1,1,17,0,0.0048247,"\int x^4 \left(a+b x^2\right) \, dx","Int[x^4*(a + b*x^2),x]","\frac{a x^5}{5}+\frac{b x^7}{7}","\frac{a x^5}{5}+\frac{b x^7}{7}",1,"(a*x^5)/5 + (b*x^7)/7","A",2,1,11,0.09091,1,"{14}"
2,1,17,0,0.0046979,"\int x^3 \left(a+b x^2\right) \, dx","Int[x^3*(a + b*x^2),x]","\frac{a x^4}{4}+\frac{b x^6}{6}","\frac{a x^4}{4}+\frac{b x^6}{6}",1,"(a*x^4)/4 + (b*x^6)/6","A",2,1,11,0.09091,1,"{14}"
3,1,17,0,0.0048836,"\int x^2 \left(a+b x^2\right) \, dx","Int[x^2*(a + b*x^2),x]","\frac{a x^3}{3}+\frac{b x^5}{5}","\frac{a x^3}{3}+\frac{b x^5}{5}",1,"(a*x^3)/3 + (b*x^5)/5","A",2,1,11,0.09091,1,"{14}"
4,1,17,0,0.0050435,"\int x \left(a+b x^2\right) \, dx","Int[x*(a + b*x^2),x]","\frac{a x^2}{2}+\frac{b x^4}{4}","\frac{a x^2}{2}+\frac{b x^4}{4}",1,"(a*x^2)/2 + (b*x^4)/4","A",2,1,9,0.1111,1,"{14}"
5,1,12,0,0.0022155,"\int \left(a+b x^2\right) \, dx","Int[a + b*x^2,x]","a x+\frac{b x^3}{3}","a x+\frac{b x^3}{3}",1,"a*x + (b*x^3)/3","A",1,0,7,0,1,"{}"
6,1,13,0,0.0038555,"\int \frac{a+b x^2}{x} \, dx","Int[(a + b*x^2)/x,x]","a \log (x)+\frac{b x^2}{2}","a \log (x)+\frac{b x^2}{2}",1,"(b*x^2)/2 + a*Log[x]","A",2,1,11,0.09091,1,"{14}"
7,1,10,0,0.0041099,"\int \frac{a+b x^2}{x^2} \, dx","Int[(a + b*x^2)/x^2,x]","b x-\frac{a}{x}","b x-\frac{a}{x}",1,"-(a/x) + b*x","A",2,1,11,0.09091,1,"{14}"
8,1,13,0,0.0044884,"\int \frac{a+b x^2}{x^3} \, dx","Int[(a + b*x^2)/x^3,x]","b \log (x)-\frac{a}{2 x^2}","b \log (x)-\frac{a}{2 x^2}",1,"-a/(2*x^2) + b*Log[x]","A",2,1,11,0.09091,1,"{14}"
9,1,15,0,0.0047591,"\int \frac{a+b x^2}{x^4} \, dx","Int[(a + b*x^2)/x^4,x]","-\frac{a}{3 x^3}-\frac{b}{x}","-\frac{a}{3 x^3}-\frac{b}{x}",1,"-a/(3*x^3) - b/x","A",2,1,11,0.09091,1,"{14}"
10,1,17,0,0.0046325,"\int \frac{a+b x^2}{x^5} \, dx","Int[(a + b*x^2)/x^5,x]","-\frac{a}{4 x^4}-\frac{b}{2 x^2}","-\frac{a}{4 x^4}-\frac{b}{2 x^2}",1,"-a/(4*x^4) - b/(2*x^2)","A",2,1,11,0.09091,1,"{14}"
11,1,17,0,0.0045444,"\int \frac{a+b x^2}{x^6} \, dx","Int[(a + b*x^2)/x^6,x]","-\frac{a}{5 x^5}-\frac{b}{3 x^3}","-\frac{a}{5 x^5}-\frac{b}{3 x^3}",1,"-a/(5*x^5) - b/(3*x^3)","A",2,1,11,0.09091,1,"{14}"
12,1,17,0,0.0047639,"\int \frac{a+b x^2}{x^7} \, dx","Int[(a + b*x^2)/x^7,x]","-\frac{a}{6 x^6}-\frac{b}{4 x^4}","-\frac{a}{6 x^6}-\frac{b}{4 x^4}",1,"-a/(6*x^6) - b/(4*x^4)","A",2,1,11,0.09091,1,"{14}"
13,1,30,0,0.0175574,"\int x^5 \left(a+b x^2\right)^2 \, dx","Int[x^5*(a + b*x^2)^2,x]","\frac{a^2 x^6}{6}+\frac{1}{4} a b x^8+\frac{b^2 x^{10}}{10}","\frac{a^2 x^6}{6}+\frac{1}{4} a b x^8+\frac{b^2 x^{10}}{10}",1,"(a^2*x^6)/6 + (a*b*x^8)/4 + (b^2*x^10)/10","A",3,2,13,0.1538,1,"{266, 43}"
14,1,30,0,0.0106896,"\int x^4 \left(a+b x^2\right)^2 \, dx","Int[x^4*(a + b*x^2)^2,x]","\frac{a^2 x^5}{5}+\frac{2}{7} a b x^7+\frac{b^2 x^9}{9}","\frac{a^2 x^5}{5}+\frac{2}{7} a b x^7+\frac{b^2 x^9}{9}",1,"(a^2*x^5)/5 + (2*a*b*x^7)/7 + (b^2*x^9)/9","A",2,1,13,0.07692,1,"{270}"
15,1,30,0,0.0177522,"\int x^3 \left(a+b x^2\right)^2 \, dx","Int[x^3*(a + b*x^2)^2,x]","\frac{a^2 x^4}{4}+\frac{1}{3} a b x^6+\frac{b^2 x^8}{8}","\frac{a^2 x^4}{4}+\frac{1}{3} a b x^6+\frac{b^2 x^8}{8}",1,"(a^2*x^4)/4 + (a*b*x^6)/3 + (b^2*x^8)/8","A",3,2,13,0.1538,1,"{266, 43}"
16,1,30,0,0.0095821,"\int x^2 \left(a+b x^2\right)^2 \, dx","Int[x^2*(a + b*x^2)^2,x]","\frac{a^2 x^3}{3}+\frac{2}{5} a b x^5+\frac{b^2 x^7}{7}","\frac{a^2 x^3}{3}+\frac{2}{5} a b x^5+\frac{b^2 x^7}{7}",1,"(a^2*x^3)/3 + (2*a*b*x^5)/5 + (b^2*x^7)/7","A",2,1,13,0.07692,1,"{270}"
17,1,16,0,0.0022917,"\int x \left(a+b x^2\right)^2 \, dx","Int[x*(a + b*x^2)^2,x]","\frac{\left(a+b x^2\right)^3}{6 b}","\frac{\left(a+b x^2\right)^3}{6 b}",1,"(a + b*x^2)^3/(6*b)","A",1,1,11,0.09091,1,"{261}"
18,1,25,0,0.0072177,"\int \left(a+b x^2\right)^2 \, dx","Int[(a + b*x^2)^2,x]","a^2 x+\frac{2}{3} a b x^3+\frac{b^2 x^5}{5}","a^2 x+\frac{2}{3} a b x^3+\frac{b^2 x^5}{5}",1,"a^2*x + (2*a*b*x^3)/3 + (b^2*x^5)/5","A",2,1,9,0.1111,1,"{194}"
19,1,23,0,0.0127247,"\int \frac{\left(a+b x^2\right)^2}{x} \, dx","Int[(a + b*x^2)^2/x,x]","a^2 \log (x)+a b x^2+\frac{b^2 x^4}{4}","a^2 \log (x)+a b x^2+\frac{b^2 x^4}{4}",1,"a*b*x^2 + (b^2*x^4)/4 + a^2*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
20,1,24,0,0.009647,"\int \frac{\left(a+b x^2\right)^2}{x^2} \, dx","Int[(a + b*x^2)^2/x^2,x]","-\frac{a^2}{x}+2 a b x+\frac{b^2 x^3}{3}","-\frac{a^2}{x}+2 a b x+\frac{b^2 x^3}{3}",1,"-(a^2/x) + 2*a*b*x + (b^2*x^3)/3","A",2,1,13,0.07692,1,"{270}"
21,1,27,0,0.0135157,"\int \frac{\left(a+b x^2\right)^2}{x^3} \, dx","Int[(a + b*x^2)^2/x^3,x]","-\frac{a^2}{2 x^2}+2 a b \log (x)+\frac{b^2 x^2}{2}","-\frac{a^2}{2 x^2}+2 a b \log (x)+\frac{b^2 x^2}{2}",1,"-a^2/(2*x^2) + (b^2*x^2)/2 + 2*a*b*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
22,1,23,0,0.0090147,"\int \frac{\left(a+b x^2\right)^2}{x^4} \, dx","Int[(a + b*x^2)^2/x^4,x]","-\frac{a^2}{3 x^3}-\frac{2 a b}{x}+b^2 x","-\frac{a^2}{3 x^3}-\frac{2 a b}{x}+b^2 x",1,"-a^2/(3*x^3) - (2*a*b)/x + b^2*x","A",2,1,13,0.07692,1,"{270}"
23,1,24,0,0.01285,"\int \frac{\left(a+b x^2\right)^2}{x^5} \, dx","Int[(a + b*x^2)^2/x^5,x]","-\frac{a^2}{4 x^4}-\frac{a b}{x^2}+b^2 \log (x)","-\frac{a^2}{4 x^4}-\frac{a b}{x^2}+b^2 \log (x)",1,"-a^2/(4*x^4) - (a*b)/x^2 + b^2*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
24,1,28,0,0.0102216,"\int \frac{\left(a+b x^2\right)^2}{x^6} \, dx","Int[(a + b*x^2)^2/x^6,x]","-\frac{a^2}{5 x^5}-\frac{2 a b}{3 x^3}-\frac{b^2}{x}","-\frac{a^2}{5 x^5}-\frac{2 a b}{3 x^3}-\frac{b^2}{x}",1,"-a^2/(5*x^5) - (2*a*b)/(3*x^3) - b^2/x","A",2,1,13,0.07692,1,"{270}"
25,1,19,0,0.0034544,"\int \frac{\left(a+b x^2\right)^2}{x^7} \, dx","Int[(a + b*x^2)^2/x^7,x]","-\frac{\left(a+b x^2\right)^3}{6 a x^6}","-\frac{\left(a+b x^2\right)^3}{6 a x^6}",1,"-(a + b*x^2)^3/(6*a*x^6)","A",1,1,13,0.07692,1,"{264}"
26,1,30,0,0.0104559,"\int \frac{\left(a+b x^2\right)^2}{x^8} \, dx","Int[(a + b*x^2)^2/x^8,x]","-\frac{a^2}{7 x^7}-\frac{2 a b}{5 x^5}-\frac{b^2}{3 x^3}","-\frac{a^2}{7 x^7}-\frac{2 a b}{5 x^5}-\frac{b^2}{3 x^3}",1,"-a^2/(7*x^7) - (2*a*b)/(5*x^5) - b^2/(3*x^3)","A",2,1,13,0.07692,1,"{270}"
27,1,30,0,0.014229,"\int \frac{\left(a+b x^2\right)^2}{x^9} \, dx","Int[(a + b*x^2)^2/x^9,x]","-\frac{a^2}{8 x^8}-\frac{a b}{3 x^6}-\frac{b^2}{4 x^4}","-\frac{a^2}{8 x^8}-\frac{a b}{3 x^6}-\frac{b^2}{4 x^4}",1,"-a^2/(8*x^8) - (a*b)/(3*x^6) - b^2/(4*x^4)","A",3,2,13,0.1538,1,"{266, 43}"
28,1,30,0,0.0099824,"\int \frac{\left(a+b x^2\right)^2}{x^{10}} \, dx","Int[(a + b*x^2)^2/x^10,x]","-\frac{a^2}{9 x^9}-\frac{2 a b}{7 x^7}-\frac{b^2}{5 x^5}","-\frac{a^2}{9 x^9}-\frac{2 a b}{7 x^7}-\frac{b^2}{5 x^5}",1,"-a^2/(9*x^9) - (2*a*b)/(7*x^7) - b^2/(5*x^5)","A",2,1,13,0.07692,1,"{270}"
29,1,43,0,0.027875,"\int x^9 \left(a+b x^2\right)^3 \, dx","Int[x^9*(a + b*x^2)^3,x]","\frac{1}{4} a^2 b x^{12}+\frac{a^3 x^{10}}{10}+\frac{3}{14} a b^2 x^{14}+\frac{b^3 x^{16}}{16}","\frac{1}{4} a^2 b x^{12}+\frac{a^3 x^{10}}{10}+\frac{3}{14} a b^2 x^{14}+\frac{b^3 x^{16}}{16}",1,"(a^3*x^10)/10 + (a^2*b*x^12)/4 + (3*a*b^2*x^14)/14 + (b^3*x^16)/16","A",3,2,13,0.1538,1,"{266, 43}"
30,1,43,0,0.0268245,"\int x^7 \left(a+b x^2\right)^3 \, dx","Int[x^7*(a + b*x^2)^3,x]","\frac{3}{10} a^2 b x^{10}+\frac{a^3 x^8}{8}+\frac{1}{4} a b^2 x^{12}+\frac{b^3 x^{14}}{14}","\frac{3}{10} a^2 b x^{10}+\frac{a^3 x^8}{8}+\frac{1}{4} a b^2 x^{12}+\frac{b^3 x^{14}}{14}",1,"(a^3*x^8)/8 + (3*a^2*b*x^10)/10 + (a*b^2*x^12)/4 + (b^3*x^14)/14","A",3,2,13,0.1538,1,"{266, 43}"
31,1,43,0,0.0251348,"\int x^5 \left(a+b x^2\right)^3 \, dx","Int[x^5*(a + b*x^2)^3,x]","\frac{3}{8} a^2 b x^8+\frac{a^3 x^6}{6}+\frac{3}{10} a b^2 x^{10}+\frac{b^3 x^{12}}{12}","\frac{3}{8} a^2 b x^8+\frac{a^3 x^6}{6}+\frac{3}{10} a b^2 x^{10}+\frac{b^3 x^{12}}{12}",1,"(a^3*x^6)/6 + (3*a^2*b*x^8)/8 + (3*a*b^2*x^10)/10 + (b^3*x^12)/12","A",3,2,13,0.1538,1,"{266, 43}"
32,1,34,0,0.0316579,"\int x^3 \left(a+b x^2\right)^3 \, dx","Int[x^3*(a + b*x^2)^3,x]","\frac{\left(a+b x^2\right)^5}{10 b^2}-\frac{a \left(a+b x^2\right)^4}{8 b^2}","\frac{\left(a+b x^2\right)^5}{10 b^2}-\frac{a \left(a+b x^2\right)^4}{8 b^2}",1,"-(a*(a + b*x^2)^4)/(8*b^2) + (a + b*x^2)^5/(10*b^2)","A",3,2,13,0.1538,1,"{266, 43}"
33,1,16,0,0.0023568,"\int x \left(a+b x^2\right)^3 \, dx","Int[x*(a + b*x^2)^3,x]","\frac{\left(a+b x^2\right)^4}{8 b}","\frac{\left(a+b x^2\right)^4}{8 b}",1,"(a + b*x^2)^4/(8*b)","A",1,1,11,0.09091,1,"{261}"
34,1,39,0,0.0184897,"\int \frac{\left(a+b x^2\right)^3}{x} \, dx","Int[(a + b*x^2)^3/x,x]","\frac{3}{2} a^2 b x^2+a^3 \log (x)+\frac{3}{4} a b^2 x^4+\frac{b^3 x^6}{6}","\frac{3}{2} a^2 b x^2+a^3 \log (x)+\frac{3}{4} a b^2 x^4+\frac{b^3 x^6}{6}",1,"(3*a^2*b*x^2)/2 + (3*a*b^2*x^4)/4 + (b^3*x^6)/6 + a^3*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
35,1,40,0,0.0206277,"\int \frac{\left(a+b x^2\right)^3}{x^3} \, dx","Int[(a + b*x^2)^3/x^3,x]","3 a^2 b \log (x)-\frac{a^3}{2 x^2}+\frac{3}{2} a b^2 x^2+\frac{b^3 x^4}{4}","3 a^2 b \log (x)-\frac{a^3}{2 x^2}+\frac{3}{2} a b^2 x^2+\frac{b^3 x^4}{4}",1,"-a^3/(2*x^2) + (3*a*b^2*x^2)/2 + (b^3*x^4)/4 + 3*a^2*b*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
36,1,40,0,0.0186338,"\int \frac{\left(a+b x^2\right)^3}{x^5} \, dx","Int[(a + b*x^2)^3/x^5,x]","-\frac{3 a^2 b}{2 x^2}-\frac{a^3}{4 x^4}+3 a b^2 \log (x)+\frac{b^3 x^2}{2}","-\frac{3 a^2 b}{2 x^2}-\frac{a^3}{4 x^4}+3 a b^2 \log (x)+\frac{b^3 x^2}{2}",1,"-a^3/(4*x^4) - (3*a^2*b)/(2*x^2) + (b^3*x^2)/2 + 3*a*b^2*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
37,1,39,0,0.0211947,"\int \frac{\left(a+b x^2\right)^3}{x^7} \, dx","Int[(a + b*x^2)^3/x^7,x]","-\frac{3 a^2 b}{4 x^4}-\frac{a^3}{6 x^6}-\frac{3 a b^2}{2 x^2}+b^3 \log (x)","-\frac{3 a^2 b}{4 x^4}-\frac{a^3}{6 x^6}-\frac{3 a b^2}{2 x^2}+b^3 \log (x)",1,"-a^3/(6*x^6) - (3*a^2*b)/(4*x^4) - (3*a*b^2)/(2*x^2) + b^3*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
38,1,19,0,0.0030151,"\int \frac{\left(a+b x^2\right)^3}{x^9} \, dx","Int[(a + b*x^2)^3/x^9,x]","-\frac{\left(a+b x^2\right)^4}{8 a x^8}","-\frac{\left(a+b x^2\right)^4}{8 a x^8}",1,"-(a + b*x^2)^4/(8*a*x^8)","A",1,1,13,0.07692,1,"{264}"
39,1,40,0,0.0193902,"\int \frac{\left(a+b x^2\right)^3}{x^{11}} \, dx","Int[(a + b*x^2)^3/x^11,x]","\frac{b \left(a+b x^2\right)^4}{40 a^2 x^8}-\frac{\left(a+b x^2\right)^4}{10 a x^{10}}","\frac{b \left(a+b x^2\right)^4}{40 a^2 x^8}-\frac{\left(a+b x^2\right)^4}{10 a x^{10}}",1,"-(a + b*x^2)^4/(10*a*x^10) + (b*(a + b*x^2)^4)/(40*a^2*x^8)","A",3,3,13,0.2308,1,"{266, 45, 37}"
40,1,43,0,0.0185851,"\int \frac{\left(a+b x^2\right)^3}{x^{13}} \, dx","Int[(a + b*x^2)^3/x^13,x]","-\frac{3 a^2 b}{10 x^{10}}-\frac{a^3}{12 x^{12}}-\frac{3 a b^2}{8 x^8}-\frac{b^3}{6 x^6}","-\frac{3 a^2 b}{10 x^{10}}-\frac{a^3}{12 x^{12}}-\frac{3 a b^2}{8 x^8}-\frac{b^3}{6 x^6}",1,"-a^3/(12*x^12) - (3*a^2*b)/(10*x^10) - (3*a*b^2)/(8*x^8) - b^3/(6*x^6)","A",3,2,13,0.1538,1,"{266, 43}"
41,1,43,0,0.0185127,"\int \frac{\left(a+b x^2\right)^3}{x^{15}} \, dx","Int[(a + b*x^2)^3/x^15,x]","-\frac{a^2 b}{4 x^{12}}-\frac{a^3}{14 x^{14}}-\frac{3 a b^2}{10 x^{10}}-\frac{b^3}{8 x^8}","-\frac{a^2 b}{4 x^{12}}-\frac{a^3}{14 x^{14}}-\frac{3 a b^2}{10 x^{10}}-\frac{b^3}{8 x^8}",1,"-a^3/(14*x^14) - (a^2*b)/(4*x^12) - (3*a*b^2)/(10*x^10) - b^3/(8*x^8)","A",3,2,13,0.1538,1,"{266, 43}"
42,1,43,0,0.0141882,"\int x^6 \left(a+b x^2\right)^3 \, dx","Int[x^6*(a + b*x^2)^3,x]","\frac{1}{3} a^2 b x^9+\frac{a^3 x^7}{7}+\frac{3}{11} a b^2 x^{11}+\frac{b^3 x^{13}}{13}","\frac{1}{3} a^2 b x^9+\frac{a^3 x^7}{7}+\frac{3}{11} a b^2 x^{11}+\frac{b^3 x^{13}}{13}",1,"(a^3*x^7)/7 + (a^2*b*x^9)/3 + (3*a*b^2*x^11)/11 + (b^3*x^13)/13","A",2,1,13,0.07692,1,"{270}"
43,1,43,0,0.0134052,"\int x^4 \left(a+b x^2\right)^3 \, dx","Int[x^4*(a + b*x^2)^3,x]","\frac{3}{7} a^2 b x^7+\frac{a^3 x^5}{5}+\frac{1}{3} a b^2 x^9+\frac{b^3 x^{11}}{11}","\frac{3}{7} a^2 b x^7+\frac{a^3 x^5}{5}+\frac{1}{3} a b^2 x^9+\frac{b^3 x^{11}}{11}",1,"(a^3*x^5)/5 + (3*a^2*b*x^7)/7 + (a*b^2*x^9)/3 + (b^3*x^11)/11","A",2,1,13,0.07692,1,"{270}"
44,1,43,0,0.0133414,"\int x^2 \left(a+b x^2\right)^3 \, dx","Int[x^2*(a + b*x^2)^3,x]","\frac{3}{5} a^2 b x^5+\frac{a^3 x^3}{3}+\frac{3}{7} a b^2 x^7+\frac{b^3 x^9}{9}","\frac{3}{5} a^2 b x^5+\frac{a^3 x^3}{3}+\frac{3}{7} a b^2 x^7+\frac{b^3 x^9}{9}",1,"(a^3*x^3)/3 + (3*a^2*b*x^5)/5 + (3*a*b^2*x^7)/7 + (b^3*x^9)/9","A",2,1,13,0.07692,1,"{270}"
45,1,35,0,0.0105425,"\int \left(a+b x^2\right)^3 \, dx","Int[(a + b*x^2)^3,x]","a^2 b x^3+a^3 x+\frac{3}{5} a b^2 x^5+\frac{b^3 x^7}{7}","a^2 b x^3+a^3 x+\frac{3}{5} a b^2 x^5+\frac{b^3 x^7}{7}",1,"a^3*x + a^2*b*x^3 + (3*a*b^2*x^5)/5 + (b^3*x^7)/7","A",2,1,9,0.1111,1,"{194}"
46,1,34,0,0.0129008,"\int \frac{\left(a+b x^2\right)^3}{x^2} \, dx","Int[(a + b*x^2)^3/x^2,x]","3 a^2 b x-\frac{a^3}{x}+a b^2 x^3+\frac{b^3 x^5}{5}","3 a^2 b x-\frac{a^3}{x}+a b^2 x^3+\frac{b^3 x^5}{5}",1,"-(a^3/x) + 3*a^2*b*x + a*b^2*x^3 + (b^3*x^5)/5","A",2,1,13,0.07692,1,"{270}"
47,1,37,0,0.0125237,"\int \frac{\left(a+b x^2\right)^3}{x^4} \, dx","Int[(a + b*x^2)^3/x^4,x]","-\frac{3 a^2 b}{x}-\frac{a^3}{3 x^3}+3 a b^2 x+\frac{b^3 x^3}{3}","-\frac{3 a^2 b}{x}-\frac{a^3}{3 x^3}+3 a b^2 x+\frac{b^3 x^3}{3}",1,"-a^3/(3*x^3) - (3*a^2*b)/x + 3*a*b^2*x + (b^3*x^3)/3","A",2,1,13,0.07692,1,"{270}"
48,1,34,0,0.0128706,"\int \frac{\left(a+b x^2\right)^3}{x^6} \, dx","Int[(a + b*x^2)^3/x^6,x]","-\frac{a^2 b}{x^3}-\frac{a^3}{5 x^5}-\frac{3 a b^2}{x}+b^3 x","-\frac{a^2 b}{x^3}-\frac{a^3}{5 x^5}-\frac{3 a b^2}{x}+b^3 x",1,"-a^3/(5*x^5) - (a^2*b)/x^3 - (3*a*b^2)/x + b^3*x","A",2,1,13,0.07692,1,"{270}"
49,1,39,0,0.0134047,"\int \frac{\left(a+b x^2\right)^3}{x^8} \, dx","Int[(a + b*x^2)^3/x^8,x]","-\frac{3 a^2 b}{5 x^5}-\frac{a^3}{7 x^7}-\frac{a b^2}{x^3}-\frac{b^3}{x}","-\frac{3 a^2 b}{5 x^5}-\frac{a^3}{7 x^7}-\frac{a b^2}{x^3}-\frac{b^3}{x}",1,"-a^3/(7*x^7) - (3*a^2*b)/(5*x^5) - (a*b^2)/x^3 - b^3/x","A",2,1,13,0.07692,1,"{270}"
50,1,43,0,0.0134588,"\int \frac{\left(a+b x^2\right)^3}{x^{10}} \, dx","Int[(a + b*x^2)^3/x^10,x]","-\frac{3 a^2 b}{7 x^7}-\frac{a^3}{9 x^9}-\frac{3 a b^2}{5 x^5}-\frac{b^3}{3 x^3}","-\frac{3 a^2 b}{7 x^7}-\frac{a^3}{9 x^9}-\frac{3 a b^2}{5 x^5}-\frac{b^3}{3 x^3}",1,"-a^3/(9*x^9) - (3*a^2*b)/(7*x^7) - (3*a*b^2)/(5*x^5) - b^3/(3*x^3)","A",2,1,13,0.07692,1,"{270}"
51,1,43,0,0.014571,"\int \frac{\left(a+b x^2\right)^3}{x^{12}} \, dx","Int[(a + b*x^2)^3/x^12,x]","-\frac{a^2 b}{3 x^9}-\frac{a^3}{11 x^{11}}-\frac{3 a b^2}{7 x^7}-\frac{b^3}{5 x^5}","-\frac{a^2 b}{3 x^9}-\frac{a^3}{11 x^{11}}-\frac{3 a b^2}{7 x^7}-\frac{b^3}{5 x^5}",1,"-a^3/(11*x^11) - (a^2*b)/(3*x^9) - (3*a*b^2)/(7*x^7) - b^3/(5*x^5)","A",2,1,13,0.07692,1,"{270}"
52,1,69,0,0.0488556,"\int x^{13} \left(a+b x^2\right)^5 \, dx","Int[x^13*(a + b*x^2)^5,x]","\frac{1}{2} a^2 b^3 x^{20}+\frac{5}{9} a^3 b^2 x^{18}+\frac{5}{16} a^4 b x^{16}+\frac{a^5 x^{14}}{14}+\frac{5}{22} a b^4 x^{22}+\frac{b^5 x^{24}}{24}","\frac{1}{2} a^2 b^3 x^{20}+\frac{5}{9} a^3 b^2 x^{18}+\frac{5}{16} a^4 b x^{16}+\frac{a^5 x^{14}}{14}+\frac{5}{22} a b^4 x^{22}+\frac{b^5 x^{24}}{24}",1,"(a^5*x^14)/14 + (5*a^4*b*x^16)/16 + (5*a^3*b^2*x^18)/9 + (a^2*b^3*x^20)/2 + (5*a*b^4*x^22)/22 + (b^5*x^24)/24","A",3,2,13,0.1538,1,"{266, 43}"
53,1,69,0,0.044137,"\int x^{11} \left(a+b x^2\right)^5 \, dx","Int[x^11*(a + b*x^2)^5,x]","\frac{5}{9} a^2 b^3 x^{18}+\frac{5}{8} a^3 b^2 x^{16}+\frac{5}{14} a^4 b x^{14}+\frac{a^5 x^{12}}{12}+\frac{1}{4} a b^4 x^{20}+\frac{b^5 x^{22}}{22}","\frac{5}{9} a^2 b^3 x^{18}+\frac{5}{8} a^3 b^2 x^{16}+\frac{5}{14} a^4 b x^{14}+\frac{a^5 x^{12}}{12}+\frac{1}{4} a b^4 x^{20}+\frac{b^5 x^{22}}{22}",1,"(a^5*x^12)/12 + (5*a^4*b*x^14)/14 + (5*a^3*b^2*x^16)/8 + (5*a^2*b^3*x^18)/9 + (a*b^4*x^20)/4 + (b^5*x^22)/22","A",3,2,13,0.1538,1,"{266, 43}"
54,1,69,0,0.0431,"\int x^9 \left(a+b x^2\right)^5 \, dx","Int[x^9*(a + b*x^2)^5,x]","\frac{5}{8} a^2 b^3 x^{16}+\frac{5}{7} a^3 b^2 x^{14}+\frac{5}{12} a^4 b x^{12}+\frac{a^5 x^{10}}{10}+\frac{5}{18} a b^4 x^{18}+\frac{b^5 x^{20}}{20}","\frac{5}{8} a^2 b^3 x^{16}+\frac{5}{7} a^3 b^2 x^{14}+\frac{5}{12} a^4 b x^{12}+\frac{a^5 x^{10}}{10}+\frac{5}{18} a b^4 x^{18}+\frac{b^5 x^{20}}{20}",1,"(a^5*x^10)/10 + (5*a^4*b*x^12)/12 + (5*a^3*b^2*x^14)/7 + (5*a^2*b^3*x^16)/8 + (5*a*b^4*x^18)/18 + (b^5*x^20)/20","A",3,2,13,0.1538,1,"{266, 43}"
55,1,72,0,0.0905814,"\int x^7 \left(a+b x^2\right)^5 \, dx","Int[x^7*(a + b*x^2)^5,x]","\frac{3 a^2 \left(a+b x^2\right)^7}{14 b^4}-\frac{a^3 \left(a+b x^2\right)^6}{12 b^4}+\frac{\left(a+b x^2\right)^9}{18 b^4}-\frac{3 a \left(a+b x^2\right)^8}{16 b^4}","\frac{3 a^2 \left(a+b x^2\right)^7}{14 b^4}-\frac{a^3 \left(a+b x^2\right)^6}{12 b^4}+\frac{\left(a+b x^2\right)^9}{18 b^4}-\frac{3 a \left(a+b x^2\right)^8}{16 b^4}",1,"-(a^3*(a + b*x^2)^6)/(12*b^4) + (3*a^2*(a + b*x^2)^7)/(14*b^4) - (3*a*(a + b*x^2)^8)/(16*b^4) + (a + b*x^2)^9/(18*b^4)","A",3,2,13,0.1538,1,"{266, 43}"
56,1,53,0,0.0647074,"\int x^5 \left(a+b x^2\right)^5 \, dx","Int[x^5*(a + b*x^2)^5,x]","\frac{a^2 \left(a+b x^2\right)^6}{12 b^3}+\frac{\left(a+b x^2\right)^8}{16 b^3}-\frac{a \left(a+b x^2\right)^7}{7 b^3}","\frac{a^2 \left(a+b x^2\right)^6}{12 b^3}+\frac{\left(a+b x^2\right)^8}{16 b^3}-\frac{a \left(a+b x^2\right)^7}{7 b^3}",1,"(a^2*(a + b*x^2)^6)/(12*b^3) - (a*(a + b*x^2)^7)/(7*b^3) + (a + b*x^2)^8/(16*b^3)","A",3,2,13,0.1538,1,"{266, 43}"
57,1,34,0,0.036031,"\int x^3 \left(a+b x^2\right)^5 \, dx","Int[x^3*(a + b*x^2)^5,x]","\frac{\left(a+b x^2\right)^7}{14 b^2}-\frac{a \left(a+b x^2\right)^6}{12 b^2}","\frac{\left(a+b x^2\right)^7}{14 b^2}-\frac{a \left(a+b x^2\right)^6}{12 b^2}",1,"-(a*(a + b*x^2)^6)/(12*b^2) + (a + b*x^2)^7/(14*b^2)","A",3,2,13,0.1538,1,"{266, 43}"
58,1,16,0,0.0024507,"\int x \left(a+b x^2\right)^5 \, dx","Int[x*(a + b*x^2)^5,x]","\frac{\left(a+b x^2\right)^6}{12 b}","\frac{\left(a+b x^2\right)^6}{12 b}",1,"(a + b*x^2)^6/(12*b)","A",1,1,11,0.09091,1,"{261}"
59,1,65,0,0.0339468,"\int \frac{\left(a+b x^2\right)^5}{x} \, dx","Int[(a + b*x^2)^5/x,x]","\frac{5}{3} a^2 b^3 x^6+\frac{5}{2} a^3 b^2 x^4+\frac{5}{2} a^4 b x^2+a^5 \log (x)+\frac{5}{8} a b^4 x^8+\frac{b^5 x^{10}}{10}","\frac{5}{3} a^2 b^3 x^6+\frac{5}{2} a^3 b^2 x^4+\frac{5}{2} a^4 b x^2+a^5 \log (x)+\frac{5}{8} a b^4 x^8+\frac{b^5 x^{10}}{10}",1,"(5*a^4*b*x^2)/2 + (5*a^3*b^2*x^4)/2 + (5*a^2*b^3*x^6)/3 + (5*a*b^4*x^8)/8 + (b^5*x^10)/10 + a^5*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
60,1,64,0,0.0366834,"\int \frac{\left(a+b x^2\right)^5}{x^3} \, dx","Int[(a + b*x^2)^5/x^3,x]","\frac{5}{2} a^2 b^3 x^4+5 a^3 b^2 x^2+5 a^4 b \log (x)-\frac{a^5}{2 x^2}+\frac{5}{6} a b^4 x^6+\frac{b^5 x^8}{8}","\frac{5}{2} a^2 b^3 x^4+5 a^3 b^2 x^2+5 a^4 b \log (x)-\frac{a^5}{2 x^2}+\frac{5}{6} a b^4 x^6+\frac{b^5 x^8}{8}",1,"-a^5/(2*x^2) + 5*a^3*b^2*x^2 + (5*a^2*b^3*x^4)/2 + (5*a*b^4*x^6)/6 + (b^5*x^8)/8 + 5*a^4*b*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
61,1,64,0,0.0361221,"\int \frac{\left(a+b x^2\right)^5}{x^5} \, dx","Int[(a + b*x^2)^5/x^5,x]","5 a^2 b^3 x^2+10 a^3 b^2 \log (x)-\frac{5 a^4 b}{2 x^2}-\frac{a^5}{4 x^4}+\frac{5}{4} a b^4 x^4+\frac{b^5 x^6}{6}","5 a^2 b^3 x^2+10 a^3 b^2 \log (x)-\frac{5 a^4 b}{2 x^2}-\frac{a^5}{4 x^4}+\frac{5}{4} a b^4 x^4+\frac{b^5 x^6}{6}",1,"-a^5/(4*x^4) - (5*a^4*b)/(2*x^2) + 5*a^2*b^3*x^2 + (5*a*b^4*x^4)/4 + (b^5*x^6)/6 + 10*a^3*b^2*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
62,1,64,0,0.0340468,"\int \frac{\left(a+b x^2\right)^5}{x^7} \, dx","Int[(a + b*x^2)^5/x^7,x]","-\frac{5 a^3 b^2}{x^2}+10 a^2 b^3 \log (x)-\frac{5 a^4 b}{4 x^4}-\frac{a^5}{6 x^6}+\frac{5}{2} a b^4 x^2+\frac{b^5 x^4}{4}","-\frac{5 a^3 b^2}{x^2}+10 a^2 b^3 \log (x)-\frac{5 a^4 b}{4 x^4}-\frac{a^5}{6 x^6}+\frac{5}{2} a b^4 x^2+\frac{b^5 x^4}{4}",1,"-a^5/(6*x^6) - (5*a^4*b)/(4*x^4) - (5*a^3*b^2)/x^2 + (5*a*b^4*x^2)/2 + (b^5*x^4)/4 + 10*a^2*b^3*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
63,1,64,0,0.0328172,"\int \frac{\left(a+b x^2\right)^5}{x^9} \, dx","Int[(a + b*x^2)^5/x^9,x]","-\frac{5 a^3 b^2}{2 x^4}-\frac{5 a^2 b^3}{x^2}-\frac{5 a^4 b}{6 x^6}-\frac{a^5}{8 x^8}+5 a b^4 \log (x)+\frac{b^5 x^2}{2}","-\frac{5 a^3 b^2}{2 x^4}-\frac{5 a^2 b^3}{x^2}-\frac{5 a^4 b}{6 x^6}-\frac{a^5}{8 x^8}+5 a b^4 \log (x)+\frac{b^5 x^2}{2}",1,"-a^5/(8*x^8) - (5*a^4*b)/(6*x^6) - (5*a^3*b^2)/(2*x^4) - (5*a^2*b^3)/x^2 + (b^5*x^2)/2 + 5*a*b^4*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
64,1,65,0,0.0310673,"\int \frac{\left(a+b x^2\right)^5}{x^{11}} \, dx","Int[(a + b*x^2)^5/x^11,x]","-\frac{5 a^3 b^2}{3 x^6}-\frac{5 a^2 b^3}{2 x^4}-\frac{5 a^4 b}{8 x^8}-\frac{a^5}{10 x^{10}}-\frac{5 a b^4}{2 x^2}+b^5 \log (x)","-\frac{5 a^3 b^2}{3 x^6}-\frac{5 a^2 b^3}{2 x^4}-\frac{5 a^4 b}{8 x^8}-\frac{a^5}{10 x^{10}}-\frac{5 a b^4}{2 x^2}+b^5 \log (x)",1,"-a^5/(10*x^10) - (5*a^4*b)/(8*x^8) - (5*a^3*b^2)/(3*x^6) - (5*a^2*b^3)/(2*x^4) - (5*a*b^4)/(2*x^2) + b^5*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
65,1,19,0,0.0035702,"\int \frac{\left(a+b x^2\right)^5}{x^{13}} \, dx","Int[(a + b*x^2)^5/x^13,x]","-\frac{\left(a+b x^2\right)^6}{12 a x^{12}}","-\frac{\left(a+b x^2\right)^6}{12 a x^{12}}",1,"-(a + b*x^2)^6/(12*a*x^12)","A",1,1,13,0.07692,1,"{264}"
66,1,40,0,0.0176447,"\int \frac{\left(a+b x^2\right)^5}{x^{15}} \, dx","Int[(a + b*x^2)^5/x^15,x]","\frac{b \left(a+b x^2\right)^6}{84 a^2 x^{12}}-\frac{\left(a+b x^2\right)^6}{14 a x^{14}}","\frac{b \left(a+b x^2\right)^6}{84 a^2 x^{12}}-\frac{\left(a+b x^2\right)^6}{14 a x^{14}}",1,"-(a + b*x^2)^6/(14*a*x^14) + (b*(a + b*x^2)^6)/(84*a^2*x^12)","A",3,3,13,0.2308,1,"{266, 45, 37}"
67,1,62,0,0.0280627,"\int \frac{\left(a+b x^2\right)^5}{x^{17}} \, dx","Int[(a + b*x^2)^5/x^17,x]","-\frac{b^2 \left(a+b x^2\right)^6}{336 a^3 x^{12}}+\frac{b \left(a+b x^2\right)^6}{56 a^2 x^{14}}-\frac{\left(a+b x^2\right)^6}{16 a x^{16}}","-\frac{b^2 \left(a+b x^2\right)^6}{336 a^3 x^{12}}+\frac{b \left(a+b x^2\right)^6}{56 a^2 x^{14}}-\frac{\left(a+b x^2\right)^6}{16 a x^{16}}",1,"-(a + b*x^2)^6/(16*a*x^16) + (b*(a + b*x^2)^6)/(56*a^2*x^14) - (b^2*(a + b*x^2)^6)/(336*a^3*x^12)","A",4,3,13,0.2308,1,"{266, 45, 37}"
68,1,69,0,0.0316203,"\int \frac{\left(a+b x^2\right)^5}{x^{19}} \, dx","Int[(a + b*x^2)^5/x^19,x]","-\frac{5 a^3 b^2}{7 x^{14}}-\frac{5 a^2 b^3}{6 x^{12}}-\frac{5 a^4 b}{16 x^{16}}-\frac{a^5}{18 x^{18}}-\frac{a b^4}{2 x^{10}}-\frac{b^5}{8 x^8}","-\frac{5 a^3 b^2}{7 x^{14}}-\frac{5 a^2 b^3}{6 x^{12}}-\frac{5 a^4 b}{16 x^{16}}-\frac{a^5}{18 x^{18}}-\frac{a b^4}{2 x^{10}}-\frac{b^5}{8 x^8}",1,"-a^5/(18*x^18) - (5*a^4*b)/(16*x^16) - (5*a^3*b^2)/(7*x^14) - (5*a^2*b^3)/(6*x^12) - (a*b^4)/(2*x^10) - b^5/(8*x^8)","A",3,2,13,0.1538,1,"{266, 43}"
69,1,69,0,0.0305198,"\int \frac{\left(a+b x^2\right)^5}{x^{21}} \, dx","Int[(a + b*x^2)^5/x^21,x]","-\frac{5 a^3 b^2}{8 x^{16}}-\frac{5 a^2 b^3}{7 x^{14}}-\frac{5 a^4 b}{18 x^{18}}-\frac{a^5}{20 x^{20}}-\frac{5 a b^4}{12 x^{12}}-\frac{b^5}{10 x^{10}}","-\frac{5 a^3 b^2}{8 x^{16}}-\frac{5 a^2 b^3}{7 x^{14}}-\frac{5 a^4 b}{18 x^{18}}-\frac{a^5}{20 x^{20}}-\frac{5 a b^4}{12 x^{12}}-\frac{b^5}{10 x^{10}}",1,"-a^5/(20*x^20) - (5*a^4*b)/(18*x^18) - (5*a^3*b^2)/(8*x^16) - (5*a^2*b^3)/(7*x^14) - (5*a*b^4)/(12*x^12) - b^5/(10*x^10)","A",3,2,13,0.1538,1,"{266, 43}"
70,1,69,0,0.0248095,"\int x^8 \left(a+b x^2\right)^5 \, dx","Int[x^8*(a + b*x^2)^5,x]","\frac{2}{3} a^2 b^3 x^{15}+\frac{10}{13} a^3 b^2 x^{13}+\frac{5}{11} a^4 b x^{11}+\frac{a^5 x^9}{9}+\frac{5}{17} a b^4 x^{17}+\frac{b^5 x^{19}}{19}","\frac{2}{3} a^2 b^3 x^{15}+\frac{10}{13} a^3 b^2 x^{13}+\frac{5}{11} a^4 b x^{11}+\frac{a^5 x^9}{9}+\frac{5}{17} a b^4 x^{17}+\frac{b^5 x^{19}}{19}",1,"(a^5*x^9)/9 + (5*a^4*b*x^11)/11 + (10*a^3*b^2*x^13)/13 + (2*a^2*b^3*x^15)/3 + (5*a*b^4*x^17)/17 + (b^5*x^19)/19","A",2,1,13,0.07692,1,"{270}"
71,1,69,0,0.0238795,"\int x^6 \left(a+b x^2\right)^5 \, dx","Int[x^6*(a + b*x^2)^5,x]","\frac{10}{13} a^2 b^3 x^{13}+\frac{10}{11} a^3 b^2 x^{11}+\frac{5}{9} a^4 b x^9+\frac{a^5 x^7}{7}+\frac{1}{3} a b^4 x^{15}+\frac{b^5 x^{17}}{17}","\frac{10}{13} a^2 b^3 x^{13}+\frac{10}{11} a^3 b^2 x^{11}+\frac{5}{9} a^4 b x^9+\frac{a^5 x^7}{7}+\frac{1}{3} a b^4 x^{15}+\frac{b^5 x^{17}}{17}",1,"(a^5*x^7)/7 + (5*a^4*b*x^9)/9 + (10*a^3*b^2*x^11)/11 + (10*a^2*b^3*x^13)/13 + (a*b^4*x^15)/3 + (b^5*x^17)/17","A",2,1,13,0.07692,1,"{270}"
72,1,69,0,0.0222111,"\int x^4 \left(a+b x^2\right)^5 \, dx","Int[x^4*(a + b*x^2)^5,x]","\frac{10}{11} a^2 b^3 x^{11}+\frac{10}{9} a^3 b^2 x^9+\frac{5}{7} a^4 b x^7+\frac{a^5 x^5}{5}+\frac{5}{13} a b^4 x^{13}+\frac{b^5 x^{15}}{15}","\frac{10}{11} a^2 b^3 x^{11}+\frac{10}{9} a^3 b^2 x^9+\frac{5}{7} a^4 b x^7+\frac{a^5 x^5}{5}+\frac{5}{13} a b^4 x^{13}+\frac{b^5 x^{15}}{15}",1,"(a^5*x^5)/5 + (5*a^4*b*x^7)/7 + (10*a^3*b^2*x^9)/9 + (10*a^2*b^3*x^11)/11 + (5*a*b^4*x^13)/13 + (b^5*x^15)/15","A",2,1,13,0.07692,1,"{270}"
73,1,66,0,0.0218526,"\int x^2 \left(a+b x^2\right)^5 \, dx","Int[x^2*(a + b*x^2)^5,x]","\frac{10}{9} a^2 b^3 x^9+\frac{10}{7} a^3 b^2 x^7+a^4 b x^5+\frac{a^5 x^3}{3}+\frac{5}{11} a b^4 x^{11}+\frac{b^5 x^{13}}{13}","\frac{10}{9} a^2 b^3 x^9+\frac{10}{7} a^3 b^2 x^7+a^4 b x^5+\frac{a^5 x^3}{3}+\frac{5}{11} a b^4 x^{11}+\frac{b^5 x^{13}}{13}",1,"(a^5*x^3)/3 + a^4*b*x^5 + (10*a^3*b^2*x^7)/7 + (10*a^2*b^3*x^9)/9 + (5*a*b^4*x^11)/11 + (b^5*x^13)/13","A",2,1,13,0.07692,1,"{270}"
74,1,62,0,0.019159,"\int \left(a+b x^2\right)^5 \, dx","Int[(a + b*x^2)^5,x]","\frac{10}{7} a^2 b^3 x^7+2 a^3 b^2 x^5+\frac{5}{3} a^4 b x^3+a^5 x+\frac{5}{9} a b^4 x^9+\frac{b^5 x^{11}}{11}","\frac{10}{7} a^2 b^3 x^7+2 a^3 b^2 x^5+\frac{5}{3} a^4 b x^3+a^5 x+\frac{5}{9} a b^4 x^9+\frac{b^5 x^{11}}{11}",1,"a^5*x + (5*a^4*b*x^3)/3 + 2*a^3*b^2*x^5 + (10*a^2*b^3*x^7)/7 + (5*a*b^4*x^9)/9 + (b^5*x^11)/11","A",2,1,9,0.1111,1,"{194}"
75,1,61,0,0.0210491,"\int \frac{\left(a+b x^2\right)^5}{x^2} \, dx","Int[(a + b*x^2)^5/x^2,x]","2 a^2 b^3 x^5+\frac{10}{3} a^3 b^2 x^3+5 a^4 b x-\frac{a^5}{x}+\frac{5}{7} a b^4 x^7+\frac{b^5 x^9}{9}","2 a^2 b^3 x^5+\frac{10}{3} a^3 b^2 x^3+5 a^4 b x-\frac{a^5}{x}+\frac{5}{7} a b^4 x^7+\frac{b^5 x^9}{9}",1,"-(a^5/x) + 5*a^4*b*x + (10*a^3*b^2*x^3)/3 + 2*a^2*b^3*x^5 + (5*a*b^4*x^7)/7 + (b^5*x^9)/9","A",2,1,13,0.07692,1,"{270}"
76,1,60,0,0.0217368,"\int \frac{\left(a+b x^2\right)^5}{x^4} \, dx","Int[(a + b*x^2)^5/x^4,x]","\frac{10}{3} a^2 b^3 x^3+10 a^3 b^2 x-\frac{5 a^4 b}{x}-\frac{a^5}{3 x^3}+a b^4 x^5+\frac{b^5 x^7}{7}","\frac{10}{3} a^2 b^3 x^3+10 a^3 b^2 x-\frac{5 a^4 b}{x}-\frac{a^5}{3 x^3}+a b^4 x^5+\frac{b^5 x^7}{7}",1,"-a^5/(3*x^3) - (5*a^4*b)/x + 10*a^3*b^2*x + (10*a^2*b^3*x^3)/3 + a*b^4*x^5 + (b^5*x^7)/7","A",2,1,13,0.07692,1,"{270}"
77,1,63,0,0.0224724,"\int \frac{\left(a+b x^2\right)^5}{x^6} \, dx","Int[(a + b*x^2)^5/x^6,x]","-\frac{10 a^3 b^2}{x}+10 a^2 b^3 x-\frac{5 a^4 b}{3 x^3}-\frac{a^5}{5 x^5}+\frac{5}{3} a b^4 x^3+\frac{b^5 x^5}{5}","-\frac{10 a^3 b^2}{x}+10 a^2 b^3 x-\frac{5 a^4 b}{3 x^3}-\frac{a^5}{5 x^5}+\frac{5}{3} a b^4 x^3+\frac{b^5 x^5}{5}",1,"-a^5/(5*x^5) - (5*a^4*b)/(3*x^3) - (10*a^3*b^2)/x + 10*a^2*b^3*x + (5*a*b^4*x^3)/3 + (b^5*x^5)/5","A",2,1,13,0.07692,1,"{270}"
78,1,61,0,0.0216362,"\int \frac{\left(a+b x^2\right)^5}{x^8} \, dx","Int[(a + b*x^2)^5/x^8,x]","-\frac{10 a^3 b^2}{3 x^3}-\frac{10 a^2 b^3}{x}-\frac{a^4 b}{x^5}-\frac{a^5}{7 x^7}+5 a b^4 x+\frac{b^5 x^3}{3}","-\frac{10 a^3 b^2}{3 x^3}-\frac{10 a^2 b^3}{x}-\frac{a^4 b}{x^5}-\frac{a^5}{7 x^7}+5 a b^4 x+\frac{b^5 x^3}{3}",1,"-a^5/(7*x^7) - (a^4*b)/x^5 - (10*a^3*b^2)/(3*x^3) - (10*a^2*b^3)/x + 5*a*b^4*x + (b^5*x^3)/3","A",2,1,13,0.07692,1,"{270}"
79,1,60,0,0.0219145,"\int \frac{\left(a+b x^2\right)^5}{x^{10}} \, dx","Int[(a + b*x^2)^5/x^10,x]","-\frac{2 a^3 b^2}{x^5}-\frac{10 a^2 b^3}{3 x^3}-\frac{5 a^4 b}{7 x^7}-\frac{a^5}{9 x^9}-\frac{5 a b^4}{x}+b^5 x","-\frac{2 a^3 b^2}{x^5}-\frac{10 a^2 b^3}{3 x^3}-\frac{5 a^4 b}{7 x^7}-\frac{a^5}{9 x^9}-\frac{5 a b^4}{x}+b^5 x",1,"-a^5/(9*x^9) - (5*a^4*b)/(7*x^7) - (2*a^3*b^2)/x^5 - (10*a^2*b^3)/(3*x^3) - (5*a*b^4)/x + b^5*x","A",2,1,13,0.07692,1,"{270}"
80,1,65,0,0.0223313,"\int \frac{\left(a+b x^2\right)^5}{x^{12}} \, dx","Int[(a + b*x^2)^5/x^12,x]","-\frac{10 a^3 b^2}{7 x^7}-\frac{2 a^2 b^3}{x^5}-\frac{5 a^4 b}{9 x^9}-\frac{a^5}{11 x^{11}}-\frac{5 a b^4}{3 x^3}-\frac{b^5}{x}","-\frac{10 a^3 b^2}{7 x^7}-\frac{2 a^2 b^3}{x^5}-\frac{5 a^4 b}{9 x^9}-\frac{a^5}{11 x^{11}}-\frac{5 a b^4}{3 x^3}-\frac{b^5}{x}",1,"-a^5/(11*x^11) - (5*a^4*b)/(9*x^9) - (10*a^3*b^2)/(7*x^7) - (2*a^2*b^3)/x^5 - (5*a*b^4)/(3*x^3) - b^5/x","A",2,1,13,0.07692,1,"{270}"
81,1,67,0,0.0230642,"\int \frac{\left(a+b x^2\right)^5}{x^{14}} \, dx","Int[(a + b*x^2)^5/x^14,x]","-\frac{10 a^3 b^2}{9 x^9}-\frac{10 a^2 b^3}{7 x^7}-\frac{5 a^4 b}{11 x^{11}}-\frac{a^5}{13 x^{13}}-\frac{a b^4}{x^5}-\frac{b^5}{3 x^3}","-\frac{10 a^3 b^2}{9 x^9}-\frac{10 a^2 b^3}{7 x^7}-\frac{5 a^4 b}{11 x^{11}}-\frac{a^5}{13 x^{13}}-\frac{a b^4}{x^5}-\frac{b^5}{3 x^3}",1,"-a^5/(13*x^13) - (5*a^4*b)/(11*x^11) - (10*a^3*b^2)/(9*x^9) - (10*a^2*b^3)/(7*x^7) - (a*b^4)/x^5 - b^5/(3*x^3)","A",2,1,13,0.07692,1,"{270}"
82,1,69,0,0.0231295,"\int \frac{\left(a+b x^2\right)^5}{x^{16}} \, dx","Int[(a + b*x^2)^5/x^16,x]","-\frac{10 a^3 b^2}{11 x^{11}}-\frac{10 a^2 b^3}{9 x^9}-\frac{5 a^4 b}{13 x^{13}}-\frac{a^5}{15 x^{15}}-\frac{5 a b^4}{7 x^7}-\frac{b^5}{5 x^5}","-\frac{10 a^3 b^2}{11 x^{11}}-\frac{10 a^2 b^3}{9 x^9}-\frac{5 a^4 b}{13 x^{13}}-\frac{a^5}{15 x^{15}}-\frac{5 a b^4}{7 x^7}-\frac{b^5}{5 x^5}",1,"-a^5/(15*x^15) - (5*a^4*b)/(13*x^13) - (10*a^3*b^2)/(11*x^11) - (10*a^2*b^3)/(9*x^9) - (5*a*b^4)/(7*x^7) - b^5/(5*x^5)","A",2,1,13,0.07692,1,"{270}"
83,1,69,0,0.0219601,"\int \frac{\left(a+b x^2\right)^5}{x^{18}} \, dx","Int[(a + b*x^2)^5/x^18,x]","-\frac{10 a^3 b^2}{13 x^{13}}-\frac{10 a^2 b^3}{11 x^{11}}-\frac{a^4 b}{3 x^{15}}-\frac{a^5}{17 x^{17}}-\frac{5 a b^4}{9 x^9}-\frac{b^5}{7 x^7}","-\frac{10 a^3 b^2}{13 x^{13}}-\frac{10 a^2 b^3}{11 x^{11}}-\frac{a^4 b}{3 x^{15}}-\frac{a^5}{17 x^{17}}-\frac{5 a b^4}{9 x^9}-\frac{b^5}{7 x^7}",1,"-a^5/(17*x^17) - (a^4*b)/(3*x^15) - (10*a^3*b^2)/(13*x^13) - (10*a^2*b^3)/(11*x^11) - (5*a*b^4)/(9*x^9) - b^5/(7*x^7)","A",2,1,13,0.07692,1,"{270}"
84,1,69,0,0.0225537,"\int \frac{\left(a+b x^2\right)^5}{x^{20}} \, dx","Int[(a + b*x^2)^5/x^20,x]","-\frac{2 a^3 b^2}{3 x^{15}}-\frac{10 a^2 b^3}{13 x^{13}}-\frac{5 a^4 b}{17 x^{17}}-\frac{a^5}{19 x^{19}}-\frac{5 a b^4}{11 x^{11}}-\frac{b^5}{9 x^9}","-\frac{2 a^3 b^2}{3 x^{15}}-\frac{10 a^2 b^3}{13 x^{13}}-\frac{5 a^4 b}{17 x^{17}}-\frac{a^5}{19 x^{19}}-\frac{5 a b^4}{11 x^{11}}-\frac{b^5}{9 x^9}",1,"-a^5/(19*x^19) - (5*a^4*b)/(17*x^17) - (2*a^3*b^2)/(3*x^15) - (10*a^2*b^3)/(13*x^13) - (5*a*b^4)/(11*x^11) - b^5/(9*x^9)","A",2,1,13,0.07692,1,"{270}"
85,1,129,0,0.2104536,"\int x^{13} \left(a+b x^2\right)^8 \, dx","Int[x^13*(a + b*x^2)^8,x]","\frac{15 a^2 \left(a+b x^2\right)^{13}}{26 b^7}-\frac{5 a^3 \left(a+b x^2\right)^{12}}{6 b^7}+\frac{15 a^4 \left(a+b x^2\right)^{11}}{22 b^7}-\frac{3 a^5 \left(a+b x^2\right)^{10}}{10 b^7}+\frac{a^6 \left(a+b x^2\right)^9}{18 b^7}+\frac{\left(a+b x^2\right)^{15}}{30 b^7}-\frac{3 a \left(a+b x^2\right)^{14}}{14 b^7}","\frac{15 a^2 \left(a+b x^2\right)^{13}}{26 b^7}-\frac{5 a^3 \left(a+b x^2\right)^{12}}{6 b^7}+\frac{15 a^4 \left(a+b x^2\right)^{11}}{22 b^7}-\frac{3 a^5 \left(a+b x^2\right)^{10}}{10 b^7}+\frac{a^6 \left(a+b x^2\right)^9}{18 b^7}+\frac{\left(a+b x^2\right)^{15}}{30 b^7}-\frac{3 a \left(a+b x^2\right)^{14}}{14 b^7}",1,"(a^6*(a + b*x^2)^9)/(18*b^7) - (3*a^5*(a + b*x^2)^10)/(10*b^7) + (15*a^4*(a + b*x^2)^11)/(22*b^7) - (5*a^3*(a + b*x^2)^12)/(6*b^7) + (15*a^2*(a + b*x^2)^13)/(26*b^7) - (3*a*(a + b*x^2)^14)/(14*b^7) + (a + b*x^2)^15/(30*b^7)","A",3,2,13,0.1538,1,"{266, 43}"
86,1,110,0,0.1709664,"\int x^{11} \left(a+b x^2\right)^8 \, dx","Int[x^11*(a + b*x^2)^8,x]","\frac{5 a^2 \left(a+b x^2\right)^{12}}{12 b^6}-\frac{5 a^3 \left(a+b x^2\right)^{11}}{11 b^6}+\frac{a^4 \left(a+b x^2\right)^{10}}{4 b^6}-\frac{a^5 \left(a+b x^2\right)^9}{18 b^6}+\frac{\left(a+b x^2\right)^{14}}{28 b^6}-\frac{5 a \left(a+b x^2\right)^{13}}{26 b^6}","\frac{5 a^2 \left(a+b x^2\right)^{12}}{12 b^6}-\frac{5 a^3 \left(a+b x^2\right)^{11}}{11 b^6}+\frac{a^4 \left(a+b x^2\right)^{10}}{4 b^6}-\frac{a^5 \left(a+b x^2\right)^9}{18 b^6}+\frac{\left(a+b x^2\right)^{14}}{28 b^6}-\frac{5 a \left(a+b x^2\right)^{13}}{26 b^6}",1,"-(a^5*(a + b*x^2)^9)/(18*b^6) + (a^4*(a + b*x^2)^10)/(4*b^6) - (5*a^3*(a + b*x^2)^11)/(11*b^6) + (5*a^2*(a + b*x^2)^12)/(12*b^6) - (5*a*(a + b*x^2)^13)/(26*b^6) + (a + b*x^2)^14/(28*b^6)","A",3,2,13,0.1538,1,"{266, 43}"
87,1,91,0,0.1417347,"\int x^9 \left(a+b x^2\right)^8 \, dx","Int[x^9*(a + b*x^2)^8,x]","\frac{3 a^2 \left(a+b x^2\right)^{11}}{11 b^5}-\frac{a^3 \left(a+b x^2\right)^{10}}{5 b^5}+\frac{a^4 \left(a+b x^2\right)^9}{18 b^5}+\frac{\left(a+b x^2\right)^{13}}{26 b^5}-\frac{a \left(a+b x^2\right)^{12}}{6 b^5}","\frac{3 a^2 \left(a+b x^2\right)^{11}}{11 b^5}-\frac{a^3 \left(a+b x^2\right)^{10}}{5 b^5}+\frac{a^4 \left(a+b x^2\right)^9}{18 b^5}+\frac{\left(a+b x^2\right)^{13}}{26 b^5}-\frac{a \left(a+b x^2\right)^{12}}{6 b^5}",1,"(a^4*(a + b*x^2)^9)/(18*b^5) - (a^3*(a + b*x^2)^10)/(5*b^5) + (3*a^2*(a + b*x^2)^11)/(11*b^5) - (a*(a + b*x^2)^12)/(6*b^5) + (a + b*x^2)^13/(26*b^5)","A",3,2,13,0.1538,1,"{266, 43}"
88,1,72,0,0.1157992,"\int x^7 \left(a+b x^2\right)^8 \, dx","Int[x^7*(a + b*x^2)^8,x]","\frac{3 a^2 \left(a+b x^2\right)^{10}}{20 b^4}-\frac{a^3 \left(a+b x^2\right)^9}{18 b^4}+\frac{\left(a+b x^2\right)^{12}}{24 b^4}-\frac{3 a \left(a+b x^2\right)^{11}}{22 b^4}","\frac{3 a^2 \left(a+b x^2\right)^{10}}{20 b^4}-\frac{a^3 \left(a+b x^2\right)^9}{18 b^4}+\frac{\left(a+b x^2\right)^{12}}{24 b^4}-\frac{3 a \left(a+b x^2\right)^{11}}{22 b^4}",1,"-(a^3*(a + b*x^2)^9)/(18*b^4) + (3*a^2*(a + b*x^2)^10)/(20*b^4) - (3*a*(a + b*x^2)^11)/(22*b^4) + (a + b*x^2)^12/(24*b^4)","A",3,2,13,0.1538,1,"{266, 43}"
89,1,53,0,0.0839906,"\int x^5 \left(a+b x^2\right)^8 \, dx","Int[x^5*(a + b*x^2)^8,x]","\frac{a^2 \left(a+b x^2\right)^9}{18 b^3}+\frac{\left(a+b x^2\right)^{11}}{22 b^3}-\frac{a \left(a+b x^2\right)^{10}}{10 b^3}","\frac{a^2 \left(a+b x^2\right)^9}{18 b^3}+\frac{\left(a+b x^2\right)^{11}}{22 b^3}-\frac{a \left(a+b x^2\right)^{10}}{10 b^3}",1,"(a^2*(a + b*x^2)^9)/(18*b^3) - (a*(a + b*x^2)^10)/(10*b^3) + (a + b*x^2)^11/(22*b^3)","A",3,2,13,0.1538,1,"{266, 43}"
90,1,34,0,0.0456613,"\int x^3 \left(a+b x^2\right)^8 \, dx","Int[x^3*(a + b*x^2)^8,x]","\frac{\left(a+b x^2\right)^{10}}{20 b^2}-\frac{a \left(a+b x^2\right)^9}{18 b^2}","\frac{\left(a+b x^2\right)^{10}}{20 b^2}-\frac{a \left(a+b x^2\right)^9}{18 b^2}",1,"-(a*(a + b*x^2)^9)/(18*b^2) + (a + b*x^2)^10/(20*b^2)","A",3,2,13,0.1538,1,"{266, 43}"
91,1,16,0,0.0023727,"\int x \left(a+b x^2\right)^8 \, dx","Int[x*(a + b*x^2)^8,x]","\frac{\left(a+b x^2\right)^9}{18 b}","\frac{\left(a+b x^2\right)^9}{18 b}",1,"(a + b*x^2)^9/(18*b)","A",1,1,11,0.09091,1,"{261}"
92,1,100,0,0.058515,"\int \frac{\left(a+b x^2\right)^8}{x} \, dx","Int[(a + b*x^2)^8/x,x]","\frac{7}{3} a^2 b^6 x^{12}+\frac{28}{5} a^3 b^5 x^{10}+\frac{35}{4} a^4 b^4 x^8+\frac{28}{3} a^5 b^3 x^6+7 a^6 b^2 x^4+4 a^7 b x^2+a^8 \log (x)+\frac{4}{7} a b^7 x^{14}+\frac{b^8 x^{16}}{16}","\frac{7}{3} a^2 b^6 x^{12}+\frac{28}{5} a^3 b^5 x^{10}+\frac{35}{4} a^4 b^4 x^8+\frac{28}{3} a^5 b^3 x^6+7 a^6 b^2 x^4+4 a^7 b x^2+a^8 \log (x)+\frac{4}{7} a b^7 x^{14}+\frac{b^8 x^{16}}{16}",1,"4*a^7*b*x^2 + 7*a^6*b^2*x^4 + (28*a^5*b^3*x^6)/3 + (35*a^4*b^4*x^8)/4 + (28*a^3*b^5*x^10)/5 + (7*a^2*b^6*x^12)/3 + (4*a*b^7*x^14)/7 + (b^8*x^16)/16 + a^8*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
93,1,99,0,0.0599015,"\int \frac{\left(a+b x^2\right)^8}{x^3} \, dx","Int[(a + b*x^2)^8/x^3,x]","\frac{14}{5} a^2 b^6 x^{10}+7 a^3 b^5 x^8+\frac{35}{3} a^4 b^4 x^6+14 a^5 b^3 x^4+14 a^6 b^2 x^2+8 a^7 b \log (x)-\frac{a^8}{2 x^2}+\frac{2}{3} a b^7 x^{12}+\frac{b^8 x^{14}}{14}","\frac{14}{5} a^2 b^6 x^{10}+7 a^3 b^5 x^8+\frac{35}{3} a^4 b^4 x^6+14 a^5 b^3 x^4+14 a^6 b^2 x^2+8 a^7 b \log (x)-\frac{a^8}{2 x^2}+\frac{2}{3} a b^7 x^{12}+\frac{b^8 x^{14}}{14}",1,"-a^8/(2*x^2) + 14*a^6*b^2*x^2 + 14*a^5*b^3*x^4 + (35*a^4*b^4*x^6)/3 + 7*a^3*b^5*x^8 + (14*a^2*b^6*x^10)/5 + (2*a*b^7*x^12)/3 + (b^8*x^14)/14 + 8*a^7*b*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
94,1,101,0,0.061354,"\int \frac{\left(a+b x^2\right)^8}{x^5} \, dx","Int[(a + b*x^2)^8/x^5,x]","\frac{7}{2} a^2 b^6 x^8+\frac{28}{3} a^3 b^5 x^6+\frac{35}{2} a^4 b^4 x^4+28 a^5 b^3 x^2+28 a^6 b^2 \log (x)-\frac{4 a^7 b}{x^2}-\frac{a^8}{4 x^4}+\frac{4}{5} a b^7 x^{10}+\frac{b^8 x^{12}}{12}","\frac{7}{2} a^2 b^6 x^8+\frac{28}{3} a^3 b^5 x^6+\frac{35}{2} a^4 b^4 x^4+28 a^5 b^3 x^2+28 a^6 b^2 \log (x)-\frac{4 a^7 b}{x^2}-\frac{a^8}{4 x^4}+\frac{4}{5} a b^7 x^{10}+\frac{b^8 x^{12}}{12}",1,"-a^8/(4*x^4) - (4*a^7*b)/x^2 + 28*a^5*b^3*x^2 + (35*a^4*b^4*x^4)/2 + (28*a^3*b^5*x^6)/3 + (7*a^2*b^6*x^8)/2 + (4*a*b^7*x^10)/5 + (b^8*x^12)/12 + 28*a^6*b^2*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
95,1,94,0,0.0570915,"\int \frac{\left(a+b x^2\right)^8}{x^7} \, dx","Int[(a + b*x^2)^8/x^7,x]","\frac{14}{3} a^2 b^6 x^6+14 a^3 b^5 x^4+35 a^4 b^4 x^2-\frac{14 a^6 b^2}{x^2}+56 a^5 b^3 \log (x)-\frac{2 a^7 b}{x^4}-\frac{a^8}{6 x^6}+a b^7 x^8+\frac{b^8 x^{10}}{10}","\frac{14}{3} a^2 b^6 x^6+14 a^3 b^5 x^4+35 a^4 b^4 x^2-\frac{14 a^6 b^2}{x^2}+56 a^5 b^3 \log (x)-\frac{2 a^7 b}{x^4}-\frac{a^8}{6 x^6}+a b^7 x^8+\frac{b^8 x^{10}}{10}",1,"-a^8/(6*x^6) - (2*a^7*b)/x^4 - (14*a^6*b^2)/x^2 + 35*a^4*b^4*x^2 + 14*a^3*b^5*x^4 + (14*a^2*b^6*x^6)/3 + a*b^7*x^8 + (b^8*x^10)/10 + 56*a^5*b^3*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
96,1,97,0,0.0568999,"\int \frac{\left(a+b x^2\right)^8}{x^9} \, dx","Int[(a + b*x^2)^8/x^9,x]","-\frac{7 a^6 b^2}{x^4}-\frac{28 a^5 b^3}{x^2}+28 a^3 b^5 x^2+7 a^2 b^6 x^4+70 a^4 b^4 \log (x)-\frac{4 a^7 b}{3 x^6}-\frac{a^8}{8 x^8}+\frac{4}{3} a b^7 x^6+\frac{b^8 x^8}{8}","-\frac{7 a^6 b^2}{x^4}-\frac{28 a^5 b^3}{x^2}+28 a^3 b^5 x^2+7 a^2 b^6 x^4+70 a^4 b^4 \log (x)-\frac{4 a^7 b}{3 x^6}-\frac{a^8}{8 x^8}+\frac{4}{3} a b^7 x^6+\frac{b^8 x^8}{8}",1,"-a^8/(8*x^8) - (4*a^7*b)/(3*x^6) - (7*a^6*b^2)/x^4 - (28*a^5*b^3)/x^2 + 28*a^3*b^5*x^2 + 7*a^2*b^6*x^4 + (4*a*b^7*x^6)/3 + (b^8*x^8)/8 + 70*a^4*b^4*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
97,1,95,0,0.0582053,"\int \frac{\left(a+b x^2\right)^8}{x^{11}} \, dx","Int[(a + b*x^2)^8/x^11,x]","-\frac{14 a^6 b^2}{3 x^6}-\frac{14 a^5 b^3}{x^4}-\frac{35 a^4 b^4}{x^2}+14 a^2 b^6 x^2+56 a^3 b^5 \log (x)-\frac{a^7 b}{x^8}-\frac{a^8}{10 x^{10}}+2 a b^7 x^4+\frac{b^8 x^6}{6}","-\frac{14 a^6 b^2}{3 x^6}-\frac{14 a^5 b^3}{x^4}-\frac{35 a^4 b^4}{x^2}+14 a^2 b^6 x^2+56 a^3 b^5 \log (x)-\frac{a^7 b}{x^8}-\frac{a^8}{10 x^{10}}+2 a b^7 x^4+\frac{b^8 x^6}{6}",1,"-a^8/(10*x^10) - (a^7*b)/x^8 - (14*a^6*b^2)/(3*x^6) - (14*a^5*b^3)/x^4 - (35*a^4*b^4)/x^2 + 14*a^2*b^6*x^2 + 2*a*b^7*x^4 + (b^8*x^6)/6 + 56*a^3*b^5*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
98,1,101,0,0.0536426,"\int \frac{\left(a+b x^2\right)^8}{x^{13}} \, dx","Int[(a + b*x^2)^8/x^13,x]","-\frac{7 a^6 b^2}{2 x^8}-\frac{28 a^5 b^3}{3 x^6}-\frac{35 a^4 b^4}{2 x^4}-\frac{28 a^3 b^5}{x^2}+28 a^2 b^6 \log (x)-\frac{4 a^7 b}{5 x^{10}}-\frac{a^8}{12 x^{12}}+4 a b^7 x^2+\frac{b^8 x^4}{4}","-\frac{7 a^6 b^2}{2 x^8}-\frac{28 a^5 b^3}{3 x^6}-\frac{35 a^4 b^4}{2 x^4}-\frac{28 a^3 b^5}{x^2}+28 a^2 b^6 \log (x)-\frac{4 a^7 b}{5 x^{10}}-\frac{a^8}{12 x^{12}}+4 a b^7 x^2+\frac{b^8 x^4}{4}",1,"-a^8/(12*x^12) - (4*a^7*b)/(5*x^10) - (7*a^6*b^2)/(2*x^8) - (28*a^5*b^3)/(3*x^6) - (35*a^4*b^4)/(2*x^4) - (28*a^3*b^5)/x^2 + 4*a*b^7*x^2 + (b^8*x^4)/4 + 28*a^2*b^6*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
99,1,99,0,0.0514795,"\int \frac{\left(a+b x^2\right)^8}{x^{15}} \, dx","Int[(a + b*x^2)^8/x^15,x]","-\frac{14 a^6 b^2}{5 x^{10}}-\frac{7 a^5 b^3}{x^8}-\frac{35 a^4 b^4}{3 x^6}-\frac{14 a^3 b^5}{x^4}-\frac{14 a^2 b^6}{x^2}-\frac{2 a^7 b}{3 x^{12}}-\frac{a^8}{14 x^{14}}+8 a b^7 \log (x)+\frac{b^8 x^2}{2}","-\frac{14 a^6 b^2}{5 x^{10}}-\frac{7 a^5 b^3}{x^8}-\frac{35 a^4 b^4}{3 x^6}-\frac{14 a^3 b^5}{x^4}-\frac{14 a^2 b^6}{x^2}-\frac{2 a^7 b}{3 x^{12}}-\frac{a^8}{14 x^{14}}+8 a b^7 \log (x)+\frac{b^8 x^2}{2}",1,"-a^8/(14*x^14) - (2*a^7*b)/(3*x^12) - (14*a^6*b^2)/(5*x^10) - (7*a^5*b^3)/x^8 - (35*a^4*b^4)/(3*x^6) - (14*a^3*b^5)/x^4 - (14*a^2*b^6)/x^2 + (b^8*x^2)/2 + 8*a*b^7*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
100,1,100,0,0.0540685,"\int \frac{\left(a+b x^2\right)^8}{x^{17}} \, dx","Int[(a + b*x^2)^8/x^17,x]","-\frac{7 a^6 b^2}{3 x^{12}}-\frac{28 a^5 b^3}{5 x^{10}}-\frac{35 a^4 b^4}{4 x^8}-\frac{28 a^3 b^5}{3 x^6}-\frac{7 a^2 b^6}{x^4}-\frac{4 a^7 b}{7 x^{14}}-\frac{a^8}{16 x^{16}}-\frac{4 a b^7}{x^2}+b^8 \log (x)","-\frac{7 a^6 b^2}{3 x^{12}}-\frac{28 a^5 b^3}{5 x^{10}}-\frac{35 a^4 b^4}{4 x^8}-\frac{28 a^3 b^5}{3 x^6}-\frac{7 a^2 b^6}{x^4}-\frac{4 a^7 b}{7 x^{14}}-\frac{a^8}{16 x^{16}}-\frac{4 a b^7}{x^2}+b^8 \log (x)",1,"-a^8/(16*x^16) - (4*a^7*b)/(7*x^14) - (7*a^6*b^2)/(3*x^12) - (28*a^5*b^3)/(5*x^10) - (35*a^4*b^4)/(4*x^8) - (28*a^3*b^5)/(3*x^6) - (7*a^2*b^6)/x^4 - (4*a*b^7)/x^2 + b^8*Log[x]","A",3,2,13,0.1538,1,"{266, 43}"
101,1,19,0,0.0031426,"\int \frac{\left(a+b x^2\right)^8}{x^{19}} \, dx","Int[(a + b*x^2)^8/x^19,x]","-\frac{\left(a+b x^2\right)^9}{18 a x^{18}}","-\frac{\left(a+b x^2\right)^9}{18 a x^{18}}",1,"-(a + b*x^2)^9/(18*a*x^18)","A",1,1,13,0.07692,1,"{264}"
102,1,40,0,0.0170586,"\int \frac{\left(a+b x^2\right)^8}{x^{21}} \, dx","Int[(a + b*x^2)^8/x^21,x]","\frac{b \left(a+b x^2\right)^9}{180 a^2 x^{18}}-\frac{\left(a+b x^2\right)^9}{20 a x^{20}}","\frac{b \left(a+b x^2\right)^9}{180 a^2 x^{18}}-\frac{\left(a+b x^2\right)^9}{20 a x^{20}}",1,"-(a + b*x^2)^9/(20*a*x^20) + (b*(a + b*x^2)^9)/(180*a^2*x^18)","A",3,3,13,0.2308,1,"{266, 45, 37}"
103,1,62,0,0.0290133,"\int \frac{\left(a+b x^2\right)^8}{x^{23}} \, dx","Int[(a + b*x^2)^8/x^23,x]","-\frac{b^2 \left(a+b x^2\right)^9}{990 a^3 x^{18}}+\frac{b \left(a+b x^2\right)^9}{110 a^2 x^{20}}-\frac{\left(a+b x^2\right)^9}{22 a x^{22}}","-\frac{b^2 \left(a+b x^2\right)^9}{990 a^3 x^{18}}+\frac{b \left(a+b x^2\right)^9}{110 a^2 x^{20}}-\frac{\left(a+b x^2\right)^9}{22 a x^{22}}",1,"-(a + b*x^2)^9/(22*a*x^22) + (b*(a + b*x^2)^9)/(110*a^2*x^20) - (b^2*(a + b*x^2)^9)/(990*a^3*x^18)","A",4,3,13,0.2308,1,"{266, 45, 37}"
104,1,84,0,0.0414562,"\int \frac{\left(a+b x^2\right)^8}{x^{25}} \, dx","Int[(a + b*x^2)^8/x^25,x]","\frac{b^3 \left(a+b x^2\right)^9}{3960 a^4 x^{18}}-\frac{b^2 \left(a+b x^2\right)^9}{440 a^3 x^{20}}+\frac{b \left(a+b x^2\right)^9}{88 a^2 x^{22}}-\frac{\left(a+b x^2\right)^9}{24 a x^{24}}","\frac{b^3 \left(a+b x^2\right)^9}{3960 a^4 x^{18}}-\frac{b^2 \left(a+b x^2\right)^9}{440 a^3 x^{20}}+\frac{b \left(a+b x^2\right)^9}{88 a^2 x^{22}}-\frac{\left(a+b x^2\right)^9}{24 a x^{24}}",1,"-(a + b*x^2)^9/(24*a*x^24) + (b*(a + b*x^2)^9)/(88*a^2*x^22) - (b^2*(a + b*x^2)^9)/(440*a^3*x^20) + (b^3*(a + b*x^2)^9)/(3960*a^4*x^18)","A",5,3,13,0.2308,1,"{266, 45, 37}"
105,1,106,0,0.054699,"\int \frac{\left(a+b x^2\right)^8}{x^{27}} \, dx","Int[(a + b*x^2)^8/x^27,x]","-\frac{b^4 \left(a+b x^2\right)^9}{12870 a^5 x^{18}}+\frac{b^3 \left(a+b x^2\right)^9}{1430 a^4 x^{20}}-\frac{b^2 \left(a+b x^2\right)^9}{286 a^3 x^{22}}+\frac{b \left(a+b x^2\right)^9}{78 a^2 x^{24}}-\frac{\left(a+b x^2\right)^9}{26 a x^{26}}","-\frac{b^4 \left(a+b x^2\right)^9}{12870 a^5 x^{18}}+\frac{b^3 \left(a+b x^2\right)^9}{1430 a^4 x^{20}}-\frac{b^2 \left(a+b x^2\right)^9}{286 a^3 x^{22}}+\frac{b \left(a+b x^2\right)^9}{78 a^2 x^{24}}-\frac{\left(a+b x^2\right)^9}{26 a x^{26}}",1,"-(a + b*x^2)^9/(26*a*x^26) + (b*(a + b*x^2)^9)/(78*a^2*x^24) - (b^2*(a + b*x^2)^9)/(286*a^3*x^22) + (b^3*(a + b*x^2)^9)/(1430*a^4*x^20) - (b^4*(a + b*x^2)^9)/(12870*a^5*x^18)","A",6,3,13,0.2308,1,"{266, 45, 37}"
106,1,108,0,0.0536761,"\int \frac{\left(a+b x^2\right)^8}{x^{29}} \, dx","Int[(a + b*x^2)^8/x^29,x]","-\frac{7 a^6 b^2}{6 x^{24}}-\frac{28 a^5 b^3}{11 x^{22}}-\frac{7 a^4 b^4}{2 x^{20}}-\frac{28 a^3 b^5}{9 x^{18}}-\frac{7 a^2 b^6}{4 x^{16}}-\frac{4 a^7 b}{13 x^{26}}-\frac{a^8}{28 x^{28}}-\frac{4 a b^7}{7 x^{14}}-\frac{b^8}{12 x^{12}}","-\frac{7 a^6 b^2}{6 x^{24}}-\frac{28 a^5 b^3}{11 x^{22}}-\frac{7 a^4 b^4}{2 x^{20}}-\frac{28 a^3 b^5}{9 x^{18}}-\frac{7 a^2 b^6}{4 x^{16}}-\frac{4 a^7 b}{13 x^{26}}-\frac{a^8}{28 x^{28}}-\frac{4 a b^7}{7 x^{14}}-\frac{b^8}{12 x^{12}}",1,"-a^8/(28*x^28) - (4*a^7*b)/(13*x^26) - (7*a^6*b^2)/(6*x^24) - (28*a^5*b^3)/(11*x^22) - (7*a^4*b^4)/(2*x^20) - (28*a^3*b^5)/(9*x^18) - (7*a^2*b^6)/(4*x^16) - (4*a*b^7)/(7*x^14) - b^8/(12*x^12)","A",3,2,13,0.1538,1,"{266, 43}"
107,1,108,0,0.0522581,"\int \frac{\left(a+b x^2\right)^8}{x^{31}} \, dx","Int[(a + b*x^2)^8/x^31,x]","-\frac{14 a^6 b^2}{13 x^{26}}-\frac{7 a^5 b^3}{3 x^{24}}-\frac{35 a^4 b^4}{11 x^{22}}-\frac{14 a^3 b^5}{5 x^{20}}-\frac{14 a^2 b^6}{9 x^{18}}-\frac{2 a^7 b}{7 x^{28}}-\frac{a^8}{30 x^{30}}-\frac{a b^7}{2 x^{16}}-\frac{b^8}{14 x^{14}}","-\frac{14 a^6 b^2}{13 x^{26}}-\frac{7 a^5 b^3}{3 x^{24}}-\frac{35 a^4 b^4}{11 x^{22}}-\frac{14 a^3 b^5}{5 x^{20}}-\frac{14 a^2 b^6}{9 x^{18}}-\frac{2 a^7 b}{7 x^{28}}-\frac{a^8}{30 x^{30}}-\frac{a b^7}{2 x^{16}}-\frac{b^8}{14 x^{14}}",1,"-a^8/(30*x^30) - (2*a^7*b)/(7*x^28) - (14*a^6*b^2)/(13*x^26) - (7*a^5*b^3)/(3*x^24) - (35*a^4*b^4)/(11*x^22) - (14*a^3*b^5)/(5*x^20) - (14*a^2*b^6)/(9*x^18) - (a*b^7)/(2*x^16) - b^8/(14*x^14)","A",3,2,13,0.1538,1,"{266, 43}"
108,1,106,0,0.0517498,"\int \frac{\left(a+b x^2\right)^8}{x^{33}} \, dx","Int[(a + b*x^2)^8/x^33,x]","-\frac{a^6 b^2}{x^{28}}-\frac{28 a^5 b^3}{13 x^{26}}-\frac{35 a^4 b^4}{12 x^{24}}-\frac{28 a^3 b^5}{11 x^{22}}-\frac{7 a^2 b^6}{5 x^{20}}-\frac{4 a^7 b}{15 x^{30}}-\frac{a^8}{32 x^{32}}-\frac{4 a b^7}{9 x^{18}}-\frac{b^8}{16 x^{16}}","-\frac{a^6 b^2}{x^{28}}-\frac{28 a^5 b^3}{13 x^{26}}-\frac{35 a^4 b^4}{12 x^{24}}-\frac{28 a^3 b^5}{11 x^{22}}-\frac{7 a^2 b^6}{5 x^{20}}-\frac{4 a^7 b}{15 x^{30}}-\frac{a^8}{32 x^{32}}-\frac{4 a b^7}{9 x^{18}}-\frac{b^8}{16 x^{16}}",1,"-a^8/(32*x^32) - (4*a^7*b)/(15*x^30) - (a^6*b^2)/x^28 - (28*a^5*b^3)/(13*x^26) - (35*a^4*b^4)/(12*x^24) - (28*a^3*b^5)/(11*x^22) - (7*a^2*b^6)/(5*x^20) - (4*a*b^7)/(9*x^18) - b^8/(16*x^16)","A",3,2,13,0.1538,1,"{266, 43}"
109,1,108,0,0.0481737,"\int x^8 \left(a+b x^2\right)^8 \, dx","Int[x^8*(a + b*x^2)^8,x]","\frac{4}{3} a^2 b^6 x^{21}+\frac{56}{19} a^3 b^5 x^{19}+\frac{70}{17} a^4 b^4 x^{17}+\frac{56}{15} a^5 b^3 x^{15}+\frac{28}{13} a^6 b^2 x^{13}+\frac{8}{11} a^7 b x^{11}+\frac{a^8 x^9}{9}+\frac{8}{23} a b^7 x^{23}+\frac{b^8 x^{25}}{25}","\frac{4}{3} a^2 b^6 x^{21}+\frac{56}{19} a^3 b^5 x^{19}+\frac{70}{17} a^4 b^4 x^{17}+\frac{56}{15} a^5 b^3 x^{15}+\frac{28}{13} a^6 b^2 x^{13}+\frac{8}{11} a^7 b x^{11}+\frac{a^8 x^9}{9}+\frac{8}{23} a b^7 x^{23}+\frac{b^8 x^{25}}{25}",1,"(a^8*x^9)/9 + (8*a^7*b*x^11)/11 + (28*a^6*b^2*x^13)/13 + (56*a^5*b^3*x^15)/15 + (70*a^4*b^4*x^17)/17 + (56*a^3*b^5*x^19)/19 + (4*a^2*b^6*x^21)/3 + (8*a*b^7*x^23)/23 + (b^8*x^25)/25","A",2,1,13,0.07692,1,"{270}"
110,1,108,0,0.0390258,"\int x^6 \left(a+b x^2\right)^8 \, dx","Int[x^6*(a + b*x^2)^8,x]","\frac{28}{19} a^2 b^6 x^{19}+\frac{56}{17} a^3 b^5 x^{17}+\frac{14}{3} a^4 b^4 x^{15}+\frac{56}{13} a^5 b^3 x^{13}+\frac{28}{11} a^6 b^2 x^{11}+\frac{8}{9} a^7 b x^9+\frac{a^8 x^7}{7}+\frac{8}{21} a b^7 x^{21}+\frac{b^8 x^{23}}{23}","\frac{28}{19} a^2 b^6 x^{19}+\frac{56}{17} a^3 b^5 x^{17}+\frac{14}{3} a^4 b^4 x^{15}+\frac{56}{13} a^5 b^3 x^{13}+\frac{28}{11} a^6 b^2 x^{11}+\frac{8}{9} a^7 b x^9+\frac{a^8 x^7}{7}+\frac{8}{21} a b^7 x^{21}+\frac{b^8 x^{23}}{23}",1,"(a^8*x^7)/7 + (8*a^7*b*x^9)/9 + (28*a^6*b^2*x^11)/11 + (56*a^5*b^3*x^13)/13 + (14*a^4*b^4*x^15)/3 + (56*a^3*b^5*x^17)/17 + (28*a^2*b^6*x^19)/19 + (8*a*b^7*x^21)/21 + (b^8*x^23)/23","A",2,1,13,0.07692,1,"{270}"
111,1,108,0,0.039408,"\int x^4 \left(a+b x^2\right)^8 \, dx","Int[x^4*(a + b*x^2)^8,x]","\frac{28}{17} a^2 b^6 x^{17}+\frac{56}{15} a^3 b^5 x^{15}+\frac{70}{13} a^4 b^4 x^{13}+\frac{56}{11} a^5 b^3 x^{11}+\frac{28}{9} a^6 b^2 x^9+\frac{8}{7} a^7 b x^7+\frac{a^8 x^5}{5}+\frac{8}{19} a b^7 x^{19}+\frac{b^8 x^{21}}{21}","\frac{28}{17} a^2 b^6 x^{17}+\frac{56}{15} a^3 b^5 x^{15}+\frac{70}{13} a^4 b^4 x^{13}+\frac{56}{11} a^5 b^3 x^{11}+\frac{28}{9} a^6 b^2 x^9+\frac{8}{7} a^7 b x^7+\frac{a^8 x^5}{5}+\frac{8}{19} a b^7 x^{19}+\frac{b^8 x^{21}}{21}",1,"(a^8*x^5)/5 + (8*a^7*b*x^7)/7 + (28*a^6*b^2*x^9)/9 + (56*a^5*b^3*x^11)/11 + (70*a^4*b^4*x^13)/13 + (56*a^3*b^5*x^15)/15 + (28*a^2*b^6*x^17)/17 + (8*a*b^7*x^19)/19 + (b^8*x^21)/21","A",2,1,13,0.07692,1,"{270}"
112,1,106,0,0.0402238,"\int x^2 \left(a+b x^2\right)^8 \, dx","Int[x^2*(a + b*x^2)^8,x]","\frac{28}{15} a^2 b^6 x^{15}+\frac{56}{13} a^3 b^5 x^{13}+\frac{70}{11} a^4 b^4 x^{11}+\frac{56}{9} a^5 b^3 x^9+4 a^6 b^2 x^7+\frac{8}{5} a^7 b x^5+\frac{a^8 x^3}{3}+\frac{8}{17} a b^7 x^{17}+\frac{b^8 x^{19}}{19}","\frac{28}{15} a^2 b^6 x^{15}+\frac{56}{13} a^3 b^5 x^{13}+\frac{70}{11} a^4 b^4 x^{11}+\frac{56}{9} a^5 b^3 x^9+4 a^6 b^2 x^7+\frac{8}{5} a^7 b x^5+\frac{a^8 x^3}{3}+\frac{8}{17} a b^7 x^{17}+\frac{b^8 x^{19}}{19}",1,"(a^8*x^3)/3 + (8*a^7*b*x^5)/5 + 4*a^6*b^2*x^7 + (56*a^5*b^3*x^9)/9 + (70*a^4*b^4*x^11)/11 + (56*a^3*b^5*x^13)/13 + (28*a^2*b^6*x^15)/15 + (8*a*b^7*x^17)/17 + (b^8*x^19)/19","A",2,1,13,0.07692,1,"{270}"
113,1,101,0,0.0373987,"\int \left(a+b x^2\right)^8 \, dx","Int[(a + b*x^2)^8,x]","\frac{28}{13} a^2 b^6 x^{13}+\frac{56}{11} a^3 b^5 x^{11}+\frac{70}{9} a^4 b^4 x^9+8 a^5 b^3 x^7+\frac{28}{5} a^6 b^2 x^5+\frac{8}{3} a^7 b x^3+a^8 x+\frac{8}{15} a b^7 x^{15}+\frac{b^8 x^{17}}{17}","\frac{28}{13} a^2 b^6 x^{13}+\frac{56}{11} a^3 b^5 x^{11}+\frac{70}{9} a^4 b^4 x^9+8 a^5 b^3 x^7+\frac{28}{5} a^6 b^2 x^5+\frac{8}{3} a^7 b x^3+a^8 x+\frac{8}{15} a b^7 x^{15}+\frac{b^8 x^{17}}{17}",1,"a^8*x + (8*a^7*b*x^3)/3 + (28*a^6*b^2*x^5)/5 + 8*a^5*b^3*x^7 + (70*a^4*b^4*x^9)/9 + (56*a^3*b^5*x^11)/11 + (28*a^2*b^6*x^13)/13 + (8*a*b^7*x^15)/15 + (b^8*x^17)/17","A",2,1,9,0.1111,1,"{194}"
114,1,100,0,0.0386043,"\int \frac{\left(a+b x^2\right)^8}{x^2} \, dx","Int[(a + b*x^2)^8/x^2,x]","\frac{28}{11} a^2 b^6 x^{11}+\frac{56}{9} a^3 b^5 x^9+10 a^4 b^4 x^7+\frac{56}{5} a^5 b^3 x^5+\frac{28}{3} a^6 b^2 x^3+8 a^7 b x-\frac{a^8}{x}+\frac{8}{13} a b^7 x^{13}+\frac{b^8 x^{15}}{15}","\frac{28}{11} a^2 b^6 x^{11}+\frac{56}{9} a^3 b^5 x^9+10 a^4 b^4 x^7+\frac{56}{5} a^5 b^3 x^5+\frac{28}{3} a^6 b^2 x^3+8 a^7 b x-\frac{a^8}{x}+\frac{8}{13} a b^7 x^{13}+\frac{b^8 x^{15}}{15}",1,"-(a^8/x) + 8*a^7*b*x + (28*a^6*b^2*x^3)/3 + (56*a^5*b^3*x^5)/5 + 10*a^4*b^4*x^7 + (56*a^3*b^5*x^9)/9 + (28*a^2*b^6*x^11)/11 + (8*a*b^7*x^13)/13 + (b^8*x^15)/15","A",2,1,13,0.07692,1,"{270}"
115,1,98,0,0.0379941,"\int \frac{\left(a+b x^2\right)^8}{x^4} \, dx","Int[(a + b*x^2)^8/x^4,x]","\frac{28}{9} a^2 b^6 x^9+8 a^3 b^5 x^7+14 a^4 b^4 x^5+\frac{56}{3} a^5 b^3 x^3+28 a^6 b^2 x-\frac{8 a^7 b}{x}-\frac{a^8}{3 x^3}+\frac{8}{11} a b^7 x^{11}+\frac{b^8 x^{13}}{13}","\frac{28}{9} a^2 b^6 x^9+8 a^3 b^5 x^7+14 a^4 b^4 x^5+\frac{56}{3} a^5 b^3 x^3+28 a^6 b^2 x-\frac{8 a^7 b}{x}-\frac{a^8}{3 x^3}+\frac{8}{11} a b^7 x^{11}+\frac{b^8 x^{13}}{13}",1,"-a^8/(3*x^3) - (8*a^7*b)/x + 28*a^6*b^2*x + (56*a^5*b^3*x^3)/3 + 14*a^4*b^4*x^5 + 8*a^3*b^5*x^7 + (28*a^2*b^6*x^9)/9 + (8*a*b^7*x^11)/11 + (b^8*x^13)/13","A",2,1,13,0.07692,1,"{270}"
116,1,100,0,0.0390975,"\int \frac{\left(a+b x^2\right)^8}{x^6} \, dx","Int[(a + b*x^2)^8/x^6,x]","4 a^2 b^6 x^7+\frac{56}{5} a^3 b^5 x^5+\frac{70}{3} a^4 b^4 x^3+56 a^5 b^3 x-\frac{28 a^6 b^2}{x}-\frac{8 a^7 b}{3 x^3}-\frac{a^8}{5 x^5}+\frac{8}{9} a b^7 x^9+\frac{b^8 x^{11}}{11}","4 a^2 b^6 x^7+\frac{56}{5} a^3 b^5 x^5+\frac{70}{3} a^4 b^4 x^3+56 a^5 b^3 x-\frac{28 a^6 b^2}{x}-\frac{8 a^7 b}{3 x^3}-\frac{a^8}{5 x^5}+\frac{8}{9} a b^7 x^9+\frac{b^8 x^{11}}{11}",1,"-a^8/(5*x^5) - (8*a^7*b)/(3*x^3) - (28*a^6*b^2)/x + 56*a^5*b^3*x + (70*a^4*b^4*x^3)/3 + (56*a^3*b^5*x^5)/5 + 4*a^2*b^6*x^7 + (8*a*b^7*x^9)/9 + (b^8*x^11)/11","A",2,1,13,0.07692,1,"{270}"
117,1,102,0,0.036847,"\int \frac{\left(a+b x^2\right)^8}{x^8} \, dx","Int[(a + b*x^2)^8/x^8,x]","\frac{28}{5} a^2 b^6 x^5+\frac{56}{3} a^3 b^5 x^3-\frac{28 a^6 b^2}{3 x^3}+70 a^4 b^4 x-\frac{56 a^5 b^3}{x}-\frac{8 a^7 b}{5 x^5}-\frac{a^8}{7 x^7}+\frac{8}{7} a b^7 x^7+\frac{b^8 x^9}{9}","\frac{28}{5} a^2 b^6 x^5+\frac{56}{3} a^3 b^5 x^3-\frac{28 a^6 b^2}{3 x^3}+70 a^4 b^4 x-\frac{56 a^5 b^3}{x}-\frac{8 a^7 b}{5 x^5}-\frac{a^8}{7 x^7}+\frac{8}{7} a b^7 x^7+\frac{b^8 x^9}{9}",1,"-a^8/(7*x^7) - (8*a^7*b)/(5*x^5) - (28*a^6*b^2)/(3*x^3) - (56*a^5*b^3)/x + 70*a^4*b^4*x + (56*a^3*b^5*x^3)/3 + (28*a^2*b^6*x^5)/5 + (8*a*b^7*x^7)/7 + (b^8*x^9)/9","A",2,1,13,0.07692,1,"{270}"
118,1,102,0,0.0390688,"\int \frac{\left(a+b x^2\right)^8}{x^{10}} \, dx","Int[(a + b*x^2)^8/x^10,x]","-\frac{28 a^6 b^2}{5 x^5}-\frac{56 a^5 b^3}{3 x^3}+\frac{28}{3} a^2 b^6 x^3-\frac{70 a^4 b^4}{x}+56 a^3 b^5 x-\frac{8 a^7 b}{7 x^7}-\frac{a^8}{9 x^9}+\frac{8}{5} a b^7 x^5+\frac{b^8 x^7}{7}","-\frac{28 a^6 b^2}{5 x^5}-\frac{56 a^5 b^3}{3 x^3}+\frac{28}{3} a^2 b^6 x^3-\frac{70 a^4 b^4}{x}+56 a^3 b^5 x-\frac{8 a^7 b}{7 x^7}-\frac{a^8}{9 x^9}+\frac{8}{5} a b^7 x^5+\frac{b^8 x^7}{7}",1,"-a^8/(9*x^9) - (8*a^7*b)/(7*x^7) - (28*a^6*b^2)/(5*x^5) - (56*a^5*b^3)/(3*x^3) - (70*a^4*b^4)/x + 56*a^3*b^5*x + (28*a^2*b^6*x^3)/3 + (8*a*b^7*x^5)/5 + (b^8*x^7)/7","A",2,1,13,0.07692,1,"{270}"
119,1,100,0,0.0398323,"\int \frac{\left(a+b x^2\right)^8}{x^{12}} \, dx","Int[(a + b*x^2)^8/x^12,x]","-\frac{4 a^6 b^2}{x^7}-\frac{56 a^5 b^3}{5 x^5}-\frac{70 a^4 b^4}{3 x^3}-\frac{56 a^3 b^5}{x}+28 a^2 b^6 x-\frac{8 a^7 b}{9 x^9}-\frac{a^8}{11 x^{11}}+\frac{8}{3} a b^7 x^3+\frac{b^8 x^5}{5}","-\frac{4 a^6 b^2}{x^7}-\frac{56 a^5 b^3}{5 x^5}-\frac{70 a^4 b^4}{3 x^3}-\frac{56 a^3 b^5}{x}+28 a^2 b^6 x-\frac{8 a^7 b}{9 x^9}-\frac{a^8}{11 x^{11}}+\frac{8}{3} a b^7 x^3+\frac{b^8 x^5}{5}",1,"-a^8/(11*x^11) - (8*a^7*b)/(9*x^9) - (4*a^6*b^2)/x^7 - (56*a^5*b^3)/(5*x^5) - (70*a^4*b^4)/(3*x^3) - (56*a^3*b^5)/x + 28*a^2*b^6*x + (8*a*b^7*x^3)/3 + (b^8*x^5)/5","A",2,1,13,0.07692,1,"{270}"
120,1,98,0,0.0377404,"\int \frac{\left(a+b x^2\right)^8}{x^{14}} \, dx","Int[(a + b*x^2)^8/x^14,x]","-\frac{28 a^6 b^2}{9 x^9}-\frac{8 a^5 b^3}{x^7}-\frac{14 a^4 b^4}{x^5}-\frac{56 a^3 b^5}{3 x^3}-\frac{28 a^2 b^6}{x}-\frac{8 a^7 b}{11 x^{11}}-\frac{a^8}{13 x^{13}}+8 a b^7 x+\frac{b^8 x^3}{3}","-\frac{28 a^6 b^2}{9 x^9}-\frac{8 a^5 b^3}{x^7}-\frac{14 a^4 b^4}{x^5}-\frac{56 a^3 b^5}{3 x^3}-\frac{28 a^2 b^6}{x}-\frac{8 a^7 b}{11 x^{11}}-\frac{a^8}{13 x^{13}}+8 a b^7 x+\frac{b^8 x^3}{3}",1,"-a^8/(13*x^13) - (8*a^7*b)/(11*x^11) - (28*a^6*b^2)/(9*x^9) - (8*a^5*b^3)/x^7 - (14*a^4*b^4)/x^5 - (56*a^3*b^5)/(3*x^3) - (28*a^2*b^6)/x + 8*a*b^7*x + (b^8*x^3)/3","A",2,1,13,0.07692,1,"{270}"
121,1,99,0,0.0393084,"\int \frac{\left(a+b x^2\right)^8}{x^{16}} \, dx","Int[(a + b*x^2)^8/x^16,x]","-\frac{28 a^6 b^2}{11 x^{11}}-\frac{56 a^5 b^3}{9 x^9}-\frac{10 a^4 b^4}{x^7}-\frac{56 a^3 b^5}{5 x^5}-\frac{28 a^2 b^6}{3 x^3}-\frac{8 a^7 b}{13 x^{13}}-\frac{a^8}{15 x^{15}}-\frac{8 a b^7}{x}+b^8 x","-\frac{28 a^6 b^2}{11 x^{11}}-\frac{56 a^5 b^3}{9 x^9}-\frac{10 a^4 b^4}{x^7}-\frac{56 a^3 b^5}{5 x^5}-\frac{28 a^2 b^6}{3 x^3}-\frac{8 a^7 b}{13 x^{13}}-\frac{a^8}{15 x^{15}}-\frac{8 a b^7}{x}+b^8 x",1,"-a^8/(15*x^15) - (8*a^7*b)/(13*x^13) - (28*a^6*b^2)/(11*x^11) - (56*a^5*b^3)/(9*x^9) - (10*a^4*b^4)/x^7 - (56*a^3*b^5)/(5*x^5) - (28*a^2*b^6)/(3*x^3) - (8*a*b^7)/x + b^8*x","A",2,1,13,0.07692,1,"{270}"
122,1,104,0,0.0393411,"\int \frac{\left(a+b x^2\right)^8}{x^{18}} \, dx","Int[(a + b*x^2)^8/x^18,x]","-\frac{28 a^6 b^2}{13 x^{13}}-\frac{56 a^5 b^3}{11 x^{11}}-\frac{70 a^4 b^4}{9 x^9}-\frac{8 a^3 b^5}{x^7}-\frac{28 a^2 b^6}{5 x^5}-\frac{8 a^7 b}{15 x^{15}}-\frac{a^8}{17 x^{17}}-\frac{8 a b^7}{3 x^3}-\frac{b^8}{x}","-\frac{28 a^6 b^2}{13 x^{13}}-\frac{56 a^5 b^3}{11 x^{11}}-\frac{70 a^4 b^4}{9 x^9}-\frac{8 a^3 b^5}{x^7}-\frac{28 a^2 b^6}{5 x^5}-\frac{8 a^7 b}{15 x^{15}}-\frac{a^8}{17 x^{17}}-\frac{8 a b^7}{3 x^3}-\frac{b^8}{x}",1,"-a^8/(17*x^17) - (8*a^7*b)/(15*x^15) - (28*a^6*b^2)/(13*x^13) - (56*a^5*b^3)/(11*x^11) - (70*a^4*b^4)/(9*x^9) - (8*a^3*b^5)/x^7 - (28*a^2*b^6)/(5*x^5) - (8*a*b^7)/(3*x^3) - b^8/x","A",2,1,13,0.07692,1,"{270}"
123,1,106,0,0.0395873,"\int \frac{\left(a+b x^2\right)^8}{x^{20}} \, dx","Int[(a + b*x^2)^8/x^20,x]","-\frac{28 a^6 b^2}{15 x^{15}}-\frac{56 a^5 b^3}{13 x^{13}}-\frac{70 a^4 b^4}{11 x^{11}}-\frac{56 a^3 b^5}{9 x^9}-\frac{4 a^2 b^6}{x^7}-\frac{8 a^7 b}{17 x^{17}}-\frac{a^8}{19 x^{19}}-\frac{8 a b^7}{5 x^5}-\frac{b^8}{3 x^3}","-\frac{28 a^6 b^2}{15 x^{15}}-\frac{56 a^5 b^3}{13 x^{13}}-\frac{70 a^4 b^4}{11 x^{11}}-\frac{56 a^3 b^5}{9 x^9}-\frac{4 a^2 b^6}{x^7}-\frac{8 a^7 b}{17 x^{17}}-\frac{a^8}{19 x^{19}}-\frac{8 a b^7}{5 x^5}-\frac{b^8}{3 x^3}",1,"-a^8/(19*x^19) - (8*a^7*b)/(17*x^17) - (28*a^6*b^2)/(15*x^15) - (56*a^5*b^3)/(13*x^13) - (70*a^4*b^4)/(11*x^11) - (56*a^3*b^5)/(9*x^9) - (4*a^2*b^6)/x^7 - (8*a*b^7)/(5*x^5) - b^8/(3*x^3)","A",2,1,13,0.07692,1,"{270}"
124,1,79,0,0.0558447,"\int \frac{x^{11}}{a+b x^2} \, dx","Int[x^11/(a + b*x^2),x]","\frac{a^2 x^6}{6 b^3}-\frac{a^3 x^4}{4 b^4}+\frac{a^4 x^2}{2 b^5}-\frac{a^5 \log \left(a+b x^2\right)}{2 b^6}-\frac{a x^8}{8 b^2}+\frac{x^{10}}{10 b}","\frac{a^2 x^6}{6 b^3}-\frac{a^3 x^4}{4 b^4}+\frac{a^4 x^2}{2 b^5}-\frac{a^5 \log \left(a+b x^2\right)}{2 b^6}-\frac{a x^8}{8 b^2}+\frac{x^{10}}{10 b}",1,"(a^4*x^2)/(2*b^5) - (a^3*x^4)/(4*b^4) + (a^2*x^6)/(6*b^3) - (a*x^8)/(8*b^2) + x^10/(10*b) - (a^5*Log[a + b*x^2])/(2*b^6)","A",3,2,13,0.1538,1,"{266, 43}"
125,1,81,0,0.0350131,"\int \frac{x^{10}}{a+b x^2} \, dx","Int[x^10/(a + b*x^2),x]","\frac{a^2 x^5}{5 b^3}-\frac{a^3 x^3}{3 b^4}+\frac{a^4 x}{b^5}-\frac{a^{9/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{11/2}}-\frac{a x^7}{7 b^2}+\frac{x^9}{9 b}","\frac{a^2 x^5}{5 b^3}-\frac{a^3 x^3}{3 b^4}+\frac{a^4 x}{b^5}-\frac{a^{9/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{11/2}}-\frac{a x^7}{7 b^2}+\frac{x^9}{9 b}",1,"(a^4*x)/b^5 - (a^3*x^3)/(3*b^4) + (a^2*x^5)/(5*b^3) - (a*x^7)/(7*b^2) + x^9/(9*b) - (a^(9/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/b^(11/2)","A",3,2,13,0.1538,1,"{302, 205}"
126,1,66,0,0.0443748,"\int \frac{x^9}{a+b x^2} \, dx","Int[x^9/(a + b*x^2),x]","\frac{a^2 x^4}{4 b^3}-\frac{a^3 x^2}{2 b^4}+\frac{a^4 \log \left(a+b x^2\right)}{2 b^5}-\frac{a x^6}{6 b^2}+\frac{x^8}{8 b}","\frac{a^2 x^4}{4 b^3}-\frac{a^3 x^2}{2 b^4}+\frac{a^4 \log \left(a+b x^2\right)}{2 b^5}-\frac{a x^6}{6 b^2}+\frac{x^8}{8 b}",1,"-(a^3*x^2)/(2*b^4) + (a^2*x^4)/(4*b^3) - (a*x^6)/(6*b^2) + x^8/(8*b) + (a^4*Log[a + b*x^2])/(2*b^5)","A",3,2,13,0.1538,1,"{266, 43}"
127,1,68,0,0.0295362,"\int \frac{x^8}{a+b x^2} \, dx","Int[x^8/(a + b*x^2),x]","\frac{a^2 x^3}{3 b^3}-\frac{a^3 x}{b^4}+\frac{a^{7/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{9/2}}-\frac{a x^5}{5 b^2}+\frac{x^7}{7 b}","\frac{a^2 x^3}{3 b^3}-\frac{a^3 x}{b^4}+\frac{a^{7/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{9/2}}-\frac{a x^5}{5 b^2}+\frac{x^7}{7 b}",1,"-((a^3*x)/b^4) + (a^2*x^3)/(3*b^3) - (a*x^5)/(5*b^2) + x^7/(7*b) + (a^(7/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/b^(9/2)","A",3,2,13,0.1538,1,"{302, 205}"
128,1,53,0,0.0350458,"\int \frac{x^7}{a+b x^2} \, dx","Int[x^7/(a + b*x^2),x]","\frac{a^2 x^2}{2 b^3}-\frac{a^3 \log \left(a+b x^2\right)}{2 b^4}-\frac{a x^4}{4 b^2}+\frac{x^6}{6 b}","\frac{a^2 x^2}{2 b^3}-\frac{a^3 \log \left(a+b x^2\right)}{2 b^4}-\frac{a x^4}{4 b^2}+\frac{x^6}{6 b}",1,"(a^2*x^2)/(2*b^3) - (a*x^4)/(4*b^2) + x^6/(6*b) - (a^3*Log[a + b*x^2])/(2*b^4)","A",3,2,13,0.1538,1,"{266, 43}"
129,1,55,0,0.0239212,"\int \frac{x^6}{a+b x^2} \, dx","Int[x^6/(a + b*x^2),x]","\frac{a^2 x}{b^3}-\frac{a^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{7/2}}-\frac{a x^3}{3 b^2}+\frac{x^5}{5 b}","\frac{a^2 x}{b^3}-\frac{a^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{7/2}}-\frac{a x^3}{3 b^2}+\frac{x^5}{5 b}",1,"(a^2*x)/b^3 - (a*x^3)/(3*b^2) + x^5/(5*b) - (a^(5/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/b^(7/2)","A",3,2,13,0.1538,1,"{302, 205}"
130,1,40,0,0.0267045,"\int \frac{x^5}{a+b x^2} \, dx","Int[x^5/(a + b*x^2),x]","\frac{a^2 \log \left(a+b x^2\right)}{2 b^3}-\frac{a x^2}{2 b^2}+\frac{x^4}{4 b}","\frac{a^2 \log \left(a+b x^2\right)}{2 b^3}-\frac{a x^2}{2 b^2}+\frac{x^4}{4 b}",1,"-(a*x^2)/(2*b^2) + x^4/(4*b) + (a^2*Log[a + b*x^2])/(2*b^3)","A",3,2,13,0.1538,1,"{266, 43}"
131,1,42,0,0.0198166,"\int \frac{x^4}{a+b x^2} \, dx","Int[x^4/(a + b*x^2),x]","\frac{a^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{5/2}}-\frac{a x}{b^2}+\frac{x^3}{3 b}","\frac{a^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{5/2}}-\frac{a x}{b^2}+\frac{x^3}{3 b}",1,"-((a*x)/b^2) + x^3/(3*b) + (a^(3/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/b^(5/2)","A",3,2,13,0.1538,1,"{302, 205}"
132,1,27,0,0.0176019,"\int \frac{x^3}{a+b x^2} \, dx","Int[x^3/(a + b*x^2),x]","\frac{x^2}{2 b}-\frac{a \log \left(a+b x^2\right)}{2 b^2}","\frac{x^2}{2 b}-\frac{a \log \left(a+b x^2\right)}{2 b^2}",1,"x^2/(2*b) - (a*Log[a + b*x^2])/(2*b^2)","A",3,2,13,0.1538,1,"{266, 43}"
133,1,31,0,0.0117742,"\int \frac{x^2}{a+b x^2} \, dx","Int[x^2/(a + b*x^2),x]","\frac{x}{b}-\frac{\sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{3/2}}","\frac{x}{b}-\frac{\sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{3/2}}",1,"x/b - (Sqrt[a]*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/b^(3/2)","A",2,2,13,0.1538,1,"{321, 205}"
134,1,15,0,0.0030103,"\int \frac{x}{a+b x^2} \, dx","Int[x/(a + b*x^2),x]","\frac{\log \left(a+b x^2\right)}{2 b}","\frac{\log \left(a+b x^2\right)}{2 b}",1,"Log[a + b*x^2]/(2*b)","A",1,1,11,0.09091,1,"{260}"
135,1,24,0,0.0050293,"\int \frac{1}{a+b x^2} \, dx","Int[(a + b*x^2)^(-1),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b}}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b}}",1,"ArcTan[(Sqrt[b]*x)/Sqrt[a]]/(Sqrt[a]*Sqrt[b])","A",1,1,9,0.1111,1,"{205}"
136,1,22,0,0.0109357,"\int \frac{1}{x \left(a+b x^2\right)} \, dx","Int[1/(x*(a + b*x^2)),x]","\frac{\log (x)}{a}-\frac{\log \left(a+b x^2\right)}{2 a}","\frac{\log (x)}{a}-\frac{\log \left(a+b x^2\right)}{2 a}",1,"Log[x]/a - Log[a + b*x^2]/(2*a)","A",4,4,13,0.3077,1,"{266, 36, 29, 31}"
137,1,34,0,0.0121051,"\int \frac{1}{x^2 \left(a+b x^2\right)} \, dx","Int[1/(x^2*(a + b*x^2)),x]","-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{3/2}}-\frac{1}{a x}","-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{3/2}}-\frac{1}{a x}",1,"-(1/(a*x)) - (Sqrt[b]*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/a^(3/2)","A",2,2,13,0.1538,1,"{325, 205}"
138,1,35,0,0.0222234,"\int \frac{1}{x^3 \left(a+b x^2\right)} \, dx","Int[1/(x^3*(a + b*x^2)),x]","\frac{b \log \left(a+b x^2\right)}{2 a^2}-\frac{b \log (x)}{a^2}-\frac{1}{2 a x^2}","\frac{b \log \left(a+b x^2\right)}{2 a^2}-\frac{b \log (x)}{a^2}-\frac{1}{2 a x^2}",1,"-1/(2*a*x^2) - (b*Log[x])/a^2 + (b*Log[a + b*x^2])/(2*a^2)","A",3,2,13,0.1538,1,"{266, 44}"
139,1,43,0,0.0172627,"\int \frac{1}{x^4 \left(a+b x^2\right)} \, dx","Int[1/(x^4*(a + b*x^2)),x]","\frac{b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{5/2}}+\frac{b}{a^2 x}-\frac{1}{3 a x^3}","\frac{b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{5/2}}+\frac{b}{a^2 x}-\frac{1}{3 a x^3}",1,"-1/(3*a*x^3) + b/(a^2*x) + (b^(3/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/a^(5/2)","A",3,2,13,0.1538,1,"{325, 205}"
140,1,49,0,0.0282816,"\int \frac{1}{x^5 \left(a+b x^2\right)} \, dx","Int[1/(x^5*(a + b*x^2)),x]","-\frac{b^2 \log \left(a+b x^2\right)}{2 a^3}+\frac{b^2 \log (x)}{a^3}+\frac{b}{2 a^2 x^2}-\frac{1}{4 a x^4}","-\frac{b^2 \log \left(a+b x^2\right)}{2 a^3}+\frac{b^2 \log (x)}{a^3}+\frac{b}{2 a^2 x^2}-\frac{1}{4 a x^4}",1,"-1/(4*a*x^4) + b/(2*a^2*x^2) + (b^2*Log[x])/a^3 - (b^2*Log[a + b*x^2])/(2*a^3)","A",3,2,13,0.1538,1,"{266, 44}"
141,1,58,0,0.0245379,"\int \frac{1}{x^6 \left(a+b x^2\right)} \, dx","Int[1/(x^6*(a + b*x^2)),x]","-\frac{b^2}{a^3 x}-\frac{b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{7/2}}+\frac{b}{3 a^2 x^3}-\frac{1}{5 a x^5}","-\frac{b^2}{a^3 x}-\frac{b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{7/2}}+\frac{b}{3 a^2 x^3}-\frac{1}{5 a x^5}",1,"-1/(5*a*x^5) + b/(3*a^2*x^3) - b^2/(a^3*x) - (b^(5/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/a^(7/2)","A",4,2,13,0.1538,1,"{325, 205}"
142,1,63,0,0.0346818,"\int \frac{1}{x^7 \left(a+b x^2\right)} \, dx","Int[1/(x^7*(a + b*x^2)),x]","-\frac{b^2}{2 a^3 x^2}+\frac{b^3 \log \left(a+b x^2\right)}{2 a^4}-\frac{b^3 \log (x)}{a^4}+\frac{b}{4 a^2 x^4}-\frac{1}{6 a x^6}","-\frac{b^2}{2 a^3 x^2}+\frac{b^3 \log \left(a+b x^2\right)}{2 a^4}-\frac{b^3 \log (x)}{a^4}+\frac{b}{4 a^2 x^4}-\frac{1}{6 a x^6}",1,"-1/(6*a*x^6) + b/(4*a^2*x^4) - b^2/(2*a^3*x^2) - (b^3*Log[x])/a^4 + (b^3*Log[a + b*x^2])/(2*a^4)","A",3,2,13,0.1538,1,"{266, 44}"
143,1,69,0,0.0346157,"\int \frac{1}{x^8 \left(a+b x^2\right)} \, dx","Int[1/(x^8*(a + b*x^2)),x]","-\frac{b^2}{3 a^3 x^3}+\frac{b^3}{a^4 x}+\frac{b^{7/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{9/2}}+\frac{b}{5 a^2 x^5}-\frac{1}{7 a x^7}","-\frac{b^2}{3 a^3 x^3}+\frac{b^3}{a^4 x}+\frac{b^{7/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{9/2}}+\frac{b}{5 a^2 x^5}-\frac{1}{7 a x^7}",1,"-1/(7*a*x^7) + b/(5*a^2*x^5) - b^2/(3*a^3*x^3) + b^3/(a^4*x) + (b^(7/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/a^(9/2)","A",5,2,13,0.1538,1,"{325, 205}"
144,1,75,0,0.0408999,"\int \frac{1}{x^9 \left(a+b x^2\right)} \, dx","Int[1/(x^9*(a + b*x^2)),x]","\frac{b^3}{2 a^4 x^2}-\frac{b^2}{4 a^3 x^4}-\frac{b^4 \log \left(a+b x^2\right)}{2 a^5}+\frac{b^4 \log (x)}{a^5}+\frac{b}{6 a^2 x^6}-\frac{1}{8 a x^8}","\frac{b^3}{2 a^4 x^2}-\frac{b^2}{4 a^3 x^4}-\frac{b^4 \log \left(a+b x^2\right)}{2 a^5}+\frac{b^4 \log (x)}{a^5}+\frac{b}{6 a^2 x^6}-\frac{1}{8 a x^8}",1,"-1/(8*a*x^8) + b/(6*a^2*x^6) - b^2/(4*a^3*x^4) + b^3/(2*a^4*x^2) + (b^4*Log[x])/a^5 - (b^4*Log[a + b*x^2])/(2*a^5)","A",3,2,13,0.1538,1,"{266, 44}"
145,1,94,0,0.0762538,"\int \frac{x^{13}}{\left(a+b x^2\right)^2} \, dx","Int[x^13/(a + b*x^2)^2,x]","\frac{a^2 x^6}{2 b^4}-\frac{a^3 x^4}{b^5}+\frac{5 a^4 x^2}{2 b^6}-\frac{a^6}{2 b^7 \left(a+b x^2\right)}-\frac{3 a^5 \log \left(a+b x^2\right)}{b^7}-\frac{a x^8}{4 b^3}+\frac{x^{10}}{10 b^2}","\frac{a^2 x^6}{2 b^4}-\frac{a^3 x^4}{b^5}+\frac{5 a^4 x^2}{2 b^6}-\frac{a^6}{2 b^7 \left(a+b x^2\right)}-\frac{3 a^5 \log \left(a+b x^2\right)}{b^7}-\frac{a x^8}{4 b^3}+\frac{x^{10}}{10 b^2}",1,"(5*a^4*x^2)/(2*b^6) - (a^3*x^4)/b^5 + (a^2*x^6)/(2*b^4) - (a*x^8)/(4*b^3) + x^10/(10*b^2) - a^6/(2*b^7*(a + b*x^2)) - (3*a^5*Log[a + b*x^2])/b^7","A",3,2,13,0.1538,1,"{266, 43}"
146,1,105,0,0.0455382,"\int \frac{x^{12}}{\left(a+b x^2\right)^2} \, dx","Int[x^12/(a + b*x^2)^2,x]","\frac{11 a^2 x^5}{10 b^4}-\frac{11 a^3 x^3}{6 b^5}+\frac{11 a^4 x}{2 b^6}-\frac{11 a^{9/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 b^{13/2}}-\frac{11 a x^7}{14 b^3}-\frac{x^{11}}{2 b \left(a+b x^2\right)}+\frac{11 x^9}{18 b^2}","\frac{11 a^2 x^5}{10 b^4}-\frac{11 a^3 x^3}{6 b^5}+\frac{11 a^4 x}{2 b^6}-\frac{11 a^{9/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 b^{13/2}}-\frac{11 a x^7}{14 b^3}-\frac{x^{11}}{2 b \left(a+b x^2\right)}+\frac{11 x^9}{18 b^2}",1,"(11*a^4*x)/(2*b^6) - (11*a^3*x^3)/(6*b^5) + (11*a^2*x^5)/(10*b^4) - (11*a*x^7)/(14*b^3) + (11*x^9)/(18*b^2) - x^11/(2*b*(a + b*x^2)) - (11*a^(9/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*b^(13/2))","A",4,3,13,0.2308,1,"{288, 302, 205}"
147,1,83,0,0.0656377,"\int \frac{x^{11}}{\left(a+b x^2\right)^2} \, dx","Int[x^11/(a + b*x^2)^2,x]","\frac{3 a^2 x^4}{4 b^4}-\frac{2 a^3 x^2}{b^5}+\frac{a^5}{2 b^6 \left(a+b x^2\right)}+\frac{5 a^4 \log \left(a+b x^2\right)}{2 b^6}-\frac{a x^6}{3 b^3}+\frac{x^8}{8 b^2}","\frac{3 a^2 x^4}{4 b^4}-\frac{2 a^3 x^2}{b^5}+\frac{a^5}{2 b^6 \left(a+b x^2\right)}+\frac{5 a^4 \log \left(a+b x^2\right)}{2 b^6}-\frac{a x^6}{3 b^3}+\frac{x^8}{8 b^2}",1,"(-2*a^3*x^2)/b^5 + (3*a^2*x^4)/(4*b^4) - (a*x^6)/(3*b^3) + x^8/(8*b^2) + a^5/(2*b^6*(a + b*x^2)) + (5*a^4*Log[a + b*x^2])/(2*b^6)","A",3,2,13,0.1538,1,"{266, 43}"
148,1,92,0,0.0369984,"\int \frac{x^{10}}{\left(a+b x^2\right)^2} \, dx","Int[x^10/(a + b*x^2)^2,x]","\frac{3 a^2 x^3}{2 b^4}-\frac{9 a^3 x}{2 b^5}+\frac{9 a^{7/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 b^{11/2}}-\frac{9 a x^5}{10 b^3}-\frac{x^9}{2 b \left(a+b x^2\right)}+\frac{9 x^7}{14 b^2}","\frac{3 a^2 x^3}{2 b^4}-\frac{9 a^3 x}{2 b^5}+\frac{9 a^{7/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 b^{11/2}}-\frac{9 a x^5}{10 b^3}-\frac{x^9}{2 b \left(a+b x^2\right)}+\frac{9 x^7}{14 b^2}",1,"(-9*a^3*x)/(2*b^5) + (3*a^2*x^3)/(2*b^4) - (9*a*x^5)/(10*b^3) + (9*x^7)/(14*b^2) - x^9/(2*b*(a + b*x^2)) + (9*a^(7/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*b^(11/2))","A",4,3,13,0.2308,1,"{288, 302, 205}"
149,1,70,0,0.0544227,"\int \frac{x^9}{\left(a+b x^2\right)^2} \, dx","Int[x^9/(a + b*x^2)^2,x]","\frac{3 a^2 x^2}{2 b^4}-\frac{a^4}{2 b^5 \left(a+b x^2\right)}-\frac{2 a^3 \log \left(a+b x^2\right)}{b^5}-\frac{a x^4}{2 b^3}+\frac{x^6}{6 b^2}","\frac{3 a^2 x^2}{2 b^4}-\frac{a^4}{2 b^5 \left(a+b x^2\right)}-\frac{2 a^3 \log \left(a+b x^2\right)}{b^5}-\frac{a x^4}{2 b^3}+\frac{x^6}{6 b^2}",1,"(3*a^2*x^2)/(2*b^4) - (a*x^4)/(2*b^3) + x^6/(6*b^2) - a^4/(2*b^5*(a + b*x^2)) - (2*a^3*Log[a + b*x^2])/b^5","A",3,2,13,0.1538,1,"{266, 43}"
150,1,79,0,0.0316641,"\int \frac{x^8}{\left(a+b x^2\right)^2} \, dx","Int[x^8/(a + b*x^2)^2,x]","\frac{7 a^2 x}{2 b^4}-\frac{7 a^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 b^{9/2}}-\frac{7 a x^3}{6 b^3}-\frac{x^7}{2 b \left(a+b x^2\right)}+\frac{7 x^5}{10 b^2}","\frac{7 a^2 x}{2 b^4}-\frac{7 a^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 b^{9/2}}-\frac{7 a x^3}{6 b^3}-\frac{x^7}{2 b \left(a+b x^2\right)}+\frac{7 x^5}{10 b^2}",1,"(7*a^2*x)/(2*b^4) - (7*a*x^3)/(6*b^3) + (7*x^5)/(10*b^2) - x^7/(2*b*(a + b*x^2)) - (7*a^(5/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*b^(9/2))","A",4,3,13,0.2308,1,"{288, 302, 205}"
151,1,57,0,0.0422548,"\int \frac{x^7}{\left(a+b x^2\right)^2} \, dx","Int[x^7/(a + b*x^2)^2,x]","\frac{a^3}{2 b^4 \left(a+b x^2\right)}+\frac{3 a^2 \log \left(a+b x^2\right)}{2 b^4}-\frac{a x^2}{b^3}+\frac{x^4}{4 b^2}","\frac{a^3}{2 b^4 \left(a+b x^2\right)}+\frac{3 a^2 \log \left(a+b x^2\right)}{2 b^4}-\frac{a x^2}{b^3}+\frac{x^4}{4 b^2}",1,"-((a*x^2)/b^3) + x^4/(4*b^2) + a^3/(2*b^4*(a + b*x^2)) + (3*a^2*Log[a + b*x^2])/(2*b^4)","A",3,2,13,0.1538,1,"{266, 43}"
152,1,66,0,0.0269408,"\int \frac{x^6}{\left(a+b x^2\right)^2} \, dx","Int[x^6/(a + b*x^2)^2,x]","\frac{5 a^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 b^{7/2}}-\frac{5 a x}{2 b^3}-\frac{x^5}{2 b \left(a+b x^2\right)}+\frac{5 x^3}{6 b^2}","\frac{5 a^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 b^{7/2}}-\frac{5 a x}{2 b^3}-\frac{x^5}{2 b \left(a+b x^2\right)}+\frac{5 x^3}{6 b^2}",1,"(-5*a*x)/(2*b^3) + (5*x^3)/(6*b^2) - x^5/(2*b*(a + b*x^2)) + (5*a^(3/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*b^(7/2))","A",4,3,13,0.2308,1,"{288, 302, 205}"
153,1,44,0,0.031901,"\int \frac{x^5}{\left(a+b x^2\right)^2} \, dx","Int[x^5/(a + b*x^2)^2,x]","-\frac{a^2}{2 b^3 \left(a+b x^2\right)}-\frac{a \log \left(a+b x^2\right)}{b^3}+\frac{x^2}{2 b^2}","-\frac{a^2}{2 b^3 \left(a+b x^2\right)}-\frac{a \log \left(a+b x^2\right)}{b^3}+\frac{x^2}{2 b^2}",1,"x^2/(2*b^2) - a^2/(2*b^3*(a + b*x^2)) - (a*Log[a + b*x^2])/b^3","A",3,2,13,0.1538,1,"{266, 43}"
154,1,55,0,0.016912,"\int \frac{x^4}{\left(a+b x^2\right)^2} \, dx","Int[x^4/(a + b*x^2)^2,x]","-\frac{3 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 b^{5/2}}-\frac{x^3}{2 b \left(a+b x^2\right)}+\frac{3 x}{2 b^2}","-\frac{3 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 b^{5/2}}-\frac{x^3}{2 b \left(a+b x^2\right)}+\frac{3 x}{2 b^2}",1,"(3*x)/(2*b^2) - x^3/(2*b*(a + b*x^2)) - (3*Sqrt[a]*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*b^(5/2))","A",3,3,13,0.2308,1,"{288, 321, 205}"
155,1,33,0,0.0237993,"\int \frac{x^3}{\left(a+b x^2\right)^2} \, dx","Int[x^3/(a + b*x^2)^2,x]","\frac{a}{2 b^2 \left(a+b x^2\right)}+\frac{\log \left(a+b x^2\right)}{2 b^2}","\frac{a}{2 b^2 \left(a+b x^2\right)}+\frac{\log \left(a+b x^2\right)}{2 b^2}",1,"a/(2*b^2*(a + b*x^2)) + Log[a + b*x^2]/(2*b^2)","A",3,2,13,0.1538,1,"{266, 43}"
156,1,45,0,0.0124618,"\int \frac{x^2}{\left(a+b x^2\right)^2} \, dx","Int[x^2/(a + b*x^2)^2,x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 \sqrt{a} b^{3/2}}-\frac{x}{2 b \left(a+b x^2\right)}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 \sqrt{a} b^{3/2}}-\frac{x}{2 b \left(a+b x^2\right)}",1,"-x/(2*b*(a + b*x^2)) + ArcTan[(Sqrt[b]*x)/Sqrt[a]]/(2*Sqrt[a]*b^(3/2))","A",2,2,13,0.1538,1,"{288, 205}"
157,1,16,0,0.0029703,"\int \frac{x}{\left(a+b x^2\right)^2} \, dx","Int[x/(a + b*x^2)^2,x]","-\frac{1}{2 b \left(a+b x^2\right)}","-\frac{1}{2 b \left(a+b x^2\right)}",1,"-1/(2*b*(a + b*x^2))","A",1,1,11,0.09091,1,"{261}"
158,1,45,0,0.0095894,"\int \frac{1}{\left(a+b x^2\right)^2} \, dx","Int[(a + b*x^2)^(-2),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b}}+\frac{x}{2 a \left(a+b x^2\right)}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b}}+\frac{x}{2 a \left(a+b x^2\right)}",1,"x/(2*a*(a + b*x^2)) + ArcTan[(Sqrt[b]*x)/Sqrt[a]]/(2*a^(3/2)*Sqrt[b])","A",2,2,9,0.2222,1,"{199, 205}"
159,1,38,0,0.0267591,"\int \frac{1}{x \left(a+b x^2\right)^2} \, dx","Int[1/(x*(a + b*x^2)^2),x]","-\frac{\log \left(a+b x^2\right)}{2 a^2}+\frac{\log (x)}{a^2}+\frac{1}{2 a \left(a+b x^2\right)}","-\frac{\log \left(a+b x^2\right)}{2 a^2}+\frac{\log (x)}{a^2}+\frac{1}{2 a \left(a+b x^2\right)}",1,"1/(2*a*(a + b*x^2)) + Log[x]/a^2 - Log[a + b*x^2]/(2*a^2)","A",3,2,13,0.1538,1,"{266, 44}"
160,1,57,0,0.0168707,"\int \frac{1}{x^2 \left(a+b x^2\right)^2} \, dx","Int[1/(x^2*(a + b*x^2)^2),x]","-\frac{3 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{5/2}}-\frac{3}{2 a^2 x}+\frac{1}{2 a x \left(a+b x^2\right)}","-\frac{3 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{5/2}}-\frac{3}{2 a^2 x}+\frac{1}{2 a x \left(a+b x^2\right)}",1,"-3/(2*a^2*x) + 1/(2*a*x*(a + b*x^2)) - (3*Sqrt[b]*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*a^(5/2))","A",3,3,13,0.2308,1,"{290, 325, 205}"
161,1,49,0,0.0361045,"\int \frac{1}{x^3 \left(a+b x^2\right)^2} \, dx","Int[1/(x^3*(a + b*x^2)^2),x]","-\frac{b}{2 a^2 \left(a+b x^2\right)}+\frac{b \log \left(a+b x^2\right)}{a^3}-\frac{2 b \log (x)}{a^3}-\frac{1}{2 a^2 x^2}","-\frac{b}{2 a^2 \left(a+b x^2\right)}+\frac{b \log \left(a+b x^2\right)}{a^3}-\frac{2 b \log (x)}{a^3}-\frac{1}{2 a^2 x^2}",1,"-1/(2*a^2*x^2) - b/(2*a^2*(a + b*x^2)) - (2*b*Log[x])/a^3 + (b*Log[a + b*x^2])/a^3","A",3,2,13,0.1538,1,"{266, 44}"
162,1,68,0,0.0257021,"\int \frac{1}{x^4 \left(a+b x^2\right)^2} \, dx","Int[1/(x^4*(a + b*x^2)^2),x]","\frac{5 b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{7/2}}+\frac{5 b}{2 a^3 x}-\frac{5}{6 a^2 x^3}+\frac{1}{2 a x^3 \left(a+b x^2\right)}","\frac{5 b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{7/2}}+\frac{5 b}{2 a^3 x}-\frac{5}{6 a^2 x^3}+\frac{1}{2 a x^3 \left(a+b x^2\right)}",1,"-5/(6*a^2*x^3) + (5*b)/(2*a^3*x) + 1/(2*a*x^3*(a + b*x^2)) + (5*b^(3/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*a^(7/2))","A",4,3,13,0.2308,1,"{290, 325, 205}"
163,1,66,0,0.0439952,"\int \frac{1}{x^5 \left(a+b x^2\right)^2} \, dx","Int[1/(x^5*(a + b*x^2)^2),x]","\frac{b^2}{2 a^3 \left(a+b x^2\right)}-\frac{3 b^2 \log \left(a+b x^2\right)}{2 a^4}+\frac{3 b^2 \log (x)}{a^4}+\frac{b}{a^3 x^2}-\frac{1}{4 a^2 x^4}","\frac{b^2}{2 a^3 \left(a+b x^2\right)}-\frac{3 b^2 \log \left(a+b x^2\right)}{2 a^4}+\frac{3 b^2 \log (x)}{a^4}+\frac{b}{a^3 x^2}-\frac{1}{4 a^2 x^4}",1,"-1/(4*a^2*x^4) + b/(a^3*x^2) + b^2/(2*a^3*(a + b*x^2)) + (3*b^2*Log[x])/a^4 - (3*b^2*Log[a + b*x^2])/(2*a^4)","A",3,2,13,0.1538,1,"{266, 44}"
164,1,81,0,0.0329955,"\int \frac{1}{x^6 \left(a+b x^2\right)^2} \, dx","Int[1/(x^6*(a + b*x^2)^2),x]","-\frac{7 b^2}{2 a^4 x}-\frac{7 b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{9/2}}+\frac{7 b}{6 a^3 x^3}-\frac{7}{10 a^2 x^5}+\frac{1}{2 a x^5 \left(a+b x^2\right)}","-\frac{7 b^2}{2 a^4 x}-\frac{7 b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{9/2}}+\frac{7 b}{6 a^3 x^3}-\frac{7}{10 a^2 x^5}+\frac{1}{2 a x^5 \left(a+b x^2\right)}",1,"-7/(10*a^2*x^5) + (7*b)/(6*a^3*x^3) - (7*b^2)/(2*a^4*x) + 1/(2*a*x^5*(a + b*x^2)) - (7*b^(5/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*a^(9/2))","A",5,3,13,0.2308,1,"{290, 325, 205}"
165,1,80,0,0.0539037,"\int \frac{1}{x^7 \left(a+b x^2\right)^2} \, dx","Int[1/(x^7*(a + b*x^2)^2),x]","-\frac{b^3}{2 a^4 \left(a+b x^2\right)}-\frac{3 b^2}{2 a^4 x^2}+\frac{2 b^3 \log \left(a+b x^2\right)}{a^5}-\frac{4 b^3 \log (x)}{a^5}+\frac{b}{2 a^3 x^4}-\frac{1}{6 a^2 x^6}","-\frac{b^3}{2 a^4 \left(a+b x^2\right)}-\frac{3 b^2}{2 a^4 x^2}+\frac{2 b^3 \log \left(a+b x^2\right)}{a^5}-\frac{4 b^3 \log (x)}{a^5}+\frac{b}{2 a^3 x^4}-\frac{1}{6 a^2 x^6}",1,"-1/(6*a^2*x^6) + b/(2*a^3*x^4) - (3*b^2)/(2*a^4*x^2) - b^3/(2*a^4*(a + b*x^2)) - (4*b^3*Log[x])/a^5 + (2*b^3*Log[a + b*x^2])/a^5","A",3,2,13,0.1538,1,"{266, 44}"
166,1,94,0,0.0431358,"\int \frac{1}{x^8 \left(a+b x^2\right)^2} \, dx","Int[1/(x^8*(a + b*x^2)^2),x]","-\frac{3 b^2}{2 a^4 x^3}+\frac{9 b^3}{2 a^5 x}+\frac{9 b^{7/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{11/2}}+\frac{9 b}{10 a^3 x^5}-\frac{9}{14 a^2 x^7}+\frac{1}{2 a x^7 \left(a+b x^2\right)}","-\frac{3 b^2}{2 a^4 x^3}+\frac{9 b^3}{2 a^5 x}+\frac{9 b^{7/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{11/2}}+\frac{9 b}{10 a^3 x^5}-\frac{9}{14 a^2 x^7}+\frac{1}{2 a x^7 \left(a+b x^2\right)}",1,"-9/(14*a^2*x^7) + (9*b)/(10*a^3*x^5) - (3*b^2)/(2*a^4*x^3) + (9*b^3)/(2*a^5*x) + 1/(2*a*x^7*(a + b*x^2)) + (9*b^(7/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*a^(11/2))","A",6,3,13,0.2308,1,"{290, 325, 205}"
167,1,93,0,0.0652697,"\int \frac{1}{x^9 \left(a+b x^2\right)^2} \, dx","Int[1/(x^9*(a + b*x^2)^2),x]","\frac{b^4}{2 a^5 \left(a+b x^2\right)}+\frac{2 b^3}{a^5 x^2}-\frac{3 b^2}{4 a^4 x^4}-\frac{5 b^4 \log \left(a+b x^2\right)}{2 a^6}+\frac{5 b^4 \log (x)}{a^6}+\frac{b}{3 a^3 x^6}-\frac{1}{8 a^2 x^8}","\frac{b^4}{2 a^5 \left(a+b x^2\right)}+\frac{2 b^3}{a^5 x^2}-\frac{3 b^2}{4 a^4 x^4}-\frac{5 b^4 \log \left(a+b x^2\right)}{2 a^6}+\frac{5 b^4 \log (x)}{a^6}+\frac{b}{3 a^3 x^6}-\frac{1}{8 a^2 x^8}",1,"-1/(8*a^2*x^8) + b/(3*a^3*x^6) - (3*b^2)/(4*a^4*x^4) + (2*b^3)/(a^5*x^2) + b^4/(2*a^5*(a + b*x^2)) + (5*b^4*Log[x])/a^6 - (5*b^4*Log[a + b*x^2])/(2*a^6)","A",3,2,13,0.1538,1,"{266, 44}"
168,1,114,0,0.1033777,"\int \frac{x^{15}}{\left(a+b x^2\right)^3} \, dx","Int[x^15/(a + b*x^2)^3,x]","\frac{a^2 x^6}{b^5}-\frac{5 a^3 x^4}{2 b^6}+\frac{15 a^4 x^2}{2 b^7}-\frac{7 a^6}{2 b^8 \left(a+b x^2\right)}+\frac{a^7}{4 b^8 \left(a+b x^2\right)^2}-\frac{21 a^5 \log \left(a+b x^2\right)}{2 b^8}-\frac{3 a x^8}{8 b^4}+\frac{x^{10}}{10 b^3}","\frac{a^2 x^6}{b^5}-\frac{5 a^3 x^4}{2 b^6}+\frac{15 a^4 x^2}{2 b^7}-\frac{7 a^6}{2 b^8 \left(a+b x^2\right)}+\frac{a^7}{4 b^8 \left(a+b x^2\right)^2}-\frac{21 a^5 \log \left(a+b x^2\right)}{2 b^8}-\frac{3 a x^8}{8 b^4}+\frac{x^{10}}{10 b^3}",1,"(15*a^4*x^2)/(2*b^7) - (5*a^3*x^4)/(2*b^6) + (a^2*x^6)/b^5 - (3*a*x^8)/(8*b^4) + x^10/(10*b^3) + a^7/(4*b^8*(a + b*x^2)^2) - (7*a^6)/(2*b^8*(a + b*x^2)) - (21*a^5*Log[a + b*x^2])/(2*b^8)","A",3,2,13,0.1538,1,"{266, 43}"
169,1,100,0,0.0821957,"\int \frac{x^{13}}{\left(a+b x^2\right)^3} \, dx","Int[x^13/(a + b*x^2)^3,x]","\frac{3 a^2 x^4}{2 b^5}-\frac{5 a^3 x^2}{b^6}+\frac{3 a^5}{b^7 \left(a+b x^2\right)}-\frac{a^6}{4 b^7 \left(a+b x^2\right)^2}+\frac{15 a^4 \log \left(a+b x^2\right)}{2 b^7}-\frac{a x^6}{2 b^4}+\frac{x^8}{8 b^3}","\frac{3 a^2 x^4}{2 b^5}-\frac{5 a^3 x^2}{b^6}+\frac{3 a^5}{b^7 \left(a+b x^2\right)}-\frac{a^6}{4 b^7 \left(a+b x^2\right)^2}+\frac{15 a^4 \log \left(a+b x^2\right)}{2 b^7}-\frac{a x^6}{2 b^4}+\frac{x^8}{8 b^3}",1,"(-5*a^3*x^2)/b^6 + (3*a^2*x^4)/(2*b^5) - (a*x^6)/(2*b^4) + x^8/(8*b^3) - a^6/(4*b^7*(a + b*x^2)^2) + (3*a^5)/(b^7*(a + b*x^2)) + (15*a^4*Log[a + b*x^2])/(2*b^7)","A",3,2,13,0.1538,1,"{266, 43}"
170,1,87,0,0.0715145,"\int \frac{x^{11}}{\left(a+b x^2\right)^3} \, dx","Int[x^11/(a + b*x^2)^3,x]","\frac{3 a^2 x^2}{b^5}-\frac{5 a^4}{2 b^6 \left(a+b x^2\right)}+\frac{a^5}{4 b^6 \left(a+b x^2\right)^2}-\frac{5 a^3 \log \left(a+b x^2\right)}{b^6}-\frac{3 a x^4}{4 b^4}+\frac{x^6}{6 b^3}","\frac{3 a^2 x^2}{b^5}-\frac{5 a^4}{2 b^6 \left(a+b x^2\right)}+\frac{a^5}{4 b^6 \left(a+b x^2\right)^2}-\frac{5 a^3 \log \left(a+b x^2\right)}{b^6}-\frac{3 a x^4}{4 b^4}+\frac{x^6}{6 b^3}",1,"(3*a^2*x^2)/b^5 - (3*a*x^4)/(4*b^4) + x^6/(6*b^3) + a^5/(4*b^6*(a + b*x^2)^2) - (5*a^4)/(2*b^6*(a + b*x^2)) - (5*a^3*Log[a + b*x^2])/b^6","A",3,2,13,0.1538,1,"{266, 43}"
171,1,74,0,0.0581404,"\int \frac{x^9}{\left(a+b x^2\right)^3} \, dx","Int[x^9/(a + b*x^2)^3,x]","-\frac{a^4}{4 b^5 \left(a+b x^2\right)^2}+\frac{2 a^3}{b^5 \left(a+b x^2\right)}+\frac{3 a^2 \log \left(a+b x^2\right)}{b^5}-\frac{3 a x^2}{2 b^4}+\frac{x^4}{4 b^3}","-\frac{a^4}{4 b^5 \left(a+b x^2\right)^2}+\frac{2 a^3}{b^5 \left(a+b x^2\right)}+\frac{3 a^2 \log \left(a+b x^2\right)}{b^5}-\frac{3 a x^2}{2 b^4}+\frac{x^4}{4 b^3}",1,"(-3*a*x^2)/(2*b^4) + x^4/(4*b^3) - a^4/(4*b^5*(a + b*x^2)^2) + (2*a^3)/(b^5*(a + b*x^2)) + (3*a^2*Log[a + b*x^2])/b^5","A",3,2,13,0.1538,1,"{266, 43}"
172,1,65,0,0.0458384,"\int \frac{x^7}{\left(a+b x^2\right)^3} \, dx","Int[x^7/(a + b*x^2)^3,x]","\frac{a^3}{4 b^4 \left(a+b x^2\right)^2}-\frac{3 a^2}{2 b^4 \left(a+b x^2\right)}-\frac{3 a \log \left(a+b x^2\right)}{2 b^4}+\frac{x^2}{2 b^3}","\frac{a^3}{4 b^4 \left(a+b x^2\right)^2}-\frac{3 a^2}{2 b^4 \left(a+b x^2\right)}-\frac{3 a \log \left(a+b x^2\right)}{2 b^4}+\frac{x^2}{2 b^3}",1,"x^2/(2*b^3) + a^3/(4*b^4*(a + b*x^2)^2) - (3*a^2)/(2*b^4*(a + b*x^2)) - (3*a*Log[a + b*x^2])/(2*b^4)","A",3,2,13,0.1538,1,"{266, 43}"
173,1,49,0,0.0377695,"\int \frac{x^5}{\left(a+b x^2\right)^3} \, dx","Int[x^5/(a + b*x^2)^3,x]","-\frac{a^2}{4 b^3 \left(a+b x^2\right)^2}+\frac{a}{b^3 \left(a+b x^2\right)}+\frac{\log \left(a+b x^2\right)}{2 b^3}","-\frac{a^2}{4 b^3 \left(a+b x^2\right)^2}+\frac{a}{b^3 \left(a+b x^2\right)}+\frac{\log \left(a+b x^2\right)}{2 b^3}",1,"-a^2/(4*b^3*(a + b*x^2)^2) + a/(b^3*(a + b*x^2)) + Log[a + b*x^2]/(2*b^3)","A",3,2,13,0.1538,1,"{266, 43}"
174,1,19,0,0.0038325,"\int \frac{x^3}{\left(a+b x^2\right)^3} \, dx","Int[x^3/(a + b*x^2)^3,x]","\frac{x^4}{4 a \left(a+b x^2\right)^2}","\frac{x^4}{4 a \left(a+b x^2\right)^2}",1,"x^4/(4*a*(a + b*x^2)^2)","A",1,1,13,0.07692,1,"{264}"
175,1,16,0,0.0028312,"\int \frac{x}{\left(a+b x^2\right)^3} \, dx","Int[x/(a + b*x^2)^3,x]","-\frac{1}{4 b \left(a+b x^2\right)^2}","-\frac{1}{4 b \left(a+b x^2\right)^2}",1,"-1/(4*b*(a + b*x^2)^2)","A",1,1,11,0.09091,1,"{261}"
176,1,54,0,0.0380604,"\int \frac{1}{x \left(a+b x^2\right)^3} \, dx","Int[1/(x*(a + b*x^2)^3),x]","\frac{1}{2 a^2 \left(a+b x^2\right)}-\frac{\log \left(a+b x^2\right)}{2 a^3}+\frac{\log (x)}{a^3}+\frac{1}{4 a \left(a+b x^2\right)^2}","\frac{1}{2 a^2 \left(a+b x^2\right)}-\frac{\log \left(a+b x^2\right)}{2 a^3}+\frac{\log (x)}{a^3}+\frac{1}{4 a \left(a+b x^2\right)^2}",1,"1/(4*a*(a + b*x^2)^2) + 1/(2*a^2*(a + b*x^2)) + Log[x]/a^3 - Log[a + b*x^2]/(2*a^3)","A",3,2,13,0.1538,1,"{266, 44}"
177,1,67,0,0.0465404,"\int \frac{1}{x^3 \left(a+b x^2\right)^3} \, dx","Int[1/(x^3*(a + b*x^2)^3),x]","-\frac{b}{a^3 \left(a+b x^2\right)}-\frac{b}{4 a^2 \left(a+b x^2\right)^2}+\frac{3 b \log \left(a+b x^2\right)}{2 a^4}-\frac{3 b \log (x)}{a^4}-\frac{1}{2 a^3 x^2}","-\frac{b}{a^3 \left(a+b x^2\right)}-\frac{b}{4 a^2 \left(a+b x^2\right)^2}+\frac{3 b \log \left(a+b x^2\right)}{2 a^4}-\frac{3 b \log (x)}{a^4}-\frac{1}{2 a^3 x^2}",1,"-1/(2*a^3*x^2) - b/(4*a^2*(a + b*x^2)^2) - b/(a^3*(a + b*x^2)) - (3*b*Log[x])/a^4 + (3*b*Log[a + b*x^2])/(2*a^4)","A",3,2,13,0.1538,1,"{266, 44}"
178,1,86,0,0.0600754,"\int \frac{1}{x^5 \left(a+b x^2\right)^3} \, dx","Int[1/(x^5*(a + b*x^2)^3),x]","\frac{3 b^2}{2 a^4 \left(a+b x^2\right)}+\frac{b^2}{4 a^3 \left(a+b x^2\right)^2}-\frac{3 b^2 \log \left(a+b x^2\right)}{a^5}+\frac{6 b^2 \log (x)}{a^5}+\frac{3 b}{2 a^4 x^2}-\frac{1}{4 a^3 x^4}","\frac{3 b^2}{2 a^4 \left(a+b x^2\right)}+\frac{b^2}{4 a^3 \left(a+b x^2\right)^2}-\frac{3 b^2 \log \left(a+b x^2\right)}{a^5}+\frac{6 b^2 \log (x)}{a^5}+\frac{3 b}{2 a^4 x^2}-\frac{1}{4 a^3 x^4}",1,"-1/(4*a^3*x^4) + (3*b)/(2*a^4*x^2) + b^2/(4*a^3*(a + b*x^2)^2) + (3*b^2)/(2*a^4*(a + b*x^2)) + (6*b^2*Log[x])/a^5 - (3*b^2*Log[a + b*x^2])/a^5","A",3,2,13,0.1538,1,"{266, 44}"
179,1,95,0,0.067537,"\int \frac{1}{x^7 \left(a+b x^2\right)^3} \, dx","Int[1/(x^7*(a + b*x^2)^3),x]","-\frac{2 b^3}{a^5 \left(a+b x^2\right)}-\frac{b^3}{4 a^4 \left(a+b x^2\right)^2}-\frac{3 b^2}{a^5 x^2}+\frac{5 b^3 \log \left(a+b x^2\right)}{a^6}-\frac{10 b^3 \log (x)}{a^6}+\frac{3 b}{4 a^4 x^4}-\frac{1}{6 a^3 x^6}","-\frac{2 b^3}{a^5 \left(a+b x^2\right)}-\frac{b^3}{4 a^4 \left(a+b x^2\right)^2}-\frac{3 b^2}{a^5 x^2}+\frac{5 b^3 \log \left(a+b x^2\right)}{a^6}-\frac{10 b^3 \log (x)}{a^6}+\frac{3 b}{4 a^4 x^4}-\frac{1}{6 a^3 x^6}",1,"-1/(6*a^3*x^6) + (3*b)/(4*a^4*x^4) - (3*b^2)/(a^5*x^2) - b^3/(4*a^4*(a + b*x^2)^2) - (2*b^3)/(a^5*(a + b*x^2)) - (10*b^3*Log[x])/a^6 + (5*b^3*Log[a + b*x^2])/a^6","A",3,2,13,0.1538,1,"{266, 44}"
180,1,112,0,0.0798041,"\int \frac{1}{x^9 \left(a+b x^2\right)^3} \, dx","Int[1/(x^9*(a + b*x^2)^3),x]","\frac{5 b^4}{2 a^6 \left(a+b x^2\right)}+\frac{b^4}{4 a^5 \left(a+b x^2\right)^2}+\frac{5 b^3}{a^6 x^2}-\frac{3 b^2}{2 a^5 x^4}-\frac{15 b^4 \log \left(a+b x^2\right)}{2 a^7}+\frac{15 b^4 \log (x)}{a^7}+\frac{b}{2 a^4 x^6}-\frac{1}{8 a^3 x^8}","\frac{5 b^4}{2 a^6 \left(a+b x^2\right)}+\frac{b^4}{4 a^5 \left(a+b x^2\right)^2}+\frac{5 b^3}{a^6 x^2}-\frac{3 b^2}{2 a^5 x^4}-\frac{15 b^4 \log \left(a+b x^2\right)}{2 a^7}+\frac{15 b^4 \log (x)}{a^7}+\frac{b}{2 a^4 x^6}-\frac{1}{8 a^3 x^8}",1,"-1/(8*a^3*x^8) + b/(2*a^4*x^6) - (3*b^2)/(2*a^5*x^4) + (5*b^3)/(a^6*x^2) + b^4/(4*a^5*(a + b*x^2)^2) + (5*b^4)/(2*a^6*(a + b*x^2)) + (15*b^4*Log[x])/a^7 - (15*b^4*Log[a + b*x^2])/(2*a^7)","A",3,2,13,0.1538,1,"{266, 44}"
181,1,111,0,0.0484199,"\int \frac{x^{12}}{\left(a+b x^2\right)^3} \, dx","Int[x^12/(a + b*x^2)^3,x]","\frac{33 a^2 x^3}{8 b^5}-\frac{99 a^3 x}{8 b^6}+\frac{99 a^{7/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 b^{13/2}}-\frac{11 x^9}{8 b^2 \left(a+b x^2\right)}-\frac{99 a x^5}{40 b^4}-\frac{x^{11}}{4 b \left(a+b x^2\right)^2}+\frac{99 x^7}{56 b^3}","\frac{33 a^2 x^3}{8 b^5}-\frac{99 a^3 x}{8 b^6}+\frac{99 a^{7/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 b^{13/2}}-\frac{11 x^9}{8 b^2 \left(a+b x^2\right)}-\frac{99 a x^5}{40 b^4}-\frac{x^{11}}{4 b \left(a+b x^2\right)^2}+\frac{99 x^7}{56 b^3}",1,"(-99*a^3*x)/(8*b^6) + (33*a^2*x^3)/(8*b^5) - (99*a*x^5)/(40*b^4) + (99*x^7)/(56*b^3) - x^11/(4*b*(a + b*x^2)^2) - (11*x^9)/(8*b^2*(a + b*x^2)) + (99*a^(7/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*b^(13/2))","A",5,3,13,0.2308,1,"{288, 302, 205}"
182,1,98,0,0.0407871,"\int \frac{x^{10}}{\left(a+b x^2\right)^3} \, dx","Int[x^10/(a + b*x^2)^3,x]","\frac{63 a^2 x}{8 b^5}-\frac{63 a^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 b^{11/2}}-\frac{9 x^7}{8 b^2 \left(a+b x^2\right)}-\frac{21 a x^3}{8 b^4}-\frac{x^9}{4 b \left(a+b x^2\right)^2}+\frac{63 x^5}{40 b^3}","\frac{63 a^2 x}{8 b^5}-\frac{63 a^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 b^{11/2}}-\frac{9 x^7}{8 b^2 \left(a+b x^2\right)}-\frac{21 a x^3}{8 b^4}-\frac{x^9}{4 b \left(a+b x^2\right)^2}+\frac{63 x^5}{40 b^3}",1,"(63*a^2*x)/(8*b^5) - (21*a*x^3)/(8*b^4) + (63*x^5)/(40*b^3) - x^9/(4*b*(a + b*x^2)^2) - (9*x^7)/(8*b^2*(a + b*x^2)) - (63*a^(5/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*b^(11/2))","A",5,3,13,0.2308,1,"{288, 302, 205}"
183,1,85,0,0.0351929,"\int \frac{x^8}{\left(a+b x^2\right)^3} \, dx","Int[x^8/(a + b*x^2)^3,x]","\frac{35 a^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 b^{9/2}}-\frac{7 x^5}{8 b^2 \left(a+b x^2\right)}-\frac{35 a x}{8 b^4}-\frac{x^7}{4 b \left(a+b x^2\right)^2}+\frac{35 x^3}{24 b^3}","\frac{35 a^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 b^{9/2}}-\frac{7 x^5}{8 b^2 \left(a+b x^2\right)}-\frac{35 a x}{8 b^4}-\frac{x^7}{4 b \left(a+b x^2\right)^2}+\frac{35 x^3}{24 b^3}",1,"(-35*a*x)/(8*b^4) + (35*x^3)/(24*b^3) - x^7/(4*b*(a + b*x^2)^2) - (7*x^5)/(8*b^2*(a + b*x^2)) + (35*a^(3/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*b^(9/2))","A",5,3,13,0.2308,1,"{288, 302, 205}"
184,1,74,0,0.0252003,"\int \frac{x^6}{\left(a+b x^2\right)^3} \, dx","Int[x^6/(a + b*x^2)^3,x]","-\frac{5 x^3}{8 b^2 \left(a+b x^2\right)}-\frac{15 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 b^{7/2}}-\frac{x^5}{4 b \left(a+b x^2\right)^2}+\frac{15 x}{8 b^3}","-\frac{5 x^3}{8 b^2 \left(a+b x^2\right)}-\frac{15 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 b^{7/2}}-\frac{x^5}{4 b \left(a+b x^2\right)^2}+\frac{15 x}{8 b^3}",1,"(15*x)/(8*b^3) - x^5/(4*b*(a + b*x^2)^2) - (5*x^3)/(8*b^2*(a + b*x^2)) - (15*Sqrt[a]*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*b^(7/2))","A",4,3,13,0.2308,1,"{288, 321, 205}"
185,1,64,0,0.0197249,"\int \frac{x^4}{\left(a+b x^2\right)^3} \, dx","Int[x^4/(a + b*x^2)^3,x]","-\frac{3 x}{8 b^2 \left(a+b x^2\right)}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 \sqrt{a} b^{5/2}}-\frac{x^3}{4 b \left(a+b x^2\right)^2}","-\frac{3 x}{8 b^2 \left(a+b x^2\right)}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 \sqrt{a} b^{5/2}}-\frac{x^3}{4 b \left(a+b x^2\right)^2}",1,"-x^3/(4*b*(a + b*x^2)^2) - (3*x)/(8*b^2*(a + b*x^2)) + (3*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*Sqrt[a]*b^(5/2))","A",3,2,13,0.1538,1,"{288, 205}"
186,1,65,0,0.0183032,"\int \frac{x^2}{\left(a+b x^2\right)^3} \, dx","Int[x^2/(a + b*x^2)^3,x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{3/2} b^{3/2}}+\frac{x}{8 a b \left(a+b x^2\right)}-\frac{x}{4 b \left(a+b x^2\right)^2}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{3/2} b^{3/2}}+\frac{x}{8 a b \left(a+b x^2\right)}-\frac{x}{4 b \left(a+b x^2\right)^2}",1,"-x/(4*b*(a + b*x^2)^2) + x/(8*a*b*(a + b*x^2)) + ArcTan[(Sqrt[b]*x)/Sqrt[a]]/(8*a^(3/2)*b^(3/2))","A",3,3,13,0.2308,1,"{288, 199, 205}"
187,1,62,0,0.0163593,"\int \frac{1}{\left(a+b x^2\right)^3} \, dx","Int[(a + b*x^2)^(-3),x]","\frac{3 x}{8 a^2 \left(a+b x^2\right)}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{b}}+\frac{x}{4 a \left(a+b x^2\right)^2}","\frac{3 x}{8 a^2 \left(a+b x^2\right)}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{b}}+\frac{x}{4 a \left(a+b x^2\right)^2}",1,"x/(4*a*(a + b*x^2)^2) + (3*x)/(8*a^2*(a + b*x^2)) + (3*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*a^(5/2)*Sqrt[b])","A",3,2,9,0.2222,1,"{199, 205}"
188,1,76,0,0.0258144,"\int \frac{1}{x^2 \left(a+b x^2\right)^3} \, dx","Int[1/(x^2*(a + b*x^2)^3),x]","\frac{5}{8 a^2 x \left(a+b x^2\right)}-\frac{15 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{7/2}}-\frac{15}{8 a^3 x}+\frac{1}{4 a x \left(a+b x^2\right)^2}","\frac{5}{8 a^2 x \left(a+b x^2\right)}-\frac{15 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{7/2}}-\frac{15}{8 a^3 x}+\frac{1}{4 a x \left(a+b x^2\right)^2}",1,"-15/(8*a^3*x) + 1/(4*a*x*(a + b*x^2)^2) + 5/(8*a^2*x*(a + b*x^2)) - (15*Sqrt[b]*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*a^(7/2))","A",4,3,13,0.2308,1,"{290, 325, 205}"
189,1,87,0,0.0336019,"\int \frac{1}{x^4 \left(a+b x^2\right)^3} \, dx","Int[1/(x^4*(a + b*x^2)^3),x]","\frac{35 b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{9/2}}+\frac{7}{8 a^2 x^3 \left(a+b x^2\right)}+\frac{35 b}{8 a^4 x}-\frac{35}{24 a^3 x^3}+\frac{1}{4 a x^3 \left(a+b x^2\right)^2}","\frac{35 b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{9/2}}+\frac{7}{8 a^2 x^3 \left(a+b x^2\right)}+\frac{35 b}{8 a^4 x}-\frac{35}{24 a^3 x^3}+\frac{1}{4 a x^3 \left(a+b x^2\right)^2}",1,"-35/(24*a^3*x^3) + (35*b)/(8*a^4*x) + 1/(4*a*x^3*(a + b*x^2)^2) + 7/(8*a^2*x^3*(a + b*x^2)) + (35*b^(3/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*a^(9/2))","A",5,3,13,0.2308,1,"{290, 325, 205}"
190,1,100,0,0.041861,"\int \frac{1}{x^6 \left(a+b x^2\right)^3} \, dx","Int[1/(x^6*(a + b*x^2)^3),x]","-\frac{63 b^2}{8 a^5 x}-\frac{63 b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{11/2}}+\frac{21 b}{8 a^4 x^3}+\frac{9}{8 a^2 x^5 \left(a+b x^2\right)}-\frac{63}{40 a^3 x^5}+\frac{1}{4 a x^5 \left(a+b x^2\right)^2}","-\frac{63 b^2}{8 a^5 x}-\frac{63 b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{11/2}}+\frac{21 b}{8 a^4 x^3}+\frac{9}{8 a^2 x^5 \left(a+b x^2\right)}-\frac{63}{40 a^3 x^5}+\frac{1}{4 a x^5 \left(a+b x^2\right)^2}",1,"-63/(40*a^3*x^5) + (21*b)/(8*a^4*x^3) - (63*b^2)/(8*a^5*x) + 1/(4*a*x^5*(a + b*x^2)^2) + 9/(8*a^2*x^5*(a + b*x^2)) - (63*b^(5/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*a^(11/2))","A",6,3,13,0.2308,1,"{290, 325, 205}"
191,1,113,0,0.0558603,"\int \frac{1}{x^8 \left(a+b x^2\right)^3} \, dx","Int[1/(x^8*(a + b*x^2)^3),x]","-\frac{33 b^2}{8 a^5 x^3}+\frac{99 b^3}{8 a^6 x}+\frac{99 b^{7/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{13/2}}+\frac{99 b}{40 a^4 x^5}+\frac{11}{8 a^2 x^7 \left(a+b x^2\right)}-\frac{99}{56 a^3 x^7}+\frac{1}{4 a x^7 \left(a+b x^2\right)^2}","-\frac{33 b^2}{8 a^5 x^3}+\frac{99 b^3}{8 a^6 x}+\frac{99 b^{7/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{13/2}}+\frac{99 b}{40 a^4 x^5}+\frac{11}{8 a^2 x^7 \left(a+b x^2\right)}-\frac{99}{56 a^3 x^7}+\frac{1}{4 a x^7 \left(a+b x^2\right)^2}",1,"-99/(56*a^3*x^7) + (99*b)/(40*a^4*x^5) - (33*b^2)/(8*a^5*x^3) + (99*b^3)/(8*a^6*x) + 1/(4*a*x^7*(a + b*x^2)^2) + 11/(8*a^2*x^7*(a + b*x^2)) + (99*b^(7/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*a^(13/2))","A",7,3,13,0.2308,1,"{290, 325, 205}"
192,1,216,0,0.2550033,"\int \frac{x^{25}}{\left(a+b x^2\right)^{10}} \, dx","Int[x^25/(a + b*x^2)^10,x]","-\frac{a^{12}}{18 b^{13} \left(a+b x^2\right)^9}+\frac{3 a^{11}}{4 b^{13} \left(a+b x^2\right)^8}-\frac{33 a^{10}}{7 b^{13} \left(a+b x^2\right)^7}+\frac{55 a^9}{3 b^{13} \left(a+b x^2\right)^6}-\frac{99 a^8}{2 b^{13} \left(a+b x^2\right)^5}+\frac{99 a^7}{b^{13} \left(a+b x^2\right)^4}-\frac{154 a^6}{b^{13} \left(a+b x^2\right)^3}+\frac{198 a^5}{b^{13} \left(a+b x^2\right)^2}-\frac{495 a^4}{2 b^{13} \left(a+b x^2\right)}+\frac{55 a^2 x^2}{2 b^{12}}-\frac{110 a^3 \log \left(a+b x^2\right)}{b^{13}}-\frac{5 a x^4}{2 b^{11}}+\frac{x^6}{6 b^{10}}","-\frac{a^{12}}{18 b^{13} \left(a+b x^2\right)^9}+\frac{3 a^{11}}{4 b^{13} \left(a+b x^2\right)^8}-\frac{33 a^{10}}{7 b^{13} \left(a+b x^2\right)^7}+\frac{55 a^9}{3 b^{13} \left(a+b x^2\right)^6}-\frac{99 a^8}{2 b^{13} \left(a+b x^2\right)^5}+\frac{99 a^7}{b^{13} \left(a+b x^2\right)^4}-\frac{154 a^6}{b^{13} \left(a+b x^2\right)^3}+\frac{198 a^5}{b^{13} \left(a+b x^2\right)^2}-\frac{495 a^4}{2 b^{13} \left(a+b x^2\right)}+\frac{55 a^2 x^2}{2 b^{12}}-\frac{110 a^3 \log \left(a+b x^2\right)}{b^{13}}-\frac{5 a x^4}{2 b^{11}}+\frac{x^6}{6 b^{10}}",1,"(55*a^2*x^2)/(2*b^12) - (5*a*x^4)/(2*b^11) + x^6/(6*b^10) - a^12/(18*b^13*(a + b*x^2)^9) + (3*a^11)/(4*b^13*(a + b*x^2)^8) - (33*a^10)/(7*b^13*(a + b*x^2)^7) + (55*a^9)/(3*b^13*(a + b*x^2)^6) - (99*a^8)/(2*b^13*(a + b*x^2)^5) + (99*a^7)/(b^13*(a + b*x^2)^4) - (154*a^6)/(b^13*(a + b*x^2)^3) + (198*a^5)/(b^13*(a + b*x^2)^2) - (495*a^4)/(2*b^13*(a + b*x^2)) - (110*a^3*Log[a + b*x^2])/b^13","A",3,2,13,0.1538,1,"{266, 43}"
193,1,205,0,0.2144398,"\int \frac{x^{23}}{\left(a+b x^2\right)^{10}} \, dx","Int[x^23/(a + b*x^2)^10,x]","\frac{a^{11}}{18 b^{12} \left(a+b x^2\right)^9}-\frac{11 a^{10}}{16 b^{12} \left(a+b x^2\right)^8}+\frac{55 a^9}{14 b^{12} \left(a+b x^2\right)^7}-\frac{55 a^8}{4 b^{12} \left(a+b x^2\right)^6}+\frac{33 a^7}{b^{12} \left(a+b x^2\right)^5}-\frac{231 a^6}{4 b^{12} \left(a+b x^2\right)^4}+\frac{77 a^5}{b^{12} \left(a+b x^2\right)^3}-\frac{165 a^4}{2 b^{12} \left(a+b x^2\right)^2}+\frac{165 a^3}{2 b^{12} \left(a+b x^2\right)}+\frac{55 a^2 \log \left(a+b x^2\right)}{2 b^{12}}-\frac{5 a x^2}{b^{11}}+\frac{x^4}{4 b^{10}}","\frac{a^{11}}{18 b^{12} \left(a+b x^2\right)^9}-\frac{11 a^{10}}{16 b^{12} \left(a+b x^2\right)^8}+\frac{55 a^9}{14 b^{12} \left(a+b x^2\right)^7}-\frac{55 a^8}{4 b^{12} \left(a+b x^2\right)^6}+\frac{33 a^7}{b^{12} \left(a+b x^2\right)^5}-\frac{231 a^6}{4 b^{12} \left(a+b x^2\right)^4}+\frac{77 a^5}{b^{12} \left(a+b x^2\right)^3}-\frac{165 a^4}{2 b^{12} \left(a+b x^2\right)^2}+\frac{165 a^3}{2 b^{12} \left(a+b x^2\right)}+\frac{55 a^2 \log \left(a+b x^2\right)}{2 b^{12}}-\frac{5 a x^2}{b^{11}}+\frac{x^4}{4 b^{10}}",1,"(-5*a*x^2)/b^11 + x^4/(4*b^10) + a^11/(18*b^12*(a + b*x^2)^9) - (11*a^10)/(16*b^12*(a + b*x^2)^8) + (55*a^9)/(14*b^12*(a + b*x^2)^7) - (55*a^8)/(4*b^12*(a + b*x^2)^6) + (33*a^7)/(b^12*(a + b*x^2)^5) - (231*a^6)/(4*b^12*(a + b*x^2)^4) + (77*a^5)/(b^12*(a + b*x^2)^3) - (165*a^4)/(2*b^12*(a + b*x^2)^2) + (165*a^3)/(2*b^12*(a + b*x^2)) + (55*a^2*Log[a + b*x^2])/(2*b^12)","A",3,2,13,0.1538,1,"{266, 43}"
194,1,188,0,0.1893999,"\int \frac{x^{21}}{\left(a+b x^2\right)^{10}} \, dx","Int[x^21/(a + b*x^2)^10,x]","-\frac{a^{10}}{18 b^{11} \left(a+b x^2\right)^9}+\frac{5 a^9}{8 b^{11} \left(a+b x^2\right)^8}-\frac{45 a^8}{14 b^{11} \left(a+b x^2\right)^7}+\frac{10 a^7}{b^{11} \left(a+b x^2\right)^6}-\frac{21 a^6}{b^{11} \left(a+b x^2\right)^5}+\frac{63 a^5}{2 b^{11} \left(a+b x^2\right)^4}-\frac{35 a^4}{b^{11} \left(a+b x^2\right)^3}+\frac{30 a^3}{b^{11} \left(a+b x^2\right)^2}-\frac{45 a^2}{2 b^{11} \left(a+b x^2\right)}-\frac{5 a \log \left(a+b x^2\right)}{b^{11}}+\frac{x^2}{2 b^{10}}","-\frac{a^{10}}{18 b^{11} \left(a+b x^2\right)^9}+\frac{5 a^9}{8 b^{11} \left(a+b x^2\right)^8}-\frac{45 a^8}{14 b^{11} \left(a+b x^2\right)^7}+\frac{10 a^7}{b^{11} \left(a+b x^2\right)^6}-\frac{21 a^6}{b^{11} \left(a+b x^2\right)^5}+\frac{63 a^5}{2 b^{11} \left(a+b x^2\right)^4}-\frac{35 a^4}{b^{11} \left(a+b x^2\right)^3}+\frac{30 a^3}{b^{11} \left(a+b x^2\right)^2}-\frac{45 a^2}{2 b^{11} \left(a+b x^2\right)}-\frac{5 a \log \left(a+b x^2\right)}{b^{11}}+\frac{x^2}{2 b^{10}}",1,"x^2/(2*b^10) - a^10/(18*b^11*(a + b*x^2)^9) + (5*a^9)/(8*b^11*(a + b*x^2)^8) - (45*a^8)/(14*b^11*(a + b*x^2)^7) + (10*a^7)/(b^11*(a + b*x^2)^6) - (21*a^6)/(b^11*(a + b*x^2)^5) + (63*a^5)/(2*b^11*(a + b*x^2)^4) - (35*a^4)/(b^11*(a + b*x^2)^3) + (30*a^3)/(b^11*(a + b*x^2)^2) - (45*a^2)/(2*b^11*(a + b*x^2)) - (5*a*Log[a + b*x^2])/b^11","A",3,2,13,0.1538,1,"{266, 43}"
195,1,179,0,0.1693556,"\int \frac{x^{19}}{\left(a+b x^2\right)^{10}} \, dx","Int[x^19/(a + b*x^2)^10,x]","\frac{a^9}{18 b^{10} \left(a+b x^2\right)^9}-\frac{9 a^8}{16 b^{10} \left(a+b x^2\right)^8}+\frac{18 a^7}{7 b^{10} \left(a+b x^2\right)^7}-\frac{7 a^6}{b^{10} \left(a+b x^2\right)^6}+\frac{63 a^5}{5 b^{10} \left(a+b x^2\right)^5}-\frac{63 a^4}{4 b^{10} \left(a+b x^2\right)^4}+\frac{14 a^3}{b^{10} \left(a+b x^2\right)^3}-\frac{9 a^2}{b^{10} \left(a+b x^2\right)^2}+\frac{9 a}{2 b^{10} \left(a+b x^2\right)}+\frac{\log \left(a+b x^2\right)}{2 b^{10}}","\frac{a^9}{18 b^{10} \left(a+b x^2\right)^9}-\frac{9 a^8}{16 b^{10} \left(a+b x^2\right)^8}+\frac{18 a^7}{7 b^{10} \left(a+b x^2\right)^7}-\frac{7 a^6}{b^{10} \left(a+b x^2\right)^6}+\frac{63 a^5}{5 b^{10} \left(a+b x^2\right)^5}-\frac{63 a^4}{4 b^{10} \left(a+b x^2\right)^4}+\frac{14 a^3}{b^{10} \left(a+b x^2\right)^3}-\frac{9 a^2}{b^{10} \left(a+b x^2\right)^2}+\frac{9 a}{2 b^{10} \left(a+b x^2\right)}+\frac{\log \left(a+b x^2\right)}{2 b^{10}}",1,"a^9/(18*b^10*(a + b*x^2)^9) - (9*a^8)/(16*b^10*(a + b*x^2)^8) + (18*a^7)/(7*b^10*(a + b*x^2)^7) - (7*a^6)/(b^10*(a + b*x^2)^6) + (63*a^5)/(5*b^10*(a + b*x^2)^5) - (63*a^4)/(4*b^10*(a + b*x^2)^4) + (14*a^3)/(b^10*(a + b*x^2)^3) - (9*a^2)/(b^10*(a + b*x^2)^2) + (9*a)/(2*b^10*(a + b*x^2)) + Log[a + b*x^2]/(2*b^10)","A",3,2,13,0.1538,1,"{266, 43}"
196,1,19,0,0.003412,"\int \frac{x^{17}}{\left(a+b x^2\right)^{10}} \, dx","Int[x^17/(a + b*x^2)^10,x]","\frac{x^{18}}{18 a \left(a+b x^2\right)^9}","\frac{x^{18}}{18 a \left(a+b x^2\right)^9}",1,"x^18/(18*a*(a + b*x^2)^9)","A",1,1,13,0.07692,1,"{264}"
197,1,39,0,0.0173839,"\int \frac{x^{15}}{\left(a+b x^2\right)^{10}} \, dx","Int[x^15/(a + b*x^2)^10,x]","\frac{x^{16}}{144 a^2 \left(a+b x^2\right)^8}+\frac{x^{16}}{18 a \left(a+b x^2\right)^9}","\frac{x^{16}}{144 a^2 \left(a+b x^2\right)^8}+\frac{x^{16}}{18 a \left(a+b x^2\right)^9}",1,"x^16/(18*a*(a + b*x^2)^9) + x^16/(144*a^2*(a + b*x^2)^8)","A",3,3,13,0.2308,1,"{266, 45, 37}"
198,1,58,0,0.0269605,"\int \frac{x^{13}}{\left(a+b x^2\right)^{10}} \, dx","Int[x^13/(a + b*x^2)^10,x]","\frac{x^{14}}{504 a^3 \left(a+b x^2\right)^7}+\frac{x^{14}}{72 a^2 \left(a+b x^2\right)^8}+\frac{x^{14}}{18 a \left(a+b x^2\right)^9}","\frac{x^{14}}{504 a^3 \left(a+b x^2\right)^7}+\frac{x^{14}}{72 a^2 \left(a+b x^2\right)^8}+\frac{x^{14}}{18 a \left(a+b x^2\right)^9}",1,"x^14/(18*a*(a + b*x^2)^9) + x^14/(72*a^2*(a + b*x^2)^8) + x^14/(504*a^3*(a + b*x^2)^7)","A",4,3,13,0.2308,1,"{266, 45, 37}"
199,1,77,0,0.0389887,"\int \frac{x^{11}}{\left(a+b x^2\right)^{10}} \, dx","Int[x^11/(a + b*x^2)^10,x]","\frac{x^{12}}{1008 a^4 \left(a+b x^2\right)^6}+\frac{x^{12}}{168 a^3 \left(a+b x^2\right)^7}+\frac{x^{12}}{48 a^2 \left(a+b x^2\right)^8}+\frac{x^{12}}{18 a \left(a+b x^2\right)^9}","\frac{x^{12}}{1008 a^4 \left(a+b x^2\right)^6}+\frac{x^{12}}{168 a^3 \left(a+b x^2\right)^7}+\frac{x^{12}}{48 a^2 \left(a+b x^2\right)^8}+\frac{x^{12}}{18 a \left(a+b x^2\right)^9}",1,"x^12/(18*a*(a + b*x^2)^9) + x^12/(48*a^2*(a + b*x^2)^8) + x^12/(168*a^3*(a + b*x^2)^7) + x^12/(1008*a^4*(a + b*x^2)^6)","A",5,3,13,0.2308,1,"{266, 45, 37}"
200,1,91,0,0.0676645,"\int \frac{x^9}{\left(a+b x^2\right)^{10}} \, dx","Int[x^9/(a + b*x^2)^10,x]","-\frac{a^4}{18 b^5 \left(a+b x^2\right)^9}+\frac{a^3}{4 b^5 \left(a+b x^2\right)^8}-\frac{3 a^2}{7 b^5 \left(a+b x^2\right)^7}+\frac{a}{3 b^5 \left(a+b x^2\right)^6}-\frac{1}{10 b^5 \left(a+b x^2\right)^5}","-\frac{a^4}{18 b^5 \left(a+b x^2\right)^9}+\frac{a^3}{4 b^5 \left(a+b x^2\right)^8}-\frac{3 a^2}{7 b^5 \left(a+b x^2\right)^7}+\frac{a}{3 b^5 \left(a+b x^2\right)^6}-\frac{1}{10 b^5 \left(a+b x^2\right)^5}",1,"-a^4/(18*b^5*(a + b*x^2)^9) + a^3/(4*b^5*(a + b*x^2)^8) - (3*a^2)/(7*b^5*(a + b*x^2)^7) + a/(3*b^5*(a + b*x^2)^6) - 1/(10*b^5*(a + b*x^2)^5)","A",3,2,13,0.1538,1,"{266, 43}"
201,1,72,0,0.0530002,"\int \frac{x^7}{\left(a+b x^2\right)^{10}} \, dx","Int[x^7/(a + b*x^2)^10,x]","\frac{a^3}{18 b^4 \left(a+b x^2\right)^9}-\frac{3 a^2}{16 b^4 \left(a+b x^2\right)^8}+\frac{3 a}{14 b^4 \left(a+b x^2\right)^7}-\frac{1}{12 b^4 \left(a+b x^2\right)^6}","\frac{a^3}{18 b^4 \left(a+b x^2\right)^9}-\frac{3 a^2}{16 b^4 \left(a+b x^2\right)^8}+\frac{3 a}{14 b^4 \left(a+b x^2\right)^7}-\frac{1}{12 b^4 \left(a+b x^2\right)^6}",1,"a^3/(18*b^4*(a + b*x^2)^9) - (3*a^2)/(16*b^4*(a + b*x^2)^8) + (3*a)/(14*b^4*(a + b*x^2)^7) - 1/(12*b^4*(a + b*x^2)^6)","A",3,2,13,0.1538,1,"{266, 43}"
202,1,53,0,0.0388855,"\int \frac{x^5}{\left(a+b x^2\right)^{10}} \, dx","Int[x^5/(a + b*x^2)^10,x]","-\frac{a^2}{18 b^3 \left(a+b x^2\right)^9}+\frac{a}{8 b^3 \left(a+b x^2\right)^8}-\frac{1}{14 b^3 \left(a+b x^2\right)^7}","-\frac{a^2}{18 b^3 \left(a+b x^2\right)^9}+\frac{a}{8 b^3 \left(a+b x^2\right)^8}-\frac{1}{14 b^3 \left(a+b x^2\right)^7}",1,"-a^2/(18*b^3*(a + b*x^2)^9) + a/(8*b^3*(a + b*x^2)^8) - 1/(14*b^3*(a + b*x^2)^7)","A",3,2,13,0.1538,1,"{266, 43}"
203,1,34,0,0.0251604,"\int \frac{x^3}{\left(a+b x^2\right)^{10}} \, dx","Int[x^3/(a + b*x^2)^10,x]","\frac{a}{18 b^2 \left(a+b x^2\right)^9}-\frac{1}{16 b^2 \left(a+b x^2\right)^8}","\frac{a}{18 b^2 \left(a+b x^2\right)^9}-\frac{1}{16 b^2 \left(a+b x^2\right)^8}",1,"a/(18*b^2*(a + b*x^2)^9) - 1/(16*b^2*(a + b*x^2)^8)","A",3,2,13,0.1538,1,"{266, 43}"
204,1,16,0,0.0027757,"\int \frac{x}{\left(a+b x^2\right)^{10}} \, dx","Int[x/(a + b*x^2)^10,x]","-\frac{1}{18 b \left(a+b x^2\right)^9}","-\frac{1}{18 b \left(a+b x^2\right)^9}",1,"-1/(18*b*(a + b*x^2)^9)","A",1,1,11,0.09091,1,"{261}"
205,1,166,0,0.1284627,"\int \frac{1}{x \left(a+b x^2\right)^{10}} \, dx","Int[1/(x*(a + b*x^2)^10),x]","\frac{1}{2 a^9 \left(a+b x^2\right)}+\frac{1}{4 a^8 \left(a+b x^2\right)^2}+\frac{1}{6 a^7 \left(a+b x^2\right)^3}+\frac{1}{8 a^6 \left(a+b x^2\right)^4}+\frac{1}{10 a^5 \left(a+b x^2\right)^5}+\frac{1}{12 a^4 \left(a+b x^2\right)^6}+\frac{1}{14 a^3 \left(a+b x^2\right)^7}+\frac{1}{16 a^2 \left(a+b x^2\right)^8}-\frac{\log \left(a+b x^2\right)}{2 a^{10}}+\frac{\log (x)}{a^{10}}+\frac{1}{18 a \left(a+b x^2\right)^9}","\frac{1}{2 a^9 \left(a+b x^2\right)}+\frac{1}{4 a^8 \left(a+b x^2\right)^2}+\frac{1}{6 a^7 \left(a+b x^2\right)^3}+\frac{1}{8 a^6 \left(a+b x^2\right)^4}+\frac{1}{10 a^5 \left(a+b x^2\right)^5}+\frac{1}{12 a^4 \left(a+b x^2\right)^6}+\frac{1}{14 a^3 \left(a+b x^2\right)^7}+\frac{1}{16 a^2 \left(a+b x^2\right)^8}-\frac{\log \left(a+b x^2\right)}{2 a^{10}}+\frac{\log (x)}{a^{10}}+\frac{1}{18 a \left(a+b x^2\right)^9}",1,"1/(18*a*(a + b*x^2)^9) + 1/(16*a^2*(a + b*x^2)^8) + 1/(14*a^3*(a + b*x^2)^7) + 1/(12*a^4*(a + b*x^2)^6) + 1/(10*a^5*(a + b*x^2)^5) + 1/(8*a^6*(a + b*x^2)^4) + 1/(6*a^7*(a + b*x^2)^3) + 1/(4*a^8*(a + b*x^2)^2) + 1/(2*a^9*(a + b*x^2)) + Log[x]/a^10 - Log[a + b*x^2]/(2*a^10)","A",3,2,13,0.1538,1,"{266, 44}"
206,1,184,0,0.1857086,"\int \frac{1}{x^3 \left(a+b x^2\right)^{10}} \, dx","Int[1/(x^3*(a + b*x^2)^10),x]","-\frac{9 b}{2 a^{10} \left(a+b x^2\right)}-\frac{2 b}{a^9 \left(a+b x^2\right)^2}-\frac{7 b}{6 a^8 \left(a+b x^2\right)^3}-\frac{3 b}{4 a^7 \left(a+b x^2\right)^4}-\frac{b}{2 a^6 \left(a+b x^2\right)^5}-\frac{b}{3 a^5 \left(a+b x^2\right)^6}-\frac{3 b}{14 a^4 \left(a+b x^2\right)^7}-\frac{b}{8 a^3 \left(a+b x^2\right)^8}-\frac{b}{18 a^2 \left(a+b x^2\right)^9}+\frac{5 b \log \left(a+b x^2\right)}{a^{11}}-\frac{10 b \log (x)}{a^{11}}-\frac{1}{2 a^{10} x^2}","-\frac{9 b}{2 a^{10} \left(a+b x^2\right)}-\frac{2 b}{a^9 \left(a+b x^2\right)^2}-\frac{7 b}{6 a^8 \left(a+b x^2\right)^3}-\frac{3 b}{4 a^7 \left(a+b x^2\right)^4}-\frac{b}{2 a^6 \left(a+b x^2\right)^5}-\frac{b}{3 a^5 \left(a+b x^2\right)^6}-\frac{3 b}{14 a^4 \left(a+b x^2\right)^7}-\frac{b}{8 a^3 \left(a+b x^2\right)^8}-\frac{b}{18 a^2 \left(a+b x^2\right)^9}+\frac{5 b \log \left(a+b x^2\right)}{a^{11}}-\frac{10 b \log (x)}{a^{11}}-\frac{1}{2 a^{10} x^2}",1,"-1/(2*a^10*x^2) - b/(18*a^2*(a + b*x^2)^9) - b/(8*a^3*(a + b*x^2)^8) - (3*b)/(14*a^4*(a + b*x^2)^7) - b/(3*a^5*(a + b*x^2)^6) - b/(2*a^6*(a + b*x^2)^5) - (3*b)/(4*a^7*(a + b*x^2)^4) - (7*b)/(6*a^8*(a + b*x^2)^3) - (2*b)/(a^9*(a + b*x^2)^2) - (9*b)/(2*a^10*(a + b*x^2)) - (10*b*Log[x])/a^11 + (5*b*Log[a + b*x^2])/a^11","A",3,2,13,0.1538,1,"{266, 44}"
207,1,217,0,0.2200027,"\int \frac{1}{x^5 \left(a+b x^2\right)^{10}} \, dx","Int[1/(x^5*(a + b*x^2)^10),x]","\frac{45 b^2}{2 a^{11} \left(a+b x^2\right)}+\frac{9 b^2}{a^{10} \left(a+b x^2\right)^2}+\frac{14 b^2}{3 a^9 \left(a+b x^2\right)^3}+\frac{21 b^2}{8 a^8 \left(a+b x^2\right)^4}+\frac{3 b^2}{2 a^7 \left(a+b x^2\right)^5}+\frac{5 b^2}{6 a^6 \left(a+b x^2\right)^6}+\frac{3 b^2}{7 a^5 \left(a+b x^2\right)^7}+\frac{3 b^2}{16 a^4 \left(a+b x^2\right)^8}+\frac{b^2}{18 a^3 \left(a+b x^2\right)^9}-\frac{55 b^2 \log \left(a+b x^2\right)}{2 a^{12}}+\frac{55 b^2 \log (x)}{a^{12}}+\frac{5 b}{a^{11} x^2}-\frac{1}{4 a^{10} x^4}","\frac{45 b^2}{2 a^{11} \left(a+b x^2\right)}+\frac{9 b^2}{a^{10} \left(a+b x^2\right)^2}+\frac{14 b^2}{3 a^9 \left(a+b x^2\right)^3}+\frac{21 b^2}{8 a^8 \left(a+b x^2\right)^4}+\frac{3 b^2}{2 a^7 \left(a+b x^2\right)^5}+\frac{5 b^2}{6 a^6 \left(a+b x^2\right)^6}+\frac{3 b^2}{7 a^5 \left(a+b x^2\right)^7}+\frac{3 b^2}{16 a^4 \left(a+b x^2\right)^8}+\frac{b^2}{18 a^3 \left(a+b x^2\right)^9}-\frac{55 b^2 \log \left(a+b x^2\right)}{2 a^{12}}+\frac{55 b^2 \log (x)}{a^{12}}+\frac{5 b}{a^{11} x^2}-\frac{1}{4 a^{10} x^4}",1,"-1/(4*a^10*x^4) + (5*b)/(a^11*x^2) + b^2/(18*a^3*(a + b*x^2)^9) + (3*b^2)/(16*a^4*(a + b*x^2)^8) + (3*b^2)/(7*a^5*(a + b*x^2)^7) + (5*b^2)/(6*a^6*(a + b*x^2)^6) + (3*b^2)/(2*a^7*(a + b*x^2)^5) + (21*b^2)/(8*a^8*(a + b*x^2)^4) + (14*b^2)/(3*a^9*(a + b*x^2)^3) + (9*b^2)/(a^10*(a + b*x^2)^2) + (45*b^2)/(2*a^11*(a + b*x^2)) + (55*b^2*Log[x])/a^12 - (55*b^2*Log[a + b*x^2])/(2*a^12)","A",3,2,13,0.1538,1,"{266, 44}"
208,1,226,0,0.2333516,"\int \frac{1}{x^7 \left(a+b x^2\right)^{10}} \, dx","Int[1/(x^7*(a + b*x^2)^10),x]","-\frac{165 b^3}{2 a^{12} \left(a+b x^2\right)}-\frac{30 b^3}{a^{11} \left(a+b x^2\right)^2}-\frac{14 b^3}{a^{10} \left(a+b x^2\right)^3}-\frac{7 b^3}{a^9 \left(a+b x^2\right)^4}-\frac{7 b^3}{2 a^8 \left(a+b x^2\right)^5}-\frac{5 b^3}{3 a^7 \left(a+b x^2\right)^6}-\frac{5 b^3}{7 a^6 \left(a+b x^2\right)^7}-\frac{b^3}{4 a^5 \left(a+b x^2\right)^8}-\frac{b^3}{18 a^4 \left(a+b x^2\right)^9}-\frac{55 b^2}{2 a^{12} x^2}+\frac{110 b^3 \log \left(a+b x^2\right)}{a^{13}}-\frac{220 b^3 \log (x)}{a^{13}}+\frac{5 b}{2 a^{11} x^4}-\frac{1}{6 a^{10} x^6}","-\frac{165 b^3}{2 a^{12} \left(a+b x^2\right)}-\frac{30 b^3}{a^{11} \left(a+b x^2\right)^2}-\frac{14 b^3}{a^{10} \left(a+b x^2\right)^3}-\frac{7 b^3}{a^9 \left(a+b x^2\right)^4}-\frac{7 b^3}{2 a^8 \left(a+b x^2\right)^5}-\frac{5 b^3}{3 a^7 \left(a+b x^2\right)^6}-\frac{5 b^3}{7 a^6 \left(a+b x^2\right)^7}-\frac{b^3}{4 a^5 \left(a+b x^2\right)^8}-\frac{b^3}{18 a^4 \left(a+b x^2\right)^9}-\frac{55 b^2}{2 a^{12} x^2}+\frac{110 b^3 \log \left(a+b x^2\right)}{a^{13}}-\frac{220 b^3 \log (x)}{a^{13}}+\frac{5 b}{2 a^{11} x^4}-\frac{1}{6 a^{10} x^6}",1,"-1/(6*a^10*x^6) + (5*b)/(2*a^11*x^4) - (55*b^2)/(2*a^12*x^2) - b^3/(18*a^4*(a + b*x^2)^9) - b^3/(4*a^5*(a + b*x^2)^8) - (5*b^3)/(7*a^6*(a + b*x^2)^7) - (5*b^3)/(3*a^7*(a + b*x^2)^6) - (7*b^3)/(2*a^8*(a + b*x^2)^5) - (7*b^3)/(a^9*(a + b*x^2)^4) - (14*b^3)/(a^10*(a + b*x^2)^3) - (30*b^3)/(a^11*(a + b*x^2)^2) - (165*b^3)/(2*a^12*(a + b*x^2)) - (220*b^3*Log[x])/a^13 + (110*b^3*Log[a + b*x^2])/a^13","A",3,2,13,0.1538,1,"{266, 44}"
209,1,231,0,0.1671873,"\int \frac{x^{24}}{\left(a+b x^2\right)^{10}} \, dx","Int[x^24/(a + b*x^2)^10,x]","\frac{7436429 a^2 x}{65536 b^{12}}-\frac{7436429 a^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 b^{25/2}}-\frac{23 x^{21}}{288 b^2 \left(a+b x^2\right)^8}-\frac{23 x^{19}}{192 b^3 \left(a+b x^2\right)^7}-\frac{437 x^{17}}{2304 b^4 \left(a+b x^2\right)^6}-\frac{7429 x^{15}}{23040 b^5 \left(a+b x^2\right)^5}-\frac{7429 x^{13}}{12288 b^6 \left(a+b x^2\right)^4}-\frac{96577 x^{11}}{73728 b^7 \left(a+b x^2\right)^3}-\frac{1062347 x^9}{294912 b^8 \left(a+b x^2\right)^2}-\frac{1062347 x^7}{65536 b^9 \left(a+b x^2\right)}-\frac{7436429 a x^3}{196608 b^{11}}-\frac{x^{23}}{18 b \left(a+b x^2\right)^9}+\frac{7436429 x^5}{327680 b^{10}}","\frac{7436429 a^2 x}{65536 b^{12}}-\frac{7436429 a^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 b^{25/2}}-\frac{23 x^{21}}{288 b^2 \left(a+b x^2\right)^8}-\frac{23 x^{19}}{192 b^3 \left(a+b x^2\right)^7}-\frac{437 x^{17}}{2304 b^4 \left(a+b x^2\right)^6}-\frac{7429 x^{15}}{23040 b^5 \left(a+b x^2\right)^5}-\frac{7429 x^{13}}{12288 b^6 \left(a+b x^2\right)^4}-\frac{96577 x^{11}}{73728 b^7 \left(a+b x^2\right)^3}-\frac{1062347 x^9}{294912 b^8 \left(a+b x^2\right)^2}-\frac{1062347 x^7}{65536 b^9 \left(a+b x^2\right)}-\frac{7436429 a x^3}{196608 b^{11}}-\frac{x^{23}}{18 b \left(a+b x^2\right)^9}+\frac{7436429 x^5}{327680 b^{10}}",1,"(7436429*a^2*x)/(65536*b^12) - (7436429*a*x^3)/(196608*b^11) + (7436429*x^5)/(327680*b^10) - x^23/(18*b*(a + b*x^2)^9) - (23*x^21)/(288*b^2*(a + b*x^2)^8) - (23*x^19)/(192*b^3*(a + b*x^2)^7) - (437*x^17)/(2304*b^4*(a + b*x^2)^6) - (7429*x^15)/(23040*b^5*(a + b*x^2)^5) - (7429*x^13)/(12288*b^6*(a + b*x^2)^4) - (96577*x^11)/(73728*b^7*(a + b*x^2)^3) - (1062347*x^9)/(294912*b^8*(a + b*x^2)^2) - (1062347*x^7)/(65536*b^9*(a + b*x^2)) - (7436429*a^(5/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(65536*b^(25/2))","A",12,3,13,0.2308,1,"{288, 302, 205}"
210,1,218,0,0.1405872,"\int \frac{x^{22}}{\left(a+b x^2\right)^{10}} \, dx","Int[x^22/(a + b*x^2)^10,x]","\frac{1616615 a^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 b^{23/2}}-\frac{7 x^{19}}{96 b^2 \left(a+b x^2\right)^8}-\frac{19 x^{17}}{192 b^3 \left(a+b x^2\right)^7}-\frac{323 x^{15}}{2304 b^4 \left(a+b x^2\right)^6}-\frac{323 x^{13}}{1536 b^5 \left(a+b x^2\right)^5}-\frac{4199 x^{11}}{12288 b^6 \left(a+b x^2\right)^4}-\frac{46189 x^9}{73728 b^7 \left(a+b x^2\right)^3}-\frac{46189 x^7}{32768 b^8 \left(a+b x^2\right)^2}-\frac{323323 x^5}{65536 b^9 \left(a+b x^2\right)}-\frac{1616615 a x}{65536 b^{11}}-\frac{x^{21}}{18 b \left(a+b x^2\right)^9}+\frac{1616615 x^3}{196608 b^{10}}","\frac{1616615 a^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 b^{23/2}}-\frac{7 x^{19}}{96 b^2 \left(a+b x^2\right)^8}-\frac{19 x^{17}}{192 b^3 \left(a+b x^2\right)^7}-\frac{323 x^{15}}{2304 b^4 \left(a+b x^2\right)^6}-\frac{323 x^{13}}{1536 b^5 \left(a+b x^2\right)^5}-\frac{4199 x^{11}}{12288 b^6 \left(a+b x^2\right)^4}-\frac{46189 x^9}{73728 b^7 \left(a+b x^2\right)^3}-\frac{46189 x^7}{32768 b^8 \left(a+b x^2\right)^2}-\frac{323323 x^5}{65536 b^9 \left(a+b x^2\right)}-\frac{1616615 a x}{65536 b^{11}}-\frac{x^{21}}{18 b \left(a+b x^2\right)^9}+\frac{1616615 x^3}{196608 b^{10}}",1,"(-1616615*a*x)/(65536*b^11) + (1616615*x^3)/(196608*b^10) - x^21/(18*b*(a + b*x^2)^9) - (7*x^19)/(96*b^2*(a + b*x^2)^8) - (19*x^17)/(192*b^3*(a + b*x^2)^7) - (323*x^15)/(2304*b^4*(a + b*x^2)^6) - (323*x^13)/(1536*b^5*(a + b*x^2)^5) - (4199*x^11)/(12288*b^6*(a + b*x^2)^4) - (46189*x^9)/(73728*b^7*(a + b*x^2)^3) - (46189*x^7)/(32768*b^8*(a + b*x^2)^2) - (323323*x^5)/(65536*b^9*(a + b*x^2)) + (1616615*a^(3/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(65536*b^(23/2))","A",12,3,13,0.2308,1,"{288, 302, 205}"
211,1,207,0,0.1241246,"\int \frac{x^{20}}{\left(a+b x^2\right)^{10}} \, dx","Int[x^20/(a + b*x^2)^10,x]","-\frac{19 x^{17}}{288 b^2 \left(a+b x^2\right)^8}-\frac{323 x^{15}}{4032 b^3 \left(a+b x^2\right)^7}-\frac{1615 x^{13}}{16128 b^4 \left(a+b x^2\right)^6}-\frac{4199 x^{11}}{32256 b^5 \left(a+b x^2\right)^5}-\frac{46189 x^9}{258048 b^6 \left(a+b x^2\right)^4}-\frac{46189 x^7}{172032 b^7 \left(a+b x^2\right)^3}-\frac{46189 x^5}{98304 b^8 \left(a+b x^2\right)^2}-\frac{230945 x^3}{196608 b^9 \left(a+b x^2\right)}-\frac{230945 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 b^{21/2}}-\frac{x^{19}}{18 b \left(a+b x^2\right)^9}+\frac{230945 x}{65536 b^{10}}","-\frac{19 x^{17}}{288 b^2 \left(a+b x^2\right)^8}-\frac{323 x^{15}}{4032 b^3 \left(a+b x^2\right)^7}-\frac{1615 x^{13}}{16128 b^4 \left(a+b x^2\right)^6}-\frac{4199 x^{11}}{32256 b^5 \left(a+b x^2\right)^5}-\frac{46189 x^9}{258048 b^6 \left(a+b x^2\right)^4}-\frac{46189 x^7}{172032 b^7 \left(a+b x^2\right)^3}-\frac{46189 x^5}{98304 b^8 \left(a+b x^2\right)^2}-\frac{230945 x^3}{196608 b^9 \left(a+b x^2\right)}-\frac{230945 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 b^{21/2}}-\frac{x^{19}}{18 b \left(a+b x^2\right)^9}+\frac{230945 x}{65536 b^{10}}",1,"(230945*x)/(65536*b^10) - x^19/(18*b*(a + b*x^2)^9) - (19*x^17)/(288*b^2*(a + b*x^2)^8) - (323*x^15)/(4032*b^3*(a + b*x^2)^7) - (1615*x^13)/(16128*b^4*(a + b*x^2)^6) - (4199*x^11)/(32256*b^5*(a + b*x^2)^5) - (46189*x^9)/(258048*b^6*(a + b*x^2)^4) - (46189*x^7)/(172032*b^7*(a + b*x^2)^3) - (46189*x^5)/(98304*b^8*(a + b*x^2)^2) - (230945*x^3)/(196608*b^9*(a + b*x^2)) - (230945*Sqrt[a]*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(65536*b^(21/2))","A",11,3,13,0.2308,1,"{288, 321, 205}"
212,1,197,0,0.1132432,"\int \frac{x^{18}}{\left(a+b x^2\right)^{10}} \, dx","Int[x^18/(a + b*x^2)^10,x]","-\frac{17 x^{15}}{288 b^2 \left(a+b x^2\right)^8}-\frac{85 x^{13}}{1344 b^3 \left(a+b x^2\right)^7}-\frac{1105 x^{11}}{16128 b^4 \left(a+b x^2\right)^6}-\frac{2431 x^9}{32256 b^5 \left(a+b x^2\right)^5}-\frac{2431 x^7}{28672 b^6 \left(a+b x^2\right)^4}-\frac{2431 x^5}{24576 b^7 \left(a+b x^2\right)^3}-\frac{12155 x^3}{98304 b^8 \left(a+b x^2\right)^2}-\frac{12155 x}{65536 b^9 \left(a+b x^2\right)}+\frac{12155 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 \sqrt{a} b^{19/2}}-\frac{x^{17}}{18 b \left(a+b x^2\right)^9}","-\frac{17 x^{15}}{288 b^2 \left(a+b x^2\right)^8}-\frac{85 x^{13}}{1344 b^3 \left(a+b x^2\right)^7}-\frac{1105 x^{11}}{16128 b^4 \left(a+b x^2\right)^6}-\frac{2431 x^9}{32256 b^5 \left(a+b x^2\right)^5}-\frac{2431 x^7}{28672 b^6 \left(a+b x^2\right)^4}-\frac{2431 x^5}{24576 b^7 \left(a+b x^2\right)^3}-\frac{12155 x^3}{98304 b^8 \left(a+b x^2\right)^2}-\frac{12155 x}{65536 b^9 \left(a+b x^2\right)}+\frac{12155 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 \sqrt{a} b^{19/2}}-\frac{x^{17}}{18 b \left(a+b x^2\right)^9}",1,"-x^17/(18*b*(a + b*x^2)^9) - (17*x^15)/(288*b^2*(a + b*x^2)^8) - (85*x^13)/(1344*b^3*(a + b*x^2)^7) - (1105*x^11)/(16128*b^4*(a + b*x^2)^6) - (2431*x^9)/(32256*b^5*(a + b*x^2)^5) - (2431*x^7)/(28672*b^6*(a + b*x^2)^4) - (2431*x^5)/(24576*b^7*(a + b*x^2)^3) - (12155*x^3)/(98304*b^8*(a + b*x^2)^2) - (12155*x)/(65536*b^9*(a + b*x^2)) + (12155*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(65536*Sqrt[a]*b^(19/2))","A",10,2,13,0.1538,1,"{288, 205}"
213,1,198,0,0.1223015,"\int \frac{x^{16}}{\left(a+b x^2\right)^{10}} \, dx","Int[x^16/(a + b*x^2)^10,x]","\frac{715 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 a^{3/2} b^{17/2}}-\frac{5 x^{13}}{96 b^2 \left(a+b x^2\right)^8}-\frac{65 x^{11}}{1344 b^3 \left(a+b x^2\right)^7}-\frac{715 x^9}{16128 b^4 \left(a+b x^2\right)^6}-\frac{143 x^7}{3584 b^5 \left(a+b x^2\right)^5}-\frac{143 x^5}{4096 b^6 \left(a+b x^2\right)^4}-\frac{715 x^3}{24576 b^7 \left(a+b x^2\right)^3}+\frac{715 x}{65536 a b^8 \left(a+b x^2\right)}-\frac{715 x}{32768 b^8 \left(a+b x^2\right)^2}-\frac{x^{15}}{18 b \left(a+b x^2\right)^9}","\frac{715 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 a^{3/2} b^{17/2}}-\frac{5 x^{13}}{96 b^2 \left(a+b x^2\right)^8}-\frac{65 x^{11}}{1344 b^3 \left(a+b x^2\right)^7}-\frac{715 x^9}{16128 b^4 \left(a+b x^2\right)^6}-\frac{143 x^7}{3584 b^5 \left(a+b x^2\right)^5}-\frac{143 x^5}{4096 b^6 \left(a+b x^2\right)^4}-\frac{715 x^3}{24576 b^7 \left(a+b x^2\right)^3}+\frac{715 x}{65536 a b^8 \left(a+b x^2\right)}-\frac{715 x}{32768 b^8 \left(a+b x^2\right)^2}-\frac{x^{15}}{18 b \left(a+b x^2\right)^9}",1,"-x^15/(18*b*(a + b*x^2)^9) - (5*x^13)/(96*b^2*(a + b*x^2)^8) - (65*x^11)/(1344*b^3*(a + b*x^2)^7) - (715*x^9)/(16128*b^4*(a + b*x^2)^6) - (143*x^7)/(3584*b^5*(a + b*x^2)^5) - (143*x^5)/(4096*b^6*(a + b*x^2)^4) - (715*x^3)/(24576*b^7*(a + b*x^2)^3) - (715*x)/(32768*b^8*(a + b*x^2)^2) + (715*x)/(65536*a*b^8*(a + b*x^2)) + (715*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(65536*a^(3/2)*b^(17/2))","A",10,3,13,0.2308,1,"{288, 199, 205}"
214,1,199,0,0.1229932,"\int \frac{x^{14}}{\left(a+b x^2\right)^{10}} \, dx","Int[x^14/(a + b*x^2)^10,x]","\frac{143 x}{65536 a^2 b^7 \left(a+b x^2\right)}+\frac{143 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 a^{5/2} b^{15/2}}-\frac{13 x^{11}}{288 b^2 \left(a+b x^2\right)^8}-\frac{143 x^9}{4032 b^3 \left(a+b x^2\right)^7}-\frac{143 x^7}{5376 b^4 \left(a+b x^2\right)^6}-\frac{143 x^5}{7680 b^5 \left(a+b x^2\right)^5}-\frac{143 x^3}{12288 b^6 \left(a+b x^2\right)^4}+\frac{143 x}{98304 a b^7 \left(a+b x^2\right)^2}-\frac{143 x}{24576 b^7 \left(a+b x^2\right)^3}-\frac{x^{13}}{18 b \left(a+b x^2\right)^9}","\frac{143 x}{65536 a^2 b^7 \left(a+b x^2\right)}+\frac{143 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 a^{5/2} b^{15/2}}-\frac{13 x^{11}}{288 b^2 \left(a+b x^2\right)^8}-\frac{143 x^9}{4032 b^3 \left(a+b x^2\right)^7}-\frac{143 x^7}{5376 b^4 \left(a+b x^2\right)^6}-\frac{143 x^5}{7680 b^5 \left(a+b x^2\right)^5}-\frac{143 x^3}{12288 b^6 \left(a+b x^2\right)^4}+\frac{143 x}{98304 a b^7 \left(a+b x^2\right)^2}-\frac{143 x}{24576 b^7 \left(a+b x^2\right)^3}-\frac{x^{13}}{18 b \left(a+b x^2\right)^9}",1,"-x^13/(18*b*(a + b*x^2)^9) - (13*x^11)/(288*b^2*(a + b*x^2)^8) - (143*x^9)/(4032*b^3*(a + b*x^2)^7) - (143*x^7)/(5376*b^4*(a + b*x^2)^6) - (143*x^5)/(7680*b^5*(a + b*x^2)^5) - (143*x^3)/(12288*b^6*(a + b*x^2)^4) - (143*x)/(24576*b^7*(a + b*x^2)^3) + (143*x)/(98304*a*b^7*(a + b*x^2)^2) + (143*x)/(65536*a^2*b^7*(a + b*x^2)) + (143*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(65536*a^(5/2)*b^(15/2))","A",10,3,13,0.2308,1,"{288, 199, 205}"
215,1,200,0,0.120337,"\int \frac{x^{12}}{\left(a+b x^2\right)^{10}} \, dx","Int[x^12/(a + b*x^2)^10,x]","\frac{55 x}{65536 a^3 b^6 \left(a+b x^2\right)}+\frac{55 x}{98304 a^2 b^6 \left(a+b x^2\right)^2}+\frac{55 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 a^{7/2} b^{13/2}}-\frac{11 x^9}{288 b^2 \left(a+b x^2\right)^8}-\frac{11 x^7}{448 b^3 \left(a+b x^2\right)^7}-\frac{11 x^5}{768 b^4 \left(a+b x^2\right)^6}-\frac{11 x^3}{1536 b^5 \left(a+b x^2\right)^5}+\frac{11 x}{24576 a b^6 \left(a+b x^2\right)^3}-\frac{11 x}{4096 b^6 \left(a+b x^2\right)^4}-\frac{x^{11}}{18 b \left(a+b x^2\right)^9}","\frac{55 x}{65536 a^3 b^6 \left(a+b x^2\right)}+\frac{55 x}{98304 a^2 b^6 \left(a+b x^2\right)^2}+\frac{55 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 a^{7/2} b^{13/2}}-\frac{11 x^9}{288 b^2 \left(a+b x^2\right)^8}-\frac{11 x^7}{448 b^3 \left(a+b x^2\right)^7}-\frac{11 x^5}{768 b^4 \left(a+b x^2\right)^6}-\frac{11 x^3}{1536 b^5 \left(a+b x^2\right)^5}+\frac{11 x}{24576 a b^6 \left(a+b x^2\right)^3}-\frac{11 x}{4096 b^6 \left(a+b x^2\right)^4}-\frac{x^{11}}{18 b \left(a+b x^2\right)^9}",1,"-x^11/(18*b*(a + b*x^2)^9) - (11*x^9)/(288*b^2*(a + b*x^2)^8) - (11*x^7)/(448*b^3*(a + b*x^2)^7) - (11*x^5)/(768*b^4*(a + b*x^2)^6) - (11*x^3)/(1536*b^5*(a + b*x^2)^5) - (11*x)/(4096*b^6*(a + b*x^2)^4) + (11*x)/(24576*a*b^6*(a + b*x^2)^3) + (55*x)/(98304*a^2*b^6*(a + b*x^2)^2) + (55*x)/(65536*a^3*b^6*(a + b*x^2)) + (55*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(65536*a^(7/2)*b^(13/2))","A",10,3,13,0.2308,1,"{288, 199, 205}"
216,1,201,0,0.1190511,"\int \frac{x^{10}}{\left(a+b x^2\right)^{10}} \, dx","Int[x^10/(a + b*x^2)^10,x]","\frac{35 x}{65536 a^4 b^5 \left(a+b x^2\right)}+\frac{35 x}{98304 a^3 b^5 \left(a+b x^2\right)^2}+\frac{7 x}{24576 a^2 b^5 \left(a+b x^2\right)^3}+\frac{35 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 a^{9/2} b^{11/2}}-\frac{x^7}{32 b^2 \left(a+b x^2\right)^8}-\frac{x^5}{64 b^3 \left(a+b x^2\right)^7}-\frac{5 x^3}{768 b^4 \left(a+b x^2\right)^6}+\frac{x}{4096 a b^5 \left(a+b x^2\right)^4}-\frac{x}{512 b^5 \left(a+b x^2\right)^5}-\frac{x^9}{18 b \left(a+b x^2\right)^9}","\frac{35 x}{65536 a^4 b^5 \left(a+b x^2\right)}+\frac{35 x}{98304 a^3 b^5 \left(a+b x^2\right)^2}+\frac{7 x}{24576 a^2 b^5 \left(a+b x^2\right)^3}+\frac{35 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 a^{9/2} b^{11/2}}-\frac{x^7}{32 b^2 \left(a+b x^2\right)^8}-\frac{x^5}{64 b^3 \left(a+b x^2\right)^7}-\frac{5 x^3}{768 b^4 \left(a+b x^2\right)^6}+\frac{x}{4096 a b^5 \left(a+b x^2\right)^4}-\frac{x}{512 b^5 \left(a+b x^2\right)^5}-\frac{x^9}{18 b \left(a+b x^2\right)^9}",1,"-x^9/(18*b*(a + b*x^2)^9) - x^7/(32*b^2*(a + b*x^2)^8) - x^5/(64*b^3*(a + b*x^2)^7) - (5*x^3)/(768*b^4*(a + b*x^2)^6) - x/(512*b^5*(a + b*x^2)^5) + x/(4096*a*b^5*(a + b*x^2)^4) + (7*x)/(24576*a^2*b^5*(a + b*x^2)^3) + (35*x)/(98304*a^3*b^5*(a + b*x^2)^2) + (35*x)/(65536*a^4*b^5*(a + b*x^2)) + (35*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(65536*a^(9/2)*b^(11/2))","A",10,3,13,0.2308,1,"{288, 199, 205}"
217,1,202,0,0.1156319,"\int \frac{x^8}{\left(a+b x^2\right)^{10}} \, dx","Int[x^8/(a + b*x^2)^10,x]","\frac{35 x}{65536 a^5 b^4 \left(a+b x^2\right)}+\frac{35 x}{98304 a^4 b^4 \left(a+b x^2\right)^2}+\frac{7 x}{24576 a^3 b^4 \left(a+b x^2\right)^3}+\frac{x}{4096 a^2 b^4 \left(a+b x^2\right)^4}+\frac{35 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 a^{11/2} b^{9/2}}-\frac{7 x^5}{288 b^2 \left(a+b x^2\right)^8}-\frac{5 x^3}{576 b^3 \left(a+b x^2\right)^7}+\frac{x}{4608 a b^4 \left(a+b x^2\right)^5}-\frac{5 x}{2304 b^4 \left(a+b x^2\right)^6}-\frac{x^7}{18 b \left(a+b x^2\right)^9}","\frac{35 x}{65536 a^5 b^4 \left(a+b x^2\right)}+\frac{35 x}{98304 a^4 b^4 \left(a+b x^2\right)^2}+\frac{7 x}{24576 a^3 b^4 \left(a+b x^2\right)^3}+\frac{x}{4096 a^2 b^4 \left(a+b x^2\right)^4}+\frac{35 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 a^{11/2} b^{9/2}}-\frac{7 x^5}{288 b^2 \left(a+b x^2\right)^8}-\frac{5 x^3}{576 b^3 \left(a+b x^2\right)^7}+\frac{x}{4608 a b^4 \left(a+b x^2\right)^5}-\frac{5 x}{2304 b^4 \left(a+b x^2\right)^6}-\frac{x^7}{18 b \left(a+b x^2\right)^9}",1,"-x^7/(18*b*(a + b*x^2)^9) - (7*x^5)/(288*b^2*(a + b*x^2)^8) - (5*x^3)/(576*b^3*(a + b*x^2)^7) - (5*x)/(2304*b^4*(a + b*x^2)^6) + x/(4608*a*b^4*(a + b*x^2)^5) + x/(4096*a^2*b^4*(a + b*x^2)^4) + (7*x)/(24576*a^3*b^4*(a + b*x^2)^3) + (35*x)/(98304*a^4*b^4*(a + b*x^2)^2) + (35*x)/(65536*a^5*b^4*(a + b*x^2)) + (35*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(65536*a^(11/2)*b^(9/2))","A",10,3,13,0.2308,1,"{288, 199, 205}"
218,1,203,0,0.1112349,"\int \frac{x^6}{\left(a+b x^2\right)^{10}} \, dx","Int[x^6/(a + b*x^2)^10,x]","\frac{55 x}{65536 a^6 b^3 \left(a+b x^2\right)}+\frac{55 x}{98304 a^5 b^3 \left(a+b x^2\right)^2}+\frac{11 x}{24576 a^4 b^3 \left(a+b x^2\right)^3}+\frac{11 x}{28672 a^3 b^3 \left(a+b x^2\right)^4}+\frac{11 x}{32256 a^2 b^3 \left(a+b x^2\right)^5}+\frac{55 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 a^{13/2} b^{7/2}}-\frac{5 x^3}{288 b^2 \left(a+b x^2\right)^8}+\frac{5 x}{16128 a b^3 \left(a+b x^2\right)^6}-\frac{5 x}{1344 b^3 \left(a+b x^2\right)^7}-\frac{x^5}{18 b \left(a+b x^2\right)^9}","\frac{55 x}{65536 a^6 b^3 \left(a+b x^2\right)}+\frac{55 x}{98304 a^5 b^3 \left(a+b x^2\right)^2}+\frac{11 x}{24576 a^4 b^3 \left(a+b x^2\right)^3}+\frac{11 x}{28672 a^3 b^3 \left(a+b x^2\right)^4}+\frac{11 x}{32256 a^2 b^3 \left(a+b x^2\right)^5}+\frac{55 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 a^{13/2} b^{7/2}}-\frac{5 x^3}{288 b^2 \left(a+b x^2\right)^8}+\frac{5 x}{16128 a b^3 \left(a+b x^2\right)^6}-\frac{5 x}{1344 b^3 \left(a+b x^2\right)^7}-\frac{x^5}{18 b \left(a+b x^2\right)^9}",1,"-x^5/(18*b*(a + b*x^2)^9) - (5*x^3)/(288*b^2*(a + b*x^2)^8) - (5*x)/(1344*b^3*(a + b*x^2)^7) + (5*x)/(16128*a*b^3*(a + b*x^2)^6) + (11*x)/(32256*a^2*b^3*(a + b*x^2)^5) + (11*x)/(28672*a^3*b^3*(a + b*x^2)^4) + (11*x)/(24576*a^4*b^3*(a + b*x^2)^3) + (55*x)/(98304*a^5*b^3*(a + b*x^2)^2) + (55*x)/(65536*a^6*b^3*(a + b*x^2)) + (55*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(65536*a^(13/2)*b^(7/2))","A",10,3,13,0.2308,1,"{288, 199, 205}"
219,1,204,0,0.1080831,"\int \frac{x^4}{\left(a+b x^2\right)^{10}} \, dx","Int[x^4/(a + b*x^2)^10,x]","\frac{143 x}{65536 a^7 b^2 \left(a+b x^2\right)}+\frac{143 x}{98304 a^6 b^2 \left(a+b x^2\right)^2}+\frac{143 x}{122880 a^5 b^2 \left(a+b x^2\right)^3}+\frac{143 x}{143360 a^4 b^2 \left(a+b x^2\right)^4}+\frac{143 x}{161280 a^3 b^2 \left(a+b x^2\right)^5}+\frac{13 x}{16128 a^2 b^2 \left(a+b x^2\right)^6}+\frac{143 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 a^{15/2} b^{5/2}}+\frac{x}{1344 a b^2 \left(a+b x^2\right)^7}-\frac{x}{96 b^2 \left(a+b x^2\right)^8}-\frac{x^3}{18 b \left(a+b x^2\right)^9}","\frac{143 x}{65536 a^7 b^2 \left(a+b x^2\right)}+\frac{143 x}{98304 a^6 b^2 \left(a+b x^2\right)^2}+\frac{143 x}{122880 a^5 b^2 \left(a+b x^2\right)^3}+\frac{143 x}{143360 a^4 b^2 \left(a+b x^2\right)^4}+\frac{143 x}{161280 a^3 b^2 \left(a+b x^2\right)^5}+\frac{13 x}{16128 a^2 b^2 \left(a+b x^2\right)^6}+\frac{143 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 a^{15/2} b^{5/2}}+\frac{x}{1344 a b^2 \left(a+b x^2\right)^7}-\frac{x}{96 b^2 \left(a+b x^2\right)^8}-\frac{x^3}{18 b \left(a+b x^2\right)^9}",1,"-x^3/(18*b*(a + b*x^2)^9) - x/(96*b^2*(a + b*x^2)^8) + x/(1344*a*b^2*(a + b*x^2)^7) + (13*x)/(16128*a^2*b^2*(a + b*x^2)^6) + (143*x)/(161280*a^3*b^2*(a + b*x^2)^5) + (143*x)/(143360*a^4*b^2*(a + b*x^2)^4) + (143*x)/(122880*a^5*b^2*(a + b*x^2)^3) + (143*x)/(98304*a^6*b^2*(a + b*x^2)^2) + (143*x)/(65536*a^7*b^2*(a + b*x^2)) + (143*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(65536*a^(15/2)*b^(5/2))","A",10,3,13,0.2308,1,"{288, 199, 205}"
220,1,205,0,0.1059709,"\int \frac{x^2}{\left(a+b x^2\right)^{10}} \, dx","Int[x^2/(a + b*x^2)^10,x]","\frac{715 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 a^{17/2} b^{3/2}}+\frac{715 x}{65536 a^8 b \left(a+b x^2\right)}+\frac{715 x}{98304 a^7 b \left(a+b x^2\right)^2}+\frac{143 x}{24576 a^6 b \left(a+b x^2\right)^3}+\frac{143 x}{28672 a^5 b \left(a+b x^2\right)^4}+\frac{143 x}{32256 a^4 b \left(a+b x^2\right)^5}+\frac{65 x}{16128 a^3 b \left(a+b x^2\right)^6}+\frac{5 x}{1344 a^2 b \left(a+b x^2\right)^7}+\frac{x}{288 a b \left(a+b x^2\right)^8}-\frac{x}{18 b \left(a+b x^2\right)^9}","\frac{715 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 a^{17/2} b^{3/2}}+\frac{715 x}{65536 a^8 b \left(a+b x^2\right)}+\frac{715 x}{98304 a^7 b \left(a+b x^2\right)^2}+\frac{143 x}{24576 a^6 b \left(a+b x^2\right)^3}+\frac{143 x}{28672 a^5 b \left(a+b x^2\right)^4}+\frac{143 x}{32256 a^4 b \left(a+b x^2\right)^5}+\frac{65 x}{16128 a^3 b \left(a+b x^2\right)^6}+\frac{5 x}{1344 a^2 b \left(a+b x^2\right)^7}+\frac{x}{288 a b \left(a+b x^2\right)^8}-\frac{x}{18 b \left(a+b x^2\right)^9}",1,"-x/(18*b*(a + b*x^2)^9) + x/(288*a*b*(a + b*x^2)^8) + (5*x)/(1344*a^2*b*(a + b*x^2)^7) + (65*x)/(16128*a^3*b*(a + b*x^2)^6) + (143*x)/(32256*a^4*b*(a + b*x^2)^5) + (143*x)/(28672*a^5*b*(a + b*x^2)^4) + (143*x)/(24576*a^6*b*(a + b*x^2)^3) + (715*x)/(98304*a^7*b*(a + b*x^2)^2) + (715*x)/(65536*a^8*b*(a + b*x^2)) + (715*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(65536*a^(17/2)*b^(3/2))","A",10,3,13,0.2308,1,"{288, 199, 205}"
221,1,181,0,0.0996333,"\int \frac{1}{\left(a+b x^2\right)^{10}} \, dx","Int[(a + b*x^2)^(-10),x]","\frac{12155 x}{65536 a^9 \left(a+b x^2\right)}+\frac{12155 x}{98304 a^8 \left(a+b x^2\right)^2}+\frac{2431 x}{24576 a^7 \left(a+b x^2\right)^3}+\frac{2431 x}{28672 a^6 \left(a+b x^2\right)^4}+\frac{2431 x}{32256 a^5 \left(a+b x^2\right)^5}+\frac{1105 x}{16128 a^4 \left(a+b x^2\right)^6}+\frac{85 x}{1344 a^3 \left(a+b x^2\right)^7}+\frac{17 x}{288 a^2 \left(a+b x^2\right)^8}+\frac{12155 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 a^{19/2} \sqrt{b}}+\frac{x}{18 a \left(a+b x^2\right)^9}","\frac{12155 x}{65536 a^9 \left(a+b x^2\right)}+\frac{12155 x}{98304 a^8 \left(a+b x^2\right)^2}+\frac{2431 x}{24576 a^7 \left(a+b x^2\right)^3}+\frac{2431 x}{28672 a^6 \left(a+b x^2\right)^4}+\frac{2431 x}{32256 a^5 \left(a+b x^2\right)^5}+\frac{1105 x}{16128 a^4 \left(a+b x^2\right)^6}+\frac{85 x}{1344 a^3 \left(a+b x^2\right)^7}+\frac{17 x}{288 a^2 \left(a+b x^2\right)^8}+\frac{12155 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 a^{19/2} \sqrt{b}}+\frac{x}{18 a \left(a+b x^2\right)^9}",1,"x/(18*a*(a + b*x^2)^9) + (17*x)/(288*a^2*(a + b*x^2)^8) + (85*x)/(1344*a^3*(a + b*x^2)^7) + (1105*x)/(16128*a^4*(a + b*x^2)^6) + (2431*x)/(32256*a^5*(a + b*x^2)^5) + (2431*x)/(28672*a^6*(a + b*x^2)^4) + (2431*x)/(24576*a^7*(a + b*x^2)^3) + (12155*x)/(98304*a^8*(a + b*x^2)^2) + (12155*x)/(65536*a^9*(a + b*x^2)) + (12155*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(65536*a^(19/2)*Sqrt[b])","A",10,2,9,0.2222,1,"{199, 205}"
222,1,209,0,0.1308136,"\int \frac{1}{x^2 \left(a+b x^2\right)^{10}} \, dx","Int[1/(x^2*(a + b*x^2)^10),x]","\frac{230945}{196608 a^9 x \left(a+b x^2\right)}+\frac{46189}{98304 a^8 x \left(a+b x^2\right)^2}+\frac{46189}{172032 a^7 x \left(a+b x^2\right)^3}+\frac{46189}{258048 a^6 x \left(a+b x^2\right)^4}+\frac{4199}{32256 a^5 x \left(a+b x^2\right)^5}+\frac{1615}{16128 a^4 x \left(a+b x^2\right)^6}+\frac{323}{4032 a^3 x \left(a+b x^2\right)^7}+\frac{19}{288 a^2 x \left(a+b x^2\right)^8}-\frac{230945 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 a^{21/2}}-\frac{230945}{65536 a^{10} x}+\frac{1}{18 a x \left(a+b x^2\right)^9}","\frac{230945}{196608 a^9 x \left(a+b x^2\right)}+\frac{46189}{98304 a^8 x \left(a+b x^2\right)^2}+\frac{46189}{172032 a^7 x \left(a+b x^2\right)^3}+\frac{46189}{258048 a^6 x \left(a+b x^2\right)^4}+\frac{4199}{32256 a^5 x \left(a+b x^2\right)^5}+\frac{1615}{16128 a^4 x \left(a+b x^2\right)^6}+\frac{323}{4032 a^3 x \left(a+b x^2\right)^7}+\frac{19}{288 a^2 x \left(a+b x^2\right)^8}-\frac{230945 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 a^{21/2}}-\frac{230945}{65536 a^{10} x}+\frac{1}{18 a x \left(a+b x^2\right)^9}",1,"-230945/(65536*a^10*x) + 1/(18*a*x*(a + b*x^2)^9) + 19/(288*a^2*x*(a + b*x^2)^8) + 323/(4032*a^3*x*(a + b*x^2)^7) + 1615/(16128*a^4*x*(a + b*x^2)^6) + 4199/(32256*a^5*x*(a + b*x^2)^5) + 46189/(258048*a^6*x*(a + b*x^2)^4) + 46189/(172032*a^7*x*(a + b*x^2)^3) + 46189/(98304*a^8*x*(a + b*x^2)^2) + 230945/(196608*a^9*x*(a + b*x^2)) - (230945*Sqrt[b]*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(65536*a^(21/2))","A",11,3,13,0.2308,1,"{290, 325, 205}"
223,1,220,0,0.1407521,"\int \frac{1}{x^4 \left(a+b x^2\right)^{10}} \, dx","Int[1/(x^4*(a + b*x^2)^10),x]","\frac{1616615 b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 a^{23/2}}+\frac{323323}{65536 a^9 x^3 \left(a+b x^2\right)}+\frac{46189}{32768 a^8 x^3 \left(a+b x^2\right)^2}+\frac{46189}{73728 a^7 x^3 \left(a+b x^2\right)^3}+\frac{4199}{12288 a^6 x^3 \left(a+b x^2\right)^4}+\frac{323}{1536 a^5 x^3 \left(a+b x^2\right)^5}+\frac{323}{2304 a^4 x^3 \left(a+b x^2\right)^6}+\frac{19}{192 a^3 x^3 \left(a+b x^2\right)^7}+\frac{7}{96 a^2 x^3 \left(a+b x^2\right)^8}+\frac{1616615 b}{65536 a^{11} x}-\frac{1616615}{196608 a^{10} x^3}+\frac{1}{18 a x^3 \left(a+b x^2\right)^9}","\frac{1616615 b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 a^{23/2}}+\frac{323323}{65536 a^9 x^3 \left(a+b x^2\right)}+\frac{46189}{32768 a^8 x^3 \left(a+b x^2\right)^2}+\frac{46189}{73728 a^7 x^3 \left(a+b x^2\right)^3}+\frac{4199}{12288 a^6 x^3 \left(a+b x^2\right)^4}+\frac{323}{1536 a^5 x^3 \left(a+b x^2\right)^5}+\frac{323}{2304 a^4 x^3 \left(a+b x^2\right)^6}+\frac{19}{192 a^3 x^3 \left(a+b x^2\right)^7}+\frac{7}{96 a^2 x^3 \left(a+b x^2\right)^8}+\frac{1616615 b}{65536 a^{11} x}-\frac{1616615}{196608 a^{10} x^3}+\frac{1}{18 a x^3 \left(a+b x^2\right)^9}",1,"-1616615/(196608*a^10*x^3) + (1616615*b)/(65536*a^11*x) + 1/(18*a*x^3*(a + b*x^2)^9) + 7/(96*a^2*x^3*(a + b*x^2)^8) + 19/(192*a^3*x^3*(a + b*x^2)^7) + 323/(2304*a^4*x^3*(a + b*x^2)^6) + 323/(1536*a^5*x^3*(a + b*x^2)^5) + 4199/(12288*a^6*x^3*(a + b*x^2)^4) + 46189/(73728*a^7*x^3*(a + b*x^2)^3) + 46189/(32768*a^8*x^3*(a + b*x^2)^2) + 323323/(65536*a^9*x^3*(a + b*x^2)) + (1616615*b^(3/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(65536*a^(23/2))","A",12,3,13,0.2308,1,"{290, 325, 205}"
224,1,233,0,0.1578447,"\int \frac{1}{x^6 \left(a+b x^2\right)^{10}} \, dx","Int[1/(x^6*(a + b*x^2)^10),x]","-\frac{7436429 b^2}{65536 a^{12} x}-\frac{7436429 b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 a^{25/2}}+\frac{7436429 b}{196608 a^{11} x^3}+\frac{1062347}{65536 a^9 x^5 \left(a+b x^2\right)}+\frac{1062347}{294912 a^8 x^5 \left(a+b x^2\right)^2}+\frac{96577}{73728 a^7 x^5 \left(a+b x^2\right)^3}+\frac{7429}{12288 a^6 x^5 \left(a+b x^2\right)^4}+\frac{7429}{23040 a^5 x^5 \left(a+b x^2\right)^5}+\frac{437}{2304 a^4 x^5 \left(a+b x^2\right)^6}+\frac{23}{192 a^3 x^5 \left(a+b x^2\right)^7}+\frac{23}{288 a^2 x^5 \left(a+b x^2\right)^8}-\frac{7436429}{327680 a^{10} x^5}+\frac{1}{18 a x^5 \left(a+b x^2\right)^9}","-\frac{7436429 b^2}{65536 a^{12} x}-\frac{7436429 b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 a^{25/2}}+\frac{7436429 b}{196608 a^{11} x^3}+\frac{1062347}{65536 a^9 x^5 \left(a+b x^2\right)}+\frac{1062347}{294912 a^8 x^5 \left(a+b x^2\right)^2}+\frac{96577}{73728 a^7 x^5 \left(a+b x^2\right)^3}+\frac{7429}{12288 a^6 x^5 \left(a+b x^2\right)^4}+\frac{7429}{23040 a^5 x^5 \left(a+b x^2\right)^5}+\frac{437}{2304 a^4 x^5 \left(a+b x^2\right)^6}+\frac{23}{192 a^3 x^5 \left(a+b x^2\right)^7}+\frac{23}{288 a^2 x^5 \left(a+b x^2\right)^8}-\frac{7436429}{327680 a^{10} x^5}+\frac{1}{18 a x^5 \left(a+b x^2\right)^9}",1,"-7436429/(327680*a^10*x^5) + (7436429*b)/(196608*a^11*x^3) - (7436429*b^2)/(65536*a^12*x) + 1/(18*a*x^5*(a + b*x^2)^9) + 23/(288*a^2*x^5*(a + b*x^2)^8) + 23/(192*a^3*x^5*(a + b*x^2)^7) + 437/(2304*a^4*x^5*(a + b*x^2)^6) + 7429/(23040*a^5*x^5*(a + b*x^2)^5) + 7429/(12288*a^6*x^5*(a + b*x^2)^4) + 96577/(73728*a^7*x^5*(a + b*x^2)^3) + 1062347/(294912*a^8*x^5*(a + b*x^2)^2) + 1062347/(65536*a^9*x^5*(a + b*x^2)) - (7436429*b^(5/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(65536*a^(25/2))","A",13,3,13,0.2308,1,"{290, 325, 205}"
225,1,28,0,0.0220877,"\int \frac{x^3}{a-b x^2} \, dx","Int[x^3/(a - b*x^2),x]","-\frac{a \log \left(a-b x^2\right)}{2 b^2}-\frac{x^2}{2 b}","-\frac{a \log \left(a-b x^2\right)}{2 b^2}-\frac{x^2}{2 b}",1,"-x^2/(2*b) - (a*Log[a - b*x^2])/(2*b^2)","A",3,2,14,0.1429,1,"{266, 43}"
226,1,31,0,0.012385,"\int \frac{x^2}{a-b x^2} \, dx","Int[x^2/(a - b*x^2),x]","\frac{\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{3/2}}-\frac{x}{b}","\frac{\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{3/2}}-\frac{x}{b}",1,"-(x/b) + (Sqrt[a]*ArcTanh[(Sqrt[b]*x)/Sqrt[a]])/b^(3/2)","A",2,2,14,0.1429,1,"{321, 208}"
227,1,16,0,0.0028838,"\int \frac{x}{a-b x^2} \, dx","Int[x/(a - b*x^2),x]","-\frac{\log \left(a-b x^2\right)}{2 b}","-\frac{\log \left(a-b x^2\right)}{2 b}",1,"-Log[a - b*x^2]/(2*b)","A",1,1,12,0.08333,1,"{260}"
228,1,24,0,0.006682,"\int \frac{1}{a-b x^2} \, dx","Int[(a - b*x^2)^(-1),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b}}",1,"ArcTanh[(Sqrt[b]*x)/Sqrt[a]]/(Sqrt[a]*Sqrt[b])","A",1,1,10,0.1000,1,"{208}"
229,1,23,0,0.0122526,"\int \frac{1}{x \left(a-b x^2\right)} \, dx","Int[1/(x*(a - b*x^2)),x]","\frac{\log (x)}{a}-\frac{\log \left(a-b x^2\right)}{2 a}","\frac{\log (x)}{a}-\frac{\log \left(a-b x^2\right)}{2 a}",1,"Log[x]/a - Log[a - b*x^2]/(2*a)","A",4,4,14,0.2857,1,"{266, 36, 29, 31}"
230,1,33,0,0.0121497,"\int \frac{1}{x^2 \left(a-b x^2\right)} \, dx","Int[1/(x^2*(a - b*x^2)),x]","\frac{\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{3/2}}-\frac{1}{a x}","\frac{\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{3/2}}-\frac{1}{a x}",1,"-(1/(a*x)) + (Sqrt[b]*ArcTanh[(Sqrt[b]*x)/Sqrt[a]])/a^(3/2)","A",2,2,14,0.1429,1,"{325, 208}"
231,1,35,0,0.0235559,"\int \frac{1}{x^3 \left(a-b x^2\right)} \, dx","Int[1/(x^3*(a - b*x^2)),x]","-\frac{b \log \left(a-b x^2\right)}{2 a^2}+\frac{b \log (x)}{a^2}-\frac{1}{2 a x^2}","-\frac{b \log \left(a-b x^2\right)}{2 a^2}+\frac{b \log (x)}{a^2}-\frac{1}{2 a x^2}",1,"-1/(2*a*x^2) + (b*Log[x])/a^2 - (b*Log[a - b*x^2])/(2*a^2)","A",3,2,14,0.1429,1,"{266, 44}"
232,1,35,0,0.0269475,"\int \frac{x^3}{\left(a-b x^2\right)^2} \, dx","Int[x^3/(a - b*x^2)^2,x]","\frac{a}{2 b^2 \left(a-b x^2\right)}+\frac{\log \left(a-b x^2\right)}{2 b^2}","\frac{a}{2 b^2 \left(a-b x^2\right)}+\frac{\log \left(a-b x^2\right)}{2 b^2}",1,"a/(2*b^2*(a - b*x^2)) + Log[a - b*x^2]/(2*b^2)","A",3,2,14,0.1429,1,"{266, 43}"
233,1,46,0,0.0135534,"\int \frac{x^2}{\left(a-b x^2\right)^2} \, dx","Int[x^2/(a - b*x^2)^2,x]","\frac{x}{2 b \left(a-b x^2\right)}-\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 \sqrt{a} b^{3/2}}","\frac{x}{2 b \left(a-b x^2\right)}-\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 \sqrt{a} b^{3/2}}",1,"x/(2*b*(a - b*x^2)) - ArcTanh[(Sqrt[b]*x)/Sqrt[a]]/(2*Sqrt[a]*b^(3/2))","A",2,2,14,0.1429,1,"{288, 208}"
234,1,17,0,0.0028674,"\int \frac{x}{\left(a-b x^2\right)^2} \, dx","Int[x/(a - b*x^2)^2,x]","\frac{1}{2 b \left(a-b x^2\right)}","\frac{1}{2 b \left(a-b x^2\right)}",1,"1/(2*b*(a - b*x^2))","A",1,1,12,0.08333,1,"{261}"
235,1,46,0,0.0122472,"\int \frac{1}{\left(a-b x^2\right)^2} \, dx","Int[(a - b*x^2)^(-2),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b}}+\frac{x}{2 a \left(a-b x^2\right)}","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b}}+\frac{x}{2 a \left(a-b x^2\right)}",1,"x/(2*a*(a - b*x^2)) + ArcTanh[(Sqrt[b]*x)/Sqrt[a]]/(2*a^(3/2)*Sqrt[b])","A",2,2,10,0.2000,1,"{199, 208}"
236,1,40,0,0.0279616,"\int \frac{1}{x \left(a-b x^2\right)^2} \, dx","Int[1/(x*(a - b*x^2)^2),x]","-\frac{\log \left(a-b x^2\right)}{2 a^2}+\frac{\log (x)}{a^2}+\frac{1}{2 a \left(a-b x^2\right)}","-\frac{\log \left(a-b x^2\right)}{2 a^2}+\frac{\log (x)}{a^2}+\frac{1}{2 a \left(a-b x^2\right)}",1,"1/(2*a*(a - b*x^2)) + Log[x]/a^2 - Log[a - b*x^2]/(2*a^2)","A",3,2,14,0.1429,1,"{266, 44}"
237,1,58,0,0.0184034,"\int \frac{1}{x^2 \left(a-b x^2\right)^2} \, dx","Int[1/(x^2*(a - b*x^2)^2),x]","\frac{3 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{5/2}}-\frac{3}{2 a^2 x}+\frac{1}{2 a x \left(a-b x^2\right)}","\frac{3 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{5/2}}-\frac{3}{2 a^2 x}+\frac{1}{2 a x \left(a-b x^2\right)}",1,"-3/(2*a^2*x) + 1/(2*a*x*(a - b*x^2)) + (3*Sqrt[b]*ArcTanh[(Sqrt[b]*x)/Sqrt[a]])/(2*a^(5/2))","A",3,3,14,0.2143,1,"{290, 325, 208}"
238,1,52,0,0.0382507,"\int \frac{1}{x^3 \left(a-b x^2\right)^2} \, dx","Int[1/(x^3*(a - b*x^2)^2),x]","\frac{b}{2 a^2 \left(a-b x^2\right)}-\frac{b \log \left(a-b x^2\right)}{a^3}+\frac{2 b \log (x)}{a^3}-\frac{1}{2 a^2 x^2}","\frac{b}{2 a^2 \left(a-b x^2\right)}-\frac{b \log \left(a-b x^2\right)}{a^3}+\frac{2 b \log (x)}{a^3}-\frac{1}{2 a^2 x^2}",1,"-1/(2*a^2*x^2) + b/(2*a^2*(a - b*x^2)) + (2*b*Log[x])/a^3 - (b*Log[a - b*x^2])/a^3","A",3,2,14,0.1429,1,"{266, 44}"
239,1,20,0,0.003635,"\int \frac{x^3}{\left(a-b x^2\right)^3} \, dx","Int[x^3/(a - b*x^2)^3,x]","\frac{x^4}{4 a \left(a-b x^2\right)^2}","\frac{x^4}{4 a \left(a-b x^2\right)^2}",1,"x^4/(4*a*(a - b*x^2)^2)","A",1,1,14,0.07143,1,"{264}"
240,1,67,0,0.0197181,"\int \frac{x^2}{\left(a-b x^2\right)^3} \, dx","Int[x^2/(a - b*x^2)^3,x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{3/2} b^{3/2}}-\frac{x}{8 a b \left(a-b x^2\right)}+\frac{x}{4 b \left(a-b x^2\right)^2}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{3/2} b^{3/2}}-\frac{x}{8 a b \left(a-b x^2\right)}+\frac{x}{4 b \left(a-b x^2\right)^2}",1,"x/(4*b*(a - b*x^2)^2) - x/(8*a*b*(a - b*x^2)) - ArcTanh[(Sqrt[b]*x)/Sqrt[a]]/(8*a^(3/2)*b^(3/2))","A",3,3,14,0.2143,1,"{288, 199, 208}"
241,1,17,0,0.0030325,"\int \frac{x}{\left(a-b x^2\right)^3} \, dx","Int[x/(a - b*x^2)^3,x]","\frac{1}{4 b \left(a-b x^2\right)^2}","\frac{1}{4 b \left(a-b x^2\right)^2}",1,"1/(4*b*(a - b*x^2)^2)","A",1,1,12,0.08333,1,"{261}"
242,1,64,0,0.0179858,"\int \frac{1}{\left(a-b x^2\right)^3} \, dx","Int[(a - b*x^2)^(-3),x]","\frac{3 x}{8 a^2 \left(a-b x^2\right)}+\frac{3 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{b}}+\frac{x}{4 a \left(a-b x^2\right)^2}","\frac{3 x}{8 a^2 \left(a-b x^2\right)}+\frac{3 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{b}}+\frac{x}{4 a \left(a-b x^2\right)^2}",1,"x/(4*a*(a - b*x^2)^2) + (3*x)/(8*a^2*(a - b*x^2)) + (3*ArcTanh[(Sqrt[b]*x)/Sqrt[a]])/(8*a^(5/2)*Sqrt[b])","A",3,2,10,0.2000,1,"{199, 208}"
243,1,57,0,0.0376401,"\int \frac{1}{x \left(a-b x^2\right)^3} \, dx","Int[1/(x*(a - b*x^2)^3),x]","\frac{1}{2 a^2 \left(a-b x^2\right)}-\frac{\log \left(a-b x^2\right)}{2 a^3}+\frac{\log (x)}{a^3}+\frac{1}{4 a \left(a-b x^2\right)^2}","\frac{1}{2 a^2 \left(a-b x^2\right)}-\frac{\log \left(a-b x^2\right)}{2 a^3}+\frac{\log (x)}{a^3}+\frac{1}{4 a \left(a-b x^2\right)^2}",1,"1/(4*a*(a - b*x^2)^2) + 1/(2*a^2*(a - b*x^2)) + Log[x]/a^3 - Log[a - b*x^2]/(2*a^3)","A",3,2,14,0.1429,1,"{266, 44}"
244,1,78,0,0.0258514,"\int \frac{1}{x^2 \left(a-b x^2\right)^3} \, dx","Int[1/(x^2*(a - b*x^2)^3),x]","\frac{5}{8 a^2 x \left(a-b x^2\right)}+\frac{15 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{7/2}}-\frac{15}{8 a^3 x}+\frac{1}{4 a x \left(a-b x^2\right)^2}","\frac{5}{8 a^2 x \left(a-b x^2\right)}+\frac{15 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{7/2}}-\frac{15}{8 a^3 x}+\frac{1}{4 a x \left(a-b x^2\right)^2}",1,"-15/(8*a^3*x) + 1/(4*a*x*(a - b*x^2)^2) + 5/(8*a^2*x*(a - b*x^2)) + (15*Sqrt[b]*ArcTanh[(Sqrt[b]*x)/Sqrt[a]])/(8*a^(7/2))","A",4,3,14,0.2143,1,"{290, 325, 208}"
245,1,69,0,0.0509335,"\int \frac{1}{x^3 \left(a-b x^2\right)^3} \, dx","Int[1/(x^3*(a - b*x^2)^3),x]","\frac{b}{a^3 \left(a-b x^2\right)}+\frac{b}{4 a^2 \left(a-b x^2\right)^2}-\frac{3 b \log \left(a-b x^2\right)}{2 a^4}+\frac{3 b \log (x)}{a^4}-\frac{1}{2 a^3 x^2}","\frac{b}{a^3 \left(a-b x^2\right)}+\frac{b}{4 a^2 \left(a-b x^2\right)^2}-\frac{3 b \log \left(a-b x^2\right)}{2 a^4}+\frac{3 b \log (x)}{a^4}-\frac{1}{2 a^3 x^2}",1,"-1/(2*a^3*x^2) + b/(4*a^2*(a - b*x^2)^2) + b/(a^3*(a - b*x^2)) + (3*b*Log[x])/a^4 - (3*b*Log[a - b*x^2])/(2*a^4)","A",3,2,14,0.1429,1,"{266, 44}"
246,1,36,0,0.0295651,"\int \frac{x^3}{\left(a-b x^2\right)^5} \, dx","Int[x^3/(a - b*x^2)^5,x]","\frac{a}{8 b^2 \left(a-b x^2\right)^4}-\frac{1}{6 b^2 \left(a-b x^2\right)^3}","\frac{a}{8 b^2 \left(a-b x^2\right)^4}-\frac{1}{6 b^2 \left(a-b x^2\right)^3}",1,"a/(8*b^2*(a - b*x^2)^4) - 1/(6*b^2*(a - b*x^2)^3)","A",3,2,14,0.1429,1,"{266, 43}"
247,1,109,0,0.0368752,"\int \frac{x^2}{\left(a-b x^2\right)^5} \, dx","Int[x^2/(a - b*x^2)^5,x]","-\frac{5 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{128 a^{7/2} b^{3/2}}-\frac{5 x}{128 a^3 b \left(a-b x^2\right)}-\frac{5 x}{192 a^2 b \left(a-b x^2\right)^2}-\frac{x}{48 a b \left(a-b x^2\right)^3}+\frac{x}{8 b \left(a-b x^2\right)^4}","-\frac{5 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{128 a^{7/2} b^{3/2}}-\frac{5 x}{128 a^3 b \left(a-b x^2\right)}-\frac{5 x}{192 a^2 b \left(a-b x^2\right)^2}-\frac{x}{48 a b \left(a-b x^2\right)^3}+\frac{x}{8 b \left(a-b x^2\right)^4}",1,"x/(8*b*(a - b*x^2)^4) - x/(48*a*b*(a - b*x^2)^3) - (5*x)/(192*a^2*b*(a - b*x^2)^2) - (5*x)/(128*a^3*b*(a - b*x^2)) - (5*ArcTanh[(Sqrt[b]*x)/Sqrt[a]])/(128*a^(7/2)*b^(3/2))","A",5,3,14,0.2143,1,"{288, 199, 208}"
248,1,17,0,0.0027673,"\int \frac{x}{\left(a-b x^2\right)^5} \, dx","Int[x/(a - b*x^2)^5,x]","\frac{1}{8 b \left(a-b x^2\right)^4}","\frac{1}{8 b \left(a-b x^2\right)^4}",1,"1/(8*b*(a - b*x^2)^4)","A",1,1,12,0.08333,1,"{261}"
249,1,100,0,0.0336952,"\int \frac{1}{\left(a-b x^2\right)^5} \, dx","Int[(a - b*x^2)^(-5),x]","\frac{35 x}{128 a^4 \left(a-b x^2\right)}+\frac{35 x}{192 a^3 \left(a-b x^2\right)^2}+\frac{7 x}{48 a^2 \left(a-b x^2\right)^3}+\frac{35 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{128 a^{9/2} \sqrt{b}}+\frac{x}{8 a \left(a-b x^2\right)^4}","\frac{35 x}{128 a^4 \left(a-b x^2\right)}+\frac{35 x}{192 a^3 \left(a-b x^2\right)^2}+\frac{7 x}{48 a^2 \left(a-b x^2\right)^3}+\frac{35 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{128 a^{9/2} \sqrt{b}}+\frac{x}{8 a \left(a-b x^2\right)^4}",1,"x/(8*a*(a - b*x^2)^4) + (7*x)/(48*a^2*(a - b*x^2)^3) + (35*x)/(192*a^3*(a - b*x^2)^2) + (35*x)/(128*a^4*(a - b*x^2)) + (35*ArcTanh[(Sqrt[b]*x)/Sqrt[a]])/(128*a^(9/2)*Sqrt[b])","A",5,2,10,0.2000,1,"{199, 208}"
250,1,91,0,0.063872,"\int \frac{1}{x \left(a-b x^2\right)^5} \, dx","Int[1/(x*(a - b*x^2)^5),x]","\frac{1}{2 a^4 \left(a-b x^2\right)}+\frac{1}{4 a^3 \left(a-b x^2\right)^2}+\frac{1}{6 a^2 \left(a-b x^2\right)^3}-\frac{\log \left(a-b x^2\right)}{2 a^5}+\frac{\log (x)}{a^5}+\frac{1}{8 a \left(a-b x^2\right)^4}","\frac{1}{2 a^4 \left(a-b x^2\right)}+\frac{1}{4 a^3 \left(a-b x^2\right)^2}+\frac{1}{6 a^2 \left(a-b x^2\right)^3}-\frac{\log \left(a-b x^2\right)}{2 a^5}+\frac{\log (x)}{a^5}+\frac{1}{8 a \left(a-b x^2\right)^4}",1,"1/(8*a*(a - b*x^2)^4) + 1/(6*a^2*(a - b*x^2)^3) + 1/(4*a^3*(a - b*x^2)^2) + 1/(2*a^4*(a - b*x^2)) + Log[x]/a^5 - Log[a - b*x^2]/(2*a^5)","A",3,2,14,0.1429,1,"{266, 44}"
251,1,118,0,0.0487778,"\int \frac{1}{x^2 \left(a-b x^2\right)^5} \, dx","Int[1/(x^2*(a - b*x^2)^5),x]","\frac{105}{128 a^4 x \left(a-b x^2\right)}+\frac{21}{64 a^3 x \left(a-b x^2\right)^2}+\frac{3}{16 a^2 x \left(a-b x^2\right)^3}+\frac{315 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{128 a^{11/2}}-\frac{315}{128 a^5 x}+\frac{1}{8 a x \left(a-b x^2\right)^4}","\frac{105}{128 a^4 x \left(a-b x^2\right)}+\frac{21}{64 a^3 x \left(a-b x^2\right)^2}+\frac{3}{16 a^2 x \left(a-b x^2\right)^3}+\frac{315 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{128 a^{11/2}}-\frac{315}{128 a^5 x}+\frac{1}{8 a x \left(a-b x^2\right)^4}",1,"-315/(128*a^5*x) + 1/(8*a*x*(a - b*x^2)^4) + 3/(16*a^2*x*(a - b*x^2)^3) + 21/(64*a^3*x*(a - b*x^2)^2) + 105/(128*a^4*x*(a - b*x^2)) + (315*Sqrt[b]*ArcTanh[(Sqrt[b]*x)/Sqrt[a]])/(128*a^(11/2))","A",6,3,14,0.2143,1,"{290, 325, 208}"
252,1,106,0,0.0870354,"\int \frac{1}{x^3 \left(a-b x^2\right)^5} \, dx","Int[1/(x^3*(a - b*x^2)^5),x]","\frac{2 b}{a^5 \left(a-b x^2\right)}+\frac{3 b}{4 a^4 \left(a-b x^2\right)^2}+\frac{b}{3 a^3 \left(a-b x^2\right)^3}+\frac{b}{8 a^2 \left(a-b x^2\right)^4}-\frac{5 b \log \left(a-b x^2\right)}{2 a^6}+\frac{5 b \log (x)}{a^6}-\frac{1}{2 a^5 x^2}","\frac{2 b}{a^5 \left(a-b x^2\right)}+\frac{3 b}{4 a^4 \left(a-b x^2\right)^2}+\frac{b}{3 a^3 \left(a-b x^2\right)^3}+\frac{b}{8 a^2 \left(a-b x^2\right)^4}-\frac{5 b \log \left(a-b x^2\right)}{2 a^6}+\frac{5 b \log (x)}{a^6}-\frac{1}{2 a^5 x^2}",1,"-1/(2*a^5*x^2) + b/(8*a^2*(a - b*x^2)^4) + b/(3*a^3*(a - b*x^2)^3) + (3*b)/(4*a^4*(a - b*x^2)^2) + (2*b)/(a^5*(a - b*x^2)) + (5*b*Log[x])/a^6 - (5*b*Log[a - b*x^2])/(2*a^6)","A",3,2,14,0.1429,1,"{266, 44}"
253,1,15,0,0.0090262,"\int \frac{1}{x \left(1+b x^2\right)} \, dx","Int[1/(x*(1 + b*x^2)),x]","\log (x)-\frac{1}{2} \log \left(b x^2+1\right)","\log (x)-\frac{1}{2} \log \left(b x^2+1\right)",1,"Log[x] - Log[1 + b*x^2]/2","A",4,4,13,0.3077,1,"{266, 36, 29, 31}"
254,1,18,0,0.0101157,"\int \frac{1}{x \left(-1+b x^2\right)} \, dx","Int[1/(x*(-1 + b*x^2)),x]","\frac{1}{2} \log \left(1-b x^2\right)-\log (x)","\frac{1}{2} \log \left(1-b x^2\right)-\log (x)",1,"-Log[x] + Log[1 - b*x^2]/2","A",4,4,13,0.3077,1,"{266, 36, 29, 31}"
255,1,26,0,0.0169842,"\int \frac{1}{x^3 \left(1+b x^2\right)} \, dx","Int[1/(x^3*(1 + b*x^2)),x]","\frac{1}{2} b \log \left(b x^2+1\right)-b \log (x)-\frac{1}{2 x^2}","\frac{1}{2} b \log \left(b x^2+1\right)-b \log (x)-\frac{1}{2 x^2}",1,"-1/(2*x^2) - b*Log[x] + (b*Log[1 + b*x^2])/2","A",3,2,13,0.1538,1,"{266, 44}"
256,1,27,0,0.017959,"\int \frac{1}{x^3 \left(-1+b x^2\right)} \, dx","Int[1/(x^3*(-1 + b*x^2)),x]","\frac{1}{2} b \log \left(1-b x^2\right)-b \log (x)+\frac{1}{2 x^2}","\frac{1}{2} b \log \left(1-b x^2\right)-b \log (x)+\frac{1}{2 x^2}",1,"1/(2*x^2) - b*Log[x] + (b*Log[1 - b*x^2])/2","A",3,2,13,0.1538,1,"{266, 44}"
257,1,30,0,0.0267875,"\int \frac{1}{-1+a+a x^2} \, dx","Int[(-1 + a + a*x^2)^(-1),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{1-a}}\right)}{\sqrt{(1-a) a}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{1-a}}\right)}{\sqrt{(1-a) a}}",1,"-(ArcTanh[(Sqrt[a]*x)/Sqrt[1 - a]]/Sqrt[(1 - a)*a])","A",1,1,10,0.1000,1,"{208}"
258,1,37,0,0.0326792,"\int \frac{1}{-c-d+(c-d) x^2} \, dx","Int[(-c - d + (c - d)*x^2)^(-1),x]","-\frac{\tanh ^{-1}\left(\frac{x \sqrt{c-d}}{\sqrt{c+d}}\right)}{\sqrt{c-d} \sqrt{c+d}}","-\frac{\tanh ^{-1}\left(\frac{x \sqrt{c-d}}{\sqrt{c+d}}\right)}{\sqrt{c-d} \sqrt{c+d}}",1,"-(ArcTanh[(Sqrt[c - d]*x)/Sqrt[c + d]]/(Sqrt[c - d]*Sqrt[c + d]))","A",1,1,18,0.05556,1,"{208}"
259,1,28,0,0.0199275,"\int \frac{1}{x \left(1+b x^2\right)^2} \, dx","Int[1/(x*(1 + b*x^2)^2),x]","\frac{1}{2 \left(b x^2+1\right)}-\frac{1}{2} \log \left(b x^2+1\right)+\log (x)","\frac{1}{2 \left(b x^2+1\right)}-\frac{1}{2} \log \left(b x^2+1\right)+\log (x)",1,"1/(2*(1 + b*x^2)) + Log[x] - Log[1 + b*x^2]/2","A",3,2,13,0.1538,1,"{266, 44}"
260,1,30,0,0.0194258,"\int \frac{1}{x \left(-1+b x^2\right)^2} \, dx","Int[1/(x*(-1 + b*x^2)^2),x]","\frac{1}{2 \left(1-b x^2\right)}-\frac{1}{2} \log \left(1-b x^2\right)+\log (x)","\frac{1}{2 \left(1-b x^2\right)}-\frac{1}{2} \log \left(1-b x^2\right)+\log (x)",1,"1/(2*(1 - b*x^2)) + Log[x] - Log[1 - b*x^2]/2","A",3,2,13,0.1538,1,"{266, 44}"
261,1,34,0,0.0253734,"\int \frac{1}{a+(b-a c) x^2} \, dx","Int[(a + (b - a*c)*x^2)^(-1),x]","\frac{\tan ^{-1}\left(\frac{x \sqrt{b-a c}}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b-a c}}","\frac{\tan ^{-1}\left(\frac{x \sqrt{b-a c}}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b-a c}}",1,"ArcTan[(Sqrt[b - a*c]*x)/Sqrt[a]]/(Sqrt[a]*Sqrt[b - a*c])","A",1,1,14,0.07143,1,"{205}"
262,1,34,0,0.0111079,"\int \frac{1}{a-(b-a c) x^2} \, dx","Int[(a - (b - a*c)*x^2)^(-1),x]","\frac{\tanh ^{-1}\left(\frac{x \sqrt{b-a c}}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b-a c}}","\frac{\tanh ^{-1}\left(\frac{x \sqrt{b-a c}}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b-a c}}",1,"ArcTanh[(Sqrt[b - a*c]*x)/Sqrt[a]]/(Sqrt[a]*Sqrt[b - a*c])","A",1,1,15,0.06667,1,"{208}"
263,1,50,0,0.0533083,"\int \frac{1}{c (a-d)-(b-c) x^2} \, dx","Int[(c*(a - d) - (b - c)*x^2)^(-1),x]","\frac{\tanh ^{-1}\left(\frac{x \sqrt{b-c}}{\sqrt{c} \sqrt{a-d}}\right)}{\sqrt{c} \sqrt{a-d} \sqrt{b-c}}","\frac{\tanh ^{-1}\left(\frac{x \sqrt{b-c}}{\sqrt{c} \sqrt{a-d}}\right)}{\sqrt{c} \sqrt{a-d} \sqrt{b-c}}",1,"ArcTanh[(Sqrt[b - c]*x)/(Sqrt[c]*Sqrt[a - d])]/(Sqrt[b - c]*Sqrt[c]*Sqrt[a - d])","A",1,1,20,0.05000,1,"{208}"
264,1,21,0,0.0043362,"\int x^{7/2} \left(a+b x^2\right) \, dx","Int[x^(7/2)*(a + b*x^2),x]","\frac{2}{9} a x^{9/2}+\frac{2}{13} b x^{13/2}","\frac{2}{9} a x^{9/2}+\frac{2}{13} b x^{13/2}",1,"(2*a*x^(9/2))/9 + (2*b*x^(13/2))/13","A",2,1,13,0.07692,1,"{14}"
265,1,21,0,0.0043558,"\int x^{5/2} \left(a+b x^2\right) \, dx","Int[x^(5/2)*(a + b*x^2),x]","\frac{2}{7} a x^{7/2}+\frac{2}{11} b x^{11/2}","\frac{2}{7} a x^{7/2}+\frac{2}{11} b x^{11/2}",1,"(2*a*x^(7/2))/7 + (2*b*x^(11/2))/11","A",2,1,13,0.07692,1,"{14}"
266,1,21,0,0.0044014,"\int x^{3/2} \left(a+b x^2\right) \, dx","Int[x^(3/2)*(a + b*x^2),x]","\frac{2}{5} a x^{5/2}+\frac{2}{9} b x^{9/2}","\frac{2}{5} a x^{5/2}+\frac{2}{9} b x^{9/2}",1,"(2*a*x^(5/2))/5 + (2*b*x^(9/2))/9","A",2,1,13,0.07692,1,"{14}"
267,1,21,0,0.0042427,"\int \sqrt{x} \left(a+b x^2\right) \, dx","Int[Sqrt[x]*(a + b*x^2),x]","\frac{2}{3} a x^{3/2}+\frac{2}{7} b x^{7/2}","\frac{2}{3} a x^{3/2}+\frac{2}{7} b x^{7/2}",1,"(2*a*x^(3/2))/3 + (2*b*x^(7/2))/7","A",2,1,13,0.07692,1,"{14}"
268,1,19,0,0.0038726,"\int \frac{a+b x^2}{\sqrt{x}} \, dx","Int[(a + b*x^2)/Sqrt[x],x]","2 a \sqrt{x}+\frac{2}{5} b x^{5/2}","2 a \sqrt{x}+\frac{2}{5} b x^{5/2}",1,"2*a*Sqrt[x] + (2*b*x^(5/2))/5","A",2,1,13,0.07692,1,"{14}"
269,1,19,0,0.0042045,"\int \frac{a+b x^2}{x^{3/2}} \, dx","Int[(a + b*x^2)/x^(3/2),x]","\frac{2}{3} b x^{3/2}-\frac{2 a}{\sqrt{x}}","\frac{2}{3} b x^{3/2}-\frac{2 a}{\sqrt{x}}",1,"(-2*a)/Sqrt[x] + (2*b*x^(3/2))/3","A",2,1,13,0.07692,1,"{14}"
270,1,19,0,0.0039198,"\int \frac{a+b x^2}{x^{5/2}} \, dx","Int[(a + b*x^2)/x^(5/2),x]","2 b \sqrt{x}-\frac{2 a}{3 x^{3/2}}","2 b \sqrt{x}-\frac{2 a}{3 x^{3/2}}",1,"(-2*a)/(3*x^(3/2)) + 2*b*Sqrt[x]","A",2,1,13,0.07692,1,"{14}"
271,1,19,0,0.0039203,"\int \frac{a+b x^2}{x^{7/2}} \, dx","Int[(a + b*x^2)/x^(7/2),x]","-\frac{2 a}{5 x^{5/2}}-\frac{2 b}{\sqrt{x}}","-\frac{2 a}{5 x^{5/2}}-\frac{2 b}{\sqrt{x}}",1,"(-2*a)/(5*x^(5/2)) - (2*b)/Sqrt[x]","A",2,1,13,0.07692,1,"{14}"
272,1,36,0,0.008615,"\int x^{7/2} \left(a+b x^2\right)^2 \, dx","Int[x^(7/2)*(a + b*x^2)^2,x]","\frac{2}{9} a^2 x^{9/2}+\frac{4}{13} a b x^{13/2}+\frac{2}{17} b^2 x^{17/2}","\frac{2}{9} a^2 x^{9/2}+\frac{4}{13} a b x^{13/2}+\frac{2}{17} b^2 x^{17/2}",1,"(2*a^2*x^(9/2))/9 + (4*a*b*x^(13/2))/13 + (2*b^2*x^(17/2))/17","A",2,1,15,0.06667,1,"{270}"
273,1,36,0,0.0084177,"\int x^{5/2} \left(a+b x^2\right)^2 \, dx","Int[x^(5/2)*(a + b*x^2)^2,x]","\frac{2}{7} a^2 x^{7/2}+\frac{4}{11} a b x^{11/2}+\frac{2}{15} b^2 x^{15/2}","\frac{2}{7} a^2 x^{7/2}+\frac{4}{11} a b x^{11/2}+\frac{2}{15} b^2 x^{15/2}",1,"(2*a^2*x^(7/2))/7 + (4*a*b*x^(11/2))/11 + (2*b^2*x^(15/2))/15","A",2,1,15,0.06667,1,"{270}"
274,1,36,0,0.0085225,"\int x^{3/2} \left(a+b x^2\right)^2 \, dx","Int[x^(3/2)*(a + b*x^2)^2,x]","\frac{2}{5} a^2 x^{5/2}+\frac{4}{9} a b x^{9/2}+\frac{2}{13} b^2 x^{13/2}","\frac{2}{5} a^2 x^{5/2}+\frac{4}{9} a b x^{9/2}+\frac{2}{13} b^2 x^{13/2}",1,"(2*a^2*x^(5/2))/5 + (4*a*b*x^(9/2))/9 + (2*b^2*x^(13/2))/13","A",2,1,15,0.06667,1,"{270}"
275,1,36,0,0.0082896,"\int \sqrt{x} \left(a+b x^2\right)^2 \, dx","Int[Sqrt[x]*(a + b*x^2)^2,x]","\frac{2}{3} a^2 x^{3/2}+\frac{4}{7} a b x^{7/2}+\frac{2}{11} b^2 x^{11/2}","\frac{2}{3} a^2 x^{3/2}+\frac{4}{7} a b x^{7/2}+\frac{2}{11} b^2 x^{11/2}",1,"(2*a^2*x^(3/2))/3 + (4*a*b*x^(7/2))/7 + (2*b^2*x^(11/2))/11","A",2,1,15,0.06667,1,"{270}"
276,1,34,0,0.0087443,"\int \frac{\left(a+b x^2\right)^2}{\sqrt{x}} \, dx","Int[(a + b*x^2)^2/Sqrt[x],x]","2 a^2 \sqrt{x}+\frac{4}{5} a b x^{5/2}+\frac{2}{9} b^2 x^{9/2}","2 a^2 \sqrt{x}+\frac{4}{5} a b x^{5/2}+\frac{2}{9} b^2 x^{9/2}",1,"2*a^2*Sqrt[x] + (4*a*b*x^(5/2))/5 + (2*b^2*x^(9/2))/9","A",2,1,15,0.06667,1,"{270}"
277,1,34,0,0.0084777,"\int \frac{\left(a+b x^2\right)^2}{x^{3/2}} \, dx","Int[(a + b*x^2)^2/x^(3/2),x]","-\frac{2 a^2}{\sqrt{x}}+\frac{4}{3} a b x^{3/2}+\frac{2}{7} b^2 x^{7/2}","-\frac{2 a^2}{\sqrt{x}}+\frac{4}{3} a b x^{3/2}+\frac{2}{7} b^2 x^{7/2}",1,"(-2*a^2)/Sqrt[x] + (4*a*b*x^(3/2))/3 + (2*b^2*x^(7/2))/7","A",2,1,15,0.06667,1,"{270}"
278,1,34,0,0.0082254,"\int \frac{\left(a+b x^2\right)^2}{x^{5/2}} \, dx","Int[(a + b*x^2)^2/x^(5/2),x]","-\frac{2 a^2}{3 x^{3/2}}+4 a b \sqrt{x}+\frac{2}{5} b^2 x^{5/2}","-\frac{2 a^2}{3 x^{3/2}}+4 a b \sqrt{x}+\frac{2}{5} b^2 x^{5/2}",1,"(-2*a^2)/(3*x^(3/2)) + 4*a*b*Sqrt[x] + (2*b^2*x^(5/2))/5","A",2,1,15,0.06667,1,"{270}"
279,1,34,0,0.008181,"\int \frac{\left(a+b x^2\right)^2}{x^{7/2}} \, dx","Int[(a + b*x^2)^2/x^(7/2),x]","-\frac{2 a^2}{5 x^{5/2}}-\frac{4 a b}{\sqrt{x}}+\frac{2}{3} b^2 x^{3/2}","-\frac{2 a^2}{5 x^{5/2}}-\frac{4 a b}{\sqrt{x}}+\frac{2}{3} b^2 x^{3/2}",1,"(-2*a^2)/(5*x^(5/2)) - (4*a*b)/Sqrt[x] + (2*b^2*x^(3/2))/3","A",2,1,15,0.06667,1,"{270}"
280,1,51,0,0.0125644,"\int x^{7/2} \left(a+b x^2\right)^3 \, dx","Int[x^(7/2)*(a + b*x^2)^3,x]","\frac{6}{13} a^2 b x^{13/2}+\frac{2}{9} a^3 x^{9/2}+\frac{6}{17} a b^2 x^{17/2}+\frac{2}{21} b^3 x^{21/2}","\frac{6}{13} a^2 b x^{13/2}+\frac{2}{9} a^3 x^{9/2}+\frac{6}{17} a b^2 x^{17/2}+\frac{2}{21} b^3 x^{21/2}",1,"(2*a^3*x^(9/2))/9 + (6*a^2*b*x^(13/2))/13 + (6*a*b^2*x^(17/2))/17 + (2*b^3*x^(21/2))/21","A",2,1,15,0.06667,1,"{270}"
281,1,51,0,0.012456,"\int x^{5/2} \left(a+b x^2\right)^3 \, dx","Int[x^(5/2)*(a + b*x^2)^3,x]","\frac{6}{11} a^2 b x^{11/2}+\frac{2}{7} a^3 x^{7/2}+\frac{2}{5} a b^2 x^{15/2}+\frac{2}{19} b^3 x^{19/2}","\frac{6}{11} a^2 b x^{11/2}+\frac{2}{7} a^3 x^{7/2}+\frac{2}{5} a b^2 x^{15/2}+\frac{2}{19} b^3 x^{19/2}",1,"(2*a^3*x^(7/2))/7 + (6*a^2*b*x^(11/2))/11 + (2*a*b^2*x^(15/2))/5 + (2*b^3*x^(19/2))/19","A",2,1,15,0.06667,1,"{270}"
282,1,51,0,0.0125412,"\int x^{3/2} \left(a+b x^2\right)^3 \, dx","Int[x^(3/2)*(a + b*x^2)^3,x]","\frac{2}{3} a^2 b x^{9/2}+\frac{2}{5} a^3 x^{5/2}+\frac{6}{13} a b^2 x^{13/2}+\frac{2}{17} b^3 x^{17/2}","\frac{2}{3} a^2 b x^{9/2}+\frac{2}{5} a^3 x^{5/2}+\frac{6}{13} a b^2 x^{13/2}+\frac{2}{17} b^3 x^{17/2}",1,"(2*a^3*x^(5/2))/5 + (2*a^2*b*x^(9/2))/3 + (6*a*b^2*x^(13/2))/13 + (2*b^3*x^(17/2))/17","A",2,1,15,0.06667,1,"{270}"
283,1,51,0,0.0127798,"\int \sqrt{x} \left(a+b x^2\right)^3 \, dx","Int[Sqrt[x]*(a + b*x^2)^3,x]","\frac{6}{7} a^2 b x^{7/2}+\frac{2}{3} a^3 x^{3/2}+\frac{6}{11} a b^2 x^{11/2}+\frac{2}{15} b^3 x^{15/2}","\frac{6}{7} a^2 b x^{7/2}+\frac{2}{3} a^3 x^{3/2}+\frac{6}{11} a b^2 x^{11/2}+\frac{2}{15} b^3 x^{15/2}",1,"(2*a^3*x^(3/2))/3 + (6*a^2*b*x^(7/2))/7 + (6*a*b^2*x^(11/2))/11 + (2*b^3*x^(15/2))/15","A",2,1,15,0.06667,1,"{270}"
284,1,49,0,0.0115788,"\int \frac{\left(a+b x^2\right)^3}{\sqrt{x}} \, dx","Int[(a + b*x^2)^3/Sqrt[x],x]","\frac{6}{5} a^2 b x^{5/2}+2 a^3 \sqrt{x}+\frac{2}{3} a b^2 x^{9/2}+\frac{2}{13} b^3 x^{13/2}","\frac{6}{5} a^2 b x^{5/2}+2 a^3 \sqrt{x}+\frac{2}{3} a b^2 x^{9/2}+\frac{2}{13} b^3 x^{13/2}",1,"2*a^3*Sqrt[x] + (6*a^2*b*x^(5/2))/5 + (2*a*b^2*x^(9/2))/3 + (2*b^3*x^(13/2))/13","A",2,1,15,0.06667,1,"{270}"
285,1,47,0,0.0116159,"\int \frac{\left(a+b x^2\right)^3}{x^{3/2}} \, dx","Int[(a + b*x^2)^3/x^(3/2),x]","2 a^2 b x^{3/2}-\frac{2 a^3}{\sqrt{x}}+\frac{6}{7} a b^2 x^{7/2}+\frac{2}{11} b^3 x^{11/2}","2 a^2 b x^{3/2}-\frac{2 a^3}{\sqrt{x}}+\frac{6}{7} a b^2 x^{7/2}+\frac{2}{11} b^3 x^{11/2}",1,"(-2*a^3)/Sqrt[x] + 2*a^2*b*x^(3/2) + (6*a*b^2*x^(7/2))/7 + (2*b^3*x^(11/2))/11","A",2,1,15,0.06667,1,"{270}"
286,1,49,0,0.011726,"\int \frac{\left(a+b x^2\right)^3}{x^{5/2}} \, dx","Int[(a + b*x^2)^3/x^(5/2),x]","6 a^2 b \sqrt{x}-\frac{2 a^3}{3 x^{3/2}}+\frac{6}{5} a b^2 x^{5/2}+\frac{2}{9} b^3 x^{9/2}","6 a^2 b \sqrt{x}-\frac{2 a^3}{3 x^{3/2}}+\frac{6}{5} a b^2 x^{5/2}+\frac{2}{9} b^3 x^{9/2}",1,"(-2*a^3)/(3*x^(3/2)) + 6*a^2*b*Sqrt[x] + (6*a*b^2*x^(5/2))/5 + (2*b^3*x^(9/2))/9","A",2,1,15,0.06667,1,"{270}"
287,1,47,0,0.0121488,"\int \frac{\left(a+b x^2\right)^3}{x^{7/2}} \, dx","Int[(a + b*x^2)^3/x^(7/2),x]","-\frac{6 a^2 b}{\sqrt{x}}-\frac{2 a^3}{5 x^{5/2}}+2 a b^2 x^{3/2}+\frac{2}{7} b^3 x^{7/2}","-\frac{6 a^2 b}{\sqrt{x}}-\frac{2 a^3}{5 x^{5/2}}+2 a b^2 x^{3/2}+\frac{2}{7} b^3 x^{7/2}",1,"(-2*a^3)/(5*x^(5/2)) - (6*a^2*b)/Sqrt[x] + 2*a*b^2*x^(3/2) + (2*b^3*x^(7/2))/7","A",2,1,15,0.06667,1,"{270}"
288,1,215,0,0.1981962,"\int \frac{x^{7/2}}{a+b x^2} \, dx","Int[x^(7/2)/(a + b*x^2),x]","-\frac{a^{5/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} b^{9/4}}+\frac{a^{5/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} b^{9/4}}-\frac{a^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} b^{9/4}}+\frac{a^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} b^{9/4}}-\frac{2 a \sqrt{x}}{b^2}+\frac{2 x^{5/2}}{5 b}","-\frac{a^{5/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} b^{9/4}}+\frac{a^{5/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} b^{9/4}}-\frac{a^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} b^{9/4}}+\frac{a^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} b^{9/4}}-\frac{2 a \sqrt{x}}{b^2}+\frac{2 x^{5/2}}{5 b}",1,"(-2*a*Sqrt[x])/b^2 + (2*x^(5/2))/(5*b) - (a^(5/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*b^(9/4)) + (a^(5/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*b^(9/4)) - (a^(5/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*b^(9/4)) + (a^(5/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*b^(9/4))","A",12,8,15,0.5333,1,"{321, 329, 211, 1165, 628, 1162, 617, 204}"
289,1,204,0,0.152454,"\int \frac{x^{5/2}}{a+b x^2} \, dx","Int[x^(5/2)/(a + b*x^2),x]","-\frac{a^{3/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} b^{7/4}}+\frac{a^{3/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} b^{7/4}}+\frac{a^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} b^{7/4}}-\frac{a^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} b^{7/4}}+\frac{2 x^{3/2}}{3 b}","-\frac{a^{3/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} b^{7/4}}+\frac{a^{3/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} b^{7/4}}+\frac{a^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} b^{7/4}}-\frac{a^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} b^{7/4}}+\frac{2 x^{3/2}}{3 b}",1,"(2*x^(3/2))/(3*b) + (a^(3/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*b^(7/4)) - (a^(3/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*b^(7/4)) - (a^(3/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*b^(7/4)) + (a^(3/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*b^(7/4))","A",11,8,15,0.5333,1,"{321, 329, 297, 1162, 617, 204, 1165, 628}"
290,1,202,0,0.1628156,"\int \frac{x^{3/2}}{a+b x^2} \, dx","Int[x^(3/2)/(a + b*x^2),x]","\frac{\sqrt[4]{a} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} b^{5/4}}-\frac{\sqrt[4]{a} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} b^{5/4}}+\frac{\sqrt[4]{a} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} b^{5/4}}-\frac{\sqrt[4]{a} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} b^{5/4}}+\frac{2 \sqrt{x}}{b}","\frac{\sqrt[4]{a} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} b^{5/4}}-\frac{\sqrt[4]{a} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} b^{5/4}}+\frac{\sqrt[4]{a} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} b^{5/4}}-\frac{\sqrt[4]{a} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} b^{5/4}}+\frac{2 \sqrt{x}}{b}",1,"(2*Sqrt[x])/b + (a^(1/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*b^(5/4)) - (a^(1/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*b^(5/4)) + (a^(1/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*b^(5/4)) - (a^(1/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*b^(5/4))","A",11,8,15,0.5333,1,"{321, 329, 211, 1165, 628, 1162, 617, 204}"
291,1,192,0,0.1443829,"\int \frac{\sqrt{x}}{a+b x^2} \, dx","Int[Sqrt[x]/(a + b*x^2),x]","\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} \sqrt[4]{a} b^{3/4}}-\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} \sqrt[4]{a} b^{3/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} \sqrt[4]{a} b^{3/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} \sqrt[4]{a} b^{3/4}}","\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} \sqrt[4]{a} b^{3/4}}-\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} \sqrt[4]{a} b^{3/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} \sqrt[4]{a} b^{3/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} \sqrt[4]{a} b^{3/4}}",1,"-(ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)]/(Sqrt[2]*a^(1/4)*b^(3/4))) + ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)]/(Sqrt[2]*a^(1/4)*b^(3/4)) + Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x]/(2*Sqrt[2]*a^(1/4)*b^(3/4)) - Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x]/(2*Sqrt[2]*a^(1/4)*b^(3/4))","A",10,7,15,0.4667,1,"{329, 297, 1162, 617, 204, 1165, 628}"
292,1,192,0,0.1461015,"\int \frac{1}{\sqrt{x} \left(a+b x^2\right)} \, dx","Int[1/(Sqrt[x]*(a + b*x^2)),x]","-\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{b}}+\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{b}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{3/4} \sqrt[4]{b}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{3/4} \sqrt[4]{b}}","-\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{b}}+\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{b}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{3/4} \sqrt[4]{b}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{3/4} \sqrt[4]{b}}",1,"-(ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)]/(Sqrt[2]*a^(3/4)*b^(1/4))) + ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)]/(Sqrt[2]*a^(3/4)*b^(1/4)) - Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x]/(2*Sqrt[2]*a^(3/4)*b^(1/4)) + Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x]/(2*Sqrt[2]*a^(3/4)*b^(1/4))","A",10,7,15,0.4667,1,"{329, 211, 1165, 628, 1162, 617, 204}"
293,1,202,0,0.1667466,"\int \frac{1}{x^{3/2} \left(a+b x^2\right)} \, dx","Int[1/(x^(3/2)*(a + b*x^2)),x]","-\frac{\sqrt[4]{b} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{5/4}}+\frac{\sqrt[4]{b} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{5/4}}+\frac{\sqrt[4]{b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{5/4}}-\frac{\sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{5/4}}-\frac{2}{a \sqrt{x}}","-\frac{\sqrt[4]{b} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{5/4}}+\frac{\sqrt[4]{b} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{5/4}}+\frac{\sqrt[4]{b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{5/4}}-\frac{\sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{5/4}}-\frac{2}{a \sqrt{x}}",1,"-2/(a*Sqrt[x]) + (b^(1/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(5/4)) - (b^(1/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(5/4)) - (b^(1/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(5/4)) + (b^(1/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(5/4))","A",11,8,15,0.5333,1,"{325, 329, 297, 1162, 617, 204, 1165, 628}"
294,1,204,0,0.1610957,"\int \frac{1}{x^{5/2} \left(a+b x^2\right)} \, dx","Int[1/(x^(5/2)*(a + b*x^2)),x]","\frac{b^{3/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{7/4}}-\frac{b^{3/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{7/4}}+\frac{b^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{7/4}}-\frac{b^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{7/4}}-\frac{2}{3 a x^{3/2}}","\frac{b^{3/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{7/4}}-\frac{b^{3/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{7/4}}+\frac{b^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{7/4}}-\frac{b^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{7/4}}-\frac{2}{3 a x^{3/2}}",1,"-2/(3*a*x^(3/2)) + (b^(3/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(7/4)) - (b^(3/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(7/4)) + (b^(3/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(7/4)) - (b^(3/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(7/4))","A",11,8,15,0.5333,1,"{325, 329, 211, 1165, 628, 1162, 617, 204}"
295,1,215,0,0.175071,"\int \frac{1}{x^{7/2} \left(a+b x^2\right)} \, dx","Int[1/(x^(7/2)*(a + b*x^2)),x]","\frac{b^{5/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{9/4}}-\frac{b^{5/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{9/4}}-\frac{b^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{9/4}}+\frac{b^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{9/4}}+\frac{2 b}{a^2 \sqrt{x}}-\frac{2}{5 a x^{5/2}}","\frac{b^{5/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{9/4}}-\frac{b^{5/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{9/4}}-\frac{b^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{9/4}}+\frac{b^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{9/4}}+\frac{2 b}{a^2 \sqrt{x}}-\frac{2}{5 a x^{5/2}}",1,"-2/(5*a*x^(5/2)) + (2*b)/(a^2*Sqrt[x]) - (b^(5/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(9/4)) + (b^(5/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(9/4)) + (b^(5/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(9/4)) - (b^(5/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(9/4))","A",12,8,15,0.5333,1,"{325, 329, 297, 1162, 617, 204, 1165, 628}"
296,1,230,0,0.1663625,"\int \frac{x^{7/2}}{\left(a+b x^2\right)^2} \, dx","Int[x^(7/2)/(a + b*x^2)^2,x]","\frac{5 \sqrt[4]{a} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} b^{9/4}}-\frac{5 \sqrt[4]{a} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} b^{9/4}}+\frac{5 \sqrt[4]{a} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} b^{9/4}}-\frac{5 \sqrt[4]{a} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} b^{9/4}}-\frac{x^{5/2}}{2 b \left(a+b x^2\right)}+\frac{5 \sqrt{x}}{2 b^2}","\frac{5 \sqrt[4]{a} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} b^{9/4}}-\frac{5 \sqrt[4]{a} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} b^{9/4}}+\frac{5 \sqrt[4]{a} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} b^{9/4}}-\frac{5 \sqrt[4]{a} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} b^{9/4}}-\frac{x^{5/2}}{2 b \left(a+b x^2\right)}+\frac{5 \sqrt{x}}{2 b^2}",1,"(5*Sqrt[x])/(2*b^2) - x^(5/2)/(2*b*(a + b*x^2)) + (5*a^(1/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*b^(9/4)) - (5*a^(1/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*b^(9/4)) + (5*a^(1/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*b^(9/4)) - (5*a^(1/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*b^(9/4))","A",12,9,15,0.6000,1,"{288, 321, 329, 211, 1165, 628, 1162, 617, 204}"
297,1,218,0,0.1484838,"\int \frac{x^{5/2}}{\left(a+b x^2\right)^2} \, dx","Int[x^(5/2)/(a + b*x^2)^2,x]","\frac{3 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} \sqrt[4]{a} b^{7/4}}-\frac{3 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} \sqrt[4]{a} b^{7/4}}-\frac{3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} \sqrt[4]{a} b^{7/4}}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} \sqrt[4]{a} b^{7/4}}-\frac{x^{3/2}}{2 b \left(a+b x^2\right)}","\frac{3 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} \sqrt[4]{a} b^{7/4}}-\frac{3 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} \sqrt[4]{a} b^{7/4}}-\frac{3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} \sqrt[4]{a} b^{7/4}}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} \sqrt[4]{a} b^{7/4}}-\frac{x^{3/2}}{2 b \left(a+b x^2\right)}",1,"-x^(3/2)/(2*b*(a + b*x^2)) - (3*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(1/4)*b^(7/4)) + (3*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(1/4)*b^(7/4)) + (3*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(1/4)*b^(7/4)) - (3*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(1/4)*b^(7/4))","A",11,8,15,0.5333,1,"{288, 329, 297, 1162, 617, 204, 1165, 628}"
298,1,218,0,0.1480166,"\int \frac{x^{3/2}}{\left(a+b x^2\right)^2} \, dx","Int[x^(3/2)/(a + b*x^2)^2,x]","-\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{3/4} b^{5/4}}+\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{3/4} b^{5/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{3/4} b^{5/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{3/4} b^{5/4}}-\frac{\sqrt{x}}{2 b \left(a+b x^2\right)}","-\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{3/4} b^{5/4}}+\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{3/4} b^{5/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{3/4} b^{5/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{3/4} b^{5/4}}-\frac{\sqrt{x}}{2 b \left(a+b x^2\right)}",1,"-Sqrt[x]/(2*b*(a + b*x^2)) - ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)]/(4*Sqrt[2]*a^(3/4)*b^(5/4)) + ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)]/(4*Sqrt[2]*a^(3/4)*b^(5/4)) - Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x]/(8*Sqrt[2]*a^(3/4)*b^(5/4)) + Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x]/(8*Sqrt[2]*a^(3/4)*b^(5/4))","A",11,8,15,0.5333,1,"{288, 329, 211, 1165, 628, 1162, 617, 204}"
299,1,218,0,0.1470906,"\int \frac{\sqrt{x}}{\left(a+b x^2\right)^2} \, dx","Int[Sqrt[x]/(a + b*x^2)^2,x]","\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{5/4} b^{3/4}}-\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{5/4} b^{3/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{5/4} b^{3/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{5/4} b^{3/4}}+\frac{x^{3/2}}{2 a \left(a+b x^2\right)}","\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{5/4} b^{3/4}}-\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{5/4} b^{3/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{5/4} b^{3/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{5/4} b^{3/4}}+\frac{x^{3/2}}{2 a \left(a+b x^2\right)}",1,"x^(3/2)/(2*a*(a + b*x^2)) - ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)]/(4*Sqrt[2]*a^(5/4)*b^(3/4)) + ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)]/(4*Sqrt[2]*a^(5/4)*b^(3/4)) + Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x]/(8*Sqrt[2]*a^(5/4)*b^(3/4)) - Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x]/(8*Sqrt[2]*a^(5/4)*b^(3/4))","A",11,8,15,0.5333,1,"{290, 329, 297, 1162, 617, 204, 1165, 628}"
300,1,218,0,0.1511826,"\int \frac{1}{\sqrt{x} \left(a+b x^2\right)^2} \, dx","Int[1/(Sqrt[x]*(a + b*x^2)^2),x]","-\frac{3 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{7/4} \sqrt[4]{b}}+\frac{3 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{7/4} \sqrt[4]{b}}-\frac{3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{7/4} \sqrt[4]{b}}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{7/4} \sqrt[4]{b}}+\frac{\sqrt{x}}{2 a \left(a+b x^2\right)}","-\frac{3 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{7/4} \sqrt[4]{b}}+\frac{3 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{7/4} \sqrt[4]{b}}-\frac{3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{7/4} \sqrt[4]{b}}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{7/4} \sqrt[4]{b}}+\frac{\sqrt{x}}{2 a \left(a+b x^2\right)}",1,"Sqrt[x]/(2*a*(a + b*x^2)) - (3*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(7/4)*b^(1/4)) + (3*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(7/4)*b^(1/4)) - (3*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(7/4)*b^(1/4)) + (3*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(7/4)*b^(1/4))","A",11,8,15,0.5333,1,"{290, 329, 211, 1165, 628, 1162, 617, 204}"
301,1,230,0,0.1878154,"\int \frac{1}{x^{3/2} \left(a+b x^2\right)^2} \, dx","Int[1/(x^(3/2)*(a + b*x^2)^2),x]","-\frac{5 \sqrt[4]{b} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{9/4}}+\frac{5 \sqrt[4]{b} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{9/4}}+\frac{5 \sqrt[4]{b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{9/4}}-\frac{5 \sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{9/4}}-\frac{5}{2 a^2 \sqrt{x}}+\frac{1}{2 a \sqrt{x} \left(a+b x^2\right)}","-\frac{5 \sqrt[4]{b} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{9/4}}+\frac{5 \sqrt[4]{b} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{9/4}}+\frac{5 \sqrt[4]{b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{9/4}}-\frac{5 \sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{9/4}}-\frac{5}{2 a^2 \sqrt{x}}+\frac{1}{2 a \sqrt{x} \left(a+b x^2\right)}",1,"-5/(2*a^2*Sqrt[x]) + 1/(2*a*Sqrt[x]*(a + b*x^2)) + (5*b^(1/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(9/4)) - (5*b^(1/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(9/4)) - (5*b^(1/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(9/4)) + (5*b^(1/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(9/4))","A",12,9,15,0.6000,1,"{290, 325, 329, 297, 1162, 617, 204, 1165, 628}"
302,1,230,0,0.1766906,"\int \frac{1}{x^{5/2} \left(a+b x^2\right)^2} \, dx","Int[1/(x^(5/2)*(a + b*x^2)^2),x]","\frac{7 b^{3/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{11/4}}-\frac{7 b^{3/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{11/4}}+\frac{7 b^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{11/4}}-\frac{7 b^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{11/4}}-\frac{7}{6 a^2 x^{3/2}}+\frac{1}{2 a x^{3/2} \left(a+b x^2\right)}","\frac{7 b^{3/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{11/4}}-\frac{7 b^{3/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{11/4}}+\frac{7 b^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{11/4}}-\frac{7 b^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{11/4}}-\frac{7}{6 a^2 x^{3/2}}+\frac{1}{2 a x^{3/2} \left(a+b x^2\right)}",1,"-7/(6*a^2*x^(3/2)) + 1/(2*a*x^(3/2)*(a + b*x^2)) + (7*b^(3/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(11/4)) - (7*b^(3/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(11/4)) + (7*b^(3/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(11/4)) - (7*b^(3/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(11/4))","A",12,9,15,0.6000,1,"{290, 325, 329, 211, 1165, 628, 1162, 617, 204}"
303,1,243,0,0.1906007,"\int \frac{1}{x^{7/2} \left(a+b x^2\right)^2} \, dx","Int[1/(x^(7/2)*(a + b*x^2)^2),x]","\frac{9 b^{5/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{13/4}}-\frac{9 b^{5/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{13/4}}-\frac{9 b^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{13/4}}+\frac{9 b^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{13/4}}+\frac{9 b}{2 a^3 \sqrt{x}}-\frac{9}{10 a^2 x^{5/2}}+\frac{1}{2 a x^{5/2} \left(a+b x^2\right)}","\frac{9 b^{5/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{13/4}}-\frac{9 b^{5/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{13/4}}-\frac{9 b^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{13/4}}+\frac{9 b^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{13/4}}+\frac{9 b}{2 a^3 \sqrt{x}}-\frac{9}{10 a^2 x^{5/2}}+\frac{1}{2 a x^{5/2} \left(a+b x^2\right)}",1,"-9/(10*a^2*x^(5/2)) + (9*b)/(2*a^3*Sqrt[x]) + 1/(2*a*x^(5/2)*(a + b*x^2)) - (9*b^(5/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(13/4)) + (9*b^(5/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(13/4)) + (9*b^(5/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(13/4)) - (9*b^(5/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(13/4))","A",13,9,15,0.6000,1,"{290, 325, 329, 297, 1162, 617, 204, 1165, 628}"
304,1,239,0,0.1774,"\int \frac{x^{7/2}}{\left(a+b x^2\right)^3} \, dx","Int[x^(7/2)/(a + b*x^2)^3,x]","-\frac{5 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{3/4} b^{9/4}}+\frac{5 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{3/4} b^{9/4}}-\frac{5 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{32 \sqrt{2} a^{3/4} b^{9/4}}+\frac{5 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{32 \sqrt{2} a^{3/4} b^{9/4}}-\frac{5 \sqrt{x}}{16 b^2 \left(a+b x^2\right)}-\frac{x^{5/2}}{4 b \left(a+b x^2\right)^2}","-\frac{5 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{3/4} b^{9/4}}+\frac{5 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{3/4} b^{9/4}}-\frac{5 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{32 \sqrt{2} a^{3/4} b^{9/4}}+\frac{5 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{32 \sqrt{2} a^{3/4} b^{9/4}}-\frac{5 \sqrt{x}}{16 b^2 \left(a+b x^2\right)}-\frac{x^{5/2}}{4 b \left(a+b x^2\right)^2}",1,"-x^(5/2)/(4*b*(a + b*x^2)^2) - (5*Sqrt[x])/(16*b^2*(a + b*x^2)) - (5*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(32*Sqrt[2]*a^(3/4)*b^(9/4)) + (5*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(32*Sqrt[2]*a^(3/4)*b^(9/4)) - (5*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(64*Sqrt[2]*a^(3/4)*b^(9/4)) + (5*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(64*Sqrt[2]*a^(3/4)*b^(9/4))","A",12,8,15,0.5333,1,"{288, 329, 211, 1165, 628, 1162, 617, 204}"
305,1,242,0,0.1697701,"\int \frac{x^{5/2}}{\left(a+b x^2\right)^3} \, dx","Int[x^(5/2)/(a + b*x^2)^3,x]","\frac{3 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{5/4} b^{7/4}}-\frac{3 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{5/4} b^{7/4}}-\frac{3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{32 \sqrt{2} a^{5/4} b^{7/4}}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{32 \sqrt{2} a^{5/4} b^{7/4}}+\frac{3 x^{3/2}}{16 a b \left(a+b x^2\right)}-\frac{x^{3/2}}{4 b \left(a+b x^2\right)^2}","\frac{3 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{5/4} b^{7/4}}-\frac{3 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{5/4} b^{7/4}}-\frac{3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{32 \sqrt{2} a^{5/4} b^{7/4}}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{32 \sqrt{2} a^{5/4} b^{7/4}}+\frac{3 x^{3/2}}{16 a b \left(a+b x^2\right)}-\frac{x^{3/2}}{4 b \left(a+b x^2\right)^2}",1,"-x^(3/2)/(4*b*(a + b*x^2)^2) + (3*x^(3/2))/(16*a*b*(a + b*x^2)) - (3*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(32*Sqrt[2]*a^(5/4)*b^(7/4)) + (3*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(32*Sqrt[2]*a^(5/4)*b^(7/4)) + (3*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(64*Sqrt[2]*a^(5/4)*b^(7/4)) - (3*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(64*Sqrt[2]*a^(5/4)*b^(7/4))","A",12,9,15,0.6000,1,"{288, 290, 329, 297, 1162, 617, 204, 1165, 628}"
306,1,242,0,0.1638164,"\int \frac{x^{3/2}}{\left(a+b x^2\right)^3} \, dx","Int[x^(3/2)/(a + b*x^2)^3,x]","-\frac{3 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{7/4} b^{5/4}}+\frac{3 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{7/4} b^{5/4}}-\frac{3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{32 \sqrt{2} a^{7/4} b^{5/4}}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{32 \sqrt{2} a^{7/4} b^{5/4}}+\frac{\sqrt{x}}{16 a b \left(a+b x^2\right)}-\frac{\sqrt{x}}{4 b \left(a+b x^2\right)^2}","-\frac{3 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{7/4} b^{5/4}}+\frac{3 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{7/4} b^{5/4}}-\frac{3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{32 \sqrt{2} a^{7/4} b^{5/4}}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{32 \sqrt{2} a^{7/4} b^{5/4}}+\frac{\sqrt{x}}{16 a b \left(a+b x^2\right)}-\frac{\sqrt{x}}{4 b \left(a+b x^2\right)^2}",1,"-Sqrt[x]/(4*b*(a + b*x^2)^2) + Sqrt[x]/(16*a*b*(a + b*x^2)) - (3*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(32*Sqrt[2]*a^(7/4)*b^(5/4)) + (3*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(32*Sqrt[2]*a^(7/4)*b^(5/4)) - (3*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(64*Sqrt[2]*a^(7/4)*b^(5/4)) + (3*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(64*Sqrt[2]*a^(7/4)*b^(5/4))","A",12,9,15,0.6000,1,"{288, 290, 329, 211, 1165, 628, 1162, 617, 204}"
307,1,239,0,0.1641888,"\int \frac{\sqrt{x}}{\left(a+b x^2\right)^3} \, dx","Int[Sqrt[x]/(a + b*x^2)^3,x]","\frac{5 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{9/4} b^{3/4}}-\frac{5 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{9/4} b^{3/4}}-\frac{5 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{32 \sqrt{2} a^{9/4} b^{3/4}}+\frac{5 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{32 \sqrt{2} a^{9/4} b^{3/4}}+\frac{5 x^{3/2}}{16 a^2 \left(a+b x^2\right)}+\frac{x^{3/2}}{4 a \left(a+b x^2\right)^2}","\frac{5 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{9/4} b^{3/4}}-\frac{5 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{9/4} b^{3/4}}-\frac{5 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{32 \sqrt{2} a^{9/4} b^{3/4}}+\frac{5 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{32 \sqrt{2} a^{9/4} b^{3/4}}+\frac{5 x^{3/2}}{16 a^2 \left(a+b x^2\right)}+\frac{x^{3/2}}{4 a \left(a+b x^2\right)^2}",1,"x^(3/2)/(4*a*(a + b*x^2)^2) + (5*x^(3/2))/(16*a^2*(a + b*x^2)) - (5*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(32*Sqrt[2]*a^(9/4)*b^(3/4)) + (5*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(32*Sqrt[2]*a^(9/4)*b^(3/4)) + (5*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(64*Sqrt[2]*a^(9/4)*b^(3/4)) - (5*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(64*Sqrt[2]*a^(9/4)*b^(3/4))","A",12,8,15,0.5333,1,"{290, 329, 297, 1162, 617, 204, 1165, 628}"
308,1,239,0,0.1722225,"\int \frac{1}{\sqrt{x} \left(a+b x^2\right)^3} \, dx","Int[1/(Sqrt[x]*(a + b*x^2)^3),x]","\frac{7 \sqrt{x}}{16 a^2 \left(a+b x^2\right)}-\frac{21 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{11/4} \sqrt[4]{b}}+\frac{21 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{11/4} \sqrt[4]{b}}-\frac{21 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{32 \sqrt{2} a^{11/4} \sqrt[4]{b}}+\frac{21 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{32 \sqrt{2} a^{11/4} \sqrt[4]{b}}+\frac{\sqrt{x}}{4 a \left(a+b x^2\right)^2}","\frac{7 \sqrt{x}}{16 a^2 \left(a+b x^2\right)}-\frac{21 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{11/4} \sqrt[4]{b}}+\frac{21 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{11/4} \sqrt[4]{b}}-\frac{21 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{32 \sqrt{2} a^{11/4} \sqrt[4]{b}}+\frac{21 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{32 \sqrt{2} a^{11/4} \sqrt[4]{b}}+\frac{\sqrt{x}}{4 a \left(a+b x^2\right)^2}",1,"Sqrt[x]/(4*a*(a + b*x^2)^2) + (7*Sqrt[x])/(16*a^2*(a + b*x^2)) - (21*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(32*Sqrt[2]*a^(11/4)*b^(1/4)) + (21*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(32*Sqrt[2]*a^(11/4)*b^(1/4)) - (21*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(64*Sqrt[2]*a^(11/4)*b^(1/4)) + (21*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(64*Sqrt[2]*a^(11/4)*b^(1/4))","A",12,8,15,0.5333,1,"{290, 329, 211, 1165, 628, 1162, 617, 204}"
309,1,251,0,0.1909517,"\int \frac{1}{x^{3/2} \left(a+b x^2\right)^3} \, dx","Int[1/(x^(3/2)*(a + b*x^2)^3),x]","\frac{9}{16 a^2 \sqrt{x} \left(a+b x^2\right)}-\frac{45 \sqrt[4]{b} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{13/4}}+\frac{45 \sqrt[4]{b} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{13/4}}+\frac{45 \sqrt[4]{b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{32 \sqrt{2} a^{13/4}}-\frac{45 \sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{32 \sqrt{2} a^{13/4}}-\frac{45}{16 a^3 \sqrt{x}}+\frac{1}{4 a \sqrt{x} \left(a+b x^2\right)^2}","\frac{9}{16 a^2 \sqrt{x} \left(a+b x^2\right)}-\frac{45 \sqrt[4]{b} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{13/4}}+\frac{45 \sqrt[4]{b} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{13/4}}+\frac{45 \sqrt[4]{b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{32 \sqrt{2} a^{13/4}}-\frac{45 \sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{32 \sqrt{2} a^{13/4}}-\frac{45}{16 a^3 \sqrt{x}}+\frac{1}{4 a \sqrt{x} \left(a+b x^2\right)^2}",1,"-45/(16*a^3*Sqrt[x]) + 1/(4*a*Sqrt[x]*(a + b*x^2)^2) + 9/(16*a^2*Sqrt[x]*(a + b*x^2)) + (45*b^(1/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(32*Sqrt[2]*a^(13/4)) - (45*b^(1/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(32*Sqrt[2]*a^(13/4)) - (45*b^(1/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(64*Sqrt[2]*a^(13/4)) + (45*b^(1/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(64*Sqrt[2]*a^(13/4))","A",13,9,15,0.6000,1,"{290, 325, 329, 297, 1162, 617, 204, 1165, 628}"
310,1,251,0,0.1845958,"\int \frac{1}{x^{5/2} \left(a+b x^2\right)^3} \, dx","Int[1/(x^(5/2)*(a + b*x^2)^3),x]","\frac{77 b^{3/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{15/4}}-\frac{77 b^{3/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{15/4}}+\frac{77 b^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{32 \sqrt{2} a^{15/4}}-\frac{77 b^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{32 \sqrt{2} a^{15/4}}+\frac{11}{16 a^2 x^{3/2} \left(a+b x^2\right)}-\frac{77}{48 a^3 x^{3/2}}+\frac{1}{4 a x^{3/2} \left(a+b x^2\right)^2}","\frac{77 b^{3/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{15/4}}-\frac{77 b^{3/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{15/4}}+\frac{77 b^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{32 \sqrt{2} a^{15/4}}-\frac{77 b^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{32 \sqrt{2} a^{15/4}}+\frac{11}{16 a^2 x^{3/2} \left(a+b x^2\right)}-\frac{77}{48 a^3 x^{3/2}}+\frac{1}{4 a x^{3/2} \left(a+b x^2\right)^2}",1,"-77/(48*a^3*x^(3/2)) + 1/(4*a*x^(3/2)*(a + b*x^2)^2) + 11/(16*a^2*x^(3/2)*(a + b*x^2)) + (77*b^(3/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(32*Sqrt[2]*a^(15/4)) - (77*b^(3/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(32*Sqrt[2]*a^(15/4)) + (77*b^(3/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(64*Sqrt[2]*a^(15/4)) - (77*b^(3/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(64*Sqrt[2]*a^(15/4))","A",13,9,15,0.6000,1,"{290, 325, 329, 211, 1165, 628, 1162, 617, 204}"
311,1,264,0,0.2117014,"\int \frac{1}{x^{7/2} \left(a+b x^2\right)^3} \, dx","Int[1/(x^(7/2)*(a + b*x^2)^3),x]","\frac{117 b^{5/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{17/4}}-\frac{117 b^{5/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{17/4}}-\frac{117 b^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{32 \sqrt{2} a^{17/4}}+\frac{117 b^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{32 \sqrt{2} a^{17/4}}+\frac{13}{16 a^2 x^{5/2} \left(a+b x^2\right)}+\frac{117 b}{16 a^4 \sqrt{x}}-\frac{117}{80 a^3 x^{5/2}}+\frac{1}{4 a x^{5/2} \left(a+b x^2\right)^2}","\frac{117 b^{5/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{17/4}}-\frac{117 b^{5/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{17/4}}-\frac{117 b^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{32 \sqrt{2} a^{17/4}}+\frac{117 b^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{32 \sqrt{2} a^{17/4}}+\frac{13}{16 a^2 x^{5/2} \left(a+b x^2\right)}+\frac{117 b}{16 a^4 \sqrt{x}}-\frac{117}{80 a^3 x^{5/2}}+\frac{1}{4 a x^{5/2} \left(a+b x^2\right)^2}",1,"-117/(80*a^3*x^(5/2)) + (117*b)/(16*a^4*Sqrt[x]) + 1/(4*a*x^(5/2)*(a + b*x^2)^2) + 13/(16*a^2*x^(5/2)*(a + b*x^2)) - (117*b^(5/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(32*Sqrt[2]*a^(17/4)) + (117*b^(5/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(32*Sqrt[2]*a^(17/4)) + (117*b^(5/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(64*Sqrt[2]*a^(17/4)) - (117*b^(5/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(64*Sqrt[2]*a^(17/4))","A",14,9,15,0.6000,1,"{290, 325, 329, 297, 1162, 617, 204, 1165, 628}"
312,1,58,0,0.0340864,"\int \frac{\sqrt{x}}{a-b x^2} \, dx","Int[Sqrt[x]/(a - b*x^2),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt[4]{a} b^{3/4}}-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt[4]{a} b^{3/4}}","\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt[4]{a} b^{3/4}}-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt[4]{a} b^{3/4}}",1,"-(ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)]/(a^(1/4)*b^(3/4))) + ArcTanh[(b^(1/4)*Sqrt[x])/a^(1/4)]/(a^(1/4)*b^(3/4))","A",4,4,16,0.2500,1,"{329, 298, 205, 208}"
313,1,108,0,0.0610106,"\int \frac{x^{7/2}}{1+x^2} \, dx","Int[x^(7/2)/(1 + x^2),x]","\frac{2 x^{5/2}}{5}-2 \sqrt{x}-\frac{\log \left(x-\sqrt{2} \sqrt{x}+1\right)}{2 \sqrt{2}}+\frac{\log \left(x+\sqrt{2} \sqrt{x}+1\right)}{2 \sqrt{2}}-\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)}{\sqrt{2}}+\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)}{\sqrt{2}}","\frac{2 x^{5/2}}{5}-2 \sqrt{x}-\frac{\log \left(x-\sqrt{2} \sqrt{x}+1\right)}{2 \sqrt{2}}+\frac{\log \left(x+\sqrt{2} \sqrt{x}+1\right)}{2 \sqrt{2}}-\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)}{\sqrt{2}}+\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)}{\sqrt{2}}",1,"-2*Sqrt[x] + (2*x^(5/2))/5 - ArcTan[1 - Sqrt[2]*Sqrt[x]]/Sqrt[2] + ArcTan[1 + Sqrt[2]*Sqrt[x]]/Sqrt[2] - Log[1 - Sqrt[2]*Sqrt[x] + x]/(2*Sqrt[2]) + Log[1 + Sqrt[2]*Sqrt[x] + x]/(2*Sqrt[2])","A",12,8,13,0.6154,1,"{321, 329, 211, 1165, 628, 1162, 617, 204}"
314,1,101,0,0.0552592,"\int \frac{x^{5/2}}{1+x^2} \, dx","Int[x^(5/2)/(1 + x^2),x]","\frac{2 x^{3/2}}{3}-\frac{\log \left(x-\sqrt{2} \sqrt{x}+1\right)}{2 \sqrt{2}}+\frac{\log \left(x+\sqrt{2} \sqrt{x}+1\right)}{2 \sqrt{2}}+\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)}{\sqrt{2}}-\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)}{\sqrt{2}}","\frac{2 x^{3/2}}{3}-\frac{\log \left(x-\sqrt{2} \sqrt{x}+1\right)}{2 \sqrt{2}}+\frac{\log \left(x+\sqrt{2} \sqrt{x}+1\right)}{2 \sqrt{2}}+\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)}{\sqrt{2}}-\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)}{\sqrt{2}}",1,"(2*x^(3/2))/3 + ArcTan[1 - Sqrt[2]*Sqrt[x]]/Sqrt[2] - ArcTan[1 + Sqrt[2]*Sqrt[x]]/Sqrt[2] - Log[1 - Sqrt[2]*Sqrt[x] + x]/(2*Sqrt[2]) + Log[1 + Sqrt[2]*Sqrt[x] + x]/(2*Sqrt[2])","A",11,8,13,0.6154,1,"{321, 329, 297, 1162, 617, 204, 1165, 628}"
315,1,99,0,0.0550577,"\int \frac{x^{3/2}}{1+x^2} \, dx","Int[x^(3/2)/(1 + x^2),x]","2 \sqrt{x}+\frac{\log \left(x-\sqrt{2} \sqrt{x}+1\right)}{2 \sqrt{2}}-\frac{\log \left(x+\sqrt{2} \sqrt{x}+1\right)}{2 \sqrt{2}}+\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)}{\sqrt{2}}-\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)}{\sqrt{2}}","2 \sqrt{x}+\frac{\log \left(x-\sqrt{2} \sqrt{x}+1\right)}{2 \sqrt{2}}-\frac{\log \left(x+\sqrt{2} \sqrt{x}+1\right)}{2 \sqrt{2}}+\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)}{\sqrt{2}}-\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)}{\sqrt{2}}",1,"2*Sqrt[x] + ArcTan[1 - Sqrt[2]*Sqrt[x]]/Sqrt[2] - ArcTan[1 + Sqrt[2]*Sqrt[x]]/Sqrt[2] + Log[1 - Sqrt[2]*Sqrt[x] + x]/(2*Sqrt[2]) - Log[1 + Sqrt[2]*Sqrt[x] + x]/(2*Sqrt[2])","A",11,8,13,0.6154,1,"{321, 329, 211, 1165, 628, 1162, 617, 204}"
316,1,92,0,0.0548459,"\int \frac{\sqrt{x}}{1+x^2} \, dx","Int[Sqrt[x]/(1 + x^2),x]","\frac{\log \left(x-\sqrt{2} \sqrt{x}+1\right)}{2 \sqrt{2}}-\frac{\log \left(x+\sqrt{2} \sqrt{x}+1\right)}{2 \sqrt{2}}-\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)}{\sqrt{2}}+\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)}{\sqrt{2}}","\frac{\log \left(x-\sqrt{2} \sqrt{x}+1\right)}{2 \sqrt{2}}-\frac{\log \left(x+\sqrt{2} \sqrt{x}+1\right)}{2 \sqrt{2}}-\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)}{\sqrt{2}}+\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)}{\sqrt{2}}",1,"-(ArcTan[1 - Sqrt[2]*Sqrt[x]]/Sqrt[2]) + ArcTan[1 + Sqrt[2]*Sqrt[x]]/Sqrt[2] + Log[1 - Sqrt[2]*Sqrt[x] + x]/(2*Sqrt[2]) - Log[1 + Sqrt[2]*Sqrt[x] + x]/(2*Sqrt[2])","A",10,7,13,0.5385,1,"{329, 297, 1162, 617, 204, 1165, 628}"
317,1,92,0,0.0532149,"\int \frac{1}{\sqrt{x} \left(1+x^2\right)} \, dx","Int[1/(Sqrt[x]*(1 + x^2)),x]","-\frac{\log \left(x-\sqrt{2} \sqrt{x}+1\right)}{2 \sqrt{2}}+\frac{\log \left(x+\sqrt{2} \sqrt{x}+1\right)}{2 \sqrt{2}}-\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)}{\sqrt{2}}+\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)}{\sqrt{2}}","-\frac{\log \left(x-\sqrt{2} \sqrt{x}+1\right)}{2 \sqrt{2}}+\frac{\log \left(x+\sqrt{2} \sqrt{x}+1\right)}{2 \sqrt{2}}-\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)}{\sqrt{2}}+\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)}{\sqrt{2}}",1,"-(ArcTan[1 - Sqrt[2]*Sqrt[x]]/Sqrt[2]) + ArcTan[1 + Sqrt[2]*Sqrt[x]]/Sqrt[2] - Log[1 - Sqrt[2]*Sqrt[x] + x]/(2*Sqrt[2]) + Log[1 + Sqrt[2]*Sqrt[x] + x]/(2*Sqrt[2])","A",10,7,13,0.5385,1,"{329, 211, 1165, 628, 1162, 617, 204}"
318,1,99,0,0.0563801,"\int \frac{1}{x^{3/2} \left(1+x^2\right)} \, dx","Int[1/(x^(3/2)*(1 + x^2)),x]","-\frac{2}{\sqrt{x}}-\frac{\log \left(x-\sqrt{2} \sqrt{x}+1\right)}{2 \sqrt{2}}+\frac{\log \left(x+\sqrt{2} \sqrt{x}+1\right)}{2 \sqrt{2}}+\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)}{\sqrt{2}}-\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)}{\sqrt{2}}","-\frac{2}{\sqrt{x}}-\frac{\log \left(x-\sqrt{2} \sqrt{x}+1\right)}{2 \sqrt{2}}+\frac{\log \left(x+\sqrt{2} \sqrt{x}+1\right)}{2 \sqrt{2}}+\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)}{\sqrt{2}}-\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)}{\sqrt{2}}",1,"-2/Sqrt[x] + ArcTan[1 - Sqrt[2]*Sqrt[x]]/Sqrt[2] - ArcTan[1 + Sqrt[2]*Sqrt[x]]/Sqrt[2] - Log[1 - Sqrt[2]*Sqrt[x] + x]/(2*Sqrt[2]) + Log[1 + Sqrt[2]*Sqrt[x] + x]/(2*Sqrt[2])","A",11,8,13,0.6154,1,"{325, 329, 297, 1162, 617, 204, 1165, 628}"
319,1,101,0,0.054339,"\int \frac{1}{x^{5/2} \left(1+x^2\right)} \, dx","Int[1/(x^(5/2)*(1 + x^2)),x]","-\frac{2}{3 x^{3/2}}+\frac{\log \left(x-\sqrt{2} \sqrt{x}+1\right)}{2 \sqrt{2}}-\frac{\log \left(x+\sqrt{2} \sqrt{x}+1\right)}{2 \sqrt{2}}+\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)}{\sqrt{2}}-\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)}{\sqrt{2}}","-\frac{2}{3 x^{3/2}}+\frac{\log \left(x-\sqrt{2} \sqrt{x}+1\right)}{2 \sqrt{2}}-\frac{\log \left(x+\sqrt{2} \sqrt{x}+1\right)}{2 \sqrt{2}}+\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)}{\sqrt{2}}-\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)}{\sqrt{2}}",1,"-2/(3*x^(3/2)) + ArcTan[1 - Sqrt[2]*Sqrt[x]]/Sqrt[2] - ArcTan[1 + Sqrt[2]*Sqrt[x]]/Sqrt[2] + Log[1 - Sqrt[2]*Sqrt[x] + x]/(2*Sqrt[2]) - Log[1 + Sqrt[2]*Sqrt[x] + x]/(2*Sqrt[2])","A",11,8,13,0.6154,1,"{325, 329, 211, 1165, 628, 1162, 617, 204}"
320,1,108,0,0.0573483,"\int \frac{1}{x^{7/2} \left(1+x^2\right)} \, dx","Int[1/(x^(7/2)*(1 + x^2)),x]","-\frac{2}{5 x^{5/2}}+\frac{2}{\sqrt{x}}+\frac{\log \left(x-\sqrt{2} \sqrt{x}+1\right)}{2 \sqrt{2}}-\frac{\log \left(x+\sqrt{2} \sqrt{x}+1\right)}{2 \sqrt{2}}-\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)}{\sqrt{2}}+\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)}{\sqrt{2}}","-\frac{2}{5 x^{5/2}}+\frac{2}{\sqrt{x}}+\frac{\log \left(x-\sqrt{2} \sqrt{x}+1\right)}{2 \sqrt{2}}-\frac{\log \left(x+\sqrt{2} \sqrt{x}+1\right)}{2 \sqrt{2}}-\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)}{\sqrt{2}}+\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)}{\sqrt{2}}",1,"-2/(5*x^(5/2)) + 2/Sqrt[x] - ArcTan[1 - Sqrt[2]*Sqrt[x]]/Sqrt[2] + ArcTan[1 + Sqrt[2]*Sqrt[x]]/Sqrt[2] + Log[1 - Sqrt[2]*Sqrt[x] + x]/(2*Sqrt[2]) - Log[1 + Sqrt[2]*Sqrt[x] + x]/(2*Sqrt[2])","A",12,8,13,0.6154,1,"{325, 329, 297, 1162, 617, 204, 1165, 628}"
321,1,122,0,0.0614054,"\int \frac{x^{7/2}}{\left(1+x^2\right)^2} \, dx","Int[x^(7/2)/(1 + x^2)^2,x]","-\frac{x^{5/2}}{2 \left(x^2+1\right)}+\frac{5 \sqrt{x}}{2}+\frac{5 \log \left(x-\sqrt{2} \sqrt{x}+1\right)}{8 \sqrt{2}}-\frac{5 \log \left(x+\sqrt{2} \sqrt{x}+1\right)}{8 \sqrt{2}}+\frac{5 \tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)}{4 \sqrt{2}}-\frac{5 \tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)}{4 \sqrt{2}}","-\frac{x^{5/2}}{2 \left(x^2+1\right)}+\frac{5 \sqrt{x}}{2}+\frac{5 \log \left(x-\sqrt{2} \sqrt{x}+1\right)}{8 \sqrt{2}}-\frac{5 \log \left(x+\sqrt{2} \sqrt{x}+1\right)}{8 \sqrt{2}}+\frac{5 \tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)}{4 \sqrt{2}}-\frac{5 \tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)}{4 \sqrt{2}}",1,"(5*Sqrt[x])/2 - x^(5/2)/(2*(1 + x^2)) + (5*ArcTan[1 - Sqrt[2]*Sqrt[x]])/(4*Sqrt[2]) - (5*ArcTan[1 + Sqrt[2]*Sqrt[x]])/(4*Sqrt[2]) + (5*Log[1 - Sqrt[2]*Sqrt[x] + x])/(8*Sqrt[2]) - (5*Log[1 + Sqrt[2]*Sqrt[x] + x])/(8*Sqrt[2])","A",12,9,13,0.6923,1,"{288, 321, 329, 211, 1165, 628, 1162, 617, 204}"
322,1,113,0,0.0587743,"\int \frac{x^{5/2}}{\left(1+x^2\right)^2} \, dx","Int[x^(5/2)/(1 + x^2)^2,x]","-\frac{x^{3/2}}{2 \left(x^2+1\right)}+\frac{3 \log \left(x-\sqrt{2} \sqrt{x}+1\right)}{8 \sqrt{2}}-\frac{3 \log \left(x+\sqrt{2} \sqrt{x}+1\right)}{8 \sqrt{2}}-\frac{3 \tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)}{4 \sqrt{2}}+\frac{3 \tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)}{4 \sqrt{2}}","-\frac{x^{3/2}}{2 \left(x^2+1\right)}+\frac{3 \log \left(x-\sqrt{2} \sqrt{x}+1\right)}{8 \sqrt{2}}-\frac{3 \log \left(x+\sqrt{2} \sqrt{x}+1\right)}{8 \sqrt{2}}-\frac{3 \tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)}{4 \sqrt{2}}+\frac{3 \tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)}{4 \sqrt{2}}",1,"-x^(3/2)/(2*(1 + x^2)) - (3*ArcTan[1 - Sqrt[2]*Sqrt[x]])/(4*Sqrt[2]) + (3*ArcTan[1 + Sqrt[2]*Sqrt[x]])/(4*Sqrt[2]) + (3*Log[1 - Sqrt[2]*Sqrt[x] + x])/(8*Sqrt[2]) - (3*Log[1 + Sqrt[2]*Sqrt[x] + x])/(8*Sqrt[2])","A",11,8,13,0.6154,1,"{288, 329, 297, 1162, 617, 204, 1165, 628}"
323,1,113,0,0.0585175,"\int \frac{x^{3/2}}{\left(1+x^2\right)^2} \, dx","Int[x^(3/2)/(1 + x^2)^2,x]","-\frac{\sqrt{x}}{2 \left(x^2+1\right)}-\frac{\log \left(x-\sqrt{2} \sqrt{x}+1\right)}{8 \sqrt{2}}+\frac{\log \left(x+\sqrt{2} \sqrt{x}+1\right)}{8 \sqrt{2}}-\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)}{4 \sqrt{2}}+\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)}{4 \sqrt{2}}","-\frac{\sqrt{x}}{2 \left(x^2+1\right)}-\frac{\log \left(x-\sqrt{2} \sqrt{x}+1\right)}{8 \sqrt{2}}+\frac{\log \left(x+\sqrt{2} \sqrt{x}+1\right)}{8 \sqrt{2}}-\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)}{4 \sqrt{2}}+\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)}{4 \sqrt{2}}",1,"-Sqrt[x]/(2*(1 + x^2)) - ArcTan[1 - Sqrt[2]*Sqrt[x]]/(4*Sqrt[2]) + ArcTan[1 + Sqrt[2]*Sqrt[x]]/(4*Sqrt[2]) - Log[1 - Sqrt[2]*Sqrt[x] + x]/(8*Sqrt[2]) + Log[1 + Sqrt[2]*Sqrt[x] + x]/(8*Sqrt[2])","A",11,8,13,0.6154,1,"{288, 329, 211, 1165, 628, 1162, 617, 204}"
324,1,113,0,0.0600187,"\int \frac{\sqrt{x}}{\left(1+x^2\right)^2} \, dx","Int[Sqrt[x]/(1 + x^2)^2,x]","\frac{x^{3/2}}{2 \left(x^2+1\right)}+\frac{\log \left(x-\sqrt{2} \sqrt{x}+1\right)}{8 \sqrt{2}}-\frac{\log \left(x+\sqrt{2} \sqrt{x}+1\right)}{8 \sqrt{2}}-\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)}{4 \sqrt{2}}+\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)}{4 \sqrt{2}}","\frac{x^{3/2}}{2 \left(x^2+1\right)}+\frac{\log \left(x-\sqrt{2} \sqrt{x}+1\right)}{8 \sqrt{2}}-\frac{\log \left(x+\sqrt{2} \sqrt{x}+1\right)}{8 \sqrt{2}}-\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)}{4 \sqrt{2}}+\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)}{4 \sqrt{2}}",1,"x^(3/2)/(2*(1 + x^2)) - ArcTan[1 - Sqrt[2]*Sqrt[x]]/(4*Sqrt[2]) + ArcTan[1 + Sqrt[2]*Sqrt[x]]/(4*Sqrt[2]) + Log[1 - Sqrt[2]*Sqrt[x] + x]/(8*Sqrt[2]) - Log[1 + Sqrt[2]*Sqrt[x] + x]/(8*Sqrt[2])","A",11,8,13,0.6154,1,"{290, 329, 297, 1162, 617, 204, 1165, 628}"
325,1,113,0,0.0591118,"\int \frac{1}{\sqrt{x} \left(1+x^2\right)^2} \, dx","Int[1/(Sqrt[x]*(1 + x^2)^2),x]","\frac{\sqrt{x}}{2 \left(x^2+1\right)}-\frac{3 \log \left(x-\sqrt{2} \sqrt{x}+1\right)}{8 \sqrt{2}}+\frac{3 \log \left(x+\sqrt{2} \sqrt{x}+1\right)}{8 \sqrt{2}}-\frac{3 \tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)}{4 \sqrt{2}}+\frac{3 \tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)}{4 \sqrt{2}}","\frac{\sqrt{x}}{2 \left(x^2+1\right)}-\frac{3 \log \left(x-\sqrt{2} \sqrt{x}+1\right)}{8 \sqrt{2}}+\frac{3 \log \left(x+\sqrt{2} \sqrt{x}+1\right)}{8 \sqrt{2}}-\frac{3 \tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)}{4 \sqrt{2}}+\frac{3 \tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)}{4 \sqrt{2}}",1,"Sqrt[x]/(2*(1 + x^2)) - (3*ArcTan[1 - Sqrt[2]*Sqrt[x]])/(4*Sqrt[2]) + (3*ArcTan[1 + Sqrt[2]*Sqrt[x]])/(4*Sqrt[2]) - (3*Log[1 - Sqrt[2]*Sqrt[x] + x])/(8*Sqrt[2]) + (3*Log[1 + Sqrt[2]*Sqrt[x] + x])/(8*Sqrt[2])","A",11,8,13,0.6154,1,"{290, 329, 211, 1165, 628, 1162, 617, 204}"
326,1,122,0,0.0648586,"\int \frac{1}{x^{3/2} \left(1+x^2\right)^2} \, dx","Int[1/(x^(3/2)*(1 + x^2)^2),x]","\frac{1}{2 \sqrt{x} \left(x^2+1\right)}-\frac{5}{2 \sqrt{x}}-\frac{5 \log \left(x-\sqrt{2} \sqrt{x}+1\right)}{8 \sqrt{2}}+\frac{5 \log \left(x+\sqrt{2} \sqrt{x}+1\right)}{8 \sqrt{2}}+\frac{5 \tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)}{4 \sqrt{2}}-\frac{5 \tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)}{4 \sqrt{2}}","\frac{1}{2 \sqrt{x} \left(x^2+1\right)}-\frac{5}{2 \sqrt{x}}-\frac{5 \log \left(x-\sqrt{2} \sqrt{x}+1\right)}{8 \sqrt{2}}+\frac{5 \log \left(x+\sqrt{2} \sqrt{x}+1\right)}{8 \sqrt{2}}+\frac{5 \tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)}{4 \sqrt{2}}-\frac{5 \tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)}{4 \sqrt{2}}",1,"-5/(2*Sqrt[x]) + 1/(2*Sqrt[x]*(1 + x^2)) + (5*ArcTan[1 - Sqrt[2]*Sqrt[x]])/(4*Sqrt[2]) - (5*ArcTan[1 + Sqrt[2]*Sqrt[x]])/(4*Sqrt[2]) - (5*Log[1 - Sqrt[2]*Sqrt[x] + x])/(8*Sqrt[2]) + (5*Log[1 + Sqrt[2]*Sqrt[x] + x])/(8*Sqrt[2])","A",12,9,13,0.6923,1,"{290, 325, 329, 297, 1162, 617, 204, 1165, 628}"
327,1,122,0,0.0608723,"\int \frac{1}{x^{5/2} \left(1+x^2\right)^2} \, dx","Int[1/(x^(5/2)*(1 + x^2)^2),x]","\frac{1}{2 x^{3/2} \left(x^2+1\right)}-\frac{7}{6 x^{3/2}}+\frac{7 \log \left(x-\sqrt{2} \sqrt{x}+1\right)}{8 \sqrt{2}}-\frac{7 \log \left(x+\sqrt{2} \sqrt{x}+1\right)}{8 \sqrt{2}}+\frac{7 \tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)}{4 \sqrt{2}}-\frac{7 \tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)}{4 \sqrt{2}}","\frac{1}{2 x^{3/2} \left(x^2+1\right)}-\frac{7}{6 x^{3/2}}+\frac{7 \log \left(x-\sqrt{2} \sqrt{x}+1\right)}{8 \sqrt{2}}-\frac{7 \log \left(x+\sqrt{2} \sqrt{x}+1\right)}{8 \sqrt{2}}+\frac{7 \tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)}{4 \sqrt{2}}-\frac{7 \tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)}{4 \sqrt{2}}",1,"-7/(6*x^(3/2)) + 1/(2*x^(3/2)*(1 + x^2)) + (7*ArcTan[1 - Sqrt[2]*Sqrt[x]])/(4*Sqrt[2]) - (7*ArcTan[1 + Sqrt[2]*Sqrt[x]])/(4*Sqrt[2]) + (7*Log[1 - Sqrt[2]*Sqrt[x] + x])/(8*Sqrt[2]) - (7*Log[1 + Sqrt[2]*Sqrt[x] + x])/(8*Sqrt[2])","A",12,9,13,0.6923,1,"{290, 325, 329, 211, 1165, 628, 1162, 617, 204}"
328,1,131,0,0.065451,"\int \frac{1}{x^{7/2} \left(1+x^2\right)^2} \, dx","Int[1/(x^(7/2)*(1 + x^2)^2),x]","\frac{1}{2 x^{5/2} \left(x^2+1\right)}-\frac{9}{10 x^{5/2}}+\frac{9}{2 \sqrt{x}}+\frac{9 \log \left(x-\sqrt{2} \sqrt{x}+1\right)}{8 \sqrt{2}}-\frac{9 \log \left(x+\sqrt{2} \sqrt{x}+1\right)}{8 \sqrt{2}}-\frac{9 \tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)}{4 \sqrt{2}}+\frac{9 \tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)}{4 \sqrt{2}}","\frac{1}{2 x^{5/2} \left(x^2+1\right)}-\frac{9}{10 x^{5/2}}+\frac{9}{2 \sqrt{x}}+\frac{9 \log \left(x-\sqrt{2} \sqrt{x}+1\right)}{8 \sqrt{2}}-\frac{9 \log \left(x+\sqrt{2} \sqrt{x}+1\right)}{8 \sqrt{2}}-\frac{9 \tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)}{4 \sqrt{2}}+\frac{9 \tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)}{4 \sqrt{2}}",1,"-9/(10*x^(5/2)) + 9/(2*Sqrt[x]) + 1/(2*x^(5/2)*(1 + x^2)) - (9*ArcTan[1 - Sqrt[2]*Sqrt[x]])/(4*Sqrt[2]) + (9*ArcTan[1 + Sqrt[2]*Sqrt[x]])/(4*Sqrt[2]) + (9*Log[1 - Sqrt[2]*Sqrt[x] + x])/(8*Sqrt[2]) - (9*Log[1 + Sqrt[2]*Sqrt[x] + x])/(8*Sqrt[2])","A",13,9,13,0.6923,1,"{290, 325, 329, 297, 1162, 617, 204, 1165, 628}"
329,1,129,0,0.068182,"\int \frac{x^{7/2}}{\left(1+x^2\right)^3} \, dx","Int[x^(7/2)/(1 + x^2)^3,x]","-\frac{x^{5/2}}{4 \left(x^2+1\right)^2}-\frac{5 \sqrt{x}}{16 \left(x^2+1\right)}-\frac{5 \log \left(x-\sqrt{2} \sqrt{x}+1\right)}{64 \sqrt{2}}+\frac{5 \log \left(x+\sqrt{2} \sqrt{x}+1\right)}{64 \sqrt{2}}-\frac{5 \tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)}{32 \sqrt{2}}+\frac{5 \tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)}{32 \sqrt{2}}","-\frac{x^{5/2}}{4 \left(x^2+1\right)^2}-\frac{5 \sqrt{x}}{16 \left(x^2+1\right)}-\frac{5 \log \left(x-\sqrt{2} \sqrt{x}+1\right)}{64 \sqrt{2}}+\frac{5 \log \left(x+\sqrt{2} \sqrt{x}+1\right)}{64 \sqrt{2}}-\frac{5 \tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)}{32 \sqrt{2}}+\frac{5 \tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)}{32 \sqrt{2}}",1,"-x^(5/2)/(4*(1 + x^2)^2) - (5*Sqrt[x])/(16*(1 + x^2)) - (5*ArcTan[1 - Sqrt[2]*Sqrt[x]])/(32*Sqrt[2]) + (5*ArcTan[1 + Sqrt[2]*Sqrt[x]])/(32*Sqrt[2]) - (5*Log[1 - Sqrt[2]*Sqrt[x] + x])/(64*Sqrt[2]) + (5*Log[1 + Sqrt[2]*Sqrt[x] + x])/(64*Sqrt[2])","A",12,8,13,0.6154,1,"{288, 329, 211, 1165, 628, 1162, 617, 204}"
330,1,129,0,0.0698324,"\int \frac{x^{5/2}}{\left(1+x^2\right)^3} \, dx","Int[x^(5/2)/(1 + x^2)^3,x]","\frac{3 x^{3/2}}{16 \left(x^2+1\right)}-\frac{x^{3/2}}{4 \left(x^2+1\right)^2}+\frac{3 \log \left(x-\sqrt{2} \sqrt{x}+1\right)}{64 \sqrt{2}}-\frac{3 \log \left(x+\sqrt{2} \sqrt{x}+1\right)}{64 \sqrt{2}}-\frac{3 \tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)}{32 \sqrt{2}}+\frac{3 \tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)}{32 \sqrt{2}}","\frac{3 x^{3/2}}{16 \left(x^2+1\right)}-\frac{x^{3/2}}{4 \left(x^2+1\right)^2}+\frac{3 \log \left(x-\sqrt{2} \sqrt{x}+1\right)}{64 \sqrt{2}}-\frac{3 \log \left(x+\sqrt{2} \sqrt{x}+1\right)}{64 \sqrt{2}}-\frac{3 \tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)}{32 \sqrt{2}}+\frac{3 \tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)}{32 \sqrt{2}}",1,"-x^(3/2)/(4*(1 + x^2)^2) + (3*x^(3/2))/(16*(1 + x^2)) - (3*ArcTan[1 - Sqrt[2]*Sqrt[x]])/(32*Sqrt[2]) + (3*ArcTan[1 + Sqrt[2]*Sqrt[x]])/(32*Sqrt[2]) + (3*Log[1 - Sqrt[2]*Sqrt[x] + x])/(64*Sqrt[2]) - (3*Log[1 + Sqrt[2]*Sqrt[x] + x])/(64*Sqrt[2])","A",12,9,13,0.6923,1,"{288, 290, 329, 297, 1162, 617, 204, 1165, 628}"
331,1,129,0,0.0679411,"\int \frac{x^{3/2}}{\left(1+x^2\right)^3} \, dx","Int[x^(3/2)/(1 + x^2)^3,x]","\frac{\sqrt{x}}{16 \left(x^2+1\right)}-\frac{\sqrt{x}}{4 \left(x^2+1\right)^2}-\frac{3 \log \left(x-\sqrt{2} \sqrt{x}+1\right)}{64 \sqrt{2}}+\frac{3 \log \left(x+\sqrt{2} \sqrt{x}+1\right)}{64 \sqrt{2}}-\frac{3 \tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)}{32 \sqrt{2}}+\frac{3 \tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)}{32 \sqrt{2}}","\frac{\sqrt{x}}{16 \left(x^2+1\right)}-\frac{\sqrt{x}}{4 \left(x^2+1\right)^2}-\frac{3 \log \left(x-\sqrt{2} \sqrt{x}+1\right)}{64 \sqrt{2}}+\frac{3 \log \left(x+\sqrt{2} \sqrt{x}+1\right)}{64 \sqrt{2}}-\frac{3 \tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)}{32 \sqrt{2}}+\frac{3 \tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)}{32 \sqrt{2}}",1,"-Sqrt[x]/(4*(1 + x^2)^2) + Sqrt[x]/(16*(1 + x^2)) - (3*ArcTan[1 - Sqrt[2]*Sqrt[x]])/(32*Sqrt[2]) + (3*ArcTan[1 + Sqrt[2]*Sqrt[x]])/(32*Sqrt[2]) - (3*Log[1 - Sqrt[2]*Sqrt[x] + x])/(64*Sqrt[2]) + (3*Log[1 + Sqrt[2]*Sqrt[x] + x])/(64*Sqrt[2])","A",12,9,13,0.6923,1,"{288, 290, 329, 211, 1165, 628, 1162, 617, 204}"
332,1,129,0,0.0690822,"\int \frac{\sqrt{x}}{\left(1+x^2\right)^3} \, dx","Int[Sqrt[x]/(1 + x^2)^3,x]","\frac{5 x^{3/2}}{16 \left(x^2+1\right)}+\frac{x^{3/2}}{4 \left(x^2+1\right)^2}+\frac{5 \log \left(x-\sqrt{2} \sqrt{x}+1\right)}{64 \sqrt{2}}-\frac{5 \log \left(x+\sqrt{2} \sqrt{x}+1\right)}{64 \sqrt{2}}-\frac{5 \tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)}{32 \sqrt{2}}+\frac{5 \tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)}{32 \sqrt{2}}","\frac{5 x^{3/2}}{16 \left(x^2+1\right)}+\frac{x^{3/2}}{4 \left(x^2+1\right)^2}+\frac{5 \log \left(x-\sqrt{2} \sqrt{x}+1\right)}{64 \sqrt{2}}-\frac{5 \log \left(x+\sqrt{2} \sqrt{x}+1\right)}{64 \sqrt{2}}-\frac{5 \tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)}{32 \sqrt{2}}+\frac{5 \tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)}{32 \sqrt{2}}",1,"x^(3/2)/(4*(1 + x^2)^2) + (5*x^(3/2))/(16*(1 + x^2)) - (5*ArcTan[1 - Sqrt[2]*Sqrt[x]])/(32*Sqrt[2]) + (5*ArcTan[1 + Sqrt[2]*Sqrt[x]])/(32*Sqrt[2]) + (5*Log[1 - Sqrt[2]*Sqrt[x] + x])/(64*Sqrt[2]) - (5*Log[1 + Sqrt[2]*Sqrt[x] + x])/(64*Sqrt[2])","A",12,8,13,0.6154,1,"{290, 329, 297, 1162, 617, 204, 1165, 628}"
333,1,129,0,0.0682552,"\int \frac{1}{\sqrt{x} \left(1+x^2\right)^3} \, dx","Int[1/(Sqrt[x]*(1 + x^2)^3),x]","\frac{7 \sqrt{x}}{16 \left(x^2+1\right)}+\frac{\sqrt{x}}{4 \left(x^2+1\right)^2}-\frac{21 \log \left(x-\sqrt{2} \sqrt{x}+1\right)}{64 \sqrt{2}}+\frac{21 \log \left(x+\sqrt{2} \sqrt{x}+1\right)}{64 \sqrt{2}}-\frac{21 \tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)}{32 \sqrt{2}}+\frac{21 \tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)}{32 \sqrt{2}}","\frac{7 \sqrt{x}}{16 \left(x^2+1\right)}+\frac{\sqrt{x}}{4 \left(x^2+1\right)^2}-\frac{21 \log \left(x-\sqrt{2} \sqrt{x}+1\right)}{64 \sqrt{2}}+\frac{21 \log \left(x+\sqrt{2} \sqrt{x}+1\right)}{64 \sqrt{2}}-\frac{21 \tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)}{32 \sqrt{2}}+\frac{21 \tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)}{32 \sqrt{2}}",1,"Sqrt[x]/(4*(1 + x^2)^2) + (7*Sqrt[x])/(16*(1 + x^2)) - (21*ArcTan[1 - Sqrt[2]*Sqrt[x]])/(32*Sqrt[2]) + (21*ArcTan[1 + Sqrt[2]*Sqrt[x]])/(32*Sqrt[2]) - (21*Log[1 - Sqrt[2]*Sqrt[x] + x])/(64*Sqrt[2]) + (21*Log[1 + Sqrt[2]*Sqrt[x] + x])/(64*Sqrt[2])","A",12,8,13,0.6154,1,"{290, 329, 211, 1165, 628, 1162, 617, 204}"
334,1,138,0,0.0703358,"\int \frac{1}{x^{3/2} \left(1+x^2\right)^3} \, dx","Int[1/(x^(3/2)*(1 + x^2)^3),x]","\frac{9}{16 \sqrt{x} \left(x^2+1\right)}+\frac{1}{4 \sqrt{x} \left(x^2+1\right)^2}-\frac{45}{16 \sqrt{x}}-\frac{45 \log \left(x-\sqrt{2} \sqrt{x}+1\right)}{64 \sqrt{2}}+\frac{45 \log \left(x+\sqrt{2} \sqrt{x}+1\right)}{64 \sqrt{2}}+\frac{45 \tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)}{32 \sqrt{2}}-\frac{45 \tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)}{32 \sqrt{2}}","\frac{9}{16 \sqrt{x} \left(x^2+1\right)}+\frac{1}{4 \sqrt{x} \left(x^2+1\right)^2}-\frac{45}{16 \sqrt{x}}-\frac{45 \log \left(x-\sqrt{2} \sqrt{x}+1\right)}{64 \sqrt{2}}+\frac{45 \log \left(x+\sqrt{2} \sqrt{x}+1\right)}{64 \sqrt{2}}+\frac{45 \tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)}{32 \sqrt{2}}-\frac{45 \tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)}{32 \sqrt{2}}",1,"-45/(16*Sqrt[x]) + 1/(4*Sqrt[x]*(1 + x^2)^2) + 9/(16*Sqrt[x]*(1 + x^2)) + (45*ArcTan[1 - Sqrt[2]*Sqrt[x]])/(32*Sqrt[2]) - (45*ArcTan[1 + Sqrt[2]*Sqrt[x]])/(32*Sqrt[2]) - (45*Log[1 - Sqrt[2]*Sqrt[x] + x])/(64*Sqrt[2]) + (45*Log[1 + Sqrt[2]*Sqrt[x] + x])/(64*Sqrt[2])","A",13,9,13,0.6923,1,"{290, 325, 329, 297, 1162, 617, 204, 1165, 628}"
335,1,138,0,0.070822,"\int \frac{1}{x^{5/2} \left(1+x^2\right)^3} \, dx","Int[1/(x^(5/2)*(1 + x^2)^3),x]","\frac{11}{16 x^{3/2} \left(x^2+1\right)}-\frac{77}{48 x^{3/2}}+\frac{1}{4 x^{3/2} \left(x^2+1\right)^2}+\frac{77 \log \left(x-\sqrt{2} \sqrt{x}+1\right)}{64 \sqrt{2}}-\frac{77 \log \left(x+\sqrt{2} \sqrt{x}+1\right)}{64 \sqrt{2}}+\frac{77 \tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)}{32 \sqrt{2}}-\frac{77 \tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)}{32 \sqrt{2}}","\frac{11}{16 x^{3/2} \left(x^2+1\right)}-\frac{77}{48 x^{3/2}}+\frac{1}{4 x^{3/2} \left(x^2+1\right)^2}+\frac{77 \log \left(x-\sqrt{2} \sqrt{x}+1\right)}{64 \sqrt{2}}-\frac{77 \log \left(x+\sqrt{2} \sqrt{x}+1\right)}{64 \sqrt{2}}+\frac{77 \tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)}{32 \sqrt{2}}-\frac{77 \tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)}{32 \sqrt{2}}",1,"-77/(48*x^(3/2)) + 1/(4*x^(3/2)*(1 + x^2)^2) + 11/(16*x^(3/2)*(1 + x^2)) + (77*ArcTan[1 - Sqrt[2]*Sqrt[x]])/(32*Sqrt[2]) - (77*ArcTan[1 + Sqrt[2]*Sqrt[x]])/(32*Sqrt[2]) + (77*Log[1 - Sqrt[2]*Sqrt[x] + x])/(64*Sqrt[2]) - (77*Log[1 + Sqrt[2]*Sqrt[x] + x])/(64*Sqrt[2])","A",13,9,13,0.6923,1,"{290, 325, 329, 211, 1165, 628, 1162, 617, 204}"
336,1,147,0,0.0745039,"\int \frac{1}{x^{7/2} \left(1+x^2\right)^3} \, dx","Int[1/(x^(7/2)*(1 + x^2)^3),x]","\frac{13}{16 x^{5/2} \left(x^2+1\right)}+\frac{1}{4 x^{5/2} \left(x^2+1\right)^2}-\frac{117}{80 x^{5/2}}+\frac{117}{16 \sqrt{x}}+\frac{117 \log \left(x-\sqrt{2} \sqrt{x}+1\right)}{64 \sqrt{2}}-\frac{117 \log \left(x+\sqrt{2} \sqrt{x}+1\right)}{64 \sqrt{2}}-\frac{117 \tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)}{32 \sqrt{2}}+\frac{117 \tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)}{32 \sqrt{2}}","\frac{13}{16 x^{5/2} \left(x^2+1\right)}+\frac{1}{4 x^{5/2} \left(x^2+1\right)^2}-\frac{117}{80 x^{5/2}}+\frac{117}{16 \sqrt{x}}+\frac{117 \log \left(x-\sqrt{2} \sqrt{x}+1\right)}{64 \sqrt{2}}-\frac{117 \log \left(x+\sqrt{2} \sqrt{x}+1\right)}{64 \sqrt{2}}-\frac{117 \tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)}{32 \sqrt{2}}+\frac{117 \tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)}{32 \sqrt{2}}",1,"-117/(80*x^(5/2)) + 117/(16*Sqrt[x]) + 1/(4*x^(5/2)*(1 + x^2)^2) + 13/(16*x^(5/2)*(1 + x^2)) - (117*ArcTan[1 - Sqrt[2]*Sqrt[x]])/(32*Sqrt[2]) + (117*ArcTan[1 + Sqrt[2]*Sqrt[x]])/(32*Sqrt[2]) + (117*Log[1 - Sqrt[2]*Sqrt[x] + x])/(64*Sqrt[2]) - (117*Log[1 + Sqrt[2]*Sqrt[x] + x])/(64*Sqrt[2])","A",14,9,13,0.6923,1,"{290, 325, 329, 297, 1162, 617, 204, 1165, 628}"
337,1,15,0,0.0074245,"\int \frac{\sqrt{x}}{1-x^2} \, dx","Int[Sqrt[x]/(1 - x^2),x]","\tanh ^{-1}\left(\sqrt{x}\right)-\tan ^{-1}\left(\sqrt{x}\right)","\tanh ^{-1}\left(\sqrt{x}\right)-\tan ^{-1}\left(\sqrt{x}\right)",1,"-ArcTan[Sqrt[x]] + ArcTanh[Sqrt[x]]","A",4,4,15,0.2667,1,"{329, 298, 203, 206}"
338,1,100,0,0.2570181,"\int \frac{x^{2/3}}{1+x^2} \, dx","Int[x^(2/3)/(1 + x^2),x]","\frac{1}{4} \sqrt{3} \log \left(x^{2/3}-\sqrt{3} \sqrt[3]{x}+1\right)-\frac{1}{4} \sqrt{3} \log \left(x^{2/3}+\sqrt{3} \sqrt[3]{x}+1\right)-\frac{1}{2} \tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{x}\right)+\frac{1}{2} \tan ^{-1}\left(2 \sqrt[3]{x}+\sqrt{3}\right)+\tan ^{-1}\left(\sqrt[3]{x}\right)","-\frac{1}{2} \sqrt{3} \tanh ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x}}{x^{2/3}+1}\right)-\frac{1}{2} \tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{x}\right)+\frac{1}{2} \tan ^{-1}\left(2 \sqrt[3]{x}+\sqrt{3}\right)+\tan ^{-1}\left(\sqrt[3]{x}\right)",1,"-ArcTan[Sqrt[3] - 2*x^(1/3)]/2 + ArcTan[Sqrt[3] + 2*x^(1/3)]/2 + ArcTan[x^(1/3)] + (Sqrt[3]*Log[1 - Sqrt[3]*x^(1/3) + x^(2/3)])/4 - (Sqrt[3]*Log[1 + Sqrt[3]*x^(1/3) + x^(2/3)])/4","A",11,7,13,0.5385,1,"{329, 295, 634, 618, 204, 628, 203}"
339,1,97,0,0.0430813,"\int x^m \left(a+b x^2\right)^5 \, dx","Int[x^m*(a + b*x^2)^5,x]","\frac{10 a^3 b^2 x^{m+5}}{m+5}+\frac{10 a^2 b^3 x^{m+7}}{m+7}+\frac{5 a^4 b x^{m+3}}{m+3}+\frac{a^5 x^{m+1}}{m+1}+\frac{5 a b^4 x^{m+9}}{m+9}+\frac{b^5 x^{m+11}}{m+11}","\frac{10 a^3 b^2 x^{m+5}}{m+5}+\frac{10 a^2 b^3 x^{m+7}}{m+7}+\frac{5 a^4 b x^{m+3}}{m+3}+\frac{a^5 x^{m+1}}{m+1}+\frac{5 a b^4 x^{m+9}}{m+9}+\frac{b^5 x^{m+11}}{m+11}",1,"(a^5*x^(1 + m))/(1 + m) + (5*a^4*b*x^(3 + m))/(3 + m) + (10*a^3*b^2*x^(5 + m))/(5 + m) + (10*a^2*b^3*x^(7 + m))/(7 + m) + (5*a*b^4*x^(9 + m))/(9 + m) + (b^5*x^(11 + m))/(11 + m)","A",2,1,13,0.07692,1,"{270}"
340,1,79,0,0.0315087,"\int x^m \left(a+b x^2\right)^4 \, dx","Int[x^m*(a + b*x^2)^4,x]","\frac{6 a^2 b^2 x^{m+5}}{m+5}+\frac{4 a^3 b x^{m+3}}{m+3}+\frac{a^4 x^{m+1}}{m+1}+\frac{4 a b^3 x^{m+7}}{m+7}+\frac{b^4 x^{m+9}}{m+9}","\frac{6 a^2 b^2 x^{m+5}}{m+5}+\frac{4 a^3 b x^{m+3}}{m+3}+\frac{a^4 x^{m+1}}{m+1}+\frac{4 a b^3 x^{m+7}}{m+7}+\frac{b^4 x^{m+9}}{m+9}",1,"(a^4*x^(1 + m))/(1 + m) + (4*a^3*b*x^(3 + m))/(3 + m) + (6*a^2*b^2*x^(5 + m))/(5 + m) + (4*a*b^3*x^(7 + m))/(7 + m) + (b^4*x^(9 + m))/(9 + m)","A",2,1,13,0.07692,1,"{270}"
341,1,61,0,0.022071,"\int x^m \left(a+b x^2\right)^3 \, dx","Int[x^m*(a + b*x^2)^3,x]","\frac{3 a^2 b x^{m+3}}{m+3}+\frac{a^3 x^{m+1}}{m+1}+\frac{3 a b^2 x^{m+5}}{m+5}+\frac{b^3 x^{m+7}}{m+7}","\frac{3 a^2 b x^{m+3}}{m+3}+\frac{a^3 x^{m+1}}{m+1}+\frac{3 a b^2 x^{m+5}}{m+5}+\frac{b^3 x^{m+7}}{m+7}",1,"(a^3*x^(1 + m))/(1 + m) + (3*a^2*b*x^(3 + m))/(3 + m) + (3*a*b^2*x^(5 + m))/(5 + m) + (b^3*x^(7 + m))/(7 + m)","A",2,1,13,0.07692,1,"{270}"
342,1,43,0,0.0151615,"\int x^m \left(a+b x^2\right)^2 \, dx","Int[x^m*(a + b*x^2)^2,x]","\frac{a^2 x^{m+1}}{m+1}+\frac{2 a b x^{m+3}}{m+3}+\frac{b^2 x^{m+5}}{m+5}","\frac{a^2 x^{m+1}}{m+1}+\frac{2 a b x^{m+3}}{m+3}+\frac{b^2 x^{m+5}}{m+5}",1,"(a^2*x^(1 + m))/(1 + m) + (2*a*b*x^(3 + m))/(3 + m) + (b^2*x^(5 + m))/(5 + m)","A",2,1,13,0.07692,1,"{270}"
343,1,25,0,0.0073573,"\int x^m \left(a+b x^2\right) \, dx","Int[x^m*(a + b*x^2),x]","\frac{a x^{m+1}}{m+1}+\frac{b x^{m+3}}{m+3}","\frac{a x^{m+1}}{m+1}+\frac{b x^{m+3}}{m+3}",1,"(a*x^(1 + m))/(1 + m) + (b*x^(3 + m))/(3 + m)","A",2,1,11,0.09091,1,"{14}"
344,1,39,0,0.0082732,"\int \frac{x^m}{a+b x^2} \, dx","Int[x^m/(a + b*x^2),x]","\frac{x^{m+1} \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a (m+1)}","\frac{x^{m+1} \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a (m+1)}",1,"(x^(1 + m)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, -((b*x^2)/a)])/(a*(1 + m))","A",1,1,13,0.07692,1,"{364}"
345,1,39,0,0.0079825,"\int \frac{x^m}{\left(a+b x^2\right)^2} \, dx","Int[x^m/(a + b*x^2)^2,x]","\frac{x^{m+1} \, _2F_1\left(2,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a^2 (m+1)}","\frac{x^{m+1} \, _2F_1\left(2,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a^2 (m+1)}",1,"(x^(1 + m)*Hypergeometric2F1[2, (1 + m)/2, (3 + m)/2, -((b*x^2)/a)])/(a^2*(1 + m))","A",1,1,13,0.07692,1,"{364}"
346,1,39,0,0.0083129,"\int \frac{x^m}{\left(a+b x^2\right)^3} \, dx","Int[x^m/(a + b*x^2)^3,x]","\frac{x^{m+1} \, _2F_1\left(3,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a^3 (m+1)}","\frac{x^{m+1} \, _2F_1\left(3,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a^3 (m+1)}",1,"(x^(1 + m)*Hypergeometric2F1[3, (1 + m)/2, (3 + m)/2, -((b*x^2)/a)])/(a^3*(1 + m))","A",1,1,13,0.07692,1,"{364}"
347,1,44,0,0.0118202,"\int \frac{(c x)^{1+m}}{a+b x^2} \, dx","Int[(c*x)^(1 + m)/(a + b*x^2),x]","\frac{(c x)^{m+2} \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};-\frac{b x^2}{a}\right)}{a c (m+2)}","\frac{(c x)^{m+2} \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};-\frac{b x^2}{a}\right)}{a c (m+2)}",1,"((c*x)^(2 + m)*Hypergeometric2F1[1, (2 + m)/2, (4 + m)/2, -((b*x^2)/a)])/(a*c*(2 + m))","A",1,1,17,0.05882,1,"{364}"
348,1,44,0,0.0096857,"\int \frac{(c x)^m}{a+b x^2} \, dx","Int[(c*x)^m/(a + b*x^2),x]","\frac{(c x)^{m+1} \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a c (m+1)}","\frac{(c x)^{m+1} \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a c (m+1)}",1,"((c*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, -((b*x^2)/a)])/(a*c*(1 + m))","A",1,1,15,0.06667,1,"{364}"
349,1,38,0,0.0085645,"\int \frac{(c x)^{-1+m}}{a+b x^2} \, dx","Int[(c*x)^(-1 + m)/(a + b*x^2),x]","\frac{(c x)^m \, _2F_1\left(1,\frac{m}{2};\frac{m+2}{2};-\frac{b x^2}{a}\right)}{a c m}","\frac{(c x)^m \, _2F_1\left(1,\frac{m}{2};\frac{m+2}{2};-\frac{b x^2}{a}\right)}{a c m}",1,"((c*x)^m*Hypergeometric2F1[1, m/2, (2 + m)/2, -((b*x^2)/a)])/(a*c*m)","A",1,1,17,0.05882,1,"{364}"
350,1,47,0,0.0118837,"\int \frac{(c x)^{-2+m}}{a+b x^2} \, dx","Int[(c*x)^(-2 + m)/(a + b*x^2),x]","-\frac{(c x)^{m-1} \, _2F_1\left(1,\frac{m-1}{2};\frac{m+1}{2};-\frac{b x^2}{a}\right)}{a c (1-m)}","-\frac{(c x)^{m-1} \, _2F_1\left(1,\frac{m-1}{2};\frac{m+1}{2};-\frac{b x^2}{a}\right)}{a c (1-m)}",1,"-(((c*x)^(-1 + m)*Hypergeometric2F1[1, (-1 + m)/2, (1 + m)/2, -((b*x^2)/a)])/(a*c*(1 - m)))","A",1,1,17,0.05882,1,"{364}"
351,1,45,0,0.01166,"\int \frac{(c x)^{-3+m}}{a+b x^2} \, dx","Int[(c*x)^(-3 + m)/(a + b*x^2),x]","-\frac{(c x)^{m-2} \, _2F_1\left(1,\frac{m-2}{2};\frac{m}{2};-\frac{b x^2}{a}\right)}{a c (2-m)}","-\frac{(c x)^{m-2} \, _2F_1\left(1,\frac{m-2}{2};\frac{m}{2};-\frac{b x^2}{a}\right)}{a c (2-m)}",1,"-(((c*x)^(-2 + m)*Hypergeometric2F1[1, (-2 + m)/2, m/2, -((b*x^2)/a)])/(a*c*(2 - m)))","A",1,1,17,0.05882,1,"{364}"
352,1,36,0,0.0078092,"\int \frac{x^m}{\left(1+\frac{a x^2}{b}\right)^2} \, dx","Int[x^m/(1 + (a*x^2)/b)^2,x]","\frac{x^{m+1} \, _2F_1\left(2,\frac{m+1}{2};\frac{m+3}{2};-\frac{a x^2}{b}\right)}{m+1}","\frac{x^{m+1} \, _2F_1\left(2,\frac{m+1}{2};\frac{m+3}{2};-\frac{a x^2}{b}\right)}{m+1}",1,"(x^(1 + m)*Hypergeometric2F1[2, (1 + m)/2, (3 + m)/2, -((a*x^2)/b)])/(1 + m)","A",1,1,16,0.06250,1,"{364}"
353,1,80,0,0.0452027,"\int x^7 \sqrt{a+b x^2} \, dx","Int[x^7*Sqrt[a + b*x^2],x]","\frac{3 a^2 \left(a+b x^2\right)^{5/2}}{5 b^4}-\frac{a^3 \left(a+b x^2\right)^{3/2}}{3 b^4}+\frac{\left(a+b x^2\right)^{9/2}}{9 b^4}-\frac{3 a \left(a+b x^2\right)^{7/2}}{7 b^4}","\frac{3 a^2 \left(a+b x^2\right)^{5/2}}{5 b^4}-\frac{a^3 \left(a+b x^2\right)^{3/2}}{3 b^4}+\frac{\left(a+b x^2\right)^{9/2}}{9 b^4}-\frac{3 a \left(a+b x^2\right)^{7/2}}{7 b^4}",1,"-(a^3*(a + b*x^2)^(3/2))/(3*b^4) + (3*a^2*(a + b*x^2)^(5/2))/(5*b^4) - (3*a*(a + b*x^2)^(7/2))/(7*b^4) + (a + b*x^2)^(9/2)/(9*b^4)","A",3,2,15,0.1333,1,"{266, 43}"
354,1,59,0,0.0327254,"\int x^5 \sqrt{a+b x^2} \, dx","Int[x^5*Sqrt[a + b*x^2],x]","\frac{a^2 \left(a+b x^2\right)^{3/2}}{3 b^3}+\frac{\left(a+b x^2\right)^{7/2}}{7 b^3}-\frac{2 a \left(a+b x^2\right)^{5/2}}{5 b^3}","\frac{a^2 \left(a+b x^2\right)^{3/2}}{3 b^3}+\frac{\left(a+b x^2\right)^{7/2}}{7 b^3}-\frac{2 a \left(a+b x^2\right)^{5/2}}{5 b^3}",1,"(a^2*(a + b*x^2)^(3/2))/(3*b^3) - (2*a*(a + b*x^2)^(5/2))/(5*b^3) + (a + b*x^2)^(7/2)/(7*b^3)","A",3,2,15,0.1333,1,"{266, 43}"
355,1,38,0,0.0216558,"\int x^3 \sqrt{a+b x^2} \, dx","Int[x^3*Sqrt[a + b*x^2],x]","\frac{\left(a+b x^2\right)^{5/2}}{5 b^2}-\frac{a \left(a+b x^2\right)^{3/2}}{3 b^2}","\frac{\left(a+b x^2\right)^{5/2}}{5 b^2}-\frac{a \left(a+b x^2\right)^{3/2}}{3 b^2}",1,"-(a*(a + b*x^2)^(3/2))/(3*b^2) + (a + b*x^2)^(5/2)/(5*b^2)","A",3,2,15,0.1333,1,"{266, 43}"
356,1,18,0,0.0030336,"\int x \sqrt{a+b x^2} \, dx","Int[x*Sqrt[a + b*x^2],x]","\frac{\left(a+b x^2\right)^{3/2}}{3 b}","\frac{\left(a+b x^2\right)^{3/2}}{3 b}",1,"(a + b*x^2)^(3/2)/(3*b)","A",1,1,13,0.07692,1,"{261}"
357,1,37,0,0.024309,"\int \frac{\sqrt{a+b x^2}}{x} \, dx","Int[Sqrt[a + b*x^2]/x,x]","\sqrt{a+b x^2}-\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)","\sqrt{a+b x^2}-\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)",1,"Sqrt[a + b*x^2] - Sqrt[a]*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]]","A",4,4,15,0.2667,1,"{266, 50, 63, 208}"
358,1,47,0,0.0249238,"\int \frac{\sqrt{a+b x^2}}{x^3} \, dx","Int[Sqrt[a + b*x^2]/x^3,x]","-\frac{\sqrt{a+b x^2}}{2 x^2}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{2 \sqrt{a}}","-\frac{\sqrt{a+b x^2}}{2 x^2}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{2 \sqrt{a}}",1,"-Sqrt[a + b*x^2]/(2*x^2) - (b*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(2*Sqrt[a])","A",4,4,15,0.2667,1,"{266, 47, 63, 208}"
359,1,71,0,0.0390252,"\int \frac{\sqrt{a+b x^2}}{x^5} \, dx","Int[Sqrt[a + b*x^2]/x^5,x]","\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{8 a^{3/2}}-\frac{b \sqrt{a+b x^2}}{8 a x^2}-\frac{\sqrt{a+b x^2}}{4 x^4}","\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{8 a^{3/2}}-\frac{b \sqrt{a+b x^2}}{8 a x^2}-\frac{\sqrt{a+b x^2}}{4 x^4}",1,"-Sqrt[a + b*x^2]/(4*x^4) - (b*Sqrt[a + b*x^2])/(8*a*x^2) + (b^2*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(8*a^(3/2))","A",5,5,15,0.3333,1,"{266, 47, 51, 63, 208}"
360,1,95,0,0.05173,"\int \frac{\sqrt{a+b x^2}}{x^7} \, dx","Int[Sqrt[a + b*x^2]/x^7,x]","\frac{b^2 \sqrt{a+b x^2}}{16 a^2 x^2}-\frac{b^3 \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{16 a^{5/2}}-\frac{b \sqrt{a+b x^2}}{24 a x^4}-\frac{\sqrt{a+b x^2}}{6 x^6}","\frac{b^2 \sqrt{a+b x^2}}{16 a^2 x^2}-\frac{b^3 \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{16 a^{5/2}}-\frac{b \sqrt{a+b x^2}}{24 a x^4}-\frac{\sqrt{a+b x^2}}{6 x^6}",1,"-Sqrt[a + b*x^2]/(6*x^6) - (b*Sqrt[a + b*x^2])/(24*a*x^4) + (b^2*Sqrt[a + b*x^2])/(16*a^2*x^2) - (b^3*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(16*a^(5/2))","A",6,5,15,0.3333,1,"{266, 47, 51, 63, 208}"
361,1,94,0,0.0327913,"\int x^4 \sqrt{a+b x^2} \, dx","Int[x^4*Sqrt[a + b*x^2],x]","-\frac{a^2 x \sqrt{a+b x^2}}{16 b^2}+\frac{a^3 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{16 b^{5/2}}+\frac{1}{6} x^5 \sqrt{a+b x^2}+\frac{a x^3 \sqrt{a+b x^2}}{24 b}","-\frac{a^2 x \sqrt{a+b x^2}}{16 b^2}+\frac{a^3 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{16 b^{5/2}}+\frac{1}{6} x^5 \sqrt{a+b x^2}+\frac{a x^3 \sqrt{a+b x^2}}{24 b}",1,"-(a^2*x*Sqrt[a + b*x^2])/(16*b^2) + (a*x^3*Sqrt[a + b*x^2])/(24*b) + (x^5*Sqrt[a + b*x^2])/6 + (a^3*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(16*b^(5/2))","A",5,4,15,0.2667,1,"{279, 321, 217, 206}"
362,1,70,0,0.0207127,"\int x^2 \sqrt{a+b x^2} \, dx","Int[x^2*Sqrt[a + b*x^2],x]","-\frac{a^2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{8 b^{3/2}}+\frac{1}{4} x^3 \sqrt{a+b x^2}+\frac{a x \sqrt{a+b x^2}}{8 b}","-\frac{a^2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{8 b^{3/2}}+\frac{1}{4} x^3 \sqrt{a+b x^2}+\frac{a x \sqrt{a+b x^2}}{8 b}",1,"(a*x*Sqrt[a + b*x^2])/(8*b) + (x^3*Sqrt[a + b*x^2])/4 - (a^2*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(8*b^(3/2))","A",4,4,15,0.2667,1,"{279, 321, 217, 206}"
363,1,46,0,0.0099707,"\int \sqrt{a+b x^2} \, dx","Int[Sqrt[a + b*x^2],x]","\frac{1}{2} x \sqrt{a+b x^2}+\frac{a \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{2 \sqrt{b}}","\frac{1}{2} x \sqrt{a+b x^2}+\frac{a \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{2 \sqrt{b}}",1,"(x*Sqrt[a + b*x^2])/2 + (a*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(2*Sqrt[b])","A",3,3,11,0.2727,1,"{195, 217, 206}"
364,1,42,0,0.0116222,"\int \frac{\sqrt{a+b x^2}}{x^2} \, dx","Int[Sqrt[a + b*x^2]/x^2,x]","\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)-\frac{\sqrt{a+b x^2}}{x}","\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)-\frac{\sqrt{a+b x^2}}{x}",1,"-(Sqrt[a + b*x^2]/x) + Sqrt[b]*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]]","A",3,3,15,0.2000,1,"{277, 217, 206}"
365,1,21,0,0.0044524,"\int \frac{\sqrt{a+b x^2}}{x^4} \, dx","Int[Sqrt[a + b*x^2]/x^4,x]","-\frac{\left(a+b x^2\right)^{3/2}}{3 a x^3}","-\frac{\left(a+b x^2\right)^{3/2}}{3 a x^3}",1,"-(a + b*x^2)^(3/2)/(3*a*x^3)","A",1,1,15,0.06667,1,"{264}"
366,1,44,0,0.0106586,"\int \frac{\sqrt{a+b x^2}}{x^6} \, dx","Int[Sqrt[a + b*x^2]/x^6,x]","\frac{2 b \left(a+b x^2\right)^{3/2}}{15 a^2 x^3}-\frac{\left(a+b x^2\right)^{3/2}}{5 a x^5}","\frac{2 b \left(a+b x^2\right)^{3/2}}{15 a^2 x^3}-\frac{\left(a+b x^2\right)^{3/2}}{5 a x^5}",1,"-(a + b*x^2)^(3/2)/(5*a*x^5) + (2*b*(a + b*x^2)^(3/2))/(15*a^2*x^3)","A",2,2,15,0.1333,1,"{271, 264}"
367,1,68,0,0.0179749,"\int \frac{\sqrt{a+b x^2}}{x^8} \, dx","Int[Sqrt[a + b*x^2]/x^8,x]","-\frac{8 b^2 \left(a+b x^2\right)^{3/2}}{105 a^3 x^3}+\frac{4 b \left(a+b x^2\right)^{3/2}}{35 a^2 x^5}-\frac{\left(a+b x^2\right)^{3/2}}{7 a x^7}","-\frac{8 b^2 \left(a+b x^2\right)^{3/2}}{105 a^3 x^3}+\frac{4 b \left(a+b x^2\right)^{3/2}}{35 a^2 x^5}-\frac{\left(a+b x^2\right)^{3/2}}{7 a x^7}",1,"-(a + b*x^2)^(3/2)/(7*a*x^7) + (4*b*(a + b*x^2)^(3/2))/(35*a^2*x^5) - (8*b^2*(a + b*x^2)^(3/2))/(105*a^3*x^3)","A",3,2,15,0.1333,1,"{271, 264}"
368,1,92,0,0.0291518,"\int \frac{\sqrt{a+b x^2}}{x^{10}} \, dx","Int[Sqrt[a + b*x^2]/x^10,x]","\frac{16 b^3 \left(a+b x^2\right)^{3/2}}{315 a^4 x^3}-\frac{8 b^2 \left(a+b x^2\right)^{3/2}}{105 a^3 x^5}+\frac{2 b \left(a+b x^2\right)^{3/2}}{21 a^2 x^7}-\frac{\left(a+b x^2\right)^{3/2}}{9 a x^9}","\frac{16 b^3 \left(a+b x^2\right)^{3/2}}{315 a^4 x^3}-\frac{8 b^2 \left(a+b x^2\right)^{3/2}}{105 a^3 x^5}+\frac{2 b \left(a+b x^2\right)^{3/2}}{21 a^2 x^7}-\frac{\left(a+b x^2\right)^{3/2}}{9 a x^9}",1,"-(a + b*x^2)^(3/2)/(9*a*x^9) + (2*b*(a + b*x^2)^(3/2))/(21*a^2*x^7) - (8*b^2*(a + b*x^2)^(3/2))/(105*a^3*x^5) + (16*b^3*(a + b*x^2)^(3/2))/(315*a^4*x^3)","A",4,2,15,0.1333,1,"{271, 264}"
369,1,80,0,0.0476189,"\int x^7 \left(a+b x^2\right)^{3/2} \, dx","Int[x^7*(a + b*x^2)^(3/2),x]","\frac{3 a^2 \left(a+b x^2\right)^{7/2}}{7 b^4}-\frac{a^3 \left(a+b x^2\right)^{5/2}}{5 b^4}+\frac{\left(a+b x^2\right)^{11/2}}{11 b^4}-\frac{a \left(a+b x^2\right)^{9/2}}{3 b^4}","\frac{3 a^2 \left(a+b x^2\right)^{7/2}}{7 b^4}-\frac{a^3 \left(a+b x^2\right)^{5/2}}{5 b^4}+\frac{\left(a+b x^2\right)^{11/2}}{11 b^4}-\frac{a \left(a+b x^2\right)^{9/2}}{3 b^4}",1,"-(a^3*(a + b*x^2)^(5/2))/(5*b^4) + (3*a^2*(a + b*x^2)^(7/2))/(7*b^4) - (a*(a + b*x^2)^(9/2))/(3*b^4) + (a + b*x^2)^(11/2)/(11*b^4)","A",3,2,15,0.1333,1,"{266, 43}"
370,1,59,0,0.0351328,"\int x^5 \left(a+b x^2\right)^{3/2} \, dx","Int[x^5*(a + b*x^2)^(3/2),x]","\frac{a^2 \left(a+b x^2\right)^{5/2}}{5 b^3}+\frac{\left(a+b x^2\right)^{9/2}}{9 b^3}-\frac{2 a \left(a+b x^2\right)^{7/2}}{7 b^3}","\frac{a^2 \left(a+b x^2\right)^{5/2}}{5 b^3}+\frac{\left(a+b x^2\right)^{9/2}}{9 b^3}-\frac{2 a \left(a+b x^2\right)^{7/2}}{7 b^3}",1,"(a^2*(a + b*x^2)^(5/2))/(5*b^3) - (2*a*(a + b*x^2)^(7/2))/(7*b^3) + (a + b*x^2)^(9/2)/(9*b^3)","A",3,2,15,0.1333,1,"{266, 43}"
371,1,38,0,0.0243898,"\int x^3 \left(a+b x^2\right)^{3/2} \, dx","Int[x^3*(a + b*x^2)^(3/2),x]","\frac{\left(a+b x^2\right)^{7/2}}{7 b^2}-\frac{a \left(a+b x^2\right)^{5/2}}{5 b^2}","\frac{\left(a+b x^2\right)^{7/2}}{7 b^2}-\frac{a \left(a+b x^2\right)^{5/2}}{5 b^2}",1,"-(a*(a + b*x^2)^(5/2))/(5*b^2) + (a + b*x^2)^(7/2)/(7*b^2)","A",3,2,15,0.1333,1,"{266, 43}"
372,1,18,0,0.0037953,"\int x \left(a+b x^2\right)^{3/2} \, dx","Int[x*(a + b*x^2)^(3/2),x]","\frac{\left(a+b x^2\right)^{5/2}}{5 b}","\frac{\left(a+b x^2\right)^{5/2}}{5 b}",1,"(a + b*x^2)^(5/2)/(5*b)","A",1,1,13,0.07692,1,"{261}"
373,1,54,0,0.0356325,"\int \frac{\left(a+b x^2\right)^{3/2}}{x} \, dx","Int[(a + b*x^2)^(3/2)/x,x]","a^{3/2} \left(-\tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)\right)+a \sqrt{a+b x^2}+\frac{1}{3} \left(a+b x^2\right)^{3/2}","a^{3/2} \left(-\tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)\right)+a \sqrt{a+b x^2}+\frac{1}{3} \left(a+b x^2\right)^{3/2}",1,"a*Sqrt[a + b*x^2] + (a + b*x^2)^(3/2)/3 - a^(3/2)*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]]","A",5,4,15,0.2667,1,"{266, 50, 63, 208}"
374,1,63,0,0.0367053,"\int \frac{\left(a+b x^2\right)^{3/2}}{x^3} \, dx","Int[(a + b*x^2)^(3/2)/x^3,x]","-\frac{\left(a+b x^2\right)^{3/2}}{2 x^2}+\frac{3}{2} b \sqrt{a+b x^2}-\frac{3}{2} \sqrt{a} b \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)","-\frac{\left(a+b x^2\right)^{3/2}}{2 x^2}+\frac{3}{2} b \sqrt{a+b x^2}-\frac{3}{2} \sqrt{a} b \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)",1,"(3*b*Sqrt[a + b*x^2])/2 - (a + b*x^2)^(3/2)/(2*x^2) - (3*Sqrt[a]*b*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/2","A",5,5,15,0.3333,1,"{266, 47, 50, 63, 208}"
375,1,68,0,0.0395221,"\int \frac{\left(a+b x^2\right)^{3/2}}{x^5} \, dx","Int[(a + b*x^2)^(3/2)/x^5,x]","-\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{8 \sqrt{a}}-\frac{3 b \sqrt{a+b x^2}}{8 x^2}-\frac{\left(a+b x^2\right)^{3/2}}{4 x^4}","-\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{8 \sqrt{a}}-\frac{3 b \sqrt{a+b x^2}}{8 x^2}-\frac{\left(a+b x^2\right)^{3/2}}{4 x^4}",1,"(-3*b*Sqrt[a + b*x^2])/(8*x^2) - (a + b*x^2)^(3/2)/(4*x^4) - (3*b^2*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(8*Sqrt[a])","A",5,4,15,0.2667,1,"{266, 47, 63, 208}"
376,1,92,0,0.0541872,"\int \frac{\left(a+b x^2\right)^{3/2}}{x^7} \, dx","Int[(a + b*x^2)^(3/2)/x^7,x]","\frac{b^3 \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{16 a^{3/2}}-\frac{b^2 \sqrt{a+b x^2}}{16 a x^2}-\frac{b \sqrt{a+b x^2}}{8 x^4}-\frac{\left(a+b x^2\right)^{3/2}}{6 x^6}","\frac{b^3 \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{16 a^{3/2}}-\frac{b^2 \sqrt{a+b x^2}}{16 a x^2}-\frac{b \sqrt{a+b x^2}}{8 x^4}-\frac{\left(a+b x^2\right)^{3/2}}{6 x^6}",1,"-(b*Sqrt[a + b*x^2])/(8*x^4) - (b^2*Sqrt[a + b*x^2])/(16*a*x^2) - (a + b*x^2)^(3/2)/(6*x^6) + (b^3*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(16*a^(3/2))","A",6,5,15,0.3333,1,"{266, 47, 51, 63, 208}"
377,1,116,0,0.0693875,"\int \frac{\left(a+b x^2\right)^{3/2}}{x^9} \, dx","Int[(a + b*x^2)^(3/2)/x^9,x]","\frac{3 b^3 \sqrt{a+b x^2}}{128 a^2 x^2}-\frac{3 b^4 \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{128 a^{5/2}}-\frac{b^2 \sqrt{a+b x^2}}{64 a x^4}-\frac{b \sqrt{a+b x^2}}{16 x^6}-\frac{\left(a+b x^2\right)^{3/2}}{8 x^8}","\frac{3 b^3 \sqrt{a+b x^2}}{128 a^2 x^2}-\frac{3 b^4 \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{128 a^{5/2}}-\frac{b^2 \sqrt{a+b x^2}}{64 a x^4}-\frac{b \sqrt{a+b x^2}}{16 x^6}-\frac{\left(a+b x^2\right)^{3/2}}{8 x^8}",1,"-(b*Sqrt[a + b*x^2])/(16*x^6) - (b^2*Sqrt[a + b*x^2])/(64*a*x^4) + (3*b^3*Sqrt[a + b*x^2])/(128*a^2*x^2) - (a + b*x^2)^(3/2)/(8*x^8) - (3*b^4*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(128*a^(5/2))","A",7,5,15,0.3333,1,"{266, 47, 51, 63, 208}"
378,1,115,0,0.0423694,"\int x^4 \left(a+b x^2\right)^{3/2} \, dx","Int[x^4*(a + b*x^2)^(3/2),x]","-\frac{3 a^3 x \sqrt{a+b x^2}}{128 b^2}+\frac{3 a^4 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{128 b^{5/2}}+\frac{a^2 x^3 \sqrt{a+b x^2}}{64 b}+\frac{1}{8} x^5 \left(a+b x^2\right)^{3/2}+\frac{1}{16} a x^5 \sqrt{a+b x^2}","-\frac{3 a^3 x \sqrt{a+b x^2}}{128 b^2}+\frac{3 a^4 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{128 b^{5/2}}+\frac{a^2 x^3 \sqrt{a+b x^2}}{64 b}+\frac{1}{8} x^5 \left(a+b x^2\right)^{3/2}+\frac{1}{16} a x^5 \sqrt{a+b x^2}",1,"(-3*a^3*x*Sqrt[a + b*x^2])/(128*b^2) + (a^2*x^3*Sqrt[a + b*x^2])/(64*b) + (a*x^5*Sqrt[a + b*x^2])/16 + (x^5*(a + b*x^2)^(3/2))/8 + (3*a^4*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(128*b^(5/2))","A",6,4,15,0.2667,1,"{279, 321, 217, 206}"
379,1,91,0,0.0306598,"\int x^2 \left(a+b x^2\right)^{3/2} \, dx","Int[x^2*(a + b*x^2)^(3/2),x]","-\frac{a^3 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{16 b^{3/2}}+\frac{a^2 x \sqrt{a+b x^2}}{16 b}+\frac{1}{8} a x^3 \sqrt{a+b x^2}+\frac{1}{6} x^3 \left(a+b x^2\right)^{3/2}","-\frac{a^3 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{16 b^{3/2}}+\frac{a^2 x \sqrt{a+b x^2}}{16 b}+\frac{1}{8} a x^3 \sqrt{a+b x^2}+\frac{1}{6} x^3 \left(a+b x^2\right)^{3/2}",1,"(a^2*x*Sqrt[a + b*x^2])/(16*b) + (a*x^3*Sqrt[a + b*x^2])/8 + (x^3*(a + b*x^2)^(3/2))/6 - (a^3*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(16*b^(3/2))","A",5,4,15,0.2667,1,"{279, 321, 217, 206}"
380,1,65,0,0.0147713,"\int \left(a+b x^2\right)^{3/2} \, dx","Int[(a + b*x^2)^(3/2),x]","\frac{3 a^2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{8 \sqrt{b}}+\frac{3}{8} a x \sqrt{a+b x^2}+\frac{1}{4} x \left(a+b x^2\right)^{3/2}","\frac{3 a^2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{8 \sqrt{b}}+\frac{3}{8} a x \sqrt{a+b x^2}+\frac{1}{4} x \left(a+b x^2\right)^{3/2}",1,"(3*a*x*Sqrt[a + b*x^2])/8 + (x*(a + b*x^2)^(3/2))/4 + (3*a^2*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(8*Sqrt[b])","A",4,3,11,0.2727,1,"{195, 217, 206}"
381,1,63,0,0.0177573,"\int \frac{\left(a+b x^2\right)^{3/2}}{x^2} \, dx","Int[(a + b*x^2)^(3/2)/x^2,x]","-\frac{\left(a+b x^2\right)^{3/2}}{x}+\frac{3}{2} b x \sqrt{a+b x^2}+\frac{3}{2} a \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)","-\frac{\left(a+b x^2\right)^{3/2}}{x}+\frac{3}{2} b x \sqrt{a+b x^2}+\frac{3}{2} a \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)",1,"(3*b*x*Sqrt[a + b*x^2])/2 - (a + b*x^2)^(3/2)/x + (3*a*Sqrt[b]*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/2","A",4,4,15,0.2667,1,"{277, 195, 217, 206}"
382,1,61,0,0.0184478,"\int \frac{\left(a+b x^2\right)^{3/2}}{x^4} \, dx","Int[(a + b*x^2)^(3/2)/x^4,x]","b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)-\frac{b \sqrt{a+b x^2}}{x}-\frac{\left(a+b x^2\right)^{3/2}}{3 x^3}","b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)-\frac{b \sqrt{a+b x^2}}{x}-\frac{\left(a+b x^2\right)^{3/2}}{3 x^3}",1,"-((b*Sqrt[a + b*x^2])/x) - (a + b*x^2)^(3/2)/(3*x^3) + b^(3/2)*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]]","A",4,3,15,0.2000,1,"{277, 217, 206}"
383,1,21,0,0.0049624,"\int \frac{\left(a+b x^2\right)^{3/2}}{x^6} \, dx","Int[(a + b*x^2)^(3/2)/x^6,x]","-\frac{\left(a+b x^2\right)^{5/2}}{5 a x^5}","-\frac{\left(a+b x^2\right)^{5/2}}{5 a x^5}",1,"-(a + b*x^2)^(5/2)/(5*a*x^5)","A",1,1,15,0.06667,1,"{264}"
384,1,44,0,0.0124121,"\int \frac{\left(a+b x^2\right)^{3/2}}{x^8} \, dx","Int[(a + b*x^2)^(3/2)/x^8,x]","\frac{2 b \left(a+b x^2\right)^{5/2}}{35 a^2 x^5}-\frac{\left(a+b x^2\right)^{5/2}}{7 a x^7}","\frac{2 b \left(a+b x^2\right)^{5/2}}{35 a^2 x^5}-\frac{\left(a+b x^2\right)^{5/2}}{7 a x^7}",1,"-(a + b*x^2)^(5/2)/(7*a*x^7) + (2*b*(a + b*x^2)^(5/2))/(35*a^2*x^5)","A",2,2,15,0.1333,1,"{271, 264}"
385,1,68,0,0.0207039,"\int \frac{\left(a+b x^2\right)^{3/2}}{x^{10}} \, dx","Int[(a + b*x^2)^(3/2)/x^10,x]","-\frac{8 b^2 \left(a+b x^2\right)^{5/2}}{315 a^3 x^5}+\frac{4 b \left(a+b x^2\right)^{5/2}}{63 a^2 x^7}-\frac{\left(a+b x^2\right)^{5/2}}{9 a x^9}","-\frac{8 b^2 \left(a+b x^2\right)^{5/2}}{315 a^3 x^5}+\frac{4 b \left(a+b x^2\right)^{5/2}}{63 a^2 x^7}-\frac{\left(a+b x^2\right)^{5/2}}{9 a x^9}",1,"-(a + b*x^2)^(5/2)/(9*a*x^9) + (4*b*(a + b*x^2)^(5/2))/(63*a^2*x^7) - (8*b^2*(a + b*x^2)^(5/2))/(315*a^3*x^5)","A",3,2,15,0.1333,1,"{271, 264}"
386,1,92,0,0.0287707,"\int \frac{\left(a+b x^2\right)^{3/2}}{x^{12}} \, dx","Int[(a + b*x^2)^(3/2)/x^12,x]","\frac{16 b^3 \left(a+b x^2\right)^{5/2}}{1155 a^4 x^5}-\frac{8 b^2 \left(a+b x^2\right)^{5/2}}{231 a^3 x^7}+\frac{2 b \left(a+b x^2\right)^{5/2}}{33 a^2 x^9}-\frac{\left(a+b x^2\right)^{5/2}}{11 a x^{11}}","\frac{16 b^3 \left(a+b x^2\right)^{5/2}}{1155 a^4 x^5}-\frac{8 b^2 \left(a+b x^2\right)^{5/2}}{231 a^3 x^7}+\frac{2 b \left(a+b x^2\right)^{5/2}}{33 a^2 x^9}-\frac{\left(a+b x^2\right)^{5/2}}{11 a x^{11}}",1,"-(a + b*x^2)^(5/2)/(11*a*x^11) + (2*b*(a + b*x^2)^(5/2))/(33*a^2*x^9) - (8*b^2*(a + b*x^2)^(5/2))/(231*a^3*x^7) + (16*b^3*(a + b*x^2)^(5/2))/(1155*a^4*x^5)","A",4,2,15,0.1333,1,"{271, 264}"
387,1,80,0,0.0467618,"\int x^7 \left(a+b x^2\right)^{5/2} \, dx","Int[x^7*(a + b*x^2)^(5/2),x]","\frac{a^2 \left(a+b x^2\right)^{9/2}}{3 b^4}-\frac{a^3 \left(a+b x^2\right)^{7/2}}{7 b^4}+\frac{\left(a+b x^2\right)^{13/2}}{13 b^4}-\frac{3 a \left(a+b x^2\right)^{11/2}}{11 b^4}","\frac{a^2 \left(a+b x^2\right)^{9/2}}{3 b^4}-\frac{a^3 \left(a+b x^2\right)^{7/2}}{7 b^4}+\frac{\left(a+b x^2\right)^{13/2}}{13 b^4}-\frac{3 a \left(a+b x^2\right)^{11/2}}{11 b^4}",1,"-(a^3*(a + b*x^2)^(7/2))/(7*b^4) + (a^2*(a + b*x^2)^(9/2))/(3*b^4) - (3*a*(a + b*x^2)^(11/2))/(11*b^4) + (a + b*x^2)^(13/2)/(13*b^4)","A",3,2,15,0.1333,1,"{266, 43}"
388,1,59,0,0.0338526,"\int x^5 \left(a+b x^2\right)^{5/2} \, dx","Int[x^5*(a + b*x^2)^(5/2),x]","\frac{a^2 \left(a+b x^2\right)^{7/2}}{7 b^3}+\frac{\left(a+b x^2\right)^{11/2}}{11 b^3}-\frac{2 a \left(a+b x^2\right)^{9/2}}{9 b^3}","\frac{a^2 \left(a+b x^2\right)^{7/2}}{7 b^3}+\frac{\left(a+b x^2\right)^{11/2}}{11 b^3}-\frac{2 a \left(a+b x^2\right)^{9/2}}{9 b^3}",1,"(a^2*(a + b*x^2)^(7/2))/(7*b^3) - (2*a*(a + b*x^2)^(9/2))/(9*b^3) + (a + b*x^2)^(11/2)/(11*b^3)","A",3,2,15,0.1333,1,"{266, 43}"
389,1,38,0,0.0236686,"\int x^3 \left(a+b x^2\right)^{5/2} \, dx","Int[x^3*(a + b*x^2)^(5/2),x]","\frac{\left(a+b x^2\right)^{9/2}}{9 b^2}-\frac{a \left(a+b x^2\right)^{7/2}}{7 b^2}","\frac{\left(a+b x^2\right)^{9/2}}{9 b^2}-\frac{a \left(a+b x^2\right)^{7/2}}{7 b^2}",1,"-(a*(a + b*x^2)^(7/2))/(7*b^2) + (a + b*x^2)^(9/2)/(9*b^2)","A",3,2,15,0.1333,1,"{266, 43}"
390,1,18,0,0.0034692,"\int x \left(a+b x^2\right)^{5/2} \, dx","Int[x*(a + b*x^2)^(5/2),x]","\frac{\left(a+b x^2\right)^{7/2}}{7 b}","\frac{\left(a+b x^2\right)^{7/2}}{7 b}",1,"(a + b*x^2)^(7/2)/(7*b)","A",1,1,13,0.07692,1,"{261}"
391,1,72,0,0.0434574,"\int \frac{\left(a+b x^2\right)^{5/2}}{x} \, dx","Int[(a + b*x^2)^(5/2)/x,x]","a^2 \sqrt{a+b x^2}+a^{5/2} \left(-\tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)\right)+\frac{1}{3} a \left(a+b x^2\right)^{3/2}+\frac{1}{5} \left(a+b x^2\right)^{5/2}","a^2 \sqrt{a+b x^2}+a^{5/2} \left(-\tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)\right)+\frac{1}{3} a \left(a+b x^2\right)^{3/2}+\frac{1}{5} \left(a+b x^2\right)^{5/2}",1,"a^2*Sqrt[a + b*x^2] + (a*(a + b*x^2)^(3/2))/3 + (a + b*x^2)^(5/2)/5 - a^(5/2)*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]]","A",6,4,15,0.2667,1,"{266, 50, 63, 208}"
392,1,80,0,0.0449643,"\int \frac{\left(a+b x^2\right)^{5/2}}{x^3} \, dx","Int[(a + b*x^2)^(5/2)/x^3,x]","-\frac{5}{2} a^{3/2} b \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)-\frac{\left(a+b x^2\right)^{5/2}}{2 x^2}+\frac{5}{6} b \left(a+b x^2\right)^{3/2}+\frac{5}{2} a b \sqrt{a+b x^2}","-\frac{5}{2} a^{3/2} b \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)-\frac{\left(a+b x^2\right)^{5/2}}{2 x^2}+\frac{5}{6} b \left(a+b x^2\right)^{3/2}+\frac{5}{2} a b \sqrt{a+b x^2}",1,"(5*a*b*Sqrt[a + b*x^2])/2 + (5*b*(a + b*x^2)^(3/2))/6 - (a + b*x^2)^(5/2)/(2*x^2) - (5*a^(3/2)*b*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/2","A",6,5,15,0.3333,1,"{266, 47, 50, 63, 208}"
393,1,86,0,0.0481995,"\int \frac{\left(a+b x^2\right)^{5/2}}{x^5} \, dx","Int[(a + b*x^2)^(5/2)/x^5,x]","\frac{15}{8} b^2 \sqrt{a+b x^2}-\frac{15}{8} \sqrt{a} b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)-\frac{\left(a+b x^2\right)^{5/2}}{4 x^4}-\frac{5 b \left(a+b x^2\right)^{3/2}}{8 x^2}","\frac{15}{8} b^2 \sqrt{a+b x^2}-\frac{15}{8} \sqrt{a} b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)-\frac{\left(a+b x^2\right)^{5/2}}{4 x^4}-\frac{5 b \left(a+b x^2\right)^{3/2}}{8 x^2}",1,"(15*b^2*Sqrt[a + b*x^2])/8 - (5*b*(a + b*x^2)^(3/2))/(8*x^2) - (a + b*x^2)^(5/2)/(4*x^4) - (15*Sqrt[a]*b^2*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/8","A",6,5,15,0.3333,1,"{266, 47, 50, 63, 208}"
394,1,89,0,0.0525926,"\int \frac{\left(a+b x^2\right)^{5/2}}{x^7} \, dx","Int[(a + b*x^2)^(5/2)/x^7,x]","-\frac{5 b^2 \sqrt{a+b x^2}}{16 x^2}-\frac{5 b^3 \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{16 \sqrt{a}}-\frac{5 b \left(a+b x^2\right)^{3/2}}{24 x^4}-\frac{\left(a+b x^2\right)^{5/2}}{6 x^6}","-\frac{5 b^2 \sqrt{a+b x^2}}{16 x^2}-\frac{5 b^3 \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{16 \sqrt{a}}-\frac{5 b \left(a+b x^2\right)^{3/2}}{24 x^4}-\frac{\left(a+b x^2\right)^{5/2}}{6 x^6}",1,"(-5*b^2*Sqrt[a + b*x^2])/(16*x^2) - (5*b*(a + b*x^2)^(3/2))/(24*x^4) - (a + b*x^2)^(5/2)/(6*x^6) - (5*b^3*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(16*Sqrt[a])","A",6,4,15,0.2667,1,"{266, 47, 63, 208}"
395,1,113,0,0.0672193,"\int \frac{\left(a+b x^2\right)^{5/2}}{x^9} \, dx","Int[(a + b*x^2)^(5/2)/x^9,x]","\frac{5 b^4 \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{128 a^{3/2}}-\frac{5 b^3 \sqrt{a+b x^2}}{128 a x^2}-\frac{5 b^2 \sqrt{a+b x^2}}{64 x^4}-\frac{5 b \left(a+b x^2\right)^{3/2}}{48 x^6}-\frac{\left(a+b x^2\right)^{5/2}}{8 x^8}","\frac{5 b^4 \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{128 a^{3/2}}-\frac{5 b^3 \sqrt{a+b x^2}}{128 a x^2}-\frac{5 b^2 \sqrt{a+b x^2}}{64 x^4}-\frac{5 b \left(a+b x^2\right)^{3/2}}{48 x^6}-\frac{\left(a+b x^2\right)^{5/2}}{8 x^8}",1,"(-5*b^2*Sqrt[a + b*x^2])/(64*x^4) - (5*b^3*Sqrt[a + b*x^2])/(128*a*x^2) - (5*b*(a + b*x^2)^(3/2))/(48*x^6) - (a + b*x^2)^(5/2)/(8*x^8) + (5*b^4*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(128*a^(3/2))","A",7,5,15,0.3333,1,"{266, 47, 51, 63, 208}"
396,1,137,0,0.0834827,"\int \frac{\left(a+b x^2\right)^{5/2}}{x^{11}} \, dx","Int[(a + b*x^2)^(5/2)/x^11,x]","\frac{3 b^4 \sqrt{a+b x^2}}{256 a^2 x^2}-\frac{3 b^5 \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{256 a^{5/2}}-\frac{b^3 \sqrt{a+b x^2}}{128 a x^4}-\frac{b^2 \sqrt{a+b x^2}}{32 x^6}-\frac{b \left(a+b x^2\right)^{3/2}}{16 x^8}-\frac{\left(a+b x^2\right)^{5/2}}{10 x^{10}}","\frac{3 b^4 \sqrt{a+b x^2}}{256 a^2 x^2}-\frac{3 b^5 \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{256 a^{5/2}}-\frac{b^3 \sqrt{a+b x^2}}{128 a x^4}-\frac{b^2 \sqrt{a+b x^2}}{32 x^6}-\frac{b \left(a+b x^2\right)^{3/2}}{16 x^8}-\frac{\left(a+b x^2\right)^{5/2}}{10 x^{10}}",1,"-(b^2*Sqrt[a + b*x^2])/(32*x^6) - (b^3*Sqrt[a + b*x^2])/(128*a*x^4) + (3*b^4*Sqrt[a + b*x^2])/(256*a^2*x^2) - (b*(a + b*x^2)^(3/2))/(16*x^8) - (a + b*x^2)^(5/2)/(10*x^10) - (3*b^5*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(256*a^(5/2))","A",8,5,15,0.3333,1,"{266, 47, 51, 63, 208}"
397,1,136,0,0.0536311,"\int x^4 \left(a+b x^2\right)^{5/2} \, dx","Int[x^4*(a + b*x^2)^(5/2),x]","-\frac{3 a^4 x \sqrt{a+b x^2}}{256 b^2}+\frac{3 a^5 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{256 b^{5/2}}+\frac{a^3 x^3 \sqrt{a+b x^2}}{128 b}+\frac{1}{32} a^2 x^5 \sqrt{a+b x^2}+\frac{1}{16} a x^5 \left(a+b x^2\right)^{3/2}+\frac{1}{10} x^5 \left(a+b x^2\right)^{5/2}","-\frac{3 a^4 x \sqrt{a+b x^2}}{256 b^2}+\frac{3 a^5 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{256 b^{5/2}}+\frac{a^3 x^3 \sqrt{a+b x^2}}{128 b}+\frac{1}{32} a^2 x^5 \sqrt{a+b x^2}+\frac{1}{16} a x^5 \left(a+b x^2\right)^{3/2}+\frac{1}{10} x^5 \left(a+b x^2\right)^{5/2}",1,"(-3*a^4*x*Sqrt[a + b*x^2])/(256*b^2) + (a^3*x^3*Sqrt[a + b*x^2])/(128*b) + (a^2*x^5*Sqrt[a + b*x^2])/32 + (a*x^5*(a + b*x^2)^(3/2))/16 + (x^5*(a + b*x^2)^(5/2))/10 + (3*a^5*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(256*b^(5/2))","A",7,4,15,0.2667,1,"{279, 321, 217, 206}"
398,1,112,0,0.0423354,"\int x^2 \left(a+b x^2\right)^{5/2} \, dx","Int[x^2*(a + b*x^2)^(5/2),x]","-\frac{5 a^4 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{128 b^{3/2}}+\frac{5 a^3 x \sqrt{a+b x^2}}{128 b}+\frac{5}{64} a^2 x^3 \sqrt{a+b x^2}+\frac{5}{48} a x^3 \left(a+b x^2\right)^{3/2}+\frac{1}{8} x^3 \left(a+b x^2\right)^{5/2}","-\frac{5 a^4 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{128 b^{3/2}}+\frac{5 a^3 x \sqrt{a+b x^2}}{128 b}+\frac{5}{64} a^2 x^3 \sqrt{a+b x^2}+\frac{5}{48} a x^3 \left(a+b x^2\right)^{3/2}+\frac{1}{8} x^3 \left(a+b x^2\right)^{5/2}",1,"(5*a^3*x*Sqrt[a + b*x^2])/(128*b) + (5*a^2*x^3*Sqrt[a + b*x^2])/64 + (5*a*x^3*(a + b*x^2)^(3/2))/48 + (x^3*(a + b*x^2)^(5/2))/8 - (5*a^4*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(128*b^(3/2))","A",6,4,15,0.2667,1,"{279, 321, 217, 206}"
399,1,84,0,0.0216615,"\int \left(a+b x^2\right)^{5/2} \, dx","Int[(a + b*x^2)^(5/2),x]","\frac{5}{16} a^2 x \sqrt{a+b x^2}+\frac{5 a^3 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{16 \sqrt{b}}+\frac{5}{24} a x \left(a+b x^2\right)^{3/2}+\frac{1}{6} x \left(a+b x^2\right)^{5/2}","\frac{5}{16} a^2 x \sqrt{a+b x^2}+\frac{5 a^3 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{16 \sqrt{b}}+\frac{5}{24} a x \left(a+b x^2\right)^{3/2}+\frac{1}{6} x \left(a+b x^2\right)^{5/2}",1,"(5*a^2*x*Sqrt[a + b*x^2])/16 + (5*a*x*(a + b*x^2)^(3/2))/24 + (x*(a + b*x^2)^(5/2))/6 + (5*a^3*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(16*Sqrt[b])","A",5,3,11,0.2727,1,"{195, 217, 206}"
400,1,83,0,0.0250642,"\int \frac{\left(a+b x^2\right)^{5/2}}{x^2} \, dx","Int[(a + b*x^2)^(5/2)/x^2,x]","\frac{15}{8} a^2 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)-\frac{\left(a+b x^2\right)^{5/2}}{x}+\frac{5}{4} b x \left(a+b x^2\right)^{3/2}+\frac{15}{8} a b x \sqrt{a+b x^2}","\frac{15}{8} a^2 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)-\frac{\left(a+b x^2\right)^{5/2}}{x}+\frac{5}{4} b x \left(a+b x^2\right)^{3/2}+\frac{15}{8} a b x \sqrt{a+b x^2}",1,"(15*a*b*x*Sqrt[a + b*x^2])/8 + (5*b*x*(a + b*x^2)^(3/2))/4 - (a + b*x^2)^(5/2)/x + (15*a^2*Sqrt[b]*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/8","A",5,4,15,0.2667,1,"{277, 195, 217, 206}"
401,1,86,0,0.0270558,"\int \frac{\left(a+b x^2\right)^{5/2}}{x^4} \, dx","Int[(a + b*x^2)^(5/2)/x^4,x]","\frac{5}{2} b^2 x \sqrt{a+b x^2}+\frac{5}{2} a b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)-\frac{\left(a+b x^2\right)^{5/2}}{3 x^3}-\frac{5 b \left(a+b x^2\right)^{3/2}}{3 x}","\frac{5}{2} b^2 x \sqrt{a+b x^2}+\frac{5}{2} a b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)-\frac{\left(a+b x^2\right)^{5/2}}{3 x^3}-\frac{5 b \left(a+b x^2\right)^{3/2}}{3 x}",1,"(5*b^2*x*Sqrt[a + b*x^2])/2 - (5*b*(a + b*x^2)^(3/2))/(3*x) - (a + b*x^2)^(5/2)/(3*x^3) + (5*a*b^(3/2)*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/2","A",5,4,15,0.2667,1,"{277, 195, 217, 206}"
402,1,82,0,0.0280164,"\int \frac{\left(a+b x^2\right)^{5/2}}{x^6} \, dx","Int[(a + b*x^2)^(5/2)/x^6,x]","-\frac{b^2 \sqrt{a+b x^2}}{x}+b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)-\frac{b \left(a+b x^2\right)^{3/2}}{3 x^3}-\frac{\left(a+b x^2\right)^{5/2}}{5 x^5}","-\frac{b^2 \sqrt{a+b x^2}}{x}+b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)-\frac{b \left(a+b x^2\right)^{3/2}}{3 x^3}-\frac{\left(a+b x^2\right)^{5/2}}{5 x^5}",1,"-((b^2*Sqrt[a + b*x^2])/x) - (b*(a + b*x^2)^(3/2))/(3*x^3) - (a + b*x^2)^(5/2)/(5*x^5) + b^(5/2)*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]]","A",5,3,15,0.2000,1,"{277, 217, 206}"
403,1,21,0,0.0046399,"\int \frac{\left(a+b x^2\right)^{5/2}}{x^8} \, dx","Int[(a + b*x^2)^(5/2)/x^8,x]","-\frac{\left(a+b x^2\right)^{7/2}}{7 a x^7}","-\frac{\left(a+b x^2\right)^{7/2}}{7 a x^7}",1,"-(a + b*x^2)^(7/2)/(7*a*x^7)","A",1,1,15,0.06667,1,"{264}"
404,1,44,0,0.0105772,"\int \frac{\left(a+b x^2\right)^{5/2}}{x^{10}} \, dx","Int[(a + b*x^2)^(5/2)/x^10,x]","\frac{2 b \left(a+b x^2\right)^{7/2}}{63 a^2 x^7}-\frac{\left(a+b x^2\right)^{7/2}}{9 a x^9}","\frac{2 b \left(a+b x^2\right)^{7/2}}{63 a^2 x^7}-\frac{\left(a+b x^2\right)^{7/2}}{9 a x^9}",1,"-(a + b*x^2)^(7/2)/(9*a*x^9) + (2*b*(a + b*x^2)^(7/2))/(63*a^2*x^7)","A",2,2,15,0.1333,1,"{271, 264}"
405,1,68,0,0.0189424,"\int \frac{\left(a+b x^2\right)^{5/2}}{x^{12}} \, dx","Int[(a + b*x^2)^(5/2)/x^12,x]","-\frac{8 b^2 \left(a+b x^2\right)^{7/2}}{693 a^3 x^7}+\frac{4 b \left(a+b x^2\right)^{7/2}}{99 a^2 x^9}-\frac{\left(a+b x^2\right)^{7/2}}{11 a x^{11}}","-\frac{8 b^2 \left(a+b x^2\right)^{7/2}}{693 a^3 x^7}+\frac{4 b \left(a+b x^2\right)^{7/2}}{99 a^2 x^9}-\frac{\left(a+b x^2\right)^{7/2}}{11 a x^{11}}",1,"-(a + b*x^2)^(7/2)/(11*a*x^11) + (4*b*(a + b*x^2)^(7/2))/(99*a^2*x^9) - (8*b^2*(a + b*x^2)^(7/2))/(693*a^3*x^7)","A",3,2,15,0.1333,1,"{271, 264}"
406,1,92,0,0.028226,"\int \frac{\left(a+b x^2\right)^{5/2}}{x^{14}} \, dx","Int[(a + b*x^2)^(5/2)/x^14,x]","\frac{16 b^3 \left(a+b x^2\right)^{7/2}}{3003 a^4 x^7}-\frac{8 b^2 \left(a+b x^2\right)^{7/2}}{429 a^3 x^9}+\frac{6 b \left(a+b x^2\right)^{7/2}}{143 a^2 x^{11}}-\frac{\left(a+b x^2\right)^{7/2}}{13 a x^{13}}","\frac{16 b^3 \left(a+b x^2\right)^{7/2}}{3003 a^4 x^7}-\frac{8 b^2 \left(a+b x^2\right)^{7/2}}{429 a^3 x^9}+\frac{6 b \left(a+b x^2\right)^{7/2}}{143 a^2 x^{11}}-\frac{\left(a+b x^2\right)^{7/2}}{13 a x^{13}}",1,"-(a + b*x^2)^(7/2)/(13*a*x^13) + (6*b*(a + b*x^2)^(7/2))/(143*a^2*x^11) - (8*b^2*(a + b*x^2)^(7/2))/(429*a^3*x^9) + (16*b^3*(a + b*x^2)^(7/2))/(3003*a^4*x^7)","A",4,2,15,0.1333,1,"{271, 264}"
407,1,116,0,0.0422674,"\int \frac{\left(a+b x^2\right)^{5/2}}{x^{16}} \, dx","Int[(a + b*x^2)^(5/2)/x^16,x]","-\frac{128 b^4 \left(a+b x^2\right)^{7/2}}{45045 a^5 x^7}+\frac{64 b^3 \left(a+b x^2\right)^{7/2}}{6435 a^4 x^9}-\frac{16 b^2 \left(a+b x^2\right)^{7/2}}{715 a^3 x^{11}}+\frac{8 b \left(a+b x^2\right)^{7/2}}{195 a^2 x^{13}}-\frac{\left(a+b x^2\right)^{7/2}}{15 a x^{15}}","-\frac{128 b^4 \left(a+b x^2\right)^{7/2}}{45045 a^5 x^7}+\frac{64 b^3 \left(a+b x^2\right)^{7/2}}{6435 a^4 x^9}-\frac{16 b^2 \left(a+b x^2\right)^{7/2}}{715 a^3 x^{11}}+\frac{8 b \left(a+b x^2\right)^{7/2}}{195 a^2 x^{13}}-\frac{\left(a+b x^2\right)^{7/2}}{15 a x^{15}}",1,"-(a + b*x^2)^(7/2)/(15*a*x^15) + (8*b*(a + b*x^2)^(7/2))/(195*a^2*x^13) - (16*b^2*(a + b*x^2)^(7/2))/(715*a^3*x^11) + (64*b^3*(a + b*x^2)^(7/2))/(6435*a^4*x^9) - (128*b^4*(a + b*x^2)^(7/2))/(45045*a^5*x^7)","A",5,2,15,0.1333,1,"{271, 264}"
408,1,140,0,0.0557573,"\int \frac{\left(a+b x^2\right)^{5/2}}{x^{18}} \, dx","Int[(a + b*x^2)^(5/2)/x^18,x]","\frac{256 b^5 \left(a+b x^2\right)^{7/2}}{153153 a^6 x^7}-\frac{128 b^4 \left(a+b x^2\right)^{7/2}}{21879 a^5 x^9}+\frac{32 b^3 \left(a+b x^2\right)^{7/2}}{2431 a^4 x^{11}}-\frac{16 b^2 \left(a+b x^2\right)^{7/2}}{663 a^3 x^{13}}+\frac{2 b \left(a+b x^2\right)^{7/2}}{51 a^2 x^{15}}-\frac{\left(a+b x^2\right)^{7/2}}{17 a x^{17}}","\frac{256 b^5 \left(a+b x^2\right)^{7/2}}{153153 a^6 x^7}-\frac{128 b^4 \left(a+b x^2\right)^{7/2}}{21879 a^5 x^9}+\frac{32 b^3 \left(a+b x^2\right)^{7/2}}{2431 a^4 x^{11}}-\frac{16 b^2 \left(a+b x^2\right)^{7/2}}{663 a^3 x^{13}}+\frac{2 b \left(a+b x^2\right)^{7/2}}{51 a^2 x^{15}}-\frac{\left(a+b x^2\right)^{7/2}}{17 a x^{17}}",1,"-(a + b*x^2)^(7/2)/(17*a*x^17) + (2*b*(a + b*x^2)^(7/2))/(51*a^2*x^15) - (16*b^2*(a + b*x^2)^(7/2))/(663*a^3*x^13) + (32*b^3*(a + b*x^2)^(7/2))/(2431*a^4*x^11) - (128*b^4*(a + b*x^2)^(7/2))/(21879*a^5*x^9) + (256*b^5*(a + b*x^2)^(7/2))/(153153*a^6*x^7)","A",6,2,15,0.1333,1,"{271, 264}"
409,1,161,0,0.0999879,"\int x^{15} \left(a+b x^2\right)^{9/2} \, dx","Int[x^15*(a + b*x^2)^(9/2),x]","\frac{a^2 \left(a+b x^2\right)^{21/2}}{b^8}-\frac{35 a^3 \left(a+b x^2\right)^{19/2}}{19 b^8}+\frac{35 a^4 \left(a+b x^2\right)^{17/2}}{17 b^8}-\frac{7 a^5 \left(a+b x^2\right)^{15/2}}{5 b^8}+\frac{7 a^6 \left(a+b x^2\right)^{13/2}}{13 b^8}-\frac{a^7 \left(a+b x^2\right)^{11/2}}{11 b^8}+\frac{\left(a+b x^2\right)^{25/2}}{25 b^8}-\frac{7 a \left(a+b x^2\right)^{23/2}}{23 b^8}","\frac{a^2 \left(a+b x^2\right)^{21/2}}{b^8}-\frac{35 a^3 \left(a+b x^2\right)^{19/2}}{19 b^8}+\frac{35 a^4 \left(a+b x^2\right)^{17/2}}{17 b^8}-\frac{7 a^5 \left(a+b x^2\right)^{15/2}}{5 b^8}+\frac{7 a^6 \left(a+b x^2\right)^{13/2}}{13 b^8}-\frac{a^7 \left(a+b x^2\right)^{11/2}}{11 b^8}+\frac{\left(a+b x^2\right)^{25/2}}{25 b^8}-\frac{7 a \left(a+b x^2\right)^{23/2}}{23 b^8}",1,"-(a^7*(a + b*x^2)^(11/2))/(11*b^8) + (7*a^6*(a + b*x^2)^(13/2))/(13*b^8) - (7*a^5*(a + b*x^2)^(15/2))/(5*b^8) + (35*a^4*(a + b*x^2)^(17/2))/(17*b^8) - (35*a^3*(a + b*x^2)^(19/2))/(19*b^8) + (a^2*(a + b*x^2)^(21/2))/b^8 - (7*a*(a + b*x^2)^(23/2))/(23*b^8) + (a + b*x^2)^(25/2)/(25*b^8)","A",3,2,15,0.1333,1,"{266, 43}"
410,1,140,0,0.0797439,"\int x^{13} \left(a+b x^2\right)^{9/2} \, dx","Int[x^13*(a + b*x^2)^(9/2),x]","\frac{15 a^2 \left(a+b x^2\right)^{19/2}}{19 b^7}-\frac{20 a^3 \left(a+b x^2\right)^{17/2}}{17 b^7}+\frac{a^4 \left(a+b x^2\right)^{15/2}}{b^7}-\frac{6 a^5 \left(a+b x^2\right)^{13/2}}{13 b^7}+\frac{a^6 \left(a+b x^2\right)^{11/2}}{11 b^7}+\frac{\left(a+b x^2\right)^{23/2}}{23 b^7}-\frac{2 a \left(a+b x^2\right)^{21/2}}{7 b^7}","\frac{15 a^2 \left(a+b x^2\right)^{19/2}}{19 b^7}-\frac{20 a^3 \left(a+b x^2\right)^{17/2}}{17 b^7}+\frac{a^4 \left(a+b x^2\right)^{15/2}}{b^7}-\frac{6 a^5 \left(a+b x^2\right)^{13/2}}{13 b^7}+\frac{a^6 \left(a+b x^2\right)^{11/2}}{11 b^7}+\frac{\left(a+b x^2\right)^{23/2}}{23 b^7}-\frac{2 a \left(a+b x^2\right)^{21/2}}{7 b^7}",1,"(a^6*(a + b*x^2)^(11/2))/(11*b^7) - (6*a^5*(a + b*x^2)^(13/2))/(13*b^7) + (a^4*(a + b*x^2)^(15/2))/b^7 - (20*a^3*(a + b*x^2)^(17/2))/(17*b^7) + (15*a^2*(a + b*x^2)^(19/2))/(19*b^7) - (2*a*(a + b*x^2)^(21/2))/(7*b^7) + (a + b*x^2)^(23/2)/(23*b^7)","A",3,2,15,0.1333,1,"{266, 43}"
411,1,122,0,0.0705596,"\int x^{11} \left(a+b x^2\right)^{9/2} \, dx","Int[x^11*(a + b*x^2)^(9/2),x]","\frac{10 a^2 \left(a+b x^2\right)^{17/2}}{17 b^6}-\frac{2 a^3 \left(a+b x^2\right)^{15/2}}{3 b^6}+\frac{5 a^4 \left(a+b x^2\right)^{13/2}}{13 b^6}-\frac{a^5 \left(a+b x^2\right)^{11/2}}{11 b^6}+\frac{\left(a+b x^2\right)^{21/2}}{21 b^6}-\frac{5 a \left(a+b x^2\right)^{19/2}}{19 b^6}","\frac{10 a^2 \left(a+b x^2\right)^{17/2}}{17 b^6}-\frac{2 a^3 \left(a+b x^2\right)^{15/2}}{3 b^6}+\frac{5 a^4 \left(a+b x^2\right)^{13/2}}{13 b^6}-\frac{a^5 \left(a+b x^2\right)^{11/2}}{11 b^6}+\frac{\left(a+b x^2\right)^{21/2}}{21 b^6}-\frac{5 a \left(a+b x^2\right)^{19/2}}{19 b^6}",1,"-(a^5*(a + b*x^2)^(11/2))/(11*b^6) + (5*a^4*(a + b*x^2)^(13/2))/(13*b^6) - (2*a^3*(a + b*x^2)^(15/2))/(3*b^6) + (10*a^2*(a + b*x^2)^(17/2))/(17*b^6) - (5*a*(a + b*x^2)^(19/2))/(19*b^6) + (a + b*x^2)^(21/2)/(21*b^6)","A",3,2,15,0.1333,1,"{266, 43}"
412,1,101,0,0.0575089,"\int x^9 \left(a+b x^2\right)^{9/2} \, dx","Int[x^9*(a + b*x^2)^(9/2),x]","\frac{2 a^2 \left(a+b x^2\right)^{15/2}}{5 b^5}-\frac{4 a^3 \left(a+b x^2\right)^{13/2}}{13 b^5}+\frac{a^4 \left(a+b x^2\right)^{11/2}}{11 b^5}+\frac{\left(a+b x^2\right)^{19/2}}{19 b^5}-\frac{4 a \left(a+b x^2\right)^{17/2}}{17 b^5}","\frac{2 a^2 \left(a+b x^2\right)^{15/2}}{5 b^5}-\frac{4 a^3 \left(a+b x^2\right)^{13/2}}{13 b^5}+\frac{a^4 \left(a+b x^2\right)^{11/2}}{11 b^5}+\frac{\left(a+b x^2\right)^{19/2}}{19 b^5}-\frac{4 a \left(a+b x^2\right)^{17/2}}{17 b^5}",1,"(a^4*(a + b*x^2)^(11/2))/(11*b^5) - (4*a^3*(a + b*x^2)^(13/2))/(13*b^5) + (2*a^2*(a + b*x^2)^(15/2))/(5*b^5) - (4*a*(a + b*x^2)^(17/2))/(17*b^5) + (a + b*x^2)^(19/2)/(19*b^5)","A",3,2,15,0.1333,1,"{266, 43}"
413,1,80,0,0.0458746,"\int x^7 \left(a+b x^2\right)^{9/2} \, dx","Int[x^7*(a + b*x^2)^(9/2),x]","\frac{3 a^2 \left(a+b x^2\right)^{13/2}}{13 b^4}-\frac{a^3 \left(a+b x^2\right)^{11/2}}{11 b^4}+\frac{\left(a+b x^2\right)^{17/2}}{17 b^4}-\frac{a \left(a+b x^2\right)^{15/2}}{5 b^4}","\frac{3 a^2 \left(a+b x^2\right)^{13/2}}{13 b^4}-\frac{a^3 \left(a+b x^2\right)^{11/2}}{11 b^4}+\frac{\left(a+b x^2\right)^{17/2}}{17 b^4}-\frac{a \left(a+b x^2\right)^{15/2}}{5 b^4}",1,"-(a^3*(a + b*x^2)^(11/2))/(11*b^4) + (3*a^2*(a + b*x^2)^(13/2))/(13*b^4) - (a*(a + b*x^2)^(15/2))/(5*b^4) + (a + b*x^2)^(17/2)/(17*b^4)","A",3,2,15,0.1333,1,"{266, 43}"
414,1,59,0,0.0350742,"\int x^5 \left(a+b x^2\right)^{9/2} \, dx","Int[x^5*(a + b*x^2)^(9/2),x]","\frac{a^2 \left(a+b x^2\right)^{11/2}}{11 b^3}+\frac{\left(a+b x^2\right)^{15/2}}{15 b^3}-\frac{2 a \left(a+b x^2\right)^{13/2}}{13 b^3}","\frac{a^2 \left(a+b x^2\right)^{11/2}}{11 b^3}+\frac{\left(a+b x^2\right)^{15/2}}{15 b^3}-\frac{2 a \left(a+b x^2\right)^{13/2}}{13 b^3}",1,"(a^2*(a + b*x^2)^(11/2))/(11*b^3) - (2*a*(a + b*x^2)^(13/2))/(13*b^3) + (a + b*x^2)^(15/2)/(15*b^3)","A",3,2,15,0.1333,1,"{266, 43}"
415,1,38,0,0.0239998,"\int x^3 \left(a+b x^2\right)^{9/2} \, dx","Int[x^3*(a + b*x^2)^(9/2),x]","\frac{\left(a+b x^2\right)^{13/2}}{13 b^2}-\frac{a \left(a+b x^2\right)^{11/2}}{11 b^2}","\frac{\left(a+b x^2\right)^{13/2}}{13 b^2}-\frac{a \left(a+b x^2\right)^{11/2}}{11 b^2}",1,"-(a*(a + b*x^2)^(11/2))/(11*b^2) + (a + b*x^2)^(13/2)/(13*b^2)","A",3,2,15,0.1333,1,"{266, 43}"
416,1,18,0,0.0034928,"\int x \left(a+b x^2\right)^{9/2} \, dx","Int[x*(a + b*x^2)^(9/2),x]","\frac{\left(a+b x^2\right)^{11/2}}{11 b}","\frac{\left(a+b x^2\right)^{11/2}}{11 b}",1,"(a + b*x^2)^(11/2)/(11*b)","A",1,1,13,0.07692,1,"{261}"
417,1,108,0,0.0702031,"\int \frac{\left(a+b x^2\right)^{9/2}}{x} \, dx","Int[(a + b*x^2)^(9/2)/x,x]","a^4 \sqrt{a+b x^2}+\frac{1}{3} a^3 \left(a+b x^2\right)^{3/2}+\frac{1}{5} a^2 \left(a+b x^2\right)^{5/2}+a^{9/2} \left(-\tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)\right)+\frac{1}{7} a \left(a+b x^2\right)^{7/2}+\frac{1}{9} \left(a+b x^2\right)^{9/2}","a^4 \sqrt{a+b x^2}+\frac{1}{3} a^3 \left(a+b x^2\right)^{3/2}+\frac{1}{5} a^2 \left(a+b x^2\right)^{5/2}+a^{9/2} \left(-\tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)\right)+\frac{1}{7} a \left(a+b x^2\right)^{7/2}+\frac{1}{9} \left(a+b x^2\right)^{9/2}",1,"a^4*Sqrt[a + b*x^2] + (a^3*(a + b*x^2)^(3/2))/3 + (a^2*(a + b*x^2)^(5/2))/5 + (a*(a + b*x^2)^(7/2))/7 + (a + b*x^2)^(9/2)/9 - a^(9/2)*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]]","A",8,4,15,0.2667,1,"{266, 50, 63, 208}"
418,1,118,0,0.071303,"\int \frac{\left(a+b x^2\right)^{9/2}}{x^3} \, dx","Int[(a + b*x^2)^(9/2)/x^3,x]","\frac{3}{2} a^2 b \left(a+b x^2\right)^{3/2}+\frac{9}{2} a^3 b \sqrt{a+b x^2}-\frac{9}{2} a^{7/2} b \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)-\frac{\left(a+b x^2\right)^{9/2}}{2 x^2}+\frac{9}{14} b \left(a+b x^2\right)^{7/2}+\frac{9}{10} a b \left(a+b x^2\right)^{5/2}","\frac{3}{2} a^2 b \left(a+b x^2\right)^{3/2}+\frac{9}{2} a^3 b \sqrt{a+b x^2}-\frac{9}{2} a^{7/2} b \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)-\frac{\left(a+b x^2\right)^{9/2}}{2 x^2}+\frac{9}{14} b \left(a+b x^2\right)^{7/2}+\frac{9}{10} a b \left(a+b x^2\right)^{5/2}",1,"(9*a^3*b*Sqrt[a + b*x^2])/2 + (3*a^2*b*(a + b*x^2)^(3/2))/2 + (9*a*b*(a + b*x^2)^(5/2))/10 + (9*b*(a + b*x^2)^(7/2))/14 - (a + b*x^2)^(9/2)/(2*x^2) - (9*a^(7/2)*b*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/2","A",8,5,15,0.3333,1,"{266, 47, 50, 63, 208}"
419,1,126,0,0.0764493,"\int \frac{\left(a+b x^2\right)^{9/2}}{x^5} \, dx","Int[(a + b*x^2)^(9/2)/x^5,x]","\frac{63}{8} a^2 b^2 \sqrt{a+b x^2}-\frac{63}{8} a^{5/2} b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)+\frac{63}{40} b^2 \left(a+b x^2\right)^{5/2}+\frac{21}{8} a b^2 \left(a+b x^2\right)^{3/2}-\frac{\left(a+b x^2\right)^{9/2}}{4 x^4}-\frac{9 b \left(a+b x^2\right)^{7/2}}{8 x^2}","\frac{63}{8} a^2 b^2 \sqrt{a+b x^2}-\frac{63}{8} a^{5/2} b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)+\frac{63}{40} b^2 \left(a+b x^2\right)^{5/2}+\frac{21}{8} a b^2 \left(a+b x^2\right)^{3/2}-\frac{\left(a+b x^2\right)^{9/2}}{4 x^4}-\frac{9 b \left(a+b x^2\right)^{7/2}}{8 x^2}",1,"(63*a^2*b^2*Sqrt[a + b*x^2])/8 + (21*a*b^2*(a + b*x^2)^(3/2))/8 + (63*b^2*(a + b*x^2)^(5/2))/40 - (9*b*(a + b*x^2)^(7/2))/(8*x^2) - (a + b*x^2)^(9/2)/(4*x^4) - (63*a^(5/2)*b^2*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/8","A",8,5,15,0.3333,1,"{266, 47, 50, 63, 208}"
420,1,126,0,0.0763166,"\int \frac{\left(a+b x^2\right)^{9/2}}{x^7} \, dx","Int[(a + b*x^2)^(9/2)/x^7,x]","-\frac{105}{16} a^{3/2} b^3 \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)-\frac{21 b^2 \left(a+b x^2\right)^{5/2}}{16 x^2}+\frac{35}{16} b^3 \left(a+b x^2\right)^{3/2}+\frac{105}{16} a b^3 \sqrt{a+b x^2}-\frac{\left(a+b x^2\right)^{9/2}}{6 x^6}-\frac{3 b \left(a+b x^2\right)^{7/2}}{8 x^4}","-\frac{105}{16} a^{3/2} b^3 \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)-\frac{21 b^2 \left(a+b x^2\right)^{5/2}}{16 x^2}+\frac{35}{16} b^3 \left(a+b x^2\right)^{3/2}+\frac{105}{16} a b^3 \sqrt{a+b x^2}-\frac{\left(a+b x^2\right)^{9/2}}{6 x^6}-\frac{3 b \left(a+b x^2\right)^{7/2}}{8 x^4}",1,"(105*a*b^3*Sqrt[a + b*x^2])/16 + (35*b^3*(a + b*x^2)^(3/2))/16 - (21*b^2*(a + b*x^2)^(5/2))/(16*x^2) - (3*b*(a + b*x^2)^(7/2))/(8*x^4) - (a + b*x^2)^(9/2)/(6*x^6) - (105*a^(3/2)*b^3*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/16","A",8,5,15,0.3333,1,"{266, 47, 50, 63, 208}"
421,1,128,0,0.0793392,"\int \frac{\left(a+b x^2\right)^{9/2}}{x^9} \, dx","Int[(a + b*x^2)^(9/2)/x^9,x]","-\frac{21 b^2 \left(a+b x^2\right)^{5/2}}{64 x^4}-\frac{105 b^3 \left(a+b x^2\right)^{3/2}}{128 x^2}+\frac{315}{128} b^4 \sqrt{a+b x^2}-\frac{315}{128} \sqrt{a} b^4 \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)-\frac{\left(a+b x^2\right)^{9/2}}{8 x^8}-\frac{3 b \left(a+b x^2\right)^{7/2}}{16 x^6}","-\frac{21 b^2 \left(a+b x^2\right)^{5/2}}{64 x^4}-\frac{105 b^3 \left(a+b x^2\right)^{3/2}}{128 x^2}+\frac{315}{128} b^4 \sqrt{a+b x^2}-\frac{315}{128} \sqrt{a} b^4 \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)-\frac{\left(a+b x^2\right)^{9/2}}{8 x^8}-\frac{3 b \left(a+b x^2\right)^{7/2}}{16 x^6}",1,"(315*b^4*Sqrt[a + b*x^2])/128 - (105*b^3*(a + b*x^2)^(3/2))/(128*x^2) - (21*b^2*(a + b*x^2)^(5/2))/(64*x^4) - (3*b*(a + b*x^2)^(7/2))/(16*x^6) - (a + b*x^2)^(9/2)/(8*x^8) - (315*Sqrt[a]*b^4*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/128","A",8,5,15,0.3333,1,"{266, 47, 50, 63, 208}"
422,1,131,0,0.0826313,"\int \frac{\left(a+b x^2\right)^{9/2}}{x^{11}} \, dx","Int[(a + b*x^2)^(9/2)/x^11,x]","-\frac{63 b^4 \sqrt{a+b x^2}}{256 x^2}-\frac{21 b^3 \left(a+b x^2\right)^{3/2}}{128 x^4}-\frac{21 b^2 \left(a+b x^2\right)^{5/2}}{160 x^6}-\frac{63 b^5 \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{256 \sqrt{a}}-\frac{9 b \left(a+b x^2\right)^{7/2}}{80 x^8}-\frac{\left(a+b x^2\right)^{9/2}}{10 x^{10}}","-\frac{63 b^4 \sqrt{a+b x^2}}{256 x^2}-\frac{21 b^3 \left(a+b x^2\right)^{3/2}}{128 x^4}-\frac{21 b^2 \left(a+b x^2\right)^{5/2}}{160 x^6}-\frac{63 b^5 \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{256 \sqrt{a}}-\frac{9 b \left(a+b x^2\right)^{7/2}}{80 x^8}-\frac{\left(a+b x^2\right)^{9/2}}{10 x^{10}}",1,"(-63*b^4*Sqrt[a + b*x^2])/(256*x^2) - (21*b^3*(a + b*x^2)^(3/2))/(128*x^4) - (21*b^2*(a + b*x^2)^(5/2))/(160*x^6) - (9*b*(a + b*x^2)^(7/2))/(80*x^8) - (a + b*x^2)^(9/2)/(10*x^10) - (63*b^5*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(256*Sqrt[a])","A",8,4,15,0.2667,1,"{266, 47, 63, 208}"
423,1,155,0,0.1010113,"\int \frac{\left(a+b x^2\right)^{9/2}}{x^{13}} \, dx","Int[(a + b*x^2)^(9/2)/x^13,x]","\frac{21 b^6 \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{1024 a^{3/2}}-\frac{21 b^5 \sqrt{a+b x^2}}{1024 a x^2}-\frac{21 b^4 \sqrt{a+b x^2}}{512 x^4}-\frac{7 b^3 \left(a+b x^2\right)^{3/2}}{128 x^6}-\frac{21 b^2 \left(a+b x^2\right)^{5/2}}{320 x^8}-\frac{3 b \left(a+b x^2\right)^{7/2}}{40 x^{10}}-\frac{\left(a+b x^2\right)^{9/2}}{12 x^{12}}","\frac{21 b^6 \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{1024 a^{3/2}}-\frac{21 b^5 \sqrt{a+b x^2}}{1024 a x^2}-\frac{21 b^4 \sqrt{a+b x^2}}{512 x^4}-\frac{7 b^3 \left(a+b x^2\right)^{3/2}}{128 x^6}-\frac{21 b^2 \left(a+b x^2\right)^{5/2}}{320 x^8}-\frac{3 b \left(a+b x^2\right)^{7/2}}{40 x^{10}}-\frac{\left(a+b x^2\right)^{9/2}}{12 x^{12}}",1,"(-21*b^4*Sqrt[a + b*x^2])/(512*x^4) - (21*b^5*Sqrt[a + b*x^2])/(1024*a*x^2) - (7*b^3*(a + b*x^2)^(3/2))/(128*x^6) - (21*b^2*(a + b*x^2)^(5/2))/(320*x^8) - (3*b*(a + b*x^2)^(7/2))/(40*x^10) - (a + b*x^2)^(9/2)/(12*x^12) + (21*b^6*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(1024*a^(3/2))","A",9,5,15,0.3333,1,"{266, 47, 51, 63, 208}"
424,1,179,0,0.1217379,"\int \frac{\left(a+b x^2\right)^{9/2}}{x^{15}} \, dx","Int[(a + b*x^2)^(9/2)/x^15,x]","\frac{9 b^6 \sqrt{a+b x^2}}{2048 a^2 x^2}-\frac{9 b^7 \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{2048 a^{5/2}}-\frac{3 b^5 \sqrt{a+b x^2}}{1024 a x^4}-\frac{3 b^4 \sqrt{a+b x^2}}{256 x^6}-\frac{3 b^3 \left(a+b x^2\right)^{3/2}}{128 x^8}-\frac{3 b^2 \left(a+b x^2\right)^{5/2}}{80 x^{10}}-\frac{3 b \left(a+b x^2\right)^{7/2}}{56 x^{12}}-\frac{\left(a+b x^2\right)^{9/2}}{14 x^{14}}","\frac{9 b^6 \sqrt{a+b x^2}}{2048 a^2 x^2}-\frac{9 b^7 \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{2048 a^{5/2}}-\frac{3 b^5 \sqrt{a+b x^2}}{1024 a x^4}-\frac{3 b^4 \sqrt{a+b x^2}}{256 x^6}-\frac{3 b^3 \left(a+b x^2\right)^{3/2}}{128 x^8}-\frac{3 b^2 \left(a+b x^2\right)^{5/2}}{80 x^{10}}-\frac{3 b \left(a+b x^2\right)^{7/2}}{56 x^{12}}-\frac{\left(a+b x^2\right)^{9/2}}{14 x^{14}}",1,"(-3*b^4*Sqrt[a + b*x^2])/(256*x^6) - (3*b^5*Sqrt[a + b*x^2])/(1024*a*x^4) + (9*b^6*Sqrt[a + b*x^2])/(2048*a^2*x^2) - (3*b^3*(a + b*x^2)^(3/2))/(128*x^8) - (3*b^2*(a + b*x^2)^(5/2))/(80*x^10) - (3*b*(a + b*x^2)^(7/2))/(56*x^12) - (a + b*x^2)^(9/2)/(14*x^14) - (9*b^7*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(2048*a^(5/2))","A",10,5,15,0.3333,1,"{266, 47, 51, 63, 208}"
425,1,202,0,0.11412,"\int x^6 \left(a+b x^2\right)^{9/2} \, dx","Int[x^6*(a + b*x^2)^(9/2),x]","\frac{45 a^7 x \sqrt{a+b x^2}}{32768 b^3}-\frac{15 a^6 x^3 \sqrt{a+b x^2}}{16384 b^2}-\frac{45 a^8 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{32768 b^{7/2}}+\frac{3 a^5 x^5 \sqrt{a+b x^2}}{4096 b}+\frac{9 a^4 x^7 \sqrt{a+b x^2}}{2048}+\frac{3}{256} a^3 x^7 \left(a+b x^2\right)^{3/2}+\frac{3}{128} a^2 x^7 \left(a+b x^2\right)^{5/2}+\frac{9}{224} a x^7 \left(a+b x^2\right)^{7/2}+\frac{1}{16} x^7 \left(a+b x^2\right)^{9/2}","\frac{45 a^7 x \sqrt{a+b x^2}}{32768 b^3}-\frac{15 a^6 x^3 \sqrt{a+b x^2}}{16384 b^2}-\frac{45 a^8 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{32768 b^{7/2}}+\frac{3 a^5 x^5 \sqrt{a+b x^2}}{4096 b}+\frac{9 a^4 x^7 \sqrt{a+b x^2}}{2048}+\frac{3}{256} a^3 x^7 \left(a+b x^2\right)^{3/2}+\frac{3}{128} a^2 x^7 \left(a+b x^2\right)^{5/2}+\frac{9}{224} a x^7 \left(a+b x^2\right)^{7/2}+\frac{1}{16} x^7 \left(a+b x^2\right)^{9/2}",1,"(45*a^7*x*Sqrt[a + b*x^2])/(32768*b^3) - (15*a^6*x^3*Sqrt[a + b*x^2])/(16384*b^2) + (3*a^5*x^5*Sqrt[a + b*x^2])/(4096*b) + (9*a^4*x^7*Sqrt[a + b*x^2])/2048 + (3*a^3*x^7*(a + b*x^2)^(3/2))/256 + (3*a^2*x^7*(a + b*x^2)^(5/2))/128 + (9*a*x^7*(a + b*x^2)^(7/2))/224 + (x^7*(a + b*x^2)^(9/2))/16 - (45*a^8*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(32768*b^(7/2))","A",10,4,15,0.2667,1,"{279, 321, 217, 206}"
426,1,178,0,0.0855914,"\int x^4 \left(a+b x^2\right)^{9/2} \, dx","Int[x^4*(a + b*x^2)^(9/2),x]","-\frac{9 a^6 x \sqrt{a+b x^2}}{2048 b^2}+\frac{9 a^7 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{2048 b^{5/2}}+\frac{3 a^5 x^3 \sqrt{a+b x^2}}{1024 b}+\frac{3}{256} a^4 x^5 \sqrt{a+b x^2}+\frac{3}{128} a^3 x^5 \left(a+b x^2\right)^{3/2}+\frac{3}{80} a^2 x^5 \left(a+b x^2\right)^{5/2}+\frac{3}{56} a x^5 \left(a+b x^2\right)^{7/2}+\frac{1}{14} x^5 \left(a+b x^2\right)^{9/2}","-\frac{9 a^6 x \sqrt{a+b x^2}}{2048 b^2}+\frac{9 a^7 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{2048 b^{5/2}}+\frac{3 a^5 x^3 \sqrt{a+b x^2}}{1024 b}+\frac{3}{256} a^4 x^5 \sqrt{a+b x^2}+\frac{3}{128} a^3 x^5 \left(a+b x^2\right)^{3/2}+\frac{3}{80} a^2 x^5 \left(a+b x^2\right)^{5/2}+\frac{3}{56} a x^5 \left(a+b x^2\right)^{7/2}+\frac{1}{14} x^5 \left(a+b x^2\right)^{9/2}",1,"(-9*a^6*x*Sqrt[a + b*x^2])/(2048*b^2) + (3*a^5*x^3*Sqrt[a + b*x^2])/(1024*b) + (3*a^4*x^5*Sqrt[a + b*x^2])/256 + (3*a^3*x^5*(a + b*x^2)^(3/2))/128 + (3*a^2*x^5*(a + b*x^2)^(5/2))/80 + (3*a*x^5*(a + b*x^2)^(7/2))/56 + (x^5*(a + b*x^2)^(9/2))/14 + (9*a^7*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(2048*b^(5/2))","A",9,4,15,0.2667,1,"{279, 321, 217, 206}"
427,1,154,0,0.0702928,"\int x^2 \left(a+b x^2\right)^{9/2} \, dx","Int[x^2*(a + b*x^2)^(9/2),x]","-\frac{21 a^6 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{1024 b^{3/2}}+\frac{21 a^5 x \sqrt{a+b x^2}}{1024 b}+\frac{21}{512} a^4 x^3 \sqrt{a+b x^2}+\frac{7}{128} a^3 x^3 \left(a+b x^2\right)^{3/2}+\frac{21}{320} a^2 x^3 \left(a+b x^2\right)^{5/2}+\frac{3}{40} a x^3 \left(a+b x^2\right)^{7/2}+\frac{1}{12} x^3 \left(a+b x^2\right)^{9/2}","-\frac{21 a^6 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{1024 b^{3/2}}+\frac{21 a^5 x \sqrt{a+b x^2}}{1024 b}+\frac{21}{512} a^4 x^3 \sqrt{a+b x^2}+\frac{7}{128} a^3 x^3 \left(a+b x^2\right)^{3/2}+\frac{21}{320} a^2 x^3 \left(a+b x^2\right)^{5/2}+\frac{3}{40} a x^3 \left(a+b x^2\right)^{7/2}+\frac{1}{12} x^3 \left(a+b x^2\right)^{9/2}",1,"(21*a^5*x*Sqrt[a + b*x^2])/(1024*b) + (21*a^4*x^3*Sqrt[a + b*x^2])/512 + (7*a^3*x^3*(a + b*x^2)^(3/2))/128 + (21*a^2*x^3*(a + b*x^2)^(5/2))/320 + (3*a*x^3*(a + b*x^2)^(7/2))/40 + (x^3*(a + b*x^2)^(9/2))/12 - (21*a^6*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(1024*b^(3/2))","A",8,4,15,0.2667,1,"{279, 321, 217, 206}"
428,1,122,0,0.0421447,"\int \left(a+b x^2\right)^{9/2} \, dx","Int[(a + b*x^2)^(9/2),x]","\frac{63}{256} a^4 x \sqrt{a+b x^2}+\frac{21}{128} a^3 x \left(a+b x^2\right)^{3/2}+\frac{21}{160} a^2 x \left(a+b x^2\right)^{5/2}+\frac{63 a^5 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{256 \sqrt{b}}+\frac{9}{80} a x \left(a+b x^2\right)^{7/2}+\frac{1}{10} x \left(a+b x^2\right)^{9/2}","\frac{63}{256} a^4 x \sqrt{a+b x^2}+\frac{21}{128} a^3 x \left(a+b x^2\right)^{3/2}+\frac{21}{160} a^2 x \left(a+b x^2\right)^{5/2}+\frac{63 a^5 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{256 \sqrt{b}}+\frac{9}{80} a x \left(a+b x^2\right)^{7/2}+\frac{1}{10} x \left(a+b x^2\right)^{9/2}",1,"(63*a^4*x*Sqrt[a + b*x^2])/256 + (21*a^3*x*(a + b*x^2)^(3/2))/128 + (21*a^2*x*(a + b*x^2)^(5/2))/160 + (9*a*x*(a + b*x^2)^(7/2))/80 + (x*(a + b*x^2)^(9/2))/10 + (63*a^5*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(256*Sqrt[b])","A",7,3,11,0.2727,1,"{195, 217, 206}"
429,1,123,0,0.0439185,"\int \frac{\left(a+b x^2\right)^{9/2}}{x^2} \, dx","Int[(a + b*x^2)^(9/2)/x^2,x]","\frac{105}{64} a^2 b x \left(a+b x^2\right)^{3/2}+\frac{315}{128} a^3 b x \sqrt{a+b x^2}+\frac{315}{128} a^4 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)-\frac{\left(a+b x^2\right)^{9/2}}{x}+\frac{9}{8} b x \left(a+b x^2\right)^{7/2}+\frac{21}{16} a b x \left(a+b x^2\right)^{5/2}","\frac{105}{64} a^2 b x \left(a+b x^2\right)^{3/2}+\frac{315}{128} a^3 b x \sqrt{a+b x^2}+\frac{315}{128} a^4 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)-\frac{\left(a+b x^2\right)^{9/2}}{x}+\frac{9}{8} b x \left(a+b x^2\right)^{7/2}+\frac{21}{16} a b x \left(a+b x^2\right)^{5/2}",1,"(315*a^3*b*x*Sqrt[a + b*x^2])/128 + (105*a^2*b*x*(a + b*x^2)^(3/2))/64 + (21*a*b*x*(a + b*x^2)^(5/2))/16 + (9*b*x*(a + b*x^2)^(7/2))/8 - (a + b*x^2)^(9/2)/x + (315*a^4*Sqrt[b]*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/128","A",7,4,15,0.2667,1,"{277, 195, 217, 206}"
430,1,128,0,0.0487097,"\int \frac{\left(a+b x^2\right)^{9/2}}{x^4} \, dx","Int[(a + b*x^2)^(9/2)/x^4,x]","\frac{105}{16} a^2 b^2 x \sqrt{a+b x^2}+\frac{105}{16} a^3 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)+\frac{7}{2} b^2 x \left(a+b x^2\right)^{5/2}+\frac{35}{8} a b^2 x \left(a+b x^2\right)^{3/2}-\frac{\left(a+b x^2\right)^{9/2}}{3 x^3}-\frac{3 b \left(a+b x^2\right)^{7/2}}{x}","\frac{105}{16} a^2 b^2 x \sqrt{a+b x^2}+\frac{105}{16} a^3 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)+\frac{7}{2} b^2 x \left(a+b x^2\right)^{5/2}+\frac{35}{8} a b^2 x \left(a+b x^2\right)^{3/2}-\frac{\left(a+b x^2\right)^{9/2}}{3 x^3}-\frac{3 b \left(a+b x^2\right)^{7/2}}{x}",1,"(105*a^2*b^2*x*Sqrt[a + b*x^2])/16 + (35*a*b^2*x*(a + b*x^2)^(3/2))/8 + (7*b^2*x*(a + b*x^2)^(5/2))/2 - (3*b*(a + b*x^2)^(7/2))/x - (a + b*x^2)^(9/2)/(3*x^3) + (105*a^3*b^(3/2)*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/16","A",7,4,15,0.2667,1,"{277, 195, 217, 206}"
431,1,129,0,0.0496843,"\int \frac{\left(a+b x^2\right)^{9/2}}{x^6} \, dx","Int[(a + b*x^2)^(9/2)/x^6,x]","\frac{63}{8} a^2 b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)-\frac{21 b^2 \left(a+b x^2\right)^{5/2}}{5 x}+\frac{21}{4} b^3 x \left(a+b x^2\right)^{3/2}+\frac{63}{8} a b^3 x \sqrt{a+b x^2}-\frac{\left(a+b x^2\right)^{9/2}}{5 x^5}-\frac{3 b \left(a+b x^2\right)^{7/2}}{5 x^3}","\frac{63}{8} a^2 b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)-\frac{21 b^2 \left(a+b x^2\right)^{5/2}}{5 x}+\frac{21}{4} b^3 x \left(a+b x^2\right)^{3/2}+\frac{63}{8} a b^3 x \sqrt{a+b x^2}-\frac{\left(a+b x^2\right)^{9/2}}{5 x^5}-\frac{3 b \left(a+b x^2\right)^{7/2}}{5 x^3}",1,"(63*a*b^3*x*Sqrt[a + b*x^2])/8 + (21*b^3*x*(a + b*x^2)^(3/2))/4 - (21*b^2*(a + b*x^2)^(5/2))/(5*x) - (3*b*(a + b*x^2)^(7/2))/(5*x^3) - (a + b*x^2)^(9/2)/(5*x^5) + (63*a^2*b^(5/2)*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/8","A",7,4,15,0.2667,1,"{277, 195, 217, 206}"
432,1,126,0,0.0509176,"\int \frac{\left(a+b x^2\right)^{9/2}}{x^8} \, dx","Int[(a + b*x^2)^(9/2)/x^8,x]","-\frac{3 b^2 \left(a+b x^2\right)^{5/2}}{5 x^3}-\frac{3 b^3 \left(a+b x^2\right)^{3/2}}{x}+\frac{9}{2} b^4 x \sqrt{a+b x^2}+\frac{9}{2} a b^{7/2} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)-\frac{\left(a+b x^2\right)^{9/2}}{7 x^7}-\frac{9 b \left(a+b x^2\right)^{7/2}}{35 x^5}","-\frac{3 b^2 \left(a+b x^2\right)^{5/2}}{5 x^3}-\frac{3 b^3 \left(a+b x^2\right)^{3/2}}{x}+\frac{9}{2} b^4 x \sqrt{a+b x^2}+\frac{9}{2} a b^{7/2} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)-\frac{\left(a+b x^2\right)^{9/2}}{7 x^7}-\frac{9 b \left(a+b x^2\right)^{7/2}}{35 x^5}",1,"(9*b^4*x*Sqrt[a + b*x^2])/2 - (3*b^3*(a + b*x^2)^(3/2))/x - (3*b^2*(a + b*x^2)^(5/2))/(5*x^3) - (9*b*(a + b*x^2)^(7/2))/(35*x^5) - (a + b*x^2)^(9/2)/(7*x^7) + (9*a*b^(7/2)*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/2","A",7,4,15,0.2667,1,"{277, 195, 217, 206}"
433,1,124,0,0.0524736,"\int \frac{\left(a+b x^2\right)^{9/2}}{x^{10}} \, dx","Int[(a + b*x^2)^(9/2)/x^10,x]","-\frac{b^4 \sqrt{a+b x^2}}{x}-\frac{b^3 \left(a+b x^2\right)^{3/2}}{3 x^3}-\frac{b^2 \left(a+b x^2\right)^{5/2}}{5 x^5}+b^{9/2} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)-\frac{b \left(a+b x^2\right)^{7/2}}{7 x^7}-\frac{\left(a+b x^2\right)^{9/2}}{9 x^9}","-\frac{b^4 \sqrt{a+b x^2}}{x}-\frac{b^3 \left(a+b x^2\right)^{3/2}}{3 x^3}-\frac{b^2 \left(a+b x^2\right)^{5/2}}{5 x^5}+b^{9/2} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)-\frac{b \left(a+b x^2\right)^{7/2}}{7 x^7}-\frac{\left(a+b x^2\right)^{9/2}}{9 x^9}",1,"-((b^4*Sqrt[a + b*x^2])/x) - (b^3*(a + b*x^2)^(3/2))/(3*x^3) - (b^2*(a + b*x^2)^(5/2))/(5*x^5) - (b*(a + b*x^2)^(7/2))/(7*x^7) - (a + b*x^2)^(9/2)/(9*x^9) + b^(9/2)*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]]","A",7,3,15,0.2000,1,"{277, 217, 206}"
434,1,21,0,0.0049336,"\int \frac{\left(a+b x^2\right)^{9/2}}{x^{12}} \, dx","Int[(a + b*x^2)^(9/2)/x^12,x]","-\frac{\left(a+b x^2\right)^{11/2}}{11 a x^{11}}","-\frac{\left(a+b x^2\right)^{11/2}}{11 a x^{11}}",1,"-(a + b*x^2)^(11/2)/(11*a*x^11)","A",1,1,15,0.06667,1,"{264}"
435,1,44,0,0.0112088,"\int \frac{\left(a+b x^2\right)^{9/2}}{x^{14}} \, dx","Int[(a + b*x^2)^(9/2)/x^14,x]","\frac{2 b \left(a+b x^2\right)^{11/2}}{143 a^2 x^{11}}-\frac{\left(a+b x^2\right)^{11/2}}{13 a x^{13}}","\frac{2 b \left(a+b x^2\right)^{11/2}}{143 a^2 x^{11}}-\frac{\left(a+b x^2\right)^{11/2}}{13 a x^{13}}",1,"-(a + b*x^2)^(11/2)/(13*a*x^13) + (2*b*(a + b*x^2)^(11/2))/(143*a^2*x^11)","A",2,2,15,0.1333,1,"{271, 264}"
436,1,68,0,0.021,"\int \frac{\left(a+b x^2\right)^{9/2}}{x^{16}} \, dx","Int[(a + b*x^2)^(9/2)/x^16,x]","-\frac{8 b^2 \left(a+b x^2\right)^{11/2}}{2145 a^3 x^{11}}+\frac{4 b \left(a+b x^2\right)^{11/2}}{195 a^2 x^{13}}-\frac{\left(a+b x^2\right)^{11/2}}{15 a x^{15}}","-\frac{8 b^2 \left(a+b x^2\right)^{11/2}}{2145 a^3 x^{11}}+\frac{4 b \left(a+b x^2\right)^{11/2}}{195 a^2 x^{13}}-\frac{\left(a+b x^2\right)^{11/2}}{15 a x^{15}}",1,"-(a + b*x^2)^(11/2)/(15*a*x^15) + (4*b*(a + b*x^2)^(11/2))/(195*a^2*x^13) - (8*b^2*(a + b*x^2)^(11/2))/(2145*a^3*x^11)","A",3,2,15,0.1333,1,"{271, 264}"
437,1,92,0,0.0296989,"\int \frac{\left(a+b x^2\right)^{9/2}}{x^{18}} \, dx","Int[(a + b*x^2)^(9/2)/x^18,x]","\frac{16 b^3 \left(a+b x^2\right)^{11/2}}{12155 a^4 x^{11}}-\frac{8 b^2 \left(a+b x^2\right)^{11/2}}{1105 a^3 x^{13}}+\frac{2 b \left(a+b x^2\right)^{11/2}}{85 a^2 x^{15}}-\frac{\left(a+b x^2\right)^{11/2}}{17 a x^{17}}","\frac{16 b^3 \left(a+b x^2\right)^{11/2}}{12155 a^4 x^{11}}-\frac{8 b^2 \left(a+b x^2\right)^{11/2}}{1105 a^3 x^{13}}+\frac{2 b \left(a+b x^2\right)^{11/2}}{85 a^2 x^{15}}-\frac{\left(a+b x^2\right)^{11/2}}{17 a x^{17}}",1,"-(a + b*x^2)^(11/2)/(17*a*x^17) + (2*b*(a + b*x^2)^(11/2))/(85*a^2*x^15) - (8*b^2*(a + b*x^2)^(11/2))/(1105*a^3*x^13) + (16*b^3*(a + b*x^2)^(11/2))/(12155*a^4*x^11)","A",4,2,15,0.1333,1,"{271, 264}"
438,1,116,0,0.0445839,"\int \frac{\left(a+b x^2\right)^{9/2}}{x^{20}} \, dx","Int[(a + b*x^2)^(9/2)/x^20,x]","-\frac{128 b^4 \left(a+b x^2\right)^{11/2}}{230945 a^5 x^{11}}+\frac{64 b^3 \left(a+b x^2\right)^{11/2}}{20995 a^4 x^{13}}-\frac{16 b^2 \left(a+b x^2\right)^{11/2}}{1615 a^3 x^{15}}+\frac{8 b \left(a+b x^2\right)^{11/2}}{323 a^2 x^{17}}-\frac{\left(a+b x^2\right)^{11/2}}{19 a x^{19}}","-\frac{128 b^4 \left(a+b x^2\right)^{11/2}}{230945 a^5 x^{11}}+\frac{64 b^3 \left(a+b x^2\right)^{11/2}}{20995 a^4 x^{13}}-\frac{16 b^2 \left(a+b x^2\right)^{11/2}}{1615 a^3 x^{15}}+\frac{8 b \left(a+b x^2\right)^{11/2}}{323 a^2 x^{17}}-\frac{\left(a+b x^2\right)^{11/2}}{19 a x^{19}}",1,"-(a + b*x^2)^(11/2)/(19*a*x^19) + (8*b*(a + b*x^2)^(11/2))/(323*a^2*x^17) - (16*b^2*(a + b*x^2)^(11/2))/(1615*a^3*x^15) + (64*b^3*(a + b*x^2)^(11/2))/(20995*a^4*x^13) - (128*b^4*(a + b*x^2)^(11/2))/(230945*a^5*x^11)","A",5,2,15,0.1333,1,"{271, 264}"
439,1,140,0,0.0562635,"\int \frac{\left(a+b x^2\right)^{9/2}}{x^{22}} \, dx","Int[(a + b*x^2)^(9/2)/x^22,x]","\frac{256 b^5 \left(a+b x^2\right)^{11/2}}{969969 a^6 x^{11}}-\frac{128 b^4 \left(a+b x^2\right)^{11/2}}{88179 a^5 x^{13}}+\frac{32 b^3 \left(a+b x^2\right)^{11/2}}{6783 a^4 x^{15}}-\frac{80 b^2 \left(a+b x^2\right)^{11/2}}{6783 a^3 x^{17}}+\frac{10 b \left(a+b x^2\right)^{11/2}}{399 a^2 x^{19}}-\frac{\left(a+b x^2\right)^{11/2}}{21 a x^{21}}","\frac{256 b^5 \left(a+b x^2\right)^{11/2}}{969969 a^6 x^{11}}-\frac{128 b^4 \left(a+b x^2\right)^{11/2}}{88179 a^5 x^{13}}+\frac{32 b^3 \left(a+b x^2\right)^{11/2}}{6783 a^4 x^{15}}-\frac{80 b^2 \left(a+b x^2\right)^{11/2}}{6783 a^3 x^{17}}+\frac{10 b \left(a+b x^2\right)^{11/2}}{399 a^2 x^{19}}-\frac{\left(a+b x^2\right)^{11/2}}{21 a x^{21}}",1,"-(a + b*x^2)^(11/2)/(21*a*x^21) + (10*b*(a + b*x^2)^(11/2))/(399*a^2*x^19) - (80*b^2*(a + b*x^2)^(11/2))/(6783*a^3*x^17) + (32*b^3*(a + b*x^2)^(11/2))/(6783*a^4*x^15) - (128*b^4*(a + b*x^2)^(11/2))/(88179*a^5*x^13) + (256*b^5*(a + b*x^2)^(11/2))/(969969*a^6*x^11)","A",6,2,15,0.1333,1,"{271, 264}"
440,1,164,0,0.0719655,"\int \frac{\left(a+b x^2\right)^{9/2}}{x^{24}} \, dx","Int[(a + b*x^2)^(9/2)/x^24,x]","-\frac{1024 b^6 \left(a+b x^2\right)^{11/2}}{7436429 a^7 x^{11}}+\frac{512 b^5 \left(a+b x^2\right)^{11/2}}{676039 a^6 x^{13}}-\frac{128 b^4 \left(a+b x^2\right)^{11/2}}{52003 a^5 x^{15}}+\frac{320 b^3 \left(a+b x^2\right)^{11/2}}{52003 a^4 x^{17}}-\frac{40 b^2 \left(a+b x^2\right)^{11/2}}{3059 a^3 x^{19}}+\frac{4 b \left(a+b x^2\right)^{11/2}}{161 a^2 x^{21}}-\frac{\left(a+b x^2\right)^{11/2}}{23 a x^{23}}","-\frac{1024 b^6 \left(a+b x^2\right)^{11/2}}{7436429 a^7 x^{11}}+\frac{512 b^5 \left(a+b x^2\right)^{11/2}}{676039 a^6 x^{13}}-\frac{128 b^4 \left(a+b x^2\right)^{11/2}}{52003 a^5 x^{15}}+\frac{320 b^3 \left(a+b x^2\right)^{11/2}}{52003 a^4 x^{17}}-\frac{40 b^2 \left(a+b x^2\right)^{11/2}}{3059 a^3 x^{19}}+\frac{4 b \left(a+b x^2\right)^{11/2}}{161 a^2 x^{21}}-\frac{\left(a+b x^2\right)^{11/2}}{23 a x^{23}}",1,"-(a + b*x^2)^(11/2)/(23*a*x^23) + (4*b*(a + b*x^2)^(11/2))/(161*a^2*x^21) - (40*b^2*(a + b*x^2)^(11/2))/(3059*a^3*x^19) + (320*b^3*(a + b*x^2)^(11/2))/(52003*a^4*x^17) - (128*b^4*(a + b*x^2)^(11/2))/(52003*a^5*x^15) + (512*b^5*(a + b*x^2)^(11/2))/(676039*a^6*x^13) - (1024*b^6*(a + b*x^2)^(11/2))/(7436429*a^7*x^11)","A",7,2,15,0.1333,1,"{271, 264}"
441,1,46,0,0.0195838,"\int x^5 \sqrt{9+4 x^2} \, dx","Int[x^5*Sqrt[9 + 4*x^2],x]","\frac{1}{448} \left(4 x^2+9\right)^{7/2}-\frac{9}{160} \left(4 x^2+9\right)^{5/2}+\frac{27}{64} \left(4 x^2+9\right)^{3/2}","\frac{1}{448} \left(4 x^2+9\right)^{7/2}-\frac{9}{160} \left(4 x^2+9\right)^{5/2}+\frac{27}{64} \left(4 x^2+9\right)^{3/2}",1,"(27*(9 + 4*x^2)^(3/2))/64 - (9*(9 + 4*x^2)^(5/2))/160 + (9 + 4*x^2)^(7/2)/448","A",3,2,15,0.1333,1,"{266, 43}"
442,1,63,0,0.0155562,"\int x^4 \sqrt{9+4 x^2} \, dx","Int[x^4*Sqrt[9 + 4*x^2],x]","\frac{1}{6} \sqrt{4 x^2+9} x^5+\frac{3}{32} \sqrt{4 x^2+9} x^3-\frac{81}{256} \sqrt{4 x^2+9} x+\frac{729}{512} \sinh ^{-1}\left(\frac{2 x}{3}\right)","\frac{1}{6} \sqrt{4 x^2+9} x^5+\frac{3}{32} \sqrt{4 x^2+9} x^3-\frac{81}{256} \sqrt{4 x^2+9} x+\frac{729}{512} \sinh ^{-1}\left(\frac{2 x}{3}\right)",1,"(-81*x*Sqrt[9 + 4*x^2])/256 + (3*x^3*Sqrt[9 + 4*x^2])/32 + (x^5*Sqrt[9 + 4*x^2])/6 + (729*ArcSinh[(2*x)/3])/512","A",4,3,15,0.2000,1,"{279, 321, 215}"
443,1,31,0,0.014846,"\int x^3 \sqrt{9+4 x^2} \, dx","Int[x^3*Sqrt[9 + 4*x^2],x]","\frac{1}{80} \left(4 x^2+9\right)^{5/2}-\frac{3}{16} \left(4 x^2+9\right)^{3/2}","\frac{1}{80} \left(4 x^2+9\right)^{5/2}-\frac{3}{16} \left(4 x^2+9\right)^{3/2}",1,"(-3*(9 + 4*x^2)^(3/2))/16 + (9 + 4*x^2)^(5/2)/80","A",3,2,15,0.1333,1,"{266, 43}"
444,1,45,0,0.0095313,"\int x^2 \sqrt{9+4 x^2} \, dx","Int[x^2*Sqrt[9 + 4*x^2],x]","\frac{1}{4} \sqrt{4 x^2+9} x^3+\frac{9}{32} \sqrt{4 x^2+9} x-\frac{81}{64} \sinh ^{-1}\left(\frac{2 x}{3}\right)","\frac{1}{4} \sqrt{4 x^2+9} x^3+\frac{9}{32} \sqrt{4 x^2+9} x-\frac{81}{64} \sinh ^{-1}\left(\frac{2 x}{3}\right)",1,"(9*x*Sqrt[9 + 4*x^2])/32 + (x^3*Sqrt[9 + 4*x^2])/4 - (81*ArcSinh[(2*x)/3])/64","A",3,3,15,0.2000,1,"{279, 321, 215}"
445,1,15,0,0.0021563,"\int x \sqrt{9+4 x^2} \, dx","Int[x*Sqrt[9 + 4*x^2],x]","\frac{1}{12} \left(4 x^2+9\right)^{3/2}","\frac{1}{12} \left(4 x^2+9\right)^{3/2}",1,"(9 + 4*x^2)^(3/2)/12","A",1,1,13,0.07692,1,"{261}"
446,1,27,0,0.0037743,"\int \sqrt{9+4 x^2} \, dx","Int[Sqrt[9 + 4*x^2],x]","\frac{1}{2} \sqrt{4 x^2+9} x+\frac{9}{4} \sinh ^{-1}\left(\frac{2 x}{3}\right)","\frac{1}{2} \sqrt{4 x^2+9} x+\frac{9}{4} \sinh ^{-1}\left(\frac{2 x}{3}\right)",1,"(x*Sqrt[9 + 4*x^2])/2 + (9*ArcSinh[(2*x)/3])/4","A",2,2,11,0.1818,1,"{195, 215}"
447,1,30,0,0.0162719,"\int \frac{\sqrt{9+4 x^2}}{x} \, dx","Int[Sqrt[9 + 4*x^2]/x,x]","\sqrt{4 x^2+9}-3 \tanh ^{-1}\left(\frac{1}{3} \sqrt{4 x^2+9}\right)","\sqrt{4 x^2+9}-3 \tanh ^{-1}\left(\frac{1}{3} \sqrt{4 x^2+9}\right)",1,"Sqrt[9 + 4*x^2] - 3*ArcTanh[Sqrt[9 + 4*x^2]/3]","A",4,4,15,0.2667,1,"{266, 50, 63, 207}"
448,1,25,0,0.0048838,"\int \frac{\sqrt{9+4 x^2}}{x^2} \, dx","Int[Sqrt[9 + 4*x^2]/x^2,x]","2 \sinh ^{-1}\left(\frac{2 x}{3}\right)-\frac{\sqrt{4 x^2+9}}{x}","2 \sinh ^{-1}\left(\frac{2 x}{3}\right)-\frac{\sqrt{4 x^2+9}}{x}",1,"-(Sqrt[9 + 4*x^2]/x) + 2*ArcSinh[(2*x)/3]","A",2,2,15,0.1333,1,"{277, 215}"
449,1,39,0,0.0164569,"\int \frac{\sqrt{9+4 x^2}}{x^3} \, dx","Int[Sqrt[9 + 4*x^2]/x^3,x]","-\frac{\sqrt{4 x^2+9}}{2 x^2}-\frac{2}{3} \tanh ^{-1}\left(\frac{1}{3} \sqrt{4 x^2+9}\right)","-\frac{\sqrt{4 x^2+9}}{2 x^2}-\frac{2}{3} \tanh ^{-1}\left(\frac{1}{3} \sqrt{4 x^2+9}\right)",1,"-Sqrt[9 + 4*x^2]/(2*x^2) - (2*ArcTanh[Sqrt[9 + 4*x^2]/3])/3","A",4,4,15,0.2667,1,"{266, 47, 63, 207}"
450,1,18,0,0.002985,"\int \frac{\sqrt{9+4 x^2}}{x^4} \, dx","Int[Sqrt[9 + 4*x^2]/x^4,x]","-\frac{\left(4 x^2+9\right)^{3/2}}{27 x^3}","-\frac{\left(4 x^2+9\right)^{3/2}}{27 x^3}",1,"-(9 + 4*x^2)^(3/2)/(27*x^3)","A",1,1,15,0.06667,1,"{264}"
451,1,57,0,0.0216427,"\int \frac{\sqrt{9+4 x^2}}{x^5} \, dx","Int[Sqrt[9 + 4*x^2]/x^5,x]","-\frac{\sqrt{4 x^2+9}}{18 x^2}-\frac{\sqrt{4 x^2+9}}{4 x^4}+\frac{2}{27} \tanh ^{-1}\left(\frac{1}{3} \sqrt{4 x^2+9}\right)","-\frac{\sqrt{4 x^2+9}}{18 x^2}-\frac{\sqrt{4 x^2+9}}{4 x^4}+\frac{2}{27} \tanh ^{-1}\left(\frac{1}{3} \sqrt{4 x^2+9}\right)",1,"-Sqrt[9 + 4*x^2]/(4*x^4) - Sqrt[9 + 4*x^2]/(18*x^2) + (2*ArcTanh[Sqrt[9 + 4*x^2]/3])/27","A",5,5,15,0.3333,1,"{266, 47, 51, 63, 207}"
452,1,46,0,0.0205247,"\int x^5 \sqrt{9-4 x^2} \, dx","Int[x^5*Sqrt[9 - 4*x^2],x]","-\frac{1}{448} \left(9-4 x^2\right)^{7/2}+\frac{9}{160} \left(9-4 x^2\right)^{5/2}-\frac{27}{64} \left(9-4 x^2\right)^{3/2}","-\frac{1}{448} \left(9-4 x^2\right)^{7/2}+\frac{9}{160} \left(9-4 x^2\right)^{5/2}-\frac{27}{64} \left(9-4 x^2\right)^{3/2}",1,"(-27*(9 - 4*x^2)^(3/2))/64 + (9*(9 - 4*x^2)^(5/2))/160 - (9 - 4*x^2)^(7/2)/448","A",3,2,15,0.1333,1,"{266, 43}"
453,1,63,0,0.0161792,"\int x^4 \sqrt{9-4 x^2} \, dx","Int[x^4*Sqrt[9 - 4*x^2],x]","\frac{1}{6} \sqrt{9-4 x^2} x^5-\frac{3}{32} \sqrt{9-4 x^2} x^3-\frac{81}{256} \sqrt{9-4 x^2} x+\frac{729}{512} \sin ^{-1}\left(\frac{2 x}{3}\right)","\frac{1}{6} \sqrt{9-4 x^2} x^5-\frac{3}{32} \sqrt{9-4 x^2} x^3-\frac{81}{256} \sqrt{9-4 x^2} x+\frac{729}{512} \sin ^{-1}\left(\frac{2 x}{3}\right)",1,"(-81*x*Sqrt[9 - 4*x^2])/256 - (3*x^3*Sqrt[9 - 4*x^2])/32 + (x^5*Sqrt[9 - 4*x^2])/6 + (729*ArcSin[(2*x)/3])/512","A",4,3,15,0.2000,1,"{279, 321, 216}"
454,1,31,0,0.0151302,"\int x^3 \sqrt{9-4 x^2} \, dx","Int[x^3*Sqrt[9 - 4*x^2],x]","\frac{1}{80} \left(9-4 x^2\right)^{5/2}-\frac{3}{16} \left(9-4 x^2\right)^{3/2}","\frac{1}{80} \left(9-4 x^2\right)^{5/2}-\frac{3}{16} \left(9-4 x^2\right)^{3/2}",1,"(-3*(9 - 4*x^2)^(3/2))/16 + (9 - 4*x^2)^(5/2)/80","A",3,2,15,0.1333,1,"{266, 43}"
455,1,45,0,0.0104155,"\int x^2 \sqrt{9-4 x^2} \, dx","Int[x^2*Sqrt[9 - 4*x^2],x]","\frac{1}{4} \sqrt{9-4 x^2} x^3-\frac{9}{32} \sqrt{9-4 x^2} x+\frac{81}{64} \sin ^{-1}\left(\frac{2 x}{3}\right)","\frac{1}{4} \sqrt{9-4 x^2} x^3-\frac{9}{32} \sqrt{9-4 x^2} x+\frac{81}{64} \sin ^{-1}\left(\frac{2 x}{3}\right)",1,"(-9*x*Sqrt[9 - 4*x^2])/32 + (x^3*Sqrt[9 - 4*x^2])/4 + (81*ArcSin[(2*x)/3])/64","A",3,3,15,0.2000,1,"{279, 321, 216}"
456,1,15,0,0.0023749,"\int x \sqrt{9-4 x^2} \, dx","Int[x*Sqrt[9 - 4*x^2],x]","-\frac{1}{12} \left(9-4 x^2\right)^{3/2}","-\frac{1}{12} \left(9-4 x^2\right)^{3/2}",1,"-(9 - 4*x^2)^(3/2)/12","A",1,1,13,0.07692,1,"{261}"
457,1,27,0,0.0032839,"\int \sqrt{9-4 x^2} \, dx","Int[Sqrt[9 - 4*x^2],x]","\frac{1}{2} \sqrt{9-4 x^2} x+\frac{9}{4} \sin ^{-1}\left(\frac{2 x}{3}\right)","\frac{1}{2} \sqrt{9-4 x^2} x+\frac{9}{4} \sin ^{-1}\left(\frac{2 x}{3}\right)",1,"(x*Sqrt[9 - 4*x^2])/2 + (9*ArcSin[(2*x)/3])/4","A",2,2,11,0.1818,1,"{195, 216}"
458,1,30,0,0.0152687,"\int \frac{\sqrt{9-4 x^2}}{x} \, dx","Int[Sqrt[9 - 4*x^2]/x,x]","\sqrt{9-4 x^2}-3 \tanh ^{-1}\left(\frac{1}{3} \sqrt{9-4 x^2}\right)","\sqrt{9-4 x^2}-3 \tanh ^{-1}\left(\frac{1}{3} \sqrt{9-4 x^2}\right)",1,"Sqrt[9 - 4*x^2] - 3*ArcTanh[Sqrt[9 - 4*x^2]/3]","A",4,4,15,0.2667,1,"{266, 50, 63, 206}"
459,1,25,0,0.0050271,"\int \frac{\sqrt{9-4 x^2}}{x^2} \, dx","Int[Sqrt[9 - 4*x^2]/x^2,x]","-\frac{\sqrt{9-4 x^2}}{x}-2 \sin ^{-1}\left(\frac{2 x}{3}\right)","-\frac{\sqrt{9-4 x^2}}{x}-2 \sin ^{-1}\left(\frac{2 x}{3}\right)",1,"-(Sqrt[9 - 4*x^2]/x) - 2*ArcSin[(2*x)/3]","A",2,2,15,0.1333,1,"{277, 216}"
460,1,39,0,0.016247,"\int \frac{\sqrt{9-4 x^2}}{x^3} \, dx","Int[Sqrt[9 - 4*x^2]/x^3,x]","\frac{2}{3} \tanh ^{-1}\left(\frac{1}{3} \sqrt{9-4 x^2}\right)-\frac{\sqrt{9-4 x^2}}{2 x^2}","\frac{2}{3} \tanh ^{-1}\left(\frac{1}{3} \sqrt{9-4 x^2}\right)-\frac{\sqrt{9-4 x^2}}{2 x^2}",1,"-Sqrt[9 - 4*x^2]/(2*x^2) + (2*ArcTanh[Sqrt[9 - 4*x^2]/3])/3","A",4,4,15,0.2667,1,"{266, 47, 63, 206}"
461,1,18,0,0.0033959,"\int \frac{\sqrt{9-4 x^2}}{x^4} \, dx","Int[Sqrt[9 - 4*x^2]/x^4,x]","-\frac{\left(9-4 x^2\right)^{3/2}}{27 x^3}","-\frac{\left(9-4 x^2\right)^{3/2}}{27 x^3}",1,"-(9 - 4*x^2)^(3/2)/(27*x^3)","A",1,1,15,0.06667,1,"{264}"
462,1,57,0,0.0219855,"\int \frac{\sqrt{9-4 x^2}}{x^5} \, dx","Int[Sqrt[9 - 4*x^2]/x^5,x]","\frac{\sqrt{9-4 x^2}}{18 x^2}-\frac{\sqrt{9-4 x^2}}{4 x^4}+\frac{2}{27} \tanh ^{-1}\left(\frac{1}{3} \sqrt{9-4 x^2}\right)","\frac{\sqrt{9-4 x^2}}{18 x^2}-\frac{\sqrt{9-4 x^2}}{4 x^4}+\frac{2}{27} \tanh ^{-1}\left(\frac{1}{3} \sqrt{9-4 x^2}\right)",1,"-Sqrt[9 - 4*x^2]/(4*x^4) + Sqrt[9 - 4*x^2]/(18*x^2) + (2*ArcTanh[Sqrt[9 - 4*x^2]/3])/27","A",5,5,15,0.3333,1,"{266, 47, 51, 63, 206}"
463,1,46,0,0.019893,"\int x^5 \sqrt{-9+4 x^2} \, dx","Int[x^5*Sqrt[-9 + 4*x^2],x]","\frac{1}{448} \left(4 x^2-9\right)^{7/2}+\frac{9}{160} \left(4 x^2-9\right)^{5/2}+\frac{27}{64} \left(4 x^2-9\right)^{3/2}","\frac{1}{448} \left(4 x^2-9\right)^{7/2}+\frac{9}{160} \left(4 x^2-9\right)^{5/2}+\frac{27}{64} \left(4 x^2-9\right)^{3/2}",1,"(27*(-9 + 4*x^2)^(3/2))/64 + (9*(-9 + 4*x^2)^(5/2))/160 + (-9 + 4*x^2)^(7/2)/448","A",3,2,15,0.1333,1,"{266, 43}"
464,1,72,0,0.0188935,"\int x^4 \sqrt{-9+4 x^2} \, dx","Int[x^4*Sqrt[-9 + 4*x^2],x]","\frac{1}{6} \sqrt{4 x^2-9} x^5-\frac{3}{32} \sqrt{4 x^2-9} x^3-\frac{81}{256} \sqrt{4 x^2-9} x-\frac{729}{512} \tanh ^{-1}\left(\frac{2 x}{\sqrt{4 x^2-9}}\right)","\frac{1}{6} \sqrt{4 x^2-9} x^5-\frac{3}{32} \sqrt{4 x^2-9} x^3-\frac{81}{256} \sqrt{4 x^2-9} x-\frac{729}{512} \tanh ^{-1}\left(\frac{2 x}{\sqrt{4 x^2-9}}\right)",1,"(-81*x*Sqrt[-9 + 4*x^2])/256 - (3*x^3*Sqrt[-9 + 4*x^2])/32 + (x^5*Sqrt[-9 + 4*x^2])/6 - (729*ArcTanh[(2*x)/Sqrt[-9 + 4*x^2]])/512","A",5,4,15,0.2667,1,"{279, 321, 217, 206}"
465,1,31,0,0.0136232,"\int x^3 \sqrt{-9+4 x^2} \, dx","Int[x^3*Sqrt[-9 + 4*x^2],x]","\frac{1}{80} \left(4 x^2-9\right)^{5/2}+\frac{3}{16} \left(4 x^2-9\right)^{3/2}","\frac{1}{80} \left(4 x^2-9\right)^{5/2}+\frac{3}{16} \left(4 x^2-9\right)^{3/2}",1,"(3*(-9 + 4*x^2)^(3/2))/16 + (-9 + 4*x^2)^(5/2)/80","A",3,2,15,0.1333,1,"{266, 43}"
466,1,54,0,0.0132831,"\int x^2 \sqrt{-9+4 x^2} \, dx","Int[x^2*Sqrt[-9 + 4*x^2],x]","\frac{1}{4} \sqrt{4 x^2-9} x^3-\frac{9}{32} \sqrt{4 x^2-9} x-\frac{81}{64} \tanh ^{-1}\left(\frac{2 x}{\sqrt{4 x^2-9}}\right)","\frac{1}{4} \sqrt{4 x^2-9} x^3-\frac{9}{32} \sqrt{4 x^2-9} x-\frac{81}{64} \tanh ^{-1}\left(\frac{2 x}{\sqrt{4 x^2-9}}\right)",1,"(-9*x*Sqrt[-9 + 4*x^2])/32 + (x^3*Sqrt[-9 + 4*x^2])/4 - (81*ArcTanh[(2*x)/Sqrt[-9 + 4*x^2]])/64","A",4,4,15,0.2667,1,"{279, 321, 217, 206}"
467,1,15,0,0.0023235,"\int x \sqrt{-9+4 x^2} \, dx","Int[x*Sqrt[-9 + 4*x^2],x]","\frac{1}{12} \left(4 x^2-9\right)^{3/2}","\frac{1}{12} \left(4 x^2-9\right)^{3/2}",1,"(-9 + 4*x^2)^(3/2)/12","A",1,1,13,0.07692,1,"{261}"
468,1,36,0,0.0056792,"\int \sqrt{-9+4 x^2} \, dx","Int[Sqrt[-9 + 4*x^2],x]","\frac{1}{2} x \sqrt{4 x^2-9}-\frac{9}{4} \tanh ^{-1}\left(\frac{2 x}{\sqrt{4 x^2-9}}\right)","\frac{1}{2} x \sqrt{4 x^2-9}-\frac{9}{4} \tanh ^{-1}\left(\frac{2 x}{\sqrt{4 x^2-9}}\right)",1,"(x*Sqrt[-9 + 4*x^2])/2 - (9*ArcTanh[(2*x)/Sqrt[-9 + 4*x^2]])/4","A",3,3,11,0.2727,1,"{195, 217, 206}"
469,1,30,0,0.0165918,"\int \frac{\sqrt{-9+4 x^2}}{x} \, dx","Int[Sqrt[-9 + 4*x^2]/x,x]","\sqrt{4 x^2-9}-3 \tan ^{-1}\left(\frac{1}{3} \sqrt{4 x^2-9}\right)","\sqrt{4 x^2-9}-3 \tan ^{-1}\left(\frac{1}{3} \sqrt{4 x^2-9}\right)",1,"Sqrt[-9 + 4*x^2] - 3*ArcTan[Sqrt[-9 + 4*x^2]/3]","A",4,4,15,0.2667,1,"{266, 50, 63, 203}"
470,1,34,0,0.0079967,"\int \frac{\sqrt{-9+4 x^2}}{x^2} \, dx","Int[Sqrt[-9 + 4*x^2]/x^2,x]","2 \tanh ^{-1}\left(\frac{2 x}{\sqrt{4 x^2-9}}\right)-\frac{\sqrt{4 x^2-9}}{x}","2 \tanh ^{-1}\left(\frac{2 x}{\sqrt{4 x^2-9}}\right)-\frac{\sqrt{4 x^2-9}}{x}",1,"-(Sqrt[-9 + 4*x^2]/x) + 2*ArcTanh[(2*x)/Sqrt[-9 + 4*x^2]]","A",3,3,15,0.2000,1,"{277, 217, 206}"
471,1,39,0,0.016156,"\int \frac{\sqrt{-9+4 x^2}}{x^3} \, dx","Int[Sqrt[-9 + 4*x^2]/x^3,x]","\frac{2}{3} \tan ^{-1}\left(\frac{1}{3} \sqrt{4 x^2-9}\right)-\frac{\sqrt{4 x^2-9}}{2 x^2}","\frac{2}{3} \tan ^{-1}\left(\frac{1}{3} \sqrt{4 x^2-9}\right)-\frac{\sqrt{4 x^2-9}}{2 x^2}",1,"-Sqrt[-9 + 4*x^2]/(2*x^2) + (2*ArcTan[Sqrt[-9 + 4*x^2]/3])/3","A",4,4,15,0.2667,1,"{266, 47, 63, 203}"
472,1,18,0,0.0030039,"\int \frac{\sqrt{-9+4 x^2}}{x^4} \, dx","Int[Sqrt[-9 + 4*x^2]/x^4,x]","\frac{\left(4 x^2-9\right)^{3/2}}{27 x^3}","\frac{\left(4 x^2-9\right)^{3/2}}{27 x^3}",1,"(-9 + 4*x^2)^(3/2)/(27*x^3)","A",1,1,15,0.06667,1,"{264}"
473,1,57,0,0.0210753,"\int \frac{\sqrt{-9+4 x^2}}{x^5} \, dx","Int[Sqrt[-9 + 4*x^2]/x^5,x]","\frac{\sqrt{4 x^2-9}}{18 x^2}-\frac{\sqrt{4 x^2-9}}{4 x^4}+\frac{2}{27} \tan ^{-1}\left(\frac{1}{3} \sqrt{4 x^2-9}\right)","\frac{\sqrt{4 x^2-9}}{18 x^2}-\frac{\sqrt{4 x^2-9}}{4 x^4}+\frac{2}{27} \tan ^{-1}\left(\frac{1}{3} \sqrt{4 x^2-9}\right)",1,"-Sqrt[-9 + 4*x^2]/(4*x^4) + Sqrt[-9 + 4*x^2]/(18*x^2) + (2*ArcTan[Sqrt[-9 + 4*x^2]/3])/27","A",5,5,15,0.3333,1,"{266, 47, 51, 63, 203}"
474,1,46,0,0.0220785,"\int x^5 \sqrt{-9-4 x^2} \, dx","Int[x^5*Sqrt[-9 - 4*x^2],x]","-\frac{1}{448} \left(-4 x^2-9\right)^{7/2}-\frac{9}{160} \left(-4 x^2-9\right)^{5/2}-\frac{27}{64} \left(-4 x^2-9\right)^{3/2}","-\frac{1}{448} \left(-4 x^2-9\right)^{7/2}-\frac{9}{160} \left(-4 x^2-9\right)^{5/2}-\frac{27}{64} \left(-4 x^2-9\right)^{3/2}",1,"(-27*(-9 - 4*x^2)^(3/2))/64 - (9*(-9 - 4*x^2)^(5/2))/160 - (-9 - 4*x^2)^(7/2)/448","A",3,2,15,0.1333,1,"{266, 43}"
475,1,72,0,0.0208599,"\int x^4 \sqrt{-9-4 x^2} \, dx","Int[x^4*Sqrt[-9 - 4*x^2],x]","\frac{1}{6} \sqrt{-4 x^2-9} x^5+\frac{3}{32} \sqrt{-4 x^2-9} x^3-\frac{81}{256} \sqrt{-4 x^2-9} x-\frac{729}{512} \tan ^{-1}\left(\frac{2 x}{\sqrt{-4 x^2-9}}\right)","\frac{1}{6} \sqrt{-4 x^2-9} x^5+\frac{3}{32} \sqrt{-4 x^2-9} x^3-\frac{81}{256} \sqrt{-4 x^2-9} x-\frac{729}{512} \tan ^{-1}\left(\frac{2 x}{\sqrt{-4 x^2-9}}\right)",1,"(-81*x*Sqrt[-9 - 4*x^2])/256 + (3*x^3*Sqrt[-9 - 4*x^2])/32 + (x^5*Sqrt[-9 - 4*x^2])/6 - (729*ArcTan[(2*x)/Sqrt[-9 - 4*x^2]])/512","A",5,4,15,0.2667,1,"{279, 321, 217, 203}"
476,1,31,0,0.0139497,"\int x^3 \sqrt{-9-4 x^2} \, dx","Int[x^3*Sqrt[-9 - 4*x^2],x]","\frac{1}{80} \left(-4 x^2-9\right)^{5/2}+\frac{3}{16} \left(-4 x^2-9\right)^{3/2}","\frac{1}{80} \left(-4 x^2-9\right)^{5/2}+\frac{3}{16} \left(-4 x^2-9\right)^{3/2}",1,"(3*(-9 - 4*x^2)^(3/2))/16 + (-9 - 4*x^2)^(5/2)/80","A",3,2,15,0.1333,1,"{266, 43}"
477,1,54,0,0.0136314,"\int x^2 \sqrt{-9-4 x^2} \, dx","Int[x^2*Sqrt[-9 - 4*x^2],x]","\frac{1}{4} \sqrt{-4 x^2-9} x^3+\frac{9}{32} \sqrt{-4 x^2-9} x+\frac{81}{64} \tan ^{-1}\left(\frac{2 x}{\sqrt{-4 x^2-9}}\right)","\frac{1}{4} \sqrt{-4 x^2-9} x^3+\frac{9}{32} \sqrt{-4 x^2-9} x+\frac{81}{64} \tan ^{-1}\left(\frac{2 x}{\sqrt{-4 x^2-9}}\right)",1,"(9*x*Sqrt[-9 - 4*x^2])/32 + (x^3*Sqrt[-9 - 4*x^2])/4 + (81*ArcTan[(2*x)/Sqrt[-9 - 4*x^2]])/64","A",4,4,15,0.2667,1,"{279, 321, 217, 203}"
478,1,15,0,0.0024286,"\int x \sqrt{-9-4 x^2} \, dx","Int[x*Sqrt[-9 - 4*x^2],x]","-\frac{1}{12} \left(-4 x^2-9\right)^{3/2}","-\frac{1}{12} \left(-4 x^2-9\right)^{3/2}",1,"-(-9 - 4*x^2)^(3/2)/12","A",1,1,13,0.07692,1,"{261}"
479,1,36,0,0.0057094,"\int \sqrt{-9-4 x^2} \, dx","Int[Sqrt[-9 - 4*x^2],x]","\frac{1}{2} x \sqrt{-4 x^2-9}-\frac{9}{4} \tan ^{-1}\left(\frac{2 x}{\sqrt{-4 x^2-9}}\right)","\frac{1}{2} x \sqrt{-4 x^2-9}-\frac{9}{4} \tan ^{-1}\left(\frac{2 x}{\sqrt{-4 x^2-9}}\right)",1,"(x*Sqrt[-9 - 4*x^2])/2 - (9*ArcTan[(2*x)/Sqrt[-9 - 4*x^2]])/4","A",3,3,11,0.2727,1,"{195, 217, 203}"
480,1,30,0,0.0151617,"\int \frac{\sqrt{-9-4 x^2}}{x} \, dx","Int[Sqrt[-9 - 4*x^2]/x,x]","\sqrt{-4 x^2-9}-3 \tan ^{-1}\left(\frac{1}{3} \sqrt{-4 x^2-9}\right)","\sqrt{-4 x^2-9}-3 \tan ^{-1}\left(\frac{1}{3} \sqrt{-4 x^2-9}\right)",1,"Sqrt[-9 - 4*x^2] - 3*ArcTan[Sqrt[-9 - 4*x^2]/3]","A",4,4,15,0.2667,1,"{266, 50, 63, 204}"
481,1,34,0,0.0076738,"\int \frac{\sqrt{-9-4 x^2}}{x^2} \, dx","Int[Sqrt[-9 - 4*x^2]/x^2,x]","-\frac{\sqrt{-4 x^2-9}}{x}-2 \tan ^{-1}\left(\frac{2 x}{\sqrt{-4 x^2-9}}\right)","-\frac{\sqrt{-4 x^2-9}}{x}-2 \tan ^{-1}\left(\frac{2 x}{\sqrt{-4 x^2-9}}\right)",1,"-(Sqrt[-9 - 4*x^2]/x) - 2*ArcTan[(2*x)/Sqrt[-9 - 4*x^2]]","A",3,3,15,0.2000,1,"{277, 217, 203}"
482,1,39,0,0.0161465,"\int \frac{\sqrt{-9-4 x^2}}{x^3} \, dx","Int[Sqrt[-9 - 4*x^2]/x^3,x]","-\frac{\sqrt{-4 x^2-9}}{2 x^2}-\frac{2}{3} \tan ^{-1}\left(\frac{1}{3} \sqrt{-4 x^2-9}\right)","-\frac{\sqrt{-4 x^2-9}}{2 x^2}-\frac{2}{3} \tan ^{-1}\left(\frac{1}{3} \sqrt{-4 x^2-9}\right)",1,"-Sqrt[-9 - 4*x^2]/(2*x^2) - (2*ArcTan[Sqrt[-9 - 4*x^2]/3])/3","A",4,4,15,0.2667,1,"{266, 47, 63, 204}"
483,1,18,0,0.003333,"\int \frac{\sqrt{-9-4 x^2}}{x^4} \, dx","Int[Sqrt[-9 - 4*x^2]/x^4,x]","\frac{\left(-4 x^2-9\right)^{3/2}}{27 x^3}","\frac{\left(-4 x^2-9\right)^{3/2}}{27 x^3}",1,"(-9 - 4*x^2)^(3/2)/(27*x^3)","A",1,1,15,0.06667,1,"{264}"
484,1,57,0,0.0211147,"\int \frac{\sqrt{-9-4 x^2}}{x^5} \, dx","Int[Sqrt[-9 - 4*x^2]/x^5,x]","-\frac{\sqrt{-4 x^2-9}}{18 x^2}-\frac{\sqrt{-4 x^2-9}}{4 x^4}+\frac{2}{27} \tan ^{-1}\left(\frac{1}{3} \sqrt{-4 x^2-9}\right)","-\frac{\sqrt{-4 x^2-9}}{18 x^2}-\frac{\sqrt{-4 x^2-9}}{4 x^4}+\frac{2}{27} \tan ^{-1}\left(\frac{1}{3} \sqrt{-4 x^2-9}\right)",1,"-Sqrt[-9 - 4*x^2]/(4*x^4) - Sqrt[-9 - 4*x^2]/(18*x^2) + (2*ArcTan[Sqrt[-9 - 4*x^2]/3])/27","A",5,5,15,0.3333,1,"{266, 47, 51, 63, 204}"
485,1,56,0,0.0307414,"\int \frac{x^5}{\sqrt{a+b x^2}} \, dx","Int[x^5/Sqrt[a + b*x^2],x]","\frac{a^2 \sqrt{a+b x^2}}{b^3}+\frac{\left(a+b x^2\right)^{5/2}}{5 b^3}-\frac{2 a \left(a+b x^2\right)^{3/2}}{3 b^3}","\frac{a^2 \sqrt{a+b x^2}}{b^3}+\frac{\left(a+b x^2\right)^{5/2}}{5 b^3}-\frac{2 a \left(a+b x^2\right)^{3/2}}{3 b^3}",1,"(a^2*Sqrt[a + b*x^2])/b^3 - (2*a*(a + b*x^2)^(3/2))/(3*b^3) + (a + b*x^2)^(5/2)/(5*b^3)","A",3,2,15,0.1333,1,"{266, 43}"
486,1,73,0,0.0195522,"\int \frac{x^4}{\sqrt{a+b x^2}} \, dx","Int[x^4/Sqrt[a + b*x^2],x]","\frac{3 a^2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{8 b^{5/2}}-\frac{3 a x \sqrt{a+b x^2}}{8 b^2}+\frac{x^3 \sqrt{a+b x^2}}{4 b}","\frac{3 a^2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{8 b^{5/2}}-\frac{3 a x \sqrt{a+b x^2}}{8 b^2}+\frac{x^3 \sqrt{a+b x^2}}{4 b}",1,"(-3*a*x*Sqrt[a + b*x^2])/(8*b^2) + (x^3*Sqrt[a + b*x^2])/(4*b) + (3*a^2*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(8*b^(5/2))","A",4,3,15,0.2000,1,"{321, 217, 206}"
487,1,36,0,0.022349,"\int \frac{x^3}{\sqrt{a+b x^2}} \, dx","Int[x^3/Sqrt[a + b*x^2],x]","\frac{\left(a+b x^2\right)^{3/2}}{3 b^2}-\frac{a \sqrt{a+b x^2}}{b^2}","\frac{\left(a+b x^2\right)^{3/2}}{3 b^2}-\frac{a \sqrt{a+b x^2}}{b^2}",1,"-((a*Sqrt[a + b*x^2])/b^2) + (a + b*x^2)^(3/2)/(3*b^2)","A",3,2,15,0.1333,1,"{266, 43}"
488,1,49,0,0.0124689,"\int \frac{x^2}{\sqrt{a+b x^2}} \, dx","Int[x^2/Sqrt[a + b*x^2],x]","\frac{x \sqrt{a+b x^2}}{2 b}-\frac{a \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{2 b^{3/2}}","\frac{x \sqrt{a+b x^2}}{2 b}-\frac{a \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{2 b^{3/2}}",1,"(x*Sqrt[a + b*x^2])/(2*b) - (a*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(2*b^(3/2))","A",3,3,15,0.2000,1,"{321, 217, 206}"
489,1,15,0,0.0033863,"\int \frac{x}{\sqrt{a+b x^2}} \, dx","Int[x/Sqrt[a + b*x^2],x]","\frac{\sqrt{a+b x^2}}{b}","\frac{\sqrt{a+b x^2}}{b}",1,"Sqrt[a + b*x^2]/b","A",1,1,13,0.07692,1,"{261}"
490,1,25,0,0.0055332,"\int \frac{1}{\sqrt{a+b x^2}} \, dx","Int[1/Sqrt[a + b*x^2],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{\sqrt{b}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{\sqrt{b}}",1,"ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]]/Sqrt[b]","A",2,2,11,0.1818,1,"{217, 206}"
491,1,25,0,0.0172745,"\int \frac{1}{x \sqrt{a+b x^2}} \, dx","Int[1/(x*Sqrt[a + b*x^2]),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{\sqrt{a}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{\sqrt{a}}",1,"-(ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]]/Sqrt[a])","A",3,3,15,0.2000,1,"{266, 63, 208}"
492,1,19,0,0.0045501,"\int \frac{1}{x^2 \sqrt{a+b x^2}} \, dx","Int[1/(x^2*Sqrt[a + b*x^2]),x]","-\frac{\sqrt{a+b x^2}}{a x}","-\frac{\sqrt{a+b x^2}}{a x}",1,"-(Sqrt[a + b*x^2]/(a*x))","A",1,1,15,0.06667,1,"{264}"
493,1,50,0,0.0261624,"\int \frac{1}{x^3 \sqrt{a+b x^2}} \, dx","Int[1/(x^3*Sqrt[a + b*x^2]),x]","\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{2 a^{3/2}}-\frac{\sqrt{a+b x^2}}{2 a x^2}","\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{2 a^{3/2}}-\frac{\sqrt{a+b x^2}}{2 a x^2}",1,"-Sqrt[a + b*x^2]/(2*a*x^2) + (b*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(2*a^(3/2))","A",4,4,15,0.2667,1,"{266, 51, 63, 208}"
494,1,44,0,0.0103251,"\int \frac{1}{x^4 \sqrt{a+b x^2}} \, dx","Int[1/(x^4*Sqrt[a + b*x^2]),x]","\frac{2 b \sqrt{a+b x^2}}{3 a^2 x}-\frac{\sqrt{a+b x^2}}{3 a x^3}","\frac{2 b \sqrt{a+b x^2}}{3 a^2 x}-\frac{\sqrt{a+b x^2}}{3 a x^3}",1,"-Sqrt[a + b*x^2]/(3*a*x^3) + (2*b*Sqrt[a + b*x^2])/(3*a^2*x)","A",2,2,15,0.1333,1,"{271, 264}"
495,1,74,0,0.0376781,"\int \frac{1}{x^5 \sqrt{a+b x^2}} \, dx","Int[1/(x^5*Sqrt[a + b*x^2]),x]","-\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{8 a^{5/2}}+\frac{3 b \sqrt{a+b x^2}}{8 a^2 x^2}-\frac{\sqrt{a+b x^2}}{4 a x^4}","-\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{8 a^{5/2}}+\frac{3 b \sqrt{a+b x^2}}{8 a^2 x^2}-\frac{\sqrt{a+b x^2}}{4 a x^4}",1,"-Sqrt[a + b*x^2]/(4*a*x^4) + (3*b*Sqrt[a + b*x^2])/(8*a^2*x^2) - (3*b^2*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(8*a^(5/2))","A",5,4,15,0.2667,1,"{266, 51, 63, 208}"
496,1,55,0,0.0327409,"\int \frac{x^5}{\left(a+b x^2\right)^{3/2}} \, dx","Int[x^5/(a + b*x^2)^(3/2),x]","-\frac{a^2}{b^3 \sqrt{a+b x^2}}-\frac{2 a \sqrt{a+b x^2}}{b^3}+\frac{\left(a+b x^2\right)^{3/2}}{3 b^3}","-\frac{a^2}{b^3 \sqrt{a+b x^2}}-\frac{2 a \sqrt{a+b x^2}}{b^3}+\frac{\left(a+b x^2\right)^{3/2}}{3 b^3}",1,"-(a^2/(b^3*Sqrt[a + b*x^2])) - (2*a*Sqrt[a + b*x^2])/b^3 + (a + b*x^2)^(3/2)/(3*b^3)","A",3,2,15,0.1333,1,"{266, 43}"
497,1,68,0,0.0225984,"\int \frac{x^4}{\left(a+b x^2\right)^{3/2}} \, dx","Int[x^4/(a + b*x^2)^(3/2),x]","\frac{3 x \sqrt{a+b x^2}}{2 b^2}-\frac{3 a \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{2 b^{5/2}}-\frac{x^3}{b \sqrt{a+b x^2}}","\frac{3 x \sqrt{a+b x^2}}{2 b^2}-\frac{3 a \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{2 b^{5/2}}-\frac{x^3}{b \sqrt{a+b x^2}}",1,"-(x^3/(b*Sqrt[a + b*x^2])) + (3*x*Sqrt[a + b*x^2])/(2*b^2) - (3*a*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(2*b^(5/2))","A",4,4,15,0.2667,1,"{288, 321, 217, 206}"
498,1,32,0,0.0223081,"\int \frac{x^3}{\left(a+b x^2\right)^{3/2}} \, dx","Int[x^3/(a + b*x^2)^(3/2),x]","\frac{a}{b^2 \sqrt{a+b x^2}}+\frac{\sqrt{a+b x^2}}{b^2}","\frac{a}{b^2 \sqrt{a+b x^2}}+\frac{\sqrt{a+b x^2}}{b^2}",1,"a/(b^2*Sqrt[a + b*x^2]) + Sqrt[a + b*x^2]/b^2","A",3,2,15,0.1333,1,"{266, 43}"
499,1,43,0,0.0131784,"\int \frac{x^2}{\left(a+b x^2\right)^{3/2}} \, dx","Int[x^2/(a + b*x^2)^(3/2),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{b^{3/2}}-\frac{x}{b \sqrt{a+b x^2}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{b^{3/2}}-\frac{x}{b \sqrt{a+b x^2}}",1,"-(x/(b*Sqrt[a + b*x^2])) + ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]]/b^(3/2)","A",3,3,15,0.2000,1,"{288, 217, 206}"
500,1,16,0,0.0033578,"\int \frac{x}{\left(a+b x^2\right)^{3/2}} \, dx","Int[x/(a + b*x^2)^(3/2),x]","-\frac{1}{b \sqrt{a+b x^2}}","-\frac{1}{b \sqrt{a+b x^2}}",1,"-(1/(b*Sqrt[a + b*x^2]))","A",1,1,13,0.07692,1,"{261}"
501,1,16,0,0.0018622,"\int \frac{1}{\left(a+b x^2\right)^{3/2}} \, dx","Int[(a + b*x^2)^(-3/2),x]","\frac{x}{a \sqrt{a+b x^2}}","\frac{x}{a \sqrt{a+b x^2}}",1,"x/(a*Sqrt[a + b*x^2])","A",1,1,11,0.09091,1,"{191}"
502,1,41,0,0.027081,"\int \frac{1}{x \left(a+b x^2\right)^{3/2}} \, dx","Int[1/(x*(a + b*x^2)^(3/2)),x]","\frac{1}{a \sqrt{a+b x^2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{a^{3/2}}","\frac{1}{a \sqrt{a+b x^2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{a^{3/2}}",1,"1/(a*Sqrt[a + b*x^2]) - ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]]/a^(3/2)","A",4,4,15,0.2667,1,"{266, 51, 63, 208}"
503,1,38,0,0.0079569,"\int \frac{1}{x^2 \left(a+b x^2\right)^{3/2}} \, dx","Int[1/(x^2*(a + b*x^2)^(3/2)),x]","-\frac{2 b x}{a^2 \sqrt{a+b x^2}}-\frac{1}{a x \sqrt{a+b x^2}}","-\frac{2 b x}{a^2 \sqrt{a+b x^2}}-\frac{1}{a x \sqrt{a+b x^2}}",1,"-(1/(a*x*Sqrt[a + b*x^2])) - (2*b*x)/(a^2*Sqrt[a + b*x^2])","A",2,2,15,0.1333,1,"{271, 191}"
504,1,68,0,0.0390216,"\int \frac{1}{x^3 \left(a+b x^2\right)^{3/2}} \, dx","Int[1/(x^3*(a + b*x^2)^(3/2)),x]","-\frac{3 \sqrt{a+b x^2}}{2 a^2 x^2}+\frac{3 b \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{2 a^{5/2}}+\frac{1}{a x^2 \sqrt{a+b x^2}}","-\frac{3 b}{2 a^2 \sqrt{a+b x^2}}+\frac{3 b \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{2 a^{5/2}}-\frac{1}{2 a x^2 \sqrt{a+b x^2}}",1,"1/(a*x^2*Sqrt[a + b*x^2]) - (3*Sqrt[a + b*x^2])/(2*a^2*x^2) + (3*b*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(2*a^(5/2))","A",5,4,15,0.2667,1,"{266, 51, 63, 208}"
505,1,66,0,0.0157467,"\int \frac{1}{x^4 \left(a+b x^2\right)^{3/2}} \, dx","Int[1/(x^4*(a + b*x^2)^(3/2)),x]","\frac{8 b^2 x}{3 a^3 \sqrt{a+b x^2}}+\frac{4 b}{3 a^2 x \sqrt{a+b x^2}}-\frac{1}{3 a x^3 \sqrt{a+b x^2}}","\frac{8 b^2 x}{3 a^3 \sqrt{a+b x^2}}+\frac{4 b}{3 a^2 x \sqrt{a+b x^2}}-\frac{1}{3 a x^3 \sqrt{a+b x^2}}",1,"-1/(3*a*x^3*Sqrt[a + b*x^2]) + (4*b)/(3*a^2*x*Sqrt[a + b*x^2]) + (8*b^2*x)/(3*a^3*Sqrt[a + b*x^2])","A",3,2,15,0.1333,1,"{271, 191}"
506,1,91,0,0.0291006,"\int \frac{x^6}{\left(a+b x^2\right)^{5/2}} \, dx","Int[x^6/(a + b*x^2)^(5/2),x]","-\frac{5 x^3}{3 b^2 \sqrt{a+b x^2}}+\frac{5 x \sqrt{a+b x^2}}{2 b^3}-\frac{5 a \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{2 b^{7/2}}-\frac{x^5}{3 b \left(a+b x^2\right)^{3/2}}","-\frac{5 x^3}{3 b^2 \sqrt{a+b x^2}}+\frac{5 x \sqrt{a+b x^2}}{2 b^3}-\frac{5 a \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{2 b^{7/2}}-\frac{x^5}{3 b \left(a+b x^2\right)^{3/2}}",1,"-x^5/(3*b*(a + b*x^2)^(3/2)) - (5*x^3)/(3*b^2*Sqrt[a + b*x^2]) + (5*x*Sqrt[a + b*x^2])/(2*b^3) - (5*a*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(2*b^(7/2))","A",5,4,15,0.2667,1,"{288, 321, 217, 206}"
507,1,54,0,0.0314975,"\int \frac{x^5}{\left(a+b x^2\right)^{5/2}} \, dx","Int[x^5/(a + b*x^2)^(5/2),x]","-\frac{a^2}{3 b^3 \left(a+b x^2\right)^{3/2}}+\frac{2 a}{b^3 \sqrt{a+b x^2}}+\frac{\sqrt{a+b x^2}}{b^3}","-\frac{a^2}{3 b^3 \left(a+b x^2\right)^{3/2}}+\frac{2 a}{b^3 \sqrt{a+b x^2}}+\frac{\sqrt{a+b x^2}}{b^3}",1,"-a^2/(3*b^3*(a + b*x^2)^(3/2)) + (2*a)/(b^3*Sqrt[a + b*x^2]) + Sqrt[a + b*x^2]/b^3","A",3,2,15,0.1333,1,"{266, 43}"
508,1,64,0,0.0204295,"\int \frac{x^4}{\left(a+b x^2\right)^{5/2}} \, dx","Int[x^4/(a + b*x^2)^(5/2),x]","-\frac{x}{b^2 \sqrt{a+b x^2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{b^{5/2}}-\frac{x^3}{3 b \left(a+b x^2\right)^{3/2}}","-\frac{x}{b^2 \sqrt{a+b x^2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{b^{5/2}}-\frac{x^3}{3 b \left(a+b x^2\right)^{3/2}}",1,"-x^3/(3*b*(a + b*x^2)^(3/2)) - x/(b^2*Sqrt[a + b*x^2]) + ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]]/b^(5/2)","A",4,3,15,0.2000,1,"{288, 217, 206}"
509,1,36,0,0.0215647,"\int \frac{x^3}{\left(a+b x^2\right)^{5/2}} \, dx","Int[x^3/(a + b*x^2)^(5/2),x]","\frac{a}{3 b^2 \left(a+b x^2\right)^{3/2}}-\frac{1}{b^2 \sqrt{a+b x^2}}","\frac{a}{3 b^2 \left(a+b x^2\right)^{3/2}}-\frac{1}{b^2 \sqrt{a+b x^2}}",1,"a/(3*b^2*(a + b*x^2)^(3/2)) - 1/(b^2*Sqrt[a + b*x^2])","A",3,2,15,0.1333,1,"{266, 43}"
510,1,21,0,0.0045606,"\int \frac{x^2}{\left(a+b x^2\right)^{5/2}} \, dx","Int[x^2/(a + b*x^2)^(5/2),x]","\frac{x^3}{3 a \left(a+b x^2\right)^{3/2}}","\frac{x^3}{3 a \left(a+b x^2\right)^{3/2}}",1,"x^3/(3*a*(a + b*x^2)^(3/2))","A",1,1,15,0.06667,1,"{264}"
511,1,18,0,0.0034343,"\int \frac{x}{\left(a+b x^2\right)^{5/2}} \, dx","Int[x/(a + b*x^2)^(5/2),x]","-\frac{1}{3 b \left(a+b x^2\right)^{3/2}}","-\frac{1}{3 b \left(a+b x^2\right)^{3/2}}",1,"-1/(3*b*(a + b*x^2)^(3/2))","A",1,1,13,0.07692,1,"{261}"
512,1,39,0,0.0051256,"\int \frac{1}{\left(a+b x^2\right)^{5/2}} \, dx","Int[(a + b*x^2)^(-5/2),x]","\frac{2 x}{3 a^2 \sqrt{a+b x^2}}+\frac{x}{3 a \left(a+b x^2\right)^{3/2}}","\frac{2 x}{3 a^2 \sqrt{a+b x^2}}+\frac{x}{3 a \left(a+b x^2\right)^{3/2}}",1,"x/(3*a*(a + b*x^2)^(3/2)) + (2*x)/(3*a^2*Sqrt[a + b*x^2])","A",2,2,11,0.1818,1,"{192, 191}"
513,1,59,0,0.0349385,"\int \frac{1}{x \left(a+b x^2\right)^{5/2}} \, dx","Int[1/(x*(a + b*x^2)^(5/2)),x]","\frac{1}{a^2 \sqrt{a+b x^2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{a^{5/2}}+\frac{1}{3 a \left(a+b x^2\right)^{3/2}}","\frac{1}{a^2 \sqrt{a+b x^2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{a^{5/2}}+\frac{1}{3 a \left(a+b x^2\right)^{3/2}}",1,"1/(3*a*(a + b*x^2)^(3/2)) + 1/(a^2*Sqrt[a + b*x^2]) - ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]]/a^(5/2)","A",5,4,15,0.2667,1,"{266, 51, 63, 208}"
514,1,60,0,0.0135271,"\int \frac{1}{x^2 \left(a+b x^2\right)^{5/2}} \, dx","Int[1/(x^2*(a + b*x^2)^(5/2)),x]","-\frac{8 b x}{3 a^3 \sqrt{a+b x^2}}-\frac{4 b x}{3 a^2 \left(a+b x^2\right)^{3/2}}-\frac{1}{a x \left(a+b x^2\right)^{3/2}}","-\frac{8 b x}{3 a^3 \sqrt{a+b x^2}}-\frac{4 b x}{3 a^2 \left(a+b x^2\right)^{3/2}}-\frac{1}{a x \left(a+b x^2\right)^{3/2}}",1,"-(1/(a*x*(a + b*x^2)^(3/2))) - (4*b*x)/(3*a^2*(a + b*x^2)^(3/2)) - (8*b*x)/(3*a^3*Sqrt[a + b*x^2])","A",3,3,15,0.2000,1,"{271, 192, 191}"
515,1,92,0,0.0495339,"\int \frac{1}{x^3 \left(a+b x^2\right)^{5/2}} \, dx","Int[1/(x^3*(a + b*x^2)^(5/2)),x]","-\frac{5 \sqrt{a+b x^2}}{2 a^3 x^2}+\frac{5}{3 a^2 x^2 \sqrt{a+b x^2}}+\frac{5 b \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{2 a^{7/2}}+\frac{1}{3 a x^2 \left(a+b x^2\right)^{3/2}}","-\frac{5 b}{2 a^3 \sqrt{a+b x^2}}-\frac{5 b}{6 a^2 \left(a+b x^2\right)^{3/2}}+\frac{5 b \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{2 a^{7/2}}-\frac{1}{2 a x^2 \left(a+b x^2\right)^{3/2}}",1,"1/(3*a*x^2*(a + b*x^2)^(3/2)) + 5/(3*a^2*x^2*Sqrt[a + b*x^2]) - (5*Sqrt[a + b*x^2])/(2*a^3*x^2) + (5*b*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(2*a^(7/2))","A",6,4,15,0.2667,1,"{266, 51, 63, 208}"
516,1,86,0,0.0224556,"\int \frac{1}{x^4 \left(a+b x^2\right)^{5/2}} \, dx","Int[1/(x^4*(a + b*x^2)^(5/2)),x]","\frac{16 b^2 x}{3 a^4 \sqrt{a+b x^2}}+\frac{8 b^2 x}{3 a^3 \left(a+b x^2\right)^{3/2}}+\frac{2 b}{a^2 x \left(a+b x^2\right)^{3/2}}-\frac{1}{3 a x^3 \left(a+b x^2\right)^{3/2}}","\frac{16 b^2 x}{3 a^4 \sqrt{a+b x^2}}+\frac{8 b^2 x}{3 a^3 \left(a+b x^2\right)^{3/2}}+\frac{2 b}{a^2 x \left(a+b x^2\right)^{3/2}}-\frac{1}{3 a x^3 \left(a+b x^2\right)^{3/2}}",1,"-1/(3*a*x^3*(a + b*x^2)^(3/2)) + (2*b)/(a^2*x*(a + b*x^2)^(3/2)) + (8*b^2*x)/(3*a^3*(a + b*x^2)^(3/2)) + (16*b^2*x)/(3*a^4*Sqrt[a + b*x^2])","A",4,3,15,0.2000,1,"{271, 192, 191}"
517,1,131,0,0.0535724,"\int \frac{x^{10}}{\left(a+b x^2\right)^{9/2}} \, dx","Int[x^10/(a + b*x^2)^(9/2),x]","-\frac{9 x^7}{35 b^2 \left(a+b x^2\right)^{5/2}}-\frac{3 x^5}{5 b^3 \left(a+b x^2\right)^{3/2}}-\frac{3 x^3}{b^4 \sqrt{a+b x^2}}+\frac{9 x \sqrt{a+b x^2}}{2 b^5}-\frac{9 a \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{2 b^{11/2}}-\frac{x^9}{7 b \left(a+b x^2\right)^{7/2}}","-\frac{9 x^7}{35 b^2 \left(a+b x^2\right)^{5/2}}-\frac{3 x^5}{5 b^3 \left(a+b x^2\right)^{3/2}}-\frac{3 x^3}{b^4 \sqrt{a+b x^2}}+\frac{9 x \sqrt{a+b x^2}}{2 b^5}-\frac{9 a \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{2 b^{11/2}}-\frac{x^9}{7 b \left(a+b x^2\right)^{7/2}}",1,"-x^9/(7*b*(a + b*x^2)^(7/2)) - (9*x^7)/(35*b^2*(a + b*x^2)^(5/2)) - (3*x^5)/(5*b^3*(a + b*x^2)^(3/2)) - (3*x^3)/(b^4*Sqrt[a + b*x^2]) + (9*x*Sqrt[a + b*x^2])/(2*b^5) - (9*a*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(2*b^(11/2))","A",7,4,15,0.2667,1,"{288, 321, 217, 206}"
518,1,94,0,0.0531119,"\int \frac{x^9}{\left(a+b x^2\right)^{9/2}} \, dx","Int[x^9/(a + b*x^2)^(9/2),x]","-\frac{a^4}{7 b^5 \left(a+b x^2\right)^{7/2}}+\frac{4 a^3}{5 b^5 \left(a+b x^2\right)^{5/2}}-\frac{2 a^2}{b^5 \left(a+b x^2\right)^{3/2}}+\frac{4 a}{b^5 \sqrt{a+b x^2}}+\frac{\sqrt{a+b x^2}}{b^5}","-\frac{a^4}{7 b^5 \left(a+b x^2\right)^{7/2}}+\frac{4 a^3}{5 b^5 \left(a+b x^2\right)^{5/2}}-\frac{2 a^2}{b^5 \left(a+b x^2\right)^{3/2}}+\frac{4 a}{b^5 \sqrt{a+b x^2}}+\frac{\sqrt{a+b x^2}}{b^5}",1,"-a^4/(7*b^5*(a + b*x^2)^(7/2)) + (4*a^3)/(5*b^5*(a + b*x^2)^(5/2)) - (2*a^2)/(b^5*(a + b*x^2)^(3/2)) + (4*a)/(b^5*Sqrt[a + b*x^2]) + Sqrt[a + b*x^2]/b^5","A",3,2,15,0.1333,1,"{266, 43}"
519,1,106,0,0.0419398,"\int \frac{x^8}{\left(a+b x^2\right)^{9/2}} \, dx","Int[x^8/(a + b*x^2)^(9/2),x]","-\frac{x^5}{5 b^2 \left(a+b x^2\right)^{5/2}}-\frac{x^3}{3 b^3 \left(a+b x^2\right)^{3/2}}-\frac{x}{b^4 \sqrt{a+b x^2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{b^{9/2}}-\frac{x^7}{7 b \left(a+b x^2\right)^{7/2}}","-\frac{x^5}{5 b^2 \left(a+b x^2\right)^{5/2}}-\frac{x^3}{3 b^3 \left(a+b x^2\right)^{3/2}}-\frac{x}{b^4 \sqrt{a+b x^2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{b^{9/2}}-\frac{x^7}{7 b \left(a+b x^2\right)^{7/2}}",1,"-x^7/(7*b*(a + b*x^2)^(7/2)) - x^5/(5*b^2*(a + b*x^2)^(5/2)) - x^3/(3*b^3*(a + b*x^2)^(3/2)) - x/(b^4*Sqrt[a + b*x^2]) + ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]]/b^(9/2)","A",6,3,15,0.2000,1,"{288, 217, 206}"
520,1,75,0,0.0447213,"\int \frac{x^7}{\left(a+b x^2\right)^{9/2}} \, dx","Int[x^7/(a + b*x^2)^(9/2),x]","\frac{a^3}{7 b^4 \left(a+b x^2\right)^{7/2}}-\frac{3 a^2}{5 b^4 \left(a+b x^2\right)^{5/2}}+\frac{a}{b^4 \left(a+b x^2\right)^{3/2}}-\frac{1}{b^4 \sqrt{a+b x^2}}","\frac{a^3}{7 b^4 \left(a+b x^2\right)^{7/2}}-\frac{3 a^2}{5 b^4 \left(a+b x^2\right)^{5/2}}+\frac{a}{b^4 \left(a+b x^2\right)^{3/2}}-\frac{1}{b^4 \sqrt{a+b x^2}}",1,"a^3/(7*b^4*(a + b*x^2)^(7/2)) - (3*a^2)/(5*b^4*(a + b*x^2)^(5/2)) + a/(b^4*(a + b*x^2)^(3/2)) - 1/(b^4*Sqrt[a + b*x^2])","A",3,2,15,0.1333,1,"{266, 43}"
521,1,21,0,0.0045666,"\int \frac{x^6}{\left(a+b x^2\right)^{9/2}} \, dx","Int[x^6/(a + b*x^2)^(9/2),x]","\frac{x^7}{7 a \left(a+b x^2\right)^{7/2}}","\frac{x^7}{7 a \left(a+b x^2\right)^{7/2}}",1,"x^7/(7*a*(a + b*x^2)^(7/2))","A",1,1,15,0.06667,1,"{264}"
522,1,59,0,0.033334,"\int \frac{x^5}{\left(a+b x^2\right)^{9/2}} \, dx","Int[x^5/(a + b*x^2)^(9/2),x]","-\frac{a^2}{7 b^3 \left(a+b x^2\right)^{7/2}}+\frac{2 a}{5 b^3 \left(a+b x^2\right)^{5/2}}-\frac{1}{3 b^3 \left(a+b x^2\right)^{3/2}}","-\frac{a^2}{7 b^3 \left(a+b x^2\right)^{7/2}}+\frac{2 a}{5 b^3 \left(a+b x^2\right)^{5/2}}-\frac{1}{3 b^3 \left(a+b x^2\right)^{3/2}}",1,"-a^2/(7*b^3*(a + b*x^2)^(7/2)) + (2*a)/(5*b^3*(a + b*x^2)^(5/2)) - 1/(3*b^3*(a + b*x^2)^(3/2))","A",3,2,15,0.1333,1,"{266, 43}"
523,1,44,0,0.0106348,"\int \frac{x^4}{\left(a+b x^2\right)^{9/2}} \, dx","Int[x^4/(a + b*x^2)^(9/2),x]","\frac{2 b x^7}{35 a^2 \left(a+b x^2\right)^{7/2}}+\frac{x^5}{5 a \left(a+b x^2\right)^{7/2}}","\frac{2 b x^7}{35 a^2 \left(a+b x^2\right)^{7/2}}+\frac{x^5}{5 a \left(a+b x^2\right)^{7/2}}",1,"x^5/(5*a*(a + b*x^2)^(7/2)) + (2*b*x^7)/(35*a^2*(a + b*x^2)^(7/2))","A",2,2,15,0.1333,1,"{271, 264}"
524,1,38,0,0.0232085,"\int \frac{x^3}{\left(a+b x^2\right)^{9/2}} \, dx","Int[x^3/(a + b*x^2)^(9/2),x]","\frac{a}{7 b^2 \left(a+b x^2\right)^{7/2}}-\frac{1}{5 b^2 \left(a+b x^2\right)^{5/2}}","\frac{a}{7 b^2 \left(a+b x^2\right)^{7/2}}-\frac{1}{5 b^2 \left(a+b x^2\right)^{5/2}}",1,"a/(7*b^2*(a + b*x^2)^(7/2)) - 1/(5*b^2*(a + b*x^2)^(5/2))","A",3,2,15,0.1333,1,"{266, 43}"
525,1,68,0,0.0205032,"\int \frac{x^2}{\left(a+b x^2\right)^{9/2}} \, dx","Int[x^2/(a + b*x^2)^(9/2),x]","\frac{8 b^2 x^7}{105 a^3 \left(a+b x^2\right)^{7/2}}+\frac{4 b x^5}{15 a^2 \left(a+b x^2\right)^{7/2}}+\frac{x^3}{3 a \left(a+b x^2\right)^{7/2}}","\frac{8 b^2 x^7}{105 a^3 \left(a+b x^2\right)^{7/2}}+\frac{4 b x^5}{15 a^2 \left(a+b x^2\right)^{7/2}}+\frac{x^3}{3 a \left(a+b x^2\right)^{7/2}}",1,"x^3/(3*a*(a + b*x^2)^(7/2)) + (4*b*x^5)/(15*a^2*(a + b*x^2)^(7/2)) + (8*b^2*x^7)/(105*a^3*(a + b*x^2)^(7/2))","A",3,2,15,0.1333,1,"{271, 264}"
526,1,18,0,0.0037261,"\int \frac{x}{\left(a+b x^2\right)^{9/2}} \, dx","Int[x/(a + b*x^2)^(9/2),x]","-\frac{1}{7 b \left(a+b x^2\right)^{7/2}}","-\frac{1}{7 b \left(a+b x^2\right)^{7/2}}",1,"-1/(7*b*(a + b*x^2)^(7/2))","A",1,1,13,0.07692,1,"{261}"
527,1,77,0,0.0160159,"\int \frac{1}{\left(a+b x^2\right)^{9/2}} \, dx","Int[(a + b*x^2)^(-9/2),x]","\frac{16 x}{35 a^4 \sqrt{a+b x^2}}+\frac{8 x}{35 a^3 \left(a+b x^2\right)^{3/2}}+\frac{6 x}{35 a^2 \left(a+b x^2\right)^{5/2}}+\frac{x}{7 a \left(a+b x^2\right)^{7/2}}","\frac{16 x}{35 a^4 \sqrt{a+b x^2}}+\frac{8 x}{35 a^3 \left(a+b x^2\right)^{3/2}}+\frac{6 x}{35 a^2 \left(a+b x^2\right)^{5/2}}+\frac{x}{7 a \left(a+b x^2\right)^{7/2}}",1,"x/(7*a*(a + b*x^2)^(7/2)) + (6*x)/(35*a^2*(a + b*x^2)^(5/2)) + (8*x)/(35*a^3*(a + b*x^2)^(3/2)) + (16*x)/(35*a^4*Sqrt[a + b*x^2])","A",4,2,11,0.1818,1,"{192, 191}"
528,1,95,0,0.0585164,"\int \frac{1}{x \left(a+b x^2\right)^{9/2}} \, dx","Int[1/(x*(a + b*x^2)^(9/2)),x]","\frac{1}{a^4 \sqrt{a+b x^2}}+\frac{1}{3 a^3 \left(a+b x^2\right)^{3/2}}+\frac{1}{5 a^2 \left(a+b x^2\right)^{5/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{a^{9/2}}+\frac{1}{7 a \left(a+b x^2\right)^{7/2}}","\frac{1}{a^4 \sqrt{a+b x^2}}+\frac{1}{3 a^3 \left(a+b x^2\right)^{3/2}}+\frac{1}{5 a^2 \left(a+b x^2\right)^{5/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{a^{9/2}}+\frac{1}{7 a \left(a+b x^2\right)^{7/2}}",1,"1/(7*a*(a + b*x^2)^(7/2)) + 1/(5*a^2*(a + b*x^2)^(5/2)) + 1/(3*a^3*(a + b*x^2)^(3/2)) + 1/(a^4*Sqrt[a + b*x^2]) - ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]]/a^(9/2)","A",7,4,15,0.2667,1,"{266, 51, 63, 208}"
529,1,100,0,0.0263844,"\int \frac{1}{x^2 \left(a+b x^2\right)^{9/2}} \, dx","Int[1/(x^2*(a + b*x^2)^(9/2)),x]","-\frac{128 b x}{35 a^5 \sqrt{a+b x^2}}-\frac{64 b x}{35 a^4 \left(a+b x^2\right)^{3/2}}-\frac{48 b x}{35 a^3 \left(a+b x^2\right)^{5/2}}-\frac{8 b x}{7 a^2 \left(a+b x^2\right)^{7/2}}-\frac{1}{a x \left(a+b x^2\right)^{7/2}}","-\frac{128 b x}{35 a^5 \sqrt{a+b x^2}}-\frac{64 b x}{35 a^4 \left(a+b x^2\right)^{3/2}}-\frac{48 b x}{35 a^3 \left(a+b x^2\right)^{5/2}}-\frac{8 b x}{7 a^2 \left(a+b x^2\right)^{7/2}}-\frac{1}{a x \left(a+b x^2\right)^{7/2}}",1,"-(1/(a*x*(a + b*x^2)^(7/2))) - (8*b*x)/(7*a^2*(a + b*x^2)^(7/2)) - (48*b*x)/(35*a^3*(a + b*x^2)^(5/2)) - (64*b*x)/(35*a^4*(a + b*x^2)^(3/2)) - (128*b*x)/(35*a^5*Sqrt[a + b*x^2])","A",5,3,15,0.2000,1,"{271, 192, 191}"
530,1,132,0,0.0780217,"\int \frac{1}{x^3 \left(a+b x^2\right)^{9/2}} \, dx","Int[1/(x^3*(a + b*x^2)^(9/2)),x]","-\frac{9 \sqrt{a+b x^2}}{2 a^5 x^2}+\frac{3}{a^4 x^2 \sqrt{a+b x^2}}+\frac{3}{5 a^3 x^2 \left(a+b x^2\right)^{3/2}}+\frac{9}{35 a^2 x^2 \left(a+b x^2\right)^{5/2}}+\frac{9 b \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{2 a^{11/2}}+\frac{1}{7 a x^2 \left(a+b x^2\right)^{7/2}}","-\frac{9 b}{2 a^5 \sqrt{a+b x^2}}-\frac{3 b}{2 a^4 \left(a+b x^2\right)^{3/2}}-\frac{9 b}{10 a^3 \left(a+b x^2\right)^{5/2}}-\frac{9 b}{14 a^2 \left(a+b x^2\right)^{7/2}}+\frac{9 b \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{2 a^{11/2}}-\frac{1}{2 a x^2 \left(a+b x^2\right)^{7/2}}",1,"1/(7*a*x^2*(a + b*x^2)^(7/2)) + 9/(35*a^2*x^2*(a + b*x^2)^(5/2)) + 3/(5*a^3*x^2*(a + b*x^2)^(3/2)) + 3/(a^4*x^2*Sqrt[a + b*x^2]) - (9*Sqrt[a + b*x^2])/(2*a^5*x^2) + (9*b*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(2*a^(11/2))","A",8,4,15,0.2667,1,"{266, 51, 63, 208}"
531,1,132,0,0.0406277,"\int \frac{1}{x^4 \left(a+b x^2\right)^{9/2}} \, dx","Int[1/(x^4*(a + b*x^2)^(9/2)),x]","\frac{256 b^2 x}{21 a^6 \sqrt{a+b x^2}}+\frac{128 b^2 x}{21 a^5 \left(a+b x^2\right)^{3/2}}+\frac{32 b^2 x}{7 a^4 \left(a+b x^2\right)^{5/2}}+\frac{80 b^2 x}{21 a^3 \left(a+b x^2\right)^{7/2}}+\frac{10 b}{3 a^2 x \left(a+b x^2\right)^{7/2}}-\frac{1}{3 a x^3 \left(a+b x^2\right)^{7/2}}","\frac{256 b^2 x}{21 a^6 \sqrt{a+b x^2}}+\frac{128 b^2 x}{21 a^5 \left(a+b x^2\right)^{3/2}}+\frac{32 b^2 x}{7 a^4 \left(a+b x^2\right)^{5/2}}+\frac{80 b^2 x}{21 a^3 \left(a+b x^2\right)^{7/2}}+\frac{10 b}{3 a^2 x \left(a+b x^2\right)^{7/2}}-\frac{1}{3 a x^3 \left(a+b x^2\right)^{7/2}}",1,"-1/(3*a*x^3*(a + b*x^2)^(7/2)) + (10*b)/(3*a^2*x*(a + b*x^2)^(7/2)) + (80*b^2*x)/(21*a^3*(a + b*x^2)^(7/2)) + (32*b^2*x)/(7*a^4*(a + b*x^2)^(5/2)) + (128*b^2*x)/(21*a^5*(a + b*x^2)^(3/2)) + (256*b^2*x)/(21*a^6*Sqrt[a + b*x^2])","A",6,3,15,0.2000,1,"{271, 192, 191}"
532,1,46,0,0.0194254,"\int \frac{x^5}{\sqrt{9+4 x^2}} \, dx","Int[x^5/Sqrt[9 + 4*x^2],x]","\frac{1}{320} \left(4 x^2+9\right)^{5/2}-\frac{3}{32} \left(4 x^2+9\right)^{3/2}+\frac{81}{64} \sqrt{4 x^2+9}","\frac{1}{320} \left(4 x^2+9\right)^{5/2}-\frac{3}{32} \left(4 x^2+9\right)^{3/2}+\frac{81}{64} \sqrt{4 x^2+9}",1,"(81*Sqrt[9 + 4*x^2])/64 - (3*(9 + 4*x^2)^(3/2))/32 + (9 + 4*x^2)^(5/2)/320","A",3,2,15,0.1333,1,"{266, 43}"
533,1,45,0,0.0093216,"\int \frac{x^4}{\sqrt{9+4 x^2}} \, dx","Int[x^4/Sqrt[9 + 4*x^2],x]","\frac{1}{16} \sqrt{4 x^2+9} x^3-\frac{27}{128} \sqrt{4 x^2+9} x+\frac{243}{256} \sinh ^{-1}\left(\frac{2 x}{3}\right)","\frac{1}{16} \sqrt{4 x^2+9} x^3-\frac{27}{128} \sqrt{4 x^2+9} x+\frac{243}{256} \sinh ^{-1}\left(\frac{2 x}{3}\right)",1,"(-27*x*Sqrt[9 + 4*x^2])/128 + (x^3*Sqrt[9 + 4*x^2])/16 + (243*ArcSinh[(2*x)/3])/256","A",3,2,15,0.1333,1,"{321, 215}"
534,1,31,0,0.0142129,"\int \frac{x^3}{\sqrt{9+4 x^2}} \, dx","Int[x^3/Sqrt[9 + 4*x^2],x]","\frac{1}{48} \left(4 x^2+9\right)^{3/2}-\frac{9}{16} \sqrt{4 x^2+9}","\frac{1}{48} \left(4 x^2+9\right)^{3/2}-\frac{9}{16} \sqrt{4 x^2+9}",1,"(-9*Sqrt[9 + 4*x^2])/16 + (9 + 4*x^2)^(3/2)/48","A",3,2,15,0.1333,1,"{266, 43}"
535,1,27,0,0.0060955,"\int \frac{x^2}{\sqrt{9+4 x^2}} \, dx","Int[x^2/Sqrt[9 + 4*x^2],x]","\frac{1}{8} x \sqrt{4 x^2+9}-\frac{9}{16} \sinh ^{-1}\left(\frac{2 x}{3}\right)","\frac{1}{8} x \sqrt{4 x^2+9}-\frac{9}{16} \sinh ^{-1}\left(\frac{2 x}{3}\right)",1,"(x*Sqrt[9 + 4*x^2])/8 - (9*ArcSinh[(2*x)/3])/16","A",2,2,15,0.1333,1,"{321, 215}"
536,1,15,0,0.0023737,"\int \frac{x}{\sqrt{9+4 x^2}} \, dx","Int[x/Sqrt[9 + 4*x^2],x]","\frac{1}{4} \sqrt{4 x^2+9}","\frac{1}{4} \sqrt{4 x^2+9}",1,"Sqrt[9 + 4*x^2]/4","A",1,1,13,0.07692,1,"{261}"
537,1,10,0,0.001411,"\int \frac{1}{\sqrt{9+4 x^2}} \, dx","Int[1/Sqrt[9 + 4*x^2],x]","\frac{1}{2} \sinh ^{-1}\left(\frac{2 x}{3}\right)","\frac{1}{2} \sinh ^{-1}\left(\frac{2 x}{3}\right)",1,"ArcSinh[(2*x)/3]/2","A",1,1,11,0.09091,1,"{215}"
538,1,20,0,0.0100864,"\int \frac{1}{x \sqrt{9+4 x^2}} \, dx","Int[1/(x*Sqrt[9 + 4*x^2]),x]","-\frac{1}{3} \tanh ^{-1}\left(\frac{1}{3} \sqrt{4 x^2+9}\right)","-\frac{1}{3} \tanh ^{-1}\left(\frac{1}{3} \sqrt{4 x^2+9}\right)",1,"-ArcTanh[Sqrt[9 + 4*x^2]/3]/3","A",3,3,15,0.2000,1,"{266, 63, 207}"
539,1,18,0,0.003062,"\int \frac{1}{x^2 \sqrt{9+4 x^2}} \, dx","Int[1/(x^2*Sqrt[9 + 4*x^2]),x]","-\frac{\sqrt{4 x^2+9}}{9 x}","-\frac{\sqrt{4 x^2+9}}{9 x}",1,"-Sqrt[9 + 4*x^2]/(9*x)","A",1,1,15,0.06667,1,"{264}"
540,1,39,0,0.0165838,"\int \frac{1}{x^3 \sqrt{9+4 x^2}} \, dx","Int[1/(x^3*Sqrt[9 + 4*x^2]),x]","\frac{2}{27} \tanh ^{-1}\left(\frac{1}{3} \sqrt{4 x^2+9}\right)-\frac{\sqrt{4 x^2+9}}{18 x^2}","\frac{2}{27} \tanh ^{-1}\left(\frac{1}{3} \sqrt{4 x^2+9}\right)-\frac{\sqrt{4 x^2+9}}{18 x^2}",1,"-Sqrt[9 + 4*x^2]/(18*x^2) + (2*ArcTanh[Sqrt[9 + 4*x^2]/3])/27","A",4,4,15,0.2667,1,"{266, 51, 63, 207}"
541,1,37,0,0.0071159,"\int \frac{1}{x^4 \sqrt{9+4 x^2}} \, dx","Int[1/(x^4*Sqrt[9 + 4*x^2]),x]","\frac{8 \sqrt{4 x^2+9}}{243 x}-\frac{\sqrt{4 x^2+9}}{27 x^3}","\frac{8 \sqrt{4 x^2+9}}{243 x}-\frac{\sqrt{4 x^2+9}}{27 x^3}",1,"-Sqrt[9 + 4*x^2]/(27*x^3) + (8*Sqrt[9 + 4*x^2])/(243*x)","A",2,2,15,0.1333,1,"{271, 264}"
542,1,57,0,0.0229079,"\int \frac{1}{x^5 \sqrt{9+4 x^2}} \, dx","Int[1/(x^5*Sqrt[9 + 4*x^2]),x]","\frac{\sqrt{4 x^2+9}}{54 x^2}-\frac{\sqrt{4 x^2+9}}{36 x^4}-\frac{2}{81} \tanh ^{-1}\left(\frac{1}{3} \sqrt{4 x^2+9}\right)","\frac{\sqrt{4 x^2+9}}{54 x^2}-\frac{\sqrt{4 x^2+9}}{36 x^4}-\frac{2}{81} \tanh ^{-1}\left(\frac{1}{3} \sqrt{4 x^2+9}\right)",1,"-Sqrt[9 + 4*x^2]/(36*x^4) + Sqrt[9 + 4*x^2]/(54*x^2) - (2*ArcTanh[Sqrt[9 + 4*x^2]/3])/81","A",5,4,15,0.2667,1,"{266, 51, 63, 207}"
543,1,46,0,0.0188897,"\int \frac{x^5}{\sqrt{9-4 x^2}} \, dx","Int[x^5/Sqrt[9 - 4*x^2],x]","-\frac{1}{320} \left(9-4 x^2\right)^{5/2}+\frac{3}{32} \left(9-4 x^2\right)^{3/2}-\frac{81}{64} \sqrt{9-4 x^2}","-\frac{1}{320} \left(9-4 x^2\right)^{5/2}+\frac{3}{32} \left(9-4 x^2\right)^{3/2}-\frac{81}{64} \sqrt{9-4 x^2}",1,"(-81*Sqrt[9 - 4*x^2])/64 + (3*(9 - 4*x^2)^(3/2))/32 - (9 - 4*x^2)^(5/2)/320","A",3,2,15,0.1333,1,"{266, 43}"
544,1,45,0,0.0096936,"\int \frac{x^4}{\sqrt{9-4 x^2}} \, dx","Int[x^4/Sqrt[9 - 4*x^2],x]","-\frac{1}{16} \sqrt{9-4 x^2} x^3-\frac{27}{128} \sqrt{9-4 x^2} x+\frac{243}{256} \sin ^{-1}\left(\frac{2 x}{3}\right)","-\frac{1}{16} \sqrt{9-4 x^2} x^3-\frac{27}{128} \sqrt{9-4 x^2} x+\frac{243}{256} \sin ^{-1}\left(\frac{2 x}{3}\right)",1,"(-27*x*Sqrt[9 - 4*x^2])/128 - (x^3*Sqrt[9 - 4*x^2])/16 + (243*ArcSin[(2*x)/3])/256","A",3,2,15,0.1333,1,"{321, 216}"
545,1,31,0,0.0135806,"\int \frac{x^3}{\sqrt{9-4 x^2}} \, dx","Int[x^3/Sqrt[9 - 4*x^2],x]","\frac{1}{48} \left(9-4 x^2\right)^{3/2}-\frac{9}{16} \sqrt{9-4 x^2}","\frac{1}{48} \left(9-4 x^2\right)^{3/2}-\frac{9}{16} \sqrt{9-4 x^2}",1,"(-9*Sqrt[9 - 4*x^2])/16 + (9 - 4*x^2)^(3/2)/48","A",3,2,15,0.1333,1,"{266, 43}"
546,1,27,0,0.0050559,"\int \frac{x^2}{\sqrt{9-4 x^2}} \, dx","Int[x^2/Sqrt[9 - 4*x^2],x]","\frac{9}{16} \sin ^{-1}\left(\frac{2 x}{3}\right)-\frac{1}{8} x \sqrt{9-4 x^2}","\frac{9}{16} \sin ^{-1}\left(\frac{2 x}{3}\right)-\frac{1}{8} x \sqrt{9-4 x^2}",1,"-(x*Sqrt[9 - 4*x^2])/8 + (9*ArcSin[(2*x)/3])/16","A",2,2,15,0.1333,1,"{321, 216}"
547,1,15,0,0.002276,"\int \frac{x}{\sqrt{9-4 x^2}} \, dx","Int[x/Sqrt[9 - 4*x^2],x]","-\frac{1}{4} \sqrt{9-4 x^2}","-\frac{1}{4} \sqrt{9-4 x^2}",1,"-Sqrt[9 - 4*x^2]/4","A",1,1,13,0.07692,1,"{261}"
548,1,10,0,0.0014207,"\int \frac{1}{\sqrt{9-4 x^2}} \, dx","Int[1/Sqrt[9 - 4*x^2],x]","\frac{1}{2} \sin ^{-1}\left(\frac{2 x}{3}\right)","\frac{1}{2} \sin ^{-1}\left(\frac{2 x}{3}\right)",1,"ArcSin[(2*x)/3]/2","A",1,1,11,0.09091,1,"{216}"
549,1,20,0,0.0101745,"\int \frac{1}{x \sqrt{9-4 x^2}} \, dx","Int[1/(x*Sqrt[9 - 4*x^2]),x]","-\frac{1}{3} \tanh ^{-1}\left(\frac{1}{3} \sqrt{9-4 x^2}\right)","-\frac{1}{3} \tanh ^{-1}\left(\frac{1}{3} \sqrt{9-4 x^2}\right)",1,"-ArcTanh[Sqrt[9 - 4*x^2]/3]/3","A",3,3,15,0.2000,1,"{266, 63, 206}"
550,1,18,0,0.0030861,"\int \frac{1}{x^2 \sqrt{9-4 x^2}} \, dx","Int[1/(x^2*Sqrt[9 - 4*x^2]),x]","-\frac{\sqrt{9-4 x^2}}{9 x}","-\frac{\sqrt{9-4 x^2}}{9 x}",1,"-Sqrt[9 - 4*x^2]/(9*x)","A",1,1,15,0.06667,1,"{264}"
551,1,39,0,0.0159081,"\int \frac{1}{x^3 \sqrt{9-4 x^2}} \, dx","Int[1/(x^3*Sqrt[9 - 4*x^2]),x]","-\frac{\sqrt{9-4 x^2}}{18 x^2}-\frac{2}{27} \tanh ^{-1}\left(\frac{1}{3} \sqrt{9-4 x^2}\right)","-\frac{\sqrt{9-4 x^2}}{18 x^2}-\frac{2}{27} \tanh ^{-1}\left(\frac{1}{3} \sqrt{9-4 x^2}\right)",1,"-Sqrt[9 - 4*x^2]/(18*x^2) - (2*ArcTanh[Sqrt[9 - 4*x^2]/3])/27","A",4,4,15,0.2667,1,"{266, 51, 63, 206}"
552,1,37,0,0.0070717,"\int \frac{1}{x^4 \sqrt{9-4 x^2}} \, dx","Int[1/(x^4*Sqrt[9 - 4*x^2]),x]","-\frac{8 \sqrt{9-4 x^2}}{243 x}-\frac{\sqrt{9-4 x^2}}{27 x^3}","-\frac{8 \sqrt{9-4 x^2}}{243 x}-\frac{\sqrt{9-4 x^2}}{27 x^3}",1,"-Sqrt[9 - 4*x^2]/(27*x^3) - (8*Sqrt[9 - 4*x^2])/(243*x)","A",2,2,15,0.1333,1,"{271, 264}"
553,1,57,0,0.0235052,"\int \frac{1}{x^5 \sqrt{9-4 x^2}} \, dx","Int[1/(x^5*Sqrt[9 - 4*x^2]),x]","-\frac{\sqrt{9-4 x^2}}{54 x^2}-\frac{\sqrt{9-4 x^2}}{36 x^4}-\frac{2}{81} \tanh ^{-1}\left(\frac{1}{3} \sqrt{9-4 x^2}\right)","-\frac{\sqrt{9-4 x^2}}{54 x^2}-\frac{\sqrt{9-4 x^2}}{36 x^4}-\frac{2}{81} \tanh ^{-1}\left(\frac{1}{3} \sqrt{9-4 x^2}\right)",1,"-Sqrt[9 - 4*x^2]/(36*x^4) - Sqrt[9 - 4*x^2]/(54*x^2) - (2*ArcTanh[Sqrt[9 - 4*x^2]/3])/81","A",5,4,15,0.2667,1,"{266, 51, 63, 206}"
554,1,46,0,0.0187101,"\int \frac{x^5}{\sqrt{-9+4 x^2}} \, dx","Int[x^5/Sqrt[-9 + 4*x^2],x]","\frac{1}{320} \left(4 x^2-9\right)^{5/2}+\frac{3}{32} \left(4 x^2-9\right)^{3/2}+\frac{81}{64} \sqrt{4 x^2-9}","\frac{1}{320} \left(4 x^2-9\right)^{5/2}+\frac{3}{32} \left(4 x^2-9\right)^{3/2}+\frac{81}{64} \sqrt{4 x^2-9}",1,"(81*Sqrt[-9 + 4*x^2])/64 + (3*(-9 + 4*x^2)^(3/2))/32 + (-9 + 4*x^2)^(5/2)/320","A",3,2,15,0.1333,1,"{266, 43}"
555,1,54,0,0.0125138,"\int \frac{x^4}{\sqrt{-9+4 x^2}} \, dx","Int[x^4/Sqrt[-9 + 4*x^2],x]","\frac{1}{16} \sqrt{4 x^2-9} x^3+\frac{27}{128} \sqrt{4 x^2-9} x+\frac{243}{256} \tanh ^{-1}\left(\frac{2 x}{\sqrt{4 x^2-9}}\right)","\frac{1}{16} \sqrt{4 x^2-9} x^3+\frac{27}{128} \sqrt{4 x^2-9} x+\frac{243}{256} \tanh ^{-1}\left(\frac{2 x}{\sqrt{4 x^2-9}}\right)",1,"(27*x*Sqrt[-9 + 4*x^2])/128 + (x^3*Sqrt[-9 + 4*x^2])/16 + (243*ArcTanh[(2*x)/Sqrt[-9 + 4*x^2]])/256","A",4,3,15,0.2000,1,"{321, 217, 206}"
556,1,31,0,0.0130457,"\int \frac{x^3}{\sqrt{-9+4 x^2}} \, dx","Int[x^3/Sqrt[-9 + 4*x^2],x]","\frac{1}{48} \left(4 x^2-9\right)^{3/2}+\frac{9}{16} \sqrt{4 x^2-9}","\frac{1}{48} \left(4 x^2-9\right)^{3/2}+\frac{9}{16} \sqrt{4 x^2-9}",1,"(9*Sqrt[-9 + 4*x^2])/16 + (-9 + 4*x^2)^(3/2)/48","A",3,2,15,0.1333,1,"{266, 43}"
557,1,36,0,0.007637,"\int \frac{x^2}{\sqrt{-9+4 x^2}} \, dx","Int[x^2/Sqrt[-9 + 4*x^2],x]","\frac{1}{8} \sqrt{4 x^2-9} x+\frac{9}{16} \tanh ^{-1}\left(\frac{2 x}{\sqrt{4 x^2-9}}\right)","\frac{1}{8} \sqrt{4 x^2-9} x+\frac{9}{16} \tanh ^{-1}\left(\frac{2 x}{\sqrt{4 x^2-9}}\right)",1,"(x*Sqrt[-9 + 4*x^2])/8 + (9*ArcTanh[(2*x)/Sqrt[-9 + 4*x^2]])/16","A",3,3,15,0.2000,1,"{321, 217, 206}"
558,1,15,0,0.0020956,"\int \frac{x}{\sqrt{-9+4 x^2}} \, dx","Int[x/Sqrt[-9 + 4*x^2],x]","\frac{1}{4} \sqrt{4 x^2-9}","\frac{1}{4} \sqrt{4 x^2-9}",1,"Sqrt[-9 + 4*x^2]/4","A",1,1,13,0.07692,1,"{261}"
559,1,19,0,0.0031291,"\int \frac{1}{\sqrt{-9+4 x^2}} \, dx","Int[1/Sqrt[-9 + 4*x^2],x]","\frac{1}{2} \tanh ^{-1}\left(\frac{2 x}{\sqrt{4 x^2-9}}\right)","\frac{1}{2} \tanh ^{-1}\left(\frac{2 x}{\sqrt{4 x^2-9}}\right)",1,"ArcTanh[(2*x)/Sqrt[-9 + 4*x^2]]/2","A",2,2,11,0.1818,1,"{217, 206}"
560,1,20,0,0.0096452,"\int \frac{1}{x \sqrt{-9+4 x^2}} \, dx","Int[1/(x*Sqrt[-9 + 4*x^2]),x]","\frac{1}{3} \tan ^{-1}\left(\frac{1}{3} \sqrt{4 x^2-9}\right)","\frac{1}{3} \tan ^{-1}\left(\frac{1}{3} \sqrt{4 x^2-9}\right)",1,"ArcTan[Sqrt[-9 + 4*x^2]/3]/3","A",3,3,15,0.2000,1,"{266, 63, 203}"
561,1,18,0,0.0029692,"\int \frac{1}{x^2 \sqrt{-9+4 x^2}} \, dx","Int[1/(x^2*Sqrt[-9 + 4*x^2]),x]","\frac{\sqrt{4 x^2-9}}{9 x}","\frac{\sqrt{4 x^2-9}}{9 x}",1,"Sqrt[-9 + 4*x^2]/(9*x)","A",1,1,15,0.06667,1,"{264}"
562,1,39,0,0.0158369,"\int \frac{1}{x^3 \sqrt{-9+4 x^2}} \, dx","Int[1/(x^3*Sqrt[-9 + 4*x^2]),x]","\frac{\sqrt{4 x^2-9}}{18 x^2}+\frac{2}{27} \tan ^{-1}\left(\frac{1}{3} \sqrt{4 x^2-9}\right)","\frac{\sqrt{4 x^2-9}}{18 x^2}+\frac{2}{27} \tan ^{-1}\left(\frac{1}{3} \sqrt{4 x^2-9}\right)",1,"Sqrt[-9 + 4*x^2]/(18*x^2) + (2*ArcTan[Sqrt[-9 + 4*x^2]/3])/27","A",4,4,15,0.2667,1,"{266, 51, 63, 203}"
563,1,37,0,0.0073577,"\int \frac{1}{x^4 \sqrt{-9+4 x^2}} \, dx","Int[1/(x^4*Sqrt[-9 + 4*x^2]),x]","\frac{8 \sqrt{4 x^2-9}}{243 x}+\frac{\sqrt{4 x^2-9}}{27 x^3}","\frac{8 \sqrt{4 x^2-9}}{243 x}+\frac{\sqrt{4 x^2-9}}{27 x^3}",1,"Sqrt[-9 + 4*x^2]/(27*x^3) + (8*Sqrt[-9 + 4*x^2])/(243*x)","A",2,2,15,0.1333,1,"{271, 264}"
564,1,57,0,0.0232267,"\int \frac{1}{x^5 \sqrt{-9+4 x^2}} \, dx","Int[1/(x^5*Sqrt[-9 + 4*x^2]),x]","\frac{\sqrt{4 x^2-9}}{54 x^2}+\frac{\sqrt{4 x^2-9}}{36 x^4}+\frac{2}{81} \tan ^{-1}\left(\frac{1}{3} \sqrt{4 x^2-9}\right)","\frac{\sqrt{4 x^2-9}}{54 x^2}+\frac{\sqrt{4 x^2-9}}{36 x^4}+\frac{2}{81} \tan ^{-1}\left(\frac{1}{3} \sqrt{4 x^2-9}\right)",1,"Sqrt[-9 + 4*x^2]/(36*x^4) + Sqrt[-9 + 4*x^2]/(54*x^2) + (2*ArcTan[Sqrt[-9 + 4*x^2]/3])/81","A",5,4,15,0.2667,1,"{266, 51, 63, 203}"
565,1,46,0,0.0194125,"\int \frac{x^5}{\sqrt{-9-4 x^2}} \, dx","Int[x^5/Sqrt[-9 - 4*x^2],x]","-\frac{1}{320} \left(-4 x^2-9\right)^{5/2}-\frac{3}{32} \left(-4 x^2-9\right)^{3/2}-\frac{81}{64} \sqrt{-4 x^2-9}","-\frac{1}{320} \left(-4 x^2-9\right)^{5/2}-\frac{3}{32} \left(-4 x^2-9\right)^{3/2}-\frac{81}{64} \sqrt{-4 x^2-9}",1,"(-81*Sqrt[-9 - 4*x^2])/64 - (3*(-9 - 4*x^2)^(3/2))/32 - (-9 - 4*x^2)^(5/2)/320","A",3,2,15,0.1333,1,"{266, 43}"
566,1,54,0,0.0129458,"\int \frac{x^4}{\sqrt{-9-4 x^2}} \, dx","Int[x^4/Sqrt[-9 - 4*x^2],x]","-\frac{1}{16} \sqrt{-4 x^2-9} x^3+\frac{27}{128} \sqrt{-4 x^2-9} x+\frac{243}{256} \tan ^{-1}\left(\frac{2 x}{\sqrt{-4 x^2-9}}\right)","-\frac{1}{16} \sqrt{-4 x^2-9} x^3+\frac{27}{128} \sqrt{-4 x^2-9} x+\frac{243}{256} \tan ^{-1}\left(\frac{2 x}{\sqrt{-4 x^2-9}}\right)",1,"(27*x*Sqrt[-9 - 4*x^2])/128 - (x^3*Sqrt[-9 - 4*x^2])/16 + (243*ArcTan[(2*x)/Sqrt[-9 - 4*x^2]])/256","A",4,3,15,0.2000,1,"{321, 217, 203}"
567,1,31,0,0.013987,"\int \frac{x^3}{\sqrt{-9-4 x^2}} \, dx","Int[x^3/Sqrt[-9 - 4*x^2],x]","\frac{1}{48} \left(-4 x^2-9\right)^{3/2}+\frac{9}{16} \sqrt{-4 x^2-9}","\frac{1}{48} \left(-4 x^2-9\right)^{3/2}+\frac{9}{16} \sqrt{-4 x^2-9}",1,"(9*Sqrt[-9 - 4*x^2])/16 + (-9 - 4*x^2)^(3/2)/48","A",3,2,15,0.1333,1,"{266, 43}"
568,1,36,0,0.0072962,"\int \frac{x^2}{\sqrt{-9-4 x^2}} \, dx","Int[x^2/Sqrt[-9 - 4*x^2],x]","-\frac{1}{8} \sqrt{-4 x^2-9} x-\frac{9}{16} \tan ^{-1}\left(\frac{2 x}{\sqrt{-4 x^2-9}}\right)","-\frac{1}{8} \sqrt{-4 x^2-9} x-\frac{9}{16} \tan ^{-1}\left(\frac{2 x}{\sqrt{-4 x^2-9}}\right)",1,"-(x*Sqrt[-9 - 4*x^2])/8 - (9*ArcTan[(2*x)/Sqrt[-9 - 4*x^2]])/16","A",3,3,15,0.2000,1,"{321, 217, 203}"
569,1,15,0,0.0022589,"\int \frac{x}{\sqrt{-9-4 x^2}} \, dx","Int[x/Sqrt[-9 - 4*x^2],x]","-\frac{1}{4} \sqrt{-4 x^2-9}","-\frac{1}{4} \sqrt{-4 x^2-9}",1,"-Sqrt[-9 - 4*x^2]/4","A",1,1,13,0.07692,1,"{261}"
570,1,19,0,0.0032778,"\int \frac{1}{\sqrt{-9-4 x^2}} \, dx","Int[1/Sqrt[-9 - 4*x^2],x]","\frac{1}{2} \tan ^{-1}\left(\frac{2 x}{\sqrt{-4 x^2-9}}\right)","\frac{1}{2} \tan ^{-1}\left(\frac{2 x}{\sqrt{-4 x^2-9}}\right)",1,"ArcTan[(2*x)/Sqrt[-9 - 4*x^2]]/2","A",2,2,11,0.1818,1,"{217, 203}"
571,1,20,0,0.0101194,"\int \frac{1}{x \sqrt{-9-4 x^2}} \, dx","Int[1/(x*Sqrt[-9 - 4*x^2]),x]","\frac{1}{3} \tan ^{-1}\left(\frac{1}{3} \sqrt{-4 x^2-9}\right)","\frac{1}{3} \tan ^{-1}\left(\frac{1}{3} \sqrt{-4 x^2-9}\right)",1,"ArcTan[Sqrt[-9 - 4*x^2]/3]/3","A",3,3,15,0.2000,1,"{266, 63, 204}"
572,1,18,0,0.0030486,"\int \frac{1}{x^2 \sqrt{-9-4 x^2}} \, dx","Int[1/(x^2*Sqrt[-9 - 4*x^2]),x]","\frac{\sqrt{-4 x^2-9}}{9 x}","\frac{\sqrt{-4 x^2-9}}{9 x}",1,"Sqrt[-9 - 4*x^2]/(9*x)","A",1,1,15,0.06667,1,"{264}"
573,1,39,0,0.0160702,"\int \frac{1}{x^3 \sqrt{-9-4 x^2}} \, dx","Int[1/(x^3*Sqrt[-9 - 4*x^2]),x]","\frac{\sqrt{-4 x^2-9}}{18 x^2}-\frac{2}{27} \tan ^{-1}\left(\frac{1}{3} \sqrt{-4 x^2-9}\right)","\frac{\sqrt{-4 x^2-9}}{18 x^2}-\frac{2}{27} \tan ^{-1}\left(\frac{1}{3} \sqrt{-4 x^2-9}\right)",1,"Sqrt[-9 - 4*x^2]/(18*x^2) - (2*ArcTan[Sqrt[-9 - 4*x^2]/3])/27","A",4,4,15,0.2667,1,"{266, 51, 63, 204}"
574,1,37,0,0.0072743,"\int \frac{1}{x^4 \sqrt{-9-4 x^2}} \, dx","Int[1/(x^4*Sqrt[-9 - 4*x^2]),x]","\frac{\sqrt{-4 x^2-9}}{27 x^3}-\frac{8 \sqrt{-4 x^2-9}}{243 x}","\frac{\sqrt{-4 x^2-9}}{27 x^3}-\frac{8 \sqrt{-4 x^2-9}}{243 x}",1,"Sqrt[-9 - 4*x^2]/(27*x^3) - (8*Sqrt[-9 - 4*x^2])/(243*x)","A",2,2,15,0.1333,1,"{271, 264}"
575,1,57,0,0.0232741,"\int \frac{1}{x^5 \sqrt{-9-4 x^2}} \, dx","Int[1/(x^5*Sqrt[-9 - 4*x^2]),x]","-\frac{\sqrt{-4 x^2-9}}{54 x^2}+\frac{\sqrt{-4 x^2-9}}{36 x^4}+\frac{2}{81} \tan ^{-1}\left(\frac{1}{3} \sqrt{-4 x^2-9}\right)","-\frac{\sqrt{-4 x^2-9}}{54 x^2}+\frac{\sqrt{-4 x^2-9}}{36 x^4}+\frac{2}{81} \tan ^{-1}\left(\frac{1}{3} \sqrt{-4 x^2-9}\right)",1,"Sqrt[-9 - 4*x^2]/(36*x^4) - Sqrt[-9 - 4*x^2]/(54*x^2) + (2*ArcTan[Sqrt[-9 - 4*x^2]/3])/81","A",5,4,15,0.2667,1,"{266, 51, 63, 204}"
576,1,17,0,0.0021277,"\int \frac{1}{\sqrt{9+b x^2}} \, dx","Int[1/Sqrt[9 + b*x^2],x]","\frac{\sinh ^{-1}\left(\frac{\sqrt{b} x}{3}\right)}{\sqrt{b}}","\frac{\sinh ^{-1}\left(\frac{\sqrt{b} x}{3}\right)}{\sqrt{b}}",1,"ArcSinh[(Sqrt[b]*x)/3]/Sqrt[b]","A",1,1,11,0.09091,1,"{215}"
577,1,17,0,0.0025019,"\int \frac{1}{\sqrt{9-b x^2}} \, dx","Int[1/Sqrt[9 - b*x^2],x]","\frac{\sin ^{-1}\left(\frac{\sqrt{b} x}{3}\right)}{\sqrt{b}}","\frac{\sin ^{-1}\left(\frac{\sqrt{b} x}{3}\right)}{\sqrt{b}}",1,"ArcSin[(Sqrt[b]*x)/3]/Sqrt[b]","A",1,1,12,0.08333,1,"{216}"
578,1,25,0,0.0055129,"\int \frac{1}{\sqrt{-9+b x^2}} \, dx","Int[1/Sqrt[-9 + b*x^2],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2-9}}\right)}{\sqrt{b}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2-9}}\right)}{\sqrt{b}}",1,"ArcTanh[(Sqrt[b]*x)/Sqrt[-9 + b*x^2]]/Sqrt[b]","A",2,2,11,0.1818,1,"{217, 206}"
579,1,26,0,0.0045402,"\int \frac{1}{\sqrt{-9-b x^2}} \, dx","Int[1/Sqrt[-9 - b*x^2],x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{-b x^2-9}}\right)}{\sqrt{b}}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{-b x^2-9}}\right)}{\sqrt{b}}",1,"ArcTan[(Sqrt[b]*x)/Sqrt[-9 - b*x^2]]/Sqrt[b]","A",2,2,12,0.1667,1,"{217, 203}"
580,1,19,0,0.005851,"\int \frac{1}{\sqrt{\pi +b x^2}} \, dx","Int[1/Sqrt[Pi + b*x^2],x]","\frac{\sinh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{\pi }}\right)}{\sqrt{b}}","\frac{\sinh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{\pi }}\right)}{\sqrt{b}}",1,"ArcSinh[(Sqrt[b]*x)/Sqrt[Pi]]/Sqrt[b]","A",1,1,11,0.09091,1,"{215}"
581,1,19,0,0.0030614,"\int \frac{1}{\sqrt{\pi -b x^2}} \, dx","Int[1/Sqrt[Pi - b*x^2],x]","\frac{\sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{\pi }}\right)}{\sqrt{b}}","\frac{\sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{\pi }}\right)}{\sqrt{b}}",1,"ArcSin[(Sqrt[b]*x)/Sqrt[Pi]]/Sqrt[b]","A",1,1,12,0.08333,1,"{216}"
582,1,27,0,0.0055478,"\int \frac{1}{\sqrt{-\pi +b x^2}} \, dx","Int[1/Sqrt[-Pi + b*x^2],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2-\pi }}\right)}{\sqrt{b}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2-\pi }}\right)}{\sqrt{b}}",1,"ArcTanh[(Sqrt[b]*x)/Sqrt[-Pi + b*x^2]]/Sqrt[b]","A",2,2,13,0.1538,1,"{217, 206}"
583,1,28,0,0.0052011,"\int \frac{1}{\sqrt{-\pi -b x^2}} \, dx","Int[1/Sqrt[-Pi - b*x^2],x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{-b x^2-\pi }}\right)}{\sqrt{b}}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{-b x^2-\pi }}\right)}{\sqrt{b}}",1,"ArcTan[(Sqrt[b]*x)/Sqrt[-Pi - b*x^2]]/Sqrt[b]","A",2,2,14,0.1429,1,"{217, 203}"
584,1,25,0,0.005355,"\int \frac{1}{\sqrt{a+b x^2}} \, dx","Int[1/Sqrt[a + b*x^2],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{\sqrt{b}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{\sqrt{b}}",1,"ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]]/Sqrt[b]","A",2,2,11,0.1818,1,"{217, 206}"
585,1,26,0,0.0048264,"\int \frac{1}{\sqrt{a-b x^2}} \, dx","Int[1/Sqrt[a - b*x^2],x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a-b x^2}}\right)}{\sqrt{b}}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a-b x^2}}\right)}{\sqrt{b}}",1,"ArcTan[(Sqrt[b]*x)/Sqrt[a - b*x^2]]/Sqrt[b]","A",2,2,12,0.1667,1,"{217, 203}"
586,1,27,0,0.0056156,"\int \frac{1}{\sqrt{-a+b x^2}} \, dx","Int[1/Sqrt[-a + b*x^2],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2-a}}\right)}{\sqrt{b}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2-a}}\right)}{\sqrt{b}}",1,"ArcTanh[(Sqrt[b]*x)/Sqrt[-a + b*x^2]]/Sqrt[b]","A",2,2,13,0.1538,1,"{217, 206}"
587,1,28,0,0.004854,"\int \frac{1}{\sqrt{-a-b x^2}} \, dx","Int[1/Sqrt[-a - b*x^2],x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{-a-b x^2}}\right)}{\sqrt{b}}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{-a-b x^2}}\right)}{\sqrt{b}}",1,"ArcTan[(Sqrt[b]*x)/Sqrt[-a - b*x^2]]/Sqrt[b]","A",2,2,14,0.1429,1,"{217, 203}"
588,1,16,0,0.0022067,"\int \frac{1}{\sqrt{a^2-x^2}} \, dx","Int[1/Sqrt[a^2 - x^2],x]","\tan ^{-1}\left(\frac{x}{\sqrt{a^2-x^2}}\right)","\tan ^{-1}\left(\frac{x}{\sqrt{a^2-x^2}}\right)",1,"ArcTan[x/Sqrt[a^2 - x^2]]","A",2,2,13,0.1538,1,"{217, 203}"
589,1,184,0,0.1329834,"\int (c x)^{7/2} \sqrt{a+b x^2} \, dx","Int[(c*x)^(7/2)*Sqrt[a + b*x^2],x]","-\frac{20 a^2 c^3 \sqrt{c x} \sqrt{a+b x^2}}{231 b^2}+\frac{10 a^{11/4} c^{7/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{231 b^{9/4} \sqrt{a+b x^2}}+\frac{2 (c x)^{9/2} \sqrt{a+b x^2}}{11 c}+\frac{4 a c (c x)^{5/2} \sqrt{a+b x^2}}{77 b}","-\frac{20 a^2 c^3 \sqrt{c x} \sqrt{a+b x^2}}{231 b^2}+\frac{10 a^{11/4} c^{7/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{231 b^{9/4} \sqrt{a+b x^2}}+\frac{2 (c x)^{9/2} \sqrt{a+b x^2}}{11 c}+\frac{4 a c (c x)^{5/2} \sqrt{a+b x^2}}{77 b}",1,"(-20*a^2*c^3*Sqrt[c*x]*Sqrt[a + b*x^2])/(231*b^2) + (4*a*c*(c*x)^(5/2)*Sqrt[a + b*x^2])/(77*b) + (2*(c*x)^(9/2)*Sqrt[a + b*x^2])/(11*c) + (10*a^(11/4)*c^(7/2)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(231*b^(9/4)*Sqrt[a + b*x^2])","A",5,4,19,0.2105,1,"{279, 321, 329, 220}"
590,1,301,0,0.2297207,"\int (c x)^{5/2} \sqrt{a+b x^2} \, dx","Int[(c*x)^(5/2)*Sqrt[a + b*x^2],x]","-\frac{4 a^2 c^2 \sqrt{c x} \sqrt{a+b x^2}}{15 b^{3/2} \left(\sqrt{a}+\sqrt{b} x\right)}-\frac{2 a^{9/4} c^{5/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{15 b^{7/4} \sqrt{a+b x^2}}+\frac{4 a^{9/4} c^{5/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{15 b^{7/4} \sqrt{a+b x^2}}+\frac{2 (c x)^{7/2} \sqrt{a+b x^2}}{9 c}+\frac{4 a c (c x)^{3/2} \sqrt{a+b x^2}}{45 b}","-\frac{4 a^2 c^2 \sqrt{c x} \sqrt{a+b x^2}}{15 b^{3/2} \left(\sqrt{a}+\sqrt{b} x\right)}-\frac{2 a^{9/4} c^{5/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{15 b^{7/4} \sqrt{a+b x^2}}+\frac{4 a^{9/4} c^{5/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{15 b^{7/4} \sqrt{a+b x^2}}+\frac{2 (c x)^{7/2} \sqrt{a+b x^2}}{9 c}+\frac{4 a c (c x)^{3/2} \sqrt{a+b x^2}}{45 b}",1,"(4*a*c*(c*x)^(3/2)*Sqrt[a + b*x^2])/(45*b) + (2*(c*x)^(7/2)*Sqrt[a + b*x^2])/(9*c) - (4*a^2*c^2*Sqrt[c*x]*Sqrt[a + b*x^2])/(15*b^(3/2)*(Sqrt[a] + Sqrt[b]*x)) + (4*a^(9/4)*c^(5/2)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(15*b^(7/4)*Sqrt[a + b*x^2]) - (2*a^(9/4)*c^(5/2)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(15*b^(7/4)*Sqrt[a + b*x^2])","A",6,6,19,0.3158,1,"{279, 321, 329, 305, 220, 1196}"
591,1,153,0,0.0904466,"\int (c x)^{3/2} \sqrt{a+b x^2} \, dx","Int[(c*x)^(3/2)*Sqrt[a + b*x^2],x]","-\frac{2 a^{7/4} c^{3/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{21 b^{5/4} \sqrt{a+b x^2}}+\frac{2 (c x)^{5/2} \sqrt{a+b x^2}}{7 c}+\frac{4 a c \sqrt{c x} \sqrt{a+b x^2}}{21 b}","-\frac{2 a^{7/4} c^{3/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{21 b^{5/4} \sqrt{a+b x^2}}+\frac{2 (c x)^{5/2} \sqrt{a+b x^2}}{7 c}+\frac{4 a c \sqrt{c x} \sqrt{a+b x^2}}{21 b}",1,"(4*a*c*Sqrt[c*x]*Sqrt[a + b*x^2])/(21*b) + (2*(c*x)^(5/2)*Sqrt[a + b*x^2])/(7*c) - (2*a^(7/4)*c^(3/2)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(21*b^(5/4)*Sqrt[a + b*x^2])","A",4,4,19,0.2105,1,"{279, 321, 329, 220}"
592,1,269,0,0.1937734,"\int \sqrt{c x} \sqrt{a+b x^2} \, dx","Int[Sqrt[c*x]*Sqrt[a + b*x^2],x]","\frac{2 a^{5/4} \sqrt{c} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{5 b^{3/4} \sqrt{a+b x^2}}-\frac{4 a^{5/4} \sqrt{c} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{5 b^{3/4} \sqrt{a+b x^2}}+\frac{2 (c x)^{3/2} \sqrt{a+b x^2}}{5 c}+\frac{4 a \sqrt{c x} \sqrt{a+b x^2}}{5 \sqrt{b} \left(\sqrt{a}+\sqrt{b} x\right)}","\frac{2 a^{5/4} \sqrt{c} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{5 b^{3/4} \sqrt{a+b x^2}}-\frac{4 a^{5/4} \sqrt{c} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{5 b^{3/4} \sqrt{a+b x^2}}+\frac{2 (c x)^{3/2} \sqrt{a+b x^2}}{5 c}+\frac{4 a \sqrt{c x} \sqrt{a+b x^2}}{5 \sqrt{b} \left(\sqrt{a}+\sqrt{b} x\right)}",1,"(2*(c*x)^(3/2)*Sqrt[a + b*x^2])/(5*c) + (4*a*Sqrt[c*x]*Sqrt[a + b*x^2])/(5*Sqrt[b]*(Sqrt[a] + Sqrt[b]*x)) - (4*a^(5/4)*Sqrt[c]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(5*b^(3/4)*Sqrt[a + b*x^2]) + (2*a^(5/4)*Sqrt[c]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(5*b^(3/4)*Sqrt[a + b*x^2])","A",5,5,19,0.2632,1,"{279, 329, 305, 220, 1196}"
593,1,126,0,0.0743437,"\int \frac{\sqrt{a+b x^2}}{\sqrt{c x}} \, dx","Int[Sqrt[a + b*x^2]/Sqrt[c*x],x]","\frac{2 a^{3/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{3 \sqrt[4]{b} \sqrt{c} \sqrt{a+b x^2}}+\frac{2 \sqrt{c x} \sqrt{a+b x^2}}{3 c}","\frac{2 a^{3/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{3 \sqrt[4]{b} \sqrt{c} \sqrt{a+b x^2}}+\frac{2 \sqrt{c x} \sqrt{a+b x^2}}{3 c}",1,"(2*Sqrt[c*x]*Sqrt[a + b*x^2])/(3*c) + (2*a^(3/4)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(3*b^(1/4)*Sqrt[c]*Sqrt[a + b*x^2])","A",3,3,19,0.1579,1,"{279, 329, 220}"
594,1,263,0,0.1942351,"\int \frac{\sqrt{a+b x^2}}{(c x)^{3/2}} \, dx","Int[Sqrt[a + b*x^2]/(c*x)^(3/2),x]","\frac{4 \sqrt{b} \sqrt{c x} \sqrt{a+b x^2}}{c^2 \left(\sqrt{a}+\sqrt{b} x\right)}+\frac{2 \sqrt[4]{a} \sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{c^{3/2} \sqrt{a+b x^2}}-\frac{4 \sqrt[4]{a} \sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{c^{3/2} \sqrt{a+b x^2}}-\frac{2 \sqrt{a+b x^2}}{c \sqrt{c x}}","\frac{4 \sqrt{b} \sqrt{c x} \sqrt{a+b x^2}}{c^2 \left(\sqrt{a}+\sqrt{b} x\right)}+\frac{2 \sqrt[4]{a} \sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{c^{3/2} \sqrt{a+b x^2}}-\frac{4 \sqrt[4]{a} \sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{c^{3/2} \sqrt{a+b x^2}}-\frac{2 \sqrt{a+b x^2}}{c \sqrt{c x}}",1,"(-2*Sqrt[a + b*x^2])/(c*Sqrt[c*x]) + (4*Sqrt[b]*Sqrt[c*x]*Sqrt[a + b*x^2])/(c^2*(Sqrt[a] + Sqrt[b]*x)) - (4*a^(1/4)*b^(1/4)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(c^(3/2)*Sqrt[a + b*x^2]) + (2*a^(1/4)*b^(1/4)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(c^(3/2)*Sqrt[a + b*x^2])","A",5,5,19,0.2632,1,"{277, 329, 305, 220, 1196}"
595,1,126,0,0.0757863,"\int \frac{\sqrt{a+b x^2}}{(c x)^{5/2}} \, dx","Int[Sqrt[a + b*x^2]/(c*x)^(5/2),x]","\frac{2 b^{3/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{3 \sqrt[4]{a} c^{5/2} \sqrt{a+b x^2}}-\frac{2 \sqrt{a+b x^2}}{3 c (c x)^{3/2}}","\frac{2 b^{3/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{3 \sqrt[4]{a} c^{5/2} \sqrt{a+b x^2}}-\frac{2 \sqrt{a+b x^2}}{3 c (c x)^{3/2}}",1,"(-2*Sqrt[a + b*x^2])/(3*c*(c*x)^(3/2)) + (2*b^(3/4)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(3*a^(1/4)*c^(5/2)*Sqrt[a + b*x^2])","A",3,3,19,0.1579,1,"{277, 329, 220}"
596,1,303,0,0.2224026,"\int \frac{\sqrt{a+b x^2}}{(c x)^{7/2}} \, dx","Int[Sqrt[a + b*x^2]/(c*x)^(7/2),x]","\frac{2 b^{5/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{5 a^{3/4} c^{7/2} \sqrt{a+b x^2}}-\frac{4 b^{5/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{5 a^{3/4} c^{7/2} \sqrt{a+b x^2}}+\frac{4 b^{3/2} \sqrt{c x} \sqrt{a+b x^2}}{5 a c^4 \left(\sqrt{a}+\sqrt{b} x\right)}-\frac{4 b \sqrt{a+b x^2}}{5 a c^3 \sqrt{c x}}-\frac{2 \sqrt{a+b x^2}}{5 c (c x)^{5/2}}","\frac{2 b^{5/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{5 a^{3/4} c^{7/2} \sqrt{a+b x^2}}-\frac{4 b^{5/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{5 a^{3/4} c^{7/2} \sqrt{a+b x^2}}+\frac{4 b^{3/2} \sqrt{c x} \sqrt{a+b x^2}}{5 a c^4 \left(\sqrt{a}+\sqrt{b} x\right)}-\frac{4 b \sqrt{a+b x^2}}{5 a c^3 \sqrt{c x}}-\frac{2 \sqrt{a+b x^2}}{5 c (c x)^{5/2}}",1,"(-2*Sqrt[a + b*x^2])/(5*c*(c*x)^(5/2)) - (4*b*Sqrt[a + b*x^2])/(5*a*c^3*Sqrt[c*x]) + (4*b^(3/2)*Sqrt[c*x]*Sqrt[a + b*x^2])/(5*a*c^4*(Sqrt[a] + Sqrt[b]*x)) - (4*b^(5/4)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(5*a^(3/4)*c^(7/2)*Sqrt[a + b*x^2]) + (2*b^(5/4)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(5*a^(3/4)*c^(7/2)*Sqrt[a + b*x^2])","A",6,6,19,0.3158,1,"{277, 325, 329, 305, 220, 1196}"
597,1,212,0,0.1301828,"\int (c x)^{7/2} \left(a+b x^2\right)^{3/2} \, dx","Int[(c*x)^(7/2)*(a + b*x^2)^(3/2),x]","-\frac{8 a^3 c^3 \sqrt{c x} \sqrt{a+b x^2}}{231 b^2}+\frac{4 a^{15/4} c^{7/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{231 b^{9/4} \sqrt{a+b x^2}}+\frac{8 a^2 c (c x)^{5/2} \sqrt{a+b x^2}}{385 b}+\frac{2 (c x)^{9/2} \left(a+b x^2\right)^{3/2}}{15 c}+\frac{4 a (c x)^{9/2} \sqrt{a+b x^2}}{55 c}","-\frac{8 a^3 c^3 \sqrt{c x} \sqrt{a+b x^2}}{231 b^2}+\frac{4 a^{15/4} c^{7/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{231 b^{9/4} \sqrt{a+b x^2}}+\frac{8 a^2 c (c x)^{5/2} \sqrt{a+b x^2}}{385 b}+\frac{2 (c x)^{9/2} \left(a+b x^2\right)^{3/2}}{15 c}+\frac{4 a (c x)^{9/2} \sqrt{a+b x^2}}{55 c}",1,"(-8*a^3*c^3*Sqrt[c*x]*Sqrt[a + b*x^2])/(231*b^2) + (8*a^2*c*(c*x)^(5/2)*Sqrt[a + b*x^2])/(385*b) + (4*a*(c*x)^(9/2)*Sqrt[a + b*x^2])/(55*c) + (2*(c*x)^(9/2)*(a + b*x^2)^(3/2))/(15*c) + (4*a^(15/4)*c^(7/2)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(231*b^(9/4)*Sqrt[a + b*x^2])","A",6,4,19,0.2105,1,"{279, 321, 329, 220}"
598,1,329,0,0.2559729,"\int (c x)^{5/2} \left(a+b x^2\right)^{3/2} \, dx","Int[(c*x)^(5/2)*(a + b*x^2)^(3/2),x]","-\frac{8 a^3 c^2 \sqrt{c x} \sqrt{a+b x^2}}{65 b^{3/2} \left(\sqrt{a}+\sqrt{b} x\right)}-\frac{4 a^{13/4} c^{5/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{65 b^{7/4} \sqrt{a+b x^2}}+\frac{8 a^{13/4} c^{5/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{65 b^{7/4} \sqrt{a+b x^2}}+\frac{8 a^2 c (c x)^{3/2} \sqrt{a+b x^2}}{195 b}+\frac{2 (c x)^{7/2} \left(a+b x^2\right)^{3/2}}{13 c}+\frac{4 a (c x)^{7/2} \sqrt{a+b x^2}}{39 c}","-\frac{8 a^3 c^2 \sqrt{c x} \sqrt{a+b x^2}}{65 b^{3/2} \left(\sqrt{a}+\sqrt{b} x\right)}-\frac{4 a^{13/4} c^{5/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{65 b^{7/4} \sqrt{a+b x^2}}+\frac{8 a^{13/4} c^{5/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{65 b^{7/4} \sqrt{a+b x^2}}+\frac{8 a^2 c (c x)^{3/2} \sqrt{a+b x^2}}{195 b}+\frac{2 (c x)^{7/2} \left(a+b x^2\right)^{3/2}}{13 c}+\frac{4 a (c x)^{7/2} \sqrt{a+b x^2}}{39 c}",1,"(8*a^2*c*(c*x)^(3/2)*Sqrt[a + b*x^2])/(195*b) + (4*a*(c*x)^(7/2)*Sqrt[a + b*x^2])/(39*c) - (8*a^3*c^2*Sqrt[c*x]*Sqrt[a + b*x^2])/(65*b^(3/2)*(Sqrt[a] + Sqrt[b]*x)) + (2*(c*x)^(7/2)*(a + b*x^2)^(3/2))/(13*c) + (8*a^(13/4)*c^(5/2)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(65*b^(7/4)*Sqrt[a + b*x^2]) - (4*a^(13/4)*c^(5/2)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(65*b^(7/4)*Sqrt[a + b*x^2])","A",7,6,19,0.3158,1,"{279, 321, 329, 305, 220, 1196}"
599,1,181,0,0.1049038,"\int (c x)^{3/2} \left(a+b x^2\right)^{3/2} \, dx","Int[(c*x)^(3/2)*(a + b*x^2)^(3/2),x]","-\frac{4 a^{11/4} c^{3/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{77 b^{5/4} \sqrt{a+b x^2}}+\frac{8 a^2 c \sqrt{c x} \sqrt{a+b x^2}}{77 b}+\frac{12 a (c x)^{5/2} \sqrt{a+b x^2}}{77 c}+\frac{2 (c x)^{5/2} \left(a+b x^2\right)^{3/2}}{11 c}","-\frac{4 a^{11/4} c^{3/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{77 b^{5/4} \sqrt{a+b x^2}}+\frac{8 a^2 c \sqrt{c x} \sqrt{a+b x^2}}{77 b}+\frac{12 a (c x)^{5/2} \sqrt{a+b x^2}}{77 c}+\frac{2 (c x)^{5/2} \left(a+b x^2\right)^{3/2}}{11 c}",1,"(8*a^2*c*Sqrt[c*x]*Sqrt[a + b*x^2])/(77*b) + (12*a*(c*x)^(5/2)*Sqrt[a + b*x^2])/(77*c) + (2*(c*x)^(5/2)*(a + b*x^2)^(3/2))/(11*c) - (4*a^(11/4)*c^(3/2)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(77*b^(5/4)*Sqrt[a + b*x^2])","A",5,4,19,0.2105,1,"{279, 321, 329, 220}"
600,1,297,0,0.2239433,"\int \sqrt{c x} \left(a+b x^2\right)^{3/2} \, dx","Int[Sqrt[c*x]*(a + b*x^2)^(3/2),x]","\frac{4 a^{9/4} \sqrt{c} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{15 b^{3/4} \sqrt{a+b x^2}}-\frac{8 a^{9/4} \sqrt{c} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{15 b^{3/4} \sqrt{a+b x^2}}+\frac{8 a^2 \sqrt{c x} \sqrt{a+b x^2}}{15 \sqrt{b} \left(\sqrt{a}+\sqrt{b} x\right)}+\frac{4 a (c x)^{3/2} \sqrt{a+b x^2}}{15 c}+\frac{2 (c x)^{3/2} \left(a+b x^2\right)^{3/2}}{9 c}","\frac{4 a^{9/4} \sqrt{c} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{15 b^{3/4} \sqrt{a+b x^2}}-\frac{8 a^{9/4} \sqrt{c} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{15 b^{3/4} \sqrt{a+b x^2}}+\frac{8 a^2 \sqrt{c x} \sqrt{a+b x^2}}{15 \sqrt{b} \left(\sqrt{a}+\sqrt{b} x\right)}+\frac{4 a (c x)^{3/2} \sqrt{a+b x^2}}{15 c}+\frac{2 (c x)^{3/2} \left(a+b x^2\right)^{3/2}}{9 c}",1,"(4*a*(c*x)^(3/2)*Sqrt[a + b*x^2])/(15*c) + (8*a^2*Sqrt[c*x]*Sqrt[a + b*x^2])/(15*Sqrt[b]*(Sqrt[a] + Sqrt[b]*x)) + (2*(c*x)^(3/2)*(a + b*x^2)^(3/2))/(9*c) - (8*a^(9/4)*Sqrt[c]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(15*b^(3/4)*Sqrt[a + b*x^2]) + (4*a^(9/4)*Sqrt[c]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(15*b^(3/4)*Sqrt[a + b*x^2])","A",6,5,19,0.2632,1,"{279, 329, 305, 220, 1196}"
601,1,152,0,0.0904508,"\int \frac{\left(a+b x^2\right)^{3/2}}{\sqrt{c x}} \, dx","Int[(a + b*x^2)^(3/2)/Sqrt[c*x],x]","\frac{4 a^{7/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{7 \sqrt[4]{b} \sqrt{c} \sqrt{a+b x^2}}+\frac{4 a \sqrt{c x} \sqrt{a+b x^2}}{7 c}+\frac{2 \sqrt{c x} \left(a+b x^2\right)^{3/2}}{7 c}","\frac{4 a^{7/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{7 \sqrt[4]{b} \sqrt{c} \sqrt{a+b x^2}}+\frac{4 a \sqrt{c x} \sqrt{a+b x^2}}{7 c}+\frac{2 \sqrt{c x} \left(a+b x^2\right)^{3/2}}{7 c}",1,"(4*a*Sqrt[c*x]*Sqrt[a + b*x^2])/(7*c) + (2*Sqrt[c*x]*(a + b*x^2)^(3/2))/(7*c) + (4*a^(7/4)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(7*b^(1/4)*Sqrt[c]*Sqrt[a + b*x^2])","A",4,3,19,0.1579,1,"{279, 329, 220}"
602,1,296,0,0.2296911,"\int \frac{\left(a+b x^2\right)^{3/2}}{(c x)^{3/2}} \, dx","Int[(a + b*x^2)^(3/2)/(c*x)^(3/2),x]","\frac{12 a^{5/4} \sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{5 c^{3/2} \sqrt{a+b x^2}}-\frac{24 a^{5/4} \sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{5 c^{3/2} \sqrt{a+b x^2}}+\frac{12 b (c x)^{3/2} \sqrt{a+b x^2}}{5 c^3}+\frac{24 a \sqrt{b} \sqrt{c x} \sqrt{a+b x^2}}{5 c^2 \left(\sqrt{a}+\sqrt{b} x\right)}-\frac{2 \left(a+b x^2\right)^{3/2}}{c \sqrt{c x}}","\frac{12 a^{5/4} \sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{5 c^{3/2} \sqrt{a+b x^2}}-\frac{24 a^{5/4} \sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{5 c^{3/2} \sqrt{a+b x^2}}+\frac{12 b (c x)^{3/2} \sqrt{a+b x^2}}{5 c^3}+\frac{24 a \sqrt{b} \sqrt{c x} \sqrt{a+b x^2}}{5 c^2 \left(\sqrt{a}+\sqrt{b} x\right)}-\frac{2 \left(a+b x^2\right)^{3/2}}{c \sqrt{c x}}",1,"(12*b*(c*x)^(3/2)*Sqrt[a + b*x^2])/(5*c^3) + (24*a*Sqrt[b]*Sqrt[c*x]*Sqrt[a + b*x^2])/(5*c^2*(Sqrt[a] + Sqrt[b]*x)) - (2*(a + b*x^2)^(3/2))/(c*Sqrt[c*x]) - (24*a^(5/4)*b^(1/4)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(5*c^(3/2)*Sqrt[a + b*x^2]) + (12*a^(5/4)*b^(1/4)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(5*c^(3/2)*Sqrt[a + b*x^2])","A",6,6,19,0.3158,1,"{277, 279, 329, 305, 220, 1196}"
603,1,152,0,0.0927667,"\int \frac{\left(a+b x^2\right)^{3/2}}{(c x)^{5/2}} \, dx","Int[(a + b*x^2)^(3/2)/(c*x)^(5/2),x]","\frac{4 a^{3/4} b^{3/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{3 c^{5/2} \sqrt{a+b x^2}}+\frac{4 b \sqrt{c x} \sqrt{a+b x^2}}{3 c^3}-\frac{2 \left(a+b x^2\right)^{3/2}}{3 c (c x)^{3/2}}","\frac{4 a^{3/4} b^{3/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{3 c^{5/2} \sqrt{a+b x^2}}+\frac{4 b \sqrt{c x} \sqrt{a+b x^2}}{3 c^3}-\frac{2 \left(a+b x^2\right)^{3/2}}{3 c (c x)^{3/2}}",1,"(4*b*Sqrt[c*x]*Sqrt[a + b*x^2])/(3*c^3) - (2*(a + b*x^2)^(3/2))/(3*c*(c*x)^(3/2)) + (4*a^(3/4)*b^(3/4)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(3*c^(5/2)*Sqrt[a + b*x^2])","A",4,4,19,0.2105,1,"{277, 279, 329, 220}"
604,1,297,0,0.227211,"\int \frac{\left(a+b x^2\right)^{3/2}}{(c x)^{7/2}} \, dx","Int[(a + b*x^2)^(3/2)/(c*x)^(7/2),x]","\frac{24 b^{3/2} \sqrt{c x} \sqrt{a+b x^2}}{5 c^4 \left(\sqrt{a}+\sqrt{b} x\right)}+\frac{12 \sqrt[4]{a} b^{5/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{5 c^{7/2} \sqrt{a+b x^2}}-\frac{24 \sqrt[4]{a} b^{5/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{5 c^{7/2} \sqrt{a+b x^2}}-\frac{12 b \sqrt{a+b x^2}}{5 c^3 \sqrt{c x}}-\frac{2 \left(a+b x^2\right)^{3/2}}{5 c (c x)^{5/2}}","\frac{24 b^{3/2} \sqrt{c x} \sqrt{a+b x^2}}{5 c^4 \left(\sqrt{a}+\sqrt{b} x\right)}+\frac{12 \sqrt[4]{a} b^{5/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{5 c^{7/2} \sqrt{a+b x^2}}-\frac{24 \sqrt[4]{a} b^{5/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{5 c^{7/2} \sqrt{a+b x^2}}-\frac{12 b \sqrt{a+b x^2}}{5 c^3 \sqrt{c x}}-\frac{2 \left(a+b x^2\right)^{3/2}}{5 c (c x)^{5/2}}",1,"(-12*b*Sqrt[a + b*x^2])/(5*c^3*Sqrt[c*x]) + (24*b^(3/2)*Sqrt[c*x]*Sqrt[a + b*x^2])/(5*c^4*(Sqrt[a] + Sqrt[b]*x)) - (2*(a + b*x^2)^(3/2))/(5*c*(c*x)^(5/2)) - (24*a^(1/4)*b^(5/4)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(5*c^(7/2)*Sqrt[a + b*x^2]) + (12*a^(1/4)*b^(5/4)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(5*c^(7/2)*Sqrt[a + b*x^2])","A",6,5,19,0.2632,1,"{277, 329, 305, 220, 1196}"
605,1,152,0,0.0917747,"\int \frac{\left(a+b x^2\right)^{3/2}}{(c x)^{9/2}} \, dx","Int[(a + b*x^2)^(3/2)/(c*x)^(9/2),x]","\frac{4 b^{7/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{7 \sqrt[4]{a} c^{9/2} \sqrt{a+b x^2}}-\frac{4 b \sqrt{a+b x^2}}{7 c^3 (c x)^{3/2}}-\frac{2 \left(a+b x^2\right)^{3/2}}{7 c (c x)^{7/2}}","\frac{4 b^{7/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{7 \sqrt[4]{a} c^{9/2} \sqrt{a+b x^2}}-\frac{4 b \sqrt{a+b x^2}}{7 c^3 (c x)^{3/2}}-\frac{2 \left(a+b x^2\right)^{3/2}}{7 c (c x)^{7/2}}",1,"(-4*b*Sqrt[a + b*x^2])/(7*c^3*(c*x)^(3/2)) - (2*(a + b*x^2)^(3/2))/(7*c*(c*x)^(7/2)) + (4*b^(7/4)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(7*a^(1/4)*c^(9/2)*Sqrt[a + b*x^2])","A",4,3,19,0.1579,1,"{277, 329, 220}"
606,1,331,0,0.2702835,"\int \frac{\left(a+b x^2\right)^{3/2}}{(c x)^{11/2}} \, dx","Int[(a + b*x^2)^(3/2)/(c*x)^(11/2),x]","\frac{4 b^{9/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{15 a^{3/4} c^{11/2} \sqrt{a+b x^2}}-\frac{8 b^{9/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{15 a^{3/4} c^{11/2} \sqrt{a+b x^2}}+\frac{8 b^{5/2} \sqrt{c x} \sqrt{a+b x^2}}{15 a c^6 \left(\sqrt{a}+\sqrt{b} x\right)}-\frac{8 b^2 \sqrt{a+b x^2}}{15 a c^5 \sqrt{c x}}-\frac{4 b \sqrt{a+b x^2}}{15 c^3 (c x)^{5/2}}-\frac{2 \left(a+b x^2\right)^{3/2}}{9 c (c x)^{9/2}}","\frac{4 b^{9/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{15 a^{3/4} c^{11/2} \sqrt{a+b x^2}}-\frac{8 b^{9/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{15 a^{3/4} c^{11/2} \sqrt{a+b x^2}}+\frac{8 b^{5/2} \sqrt{c x} \sqrt{a+b x^2}}{15 a c^6 \left(\sqrt{a}+\sqrt{b} x\right)}-\frac{8 b^2 \sqrt{a+b x^2}}{15 a c^5 \sqrt{c x}}-\frac{4 b \sqrt{a+b x^2}}{15 c^3 (c x)^{5/2}}-\frac{2 \left(a+b x^2\right)^{3/2}}{9 c (c x)^{9/2}}",1,"(-4*b*Sqrt[a + b*x^2])/(15*c^3*(c*x)^(5/2)) - (8*b^2*Sqrt[a + b*x^2])/(15*a*c^5*Sqrt[c*x]) + (8*b^(5/2)*Sqrt[c*x]*Sqrt[a + b*x^2])/(15*a*c^6*(Sqrt[a] + Sqrt[b]*x)) - (2*(a + b*x^2)^(3/2))/(9*c*(c*x)^(9/2)) - (8*b^(9/4)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(15*a^(3/4)*c^(11/2)*Sqrt[a + b*x^2]) + (4*b^(9/4)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(15*a^(3/4)*c^(11/2)*Sqrt[a + b*x^2])","A",7,6,19,0.3158,1,"{277, 325, 329, 305, 220, 1196}"
607,1,128,0,0.0639806,"\int (c x)^{5/2} \sqrt{3 a-2 a x^2} \, dx","Int[(c*x)^(5/2)*Sqrt[3*a - 2*a*x^2],x]","-\frac{3 \sqrt[4]{6} a c^2 \sqrt{3-2 x^2} \sqrt{c x} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{3-\sqrt{6} x}}{\sqrt{6}}\right)\right|2\right)}{5 \sqrt{x} \sqrt{3 a-2 a x^2}}+\frac{2 \sqrt{3 a-2 a x^2} (c x)^{7/2}}{9 c}-\frac{2}{15} c \sqrt{3 a-2 a x^2} (c x)^{3/2}","-\frac{3 \sqrt[4]{6} a c^2 \sqrt{3-2 x^2} \sqrt{c x} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{3-\sqrt{6} x}}{\sqrt{6}}\right)\right|2\right)}{5 \sqrt{x} \sqrt{3 a-2 a x^2}}+\frac{2 \sqrt{3 a-2 a x^2} (c x)^{7/2}}{9 c}-\frac{2}{15} c \sqrt{3 a-2 a x^2} (c x)^{3/2}",1,"(-2*c*(c*x)^(3/2)*Sqrt[3*a - 2*a*x^2])/15 + (2*(c*x)^(7/2)*Sqrt[3*a - 2*a*x^2])/(9*c) - (3*6^(1/4)*a*c^2*Sqrt[c*x]*Sqrt[3 - 2*x^2]*EllipticE[ArcSin[Sqrt[3 - Sqrt[6]*x]/Sqrt[6]], 2])/(5*Sqrt[x]*Sqrt[3*a - 2*a*x^2])","A",6,6,22,0.2727,1,"{279, 321, 320, 319, 318, 424}"
608,1,117,0,0.0774048,"\int (c x)^{3/2} \sqrt{3 a-2 a x^2} \, dx","Int[(c*x)^(3/2)*Sqrt[3*a - 2*a*x^2],x]","\frac{6^{3/4} a c^{3/2} \sqrt{3-2 x^2} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{\frac{2}{3}} \sqrt{c x}}{\sqrt{c}}\right)\right|-1\right)}{7 \sqrt{a \left(3-2 x^2\right)}}+\frac{2 \sqrt{3 a-2 a x^2} (c x)^{5/2}}{7 c}-\frac{2}{7} c \sqrt{3 a-2 a x^2} \sqrt{c x}","\frac{6^{3/4} a c^{3/2} \sqrt{3-2 x^2} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{\frac{2}{3}} \sqrt{c x}}{\sqrt{c}}\right)\right|-1\right)}{7 \sqrt{a \left(3-2 x^2\right)}}+\frac{2 \sqrt{3 a-2 a x^2} (c x)^{5/2}}{7 c}-\frac{2}{7} c \sqrt{3 a-2 a x^2} \sqrt{c x}",1,"(-2*c*Sqrt[c*x]*Sqrt[3*a - 2*a*x^2])/7 + (2*(c*x)^(5/2)*Sqrt[3*a - 2*a*x^2])/(7*c) + (6^(3/4)*a*c^(3/2)*Sqrt[3 - 2*x^2]*EllipticF[ArcSin[((2/3)^(1/4)*Sqrt[c*x])/Sqrt[c]], -1])/(7*Sqrt[a*(3 - 2*x^2)])","A",5,5,22,0.2273,1,"{279, 321, 329, 224, 221}"
609,1,99,0,0.0428037,"\int \sqrt{c x} \sqrt{3 a-2 a x^2} \, dx","Int[Sqrt[c*x]*Sqrt[3*a - 2*a*x^2],x]","\frac{2 \sqrt{3 a-2 a x^2} (c x)^{3/2}}{5 c}-\frac{6 \sqrt[4]{6} a \sqrt{3-2 x^2} \sqrt{c x} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{3-\sqrt{6} x}}{\sqrt{6}}\right)\right|2\right)}{5 \sqrt{x} \sqrt{3 a-2 a x^2}}","\frac{2 \sqrt{3 a-2 a x^2} (c x)^{3/2}}{5 c}-\frac{6 \sqrt[4]{6} a \sqrt{3-2 x^2} \sqrt{c x} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{3-\sqrt{6} x}}{\sqrt{6}}\right)\right|2\right)}{5 \sqrt{x} \sqrt{3 a-2 a x^2}}",1,"(2*(c*x)^(3/2)*Sqrt[3*a - 2*a*x^2])/(5*c) - (6*6^(1/4)*a*Sqrt[c*x]*Sqrt[3 - 2*x^2]*EllipticE[ArcSin[Sqrt[3 - Sqrt[6]*x]/Sqrt[6]], 2])/(5*Sqrt[x]*Sqrt[3*a - 2*a*x^2])","A",5,5,22,0.2273,1,"{279, 320, 319, 318, 424}"
610,1,94,0,0.0468306,"\int \frac{\sqrt{3 a-2 a x^2}}{\sqrt{c x}} \, dx","Int[Sqrt[3*a - 2*a*x^2]/Sqrt[c*x],x]","\frac{2 \sqrt{3 a-2 a x^2} \sqrt{c x}}{3 c}+\frac{2\ 2^{3/4} a \sqrt{3-2 x^2} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{\frac{2}{3}} \sqrt{c x}}{\sqrt{c}}\right)\right|-1\right)}{\sqrt[4]{3} \sqrt{c} \sqrt{a \left(3-2 x^2\right)}}","\frac{2 \sqrt{3 a-2 a x^2} \sqrt{c x}}{3 c}+\frac{2\ 2^{3/4} a \sqrt{3-2 x^2} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{\frac{2}{3}} \sqrt{c x}}{\sqrt{c}}\right)\right|-1\right)}{\sqrt[4]{3} \sqrt{c} \sqrt{a \left(3-2 x^2\right)}}",1,"(2*Sqrt[c*x]*Sqrt[3*a - 2*a*x^2])/(3*c) + (2*2^(3/4)*a*Sqrt[3 - 2*x^2]*EllipticF[ArcSin[((2/3)^(1/4)*Sqrt[c*x])/Sqrt[c]], -1])/(3^(1/4)*Sqrt[c]*Sqrt[a*(3 - 2*x^2)])","A",4,4,22,0.1818,1,"{279, 329, 224, 221}"
611,1,98,0,0.0416983,"\int \frac{\sqrt{3 a-2 a x^2}}{(c x)^{3/2}} \, dx","Int[Sqrt[3*a - 2*a*x^2]/(c*x)^(3/2),x]","\frac{4 \sqrt[4]{6} a \sqrt{3-2 x^2} \sqrt{c x} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{3-\sqrt{6} x}}{\sqrt{6}}\right)\right|2\right)}{c^2 \sqrt{x} \sqrt{3 a-2 a x^2}}-\frac{2 \sqrt{3 a-2 a x^2}}{c \sqrt{c x}}","\frac{4 \sqrt[4]{6} a \sqrt{3-2 x^2} \sqrt{c x} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{3-\sqrt{6} x}}{\sqrt{6}}\right)\right|2\right)}{c^2 \sqrt{x} \sqrt{3 a-2 a x^2}}-\frac{2 \sqrt{3 a-2 a x^2}}{c \sqrt{c x}}",1,"(-2*Sqrt[3*a - 2*a*x^2])/(c*Sqrt[c*x]) + (4*6^(1/4)*a*Sqrt[c*x]*Sqrt[3 - 2*x^2]*EllipticE[ArcSin[Sqrt[3 - Sqrt[6]*x]/Sqrt[6]], 2])/(c^2*Sqrt[x]*Sqrt[3*a - 2*a*x^2])","A",5,5,22,0.2273,1,"{277, 320, 319, 318, 424}"
612,1,96,0,0.0482166,"\int \frac{\sqrt{3 a-2 a x^2}}{(c x)^{5/2}} \, dx","Int[Sqrt[3*a - 2*a*x^2]/(c*x)^(5/2),x]","-\frac{4\ 2^{3/4} a \sqrt{3-2 x^2} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{\frac{2}{3}} \sqrt{c x}}{\sqrt{c}}\right)\right|-1\right)}{3 \sqrt[4]{3} c^{5/2} \sqrt{a \left(3-2 x^2\right)}}-\frac{2 \sqrt{3 a-2 a x^2}}{3 c (c x)^{3/2}}","-\frac{4\ 2^{3/4} a \sqrt{3-2 x^2} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{\frac{2}{3}} \sqrt{c x}}{\sqrt{c}}\right)\right|-1\right)}{3 \sqrt[4]{3} c^{5/2} \sqrt{a \left(3-2 x^2\right)}}-\frac{2 \sqrt{3 a-2 a x^2}}{3 c (c x)^{3/2}}",1,"(-2*Sqrt[3*a - 2*a*x^2])/(3*c*(c*x)^(3/2)) - (4*2^(3/4)*a*Sqrt[3 - 2*x^2]*EllipticF[ArcSin[((2/3)^(1/4)*Sqrt[c*x])/Sqrt[c]], -1])/(3*3^(1/4)*c^(5/2)*Sqrt[a*(3 - 2*x^2)])","A",4,4,22,0.1818,1,"{277, 329, 224, 221}"
613,1,156,0,0.0897231,"\int \frac{(c x)^{7/2}}{\sqrt{a+b x^2}} \, dx","Int[(c*x)^(7/2)/Sqrt[a + b*x^2],x]","\frac{5 a^{7/4} c^{7/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{21 b^{9/4} \sqrt{a+b x^2}}-\frac{10 a c^3 \sqrt{c x} \sqrt{a+b x^2}}{21 b^2}+\frac{2 c (c x)^{5/2} \sqrt{a+b x^2}}{7 b}","\frac{5 a^{7/4} c^{7/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{21 b^{9/4} \sqrt{a+b x^2}}-\frac{10 a c^3 \sqrt{c x} \sqrt{a+b x^2}}{21 b^2}+\frac{2 c (c x)^{5/2} \sqrt{a+b x^2}}{7 b}",1,"(-10*a*c^3*Sqrt[c*x]*Sqrt[a + b*x^2])/(21*b^2) + (2*c*(c*x)^(5/2)*Sqrt[a + b*x^2])/(7*b) + (5*a^(7/4)*c^(7/2)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(21*b^(9/4)*Sqrt[a + b*x^2])","A",4,3,19,0.1579,1,"{321, 329, 220}"
614,1,273,0,0.1864989,"\int \frac{(c x)^{5/2}}{\sqrt{a+b x^2}} \, dx","Int[(c*x)^(5/2)/Sqrt[a + b*x^2],x]","-\frac{3 a^{5/4} c^{5/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{5 b^{7/4} \sqrt{a+b x^2}}+\frac{6 a^{5/4} c^{5/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{5 b^{7/4} \sqrt{a+b x^2}}-\frac{6 a c^2 \sqrt{c x} \sqrt{a+b x^2}}{5 b^{3/2} \left(\sqrt{a}+\sqrt{b} x\right)}+\frac{2 c (c x)^{3/2} \sqrt{a+b x^2}}{5 b}","-\frac{3 a^{5/4} c^{5/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{5 b^{7/4} \sqrt{a+b x^2}}+\frac{6 a^{5/4} c^{5/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{5 b^{7/4} \sqrt{a+b x^2}}-\frac{6 a c^2 \sqrt{c x} \sqrt{a+b x^2}}{5 b^{3/2} \left(\sqrt{a}+\sqrt{b} x\right)}+\frac{2 c (c x)^{3/2} \sqrt{a+b x^2}}{5 b}",1,"(2*c*(c*x)^(3/2)*Sqrt[a + b*x^2])/(5*b) - (6*a*c^2*Sqrt[c*x]*Sqrt[a + b*x^2])/(5*b^(3/2)*(Sqrt[a] + Sqrt[b]*x)) + (6*a^(5/4)*c^(5/2)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(5*b^(7/4)*Sqrt[a + b*x^2]) - (3*a^(5/4)*c^(5/2)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(5*b^(7/4)*Sqrt[a + b*x^2])","A",5,5,19,0.2632,1,"{321, 329, 305, 220, 1196}"
615,1,127,0,0.070928,"\int \frac{(c x)^{3/2}}{\sqrt{a+b x^2}} \, dx","Int[(c*x)^(3/2)/Sqrt[a + b*x^2],x]","\frac{2 c \sqrt{c x} \sqrt{a+b x^2}}{3 b}-\frac{a^{3/4} c^{3/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{3 b^{5/4} \sqrt{a+b x^2}}","\frac{2 c \sqrt{c x} \sqrt{a+b x^2}}{3 b}-\frac{a^{3/4} c^{3/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{3 b^{5/4} \sqrt{a+b x^2}}",1,"(2*c*Sqrt[c*x]*Sqrt[a + b*x^2])/(3*b) - (a^(3/4)*c^(3/2)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(3*b^(5/4)*Sqrt[a + b*x^2])","A",3,3,19,0.1579,1,"{321, 329, 220}"
616,1,236,0,0.1661724,"\int \frac{\sqrt{c x}}{\sqrt{a+b x^2}} \, dx","Int[Sqrt[c*x]/Sqrt[a + b*x^2],x]","\frac{\sqrt[4]{a} \sqrt{c} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{b^{3/4} \sqrt{a+b x^2}}-\frac{2 \sqrt[4]{a} \sqrt{c} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{b^{3/4} \sqrt{a+b x^2}}+\frac{2 \sqrt{c x} \sqrt{a+b x^2}}{\sqrt{b} \left(\sqrt{a}+\sqrt{b} x\right)}","\frac{\sqrt[4]{a} \sqrt{c} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{b^{3/4} \sqrt{a+b x^2}}-\frac{2 \sqrt[4]{a} \sqrt{c} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{b^{3/4} \sqrt{a+b x^2}}+\frac{2 \sqrt{c x} \sqrt{a+b x^2}}{\sqrt{b} \left(\sqrt{a}+\sqrt{b} x\right)}",1,"(2*Sqrt[c*x]*Sqrt[a + b*x^2])/(Sqrt[b]*(Sqrt[a] + Sqrt[b]*x)) - (2*a^(1/4)*Sqrt[c]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(b^(3/4)*Sqrt[a + b*x^2]) + (a^(1/4)*Sqrt[c]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(b^(3/4)*Sqrt[a + b*x^2])","A",4,4,19,0.2105,1,"{329, 305, 220, 1196}"
617,1,97,0,0.0577287,"\int \frac{1}{\sqrt{c x} \sqrt{a+b x^2}} \, dx","Int[1/(Sqrt[c*x]*Sqrt[a + b*x^2]),x]","\frac{\left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{\sqrt[4]{a} \sqrt[4]{b} \sqrt{c} \sqrt{a+b x^2}}","\frac{\left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{\sqrt[4]{a} \sqrt[4]{b} \sqrt{c} \sqrt{a+b x^2}}",1,"((Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(a^(1/4)*b^(1/4)*Sqrt[c]*Sqrt[a + b*x^2])","A",2,2,19,0.1053,1,"{329, 220}"
618,1,268,0,0.1883724,"\int \frac{1}{(c x)^{3/2} \sqrt{a+b x^2}} \, dx","Int[1/((c*x)^(3/2)*Sqrt[a + b*x^2]),x]","\frac{\sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{a^{3/4} c^{3/2} \sqrt{a+b x^2}}-\frac{2 \sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{a^{3/4} c^{3/2} \sqrt{a+b x^2}}+\frac{2 \sqrt{b} \sqrt{c x} \sqrt{a+b x^2}}{a c^2 \left(\sqrt{a}+\sqrt{b} x\right)}-\frac{2 \sqrt{a+b x^2}}{a c \sqrt{c x}}","\frac{\sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{a^{3/4} c^{3/2} \sqrt{a+b x^2}}-\frac{2 \sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{a^{3/4} c^{3/2} \sqrt{a+b x^2}}+\frac{2 \sqrt{b} \sqrt{c x} \sqrt{a+b x^2}}{a c^2 \left(\sqrt{a}+\sqrt{b} x\right)}-\frac{2 \sqrt{a+b x^2}}{a c \sqrt{c x}}",1,"(-2*Sqrt[a + b*x^2])/(a*c*Sqrt[c*x]) + (2*Sqrt[b]*Sqrt[c*x]*Sqrt[a + b*x^2])/(a*c^2*(Sqrt[a] + Sqrt[b]*x)) - (2*b^(1/4)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(a^(3/4)*c^(3/2)*Sqrt[a + b*x^2]) + (b^(1/4)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(a^(3/4)*c^(3/2)*Sqrt[a + b*x^2])","A",5,5,19,0.2632,1,"{325, 329, 305, 220, 1196}"
619,1,129,0,0.0730192,"\int \frac{1}{(c x)^{5/2} \sqrt{a+b x^2}} \, dx","Int[1/((c*x)^(5/2)*Sqrt[a + b*x^2]),x]","-\frac{b^{3/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{3 a^{5/4} c^{5/2} \sqrt{a+b x^2}}-\frac{2 \sqrt{a+b x^2}}{3 a c (c x)^{3/2}}","-\frac{b^{3/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{3 a^{5/4} c^{5/2} \sqrt{a+b x^2}}-\frac{2 \sqrt{a+b x^2}}{3 a c (c x)^{3/2}}",1,"(-2*Sqrt[a + b*x^2])/(3*a*c*(c*x)^(3/2)) - (b^(3/4)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(3*a^(5/4)*c^(5/2)*Sqrt[a + b*x^2])","A",3,3,19,0.1579,1,"{325, 329, 220}"
620,1,306,0,0.2202734,"\int \frac{1}{(c x)^{7/2} \sqrt{a+b x^2}} \, dx","Int[1/((c*x)^(7/2)*Sqrt[a + b*x^2]),x]","-\frac{6 b^{3/2} \sqrt{c x} \sqrt{a+b x^2}}{5 a^2 c^4 \left(\sqrt{a}+\sqrt{b} x\right)}-\frac{3 b^{5/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{5 a^{7/4} c^{7/2} \sqrt{a+b x^2}}+\frac{6 b^{5/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{5 a^{7/4} c^{7/2} \sqrt{a+b x^2}}+\frac{6 b \sqrt{a+b x^2}}{5 a^2 c^3 \sqrt{c x}}-\frac{2 \sqrt{a+b x^2}}{5 a c (c x)^{5/2}}","-\frac{6 b^{3/2} \sqrt{c x} \sqrt{a+b x^2}}{5 a^2 c^4 \left(\sqrt{a}+\sqrt{b} x\right)}-\frac{3 b^{5/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{5 a^{7/4} c^{7/2} \sqrt{a+b x^2}}+\frac{6 b^{5/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{5 a^{7/4} c^{7/2} \sqrt{a+b x^2}}+\frac{6 b \sqrt{a+b x^2}}{5 a^2 c^3 \sqrt{c x}}-\frac{2 \sqrt{a+b x^2}}{5 a c (c x)^{5/2}}",1,"(-2*Sqrt[a + b*x^2])/(5*a*c*(c*x)^(5/2)) + (6*b*Sqrt[a + b*x^2])/(5*a^2*c^3*Sqrt[c*x]) - (6*b^(3/2)*Sqrt[c*x]*Sqrt[a + b*x^2])/(5*a^2*c^4*(Sqrt[a] + Sqrt[b]*x)) + (6*b^(5/4)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(5*a^(7/4)*c^(7/2)*Sqrt[a + b*x^2]) - (3*b^(5/4)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(5*a^(7/4)*c^(7/2)*Sqrt[a + b*x^2])","A",6,5,19,0.2632,1,"{325, 329, 305, 220, 1196}"
621,1,153,0,0.0866138,"\int \frac{(c x)^{7/2}}{\left(a+b x^2\right)^{3/2}} \, dx","Int[(c*x)^(7/2)/(a + b*x^2)^(3/2),x]","-\frac{5 a^{3/4} c^{7/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{6 b^{9/4} \sqrt{a+b x^2}}+\frac{5 c^3 \sqrt{c x} \sqrt{a+b x^2}}{3 b^2}-\frac{c (c x)^{5/2}}{b \sqrt{a+b x^2}}","-\frac{5 a^{3/4} c^{7/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{6 b^{9/4} \sqrt{a+b x^2}}+\frac{5 c^3 \sqrt{c x} \sqrt{a+b x^2}}{3 b^2}-\frac{c (c x)^{5/2}}{b \sqrt{a+b x^2}}",1,"-((c*(c*x)^(5/2))/(b*Sqrt[a + b*x^2])) + (5*c^3*Sqrt[c*x]*Sqrt[a + b*x^2])/(3*b^2) - (5*a^(3/4)*c^(7/2)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(6*b^(9/4)*Sqrt[a + b*x^2])","A",4,4,19,0.2105,1,"{288, 321, 329, 220}"
622,1,266,0,0.1890333,"\int \frac{(c x)^{5/2}}{\left(a+b x^2\right)^{3/2}} \, dx","Int[(c*x)^(5/2)/(a + b*x^2)^(3/2),x]","\frac{3 c^2 \sqrt{c x} \sqrt{a+b x^2}}{b^{3/2} \left(\sqrt{a}+\sqrt{b} x\right)}+\frac{3 \sqrt[4]{a} c^{5/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{2 b^{7/4} \sqrt{a+b x^2}}-\frac{3 \sqrt[4]{a} c^{5/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{b^{7/4} \sqrt{a+b x^2}}-\frac{c (c x)^{3/2}}{b \sqrt{a+b x^2}}","\frac{3 c^2 \sqrt{c x} \sqrt{a+b x^2}}{b^{3/2} \left(\sqrt{a}+\sqrt{b} x\right)}+\frac{3 \sqrt[4]{a} c^{5/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{2 b^{7/4} \sqrt{a+b x^2}}-\frac{3 \sqrt[4]{a} c^{5/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{b^{7/4} \sqrt{a+b x^2}}-\frac{c (c x)^{3/2}}{b \sqrt{a+b x^2}}",1,"-((c*(c*x)^(3/2))/(b*Sqrt[a + b*x^2])) + (3*c^2*Sqrt[c*x]*Sqrt[a + b*x^2])/(b^(3/2)*(Sqrt[a] + Sqrt[b]*x)) - (3*a^(1/4)*c^(5/2)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(b^(7/4)*Sqrt[a + b*x^2]) + (3*a^(1/4)*c^(5/2)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(2*b^(7/4)*Sqrt[a + b*x^2])","A",5,5,19,0.2632,1,"{288, 329, 305, 220, 1196}"
623,1,125,0,0.0707704,"\int \frac{(c x)^{3/2}}{\left(a+b x^2\right)^{3/2}} \, dx","Int[(c*x)^(3/2)/(a + b*x^2)^(3/2),x]","\frac{c^{3/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a} b^{5/4} \sqrt{a+b x^2}}-\frac{c \sqrt{c x}}{b \sqrt{a+b x^2}}","\frac{c^{3/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a} b^{5/4} \sqrt{a+b x^2}}-\frac{c \sqrt{c x}}{b \sqrt{a+b x^2}}",1,"-((c*Sqrt[c*x])/(b*Sqrt[a + b*x^2])) + (c^(3/2)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(2*a^(1/4)*b^(5/4)*Sqrt[a + b*x^2])","A",3,3,19,0.1579,1,"{288, 329, 220}"
624,1,266,0,0.1865921,"\int \frac{\sqrt{c x}}{\left(a+b x^2\right)^{3/2}} \, dx","Int[Sqrt[c*x]/(a + b*x^2)^(3/2),x]","-\frac{\sqrt{c} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{2 a^{3/4} b^{3/4} \sqrt{a+b x^2}}+\frac{\sqrt{c} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{a^{3/4} b^{3/4} \sqrt{a+b x^2}}+\frac{(c x)^{3/2}}{a c \sqrt{a+b x^2}}-\frac{\sqrt{c x} \sqrt{a+b x^2}}{a \sqrt{b} \left(\sqrt{a}+\sqrt{b} x\right)}","-\frac{\sqrt{c} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{2 a^{3/4} b^{3/4} \sqrt{a+b x^2}}+\frac{\sqrt{c} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{a^{3/4} b^{3/4} \sqrt{a+b x^2}}+\frac{(c x)^{3/2}}{a c \sqrt{a+b x^2}}-\frac{\sqrt{c x} \sqrt{a+b x^2}}{a \sqrt{b} \left(\sqrt{a}+\sqrt{b} x\right)}",1,"(c*x)^(3/2)/(a*c*Sqrt[a + b*x^2]) - (Sqrt[c*x]*Sqrt[a + b*x^2])/(a*Sqrt[b]*(Sqrt[a] + Sqrt[b]*x)) + (Sqrt[c]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(a^(3/4)*b^(3/4)*Sqrt[a + b*x^2]) - (Sqrt[c]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(2*a^(3/4)*b^(3/4)*Sqrt[a + b*x^2])","A",5,5,19,0.2632,1,"{290, 329, 305, 220, 1196}"
625,1,126,0,0.0700747,"\int \frac{1}{\sqrt{c x} \left(a+b x^2\right)^{3/2}} \, dx","Int[1/(Sqrt[c*x]*(a + b*x^2)^(3/2)),x]","\frac{\left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{2 a^{5/4} \sqrt[4]{b} \sqrt{c} \sqrt{a+b x^2}}+\frac{\sqrt{c x}}{a c \sqrt{a+b x^2}}","\frac{\left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{2 a^{5/4} \sqrt[4]{b} \sqrt{c} \sqrt{a+b x^2}}+\frac{\sqrt{c x}}{a c \sqrt{a+b x^2}}",1,"Sqrt[c*x]/(a*c*Sqrt[a + b*x^2]) + ((Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(2*a^(5/4)*b^(1/4)*Sqrt[c]*Sqrt[a + b*x^2])","A",3,3,19,0.1579,1,"{290, 329, 220}"
626,1,296,0,0.2194427,"\int \frac{1}{(c x)^{3/2} \left(a+b x^2\right)^{3/2}} \, dx","Int[1/((c*x)^(3/2)*(a + b*x^2)^(3/2)),x]","\frac{3 \sqrt{b} \sqrt{c x} \sqrt{a+b x^2}}{a^2 c^2 \left(\sqrt{a}+\sqrt{b} x\right)}+\frac{3 \sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{2 a^{7/4} c^{3/2} \sqrt{a+b x^2}}-\frac{3 \sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{a^{7/4} c^{3/2} \sqrt{a+b x^2}}-\frac{3 \sqrt{a+b x^2}}{a^2 c \sqrt{c x}}+\frac{1}{a c \sqrt{c x} \sqrt{a+b x^2}}","\frac{3 \sqrt{b} \sqrt{c x} \sqrt{a+b x^2}}{a^2 c^2 \left(\sqrt{a}+\sqrt{b} x\right)}+\frac{3 \sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{2 a^{7/4} c^{3/2} \sqrt{a+b x^2}}-\frac{3 \sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{a^{7/4} c^{3/2} \sqrt{a+b x^2}}-\frac{3 \sqrt{a+b x^2}}{a^2 c \sqrt{c x}}+\frac{1}{a c \sqrt{c x} \sqrt{a+b x^2}}",1,"1/(a*c*Sqrt[c*x]*Sqrt[a + b*x^2]) - (3*Sqrt[a + b*x^2])/(a^2*c*Sqrt[c*x]) + (3*Sqrt[b]*Sqrt[c*x]*Sqrt[a + b*x^2])/(a^2*c^2*(Sqrt[a] + Sqrt[b]*x)) - (3*b^(1/4)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(a^(7/4)*c^(3/2)*Sqrt[a + b*x^2]) + (3*b^(1/4)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(2*a^(7/4)*c^(3/2)*Sqrt[a + b*x^2])","A",6,6,19,0.3158,1,"{290, 325, 329, 305, 220, 1196}"
627,1,154,0,0.0897644,"\int \frac{1}{(c x)^{5/2} \left(a+b x^2\right)^{3/2}} \, dx","Int[1/((c*x)^(5/2)*(a + b*x^2)^(3/2)),x]","-\frac{5 b^{3/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{6 a^{9/4} c^{5/2} \sqrt{a+b x^2}}-\frac{5 \sqrt{a+b x^2}}{3 a^2 c (c x)^{3/2}}+\frac{1}{a c (c x)^{3/2} \sqrt{a+b x^2}}","-\frac{5 b^{3/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{6 a^{9/4} c^{5/2} \sqrt{a+b x^2}}-\frac{5 \sqrt{a+b x^2}}{3 a^2 c (c x)^{3/2}}+\frac{1}{a c (c x)^{3/2} \sqrt{a+b x^2}}",1,"1/(a*c*(c*x)^(3/2)*Sqrt[a + b*x^2]) - (5*Sqrt[a + b*x^2])/(3*a^2*c*(c*x)^(3/2)) - (5*b^(3/4)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(6*a^(9/4)*c^(5/2)*Sqrt[a + b*x^2])","A",4,4,19,0.2105,1,"{290, 325, 329, 220}"
628,1,331,0,0.2542665,"\int \frac{1}{(c x)^{7/2} \left(a+b x^2\right)^{3/2}} \, dx","Int[1/((c*x)^(7/2)*(a + b*x^2)^(3/2)),x]","-\frac{21 b^{3/2} \sqrt{c x} \sqrt{a+b x^2}}{5 a^3 c^4 \left(\sqrt{a}+\sqrt{b} x\right)}-\frac{21 b^{5/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{10 a^{11/4} c^{7/2} \sqrt{a+b x^2}}+\frac{21 b^{5/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{5 a^{11/4} c^{7/2} \sqrt{a+b x^2}}+\frac{21 b \sqrt{a+b x^2}}{5 a^3 c^3 \sqrt{c x}}-\frac{7 \sqrt{a+b x^2}}{5 a^2 c (c x)^{5/2}}+\frac{1}{a c (c x)^{5/2} \sqrt{a+b x^2}}","-\frac{21 b^{3/2} \sqrt{c x} \sqrt{a+b x^2}}{5 a^3 c^4 \left(\sqrt{a}+\sqrt{b} x\right)}-\frac{21 b^{5/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{10 a^{11/4} c^{7/2} \sqrt{a+b x^2}}+\frac{21 b^{5/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{5 a^{11/4} c^{7/2} \sqrt{a+b x^2}}+\frac{21 b \sqrt{a+b x^2}}{5 a^3 c^3 \sqrt{c x}}-\frac{7 \sqrt{a+b x^2}}{5 a^2 c (c x)^{5/2}}+\frac{1}{a c (c x)^{5/2} \sqrt{a+b x^2}}",1,"1/(a*c*(c*x)^(5/2)*Sqrt[a + b*x^2]) - (7*Sqrt[a + b*x^2])/(5*a^2*c*(c*x)^(5/2)) + (21*b*Sqrt[a + b*x^2])/(5*a^3*c^3*Sqrt[c*x]) - (21*b^(3/2)*Sqrt[c*x]*Sqrt[a + b*x^2])/(5*a^3*c^4*(Sqrt[a] + Sqrt[b]*x)) + (21*b^(5/4)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(5*a^(11/4)*c^(7/2)*Sqrt[a + b*x^2]) - (21*b^(5/4)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(10*a^(11/4)*c^(7/2)*Sqrt[a + b*x^2])","A",7,6,19,0.3158,1,"{290, 325, 329, 305, 220, 1196}"
629,1,155,0,0.0887926,"\int \frac{(c x)^{7/2}}{\left(a+b x^2\right)^{5/2}} \, dx","Int[(c*x)^(7/2)/(a + b*x^2)^(5/2),x]","-\frac{5 c^3 \sqrt{c x}}{6 b^2 \sqrt{a+b x^2}}+\frac{5 c^{7/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{12 \sqrt[4]{a} b^{9/4} \sqrt{a+b x^2}}-\frac{c (c x)^{5/2}}{3 b \left(a+b x^2\right)^{3/2}}","-\frac{5 c^3 \sqrt{c x}}{6 b^2 \sqrt{a+b x^2}}+\frac{5 c^{7/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{12 \sqrt[4]{a} b^{9/4} \sqrt{a+b x^2}}-\frac{c (c x)^{5/2}}{3 b \left(a+b x^2\right)^{3/2}}",1,"-(c*(c*x)^(5/2))/(3*b*(a + b*x^2)^(3/2)) - (5*c^3*Sqrt[c*x])/(6*b^2*Sqrt[a + b*x^2]) + (5*c^(7/2)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(12*a^(1/4)*b^(9/4)*Sqrt[a + b*x^2])","A",4,3,19,0.1579,1,"{288, 329, 220}"
630,1,304,0,0.2158714,"\int \frac{(c x)^{5/2}}{\left(a+b x^2\right)^{5/2}} \, dx","Int[(c*x)^(5/2)/(a + b*x^2)^(5/2),x]","-\frac{c^{5/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{4 a^{3/4} b^{7/4} \sqrt{a+b x^2}}+\frac{c^{5/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{2 a^{3/4} b^{7/4} \sqrt{a+b x^2}}-\frac{c^2 \sqrt{c x} \sqrt{a+b x^2}}{2 a b^{3/2} \left(\sqrt{a}+\sqrt{b} x\right)}+\frac{c (c x)^{3/2}}{2 a b \sqrt{a+b x^2}}-\frac{c (c x)^{3/2}}{3 b \left(a+b x^2\right)^{3/2}}","-\frac{c^{5/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{4 a^{3/4} b^{7/4} \sqrt{a+b x^2}}+\frac{c^{5/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{2 a^{3/4} b^{7/4} \sqrt{a+b x^2}}-\frac{c^2 \sqrt{c x} \sqrt{a+b x^2}}{2 a b^{3/2} \left(\sqrt{a}+\sqrt{b} x\right)}+\frac{c (c x)^{3/2}}{2 a b \sqrt{a+b x^2}}-\frac{c (c x)^{3/2}}{3 b \left(a+b x^2\right)^{3/2}}",1,"-(c*(c*x)^(3/2))/(3*b*(a + b*x^2)^(3/2)) + (c*(c*x)^(3/2))/(2*a*b*Sqrt[a + b*x^2]) - (c^2*Sqrt[c*x]*Sqrt[a + b*x^2])/(2*a*b^(3/2)*(Sqrt[a] + Sqrt[b]*x)) + (c^(5/2)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(2*a^(3/4)*b^(7/4)*Sqrt[a + b*x^2]) - (c^(5/2)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(4*a^(3/4)*b^(7/4)*Sqrt[a + b*x^2])","A",6,6,19,0.3158,1,"{288, 290, 329, 305, 220, 1196}"
631,1,156,0,0.0882295,"\int \frac{(c x)^{3/2}}{\left(a+b x^2\right)^{5/2}} \, dx","Int[(c*x)^(3/2)/(a + b*x^2)^(5/2),x]","\frac{c^{3/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{12 a^{5/4} b^{5/4} \sqrt{a+b x^2}}+\frac{c \sqrt{c x}}{6 a b \sqrt{a+b x^2}}-\frac{c \sqrt{c x}}{3 b \left(a+b x^2\right)^{3/2}}","\frac{c^{3/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{12 a^{5/4} b^{5/4} \sqrt{a+b x^2}}+\frac{c \sqrt{c x}}{6 a b \sqrt{a+b x^2}}-\frac{c \sqrt{c x}}{3 b \left(a+b x^2\right)^{3/2}}",1,"-(c*Sqrt[c*x])/(3*b*(a + b*x^2)^(3/2)) + (c*Sqrt[c*x])/(6*a*b*Sqrt[a + b*x^2]) + (c^(3/2)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(12*a^(5/4)*b^(5/4)*Sqrt[a + b*x^2])","A",4,4,19,0.2105,1,"{288, 290, 329, 220}"
632,1,302,0,0.2239842,"\int \frac{\sqrt{c x}}{\left(a+b x^2\right)^{5/2}} \, dx","Int[Sqrt[c*x]/(a + b*x^2)^(5/2),x]","-\frac{\sqrt{c} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{4 a^{7/4} b^{3/4} \sqrt{a+b x^2}}+\frac{\sqrt{c} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{2 a^{7/4} b^{3/4} \sqrt{a+b x^2}}+\frac{(c x)^{3/2}}{2 a^2 c \sqrt{a+b x^2}}-\frac{\sqrt{c x} \sqrt{a+b x^2}}{2 a^2 \sqrt{b} \left(\sqrt{a}+\sqrt{b} x\right)}+\frac{(c x)^{3/2}}{3 a c \left(a+b x^2\right)^{3/2}}","-\frac{\sqrt{c} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{4 a^{7/4} b^{3/4} \sqrt{a+b x^2}}+\frac{\sqrt{c} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{2 a^{7/4} b^{3/4} \sqrt{a+b x^2}}+\frac{(c x)^{3/2}}{2 a^2 c \sqrt{a+b x^2}}-\frac{\sqrt{c x} \sqrt{a+b x^2}}{2 a^2 \sqrt{b} \left(\sqrt{a}+\sqrt{b} x\right)}+\frac{(c x)^{3/2}}{3 a c \left(a+b x^2\right)^{3/2}}",1,"(c*x)^(3/2)/(3*a*c*(a + b*x^2)^(3/2)) + (c*x)^(3/2)/(2*a^2*c*Sqrt[a + b*x^2]) - (Sqrt[c*x]*Sqrt[a + b*x^2])/(2*a^2*Sqrt[b]*(Sqrt[a] + Sqrt[b]*x)) + (Sqrt[c]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(2*a^(7/4)*b^(3/4)*Sqrt[a + b*x^2]) - (Sqrt[c]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(4*a^(7/4)*b^(3/4)*Sqrt[a + b*x^2])","A",6,5,19,0.2632,1,"{290, 329, 305, 220, 1196}"
633,1,157,0,0.0882105,"\int \frac{1}{\sqrt{c x} \left(a+b x^2\right)^{5/2}} \, dx","Int[1/(Sqrt[c*x]*(a + b*x^2)^(5/2)),x]","\frac{5 \sqrt{c x}}{6 a^2 c \sqrt{a+b x^2}}+\frac{5 \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{12 a^{9/4} \sqrt[4]{b} \sqrt{c} \sqrt{a+b x^2}}+\frac{\sqrt{c x}}{3 a c \left(a+b x^2\right)^{3/2}}","\frac{5 \sqrt{c x}}{6 a^2 c \sqrt{a+b x^2}}+\frac{5 \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{12 a^{9/4} \sqrt[4]{b} \sqrt{c} \sqrt{a+b x^2}}+\frac{\sqrt{c x}}{3 a c \left(a+b x^2\right)^{3/2}}",1,"Sqrt[c*x]/(3*a*c*(a + b*x^2)^(3/2)) + (5*Sqrt[c*x])/(6*a^2*c*Sqrt[a + b*x^2]) + (5*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(12*a^(9/4)*b^(1/4)*Sqrt[c]*Sqrt[a + b*x^2])","A",4,3,19,0.1579,1,"{290, 329, 220}"
634,1,333,0,0.255224,"\int \frac{1}{(c x)^{3/2} \left(a+b x^2\right)^{5/2}} \, dx","Int[1/((c*x)^(3/2)*(a + b*x^2)^(5/2)),x]","\frac{7 \sqrt{b} \sqrt{c x} \sqrt{a+b x^2}}{2 a^3 c^2 \left(\sqrt{a}+\sqrt{b} x\right)}+\frac{7 \sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{4 a^{11/4} c^{3/2} \sqrt{a+b x^2}}-\frac{7 \sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{2 a^{11/4} c^{3/2} \sqrt{a+b x^2}}-\frac{7 \sqrt{a+b x^2}}{2 a^3 c \sqrt{c x}}+\frac{7}{6 a^2 c \sqrt{c x} \sqrt{a+b x^2}}+\frac{1}{3 a c \sqrt{c x} \left(a+b x^2\right)^{3/2}}","\frac{7 \sqrt{b} \sqrt{c x} \sqrt{a+b x^2}}{2 a^3 c^2 \left(\sqrt{a}+\sqrt{b} x\right)}+\frac{7 \sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{4 a^{11/4} c^{3/2} \sqrt{a+b x^2}}-\frac{7 \sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{2 a^{11/4} c^{3/2} \sqrt{a+b x^2}}-\frac{7 \sqrt{a+b x^2}}{2 a^3 c \sqrt{c x}}+\frac{7}{6 a^2 c \sqrt{c x} \sqrt{a+b x^2}}+\frac{1}{3 a c \sqrt{c x} \left(a+b x^2\right)^{3/2}}",1,"1/(3*a*c*Sqrt[c*x]*(a + b*x^2)^(3/2)) + 7/(6*a^2*c*Sqrt[c*x]*Sqrt[a + b*x^2]) - (7*Sqrt[a + b*x^2])/(2*a^3*c*Sqrt[c*x]) + (7*Sqrt[b]*Sqrt[c*x]*Sqrt[a + b*x^2])/(2*a^3*c^2*(Sqrt[a] + Sqrt[b]*x)) - (7*b^(1/4)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(2*a^(11/4)*c^(3/2)*Sqrt[a + b*x^2]) + (7*b^(1/4)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(4*a^(11/4)*c^(3/2)*Sqrt[a + b*x^2])","A",7,6,19,0.3158,1,"{290, 325, 329, 305, 220, 1196}"
635,1,185,0,0.1103333,"\int \frac{1}{(c x)^{5/2} \left(a+b x^2\right)^{5/2}} \, dx","Int[1/((c*x)^(5/2)*(a + b*x^2)^(5/2)),x]","-\frac{5 b^{3/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{4 a^{13/4} c^{5/2} \sqrt{a+b x^2}}-\frac{5 \sqrt{a+b x^2}}{2 a^3 c (c x)^{3/2}}+\frac{3}{2 a^2 c (c x)^{3/2} \sqrt{a+b x^2}}+\frac{1}{3 a c (c x)^{3/2} \left(a+b x^2\right)^{3/2}}","-\frac{5 b^{3/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{4 a^{13/4} c^{5/2} \sqrt{a+b x^2}}-\frac{5 \sqrt{a+b x^2}}{2 a^3 c (c x)^{3/2}}+\frac{3}{2 a^2 c (c x)^{3/2} \sqrt{a+b x^2}}+\frac{1}{3 a c (c x)^{3/2} \left(a+b x^2\right)^{3/2}}",1,"1/(3*a*c*(c*x)^(3/2)*(a + b*x^2)^(3/2)) + 3/(2*a^2*c*(c*x)^(3/2)*Sqrt[a + b*x^2]) - (5*Sqrt[a + b*x^2])/(2*a^3*c*(c*x)^(3/2)) - (5*b^(3/4)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(4*a^(13/4)*c^(5/2)*Sqrt[a + b*x^2])","A",5,4,19,0.2105,1,"{290, 325, 329, 220}"
636,1,362,0,0.2950314,"\int \frac{1}{(c x)^{7/2} \left(a+b x^2\right)^{5/2}} \, dx","Int[1/((c*x)^(7/2)*(a + b*x^2)^(5/2)),x]","-\frac{77 b^{3/2} \sqrt{c x} \sqrt{a+b x^2}}{10 a^4 c^4 \left(\sqrt{a}+\sqrt{b} x\right)}-\frac{77 b^{5/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{20 a^{15/4} c^{7/2} \sqrt{a+b x^2}}+\frac{77 b^{5/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{10 a^{15/4} c^{7/2} \sqrt{a+b x^2}}+\frac{77 b \sqrt{a+b x^2}}{10 a^4 c^3 \sqrt{c x}}-\frac{77 \sqrt{a+b x^2}}{30 a^3 c (c x)^{5/2}}+\frac{11}{6 a^2 c (c x)^{5/2} \sqrt{a+b x^2}}+\frac{1}{3 a c (c x)^{5/2} \left(a+b x^2\right)^{3/2}}","-\frac{77 b^{3/2} \sqrt{c x} \sqrt{a+b x^2}}{10 a^4 c^4 \left(\sqrt{a}+\sqrt{b} x\right)}-\frac{77 b^{5/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{20 a^{15/4} c^{7/2} \sqrt{a+b x^2}}+\frac{77 b^{5/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a} \sqrt{c}}\right)|\frac{1}{2}\right)}{10 a^{15/4} c^{7/2} \sqrt{a+b x^2}}+\frac{77 b \sqrt{a+b x^2}}{10 a^4 c^3 \sqrt{c x}}-\frac{77 \sqrt{a+b x^2}}{30 a^3 c (c x)^{5/2}}+\frac{11}{6 a^2 c (c x)^{5/2} \sqrt{a+b x^2}}+\frac{1}{3 a c (c x)^{5/2} \left(a+b x^2\right)^{3/2}}",1,"1/(3*a*c*(c*x)^(5/2)*(a + b*x^2)^(3/2)) + 11/(6*a^2*c*(c*x)^(5/2)*Sqrt[a + b*x^2]) - (77*Sqrt[a + b*x^2])/(30*a^3*c*(c*x)^(5/2)) + (77*b*Sqrt[a + b*x^2])/(10*a^4*c^3*Sqrt[c*x]) - (77*b^(3/2)*Sqrt[c*x]*Sqrt[a + b*x^2])/(10*a^4*c^4*(Sqrt[a] + Sqrt[b]*x)) + (77*b^(5/4)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(10*a^(15/4)*c^(7/2)*Sqrt[a + b*x^2]) - (77*b^(5/4)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[c*x])/(a^(1/4)*Sqrt[c])], 1/2])/(20*a^(15/4)*c^(7/2)*Sqrt[a + b*x^2])","A",8,6,19,0.3158,1,"{290, 325, 329, 305, 220, 1196}"
637,1,107,0,0.0428406,"\int \frac{(c x)^{5/2}}{\sqrt{3 a-2 a x^2}} \, dx","Int[(c*x)^(5/2)/Sqrt[3*a - 2*a*x^2],x]","-\frac{9 \sqrt[4]{3} c^2 \sqrt{3-2 x^2} \sqrt{c x} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{3-\sqrt{6} x}}{\sqrt{6}}\right)\right|2\right)}{5\ 2^{3/4} \sqrt{x} \sqrt{3 a-2 a x^2}}-\frac{c \sqrt{3 a-2 a x^2} (c x)^{3/2}}{5 a}","-\frac{9 \sqrt[4]{3} c^2 \sqrt{3-2 x^2} \sqrt{c x} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{3-\sqrt{6} x}}{\sqrt{6}}\right)\right|2\right)}{5\ 2^{3/4} \sqrt{x} \sqrt{3 a-2 a x^2}}-\frac{c \sqrt{3 a-2 a x^2} (c x)^{3/2}}{5 a}",1,"-(c*(c*x)^(3/2)*Sqrt[3*a - 2*a*x^2])/(5*a) - (9*3^(1/4)*c^2*Sqrt[c*x]*Sqrt[3 - 2*x^2]*EllipticE[ArcSin[Sqrt[3 - Sqrt[6]*x]/Sqrt[6]], 2])/(5*2^(3/4)*Sqrt[x]*Sqrt[3*a - 2*a*x^2])","A",5,5,22,0.2273,1,"{321, 320, 319, 318, 424}"
638,1,88,0,0.0466644,"\int \frac{(c x)^{3/2}}{\sqrt{3 a-2 a x^2}} \, dx","Int[(c*x)^(3/2)/Sqrt[3*a - 2*a*x^2],x]","\frac{c^{3/2} \sqrt{3-2 x^2} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{\frac{2}{3}} \sqrt{c x}}{\sqrt{c}}\right)\right|-1\right)}{\sqrt[4]{6} \sqrt{a \left(3-2 x^2\right)}}-\frac{c \sqrt{3 a-2 a x^2} \sqrt{c x}}{3 a}","\frac{c^{3/2} \sqrt{3-2 x^2} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{\frac{2}{3}} \sqrt{c x}}{\sqrt{c}}\right)\right|-1\right)}{\sqrt[4]{6} \sqrt{a \left(3-2 x^2\right)}}-\frac{c \sqrt{3 a-2 a x^2} \sqrt{c x}}{3 a}",1,"-(c*Sqrt[c*x]*Sqrt[3*a - 2*a*x^2])/(3*a) + (c^(3/2)*Sqrt[3 - 2*x^2]*EllipticF[ArcSin[((2/3)^(1/4)*Sqrt[c*x])/Sqrt[c]], -1])/(6^(1/4)*Sqrt[a*(3 - 2*x^2)])","A",4,4,22,0.1818,1,"{321, 329, 224, 221}"
639,1,67,0,0.0298237,"\int \frac{\sqrt{c x}}{\sqrt{3 a-2 a x^2}} \, dx","Int[Sqrt[c*x]/Sqrt[3*a - 2*a*x^2],x]","-\frac{\sqrt[4]{6} \sqrt{3-2 x^2} \sqrt{c x} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{3-\sqrt{6} x}}{\sqrt{6}}\right)\right|2\right)}{\sqrt{x} \sqrt{3 a-2 a x^2}}","-\frac{\sqrt[4]{6} \sqrt{3-2 x^2} \sqrt{c x} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{3-\sqrt{6} x}}{\sqrt{6}}\right)\right|2\right)}{\sqrt{x} \sqrt{3 a-2 a x^2}}",1,"-((6^(1/4)*Sqrt[c*x]*Sqrt[3 - 2*x^2]*EllipticE[ArcSin[Sqrt[3 - Sqrt[6]*x]/Sqrt[6]], 2])/(Sqrt[x]*Sqrt[3*a - 2*a*x^2]))","A",4,4,22,0.1818,1,"{320, 319, 318, 424}"
640,1,63,0,0.0341655,"\int \frac{1}{\sqrt{c x} \sqrt{3 a-2 a x^2}} \, dx","Int[1/(Sqrt[c*x]*Sqrt[3*a - 2*a*x^2]),x]","\frac{2^{3/4} \sqrt{3-2 x^2} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{\frac{2}{3}} \sqrt{c x}}{\sqrt{c}}\right)\right|-1\right)}{\sqrt[4]{3} \sqrt{c} \sqrt{a \left(3-2 x^2\right)}}","\frac{2^{3/4} \sqrt{3-2 x^2} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{\frac{2}{3}} \sqrt{c x}}{\sqrt{c}}\right)\right|-1\right)}{\sqrt[4]{3} \sqrt{c} \sqrt{a \left(3-2 x^2\right)}}",1,"(2^(3/4)*Sqrt[3 - 2*x^2]*EllipticF[ArcSin[((2/3)^(1/4)*Sqrt[c*x])/Sqrt[c]], -1])/(3^(1/4)*Sqrt[c]*Sqrt[a*(3 - 2*x^2)])","A",3,3,22,0.1364,1,"{329, 224, 221}"
641,1,107,0,0.042602,"\int \frac{1}{(c x)^{3/2} \sqrt{3 a-2 a x^2}} \, dx","Int[1/((c*x)^(3/2)*Sqrt[3*a - 2*a*x^2]),x]","\frac{2 \sqrt[4]{2} \sqrt{3-2 x^2} \sqrt{c x} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{3-\sqrt{6} x}}{\sqrt{6}}\right)\right|2\right)}{3^{3/4} c^2 \sqrt{x} \sqrt{3 a-2 a x^2}}-\frac{2 \sqrt{3 a-2 a x^2}}{3 a c \sqrt{c x}}","\frac{2 \sqrt[4]{2} \sqrt{3-2 x^2} \sqrt{c x} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{3-\sqrt{6} x}}{\sqrt{6}}\right)\right|2\right)}{3^{3/4} c^2 \sqrt{x} \sqrt{3 a-2 a x^2}}-\frac{2 \sqrt{3 a-2 a x^2}}{3 a c \sqrt{c x}}",1,"(-2*Sqrt[3*a - 2*a*x^2])/(3*a*c*Sqrt[c*x]) + (2*2^(1/4)*Sqrt[c*x]*Sqrt[3 - 2*x^2]*EllipticE[ArcSin[Sqrt[3 - Sqrt[6]*x]/Sqrt[6]], 2])/(3^(3/4)*c^2*Sqrt[x]*Sqrt[3*a - 2*a*x^2])","A",5,5,22,0.2273,1,"{325, 320, 319, 318, 424}"
642,1,98,0,0.0459691,"\int \frac{1}{(c x)^{5/2} \sqrt{3 a-2 a x^2}} \, dx","Int[1/((c*x)^(5/2)*Sqrt[3*a - 2*a*x^2]),x]","\frac{2\ 2^{3/4} \sqrt{3-2 x^2} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{\frac{2}{3}} \sqrt{c x}}{\sqrt{c}}\right)\right|-1\right)}{9 \sqrt[4]{3} c^{5/2} \sqrt{a \left(3-2 x^2\right)}}-\frac{2 \sqrt{3 a-2 a x^2}}{9 a c (c x)^{3/2}}","\frac{2\ 2^{3/4} \sqrt{3-2 x^2} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{\frac{2}{3}} \sqrt{c x}}{\sqrt{c}}\right)\right|-1\right)}{9 \sqrt[4]{3} c^{5/2} \sqrt{a \left(3-2 x^2\right)}}-\frac{2 \sqrt{3 a-2 a x^2}}{9 a c (c x)^{3/2}}",1,"(-2*Sqrt[3*a - 2*a*x^2])/(9*a*c*(c*x)^(3/2)) + (2*2^(3/4)*Sqrt[3 - 2*x^2]*EllipticF[ArcSin[((2/3)^(1/4)*Sqrt[c*x])/Sqrt[c]], -1])/(9*3^(1/4)*c^(5/2)*Sqrt[a*(3 - 2*x^2)])","A",4,4,22,0.1818,1,"{325, 329, 224, 221}"
643,1,110,0,0.0420811,"\int \frac{(c x)^{5/2}}{\left(3 a-2 a x^2\right)^{3/2}} \, dx","Int[(c*x)^(5/2)/(3*a - 2*a*x^2)^(3/2),x]","\frac{3 \sqrt[4]{3} c^2 \sqrt{3-2 x^2} \sqrt{c x} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{3-\sqrt{6} x}}{\sqrt{6}}\right)\right|2\right)}{2\ 2^{3/4} a \sqrt{x} \sqrt{3 a-2 a x^2}}+\frac{c (c x)^{3/2}}{2 a \sqrt{3 a-2 a x^2}}","\frac{3 \sqrt[4]{3} c^2 \sqrt{3-2 x^2} \sqrt{c x} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{3-\sqrt{6} x}}{\sqrt{6}}\right)\right|2\right)}{2\ 2^{3/4} a \sqrt{x} \sqrt{3 a-2 a x^2}}+\frac{c (c x)^{3/2}}{2 a \sqrt{3 a-2 a x^2}}",1,"(c*(c*x)^(3/2))/(2*a*Sqrt[3*a - 2*a*x^2]) + (3*3^(1/4)*c^2*Sqrt[c*x]*Sqrt[3 - 2*x^2]*EllipticE[ArcSin[Sqrt[3 - Sqrt[6]*x]/Sqrt[6]], 2])/(2*2^(3/4)*a*Sqrt[x]*Sqrt[3*a - 2*a*x^2])","A",5,5,22,0.2273,1,"{288, 320, 319, 318, 424}"
644,1,94,0,0.0484398,"\int \frac{(c x)^{3/2}}{\left(3 a-2 a x^2\right)^{3/2}} \, dx","Int[(c*x)^(3/2)/(3*a - 2*a*x^2)^(3/2),x]","\frac{c \sqrt{c x}}{2 a \sqrt{3 a-2 a x^2}}-\frac{c^{3/2} \sqrt{3-2 x^2} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{\frac{2}{3}} \sqrt{c x}}{\sqrt{c}}\right)\right|-1\right)}{2 \sqrt[4]{6} a \sqrt{a \left(3-2 x^2\right)}}","\frac{c \sqrt{c x}}{2 a \sqrt{3 a-2 a x^2}}-\frac{c^{3/2} \sqrt{3-2 x^2} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{\frac{2}{3}} \sqrt{c x}}{\sqrt{c}}\right)\right|-1\right)}{2 \sqrt[4]{6} a \sqrt{a \left(3-2 x^2\right)}}",1,"(c*Sqrt[c*x])/(2*a*Sqrt[3*a - 2*a*x^2]) - (c^(3/2)*Sqrt[3 - 2*x^2]*EllipticF[ArcSin[((2/3)^(1/4)*Sqrt[c*x])/Sqrt[c]], -1])/(2*6^(1/4)*a*Sqrt[a*(3 - 2*x^2)])","A",4,4,22,0.1818,1,"{288, 329, 224, 221}"
645,1,101,0,0.0393555,"\int \frac{\sqrt{c x}}{\left(3 a-2 a x^2\right)^{3/2}} \, dx","Int[Sqrt[c*x]/(3*a - 2*a*x^2)^(3/2),x]","\frac{(c x)^{3/2}}{3 a c \sqrt{3 a-2 a x^2}}+\frac{\sqrt{3-2 x^2} \sqrt{c x} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{3-\sqrt{6} x}}{\sqrt{6}}\right)\right|2\right)}{6^{3/4} a \sqrt{x} \sqrt{3 a-2 a x^2}}","\frac{(c x)^{3/2}}{3 a c \sqrt{3 a-2 a x^2}}+\frac{\sqrt{3-2 x^2} \sqrt{c x} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{3-\sqrt{6} x}}{\sqrt{6}}\right)\right|2\right)}{6^{3/4} a \sqrt{x} \sqrt{3 a-2 a x^2}}",1,"(c*x)^(3/2)/(3*a*c*Sqrt[3*a - 2*a*x^2]) + (Sqrt[c*x]*Sqrt[3 - 2*x^2]*EllipticE[ArcSin[Sqrt[3 - Sqrt[6]*x]/Sqrt[6]], 2])/(6^(3/4)*a*Sqrt[x]*Sqrt[3*a - 2*a*x^2])","A",5,5,22,0.2273,1,"{290, 320, 319, 318, 424}"
646,1,96,0,0.0463873,"\int \frac{1}{\sqrt{c x} \left(3 a-2 a x^2\right)^{3/2}} \, dx","Int[1/(Sqrt[c*x]*(3*a - 2*a*x^2)^(3/2)),x]","\frac{\sqrt{c x}}{3 a c \sqrt{3 a-2 a x^2}}+\frac{\sqrt{3-2 x^2} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{\frac{2}{3}} \sqrt{c x}}{\sqrt{c}}\right)\right|-1\right)}{3 \sqrt[4]{6} a \sqrt{c} \sqrt{a \left(3-2 x^2\right)}}","\frac{\sqrt{c x}}{3 a c \sqrt{3 a-2 a x^2}}+\frac{\sqrt{3-2 x^2} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{\frac{2}{3}} \sqrt{c x}}{\sqrt{c}}\right)\right|-1\right)}{3 \sqrt[4]{6} a \sqrt{c} \sqrt{a \left(3-2 x^2\right)}}",1,"Sqrt[c*x]/(3*a*c*Sqrt[3*a - 2*a*x^2]) + (Sqrt[3 - 2*x^2]*EllipticF[ArcSin[((2/3)^(1/4)*Sqrt[c*x])/Sqrt[c]], -1])/(3*6^(1/4)*a*Sqrt[c]*Sqrt[a*(3 - 2*x^2)])","A",4,4,22,0.1818,1,"{290, 329, 224, 221}"
647,1,140,0,0.0561087,"\int \frac{1}{(c x)^{3/2} \left(3 a-2 a x^2\right)^{3/2}} \, dx","Int[1/((c*x)^(3/2)*(3*a - 2*a*x^2)^(3/2)),x]","-\frac{\sqrt{3 a-2 a x^2}}{3 a^2 c \sqrt{c x}}+\frac{\sqrt[4]{2} \sqrt{3-2 x^2} \sqrt{c x} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{3-\sqrt{6} x}}{\sqrt{6}}\right)\right|2\right)}{3^{3/4} a c^2 \sqrt{x} \sqrt{3 a-2 a x^2}}+\frac{1}{3 a c \sqrt{3 a-2 a x^2} \sqrt{c x}}","-\frac{\sqrt{3 a-2 a x^2}}{3 a^2 c \sqrt{c x}}+\frac{\sqrt[4]{2} \sqrt{3-2 x^2} \sqrt{c x} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{3-\sqrt{6} x}}{\sqrt{6}}\right)\right|2\right)}{3^{3/4} a c^2 \sqrt{x} \sqrt{3 a-2 a x^2}}+\frac{1}{3 a c \sqrt{3 a-2 a x^2} \sqrt{c x}}",1,"1/(3*a*c*Sqrt[c*x]*Sqrt[3*a - 2*a*x^2]) - Sqrt[3*a - 2*a*x^2]/(3*a^2*c*Sqrt[c*x]) + (2^(1/4)*Sqrt[c*x]*Sqrt[3 - 2*x^2]*EllipticE[ArcSin[Sqrt[3 - Sqrt[6]*x]/Sqrt[6]], 2])/(3^(3/4)*a*c^2*Sqrt[x]*Sqrt[3*a - 2*a*x^2])","A",6,6,22,0.2727,1,"{290, 325, 320, 319, 318, 424}"
648,1,132,0,0.0631519,"\int \frac{1}{(c x)^{5/2} \left(3 a-2 a x^2\right)^{3/2}} \, dx","Int[1/((c*x)^(5/2)*(3*a - 2*a*x^2)^(3/2)),x]","-\frac{5 \sqrt{3 a-2 a x^2}}{27 a^2 c (c x)^{3/2}}+\frac{5\ 2^{3/4} \sqrt{3-2 x^2} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{\frac{2}{3}} \sqrt{c x}}{\sqrt{c}}\right)\right|-1\right)}{27 \sqrt[4]{3} a c^{5/2} \sqrt{a \left(3-2 x^2\right)}}+\frac{1}{3 a c \sqrt{3 a-2 a x^2} (c x)^{3/2}}","-\frac{5 \sqrt{3 a-2 a x^2}}{27 a^2 c (c x)^{3/2}}+\frac{5\ 2^{3/4} \sqrt{3-2 x^2} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{\frac{2}{3}} \sqrt{c x}}{\sqrt{c}}\right)\right|-1\right)}{27 \sqrt[4]{3} a c^{5/2} \sqrt{a \left(3-2 x^2\right)}}+\frac{1}{3 a c \sqrt{3 a-2 a x^2} (c x)^{3/2}}",1,"1/(3*a*c*(c*x)^(3/2)*Sqrt[3*a - 2*a*x^2]) - (5*Sqrt[3*a - 2*a*x^2])/(27*a^2*c*(c*x)^(3/2)) + (5*2^(3/4)*Sqrt[3 - 2*x^2]*EllipticF[ArcSin[((2/3)^(1/4)*Sqrt[c*x])/Sqrt[c]], -1])/(27*3^(1/4)*a*c^(5/2)*Sqrt[a*(3 - 2*x^2)])","A",5,5,22,0.2273,1,"{290, 325, 329, 224, 221}"
649,1,21,0,0.008636,"\int \frac{1}{\sqrt{x} \sqrt{1-a^2 x^2}} \, dx","Int[1/(Sqrt[x]*Sqrt[1 - a^2*x^2]),x]","\frac{2 F\left(\left.\sin ^{-1}\left(\sqrt{a} \sqrt{x}\right)\right|-1\right)}{\sqrt{a}}","\frac{2 F\left(\left.\sin ^{-1}\left(\sqrt{a} \sqrt{x}\right)\right|-1\right)}{\sqrt{a}}",1,"(2*EllipticF[ArcSin[Sqrt[a]*Sqrt[x]], -1])/Sqrt[a]","A",2,2,20,0.1000,1,"{329, 221}"
650,1,67,0,0.0377915,"\int \frac{1}{\sqrt{x} \sqrt{1+a x^2}} \, dx","Int[1/(Sqrt[x]*Sqrt[1 + a*x^2]),x]","\frac{\left(\sqrt{a} x+1\right) \sqrt{\frac{a x^2+1}{\left(\sqrt{a} x+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{a} \sqrt{x}\right)|\frac{1}{2}\right)}{\sqrt[4]{a} \sqrt{a x^2+1}}","\frac{\left(\sqrt{a} x+1\right) \sqrt{\frac{a x^2+1}{\left(\sqrt{a} x+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{a} \sqrt{x}\right)|\frac{1}{2}\right)}{\sqrt[4]{a} \sqrt{a x^2+1}}",1,"((1 + Sqrt[a]*x)*Sqrt[(1 + a*x^2)/(1 + Sqrt[a]*x)^2]*EllipticF[2*ArcTan[a^(1/4)*Sqrt[x]], 1/2])/(a^(1/4)*Sqrt[1 + a*x^2])","A",2,2,17,0.1176,1,"{329, 220}"
651,1,64,0,0.0192922,"\int x^m \left(a+b x^2\right)^{3/2} \, dx","Int[x^m*(a + b*x^2)^(3/2),x]","\frac{a x^{m+1} \sqrt{a+b x^2} \, _2F_1\left(-\frac{3}{2},\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{(m+1) \sqrt{\frac{b x^2}{a}+1}}","\frac{x^{m+1} \left(a+b x^2\right)^{5/2} \, _2F_1\left(1,\frac{m+6}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a (m+1)}",1,"(a*x^(1 + m)*Sqrt[a + b*x^2]*Hypergeometric2F1[-3/2, (1 + m)/2, (3 + m)/2, -((b*x^2)/a)])/((1 + m)*Sqrt[1 + (b*x^2)/a])","A",2,2,15,0.1333,1,"{365, 364}"
652,1,63,0,0.0178072,"\int x^m \sqrt{a+b x^2} \, dx","Int[x^m*Sqrt[a + b*x^2],x]","\frac{x^{m+1} \sqrt{a+b x^2} \, _2F_1\left(-\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{(m+1) \sqrt{\frac{b x^2}{a}+1}}","\frac{x^{m+1} \left(a+b x^2\right)^{3/2} \, _2F_1\left(1,\frac{m+4}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a (m+1)}",1,"(x^(1 + m)*Sqrt[a + b*x^2]*Hypergeometric2F1[-1/2, (1 + m)/2, (3 + m)/2, -((b*x^2)/a)])/((1 + m)*Sqrt[1 + (b*x^2)/a])","A",2,2,15,0.1333,1,"{365, 364}"
653,1,63,0,0.0179431,"\int \frac{x^m}{\sqrt{a+b x^2}} \, dx","Int[x^m/Sqrt[a + b*x^2],x]","\frac{x^{m+1} \sqrt{\frac{b x^2}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{(m+1) \sqrt{a+b x^2}}","\frac{x^{m+1} \sqrt{a+b x^2} \, _2F_1\left(1,\frac{m+2}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a (m+1)}",1,"(x^(1 + m)*Sqrt[1 + (b*x^2)/a]*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, -((b*x^2)/a)])/((1 + m)*Sqrt[a + b*x^2])","A",2,2,15,0.1333,1,"{365, 364}"
654,1,66,0,0.0195241,"\int \frac{x^m}{\left(a+b x^2\right)^{3/2}} \, dx","Int[x^m/(a + b*x^2)^(3/2),x]","\frac{x^{m+1} \sqrt{\frac{b x^2}{a}+1} \, _2F_1\left(\frac{3}{2},\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a (m+1) \sqrt{a+b x^2}}","\frac{x^{m+1} \, _2F_1\left(1,\frac{m}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a (m+1) \sqrt{a+b x^2}}",1,"(x^(1 + m)*Sqrt[1 + (b*x^2)/a]*Hypergeometric2F1[3/2, (1 + m)/2, (3 + m)/2, -((b*x^2)/a)])/(a*(1 + m)*Sqrt[a + b*x^2])","A",2,2,15,0.1333,1,"{365, 364}"
655,1,66,0,0.0197179,"\int \frac{x^m}{\left(a+b x^2\right)^{5/2}} \, dx","Int[x^m/(a + b*x^2)^(5/2),x]","\frac{x^{m+1} \sqrt{\frac{b x^2}{a}+1} \, _2F_1\left(\frac{5}{2},\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a^2 (m+1) \sqrt{a+b x^2}}","\frac{x^{m+1} \, _2F_1\left(1,\frac{m-2}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a (m+1) \left(a+b x^2\right)^{3/2}}",1,"(x^(1 + m)*Sqrt[1 + (b*x^2)/a]*Hypergeometric2F1[5/2, (1 + m)/2, (3 + m)/2, -((b*x^2)/a)])/(a^2*(1 + m)*Sqrt[a + b*x^2])","A",2,2,15,0.1333,1,"{365, 364}"
656,1,63,0,0.0195211,"\int \frac{x^{2+m}}{\sqrt{a+b x^2}} \, dx","Int[x^(2 + m)/Sqrt[a + b*x^2],x]","\frac{x^{m+3} \sqrt{\frac{b x^2}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{m+3}{2};\frac{m+5}{2};-\frac{b x^2}{a}\right)}{(m+3) \sqrt{a+b x^2}}","\frac{x^{m+3} \sqrt{a+b x^2} \, _2F_1\left(1,\frac{m+4}{2};\frac{m+5}{2};-\frac{b x^2}{a}\right)}{a (m+3)}",1,"(x^(3 + m)*Sqrt[1 + (b*x^2)/a]*Hypergeometric2F1[1/2, (3 + m)/2, (5 + m)/2, -((b*x^2)/a)])/((3 + m)*Sqrt[a + b*x^2])","A",2,2,17,0.1176,1,"{365, 364}"
657,1,63,0,0.019524,"\int \frac{x^{1+m}}{\sqrt{a+b x^2}} \, dx","Int[x^(1 + m)/Sqrt[a + b*x^2],x]","\frac{x^{m+2} \sqrt{\frac{b x^2}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};-\frac{b x^2}{a}\right)}{(m+2) \sqrt{a+b x^2}}","\frac{x^{m+2} \sqrt{a+b x^2} \, _2F_1\left(1,\frac{m+3}{2};\frac{m+4}{2};-\frac{b x^2}{a}\right)}{a (m+2)}",1,"(x^(2 + m)*Sqrt[1 + (b*x^2)/a]*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, -((b*x^2)/a)])/((2 + m)*Sqrt[a + b*x^2])","A",2,2,17,0.1176,1,"{365, 364}"
658,1,63,0,0.0171533,"\int \frac{x^m}{\sqrt{a+b x^2}} \, dx","Int[x^m/Sqrt[a + b*x^2],x]","\frac{x^{m+1} \sqrt{\frac{b x^2}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{(m+1) \sqrt{a+b x^2}}","\frac{x^{m+1} \sqrt{a+b x^2} \, _2F_1\left(1,\frac{m+2}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a (m+1)}",1,"(x^(1 + m)*Sqrt[1 + (b*x^2)/a]*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, -((b*x^2)/a)])/((1 + m)*Sqrt[a + b*x^2])","A",2,2,15,0.1333,1,"{365, 364}"
659,1,57,0,0.0186178,"\int \frac{x^{-1+m}}{\sqrt{a+b x^2}} \, dx","Int[x^(-1 + m)/Sqrt[a + b*x^2],x]","\frac{x^m \sqrt{\frac{b x^2}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{m}{2};\frac{m+2}{2};-\frac{b x^2}{a}\right)}{m \sqrt{a+b x^2}}","\frac{x^m \sqrt{a+b x^2} \, _2F_1\left(1,\frac{m+1}{2};\frac{m+2}{2};-\frac{b x^2}{a}\right)}{a m}",1,"(x^m*Sqrt[1 + (b*x^2)/a]*Hypergeometric2F1[1/2, m/2, (2 + m)/2, -((b*x^2)/a)])/(m*Sqrt[a + b*x^2])","A",2,2,17,0.1176,1,"{365, 364}"
660,1,66,0,0.0199039,"\int \frac{x^{-2+m}}{\sqrt{a+b x^2}} \, dx","Int[x^(-2 + m)/Sqrt[a + b*x^2],x]","-\frac{x^{m-1} \sqrt{\frac{b x^2}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{m-1}{2};\frac{m+1}{2};-\frac{b x^2}{a}\right)}{(1-m) \sqrt{a+b x^2}}","-\frac{x^{m-1} \sqrt{a+b x^2} \, _2F_1\left(1,\frac{m}{2};\frac{m+1}{2};-\frac{b x^2}{a}\right)}{a (1-m)}",1,"-((x^(-1 + m)*Sqrt[1 + (b*x^2)/a]*Hypergeometric2F1[1/2, (-1 + m)/2, (1 + m)/2, -((b*x^2)/a)])/((1 - m)*Sqrt[a + b*x^2]))","A",2,2,17,0.1176,1,"{365, 364}"
661,1,17,0,0.0113457,"\int \frac{x^{1+m} \left(a (2+m)+b (3+m) x^2\right)}{\sqrt{a+b x^2}} \, dx","Int[(x^(1 + m)*(a*(2 + m) + b*(3 + m)*x^2))/Sqrt[a + b*x^2],x]","x^{m+2} \sqrt{a+b x^2}","x^{m+2} \sqrt{a+b x^2}",1,"x^(2 + m)*Sqrt[a + b*x^2]","A",1,1,31,0.03226,1,"{449}"
662,1,127,0,0.0659783,"\int \left(\frac{a (2+m) x^{1+m}}{\sqrt{a+b x^2}}+\frac{b (3+m) x^{3+m}}{\sqrt{a+b x^2}}\right) \, dx","Int[(a*(2 + m)*x^(1 + m))/Sqrt[a + b*x^2] + (b*(3 + m)*x^(3 + m))/Sqrt[a + b*x^2],x]","\frac{a x^{m+2} \sqrt{\frac{b x^2}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};-\frac{b x^2}{a}\right)}{\sqrt{a+b x^2}}+\frac{b (m+3) x^{m+4} \sqrt{\frac{b x^2}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{m+4}{2};\frac{m+6}{2};-\frac{b x^2}{a}\right)}{(m+4) \sqrt{a+b x^2}}","x^{m+2} \sqrt{a+b x^2}",1,"(a*x^(2 + m)*Sqrt[1 + (b*x^2)/a]*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, -((b*x^2)/a)])/Sqrt[a + b*x^2] + (b*(3 + m)*x^(4 + m)*Sqrt[1 + (b*x^2)/a]*Hypergeometric2F1[1/2, (4 + m)/2, (6 + m)/2, -((b*x^2)/a)])/((4 + m)*Sqrt[a + b*x^2])","C",5,2,43,0.04651,1,"{365, 364}"
663,1,15,0,0.0118946,"\int \frac{x^{-1+m} \left(a m+b (-1+m) x^2\right)}{\left(a+b x^2\right)^{3/2}} \, dx","Int[(x^(-1 + m)*(a*m + b*(-1 + m)*x^2))/(a + b*x^2)^(3/2),x]","\frac{x^m}{\sqrt{a+b x^2}}","\frac{x^m}{\sqrt{a+b x^2}}",1,"x^m/Sqrt[a + b*x^2]","A",1,1,29,0.03448,1,"{449}"
664,1,123,0,0.0650502,"\int \left(-\frac{b x^{1+m}}{\left(a+b x^2\right)^{3/2}}+\frac{m x^{-1+m}}{\sqrt{a+b x^2}}\right) \, dx","Int[-((b*x^(1 + m))/(a + b*x^2)^(3/2)) + (m*x^(-1 + m))/Sqrt[a + b*x^2],x]","\frac{x^m \sqrt{\frac{b x^2}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{m}{2};\frac{m+2}{2};-\frac{b x^2}{a}\right)}{\sqrt{a+b x^2}}-\frac{b x^{m+2} \sqrt{\frac{b x^2}{a}+1} \, _2F_1\left(\frac{3}{2},\frac{m+2}{2};\frac{m+4}{2};-\frac{b x^2}{a}\right)}{a (m+2) \sqrt{a+b x^2}}","\frac{x^m}{\sqrt{a+b x^2}}",1,"(x^m*Sqrt[1 + (b*x^2)/a]*Hypergeometric2F1[1/2, m/2, (2 + m)/2, -((b*x^2)/a)])/Sqrt[a + b*x^2] - (b*x^(2 + m)*Sqrt[1 + (b*x^2)/a]*Hypergeometric2F1[3/2, (2 + m)/2, (4 + m)/2, -((b*x^2)/a)])/(a*(2 + m)*Sqrt[a + b*x^2])","C",5,2,38,0.05263,1,"{365, 364}"
665,1,80,0,0.0491851,"\int x^7 \sqrt[3]{a+b x^2} \, dx","Int[x^7*(a + b*x^2)^(1/3),x]","\frac{9 a^2 \left(a+b x^2\right)^{7/3}}{14 b^4}-\frac{3 a^3 \left(a+b x^2\right)^{4/3}}{8 b^4}+\frac{3 \left(a+b x^2\right)^{13/3}}{26 b^4}-\frac{9 a \left(a+b x^2\right)^{10/3}}{20 b^4}","\frac{9 a^2 \left(a+b x^2\right)^{7/3}}{14 b^4}-\frac{3 a^3 \left(a+b x^2\right)^{4/3}}{8 b^4}+\frac{3 \left(a+b x^2\right)^{13/3}}{26 b^4}-\frac{9 a \left(a+b x^2\right)^{10/3}}{20 b^4}",1,"(-3*a^3*(a + b*x^2)^(4/3))/(8*b^4) + (9*a^2*(a + b*x^2)^(7/3))/(14*b^4) - (9*a*(a + b*x^2)^(10/3))/(20*b^4) + (3*(a + b*x^2)^(13/3))/(26*b^4)","A",3,2,15,0.1333,1,"{266, 43}"
666,1,59,0,0.034617,"\int x^5 \sqrt[3]{a+b x^2} \, dx","Int[x^5*(a + b*x^2)^(1/3),x]","\frac{3 a^2 \left(a+b x^2\right)^{4/3}}{8 b^3}+\frac{3 \left(a+b x^2\right)^{10/3}}{20 b^3}-\frac{3 a \left(a+b x^2\right)^{7/3}}{7 b^3}","\frac{3 a^2 \left(a+b x^2\right)^{4/3}}{8 b^3}+\frac{3 \left(a+b x^2\right)^{10/3}}{20 b^3}-\frac{3 a \left(a+b x^2\right)^{7/3}}{7 b^3}",1,"(3*a^2*(a + b*x^2)^(4/3))/(8*b^3) - (3*a*(a + b*x^2)^(7/3))/(7*b^3) + (3*(a + b*x^2)^(10/3))/(20*b^3)","A",3,2,15,0.1333,1,"{266, 43}"
667,1,38,0,0.0231805,"\int x^3 \sqrt[3]{a+b x^2} \, dx","Int[x^3*(a + b*x^2)^(1/3),x]","\frac{3 \left(a+b x^2\right)^{7/3}}{14 b^2}-\frac{3 a \left(a+b x^2\right)^{4/3}}{8 b^2}","\frac{3 \left(a+b x^2\right)^{7/3}}{14 b^2}-\frac{3 a \left(a+b x^2\right)^{4/3}}{8 b^2}",1,"(-3*a*(a + b*x^2)^(4/3))/(8*b^2) + (3*(a + b*x^2)^(7/3))/(14*b^2)","A",3,2,15,0.1333,1,"{266, 43}"
668,1,18,0,0.003245,"\int x \sqrt[3]{a+b x^2} \, dx","Int[x*(a + b*x^2)^(1/3),x]","\frac{3 \left(a+b x^2\right)^{4/3}}{8 b}","\frac{3 \left(a+b x^2\right)^{4/3}}{8 b}",1,"(3*(a + b*x^2)^(4/3))/(8*b)","A",1,1,13,0.07692,1,"{261}"
669,1,101,0,0.0791417,"\int \frac{\sqrt[3]{a+b x^2}}{x} \, dx","Int[(a + b*x^2)^(1/3)/x,x]","\frac{3}{2} \sqrt[3]{a+b x^2}+\frac{3}{4} \sqrt[3]{a} \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)-\frac{1}{2} \sqrt{3} \sqrt[3]{a} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)-\frac{1}{2} \sqrt[3]{a} \log (x)","\frac{3}{2} \sqrt[3]{a+b x^2}+\frac{3}{4} \sqrt[3]{a} \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)-\frac{1}{2} \sqrt{3} \sqrt[3]{a} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)-\frac{1}{2} \sqrt[3]{a} \log (x)",1,"(3*(a + b*x^2)^(1/3))/2 - (Sqrt[3]*a^(1/3)*ArcTan[(a^(1/3) + 2*(a + b*x^2)^(1/3))/(Sqrt[3]*a^(1/3))])/2 - (a^(1/3)*Log[x])/2 + (3*a^(1/3)*Log[a^(1/3) - (a + b*x^2)^(1/3)])/4","A",6,6,15,0.4000,1,"{266, 50, 57, 617, 204, 31}"
670,1,107,0,0.0713732,"\int \frac{\sqrt[3]{a+b x^2}}{x^3} \, dx","Int[(a + b*x^2)^(1/3)/x^3,x]","\frac{b \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{4 a^{2/3}}-\frac{b \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{2 \sqrt{3} a^{2/3}}-\frac{b \log (x)}{6 a^{2/3}}-\frac{\sqrt[3]{a+b x^2}}{2 x^2}","\frac{b \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{4 a^{2/3}}-\frac{b \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{2 \sqrt{3} a^{2/3}}-\frac{b \log (x)}{6 a^{2/3}}-\frac{\sqrt[3]{a+b x^2}}{2 x^2}",1,"-(a + b*x^2)^(1/3)/(2*x^2) - (b*ArcTan[(a^(1/3) + 2*(a + b*x^2)^(1/3))/(Sqrt[3]*a^(1/3))])/(2*Sqrt[3]*a^(2/3)) - (b*Log[x])/(6*a^(2/3)) + (b*Log[a^(1/3) - (a + b*x^2)^(1/3)])/(4*a^(2/3))","A",6,6,15,0.4000,1,"{266, 47, 57, 617, 204, 31}"
671,1,135,0,0.0941841,"\int \frac{\sqrt[3]{a+b x^2}}{x^5} \, dx","Int[(a + b*x^2)^(1/3)/x^5,x]","-\frac{b^2 \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{12 a^{5/3}}+\frac{b^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{6 \sqrt{3} a^{5/3}}+\frac{b^2 \log (x)}{18 a^{5/3}}-\frac{b \sqrt[3]{a+b x^2}}{12 a x^2}-\frac{\sqrt[3]{a+b x^2}}{4 x^4}","-\frac{b^2 \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{12 a^{5/3}}+\frac{b^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{6 \sqrt{3} a^{5/3}}+\frac{b^2 \log (x)}{18 a^{5/3}}-\frac{b \sqrt[3]{a+b x^2}}{12 a x^2}-\frac{\sqrt[3]{a+b x^2}}{4 x^4}",1,"-(a + b*x^2)^(1/3)/(4*x^4) - (b*(a + b*x^2)^(1/3))/(12*a*x^2) + (b^2*ArcTan[(a^(1/3) + 2*(a + b*x^2)^(1/3))/(Sqrt[3]*a^(1/3))])/(6*Sqrt[3]*a^(5/3)) + (b^2*Log[x])/(18*a^(5/3)) - (b^2*Log[a^(1/3) - (a + b*x^2)^(1/3)])/(12*a^(5/3))","A",7,7,15,0.4667,1,"{266, 47, 51, 57, 617, 204, 31}"
672,1,314,0,0.282635,"\int x^4 \sqrt[3]{a+b x^2} \, dx","Int[x^4*(a + b*x^2)^(1/3),x]","-\frac{54 a^2 x \sqrt[3]{a+b x^2}}{935 b^2}-\frac{54\ 3^{3/4} \sqrt{2-\sqrt{3}} a^3 \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{935 b^3 x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}+\frac{3}{17} x^5 \sqrt[3]{a+b x^2}+\frac{6 a x^3 \sqrt[3]{a+b x^2}}{187 b}","-\frac{54 a^2 x \sqrt[3]{a+b x^2}}{935 b^2}-\frac{54\ 3^{3/4} \sqrt{2-\sqrt{3}} a^3 \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{935 b^3 x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}+\frac{3}{17} x^5 \sqrt[3]{a+b x^2}+\frac{6 a x^3 \sqrt[3]{a+b x^2}}{187 b}",1,"(-54*a^2*x*(a + b*x^2)^(1/3))/(935*b^2) + (6*a*x^3*(a + b*x^2)^(1/3))/(187*b) + (3*x^5*(a + b*x^2)^(1/3))/17 - (54*3^(3/4)*Sqrt[2 - Sqrt[3]]*a^3*(a^(1/3) - (a + b*x^2)^(1/3))*Sqrt[(a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(935*b^3*x*Sqrt[-((a^(1/3)*(a^(1/3) - (a + b*x^2)^(1/3)))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2)])","A",5,4,15,0.2667,1,"{279, 321, 236, 219}"
673,1,290,0,0.1613554,"\int x^2 \sqrt[3]{a+b x^2} \, dx","Int[x^2*(a + b*x^2)^(1/3),x]","\frac{6\ 3^{3/4} \sqrt{2-\sqrt{3}} a^2 \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{55 b^2 x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}+\frac{3}{11} x^3 \sqrt[3]{a+b x^2}+\frac{6 a x \sqrt[3]{a+b x^2}}{55 b}","\frac{6\ 3^{3/4} \sqrt{2-\sqrt{3}} a^2 \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{55 b^2 x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}+\frac{3}{11} x^3 \sqrt[3]{a+b x^2}+\frac{6 a x \sqrt[3]{a+b x^2}}{55 b}",1,"(6*a*x*(a + b*x^2)^(1/3))/(55*b) + (3*x^3*(a + b*x^2)^(1/3))/11 + (6*3^(3/4)*Sqrt[2 - Sqrt[3]]*a^2*(a^(1/3) - (a + b*x^2)^(1/3))*Sqrt[(a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(55*b^2*x*Sqrt[-((a^(1/3)*(a^(1/3) - (a + b*x^2)^(1/3)))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2)])","A",4,4,15,0.2667,1,"{279, 321, 236, 219}"
674,1,266,0,0.1244848,"\int \sqrt[3]{a+b x^2} \, dx","Int[(a + b*x^2)^(1/3),x]","\frac{3}{5} x \sqrt[3]{a+b x^2}-\frac{2\ 3^{3/4} \sqrt{2-\sqrt{3}} a \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{5 b x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}","\frac{3}{5} x \sqrt[3]{a+b x^2}-\frac{2\ 3^{3/4} \sqrt{2-\sqrt{3}} a \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{5 b x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}",1,"(3*x*(a + b*x^2)^(1/3))/5 - (2*3^(3/4)*Sqrt[2 - Sqrt[3]]*a*(a^(1/3) - (a + b*x^2)^(1/3))*Sqrt[(a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(5*b*x*Sqrt[-((a^(1/3)*(a^(1/3) - (a + b*x^2)^(1/3)))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2)])","A",3,3,11,0.2727,1,"{195, 236, 219}"
675,1,260,0,0.1254273,"\int \frac{\sqrt[3]{a+b x^2}}{x^2} \, dx","Int[(a + b*x^2)^(1/3)/x^2,x]","-\frac{2 \sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}-\frac{\sqrt[3]{a+b x^2}}{x}","-\frac{2 \sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}-\frac{\sqrt[3]{a+b x^2}}{x}",1,"-((a + b*x^2)^(1/3)/x) - (2*Sqrt[2 - Sqrt[3]]*(a^(1/3) - (a + b*x^2)^(1/3))*Sqrt[(a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(3^(1/4)*x*Sqrt[-((a^(1/3)*(a^(1/3) - (a + b*x^2)^(1/3)))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2)])","A",3,3,15,0.2000,1,"{277, 236, 219}"
676,1,290,0,0.1578588,"\int \frac{\sqrt[3]{a+b x^2}}{x^4} \, dx","Int[(a + b*x^2)^(1/3)/x^4,x]","\frac{2 \sqrt{2-\sqrt{3}} b \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{9 \sqrt[4]{3} a x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}-\frac{2 b \sqrt[3]{a+b x^2}}{9 a x}-\frac{\sqrt[3]{a+b x^2}}{3 x^3}","\frac{2 \sqrt{2-\sqrt{3}} b \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{9 \sqrt[4]{3} a x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}-\frac{2 b \sqrt[3]{a+b x^2}}{9 a x}-\frac{\sqrt[3]{a+b x^2}}{3 x^3}",1,"-(a + b*x^2)^(1/3)/(3*x^3) - (2*b*(a + b*x^2)^(1/3))/(9*a*x) + (2*Sqrt[2 - Sqrt[3]]*b*(a^(1/3) - (a + b*x^2)^(1/3))*Sqrt[(a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(9*3^(1/4)*a*x*Sqrt[-((a^(1/3)*(a^(1/3) - (a + b*x^2)^(1/3)))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2)])","A",4,4,15,0.2667,1,"{277, 325, 236, 219}"
677,1,80,0,0.0473386,"\int x^7 \left(a+b x^2\right)^{2/3} \, dx","Int[x^7*(a + b*x^2)^(2/3),x]","\frac{9 a^2 \left(a+b x^2\right)^{8/3}}{16 b^4}-\frac{3 a^3 \left(a+b x^2\right)^{5/3}}{10 b^4}+\frac{3 \left(a+b x^2\right)^{14/3}}{28 b^4}-\frac{9 a \left(a+b x^2\right)^{11/3}}{22 b^4}","\frac{9 a^2 \left(a+b x^2\right)^{8/3}}{16 b^4}-\frac{3 a^3 \left(a+b x^2\right)^{5/3}}{10 b^4}+\frac{3 \left(a+b x^2\right)^{14/3}}{28 b^4}-\frac{9 a \left(a+b x^2\right)^{11/3}}{22 b^4}",1,"(-3*a^3*(a + b*x^2)^(5/3))/(10*b^4) + (9*a^2*(a + b*x^2)^(8/3))/(16*b^4) - (9*a*(a + b*x^2)^(11/3))/(22*b^4) + (3*(a + b*x^2)^(14/3))/(28*b^4)","A",3,2,15,0.1333,1,"{266, 43}"
678,1,59,0,0.0359452,"\int x^5 \left(a+b x^2\right)^{2/3} \, dx","Int[x^5*(a + b*x^2)^(2/3),x]","\frac{3 a^2 \left(a+b x^2\right)^{5/3}}{10 b^3}+\frac{3 \left(a+b x^2\right)^{11/3}}{22 b^3}-\frac{3 a \left(a+b x^2\right)^{8/3}}{8 b^3}","\frac{3 a^2 \left(a+b x^2\right)^{5/3}}{10 b^3}+\frac{3 \left(a+b x^2\right)^{11/3}}{22 b^3}-\frac{3 a \left(a+b x^2\right)^{8/3}}{8 b^3}",1,"(3*a^2*(a + b*x^2)^(5/3))/(10*b^3) - (3*a*(a + b*x^2)^(8/3))/(8*b^3) + (3*(a + b*x^2)^(11/3))/(22*b^3)","A",3,2,15,0.1333,1,"{266, 43}"
679,1,38,0,0.0234761,"\int x^3 \left(a+b x^2\right)^{2/3} \, dx","Int[x^3*(a + b*x^2)^(2/3),x]","\frac{3 \left(a+b x^2\right)^{8/3}}{16 b^2}-\frac{3 a \left(a+b x^2\right)^{5/3}}{10 b^2}","\frac{3 \left(a+b x^2\right)^{8/3}}{16 b^2}-\frac{3 a \left(a+b x^2\right)^{5/3}}{10 b^2}",1,"(-3*a*(a + b*x^2)^(5/3))/(10*b^2) + (3*(a + b*x^2)^(8/3))/(16*b^2)","A",3,2,15,0.1333,1,"{266, 43}"
680,1,18,0,0.0036006,"\int x \left(a+b x^2\right)^{2/3} \, dx","Int[x*(a + b*x^2)^(2/3),x]","\frac{3 \left(a+b x^2\right)^{5/3}}{10 b}","\frac{3 \left(a+b x^2\right)^{5/3}}{10 b}",1,"(3*(a + b*x^2)^(5/3))/(10*b)","A",1,1,13,0.07692,1,"{261}"
681,1,101,0,0.0664327,"\int \frac{\left(a+b x^2\right)^{2/3}}{x} \, dx","Int[(a + b*x^2)^(2/3)/x,x]","\frac{3}{4} a^{2/3} \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)+\frac{1}{2} \sqrt{3} a^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)-\frac{1}{2} a^{2/3} \log (x)+\frac{3}{4} \left(a+b x^2\right)^{2/3}","\frac{3}{4} a^{2/3} \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)+\frac{1}{2} \sqrt{3} a^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)-\frac{1}{2} a^{2/3} \log (x)+\frac{3}{4} \left(a+b x^2\right)^{2/3}",1,"(3*(a + b*x^2)^(2/3))/4 + (Sqrt[3]*a^(2/3)*ArcTan[(a^(1/3) + 2*(a + b*x^2)^(1/3))/(Sqrt[3]*a^(1/3))])/2 - (a^(2/3)*Log[x])/2 + (3*a^(2/3)*Log[a^(1/3) - (a + b*x^2)^(1/3)])/4","A",6,6,15,0.4000,1,"{266, 50, 55, 617, 204, 31}"
682,1,104,0,0.0663066,"\int \frac{\left(a+b x^2\right)^{2/3}}{x^3} \, dx","Int[(a + b*x^2)^(2/3)/x^3,x]","-\frac{\left(a+b x^2\right)^{2/3}}{2 x^2}+\frac{b \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{2 \sqrt[3]{a}}+\frac{b \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} \sqrt[3]{a}}-\frac{b \log (x)}{3 \sqrt[3]{a}}","-\frac{\left(a+b x^2\right)^{2/3}}{2 x^2}+\frac{b \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{2 \sqrt[3]{a}}+\frac{b \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} \sqrt[3]{a}}-\frac{b \log (x)}{3 \sqrt[3]{a}}",1,"-(a + b*x^2)^(2/3)/(2*x^2) + (b*ArcTan[(a^(1/3) + 2*(a + b*x^2)^(1/3))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(1/3)) - (b*Log[x])/(3*a^(1/3)) + (b*Log[a^(1/3) - (a + b*x^2)^(1/3)])/(2*a^(1/3))","A",6,6,15,0.4000,1,"{266, 47, 55, 617, 204, 31}"
683,1,135,0,0.0877556,"\int \frac{\left(a+b x^2\right)^{2/3}}{x^5} \, dx","Int[(a + b*x^2)^(2/3)/x^5,x]","-\frac{b^2 \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{12 a^{4/3}}-\frac{b^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{6 \sqrt{3} a^{4/3}}+\frac{b^2 \log (x)}{18 a^{4/3}}-\frac{b \left(a+b x^2\right)^{2/3}}{6 a x^2}-\frac{\left(a+b x^2\right)^{2/3}}{4 x^4}","-\frac{b^2 \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{12 a^{4/3}}-\frac{b^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{6 \sqrt{3} a^{4/3}}+\frac{b^2 \log (x)}{18 a^{4/3}}-\frac{b \left(a+b x^2\right)^{2/3}}{6 a x^2}-\frac{\left(a+b x^2\right)^{2/3}}{4 x^4}",1,"-(a + b*x^2)^(2/3)/(4*x^4) - (b*(a + b*x^2)^(2/3))/(6*a*x^2) - (b^2*ArcTan[(a^(1/3) + 2*(a + b*x^2)^(1/3))/(Sqrt[3]*a^(1/3))])/(6*Sqrt[3]*a^(4/3)) + (b^2*Log[x])/(18*a^(4/3)) - (b^2*Log[a^(1/3) - (a + b*x^2)^(1/3)])/(12*a^(4/3))","A",7,7,15,0.4667,1,"{266, 47, 51, 55, 617, 204, 31}"
684,1,601,0,0.4622921,"\int x^4 \left(a+b x^2\right)^{2/3} \, dx","Int[x^4*(a + b*x^2)^(2/3),x]","-\frac{108 a^2 x \left(a+b x^2\right)^{2/3}}{1729 b^2}-\frac{324 a^3 x}{1729 b^2 \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}-\frac{108 \sqrt{2} 3^{3/4} a^{10/3} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{1729 b^3 x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}+\frac{162 \sqrt[4]{3} \sqrt{2+\sqrt{3}} a^{10/3} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{1729 b^3 x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}+\frac{3}{19} x^5 \left(a+b x^2\right)^{2/3}+\frac{12 a x^3 \left(a+b x^2\right)^{2/3}}{247 b}","-\frac{108 a^2 x \left(a+b x^2\right)^{2/3}}{1729 b^2}-\frac{324 a^3 x}{1729 b^2 \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}-\frac{108 \sqrt{2} 3^{3/4} a^{10/3} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{1729 b^3 x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}+\frac{162 \sqrt[4]{3} \sqrt{2+\sqrt{3}} a^{10/3} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{1729 b^3 x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}+\frac{3}{19} x^5 \left(a+b x^2\right)^{2/3}+\frac{12 a x^3 \left(a+b x^2\right)^{2/3}}{247 b}",1,"(-108*a^2*x*(a + b*x^2)^(2/3))/(1729*b^2) + (12*a*x^3*(a + b*x^2)^(2/3))/(247*b) + (3*x^5*(a + b*x^2)^(2/3))/19 - (324*a^3*x)/(1729*b^2*((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))) + (162*3^(1/4)*Sqrt[2 + Sqrt[3]]*a^(10/3)*(a^(1/3) - (a + b*x^2)^(1/3))*Sqrt[(a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2]*EllipticE[ArcSin[((1 + Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(1729*b^3*x*Sqrt[-((a^(1/3)*(a^(1/3) - (a + b*x^2)^(1/3)))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2)]) - (108*Sqrt[2]*3^(3/4)*a^(10/3)*(a^(1/3) - (a + b*x^2)^(1/3))*Sqrt[(a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(1729*b^3*x*Sqrt[-((a^(1/3)*(a^(1/3) - (a + b*x^2)^(1/3)))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2)])","A",7,6,15,0.4000,1,"{279, 321, 235, 304, 219, 1879}"
685,1,577,0,0.3686258,"\int x^2 \left(a+b x^2\right)^{2/3} \, dx","Int[x^2*(a + b*x^2)^(2/3),x]","\frac{12 \sqrt{2} 3^{3/4} a^{7/3} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{91 b^2 x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}-\frac{18 \sqrt[4]{3} \sqrt{2+\sqrt{3}} a^{7/3} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{91 b^2 x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}+\frac{36 a^2 x}{91 b \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}+\frac{3}{13} x^3 \left(a+b x^2\right)^{2/3}+\frac{12 a x \left(a+b x^2\right)^{2/3}}{91 b}","\frac{12 \sqrt{2} 3^{3/4} a^{7/3} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{91 b^2 x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}-\frac{18 \sqrt[4]{3} \sqrt{2+\sqrt{3}} a^{7/3} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{91 b^2 x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}+\frac{36 a^2 x}{91 b \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}+\frac{3}{13} x^3 \left(a+b x^2\right)^{2/3}+\frac{12 a x \left(a+b x^2\right)^{2/3}}{91 b}",1,"(12*a*x*(a + b*x^2)^(2/3))/(91*b) + (3*x^3*(a + b*x^2)^(2/3))/13 + (36*a^2*x)/(91*b*((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))) - (18*3^(1/4)*Sqrt[2 + Sqrt[3]]*a^(7/3)*(a^(1/3) - (a + b*x^2)^(1/3))*Sqrt[(a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2]*EllipticE[ArcSin[((1 + Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(91*b^2*x*Sqrt[-((a^(1/3)*(a^(1/3) - (a + b*x^2)^(1/3)))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2)]) + (12*Sqrt[2]*3^(3/4)*a^(7/3)*(a^(1/3) - (a + b*x^2)^(1/3))*Sqrt[(a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(91*b^2*x*Sqrt[-((a^(1/3)*(a^(1/3) - (a + b*x^2)^(1/3)))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2)])","A",6,6,15,0.4000,1,"{279, 321, 235, 304, 219, 1879}"
686,1,550,0,0.3071882,"\int \left(a+b x^2\right)^{2/3} \, dx","Int[(a + b*x^2)^(2/3),x]","-\frac{4 \sqrt{2} 3^{3/4} a^{4/3} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{7 b x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}+\frac{6 \sqrt[4]{3} \sqrt{2+\sqrt{3}} a^{4/3} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{7 b x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}-\frac{12 a x}{7 \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}+\frac{3}{7} x \left(a+b x^2\right)^{2/3}","-\frac{4 \sqrt{2} 3^{3/4} a^{4/3} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{7 b x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}+\frac{6 \sqrt[4]{3} \sqrt{2+\sqrt{3}} a^{4/3} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{7 b x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}-\frac{12 a x}{7 \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}+\frac{3}{7} x \left(a+b x^2\right)^{2/3}",1,"(3*x*(a + b*x^2)^(2/3))/7 - (12*a*x)/(7*((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))) + (6*3^(1/4)*Sqrt[2 + Sqrt[3]]*a^(4/3)*(a^(1/3) - (a + b*x^2)^(1/3))*Sqrt[(a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2]*EllipticE[ArcSin[((1 + Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(7*b*x*Sqrt[-((a^(1/3)*(a^(1/3) - (a + b*x^2)^(1/3)))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2)]) - (4*Sqrt[2]*3^(3/4)*a^(4/3)*(a^(1/3) - (a + b*x^2)^(1/3))*Sqrt[(a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(7*b*x*Sqrt[-((a^(1/3)*(a^(1/3) - (a + b*x^2)^(1/3)))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2)])","A",5,5,11,0.4545,1,"{195, 235, 304, 219, 1879}"
687,1,538,0,0.3030274,"\int \frac{\left(a+b x^2\right)^{2/3}}{x^2} \, dx","Int[(a + b*x^2)^(2/3)/x^2,x]","-\frac{4 \sqrt{2} \sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}+\frac{2 \sqrt[4]{3} \sqrt{2+\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}-\frac{4 b x}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}}-\frac{\left(a+b x^2\right)^{2/3}}{x}","-\frac{4 \sqrt{2} \sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}+\frac{2 \sqrt[4]{3} \sqrt{2+\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}-\frac{4 b x}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}}-\frac{\left(a+b x^2\right)^{2/3}}{x}",1,"-((a + b*x^2)^(2/3)/x) - (4*b*x)/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3)) + (2*3^(1/4)*Sqrt[2 + Sqrt[3]]*a^(1/3)*(a^(1/3) - (a + b*x^2)^(1/3))*Sqrt[(a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2]*EllipticE[ArcSin[((1 + Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(x*Sqrt[-((a^(1/3)*(a^(1/3) - (a + b*x^2)^(1/3)))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2)]) - (4*Sqrt[2]*a^(1/3)*(a^(1/3) - (a + b*x^2)^(1/3))*Sqrt[(a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(3^(1/4)*x*Sqrt[-((a^(1/3)*(a^(1/3) - (a + b*x^2)^(1/3)))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2)])","A",5,5,15,0.3333,1,"{277, 235, 304, 219, 1879}"
688,1,575,0,0.3730066,"\int \frac{\left(a+b x^2\right)^{2/3}}{x^4} \, dx","Int[(a + b*x^2)^(2/3)/x^4,x]","-\frac{4 \sqrt{2} b \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{9 \sqrt[4]{3} a^{2/3} x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}+\frac{2 \sqrt{2+\sqrt{3}} b \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{3\ 3^{3/4} a^{2/3} x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}-\frac{4 b^2 x}{9 a \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}-\frac{4 b \left(a+b x^2\right)^{2/3}}{9 a x}-\frac{\left(a+b x^2\right)^{2/3}}{3 x^3}","-\frac{4 \sqrt{2} b \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{9 \sqrt[4]{3} a^{2/3} x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}+\frac{2 \sqrt{2+\sqrt{3}} b \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{3\ 3^{3/4} a^{2/3} x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}-\frac{4 b^2 x}{9 a \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}-\frac{4 b \left(a+b x^2\right)^{2/3}}{9 a x}-\frac{\left(a+b x^2\right)^{2/3}}{3 x^3}",1,"-(a + b*x^2)^(2/3)/(3*x^3) - (4*b*(a + b*x^2)^(2/3))/(9*a*x) - (4*b^2*x)/(9*a*((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))) + (2*Sqrt[2 + Sqrt[3]]*b*(a^(1/3) - (a + b*x^2)^(1/3))*Sqrt[(a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2]*EllipticE[ArcSin[((1 + Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(3*3^(3/4)*a^(2/3)*x*Sqrt[-((a^(1/3)*(a^(1/3) - (a + b*x^2)^(1/3)))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2)]) - (4*Sqrt[2]*b*(a^(1/3) - (a + b*x^2)^(1/3))*Sqrt[(a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(9*3^(1/4)*a^(2/3)*x*Sqrt[-((a^(1/3)*(a^(1/3) - (a + b*x^2)^(1/3)))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2)])","A",6,6,15,0.4000,1,"{277, 325, 235, 304, 219, 1879}"
689,1,80,0,0.048907,"\int x^7 \left(a+b x^2\right)^{4/3} \, dx","Int[x^7*(a + b*x^2)^(4/3),x]","\frac{9 a^2 \left(a+b x^2\right)^{10/3}}{20 b^4}-\frac{3 a^3 \left(a+b x^2\right)^{7/3}}{14 b^4}+\frac{3 \left(a+b x^2\right)^{16/3}}{32 b^4}-\frac{9 a \left(a+b x^2\right)^{13/3}}{26 b^4}","\frac{9 a^2 \left(a+b x^2\right)^{10/3}}{20 b^4}-\frac{3 a^3 \left(a+b x^2\right)^{7/3}}{14 b^4}+\frac{3 \left(a+b x^2\right)^{16/3}}{32 b^4}-\frac{9 a \left(a+b x^2\right)^{13/3}}{26 b^4}",1,"(-3*a^3*(a + b*x^2)^(7/3))/(14*b^4) + (9*a^2*(a + b*x^2)^(10/3))/(20*b^4) - (9*a*(a + b*x^2)^(13/3))/(26*b^4) + (3*(a + b*x^2)^(16/3))/(32*b^4)","A",3,2,15,0.1333,1,"{266, 43}"
690,1,59,0,0.0377544,"\int x^5 \left(a+b x^2\right)^{4/3} \, dx","Int[x^5*(a + b*x^2)^(4/3),x]","\frac{3 a^2 \left(a+b x^2\right)^{7/3}}{14 b^3}+\frac{3 \left(a+b x^2\right)^{13/3}}{26 b^3}-\frac{3 a \left(a+b x^2\right)^{10/3}}{10 b^3}","\frac{3 a^2 \left(a+b x^2\right)^{7/3}}{14 b^3}+\frac{3 \left(a+b x^2\right)^{13/3}}{26 b^3}-\frac{3 a \left(a+b x^2\right)^{10/3}}{10 b^3}",1,"(3*a^2*(a + b*x^2)^(7/3))/(14*b^3) - (3*a*(a + b*x^2)^(10/3))/(10*b^3) + (3*(a + b*x^2)^(13/3))/(26*b^3)","A",3,2,15,0.1333,1,"{266, 43}"
691,1,38,0,0.0242434,"\int x^3 \left(a+b x^2\right)^{4/3} \, dx","Int[x^3*(a + b*x^2)^(4/3),x]","\frac{3 \left(a+b x^2\right)^{10/3}}{20 b^2}-\frac{3 a \left(a+b x^2\right)^{7/3}}{14 b^2}","\frac{3 \left(a+b x^2\right)^{10/3}}{20 b^2}-\frac{3 a \left(a+b x^2\right)^{7/3}}{14 b^2}",1,"(-3*a*(a + b*x^2)^(7/3))/(14*b^2) + (3*(a + b*x^2)^(10/3))/(20*b^2)","A",3,2,15,0.1333,1,"{266, 43}"
692,1,18,0,0.0038096,"\int x \left(a+b x^2\right)^{4/3} \, dx","Int[x*(a + b*x^2)^(4/3),x]","\frac{3 \left(a+b x^2\right)^{7/3}}{14 b}","\frac{3 \left(a+b x^2\right)^{7/3}}{14 b}",1,"(3*(a + b*x^2)^(7/3))/(14*b)","A",1,1,13,0.07692,1,"{261}"
693,1,117,0,0.0819629,"\int \frac{\left(a+b x^2\right)^{4/3}}{x} \, dx","Int[(a + b*x^2)^(4/3)/x,x]","\frac{3}{4} a^{4/3} \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)-\frac{1}{2} \sqrt{3} a^{4/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)-\frac{1}{2} a^{4/3} \log (x)+\frac{3}{2} a \sqrt[3]{a+b x^2}+\frac{3}{8} \left(a+b x^2\right)^{4/3}","\frac{3}{4} a^{4/3} \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)-\frac{1}{2} \sqrt{3} a^{4/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)-\frac{1}{2} a^{4/3} \log (x)+\frac{3}{2} a \sqrt[3]{a+b x^2}+\frac{3}{8} \left(a+b x^2\right)^{4/3}",1,"(3*a*(a + b*x^2)^(1/3))/2 + (3*(a + b*x^2)^(4/3))/8 - (Sqrt[3]*a^(4/3)*ArcTan[(a^(1/3) + 2*(a + b*x^2)^(1/3))/(Sqrt[3]*a^(1/3))])/2 - (a^(4/3)*Log[x])/2 + (3*a^(4/3)*Log[a^(1/3) - (a + b*x^2)^(1/3)])/4","A",7,6,15,0.4000,1,"{266, 50, 57, 617, 204, 31}"
694,1,116,0,0.0840763,"\int \frac{\left(a+b x^2\right)^{4/3}}{x^3} \, dx","Int[(a + b*x^2)^(4/3)/x^3,x]","-\frac{\left(a+b x^2\right)^{4/3}}{2 x^2}+2 b \sqrt[3]{a+b x^2}+\sqrt[3]{a} b \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)-\frac{2 \sqrt[3]{a} b \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3}}-\frac{2}{3} \sqrt[3]{a} b \log (x)","-\frac{\left(a+b x^2\right)^{4/3}}{2 x^2}+2 b \sqrt[3]{a+b x^2}+\sqrt[3]{a} b \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)-\frac{2 \sqrt[3]{a} b \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3}}-\frac{2}{3} \sqrt[3]{a} b \log (x)",1,"2*b*(a + b*x^2)^(1/3) - (a + b*x^2)^(4/3)/(2*x^2) - (2*a^(1/3)*b*ArcTan[(a^(1/3) + 2*(a + b*x^2)^(1/3))/(Sqrt[3]*a^(1/3))])/Sqrt[3] - (2*a^(1/3)*b*Log[x])/3 + a^(1/3)*b*Log[a^(1/3) - (a + b*x^2)^(1/3)]","A",7,7,15,0.4667,1,"{266, 47, 50, 57, 617, 204, 31}"
695,1,132,0,0.087383,"\int \frac{\left(a+b x^2\right)^{4/3}}{x^5} \, dx","Int[(a + b*x^2)^(4/3)/x^5,x]","\frac{b^2 \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{6 a^{2/3}}-\frac{b^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{2/3}}-\frac{b^2 \log (x)}{9 a^{2/3}}-\frac{b \sqrt[3]{a+b x^2}}{3 x^2}-\frac{\left(a+b x^2\right)^{4/3}}{4 x^4}","\frac{b^2 \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{6 a^{2/3}}-\frac{b^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{2/3}}-\frac{b^2 \log (x)}{9 a^{2/3}}-\frac{b \sqrt[3]{a+b x^2}}{3 x^2}-\frac{\left(a+b x^2\right)^{4/3}}{4 x^4}",1,"-(b*(a + b*x^2)^(1/3))/(3*x^2) - (a + b*x^2)^(4/3)/(4*x^4) - (b^2*ArcTan[(a^(1/3) + 2*(a + b*x^2)^(1/3))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(2/3)) - (b^2*Log[x])/(9*a^(2/3)) + (b^2*Log[a^(1/3) - (a + b*x^2)^(1/3)])/(6*a^(2/3))","A",7,6,15,0.4000,1,"{266, 47, 57, 617, 204, 31}"
696,1,335,0,0.2282817,"\int x^4 \left(a+b x^2\right)^{4/3} \, dx","Int[x^4*(a + b*x^2)^(4/3),x]","-\frac{432 a^3 x \sqrt[3]{a+b x^2}}{21505 b^2}-\frac{432\ 3^{3/4} \sqrt{2-\sqrt{3}} a^4 \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{21505 b^3 x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}+\frac{48 a^2 x^3 \sqrt[3]{a+b x^2}}{4301 b}+\frac{3}{23} x^5 \left(a+b x^2\right)^{4/3}+\frac{24}{391} a x^5 \sqrt[3]{a+b x^2}","-\frac{432 a^3 x \sqrt[3]{a+b x^2}}{21505 b^2}-\frac{432\ 3^{3/4} \sqrt{2-\sqrt{3}} a^4 \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{21505 b^3 x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}+\frac{48 a^2 x^3 \sqrt[3]{a+b x^2}}{4301 b}+\frac{3}{23} x^5 \left(a+b x^2\right)^{4/3}+\frac{24}{391} a x^5 \sqrt[3]{a+b x^2}",1,"(-432*a^3*x*(a + b*x^2)^(1/3))/(21505*b^2) + (48*a^2*x^3*(a + b*x^2)^(1/3))/(4301*b) + (24*a*x^5*(a + b*x^2)^(1/3))/391 + (3*x^5*(a + b*x^2)^(4/3))/23 - (432*3^(3/4)*Sqrt[2 - Sqrt[3]]*a^4*(a^(1/3) - (a + b*x^2)^(1/3))*Sqrt[(a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(21505*b^3*x*Sqrt[-((a^(1/3)*(a^(1/3) - (a + b*x^2)^(1/3)))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2)])","A",6,4,15,0.2667,1,"{279, 321, 236, 219}"
697,1,311,0,0.1854068,"\int x^2 \left(a+b x^2\right)^{4/3} \, dx","Int[x^2*(a + b*x^2)^(4/3),x]","\frac{48\ 3^{3/4} \sqrt{2-\sqrt{3}} a^3 \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{935 b^2 x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}+\frac{48 a^2 x \sqrt[3]{a+b x^2}}{935 b}+\frac{24}{187} a x^3 \sqrt[3]{a+b x^2}+\frac{3}{17} x^3 \left(a+b x^2\right)^{4/3}","\frac{48\ 3^{3/4} \sqrt{2-\sqrt{3}} a^3 \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{935 b^2 x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}+\frac{48 a^2 x \sqrt[3]{a+b x^2}}{935 b}+\frac{24}{187} a x^3 \sqrt[3]{a+b x^2}+\frac{3}{17} x^3 \left(a+b x^2\right)^{4/3}",1,"(48*a^2*x*(a + b*x^2)^(1/3))/(935*b) + (24*a*x^3*(a + b*x^2)^(1/3))/187 + (3*x^3*(a + b*x^2)^(4/3))/17 + (48*3^(3/4)*Sqrt[2 - Sqrt[3]]*a^3*(a^(1/3) - (a + b*x^2)^(1/3))*Sqrt[(a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(935*b^2*x*Sqrt[-((a^(1/3)*(a^(1/3) - (a + b*x^2)^(1/3)))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2)])","A",5,4,15,0.2667,1,"{279, 321, 236, 219}"
698,1,285,0,0.1661354,"\int \left(a+b x^2\right)^{4/3} \, dx","Int[(a + b*x^2)^(4/3),x]","-\frac{16\ 3^{3/4} \sqrt{2-\sqrt{3}} a^2 \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{55 b x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}+\frac{24}{55} a x \sqrt[3]{a+b x^2}+\frac{3}{11} x \left(a+b x^2\right)^{4/3}","-\frac{16\ 3^{3/4} \sqrt{2-\sqrt{3}} a^2 \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{55 b x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}+\frac{24}{55} a x \sqrt[3]{a+b x^2}+\frac{3}{11} x \left(a+b x^2\right)^{4/3}",1,"(24*a*x*(a + b*x^2)^(1/3))/55 + (3*x*(a + b*x^2)^(4/3))/11 - (16*3^(3/4)*Sqrt[2 - Sqrt[3]]*a^2*(a^(1/3) - (a + b*x^2)^(1/3))*Sqrt[(a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(55*b*x*Sqrt[-((a^(1/3)*(a^(1/3) - (a + b*x^2)^(1/3)))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2)])","A",4,3,11,0.2727,1,"{195, 236, 219}"
699,1,280,0,0.1540804,"\int \frac{\left(a+b x^2\right)^{4/3}}{x^2} \, dx","Int[(a + b*x^2)^(4/3)/x^2,x]","-\frac{16 \sqrt{2-\sqrt{3}} a \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{5 \sqrt[4]{3} x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}-\frac{\left(a+b x^2\right)^{4/3}}{x}+\frac{8}{5} b x \sqrt[3]{a+b x^2}","-\frac{16 \sqrt{2-\sqrt{3}} a \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{5 \sqrt[4]{3} x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}-\frac{\left(a+b x^2\right)^{4/3}}{x}+\frac{8}{5} b x \sqrt[3]{a+b x^2}",1,"(8*b*x*(a + b*x^2)^(1/3))/5 - (a + b*x^2)^(4/3)/x - (16*Sqrt[2 - Sqrt[3]]*a*(a^(1/3) - (a + b*x^2)^(1/3))*Sqrt[(a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(5*3^(1/4)*x*Sqrt[-((a^(1/3)*(a^(1/3) - (a + b*x^2)^(1/3)))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2)])","A",4,4,15,0.2667,1,"{277, 195, 236, 219}"
700,1,284,0,0.1503232,"\int \frac{\left(a+b x^2\right)^{4/3}}{x^4} \, dx","Int[(a + b*x^2)^(4/3)/x^4,x]","-\frac{16 \sqrt{2-\sqrt{3}} b \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{9 \sqrt[4]{3} x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}-\frac{\left(a+b x^2\right)^{4/3}}{3 x^3}-\frac{8 b \sqrt[3]{a+b x^2}}{9 x}","-\frac{16 \sqrt{2-\sqrt{3}} b \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{9 \sqrt[4]{3} x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}-\frac{\left(a+b x^2\right)^{4/3}}{3 x^3}-\frac{8 b \sqrt[3]{a+b x^2}}{9 x}",1,"(-8*b*(a + b*x^2)^(1/3))/(9*x) - (a + b*x^2)^(4/3)/(3*x^3) - (16*Sqrt[2 - Sqrt[3]]*b*(a^(1/3) - (a + b*x^2)^(1/3))*Sqrt[(a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(9*3^(1/4)*x*Sqrt[-((a^(1/3)*(a^(1/3) - (a + b*x^2)^(1/3)))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2)])","A",4,3,15,0.2000,1,"{277, 236, 219}"
701,1,13,0,0.0021335,"\int x \left(-1+x^2\right)^{7/3} \, dx","Int[x*(-1 + x^2)^(7/3),x]","\frac{3}{20} \left(x^2-1\right)^{10/3}","\frac{3}{20} \left(x^2-1\right)^{10/3}",1,"(3*(-1 + x^2)^(10/3))/20","A",1,1,11,0.09091,1,"{261}"
702,1,80,0,0.0463976,"\int \frac{x^7}{\sqrt[3]{a+b x^2}} \, dx","Int[x^7/(a + b*x^2)^(1/3),x]","\frac{9 a^2 \left(a+b x^2\right)^{5/3}}{10 b^4}-\frac{3 a^3 \left(a+b x^2\right)^{2/3}}{4 b^4}+\frac{3 \left(a+b x^2\right)^{11/3}}{22 b^4}-\frac{9 a \left(a+b x^2\right)^{8/3}}{16 b^4}","\frac{9 a^2 \left(a+b x^2\right)^{5/3}}{10 b^4}-\frac{3 a^3 \left(a+b x^2\right)^{2/3}}{4 b^4}+\frac{3 \left(a+b x^2\right)^{11/3}}{22 b^4}-\frac{9 a \left(a+b x^2\right)^{8/3}}{16 b^4}",1,"(-3*a^3*(a + b*x^2)^(2/3))/(4*b^4) + (9*a^2*(a + b*x^2)^(5/3))/(10*b^4) - (9*a*(a + b*x^2)^(8/3))/(16*b^4) + (3*(a + b*x^2)^(11/3))/(22*b^4)","A",3,2,15,0.1333,1,"{266, 43}"
703,1,59,0,0.0343872,"\int \frac{x^5}{\sqrt[3]{a+b x^2}} \, dx","Int[x^5/(a + b*x^2)^(1/3),x]","\frac{3 a^2 \left(a+b x^2\right)^{2/3}}{4 b^3}+\frac{3 \left(a+b x^2\right)^{8/3}}{16 b^3}-\frac{3 a \left(a+b x^2\right)^{5/3}}{5 b^3}","\frac{3 a^2 \left(a+b x^2\right)^{2/3}}{4 b^3}+\frac{3 \left(a+b x^2\right)^{8/3}}{16 b^3}-\frac{3 a \left(a+b x^2\right)^{5/3}}{5 b^3}",1,"(3*a^2*(a + b*x^2)^(2/3))/(4*b^3) - (3*a*(a + b*x^2)^(5/3))/(5*b^3) + (3*(a + b*x^2)^(8/3))/(16*b^3)","A",3,2,15,0.1333,1,"{266, 43}"
704,1,38,0,0.0225681,"\int \frac{x^3}{\sqrt[3]{a+b x^2}} \, dx","Int[x^3/(a + b*x^2)^(1/3),x]","\frac{3 \left(a+b x^2\right)^{5/3}}{10 b^2}-\frac{3 a \left(a+b x^2\right)^{2/3}}{4 b^2}","\frac{3 \left(a+b x^2\right)^{5/3}}{10 b^2}-\frac{3 a \left(a+b x^2\right)^{2/3}}{4 b^2}",1,"(-3*a*(a + b*x^2)^(2/3))/(4*b^2) + (3*(a + b*x^2)^(5/3))/(10*b^2)","A",3,2,15,0.1333,1,"{266, 43}"
705,1,18,0,0.0032547,"\int \frac{x}{\sqrt[3]{a+b x^2}} \, dx","Int[x/(a + b*x^2)^(1/3),x]","\frac{3 \left(a+b x^2\right)^{2/3}}{4 b}","\frac{3 \left(a+b x^2\right)^{2/3}}{4 b}",1,"(3*(a + b*x^2)^(2/3))/(4*b)","A",1,1,13,0.07692,1,"{261}"
706,1,86,0,0.0508861,"\int \frac{1}{x \sqrt[3]{a+b x^2}} \, dx","Int[1/(x*(a + b*x^2)^(1/3)),x]","\frac{3 \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{4 \sqrt[3]{a}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{2 \sqrt[3]{a}}-\frac{\log (x)}{2 \sqrt[3]{a}}","\frac{3 \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{4 \sqrt[3]{a}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{2 \sqrt[3]{a}}-\frac{\log (x)}{2 \sqrt[3]{a}}",1,"(Sqrt[3]*ArcTan[(a^(1/3) + 2*(a + b*x^2)^(1/3))/(Sqrt[3]*a^(1/3))])/(2*a^(1/3)) - Log[x]/(2*a^(1/3)) + (3*Log[a^(1/3) - (a + b*x^2)^(1/3)])/(4*a^(1/3))","A",5,5,15,0.3333,1,"{266, 55, 617, 204, 31}"
707,1,110,0,0.065413,"\int \frac{1}{x^3 \sqrt[3]{a+b x^2}} \, dx","Int[1/(x^3*(a + b*x^2)^(1/3)),x]","-\frac{b \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{4 a^{4/3}}-\frac{b \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{2 \sqrt{3} a^{4/3}}+\frac{b \log (x)}{6 a^{4/3}}-\frac{\left(a+b x^2\right)^{2/3}}{2 a x^2}","-\frac{b \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{4 a^{4/3}}-\frac{b \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{2 \sqrt{3} a^{4/3}}+\frac{b \log (x)}{6 a^{4/3}}-\frac{\left(a+b x^2\right)^{2/3}}{2 a x^2}",1,"-(a + b*x^2)^(2/3)/(2*a*x^2) - (b*ArcTan[(a^(1/3) + 2*(a + b*x^2)^(1/3))/(Sqrt[3]*a^(1/3))])/(2*Sqrt[3]*a^(4/3)) + (b*Log[x])/(6*a^(4/3)) - (b*Log[a^(1/3) - (a + b*x^2)^(1/3)])/(4*a^(4/3))","A",6,6,15,0.4000,1,"{266, 51, 55, 617, 204, 31}"
708,1,138,0,0.0933155,"\int \frac{1}{x^5 \sqrt[3]{a+b x^2}} \, dx","Int[1/(x^5*(a + b*x^2)^(1/3)),x]","\frac{b^2 \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{6 a^{7/3}}+\frac{b^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{7/3}}-\frac{b^2 \log (x)}{9 a^{7/3}}+\frac{b \left(a+b x^2\right)^{2/3}}{3 a^2 x^2}-\frac{\left(a+b x^2\right)^{2/3}}{4 a x^4}","\frac{b^2 \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{6 a^{7/3}}+\frac{b^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{7/3}}-\frac{b^2 \log (x)}{9 a^{7/3}}+\frac{b \left(a+b x^2\right)^{2/3}}{3 a^2 x^2}-\frac{\left(a+b x^2\right)^{2/3}}{4 a x^4}",1,"-(a + b*x^2)^(2/3)/(4*a*x^4) + (b*(a + b*x^2)^(2/3))/(3*a^2*x^2) + (b^2*ArcTan[(a^(1/3) + 2*(a + b*x^2)^(1/3))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(7/3)) - (b^2*Log[x])/(9*a^(7/3)) + (b^2*Log[a^(1/3) - (a + b*x^2)^(1/3)])/(6*a^(7/3))","A",7,6,15,0.4000,1,"{266, 51, 55, 617, 204, 31}"
709,1,580,0,0.3663726,"\int \frac{x^4}{\sqrt[3]{a+b x^2}} \, dx","Int[x^4/(a + b*x^2)^(1/3),x]","-\frac{81 a^2 x}{91 b^2 \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}-\frac{27 \sqrt{2} 3^{3/4} a^{7/3} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{91 b^3 x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}+\frac{81 \sqrt[4]{3} \sqrt{2+\sqrt{3}} a^{7/3} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{182 b^3 x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}-\frac{27 a x \left(a+b x^2\right)^{2/3}}{91 b^2}+\frac{3 x^3 \left(a+b x^2\right)^{2/3}}{13 b}","-\frac{81 a^2 x}{91 b^2 \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}-\frac{27 \sqrt{2} 3^{3/4} a^{7/3} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{91 b^3 x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}+\frac{81 \sqrt[4]{3} \sqrt{2+\sqrt{3}} a^{7/3} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{182 b^3 x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}-\frac{27 a x \left(a+b x^2\right)^{2/3}}{91 b^2}+\frac{3 x^3 \left(a+b x^2\right)^{2/3}}{13 b}",1,"(-27*a*x*(a + b*x^2)^(2/3))/(91*b^2) + (3*x^3*(a + b*x^2)^(2/3))/(13*b) - (81*a^2*x)/(91*b^2*((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))) + (81*3^(1/4)*Sqrt[2 + Sqrt[3]]*a^(7/3)*(a^(1/3) - (a + b*x^2)^(1/3))*Sqrt[(a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2]*EllipticE[ArcSin[((1 + Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(182*b^3*x*Sqrt[-((a^(1/3)*(a^(1/3) - (a + b*x^2)^(1/3)))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2)]) - (27*Sqrt[2]*3^(3/4)*a^(7/3)*(a^(1/3) - (a + b*x^2)^(1/3))*Sqrt[(a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(91*b^3*x*Sqrt[-((a^(1/3)*(a^(1/3) - (a + b*x^2)^(1/3)))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2)])","A",6,5,15,0.3333,1,"{321, 235, 304, 219, 1879}"
710,1,556,0,0.3094786,"\int \frac{x^2}{\sqrt[3]{a+b x^2}} \, dx","Int[x^2/(a + b*x^2)^(1/3),x]","\frac{3 \sqrt{2} 3^{3/4} a^{4/3} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{7 b^2 x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}-\frac{9 \sqrt[4]{3} \sqrt{2+\sqrt{3}} a^{4/3} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{14 b^2 x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}+\frac{9 a x}{7 b \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}+\frac{3 x \left(a+b x^2\right)^{2/3}}{7 b}","\frac{3 \sqrt{2} 3^{3/4} a^{4/3} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{7 b^2 x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}-\frac{9 \sqrt[4]{3} \sqrt{2+\sqrt{3}} a^{4/3} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{14 b^2 x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}+\frac{9 a x}{7 b \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}+\frac{3 x \left(a+b x^2\right)^{2/3}}{7 b}",1,"(3*x*(a + b*x^2)^(2/3))/(7*b) + (9*a*x)/(7*b*((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))) - (9*3^(1/4)*Sqrt[2 + Sqrt[3]]*a^(4/3)*(a^(1/3) - (a + b*x^2)^(1/3))*Sqrt[(a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2]*EllipticE[ArcSin[((1 + Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(14*b^2*x*Sqrt[-((a^(1/3)*(a^(1/3) - (a + b*x^2)^(1/3)))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2)]) + (3*Sqrt[2]*3^(3/4)*a^(4/3)*(a^(1/3) - (a + b*x^2)^(1/3))*Sqrt[(a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(7*b^2*x*Sqrt[-((a^(1/3)*(a^(1/3) - (a + b*x^2)^(1/3)))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2)])","A",5,5,15,0.3333,1,"{321, 235, 304, 219, 1879}"
711,1,529,0,0.2498893,"\int \frac{1}{\sqrt[3]{a+b x^2}} \, dx","Int[(a + b*x^2)^(-1/3),x]","-\frac{\sqrt{2} 3^{3/4} \sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{b x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}+\frac{3 \sqrt[4]{3} \sqrt{2+\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{2 b x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}-\frac{3 x}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}}","-\frac{\sqrt{2} 3^{3/4} \sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{b x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}+\frac{3 \sqrt[4]{3} \sqrt{2+\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{2 b x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}-\frac{3 x}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}}",1,"(-3*x)/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3)) + (3*3^(1/4)*Sqrt[2 + Sqrt[3]]*a^(1/3)*(a^(1/3) - (a + b*x^2)^(1/3))*Sqrt[(a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2]*EllipticE[ArcSin[((1 + Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(2*b*x*Sqrt[-((a^(1/3)*(a^(1/3) - (a + b*x^2)^(1/3)))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2)]) - (Sqrt[2]*3^(3/4)*a^(1/3)*(a^(1/3) - (a + b*x^2)^(1/3))*Sqrt[(a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(b*x*Sqrt[-((a^(1/3)*(a^(1/3) - (a + b*x^2)^(1/3)))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2)])","A",4,4,11,0.3636,1,"{235, 304, 219, 1879}"
712,1,546,0,0.2997048,"\int \frac{1}{x^2 \sqrt[3]{a+b x^2}} \, dx","Int[1/(x^2*(a + b*x^2)^(1/3)),x]","-\frac{\sqrt{2} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} a^{2/3} x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}+\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{2 a^{2/3} x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}-\frac{b x}{a \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}-\frac{\left(a+b x^2\right)^{2/3}}{a x}","-\frac{\sqrt{2} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} a^{2/3} x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}+\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{2 a^{2/3} x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}-\frac{b x}{a \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}-\frac{\left(a+b x^2\right)^{2/3}}{a x}",1,"-((a + b*x^2)^(2/3)/(a*x)) - (b*x)/(a*((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))) + (3^(1/4)*Sqrt[2 + Sqrt[3]]*(a^(1/3) - (a + b*x^2)^(1/3))*Sqrt[(a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2]*EllipticE[ArcSin[((1 + Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(2*a^(2/3)*x*Sqrt[-((a^(1/3)*(a^(1/3) - (a + b*x^2)^(1/3)))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2)]) - (Sqrt[2]*(a^(1/3) - (a + b*x^2)^(1/3))*Sqrt[(a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(3^(1/4)*a^(2/3)*x*Sqrt[-((a^(1/3)*(a^(1/3) - (a + b*x^2)^(1/3)))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2)])","A",5,5,15,0.3333,1,"{325, 235, 304, 219, 1879}"
713,1,578,0,0.3571958,"\int \frac{1}{x^4 \sqrt[3]{a+b x^2}} \, dx","Int[1/(x^4*(a + b*x^2)^(1/3)),x]","\frac{5 b^2 x}{9 a^2 \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}+\frac{5 b \left(a+b x^2\right)^{2/3}}{9 a^2 x}+\frac{5 \sqrt{2} b \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{9 \sqrt[4]{3} a^{5/3} x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}-\frac{5 \sqrt{2+\sqrt{3}} b \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{6\ 3^{3/4} a^{5/3} x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}-\frac{\left(a+b x^2\right)^{2/3}}{3 a x^3}","\frac{5 b^2 x}{9 a^2 \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}+\frac{5 b \left(a+b x^2\right)^{2/3}}{9 a^2 x}+\frac{5 \sqrt{2} b \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{9 \sqrt[4]{3} a^{5/3} x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}-\frac{5 \sqrt{2+\sqrt{3}} b \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{6\ 3^{3/4} a^{5/3} x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}-\frac{\left(a+b x^2\right)^{2/3}}{3 a x^3}",1,"-(a + b*x^2)^(2/3)/(3*a*x^3) + (5*b*(a + b*x^2)^(2/3))/(9*a^2*x) + (5*b^2*x)/(9*a^2*((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))) - (5*Sqrt[2 + Sqrt[3]]*b*(a^(1/3) - (a + b*x^2)^(1/3))*Sqrt[(a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2]*EllipticE[ArcSin[((1 + Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(6*3^(3/4)*a^(5/3)*x*Sqrt[-((a^(1/3)*(a^(1/3) - (a + b*x^2)^(1/3)))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2)]) + (5*Sqrt[2]*b*(a^(1/3) - (a + b*x^2)^(1/3))*Sqrt[(a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(9*3^(1/4)*a^(5/3)*x*Sqrt[-((a^(1/3)*(a^(1/3) - (a + b*x^2)^(1/3)))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2)])","A",6,5,15,0.3333,1,"{325, 235, 304, 219, 1879}"
714,1,80,0,0.045896,"\int \frac{x^7}{\left(a+b x^2\right)^{2/3}} \, dx","Int[x^7/(a + b*x^2)^(2/3),x]","\frac{9 a^2 \left(a+b x^2\right)^{4/3}}{8 b^4}-\frac{3 a^3 \sqrt[3]{a+b x^2}}{2 b^4}+\frac{3 \left(a+b x^2\right)^{10/3}}{20 b^4}-\frac{9 a \left(a+b x^2\right)^{7/3}}{14 b^4}","\frac{9 a^2 \left(a+b x^2\right)^{4/3}}{8 b^4}-\frac{3 a^3 \sqrt[3]{a+b x^2}}{2 b^4}+\frac{3 \left(a+b x^2\right)^{10/3}}{20 b^4}-\frac{9 a \left(a+b x^2\right)^{7/3}}{14 b^4}",1,"(-3*a^3*(a + b*x^2)^(1/3))/(2*b^4) + (9*a^2*(a + b*x^2)^(4/3))/(8*b^4) - (9*a*(a + b*x^2)^(7/3))/(14*b^4) + (3*(a + b*x^2)^(10/3))/(20*b^4)","A",3,2,15,0.1333,1,"{266, 43}"
715,1,59,0,0.0335988,"\int \frac{x^5}{\left(a+b x^2\right)^{2/3}} \, dx","Int[x^5/(a + b*x^2)^(2/3),x]","\frac{3 a^2 \sqrt[3]{a+b x^2}}{2 b^3}+\frac{3 \left(a+b x^2\right)^{7/3}}{14 b^3}-\frac{3 a \left(a+b x^2\right)^{4/3}}{4 b^3}","\frac{3 a^2 \sqrt[3]{a+b x^2}}{2 b^3}+\frac{3 \left(a+b x^2\right)^{7/3}}{14 b^3}-\frac{3 a \left(a+b x^2\right)^{4/3}}{4 b^3}",1,"(3*a^2*(a + b*x^2)^(1/3))/(2*b^3) - (3*a*(a + b*x^2)^(4/3))/(4*b^3) + (3*(a + b*x^2)^(7/3))/(14*b^3)","A",3,2,15,0.1333,1,"{266, 43}"
716,1,38,0,0.0235036,"\int \frac{x^3}{\left(a+b x^2\right)^{2/3}} \, dx","Int[x^3/(a + b*x^2)^(2/3),x]","\frac{3 \left(a+b x^2\right)^{4/3}}{8 b^2}-\frac{3 a \sqrt[3]{a+b x^2}}{2 b^2}","\frac{3 \left(a+b x^2\right)^{4/3}}{8 b^2}-\frac{3 a \sqrt[3]{a+b x^2}}{2 b^2}",1,"(-3*a*(a + b*x^2)^(1/3))/(2*b^2) + (3*(a + b*x^2)^(4/3))/(8*b^2)","A",3,2,15,0.1333,1,"{266, 43}"
717,1,18,0,0.0035487,"\int \frac{x}{\left(a+b x^2\right)^{2/3}} \, dx","Int[x/(a + b*x^2)^(2/3),x]","\frac{3 \sqrt[3]{a+b x^2}}{2 b}","\frac{3 \sqrt[3]{a+b x^2}}{2 b}",1,"(3*(a + b*x^2)^(1/3))/(2*b)","A",1,1,13,0.07692,1,"{261}"
718,1,86,0,0.0518777,"\int \frac{1}{x \left(a+b x^2\right)^{2/3}} \, dx","Int[1/(x*(a + b*x^2)^(2/3)),x]","\frac{3 \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{4 a^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{2 a^{2/3}}-\frac{\log (x)}{2 a^{2/3}}","\frac{3 \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{4 a^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{2 a^{2/3}}-\frac{\log (x)}{2 a^{2/3}}",1,"-(Sqrt[3]*ArcTan[(a^(1/3) + 2*(a + b*x^2)^(1/3))/(Sqrt[3]*a^(1/3))])/(2*a^(2/3)) - Log[x]/(2*a^(2/3)) + (3*Log[a^(1/3) - (a + b*x^2)^(1/3)])/(4*a^(2/3))","A",5,5,15,0.3333,1,"{266, 57, 617, 204, 31}"
719,1,107,0,0.0658551,"\int \frac{1}{x^3 \left(a+b x^2\right)^{2/3}} \, dx","Int[1/(x^3*(a + b*x^2)^(2/3)),x]","-\frac{b \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{2 a^{5/3}}+\frac{b \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{5/3}}+\frac{b \log (x)}{3 a^{5/3}}-\frac{\sqrt[3]{a+b x^2}}{2 a x^2}","-\frac{b \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{2 a^{5/3}}+\frac{b \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{5/3}}+\frac{b \log (x)}{3 a^{5/3}}-\frac{\sqrt[3]{a+b x^2}}{2 a x^2}",1,"-(a + b*x^2)^(1/3)/(2*a*x^2) + (b*ArcTan[(a^(1/3) + 2*(a + b*x^2)^(1/3))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(5/3)) + (b*Log[x])/(3*a^(5/3)) - (b*Log[a^(1/3) - (a + b*x^2)^(1/3)])/(2*a^(5/3))","A",6,6,15,0.4000,1,"{266, 51, 57, 617, 204, 31}"
720,1,138,0,0.0883603,"\int \frac{1}{x^5 \left(a+b x^2\right)^{2/3}} \, dx","Int[1/(x^5*(a + b*x^2)^(2/3)),x]","\frac{5 b^2 \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{12 a^{8/3}}-\frac{5 b^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{6 \sqrt{3} a^{8/3}}-\frac{5 b^2 \log (x)}{18 a^{8/3}}+\frac{5 b \sqrt[3]{a+b x^2}}{12 a^2 x^2}-\frac{\sqrt[3]{a+b x^2}}{4 a x^4}","\frac{5 b^2 \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{12 a^{8/3}}-\frac{5 b^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{6 \sqrt{3} a^{8/3}}-\frac{5 b^2 \log (x)}{18 a^{8/3}}+\frac{5 b \sqrt[3]{a+b x^2}}{12 a^2 x^2}-\frac{\sqrt[3]{a+b x^2}}{4 a x^4}",1,"-(a + b*x^2)^(1/3)/(4*a*x^4) + (5*b*(a + b*x^2)^(1/3))/(12*a^2*x^2) - (5*b^2*ArcTan[(a^(1/3) + 2*(a + b*x^2)^(1/3))/(Sqrt[3]*a^(1/3))])/(6*Sqrt[3]*a^(8/3)) - (5*b^2*Log[x])/(18*a^(8/3)) + (5*b^2*Log[a^(1/3) - (a + b*x^2)^(1/3)])/(12*a^(8/3))","A",7,6,15,0.4000,1,"{266, 51, 57, 617, 204, 31}"
721,1,293,0,0.1575266,"\int \frac{x^4}{\left(a+b x^2\right)^{2/3}} \, dx","Int[x^4/(a + b*x^2)^(2/3),x]","-\frac{27\ 3^{3/4} \sqrt{2-\sqrt{3}} a^2 \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{55 b^3 x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}-\frac{27 a x \sqrt[3]{a+b x^2}}{55 b^2}+\frac{3 x^3 \sqrt[3]{a+b x^2}}{11 b}","-\frac{27\ 3^{3/4} \sqrt{2-\sqrt{3}} a^2 \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{55 b^3 x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}-\frac{27 a x \sqrt[3]{a+b x^2}}{55 b^2}+\frac{3 x^3 \sqrt[3]{a+b x^2}}{11 b}",1,"(-27*a*x*(a + b*x^2)^(1/3))/(55*b^2) + (3*x^3*(a + b*x^2)^(1/3))/(11*b) - (27*3^(3/4)*Sqrt[2 - Sqrt[3]]*a^2*(a^(1/3) - (a + b*x^2)^(1/3))*Sqrt[(a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(55*b^3*x*Sqrt[-((a^(1/3)*(a^(1/3) - (a + b*x^2)^(1/3)))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2)])","A",4,3,15,0.2000,1,"{321, 236, 219}"
722,1,269,0,0.1234666,"\int \frac{x^2}{\left(a+b x^2\right)^{2/3}} \, dx","Int[x^2/(a + b*x^2)^(2/3),x]","\frac{3\ 3^{3/4} \sqrt{2-\sqrt{3}} a \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{5 b^2 x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}+\frac{3 x \sqrt[3]{a+b x^2}}{5 b}","\frac{3\ 3^{3/4} \sqrt{2-\sqrt{3}} a \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{5 b^2 x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}+\frac{3 x \sqrt[3]{a+b x^2}}{5 b}",1,"(3*x*(a + b*x^2)^(1/3))/(5*b) + (3*3^(3/4)*Sqrt[2 - Sqrt[3]]*a*(a^(1/3) - (a + b*x^2)^(1/3))*Sqrt[(a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(5*b^2*x*Sqrt[-((a^(1/3)*(a^(1/3) - (a + b*x^2)^(1/3)))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2)])","A",3,3,15,0.2000,1,"{321, 236, 219}"
723,1,246,0,0.0955809,"\int \frac{1}{\left(a+b x^2\right)^{2/3}} \, dx","Int[(a + b*x^2)^(-2/3),x]","-\frac{3^{3/4} \sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{b x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}","-\frac{3^{3/4} \sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{b x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}",1,"-((3^(3/4)*Sqrt[2 - Sqrt[3]]*(a^(1/3) - (a + b*x^2)^(1/3))*Sqrt[(a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(b*x*Sqrt[-((a^(1/3)*(a^(1/3) - (a + b*x^2)^(1/3)))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2)]))","A",2,2,11,0.1818,1,"{236, 219}"
724,1,265,0,0.1205466,"\int \frac{1}{x^2 \left(a+b x^2\right)^{2/3}} \, dx","Int[1/(x^2*(a + b*x^2)^(2/3)),x]","\frac{\sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} a x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}-\frac{\sqrt[3]{a+b x^2}}{a x}","\frac{\sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} a x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}-\frac{\sqrt[3]{a+b x^2}}{a x}",1,"-((a + b*x^2)^(1/3)/(a*x)) + (Sqrt[2 - Sqrt[3]]*(a^(1/3) - (a + b*x^2)^(1/3))*Sqrt[(a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(3^(1/4)*a*x*Sqrt[-((a^(1/3)*(a^(1/3) - (a + b*x^2)^(1/3)))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2)])","A",3,3,15,0.2000,1,"{325, 236, 219}"
725,1,293,0,0.1499034,"\int \frac{1}{x^4 \left(a+b x^2\right)^{2/3}} \, dx","Int[1/(x^4*(a + b*x^2)^(2/3)),x]","\frac{7 b \sqrt[3]{a+b x^2}}{9 a^2 x}-\frac{7 \sqrt{2-\sqrt{3}} b \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{9 \sqrt[4]{3} a^2 x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}-\frac{\sqrt[3]{a+b x^2}}{3 a x^3}","\frac{7 b \sqrt[3]{a+b x^2}}{9 a^2 x}-\frac{7 \sqrt{2-\sqrt{3}} b \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{9 \sqrt[4]{3} a^2 x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}-\frac{\sqrt[3]{a+b x^2}}{3 a x^3}",1,"-(a + b*x^2)^(1/3)/(3*a*x^3) + (7*b*(a + b*x^2)^(1/3))/(9*a^2*x) - (7*Sqrt[2 - Sqrt[3]]*b*(a^(1/3) - (a + b*x^2)^(1/3))*Sqrt[(a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(9*3^(1/4)*a^2*x*Sqrt[-((a^(1/3)*(a^(1/3) - (a + b*x^2)^(1/3)))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2)])","A",4,3,15,0.2000,1,"{325, 236, 219}"
726,1,80,0,0.0438257,"\int \frac{x^7}{\left(a+b x^2\right)^{4/3}} \, dx","Int[x^7/(a + b*x^2)^(4/3),x]","\frac{3 a^3}{2 b^4 \sqrt[3]{a+b x^2}}+\frac{9 a^2 \left(a+b x^2\right)^{2/3}}{4 b^4}-\frac{9 a \left(a+b x^2\right)^{5/3}}{10 b^4}+\frac{3 \left(a+b x^2\right)^{8/3}}{16 b^4}","\frac{3 a^3}{2 b^4 \sqrt[3]{a+b x^2}}+\frac{9 a^2 \left(a+b x^2\right)^{2/3}}{4 b^4}-\frac{9 a \left(a+b x^2\right)^{5/3}}{10 b^4}+\frac{3 \left(a+b x^2\right)^{8/3}}{16 b^4}",1,"(3*a^3)/(2*b^4*(a + b*x^2)^(1/3)) + (9*a^2*(a + b*x^2)^(2/3))/(4*b^4) - (9*a*(a + b*x^2)^(5/3))/(10*b^4) + (3*(a + b*x^2)^(8/3))/(16*b^4)","A",3,2,15,0.1333,1,"{266, 43}"
727,1,59,0,0.0332049,"\int \frac{x^5}{\left(a+b x^2\right)^{4/3}} \, dx","Int[x^5/(a + b*x^2)^(4/3),x]","-\frac{3 a^2}{2 b^3 \sqrt[3]{a+b x^2}}-\frac{3 a \left(a+b x^2\right)^{2/3}}{2 b^3}+\frac{3 \left(a+b x^2\right)^{5/3}}{10 b^3}","-\frac{3 a^2}{2 b^3 \sqrt[3]{a+b x^2}}-\frac{3 a \left(a+b x^2\right)^{2/3}}{2 b^3}+\frac{3 \left(a+b x^2\right)^{5/3}}{10 b^3}",1,"(-3*a^2)/(2*b^3*(a + b*x^2)^(1/3)) - (3*a*(a + b*x^2)^(2/3))/(2*b^3) + (3*(a + b*x^2)^(5/3))/(10*b^3)","A",3,2,15,0.1333,1,"{266, 43}"
728,1,38,0,0.0234592,"\int \frac{x^3}{\left(a+b x^2\right)^{4/3}} \, dx","Int[x^3/(a + b*x^2)^(4/3),x]","\frac{3 a}{2 b^2 \sqrt[3]{a+b x^2}}+\frac{3 \left(a+b x^2\right)^{2/3}}{4 b^2}","\frac{3 a}{2 b^2 \sqrt[3]{a+b x^2}}+\frac{3 \left(a+b x^2\right)^{2/3}}{4 b^2}",1,"(3*a)/(2*b^2*(a + b*x^2)^(1/3)) + (3*(a + b*x^2)^(2/3))/(4*b^2)","A",3,2,15,0.1333,1,"{266, 43}"
729,1,18,0,0.0035819,"\int \frac{x}{\left(a+b x^2\right)^{4/3}} \, dx","Int[x/(a + b*x^2)^(4/3),x]","-\frac{3}{2 b \sqrt[3]{a+b x^2}}","-\frac{3}{2 b \sqrt[3]{a+b x^2}}",1,"-3/(2*b*(a + b*x^2)^(1/3))","A",1,1,13,0.07692,1,"{261}"
730,1,104,0,0.0648134,"\int \frac{1}{x \left(a+b x^2\right)^{4/3}} \, dx","Int[1/(x*(a + b*x^2)^(4/3)),x]","\frac{3 \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{4 a^{4/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{2 a^{4/3}}-\frac{\log (x)}{2 a^{4/3}}+\frac{3}{2 a \sqrt[3]{a+b x^2}}","\frac{3 \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{4 a^{4/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{2 a^{4/3}}-\frac{\log (x)}{2 a^{4/3}}+\frac{3}{2 a \sqrt[3]{a+b x^2}}",1,"3/(2*a*(a + b*x^2)^(1/3)) + (Sqrt[3]*ArcTan[(a^(1/3) + 2*(a + b*x^2)^(1/3))/(Sqrt[3]*a^(1/3))])/(2*a^(4/3)) - Log[x]/(2*a^(4/3)) + (3*Log[a^(1/3) - (a + b*x^2)^(1/3)])/(4*a^(4/3))","A",6,6,15,0.4000,1,"{266, 51, 55, 617, 204, 31}"
731,1,125,0,0.0801575,"\int \frac{1}{x^3 \left(a+b x^2\right)^{4/3}} \, dx","Int[1/(x^3*(a + b*x^2)^(4/3)),x]","-\frac{2 \left(a+b x^2\right)^{2/3}}{a^2 x^2}-\frac{b \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{a^{7/3}}-\frac{2 b \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{7/3}}+\frac{2 b \log (x)}{3 a^{7/3}}+\frac{3}{2 a x^2 \sqrt[3]{a+b x^2}}","-\frac{2 b}{a^2 \sqrt[3]{a+b x^2}}-\frac{b \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{a^{7/3}}-\frac{2 b \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{7/3}}+\frac{2 b \log (x)}{3 a^{7/3}}-\frac{1}{2 a x^2 \sqrt[3]{a+b x^2}}",1,"3/(2*a*x^2*(a + b*x^2)^(1/3)) - (2*(a + b*x^2)^(2/3))/(a^2*x^2) - (2*b*ArcTan[(a^(1/3) + 2*(a + b*x^2)^(1/3))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(7/3)) + (2*b*Log[x])/(3*a^(7/3)) - (b*Log[a^(1/3) - (a + b*x^2)^(1/3)])/a^(7/3)","A",7,6,15,0.4000,1,"{266, 51, 55, 617, 204, 31}"
732,1,159,0,0.1055789,"\int \frac{1}{x^5 \left(a+b x^2\right)^{4/3}} \, dx","Int[1/(x^5*(a + b*x^2)^(4/3)),x]","\frac{7 b^2 \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{6 a^{10/3}}+\frac{7 b^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{10/3}}-\frac{7 b^2 \log (x)}{9 a^{10/3}}+\frac{7 b \left(a+b x^2\right)^{2/3}}{3 a^3 x^2}-\frac{7 \left(a+b x^2\right)^{2/3}}{4 a^2 x^4}+\frac{3}{2 a x^4 \sqrt[3]{a+b x^2}}","\frac{7 b^2}{3 a^3 \sqrt[3]{a+b x^2}}+\frac{7 b^2 \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{6 a^{10/3}}+\frac{7 b^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{10/3}}-\frac{7 b^2 \log (x)}{9 a^{10/3}}+\frac{7 b}{12 a^2 x^2 \sqrt[3]{a+b x^2}}-\frac{1}{4 a x^4 \sqrt[3]{a+b x^2}}",1,"3/(2*a*x^4*(a + b*x^2)^(1/3)) - (7*(a + b*x^2)^(2/3))/(4*a^2*x^4) + (7*b*(a + b*x^2)^(2/3))/(3*a^3*x^2) + (7*b^2*ArcTan[(a^(1/3) + 2*(a + b*x^2)^(1/3))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(10/3)) - (7*b^2*Log[x])/(9*a^(10/3)) + (7*b^2*Log[a^(1/3) - (a + b*x^2)^(1/3)])/(6*a^(10/3))","A",8,6,15,0.4000,1,"{266, 51, 55, 617, 204, 31}"
733,1,577,0,0.3653008,"\int \frac{x^4}{\left(a+b x^2\right)^{4/3}} \, dx","Int[x^4/(a + b*x^2)^(4/3),x]","\frac{27\ 3^{3/4} a^{4/3} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{7 \sqrt{2} b^3 x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}-\frac{81 \sqrt[4]{3} \sqrt{2+\sqrt{3}} a^{4/3} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{28 b^3 x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}+\frac{27 x \left(a+b x^2\right)^{2/3}}{14 b^2}+\frac{81 a x}{14 b^2 \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}-\frac{3 x^3}{2 b \sqrt[3]{a+b x^2}}","\frac{27\ 3^{3/4} a^{4/3} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{7 \sqrt{2} b^3 x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}-\frac{81 \sqrt[4]{3} \sqrt{2+\sqrt{3}} a^{4/3} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{28 b^3 x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}+\frac{27 x \left(a+b x^2\right)^{2/3}}{14 b^2}+\frac{81 a x}{14 b^2 \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}-\frac{3 x^3}{2 b \sqrt[3]{a+b x^2}}",1,"(-3*x^3)/(2*b*(a + b*x^2)^(1/3)) + (27*x*(a + b*x^2)^(2/3))/(14*b^2) + (81*a*x)/(14*b^2*((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))) - (81*3^(1/4)*Sqrt[2 + Sqrt[3]]*a^(4/3)*(a^(1/3) - (a + b*x^2)^(1/3))*Sqrt[(a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2]*EllipticE[ArcSin[((1 + Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(28*b^3*x*Sqrt[-((a^(1/3)*(a^(1/3) - (a + b*x^2)^(1/3)))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2)]) + (27*3^(3/4)*a^(4/3)*(a^(1/3) - (a + b*x^2)^(1/3))*Sqrt[(a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(7*Sqrt[2]*b^3*x*Sqrt[-((a^(1/3)*(a^(1/3) - (a + b*x^2)^(1/3)))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2)])","A",6,6,15,0.4000,1,"{288, 321, 235, 304, 219, 1879}"
734,1,553,0,0.3032324,"\int \frac{x^2}{\left(a+b x^2\right)^{4/3}} \, dx","Int[x^2/(a + b*x^2)^(4/3),x]","-\frac{3\ 3^{3/4} \sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{\sqrt{2} b^2 x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}+\frac{9 \sqrt[4]{3} \sqrt{2+\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{4 b^2 x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}-\frac{3 x}{2 b \sqrt[3]{a+b x^2}}-\frac{9 x}{2 b \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}","-\frac{3\ 3^{3/4} \sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{\sqrt{2} b^2 x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}+\frac{9 \sqrt[4]{3} \sqrt{2+\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{4 b^2 x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}-\frac{3 x}{2 b \sqrt[3]{a+b x^2}}-\frac{9 x}{2 b \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}",1,"(-3*x)/(2*b*(a + b*x^2)^(1/3)) - (9*x)/(2*b*((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))) + (9*3^(1/4)*Sqrt[2 + Sqrt[3]]*a^(1/3)*(a^(1/3) - (a + b*x^2)^(1/3))*Sqrt[(a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2]*EllipticE[ArcSin[((1 + Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(4*b^2*x*Sqrt[-((a^(1/3)*(a^(1/3) - (a + b*x^2)^(1/3)))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2)]) - (3*3^(3/4)*a^(1/3)*(a^(1/3) - (a + b*x^2)^(1/3))*Sqrt[(a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(Sqrt[2]*b^2*x*Sqrt[-((a^(1/3)*(a^(1/3) - (a + b*x^2)^(1/3)))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2)])","A",5,5,15,0.3333,1,"{288, 235, 304, 219, 1879}"
735,1,552,0,0.2977323,"\int \frac{1}{\left(a+b x^2\right)^{4/3}} \, dx","Int[(a + b*x^2)^(-4/3),x]","\frac{3^{3/4} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{\sqrt{2} a^{2/3} b x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}-\frac{3 \sqrt[4]{3} \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{4 a^{2/3} b x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}+\frac{3 x}{2 a \sqrt[3]{a+b x^2}}+\frac{3 x}{2 a \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}","\frac{3^{3/4} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{\sqrt{2} a^{2/3} b x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}-\frac{3 \sqrt[4]{3} \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{4 a^{2/3} b x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}+\frac{3 x}{2 a \sqrt[3]{a+b x^2}}+\frac{3 x}{2 a \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}",1,"(3*x)/(2*a*(a + b*x^2)^(1/3)) + (3*x)/(2*a*((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))) - (3*3^(1/4)*Sqrt[2 + Sqrt[3]]*(a^(1/3) - (a + b*x^2)^(1/3))*Sqrt[(a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2]*EllipticE[ArcSin[((1 + Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(4*a^(2/3)*b*x*Sqrt[-((a^(1/3)*(a^(1/3) - (a + b*x^2)^(1/3)))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2)]) + (3^(3/4)*(a^(1/3) - (a + b*x^2)^(1/3))*Sqrt[(a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(Sqrt[2]*a^(2/3)*b*x*Sqrt[-((a^(1/3)*(a^(1/3) - (a + b*x^2)^(1/3)))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2)])","A",5,5,11,0.4545,1,"{199, 235, 304, 219, 1879}"
736,1,571,0,0.3522246,"\int \frac{1}{x^2 \left(a+b x^2\right)^{4/3}} \, dx","Int[1/(x^2*(a + b*x^2)^(4/3)),x]","-\frac{5 b x}{2 a^2 \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}-\frac{5 \left(a+b x^2\right)^{2/3}}{2 a^2 x}-\frac{5 \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{\sqrt{2} \sqrt[4]{3} a^{5/3} x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}+\frac{5 \sqrt[4]{3} \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{4 a^{5/3} x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}+\frac{3}{2 a x \sqrt[3]{a+b x^2}}","-\frac{5 b x}{2 a^2 \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}-\frac{5 \left(a+b x^2\right)^{2/3}}{2 a^2 x}-\frac{5 \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{\sqrt{2} \sqrt[4]{3} a^{5/3} x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}+\frac{5 \sqrt[4]{3} \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{4 a^{5/3} x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}+\frac{3}{2 a x \sqrt[3]{a+b x^2}}",1,"3/(2*a*x*(a + b*x^2)^(1/3)) - (5*(a + b*x^2)^(2/3))/(2*a^2*x) - (5*b*x)/(2*a^2*((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))) + (5*3^(1/4)*Sqrt[2 + Sqrt[3]]*(a^(1/3) - (a + b*x^2)^(1/3))*Sqrt[(a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2]*EllipticE[ArcSin[((1 + Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(4*a^(5/3)*x*Sqrt[-((a^(1/3)*(a^(1/3) - (a + b*x^2)^(1/3)))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2)]) - (5*(a^(1/3) - (a + b*x^2)^(1/3))*Sqrt[(a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(Sqrt[2]*3^(1/4)*a^(5/3)*x*Sqrt[-((a^(1/3)*(a^(1/3) - (a + b*x^2)^(1/3)))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2)])","A",6,6,15,0.4000,1,"{290, 325, 235, 304, 219, 1879}"
737,1,599,0,0.4182463,"\int \frac{1}{x^4 \left(a+b x^2\right)^{4/3}} \, dx","Int[1/(x^4*(a + b*x^2)^(4/3)),x]","\frac{55 b^2 x}{18 a^3 \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}+\frac{55 b \left(a+b x^2\right)^{2/3}}{18 a^3 x}-\frac{11 \left(a+b x^2\right)^{2/3}}{6 a^2 x^3}+\frac{55 b \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{9 \sqrt{2} \sqrt[4]{3} a^{8/3} x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}-\frac{55 \sqrt{2+\sqrt{3}} b \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{12\ 3^{3/4} a^{8/3} x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}+\frac{3}{2 a x^3 \sqrt[3]{a+b x^2}}","\frac{55 b^2 x}{18 a^3 \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}+\frac{55 b \left(a+b x^2\right)^{2/3}}{18 a^3 x}-\frac{11 \left(a+b x^2\right)^{2/3}}{6 a^2 x^3}+\frac{55 b \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{9 \sqrt{2} \sqrt[4]{3} a^{8/3} x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}-\frac{55 \sqrt{2+\sqrt{3}} b \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b x^2+a}}\right)|-7+4 \sqrt{3}\right)}{12\ 3^{3/4} a^{8/3} x \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{a+b x^2}\right)^2}}}+\frac{3}{2 a x^3 \sqrt[3]{a+b x^2}}",1,"3/(2*a*x^3*(a + b*x^2)^(1/3)) - (11*(a + b*x^2)^(2/3))/(6*a^2*x^3) + (55*b*(a + b*x^2)^(2/3))/(18*a^3*x) + (55*b^2*x)/(18*a^3*((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))) - (55*Sqrt[2 + Sqrt[3]]*b*(a^(1/3) - (a + b*x^2)^(1/3))*Sqrt[(a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2]*EllipticE[ArcSin[((1 + Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(12*3^(3/4)*a^(8/3)*x*Sqrt[-((a^(1/3)*(a^(1/3) - (a + b*x^2)^(1/3)))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2)]) + (55*b*(a^(1/3) - (a + b*x^2)^(1/3))*Sqrt[(a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))], -7 + 4*Sqrt[3]])/(9*Sqrt[2]*3^(1/4)*a^(8/3)*x*Sqrt[-((a^(1/3)*(a^(1/3) - (a + b*x^2)^(1/3)))/((1 - Sqrt[3])*a^(1/3) - (a + b*x^2)^(1/3))^2)])","A",7,6,15,0.4000,1,"{290, 325, 235, 304, 219, 1879}"
738,1,275,0,0.3908679,"\int (c x)^{13/3} \sqrt[3]{a+b x^2} \, dx","Int[(c*x)^(13/3)*(a + b*x^2)^(1/3),x]","-\frac{5 a^2 c^3 (c x)^{4/3} \sqrt[3]{a+b x^2}}{108 b^2}-\frac{5 a^3 c^{13/3} \log \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)}{162 b^{8/3}}+\frac{5 a^3 c^{13/3} \log \left(\frac{b^{2/3} (c x)^{4/3}}{\left(a+b x^2\right)^{2/3}}+\frac{\sqrt[3]{b} c^{2/3} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{4/3}\right)}{324 b^{8/3}}-\frac{5 a^3 c^{13/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{2/3}}{\sqrt{3} c^{2/3}}\right)}{54 \sqrt{3} b^{8/3}}+\frac{(c x)^{16/3} \sqrt[3]{a+b x^2}}{6 c}+\frac{a c (c x)^{10/3} \sqrt[3]{a+b x^2}}{36 b}","-\frac{5 a^2 c^3 (c x)^{4/3} \sqrt[3]{a+b x^2}}{108 b^2}-\frac{5 a^3 c^{13/3} \log \left(\sqrt[3]{b} (c x)^{2/3}-c^{2/3} \sqrt[3]{a+b x^2}\right)}{108 b^{8/3}}-\frac{5 a^3 c^{13/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} (c x)^{2/3}}{c^{2/3} \sqrt[3]{a+b x^2}}+1}{\sqrt{3}}\right)}{54 \sqrt{3} b^{8/3}}+\frac{(c x)^{16/3} \sqrt[3]{a+b x^2}}{6 c}+\frac{a c (c x)^{10/3} \sqrt[3]{a+b x^2}}{36 b}",1,"(-5*a^2*c^3*(c*x)^(4/3)*(a + b*x^2)^(1/3))/(108*b^2) + (a*c*(c*x)^(10/3)*(a + b*x^2)^(1/3))/(36*b) + ((c*x)^(16/3)*(a + b*x^2)^(1/3))/(6*c) - (5*a^3*c^(13/3)*ArcTan[(c^(2/3) + (2*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))/(Sqrt[3]*c^(2/3))])/(54*Sqrt[3]*b^(8/3)) - (5*a^3*c^(13/3)*Log[c^(2/3) - (b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3)])/(162*b^(8/3)) + (5*a^3*c^(13/3)*Log[c^(4/3) + (b^(2/3)*(c*x)^(4/3))/(a + b*x^2)^(2/3) + (b^(1/3)*c^(2/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3)])/(324*b^(8/3))","A",12,11,19,0.5789,1,"{279, 321, 329, 275, 331, 292, 31, 634, 617, 204, 628}"
739,1,244,0,0.3017058,"\int (c x)^{7/3} \sqrt[3]{a+b x^2} \, dx","Int[(c*x)^(7/3)*(a + b*x^2)^(1/3),x]","\frac{a^2 c^{7/3} \log \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)}{18 b^{5/3}}-\frac{a^2 c^{7/3} \log \left(\frac{b^{2/3} (c x)^{4/3}}{\left(a+b x^2\right)^{2/3}}+\frac{\sqrt[3]{b} c^{2/3} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{4/3}\right)}{36 b^{5/3}}+\frac{a^2 c^{7/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{2/3}}{\sqrt{3} c^{2/3}}\right)}{6 \sqrt{3} b^{5/3}}+\frac{(c x)^{10/3} \sqrt[3]{a+b x^2}}{4 c}+\frac{a c (c x)^{4/3} \sqrt[3]{a+b x^2}}{12 b}","\frac{a^2 c^{7/3} \log \left(\sqrt[3]{b} (c x)^{2/3}-c^{2/3} \sqrt[3]{a+b x^2}\right)}{12 b^{5/3}}+\frac{a^2 c^{7/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} (c x)^{2/3}}{c^{2/3} \sqrt[3]{a+b x^2}}+1}{\sqrt{3}}\right)}{6 \sqrt{3} b^{5/3}}+\frac{(c x)^{10/3} \sqrt[3]{a+b x^2}}{4 c}+\frac{a c (c x)^{4/3} \sqrt[3]{a+b x^2}}{12 b}",1,"(a*c*(c*x)^(4/3)*(a + b*x^2)^(1/3))/(12*b) + ((c*x)^(10/3)*(a + b*x^2)^(1/3))/(4*c) + (a^2*c^(7/3)*ArcTan[(c^(2/3) + (2*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))/(Sqrt[3]*c^(2/3))])/(6*Sqrt[3]*b^(5/3)) + (a^2*c^(7/3)*Log[c^(2/3) - (b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3)])/(18*b^(5/3)) - (a^2*c^(7/3)*Log[c^(4/3) + (b^(2/3)*(c*x)^(4/3))/(a + b*x^2)^(2/3) + (b^(1/3)*c^(2/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3)])/(36*b^(5/3))","A",11,11,19,0.5789,1,"{279, 321, 329, 275, 331, 292, 31, 634, 617, 204, 628}"
740,1,211,0,0.273921,"\int \sqrt[3]{c x} \sqrt[3]{a+b x^2} \, dx","Int[(c*x)^(1/3)*(a + b*x^2)^(1/3),x]","-\frac{a \sqrt[3]{c} \log \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)}{6 b^{2/3}}+\frac{a \sqrt[3]{c} \log \left(\frac{b^{2/3} (c x)^{4/3}}{\left(a+b x^2\right)^{2/3}}+\frac{\sqrt[3]{b} c^{2/3} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{4/3}\right)}{12 b^{2/3}}-\frac{a \sqrt[3]{c} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{2/3}}{\sqrt{3} c^{2/3}}\right)}{2 \sqrt{3} b^{2/3}}+\frac{(c x)^{4/3} \sqrt[3]{a+b x^2}}{2 c}","-\frac{a \sqrt[3]{c} \log \left(\sqrt[3]{b} (c x)^{2/3}-c^{2/3} \sqrt[3]{a+b x^2}\right)}{4 b^{2/3}}-\frac{a \sqrt[3]{c} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} (c x)^{2/3}}{c^{2/3} \sqrt[3]{a+b x^2}}+1}{\sqrt{3}}\right)}{2 \sqrt{3} b^{2/3}}+\frac{(c x)^{4/3} \sqrt[3]{a+b x^2}}{2 c}",1,"((c*x)^(4/3)*(a + b*x^2)^(1/3))/(2*c) - (a*c^(1/3)*ArcTan[(c^(2/3) + (2*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))/(Sqrt[3]*c^(2/3))])/(2*Sqrt[3]*b^(2/3)) - (a*c^(1/3)*Log[c^(2/3) - (b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3)])/(6*b^(2/3)) + (a*c^(1/3)*Log[c^(4/3) + (b^(2/3)*(c*x)^(4/3))/(a + b*x^2)^(2/3) + (b^(1/3)*c^(2/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3)])/(12*b^(2/3))","A",10,10,19,0.5263,1,"{279, 329, 275, 331, 292, 31, 634, 617, 204, 628}"
741,1,208,0,0.2744347,"\int \frac{\sqrt[3]{a+b x^2}}{(c x)^{5/3}} \, dx","Int[(a + b*x^2)^(1/3)/(c*x)^(5/3),x]","\frac{\sqrt[3]{b} \log \left(\frac{b^{2/3} (c x)^{4/3}}{\left(a+b x^2\right)^{2/3}}+\frac{\sqrt[3]{b} c^{2/3} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{4/3}\right)}{4 c^{5/3}}-\frac{\sqrt[3]{b} \log \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)}{2 c^{5/3}}-\frac{\sqrt{3} \sqrt[3]{b} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{2/3}}{\sqrt{3} c^{2/3}}\right)}{2 c^{5/3}}-\frac{3 \sqrt[3]{a+b x^2}}{2 c (c x)^{2/3}}","-\frac{3 \sqrt[3]{b} \log \left(\sqrt[3]{b} (c x)^{2/3}-c^{2/3} \sqrt[3]{a+b x^2}\right)}{4 c^{5/3}}-\frac{\sqrt{3} \sqrt[3]{b} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} (c x)^{2/3}}{c^{2/3} \sqrt[3]{a+b x^2}}+1}{\sqrt{3}}\right)}{2 c^{5/3}}-\frac{3 \sqrt[3]{a+b x^2}}{2 c (c x)^{2/3}}",1,"(-3*(a + b*x^2)^(1/3))/(2*c*(c*x)^(2/3)) - (Sqrt[3]*b^(1/3)*ArcTan[(c^(2/3) + (2*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))/(Sqrt[3]*c^(2/3))])/(2*c^(5/3)) - (b^(1/3)*Log[c^(2/3) - (b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3)])/(2*c^(5/3)) + (b^(1/3)*Log[c^(4/3) + (b^(2/3)*(c*x)^(4/3))/(a + b*x^2)^(2/3) + (b^(1/3)*c^(2/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3)])/(4*c^(5/3))","A",10,10,19,0.5263,1,"{277, 329, 275, 331, 292, 31, 634, 617, 204, 628}"
742,1,28,0,0.0056703,"\int \frac{\sqrt[3]{a+b x^2}}{(c x)^{11/3}} \, dx","Int[(a + b*x^2)^(1/3)/(c*x)^(11/3),x]","-\frac{3 \left(a+b x^2\right)^{4/3}}{8 a c (c x)^{8/3}}","-\frac{3 \left(a+b x^2\right)^{4/3}}{8 a c (c x)^{8/3}}",1,"(-3*(a + b*x^2)^(4/3))/(8*a*c*(c*x)^(8/3))","A",1,1,19,0.05263,1,"{264}"
743,1,57,0,0.0147292,"\int \frac{\sqrt[3]{a+b x^2}}{(c x)^{17/3}} \, dx","Int[(a + b*x^2)^(1/3)/(c*x)^(17/3),x]","\frac{9 \left(a+b x^2\right)^{7/3}}{56 a^2 c (c x)^{14/3}}-\frac{3 \left(a+b x^2\right)^{4/3}}{8 a c (c x)^{14/3}}","\frac{9 \left(a+b x^2\right)^{7/3}}{56 a^2 c (c x)^{14/3}}-\frac{3 \left(a+b x^2\right)^{4/3}}{8 a c (c x)^{14/3}}",1,"(-3*(a + b*x^2)^(4/3))/(8*a*c*(c*x)^(14/3)) + (9*(a + b*x^2)^(7/3))/(56*a^2*c*(c*x)^(14/3))","A",2,2,19,0.1053,1,"{273, 264}"
744,1,85,0,0.0247993,"\int \frac{\sqrt[3]{a+b x^2}}{(c x)^{23/3}} \, dx","Int[(a + b*x^2)^(1/3)/(c*x)^(23/3),x]","-\frac{27 \left(a+b x^2\right)^{10/3}}{280 a^3 c (c x)^{20/3}}+\frac{9 \left(a+b x^2\right)^{7/3}}{28 a^2 c (c x)^{20/3}}-\frac{3 \left(a+b x^2\right)^{4/3}}{8 a c (c x)^{20/3}}","-\frac{27 \left(a+b x^2\right)^{10/3}}{280 a^3 c (c x)^{20/3}}+\frac{9 \left(a+b x^2\right)^{7/3}}{28 a^2 c (c x)^{20/3}}-\frac{3 \left(a+b x^2\right)^{4/3}}{8 a c (c x)^{20/3}}",1,"(-3*(a + b*x^2)^(4/3))/(8*a*c*(c*x)^(20/3)) + (9*(a + b*x^2)^(7/3))/(28*a^2*c*(c*x)^(20/3)) - (27*(a + b*x^2)^(10/3))/(280*a^3*c*(c*x)^(20/3))","A",3,2,19,0.1053,1,"{273, 264}"
745,1,113,0,0.0394777,"\int \frac{\sqrt[3]{a+b x^2}}{(c x)^{29/3}} \, dx","Int[(a + b*x^2)^(1/3)/(c*x)^(29/3),x]","\frac{243 \left(a+b x^2\right)^{13/3}}{3640 a^4 c (c x)^{26/3}}-\frac{81 \left(a+b x^2\right)^{10/3}}{280 a^3 c (c x)^{26/3}}+\frac{27 \left(a+b x^2\right)^{7/3}}{56 a^2 c (c x)^{26/3}}-\frac{3 \left(a+b x^2\right)^{4/3}}{8 a c (c x)^{26/3}}","\frac{243 \left(a+b x^2\right)^{13/3}}{3640 a^4 c (c x)^{26/3}}-\frac{81 \left(a+b x^2\right)^{10/3}}{280 a^3 c (c x)^{26/3}}+\frac{27 \left(a+b x^2\right)^{7/3}}{56 a^2 c (c x)^{26/3}}-\frac{3 \left(a+b x^2\right)^{4/3}}{8 a c (c x)^{26/3}}",1,"(-3*(a + b*x^2)^(4/3))/(8*a*c*(c*x)^(26/3)) + (27*(a + b*x^2)^(7/3))/(56*a^2*c*(c*x)^(26/3)) - (81*(a + b*x^2)^(10/3))/(280*a^3*c*(c*x)^(26/3)) + (243*(a + b*x^2)^(13/3))/(3640*a^4*c*(c*x)^(26/3))","A",4,2,19,0.1053,1,"{273, 264}"
746,1,451,0,0.9705882,"\int (c x)^{10/3} \sqrt[3]{a+b x^2} \, dx","Int[(c*x)^(10/3)*(a + b*x^2)^(1/3),x]","-\frac{14 a^2 c^3 \sqrt[3]{c x} \sqrt[3]{a+b x^2}}{135 b^2}+\frac{7 a^2 c^{7/3} \sqrt[3]{c x} \sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right) \sqrt{\frac{\frac{b^{2/3} (c x)^{4/3}}{\left(a+b x^2\right)^{2/3}}+\frac{\sqrt[3]{b} c^{2/3} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{4/3}}{\left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}} F\left(\cos ^{-1}\left(\frac{c^{2/3}-\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}{c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{135 \sqrt[4]{3} b^2 \sqrt{-\frac{\sqrt[3]{b} (c x)^{2/3} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)}{\sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}}}+\frac{(c x)^{13/3} \sqrt[3]{a+b x^2}}{5 c}+\frac{2 a c (c x)^{7/3} \sqrt[3]{a+b x^2}}{45 b}","-\frac{14 a^2 c^3 \sqrt[3]{c x} \sqrt[3]{a+b x^2}}{135 b^2}+\frac{7 a^2 c^{7/3} \sqrt[3]{c x} \sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right) \sqrt{\frac{\frac{b^{2/3} (c x)^{4/3}}{\left(a+b x^2\right)^{2/3}}+\frac{\sqrt[3]{b} c^{2/3} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{4/3}}{\left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}} F\left(\cos ^{-1}\left(\frac{c^{2/3}-\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}{c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{135 \sqrt[4]{3} b^2 \sqrt{-\frac{\sqrt[3]{b} (c x)^{2/3} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)}{\sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}}}+\frac{(c x)^{13/3} \sqrt[3]{a+b x^2}}{5 c}+\frac{2 a c (c x)^{7/3} \sqrt[3]{a+b x^2}}{45 b}",1,"(-14*a^2*c^3*(c*x)^(1/3)*(a + b*x^2)^(1/3))/(135*b^2) + (2*a*c*(c*x)^(7/3)*(a + b*x^2)^(1/3))/(45*b) + ((c*x)^(13/3)*(a + b*x^2)^(1/3))/(5*c) + (7*a^2*c^(7/3)*(c*x)^(1/3)*(a + b*x^2)^(1/3)*(c^(2/3) - (b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))*Sqrt[(c^(4/3) + (b^(2/3)*(c*x)^(4/3))/(a + b*x^2)^(2/3) + (b^(1/3)*c^(2/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))/(c^(2/3) - ((1 + Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))^2]*EllipticF[ArcCos[(c^(2/3) - ((1 - Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))/(c^(2/3) - ((1 + Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))], (2 + Sqrt[3])/4])/(135*3^(1/4)*b^2*Sqrt[-((b^(1/3)*(c*x)^(2/3)*(c^(2/3) - (b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3)))/((a + b*x^2)^(1/3)*(c^(2/3) - ((1 + Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))^2))])","A",6,5,19,0.2632,1,"{279, 321, 329, 241, 225}"
747,1,418,0,0.7134108,"\int (c x)^{4/3} \sqrt[3]{a+b x^2} \, dx","Int[(c*x)^(4/3)*(a + b*x^2)^(1/3),x]","-\frac{a \sqrt[3]{c} \sqrt[3]{c x} \sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right) \sqrt{\frac{\frac{b^{2/3} (c x)^{4/3}}{\left(a+b x^2\right)^{2/3}}+\frac{\sqrt[3]{b} c^{2/3} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{4/3}}{\left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}} F\left(\cos ^{-1}\left(\frac{c^{2/3}-\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}{c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{9 \sqrt[4]{3} b \sqrt{-\frac{\sqrt[3]{b} (c x)^{2/3} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)}{\sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}}}+\frac{(c x)^{7/3} \sqrt[3]{a+b x^2}}{3 c}+\frac{2 a c \sqrt[3]{c x} \sqrt[3]{a+b x^2}}{9 b}","-\frac{a \sqrt[3]{c} \sqrt[3]{c x} \sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right) \sqrt{\frac{\frac{b^{2/3} (c x)^{4/3}}{\left(a+b x^2\right)^{2/3}}+\frac{\sqrt[3]{b} c^{2/3} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{4/3}}{\left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}} F\left(\cos ^{-1}\left(\frac{c^{2/3}-\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}{c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{9 \sqrt[4]{3} b \sqrt{-\frac{\sqrt[3]{b} (c x)^{2/3} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)}{\sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}}}+\frac{(c x)^{7/3} \sqrt[3]{a+b x^2}}{3 c}+\frac{2 a c \sqrt[3]{c x} \sqrt[3]{a+b x^2}}{9 b}",1,"(2*a*c*(c*x)^(1/3)*(a + b*x^2)^(1/3))/(9*b) + ((c*x)^(7/3)*(a + b*x^2)^(1/3))/(3*c) - (a*c^(1/3)*(c*x)^(1/3)*(a + b*x^2)^(1/3)*(c^(2/3) - (b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))*Sqrt[(c^(4/3) + (b^(2/3)*(c*x)^(4/3))/(a + b*x^2)^(2/3) + (b^(1/3)*c^(2/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))/(c^(2/3) - ((1 + Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))^2]*EllipticF[ArcCos[(c^(2/3) - ((1 - Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))/(c^(2/3) - ((1 + Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))], (2 + Sqrt[3])/4])/(9*3^(1/4)*b*Sqrt[-((b^(1/3)*(c*x)^(2/3)*(c^(2/3) - (b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3)))/((a + b*x^2)^(1/3)*(c^(2/3) - ((1 + Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))^2))])","A",5,5,19,0.2632,1,"{279, 321, 329, 241, 225}"
748,1,381,0,0.6585997,"\int \frac{\sqrt[3]{a+b x^2}}{(c x)^{2/3}} \, dx","Int[(a + b*x^2)^(1/3)/(c*x)^(2/3),x]","\frac{\sqrt[3]{c x} \sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right) \sqrt{\frac{\frac{b^{2/3} (c x)^{4/3}}{\left(a+b x^2\right)^{2/3}}+\frac{\sqrt[3]{b} c^{2/3} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{4/3}}{\left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}} F\left(\cos ^{-1}\left(\frac{c^{2/3}-\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}{c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{\sqrt[4]{3} c^{5/3} \sqrt{-\frac{\sqrt[3]{b} (c x)^{2/3} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)}{\sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}}}+\frac{\sqrt[3]{c x} \sqrt[3]{a+b x^2}}{c}","\frac{\sqrt[3]{c x} \sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right) \sqrt{\frac{\frac{b^{2/3} (c x)^{4/3}}{\left(a+b x^2\right)^{2/3}}+\frac{\sqrt[3]{b} c^{2/3} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{4/3}}{\left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}} F\left(\cos ^{-1}\left(\frac{c^{2/3}-\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}{c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{\sqrt[4]{3} c^{5/3} \sqrt{-\frac{\sqrt[3]{b} (c x)^{2/3} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)}{\sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}}}+\frac{\sqrt[3]{c x} \sqrt[3]{a+b x^2}}{c}",1,"((c*x)^(1/3)*(a + b*x^2)^(1/3))/c + ((c*x)^(1/3)*(a + b*x^2)^(1/3)*(c^(2/3) - (b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))*Sqrt[(c^(4/3) + (b^(2/3)*(c*x)^(4/3))/(a + b*x^2)^(2/3) + (b^(1/3)*c^(2/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))/(c^(2/3) - ((1 + Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))^2]*EllipticF[ArcCos[(c^(2/3) - ((1 - Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))/(c^(2/3) - ((1 + Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))], (2 + Sqrt[3])/4])/(3^(1/4)*c^(5/3)*Sqrt[-((b^(1/3)*(c*x)^(2/3)*(c^(2/3) - (b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3)))/((a + b*x^2)^(1/3)*(c^(2/3) - ((1 + Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))^2))])","A",4,4,19,0.2105,1,"{279, 329, 241, 225}"
749,1,391,0,0.6645209,"\int \frac{\sqrt[3]{a+b x^2}}{(c x)^{8/3}} \, dx","Int[(a + b*x^2)^(1/3)/(c*x)^(8/3),x]","\frac{3^{3/4} b \sqrt[3]{c x} \sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right) \sqrt{\frac{\frac{b^{2/3} (c x)^{4/3}}{\left(a+b x^2\right)^{2/3}}+\frac{\sqrt[3]{b} c^{2/3} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{4/3}}{\left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}} F\left(\cos ^{-1}\left(\frac{c^{2/3}-\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}{c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{5 a c^{11/3} \sqrt{-\frac{\sqrt[3]{b} (c x)^{2/3} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)}{\sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}}}-\frac{3 \sqrt[3]{a+b x^2}}{5 c (c x)^{5/3}}","\frac{3^{3/4} b \sqrt[3]{c x} \sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right) \sqrt{\frac{\frac{b^{2/3} (c x)^{4/3}}{\left(a+b x^2\right)^{2/3}}+\frac{\sqrt[3]{b} c^{2/3} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{4/3}}{\left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}} F\left(\cos ^{-1}\left(\frac{c^{2/3}-\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}{c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{5 a c^{11/3} \sqrt{-\frac{\sqrt[3]{b} (c x)^{2/3} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)}{\sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}}}-\frac{3 \sqrt[3]{a+b x^2}}{5 c (c x)^{5/3}}",1,"(-3*(a + b*x^2)^(1/3))/(5*c*(c*x)^(5/3)) + (3^(3/4)*b*(c*x)^(1/3)*(a + b*x^2)^(1/3)*(c^(2/3) - (b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))*Sqrt[(c^(4/3) + (b^(2/3)*(c*x)^(4/3))/(a + b*x^2)^(2/3) + (b^(1/3)*c^(2/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))/(c^(2/3) - ((1 + Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))^2]*EllipticF[ArcCos[(c^(2/3) - ((1 - Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))/(c^(2/3) - ((1 + Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))], (2 + Sqrt[3])/4])/(5*a*c^(11/3)*Sqrt[-((b^(1/3)*(c*x)^(2/3)*(c^(2/3) - (b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3)))/((a + b*x^2)^(1/3)*(c^(2/3) - ((1 + Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))^2))])","A",4,4,19,0.2105,1,"{277, 329, 241, 225}"
750,1,422,0,0.7197395,"\int \frac{\sqrt[3]{a+b x^2}}{(c x)^{14/3}} \, dx","Int[(a + b*x^2)^(1/3)/(c*x)^(14/3),x]","-\frac{3\ 3^{3/4} b^2 \sqrt[3]{c x} \sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right) \sqrt{\frac{\frac{b^{2/3} (c x)^{4/3}}{\left(a+b x^2\right)^{2/3}}+\frac{\sqrt[3]{b} c^{2/3} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{4/3}}{\left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}} F\left(\cos ^{-1}\left(\frac{c^{2/3}-\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}{c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{55 a^2 c^{17/3} \sqrt{-\frac{\sqrt[3]{b} (c x)^{2/3} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)}{\sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}}}-\frac{6 b \sqrt[3]{a+b x^2}}{55 a c^3 (c x)^{5/3}}-\frac{3 \sqrt[3]{a+b x^2}}{11 c (c x)^{11/3}}","-\frac{3\ 3^{3/4} b^2 \sqrt[3]{c x} \sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right) \sqrt{\frac{\frac{b^{2/3} (c x)^{4/3}}{\left(a+b x^2\right)^{2/3}}+\frac{\sqrt[3]{b} c^{2/3} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{4/3}}{\left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}} F\left(\cos ^{-1}\left(\frac{c^{2/3}-\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}{c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{55 a^2 c^{17/3} \sqrt{-\frac{\sqrt[3]{b} (c x)^{2/3} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)}{\sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}}}-\frac{6 b \sqrt[3]{a+b x^2}}{55 a c^3 (c x)^{5/3}}-\frac{3 \sqrt[3]{a+b x^2}}{11 c (c x)^{11/3}}",1,"(-3*(a + b*x^2)^(1/3))/(11*c*(c*x)^(11/3)) - (6*b*(a + b*x^2)^(1/3))/(55*a*c^3*(c*x)^(5/3)) - (3*3^(3/4)*b^2*(c*x)^(1/3)*(a + b*x^2)^(1/3)*(c^(2/3) - (b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))*Sqrt[(c^(4/3) + (b^(2/3)*(c*x)^(4/3))/(a + b*x^2)^(2/3) + (b^(1/3)*c^(2/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))/(c^(2/3) - ((1 + Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))^2]*EllipticF[ArcCos[(c^(2/3) - ((1 - Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))/(c^(2/3) - ((1 + Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))], (2 + Sqrt[3])/4])/(55*a^2*c^(17/3)*Sqrt[-((b^(1/3)*(c*x)^(2/3)*(c^(2/3) - (b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3)))/((a + b*x^2)^(1/3)*(c^(2/3) - ((1 + Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))^2))])","A",5,5,19,0.2632,1,"{277, 325, 329, 241, 225}"
751,1,58,0,0.0173999,"\int (c x)^{2/3} \sqrt[3]{a+b x^2} \, dx","Int[(c*x)^(2/3)*(a + b*x^2)^(1/3),x]","\frac{3 (c x)^{5/3} \sqrt[3]{a+b x^2} \, _2F_1\left(-\frac{1}{3},\frac{5}{6};\frac{11}{6};-\frac{b x^2}{a}\right)}{5 c \sqrt[3]{\frac{b x^2}{a}+1}}","\frac{3 (c x)^{5/3} \sqrt[3]{a+b x^2} \, _2F_1\left(-\frac{1}{3},\frac{5}{6};\frac{11}{6};-\frac{b x^2}{a}\right)}{5 c \sqrt[3]{\frac{b x^2}{a}+1}}",1,"(3*(c*x)^(5/3)*(a + b*x^2)^(1/3)*Hypergeometric2F1[-1/3, 5/6, 11/6, -((b*x^2)/a)])/(5*c*(1 + (b*x^2)/a)^(1/3))","A",2,2,19,0.1053,1,"{365, 364}"
752,1,58,0,0.0174453,"\int \frac{\sqrt[3]{a+b x^2}}{\sqrt[3]{c x}} \, dx","Int[(a + b*x^2)^(1/3)/(c*x)^(1/3),x]","\frac{3 (c x)^{2/3} \sqrt[3]{a+b x^2} \, _2F_1\left(-\frac{1}{3},\frac{1}{3};\frac{4}{3};-\frac{b x^2}{a}\right)}{2 c \sqrt[3]{\frac{b x^2}{a}+1}}","\frac{3 (c x)^{2/3} \sqrt[3]{a+b x^2} \, _2F_1\left(-\frac{1}{3},\frac{1}{3};\frac{4}{3};-\frac{b x^2}{a}\right)}{2 c \sqrt[3]{\frac{b x^2}{a}+1}}",1,"(3*(c*x)^(2/3)*(a + b*x^2)^(1/3)*Hypergeometric2F1[-1/3, 1/3, 4/3, -((b*x^2)/a)])/(2*c*(1 + (b*x^2)/a)^(1/3))","A",2,2,19,0.1053,1,"{365, 364}"
753,1,56,0,0.0182894,"\int \frac{\sqrt[3]{a+b x^2}}{(c x)^{4/3}} \, dx","Int[(a + b*x^2)^(1/3)/(c*x)^(4/3),x]","-\frac{3 \sqrt[3]{a+b x^2} \, _2F_1\left(-\frac{1}{3},-\frac{1}{6};\frac{5}{6};-\frac{b x^2}{a}\right)}{c \sqrt[3]{c x} \sqrt[3]{\frac{b x^2}{a}+1}}","-\frac{3 \sqrt[3]{a+b x^2} \, _2F_1\left(-\frac{1}{3},-\frac{1}{6};\frac{5}{6};-\frac{b x^2}{a}\right)}{c \sqrt[3]{c x} \sqrt[3]{\frac{b x^2}{a}+1}}",1,"(-3*(a + b*x^2)^(1/3)*Hypergeometric2F1[-1/3, -1/6, 5/6, -((b*x^2)/a)])/(c*(c*x)^(1/3)*(1 + (b*x^2)/a)^(1/3))","A",2,2,19,0.1053,1,"{365, 364}"
754,1,303,0,0.3663375,"\int (c x)^{13/3} \left(a+b x^2\right)^{4/3} \, dx","Int[(c*x)^(13/3)*(a + b*x^2)^(4/3),x]","-\frac{5 a^3 c^3 (c x)^{4/3} \sqrt[3]{a+b x^2}}{324 b^2}-\frac{5 a^4 c^{13/3} \log \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)}{486 b^{8/3}}+\frac{5 a^4 c^{13/3} \log \left(\frac{b^{2/3} (c x)^{4/3}}{\left(a+b x^2\right)^{2/3}}+\frac{\sqrt[3]{b} c^{2/3} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{4/3}\right)}{972 b^{8/3}}-\frac{5 a^4 c^{13/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{2/3}}{\sqrt{3} c^{2/3}}\right)}{162 \sqrt{3} b^{8/3}}+\frac{a^2 c (c x)^{10/3} \sqrt[3]{a+b x^2}}{108 b}+\frac{(c x)^{16/3} \left(a+b x^2\right)^{4/3}}{8 c}+\frac{a (c x)^{16/3} \sqrt[3]{a+b x^2}}{18 c}","-\frac{5 a^3 c^3 (c x)^{4/3} \sqrt[3]{a+b x^2}}{324 b^2}-\frac{5 a^4 c^{13/3} \log \left(\sqrt[3]{b} (c x)^{2/3}-c^{2/3} \sqrt[3]{a+b x^2}\right)}{324 b^{8/3}}-\frac{5 a^4 c^{13/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} (c x)^{2/3}}{c^{2/3} \sqrt[3]{a+b x^2}}+1}{\sqrt{3}}\right)}{162 \sqrt{3} b^{8/3}}+\frac{a^2 c (c x)^{10/3} \sqrt[3]{a+b x^2}}{108 b}+\frac{(c x)^{16/3} \left(a+b x^2\right)^{4/3}}{8 c}+\frac{a (c x)^{16/3} \sqrt[3]{a+b x^2}}{18 c}",1,"(-5*a^3*c^3*(c*x)^(4/3)*(a + b*x^2)^(1/3))/(324*b^2) + (a^2*c*(c*x)^(10/3)*(a + b*x^2)^(1/3))/(108*b) + (a*(c*x)^(16/3)*(a + b*x^2)^(1/3))/(18*c) + ((c*x)^(16/3)*(a + b*x^2)^(4/3))/(8*c) - (5*a^4*c^(13/3)*ArcTan[(c^(2/3) + (2*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))/(Sqrt[3]*c^(2/3))])/(162*Sqrt[3]*b^(8/3)) - (5*a^4*c^(13/3)*Log[c^(2/3) - (b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3)])/(486*b^(8/3)) + (5*a^4*c^(13/3)*Log[c^(4/3) + (b^(2/3)*(c*x)^(4/3))/(a + b*x^2)^(2/3) + (b^(1/3)*c^(2/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3)])/(972*b^(8/3))","A",13,11,19,0.5789,1,"{279, 321, 329, 275, 331, 292, 31, 634, 617, 204, 628}"
755,1,272,0,0.3229926,"\int (c x)^{7/3} \left(a+b x^2\right)^{4/3} \, dx","Int[(c*x)^(7/3)*(a + b*x^2)^(4/3),x]","\frac{2 a^3 c^{7/3} \log \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)}{81 b^{5/3}}-\frac{a^3 c^{7/3} \log \left(\frac{b^{2/3} (c x)^{4/3}}{\left(a+b x^2\right)^{2/3}}+\frac{\sqrt[3]{b} c^{2/3} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{4/3}\right)}{81 b^{5/3}}+\frac{2 a^3 c^{7/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{2/3}}{\sqrt{3} c^{2/3}}\right)}{27 \sqrt{3} b^{5/3}}+\frac{a^2 c (c x)^{4/3} \sqrt[3]{a+b x^2}}{27 b}+\frac{(c x)^{10/3} \left(a+b x^2\right)^{4/3}}{6 c}+\frac{a (c x)^{10/3} \sqrt[3]{a+b x^2}}{9 c}","\frac{a^3 c^{7/3} \log \left(\sqrt[3]{b} (c x)^{2/3}-c^{2/3} \sqrt[3]{a+b x^2}\right)}{27 b^{5/3}}+\frac{2 a^3 c^{7/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} (c x)^{2/3}}{c^{2/3} \sqrt[3]{a+b x^2}}+1}{\sqrt{3}}\right)}{27 \sqrt{3} b^{5/3}}+\frac{a^2 c (c x)^{4/3} \sqrt[3]{a+b x^2}}{27 b}+\frac{(c x)^{10/3} \left(a+b x^2\right)^{4/3}}{6 c}+\frac{a (c x)^{10/3} \sqrt[3]{a+b x^2}}{9 c}",1,"(a^2*c*(c*x)^(4/3)*(a + b*x^2)^(1/3))/(27*b) + (a*(c*x)^(10/3)*(a + b*x^2)^(1/3))/(9*c) + ((c*x)^(10/3)*(a + b*x^2)^(4/3))/(6*c) + (2*a^3*c^(7/3)*ArcTan[(c^(2/3) + (2*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))/(Sqrt[3]*c^(2/3))])/(27*Sqrt[3]*b^(5/3)) + (2*a^3*c^(7/3)*Log[c^(2/3) - (b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3)])/(81*b^(5/3)) - (a^3*c^(7/3)*Log[c^(4/3) + (b^(2/3)*(c*x)^(4/3))/(a + b*x^2)^(2/3) + (b^(1/3)*c^(2/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3)])/(81*b^(5/3))","A",12,11,19,0.5789,1,"{279, 321, 329, 275, 331, 292, 31, 634, 617, 204, 628}"
756,1,243,0,0.2899624,"\int \sqrt[3]{c x} \left(a+b x^2\right)^{4/3} \, dx","Int[(c*x)^(1/3)*(a + b*x^2)^(4/3),x]","-\frac{a^2 \sqrt[3]{c} \log \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)}{9 b^{2/3}}+\frac{a^2 \sqrt[3]{c} \log \left(\frac{b^{2/3} (c x)^{4/3}}{\left(a+b x^2\right)^{2/3}}+\frac{\sqrt[3]{b} c^{2/3} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{4/3}\right)}{18 b^{2/3}}-\frac{a^2 \sqrt[3]{c} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{2/3}}{\sqrt{3} c^{2/3}}\right)}{3 \sqrt{3} b^{2/3}}+\frac{a (c x)^{4/3} \sqrt[3]{a+b x^2}}{3 c}+\frac{(c x)^{4/3} \left(a+b x^2\right)^{4/3}}{4 c}","-\frac{a^2 \sqrt[3]{c} \log \left(\sqrt[3]{b} (c x)^{2/3}-c^{2/3} \sqrt[3]{a+b x^2}\right)}{6 b^{2/3}}-\frac{a^2 \sqrt[3]{c} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} (c x)^{2/3}}{c^{2/3} \sqrt[3]{a+b x^2}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} b^{2/3}}+\frac{a (c x)^{4/3} \sqrt[3]{a+b x^2}}{3 c}+\frac{(c x)^{4/3} \left(a+b x^2\right)^{4/3}}{4 c}",1,"(a*(c*x)^(4/3)*(a + b*x^2)^(1/3))/(3*c) + ((c*x)^(4/3)*(a + b*x^2)^(4/3))/(4*c) - (a^2*c^(1/3)*ArcTan[(c^(2/3) + (2*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))/(Sqrt[3]*c^(2/3))])/(3*Sqrt[3]*b^(2/3)) - (a^2*c^(1/3)*Log[c^(2/3) - (b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3)])/(9*b^(2/3)) + (a^2*c^(1/3)*Log[c^(4/3) + (b^(2/3)*(c*x)^(4/3))/(a + b*x^2)^(2/3) + (b^(1/3)*c^(2/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3)])/(18*b^(2/3))","A",11,10,19,0.5263,1,"{279, 329, 275, 331, 292, 31, 634, 617, 204, 628}"
757,1,233,0,0.2870071,"\int \frac{\left(a+b x^2\right)^{4/3}}{(c x)^{5/3}} \, dx","Int[(a + b*x^2)^(4/3)/(c*x)^(5/3),x]","\frac{a \sqrt[3]{b} \log \left(\frac{b^{2/3} (c x)^{4/3}}{\left(a+b x^2\right)^{2/3}}+\frac{\sqrt[3]{b} c^{2/3} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{4/3}\right)}{3 c^{5/3}}+\frac{2 b (c x)^{4/3} \sqrt[3]{a+b x^2}}{c^3}-\frac{2 a \sqrt[3]{b} \log \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)}{3 c^{5/3}}-\frac{2 a \sqrt[3]{b} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{2/3}}{\sqrt{3} c^{2/3}}\right)}{\sqrt{3} c^{5/3}}-\frac{3 \left(a+b x^2\right)^{4/3}}{2 c (c x)^{2/3}}","\frac{2 b (c x)^{4/3} \sqrt[3]{a+b x^2}}{c^3}-\frac{a \sqrt[3]{b} \log \left(\sqrt[3]{b} (c x)^{2/3}-c^{2/3} \sqrt[3]{a+b x^2}\right)}{c^{5/3}}-\frac{2 a \sqrt[3]{b} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} (c x)^{2/3}}{c^{2/3} \sqrt[3]{a+b x^2}}+1}{\sqrt{3}}\right)}{\sqrt{3} c^{5/3}}-\frac{3 \left(a+b x^2\right)^{4/3}}{2 c (c x)^{2/3}}",1,"(2*b*(c*x)^(4/3)*(a + b*x^2)^(1/3))/c^3 - (3*(a + b*x^2)^(4/3))/(2*c*(c*x)^(2/3)) - (2*a*b^(1/3)*ArcTan[(c^(2/3) + (2*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))/(Sqrt[3]*c^(2/3))])/(Sqrt[3]*c^(5/3)) - (2*a*b^(1/3)*Log[c^(2/3) - (b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3)])/(3*c^(5/3)) + (a*b^(1/3)*Log[c^(4/3) + (b^(2/3)*(c*x)^(4/3))/(a + b*x^2)^(2/3) + (b^(1/3)*c^(2/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3)])/(3*c^(5/3))","A",11,11,19,0.5789,1,"{277, 279, 329, 275, 331, 292, 31, 634, 617, 204, 628}"
758,1,234,0,0.2908335,"\int \frac{\left(a+b x^2\right)^{4/3}}{(c x)^{11/3}} \, dx","Int[(a + b*x^2)^(4/3)/(c*x)^(11/3),x]","-\frac{b^{4/3} \log \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)}{2 c^{11/3}}+\frac{b^{4/3} \log \left(\frac{b^{2/3} (c x)^{4/3}}{\left(a+b x^2\right)^{2/3}}+\frac{\sqrt[3]{b} c^{2/3} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{4/3}\right)}{4 c^{11/3}}-\frac{\sqrt{3} b^{4/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{2/3}}{\sqrt{3} c^{2/3}}\right)}{2 c^{11/3}}-\frac{3 b \sqrt[3]{a+b x^2}}{2 c^3 (c x)^{2/3}}-\frac{3 \left(a+b x^2\right)^{4/3}}{8 c (c x)^{8/3}}","-\frac{3 b^{4/3} \log \left(\sqrt[3]{b} (c x)^{2/3}-c^{2/3} \sqrt[3]{a+b x^2}\right)}{4 c^{11/3}}-\frac{\sqrt{3} b^{4/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} (c x)^{2/3}}{c^{2/3} \sqrt[3]{a+b x^2}}+1}{\sqrt{3}}\right)}{2 c^{11/3}}-\frac{3 b \sqrt[3]{a+b x^2}}{2 c^3 (c x)^{2/3}}-\frac{3 \left(a+b x^2\right)^{4/3}}{8 c (c x)^{8/3}}",1,"(-3*b*(a + b*x^2)^(1/3))/(2*c^3*(c*x)^(2/3)) - (3*(a + b*x^2)^(4/3))/(8*c*(c*x)^(8/3)) - (Sqrt[3]*b^(4/3)*ArcTan[(c^(2/3) + (2*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))/(Sqrt[3]*c^(2/3))])/(2*c^(11/3)) - (b^(4/3)*Log[c^(2/3) - (b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3)])/(2*c^(11/3)) + (b^(4/3)*Log[c^(4/3) + (b^(2/3)*(c*x)^(4/3))/(a + b*x^2)^(2/3) + (b^(1/3)*c^(2/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3)])/(4*c^(11/3))","A",11,10,19,0.5263,1,"{277, 329, 275, 331, 292, 31, 634, 617, 204, 628}"
759,1,28,0,0.0060914,"\int \frac{\left(a+b x^2\right)^{4/3}}{(c x)^{17/3}} \, dx","Int[(a + b*x^2)^(4/3)/(c*x)^(17/3),x]","-\frac{3 \left(a+b x^2\right)^{7/3}}{14 a c (c x)^{14/3}}","-\frac{3 \left(a+b x^2\right)^{7/3}}{14 a c (c x)^{14/3}}",1,"(-3*(a + b*x^2)^(7/3))/(14*a*c*(c*x)^(14/3))","A",1,1,19,0.05263,1,"{264}"
760,1,57,0,0.0148183,"\int \frac{\left(a+b x^2\right)^{4/3}}{(c x)^{23/3}} \, dx","Int[(a + b*x^2)^(4/3)/(c*x)^(23/3),x]","\frac{9 \left(a+b x^2\right)^{10/3}}{140 a^2 c (c x)^{20/3}}-\frac{3 \left(a+b x^2\right)^{7/3}}{14 a c (c x)^{20/3}}","\frac{9 \left(a+b x^2\right)^{10/3}}{140 a^2 c (c x)^{20/3}}-\frac{3 \left(a+b x^2\right)^{7/3}}{14 a c (c x)^{20/3}}",1,"(-3*(a + b*x^2)^(7/3))/(14*a*c*(c*x)^(20/3)) + (9*(a + b*x^2)^(10/3))/(140*a^2*c*(c*x)^(20/3))","A",2,2,19,0.1053,1,"{273, 264}"
761,1,85,0,0.027316,"\int \frac{\left(a+b x^2\right)^{4/3}}{(c x)^{29/3}} \, dx","Int[(a + b*x^2)^(4/3)/(c*x)^(29/3),x]","-\frac{27 \left(a+b x^2\right)^{13/3}}{910 a^3 c (c x)^{26/3}}+\frac{9 \left(a+b x^2\right)^{10/3}}{70 a^2 c (c x)^{26/3}}-\frac{3 \left(a+b x^2\right)^{7/3}}{14 a c (c x)^{26/3}}","-\frac{27 \left(a+b x^2\right)^{13/3}}{910 a^3 c (c x)^{26/3}}+\frac{9 \left(a+b x^2\right)^{10/3}}{70 a^2 c (c x)^{26/3}}-\frac{3 \left(a+b x^2\right)^{7/3}}{14 a c (c x)^{26/3}}",1,"(-3*(a + b*x^2)^(7/3))/(14*a*c*(c*x)^(26/3)) + (9*(a + b*x^2)^(10/3))/(70*a^2*c*(c*x)^(26/3)) - (27*(a + b*x^2)^(13/3))/(910*a^3*c*(c*x)^(26/3))","A",3,2,19,0.1053,1,"{273, 264}"
762,1,479,0,0.8295005,"\int (c x)^{10/3} \left(a+b x^2\right)^{4/3} \, dx","Int[(c*x)^(10/3)*(a + b*x^2)^(4/3),x]","-\frac{16 a^3 c^3 \sqrt[3]{c x} \sqrt[3]{a+b x^2}}{405 b^2}+\frac{8 a^3 c^{7/3} \sqrt[3]{c x} \sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right) \sqrt{\frac{\frac{b^{2/3} (c x)^{4/3}}{\left(a+b x^2\right)^{2/3}}+\frac{\sqrt[3]{b} c^{2/3} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{4/3}}{\left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}} F\left(\cos ^{-1}\left(\frac{c^{2/3}-\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}{c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{405 \sqrt[4]{3} b^2 \sqrt{-\frac{\sqrt[3]{b} (c x)^{2/3} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)}{\sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}}}+\frac{16 a^2 c (c x)^{7/3} \sqrt[3]{a+b x^2}}{945 b}+\frac{(c x)^{13/3} \left(a+b x^2\right)^{4/3}}{7 c}+\frac{8 a (c x)^{13/3} \sqrt[3]{a+b x^2}}{105 c}","-\frac{16 a^3 c^3 \sqrt[3]{c x} \sqrt[3]{a+b x^2}}{405 b^2}+\frac{8 a^3 c^{7/3} \sqrt[3]{c x} \sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right) \sqrt{\frac{\frac{b^{2/3} (c x)^{4/3}}{\left(a+b x^2\right)^{2/3}}+\frac{\sqrt[3]{b} c^{2/3} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{4/3}}{\left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}} F\left(\cos ^{-1}\left(\frac{c^{2/3}-\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}{c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{405 \sqrt[4]{3} b^2 \sqrt{-\frac{\sqrt[3]{b} (c x)^{2/3} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)}{\sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}}}+\frac{16 a^2 c (c x)^{7/3} \sqrt[3]{a+b x^2}}{945 b}+\frac{(c x)^{13/3} \left(a+b x^2\right)^{4/3}}{7 c}+\frac{8 a (c x)^{13/3} \sqrt[3]{a+b x^2}}{105 c}",1,"(-16*a^3*c^3*(c*x)^(1/3)*(a + b*x^2)^(1/3))/(405*b^2) + (16*a^2*c*(c*x)^(7/3)*(a + b*x^2)^(1/3))/(945*b) + (8*a*(c*x)^(13/3)*(a + b*x^2)^(1/3))/(105*c) + ((c*x)^(13/3)*(a + b*x^2)^(4/3))/(7*c) + (8*a^3*c^(7/3)*(c*x)^(1/3)*(a + b*x^2)^(1/3)*(c^(2/3) - (b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))*Sqrt[(c^(4/3) + (b^(2/3)*(c*x)^(4/3))/(a + b*x^2)^(2/3) + (b^(1/3)*c^(2/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))/(c^(2/3) - ((1 + Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))^2]*EllipticF[ArcCos[(c^(2/3) - ((1 - Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))/(c^(2/3) - ((1 + Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))], (2 + Sqrt[3])/4])/(405*3^(1/4)*b^2*Sqrt[-((b^(1/3)*(c*x)^(2/3)*(c^(2/3) - (b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3)))/((a + b*x^2)^(1/3)*(c^(2/3) - ((1 + Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))^2))])","A",7,5,19,0.2632,1,"{279, 321, 329, 241, 225}"
763,1,448,0,0.7456425,"\int (c x)^{4/3} \left(a+b x^2\right)^{4/3} \, dx","Int[(c*x)^(4/3)*(a + b*x^2)^(4/3),x]","-\frac{8 a^2 \sqrt[3]{c} \sqrt[3]{c x} \sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right) \sqrt{\frac{\frac{b^{2/3} (c x)^{4/3}}{\left(a+b x^2\right)^{2/3}}+\frac{\sqrt[3]{b} c^{2/3} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{4/3}}{\left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}} F\left(\cos ^{-1}\left(\frac{c^{2/3}-\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}{c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{135 \sqrt[4]{3} b \sqrt{-\frac{\sqrt[3]{b} (c x)^{2/3} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)}{\sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}}}+\frac{16 a^2 c \sqrt[3]{c x} \sqrt[3]{a+b x^2}}{135 b}+\frac{(c x)^{7/3} \left(a+b x^2\right)^{4/3}}{5 c}+\frac{8 a (c x)^{7/3} \sqrt[3]{a+b x^2}}{45 c}","-\frac{8 a^2 \sqrt[3]{c} \sqrt[3]{c x} \sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right) \sqrt{\frac{\frac{b^{2/3} (c x)^{4/3}}{\left(a+b x^2\right)^{2/3}}+\frac{\sqrt[3]{b} c^{2/3} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{4/3}}{\left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}} F\left(\cos ^{-1}\left(\frac{c^{2/3}-\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}{c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{135 \sqrt[4]{3} b \sqrt{-\frac{\sqrt[3]{b} (c x)^{2/3} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)}{\sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}}}+\frac{16 a^2 c \sqrt[3]{c x} \sqrt[3]{a+b x^2}}{135 b}+\frac{(c x)^{7/3} \left(a+b x^2\right)^{4/3}}{5 c}+\frac{8 a (c x)^{7/3} \sqrt[3]{a+b x^2}}{45 c}",1,"(16*a^2*c*(c*x)^(1/3)*(a + b*x^2)^(1/3))/(135*b) + (8*a*(c*x)^(7/3)*(a + b*x^2)^(1/3))/(45*c) + ((c*x)^(7/3)*(a + b*x^2)^(4/3))/(5*c) - (8*a^2*c^(1/3)*(c*x)^(1/3)*(a + b*x^2)^(1/3)*(c^(2/3) - (b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))*Sqrt[(c^(4/3) + (b^(2/3)*(c*x)^(4/3))/(a + b*x^2)^(2/3) + (b^(1/3)*c^(2/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))/(c^(2/3) - ((1 + Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))^2]*EllipticF[ArcCos[(c^(2/3) - ((1 - Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))/(c^(2/3) - ((1 + Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))], (2 + Sqrt[3])/4])/(135*3^(1/4)*b*Sqrt[-((b^(1/3)*(c*x)^(2/3)*(c^(2/3) - (b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3)))/((a + b*x^2)^(1/3)*(c^(2/3) - ((1 + Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))^2))])","A",6,5,19,0.2632,1,"{279, 321, 329, 241, 225}"
764,1,414,0,0.6945286,"\int \frac{\left(a+b x^2\right)^{4/3}}{(c x)^{2/3}} \, dx","Int[(a + b*x^2)^(4/3)/(c*x)^(2/3),x]","\frac{8 a \sqrt[3]{c x} \sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right) \sqrt{\frac{\frac{b^{2/3} (c x)^{4/3}}{\left(a+b x^2\right)^{2/3}}+\frac{\sqrt[3]{b} c^{2/3} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{4/3}}{\left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}} F\left(\cos ^{-1}\left(\frac{c^{2/3}-\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}{c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{9 \sqrt[4]{3} c^{5/3} \sqrt{-\frac{\sqrt[3]{b} (c x)^{2/3} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)}{\sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}}}+\frac{\sqrt[3]{c x} \left(a+b x^2\right)^{4/3}}{3 c}+\frac{8 a \sqrt[3]{c x} \sqrt[3]{a+b x^2}}{9 c}","\frac{8 a \sqrt[3]{c x} \sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right) \sqrt{\frac{\frac{b^{2/3} (c x)^{4/3}}{\left(a+b x^2\right)^{2/3}}+\frac{\sqrt[3]{b} c^{2/3} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{4/3}}{\left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}} F\left(\cos ^{-1}\left(\frac{c^{2/3}-\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}{c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{9 \sqrt[4]{3} c^{5/3} \sqrt{-\frac{\sqrt[3]{b} (c x)^{2/3} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)}{\sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}}}+\frac{\sqrt[3]{c x} \left(a+b x^2\right)^{4/3}}{3 c}+\frac{8 a \sqrt[3]{c x} \sqrt[3]{a+b x^2}}{9 c}",1,"(8*a*(c*x)^(1/3)*(a + b*x^2)^(1/3))/(9*c) + ((c*x)^(1/3)*(a + b*x^2)^(4/3))/(3*c) + (8*a*(c*x)^(1/3)*(a + b*x^2)^(1/3)*(c^(2/3) - (b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))*Sqrt[(c^(4/3) + (b^(2/3)*(c*x)^(4/3))/(a + b*x^2)^(2/3) + (b^(1/3)*c^(2/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))/(c^(2/3) - ((1 + Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))^2]*EllipticF[ArcCos[(c^(2/3) - ((1 - Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))/(c^(2/3) - ((1 + Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))], (2 + Sqrt[3])/4])/(9*3^(1/4)*c^(5/3)*Sqrt[-((b^(1/3)*(c*x)^(2/3)*(c^(2/3) - (b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3)))/((a + b*x^2)^(1/3)*(c^(2/3) - ((1 + Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))^2))])","A",5,4,19,0.2105,1,"{279, 329, 241, 225}"
765,1,414,0,0.697927,"\int \frac{\left(a+b x^2\right)^{4/3}}{(c x)^{8/3}} \, dx","Int[(a + b*x^2)^(4/3)/(c*x)^(8/3),x]","\frac{8 b \sqrt[3]{c x} \sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right) \sqrt{\frac{\frac{b^{2/3} (c x)^{4/3}}{\left(a+b x^2\right)^{2/3}}+\frac{\sqrt[3]{b} c^{2/3} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{4/3}}{\left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}} F\left(\cos ^{-1}\left(\frac{c^{2/3}-\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}{c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{5 \sqrt[4]{3} c^{11/3} \sqrt{-\frac{\sqrt[3]{b} (c x)^{2/3} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)}{\sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}}}+\frac{8 b \sqrt[3]{c x} \sqrt[3]{a+b x^2}}{5 c^3}-\frac{3 \left(a+b x^2\right)^{4/3}}{5 c (c x)^{5/3}}","\frac{8 b \sqrt[3]{c x} \sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right) \sqrt{\frac{\frac{b^{2/3} (c x)^{4/3}}{\left(a+b x^2\right)^{2/3}}+\frac{\sqrt[3]{b} c^{2/3} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{4/3}}{\left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}} F\left(\cos ^{-1}\left(\frac{c^{2/3}-\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}{c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{5 \sqrt[4]{3} c^{11/3} \sqrt{-\frac{\sqrt[3]{b} (c x)^{2/3} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)}{\sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}}}+\frac{8 b \sqrt[3]{c x} \sqrt[3]{a+b x^2}}{5 c^3}-\frac{3 \left(a+b x^2\right)^{4/3}}{5 c (c x)^{5/3}}",1,"(8*b*(c*x)^(1/3)*(a + b*x^2)^(1/3))/(5*c^3) - (3*(a + b*x^2)^(4/3))/(5*c*(c*x)^(5/3)) + (8*b*(c*x)^(1/3)*(a + b*x^2)^(1/3)*(c^(2/3) - (b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))*Sqrt[(c^(4/3) + (b^(2/3)*(c*x)^(4/3))/(a + b*x^2)^(2/3) + (b^(1/3)*c^(2/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))/(c^(2/3) - ((1 + Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))^2]*EllipticF[ArcCos[(c^(2/3) - ((1 - Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))/(c^(2/3) - ((1 + Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))], (2 + Sqrt[3])/4])/(5*3^(1/4)*c^(11/3)*Sqrt[-((b^(1/3)*(c*x)^(2/3)*(c^(2/3) - (b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3)))/((a + b*x^2)^(1/3)*(c^(2/3) - ((1 + Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))^2))])","A",5,5,19,0.2632,1,"{277, 279, 329, 241, 225}"
766,1,419,0,0.7021605,"\int \frac{\left(a+b x^2\right)^{4/3}}{(c x)^{14/3}} \, dx","Int[(a + b*x^2)^(4/3)/(c*x)^(14/3),x]","\frac{8\ 3^{3/4} b^2 \sqrt[3]{c x} \sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right) \sqrt{\frac{\frac{b^{2/3} (c x)^{4/3}}{\left(a+b x^2\right)^{2/3}}+\frac{\sqrt[3]{b} c^{2/3} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{4/3}}{\left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}} F\left(\cos ^{-1}\left(\frac{c^{2/3}-\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}{c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{55 a c^{17/3} \sqrt{-\frac{\sqrt[3]{b} (c x)^{2/3} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)}{\sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}}}-\frac{24 b \sqrt[3]{a+b x^2}}{55 c^3 (c x)^{5/3}}-\frac{3 \left(a+b x^2\right)^{4/3}}{11 c (c x)^{11/3}}","\frac{8\ 3^{3/4} b^2 \sqrt[3]{c x} \sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right) \sqrt{\frac{\frac{b^{2/3} (c x)^{4/3}}{\left(a+b x^2\right)^{2/3}}+\frac{\sqrt[3]{b} c^{2/3} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{4/3}}{\left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}} F\left(\cos ^{-1}\left(\frac{c^{2/3}-\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}{c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{55 a c^{17/3} \sqrt{-\frac{\sqrt[3]{b} (c x)^{2/3} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)}{\sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}}}-\frac{24 b \sqrt[3]{a+b x^2}}{55 c^3 (c x)^{5/3}}-\frac{3 \left(a+b x^2\right)^{4/3}}{11 c (c x)^{11/3}}",1,"(-24*b*(a + b*x^2)^(1/3))/(55*c^3*(c*x)^(5/3)) - (3*(a + b*x^2)^(4/3))/(11*c*(c*x)^(11/3)) + (8*3^(3/4)*b^2*(c*x)^(1/3)*(a + b*x^2)^(1/3)*(c^(2/3) - (b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))*Sqrt[(c^(4/3) + (b^(2/3)*(c*x)^(4/3))/(a + b*x^2)^(2/3) + (b^(1/3)*c^(2/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))/(c^(2/3) - ((1 + Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))^2]*EllipticF[ArcCos[(c^(2/3) - ((1 - Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))/(c^(2/3) - ((1 + Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))], (2 + Sqrt[3])/4])/(55*a*c^(17/3)*Sqrt[-((b^(1/3)*(c*x)^(2/3)*(c^(2/3) - (b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3)))/((a + b*x^2)^(1/3)*(c^(2/3) - ((1 + Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))^2))])","A",5,4,19,0.2105,1,"{277, 329, 241, 225}"
767,1,450,0,0.7666482,"\int \frac{\left(a+b x^2\right)^{4/3}}{(c x)^{20/3}} \, dx","Int[(a + b*x^2)^(4/3)/(c*x)^(20/3),x]","-\frac{24\ 3^{3/4} b^3 \sqrt[3]{c x} \sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right) \sqrt{\frac{\frac{b^{2/3} (c x)^{4/3}}{\left(a+b x^2\right)^{2/3}}+\frac{\sqrt[3]{b} c^{2/3} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{4/3}}{\left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}} F\left(\cos ^{-1}\left(\frac{c^{2/3}-\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}{c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{935 a^2 c^{23/3} \sqrt{-\frac{\sqrt[3]{b} (c x)^{2/3} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)}{\sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}}}-\frac{48 b^2 \sqrt[3]{a+b x^2}}{935 a c^5 (c x)^{5/3}}-\frac{24 b \sqrt[3]{a+b x^2}}{187 c^3 (c x)^{11/3}}-\frac{3 \left(a+b x^2\right)^{4/3}}{17 c (c x)^{17/3}}","-\frac{24\ 3^{3/4} b^3 \sqrt[3]{c x} \sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right) \sqrt{\frac{\frac{b^{2/3} (c x)^{4/3}}{\left(a+b x^2\right)^{2/3}}+\frac{\sqrt[3]{b} c^{2/3} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{4/3}}{\left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}} F\left(\cos ^{-1}\left(\frac{c^{2/3}-\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}{c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{935 a^2 c^{23/3} \sqrt{-\frac{\sqrt[3]{b} (c x)^{2/3} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)}{\sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}}}-\frac{48 b^2 \sqrt[3]{a+b x^2}}{935 a c^5 (c x)^{5/3}}-\frac{24 b \sqrt[3]{a+b x^2}}{187 c^3 (c x)^{11/3}}-\frac{3 \left(a+b x^2\right)^{4/3}}{17 c (c x)^{17/3}}",1,"(-24*b*(a + b*x^2)^(1/3))/(187*c^3*(c*x)^(11/3)) - (48*b^2*(a + b*x^2)^(1/3))/(935*a*c^5*(c*x)^(5/3)) - (3*(a + b*x^2)^(4/3))/(17*c*(c*x)^(17/3)) - (24*3^(3/4)*b^3*(c*x)^(1/3)*(a + b*x^2)^(1/3)*(c^(2/3) - (b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))*Sqrt[(c^(4/3) + (b^(2/3)*(c*x)^(4/3))/(a + b*x^2)^(2/3) + (b^(1/3)*c^(2/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))/(c^(2/3) - ((1 + Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))^2]*EllipticF[ArcCos[(c^(2/3) - ((1 - Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))/(c^(2/3) - ((1 + Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))], (2 + Sqrt[3])/4])/(935*a^2*c^(23/3)*Sqrt[-((b^(1/3)*(c*x)^(2/3)*(c^(2/3) - (b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3)))/((a + b*x^2)^(1/3)*(c^(2/3) - ((1 + Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))^2))])","A",6,5,19,0.2632,1,"{277, 325, 329, 241, 225}"
768,1,59,0,0.0192229,"\int (c x)^{2/3} \left(a+b x^2\right)^{4/3} \, dx","Int[(c*x)^(2/3)*(a + b*x^2)^(4/3),x]","\frac{3 a (c x)^{5/3} \sqrt[3]{a+b x^2} \, _2F_1\left(-\frac{4}{3},\frac{5}{6};\frac{11}{6};-\frac{b x^2}{a}\right)}{5 c \sqrt[3]{\frac{b x^2}{a}+1}}","\frac{3 a (c x)^{5/3} \sqrt[3]{a+b x^2} \, _2F_1\left(-\frac{4}{3},\frac{5}{6};\frac{11}{6};-\frac{b x^2}{a}\right)}{5 c \sqrt[3]{\frac{b x^2}{a}+1}}",1,"(3*a*(c*x)^(5/3)*(a + b*x^2)^(1/3)*Hypergeometric2F1[-4/3, 5/6, 11/6, -((b*x^2)/a)])/(5*c*(1 + (b*x^2)/a)^(1/3))","A",2,2,19,0.1053,1,"{365, 364}"
769,1,59,0,0.0185268,"\int \frac{\left(a+b x^2\right)^{4/3}}{\sqrt[3]{c x}} \, dx","Int[(a + b*x^2)^(4/3)/(c*x)^(1/3),x]","\frac{3 a (c x)^{2/3} \sqrt[3]{a+b x^2} \, _2F_1\left(-\frac{4}{3},\frac{1}{3};\frac{4}{3};-\frac{b x^2}{a}\right)}{2 c \sqrt[3]{\frac{b x^2}{a}+1}}","\frac{3 a (c x)^{2/3} \sqrt[3]{a+b x^2} \, _2F_1\left(-\frac{4}{3},\frac{1}{3};\frac{4}{3};-\frac{b x^2}{a}\right)}{2 c \sqrt[3]{\frac{b x^2}{a}+1}}",1,"(3*a*(c*x)^(2/3)*(a + b*x^2)^(1/3)*Hypergeometric2F1[-4/3, 1/3, 4/3, -((b*x^2)/a)])/(2*c*(1 + (b*x^2)/a)^(1/3))","A",2,2,19,0.1053,1,"{365, 364}"
770,1,57,0,0.0189494,"\int \frac{\left(a+b x^2\right)^{4/3}}{(c x)^{4/3}} \, dx","Int[(a + b*x^2)^(4/3)/(c*x)^(4/3),x]","-\frac{3 a \sqrt[3]{a+b x^2} \, _2F_1\left(-\frac{4}{3},-\frac{1}{6};\frac{5}{6};-\frac{b x^2}{a}\right)}{c \sqrt[3]{c x} \sqrt[3]{\frac{b x^2}{a}+1}}","-\frac{3 a \sqrt[3]{a+b x^2} \, _2F_1\left(-\frac{4}{3},-\frac{1}{6};\frac{5}{6};-\frac{b x^2}{a}\right)}{c \sqrt[3]{c x} \sqrt[3]{\frac{b x^2}{a}+1}}",1,"(-3*a*(a + b*x^2)^(1/3)*Hypergeometric2F1[-4/3, -1/6, 5/6, -((b*x^2)/a)])/(c*(c*x)^(1/3)*(1 + (b*x^2)/a)^(1/3))","A",2,2,19,0.1053,1,"{365, 364}"
771,1,278,0,0.3379183,"\int \frac{(c x)^{19/3}}{\left(a+b x^2\right)^{2/3}} \, dx","Int[(c*x)^(19/3)/(a + b*x^2)^(2/3),x]","\frac{10 a^2 c^5 (c x)^{4/3} \sqrt[3]{a+b x^2}}{27 b^3}+\frac{20 a^3 c^{19/3} \log \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)}{81 b^{11/3}}-\frac{10 a^3 c^{19/3} \log \left(\frac{b^{2/3} (c x)^{4/3}}{\left(a+b x^2\right)^{2/3}}+\frac{\sqrt[3]{b} c^{2/3} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{4/3}\right)}{81 b^{11/3}}+\frac{20 a^3 c^{19/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{2/3}}{\sqrt{3} c^{2/3}}\right)}{27 \sqrt{3} b^{11/3}}-\frac{2 a c^3 (c x)^{10/3} \sqrt[3]{a+b x^2}}{9 b^2}+\frac{c (c x)^{16/3} \sqrt[3]{a+b x^2}}{6 b}","\frac{10 a^2 c^5 (c x)^{4/3} \sqrt[3]{a+b x^2}}{27 b^3}+\frac{10 a^3 c^{19/3} \log \left(\sqrt[3]{b} (c x)^{2/3}-c^{2/3} \sqrt[3]{a+b x^2}\right)}{27 b^{11/3}}+\frac{20 a^3 c^{19/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} (c x)^{2/3}}{c^{2/3} \sqrt[3]{a+b x^2}}+1}{\sqrt{3}}\right)}{27 \sqrt{3} b^{11/3}}-\frac{2 a c^3 (c x)^{10/3} \sqrt[3]{a+b x^2}}{9 b^2}+\frac{c (c x)^{16/3} \sqrt[3]{a+b x^2}}{6 b}",1,"(10*a^2*c^5*(c*x)^(4/3)*(a + b*x^2)^(1/3))/(27*b^3) - (2*a*c^3*(c*x)^(10/3)*(a + b*x^2)^(1/3))/(9*b^2) + (c*(c*x)^(16/3)*(a + b*x^2)^(1/3))/(6*b) + (20*a^3*c^(19/3)*ArcTan[(c^(2/3) + (2*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))/(Sqrt[3]*c^(2/3))])/(27*Sqrt[3]*b^(11/3)) + (20*a^3*c^(19/3)*Log[c^(2/3) - (b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3)])/(81*b^(11/3)) - (10*a^3*c^(19/3)*Log[c^(4/3) + (b^(2/3)*(c*x)^(4/3))/(a + b*x^2)^(2/3) + (b^(1/3)*c^(2/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3)])/(81*b^(11/3))","A",12,10,19,0.5263,1,"{321, 329, 275, 331, 292, 31, 634, 617, 204, 628}"
772,1,247,0,0.2899667,"\int \frac{(c x)^{13/3}}{\left(a+b x^2\right)^{2/3}} \, dx","Int[(c*x)^(13/3)/(a + b*x^2)^(2/3),x]","-\frac{5 a^2 c^{13/3} \log \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)}{18 b^{8/3}}+\frac{5 a^2 c^{13/3} \log \left(\frac{b^{2/3} (c x)^{4/3}}{\left(a+b x^2\right)^{2/3}}+\frac{\sqrt[3]{b} c^{2/3} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{4/3}\right)}{36 b^{8/3}}-\frac{5 a^2 c^{13/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{2/3}}{\sqrt{3} c^{2/3}}\right)}{6 \sqrt{3} b^{8/3}}-\frac{5 a c^3 (c x)^{4/3} \sqrt[3]{a+b x^2}}{12 b^2}+\frac{c (c x)^{10/3} \sqrt[3]{a+b x^2}}{4 b}","-\frac{5 a^2 c^{13/3} \log \left(\sqrt[3]{b} (c x)^{2/3}-c^{2/3} \sqrt[3]{a+b x^2}\right)}{12 b^{8/3}}-\frac{5 a^2 c^{13/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} (c x)^{2/3}}{c^{2/3} \sqrt[3]{a+b x^2}}+1}{\sqrt{3}}\right)}{6 \sqrt{3} b^{8/3}}-\frac{5 a c^3 (c x)^{4/3} \sqrt[3]{a+b x^2}}{12 b^2}+\frac{c (c x)^{10/3} \sqrt[3]{a+b x^2}}{4 b}",1,"(-5*a*c^3*(c*x)^(4/3)*(a + b*x^2)^(1/3))/(12*b^2) + (c*(c*x)^(10/3)*(a + b*x^2)^(1/3))/(4*b) - (5*a^2*c^(13/3)*ArcTan[(c^(2/3) + (2*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))/(Sqrt[3]*c^(2/3))])/(6*Sqrt[3]*b^(8/3)) - (5*a^2*c^(13/3)*Log[c^(2/3) - (b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3)])/(18*b^(8/3)) + (5*a^2*c^(13/3)*Log[c^(4/3) + (b^(2/3)*(c*x)^(4/3))/(a + b*x^2)^(2/3) + (b^(1/3)*c^(2/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3)])/(36*b^(8/3))","A",11,10,19,0.5263,1,"{321, 329, 275, 331, 292, 31, 634, 617, 204, 628}"
773,1,209,0,0.2616096,"\int \frac{(c x)^{7/3}}{\left(a+b x^2\right)^{2/3}} \, dx","Int[(c*x)^(7/3)/(a + b*x^2)^(2/3),x]","\frac{a c^{7/3} \log \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)}{3 b^{5/3}}-\frac{a c^{7/3} \log \left(\frac{b^{2/3} (c x)^{4/3}}{\left(a+b x^2\right)^{2/3}}+\frac{\sqrt[3]{b} c^{2/3} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{4/3}\right)}{6 b^{5/3}}+\frac{a c^{7/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{2/3}}{\sqrt{3} c^{2/3}}\right)}{\sqrt{3} b^{5/3}}+\frac{c (c x)^{4/3} \sqrt[3]{a+b x^2}}{2 b}","\frac{a c^{7/3} \log \left(\sqrt[3]{b} (c x)^{2/3}-c^{2/3} \sqrt[3]{a+b x^2}\right)}{2 b^{5/3}}+\frac{a c^{7/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} (c x)^{2/3}}{c^{2/3} \sqrt[3]{a+b x^2}}+1}{\sqrt{3}}\right)}{\sqrt{3} b^{5/3}}+\frac{c (c x)^{4/3} \sqrt[3]{a+b x^2}}{2 b}",1,"(c*(c*x)^(4/3)*(a + b*x^2)^(1/3))/(2*b) + (a*c^(7/3)*ArcTan[(c^(2/3) + (2*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))/(Sqrt[3]*c^(2/3))])/(Sqrt[3]*b^(5/3)) + (a*c^(7/3)*Log[c^(2/3) - (b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3)])/(3*b^(5/3)) - (a*c^(7/3)*Log[c^(4/3) + (b^(2/3)*(c*x)^(4/3))/(a + b*x^2)^(2/3) + (b^(1/3)*c^(2/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3)])/(6*b^(5/3))","A",10,10,19,0.5263,1,"{321, 329, 275, 331, 292, 31, 634, 617, 204, 628}"
774,1,183,0,0.244622,"\int \frac{\sqrt[3]{c x}}{\left(a+b x^2\right)^{2/3}} \, dx","Int[(c*x)^(1/3)/(a + b*x^2)^(2/3),x]","-\frac{\sqrt[3]{c} \log \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)}{2 b^{2/3}}+\frac{\sqrt[3]{c} \log \left(\frac{b^{2/3} (c x)^{4/3}}{\left(a+b x^2\right)^{2/3}}+\frac{\sqrt[3]{b} c^{2/3} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{4/3}\right)}{4 b^{2/3}}-\frac{\sqrt{3} \sqrt[3]{c} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{2/3}}{\sqrt{3} c^{2/3}}\right)}{2 b^{2/3}}","-\frac{3 \sqrt[3]{c} \log \left(\sqrt[3]{b} (c x)^{2/3}-c^{2/3} \sqrt[3]{a+b x^2}\right)}{4 b^{2/3}}-\frac{\sqrt{3} \sqrt[3]{c} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} (c x)^{2/3}}{c^{2/3} \sqrt[3]{a+b x^2}}+1}{\sqrt{3}}\right)}{2 b^{2/3}}",1,"-(Sqrt[3]*c^(1/3)*ArcTan[(c^(2/3) + (2*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))/(Sqrt[3]*c^(2/3))])/(2*b^(2/3)) - (c^(1/3)*Log[c^(2/3) - (b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3)])/(2*b^(2/3)) + (c^(1/3)*Log[c^(4/3) + (b^(2/3)*(c*x)^(4/3))/(a + b*x^2)^(2/3) + (b^(1/3)*c^(2/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3)])/(4*b^(2/3))","A",9,9,19,0.4737,1,"{329, 275, 331, 292, 31, 634, 617, 204, 628}"
775,1,28,0,0.0062157,"\int \frac{1}{(c x)^{5/3} \left(a+b x^2\right)^{2/3}} \, dx","Int[1/((c*x)^(5/3)*(a + b*x^2)^(2/3)),x]","-\frac{3 \sqrt[3]{a+b x^2}}{2 a c (c x)^{2/3}}","-\frac{3 \sqrt[3]{a+b x^2}}{2 a c (c x)^{2/3}}",1,"(-3*(a + b*x^2)^(1/3))/(2*a*c*(c*x)^(2/3))","A",1,1,19,0.05263,1,"{264}"
776,1,57,0,0.0153678,"\int \frac{1}{(c x)^{11/3} \left(a+b x^2\right)^{2/3}} \, dx","Int[1/((c*x)^(11/3)*(a + b*x^2)^(2/3)),x]","\frac{9 \left(a+b x^2\right)^{4/3}}{8 a^2 c (c x)^{8/3}}-\frac{3 \sqrt[3]{a+b x^2}}{2 a c (c x)^{8/3}}","\frac{9 \left(a+b x^2\right)^{4/3}}{8 a^2 c (c x)^{8/3}}-\frac{3 \sqrt[3]{a+b x^2}}{2 a c (c x)^{8/3}}",1,"(-3*(a + b*x^2)^(1/3))/(2*a*c*(c*x)^(8/3)) + (9*(a + b*x^2)^(4/3))/(8*a^2*c*(c*x)^(8/3))","A",2,2,19,0.1053,1,"{273, 264}"
777,1,85,0,0.0254695,"\int \frac{1}{(c x)^{17/3} \left(a+b x^2\right)^{2/3}} \, dx","Int[1/((c*x)^(17/3)*(a + b*x^2)^(2/3)),x]","-\frac{27 \left(a+b x^2\right)^{7/3}}{28 a^3 c (c x)^{14/3}}+\frac{9 \left(a+b x^2\right)^{4/3}}{4 a^2 c (c x)^{14/3}}-\frac{3 \sqrt[3]{a+b x^2}}{2 a c (c x)^{14/3}}","-\frac{27 \left(a+b x^2\right)^{7/3}}{28 a^3 c (c x)^{14/3}}+\frac{9 \left(a+b x^2\right)^{4/3}}{4 a^2 c (c x)^{14/3}}-\frac{3 \sqrt[3]{a+b x^2}}{2 a c (c x)^{14/3}}",1,"(-3*(a + b*x^2)^(1/3))/(2*a*c*(c*x)^(14/3)) + (9*(a + b*x^2)^(4/3))/(4*a^2*c*(c*x)^(14/3)) - (27*(a + b*x^2)^(7/3))/(28*a^3*c*(c*x)^(14/3))","A",3,2,19,0.1053,1,"{273, 264}"
778,1,113,0,0.0393894,"\int \frac{1}{(c x)^{23/3} \left(a+b x^2\right)^{2/3}} \, dx","Int[1/((c*x)^(23/3)*(a + b*x^2)^(2/3)),x]","\frac{243 \left(a+b x^2\right)^{10/3}}{280 a^4 c (c x)^{20/3}}-\frac{81 \left(a+b x^2\right)^{7/3}}{28 a^3 c (c x)^{20/3}}+\frac{27 \left(a+b x^2\right)^{4/3}}{8 a^2 c (c x)^{20/3}}-\frac{3 \sqrt[3]{a+b x^2}}{2 a c (c x)^{20/3}}","\frac{243 \left(a+b x^2\right)^{10/3}}{280 a^4 c (c x)^{20/3}}-\frac{81 \left(a+b x^2\right)^{7/3}}{28 a^3 c (c x)^{20/3}}+\frac{27 \left(a+b x^2\right)^{4/3}}{8 a^2 c (c x)^{20/3}}-\frac{3 \sqrt[3]{a+b x^2}}{2 a c (c x)^{20/3}}",1,"(-3*(a + b*x^2)^(1/3))/(2*a*c*(c*x)^(20/3)) + (27*(a + b*x^2)^(4/3))/(8*a^2*c*(c*x)^(20/3)) - (81*(a + b*x^2)^(7/3))/(28*a^3*c*(c*x)^(20/3)) + (243*(a + b*x^2)^(10/3))/(280*a^4*c*(c*x)^(20/3))","A",4,2,19,0.1053,1,"{273, 264}"
779,1,421,0,0.6888027,"\int \frac{(c x)^{10/3}}{\left(a+b x^2\right)^{2/3}} \, dx","Int[(c*x)^(10/3)/(a + b*x^2)^(2/3),x]","-\frac{7 a c^3 \sqrt[3]{c x} \sqrt[3]{a+b x^2}}{9 b^2}+\frac{7 a c^{7/3} \sqrt[3]{c x} \sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right) \sqrt{\frac{\frac{b^{2/3} (c x)^{4/3}}{\left(a+b x^2\right)^{2/3}}+\frac{\sqrt[3]{b} c^{2/3} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{4/3}}{\left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}} F\left(\cos ^{-1}\left(\frac{c^{2/3}-\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}{c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{18 \sqrt[4]{3} b^2 \sqrt{-\frac{\sqrt[3]{b} (c x)^{2/3} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)}{\sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}}}+\frac{c (c x)^{7/3} \sqrt[3]{a+b x^2}}{3 b}","-\frac{7 a c^3 \sqrt[3]{c x} \sqrt[3]{a+b x^2}}{9 b^2}+\frac{7 a c^{7/3} \sqrt[3]{c x} \sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right) \sqrt{\frac{\frac{b^{2/3} (c x)^{4/3}}{\left(a+b x^2\right)^{2/3}}+\frac{\sqrt[3]{b} c^{2/3} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{4/3}}{\left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}} F\left(\cos ^{-1}\left(\frac{c^{2/3}-\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}{c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{18 \sqrt[4]{3} b^2 \sqrt{-\frac{\sqrt[3]{b} (c x)^{2/3} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)}{\sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}}}+\frac{c (c x)^{7/3} \sqrt[3]{a+b x^2}}{3 b}",1,"(-7*a*c^3*(c*x)^(1/3)*(a + b*x^2)^(1/3))/(9*b^2) + (c*(c*x)^(7/3)*(a + b*x^2)^(1/3))/(3*b) + (7*a*c^(7/3)*(c*x)^(1/3)*(a + b*x^2)^(1/3)*(c^(2/3) - (b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))*Sqrt[(c^(4/3) + (b^(2/3)*(c*x)^(4/3))/(a + b*x^2)^(2/3) + (b^(1/3)*c^(2/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))/(c^(2/3) - ((1 + Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))^2]*EllipticF[ArcCos[(c^(2/3) - ((1 - Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))/(c^(2/3) - ((1 + Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))], (2 + Sqrt[3])/4])/(18*3^(1/4)*b^2*Sqrt[-((b^(1/3)*(c*x)^(2/3)*(c^(2/3) - (b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3)))/((a + b*x^2)^(1/3)*(c^(2/3) - ((1 + Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))^2))])","A",5,4,19,0.2105,1,"{321, 329, 241, 225}"
780,1,388,0,0.6395571,"\int \frac{(c x)^{4/3}}{\left(a+b x^2\right)^{2/3}} \, dx","Int[(c*x)^(4/3)/(a + b*x^2)^(2/3),x]","\frac{c \sqrt[3]{c x} \sqrt[3]{a+b x^2}}{b}-\frac{\sqrt[3]{c} \sqrt[3]{c x} \sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right) \sqrt{\frac{\frac{b^{2/3} (c x)^{4/3}}{\left(a+b x^2\right)^{2/3}}+\frac{\sqrt[3]{b} c^{2/3} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{4/3}}{\left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}} F\left(\cos ^{-1}\left(\frac{c^{2/3}-\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}{c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{2 \sqrt[4]{3} b \sqrt{-\frac{\sqrt[3]{b} (c x)^{2/3} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)}{\sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}}}","\frac{c \sqrt[3]{c x} \sqrt[3]{a+b x^2}}{b}-\frac{\sqrt[3]{c} \sqrt[3]{c x} \sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right) \sqrt{\frac{\frac{b^{2/3} (c x)^{4/3}}{\left(a+b x^2\right)^{2/3}}+\frac{\sqrt[3]{b} c^{2/3} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{4/3}}{\left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}} F\left(\cos ^{-1}\left(\frac{c^{2/3}-\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}{c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{2 \sqrt[4]{3} b \sqrt{-\frac{\sqrt[3]{b} (c x)^{2/3} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)}{\sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}}}",1,"(c*(c*x)^(1/3)*(a + b*x^2)^(1/3))/b - (c^(1/3)*(c*x)^(1/3)*(a + b*x^2)^(1/3)*(c^(2/3) - (b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))*Sqrt[(c^(4/3) + (b^(2/3)*(c*x)^(4/3))/(a + b*x^2)^(2/3) + (b^(1/3)*c^(2/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))/(c^(2/3) - ((1 + Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))^2]*EllipticF[ArcCos[(c^(2/3) - ((1 - Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))/(c^(2/3) - ((1 + Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))], (2 + Sqrt[3])/4])/(2*3^(1/4)*b*Sqrt[-((b^(1/3)*(c*x)^(2/3)*(c^(2/3) - (b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3)))/((a + b*x^2)^(1/3)*(c^(2/3) - ((1 + Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))^2))])","A",4,4,19,0.2105,1,"{321, 329, 241, 225}"
781,1,364,0,0.5912757,"\int \frac{1}{(c x)^{2/3} \left(a+b x^2\right)^{2/3}} \, dx","Int[1/((c*x)^(2/3)*(a + b*x^2)^(2/3)),x]","\frac{3^{3/4} \sqrt[3]{c x} \sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right) \sqrt{\frac{\frac{b^{2/3} (c x)^{4/3}}{\left(a+b x^2\right)^{2/3}}+\frac{\sqrt[3]{b} c^{2/3} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{4/3}}{\left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}} F\left(\cos ^{-1}\left(\frac{c^{2/3}-\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}{c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{2 a c^{5/3} \sqrt{-\frac{\sqrt[3]{b} (c x)^{2/3} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)}{\sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}}}","\frac{3^{3/4} \sqrt[3]{c x} \sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right) \sqrt{\frac{\frac{b^{2/3} (c x)^{4/3}}{\left(a+b x^2\right)^{2/3}}+\frac{\sqrt[3]{b} c^{2/3} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{4/3}}{\left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}} F\left(\cos ^{-1}\left(\frac{c^{2/3}-\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}{c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{2 a c^{5/3} \sqrt{-\frac{\sqrt[3]{b} (c x)^{2/3} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)}{\sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}}}",1,"(3^(3/4)*(c*x)^(1/3)*(a + b*x^2)^(1/3)*(c^(2/3) - (b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))*Sqrt[(c^(4/3) + (b^(2/3)*(c*x)^(4/3))/(a + b*x^2)^(2/3) + (b^(1/3)*c^(2/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))/(c^(2/3) - ((1 + Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))^2]*EllipticF[ArcCos[(c^(2/3) - ((1 - Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))/(c^(2/3) - ((1 + Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))], (2 + Sqrt[3])/4])/(2*a*c^(5/3)*Sqrt[-((b^(1/3)*(c*x)^(2/3)*(c^(2/3) - (b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3)))/((a + b*x^2)^(1/3)*(c^(2/3) - ((1 + Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))^2))])","A",3,3,19,0.1579,1,"{329, 241, 225}"
782,1,394,0,0.6416427,"\int \frac{1}{(c x)^{8/3} \left(a+b x^2\right)^{2/3}} \, dx","Int[1/((c*x)^(8/3)*(a + b*x^2)^(2/3)),x]","-\frac{3\ 3^{3/4} b \sqrt[3]{c x} \sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right) \sqrt{\frac{\frac{b^{2/3} (c x)^{4/3}}{\left(a+b x^2\right)^{2/3}}+\frac{\sqrt[3]{b} c^{2/3} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{4/3}}{\left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}} F\left(\cos ^{-1}\left(\frac{c^{2/3}-\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}{c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{10 a^2 c^{11/3} \sqrt{-\frac{\sqrt[3]{b} (c x)^{2/3} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)}{\sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}}}-\frac{3 \sqrt[3]{a+b x^2}}{5 a c (c x)^{5/3}}","-\frac{3\ 3^{3/4} b \sqrt[3]{c x} \sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right) \sqrt{\frac{\frac{b^{2/3} (c x)^{4/3}}{\left(a+b x^2\right)^{2/3}}+\frac{\sqrt[3]{b} c^{2/3} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{4/3}}{\left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}} F\left(\cos ^{-1}\left(\frac{c^{2/3}-\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}{c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{10 a^2 c^{11/3} \sqrt{-\frac{\sqrt[3]{b} (c x)^{2/3} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)}{\sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}}}-\frac{3 \sqrt[3]{a+b x^2}}{5 a c (c x)^{5/3}}",1,"(-3*(a + b*x^2)^(1/3))/(5*a*c*(c*x)^(5/3)) - (3*3^(3/4)*b*(c*x)^(1/3)*(a + b*x^2)^(1/3)*(c^(2/3) - (b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))*Sqrt[(c^(4/3) + (b^(2/3)*(c*x)^(4/3))/(a + b*x^2)^(2/3) + (b^(1/3)*c^(2/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))/(c^(2/3) - ((1 + Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))^2]*EllipticF[ArcCos[(c^(2/3) - ((1 - Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))/(c^(2/3) - ((1 + Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))], (2 + Sqrt[3])/4])/(10*a^2*c^(11/3)*Sqrt[-((b^(1/3)*(c*x)^(2/3)*(c^(2/3) - (b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3)))/((a + b*x^2)^(1/3)*(c^(2/3) - ((1 + Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))^2))])","A",4,4,19,0.2105,1,"{325, 329, 241, 225}"
783,1,425,0,0.691575,"\int \frac{1}{(c x)^{14/3} \left(a+b x^2\right)^{2/3}} \, dx","Int[1/((c*x)^(14/3)*(a + b*x^2)^(2/3)),x]","\frac{27\ 3^{3/4} b^2 \sqrt[3]{c x} \sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right) \sqrt{\frac{\frac{b^{2/3} (c x)^{4/3}}{\left(a+b x^2\right)^{2/3}}+\frac{\sqrt[3]{b} c^{2/3} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{4/3}}{\left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}} F\left(\cos ^{-1}\left(\frac{c^{2/3}-\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}{c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{110 a^3 c^{17/3} \sqrt{-\frac{\sqrt[3]{b} (c x)^{2/3} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)}{\sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}}}+\frac{27 b \sqrt[3]{a+b x^2}}{55 a^2 c^3 (c x)^{5/3}}-\frac{3 \sqrt[3]{a+b x^2}}{11 a c (c x)^{11/3}}","\frac{27\ 3^{3/4} b^2 \sqrt[3]{c x} \sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right) \sqrt{\frac{\frac{b^{2/3} (c x)^{4/3}}{\left(a+b x^2\right)^{2/3}}+\frac{\sqrt[3]{b} c^{2/3} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}+c^{4/3}}{\left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}} F\left(\cos ^{-1}\left(\frac{c^{2/3}-\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}{c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{b x^2+a}}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{110 a^3 c^{17/3} \sqrt{-\frac{\sqrt[3]{b} (c x)^{2/3} \left(c^{2/3}-\frac{\sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)}{\sqrt[3]{a+b x^2} \left(c^{2/3}-\frac{\left(1+\sqrt{3}\right) \sqrt[3]{b} (c x)^{2/3}}{\sqrt[3]{a+b x^2}}\right)^2}}}+\frac{27 b \sqrt[3]{a+b x^2}}{55 a^2 c^3 (c x)^{5/3}}-\frac{3 \sqrt[3]{a+b x^2}}{11 a c (c x)^{11/3}}",1,"(-3*(a + b*x^2)^(1/3))/(11*a*c*(c*x)^(11/3)) + (27*b*(a + b*x^2)^(1/3))/(55*a^2*c^3*(c*x)^(5/3)) + (27*3^(3/4)*b^2*(c*x)^(1/3)*(a + b*x^2)^(1/3)*(c^(2/3) - (b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))*Sqrt[(c^(4/3) + (b^(2/3)*(c*x)^(4/3))/(a + b*x^2)^(2/3) + (b^(1/3)*c^(2/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))/(c^(2/3) - ((1 + Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))^2]*EllipticF[ArcCos[(c^(2/3) - ((1 - Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))/(c^(2/3) - ((1 + Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))], (2 + Sqrt[3])/4])/(110*a^3*c^(17/3)*Sqrt[-((b^(1/3)*(c*x)^(2/3)*(c^(2/3) - (b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3)))/((a + b*x^2)^(1/3)*(c^(2/3) - ((1 + Sqrt[3])*b^(1/3)*(c*x)^(2/3))/(a + b*x^2)^(1/3))^2))])","A",5,4,19,0.2105,1,"{325, 329, 241, 225}"
784,1,58,0,0.0183455,"\int \frac{(c x)^{2/3}}{\left(a+b x^2\right)^{2/3}} \, dx","Int[(c*x)^(2/3)/(a + b*x^2)^(2/3),x]","\frac{3 (c x)^{5/3} \left(\frac{b x^2}{a}+1\right)^{2/3} \, _2F_1\left(\frac{2}{3},\frac{5}{6};\frac{11}{6};-\frac{b x^2}{a}\right)}{5 c \left(a+b x^2\right)^{2/3}}","\frac{3 (c x)^{5/3} \left(\frac{b x^2}{a}+1\right)^{2/3} \, _2F_1\left(\frac{2}{3},\frac{5}{6};\frac{11}{6};-\frac{b x^2}{a}\right)}{5 c \left(a+b x^2\right)^{2/3}}",1,"(3*(c*x)^(5/3)*(1 + (b*x^2)/a)^(2/3)*Hypergeometric2F1[2/3, 5/6, 11/6, -((b*x^2)/a)])/(5*c*(a + b*x^2)^(2/3))","A",2,2,19,0.1053,1,"{365, 364}"
785,1,58,0,0.0189458,"\int \frac{1}{\sqrt[3]{c x} \left(a+b x^2\right)^{2/3}} \, dx","Int[1/((c*x)^(1/3)*(a + b*x^2)^(2/3)),x]","\frac{3 (c x)^{2/3} \left(\frac{b x^2}{a}+1\right)^{2/3} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};-\frac{b x^2}{a}\right)}{2 c \left(a+b x^2\right)^{2/3}}","\frac{3 (c x)^{2/3} \left(\frac{b x^2}{a}+1\right)^{2/3} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};-\frac{b x^2}{a}\right)}{2 c \left(a+b x^2\right)^{2/3}}",1,"(3*(c*x)^(2/3)*(1 + (b*x^2)/a)^(2/3)*Hypergeometric2F1[1/3, 2/3, 4/3, -((b*x^2)/a)])/(2*c*(a + b*x^2)^(2/3))","A",2,2,19,0.1053,1,"{365, 364}"
786,1,56,0,0.0193969,"\int \frac{1}{(c x)^{4/3} \left(a+b x^2\right)^{2/3}} \, dx","Int[1/((c*x)^(4/3)*(a + b*x^2)^(2/3)),x]","-\frac{3 \left(\frac{b x^2}{a}+1\right)^{2/3} \, _2F_1\left(-\frac{1}{6},\frac{2}{3};\frac{5}{6};-\frac{b x^2}{a}\right)}{c \sqrt[3]{c x} \left(a+b x^2\right)^{2/3}}","-\frac{3 \left(\frac{b x^2}{a}+1\right)^{2/3} \, _2F_1\left(-\frac{1}{6},\frac{2}{3};\frac{5}{6};-\frac{b x^2}{a}\right)}{c \sqrt[3]{c x} \left(a+b x^2\right)^{2/3}}",1,"(-3*(1 + (b*x^2)/a)^(2/3)*Hypergeometric2F1[-1/6, 2/3, 5/6, -((b*x^2)/a)])/(c*(c*x)^(1/3)*(a + b*x^2)^(2/3))","A",2,2,19,0.1053,1,"{365, 364}"
787,1,121,0,0.0487949,"\int x^4 \sqrt[4]{a+b x^2} \, dx","Int[x^4*(a + b*x^2)^(1/4),x]","-\frac{4 a^2 x \sqrt[4]{a+b x^2}}{77 b^2}+\frac{8 a^{7/2} \left(\frac{b x^2}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{77 b^{5/2} \left(a+b x^2\right)^{3/4}}+\frac{2}{11} x^5 \sqrt[4]{a+b x^2}+\frac{2 a x^3 \sqrt[4]{a+b x^2}}{77 b}","-\frac{4 a^2 x \sqrt[4]{a+b x^2}}{77 b^2}+\frac{8 a^{7/2} \left(\frac{b x^2}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{77 b^{5/2} \left(a+b x^2\right)^{3/4}}+\frac{2}{11} x^5 \sqrt[4]{a+b x^2}+\frac{2 a x^3 \sqrt[4]{a+b x^2}}{77 b}",1,"(-4*a^2*x*(a + b*x^2)^(1/4))/(77*b^2) + (2*a*x^3*(a + b*x^2)^(1/4))/(77*b) + (2*x^5*(a + b*x^2)^(1/4))/11 + (8*a^(7/2)*(1 + (b*x^2)/a)^(3/4)*EllipticF[ArcTan[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(77*b^(5/2)*(a + b*x^2)^(3/4))","A",5,4,15,0.2667,1,"{279, 321, 233, 231}"
788,1,97,0,0.0329361,"\int x^2 \sqrt[4]{a+b x^2} \, dx","Int[x^2*(a + b*x^2)^(1/4),x]","-\frac{4 a^{5/2} \left(\frac{b x^2}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{21 b^{3/2} \left(a+b x^2\right)^{3/4}}+\frac{2}{7} x^3 \sqrt[4]{a+b x^2}+\frac{2 a x \sqrt[4]{a+b x^2}}{21 b}","-\frac{4 a^{5/2} \left(\frac{b x^2}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{21 b^{3/2} \left(a+b x^2\right)^{3/4}}+\frac{2}{7} x^3 \sqrt[4]{a+b x^2}+\frac{2 a x \sqrt[4]{a+b x^2}}{21 b}",1,"(2*a*x*(a + b*x^2)^(1/4))/(21*b) + (2*x^3*(a + b*x^2)^(1/4))/7 - (4*a^(5/2)*(1 + (b*x^2)/a)^(3/4)*EllipticF[ArcTan[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(21*b^(3/2)*(a + b*x^2)^(3/4))","A",4,4,15,0.2667,1,"{279, 321, 233, 231}"
789,1,75,0,0.0178442,"\int \sqrt[4]{a+b x^2} \, dx","Int[(a + b*x^2)^(1/4),x]","\frac{2 a^{3/2} \left(\frac{b x^2}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{3 \sqrt{b} \left(a+b x^2\right)^{3/4}}+\frac{2}{3} x \sqrt[4]{a+b x^2}","\frac{2 a^{3/2} \left(\frac{b x^2}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{3 \sqrt{b} \left(a+b x^2\right)^{3/4}}+\frac{2}{3} x \sqrt[4]{a+b x^2}",1,"(2*x*(a + b*x^2)^(1/4))/3 + (2*a^(3/2)*(1 + (b*x^2)/a)^(3/4)*EllipticF[ArcTan[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(3*Sqrt[b]*(a + b*x^2)^(3/4))","A",3,3,11,0.2727,1,"{195, 233, 231}"
790,1,72,0,0.0205531,"\int \frac{\sqrt[4]{a+b x^2}}{x^2} \, dx","Int[(a + b*x^2)^(1/4)/x^2,x]","\frac{\sqrt{a} \sqrt{b} \left(\frac{b x^2}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{\left(a+b x^2\right)^{3/4}}-\frac{\sqrt[4]{a+b x^2}}{x}","\frac{\sqrt{a} \sqrt{b} \left(\frac{b x^2}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{\left(a+b x^2\right)^{3/4}}-\frac{\sqrt[4]{a+b x^2}}{x}",1,"-((a + b*x^2)^(1/4)/x) + (Sqrt[a]*Sqrt[b]*(1 + (b*x^2)/a)^(3/4)*EllipticF[ArcTan[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(a + b*x^2)^(3/4)","A",3,3,15,0.2000,1,"{277, 233, 231}"
791,1,99,0,0.0310681,"\int \frac{\sqrt[4]{a+b x^2}}{x^4} \, dx","Int[(a + b*x^2)^(1/4)/x^4,x]","-\frac{b^{3/2} \left(\frac{b x^2}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{6 \sqrt{a} \left(a+b x^2\right)^{3/4}}-\frac{b \sqrt[4]{a+b x^2}}{6 a x}-\frac{\sqrt[4]{a+b x^2}}{3 x^3}","-\frac{b^{3/2} \left(\frac{b x^2}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{6 \sqrt{a} \left(a+b x^2\right)^{3/4}}-\frac{b \sqrt[4]{a+b x^2}}{6 a x}-\frac{\sqrt[4]{a+b x^2}}{3 x^3}",1,"-(a + b*x^2)^(1/4)/(3*x^3) - (b*(a + b*x^2)^(1/4))/(6*a*x) - (b^(3/2)*(1 + (b*x^2)/a)^(3/4)*EllipticF[ArcTan[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(6*Sqrt[a]*(a + b*x^2)^(3/4))","A",4,4,15,0.2667,1,"{277, 325, 233, 231}"
792,1,123,0,0.0463112,"\int \frac{\sqrt[4]{a+b x^2}}{x^6} \, dx","Int[(a + b*x^2)^(1/4)/x^6,x]","\frac{b^2 \sqrt[4]{a+b x^2}}{12 a^2 x}+\frac{b^{5/2} \left(\frac{b x^2}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{12 a^{3/2} \left(a+b x^2\right)^{3/4}}-\frac{b \sqrt[4]{a+b x^2}}{30 a x^3}-\frac{\sqrt[4]{a+b x^2}}{5 x^5}","\frac{b^2 \sqrt[4]{a+b x^2}}{12 a^2 x}+\frac{b^{5/2} \left(\frac{b x^2}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{12 a^{3/2} \left(a+b x^2\right)^{3/4}}-\frac{b \sqrt[4]{a+b x^2}}{30 a x^3}-\frac{\sqrt[4]{a+b x^2}}{5 x^5}",1,"-(a + b*x^2)^(1/4)/(5*x^5) - (b*(a + b*x^2)^(1/4))/(30*a*x^3) + (b^2*(a + b*x^2)^(1/4))/(12*a^2*x) + (b^(5/2)*(1 + (b*x^2)/a)^(3/4)*EllipticF[ArcTan[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(12*a^(3/2)*(a + b*x^2)^(3/4))","A",5,4,15,0.2667,1,"{277, 325, 233, 231}"
793,1,126,0,0.0458994,"\int x^4 \sqrt[4]{a-b x^2} \, dx","Int[x^4*(a - b*x^2)^(1/4),x]","-\frac{4 a^2 x \sqrt[4]{a-b x^2}}{77 b^2}+\frac{8 a^{7/2} \left(1-\frac{b x^2}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{77 b^{5/2} \left(a-b x^2\right)^{3/4}}+\frac{2}{11} x^5 \sqrt[4]{a-b x^2}-\frac{2 a x^3 \sqrt[4]{a-b x^2}}{77 b}","-\frac{4 a^2 x \sqrt[4]{a-b x^2}}{77 b^2}+\frac{8 a^{7/2} \left(1-\frac{b x^2}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{77 b^{5/2} \left(a-b x^2\right)^{3/4}}+\frac{2}{11} x^5 \sqrt[4]{a-b x^2}-\frac{2 a x^3 \sqrt[4]{a-b x^2}}{77 b}",1,"(-4*a^2*x*(a - b*x^2)^(1/4))/(77*b^2) - (2*a*x^3*(a - b*x^2)^(1/4))/(77*b) + (2*x^5*(a - b*x^2)^(1/4))/11 + (8*a^(7/2)*(1 - (b*x^2)/a)^(3/4)*EllipticF[ArcSin[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(77*b^(5/2)*(a - b*x^2)^(3/4))","A",5,4,16,0.2500,1,"{279, 321, 233, 232}"
794,1,101,0,0.0329024,"\int x^2 \sqrt[4]{a-b x^2} \, dx","Int[x^2*(a - b*x^2)^(1/4),x]","\frac{4 a^{5/2} \left(1-\frac{b x^2}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{21 b^{3/2} \left(a-b x^2\right)^{3/4}}+\frac{2}{7} x^3 \sqrt[4]{a-b x^2}-\frac{2 a x \sqrt[4]{a-b x^2}}{21 b}","\frac{4 a^{5/2} \left(1-\frac{b x^2}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{21 b^{3/2} \left(a-b x^2\right)^{3/4}}+\frac{2}{7} x^3 \sqrt[4]{a-b x^2}-\frac{2 a x \sqrt[4]{a-b x^2}}{21 b}",1,"(-2*a*x*(a - b*x^2)^(1/4))/(21*b) + (2*x^3*(a - b*x^2)^(1/4))/7 + (4*a^(5/2)*(1 - (b*x^2)/a)^(3/4)*EllipticF[ArcSin[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(21*b^(3/2)*(a - b*x^2)^(3/4))","A",4,4,16,0.2500,1,"{279, 321, 233, 232}"
795,1,78,0,0.0178637,"\int \sqrt[4]{a-b x^2} \, dx","Int[(a - b*x^2)^(1/4),x]","\frac{2 a^{3/2} \left(1-\frac{b x^2}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{3 \sqrt{b} \left(a-b x^2\right)^{3/4}}+\frac{2}{3} x \sqrt[4]{a-b x^2}","\frac{2 a^{3/2} \left(1-\frac{b x^2}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{3 \sqrt{b} \left(a-b x^2\right)^{3/4}}+\frac{2}{3} x \sqrt[4]{a-b x^2}",1,"(2*x*(a - b*x^2)^(1/4))/3 + (2*a^(3/2)*(1 - (b*x^2)/a)^(3/4)*EllipticF[ArcSin[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(3*Sqrt[b]*(a - b*x^2)^(3/4))","A",3,3,12,0.2500,1,"{195, 233, 232}"
796,1,76,0,0.0198882,"\int \frac{\sqrt[4]{a-b x^2}}{x^2} \, dx","Int[(a - b*x^2)^(1/4)/x^2,x]","-\frac{\sqrt[4]{a-b x^2}}{x}-\frac{\sqrt{a} \sqrt{b} \left(1-\frac{b x^2}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{\left(a-b x^2\right)^{3/4}}","-\frac{\sqrt[4]{a-b x^2}}{x}-\frac{\sqrt{a} \sqrt{b} \left(1-\frac{b x^2}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{\left(a-b x^2\right)^{3/4}}",1,"-((a - b*x^2)^(1/4)/x) - (Sqrt[a]*Sqrt[b]*(1 - (b*x^2)/a)^(3/4)*EllipticF[ArcSin[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(a - b*x^2)^(3/4)","A",3,3,16,0.1875,1,"{277, 233, 232}"
797,1,103,0,0.0319621,"\int \frac{\sqrt[4]{a-b x^2}}{x^4} \, dx","Int[(a - b*x^2)^(1/4)/x^4,x]","-\frac{b^{3/2} \left(1-\frac{b x^2}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{6 \sqrt{a} \left(a-b x^2\right)^{3/4}}+\frac{b \sqrt[4]{a-b x^2}}{6 a x}-\frac{\sqrt[4]{a-b x^2}}{3 x^3}","-\frac{b^{3/2} \left(1-\frac{b x^2}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{6 \sqrt{a} \left(a-b x^2\right)^{3/4}}+\frac{b \sqrt[4]{a-b x^2}}{6 a x}-\frac{\sqrt[4]{a-b x^2}}{3 x^3}",1,"-(a - b*x^2)^(1/4)/(3*x^3) + (b*(a - b*x^2)^(1/4))/(6*a*x) - (b^(3/2)*(1 - (b*x^2)/a)^(3/4)*EllipticF[ArcSin[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(6*Sqrt[a]*(a - b*x^2)^(3/4))","A",4,4,16,0.2500,1,"{277, 325, 233, 232}"
798,1,128,0,0.0455706,"\int \frac{\sqrt[4]{a-b x^2}}{x^6} \, dx","Int[(a - b*x^2)^(1/4)/x^6,x]","\frac{b^2 \sqrt[4]{a-b x^2}}{12 a^2 x}-\frac{b^{5/2} \left(1-\frac{b x^2}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{12 a^{3/2} \left(a-b x^2\right)^{3/4}}+\frac{b \sqrt[4]{a-b x^2}}{30 a x^3}-\frac{\sqrt[4]{a-b x^2}}{5 x^5}","\frac{b^2 \sqrt[4]{a-b x^2}}{12 a^2 x}-\frac{b^{5/2} \left(1-\frac{b x^2}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{12 a^{3/2} \left(a-b x^2\right)^{3/4}}+\frac{b \sqrt[4]{a-b x^2}}{30 a x^3}-\frac{\sqrt[4]{a-b x^2}}{5 x^5}",1,"-(a - b*x^2)^(1/4)/(5*x^5) + (b*(a - b*x^2)^(1/4))/(30*a*x^3) + (b^2*(a - b*x^2)^(1/4))/(12*a^2*x) - (b^(5/2)*(1 - (b*x^2)/a)^(3/4)*EllipticF[ArcSin[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(12*a^(3/2)*(a - b*x^2)^(3/4))","A",5,4,16,0.2500,1,"{277, 325, 233, 232}"
799,1,143,0,0.0514642,"\int x^4 \left(a+b x^2\right)^{3/4} \, dx","Int[x^4*(a + b*x^2)^(3/4),x]","-\frac{4 a^2 x \left(a+b x^2\right)^{3/4}}{65 b^2}+\frac{8 a^3 x}{65 b^2 \sqrt[4]{a+b x^2}}-\frac{8 a^{7/2} \sqrt[4]{\frac{b x^2}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{65 b^{5/2} \sqrt[4]{a+b x^2}}+\frac{2}{13} x^5 \left(a+b x^2\right)^{3/4}+\frac{2 a x^3 \left(a+b x^2\right)^{3/4}}{39 b}","-\frac{4 a^2 x \left(a+b x^2\right)^{3/4}}{65 b^2}+\frac{8 a^3 x}{65 b^2 \sqrt[4]{a+b x^2}}-\frac{8 a^{7/2} \sqrt[4]{\frac{b x^2}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{65 b^{5/2} \sqrt[4]{a+b x^2}}+\frac{2}{13} x^5 \left(a+b x^2\right)^{3/4}+\frac{2 a x^3 \left(a+b x^2\right)^{3/4}}{39 b}",1,"(8*a^3*x)/(65*b^2*(a + b*x^2)^(1/4)) - (4*a^2*x*(a + b*x^2)^(3/4))/(65*b^2) + (2*a*x^3*(a + b*x^2)^(3/4))/(39*b) + (2*x^5*(a + b*x^2)^(3/4))/13 - (8*a^(7/2)*(1 + (b*x^2)/a)^(1/4)*EllipticE[ArcTan[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(65*b^(5/2)*(a + b*x^2)^(1/4))","A",6,5,15,0.3333,1,"{279, 321, 229, 227, 196}"
800,1,119,0,0.0377391,"\int x^2 \left(a+b x^2\right)^{3/4} \, dx","Int[x^2*(a + b*x^2)^(3/4),x]","\frac{4 a^{5/2} \sqrt[4]{\frac{b x^2}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{15 b^{3/2} \sqrt[4]{a+b x^2}}-\frac{4 a^2 x}{15 b \sqrt[4]{a+b x^2}}+\frac{2}{9} x^3 \left(a+b x^2\right)^{3/4}+\frac{2 a x \left(a+b x^2\right)^{3/4}}{15 b}","\frac{4 a^{5/2} \sqrt[4]{\frac{b x^2}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{15 b^{3/2} \sqrt[4]{a+b x^2}}-\frac{4 a^2 x}{15 b \sqrt[4]{a+b x^2}}+\frac{2}{9} x^3 \left(a+b x^2\right)^{3/4}+\frac{2 a x \left(a+b x^2\right)^{3/4}}{15 b}",1,"(-4*a^2*x)/(15*b*(a + b*x^2)^(1/4)) + (2*a*x*(a + b*x^2)^(3/4))/(15*b) + (2*x^3*(a + b*x^2)^(3/4))/9 + (4*a^(5/2)*(1 + (b*x^2)/a)^(1/4)*EllipticE[ArcTan[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(15*b^(3/2)*(a + b*x^2)^(1/4))","A",5,5,15,0.3333,1,"{279, 321, 229, 227, 196}"
801,1,92,0,0.0209407,"\int \left(a+b x^2\right)^{3/4} \, dx","Int[(a + b*x^2)^(3/4),x]","-\frac{6 a^{3/2} \sqrt[4]{\frac{b x^2}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{5 \sqrt{b} \sqrt[4]{a+b x^2}}+\frac{6 a x}{5 \sqrt[4]{a+b x^2}}+\frac{2}{5} x \left(a+b x^2\right)^{3/4}","-\frac{6 a^{3/2} \sqrt[4]{\frac{b x^2}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{5 \sqrt{b} \sqrt[4]{a+b x^2}}+\frac{6 a x}{5 \sqrt[4]{a+b x^2}}+\frac{2}{5} x \left(a+b x^2\right)^{3/4}",1,"(6*a*x)/(5*(a + b*x^2)^(1/4)) + (2*x*(a + b*x^2)^(3/4))/5 - (6*a^(3/2)*(1 + (b*x^2)/a)^(1/4)*EllipticE[ArcTan[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(5*Sqrt[b]*(a + b*x^2)^(1/4))","A",4,4,11,0.3636,1,"{195, 229, 227, 196}"
802,1,88,0,0.0238425,"\int \frac{\left(a+b x^2\right)^{3/4}}{x^2} \, dx","Int[(a + b*x^2)^(3/4)/x^2,x]","\frac{3 b x}{\sqrt[4]{a+b x^2}}-\frac{\left(a+b x^2\right)^{3/4}}{x}-\frac{3 \sqrt{a} \sqrt{b} \sqrt[4]{\frac{b x^2}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{\sqrt[4]{a+b x^2}}","\frac{3 b x}{\sqrt[4]{a+b x^2}}-\frac{\left(a+b x^2\right)^{3/4}}{x}-\frac{3 \sqrt{a} \sqrt{b} \sqrt[4]{\frac{b x^2}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{\sqrt[4]{a+b x^2}}",1,"(3*b*x)/(a + b*x^2)^(1/4) - (a + b*x^2)^(3/4)/x - (3*Sqrt[a]*Sqrt[b]*(1 + (b*x^2)/a)^(1/4)*EllipticE[ArcTan[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(a + b*x^2)^(1/4)","A",4,4,15,0.2667,1,"{277, 229, 227, 196}"
803,1,121,0,0.0378355,"\int \frac{\left(a+b x^2\right)^{3/4}}{x^4} \, dx","Int[(a + b*x^2)^(3/4)/x^4,x]","\frac{b^2 x}{2 a \sqrt[4]{a+b x^2}}-\frac{b^{3/2} \sqrt[4]{\frac{b x^2}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{2 \sqrt{a} \sqrt[4]{a+b x^2}}-\frac{b \left(a+b x^2\right)^{3/4}}{2 a x}-\frac{\left(a+b x^2\right)^{3/4}}{3 x^3}","\frac{b^2 x}{2 a \sqrt[4]{a+b x^2}}-\frac{b^{3/2} \sqrt[4]{\frac{b x^2}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{2 \sqrt{a} \sqrt[4]{a+b x^2}}-\frac{b \left(a+b x^2\right)^{3/4}}{2 a x}-\frac{\left(a+b x^2\right)^{3/4}}{3 x^3}",1,"(b^2*x)/(2*a*(a + b*x^2)^(1/4)) - (a + b*x^2)^(3/4)/(3*x^3) - (b*(a + b*x^2)^(3/4))/(2*a*x) - (b^(3/2)*(1 + (b*x^2)/a)^(1/4)*EllipticE[ArcTan[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(2*Sqrt[a]*(a + b*x^2)^(1/4))","A",5,5,15,0.3333,1,"{277, 325, 229, 227, 196}"
804,1,145,0,0.0505805,"\int \frac{\left(a+b x^2\right)^{3/4}}{x^6} \, dx","Int[(a + b*x^2)^(3/4)/x^6,x]","-\frac{3 b^3 x}{20 a^2 \sqrt[4]{a+b x^2}}+\frac{3 b^2 \left(a+b x^2\right)^{3/4}}{20 a^2 x}+\frac{3 b^{5/2} \sqrt[4]{\frac{b x^2}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{20 a^{3/2} \sqrt[4]{a+b x^2}}-\frac{b \left(a+b x^2\right)^{3/4}}{10 a x^3}-\frac{\left(a+b x^2\right)^{3/4}}{5 x^5}","-\frac{3 b^3 x}{20 a^2 \sqrt[4]{a+b x^2}}+\frac{3 b^2 \left(a+b x^2\right)^{3/4}}{20 a^2 x}+\frac{3 b^{5/2} \sqrt[4]{\frac{b x^2}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{20 a^{3/2} \sqrt[4]{a+b x^2}}-\frac{b \left(a+b x^2\right)^{3/4}}{10 a x^3}-\frac{\left(a+b x^2\right)^{3/4}}{5 x^5}",1,"(-3*b^3*x)/(20*a^2*(a + b*x^2)^(1/4)) - (a + b*x^2)^(3/4)/(5*x^5) - (b*(a + b*x^2)^(3/4))/(10*a*x^3) + (3*b^2*(a + b*x^2)^(3/4))/(20*a^2*x) + (3*b^(5/2)*(1 + (b*x^2)/a)^(1/4)*EllipticE[ArcTan[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(20*a^(3/2)*(a + b*x^2)^(1/4))","A",6,5,15,0.3333,1,"{277, 325, 229, 227, 196}"
805,1,126,0,0.0445159,"\int x^4 \left(a-b x^2\right)^{3/4} \, dx","Int[x^4*(a - b*x^2)^(3/4),x]","-\frac{4 a^2 x \left(a-b x^2\right)^{3/4}}{65 b^2}+\frac{8 a^{7/2} \sqrt[4]{1-\frac{b x^2}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{65 b^{5/2} \sqrt[4]{a-b x^2}}+\frac{2}{13} x^5 \left(a-b x^2\right)^{3/4}-\frac{2 a x^3 \left(a-b x^2\right)^{3/4}}{39 b}","-\frac{4 a^2 x \left(a-b x^2\right)^{3/4}}{65 b^2}+\frac{8 a^{7/2} \sqrt[4]{1-\frac{b x^2}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{65 b^{5/2} \sqrt[4]{a-b x^2}}+\frac{2}{13} x^5 \left(a-b x^2\right)^{3/4}-\frac{2 a x^3 \left(a-b x^2\right)^{3/4}}{39 b}",1,"(-4*a^2*x*(a - b*x^2)^(3/4))/(65*b^2) - (2*a*x^3*(a - b*x^2)^(3/4))/(39*b) + (2*x^5*(a - b*x^2)^(3/4))/13 + (8*a^(7/2)*(1 - (b*x^2)/a)^(1/4)*EllipticE[ArcSin[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(65*b^(5/2)*(a - b*x^2)^(1/4))","A",5,4,16,0.2500,1,"{279, 321, 229, 228}"
806,1,101,0,0.0329896,"\int x^2 \left(a-b x^2\right)^{3/4} \, dx","Int[x^2*(a - b*x^2)^(3/4),x]","\frac{4 a^{5/2} \sqrt[4]{1-\frac{b x^2}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{15 b^{3/2} \sqrt[4]{a-b x^2}}+\frac{2}{9} x^3 \left(a-b x^2\right)^{3/4}-\frac{2 a x \left(a-b x^2\right)^{3/4}}{15 b}","\frac{4 a^{5/2} \sqrt[4]{1-\frac{b x^2}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{15 b^{3/2} \sqrt[4]{a-b x^2}}+\frac{2}{9} x^3 \left(a-b x^2\right)^{3/4}-\frac{2 a x \left(a-b x^2\right)^{3/4}}{15 b}",1,"(-2*a*x*(a - b*x^2)^(3/4))/(15*b) + (2*x^3*(a - b*x^2)^(3/4))/9 + (4*a^(5/2)*(1 - (b*x^2)/a)^(1/4)*EllipticE[ArcSin[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(15*b^(3/2)*(a - b*x^2)^(1/4))","A",4,4,16,0.2500,1,"{279, 321, 229, 228}"
807,1,78,0,0.0187742,"\int \left(a-b x^2\right)^{3/4} \, dx","Int[(a - b*x^2)^(3/4),x]","\frac{6 a^{3/2} \sqrt[4]{1-\frac{b x^2}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{5 \sqrt{b} \sqrt[4]{a-b x^2}}+\frac{2}{5} x \left(a-b x^2\right)^{3/4}","\frac{6 a^{3/2} \sqrt[4]{1-\frac{b x^2}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{5 \sqrt{b} \sqrt[4]{a-b x^2}}+\frac{2}{5} x \left(a-b x^2\right)^{3/4}",1,"(2*x*(a - b*x^2)^(3/4))/5 + (6*a^(3/2)*(1 - (b*x^2)/a)^(1/4)*EllipticE[ArcSin[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(5*Sqrt[b]*(a - b*x^2)^(1/4))","A",3,3,12,0.2500,1,"{195, 229, 228}"
808,1,76,0,0.0204751,"\int \frac{\left(a-b x^2\right)^{3/4}}{x^2} \, dx","Int[(a - b*x^2)^(3/4)/x^2,x]","-\frac{\left(a-b x^2\right)^{3/4}}{x}-\frac{3 \sqrt{a} \sqrt{b} \sqrt[4]{1-\frac{b x^2}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{\sqrt[4]{a-b x^2}}","-\frac{\left(a-b x^2\right)^{3/4}}{x}-\frac{3 \sqrt{a} \sqrt{b} \sqrt[4]{1-\frac{b x^2}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{\sqrt[4]{a-b x^2}}",1,"-((a - b*x^2)^(3/4)/x) - (3*Sqrt[a]*Sqrt[b]*(1 - (b*x^2)/a)^(1/4)*EllipticE[ArcSin[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(a - b*x^2)^(1/4)","A",3,3,16,0.1875,1,"{277, 229, 228}"
809,1,103,0,0.0317913,"\int \frac{\left(a-b x^2\right)^{3/4}}{x^4} \, dx","Int[(a - b*x^2)^(3/4)/x^4,x]","\frac{b^{3/2} \sqrt[4]{1-\frac{b x^2}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{2 \sqrt{a} \sqrt[4]{a-b x^2}}+\frac{b \left(a-b x^2\right)^{3/4}}{2 a x}-\frac{\left(a-b x^2\right)^{3/4}}{3 x^3}","\frac{b^{3/2} \sqrt[4]{1-\frac{b x^2}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{2 \sqrt{a} \sqrt[4]{a-b x^2}}+\frac{b \left(a-b x^2\right)^{3/4}}{2 a x}-\frac{\left(a-b x^2\right)^{3/4}}{3 x^3}",1,"-(a - b*x^2)^(3/4)/(3*x^3) + (b*(a - b*x^2)^(3/4))/(2*a*x) + (b^(3/2)*(1 - (b*x^2)/a)^(1/4)*EllipticE[ArcSin[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(2*Sqrt[a]*(a - b*x^2)^(1/4))","A",4,4,16,0.2500,1,"{277, 325, 229, 228}"
810,1,128,0,0.0450154,"\int \frac{\left(a-b x^2\right)^{3/4}}{x^6} \, dx","Int[(a - b*x^2)^(3/4)/x^6,x]","\frac{3 b^2 \left(a-b x^2\right)^{3/4}}{20 a^2 x}+\frac{3 b^{5/2} \sqrt[4]{1-\frac{b x^2}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{20 a^{3/2} \sqrt[4]{a-b x^2}}+\frac{b \left(a-b x^2\right)^{3/4}}{10 a x^3}-\frac{\left(a-b x^2\right)^{3/4}}{5 x^5}","\frac{3 b^2 \left(a-b x^2\right)^{3/4}}{20 a^2 x}+\frac{3 b^{5/2} \sqrt[4]{1-\frac{b x^2}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{20 a^{3/2} \sqrt[4]{a-b x^2}}+\frac{b \left(a-b x^2\right)^{3/4}}{10 a x^3}-\frac{\left(a-b x^2\right)^{3/4}}{5 x^5}",1,"-(a - b*x^2)^(3/4)/(5*x^5) + (b*(a - b*x^2)^(3/4))/(10*a*x^3) + (3*b^2*(a - b*x^2)^(3/4))/(20*a^2*x) + (3*b^(5/2)*(1 - (b*x^2)/a)^(1/4)*EllipticE[ArcSin[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(20*a^(3/2)*(a - b*x^2)^(1/4))","A",5,4,16,0.2500,1,"{277, 325, 229, 228}"
811,1,92,0,0.0242793,"\int \left(a+b x^2\right)^{5/4} \, dx","Int[(a + b*x^2)^(5/4),x]","\frac{10 a^{5/2} \left(\frac{b x^2}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{21 \sqrt{b} \left(a+b x^2\right)^{3/4}}+\frac{10}{21} a x \sqrt[4]{a+b x^2}+\frac{2}{7} x \left(a+b x^2\right)^{5/4}","\frac{10 a^{5/2} \left(\frac{b x^2}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{21 \sqrt{b} \left(a+b x^2\right)^{3/4}}+\frac{10}{21} a x \sqrt[4]{a+b x^2}+\frac{2}{7} x \left(a+b x^2\right)^{5/4}",1,"(10*a*x*(a + b*x^2)^(1/4))/21 + (2*x*(a + b*x^2)^(5/4))/7 + (10*a^(5/2)*(1 + (b*x^2)/a)^(3/4)*EllipticF[ArcTan[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(21*Sqrt[b]*(a + b*x^2)^(3/4))","A",4,3,11,0.2727,1,"{195, 233, 231}"
812,1,96,0,0.0251112,"\int \left(a-b x^2\right)^{5/4} \, dx","Int[(a - b*x^2)^(5/4),x]","\frac{10 a^{5/2} \left(1-\frac{b x^2}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{21 \sqrt{b} \left(a-b x^2\right)^{3/4}}+\frac{10}{21} a x \sqrt[4]{a-b x^2}+\frac{2}{7} x \left(a-b x^2\right)^{5/4}","\frac{10 a^{5/2} \left(1-\frac{b x^2}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{21 \sqrt{b} \left(a-b x^2\right)^{3/4}}+\frac{10}{21} a x \sqrt[4]{a-b x^2}+\frac{2}{7} x \left(a-b x^2\right)^{5/4}",1,"(10*a*x*(a - b*x^2)^(1/4))/21 + (2*x*(a - b*x^2)^(5/4))/7 + (10*a^(5/2)*(1 - (b*x^2)/a)^(3/4)*EllipticF[ArcSin[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(21*Sqrt[b]*(a - b*x^2)^(3/4))","A",4,3,12,0.2500,1,"{195, 233, 232}"
813,1,111,0,0.0291233,"\int \left(a+b x^2\right)^{7/4} \, dx","Int[(a + b*x^2)^(7/4),x]","\frac{14 a^2 x}{15 \sqrt[4]{a+b x^2}}-\frac{14 a^{5/2} \sqrt[4]{\frac{b x^2}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{15 \sqrt{b} \sqrt[4]{a+b x^2}}+\frac{14}{45} a x \left(a+b x^2\right)^{3/4}+\frac{2}{9} x \left(a+b x^2\right)^{7/4}","\frac{14 a^2 x}{15 \sqrt[4]{a+b x^2}}-\frac{14 a^{5/2} \sqrt[4]{\frac{b x^2}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{15 \sqrt{b} \sqrt[4]{a+b x^2}}+\frac{14}{45} a x \left(a+b x^2\right)^{3/4}+\frac{2}{9} x \left(a+b x^2\right)^{7/4}",1,"(14*a^2*x)/(15*(a + b*x^2)^(1/4)) + (14*a*x*(a + b*x^2)^(3/4))/45 + (2*x*(a + b*x^2)^(7/4))/9 - (14*a^(5/2)*(1 + (b*x^2)/a)^(1/4)*EllipticE[ArcTan[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(15*Sqrt[b]*(a + b*x^2)^(1/4))","A",5,4,11,0.3636,1,"{195, 229, 227, 196}"
814,1,96,0,0.0256642,"\int \left(a-b x^2\right)^{7/4} \, dx","Int[(a - b*x^2)^(7/4),x]","\frac{14 a^{5/2} \sqrt[4]{1-\frac{b x^2}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{15 \sqrt{b} \sqrt[4]{a-b x^2}}+\frac{14}{45} a x \left(a-b x^2\right)^{3/4}+\frac{2}{9} x \left(a-b x^2\right)^{7/4}","\frac{14 a^{5/2} \sqrt[4]{1-\frac{b x^2}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{15 \sqrt{b} \sqrt[4]{a-b x^2}}+\frac{14}{45} a x \left(a-b x^2\right)^{3/4}+\frac{2}{9} x \left(a-b x^2\right)^{7/4}",1,"(14*a*x*(a - b*x^2)^(3/4))/45 + (2*x*(a - b*x^2)^(7/4))/9 + (14*a^(5/2)*(1 - (b*x^2)/a)^(1/4)*EllipticE[ArcSin[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(15*Sqrt[b]*(a - b*x^2)^(1/4))","A",4,3,12,0.2500,1,"{195, 229, 228}"
815,1,146,0,0.0518924,"\int \frac{x^6}{\sqrt[4]{a+b x^2}} \, dx","Int[x^6/(a + b*x^2)^(1/4),x]","\frac{8 a^2 x \left(a+b x^2\right)^{3/4}}{39 b^3}-\frac{16 a^3 x}{39 b^3 \sqrt[4]{a+b x^2}}+\frac{16 a^{7/2} \sqrt[4]{\frac{b x^2}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{39 b^{7/2} \sqrt[4]{a+b x^2}}-\frac{20 a x^3 \left(a+b x^2\right)^{3/4}}{117 b^2}+\frac{2 x^5 \left(a+b x^2\right)^{3/4}}{13 b}","\frac{8 a^2 x \left(a+b x^2\right)^{3/4}}{39 b^3}-\frac{16 a^3 x}{39 b^3 \sqrt[4]{a+b x^2}}+\frac{16 a^{7/2} \sqrt[4]{\frac{b x^2}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{39 b^{7/2} \sqrt[4]{a+b x^2}}-\frac{20 a x^3 \left(a+b x^2\right)^{3/4}}{117 b^2}+\frac{2 x^5 \left(a+b x^2\right)^{3/4}}{13 b}",1,"(-16*a^3*x)/(39*b^3*(a + b*x^2)^(1/4)) + (8*a^2*x*(a + b*x^2)^(3/4))/(39*b^3) - (20*a*x^3*(a + b*x^2)^(3/4))/(117*b^2) + (2*x^5*(a + b*x^2)^(3/4))/(13*b) + (16*a^(7/2)*(1 + (b*x^2)/a)^(1/4)*EllipticE[ArcTan[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(39*b^(7/2)*(a + b*x^2)^(1/4))","A",6,4,15,0.2667,1,"{321, 229, 227, 196}"
816,1,122,0,0.0362143,"\int \frac{x^4}{\sqrt[4]{a+b x^2}} \, dx","Int[x^4/(a + b*x^2)^(1/4),x]","\frac{8 a^2 x}{15 b^2 \sqrt[4]{a+b x^2}}-\frac{8 a^{5/2} \sqrt[4]{\frac{b x^2}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{15 b^{5/2} \sqrt[4]{a+b x^2}}-\frac{4 a x \left(a+b x^2\right)^{3/4}}{15 b^2}+\frac{2 x^3 \left(a+b x^2\right)^{3/4}}{9 b}","\frac{8 a^2 x}{15 b^2 \sqrt[4]{a+b x^2}}-\frac{8 a^{5/2} \sqrt[4]{\frac{b x^2}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{15 b^{5/2} \sqrt[4]{a+b x^2}}-\frac{4 a x \left(a+b x^2\right)^{3/4}}{15 b^2}+\frac{2 x^3 \left(a+b x^2\right)^{3/4}}{9 b}",1,"(8*a^2*x)/(15*b^2*(a + b*x^2)^(1/4)) - (4*a*x*(a + b*x^2)^(3/4))/(15*b^2) + (2*x^3*(a + b*x^2)^(3/4))/(9*b) - (8*a^(5/2)*(1 + (b*x^2)/a)^(1/4)*EllipticE[ArcTan[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(15*b^(5/2)*(a + b*x^2)^(1/4))","A",5,4,15,0.2667,1,"{321, 229, 227, 196}"
817,1,98,0,0.0239423,"\int \frac{x^2}{\sqrt[4]{a+b x^2}} \, dx","Int[x^2/(a + b*x^2)^(1/4),x]","\frac{4 a^{3/2} \sqrt[4]{\frac{b x^2}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{5 b^{3/2} \sqrt[4]{a+b x^2}}-\frac{4 a x}{5 b \sqrt[4]{a+b x^2}}+\frac{2 x \left(a+b x^2\right)^{3/4}}{5 b}","\frac{4 a^{3/2} \sqrt[4]{\frac{b x^2}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{5 b^{3/2} \sqrt[4]{a+b x^2}}-\frac{4 a x}{5 b \sqrt[4]{a+b x^2}}+\frac{2 x \left(a+b x^2\right)^{3/4}}{5 b}",1,"(-4*a*x)/(5*b*(a + b*x^2)^(1/4)) + (2*x*(a + b*x^2)^(3/4))/(5*b) + (4*a^(3/2)*(1 + (b*x^2)/a)^(1/4)*EllipticE[ArcTan[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(5*b^(3/2)*(a + b*x^2)^(1/4))","A",4,4,15,0.2667,1,"{321, 229, 227, 196}"
818,1,71,0,0.0138555,"\int \frac{1}{\sqrt[4]{a+b x^2}} \, dx","Int[(a + b*x^2)^(-1/4),x]","\frac{2 x}{\sqrt[4]{a+b x^2}}-\frac{2 \sqrt{a} \sqrt[4]{\frac{b x^2}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{\sqrt{b} \sqrt[4]{a+b x^2}}","\frac{2 x}{\sqrt[4]{a+b x^2}}-\frac{2 \sqrt{a} \sqrt[4]{\frac{b x^2}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{\sqrt{b} \sqrt[4]{a+b x^2}}",1,"(2*x)/(a + b*x^2)^(1/4) - (2*Sqrt[a]*(1 + (b*x^2)/a)^(1/4)*EllipticE[ArcTan[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(Sqrt[b]*(a + b*x^2)^(1/4))","A",3,3,11,0.2727,1,"{229, 227, 196}"
819,1,93,0,0.0252727,"\int \frac{1}{x^2 \sqrt[4]{a+b x^2}} \, dx","Int[1/(x^2*(a + b*x^2)^(1/4)),x]","\frac{b x}{a \sqrt[4]{a+b x^2}}-\frac{\left(a+b x^2\right)^{3/4}}{a x}-\frac{\sqrt{b} \sqrt[4]{\frac{b x^2}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{\sqrt{a} \sqrt[4]{a+b x^2}}","\frac{b x}{a \sqrt[4]{a+b x^2}}-\frac{\left(a+b x^2\right)^{3/4}}{a x}-\frac{\sqrt{b} \sqrt[4]{\frac{b x^2}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{\sqrt{a} \sqrt[4]{a+b x^2}}",1,"(b*x)/(a*(a + b*x^2)^(1/4)) - (a + b*x^2)^(3/4)/(a*x) - (Sqrt[b]*(1 + (b*x^2)/a)^(1/4)*EllipticE[ArcTan[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(Sqrt[a]*(a + b*x^2)^(1/4))","A",4,4,15,0.2667,1,"{325, 229, 227, 196}"
820,1,124,0,0.0361695,"\int \frac{1}{x^4 \sqrt[4]{a+b x^2}} \, dx","Int[1/(x^4*(a + b*x^2)^(1/4)),x]","-\frac{b^2 x}{2 a^2 \sqrt[4]{a+b x^2}}+\frac{b^{3/2} \sqrt[4]{\frac{b x^2}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{2 a^{3/2} \sqrt[4]{a+b x^2}}+\frac{b \left(a+b x^2\right)^{3/4}}{2 a^2 x}-\frac{\left(a+b x^2\right)^{3/4}}{3 a x^3}","-\frac{b^2 x}{2 a^2 \sqrt[4]{a+b x^2}}+\frac{b^{3/2} \sqrt[4]{\frac{b x^2}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{2 a^{3/2} \sqrt[4]{a+b x^2}}+\frac{b \left(a+b x^2\right)^{3/4}}{2 a^2 x}-\frac{\left(a+b x^2\right)^{3/4}}{3 a x^3}",1,"-(b^2*x)/(2*a^2*(a + b*x^2)^(1/4)) - (a + b*x^2)^(3/4)/(3*a*x^3) + (b*(a + b*x^2)^(3/4))/(2*a^2*x) + (b^(3/2)*(1 + (b*x^2)/a)^(1/4)*EllipticE[ArcTan[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(2*a^(3/2)*(a + b*x^2)^(1/4))","A",5,4,15,0.2667,1,"{325, 229, 227, 196}"
821,1,148,0,0.0508354,"\int \frac{1}{x^6 \sqrt[4]{a+b x^2}} \, dx","Int[1/(x^6*(a + b*x^2)^(1/4)),x]","\frac{7 b^3 x}{20 a^3 \sqrt[4]{a+b x^2}}-\frac{7 b^2 \left(a+b x^2\right)^{3/4}}{20 a^3 x}-\frac{7 b^{5/2} \sqrt[4]{\frac{b x^2}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{20 a^{5/2} \sqrt[4]{a+b x^2}}+\frac{7 b \left(a+b x^2\right)^{3/4}}{30 a^2 x^3}-\frac{\left(a+b x^2\right)^{3/4}}{5 a x^5}","\frac{7 b^3 x}{20 a^3 \sqrt[4]{a+b x^2}}-\frac{7 b^2 \left(a+b x^2\right)^{3/4}}{20 a^3 x}-\frac{7 b^{5/2} \sqrt[4]{\frac{b x^2}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{20 a^{5/2} \sqrt[4]{a+b x^2}}+\frac{7 b \left(a+b x^2\right)^{3/4}}{30 a^2 x^3}-\frac{\left(a+b x^2\right)^{3/4}}{5 a x^5}",1,"(7*b^3*x)/(20*a^3*(a + b*x^2)^(1/4)) - (a + b*x^2)^(3/4)/(5*a*x^5) + (7*b*(a + b*x^2)^(3/4))/(30*a^2*x^3) - (7*b^2*(a + b*x^2)^(3/4))/(20*a^3*x) - (7*b^(5/2)*(1 + (b*x^2)/a)^(1/4)*EllipticE[ArcTan[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(20*a^(5/2)*(a + b*x^2)^(1/4))","A",6,4,15,0.2667,1,"{325, 229, 227, 196}"
822,1,129,0,0.0447899,"\int \frac{x^6}{\sqrt[4]{a-b x^2}} \, dx","Int[x^6/(a - b*x^2)^(1/4),x]","-\frac{8 a^2 x \left(a-b x^2\right)^{3/4}}{39 b^3}+\frac{16 a^{7/2} \sqrt[4]{1-\frac{b x^2}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{39 b^{7/2} \sqrt[4]{a-b x^2}}-\frac{20 a x^3 \left(a-b x^2\right)^{3/4}}{117 b^2}-\frac{2 x^5 \left(a-b x^2\right)^{3/4}}{13 b}","-\frac{8 a^2 x \left(a-b x^2\right)^{3/4}}{39 b^3}+\frac{16 a^{7/2} \sqrt[4]{1-\frac{b x^2}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{39 b^{7/2} \sqrt[4]{a-b x^2}}-\frac{20 a x^3 \left(a-b x^2\right)^{3/4}}{117 b^2}-\frac{2 x^5 \left(a-b x^2\right)^{3/4}}{13 b}",1,"(-8*a^2*x*(a - b*x^2)^(3/4))/(39*b^3) - (20*a*x^3*(a - b*x^2)^(3/4))/(117*b^2) - (2*x^5*(a - b*x^2)^(3/4))/(13*b) + (16*a^(7/2)*(1 - (b*x^2)/a)^(1/4)*EllipticE[ArcSin[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(39*b^(7/2)*(a - b*x^2)^(1/4))","A",5,3,16,0.1875,1,"{321, 229, 228}"
823,1,104,0,0.0336114,"\int \frac{x^4}{\sqrt[4]{a-b x^2}} \, dx","Int[x^4/(a - b*x^2)^(1/4),x]","\frac{8 a^{5/2} \sqrt[4]{1-\frac{b x^2}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{15 b^{5/2} \sqrt[4]{a-b x^2}}-\frac{4 a x \left(a-b x^2\right)^{3/4}}{15 b^2}-\frac{2 x^3 \left(a-b x^2\right)^{3/4}}{9 b}","\frac{8 a^{5/2} \sqrt[4]{1-\frac{b x^2}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{15 b^{5/2} \sqrt[4]{a-b x^2}}-\frac{4 a x \left(a-b x^2\right)^{3/4}}{15 b^2}-\frac{2 x^3 \left(a-b x^2\right)^{3/4}}{9 b}",1,"(-4*a*x*(a - b*x^2)^(3/4))/(15*b^2) - (2*x^3*(a - b*x^2)^(3/4))/(9*b) + (8*a^(5/2)*(1 - (b*x^2)/a)^(1/4)*EllipticE[ArcSin[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(15*b^(5/2)*(a - b*x^2)^(1/4))","A",4,3,16,0.1875,1,"{321, 229, 228}"
824,1,81,0,0.021667,"\int \frac{x^2}{\sqrt[4]{a-b x^2}} \, dx","Int[x^2/(a - b*x^2)^(1/4),x]","\frac{4 a^{3/2} \sqrt[4]{1-\frac{b x^2}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{5 b^{3/2} \sqrt[4]{a-b x^2}}-\frac{2 x \left(a-b x^2\right)^{3/4}}{5 b}","\frac{4 a^{3/2} \sqrt[4]{1-\frac{b x^2}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{5 b^{3/2} \sqrt[4]{a-b x^2}}-\frac{2 x \left(a-b x^2\right)^{3/4}}{5 b}",1,"(-2*x*(a - b*x^2)^(3/4))/(5*b) + (4*a^(3/2)*(1 - (b*x^2)/a)^(1/4)*EllipticE[ArcSin[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(5*b^(3/2)*(a - b*x^2)^(1/4))","A",3,3,16,0.1875,1,"{321, 229, 228}"
825,1,58,0,0.0112114,"\int \frac{1}{\sqrt[4]{a-b x^2}} \, dx","Int[(a - b*x^2)^(-1/4),x]","\frac{2 \sqrt{a} \sqrt[4]{1-\frac{b x^2}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{\sqrt{b} \sqrt[4]{a-b x^2}}","\frac{2 \sqrt{a} \sqrt[4]{1-\frac{b x^2}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{\sqrt{b} \sqrt[4]{a-b x^2}}",1,"(2*Sqrt[a]*(1 - (b*x^2)/a)^(1/4)*EllipticE[ArcSin[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(Sqrt[b]*(a - b*x^2)^(1/4))","A",2,2,12,0.1667,1,"{229, 228}"
826,1,79,0,0.0202877,"\int \frac{1}{x^2 \sqrt[4]{a-b x^2}} \, dx","Int[1/(x^2*(a - b*x^2)^(1/4)),x]","-\frac{\left(a-b x^2\right)^{3/4}}{a x}-\frac{\sqrt{b} \sqrt[4]{1-\frac{b x^2}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{\sqrt{a} \sqrt[4]{a-b x^2}}","-\frac{\left(a-b x^2\right)^{3/4}}{a x}-\frac{\sqrt{b} \sqrt[4]{1-\frac{b x^2}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{\sqrt{a} \sqrt[4]{a-b x^2}}",1,"-((a - b*x^2)^(3/4)/(a*x)) - (Sqrt[b]*(1 - (b*x^2)/a)^(1/4)*EllipticE[ArcSin[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(Sqrt[a]*(a - b*x^2)^(1/4))","A",3,3,16,0.1875,1,"{325, 229, 228}"
827,1,106,0,0.0313681,"\int \frac{1}{x^4 \sqrt[4]{a-b x^2}} \, dx","Int[1/(x^4*(a - b*x^2)^(1/4)),x]","-\frac{b^{3/2} \sqrt[4]{1-\frac{b x^2}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{2 a^{3/2} \sqrt[4]{a-b x^2}}-\frac{b \left(a-b x^2\right)^{3/4}}{2 a^2 x}-\frac{\left(a-b x^2\right)^{3/4}}{3 a x^3}","-\frac{b^{3/2} \sqrt[4]{1-\frac{b x^2}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{2 a^{3/2} \sqrt[4]{a-b x^2}}-\frac{b \left(a-b x^2\right)^{3/4}}{2 a^2 x}-\frac{\left(a-b x^2\right)^{3/4}}{3 a x^3}",1,"-(a - b*x^2)^(3/4)/(3*a*x^3) - (b*(a - b*x^2)^(3/4))/(2*a^2*x) - (b^(3/2)*(1 - (b*x^2)/a)^(1/4)*EllipticE[ArcSin[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(2*a^(3/2)*(a - b*x^2)^(1/4))","A",4,3,16,0.1875,1,"{325, 229, 228}"
828,1,131,0,0.0443256,"\int \frac{1}{x^6 \sqrt[4]{a-b x^2}} \, dx","Int[1/(x^6*(a - b*x^2)^(1/4)),x]","-\frac{7 b^2 \left(a-b x^2\right)^{3/4}}{20 a^3 x}-\frac{7 b^{5/2} \sqrt[4]{1-\frac{b x^2}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{20 a^{5/2} \sqrt[4]{a-b x^2}}-\frac{7 b \left(a-b x^2\right)^{3/4}}{30 a^2 x^3}-\frac{\left(a-b x^2\right)^{3/4}}{5 a x^5}","-\frac{7 b^2 \left(a-b x^2\right)^{3/4}}{20 a^3 x}-\frac{7 b^{5/2} \sqrt[4]{1-\frac{b x^2}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{20 a^{5/2} \sqrt[4]{a-b x^2}}-\frac{7 b \left(a-b x^2\right)^{3/4}}{30 a^2 x^3}-\frac{\left(a-b x^2\right)^{3/4}}{5 a x^5}",1,"-(a - b*x^2)^(3/4)/(5*a*x^5) - (7*b*(a - b*x^2)^(3/4))/(30*a^2*x^3) - (7*b^2*(a - b*x^2)^(3/4))/(20*a^3*x) - (7*b^(5/2)*(1 - (b*x^2)/a)^(1/4)*EllipticE[ArcSin[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(20*a^(5/2)*(a - b*x^2)^(1/4))","A",5,3,16,0.1875,1,"{325, 229, 228}"
829,1,124,0,0.0429373,"\int \frac{x^6}{\left(a+b x^2\right)^{3/4}} \, dx","Int[x^6/(a + b*x^2)^(3/4),x]","\frac{40 a^2 x \sqrt[4]{a+b x^2}}{77 b^3}-\frac{80 a^{7/2} \left(\frac{b x^2}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{77 b^{7/2} \left(a+b x^2\right)^{3/4}}-\frac{20 a x^3 \sqrt[4]{a+b x^2}}{77 b^2}+\frac{2 x^5 \sqrt[4]{a+b x^2}}{11 b}","\frac{40 a^2 x \sqrt[4]{a+b x^2}}{77 b^3}-\frac{80 a^{7/2} \left(\frac{b x^2}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{77 b^{7/2} \left(a+b x^2\right)^{3/4}}-\frac{20 a x^3 \sqrt[4]{a+b x^2}}{77 b^2}+\frac{2 x^5 \sqrt[4]{a+b x^2}}{11 b}",1,"(40*a^2*x*(a + b*x^2)^(1/4))/(77*b^3) - (20*a*x^3*(a + b*x^2)^(1/4))/(77*b^2) + (2*x^5*(a + b*x^2)^(1/4))/(11*b) - (80*a^(7/2)*(1 + (b*x^2)/a)^(3/4)*EllipticF[ArcTan[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(77*b^(7/2)*(a + b*x^2)^(3/4))","A",5,3,15,0.2000,1,"{321, 233, 231}"
830,1,100,0,0.0314355,"\int \frac{x^4}{\left(a+b x^2\right)^{3/4}} \, dx","Int[x^4/(a + b*x^2)^(3/4),x]","\frac{8 a^{5/2} \left(\frac{b x^2}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{7 b^{5/2} \left(a+b x^2\right)^{3/4}}-\frac{4 a x \sqrt[4]{a+b x^2}}{7 b^2}+\frac{2 x^3 \sqrt[4]{a+b x^2}}{7 b}","\frac{8 a^{5/2} \left(\frac{b x^2}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{7 b^{5/2} \left(a+b x^2\right)^{3/4}}-\frac{4 a x \sqrt[4]{a+b x^2}}{7 b^2}+\frac{2 x^3 \sqrt[4]{a+b x^2}}{7 b}",1,"(-4*a*x*(a + b*x^2)^(1/4))/(7*b^2) + (2*x^3*(a + b*x^2)^(1/4))/(7*b) + (8*a^(5/2)*(1 + (b*x^2)/a)^(3/4)*EllipticF[ArcTan[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(7*b^(5/2)*(a + b*x^2)^(3/4))","A",4,3,15,0.2000,1,"{321, 233, 231}"
831,1,78,0,0.0195595,"\int \frac{x^2}{\left(a+b x^2\right)^{3/4}} \, dx","Int[x^2/(a + b*x^2)^(3/4),x]","\frac{2 x \sqrt[4]{a+b x^2}}{3 b}-\frac{4 a^{3/2} \left(\frac{b x^2}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{3 b^{3/2} \left(a+b x^2\right)^{3/4}}","\frac{2 x \sqrt[4]{a+b x^2}}{3 b}-\frac{4 a^{3/2} \left(\frac{b x^2}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{3 b^{3/2} \left(a+b x^2\right)^{3/4}}",1,"(2*x*(a + b*x^2)^(1/4))/(3*b) - (4*a^(3/2)*(1 + (b*x^2)/a)^(3/4)*EllipticF[ArcTan[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(3*b^(3/2)*(a + b*x^2)^(3/4))","A",3,3,15,0.2000,1,"{321, 233, 231}"
832,1,56,0,0.0096891,"\int \frac{1}{\left(a+b x^2\right)^{3/4}} \, dx","Int[(a + b*x^2)^(-3/4),x]","\frac{2 \sqrt{a} \left(\frac{b x^2}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{\sqrt{b} \left(a+b x^2\right)^{3/4}}","\frac{2 \sqrt{a} \left(\frac{b x^2}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{\sqrt{b} \left(a+b x^2\right)^{3/4}}",1,"(2*Sqrt[a]*(1 + (b*x^2)/a)^(3/4)*EllipticF[ArcTan[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(Sqrt[b]*(a + b*x^2)^(3/4))","A",2,2,11,0.1818,1,"{233, 231}"
833,1,76,0,0.0186475,"\int \frac{1}{x^2 \left(a+b x^2\right)^{3/4}} \, dx","Int[1/(x^2*(a + b*x^2)^(3/4)),x]","-\frac{\sqrt[4]{a+b x^2}}{a x}-\frac{\sqrt{b} \left(\frac{b x^2}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{\sqrt{a} \left(a+b x^2\right)^{3/4}}","-\frac{\sqrt[4]{a+b x^2}}{a x}-\frac{\sqrt{b} \left(\frac{b x^2}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{\sqrt{a} \left(a+b x^2\right)^{3/4}}",1,"-((a + b*x^2)^(1/4)/(a*x)) - (Sqrt[b]*(1 + (b*x^2)/a)^(3/4)*EllipticF[ArcTan[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(Sqrt[a]*(a + b*x^2)^(3/4))","A",3,3,15,0.2000,1,"{325, 233, 231}"
834,1,102,0,0.0314378,"\int \frac{1}{x^4 \left(a+b x^2\right)^{3/4}} \, dx","Int[1/(x^4*(a + b*x^2)^(3/4)),x]","\frac{5 b^{3/2} \left(\frac{b x^2}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{6 a^{3/2} \left(a+b x^2\right)^{3/4}}+\frac{5 b \sqrt[4]{a+b x^2}}{6 a^2 x}-\frac{\sqrt[4]{a+b x^2}}{3 a x^3}","\frac{5 b^{3/2} \left(\frac{b x^2}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{6 a^{3/2} \left(a+b x^2\right)^{3/4}}+\frac{5 b \sqrt[4]{a+b x^2}}{6 a^2 x}-\frac{\sqrt[4]{a+b x^2}}{3 a x^3}",1,"-(a + b*x^2)^(1/4)/(3*a*x^3) + (5*b*(a + b*x^2)^(1/4))/(6*a^2*x) + (5*b^(3/2)*(1 + (b*x^2)/a)^(3/4)*EllipticF[ArcTan[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(6*a^(3/2)*(a + b*x^2)^(3/4))","A",4,3,15,0.2000,1,"{325, 233, 231}"
835,1,126,0,0.0427865,"\int \frac{1}{x^6 \left(a+b x^2\right)^{3/4}} \, dx","Int[1/(x^6*(a + b*x^2)^(3/4)),x]","-\frac{3 b^2 \sqrt[4]{a+b x^2}}{4 a^3 x}-\frac{3 b^{5/2} \left(\frac{b x^2}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{4 a^{5/2} \left(a+b x^2\right)^{3/4}}+\frac{3 b \sqrt[4]{a+b x^2}}{10 a^2 x^3}-\frac{\sqrt[4]{a+b x^2}}{5 a x^5}","-\frac{3 b^2 \sqrt[4]{a+b x^2}}{4 a^3 x}-\frac{3 b^{5/2} \left(\frac{b x^2}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{4 a^{5/2} \left(a+b x^2\right)^{3/4}}+\frac{3 b \sqrt[4]{a+b x^2}}{10 a^2 x^3}-\frac{\sqrt[4]{a+b x^2}}{5 a x^5}",1,"-(a + b*x^2)^(1/4)/(5*a*x^5) + (3*b*(a + b*x^2)^(1/4))/(10*a^2*x^3) - (3*b^2*(a + b*x^2)^(1/4))/(4*a^3*x) - (3*b^(5/2)*(1 + (b*x^2)/a)^(3/4)*EllipticF[ArcTan[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(4*a^(5/2)*(a + b*x^2)^(3/4))","A",5,3,15,0.2000,1,"{325, 233, 231}"
836,1,129,0,0.0464821,"\int \frac{x^6}{\left(a-b x^2\right)^{3/4}} \, dx","Int[x^6/(a - b*x^2)^(3/4),x]","-\frac{40 a^2 x \sqrt[4]{a-b x^2}}{77 b^3}+\frac{80 a^{7/2} \left(1-\frac{b x^2}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{77 b^{7/2} \left(a-b x^2\right)^{3/4}}-\frac{20 a x^3 \sqrt[4]{a-b x^2}}{77 b^2}-\frac{2 x^5 \sqrt[4]{a-b x^2}}{11 b}","-\frac{40 a^2 x \sqrt[4]{a-b x^2}}{77 b^3}+\frac{80 a^{7/2} \left(1-\frac{b x^2}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{77 b^{7/2} \left(a-b x^2\right)^{3/4}}-\frac{20 a x^3 \sqrt[4]{a-b x^2}}{77 b^2}-\frac{2 x^5 \sqrt[4]{a-b x^2}}{11 b}",1,"(-40*a^2*x*(a - b*x^2)^(1/4))/(77*b^3) - (20*a*x^3*(a - b*x^2)^(1/4))/(77*b^2) - (2*x^5*(a - b*x^2)^(1/4))/(11*b) + (80*a^(7/2)*(1 - (b*x^2)/a)^(3/4)*EllipticF[ArcSin[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(77*b^(7/2)*(a - b*x^2)^(3/4))","A",5,3,16,0.1875,1,"{321, 233, 232}"
837,1,104,0,0.0318736,"\int \frac{x^4}{\left(a-b x^2\right)^{3/4}} \, dx","Int[x^4/(a - b*x^2)^(3/4),x]","\frac{8 a^{5/2} \left(1-\frac{b x^2}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{7 b^{5/2} \left(a-b x^2\right)^{3/4}}-\frac{4 a x \sqrt[4]{a-b x^2}}{7 b^2}-\frac{2 x^3 \sqrt[4]{a-b x^2}}{7 b}","\frac{8 a^{5/2} \left(1-\frac{b x^2}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{7 b^{5/2} \left(a-b x^2\right)^{3/4}}-\frac{4 a x \sqrt[4]{a-b x^2}}{7 b^2}-\frac{2 x^3 \sqrt[4]{a-b x^2}}{7 b}",1,"(-4*a*x*(a - b*x^2)^(1/4))/(7*b^2) - (2*x^3*(a - b*x^2)^(1/4))/(7*b) + (8*a^(5/2)*(1 - (b*x^2)/a)^(3/4)*EllipticF[ArcSin[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(7*b^(5/2)*(a - b*x^2)^(3/4))","A",4,3,16,0.1875,1,"{321, 233, 232}"
838,1,81,0,0.0216295,"\int \frac{x^2}{\left(a-b x^2\right)^{3/4}} \, dx","Int[x^2/(a - b*x^2)^(3/4),x]","\frac{4 a^{3/2} \left(1-\frac{b x^2}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{3 b^{3/2} \left(a-b x^2\right)^{3/4}}-\frac{2 x \sqrt[4]{a-b x^2}}{3 b}","\frac{4 a^{3/2} \left(1-\frac{b x^2}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{3 b^{3/2} \left(a-b x^2\right)^{3/4}}-\frac{2 x \sqrt[4]{a-b x^2}}{3 b}",1,"(-2*x*(a - b*x^2)^(1/4))/(3*b) + (4*a^(3/2)*(1 - (b*x^2)/a)^(3/4)*EllipticF[ArcSin[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(3*b^(3/2)*(a - b*x^2)^(3/4))","A",3,3,16,0.1875,1,"{321, 233, 232}"
839,1,58,0,0.010857,"\int \frac{1}{\left(a-b x^2\right)^{3/4}} \, dx","Int[(a - b*x^2)^(-3/4),x]","\frac{2 \sqrt{a} \left(1-\frac{b x^2}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{\sqrt{b} \left(a-b x^2\right)^{3/4}}","\frac{2 \sqrt{a} \left(1-\frac{b x^2}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{\sqrt{b} \left(a-b x^2\right)^{3/4}}",1,"(2*Sqrt[a]*(1 - (b*x^2)/a)^(3/4)*EllipticF[ArcSin[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(Sqrt[b]*(a - b*x^2)^(3/4))","A",2,2,12,0.1667,1,"{233, 232}"
840,1,78,0,0.0209561,"\int \frac{1}{x^2 \left(a-b x^2\right)^{3/4}} \, dx","Int[1/(x^2*(a - b*x^2)^(3/4)),x]","\frac{\sqrt{b} \left(1-\frac{b x^2}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{\sqrt{a} \left(a-b x^2\right)^{3/4}}-\frac{\sqrt[4]{a-b x^2}}{a x}","\frac{\sqrt{b} \left(1-\frac{b x^2}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{\sqrt{a} \left(a-b x^2\right)^{3/4}}-\frac{\sqrt[4]{a-b x^2}}{a x}",1,"-((a - b*x^2)^(1/4)/(a*x)) + (Sqrt[b]*(1 - (b*x^2)/a)^(3/4)*EllipticF[ArcSin[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(Sqrt[a]*(a - b*x^2)^(3/4))","A",3,3,16,0.1875,1,"{325, 233, 232}"
841,1,106,0,0.0323221,"\int \frac{1}{x^4 \left(a-b x^2\right)^{3/4}} \, dx","Int[1/(x^4*(a - b*x^2)^(3/4)),x]","\frac{5 b^{3/2} \left(1-\frac{b x^2}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{6 a^{3/2} \left(a-b x^2\right)^{3/4}}-\frac{5 b \sqrt[4]{a-b x^2}}{6 a^2 x}-\frac{\sqrt[4]{a-b x^2}}{3 a x^3}","\frac{5 b^{3/2} \left(1-\frac{b x^2}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{6 a^{3/2} \left(a-b x^2\right)^{3/4}}-\frac{5 b \sqrt[4]{a-b x^2}}{6 a^2 x}-\frac{\sqrt[4]{a-b x^2}}{3 a x^3}",1,"-(a - b*x^2)^(1/4)/(3*a*x^3) - (5*b*(a - b*x^2)^(1/4))/(6*a^2*x) + (5*b^(3/2)*(1 - (b*x^2)/a)^(3/4)*EllipticF[ArcSin[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(6*a^(3/2)*(a - b*x^2)^(3/4))","A",4,3,16,0.1875,1,"{325, 233, 232}"
842,1,131,0,0.046621,"\int \frac{1}{x^6 \left(a-b x^2\right)^{3/4}} \, dx","Int[1/(x^6*(a - b*x^2)^(3/4)),x]","-\frac{3 b^2 \sqrt[4]{a-b x^2}}{4 a^3 x}+\frac{3 b^{5/2} \left(1-\frac{b x^2}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{4 a^{5/2} \left(a-b x^2\right)^{3/4}}-\frac{3 b \sqrt[4]{a-b x^2}}{10 a^2 x^3}-\frac{\sqrt[4]{a-b x^2}}{5 a x^5}","-\frac{3 b^2 \sqrt[4]{a-b x^2}}{4 a^3 x}+\frac{3 b^{5/2} \left(1-\frac{b x^2}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{4 a^{5/2} \left(a-b x^2\right)^{3/4}}-\frac{3 b \sqrt[4]{a-b x^2}}{10 a^2 x^3}-\frac{\sqrt[4]{a-b x^2}}{5 a x^5}",1,"-(a - b*x^2)^(1/4)/(5*a*x^5) - (3*b*(a - b*x^2)^(1/4))/(10*a^2*x^3) - (3*b^2*(a - b*x^2)^(1/4))/(4*a^3*x) + (3*b^(5/2)*(1 - (b*x^2)/a)^(3/4)*EllipticF[ArcSin[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(4*a^(5/2)*(a - b*x^2)^(3/4))","A",5,3,16,0.1875,1,"{325, 233, 232}"
843,1,124,0,0.0434474,"\int \frac{x^6}{\left(a+b x^2\right)^{5/4}} \, dx","Int[x^6/(a + b*x^2)^(5/4),x]","\frac{8 a^2 x}{3 b^3 \sqrt[4]{a+b x^2}}-\frac{16 a^{5/2} \sqrt[4]{\frac{b x^2}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{3 b^{7/2} \sqrt[4]{a+b x^2}}-\frac{4 a x^3}{9 b^2 \sqrt[4]{a+b x^2}}+\frac{2 x^5}{9 b \sqrt[4]{a+b x^2}}","\frac{8 a^2 x}{3 b^3 \sqrt[4]{a+b x^2}}-\frac{16 a^{5/2} \sqrt[4]{\frac{b x^2}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{3 b^{7/2} \sqrt[4]{a+b x^2}}-\frac{4 a x^3}{9 b^2 \sqrt[4]{a+b x^2}}+\frac{2 x^5}{9 b \sqrt[4]{a+b x^2}}",1,"(8*a^2*x)/(3*b^3*(a + b*x^2)^(1/4)) - (4*a*x^3)/(9*b^2*(a + b*x^2)^(1/4)) + (2*x^5)/(9*b*(a + b*x^2)^(1/4)) - (16*a^(5/2)*(1 + (b*x^2)/a)^(1/4)*EllipticE[ArcTan[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(3*b^(7/2)*(a + b*x^2)^(1/4))","A",5,3,15,0.2000,1,"{285, 197, 196}"
844,1,100,0,0.0314686,"\int \frac{x^4}{\left(a+b x^2\right)^{5/4}} \, dx","Int[x^4/(a + b*x^2)^(5/4),x]","\frac{24 a^{3/2} \sqrt[4]{\frac{b x^2}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{5 b^{5/2} \sqrt[4]{a+b x^2}}-\frac{12 a x}{5 b^2 \sqrt[4]{a+b x^2}}+\frac{2 x^3}{5 b \sqrt[4]{a+b x^2}}","\frac{24 a^{3/2} \sqrt[4]{\frac{b x^2}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{5 b^{5/2} \sqrt[4]{a+b x^2}}-\frac{12 a x}{5 b^2 \sqrt[4]{a+b x^2}}+\frac{2 x^3}{5 b \sqrt[4]{a+b x^2}}",1,"(-12*a*x)/(5*b^2*(a + b*x^2)^(1/4)) + (2*x^3)/(5*b*(a + b*x^2)^(1/4)) + (24*a^(3/2)*(1 + (b*x^2)/a)^(1/4)*EllipticE[ArcTan[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(5*b^(5/2)*(a + b*x^2)^(1/4))","A",4,3,15,0.2000,1,"{285, 197, 196}"
845,1,74,0,0.0190679,"\int \frac{x^2}{\left(a+b x^2\right)^{5/4}} \, dx","Int[x^2/(a + b*x^2)^(5/4),x]","\frac{2 x}{b \sqrt[4]{a+b x^2}}-\frac{4 \sqrt{a} \sqrt[4]{\frac{b x^2}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{b^{3/2} \sqrt[4]{a+b x^2}}","\frac{2 x}{b \sqrt[4]{a+b x^2}}-\frac{4 \sqrt{a} \sqrt[4]{\frac{b x^2}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{b^{3/2} \sqrt[4]{a+b x^2}}",1,"(2*x)/(b*(a + b*x^2)^(1/4)) - (4*Sqrt[a]*(1 + (b*x^2)/a)^(1/4)*EllipticE[ArcTan[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(b^(3/2)*(a + b*x^2)^(1/4))","A",3,3,15,0.2000,1,"{285, 197, 196}"
846,1,56,0,0.0101319,"\int \frac{1}{\left(a+b x^2\right)^{5/4}} \, dx","Int[(a + b*x^2)^(-5/4),x]","\frac{2 \sqrt[4]{\frac{b x^2}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{\sqrt{a} \sqrt{b} \sqrt[4]{a+b x^2}}","\frac{2 \sqrt[4]{\frac{b x^2}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{\sqrt{a} \sqrt{b} \sqrt[4]{a+b x^2}}",1,"(2*(1 + (b*x^2)/a)^(1/4)*EllipticE[ArcTan[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(Sqrt[a]*Sqrt[b]*(a + b*x^2)^(1/4))","A",2,2,11,0.1818,1,"{197, 196}"
847,1,76,0,0.0201927,"\int \frac{1}{x^2 \left(a+b x^2\right)^{5/4}} \, dx","Int[1/(x^2*(a + b*x^2)^(5/4)),x]","-\frac{3 \sqrt{b} \sqrt[4]{\frac{b x^2}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{a^{3/2} \sqrt[4]{a+b x^2}}-\frac{1}{a x \sqrt[4]{a+b x^2}}","-\frac{3 \sqrt{b} \sqrt[4]{\frac{b x^2}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{a^{3/2} \sqrt[4]{a+b x^2}}-\frac{1}{a x \sqrt[4]{a+b x^2}}",1,"-(1/(a*x*(a + b*x^2)^(1/4))) - (3*Sqrt[b]*(1 + (b*x^2)/a)^(1/4)*EllipticE[ArcTan[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(a^(3/2)*(a + b*x^2)^(1/4))","A",3,3,15,0.2000,1,"{286, 197, 196}"
848,1,102,0,0.0303397,"\int \frac{1}{x^4 \left(a+b x^2\right)^{5/4}} \, dx","Int[1/(x^4*(a + b*x^2)^(5/4)),x]","\frac{7 b^{3/2} \sqrt[4]{\frac{b x^2}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{2 a^{5/2} \sqrt[4]{a+b x^2}}+\frac{7 b}{6 a^2 x \sqrt[4]{a+b x^2}}-\frac{1}{3 a x^3 \sqrt[4]{a+b x^2}}","\frac{7 b^{3/2} \sqrt[4]{\frac{b x^2}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{2 a^{5/2} \sqrt[4]{a+b x^2}}+\frac{7 b}{6 a^2 x \sqrt[4]{a+b x^2}}-\frac{1}{3 a x^3 \sqrt[4]{a+b x^2}}",1,"-1/(3*a*x^3*(a + b*x^2)^(1/4)) + (7*b)/(6*a^2*x*(a + b*x^2)^(1/4)) + (7*b^(3/2)*(1 + (b*x^2)/a)^(1/4)*EllipticE[ArcTan[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(2*a^(5/2)*(a + b*x^2)^(1/4))","A",4,3,15,0.2000,1,"{286, 197, 196}"
849,1,126,0,0.0424427,"\int \frac{1}{x^6 \left(a+b x^2\right)^{5/4}} \, dx","Int[1/(x^6*(a + b*x^2)^(5/4)),x]","-\frac{77 b^2}{60 a^3 x \sqrt[4]{a+b x^2}}-\frac{77 b^{5/2} \sqrt[4]{\frac{b x^2}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{20 a^{7/2} \sqrt[4]{a+b x^2}}+\frac{11 b}{30 a^2 x^3 \sqrt[4]{a+b x^2}}-\frac{1}{5 a x^5 \sqrt[4]{a+b x^2}}","-\frac{77 b^2}{60 a^3 x \sqrt[4]{a+b x^2}}-\frac{77 b^{5/2} \sqrt[4]{\frac{b x^2}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{20 a^{7/2} \sqrt[4]{a+b x^2}}+\frac{11 b}{30 a^2 x^3 \sqrt[4]{a+b x^2}}-\frac{1}{5 a x^5 \sqrt[4]{a+b x^2}}",1,"-1/(5*a*x^5*(a + b*x^2)^(1/4)) + (11*b)/(30*a^2*x^3*(a + b*x^2)^(1/4)) - (77*b^2)/(60*a^3*x*(a + b*x^2)^(1/4)) - (77*b^(5/2)*(1 + (b*x^2)/a)^(1/4)*EllipticE[ArcTan[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(20*a^(7/2)*(a + b*x^2)^(1/4))","A",5,3,15,0.2000,1,"{286, 197, 196}"
850,1,124,0,0.0474167,"\int \frac{x^6}{\left(a-b x^2\right)^{5/4}} \, dx","Int[x^6/(a - b*x^2)^(5/4),x]","-\frac{16 a^{5/2} \sqrt[4]{1-\frac{b x^2}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{3 b^{7/2} \sqrt[4]{a-b x^2}}+\frac{20 x^3 \left(a-b x^2\right)^{3/4}}{9 b^2}+\frac{8 a x \left(a-b x^2\right)^{3/4}}{3 b^3}+\frac{2 x^5}{b \sqrt[4]{a-b x^2}}","-\frac{16 a^{5/2} \sqrt[4]{1-\frac{b x^2}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{3 b^{7/2} \sqrt[4]{a-b x^2}}+\frac{20 x^3 \left(a-b x^2\right)^{3/4}}{9 b^2}+\frac{8 a x \left(a-b x^2\right)^{3/4}}{3 b^3}+\frac{2 x^5}{b \sqrt[4]{a-b x^2}}",1,"(2*x^5)/(b*(a - b*x^2)^(1/4)) + (8*a*x*(a - b*x^2)^(3/4))/(3*b^3) + (20*x^3*(a - b*x^2)^(3/4))/(9*b^2) - (16*a^(5/2)*(1 - (b*x^2)/a)^(1/4)*EllipticE[ArcSin[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(3*b^(7/2)*(a - b*x^2)^(1/4))","A",5,4,16,0.2500,1,"{288, 321, 229, 228}"
851,1,101,0,0.0313051,"\int \frac{x^4}{\left(a-b x^2\right)^{5/4}} \, dx","Int[x^4/(a - b*x^2)^(5/4),x]","-\frac{24 a^{3/2} \sqrt[4]{1-\frac{b x^2}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{5 b^{5/2} \sqrt[4]{a-b x^2}}+\frac{12 x \left(a-b x^2\right)^{3/4}}{5 b^2}+\frac{2 x^3}{b \sqrt[4]{a-b x^2}}","-\frac{24 a^{3/2} \sqrt[4]{1-\frac{b x^2}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{5 b^{5/2} \sqrt[4]{a-b x^2}}+\frac{12 x \left(a-b x^2\right)^{3/4}}{5 b^2}+\frac{2 x^3}{b \sqrt[4]{a-b x^2}}",1,"(2*x^3)/(b*(a - b*x^2)^(1/4)) + (12*x*(a - b*x^2)^(3/4))/(5*b^2) - (24*a^(3/2)*(1 - (b*x^2)/a)^(1/4)*EllipticE[ArcSin[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(5*b^(5/2)*(a - b*x^2)^(1/4))","A",4,4,16,0.2500,1,"{288, 321, 229, 228}"
852,1,77,0,0.021773,"\int \frac{x^2}{\left(a-b x^2\right)^{5/4}} \, dx","Int[x^2/(a - b*x^2)^(5/4),x]","\frac{2 x}{b \sqrt[4]{a-b x^2}}-\frac{4 \sqrt{a} \sqrt[4]{1-\frac{b x^2}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{b^{3/2} \sqrt[4]{a-b x^2}}","\frac{2 x}{b \sqrt[4]{a-b x^2}}-\frac{4 \sqrt{a} \sqrt[4]{1-\frac{b x^2}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{b^{3/2} \sqrt[4]{a-b x^2}}",1,"(2*x)/(b*(a - b*x^2)^(1/4)) - (4*Sqrt[a]*(1 - (b*x^2)/a)^(1/4)*EllipticE[ArcSin[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(b^(3/2)*(a - b*x^2)^(1/4))","A",3,3,16,0.1875,1,"{288, 229, 228}"
853,1,77,0,0.0193488,"\int \frac{1}{\left(a-b x^2\right)^{5/4}} \, dx","Int[(a - b*x^2)^(-5/4),x]","\frac{2 x}{a \sqrt[4]{a-b x^2}}-\frac{2 \sqrt[4]{1-\frac{b x^2}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{\sqrt{a} \sqrt{b} \sqrt[4]{a-b x^2}}","\frac{2 x}{a \sqrt[4]{a-b x^2}}-\frac{2 \sqrt[4]{1-\frac{b x^2}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{\sqrt{a} \sqrt{b} \sqrt[4]{a-b x^2}}",1,"(2*x)/(a*(a - b*x^2)^(1/4)) - (2*(1 - (b*x^2)/a)^(1/4)*EllipticE[ArcSin[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(Sqrt[a]*Sqrt[b]*(a - b*x^2)^(1/4))","A",3,3,12,0.2500,1,"{199, 229, 228}"
854,1,99,0,0.031739,"\int \frac{1}{x^2 \left(a-b x^2\right)^{5/4}} \, dx","Int[1/(x^2*(a - b*x^2)^(5/4)),x]","-\frac{3 \left(a-b x^2\right)^{3/4}}{a^2 x}-\frac{3 \sqrt{b} \sqrt[4]{1-\frac{b x^2}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{a^{3/2} \sqrt[4]{a-b x^2}}+\frac{2}{a x \sqrt[4]{a-b x^2}}","-\frac{3 \left(a-b x^2\right)^{3/4}}{a^2 x}-\frac{3 \sqrt{b} \sqrt[4]{1-\frac{b x^2}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{a^{3/2} \sqrt[4]{a-b x^2}}+\frac{2}{a x \sqrt[4]{a-b x^2}}",1,"2/(a*x*(a - b*x^2)^(1/4)) - (3*(a - b*x^2)^(3/4))/(a^2*x) - (3*Sqrt[b]*(1 - (b*x^2)/a)^(1/4)*EllipticE[ArcSin[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(a^(3/2)*(a - b*x^2)^(1/4))","A",4,4,16,0.2500,1,"{290, 325, 229, 228}"
855,1,126,0,0.0451057,"\int \frac{1}{x^4 \left(a-b x^2\right)^{5/4}} \, dx","Int[1/(x^4*(a - b*x^2)^(5/4)),x]","-\frac{7 b^{3/2} \sqrt[4]{1-\frac{b x^2}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{2 a^{5/2} \sqrt[4]{a-b x^2}}-\frac{7 b \left(a-b x^2\right)^{3/4}}{2 a^3 x}-\frac{7 \left(a-b x^2\right)^{3/4}}{3 a^2 x^3}+\frac{2}{a x^3 \sqrt[4]{a-b x^2}}","-\frac{7 b^{3/2} \sqrt[4]{1-\frac{b x^2}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{2 a^{5/2} \sqrt[4]{a-b x^2}}-\frac{7 b \left(a-b x^2\right)^{3/4}}{2 a^3 x}-\frac{7 \left(a-b x^2\right)^{3/4}}{3 a^2 x^3}+\frac{2}{a x^3 \sqrt[4]{a-b x^2}}",1,"2/(a*x^3*(a - b*x^2)^(1/4)) - (7*(a - b*x^2)^(3/4))/(3*a^2*x^3) - (7*b*(a - b*x^2)^(3/4))/(2*a^3*x) - (7*b^(3/2)*(1 - (b*x^2)/a)^(1/4)*EllipticE[ArcSin[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(2*a^(5/2)*(a - b*x^2)^(1/4))","A",5,4,16,0.2500,1,"{290, 325, 229, 228}"
856,1,151,0,0.0610959,"\int \frac{1}{x^6 \left(a-b x^2\right)^{5/4}} \, dx","Int[1/(x^6*(a - b*x^2)^(5/4)),x]","-\frac{77 b^2 \left(a-b x^2\right)^{3/4}}{20 a^4 x}-\frac{77 b^{5/2} \sqrt[4]{1-\frac{b x^2}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{20 a^{7/2} \sqrt[4]{a-b x^2}}-\frac{77 b \left(a-b x^2\right)^{3/4}}{30 a^3 x^3}-\frac{11 \left(a-b x^2\right)^{3/4}}{5 a^2 x^5}+\frac{2}{a x^5 \sqrt[4]{a-b x^2}}","-\frac{77 b^2 \left(a-b x^2\right)^{3/4}}{20 a^4 x}-\frac{77 b^{5/2} \sqrt[4]{1-\frac{b x^2}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{20 a^{7/2} \sqrt[4]{a-b x^2}}-\frac{77 b \left(a-b x^2\right)^{3/4}}{30 a^3 x^3}-\frac{11 \left(a-b x^2\right)^{3/4}}{5 a^2 x^5}+\frac{2}{a x^5 \sqrt[4]{a-b x^2}}",1,"2/(a*x^5*(a - b*x^2)^(1/4)) - (11*(a - b*x^2)^(3/4))/(5*a^2*x^5) - (77*b*(a - b*x^2)^(3/4))/(30*a^3*x^3) - (77*b^2*(a - b*x^2)^(3/4))/(20*a^4*x) - (77*b^(5/2)*(1 - (b*x^2)/a)^(1/4)*EllipticE[ArcSin[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(20*a^(7/2)*(a - b*x^2)^(1/4))","A",6,4,16,0.2500,1,"{290, 325, 229, 228}"
857,1,78,0,0.0166227,"\int \frac{1}{\left(a+b x^2\right)^{7/4}} \, dx","Int[(a + b*x^2)^(-7/4),x]","\frac{2 x}{3 a \left(a+b x^2\right)^{3/4}}+\frac{2 \left(\frac{b x^2}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{3 \sqrt{a} \sqrt{b} \left(a+b x^2\right)^{3/4}}","\frac{2 x}{3 a \left(a+b x^2\right)^{3/4}}+\frac{2 \left(\frac{b x^2}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{3 \sqrt{a} \sqrt{b} \left(a+b x^2\right)^{3/4}}",1,"(2*x)/(3*a*(a + b*x^2)^(3/4)) + (2*(1 + (b*x^2)/a)^(3/4)*EllipticF[ArcTan[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(3*Sqrt[a]*Sqrt[b]*(a + b*x^2)^(3/4))","A",3,3,11,0.2727,1,"{199, 233, 231}"
858,1,78,0,0.0173645,"\int \frac{1}{\left(a+b x^2\right)^{9/4}} \, dx","Int[(a + b*x^2)^(-9/4),x]","\frac{6 \sqrt[4]{\frac{b x^2}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{5 a^{3/2} \sqrt{b} \sqrt[4]{a+b x^2}}+\frac{2 x}{5 a \left(a+b x^2\right)^{5/4}}","\frac{6 \sqrt[4]{\frac{b x^2}{a}+1} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{5 a^{3/2} \sqrt{b} \sqrt[4]{a+b x^2}}+\frac{2 x}{5 a \left(a+b x^2\right)^{5/4}}",1,"(2*x)/(5*a*(a + b*x^2)^(5/4)) + (6*(1 + (b*x^2)/a)^(1/4)*EllipticE[ArcTan[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(5*a^(3/2)*Sqrt[b]*(a + b*x^2)^(1/4))","A",3,3,11,0.2727,1,"{199, 197, 196}"
859,1,97,0,0.0235896,"\int \frac{1}{\left(a+b x^2\right)^{11/4}} \, dx","Int[(a + b*x^2)^(-11/4),x]","\frac{10 x}{21 a^2 \left(a+b x^2\right)^{3/4}}+\frac{10 \left(\frac{b x^2}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{21 a^{3/2} \sqrt{b} \left(a+b x^2\right)^{3/4}}+\frac{2 x}{7 a \left(a+b x^2\right)^{7/4}}","\frac{10 x}{21 a^2 \left(a+b x^2\right)^{3/4}}+\frac{10 \left(\frac{b x^2}{a}+1\right)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{21 a^{3/2} \sqrt{b} \left(a+b x^2\right)^{3/4}}+\frac{2 x}{7 a \left(a+b x^2\right)^{7/4}}",1,"(2*x)/(7*a*(a + b*x^2)^(7/4)) + (10*x)/(21*a^2*(a + b*x^2)^(3/4)) + (10*(1 + (b*x^2)/a)^(3/4)*EllipticF[ArcTan[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(21*a^(3/2)*Sqrt[b]*(a + b*x^2)^(3/4))","A",4,3,11,0.2727,1,"{199, 233, 231}"
860,1,81,0,0.0178061,"\int \frac{1}{\left(a-b x^2\right)^{7/4}} \, dx","Int[(a - b*x^2)^(-7/4),x]","\frac{2 x}{3 a \left(a-b x^2\right)^{3/4}}+\frac{2 \left(1-\frac{b x^2}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{3 \sqrt{a} \sqrt{b} \left(a-b x^2\right)^{3/4}}","\frac{2 x}{3 a \left(a-b x^2\right)^{3/4}}+\frac{2 \left(1-\frac{b x^2}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{3 \sqrt{a} \sqrt{b} \left(a-b x^2\right)^{3/4}}",1,"(2*x)/(3*a*(a - b*x^2)^(3/4)) + (2*(1 - (b*x^2)/a)^(3/4)*EllipticF[ArcSin[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(3*Sqrt[a]*Sqrt[b]*(a - b*x^2)^(3/4))","A",3,3,12,0.2500,1,"{199, 233, 232}"
861,1,101,0,0.02682,"\int \frac{1}{\left(a-b x^2\right)^{9/4}} \, dx","Int[(a - b*x^2)^(-9/4),x]","\frac{6 x}{5 a^2 \sqrt[4]{a-b x^2}}-\frac{6 \sqrt[4]{1-\frac{b x^2}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{5 a^{3/2} \sqrt{b} \sqrt[4]{a-b x^2}}+\frac{2 x}{5 a \left(a-b x^2\right)^{5/4}}","\frac{6 x}{5 a^2 \sqrt[4]{a-b x^2}}-\frac{6 \sqrt[4]{1-\frac{b x^2}{a}} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{5 a^{3/2} \sqrt{b} \sqrt[4]{a-b x^2}}+\frac{2 x}{5 a \left(a-b x^2\right)^{5/4}}",1,"(2*x)/(5*a*(a - b*x^2)^(5/4)) + (6*x)/(5*a^2*(a - b*x^2)^(1/4)) - (6*(1 - (b*x^2)/a)^(1/4)*EllipticE[ArcSin[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(5*a^(3/2)*Sqrt[b]*(a - b*x^2)^(1/4))","A",4,3,12,0.2500,1,"{199, 229, 228}"
862,1,101,0,0.0258074,"\int \frac{1}{\left(a-b x^2\right)^{11/4}} \, dx","Int[(a - b*x^2)^(-11/4),x]","\frac{10 x}{21 a^2 \left(a-b x^2\right)^{3/4}}+\frac{10 \left(1-\frac{b x^2}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{21 a^{3/2} \sqrt{b} \left(a-b x^2\right)^{3/4}}+\frac{2 x}{7 a \left(a-b x^2\right)^{7/4}}","\frac{10 x}{21 a^2 \left(a-b x^2\right)^{3/4}}+\frac{10 \left(1-\frac{b x^2}{a}\right)^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{21 a^{3/2} \sqrt{b} \left(a-b x^2\right)^{3/4}}+\frac{2 x}{7 a \left(a-b x^2\right)^{7/4}}",1,"(2*x)/(7*a*(a - b*x^2)^(7/4)) + (10*x)/(21*a^2*(a - b*x^2)^(3/4)) + (10*(1 - (b*x^2)/a)^(3/4)*EllipticF[ArcSin[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(21*a^(3/2)*Sqrt[b]*(a - b*x^2)^(3/4))","A",4,3,12,0.2500,1,"{199, 233, 232}"
863,1,99,0,0.0282477,"\int \frac{x^6}{\sqrt[4]{2+3 x^2}} \, dx","Int[x^6/(2 + 3*x^2)^(1/4),x]","\frac{2}{39} \left(3 x^2+2\right)^{3/4} x^5-\frac{40 \left(3 x^2+2\right)^{3/4} x^3}{1053}+\frac{32 \left(3 x^2+2\right)^{3/4} x}{1053}-\frac{128 x}{1053 \sqrt[4]{3 x^2+2}}+\frac{128 \sqrt[4]{2} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{1053 \sqrt{3}}","\frac{2}{39} \left(3 x^2+2\right)^{3/4} x^5-\frac{40 \left(3 x^2+2\right)^{3/4} x^3}{1053}+\frac{32 \left(3 x^2+2\right)^{3/4} x}{1053}-\frac{128 x}{1053 \sqrt[4]{3 x^2+2}}+\frac{128 \sqrt[4]{2} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{1053 \sqrt{3}}",1,"(-128*x)/(1053*(2 + 3*x^2)^(1/4)) + (32*x*(2 + 3*x^2)^(3/4))/1053 - (40*x^3*(2 + 3*x^2)^(3/4))/1053 + (2*x^5*(2 + 3*x^2)^(3/4))/39 + (128*2^(1/4)*EllipticE[ArcTan[Sqrt[3/2]*x]/2, 2])/(1053*Sqrt[3])","A",5,3,15,0.2000,1,"{321, 227, 196}"
864,1,81,0,0.0201116,"\int \frac{x^4}{\sqrt[4]{2+3 x^2}} \, dx","Int[x^4/(2 + 3*x^2)^(1/4),x]","\frac{2}{27} \left(3 x^2+2\right)^{3/4} x^3-\frac{8}{135} \left(3 x^2+2\right)^{3/4} x+\frac{32 x}{135 \sqrt[4]{3 x^2+2}}-\frac{32 \sqrt[4]{2} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{135 \sqrt{3}}","\frac{2}{27} \left(3 x^2+2\right)^{3/4} x^3-\frac{8}{135} \left(3 x^2+2\right)^{3/4} x+\frac{32 x}{135 \sqrt[4]{3 x^2+2}}-\frac{32 \sqrt[4]{2} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{135 \sqrt{3}}",1,"(32*x)/(135*(2 + 3*x^2)^(1/4)) - (8*x*(2 + 3*x^2)^(3/4))/135 + (2*x^3*(2 + 3*x^2)^(3/4))/27 - (32*2^(1/4)*EllipticE[ArcTan[Sqrt[3/2]*x]/2, 2])/(135*Sqrt[3])","A",4,3,15,0.2000,1,"{321, 227, 196}"
865,1,63,0,0.012527,"\int \frac{x^2}{\sqrt[4]{2+3 x^2}} \, dx","Int[x^2/(2 + 3*x^2)^(1/4),x]","\frac{2}{15} \left(3 x^2+2\right)^{3/4} x-\frac{8 x}{15 \sqrt[4]{3 x^2+2}}+\frac{8 \sqrt[4]{2} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{15 \sqrt{3}}","\frac{2}{15} \left(3 x^2+2\right)^{3/4} x-\frac{8 x}{15 \sqrt[4]{3 x^2+2}}+\frac{8 \sqrt[4]{2} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{15 \sqrt{3}}",1,"(-8*x)/(15*(2 + 3*x^2)^(1/4)) + (2*x*(2 + 3*x^2)^(3/4))/15 + (8*2^(1/4)*EllipticE[ArcTan[Sqrt[3/2]*x]/2, 2])/(15*Sqrt[3])","A",3,3,15,0.2000,1,"{321, 227, 196}"
866,1,43,0,0.0069099,"\int \frac{1}{\sqrt[4]{2+3 x^2}} \, dx","Int[(2 + 3*x^2)^(-1/4),x]","\frac{2 x}{\sqrt[4]{3 x^2+2}}-\frac{2 \sqrt[4]{2} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{\sqrt{3}}","\frac{2 x}{\sqrt[4]{3 x^2+2}}-\frac{2 \sqrt[4]{2} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{\sqrt{3}}",1,"(2*x)/(2 + 3*x^2)^(1/4) - (2*2^(1/4)*EllipticE[ArcTan[Sqrt[3/2]*x]/2, 2])/Sqrt[3]","A",2,2,11,0.1818,1,"{227, 196}"
867,1,63,0,0.0127797,"\int \frac{1}{x^2 \sqrt[4]{2+3 x^2}} \, dx","Int[1/(x^2*(2 + 3*x^2)^(1/4)),x]","\frac{3 x}{2 \sqrt[4]{3 x^2+2}}-\frac{\left(3 x^2+2\right)^{3/4}}{2 x}-\frac{\sqrt{3} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{2^{3/4}}","\frac{3 x}{2 \sqrt[4]{3 x^2+2}}-\frac{\left(3 x^2+2\right)^{3/4}}{2 x}-\frac{\sqrt{3} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{2^{3/4}}",1,"(3*x)/(2*(2 + 3*x^2)^(1/4)) - (2 + 3*x^2)^(3/4)/(2*x) - (Sqrt[3]*EllipticE[ArcTan[Sqrt[3/2]*x]/2, 2])/2^(3/4)","A",3,3,15,0.2000,1,"{325, 227, 196}"
868,1,83,0,0.0192217,"\int \frac{1}{x^4 \sqrt[4]{2+3 x^2}} \, dx","Int[1/(x^4*(2 + 3*x^2)^(1/4)),x]","-\frac{9 x}{8 \sqrt[4]{3 x^2+2}}+\frac{3 \left(3 x^2+2\right)^{3/4}}{8 x}-\frac{\left(3 x^2+2\right)^{3/4}}{6 x^3}+\frac{3 \sqrt{3} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{4\ 2^{3/4}}","-\frac{9 x}{8 \sqrt[4]{3 x^2+2}}+\frac{3 \left(3 x^2+2\right)^{3/4}}{8 x}-\frac{\left(3 x^2+2\right)^{3/4}}{6 x^3}+\frac{3 \sqrt{3} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{4\ 2^{3/4}}",1,"(-9*x)/(8*(2 + 3*x^2)^(1/4)) - (2 + 3*x^2)^(3/4)/(6*x^3) + (3*(2 + 3*x^2)^(3/4))/(8*x) + (3*Sqrt[3]*EllipticE[ArcTan[Sqrt[3/2]*x]/2, 2])/(4*2^(3/4))","A",4,3,15,0.2000,1,"{325, 227, 196}"
869,1,101,0,0.0295966,"\int \frac{1}{x^6 \sqrt[4]{2+3 x^2}} \, dx","Int[1/(x^6*(2 + 3*x^2)^(1/4)),x]","\frac{189 x}{160 \sqrt[4]{3 x^2+2}}-\frac{63 \left(3 x^2+2\right)^{3/4}}{160 x}+\frac{7 \left(3 x^2+2\right)^{3/4}}{40 x^3}-\frac{\left(3 x^2+2\right)^{3/4}}{10 x^5}-\frac{63 \sqrt{3} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{80\ 2^{3/4}}","\frac{189 x}{160 \sqrt[4]{3 x^2+2}}-\frac{63 \left(3 x^2+2\right)^{3/4}}{160 x}+\frac{7 \left(3 x^2+2\right)^{3/4}}{40 x^3}-\frac{\left(3 x^2+2\right)^{3/4}}{10 x^5}-\frac{63 \sqrt{3} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{80\ 2^{3/4}}",1,"(189*x)/(160*(2 + 3*x^2)^(1/4)) - (2 + 3*x^2)^(3/4)/(10*x^5) + (7*(2 + 3*x^2)^(3/4))/(40*x^3) - (63*(2 + 3*x^2)^(3/4))/(160*x) - (63*Sqrt[3]*EllipticE[ArcTan[Sqrt[3/2]*x]/2, 2])/(80*2^(3/4))","A",5,3,15,0.2000,1,"{325, 227, 196}"
870,1,83,0,0.0224705,"\int \frac{x^6}{\sqrt[4]{2-3 x^2}} \, dx","Int[x^6/(2 - 3*x^2)^(1/4),x]","-\frac{2}{39} \left(2-3 x^2\right)^{3/4} x^5-\frac{40 \left(2-3 x^2\right)^{3/4} x^3}{1053}-\frac{32 \left(2-3 x^2\right)^{3/4} x}{1053}+\frac{128 \sqrt[4]{2} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{1053 \sqrt{3}}","-\frac{2}{39} \left(2-3 x^2\right)^{3/4} x^5-\frac{40 \left(2-3 x^2\right)^{3/4} x^3}{1053}-\frac{32 \left(2-3 x^2\right)^{3/4} x}{1053}+\frac{128 \sqrt[4]{2} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{1053 \sqrt{3}}",1,"(-32*x*(2 - 3*x^2)^(3/4))/1053 - (40*x^3*(2 - 3*x^2)^(3/4))/1053 - (2*x^5*(2 - 3*x^2)^(3/4))/39 + (128*2^(1/4)*EllipticE[ArcSin[Sqrt[3/2]*x]/2, 2])/(1053*Sqrt[3])","A",4,2,15,0.1333,1,"{321, 228}"
871,1,65,0,0.0144044,"\int \frac{x^4}{\sqrt[4]{2-3 x^2}} \, dx","Int[x^4/(2 - 3*x^2)^(1/4),x]","-\frac{2}{27} \left(2-3 x^2\right)^{3/4} x^3-\frac{8}{135} \left(2-3 x^2\right)^{3/4} x+\frac{32 \sqrt[4]{2} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{135 \sqrt{3}}","-\frac{2}{27} \left(2-3 x^2\right)^{3/4} x^3-\frac{8}{135} \left(2-3 x^2\right)^{3/4} x+\frac{32 \sqrt[4]{2} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{135 \sqrt{3}}",1,"(-8*x*(2 - 3*x^2)^(3/4))/135 - (2*x^3*(2 - 3*x^2)^(3/4))/27 + (32*2^(1/4)*EllipticE[ArcSin[Sqrt[3/2]*x]/2, 2])/(135*Sqrt[3])","A",3,2,15,0.1333,1,"{321, 228}"
872,1,47,0,0.0083717,"\int \frac{x^2}{\sqrt[4]{2-3 x^2}} \, dx","Int[x^2/(2 - 3*x^2)^(1/4),x]","\frac{8 \sqrt[4]{2} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{15 \sqrt{3}}-\frac{2}{15} x \left(2-3 x^2\right)^{3/4}","\frac{8 \sqrt[4]{2} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{15 \sqrt{3}}-\frac{2}{15} x \left(2-3 x^2\right)^{3/4}",1,"(-2*x*(2 - 3*x^2)^(3/4))/15 + (8*2^(1/4)*EllipticE[ArcSin[Sqrt[3/2]*x]/2, 2])/(15*Sqrt[3])","A",2,2,15,0.1333,1,"{321, 228}"
873,1,28,0,0.0030895,"\int \frac{1}{\sqrt[4]{2-3 x^2}} \, dx","Int[(2 - 3*x^2)^(-1/4),x]","\frac{2 \sqrt[4]{2} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{\sqrt{3}}","\frac{2 \sqrt[4]{2} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{\sqrt{3}}",1,"(2*2^(1/4)*EllipticE[ArcSin[Sqrt[3/2]*x]/2, 2])/Sqrt[3]","A",1,1,11,0.09091,1,"{228}"
874,1,47,0,0.0082851,"\int \frac{1}{x^2 \sqrt[4]{2-3 x^2}} \, dx","Int[1/(x^2*(2 - 3*x^2)^(1/4)),x]","-\frac{\left(2-3 x^2\right)^{3/4}}{2 x}-\frac{\sqrt{3} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{2^{3/4}}","-\frac{\left(2-3 x^2\right)^{3/4}}{2 x}-\frac{\sqrt{3} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{2^{3/4}}",1,"-(2 - 3*x^2)^(3/4)/(2*x) - (Sqrt[3]*EllipticE[ArcSin[Sqrt[3/2]*x]/2, 2])/2^(3/4)","A",2,2,15,0.1333,1,"{325, 228}"
875,1,67,0,0.0144736,"\int \frac{1}{x^4 \sqrt[4]{2-3 x^2}} \, dx","Int[1/(x^4*(2 - 3*x^2)^(1/4)),x]","-\frac{3 \left(2-3 x^2\right)^{3/4}}{8 x}-\frac{\left(2-3 x^2\right)^{3/4}}{6 x^3}-\frac{3 \sqrt{3} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{4\ 2^{3/4}}","-\frac{3 \left(2-3 x^2\right)^{3/4}}{8 x}-\frac{\left(2-3 x^2\right)^{3/4}}{6 x^3}-\frac{3 \sqrt{3} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{4\ 2^{3/4}}",1,"-(2 - 3*x^2)^(3/4)/(6*x^3) - (3*(2 - 3*x^2)^(3/4))/(8*x) - (3*Sqrt[3]*EllipticE[ArcSin[Sqrt[3/2]*x]/2, 2])/(4*2^(3/4))","A",3,2,15,0.1333,1,"{325, 228}"
876,1,85,0,0.0212376,"\int \frac{1}{x^6 \sqrt[4]{2-3 x^2}} \, dx","Int[1/(x^6*(2 - 3*x^2)^(1/4)),x]","-\frac{63 \left(2-3 x^2\right)^{3/4}}{160 x}-\frac{7 \left(2-3 x^2\right)^{3/4}}{40 x^3}-\frac{\left(2-3 x^2\right)^{3/4}}{10 x^5}-\frac{63 \sqrt{3} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{80\ 2^{3/4}}","-\frac{63 \left(2-3 x^2\right)^{3/4}}{160 x}-\frac{7 \left(2-3 x^2\right)^{3/4}}{40 x^3}-\frac{\left(2-3 x^2\right)^{3/4}}{10 x^5}-\frac{63 \sqrt{3} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{80\ 2^{3/4}}",1,"-(2 - 3*x^2)^(3/4)/(10*x^5) - (7*(2 - 3*x^2)^(3/4))/(40*x^3) - (63*(2 - 3*x^2)^(3/4))/(160*x) - (63*Sqrt[3]*EllipticE[ArcSin[Sqrt[3/2]*x]/2, 2])/(80*2^(3/4))","A",4,2,15,0.1333,1,"{325, 228}"
877,1,83,0,0.0249696,"\int \frac{x^6}{\left(2+3 x^2\right)^{3/4}} \, dx","Int[x^6/(2 + 3*x^2)^(3/4),x]","\frac{2}{33} \sqrt[4]{3 x^2+2} x^5-\frac{40}{693} \sqrt[4]{3 x^2+2} x^3+\frac{160 \sqrt[4]{3 x^2+2} x}{2079}-\frac{320\ 2^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{2079 \sqrt{3}}","\frac{2}{33} \sqrt[4]{3 x^2+2} x^5-\frac{40}{693} \sqrt[4]{3 x^2+2} x^3+\frac{160 \sqrt[4]{3 x^2+2} x}{2079}-\frac{320\ 2^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{2079 \sqrt{3}}",1,"(160*x*(2 + 3*x^2)^(1/4))/2079 - (40*x^3*(2 + 3*x^2)^(1/4))/693 + (2*x^5*(2 + 3*x^2)^(1/4))/33 - (320*2^(3/4)*EllipticF[ArcTan[Sqrt[3/2]*x]/2, 2])/(2079*Sqrt[3])","A",4,2,15,0.1333,1,"{321, 231}"
878,1,65,0,0.0148995,"\int \frac{x^4}{\left(2+3 x^2\right)^{3/4}} \, dx","Int[x^4/(2 + 3*x^2)^(3/4),x]","\frac{2}{21} \sqrt[4]{3 x^2+2} x^3-\frac{8}{63} \sqrt[4]{3 x^2+2} x+\frac{16\ 2^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{63 \sqrt{3}}","\frac{2}{21} \sqrt[4]{3 x^2+2} x^3-\frac{8}{63} \sqrt[4]{3 x^2+2} x+\frac{16\ 2^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{63 \sqrt{3}}",1,"(-8*x*(2 + 3*x^2)^(1/4))/63 + (2*x^3*(2 + 3*x^2)^(1/4))/21 + (16*2^(3/4)*EllipticF[ArcTan[Sqrt[3/2]*x]/2, 2])/(63*Sqrt[3])","A",3,2,15,0.1333,1,"{321, 231}"
879,1,47,0,0.0086441,"\int \frac{x^2}{\left(2+3 x^2\right)^{3/4}} \, dx","Int[x^2/(2 + 3*x^2)^(3/4),x]","\frac{2}{9} x \sqrt[4]{3 x^2+2}-\frac{4\ 2^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{9 \sqrt{3}}","\frac{2}{9} x \sqrt[4]{3 x^2+2}-\frac{4\ 2^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{9 \sqrt{3}}",1,"(2*x*(2 + 3*x^2)^(1/4))/9 - (4*2^(3/4)*EllipticF[ArcTan[Sqrt[3/2]*x]/2, 2])/(9*Sqrt[3])","A",2,2,15,0.1333,1,"{321, 231}"
880,1,27,0,0.0029293,"\int \frac{1}{\left(2+3 x^2\right)^{3/4}} \, dx","Int[(2 + 3*x^2)^(-3/4),x]","\frac{2^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{\sqrt{3}}","\frac{2^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{\sqrt{3}}",1,"(2^(3/4)*EllipticF[ArcTan[Sqrt[3/2]*x]/2, 2])/Sqrt[3]","A",1,1,11,0.09091,1,"{231}"
881,1,49,0,0.0083085,"\int \frac{1}{x^2 \left(2+3 x^2\right)^{3/4}} \, dx","Int[1/(x^2*(2 + 3*x^2)^(3/4)),x]","-\frac{\sqrt[4]{3 x^2+2}}{2 x}-\frac{\sqrt{3} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{2 \sqrt[4]{2}}","-\frac{\sqrt[4]{3 x^2+2}}{2 x}-\frac{\sqrt{3} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{2 \sqrt[4]{2}}",1,"-(2 + 3*x^2)^(1/4)/(2*x) - (Sqrt[3]*EllipticF[ArcTan[Sqrt[3/2]*x]/2, 2])/(2*2^(1/4))","A",2,2,15,0.1333,1,"{325, 231}"
882,1,67,0,0.0148175,"\int \frac{1}{x^4 \left(2+3 x^2\right)^{3/4}} \, dx","Int[1/(x^4*(2 + 3*x^2)^(3/4)),x]","\frac{5 \sqrt[4]{3 x^2+2}}{8 x}-\frac{\sqrt[4]{3 x^2+2}}{6 x^3}+\frac{5 \sqrt{3} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{8 \sqrt[4]{2}}","\frac{5 \sqrt[4]{3 x^2+2}}{8 x}-\frac{\sqrt[4]{3 x^2+2}}{6 x^3}+\frac{5 \sqrt{3} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{8 \sqrt[4]{2}}",1,"-(2 + 3*x^2)^(1/4)/(6*x^3) + (5*(2 + 3*x^2)^(1/4))/(8*x) + (5*Sqrt[3]*EllipticF[ArcTan[Sqrt[3/2]*x]/2, 2])/(8*2^(1/4))","A",3,2,15,0.1333,1,"{325, 231}"
883,1,85,0,0.0227747,"\int \frac{1}{x^6 \left(2+3 x^2\right)^{3/4}} \, dx","Int[1/(x^6*(2 + 3*x^2)^(3/4)),x]","-\frac{27 \sqrt[4]{3 x^2+2}}{32 x}+\frac{9 \sqrt[4]{3 x^2+2}}{40 x^3}-\frac{\sqrt[4]{3 x^2+2}}{10 x^5}-\frac{27 \sqrt{3} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{32 \sqrt[4]{2}}","-\frac{27 \sqrt[4]{3 x^2+2}}{32 x}+\frac{9 \sqrt[4]{3 x^2+2}}{40 x^3}-\frac{\sqrt[4]{3 x^2+2}}{10 x^5}-\frac{27 \sqrt{3} F\left(\left.\frac{1}{2} \tan ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{32 \sqrt[4]{2}}",1,"-(2 + 3*x^2)^(1/4)/(10*x^5) + (9*(2 + 3*x^2)^(1/4))/(40*x^3) - (27*(2 + 3*x^2)^(1/4))/(32*x) - (27*Sqrt[3]*EllipticF[ArcTan[Sqrt[3/2]*x]/2, 2])/(32*2^(1/4))","A",4,2,15,0.1333,1,"{325, 231}"
884,1,83,0,0.0226623,"\int \frac{x^6}{\left(2-3 x^2\right)^{3/4}} \, dx","Int[x^6/(2 - 3*x^2)^(3/4),x]","-\frac{2}{33} \sqrt[4]{2-3 x^2} x^5-\frac{40}{693} \sqrt[4]{2-3 x^2} x^3-\frac{160 \sqrt[4]{2-3 x^2} x}{2079}+\frac{320\ 2^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{2079 \sqrt{3}}","-\frac{2}{33} \sqrt[4]{2-3 x^2} x^5-\frac{40}{693} \sqrt[4]{2-3 x^2} x^3-\frac{160 \sqrt[4]{2-3 x^2} x}{2079}+\frac{320\ 2^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{2079 \sqrt{3}}",1,"(-160*x*(2 - 3*x^2)^(1/4))/2079 - (40*x^3*(2 - 3*x^2)^(1/4))/693 - (2*x^5*(2 - 3*x^2)^(1/4))/33 + (320*2^(3/4)*EllipticF[ArcSin[Sqrt[3/2]*x]/2, 2])/(2079*Sqrt[3])","A",4,2,15,0.1333,1,"{321, 232}"
885,1,65,0,0.0155594,"\int \frac{x^4}{\left(2-3 x^2\right)^{3/4}} \, dx","Int[x^4/(2 - 3*x^2)^(3/4),x]","-\frac{2}{21} \sqrt[4]{2-3 x^2} x^3-\frac{8}{63} \sqrt[4]{2-3 x^2} x+\frac{16\ 2^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{63 \sqrt{3}}","-\frac{2}{21} \sqrt[4]{2-3 x^2} x^3-\frac{8}{63} \sqrt[4]{2-3 x^2} x+\frac{16\ 2^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{63 \sqrt{3}}",1,"(-8*x*(2 - 3*x^2)^(1/4))/63 - (2*x^3*(2 - 3*x^2)^(1/4))/21 + (16*2^(3/4)*EllipticF[ArcSin[Sqrt[3/2]*x]/2, 2])/(63*Sqrt[3])","A",3,2,15,0.1333,1,"{321, 232}"
886,1,47,0,0.0085179,"\int \frac{x^2}{\left(2-3 x^2\right)^{3/4}} \, dx","Int[x^2/(2 - 3*x^2)^(3/4),x]","\frac{4\ 2^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{9 \sqrt{3}}-\frac{2}{9} x \sqrt[4]{2-3 x^2}","\frac{4\ 2^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{9 \sqrt{3}}-\frac{2}{9} x \sqrt[4]{2-3 x^2}",1,"(-2*x*(2 - 3*x^2)^(1/4))/9 + (4*2^(3/4)*EllipticF[ArcSin[Sqrt[3/2]*x]/2, 2])/(9*Sqrt[3])","A",2,2,15,0.1333,1,"{321, 232}"
887,1,27,0,0.0033811,"\int \frac{1}{\left(2-3 x^2\right)^{3/4}} \, dx","Int[(2 - 3*x^2)^(-3/4),x]","\frac{2^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{\sqrt{3}}","\frac{2^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{\sqrt{3}}",1,"(2^(3/4)*EllipticF[ArcSin[Sqrt[3/2]*x]/2, 2])/Sqrt[3]","A",1,1,11,0.09091,1,"{232}"
888,1,49,0,0.0089599,"\int \frac{1}{x^2 \left(2-3 x^2\right)^{3/4}} \, dx","Int[1/(x^2*(2 - 3*x^2)^(3/4)),x]","\frac{\sqrt{3} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{2 \sqrt[4]{2}}-\frac{\sqrt[4]{2-3 x^2}}{2 x}","\frac{\sqrt{3} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{2 \sqrt[4]{2}}-\frac{\sqrt[4]{2-3 x^2}}{2 x}",1,"-(2 - 3*x^2)^(1/4)/(2*x) + (Sqrt[3]*EllipticF[ArcSin[Sqrt[3/2]*x]/2, 2])/(2*2^(1/4))","A",2,2,15,0.1333,1,"{325, 232}"
889,1,67,0,0.0150862,"\int \frac{1}{x^4 \left(2-3 x^2\right)^{3/4}} \, dx","Int[1/(x^4*(2 - 3*x^2)^(3/4)),x]","-\frac{5 \sqrt[4]{2-3 x^2}}{8 x}-\frac{\sqrt[4]{2-3 x^2}}{6 x^3}+\frac{5 \sqrt{3} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{8 \sqrt[4]{2}}","-\frac{5 \sqrt[4]{2-3 x^2}}{8 x}-\frac{\sqrt[4]{2-3 x^2}}{6 x^3}+\frac{5 \sqrt{3} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{8 \sqrt[4]{2}}",1,"-(2 - 3*x^2)^(1/4)/(6*x^3) - (5*(2 - 3*x^2)^(1/4))/(8*x) + (5*Sqrt[3]*EllipticF[ArcSin[Sqrt[3/2]*x]/2, 2])/(8*2^(1/4))","A",3,2,15,0.1333,1,"{325, 232}"
890,1,85,0,0.0218717,"\int \frac{1}{x^6 \left(2-3 x^2\right)^{3/4}} \, dx","Int[1/(x^6*(2 - 3*x^2)^(3/4)),x]","-\frac{27 \sqrt[4]{2-3 x^2}}{32 x}-\frac{9 \sqrt[4]{2-3 x^2}}{40 x^3}-\frac{\sqrt[4]{2-3 x^2}}{10 x^5}+\frac{27 \sqrt{3} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{32 \sqrt[4]{2}}","-\frac{27 \sqrt[4]{2-3 x^2}}{32 x}-\frac{9 \sqrt[4]{2-3 x^2}}{40 x^3}-\frac{\sqrt[4]{2-3 x^2}}{10 x^5}+\frac{27 \sqrt{3} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{32 \sqrt[4]{2}}",1,"-(2 - 3*x^2)^(1/4)/(10*x^5) - (9*(2 - 3*x^2)^(1/4))/(40*x^3) - (27*(2 - 3*x^2)^(1/4))/(32*x) + (27*Sqrt[3]*EllipticF[ArcSin[Sqrt[3/2]*x]/2, 2])/(32*2^(1/4))","A",4,2,15,0.1333,1,"{325, 232}"
891,1,258,0,0.1436203,"\int \frac{x^6}{\sqrt[4]{-2+3 x^2}} \, dx","Int[x^6/(-2 + 3*x^2)^(1/4),x]","\frac{2}{39} \left(3 x^2-2\right)^{3/4} x^5+\frac{40 \left(3 x^2-2\right)^{3/4} x^3}{1053}+\frac{32 \left(3 x^2-2\right)^{3/4} x}{1053}+\frac{128 \sqrt[4]{3 x^2-2} x}{1053 \left(\sqrt{3 x^2-2}+\sqrt{2}\right)}+\frac{64 \sqrt[4]{2} \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{1053 \sqrt{3} x}-\frac{128 \sqrt[4]{2} \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{3 x^2-2}+\sqrt{2}\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{1053 \sqrt{3} x}","\frac{2}{39} \left(3 x^2-2\right)^{3/4} x^5+\frac{40 \left(3 x^2-2\right)^{3/4} x^3}{1053}+\frac{32 \left(3 x^2-2\right)^{3/4} x}{1053}+\frac{128 \sqrt[4]{3 x^2-2} x}{1053 \left(\sqrt{3 x^2-2}+\sqrt{2}\right)}+\frac{64 \sqrt[4]{2} \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{1053 \sqrt{3} x}-\frac{128 \sqrt[4]{2} \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{3 x^2-2}+\sqrt{2}\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{1053 \sqrt{3} x}",1,"(32*x*(-2 + 3*x^2)^(3/4))/1053 + (40*x^3*(-2 + 3*x^2)^(3/4))/1053 + (2*x^5*(-2 + 3*x^2)^(3/4))/39 + (128*x*(-2 + 3*x^2)^(1/4))/(1053*(Sqrt[2] + Sqrt[-2 + 3*x^2])) - (128*2^(1/4)*Sqrt[x^2/(Sqrt[2] + Sqrt[-2 + 3*x^2])^2]*(Sqrt[2] + Sqrt[-2 + 3*x^2])*EllipticE[2*ArcTan[(-2 + 3*x^2)^(1/4)/2^(1/4)], 1/2])/(1053*Sqrt[3]*x) + (64*2^(1/4)*Sqrt[x^2/(Sqrt[2] + Sqrt[-2 + 3*x^2])^2]*(Sqrt[2] + Sqrt[-2 + 3*x^2])*EllipticF[2*ArcTan[(-2 + 3*x^2)^(1/4)/2^(1/4)], 1/2])/(1053*Sqrt[3]*x)","A",7,5,15,0.3333,1,"{321, 230, 305, 220, 1196}"
892,1,240,0,0.1117577,"\int \frac{x^4}{\sqrt[4]{-2+3 x^2}} \, dx","Int[x^4/(-2 + 3*x^2)^(1/4),x]","\frac{2}{27} \left(3 x^2-2\right)^{3/4} x^3+\frac{8}{135} \left(3 x^2-2\right)^{3/4} x+\frac{32 \sqrt[4]{3 x^2-2} x}{135 \left(\sqrt{3 x^2-2}+\sqrt{2}\right)}+\frac{16 \sqrt[4]{2} \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{135 \sqrt{3} x}-\frac{32 \sqrt[4]{2} \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{3 x^2-2}+\sqrt{2}\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{135 \sqrt{3} x}","\frac{2}{27} \left(3 x^2-2\right)^{3/4} x^3+\frac{8}{135} \left(3 x^2-2\right)^{3/4} x+\frac{32 \sqrt[4]{3 x^2-2} x}{135 \left(\sqrt{3 x^2-2}+\sqrt{2}\right)}+\frac{16 \sqrt[4]{2} \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{135 \sqrt{3} x}-\frac{32 \sqrt[4]{2} \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{3 x^2-2}+\sqrt{2}\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{135 \sqrt{3} x}",1,"(8*x*(-2 + 3*x^2)^(3/4))/135 + (2*x^3*(-2 + 3*x^2)^(3/4))/27 + (32*x*(-2 + 3*x^2)^(1/4))/(135*(Sqrt[2] + Sqrt[-2 + 3*x^2])) - (32*2^(1/4)*Sqrt[x^2/(Sqrt[2] + Sqrt[-2 + 3*x^2])^2]*(Sqrt[2] + Sqrt[-2 + 3*x^2])*EllipticE[2*ArcTan[(-2 + 3*x^2)^(1/4)/2^(1/4)], 1/2])/(135*Sqrt[3]*x) + (16*2^(1/4)*Sqrt[x^2/(Sqrt[2] + Sqrt[-2 + 3*x^2])^2]*(Sqrt[2] + Sqrt[-2 + 3*x^2])*EllipticF[2*ArcTan[(-2 + 3*x^2)^(1/4)/2^(1/4)], 1/2])/(135*Sqrt[3]*x)","A",6,5,15,0.3333,1,"{321, 230, 305, 220, 1196}"
893,1,222,0,0.090511,"\int \frac{x^2}{\sqrt[4]{-2+3 x^2}} \, dx","Int[x^2/(-2 + 3*x^2)^(1/4),x]","\frac{2}{15} \left(3 x^2-2\right)^{3/4} x+\frac{8 \sqrt[4]{3 x^2-2} x}{15 \left(\sqrt{3 x^2-2}+\sqrt{2}\right)}+\frac{4 \sqrt[4]{2} \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{15 \sqrt{3} x}-\frac{8 \sqrt[4]{2} \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{3 x^2-2}+\sqrt{2}\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{15 \sqrt{3} x}","\frac{2}{15} \left(3 x^2-2\right)^{3/4} x+\frac{8 \sqrt[4]{3 x^2-2} x}{15 \left(\sqrt{3 x^2-2}+\sqrt{2}\right)}+\frac{4 \sqrt[4]{2} \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{15 \sqrt{3} x}-\frac{8 \sqrt[4]{2} \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{3 x^2-2}+\sqrt{2}\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{15 \sqrt{3} x}",1,"(2*x*(-2 + 3*x^2)^(3/4))/15 + (8*x*(-2 + 3*x^2)^(1/4))/(15*(Sqrt[2] + Sqrt[-2 + 3*x^2])) - (8*2^(1/4)*Sqrt[x^2/(Sqrt[2] + Sqrt[-2 + 3*x^2])^2]*(Sqrt[2] + Sqrt[-2 + 3*x^2])*EllipticE[2*ArcTan[(-2 + 3*x^2)^(1/4)/2^(1/4)], 1/2])/(15*Sqrt[3]*x) + (4*2^(1/4)*Sqrt[x^2/(Sqrt[2] + Sqrt[-2 + 3*x^2])^2]*(Sqrt[2] + Sqrt[-2 + 3*x^2])*EllipticF[2*ArcTan[(-2 + 3*x^2)^(1/4)/2^(1/4)], 1/2])/(15*Sqrt[3]*x)","A",5,5,15,0.3333,1,"{321, 230, 305, 220, 1196}"
894,1,199,0,0.0741029,"\int \frac{1}{\sqrt[4]{-2+3 x^2}} \, dx","Int[(-2 + 3*x^2)^(-1/4),x]","\frac{2 \sqrt[4]{3 x^2-2} x}{\sqrt{3 x^2-2}+\sqrt{2}}+\frac{\sqrt[4]{2} \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{\sqrt{3} x}-\frac{2 \sqrt[4]{2} \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{3 x^2-2}+\sqrt{2}\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{\sqrt{3} x}","\frac{2 \sqrt[4]{3 x^2-2} x}{\sqrt{3 x^2-2}+\sqrt{2}}+\frac{\sqrt[4]{2} \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{\sqrt{3} x}-\frac{2 \sqrt[4]{2} \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{3 x^2-2}+\sqrt{2}\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{\sqrt{3} x}",1,"(2*x*(-2 + 3*x^2)^(1/4))/(Sqrt[2] + Sqrt[-2 + 3*x^2]) - (2*2^(1/4)*Sqrt[x^2/(Sqrt[2] + Sqrt[-2 + 3*x^2])^2]*(Sqrt[2] + Sqrt[-2 + 3*x^2])*EllipticE[2*ArcTan[(-2 + 3*x^2)^(1/4)/2^(1/4)], 1/2])/(Sqrt[3]*x) + (2^(1/4)*Sqrt[x^2/(Sqrt[2] + Sqrt[-2 + 3*x^2])^2]*(Sqrt[2] + Sqrt[-2 + 3*x^2])*EllipticF[2*ArcTan[(-2 + 3*x^2)^(1/4)/2^(1/4)], 1/2])/(Sqrt[3]*x)","A",4,4,11,0.3636,1,"{230, 305, 220, 1196}"
895,1,221,0,0.0896784,"\int \frac{1}{x^2 \sqrt[4]{-2+3 x^2}} \, dx","Int[1/(x^2*(-2 + 3*x^2)^(1/4)),x]","-\frac{3 \sqrt[4]{3 x^2-2} x}{2 \left(\sqrt{3 x^2-2}+\sqrt{2}\right)}+\frac{\left(3 x^2-2\right)^{3/4}}{2 x}-\frac{\sqrt{3} \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{2\ 2^{3/4} x}+\frac{\sqrt{3} \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{3 x^2-2}+\sqrt{2}\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{2^{3/4} x}","-\frac{3 \sqrt[4]{3 x^2-2} x}{2 \left(\sqrt{3 x^2-2}+\sqrt{2}\right)}+\frac{\left(3 x^2-2\right)^{3/4}}{2 x}-\frac{\sqrt{3} \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{2\ 2^{3/4} x}+\frac{\sqrt{3} \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{3 x^2-2}+\sqrt{2}\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{2^{3/4} x}",1,"(-2 + 3*x^2)^(3/4)/(2*x) - (3*x*(-2 + 3*x^2)^(1/4))/(2*(Sqrt[2] + Sqrt[-2 + 3*x^2])) + (Sqrt[3]*Sqrt[x^2/(Sqrt[2] + Sqrt[-2 + 3*x^2])^2]*(Sqrt[2] + Sqrt[-2 + 3*x^2])*EllipticE[2*ArcTan[(-2 + 3*x^2)^(1/4)/2^(1/4)], 1/2])/(2^(3/4)*x) - (Sqrt[3]*Sqrt[x^2/(Sqrt[2] + Sqrt[-2 + 3*x^2])^2]*(Sqrt[2] + Sqrt[-2 + 3*x^2])*EllipticF[2*ArcTan[(-2 + 3*x^2)^(1/4)/2^(1/4)], 1/2])/(2*2^(3/4)*x)","A",5,5,15,0.3333,1,"{325, 230, 305, 220, 1196}"
896,1,242,0,0.109254,"\int \frac{1}{x^4 \sqrt[4]{-2+3 x^2}} \, dx","Int[1/(x^4*(-2 + 3*x^2)^(1/4)),x]","-\frac{9 \sqrt[4]{3 x^2-2} x}{8 \left(\sqrt{3 x^2-2}+\sqrt{2}\right)}+\frac{3 \left(3 x^2-2\right)^{3/4}}{8 x}+\frac{\left(3 x^2-2\right)^{3/4}}{6 x^3}-\frac{3 \sqrt{3} \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{8\ 2^{3/4} x}+\frac{3 \sqrt{3} \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{3 x^2-2}+\sqrt{2}\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{4\ 2^{3/4} x}","-\frac{9 \sqrt[4]{3 x^2-2} x}{8 \left(\sqrt{3 x^2-2}+\sqrt{2}\right)}+\frac{3 \left(3 x^2-2\right)^{3/4}}{8 x}+\frac{\left(3 x^2-2\right)^{3/4}}{6 x^3}-\frac{3 \sqrt{3} \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{8\ 2^{3/4} x}+\frac{3 \sqrt{3} \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{3 x^2-2}+\sqrt{2}\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{4\ 2^{3/4} x}",1,"(-2 + 3*x^2)^(3/4)/(6*x^3) + (3*(-2 + 3*x^2)^(3/4))/(8*x) - (9*x*(-2 + 3*x^2)^(1/4))/(8*(Sqrt[2] + Sqrt[-2 + 3*x^2])) + (3*Sqrt[3]*Sqrt[x^2/(Sqrt[2] + Sqrt[-2 + 3*x^2])^2]*(Sqrt[2] + Sqrt[-2 + 3*x^2])*EllipticE[2*ArcTan[(-2 + 3*x^2)^(1/4)/2^(1/4)], 1/2])/(4*2^(3/4)*x) - (3*Sqrt[3]*Sqrt[x^2/(Sqrt[2] + Sqrt[-2 + 3*x^2])^2]*(Sqrt[2] + Sqrt[-2 + 3*x^2])*EllipticF[2*ArcTan[(-2 + 3*x^2)^(1/4)/2^(1/4)], 1/2])/(8*2^(3/4)*x)","A",6,5,15,0.3333,1,"{325, 230, 305, 220, 1196}"
897,1,260,0,0.1263156,"\int \frac{1}{x^6 \sqrt[4]{-2+3 x^2}} \, dx","Int[1/(x^6*(-2 + 3*x^2)^(1/4)),x]","-\frac{189 \sqrt[4]{3 x^2-2} x}{160 \left(\sqrt{3 x^2-2}+\sqrt{2}\right)}+\frac{63 \left(3 x^2-2\right)^{3/4}}{160 x}+\frac{7 \left(3 x^2-2\right)^{3/4}}{40 x^3}+\frac{\left(3 x^2-2\right)^{3/4}}{10 x^5}-\frac{63 \sqrt{3} \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{160\ 2^{3/4} x}+\frac{63 \sqrt{3} \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{3 x^2-2}+\sqrt{2}\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{80\ 2^{3/4} x}","-\frac{189 \sqrt[4]{3 x^2-2} x}{160 \left(\sqrt{3 x^2-2}+\sqrt{2}\right)}+\frac{63 \left(3 x^2-2\right)^{3/4}}{160 x}+\frac{7 \left(3 x^2-2\right)^{3/4}}{40 x^3}+\frac{\left(3 x^2-2\right)^{3/4}}{10 x^5}-\frac{63 \sqrt{3} \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{160\ 2^{3/4} x}+\frac{63 \sqrt{3} \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{3 x^2-2}+\sqrt{2}\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{80\ 2^{3/4} x}",1,"(-2 + 3*x^2)^(3/4)/(10*x^5) + (7*(-2 + 3*x^2)^(3/4))/(40*x^3) + (63*(-2 + 3*x^2)^(3/4))/(160*x) - (189*x*(-2 + 3*x^2)^(1/4))/(160*(Sqrt[2] + Sqrt[-2 + 3*x^2])) + (63*Sqrt[3]*Sqrt[x^2/(Sqrt[2] + Sqrt[-2 + 3*x^2])^2]*(Sqrt[2] + Sqrt[-2 + 3*x^2])*EllipticE[2*ArcTan[(-2 + 3*x^2)^(1/4)/2^(1/4)], 1/2])/(80*2^(3/4)*x) - (63*Sqrt[3]*Sqrt[x^2/(Sqrt[2] + Sqrt[-2 + 3*x^2])^2]*(Sqrt[2] + Sqrt[-2 + 3*x^2])*EllipticF[2*ArcTan[(-2 + 3*x^2)^(1/4)/2^(1/4)], 1/2])/(160*2^(3/4)*x)","A",7,5,15,0.3333,1,"{325, 230, 305, 220, 1196}"
898,1,260,0,0.1337889,"\int \frac{x^6}{\sqrt[4]{-2-3 x^2}} \, dx","Int[x^6/(-2 - 3*x^2)^(1/4),x]","-\frac{2}{39} \left(-3 x^2-2\right)^{3/4} x^5+\frac{40 \left(-3 x^2-2\right)^{3/4} x^3}{1053}-\frac{32 \left(-3 x^2-2\right)^{3/4} x}{1053}-\frac{128 \sqrt[4]{-3 x^2-2} x}{1053 \left(\sqrt{-3 x^2-2}+\sqrt{2}\right)}+\frac{64 \sqrt[4]{2} \sqrt{-\frac{x^2}{\left(\sqrt{-3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{-3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{-3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{1053 \sqrt{3} x}-\frac{128 \sqrt[4]{2} \sqrt{-\frac{x^2}{\left(\sqrt{-3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{-3 x^2-2}+\sqrt{2}\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{-3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{1053 \sqrt{3} x}","-\frac{2}{39} \left(-3 x^2-2\right)^{3/4} x^5+\frac{40 \left(-3 x^2-2\right)^{3/4} x^3}{1053}-\frac{32 \left(-3 x^2-2\right)^{3/4} x}{1053}-\frac{128 \sqrt[4]{-3 x^2-2} x}{1053 \left(\sqrt{-3 x^2-2}+\sqrt{2}\right)}+\frac{64 \sqrt[4]{2} \sqrt{-\frac{x^2}{\left(\sqrt{-3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{-3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{-3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{1053 \sqrt{3} x}-\frac{128 \sqrt[4]{2} \sqrt{-\frac{x^2}{\left(\sqrt{-3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{-3 x^2-2}+\sqrt{2}\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{-3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{1053 \sqrt{3} x}",1,"(-32*x*(-2 - 3*x^2)^(3/4))/1053 + (40*x^3*(-2 - 3*x^2)^(3/4))/1053 - (2*x^5*(-2 - 3*x^2)^(3/4))/39 - (128*x*(-2 - 3*x^2)^(1/4))/(1053*(Sqrt[2] + Sqrt[-2 - 3*x^2])) - (128*2^(1/4)*Sqrt[-(x^2/(Sqrt[2] + Sqrt[-2 - 3*x^2])^2)]*(Sqrt[2] + Sqrt[-2 - 3*x^2])*EllipticE[2*ArcTan[(-2 - 3*x^2)^(1/4)/2^(1/4)], 1/2])/(1053*Sqrt[3]*x) + (64*2^(1/4)*Sqrt[-(x^2/(Sqrt[2] + Sqrt[-2 - 3*x^2])^2)]*(Sqrt[2] + Sqrt[-2 - 3*x^2])*EllipticF[2*ArcTan[(-2 - 3*x^2)^(1/4)/2^(1/4)], 1/2])/(1053*Sqrt[3]*x)","A",7,5,15,0.3333,1,"{321, 230, 305, 220, 1196}"
899,1,242,0,0.1104688,"\int \frac{x^4}{\sqrt[4]{-2-3 x^2}} \, dx","Int[x^4/(-2 - 3*x^2)^(1/4),x]","-\frac{2}{27} \left(-3 x^2-2\right)^{3/4} x^3+\frac{8}{135} \left(-3 x^2-2\right)^{3/4} x+\frac{32 \sqrt[4]{-3 x^2-2} x}{135 \left(\sqrt{-3 x^2-2}+\sqrt{2}\right)}-\frac{16 \sqrt[4]{2} \sqrt{-\frac{x^2}{\left(\sqrt{-3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{-3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{-3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{135 \sqrt{3} x}+\frac{32 \sqrt[4]{2} \sqrt{-\frac{x^2}{\left(\sqrt{-3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{-3 x^2-2}+\sqrt{2}\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{-3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{135 \sqrt{3} x}","-\frac{2}{27} \left(-3 x^2-2\right)^{3/4} x^3+\frac{8}{135} \left(-3 x^2-2\right)^{3/4} x+\frac{32 \sqrt[4]{-3 x^2-2} x}{135 \left(\sqrt{-3 x^2-2}+\sqrt{2}\right)}-\frac{16 \sqrt[4]{2} \sqrt{-\frac{x^2}{\left(\sqrt{-3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{-3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{-3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{135 \sqrt{3} x}+\frac{32 \sqrt[4]{2} \sqrt{-\frac{x^2}{\left(\sqrt{-3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{-3 x^2-2}+\sqrt{2}\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{-3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{135 \sqrt{3} x}",1,"(8*x*(-2 - 3*x^2)^(3/4))/135 - (2*x^3*(-2 - 3*x^2)^(3/4))/27 + (32*x*(-2 - 3*x^2)^(1/4))/(135*(Sqrt[2] + Sqrt[-2 - 3*x^2])) + (32*2^(1/4)*Sqrt[-(x^2/(Sqrt[2] + Sqrt[-2 - 3*x^2])^2)]*(Sqrt[2] + Sqrt[-2 - 3*x^2])*EllipticE[2*ArcTan[(-2 - 3*x^2)^(1/4)/2^(1/4)], 1/2])/(135*Sqrt[3]*x) - (16*2^(1/4)*Sqrt[-(x^2/(Sqrt[2] + Sqrt[-2 - 3*x^2])^2)]*(Sqrt[2] + Sqrt[-2 - 3*x^2])*EllipticF[2*ArcTan[(-2 - 3*x^2)^(1/4)/2^(1/4)], 1/2])/(135*Sqrt[3]*x)","A",6,5,15,0.3333,1,"{321, 230, 305, 220, 1196}"
900,1,224,0,0.0939805,"\int \frac{x^2}{\sqrt[4]{-2-3 x^2}} \, dx","Int[x^2/(-2 - 3*x^2)^(1/4),x]","-\frac{2}{15} \left(-3 x^2-2\right)^{3/4} x-\frac{8 \sqrt[4]{-3 x^2-2} x}{15 \left(\sqrt{-3 x^2-2}+\sqrt{2}\right)}+\frac{4 \sqrt[4]{2} \sqrt{-\frac{x^2}{\left(\sqrt{-3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{-3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{-3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{15 \sqrt{3} x}-\frac{8 \sqrt[4]{2} \sqrt{-\frac{x^2}{\left(\sqrt{-3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{-3 x^2-2}+\sqrt{2}\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{-3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{15 \sqrt{3} x}","-\frac{2}{15} \left(-3 x^2-2\right)^{3/4} x-\frac{8 \sqrt[4]{-3 x^2-2} x}{15 \left(\sqrt{-3 x^2-2}+\sqrt{2}\right)}+\frac{4 \sqrt[4]{2} \sqrt{-\frac{x^2}{\left(\sqrt{-3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{-3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{-3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{15 \sqrt{3} x}-\frac{8 \sqrt[4]{2} \sqrt{-\frac{x^2}{\left(\sqrt{-3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{-3 x^2-2}+\sqrt{2}\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{-3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{15 \sqrt{3} x}",1,"(-2*x*(-2 - 3*x^2)^(3/4))/15 - (8*x*(-2 - 3*x^2)^(1/4))/(15*(Sqrt[2] + Sqrt[-2 - 3*x^2])) - (8*2^(1/4)*Sqrt[-(x^2/(Sqrt[2] + Sqrt[-2 - 3*x^2])^2)]*(Sqrt[2] + Sqrt[-2 - 3*x^2])*EllipticE[2*ArcTan[(-2 - 3*x^2)^(1/4)/2^(1/4)], 1/2])/(15*Sqrt[3]*x) + (4*2^(1/4)*Sqrt[-(x^2/(Sqrt[2] + Sqrt[-2 - 3*x^2])^2)]*(Sqrt[2] + Sqrt[-2 - 3*x^2])*EllipticF[2*ArcTan[(-2 - 3*x^2)^(1/4)/2^(1/4)], 1/2])/(15*Sqrt[3]*x)","A",5,5,15,0.3333,1,"{321, 230, 305, 220, 1196}"
901,1,202,0,0.0784781,"\int \frac{1}{\sqrt[4]{-2-3 x^2}} \, dx","Int[(-2 - 3*x^2)^(-1/4),x]","\frac{2 \sqrt[4]{-3 x^2-2} x}{\sqrt{-3 x^2-2}+\sqrt{2}}-\frac{\sqrt[4]{2} \sqrt{-\frac{x^2}{\left(\sqrt{-3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{-3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{-3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{\sqrt{3} x}+\frac{2 \sqrt[4]{2} \sqrt{-\frac{x^2}{\left(\sqrt{-3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{-3 x^2-2}+\sqrt{2}\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{-3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{\sqrt{3} x}","\frac{2 \sqrt[4]{-3 x^2-2} x}{\sqrt{-3 x^2-2}+\sqrt{2}}-\frac{\sqrt[4]{2} \sqrt{-\frac{x^2}{\left(\sqrt{-3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{-3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{-3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{\sqrt{3} x}+\frac{2 \sqrt[4]{2} \sqrt{-\frac{x^2}{\left(\sqrt{-3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{-3 x^2-2}+\sqrt{2}\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{-3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{\sqrt{3} x}",1,"(2*x*(-2 - 3*x^2)^(1/4))/(Sqrt[2] + Sqrt[-2 - 3*x^2]) + (2*2^(1/4)*Sqrt[-(x^2/(Sqrt[2] + Sqrt[-2 - 3*x^2])^2)]*(Sqrt[2] + Sqrt[-2 - 3*x^2])*EllipticE[2*ArcTan[(-2 - 3*x^2)^(1/4)/2^(1/4)], 1/2])/(Sqrt[3]*x) - (2^(1/4)*Sqrt[-(x^2/(Sqrt[2] + Sqrt[-2 - 3*x^2])^2)]*(Sqrt[2] + Sqrt[-2 - 3*x^2])*EllipticF[2*ArcTan[(-2 - 3*x^2)^(1/4)/2^(1/4)], 1/2])/(Sqrt[3]*x)","A",4,4,11,0.3636,1,"{230, 305, 220, 1196}"
902,1,223,0,0.092718,"\int \frac{1}{x^2 \sqrt[4]{-2-3 x^2}} \, dx","Int[1/(x^2*(-2 - 3*x^2)^(1/4)),x]","\frac{3 \sqrt[4]{-3 x^2-2} x}{2 \left(\sqrt{-3 x^2-2}+\sqrt{2}\right)}+\frac{\left(-3 x^2-2\right)^{3/4}}{2 x}-\frac{\sqrt{3} \sqrt{-\frac{x^2}{\left(\sqrt{-3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{-3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{-3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{2\ 2^{3/4} x}+\frac{\sqrt{3} \sqrt{-\frac{x^2}{\left(\sqrt{-3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{-3 x^2-2}+\sqrt{2}\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{-3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{2^{3/4} x}","\frac{3 \sqrt[4]{-3 x^2-2} x}{2 \left(\sqrt{-3 x^2-2}+\sqrt{2}\right)}+\frac{\left(-3 x^2-2\right)^{3/4}}{2 x}-\frac{\sqrt{3} \sqrt{-\frac{x^2}{\left(\sqrt{-3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{-3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{-3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{2\ 2^{3/4} x}+\frac{\sqrt{3} \sqrt{-\frac{x^2}{\left(\sqrt{-3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{-3 x^2-2}+\sqrt{2}\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{-3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{2^{3/4} x}",1,"(-2 - 3*x^2)^(3/4)/(2*x) + (3*x*(-2 - 3*x^2)^(1/4))/(2*(Sqrt[2] + Sqrt[-2 - 3*x^2])) + (Sqrt[3]*Sqrt[-(x^2/(Sqrt[2] + Sqrt[-2 - 3*x^2])^2)]*(Sqrt[2] + Sqrt[-2 - 3*x^2])*EllipticE[2*ArcTan[(-2 - 3*x^2)^(1/4)/2^(1/4)], 1/2])/(2^(3/4)*x) - (Sqrt[3]*Sqrt[-(x^2/(Sqrt[2] + Sqrt[-2 - 3*x^2])^2)]*(Sqrt[2] + Sqrt[-2 - 3*x^2])*EllipticF[2*ArcTan[(-2 - 3*x^2)^(1/4)/2^(1/4)], 1/2])/(2*2^(3/4)*x)","A",5,5,15,0.3333,1,"{325, 230, 305, 220, 1196}"
903,1,244,0,0.1105424,"\int \frac{1}{x^4 \sqrt[4]{-2-3 x^2}} \, dx","Int[1/(x^4*(-2 - 3*x^2)^(1/4)),x]","-\frac{9 \sqrt[4]{-3 x^2-2} x}{8 \left(\sqrt{-3 x^2-2}+\sqrt{2}\right)}-\frac{3 \left(-3 x^2-2\right)^{3/4}}{8 x}+\frac{\left(-3 x^2-2\right)^{3/4}}{6 x^3}+\frac{3 \sqrt{3} \sqrt{-\frac{x^2}{\left(\sqrt{-3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{-3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{-3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{8\ 2^{3/4} x}-\frac{3 \sqrt{3} \sqrt{-\frac{x^2}{\left(\sqrt{-3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{-3 x^2-2}+\sqrt{2}\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{-3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{4\ 2^{3/4} x}","-\frac{9 \sqrt[4]{-3 x^2-2} x}{8 \left(\sqrt{-3 x^2-2}+\sqrt{2}\right)}-\frac{3 \left(-3 x^2-2\right)^{3/4}}{8 x}+\frac{\left(-3 x^2-2\right)^{3/4}}{6 x^3}+\frac{3 \sqrt{3} \sqrt{-\frac{x^2}{\left(\sqrt{-3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{-3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{-3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{8\ 2^{3/4} x}-\frac{3 \sqrt{3} \sqrt{-\frac{x^2}{\left(\sqrt{-3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{-3 x^2-2}+\sqrt{2}\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{-3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{4\ 2^{3/4} x}",1,"(-2 - 3*x^2)^(3/4)/(6*x^3) - (3*(-2 - 3*x^2)^(3/4))/(8*x) - (9*x*(-2 - 3*x^2)^(1/4))/(8*(Sqrt[2] + Sqrt[-2 - 3*x^2])) - (3*Sqrt[3]*Sqrt[-(x^2/(Sqrt[2] + Sqrt[-2 - 3*x^2])^2)]*(Sqrt[2] + Sqrt[-2 - 3*x^2])*EllipticE[2*ArcTan[(-2 - 3*x^2)^(1/4)/2^(1/4)], 1/2])/(4*2^(3/4)*x) + (3*Sqrt[3]*Sqrt[-(x^2/(Sqrt[2] + Sqrt[-2 - 3*x^2])^2)]*(Sqrt[2] + Sqrt[-2 - 3*x^2])*EllipticF[2*ArcTan[(-2 - 3*x^2)^(1/4)/2^(1/4)], 1/2])/(8*2^(3/4)*x)","A",6,5,15,0.3333,1,"{325, 230, 305, 220, 1196}"
904,1,262,0,0.1288806,"\int \frac{1}{x^6 \sqrt[4]{-2-3 x^2}} \, dx","Int[1/(x^6*(-2 - 3*x^2)^(1/4)),x]","\frac{189 \sqrt[4]{-3 x^2-2} x}{160 \left(\sqrt{-3 x^2-2}+\sqrt{2}\right)}+\frac{63 \left(-3 x^2-2\right)^{3/4}}{160 x}-\frac{7 \left(-3 x^2-2\right)^{3/4}}{40 x^3}+\frac{\left(-3 x^2-2\right)^{3/4}}{10 x^5}-\frac{63 \sqrt{3} \sqrt{-\frac{x^2}{\left(\sqrt{-3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{-3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{-3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{160\ 2^{3/4} x}+\frac{63 \sqrt{3} \sqrt{-\frac{x^2}{\left(\sqrt{-3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{-3 x^2-2}+\sqrt{2}\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{-3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{80\ 2^{3/4} x}","\frac{189 \sqrt[4]{-3 x^2-2} x}{160 \left(\sqrt{-3 x^2-2}+\sqrt{2}\right)}+\frac{63 \left(-3 x^2-2\right)^{3/4}}{160 x}-\frac{7 \left(-3 x^2-2\right)^{3/4}}{40 x^3}+\frac{\left(-3 x^2-2\right)^{3/4}}{10 x^5}-\frac{63 \sqrt{3} \sqrt{-\frac{x^2}{\left(\sqrt{-3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{-3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{-3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{160\ 2^{3/4} x}+\frac{63 \sqrt{3} \sqrt{-\frac{x^2}{\left(\sqrt{-3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{-3 x^2-2}+\sqrt{2}\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{-3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{80\ 2^{3/4} x}",1,"(-2 - 3*x^2)^(3/4)/(10*x^5) - (7*(-2 - 3*x^2)^(3/4))/(40*x^3) + (63*(-2 - 3*x^2)^(3/4))/(160*x) + (189*x*(-2 - 3*x^2)^(1/4))/(160*(Sqrt[2] + Sqrt[-2 - 3*x^2])) + (63*Sqrt[3]*Sqrt[-(x^2/(Sqrt[2] + Sqrt[-2 - 3*x^2])^2)]*(Sqrt[2] + Sqrt[-2 - 3*x^2])*EllipticE[2*ArcTan[(-2 - 3*x^2)^(1/4)/2^(1/4)], 1/2])/(80*2^(3/4)*x) - (63*Sqrt[3]*Sqrt[-(x^2/(Sqrt[2] + Sqrt[-2 - 3*x^2])^2)]*(Sqrt[2] + Sqrt[-2 - 3*x^2])*EllipticF[2*ArcTan[(-2 - 3*x^2)^(1/4)/2^(1/4)], 1/2])/(160*2^(3/4)*x)","A",7,5,15,0.3333,1,"{325, 230, 305, 220, 1196}"
905,1,138,0,0.0568948,"\int \frac{x^6}{\left(-2+3 x^2\right)^{3/4}} \, dx","Int[x^6/(-2 + 3*x^2)^(3/4),x]","\frac{2}{33} \sqrt[4]{3 x^2-2} x^5+\frac{40}{693} \sqrt[4]{3 x^2-2} x^3+\frac{160 \sqrt[4]{3 x^2-2} x}{2079}+\frac{160\ 2^{3/4} \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{2079 \sqrt{3} x}","\frac{2}{33} \sqrt[4]{3 x^2-2} x^5+\frac{40}{693} \sqrt[4]{3 x^2-2} x^3+\frac{160 \sqrt[4]{3 x^2-2} x}{2079}+\frac{160\ 2^{3/4} \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{2079 \sqrt{3} x}",1,"(160*x*(-2 + 3*x^2)^(1/4))/2079 + (40*x^3*(-2 + 3*x^2)^(1/4))/693 + (2*x^5*(-2 + 3*x^2)^(1/4))/33 + (160*2^(3/4)*Sqrt[x^2/(Sqrt[2] + Sqrt[-2 + 3*x^2])^2]*(Sqrt[2] + Sqrt[-2 + 3*x^2])*EllipticF[2*ArcTan[(-2 + 3*x^2)^(1/4)/2^(1/4)], 1/2])/(2079*Sqrt[3]*x)","A",5,3,15,0.2000,1,"{321, 234, 220}"
906,1,120,0,0.0456249,"\int \frac{x^4}{\left(-2+3 x^2\right)^{3/4}} \, dx","Int[x^4/(-2 + 3*x^2)^(3/4),x]","\frac{2}{21} \sqrt[4]{3 x^2-2} x^3+\frac{8}{63} \sqrt[4]{3 x^2-2} x+\frac{8\ 2^{3/4} \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{63 \sqrt{3} x}","\frac{2}{21} \sqrt[4]{3 x^2-2} x^3+\frac{8}{63} \sqrt[4]{3 x^2-2} x+\frac{8\ 2^{3/4} \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{63 \sqrt{3} x}",1,"(8*x*(-2 + 3*x^2)^(1/4))/63 + (2*x^3*(-2 + 3*x^2)^(1/4))/21 + (8*2^(3/4)*Sqrt[x^2/(Sqrt[2] + Sqrt[-2 + 3*x^2])^2]*(Sqrt[2] + Sqrt[-2 + 3*x^2])*EllipticF[2*ArcTan[(-2 + 3*x^2)^(1/4)/2^(1/4)], 1/2])/(63*Sqrt[3]*x)","A",4,3,15,0.2000,1,"{321, 234, 220}"
907,1,102,0,0.0367001,"\int \frac{x^2}{\left(-2+3 x^2\right)^{3/4}} \, dx","Int[x^2/(-2 + 3*x^2)^(3/4),x]","\frac{2}{9} \sqrt[4]{3 x^2-2} x+\frac{2\ 2^{3/4} \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{9 \sqrt{3} x}","\frac{2}{9} \sqrt[4]{3 x^2-2} x+\frac{2\ 2^{3/4} \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{9 \sqrt{3} x}",1,"(2*x*(-2 + 3*x^2)^(1/4))/9 + (2*2^(3/4)*Sqrt[x^2/(Sqrt[2] + Sqrt[-2 + 3*x^2])^2]*(Sqrt[2] + Sqrt[-2 + 3*x^2])*EllipticF[2*ArcTan[(-2 + 3*x^2)^(1/4)/2^(1/4)], 1/2])/(9*Sqrt[3]*x)","A",3,3,15,0.2000,1,"{321, 234, 220}"
908,1,82,0,0.0259494,"\int \frac{1}{\left(-2+3 x^2\right)^{3/4}} \, dx","Int[(-2 + 3*x^2)^(-3/4),x]","\frac{\sqrt{\frac{x^2}{\left(\sqrt{3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{\sqrt[4]{2} \sqrt{3} x}","\frac{\sqrt{\frac{x^2}{\left(\sqrt{3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{\sqrt[4]{2} \sqrt{3} x}",1,"(Sqrt[x^2/(Sqrt[2] + Sqrt[-2 + 3*x^2])^2]*(Sqrt[2] + Sqrt[-2 + 3*x^2])*EllipticF[2*ArcTan[(-2 + 3*x^2)^(1/4)/2^(1/4)], 1/2])/(2^(1/4)*Sqrt[3]*x)","A",2,2,11,0.1818,1,"{234, 220}"
909,1,104,0,0.0353238,"\int \frac{1}{x^2 \left(-2+3 x^2\right)^{3/4}} \, dx","Int[1/(x^2*(-2 + 3*x^2)^(3/4)),x]","\frac{\sqrt[4]{3 x^2-2}}{2 x}+\frac{\sqrt{3} \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{2} x}","\frac{\sqrt[4]{3 x^2-2}}{2 x}+\frac{\sqrt{3} \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{2} x}",1,"(-2 + 3*x^2)^(1/4)/(2*x) + (Sqrt[3]*Sqrt[x^2/(Sqrt[2] + Sqrt[-2 + 3*x^2])^2]*(Sqrt[2] + Sqrt[-2 + 3*x^2])*EllipticF[2*ArcTan[(-2 + 3*x^2)^(1/4)/2^(1/4)], 1/2])/(4*2^(1/4)*x)","A",3,3,15,0.2000,1,"{325, 234, 220}"
910,1,122,0,0.0463736,"\int \frac{1}{x^4 \left(-2+3 x^2\right)^{3/4}} \, dx","Int[1/(x^4*(-2 + 3*x^2)^(3/4)),x]","\frac{5 \sqrt[4]{3 x^2-2}}{8 x}+\frac{\sqrt[4]{3 x^2-2}}{6 x^3}+\frac{5 \sqrt{3} \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{16 \sqrt[4]{2} x}","\frac{5 \sqrt[4]{3 x^2-2}}{8 x}+\frac{\sqrt[4]{3 x^2-2}}{6 x^3}+\frac{5 \sqrt{3} \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{16 \sqrt[4]{2} x}",1,"(-2 + 3*x^2)^(1/4)/(6*x^3) + (5*(-2 + 3*x^2)^(1/4))/(8*x) + (5*Sqrt[3]*Sqrt[x^2/(Sqrt[2] + Sqrt[-2 + 3*x^2])^2]*(Sqrt[2] + Sqrt[-2 + 3*x^2])*EllipticF[2*ArcTan[(-2 + 3*x^2)^(1/4)/2^(1/4)], 1/2])/(16*2^(1/4)*x)","A",4,3,15,0.2000,1,"{325, 234, 220}"
911,1,140,0,0.056775,"\int \frac{1}{x^6 \left(-2+3 x^2\right)^{3/4}} \, dx","Int[1/(x^6*(-2 + 3*x^2)^(3/4)),x]","\frac{27 \sqrt[4]{3 x^2-2}}{32 x}+\frac{9 \sqrt[4]{3 x^2-2}}{40 x^3}+\frac{\sqrt[4]{3 x^2-2}}{10 x^5}+\frac{27 \sqrt{3} \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{64 \sqrt[4]{2} x}","\frac{27 \sqrt[4]{3 x^2-2}}{32 x}+\frac{9 \sqrt[4]{3 x^2-2}}{40 x^3}+\frac{\sqrt[4]{3 x^2-2}}{10 x^5}+\frac{27 \sqrt{3} \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{64 \sqrt[4]{2} x}",1,"(-2 + 3*x^2)^(1/4)/(10*x^5) + (9*(-2 + 3*x^2)^(1/4))/(40*x^3) + (27*(-2 + 3*x^2)^(1/4))/(32*x) + (27*Sqrt[3]*Sqrt[x^2/(Sqrt[2] + Sqrt[-2 + 3*x^2])^2]*(Sqrt[2] + Sqrt[-2 + 3*x^2])*EllipticF[2*ArcTan[(-2 + 3*x^2)^(1/4)/2^(1/4)], 1/2])/(64*2^(1/4)*x)","A",5,3,15,0.2000,1,"{325, 234, 220}"
912,1,139,0,0.0575328,"\int \frac{x^6}{\left(-2-3 x^2\right)^{3/4}} \, dx","Int[x^6/(-2 - 3*x^2)^(3/4),x]","-\frac{2}{33} \sqrt[4]{-3 x^2-2} x^5+\frac{40}{693} \sqrt[4]{-3 x^2-2} x^3-\frac{160 \sqrt[4]{-3 x^2-2} x}{2079}+\frac{160\ 2^{3/4} \sqrt{-\frac{x^2}{\left(\sqrt{-3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{-3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{-3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{2079 \sqrt{3} x}","-\frac{2}{33} \sqrt[4]{-3 x^2-2} x^5+\frac{40}{693} \sqrt[4]{-3 x^2-2} x^3-\frac{160 \sqrt[4]{-3 x^2-2} x}{2079}+\frac{160\ 2^{3/4} \sqrt{-\frac{x^2}{\left(\sqrt{-3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{-3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{-3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{2079 \sqrt{3} x}",1,"(-160*x*(-2 - 3*x^2)^(1/4))/2079 + (40*x^3*(-2 - 3*x^2)^(1/4))/693 - (2*x^5*(-2 - 3*x^2)^(1/4))/33 + (160*2^(3/4)*Sqrt[-(x^2/(Sqrt[2] + Sqrt[-2 - 3*x^2])^2)]*(Sqrt[2] + Sqrt[-2 - 3*x^2])*EllipticF[2*ArcTan[(-2 - 3*x^2)^(1/4)/2^(1/4)], 1/2])/(2079*Sqrt[3]*x)","A",5,3,15,0.2000,1,"{321, 234, 220}"
913,1,121,0,0.0461336,"\int \frac{x^4}{\left(-2-3 x^2\right)^{3/4}} \, dx","Int[x^4/(-2 - 3*x^2)^(3/4),x]","-\frac{2}{21} \sqrt[4]{-3 x^2-2} x^3+\frac{8}{63} \sqrt[4]{-3 x^2-2} x-\frac{8\ 2^{3/4} \sqrt{-\frac{x^2}{\left(\sqrt{-3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{-3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{-3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{63 \sqrt{3} x}","-\frac{2}{21} \sqrt[4]{-3 x^2-2} x^3+\frac{8}{63} \sqrt[4]{-3 x^2-2} x-\frac{8\ 2^{3/4} \sqrt{-\frac{x^2}{\left(\sqrt{-3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{-3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{-3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{63 \sqrt{3} x}",1,"(8*x*(-2 - 3*x^2)^(1/4))/63 - (2*x^3*(-2 - 3*x^2)^(1/4))/21 - (8*2^(3/4)*Sqrt[-(x^2/(Sqrt[2] + Sqrt[-2 - 3*x^2])^2)]*(Sqrt[2] + Sqrt[-2 - 3*x^2])*EllipticF[2*ArcTan[(-2 - 3*x^2)^(1/4)/2^(1/4)], 1/2])/(63*Sqrt[3]*x)","A",4,3,15,0.2000,1,"{321, 234, 220}"
914,1,103,0,0.0355607,"\int \frac{x^2}{\left(-2-3 x^2\right)^{3/4}} \, dx","Int[x^2/(-2 - 3*x^2)^(3/4),x]","\frac{2\ 2^{3/4} \sqrt{-\frac{x^2}{\left(\sqrt{-3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{-3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{-3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{9 \sqrt{3} x}-\frac{2}{9} x \sqrt[4]{-3 x^2-2}","\frac{2\ 2^{3/4} \sqrt{-\frac{x^2}{\left(\sqrt{-3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{-3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{-3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{9 \sqrt{3} x}-\frac{2}{9} x \sqrt[4]{-3 x^2-2}",1,"(-2*x*(-2 - 3*x^2)^(1/4))/9 + (2*2^(3/4)*Sqrt[-(x^2/(Sqrt[2] + Sqrt[-2 - 3*x^2])^2)]*(Sqrt[2] + Sqrt[-2 - 3*x^2])*EllipticF[2*ArcTan[(-2 - 3*x^2)^(1/4)/2^(1/4)], 1/2])/(9*Sqrt[3]*x)","A",3,3,15,0.2000,1,"{321, 234, 220}"
915,1,84,0,0.0270031,"\int \frac{1}{\left(-2-3 x^2\right)^{3/4}} \, dx","Int[(-2 - 3*x^2)^(-3/4),x]","-\frac{\sqrt{-\frac{x^2}{\left(\sqrt{-3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{-3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{-3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{\sqrt[4]{2} \sqrt{3} x}","-\frac{\sqrt{-\frac{x^2}{\left(\sqrt{-3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{-3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{-3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{\sqrt[4]{2} \sqrt{3} x}",1,"-((Sqrt[-(x^2/(Sqrt[2] + Sqrt[-2 - 3*x^2])^2)]*(Sqrt[2] + Sqrt[-2 - 3*x^2])*EllipticF[2*ArcTan[(-2 - 3*x^2)^(1/4)/2^(1/4)], 1/2])/(2^(1/4)*Sqrt[3]*x))","A",2,2,11,0.1818,1,"{234, 220}"
916,1,105,0,0.0353193,"\int \frac{1}{x^2 \left(-2-3 x^2\right)^{3/4}} \, dx","Int[1/(x^2*(-2 - 3*x^2)^(3/4)),x]","\frac{\sqrt[4]{-3 x^2-2}}{2 x}+\frac{\sqrt{3} \sqrt{-\frac{x^2}{\left(\sqrt{-3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{-3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{-3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{2} x}","\frac{\sqrt[4]{-3 x^2-2}}{2 x}+\frac{\sqrt{3} \sqrt{-\frac{x^2}{\left(\sqrt{-3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{-3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{-3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{2} x}",1,"(-2 - 3*x^2)^(1/4)/(2*x) + (Sqrt[3]*Sqrt[-(x^2/(Sqrt[2] + Sqrt[-2 - 3*x^2])^2)]*(Sqrt[2] + Sqrt[-2 - 3*x^2])*EllipticF[2*ArcTan[(-2 - 3*x^2)^(1/4)/2^(1/4)], 1/2])/(4*2^(1/4)*x)","A",3,3,15,0.2000,1,"{325, 234, 220}"
917,1,123,0,0.0485651,"\int \frac{1}{x^4 \left(-2-3 x^2\right)^{3/4}} \, dx","Int[1/(x^4*(-2 - 3*x^2)^(3/4)),x]","-\frac{5 \sqrt[4]{-3 x^2-2}}{8 x}+\frac{\sqrt[4]{-3 x^2-2}}{6 x^3}-\frac{5 \sqrt{3} \sqrt{-\frac{x^2}{\left(\sqrt{-3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{-3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{-3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{16 \sqrt[4]{2} x}","-\frac{5 \sqrt[4]{-3 x^2-2}}{8 x}+\frac{\sqrt[4]{-3 x^2-2}}{6 x^3}-\frac{5 \sqrt{3} \sqrt{-\frac{x^2}{\left(\sqrt{-3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{-3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{-3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{16 \sqrt[4]{2} x}",1,"(-2 - 3*x^2)^(1/4)/(6*x^3) - (5*(-2 - 3*x^2)^(1/4))/(8*x) - (5*Sqrt[3]*Sqrt[-(x^2/(Sqrt[2] + Sqrt[-2 - 3*x^2])^2)]*(Sqrt[2] + Sqrt[-2 - 3*x^2])*EllipticF[2*ArcTan[(-2 - 3*x^2)^(1/4)/2^(1/4)], 1/2])/(16*2^(1/4)*x)","A",4,3,15,0.2000,1,"{325, 234, 220}"
918,1,141,0,0.057696,"\int \frac{1}{x^6 \left(-2-3 x^2\right)^{3/4}} \, dx","Int[1/(x^6*(-2 - 3*x^2)^(3/4)),x]","\frac{27 \sqrt[4]{-3 x^2-2}}{32 x}-\frac{9 \sqrt[4]{-3 x^2-2}}{40 x^3}+\frac{\sqrt[4]{-3 x^2-2}}{10 x^5}+\frac{27 \sqrt{3} \sqrt{-\frac{x^2}{\left(\sqrt{-3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{-3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{-3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{64 \sqrt[4]{2} x}","\frac{27 \sqrt[4]{-3 x^2-2}}{32 x}-\frac{9 \sqrt[4]{-3 x^2-2}}{40 x^3}+\frac{\sqrt[4]{-3 x^2-2}}{10 x^5}+\frac{27 \sqrt{3} \sqrt{-\frac{x^2}{\left(\sqrt{-3 x^2-2}+\sqrt{2}\right)^2}} \left(\sqrt{-3 x^2-2}+\sqrt{2}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{-3 x^2-2}}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{64 \sqrt[4]{2} x}",1,"(-2 - 3*x^2)^(1/4)/(10*x^5) - (9*(-2 - 3*x^2)^(1/4))/(40*x^3) + (27*(-2 - 3*x^2)^(1/4))/(32*x) + (27*Sqrt[3]*Sqrt[-(x^2/(Sqrt[2] + Sqrt[-2 - 3*x^2])^2)]*(Sqrt[2] + Sqrt[-2 - 3*x^2])*EllipticF[2*ArcTan[(-2 - 3*x^2)^(1/4)/2^(1/4)], 1/2])/(64*2^(1/4)*x)","A",5,3,15,0.2000,1,"{325, 234, 220}"
919,1,152,0,0.1077689,"\int (c x)^{7/2} \sqrt[4]{a+b x^2} \, dx","Int[(c*x)^(7/2)*(a + b*x^2)^(1/4),x]","-\frac{a^2 c^3 \sqrt{c x} \sqrt[4]{a+b x^2}}{12 b^2}-\frac{a^{5/2} c^2 (c x)^{3/2} \left(\frac{a}{b x^2}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{12 b^{3/2} \left(a+b x^2\right)^{3/4}}+\frac{(c x)^{9/2} \sqrt[4]{a+b x^2}}{5 c}+\frac{a c (c x)^{5/2} \sqrt[4]{a+b x^2}}{30 b}","-\frac{a^2 c^3 \sqrt{c x} \sqrt[4]{a+b x^2}}{12 b^2}-\frac{a^{5/2} c^2 (c x)^{3/2} \left(\frac{a}{b x^2}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{12 b^{3/2} \left(a+b x^2\right)^{3/4}}+\frac{(c x)^{9/2} \sqrt[4]{a+b x^2}}{5 c}+\frac{a c (c x)^{5/2} \sqrt[4]{a+b x^2}}{30 b}",1,"-(a^2*c^3*Sqrt[c*x]*(a + b*x^2)^(1/4))/(12*b^2) + (a*c*(c*x)^(5/2)*(a + b*x^2)^(1/4))/(30*b) + ((c*x)^(9/2)*(a + b*x^2)^(1/4))/(5*c) - (a^(5/2)*c^2*(1 + a/(b*x^2))^(3/4)*(c*x)^(3/2)*EllipticF[ArcCot[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(12*b^(3/2)*(a + b*x^2)^(3/4))","A",8,7,19,0.3684,1,"{279, 321, 329, 237, 335, 275, 231}"
920,1,118,0,0.0845446,"\int (c x)^{3/2} \sqrt[4]{a+b x^2} \, dx","Int[(c*x)^(3/2)*(a + b*x^2)^(1/4),x]","\frac{a^{3/2} (c x)^{3/2} \left(\frac{a}{b x^2}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{6 \sqrt{b} \left(a+b x^2\right)^{3/4}}+\frac{(c x)^{5/2} \sqrt[4]{a+b x^2}}{3 c}+\frac{a c \sqrt{c x} \sqrt[4]{a+b x^2}}{6 b}","\frac{a^{3/2} (c x)^{3/2} \left(\frac{a}{b x^2}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{6 \sqrt{b} \left(a+b x^2\right)^{3/4}}+\frac{(c x)^{5/2} \sqrt[4]{a+b x^2}}{3 c}+\frac{a c \sqrt{c x} \sqrt[4]{a+b x^2}}{6 b}",1,"(a*c*Sqrt[c*x]*(a + b*x^2)^(1/4))/(6*b) + ((c*x)^(5/2)*(a + b*x^2)^(1/4))/(3*c) + (a^(3/2)*(1 + a/(b*x^2))^(3/4)*(c*x)^(3/2)*EllipticF[ArcCot[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(6*Sqrt[b]*(a + b*x^2)^(3/4))","A",7,7,19,0.3684,1,"{279, 321, 329, 237, 335, 275, 231}"
921,1,89,0,0.0728459,"\int \frac{\sqrt[4]{a+b x^2}}{\sqrt{c x}} \, dx","Int[(a + b*x^2)^(1/4)/Sqrt[c*x],x]","\frac{\sqrt{c x} \sqrt[4]{a+b x^2}}{c}-\frac{\sqrt{a} \sqrt{b} (c x)^{3/2} \left(\frac{a}{b x^2}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{c^2 \left(a+b x^2\right)^{3/4}}","\frac{\sqrt{c x} \sqrt[4]{a+b x^2}}{c}-\frac{\sqrt{a} \sqrt{b} (c x)^{3/2} \left(\frac{a}{b x^2}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{c^2 \left(a+b x^2\right)^{3/4}}",1,"(Sqrt[c*x]*(a + b*x^2)^(1/4))/c - (Sqrt[a]*Sqrt[b]*(1 + a/(b*x^2))^(3/4)*(c*x)^(3/2)*EllipticF[ArcCot[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(c^2*(a + b*x^2)^(3/4))","A",6,6,19,0.3158,1,"{279, 329, 237, 335, 275, 231}"
922,1,94,0,0.0742942,"\int \frac{\sqrt[4]{a+b x^2}}{(c x)^{5/2}} \, dx","Int[(a + b*x^2)^(1/4)/(c*x)^(5/2),x]","-\frac{2 b^{3/2} (c x)^{3/2} \left(\frac{a}{b x^2}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{3 \sqrt{a} c^4 \left(a+b x^2\right)^{3/4}}-\frac{2 \sqrt[4]{a+b x^2}}{3 c (c x)^{3/2}}","-\frac{2 b^{3/2} (c x)^{3/2} \left(\frac{a}{b x^2}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{3 \sqrt{a} c^4 \left(a+b x^2\right)^{3/4}}-\frac{2 \sqrt[4]{a+b x^2}}{3 c (c x)^{3/2}}",1,"(-2*(a + b*x^2)^(1/4))/(3*c*(c*x)^(3/2)) - (2*b^(3/2)*(1 + a/(b*x^2))^(3/4)*(c*x)^(3/2)*EllipticF[ArcCot[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(3*Sqrt[a]*c^4*(a + b*x^2)^(3/4))","A",6,6,19,0.3158,1,"{277, 329, 237, 335, 275, 231}"
923,1,123,0,0.088923,"\int \frac{\sqrt[4]{a+b x^2}}{(c x)^{9/2}} \, dx","Int[(a + b*x^2)^(1/4)/(c*x)^(9/2),x]","\frac{4 b^{5/2} (c x)^{3/2} \left(\frac{a}{b x^2}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{21 a^{3/2} c^6 \left(a+b x^2\right)^{3/4}}-\frac{2 b \sqrt[4]{a+b x^2}}{21 a c^3 (c x)^{3/2}}-\frac{2 \sqrt[4]{a+b x^2}}{7 c (c x)^{7/2}}","\frac{4 b^{5/2} (c x)^{3/2} \left(\frac{a}{b x^2}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{21 a^{3/2} c^6 \left(a+b x^2\right)^{3/4}}-\frac{2 b \sqrt[4]{a+b x^2}}{21 a c^3 (c x)^{3/2}}-\frac{2 \sqrt[4]{a+b x^2}}{7 c (c x)^{7/2}}",1,"(-2*(a + b*x^2)^(1/4))/(7*c*(c*x)^(7/2)) - (2*b*(a + b*x^2)^(1/4))/(21*a*c^3*(c*x)^(3/2)) + (4*b^(5/2)*(1 + a/(b*x^2))^(3/4)*(c*x)^(3/2)*EllipticF[ArcCot[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(21*a^(3/2)*c^6*(a + b*x^2)^(3/4))","A",7,7,19,0.3684,1,"{277, 325, 329, 237, 335, 275, 231}"
924,1,154,0,0.1100385,"\int \frac{\sqrt[4]{a+b x^2}}{(c x)^{13/2}} \, dx","Int[(a + b*x^2)^(1/4)/(c*x)^(13/2),x]","\frac{4 b^2 \sqrt[4]{a+b x^2}}{77 a^2 c^5 (c x)^{3/2}}-\frac{8 b^{7/2} (c x)^{3/2} \left(\frac{a}{b x^2}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{77 a^{5/2} c^8 \left(a+b x^2\right)^{3/4}}-\frac{2 b \sqrt[4]{a+b x^2}}{77 a c^3 (c x)^{7/2}}-\frac{2 \sqrt[4]{a+b x^2}}{11 c (c x)^{11/2}}","\frac{4 b^2 \sqrt[4]{a+b x^2}}{77 a^2 c^5 (c x)^{3/2}}-\frac{8 b^{7/2} (c x)^{3/2} \left(\frac{a}{b x^2}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{77 a^{5/2} c^8 \left(a+b x^2\right)^{3/4}}-\frac{2 b \sqrt[4]{a+b x^2}}{77 a c^3 (c x)^{7/2}}-\frac{2 \sqrt[4]{a+b x^2}}{11 c (c x)^{11/2}}",1,"(-2*(a + b*x^2)^(1/4))/(11*c*(c*x)^(11/2)) - (2*b*(a + b*x^2)^(1/4))/(77*a*c^3*(c*x)^(7/2)) + (4*b^2*(a + b*x^2)^(1/4))/(77*a^2*c^5*(c*x)^(3/2)) - (8*b^(7/2)*(1 + a/(b*x^2))^(3/4)*(c*x)^(3/2)*EllipticF[ArcCot[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(77*a^(5/2)*c^8*(a + b*x^2)^(3/4))","A",8,7,19,0.3684,1,"{277, 325, 329, 237, 335, 275, 231}"
925,1,147,0,0.0921969,"\int (c x)^{5/2} \sqrt[4]{a+b x^2} \, dx","Int[(c*x)^(5/2)*(a + b*x^2)^(1/4),x]","\frac{3 a^2 c^{5/2} \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a+b x^2}}\right)}{32 b^{7/4}}-\frac{3 a^2 c^{5/2} \tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a+b x^2}}\right)}{32 b^{7/4}}+\frac{(c x)^{7/2} \sqrt[4]{a+b x^2}}{4 c}+\frac{a c (c x)^{3/2} \sqrt[4]{a+b x^2}}{16 b}","\frac{3 a^2 c^{5/2} \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a+b x^2}}\right)}{32 b^{7/4}}-\frac{3 a^2 c^{5/2} \tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a+b x^2}}\right)}{32 b^{7/4}}+\frac{(c x)^{7/2} \sqrt[4]{a+b x^2}}{4 c}+\frac{a c (c x)^{3/2} \sqrt[4]{a+b x^2}}{16 b}",1,"(a*c*(c*x)^(3/2)*(a + b*x^2)^(1/4))/(16*b) + ((c*x)^(7/2)*(a + b*x^2)^(1/4))/(4*c) + (3*a^2*c^(5/2)*ArcTan[(b^(1/4)*Sqrt[c*x])/(Sqrt[c]*(a + b*x^2)^(1/4))])/(32*b^(7/4)) - (3*a^2*c^(5/2)*ArcTanh[(b^(1/4)*Sqrt[c*x])/(Sqrt[c]*(a + b*x^2)^(1/4))])/(32*b^(7/4))","A",7,7,19,0.3684,1,"{279, 321, 329, 331, 298, 205, 208}"
926,1,116,0,0.0698382,"\int \sqrt{c x} \sqrt[4]{a+b x^2} \, dx","Int[Sqrt[c*x]*(a + b*x^2)^(1/4),x]","-\frac{a \sqrt{c} \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a+b x^2}}\right)}{4 b^{3/4}}+\frac{a \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a+b x^2}}\right)}{4 b^{3/4}}+\frac{(c x)^{3/2} \sqrt[4]{a+b x^2}}{2 c}","-\frac{a \sqrt{c} \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a+b x^2}}\right)}{4 b^{3/4}}+\frac{a \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a+b x^2}}\right)}{4 b^{3/4}}+\frac{(c x)^{3/2} \sqrt[4]{a+b x^2}}{2 c}",1,"((c*x)^(3/2)*(a + b*x^2)^(1/4))/(2*c) - (a*Sqrt[c]*ArcTan[(b^(1/4)*Sqrt[c*x])/(Sqrt[c]*(a + b*x^2)^(1/4))])/(4*b^(3/4)) + (a*Sqrt[c]*ArcTanh[(b^(1/4)*Sqrt[c*x])/(Sqrt[c]*(a + b*x^2)^(1/4))])/(4*b^(3/4))","A",6,6,19,0.3158,1,"{279, 329, 331, 298, 205, 208}"
927,1,107,0,0.0692396,"\int \frac{\sqrt[4]{a+b x^2}}{(c x)^{3/2}} \, dx","Int[(a + b*x^2)^(1/4)/(c*x)^(3/2),x]","-\frac{\sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a+b x^2}}\right)}{c^{3/2}}+\frac{\sqrt[4]{b} \tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a+b x^2}}\right)}{c^{3/2}}-\frac{2 \sqrt[4]{a+b x^2}}{c \sqrt{c x}}","-\frac{\sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a+b x^2}}\right)}{c^{3/2}}+\frac{\sqrt[4]{b} \tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a+b x^2}}\right)}{c^{3/2}}-\frac{2 \sqrt[4]{a+b x^2}}{c \sqrt{c x}}",1,"(-2*(a + b*x^2)^(1/4))/(c*Sqrt[c*x]) - (b^(1/4)*ArcTan[(b^(1/4)*Sqrt[c*x])/(Sqrt[c]*(a + b*x^2)^(1/4))])/c^(3/2) + (b^(1/4)*ArcTanh[(b^(1/4)*Sqrt[c*x])/(Sqrt[c]*(a + b*x^2)^(1/4))])/c^(3/2)","A",6,6,19,0.3158,1,"{277, 329, 331, 298, 205, 208}"
928,1,28,0,0.0060003,"\int \frac{\sqrt[4]{a+b x^2}}{(c x)^{7/2}} \, dx","Int[(a + b*x^2)^(1/4)/(c*x)^(7/2),x]","-\frac{2 \left(a+b x^2\right)^{5/4}}{5 a c (c x)^{5/2}}","-\frac{2 \left(a+b x^2\right)^{5/4}}{5 a c (c x)^{5/2}}",1,"(-2*(a + b*x^2)^(5/4))/(5*a*c*(c*x)^(5/2))","A",1,1,19,0.05263,1,"{264}"
929,1,57,0,0.0145266,"\int \frac{\sqrt[4]{a+b x^2}}{(c x)^{11/2}} \, dx","Int[(a + b*x^2)^(1/4)/(c*x)^(11/2),x]","\frac{8 \left(a+b x^2\right)^{9/4}}{45 a^2 c (c x)^{9/2}}-\frac{2 \left(a+b x^2\right)^{5/4}}{5 a c (c x)^{9/2}}","\frac{8 \left(a+b x^2\right)^{9/4}}{45 a^2 c (c x)^{9/2}}-\frac{2 \left(a+b x^2\right)^{5/4}}{5 a c (c x)^{9/2}}",1,"(-2*(a + b*x^2)^(5/4))/(5*a*c*(c*x)^(9/2)) + (8*(a + b*x^2)^(9/4))/(45*a^2*c*(c*x)^(9/2))","A",2,2,19,0.1053,1,"{273, 264}"
930,1,85,0,0.0244733,"\int \frac{\sqrt[4]{a+b x^2}}{(c x)^{15/2}} \, dx","Int[(a + b*x^2)^(1/4)/(c*x)^(15/2),x]","-\frac{64 \left(a+b x^2\right)^{13/4}}{585 a^3 c (c x)^{13/2}}+\frac{16 \left(a+b x^2\right)^{9/4}}{45 a^2 c (c x)^{13/2}}-\frac{2 \left(a+b x^2\right)^{5/4}}{5 a c (c x)^{13/2}}","-\frac{64 \left(a+b x^2\right)^{13/4}}{585 a^3 c (c x)^{13/2}}+\frac{16 \left(a+b x^2\right)^{9/4}}{45 a^2 c (c x)^{13/2}}-\frac{2 \left(a+b x^2\right)^{5/4}}{5 a c (c x)^{13/2}}",1,"(-2*(a + b*x^2)^(5/4))/(5*a*c*(c*x)^(13/2)) + (16*(a + b*x^2)^(9/4))/(45*a^2*c*(c*x)^(13/2)) - (64*(a + b*x^2)^(13/4))/(585*a^3*c*(c*x)^(13/2))","A",3,2,19,0.1053,1,"{273, 264}"
931,1,113,0,0.0384764,"\int \frac{\sqrt[4]{a+b x^2}}{(c x)^{19/2}} \, dx","Int[(a + b*x^2)^(1/4)/(c*x)^(19/2),x]","\frac{256 \left(a+b x^2\right)^{17/4}}{3315 a^4 c (c x)^{17/2}}-\frac{64 \left(a+b x^2\right)^{13/4}}{195 a^3 c (c x)^{17/2}}+\frac{8 \left(a+b x^2\right)^{9/4}}{15 a^2 c (c x)^{17/2}}-\frac{2 \left(a+b x^2\right)^{5/4}}{5 a c (c x)^{17/2}}","\frac{256 \left(a+b x^2\right)^{17/4}}{3315 a^4 c (c x)^{17/2}}-\frac{64 \left(a+b x^2\right)^{13/4}}{195 a^3 c (c x)^{17/2}}+\frac{8 \left(a+b x^2\right)^{9/4}}{15 a^2 c (c x)^{17/2}}-\frac{2 \left(a+b x^2\right)^{5/4}}{5 a c (c x)^{17/2}}",1,"(-2*(a + b*x^2)^(5/4))/(5*a*c*(c*x)^(17/2)) + (8*(a + b*x^2)^(9/4))/(15*a^2*c*(c*x)^(17/2)) - (64*(a + b*x^2)^(13/4))/(195*a^3*c*(c*x)^(17/2)) + (256*(a + b*x^2)^(17/4))/(3315*a^4*c*(c*x)^(17/2))","A",4,2,19,0.1053,1,"{273, 264}"
932,1,122,0,0.0920301,"\int (c x)^{3/2} \sqrt[4]{a-b x^2} \, dx","Int[(c*x)^(3/2)*(a - b*x^2)^(1/4),x]","-\frac{a^{3/2} (c x)^{3/2} \left(1-\frac{a}{b x^2}\right)^{3/4} F\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{6 \sqrt{b} \left(a-b x^2\right)^{3/4}}+\frac{(c x)^{5/2} \sqrt[4]{a-b x^2}}{3 c}-\frac{a c \sqrt{c x} \sqrt[4]{a-b x^2}}{6 b}","-\frac{a^{3/2} (c x)^{3/2} \left(1-\frac{a}{b x^2}\right)^{3/4} F\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{6 \sqrt{b} \left(a-b x^2\right)^{3/4}}+\frac{(c x)^{5/2} \sqrt[4]{a-b x^2}}{3 c}-\frac{a c \sqrt{c x} \sqrt[4]{a-b x^2}}{6 b}",1,"-(a*c*Sqrt[c*x]*(a - b*x^2)^(1/4))/(6*b) + ((c*x)^(5/2)*(a - b*x^2)^(1/4))/(3*c) - (a^(3/2)*(1 - a/(b*x^2))^(3/4)*(c*x)^(3/2)*EllipticF[ArcCsc[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(6*Sqrt[b]*(a - b*x^2)^(3/4))","A",7,7,20,0.3500,1,"{279, 321, 329, 237, 335, 275, 232}"
933,1,92,0,0.0791617,"\int \frac{\sqrt[4]{a-b x^2}}{\sqrt{c x}} \, dx","Int[(a - b*x^2)^(1/4)/Sqrt[c*x],x]","\frac{\sqrt{c x} \sqrt[4]{a-b x^2}}{c}-\frac{\sqrt{a} \sqrt{b} (c x)^{3/2} \left(1-\frac{a}{b x^2}\right)^{3/4} F\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{c^2 \left(a-b x^2\right)^{3/4}}","\frac{\sqrt{c x} \sqrt[4]{a-b x^2}}{c}-\frac{\sqrt{a} \sqrt{b} (c x)^{3/2} \left(1-\frac{a}{b x^2}\right)^{3/4} F\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{c^2 \left(a-b x^2\right)^{3/4}}",1,"(Sqrt[c*x]*(a - b*x^2)^(1/4))/c - (Sqrt[a]*Sqrt[b]*(1 - a/(b*x^2))^(3/4)*(c*x)^(3/2)*EllipticF[ArcCsc[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(c^2*(a - b*x^2)^(3/4))","A",6,6,20,0.3000,1,"{279, 329, 237, 335, 275, 232}"
934,1,97,0,0.0785771,"\int \frac{\sqrt[4]{a-b x^2}}{(c x)^{5/2}} \, dx","Int[(a - b*x^2)^(1/4)/(c*x)^(5/2),x]","\frac{2 b^{3/2} (c x)^{3/2} \left(1-\frac{a}{b x^2}\right)^{3/4} F\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{3 \sqrt{a} c^4 \left(a-b x^2\right)^{3/4}}-\frac{2 \sqrt[4]{a-b x^2}}{3 c (c x)^{3/2}}","\frac{2 b^{3/2} (c x)^{3/2} \left(1-\frac{a}{b x^2}\right)^{3/4} F\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{3 \sqrt{a} c^4 \left(a-b x^2\right)^{3/4}}-\frac{2 \sqrt[4]{a-b x^2}}{3 c (c x)^{3/2}}",1,"(-2*(a - b*x^2)^(1/4))/(3*c*(c*x)^(3/2)) + (2*b^(3/2)*(1 - a/(b*x^2))^(3/4)*(c*x)^(3/2)*EllipticF[ArcCsc[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(3*Sqrt[a]*c^4*(a - b*x^2)^(3/4))","A",6,6,20,0.3000,1,"{277, 329, 237, 335, 275, 232}"
935,1,127,0,0.0958838,"\int \frac{\sqrt[4]{a-b x^2}}{(c x)^{9/2}} \, dx","Int[(a - b*x^2)^(1/4)/(c*x)^(9/2),x]","\frac{4 b^{5/2} (c x)^{3/2} \left(1-\frac{a}{b x^2}\right)^{3/4} F\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{21 a^{3/2} c^6 \left(a-b x^2\right)^{3/4}}+\frac{2 b \sqrt[4]{a-b x^2}}{21 a c^3 (c x)^{3/2}}-\frac{2 \sqrt[4]{a-b x^2}}{7 c (c x)^{7/2}}","\frac{4 b^{5/2} (c x)^{3/2} \left(1-\frac{a}{b x^2}\right)^{3/4} F\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{21 a^{3/2} c^6 \left(a-b x^2\right)^{3/4}}+\frac{2 b \sqrt[4]{a-b x^2}}{21 a c^3 (c x)^{3/2}}-\frac{2 \sqrt[4]{a-b x^2}}{7 c (c x)^{7/2}}",1,"(-2*(a - b*x^2)^(1/4))/(7*c*(c*x)^(7/2)) + (2*b*(a - b*x^2)^(1/4))/(21*a*c^3*(c*x)^(3/2)) + (4*b^(5/2)*(1 - a/(b*x^2))^(3/4)*(c*x)^(3/2)*EllipticF[ArcCsc[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(21*a^(3/2)*c^6*(a - b*x^2)^(3/4))","A",7,7,20,0.3500,1,"{277, 325, 329, 237, 335, 275, 232}"
936,1,159,0,0.1110306,"\int \frac{\sqrt[4]{a-b x^2}}{(c x)^{13/2}} \, dx","Int[(a - b*x^2)^(1/4)/(c*x)^(13/2),x]","\frac{4 b^2 \sqrt[4]{a-b x^2}}{77 a^2 c^5 (c x)^{3/2}}+\frac{8 b^{7/2} (c x)^{3/2} \left(1-\frac{a}{b x^2}\right)^{3/4} F\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{77 a^{5/2} c^8 \left(a-b x^2\right)^{3/4}}+\frac{2 b \sqrt[4]{a-b x^2}}{77 a c^3 (c x)^{7/2}}-\frac{2 \sqrt[4]{a-b x^2}}{11 c (c x)^{11/2}}","\frac{4 b^2 \sqrt[4]{a-b x^2}}{77 a^2 c^5 (c x)^{3/2}}+\frac{8 b^{7/2} (c x)^{3/2} \left(1-\frac{a}{b x^2}\right)^{3/4} F\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{77 a^{5/2} c^8 \left(a-b x^2\right)^{3/4}}+\frac{2 b \sqrt[4]{a-b x^2}}{77 a c^3 (c x)^{7/2}}-\frac{2 \sqrt[4]{a-b x^2}}{11 c (c x)^{11/2}}",1,"(-2*(a - b*x^2)^(1/4))/(11*c*(c*x)^(11/2)) + (2*b*(a - b*x^2)^(1/4))/(77*a*c^3*(c*x)^(7/2)) + (4*b^2*(a - b*x^2)^(1/4))/(77*a^2*c^5*(c*x)^(3/2)) + (8*b^(7/2)*(1 - a/(b*x^2))^(3/4)*(c*x)^(3/2)*EllipticF[ArcCsc[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(77*a^(5/2)*c^8*(a - b*x^2)^(3/4))","A",8,7,20,0.3500,1,"{277, 325, 329, 237, 335, 275, 232}"
937,1,343,0,0.3676337,"\int (c x)^{5/2} \sqrt[4]{a-b x^2} \, dx","Int[(c*x)^(5/2)*(a - b*x^2)^(1/4),x]","\frac{3 a^2 c^{5/2} \log \left(\frac{\sqrt{b} \sqrt{c} x}{\sqrt{a-b x^2}}-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a-b x^2}}+\sqrt{c}\right)}{64 \sqrt{2} b^{7/4}}-\frac{3 a^2 c^{5/2} \log \left(\frac{\sqrt{b} \sqrt{c} x}{\sqrt{a-b x^2}}+\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a-b x^2}}+\sqrt{c}\right)}{64 \sqrt{2} b^{7/4}}-\frac{3 a^2 c^{5/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a-b x^2}}\right)}{32 \sqrt{2} b^{7/4}}+\frac{3 a^2 c^{5/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a-b x^2}}+1\right)}{32 \sqrt{2} b^{7/4}}+\frac{(c x)^{7/2} \sqrt[4]{a-b x^2}}{4 c}-\frac{a c (c x)^{3/2} \sqrt[4]{a-b x^2}}{16 b}","\frac{3 a^2 c^{5/2} \log \left(\frac{\sqrt{b} \sqrt{c} x}{\sqrt{a-b x^2}}-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a-b x^2}}+\sqrt{c}\right)}{64 \sqrt{2} b^{7/4}}-\frac{3 a^2 c^{5/2} \log \left(\frac{\sqrt{b} \sqrt{c} x}{\sqrt{a-b x^2}}+\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a-b x^2}}+\sqrt{c}\right)}{64 \sqrt{2} b^{7/4}}-\frac{3 a^2 c^{5/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a-b x^2}}\right)}{32 \sqrt{2} b^{7/4}}+\frac{3 a^2 c^{5/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a-b x^2}}+1\right)}{32 \sqrt{2} b^{7/4}}+\frac{(c x)^{7/2} \sqrt[4]{a-b x^2}}{4 c}-\frac{a c (c x)^{3/2} \sqrt[4]{a-b x^2}}{16 b}",1,"-(a*c*(c*x)^(3/2)*(a - b*x^2)^(1/4))/(16*b) + ((c*x)^(7/2)*(a - b*x^2)^(1/4))/(4*c) - (3*a^2*c^(5/2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[c*x])/(Sqrt[c]*(a - b*x^2)^(1/4))])/(32*Sqrt[2]*b^(7/4)) + (3*a^2*c^(5/2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[c*x])/(Sqrt[c]*(a - b*x^2)^(1/4))])/(32*Sqrt[2]*b^(7/4)) + (3*a^2*c^(5/2)*Log[Sqrt[c] + (Sqrt[b]*Sqrt[c]*x)/Sqrt[a - b*x^2] - (Sqrt[2]*b^(1/4)*Sqrt[c*x])/(a - b*x^2)^(1/4)])/(64*Sqrt[2]*b^(7/4)) - (3*a^2*c^(5/2)*Log[Sqrt[c] + (Sqrt[b]*Sqrt[c]*x)/Sqrt[a - b*x^2] + (Sqrt[2]*b^(1/4)*Sqrt[c*x])/(a - b*x^2)^(1/4)])/(64*Sqrt[2]*b^(7/4))","A",13,10,20,0.5000,1,"{279, 321, 329, 331, 297, 1162, 617, 204, 1165, 628}"
938,1,307,0,0.2683613,"\int \sqrt{c x} \sqrt[4]{a-b x^2} \, dx","Int[Sqrt[c*x]*(a - b*x^2)^(1/4),x]","\frac{a \sqrt{c} \log \left(\frac{\sqrt{b} \sqrt{c} x}{\sqrt{a-b x^2}}-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a-b x^2}}+\sqrt{c}\right)}{8 \sqrt{2} b^{3/4}}-\frac{a \sqrt{c} \log \left(\frac{\sqrt{b} \sqrt{c} x}{\sqrt{a-b x^2}}+\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a-b x^2}}+\sqrt{c}\right)}{8 \sqrt{2} b^{3/4}}-\frac{a \sqrt{c} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a-b x^2}}\right)}{4 \sqrt{2} b^{3/4}}+\frac{a \sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a-b x^2}}+1\right)}{4 \sqrt{2} b^{3/4}}+\frac{(c x)^{3/2} \sqrt[4]{a-b x^2}}{2 c}","\frac{a \sqrt{c} \log \left(\frac{\sqrt{b} \sqrt{c} x}{\sqrt{a-b x^2}}-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a-b x^2}}+\sqrt{c}\right)}{8 \sqrt{2} b^{3/4}}-\frac{a \sqrt{c} \log \left(\frac{\sqrt{b} \sqrt{c} x}{\sqrt{a-b x^2}}+\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a-b x^2}}+\sqrt{c}\right)}{8 \sqrt{2} b^{3/4}}-\frac{a \sqrt{c} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a-b x^2}}\right)}{4 \sqrt{2} b^{3/4}}+\frac{a \sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a-b x^2}}+1\right)}{4 \sqrt{2} b^{3/4}}+\frac{(c x)^{3/2} \sqrt[4]{a-b x^2}}{2 c}",1,"((c*x)^(3/2)*(a - b*x^2)^(1/4))/(2*c) - (a*Sqrt[c]*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[c*x])/(Sqrt[c]*(a - b*x^2)^(1/4))])/(4*Sqrt[2]*b^(3/4)) + (a*Sqrt[c]*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[c*x])/(Sqrt[c]*(a - b*x^2)^(1/4))])/(4*Sqrt[2]*b^(3/4)) + (a*Sqrt[c]*Log[Sqrt[c] + (Sqrt[b]*Sqrt[c]*x)/Sqrt[a - b*x^2] - (Sqrt[2]*b^(1/4)*Sqrt[c*x])/(a - b*x^2)^(1/4)])/(8*Sqrt[2]*b^(3/4)) - (a*Sqrt[c]*Log[Sqrt[c] + (Sqrt[b]*Sqrt[c]*x)/Sqrt[a - b*x^2] + (Sqrt[2]*b^(1/4)*Sqrt[c*x])/(a - b*x^2)^(1/4)])/(8*Sqrt[2]*b^(3/4))","A",12,9,20,0.4500,1,"{279, 329, 331, 297, 1162, 617, 204, 1165, 628}"
939,1,296,0,0.2747092,"\int \frac{\sqrt[4]{a-b x^2}}{(c x)^{3/2}} \, dx","Int[(a - b*x^2)^(1/4)/(c*x)^(3/2),x]","-\frac{\sqrt[4]{b} \log \left(\frac{\sqrt{b} \sqrt{c} x}{\sqrt{a-b x^2}}-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a-b x^2}}+\sqrt{c}\right)}{2 \sqrt{2} c^{3/2}}+\frac{\sqrt[4]{b} \log \left(\frac{\sqrt{b} \sqrt{c} x}{\sqrt{a-b x^2}}+\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a-b x^2}}+\sqrt{c}\right)}{2 \sqrt{2} c^{3/2}}+\frac{\sqrt[4]{b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a-b x^2}}\right)}{\sqrt{2} c^{3/2}}-\frac{\sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a-b x^2}}+1\right)}{\sqrt{2} c^{3/2}}-\frac{2 \sqrt[4]{a-b x^2}}{c \sqrt{c x}}","-\frac{\sqrt[4]{b} \log \left(\frac{\sqrt{b} \sqrt{c} x}{\sqrt{a-b x^2}}-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a-b x^2}}+\sqrt{c}\right)}{2 \sqrt{2} c^{3/2}}+\frac{\sqrt[4]{b} \log \left(\frac{\sqrt{b} \sqrt{c} x}{\sqrt{a-b x^2}}+\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a-b x^2}}+\sqrt{c}\right)}{2 \sqrt{2} c^{3/2}}+\frac{\sqrt[4]{b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a-b x^2}}\right)}{\sqrt{2} c^{3/2}}-\frac{\sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a-b x^2}}+1\right)}{\sqrt{2} c^{3/2}}-\frac{2 \sqrt[4]{a-b x^2}}{c \sqrt{c x}}",1,"(-2*(a - b*x^2)^(1/4))/(c*Sqrt[c*x]) + (b^(1/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[c*x])/(Sqrt[c]*(a - b*x^2)^(1/4))])/(Sqrt[2]*c^(3/2)) - (b^(1/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[c*x])/(Sqrt[c]*(a - b*x^2)^(1/4))])/(Sqrt[2]*c^(3/2)) - (b^(1/4)*Log[Sqrt[c] + (Sqrt[b]*Sqrt[c]*x)/Sqrt[a - b*x^2] - (Sqrt[2]*b^(1/4)*Sqrt[c*x])/(a - b*x^2)^(1/4)])/(2*Sqrt[2]*c^(3/2)) + (b^(1/4)*Log[Sqrt[c] + (Sqrt[b]*Sqrt[c]*x)/Sqrt[a - b*x^2] + (Sqrt[2]*b^(1/4)*Sqrt[c*x])/(a - b*x^2)^(1/4)])/(2*Sqrt[2]*c^(3/2))","A",12,9,20,0.4500,1,"{277, 329, 331, 297, 1162, 617, 204, 1165, 628}"
940,1,29,0,0.0061529,"\int \frac{\sqrt[4]{a-b x^2}}{(c x)^{7/2}} \, dx","Int[(a - b*x^2)^(1/4)/(c*x)^(7/2),x]","-\frac{2 \left(a-b x^2\right)^{5/4}}{5 a c (c x)^{5/2}}","-\frac{2 \left(a-b x^2\right)^{5/4}}{5 a c (c x)^{5/2}}",1,"(-2*(a - b*x^2)^(5/4))/(5*a*c*(c*x)^(5/2))","A",1,1,20,0.05000,1,"{264}"
941,1,59,0,0.0162985,"\int \frac{\sqrt[4]{a-b x^2}}{(c x)^{11/2}} \, dx","Int[(a - b*x^2)^(1/4)/(c*x)^(11/2),x]","\frac{8 \left(a-b x^2\right)^{9/4}}{45 a^2 c (c x)^{9/2}}-\frac{2 \left(a-b x^2\right)^{5/4}}{5 a c (c x)^{9/2}}","\frac{8 \left(a-b x^2\right)^{9/4}}{45 a^2 c (c x)^{9/2}}-\frac{2 \left(a-b x^2\right)^{5/4}}{5 a c (c x)^{9/2}}",1,"(-2*(a - b*x^2)^(5/4))/(5*a*c*(c*x)^(9/2)) + (8*(a - b*x^2)^(9/4))/(45*a^2*c*(c*x)^(9/2))","A",2,2,20,0.1000,1,"{273, 264}"
942,1,88,0,0.0278238,"\int \frac{\sqrt[4]{a-b x^2}}{(c x)^{15/2}} \, dx","Int[(a - b*x^2)^(1/4)/(c*x)^(15/2),x]","-\frac{64 \left(a-b x^2\right)^{13/4}}{585 a^3 c (c x)^{13/2}}+\frac{16 \left(a-b x^2\right)^{9/4}}{45 a^2 c (c x)^{13/2}}-\frac{2 \left(a-b x^2\right)^{5/4}}{5 a c (c x)^{13/2}}","-\frac{64 \left(a-b x^2\right)^{13/4}}{585 a^3 c (c x)^{13/2}}+\frac{16 \left(a-b x^2\right)^{9/4}}{45 a^2 c (c x)^{13/2}}-\frac{2 \left(a-b x^2\right)^{5/4}}{5 a c (c x)^{13/2}}",1,"(-2*(a - b*x^2)^(5/4))/(5*a*c*(c*x)^(13/2)) + (16*(a - b*x^2)^(9/4))/(45*a^2*c*(c*x)^(13/2)) - (64*(a - b*x^2)^(13/4))/(585*a^3*c*(c*x)^(13/2))","A",3,2,20,0.1000,1,"{273, 264}"
943,1,117,0,0.0402291,"\int \frac{\sqrt[4]{a-b x^2}}{(c x)^{19/2}} \, dx","Int[(a - b*x^2)^(1/4)/(c*x)^(19/2),x]","\frac{256 \left(a-b x^2\right)^{17/4}}{3315 a^4 c (c x)^{17/2}}-\frac{64 \left(a-b x^2\right)^{13/4}}{195 a^3 c (c x)^{17/2}}+\frac{8 \left(a-b x^2\right)^{9/4}}{15 a^2 c (c x)^{17/2}}-\frac{2 \left(a-b x^2\right)^{5/4}}{5 a c (c x)^{17/2}}","\frac{256 \left(a-b x^2\right)^{17/4}}{3315 a^4 c (c x)^{17/2}}-\frac{64 \left(a-b x^2\right)^{13/4}}{195 a^3 c (c x)^{17/2}}+\frac{8 \left(a-b x^2\right)^{9/4}}{15 a^2 c (c x)^{17/2}}-\frac{2 \left(a-b x^2\right)^{5/4}}{5 a c (c x)^{17/2}}",1,"(-2*(a - b*x^2)^(5/4))/(5*a*c*(c*x)^(17/2)) + (8*(a - b*x^2)^(9/4))/(15*a^2*c*(c*x)^(17/2)) - (64*(a - b*x^2)^(13/4))/(195*a^3*c*(c*x)^(17/2)) + (256*(a - b*x^2)^(17/4))/(3315*a^4*c*(c*x)^(17/2))","A",4,2,20,0.1000,1,"{273, 264}"
944,1,117,0,0.0648402,"\int \frac{(c x)^{3/2}}{\sqrt[4]{a+b x^2}} \, dx","Int[(c*x)^(3/2)/(a + b*x^2)^(1/4),x]","-\frac{a c^{3/2} \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a+b x^2}}\right)}{4 b^{5/4}}-\frac{a c^{3/2} \tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a+b x^2}}\right)}{4 b^{5/4}}+\frac{c \sqrt{c x} \left(a+b x^2\right)^{3/4}}{2 b}","-\frac{a c^{3/2} \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a+b x^2}}\right)}{4 b^{5/4}}-\frac{a c^{3/2} \tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a+b x^2}}\right)}{4 b^{5/4}}+\frac{c \sqrt{c x} \left(a+b x^2\right)^{3/4}}{2 b}",1,"(c*Sqrt[c*x]*(a + b*x^2)^(3/4))/(2*b) - (a*c^(3/2)*ArcTan[(b^(1/4)*Sqrt[c*x])/(Sqrt[c]*(a + b*x^2)^(1/4))])/(4*b^(5/4)) - (a*c^(3/2)*ArcTanh[(b^(1/4)*Sqrt[c*x])/(Sqrt[c]*(a + b*x^2)^(1/4))])/(4*b^(5/4))","A",6,6,19,0.3158,1,"{321, 329, 240, 212, 208, 205}"
945,1,83,0,0.0502655,"\int \frac{1}{\sqrt{c x} \sqrt[4]{a+b x^2}} \, dx","Int[1/(Sqrt[c*x]*(a + b*x^2)^(1/4)),x]","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a+b x^2}}\right)}{\sqrt[4]{b} \sqrt{c}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a+b x^2}}\right)}{\sqrt[4]{b} \sqrt{c}}","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a+b x^2}}\right)}{\sqrt[4]{b} \sqrt{c}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a+b x^2}}\right)}{\sqrt[4]{b} \sqrt{c}}",1,"ArcTan[(b^(1/4)*Sqrt[c*x])/(Sqrt[c]*(a + b*x^2)^(1/4))]/(b^(1/4)*Sqrt[c]) + ArcTanh[(b^(1/4)*Sqrt[c*x])/(Sqrt[c]*(a + b*x^2)^(1/4))]/(b^(1/4)*Sqrt[c])","A",5,5,19,0.2632,1,"{329, 240, 212, 208, 205}"
946,1,28,0,0.005981,"\int \frac{1}{(c x)^{5/2} \sqrt[4]{a+b x^2}} \, dx","Int[1/((c*x)^(5/2)*(a + b*x^2)^(1/4)),x]","-\frac{2 \left(a+b x^2\right)^{3/4}}{3 a c (c x)^{3/2}}","-\frac{2 \left(a+b x^2\right)^{3/4}}{3 a c (c x)^{3/2}}",1,"(-2*(a + b*x^2)^(3/4))/(3*a*c*(c*x)^(3/2))","A",1,1,19,0.05263,1,"{264}"
947,1,57,0,0.0158406,"\int \frac{1}{(c x)^{9/2} \sqrt[4]{a+b x^2}} \, dx","Int[1/((c*x)^(9/2)*(a + b*x^2)^(1/4)),x]","\frac{8 \left(a+b x^2\right)^{7/4}}{21 a^2 c (c x)^{7/2}}-\frac{2 \left(a+b x^2\right)^{3/4}}{3 a c (c x)^{7/2}}","\frac{8 \left(a+b x^2\right)^{7/4}}{21 a^2 c (c x)^{7/2}}-\frac{2 \left(a+b x^2\right)^{3/4}}{3 a c (c x)^{7/2}}",1,"(-2*(a + b*x^2)^(3/4))/(3*a*c*(c*x)^(7/2)) + (8*(a + b*x^2)^(7/4))/(21*a^2*c*(c*x)^(7/2))","A",2,2,19,0.1053,1,"{273, 264}"
948,1,85,0,0.0264572,"\int \frac{1}{(c x)^{13/2} \sqrt[4]{a+b x^2}} \, dx","Int[1/((c*x)^(13/2)*(a + b*x^2)^(1/4)),x]","-\frac{64 \left(a+b x^2\right)^{11/4}}{231 a^3 c (c x)^{11/2}}+\frac{16 \left(a+b x^2\right)^{7/4}}{21 a^2 c (c x)^{11/2}}-\frac{2 \left(a+b x^2\right)^{3/4}}{3 a c (c x)^{11/2}}","-\frac{64 \left(a+b x^2\right)^{11/4}}{231 a^3 c (c x)^{11/2}}+\frac{16 \left(a+b x^2\right)^{7/4}}{21 a^2 c (c x)^{11/2}}-\frac{2 \left(a+b x^2\right)^{3/4}}{3 a c (c x)^{11/2}}",1,"(-2*(a + b*x^2)^(3/4))/(3*a*c*(c*x)^(11/2)) + (16*(a + b*x^2)^(7/4))/(21*a^2*c*(c*x)^(11/2)) - (64*(a + b*x^2)^(11/4))/(231*a^3*c*(c*x)^(11/2))","A",3,2,19,0.1053,1,"{273, 264}"
949,1,156,0,0.0671365,"\int \frac{(c x)^{9/2}}{\sqrt[4]{a+b x^2}} \, dx","Int[(c*x)^(9/2)/(a + b*x^2)^(1/4),x]","\frac{7 a^2 c^4 x \sqrt{c x}}{20 b^2 \sqrt[4]{a+b x^2}}+\frac{7 a^{5/2} c^4 \sqrt{c x} \sqrt[4]{\frac{a}{b x^2}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{20 b^{5/2} \sqrt[4]{a+b x^2}}-\frac{7 a c^3 (c x)^{3/2} \left(a+b x^2\right)^{3/4}}{30 b^2}+\frac{c (c x)^{7/2} \left(a+b x^2\right)^{3/4}}{5 b}","\frac{7 a^2 c^4 x \sqrt{c x}}{20 b^2 \sqrt[4]{a+b x^2}}+\frac{7 a^{5/2} c^4 \sqrt{c x} \sqrt[4]{\frac{a}{b x^2}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{20 b^{5/2} \sqrt[4]{a+b x^2}}-\frac{7 a c^3 (c x)^{3/2} \left(a+b x^2\right)^{3/4}}{30 b^2}+\frac{c (c x)^{7/2} \left(a+b x^2\right)^{3/4}}{5 b}",1,"(7*a^2*c^4*x*Sqrt[c*x])/(20*b^2*(a + b*x^2)^(1/4)) - (7*a*c^3*(c*x)^(3/2)*(a + b*x^2)^(3/4))/(30*b^2) + (c*(c*x)^(7/2)*(a + b*x^2)^(3/4))/(5*b) + (7*a^(5/2)*c^4*(1 + a/(b*x^2))^(1/4)*Sqrt[c*x]*EllipticE[ArcCot[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(20*b^(5/2)*(a + b*x^2)^(1/4))","A",6,5,19,0.2632,1,"{321, 314, 284, 335, 196}"
950,1,125,0,0.0465621,"\int \frac{(c x)^{5/2}}{\sqrt[4]{a+b x^2}} \, dx","Int[(c*x)^(5/2)/(a + b*x^2)^(1/4),x]","-\frac{a^{3/2} c^2 \sqrt{c x} \sqrt[4]{\frac{a}{b x^2}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{2 b^{3/2} \sqrt[4]{a+b x^2}}-\frac{a c^2 x \sqrt{c x}}{2 b \sqrt[4]{a+b x^2}}+\frac{c (c x)^{3/2} \left(a+b x^2\right)^{3/4}}{3 b}","-\frac{a^{3/2} c^2 \sqrt{c x} \sqrt[4]{\frac{a}{b x^2}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{2 b^{3/2} \sqrt[4]{a+b x^2}}-\frac{a c^2 x \sqrt{c x}}{2 b \sqrt[4]{a+b x^2}}+\frac{c (c x)^{3/2} \left(a+b x^2\right)^{3/4}}{3 b}",1,"-(a*c^2*x*Sqrt[c*x])/(2*b*(a + b*x^2)^(1/4)) + (c*(c*x)^(3/2)*(a + b*x^2)^(3/4))/(3*b) - (a^(3/2)*c^2*(1 + a/(b*x^2))^(1/4)*Sqrt[c*x]*EllipticE[ArcCot[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(2*b^(3/2)*(a + b*x^2)^(1/4))","A",5,5,19,0.2632,1,"{321, 314, 284, 335, 196}"
951,1,83,0,0.0324452,"\int \frac{\sqrt{c x}}{\sqrt[4]{a+b x^2}} \, dx","Int[Sqrt[c*x]/(a + b*x^2)^(1/4),x]","\frac{x \sqrt{c x}}{\sqrt[4]{a+b x^2}}+\frac{\sqrt{a} \sqrt{c x} \sqrt[4]{\frac{a}{b x^2}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{\sqrt{b} \sqrt[4]{a+b x^2}}","\frac{x \sqrt{c x}}{\sqrt[4]{a+b x^2}}+\frac{\sqrt{a} \sqrt{c x} \sqrt[4]{\frac{a}{b x^2}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{\sqrt{b} \sqrt[4]{a+b x^2}}",1,"(x*Sqrt[c*x])/(a + b*x^2)^(1/4) + (Sqrt[a]*(1 + a/(b*x^2))^(1/4)*Sqrt[c*x]*EllipticE[ArcCot[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(Sqrt[b]*(a + b*x^2)^(1/4))","A",4,4,19,0.2105,1,"{314, 284, 335, 196}"
952,1,90,0,0.0345417,"\int \frac{1}{(c x)^{3/2} \sqrt[4]{a+b x^2}} \, dx","Int[1/((c*x)^(3/2)*(a + b*x^2)^(1/4)),x]","\frac{2 \sqrt{b} \sqrt{c x} \sqrt[4]{\frac{a}{b x^2}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{\sqrt{a} c^2 \sqrt[4]{a+b x^2}}-\frac{2}{c \sqrt{c x} \sqrt[4]{a+b x^2}}","\frac{2 \sqrt{b} \sqrt{c x} \sqrt[4]{\frac{a}{b x^2}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{\sqrt{a} c^2 \sqrt[4]{a+b x^2}}-\frac{2}{c \sqrt{c x} \sqrt[4]{a+b x^2}}",1,"-2/(c*Sqrt[c*x]*(a + b*x^2)^(1/4)) + (2*Sqrt[b]*(1 + a/(b*x^2))^(1/4)*Sqrt[c*x]*EllipticE[ArcCot[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(Sqrt[a]*c^2*(a + b*x^2)^(1/4))","A",4,4,19,0.2105,1,"{316, 284, 335, 196}"
953,1,126,0,0.0490704,"\int \frac{1}{(c x)^{7/2} \sqrt[4]{a+b x^2}} \, dx","Int[1/((c*x)^(7/2)*(a + b*x^2)^(1/4)),x]","-\frac{4 b^{3/2} \sqrt{c x} \sqrt[4]{\frac{a}{b x^2}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{5 a^{3/2} c^4 \sqrt[4]{a+b x^2}}+\frac{4 b}{5 a c^3 \sqrt{c x} \sqrt[4]{a+b x^2}}-\frac{2 \left(a+b x^2\right)^{3/4}}{5 a c (c x)^{5/2}}","-\frac{4 b^{3/2} \sqrt{c x} \sqrt[4]{\frac{a}{b x^2}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{5 a^{3/2} c^4 \sqrt[4]{a+b x^2}}+\frac{4 b}{5 a c^3 \sqrt{c x} \sqrt[4]{a+b x^2}}-\frac{2 \left(a+b x^2\right)^{3/4}}{5 a c (c x)^{5/2}}",1,"(4*b)/(5*a*c^3*Sqrt[c*x]*(a + b*x^2)^(1/4)) - (2*(a + b*x^2)^(3/4))/(5*a*c*(c*x)^(5/2)) - (4*b^(3/2)*(1 + a/(b*x^2))^(1/4)*Sqrt[c*x]*EllipticE[ArcCot[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(5*a^(3/2)*c^4*(a + b*x^2)^(1/4))","A",5,5,19,0.2632,1,"{325, 316, 284, 335, 196}"
954,1,157,0,0.0678214,"\int \frac{1}{(c x)^{11/2} \sqrt[4]{a+b x^2}} \, dx","Int[1/((c*x)^(11/2)*(a + b*x^2)^(1/4)),x]","-\frac{8 b^2}{15 a^2 c^5 \sqrt{c x} \sqrt[4]{a+b x^2}}+\frac{8 b^{5/2} \sqrt{c x} \sqrt[4]{\frac{a}{b x^2}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{15 a^{5/2} c^6 \sqrt[4]{a+b x^2}}+\frac{4 b \left(a+b x^2\right)^{3/4}}{15 a^2 c^3 (c x)^{5/2}}-\frac{2 \left(a+b x^2\right)^{3/4}}{9 a c (c x)^{9/2}}","-\frac{8 b^2}{15 a^2 c^5 \sqrt{c x} \sqrt[4]{a+b x^2}}+\frac{8 b^{5/2} \sqrt{c x} \sqrt[4]{\frac{a}{b x^2}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{15 a^{5/2} c^6 \sqrt[4]{a+b x^2}}+\frac{4 b \left(a+b x^2\right)^{3/4}}{15 a^2 c^3 (c x)^{5/2}}-\frac{2 \left(a+b x^2\right)^{3/4}}{9 a c (c x)^{9/2}}",1,"(-8*b^2)/(15*a^2*c^5*Sqrt[c*x]*(a + b*x^2)^(1/4)) - (2*(a + b*x^2)^(3/4))/(9*a*c*(c*x)^(9/2)) + (4*b*(a + b*x^2)^(3/4))/(15*a^2*c^3*(c*x)^(5/2)) + (8*b^(5/2)*(1 + a/(b*x^2))^(1/4)*Sqrt[c*x]*EllipticE[ArcCot[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(15*a^(5/2)*c^6*(a + b*x^2)^(1/4))","A",6,5,19,0.2632,1,"{325, 316, 284, 335, 196}"
955,1,308,0,0.2651208,"\int \frac{(c x)^{3/2}}{\sqrt[4]{a-b x^2}} \, dx","Int[(c*x)^(3/2)/(a - b*x^2)^(1/4),x]","-\frac{a c^{3/2} \log \left(\frac{\sqrt{b} \sqrt{c} x}{\sqrt{a-b x^2}}-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a-b x^2}}+\sqrt{c}\right)}{8 \sqrt{2} b^{5/4}}+\frac{a c^{3/2} \log \left(\frac{\sqrt{b} \sqrt{c} x}{\sqrt{a-b x^2}}+\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a-b x^2}}+\sqrt{c}\right)}{8 \sqrt{2} b^{5/4}}-\frac{a c^{3/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a-b x^2}}\right)}{4 \sqrt{2} b^{5/4}}+\frac{a c^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a-b x^2}}+1\right)}{4 \sqrt{2} b^{5/4}}-\frac{c \sqrt{c x} \left(a-b x^2\right)^{3/4}}{2 b}","-\frac{a c^{3/2} \log \left(\frac{\sqrt{b} \sqrt{c} x}{\sqrt{a-b x^2}}-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a-b x^2}}+\sqrt{c}\right)}{8 \sqrt{2} b^{5/4}}+\frac{a c^{3/2} \log \left(\frac{\sqrt{b} \sqrt{c} x}{\sqrt{a-b x^2}}+\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a-b x^2}}+\sqrt{c}\right)}{8 \sqrt{2} b^{5/4}}-\frac{a c^{3/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a-b x^2}}\right)}{4 \sqrt{2} b^{5/4}}+\frac{a c^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a-b x^2}}+1\right)}{4 \sqrt{2} b^{5/4}}-\frac{c \sqrt{c x} \left(a-b x^2\right)^{3/4}}{2 b}",1,"-(c*Sqrt[c*x]*(a - b*x^2)^(3/4))/(2*b) - (a*c^(3/2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[c*x])/(Sqrt[c]*(a - b*x^2)^(1/4))])/(4*Sqrt[2]*b^(5/4)) + (a*c^(3/2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[c*x])/(Sqrt[c]*(a - b*x^2)^(1/4))])/(4*Sqrt[2]*b^(5/4)) - (a*c^(3/2)*Log[Sqrt[c] + (Sqrt[b]*Sqrt[c]*x)/Sqrt[a - b*x^2] - (Sqrt[2]*b^(1/4)*Sqrt[c*x])/(a - b*x^2)^(1/4)])/(8*Sqrt[2]*b^(5/4)) + (a*c^(3/2)*Log[Sqrt[c] + (Sqrt[b]*Sqrt[c]*x)/Sqrt[a - b*x^2] + (Sqrt[2]*b^(1/4)*Sqrt[c*x])/(a - b*x^2)^(1/4)])/(8*Sqrt[2]*b^(5/4))","A",12,9,20,0.4500,1,"{321, 329, 240, 211, 1165, 628, 1162, 617, 204}"
956,1,272,0,0.227996,"\int \frac{1}{\sqrt{c x} \sqrt[4]{a-b x^2}} \, dx","Int[1/(Sqrt[c*x]*(a - b*x^2)^(1/4)),x]","-\frac{\log \left(\frac{\sqrt{b} \sqrt{c} x}{\sqrt{a-b x^2}}-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a-b x^2}}+\sqrt{c}\right)}{2 \sqrt{2} \sqrt[4]{b} \sqrt{c}}+\frac{\log \left(\frac{\sqrt{b} \sqrt{c} x}{\sqrt{a-b x^2}}+\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a-b x^2}}+\sqrt{c}\right)}{2 \sqrt{2} \sqrt[4]{b} \sqrt{c}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a-b x^2}}\right)}{\sqrt{2} \sqrt[4]{b} \sqrt{c}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a-b x^2}}+1\right)}{\sqrt{2} \sqrt[4]{b} \sqrt{c}}","-\frac{\log \left(\frac{\sqrt{b} \sqrt{c} x}{\sqrt{a-b x^2}}-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a-b x^2}}+\sqrt{c}\right)}{2 \sqrt{2} \sqrt[4]{b} \sqrt{c}}+\frac{\log \left(\frac{\sqrt{b} \sqrt{c} x}{\sqrt{a-b x^2}}+\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a-b x^2}}+\sqrt{c}\right)}{2 \sqrt{2} \sqrt[4]{b} \sqrt{c}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a-b x^2}}\right)}{\sqrt{2} \sqrt[4]{b} \sqrt{c}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a-b x^2}}+1\right)}{\sqrt{2} \sqrt[4]{b} \sqrt{c}}",1,"-(ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[c*x])/(Sqrt[c]*(a - b*x^2)^(1/4))]/(Sqrt[2]*b^(1/4)*Sqrt[c])) + ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[c*x])/(Sqrt[c]*(a - b*x^2)^(1/4))]/(Sqrt[2]*b^(1/4)*Sqrt[c]) - Log[Sqrt[c] + (Sqrt[b]*Sqrt[c]*x)/Sqrt[a - b*x^2] - (Sqrt[2]*b^(1/4)*Sqrt[c*x])/(a - b*x^2)^(1/4)]/(2*Sqrt[2]*b^(1/4)*Sqrt[c]) + Log[Sqrt[c] + (Sqrt[b]*Sqrt[c]*x)/Sqrt[a - b*x^2] + (Sqrt[2]*b^(1/4)*Sqrt[c*x])/(a - b*x^2)^(1/4)]/(2*Sqrt[2]*b^(1/4)*Sqrt[c])","A",11,8,20,0.4000,1,"{329, 240, 211, 1165, 628, 1162, 617, 204}"
957,1,29,0,0.0060532,"\int \frac{1}{(c x)^{5/2} \sqrt[4]{a-b x^2}} \, dx","Int[1/((c*x)^(5/2)*(a - b*x^2)^(1/4)),x]","-\frac{2 \left(a-b x^2\right)^{3/4}}{3 a c (c x)^{3/2}}","-\frac{2 \left(a-b x^2\right)^{3/4}}{3 a c (c x)^{3/2}}",1,"(-2*(a - b*x^2)^(3/4))/(3*a*c*(c*x)^(3/2))","A",1,1,20,0.05000,1,"{264}"
958,1,59,0,0.0153705,"\int \frac{1}{(c x)^{9/2} \sqrt[4]{a-b x^2}} \, dx","Int[1/((c*x)^(9/2)*(a - b*x^2)^(1/4)),x]","\frac{8 \left(a-b x^2\right)^{7/4}}{21 a^2 c (c x)^{7/2}}-\frac{2 \left(a-b x^2\right)^{3/4}}{3 a c (c x)^{7/2}}","\frac{8 \left(a-b x^2\right)^{7/4}}{21 a^2 c (c x)^{7/2}}-\frac{2 \left(a-b x^2\right)^{3/4}}{3 a c (c x)^{7/2}}",1,"(-2*(a - b*x^2)^(3/4))/(3*a*c*(c*x)^(7/2)) + (8*(a - b*x^2)^(7/4))/(21*a^2*c*(c*x)^(7/2))","A",2,2,20,0.1000,1,"{273, 264}"
959,1,88,0,0.0269606,"\int \frac{1}{(c x)^{13/2} \sqrt[4]{a-b x^2}} \, dx","Int[1/((c*x)^(13/2)*(a - b*x^2)^(1/4)),x]","-\frac{64 \left(a-b x^2\right)^{11/4}}{231 a^3 c (c x)^{11/2}}+\frac{16 \left(a-b x^2\right)^{7/4}}{21 a^2 c (c x)^{11/2}}-\frac{2 \left(a-b x^2\right)^{3/4}}{3 a c (c x)^{11/2}}","-\frac{64 \left(a-b x^2\right)^{11/4}}{231 a^3 c (c x)^{11/2}}+\frac{16 \left(a-b x^2\right)^{7/4}}{21 a^2 c (c x)^{11/2}}-\frac{2 \left(a-b x^2\right)^{3/4}}{3 a c (c x)^{11/2}}",1,"(-2*(a - b*x^2)^(3/4))/(3*a*c*(c*x)^(11/2)) + (16*(a - b*x^2)^(7/4))/(21*a^2*c*(c*x)^(11/2)) - (64*(a - b*x^2)^(11/4))/(231*a^3*c*(c*x)^(11/2))","A",3,2,20,0.1000,1,"{273, 264}"
960,1,128,0,0.0494462,"\int \frac{(c x)^{5/2}}{\sqrt[4]{a-b x^2}} \, dx","Int[(c*x)^(5/2)/(a - b*x^2)^(1/4),x]","\frac{a^{3/2} c^2 \sqrt{c x} \sqrt[4]{1-\frac{a}{b x^2}} E\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{2 b^{3/2} \sqrt[4]{a-b x^2}}-\frac{a c^3 \left(a-b x^2\right)^{3/4}}{2 b^2 \sqrt{c x}}-\frac{c (c x)^{3/2} \left(a-b x^2\right)^{3/4}}{3 b}","\frac{a^{3/2} c^2 \sqrt{c x} \sqrt[4]{1-\frac{a}{b x^2}} E\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{2 b^{3/2} \sqrt[4]{a-b x^2}}-\frac{a c^3 \left(a-b x^2\right)^{3/4}}{2 b^2 \sqrt{c x}}-\frac{c (c x)^{3/2} \left(a-b x^2\right)^{3/4}}{3 b}",1,"-(a*c^3*(a - b*x^2)^(3/4))/(2*b^2*Sqrt[c*x]) - (c*(c*x)^(3/2)*(a - b*x^2)^(3/4))/(3*b) + (a^(3/2)*c^2*(1 - a/(b*x^2))^(1/4)*Sqrt[c*x]*EllipticE[ArcCsc[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(2*b^(3/2)*(a - b*x^2)^(1/4))","A",5,5,20,0.2500,1,"{321, 315, 317, 335, 228}"
961,1,90,0,0.0357489,"\int \frac{\sqrt{c x}}{\sqrt[4]{a-b x^2}} \, dx","Int[Sqrt[c*x]/(a - b*x^2)^(1/4),x]","\frac{\sqrt{a} \sqrt{c x} \sqrt[4]{1-\frac{a}{b x^2}} E\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{\sqrt{b} \sqrt[4]{a-b x^2}}-\frac{c \left(a-b x^2\right)^{3/4}}{b \sqrt{c x}}","\frac{\sqrt{a} \sqrt{c x} \sqrt[4]{1-\frac{a}{b x^2}} E\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{\sqrt{b} \sqrt[4]{a-b x^2}}-\frac{c \left(a-b x^2\right)^{3/4}}{b \sqrt{c x}}",1,"-((c*(a - b*x^2)^(3/4))/(b*Sqrt[c*x])) + (Sqrt[a]*(1 - a/(b*x^2))^(1/4)*Sqrt[c*x]*EllipticE[ArcCsc[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(Sqrt[b]*(a - b*x^2)^(1/4))","A",4,4,20,0.2000,1,"{315, 317, 335, 228}"
962,1,68,0,0.0235431,"\int \frac{1}{(c x)^{3/2} \sqrt[4]{a-b x^2}} \, dx","Int[1/((c*x)^(3/2)*(a - b*x^2)^(1/4)),x]","-\frac{2 \sqrt{b} \sqrt{c x} \sqrt[4]{1-\frac{a}{b x^2}} E\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{\sqrt{a} c^2 \sqrt[4]{a-b x^2}}","-\frac{2 \sqrt{b} \sqrt{c x} \sqrt[4]{1-\frac{a}{b x^2}} E\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{\sqrt{a} c^2 \sqrt[4]{a-b x^2}}",1,"(-2*Sqrt[b]*(1 - a/(b*x^2))^(1/4)*Sqrt[c*x]*EllipticE[ArcCsc[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(Sqrt[a]*c^2*(a - b*x^2)^(1/4))","A",3,3,20,0.1500,1,"{317, 335, 228}"
963,1,100,0,0.0358012,"\int \frac{1}{(c x)^{7/2} \sqrt[4]{a-b x^2}} \, dx","Int[1/((c*x)^(7/2)*(a - b*x^2)^(1/4)),x]","-\frac{4 b^{3/2} \sqrt{c x} \sqrt[4]{1-\frac{a}{b x^2}} E\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{5 a^{3/2} c^4 \sqrt[4]{a-b x^2}}-\frac{2 \left(a-b x^2\right)^{3/4}}{5 a c (c x)^{5/2}}","-\frac{4 b^{3/2} \sqrt{c x} \sqrt[4]{1-\frac{a}{b x^2}} E\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{5 a^{3/2} c^4 \sqrt[4]{a-b x^2}}-\frac{2 \left(a-b x^2\right)^{3/4}}{5 a c (c x)^{5/2}}",1,"(-2*(a - b*x^2)^(3/4))/(5*a*c*(c*x)^(5/2)) - (4*b^(3/2)*(1 - a/(b*x^2))^(1/4)*Sqrt[c*x]*EllipticE[ArcCsc[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(5*a^(3/2)*c^4*(a - b*x^2)^(1/4))","A",4,4,20,0.2000,1,"{325, 317, 335, 228}"
964,1,130,0,0.051073,"\int \frac{1}{(c x)^{11/2} \sqrt[4]{a-b x^2}} \, dx","Int[1/((c*x)^(11/2)*(a - b*x^2)^(1/4)),x]","-\frac{8 b^{5/2} \sqrt{c x} \sqrt[4]{1-\frac{a}{b x^2}} E\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{15 a^{5/2} c^6 \sqrt[4]{a-b x^2}}-\frac{4 b \left(a-b x^2\right)^{3/4}}{15 a^2 c^3 (c x)^{5/2}}-\frac{2 \left(a-b x^2\right)^{3/4}}{9 a c (c x)^{9/2}}","-\frac{8 b^{5/2} \sqrt{c x} \sqrt[4]{1-\frac{a}{b x^2}} E\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{15 a^{5/2} c^6 \sqrt[4]{a-b x^2}}-\frac{4 b \left(a-b x^2\right)^{3/4}}{15 a^2 c^3 (c x)^{5/2}}-\frac{2 \left(a-b x^2\right)^{3/4}}{9 a c (c x)^{9/2}}",1,"(-2*(a - b*x^2)^(3/4))/(9*a*c*(c*x)^(9/2)) - (4*b*(a - b*x^2)^(3/4))/(15*a^2*c^3*(c*x)^(5/2)) - (8*b^(5/2)*(1 - a/(b*x^2))^(1/4)*Sqrt[c*x]*EllipticE[ArcCsc[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(15*a^(5/2)*c^6*(a - b*x^2)^(1/4))","A",5,4,20,0.2000,1,"{325, 317, 335, 228}"
965,1,86,0,0.0696213,"\int \frac{(c x)^{3/2}}{\left(a+b x^2\right)^{3/4}} \, dx","Int[(c*x)^(3/2)/(a + b*x^2)^(3/4),x]","\frac{c \sqrt{c x} \sqrt[4]{a+b x^2}}{b}+\frac{\sqrt{a} (c x)^{3/2} \left(\frac{a}{b x^2}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{\sqrt{b} \left(a+b x^2\right)^{3/4}}","\frac{c \sqrt{c x} \sqrt[4]{a+b x^2}}{b}+\frac{\sqrt{a} (c x)^{3/2} \left(\frac{a}{b x^2}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{\sqrt{b} \left(a+b x^2\right)^{3/4}}",1,"(c*Sqrt[c*x]*(a + b*x^2)^(1/4))/b + (Sqrt[a]*(1 + a/(b*x^2))^(3/4)*(c*x)^(3/2)*EllipticF[ArcCot[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(Sqrt[b]*(a + b*x^2)^(3/4))","A",6,6,19,0.3158,1,"{321, 329, 237, 335, 275, 231}"
966,1,66,0,0.0629385,"\int \frac{1}{\sqrt{c x} \left(a+b x^2\right)^{3/4}} \, dx","Int[1/(Sqrt[c*x]*(a + b*x^2)^(3/4)),x]","-\frac{2 \sqrt{b} (c x)^{3/2} \left(\frac{a}{b x^2}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{\sqrt{a} c^2 \left(a+b x^2\right)^{3/4}}","-\frac{2 \sqrt{b} (c x)^{3/2} \left(\frac{a}{b x^2}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{\sqrt{a} c^2 \left(a+b x^2\right)^{3/4}}",1,"(-2*Sqrt[b]*(1 + a/(b*x^2))^(3/4)*(c*x)^(3/2)*EllipticF[ArcCot[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(Sqrt[a]*c^2*(a + b*x^2)^(3/4))","A",5,5,19,0.2632,1,"{329, 237, 335, 275, 231}"
967,1,97,0,0.0734007,"\int \frac{1}{(c x)^{5/2} \left(a+b x^2\right)^{3/4}} \, dx","Int[1/((c*x)^(5/2)*(a + b*x^2)^(3/4)),x]","\frac{4 b^{3/2} (c x)^{3/2} \left(\frac{a}{b x^2}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{3 a^{3/2} c^4 \left(a+b x^2\right)^{3/4}}-\frac{2 \sqrt[4]{a+b x^2}}{3 a c (c x)^{3/2}}","\frac{4 b^{3/2} (c x)^{3/2} \left(\frac{a}{b x^2}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{3 a^{3/2} c^4 \left(a+b x^2\right)^{3/4}}-\frac{2 \sqrt[4]{a+b x^2}}{3 a c (c x)^{3/2}}",1,"(-2*(a + b*x^2)^(1/4))/(3*a*c*(c*x)^(3/2)) + (4*b^(3/2)*(1 + a/(b*x^2))^(3/4)*(c*x)^(3/2)*EllipticF[ArcCot[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(3*a^(3/2)*c^4*(a + b*x^2)^(3/4))","A",6,6,19,0.3158,1,"{325, 329, 237, 335, 275, 231}"
968,1,126,0,0.0876074,"\int \frac{1}{(c x)^{9/2} \left(a+b x^2\right)^{3/4}} \, dx","Int[1/((c*x)^(9/2)*(a + b*x^2)^(3/4)),x]","-\frac{8 b^{5/2} (c x)^{3/2} \left(\frac{a}{b x^2}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{7 a^{5/2} c^6 \left(a+b x^2\right)^{3/4}}+\frac{4 b \sqrt[4]{a+b x^2}}{7 a^2 c^3 (c x)^{3/2}}-\frac{2 \sqrt[4]{a+b x^2}}{7 a c (c x)^{7/2}}","-\frac{8 b^{5/2} (c x)^{3/2} \left(\frac{a}{b x^2}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{7 a^{5/2} c^6 \left(a+b x^2\right)^{3/4}}+\frac{4 b \sqrt[4]{a+b x^2}}{7 a^2 c^3 (c x)^{3/2}}-\frac{2 \sqrt[4]{a+b x^2}}{7 a c (c x)^{7/2}}",1,"(-2*(a + b*x^2)^(1/4))/(7*a*c*(c*x)^(7/2)) + (4*b*(a + b*x^2)^(1/4))/(7*a^2*c^3*(c*x)^(3/2)) - (8*b^(5/2)*(1 + a/(b*x^2))^(3/4)*(c*x)^(3/2)*EllipticF[ArcCot[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(7*a^(5/2)*c^6*(a + b*x^2)^(3/4))","A",7,6,19,0.3158,1,"{325, 329, 237, 335, 275, 231}"
969,1,157,0,0.1074421,"\int \frac{1}{(c x)^{13/2} \left(a+b x^2\right)^{3/4}} \, dx","Int[1/((c*x)^(13/2)*(a + b*x^2)^(3/4)),x]","-\frac{40 b^2 \sqrt[4]{a+b x^2}}{77 a^3 c^5 (c x)^{3/2}}+\frac{80 b^{7/2} (c x)^{3/2} \left(\frac{a}{b x^2}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{77 a^{7/2} c^8 \left(a+b x^2\right)^{3/4}}+\frac{20 b \sqrt[4]{a+b x^2}}{77 a^2 c^3 (c x)^{7/2}}-\frac{2 \sqrt[4]{a+b x^2}}{11 a c (c x)^{11/2}}","-\frac{40 b^2 \sqrt[4]{a+b x^2}}{77 a^3 c^5 (c x)^{3/2}}+\frac{80 b^{7/2} (c x)^{3/2} \left(\frac{a}{b x^2}+1\right)^{3/4} F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{77 a^{7/2} c^8 \left(a+b x^2\right)^{3/4}}+\frac{20 b \sqrt[4]{a+b x^2}}{77 a^2 c^3 (c x)^{7/2}}-\frac{2 \sqrt[4]{a+b x^2}}{11 a c (c x)^{11/2}}",1,"(-2*(a + b*x^2)^(1/4))/(11*a*c*(c*x)^(11/2)) + (20*b*(a + b*x^2)^(1/4))/(77*a^2*c^3*(c*x)^(7/2)) - (40*b^2*(a + b*x^2)^(1/4))/(77*a^3*c^5*(c*x)^(3/2)) + (80*b^(7/2)*(1 + a/(b*x^2))^(3/4)*(c*x)^(3/2)*EllipticF[ArcCot[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(77*a^(7/2)*c^8*(a + b*x^2)^(3/4))","A",8,6,19,0.3158,1,"{325, 329, 237, 335, 275, 231}"
970,1,117,0,0.0668808,"\int \frac{(c x)^{5/2}}{\left(a+b x^2\right)^{3/4}} \, dx","Int[(c*x)^(5/2)/(a + b*x^2)^(3/4),x]","\frac{3 a c^{5/2} \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a+b x^2}}\right)}{4 b^{7/4}}-\frac{3 a c^{5/2} \tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a+b x^2}}\right)}{4 b^{7/4}}+\frac{c (c x)^{3/2} \sqrt[4]{a+b x^2}}{2 b}","\frac{3 a c^{5/2} \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a+b x^2}}\right)}{4 b^{7/4}}-\frac{3 a c^{5/2} \tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a+b x^2}}\right)}{4 b^{7/4}}+\frac{c (c x)^{3/2} \sqrt[4]{a+b x^2}}{2 b}",1,"(c*(c*x)^(3/2)*(a + b*x^2)^(1/4))/(2*b) + (3*a*c^(5/2)*ArcTan[(b^(1/4)*Sqrt[c*x])/(Sqrt[c]*(a + b*x^2)^(1/4))])/(4*b^(7/4)) - (3*a*c^(5/2)*ArcTanh[(b^(1/4)*Sqrt[c*x])/(Sqrt[c]*(a + b*x^2)^(1/4))])/(4*b^(7/4))","A",6,6,19,0.3158,1,"{321, 329, 331, 298, 205, 208}"
971,1,84,0,0.0557165,"\int \frac{\sqrt{c x}}{\left(a+b x^2\right)^{3/4}} \, dx","Int[Sqrt[c*x]/(a + b*x^2)^(3/4),x]","\frac{\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a+b x^2}}\right)}{b^{3/4}}-\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a+b x^2}}\right)}{b^{3/4}}","\frac{\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a+b x^2}}\right)}{b^{3/4}}-\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a+b x^2}}\right)}{b^{3/4}}",1,"-((Sqrt[c]*ArcTan[(b^(1/4)*Sqrt[c*x])/(Sqrt[c]*(a + b*x^2)^(1/4))])/b^(3/4)) + (Sqrt[c]*ArcTanh[(b^(1/4)*Sqrt[c*x])/(Sqrt[c]*(a + b*x^2)^(1/4))])/b^(3/4)","A",5,5,19,0.2632,1,"{329, 331, 298, 205, 208}"
972,1,26,0,0.0059991,"\int \frac{1}{(c x)^{3/2} \left(a+b x^2\right)^{3/4}} \, dx","Int[1/((c*x)^(3/2)*(a + b*x^2)^(3/4)),x]","-\frac{2 \sqrt[4]{a+b x^2}}{a c \sqrt{c x}}","-\frac{2 \sqrt[4]{a+b x^2}}{a c \sqrt{c x}}",1,"(-2*(a + b*x^2)^(1/4))/(a*c*Sqrt[c*x])","A",1,1,19,0.05263,1,"{264}"
973,1,55,0,0.0143003,"\int \frac{1}{(c x)^{7/2} \left(a+b x^2\right)^{3/4}} \, dx","Int[1/((c*x)^(7/2)*(a + b*x^2)^(3/4)),x]","\frac{8 \left(a+b x^2\right)^{5/4}}{5 a^2 c (c x)^{5/2}}-\frac{2 \sqrt[4]{a+b x^2}}{a c (c x)^{5/2}}","\frac{8 \left(a+b x^2\right)^{5/4}}{5 a^2 c (c x)^{5/2}}-\frac{2 \sqrt[4]{a+b x^2}}{a c (c x)^{5/2}}",1,"(-2*(a + b*x^2)^(1/4))/(a*c*(c*x)^(5/2)) + (8*(a + b*x^2)^(5/4))/(5*a^2*c*(c*x)^(5/2))","A",2,2,19,0.1053,1,"{273, 264}"
974,1,83,0,0.024621,"\int \frac{1}{(c x)^{11/2} \left(a+b x^2\right)^{3/4}} \, dx","Int[1/((c*x)^(11/2)*(a + b*x^2)^(3/4)),x]","-\frac{64 \left(a+b x^2\right)^{9/4}}{45 a^3 c (c x)^{9/2}}+\frac{16 \left(a+b x^2\right)^{5/4}}{5 a^2 c (c x)^{9/2}}-\frac{2 \sqrt[4]{a+b x^2}}{a c (c x)^{9/2}}","-\frac{64 \left(a+b x^2\right)^{9/4}}{45 a^3 c (c x)^{9/2}}+\frac{16 \left(a+b x^2\right)^{5/4}}{5 a^2 c (c x)^{9/2}}-\frac{2 \sqrt[4]{a+b x^2}}{a c (c x)^{9/2}}",1,"(-2*(a + b*x^2)^(1/4))/(a*c*(c*x)^(9/2)) + (16*(a + b*x^2)^(5/4))/(5*a^2*c*(c*x)^(9/2)) - (64*(a + b*x^2)^(9/4))/(45*a^3*c*(c*x)^(9/2))","A",3,2,19,0.1053,1,"{273, 264}"
975,1,91,0,0.0764107,"\int \frac{(c x)^{3/2}}{\left(a-b x^2\right)^{3/4}} \, dx","Int[(c*x)^(3/2)/(a - b*x^2)^(3/4),x]","-\frac{c \sqrt{c x} \sqrt[4]{a-b x^2}}{b}-\frac{\sqrt{a} (c x)^{3/2} \left(1-\frac{a}{b x^2}\right)^{3/4} F\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{\sqrt{b} \left(a-b x^2\right)^{3/4}}","-\frac{c \sqrt{c x} \sqrt[4]{a-b x^2}}{b}-\frac{\sqrt{a} (c x)^{3/2} \left(1-\frac{a}{b x^2}\right)^{3/4} F\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{\sqrt{b} \left(a-b x^2\right)^{3/4}}",1,"-((c*Sqrt[c*x]*(a - b*x^2)^(1/4))/b) - (Sqrt[a]*(1 - a/(b*x^2))^(3/4)*(c*x)^(3/2)*EllipticF[ArcCsc[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(Sqrt[b]*(a - b*x^2)^(3/4))","A",6,6,20,0.3000,1,"{321, 329, 237, 335, 275, 232}"
976,1,68,0,0.0635725,"\int \frac{1}{\sqrt{c x} \left(a-b x^2\right)^{3/4}} \, dx","Int[1/(Sqrt[c*x]*(a - b*x^2)^(3/4)),x]","-\frac{2 \sqrt{b} (c x)^{3/2} \left(1-\frac{a}{b x^2}\right)^{3/4} F\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{\sqrt{a} c^2 \left(a-b x^2\right)^{3/4}}","-\frac{2 \sqrt{b} (c x)^{3/2} \left(1-\frac{a}{b x^2}\right)^{3/4} F\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{\sqrt{a} c^2 \left(a-b x^2\right)^{3/4}}",1,"(-2*Sqrt[b]*(1 - a/(b*x^2))^(3/4)*(c*x)^(3/2)*EllipticF[ArcCsc[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(Sqrt[a]*c^2*(a - b*x^2)^(3/4))","A",5,5,20,0.2500,1,"{329, 237, 335, 275, 232}"
977,1,100,0,0.0761773,"\int \frac{1}{(c x)^{5/2} \left(a-b x^2\right)^{3/4}} \, dx","Int[1/((c*x)^(5/2)*(a - b*x^2)^(3/4)),x]","-\frac{4 b^{3/2} (c x)^{3/2} \left(1-\frac{a}{b x^2}\right)^{3/4} F\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{3 a^{3/2} c^4 \left(a-b x^2\right)^{3/4}}-\frac{2 \sqrt[4]{a-b x^2}}{3 a c (c x)^{3/2}}","-\frac{4 b^{3/2} (c x)^{3/2} \left(1-\frac{a}{b x^2}\right)^{3/4} F\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{3 a^{3/2} c^4 \left(a-b x^2\right)^{3/4}}-\frac{2 \sqrt[4]{a-b x^2}}{3 a c (c x)^{3/2}}",1,"(-2*(a - b*x^2)^(1/4))/(3*a*c*(c*x)^(3/2)) - (4*b^(3/2)*(1 - a/(b*x^2))^(3/4)*(c*x)^(3/2)*EllipticF[ArcCsc[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(3*a^(3/2)*c^4*(a - b*x^2)^(3/4))","A",6,6,20,0.3000,1,"{325, 329, 237, 335, 275, 232}"
978,1,130,0,0.0943923,"\int \frac{1}{(c x)^{9/2} \left(a-b x^2\right)^{3/4}} \, dx","Int[1/((c*x)^(9/2)*(a - b*x^2)^(3/4)),x]","-\frac{8 b^{5/2} (c x)^{3/2} \left(1-\frac{a}{b x^2}\right)^{3/4} F\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{7 a^{5/2} c^6 \left(a-b x^2\right)^{3/4}}-\frac{4 b \sqrt[4]{a-b x^2}}{7 a^2 c^3 (c x)^{3/2}}-\frac{2 \sqrt[4]{a-b x^2}}{7 a c (c x)^{7/2}}","-\frac{8 b^{5/2} (c x)^{3/2} \left(1-\frac{a}{b x^2}\right)^{3/4} F\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{7 a^{5/2} c^6 \left(a-b x^2\right)^{3/4}}-\frac{4 b \sqrt[4]{a-b x^2}}{7 a^2 c^3 (c x)^{3/2}}-\frac{2 \sqrt[4]{a-b x^2}}{7 a c (c x)^{7/2}}",1,"(-2*(a - b*x^2)^(1/4))/(7*a*c*(c*x)^(7/2)) - (4*b*(a - b*x^2)^(1/4))/(7*a^2*c^3*(c*x)^(3/2)) - (8*b^(5/2)*(1 - a/(b*x^2))^(3/4)*(c*x)^(3/2)*EllipticF[ArcCsc[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(7*a^(5/2)*c^6*(a - b*x^2)^(3/4))","A",7,6,20,0.3000,1,"{325, 329, 237, 335, 275, 232}"
979,1,162,0,0.1111491,"\int \frac{1}{(c x)^{13/2} \left(a-b x^2\right)^{3/4}} \, dx","Int[1/((c*x)^(13/2)*(a - b*x^2)^(3/4)),x]","-\frac{40 b^2 \sqrt[4]{a-b x^2}}{77 a^3 c^5 (c x)^{3/2}}-\frac{80 b^{7/2} (c x)^{3/2} \left(1-\frac{a}{b x^2}\right)^{3/4} F\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{77 a^{7/2} c^8 \left(a-b x^2\right)^{3/4}}-\frac{20 b \sqrt[4]{a-b x^2}}{77 a^2 c^3 (c x)^{7/2}}-\frac{2 \sqrt[4]{a-b x^2}}{11 a c (c x)^{11/2}}","-\frac{40 b^2 \sqrt[4]{a-b x^2}}{77 a^3 c^5 (c x)^{3/2}}-\frac{80 b^{7/2} (c x)^{3/2} \left(1-\frac{a}{b x^2}\right)^{3/4} F\left(\left.\frac{1}{2} \csc ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{77 a^{7/2} c^8 \left(a-b x^2\right)^{3/4}}-\frac{20 b \sqrt[4]{a-b x^2}}{77 a^2 c^3 (c x)^{7/2}}-\frac{2 \sqrt[4]{a-b x^2}}{11 a c (c x)^{11/2}}",1,"(-2*(a - b*x^2)^(1/4))/(11*a*c*(c*x)^(11/2)) - (20*b*(a - b*x^2)^(1/4))/(77*a^2*c^3*(c*x)^(7/2)) - (40*b^2*(a - b*x^2)^(1/4))/(77*a^3*c^5*(c*x)^(3/2)) - (80*b^(7/2)*(1 - a/(b*x^2))^(3/4)*(c*x)^(3/2)*EllipticF[ArcCsc[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(77*a^(7/2)*c^8*(a - b*x^2)^(3/4))","A",8,6,20,0.3000,1,"{325, 329, 237, 335, 275, 232}"
980,1,308,0,0.2615052,"\int \frac{(c x)^{5/2}}{\left(a-b x^2\right)^{3/4}} \, dx","Int[(c*x)^(5/2)/(a - b*x^2)^(3/4),x]","\frac{3 a c^{5/2} \log \left(\frac{\sqrt{b} \sqrt{c} x}{\sqrt{a-b x^2}}-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a-b x^2}}+\sqrt{c}\right)}{8 \sqrt{2} b^{7/4}}-\frac{3 a c^{5/2} \log \left(\frac{\sqrt{b} \sqrt{c} x}{\sqrt{a-b x^2}}+\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a-b x^2}}+\sqrt{c}\right)}{8 \sqrt{2} b^{7/4}}-\frac{3 a c^{5/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a-b x^2}}\right)}{4 \sqrt{2} b^{7/4}}+\frac{3 a c^{5/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a-b x^2}}+1\right)}{4 \sqrt{2} b^{7/4}}-\frac{c (c x)^{3/2} \sqrt[4]{a-b x^2}}{2 b}","\frac{3 a c^{5/2} \log \left(\frac{\sqrt{b} \sqrt{c} x}{\sqrt{a-b x^2}}-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a-b x^2}}+\sqrt{c}\right)}{8 \sqrt{2} b^{7/4}}-\frac{3 a c^{5/2} \log \left(\frac{\sqrt{b} \sqrt{c} x}{\sqrt{a-b x^2}}+\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a-b x^2}}+\sqrt{c}\right)}{8 \sqrt{2} b^{7/4}}-\frac{3 a c^{5/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a-b x^2}}\right)}{4 \sqrt{2} b^{7/4}}+\frac{3 a c^{5/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a-b x^2}}+1\right)}{4 \sqrt{2} b^{7/4}}-\frac{c (c x)^{3/2} \sqrt[4]{a-b x^2}}{2 b}",1,"-(c*(c*x)^(3/2)*(a - b*x^2)^(1/4))/(2*b) - (3*a*c^(5/2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[c*x])/(Sqrt[c]*(a - b*x^2)^(1/4))])/(4*Sqrt[2]*b^(7/4)) + (3*a*c^(5/2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[c*x])/(Sqrt[c]*(a - b*x^2)^(1/4))])/(4*Sqrt[2]*b^(7/4)) + (3*a*c^(5/2)*Log[Sqrt[c] + (Sqrt[b]*Sqrt[c]*x)/Sqrt[a - b*x^2] - (Sqrt[2]*b^(1/4)*Sqrt[c*x])/(a - b*x^2)^(1/4)])/(8*Sqrt[2]*b^(7/4)) - (3*a*c^(5/2)*Log[Sqrt[c] + (Sqrt[b]*Sqrt[c]*x)/Sqrt[a - b*x^2] + (Sqrt[2]*b^(1/4)*Sqrt[c*x])/(a - b*x^2)^(1/4)])/(8*Sqrt[2]*b^(7/4))","A",12,9,20,0.4500,1,"{321, 329, 331, 297, 1162, 617, 204, 1165, 628}"
981,1,272,0,0.2317782,"\int \frac{\sqrt{c x}}{\left(a-b x^2\right)^{3/4}} \, dx","Int[Sqrt[c*x]/(a - b*x^2)^(3/4),x]","\frac{\sqrt{c} \log \left(\frac{\sqrt{b} \sqrt{c} x}{\sqrt{a-b x^2}}-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a-b x^2}}+\sqrt{c}\right)}{2 \sqrt{2} b^{3/4}}-\frac{\sqrt{c} \log \left(\frac{\sqrt{b} \sqrt{c} x}{\sqrt{a-b x^2}}+\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a-b x^2}}+\sqrt{c}\right)}{2 \sqrt{2} b^{3/4}}-\frac{\sqrt{c} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a-b x^2}}\right)}{\sqrt{2} b^{3/4}}+\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a-b x^2}}+1\right)}{\sqrt{2} b^{3/4}}","\frac{\sqrt{c} \log \left(\frac{\sqrt{b} \sqrt{c} x}{\sqrt{a-b x^2}}-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a-b x^2}}+\sqrt{c}\right)}{2 \sqrt{2} b^{3/4}}-\frac{\sqrt{c} \log \left(\frac{\sqrt{b} \sqrt{c} x}{\sqrt{a-b x^2}}+\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt[4]{a-b x^2}}+\sqrt{c}\right)}{2 \sqrt{2} b^{3/4}}-\frac{\sqrt{c} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a-b x^2}}\right)}{\sqrt{2} b^{3/4}}+\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a-b x^2}}+1\right)}{\sqrt{2} b^{3/4}}",1,"-((Sqrt[c]*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[c*x])/(Sqrt[c]*(a - b*x^2)^(1/4))])/(Sqrt[2]*b^(3/4))) + (Sqrt[c]*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[c*x])/(Sqrt[c]*(a - b*x^2)^(1/4))])/(Sqrt[2]*b^(3/4)) + (Sqrt[c]*Log[Sqrt[c] + (Sqrt[b]*Sqrt[c]*x)/Sqrt[a - b*x^2] - (Sqrt[2]*b^(1/4)*Sqrt[c*x])/(a - b*x^2)^(1/4)])/(2*Sqrt[2]*b^(3/4)) - (Sqrt[c]*Log[Sqrt[c] + (Sqrt[b]*Sqrt[c]*x)/Sqrt[a - b*x^2] + (Sqrt[2]*b^(1/4)*Sqrt[c*x])/(a - b*x^2)^(1/4)])/(2*Sqrt[2]*b^(3/4))","A",11,8,20,0.4000,1,"{329, 331, 297, 1162, 617, 204, 1165, 628}"
982,1,27,0,0.0067443,"\int \frac{1}{(c x)^{3/2} \left(a-b x^2\right)^{3/4}} \, dx","Int[1/((c*x)^(3/2)*(a - b*x^2)^(3/4)),x]","-\frac{2 \sqrt[4]{a-b x^2}}{a c \sqrt{c x}}","-\frac{2 \sqrt[4]{a-b x^2}}{a c \sqrt{c x}}",1,"(-2*(a - b*x^2)^(1/4))/(a*c*Sqrt[c*x])","A",1,1,20,0.05000,1,"{264}"
983,1,57,0,0.0140473,"\int \frac{1}{(c x)^{7/2} \left(a-b x^2\right)^{3/4}} \, dx","Int[1/((c*x)^(7/2)*(a - b*x^2)^(3/4)),x]","\frac{8 \left(a-b x^2\right)^{5/4}}{5 a^2 c (c x)^{5/2}}-\frac{2 \sqrt[4]{a-b x^2}}{a c (c x)^{5/2}}","\frac{8 \left(a-b x^2\right)^{5/4}}{5 a^2 c (c x)^{5/2}}-\frac{2 \sqrt[4]{a-b x^2}}{a c (c x)^{5/2}}",1,"(-2*(a - b*x^2)^(1/4))/(a*c*(c*x)^(5/2)) + (8*(a - b*x^2)^(5/4))/(5*a^2*c*(c*x)^(5/2))","A",2,2,20,0.1000,1,"{273, 264}"
984,1,86,0,0.025203,"\int \frac{1}{(c x)^{11/2} \left(a-b x^2\right)^{3/4}} \, dx","Int[1/((c*x)^(11/2)*(a - b*x^2)^(3/4)),x]","-\frac{64 \left(a-b x^2\right)^{9/4}}{45 a^3 c (c x)^{9/2}}+\frac{16 \left(a-b x^2\right)^{5/4}}{5 a^2 c (c x)^{9/2}}-\frac{2 \sqrt[4]{a-b x^2}}{a c (c x)^{9/2}}","-\frac{64 \left(a-b x^2\right)^{9/4}}{45 a^3 c (c x)^{9/2}}+\frac{16 \left(a-b x^2\right)^{5/4}}{5 a^2 c (c x)^{9/2}}-\frac{2 \sqrt[4]{a-b x^2}}{a c (c x)^{9/2}}",1,"(-2*(a - b*x^2)^(1/4))/(a*c*(c*x)^(9/2)) + (16*(a - b*x^2)^(5/4))/(5*a^2*c*(c*x)^(9/2)) - (64*(a - b*x^2)^(9/4))/(45*a^3*c*(c*x)^(9/2))","A",3,2,20,0.1000,1,"{273, 264}"
985,1,146,0,0.0763353,"\int \frac{(c x)^{7/2}}{\left(a+b x^2\right)^{5/4}} \, dx","Int[(c*x)^(7/2)/(a + b*x^2)^(5/4),x]","\frac{5 a c^3 \sqrt{c x}}{2 b^2 \sqrt[4]{a+b x^2}}-\frac{5 a c^{7/2} \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a+b x^2}}\right)}{4 b^{9/4}}-\frac{5 a c^{7/2} \tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a+b x^2}}\right)}{4 b^{9/4}}+\frac{c (c x)^{5/2}}{2 b \sqrt[4]{a+b x^2}}","\frac{5 a c^3 \sqrt{c x}}{2 b^2 \sqrt[4]{a+b x^2}}-\frac{5 a c^{7/2} \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a+b x^2}}\right)}{4 b^{9/4}}-\frac{5 a c^{7/2} \tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a+b x^2}}\right)}{4 b^{9/4}}+\frac{c (c x)^{5/2}}{2 b \sqrt[4]{a+b x^2}}",1,"(5*a*c^3*Sqrt[c*x])/(2*b^2*(a + b*x^2)^(1/4)) + (c*(c*x)^(5/2))/(2*b*(a + b*x^2)^(1/4)) - (5*a*c^(7/2)*ArcTan[(b^(1/4)*Sqrt[c*x])/(Sqrt[c]*(a + b*x^2)^(1/4))])/(4*b^(9/4)) - (5*a*c^(7/2)*ArcTanh[(b^(1/4)*Sqrt[c*x])/(Sqrt[c]*(a + b*x^2)^(1/4))])/(4*b^(9/4))","A",7,7,19,0.3684,1,"{285, 288, 329, 240, 212, 208, 205}"
986,1,107,0,0.0594885,"\int \frac{(c x)^{3/2}}{\left(a+b x^2\right)^{5/4}} \, dx","Int[(c*x)^(3/2)/(a + b*x^2)^(5/4),x]","\frac{c^{3/2} \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a+b x^2}}\right)}{b^{5/4}}+\frac{c^{3/2} \tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a+b x^2}}\right)}{b^{5/4}}-\frac{2 c \sqrt{c x}}{b \sqrt[4]{a+b x^2}}","\frac{c^{3/2} \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a+b x^2}}\right)}{b^{5/4}}+\frac{c^{3/2} \tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{c x}}{\sqrt{c} \sqrt[4]{a+b x^2}}\right)}{b^{5/4}}-\frac{2 c \sqrt{c x}}{b \sqrt[4]{a+b x^2}}",1,"(-2*c*Sqrt[c*x])/(b*(a + b*x^2)^(1/4)) + (c^(3/2)*ArcTan[(b^(1/4)*Sqrt[c*x])/(Sqrt[c]*(a + b*x^2)^(1/4))])/b^(5/4) + (c^(3/2)*ArcTanh[(b^(1/4)*Sqrt[c*x])/(Sqrt[c]*(a + b*x^2)^(1/4))])/b^(5/4)","A",6,6,19,0.3158,1,"{288, 329, 240, 212, 208, 205}"
987,1,26,0,0.0055901,"\int \frac{1}{\sqrt{c x} \left(a+b x^2\right)^{5/4}} \, dx","Int[1/(Sqrt[c*x]*(a + b*x^2)^(5/4)),x]","\frac{2 \sqrt{c x}}{a c \sqrt[4]{a+b x^2}}","\frac{2 \sqrt{c x}}{a c \sqrt[4]{a+b x^2}}",1,"(2*Sqrt[c*x])/(a*c*(a + b*x^2)^(1/4))","A",1,1,19,0.05263,1,"{264}"
988,1,55,0,0.0148584,"\int \frac{1}{(c x)^{5/2} \left(a+b x^2\right)^{5/4}} \, dx","Int[1/((c*x)^(5/2)*(a + b*x^2)^(5/4)),x]","\frac{2}{a c (c x)^{3/2} \sqrt[4]{a+b x^2}}-\frac{8 \left(a+b x^2\right)^{3/4}}{3 a^2 c (c x)^{3/2}}","\frac{2}{a c (c x)^{3/2} \sqrt[4]{a+b x^2}}-\frac{8 \left(a+b x^2\right)^{3/4}}{3 a^2 c (c x)^{3/2}}",1,"2/(a*c*(c*x)^(3/2)*(a + b*x^2)^(1/4)) - (8*(a + b*x^2)^(3/4))/(3*a^2*c*(c*x)^(3/2))","A",2,2,19,0.1053,1,"{273, 264}"
989,1,83,0,0.0235764,"\int \frac{1}{(c x)^{9/2} \left(a+b x^2\right)^{5/4}} \, dx","Int[1/((c*x)^(9/2)*(a + b*x^2)^(5/4)),x]","\frac{64 \left(a+b x^2\right)^{7/4}}{21 a^3 c (c x)^{7/2}}-\frac{16 \left(a+b x^2\right)^{3/4}}{3 a^2 c (c x)^{7/2}}+\frac{2}{a c (c x)^{7/2} \sqrt[4]{a+b x^2}}","\frac{64 \left(a+b x^2\right)^{7/4}}{21 a^3 c (c x)^{7/2}}-\frac{16 \left(a+b x^2\right)^{3/4}}{3 a^2 c (c x)^{7/2}}+\frac{2}{a c (c x)^{7/2} \sqrt[4]{a+b x^2}}",1,"2/(a*c*(c*x)^(7/2)*(a + b*x^2)^(1/4)) - (16*(a + b*x^2)^(3/4))/(3*a^2*c*(c*x)^(7/2)) + (64*(a + b*x^2)^(7/4))/(21*a^3*c*(c*x)^(7/2))","A",3,2,19,0.1053,1,"{273, 264}"
990,1,109,0,0.0374668,"\int \frac{1}{(c x)^{13/2} \left(a+b x^2\right)^{5/4}} \, dx","Int[1/((c*x)^(13/2)*(a + b*x^2)^(5/4)),x]","-\frac{256 \left(a+b x^2\right)^{11/4}}{77 a^4 c (c x)^{11/2}}+\frac{64 \left(a+b x^2\right)^{7/4}}{7 a^3 c (c x)^{11/2}}-\frac{8 \left(a+b x^2\right)^{3/4}}{a^2 c (c x)^{11/2}}+\frac{2}{a c (c x)^{11/2} \sqrt[4]{a+b x^2}}","-\frac{256 \left(a+b x^2\right)^{11/4}}{77 a^4 c (c x)^{11/2}}+\frac{64 \left(a+b x^2\right)^{7/4}}{7 a^3 c (c x)^{11/2}}-\frac{8 \left(a+b x^2\right)^{3/4}}{a^2 c (c x)^{11/2}}+\frac{2}{a c (c x)^{11/2} \sqrt[4]{a+b x^2}}",1,"2/(a*c*(c*x)^(11/2)*(a + b*x^2)^(1/4)) - (8*(a + b*x^2)^(3/4))/(a^2*c*(c*x)^(11/2)) + (64*(a + b*x^2)^(7/4))/(7*a^3*c*(c*x)^(11/2)) - (256*(a + b*x^2)^(11/4))/(77*a^4*c*(c*x)^(11/2))","A",4,2,19,0.1053,1,"{273, 264}"
991,1,155,0,0.0678403,"\int \frac{(c x)^{13/2}}{\left(a+b x^2\right)^{5/4}} \, dx","Int[(c*x)^(13/2)/(a + b*x^2)^(5/4),x]","\frac{77 a^2 c^5 (c x)^{3/2}}{60 b^3 \sqrt[4]{a+b x^2}}+\frac{77 a^{5/2} c^6 \sqrt{c x} \sqrt[4]{\frac{a}{b x^2}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{20 b^{7/2} \sqrt[4]{a+b x^2}}-\frac{11 a c^3 (c x)^{7/2}}{30 b^2 \sqrt[4]{a+b x^2}}+\frac{c (c x)^{11/2}}{5 b \sqrt[4]{a+b x^2}}","\frac{77 a^2 c^5 (c x)^{3/2}}{60 b^3 \sqrt[4]{a+b x^2}}+\frac{77 a^{5/2} c^6 \sqrt{c x} \sqrt[4]{\frac{a}{b x^2}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{20 b^{7/2} \sqrt[4]{a+b x^2}}-\frac{11 a c^3 (c x)^{7/2}}{30 b^2 \sqrt[4]{a+b x^2}}+\frac{c (c x)^{11/2}}{5 b \sqrt[4]{a+b x^2}}",1,"(77*a^2*c^5*(c*x)^(3/2))/(60*b^3*(a + b*x^2)^(1/4)) - (11*a*c^3*(c*x)^(7/2))/(30*b^2*(a + b*x^2)^(1/4)) + (c*(c*x)^(11/2))/(5*b*(a + b*x^2)^(1/4)) + (77*a^(5/2)*c^6*(1 + a/(b*x^2))^(1/4)*Sqrt[c*x]*EllipticE[ArcCot[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(20*b^(7/2)*(a + b*x^2)^(1/4))","A",6,4,19,0.2105,1,"{285, 284, 335, 196}"
992,1,124,0,0.048874,"\int \frac{(c x)^{9/2}}{\left(a+b x^2\right)^{5/4}} \, dx","Int[(c*x)^(9/2)/(a + b*x^2)^(5/4),x]","-\frac{7 a^{3/2} c^4 \sqrt{c x} \sqrt[4]{\frac{a}{b x^2}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{2 b^{5/2} \sqrt[4]{a+b x^2}}-\frac{7 a c^3 (c x)^{3/2}}{6 b^2 \sqrt[4]{a+b x^2}}+\frac{c (c x)^{7/2}}{3 b \sqrt[4]{a+b x^2}}","-\frac{7 a^{3/2} c^4 \sqrt{c x} \sqrt[4]{\frac{a}{b x^2}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{2 b^{5/2} \sqrt[4]{a+b x^2}}-\frac{7 a c^3 (c x)^{3/2}}{6 b^2 \sqrt[4]{a+b x^2}}+\frac{c (c x)^{7/2}}{3 b \sqrt[4]{a+b x^2}}",1,"(-7*a*c^3*(c*x)^(3/2))/(6*b^2*(a + b*x^2)^(1/4)) + (c*(c*x)^(7/2))/(3*b*(a + b*x^2)^(1/4)) - (7*a^(3/2)*c^4*(1 + a/(b*x^2))^(1/4)*Sqrt[c*x]*EllipticE[ArcCot[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(2*b^(5/2)*(a + b*x^2)^(1/4))","A",5,4,19,0.2105,1,"{285, 284, 335, 196}"
993,1,90,0,0.0330505,"\int \frac{(c x)^{5/2}}{\left(a+b x^2\right)^{5/4}} \, dx","Int[(c*x)^(5/2)/(a + b*x^2)^(5/4),x]","\frac{3 \sqrt{a} c^2 \sqrt{c x} \sqrt[4]{\frac{a}{b x^2}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{b^{3/2} \sqrt[4]{a+b x^2}}+\frac{c (c x)^{3/2}}{b \sqrt[4]{a+b x^2}}","\frac{3 \sqrt{a} c^2 \sqrt{c x} \sqrt[4]{\frac{a}{b x^2}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{b^{3/2} \sqrt[4]{a+b x^2}}+\frac{c (c x)^{3/2}}{b \sqrt[4]{a+b x^2}}",1,"(c*(c*x)^(3/2))/(b*(a + b*x^2)^(1/4)) + (3*Sqrt[a]*c^2*(1 + a/(b*x^2))^(1/4)*Sqrt[c*x]*EllipticE[ArcCot[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(b^(3/2)*(a + b*x^2)^(1/4))","A",4,4,19,0.2105,1,"{285, 284, 335, 196}"
994,1,63,0,0.0202479,"\int \frac{\sqrt{c x}}{\left(a+b x^2\right)^{5/4}} \, dx","Int[Sqrt[c*x]/(a + b*x^2)^(5/4),x]","-\frac{2 \sqrt{c x} \sqrt[4]{\frac{a}{b x^2}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{\sqrt{a} \sqrt{b} \sqrt[4]{a+b x^2}}","-\frac{2 \sqrt{c x} \sqrt[4]{\frac{a}{b x^2}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{\sqrt{a} \sqrt{b} \sqrt[4]{a+b x^2}}",1,"(-2*(1 + a/(b*x^2))^(1/4)*Sqrt[c*x]*EllipticE[ArcCot[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(Sqrt[a]*Sqrt[b]*(a + b*x^2)^(1/4))","A",3,3,19,0.1579,1,"{284, 335, 196}"
995,1,93,0,0.0346462,"\int \frac{1}{(c x)^{3/2} \left(a+b x^2\right)^{5/4}} \, dx","Int[1/((c*x)^(3/2)*(a + b*x^2)^(5/4)),x]","\frac{4 \sqrt{b} \sqrt{c x} \sqrt[4]{\frac{a}{b x^2}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{a^{3/2} c^2 \sqrt[4]{a+b x^2}}-\frac{2}{a c \sqrt{c x} \sqrt[4]{a+b x^2}}","\frac{4 \sqrt{b} \sqrt{c x} \sqrt[4]{\frac{a}{b x^2}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{a^{3/2} c^2 \sqrt[4]{a+b x^2}}-\frac{2}{a c \sqrt{c x} \sqrt[4]{a+b x^2}}",1,"-2/(a*c*Sqrt[c*x]*(a + b*x^2)^(1/4)) + (4*Sqrt[b]*(1 + a/(b*x^2))^(1/4)*Sqrt[c*x]*EllipticE[ArcCot[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(a^(3/2)*c^2*(a + b*x^2)^(1/4))","A",4,4,19,0.2105,1,"{286, 284, 335, 196}"
996,1,126,0,0.0510784,"\int \frac{1}{(c x)^{7/2} \left(a+b x^2\right)^{5/4}} \, dx","Int[1/((c*x)^(7/2)*(a + b*x^2)^(5/4)),x]","-\frac{24 b^{3/2} \sqrt{c x} \sqrt[4]{\frac{a}{b x^2}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{5 a^{5/2} c^4 \sqrt[4]{a+b x^2}}+\frac{12 b}{5 a^2 c^3 \sqrt{c x} \sqrt[4]{a+b x^2}}-\frac{2}{5 a c (c x)^{5/2} \sqrt[4]{a+b x^2}}","-\frac{24 b^{3/2} \sqrt{c x} \sqrt[4]{\frac{a}{b x^2}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{5 a^{5/2} c^4 \sqrt[4]{a+b x^2}}+\frac{12 b}{5 a^2 c^3 \sqrt{c x} \sqrt[4]{a+b x^2}}-\frac{2}{5 a c (c x)^{5/2} \sqrt[4]{a+b x^2}}",1,"-2/(5*a*c*(c*x)^(5/2)*(a + b*x^2)^(1/4)) + (12*b)/(5*a^2*c^3*Sqrt[c*x]*(a + b*x^2)^(1/4)) - (24*b^(3/2)*(1 + a/(b*x^2))^(1/4)*Sqrt[c*x]*EllipticE[ArcCot[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(5*a^(5/2)*c^4*(a + b*x^2)^(1/4))","A",5,4,19,0.2105,1,"{286, 284, 335, 196}"
997,1,157,0,0.0674036,"\int \frac{1}{(c x)^{11/2} \left(a+b x^2\right)^{5/4}} \, dx","Int[1/((c*x)^(11/2)*(a + b*x^2)^(5/4)),x]","-\frac{8 b^2}{3 a^3 c^5 \sqrt{c x} \sqrt[4]{a+b x^2}}+\frac{16 b^{5/2} \sqrt{c x} \sqrt[4]{\frac{a}{b x^2}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{3 a^{7/2} c^6 \sqrt[4]{a+b x^2}}+\frac{4 b}{9 a^2 c^3 (c x)^{5/2} \sqrt[4]{a+b x^2}}-\frac{2}{9 a c (c x)^{9/2} \sqrt[4]{a+b x^2}}","-\frac{8 b^2}{3 a^3 c^5 \sqrt{c x} \sqrt[4]{a+b x^2}}+\frac{16 b^{5/2} \sqrt{c x} \sqrt[4]{\frac{a}{b x^2}+1} E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{3 a^{7/2} c^6 \sqrt[4]{a+b x^2}}+\frac{4 b}{9 a^2 c^3 (c x)^{5/2} \sqrt[4]{a+b x^2}}-\frac{2}{9 a c (c x)^{9/2} \sqrt[4]{a+b x^2}}",1,"-2/(9*a*c*(c*x)^(9/2)*(a + b*x^2)^(1/4)) + (4*b)/(9*a^2*c^3*(c*x)^(5/2)*(a + b*x^2)^(1/4)) - (8*b^2)/(3*a^3*c^5*Sqrt[c*x]*(a + b*x^2)^(1/4)) + (16*b^(5/2)*(1 + a/(b*x^2))^(1/4)*Sqrt[c*x]*EllipticE[ArcCot[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(3*a^(7/2)*c^6*(a + b*x^2)^(1/4))","A",6,4,19,0.2105,1,"{286, 284, 335, 196}"
998,1,58,0,0.017512,"\int \frac{(c x)^{5/4}}{\sqrt[4]{a+b x^2}} \, dx","Int[(c*x)^(5/4)/(a + b*x^2)^(1/4),x]","\frac{4 (c x)^{9/4} \sqrt[4]{\frac{b x^2}{a}+1} \, _2F_1\left(\frac{1}{4},\frac{9}{8};\frac{17}{8};-\frac{b x^2}{a}\right)}{9 c \sqrt[4]{a+b x^2}}","\frac{4 (c x)^{9/4} \sqrt[4]{\frac{b x^2}{a}+1} \, _2F_1\left(\frac{1}{4},\frac{9}{8};\frac{17}{8};-\frac{b x^2}{a}\right)}{9 c \sqrt[4]{a+b x^2}}",1,"(4*(c*x)^(9/4)*(1 + (b*x^2)/a)^(1/4)*Hypergeometric2F1[1/4, 9/8, 17/8, -((b*x^2)/a)])/(9*c*(a + b*x^2)^(1/4))","A",2,2,19,0.1053,1,"{365, 364}"
999,1,58,0,0.0168453,"\int \frac{(c x)^{3/4}}{\sqrt[4]{a+b x^2}} \, dx","Int[(c*x)^(3/4)/(a + b*x^2)^(1/4),x]","\frac{4 (c x)^{7/4} \sqrt[4]{\frac{b x^2}{a}+1} \, _2F_1\left(\frac{1}{4},\frac{7}{8};\frac{15}{8};-\frac{b x^2}{a}\right)}{7 c \sqrt[4]{a+b x^2}}","\frac{4 (c x)^{7/4} \sqrt[4]{\frac{b x^2}{a}+1} \, _2F_1\left(\frac{1}{4},\frac{7}{8};\frac{15}{8};-\frac{b x^2}{a}\right)}{7 c \sqrt[4]{a+b x^2}}",1,"(4*(c*x)^(7/4)*(1 + (b*x^2)/a)^(1/4)*Hypergeometric2F1[1/4, 7/8, 15/8, -((b*x^2)/a)])/(7*c*(a + b*x^2)^(1/4))","A",2,2,19,0.1053,1,"{365, 364}"
1000,1,58,0,0.0166135,"\int \frac{\sqrt[4]{c x}}{\sqrt[4]{a+b x^2}} \, dx","Int[(c*x)^(1/4)/(a + b*x^2)^(1/4),x]","\frac{4 (c x)^{5/4} \sqrt[4]{\frac{b x^2}{a}+1} \, _2F_1\left(\frac{1}{4},\frac{5}{8};\frac{13}{8};-\frac{b x^2}{a}\right)}{5 c \sqrt[4]{a+b x^2}}","\frac{4 (c x)^{5/4} \sqrt[4]{\frac{b x^2}{a}+1} \, _2F_1\left(\frac{1}{4},\frac{5}{8};\frac{13}{8};-\frac{b x^2}{a}\right)}{5 c \sqrt[4]{a+b x^2}}",1,"(4*(c*x)^(5/4)*(1 + (b*x^2)/a)^(1/4)*Hypergeometric2F1[1/4, 5/8, 13/8, -((b*x^2)/a)])/(5*c*(a + b*x^2)^(1/4))","A",2,2,19,0.1053,1,"{365, 364}"
1001,1,58,0,0.018118,"\int \frac{1}{\sqrt[4]{c x} \sqrt[4]{a+b x^2}} \, dx","Int[1/((c*x)^(1/4)*(a + b*x^2)^(1/4)),x]","\frac{4 (c x)^{3/4} \sqrt[4]{\frac{b x^2}{a}+1} \, _2F_1\left(\frac{1}{4},\frac{3}{8};\frac{11}{8};-\frac{b x^2}{a}\right)}{3 c \sqrt[4]{a+b x^2}}","\frac{4 (c x)^{3/4} \sqrt[4]{\frac{b x^2}{a}+1} \, _2F_1\left(\frac{1}{4},\frac{3}{8};\frac{11}{8};-\frac{b x^2}{a}\right)}{3 c \sqrt[4]{a+b x^2}}",1,"(4*(c*x)^(3/4)*(1 + (b*x^2)/a)^(1/4)*Hypergeometric2F1[1/4, 3/8, 11/8, -((b*x^2)/a)])/(3*c*(a + b*x^2)^(1/4))","A",2,2,19,0.1053,1,"{365, 364}"
1002,1,56,0,0.0168982,"\int \frac{1}{(c x)^{3/4} \sqrt[4]{a+b x^2}} \, dx","Int[1/((c*x)^(3/4)*(a + b*x^2)^(1/4)),x]","\frac{4 \sqrt[4]{c x} \sqrt[4]{\frac{b x^2}{a}+1} \, _2F_1\left(\frac{1}{8},\frac{1}{4};\frac{9}{8};-\frac{b x^2}{a}\right)}{c \sqrt[4]{a+b x^2}}","\frac{4 \sqrt[4]{c x} \sqrt[4]{\frac{b x^2}{a}+1} \, _2F_1\left(\frac{1}{8},\frac{1}{4};\frac{9}{8};-\frac{b x^2}{a}\right)}{c \sqrt[4]{a+b x^2}}",1,"(4*(c*x)^(1/4)*(1 + (b*x^2)/a)^(1/4)*Hypergeometric2F1[1/8, 1/4, 9/8, -((b*x^2)/a)])/(c*(a + b*x^2)^(1/4))","A",2,2,19,0.1053,1,"{365, 364}"
1003,1,56,0,0.0170952,"\int \frac{1}{(c x)^{5/4} \sqrt[4]{a+b x^2}} \, dx","Int[1/((c*x)^(5/4)*(a + b*x^2)^(1/4)),x]","-\frac{4 \sqrt[4]{\frac{b x^2}{a}+1} \, _2F_1\left(-\frac{1}{8},\frac{1}{4};\frac{7}{8};-\frac{b x^2}{a}\right)}{c \sqrt[4]{c x} \sqrt[4]{a+b x^2}}","-\frac{4 \sqrt[4]{\frac{b x^2}{a}+1} \, _2F_1\left(-\frac{1}{8},\frac{1}{4};\frac{7}{8};-\frac{b x^2}{a}\right)}{c \sqrt[4]{c x} \sqrt[4]{a+b x^2}}",1,"(-4*(1 + (b*x^2)/a)^(1/4)*Hypergeometric2F1[-1/8, 1/4, 7/8, -((b*x^2)/a)])/(c*(c*x)^(1/4)*(a + b*x^2)^(1/4))","A",2,2,19,0.1053,1,"{365, 364}"
1004,1,61,0,0.0185229,"\int \frac{(c x)^{5/4}}{\left(a+b x^2\right)^{7/4}} \, dx","Int[(c*x)^(5/4)/(a + b*x^2)^(7/4),x]","\frac{4 (c x)^{9/4} \left(\frac{b x^2}{a}+1\right)^{3/4} \, _2F_1\left(\frac{9}{8},\frac{7}{4};\frac{17}{8};-\frac{b x^2}{a}\right)}{9 a c \left(a+b x^2\right)^{3/4}}","\frac{4 (c x)^{9/4} \left(\frac{b x^2}{a}+1\right)^{3/4} \, _2F_1\left(\frac{9}{8},\frac{7}{4};\frac{17}{8};-\frac{b x^2}{a}\right)}{9 a c \left(a+b x^2\right)^{3/4}}",1,"(4*(c*x)^(9/4)*(1 + (b*x^2)/a)^(3/4)*Hypergeometric2F1[9/8, 7/4, 17/8, -((b*x^2)/a)])/(9*a*c*(a + b*x^2)^(3/4))","A",2,2,19,0.1053,1,"{365, 364}"
1005,1,61,0,0.018248,"\int \frac{(c x)^{3/4}}{\left(a+b x^2\right)^{7/4}} \, dx","Int[(c*x)^(3/4)/(a + b*x^2)^(7/4),x]","\frac{4 (c x)^{7/4} \left(\frac{b x^2}{a}+1\right)^{3/4} \, _2F_1\left(\frac{7}{8},\frac{7}{4};\frac{15}{8};-\frac{b x^2}{a}\right)}{7 a c \left(a+b x^2\right)^{3/4}}","\frac{4 (c x)^{7/4} \left(\frac{b x^2}{a}+1\right)^{3/4} \, _2F_1\left(\frac{7}{8},\frac{7}{4};\frac{15}{8};-\frac{b x^2}{a}\right)}{7 a c \left(a+b x^2\right)^{3/4}}",1,"(4*(c*x)^(7/4)*(1 + (b*x^2)/a)^(3/4)*Hypergeometric2F1[7/8, 7/4, 15/8, -((b*x^2)/a)])/(7*a*c*(a + b*x^2)^(3/4))","A",2,2,19,0.1053,1,"{365, 364}"
1006,1,61,0,0.0185868,"\int \frac{\sqrt[4]{c x}}{\left(a+b x^2\right)^{7/4}} \, dx","Int[(c*x)^(1/4)/(a + b*x^2)^(7/4),x]","\frac{4 (c x)^{5/4} \left(\frac{b x^2}{a}+1\right)^{3/4} \, _2F_1\left(\frac{5}{8},\frac{7}{4};\frac{13}{8};-\frac{b x^2}{a}\right)}{5 a c \left(a+b x^2\right)^{3/4}}","\frac{4 (c x)^{5/4} \left(\frac{b x^2}{a}+1\right)^{3/4} \, _2F_1\left(\frac{5}{8},\frac{7}{4};\frac{13}{8};-\frac{b x^2}{a}\right)}{5 a c \left(a+b x^2\right)^{3/4}}",1,"(4*(c*x)^(5/4)*(1 + (b*x^2)/a)^(3/4)*Hypergeometric2F1[5/8, 7/4, 13/8, -((b*x^2)/a)])/(5*a*c*(a + b*x^2)^(3/4))","A",2,2,19,0.1053,1,"{365, 364}"
1007,1,61,0,0.0183507,"\int \frac{1}{\sqrt[4]{c x} \left(a+b x^2\right)^{7/4}} \, dx","Int[1/((c*x)^(1/4)*(a + b*x^2)^(7/4)),x]","\frac{4 (c x)^{3/4} \left(\frac{b x^2}{a}+1\right)^{3/4} \, _2F_1\left(\frac{3}{8},\frac{7}{4};\frac{11}{8};-\frac{b x^2}{a}\right)}{3 a c \left(a+b x^2\right)^{3/4}}","\frac{4 (c x)^{3/4} \left(\frac{b x^2}{a}+1\right)^{3/4} \, _2F_1\left(\frac{3}{8},\frac{7}{4};\frac{11}{8};-\frac{b x^2}{a}\right)}{3 a c \left(a+b x^2\right)^{3/4}}",1,"(4*(c*x)^(3/4)*(1 + (b*x^2)/a)^(3/4)*Hypergeometric2F1[3/8, 7/4, 11/8, -((b*x^2)/a)])/(3*a*c*(a + b*x^2)^(3/4))","A",2,2,19,0.1053,1,"{365, 364}"
1008,1,59,0,0.0181921,"\int \frac{1}{(c x)^{3/4} \left(a+b x^2\right)^{7/4}} \, dx","Int[1/((c*x)^(3/4)*(a + b*x^2)^(7/4)),x]","\frac{4 \sqrt[4]{c x} \left(\frac{b x^2}{a}+1\right)^{3/4} \, _2F_1\left(\frac{1}{8},\frac{7}{4};\frac{9}{8};-\frac{b x^2}{a}\right)}{a c \left(a+b x^2\right)^{3/4}}","\frac{4 \sqrt[4]{c x} \left(\frac{b x^2}{a}+1\right)^{3/4} \, _2F_1\left(\frac{1}{8},\frac{7}{4};\frac{9}{8};-\frac{b x^2}{a}\right)}{a c \left(a+b x^2\right)^{3/4}}",1,"(4*(c*x)^(1/4)*(1 + (b*x^2)/a)^(3/4)*Hypergeometric2F1[1/8, 7/4, 9/8, -((b*x^2)/a)])/(a*c*(a + b*x^2)^(3/4))","A",2,2,19,0.1053,1,"{365, 364}"
1009,1,59,0,0.0190109,"\int \frac{1}{(c x)^{5/4} \left(a+b x^2\right)^{7/4}} \, dx","Int[1/((c*x)^(5/4)*(a + b*x^2)^(7/4)),x]","-\frac{4 \left(\frac{b x^2}{a}+1\right)^{3/4} \, _2F_1\left(-\frac{1}{8},\frac{7}{4};\frac{7}{8};-\frac{b x^2}{a}\right)}{a c \sqrt[4]{c x} \left(a+b x^2\right)^{3/4}}","-\frac{4 \left(\frac{b x^2}{a}+1\right)^{3/4} \, _2F_1\left(-\frac{1}{8},\frac{7}{4};\frac{7}{8};-\frac{b x^2}{a}\right)}{a c \sqrt[4]{c x} \left(a+b x^2\right)^{3/4}}",1,"(-4*(1 + (b*x^2)/a)^(3/4)*Hypergeometric2F1[-1/8, 7/4, 7/8, -((b*x^2)/a)])/(a*c*(c*x)^(1/4)*(a + b*x^2)^(3/4))","A",2,2,19,0.1053,1,"{365, 364}"
1010,1,345,0,0.425017,"\int x^6 \sqrt[6]{a+b x^2} \, dx","Int[x^6*(a + b*x^2)^(1/6),x]","-\frac{9 a^2 x^3 \sqrt[6]{a+b x^2}}{704 b^2}+\frac{81 a^3 x \sqrt[6]{a+b x^2}}{2816 b^3}-\frac{81\ 3^{3/4} \sqrt{2-\sqrt{3}} a^4 \sqrt[6]{a+b x^2} \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{2816 b^4 x \sqrt[3]{\frac{a}{a+b x^2}} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}+\frac{3}{22} x^7 \sqrt[6]{a+b x^2}+\frac{3 a x^5 \sqrt[6]{a+b x^2}}{352 b}","-\frac{9 a^2 x^3 \sqrt[6]{a+b x^2}}{704 b^2}+\frac{81 a^3 x \sqrt[6]{a+b x^2}}{2816 b^3}-\frac{81\ 3^{3/4} \sqrt{2-\sqrt{3}} a^4 \sqrt[6]{a+b x^2} \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{2816 b^4 x \sqrt[3]{\frac{a}{a+b x^2}} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}+\frac{3}{22} x^7 \sqrt[6]{a+b x^2}+\frac{3 a x^5 \sqrt[6]{a+b x^2}}{352 b}",1,"(81*a^3*x*(a + b*x^2)^(1/6))/(2816*b^3) - (9*a^2*x^3*(a + b*x^2)^(1/6))/(704*b^2) + (3*a*x^5*(a + b*x^2)^(1/6))/(352*b) + (3*x^7*(a + b*x^2)^(1/6))/22 - (81*3^(3/4)*Sqrt[2 - Sqrt[3]]*a^4*(a + b*x^2)^(1/6)*(1 - (a/(a + b*x^2))^(1/3))*Sqrt[(1 + (a/(a + b*x^2))^(1/3) + (a/(a + b*x^2))^(2/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))], -7 + 4*Sqrt[3]])/(2816*b^4*x*(a/(a + b*x^2))^(1/3)*Sqrt[-((1 - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2)])","A",7,5,15,0.3333,1,"{279, 321, 241, 236, 219}"
1011,1,321,0,0.2910739,"\int x^4 \sqrt[6]{a+b x^2} \, dx","Int[x^4*(a + b*x^2)^(1/6),x]","-\frac{27 a^2 x \sqrt[6]{a+b x^2}}{640 b^2}+\frac{27\ 3^{3/4} \sqrt{2-\sqrt{3}} a^3 \sqrt[6]{a+b x^2} \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{640 b^3 x \sqrt[3]{\frac{a}{a+b x^2}} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}+\frac{3}{16} x^5 \sqrt[6]{a+b x^2}+\frac{3 a x^3 \sqrt[6]{a+b x^2}}{160 b}","-\frac{27 a^2 x \sqrt[6]{a+b x^2}}{640 b^2}+\frac{27\ 3^{3/4} \sqrt{2-\sqrt{3}} a^3 \sqrt[6]{a+b x^2} \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{640 b^3 x \sqrt[3]{\frac{a}{a+b x^2}} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}+\frac{3}{16} x^5 \sqrt[6]{a+b x^2}+\frac{3 a x^3 \sqrt[6]{a+b x^2}}{160 b}",1,"(-27*a^2*x*(a + b*x^2)^(1/6))/(640*b^2) + (3*a*x^3*(a + b*x^2)^(1/6))/(160*b) + (3*x^5*(a + b*x^2)^(1/6))/16 + (27*3^(3/4)*Sqrt[2 - Sqrt[3]]*a^3*(a + b*x^2)^(1/6)*(1 - (a/(a + b*x^2))^(1/3))*Sqrt[(1 + (a/(a + b*x^2))^(1/3) + (a/(a + b*x^2))^(2/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))], -7 + 4*Sqrt[3]])/(640*b^3*x*(a/(a + b*x^2))^(1/3)*Sqrt[-((1 - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2)])","A",6,5,15,0.3333,1,"{279, 321, 241, 236, 219}"
1012,1,297,0,0.2472366,"\int x^2 \sqrt[6]{a+b x^2} \, dx","Int[x^2*(a + b*x^2)^(1/6),x]","-\frac{3\ 3^{3/4} \sqrt{2-\sqrt{3}} a^2 \sqrt[6]{a+b x^2} \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{40 b^2 x \sqrt[3]{\frac{a}{a+b x^2}} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}+\frac{3}{10} x^3 \sqrt[6]{a+b x^2}+\frac{3 a x \sqrt[6]{a+b x^2}}{40 b}","-\frac{3\ 3^{3/4} \sqrt{2-\sqrt{3}} a^2 \sqrt[6]{a+b x^2} \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{40 b^2 x \sqrt[3]{\frac{a}{a+b x^2}} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}+\frac{3}{10} x^3 \sqrt[6]{a+b x^2}+\frac{3 a x \sqrt[6]{a+b x^2}}{40 b}",1,"(3*a*x*(a + b*x^2)^(1/6))/(40*b) + (3*x^3*(a + b*x^2)^(1/6))/10 - (3*3^(3/4)*Sqrt[2 - Sqrt[3]]*a^2*(a + b*x^2)^(1/6)*(1 - (a/(a + b*x^2))^(1/3))*Sqrt[(1 + (a/(a + b*x^2))^(1/3) + (a/(a + b*x^2))^(2/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))], -7 + 4*Sqrt[3]])/(40*b^2*x*(a/(a + b*x^2))^(1/3)*Sqrt[-((1 - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2)])","A",5,5,15,0.3333,1,"{279, 321, 241, 236, 219}"
1013,1,273,0,0.2085862,"\int \sqrt[6]{a+b x^2} \, dx","Int[(a + b*x^2)^(1/6),x]","\frac{3}{4} x \sqrt[6]{a+b x^2}+\frac{3^{3/4} \sqrt{2-\sqrt{3}} a \sqrt[6]{a+b x^2} \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{4 b x \sqrt[3]{\frac{a}{a+b x^2}} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}","\frac{3}{4} x \sqrt[6]{a+b x^2}+\frac{3^{3/4} \sqrt{2-\sqrt{3}} a \sqrt[6]{a+b x^2} \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{4 b x \sqrt[3]{\frac{a}{a+b x^2}} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}",1,"(3*x*(a + b*x^2)^(1/6))/4 + (3^(3/4)*Sqrt[2 - Sqrt[3]]*a*(a + b*x^2)^(1/6)*(1 - (a/(a + b*x^2))^(1/3))*Sqrt[(1 + (a/(a + b*x^2))^(1/3) + (a/(a + b*x^2))^(2/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))], -7 + 4*Sqrt[3]])/(4*b*x*(a/(a + b*x^2))^(1/3)*Sqrt[-((1 - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2)])","A",4,4,11,0.3636,1,"{195, 241, 236, 219}"
1014,1,266,0,0.2099543,"\int \frac{\sqrt[6]{a+b x^2}}{x^2} \, dx","Int[(a + b*x^2)^(1/6)/x^2,x]","\frac{\sqrt{2-\sqrt{3}} \sqrt[6]{a+b x^2} \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} x \sqrt[3]{\frac{a}{a+b x^2}} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}-\frac{\sqrt[6]{a+b x^2}}{x}","\frac{\sqrt{2-\sqrt{3}} \sqrt[6]{a+b x^2} \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} x \sqrt[3]{\frac{a}{a+b x^2}} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}-\frac{\sqrt[6]{a+b x^2}}{x}",1,"-((a + b*x^2)^(1/6)/x) + (Sqrt[2 - Sqrt[3]]*(a + b*x^2)^(1/6)*(1 - (a/(a + b*x^2))^(1/3))*Sqrt[(1 + (a/(a + b*x^2))^(1/3) + (a/(a + b*x^2))^(2/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))], -7 + 4*Sqrt[3]])/(3^(1/4)*x*(a/(a + b*x^2))^(1/3)*Sqrt[-((1 - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2)])","A",4,4,15,0.2667,1,"{277, 241, 236, 219}"
1015,1,297,0,0.2481828,"\int \frac{\sqrt[6]{a+b x^2}}{x^4} \, dx","Int[(a + b*x^2)^(1/6)/x^4,x]","-\frac{b \sqrt[6]{a+b x^2}}{9 a x}-\frac{\sqrt[6]{a+b x^2}}{3 x^3}-\frac{2 \sqrt{2-\sqrt{3}} b \sqrt[6]{a+b x^2} \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{9 \sqrt[4]{3} a x \sqrt[3]{\frac{a}{a+b x^2}} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}","-\frac{b \sqrt[6]{a+b x^2}}{9 a x}-\frac{\sqrt[6]{a+b x^2}}{3 x^3}-\frac{2 \sqrt{2-\sqrt{3}} b \sqrt[6]{a+b x^2} \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{9 \sqrt[4]{3} a x \sqrt[3]{\frac{a}{a+b x^2}} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}",1,"-(a + b*x^2)^(1/6)/(3*x^3) - (b*(a + b*x^2)^(1/6))/(9*a*x) - (2*Sqrt[2 - Sqrt[3]]*b*(a + b*x^2)^(1/6)*(1 - (a/(a + b*x^2))^(1/3))*Sqrt[(1 + (a/(a + b*x^2))^(1/3) + (a/(a + b*x^2))^(2/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))], -7 + 4*Sqrt[3]])/(9*3^(1/4)*a*x*(a/(a + b*x^2))^(1/3)*Sqrt[-((1 - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2)])","A",5,5,15,0.3333,1,"{277, 325, 241, 236, 219}"
1016,1,323,0,0.282843,"\int \frac{\sqrt[6]{a+b x^2}}{x^6} \, dx","Int[(a + b*x^2)^(1/6)/x^6,x]","\frac{8 b^2 \sqrt[6]{a+b x^2}}{135 a^2 x}+\frac{16 \sqrt{2-\sqrt{3}} b^2 \sqrt[6]{a+b x^2} \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{135 \sqrt[4]{3} a^2 x \sqrt[3]{\frac{a}{a+b x^2}} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}-\frac{b \sqrt[6]{a+b x^2}}{45 a x^3}-\frac{\sqrt[6]{a+b x^2}}{5 x^5}","\frac{8 b^2 \sqrt[6]{a+b x^2}}{135 a^2 x}+\frac{16 \sqrt{2-\sqrt{3}} b^2 \sqrt[6]{a+b x^2} \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{135 \sqrt[4]{3} a^2 x \sqrt[3]{\frac{a}{a+b x^2}} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}-\frac{b \sqrt[6]{a+b x^2}}{45 a x^3}-\frac{\sqrt[6]{a+b x^2}}{5 x^5}",1,"-(a + b*x^2)^(1/6)/(5*x^5) - (b*(a + b*x^2)^(1/6))/(45*a*x^3) + (8*b^2*(a + b*x^2)^(1/6))/(135*a^2*x) + (16*Sqrt[2 - Sqrt[3]]*b^2*(a + b*x^2)^(1/6)*(1 - (a/(a + b*x^2))^(1/3))*Sqrt[(1 + (a/(a + b*x^2))^(1/3) + (a/(a + b*x^2))^(2/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))], -7 + 4*Sqrt[3]])/(135*3^(1/4)*a^2*x*(a/(a + b*x^2))^(1/3)*Sqrt[-((1 - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2)])","A",6,5,15,0.3333,1,"{277, 325, 241, 236, 219}"
1017,1,347,0,0.3177643,"\int \frac{\sqrt[6]{a+b x^2}}{x^8} \, dx","Int[(a + b*x^2)^(1/6)/x^8,x]","-\frac{16 b^3 \sqrt[6]{a+b x^2}}{405 a^3 x}+\frac{2 b^2 \sqrt[6]{a+b x^2}}{135 a^2 x^3}-\frac{32 \sqrt{2-\sqrt{3}} b^3 \sqrt[6]{a+b x^2} \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{405 \sqrt[4]{3} a^3 x \sqrt[3]{\frac{a}{a+b x^2}} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}-\frac{b \sqrt[6]{a+b x^2}}{105 a x^5}-\frac{\sqrt[6]{a+b x^2}}{7 x^7}","-\frac{16 b^3 \sqrt[6]{a+b x^2}}{405 a^3 x}+\frac{2 b^2 \sqrt[6]{a+b x^2}}{135 a^2 x^3}-\frac{32 \sqrt{2-\sqrt{3}} b^3 \sqrt[6]{a+b x^2} \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{405 \sqrt[4]{3} a^3 x \sqrt[3]{\frac{a}{a+b x^2}} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}-\frac{b \sqrt[6]{a+b x^2}}{105 a x^5}-\frac{\sqrt[6]{a+b x^2}}{7 x^7}",1,"-(a + b*x^2)^(1/6)/(7*x^7) - (b*(a + b*x^2)^(1/6))/(105*a*x^5) + (2*b^2*(a + b*x^2)^(1/6))/(135*a^2*x^3) - (16*b^3*(a + b*x^2)^(1/6))/(405*a^3*x) - (32*Sqrt[2 - Sqrt[3]]*b^3*(a + b*x^2)^(1/6)*(1 - (a/(a + b*x^2))^(1/3))*Sqrt[(1 + (a/(a + b*x^2))^(1/3) + (a/(a + b*x^2))^(2/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))], -7 + 4*Sqrt[3]])/(405*3^(1/4)*a^3*x*(a/(a + b*x^2))^(1/3)*Sqrt[-((1 - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2)])","A",7,5,15,0.3333,1,"{277, 325, 241, 236, 219}"
1018,1,659,0,0.6932898,"\int \frac{x^6}{\sqrt[6]{a+b x^2}} \, dx","Int[x^6/(a + b*x^2)^(1/6),x]","\frac{81 a^2 x \left(a+b x^2\right)^{5/6}}{448 b^3}-\frac{243 a^3 x}{896 b^3 \sqrt[6]{a+b x^2}}-\frac{243 a^4 x}{896 b^3 \left(\frac{a}{a+b x^2}\right)^{2/3} \left(a+b x^2\right)^{7/6} \left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)}+\frac{81\ 3^{3/4} a^4 \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{448 \sqrt{2} b^4 x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}-\frac{243 \sqrt[4]{3} \sqrt{2+\sqrt{3}} a^4 \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{1792 b^4 x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}-\frac{9 a x^3 \left(a+b x^2\right)^{5/6}}{56 b^2}+\frac{3 x^5 \left(a+b x^2\right)^{5/6}}{20 b}","\frac{81 a^2 x \left(a+b x^2\right)^{5/6}}{448 b^3}-\frac{243 a^3 x}{896 b^3 \sqrt[6]{a+b x^2}}-\frac{243 a^4 x}{896 b^3 \left(\frac{a}{a+b x^2}\right)^{2/3} \left(a+b x^2\right)^{7/6} \left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)}+\frac{81\ 3^{3/4} a^4 \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{448 \sqrt{2} b^4 x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}-\frac{243 \sqrt[4]{3} \sqrt{2+\sqrt{3}} a^4 \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{1792 b^4 x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}-\frac{9 a x^3 \left(a+b x^2\right)^{5/6}}{56 b^2}+\frac{3 x^5 \left(a+b x^2\right)^{5/6}}{20 b}",1,"(-243*a^3*x)/(896*b^3*(a + b*x^2)^(1/6)) + (81*a^2*x*(a + b*x^2)^(5/6))/(448*b^3) - (9*a*x^3*(a + b*x^2)^(5/6))/(56*b^2) + (3*x^5*(a + b*x^2)^(5/6))/(20*b) - (243*a^4*x)/(896*b^3*(a/(a + b*x^2))^(2/3)*(a + b*x^2)^(7/6)*(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))) - (243*3^(1/4)*Sqrt[2 + Sqrt[3]]*a^4*(1 - (a/(a + b*x^2))^(1/3))*Sqrt[(1 + (a/(a + b*x^2))^(1/3) + (a/(a + b*x^2))^(2/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2]*EllipticE[ArcSin[(1 + Sqrt[3] - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))], -7 + 4*Sqrt[3]])/(1792*b^4*x*(a/(a + b*x^2))^(2/3)*(a + b*x^2)^(1/6)*Sqrt[-((1 - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2)]) + (81*3^(3/4)*a^4*(1 - (a/(a + b*x^2))^(1/3))*Sqrt[(1 + (a/(a + b*x^2))^(1/3) + (a/(a + b*x^2))^(2/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))], -7 + 4*Sqrt[3]])/(448*Sqrt[2]*b^4*x*(a/(a + b*x^2))^(2/3)*(a + b*x^2)^(1/6)*Sqrt[-((1 - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2)])","A",9,7,15,0.4667,1,"{321, 238, 198, 235, 304, 219, 1879}"
1019,1,635,0,0.6087327,"\int \frac{x^4}{\sqrt[6]{a+b x^2}} \, dx","Int[x^4/(a + b*x^2)^(1/6),x]","\frac{81 a^3 x}{224 b^2 \left(\frac{a}{a+b x^2}\right)^{2/3} \left(a+b x^2\right)^{7/6} \left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)}+\frac{81 a^2 x}{224 b^2 \sqrt[6]{a+b x^2}}-\frac{27\ 3^{3/4} a^3 \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{112 \sqrt{2} b^3 x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}+\frac{81 \sqrt[4]{3} \sqrt{2+\sqrt{3}} a^3 \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{448 b^3 x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}-\frac{27 a x \left(a+b x^2\right)^{5/6}}{112 b^2}+\frac{3 x^3 \left(a+b x^2\right)^{5/6}}{14 b}","\frac{81 a^3 x}{224 b^2 \left(\frac{a}{a+b x^2}\right)^{2/3} \left(a+b x^2\right)^{7/6} \left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)}+\frac{81 a^2 x}{224 b^2 \sqrt[6]{a+b x^2}}-\frac{27\ 3^{3/4} a^3 \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{112 \sqrt{2} b^3 x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}+\frac{81 \sqrt[4]{3} \sqrt{2+\sqrt{3}} a^3 \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{448 b^3 x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}-\frac{27 a x \left(a+b x^2\right)^{5/6}}{112 b^2}+\frac{3 x^3 \left(a+b x^2\right)^{5/6}}{14 b}",1,"(81*a^2*x)/(224*b^2*(a + b*x^2)^(1/6)) - (27*a*x*(a + b*x^2)^(5/6))/(112*b^2) + (3*x^3*(a + b*x^2)^(5/6))/(14*b) + (81*a^3*x)/(224*b^2*(a/(a + b*x^2))^(2/3)*(a + b*x^2)^(7/6)*(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))) + (81*3^(1/4)*Sqrt[2 + Sqrt[3]]*a^3*(1 - (a/(a + b*x^2))^(1/3))*Sqrt[(1 + (a/(a + b*x^2))^(1/3) + (a/(a + b*x^2))^(2/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2]*EllipticE[ArcSin[(1 + Sqrt[3] - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))], -7 + 4*Sqrt[3]])/(448*b^3*x*(a/(a + b*x^2))^(2/3)*(a + b*x^2)^(1/6)*Sqrt[-((1 - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2)]) - (27*3^(3/4)*a^3*(1 - (a/(a + b*x^2))^(1/3))*Sqrt[(1 + (a/(a + b*x^2))^(1/3) + (a/(a + b*x^2))^(2/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))], -7 + 4*Sqrt[3]])/(112*Sqrt[2]*b^3*x*(a/(a + b*x^2))^(2/3)*(a + b*x^2)^(1/6)*Sqrt[-((1 - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2)])","A",8,7,15,0.4667,1,"{321, 238, 198, 235, 304, 219, 1879}"
1020,1,611,0,0.546757,"\int \frac{x^2}{\sqrt[6]{a+b x^2}} \, dx","Int[x^2/(a + b*x^2)^(1/6),x]","\frac{3\ 3^{3/4} a^2 \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{8 \sqrt{2} b^2 x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}-\frac{9 \sqrt[4]{3} \sqrt{2+\sqrt{3}} a^2 \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{32 b^2 x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}-\frac{9 a^2 x}{16 b \left(\frac{a}{a+b x^2}\right)^{2/3} \left(a+b x^2\right)^{7/6} \left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)}-\frac{9 a x}{16 b \sqrt[6]{a+b x^2}}+\frac{3 x \left(a+b x^2\right)^{5/6}}{8 b}","\frac{3\ 3^{3/4} a^2 \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{8 \sqrt{2} b^2 x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}-\frac{9 \sqrt[4]{3} \sqrt{2+\sqrt{3}} a^2 \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{32 b^2 x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}-\frac{9 a^2 x}{16 b \left(\frac{a}{a+b x^2}\right)^{2/3} \left(a+b x^2\right)^{7/6} \left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)}-\frac{9 a x}{16 b \sqrt[6]{a+b x^2}}+\frac{3 x \left(a+b x^2\right)^{5/6}}{8 b}",1,"(-9*a*x)/(16*b*(a + b*x^2)^(1/6)) + (3*x*(a + b*x^2)^(5/6))/(8*b) - (9*a^2*x)/(16*b*(a/(a + b*x^2))^(2/3)*(a + b*x^2)^(7/6)*(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))) - (9*3^(1/4)*Sqrt[2 + Sqrt[3]]*a^2*(1 - (a/(a + b*x^2))^(1/3))*Sqrt[(1 + (a/(a + b*x^2))^(1/3) + (a/(a + b*x^2))^(2/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2]*EllipticE[ArcSin[(1 + Sqrt[3] - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))], -7 + 4*Sqrt[3]])/(32*b^2*x*(a/(a + b*x^2))^(2/3)*(a + b*x^2)^(1/6)*Sqrt[-((1 - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2)]) + (3*3^(3/4)*a^2*(1 - (a/(a + b*x^2))^(1/3))*Sqrt[(1 + (a/(a + b*x^2))^(1/3) + (a/(a + b*x^2))^(2/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))], -7 + 4*Sqrt[3]])/(8*Sqrt[2]*b^2*x*(a/(a + b*x^2))^(2/3)*(a + b*x^2)^(1/6)*Sqrt[-((1 - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2)])","A",7,7,15,0.4667,1,"{321, 238, 198, 235, 304, 219, 1879}"
1021,1,577,0,0.4672358,"\int \frac{1}{\sqrt[6]{a+b x^2}} \, dx","Int[(a + b*x^2)^(-1/6),x]","\frac{3 x}{2 \sqrt[6]{a+b x^2}}+\frac{3 a x}{2 \left(\frac{a}{a+b x^2}\right)^{2/3} \left(a+b x^2\right)^{7/6} \left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)}-\frac{3^{3/4} a \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt{2} b x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}+\frac{3 \sqrt[4]{3} \sqrt{2+\sqrt{3}} a \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{4 b x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}","\frac{3 x}{2 \sqrt[6]{a+b x^2}}+\frac{3 a x}{2 \left(\frac{a}{a+b x^2}\right)^{2/3} \left(a+b x^2\right)^{7/6} \left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)}-\frac{3^{3/4} a \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt{2} b x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}+\frac{3 \sqrt[4]{3} \sqrt{2+\sqrt{3}} a \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{4 b x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}",1,"(3*x)/(2*(a + b*x^2)^(1/6)) + (3*a*x)/(2*(a/(a + b*x^2))^(2/3)*(a + b*x^2)^(7/6)*(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))) + (3*3^(1/4)*Sqrt[2 + Sqrt[3]]*a*(1 - (a/(a + b*x^2))^(1/3))*Sqrt[(1 + (a/(a + b*x^2))^(1/3) + (a/(a + b*x^2))^(2/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2]*EllipticE[ArcSin[(1 + Sqrt[3] - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))], -7 + 4*Sqrt[3]])/(4*b*x*(a/(a + b*x^2))^(2/3)*(a + b*x^2)^(1/6)*Sqrt[-((1 - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2)]) - (3^(3/4)*a*(1 - (a/(a + b*x^2))^(1/3))*Sqrt[(1 + (a/(a + b*x^2))^(1/3) + (a/(a + b*x^2))^(2/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))], -7 + 4*Sqrt[3]])/(Sqrt[2]*b*x*(a/(a + b*x^2))^(2/3)*(a + b*x^2)^(1/6)*Sqrt[-((1 - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2)])","A",6,6,11,0.5455,1,"{238, 198, 235, 304, 219, 1879}"
1022,1,586,0,0.5329923,"\int \frac{1}{x^2 \sqrt[6]{a+b x^2}} \, dx","Int[1/(x^2*(a + b*x^2)^(1/6)),x]","\frac{b x}{a \sqrt[6]{a+b x^2}}+\frac{b x}{\left(\frac{a}{a+b x^2}\right)^{2/3} \left(a+b x^2\right)^{7/6} \left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)}-\frac{\left(a+b x^2\right)^{5/6}}{a x}-\frac{\sqrt{2} \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}+\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{2 x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}","\frac{b x}{a \sqrt[6]{a+b x^2}}+\frac{b x}{\left(\frac{a}{a+b x^2}\right)^{2/3} \left(a+b x^2\right)^{7/6} \left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)}-\frac{\left(a+b x^2\right)^{5/6}}{a x}-\frac{\sqrt{2} \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}+\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{2 x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}",1,"(b*x)/(a*(a + b*x^2)^(1/6)) - (a + b*x^2)^(5/6)/(a*x) + (b*x)/((a/(a + b*x^2))^(2/3)*(a + b*x^2)^(7/6)*(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))) + (3^(1/4)*Sqrt[2 + Sqrt[3]]*(1 - (a/(a + b*x^2))^(1/3))*Sqrt[(1 + (a/(a + b*x^2))^(1/3) + (a/(a + b*x^2))^(2/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2]*EllipticE[ArcSin[(1 + Sqrt[3] - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))], -7 + 4*Sqrt[3]])/(2*x*(a/(a + b*x^2))^(2/3)*(a + b*x^2)^(1/6)*Sqrt[-((1 - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2)]) - (Sqrt[2]*(1 - (a/(a + b*x^2))^(1/3))*Sqrt[(1 + (a/(a + b*x^2))^(1/3) + (a/(a + b*x^2))^(2/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))], -7 + 4*Sqrt[3]])/(3^(1/4)*x*(a/(a + b*x^2))^(2/3)*(a + b*x^2)^(1/6)*Sqrt[-((1 - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2)])","A",7,7,15,0.4667,1,"{325, 238, 198, 235, 304, 219, 1879}"
1023,1,633,0,0.5946302,"\int \frac{1}{x^4 \sqrt[6]{a+b x^2}} \, dx","Int[1/(x^4*(a + b*x^2)^(1/6)),x]","-\frac{4 b^2 x}{9 a^2 \sqrt[6]{a+b x^2}}+\frac{4 b \left(a+b x^2\right)^{5/6}}{9 a^2 x}-\frac{4 b^2 x}{9 a \left(\frac{a}{a+b x^2}\right)^{2/3} \left(a+b x^2\right)^{7/6} \left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)}-\frac{\left(a+b x^2\right)^{5/6}}{3 a x^3}+\frac{4 \sqrt{2} b \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{9 \sqrt[4]{3} a x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}-\frac{2 \sqrt{2+\sqrt{3}} b \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{3\ 3^{3/4} a x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}","-\frac{4 b^2 x}{9 a^2 \sqrt[6]{a+b x^2}}+\frac{4 b \left(a+b x^2\right)^{5/6}}{9 a^2 x}-\frac{4 b^2 x}{9 a \left(\frac{a}{a+b x^2}\right)^{2/3} \left(a+b x^2\right)^{7/6} \left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)}-\frac{\left(a+b x^2\right)^{5/6}}{3 a x^3}+\frac{4 \sqrt{2} b \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{9 \sqrt[4]{3} a x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}-\frac{2 \sqrt{2+\sqrt{3}} b \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{3\ 3^{3/4} a x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}",1,"(-4*b^2*x)/(9*a^2*(a + b*x^2)^(1/6)) - (a + b*x^2)^(5/6)/(3*a*x^3) + (4*b*(a + b*x^2)^(5/6))/(9*a^2*x) - (4*b^2*x)/(9*a*(a/(a + b*x^2))^(2/3)*(a + b*x^2)^(7/6)*(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))) - (2*Sqrt[2 + Sqrt[3]]*b*(1 - (a/(a + b*x^2))^(1/3))*Sqrt[(1 + (a/(a + b*x^2))^(1/3) + (a/(a + b*x^2))^(2/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2]*EllipticE[ArcSin[(1 + Sqrt[3] - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))], -7 + 4*Sqrt[3]])/(3*3^(3/4)*a*x*(a/(a + b*x^2))^(2/3)*(a + b*x^2)^(1/6)*Sqrt[-((1 - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2)]) + (4*Sqrt[2]*b*(1 - (a/(a + b*x^2))^(1/3))*Sqrt[(1 + (a/(a + b*x^2))^(1/3) + (a/(a + b*x^2))^(2/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))], -7 + 4*Sqrt[3]])/(9*3^(1/4)*a*x*(a/(a + b*x^2))^(2/3)*(a + b*x^2)^(1/6)*Sqrt[-((1 - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2)])","A",8,7,15,0.4667,1,"{325, 238, 198, 235, 304, 219, 1879}"
1024,1,661,0,0.6721802,"\int \frac{1}{x^6 \sqrt[6]{a+b x^2}} \, dx","Int[1/(x^6*(a + b*x^2)^(1/6)),x]","\frac{8 b^3 x}{27 a^3 \sqrt[6]{a+b x^2}}+\frac{8 b^3 x}{27 a^2 \left(\frac{a}{a+b x^2}\right)^{2/3} \left(a+b x^2\right)^{7/6} \left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)}-\frac{8 b^2 \left(a+b x^2\right)^{5/6}}{27 a^3 x}-\frac{8 \sqrt{2} b^2 \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{27 \sqrt[4]{3} a^2 x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}+\frac{4 \sqrt{2+\sqrt{3}} b^2 \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{9\ 3^{3/4} a^2 x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}+\frac{2 b \left(a+b x^2\right)^{5/6}}{9 a^2 x^3}-\frac{\left(a+b x^2\right)^{5/6}}{5 a x^5}","\frac{8 b^3 x}{27 a^3 \sqrt[6]{a+b x^2}}+\frac{8 b^3 x}{27 a^2 \left(\frac{a}{a+b x^2}\right)^{2/3} \left(a+b x^2\right)^{7/6} \left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)}-\frac{8 b^2 \left(a+b x^2\right)^{5/6}}{27 a^3 x}-\frac{8 \sqrt{2} b^2 \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{27 \sqrt[4]{3} a^2 x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}+\frac{4 \sqrt{2+\sqrt{3}} b^2 \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{9\ 3^{3/4} a^2 x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}+\frac{2 b \left(a+b x^2\right)^{5/6}}{9 a^2 x^3}-\frac{\left(a+b x^2\right)^{5/6}}{5 a x^5}",1,"(8*b^3*x)/(27*a^3*(a + b*x^2)^(1/6)) - (a + b*x^2)^(5/6)/(5*a*x^5) + (2*b*(a + b*x^2)^(5/6))/(9*a^2*x^3) - (8*b^2*(a + b*x^2)^(5/6))/(27*a^3*x) + (8*b^3*x)/(27*a^2*(a/(a + b*x^2))^(2/3)*(a + b*x^2)^(7/6)*(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))) + (4*Sqrt[2 + Sqrt[3]]*b^2*(1 - (a/(a + b*x^2))^(1/3))*Sqrt[(1 + (a/(a + b*x^2))^(1/3) + (a/(a + b*x^2))^(2/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2]*EllipticE[ArcSin[(1 + Sqrt[3] - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))], -7 + 4*Sqrt[3]])/(9*3^(3/4)*a^2*x*(a/(a + b*x^2))^(2/3)*(a + b*x^2)^(1/6)*Sqrt[-((1 - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2)]) - (8*Sqrt[2]*b^2*(1 - (a/(a + b*x^2))^(1/3))*Sqrt[(1 + (a/(a + b*x^2))^(1/3) + (a/(a + b*x^2))^(2/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))], -7 + 4*Sqrt[3]])/(27*3^(1/4)*a^2*x*(a/(a + b*x^2))^(2/3)*(a + b*x^2)^(1/6)*Sqrt[-((1 - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2)])","A",9,7,15,0.4667,1,"{325, 238, 198, 235, 304, 219, 1879}"
1025,1,324,0,0.2920846,"\int \frac{x^6}{\left(a+b x^2\right)^{5/6}} \, dx","Int[x^6/(a + b*x^2)^(5/6),x]","\frac{81 a^2 x \sqrt[6]{a+b x^2}}{128 b^3}-\frac{81\ 3^{3/4} \sqrt{2-\sqrt{3}} a^3 \sqrt[6]{a+b x^2} \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{128 b^4 x \sqrt[3]{\frac{a}{a+b x^2}} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}-\frac{9 a x^3 \sqrt[6]{a+b x^2}}{32 b^2}+\frac{3 x^5 \sqrt[6]{a+b x^2}}{16 b}","\frac{81 a^2 x \sqrt[6]{a+b x^2}}{128 b^3}-\frac{81\ 3^{3/4} \sqrt{2-\sqrt{3}} a^3 \sqrt[6]{a+b x^2} \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{128 b^4 x \sqrt[3]{\frac{a}{a+b x^2}} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}-\frac{9 a x^3 \sqrt[6]{a+b x^2}}{32 b^2}+\frac{3 x^5 \sqrt[6]{a+b x^2}}{16 b}",1,"(81*a^2*x*(a + b*x^2)^(1/6))/(128*b^3) - (9*a*x^3*(a + b*x^2)^(1/6))/(32*b^2) + (3*x^5*(a + b*x^2)^(1/6))/(16*b) - (81*3^(3/4)*Sqrt[2 - Sqrt[3]]*a^3*(a + b*x^2)^(1/6)*(1 - (a/(a + b*x^2))^(1/3))*Sqrt[(1 + (a/(a + b*x^2))^(1/3) + (a/(a + b*x^2))^(2/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))], -7 + 4*Sqrt[3]])/(128*b^4*x*(a/(a + b*x^2))^(1/3)*Sqrt[-((1 - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2)])","A",6,4,15,0.2667,1,"{321, 241, 236, 219}"
1026,1,300,0,0.2514144,"\int \frac{x^4}{\left(a+b x^2\right)^{5/6}} \, dx","Int[x^4/(a + b*x^2)^(5/6),x]","\frac{27\ 3^{3/4} \sqrt{2-\sqrt{3}} a^2 \sqrt[6]{a+b x^2} \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{40 b^3 x \sqrt[3]{\frac{a}{a+b x^2}} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}-\frac{27 a x \sqrt[6]{a+b x^2}}{40 b^2}+\frac{3 x^3 \sqrt[6]{a+b x^2}}{10 b}","\frac{27\ 3^{3/4} \sqrt{2-\sqrt{3}} a^2 \sqrt[6]{a+b x^2} \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{40 b^3 x \sqrt[3]{\frac{a}{a+b x^2}} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}-\frac{27 a x \sqrt[6]{a+b x^2}}{40 b^2}+\frac{3 x^3 \sqrt[6]{a+b x^2}}{10 b}",1,"(-27*a*x*(a + b*x^2)^(1/6))/(40*b^2) + (3*x^3*(a + b*x^2)^(1/6))/(10*b) + (27*3^(3/4)*Sqrt[2 - Sqrt[3]]*a^2*(a + b*x^2)^(1/6)*(1 - (a/(a + b*x^2))^(1/3))*Sqrt[(1 + (a/(a + b*x^2))^(1/3) + (a/(a + b*x^2))^(2/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))], -7 + 4*Sqrt[3]])/(40*b^3*x*(a/(a + b*x^2))^(1/3)*Sqrt[-((1 - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2)])","A",5,4,15,0.2667,1,"{321, 241, 236, 219}"
1027,1,276,0,0.2121472,"\int \frac{x^2}{\left(a+b x^2\right)^{5/6}} \, dx","Int[x^2/(a + b*x^2)^(5/6),x]","\frac{3 x \sqrt[6]{a+b x^2}}{4 b}-\frac{3\ 3^{3/4} \sqrt{2-\sqrt{3}} a \sqrt[6]{a+b x^2} \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{4 b^2 x \sqrt[3]{\frac{a}{a+b x^2}} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}","\frac{3 x \sqrt[6]{a+b x^2}}{4 b}-\frac{3\ 3^{3/4} \sqrt{2-\sqrt{3}} a \sqrt[6]{a+b x^2} \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{4 b^2 x \sqrt[3]{\frac{a}{a+b x^2}} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}",1,"(3*x*(a + b*x^2)^(1/6))/(4*b) - (3*3^(3/4)*Sqrt[2 - Sqrt[3]]*a*(a + b*x^2)^(1/6)*(1 - (a/(a + b*x^2))^(1/3))*Sqrt[(1 + (a/(a + b*x^2))^(1/3) + (a/(a + b*x^2))^(2/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))], -7 + 4*Sqrt[3]])/(4*b^2*x*(a/(a + b*x^2))^(1/3)*Sqrt[-((1 - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2)])","A",4,4,15,0.2667,1,"{321, 241, 236, 219}"
1028,1,252,0,0.1839527,"\int \frac{1}{\left(a+b x^2\right)^{5/6}} \, dx","Int[(a + b*x^2)^(-5/6),x]","\frac{3^{3/4} \sqrt{2-\sqrt{3}} \sqrt[6]{a+b x^2} \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{b x \sqrt[3]{\frac{a}{a+b x^2}} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}","\frac{3^{3/4} \sqrt{2-\sqrt{3}} \sqrt[6]{a+b x^2} \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{b x \sqrt[3]{\frac{a}{a+b x^2}} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}",1,"(3^(3/4)*Sqrt[2 - Sqrt[3]]*(a + b*x^2)^(1/6)*(1 - (a/(a + b*x^2))^(1/3))*Sqrt[(1 + (a/(a + b*x^2))^(1/3) + (a/(a + b*x^2))^(2/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))], -7 + 4*Sqrt[3]])/(b*x*(a/(a + b*x^2))^(1/3)*Sqrt[-((1 - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2)])","A",3,3,11,0.2727,1,"{241, 236, 219}"
1029,1,273,0,0.211623,"\int \frac{1}{x^2 \left(a+b x^2\right)^{5/6}} \, dx","Int[1/(x^2*(a + b*x^2)^(5/6)),x]","-\frac{\sqrt[6]{a+b x^2}}{a x}-\frac{2 \sqrt{2-\sqrt{3}} \sqrt[6]{a+b x^2} \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} a x \sqrt[3]{\frac{a}{a+b x^2}} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}","-\frac{\sqrt[6]{a+b x^2}}{a x}-\frac{2 \sqrt{2-\sqrt{3}} \sqrt[6]{a+b x^2} \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} a x \sqrt[3]{\frac{a}{a+b x^2}} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}",1,"-((a + b*x^2)^(1/6)/(a*x)) - (2*Sqrt[2 - Sqrt[3]]*(a + b*x^2)^(1/6)*(1 - (a/(a + b*x^2))^(1/3))*Sqrt[(1 + (a/(a + b*x^2))^(1/3) + (a/(a + b*x^2))^(2/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))], -7 + 4*Sqrt[3]])/(3^(1/4)*a*x*(a/(a + b*x^2))^(1/3)*Sqrt[-((1 - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2)])","A",4,4,15,0.2667,1,"{325, 241, 236, 219}"
1030,1,300,0,0.2429567,"\int \frac{1}{x^4 \left(a+b x^2\right)^{5/6}} \, dx","Int[1/(x^4*(a + b*x^2)^(5/6)),x]","\frac{8 b \sqrt[6]{a+b x^2}}{9 a^2 x}+\frac{16 \sqrt{2-\sqrt{3}} b \sqrt[6]{a+b x^2} \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{9 \sqrt[4]{3} a^2 x \sqrt[3]{\frac{a}{a+b x^2}} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}-\frac{\sqrt[6]{a+b x^2}}{3 a x^3}","\frac{8 b \sqrt[6]{a+b x^2}}{9 a^2 x}+\frac{16 \sqrt{2-\sqrt{3}} b \sqrt[6]{a+b x^2} \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{9 \sqrt[4]{3} a^2 x \sqrt[3]{\frac{a}{a+b x^2}} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}-\frac{\sqrt[6]{a+b x^2}}{3 a x^3}",1,"-(a + b*x^2)^(1/6)/(3*a*x^3) + (8*b*(a + b*x^2)^(1/6))/(9*a^2*x) + (16*Sqrt[2 - Sqrt[3]]*b*(a + b*x^2)^(1/6)*(1 - (a/(a + b*x^2))^(1/3))*Sqrt[(1 + (a/(a + b*x^2))^(1/3) + (a/(a + b*x^2))^(2/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))], -7 + 4*Sqrt[3]])/(9*3^(1/4)*a^2*x*(a/(a + b*x^2))^(1/3)*Sqrt[-((1 - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2)])","A",5,4,15,0.2667,1,"{325, 241, 236, 219}"
1031,1,326,0,0.2788218,"\int \frac{1}{x^6 \left(a+b x^2\right)^{5/6}} \, dx","Int[1/(x^6*(a + b*x^2)^(5/6)),x]","-\frac{112 b^2 \sqrt[6]{a+b x^2}}{135 a^3 x}-\frac{224 \sqrt{2-\sqrt{3}} b^2 \sqrt[6]{a+b x^2} \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{135 \sqrt[4]{3} a^3 x \sqrt[3]{\frac{a}{a+b x^2}} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}+\frac{14 b \sqrt[6]{a+b x^2}}{45 a^2 x^3}-\frac{\sqrt[6]{a+b x^2}}{5 a x^5}","-\frac{112 b^2 \sqrt[6]{a+b x^2}}{135 a^3 x}-\frac{224 \sqrt{2-\sqrt{3}} b^2 \sqrt[6]{a+b x^2} \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{135 \sqrt[4]{3} a^3 x \sqrt[3]{\frac{a}{a+b x^2}} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}+\frac{14 b \sqrt[6]{a+b x^2}}{45 a^2 x^3}-\frac{\sqrt[6]{a+b x^2}}{5 a x^5}",1,"-(a + b*x^2)^(1/6)/(5*a*x^5) + (14*b*(a + b*x^2)^(1/6))/(45*a^2*x^3) - (112*b^2*(a + b*x^2)^(1/6))/(135*a^3*x) - (224*Sqrt[2 - Sqrt[3]]*b^2*(a + b*x^2)^(1/6)*(1 - (a/(a + b*x^2))^(1/3))*Sqrt[(1 + (a/(a + b*x^2))^(1/3) + (a/(a + b*x^2))^(2/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))], -7 + 4*Sqrt[3]])/(135*3^(1/4)*a^3*x*(a/(a + b*x^2))^(1/3)*Sqrt[-((1 - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2)])","A",6,4,15,0.2667,1,"{325, 241, 236, 219}"
1032,1,654,0,0.6688256,"\int \frac{x^6}{\left(a+b x^2\right)^{7/6}} \, dx","Int[x^6/(a + b*x^2)^(7/6),x]","\frac{1215 a^2 x}{224 b^3 \sqrt[6]{a+b x^2}}+\frac{1215 a^3 x}{224 b^3 \left(\frac{a}{a+b x^2}\right)^{2/3} \left(a+b x^2\right)^{7/6} \left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)}-\frac{405\ 3^{3/4} a^3 \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{112 \sqrt{2} b^4 x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}+\frac{1215 \sqrt[4]{3} \sqrt{2+\sqrt{3}} a^3 \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{448 b^4 x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}+\frac{45 x^3 \left(a+b x^2\right)^{5/6}}{14 b^2}-\frac{405 a x \left(a+b x^2\right)^{5/6}}{112 b^3}-\frac{3 x^5}{b \sqrt[6]{a+b x^2}}","\frac{1215 a^2 x}{224 b^3 \sqrt[6]{a+b x^2}}+\frac{1215 a^3 x}{224 b^3 \left(\frac{a}{a+b x^2}\right)^{2/3} \left(a+b x^2\right)^{7/6} \left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)}-\frac{405\ 3^{3/4} a^3 \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{112 \sqrt{2} b^4 x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}+\frac{1215 \sqrt[4]{3} \sqrt{2+\sqrt{3}} a^3 \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{448 b^4 x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}+\frac{45 x^3 \left(a+b x^2\right)^{5/6}}{14 b^2}-\frac{405 a x \left(a+b x^2\right)^{5/6}}{112 b^3}-\frac{3 x^5}{b \sqrt[6]{a+b x^2}}",1,"(1215*a^2*x)/(224*b^3*(a + b*x^2)^(1/6)) - (3*x^5)/(b*(a + b*x^2)^(1/6)) - (405*a*x*(a + b*x^2)^(5/6))/(112*b^3) + (45*x^3*(a + b*x^2)^(5/6))/(14*b^2) + (1215*a^3*x)/(224*b^3*(a/(a + b*x^2))^(2/3)*(a + b*x^2)^(7/6)*(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))) + (1215*3^(1/4)*Sqrt[2 + Sqrt[3]]*a^3*(1 - (a/(a + b*x^2))^(1/3))*Sqrt[(1 + (a/(a + b*x^2))^(1/3) + (a/(a + b*x^2))^(2/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2]*EllipticE[ArcSin[(1 + Sqrt[3] - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))], -7 + 4*Sqrt[3]])/(448*b^4*x*(a/(a + b*x^2))^(2/3)*(a + b*x^2)^(1/6)*Sqrt[-((1 - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2)]) - (405*3^(3/4)*a^3*(1 - (a/(a + b*x^2))^(1/3))*Sqrt[(1 + (a/(a + b*x^2))^(1/3) + (a/(a + b*x^2))^(2/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))], -7 + 4*Sqrt[3]])/(112*Sqrt[2]*b^4*x*(a/(a + b*x^2))^(2/3)*(a + b*x^2)^(1/6)*Sqrt[-((1 - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2)])","A",9,8,15,0.5333,1,"{288, 321, 238, 198, 235, 304, 219, 1879}"
1033,1,630,0,0.5916132,"\int \frac{x^4}{\left(a+b x^2\right)^{7/6}} \, dx","Int[x^4/(a + b*x^2)^(7/6),x]","-\frac{81 a^2 x}{16 b^2 \left(\frac{a}{a+b x^2}\right)^{2/3} \left(a+b x^2\right)^{7/6} \left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)}+\frac{27\ 3^{3/4} a^2 \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{8 \sqrt{2} b^3 x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}-\frac{81 \sqrt[4]{3} \sqrt{2+\sqrt{3}} a^2 \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{32 b^3 x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}+\frac{27 x \left(a+b x^2\right)^{5/6}}{8 b^2}-\frac{81 a x}{16 b^2 \sqrt[6]{a+b x^2}}-\frac{3 x^3}{b \sqrt[6]{a+b x^2}}","-\frac{81 a^2 x}{16 b^2 \left(\frac{a}{a+b x^2}\right)^{2/3} \left(a+b x^2\right)^{7/6} \left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)}+\frac{27\ 3^{3/4} a^2 \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{8 \sqrt{2} b^3 x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}-\frac{81 \sqrt[4]{3} \sqrt{2+\sqrt{3}} a^2 \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{32 b^3 x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}+\frac{27 x \left(a+b x^2\right)^{5/6}}{8 b^2}-\frac{81 a x}{16 b^2 \sqrt[6]{a+b x^2}}-\frac{3 x^3}{b \sqrt[6]{a+b x^2}}",1,"(-81*a*x)/(16*b^2*(a + b*x^2)^(1/6)) - (3*x^3)/(b*(a + b*x^2)^(1/6)) + (27*x*(a + b*x^2)^(5/6))/(8*b^2) - (81*a^2*x)/(16*b^2*(a/(a + b*x^2))^(2/3)*(a + b*x^2)^(7/6)*(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))) - (81*3^(1/4)*Sqrt[2 + Sqrt[3]]*a^2*(1 - (a/(a + b*x^2))^(1/3))*Sqrt[(1 + (a/(a + b*x^2))^(1/3) + (a/(a + b*x^2))^(2/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2]*EllipticE[ArcSin[(1 + Sqrt[3] - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))], -7 + 4*Sqrt[3]])/(32*b^3*x*(a/(a + b*x^2))^(2/3)*(a + b*x^2)^(1/6)*Sqrt[-((1 - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2)]) + (27*3^(3/4)*a^2*(1 - (a/(a + b*x^2))^(1/3))*Sqrt[(1 + (a/(a + b*x^2))^(1/3) + (a/(a + b*x^2))^(2/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))], -7 + 4*Sqrt[3]])/(8*Sqrt[2]*b^3*x*(a/(a + b*x^2))^(2/3)*(a + b*x^2)^(1/6)*Sqrt[-((1 - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2)])","A",8,8,15,0.5333,1,"{288, 321, 238, 198, 235, 304, 219, 1879}"
1034,1,583,0,0.5224276,"\int \frac{x^2}{\left(a+b x^2\right)^{7/6}} \, dx","Int[x^2/(a + b*x^2)^(7/6),x]","-\frac{3\ 3^{3/4} a \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt{2} b^2 x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}+\frac{9 \sqrt[4]{3} \sqrt{2+\sqrt{3}} a \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{4 b^2 x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}+\frac{3 x}{2 b \sqrt[6]{a+b x^2}}+\frac{9 a x}{2 b \left(\frac{a}{a+b x^2}\right)^{2/3} \left(a+b x^2\right)^{7/6} \left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)}","-\frac{3\ 3^{3/4} a \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt{2} b^2 x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}+\frac{9 \sqrt[4]{3} \sqrt{2+\sqrt{3}} a \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{4 b^2 x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}+\frac{3 x}{2 b \sqrt[6]{a+b x^2}}+\frac{9 a x}{2 b \left(\frac{a}{a+b x^2}\right)^{2/3} \left(a+b x^2\right)^{7/6} \left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)}",1,"(3*x)/(2*b*(a + b*x^2)^(1/6)) + (9*a*x)/(2*b*(a/(a + b*x^2))^(2/3)*(a + b*x^2)^(7/6)*(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))) + (9*3^(1/4)*Sqrt[2 + Sqrt[3]]*a*(1 - (a/(a + b*x^2))^(1/3))*Sqrt[(1 + (a/(a + b*x^2))^(1/3) + (a/(a + b*x^2))^(2/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2]*EllipticE[ArcSin[(1 + Sqrt[3] - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))], -7 + 4*Sqrt[3]])/(4*b^2*x*(a/(a + b*x^2))^(2/3)*(a + b*x^2)^(1/6)*Sqrt[-((1 - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2)]) - (3*3^(3/4)*a*(1 - (a/(a + b*x^2))^(1/3))*Sqrt[(1 + (a/(a + b*x^2))^(1/3) + (a/(a + b*x^2))^(2/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))], -7 + 4*Sqrt[3]])/(Sqrt[2]*b^2*x*(a/(a + b*x^2))^(2/3)*(a + b*x^2)^(1/6)*Sqrt[-((1 - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2)])","A",7,7,15,0.4667,1,"{288, 238, 198, 235, 304, 219, 1879}"
1035,1,555,0,0.3941794,"\int \frac{1}{\left(a+b x^2\right)^{7/6}} \, dx","Int[(a + b*x^2)^(-7/6),x]","-\frac{3 x}{\left(\frac{a}{a+b x^2}\right)^{2/3} \left(a+b x^2\right)^{7/6} \left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)}+\frac{\sqrt{2} 3^{3/4} \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{b x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}-\frac{3 \sqrt[4]{3} \sqrt{2+\sqrt{3}} \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{2 b x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}","-\frac{3 x}{\left(\frac{a}{a+b x^2}\right)^{2/3} \left(a+b x^2\right)^{7/6} \left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)}+\frac{\sqrt{2} 3^{3/4} \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{b x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}-\frac{3 \sqrt[4]{3} \sqrt{2+\sqrt{3}} \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{2 b x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}",1,"(-3*x)/((a/(a + b*x^2))^(2/3)*(a + b*x^2)^(7/6)*(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))) - (3*3^(1/4)*Sqrt[2 + Sqrt[3]]*(1 - (a/(a + b*x^2))^(1/3))*Sqrt[(1 + (a/(a + b*x^2))^(1/3) + (a/(a + b*x^2))^(2/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2]*EllipticE[ArcSin[(1 + Sqrt[3] - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))], -7 + 4*Sqrt[3]])/(2*b*x*(a/(a + b*x^2))^(2/3)*(a + b*x^2)^(1/6)*Sqrt[-((1 - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2)]) + (Sqrt[2]*3^(3/4)*(1 - (a/(a + b*x^2))^(1/3))*Sqrt[(1 + (a/(a + b*x^2))^(1/3) + (a/(a + b*x^2))^(2/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))], -7 + 4*Sqrt[3]])/(b*x*(a/(a + b*x^2))^(2/3)*(a + b*x^2)^(1/6)*Sqrt[-((1 - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2)])","A",5,5,11,0.4545,1,"{198, 235, 304, 219, 1879}"
1036,1,614,0,0.5739681,"\int \frac{1}{x^2 \left(a+b x^2\right)^{7/6}} \, dx","Int[1/(x^2*(a + b*x^2)^(7/6)),x]","\frac{4 b x}{a^2 \sqrt[6]{a+b x^2}}-\frac{4 \left(a+b x^2\right)^{5/6}}{a^2 x}+\frac{4 b x}{a \left(\frac{a}{a+b x^2}\right)^{2/3} \left(a+b x^2\right)^{7/6} \left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)}+\frac{3}{a x \sqrt[6]{a+b x^2}}-\frac{4 \sqrt{2} \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} a x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}+\frac{2 \sqrt[4]{3} \sqrt{2+\sqrt{3}} \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{a x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}","\frac{4 b x}{a^2 \sqrt[6]{a+b x^2}}-\frac{4 \left(a+b x^2\right)^{5/6}}{a^2 x}+\frac{4 b x}{a \left(\frac{a}{a+b x^2}\right)^{2/3} \left(a+b x^2\right)^{7/6} \left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)}+\frac{3}{a x \sqrt[6]{a+b x^2}}-\frac{4 \sqrt{2} \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} a x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}+\frac{2 \sqrt[4]{3} \sqrt{2+\sqrt{3}} \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{a x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}",1,"3/(a*x*(a + b*x^2)^(1/6)) + (4*b*x)/(a^2*(a + b*x^2)^(1/6)) - (4*(a + b*x^2)^(5/6))/(a^2*x) + (4*b*x)/(a*(a/(a + b*x^2))^(2/3)*(a + b*x^2)^(7/6)*(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))) + (2*3^(1/4)*Sqrt[2 + Sqrt[3]]*(1 - (a/(a + b*x^2))^(1/3))*Sqrt[(1 + (a/(a + b*x^2))^(1/3) + (a/(a + b*x^2))^(2/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2]*EllipticE[ArcSin[(1 + Sqrt[3] - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))], -7 + 4*Sqrt[3]])/(a*x*(a/(a + b*x^2))^(2/3)*(a + b*x^2)^(1/6)*Sqrt[-((1 - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2)]) - (4*Sqrt[2]*(1 - (a/(a + b*x^2))^(1/3))*Sqrt[(1 + (a/(a + b*x^2))^(1/3) + (a/(a + b*x^2))^(2/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))], -7 + 4*Sqrt[3]])/(3^(1/4)*a*x*(a/(a + b*x^2))^(2/3)*(a + b*x^2)^(1/6)*Sqrt[-((1 - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2)])","A",8,8,15,0.5333,1,"{290, 325, 238, 198, 235, 304, 219, 1879}"
1037,1,652,0,0.6538086,"\int \frac{1}{x^4 \left(a+b x^2\right)^{7/6}} \, dx","Int[1/(x^4*(a + b*x^2)^(7/6)),x]","-\frac{40 b^2 x}{9 a^3 \sqrt[6]{a+b x^2}}-\frac{40 b^2 x}{9 a^2 \left(\frac{a}{a+b x^2}\right)^{2/3} \left(a+b x^2\right)^{7/6} \left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)}+\frac{40 b \left(a+b x^2\right)^{5/6}}{9 a^3 x}-\frac{10 \left(a+b x^2\right)^{5/6}}{3 a^2 x^3}+\frac{40 \sqrt{2} b \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{9 \sqrt[4]{3} a^2 x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}-\frac{20 \sqrt{2+\sqrt{3}} b \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{3\ 3^{3/4} a^2 x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}+\frac{3}{a x^3 \sqrt[6]{a+b x^2}}","-\frac{40 b^2 x}{9 a^3 \sqrt[6]{a+b x^2}}-\frac{40 b^2 x}{9 a^2 \left(\frac{a}{a+b x^2}\right)^{2/3} \left(a+b x^2\right)^{7/6} \left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)}+\frac{40 b \left(a+b x^2\right)^{5/6}}{9 a^3 x}-\frac{10 \left(a+b x^2\right)^{5/6}}{3 a^2 x^3}+\frac{40 \sqrt{2} b \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{9 \sqrt[4]{3} a^2 x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}-\frac{20 \sqrt{2+\sqrt{3}} b \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{3\ 3^{3/4} a^2 x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}+\frac{3}{a x^3 \sqrt[6]{a+b x^2}}",1,"3/(a*x^3*(a + b*x^2)^(1/6)) - (40*b^2*x)/(9*a^3*(a + b*x^2)^(1/6)) - (10*(a + b*x^2)^(5/6))/(3*a^2*x^3) + (40*b*(a + b*x^2)^(5/6))/(9*a^3*x) - (40*b^2*x)/(9*a^2*(a/(a + b*x^2))^(2/3)*(a + b*x^2)^(7/6)*(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))) - (20*Sqrt[2 + Sqrt[3]]*b*(1 - (a/(a + b*x^2))^(1/3))*Sqrt[(1 + (a/(a + b*x^2))^(1/3) + (a/(a + b*x^2))^(2/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2]*EllipticE[ArcSin[(1 + Sqrt[3] - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))], -7 + 4*Sqrt[3]])/(3*3^(3/4)*a^2*x*(a/(a + b*x^2))^(2/3)*(a + b*x^2)^(1/6)*Sqrt[-((1 - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2)]) + (40*Sqrt[2]*b*(1 - (a/(a + b*x^2))^(1/3))*Sqrt[(1 + (a/(a + b*x^2))^(1/3) + (a/(a + b*x^2))^(2/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))], -7 + 4*Sqrt[3]])/(9*3^(1/4)*a^2*x*(a/(a + b*x^2))^(2/3)*(a + b*x^2)^(1/6)*Sqrt[-((1 - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2)])","A",9,8,15,0.5333,1,"{290, 325, 238, 198, 235, 304, 219, 1879}"
1038,1,680,0,0.7414268,"\int \frac{1}{x^6 \left(a+b x^2\right)^{7/6}} \, dx","Int[1/(x^6*(a + b*x^2)^(7/6)),x]","\frac{128 b^3 x}{27 a^4 \sqrt[6]{a+b x^2}}+\frac{128 b^3 x}{27 a^3 \left(\frac{a}{a+b x^2}\right)^{2/3} \left(a+b x^2\right)^{7/6} \left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)}-\frac{128 b^2 \left(a+b x^2\right)^{5/6}}{27 a^4 x}-\frac{128 \sqrt{2} b^2 \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{27 \sqrt[4]{3} a^3 x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}+\frac{64 \sqrt{2+\sqrt{3}} b^2 \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{9\ 3^{3/4} a^3 x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}+\frac{32 b \left(a+b x^2\right)^{5/6}}{9 a^3 x^3}-\frac{16 \left(a+b x^2\right)^{5/6}}{5 a^2 x^5}+\frac{3}{a x^5 \sqrt[6]{a+b x^2}}","\frac{128 b^3 x}{27 a^4 \sqrt[6]{a+b x^2}}+\frac{128 b^3 x}{27 a^3 \left(\frac{a}{a+b x^2}\right)^{2/3} \left(a+b x^2\right)^{7/6} \left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)}-\frac{128 b^2 \left(a+b x^2\right)^{5/6}}{27 a^4 x}-\frac{128 \sqrt{2} b^2 \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{27 \sqrt[4]{3} a^3 x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}+\frac{64 \sqrt{2+\sqrt{3}} b^2 \left(1-\sqrt[3]{\frac{a}{a+b x^2}}\right) \sqrt{\frac{\left(\frac{a}{a+b x^2}\right)^{2/3}+\sqrt[3]{\frac{a}{a+b x^2}}+1}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{a}{b x^2+a}}+\sqrt{3}+1}{-\sqrt[3]{\frac{a}{b x^2+a}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{9\ 3^{3/4} a^3 x \left(\frac{a}{a+b x^2}\right)^{2/3} \sqrt[6]{a+b x^2} \sqrt{-\frac{1-\sqrt[3]{\frac{a}{a+b x^2}}}{\left(-\sqrt[3]{\frac{a}{a+b x^2}}-\sqrt{3}+1\right)^2}}}+\frac{32 b \left(a+b x^2\right)^{5/6}}{9 a^3 x^3}-\frac{16 \left(a+b x^2\right)^{5/6}}{5 a^2 x^5}+\frac{3}{a x^5 \sqrt[6]{a+b x^2}}",1,"3/(a*x^5*(a + b*x^2)^(1/6)) + (128*b^3*x)/(27*a^4*(a + b*x^2)^(1/6)) - (16*(a + b*x^2)^(5/6))/(5*a^2*x^5) + (32*b*(a + b*x^2)^(5/6))/(9*a^3*x^3) - (128*b^2*(a + b*x^2)^(5/6))/(27*a^4*x) + (128*b^3*x)/(27*a^3*(a/(a + b*x^2))^(2/3)*(a + b*x^2)^(7/6)*(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))) + (64*Sqrt[2 + Sqrt[3]]*b^2*(1 - (a/(a + b*x^2))^(1/3))*Sqrt[(1 + (a/(a + b*x^2))^(1/3) + (a/(a + b*x^2))^(2/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2]*EllipticE[ArcSin[(1 + Sqrt[3] - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))], -7 + 4*Sqrt[3]])/(9*3^(3/4)*a^3*x*(a/(a + b*x^2))^(2/3)*(a + b*x^2)^(1/6)*Sqrt[-((1 - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2)]) - (128*Sqrt[2]*b^2*(1 - (a/(a + b*x^2))^(1/3))*Sqrt[(1 + (a/(a + b*x^2))^(1/3) + (a/(a + b*x^2))^(2/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))], -7 + 4*Sqrt[3]])/(27*3^(1/4)*a^3*x*(a/(a + b*x^2))^(2/3)*(a + b*x^2)^(1/6)*Sqrt[-((1 - (a/(a + b*x^2))^(1/3))/(1 - Sqrt[3] - (a/(a + b*x^2))^(1/3))^2)])","A",10,8,15,0.5333,1,"{290, 325, 238, 198, 235, 304, 219, 1879}"
1039,1,100,0,0.0635418,"\int x^7 \left(a+b x^2\right)^p \, dx","Int[x^7*(a + b*x^2)^p,x]","-\frac{a^3 \left(a+b x^2\right)^{p+1}}{2 b^4 (p+1)}+\frac{3 a^2 \left(a+b x^2\right)^{p+2}}{2 b^4 (p+2)}-\frac{3 a \left(a+b x^2\right)^{p+3}}{2 b^4 (p+3)}+\frac{\left(a+b x^2\right)^{p+4}}{2 b^4 (p+4)}","-\frac{a^3 \left(a+b x^2\right)^{p+1}}{2 b^4 (p+1)}+\frac{3 a^2 \left(a+b x^2\right)^{p+2}}{2 b^4 (p+2)}-\frac{3 a \left(a+b x^2\right)^{p+3}}{2 b^4 (p+3)}+\frac{\left(a+b x^2\right)^{p+4}}{2 b^4 (p+4)}",1,"-(a^3*(a + b*x^2)^(1 + p))/(2*b^4*(1 + p)) + (3*a^2*(a + b*x^2)^(2 + p))/(2*b^4*(2 + p)) - (3*a*(a + b*x^2)^(3 + p))/(2*b^4*(3 + p)) + (a + b*x^2)^(4 + p)/(2*b^4*(4 + p))","A",3,2,13,0.1538,1,"{266, 43}"
1040,1,72,0,0.0431496,"\int x^5 \left(a+b x^2\right)^p \, dx","Int[x^5*(a + b*x^2)^p,x]","\frac{a^2 \left(a+b x^2\right)^{p+1}}{2 b^3 (p+1)}-\frac{a \left(a+b x^2\right)^{p+2}}{b^3 (p+2)}+\frac{\left(a+b x^2\right)^{p+3}}{2 b^3 (p+3)}","\frac{a^2 \left(a+b x^2\right)^{p+1}}{2 b^3 (p+1)}-\frac{a \left(a+b x^2\right)^{p+2}}{b^3 (p+2)}+\frac{\left(a+b x^2\right)^{p+3}}{2 b^3 (p+3)}",1,"(a^2*(a + b*x^2)^(1 + p))/(2*b^3*(1 + p)) - (a*(a + b*x^2)^(2 + p))/(b^3*(2 + p)) + (a + b*x^2)^(3 + p)/(2*b^3*(3 + p))","A",3,2,13,0.1538,1,"{266, 43}"
1041,1,48,0,0.0289054,"\int x^3 \left(a+b x^2\right)^p \, dx","Int[x^3*(a + b*x^2)^p,x]","\frac{\left(a+b x^2\right)^{p+2}}{2 b^2 (p+2)}-\frac{a \left(a+b x^2\right)^{p+1}}{2 b^2 (p+1)}","\frac{\left(a+b x^2\right)^{p+2}}{2 b^2 (p+2)}-\frac{a \left(a+b x^2\right)^{p+1}}{2 b^2 (p+1)}",1,"-(a*(a + b*x^2)^(1 + p))/(2*b^2*(1 + p)) + (a + b*x^2)^(2 + p)/(2*b^2*(2 + p))","A",3,2,13,0.1538,1,"{266, 43}"
1042,1,23,0,0.0047815,"\int x \left(a+b x^2\right)^p \, dx","Int[x*(a + b*x^2)^p,x]","\frac{\left(a+b x^2\right)^{p+1}}{2 b (p+1)}","\frac{\left(a+b x^2\right)^{p+1}}{2 b (p+1)}",1,"(a + b*x^2)^(1 + p)/(2*b*(1 + p))","A",1,1,11,0.09091,1,"{261}"
1043,1,41,0,0.0222451,"\int \frac{\left(a+b x^2\right)^p}{x} \, dx","Int[(a + b*x^2)^p/x,x]","-\frac{\left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{b x^2}{a}+1\right)}{2 a (p+1)}","-\frac{\left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{b x^2}{a}+1\right)}{2 a (p+1)}",1,"-((a + b*x^2)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, 1 + (b*x^2)/a])/(2*a*(1 + p))","A",2,2,13,0.1538,1,"{266, 65}"
1044,1,42,0,0.0225637,"\int \frac{\left(a+b x^2\right)^p}{x^3} \, dx","Int[(a + b*x^2)^p/x^3,x]","\frac{b \left(a+b x^2\right)^{p+1} \, _2F_1\left(2,p+1;p+2;\frac{b x^2}{a}+1\right)}{2 a^2 (p+1)}","\frac{b \left(a+b x^2\right)^{p+1} \, _2F_1\left(2,p+1;p+2;\frac{b x^2}{a}+1\right)}{2 a^2 (p+1)}",1,"(b*(a + b*x^2)^(1 + p)*Hypergeometric2F1[2, 1 + p, 2 + p, 1 + (b*x^2)/a])/(2*a^2*(1 + p))","A",2,2,13,0.1538,1,"{266, 65}"
1045,1,49,0,0.0129535,"\int x^6 \left(a+b x^2\right)^p \, dx","Int[x^6*(a + b*x^2)^p,x]","\frac{1}{7} x^7 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{7}{2},-p;\frac{9}{2};-\frac{b x^2}{a}\right)","\frac{x^7 \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+\frac{9}{2};\frac{9}{2};-\frac{b x^2}{a}\right)}{7 a}",1,"(x^7*(a + b*x^2)^p*Hypergeometric2F1[7/2, -p, 9/2, -((b*x^2)/a)])/(7*(1 + (b*x^2)/a)^p)","A",2,2,13,0.1538,1,"{365, 364}"
1046,1,49,0,0.0129529,"\int x^4 \left(a+b x^2\right)^p \, dx","Int[x^4*(a + b*x^2)^p,x]","\frac{1}{5} x^5 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{5}{2},-p;\frac{7}{2};-\frac{b x^2}{a}\right)","\frac{x^5 \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+\frac{7}{2};\frac{7}{2};-\frac{b x^2}{a}\right)}{5 a}",1,"(x^5*(a + b*x^2)^p*Hypergeometric2F1[5/2, -p, 7/2, -((b*x^2)/a)])/(5*(1 + (b*x^2)/a)^p)","A",2,2,13,0.1538,1,"{365, 364}"
1047,1,49,0,0.0138384,"\int x^2 \left(a+b x^2\right)^p \, dx","Int[x^2*(a + b*x^2)^p,x]","\frac{1}{3} x^3 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{3}{2},-p;\frac{5}{2};-\frac{b x^2}{a}\right)","\frac{x^3 \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+\frac{5}{2};\frac{5}{2};-\frac{b x^2}{a}\right)}{3 a}",1,"(x^3*(a + b*x^2)^p*Hypergeometric2F1[3/2, -p, 5/2, -((b*x^2)/a)])/(3*(1 + (b*x^2)/a)^p)","A",2,2,13,0.1538,1,"{365, 364}"
1048,1,44,0,0.0094728,"\int \left(a+b x^2\right)^p \, dx","Int[(a + b*x^2)^p,x]","x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{b x^2}{a}\right)","\frac{x \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+\frac{3}{2};\frac{3}{2};-\frac{b x^2}{a}\right)}{a}",1,"(x*(a + b*x^2)^p*Hypergeometric2F1[1/2, -p, 3/2, -((b*x^2)/a)])/(1 + (b*x^2)/a)^p","A",2,2,9,0.2222,1,"{246, 245}"
1049,1,47,0,0.0133995,"\int \frac{\left(a+b x^2\right)^p}{x^2} \, dx","Int[(a + b*x^2)^p/x^2,x]","-\frac{\left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(-\frac{1}{2},-p;\frac{1}{2};-\frac{b x^2}{a}\right)}{x}","-\frac{\left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+\frac{1}{2};\frac{1}{2};-\frac{b x^2}{a}\right)}{a x}",1,"-(((a + b*x^2)^p*Hypergeometric2F1[-1/2, -p, 1/2, -((b*x^2)/a)])/(x*(1 + (b*x^2)/a)^p))","A",2,2,13,0.1538,1,"{365, 364}"
1050,1,51,0,0.0134661,"\int x^{7/2} \left(a+b x^2\right)^p \, dx","Int[x^(7/2)*(a + b*x^2)^p,x]","\frac{2}{9} x^{9/2} \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{9}{4},-p;\frac{13}{4};-\frac{b x^2}{a}\right)","\frac{2 x^{9/2} \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+\frac{13}{4};\frac{13}{4};-\frac{b x^2}{a}\right)}{9 a}",1,"(2*x^(9/2)*(a + b*x^2)^p*Hypergeometric2F1[9/4, -p, 13/4, -((b*x^2)/a)])/(9*(1 + (b*x^2)/a)^p)","A",2,2,15,0.1333,1,"{365, 364}"
1051,1,51,0,0.0137521,"\int x^{5/2} \left(a+b x^2\right)^p \, dx","Int[x^(5/2)*(a + b*x^2)^p,x]","\frac{2}{7} x^{7/2} \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{7}{4},-p;\frac{11}{4};-\frac{b x^2}{a}\right)","\frac{2 x^{7/2} \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+\frac{11}{4};\frac{11}{4};-\frac{b x^2}{a}\right)}{7 a}",1,"(2*x^(7/2)*(a + b*x^2)^p*Hypergeometric2F1[7/4, -p, 11/4, -((b*x^2)/a)])/(7*(1 + (b*x^2)/a)^p)","A",2,2,15,0.1333,1,"{365, 364}"
1052,1,51,0,0.0133974,"\int x^{3/2} \left(a+b x^2\right)^p \, dx","Int[x^(3/2)*(a + b*x^2)^p,x]","\frac{2}{5} x^{5/2} \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{5}{4},-p;\frac{9}{4};-\frac{b x^2}{a}\right)","\frac{2 x^{5/2} \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+\frac{9}{4};\frac{9}{4};-\frac{b x^2}{a}\right)}{5 a}",1,"(2*x^(5/2)*(a + b*x^2)^p*Hypergeometric2F1[5/4, -p, 9/4, -((b*x^2)/a)])/(5*(1 + (b*x^2)/a)^p)","A",2,2,15,0.1333,1,"{365, 364}"
1053,1,51,0,0.012401,"\int \sqrt{x} \left(a+b x^2\right)^p \, dx","Int[Sqrt[x]*(a + b*x^2)^p,x]","\frac{2}{3} x^{3/2} \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{3}{4},-p;\frac{7}{4};-\frac{b x^2}{a}\right)","\frac{2 x^{3/2} \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+\frac{7}{4};\frac{7}{4};-\frac{b x^2}{a}\right)}{3 a}",1,"(2*x^(3/2)*(a + b*x^2)^p*Hypergeometric2F1[3/4, -p, 7/4, -((b*x^2)/a)])/(3*(1 + (b*x^2)/a)^p)","A",2,2,15,0.1333,1,"{365, 364}"
1054,1,49,0,0.0125484,"\int \frac{\left(a+b x^2\right)^p}{\sqrt{x}} \, dx","Int[(a + b*x^2)^p/Sqrt[x],x]","2 \sqrt{x} \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{1}{4},-p;\frac{5}{4};-\frac{b x^2}{a}\right)","\frac{2 \sqrt{x} \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+\frac{5}{4};\frac{5}{4};-\frac{b x^2}{a}\right)}{a}",1,"(2*Sqrt[x]*(a + b*x^2)^p*Hypergeometric2F1[1/4, -p, 5/4, -((b*x^2)/a)])/(1 + (b*x^2)/a)^p","A",2,2,15,0.1333,1,"{365, 364}"
1055,1,49,0,0.0131761,"\int \frac{\left(a+b x^2\right)^p}{x^{3/2}} \, dx","Int[(a + b*x^2)^p/x^(3/2),x]","-\frac{2 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(-\frac{1}{4},-p;\frac{3}{4};-\frac{b x^2}{a}\right)}{\sqrt{x}}","-\frac{2 \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+\frac{3}{4};\frac{3}{4};-\frac{b x^2}{a}\right)}{a \sqrt{x}}",1,"(-2*(a + b*x^2)^p*Hypergeometric2F1[-1/4, -p, 3/4, -((b*x^2)/a)])/(Sqrt[x]*(1 + (b*x^2)/a)^p)","A",2,2,15,0.1333,1,"{365, 364}"
1056,1,51,0,0.0135999,"\int \frac{\left(a+b x^2\right)^p}{x^{5/2}} \, dx","Int[(a + b*x^2)^p/x^(5/2),x]","-\frac{2 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(-\frac{3}{4},-p;\frac{1}{4};-\frac{b x^2}{a}\right)}{3 x^{3/2}}","-\frac{2 \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p+\frac{1}{4};\frac{1}{4};-\frac{b x^2}{a}\right)}{3 a x^{3/2}}",1,"(-2*(a + b*x^2)^p*Hypergeometric2F1[-3/4, -p, 1/4, -((b*x^2)/a)])/(3*x^(3/2)*(1 + (b*x^2)/a)^p)","A",2,2,15,0.1333,1,"{365, 364}"
1057,1,51,0,0.0130226,"\int \frac{\left(a+b x^2\right)^p}{x^{7/2}} \, dx","Int[(a + b*x^2)^p/x^(7/2),x]","-\frac{2 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(-\frac{5}{4},-p;-\frac{1}{4};-\frac{b x^2}{a}\right)}{5 x^{5/2}}","-\frac{2 \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,p-\frac{1}{4};-\frac{1}{4};-\frac{b x^2}{a}\right)}{5 a x^{5/2}}",1,"(-2*(a + b*x^2)^p*Hypergeometric2F1[-5/4, -p, -1/4, -((b*x^2)/a)])/(5*x^(5/2)*(1 + (b*x^2)/a)^p)","A",2,2,15,0.1333,1,"{365, 364}"
1058,1,61,0,0.0167581,"\int x^m \left(a+b x^2\right)^p \, dx","Int[x^m*(a + b*x^2)^p,x]","\frac{x^{m+1} \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+1}{2},-p;\frac{m+3}{2};-\frac{b x^2}{a}\right)}{m+1}","\frac{x^{m+1} \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,\frac{1}{2} (m+2 p+3);\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a (m+1)}",1,"(x^(1 + m)*(a + b*x^2)^p*Hypergeometric2F1[(1 + m)/2, -p, (3 + m)/2, -((b*x^2)/a)])/((1 + m)*(1 + (b*x^2)/a)^p)","A",2,2,13,0.1538,1,"{365, 364}"
1059,1,66,0,0.0189753,"\int (c x)^m \left(a+b x^2\right)^p \, dx","Int[(c*x)^m*(a + b*x^2)^p,x]","\frac{(c x)^{m+1} \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+1}{2},-p;\frac{m+3}{2};-\frac{b x^2}{a}\right)}{c (m+1)}","\frac{(c x)^{m+1} \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+1}{2},-p;\frac{m+3}{2};-\frac{b x^2}{a}\right)}{c (m+1)}",1,"((c*x)^(1 + m)*(a + b*x^2)^p*Hypergeometric2F1[(1 + m)/2, -p, (3 + m)/2, -((b*x^2)/a)])/(c*(1 + m)*(1 + (b*x^2)/a)^p)","A",2,2,15,0.1333,1,"{365, 364}"
1060,1,70,0,0.0208351,"\int x^{-8-2 p} \left(a+b x^2\right)^p \, dx","Int[x^(-8 - 2*p)*(a + b*x^2)^p,x]","-\frac{x^{-2 p-7} \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{1}{2} (-2 p-7),-p;\frac{1}{2} (-2 p-5);-\frac{b x^2}{a}\right)}{2 p+7}","-\frac{x^{-2 p-7} \left(a+b x^2\right)^{p+1} \, _2F_1\left(-\frac{5}{2},1;\frac{1}{2} (-2 p-5);-\frac{b x^2}{a}\right)}{a (2 p+7)}",1,"-((x^(-7 - 2*p)*(a + b*x^2)^p*Hypergeometric2F1[(-7 - 2*p)/2, -p, (-5 - 2*p)/2, -((b*x^2)/a)])/((7 + 2*p)*(1 + (b*x^2)/a)^p))","A",2,2,17,0.1176,1,"{365, 364}"
1061,1,105,0,0.0571453,"\int x^{-7-2 p} \left(a+b x^2\right)^p \, dx","Int[x^(-7 - 2*p)*(a + b*x^2)^p,x]","-\frac{b^2 x^{-2 (p+1)} \left(a+b x^2\right)^{p+1}}{a^3 (p+1) (p+2) (p+3)}+\frac{b x^{-2 (p+2)} \left(a+b x^2\right)^{p+1}}{a^2 (p+2) (p+3)}-\frac{x^{-2 (p+3)} \left(a+b x^2\right)^{p+1}}{2 a (p+3)}","-\frac{b^2 x^{-2 (p+1)} \left(a+b x^2\right)^{p+1}}{a^3 (p+1) (p+2) (p+3)}+\frac{b x^{-2 (p+2)} \left(a+b x^2\right)^{p+1}}{a^2 (p+2) (p+3)}-\frac{x^{-2 (p+3)} \left(a+b x^2\right)^{p+1}}{2 a (p+3)}",1,"-((b^2*(a + b*x^2)^(1 + p))/(a^3*(1 + p)*(2 + p)*(3 + p)*x^(2*(1 + p)))) + (b*(a + b*x^2)^(1 + p))/(a^2*(2 + p)*(3 + p)*x^(2*(2 + p))) - (a + b*x^2)^(1 + p)/(2*a*(3 + p)*x^(2*(3 + p)))","A",3,2,17,0.1176,1,"{271, 264}"
1062,1,70,0,0.0203274,"\int x^{-6-2 p} \left(a+b x^2\right)^p \, dx","Int[x^(-6 - 2*p)*(a + b*x^2)^p,x]","-\frac{x^{-2 p-5} \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{1}{2} (-2 p-5),-p;\frac{1}{2} (-2 p-3);-\frac{b x^2}{a}\right)}{2 p+5}","-\frac{x^{-2 p-5} \left(a+b x^2\right)^{p+1} \, _2F_1\left(-\frac{3}{2},1;\frac{1}{2} (-2 p-3);-\frac{b x^2}{a}\right)}{a (2 p+5)}",1,"-((x^(-5 - 2*p)*(a + b*x^2)^p*Hypergeometric2F1[(-5 - 2*p)/2, -p, (-3 - 2*p)/2, -((b*x^2)/a)])/((5 + 2*p)*(1 + (b*x^2)/a)^p))","A",2,2,17,0.1176,1,"{365, 364}"
1063,1,67,0,0.0202722,"\int x^{-5-2 p} \left(a+b x^2\right)^p \, dx","Int[x^(-5 - 2*p)*(a + b*x^2)^p,x]","\frac{b x^{-2 (p+1)} \left(a+b x^2\right)^{p+1}}{2 a^2 (p+1) (p+2)}-\frac{x^{-2 (p+2)} \left(a+b x^2\right)^{p+1}}{2 a (p+2)}","\frac{b x^{-2 (p+1)} \left(a+b x^2\right)^{p+1}}{2 a^2 (p+1) (p+2)}-\frac{x^{-2 (p+2)} \left(a+b x^2\right)^{p+1}}{2 a (p+2)}",1,"(b*(a + b*x^2)^(1 + p))/(2*a^2*(1 + p)*(2 + p)*x^(2*(1 + p))) - (a + b*x^2)^(1 + p)/(2*a*(2 + p)*x^(2*(2 + p)))","A",2,2,17,0.1176,1,"{271, 264}"
1064,1,70,0,0.0210447,"\int x^{-4-2 p} \left(a+b x^2\right)^p \, dx","Int[x^(-4 - 2*p)*(a + b*x^2)^p,x]","-\frac{x^{-2 p-3} \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{1}{2} (-2 p-3),-p;\frac{1}{2} (-2 p-1);-\frac{b x^2}{a}\right)}{2 p+3}","-\frac{x^{-2 p-3} \left(a+b x^2\right)^{p+1} \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2} (-2 p-1);-\frac{b x^2}{a}\right)}{a (2 p+3)}",1,"-((x^(-3 - 2*p)*(a + b*x^2)^p*Hypergeometric2F1[(-3 - 2*p)/2, -p, (-1 - 2*p)/2, -((b*x^2)/a)])/((3 + 2*p)*(1 + (b*x^2)/a)^p))","A",2,2,17,0.1176,1,"{365, 364}"
1065,1,30,0,0.0060034,"\int x^{-3-2 p} \left(a+b x^2\right)^p \, dx","Int[x^(-3 - 2*p)*(a + b*x^2)^p,x]","-\frac{x^{-2 (p+1)} \left(a+b x^2\right)^{p+1}}{2 a (p+1)}","-\frac{x^{-2 (p+1)} \left(a+b x^2\right)^{p+1}}{2 a (p+1)}",1,"-(a + b*x^2)^(1 + p)/(2*a*(1 + p)*x^(2*(1 + p)))","A",1,1,17,0.05882,1,"{264}"
1066,1,70,0,0.0211372,"\int x^{-2-2 p} \left(a+b x^2\right)^p \, dx","Int[x^(-2 - 2*p)*(a + b*x^2)^p,x]","-\frac{x^{-2 p-1} \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{1}{2} (-2 p-1),-p;\frac{1}{2} (1-2 p);-\frac{b x^2}{a}\right)}{2 p+1}","-\frac{x^{-2 p-1} \left(a+b x^2\right)^{p+1} \, _2F_1\left(\frac{1}{2},1;\frac{1}{2} (1-2 p);-\frac{b x^2}{a}\right)}{a (2 p+1)}",1,"-((x^(-1 - 2*p)*(a + b*x^2)^p*Hypergeometric2F1[(-1 - 2*p)/2, -p, (1 - 2*p)/2, -((b*x^2)/a)])/((1 + 2*p)*(1 + (b*x^2)/a)^p))","A",2,2,17,0.1176,1,"{365, 364}"
1067,1,56,0,0.0157644,"\int x^{-1-2 p} \left(a+b x^2\right)^p \, dx","Int[x^(-1 - 2*p)*(a + b*x^2)^p,x]","-\frac{x^{-2 p} \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(-p,-p;1-p;-\frac{b x^2}{a}\right)}{2 p}","-\frac{x^{-2 p} \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,1;1-p;-\frac{b x^2}{a}\right)}{2 a p}",1,"-((a + b*x^2)^p*Hypergeometric2F1[-p, -p, 1 - p, -((b*x^2)/a)])/(2*p*x^(2*p)*(1 + (b*x^2)/a)^p)","A",2,2,17,0.1176,1,"{365, 364}"
1068,1,69,0,0.0191409,"\int x^{-2 p} \left(a+b x^2\right)^p \, dx","Int[(a + b*x^2)^p/x^(2*p),x]","\frac{x^{1-2 p} \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{1}{2} (1-2 p),-p;\frac{1}{2} (3-2 p);-\frac{b x^2}{a}\right)}{1-2 p}","\frac{x^{1-2 p} \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,\frac{3}{2};\frac{1}{2} (3-2 p);-\frac{b x^2}{a}\right)}{a (1-2 p)}",1,"(x^(1 - 2*p)*(a + b*x^2)^p*Hypergeometric2F1[(1 - 2*p)/2, -p, (3 - 2*p)/2, -((b*x^2)/a)])/((1 - 2*p)*(1 + (b*x^2)/a)^p)","A",2,2,15,0.1333,1,"{365, 364}"
1069,1,64,0,0.0208196,"\int x^{1-2 p} \left(a+b x^2\right)^p \, dx","Int[x^(1 - 2*p)*(a + b*x^2)^p,x]","\frac{x^{2-2 p} \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(1-p,-p;2-p;-\frac{b x^2}{a}\right)}{2 (1-p)}","\frac{x^{2-2 p} \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,2;2-p;-\frac{b x^2}{a}\right)}{2 a (1-p)}",1,"(x^(2 - 2*p)*(a + b*x^2)^p*Hypergeometric2F1[1 - p, -p, 2 - p, -((b*x^2)/a)])/(2*(1 - p)*(1 + (b*x^2)/a)^p)","A",2,2,17,0.1176,1,"{365, 364}"
1070,1,69,0,0.0196595,"\int x^{2-2 p} \left(a+b x^2\right)^p \, dx","Int[x^(2 - 2*p)*(a + b*x^2)^p,x]","\frac{x^{3-2 p} \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{1}{2} (3-2 p),-p;\frac{1}{2} (5-2 p);-\frac{b x^2}{a}\right)}{3-2 p}","\frac{x^{3-2 p} \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,\frac{5}{2};\frac{1}{2} (5-2 p);-\frac{b x^2}{a}\right)}{a (3-2 p)}",1,"(x^(3 - 2*p)*(a + b*x^2)^p*Hypergeometric2F1[(3 - 2*p)/2, -p, (5 - 2*p)/2, -((b*x^2)/a)])/((3 - 2*p)*(1 + (b*x^2)/a)^p)","A",2,2,17,0.1176,1,"{365, 364}"
1071,1,64,0,0.0206146,"\int x^{3-2 p} \left(a+b x^2\right)^p \, dx","Int[x^(3 - 2*p)*(a + b*x^2)^p,x]","\frac{x^{4-2 p} \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(2-p,-p;3-p;-\frac{b x^2}{a}\right)}{2 (2-p)}","\frac{x^{4-2 p} \left(a+b x^2\right)^{p+1} \, _2F_1\left(1,3;3-p;-\frac{b x^2}{a}\right)}{2 a (2-p)}",1,"(x^(4 - 2*p)*(a + b*x^2)^p*Hypergeometric2F1[2 - p, -p, 3 - p, -((b*x^2)/a)])/(2*(2 - p)*(1 + (b*x^2)/a)^p)","A",2,2,17,0.1176,1,"{365, 364}"