2*n) + a^2*Log[x]","A",1
2463,1,38,44,0.0414666,"\int \frac{\left(a+b x^n\right)^2}{x^2} \, dx","Integrate[(a + b*x^n)^2/x^2,x]","\frac{-a^2+\frac{2 a b x^n}{n-1}+\frac{b^2 x^{2 n}}{2 n-1}}{x}","-\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 + (2*a*b*x^n)/(-1 + n) + (b^2*x^(2*n))/(-1 + 2*n))/x","A",1
2464,1,39,50,0.04053,"\int \frac{\left(a+b x^n\right)^2}{x^3} \, dx","Integrate[(a + b*x^n)^2/x^3,x]","\frac{-a^2+\frac{4 a b x^n}{n-2}+\frac{b^2 x^{2 n}}{n-1}}{2 x^2}","-\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 + (4*a*b*x^n)/(-2 + n) + (b^2*x^(2*n))/(-1 + n))/(2*x^2)","A",1
2465,1,58,65,0.0445793,"\int x^3 \left(a+b x^n\right)^3 \, dx","Integrate[x^3*(a + b*x^n)^3,x]","\frac{1}{4} x^4 \left(a^3+\frac{12 a^2 b x^n}{n+4}+\frac{6 a b^2 x^{2 n}}{n+2}+\frac{4 b^3 x^{3 n}}{3 n+4}\right)","\frac{a^3 x^4}{4}+\frac{3 a^2 b x^{n+4}}{n+4}+\frac{3 a b^2 x^{2 (n+2)}}{2 (n+2)}+\frac{b^3 x^{3 n+4}}{3 n+4}",1,"(x^4*(a^3 + (12*a^2*b*x^n)/(4 + n) + (6*a*b^2*x^(2*n))/(2 + n) + (4*b^3*x^(3*n))/(4 + 3*n)))/4","A",1
2466,1,57,66,0.038891,"\int x^2 \left(a+b x^n\right)^3 \, dx","Integrate[x^2*(a + b*x^n)^3,x]","\frac{1}{3} x^3 \left(a^3+\frac{9 a^2 b x^n}{n+3}+\frac{9 a b^2 x^{2 n}}{2 n+3}+\frac{b^3 x^{3 n}}{n+1}\right)","\frac{a^3 x^3}{3}+\frac{3 a^2 b x^{n+3}}{n+3}+\frac{3 a b^2 x^{2 n+3}}{2 n+3}+\frac{b^3 x^{3 (n+1)}}{3 (n+1)}",1,"(x^3*(a^3 + (9*a^2*b*x^n)/(3 + n) + (9*a*b^2*x^(2*n))/(3 + 2*n) + (b^3*x^(3*n))/(1 + n)))/3","A",1
2467,1,58,65,0.0387894,"\int x \left(a+b x^n\right)^3 \, dx","Integrate[x*(a + b*x^n)^3,x]","\frac{1}{2} x^2 \left(a^3+\frac{6 a^2 b x^n}{n+2}+\frac{3 a b^2 x^{2 n}}{n+1}+\frac{2 b^3 x^{3 n}}{3 n+2}\right)","\frac{a^3 x^2}{2}+\frac{3 a^2 b x^{n+2}}{n+2}+\frac{3 a b^2 x^{2 (n+1)}}{2 (n+1)}+\frac{b^3 x^{3 n+2}}{3 n+2}",1,"(x^2*(a^3 + (6*a^2*b*x^n)/(2 + n) + (3*a*b^2*x^(2*n))/(1 + n) + (2*b^3*x^(3*n))/(2 + 3*n)))/2","A",1
2468,1,54,60,0.0343959,"\int \left(a+b x^n\right)^3 \, dx","Integrate[(a + b*x^n)^3,x]","x \left(a^3+\frac{3 a^2 b x^n}{n+1}+\frac{3 a b^2 x^{2 n}}{2 n+1}+\frac{b^3 x^{3 n}}{3 n+1}\right)","a^3 x+\frac{3 a^2 b x^{n+1}}{n+1}+\frac{3 a b^2 x^{2 n+1}}{2 n+1}+\frac{b^3 x^{3 n+1}}{3 n+1}",1,"x*(a^3 + (3*a^2*b*x^n)/(1 + n) + (3*a*b^2*x^(2*n))/(1 + 2*n) + (b^3*x^(3*n))/(1 + 3*n))","A",1
2469,1,41,50,0.0259728,"\int \frac{\left(a+b x^n\right)^3}{x} \, dx","Integrate[(a + b*x^n)^3/x,x]","a^3 \log (x)+\frac{b x^n \left(18 a^2+9 a b x^n+2 b^2 x^{2 n}\right)}{6 n}","a^3 \log (x)+\frac{3 a^2 b x^n}{n}+\frac{3 a b^2 x^{2 n}}{2 n}+\frac{b^3 x^{3 n}}{3 n}",1,"(b*x^n*(18*a^2 + 9*a*b*x^n + 2*b^2*x^(2*n)))/(6*n) + a^3*Log[x]","A",1
2470,1,58,66,0.0541878,"\int \frac{\left(a+b x^n\right)^3}{x^2} \, dx","Integrate[(a + b*x^n)^3/x^2,x]","\frac{-a^3+\frac{3 a^2 b x^n}{n-1}+\frac{3 a b^2 x^{2 n}}{2 n-1}+\frac{b^3 x^{3 n}}{3 n-1}}{x}","-\frac{a^3}{x}-\frac{3 a^2 b x^{n-1}}{1-n}-\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 + (3*a^2*b*x^n)/(-1 + n) + (3*a*b^2*x^(2*n))/(-1 + 2*n) + (b^3*x^(3*n))/(-1 + 3*n))/x","A",1
2471,1,60,72,0.053144,"\int \frac{\left(a+b x^n\right)^3}{x^3} \, dx","Integrate[(a + b*x^n)^3/x^3,x]","\frac{-a^3+\frac{6 a^2 b x^n}{n-2}+\frac{3 a b^2 x^{2 n}}{n-1}+\frac{2 b^3 x^{3 n}}{3 n-2}}{2 x^2}","-\frac{a^3}{2 x^2}-\frac{3 a^2 b x^{n-2}}{2-n}-\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 + (6*a^2*b*x^n)/(-2 + n) + (3*a*b^2*x^(2*n))/(-1 + n) + (2*b^3*x^(3*n))/(-2 + 3*n))/(2*x^2)","A",1
2472,1,33,33,0.003091,"\int \frac{x}{a+b x^n} \, dx","Integrate[x/(a + b*x^n),x]","\frac{x^2 \, _2F_1\left(1,\frac{2}{n};1+\frac{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, 1 + 2/n, -((b*x^n)/a)])/(2*a)","A",1
2473,1,24,24,0.0022848,"\int \frac{1}{a+b x^n} \, dx","Integrate[(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
2474,1,22,23,0.0069885,"\int \frac{1}{x \left(a+b x^n\right)} \, dx","Integrate[1/(x*(a + b*x^n)),x]","\frac{n \log (x)-\log \left(a+b x^n\right)}{a n}","\frac{\log (x)}{a}-\frac{\log \left(a+b x^n\right)}{a n}",1,"(n*Log[x] - Log[a + b*x^n])/(a*n)","A",1
2475,1,31,34,0.0031325,"\int \frac{1}{x^2 \left(a+b x^n\right)} \, dx","Integrate[1/(x^2*(a + b*x^n)),x]","-\frac{\, _2F_1\left(1,-\frac{1}{n};1-\frac{1}{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^(-1), -((b*x^n)/a)]/(a*x))","A",1
2476,1,33,36,0.0029617,"\int \frac{1}{x^3 \left(a+b x^n\right)} \, dx","Integrate[1/(x^3*(a + b*x^n)),x]","-\frac{\, _2F_1\left(1,-\frac{2}{n};1-\frac{2}{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,"-1/2*Hypergeometric2F1[1, -2/n, 1 - 2/n, -((b*x^n)/a)]/(a*x^2)","A",1
2477,1,33,33,0.0033022,"\int \frac{x}{\left(a+b x^n\right)^2} \, dx","Integrate[x/(a + b*x^n)^2,x]","\frac{x^2 \, _2F_1\left(2,\frac{2}{n};1+\frac{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, 1 + 2/n, -((b*x^n)/a)])/(2*a^2)","A",1
2478,1,24,24,0.0021989,"\int \frac{1}{\left(a+b x^n\right)^2} \, dx","Integrate[(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
2479,1,33,39,0.0620246,"\int \frac{1}{x \left(a+b x^n\right)^2} \, dx","Integrate[1/(x*(a + b*x^n)^2),x]","\frac{\frac{a}{a+b x^n}-\log \left(a+b x^n\right)+n \log (x)}{a^2 n}","-\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,"(a/(a + b*x^n) + n*Log[x] - Log[a + b*x^n])/(a^2*n)","A",1
2480,1,31,34,0.003916,"\int \frac{1}{x^2 \left(a+b x^n\right)^2} \, dx","Integrate[1/(x^2*(a + b*x^n)^2),x]","-\frac{\, _2F_1\left(2,-\frac{1}{n};1-\frac{1}{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^(-1), -((b*x^n)/a)]/(a^2*x))","A",1
2481,1,33,36,0.0031925,"\int \frac{1}{x^3 \left(a+b x^n\right)^2} \, dx","Integrate[1/(x^3*(a + b*x^n)^2),x]","-\frac{\, _2F_1\left(2,-\frac{2}{n};1-\frac{2}{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,"-1/2*Hypergeometric2F1[2, -2/n, 1 - 2/n, -((b*x^n)/a)]/(a^2*x^2)","A",1
2482,1,33,33,0.0034174,"\int \frac{x}{\left(a+b x^n\right)^3} \, dx","Integrate[x/(a + b*x^n)^3,x]","\frac{x^2 \, _2F_1\left(3,\frac{2}{n};1+\frac{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, 1 + 2/n, -((b*x^n)/a)])/(2*a^3)","A",1
2483,1,24,24,0.0021229,"\int \frac{1}{\left(a+b x^n\right)^3} \, dx","Integrate[(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
2484,1,47,58,0.1225294,"\int \frac{1}{x \left(a+b x^n\right)^3} \, dx","Integrate[1/(x*(a + b*x^n)^3),x]","\frac{\frac{a \left(3 a+2 b x^n\right)}{\left(a+b x^n\right)^2}-2 \log \left(a+b x^n\right)+2 n \log (x)}{2 a^3 n}","-\frac{\log \left(a+b x^n\right)}{a^3 n}+\frac{\log (x)}{a^3}+\frac{1}{a^2 n \left(a+b x^n\right)}+\frac{1}{2 a n \left(a+b x^n\right)^2}",1,"((a*(3*a + 2*b*x^n))/(a + b*x^n)^2 + 2*n*Log[x] - 2*Log[a + b*x^n])/(2*a^3*n)","A",1
2485,1,31,34,0.0036575,"\int \frac{1}{x^2 \left(a+b x^n\right)^3} \, dx","Integrate[1/(x^2*(a + b*x^n)^3),x]","-\frac{\, _2F_1\left(3,-\frac{1}{n};1-\frac{1}{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^(-1), -((b*x^n)/a)]/(a^3*x))","A",1
2486,1,33,36,0.0035983,"\int \frac{1}{x^3 \left(a+b x^n\right)^3} \, dx","Integrate[1/(x^3*(a + b*x^n)^3),x]","-\frac{\, _2F_1\left(3,-\frac{2}{n};1-\frac{2}{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,"-1/2*Hypergeometric2F1[3, -2/n, 1 - 2/n, -((b*x^n)/a)]/(a^3*x^2)","A",1
2487,1,57,48,0.0189623,"\int x \sqrt{a+b x^n} \, dx","Integrate[x*Sqrt[a + b*x^n],x]","\frac{x^2 \sqrt{a+b x^n} \, _2F_1\left(-\frac{1}{2},\frac{2}{n};1+\frac{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, 1 + 2/n, -((b*x^n)/a)])/(2*Sqrt[1 + (b*x^n)/a])","A",1
2488,1,48,39,0.008084,"\int \sqrt{a+b x^n} \, dx","Integrate[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",1
2489,1,43,45,0.0123711,"\int \frac{\sqrt{a+b x^n}}{x} \, dx","Integrate[Sqrt[a + b*x^n]/x,x]","\frac{2 \sqrt{a+b x^n}-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] - 2*Sqrt[a]*ArcTanh[Sqrt[a + b*x^n]/Sqrt[a]])/n","A",1
2490,1,55,49,0.0134737,"\int \frac{\sqrt{a+b x^n}}{x^2} \, dx","Integrate[Sqrt[a + b*x^n]/x^2,x]","-\frac{\sqrt{a+b x^n} \, _2F_1\left(-\frac{1}{2},-\frac{1}{n};1-\frac{1}{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^(-1), -((b*x^n)/a)])/(x*Sqrt[1 + (b*x^n)/a]))","A",1
2491,1,57,51,0.0136222,"\int \frac{\sqrt{a+b x^n}}{x^3} \, dx","Integrate[Sqrt[a + b*x^n]/x^3,x]","-\frac{\sqrt{a+b x^n} \, _2F_1\left(-\frac{1}{2},-\frac{2}{n};1-\frac{2}{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,"-1/2*(Sqrt[a + b*x^n]*Hypergeometric2F1[-1/2, -2/n, 1 - 2/n, -((b*x^n)/a)])/(x^2*Sqrt[1 + (b*x^n)/a])","A",1
2492,1,58,48,0.0295977,"\int x \left(a+b x^n\right)^{3/2} \, dx","Integrate[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};1+\frac{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, 1 + 2/n, -((b*x^n)/a)])/(2*Sqrt[1 + (b*x^n)/a])","A",1
2493,1,49,39,0.0073521,"\int \left(a+b x^n\right)^{3/2} \, dx","Integrate[(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",1
2494,1,55,64,0.0246256,"\int \frac{\left(a+b x^n\right)^{3/2}}{x} \, dx","Integrate[(a + b*x^n)^(3/2)/x,x]","\frac{2 \sqrt{a+b x^n} \left(4 a+b x^n\right)-6 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b x^n}}{\sqrt{a}}\right)}{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*Sqrt[a + b*x^n]*(4*a + b*x^n) - 6*a^(3/2)*ArcTanh[Sqrt[a + b*x^n]/Sqrt[a]])/(3*n)","A",1
2495,1,56,49,0.0144134,"\int \frac{\left(a+b x^n\right)^{3/2}}{x^2} \, dx","Integrate[(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};1-\frac{1}{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^(-1), -((b*x^n)/a)])/(x*Sqrt[1 + (b*x^n)/a]))","A",1
2496,1,58,51,0.0123827,"\int \frac{\left(a+b x^n\right)^{3/2}}{x^3} \, dx","Integrate[(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};1-\frac{2}{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,"-1/2*(a*Sqrt[a + b*x^n]*Hypergeometric2F1[-3/2, -2/n, 1 - 2/n, -((b*x^n)/a)])/(x^2*Sqrt[1 + (b*x^n)/a])","A",1
2497,1,60,48,0.0146685,"\int x \left(a+b x^n\right)^{5/2} \, dx","Integrate[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};1+\frac{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, 1 + 2/n, -((b*x^n)/a)])/(2*Sqrt[1 + (b*x^n)/a])","A",1
2498,1,51,39,0.008114,"\int \left(a+b x^n\right)^{5/2} \, dx","Integrate[(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",1
2499,1,69,85,0.0453081,"\int \frac{\left(a+b x^n\right)^{5/2}}{x} \, dx","Integrate[(a + b*x^n)^(5/2)/x,x]","\frac{2 \sqrt{a+b x^n} \left(23 a^2+11 a b x^n+3 b^2 x^{2 n}\right)-30 a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+b x^n}}{\sqrt{a}}\right)}{15 n}","-\frac{2 a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+b x^n}}{\sqrt{a}}\right)}{n}+\frac{2 a^2 \sqrt{a+b x^n}}{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*Sqrt[a + b*x^n]*(23*a^2 + 11*a*b*x^n + 3*b^2*x^(2*n)) - 30*a^(5/2)*ArcTanh[Sqrt[a + b*x^n]/Sqrt[a]])/(15*n)","A",1
2500,1,58,49,0.036573,"\int \frac{\left(a+b x^n\right)^{5/2}}{x^2} \, dx","Integrate[(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};1-\frac{1}{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^(-1), -((b*x^n)/a)])/(x*Sqrt[1 + (b*x^n)/a]))","A",1
2501,1,60,51,0.0133774,"\int \frac{\left(a+b x^n\right)^{5/2}}{x^3} \, dx","Integrate[(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};1-\frac{2}{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,"-1/2*(a^2*Sqrt[a + b*x^n]*Hypergeometric2F1[-5/2, -2/n, 1 - 2/n, -((b*x^n)/a)])/(x^2*Sqrt[1 + (b*x^n)/a])","A",1
2502,1,57,48,0.0156077,"\int \frac{x}{\sqrt{a+b x^n}} \, dx","Integrate[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};1+\frac{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, 1 + 2/n, -((b*x^n)/a)])/(2*Sqrt[a + b*x^n])","A",1
2503,1,48,39,0.0094376,"\int \frac{1}{\sqrt{a+b x^n}} \, dx","Integrate[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",1
2504,1,28,28,0.0051168,"\int \frac{1}{x \sqrt{a+b x^n}} \, dx","Integrate[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",1
2505,1,55,49,0.0229907,"\int \frac{1}{x^2 \sqrt{a+b x^n}} \, dx","Integrate[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};1-\frac{1}{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^(-1), -((b*x^n)/a)])/(x*Sqrt[a + b*x^n]))","A",1
2506,1,57,51,0.0163483,"\int \frac{1}{x^3 \sqrt{a+b x^n}} \, dx","Integrate[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};1-\frac{2}{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,"-1/2*(Sqrt[1 + (b*x^n)/a]*Hypergeometric2F1[1/2, -2/n, 1 - 2/n, -((b*x^n)/a)])/(x^2*Sqrt[a + b*x^n])","A",1
2507,1,60,48,0.0164356,"\int \frac{x}{\left(a+b x^n\right)^{3/2}} \, dx","Integrate[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};1+\frac{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, 1 + 2/n, -((b*x^n)/a)])/(2*a*Sqrt[a + b*x^n])","A",1
2508,1,51,39,0.0142834,"\int \frac{1}{\left(a+b x^n\right)^{3/2}} \, dx","Integrate[(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",1
2509,1,37,48,0.009605,"\int \frac{1}{x \left(a+b x^n\right)^{3/2}} \, dx","Integrate[1/(x*(a + b*x^n)^(3/2)),x]","\frac{2 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{b x^n}{a}+1\right)}{a n \sqrt{a+b x^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*Hypergeometric2F1[-1/2, 1, 1/2, 1 + (b*x^n)/a])/(a*n*Sqrt[a + b*x^n])","C",1
2510,1,58,49,0.0155652,"\int \frac{1}{x^2 \left(a+b x^n\right)^{3/2}} \, dx","Integrate[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};1-\frac{1}{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^(-1), -((b*x^n)/a)])/(a*x*Sqrt[a + b*x^n]))","A",1
2511,1,60,51,0.0151841,"\int \frac{1}{x^3 \left(a+b x^n\right)^{3/2}} \, dx","Integrate[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};1-\frac{2}{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,"-1/2*(Sqrt[1 + (b*x^n)/a]*Hypergeometric2F1[3/2, -2/n, 1 - 2/n, -((b*x^n)/a)])/(a*x^2*Sqrt[a + b*x^n])","A",1
2512,1,60,48,0.016419,"\int \frac{x}{\left(a+b x^n\right)^{5/2}} \, dx","Integrate[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};1+\frac{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, 1 + 2/n, -((b*x^n)/a)])/(2*a^2*Sqrt[a + b*x^n])","A",1
2513,1,51,39,0.0239732,"\int \frac{1}{\left(a+b x^n\right)^{5/2}} \, dx","Integrate[(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",1
2514,1,39,69,0.0106313,"\int \frac{1}{x \left(a+b x^n\right)^{5/2}} \, dx","Integrate[1/(x*(a + b*x^n)^(5/2)),x]","\frac{2 \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{b x^n}{a}+1\right)}{3 a n \left(a+b x^n\right)^{3/2}}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b x^n}}{\sqrt{a}}\right)}{a^{5/2} n}+\frac{2}{a^2 n \sqrt{a+b x^n}}+\frac{2}{3 a n \left(a+b x^n\right)^{3/2}}",1,"(2*Hypergeometric2F1[-3/2, 1, -1/2, 1 + (b*x^n)/a])/(3*a*n*(a + b*x^n)^(3/2))","C",1
2515,1,58,49,0.026781,"\int \frac{1}{x^2 \left(a+b x^n\right)^{5/2}} \, dx","Integrate[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};1-\frac{1}{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^(-1), -((b*x^n)/a)])/(a^2*x*Sqrt[a + b*x^n]))","A",1
2516,1,60,51,0.0303755,"\int \frac{1}{x^3 \left(a+b x^n\right)^{5/2}} \, dx","Integrate[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};1-\frac{2}{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,"-1/2*(Sqrt[1 + (b*x^n)/a]*Hypergeometric2F1[5/2, -2/n, 1 - 2/n, -((b*x^n)/a)])/(a^2*x^2*Sqrt[a + b*x^n])","A",1
2517,1,129,106,0.0728903,"\int \frac{\sqrt[3]{a+b x^n}}{x} \, dx","Integrate[(a + b*x^n)^(1/3)/x,x]","\frac{-\sqrt[3]{a} \log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^n}+\left(a+b x^n\right)^{2/3}\right)+6 \sqrt[3]{a+b x^n}+2 \sqrt[3]{a} \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^n}\right)-2 \sqrt{3} \sqrt[3]{a} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{a+b x^n}}{\sqrt[3]{a}}+1}{\sqrt{3}}\right)}{2 n}","\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,"(6*(a + b*x^n)^(1/3) - 2*Sqrt[3]*a^(1/3)*ArcTan[(1 + (2*(a + b*x^n)^(1/3))/a^(1/3))/Sqrt[3]] + 2*a^(1/3)*Log[a^(1/3) - (a + b*x^n)^(1/3)] - a^(1/3)*Log[a^(2/3) + a^(1/3)*(a + b*x^n)^(1/3) + (a + b*x^n)^(2/3)])/(2*n)","A",1
2518,1,22,27,0.0134455,"\int x^{-1+4 n} \left(a+b x^n\right) \, dx","Integrate[x^(-1 + 4*n)*(a + b*x^n),x]","\frac{x^{4 n} \left(5 a+4 b x^n\right)}{20 n}","\frac{a x^{4 n}}{4 n}+\frac{b x^{5 n}}{5 n}",1,"(x^(4*n)*(5*a + 4*b*x^n))/(20*n)","A",1
2519,1,22,27,0.0103365,"\int x^{-1+3 n} \left(a+b x^n\right) \, dx","Integrate[x^(-1 + 3*n)*(a + b*x^n),x]","\frac{x^{3 n} \left(4 a+3 b x^n\right)}{12 n}","\frac{a x^{3 n}}{3 n}+\frac{b x^{4 n}}{4 n}",1,"(x^(3*n)*(4*a + 3*b*x^n))/(12*n)","A",1
2520,1,22,27,0.0103213,"\int x^{-1+2 n} \left(a+b x^n\right) \, dx","Integrate[x^(-1 + 2*n)*(a + b*x^n),x]","\frac{x^{2 n} \left(3 a+2 b x^n\right)}{6 n}","\frac{a x^{2 n}}{2 n}+\frac{b x^{3 n}}{3 n}",1,"(x^(2*n)*(3*a + 2*b*x^n))/(6*n)","A",1
2521,1,19,22,0.0084259,"\int x^{-1+n} \left(a+b x^n\right) \, dx","Integrate[x^(-1 + n)*(a + b*x^n),x]","\frac{x^n \left(2 a+b x^n\right)}{2 n}","\frac{a x^n}{n}+\frac{b x^{2 n}}{2 n}",1,"(x^n*(2*a + b*x^n))/(2*n)","A",1
2522,1,13,13,0.0084676,"\int \frac{a+b x^n}{x} \, dx","Integrate[(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",1
2523,1,16,16,0.0102032,"\int x^{-1-n} \left(a+b x^n\right) \, dx","Integrate[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",1
2524,1,20,25,0.0108545,"\int x^{-1-2 n} \left(a+b x^n\right) \, dx","Integrate[x^(-1 - 2*n)*(a + b*x^n),x]","-\frac{x^{-2 n} \left(a+2 b x^n\right)}{2 n}","-\frac{a x^{-2 n}}{2 n}-\frac{b x^{-n}}{n}",1,"-1/2*(a + 2*b*x^n)/(n*x^(2*n))","A",1
2525,1,22,27,0.0351754,"\int x^{-1-3 n} \left(a+b x^n\right) \, dx","Integrate[x^(-1 - 3*n)*(a + b*x^n),x]","-\frac{x^{-3 n} \left(2 a+3 b x^n\right)}{6 n}","-\frac{a x^{-3 n}}{3 n}-\frac{b x^{-2 n}}{2 n}",1,"-1/6*(2*a + 3*b*x^n)/(n*x^(3*n))","A",1
2526,1,22,27,0.0107333,"\int x^{-1-4 n} \left(a+b x^n\right) \, dx","Integrate[x^(-1 - 4*n)*(a + b*x^n),x]","-\frac{x^{-4 n} \left(3 a+4 b x^n\right)}{12 n}","-\frac{a x^{-4 n}}{4 n}-\frac{b x^{-3 n}}{3 n}",1,"-1/12*(3*a + 4*b*x^n)/(n*x^(4*n))","A",1
2527,1,22,27,0.011375,"\int x^{-1-5 n} \left(a+b x^n\right) \, dx","Integrate[x^(-1 - 5*n)*(a + b*x^n),x]","-\frac{x^{-5 n} \left(4 a+5 b x^n\right)}{20 n}","-\frac{a x^{-5 n}}{5 n}-\frac{b x^{-4 n}}{4 n}",1,"-1/20*(4*a + 5*b*x^n)/(n*x^(5*n))","A",1
2528,1,35,45,0.0228507,"\int x^{-1+4 n} \left(a+b x^n\right)^2 \, dx","Integrate[x^(-1 + 4*n)*(a + b*x^n)^2,x]","\frac{x^{4 n} \left(15 a^2+24 a b x^n+10 b^2 x^{2 n}\right)}{60 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,"(x^(4*n)*(15*a^2 + 24*a*b*x^n + 10*b^2*x^(2*n)))/(60*n)","A",1
2529,1,35,45,0.040678,"\int x^{-1+3 n} \left(a+b x^n\right)^2 \, dx","Integrate[x^(-1 + 3*n)*(a + b*x^n)^2,x]","\frac{x^{3 n} \left(10 a^2+15 a b x^n+6 b^2 x^{2 n}\right)}{30 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,"(x^(3*n)*(10*a^2 + 15*a*b*x^n + 6*b^2*x^(2*n)))/(30*n)","A",1
2530,1,35,45,0.0193773,"\int x^{-1+2 n} \left(a+b x^n\right)^2 \, dx","Integrate[x^(-1 + 2*n)*(a + b*x^n)^2,x]","\frac{x^{2 n} \left(6 a^2+8 a b x^n+3 b^2 x^{2 n}\right)}{12 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,"(x^(2*n)*(6*a^2 + 8*a*b*x^n + 3*b^2*x^(2*n)))/(12*n)","A",1
2531,1,19,19,0.0045974,"\int x^{-1+n} \left(a+b x^n\right)^2 \, dx","Integrate[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
2532,1,27,32,0.0231578,"\int \frac{\left(a+b x^n\right)^2}{x} \, dx","Integrate[(a + b*x^n)^2/x,x]","a^2 \log (x)+\frac{b x^n \left(4 a+b x^n\right)}{2 n}","a^2 \log (x)+\frac{2 a b x^n}{n}+\frac{b^2 x^{2 n}}{2 n}",1,"(b*x^n*(4*a + b*x^n))/(2*n) + a^2*Log[x]","A",1
2533,1,29,30,0.0434353,"\int x^{-1-n} \left(a+b x^n\right)^2 \, dx","Integrate[x^(-1 - n)*(a + b*x^n)^2,x]","\frac{-a^2 x^{-n}+2 a b n \log (x)+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/x^n) + b^2*x^n + 2*a*b*n*Log[x])/n","A",1
2534,1,28,34,0.0375608,"\int x^{-1-2 n} \left(a+b x^n\right)^2 \, dx","Integrate[x^(-1 - 2*n)*(a + b*x^n)^2,x]","b^2 \log (x)-\frac{a x^{-2 n} \left(a+4 b x^n\right)}{2 n}","-\frac{a^2 x^{-2 n}}{2 n}-\frac{2 a b x^{-n}}{n}+b^2 \log (x)",1,"-1/2*(a*(a + 4*b*x^n))/(n*x^(2*n)) + b^2*Log[x]","A",1
2535,1,24,24,0.0065892,"\int x^{-1-3 n} \left(a+b x^n\right)^2 \, dx","Integrate[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,"-1/3*(a + b*x^n)^3/(a*n*x^(3*n))","A",1
2536,1,35,45,0.0148714,"\int x^{-1-4 n} \left(a+b x^n\right)^2 \, dx","Integrate[x^(-1 - 4*n)*(a + b*x^n)^2,x]","-\frac{x^{-4 n} \left(3 a^2+8 a b x^n+6 b^2 x^{2 n}\right)}{12 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,"-1/12*(3*a^2 + 8*a*b*x^n + 6*b^2*x^(2*n))/(n*x^(4*n))","A",1
2537,1,35,45,0.0145273,"\int x^{-1-5 n} \left(a+b x^n\right)^2 \, dx","Integrate[x^(-1 - 5*n)*(a + b*x^n)^2,x]","-\frac{x^{-5 n} \left(6 a^2+15 a b x^n+10 b^2 x^{2 n}\right)}{30 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,"-1/30*(6*a^2 + 15*a*b*x^n + 10*b^2*x^(2*n))/(n*x^(5*n))","A",1
2538,1,35,45,0.0171818,"\int x^{-1-6 n} \left(a+b x^n\right)^2 \, dx","Integrate[x^(-1 - 6*n)*(a + b*x^n)^2,x]","-\frac{x^{-6 n} \left(10 a^2+24 a b x^n+15 b^2 x^{2 n}\right)}{60 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,"-1/60*(10*a^2 + 24*a*b*x^n + 15*b^2*x^(2*n))/(n*x^(6*n))","A",1
2539,1,48,63,0.0235061,"\int x^{-1+4 n} \left(a+b x^n\right)^3 \, dx","Integrate[x^(-1 + 4*n)*(a + b*x^n)^3,x]","\frac{x^{4 n} \left(35 a^3+84 a^2 b x^n+70 a b^2 x^{2 n}+20 b^3 x^{3 n}\right)}{140 n}","\frac{a^3 x^{4 n}}{4 n}+\frac{3 a^2 b x^{5 n}}{5 n}+\frac{a b^2 x^{6 n}}{2 n}+\frac{b^3 x^{7 n}}{7 n}",1,"(x^(4*n)*(35*a^3 + 84*a^2*b*x^n + 70*a*b^2*x^(2*n) + 20*b^3*x^(3*n)))/(140*n)","A",1
2540,1,48,63,0.0286871,"\int x^{-1+3 n} \left(a+b x^n\right)^3 \, dx","Integrate[x^(-1 + 3*n)*(a + b*x^n)^3,x]","\frac{x^{3 n} \left(20 a^3+45 a^2 b x^n+36 a b^2 x^{2 n}+10 b^3 x^{3 n}\right)}{60 n}","\frac{a^3 x^{3 n}}{3 n}+\frac{3 a^2 b x^{4 n}}{4 n}+\frac{3 a b^2 x^{5 n}}{5 n}+\frac{b^3 x^{6 n}}{6 n}",1,"(x^(3*n)*(20*a^3 + 45*a^2*b*x^n + 36*a*b^2*x^(2*n) + 10*b^3*x^(3*n)))/(60*n)","A",1
2541,1,27,40,0.0266499,"\int x^{-1+2 n} \left(a+b x^n\right)^3 \, dx","Integrate[x^(-1 + 2*n)*(a + b*x^n)^3,x]","-\frac{\left(a-4 b x^n\right) \left(a+b x^n\right)^4}{20 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,"-1/20*((a - 4*b*x^n)*(a + b*x^n)^4)/(b^2*n)","A",1
2542,1,19,19,0.003927,"\int x^{-1+n} \left(a+b x^n\right)^3 \, dx","Integrate[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
2543,1,41,50,0.0426796,"\int \frac{\left(a+b x^n\right)^3}{x} \, dx","Integrate[(a + b*x^n)^3/x,x]","a^3 \log (x)+\frac{b x^n \left(18 a^2+9 a b x^n+2 b^2 x^{2 n}\right)}{6 n}","a^3 \log (x)+\frac{3 a^2 b x^n}{n}+\frac{3 a b^2 x^{2 n}}{2 n}+\frac{b^3 x^{3 n}}{3 n}",1,"(b*x^n*(18*a^2 + 9*a*b*x^n + 2*b^2*x^(2*n)))/(6*n) + a^3*Log[x]","A",1
2544,1,45,49,0.0305894,"\int x^{-1-n} \left(a+b x^n\right)^3 \, dx","Integrate[x^(-1 - n)*(a + b*x^n)^3,x]","\frac{-a^3 x^{-n}+3 a^2 b n \log (x)+3 a b^2 x^n+\frac{1}{2} b^3 x^{2 n}}{n}","-\frac{a^3 x^{-n}}{n}+3 a^2 b \log (x)+\frac{3 a b^2 x^n}{n}+\frac{b^3 x^{2 n}}{2 n}",1,"(-(a^3/x^n) + 3*a*b^2*x^n + (b^3*x^(2*n))/2 + 3*a^2*b*n*Log[x])/n","A",1
2545,1,44,48,0.0459464,"\int x^{-1-2 n} \left(a+b x^n\right)^3 \, dx","Integrate[x^(-1 - 2*n)*(a + b*x^n)^3,x]","\frac{-\frac{1}{2} a^3 x^{-2 n}-3 a^2 b x^{-n}+3 a b^2 n \log (x)+b^3 x^n}{n}","-\frac{a^3 x^{-2 n}}{2 n}-\frac{3 a^2 b x^{-n}}{n}+3 a b^2 \log (x)+\frac{b^3 x^n}{n}",1,"(-1/2*a^3/x^(2*n) - (3*a^2*b)/x^n + b^3*x^n + 3*a*b^2*n*Log[x])/n","A",1
2546,1,43,52,0.058354,"\int x^{-1-3 n} \left(a+b x^n\right)^3 \, dx","Integrate[x^(-1 - 3*n)*(a + b*x^n)^3,x]","b^3 \log (x)-\frac{a x^{-3 n} \left(2 a^2+9 a b x^n+18 b^2 x^{2 n}\right)}{6 n}","-\frac{a^3 x^{-3 n}}{3 n}-\frac{3 a^2 b x^{-2 n}}{2 n}-\frac{3 a b^2 x^{-n}}{n}+b^3 \log (x)",1,"-1/6*(a*(2*a^2 + 9*a*b*x^n + 18*b^2*x^(2*n)))/(n*x^(3*n)) + b^3*Log[x]","A",1
2547,1,24,24,0.007492,"\int x^{-1-4 n} \left(a+b x^n\right)^3 \, dx","Integrate[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,"-1/4*(a + b*x^n)^4/(a*n*x^(4*n))","A",1
2548,1,48,50,0.0215897,"\int x^{-1-5 n} \left(a+b x^n\right)^3 \, dx","Integrate[x^(-1 - 5*n)*(a + b*x^n)^3,x]","-\frac{x^{-5 n} \left(4 a^3+15 a^2 b x^n+20 a b^2 x^{2 n}+10 b^3 x^{3 n}\right)}{20 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,"-1/20*(4*a^3 + 15*a^2*b*x^n + 20*a*b^2*x^(2*n) + 10*b^3*x^(3*n))/(n*x^(5*n))","A",1
2549,1,48,63,0.020875,"\int x^{-1-6 n} \left(a+b x^n\right)^3 \, dx","Integrate[x^(-1 - 6*n)*(a + b*x^n)^3,x]","-\frac{x^{-6 n} \left(10 a^3+36 a^2 b x^n+45 a b^2 x^{2 n}+20 b^3 x^{3 n}\right)}{60 n}","-\frac{a^3 x^{-6 n}}{6 n}-\frac{3 a^2 b x^{-5 n}}{5 n}-\frac{3 a b^2 x^{-4 n}}{4 n}-\frac{b^3 x^{-3 n}}{3 n}",1,"-1/60*(10*a^3 + 36*a^2*b*x^n + 45*a*b^2*x^(2*n) + 20*b^3*x^(3*n))/(n*x^(6*n))","A",1
2550,1,48,63,0.0385783,"\int x^{-1-7 n} \left(a+b x^n\right)^3 \, dx","Integrate[x^(-1 - 7*n)*(a + b*x^n)^3,x]","-\frac{x^{-7 n} \left(20 a^3+70 a^2 b x^n+84 a b^2 x^{2 n}+35 b^3 x^{3 n}\right)}{140 n}","-\frac{a^3 x^{-7 n}}{7 n}-\frac{a^2 b x^{-6 n}}{2 n}-\frac{3 a b^2 x^{-5 n}}{5 n}-\frac{b^3 x^{-4 n}}{4 n}",1,"-1/140*(20*a^3 + 70*a^2*b*x^n + 84*a*b^2*x^(2*n) + 35*b^3*x^(3*n))/(n*x^(7*n))","A",1
2551,1,82,84,0.0598788,"\int x^{-1+4 n} \left(a+b x^n\right)^5 \, dx","Integrate[x^(-1 + 4*n)*(a + b*x^n)^5,x]","\frac{\frac{1}{4} a^5 x^{4 n}+a^4 b x^{5 n}+\frac{5}{3} a^3 b^2 x^{6 n}+\frac{10}{7} a^2 b^3 x^{7 n}+\frac{5}{8} a b^4 x^{8 n}+\frac{1}{9} b^5 x^{9 n}}{n}","-\frac{a^3 \left(a+b x^n\right)^6}{6 b^4 n}+\frac{3 a^2 \left(a+b x^n\right)^7}{7 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^5*x^(4*n))/4 + a^4*b*x^(5*n) + (5*a^3*b^2*x^(6*n))/3 + (10*a^2*b^3*x^(7*n))/7 + (5*a*b^4*x^(8*n))/8 + (b^5*x^(9*n))/9)/n","A",1
2552,1,40,62,0.0440653,"\int x^{-1+3 n} \left(a+b x^n\right)^5 \, dx","Integrate[x^(-1 + 3*n)*(a + b*x^n)^5,x]","\frac{\left(a+b x^n\right)^6 \left(a^2-6 a b x^n+21 b^2 x^{2 n}\right)}{168 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 + b*x^n)^6*(a^2 - 6*a*b*x^n + 21*b^2*x^(2*n)))/(168*b^3*n)","A",1
2553,1,27,40,0.0291678,"\int x^{-1+2 n} \left(a+b x^n\right)^5 \, dx","Integrate[x^(-1 + 2*n)*(a + b*x^n)^5,x]","-\frac{\left(a-6 b x^n\right) \left(a+b x^n\right)^6}{42 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,"-1/42*((a - 6*b*x^n)*(a + b*x^n)^6)/(b^2*n)","A",1
2554,1,19,19,0.0049768,"\int x^{-1+n} \left(a+b x^n\right)^5 \, dx","Integrate[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
2555,1,74,84,0.0724326,"\int \frac{\left(a+b x^n\right)^5}{x} \, dx","Integrate[(a + b*x^n)^5/x,x]","\frac{a^5 n \log (x)+5 a^4 b x^n+5 a^3 b^2 x^{2 n}+\frac{10}{3} a^2 b^3 x^{3 n}+\frac{5}{4} a b^4 x^{4 n}+\frac{1}{5} b^5 x^{5 n}}{n}","a^5 \log (x)+\frac{5 a^4 b x^n}{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 b^4 x^{4 n}}{4 n}+\frac{b^5 x^{5 n}}{5 n}",1,"(5*a^4*b*x^n + 5*a^3*b^2*x^(2*n) + (10*a^2*b^3*x^(3*n))/3 + (5*a*b^4*x^(4*n))/4 + (b^5*x^(5*n))/5 + a^5*n*Log[x])/n","A",1
2556,1,73,83,0.0568365,"\int x^{-1-n} \left(a+b x^n\right)^5 \, dx","Integrate[x^(-1 - n)*(a + b*x^n)^5,x]","\frac{-a^5 x^{-n}+5 a^4 b n \log (x)+10 a^3 b^2 x^n+5 a^2 b^3 x^{2 n}+\frac{5}{3} a b^4 x^{3 n}+\frac{1}{4} b^5 x^{4 n}}{n}","-\frac{a^5 x^{-n}}{n}+5 a^4 b \log (x)+\frac{10 a^3 b^2 x^n}{n}+\frac{5 a^2 b^3 x^{2 n}}{n}+\frac{5 a b^4 x^{3 n}}{3 n}+\frac{b^5 x^{4 n}}{4 n}",1,"(-(a^5/x^n) + 10*a^3*b^2*x^n + 5*a^2*b^3*x^(2*n) + (5*a*b^4*x^(3*n))/3 + (b^5*x^(4*n))/4 + 5*a^4*b*n*Log[x])/n","A",1
2557,1,72,85,0.0797558,"\int x^{-1-2 n} \left(a+b x^n\right)^5 \, dx","Integrate[x^(-1 - 2*n)*(a + b*x^n)^5,x]","10 a^3 b^2 \log (x)+\frac{x^{-2 n} \left(-3 a^5-30 a^4 b x^n+60 a^2 b^3 x^{3 n}+15 a b^4 x^{4 n}+2 b^5 x^{5 n}\right)}{6 n}","-\frac{a^5 x^{-2 n}}{2 n}-\frac{5 a^4 b x^{-n}}{n}+10 a^3 b^2 \log (x)+\frac{10 a^2 b^3 x^n}{n}+\frac{5 a b^4 x^{2 n}}{2 n}+\frac{b^5 x^{3 n}}{3 n}",1,"(-3*a^5 - 30*a^4*b*x^n + 60*a^2*b^3*x^(3*n) + 15*a*b^4*x^(4*n) + 2*b^5*x^(5*n))/(6*n*x^(2*n)) + 10*a^3*b^2*Log[x]","A",1
2558,1,72,85,0.0656634,"\int x^{-1-3 n} \left(a+b x^n\right)^5 \, dx","Integrate[x^(-1 - 3*n)*(a + b*x^n)^5,x]","10 a^2 b^3 \log (x)+\frac{x^{-3 n} \left(-2 a^5-15 a^4 b x^n-60 a^3 b^2 x^{2 n}+30 a b^4 x^{4 n}+3 b^5 x^{5 n}\right)}{6 n}","-\frac{a^5 x^{-3 n}}{3 n}-\frac{5 a^4 b x^{-2 n}}{2 n}-\frac{10 a^3 b^2 x^{-n}}{n}+10 a^2 b^3 \log (x)+\frac{5 a b^4 x^n}{n}+\frac{b^5 x^{2 n}}{2 n}",1,"(-2*a^5 - 15*a^4*b*x^n - 60*a^3*b^2*x^(2*n) + 30*a*b^4*x^(4*n) + 3*b^5*x^(5*n))/(6*n*x^(3*n)) + 10*a^2*b^3*Log[x]","A",1
2559,1,72,82,0.0545211,"\int x^{-1-4 n} \left(a+b x^n\right)^5 \, dx","Integrate[x^(-1 - 4*n)*(a + b*x^n)^5,x]","\frac{-\frac{1}{4} a^5 x^{-4 n}-\frac{5}{3} a^4 b x^{-3 n}-5 a^3 b^2 x^{-2 n}-10 a^2 b^3 x^{-n}+5 a b^4 n \log (x)+b^5 x^n}{n}","-\frac{a^5 x^{-4 n}}{4 n}-\frac{5 a^4 b x^{-3 n}}{3 n}-\frac{5 a^3 b^2 x^{-2 n}}{n}-\frac{10 a^2 b^3 x^{-n}}{n}+5 a b^4 \log (x)+\frac{b^5 x^n}{n}",1,"(-1/4*a^5/x^(4*n) - (5*a^4*b)/(3*x^(3*n)) - (5*a^3*b^2)/x^(2*n) - (10*a^2*b^3)/x^n + b^5*x^n + 5*a*b^4*n*Log[x])/n","A",1
2560,1,69,86,0.0840016,"\int x^{-1-5 n} \left(a+b x^n\right)^5 \, dx","Integrate[x^(-1 - 5*n)*(a + b*x^n)^5,x]","b^5 \log (x)-\frac{a x^{-5 n} \left(12 a^4+75 a^3 b x^n+200 a^2 b^2 x^{2 n}+300 a b^3 x^{3 n}+300 b^4 x^{4 n}\right)}{60 n}","-\frac{a^5 x^{-5 n}}{5 n}-\frac{5 a^4 b x^{-4 n}}{4 n}-\frac{10 a^3 b^2 x^{-3 n}}{3 n}-\frac{5 a^2 b^3 x^{-2 n}}{n}-\frac{5 a b^4 x^{-n}}{n}+b^5 \log (x)",1,"-1/60*(a*(12*a^4 + 75*a^3*b*x^n + 200*a^2*b^2*x^(2*n) + 300*a*b^3*x^(3*n) + 300*b^4*x^(4*n)))/(n*x^(5*n)) + b^5*Log[x]","A",1
2561,1,24,24,0.0086524,"\int x^{-1-6 n} \left(a+b x^n\right)^5 \, dx","Integrate[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,"-1/6*(a + b*x^n)^6/(a*n*x^(6*n))","A",1
2562,1,33,50,0.0245342,"\int x^{-1-7 n} \left(a+b x^n\right)^5 \, dx","Integrate[x^(-1 - 7*n)*(a + b*x^n)^5,x]","\frac{x^{-7 n} \left(b x^n-6 a\right) \left(a+b x^n\right)^6}{42 a^2 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,"((-6*a + b*x^n)*(a + b*x^n)^6)/(42*a^2*n*x^(7*n))","A",1
2563,1,74,77,0.0393926,"\int x^{-1-8 n} \left(a+b x^n\right)^5 \, dx","Integrate[x^(-1 - 8*n)*(a + b*x^n)^5,x]","-\frac{x^{-8 n} \left(21 a^5+120 a^4 b x^n+280 a^3 b^2 x^{2 n}+336 a^2 b^3 x^{3 n}+210 a b^4 x^{4 n}+56 b^5 x^{5 n}\right)}{168 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,"-1/168*(21*a^5 + 120*a^4*b*x^n + 280*a^3*b^2*x^(2*n) + 336*a^2*b^3*x^(3*n) + 210*a*b^4*x^(4*n) + 56*b^5*x^(5*n))/(n*x^(8*n))","A",1
2564,1,74,97,0.0458406,"\int x^{-1-9 n} \left(a+b x^n\right)^5 \, dx","Integrate[x^(-1 - 9*n)*(a + b*x^n)^5,x]","-\frac{x^{-9 n} \left(56 a^5+315 a^4 b x^n+720 a^3 b^2 x^{2 n}+840 a^2 b^3 x^{3 n}+504 a b^4 x^{4 n}+126 b^5 x^{5 n}\right)}{504 n}","-\frac{a^5 x^{-9 n}}{9 n}-\frac{5 a^4 b x^{-8 n}}{8 n}-\frac{10 a^3 b^2 x^{-7 n}}{7 n}-\frac{5 a^2 b^3 x^{-6 n}}{3 n}-\frac{a b^4 x^{-5 n}}{n}-\frac{b^5 x^{-4 n}}{4 n}",1,"-1/504*(56*a^5 + 315*a^4*b*x^n + 720*a^3*b^2*x^(2*n) + 840*a^2*b^3*x^(3*n) + 504*a*b^4*x^(4*n) + 126*b^5*x^(5*n))/(n*x^(9*n))","A",1
2565,1,74,99,0.0483622,"\int x^{-1-10 n} \left(a+b x^n\right)^5 \, dx","Integrate[x^(-1 - 10*n)*(a + b*x^n)^5,x]","-\frac{x^{-10 n} \left(126 a^5+700 a^4 b x^n+1575 a^3 b^2 x^{2 n}+1800 a^2 b^3 x^{3 n}+1050 a b^4 x^{4 n}+252 b^5 x^{5 n}\right)}{1260 n}","-\frac{a^5 x^{-10 n}}{10 n}-\frac{5 a^4 b x^{-9 n}}{9 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 b^4 x^{-6 n}}{6 n}-\frac{b^5 x^{-5 n}}{5 n}",1,"-1/1260*(126*a^5 + 700*a^4*b*x^n + 1575*a^3*b^2*x^(2*n) + 1800*a^2*b^3*x^(3*n) + 1050*a*b^4*x^(4*n) + 252*b^5*x^(5*n))/(n*x^(10*n))","A",1
2566,1,128,151,0.0931564,"\int x^{-1+9 n} \left(a+b x^n\right)^8 \, dx","Integrate[x^(-1 + 9*n)*(a + b*x^n)^8,x]","\frac{\frac{1}{9} a^8 x^{9 n}+\frac{4}{5} a^7 b x^{10 n}+\frac{28}{11} a^6 b^2 x^{11 n}+\frac{14}{3} a^5 b^3 x^{12 n}+\frac{70}{13} a^4 b^4 x^{13 n}+4 a^3 b^5 x^{14 n}+\frac{28}{15} a^2 b^6 x^{15 n}+\frac{1}{2} a b^7 x^{16 n}+\frac{1}{17} b^8 x^{17 n}}{n}","\frac{a^8 x^{9 n}}{9 n}+\frac{4 a^7 b x^{10 n}}{5 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{a b^7 x^{16 n}}{2 n}+\frac{b^8 x^{17 n}}{17 n}",1,"((a^8*x^(9*n))/9 + (4*a^7*b*x^(10*n))/5 + (28*a^6*b^2*x^(11*n))/11 + (14*a^5*b^3*x^(12*n))/3 + (70*a^4*b^4*x^(13*n))/13 + 4*a^3*b^5*x^(14*n) + (28*a^2*b^6*x^(15*n))/15 + (a*b^7*x^(16*n))/2 + (b^8*x^(17*n))/17)/n","A",1
2567,1,128,151,0.081279,"\int x^{-1+8 n} \left(a+b x^n\right)^8 \, dx","Integrate[x^(-1 + 8*n)*(a + b*x^n)^8,x]","\frac{\frac{1}{8} a^8 x^{8 n}+\frac{8}{9} a^7 b x^{9 n}+\frac{14}{5} a^6 b^2 x^{10 n}+\frac{56}{11} a^5 b^3 x^{11 n}+\frac{35}{6} a^4 b^4 x^{12 n}+\frac{56}{13} a^3 b^5 x^{13 n}+2 a^2 b^6 x^{14 n}+\frac{8}{15} a b^7 x^{15 n}+\frac{1}{16} b^8 x^{16 n}}{n}","\frac{a^8 x^{8 n}}{8 n}+\frac{8 a^7 b x^{9 n}}{9 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 b^7 x^{15 n}}{15 n}+\frac{b^8 x^{16 n}}{16 n}",1,"((a^8*x^(8*n))/8 + (8*a^7*b*x^(9*n))/9 + (14*a^6*b^2*x^(10*n))/5 + (56*a^5*b^3*x^(11*n))/11 + (35*a^4*b^4*x^(12*n))/6 + (56*a^3*b^5*x^(13*n))/13 + 2*a^2*b^6*x^(14*n) + (8*a*b^7*x^(15*n))/15 + (b^8*x^(16*n))/16)/n","A",1
2568,1,127,150,0.0845056,"\int x^{-1+7 n} \left(a+b x^n\right)^8 \, dx","Integrate[x^(-1 + 7*n)*(a + b*x^n)^8,x]","\frac{\frac{1}{7} a^8 x^{7 n}+a^7 b x^{8 n}+\frac{28}{9} a^6 b^2 x^{9 n}+\frac{28}{5} a^5 b^3 x^{10 n}+\frac{70}{11} a^4 b^4 x^{11 n}+\frac{14}{3} a^3 b^5 x^{12 n}+\frac{28}{13} a^2 b^6 x^{13 n}+\frac{4}{7} a b^7 x^{14 n}+\frac{1}{15} b^8 x^{15 n}}{n}","\frac{a^6 \left(a+b x^n\right)^9}{9 b^7 n}-\frac{3 a^5 \left(a+b x^n\right)^{10}}{5 b^7 n}+\frac{15 a^4 \left(a+b x^n\right)^{11}}{11 b^7 n}-\frac{5 a^3 \left(a+b x^n\right)^{12}}{3 b^7 n}+\frac{15 a^2 \left(a+b x^n\right)^{13}}{13 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^8*x^(7*n))/7 + a^7*b*x^(8*n) + (28*a^6*b^2*x^(9*n))/9 + (28*a^5*b^3*x^(10*n))/5 + (70*a^4*b^4*x^(11*n))/11 + (14*a^3*b^5*x^(12*n))/3 + (28*a^2*b^6*x^(13*n))/13 + (4*a*b^7*x^(14*n))/7 + (b^8*x^(15*n))/15)/n","A",1
2569,1,79,128,0.0999133,"\int x^{-1+6 n} \left(a+b x^n\right)^8 \, dx","Integrate[x^(-1 + 6*n)*(a + b*x^n)^8,x]","-\frac{\left(a+b x^n\right)^9 \left(a^5-9 a^4 b x^n+45 a^3 b^2 x^{2 n}-165 a^2 b^3 x^{3 n}+495 a b^4 x^{4 n}-1287 b^5 x^{5 n}\right)}{18018 b^6 n}","-\frac{a^5 \left(a+b x^n\right)^9}{9 b^6 n}+\frac{a^4 \left(a+b x^n\right)^{10}}{2 b^6 n}-\frac{10 a^3 \left(a+b x^n\right)^{11}}{11 b^6 n}+\frac{5 a^2 \left(a+b x^n\right)^{12}}{6 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,"-1/18018*((a + b*x^n)^9*(a^5 - 9*a^4*b*x^n + 45*a^3*b^2*x^(2*n) - 165*a^2*b^3*x^(3*n) + 495*a*b^4*x^(4*n) - 1287*b^5*x^(5*n)))/(b^6*n)","A",1
2570,1,66,106,0.0609483,"\int x^{-1+5 n} \left(a+b x^n\right)^8 \, dx","Integrate[x^(-1 + 5*n)*(a + b*x^n)^8,x]","\frac{\left(a+b x^n\right)^9 \left(a^4-9 a^3 b x^n+45 a^2 b^2 x^{2 n}-165 a b^3 x^{3 n}+495 b^4 x^{4 n}\right)}{6435 b^5 n}","\frac{a^4 \left(a+b x^n\right)^9}{9 b^5 n}-\frac{2 a^3 \left(a+b x^n\right)^{10}}{5 b^5 n}+\frac{6 a^2 \left(a+b x^n\right)^{11}}{11 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 + b*x^n)^9*(a^4 - 9*a^3*b*x^n + 45*a^2*b^2*x^(2*n) - 165*a*b^3*x^(3*n) + 495*b^4*x^(4*n)))/(6435*b^5*n)","A",1
2571,1,53,84,0.0586994,"\int x^{-1+4 n} \left(a+b x^n\right)^8 \, dx","Integrate[x^(-1 + 4*n)*(a + b*x^n)^8,x]","-\frac{\left(a+b x^n\right)^9 \left(a^3-9 a^2 b x^n+45 a b^2 x^{2 n}-165 b^3 x^{3 n}\right)}{1980 b^4 n}","-\frac{a^3 \left(a+b x^n\right)^9}{9 b^4 n}+\frac{3 a^2 \left(a+b x^n\right)^{10}}{10 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,"-1/1980*((a + b*x^n)^9*(a^3 - 9*a^2*b*x^n + 45*a*b^2*x^(2*n) - 165*b^3*x^(3*n)))/(b^4*n)","A",1
2572,1,40,62,0.0353291,"\int x^{-1+3 n} \left(a+b x^n\right)^8 \, dx","Integrate[x^(-1 + 3*n)*(a + b*x^n)^8,x]","\frac{\left(a+b x^n\right)^9 \left(a^2-9 a b x^n+45 b^2 x^{2 n}\right)}{495 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 + b*x^n)^9*(a^2 - 9*a*b*x^n + 45*b^2*x^(2*n)))/(495*b^3*n)","A",1
2573,1,27,40,0.0411271,"\int x^{-1+2 n} \left(a+b x^n\right)^8 \, dx","Integrate[x^(-1 + 2*n)*(a + b*x^n)^8,x]","-\frac{\left(a-9 b x^n\right) \left(a+b x^n\right)^9}{90 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,"-1/90*((a - 9*b*x^n)*(a + b*x^n)^9)/(b^2*n)","A",1
2574,1,19,19,0.0109672,"\int x^{-1+n} \left(a+b x^n\right)^8 \, dx","Integrate[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
2575,1,119,138,0.0842045,"\int \frac{\left(a+b x^n\right)^8}{x} \, dx","Integrate[(a + b*x^n)^8/x,x]","\frac{a^8 n \log (x)+8 a^7 b x^n+14 a^6 b^2 x^{2 n}+\frac{56}{3} a^5 b^3 x^{3 n}+\frac{35}{2} a^4 b^4 x^{4 n}+\frac{56}{5} a^3 b^5 x^{5 n}+\frac{14}{3} a^2 b^6 x^{6 n}+\frac{8}{7} a b^7 x^{7 n}+\frac{1}{8} b^8 x^{8 n}}{n}","a^8 \log (x)+\frac{8 a^7 b x^n}{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 b^7 x^{7 n}}{7 n}+\frac{b^8 x^{8 n}}{8 n}",1,"(8*a^7*b*x^n + 14*a^6*b^2*x^(2*n) + (56*a^5*b^3*x^(3*n))/3 + (35*a^4*b^4*x^(4*n))/2 + (56*a^3*b^5*x^(5*n))/5 + (14*a^2*b^6*x^(6*n))/3 + (8*a*b^7*x^(7*n))/7 + (b^8*x^(8*n))/8 + a^8*n*Log[x])/n","A",1
2576,1,116,135,0.1003521,"\int x^{-1-n} \left(a+b x^n\right)^8 \, dx","Integrate[x^(-1 - n)*(a + b*x^n)^8,x]","\frac{-a^8 x^{-n}+8 a^7 b n \log (x)+28 a^6 b^2 x^n+28 a^5 b^3 x^{2 n}+\frac{70}{3} a^4 b^4 x^{3 n}+14 a^3 b^5 x^{4 n}+\frac{28}{5} a^2 b^6 x^{5 n}+\frac{4}{3} a b^7 x^{6 n}+\frac{1}{7} b^8 x^{7 n}}{n}","-\frac{a^8 x^{-n}}{n}+8 a^7 b \log (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}+\frac{4 a b^7 x^{6 n}}{3 n}+\frac{b^8 x^{7 n}}{7 n}",1,"(-(a^8/x^n) + 28*a^6*b^2*x^n + 28*a^5*b^3*x^(2*n) + (70*a^4*b^4*x^(3*n))/3 + 14*a^3*b^5*x^(4*n) + (28*a^2*b^6*x^(5*n))/5 + (4*a*b^7*x^(6*n))/3 + (b^8*x^(7*n))/7 + 8*a^7*b*n*Log[x])/n","A",1
2577,1,116,135,0.1081584,"\int x^{-1-2 n} \left(a+b x^n\right)^8 \, dx","Integrate[x^(-1 - 2*n)*(a + b*x^n)^8,x]","\frac{-\frac{1}{2} a^8 x^{-2 n}-8 a^7 b x^{-n}+28 a^6 b^2 n \log (x)+56 a^5 b^3 x^n+35 a^4 b^4 x^{2 n}+\frac{56}{3} a^3 b^5 x^{3 n}+7 a^2 b^6 x^{4 n}+\frac{8}{5} a b^7 x^{5 n}+\frac{1}{6} b^8 x^{6 n}}{n}","-\frac{a^8 x^{-2 n}}{2 n}-\frac{8 a^7 b x^{-n}}{n}+28 a^6 b^2 \log (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}+\frac{8 a b^7 x^{5 n}}{5 n}+\frac{b^8 x^{6 n}}{6 n}",1,"(-1/2*a^8/x^(2*n) - (8*a^7*b)/x^n + 56*a^5*b^3*x^n + 35*a^4*b^4*x^(2*n) + (56*a^3*b^5*x^(3*n))/3 + 7*a^2*b^6*x^(4*n) + (8*a*b^7*x^(5*n))/5 + (b^8*x^(6*n))/6 + 28*a^6*b^2*n*Log[x])/n","A",1
2578,1,114,133,0.0792926,"\int x^{-1-3 n} \left(a+b x^n\right)^8 \, dx","Integrate[x^(-1 - 3*n)*(a + b*x^n)^8,x]","\frac{-\frac{1}{3} a^8 x^{-3 n}-4 a^7 b x^{-2 n}-28 a^6 b^2 x^{-n}+56 a^5 b^3 n \log (x)+70 a^4 b^4 x^n+28 a^3 b^5 x^{2 n}+\frac{28}{3} a^2 b^6 x^{3 n}+2 a b^7 x^{4 n}+\frac{1}{5} b^8 x^{5 n}}{n}","-\frac{a^8 x^{-3 n}}{3 n}-\frac{4 a^7 b x^{-2 n}}{n}-\frac{28 a^6 b^2 x^{-n}}{n}+56 a^5 b^3 \log (x)+\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}+\frac{2 a b^7 x^{4 n}}{n}+\frac{b^8 x^{5 n}}{5 n}",1,"(-1/3*a^8/x^(3*n) - (4*a^7*b)/x^(2*n) - (28*a^6*b^2)/x^n + 70*a^4*b^4*x^n + 28*a^3*b^5*x^(2*n) + (28*a^2*b^6*x^(3*n))/3 + 2*a*b^7*x^(4*n) + (b^8*x^(5*n))/5 + 56*a^5*b^3*n*Log[x])/n","A",1
2579,1,116,135,0.0936879,"\int x^{-1-4 n} \left(a+b x^n\right)^8 \, dx","Integrate[x^(-1 - 4*n)*(a + b*x^n)^8,x]","\frac{-\frac{1}{4} a^8 x^{-4 n}-\frac{8}{3} a^7 b x^{-3 n}-14 a^6 b^2 x^{-2 n}-56 a^5 b^3 x^{-n}+70 a^4 b^4 n \log (x)+56 a^3 b^5 x^n+14 a^2 b^6 x^{2 n}+\frac{8}{3} a b^7 x^{3 n}+\frac{1}{4} b^8 x^{4 n}}{n}","-\frac{a^8 x^{-4 n}}{4 n}-\frac{8 a^7 b x^{-3 n}}{3 n}-\frac{14 a^6 b^2 x^{-2 n}}{n}-\frac{56 a^5 b^3 x^{-n}}{n}+70 a^4 b^4 \log (x)+\frac{56 a^3 b^5 x^n}{n}+\frac{14 a^2 b^6 x^{2 n}}{n}+\frac{8 a b^7 x^{3 n}}{3 n}+\frac{b^8 x^{4 n}}{4 n}",1,"(-1/4*a^8/x^(4*n) - (8*a^7*b)/(3*x^(3*n)) - (14*a^6*b^2)/x^(2*n) - (56*a^5*b^3)/x^n + 56*a^3*b^5*x^n + 14*a^2*b^6*x^(2*n) + (8*a*b^7*x^(3*n))/3 + (b^8*x^(4*n))/4 + 70*a^4*b^4*n*Log[x])/n","A",1
2580,1,114,133,0.100813,"\int x^{-1-5 n} \left(a+b x^n\right)^8 \, dx","Integrate[x^(-1 - 5*n)*(a + b*x^n)^8,x]","\frac{-\frac{1}{5} a^8 x^{-5 n}-2 a^7 b x^{-4 n}-\frac{28}{3} a^6 b^2 x^{-3 n}-28 a^5 b^3 x^{-2 n}-70 a^4 b^4 x^{-n}+56 a^3 b^5 n \log (x)+28 a^2 b^6 x^n+4 a b^7 x^{2 n}+\frac{1}{3} b^8 x^{3 n}}{n}","-\frac{a^8 x^{-5 n}}{5 n}-\frac{2 a^7 b x^{-4 n}}{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}+56 a^3 b^5 \log (x)+\frac{28 a^2 b^6 x^n}{n}+\frac{4 a b^7 x^{2 n}}{n}+\frac{b^8 x^{3 n}}{3 n}",1,"(-1/5*a^8/x^(5*n) - (2*a^7*b)/x^(4*n) - (28*a^6*b^2)/(3*x^(3*n)) - (28*a^5*b^3)/x^(2*n) - (70*a^4*b^4)/x^n + 28*a^2*b^6*x^n + 4*a*b^7*x^(2*n) + (b^8*x^(3*n))/3 + 56*a^3*b^5*n*Log[x])/n","A",1
2581,1,116,135,0.1364191,"\int x^{-1-6 n} \left(a+b x^n\right)^8 \, dx","Integrate[x^(-1 - 6*n)*(a + b*x^n)^8,x]","\frac{-\frac{1}{6} a^8 x^{-6 n}-\frac{8}{5} a^7 b x^{-5 n}-7 a^6 b^2 x^{-4 n}-\frac{56}{3} a^5 b^3 x^{-3 n}-35 a^4 b^4 x^{-2 n}-56 a^3 b^5 x^{-n}+28 a^2 b^6 n \log (x)+8 a b^7 x^n+\frac{1}{2} b^8 x^{2 n}}{n}","-\frac{a^8 x^{-6 n}}{6 n}-\frac{8 a^7 b x^{-5 n}}{5 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 b^7 x^n}{n}+\frac{b^8 x^{2 n}}{2 n}",1,"(-1/6*a^8/x^(6*n) - (8*a^7*b)/(5*x^(5*n)) - (7*a^6*b^2)/x^(4*n) - (56*a^5*b^3)/(3*x^(3*n)) - (35*a^4*b^4)/x^(2*n) - (56*a^3*b^5)/x^n + 8*a*b^7*x^n + (b^8*x^(2*n))/2 + 28*a^2*b^6*n*Log[x])/n","A",1
2582,1,115,134,0.14436,"\int x^{-1-7 n} \left(a+b x^n\right)^8 \, dx","Integrate[x^(-1 - 7*n)*(a + b*x^n)^8,x]","\frac{-\frac{1}{7} a^8 x^{-7 n}-\frac{4}{3} a^7 b x^{-6 n}-\frac{28}{5} a^6 b^2 x^{-5 n}-14 a^5 b^3 x^{-4 n}-\frac{70}{3} a^4 b^4 x^{-3 n}-28 a^3 b^5 x^{-2 n}-28 a^2 b^6 x^{-n}+8 a b^7 n \log (x)+b^8 x^n}{n}","-\frac{a^8 x^{-7 n}}{7 n}-\frac{4 a^7 b x^{-6 n}}{3 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}+8 a b^7 \log (x)+\frac{b^8 x^n}{n}",1,"(-1/7*a^8/x^(7*n) - (4*a^7*b)/(3*x^(6*n)) - (28*a^6*b^2)/(5*x^(5*n)) - (14*a^5*b^3)/x^(4*n) - (70*a^4*b^4)/(3*x^(3*n)) - (28*a^3*b^5)/x^(2*n) - (28*a^2*b^6)/x^n + b^8*x^n + 8*a*b^7*n*Log[x])/n","A",1
2583,1,108,140,0.135611,"\int x^{-1-8 n} \left(a+b x^n\right)^8 \, dx","Integrate[x^(-1 - 8*n)*(a + b*x^n)^8,x]","b^8 \log (x)-\frac{a x^{-8 n} \left(105 a^7+960 a^6 b x^n+3920 a^5 b^2 x^{2 n}+9408 a^4 b^3 x^{3 n}+14700 a^3 b^4 x^{4 n}+15680 a^2 b^5 x^{5 n}+11760 a b^6 x^{6 n}+6720 b^7 x^{7 n}\right)}{840 n}","-\frac{a^8 x^{-8 n}}{8 n}-\frac{8 a^7 b x^{-7 n}}{7 n}-\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 b^7 x^{-n}}{n}+b^8 \log (x)",1,"-1/840*(a*(105*a^7 + 960*a^6*b*x^n + 3920*a^5*b^2*x^(2*n) + 9408*a^4*b^3*x^(3*n) + 14700*a^3*b^4*x^(4*n) + 15680*a^2*b^5*x^(5*n) + 11760*a*b^6*x^(6*n) + 6720*b^7*x^(7*n)))/(n*x^(8*n)) + b^8*Log[x]","A",1
2584,1,24,24,0.0108504,"\int x^{-1-9 n} \left(a+b x^n\right)^8 \, dx","Integrate[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,"-1/9*(a + b*x^n)^9/(a*n*x^(9*n))","A",1
2585,1,33,50,0.03872,"\int x^{-1-10 n} \left(a+b x^n\right)^8 \, dx","Integrate[x^(-1 - 10*n)*(a + b*x^n)^8,x]","\frac{x^{-10 n} \left(b x^n-9 a\right) \left(a+b x^n\right)^9}{90 a^2 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,"((-9*a + b*x^n)*(a + b*x^n)^9)/(90*a^2*n*x^(10*n))","A",1
2586,1,46,77,0.0257773,"\int x^{-1-11 n} \left(a+b x^n\right)^8 \, dx","Integrate[x^(-1 - 11*n)*(a + b*x^n)^8,x]","-\frac{x^{-11 n} \left(a+b x^n\right)^9 \left(45 a^2-9 a b x^n+b^2 x^{2 n}\right)}{495 a^3 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,"-1/495*((a + b*x^n)^9*(45*a^2 - 9*a*b*x^n + b^2*x^(2*n)))/(a^3*n*x^(11*n))","A",1
2587,1,59,104,0.0206353,"\int x^{-1-12 n} \left(a+b x^n\right)^8 \, dx","Integrate[x^(-1 - 12*n)*(a + b*x^n)^8,x]","\frac{x^{-12 n} \left(a+b x^n\right)^9 \left(-165 a^3+45 a^2 b x^n-9 a b^2 x^{2 n}+b^3 x^{3 n}\right)}{1980 a^4 n}","\frac{b^3 x^{-9 n} \left(a+b x^n\right)^9}{1980 a^4 n}-\frac{b^2 x^{-10 n} \left(a+b x^n\right)^9}{220 a^3 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*(-165*a^3 + 45*a^2*b*x^n - 9*a*b^2*x^(2*n) + b^3*x^(3*n)))/(1980*a^4*n*x^(12*n))","A",1
2588,1,113,131,0.0607169,"\int x^{-1-13 n} \left(a+b x^n\right)^8 \, dx","Integrate[x^(-1 - 13*n)*(a + b*x^n)^8,x]","-\frac{x^{-13 n} \left(495 a^8+4290 a^7 b x^n+16380 a^6 b^2 x^{2 n}+36036 a^5 b^3 x^{3 n}+50050 a^4 b^4 x^{4 n}+45045 a^3 b^5 x^{5 n}+25740 a^2 b^6 x^{6 n}+8580 a b^7 x^{7 n}+1287 b^8 x^{8 n}\right)}{6435 n}","-\frac{b^4 x^{-9 n} \left(a+b x^n\right)^9}{6435 a^5 n}+\frac{b^3 x^{-10 n} \left(a+b x^n\right)^9}{715 a^4 n}-\frac{b^2 x^{-11 n} \left(a+b x^n\right)^9}{143 a^3 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,"-1/6435*(495*a^8 + 4290*a^7*b*x^n + 16380*a^6*b^2*x^(2*n) + 36036*a^5*b^3*x^(3*n) + 50050*a^4*b^4*x^(4*n) + 45045*a^3*b^5*x^(5*n) + 25740*a^2*b^6*x^(6*n) + 8580*a*b^7*x^(7*n) + 1287*b^8*x^(8*n))/(n*x^(13*n))","A",1
2589,1,113,151,0.0540915,"\int x^{-1-14 n} \left(a+b x^n\right)^8 \, dx","Integrate[x^(-1 - 14*n)*(a + b*x^n)^8,x]","-\frac{x^{-14 n} \left(1287 a^8+11088 a^7 b x^n+42042 a^6 b^2 x^{2 n}+91728 a^5 b^3 x^{3 n}+126126 a^4 b^4 x^{4 n}+112112 a^3 b^5 x^{5 n}+63063 a^2 b^6 x^{6 n}+20592 a b^7 x^{7 n}+3003 b^8 x^{8 n}\right)}{18018 n}","-\frac{a^8 x^{-14 n}}{14 n}-\frac{8 a^7 b x^{-13 n}}{13 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 b^7 x^{-7 n}}{7 n}-\frac{b^8 x^{-6 n}}{6 n}",1,"-1/18018*(1287*a^8 + 11088*a^7*b*x^n + 42042*a^6*b^2*x^(2*n) + 91728*a^5*b^3*x^(3*n) + 126126*a^4*b^4*x^(4*n) + 112112*a^3*b^5*x^(5*n) + 63063*a^2*b^6*x^(6*n) + 20592*a*b^7*x^(7*n) + 3003*b^8*x^(8*n))/(n*x^(14*n))","A",1
2590,1,113,151,0.0594166,"\int x^{-1-15 n} \left(a+b x^n\right)^8 \, dx","Integrate[x^(-1 - 15*n)*(a + b*x^n)^8,x]","-\frac{x^{-15 n} \left(3003 a^8+25740 a^7 b x^n+97020 a^6 b^2 x^{2 n}+210210 a^5 b^3 x^{3 n}+286650 a^4 b^4 x^{4 n}+252252 a^3 b^5 x^{5 n}+140140 a^2 b^6 x^{6 n}+45045 a b^7 x^{7 n}+6435 b^8 x^{8 n}\right)}{45045 n}","-\frac{a^8 x^{-15 n}}{15 n}-\frac{4 a^7 b x^{-14 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{a b^7 x^{-8 n}}{n}-\frac{b^8 x^{-7 n}}{7 n}",1,"-1/45045*(3003*a^8 + 25740*a^7*b*x^n + 97020*a^6*b^2*x^(2*n) + 210210*a^5*b^3*x^(3*n) + 286650*a^4*b^4*x^(4*n) + 252252*a^3*b^5*x^(5*n) + 140140*a^2*b^6*x^(6*n) + 45045*a*b^7*x^(7*n) + 6435*b^8*x^(8*n))/(n*x^(15*n))","A",1
2591,1,19,19,0.0075997,"\int x^{-1+n} \left(a+b x^n\right)^{16} \, dx","Integrate[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
2592,1,160,16,0.0060588,"\int x^{12} \left(a+b x^{13}\right)^{12} \, dx","Integrate[x^12*(a + b*x^13)^12,x]","\frac{a^{12} x^{13}}{13}+\frac{6}{13} a^{11} b x^{26}+\frac{22}{13} a^{10} b^2 x^{39}+\frac{55}{13} a^9 b^3 x^{52}+\frac{99}{13} a^8 b^4 x^{65}+\frac{132}{13} a^7 b^5 x^{78}+\frac{132}{13} a^6 b^6 x^{91}+\frac{99}{13} a^5 b^7 x^{104}+\frac{55}{13} a^4 b^8 x^{117}+\frac{22}{13} a^3 b^9 x^{130}+\frac{6}{13} a^2 b^{10} x^{143}+\frac{1}{13} a b^{11} x^{156}+\frac{b^{12} x^{169}}{169}","\frac{\left(a+b x^{13}\right)^{13}}{169 b}",1,"(a^12*x^13)/13 + (6*a^11*b*x^26)/13 + (22*a^10*b^2*x^39)/13 + (55*a^9*b^3*x^52)/13 + (99*a^8*b^4*x^65)/13 + (132*a^7*b^5*x^78)/13 + (132*a^6*b^6*x^91)/13 + (99*a^5*b^7*x^104)/13 + (55*a^4*b^8*x^117)/13 + (22*a^3*b^9*x^130)/13 + (6*a^2*b^10*x^143)/13 + (a*b^11*x^156)/13 + (b^12*x^169)/169","B",1
2593,1,160,16,0.0068477,"\int x^{24} \left(a+b x^{25}\right)^{12} \, dx","Integrate[x^24*(a + b*x^25)^12,x]","\frac{a^{12} x^{25}}{25}+\frac{6}{25} a^{11} b x^{50}+\frac{22}{25} a^{10} b^2 x^{75}+\frac{11}{5} a^9 b^3 x^{100}+\frac{99}{25} a^8 b^4 x^{125}+\frac{132}{25} a^7 b^5 x^{150}+\frac{132}{25} a^6 b^6 x^{175}+\frac{99}{25} a^5 b^7 x^{200}+\frac{11}{5} a^4 b^8 x^{225}+\frac{22}{25} a^3 b^9 x^{250}+\frac{6}{25} a^2 b^{10} x^{275}+\frac{1}{25} a b^{11} x^{300}+\frac{b^{12} x^{325}}{325}","\frac{\left(a+b x^{25}\right)^{13}}{325 b}",1,"(a^12*x^25)/25 + (6*a^11*b*x^50)/25 + (22*a^10*b^2*x^75)/25 + (11*a^9*b^3*x^100)/5 + (99*a^8*b^4*x^125)/25 + (132*a^7*b^5*x^150)/25 + (132*a^6*b^6*x^175)/25 + (99*a^5*b^7*x^200)/25 + (11*a^4*b^8*x^225)/5 + (22*a^3*b^9*x^250)/25 + (6*a^2*b^10*x^275)/25 + (a*b^11*x^300)/25 + (b^12*x^325)/325","B",1
2594,1,160,16,0.0322399,"\int x^{36} \left(a+b x^{37}\right)^{12} \, dx","Integrate[x^36*(a + b*x^37)^12,x]","\frac{a^{12} x^{37}}{37}+\frac{6}{37} a^{11} b x^{74}+\frac{22}{37} a^{10} b^2 x^{111}+\frac{55}{37} a^9 b^3 x^{148}+\frac{99}{37} a^8 b^4 x^{185}+\frac{132}{37} a^7 b^5 x^{222}+\frac{132}{37} a^6 b^6 x^{259}+\frac{99}{37} a^5 b^7 x^{296}+\frac{55}{37} a^4 b^8 x^{333}+\frac{22}{37} a^3 b^9 x^{370}+\frac{6}{37} a^2 b^{10} x^{407}+\frac{1}{37} a b^{11} x^{444}+\frac{b^{12} x^{481}}{481}","\frac{\left(a+b x^{37}\right)^{13}}{481 b}",1,"(a^12*x^37)/37 + (6*a^11*b*x^74)/37 + (22*a^10*b^2*x^111)/37 + (55*a^9*b^3*x^148)/37 + (99*a^8*b^4*x^185)/37 + (132*a^7*b^5*x^222)/37 + (132*a^6*b^6*x^259)/37 + (99*a^5*b^7*x^296)/37 + (55*a^4*b^8*x^333)/37 + (22*a^3*b^9*x^370)/37 + (6*a^2*b^10*x^407)/37 + (a*b^11*x^444)/37 + (b^12*x^481)/481","B",1
2595,1,24,27,0.0159651,"\int x^{12 m} \left(a+b x^{1+12 m}\right)^{12} \, dx","Integrate[x^(12*m)*(a + b*x^(1 + 12*m))^12,x]","\frac{\left(a+b x^{12 m+1}\right)^{13}}{156 b m+13 b}","\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 + 156*b*m)","A",1
2596,1,24,27,0.0031009,"\int x^{12+12 (-1+m)} \left(a+b x^{1+12 m}\right)^{12} \, dx","Integrate[x^(12 + 12*(-1 + m))*(a + b*x^(1 + 12*m))^12,x]","\frac{\left(a+b x^{12 m+1}\right)^{13}}{156 b m+13 b}","\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 + 156*b*m)","A",1
2597,1,65,82,0.0774624,"\int \frac{x^{-1+5 n}}{a+b x^n} \, dx","Integrate[x^(-1 + 5*n)/(a + b*x^n),x]","\frac{12 a^4 \log \left(a+b x^n\right)+b x^n \left(-12 a^3+6 a^2 b x^n-4 a b^2 x^{2 n}+3 b^3 x^{3 n}\right)}{12 b^5 n}","\frac{a^4 \log \left(a+b x^n\right)}{b^5 n}-\frac{a^3 x^n}{b^4 n}+\frac{a^2 x^{2 n}}{2 b^3 n}-\frac{a x^{3 n}}{3 b^2 n}+\frac{x^{4 n}}{4 b n}",1,"(b*x^n*(-12*a^3 + 6*a^2*b*x^n - 4*a*b^2*x^(2*n) + 3*b^3*x^(3*n)) + 12*a^4*Log[a + b*x^n])/(12*b^5*n)","A",1
2598,1,52,64,0.0388379,"\int \frac{x^{-1+4 n}}{a+b x^n} \, dx","Integrate[x^(-1 + 4*n)/(a + b*x^n),x]","\frac{b x^n \left(6 a^2-3 a b x^n+2 b^2 x^{2 n}\right)-6 a^3 \log \left(a+b x^n\right)}{6 b^4 n}","-\frac{a^3 \log \left(a+b x^n\right)}{b^4 n}+\frac{a^2 x^n}{b^3 n}-\frac{a x^{2 n}}{2 b^2 n}+\frac{x^{3 n}}{3 b n}",1,"(b*x^n*(6*a^2 - 3*a*b*x^n + 2*b^2*x^(2*n)) - 6*a^3*Log[a + b*x^n])/(6*b^4*n)","A",1
2599,1,38,46,0.0476383,"\int \frac{x^{-1+3 n}}{a+b x^n} \, dx","Integrate[x^(-1 + 3*n)/(a + b*x^n),x]","\frac{2 a^2 \log \left(a+b x^n\right)+b x^n \left(b x^n-2 a\right)}{2 b^3 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,"(b*x^n*(-2*a + b*x^n) + 2*a^2*Log[a + b*x^n])/(2*b^3*n)","A",1
2600,1,26,28,0.0170693,"\int \frac{x^{-1+2 n}}{a+b x^n} \, dx","Integrate[x^(-1 + 2*n)/(a + b*x^n),x]","\frac{\frac{x^n}{b}-\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 - (a*Log[a + b*x^n])/b^2)/n","A",1
2601,1,15,15,0.0024985,"\int \frac{x^{-1+n}}{a+b x^n} \, dx","Integrate[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
2602,1,22,23,0.0111895,"\int \frac{1}{x \left(a+b x^n\right)} \, dx","Integrate[1/(x*(a + b*x^n)),x]","\frac{n \log (x)-\log \left(a+b x^n\right)}{a n}","\frac{\log (x)}{a}-\frac{\log \left(a+b x^n\right)}{a n}",1,"(n*Log[x] - Log[a + b*x^n])/(a*n)","A",1
2603,1,32,38,0.0528024,"\int \frac{x^{-1-n}}{a+b x^n} \, dx","Integrate[x^(-1 - n)/(a + b*x^n),x]","-\frac{-b \log \left(a+b x^n\right)+a x^{-n}+b n \log (x)}{a^2 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,"-((a/x^n + b*n*Log[x] - b*Log[a + b*x^n])/(a^2*n))","A",1
2604,1,49,57,0.0682229,"\int \frac{x^{-1-2 n}}{a+b x^n} \, dx","Integrate[x^(-1 - 2*n)/(a + b*x^n),x]","\frac{-2 b^2 \log \left(a+b x^n\right)+a x^{-2 n} \left(2 b x^n-a\right)+2 b^2 n \log (x)}{2 a^3 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,"((a*(-a + 2*b*x^n))/x^(2*n) + 2*b^2*n*Log[x] - 2*b^2*Log[a + b*x^n])/(2*a^3*n)","A",1
2605,1,62,76,0.1110808,"\int \frac{x^{-1-3 n}}{a+b x^n} \, dx","Integrate[x^(-1 - 3*n)/(a + b*x^n),x]","-\frac{a x^{-3 n} \left(2 a^2-3 a b x^n+6 b^2 x^{2 n}\right)-6 b^3 \log \left(a+b x^n\right)+6 b^3 n \log (x)}{6 a^4 n}","\frac{b^3 \log \left(a+b x^n\right)}{a^4 n}-\frac{b^3 \log (x)}{a^4}-\frac{b^2 x^{-n}}{a^3 n}+\frac{b x^{-2 n}}{2 a^2 n}-\frac{x^{-3 n}}{3 a n}",1,"-1/6*((a*(2*a^2 - 3*a*b*x^n + 6*b^2*x^(2*n)))/x^(3*n) + 6*b^3*n*Log[x] - 6*b^3*Log[a + b*x^n])/(a^4*n)","A",1
2606,1,65,82,0.0339126,"\int \frac{x^{4+5 (-1+n)}}{a+b x^n} \, dx","Integrate[x^(4 + 5*(-1 + n))/(a + b*x^n),x]","\frac{12 a^4 \log \left(a+b x^n\right)+b x^n \left(-12 a^3+6 a^2 b x^n-4 a b^2 x^{2 n}+3 b^3 x^{3 n}\right)}{12 b^5 n}","\frac{a^4 \log \left(a+b x^n\right)}{b^5 n}-\frac{a^3 x^n}{b^4 n}+\frac{a^2 x^{2 n}}{2 b^3 n}-\frac{a x^{3 n}}{3 b^2 n}+\frac{x^{4 n}}{4 b n}",1,"(b*x^n*(-12*a^3 + 6*a^2*b*x^n - 4*a*b^2*x^(2*n) + 3*b^3*x^(3*n)) + 12*a^4*Log[a + b*x^n])/(12*b^5*n)","A",1
2607,1,52,64,0.0420141,"\int \frac{x^{3+4 (-1+n)}}{a+b x^n} \, dx","Integrate[x^(3 + 4*(-1 + n))/(a + b*x^n),x]","\frac{b x^n \left(6 a^2-3 a b x^n+2 b^2 x^{2 n}\right)-6 a^3 \log \left(a+b x^n\right)}{6 b^4 n}","-\frac{a^3 \log \left(a+b x^n\right)}{b^4 n}+\frac{a^2 x^n}{b^3 n}-\frac{a x^{2 n}}{2 b^2 n}+\frac{x^{3 n}}{3 b n}",1,"(b*x^n*(6*a^2 - 3*a*b*x^n + 2*b^2*x^(2*n)) - 6*a^3*Log[a + b*x^n])/(6*b^4*n)","A",1
2608,1,38,46,0.0136089,"\int \frac{x^{2+3 (-1+n)}}{a+b x^n} \, dx","Integrate[x^(2 + 3*(-1 + n))/(a + b*x^n),x]","\frac{2 a^2 \log \left(a+b x^n\right)+b x^n \left(b x^n-2 a\right)}{2 b^3 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,"(b*x^n*(-2*a + b*x^n) + 2*a^2*Log[a + b*x^n])/(2*b^3*n)","A",1
2609,1,26,28,0.0115501,"\int \frac{x^{1+2 (-1+n)}}{a+b x^n} \, dx","Integrate[x^(1 + 2*(-1 + n))/(a + b*x^n),x]","\frac{\frac{x^n}{b}-\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 - (a*Log[a + b*x^n])/b^2)/n","A",1
2610,1,15,15,0.00151,"\int \frac{x^{-1+n}}{a+b x^n} \, dx","Integrate[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
2611,1,22,23,0.0232347,"\int \frac{1}{x \left(a+b x^n\right)} \, dx","Integrate[1/(x*(a + b*x^n)),x]","\frac{n \log (x)-\log \left(a+b x^n\right)}{a n}","\frac{\log (x)}{a}-\frac{\log \left(a+b x^n\right)}{a n}",1,"(n*Log[x] - Log[a + b*x^n])/(a*n)","A",1
2612,1,32,38,0.0099621,"\int \frac{x^{-1-n}}{a+b x^n} \, dx","Integrate[x^(-1 - n)/(a + b*x^n),x]","-\frac{-b \log \left(a+b x^n\right)+a x^{-n}+b n \log (x)}{a^2 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,"-((a/x^n + b*n*Log[x] - b*Log[a + b*x^n])/(a^2*n))","A",1
2613,1,49,57,0.0165079,"\int \frac{x^{-3-2 (-1+n)}}{a+b x^n} \, dx","Integrate[x^(-3 - 2*(-1 + n))/(a + b*x^n),x]","\frac{-2 b^2 \log \left(a+b x^n\right)+a x^{-2 n} \left(2 b x^n-a\right)+2 b^2 n \log (x)}{2 a^3 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,"((a*(-a + 2*b*x^n))/x^(2*n) + 2*b^2*n*Log[x] - 2*b^2*Log[a + b*x^n])/(2*a^3*n)","A",1
2614,1,62,76,0.0174631,"\int \frac{x^{-4-3 (-1+n)}}{a+b x^n} \, dx","Integrate[x^(-4 - 3*(-1 + n))/(a + b*x^n),x]","-\frac{a x^{-3 n} \left(2 a^2-3 a b x^n+6 b^2 x^{2 n}\right)-6 b^3 \log \left(a+b x^n\right)+6 b^3 n \log (x)}{6 a^4 n}","\frac{b^3 \log \left(a+b x^n\right)}{a^4 n}-\frac{b^3 \log (x)}{a^4}-\frac{b^2 x^{-n}}{a^3 n}+\frac{b x^{-2 n}}{2 a^2 n}-\frac{x^{-3 n}}{3 a n}",1,"-1/6*((a*(2*a^2 - 3*a*b*x^n + 6*b^2*x^(2*n)))/x^(3*n) + 6*b^3*n*Log[x] - 6*b^3*Log[a + b*x^n])/(a^4*n)","A",1
2615,1,54,71,0.0474317,"\int \frac{x^{-1+5 n}}{2+b x^n} \, dx","Integrate[x^(-1 + 5*n)/(2 + b*x^n),x]","\frac{b x^n \left(3 b^3 x^{3 n}-8 b^2 x^{2 n}+24 b x^n-96\right)+192 \log \left(b x^n+2\right)}{12 b^5 n}","\frac{16 \log \left(b x^n+2\right)}{b^5 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{x^{4 n}}{4 b n}",1,"(b*x^n*(-96 + 24*b*x^n - 8*b^2*x^(2*n) + 3*b^3*x^(3*n)) + 192*Log[2 + b*x^n])/(12*b^5*n)","A",1
2616,1,43,56,0.0246041,"\int \frac{x^{-1+4 n}}{2+b x^n} \, dx","Integrate[x^(-1 + 4*n)/(2 + b*x^n),x]","\frac{b x^n \left(b^2 x^{2 n}-3 b x^n+12\right)-24 \log \left(b x^n+2\right)}{3 b^4 n}","-\frac{8 \log \left(b x^n+2\right)}{b^4 n}+\frac{4 x^n}{b^3 n}-\frac{x^{2 n}}{b^2 n}+\frac{x^{3 n}}{3 b n}",1,"(b*x^n*(12 - 3*b*x^n + b^2*x^(2*n)) - 24*Log[2 + b*x^n])/(3*b^4*n)","A",1
2617,1,33,43,0.0188787,"\int \frac{x^{-1+3 n}}{2+b x^n} \, dx","Integrate[x^(-1 + 3*n)/(2 + b*x^n),x]","\frac{b x^n \left(b x^n-4\right)+8 \log \left(b x^n+2\right)}{2 b^3 n}","\frac{4 \log \left(b x^n+2\right)}{b^3 n}-\frac{2 x^n}{b^2 n}+\frac{x^{2 n}}{2 b n}",1,"(b*x^n*(-4 + b*x^n) + 8*Log[2 + b*x^n])/(2*b^3*n)","A",1
2618,1,25,27,0.0118613,"\int \frac{x^{-1+2 n}}{2+b x^n} \, dx","Integrate[x^(-1 + 2*n)/(2 + b*x^n),x]","\frac{\frac{x^n}{b}-\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 - (2*Log[2 + b*x^n])/b^2)/n","A",1
2619,1,15,15,0.0022808,"\int \frac{x^{-1+n}}{2+b x^n} \, dx","Integrate[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
2620,1,22,22,0.0055789,"\int \frac{1}{x \left(2+b x^n\right)} \, dx","Integrate[1/(x*(2 + b*x^n)),x]","\frac{n \log (x)-\log \left(b x^n+2\right)}{2 n}","\frac{\log (x)}{2}-\frac{\log \left(b x^n+2\right)}{2 n}",1,"(n*Log[x] - Log[2 + b*x^n])/(2*n)","A",1
2621,1,31,36,0.0450611,"\int \frac{x^{-1-n}}{2+b x^n} \, dx","Integrate[x^(-1 - n)/(2 + b*x^n),x]","-\frac{-b \log \left(b x^n+2\right)+b n \log (x)+2 x^{-n}}{4 n}","\frac{b \log \left(b x^n+2\right)}{4 n}-\frac{1}{4} b \log (x)-\frac{x^{-n}}{2 n}",1,"-1/4*(2/x^n + b*n*Log[x] - b*Log[2 + b*x^n])/n","A",1
2622,1,42,53,0.0528407,"\int \frac{x^{-1-2 n}}{2+b x^n} \, dx","Integrate[x^(-1 - 2*n)/(2 + b*x^n),x]","-\frac{b^2 \log \left(b x^n+2\right)-b^2 n \log (x)+x^{-2 n} \left(2-2 b x^n\right)}{8 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,"-1/8*((2 - 2*b*x^n)/x^(2*n) - b^2*n*Log[x] + b^2*Log[2 + b*x^n])/n","A",1
2623,1,53,68,0.082143,"\int \frac{x^{-1-3 n}}{2+b x^n} \, dx","Integrate[x^(-1 - 3*n)/(2 + b*x^n),x]","-\frac{-3 b^3 \log \left(b x^n+2\right)+3 b^3 n \log (x)+x^{-3 n} \left(6 b^2 x^{2 n}-6 b x^n+8\right)}{48 n}","\frac{b^3 \log \left(b x^n+2\right)}{16 n}-\frac{1}{16} b^3 \log (x)-\frac{b^2 x^{-n}}{8 n}+\frac{b x^{-2 n}}{8 n}-\frac{x^{-3 n}}{6 n}",1,"-1/48*((8 - 6*b*x^n + 6*b^2*x^(2*n))/x^(3*n) + 3*b^3*n*Log[x] - 3*b^3*Log[2 + b*x^n])/n","A",1
2624,1,54,66,0.0727996,"\int \frac{x^{-1+4 n}}{\left(a+b x^n\right)^2} \, dx","Integrate[x^(-1 + 4*n)/(a + b*x^n)^2,x]","\frac{\frac{2 a^3}{a+b x^n}+6 a^2 \log \left(a+b x^n\right)-4 a b x^n+b^2 x^{2 n}}{2 b^4 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,"(-4*a*b*x^n + b^2*x^(2*n) + (2*a^3)/(a + b*x^n) + 6*a^2*Log[a + b*x^n])/(2*b^4*n)","A",1
2625,1,38,48,0.0496816,"\int \frac{x^{-1+3 n}}{\left(a+b x^n\right)^2} \, dx","Integrate[x^(-1 + 3*n)/(a + b*x^n)^2,x]","\frac{-\frac{a^2}{a+b x^n}-2 a \log \left(a+b x^n\right)+b x^n}{b^3 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,"(b*x^n - a^2/(a + b*x^n) - 2*a*Log[a + b*x^n])/(b^3*n)","A",1
2626,1,27,33,0.0276751,"\int \frac{x^{-1+2 n}}{\left(a+b x^n\right)^2} \, dx","Integrate[x^(-1 + 2*n)/(a + b*x^n)^2,x]","\frac{\frac{a}{a+b x^n}+\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/(a + b*x^n) + Log[a + b*x^n])/(b^2*n)","A",1
2627,1,17,17,0.0059162,"\int \frac{x^{-1+n}}{\left(a+b x^n\right)^2} \, dx","Integrate[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
2628,1,33,39,0.0695372,"\int \frac{1}{x \left(a+b x^n\right)^2} \, dx","Integrate[1/(x*(a + b*x^n)^2),x]","\frac{\frac{a}{a+b x^n}-\log \left(a+b x^n\right)+n \log (x)}{a^2 n}","-\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,"(a/(a + b*x^n) + n*Log[x] - Log[a + b*x^n])/(a^2*n)","A",1
2629,1,45,57,0.1528354,"\int \frac{x^{-1-n}}{\left(a+b x^n\right)^2} \, dx","Integrate[x^(-1 - n)/(a + b*x^n)^2,x]","-\frac{-2 b \log \left(a+b x^n\right)+a \left(\frac{b}{a+b x^n}+x^{-n}\right)+2 b n \log (x)}{a^3 n}","\frac{2 b \log \left(a+b x^n\right)}{a^3 n}-\frac{2 b \log (x)}{a^3}-\frac{b}{a^2 n \left(a+b x^n\right)}-\frac{x^{-n}}{a^2 n}",1,"-((a*(x^(-n) + b/(a + b*x^n)) + 2*b*n*Log[x] - 2*b*Log[a + b*x^n])/(a^3*n))","A",1
2630,1,65,78,0.2099051,"\int \frac{x^{-1-2 n}}{\left(a+b x^n\right)^2} \, dx","Integrate[x^(-1 - 2*n)/(a + b*x^n)^2,x]","\frac{-6 b^2 \log \left(a+b x^n\right)+a \left(\frac{2 b^2}{a+b x^n}-a x^{-2 n}+4 b x^{-n}\right)+6 b^2 n \log (x)}{2 a^4 n}","-\frac{3 b^2 \log \left(a+b x^n\right)}{a^4 n}+\frac{3 b^2 \log (x)}{a^4}+\frac{b^2}{a^3 n \left(a+b x^n\right)}+\frac{2 b x^{-n}}{a^3 n}-\frac{x^{-2 n}}{2 a^2 n}",1,"(a*(-(a/x^(2*n)) + (4*b)/x^n + (2*b^2)/(a + b*x^n)) + 6*b^2*n*Log[x] - 6*b^2*Log[a + b*x^n])/(2*a^4*n)","A",1
2631,1,78,94,0.2213055,"\int \frac{x^{-1-3 n}}{\left(a+b x^n\right)^2} \, dx","Integrate[x^(-1 - 3*n)/(a + b*x^n)^2,x]","\frac{a \left(-a^2 x^{-3 n}-\frac{3 b^3}{a+b x^n}+3 a b x^{-2 n}-9 b^2 x^{-n}\right)+12 b^3 \log \left(a+b x^n\right)-12 b^3 n \log (x)}{3 a^5 n}","\frac{4 b^3 \log \left(a+b x^n\right)}{a^5 n}-\frac{4 b^3 \log (x)}{a^5}-\frac{b^3}{a^4 n \left(a+b x^n\right)}-\frac{3 b^2 x^{-n}}{a^4 n}+\frac{b x^{-2 n}}{a^3 n}-\frac{x^{-3 n}}{3 a^2 n}",1,"(a*(-(a^2/x^(3*n)) + (3*a*b)/x^(2*n) - (9*b^2)/x^n - (3*b^3)/(a + b*x^n)) - 12*b^3*n*Log[x] + 12*b^3*Log[a + b*x^n])/(3*a^5*n)","A",1
2632,1,51,70,0.180743,"\int \frac{x^{-1+4 n}}{\left(a+b x^n\right)^3} \, dx","Integrate[x^(-1 + 4*n)/(a + b*x^n)^3,x]","-\frac{\frac{a^2 \left(5 a+6 b x^n\right)}{\left(a+b x^n\right)^2}+6 a \log \left(a+b x^n\right)-2 b x^n}{2 b^4 n}","\frac{a^3}{2 b^4 n \left(a+b x^n\right)^2}-\frac{3 a^2}{b^4 n \left(a+b x^n\right)}-\frac{3 a \log \left(a+b x^n\right)}{b^4 n}+\frac{x^n}{b^3 n}",1,"-1/2*(-2*b*x^n + (a^2*(5*a + 6*b*x^n))/(a + b*x^n)^2 + 6*a*Log[a + b*x^n])/(b^4*n)","A",1
2633,1,42,56,0.0476675,"\int \frac{x^{-1+3 n}}{\left(a+b x^n\right)^3} \, dx","Integrate[x^(-1 + 3*n)/(a + b*x^n)^3,x]","\frac{\frac{a \left(3 a+4 b x^n\right)}{\left(a+b x^n\right)^2}+2 \log \left(a+b x^n\right)}{2 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*(3*a + 4*b*x^n))/(a + b*x^n)^2 + 2*Log[a + b*x^n])/(2*b^3*n)","A",1
2634,1,24,24,0.0074639,"\int \frac{x^{-1+2 n}}{\left(a+b x^n\right)^3} \, dx","Integrate[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
2635,1,19,19,0.0047064,"\int \frac{x^{-1+n}}{\left(a+b x^n\right)^3} \, dx","Integrate[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*1/(b*n*(a + b*x^n)^2)","A",1
2636,1,47,58,0.1217917,"\int \frac{1}{x \left(a+b x^n\right)^3} \, dx","Integrate[1/(x*(a + b*x^n)^3),x]","\frac{\frac{a \left(3 a+2 b x^n\right)}{\left(a+b x^n\right)^2}-2 \log \left(a+b x^n\right)+2 n \log (x)}{2 a^3 n}","-\frac{\log \left(a+b x^n\right)}{a^3 n}+\frac{\log (x)}{a^3}+\frac{1}{a^2 n \left(a+b x^n\right)}+\frac{1}{2 a n \left(a+b x^n\right)^2}",1,"((a*(3*a + 2*b*x^n))/(a + b*x^n)^2 + 2*n*Log[x] - 2*Log[a + b*x^n])/(2*a^3*n)","A",1
2637,1,58,77,0.2156171,"\int \frac{x^{-1-n}}{\left(a+b x^n\right)^3} \, dx","Integrate[x^(-1 - n)/(a + b*x^n)^3,x]","-\frac{\frac{a b \left(5 a+4 b x^n\right)}{\left(a+b x^n\right)^2}-6 b \log \left(a+b x^n\right)+2 a x^{-n}+6 b n \log (x)}{2 a^4 n}","\frac{3 b \log \left(a+b x^n\right)}{a^4 n}-\frac{3 b \log (x)}{a^4}-\frac{2 b}{a^3 n \left(a+b x^n\right)}-\frac{x^{-n}}{a^3 n}-\frac{b}{2 a^2 n \left(a+b x^n\right)^2}",1,"-1/2*((2*a)/x^n + (a*b*(5*a + 4*b*x^n))/(a + b*x^n)^2 + 6*b*n*Log[x] - 6*b*Log[a + b*x^n])/(a^4*n)","A",1
2638,1,79,101,0.2661544,"\int \frac{x^{-1-2 n}}{\left(a+b x^n\right)^3} \, dx","Integrate[x^(-1 - 2*n)/(a + b*x^n)^3,x]","\frac{\frac{a x^{-2 n} \left(a+2 b x^n\right) \left(-a^2+6 a b x^n+6 b^2 x^{2 n}\right)}{\left(a+b x^n\right)^2}-12 b^2 \log \left(a+b x^n\right)+12 b^2 n \log (x)}{2 a^5 n}","-\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^2}{a^4 n \left(a+b x^n\right)}+\frac{3 b x^{-n}}{a^4 n}+\frac{b^2}{2 a^3 n \left(a+b x^n\right)^2}-\frac{x^{-2 n}}{2 a^3 n}",1,"((a*(a + 2*b*x^n)*(-a^2 + 6*a*b*x^n + 6*b^2*x^(2*n)))/(x^(2*n)*(a + b*x^n)^2) + 12*b^2*n*Log[x] - 12*b^2*Log[a + b*x^n])/(2*a^5*n)","A",1
2639,1,32,50,0.0074785,"\int \frac{x^{-1-\frac{n}{2}}}{a+b x^n} \, dx","Integrate[x^(-1 - n/2)/(a + b*x^n),x]","-\frac{2 x^{-n/2} \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};-\frac{b x^n}{a}\right)}{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*Hypergeometric2F1[-1/2, 1, 1/2, -((b*x^n)/a)])/(a*n*x^(n/2))","C",1
2640,1,34,160,0.0176813,"\int \frac{x^{-1-\frac{2 n}{3}}}{a+b x^n} \, dx","Integrate[x^(-1 - (2*n)/3)/(a + b*x^n),x]","-\frac{3 x^{-2 n/3} \, _2F_1\left(-\frac{2}{3},1;\frac{1}{3};-\frac{b x^n}{a}\right)}{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*Hypergeometric2F1[-2/3, 1, 1/3, -((b*x^n)/a)])/(2*a*n*x^((2*n)/3))","C",1
2641,1,34,236,0.0077691,"\int \frac{x^{-1-\frac{3 n}{4}}}{a+b x^n} \, dx","Integrate[x^(-1 - (3*n)/4)/(a + b*x^n),x]","-\frac{4 x^{-3 n/4} \, _2F_1\left(-\frac{3}{4},1;\frac{1}{4};-\frac{b x^n}{a}\right)}{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*Hypergeometric2F1[-3/4, 1, 1/4, -((b*x^n)/a)])/(3*a*n*x^((3*n)/4))","C",1
2642,1,32,38,0.0283784,"\int \frac{x^{-1-n}}{a+b x^n} \, dx","Integrate[x^(-1 - n)/(a + b*x^n),x]","-\frac{-b \log \left(a+b x^n\right)+a x^{-n}+b n \log (x)}{a^2 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,"-((a/x^n + b*n*Log[x] - b*Log[a + b*x^n])/(a^2*n))","A",1
2643,1,32,50,0.0040775,"\int \frac{x^{-1-\frac{n}{2}}}{a+b x^n} \, dx","Integrate[x^(-1 - n/2)/(a + b*x^n),x]","-\frac{2 x^{-n/2} \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};-\frac{b x^n}{a}\right)}{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*Hypergeometric2F1[-1/2, 1, 1/2, -((b*x^n)/a)])/(a*n*x^(n/2))","C",1
2644,1,32,158,0.0069701,"\int \frac{x^{-1-\frac{n}{3}}}{a+b x^n} \, dx","Integrate[x^(-1 - n/3)/(a + b*x^n),x]","-\frac{3 x^{-n/3} \, _2F_1\left(-\frac{1}{3},1;\frac{2}{3};-\frac{b x^n}{a}\right)}{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*Hypergeometric2F1[-1/3, 1, 2/3, -((b*x^n)/a)])/(a*n*x^(n/3))","C",1
2645,1,32,234,0.0070139,"\int \frac{x^{-1-\frac{n}{4}}}{a+b x^n} \, dx","Integrate[x^(-1 - n/4)/(a + b*x^n),x]","-\frac{4 x^{-n/4} \, _2F_1\left(-\frac{1}{4},1;\frac{3}{4};-\frac{b x^n}{a}\right)}{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*Hypergeometric2F1[-1/4, 1, 3/4, -((b*x^n)/a)])/(a*n*x^(n/4))","C",1
2646,1,34,68,0.0077407,"\int \frac{x^{-1-\frac{3 n}{2}}}{a+b x^n} \, dx","Integrate[x^(-1 - (3*n)/2)/(a + b*x^n),x]","-\frac{2 x^{-3 n/2} \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};-\frac{b x^n}{a}\right)}{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*Hypergeometric2F1[-3/2, 1, -1/2, -((b*x^n)/a)])/(3*a*n*x^((3*n)/2))","C",1
2647,1,34,176,0.007738,"\int \frac{x^{-1-\frac{4 n}{3}}}{a+b x^n} \, dx","Integrate[x^(-1 - (4*n)/3)/(a + b*x^n),x]","-\frac{3 x^{-4 n/3} \, _2F_1\left(-\frac{4}{3},1;-\frac{1}{3};-\frac{b x^n}{a}\right)}{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*Hypergeometric2F1[-4/3, 1, -1/3, -((b*x^n)/a)])/(4*a*n*x^((4*n)/3))","C",1
2648,1,34,252,0.0077264,"\int \frac{x^{-1-\frac{5 n}{4}}}{a+b x^n} \, dx","Integrate[x^(-1 - (5*n)/4)/(a + b*x^n),x]","-\frac{4 x^{-5 n/4} \, _2F_1\left(-\frac{5}{4},1;-\frac{1}{4};-\frac{b x^n}{a}\right)}{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*Hypergeometric2F1[-5/4, 1, -1/4, -((b*x^n)/a)])/(5*a*n*x^((5*n)/4))","C",1
2649,1,57,92,0.0493615,"\int x^{-1+4 n} \sqrt{a+b x^n} \, dx","Integrate[x^(-1 + 4*n)*Sqrt[a + b*x^n],x]","\frac{2 \left(a+b x^n\right)^{3/2} \left(-16 a^3+24 a^2 b x^n-30 a b^2 x^{2 n}+35 b^3 x^{3 n}\right)}{315 b^4 n}","-\frac{2 a^3 \left(a+b x^n\right)^{3/2}}{3 b^4 n}+\frac{6 a^2 \left(a+b x^n\right)^{5/2}}{5 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 + b*x^n)^(3/2)*(-16*a^3 + 24*a^2*b*x^n - 30*a*b^2*x^(2*n) + 35*b^3*x^(3*n)))/(315*b^4*n)","A",1
2650,1,44,68,0.0370389,"\int x^{-1+3 n} \sqrt{a+b x^n} \, dx","Integrate[x^(-1 + 3*n)*Sqrt[a + b*x^n],x]","\frac{2 \left(a+b x^n\right)^{3/2} \left(8 a^2-12 a b x^n+15 b^2 x^{2 n}\right)}{105 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 + b*x^n)^(3/2)*(8*a^2 - 12*a*b*x^n + 15*b^2*x^(2*n)))/(105*b^3*n)","A",1
2651,1,31,44,0.0340603,"\int x^{-1+2 n} \sqrt{a+b x^n} \, dx","Integrate[x^(-1 + 2*n)*Sqrt[a + b*x^n],x]","\frac{2 \left(a+b x^n\right)^{3/2} \left(3 b x^n-2 a\right)}{15 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 + b*x^n)^(3/2)*(-2*a + 3*b*x^n))/(15*b^2*n)","A",1
2652,1,21,21,0.011653,"\int x^{-1+n} \sqrt{a+b x^n} \, dx","Integrate[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
2653,1,43,45,0.0128501,"\int \frac{\sqrt{a+b x^n}}{x} \, dx","Integrate[Sqrt[a + b*x^n]/x,x]","\frac{2 \sqrt{a+b x^n}-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] - 2*Sqrt[a]*ArcTanh[Sqrt[a + b*x^n]/Sqrt[a]])/n","A",1
2654,1,62,51,0.0557455,"\int x^{-1-n} \sqrt{a+b x^n} \, dx","Integrate[x^(-1 - n)*Sqrt[a + b*x^n],x]","-\frac{x^{-n} \left(b x^n \sqrt{\frac{b x^n}{a}+1} \tanh ^{-1}\left(\sqrt{\frac{b x^n}{a}+1}\right)+a+b x^n\right)}{n \sqrt{a+b x^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}",1,"-((a + b*x^n + b*x^n*Sqrt[1 + (b*x^n)/a]*ArcTanh[Sqrt[1 + (b*x^n)/a]])/(n*x^n*Sqrt[a + b*x^n]))","A",1
2655,1,42,84,0.0131975,"\int x^{-1-2 n} \sqrt{a+b x^n} \, dx","Integrate[x^(-1 - 2*n)*Sqrt[a + b*x^n],x]","-\frac{2 b^2 \left(a+b x^n\right)^{3/2} \, _2F_1\left(\frac{3}{2},3;\frac{5}{2};\frac{b x^n}{a}+1\right)}{3 a^3 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,"(-2*b^2*(a + b*x^n)^(3/2)*Hypergeometric2F1[3/2, 3, 5/2, 1 + (b*x^n)/a])/(3*a^3*n)","C",1
2656,1,42,113,0.0115601,"\int x^{-1-3 n} \sqrt{a+b x^n} \, dx","Integrate[x^(-1 - 3*n)*Sqrt[a + b*x^n],x]","\frac{2 b^3 \left(a+b x^n\right)^{3/2} \, _2F_1\left(\frac{3}{2},4;\frac{5}{2};\frac{b x^n}{a}+1\right)}{3 a^4 n}","-\frac{b^3 \tanh ^{-1}\left(\frac{\sqrt{a+b x^n}}{\sqrt{a}}\right)}{8 a^{5/2} n}+\frac{b^2 x^{-n} \sqrt{a+b x^n}}{8 a^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,"(2*b^3*(a + b*x^n)^(3/2)*Hypergeometric2F1[3/2, 4, 5/2, 1 + (b*x^n)/a])/(3*a^4*n)","C",1
2657,1,42,142,0.0124495,"\int x^{-1-4 n} \sqrt{a+b x^n} \, dx","Integrate[x^(-1 - 4*n)*Sqrt[a + b*x^n],x]","-\frac{2 b^4 \left(a+b x^n\right)^{3/2} \, _2F_1\left(\frac{3}{2},5;\frac{5}{2};\frac{b x^n}{a}+1\right)}{3 a^5 n}","\frac{5 b^4 \tanh ^{-1}\left(\frac{\sqrt{a+b x^n}}{\sqrt{a}}\right)}{64 a^{7/2} n}-\frac{5 b^3 x^{-n} \sqrt{a+b x^n}}{64 a^3 n}+\frac{5 b^2 x^{-2 n} \sqrt{a+b x^n}}{96 a^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,"(-2*b^4*(a + b*x^n)^(3/2)*Hypergeometric2F1[3/2, 5, 5/2, 1 + (b*x^n)/a])/(3*a^5*n)","C",1
2658,1,57,88,0.0506775,"\int \frac{x^{-1+4 n}}{\sqrt{a+b x^n}} \, dx","Integrate[x^(-1 + 4*n)/Sqrt[a + b*x^n],x]","\frac{2 \sqrt{a+b x^n} \left(-16 a^3+8 a^2 b x^n-6 a b^2 x^{2 n}+5 b^3 x^{3 n}\right)}{35 b^4 n}","-\frac{2 a^3 \sqrt{a+b x^n}}{b^4 n}+\frac{2 a^2 \left(a+b x^n\right)^{3/2}}{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*Sqrt[a + b*x^n]*(-16*a^3 + 8*a^2*b*x^n - 6*a*b^2*x^(2*n) + 5*b^3*x^(3*n)))/(35*b^4*n)","A",1
2659,1,44,66,0.0248276,"\int \frac{x^{-1+3 n}}{\sqrt{a+b x^n}} \, dx","Integrate[x^(-1 + 3*n)/Sqrt[a + b*x^n],x]","\frac{2 \sqrt{a+b x^n} \left(8 a^2-4 a b x^n+3 b^2 x^{2 n}\right)}{15 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*Sqrt[a + b*x^n]*(8*a^2 - 4*a*b*x^n + 3*b^2*x^(2*n)))/(15*b^3*n)","A",1
2660,1,30,42,0.0405563,"\int \frac{x^{-1+2 n}}{\sqrt{a+b x^n}} \, dx","Integrate[x^(-1 + 2*n)/Sqrt[a + b*x^n],x]","\frac{2 \left(b x^n-2 a\right) \sqrt{a+b x^n}}{3 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*(-2*a + b*x^n)*Sqrt[a + b*x^n])/(3*b^2*n)","A",1
2661,1,19,19,0.0036786,"\int \frac{x^{-1+n}}{\sqrt{a+b x^n}} \, dx","Integrate[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
2662,1,28,28,0.0099131,"\int \frac{1}{x \sqrt{a+b x^n}} \, dx","Integrate[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",1
2663,1,67,53,0.0893292,"\int \frac{x^{-1-n}}{\sqrt{a+b x^n}} \, dx","Integrate[x^(-1 - n)/Sqrt[a + b*x^n],x]","\frac{2 b \sqrt{a+b x^n} \left(\frac{\tanh ^{-1}\left(\sqrt{\frac{b x^n}{a}+1}\right)}{2 \sqrt{\frac{b x^n}{a}+1}}-\frac{a x^{-n}}{2 b}\right)}{a^2 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,"(2*b*Sqrt[a + b*x^n]*(-1/2*a/(b*x^n) + ArcTanh[Sqrt[1 + (b*x^n)/a]]/(2*Sqrt[1 + (b*x^n)/a])))/(a^2*n)","A",1
2664,1,40,87,0.0153311,"\int \frac{x^{-1-2 n}}{\sqrt{a+b x^n}} \, dx","Integrate[x^(-1 - 2*n)/Sqrt[a + b*x^n],x]","-\frac{2 b^2 \sqrt{a+b x^n} \, _2F_1\left(\frac{1}{2},3;\frac{3}{2};\frac{b x^n}{a}+1\right)}{a^3 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,"(-2*b^2*Sqrt[a + b*x^n]*Hypergeometric2F1[1/2, 3, 3/2, 1 + (b*x^n)/a])/(a^3*n)","C",1
2665,1,40,116,0.0094054,"\int \frac{x^{-1-3 n}}{\sqrt{a+b x^n}} \, dx","Integrate[x^(-1 - 3*n)/Sqrt[a + b*x^n],x]","\frac{2 b^3 \sqrt{a+b x^n} \, _2F_1\left(\frac{1}{2},4;\frac{3}{2};\frac{b x^n}{a}+1\right)}{a^4 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^2 x^{-n} \sqrt{a+b x^n}}{8 a^3 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,"(2*b^3*Sqrt[a + b*x^n]*Hypergeometric2F1[1/2, 4, 3/2, 1 + (b*x^n)/a])/(a^4*n)","C",1
2666,1,40,145,0.0102177,"\int \frac{x^{-1-4 n}}{\sqrt{a+b x^n}} \, dx","Integrate[x^(-1 - 4*n)/Sqrt[a + b*x^n],x]","-\frac{2 b^4 \sqrt{a+b x^n} \, _2F_1\left(\frac{1}{2},5;\frac{3}{2};\frac{b x^n}{a}+1\right)}{a^5 n}","-\frac{35 b^4 \tanh ^{-1}\left(\frac{\sqrt{a+b x^n}}{\sqrt{a}}\right)}{64 a^{9/2} n}+\frac{35 b^3 x^{-n} \sqrt{a+b x^n}}{64 a^4 n}-\frac{35 b^2 x^{-2 n} \sqrt{a+b x^n}}{96 a^3 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,"(-2*b^4*Sqrt[a + b*x^n]*Hypergeometric2F1[1/2, 5, 3/2, 1 + (b*x^n)/a])/(a^5*n)","C",1
2667,1,67,75,0.0620432,"\int x^m \left(a+b x^n\right)^3 \, dx","Integrate[x^m*(a + b*x^n)^3,x]","x^{m+1} \left(\frac{a^3}{m+1}+\frac{3 a^2 b x^n}{m+n+1}+\frac{3 a b^2 x^{2 n}}{m+2 n+1}+\frac{b^3 x^{3 n}}{m+3 n+1}\right)","\frac{a^3 x^{m+1}}{m+1}+\frac{3 a^2 b x^{m+n+1}}{m+n+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,"x^(1 + m)*(a^3/(1 + m) + (3*a^2*b*x^n)/(1 + m + n) + (3*a*b^2*x^(2*n))/(1 + m + 2*n) + (b^3*x^(3*n))/(1 + m + 3*n))","A",1
2668,1,46,51,0.0393709,"\int x^m \left(a+b x^n\right)^2 \, dx","Integrate[x^m*(a + b*x^n)^2,x]","x^{m+1} \left(\frac{a^2}{m+1}+\frac{2 a b x^n}{m+n+1}+\frac{b^2 x^{2 n}}{m+2 n+1}\right)","\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,"x^(1 + m)*(a^2/(1 + m) + (2*a*b*x^n)/(1 + m + n) + (b^2*x^(2*n))/(1 + m + 2*n))","A",1
2669,1,27,27,0.0209283,"\int x^m \left(a+b x^n\right) \, dx","Integrate[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",1
2670,1,41,40,0.0079184,"\int \frac{x^m}{a+b x^n} \, dx","Integrate[x^m/(a + b*x^n),x]","\frac{x^{m+1} \, _2F_1\left(1,\frac{m+1}{n};\frac{m+1}{n}+1;-\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 + (1 + m)/n, -((b*x^n)/a)])/(a*(1 + m))","A",1
2671,1,41,40,0.0151914,"\int \frac{x^m}{\left(a+b x^n\right)^2} \, dx","Integrate[x^m/(a + b*x^n)^2,x]","\frac{x^{m+1} \, _2F_1\left(2,\frac{m+1}{n};\frac{m+1}{n}+1;-\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 + (1 + m)/n, -((b*x^n)/a)])/(a^2*(1 + m))","A",1
2672,1,41,40,0.007095,"\int \frac{x^m}{\left(a+b x^n\right)^3} \, dx","Integrate[x^m/(a + b*x^n)^3,x]","\frac{x^{m+1} \, _2F_1\left(3,\frac{m+1}{n};\frac{m+1}{n}+1;-\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 + (1 + m)/n, -((b*x^n)/a)])/(a^3*(1 + m))","A",1
2673,1,66,55,0.0216771,"\int x^m \left(a+b x^n\right)^{3/2} \, dx","Integrate[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+1}{n}+1;-\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 + (1 + m)/n, -((b*x^n)/a)])/((1 + m)*Sqrt[1 + (b*x^n)/a])","A",1
2674,1,65,55,0.0163961,"\int x^m \sqrt{a+b x^n} \, dx","Integrate[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+1}{n}+1;-\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 + (1 + m)/n, -((b*x^n)/a)])/((1 + m)*Sqrt[1 + (b*x^n)/a])","A",1
2675,1,65,55,0.0244258,"\int \frac{x^m}{\sqrt{a+b x^n}} \, dx","Integrate[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+1}{n}+1;-\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 + (1 + m)/n, -((b*x^n)/a)])/((1 + m)*Sqrt[a + b*x^n])","A",1
2676,1,68,55,0.0350169,"\int \frac{x^m}{\left(a+b x^n\right)^{3/2}} \, dx","Integrate[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+1}{n}+1;-\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 + (1 + m)/n, -((b*x^n)/a)])/(a*(1 + m)*Sqrt[a + b*x^n])","A",1
2677,1,68,55,0.0206176,"\int \frac{x^m}{\left(a+b x^n\right)^{5/2}} \, dx","Integrate[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+1}{n}+1;-\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 + (1 + m)/n, -((b*x^n)/a)])/(a^2*(1 + m)*Sqrt[a + b*x^n])","A",1
2678,1,68,59,0.0308316,"\int \frac{x^{3+2 n}}{\sqrt{a+b x^n}} \, dx","Integrate[x^(3 + 2*n)/Sqrt[a + b*x^n],x]","\frac{x^{2 n+4} \sqrt{\frac{b x^n}{a}+1} \, _2F_1\left(\frac{1}{2},2+\frac{4}{n};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^(4 + 2*n)*Sqrt[1 + (b*x^n)/a]*Hypergeometric2F1[1/2, 2 + 4/n, 3 + 4/n, -((b*x^n)/a)])/(2*(2 + n)*Sqrt[a + b*x^n])","A",1
2679,1,65,56,0.0421024,"\int \frac{x^{3+n}}{\sqrt{a+b x^n}} \, dx","Integrate[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};\frac{n+4}{n}+1;-\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, 1 + (4 + n)/n, -((b*x^n)/a)])/((4 + n)*Sqrt[a + b*x^n])","A",1
2680,1,64,56,0.0288005,"\int \frac{x^{3-n}}{\sqrt{a+b x^n}} \, dx","Integrate[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)}{(n-4) \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",1
2681,1,68,61,0.0237573,"\int \frac{x^{3-2 n}}{\sqrt{a+b x^n}} \, dx","Integrate[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},\frac{4}{n}-2;\frac{4}{n}-1;-\frac{b x^n}{a}\right)}{2 (n-2) \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,"-1/2*(x^(4 - 2*n)*Sqrt[1 + (b*x^n)/a]*Hypergeometric2F1[1/2, -2 + 4/n, -1 + 4/n, -((b*x^n)/a)])/((-2 + n)*Sqrt[a + b*x^n])","A",1
2682,1,77,66,0.0234726,"\int \frac{x^{m+2 n}}{\sqrt{a+b x^n}} \, dx","Integrate[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+2 n+1}{n}+1;-\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 + (1 + m + 2*n)/n, -((b*x^n)/a)])/((1 + m + 2*n)*Sqrt[a + b*x^n])","A",1
2683,1,69,60,0.0282416,"\int \frac{x^{m+n}}{\sqrt{a+b x^n}} \, dx","Integrate[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+n+1}{n}+1;-\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 + (1 + m + n)/n, -((b*x^n)/a)])/((1 + m + n)*Sqrt[a + b*x^n])","A",1
2684,1,72,63,0.0253408,"\int \frac{x^{m-n}}{\sqrt{a+b x^n}} \, dx","Integrate[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",1
2685,1,77,66,0.028677,"\int \frac{x^{m-2 n}}{\sqrt{a+b x^n}} \, dx","Integrate[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-2 n+1}{n}+1;-\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 + (1 + m - 2*n)/n, -((b*x^n)/a)])/((1 + m - 2*n)*Sqrt[a + b*x^n])","A",1
2686,1,111,15,0.2266442,"\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","Integrate[-1/2*(b*n*x^(-1 + m + n))/(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} \left(b (2 m-n) x^n \, _2F_1\left(\frac{3}{2},\frac{m+n}{n};\frac{m}{n}+2;-\frac{b x^n}{a}\right)+2 a (m+n) \, _2F_1\left(\frac{3}{2},\frac{m}{n};\frac{m+n}{n};-\frac{b x^n}{a}\right)\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]*(2*a*(m + n)*Hypergeometric2F1[3/2, m/n, (m + n)/n, -((b*x^n)/a)] + b*(2*m - n)*x^n*Hypergeometric2F1[3/2, (m + n)/n, 2 + m/n, -((b*x^n)/a)]))/(2*a*(m + n)*Sqrt[a + b*x^n])","C",1
2687,1,100,129,0.2259178,"\int \frac{x^{-1+\frac{7 n}{2}}}{\sqrt{a+b x^n}} \, dx","Integrate[x^(-1 + (7*n)/2)/Sqrt[a + b*x^n],x]","\frac{\sqrt{a+b x^n} \left(\sqrt{b} x^{n/2} \left(15 a^2-10 a b x^n+8 b^2 x^{2 n}\right)-\frac{15 a^{5/2} \sinh ^{-1}\left(\frac{\sqrt{b} x^{n/2}}{\sqrt{a}}\right)}{\sqrt{\frac{b x^n}{a}+1}}\right)}{24 b^{7/2} 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^2 x^{n/2} \sqrt{a+b x^n}}{8 b^3 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,"(Sqrt[a + b*x^n]*(Sqrt[b]*x^(n/2)*(15*a^2 - 10*a*b*x^n + 8*b^2*x^(2*n)) - (15*a^(5/2)*ArcSinh[(Sqrt[b]*x^(n/2))/Sqrt[a]])/Sqrt[1 + (b*x^n)/a]))/(24*b^(7/2)*n)","A",1
2688,1,100,98,0.0675661,"\int \frac{x^{-1+\frac{5 n}{2}}}{\sqrt{a+b x^n}} \, dx","Integrate[x^(-1 + (5*n)/2)/Sqrt[a + b*x^n],x]","\frac{3 a^{5/2} \sqrt{\frac{b x^n}{a}+1} \sinh ^{-1}\left(\frac{\sqrt{b} x^{n/2}}{\sqrt{a}}\right)+\sqrt{b} x^{n/2} \left(-3 a^2-a b x^n+2 b^2 x^{2 n}\right)}{4 b^{5/2} n \sqrt{a+b x^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,"(Sqrt[b]*x^(n/2)*(-3*a^2 - a*b*x^n + 2*b^2*x^(2*n)) + 3*a^(5/2)*Sqrt[1 + (b*x^n)/a]*ArcSinh[(Sqrt[b]*x^(n/2))/Sqrt[a]])/(4*b^(5/2)*n*Sqrt[a + b*x^n])","A",1
2689,1,81,62,0.0545758,"\int \frac{x^{-1+\frac{3 n}{2}}}{\sqrt{a+b x^n}} \, dx","Integrate[x^(-1 + (3*n)/2)/Sqrt[a + b*x^n],x]","\frac{\sqrt{b} x^{n/2} \left(a+b x^n\right)-a^{3/2} \sqrt{\frac{b x^n}{a}+1} \sinh ^{-1}\left(\frac{\sqrt{b} x^{n/2}}{\sqrt{a}}\right)}{b^{3/2} n \sqrt{a+b x^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,"(Sqrt[b]*x^(n/2)*(a + b*x^n) - a^(3/2)*Sqrt[1 + (b*x^n)/a]*ArcSinh[(Sqrt[b]*x^(n/2))/Sqrt[a]])/(b^(3/2)*n*Sqrt[a + b*x^n])","A",1
2690,1,59,35,0.0188361,"\int \frac{x^{-1+\frac{n}{2}}}{\sqrt{a+b x^n}} \, dx","Integrate[x^(-1 + n/2)/Sqrt[a + b*x^n],x]","\frac{2 \sqrt{a} \sqrt{\frac{b x^n}{a}+1} \sinh ^{-1}\left(\frac{\sqrt{b} x^{n/2}}{\sqrt{a}}\right)}{\sqrt{b} n \sqrt{a+b x^n}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} x^{n/2}}{\sqrt{a+b x^n}}\right)}{\sqrt{b} n}",1,"(2*Sqrt[a]*Sqrt[1 + (b*x^n)/a]*ArcSinh[(Sqrt[b]*x^(n/2))/Sqrt[a]])/(Sqrt[b]*n*Sqrt[a + b*x^n])","A",1
2691,1,26,26,0.0074722,"\int \frac{x^{-1-\frac{n}{2}}}{\sqrt{a+b x^n}} \, dx","Integrate[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
2692,1,36,58,0.013278,"\int \frac{x^{-1-\frac{3 n}{2}}}{\sqrt{a+b x^n}} \, dx","Integrate[x^(-1 - (3*n)/2)/Sqrt[a + b*x^n],x]","-\frac{2 x^{-3 n/2} \left(a-2 b x^n\right) \sqrt{a+b x^n}}{3 a^2 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*(a - 2*b*x^n)*Sqrt[a + b*x^n])/(3*a^2*n*x^((3*n)/2))","A",1
2693,1,51,89,0.0183235,"\int \frac{x^{-1-\frac{5 n}{2}}}{\sqrt{a+b x^n}} \, dx","Integrate[x^(-1 - (5*n)/2)/Sqrt[a + b*x^n],x]","-\frac{2 x^{-5 n/2} \sqrt{a+b x^n} \left(3 a^2-4 a b x^n+8 b^2 x^{2 n}\right)}{15 a^3 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]*(3*a^2 - 4*a*b*x^n + 8*b^2*x^(2*n)))/(15*a^3*n*x^((5*n)/2))","A",1
2694,1,64,120,0.0231729,"\int \frac{x^{-1-\frac{7 n}{2}}}{\sqrt{a+b x^n}} \, dx","Integrate[x^(-1 - (7*n)/2)/Sqrt[a + b*x^n],x]","-\frac{2 x^{-7 n/2} \sqrt{a+b x^n} \left(5 a^3-6 a^2 b x^n+8 a b^2 x^{2 n}-16 b^3 x^{3 n}\right)}{35 a^4 n}","\frac{32 b^3 x^{-n/2} \sqrt{a+b x^n}}{35 a^4 n}-\frac{16 b^2 x^{-3 n/2} \sqrt{a+b x^n}}{35 a^3 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]*(5*a^3 - 6*a^2*b*x^n + 8*a*b^2*x^(2*n) - 16*b^3*x^(3*n)))/(35*a^4*n*x^((7*n)/2))","A",1
2695,1,110,65,0.1766941,"\int \frac{x^m}{\sqrt{a+b x^{-2+m}}} \, dx","Integrate[x^m/Sqrt[a + b*x^(-2 + m)],x]","\frac{2 x \left(6 a x^2 \sqrt{\frac{a x^{2-m}}{b}+1} \, _2F_1\left(\frac{1}{2},\frac{m-8}{2 (m-2)};\frac{3 (m-4)}{2 (m-2)};-\frac{a x^{2-m}}{b}\right)+(m-8) \left(a x^2+b x^m\right)\right)}{b (m-8) (m+4) \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,"(2*x*((-8 + m)*(a*x^2 + b*x^m) + 6*a*x^2*Sqrt[1 + (a*x^(2 - m))/b]*Hypergeometric2F1[1/2, (-8 + m)/(2*(-2 + m)), (3*(-4 + m))/(2*(-2 + m)), -((a*x^(2 - m))/b)]))/(b*(-8 + m)*(4 + m)*Sqrt[a + b*x^(-2 + m)])","A",1
2696,1,79,67,0.0502622,"\int \frac{x^m}{\sqrt{a+b x^{2-m}}} \, dx","Integrate[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}{m-2};-\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",1
2697,1,26,26,0.1977801,"\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","Integrate[(6*a*x^2)/(b*(4 + m)*Sqrt[a + b*x^(-2 + m)]) + x^m/Sqrt[a + b*x^(-2 + m)],x]","\frac{2 x^3 \sqrt{a+b x^{m-2}}}{b (m+4)}","\frac{2 x^3 \sqrt{a+b x^{m-2}}}{b (m+4)}",1,"(2*x^3*Sqrt[a + b*x^(-2 + m)])/(b*(4 + m))","A",1
2698,1,111,15,0.1316058,"\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","Integrate[(x^(-1 + m)*(2*a*m + b*(2*m - n)*x^n))/(2*(a + b*x^n)^(3/2)),x]","\frac{x^m \sqrt{\frac{b x^n}{a}+1} \left(b (2 m-n) x^n \, _2F_1\left(\frac{3}{2},\frac{m+n}{n};\frac{m}{n}+2;-\frac{b x^n}{a}\right)+2 a (m+n) \, _2F_1\left(\frac{3}{2},\frac{m}{n};\frac{m+n}{n};-\frac{b x^n}{a}\right)\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]*(2*a*(m + n)*Hypergeometric2F1[3/2, m/n, (m + n)/n, -((b*x^n)/a)] + b*(2*m - n)*x^n*Hypergeometric2F1[3/2, (m + n)/n, 2 + m/n, -((b*x^n)/a)]))/(2*a*(m + n)*Sqrt[a + b*x^n])","C",1
2699,1,111,15,0.0963714,"\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","Integrate[-1/2*(b*n*x^(-1 + m + n))/(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} \left(b (2 m-n) x^n \, _2F_1\left(\frac{3}{2},\frac{m+n}{n};\frac{m}{n}+2;-\frac{b x^n}{a}\right)+2 a (m+n) \, _2F_1\left(\frac{3}{2},\frac{m}{n};\frac{m+n}{n};-\frac{b x^n}{a}\right)\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]*(2*a*(m + n)*Hypergeometric2F1[3/2, m/n, (m + n)/n, -((b*x^n)/a)] + b*(2*m - n)*x^n*Hypergeometric2F1[3/2, (m + n)/n, 2 + m/n, -((b*x^n)/a)]))/(2*a*(m + n)*Sqrt[a + b*x^n])","C",1
2700,1,67,97,0.0389981,"\int \frac{x^m}{\sqrt[3]{a+b x^{3 (1+m)}}} \, dx","Integrate[x^m/(a + b*x^(3*(1 + m)))^(1/3),x]","\frac{x^{m+1} \sqrt[3]{\frac{b x^{3 m+3}}{a}+1} \, _2F_1\left(\frac{1}{3},\frac{1}{3};\frac{4}{3};-\frac{b x^{3 m+3}}{a}\right)}{(m+1) \sqrt[3]{a+b x^{3 m+3}}}","\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,"(x^(1 + m)*(1 + (b*x^(3 + 3*m))/a)^(1/3)*Hypergeometric2F1[1/3, 1/3, 4/3, -((b*x^(3 + 3*m))/a)])/((1 + m)*(a + b*x^(3 + 3*m))^(1/3))","C",1
2701,1,73,139,0.0791112,"\int x^m \left(a+b x^{-\frac{3}{2} (1+m)}\right)^{2/3} \, dx","Integrate[x^m*(a + b/x^((3*(1 + m))/2))^(2/3),x]","\frac{x^{m+1} \left(a+b x^{-\frac{3}{2} (m+1)}\right)^{2/3} \, _2F_1\left(-\frac{2}{3},-\frac{2}{3};\frac{1}{3};-\frac{b x^{-\frac{3}{2} (m+1)}}{a}\right)}{(m+1) \left(\frac{b x^{-\frac{3}{2} (m+1)}}{a}+1\right)^{2/3}}","\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)*Hypergeometric2F1[-2/3, -2/3, 1/3, -(b/(a*x^((3*(1 + m))/2)))])/((1 + m)*(1 + b/(a*x^((3*(1 + m))/2)))^(2/3))","C",1
2702,1,56,89,0.0185545,"\int \frac{x^{-1+\frac{n}{3}}}{\sqrt[3]{a+b x^n}} \, dx","Integrate[x^(-1 + n/3)/(a + b*x^n)^(1/3),x]","\frac{3 x^{n/3} \sqrt[3]{\frac{b x^n}{a}+1} \, _2F_1\left(\frac{1}{3},\frac{1}{3};\frac{4}{3};-\frac{b x^n}{a}\right)}{n \sqrt[3]{a+b x^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,"(3*x^(n/3)*(1 + (b*x^n)/a)^(1/3)*Hypergeometric2F1[1/3, 1/3, 4/3, -((b*x^n)/a)])/(n*(a + b*x^n)^(1/3))","C",1
2703,1,58,114,0.0275827,"\int x^{-1-\frac{2 n}{3}} \left(a+b x^n\right)^{2/3} \, dx","Integrate[x^(-1 - (2*n)/3)*(a + b*x^n)^(2/3),x]","-\frac{3 x^{-2 n/3} \left(a+b x^n\right)^{2/3} \, _2F_1\left(-\frac{2}{3},-\frac{2}{3};\frac{1}{3};-\frac{b x^n}{a}\right)}{2 n \left(\frac{b x^n}{a}+1\right)^{2/3}}","-\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)*Hypergeometric2F1[-2/3, -2/3, 1/3, -((b*x^n)/a)])/(2*n*x^((2*n)/3)*(1 + (b*x^n)/a)^(2/3))","C",1
2704,1,63,54,0.0329915,"\int x^m \left(a+b x^n\right)^p \, dx","Integrate[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+1}{n}+1;-\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 + (1 + m)/n, -((b*x^n)/a)])/((1 + m)*(1 + (b*x^n)/a)^p)","A",1
2705,1,55,146,0.0744552,"\int \left(a+b x^n\right)^{-4-\frac{1}{n}} \, dx","Integrate[(a + b*x^n)^(-4 - n^(-1)),x]","\frac{x \left(a+b x^n\right)^{-1/n} \left(\frac{b x^n}{a}+1\right)^{\frac{1}{n}} \, _2F_1\left(4+\frac{1}{n},\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a^4}","\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{1}{n}-1}}{a^3 (n+1) (2 n+1) (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{x \left(a+b x^n\right)^{-\frac{1}{n}-3}}{a (3 n+1)}",1,"(x*(1 + (b*x^n)/a)^n^(-1)*Hypergeometric2F1[4 + n^(-1), n^(-1), 1 + n^(-1), -((b*x^n)/a)])/(a^4*(a + b*x^n)^n^(-1))","C",1
2706,1,55,96,0.0414175,"\int \left(a+b x^n\right)^{-3-\frac{1}{n}} \, dx","Integrate[(a + b*x^n)^(-3 - n^(-1)),x]","\frac{x \left(a+b x^n\right)^{-1/n} \left(\frac{b x^n}{a}+1\right)^{\frac{1}{n}} \, _2F_1\left(3+\frac{1}{n},\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a^3}","\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*(1 + (b*x^n)/a)^n^(-1)*Hypergeometric2F1[3 + n^(-1), n^(-1), 1 + n^(-1), -((b*x^n)/a)])/(a^3*(a + b*x^n)^n^(-1))","C",1
2707,1,55,50,0.0457609,"\int \left(a+b x^n\right)^{-2-\frac{1}{n}} \, dx","Integrate[(a + b*x^n)^(-2 - n^(-1)),x]","\frac{x \left(a+b x^n\right)^{-1/n} \left(\frac{b x^n}{a}+1\right)^{\frac{1}{n}} \, _2F_1\left(2+\frac{1}{n},\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a^2}","\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*(1 + (b*x^n)/a)^n^(-1)*Hypergeometric2F1[2 + n^(-1), n^(-1), 1 + n^(-1), -((b*x^n)/a)])/(a^2*(a + b*x^n)^n^(-1))","C",1
2708,1,18,18,0.063666,"\int \left(a+b x^n\right)^{-1-\frac{1}{n}} \, dx","Integrate[(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
2709,1,50,50,0.0138043,"\int \left(a+b x^n\right)^{-1/n} \, dx","Integrate[(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",1
2710,1,53,53,0.011577,"\int \left(a+b x^n\right)^{1-\frac{1}{n}} \, dx","Integrate[(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",1
2711,1,55,55,0.0080751,"\int \left(a+b x^n\right)^{2-\frac{1}{n}} \, dx","Integrate[(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",1
2712,1,21,21,0.004366,"\int x^m \left(b x^n\right)^p \, dx","Integrate[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",1
2713,1,18,18,0.0030282,"\int x^2 \left(b x^n\right)^p \, dx","Integrate[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",1
2714,1,18,18,0.0203619,"\int x \left(b x^n\right)^p \, dx","Integrate[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",1
2715,1,16,16,0.0019431,"\int \left(b x^n\right)^p \, dx","Integrate[(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",1
2716,1,14,14,0.001398,"\int \frac{\left(b x^n\right)^p}{x} \, dx","Integrate[(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",1
2717,1,18,20,0.0035788,"\int \frac{\left(b x^n\right)^p}{x^2} \, dx","Integrate[(b*x^n)^p/x^2,x]","\frac{\left(b x^n\right)^p}{x (n p-1)}","-\frac{\left(b x^n\right)^p}{x (1-n p)}",1,"(b*x^n)^p/((-1 + n*p)*x)","A",1
2718,1,18,20,0.0026574,"\int \frac{\left(b x^n\right)^p}{x^3} \, dx","Integrate[(b*x^n)^p/x^3,x]","\frac{\left(b x^n\right)^p}{x^2 (n p-2)}","-\frac{\left(b x^n\right)^p}{x^2 (2-n p)}",1,"(b*x^n)^p/((-2 + n*p)*x^2)","A",1
2719,1,18,20,0.0027726,"\int \frac{\left(b x^n\right)^p}{x^4} \, dx","Integrate[(b*x^n)^p/x^4,x]","\frac{\left(b x^n\right)^p}{x^3 (n p-3)}","-\frac{\left(b x^n\right)^p}{x^3 (3-n p)}",1,"(b*x^n)^p/((-3 + n*p)*x^3)","A",1
2720,1,23,23,0.0071799,"\int x^{-1+n} \left(a+b x^n\right)^p \, dx","Integrate[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
2721,1,40,49,0.0244238,"\int x^{-1+2 n} \left(a+b x^n\right)^p \, dx","Integrate[x^(-1 + 2*n)*(a + b*x^n)^p,x]","\frac{\left(a+b x^n\right)^{p+1} \left(b (p+1) x^n-a\right)}{b^2 n (p+1) (p+2)}","\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 + b*x^n)^(1 + p)*(-a + b*(1 + p)*x^n))/(b^2*n*(1 + p)*(2 + p))","A",1
2722,1,66,75,0.0462592,"\int x^{-1+3 n} \left(a+b x^n\right)^p \, dx","Integrate[x^(-1 + 3*n)*(a + b*x^n)^p,x]","\frac{\left(a+b x^n\right)^{p+1} \left(2 a^2-2 a b (p+1) x^n+b^2 \left(p^2+3 p+2\right) x^{2 n}\right)}{b^3 n (p+1) (p+2) (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 + b*x^n)^(1 + p)*(2*a^2 - 2*a*b*(1 + p)*x^n + b^2*(2 + 3*p + p^2)*x^(2*n)))/(b^3*n*(1 + p)*(2 + p)*(3 + p))","A",1
2723,1,78,103,0.0879773,"\int x^{-1+4 n} \left(a+b x^n\right)^p \, dx","Integrate[x^(-1 + 4*n)*(a + b*x^n)^p,x]","\frac{\left(a+b x^n\right)^{p+1} \left(-\frac{a^3}{p+1}+\frac{3 a^2 \left(a+b x^n\right)}{p+2}-\frac{3 a \left(a+b x^n\right)^2}{p+3}+\frac{\left(a+b x^n\right)^3}{p+4}\right)}{b^4 n}","-\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 + b*x^n)^(1 + p)*(-(a^3/(1 + p)) + (3*a^2*(a + b*x^n))/(2 + p) - (3*a*(a + b*x^n)^2)/(3 + p) + (a + b*x^n)^3/(4 + p)))/(b^4*n)","A",1
2724,1,32,32,0.0226483,"\int x^{-1-n-n p} \left(a+b x^n\right)^p \, dx","Integrate[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
2725,1,24,24,0.0109748,"\int x^{-1-9 n} \left(a+b x^n\right)^8 \, dx","Integrate[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,"-1/9*(a + b*x^n)^9/(a*n*x^(9*n))","A",1
2726,1,29,30,0.0154513,"\int x^{-4-3 p} \left(a+b x^3\right)^p \, dx","Integrate[x^(-4 - 3*p)*(a + b*x^3)^p,x]","\frac{x^{-3 p-3} \left(a+b x^3\right)^{p+1}}{a (-3 p-3)}","-\frac{x^{-3 (p+1)} \left(a+b x^3\right)^{p+1}}{3 a (p+1)}",1,"(x^(-3 - 3*p)*(a + b*x^3)^(1 + p))/(a*(-3 - 3*p))","A",1
2727,1,108,19,0.0103179,"\int \frac{\left(a+b x^3\right)^8}{x^{28}} \, dx","Integrate[(a + b*x^3)^8/x^28,x]","-\frac{a^8}{27 x^{27}}-\frac{a^7 b}{3 x^{24}}-\frac{4 a^6 b^2}{3 x^{21}}-\frac{28 a^5 b^3}{9 x^{18}}-\frac{14 a^4 b^4}{3 x^{15}}-\frac{14 a^3 b^5}{3 x^{12}}-\frac{28 a^2 b^6}{9 x^9}-\frac{4 a b^7}{3 x^6}-\frac{b^8}{3 x^3}","-\frac{\left(a+b x^3\right)^9}{27 a x^{27}}",1,"-1/27*a^8/x^27 - (a^7*b)/(3*x^24) - (4*a^6*b^2)/(3*x^21) - (28*a^5*b^3)/(9*x^18) - (14*a^4*b^4)/(3*x^15) - (14*a^3*b^5)/(3*x^12) - (28*a^2*b^6)/(9*x^9) - (4*a*b^7)/(3*x^6) - b^8/(3*x^3)","B",1
2728,1,22,23,0.0049117,"\int \frac{1}{x \left(a+b x^n\right)} \, dx","Integrate[1/(x*(a + b*x^n)),x]","\frac{n \log (x)-\log \left(a+b x^n\right)}{a n}","\frac{\log (x)}{a}-\frac{\log \left(a+b x^n\right)}{a n}",1,"(n*Log[x] - Log[a + b*x^n])/(a*n)","A",1
2729,1,22,22,0.0060989,"\int \frac{1}{x \left(a+b x^3\right)} \, dx","Integrate[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",1
2730,1,55,147,0.0447288,"\int \left(a+b x^n\right)^{-\frac{1+4 n}{n}} \, dx","Integrate[(a + b*x^n)^(-((1 + 4*n)/n)),x]","\frac{x \left(a+b x^n\right)^{-1/n} \left(\frac{b x^n}{a}+1\right)^{\frac{1}{n}} \, _2F_1\left(4+\frac{1}{n},\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a^4}","\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{3 n x \left(a+b x^n\right)^{-\frac{1}{n}-2}}{a^2 \left(6 n^2+5 n+1\right)}+\frac{x \left(a+b x^n\right)^{-\frac{1}{n}-3}}{a (3 n+1)}",1,"(x*(1 + (b*x^n)/a)^n^(-1)*Hypergeometric2F1[4 + n^(-1), n^(-1), 1 + n^(-1), -((b*x^n)/a)])/(a^4*(a + b*x^n)^n^(-1))","C",1
2731,1,55,97,0.0369555,"\int \left(a+b x^n\right)^{-\frac{1+3 n}{n}} \, dx","Integrate[(a + b*x^n)^(-((1 + 3*n)/n)),x]","\frac{x \left(a+b x^n\right)^{-1/n} \left(\frac{b x^n}{a}+1\right)^{\frac{1}{n}} \, _2F_1\left(3+\frac{1}{n},\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a^3}","\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*(1 + (b*x^n)/a)^n^(-1)*Hypergeometric2F1[3 + n^(-1), n^(-1), 1 + n^(-1), -((b*x^n)/a)])/(a^3*(a + b*x^n)^n^(-1))","C",1
2732,1,55,51,0.0475046,"\int \left(a+b x^n\right)^{-\frac{1+2 n}{n}} \, dx","Integrate[(a + b*x^n)^(-((1 + 2*n)/n)),x]","\frac{x \left(a+b x^n\right)^{-1/n} \left(\frac{b x^n}{a}+1\right)^{\frac{1}{n}} \, _2F_1\left(2+\frac{1}{n},\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a^2}","\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,"(x*(1 + (b*x^n)/a)^n^(-1)*Hypergeometric2F1[2 + n^(-1), n^(-1), 1 + n^(-1), -((b*x^n)/a)])/(a^2*(a + b*x^n)^n^(-1))","C",1
2733,1,18,18,0.0416246,"\int \left(a+b x^n\right)^{-\frac{1+n}{n}} \, dx","Integrate[(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
2734,1,50,50,0.0026765,"\int \left(a+b x^n\right)^{-1/n} \, dx","Integrate[(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",1
2735,1,53,59,0.0047658,"\int \left(a+b x^n\right)^{-\frac{1-n}{n}} \, dx","Integrate[(a + b*x^n)^(-((1 - n)/n)),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)","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,"(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",1
2736,1,55,56,0.0030794,"\int \left(a+b x^n\right)^{-\frac{1-2 n}{n}} \, dx","Integrate[(a + b*x^n)^(-((1 - 2*n)/n)),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)","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,"(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",1
2737,1,15,15,0.004019,"\int \frac{1}{x \left(a+b x^{-n}\right)} \, dx","Integrate[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",1
2738,1,19,19,0.0057471,"\int \frac{x^m}{a+b x^{1+m}} \, dx","Integrate[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
2739,1,27,27,0.0117363,"\int x^m \left(a+b x^{1+m}\right)^n \, dx","Integrate[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
2740,1,57,71,0.0583384,"\int x^m \left(a+b x^{2+2 m}\right)^3 \, dx","Integrate[x^m*(a + b*x^(2 + 2*m))^3,x]","\frac{35 a^3 x^{m+1}+35 a^2 b x^{3 m+3}+21 a b^2 x^{5 m+5}+5 b^3 x^{7 m+7}}{35 m+35}","\frac{a^3 x^{m+1}}{m+1}+\frac{a^2 b x^{3 (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,"(35*a^3*x^(1 + m) + 35*a^2*b*x^(3 + 3*m) + 21*a*b^2*x^(5 + 5*m) + 5*b^3*x^(7 + 7*m))/(35 + 35*m)","A",1
2741,1,42,52,0.0254907,"\int x^m \left(a+b x^{2+2 m}\right)^2 \, dx","Integrate[x^m*(a + b*x^(2 + 2*m))^2,x]","\frac{15 a^2 x^{m+1}+10 a b x^{3 m+3}+3 b^2 x^{5 m+5}}{15 m+15}","\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,"(15*a^2*x^(1 + m) + 10*a*b*x^(3 + 3*m) + 3*b^2*x^(5 + 5*m))/(15 + 15*m)","A",1
2742,1,26,30,0.0137659,"\int x^m \left(a+b x^{2+2 m}\right) \, dx","Integrate[x^m*(a + b*x^(2 + 2*m)),x]","\frac{3 a x^{m+1}+b x^{3 m+3}}{3 m+3}","\frac{a x^{m+1}}{m+1}+\frac{b x^{3 (m+1)}}{3 (m+1)}",1,"(3*a*x^(1 + m) + b*x^(3 + 3*m))/(3 + 3*m)","A",1
2743,1,33,33,0.0136311,"\int \frac{x^m}{a+b x^{2+2 m}} \, dx","Integrate[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",1
2744,1,53,67,0.0145115,"\int \frac{x^m}{\left(a+b x^{2+2 m}\right)^2} \, dx","Integrate[x^m/(a + b*x^(2 + 2*m))^2,x]","\frac{x^{m+1} \, _2F_1\left(2,\frac{m+1}{2 m+2};\frac{m+1}{2 m+2}+1;-\frac{b x^{2 m+2}}{a}\right)}{a^2 (m+1)}","\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)*Hypergeometric2F1[2, (1 + m)/(2 + 2*m), 1 + (1 + m)/(2 + 2*m), -((b*x^(2 + 2*m))/a)])/(a^2*(1 + m))","C",1
2745,1,35,97,0.0085464,"\int \frac{x^m}{\left(a+b x^{2+2 m}\right)^3} \, dx","Integrate[x^m/(a + b*x^(2 + 2*m))^3,x]","\frac{x^{m+1} \, _2F_1\left(\frac{1}{2},3;\frac{3}{2};-\frac{b x^{2 m+2}}{a}\right)}{a^3 (m+1)}","\frac{3 \tan ^{-1}\left(\frac{\sqrt{b} x^{m+1}}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{b} (m+1)}+\frac{3 x^{m+1}}{8 a^2 (m+1) \left(a+b x^{2 (m+1)}\right)}+\frac{x^{m+1}}{4 a (m+1) \left(a+b x^{2 (m+1)}\right)^2}",1,"(x^(1 + m)*Hypergeometric2F1[1/2, 3, 3/2, -((b*x^(2 + 2*m))/a)])/(a^3*(1 + m))","C",1
2746,1,88,136,0.0938599,"\int x^m \left(a+b x^{2+2 m}\right)^{5/2} \, dx","Integrate[x^m*(a + b*x^(2 + 2*m))^(5/2),x]","\frac{a^2 x^{m+1} \sqrt{a+b x^{2 m+2}} \, _2F_1\left(-\frac{5}{2},\frac{m+1}{2 m+2};\frac{m+1}{2 m+2}+1;-\frac{b x^{2 m+2}}{a}\right)}{(m+1) \sqrt{\frac{b x^{2 m+2}}{a}+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{5 a^2 x^{m+1} \sqrt{a+b x^{2 (m+1)}}}{16 (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,"(a^2*x^(1 + m)*Sqrt[a + b*x^(2 + 2*m)]*Hypergeometric2F1[-5/2, (1 + m)/(2 + 2*m), 1 + (1 + m)/(2 + 2*m), -((b*x^(2 + 2*m))/a)])/((1 + m)*Sqrt[1 + (b*x^(2 + 2*m))/a])","C",1
2747,1,86,104,0.0476774,"\int x^m \left(a+b x^{2+2 m}\right)^{3/2} \, dx","Integrate[x^m*(a + b*x^(2 + 2*m))^(3/2),x]","\frac{a x^{m+1} \sqrt{a+b x^{2 m+2}} \, _2F_1\left(-\frac{3}{2},\frac{m+1}{2 m+2};\frac{m+1}{2 m+2}+1;-\frac{b x^{2 m+2}}{a}\right)}{(m+1) \sqrt{\frac{b x^{2 m+2}}{a}+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,"(a*x^(1 + m)*Sqrt[a + b*x^(2 + 2*m)]*Hypergeometric2F1[-3/2, (1 + m)/(2 + 2*m), 1 + (1 + m)/(2 + 2*m), -((b*x^(2 + 2*m))/a)])/((1 + m)*Sqrt[1 + (b*x^(2 + 2*m))/a])","C",1
2748,1,85,72,0.0301963,"\int x^m \sqrt{a+b x^{2+2 m}} \, dx","Integrate[x^m*Sqrt[a + b*x^(2 + 2*m)],x]","\frac{x^{m+1} \sqrt{a+b x^{2 m+2}} \, _2F_1\left(-\frac{1}{2},\frac{m+1}{2 m+2};\frac{m+1}{2 m+2}+1;-\frac{b x^{2 m+2}}{a}\right)}{(m+1) \sqrt{\frac{b x^{2 m+2}}{a}+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 + 2*m)]*Hypergeometric2F1[-1/2, (1 + m)/(2 + 2*m), 1 + (1 + m)/(2 + 2*m), -((b*x^(2 + 2*m))/a)])/((1 + m)*Sqrt[1 + (b*x^(2 + 2*m))/a])","C",1
2749,1,66,38,0.0391892,"\int \frac{x^m}{\sqrt{a+b x^{2+2 m}}} \, dx","Integrate[x^m/Sqrt[a + b*x^(2 + 2*m)],x]","\frac{\sqrt{a} \sqrt{\frac{b x^{2 m+2}}{a}+1} \sinh ^{-1}\left(\frac{\sqrt{b} x^{m+1}}{\sqrt{a}}\right)}{\sqrt{b} (m+1) \sqrt{a+b x^{2 m+2}}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x^{m+1}}{\sqrt{a+b x^{2 (m+1)}}}\right)}{\sqrt{b} (m+1)}",1,"(Sqrt[a]*Sqrt[1 + (b*x^(2 + 2*m))/a]*ArcSinh[(Sqrt[b]*x^(1 + m))/Sqrt[a]])/(Sqrt[b]*(1 + m)*Sqrt[a + b*x^(2 + 2*m)])","A",1
2750,1,29,29,0.0126541,"\int \frac{x^m}{\left(a+b x^{2+2 m}\right)^{3/2}} \, dx","Integrate[x^m/(a + b*x^(2 + 2*m))^(3/2),x]","\frac{x^{m+1}}{a (m+1) \sqrt{a+b x^{2 m+2}}}","\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 + 2*m)])","A",1
2751,1,46,65,0.0557449,"\int \frac{x^m}{\left(a+b x^{2+2 m}\right)^{5/2}} \, dx","Integrate[x^m/(a + b*x^(2 + 2*m))^(5/2),x]","\frac{x^{m+1} \left(3 a+2 b x^{2 m+2}\right)}{3 a^2 (m+1) \left(a+b x^{2 m+2}\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)*(3*a + 2*b*x^(2 + 2*m)))/(3*a^2*(1 + m)*(a + b*x^(2 + 2*m))^(3/2))","A",1
2752,1,61,102,0.0587356,"\int \frac{x^m}{\left(a+b x^{2+2 m}\right)^{7/2}} \, dx","Integrate[x^m/(a + b*x^(2 + 2*m))^(7/2),x]","\frac{x^{m+1} \left(15 a^2+20 a b x^{2 m+2}+8 b^2 x^{4 m+4}\right)}{15 a^3 (m+1) \left(a+b x^{2 m+2}\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)*(15*a^2 + 20*a*b*x^(2 + 2*m) + 8*b^2*x^(4 + 4*m)))/(15*a^3*(1 + m)*(a + b*x^(2 + 2*m))^(5/2))","A",1
2753,1,20,20,0.0150799,"\int x^n \sqrt{1+x^{1+n}} \, dx","Integrate[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
2754,1,22,22,0.0128242,"\int x^n \sqrt{a^2+x^{1+n}} \, dx","Integrate[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
2755,1,47,64,0.0458837,"\int (c x)^m \left(a+b x^n\right)^2 \, dx","Integrate[(c*x)^m*(a + b*x^n)^2,x]","x (c x)^m \left(\frac{a^2}{m+1}+\frac{2 a b x^n}{m+n+1}+\frac{b^2 x^{2 n}}{m+2 n+1}\right)","\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,"x*(c*x)^m*(a^2/(1 + m) + (2*a*b*x^n)/(1 + m + n) + (b^2*x^(2*n))/(1 + m + 2*n))","A",1
2756,1,41,58,0.0337719,"\int (c x)^m \left(a+b x^3\right)^2 \, dx","Integrate[(c*x)^m*(a + b*x^3)^2,x]","x (c x)^m \left(\frac{a^2}{m+1}+\frac{2 a b x^3}{m+4}+\frac{b^2 x^6}{m+7}\right)","\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,"x*(c*x)^m*(a^2/(1 + m) + (2*a*b*x^3)/(4 + m) + (b^2*x^6)/(7 + m))","A",1
2757,1,41,58,0.0720133,"\int (c x)^m \left(a+b x^2\right)^2 \, dx","Integrate[(c*x)^m*(a + b*x^2)^2,x]","x (c x)^m \left(\frac{a^2}{m+1}+\frac{2 a b x^2}{m+3}+\frac{b^2 x^4}{m+5}\right)","\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,"x*(c*x)^m*(a^2/(1 + m) + (2*a*b*x^2)/(3 + m) + (b^2*x^4)/(5 + m))","A",1
2758,1,39,58,0.0610715,"\int (c x)^m (a+b x)^2 \, dx","Integrate[(c*x)^m*(a + b*x)^2,x]","x (c x)^m \left(\frac{a^2}{m+1}+\frac{2 a b x}{m+2}+\frac{b^2 x^2}{m+3}\right)","\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,"x*(c*x)^m*(a^2/(1 + m) + (2*a*b*x)/(2 + m) + (b^2*x^2)/(3 + m))","A",1
2759,1,36,52,0.0512817,"\int \left(a+\frac{b}{x}\right)^2 (c x)^m \, dx","Integrate[(a + b/x)^2*(c*x)^m,x]","(c x)^m \left(\frac{a^2 x}{m+1}+\frac{2 a b}{m}+\frac{b^2}{(m-1) x}\right)","\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,"(c*x)^m*((2*a*b)/m + b^2/((-1 + m)*x) + (a^2*x)/(1 + m))","A",1
2760,1,64,61,0.0336464,"\int \left(a+\frac{b}{x^2}\right)^2 (c x)^m \, dx","Integrate[(a + b/x^2)^2*(c*x)^m,x]","\frac{(c x)^m \left(a^2 \left(m^2-4 m+3\right) x^4+2 a b \left(m^2-2 m-3\right) x^2+b^2 \left(m^2-1\right)\right)}{(m-3) (m-1) (m+1) x^3}","\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,"((c*x)^m*(b^2*(-1 + m^2) + 2*a*b*(-3 - 2*m + m^2)*x^2 + a^2*(3 - 4*m + m^2)*x^4))/((-3 + m)*(-1 + m)*(1 + m)*x^3)","A",1
2761,1,67,63,0.0368597,"\int \left(a+\frac{b}{x^3}\right)^2 (c x)^m \, dx","Integrate[(a + b/x^3)^2*(c*x)^m,x]","\frac{(c x)^m \left(a^2 \left(m^2-7 m+10\right) x^6+2 a b \left(m^2-4 m-5\right) x^3+b^2 \left(m^2-m-2\right)\right)}{(m-5) (m-2) (m+1) x^5}","\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,"((c*x)^m*(b^2*(-2 - m + m^2) + 2*a*b*(-5 - 4*m + m^2)*x^3 + a^2*(10 - 7*m + m^2)*x^6))/((-5 + m)*(-2 + m)*(1 + m)*x^5)","A",1
2762,1,37,74,0.0117731,"\int \frac{(c x)^{-1-\frac{n}{2}}}{a+b x^n} \, dx","Integrate[(c*x)^(-1 - n/2)/(a + b*x^n),x]","-\frac{2 x (c x)^{-\frac{n}{2}-1} \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};-\frac{b x^n}{a}\right)}{a 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*x*(c*x)^(-1 - n/2)*Hypergeometric2F1[-1/2, 1, 1/2, -((b*x^n)/a)])/(a*n)","C",1
2763,1,39,222,0.0119698,"\int \frac{(c x)^{-1-\frac{2 n}{3}}}{a+b x^n} \, dx","Integrate[(c*x)^(-1 - (2*n)/3)/(a + b*x^n),x]","-\frac{3 x (c x)^{-\frac{2 n}{3}-1} \, _2F_1\left(-\frac{2}{3},1;\frac{1}{3};-\frac{b x^n}{a}\right)}{2 a 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*x*(c*x)^(-1 - (2*n)/3)*Hypergeometric2F1[-2/3, 1, 1/3, -((b*x^n)/a)])/(2*a*n)","C",1
2764,1,39,317,0.0111007,"\int \frac{(c x)^{-1-\frac{3 n}{4}}}{a+b x^n} \, dx","Integrate[(c*x)^(-1 - (3*n)/4)/(a + b*x^n),x]","-\frac{4 x (c x)^{-\frac{3 n}{4}-1} \, _2F_1\left(-\frac{3}{4},1;\frac{1}{4};-\frac{b x^n}{a}\right)}{3 a 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*x*(c*x)^(-1 - (3*n)/4)*Hypergeometric2F1[-3/4, 1, 1/4, -((b*x^n)/a)])/(3*a*n)","C",1
2765,1,42,69,0.043783,"\int \frac{(c x)^{-1-n}}{a+b x^n} \, dx","Integrate[(c*x)^(-1 - n)/(a + b*x^n),x]","-\frac{(c x)^{-n} \left(-b x^n \log \left(a+b x^n\right)+a+b n x^n \log (x)\right)}{a^2 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,"-((a + b*n*x^n*Log[x] - b*x^n*Log[a + b*x^n])/(a^2*c*n*(c*x)^n))","A",1
2766,1,37,74,0.0033262,"\int \frac{(c x)^{-1-\frac{n}{2}}}{a+b x^n} \, dx","Integrate[(c*x)^(-1 - n/2)/(a + b*x^n),x]","-\frac{2 x (c x)^{-\frac{n}{2}-1} \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};-\frac{b x^n}{a}\right)}{a 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*x*(c*x)^(-1 - n/2)*Hypergeometric2F1[-1/2, 1, 1/2, -((b*x^n)/a)])/(a*n)","C",1
2767,1,37,220,0.0111101,"\int \frac{(c x)^{-1-\frac{n}{3}}}{a+b x^n} \, dx","Integrate[(c*x)^(-1 - n/3)/(a + b*x^n),x]","-\frac{3 x (c x)^{-\frac{n}{3}-1} \, _2F_1\left(-\frac{1}{3},1;\frac{2}{3};-\frac{b x^n}{a}\right)}{a 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*x*(c*x)^(-1 - n/3)*Hypergeometric2F1[-1/3, 1, 2/3, -((b*x^n)/a)])/(a*n)","C",1
2768,1,37,315,0.01177,"\int \frac{(c x)^{-1-\frac{n}{4}}}{a+b x^n} \, dx","Integrate[(c*x)^(-1 - n/4)/(a + b*x^n),x]","-\frac{4 x (c x)^{-\frac{n}{4}-1} \, _2F_1\left(-\frac{1}{4},1;\frac{3}{4};-\frac{b x^n}{a}\right)}{a 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*x*(c*x)^(-1 - n/4)*Hypergeometric2F1[-1/4, 1, 3/4, -((b*x^n)/a)])/(a*n)","C",1
2769,1,39,100,0.0119164,"\int \frac{(c x)^{-1-\frac{3 n}{2}}}{a+b x^n} \, dx","Integrate[(c*x)^(-1 - (3*n)/2)/(a + b*x^n),x]","-\frac{2 x (c x)^{-\frac{3 n}{2}-1} \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};-\frac{b x^n}{a}\right)}{3 a 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*x*(c*x)^(-1 - (3*n)/2)*Hypergeometric2F1[-3/2, 1, -1/2, -((b*x^n)/a)])/(3*a*n)","C",1
2770,1,39,246,0.014554,"\int \frac{(c x)^{-1-\frac{4 n}{3}}}{a+b x^n} \, dx","Integrate[(c*x)^(-1 - (4*n)/3)/(a + b*x^n),x]","-\frac{3 x (c x)^{-\frac{4 n}{3}-1} \, _2F_1\left(-\frac{4}{3},1;-\frac{1}{3};-\frac{b x^n}{a}\right)}{4 a 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*x*(c*x)^(-1 - (4*n)/3)*Hypergeometric2F1[-4/3, 1, -1/3, -((b*x^n)/a)])/(4*a*n)","C",1
2771,1,39,341,0.0122624,"\int \frac{(c x)^{-1-\frac{5 n}{4}}}{a+b x^n} \, dx","Integrate[(c*x)^(-1 - (5*n)/4)/(a + b*x^n),x]","-\frac{4 x (c x)^{-\frac{5 n}{4}-1} \, _2F_1\left(-\frac{5}{4},1;-\frac{1}{4};-\frac{b x^n}{a}\right)}{5 a 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*x*(c*x)^(-1 - (5*n)/4)*Hypergeometric2F1[-5/4, 1, -1/4, -((b*x^n)/a)])/(5*a*n)","C",1
2772,1,44,44,0.0130453,"\int \frac{(c x)^{4+n}}{a+b x^n} \, dx","Integrate[(c*x)^(4 + n)/(a + b*x^n),x]","\frac{x (c x)^{n+4} \, _2F_1\left(1,\frac{n+5}{n};\frac{n+5}{n}+1;-\frac{b x^n}{a}\right)}{a (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,"(x*(c*x)^(4 + n)*Hypergeometric2F1[1, (5 + n)/n, 1 + (5 + n)/n, -((b*x^n)/a)])/(a*(5 + n))","A",1
2773,1,44,46,0.0197791,"\int \frac{(c x)^{3+n}}{a+b x^n} \, dx","Integrate[(c*x)^(3 + n)/(a + b*x^n),x]","\frac{x (c x)^{n+3} \, _2F_1\left(1,\frac{n+4}{n};\frac{n+4}{n}+1;-\frac{b x^n}{a}\right)}{a (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,"(x*(c*x)^(3 + n)*Hypergeometric2F1[1, (4 + n)/n, 1 + (4 + n)/n, -((b*x^n)/a)])/(a*(4 + n))","A",1
2774,1,44,44,0.0119813,"\int \frac{(c x)^{2+n}}{a+b x^n} \, dx","Integrate[(c*x)^(2 + n)/(a + b*x^n),x]","\frac{x (c x)^{n+2} \, _2F_1\left(1,\frac{n+3}{n};\frac{n+3}{n}+1;-\frac{b x^n}{a}\right)}{a (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,"(x*(c*x)^(2 + n)*Hypergeometric2F1[1, (3 + n)/n, 1 + (3 + n)/n, -((b*x^n)/a)])/(a*(3 + n))","A",1
2775,1,45,44,0.0106597,"\int \frac{(c x)^{1+n}}{a+b x^n} \, dx","Integrate[(c*x)^(1 + n)/(a + b*x^n),x]","\frac{c x^2 (c x)^n \, _2F_1\left(1,\frac{n+2}{n};\frac{n+2}{n}+1;-\frac{b x^n}{a}\right)}{a (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*(c*x)^n*Hypergeometric2F1[1, (2 + n)/n, 1 + (2 + n)/n, -((b*x^n)/a)])/(a*(2 + n))","A",1
2776,1,36,40,0.0086029,"\int \frac{(c x)^n}{a+b x^n} \, dx","Integrate[(c*x)^n/(a + b*x^n),x]","\frac{x (c x)^n \, _2F_1\left(1,1+\frac{1}{n};2+\frac{1}{n};-\frac{b x^n}{a}\right)}{a (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,"(x*(c*x)^n*Hypergeometric2F1[1, 1 + n^(-1), 2 + n^(-1), -((b*x^n)/a)])/(a*(1 + n))","A",1
2777,1,29,28,0.0056983,"\int \frac{(c x)^{-1+n}}{a+b x^n} \, dx","Integrate[(c*x)^(-1 + n)/(a + b*x^n),x]","\frac{x^{1-n} (c x)^{n-1} \log \left(a+b x^n\right)}{b n}","\frac{x^{-n} (c x)^n \log \left(a+b x^n\right)}{b c n}",1,"(x^(1 - n)*(c*x)^(-1 + n)*Log[a + b*x^n])/(b*n)","A",1
2778,1,44,50,0.0127267,"\int \frac{(c x)^{-2+n}}{a+b x^n} \, dx","Integrate[(c*x)^(-2 + n)/(a + b*x^n),x]","\frac{x (c x)^{n-2} \, _2F_1\left(1,\frac{n-1}{n};\frac{n-1}{n}+1;-\frac{b x^n}{a}\right)}{a (n-1)}","-\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,"(x*(c*x)^(-2 + n)*Hypergeometric2F1[1, (-1 + n)/n, 1 + (-1 + n)/n, -((b*x^n)/a)])/(a*(-1 + n))","A",1
2779,1,44,52,0.0125565,"\int \frac{(c x)^{-3+n}}{a+b x^n} \, dx","Integrate[(c*x)^(-3 + n)/(a + b*x^n),x]","\frac{x (c x)^{n-3} \, _2F_1\left(1,\frac{n-2}{n};\frac{n-2}{n}+1;-\frac{b x^n}{a}\right)}{a (n-2)}","-\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,"(x*(c*x)^(-3 + n)*Hypergeometric2F1[1, (-2 + n)/n, 1 + (-2 + n)/n, -((b*x^n)/a)])/(a*(-2 + n))","A",1
2780,1,31,24,0.0151203,"\int \frac{(c x)^{-1+n}}{\left(a+b x^n\right)^2} \, dx","Integrate[(c*x)^(-1 + n)/(a + b*x^n)^2,x]","-\frac{x^{1-n} (c x)^{n-1}}{b n \left(a+b x^n\right)}","\frac{(c x)^n}{a c n \left(a+b x^n\right)}",1,"-((x^(1 - n)*(c*x)^(-1 + n))/(b*n*(a + b*x^n)))","A",1
2781,1,133,178,0.2675112,"\int \frac{(c x)^{-1+\frac{7 n}{2}}}{\sqrt{a+b x^n}} \, dx","Integrate[(c*x)^(-1 + (7*n)/2)/Sqrt[a + b*x^n],x]","\frac{x^{-7 n/2} (c x)^{7 n/2} \sqrt{a+b x^n} \left(\sqrt{b} x^{n/2} \sqrt{\frac{b x^n}{a}+1} \left(15 a^2-10 a b x^n+8 b^2 x^{2 n}\right)-15 a^{5/2} \sinh ^{-1}\left(\frac{\sqrt{b} x^{n/2}}{\sqrt{a}}\right)\right)}{24 b^{7/2} c n \sqrt{\frac{b x^n}{a}+1}}","-\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^2 x^{-3 n} (c x)^{7 n/2} \sqrt{a+b x^n}}{8 b^3 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,"((c*x)^((7*n)/2)*Sqrt[a + b*x^n]*(Sqrt[b]*x^(n/2)*Sqrt[1 + (b*x^n)/a]*(15*a^2 - 10*a*b*x^n + 8*b^2*x^(2*n)) - 15*a^(5/2)*ArcSinh[(Sqrt[b]*x^(n/2))/Sqrt[a]]))/(24*b^(7/2)*c*n*x^((7*n)/2)*Sqrt[1 + (b*x^n)/a])","A",1
2782,1,121,137,0.118236,"\int \frac{(c x)^{-1+\frac{5 n}{2}}}{\sqrt{a+b x^n}} \, dx","Integrate[(c*x)^(-1 + (5*n)/2)/Sqrt[a + b*x^n],x]","\frac{a x^{-5 n/2} (c x)^{5 n/2} \sqrt{\frac{b x^n}{a}+1} \left(3 a^{3/2} \sinh ^{-1}\left(\frac{\sqrt{b} x^{n/2}}{\sqrt{a}}\right)+\sqrt{b} x^{n/2} \left(2 b x^n-3 a\right) \sqrt{\frac{b x^n}{a}+1}\right)}{4 b^{5/2} c n \sqrt{a+b x^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,"(a*(c*x)^((5*n)/2)*Sqrt[1 + (b*x^n)/a]*(Sqrt[b]*x^(n/2)*(-3*a + 2*b*x^n)*Sqrt[1 + (b*x^n)/a] + 3*a^(3/2)*ArcSinh[(Sqrt[b]*x^(n/2))/Sqrt[a]]))/(4*b^(5/2)*c*n*x^((5*n)/2)*Sqrt[a + b*x^n])","A",1
2783,1,110,91,0.0614093,"\int \frac{(c x)^{-1+\frac{3 n}{2}}}{\sqrt{a+b x^n}} \, dx","Integrate[(c*x)^(-1 + (3*n)/2)/Sqrt[a + b*x^n],x]","\frac{a x^{1-\frac{3 n}{2}} (c x)^{\frac{3 n}{2}-1} \sqrt{\frac{b x^n}{a}+1} \left(\sqrt{b} x^{n/2} \sqrt{\frac{a+b x^n}{a}}-\sqrt{a} \sinh ^{-1}\left(\frac{\sqrt{b} x^{n/2}}{\sqrt{a}}\right)\right)}{b^{3/2} n \sqrt{a+b x^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,"(a*x^(1 - (3*n)/2)*(c*x)^(-1 + (3*n)/2)*Sqrt[1 + (b*x^n)/a]*(Sqrt[b]*x^(n/2)*Sqrt[(a + b*x^n)/a] - Sqrt[a]*ArcSinh[(Sqrt[b]*x^(n/2))/Sqrt[a]]))/(b^(3/2)*n*Sqrt[a + b*x^n])","A",1
2784,1,78,54,0.0318046,"\int \frac{(c x)^{-1+\frac{n}{2}}}{\sqrt{a+b x^n}} \, dx","Integrate[(c*x)^(-1 + n/2)/Sqrt[a + b*x^n],x]","\frac{2 \sqrt{a} x^{-n/2} (c x)^{n/2} \sqrt{\frac{b x^n}{a}+1} \sinh ^{-1}\left(\frac{\sqrt{b} x^{n/2}}{\sqrt{a}}\right)}{\sqrt{b} c n \sqrt{a+b x^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*Sqrt[a]*(c*x)^(n/2)*Sqrt[1 + (b*x^n)/a]*ArcSinh[(Sqrt[b]*x^(n/2))/Sqrt[a]])/(Sqrt[b]*c*n*x^(n/2)*Sqrt[a + b*x^n])","A",1
2785,1,31,31,0.0117594,"\int \frac{(c x)^{-1-\frac{n}{2}}}{\sqrt{a+b x^n}} \, dx","Integrate[(c*x)^(-1 - n/2)/Sqrt[a + b*x^n],x]","-\frac{2 x (c x)^{-\frac{n}{2}-1} \sqrt{a+b x^n}}{a n}","-\frac{2 (c x)^{-n/2} \sqrt{a+b x^n}}{a c n}",1,"(-2*x*(c*x)^(-1 - n/2)*Sqrt[a + b*x^n])/(a*n)","A",1
2786,1,41,65,0.016875,"\int \frac{(c x)^{-1-\frac{3 n}{2}}}{\sqrt{a+b x^n}} \, dx","Integrate[(c*x)^(-1 - (3*n)/2)/Sqrt[a + b*x^n],x]","-\frac{2 (c x)^{-3 n/2} \left(a-2 b x^n\right) \sqrt{a+b x^n}}{3 a^2 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*(a - 2*b*x^n)*Sqrt[a + b*x^n])/(3*a^2*c*n*(c*x)^((3*n)/2))","A",1
2787,1,56,98,0.0203805,"\int \frac{(c x)^{-1-\frac{5 n}{2}}}{\sqrt{a+b x^n}} \, dx","Integrate[(c*x)^(-1 - (5*n)/2)/Sqrt[a + b*x^n],x]","-\frac{2 (c x)^{-5 n/2} \sqrt{a+b x^n} \left(3 a^2-4 a b x^n+8 b^2 x^{2 n}\right)}{15 a^3 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]*(3*a^2 - 4*a*b*x^n + 8*b^2*x^(2*n)))/(15*a^3*c*n*(c*x)^((5*n)/2))","A",1
2788,1,69,129,0.0269584,"\int \frac{(c x)^{-1-\frac{7 n}{2}}}{\sqrt{a+b x^n}} \, dx","Integrate[(c*x)^(-1 - (7*n)/2)/Sqrt[a + b*x^n],x]","-\frac{2 (c x)^{-7 n/2} \sqrt{a+b x^n} \left(5 a^3-6 a^2 b x^n+8 a b^2 x^{2 n}-16 b^3 x^{3 n}\right)}{35 a^4 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]*(5*a^3 - 6*a^2*b*x^n + 8*a*b^2*x^(2*n) - 16*b^3*x^(3*n)))/(35*a^4*c*n*(c*x)^((7*n)/2))","A",1
2789,1,64,59,0.0171594,"\int (c x)^m \left(a+b x^n\right)^p \, dx","Integrate[(c*x)^m*(a + b*x^n)^p,x]","\frac{x (c x)^m \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+1}{n}+1;-\frac{b x^n}{a}\right)}{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,"(x*(c*x)^m*(a + b*x^n)^p*Hypergeometric2F1[(1 + m)/n, -p, 1 + (1 + m)/n, -((b*x^n)/a)])/((1 + m)*(1 + (b*x^n)/a)^p)","A",1
2790,1,62,56,0.0166198,"\int (c x)^{3 n} \left(a+b x^n\right)^p \, dx","Integrate[(c*x)^(3*n)*(a + b*x^n)^p,x]","\frac{x (c x)^{3 n} \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)}{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,"(x*(c*x)^(3*n)*(a + b*x^n)^p*Hypergeometric2F1[3 + n^(-1), -p, 4 + n^(-1), -((b*x^n)/a)])/((1 + 3*n)*(1 + (b*x^n)/a)^p)","A",1
2791,1,62,56,0.0165893,"\int (c x)^{2 n} \left(a+b x^n\right)^p \, dx","Integrate[(c*x)^(2*n)*(a + b*x^n)^p,x]","\frac{x (c x)^{2 n} \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)}{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,"(x*(c*x)^(2*n)*(a + b*x^n)^p*Hypergeometric2F1[2 + n^(-1), -p, 3 + n^(-1), -((b*x^n)/a)])/((1 + 2*n)*(1 + (b*x^n)/a)^p)","A",1
2792,1,58,52,0.0135976,"\int (c x)^n \left(a+b x^n\right)^p \, dx","Integrate[(c*x)^n*(a + b*x^n)^p,x]","\frac{x (c x)^n \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)}{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,"(x*(c*x)^n*(a + b*x^n)^p*Hypergeometric2F1[1 + n^(-1), -p, 2 + n^(-1), -((b*x^n)/a)])/((1 + n)*(1 + (b*x^n)/a)^p)","A",1
2793,1,46,38,0.006222,"\int \left(a+b x^n\right)^p \, dx","Integrate[(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",1
2794,1,59,53,0.0162563,"\int (c x)^{-n} \left(a+b x^n\right)^p \, dx","Integrate[(a + b*x^n)^p/(c*x)^n,x]","-\frac{x (c x)^{-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)}{n-1}","\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,"-((x*(a + b*x^n)^p*Hypergeometric2F1[-1 + n^(-1), -p, n^(-1), -((b*x^n)/a)])/((-1 + n)*(c*x)^n*(1 + (b*x^n)/a)^p))","A",1
2795,1,63,56,0.0166206,"\int (c x)^{-2 n} \left(a+b x^n\right)^p \, dx","Integrate[(a + b*x^n)^p/(c*x)^(2*n),x]","-\frac{x (c x)^{-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)}{2 n-1}","\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,"-((x*(a + b*x^n)^p*Hypergeometric2F1[-2 + n^(-1), -p, -1 + n^(-1), -((b*x^n)/a)])/((-1 + 2*n)*(c*x)^(2*n)*(1 + (b*x^n)/a)^p))","A",1
2796,1,63,56,0.0170152,"\int (c x)^{-3 n} \left(a+b x^n\right)^p \, dx","Integrate[(a + b*x^n)^p/(c*x)^(3*n),x]","-\frac{x (c x)^{-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)}{3 n-1}","\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,"-((x*(a + b*x^n)^p*Hypergeometric2F1[-3 + n^(-1), -p, -2 + n^(-1), -((b*x^n)/a)])/((-1 + 3*n)*(c*x)^(3*n)*(1 + (b*x^n)/a)^p))","A",1
2797,1,63,63,0.0142426,"\int (c x)^{-1-n p} \left(a+b x^n\right)^p \, dx","Integrate[(c*x)^(-1 - n*p)*(a + b*x^n)^p,x]","-\frac{x (c x)^{-n p-1} \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)}{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,"-((x*(c*x)^(-1 - n*p)*(a + b*x^n)^p*Hypergeometric2F1[-p, -p, 1 - p, -((b*x^n)/a)])/(n*p*(1 + (b*x^n)/a)^p))","A",1
2798,1,37,37,0.0277578,"\int (c x)^{-1-n-n p} \left(a+b x^n\right)^p \, dx","Integrate[(c*x)^(-1 - n - n*p)*(a + b*x^n)^p,x]","-\frac{x (c x)^{-n (p+1)-1} \left(a+b x^n\right)^{p+1}}{a n (p+1)}","-\frac{(c x)^{-n (p+1)} \left(a+b x^n\right)^{p+1}}{a c n (p+1)}",1,"-((x*(c*x)^(-1 - n*(1 + p))*(a + b*x^n)^(1 + p))/(a*n*(1 + p)))","A",1
2799,1,69,79,0.0492747,"\int (c x)^{-1-2 n-n p} \left(a+b x^n\right)^p \, dx","Integrate[(c*x)^(-1 - 2*n - n*p)*(a + b*x^n)^p,x]","-\frac{x (c x)^{-n (p+2)-1} \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} \, _2F_1\left(-p-2,-p;-p-1;-\frac{b x^n}{a}\right)}{n (p+2)}","\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,"-((x*(c*x)^(-1 - n*(2 + p))*(a + b*x^n)^p*Hypergeometric2F1[-2 - p, -p, -1 - p, -((b*x^n)/a)])/(n*(2 + p)*(1 + (b*x^n)/a)^p))","C",1
2800,1,69,127,0.0373086,"\int (c x)^{-1-3 n-n p} \left(a+b x^n\right)^p \, dx","Integrate[(c*x)^(-1 - 3*n - n*p)*(a + b*x^n)^p,x]","-\frac{x (c x)^{-n (p+3)-1} \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} \, _2F_1\left(-p-3,-p;-p-2;-\frac{b x^n}{a}\right)}{n (p+3)}","-\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{2 (c x)^{-n (p+3)} \left(a+b x^n\right)^{p+2}}{a^2 c n (p+1) (p+2)}-\frac{(c x)^{-n (p+3)} \left(a+b x^n\right)^{p+1}}{a c n (p+1)}",1,"-((x*(c*x)^(-1 - n*(3 + p))*(a + b*x^n)^p*Hypergeometric2F1[-3 - p, -p, -2 - p, -((b*x^n)/a)])/(n*(3 + p)*(1 + (b*x^n)/a)^p))","C",1
2801,1,69,179,0.0280412,"\int (c x)^{-1-4 n-n p} \left(a+b x^n\right)^p \, dx","Integrate[(c*x)^(-1 - 4*n - n*p)*(a + b*x^n)^p,x]","-\frac{x (c x)^{-n (p+4)-1} \left(a+b x^n\right)^p \left(\frac{b x^n}{a}+1\right)^{-p} \, _2F_1\left(-p-4,-p;-p-3;-\frac{b x^n}{a}\right)}{n (p+4)}","\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{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{3 (c x)^{-n (p+4)} \left(a+b x^n\right)^{p+2}}{a^2 c n (p+1) (p+2)}-\frac{(c x)^{-n (p+4)} \left(a+b x^n\right)^{p+1}}{a c n (p+1)}",1,"-((x*(c*x)^(-1 - n*(4 + p))*(a + b*x^n)^p*Hypergeometric2F1[-4 - p, -p, -3 - p, -((b*x^n)/a)])/(n*(4 + p)*(1 + (b*x^n)/a)^p))","C",1
2802,1,25,30,0.0225668,"\int \left(c (a+b x)^2\right)^{5/2} \, dx","Integrate[(c*(a + b*x)^2)^(5/2),x]","\frac{(a+b x) \left(c (a+b x)^2\right)^{5/2}}{6 b}","\frac{c^2 (a+b x)^5 \sqrt{c (a+b x)^2}}{6 b}",1,"((a + b*x)*(c*(a + b*x)^2)^(5/2))/(6*b)","A",1
2803,1,25,28,0.0098644,"\int \left(c (a+b x)^2\right)^{3/2} \, dx","Integrate[(c*(a + b*x)^2)^(3/2),x]","\frac{(a+b x) \left(c (a+b x)^2\right)^{3/2}}{4 b}","\frac{c (a+b x)^3 \sqrt{c (a+b x)^2}}{4 b}",1,"((a + b*x)*(c*(a + b*x)^2)^(3/2))/(4*b)","A",1
2804,1,31,25,0.0136182,"\int \sqrt{c (a+b x)^2} \, dx","Integrate[Sqrt[c*(a + b*x)^2],x]","\frac{c x (a+b x) (2 a+b x)}{2 \sqrt{c (a+b x)^2}}","\frac{(a+b x) \sqrt{c (a+b x)^2}}{2 b}",1,"(c*x*(a + b*x)*(2*a + b*x))/(2*Sqrt[c*(a + b*x)^2])","A",1
2805,1,28,28,0.0070967,"\int \frac{1}{\sqrt{c (a+b x)^2}} \, dx","Integrate[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",1
2806,1,25,30,0.0092878,"\int \frac{1}{\left(c (a+b x)^2\right)^{3/2}} \, dx","Integrate[(c*(a + b*x)^2)^(-3/2),x]","-\frac{a+b x}{2 b \left(c (a+b x)^2\right)^{3/2}}","-\frac{1}{2 b c (a+b x) \sqrt{c (a+b x)^2}}",1,"-1/2*(a + b*x)/(b*(c*(a + b*x)^2)^(3/2))","A",1
2807,1,25,30,0.0134737,"\int \frac{1}{\left(c (a+b x)^2\right)^{5/2}} \, dx","Integrate[(c*(a + b*x)^2)^(-5/2),x]","-\frac{a+b x}{4 b \left(c (a+b x)^2\right)^{5/2}}","-\frac{1}{4 b c^2 (a+b x)^3 \sqrt{c (a+b x)^2}}",1,"-1/4*(a + b*x)/(b*(c*(a + b*x)^2)^(5/2))","A",1
2808,1,25,20,0.0092444,"\int \sqrt{(3+5 x)^2} \, dx","Integrate[Sqrt[(3 + 5*x)^2],x]","\frac{x \sqrt{(5 x+3)^2} (5 x+6)}{10 x+6}","\frac{1}{10} (5 x+3) \sqrt{(5 x+3)^2}",1,"(x*Sqrt[(3 + 5*x)^2]*(6 + 5*x))/(6 + 10*x)","A",1
2809,1,25,20,0.0057983,"\int \sqrt{(6+10 x)^2} \, dx","Integrate[Sqrt[(6 + 10*x)^2],x]","\frac{x \sqrt{(5 x+3)^2} (5 x+6)}{5 x+3}","\frac{1}{5} (5 x+3) \sqrt{(5 x+3)^2}",1,"(x*Sqrt[(3 + 5*x)^2]*(6 + 5*x))/(3 + 5*x)","A",1
2810,1,26,26,0.0090459,"\int \frac{1}{\sqrt{(3+5 x)^2}} \, dx","Integrate[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",1
2811,1,26,26,0.0069023,"\int \frac{1}{\sqrt{(6+10 x)^2}} \, dx","Integrate[1/Sqrt[(6 + 10*x)^2],x]","\frac{(10 x+6) \log (10 x+6)}{10 \sqrt{(10 x+6)^2}}","\frac{(5 x+3) \log (5 x+3)}{10 \sqrt{(5 x+3)^2}}",1,"((6 + 10*x)*Log[6 + 10*x])/(10*Sqrt[(6 + 10*x)^2])","A",1
2812,1,28,28,0.006365,"\int \frac{1}{\sqrt{-(2+3 x)^2}} \, dx","Integrate[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",1
2813,1,25,30,0.0328455,"\int \left(c (a+b x)^3\right)^{5/2} \, dx","Integrate[(c*(a + b*x)^3)^(5/2),x]","\frac{2 (a+b x) \left(c (a+b x)^3\right)^{5/2}}{17 b}","\frac{2 c^2 (a+b x)^7 \sqrt{c (a+b x)^3}}{17 b}",1,"(2*(a + b*x)*(c*(a + b*x)^3)^(5/2))/(17*b)","A",1
2814,1,25,28,0.0153434,"\int \left(c (a+b x)^3\right)^{3/2} \, dx","Integrate[(c*(a + b*x)^3)^(3/2),x]","\frac{2 (a+b x) \left(c (a+b x)^3\right)^{3/2}}{11 b}","\frac{2 c (a+b x)^4 \sqrt{c (a+b x)^3}}{11 b}",1,"(2*(a + b*x)*(c*(a + b*x)^3)^(3/2))/(11*b)","A",1
2815,1,25,25,0.0080456,"\int \sqrt{c (a+b x)^3} \, dx","Integrate[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",1
2816,1,23,23,0.0100518,"\int \frac{1}{\sqrt{c (a+b x)^3}} \, dx","Integrate[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",1
2817,1,25,30,0.0123128,"\int \frac{1}{\left(c (a+b x)^3\right)^{3/2}} \, dx","Integrate[(c*(a + b*x)^3)^(-3/2),x]","-\frac{2 (a+b x)}{7 b \left(c (a+b x)^3\right)^{3/2}}","-\frac{2}{7 b c (a+b x)^2 \sqrt{c (a+b x)^3}}",1,"(-2*(a + b*x))/(7*b*(c*(a + b*x)^3)^(3/2))","A",1
2818,1,25,30,0.0178564,"\int \frac{1}{\left(c (a+b x)^3\right)^{5/2}} \, dx","Integrate[(c*(a + b*x)^3)^(-5/2),x]","-\frac{2 (a+b x)}{13 b \left(c (a+b x)^3\right)^{5/2}}","-\frac{2}{13 b c^2 (a+b x)^5 \sqrt{c (a+b x)^3}}",1,"(-2*(a + b*x))/(13*b*(c*(a + b*x)^3)^(5/2))","A",1
2819,1,21,30,0.0132896,"\int \left(\frac{c}{a+b x}\right)^{5/2} \, dx","Integrate[(c/(a + b*x))^(5/2),x]","-\frac{2 c \left(\frac{c}{a+b x}\right)^{3/2}}{3 b}","-\frac{2 c^2 \sqrt{\frac{c}{a+b x}}}{3 b (a+b x)}",1,"(-2*c*(c/(a + b*x))^(3/2))/(3*b)","A",1
2820,1,19,19,0.0064461,"\int \left(\frac{c}{a+b x}\right)^{3/2} \, dx","Integrate[(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",1
2821,1,19,23,0.0127199,"\int \sqrt{\frac{c}{a+b x}} \, dx","Integrate[Sqrt[c/(a + b*x)],x]","\frac{2 c}{b \sqrt{\frac{c}{a+b x}}}","\frac{2 (a+b x) \sqrt{\frac{c}{a+b x}}}{b}",1,"(2*c)/(b*Sqrt[c/(a + b*x)])","A",1
2822,1,21,25,0.0132418,"\int \frac{1}{\sqrt{\frac{c}{a+b x}}} \, dx","Integrate[1/Sqrt[c/(a + b*x)],x]","\frac{2 c}{3 b \left(\frac{c}{a+b x}\right)^{3/2}}","\frac{2 (a+b x)}{3 b \sqrt{\frac{c}{a+b x}}}",1,"(2*c)/(3*b*(c/(a + b*x))^(3/2))","A",1
2823,1,21,30,0.0150834,"\int \frac{1}{\left(\frac{c}{a+b x}\right)^{3/2}} \, dx","Integrate[(c/(a + b*x))^(-3/2),x]","\frac{2 c}{5 b \left(\frac{c}{a+b x}\right)^{5/2}}","\frac{2 (a+b x)^2}{5 b c \sqrt{\frac{c}{a+b x}}}",1,"(2*c)/(5*b*(c/(a + b*x))^(5/2))","A",1
2824,1,21,30,0.0177359,"\int \frac{1}{\left(\frac{c}{a+b x}\right)^{5/2}} \, dx","Integrate[(c/(a + b*x))^(-5/2),x]","\frac{2 c}{7 b \left(\frac{c}{a+b x}\right)^{7/2}}","\frac{2 (a+b x)^3}{7 b c^2 \sqrt{\frac{c}{a+b x}}}",1,"(2*c)/(7*b*(c/(a + b*x))^(7/2))","A",1
2825,1,25,30,0.0115437,"\int \left(\frac{c}{(a+b x)^2}\right)^{5/2} \, dx","Integrate[(c/(a + b*x)^2)^(5/2),x]","-\frac{(a+b x) \left(\frac{c}{(a+b x)^2}\right)^{5/2}}{4 b}","-\frac{c^2 \sqrt{\frac{c}{(a+b x)^2}}}{4 b (a+b x)^3}",1,"-1/4*((c/(a + b*x)^2)^(5/2)*(a + b*x))/b","A",1
2826,1,25,28,0.0082078,"\int \left(\frac{c}{(a+b x)^2}\right)^{3/2} \, dx","Integrate[(c/(a + b*x)^2)^(3/2),x]","-\frac{(a+b x) \left(\frac{c}{(a+b x)^2}\right)^{3/2}}{2 b}","-\frac{c \sqrt{\frac{c}{(a+b x)^2}}}{2 b (a+b x)}",1,"-1/2*((c/(a + b*x)^2)^(3/2)*(a + b*x))/b","A",1
2827,1,28,28,0.0075459,"\int \sqrt{\frac{c}{(a+b x)^2}} \, dx","Integrate[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",1
2828,1,32,25,0.0138952,"\int \frac{1}{\sqrt{\frac{c}{(a+b x)^2}}} \, dx","Integrate[1/Sqrt[c/(a + b*x)^2],x]","\frac{x (2 a+b x)}{2 (a+b x) \sqrt{\frac{c}{(a+b x)^2}}}","\frac{a+b x}{2 b \sqrt{\frac{c}{(a+b x)^2}}}",1,"(x*(2*a + b*x))/(2*Sqrt[c/(a + b*x)^2]*(a + b*x))","A",1
2829,1,25,30,0.0147273,"\int \frac{1}{\left(\frac{c}{(a+b x)^2}\right)^{3/2}} \, dx","Integrate[(c/(a + b*x)^2)^(-3/2),x]","\frac{a+b x}{4 b \left(\frac{c}{(a+b x)^2}\right)^{3/2}}","\frac{(a+b x)^3}{4 b c \sqrt{\frac{c}{(a+b x)^2}}}",1,"(a + b*x)/(4*b*(c/(a + b*x)^2)^(3/2))","A",1
2830,1,25,30,0.017838,"\int \frac{1}{\left(\frac{c}{(a+b x)^2}\right)^{5/2}} \, dx","Integrate[(c/(a + b*x)^2)^(-5/2),x]","\frac{a+b x}{6 b \left(\frac{c}{(a+b x)^2}\right)^{5/2}}","\frac{(a+b x)^5}{6 b c^2 \sqrt{\frac{c}{(a+b x)^2}}}",1,"(a + b*x)/(6*b*(c/(a + b*x)^2)^(5/2))","A",1
2831,1,25,30,0.0139428,"\int \left(\frac{c}{(a+b x)^3}\right)^{5/2} \, dx","Integrate[(c/(a + b*x)^3)^(5/2),x]","-\frac{2 (a+b x) \left(\frac{c}{(a+b x)^3}\right)^{5/2}}{13 b}","-\frac{2 c^2 \sqrt{\frac{c}{(a+b x)^3}}}{13 b (a+b x)^5}",1,"(-2*(c/(a + b*x)^3)^(5/2)*(a + b*x))/(13*b)","A",1
2832,1,25,28,0.0106507,"\int \left(\frac{c}{(a+b x)^3}\right)^{3/2} \, dx","Integrate[(c/(a + b*x)^3)^(3/2),x]","-\frac{2 (a+b x) \left(\frac{c}{(a+b x)^3}\right)^{3/2}}{7 b}","-\frac{2 c \sqrt{\frac{c}{(a+b x)^3}}}{7 b (a+b x)^2}",1,"(-2*(c/(a + b*x)^3)^(3/2)*(a + b*x))/(7*b)","A",1
2833,1,23,23,0.0087276,"\int \sqrt{\frac{c}{(a+b x)^3}} \, dx","Integrate[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",1
2834,1,25,25,0.0192336,"\int \frac{1}{\sqrt{\frac{c}{(a+b x)^3}}} \, dx","Integrate[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",1
2835,1,25,30,0.0242499,"\int \frac{1}{\left(\frac{c}{(a+b x)^3}\right)^{3/2}} \, dx","Integrate[(c/(a + b*x)^3)^(-3/2),x]","\frac{2 (a+b x)}{11 b \left(\frac{c}{(a+b x)^3}\right)^{3/2}}","\frac{2 (a+b x)^4}{11 b c \sqrt{\frac{c}{(a+b x)^3}}}",1,"(2*(a + b*x))/(11*b*(c/(a + b*x)^3)^(3/2))","A",1
2836,1,25,30,0.0175753,"\int \frac{1}{\left(\frac{c}{(a+b x)^3}\right)^{5/2}} \, dx","Integrate[(c/(a + b*x)^3)^(-5/2),x]","\frac{2 (a+b x)}{17 b \left(\frac{c}{(a+b x)^3}\right)^{5/2}}","\frac{2 (a+b x)^7}{17 b c^2 \sqrt{\frac{c}{(a+b x)^3}}}",1,"(2*(a + b*x))/(17*b*(c/(a + b*x)^3)^(5/2))","A",1
2837,1,34,27,0.017145,"\int \left(c (a+b x)^{3/2}\right)^{2/3} \, dx","Integrate[(c*(a + b*x)^(3/2))^(2/3),x]","\frac{x (2 a+b x) \left(c (a+b x)^{3/2}\right)^{2/3}}{2 (a+b x)}","\frac{(a+b x) \left(c (a+b x)^{3/2}\right)^{2/3}}{2 b}",1,"(x*(c*(a + b*x)^(3/2))^(2/3)*(2*a + b*x))/(2*(a + b*x))","A",1
2838,1,34,32,0.0194171,"\int \left(c (a+b x)^{2/3}\right)^{3/2} \, dx","Integrate[(c*(a + b*x)^(2/3))^(3/2),x]","\frac{x (2 a+b x) \left(c (a+b x)^{2/3}\right)^{3/2}}{2 (a+b x)}","\frac{c (a+b x)^{5/3} \sqrt{c (a+b x)^{2/3}}}{2 b}",1,"(x*(c*(a + b*x)^(2/3))^(3/2)*(2*a + b*x))/(2*(a + b*x))","A",1
2839,1,34,27,0.0255672,"\int \frac{1}{\left(\frac{c}{(a+b x)^{3/2}}\right)^{2/3}} \, dx","Integrate[(c/(a + b*x)^(3/2))^(-2/3),x]","\frac{x (2 a+b x)}{2 (a+b x) \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,"(x*(2*a + b*x))/(2*(c/(a + b*x)^(3/2))^(2/3)*(a + b*x))","A",1
2840,1,34,34,0.0261679,"\int \frac{1}{\left(\frac{c}{(a+b x)^{2/3}}\right)^{3/2}} \, dx","Integrate[(c/(a + b*x)^(2/3))^(-3/2),x]","\frac{x (2 a+b x)}{2 (a+b x) \left(\frac{c}{(a+b x)^{2/3}}\right)^{3/2}}","\frac{(a+b x)^{5/3}}{2 b c \sqrt{\frac{c}{(a+b x)^{2/3}}}}",1,"(x*(2*a + b*x))/(2*(c/(a + b*x)^(2/3))^(3/2)*(a + b*x))","A",1
2841,1,77,31,0.0252145,"\int (c+d x)^3 \left(a+b (c+d x)^2\right) \, dx","Integrate[(c + d*x)^3*(a + b*(c + d*x)^2),x]","\frac{1}{12} x (2 c+d x) \left(3 a \left(2 c^2+2 c d x+d^2 x^2\right)+2 b \left(3 c^4+6 c^3 d x+7 c^2 d^2 x^2+4 c d^3 x^3+d^4 x^4\right)\right)","\frac{a (c+d x)^4}{4 d}+\frac{b (c+d x)^6}{6 d}",1,"(x*(2*c + d*x)*(3*a*(2*c^2 + 2*c*d*x + d^2*x^2) + 2*b*(3*c^4 + 6*c^3*d*x + 7*c^2*d^2*x^2 + 4*c*d^3*x^3 + d^4*x^4)))/12","B",1
2842,1,172,51,0.0345059,"\int (c+d x)^3 \left(a+b (c+d x)^2\right)^2 \, dx","Integrate[(c + d*x)^3*(a + b*(c + d*x)^2)^2,x]","\frac{1}{4} d^3 x^4 \left(a^2+20 a b c^2+35 b^2 c^4\right)+\frac{1}{3} c d^2 x^3 \left(3 a^2+20 a b c^2+21 b^2 c^4\right)+\frac{1}{2} c^2 d x^2 \left(3 a^2+10 a b c^2+7 b^2 c^4\right)+\frac{1}{6} b d^5 x^6 \left(2 a+21 b c^2\right)+b c d^4 x^5 \left(2 a+7 b c^2\right)+c^3 x \left(a+b c^2\right)^2+b^2 c d^6 x^7+\frac{1}{8} b^2 d^7 x^8","\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,"c^3*(a + b*c^2)^2*x + (c^2*(3*a^2 + 10*a*b*c^2 + 7*b^2*c^4)*d*x^2)/2 + (c*(3*a^2 + 20*a*b*c^2 + 21*b^2*c^4)*d^2*x^3)/3 + ((a^2 + 20*a*b*c^2 + 35*b^2*c^4)*d^3*x^4)/4 + b*c*(2*a + 7*b*c^2)*d^4*x^5 + (b*(2*a + 21*b*c^2)*d^5*x^6)/6 + b^2*c*d^6*x^7 + (b^2*d^7*x^8)/8","B",1
2843,1,249,48,0.0504074,"\int (c+d x)^3 \left(a+b (c+d x)^2\right)^3 \, dx","Integrate[(c + d*x)^3*(a + b*(c + d*x)^2)^3,x]","\frac{1}{2} b d^5 x^6 \left(a^2+21 a b c^2+42 b^2 c^4\right)+\frac{3}{5} b c d^4 x^5 \left(5 a^2+35 a b c^2+42 b^2 c^4\right)+\frac{1}{4} d^3 x^4 \left(a^3+30 a^2 b c^2+105 a b^2 c^4+84 b^3 c^6\right)+c d^2 x^3 \left(a^3+10 a^2 b c^2+21 a b^2 c^4+12 b^3 c^6\right)+\frac{3}{8} b^2 d^7 x^8 \left(a+12 b c^2\right)+3 b^2 c d^6 x^7 \left(a+4 b c^2\right)+\frac{3}{2} c^2 d x^2 \left(a+b c^2\right)^2 \left(a+3 b c^2\right)+c^3 x \left(a+b c^2\right)^3+b^3 c d^8 x^9+\frac{1}{10} b^3 d^9 x^{10}","\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,"c^3*(a + b*c^2)^3*x + (3*c^2*(a + b*c^2)^2*(a + 3*b*c^2)*d*x^2)/2 + c*(a^3 + 10*a^2*b*c^2 + 21*a*b^2*c^4 + 12*b^3*c^6)*d^2*x^3 + ((a^3 + 30*a^2*b*c^2 + 105*a*b^2*c^4 + 84*b^3*c^6)*d^3*x^4)/4 + (3*b*c*(5*a^2 + 35*a*b*c^2 + 42*b^2*c^4)*d^4*x^5)/5 + (b*(a^2 + 21*a*b*c^2 + 42*b^2*c^4)*d^5*x^6)/2 + 3*b^2*c*(a + 4*b*c^2)*d^6*x^7 + (3*b^2*(a + 12*b*c^2)*d^7*x^8)/8 + b^3*c*d^8*x^9 + (b^3*d^9*x^10)/10","B",1
2844,1,12,12,0.0032141,"\int \frac{2+x}{1+(2+x)^2} \, dx","Integrate[(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",1
2845,1,13,13,0.0029379,"\int \frac{2+x}{\left(1+(2+x)^2\right)^2} \, dx","Integrate[(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/(1 + (2 + x)^2)","A",1
2846,1,13,13,0.003283,"\int \frac{2+x}{\left(1+(2+x)^2\right)^3} \, dx","Integrate[(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/(1 + (2 + x)^2)^2","A",1
2847,1,73,93,0.096293,"\int (c+d x)^5 \left(a+b (c+d x)^2\right)^p \, dx","Integrate[(c + d*x)^5*(a + b*(c + d*x)^2)^p,x]","\frac{\left(a+b (c+d x)^2\right)^{p+1} \left(\frac{a^2}{p+1}-\frac{2 a \left(a+b (c+d x)^2\right)}{p+2}+\frac{\left(a+b (c+d x)^2\right)^2}{p+3}\right)}{2 b^3 d}","\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 + b*(c + d*x)^2)^(1 + p)*(a^2/(1 + p) - (2*a*(a + b*(c + d*x)^2))/(2 + p) + (a + b*(c + d*x)^2)^2/(3 + p)))/(2*b^3*d)","A",1
2848,1,68,55,0.0391318,"\int (c+d x)^4 \left(a+b (c+d x)^2\right)^p \, dx","Integrate[(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",1
2849,1,51,62,0.0536859,"\int (c+d x)^3 \left(a+b (c+d x)^2\right)^p \, dx","Integrate[(c + d*x)^3*(a + b*(c + d*x)^2)^p,x]","\frac{\left(a+b (c+d x)^2\right)^{p+1} \left(b (p+1) (c+d x)^2-a\right)}{2 b^2 d (p+1) (p+2)}","\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 + b*(c + d*x)^2)^(1 + p)*(-a + b*(1 + p)*(c + d*x)^2))/(2*b^2*d*(1 + p)*(2 + p))","A",1
2850,1,68,55,0.0175828,"\int (c+d x)^2 \left(a+b (c+d x)^2\right)^p \, dx","Integrate[(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",1
2851,1,30,30,0.0091722,"\int (c+d x) \left(a+b (c+d x)^2\right)^p \, dx","Integrate[(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",1
2852,1,52,52,0.03789,"\int \frac{\left(a+b (c+d x)^2\right)^p}{c+d x} \, dx","Integrate[(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,"-1/2*((a + b*(c + d*x)^2)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, 1 + (b*(c + d*x)^2)/a])/(a*d*(1 + p))","A",1
2853,1,98,31,0.0135086,"\int (c+d x)^3 \left(a+b (c+d x)^3\right) \, dx","Integrate[(c + d*x)^3*(a + b*(c + d*x)^3),x]","\frac{1}{4} d^3 x^4 \left(a+20 b c^3\right)+c d^2 x^3 \left(a+5 b c^3\right)+c^3 x \left(a+b c^3\right)+\frac{3}{2} c^2 d x^2 \left(a+2 b c^3\right)+3 b c^2 d^4 x^5+b c d^5 x^6+\frac{1}{7} b d^6 x^7","\frac{a (c+d x)^4}{4 d}+\frac{b (c+d x)^7}{7 d}",1,"c^3*(a + b*c^3)*x + (3*c^2*(a + 2*b*c^3)*d*x^2)/2 + c*(a + 5*b*c^3)*d^2*x^3 + ((a + 20*b*c^3)*d^3*x^4)/4 + 3*b*c^2*d^4*x^5 + b*c*d^5*x^6 + (b*d^6*x^7)/7","B",1
2854,1,203,51,0.0299657,"\int (c+d x)^3 \left(a+b (c+d x)^3\right)^2 \, dx","Integrate[(c + d*x)^3*(a + b*(c + d*x)^3)^2,x]","\frac{1}{4} d^3 x^4 \left(a^2+40 a b c^3+84 b^2 c^6\right)+c d^2 x^3 \left(a^2+10 a b c^3+12 b^2 c^6\right)+\frac{3}{2} c^2 d x^2 \left(a^2+4 a b c^3+3 b^2 c^6\right)+\frac{2}{7} b d^6 x^7 \left(a+42 b c^3\right)+b c d^5 x^6 \left(2 a+21 b c^3\right)+c^3 x \left(a+b c^3\right)^2+\frac{6}{5} b c^2 d^4 x^5 \left(5 a+21 b c^3\right)+\frac{9}{2} b^2 c^2 d^7 x^8+b^2 c d^8 x^9+\frac{1}{10} b^2 d^9 x^{10}","\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,"c^3*(a + b*c^3)^2*x + (3*c^2*(a^2 + 4*a*b*c^3 + 3*b^2*c^6)*d*x^2)/2 + c*(a^2 + 10*a*b*c^3 + 12*b^2*c^6)*d^2*x^3 + ((a^2 + 40*a*b*c^3 + 84*b^2*c^6)*d^3*x^4)/4 + (6*b*c^2*(5*a + 21*b*c^3)*d^4*x^5)/5 + b*c*(2*a + 21*b*c^3)*d^5*x^6 + (2*b*(a + 42*b*c^3)*d^6*x^7)/7 + (9*b^2*c^2*d^7*x^8)/2 + b^2*c*d^8*x^9 + (b^2*d^9*x^10)/10","B",1
2855,1,323,71,0.0808461,"\int (c+d x)^3 \left(a+b (c+d x)^3\right)^3 \, dx","Integrate[(c + d*x)^3*(a + b*(c + d*x)^3)^3,x]","\frac{3}{7} b d^6 x^7 \left(a^2+84 a b c^3+308 b^2 c^6\right)+3 b c d^5 x^6 \left(a^2+21 a b c^3+44 b^2 c^6\right)+\frac{9}{5} b c^2 d^4 x^5 \left(5 a^2+42 a b c^3+55 b^2 c^6\right)+\frac{1}{4} d^3 x^4 \left(a^3+60 a^2 b c^3+252 a b^2 c^6+220 b^3 c^9\right)+c d^2 x^3 \left(a^3+15 a^2 b c^3+36 a b^2 c^6+22 b^3 c^9\right)+\frac{1}{10} b^2 d^9 x^{10} \left(3 a+220 b c^3\right)+b^2 c d^8 x^9 \left(3 a+55 b c^3\right)+\frac{9}{2} b^2 c^2 d^7 x^8 \left(3 a+22 b c^3\right)+c^3 x \left(a+b c^3\right)^3+\frac{3}{2} c^2 d x^2 \left(a+b c^3\right)^2 \left(a+4 b c^3\right)+6 b^3 c^2 d^{10} x^{11}+b^3 c d^{11} x^{12}+\frac{1}{13} b^3 d^{12} x^{13}","\frac{a^3 (c+d x)^4}{4 d}+\frac{3 a^2 b (c+d x)^7}{7 d}+\frac{3 a b^2 (c+d x)^{10}}{10 d}+\frac{b^3 (c+d x)^{13}}{13 d}",1,"c^3*(a + b*c^3)^3*x + (3*c^2*(a + b*c^3)^2*(a + 4*b*c^3)*d*x^2)/2 + c*(a^3 + 15*a^2*b*c^3 + 36*a*b^2*c^6 + 22*b^3*c^9)*d^2*x^3 + ((a^3 + 60*a^2*b*c^3 + 252*a*b^2*c^6 + 220*b^3*c^9)*d^3*x^4)/4 + (9*b*c^2*(5*a^2 + 42*a*b*c^3 + 55*b^2*c^6)*d^4*x^5)/5 + 3*b*c*(a^2 + 21*a*b*c^3 + 44*b^2*c^6)*d^5*x^6 + (3*b*(a^2 + 84*a*b*c^3 + 308*b^2*c^6)*d^6*x^7)/7 + (9*b^2*c^2*(3*a + 22*b*c^3)*d^7*x^8)/2 + b^2*c*(3*a + 55*b*c^3)*d^8*x^9 + (b^2*(3*a + 220*b*c^3)*d^9*x^10)/10 + 6*b^3*c^2*d^10*x^11 + b^3*c*d^11*x^12 + (b^3*d^12*x^13)/13","B",1
2856,1,102,37,0.0064888,"\int (c e+d e x)^3 \left(a+b (c+d x)^3\right) \, dx","Integrate[(c*e + d*e*x)^3*(a + b*(c + d*x)^3),x]","e^3 \left(\frac{1}{4} d^3 x^4 \left(a+20 b c^3\right)+c d^2 x^3 \left(a+5 b c^3\right)+c^3 x \left(a+b c^3\right)+\frac{3}{2} c^2 d x^2 \left(a+2 b c^3\right)+3 b c^2 d^4 x^5+b c d^5 x^6+\frac{1}{7} b d^6 x^7\right)","\frac{a e^3 (c+d x)^4}{4 d}+\frac{b e^3 (c+d x)^7}{7 d}",1,"e^3*(c^3*(a + b*c^3)*x + (3*c^2*(a + 2*b*c^3)*d*x^2)/2 + c*(a + 5*b*c^3)*d^2*x^3 + ((a + 20*b*c^3)*d^3*x^4)/4 + 3*b*c^2*d^4*x^5 + b*c*d^5*x^6 + (b*d^6*x^7)/7)","B",1
2857,1,207,60,0.0116819,"\int (c e+d e x)^3 \left(a+b (c+d x)^3\right)^2 \, dx","Integrate[(c*e + d*e*x)^3*(a + b*(c + d*x)^3)^2,x]","e^3 \left(\frac{1}{4} d^3 x^4 \left(a^2+40 a b c^3+84 b^2 c^6\right)+c d^2 x^3 \left(a^2+10 a b c^3+12 b^2 c^6\right)+\frac{3}{2} c^2 d x^2 \left(a^2+4 a b c^3+3 b^2 c^6\right)+\frac{2}{7} b d^6 x^7 \left(a+42 b c^3\right)+b c d^5 x^6 \left(2 a+21 b c^3\right)+c^3 x \left(a+b c^3\right)^2+\frac{6}{5} b c^2 d^4 x^5 \left(5 a+21 b c^3\right)+\frac{9}{2} b^2 c^2 d^7 x^8+b^2 c d^8 x^9+\frac{1}{10} b^2 d^9 x^{10}\right)","\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,"e^3*(c^3*(a + b*c^3)^2*x + (3*c^2*(a^2 + 4*a*b*c^3 + 3*b^2*c^6)*d*x^2)/2 + c*(a^2 + 10*a*b*c^3 + 12*b^2*c^6)*d^2*x^3 + ((a^2 + 40*a*b*c^3 + 84*b^2*c^6)*d^3*x^4)/4 + (6*b*c^2*(5*a + 21*b*c^3)*d^4*x^5)/5 + b*c*(2*a + 21*b*c^3)*d^5*x^6 + (2*b*(a + 42*b*c^3)*d^6*x^7)/7 + (9*b^2*c^2*d^7*x^8)/2 + b^2*c*d^8*x^9 + (b^2*d^9*x^10)/10)","B",1
2858,1,327,83,0.018035,"\int (c e+d e x)^3 \left(a+b (c+d x)^3\right)^3 \, dx","Integrate[(c*e + d*e*x)^3*(a + b*(c + d*x)^3)^3,x]","e^3 \left(\frac{3}{7} b d^6 x^7 \left(a^2+84 a b c^3+308 b^2 c^6\right)+3 b c d^5 x^6 \left(a^2+21 a b c^3+44 b^2 c^6\right)+\frac{9}{5} b c^2 d^4 x^5 \left(5 a^2+42 a b c^3+55 b^2 c^6\right)+\frac{1}{4} d^3 x^4 \left(a^3+60 a^2 b c^3+252 a b^2 c^6+220 b^3 c^9\right)+c d^2 x^3 \left(a^3+15 a^2 b c^3+36 a b^2 c^6+22 b^3 c^9\right)+\frac{1}{10} b^2 d^9 x^{10} \left(3 a+220 b c^3\right)+b^2 c d^8 x^9 \left(3 a+55 b c^3\right)+\frac{9}{2} b^2 c^2 d^7 x^8 \left(3 a+22 b c^3\right)+c^3 x \left(a+b c^3\right)^3+\frac{3}{2} c^2 d x^2 \left(a+b c^3\right)^2 \left(a+4 b c^3\right)+6 b^3 c^2 d^{10} x^{11}+b^3 c d^{11} x^{12}+\frac{1}{13} b^3 d^{12} x^{13}\right)","\frac{a^3 e^3 (c+d x)^4}{4 d}+\frac{3 a^2 b e^3 (c+d x)^7}{7 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,"e^3*(c^3*(a + b*c^3)^3*x + (3*c^2*(a + b*c^3)^2*(a + 4*b*c^3)*d*x^2)/2 + c*(a^3 + 15*a^2*b*c^3 + 36*a*b^2*c^6 + 22*b^3*c^9)*d^2*x^3 + ((a^3 + 60*a^2*b*c^3 + 252*a*b^2*c^6 + 220*b^3*c^9)*d^3*x^4)/4 + (9*b*c^2*(5*a^2 + 42*a*b*c^3 + 55*b^2*c^6)*d^4*x^5)/5 + 3*b*c*(a^2 + 21*a*b*c^3 + 44*b^2*c^6)*d^5*x^6 + (3*b*(a^2 + 84*a*b*c^3 + 308*b^2*c^6)*d^6*x^7)/7 + (9*b^2*c^2*(3*a + 22*b*c^3)*d^7*x^8)/2 + b^2*c*(3*a + 55*b*c^3)*d^8*x^9 + (b^2*(3*a + 220*b*c^3)*d^9*x^10)/10 + 6*b^3*c^2*d^10*x^11 + b^3*c*d^11*x^12 + (b^3*d^12*x^13)/13)","B",1
2859,1,159,156,0.0529403,"\int \frac{(c+d x)^4}{a+b (c+d x)^3} \, dx","Integrate[(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{2 \sqrt[3]{b} (c+d x)-\sqrt[3]{a}}{\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",1
2860,1,142,144,0.0217794,"\int \frac{(c+d x)^3}{a+b (c+d x)^3} \, dx","Integrate[(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)-2 \sqrt[3]{a} \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)-2 \sqrt{3} \sqrt[3]{a} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} (c+d x)-\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)+6 \sqrt[3]{b} c+6 \sqrt[3]{b} d x}{6 b^{4/3} d}","\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,"(6*b^(1/3)*c + 6*b^(1/3)*d*x - 2*Sqrt[3]*a^(1/3)*ArcTan[(-a^(1/3) + 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))] - 2*a^(1/3)*Log[a^(1/3) + b^(1/3)*(c + d*x)] + 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",1
2861,1,22,22,0.0082351,"\int \frac{(c+d x)^2}{a+b (c+d x)^3} \, dx","Integrate[(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",1
2862,1,114,140,0.0142058,"\int \frac{c+d x}{a+b (c+d x)^3} \, dx","Integrate[(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)-2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} (c+d x)-\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{6 \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,"(2*Sqrt[3]*ArcTan[(-a^(1/3) + 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))] - 2*Log[a^(1/3) + b^(1/3)*(c + d*x)] + 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",1
2863,1,116,140,0.0118588,"\int \frac{1}{a+b (c+d x)^3} \, dx","Integrate[(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)+2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} (c+d x)-\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{6 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,"(2*Sqrt[3]*ArcTan[(-a^(1/3) + 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))] + 2*Log[a^(1/3) + b^(1/3)*(c + d*x)] - 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",1
2864,1,36,36,0.0092279,"\int \frac{1}{(c+d x) \left(a+b (c+d x)^3\right)} \, dx","Integrate[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",1
2865,1,140,154,0.0479129,"\int \frac{1}{(c+d x)^2 \left(a+b (c+d x)^3\right)} \, dx","Integrate[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)+2 \sqrt[3]{b} \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)-2 \sqrt{3} \sqrt[3]{b} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} (c+d x)-\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)-\frac{6 \sqrt[3]{a}}{c+d x}}{6 a^{4/3} d}","-\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,"((-6*a^(1/3))/(c + d*x) - 2*Sqrt[3]*b^(1/3)*ArcTan[(-a^(1/3) + 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))] + 2*b^(1/3)*Log[a^(1/3) + b^(1/3)*(c + d*x)] - 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",1
2866,1,139,156,0.037405,"\int \frac{1}{(c+d x)^3 \left(a+b (c+d x)^3\right)} \, dx","Integrate[1/((c + d*x)^3*(a + b*(c + d*x)^3)),x]","\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)-\frac{3 a^{2/3}}{(c+d x)^2}-2 b^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)-2 \sqrt{3} b^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} (c+d x)-\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{6 a^{5/3} d}","-\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,"((-3*a^(2/3))/(c + d*x)^2 - 2*Sqrt[3]*b^(2/3)*ArcTan[(-a^(1/3) + 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))] - 2*b^(2/3)*Log[a^(1/3) + b^(1/3)*(c + d*x)] + 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",1
2867,1,44,56,0.0242652,"\int \frac{1}{(c+d x)^4 \left(a+b (c+d x)^3\right)} \, dx","Integrate[1/((c + d*x)^4*(a + b*(c + d*x)^3)),x]","\frac{b \log \left(a+b (c+d x)^3\right)-\frac{a}{(c+d x)^3}-3 b \log (c+d x)}{3 a^2 d}","-\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,"(-(a/(c + d*x)^3) - 3*b*Log[c + d*x] + b*Log[a + b*(c + d*x)^3])/(3*a^2*d)","A",1
2868,1,152,172,0.10458,"\int \frac{(c+d x)^4}{\left(a+b (c+d x)^3\right)^2} \, dx","Integrate[(c + d*x)^4/(a + b*(c + d*x)^3)^2,x]","\frac{\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{\sqrt[3]{a}}-\frac{3 b^{2/3} (c+d x)^2}{a+b (c+d x)^3}-\frac{2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{\sqrt[3]{a}}+\frac{2 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} (c+d x)-\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt[3]{a}}}{9 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)}{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,"((-3*b^(2/3)*(c + d*x)^2)/(a + b*(c + d*x)^3) + (2*Sqrt[3]*ArcTan[(-a^(1/3) + 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))])/a^(1/3) - (2*Log[a^(1/3) + b^(1/3)*(c + d*x)])/a^(1/3) + Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2]/a^(1/3))/(9*b^(5/3)*d)","A",1
2869,1,151,170,0.0694847,"\int \frac{(c+d x)^3}{\left(a+b (c+d x)^3\right)^2} \, dx","Integrate[(c + d*x)^3/(a + b*(c + d*x)^3)^2,x]","\frac{-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{a^{2/3}}+\frac{2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{a^{2/3}}+\frac{2 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} (c+d x)-\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{a^{2/3}}-\frac{6 \sqrt[3]{b} (c+d x)}{a+b (c+d x)^3}}{18 b^{4/3} d}","\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,"((-6*b^(1/3)*(c + d*x))/(a + b*(c + d*x)^3) + (2*Sqrt[3]*ArcTan[(-a^(1/3) + 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))])/a^(2/3) + (2*Log[a^(1/3) + b^(1/3)*(c + d*x)])/a^(2/3) - Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2]/a^(2/3))/(18*b^(4/3)*d)","A",1
2870,1,23,23,0.014159,"\int \frac{(c+d x)^2}{\left(a+b (c+d x)^3\right)^2} \, dx","Integrate[(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*1/(b*d*(a + b*(c + d*x)^3))","A",1
2871,1,152,172,0.0890226,"\int \frac{c+d x}{\left(a+b (c+d x)^3\right)^2} \, dx","Integrate[(c + d*x)/(a + b*(c + d*x)^3)^2,x]","\frac{\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{b^{2/3}}-\frac{2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{b^{2/3}}+\frac{2 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} (c+d x)-\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{b^{2/3}}+\frac{6 \sqrt[3]{a} (c+d x)^2}{a+b (c+d x)^3}}{18 a^{4/3} d}","-\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,"((6*a^(1/3)*(c + d*x)^2)/(a + b*(c + d*x)^3) + (2*Sqrt[3]*ArcTan[(-a^(1/3) + 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))])/b^(2/3) - (2*Log[a^(1/3) + b^(1/3)*(c + d*x)])/b^(2/3) + Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2]/b^(2/3))/(18*a^(4/3)*d)","A",1
2872,1,151,170,0.059217,"\int \frac{1}{\left(a+b (c+d x)^3\right)^2} \, dx","Integrate[(a + b*(c + d*x)^3)^(-2),x]","\frac{-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{\sqrt[3]{b}}+\frac{3 a^{2/3} (c+d x)}{a+b (c+d x)^3}+\frac{2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{\sqrt[3]{b}}+\frac{2 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} (c+d x)-\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt[3]{b}}}{9 a^{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)}{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,"((3*a^(2/3)*(c + d*x))/(a + b*(c + d*x)^3) + (2*Sqrt[3]*ArcTan[(-a^(1/3) + 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))])/b^(1/3) + (2*Log[a^(1/3) + b^(1/3)*(c + d*x)])/b^(1/3) - Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2]/b^(1/3))/(9*a^(5/3)*d)","A",1
2873,1,48,59,0.026327,"\int \frac{1}{(c+d x) \left(a+b (c+d x)^3\right)^2} \, dx","Integrate[1/((c + d*x)*(a + b*(c + d*x)^3)^2),x]","\frac{\frac{a}{a+b (c+d x)^3}-\log \left(a+b (c+d x)^3\right)+3 \log (c+d x)}{3 a^2 d}","-\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,"(a/(a + b*(c + d*x)^3) + 3*Log[c + d*x] - Log[a + b*(c + d*x)^3])/(3*a^2*d)","A",1
2874,1,168,189,0.0933934,"\int \frac{1}{(c+d x)^2 \left(a+b (c+d x)^3\right)^2} \, dx","Integrate[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)-\frac{3 \sqrt[3]{a} b (c+d x)^2}{a+b (c+d x)^3}+4 \sqrt[3]{b} \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)-4 \sqrt{3} \sqrt[3]{b} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} (c+d x)-\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)-\frac{9 \sqrt[3]{a}}{c+d x}}{9 a^{7/3} d}","-\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,"((-9*a^(1/3))/(c + d*x) - (3*a^(1/3)*b*(c + d*x)^2)/(a + b*(c + d*x)^3) - 4*Sqrt[3]*b^(1/3)*ArcTan[(-a^(1/3) + 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))] + 4*b^(1/3)*Log[a^(1/3) + b^(1/3)*(c + d*x)] - 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",1
2875,1,166,189,0.0858084,"\int \frac{1}{(c+d x)^3 \left(a+b (c+d x)^3\right)^2} \, dx","Integrate[1/((c + d*x)^3*(a + b*(c + d*x)^3)^2),x]","\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)-\frac{6 a^{2/3} b (c+d x)}{a+b (c+d x)^3}-\frac{9 a^{2/3}}{(c+d x)^2}-10 b^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)-10 \sqrt{3} b^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} (c+d x)-\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{18 a^{8/3} d}","-\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,"((-9*a^(2/3))/(c + d*x)^2 - (6*a^(2/3)*b*(c + d*x))/(a + b*(c + d*x)^3) - 10*Sqrt[3]*b^(2/3)*ArcTan[(-a^(1/3) + 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))] - 10*b^(2/3)*Log[a^(1/3) + b^(1/3)*(c + d*x)] + 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",1
2876,1,60,80,0.0782336,"\int \frac{1}{(c+d x)^4 \left(a+b (c+d x)^3\right)^2} \, dx","Integrate[1/((c + d*x)^4*(a + b*(c + d*x)^3)^2),x]","-\frac{a \left(\frac{b}{a+b (c+d x)^3}+\frac{1}{(c+d x)^3}\right)-2 b \log \left(a+b (c+d x)^3\right)+6 b \log (c+d x)}{3 a^3 d}","-\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{b}{3 a^2 d \left(a+b (c+d x)^3\right)}-\frac{1}{3 a^2 d (c+d x)^3}",1,"-1/3*(a*((c + d*x)^(-3) + b/(a + b*(c + d*x)^3)) + 6*b*Log[c + d*x] - 2*b*Log[a + b*(c + d*x)^3])/(a^3*d)","A",1
2877,1,182,205,0.1825767,"\int \frac{(c+d x)^4}{\left(a+b (c+d x)^3\right)^3} \, dx","Integrate[(c + d*x)^4/(a + b*(c + d*x)^3)^3,x]","\frac{\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{a^{4/3}}-\frac{2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{a^{4/3}}+\frac{2 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} (c+d x)-\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{a^{4/3}}+\frac{6 b^{2/3} (c+d x)^2}{a \left(a+b (c+d x)^3\right)}-\frac{9 b^{2/3} (c+d x)^2}{\left(a+b (c+d x)^3\right)^2}}{54 b^{5/3} d}","-\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,"((-9*b^(2/3)*(c + d*x)^2)/(a + b*(c + d*x)^3)^2 + (6*b^(2/3)*(c + d*x)^2)/(a*(a + b*(c + d*x)^3)) + (2*Sqrt[3]*ArcTan[(-a^(1/3) + 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))])/a^(4/3) - (2*Log[a^(1/3) + b^(1/3)*(c + d*x)])/a^(4/3) + Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2]/a^(4/3))/(54*b^(5/3)*d)","A",1
2878,1,179,201,0.122029,"\int \frac{(c+d x)^3}{\left(a+b (c+d x)^3\right)^3} \, dx","Integrate[(c + d*x)^3/(a + b*(c + d*x)^3)^3,x]","\frac{-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{a^{5/3}}+\frac{2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{a^{5/3}}+\frac{2 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} (c+d x)-\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{a^{5/3}}+\frac{3 \sqrt[3]{b} (c+d x)}{a \left(a+b (c+d x)^3\right)}-\frac{9 \sqrt[3]{b} (c+d x)}{\left(a+b (c+d x)^3\right)^2}}{54 b^{4/3} d}","\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,"((-9*b^(1/3)*(c + d*x))/(a + b*(c + d*x)^3)^2 + (3*b^(1/3)*(c + d*x))/(a*(a + b*(c + d*x)^3)) + (2*Sqrt[3]*ArcTan[(-a^(1/3) + 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))])/a^(5/3) + (2*Log[a^(1/3) + b^(1/3)*(c + d*x)])/a^(5/3) - Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2]/a^(5/3))/(54*b^(4/3)*d)","A",1
2879,1,23,23,0.0142578,"\int \frac{(c+d x)^2}{\left(a+b (c+d x)^3\right)^3} \, dx","Integrate[(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*1/(b*d*(a + b*(c + d*x)^3)^2)","A",1
2880,1,180,202,0.1288256,"\int \frac{c+d x}{\left(a+b (c+d x)^3\right)^3} \, dx","Integrate[(c + d*x)/(a + b*(c + d*x)^3)^3,x]","\frac{\frac{2 \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{b^{2/3}}+\frac{9 a^{4/3} (c+d x)^2}{\left(a+b (c+d x)^3\right)^2}-\frac{4 \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{b^{2/3}}+\frac{4 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} (c+d x)-\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{b^{2/3}}+\frac{12 \sqrt[3]{a} (c+d x)^2}{a+b (c+d x)^3}}{54 a^{7/3} d}","-\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,"((9*a^(4/3)*(c + d*x)^2)/(a + b*(c + d*x)^3)^2 + (12*a^(1/3)*(c + d*x)^2)/(a + b*(c + d*x)^3) + (4*Sqrt[3]*ArcTan[(-a^(1/3) + 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))])/b^(2/3) - (4*Log[a^(1/3) + b^(1/3)*(c + d*x)])/b^(2/3) + (2*Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2])/b^(2/3))/(54*a^(7/3)*d)","A",1
2881,1,176,198,0.1056786,"\int \frac{1}{\left(a+b (c+d x)^3\right)^3} \, dx","Integrate[(a + b*(c + d*x)^3)^(-3),x]","\frac{-\frac{5 \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{\sqrt[3]{b}}+\frac{9 a^{5/3} (c+d x)}{\left(a+b (c+d x)^3\right)^2}+\frac{15 a^{2/3} (c+d x)}{a+b (c+d x)^3}+\frac{10 \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{\sqrt[3]{b}}+\frac{10 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} (c+d x)-\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt[3]{b}}}{54 a^{8/3} d}","-\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 \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{5 (c+d x)}{18 a^2 d \left(a+b (c+d x)^3\right)}+\frac{c+d x}{6 a d \left(a+b (c+d x)^3\right)^2}",1,"((9*a^(5/3)*(c + d*x))/(a + b*(c + d*x)^3)^2 + (15*a^(2/3)*(c + d*x))/(a + b*(c + d*x)^3) + (10*Sqrt[3]*ArcTan[(-a^(1/3) + 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))])/b^(1/3) + (10*Log[a^(1/3) + b^(1/3)*(c + d*x)])/b^(1/3) - (5*Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2])/b^(1/3))/(54*a^(8/3)*d)","A",1
2882,1,63,82,0.0557452,"\int \frac{1}{(c+d x) \left(a+b (c+d x)^3\right)^3} \, dx","Integrate[1/((c + d*x)*(a + b*(c + d*x)^3)^3),x]","\frac{\frac{a \left(2 \left(a+b (c+d x)^3\right)+a\right)}{\left(a+b (c+d x)^3\right)^2}-2 \log \left(a+b (c+d x)^3\right)+6 \log (c+d x)}{6 a^3 d}","-\frac{\log \left(a+b (c+d x)^3\right)}{3 a^3 d}+\frac{\log (c+d x)}{a^3 d}+\frac{1}{3 a^2 d \left(a+b (c+d x)^3\right)}+\frac{1}{6 a d \left(a+b (c+d x)^3\right)^2}",1,"((a*(a + 2*(a + b*(c + d*x)^3)))/(a + b*(c + d*x)^3)^2 + 6*Log[c + d*x] - 2*Log[a + b*(c + d*x)^3])/(6*a^3*d)","A",1
2883,1,196,219,0.1558639,"\int \frac{1}{(c+d x)^2 \left(a+b (c+d x)^3\right)^3} \, dx","Integrate[1/((c + d*x)^2*(a + b*(c + d*x)^3)^3),x]","\frac{-14 \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)-\frac{9 a^{4/3} b (c+d x)^2}{\left(a+b (c+d x)^3\right)^2}-\frac{30 \sqrt[3]{a} b (c+d x)^2}{a+b (c+d x)^3}+28 \sqrt[3]{b} \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)-28 \sqrt{3} \sqrt[3]{b} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} (c+d x)-\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)-\frac{54 \sqrt[3]{a}}{c+d x}}{54 a^{10/3} d}","-\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{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{7}{18 a^2 d (c+d x) \left(a+b (c+d x)^3\right)}+\frac{1}{6 a d (c+d x) \left(a+b (c+d x)^3\right)^2}",1,"((-54*a^(1/3))/(c + d*x) - (9*a^(4/3)*b*(c + d*x)^2)/(a + b*(c + d*x)^3)^2 - (30*a^(1/3)*b*(c + d*x)^2)/(a + b*(c + d*x)^3) - 28*Sqrt[3]*b^(1/3)*ArcTan[(-a^(1/3) + 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))] + 28*b^(1/3)*Log[a^(1/3) + b^(1/3)*(c + d*x)] - 14*b^(1/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2])/(54*a^(10/3)*d)","A",1
2884,1,192,219,0.1578096,"\int \frac{1}{(c+d x)^3 \left(a+b (c+d x)^3\right)^3} \, dx","Integrate[1/((c + d*x)^3*(a + b*(c + d*x)^3)^3),x]","\frac{20 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)-\frac{9 a^{5/3} b (c+d x)}{\left(a+b (c+d x)^3\right)^2}-\frac{33 a^{2/3} b (c+d x)}{a+b (c+d x)^3}-\frac{27 a^{2/3}}{(c+d x)^2}-40 b^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)-40 \sqrt{3} b^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} (c+d x)-\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{54 a^{11/3} d}","-\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{10}{9 a^3 d (c+d x)^2}+\frac{4}{9 a^2 d (c+d x)^2 \left(a+b (c+d x)^3\right)}+\frac{1}{6 a d (c+d x)^2 \left(a+b (c+d x)^3\right)^2}",1,"((-27*a^(2/3))/(c + d*x)^2 - (9*a^(5/3)*b*(c + d*x))/(a + b*(c + d*x)^3)^2 - (33*a^(2/3)*b*(c + d*x))/(a + b*(c + d*x)^3) - 40*Sqrt[3]*b^(2/3)*ArcTan[(-a^(1/3) + 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))] - 40*b^(2/3)*Log[a^(1/3) + b^(1/3)*(c + d*x)] + 20*b^(2/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2])/(54*a^(11/3)*d)","A",1
2885,1,80,101,0.1193489,"\int \frac{1}{(c+d x)^4 \left(a+b (c+d x)^3\right)^3} \, dx","Integrate[1/((c + d*x)^4*(a + b*(c + d*x)^3)^3),x]","\frac{a \left(-\frac{4 b}{a+b (c+d x)^3}-\frac{a b}{\left(a+b (c+d x)^3\right)^2}-\frac{2}{(c+d x)^3}\right)+6 b \log \left(a+b (c+d x)^3\right)-18 b \log (c+d x)}{6 a^4 d}","-\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{2 b}{3 a^3 d \left(a+b (c+d x)^3\right)}-\frac{1}{3 a^3 d (c+d x)^3}-\frac{b}{6 a^2 d \left(a+b (c+d x)^3\right)^2}",1,"(a*(-2/(c + d*x)^3 - (a*b)/(a + b*(c + d*x)^3)^2 - (4*b)/(a + b*(c + d*x)^3)) - 18*b*Log[c + d*x] + 6*b*Log[a + b*(c + d*x)^3])/(6*a^4*d)","A",1
2886,1,163,168,0.0163707,"\int \frac{(c e+d e x)^4}{a+b (c+d x)^3} \, dx","Integrate[(c*e + d*e*x)^4/(a + b*(c + d*x)^3),x]","e^4 \left(\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{2 \sqrt[3]{b} (c+d x)-\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^{5/3} d}+\frac{(c+d x)^2}{2 b d}\right)","\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)*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",1
2887,1,145,156,0.0197098,"\int \frac{(c e+d e x)^3}{a+b (c+d x)^3} \, dx","Integrate[(c*e + d*e*x)^3/(a + b*(c + d*x)^3),x]","\frac{e^3 \left(\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)-2 \sqrt[3]{a} \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)-2 \sqrt{3} \sqrt[3]{a} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} (c+d x)-\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)+6 \sqrt[3]{b} c+6 \sqrt[3]{b} d x\right)}{6 b^{4/3} d}","\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*(6*b^(1/3)*c + 6*b^(1/3)*d*x - 2*Sqrt[3]*a^(1/3)*ArcTan[(-a^(1/3) + 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))] - 2*a^(1/3)*Log[a^(1/3) + b^(1/3)*(c + d*x)] + 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",1
2888,1,25,25,0.0091555,"\int \frac{(c e+d e x)^2}{a+b (c+d x)^3} \, dx","Integrate[(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",1
2889,1,115,143,0.0137131,"\int \frac{c e+d e x}{a+b (c+d x)^3} \, dx","Integrate[(c*e + d*e*x)/(a + b*(c + d*x)^3),x]","\frac{e \left(\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)-2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} (c+d x)-\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)\right)}{6 \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*(2*Sqrt[3]*ArcTan[(-a^(1/3) + 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))] - 2*Log[a^(1/3) + b^(1/3)*(c + d*x)] + 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",1
2890,1,42,42,0.0104023,"\int \frac{1}{(c e+d e x) \left(a+b (c+d x)^3\right)} \, dx","Integrate[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",1
2891,1,143,166,0.038379,"\int \frac{1}{(c e+d e x)^2 \left(a+b (c+d x)^3\right)} \, dx","Integrate[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)+2 \sqrt[3]{b} \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)-2 \sqrt{3} \sqrt[3]{b} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} (c+d x)-\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)-\frac{6 \sqrt[3]{a}}{c+d x}}{6 a^{4/3} d e^2}","-\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,"((-6*a^(1/3))/(c + d*x) - 2*Sqrt[3]*b^(1/3)*ArcTan[(-a^(1/3) + 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))] + 2*b^(1/3)*Log[a^(1/3) + b^(1/3)*(c + d*x)] - 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",1
2892,1,142,168,0.0386468,"\int \frac{1}{(c e+d e x)^3 \left(a+b (c+d x)^3\right)} \, dx","Integrate[1/((c*e + d*e*x)^3*(a + b*(c + d*x)^3)),x]","\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)-\frac{3 a^{2/3}}{(c+d x)^2}-2 b^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)-2 \sqrt{3} b^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} (c+d x)-\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{6 a^{5/3} d e^3}","-\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,"((-3*a^(2/3))/(c + d*x)^2 - 2*Sqrt[3]*b^(2/3)*ArcTan[(-a^(1/3) + 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))] - 2*b^(2/3)*Log[a^(1/3) + b^(1/3)*(c + d*x)] + 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",1
2893,1,47,65,0.0179015,"\int \frac{1}{(c e+d e x)^4 \left(a+b (c+d x)^3\right)} \, dx","Integrate[1/((c*e + d*e*x)^4*(a + b*(c + d*x)^3)),x]","\frac{b \log \left(a+b (c+d x)^3\right)-\frac{a}{(c+d x)^3}-3 b \log (c+d x)}{3 a^2 d e^4}","-\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,"(-(a/(c + d*x)^3) - 3*b*Log[c + d*x] + b*Log[a + b*(c + d*x)^3])/(3*a^2*d*e^4)","A",1
2894,1,155,184,0.0914828,"\int \frac{(c e+d e x)^4}{\left(a+b (c+d x)^3\right)^2} \, dx","Integrate[(c*e + d*e*x)^4/(a + b*(c + d*x)^3)^2,x]","\frac{e^4 \left(\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{\sqrt[3]{a}}-\frac{3 b^{2/3} (c+d x)^2}{a+b (c+d x)^3}-\frac{2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{\sqrt[3]{a}}+\frac{2 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} (c+d x)-\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt[3]{a}}\right)}{9 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)}{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*((-3*b^(2/3)*(c + d*x)^2)/(a + b*(c + d*x)^3) + (2*Sqrt[3]*ArcTan[(-a^(1/3) + 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))])/a^(1/3) - (2*Log[a^(1/3) + b^(1/3)*(c + d*x)])/a^(1/3) + Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2]/a^(1/3)))/(9*b^(5/3)*d)","A",1
2895,1,154,182,0.06777,"\int \frac{(c e+d e x)^3}{\left(a+b (c+d x)^3\right)^2} \, dx","Integrate[(c*e + d*e*x)^3/(a + b*(c + d*x)^3)^2,x]","\frac{e^3 \left(-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{a^{2/3}}+\frac{2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{a^{2/3}}+\frac{2 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} (c+d x)-\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{a^{2/3}}-\frac{6 \sqrt[3]{b} (c+d x)}{a+b (c+d x)^3}\right)}{18 b^{4/3} d}","\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*((-6*b^(1/3)*(c + d*x))/(a + b*(c + d*x)^3) + (2*Sqrt[3]*ArcTan[(-a^(1/3) + 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))])/a^(2/3) + (2*Log[a^(1/3) + b^(1/3)*(c + d*x)])/a^(2/3) - Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2]/a^(2/3)))/(18*b^(4/3)*d)","A",1
2896,1,26,26,0.014307,"\int \frac{(c e+d e x)^2}{\left(a+b (c+d x)^3\right)^2} \, dx","Integrate[(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,"-1/3*e^2/(b*d*(a + b*(c + d*x)^3))","A",1
2897,1,153,176,0.013491,"\int \frac{c e+d e x}{\left(a+b (c+d x)^3\right)^2} \, dx","Integrate[(c*e + d*e*x)/(a + b*(c + d*x)^3)^2,x]","\frac{e \left(\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{b^{2/3}}-\frac{2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{b^{2/3}}+\frac{2 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} (c+d x)-\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{b^{2/3}}+\frac{6 \sqrt[3]{a} (c+d x)^2}{a+b (c+d x)^3}\right)}{18 a^{4/3} d}","-\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*((6*a^(1/3)*(c + d*x)^2)/(a + b*(c + d*x)^3) + (2*Sqrt[3]*ArcTan[(-a^(1/3) + 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))])/b^(2/3) - (2*Log[a^(1/3) + b^(1/3)*(c + d*x)])/b^(2/3) + Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2]/b^(2/3)))/(18*a^(4/3)*d)","A",1
2898,1,51,68,0.0225983,"\int \frac{1}{(c e+d e x) \left(a+b (c+d x)^3\right)^2} \, dx","Integrate[1/((c*e + d*e*x)*(a + b*(c + d*x)^3)^2),x]","\frac{\frac{a}{a+b (c+d x)^3}-\log \left(a+b (c+d x)^3\right)+3 \log (c+d x)}{3 a^2 d e}","-\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,"(a/(a + b*(c + d*x)^3) + 3*Log[c + d*x] - Log[a + b*(c + d*x)^3])/(3*a^2*d*e)","A",1
2899,1,171,204,0.0863957,"\int \frac{1}{(c e+d e x)^2 \left(a+b (c+d x)^3\right)^2} \, dx","Integrate[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)-\frac{3 \sqrt[3]{a} b (c+d x)^2}{a+b (c+d x)^3}+4 \sqrt[3]{b} \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)-4 \sqrt{3} \sqrt[3]{b} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} (c+d x)-\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)-\frac{9 \sqrt[3]{a}}{c+d x}}{9 a^{7/3} d e^2}","-\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,"((-9*a^(1/3))/(c + d*x) - (3*a^(1/3)*b*(c + d*x)^2)/(a + b*(c + d*x)^3) - 4*Sqrt[3]*b^(1/3)*ArcTan[(-a^(1/3) + 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))] + 4*b^(1/3)*Log[a^(1/3) + b^(1/3)*(c + d*x)] - 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",1
2900,1,169,204,0.0649657,"\int \frac{1}{(c e+d e x)^3 \left(a+b (c+d x)^3\right)^2} \, dx","Integrate[1/((c*e + d*e*x)^3*(a + b*(c + d*x)^3)^2),x]","\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)-\frac{6 a^{2/3} b (c+d x)}{a+b (c+d x)^3}-\frac{9 a^{2/3}}{(c+d x)^2}-10 b^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)-10 \sqrt{3} b^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} (c+d x)-\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{18 a^{8/3} d e^3}","-\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,"((-9*a^(2/3))/(c + d*x)^2 - (6*a^(2/3)*b*(c + d*x))/(a + b*(c + d*x)^3) - 10*Sqrt[3]*b^(2/3)*ArcTan[(-a^(1/3) + 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))] - 10*b^(2/3)*Log[a^(1/3) + b^(1/3)*(c + d*x)] + 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",1
2901,1,63,92,0.0601424,"\int \frac{1}{(c e+d e x)^4 \left(a+b (c+d x)^3\right)^2} \, dx","Integrate[1/((c*e + d*e*x)^4*(a + b*(c + d*x)^3)^2),x]","-\frac{a \left(\frac{b}{a+b (c+d x)^3}+\frac{1}{(c+d x)^3}\right)-2 b \log \left(a+b (c+d x)^3\right)+6 b \log (c+d x)}{3 a^3 d e^4}","-\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{b}{3 a^2 d e^4 \left(a+b (c+d x)^3\right)}-\frac{1}{3 a^2 d e^4 (c+d x)^3}",1,"-1/3*(a*((c + d*x)^(-3) + b/(a + b*(c + d*x)^3)) + 6*b*Log[c + d*x] - 2*b*Log[a + b*(c + d*x)^3])/(a^3*d*e^4)","A",1
2902,1,185,220,0.0157038,"\int \frac{(c e+d e x)^4}{\left(a+b (c+d x)^3\right)^3} \, dx","Integrate[(c*e + d*e*x)^4/(a + b*(c + d*x)^3)^3,x]","\frac{e^4 \left(\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{a^{4/3}}-\frac{2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{a^{4/3}}+\frac{2 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} (c+d x)-\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{a^{4/3}}+\frac{6 b^{2/3} (c+d x)^2}{a \left(a+b (c+d x)^3\right)}-\frac{9 b^{2/3} (c+d x)^2}{\left(a+b (c+d x)^3\right)^2}\right)}{54 b^{5/3} d}","-\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*((-9*b^(2/3)*(c + d*x)^2)/(a + b*(c + d*x)^3)^2 + (6*b^(2/3)*(c + d*x)^2)/(a*(a + b*(c + d*x)^3)) + (2*Sqrt[3]*ArcTan[(-a^(1/3) + 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))])/a^(4/3) - (2*Log[a^(1/3) + b^(1/3)*(c + d*x)])/a^(4/3) + Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2]/a^(4/3)))/(54*b^(5/3)*d)","A",1
2903,1,182,216,0.0193098,"\int \frac{(c e+d e x)^3}{\left(a+b (c+d x)^3\right)^3} \, dx","Integrate[(c*e + d*e*x)^3/(a + b*(c + d*x)^3)^3,x]","\frac{e^3 \left(-\frac{\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{a^{5/3}}+\frac{2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{a^{5/3}}+\frac{2 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} (c+d x)-\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{a^{5/3}}+\frac{3 \sqrt[3]{b} (c+d x)}{a \left(a+b (c+d x)^3\right)}-\frac{9 \sqrt[3]{b} (c+d x)}{\left(a+b (c+d x)^3\right)^2}\right)}{54 b^{4/3} d}","\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*((-9*b^(1/3)*(c + d*x))/(a + b*(c + d*x)^3)^2 + (3*b^(1/3)*(c + d*x))/(a*(a + b*(c + d*x)^3)) + (2*Sqrt[3]*ArcTan[(-a^(1/3) + 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))])/a^(5/3) + (2*Log[a^(1/3) + b^(1/3)*(c + d*x)])/a^(5/3) - Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2]/a^(5/3)))/(54*b^(4/3)*d)","A",1
2904,1,26,26,0.0135276,"\int \frac{(c e+d e x)^2}{\left(a+b (c+d x)^3\right)^3} \, dx","Integrate[(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,"-1/6*e^2/(b*d*(a + b*(c + d*x)^3)^2)","A",1
2905,1,181,207,0.0130187,"\int \frac{c e+d e x}{\left(a+b (c+d x)^3\right)^3} \, dx","Integrate[(c*e + d*e*x)/(a + b*(c + d*x)^3)^3,x]","\frac{e \left(\frac{2 \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} (c+d x)+b^{2/3} (c+d x)^2\right)}{b^{2/3}}+\frac{9 a^{4/3} (c+d x)^2}{\left(a+b (c+d x)^3\right)^2}-\frac{4 \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)}{b^{2/3}}+\frac{4 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} (c+d x)-\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{b^{2/3}}+\frac{12 \sqrt[3]{a} (c+d x)^2}{a+b (c+d x)^3}\right)}{54 a^{7/3} d}","-\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*((9*a^(4/3)*(c + d*x)^2)/(a + b*(c + d*x)^3)^2 + (12*a^(1/3)*(c + d*x)^2)/(a + b*(c + d*x)^3) + (4*Sqrt[3]*ArcTan[(-a^(1/3) + 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))])/b^(2/3) - (4*Log[a^(1/3) + b^(1/3)*(c + d*x)])/b^(2/3) + (2*Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2])/b^(2/3)))/(54*a^(7/3)*d)","A",1
2906,1,66,94,0.0378631,"\int \frac{1}{(c e+d e x) \left(a+b (c+d x)^3\right)^3} \, dx","Integrate[1/((c*e + d*e*x)*(a + b*(c + d*x)^3)^3),x]","\frac{\frac{a \left(2 \left(a+b (c+d x)^3\right)+a\right)}{\left(a+b (c+d x)^3\right)^2}-2 \log \left(a+b (c+d x)^3\right)+6 \log (c+d x)}{6 a^3 d e}","-\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}{3 a^2 d e \left(a+b (c+d x)^3\right)}+\frac{1}{6 a d e \left(a+b (c+d x)^3\right)^2}",1,"((a*(a + 2*(a + b*(c + d*x)^3)))/(a + b*(c + d*x)^3)^2 + 6*Log[c + d*x] - 2*Log[a + b*(c + d*x)^3])/(6*a^3*d*e)","A",1
2907,1,199,237,0.0980257,"\int \frac{1}{(c e+d e x)^2 \left(a+b (c+d x)^3\right)^3} \, dx","Integrate[1/((c*e + d*e*x)^2*(a + b*(c + d*x)^3)^3),x]","\frac{-14 \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)-\frac{9 a^{4/3} b (c+d x)^2}{\left(a+b (c+d x)^3\right)^2}-\frac{30 \sqrt[3]{a} b (c+d x)^2}{a+b (c+d x)^3}+28 \sqrt[3]{b} \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)-28 \sqrt{3} \sqrt[3]{b} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} (c+d x)-\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)-\frac{54 \sqrt[3]{a}}{c+d x}}{54 a^{10/3} d e^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{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{7}{18 a^2 d e^2 (c+d x) \left(a+b (c+d x)^3\right)}+\frac{1}{6 a d e^2 (c+d x) \left(a+b (c+d x)^3\right)^2}",1,"((-54*a^(1/3))/(c + d*x) - (9*a^(4/3)*b*(c + d*x)^2)/(a + b*(c + d*x)^3)^2 - (30*a^(1/3)*b*(c + d*x)^2)/(a + b*(c + d*x)^3) - 28*Sqrt[3]*b^(1/3)*ArcTan[(-a^(1/3) + 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))] + 28*b^(1/3)*Log[a^(1/3) + b^(1/3)*(c + d*x)] - 14*b^(1/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2])/(54*a^(10/3)*d*e^2)","A",1
2908,1,195,237,0.0594224,"\int \frac{1}{(c e+d e x)^3 \left(a+b (c+d x)^3\right)^3} \, dx","Integrate[1/((c*e + d*e*x)^3*(a + b*(c + d*x)^3)^3),x]","\frac{20 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)-\frac{9 a^{5/3} b (c+d x)}{\left(a+b (c+d x)^3\right)^2}-\frac{33 a^{2/3} b (c+d x)}{a+b (c+d x)^3}-\frac{27 a^{2/3}}{(c+d x)^2}-40 b^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} (c+d x)\right)-40 \sqrt{3} b^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} (c+d x)-\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{54 a^{11/3} d e^3}","-\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{10}{9 a^3 d e^3 (c+d x)^2}+\frac{4}{9 a^2 d e^3 (c+d x)^2 \left(a+b (c+d x)^3\right)}+\frac{1}{6 a d e^3 (c+d x)^2 \left(a+b (c+d x)^3\right)^2}",1,"((-27*a^(2/3))/(c + d*x)^2 - (9*a^(5/3)*b*(c + d*x))/(a + b*(c + d*x)^3)^2 - (33*a^(2/3)*b*(c + d*x))/(a + b*(c + d*x)^3) - 40*Sqrt[3]*b^(2/3)*ArcTan[(-a^(1/3) + 2*b^(1/3)*(c + d*x))/(Sqrt[3]*a^(1/3))] - 40*b^(2/3)*Log[a^(1/3) + b^(1/3)*(c + d*x)] + 20*b^(2/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*(c + d*x) + b^(2/3)*(c + d*x)^2])/(54*a^(11/3)*d*e^3)","A",1
2909,1,83,116,0.0560436,"\int \frac{1}{(c e+d e x)^4 \left(a+b (c+d x)^3\right)^3} \, dx","Integrate[1/((c*e + d*e*x)^4*(a + b*(c + d*x)^3)^3),x]","\frac{a \left(-\frac{4 b}{a+b (c+d x)^3}-\frac{a b}{\left(a+b (c+d x)^3\right)^2}-\frac{2}{(c+d x)^3}\right)+6 b \log \left(a+b (c+d x)^3\right)-18 b \log (c+d x)}{6 a^4 d e^4}","-\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{2 b}{3 a^3 d e^4 \left(a+b (c+d x)^3\right)}-\frac{1}{3 a^3 d e^4 (c+d x)^3}-\frac{b}{6 a^2 d e^4 \left(a+b (c+d x)^3\right)^2}",1,"(a*(-2/(c + d*x)^3 - (a*b)/(a + b*(c + d*x)^3)^2 - (4*b)/(a + b*(c + d*x)^3)) - 18*b*Log[c + d*x] + 6*b*Log[a + b*(c + d*x)^3])/(6*a^4*d*e^4)","A",1
2910,1,30,30,0.0193016,"\int (c+d x)^3 \left(a+b (c+d x)^4\right)^p \, dx","Integrate[(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",1
2911,1,80,23,0.0199047,"\int (c+d x)^3 \left(a+b (c+d x)^4\right) \, dx","Integrate[(c + d*x)^3*(a + b*(c + d*x)^4),x]","\frac{1}{8} x \left(4 c^3+6 c^2 d x+4 c d^2 x^2+d^3 x^3\right) \left(2 a+b \left(2 c^4+4 c^3 d x+6 c^2 d^2 x^2+4 c d^3 x^3+d^4 x^4\right)\right)","\frac{\left(a+b (c+d x)^4\right)^2}{8 b d}",1,"(x*(4*c^3 + 6*c^2*d*x + 4*c*d^2*x^2 + d^3*x^3)*(2*a + b*(2*c^4 + 4*c^3*d*x + 6*c^2*d^2*x^2 + 4*c*d^3*x^3 + d^4*x^4)))/8","B",1
2912,1,172,23,0.0404201,"\int (c+d x)^3 \left(a+b (c+d x)^4\right)^2 \, dx","Integrate[(c + d*x)^3*(a + b*(c + d*x)^4)^2,x]","\frac{1}{12} x \left(4 c^3+6 c^2 d x+4 c d^2 x^2+d^3 x^3\right) \left(3 a^2+3 a b \left(2 c^4+4 c^3 d x+6 c^2 d^2 x^2+4 c d^3 x^3+d^4 x^4\right)+b^2 \left(3 c^8+12 c^7 d x+34 c^6 d^2 x^2+60 c^5 d^3 x^3+71 c^4 d^4 x^4+56 c^3 d^5 x^5+28 c^2 d^6 x^6+8 c d^7 x^7+d^8 x^8\right)\right)","\frac{\left(a+b (c+d x)^4\right)^3}{12 b d}",1,"(x*(4*c^3 + 6*c^2*d*x + 4*c*d^2*x^2 + d^3*x^3)*(3*a^2 + 3*a*b*(2*c^4 + 4*c^3*d*x + 6*c^2*d^2*x^2 + 4*c*d^3*x^3 + d^4*x^4) + b^2*(3*c^8 + 12*c^7*d*x + 34*c^6*d^2*x^2 + 60*c^5*d^3*x^3 + 71*c^4*d^4*x^4 + 56*c^3*d^5*x^5 + 28*c^2*d^6*x^6 + 8*c*d^7*x^7 + d^8*x^8)))/12","B",1
2913,1,308,23,0.0749851,"\int (c+d x)^3 \left(a+b (c+d x)^4\right)^3 \, dx","Integrate[(c + d*x)^3*(a + b*(c + d*x)^4)^3,x]","\frac{1}{16} x \left(4 c^3+6 c^2 d x+4 c d^2 x^2+d^3 x^3\right) \left(4 a^3+6 a^2 b \left(2 c^4+4 c^3 d x+6 c^2 d^2 x^2+4 c d^3 x^3+d^4 x^4\right)+4 a b^2 \left(3 c^8+12 c^7 d x+34 c^6 d^2 x^2+60 c^5 d^3 x^3+71 c^4 d^4 x^4+56 c^3 d^5 x^5+28 c^2 d^6 x^6+8 c d^7 x^7+d^8 x^8\right)+b^3 \left(4 c^{12}+24 c^{11} d x+100 c^{10} d^2 x^2+280 c^9 d^3 x^3+566 c^8 d^4 x^4+848 c^7 d^5 x^5+952 c^6 d^6 x^6+800 c^5 d^7 x^7+496 c^4 d^8 x^8+220 c^3 d^9 x^9+66 c^2 d^{10} x^{10}+12 c d^{11} x^{11}+d^{12} x^{12}\right)\right)","\frac{\left(a+b (c+d x)^4\right)^4}{16 b d}",1,"(x*(4*c^3 + 6*c^2*d*x + 4*c*d^2*x^2 + d^3*x^3)*(4*a^3 + 6*a^2*b*(2*c^4 + 4*c^3*d*x + 6*c^2*d^2*x^2 + 4*c*d^3*x^3 + d^4*x^4) + 4*a*b^2*(3*c^8 + 12*c^7*d*x + 34*c^6*d^2*x^2 + 60*c^5*d^3*x^3 + 71*c^4*d^4*x^4 + 56*c^3*d^5*x^5 + 28*c^2*d^6*x^6 + 8*c*d^7*x^7 + d^8*x^8) + b^3*(4*c^12 + 24*c^11*d*x + 100*c^10*d^2*x^2 + 280*c^9*d^3*x^3 + 566*c^8*d^4*x^4 + 848*c^7*d^5*x^5 + 952*c^6*d^6*x^6 + 800*c^5*d^7*x^7 + 496*c^4*d^8*x^8 + 220*c^3*d^9*x^9 + 66*c^2*d^10*x^10 + 12*c*d^11*x^11 + d^12*x^12)))/16","B",1
2914,1,22,22,0.0094172,"\int \frac{(c+d x)^3}{a+b (c+d x)^4} \, dx","Integrate[(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",1
2915,1,23,23,0.0123465,"\int \frac{(c+d x)^3}{\left(a+b (c+d x)^4\right)^2} \, dx","Integrate[(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*1/(b*d*(a + b*(c + d*x)^4))","A",1
2916,1,23,23,0.0126318,"\int \frac{(c+d x)^3}{\left(a+b (c+d x)^4\right)^3} \, dx","Integrate[(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*1/(b*d*(a + b*(c + d*x)^4)^2)","A",1
2917,1,90,111,0.0603971,"\int \frac{1}{\sqrt{a+b (c+d x)^4}} \, dx","Integrate[1/Sqrt[a + b*(c + d*x)^4],x]","-\frac{i \sqrt{\frac{a+b (c+d x)^4}{a}} F\left(\left.i \sinh ^{-1}\left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}} (c+d x)\right)\right|-1\right)}{d \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}} \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,"((-I)*Sqrt[(a + b*(c + d*x)^4)/a]*EllipticF[I*ArcSinh[Sqrt[(I*Sqrt[b])/Sqrt[a]]*(c + d*x)], -1])/(Sqrt[(I*Sqrt[b])/Sqrt[a]]*d*Sqrt[a + b*(c + d*x)^4])","C",1
2918,1,330,154,1.0087482,"\int \frac{x}{\sqrt{a+b (c+d x)^4}} \, dx","Integrate[x/Sqrt[a + b*(c + d*x)^4],x]","\frac{\sqrt[4]{-1} \sqrt{2} \sqrt{-\frac{i \left(\sqrt[4]{-1} \sqrt[4]{a}+\sqrt[4]{b} (c+d x)\right)}{\sqrt[4]{-1} \sqrt[4]{a}-\sqrt[4]{b} (c+d x)}} \left(\sqrt{b} (c+d x)^2+i \sqrt{a}\right) \left(\left(\sqrt[4]{-1} \sqrt[4]{a}-\sqrt[4]{b} c\right) F\left(\left.\sin ^{-1}\left(\sqrt{-\frac{i \left(\sqrt[4]{b} (c+d x)+\sqrt[4]{-1} \sqrt[4]{a}\right)}{\sqrt[4]{-1} \sqrt[4]{a}-\sqrt[4]{b} (c+d x)}}\right)\right|-1\right)-2 \sqrt[4]{-1} \sqrt[4]{a} \Pi \left(-i;\left.\sin ^{-1}\left(\sqrt{-\frac{i \left(\sqrt[4]{b} (c+d x)+\sqrt[4]{-1} \sqrt[4]{a}\right)}{\sqrt[4]{-1} \sqrt[4]{a}-\sqrt[4]{b} (c+d x)}}\right)\right|-1\right)\right)}{\sqrt[4]{a} \sqrt{b} d^2 \sqrt{\frac{\sqrt{b} (c+d x)^2+i \sqrt{a}}{\left(\sqrt[4]{-1} \sqrt[4]{a}-\sqrt[4]{b} (c+d x)\right)^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,"((-1)^(1/4)*Sqrt[2]*Sqrt[((-I)*((-1)^(1/4)*a^(1/4) + b^(1/4)*(c + d*x)))/((-1)^(1/4)*a^(1/4) - b^(1/4)*(c + d*x))]*(I*Sqrt[a] + Sqrt[b]*(c + d*x)^2)*(((-1)^(1/4)*a^(1/4) - b^(1/4)*c)*EllipticF[ArcSin[Sqrt[((-I)*((-1)^(1/4)*a^(1/4) + b^(1/4)*(c + d*x)))/((-1)^(1/4)*a^(1/4) - b^(1/4)*(c + d*x))]], -1] - 2*(-1)^(1/4)*a^(1/4)*EllipticPi[-I, ArcSin[Sqrt[((-I)*((-1)^(1/4)*a^(1/4) + b^(1/4)*(c + d*x)))/((-1)^(1/4)*a^(1/4) - b^(1/4)*(c + d*x))]], -1]))/(a^(1/4)*Sqrt[b]*d^2*Sqrt[(I*Sqrt[a] + Sqrt[b]*(c + d*x)^2)/((-1)^(1/4)*a^(1/4) - b^(1/4)*(c + d*x))^2]*Sqrt[a + b*(c + d*x)^4])","C",1
2919,1,79,78,0.1108532,"\int (d x)^m \sqrt{a+b (c x)^{3/2}} \, dx","Integrate[(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{a+b (c x)^{3/2}}{a}}}","\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[(a + b*(c*x)^(3/2))/a])","A",1
2920,1,112,74,0.2241825,"\int (d x)^m \sqrt{a+b \sqrt{c x}} \, dx","Integrate[(d*x)^m*Sqrt[a + b*Sqrt[c*x]],x]","\frac{4 (d x)^m \left(a+b \sqrt{c x}\right)^{3/2} \left(-\frac{b \sqrt{c x}}{a}\right)^{-2 m} \left(3 \left(a+b \sqrt{c x}\right) \, _2F_1\left(\frac{5}{2},-2 m;\frac{7}{2};\frac{\sqrt{c x} b}{a}+1\right)-5 a \, _2F_1\left(\frac{3}{2},-2 m;\frac{5}{2};\frac{\sqrt{c x} b}{a}+1\right)\right)}{15 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*(d*x)^m*(a + b*Sqrt[c*x])^(3/2)*(-5*a*Hypergeometric2F1[3/2, -2*m, 5/2, 1 + (b*Sqrt[c*x])/a] + 3*(a + b*Sqrt[c*x])*Hypergeometric2F1[5/2, -2*m, 7/2, 1 + (b*Sqrt[c*x])/a]))/(15*b^2*c*(-((b*Sqrt[c*x])/a))^(2*m))","A",1
2921,1,135,76,0.3437459,"\int (d x)^m \sqrt{a+\frac{b}{\sqrt{c x}}} \, dx","Integrate[(d*x)^m*Sqrt[a + b/Sqrt[c*x]],x]","\frac{4 (d x)^m \sqrt{a+\frac{b}{\sqrt{c x}}} \left(a \sqrt{c x}+b\right) \left(-\frac{a \sqrt{c x}}{b}\right)^{\frac{1}{2}-2 m} \left(3 \left(a \sqrt{c x}+b\right) \, _2F_1\left(\frac{5}{2},\frac{1}{2}-2 m;\frac{7}{2};\frac{\sqrt{c x} a}{b}+1\right)-5 b \, _2F_1\left(\frac{3}{2},\frac{1}{2}-2 m;\frac{5}{2};\frac{\sqrt{c x} a}{b}+1\right)\right)}{15 a^2 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*(d*x)^m*(-((a*Sqrt[c*x])/b))^(1/2 - 2*m)*Sqrt[a + b/Sqrt[c*x]]*(b + a*Sqrt[c*x])*(-5*b*Hypergeometric2F1[3/2, 1/2 - 2*m, 5/2, 1 + (a*Sqrt[c*x])/b] + 3*(b + a*Sqrt[c*x])*Hypergeometric2F1[5/2, 1/2 - 2*m, 7/2, 1 + (a*Sqrt[c*x])/b]))/(15*a^2*c)","A",1
2922,1,84,78,0.1627002,"\int (d x)^m \sqrt{a+\frac{b}{(c x)^{3/2}}} \, dx","Integrate[(d*x)^m*Sqrt[a + b/(c*x)^(3/2)],x]","\frac{4 x (d x)^m \sqrt{a+\frac{b}{(c x)^{3/2}}} \, _2F_1\left(-\frac{1}{2},\frac{1}{6} (4 m+1);\frac{1}{6} (4 m+7);-\frac{a (c x)^{3/2}}{b}\right)}{(4 m+1) \sqrt{\frac{a (c x)^{3/2}+b}{b}}}","\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,"(4*x*(d*x)^m*Sqrt[a + b/(c*x)^(3/2)]*Hypergeometric2F1[-1/2, (1 + 4*m)/6, (7 + 4*m)/6, -((a*(c*x)^(3/2))/b)])/((1 + 4*m)*Sqrt[(b + a*(c*x)^(3/2))/b])","A",1
2923,1,70,73,0.1232561,"\int (d x)^m \left(a+b (c x)^n\right)^p \, dx","Integrate[(d*x)^m*(a + b*(c*x)^n)^p,x]","\frac{x (d x)^m \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+1}{n}+1;-\frac{b (c x)^n}{a}\right)}{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,"(x*(d*x)^m*(a + b*(c*x)^n)^p*Hypergeometric2F1[(1 + m)/n, -p, 1 + (1 + m)/n, -((b*(c*x)^n)/a)])/((1 + m)*(1 + (b*(c*x)^n)/a)^p)","A",1
2924,1,61,61,0.0610596,"\int x^2 \left(a+b (c x)^n\right)^p \, dx","Integrate[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;1+\frac{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, 1 + 3/n, -((b*(c*x)^n)/a)])/(3*(1 + (b*(c*x)^n)/a)^p)","A",1
2925,1,61,61,0.0408878,"\int x \left(a+b (c x)^n\right)^p \, dx","Integrate[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;1+\frac{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, 1 + 2/n, -((b*(c*x)^n)/a)])/(2*(1 + (b*(c*x)^n)/a)^p)","A",1
2926,1,52,52,0.0074149,"\int \left(a+b (c x)^n\right)^p \, dx","Integrate[(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",1
2927,1,46,46,0.0424421,"\int \frac{\left(a+b (c x)^n\right)^p}{x} \, dx","Integrate[(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",1
2928,1,59,62,0.0538221,"\int \frac{\left(a+b (c x)^n\right)^p}{x^2} \, dx","Integrate[(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;1-\frac{1}{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^(-1), -((b*(c*x)^n)/a)])/(x*(1 + (b*(c*x)^n)/a)^p))","A",1
2929,1,67,83,0.0289334,"\int \frac{1}{1+\left(x^2\right)^{3/2}} \, dx","Integrate[(1 + (x^2)^(3/2))^(-1),x]","\frac{x \left(-\log \left(x^2-\sqrt{x^2}+1\right)+2 \log \left(\sqrt{x^2}+1\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt{x^2}-1}{\sqrt{3}}\right)\right)}{6 \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*(2*Sqrt[3]*ArcTan[(-1 + 2*Sqrt[x^2])/Sqrt[3]] - Log[1 + x^2 - Sqrt[x^2]] + 2*Log[1 + Sqrt[x^2]]))/(6*Sqrt[x^2])","A",1
2930,1,103,174,0.0885154,"\int x^5 \sqrt{a+b \sqrt{c x^2}} \, dx","Integrate[x^5*Sqrt[a + b*Sqrt[c*x^2]],x]","\frac{2 \left(a+b \sqrt{c x^2}\right)^{3/2} \left(-256 a^5+384 a^4 b \sqrt{c x^2}-480 a^3 b^2 c x^2+560 a^2 b^3 \left(c x^2\right)^{3/2}-630 a b^4 c^2 x^4+693 b^5 \left(c x^2\right)^{5/2}\right)}{9009 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 a^4 \left(a+b \sqrt{c x^2}\right)^{5/2}}{b^6 c^3}-\frac{20 a^3 \left(a+b \sqrt{c x^2}\right)^{7/2}}{7 b^6 c^3}+\frac{20 a^2 \left(a+b \sqrt{c x^2}\right)^{9/2}}{9 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 + b*Sqrt[c*x^2])^(3/2)*(-256*a^5 - 480*a^3*b^2*c*x^2 - 630*a*b^4*c^2*x^4 + 384*a^4*b*Sqrt[c*x^2] + 560*a^2*b^3*(c*x^2)^(3/2) + 693*b^5*(c*x^2)^(5/2)))/(9009*b^6*c^3)","A",1
2931,1,72,116,0.0580545,"\int x^3 \sqrt{a+b \sqrt{c x^2}} \, dx","Integrate[x^3*Sqrt[a + b*Sqrt[c*x^2]],x]","\frac{2 \left(a+b \sqrt{c x^2}\right)^{3/2} \left(-16 a^3+24 a^2 b \sqrt{c x^2}-30 a b^2 c x^2+35 b^3 \left(c x^2\right)^{3/2}\right)}{315 b^4 c^2}","-\frac{2 a^3 \left(a+b \sqrt{c x^2}\right)^{3/2}}{3 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 \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 + b*Sqrt[c*x^2])^(3/2)*(-16*a^3 - 30*a*b^2*c*x^2 + 24*a^2*b*Sqrt[c*x^2] + 35*b^3*(c*x^2)^(3/2)))/(315*b^4*c^2)","A",1
2932,1,43,56,0.0272246,"\int x \sqrt{a+b \sqrt{c x^2}} \, dx","Integrate[x*Sqrt[a + b*Sqrt[c*x^2]],x]","\frac{2 \left(a+b \sqrt{c x^2}\right)^{3/2} \left(3 b \sqrt{c x^2}-2 a\right)}{15 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 + b*Sqrt[c*x^2])^(3/2)*(-2*a + 3*b*Sqrt[c*x^2]))/(15*b^2*c)","A",1
2933,1,51,51,0.0318629,"\int \frac{\sqrt{a+b \sqrt{c x^2}}}{x} \, dx","Integrate[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",1
2934,1,52,97,0.0190534,"\int \frac{\sqrt{a+b \sqrt{c x^2}}}{x^3} \, dx","Integrate[Sqrt[a + b*Sqrt[c*x^2]]/x^3,x]","-\frac{2 b^2 c \left(a+b \sqrt{c x^2}\right)^{3/2} \, _2F_1\left(\frac{3}{2},3;\frac{5}{2};\frac{\sqrt{c x^2} b}{a}+1\right)}{3 a^3}","\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,"(-2*b^2*c*(a + b*Sqrt[c*x^2])^(3/2)*Hypergeometric2F1[3/2, 3, 5/2, 1 + (b*Sqrt[c*x^2])/a])/(3*a^3)","C",1
2935,1,54,171,0.0201424,"\int \frac{\sqrt{a+b \sqrt{c x^2}}}{x^5} \, dx","Integrate[Sqrt[a + b*Sqrt[c*x^2]]/x^5,x]","-\frac{2 b^4 c^2 \left(a+b \sqrt{c x^2}\right)^{3/2} \, _2F_1\left(\frac{3}{2},5;\frac{5}{2};\frac{\sqrt{c x^2} b}{a}+1\right)}{3 a^5}","\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^3 c^2 \sqrt{a+b \sqrt{c x^2}}}{64 a^3 \sqrt{c x^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,"(-2*b^4*c^2*(a + b*Sqrt[c*x^2])^(3/2)*Hypergeometric2F1[3/2, 5, 5/2, 1 + (b*Sqrt[c*x^2])/a])/(3*a^5)","C",1
2936,1,96,191,0.0518971,"\int x^4 \sqrt{a+b \sqrt{c x^2}} \, dx","Integrate[x^4*Sqrt[a + b*Sqrt[c*x^2]],x]","\frac{2 x \left(a+b \sqrt{c x^2}\right)^{3/2} \left(128 a^4-192 a^3 b \sqrt{c x^2}+240 a^2 b^2 c x^2-280 a b^3 \left(c x^2\right)^{3/2}+315 b^4 c^2 x^4\right)}{3465 b^5 c^2 \sqrt{c x^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{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{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{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*x*(a + b*Sqrt[c*x^2])^(3/2)*(128*a^4 + 240*a^2*b^2*c*x^2 + 315*b^4*c^2*x^4 - 192*a^3*b*Sqrt[c*x^2] - 280*a*b^3*(c*x^2)^(3/2)))/(3465*b^5*c^2*Sqrt[c*x^2])","A",1
2937,1,64,113,0.031493,"\int x^2 \sqrt{a+b \sqrt{c x^2}} \, dx","Integrate[x^2*Sqrt[a + b*Sqrt[c*x^2]],x]","\frac{2 x^3 \left(a+b \sqrt{c x^2}\right)^{3/2} \left(8 a^2-12 a b \sqrt{c x^2}+15 b^2 c x^2\right)}{105 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*x^3*(a + b*Sqrt[c*x^2])^(3/2)*(8*a^2 + 15*b^2*c*x^2 - 12*a*b*Sqrt[c*x^2]))/(105*b^3*(c*x^2)^(3/2))","A",1
2938,1,34,34,0.0081531,"\int \sqrt{a+b \sqrt{c x^2}} \, dx","Integrate[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",1
2939,1,87,67,0.0515757,"\int \frac{\sqrt{a+b \sqrt{c x^2}}}{x^2} \, dx","Integrate[Sqrt[a + b*Sqrt[c*x^2]]/x^2,x]","-\frac{b \sqrt{c x^2} \sqrt{\frac{b \sqrt{c x^2}}{a}+1} \tanh ^{-1}\left(\sqrt{\frac{b \sqrt{c x^2}}{a}+1}\right)+a+b \sqrt{c x^2}}{x \sqrt{a+b \sqrt{c x^2}}}","-\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,"-((a + b*Sqrt[c*x^2] + b*Sqrt[c*x^2]*Sqrt[1 + (b*Sqrt[c*x^2])/a]*ArcTanh[Sqrt[1 + (b*Sqrt[c*x^2])/a]])/(x*Sqrt[a + b*Sqrt[c*x^2]]))","A",1
2940,1,63,144,0.0147477,"\int \frac{\sqrt{a+b \sqrt{c x^2}}}{x^4} \, dx","Integrate[Sqrt[a + b*Sqrt[c*x^2]]/x^4,x]","\frac{2 b^3 \left(c x^2\right)^{3/2} \left(a+b \sqrt{c x^2}\right)^{3/2} \, _2F_1\left(\frac{3}{2},4;\frac{5}{2};\frac{\sqrt{c x^2} b}{a}+1\right)}{3 a^4 x^3}","-\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^2 c \sqrt{a+b \sqrt{c x^2}}}{8 a^2 x}-\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,"(2*b^3*(c*x^2)^(3/2)*(a + b*Sqrt[c*x^2])^(3/2)*Hypergeometric2F1[3/2, 4, 5/2, 1 + (b*Sqrt[c*x^2])/a])/(3*a^4*x^3)","C",1
2941,1,63,219,0.014157,"\int \frac{\sqrt{a+b \sqrt{c x^2}}}{x^6} \, dx","Integrate[Sqrt[a + b*Sqrt[c*x^2]]/x^6,x]","\frac{2 b^5 \left(c x^2\right)^{5/2} \left(a+b \sqrt{c x^2}\right)^{3/2} \, _2F_1\left(\frac{3}{2},6;\frac{5}{2};\frac{\sqrt{c x^2} b}{a}+1\right)}{3 a^6 x^5}","-\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{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{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,"(2*b^5*(c*x^2)^(5/2)*(a + b*Sqrt[c*x^2])^(3/2)*Hypergeometric2F1[3/2, 6, 5/2, 1 + (b*Sqrt[c*x^2])/a])/(3*a^6*x^5)","C",1
2942,1,67,113,0.0430634,"\int x^8 \sqrt{a+b \left(c x^2\right)^{3/2}} \, dx","Integrate[x^8*Sqrt[a + b*(c*x^2)^(3/2)],x]","\frac{2 x \left(a+b \left(c x^2\right)^{3/2}\right)^{3/2} \left(8 a^2-12 a b \left(c x^2\right)^{3/2}+15 b^2 c^3 x^6\right)}{315 b^3 c^4 \sqrt{c x^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*x*(a + b*(c*x^2)^(3/2))^(3/2)*(8*a^2 + 15*b^2*c^3*x^6 - 12*a*b*(c*x^2)^(3/2)))/(315*b^3*c^4*Sqrt[c*x^2])","A",1
2943,1,43,56,0.0236479,"\int x^5 \sqrt{a+b \left(c x^2\right)^{3/2}} \, dx","Integrate[x^5*Sqrt[a + b*(c*x^2)^(3/2)],x]","\frac{2 \left(a+b \left(c x^2\right)^{3/2}\right)^{3/2} \left(3 b \left(c x^2\right)^{3/2}-2 a\right)}{45 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 + b*(c*x^2)^(3/2))^(3/2)*(-2*a + 3*b*(c*x^2)^(3/2)))/(45*b^2*c^3)","A",1
2944,1,36,36,0.0112559,"\int x^2 \sqrt{a+b \left(c x^2\right)^{3/2}} \, dx","Integrate[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",1
2945,1,55,55,0.0254776,"\int \frac{\sqrt{a+b \left(c x^2\right)^{3/2}}}{x} \, dx","Integrate[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",1
2946,1,93,71,0.087542,"\int \frac{\sqrt{a+b \left(c x^2\right)^{3/2}}}{x^4} \, dx","Integrate[Sqrt[a + b*(c*x^2)^(3/2)]/x^4,x]","\frac{-b \left(c x^2\right)^{3/2} \sqrt{\frac{b \left(c x^2\right)^{3/2}}{a}+1} \tanh ^{-1}\left(\sqrt{\frac{b \left(c x^2\right)^{3/2}}{a}+1}\right)-a-b \left(c x^2\right)^{3/2}}{3 x^3 \sqrt{a+b \left(c x^2\right)^{3/2}}}","-\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,"(-a - b*(c*x^2)^(3/2) - b*(c*x^2)^(3/2)*Sqrt[1 + (b*(c*x^2)^(3/2))/a]*ArcTanh[Sqrt[1 + (b*(c*x^2)^(3/2))/a]])/(3*x^3*Sqrt[a + b*(c*x^2)^(3/2)])","A",1
2947,1,109,340,0.1116693,"\int x^3 \sqrt{a+b \left(c x^2\right)^{3/2}} \, dx","Integrate[x^3*Sqrt[a + b*(c*x^2)^(3/2)],x]","\frac{2 \sqrt{c x^2} \sqrt{a+b \left(c x^2\right)^{3/2}} \left(a \left(\frac{a+b \left(c x^2\right)^{3/2}}{a}\right)^{3/2}-a \, _2F_1\left(-\frac{1}{2},\frac{1}{3};\frac{4}{3};-\frac{b \left(c x^2\right)^{3/2}}{a}\right)\right)}{11 b c^2 \sqrt{\frac{a+b \left(c x^2\right)^{3/2}}{a}}}","-\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*Sqrt[c*x^2]*Sqrt[a + b*(c*x^2)^(3/2)]*(a*((a + b*(c*x^2)^(3/2))/a)^(3/2) - a*Hypergeometric2F1[-1/2, 1/3, 4/3, -((b*(c*x^2)^(3/2))/a)]))/(11*b*c^2*Sqrt[(a + b*(c*x^2)^(3/2))/a])","C",1
2948,1,64,306,0.0132293,"\int \sqrt{a+b \left(c x^2\right)^{3/2}} \, dx","Integrate[Sqrt[a + b*(c*x^2)^(3/2)],x]","\frac{x \sqrt{a+b \left(c x^2\right)^{3/2}} \, _2F_1\left(-\frac{1}{2},\frac{1}{3};\frac{4}{3};-\frac{b \left(c x^2\right)^{3/2}}{a}\right)}{\sqrt{\frac{b \left(c x^2\right)^{3/2}}{a}+1}}","\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,"(x*Sqrt[a + b*(c*x^2)^(3/2)]*Hypergeometric2F1[-1/2, 1/3, 4/3, -((b*(c*x^2)^(3/2))/a)])/Sqrt[1 + (b*(c*x^2)^(3/2))/a]","C",1
2949,1,69,298,0.019792,"\int \frac{\sqrt{a+b \left(c x^2\right)^{3/2}}}{x^3} \, dx","Integrate[Sqrt[a + b*(c*x^2)^(3/2)]/x^3,x]","-\frac{\sqrt{a+b \left(c x^2\right)^{3/2}} \, _2F_1\left(-\frac{2}{3},-\frac{1}{2};\frac{1}{3};-\frac{b \left(c x^2\right)^{3/2}}{a}\right)}{2 x^2 \sqrt{\frac{b \left(c x^2\right)^{3/2}}{a}+1}}","\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,"-1/2*(Sqrt[a + b*(c*x^2)^(3/2)]*Hypergeometric2F1[-2/3, -1/2, 1/3, -((b*(c*x^2)^(3/2))/a)])/(x^2*Sqrt[1 + (b*(c*x^2)^(3/2))/a])","C",1
2950,1,69,352,0.0169303,"\int \frac{\sqrt{a+b \left(c x^2\right)^{3/2}}}{x^6} \, dx","Integrate[Sqrt[a + b*(c*x^2)^(3/2)]/x^6,x]","-\frac{\sqrt{a+b \left(c x^2\right)^{3/2}} \, _2F_1\left(-\frac{5}{3},-\frac{1}{2};-\frac{2}{3};-\frac{b \left(c x^2\right)^{3/2}}{a}\right)}{5 x^5 \sqrt{\frac{b \left(c x^2\right)^{3/2}}{a}+1}}","-\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,"-1/5*(Sqrt[a + b*(c*x^2)^(3/2)]*Hypergeometric2F1[-5/3, -1/2, -2/3, -((b*(c*x^2)^(3/2))/a)])/(x^5*Sqrt[1 + (b*(c*x^2)^(3/2))/a])","C",1
2951,1,109,709,0.0946812,"\int x^4 \sqrt{a+b \left(c x^2\right)^{3/2}} \, dx","Integrate[x^4*Sqrt[a + b*(c*x^2)^(3/2)],x]","\frac{2 x^5 \sqrt{a+b \left(c x^2\right)^{3/2}} \left(a \left(\frac{a+b \left(c x^2\right)^{3/2}}{a}\right)^{3/2}-a \, _2F_1\left(-\frac{1}{2},\frac{2}{3};\frac{5}{3};-\frac{b \left(c x^2\right)^{3/2}}{a}\right)\right)}{13 b \left(c x^2\right)^{3/2} \sqrt{\frac{a+b \left(c x^2\right)^{3/2}}{a}}}","-\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{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{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)]*(a*((a + b*(c*x^2)^(3/2))/a)^(3/2) - a*Hypergeometric2F1[-1/2, 2/3, 5/3, -((b*(c*x^2)^(3/2))/a)]))/(13*b*(c*x^2)^(3/2)*Sqrt[(a + b*(c*x^2)^(3/2))/a])","C",1
2952,1,69,642,0.0192436,"\int x \sqrt{a+b \left(c x^2\right)^{3/2}} \, dx","Integrate[x*Sqrt[a + b*(c*x^2)^(3/2)],x]","\frac{x^2 \sqrt{a+b \left(c x^2\right)^{3/2}} \, _2F_1\left(-\frac{1}{2},\frac{2}{3};\frac{5}{3};-\frac{b \left(c x^2\right)^{3/2}}{a}\right)}{2 \sqrt{\frac{b \left(c x^2\right)^{3/2}}{a}+1}}","\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,"(x^2*Sqrt[a + b*(c*x^2)^(3/2)]*Hypergeometric2F1[-1/2, 2/3, 5/3, -((b*(c*x^2)^(3/2))/a)])/(2*Sqrt[1 + (b*(c*x^2)^(3/2))/a])","C",1
2953,1,67,661,0.0194752,"\int \frac{\sqrt{a+b \left(c x^2\right)^{3/2}}}{x^2} \, dx","Integrate[Sqrt[a + b*(c*x^2)^(3/2)]/x^2,x]","-\frac{\sqrt{a+b \left(c x^2\right)^{3/2}} \, _2F_1\left(-\frac{1}{2},-\frac{1}{3};\frac{2}{3};-\frac{b \left(c x^2\right)^{3/2}}{a}\right)}{x \sqrt{\frac{b \left(c x^2\right)^{3/2}}{a}+1}}","\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)]*Hypergeometric2F1[-1/2, -1/3, 2/3, -((b*(c*x^2)^(3/2))/a)])/(x*Sqrt[1 + (b*(c*x^2)^(3/2))/a]))","C",1
2954,1,69,681,0.0415108,"\int \frac{\sqrt{a+b \left(c x^2\right)^{3/2}}}{x^5} \, dx","Integrate[Sqrt[a + b*(c*x^2)^(3/2)]/x^5,x]","-\frac{\sqrt{a+b \left(c x^2\right)^{3/2}} \, _2F_1\left(-\frac{4}{3},-\frac{1}{2};-\frac{1}{3};-\frac{b \left(c x^2\right)^{3/2}}{a}\right)}{4 x^4 \sqrt{\frac{b \left(c x^2\right)^{3/2}}{a}+1}}","\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,"-1/4*(Sqrt[a + b*(c*x^2)^(3/2)]*Hypergeometric2F1[-4/3, -1/2, -1/3, -((b*(c*x^2)^(3/2))/a)])/(x^4*Sqrt[1 + (b*(c*x^2)^(3/2))/a])","C",1
2955,0,0,86,0.0810615,"\int (d x)^m \sqrt{a+b \left(c x^2\right)^{3/2}} \, dx","Integrate[(d*x)^m*Sqrt[a + b*(c*x^2)^(3/2)],x]","\int (d x)^m \sqrt{a+b \left(c x^2\right)^{3/2}} \, dx","\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,"Integrate[(d*x)^m*Sqrt[a + b*(c*x^2)^(3/2)], x]","F",-1
2956,1,74,88,0.0811576,"\int (d x)^m \sqrt{a+b \sqrt{c x^2}} \, dx","Integrate[(d*x)^m*Sqrt[a + b*Sqrt[c*x^2]],x]","\frac{x (d x)^m \sqrt{a+b \sqrt{c x^2}} \, _2F_1\left(-\frac{1}{2},m+1;m+2;-\frac{b \sqrt{c x^2}}{a}\right)}{(m+1) \sqrt{\frac{b \sqrt{c x^2}}{a}+1}}","\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,"(x*(d*x)^m*Sqrt[a + b*Sqrt[c*x^2]]*Hypergeometric2F1[-1/2, 1 + m, 2 + m, -((b*Sqrt[c*x^2])/a)])/((1 + m)*Sqrt[1 + (b*Sqrt[c*x^2])/a])","A",1
2957,1,81,87,0.1233212,"\int (d x)^m \sqrt{a+\frac{b}{\sqrt{c x^2}}} \, dx","Integrate[(d*x)^m*Sqrt[a + b/Sqrt[c*x^2]],x]","\frac{2 x (d x)^m \sqrt{a+\frac{b}{\sqrt{c x^2}}} \, _2F_1\left(-\frac{1}{2},m+\frac{1}{2};m+\frac{3}{2};-\frac{a \sqrt{c x^2}}{b}\right)}{(2 m+1) \sqrt{\frac{a \sqrt{c x^2}}{b}+1}}","-\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*x*(d*x)^m*Sqrt[a + b/Sqrt[c*x^2]]*Hypergeometric2F1[-1/2, 1/2 + m, 3/2 + m, -((a*Sqrt[c*x^2])/b)])/((1 + 2*m)*Sqrt[1 + (a*Sqrt[c*x^2])/b])","A",1
2958,0,0,90,0.1616816,"\int (d x)^m \sqrt{a+\frac{b}{\left(c x^2\right)^{3/2}}} \, dx","Integrate[(d*x)^m*Sqrt[a + b/(c*x^2)^(3/2)],x]","\int (d x)^m \sqrt{a+\frac{b}{\left(c x^2\right)^{3/2}}} \, dx","\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,"Integrate[(d*x)^m*Sqrt[a + b/(c*x^2)^(3/2)], x]","F",-1
2959,1,17,17,0.0113135,"\int \frac{1}{1+\left(x^3\right)^{2/3}} \, dx","Integrate[(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",1
2960,1,72,116,0.0976659,"\int x^5 \sqrt{a+b \sqrt{c x^3}} \, dx","Integrate[x^5*Sqrt[a + b*Sqrt[c*x^3]],x]","\frac{4 \left(a+b \sqrt{c x^3}\right)^{3/2} \left(-16 a^3+24 a^2 b \sqrt{c x^3}-30 a b^2 c x^3+35 b^3 \left(c x^3\right)^{3/2}\right)}{945 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 a^2 \left(a+b \sqrt{c x^3}\right)^{5/2}}{5 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 + b*Sqrt[c*x^3])^(3/2)*(-16*a^3 - 30*a*b^2*c*x^3 + 24*a^2*b*Sqrt[c*x^3] + 35*b^3*(c*x^3)^(3/2)))/(945*b^4*c^2)","A",1
2961,1,43,56,0.0355091,"\int x^2 \sqrt{a+b \sqrt{c x^3}} \, dx","Integrate[x^2*Sqrt[a + b*Sqrt[c*x^3]],x]","\frac{4 \left(a+b \sqrt{c x^3}\right)^{3/2} \left(3 b \sqrt{c x^3}-2 a\right)}{45 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 + b*Sqrt[c*x^3])^(3/2)*(-2*a + 3*b*Sqrt[c*x^3]))/(45*b^2*c)","A",1
2962,1,55,55,0.0464772,"\int \frac{\sqrt{a+b \sqrt{c x^3}}}{x} \, dx","Integrate[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",1
2963,0,0,97,0.0478811,"\int \frac{\sqrt{a+b \sqrt{c x^3}}}{x^4} \, dx","Integrate[Sqrt[a + b*Sqrt[c*x^3]]/x^4,x]","\int \frac{\sqrt{a+b \sqrt{c x^3}}}{x^4} \, dx","\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,"Integrate[Sqrt[a + b*Sqrt[c*x^3]]/x^4, x]","F",-1
2964,0,0,400,0.0443115,"\int x \sqrt{a+b \sqrt{c x^3}} \, dx","Integrate[x*Sqrt[a + b*Sqrt[c*x^3]],x]","\int x \sqrt{a+b \sqrt{c x^3}} \, dx","-\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,"Integrate[x*Sqrt[a + b*Sqrt[c*x^3]], x]","F",-1
2965,0,0,355,0.043325,"\int \frac{\sqrt{a+b \sqrt{c x^3}}}{x^2} \, dx","Integrate[Sqrt[a + b*Sqrt[c*x^3]]/x^2,x]","\int \frac{\sqrt{a+b \sqrt{c x^3}}}{x^2} \, dx","\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,"Integrate[Sqrt[a + b*Sqrt[c*x^3]]/x^2, x]","F",-1
2966,0,0,434,0.0442938,"\int \frac{\sqrt{a+b \sqrt{c x^3}}}{x^5} \, dx","Integrate[Sqrt[a + b*Sqrt[c*x^3]]/x^5,x]","\int \frac{\sqrt{a+b \sqrt{c x^3}}}{x^5} \, dx","\frac{21 b^2 c \sqrt{a+b \sqrt{c x^3}}}{160 a^2 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{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,"Integrate[Sqrt[a + b*Sqrt[c*x^3]]/x^5, x]","F",-1
2967,0,0,843,0.057582,"\int x^3 \sqrt{a+b \sqrt{c x^3}} \, dx","Integrate[x^3*Sqrt[a + b*Sqrt[c*x^3]],x]","\int x^3 \sqrt{a+b \sqrt{c x^3}} \, dx","\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,"Integrate[x^3*Sqrt[a + b*Sqrt[c*x^3]], x]","F",-1
2968,0,0,770,0.0127154,"\int \sqrt{a+b \sqrt{c x^3}} \, dx","Integrate[Sqrt[a + b*Sqrt[c*x^3]],x]","\int \sqrt{a+b \sqrt{c x^3}} \, dx","\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,"Integrate[Sqrt[a + b*Sqrt[c*x^3]], x]","F",-1
2969,0,0,810,0.0595758,"\int \frac{\sqrt{a+b \sqrt{c x^3}}}{x^3} \, dx","Integrate[Sqrt[a + b*Sqrt[c*x^3]]/x^3,x]","\int \frac{\sqrt{a+b \sqrt{c x^3}}}{x^3} \, dx","-\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,"Integrate[Sqrt[a + b*Sqrt[c*x^3]]/x^3, x]","F",-1
2970,1,80,116,0.1502513,"\int x^{17} \sqrt{a+b \left(c x^3\right)^{3/2}} \, dx","Integrate[x^17*Sqrt[a + b*(c*x^3)^(3/2)],x]","\frac{4 \left(a+b \left(c x^3\right)^{3/2}\right)^{3/2} \left(-16 a^3+24 a^2 b \left(c x^3\right)^{3/2}-30 a b^2 c^3 x^9+35 b^3 c^3 x^9 \left(c x^3\right)^{3/2}\right)}{2835 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 a^2 \left(a+b \left(c x^3\right)^{3/2}\right)^{5/2}}{15 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 + b*(c*x^3)^(3/2))^(3/2)*(-16*a^3 - 30*a*b^2*c^3*x^9 + 24*a^2*b*(c*x^3)^(3/2) + 35*b^3*c^3*x^9*(c*x^3)^(3/2)))/(2835*b^4*c^6)","A",1
2971,1,43,56,0.0758763,"\int x^8 \sqrt{a+b \left(c x^3\right)^{3/2}} \, dx","Integrate[x^8*Sqrt[a + b*(c*x^3)^(3/2)],x]","\frac{4 \left(a+b \left(c x^3\right)^{3/2}\right)^{3/2} \left(3 b \left(c x^3\right)^{3/2}-2 a\right)}{135 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 + b*(c*x^3)^(3/2))^(3/2)*(-2*a + 3*b*(c*x^3)^(3/2)))/(135*b^2*c^3)","A",1
2972,1,55,55,0.070806,"\int \frac{\sqrt{a+b \left(c x^3\right)^{3/2}}}{x} \, dx","Integrate[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",1
2973,0,0,101,0.0653348,"\int \frac{\sqrt{a+b \left(c x^3\right)^{3/2}}}{x^{10}} \, dx","Integrate[Sqrt[a + b*(c*x^3)^(3/2)]/x^10,x]","\int \frac{\sqrt{a+b \left(c x^3\right)^{3/2}}}{x^{10}} \, dx","\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,"Integrate[Sqrt[a + b*(c*x^3)^(3/2)]/x^10, x]","F",-1
2974,1,69,642,0.0534069,"\int x^2 \sqrt{a+b \left(c x^3\right)^{3/2}} \, dx","Integrate[x^2*Sqrt[a + b*(c*x^3)^(3/2)],x]","\frac{x^3 \sqrt{a+b \left(c x^3\right)^{3/2}} \, _2F_1\left(-\frac{1}{2},\frac{2}{3};\frac{5}{3};-\frac{b \left(c x^3\right)^{3/2}}{a}\right)}{3 \sqrt{\frac{b \left(c x^3\right)^{3/2}}{a}+1}}","\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,"(x^3*Sqrt[a + b*(c*x^3)^(3/2)]*Hypergeometric2F1[-1/2, 2/3, 5/3, -((b*(c*x^3)^(3/2))/a)])/(3*Sqrt[1 + (b*(c*x^3)^(3/2))/a])","C",1
2975,0,0,170,0.0679355,"\int x^9 \sqrt{a+b \left(c x^3\right)^{3/2}} \, dx","Integrate[x^9*Sqrt[a + b*(c*x^3)^(3/2)],x]","\int x^9 \sqrt{a+b \left(c x^3\right)^{3/2}} \, dx","\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,"Integrate[x^9*Sqrt[a + b*(c*x^3)^(3/2)], x]","F",-1
2976,0,0,91,0.0169402,"\int \sqrt{a+b \left(c x^3\right)^{3/2}} \, dx","Integrate[Sqrt[a + b*(c*x^3)^(3/2)],x]","\int \sqrt{a+b \left(c x^3\right)^{3/2}} \, dx","\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,"Integrate[Sqrt[a + b*(c*x^3)^(3/2)], x]","F",-1
2977,0,0,139,0.0560117,"\int \frac{\sqrt{a+b \left(c x^3\right)^{3/2}}}{x^9} \, dx","Integrate[Sqrt[a + b*(c*x^3)^(3/2)]/x^9,x]","\int \frac{\sqrt{a+b \left(c x^3\right)^{3/2}}}{x^9} \, dx","-\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,"Integrate[Sqrt[a + b*(c*x^3)^(3/2)]/x^9, x]","F",-1
2978,0,0,84,0.085082,"\int (d x)^m \sqrt{a+b \left(c x^3\right)^{3/2}} \, dx","Integrate[(d*x)^m*Sqrt[a + b*(c*x^3)^(3/2)],x]","\int (d x)^m \sqrt{a+b \left(c x^3\right)^{3/2}} \, dx","\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,"Integrate[(d*x)^m*Sqrt[a + b*(c*x^3)^(3/2)], x]","F",-1
2979,1,84,84,0.0959128,"\int (d x)^m \sqrt{a+b \sqrt{c x^3}} \, dx","Integrate[(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",1
2980,1,89,84,0.1510367,"\int (d x)^m \sqrt{a+\frac{b}{\sqrt{c x^3}}} \, dx","Integrate[(d*x)^m*Sqrt[a + b/Sqrt[c*x^3]],x]","\frac{4 x (d x)^m \sqrt{a+\frac{b}{\sqrt{c x^3}}} \, _2F_1\left(-\frac{1}{2},\frac{2 m}{3}+\frac{1}{6};\frac{2 m}{3}+\frac{7}{6};-\frac{a \sqrt{c x^3}}{b}\right)}{(4 m+1) \sqrt{\frac{a \sqrt{c x^3}}{b}+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,"(4*x*(d*x)^m*Sqrt[a + b/Sqrt[c*x^3]]*Hypergeometric2F1[-1/2, 1/6 + (2*m)/3, 7/6 + (2*m)/3, -((a*Sqrt[c*x^3])/b)])/((1 + 4*m)*Sqrt[1 + (a*Sqrt[c*x^3])/b])","A",1
2981,0,0,102,0.1888116,"\int (d x)^m \sqrt{a+\frac{b}{\left(c x^3\right)^{3/2}}} \, dx","Integrate[(d*x)^m*Sqrt[a + b/(c*x^3)^(3/2)],x]","\int (d x)^m \sqrt{a+\frac{b}{\left(c x^3\right)^{3/2}}} \, dx","\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,"Integrate[(d*x)^m*Sqrt[a + b/(c*x^3)^(3/2)], x]","F",-1
2982,1,111,169,0.160667,"\int \sqrt{a+b \sqrt{\frac{c}{x}}} x \, dx","Integrate[Sqrt[a + b*Sqrt[c/x]]*x,x]","\frac{\sqrt{a} x \sqrt{a+b \sqrt{\frac{c}{x}}} \left(48 a^3 x+8 a^2 b x \sqrt{\frac{c}{x}}-10 a b^2 c+15 b^3 c \sqrt{\frac{c}{x}}\right)-15 b^4 c^2 \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{\frac{c}{x}}}}{\sqrt{a}}\right)}{96 a^{7/2}}","-\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^3 c^2 \sqrt{a+b \sqrt{\frac{c}{x}}}}{32 a^3 \sqrt{\frac{c}{x}}}-\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,"(Sqrt[a]*Sqrt[a + b*Sqrt[c/x]]*x*(-10*a*b^2*c + 15*b^3*c*Sqrt[c/x] + 48*a^3*x + 8*a^2*b*Sqrt[c/x]*x) - 15*b^4*c^2*ArcTanh[Sqrt[a + b*Sqrt[c/x]]/Sqrt[a]])/(96*a^(7/2))","A",1
2983,1,79,92,0.073641,"\int \sqrt{a+b \sqrt{\frac{c}{x}}} \, dx","Integrate[Sqrt[a + b*Sqrt[c/x]],x]","\frac{\sqrt{a} x \sqrt{a+b \sqrt{\frac{c}{x}}} \left(2 a+b \sqrt{\frac{c}{x}}\right)-b^2 c \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{\frac{c}{x}}}}{\sqrt{a}}\right)}{2 a^{3/2}}","-\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,"(Sqrt[a]*Sqrt[a + b*Sqrt[c/x]]*(2*a + b*Sqrt[c/x])*x - b^2*c*ArcTanh[Sqrt[a + b*Sqrt[c/x]]/Sqrt[a]])/(2*a^(3/2))","A",1
2984,1,51,51,0.0488475,"\int \frac{\sqrt{a+b \sqrt{\frac{c}{x}}}}{x} \, dx","Integrate[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",1
2985,1,43,56,0.0359246,"\int \frac{\sqrt{a+b \sqrt{\frac{c}{x}}}}{x^2} \, dx","Integrate[Sqrt[a + b*Sqrt[c/x]]/x^2,x]","\frac{4 \left(2 a-3 b \sqrt{\frac{c}{x}}\right) \left(a+b \sqrt{\frac{c}{x}}\right)^{3/2}}{15 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*(2*a - 3*b*Sqrt[c/x])*(a + b*Sqrt[c/x])^(3/2))/(15*b^2*c)","A",1
2986,1,75,116,0.0540429,"\int \frac{\sqrt{a+b \sqrt{\frac{c}{x}}}}{x^3} \, dx","Integrate[Sqrt[a + b*Sqrt[c/x]]/x^3,x]","\frac{4 \left(a+b \sqrt{\frac{c}{x}}\right)^{3/2} \left(16 a^3 x-24 a^2 b x \sqrt{\frac{c}{x}}+30 a b^2 c-35 b^3 c \sqrt{\frac{c}{x}}\right)}{315 b^4 c^2 x}","\frac{4 a^3 \left(a+b \sqrt{\frac{c}{x}}\right)^{3/2}}{3 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 \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 + b*Sqrt[c/x])^(3/2)*(30*a*b^2*c - 35*b^3*c*Sqrt[c/x] + 16*a^3*x - 24*a^2*b*Sqrt[c/x]*x))/(315*b^4*c^2*x)","A",1
2987,1,111,174,0.0649794,"\int \frac{\sqrt{a+b \sqrt{\frac{c}{x}}}}{x^4} \, dx","Integrate[Sqrt[a + b*Sqrt[c/x]]/x^4,x]","\frac{4 \left(a+b \sqrt{\frac{c}{x}}\right)^{3/2} \left(256 a^5 x^2-384 a^4 b x^2 \sqrt{\frac{c}{x}}+480 a^3 b^2 c x-560 a^2 b^3 c x \sqrt{\frac{c}{x}}+630 a b^4 c^2-693 b^5 c x \left(\frac{c}{x}\right)^{3/2}\right)}{9009 b^6 c^3 x^2}","\frac{4 a^5 \left(a+b \sqrt{\frac{c}{x}}\right)^{3/2}}{3 b^6 c^3}-\frac{4 a^4 \left(a+b \sqrt{\frac{c}{x}}\right)^{5/2}}{b^6 c^3}+\frac{40 a^3 \left(a+b \sqrt{\frac{c}{x}}\right)^{7/2}}{7 b^6 c^3}-\frac{40 a^2 \left(a+b \sqrt{\frac{c}{x}}\right)^{9/2}}{9 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 + b*Sqrt[c/x])^(3/2)*(630*a*b^4*c^2 + 480*a^3*b^2*c*x - 560*a^2*b^3*c*Sqrt[c/x]*x - 693*b^5*c*(c/x)^(3/2)*x + 256*a^5*x^2 - 384*a^4*b*Sqrt[c/x]*x^2))/(9009*b^6*c^3*x^2)","A",1
2988,1,126,172,0.1615656,"\int \frac{x}{\sqrt{a+b \sqrt{\frac{c}{x}}}} \, dx","Integrate[x/Sqrt[a + b*Sqrt[c/x]],x]","\frac{35 b^4 c^2 \tanh ^{-1}\left(\frac{\sqrt{a}}{\sqrt{a+b \sqrt{\frac{c}{x}}}}\right)}{32 a^{9/2}}+\frac{48 a^4 x^2-8 a^3 b x^2 \sqrt{\frac{c}{x}}+14 a^2 b^2 c x-35 a b^3 c x \sqrt{\frac{c}{x}}-105 b^4 c^2}{96 a^4 \sqrt{a+b \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^3 c^2 \sqrt{a+b \sqrt{\frac{c}{x}}}}{32 a^4 \sqrt{\frac{c}{x}}}+\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,"(-105*b^4*c^2 + 14*a^2*b^2*c*x - 35*a*b^3*c*Sqrt[c/x]*x + 48*a^4*x^2 - 8*a^3*b*Sqrt[c/x]*x^2)/(96*a^4*Sqrt[a + b*Sqrt[c/x]]) + (35*b^4*c^2*ArcTanh[Sqrt[a]/Sqrt[a + b*Sqrt[c/x]]])/(32*a^(9/2))","A",1
2989,1,89,95,0.100617,"\int \frac{1}{\sqrt{a+b \sqrt{\frac{c}{x}}}} \, dx","Integrate[1/Sqrt[a + b*Sqrt[c/x]],x]","\frac{3 b^2 c \tanh ^{-1}\left(\frac{\sqrt{a}}{\sqrt{a+b \sqrt{\frac{c}{x}}}}\right)}{2 a^{5/2}}+\frac{2 a^2 x-a b x \sqrt{\frac{c}{x}}-3 b^2 c}{2 a^2 \sqrt{a+b \sqrt{\frac{c}{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}",1,"(-3*b^2*c + 2*a^2*x - a*b*Sqrt[c/x]*x)/(2*a^2*Sqrt[a + b*Sqrt[c/x]]) + (3*b^2*c*ArcTanh[Sqrt[a]/Sqrt[a + b*Sqrt[c/x]]])/(2*a^(5/2))","A",1
2990,1,31,31,0.0458323,"\int \frac{1}{\sqrt{a+b \sqrt{\frac{c}{x}}} x} \, dx","Integrate[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",1
2991,1,42,54,0.0360845,"\int \frac{1}{\sqrt{a+b \sqrt{\frac{c}{x}}} x^2} \, dx","Integrate[1/(Sqrt[a + b*Sqrt[c/x]]*x^2),x]","-\frac{4 \left(b \sqrt{\frac{c}{x}}-2 a\right) \sqrt{a+b \sqrt{\frac{c}{x}}}}{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*(-2*a + b*Sqrt[c/x])*Sqrt[a + b*Sqrt[c/x]])/(3*b^2*c)","A",1
2992,1,75,112,0.0775615,"\int \frac{1}{\sqrt{a+b \sqrt{\frac{c}{x}}} x^3} \, dx","Integrate[1/(Sqrt[a + b*Sqrt[c/x]]*x^3),x]","\frac{4 \sqrt{a+b \sqrt{\frac{c}{x}}} \left(16 a^3 x-8 a^2 b x \sqrt{\frac{c}{x}}+6 a b^2 c-5 b^3 c \sqrt{\frac{c}{x}}\right)}{35 b^4 c^2 x}","\frac{4 a^3 \sqrt{a+b \sqrt{\frac{c}{x}}}}{b^4 c^2}-\frac{4 a^2 \left(a+b \sqrt{\frac{c}{x}}\right)^{3/2}}{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*Sqrt[a + b*Sqrt[c/x]]*(6*a*b^2*c - 5*b^3*c*Sqrt[c/x] + 16*a^3*x - 8*a^2*b*Sqrt[c/x]*x))/(35*b^4*c^2*x)","A",1
2993,1,111,172,0.0919137,"\int \frac{1}{\sqrt{a+b \sqrt{\frac{c}{x}}} x^4} \, dx","Integrate[1/(Sqrt[a + b*Sqrt[c/x]]*x^4),x]","\frac{4 \sqrt{a+b \sqrt{\frac{c}{x}}} \left(256 a^5 x^2-128 a^4 b x^2 \sqrt{\frac{c}{x}}+96 a^3 b^2 c x-80 a^2 b^3 c x \sqrt{\frac{c}{x}}+70 a b^4 c^2-63 b^5 c x \left(\frac{c}{x}\right)^{3/2}\right)}{693 b^6 c^3 x^2}","\frac{4 a^5 \sqrt{a+b \sqrt{\frac{c}{x}}}}{b^6 c^3}-\frac{20 a^4 \left(a+b \sqrt{\frac{c}{x}}\right)^{3/2}}{3 b^6 c^3}+\frac{8 a^3 \left(a+b \sqrt{\frac{c}{x}}\right)^{5/2}}{b^6 c^3}-\frac{40 a^2 \left(a+b \sqrt{\frac{c}{x}}\right)^{7/2}}{7 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*Sqrt[a + b*Sqrt[c/x]]*(70*a*b^4*c^2 + 96*a^3*b^2*c*x - 80*a^2*b^3*c*Sqrt[c/x]*x - 63*b^5*c*(c/x)^(3/2)*x + 256*a^5*x^2 - 128*a^4*b*Sqrt[c/x]*x^2))/(693*b^6*c^3*x^2)","A",1
2994,1,70,58,0.1433679,"\int \frac{1}{\sqrt{1+\sqrt{\frac{1}{x}}}} \, dx","Integrate[1/Sqrt[1 + Sqrt[x^(-1)]],x]","\frac{1}{4} \left(2 \left(2-3 \sqrt{\frac{1}{x}}\right) \sqrt{\sqrt{\frac{1}{x}}+1} x-3 \log \left(1-\frac{1}{\sqrt{\sqrt{\frac{1}{x}}+1}}\right)+3 \log \left(\frac{1}{\sqrt{\sqrt{\frac{1}{x}}+1}}+1\right)\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,"(2*(2 - 3*Sqrt[x^(-1)])*Sqrt[1 + Sqrt[x^(-1)]]*x - 3*Log[1 - 1/Sqrt[1 + Sqrt[x^(-1)]]] + 3*Log[1 + 1/Sqrt[1 + Sqrt[x^(-1)]]])/4","A",1
2995,0,0,102,0.1514213,"\int \sqrt{a+b \left(\frac{c}{x}\right)^{3/2}} (d x)^m \, dx","Integrate[Sqrt[a + b*(c/x)^(3/2)]*(d*x)^m,x]","\int \sqrt{a+b \left(\frac{c}{x}\right)^{3/2}} (d x)^m \, dx","\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,"Integrate[Sqrt[a + b*(c/x)^(3/2)]*(d*x)^m, x]","F",-1
2996,1,78,60,0.0967935,"\int \sqrt{a+b \sqrt{\frac{c}{x}}} (d x)^m \, dx","Integrate[Sqrt[a + b*Sqrt[c/x]]*(d*x)^m,x]","\frac{x (d x)^m \sqrt{a+b \sqrt{\frac{c}{x}}} \, _2F_1\left(-\frac{1}{2},-2 (m+1);-2 m-1;-\frac{b \sqrt{\frac{c}{x}}}{a}\right)}{(m+1) \sqrt{\frac{b \sqrt{\frac{c}{x}}}{a}+1}}","\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,"(Sqrt[a + b*Sqrt[c/x]]*x*(d*x)^m*Hypergeometric2F1[-1/2, -2*(1 + m), -1 - 2*m, -((b*Sqrt[c/x])/a)])/((1 + m)*Sqrt[1 + (b*Sqrt[c/x])/a])","A",1
2997,1,85,78,0.1175766,"\int \sqrt{a+\frac{b}{\sqrt{\frac{c}{x}}}} (d x)^m \, dx","Integrate[Sqrt[a + b/Sqrt[c/x]]*(d*x)^m,x]","\frac{4 x (d x)^m \sqrt{a+\frac{b}{\sqrt{\frac{c}{x}}}} \, _2F_1\left(-\frac{1}{2},-2 m-\frac{5}{2};-2 m-\frac{3}{2};-\frac{a \sqrt{\frac{c}{x}}}{b}\right)}{(4 m+5) \sqrt{\frac{a \sqrt{\frac{c}{x}}}{b}+1}}","-\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*Sqrt[a + b/Sqrt[c/x]]*x*(d*x)^m*Hypergeometric2F1[-1/2, -5/2 - 2*m, -3/2 - 2*m, -((a*Sqrt[c/x])/b)])/((5 + 4*m)*Sqrt[1 + (a*Sqrt[c/x])/b])","A",1
2998,0,0,102,0.2224416,"\int \sqrt{a+\frac{b}{\left(\frac{c}{x}\right)^{3/2}}} (d x)^m \, dx","Integrate[Sqrt[a + b/(c/x)^(3/2)]*(d*x)^m,x]","\int \sqrt{a+\frac{b}{\left(\frac{c}{x}\right)^{3/2}}} (d x)^m \, dx","\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,"Integrate[Sqrt[a + b/(c/x)^(3/2)]*(d*x)^m, x]","F",-1
2999,0,0,102,0.2473591,"\int \frac{(d x)^m}{\sqrt{a+b \left(\frac{c}{x}\right)^{3/2}}} \, dx","Integrate[(d*x)^m/Sqrt[a + b*(c/x)^(3/2)],x]","\int \frac{(d x)^m}{\sqrt{a+b \left(\frac{c}{x}\right)^{3/2}}} \, dx","\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,"Integrate[(d*x)^m/Sqrt[a + b*(c/x)^(3/2)], x]","F",-1
3000,1,96,58,0.2483942,"\int \frac{(d x)^m}{\sqrt{a+b \sqrt{\frac{c}{x}}}} \, dx","Integrate[(d*x)^m/Sqrt[a + b*Sqrt[c/x]],x]","\frac{4 b^2 c (d x)^m \left(1-\frac{a}{a+b \sqrt{\frac{c}{x}}}\right)^{2 m} \, _2F_1\left(2 m+\frac{5}{2},2 m+3;2 m+\frac{7}{2};\frac{a}{a+b \sqrt{\frac{c}{x}}}\right)}{(4 m+5) \left(a+b \sqrt{\frac{c}{x}}\right)^{5/2}}","\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*(1 - a/(a + b*Sqrt[c/x]))^(2*m)*(d*x)^m*Hypergeometric2F1[5/2 + 2*m, 3 + 2*m, 7/2 + 2*m, a/(a + b*Sqrt[c/x])])/((5 + 4*m)*(a + b*Sqrt[c/x])^(5/2))","A",1
3001,1,116,76,0.4348694,"\int \frac{(d x)^m}{\sqrt{a+\frac{b}{\sqrt{\frac{c}{x}}}}} \, dx","Integrate[(d*x)^m/Sqrt[a + b/Sqrt[c/x]],x]","\frac{a^2 c (d x)^m \left(\frac{a \sqrt{\frac{c}{x}}}{a \sqrt{\frac{c}{x}}+b}\right)^{2 m-\frac{1}{2}} \, _2F_1\left(2 m+2,2 m+\frac{5}{2};2 m+3;\frac{b}{\sqrt{\frac{c}{x}} a+b}\right)}{(m+1) \sqrt{a+\frac{b}{\sqrt{\frac{c}{x}}}} \left(a \sqrt{\frac{c}{x}}+b\right)^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,"(a^2*c*((a*Sqrt[c/x])/(b + a*Sqrt[c/x]))^(-1/2 + 2*m)*(d*x)^m*Hypergeometric2F1[2 + 2*m, 5/2 + 2*m, 3 + 2*m, b/(b + a*Sqrt[c/x])])/((1 + m)*Sqrt[a + b/Sqrt[c/x]]*(b + a*Sqrt[c/x])^2)","A",1
3002,0,0,102,0.2911215,"\int \frac{(d x)^m}{\sqrt{a+\frac{b}{\left(\frac{c}{x}\right)^{3/2}}}} \, dx","Integrate[(d*x)^m/Sqrt[a + b/(c/x)^(3/2)],x]","\int \frac{(d x)^m}{\sqrt{a+\frac{b}{\left(\frac{c}{x}\right)^{3/2}}}} \, dx","\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,"Integrate[(d*x)^m/Sqrt[a + b/(c/x)^(3/2)], x]","F",-1
3003,1,19,19,0.0058694,"\int \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right) \, dx","Integrate[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",1
3004,1,38,34,0.01975,"\int \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^2 \, dx","Integrate[(a + b*(c*x^n)^n^(-1))^2,x]","a^2 x+a b x \left(c x^n\right)^{\frac{1}{n}}+\frac{1}{3} b^2 x \left(c x^n\right)^{2/n}","\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,"a^2*x + a*b*x*(c*x^n)^n^(-1) + (b^2*x*(c*x^n)^(2/n))/3","A",1
3005,1,60,34,0.0365395,"\int \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^3 \, dx","Integrate[(a + b*(c*x^n)^n^(-1))^3,x]","a^3 x+\frac{3}{2} a^2 b x \left(c x^n\right)^{\frac{1}{n}}+a b^2 x \left(c x^n\right)^{2/n}+\frac{1}{4} b^3 x \left(c x^n\right)^{3/n}","\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,"a^3*x + (3*a^2*b*x*(c*x^n)^n^(-1))/2 + a*b^2*x*(c*x^n)^(2/n) + (b^3*x*(c*x^n)^(3/n))/4","A",1
3006,1,87,101,0.0632105,"\int \frac{x^3}{a+b \left(c x^n\right)^{\frac{1}{n}}} \, dx","Integrate[x^3/(a + b*(c*x^n)^n^(-1)),x]","\frac{x^4 \left(c x^n\right)^{-4/n} \left(b \left(c x^n\right)^{\frac{1}{n}} \left(6 a^2-3 a b \left(c x^n\right)^{\frac{1}{n}}+2 b^2 \left(c x^n\right)^{2/n}\right)-6 a^3 \log \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)\right)}{6 b^4}","-\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^2 x^4 \left(c x^n\right)^{-3/n}}{b^3}-\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,"(x^4*(b*(c*x^n)^n^(-1)*(6*a^2 - 3*a*b*(c*x^n)^n^(-1) + 2*b^2*(c*x^n)^(2/n)) - 6*a^3*Log[a + b*(c*x^n)^n^(-1)]))/(6*b^4*(c*x^n)^(4/n))","A",1
3007,1,67,77,0.0435985,"\int \frac{x^2}{a+b \left(c x^n\right)^{\frac{1}{n}}} \, dx","Integrate[x^2/(a + b*(c*x^n)^n^(-1)),x]","\frac{x^3 \left(c x^n\right)^{-3/n} \left(2 a^2 \log \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)+b \left(c x^n\right)^{\frac{1}{n}} \left(b \left(c x^n\right)^{\frac{1}{n}}-2 a\right)\right)}{2 b^3}","\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,"(x^3*(b*(c*x^n)^n^(-1)*(-2*a + b*(c*x^n)^n^(-1)) + 2*a^2*Log[a + b*(c*x^n)^n^(-1)]))/(2*b^3*(c*x^n)^(3/n))","A",1
3008,1,49,53,0.0182525,"\int \frac{x}{a+b \left(c x^n\right)^{\frac{1}{n}}} \, dx","Integrate[x/(a + b*(c*x^n)^n^(-1)),x]","x^2 \left(c x^n\right)^{-2/n} \left(\frac{\left(c x^n\right)^{\frac{1}{n}}}{b}-\frac{a \log \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)}{b^2}\right)","\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*((c*x^n)^n^(-1)/b - (a*Log[a + b*(c*x^n)^n^(-1)])/b^2))/(c*x^n)^(2/n)","A",1
3009,1,30,30,0.004086,"\int \frac{1}{a+b \left(c x^n\right)^{\frac{1}{n}}} \, dx","Integrate[(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",1
3010,1,23,26,0.010145,"\int \frac{1}{x \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)} \, dx","Integrate[1/(x*(a + b*(c*x^n)^n^(-1))),x]","\frac{\log (x)-\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] - Log[a + b*(c*x^n)^n^(-1)])/a","A",1
3011,1,49,60,0.024887,"\int \frac{1}{x^2 \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)} \, dx","Integrate[1/(x^2*(a + b*(c*x^n)^n^(-1))),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+b \log (x) \left(c x^n\right)^{\frac{1}{n}}}{a^2 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,"-((a + b*(c*x^n)^n^(-1)*Log[x] - b*(c*x^n)^n^(-1)*Log[a + b*(c*x^n)^n^(-1)])/(a^2*x))","A",1
3012,1,75,87,0.0517355,"\int \frac{1}{x^3 \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)} \, dx","Integrate[1/(x^3*(a + b*(c*x^n)^n^(-1))),x]","-\frac{a^2+2 b^2 \left(c x^n\right)^{2/n} \log \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)-2 a b \left(c x^n\right)^{\frac{1}{n}}-2 b^2 \log (x) \left(c x^n\right)^{2/n}}{2 a^3 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^2 - 2*a*b*(c*x^n)^n^(-1) - 2*b^2*(c*x^n)^(2/n)*Log[x] + 2*b^2*(c*x^n)^(2/n)*Log[a + b*(c*x^n)^n^(-1)])/(a^3*x^2)","A",1
3013,1,89,114,0.0801954,"\int \frac{x^3}{\left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^2} \, dx","Integrate[x^3/(a + b*(c*x^n)^n^(-1))^2,x]","\frac{x^4 \left(c x^n\right)^{-4/n} \left(\frac{2 a^3}{a+b \left(c x^n\right)^{\frac{1}{n}}}+6 a^2 \log \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)-4 a b \left(c x^n\right)^{\frac{1}{n}}+b^2 \left(c x^n\right)^{2/n}\right)}{2 b^4}","\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,"(x^4*(-4*a*b*(c*x^n)^n^(-1) + b^2*(c*x^n)^(2/n) + (2*a^3)/(a + b*(c*x^n)^n^(-1)) + 6*a^2*Log[a + b*(c*x^n)^n^(-1)]))/(2*b^4*(c*x^n)^(4/n))","A",1
3014,1,67,90,0.0655582,"\int \frac{x^2}{\left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^2} \, dx","Integrate[x^2/(a + b*(c*x^n)^n^(-1))^2,x]","\frac{x^3 \left(c x^n\right)^{-3/n} \left(-\frac{a^2}{a+b \left(c x^n\right)^{\frac{1}{n}}}-2 a \log \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)+b \left(c x^n\right)^{\frac{1}{n}}\right)}{b^3}","-\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*(c*x^n)^n^(-1) - a^2/(a + b*(c*x^n)^n^(-1)) - 2*a*Log[a + b*(c*x^n)^n^(-1)]))/(b^3*(c*x^n)^(3/n))","A",1
3015,1,50,67,0.0357374,"\int \frac{x}{\left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^2} \, dx","Integrate[x/(a + b*(c*x^n)^n^(-1))^2,x]","\frac{x^2 \left(c x^n\right)^{-2/n} \left(\frac{a}{a+b \left(c x^n\right)^{\frac{1}{n}}}+\log \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)\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,"(x^2*(a/(a + b*(c*x^n)^n^(-1)) + Log[a + b*(c*x^n)^n^(-1)]))/(b^2*(c*x^n)^(2/n))","A",1
3016,1,33,20,0.0184939,"\int \frac{1}{\left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^2} \, dx","Integrate[(a + b*(c*x^n)^n^(-1))^(-2),x]","-\frac{x \left(c x^n\right)^{-1/n}}{a b+b^2 \left(c x^n\right)^{\frac{1}{n}}}","\frac{x}{a^2+a b \left(c x^n\right)^{\frac{1}{n}}}",1,"-(x/((c*x^n)^n^(-1)*(a*b + b^2*(c*x^n)^n^(-1))))","A",1
3017,1,40,45,0.0392673,"\int \frac{1}{x \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^2} \, dx","Integrate[1/(x*(a + b*(c*x^n)^n^(-1))^2),x]","\frac{\frac{a}{a+b \left(c x^n\right)^{\frac{1}{n}}}-\log \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)+\log (x)}{a^2}","-\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,"(a/(a + b*(c*x^n)^n^(-1)) + Log[x] - Log[a + b*(c*x^n)^n^(-1)])/a^2","A",1
3018,1,71,94,0.13115,"\int \frac{1}{x^2 \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^2} \, dx","Integrate[1/(x^2*(a + b*(c*x^n)^n^(-1))^2),x]","-\frac{\left(c x^n\right)^{\frac{1}{n}} \left(a \left(\frac{b}{a+b \left(c x^n\right)^{\frac{1}{n}}}+\left(c x^n\right)^{-1/n}\right)-2 b \log \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)+2 b \log (x)\right)}{a^3 x}","-\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{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{1}{a^2 x}",1,"-(((c*x^n)^n^(-1)*(a*((c*x^n)^(-n^(-1)) + b/(a + b*(c*x^n)^n^(-1))) + 2*b*Log[x] - 2*b*Log[a + b*(c*x^n)^n^(-1)]))/(a^3*x))","A",1
3019,1,99,125,0.2121179,"\int \frac{1}{x^3 \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^2} \, dx","Integrate[1/(x^3*(a + b*(c*x^n)^n^(-1))^2),x]","\frac{\left(c x^n\right)^{2/n} \left(a \left(\frac{2 b^2}{a+b \left(c x^n\right)^{\frac{1}{n}}}-a \left(c x^n\right)^{-2/n}+4 b \left(c x^n\right)^{-1/n}\right)-6 b^2 \log \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)+6 b^2 \log (x)\right)}{2 a^4 x^2}","\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{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{2 b \left(c x^n\right)^{\frac{1}{n}}}{a^3 x^2}-\frac{1}{2 a^2 x^2}",1,"((c*x^n)^(2/n)*(a*(-(a/(c*x^n)^(2/n)) + (4*b)/(c*x^n)^n^(-1) + (2*b^2)/(a + b*(c*x^n)^n^(-1))) + 6*b^2*Log[x] - 6*b^2*Log[a + b*(c*x^n)^n^(-1)]))/(2*a^4*x^2)","A",1
3020,1,34,34,0.015306,"\int \frac{1}{\left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^3} \, dx","Integrate[(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,"-1/2*x/(b*(c*x^n)^n^(-1)*(a + b*(c*x^n)^n^(-1))^2)","A",1
3021,1,35,48,0.0210959,"\int \frac{x}{\left(1+\left(x^n\right)^{\frac{1}{n}}\right)^2} \, dx","Integrate[x/(1 + (x^n)^n^(-1))^2,x]","x^2 \left(x^n\right)^{-2/n} \left(\frac{1}{\left(x^n\right)^{\frac{1}{n}}+1}+\log \left(\left(x^n\right)^{\frac{1}{n}}+1\right)\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*((1 + (x^n)^n^(-1))^(-1) + Log[1 + (x^n)^n^(-1)]))/(x^n)^(2/n)","A",1
3022,1,113,171,0.1310626,"\int x^3 \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^p \, dx","Integrate[x^3*(a + b*(c*x^n)^n^(-1))^p,x]","\frac{x^4 \left(c x^n\right)^{-4/n} \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^{p+1} \left(-\frac{a^3}{p+1}+\frac{3 a^2 \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)}{p+2}-\frac{3 a \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^2}{p+3}+\frac{\left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^3}{p+4}\right)}{b^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,"(x^4*(a + b*(c*x^n)^n^(-1))^(1 + p)*(-(a^3/(1 + p)) + (3*a^2*(a + b*(c*x^n)^n^(-1)))/(2 + p) - (3*a*(a + b*(c*x^n)^n^(-1))^2)/(3 + p) + (a + b*(c*x^n)^n^(-1))^3/(4 + p)))/(b^4*(c*x^n)^(4/n))","A",1
3023,1,95,126,0.0527296,"\int x^2 \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^p \, dx","Integrate[x^2*(a + b*(c*x^n)^n^(-1))^p,x]","\frac{x^3 \left(c x^n\right)^{-3/n} \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^{p+1} \left(2 a^2-2 a b (p+1) \left(c x^n\right)^{\frac{1}{n}}+b^2 \left(p^2+3 p+2\right) \left(c x^n\right)^{2/n}\right)}{b^3 (p+1) (p+2) (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,"(x^3*(a + b*(c*x^n)^n^(-1))^(1 + p)*(2*a^2 - 2*a*b*(1 + p)*(c*x^n)^n^(-1) + b^2*(2 + 3*p + p^2)*(c*x^n)^(2/n)))/(b^3*(1 + p)*(2 + p)*(3 + p)*(c*x^n)^(3/n))","A",1
3024,1,63,83,0.0300597,"\int x \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^p \, dx","Integrate[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+1} \left(b (p+1) \left(c x^n\right)^{\frac{1}{n}}-a\right)}{b^2 (p+1) (p+2)}","\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,"(x^2*(a + b*(c*x^n)^n^(-1))^(1 + p)*(-a + b*(1 + p)*(c*x^n)^n^(-1)))/(b^2*(1 + p)*(2 + p)*(c*x^n)^(2/n))","A",1
3025,1,64,38,0.1473426,"\int \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^p \, dx","Integrate[(a + b*(c*x^n)^n^(-1))^p,x]","\frac{x \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^p \left(\frac{a \left(c x^n\right)^{-1/n} \left(1-\left(\frac{b \left(c x^n\right)^{\frac{1}{n}}}{a}+1\right)^{-p}\right)}{b}+1\right)}{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))^p*(1 + (a*(1 - (1 + (b*(c*x^n)^n^(-1))/a)^(-p)))/(b*(c*x^n)^n^(-1))))/(1 + p)","A",1
3026,1,51,51,0.017217,"\int \frac{\left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^p}{x} \, dx","Integrate[(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",1
3027,1,63,63,0.0118468,"\int \frac{\left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^p}{x^2} \, dx","Integrate[(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",1
3028,1,62,62,0.0422209,"\int \left(a+b \left(c x^n\right)^{2/n}\right)^3 \, dx","Integrate[(a + b*(c*x^n)^(2/n))^3,x]","a^3 x+a^2 b x \left(c x^n\right)^{2/n}+\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^3 x+a^2 b x \left(c x^n\right)^{2/n}+\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",1
3029,1,43,43,0.0155828,"\int \left(a+b \left(c x^n\right)^{2/n}\right)^2 \, dx","Integrate[(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",1
3030,1,21,21,0.002388,"\int \left(a+b \left(c x^n\right)^{2/n}\right) \, dx","Integrate[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",1
3031,1,44,44,0.009766,"\int \frac{1}{a+b \left(c x^n\right)^{2/n}} \, dx","Integrate[(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",1
3032,1,73,73,0.0642231,"\int \frac{1}{\left(a+b \left(c x^n\right)^{2/n}\right)^2} \, dx","Integrate[(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",1
3033,1,91,98,0.1368134,"\int \frac{1}{\left(a+b \left(c x^n\right)^{2/n}\right)^3} \, dx","Integrate[(a + b*(c*x^n)^(2/n))^(-3),x]","\frac{x \left(\frac{\sqrt{a} \left(5 a+3 b \left(c x^n\right)^{2/n}\right)}{\left(a+b \left(c x^n\right)^{2/n}\right)^2}+\frac{3 \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{b}}\right)}{8 a^{5/2}}","\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{3 x}{8 a^2 \left(a+b \left(c x^n\right)^{2/n}\right)}+\frac{x}{4 a \left(a+b \left(c x^n\right)^{2/n}\right)^2}",1,"(x*((Sqrt[a]*(5*a + 3*b*(c*x^n)^(2/n)))/(a + b*(c*x^n)^(2/n))^2 + (3*ArcTan[(Sqrt[b]*(c*x^n)^n^(-1))/Sqrt[a]])/(Sqrt[b]*(c*x^n)^n^(-1))))/(8*a^(5/2))","A",1
3034,1,22,22,0.0101787,"\int \frac{1}{1+4 \sqrt{x^4}} \, dx","Integrate[(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",1
3035,1,22,22,0.004541,"\int \frac{1}{1-4 \sqrt{x^4}} \, dx","Integrate[(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",1
3036,1,22,22,0.0168361,"\int \frac{1}{1+4 \sqrt[3]{x^6}} \, dx","Integrate[(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",1
3037,1,22,22,0.0187051,"\int \frac{1}{1-4 \sqrt[3]{x^6}} \, dx","Integrate[(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",1
3038,1,34,34,0.0088148,"\int \frac{1}{1+4 \left(x^{2 n}\right)^{\frac{1}{n}}} \, dx","Integrate[(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",1
3039,1,34,34,0.0049879,"\int \frac{1}{1-4 \left(x^{2 n}\right)^{\frac{1}{n}}} \, dx","Integrate[(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",1
3040,1,65,65,0.0235189,"\int \left(a+b \left(c x^n\right)^{3/n}\right)^3 \, dx","Integrate[(a + b*(c*x^n)^(3/n))^3,x]","a^3 x+\frac{3}{4} a^2 b x \left(c x^n\right)^{3/n}+\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}","a^3 x+\frac{3}{4} a^2 b x \left(c x^n\right)^{3/n}+\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",1
3041,1,43,43,0.0140918,"\int \left(a+b \left(c x^n\right)^{3/n}\right)^2 \, dx","Integrate[(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",1
3042,1,21,21,0.0020025,"\int \left(a+b \left(c x^n\right)^{3/n}\right) \, dx","Integrate[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",1
3043,1,133,183,0.0904439,"\int \frac{1}{a+b \left(c x^n\right)^{3/n}} \, dx","Integrate[(a + b*(c*x^n)^(3/n))^(-1),x]","-\frac{x \left(c x^n\right)^{-1/n} \left(\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)-2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} \left(c x^n\right)^{\frac{1}{n}}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} \left(c x^n\right)^{\frac{1}{n}}}{\sqrt[3]{a}}}{\sqrt{3}}\right)\right)}{6 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,"-1/6*(x*(2*Sqrt[3]*ArcTan[(1 - (2*b^(1/3)*(c*x^n)^n^(-1))/a^(1/3))/Sqrt[3]] - 2*Log[a^(1/3) + b^(1/3)*(c*x^n)^n^(-1)] + Log[a^(2/3) - a^(1/3)*b^(1/3)*(c*x^n)^n^(-1) + b^(2/3)*(c*x^n)^(2/n)]))/(a^(2/3)*b^(1/3)*(c*x^n)^n^(-1))","A",1
3044,1,158,210,0.3359578,"\int \frac{1}{\left(a+b \left(c x^n\right)^{3/n}\right)^2} \, dx","Integrate[(a + b*(c*x^n)^(3/n))^(-2),x]","\frac{x \left(\frac{1}{a+b \left(c x^n\right)^{3/n}}-\frac{\left(c x^n\right)^{-1/n} \left(\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)-2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} \left(c x^n\right)^{\frac{1}{n}}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} \left(c x^n\right)^{\frac{1}{n}}}{\sqrt[3]{a}}}{\sqrt{3}}\right)\right)}{3 a^{2/3} \sqrt[3]{b}}\right)}{3 a}","-\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*((a + b*(c*x^n)^(3/n))^(-1) - (2*Sqrt[3]*ArcTan[(1 - (2*b^(1/3)*(c*x^n)^n^(-1))/a^(1/3))/Sqrt[3]] - 2*Log[a^(1/3) + b^(1/3)*(c*x^n)^n^(-1)] + Log[a^(2/3) - a^(1/3)*b^(1/3)*(c*x^n)^n^(-1) + b^(2/3)*(c*x^n)^(2/n)])/(3*a^(2/3)*b^(1/3)*(c*x^n)^n^(-1))))/(3*a)","A",1
3045,1,215,235,0.2257212,"\int \frac{1}{\left(a+b \left(c x^n\right)^{3/n}\right)^3} \, dx","Integrate[(a + b*(c*x^n)^(3/n))^(-3),x]","\frac{x \left(-\frac{5 \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)}{\sqrt[3]{b}}+\frac{15 a^{2/3}}{a+b \left(c x^n\right)^{3/n}}+\frac{9 a^{5/3}}{\left(a+b \left(c x^n\right)^{3/n}\right)^2}+\frac{10 \left(c x^n\right)^{-1/n} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \left(c x^n\right)^{\frac{1}{n}}\right)}{\sqrt[3]{b}}-\frac{10 \sqrt{3} \left(c x^n\right)^{-1/n} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} \left(c x^n\right)^{\frac{1}{n}}}{\sqrt[3]{a}}}{\sqrt{3}}\right)}{\sqrt[3]{b}}\right)}{54 a^{8/3}}","-\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 \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{5 x}{18 a^2 \left(a+b \left(c x^n\right)^{3/n}\right)}+\frac{x}{6 a \left(a+b \left(c x^n\right)^{3/n}\right)^2}",1,"(x*((9*a^(5/3))/(a + b*(c*x^n)^(3/n))^2 + (15*a^(2/3))/(a + b*(c*x^n)^(3/n)) - (10*Sqrt[3]*ArcTan[(1 - (2*b^(1/3)*(c*x^n)^n^(-1))/a^(1/3))/Sqrt[3]])/(b^(1/3)*(c*x^n)^n^(-1)) + (10*Log[a^(1/3) + b^(1/3)*(c*x^n)^n^(-1)])/(b^(1/3)*(c*x^n)^n^(-1)) - (5*Log[a^(2/3) - a^(1/3)*b^(1/3)*(c*x^n)^n^(-1) + b^(2/3)*(c*x^n)^(2/n)])/(b^(1/3)*(c*x^n)^n^(-1))))/(54*a^(8/3))","A",1
3046,1,82,86,0.2292383,"\int (d x)^m \left(a+b \left(c x^q\right)^n\right)^p \, dx","Integrate[(d*x)^m*(a + b*(c*x^q)^n)^p,x]","\frac{x (d x)^m \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)}{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,"(x*(d*x)^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)])/((1 + m)*(1 + (b*(c*x^q)^n)/a)^p)","A",1
3047,1,73,73,0.1008956,"\int x^2 \left(a+b \left(c x^q\right)^n\right)^p \, dx","Integrate[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",1
3048,1,73,73,0.0856744,"\int x \left(a+b \left(c x^q\right)^n\right)^p \, dx","Integrate[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",1
3049,1,66,66,0.0716967,"\int \left(a+b \left(c x^q\right)^n\right)^p \, dx","Integrate[(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",1
3050,1,53,53,0.0591372,"\int \frac{\left(a+b \left(c x^q\right)^n\right)^p}{x} \, dx","Integrate[(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",1
3051,1,71,71,0.1081205,"\int \frac{\left(a+b \left(c x^q\right)^n\right)^p}{x^2} \, dx","Integrate[(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",1
3052,0,0,230,0.1827439,"\int \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}} x^m \, dx","Integrate[Sqrt[a + b*Sqrt[d/x] + c/x]*x^m,x]","\int \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}} x^m \, dx","\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,"Integrate[Sqrt[a + b*Sqrt[d/x] + c/x]*x^m, x]","F",-1
3053,0,0,333,0.2142274,"\int \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}} x^2 \, dx","Integrate[Sqrt[a + b*Sqrt[d/x] + c/x]*x^2,x]","\int \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}} x^2 \, dx","\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{\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{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{x^3 \left(a+b \sqrt{\frac{d}{x}}+\frac{c}{x}\right)^{3/2}}{3 a}",1,"Integrate[Sqrt[a + b*Sqrt[d/x] + c/x]*x^2, x]","F",-1
3054,0,0,209,0.3301405,"\int \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}} x \, dx","Integrate[Sqrt[a + b*Sqrt[d/x] + c/x]*x,x]","\int \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}} x \, dx","-\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{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{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,"Integrate[Sqrt[a + b*Sqrt[d/x] + c/x]*x, x]","F",-1
3055,0,0,113,0.1720482,"\int \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}} \, dx","Integrate[Sqrt[a + b*Sqrt[d/x] + c/x],x]","\int \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}} \, dx","\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,"Integrate[Sqrt[a + b*Sqrt[d/x] + c/x], x]","F",-1
3056,0,0,145,0.1478184,"\int \frac{\sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{x} \, dx","Integrate[Sqrt[a + b*Sqrt[d/x] + c/x]/x,x]","\int \frac{\sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{x} \, dx","-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,"Integrate[Sqrt[a + b*Sqrt[d/x] + c/x]/x, x]","F",-1
3057,0,0,155,0.1342239,"\int \frac{\sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{x^2} \, dx","Integrate[Sqrt[a + b*Sqrt[d/x] + c/x]/x^2,x]","\int \frac{\sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{x^2} \, dx","\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,"Integrate[Sqrt[a + b*Sqrt[d/x] + c/x]/x^2, x]","F",-1
3058,0,0,233,0.1324478,"\int \frac{\sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{x^3} \, dx","Integrate[Sqrt[a + b*Sqrt[d/x] + c/x]/x^3,x]","\int \frac{\sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{x^3} \, dx","-\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{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{\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{2 \left(a+b \sqrt{\frac{d}{x}}+\frac{c}{x}\right)^{3/2}}{5 c x}",1,"Integrate[Sqrt[a + b*Sqrt[d/x] + c/x]/x^3, x]","F",-1
3059,0,0,371,0.1411493,"\int \frac{\sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{x^4} \, dx","Integrate[Sqrt[a + b*Sqrt[d/x] + c/x]/x^4,x]","\int \frac{\sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{x^4} \, dx","\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{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{\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{\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,"Integrate[Sqrt[a + b*Sqrt[d/x] + c/x]/x^4, x]","F",-1
3060,0,0,230,0.2565427,"\int \frac{x^m}{\sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}} \, dx","Integrate[x^m/Sqrt[a + b*Sqrt[d/x] + c/x],x]","\int \frac{x^m}{\sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}} \, dx","\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,"Integrate[x^m/Sqrt[a + b*Sqrt[d/x] + c/x], x]","F",-1
3061,0,0,386,0.4144585,"\int \frac{x^2}{\sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}} \, dx","Integrate[x^2/Sqrt[a + b*Sqrt[d/x] + c/x],x]","\int \frac{x^2}{\sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}} \, dx","\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{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(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\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{x^3 \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{3 a}",1,"Integrate[x^2/Sqrt[a + b*Sqrt[d/x] + c/x], x]","F",-1
3062,0,0,248,0.3293245,"\int \frac{x}{\sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}} \, dx","Integrate[x/Sqrt[a + b*Sqrt[d/x] + c/x],x]","\int \frac{x}{\sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}} \, dx","\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{\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{x^2 \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{2 a}",1,"Integrate[x/Sqrt[a + b*Sqrt[d/x] + c/x], x]","F",-1
3063,0,0,135,0.3779091,"\int \frac{1}{\sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}} \, dx","Integrate[1/Sqrt[a + b*Sqrt[d/x] + c/x],x]","\int \frac{1}{\sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}} \, dx","-\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,"Integrate[1/Sqrt[a + b*Sqrt[d/x] + c/x], x]","F",-1
3064,1,54,54,0.3852291,"\int \frac{1}{\sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}} x} \, dx","Integrate[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",1
3065,0,0,93,0.199558,"\int \frac{1}{\sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}} x^2} \, dx","Integrate[1/(Sqrt[a + b*Sqrt[d/x] + c/x]*x^2),x]","\int \frac{1}{\sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}} x^2} \, dx","\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,"Integrate[1/(Sqrt[a + b*Sqrt[d/x] + c/x]*x^2), x]","F",-1
3066,0,0,165,0.2008831,"\int \frac{1}{\sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}} x^3} \, dx","Integrate[1/(Sqrt[a + b*Sqrt[d/x] + c/x]*x^3),x]","\int \frac{1}{\sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}} x^3} \, dx","-\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{\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{2 \sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}}}{3 c x}",1,"Integrate[1/(Sqrt[a + b*Sqrt[d/x] + c/x]*x^3), x]","F",-1
3067,0,0,289,0.2095165,"\int \frac{1}{\sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}} x^4} \, dx","Integrate[1/(Sqrt[a + b*Sqrt[d/x] + c/x]*x^4),x]","\int \frac{1}{\sqrt{a+b \sqrt{\frac{d}{x}}+\frac{c}{x}} x^4} \, dx","\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(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{\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,"Integrate[1/(Sqrt[a + b*Sqrt[d/x] + c/x]*x^4), x]","F",-1
3068,1,26,26,0.018131,"\int \sqrt{\sqrt{\frac{1}{x}}+\frac{1}{x}} \, dx","Integrate[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",1
3069,1,75,75,0.0826023,"\int \sqrt{2+\sqrt{\frac{1}{x}}+\frac{1}{x}} \, dx","Integrate[Sqrt[2 + Sqrt[x^(-1)] + x^(-1)],x]","\frac{1}{16} \left(4 \left(\sqrt{\frac{1}{x}}+4\right) \sqrt{\sqrt{\frac{1}{x}}+\frac{1}{x}+2} x+7 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{x}}+4}{2 \sqrt{2} \sqrt{\sqrt{\frac{1}{x}}+\frac{1}{x}+2}}\right)\right)","\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*(4 + Sqrt[x^(-1)])*Sqrt[2 + Sqrt[x^(-1)] + x^(-1)]*x + 7*Sqrt[2]*ArcTanh[(4 + Sqrt[x^(-1)])/(2*Sqrt[2]*Sqrt[2 + Sqrt[x^(-1)] + x^(-1)])])/16","A",1
3070,1,61,79,0.0535853,"\int \left(c x^n\right)^{\frac{1}{n}} \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^p \, dx","Integrate[(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+1} \left(b (p+1) \left(c x^n\right)^{\frac{1}{n}}-a\right)}{b^2 (p+1) (p+2)}","\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,"(x*(a + b*(c*x^n)^n^(-1))^(1 + p)*(-a + b*(1 + p)*(c*x^n)^n^(-1)))/(b^2*(1 + p)*(2 + p)*(c*x^n)^n^(-1))","A",1
3071,1,48,70,0.0386637,"\int \left(c x^n\right)^{\frac{1}{n}} \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^3 \, dx","Integrate[(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-4 b \left(c x^n\right)^{\frac{1}{n}}\right) \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^4}{20 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,"-1/20*(x*(a - 4*b*(c*x^n)^n^(-1))*(a + b*(c*x^n)^n^(-1))^4)/(b^2*(c*x^n)^n^(-1))","A",1
3072,1,49,55,0.0202215,"\int \left(c x^n\right)^{\frac{1}{n}} \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^2 \, dx","Integrate[(c*x^n)^n^(-1)*(a + b*(c*x^n)^n^(-1))^2,x]","\frac{1}{12} x \left(c x^n\right)^{\frac{1}{n}} \left(6 a^2+8 a b \left(c x^n\right)^{\frac{1}{n}}+3 b^2 \left(c x^n\right)^{2/n}\right)","\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,"(x*(c*x^n)^n^(-1)*(6*a^2 + 8*a*b*(c*x^n)^n^(-1) + 3*b^2*(c*x^n)^(2/n)))/12","A",1
3073,1,30,33,0.0124408,"\int \left(c x^n\right)^{\frac{1}{n}} \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right) \, dx","Integrate[(c*x^n)^n^(-1)*(a + b*(c*x^n)^n^(-1)),x]","\frac{1}{6} x \left(c x^n\right)^{\frac{1}{n}} \left(3 a+2 b \left(c x^n\right)^{\frac{1}{n}}\right)","\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,"(x*(c*x^n)^n^(-1)*(3*a + 2*b*(c*x^n)^n^(-1)))/6","A",1
3074,1,35,38,0.0317437,"\int \frac{\left(c x^n\right)^{\frac{1}{n}}}{a+b \left(c x^n\right)^{\frac{1}{n}}} \, dx","Integrate[(c*x^n)^n^(-1)/(a + b*(c*x^n)^n^(-1)),x]","\frac{x \left(b-a \left(c x^n\right)^{-1/n} \log \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)\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*Log[a + b*(c*x^n)^n^(-1)])/(c*x^n)^n^(-1)))/b^2","A",1
3075,1,48,63,0.0367436,"\int \frac{\left(c x^n\right)^{\frac{1}{n}}}{\left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^2} \, dx","Integrate[(c*x^n)^n^(-1)/(a + b*(c*x^n)^n^(-1))^2,x]","\frac{x \left(c x^n\right)^{-1/n} \left(\frac{a}{a+b \left(c x^n\right)^{\frac{1}{n}}}+\log \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)\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,"(x*(a/(a + b*(c*x^n)^n^(-1)) + Log[a + b*(c*x^n)^n^(-1)]))/(b^2*(c*x^n)^n^(-1))","A",1
3076,1,32,32,0.0086394,"\int \frac{\left(c x^n\right)^{\frac{1}{n}}}{\left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^3} \, dx","Integrate[(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",1
3077,1,48,70,0.0452701,"\int \frac{\left(c x^n\right)^{\frac{1}{n}}}{\left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^4} \, dx","Integrate[(c*x^n)^n^(-1)/(a + b*(c*x^n)^n^(-1))^4,x]","-\frac{x \left(c x^n\right)^{-1/n} \left(a+3 b \left(c x^n\right)^{\frac{1}{n}}\right)}{6 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}}{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,"-1/6*(x*(a + 3*b*(c*x^n)^n^(-1)))/(b^2*(c*x^n)^n^(-1)*(a + b*(c*x^n)^n^(-1))^3)","A",1
3078,1,48,70,0.0336635,"\int \frac{\left(c x^n\right)^{\frac{1}{n}}}{\left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^5} \, dx","Integrate[(c*x^n)^n^(-1)/(a + b*(c*x^n)^n^(-1))^5,x]","-\frac{x \left(c x^n\right)^{-1/n} \left(a+4 b \left(c x^n\right)^{\frac{1}{n}}\right)}{12 b^2 \left(a+b \left(c x^n\right)^{\frac{1}{n}}\right)^4}","\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,"-1/12*(x*(a + 4*b*(c*x^n)^n^(-1)))/(b^2*(c*x^n)^n^(-1)*(a + b*(c*x^n)^n^(-1))^4)","A",1