1,1,17,17,0.0053394,"\int x^4 \left(a+b x^2\right) \, dx","IntegrateAlgebraic[x^4*(a + b*x^2),x]","\frac{1}{35} \left(7 a x^5+5 b x^7\right)","\frac{a x^5}{5}+\frac{b x^7}{7}",1,"(7*a*x^5 + 5*b*x^7)/35","A",1
2,1,17,17,0.0048566,"\int x^3 \left(a+b x^2\right) \, dx","IntegrateAlgebraic[x^3*(a + b*x^2),x]","\frac{1}{12} \left(3 a x^4+2 b x^6\right)","\frac{a x^4}{4}+\frac{b x^6}{6}",1,"(3*a*x^4 + 2*b*x^6)/12","A",1
3,1,17,17,0.0047108,"\int x^2 \left(a+b x^2\right) \, dx","IntegrateAlgebraic[x^2*(a + b*x^2),x]","\frac{1}{15} \left(5 a x^3+3 b x^5\right)","\frac{a x^3}{3}+\frac{b x^5}{5}",1,"(5*a*x^3 + 3*b*x^5)/15","A",1
4,1,16,17,0.0045187,"\int x \left(a+b x^2\right) \, dx","IntegrateAlgebraic[x*(a + b*x^2),x]","\frac{1}{4} \left(2 a x^2+b x^4\right)","\frac{a x^2}{2}+\frac{b x^4}{4}",1,"(2*a*x^2 + b*x^4)/4","A",1
5,1,14,12,0.0032538,"\int \left(a+b x^2\right) \, dx","IntegrateAlgebraic[a + b*x^2,x]","\frac{1}{3} \left(3 a x+b x^3\right)","a x+\frac{b x^3}{3}",1,"(3*a*x + b*x^3)/3","A",1
6,1,13,13,0.0041039,"\int \frac{a+b x^2}{x} \, dx","IntegrateAlgebraic[(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",1
7,1,13,10,0.003449,"\int \frac{a+b x^2}{x^2} \, dx","IntegrateAlgebraic[(a + b*x^2)/x^2,x]","\frac{b x^2-a}{x}","b x-\frac{a}{x}",1,"(-a + b*x^2)/x","A",1
8,1,13,13,0.005428,"\int \frac{a+b x^2}{x^3} \, dx","IntegrateAlgebraic[(a + b*x^2)/x^3,x]","b \log (x)-\frac{a}{2 x^2}","b \log (x)-\frac{a}{2 x^2}",1,"-1/2*a/x^2 + b*Log[x]","A",1
9,1,17,15,0.0051495,"\int \frac{a+b x^2}{x^4} \, dx","IntegrateAlgebraic[(a + b*x^2)/x^4,x]","\frac{-a-3 b x^2}{3 x^3}","-\frac{a}{3 x^3}-\frac{b}{x}",1,"(-a - 3*b*x^2)/(3*x^3)","A",1
10,1,17,17,0.0049964,"\int \frac{a+b x^2}{x^5} \, dx","IntegrateAlgebraic[(a + b*x^2)/x^5,x]","\frac{-a-2 b x^2}{4 x^4}","-\frac{a}{4 x^4}-\frac{b}{2 x^2}",1,"(-a - 2*b*x^2)/(4*x^4)","A",1
11,1,17,17,0.0050735,"\int \frac{a+b x^2}{x^6} \, dx","IntegrateAlgebraic[(a + b*x^2)/x^6,x]","\frac{-3 a-5 b x^2}{15 x^5}","-\frac{a}{5 x^5}-\frac{b}{3 x^3}",1,"(-3*a - 5*b*x^2)/(15*x^5)","A",1
12,1,17,17,0.0051314,"\int \frac{a+b x^2}{x^7} \, dx","IntegrateAlgebraic[(a + b*x^2)/x^7,x]","\frac{-2 a-3 b x^2}{12 x^6}","-\frac{a}{6 x^6}-\frac{b}{4 x^4}",1,"(-2*a - 3*b*x^2)/(12*x^6)","A",1
13,1,28,30,0.0062951,"\int x^5 \left(a+b x^2\right)^2 \, dx","IntegrateAlgebraic[x^5*(a + b*x^2)^2,x]","\frac{1}{60} x^6 \left(10 a^2+15 a b x^2+6 b^2 x^4\right)","\frac{a^2 x^6}{6}+\frac{1}{4} a b x^8+\frac{b^2 x^{10}}{10}",1,"(x^6*(10*a^2 + 15*a*b*x^2 + 6*b^2*x^4))/60","A",1
14,1,28,30,0.005766,"\int x^4 \left(a+b x^2\right)^2 \, dx","IntegrateAlgebraic[x^4*(a + b*x^2)^2,x]","\frac{1}{315} \left(63 a^2 x^5+90 a b x^7+35 b^2 x^9\right)","\frac{a^2 x^5}{5}+\frac{2}{7} a b x^7+\frac{b^2 x^9}{9}",1,"(63*a^2*x^5 + 90*a*b*x^7 + 35*b^2*x^9)/315","A",1
15,1,28,30,0.0061591,"\int x^3 \left(a+b x^2\right)^2 \, dx","IntegrateAlgebraic[x^3*(a + b*x^2)^2,x]","\frac{1}{24} \left(6 a^2 x^4+8 a b x^6+3 b^2 x^8\right)","\frac{a^2 x^4}{4}+\frac{1}{3} a b x^6+\frac{b^2 x^8}{8}",1,"(6*a^2*x^4 + 8*a*b*x^6 + 3*b^2*x^8)/24","A",1
16,1,28,30,0.0058155,"\int x^2 \left(a+b x^2\right)^2 \, dx","IntegrateAlgebraic[x^2*(a + b*x^2)^2,x]","\frac{1}{105} \left(35 a^2 x^3+42 a b x^5+15 b^2 x^7\right)","\frac{a^2 x^3}{3}+\frac{2}{5} a b x^5+\frac{b^2 x^7}{7}",1,"(35*a^2*x^3 + 42*a*b*x^5 + 15*b^2*x^7)/105","A",1
17,1,16,16,0.0064914,"\int x \left(a+b x^2\right)^2 \, dx","IntegrateAlgebraic[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
18,1,26,25,0.0055584,"\int \left(a+b x^2\right)^2 \, dx","IntegrateAlgebraic[(a + b*x^2)^2,x]","\frac{1}{15} \left(15 a^2 x+10 a b x^3+3 b^2 x^5\right)","a^2 x+\frac{2}{3} a b x^3+\frac{b^2 x^5}{5}",1,"(15*a^2*x + 10*a*b*x^3 + 3*b^2*x^5)/15","A",1
19,1,26,23,0.0060016,"\int \frac{\left(a+b x^2\right)^2}{x} \, dx","IntegrateAlgebraic[(a + b*x^2)^2/x,x]","a^2 \log (x)+\frac{1}{4} \left(4 a b x^2+b^2 x^4\right)","a^2 \log (x)+a b x^2+\frac{b^2 x^4}{4}",1,"(4*a*b*x^2 + b^2*x^4)/4 + a^2*Log[x]","A",1
20,1,27,24,0.0044921,"\int \frac{\left(a+b x^2\right)^2}{x^2} \, dx","IntegrateAlgebraic[(a + b*x^2)^2/x^2,x]","\frac{-3 a^2+6 a b x^2+b^2 x^4}{3 x}","-\frac{a^2}{x}+2 a b x+\frac{b^2 x^3}{3}",1,"(-3*a^2 + 6*a*b*x^2 + b^2*x^4)/(3*x)","A",1
21,1,27,27,0.0065125,"\int \frac{\left(a+b x^2\right)^2}{x^3} \, dx","IntegrateAlgebraic[(a + b*x^2)^2/x^3,x]","\frac{b^2 x^4-a^2}{2 x^2}+2 a b \log (x)","-\frac{a^2}{2 x^2}+2 a b \log (x)+\frac{b^2 x^2}{2}",1,"(-a^2 + b^2*x^4)/(2*x^2) + 2*a*b*Log[x]","A",1
22,1,28,23,0.0048273,"\int \frac{\left(a+b x^2\right)^2}{x^4} \, dx","IntegrateAlgebraic[(a + b*x^2)^2/x^4,x]","\frac{-a^2-6 a b x^2+3 b^2 x^4}{3 x^3}","-\frac{a^2}{3 x^3}-\frac{2 a b}{x}+b^2 x",1,"(-a^2 - 6*a*b*x^2 + 3*b^2*x^4)/(3*x^3)","A",1
23,1,23,24,0.0070611,"\int \frac{\left(a+b x^2\right)^2}{x^5} \, dx","IntegrateAlgebraic[(a + b*x^2)^2/x^5,x]","b^2 \log (x)-\frac{a \left(a+4 b x^2\right)}{4 x^4}","-\frac{a^2}{4 x^4}-\frac{a b}{x^2}+b^2 \log (x)",1,"-1/4*(a*(a + 4*b*x^2))/x^4 + b^2*Log[x]","A",1
24,1,28,28,0.0049702,"\int \frac{\left(a+b x^2\right)^2}{x^6} \, dx","IntegrateAlgebraic[(a + b*x^2)^2/x^6,x]","\frac{-3 a^2-10 a b x^2-15 b^2 x^4}{15 x^5}","-\frac{a^2}{5 x^5}-\frac{2 a b}{3 x^3}-\frac{b^2}{x}",1,"(-3*a^2 - 10*a*b*x^2 - 15*b^2*x^4)/(15*x^5)","A",1
25,1,28,19,0.0049291,"\int \frac{\left(a+b x^2\right)^2}{x^7} \, dx","IntegrateAlgebraic[(a + b*x^2)^2/x^7,x]","\frac{-a^2-3 a b x^2-3 b^2 x^4}{6 x^6}","-\frac{\left(a+b x^2\right)^3}{6 a x^6}",1,"(-a^2 - 3*a*b*x^2 - 3*b^2*x^4)/(6*x^6)","A",1
26,1,28,30,0.0051439,"\int \frac{\left(a+b x^2\right)^2}{x^8} \, dx","IntegrateAlgebraic[(a + b*x^2)^2/x^8,x]","\frac{-15 a^2-42 a b x^2-35 b^2 x^4}{105 x^7}","-\frac{a^2}{7 x^7}-\frac{2 a b}{5 x^5}-\frac{b^2}{3 x^3}",1,"(-15*a^2 - 42*a*b*x^2 - 35*b^2*x^4)/(105*x^7)","A",1
27,1,28,30,0.0048276,"\int \frac{\left(a+b x^2\right)^2}{x^9} \, dx","IntegrateAlgebraic[(a + b*x^2)^2/x^9,x]","\frac{-3 a^2-8 a b x^2-6 b^2 x^4}{24 x^8}","-\frac{a^2}{8 x^8}-\frac{a b}{3 x^6}-\frac{b^2}{4 x^4}",1,"(-3*a^2 - 8*a*b*x^2 - 6*b^2*x^4)/(24*x^8)","A",1
28,1,28,30,0.0049663,"\int \frac{\left(a+b x^2\right)^2}{x^{10}} \, dx","IntegrateAlgebraic[(a + b*x^2)^2/x^10,x]","\frac{-35 a^2-90 a b x^2-63 b^2 x^4}{315 x^9}","-\frac{a^2}{9 x^9}-\frac{2 a b}{7 x^7}-\frac{b^2}{5 x^5}",1,"(-35*a^2 - 90*a*b*x^2 - 63*b^2*x^4)/(315*x^9)","A",1
29,1,39,43,0.0086766,"\int x^9 \left(a+b x^2\right)^3 \, dx","IntegrateAlgebraic[x^9*(a + b*x^2)^3,x]","\frac{1}{560} x^{10} \left(56 a^3+140 a^2 b x^2+120 a b^2 x^4+35 b^3 x^6\right)","\frac{a^3 x^{10}}{10}+\frac{1}{4} a^2 b x^{12}+\frac{3}{14} a b^2 x^{14}+\frac{b^3 x^{16}}{16}",1,"(x^10*(56*a^3 + 140*a^2*b*x^2 + 120*a*b^2*x^4 + 35*b^3*x^6))/560","A",1
30,1,39,43,0.0084294,"\int x^7 \left(a+b x^2\right)^3 \, dx","IntegrateAlgebraic[x^7*(a + b*x^2)^3,x]","\frac{1}{280} x^8 \left(35 a^3+84 a^2 b x^2+70 a b^2 x^4+20 b^3 x^6\right)","\frac{a^3 x^8}{8}+\frac{3}{10} a^2 b x^{10}+\frac{1}{4} a b^2 x^{12}+\frac{b^3 x^{14}}{14}",1,"(x^8*(35*a^3 + 84*a^2*b*x^2 + 70*a*b^2*x^4 + 20*b^3*x^6))/280","A",1
31,1,39,43,0.0084313,"\int x^5 \left(a+b x^2\right)^3 \, dx","IntegrateAlgebraic[x^5*(a + b*x^2)^3,x]","\frac{1}{120} x^6 \left(20 a^3+45 a^2 b x^2+36 a b^2 x^4+10 b^3 x^6\right)","\frac{a^3 x^6}{6}+\frac{3}{8} a^2 b x^8+\frac{3}{10} a b^2 x^{10}+\frac{b^3 x^{12}}{12}",1,"(x^6*(20*a^3 + 45*a^2*b*x^2 + 36*a*b^2*x^4 + 10*b^3*x^6))/120","A",1
32,1,39,34,0.0092986,"\int x^3 \left(a+b x^2\right)^3 \, dx","IntegrateAlgebraic[x^3*(a + b*x^2)^3,x]","\frac{1}{40} x^4 \left(10 a^3+20 a^2 b x^2+15 a b^2 x^4+4 b^3 x^6\right)","\frac{\left(a+b x^2\right)^5}{10 b^2}-\frac{a \left(a+b x^2\right)^4}{8 b^2}",1,"(x^4*(10*a^3 + 20*a^2*b*x^2 + 15*a*b^2*x^4 + 4*b^3*x^6))/40","A",1
33,1,16,16,0.0063427,"\int x \left(a+b x^2\right)^3 \, dx","IntegrateAlgebraic[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
34,1,36,39,0.0107562,"\int \frac{\left(a+b x^2\right)^3}{x} \, dx","IntegrateAlgebraic[(a + b*x^2)^3/x,x]","a^3 \log (x)+\frac{1}{12} b x^2 \left(18 a^2+9 a b x^2+2 b^2 x^4\right)","a^3 \log (x)+\frac{3}{2} a^2 b x^2+\frac{3}{4} a b^2 x^4+\frac{b^3 x^6}{6}",1,"(b*x^2*(18*a^2 + 9*a*b*x^2 + 2*b^2*x^4))/12 + a^3*Log[x]","A",1
35,1,38,40,0.0145254,"\int \frac{\left(a+b x^2\right)^3}{x^3} \, dx","IntegrateAlgebraic[(a + b*x^2)^3/x^3,x]","\frac{-2 a^3+6 a b^2 x^4+b^3 x^6}{4 x^2}+3 a^2 b \log (x)","-\frac{a^3}{2 x^2}+3 a^2 b \log (x)+\frac{3}{2} a b^2 x^2+\frac{b^3 x^4}{4}",1,"(-2*a^3 + 6*a*b^2*x^4 + b^3*x^6)/(4*x^2) + 3*a^2*b*Log[x]","A",1
36,1,39,40,0.0134468,"\int \frac{\left(a+b x^2\right)^3}{x^5} \, dx","IntegrateAlgebraic[(a + b*x^2)^3/x^5,x]","\frac{-a^3-6 a^2 b x^2+2 b^3 x^6}{4 x^4}+3 a b^2 \log (x)","-\frac{a^3}{4 x^4}-\frac{3 a^2 b}{2 x^2}+3 a b^2 \log (x)+\frac{b^3 x^2}{2}",1,"(-a^3 - 6*a^2*b*x^2 + 2*b^3*x^6)/(4*x^4) + 3*a*b^2*Log[x]","A",1
37,1,36,39,0.0125567,"\int \frac{\left(a+b x^2\right)^3}{x^7} \, dx","IntegrateAlgebraic[(a + b*x^2)^3/x^7,x]","b^3 \log (x)-\frac{a \left(2 a^2+9 a b x^2+18 b^2 x^4\right)}{12 x^6}","-\frac{a^3}{6 x^6}-\frac{3 a^2 b}{4 x^4}-\frac{3 a b^2}{2 x^2}+b^3 \log (x)",1,"-1/12*(a*(2*a^2 + 9*a*b*x^2 + 18*b^2*x^4))/x^6 + b^3*Log[x]","A",1
38,1,39,19,0.0119486,"\int \frac{\left(a+b x^2\right)^3}{x^9} \, dx","IntegrateAlgebraic[(a + b*x^2)^3/x^9,x]","\frac{-a^3-4 a^2 b x^2-6 a b^2 x^4-4 b^3 x^6}{8 x^8}","-\frac{\left(a+b x^2\right)^4}{8 a x^8}",1,"(-a^3 - 4*a^2*b*x^2 - 6*a*b^2*x^4 - 4*b^3*x^6)/(8*x^8)","B",1
39,1,39,40,0.0090359,"\int \frac{\left(a+b x^2\right)^3}{x^{11}} \, dx","IntegrateAlgebraic[(a + b*x^2)^3/x^11,x]","\frac{-4 a^3-15 a^2 b x^2-20 a b^2 x^4-10 b^3 x^6}{40 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,"(-4*a^3 - 15*a^2*b*x^2 - 20*a*b^2*x^4 - 10*b^3*x^6)/(40*x^10)","A",1
40,1,39,43,0.0090917,"\int \frac{\left(a+b x^2\right)^3}{x^{13}} \, dx","IntegrateAlgebraic[(a + b*x^2)^3/x^13,x]","\frac{-10 a^3-36 a^2 b x^2-45 a b^2 x^4-20 b^3 x^6}{120 x^{12}}","-\frac{a^3}{12 x^{12}}-\frac{3 a^2 b}{10 x^{10}}-\frac{3 a b^2}{8 x^8}-\frac{b^3}{6 x^6}",1,"(-10*a^3 - 36*a^2*b*x^2 - 45*a*b^2*x^4 - 20*b^3*x^6)/(120*x^12)","A",1
41,1,39,43,0.011746,"\int \frac{\left(a+b x^2\right)^3}{x^{15}} \, dx","IntegrateAlgebraic[(a + b*x^2)^3/x^15,x]","\frac{-20 a^3-70 a^2 b x^2-84 a b^2 x^4-35 b^3 x^6}{280 x^{14}}","-\frac{a^3}{14 x^{14}}-\frac{a^2 b}{4 x^{12}}-\frac{3 a b^2}{10 x^{10}}-\frac{b^3}{8 x^8}",1,"(-20*a^3 - 70*a^2*b*x^2 - 84*a*b^2*x^4 - 35*b^3*x^6)/(280*x^14)","A",1
42,1,39,43,0.0083108,"\int x^6 \left(a+b x^2\right)^3 \, dx","IntegrateAlgebraic[x^6*(a + b*x^2)^3,x]","\frac{429 a^3 x^7+1001 a^2 b x^9+819 a b^2 x^{11}+231 b^3 x^{13}}{3003}","\frac{a^3 x^7}{7}+\frac{1}{3} a^2 b x^9+\frac{3}{11} a b^2 x^{11}+\frac{b^3 x^{13}}{13}",1,"(429*a^3*x^7 + 1001*a^2*b*x^9 + 819*a*b^2*x^11 + 231*b^3*x^13)/3003","A",1
43,1,39,43,0.0085194,"\int x^4 \left(a+b x^2\right)^3 \, dx","IntegrateAlgebraic[x^4*(a + b*x^2)^3,x]","\frac{231 a^3 x^5+495 a^2 b x^7+385 a b^2 x^9+105 b^3 x^{11}}{1155}","\frac{a^3 x^5}{5}+\frac{3}{7} a^2 b x^7+\frac{1}{3} a b^2 x^9+\frac{b^3 x^{11}}{11}",1,"(231*a^3*x^5 + 495*a^2*b*x^7 + 385*a*b^2*x^9 + 105*b^3*x^11)/1155","A",1
44,1,39,43,0.0084872,"\int x^2 \left(a+b x^2\right)^3 \, dx","IntegrateAlgebraic[x^2*(a + b*x^2)^3,x]","\frac{1}{315} \left(105 a^3 x^3+189 a^2 b x^5+135 a b^2 x^7+35 b^3 x^9\right)","\frac{a^3 x^3}{3}+\frac{3}{5} a^2 b x^5+\frac{3}{7} a b^2 x^7+\frac{b^3 x^9}{9}",1,"(105*a^3*x^3 + 189*a^2*b*x^5 + 135*a*b^2*x^7 + 35*b^3*x^9)/315","A",1
45,1,37,35,0.0070213,"\int \left(a+b x^2\right)^3 \, dx","IntegrateAlgebraic[(a + b*x^2)^3,x]","\frac{1}{35} \left(35 a^3 x+35 a^2 b x^3+21 a b^2 x^5+5 b^3 x^7\right)","a^3 x+a^2 b x^3+\frac{3}{5} a b^2 x^5+\frac{b^3 x^7}{7}",1,"(35*a^3*x + 35*a^2*b*x^3 + 21*a*b^2*x^5 + 5*b^3*x^7)/35","A",1
46,1,38,34,0.0083061,"\int \frac{\left(a+b x^2\right)^3}{x^2} \, dx","IntegrateAlgebraic[(a + b*x^2)^3/x^2,x]","\frac{-5 a^3+15 a^2 b x^2+5 a b^2 x^4+b^3 x^6}{5 x}","-\frac{a^3}{x}+3 a^2 b x+a b^2 x^3+\frac{b^3 x^5}{5}",1,"(-5*a^3 + 15*a^2*b*x^2 + 5*a*b^2*x^4 + b^3*x^6)/(5*x)","A",1
47,1,38,37,0.0083923,"\int \frac{\left(a+b x^2\right)^3}{x^4} \, dx","IntegrateAlgebraic[(a + b*x^2)^3/x^4,x]","\frac{-a^3-9 a^2 b x^2+9 a b^2 x^4+b^3 x^6}{3 x^3}","-\frac{a^3}{3 x^3}-\frac{3 a^2 b}{x}+3 a b^2 x+\frac{b^3 x^3}{3}",1,"(-a^3 - 9*a^2*b*x^2 + 9*a*b^2*x^4 + b^3*x^6)/(3*x^3)","A",1
48,1,39,34,0.0099927,"\int \frac{\left(a+b x^2\right)^3}{x^6} \, dx","IntegrateAlgebraic[(a + b*x^2)^3/x^6,x]","\frac{-a^3-5 a^2 b x^2-15 a b^2 x^4+5 b^3 x^6}{5 x^5}","-\frac{a^3}{5 x^5}-\frac{a^2 b}{x^3}-\frac{3 a b^2}{x}+b^3 x",1,"(-a^3 - 5*a^2*b*x^2 - 15*a*b^2*x^4 + 5*b^3*x^6)/(5*x^5)","A",1
49,1,39,39,0.0088105,"\int \frac{\left(a+b x^2\right)^3}{x^8} \, dx","IntegrateAlgebraic[(a + b*x^2)^3/x^8,x]","\frac{-5 a^3-21 a^2 b x^2-35 a b^2 x^4-35 b^3 x^6}{35 x^7}","-\frac{a^3}{7 x^7}-\frac{3 a^2 b}{5 x^5}-\frac{a b^2}{x^3}-\frac{b^3}{x}",1,"(-5*a^3 - 21*a^2*b*x^2 - 35*a*b^2*x^4 - 35*b^3*x^6)/(35*x^7)","A",1
50,1,39,43,0.008873,"\int \frac{\left(a+b x^2\right)^3}{x^{10}} \, dx","IntegrateAlgebraic[(a + b*x^2)^3/x^10,x]","\frac{-35 a^3-135 a^2 b x^2-189 a b^2 x^4-105 b^3 x^6}{315 x^9}","-\frac{a^3}{9 x^9}-\frac{3 a^2 b}{7 x^7}-\frac{3 a b^2}{5 x^5}-\frac{b^3}{3 x^3}",1,"(-35*a^3 - 135*a^2*b*x^2 - 189*a*b^2*x^4 - 105*b^3*x^6)/(315*x^9)","A",1
51,1,39,43,0.0121744,"\int \frac{\left(a+b x^2\right)^3}{x^{12}} \, dx","IntegrateAlgebraic[(a + b*x^2)^3/x^12,x]","\frac{-105 a^3-385 a^2 b x^2-495 a b^2 x^4-231 b^3 x^6}{1155 x^{11}}","-\frac{a^3}{11 x^{11}}-\frac{a^2 b}{3 x^9}-\frac{3 a b^2}{7 x^7}-\frac{b^3}{5 x^5}",1,"(-105*a^3 - 385*a^2*b*x^2 - 495*a*b^2*x^4 - 231*b^3*x^6)/(1155*x^11)","A",1
52,1,61,69,0.0114667,"\int x^{13} \left(a+b x^2\right)^5 \, dx","IntegrateAlgebraic[x^13*(a + b*x^2)^5,x]","\frac{792 a^5 x^{14}+3465 a^4 b x^{16}+6160 a^3 b^2 x^{18}+5544 a^2 b^3 x^{20}+2520 a b^4 x^{22}+462 b^5 x^{24}}{11088}","\frac{a^5 x^{14}}{14}+\frac{5}{16} a^4 b x^{16}+\frac{5}{9} a^3 b^2 x^{18}+\frac{1}{2} a^2 b^3 x^{20}+\frac{5}{22} a b^4 x^{22}+\frac{b^5 x^{24}}{24}",1,"(792*a^5*x^14 + 3465*a^4*b*x^16 + 6160*a^3*b^2*x^18 + 5544*a^2*b^3*x^20 + 2520*a*b^4*x^22 + 462*b^5*x^24)/11088","A",1
53,1,61,69,0.0109176,"\int x^{11} \left(a+b x^2\right)^5 \, dx","IntegrateAlgebraic[x^11*(a + b*x^2)^5,x]","\frac{462 a^5 x^{12}+1980 a^4 b x^{14}+3465 a^3 b^2 x^{16}+3080 a^2 b^3 x^{18}+1386 a b^4 x^{20}+252 b^5 x^{22}}{5544}","\frac{a^5 x^{12}}{12}+\frac{5}{14} a^4 b x^{14}+\frac{5}{8} a^3 b^2 x^{16}+\frac{5}{9} a^2 b^3 x^{18}+\frac{1}{4} a b^4 x^{20}+\frac{b^5 x^{22}}{22}",1,"(462*a^5*x^12 + 1980*a^4*b*x^14 + 3465*a^3*b^2*x^16 + 3080*a^2*b^3*x^18 + 1386*a*b^4*x^20 + 252*b^5*x^22)/5544","A",1
54,1,61,69,0.0105005,"\int x^9 \left(a+b x^2\right)^5 \, dx","IntegrateAlgebraic[x^9*(a + b*x^2)^5,x]","\frac{252 a^5 x^{10}+1050 a^4 b x^{12}+1800 a^3 b^2 x^{14}+1575 a^2 b^3 x^{16}+700 a b^4 x^{18}+126 b^5 x^{20}}{2520}","\frac{a^5 x^{10}}{10}+\frac{5}{12} a^4 b x^{12}+\frac{5}{7} a^3 b^2 x^{14}+\frac{5}{8} a^2 b^3 x^{16}+\frac{5}{18} a b^4 x^{18}+\frac{b^5 x^{20}}{20}",1,"(252*a^5*x^10 + 1050*a^4*b*x^12 + 1800*a^3*b^2*x^14 + 1575*a^2*b^3*x^16 + 700*a*b^4*x^18 + 126*b^5*x^20)/2520","A",1
55,1,61,72,0.0114608,"\int x^7 \left(a+b x^2\right)^5 \, dx","IntegrateAlgebraic[x^7*(a + b*x^2)^5,x]","\frac{x^8 \left(126 a^5+504 a^4 b x^2+840 a^3 b^2 x^4+720 a^2 b^3 x^6+315 a b^4 x^8+56 b^5 x^{10}\right)}{1008}","-\frac{a^3 \left(a+b x^2\right)^6}{12 b^4}+\frac{3 a^2 \left(a+b x^2\right)^7}{14 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,"(x^8*(126*a^5 + 504*a^4*b*x^2 + 840*a^3*b^2*x^4 + 720*a^2*b^3*x^6 + 315*a*b^4*x^8 + 56*b^5*x^10))/1008","A",1
56,1,61,53,0.0108858,"\int x^5 \left(a+b x^2\right)^5 \, dx","IntegrateAlgebraic[x^5*(a + b*x^2)^5,x]","\frac{1}{336} \left(56 a^5 x^6+210 a^4 b x^8+336 a^3 b^2 x^{10}+280 a^2 b^3 x^{12}+120 a b^4 x^{14}+21 b^5 x^{16}\right)","\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,"(56*a^5*x^6 + 210*a^4*b*x^8 + 336*a^3*b^2*x^10 + 280*a^2*b^3*x^12 + 120*a*b^4*x^14 + 21*b^5*x^16)/336","A",1
57,1,61,34,0.0111128,"\int x^3 \left(a+b x^2\right)^5 \, dx","IntegrateAlgebraic[x^3*(a + b*x^2)^5,x]","\frac{1}{84} x^4 \left(21 a^5+70 a^4 b x^2+105 a^3 b^2 x^4+84 a^2 b^3 x^6+35 a b^4 x^8+6 b^5 x^{10}\right)","\frac{\left(a+b x^2\right)^7}{14 b^2}-\frac{a \left(a+b x^2\right)^6}{12 b^2}",1,"(x^4*(21*a^5 + 70*a^4*b*x^2 + 105*a^3*b^2*x^4 + 84*a^2*b^3*x^6 + 35*a*b^4*x^8 + 6*b^5*x^10))/84","A",1
58,1,16,16,0.0074101,"\int x \left(a+b x^2\right)^5 \, dx","IntegrateAlgebraic[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
59,1,58,65,0.0138647,"\int \frac{\left(a+b x^2\right)^5}{x} \, dx","IntegrateAlgebraic[(a + b*x^2)^5/x,x]","a^5 \log (x)+\frac{1}{120} b x^2 \left(300 a^4+300 a^3 b x^2+200 a^2 b^2 x^4+75 a b^3 x^6+12 b^4 x^8\right)","a^5 \log (x)+\frac{5}{2} a^4 b x^2+\frac{5}{2} a^3 b^2 x^4+\frac{5}{3} a^2 b^3 x^6+\frac{5}{8} a b^4 x^8+\frac{b^5 x^{10}}{10}",1,"(b*x^2*(300*a^4 + 300*a^3*b*x^2 + 200*a^2*b^2*x^4 + 75*a*b^3*x^6 + 12*b^4*x^8))/120 + a^5*Log[x]","A",1
60,1,61,64,0.0164202,"\int \frac{\left(a+b x^2\right)^5}{x^3} \, dx","IntegrateAlgebraic[(a + b*x^2)^5/x^3,x]","5 a^4 b \log (x)+\frac{-12 a^5+120 a^3 b^2 x^4+60 a^2 b^3 x^6+20 a b^4 x^8+3 b^5 x^{10}}{24 x^2}","-\frac{a^5}{2 x^2}+5 a^4 b \log (x)+5 a^3 b^2 x^2+\frac{5}{2} a^2 b^3 x^4+\frac{5}{6} a b^4 x^6+\frac{b^5 x^8}{8}",1,"(-12*a^5 + 120*a^3*b^2*x^4 + 60*a^2*b^3*x^6 + 20*a*b^4*x^8 + 3*b^5*x^10)/(24*x^2) + 5*a^4*b*Log[x]","A",1
61,1,61,64,0.0166507,"\int \frac{\left(a+b x^2\right)^5}{x^5} \, dx","IntegrateAlgebraic[(a + b*x^2)^5/x^5,x]","10 a^3 b^2 \log (x)+\frac{-3 a^5-30 a^4 b x^2+60 a^2 b^3 x^6+15 a b^4 x^8+2 b^5 x^{10}}{12 x^4}","-\frac{a^5}{4 x^4}-\frac{5 a^4 b}{2 x^2}+10 a^3 b^2 \log (x)+5 a^2 b^3 x^2+\frac{5}{4} a b^4 x^4+\frac{b^5 x^6}{6}",1,"(-3*a^5 - 30*a^4*b*x^2 + 60*a^2*b^3*x^6 + 15*a*b^4*x^8 + 2*b^5*x^10)/(12*x^4) + 10*a^3*b^2*Log[x]","A",1
62,1,61,64,0.0151581,"\int \frac{\left(a+b x^2\right)^5}{x^7} \, dx","IntegrateAlgebraic[(a + b*x^2)^5/x^7,x]","10 a^2 b^3 \log (x)+\frac{-2 a^5-15 a^4 b x^2-60 a^3 b^2 x^4+30 a b^4 x^8+3 b^5 x^{10}}{12 x^6}","-\frac{a^5}{6 x^6}-\frac{5 a^4 b}{4 x^4}-\frac{5 a^3 b^2}{x^2}+10 a^2 b^3 \log (x)+\frac{5}{2} a b^4 x^2+\frac{b^5 x^4}{4}",1,"(-2*a^5 - 15*a^4*b*x^2 - 60*a^3*b^2*x^4 + 30*a*b^4*x^8 + 3*b^5*x^10)/(12*x^6) + 10*a^2*b^3*Log[x]","A",1
63,1,61,64,0.0204555,"\int \frac{\left(a+b x^2\right)^5}{x^9} \, dx","IntegrateAlgebraic[(a + b*x^2)^5/x^9,x]","\frac{-3 a^5-20 a^4 b x^2-60 a^3 b^2 x^4-120 a^2 b^3 x^6+12 b^5 x^{10}}{24 x^8}+5 a b^4 \log (x)","-\frac{a^5}{8 x^8}-\frac{5 a^4 b}{6 x^6}-\frac{5 a^3 b^2}{2 x^4}-\frac{5 a^2 b^3}{x^2}+5 a b^4 \log (x)+\frac{b^5 x^2}{2}",1,"(-3*a^5 - 20*a^4*b*x^2 - 60*a^3*b^2*x^4 - 120*a^2*b^3*x^6 + 12*b^5*x^10)/(24*x^8) + 5*a*b^4*Log[x]","A",1
64,1,58,65,0.0151487,"\int \frac{\left(a+b x^2\right)^5}{x^{11}} \, dx","IntegrateAlgebraic[(a + b*x^2)^5/x^11,x]","b^5 \log (x)-\frac{a \left(12 a^4+75 a^3 b x^2+200 a^2 b^2 x^4+300 a b^3 x^6+300 b^4 x^8\right)}{120 x^{10}}","-\frac{a^5}{10 x^{10}}-\frac{5 a^4 b}{8 x^8}-\frac{5 a^3 b^2}{3 x^6}-\frac{5 a^2 b^3}{2 x^4}-\frac{5 a b^4}{2 x^2}+b^5 \log (x)",1,"-1/120*(a*(12*a^4 + 75*a^3*b*x^2 + 200*a^2*b^2*x^4 + 300*a*b^3*x^6 + 300*b^4*x^8))/x^10 + b^5*Log[x]","A",1
65,1,61,19,0.0106177,"\int \frac{\left(a+b x^2\right)^5}{x^{13}} \, dx","IntegrateAlgebraic[(a + b*x^2)^5/x^13,x]","\frac{-a^5-6 a^4 b x^2-15 a^3 b^2 x^4-20 a^2 b^3 x^6-15 a b^4 x^8-6 b^5 x^{10}}{12 x^{12}}","-\frac{\left(a+b x^2\right)^6}{12 a x^{12}}",1,"(-a^5 - 6*a^4*b*x^2 - 15*a^3*b^2*x^4 - 20*a^2*b^3*x^6 - 15*a*b^4*x^8 - 6*b^5*x^10)/(12*x^12)","B",1
66,1,61,40,0.0135192,"\int \frac{\left(a+b x^2\right)^5}{x^{15}} \, dx","IntegrateAlgebraic[(a + b*x^2)^5/x^15,x]","\frac{-6 a^5-35 a^4 b x^2-84 a^3 b^2 x^4-105 a^2 b^3 x^6-70 a b^4 x^8-21 b^5 x^{10}}{84 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,"(-6*a^5 - 35*a^4*b*x^2 - 84*a^3*b^2*x^4 - 105*a^2*b^3*x^6 - 70*a*b^4*x^8 - 21*b^5*x^10)/(84*x^14)","A",1
67,1,61,62,0.0109291,"\int \frac{\left(a+b x^2\right)^5}{x^{17}} \, dx","IntegrateAlgebraic[(a + b*x^2)^5/x^17,x]","\frac{-21 a^5-120 a^4 b x^2-280 a^3 b^2 x^4-336 a^2 b^3 x^6-210 a b^4 x^8-56 b^5 x^{10}}{336 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,"(-21*a^5 - 120*a^4*b*x^2 - 280*a^3*b^2*x^4 - 336*a^2*b^3*x^6 - 210*a*b^4*x^8 - 56*b^5*x^10)/(336*x^16)","A",1
68,1,61,69,0.0105481,"\int \frac{\left(a+b x^2\right)^5}{x^{19}} \, dx","IntegrateAlgebraic[(a + b*x^2)^5/x^19,x]","\frac{-56 a^5-315 a^4 b x^2-720 a^3 b^2 x^4-840 a^2 b^3 x^6-504 a b^4 x^8-126 b^5 x^{10}}{1008 x^{18}}","-\frac{a^5}{18 x^{18}}-\frac{5 a^4 b}{16 x^{16}}-\frac{5 a^3 b^2}{7 x^{14}}-\frac{5 a^2 b^3}{6 x^{12}}-\frac{a b^4}{2 x^{10}}-\frac{b^5}{8 x^8}",1,"(-56*a^5 - 315*a^4*b*x^2 - 720*a^3*b^2*x^4 - 840*a^2*b^3*x^6 - 504*a*b^4*x^8 - 126*b^5*x^10)/(1008*x^18)","A",1
69,1,61,69,0.0107141,"\int \frac{\left(a+b x^2\right)^5}{x^{21}} \, dx","IntegrateAlgebraic[(a + b*x^2)^5/x^21,x]","\frac{-126 a^5-700 a^4 b x^2-1575 a^3 b^2 x^4-1800 a^2 b^3 x^6-1050 a b^4 x^8-252 b^5 x^{10}}{2520 x^{20}}","-\frac{a^5}{20 x^{20}}-\frac{5 a^4 b}{18 x^{18}}-\frac{5 a^3 b^2}{8 x^{16}}-\frac{5 a^2 b^3}{7 x^{14}}-\frac{5 a b^4}{12 x^{12}}-\frac{b^5}{10 x^{10}}",1,"(-126*a^5 - 700*a^4*b*x^2 - 1575*a^3*b^2*x^4 - 1800*a^2*b^3*x^6 - 1050*a*b^4*x^8 - 252*b^5*x^10)/(2520*x^20)","A",1
70,1,61,69,0.0110212,"\int x^8 \left(a+b x^2\right)^5 \, dx","IntegrateAlgebraic[x^8*(a + b*x^2)^5,x]","\frac{46189 a^5 x^9+188955 a^4 b x^{11}+319770 a^3 b^2 x^{13}+277134 a^2 b^3 x^{15}+122265 a b^4 x^{17}+21879 b^5 x^{19}}{415701}","\frac{a^5 x^9}{9}+\frac{5}{11} a^4 b x^{11}+\frac{10}{13} a^3 b^2 x^{13}+\frac{2}{3} a^2 b^3 x^{15}+\frac{5}{17} a b^4 x^{17}+\frac{b^5 x^{19}}{19}",1,"(46189*a^5*x^9 + 188955*a^4*b*x^11 + 319770*a^3*b^2*x^13 + 277134*a^2*b^3*x^15 + 122265*a*b^4*x^17 + 21879*b^5*x^19)/415701","A",1
71,1,61,69,0.0120638,"\int x^6 \left(a+b x^2\right)^5 \, dx","IntegrateAlgebraic[x^6*(a + b*x^2)^5,x]","\frac{21879 a^5 x^7+85085 a^4 b x^9+139230 a^3 b^2 x^{11}+117810 a^2 b^3 x^{13}+51051 a b^4 x^{15}+9009 b^5 x^{17}}{153153}","\frac{a^5 x^7}{7}+\frac{5}{9} a^4 b x^9+\frac{10}{11} a^3 b^2 x^{11}+\frac{10}{13} a^2 b^3 x^{13}+\frac{1}{3} a b^4 x^{15}+\frac{b^5 x^{17}}{17}",1,"(21879*a^5*x^7 + 85085*a^4*b*x^9 + 139230*a^3*b^2*x^11 + 117810*a^2*b^3*x^13 + 51051*a*b^4*x^15 + 9009*b^5*x^17)/153153","A",1
72,1,61,69,0.0109747,"\int x^4 \left(a+b x^2\right)^5 \, dx","IntegrateAlgebraic[x^4*(a + b*x^2)^5,x]","\frac{9009 a^5 x^5+32175 a^4 b x^7+50050 a^3 b^2 x^9+40950 a^2 b^3 x^{11}+17325 a b^4 x^{13}+3003 b^5 x^{15}}{45045}","\frac{a^5 x^5}{5}+\frac{5}{7} a^4 b x^7+\frac{10}{9} a^3 b^2 x^9+\frac{10}{11} a^2 b^3 x^{11}+\frac{5}{13} a b^4 x^{13}+\frac{b^5 x^{15}}{15}",1,"(9009*a^5*x^5 + 32175*a^4*b*x^7 + 50050*a^3*b^2*x^9 + 40950*a^2*b^3*x^11 + 17325*a*b^4*x^13 + 3003*b^5*x^15)/45045","A",1
73,1,61,66,0.0103935,"\int x^2 \left(a+b x^2\right)^5 \, dx","IntegrateAlgebraic[x^2*(a + b*x^2)^5,x]","\frac{3003 a^5 x^3+9009 a^4 b x^5+12870 a^3 b^2 x^7+10010 a^2 b^3 x^9+4095 a b^4 x^{11}+693 b^5 x^{13}}{9009}","\frac{a^5 x^3}{3}+a^4 b x^5+\frac{10}{7} a^3 b^2 x^7+\frac{10}{9} a^2 b^3 x^9+\frac{5}{11} a b^4 x^{11}+\frac{b^5 x^{13}}{13}",1,"(3003*a^5*x^3 + 9009*a^4*b*x^5 + 12870*a^3*b^2*x^7 + 10010*a^2*b^3*x^9 + 4095*a*b^4*x^11 + 693*b^5*x^13)/9009","A",1
74,1,59,62,0.0093227,"\int \left(a+b x^2\right)^5 \, dx","IntegrateAlgebraic[(a + b*x^2)^5,x]","\frac{1}{693} \left(693 a^5 x+1155 a^4 b x^3+1386 a^3 b^2 x^5+990 a^2 b^3 x^7+385 a b^4 x^9+63 b^5 x^{11}\right)","a^5 x+\frac{5}{3} a^4 b x^3+2 a^3 b^2 x^5+\frac{10}{7} a^2 b^3 x^7+\frac{5}{9} a b^4 x^9+\frac{b^5 x^{11}}{11}",1,"(693*a^5*x + 1155*a^4*b*x^3 + 1386*a^3*b^2*x^5 + 990*a^2*b^3*x^7 + 385*a*b^4*x^9 + 63*b^5*x^11)/693","A",1
75,1,61,61,0.0097531,"\int \frac{\left(a+b x^2\right)^5}{x^2} \, dx","IntegrateAlgebraic[(a + b*x^2)^5/x^2,x]","\frac{-63 a^5+315 a^4 b x^2+210 a^3 b^2 x^4+126 a^2 b^3 x^6+45 a b^4 x^8+7 b^5 x^{10}}{63 x}","-\frac{a^5}{x}+5 a^4 b x+\frac{10}{3} a^3 b^2 x^3+2 a^2 b^3 x^5+\frac{5}{7} a b^4 x^7+\frac{b^5 x^9}{9}",1,"(-63*a^5 + 315*a^4*b*x^2 + 210*a^3*b^2*x^4 + 126*a^2*b^3*x^6 + 45*a*b^4*x^8 + 7*b^5*x^10)/(63*x)","A",1
76,1,61,60,0.0100566,"\int \frac{\left(a+b x^2\right)^5}{x^4} \, dx","IntegrateAlgebraic[(a + b*x^2)^5/x^4,x]","\frac{-7 a^5-105 a^4 b x^2+210 a^3 b^2 x^4+70 a^2 b^3 x^6+21 a b^4 x^8+3 b^5 x^{10}}{21 x^3}","-\frac{a^5}{3 x^3}-\frac{5 a^4 b}{x}+10 a^3 b^2 x+\frac{10}{3} a^2 b^3 x^3+a b^4 x^5+\frac{b^5 x^7}{7}",1,"(-7*a^5 - 105*a^4*b*x^2 + 210*a^3*b^2*x^4 + 70*a^2*b^3*x^6 + 21*a*b^4*x^8 + 3*b^5*x^10)/(21*x^3)","A",1
77,1,61,63,0.010425,"\int \frac{\left(a+b x^2\right)^5}{x^6} \, dx","IntegrateAlgebraic[(a + b*x^2)^5/x^6,x]","\frac{-3 a^5-25 a^4 b x^2-150 a^3 b^2 x^4+150 a^2 b^3 x^6+25 a b^4 x^8+3 b^5 x^{10}}{15 x^5}","-\frac{a^5}{5 x^5}-\frac{5 a^4 b}{3 x^3}-\frac{10 a^3 b^2}{x}+10 a^2 b^3 x+\frac{5}{3} a b^4 x^3+\frac{b^5 x^5}{5}",1,"(-3*a^5 - 25*a^4*b*x^2 - 150*a^3*b^2*x^4 + 150*a^2*b^3*x^6 + 25*a*b^4*x^8 + 3*b^5*x^10)/(15*x^5)","A",1
78,1,61,61,0.0113115,"\int \frac{\left(a+b x^2\right)^5}{x^8} \, dx","IntegrateAlgebraic[(a + b*x^2)^5/x^8,x]","\frac{-3 a^5-21 a^4 b x^2-70 a^3 b^2 x^4-210 a^2 b^3 x^6+105 a b^4 x^8+7 b^5 x^{10}}{21 x^7}","-\frac{a^5}{7 x^7}-\frac{a^4 b}{x^5}-\frac{10 a^3 b^2}{3 x^3}-\frac{10 a^2 b^3}{x}+5 a b^4 x+\frac{b^5 x^3}{3}",1,"(-3*a^5 - 21*a^4*b*x^2 - 70*a^3*b^2*x^4 - 210*a^2*b^3*x^6 + 105*a*b^4*x^8 + 7*b^5*x^10)/(21*x^7)","A",1
79,1,61,60,0.0116305,"\int \frac{\left(a+b x^2\right)^5}{x^{10}} \, dx","IntegrateAlgebraic[(a + b*x^2)^5/x^10,x]","\frac{-7 a^5-45 a^4 b x^2-126 a^3 b^2 x^4-210 a^2 b^3 x^6-315 a b^4 x^8+63 b^5 x^{10}}{63 x^9}","-\frac{a^5}{9 x^9}-\frac{5 a^4 b}{7 x^7}-\frac{2 a^3 b^2}{x^5}-\frac{10 a^2 b^3}{3 x^3}-\frac{5 a b^4}{x}+b^5 x",1,"(-7*a^5 - 45*a^4*b*x^2 - 126*a^3*b^2*x^4 - 210*a^2*b^3*x^6 - 315*a*b^4*x^8 + 63*b^5*x^10)/(63*x^9)","A",1
80,1,61,65,0.0107574,"\int \frac{\left(a+b x^2\right)^5}{x^{12}} \, dx","IntegrateAlgebraic[(a + b*x^2)^5/x^12,x]","\frac{-63 a^5-385 a^4 b x^2-990 a^3 b^2 x^4-1386 a^2 b^3 x^6-1155 a b^4 x^8-693 b^5 x^{10}}{693 x^{11}}","-\frac{a^5}{11 x^{11}}-\frac{5 a^4 b}{9 x^9}-\frac{10 a^3 b^2}{7 x^7}-\frac{2 a^2 b^3}{x^5}-\frac{5 a b^4}{3 x^3}-\frac{b^5}{x}",1,"(-63*a^5 - 385*a^4*b*x^2 - 990*a^3*b^2*x^4 - 1386*a^2*b^3*x^6 - 1155*a*b^4*x^8 - 693*b^5*x^10)/(693*x^11)","A",1
81,1,61,67,0.0106693,"\int \frac{\left(a+b x^2\right)^5}{x^{14}} \, dx","IntegrateAlgebraic[(a + b*x^2)^5/x^14,x]","\frac{-693 a^5-4095 a^4 b x^2-10010 a^3 b^2 x^4-12870 a^2 b^3 x^6-9009 a b^4 x^8-3003 b^5 x^{10}}{9009 x^{13}}","-\frac{a^5}{13 x^{13}}-\frac{5 a^4 b}{11 x^{11}}-\frac{10 a^3 b^2}{9 x^9}-\frac{10 a^2 b^3}{7 x^7}-\frac{a b^4}{x^5}-\frac{b^5}{3 x^3}",1,"(-693*a^5 - 4095*a^4*b*x^2 - 10010*a^3*b^2*x^4 - 12870*a^2*b^3*x^6 - 9009*a*b^4*x^8 - 3003*b^5*x^10)/(9009*x^13)","A",1
82,1,61,69,0.0106843,"\int \frac{\left(a+b x^2\right)^5}{x^{16}} \, dx","IntegrateAlgebraic[(a + b*x^2)^5/x^16,x]","\frac{-3003 a^5-17325 a^4 b x^2-40950 a^3 b^2 x^4-50050 a^2 b^3 x^6-32175 a b^4 x^8-9009 b^5 x^{10}}{45045 x^{15}}","-\frac{a^5}{15 x^{15}}-\frac{5 a^4 b}{13 x^{13}}-\frac{10 a^3 b^2}{11 x^{11}}-\frac{10 a^2 b^3}{9 x^9}-\frac{5 a b^4}{7 x^7}-\frac{b^5}{5 x^5}",1,"(-3003*a^5 - 17325*a^4*b*x^2 - 40950*a^3*b^2*x^4 - 50050*a^2*b^3*x^6 - 32175*a*b^4*x^8 - 9009*b^5*x^10)/(45045*x^15)","A",1
83,1,61,69,0.0105038,"\int \frac{\left(a+b x^2\right)^5}{x^{18}} \, dx","IntegrateAlgebraic[(a + b*x^2)^5/x^18,x]","\frac{-9009 a^5-51051 a^4 b x^2-117810 a^3 b^2 x^4-139230 a^2 b^3 x^6-85085 a b^4 x^8-21879 b^5 x^{10}}{153153 x^{17}}","-\frac{a^5}{17 x^{17}}-\frac{a^4 b}{3 x^{15}}-\frac{10 a^3 b^2}{13 x^{13}}-\frac{10 a^2 b^3}{11 x^{11}}-\frac{5 a b^4}{9 x^9}-\frac{b^5}{7 x^7}",1,"(-9009*a^5 - 51051*a^4*b*x^2 - 117810*a^3*b^2*x^4 - 139230*a^2*b^3*x^6 - 85085*a*b^4*x^8 - 21879*b^5*x^10)/(153153*x^17)","A",1
84,1,61,69,0.0129621,"\int \frac{\left(a+b x^2\right)^5}{x^{20}} \, dx","IntegrateAlgebraic[(a + b*x^2)^5/x^20,x]","\frac{-21879 a^5-122265 a^4 b x^2-277134 a^3 b^2 x^4-319770 a^2 b^3 x^6-188955 a b^4 x^8-46189 b^5 x^{10}}{415701 x^{19}}","-\frac{a^5}{19 x^{19}}-\frac{5 a^4 b}{17 x^{17}}-\frac{2 a^3 b^2}{3 x^{15}}-\frac{10 a^2 b^3}{13 x^{13}}-\frac{5 a b^4}{11 x^{11}}-\frac{b^5}{9 x^9}",1,"(-21879*a^5 - 122265*a^4*b*x^2 - 277134*a^3*b^2*x^4 - 319770*a^2*b^3*x^6 - 188955*a*b^4*x^8 - 46189*b^5*x^10)/(415701*x^19)","A",1
85,1,94,129,0.0151429,"\int x^{13} \left(a+b x^2\right)^8 \, dx","IntegrateAlgebraic[x^13*(a + b*x^2)^8,x]","\frac{6435 a^8 x^{14}+45045 a^7 b x^{16}+140140 a^6 b^2 x^{18}+252252 a^5 b^3 x^{20}+286650 a^4 b^4 x^{22}+210210 a^3 b^5 x^{24}+97020 a^2 b^6 x^{26}+25740 a b^7 x^{28}+3003 b^8 x^{30}}{90090}","\frac{a^6 \left(a+b x^2\right)^9}{18 b^7}-\frac{3 a^5 \left(a+b x^2\right)^{10}}{10 b^7}+\frac{15 a^4 \left(a+b x^2\right)^{11}}{22 b^7}-\frac{5 a^3 \left(a+b x^2\right)^{12}}{6 b^7}+\frac{15 a^2 \left(a+b x^2\right)^{13}}{26 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,"(6435*a^8*x^14 + 45045*a^7*b*x^16 + 140140*a^6*b^2*x^18 + 252252*a^5*b^3*x^20 + 286650*a^4*b^4*x^22 + 210210*a^3*b^5*x^24 + 97020*a^2*b^6*x^26 + 25740*a*b^7*x^28 + 3003*b^8*x^30)/90090","A",1
86,1,94,110,0.014698,"\int x^{11} \left(a+b x^2\right)^8 \, dx","IntegrateAlgebraic[x^11*(a + b*x^2)^8,x]","\frac{3003 a^8 x^{12}+20592 a^7 b x^{14}+63063 a^6 b^2 x^{16}+112112 a^5 b^3 x^{18}+126126 a^4 b^4 x^{20}+91728 a^3 b^5 x^{22}+42042 a^2 b^6 x^{24}+11088 a b^7 x^{26}+1287 b^8 x^{28}}{36036}","-\frac{a^5 \left(a+b x^2\right)^9}{18 b^6}+\frac{a^4 \left(a+b x^2\right)^{10}}{4 b^6}-\frac{5 a^3 \left(a+b x^2\right)^{11}}{11 b^6}+\frac{5 a^2 \left(a+b x^2\right)^{12}}{12 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,"(3003*a^8*x^12 + 20592*a^7*b*x^14 + 63063*a^6*b^2*x^16 + 112112*a^5*b^3*x^18 + 126126*a^4*b^4*x^20 + 91728*a^3*b^5*x^22 + 42042*a^2*b^6*x^24 + 11088*a*b^7*x^26 + 1287*b^8*x^28)/36036","A",1
87,1,94,91,0.014361,"\int x^9 \left(a+b x^2\right)^8 \, dx","IntegrateAlgebraic[x^9*(a + b*x^2)^8,x]","\frac{1287 a^8 x^{10}+8580 a^7 b x^{12}+25740 a^6 b^2 x^{14}+45045 a^5 b^3 x^{16}+50050 a^4 b^4 x^{18}+36036 a^3 b^5 x^{20}+16380 a^2 b^6 x^{22}+4290 a b^7 x^{24}+495 b^8 x^{26}}{12870}","\frac{a^4 \left(a+b x^2\right)^9}{18 b^5}-\frac{a^3 \left(a+b x^2\right)^{10}}{5 b^5}+\frac{3 a^2 \left(a+b x^2\right)^{11}}{11 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,"(1287*a^8*x^10 + 8580*a^7*b*x^12 + 25740*a^6*b^2*x^14 + 45045*a^5*b^3*x^16 + 50050*a^4*b^4*x^18 + 36036*a^3*b^5*x^20 + 16380*a^2*b^6*x^22 + 4290*a*b^7*x^24 + 495*b^8*x^26)/12870","A",1
88,1,94,72,0.0141276,"\int x^7 \left(a+b x^2\right)^8 \, dx","IntegrateAlgebraic[x^7*(a + b*x^2)^8,x]","\frac{495 a^8 x^8+3168 a^7 b x^{10}+9240 a^6 b^2 x^{12}+15840 a^5 b^3 x^{14}+17325 a^4 b^4 x^{16}+12320 a^3 b^5 x^{18}+5544 a^2 b^6 x^{20}+1440 a b^7 x^{22}+165 b^8 x^{24}}{3960}","-\frac{a^3 \left(a+b x^2\right)^9}{18 b^4}+\frac{3 a^2 \left(a+b x^2\right)^{10}}{20 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,"(495*a^8*x^8 + 3168*a^7*b*x^10 + 9240*a^6*b^2*x^12 + 15840*a^5*b^3*x^14 + 17325*a^4*b^4*x^16 + 12320*a^3*b^5*x^18 + 5544*a^2*b^6*x^20 + 1440*a*b^7*x^22 + 165*b^8*x^24)/3960","A",1
89,1,94,53,0.014054,"\int x^5 \left(a+b x^2\right)^8 \, dx","IntegrateAlgebraic[x^5*(a + b*x^2)^8,x]","\frac{1}{990} \left(165 a^8 x^6+990 a^7 b x^8+2772 a^6 b^2 x^{10}+4620 a^5 b^3 x^{12}+4950 a^4 b^4 x^{14}+3465 a^3 b^5 x^{16}+1540 a^2 b^6 x^{18}+396 a b^7 x^{20}+45 b^8 x^{22}\right)","\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,"(165*a^8*x^6 + 990*a^7*b*x^8 + 2772*a^6*b^2*x^10 + 4620*a^5*b^3*x^12 + 4950*a^4*b^4*x^14 + 3465*a^3*b^5*x^16 + 1540*a^2*b^6*x^18 + 396*a*b^7*x^20 + 45*b^8*x^22)/990","A",1
90,1,94,34,0.0139931,"\int x^3 \left(a+b x^2\right)^8 \, dx","IntegrateAlgebraic[x^3*(a + b*x^2)^8,x]","\frac{1}{180} \left(45 a^8 x^4+240 a^7 b x^6+630 a^6 b^2 x^8+1008 a^5 b^3 x^{10}+1050 a^4 b^4 x^{12}+720 a^3 b^5 x^{14}+315 a^2 b^6 x^{16}+80 a b^7 x^{18}+9 b^8 x^{20}\right)","\frac{\left(a+b x^2\right)^{10}}{20 b^2}-\frac{a \left(a+b x^2\right)^9}{18 b^2}",1,"(45*a^8*x^4 + 240*a^7*b*x^6 + 630*a^6*b^2*x^8 + 1008*a^5*b^3*x^10 + 1050*a^4*b^4*x^12 + 720*a^3*b^5*x^14 + 315*a^2*b^6*x^16 + 80*a*b^7*x^18 + 9*b^8*x^20)/180","B",1
91,1,16,16,0.0072539,"\int x \left(a+b x^2\right)^8 \, dx","IntegrateAlgebraic[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
92,1,93,100,0.0168825,"\int \frac{\left(a+b x^2\right)^8}{x} \, dx","IntegrateAlgebraic[(a + b*x^2)^8/x,x]","a^8 \log (x)+\frac{6720 a^7 b x^2+11760 a^6 b^2 x^4+15680 a^5 b^3 x^6+14700 a^4 b^4 x^8+9408 a^3 b^5 x^{10}+3920 a^2 b^6 x^{12}+960 a b^7 x^{14}+105 b^8 x^{16}}{1680}","a^8 \log (x)+4 a^7 b x^2+7 a^6 b^2 x^4+\frac{28}{3} a^5 b^3 x^6+\frac{35}{4} a^4 b^4 x^8+\frac{28}{5} a^3 b^5 x^{10}+\frac{7}{3} a^2 b^6 x^{12}+\frac{4}{7} a b^7 x^{14}+\frac{b^8 x^{16}}{16}",1,"(6720*a^7*b*x^2 + 11760*a^6*b^2*x^4 + 15680*a^5*b^3*x^6 + 14700*a^4*b^4*x^8 + 9408*a^3*b^5*x^10 + 3920*a^2*b^6*x^12 + 960*a*b^7*x^14 + 105*b^8*x^16)/1680 + a^8*Log[x]","A",1
93,1,94,99,0.0219365,"\int \frac{\left(a+b x^2\right)^8}{x^3} \, dx","IntegrateAlgebraic[(a + b*x^2)^8/x^3,x]","8 a^7 b \log (x)+\frac{-105 a^8+2940 a^6 b^2 x^4+2940 a^5 b^3 x^6+2450 a^4 b^4 x^8+1470 a^3 b^5 x^{10}+588 a^2 b^6 x^{12}+140 a b^7 x^{14}+15 b^8 x^{16}}{210 x^2}","-\frac{a^8}{2 x^2}+8 a^7 b \log (x)+14 a^6 b^2 x^2+14 a^5 b^3 x^4+\frac{35}{3} a^4 b^4 x^6+7 a^3 b^5 x^8+\frac{14}{5} a^2 b^6 x^{10}+\frac{2}{3} a b^7 x^{12}+\frac{b^8 x^{14}}{14}",1,"(-105*a^8 + 2940*a^6*b^2*x^4 + 2940*a^5*b^3*x^6 + 2450*a^4*b^4*x^8 + 1470*a^3*b^5*x^10 + 588*a^2*b^6*x^12 + 140*a*b^7*x^14 + 15*b^8*x^16)/(210*x^2) + 8*a^7*b*Log[x]","A",1
94,1,94,101,0.0220929,"\int \frac{\left(a+b x^2\right)^8}{x^5} \, dx","IntegrateAlgebraic[(a + b*x^2)^8/x^5,x]","28 a^6 b^2 \log (x)+\frac{-15 a^8-240 a^7 b x^2+1680 a^5 b^3 x^6+1050 a^4 b^4 x^8+560 a^3 b^5 x^{10}+210 a^2 b^6 x^{12}+48 a b^7 x^{14}+5 b^8 x^{16}}{60 x^4}","-\frac{a^8}{4 x^4}-\frac{4 a^7 b}{x^2}+28 a^6 b^2 \log (x)+28 a^5 b^3 x^2+\frac{35}{2} a^4 b^4 x^4+\frac{28}{3} a^3 b^5 x^6+\frac{7}{2} a^2 b^6 x^8+\frac{4}{5} a b^7 x^{10}+\frac{b^8 x^{12}}{12}",1,"(-15*a^8 - 240*a^7*b*x^2 + 1680*a^5*b^3*x^6 + 1050*a^4*b^4*x^8 + 560*a^3*b^5*x^10 + 210*a^2*b^6*x^12 + 48*a*b^7*x^14 + 5*b^8*x^16)/(60*x^4) + 28*a^6*b^2*Log[x]","A",1
95,1,94,94,0.0227646,"\int \frac{\left(a+b x^2\right)^8}{x^7} \, dx","IntegrateAlgebraic[(a + b*x^2)^8/x^7,x]","56 a^5 b^3 \log (x)+\frac{-5 a^8-60 a^7 b x^2-420 a^6 b^2 x^4+1050 a^4 b^4 x^8+420 a^3 b^5 x^{10}+140 a^2 b^6 x^{12}+30 a b^7 x^{14}+3 b^8 x^{16}}{30 x^6}","-\frac{a^8}{6 x^6}-\frac{2 a^7 b}{x^4}-\frac{14 a^6 b^2}{x^2}+56 a^5 b^3 \log (x)+35 a^4 b^4 x^2+14 a^3 b^5 x^4+\frac{14}{3} a^2 b^6 x^6+a b^7 x^8+\frac{b^8 x^{10}}{10}",1,"(-5*a^8 - 60*a^7*b*x^2 - 420*a^6*b^2*x^4 + 1050*a^4*b^4*x^8 + 420*a^3*b^5*x^10 + 140*a^2*b^6*x^12 + 30*a*b^7*x^14 + 3*b^8*x^16)/(30*x^6) + 56*a^5*b^3*Log[x]","A",1
96,1,94,97,0.0219102,"\int \frac{\left(a+b x^2\right)^8}{x^9} \, dx","IntegrateAlgebraic[(a + b*x^2)^8/x^9,x]","70 a^4 b^4 \log (x)+\frac{-3 a^8-32 a^7 b x^2-168 a^6 b^2 x^4-672 a^5 b^3 x^6+672 a^3 b^5 x^{10}+168 a^2 b^6 x^{12}+32 a b^7 x^{14}+3 b^8 x^{16}}{24 x^8}","-\frac{a^8}{8 x^8}-\frac{4 a^7 b}{3 x^6}-\frac{7 a^6 b^2}{x^4}-\frac{28 a^5 b^3}{x^2}+70 a^4 b^4 \log (x)+28 a^3 b^5 x^2+7 a^2 b^6 x^4+\frac{4}{3} a b^7 x^6+\frac{b^8 x^8}{8}",1,"(-3*a^8 - 32*a^7*b*x^2 - 168*a^6*b^2*x^4 - 672*a^5*b^3*x^6 + 672*a^3*b^5*x^10 + 168*a^2*b^6*x^12 + 32*a*b^7*x^14 + 3*b^8*x^16)/(24*x^8) + 70*a^4*b^4*Log[x]","A",1
97,1,94,95,0.0237294,"\int \frac{\left(a+b x^2\right)^8}{x^{11}} \, dx","IntegrateAlgebraic[(a + b*x^2)^8/x^11,x]","56 a^3 b^5 \log (x)+\frac{-3 a^8-30 a^7 b x^2-140 a^6 b^2 x^4-420 a^5 b^3 x^6-1050 a^4 b^4 x^8+420 a^2 b^6 x^{12}+60 a b^7 x^{14}+5 b^8 x^{16}}{30 x^{10}}","-\frac{a^8}{10 x^{10}}-\frac{a^7 b}{x^8}-\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}+56 a^3 b^5 \log (x)+14 a^2 b^6 x^2+2 a b^7 x^4+\frac{b^8 x^6}{6}",1,"(-3*a^8 - 30*a^7*b*x^2 - 140*a^6*b^2*x^4 - 420*a^5*b^3*x^6 - 1050*a^4*b^4*x^8 + 420*a^2*b^6*x^12 + 60*a*b^7*x^14 + 5*b^8*x^16)/(30*x^10) + 56*a^3*b^5*Log[x]","A",1
98,1,94,101,0.0235849,"\int \frac{\left(a+b x^2\right)^8}{x^{13}} \, dx","IntegrateAlgebraic[(a + b*x^2)^8/x^13,x]","28 a^2 b^6 \log (x)+\frac{-5 a^8-48 a^7 b x^2-210 a^6 b^2 x^4-560 a^5 b^3 x^6-1050 a^4 b^4 x^8-1680 a^3 b^5 x^{10}+240 a b^7 x^{14}+15 b^8 x^{16}}{60 x^{12}}","-\frac{a^8}{12 x^{12}}-\frac{4 a^7 b}{5 x^{10}}-\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)+4 a b^7 x^2+\frac{b^8 x^4}{4}",1,"(-5*a^8 - 48*a^7*b*x^2 - 210*a^6*b^2*x^4 - 560*a^5*b^3*x^6 - 1050*a^4*b^4*x^8 - 1680*a^3*b^5*x^10 + 240*a*b^7*x^14 + 15*b^8*x^16)/(60*x^12) + 28*a^2*b^6*Log[x]","A",1
99,1,94,99,0.0240895,"\int \frac{\left(a+b x^2\right)^8}{x^{15}} \, dx","IntegrateAlgebraic[(a + b*x^2)^8/x^15,x]","\frac{-15 a^8-140 a^7 b x^2-588 a^6 b^2 x^4-1470 a^5 b^3 x^6-2450 a^4 b^4 x^8-2940 a^3 b^5 x^{10}-2940 a^2 b^6 x^{12}+105 b^8 x^{16}}{210 x^{14}}+8 a b^7 \log (x)","-\frac{a^8}{14 x^{14}}-\frac{2 a^7 b}{3 x^{12}}-\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}+8 a b^7 \log (x)+\frac{b^8 x^2}{2}",1,"(-15*a^8 - 140*a^7*b*x^2 - 588*a^6*b^2*x^4 - 1470*a^5*b^3*x^6 - 2450*a^4*b^4*x^8 - 2940*a^3*b^5*x^10 - 2940*a^2*b^6*x^12 + 105*b^8*x^16)/(210*x^14) + 8*a*b^7*Log[x]","A",1
100,1,93,100,0.0251299,"\int \frac{\left(a+b x^2\right)^8}{x^{17}} \, dx","IntegrateAlgebraic[(a + b*x^2)^8/x^17,x]","\frac{-105 a^8-960 a^7 b x^2-3920 a^6 b^2 x^4-9408 a^5 b^3 x^6-14700 a^4 b^4 x^8-15680 a^3 b^5 x^{10}-11760 a^2 b^6 x^{12}-6720 a b^7 x^{14}}{1680 x^{16}}+b^8 \log (x)","-\frac{a^8}{16 x^{16}}-\frac{4 a^7 b}{7 x^{14}}-\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 b^7}{x^2}+b^8 \log (x)",1,"(-105*a^8 - 960*a^7*b*x^2 - 3920*a^6*b^2*x^4 - 9408*a^5*b^3*x^6 - 14700*a^4*b^4*x^8 - 15680*a^3*b^5*x^10 - 11760*a^2*b^6*x^12 - 6720*a*b^7*x^14)/(1680*x^16) + b^8*Log[x]","A",1
101,1,94,19,0.0127147,"\int \frac{\left(a+b x^2\right)^8}{x^{19}} \, dx","IntegrateAlgebraic[(a + b*x^2)^8/x^19,x]","\frac{-a^8-9 a^7 b x^2-36 a^6 b^2 x^4-84 a^5 b^3 x^6-126 a^4 b^4 x^8-126 a^3 b^5 x^{10}-84 a^2 b^6 x^{12}-36 a b^7 x^{14}-9 b^8 x^{16}}{18 x^{18}}","-\frac{\left(a+b x^2\right)^9}{18 a x^{18}}",1,"(-a^8 - 9*a^7*b*x^2 - 36*a^6*b^2*x^4 - 84*a^5*b^3*x^6 - 126*a^4*b^4*x^8 - 126*a^3*b^5*x^10 - 84*a^2*b^6*x^12 - 36*a*b^7*x^14 - 9*b^8*x^16)/(18*x^18)","B",1
102,1,94,40,0.0127244,"\int \frac{\left(a+b x^2\right)^8}{x^{21}} \, dx","IntegrateAlgebraic[(a + b*x^2)^8/x^21,x]","\frac{-9 a^8-80 a^7 b x^2-315 a^6 b^2 x^4-720 a^5 b^3 x^6-1050 a^4 b^4 x^8-1008 a^3 b^5 x^{10}-630 a^2 b^6 x^{12}-240 a b^7 x^{14}-45 b^8 x^{16}}{180 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,"(-9*a^8 - 80*a^7*b*x^2 - 315*a^6*b^2*x^4 - 720*a^5*b^3*x^6 - 1050*a^4*b^4*x^8 - 1008*a^3*b^5*x^10 - 630*a^2*b^6*x^12 - 240*a*b^7*x^14 - 45*b^8*x^16)/(180*x^20)","B",1
103,1,94,62,0.0131695,"\int \frac{\left(a+b x^2\right)^8}{x^{23}} \, dx","IntegrateAlgebraic[(a + b*x^2)^8/x^23,x]","\frac{-45 a^8-396 a^7 b x^2-1540 a^6 b^2 x^4-3465 a^5 b^3 x^6-4950 a^4 b^4 x^8-4620 a^3 b^5 x^{10}-2772 a^2 b^6 x^{12}-990 a b^7 x^{14}-165 b^8 x^{16}}{990 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,"(-45*a^8 - 396*a^7*b*x^2 - 1540*a^6*b^2*x^4 - 3465*a^5*b^3*x^6 - 4950*a^4*b^4*x^8 - 4620*a^3*b^5*x^10 - 2772*a^2*b^6*x^12 - 990*a*b^7*x^14 - 165*b^8*x^16)/(990*x^22)","A",1
104,1,94,84,0.0130548,"\int \frac{\left(a+b x^2\right)^8}{x^{25}} \, dx","IntegrateAlgebraic[(a + b*x^2)^8/x^25,x]","\frac{-165 a^8-1440 a^7 b x^2-5544 a^6 b^2 x^4-12320 a^5 b^3 x^6-17325 a^4 b^4 x^8-15840 a^3 b^5 x^{10}-9240 a^2 b^6 x^{12}-3168 a b^7 x^{14}-495 b^8 x^{16}}{3960 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,"(-165*a^8 - 1440*a^7*b*x^2 - 5544*a^6*b^2*x^4 - 12320*a^5*b^3*x^6 - 17325*a^4*b^4*x^8 - 15840*a^3*b^5*x^10 - 9240*a^2*b^6*x^12 - 3168*a*b^7*x^14 - 495*b^8*x^16)/(3960*x^24)","A",1
105,1,94,106,0.0132569,"\int \frac{\left(a+b x^2\right)^8}{x^{27}} \, dx","IntegrateAlgebraic[(a + b*x^2)^8/x^27,x]","\frac{-495 a^8-4290 a^7 b x^2-16380 a^6 b^2 x^4-36036 a^5 b^3 x^6-50050 a^4 b^4 x^8-45045 a^3 b^5 x^{10}-25740 a^2 b^6 x^{12}-8580 a b^7 x^{14}-1287 b^8 x^{16}}{12870 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,"(-495*a^8 - 4290*a^7*b*x^2 - 16380*a^6*b^2*x^4 - 36036*a^5*b^3*x^6 - 50050*a^4*b^4*x^8 - 45045*a^3*b^5*x^10 - 25740*a^2*b^6*x^12 - 8580*a*b^7*x^14 - 1287*b^8*x^16)/(12870*x^26)","A",1
106,1,94,108,0.0128171,"\int \frac{\left(a+b x^2\right)^8}{x^{29}} \, dx","IntegrateAlgebraic[(a + b*x^2)^8/x^29,x]","\frac{-1287 a^8-11088 a^7 b x^2-42042 a^6 b^2 x^4-91728 a^5 b^3 x^6-126126 a^4 b^4 x^8-112112 a^3 b^5 x^{10}-63063 a^2 b^6 x^{12}-20592 a b^7 x^{14}-3003 b^8 x^{16}}{36036 x^{28}}","-\frac{a^8}{28 x^{28}}-\frac{4 a^7 b}{13 x^{26}}-\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 b^7}{7 x^{14}}-\frac{b^8}{12 x^{12}}",1,"(-1287*a^8 - 11088*a^7*b*x^2 - 42042*a^6*b^2*x^4 - 91728*a^5*b^3*x^6 - 126126*a^4*b^4*x^8 - 112112*a^3*b^5*x^10 - 63063*a^2*b^6*x^12 - 20592*a*b^7*x^14 - 3003*b^8*x^16)/(36036*x^28)","A",1
107,1,94,108,0.0129442,"\int \frac{\left(a+b x^2\right)^8}{x^{31}} \, dx","IntegrateAlgebraic[(a + b*x^2)^8/x^31,x]","\frac{-3003 a^8-25740 a^7 b x^2-97020 a^6 b^2 x^4-210210 a^5 b^3 x^6-286650 a^4 b^4 x^8-252252 a^3 b^5 x^{10}-140140 a^2 b^6 x^{12}-45045 a b^7 x^{14}-6435 b^8 x^{16}}{90090 x^{30}}","-\frac{a^8}{30 x^{30}}-\frac{2 a^7 b}{7 x^{28}}-\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{a b^7}{2 x^{16}}-\frac{b^8}{14 x^{14}}",1,"(-3003*a^8 - 25740*a^7*b*x^2 - 97020*a^6*b^2*x^4 - 210210*a^5*b^3*x^6 - 286650*a^4*b^4*x^8 - 252252*a^3*b^5*x^10 - 140140*a^2*b^6*x^12 - 45045*a*b^7*x^14 - 6435*b^8*x^16)/(90090*x^30)","A",1
108,1,94,106,0.0130242,"\int \frac{\left(a+b x^2\right)^8}{x^{33}} \, dx","IntegrateAlgebraic[(a + b*x^2)^8/x^33,x]","\frac{-6435 a^8-54912 a^7 b x^2-205920 a^6 b^2 x^4-443520 a^5 b^3 x^6-600600 a^4 b^4 x^8-524160 a^3 b^5 x^{10}-288288 a^2 b^6 x^{12}-91520 a b^7 x^{14}-12870 b^8 x^{16}}{205920 x^{32}}","-\frac{a^8}{32 x^{32}}-\frac{4 a^7 b}{15 x^{30}}-\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 b^7}{9 x^{18}}-\frac{b^8}{16 x^{16}}",1,"(-6435*a^8 - 54912*a^7*b*x^2 - 205920*a^6*b^2*x^4 - 443520*a^5*b^3*x^6 - 600600*a^4*b^4*x^8 - 524160*a^3*b^5*x^10 - 288288*a^2*b^6*x^12 - 91520*a*b^7*x^14 - 12870*b^8*x^16)/(205920*x^32)","A",1
109,1,94,108,0.0153301,"\int x^8 \left(a+b x^2\right)^8 \, dx","IntegrateAlgebraic[x^8*(a + b*x^2)^8,x]","\frac{26558675 a^8 x^9+173838600 a^7 b x^{11}+514829700 a^6 b^2 x^{13}+892371480 a^5 b^3 x^{15}+984233250 a^4 b^4 x^{17}+704503800 a^3 b^5 x^{19}+318704100 a^2 b^6 x^{21}+83140200 a b^7 x^{23}+9561123 b^8 x^{25}}{239028075}","\frac{a^8 x^9}{9}+\frac{8}{11} a^7 b x^{11}+\frac{28}{13} a^6 b^2 x^{13}+\frac{56}{15} a^5 b^3 x^{15}+\frac{70}{17} a^4 b^4 x^{17}+\frac{56}{19} a^3 b^5 x^{19}+\frac{4}{3} a^2 b^6 x^{21}+\frac{8}{23} a b^7 x^{23}+\frac{b^8 x^{25}}{25}",1,"(26558675*a^8*x^9 + 173838600*a^7*b*x^11 + 514829700*a^6*b^2*x^13 + 892371480*a^5*b^3*x^15 + 984233250*a^4*b^4*x^17 + 704503800*a^3*b^5*x^19 + 318704100*a^2*b^6*x^21 + 83140200*a*b^7*x^23 + 9561123*b^8*x^25)/239028075","A",1
110,1,94,108,0.0143069,"\int x^6 \left(a+b x^2\right)^8 \, dx","IntegrateAlgebraic[x^6*(a + b*x^2)^8,x]","\frac{9561123 a^8 x^7+59491432 a^7 b x^9+170361828 a^6 b^2 x^{11}+288304632 a^5 b^3 x^{13}+312330018 a^4 b^4 x^{15}+220468248 a^3 b^5 x^{17}+98630532 a^2 b^6 x^{19}+25496328 a b^7 x^{21}+2909907 b^8 x^{23}}{66927861}","\frac{a^8 x^7}{7}+\frac{8}{9} a^7 b x^9+\frac{28}{11} a^6 b^2 x^{11}+\frac{56}{13} a^5 b^3 x^{13}+\frac{14}{3} a^4 b^4 x^{15}+\frac{56}{17} a^3 b^5 x^{17}+\frac{28}{19} a^2 b^6 x^{19}+\frac{8}{21} a b^7 x^{21}+\frac{b^8 x^{23}}{23}",1,"(9561123*a^8*x^7 + 59491432*a^7*b*x^9 + 170361828*a^6*b^2*x^11 + 288304632*a^5*b^3*x^13 + 312330018*a^4*b^4*x^15 + 220468248*a^3*b^5*x^17 + 98630532*a^2*b^6*x^19 + 25496328*a*b^7*x^21 + 2909907*b^8*x^23)/66927861","A",1
111,1,94,108,0.0142309,"\int x^4 \left(a+b x^2\right)^8 \, dx","IntegrateAlgebraic[x^4*(a + b*x^2)^8,x]","\frac{2909907 a^8 x^5+16628040 a^7 b x^7+45265220 a^6 b^2 x^9+74070360 a^5 b^3 x^{11}+78343650 a^4 b^4 x^{13}+54318264 a^3 b^5 x^{15}+23963940 a^2 b^6 x^{17}+6126120 a b^7 x^{19}+692835 b^8 x^{21}}{14549535}","\frac{a^8 x^5}{5}+\frac{8}{7} a^7 b x^7+\frac{28}{9} a^6 b^2 x^9+\frac{56}{11} a^5 b^3 x^{11}+\frac{70}{13} a^4 b^4 x^{13}+\frac{56}{15} a^3 b^5 x^{15}+\frac{28}{17} a^2 b^6 x^{17}+\frac{8}{19} a b^7 x^{19}+\frac{b^8 x^{21}}{21}",1,"(2909907*a^8*x^5 + 16628040*a^7*b*x^7 + 45265220*a^6*b^2*x^9 + 74070360*a^5*b^3*x^11 + 78343650*a^4*b^4*x^13 + 54318264*a^3*b^5*x^15 + 23963940*a^2*b^6*x^17 + 6126120*a*b^7*x^19 + 692835*b^8*x^21)/14549535","A",1
112,1,94,106,0.0143264,"\int x^2 \left(a+b x^2\right)^8 \, dx","IntegrateAlgebraic[x^2*(a + b*x^2)^8,x]","\frac{692835 a^8 x^3+3325608 a^7 b x^5+8314020 a^6 b^2 x^7+12932920 a^5 b^3 x^9+13226850 a^4 b^4 x^{11}+8953560 a^3 b^5 x^{13}+3879876 a^2 b^6 x^{15}+978120 a b^7 x^{17}+109395 b^8 x^{19}}{2078505}","\frac{a^8 x^3}{3}+\frac{8}{5} a^7 b x^5+4 a^6 b^2 x^7+\frac{56}{9} a^5 b^3 x^9+\frac{70}{11} a^4 b^4 x^{11}+\frac{56}{13} a^3 b^5 x^{13}+\frac{28}{15} a^2 b^6 x^{15}+\frac{8}{17} a b^7 x^{17}+\frac{b^8 x^{19}}{19}",1,"(692835*a^8*x^3 + 3325608*a^7*b*x^5 + 8314020*a^6*b^2*x^7 + 12932920*a^5*b^3*x^9 + 13226850*a^4*b^4*x^11 + 8953560*a^3*b^5*x^13 + 3879876*a^2*b^6*x^15 + 978120*a*b^7*x^17 + 109395*b^8*x^19)/2078505","A",1
113,1,92,101,0.0128245,"\int \left(a+b x^2\right)^8 \, dx","IntegrateAlgebraic[(a + b*x^2)^8,x]","\frac{109395 a^8 x+291720 a^7 b x^3+612612 a^6 b^2 x^5+875160 a^5 b^3 x^7+850850 a^4 b^4 x^9+556920 a^3 b^5 x^{11}+235620 a^2 b^6 x^{13}+58344 a b^7 x^{15}+6435 b^8 x^{17}}{109395}","a^8 x+\frac{8}{3} a^7 b x^3+\frac{28}{5} a^6 b^2 x^5+8 a^5 b^3 x^7+\frac{70}{9} a^4 b^4 x^9+\frac{56}{11} a^3 b^5 x^{11}+\frac{28}{13} a^2 b^6 x^{13}+\frac{8}{15} a b^7 x^{15}+\frac{b^8 x^{17}}{17}",1,"(109395*a^8*x + 291720*a^7*b*x^3 + 612612*a^6*b^2*x^5 + 875160*a^5*b^3*x^7 + 850850*a^4*b^4*x^9 + 556920*a^3*b^5*x^11 + 235620*a^2*b^6*x^13 + 58344*a*b^7*x^15 + 6435*b^8*x^17)/109395","A",1
114,1,94,100,0.0167436,"\int \frac{\left(a+b x^2\right)^8}{x^2} \, dx","IntegrateAlgebraic[(a + b*x^2)^8/x^2,x]","\frac{-6435 a^8+51480 a^7 b x^2+60060 a^6 b^2 x^4+72072 a^5 b^3 x^6+64350 a^4 b^4 x^8+40040 a^3 b^5 x^{10}+16380 a^2 b^6 x^{12}+3960 a b^7 x^{14}+429 b^8 x^{16}}{6435 x}","-\frac{a^8}{x}+8 a^7 b x+\frac{28}{3} a^6 b^2 x^3+\frac{56}{5} a^5 b^3 x^5+10 a^4 b^4 x^7+\frac{56}{9} a^3 b^5 x^9+\frac{28}{11} a^2 b^6 x^{11}+\frac{8}{13} a b^7 x^{13}+\frac{b^8 x^{15}}{15}",1,"(-6435*a^8 + 51480*a^7*b*x^2 + 60060*a^6*b^2*x^4 + 72072*a^5*b^3*x^6 + 64350*a^4*b^4*x^8 + 40040*a^3*b^5*x^10 + 16380*a^2*b^6*x^12 + 3960*a*b^7*x^14 + 429*b^8*x^16)/(6435*x)","A",1
115,1,94,98,0.0156105,"\int \frac{\left(a+b x^2\right)^8}{x^4} \, dx","IntegrateAlgebraic[(a + b*x^2)^8/x^4,x]","\frac{-429 a^8-10296 a^7 b x^2+36036 a^6 b^2 x^4+24024 a^5 b^3 x^6+18018 a^4 b^4 x^8+10296 a^3 b^5 x^{10}+4004 a^2 b^6 x^{12}+936 a b^7 x^{14}+99 b^8 x^{16}}{1287 x^3}","-\frac{a^8}{3 x^3}-\frac{8 a^7 b}{x}+28 a^6 b^2 x+\frac{56}{3} a^5 b^3 x^3+14 a^4 b^4 x^5+8 a^3 b^5 x^7+\frac{28}{9} a^2 b^6 x^9+\frac{8}{11} a b^7 x^{11}+\frac{b^8 x^{13}}{13}",1,"(-429*a^8 - 10296*a^7*b*x^2 + 36036*a^6*b^2*x^4 + 24024*a^5*b^3*x^6 + 18018*a^4*b^4*x^8 + 10296*a^3*b^5*x^10 + 4004*a^2*b^6*x^12 + 936*a*b^7*x^14 + 99*b^8*x^16)/(1287*x^3)","A",1
116,1,94,100,0.0178403,"\int \frac{\left(a+b x^2\right)^8}{x^6} \, dx","IntegrateAlgebraic[(a + b*x^2)^8/x^6,x]","\frac{-99 a^8-1320 a^7 b x^2-13860 a^6 b^2 x^4+27720 a^5 b^3 x^6+11550 a^4 b^4 x^8+5544 a^3 b^5 x^{10}+1980 a^2 b^6 x^{12}+440 a b^7 x^{14}+45 b^8 x^{16}}{495 x^5}","-\frac{a^8}{5 x^5}-\frac{8 a^7 b}{3 x^3}-\frac{28 a^6 b^2}{x}+56 a^5 b^3 x+\frac{70}{3} a^4 b^4 x^3+\frac{56}{5} a^3 b^5 x^5+4 a^2 b^6 x^7+\frac{8}{9} a b^7 x^9+\frac{b^8 x^{11}}{11}",1,"(-99*a^8 - 1320*a^7*b*x^2 - 13860*a^6*b^2*x^4 + 27720*a^5*b^3*x^6 + 11550*a^4*b^4*x^8 + 5544*a^3*b^5*x^10 + 1980*a^2*b^6*x^12 + 440*a*b^7*x^14 + 45*b^8*x^16)/(495*x^5)","A",1
117,1,94,102,0.0147052,"\int \frac{\left(a+b x^2\right)^8}{x^8} \, dx","IntegrateAlgebraic[(a + b*x^2)^8/x^8,x]","\frac{-45 a^8-504 a^7 b x^2-2940 a^6 b^2 x^4-17640 a^5 b^3 x^6+22050 a^4 b^4 x^8+5880 a^3 b^5 x^{10}+1764 a^2 b^6 x^{12}+360 a b^7 x^{14}+35 b^8 x^{16}}{315 x^7}","-\frac{a^8}{7 x^7}-\frac{8 a^7 b}{5 x^5}-\frac{28 a^6 b^2}{3 x^3}-\frac{56 a^5 b^3}{x}+70 a^4 b^4 x+\frac{56}{3} a^3 b^5 x^3+\frac{28}{5} a^2 b^6 x^5+\frac{8}{7} a b^7 x^7+\frac{b^8 x^9}{9}",1,"(-45*a^8 - 504*a^7*b*x^2 - 2940*a^6*b^2*x^4 - 17640*a^5*b^3*x^6 + 22050*a^4*b^4*x^8 + 5880*a^3*b^5*x^10 + 1764*a^2*b^6*x^12 + 360*a*b^7*x^14 + 35*b^8*x^16)/(315*x^7)","A",1
118,1,94,102,0.0178568,"\int \frac{\left(a+b x^2\right)^8}{x^{10}} \, dx","IntegrateAlgebraic[(a + b*x^2)^8/x^10,x]","\frac{-35 a^8-360 a^7 b x^2-1764 a^6 b^2 x^4-5880 a^5 b^3 x^6-22050 a^4 b^4 x^8+17640 a^3 b^5 x^{10}+2940 a^2 b^6 x^{12}+504 a b^7 x^{14}+45 b^8 x^{16}}{315 x^9}","-\frac{a^8}{9 x^9}-\frac{8 a^7 b}{7 x^7}-\frac{28 a^6 b^2}{5 x^5}-\frac{56 a^5 b^3}{3 x^3}-\frac{70 a^4 b^4}{x}+56 a^3 b^5 x+\frac{28}{3} a^2 b^6 x^3+\frac{8}{5} a b^7 x^5+\frac{b^8 x^7}{7}",1,"(-35*a^8 - 360*a^7*b*x^2 - 1764*a^6*b^2*x^4 - 5880*a^5*b^3*x^6 - 22050*a^4*b^4*x^8 + 17640*a^3*b^5*x^10 + 2940*a^2*b^6*x^12 + 504*a*b^7*x^14 + 45*b^8*x^16)/(315*x^9)","A",1
119,1,94,100,0.0170014,"\int \frac{\left(a+b x^2\right)^8}{x^{12}} \, dx","IntegrateAlgebraic[(a + b*x^2)^8/x^12,x]","\frac{-45 a^8-440 a^7 b x^2-1980 a^6 b^2 x^4-5544 a^5 b^3 x^6-11550 a^4 b^4 x^8-27720 a^3 b^5 x^{10}+13860 a^2 b^6 x^{12}+1320 a b^7 x^{14}+99 b^8 x^{16}}{495 x^{11}}","-\frac{a^8}{11 x^{11}}-\frac{8 a^7 b}{9 x^9}-\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}{3} a b^7 x^3+\frac{b^8 x^5}{5}",1,"(-45*a^8 - 440*a^7*b*x^2 - 1980*a^6*b^2*x^4 - 5544*a^5*b^3*x^6 - 11550*a^4*b^4*x^8 - 27720*a^3*b^5*x^10 + 13860*a^2*b^6*x^12 + 1320*a*b^7*x^14 + 99*b^8*x^16)/(495*x^11)","A",1
120,1,94,98,0.0179161,"\int \frac{\left(a+b x^2\right)^8}{x^{14}} \, dx","IntegrateAlgebraic[(a + b*x^2)^8/x^14,x]","\frac{-99 a^8-936 a^7 b x^2-4004 a^6 b^2 x^4-10296 a^5 b^3 x^6-18018 a^4 b^4 x^8-24024 a^3 b^5 x^{10}-36036 a^2 b^6 x^{12}+10296 a b^7 x^{14}+429 b^8 x^{16}}{1287 x^{13}}","-\frac{a^8}{13 x^{13}}-\frac{8 a^7 b}{11 x^{11}}-\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}+8 a b^7 x+\frac{b^8 x^3}{3}",1,"(-99*a^8 - 936*a^7*b*x^2 - 4004*a^6*b^2*x^4 - 10296*a^5*b^3*x^6 - 18018*a^4*b^4*x^8 - 24024*a^3*b^5*x^10 - 36036*a^2*b^6*x^12 + 10296*a*b^7*x^14 + 429*b^8*x^16)/(1287*x^13)","A",1
121,1,94,99,0.0140112,"\int \frac{\left(a+b x^2\right)^8}{x^{16}} \, dx","IntegrateAlgebraic[(a + b*x^2)^8/x^16,x]","\frac{-429 a^8-3960 a^7 b x^2-16380 a^6 b^2 x^4-40040 a^5 b^3 x^6-64350 a^4 b^4 x^8-72072 a^3 b^5 x^{10}-60060 a^2 b^6 x^{12}-51480 a b^7 x^{14}+6435 b^8 x^{16}}{6435 x^{15}}","-\frac{a^8}{15 x^{15}}-\frac{8 a^7 b}{13 x^{13}}-\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 b^7}{x}+b^8 x",1,"(-429*a^8 - 3960*a^7*b*x^2 - 16380*a^6*b^2*x^4 - 40040*a^5*b^3*x^6 - 64350*a^4*b^4*x^8 - 72072*a^3*b^5*x^10 - 60060*a^2*b^6*x^12 - 51480*a*b^7*x^14 + 6435*b^8*x^16)/(6435*x^15)","A",1
122,1,94,104,0.0182519,"\int \frac{\left(a+b x^2\right)^8}{x^{18}} \, dx","IntegrateAlgebraic[(a + b*x^2)^8/x^18,x]","\frac{-6435 a^8-58344 a^7 b x^2-235620 a^6 b^2 x^4-556920 a^5 b^3 x^6-850850 a^4 b^4 x^8-875160 a^3 b^5 x^{10}-612612 a^2 b^6 x^{12}-291720 a b^7 x^{14}-109395 b^8 x^{16}}{109395 x^{17}}","-\frac{a^8}{17 x^{17}}-\frac{8 a^7 b}{15 x^{15}}-\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 b^7}{3 x^3}-\frac{b^8}{x}",1,"(-6435*a^8 - 58344*a^7*b*x^2 - 235620*a^6*b^2*x^4 - 556920*a^5*b^3*x^6 - 850850*a^4*b^4*x^8 - 875160*a^3*b^5*x^10 - 612612*a^2*b^6*x^12 - 291720*a*b^7*x^14 - 109395*b^8*x^16)/(109395*x^17)","A",1
123,1,94,106,0.0172746,"\int \frac{\left(a+b x^2\right)^8}{x^{20}} \, dx","IntegrateAlgebraic[(a + b*x^2)^8/x^20,x]","\frac{-109395 a^8-978120 a^7 b x^2-3879876 a^6 b^2 x^4-8953560 a^5 b^3 x^6-13226850 a^4 b^4 x^8-12932920 a^3 b^5 x^{10}-8314020 a^2 b^6 x^{12}-3325608 a b^7 x^{14}-692835 b^8 x^{16}}{2078505 x^{19}}","-\frac{a^8}{19 x^{19}}-\frac{8 a^7 b}{17 x^{17}}-\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 b^7}{5 x^5}-\frac{b^8}{3 x^3}",1,"(-109395*a^8 - 978120*a^7*b*x^2 - 3879876*a^6*b^2*x^4 - 8953560*a^5*b^3*x^6 - 13226850*a^4*b^4*x^8 - 12932920*a^3*b^5*x^10 - 8314020*a^2*b^6*x^12 - 3325608*a*b^7*x^14 - 692835*b^8*x^16)/(2078505*x^19)","A",1
124,1,72,79,0.0185969,"\int \frac{x^{11}}{a+b x^2} \, dx","IntegrateAlgebraic[x^11/(a + b*x^2),x]","\frac{x^2 \left(60 a^4-30 a^3 b x^2+20 a^2 b^2 x^4-15 a b^3 x^6+12 b^4 x^8\right)}{120 b^5}-\frac{a^5 \log \left(a+b x^2\right)}{2 b^6}","-\frac{a^5 \log \left(a+b x^2\right)}{2 b^6}+\frac{a^4 x^2}{2 b^5}-\frac{a^3 x^4}{4 b^4}+\frac{a^2 x^6}{6 b^3}-\frac{a x^8}{8 b^2}+\frac{x^{10}}{10 b}",1,"(x^2*(60*a^4 - 30*a^3*b*x^2 + 20*a^2*b^2*x^4 - 15*a*b^3*x^6 + 12*b^4*x^8))/(120*b^5) - (a^5*Log[a + b*x^2])/(2*b^6)","A",1
125,1,77,81,0.0467251,"\int \frac{x^{10}}{a+b x^2} \, dx","IntegrateAlgebraic[x^10/(a + b*x^2),x]","\frac{315 a^4 x-105 a^3 b x^3+63 a^2 b^2 x^5-45 a b^3 x^7+35 b^4 x^9}{315 b^5}-\frac{a^{9/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{11/2}}","-\frac{a^{9/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{11/2}}+\frac{a^4 x}{b^5}-\frac{a^3 x^3}{3 b^4}+\frac{a^2 x^5}{5 b^3}-\frac{a x^7}{7 b^2}+\frac{x^9}{9 b}",1,"(315*a^4*x - 105*a^3*b*x^3 + 63*a^2*b^2*x^5 - 45*a*b^3*x^7 + 35*b^4*x^9)/(315*b^5) - (a^(9/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/b^(11/2)","A",1
126,1,61,66,0.0165858,"\int \frac{x^9}{a+b x^2} \, dx","IntegrateAlgebraic[x^9/(a + b*x^2),x]","\frac{a^4 \log \left(a+b x^2\right)}{2 b^5}+\frac{-12 a^3 x^2+6 a^2 b x^4-4 a b^2 x^6+3 b^3 x^8}{24 b^4}","\frac{a^4 \log \left(a+b x^2\right)}{2 b^5}-\frac{a^3 x^2}{2 b^4}+\frac{a^2 x^4}{4 b^3}-\frac{a x^6}{6 b^2}+\frac{x^8}{8 b}",1,"(-12*a^3*x^2 + 6*a^2*b*x^4 - 4*a*b^2*x^6 + 3*b^3*x^8)/(24*b^4) + (a^4*Log[a + b*x^2])/(2*b^5)","A",1
127,1,65,68,0.0368762,"\int \frac{x^8}{a+b x^2} \, dx","IntegrateAlgebraic[x^8/(a + b*x^2),x]","\frac{a^{7/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{9/2}}+\frac{-105 a^3 x+35 a^2 b x^3-21 a b^2 x^5+15 b^3 x^7}{105 b^4}","\frac{a^{7/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{9/2}}-\frac{a^3 x}{b^4}+\frac{a^2 x^3}{3 b^3}-\frac{a x^5}{5 b^2}+\frac{x^7}{7 b}",1,"(-105*a^3*x + 35*a^2*b*x^3 - 21*a*b^2*x^5 + 15*b^3*x^7)/(105*b^4) + (a^(7/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/b^(9/2)","A",1
128,1,50,53,0.0139286,"\int \frac{x^7}{a+b x^2} \, dx","IntegrateAlgebraic[x^7/(a + b*x^2),x]","\frac{6 a^2 x^2-3 a b x^4+2 b^2 x^6}{12 b^3}-\frac{a^3 \log \left(a+b x^2\right)}{2 b^4}","-\frac{a^3 \log \left(a+b x^2\right)}{2 b^4}+\frac{a^2 x^2}{2 b^3}-\frac{a x^4}{4 b^2}+\frac{x^6}{6 b}",1,"(6*a^2*x^2 - 3*a*b*x^4 + 2*b^2*x^6)/(12*b^3) - (a^3*Log[a + b*x^2])/(2*b^4)","A",1
129,1,55,55,0.0328825,"\int \frac{x^6}{a+b x^2} \, dx","IntegrateAlgebraic[x^6/(a + b*x^2),x]","\frac{15 a^2 x-5 a b x^3+3 b^2 x^5}{15 b^3}-\frac{a^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{7/2}}","-\frac{a^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{7/2}}+\frac{a^2 x}{b^3}-\frac{a x^3}{3 b^2}+\frac{x^5}{5 b}",1,"(15*a^2*x - 5*a*b*x^3 + 3*b^2*x^5)/(15*b^3) - (a^(5/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/b^(7/2)","A",1
130,1,38,40,0.0128627,"\int \frac{x^5}{a+b x^2} \, dx","IntegrateAlgebraic[x^5/(a + b*x^2),x]","\frac{a^2 \log \left(a+b x^2\right)}{2 b^3}+\frac{b x^4-2 a x^2}{4 b^2}","\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,"(-2*a*x^2 + b*x^4)/(4*b^2) + (a^2*Log[a + b*x^2])/(2*b^3)","A",1
131,1,42,42,0.027292,"\int \frac{x^4}{a+b x^2} \, dx","IntegrateAlgebraic[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{b x^3-3 a x}{3 b^2}","\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,"(-3*a*x + b*x^3)/(3*b^2) + (a^(3/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/b^(5/2)","A",1
132,1,27,27,0.0088966,"\int \frac{x^3}{a+b x^2} \, dx","IntegrateAlgebraic[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",1
133,1,31,31,0.0141767,"\int \frac{x^2}{a+b x^2} \, dx","IntegrateAlgebraic[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",1
134,1,15,15,0.0052357,"\int \frac{x}{a+b x^2} \, dx","IntegrateAlgebraic[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
135,1,24,24,0.0082989,"\int \frac{1}{a+b x^2} \, dx","IntegrateAlgebraic[(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
136,1,22,22,0.009261,"\int \frac{1}{x \left(a+b x^2\right)} \, dx","IntegrateAlgebraic[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",1
137,1,34,34,0.0187103,"\int \frac{1}{x^2 \left(a+b x^2\right)} \, dx","IntegrateAlgebraic[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",1
138,1,35,35,0.0126877,"\int \frac{1}{x^3 \left(a+b x^2\right)} \, dx","IntegrateAlgebraic[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*1/(a*x^2) - (b*Log[x])/a^2 + (b*Log[a + b*x^2])/(2*a^2)","A",1
139,1,45,43,0.0298053,"\int \frac{1}{x^4 \left(a+b x^2\right)} \, dx","IntegrateAlgebraic[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{3 b x^2-a}{3 a^2 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,"(-a + 3*b*x^2)/(3*a^2*x^3) + (b^(3/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/a^(5/2)","A",1
140,1,48,49,0.0154912,"\int \frac{1}{x^5 \left(a+b x^2\right)} \, dx","IntegrateAlgebraic[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{2 b x^2-a}{4 a^2 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,"(-a + 2*b*x^2)/(4*a^2*x^4) + (b^2*Log[x])/a^3 - (b^2*Log[a + b*x^2])/(2*a^3)","A",1
141,1,57,58,0.0337648,"\int \frac{1}{x^6 \left(a+b x^2\right)} \, dx","IntegrateAlgebraic[1/(x^6*(a + b*x^2)),x]","\frac{-3 a^2+5 a b x^2-15 b^2 x^4}{15 a^3 x^5}-\frac{b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{7/2}}","-\frac{b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{7/2}}-\frac{b^2}{a^3 x}+\frac{b}{3 a^2 x^3}-\frac{1}{5 a x^5}",1,"(-3*a^2 + 5*a*b*x^2 - 15*b^2*x^4)/(15*a^3*x^5) - (b^(5/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/a^(7/2)","A",1
142,1,60,63,0.0174841,"\int \frac{1}{x^7 \left(a+b x^2\right)} \, dx","IntegrateAlgebraic[1/(x^7*(a + b*x^2)),x]","\frac{b^3 \log \left(a+b x^2\right)}{2 a^4}-\frac{b^3 \log (x)}{a^4}+\frac{-2 a^2+3 a b x^2-6 b^2 x^4}{12 a^3 x^6}","\frac{b^3 \log \left(a+b x^2\right)}{2 a^4}-\frac{b^3 \log (x)}{a^4}-\frac{b^2}{2 a^3 x^2}+\frac{b}{4 a^2 x^4}-\frac{1}{6 a x^6}",1,"(-2*a^2 + 3*a*b*x^2 - 6*b^2*x^4)/(12*a^3*x^6) - (b^3*Log[x])/a^4 + (b^3*Log[a + b*x^2])/(2*a^4)","A",1
143,1,67,69,0.0383209,"\int \frac{1}{x^8 \left(a+b x^2\right)} \, dx","IntegrateAlgebraic[1/(x^8*(a + b*x^2)),x]","\frac{b^{7/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{9/2}}+\frac{-15 a^3+21 a^2 b x^2-35 a b^2 x^4+105 b^3 x^6}{105 a^4 x^7}","\frac{b^{7/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{9/2}}+\frac{b^3}{a^4 x}-\frac{b^2}{3 a^3 x^3}+\frac{b}{5 a^2 x^5}-\frac{1}{7 a x^7}",1,"(-15*a^3 + 21*a^2*b*x^2 - 35*a*b^2*x^4 + 105*b^3*x^6)/(105*a^4*x^7) + (b^(7/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/a^(9/2)","A",1
144,1,70,75,0.0180115,"\int \frac{1}{x^9 \left(a+b x^2\right)} \, dx","IntegrateAlgebraic[1/(x^9*(a + b*x^2)),x]","-\frac{b^4 \log \left(a+b x^2\right)}{2 a^5}+\frac{b^4 \log (x)}{a^5}+\frac{-3 a^3+4 a^2 b x^2-6 a b^2 x^4+12 b^3 x^6}{24 a^4 x^8}","-\frac{b^4 \log \left(a+b x^2\right)}{2 a^5}+\frac{b^4 \log (x)}{a^5}+\frac{b^3}{2 a^4 x^2}-\frac{b^2}{4 a^3 x^4}+\frac{b}{6 a^2 x^6}-\frac{1}{8 a x^8}",1,"(-3*a^3 + 4*a^2*b*x^2 - 6*a*b^2*x^4 + 12*b^3*x^6)/(24*a^4*x^8) + (b^4*Log[x])/a^5 - (b^4*Log[a + b*x^2])/(2*a^5)","A",1
145,1,98,94,0.0417839,"\int \frac{x^{13}}{\left(a+b x^2\right)^2} \, dx","IntegrateAlgebraic[x^13/(a + b*x^2)^2,x]","\frac{-10 a^6+50 a^5 b x^2+30 a^4 b^2 x^4-10 a^3 b^3 x^6+5 a^2 b^4 x^8-3 a b^5 x^{10}+2 b^6 x^{12}}{20 b^7 \left(a+b x^2\right)}-\frac{3 a^5 \log \left(a+b x^2\right)}{b^7}","-\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{5 a^4 x^2}{2 b^6}-\frac{a^3 x^4}{b^5}+\frac{a^2 x^6}{2 b^4}-\frac{a x^8}{4 b^3}+\frac{x^{10}}{10 b^2}",1,"(-10*a^6 + 50*a^5*b*x^2 + 30*a^4*b^2*x^4 - 10*a^3*b^3*x^6 + 5*a^2*b^4*x^8 - 3*a*b^5*x^10 + 2*b^6*x^12)/(20*b^7*(a + b*x^2)) - (3*a^5*Log[a + b*x^2])/b^7","A",1
146,1,99,105,0.0764384,"\int \frac{x^{12}}{\left(a+b x^2\right)^2} \, dx","IntegrateAlgebraic[x^12/(a + b*x^2)^2,x]","\frac{x \left(3465 a^5+2310 a^4 b x^2-462 a^3 b^2 x^4+198 a^2 b^3 x^6-110 a b^4 x^8+70 b^5 x^{10}\right)}{630 b^6 \left(a+b x^2\right)}-\frac{11 a^{9/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 b^{13/2}}","-\frac{11 a^{9/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 b^{13/2}}+\frac{11 a^4 x}{2 b^6}-\frac{11 a^3 x^3}{6 b^5}+\frac{11 a^2 x^5}{10 b^4}-\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,"(x*(3465*a^5 + 2310*a^4*b*x^2 - 462*a^3*b^2*x^4 + 198*a^2*b^3*x^6 - 110*a*b^4*x^8 + 70*b^5*x^10))/(630*b^6*(a + b*x^2)) - (11*a^(9/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*b^(13/2))","A",1
147,1,89,83,0.0334967,"\int \frac{x^{11}}{\left(a+b x^2\right)^2} \, dx","IntegrateAlgebraic[x^11/(a + b*x^2)^2,x]","\frac{5 a^4 \log \left(a+b x^2\right)}{2 b^6}+\frac{12 a^5-48 a^4 b x^2-30 a^3 b^2 x^4+10 a^2 b^3 x^6-5 a b^4 x^8+3 b^5 x^{10}}{24 b^6 \left(a+b x^2\right)}","\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{2 a^3 x^2}{b^5}+\frac{3 a^2 x^4}{4 b^4}-\frac{a x^6}{3 b^3}+\frac{x^8}{8 b^2}",1,"(12*a^5 - 48*a^4*b*x^2 - 30*a^3*b^2*x^4 + 10*a^2*b^3*x^6 - 5*a*b^4*x^8 + 3*b^5*x^10)/(24*b^6*(a + b*x^2)) + (5*a^4*Log[a + b*x^2])/(2*b^6)","A",1
148,1,88,92,0.071537,"\int \frac{x^{10}}{\left(a+b x^2\right)^2} \, dx","IntegrateAlgebraic[x^10/(a + b*x^2)^2,x]","\frac{9 a^{7/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 b^{11/2}}+\frac{x \left(-315 a^4-210 a^3 b x^2+42 a^2 b^2 x^4-18 a b^3 x^6+10 b^4 x^8\right)}{70 b^5 \left(a+b x^2\right)}","\frac{9 a^{7/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 b^{11/2}}-\frac{9 a^3 x}{2 b^5}+\frac{3 a^2 x^3}{2 b^4}-\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,"(x*(-315*a^4 - 210*a^3*b*x^2 + 42*a^2*b^2*x^4 - 18*a*b^3*x^6 + 10*b^4*x^8))/(70*b^5*(a + b*x^2)) + (9*a^(7/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*b^(11/2))","A",1
149,1,75,70,0.0337856,"\int \frac{x^9}{\left(a+b x^2\right)^2} \, dx","IntegrateAlgebraic[x^9/(a + b*x^2)^2,x]","\frac{-3 a^4+9 a^3 b x^2+6 a^2 b^2 x^4-2 a b^3 x^6+b^4 x^8}{6 b^5 \left(a+b x^2\right)}-\frac{2 a^3 \log \left(a+b x^2\right)}{b^5}","-\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{3 a^2 x^2}{2 b^4}-\frac{a x^4}{2 b^3}+\frac{x^6}{6 b^2}",1,"(-3*a^4 + 9*a^3*b*x^2 + 6*a^2*b^2*x^4 - 2*a*b^3*x^6 + b^4*x^8)/(6*b^5*(a + b*x^2)) - (2*a^3*Log[a + b*x^2])/b^5","A",1
150,1,77,79,0.0636644,"\int \frac{x^8}{\left(a+b x^2\right)^2} \, dx","IntegrateAlgebraic[x^8/(a + b*x^2)^2,x]","\frac{x \left(105 a^3+70 a^2 b x^2-14 a b^2 x^4+6 b^3 x^6\right)}{30 b^4 \left(a+b x^2\right)}-\frac{7 a^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 b^{9/2}}","-\frac{7 a^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 b^{9/2}}+\frac{7 a^2 x}{2 b^4}-\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,"(x*(105*a^3 + 70*a^2*b*x^2 - 14*a*b^2*x^4 + 6*b^3*x^6))/(30*b^4*(a + b*x^2)) - (7*a^(5/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*b^(9/2))","A",1
151,1,66,57,0.027668,"\int \frac{x^7}{\left(a+b x^2\right)^2} \, dx","IntegrateAlgebraic[x^7/(a + b*x^2)^2,x]","\frac{3 a^2 \log \left(a+b x^2\right)}{2 b^4}+\frac{2 a^3-4 a^2 b x^2-3 a b^2 x^4+b^3 x^6}{4 b^4 \left(a+b x^2\right)}","\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,"(2*a^3 - 4*a^2*b*x^2 - 3*a*b^2*x^4 + b^3*x^6)/(4*b^4*(a + b*x^2)) + (3*a^2*Log[a + b*x^2])/(2*b^4)","A",1
152,1,66,66,0.0560113,"\int \frac{x^6}{\left(a+b x^2\right)^2} \, dx","IntegrateAlgebraic[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{x \left(-15 a^2-10 a b x^2+2 b^2 x^4\right)}{6 b^3 \left(a+b x^2\right)}","\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,"(x*(-15*a^2 - 10*a*b*x^2 + 2*b^2*x^4))/(6*b^3*(a + b*x^2)) + (5*a^(3/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*b^(7/2))","A",1
153,1,50,44,0.0267718,"\int \frac{x^5}{\left(a+b x^2\right)^2} \, dx","IntegrateAlgebraic[x^5/(a + b*x^2)^2,x]","\frac{-a^2+a b x^2+b^2 x^4}{2 b^3 \left(a+b x^2\right)}-\frac{a \log \left(a+b x^2\right)}{b^3}","-\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,"(-a^2 + a*b*x^2 + b^2*x^4)/(2*b^3*(a + b*x^2)) - (a*Log[a + b*x^2])/b^3","A",1
154,1,55,55,0.0445968,"\int \frac{x^4}{\left(a+b x^2\right)^2} \, dx","IntegrateAlgebraic[x^4/(a + b*x^2)^2,x]","\frac{x \left(3 a+2 b x^2\right)}{2 b^2 \left(a+b x^2\right)}-\frac{3 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 b^{5/2}}","-\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,"(x*(3*a + 2*b*x^2))/(2*b^2*(a + b*x^2)) - (3*Sqrt[a]*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*b^(5/2))","A",1
155,1,33,33,0.0151691,"\int \frac{x^3}{\left(a+b x^2\right)^2} \, dx","IntegrateAlgebraic[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",1
156,1,45,45,0.0305816,"\int \frac{x^2}{\left(a+b x^2\right)^2} \, dx","IntegrateAlgebraic[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,"-1/2*x/(b*(a + b*x^2)) + ArcTan[(Sqrt[b]*x)/Sqrt[a]]/(2*Sqrt[a]*b^(3/2))","A",1
157,1,16,16,0.0060118,"\int \frac{x}{\left(a+b x^2\right)^2} \, dx","IntegrateAlgebraic[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*1/(b*(a + b*x^2))","A",1
158,1,45,45,0.0328361,"\int \frac{1}{\left(a+b x^2\right)^2} \, dx","IntegrateAlgebraic[(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",1
159,1,38,38,0.02263,"\int \frac{1}{x \left(a+b x^2\right)^2} \, dx","IntegrateAlgebraic[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",1
160,1,57,57,0.0507535,"\int \frac{1}{x^2 \left(a+b x^2\right)^2} \, dx","IntegrateAlgebraic[1/(x^2*(a + b*x^2)^2),x]","\frac{-2 a-3 b x^2}{2 a^2 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 \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,"(-2*a - 3*b*x^2)/(2*a^2*x*(a + b*x^2)) - (3*Sqrt[b]*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*a^(5/2))","A",1
161,1,51,49,0.0472744,"\int \frac{1}{x^3 \left(a+b x^2\right)^2} \, dx","IntegrateAlgebraic[1/(x^3*(a + b*x^2)^2),x]","\frac{b \log \left(a+b x^2\right)}{a^3}-\frac{2 b \log (x)}{a^3}+\frac{-a-2 b x^2}{2 a^2 x^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{b}{2 a^2 \left(a+b x^2\right)}-\frac{1}{2 a^2 x^2}",1,"(-a - 2*b*x^2)/(2*a^2*x^2*(a + b*x^2)) - (2*b*Log[x])/a^3 + (b*Log[a + b*x^2])/a^3","A",1
162,1,68,68,0.0509546,"\int \frac{1}{x^4 \left(a+b x^2\right)^2} \, dx","IntegrateAlgebraic[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{-2 a^2+10 a b x^2+15 b^2 x^4}{6 a^3 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,"(-2*a^2 + 10*a*b*x^2 + 15*b^2*x^4)/(6*a^3*x^3*(a + b*x^2)) + (5*b^(3/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*a^(7/2))","A",1
163,1,69,66,0.0640815,"\int \frac{1}{x^5 \left(a+b x^2\right)^2} \, dx","IntegrateAlgebraic[1/(x^5*(a + b*x^2)^2),x]","-\frac{3 b^2 \log \left(a+b x^2\right)}{2 a^4}+\frac{3 b^2 \log (x)}{a^4}+\frac{-a^2+3 a b x^2+6 b^2 x^4}{4 a^3 x^4 \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^2}{2 a^3 \left(a+b x^2\right)}+\frac{b}{a^3 x^2}-\frac{1}{4 a^2 x^4}",1,"(-a^2 + 3*a*b*x^2 + 6*b^2*x^4)/(4*a^3*x^4*(a + b*x^2)) + (3*b^2*Log[x])/a^4 - (3*b^2*Log[a + b*x^2])/(2*a^4)","A",1
164,1,79,81,0.0608394,"\int \frac{1}{x^6 \left(a+b x^2\right)^2} \, dx","IntegrateAlgebraic[1/(x^6*(a + b*x^2)^2),x]","\frac{-6 a^3+14 a^2 b x^2-70 a b^2 x^4-105 b^3 x^6}{30 a^4 x^5 \left(a+b x^2\right)}-\frac{7 b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{9/2}}","-\frac{7 b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{9/2}}-\frac{7 b^2}{2 a^4 x}+\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,"(-6*a^3 + 14*a^2*b*x^2 - 70*a*b^2*x^4 - 105*b^3*x^6)/(30*a^4*x^5*(a + b*x^2)) - (7*b^(5/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*a^(9/2))","A",1
165,1,78,80,0.069676,"\int \frac{1}{x^7 \left(a+b x^2\right)^2} \, dx","IntegrateAlgebraic[1/(x^7*(a + b*x^2)^2),x]","\frac{2 b^3 \log \left(a+b x^2\right)}{a^5}-\frac{4 b^3 \log (x)}{a^5}+\frac{-a^3+2 a^2 b x^2-6 a b^2 x^4-12 b^3 x^6}{6 a^4 x^6 \left(a+b x^2\right)}","\frac{2 b^3 \log \left(a+b x^2\right)}{a^5}-\frac{4 b^3 \log (x)}{a^5}-\frac{b^3}{2 a^4 \left(a+b x^2\right)}-\frac{3 b^2}{2 a^4 x^2}+\frac{b}{2 a^3 x^4}-\frac{1}{6 a^2 x^6}",1,"(-a^3 + 2*a^2*b*x^2 - 6*a*b^2*x^4 - 12*b^3*x^6)/(6*a^4*x^6*(a + b*x^2)) - (4*b^3*Log[x])/a^5 + (2*b^3*Log[a + b*x^2])/a^5","A",1
166,1,90,94,0.0655527,"\int \frac{1}{x^8 \left(a+b x^2\right)^2} \, dx","IntegrateAlgebraic[1/(x^8*(a + b*x^2)^2),x]","\frac{9 b^{7/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{11/2}}+\frac{-10 a^4+18 a^3 b x^2-42 a^2 b^2 x^4+210 a b^3 x^6+315 b^4 x^8}{70 a^5 x^7 \left(a+b x^2\right)}","\frac{9 b^{7/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{11/2}}+\frac{9 b^3}{2 a^5 x}-\frac{3 b^2}{2 a^4 x^3}+\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,"(-10*a^4 + 18*a^3*b*x^2 - 42*a^2*b^2*x^4 + 210*a*b^3*x^6 + 315*b^4*x^8)/(70*a^5*x^7*(a + b*x^2)) + (9*b^(7/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*a^(11/2))","A",1
167,1,91,93,0.0922655,"\int \frac{1}{x^9 \left(a+b x^2\right)^2} \, dx","IntegrateAlgebraic[1/(x^9*(a + b*x^2)^2),x]","-\frac{5 b^4 \log \left(a+b x^2\right)}{2 a^6}+\frac{5 b^4 \log (x)}{a^6}+\frac{-3 a^4+5 a^3 b x^2-10 a^2 b^2 x^4+30 a b^3 x^6+60 b^4 x^8}{24 a^5 x^8 \left(a+b x^2\right)}","-\frac{5 b^4 \log \left(a+b x^2\right)}{2 a^6}+\frac{5 b^4 \log (x)}{a^6}+\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{b}{3 a^3 x^6}-\frac{1}{8 a^2 x^8}",1,"(-3*a^4 + 5*a^3*b*x^2 - 10*a^2*b^2*x^4 + 30*a*b^3*x^6 + 60*b^4*x^8)/(24*a^5*x^8*(a + b*x^2)) + (5*b^4*Log[x])/a^6 - (5*b^4*Log[a + b*x^2])/(2*a^6)","A",1
168,1,111,114,0.0468527,"\int \frac{x^{15}}{\left(a+b x^2\right)^3} \, dx","IntegrateAlgebraic[x^15/(a + b*x^2)^3,x]","\frac{-130 a^7+160 a^6 b x^2+500 a^5 b^2 x^4+140 a^4 b^3 x^6-35 a^3 b^4 x^8+14 a^2 b^5 x^{10}-7 a b^6 x^{12}+4 b^7 x^{14}}{40 b^8 \left(a+b x^2\right)^2}-\frac{21 a^5 \log \left(a+b x^2\right)}{2 b^8}","\frac{a^7}{4 b^8 \left(a+b x^2\right)^2}-\frac{7 a^6}{2 b^8 \left(a+b x^2\right)}-\frac{21 a^5 \log \left(a+b x^2\right)}{2 b^8}+\frac{15 a^4 x^2}{2 b^7}-\frac{5 a^3 x^4}{2 b^6}+\frac{a^2 x^6}{b^5}-\frac{3 a x^8}{8 b^4}+\frac{x^{10}}{10 b^3}",1,"(-130*a^7 + 160*a^6*b*x^2 + 500*a^5*b^2*x^4 + 140*a^4*b^3*x^6 - 35*a^3*b^4*x^8 + 14*a^2*b^5*x^10 - 7*a*b^6*x^12 + 4*b^7*x^14)/(40*b^8*(a + b*x^2)^2) - (21*a^5*Log[a + b*x^2])/(2*b^8)","A",1
169,1,99,100,0.0444571,"\int \frac{x^{13}}{\left(a+b x^2\right)^3} \, dx","IntegrateAlgebraic[x^13/(a + b*x^2)^3,x]","\frac{15 a^4 \log \left(a+b x^2\right)}{2 b^7}+\frac{22 a^6-16 a^5 b x^2-68 a^4 b^2 x^4-20 a^3 b^3 x^6+5 a^2 b^4 x^8-2 a b^5 x^{10}+b^6 x^{12}}{8 b^7 \left(a+b x^2\right)^2}","-\frac{a^6}{4 b^7 \left(a+b x^2\right)^2}+\frac{3 a^5}{b^7 \left(a+b x^2\right)}+\frac{15 a^4 \log \left(a+b x^2\right)}{2 b^7}-\frac{5 a^3 x^2}{b^6}+\frac{3 a^2 x^4}{2 b^5}-\frac{a x^6}{2 b^4}+\frac{x^8}{8 b^3}",1,"(22*a^6 - 16*a^5*b*x^2 - 68*a^4*b^2*x^4 - 20*a^3*b^3*x^6 + 5*a^2*b^4*x^8 - 2*a*b^5*x^10 + b^6*x^12)/(8*b^7*(a + b*x^2)^2) + (15*a^4*Log[a + b*x^2])/(2*b^7)","A",1
170,1,87,87,0.0386795,"\int \frac{x^{11}}{\left(a+b x^2\right)^3} \, dx","IntegrateAlgebraic[x^11/(a + b*x^2)^3,x]","\frac{-27 a^5+6 a^4 b x^2+63 a^3 b^2 x^4+20 a^2 b^3 x^6-5 a b^4 x^8+2 b^5 x^{10}}{12 b^6 \left(a+b x^2\right)^2}-\frac{5 a^3 \log \left(a+b x^2\right)}{b^6}","\frac{a^5}{4 b^6 \left(a+b x^2\right)^2}-\frac{5 a^4}{2 b^6 \left(a+b x^2\right)}-\frac{5 a^3 \log \left(a+b x^2\right)}{b^6}+\frac{3 a^2 x^2}{b^5}-\frac{3 a x^4}{4 b^4}+\frac{x^6}{6 b^3}",1,"(-27*a^5 + 6*a^4*b*x^2 + 63*a^3*b^2*x^4 + 20*a^2*b^3*x^6 - 5*a*b^4*x^8 + 2*b^5*x^10)/(12*b^6*(a + b*x^2)^2) - (5*a^3*Log[a + b*x^2])/b^6","A",1
171,1,75,74,0.0358534,"\int \frac{x^9}{\left(a+b x^2\right)^3} \, dx","IntegrateAlgebraic[x^9/(a + b*x^2)^3,x]","\frac{3 a^2 \log \left(a+b x^2\right)}{b^5}+\frac{7 a^4+2 a^3 b x^2-11 a^2 b^2 x^4-4 a b^3 x^6+b^4 x^8}{4 b^5 \left(a+b x^2\right)^2}","-\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,"(7*a^4 + 2*a^3*b*x^2 - 11*a^2*b^2*x^4 - 4*a*b^3*x^6 + b^4*x^8)/(4*b^5*(a + b*x^2)^2) + (3*a^2*Log[a + b*x^2])/b^5","A",1
172,1,65,65,0.0675239,"\int \frac{x^7}{\left(a+b x^2\right)^3} \, dx","IntegrateAlgebraic[x^7/(a + b*x^2)^3,x]","\frac{-5 a^3-4 a^2 b x^2+4 a b^2 x^4+2 b^3 x^6}{4 b^4 \left(a+b x^2\right)^2}-\frac{3 a \log \left(a+b x^2\right)}{2 b^4}","\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,"(-5*a^3 - 4*a^2*b*x^2 + 4*a*b^2*x^4 + 2*b^3*x^6)/(4*b^4*(a + b*x^2)^2) - (3*a*Log[a + b*x^2])/(2*b^4)","A",1
173,1,43,49,0.025826,"\int \frac{x^5}{\left(a+b x^2\right)^3} \, dx","IntegrateAlgebraic[x^5/(a + b*x^2)^3,x]","\frac{a \left(3 a+4 b x^2\right)}{4 b^3 \left(a+b x^2\right)^2}+\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*(3*a + 4*b*x^2))/(4*b^3*(a + b*x^2)^2) + Log[a + b*x^2]/(2*b^3)","A",1
174,1,26,19,0.0119808,"\int \frac{x^3}{\left(a+b x^2\right)^3} \, dx","IntegrateAlgebraic[x^3/(a + b*x^2)^3,x]","\frac{-a-2 b x^2}{4 b^2 \left(a+b x^2\right)^2}","\frac{x^4}{4 a \left(a+b x^2\right)^2}",1,"(-a - 2*b*x^2)/(4*b^2*(a + b*x^2)^2)","A",1
175,1,16,16,0.0064639,"\int \frac{x}{\left(a+b x^2\right)^3} \, dx","IntegrateAlgebraic[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*1/(b*(a + b*x^2)^2)","A",1
176,1,48,54,0.0430531,"\int \frac{1}{x \left(a+b x^2\right)^3} \, dx","IntegrateAlgebraic[1/(x*(a + b*x^2)^3),x]","-\frac{\log \left(a+b x^2\right)}{2 a^3}+\frac{\log (x)}{a^3}+\frac{3 a+2 b x^2}{4 a^2 \left(a+b x^2\right)^2}","-\frac{\log \left(a+b x^2\right)}{2 a^3}+\frac{\log (x)}{a^3}+\frac{1}{2 a^2 \left(a+b x^2\right)}+\frac{1}{4 a \left(a+b x^2\right)^2}",1,"(3*a + 2*b*x^2)/(4*a^2*(a + b*x^2)^2) + Log[x]/a^3 - Log[a + b*x^2]/(2*a^3)","A",1
177,1,65,67,0.0698166,"\int \frac{1}{x^3 \left(a+b x^2\right)^3} \, dx","IntegrateAlgebraic[1/(x^3*(a + b*x^2)^3),x]","\frac{3 b \log \left(a+b x^2\right)}{2 a^4}-\frac{3 b \log (x)}{a^4}+\frac{-2 a^2-9 a b x^2-6 b^2 x^4}{4 a^3 x^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{b}{a^3 \left(a+b x^2\right)}-\frac{1}{2 a^3 x^2}-\frac{b}{4 a^2 \left(a+b x^2\right)^2}",1,"(-2*a^2 - 9*a*b*x^2 - 6*b^2*x^4)/(4*a^3*x^2*(a + b*x^2)^2) - (3*b*Log[x])/a^4 + (3*b*Log[a + b*x^2])/(2*a^4)","A",1
178,1,78,86,0.0612654,"\int \frac{1}{x^5 \left(a+b x^2\right)^3} \, dx","IntegrateAlgebraic[1/(x^5*(a + b*x^2)^3),x]","-\frac{3 b^2 \log \left(a+b x^2\right)}{a^5}+\frac{6 b^2 \log (x)}{a^5}+\frac{-a^3+4 a^2 b x^2+18 a b^2 x^4+12 b^3 x^6}{4 a^4 x^4 \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}{2 a^4 \left(a+b x^2\right)}+\frac{3 b}{2 a^4 x^2}+\frac{b^2}{4 a^3 \left(a+b x^2\right)^2}-\frac{1}{4 a^3 x^4}",1,"(-a^3 + 4*a^2*b*x^2 + 18*a*b^2*x^4 + 12*b^3*x^6)/(4*a^4*x^4*(a + b*x^2)^2) + (6*b^2*Log[x])/a^5 - (3*b^2*Log[a + b*x^2])/a^5","A",1
179,1,89,95,0.0899711,"\int \frac{1}{x^7 \left(a+b x^2\right)^3} \, dx","IntegrateAlgebraic[1/(x^7*(a + b*x^2)^3),x]","\frac{5 b^3 \log \left(a+b x^2\right)}{a^6}-\frac{10 b^3 \log (x)}{a^6}+\frac{-2 a^4+5 a^3 b x^2-20 a^2 b^2 x^4-90 a b^3 x^6-60 b^4 x^8}{12 a^5 x^6 \left(a+b x^2\right)^2}","\frac{5 b^3 \log \left(a+b x^2\right)}{a^6}-\frac{10 b^3 \log (x)}{a^6}-\frac{2 b^3}{a^5 \left(a+b x^2\right)}-\frac{3 b^2}{a^5 x^2}-\frac{b^3}{4 a^4 \left(a+b x^2\right)^2}+\frac{3 b}{4 a^4 x^4}-\frac{1}{6 a^3 x^6}",1,"(-2*a^4 + 5*a^3*b*x^2 - 20*a^2*b^2*x^4 - 90*a*b^3*x^6 - 60*b^4*x^8)/(12*a^5*x^6*(a + b*x^2)^2) - (10*b^3*Log[x])/a^6 + (5*b^3*Log[a + b*x^2])/a^6","A",1
180,1,102,112,0.0776632,"\int \frac{1}{x^9 \left(a+b x^2\right)^3} \, dx","IntegrateAlgebraic[1/(x^9*(a + b*x^2)^3),x]","-\frac{15 b^4 \log \left(a+b x^2\right)}{2 a^7}+\frac{15 b^4 \log (x)}{a^7}+\frac{-a^5+2 a^4 b x^2-5 a^3 b^2 x^4+20 a^2 b^3 x^6+90 a b^4 x^8+60 b^5 x^{10}}{8 a^6 x^8 \left(a+b x^2\right)^2}","-\frac{15 b^4 \log \left(a+b x^2\right)}{2 a^7}+\frac{15 b^4 \log (x)}{a^7}+\frac{5 b^4}{2 a^6 \left(a+b x^2\right)}+\frac{5 b^3}{a^6 x^2}+\frac{b^4}{4 a^5 \left(a+b x^2\right)^2}-\frac{3 b^2}{2 a^5 x^4}+\frac{b}{2 a^4 x^6}-\frac{1}{8 a^3 x^8}",1,"(-a^5 + 2*a^4*b*x^2 - 5*a^3*b^2*x^4 + 20*a^2*b^3*x^6 + 90*a*b^4*x^8 + 60*b^5*x^10)/(8*a^6*x^8*(a + b*x^2)^2) + (15*b^4*Log[x])/a^7 - (15*b^4*Log[a + b*x^2])/(2*a^7)","A",1
181,1,99,111,0.0839419,"\int \frac{x^{12}}{\left(a+b x^2\right)^3} \, dx","IntegrateAlgebraic[x^12/(a + b*x^2)^3,x]","\frac{99 a^{7/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 b^{13/2}}+\frac{-3465 a^5 x-5775 a^4 b x^3-1848 a^3 b^2 x^5+264 a^2 b^3 x^7-88 a b^4 x^9+40 b^5 x^{11}}{280 b^6 \left(a+b x^2\right)^2}","\frac{99 a^{7/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 b^{13/2}}-\frac{99 a^3 x}{8 b^6}+\frac{33 a^2 x^3}{8 b^5}-\frac{99 a x^5}{40 b^4}-\frac{11 x^9}{8 b^2 \left(a+b x^2\right)}-\frac{x^{11}}{4 b \left(a+b x^2\right)^2}+\frac{99 x^7}{56 b^3}",1,"(-3465*a^5*x - 5775*a^4*b*x^3 - 1848*a^3*b^2*x^5 + 264*a^2*b^3*x^7 - 88*a*b^4*x^9 + 40*b^5*x^11)/(280*b^6*(a + b*x^2)^2) + (99*a^(7/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*b^(13/2))","A",1
182,1,88,98,0.0647636,"\int \frac{x^{10}}{\left(a+b x^2\right)^3} \, dx","IntegrateAlgebraic[x^10/(a + b*x^2)^3,x]","\frac{315 a^4 x+525 a^3 b x^3+168 a^2 b^2 x^5-24 a b^3 x^7+8 b^4 x^9}{40 b^5 \left(a+b x^2\right)^2}-\frac{63 a^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 b^{11/2}}","-\frac{63 a^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 b^{11/2}}+\frac{63 a^2 x}{8 b^5}-\frac{21 a x^3}{8 b^4}-\frac{9 x^7}{8 b^2 \left(a+b x^2\right)}-\frac{x^9}{4 b \left(a+b x^2\right)^2}+\frac{63 x^5}{40 b^3}",1,"(315*a^4*x + 525*a^3*b*x^3 + 168*a^2*b^2*x^5 - 24*a*b^3*x^7 + 8*b^4*x^9)/(40*b^5*(a + b*x^2)^2) - (63*a^(5/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*b^(11/2))","A",1
183,1,77,85,0.0634792,"\int \frac{x^8}{\left(a+b x^2\right)^3} \, dx","IntegrateAlgebraic[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{-105 a^3 x-175 a^2 b x^3-56 a b^2 x^5+8 b^3 x^7}{24 b^4 \left(a+b x^2\right)^2}","\frac{35 a^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 b^{9/2}}-\frac{35 a x}{8 b^4}-\frac{7 x^5}{8 b^2 \left(a+b x^2\right)}-\frac{x^7}{4 b \left(a+b x^2\right)^2}+\frac{35 x^3}{24 b^3}",1,"(-105*a^3*x - 175*a^2*b*x^3 - 56*a*b^2*x^5 + 8*b^3*x^7)/(24*b^4*(a + b*x^2)^2) + (35*a^(3/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*b^(9/2))","A",1
184,1,66,74,0.0598832,"\int \frac{x^6}{\left(a+b x^2\right)^3} \, dx","IntegrateAlgebraic[x^6/(a + b*x^2)^3,x]","\frac{15 a^2 x+25 a b x^3+8 b^2 x^5}{8 b^3 \left(a+b x^2\right)^2}-\frac{15 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 b^{7/2}}","-\frac{15 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 b^{7/2}}-\frac{5 x^3}{8 b^2 \left(a+b x^2\right)}-\frac{x^5}{4 b \left(a+b x^2\right)^2}+\frac{15 x}{8 b^3}",1,"(15*a^2*x + 25*a*b*x^3 + 8*b^2*x^5)/(8*b^3*(a + b*x^2)^2) - (15*Sqrt[a]*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*b^(7/2))","A",1
185,1,55,64,0.0533853,"\int \frac{x^4}{\left(a+b x^2\right)^3} \, dx","IntegrateAlgebraic[x^4/(a + b*x^2)^3,x]","\frac{3 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 \sqrt{a} b^{5/2}}+\frac{-3 a x-5 b x^3}{8 b^2 \left(a+b x^2\right)^2}","\frac{3 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 \sqrt{a} b^{5/2}}-\frac{3 x}{8 b^2 \left(a+b x^2\right)}-\frac{x^3}{4 b \left(a+b x^2\right)^2}",1,"(-3*a*x - 5*b*x^3)/(8*b^2*(a + b*x^2)^2) + (3*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*Sqrt[a]*b^(5/2))","A",1
186,1,56,65,0.042021,"\int \frac{x^2}{\left(a+b x^2\right)^3} \, dx","IntegrateAlgebraic[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 \left(a-b x^2\right)}{8 a 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,"-1/8*(x*(a - b*x^2))/(a*b*(a + b*x^2)^2) + ArcTan[(Sqrt[b]*x)/Sqrt[a]]/(8*a^(3/2)*b^(3/2))","A",1
187,1,55,62,0.0487406,"\int \frac{1}{\left(a+b x^2\right)^3} \, dx","IntegrateAlgebraic[(a + b*x^2)^(-3),x]","\frac{3 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{b}}+\frac{5 a x+3 b x^3}{8 a^2 \left(a+b x^2\right)^2}","\frac{3 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{b}}+\frac{3 x}{8 a^2 \left(a+b x^2\right)}+\frac{x}{4 a \left(a+b x^2\right)^2}",1,"(5*a*x + 3*b*x^3)/(8*a^2*(a + b*x^2)^2) + (3*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*a^(5/2)*Sqrt[b])","A",1
188,1,68,76,0.0543934,"\int \frac{1}{x^2 \left(a+b x^2\right)^3} \, dx","IntegrateAlgebraic[1/(x^2*(a + b*x^2)^3),x]","\frac{-8 a^2-25 a b x^2-15 b^2 x^4}{8 a^3 x \left(a+b x^2\right)^2}-\frac{15 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{7/2}}","-\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{5}{8 a^2 x \left(a+b x^2\right)}+\frac{1}{4 a x \left(a+b x^2\right)^2}",1,"(-8*a^2 - 25*a*b*x^2 - 15*b^2*x^4)/(8*a^3*x*(a + b*x^2)^2) - (15*Sqrt[b]*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*a^(7/2))","A",1
189,1,79,87,0.0618598,"\int \frac{1}{x^4 \left(a+b x^2\right)^3} \, dx","IntegrateAlgebraic[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{-8 a^3+56 a^2 b x^2+175 a b^2 x^4+105 b^3 x^6}{24 a^4 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{35 b}{8 a^4 x}-\frac{35}{24 a^3 x^3}+\frac{7}{8 a^2 x^3 \left(a+b x^2\right)}+\frac{1}{4 a x^3 \left(a+b x^2\right)^2}",1,"(-8*a^3 + 56*a^2*b*x^2 + 175*a*b^2*x^4 + 105*b^3*x^6)/(24*a^4*x^3*(a + b*x^2)^2) + (35*b^(3/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*a^(9/2))","A",1
190,1,90,100,0.0714145,"\int \frac{1}{x^6 \left(a+b x^2\right)^3} \, dx","IntegrateAlgebraic[1/(x^6*(a + b*x^2)^3),x]","\frac{-8 a^4+24 a^3 b x^2-168 a^2 b^2 x^4-525 a b^3 x^6-315 b^4 x^8}{40 a^5 x^5 \left(a+b x^2\right)^2}-\frac{63 b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{11/2}}","-\frac{63 b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{11/2}}-\frac{63 b^2}{8 a^5 x}+\frac{21 b}{8 a^4 x^3}-\frac{63}{40 a^3 x^5}+\frac{9}{8 a^2 x^5 \left(a+b x^2\right)}+\frac{1}{4 a x^5 \left(a+b x^2\right)^2}",1,"(-8*a^4 + 24*a^3*b*x^2 - 168*a^2*b^2*x^4 - 525*a*b^3*x^6 - 315*b^4*x^8)/(40*a^5*x^5*(a + b*x^2)^2) - (63*b^(5/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*a^(11/2))","A",1
191,1,101,113,0.0736789,"\int \frac{1}{x^8 \left(a+b x^2\right)^3} \, dx","IntegrateAlgebraic[1/(x^8*(a + b*x^2)^3),x]","\frac{99 b^{7/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{13/2}}+\frac{-40 a^5+88 a^4 b x^2-264 a^3 b^2 x^4+1848 a^2 b^3 x^6+5775 a b^4 x^8+3465 b^5 x^{10}}{280 a^6 x^7 \left(a+b x^2\right)^2}","\frac{99 b^{7/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{13/2}}+\frac{99 b^3}{8 a^6 x}-\frac{33 b^2}{8 a^5 x^3}+\frac{99 b}{40 a^4 x^5}-\frac{99}{56 a^3 x^7}+\frac{11}{8 a^2 x^7 \left(a+b x^2\right)}+\frac{1}{4 a x^7 \left(a+b x^2\right)^2}",1,"(-40*a^5 + 88*a^4*b*x^2 - 264*a^3*b^2*x^4 + 1848*a^2*b^3*x^6 + 5775*a*b^4*x^8 + 3465*b^5*x^10)/(280*a^6*x^7*(a + b*x^2)^2) + (99*b^(7/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*a^(13/2))","A",1
192,1,164,216,0.0765918,"\int \frac{x^{25}}{\left(a+b x^2\right)^{10}} \, dx","IntegrateAlgebraic[x^25/(a + b*x^2)^10,x]","\frac{-35201 a^{12}-289089 a^{11} b x^2-1031616 a^{10} b^2 x^4-2074464 a^9 b^3 x^6-2529576 a^8 b^4 x^8-1831032 a^7 b^5 x^{10}-638568 a^6 b^6 x^{12}+58968 a^5 b^7 x^{14}+139482 a^4 b^8 x^{16}+43218 a^3 b^9 x^{18}+2772 a^2 b^{10} x^{20}-252 a b^{11} x^{22}+42 b^{12} x^{24}}{252 b^{13} \left(a+b x^2\right)^9}-\frac{110 a^3 \log \left(a+b x^2\right)}{b^{13}}","-\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{110 a^3 \log \left(a+b x^2\right)}{b^{13}}+\frac{55 a^2 x^2}{2 b^{12}}-\frac{5 a x^4}{2 b^{11}}+\frac{x^6}{6 b^{10}}",1,"(-35201*a^12 - 289089*a^11*b*x^2 - 1031616*a^10*b^2*x^4 - 2074464*a^9*b^3*x^6 - 2529576*a^8*b^4*x^8 - 1831032*a^7*b^5*x^10 - 638568*a^6*b^6*x^12 + 58968*a^5*b^7*x^14 + 139482*a^4*b^8*x^16 + 43218*a^3*b^9*x^18 + 2772*a^2*b^10*x^20 - 252*a*b^11*x^22 + 42*b^12*x^24)/(252*b^13*(a + b*x^2)^9) - (110*a^3*Log[a + b*x^2])/b^13","A",1
193,1,155,205,0.0538391,"\int \frac{x^{23}}{\left(a+b x^2\right)^{10}} \, dx","IntegrateAlgebraic[x^23/(a + b*x^2)^10,x]","\frac{55 a^2 \log \left(a+b x^2\right)}{2 b^{12}}+\frac{42131 a^{11}+351459 a^{10} b x^2+1281096 a^9 b^2 x^4+2656584 a^8 b^3 x^6+3402756 a^7 b^4 x^8+2704212 a^6 b^5 x^{10}+1220688 a^5 b^6 x^{12}+190512 a^4 b^7 x^{14}-77112 a^3 b^8 x^{16}-36288 a^2 b^9 x^{18}-2772 a b^{10} x^{20}+252 b^{11} x^{22}}{1008 b^{12} \left(a+b x^2\right)^9}","\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,"(42131*a^11 + 351459*a^10*b*x^2 + 1281096*a^9*b^2*x^4 + 2656584*a^8*b^3*x^6 + 3402756*a^7*b^4*x^8 + 2704212*a^6*b^5*x^10 + 1220688*a^5*b^6*x^12 + 190512*a^4*b^7*x^14 - 77112*a^3*b^8*x^16 - 36288*a^2*b^9*x^18 - 2772*a*b^10*x^20 + 252*b^11*x^22)/(1008*b^12*(a + b*x^2)^9) + (55*a^2*Log[a + b*x^2])/(2*b^12)","A",1
194,1,140,188,0.0594757,"\int \frac{x^{21}}{\left(a+b x^2\right)^{10}} \, dx","IntegrateAlgebraic[x^21/(a + b*x^2)^10,x]","\frac{-4861 a^{10}-41229 a^9 b x^2-153576 a^8 b^2 x^4-328104 a^7 b^3 x^6-439236 a^6 b^4 x^8-375732 a^5 b^5 x^{10}-197568 a^4 b^6 x^{12}-54432 a^3 b^7 x^{14}-2268 a^2 b^8 x^{16}+2268 a b^9 x^{18}+252 b^{10} x^{20}}{504 b^{11} \left(a+b x^2\right)^9}-\frac{5 a \log \left(a+b x^2\right)}{b^{11}}","-\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,"(-4861*a^10 - 41229*a^9*b*x^2 - 153576*a^8*b^2*x^4 - 328104*a^7*b^3*x^6 - 439236*a^6*b^4*x^8 - 375732*a^5*b^5*x^10 - 197568*a^4*b^6*x^12 - 54432*a^3*b^7*x^14 - 2268*a^2*b^8*x^16 + 2268*a*b^9*x^18 + 252*b^10*x^20)/(504*b^11*(a + b*x^2)^9) - (5*a*Log[a + b*x^2])/b^11","A",1
195,1,120,179,0.0529399,"\int \frac{x^{19}}{\left(a+b x^2\right)^{10}} \, dx","IntegrateAlgebraic[x^19/(a + b*x^2)^10,x]","\frac{a \left(7129 a^8+61641 a^7 b x^2+235224 a^6 b^2 x^4+518616 a^5 b^3 x^6+725004 a^4 b^4 x^8+661500 a^3 b^5 x^{10}+388080 a^2 b^6 x^{12}+136080 a b^7 x^{14}+22680 b^8 x^{16}\right)}{5040 b^{10} \left(a+b x^2\right)^9}+\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*(7129*a^8 + 61641*a^7*b*x^2 + 235224*a^6*b^2*x^4 + 518616*a^5*b^3*x^6 + 725004*a^4*b^4*x^8 + 661500*a^3*b^5*x^10 + 388080*a^2*b^6*x^12 + 136080*a*b^7*x^14 + 22680*b^8*x^16))/(5040*b^10*(a + b*x^2)^9) + Log[a + b*x^2]/(2*b^10)","A",1
196,1,103,19,0.0318709,"\int \frac{x^{17}}{\left(a+b x^2\right)^{10}} \, dx","IntegrateAlgebraic[x^17/(a + b*x^2)^10,x]","\frac{-a^8-9 a^7 b x^2-36 a^6 b^2 x^4-84 a^5 b^3 x^6-126 a^4 b^4 x^8-126 a^3 b^5 x^{10}-84 a^2 b^6 x^{12}-36 a b^7 x^{14}-9 b^8 x^{16}}{18 b^9 \left(a+b x^2\right)^9}","\frac{x^{18}}{18 a \left(a+b x^2\right)^9}",1,"(-a^8 - 9*a^7*b*x^2 - 36*a^6*b^2*x^4 - 84*a^5*b^3*x^6 - 126*a^4*b^4*x^8 - 126*a^3*b^5*x^10 - 84*a^2*b^6*x^12 - 36*a*b^7*x^14 - 9*b^8*x^16)/(18*b^9*(a + b*x^2)^9)","B",1
197,1,92,39,0.0262848,"\int \frac{x^{15}}{\left(a+b x^2\right)^{10}} \, dx","IntegrateAlgebraic[x^15/(a + b*x^2)^10,x]","\frac{-a^7-9 a^6 b x^2-36 a^5 b^2 x^4-84 a^4 b^3 x^6-126 a^3 b^4 x^8-126 a^2 b^5 x^{10}-84 a b^6 x^{12}-36 b^7 x^{14}}{144 b^8 \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,"(-a^7 - 9*a^6*b*x^2 - 36*a^5*b^2*x^4 - 84*a^4*b^3*x^6 - 126*a^3*b^4*x^8 - 126*a^2*b^5*x^10 - 84*a*b^6*x^12 - 36*b^7*x^14)/(144*b^8*(a + b*x^2)^9)","B",1
198,1,81,58,0.0266995,"\int \frac{x^{13}}{\left(a+b x^2\right)^{10}} \, dx","IntegrateAlgebraic[x^13/(a + b*x^2)^10,x]","\frac{-a^6-9 a^5 b x^2-36 a^4 b^2 x^4-84 a^3 b^3 x^6-126 a^2 b^4 x^8-126 a b^5 x^{10}-84 b^6 x^{12}}{504 b^7 \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,"(-a^6 - 9*a^5*b*x^2 - 36*a^4*b^2*x^4 - 84*a^3*b^3*x^6 - 126*a^2*b^4*x^8 - 126*a*b^5*x^10 - 84*b^6*x^12)/(504*b^7*(a + b*x^2)^9)","A",1
199,1,70,77,0.0247021,"\int \frac{x^{11}}{\left(a+b x^2\right)^{10}} \, dx","IntegrateAlgebraic[x^11/(a + b*x^2)^10,x]","\frac{-a^5-9 a^4 b x^2-36 a^3 b^2 x^4-84 a^2 b^3 x^6-126 a b^4 x^8-126 b^5 x^{10}}{1008 b^6 \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,"(-a^5 - 9*a^4*b*x^2 - 36*a^3*b^2*x^4 - 84*a^2*b^3*x^6 - 126*a*b^4*x^8 - 126*b^5*x^10)/(1008*b^6*(a + b*x^2)^9)","A",1
200,1,59,91,0.0235197,"\int \frac{x^9}{\left(a+b x^2\right)^{10}} \, dx","IntegrateAlgebraic[x^9/(a + b*x^2)^10,x]","\frac{-a^4-9 a^3 b x^2-36 a^2 b^2 x^4-84 a b^3 x^6-126 b^4 x^8}{1260 b^5 \left(a+b x^2\right)^9}","-\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 - 9*a^3*b*x^2 - 36*a^2*b^2*x^4 - 84*a*b^3*x^6 - 126*b^4*x^8)/(1260*b^5*(a + b*x^2)^9)","A",1
201,1,48,72,0.0183291,"\int \frac{x^7}{\left(a+b x^2\right)^{10}} \, dx","IntegrateAlgebraic[x^7/(a + b*x^2)^10,x]","\frac{-a^3-9 a^2 b x^2-36 a b^2 x^4-84 b^3 x^6}{1008 b^4 \left(a+b x^2\right)^9}","\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 - 9*a^2*b*x^2 - 36*a*b^2*x^4 - 84*b^3*x^6)/(1008*b^4*(a + b*x^2)^9)","A",1
202,1,37,53,0.0192242,"\int \frac{x^5}{\left(a+b x^2\right)^{10}} \, dx","IntegrateAlgebraic[x^5/(a + b*x^2)^10,x]","\frac{-a^2-9 a b x^2-36 b^2 x^4}{504 b^3 \left(a+b x^2\right)^9}","-\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 - 9*a*b*x^2 - 36*b^2*x^4)/(504*b^3*(a + b*x^2)^9)","A",1
203,1,26,34,0.0135875,"\int \frac{x^3}{\left(a+b x^2\right)^{10}} \, dx","IntegrateAlgebraic[x^3/(a + b*x^2)^10,x]","\frac{-a-9 b x^2}{144 b^2 \left(a+b x^2\right)^9}","\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 - 9*b*x^2)/(144*b^2*(a + b*x^2)^9)","A",1
204,1,16,16,0.0067941,"\int \frac{x}{\left(a+b x^2\right)^{10}} \, dx","IntegrateAlgebraic[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*1/(b*(a + b*x^2)^9)","A",1
205,1,125,166,0.12089,"\int \frac{1}{x \left(a+b x^2\right)^{10}} \, dx","IntegrateAlgebraic[1/(x*(a + b*x^2)^10),x]","-\frac{\log \left(a+b x^2\right)}{2 a^{10}}+\frac{\log (x)}{a^{10}}+\frac{7129 a^8+41481 a^7 b x^2+120564 a^6 b^2 x^4+210756 a^5 b^3 x^6+236754 a^4 b^4 x^8+173250 a^3 b^5 x^{10}+80220 a^2 b^6 x^{12}+21420 a b^7 x^{14}+2520 b^8 x^{16}}{5040 a^9 \left(a+b x^2\right)^9}","-\frac{\log \left(a+b x^2\right)}{2 a^{10}}+\frac{\log (x)}{a^{10}}+\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{1}{18 a \left(a+b x^2\right)^9}",1,"(7129*a^8 + 41481*a^7*b*x^2 + 120564*a^6*b^2*x^4 + 210756*a^5*b^3*x^6 + 236754*a^4*b^4*x^8 + 173250*a^3*b^5*x^10 + 80220*a^2*b^6*x^12 + 21420*a*b^7*x^14 + 2520*b^8*x^16)/(5040*a^9*(a + b*x^2)^9) + Log[x]/a^10 - Log[a + b*x^2]/(2*a^10)","A",1
206,1,140,184,0.1573751,"\int \frac{1}{x^3 \left(a+b x^2\right)^{10}} \, dx","IntegrateAlgebraic[1/(x^3*(a + b*x^2)^10),x]","\frac{5 b \log \left(a+b x^2\right)}{a^{11}}-\frac{10 b \log (x)}{a^{11}}+\frac{-252 a^9-7129 a^8 b x^2-41481 a^7 b^2 x^4-120564 a^6 b^3 x^6-210756 a^5 b^4 x^8-236754 a^4 b^5 x^{10}-173250 a^3 b^6 x^{12}-80220 a^2 b^7 x^{14}-21420 a b^8 x^{16}-2520 b^9 x^{18}}{504 a^{10} x^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{9 b}{2 a^{10} \left(a+b x^2\right)}-\frac{1}{2 a^{10} x^2}-\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}",1,"(-252*a^9 - 7129*a^8*b*x^2 - 41481*a^7*b^2*x^4 - 120564*a^6*b^3*x^6 - 210756*a^5*b^4*x^8 - 236754*a^4*b^5*x^10 - 173250*a^3*b^6*x^12 - 80220*a^2*b^7*x^14 - 21420*a*b^8*x^16 - 2520*b^9*x^18)/(504*a^10*x^2*(a + b*x^2)^9) - (10*b*Log[x])/a^11 + (5*b*Log[a + b*x^2])/a^11","A",1
207,1,157,217,0.1263846,"\int \frac{1}{x^5 \left(a+b x^2\right)^{10}} \, dx","IntegrateAlgebraic[1/(x^5*(a + b*x^2)^10),x]","-\frac{55 b^2 \log \left(a+b x^2\right)}{2 a^{12}}+\frac{55 b^2 \log (x)}{a^{12}}+\frac{-252 a^{10}+2772 a^9 b x^2+78419 a^8 b^2 x^4+456291 a^7 b^3 x^6+1326204 a^6 b^4 x^8+2318316 a^5 b^5 x^{10}+2604294 a^4 b^6 x^{12}+1905750 a^3 b^7 x^{14}+882420 a^2 b^8 x^{16}+235620 a b^9 x^{18}+27720 b^{10} x^{20}}{1008 a^{11} x^4 \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{45 b^2}{2 a^{11} \left(a+b x^2\right)}+\frac{5 b}{a^{11} x^2}+\frac{9 b^2}{a^{10} \left(a+b x^2\right)^2}-\frac{1}{4 a^{10} x^4}+\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}",1,"(-252*a^10 + 2772*a^9*b*x^2 + 78419*a^8*b^2*x^4 + 456291*a^7*b^3*x^6 + 1326204*a^6*b^4*x^8 + 2318316*a^5*b^5*x^10 + 2604294*a^4*b^6*x^12 + 1905750*a^3*b^7*x^14 + 882420*a^2*b^8*x^16 + 235620*a*b^9*x^18 + 27720*b^10*x^20)/(1008*a^11*x^4*(a + b*x^2)^9) + (55*b^2*Log[x])/a^12 - (55*b^2*Log[a + b*x^2])/(2*a^12)","A",1
208,1,166,226,0.1564293,"\int \frac{1}{x^7 \left(a+b x^2\right)^{10}} \, dx","IntegrateAlgebraic[1/(x^7*(a + b*x^2)^10),x]","\frac{110 b^3 \log \left(a+b x^2\right)}{a^{13}}-\frac{220 b^3 \log (x)}{a^{13}}+\frac{-42 a^{11}+252 a^{10} b x^2-2772 a^9 b^2 x^4-78419 a^8 b^3 x^6-456291 a^7 b^4 x^8-1326204 a^6 b^5 x^{10}-2318316 a^5 b^6 x^{12}-2604294 a^4 b^7 x^{14}-1905750 a^3 b^8 x^{16}-882420 a^2 b^9 x^{18}-235620 a b^{10} x^{20}-27720 b^{11} x^{22}}{252 a^{12} x^6 \left(a+b x^2\right)^9}","\frac{110 b^3 \log \left(a+b x^2\right)}{a^{13}}-\frac{220 b^3 \log (x)}{a^{13}}-\frac{165 b^3}{2 a^{12} \left(a+b x^2\right)}-\frac{55 b^2}{2 a^{12} x^2}-\frac{30 b^3}{a^{11} \left(a+b x^2\right)^2}+\frac{5 b}{2 a^{11} x^4}-\frac{14 b^3}{a^{10} \left(a+b x^2\right)^3}-\frac{1}{6 a^{10} x^6}-\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}",1,"(-42*a^11 + 252*a^10*b*x^2 - 2772*a^9*b^2*x^4 - 78419*a^8*b^3*x^6 - 456291*a^7*b^4*x^8 - 1326204*a^6*b^5*x^10 - 2318316*a^5*b^6*x^12 - 2604294*a^4*b^7*x^14 - 1905750*a^3*b^8*x^16 - 882420*a^2*b^9*x^18 - 235620*a*b^10*x^20 - 27720*b^11*x^22)/(252*a^12*x^6*(a + b*x^2)^9) - (220*b^3*Log[x])/a^13 + (110*b^3*Log[a + b*x^2])/a^13","A",1
209,1,165,231,0.1207458,"\int \frac{x^{24}}{\left(a+b x^2\right)^{10}} \, dx","IntegrateAlgebraic[x^24/(a + b*x^2)^10,x]","\frac{x \left(334639305 a^{11}+2900207310 a^{10} b x^2+11110024926 a^9 b^2 x^4+24648575094 a^8 b^3 x^6+34810986496 a^7 b^4 x^8+32314857354 a^6 b^5 x^{10}+19562592546 a^5 b^6 x^{12}+7323998514 a^4 b^7 x^{14}+1469632311 a^3 b^8 x^{16}+94961664 a^2 b^9 x^{18}-4521984 a b^{10} x^{20}+589824 b^{11} x^{22}\right)}{2949120 b^{12} \left(a+b x^2\right)^9}-\frac{7436429 a^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 b^{25/2}}","-\frac{7436429 a^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 b^{25/2}}+\frac{7436429 a^2 x}{65536 b^{12}}-\frac{7436429 a x^3}{196608 b^{11}}-\frac{1062347 x^7}{65536 b^9 \left(a+b x^2\right)}-\frac{1062347 x^9}{294912 b^8 \left(a+b x^2\right)^2}-\frac{96577 x^{11}}{73728 b^7 \left(a+b x^2\right)^3}-\frac{7429 x^{13}}{12288 b^6 \left(a+b x^2\right)^4}-\frac{7429 x^{15}}{23040 b^5 \left(a+b x^2\right)^5}-\frac{437 x^{17}}{2304 b^4 \left(a+b x^2\right)^6}-\frac{23 x^{19}}{192 b^3 \left(a+b x^2\right)^7}-\frac{23 x^{21}}{288 b^2 \left(a+b x^2\right)^8}-\frac{x^{23}}{18 b \left(a+b x^2\right)^9}+\frac{7436429 x^5}{327680 b^{10}}",1,"(x*(334639305*a^11 + 2900207310*a^10*b*x^2 + 11110024926*a^9*b^2*x^4 + 24648575094*a^8*b^3*x^6 + 34810986496*a^7*b^4*x^8 + 32314857354*a^6*b^5*x^10 + 19562592546*a^5*b^6*x^12 + 7323998514*a^4*b^7*x^14 + 1469632311*a^3*b^8*x^16 + 94961664*a^2*b^9*x^18 - 4521984*a*b^10*x^20 + 589824*b^11*x^22))/(2949120*b^12*(a + b*x^2)^9) - (7436429*a^(5/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(65536*b^(25/2))","A",1
210,1,154,218,0.1089406,"\int \frac{x^{22}}{\left(a+b x^2\right)^{10}} \, dx","IntegrateAlgebraic[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{x \left(-14549535 a^{10}-126095970 a^9 b x^2-483044562 a^8 b^2 x^4-1071677178 a^7 b^3 x^6-1513521152 a^6 b^4 x^8-1404993798 a^5 b^5 x^{10}-850547502 a^4 b^6 x^{12}-318434718 a^3 b^7 x^{14}-63897057 a^2 b^8 x^{16}-4128768 a b^9 x^{18}+196608 b^{10} x^{20}\right)}{589824 b^{11} \left(a+b x^2\right)^9}","\frac{1616615 a^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 b^{23/2}}-\frac{1616615 a x}{65536 b^{11}}-\frac{323323 x^5}{65536 b^9 \left(a+b x^2\right)}-\frac{46189 x^7}{32768 b^8 \left(a+b x^2\right)^2}-\frac{46189 x^9}{73728 b^7 \left(a+b x^2\right)^3}-\frac{4199 x^{11}}{12288 b^6 \left(a+b x^2\right)^4}-\frac{323 x^{13}}{1536 b^5 \left(a+b x^2\right)^5}-\frac{323 x^{15}}{2304 b^4 \left(a+b x^2\right)^6}-\frac{19 x^{17}}{192 b^3 \left(a+b x^2\right)^7}-\frac{7 x^{19}}{96 b^2 \left(a+b x^2\right)^8}-\frac{x^{21}}{18 b \left(a+b x^2\right)^9}+\frac{1616615 x^3}{196608 b^{10}}",1,"(x*(-14549535*a^10 - 126095970*a^9*b*x^2 - 483044562*a^8*b^2*x^4 - 1071677178*a^7*b^3*x^6 - 1513521152*a^6*b^4*x^8 - 1404993798*a^5*b^5*x^10 - 850547502*a^4*b^6*x^12 - 318434718*a^3*b^7*x^14 - 63897057*a^2*b^8*x^16 - 4128768*a*b^9*x^18 + 196608*b^10*x^20))/(589824*b^11*(a + b*x^2)^9) + (1616615*a^(3/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(65536*b^(23/2))","A",1
211,1,143,207,0.1016545,"\int \frac{x^{20}}{\left(a+b x^2\right)^{10}} \, dx","IntegrateAlgebraic[x^20/(a + b*x^2)^10,x]","\frac{x \left(14549535 a^9+126095970 a^8 b x^2+483044562 a^7 b^2 x^4+1071677178 a^6 b^3 x^6+1513521152 a^5 b^4 x^8+1404993798 a^4 b^5 x^{10}+850547502 a^3 b^6 x^{12}+318434718 a^2 b^7 x^{14}+63897057 a b^8 x^{16}+4128768 b^9 x^{18}\right)}{4128768 b^{10} \left(a+b x^2\right)^9}-\frac{230945 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 b^{21/2}}","-\frac{230945 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 b^{21/2}}-\frac{230945 x^3}{196608 b^9 \left(a+b x^2\right)}-\frac{46189 x^5}{98304 b^8 \left(a+b x^2\right)^2}-\frac{46189 x^7}{172032 b^7 \left(a+b x^2\right)^3}-\frac{46189 x^9}{258048 b^6 \left(a+b x^2\right)^4}-\frac{4199 x^{11}}{32256 b^5 \left(a+b x^2\right)^5}-\frac{1615 x^{13}}{16128 b^4 \left(a+b x^2\right)^6}-\frac{323 x^{15}}{4032 b^3 \left(a+b x^2\right)^7}-\frac{19 x^{17}}{288 b^2 \left(a+b x^2\right)^8}-\frac{x^{19}}{18 b \left(a+b x^2\right)^9}+\frac{230945 x}{65536 b^{10}}",1,"(x*(14549535*a^9 + 126095970*a^8*b*x^2 + 483044562*a^7*b^2*x^4 + 1071677178*a^6*b^3*x^6 + 1513521152*a^5*b^4*x^8 + 1404993798*a^4*b^5*x^10 + 850547502*a^3*b^6*x^12 + 318434718*a^2*b^7*x^14 + 63897057*a*b^8*x^16 + 4128768*b^9*x^18))/(4128768*b^10*(a + b*x^2)^9) - (230945*Sqrt[a]*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(65536*b^(21/2))","A",1
212,1,132,197,0.1032803,"\int \frac{x^{18}}{\left(a+b x^2\right)^{10}} \, dx","IntegrateAlgebraic[x^18/(a + b*x^2)^10,x]","\frac{12155 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 \sqrt{a} b^{19/2}}-\frac{x \left(765765 a^8+6636630 a^7 b x^2+25423398 a^6 b^2 x^4+56404062 a^5 b^3 x^6+79659008 a^4 b^4 x^8+73947042 a^3 b^5 x^{10}+44765658 a^2 b^6 x^{12}+16759722 a b^7 x^{14}+3363003 b^8 x^{16}\right)}{4128768 b^9 \left(a+b x^2\right)^9}","\frac{12155 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 \sqrt{a} b^{19/2}}-\frac{12155 x}{65536 b^9 \left(a+b x^2\right)}-\frac{12155 x^3}{98304 b^8 \left(a+b x^2\right)^2}-\frac{2431 x^5}{24576 b^7 \left(a+b x^2\right)^3}-\frac{2431 x^7}{28672 b^6 \left(a+b x^2\right)^4}-\frac{2431 x^9}{32256 b^5 \left(a+b x^2\right)^5}-\frac{1105 x^{11}}{16128 b^4 \left(a+b x^2\right)^6}-\frac{85 x^{13}}{1344 b^3 \left(a+b x^2\right)^7}-\frac{17 x^{15}}{288 b^2 \left(a+b x^2\right)^8}-\frac{x^{17}}{18 b \left(a+b x^2\right)^9}",1,"-1/4128768*(x*(765765*a^8 + 6636630*a^7*b*x^2 + 25423398*a^6*b^2*x^4 + 56404062*a^5*b^3*x^6 + 79659008*a^4*b^4*x^8 + 73947042*a^3*b^5*x^10 + 44765658*a^2*b^6*x^12 + 16759722*a*b^7*x^14 + 3363003*b^8*x^16))/(b^9*(a + b*x^2)^9) + (12155*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(65536*Sqrt[a]*b^(19/2))","A",1
213,1,135,198,0.0954151,"\int \frac{x^{16}}{\left(a+b x^2\right)^{10}} \, dx","IntegrateAlgebraic[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{x \left(45045 a^8+390390 a^7 b x^2+1495494 a^6 b^2 x^4+3317886 a^5 b^3 x^6+4685824 a^4 b^4 x^8+4349826 a^3 b^5 x^{10}+2633274 a^2 b^6 x^{12}+985866 a b^7 x^{14}-45045 b^8 x^{16}\right)}{4128768 a b^8 \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{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{715 x^3}{24576 b^7 \left(a+b x^2\right)^3}-\frac{143 x^5}{4096 b^6 \left(a+b x^2\right)^4}-\frac{143 x^7}{3584 b^5 \left(a+b x^2\right)^5}-\frac{715 x^9}{16128 b^4 \left(a+b x^2\right)^6}-\frac{65 x^{11}}{1344 b^3 \left(a+b x^2\right)^7}-\frac{5 x^{13}}{96 b^2 \left(a+b x^2\right)^8}-\frac{x^{15}}{18 b \left(a+b x^2\right)^9}",1,"-1/4128768*(x*(45045*a^8 + 390390*a^7*b*x^2 + 1495494*a^6*b^2*x^4 + 3317886*a^5*b^3*x^6 + 4685824*a^4*b^4*x^8 + 4349826*a^3*b^5*x^10 + 2633274*a^2*b^6*x^12 + 985866*a*b^7*x^14 - 45045*b^8*x^16))/(a*b^8*(a + b*x^2)^9) + (715*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(65536*a^(3/2)*b^(17/2))","A",1
214,1,135,199,0.0842603,"\int \frac{x^{14}}{\left(a+b x^2\right)^{10}} \, dx","IntegrateAlgebraic[x^14/(a + b*x^2)^10,x]","\frac{143 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 a^{5/2} b^{15/2}}-\frac{x \left(45045 a^8+390390 a^7 b x^2+1495494 a^6 b^2 x^4+3317886 a^5 b^3 x^6+4685824 a^4 b^4 x^8+4349826 a^3 b^5 x^{10}+2633274 a^2 b^6 x^{12}-390390 a b^7 x^{14}-45045 b^8 x^{16}\right)}{20643840 a^2 b^7 \left(a+b x^2\right)^9}","\frac{143 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 a^{5/2} b^{15/2}}+\frac{143 x}{65536 a^2 b^7 \left(a+b x^2\right)}+\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{143 x^3}{12288 b^6 \left(a+b x^2\right)^4}-\frac{143 x^5}{7680 b^5 \left(a+b x^2\right)^5}-\frac{143 x^7}{5376 b^4 \left(a+b x^2\right)^6}-\frac{143 x^9}{4032 b^3 \left(a+b x^2\right)^7}-\frac{13 x^{11}}{288 b^2 \left(a+b x^2\right)^8}-\frac{x^{13}}{18 b \left(a+b x^2\right)^9}",1,"-1/20643840*(x*(45045*a^8 + 390390*a^7*b*x^2 + 1495494*a^6*b^2*x^4 + 3317886*a^5*b^3*x^6 + 4685824*a^4*b^4*x^8 + 4349826*a^3*b^5*x^10 + 2633274*a^2*b^6*x^12 - 390390*a*b^7*x^14 - 45045*b^8*x^16))/(a^2*b^7*(a + b*x^2)^9) + (143*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(65536*a^(5/2)*b^(15/2))","A",1
215,1,135,200,0.096653,"\int \frac{x^{12}}{\left(a+b x^2\right)^{10}} \, dx","IntegrateAlgebraic[x^12/(a + b*x^2)^10,x]","\frac{55 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 a^{7/2} b^{13/2}}-\frac{x \left(3465 a^8+30030 a^7 b x^2+115038 a^6 b^2 x^4+255222 a^5 b^3 x^6+360448 a^4 b^4 x^8+334602 a^3 b^5 x^{10}-115038 a^2 b^6 x^{12}-30030 a b^7 x^{14}-3465 b^8 x^{16}\right)}{4128768 a^3 b^6 \left(a+b x^2\right)^9}","\frac{55 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 a^{7/2} b^{13/2}}+\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{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{11 x^3}{1536 b^5 \left(a+b x^2\right)^5}-\frac{11 x^5}{768 b^4 \left(a+b x^2\right)^6}-\frac{11 x^7}{448 b^3 \left(a+b x^2\right)^7}-\frac{11 x^9}{288 b^2 \left(a+b x^2\right)^8}-\frac{x^{11}}{18 b \left(a+b x^2\right)^9}",1,"-1/4128768*(x*(3465*a^8 + 30030*a^7*b*x^2 + 115038*a^6*b^2*x^4 + 255222*a^5*b^3*x^6 + 360448*a^4*b^4*x^8 + 334602*a^3*b^5*x^10 - 115038*a^2*b^6*x^12 - 30030*a*b^7*x^14 - 3465*b^8*x^16))/(a^3*b^6*(a + b*x^2)^9) + (55*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(65536*a^(7/2)*b^(13/2))","A",1
216,1,135,201,0.0977598,"\int \frac{x^{10}}{\left(a+b x^2\right)^{10}} \, dx","IntegrateAlgebraic[x^10/(a + b*x^2)^10,x]","\frac{35 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 a^{9/2} b^{11/2}}-\frac{x \left(315 a^8+2730 a^7 b x^2+10458 a^6 b^2 x^4+23202 a^5 b^3 x^6+32768 a^4 b^4 x^8-23202 a^3 b^5 x^{10}-10458 a^2 b^6 x^{12}-2730 a b^7 x^{14}-315 b^8 x^{16}\right)}{589824 a^4 b^5 \left(a+b x^2\right)^9}","\frac{35 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 a^{9/2} b^{11/2}}+\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{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{5 x^3}{768 b^4 \left(a+b x^2\right)^6}-\frac{x^5}{64 b^3 \left(a+b x^2\right)^7}-\frac{x^7}{32 b^2 \left(a+b x^2\right)^8}-\frac{x^9}{18 b \left(a+b x^2\right)^9}",1,"-1/589824*(x*(315*a^8 + 2730*a^7*b*x^2 + 10458*a^6*b^2*x^4 + 23202*a^5*b^3*x^6 + 32768*a^4*b^4*x^8 - 23202*a^3*b^5*x^10 - 10458*a^2*b^6*x^12 - 2730*a*b^7*x^14 - 315*b^8*x^16))/(a^4*b^5*(a + b*x^2)^9) + (35*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(65536*a^(9/2)*b^(11/2))","A",1
217,1,135,202,0.0861979,"\int \frac{x^8}{\left(a+b x^2\right)^{10}} \, dx","IntegrateAlgebraic[x^8/(a + b*x^2)^10,x]","\frac{35 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 a^{11/2} b^{9/2}}-\frac{x \left(315 a^8+2730 a^7 b x^2+10458 a^6 b^2 x^4+23202 a^5 b^3 x^6-32768 a^4 b^4 x^8-23202 a^3 b^5 x^{10}-10458 a^2 b^6 x^{12}-2730 a b^7 x^{14}-315 b^8 x^{16}\right)}{589824 a^5 b^4 \left(a+b x^2\right)^9}","\frac{35 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 a^{11/2} b^{9/2}}+\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{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{5 x^3}{576 b^3 \left(a+b x^2\right)^7}-\frac{7 x^5}{288 b^2 \left(a+b x^2\right)^8}-\frac{x^7}{18 b \left(a+b x^2\right)^9}",1,"-1/589824*(x*(315*a^8 + 2730*a^7*b*x^2 + 10458*a^6*b^2*x^4 + 23202*a^5*b^3*x^6 - 32768*a^4*b^4*x^8 - 23202*a^3*b^5*x^10 - 10458*a^2*b^6*x^12 - 2730*a*b^7*x^14 - 315*b^8*x^16))/(a^5*b^4*(a + b*x^2)^9) + (35*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(65536*a^(11/2)*b^(9/2))","A",1
218,1,135,203,0.0908718,"\int \frac{x^6}{\left(a+b x^2\right)^{10}} \, dx","IntegrateAlgebraic[x^6/(a + b*x^2)^10,x]","\frac{55 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 a^{13/2} b^{7/2}}-\frac{x \left(3465 a^8+30030 a^7 b x^2+115038 a^6 b^2 x^4-334602 a^5 b^3 x^6-360448 a^4 b^4 x^8-255222 a^3 b^5 x^{10}-115038 a^2 b^6 x^{12}-30030 a b^7 x^{14}-3465 b^8 x^{16}\right)}{4128768 a^6 b^3 \left(a+b x^2\right)^9}","\frac{55 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 a^{13/2} b^{7/2}}+\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{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{5 x^3}{288 b^2 \left(a+b x^2\right)^8}-\frac{x^5}{18 b \left(a+b x^2\right)^9}",1,"-1/4128768*(x*(3465*a^8 + 30030*a^7*b*x^2 + 115038*a^6*b^2*x^4 - 334602*a^5*b^3*x^6 - 360448*a^4*b^4*x^8 - 255222*a^3*b^5*x^10 - 115038*a^2*b^6*x^12 - 30030*a*b^7*x^14 - 3465*b^8*x^16))/(a^6*b^3*(a + b*x^2)^9) + (55*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(65536*a^(13/2)*b^(7/2))","A",1
219,1,135,204,0.0899586,"\int \frac{x^4}{\left(a+b x^2\right)^{10}} \, dx","IntegrateAlgebraic[x^4/(a + b*x^2)^10,x]","\frac{143 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 a^{15/2} b^{5/2}}-\frac{x \left(45045 a^8+390390 a^7 b x^2-2633274 a^6 b^2 x^4-4349826 a^5 b^3 x^6-4685824 a^4 b^4 x^8-3317886 a^3 b^5 x^{10}-1495494 a^2 b^6 x^{12}-390390 a b^7 x^{14}-45045 b^8 x^{16}\right)}{20643840 a^7 b^2 \left(a+b x^2\right)^9}","\frac{143 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 a^{15/2} b^{5/2}}+\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{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,"-1/20643840*(x*(45045*a^8 + 390390*a^7*b*x^2 - 2633274*a^6*b^2*x^4 - 4349826*a^5*b^3*x^6 - 4685824*a^4*b^4*x^8 - 3317886*a^3*b^5*x^10 - 1495494*a^2*b^6*x^12 - 390390*a*b^7*x^14 - 45045*b^8*x^16))/(a^7*b^2*(a + b*x^2)^9) + (143*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(65536*a^(15/2)*b^(5/2))","A",1
220,1,135,205,0.0814553,"\int \frac{x^2}{\left(a+b x^2\right)^{10}} \, dx","IntegrateAlgebraic[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{x \left(45045 a^8-985866 a^7 b x^2-2633274 a^6 b^2 x^4-4349826 a^5 b^3 x^6-4685824 a^4 b^4 x^8-3317886 a^3 b^5 x^{10}-1495494 a^2 b^6 x^{12}-390390 a b^7 x^{14}-45045 b^8 x^{16}\right)}{4128768 a^8 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,"-1/4128768*(x*(45045*a^8 - 985866*a^7*b*x^2 - 2633274*a^6*b^2*x^4 - 4349826*a^5*b^3*x^6 - 4685824*a^4*b^4*x^8 - 3317886*a^3*b^5*x^10 - 1495494*a^2*b^6*x^12 - 390390*a*b^7*x^14 - 45045*b^8*x^16))/(a^8*b*(a + b*x^2)^9) + (715*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(65536*a^(17/2)*b^(3/2))","A",1
221,1,132,181,0.1198351,"\int \frac{1}{\left(a+b x^2\right)^{10}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(-10),x]","\frac{12155 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 a^{19/2} \sqrt{b}}+\frac{3363003 a^8 x+16759722 a^7 b x^3+44765658 a^6 b^2 x^5+73947042 a^5 b^3 x^7+79659008 a^4 b^4 x^9+56404062 a^3 b^5 x^{11}+25423398 a^2 b^6 x^{13}+6636630 a b^7 x^{15}+765765 b^8 x^{17}}{4128768 a^9 \left(a+b x^2\right)^9}","\frac{12155 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 a^{19/2} \sqrt{b}}+\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{x}{18 a \left(a+b x^2\right)^9}",1,"(3363003*a^8*x + 16759722*a^7*b*x^3 + 44765658*a^6*b^2*x^5 + 73947042*a^5*b^3*x^7 + 79659008*a^4*b^4*x^9 + 56404062*a^3*b^5*x^11 + 25423398*a^2*b^6*x^13 + 6636630*a*b^7*x^15 + 765765*b^8*x^17)/(4128768*a^9*(a + b*x^2)^9) + (12155*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(65536*a^(19/2)*Sqrt[b])","A",1
222,1,145,209,0.1251267,"\int \frac{1}{x^2 \left(a+b x^2\right)^{10}} \, dx","IntegrateAlgebraic[1/(x^2*(a + b*x^2)^10),x]","\frac{-4128768 a^9-63897057 a^8 b x^2-318434718 a^7 b^2 x^4-850547502 a^6 b^3 x^6-1404993798 a^5 b^4 x^8-1513521152 a^4 b^5 x^{10}-1071677178 a^3 b^6 x^{12}-483044562 a^2 b^7 x^{14}-126095970 a b^8 x^{16}-14549535 b^9 x^{18}}{4128768 a^{10} x \left(a+b x^2\right)^9}-\frac{230945 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 a^{21/2}}","-\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{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{1}{18 a x \left(a+b x^2\right)^9}",1,"(-4128768*a^9 - 63897057*a^8*b*x^2 - 318434718*a^7*b^2*x^4 - 850547502*a^6*b^3*x^6 - 1404993798*a^5*b^4*x^8 - 1513521152*a^4*b^5*x^10 - 1071677178*a^3*b^6*x^12 - 483044562*a^2*b^7*x^14 - 126095970*a*b^8*x^16 - 14549535*b^9*x^18)/(4128768*a^10*x*(a + b*x^2)^9) - (230945*Sqrt[b]*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(65536*a^(21/2))","A",1
223,1,156,220,0.1119355,"\int \frac{1}{x^4 \left(a+b x^2\right)^{10}} \, dx","IntegrateAlgebraic[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{-196608 a^{10}+4128768 a^9 b x^2+63897057 a^8 b^2 x^4+318434718 a^7 b^3 x^6+850547502 a^6 b^4 x^8+1404993798 a^5 b^5 x^{10}+1513521152 a^4 b^6 x^{12}+1071677178 a^3 b^7 x^{14}+483044562 a^2 b^8 x^{16}+126095970 a b^9 x^{18}+14549535 b^{10} x^{20}}{589824 a^{11} 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{1616615 b}{65536 a^{11} x}-\frac{1616615}{196608 a^{10} x^3}+\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{1}{18 a x^3 \left(a+b x^2\right)^9}",1,"(-196608*a^10 + 4128768*a^9*b*x^2 + 63897057*a^8*b^2*x^4 + 318434718*a^7*b^3*x^6 + 850547502*a^6*b^4*x^8 + 1404993798*a^5*b^5*x^10 + 1513521152*a^4*b^6*x^12 + 1071677178*a^3*b^7*x^14 + 483044562*a^2*b^8*x^16 + 126095970*a*b^9*x^18 + 14549535*b^10*x^20)/(589824*a^11*x^3*(a + b*x^2)^9) + (1616615*b^(3/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(65536*a^(23/2))","A",1
224,1,167,233,0.1217864,"\int \frac{1}{x^6 \left(a+b x^2\right)^{10}} \, dx","IntegrateAlgebraic[1/(x^6*(a + b*x^2)^10),x]","\frac{-589824 a^{11}+4521984 a^{10} b x^2-94961664 a^9 b^2 x^4-1469632311 a^8 b^3 x^6-7323998514 a^7 b^4 x^8-19562592546 a^6 b^5 x^{10}-32314857354 a^5 b^6 x^{12}-34810986496 a^4 b^7 x^{14}-24648575094 a^3 b^8 x^{16}-11110024926 a^2 b^9 x^{18}-2900207310 a b^{10} x^{20}-334639305 b^{11} x^{22}}{2949120 a^{12} x^5 \left(a+b x^2\right)^9}-\frac{7436429 b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 a^{25/2}}","-\frac{7436429 b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{65536 a^{25/2}}-\frac{7436429 b^2}{65536 a^{12} x}+\frac{7436429 b}{196608 a^{11} x^3}-\frac{7436429}{327680 a^{10} x^5}+\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{1}{18 a x^5 \left(a+b x^2\right)^9}",1,"(-589824*a^11 + 4521984*a^10*b*x^2 - 94961664*a^9*b^2*x^4 - 1469632311*a^8*b^3*x^6 - 7323998514*a^7*b^4*x^8 - 19562592546*a^6*b^5*x^10 - 32314857354*a^5*b^6*x^12 - 34810986496*a^4*b^7*x^14 - 24648575094*a^3*b^8*x^16 - 11110024926*a^2*b^9*x^18 - 2900207310*a*b^10*x^20 - 334639305*b^11*x^22)/(2949120*a^12*x^5*(a + b*x^2)^9) - (7436429*b^(5/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(65536*a^(25/2))","A",1
225,1,28,28,0.0099913,"\int \frac{x^3}{a-b x^2} \, dx","IntegrateAlgebraic[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,"-1/2*x^2/b - (a*Log[a - b*x^2])/(2*b^2)","A",1
226,1,31,31,0.0155877,"\int \frac{x^2}{a-b x^2} \, dx","IntegrateAlgebraic[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",1
227,1,16,16,0.0058209,"\int \frac{x}{a-b x^2} \, dx","IntegrateAlgebraic[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,"-1/2*Log[a - b*x^2]/b","A",1
228,1,24,24,0.0088796,"\int \frac{1}{a-b x^2} \, dx","IntegrateAlgebraic[(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
229,1,23,23,0.0110117,"\int \frac{1}{x \left(a-b x^2\right)} \, dx","IntegrateAlgebraic[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",1
230,1,33,33,0.017528,"\int \frac{1}{x^2 \left(a-b x^2\right)} \, dx","IntegrateAlgebraic[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",1
231,1,35,35,0.013973,"\int \frac{1}{x^3 \left(a-b x^2\right)} \, dx","IntegrateAlgebraic[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*1/(a*x^2) + (b*Log[x])/a^2 - (b*Log[a - b*x^2])/(2*a^2)","A",1
232,1,36,35,0.0236392,"\int \frac{x^3}{\left(a-b x^2\right)^2} \, dx","IntegrateAlgebraic[x^3/(a - b*x^2)^2,x]","\frac{\log \left(a-b x^2\right)}{2 b^2}-\frac{a}{2 b^2 \left(b x^2-a\right)}","\frac{a}{2 b^2 \left(a-b x^2\right)}+\frac{\log \left(a-b x^2\right)}{2 b^2}",1,"-1/2*a/(b^2*(-a + b*x^2)) + Log[a - b*x^2]/(2*b^2)","A",1
233,1,47,46,0.041501,"\int \frac{x^2}{\left(a-b x^2\right)^2} \, dx","IntegrateAlgebraic[x^2/(a - b*x^2)^2,x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 \sqrt{a} b^{3/2}}-\frac{x}{2 b \left(b x^2-a\right)}","\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,"-1/2*x/(b*(-a + b*x^2)) - ArcTanh[(Sqrt[b]*x)/Sqrt[a]]/(2*Sqrt[a]*b^(3/2))","A",1
234,1,18,17,0.0065887,"\int \frac{x}{\left(a-b x^2\right)^2} \, dx","IntegrateAlgebraic[x/(a - b*x^2)^2,x]","-\frac{1}{2 b \left(b x^2-a\right)}","\frac{1}{2 b \left(a-b x^2\right)}",1,"-1/2*1/(b*(-a + b*x^2))","A",1
235,1,46,46,0.0258515,"\int \frac{1}{\left(a-b x^2\right)^2} \, dx","IntegrateAlgebraic[(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",1
236,1,40,40,0.0274435,"\int \frac{1}{x \left(a-b x^2\right)^2} \, dx","IntegrateAlgebraic[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",1
237,1,58,58,0.0489826,"\int \frac{1}{x^2 \left(a-b x^2\right)^2} \, dx","IntegrateAlgebraic[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 b x^2-2 a}{2 a^2 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,"(-2*a + 3*b*x^2)/(2*a^2*x*(a - b*x^2)) + (3*Sqrt[b]*ArcTanh[(Sqrt[b]*x)/Sqrt[a]])/(2*a^(5/2))","A",1
238,1,53,52,0.0448109,"\int \frac{1}{x^3 \left(a-b x^2\right)^2} \, dx","IntegrateAlgebraic[1/(x^3*(a - b*x^2)^2),x]","-\frac{b \log \left(a-b x^2\right)}{a^3}+\frac{2 b \log (x)}{a^3}+\frac{a-2 b x^2}{2 a^2 x^2 \left(b x^2-a\right)}","-\frac{b \log \left(a-b x^2\right)}{a^3}+\frac{2 b \log (x)}{a^3}+\frac{b}{2 a^2 \left(a-b x^2\right)}-\frac{1}{2 a^2 x^2}",1,"(a - 2*b*x^2)/(2*a^2*x^2*(-a + b*x^2)) + (2*b*Log[x])/a^3 - (b*Log[a - b*x^2])/a^3","A",1
239,1,28,20,0.0144112,"\int \frac{x^3}{\left(a-b x^2\right)^3} \, dx","IntegrateAlgebraic[x^3/(a - b*x^2)^3,x]","\frac{2 b x^2-a}{4 b^2 \left(b x^2-a\right)^2}","\frac{x^4}{4 a \left(a-b x^2\right)^2}",1,"(-a + 2*b*x^2)/(4*b^2*(-a + b*x^2)^2)","A",1
240,1,56,67,0.0428963,"\int \frac{x^2}{\left(a-b x^2\right)^3} \, dx","IntegrateAlgebraic[x^2/(a - b*x^2)^3,x]","\frac{x \left(a+b x^2\right)}{8 a 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{\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*(a + b*x^2))/(8*a*b*(a - b*x^2)^2) - ArcTanh[(Sqrt[b]*x)/Sqrt[a]]/(8*a^(3/2)*b^(3/2))","A",1
241,1,18,17,0.0058647,"\int \frac{x}{\left(a-b x^2\right)^3} \, dx","IntegrateAlgebraic[x/(a - b*x^2)^3,x]","\frac{1}{4 b \left(b x^2-a\right)^2}","\frac{1}{4 b \left(a-b x^2\right)^2}",1,"1/(4*b*(-a + b*x^2)^2)","A",1
242,1,56,64,0.0512207,"\int \frac{1}{\left(a-b x^2\right)^3} \, dx","IntegrateAlgebraic[(a - b*x^2)^(-3),x]","\frac{3 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{b}}+\frac{5 a x-3 b x^3}{8 a^2 \left(a-b x^2\right)^2}","\frac{3 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{b}}+\frac{3 x}{8 a^2 \left(a-b x^2\right)}+\frac{x}{4 a \left(a-b x^2\right)^2}",1,"(5*a*x - 3*b*x^3)/(8*a^2*(a - b*x^2)^2) + (3*ArcTanh[(Sqrt[b]*x)/Sqrt[a]])/(8*a^(5/2)*Sqrt[b])","A",1
243,1,50,57,0.046697,"\int \frac{1}{x \left(a-b x^2\right)^3} \, dx","IntegrateAlgebraic[1/(x*(a - b*x^2)^3),x]","-\frac{\log \left(a-b x^2\right)}{2 a^3}+\frac{\log (x)}{a^3}+\frac{3 a-2 b x^2}{4 a^2 \left(a-b x^2\right)^2}","-\frac{\log \left(a-b x^2\right)}{2 a^3}+\frac{\log (x)}{a^3}+\frac{1}{2 a^2 \left(a-b x^2\right)}+\frac{1}{4 a \left(a-b x^2\right)^2}",1,"(3*a - 2*b*x^2)/(4*a^2*(a - b*x^2)^2) + Log[x]/a^3 - Log[a - b*x^2]/(2*a^3)","A",1
244,1,69,78,0.0608836,"\int \frac{1}{x^2 \left(a-b x^2\right)^3} \, dx","IntegrateAlgebraic[1/(x^2*(a - b*x^2)^3),x]","\frac{15 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{7/2}}+\frac{-8 a^2+25 a b x^2-15 b^2 x^4}{8 a^3 x \left(a-b x^2\right)^2}","\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{5}{8 a^2 x \left(a-b x^2\right)}+\frac{1}{4 a x \left(a-b x^2\right)^2}",1,"(-8*a^2 + 25*a*b*x^2 - 15*b^2*x^4)/(8*a^3*x*(a - b*x^2)^2) + (15*Sqrt[b]*ArcTanh[(Sqrt[b]*x)/Sqrt[a]])/(8*a^(7/2))","A",1
245,1,67,69,0.0716726,"\int \frac{1}{x^3 \left(a-b x^2\right)^3} \, dx","IntegrateAlgebraic[1/(x^3*(a - b*x^2)^3),x]","-\frac{3 b \log \left(a-b x^2\right)}{2 a^4}+\frac{3 b \log (x)}{a^4}+\frac{-2 a^2+9 a b x^2-6 b^2 x^4}{4 a^3 x^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{b}{a^3 \left(a-b x^2\right)}-\frac{1}{2 a^3 x^2}+\frac{b}{4 a^2 \left(a-b x^2\right)^2}",1,"(-2*a^2 + 9*a*b*x^2 - 6*b^2*x^4)/(4*a^3*x^2*(a - b*x^2)^2) + (3*b*Log[x])/a^4 - (3*b*Log[a - b*x^2])/(2*a^4)","A",1
246,1,28,36,0.0157091,"\int \frac{x^3}{\left(a-b x^2\right)^5} \, dx","IntegrateAlgebraic[x^3/(a - b*x^2)^5,x]","\frac{4 b x^2-a}{24 b^2 \left(b x^2-a\right)^4}","\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 + 4*b*x^2)/(24*b^2*(-a + b*x^2)^4)","A",1
247,1,81,109,0.0661588,"\int \frac{x^2}{\left(a-b x^2\right)^5} \, dx","IntegrateAlgebraic[x^2/(a - b*x^2)^5,x]","\frac{15 a^3 x+73 a^2 b x^3-55 a b^2 x^5+15 b^3 x^7}{384 a^3 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 \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,"(15*a^3*x + 73*a^2*b*x^3 - 55*a*b^2*x^5 + 15*b^3*x^7)/(384*a^3*b*(a - b*x^2)^4) - (5*ArcTanh[(Sqrt[b]*x)/Sqrt[a]])/(128*a^(7/2)*b^(3/2))","A",1
248,1,18,17,0.0071043,"\int \frac{x}{\left(a-b x^2\right)^5} \, dx","IntegrateAlgebraic[x/(a - b*x^2)^5,x]","\frac{1}{8 b \left(b x^2-a\right)^4}","\frac{1}{8 b \left(a-b x^2\right)^4}",1,"1/(8*b*(-a + b*x^2)^4)","A",1
249,1,78,100,0.0607769,"\int \frac{1}{\left(a-b x^2\right)^5} \, dx","IntegrateAlgebraic[(a - b*x^2)^(-5),x]","\frac{35 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{128 a^{9/2} \sqrt{b}}+\frac{x \left(279 a^3-511 a^2 b x^2+385 a b^2 x^4-105 b^3 x^6\right)}{384 a^4 \left(a-b x^2\right)^4}","\frac{35 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{128 a^{9/2} \sqrt{b}}+\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{x}{8 a \left(a-b x^2\right)^4}",1,"(x*(279*a^3 - 511*a^2*b*x^2 + 385*a*b^2*x^4 - 105*b^3*x^6))/(384*a^4*(a - b*x^2)^4) + (35*ArcTanh[(Sqrt[b]*x)/Sqrt[a]])/(128*a^(9/2)*Sqrt[b])","A",1
250,1,72,91,0.0498965,"\int \frac{1}{x \left(a-b x^2\right)^5} \, dx","IntegrateAlgebraic[1/(x*(a - b*x^2)^5),x]","-\frac{\log \left(a-b x^2\right)}{2 a^5}+\frac{\log (x)}{a^5}+\frac{25 a^3-52 a^2 b x^2+42 a b^2 x^4-12 b^3 x^6}{24 a^4 \left(a-b x^2\right)^4}","-\frac{\log \left(a-b x^2\right)}{2 a^5}+\frac{\log (x)}{a^5}+\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{1}{8 a \left(a-b x^2\right)^4}",1,"(25*a^3 - 52*a^2*b*x^2 + 42*a*b^2*x^4 - 12*b^3*x^6)/(24*a^4*(a - b*x^2)^4) + Log[x]/a^5 - Log[a - b*x^2]/(2*a^5)","A",1
251,1,91,118,0.0710211,"\int \frac{1}{x^2 \left(a-b x^2\right)^5} \, dx","IntegrateAlgebraic[1/(x^2*(a - b*x^2)^5),x]","\frac{315 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{128 a^{11/2}}+\frac{-128 a^4+837 a^3 b x^2-1533 a^2 b^2 x^4+1155 a b^3 x^6-315 b^4 x^8}{128 a^5 x \left(a-b x^2\right)^4}","\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{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{1}{8 a x \left(a-b x^2\right)^4}",1,"(-128*a^4 + 837*a^3*b*x^2 - 1533*a^2*b^2*x^4 + 1155*a*b^3*x^6 - 315*b^4*x^8)/(128*a^5*x*(a - b*x^2)^4) + (315*Sqrt[b]*ArcTanh[(Sqrt[b]*x)/Sqrt[a]])/(128*a^(11/2))","A",1
252,1,89,106,0.0861246,"\int \frac{1}{x^3 \left(a-b x^2\right)^5} \, dx","IntegrateAlgebraic[1/(x^3*(a - b*x^2)^5),x]","-\frac{5 b \log \left(a-b x^2\right)}{2 a^6}+\frac{5 b \log (x)}{a^6}+\frac{-12 a^4+125 a^3 b x^2-260 a^2 b^2 x^4+210 a b^3 x^6-60 b^4 x^8}{24 a^5 x^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{2 b}{a^5 \left(a-b x^2\right)}-\frac{1}{2 a^5 x^2}+\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}",1,"(-12*a^4 + 125*a^3*b*x^2 - 260*a^2*b^2*x^4 + 210*a*b^3*x^6 - 60*b^4*x^8)/(24*a^5*x^2*(a - b*x^2)^4) + (5*b*Log[x])/a^6 - (5*b*Log[a - b*x^2])/(2*a^6)","A",1
253,1,15,15,0.0077036,"\int \frac{1}{x \left(1+b x^2\right)} \, dx","IntegrateAlgebraic[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",1
254,1,17,18,0.0088878,"\int \frac{1}{x \left(-1+b x^2\right)} \, dx","IntegrateAlgebraic[1/(x*(-1 + b*x^2)),x]","\frac{1}{2} \log \left(b x^2-1\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",1
255,1,26,26,0.0108437,"\int \frac{1}{x^3 \left(1+b x^2\right)} \, dx","IntegrateAlgebraic[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*1/x^2 - b*Log[x] + (b*Log[1 + b*x^2])/2","A",1
256,1,26,27,0.0092733,"\int \frac{1}{x^3 \left(-1+b x^2\right)} \, dx","IntegrateAlgebraic[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(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",1
257,1,28,30,0.0187967,"\int \frac{1}{-1+a+a x^2} \, dx","IntegrateAlgebraic[(-1 + a + a*x^2)^(-1),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a-1}}\right)}{\sqrt{a-1} \sqrt{a}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{1-a}}\right)}{\sqrt{(1-a) a}}",1,"ArcTan[(Sqrt[a]*x)/Sqrt[-1 + a]]/(Sqrt[-1 + a]*Sqrt[a])","A",1
258,1,50,37,0.0298052,"\int \frac{1}{-c-d+(c-d) x^2} \, dx","IntegrateAlgebraic[(-c - d + (c - d)*x^2)^(-1),x]","-\frac{\tan ^{-1}\left(\frac{x \sqrt{-c-d} \sqrt{c-d}}{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,"-(ArcTan[(Sqrt[-c - d]*Sqrt[c - d]*x)/(c + d)]/(Sqrt[-c - d]*Sqrt[c - d]))","A",1
259,1,28,28,0.0201356,"\int \frac{1}{x \left(1+b x^2\right)^2} \, dx","IntegrateAlgebraic[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",1
260,1,28,30,0.020378,"\int \frac{1}{x \left(-1+b x^2\right)^2} \, dx","IntegrateAlgebraic[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(1-b x^2\right)}-\frac{1}{2} \log \left(1-b x^2\right)+\log (x)",1,"-1/2*1/(-1 + b*x^2) + Log[x] - Log[-1 + b*x^2]/2","A",1
261,1,36,34,0.027248,"\int \frac{1}{a+(b-a c) x^2} \, dx","IntegrateAlgebraic[(a + (b - a*c)*x^2)^(-1),x]","\frac{\tanh ^{-1}\left(\frac{x \sqrt{a c-b}}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{a c-b}}","\frac{\tan ^{-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
262,1,36,34,0.0213675,"\int \frac{1}{a-(b-a c) x^2} \, dx","IntegrateAlgebraic[(a - (b - a*c)*x^2)^(-1),x]","\frac{\tan ^{-1}\left(\frac{x \sqrt{a c-b}}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{a c-b}}","\frac{\tanh ^{-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
263,1,50,50,0.0378267,"\int \frac{1}{c (a-d)-(b-c) x^2} \, dx","IntegrateAlgebraic[(c*(a - d) - (b - c)*x^2)^(-1),x]","\frac{\tan ^{-1}\left(\frac{x \sqrt{c-b}}{\sqrt{c} \sqrt{a-d}}\right)}{\sqrt{c} \sqrt{a-d} \sqrt{c-b}}","\frac{\tanh ^{-1}\left(\frac{x \sqrt{b-c}}{\sqrt{c} \sqrt{a-d}}\right)}{\sqrt{c} \sqrt{a-d} \sqrt{b-c}}",1,"ArcTan[(Sqrt[-b + c]*x)/(Sqrt[c]*Sqrt[a - d])]/(Sqrt[c]*Sqrt[-b + c]*Sqrt[a - d])","A",1
264,1,21,21,0.0085978,"\int x^{7/2} \left(a+b x^2\right) \, dx","IntegrateAlgebraic[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",1
265,1,21,21,0.008209,"\int x^{5/2} \left(a+b x^2\right) \, dx","IntegrateAlgebraic[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",1
266,1,21,21,0.0079959,"\int x^{3/2} \left(a+b x^2\right) \, dx","IntegrateAlgebraic[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",1
267,1,21,21,0.0077336,"\int \sqrt{x} \left(a+b x^2\right) \, dx","IntegrateAlgebraic[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",1
268,1,19,19,0.0071044,"\int \frac{a+b x^2}{\sqrt{x}} \, dx","IntegrateAlgebraic[(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",1
269,1,19,19,0.0102236,"\int \frac{a+b x^2}{x^{3/2}} \, dx","IntegrateAlgebraic[(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",1
270,1,19,19,0.0093681,"\int \frac{a+b x^2}{x^{5/2}} \, dx","IntegrateAlgebraic[(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",1
271,1,19,19,0.0101621,"\int \frac{a+b x^2}{x^{7/2}} \, dx","IntegrateAlgebraic[(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",1
272,1,36,36,0.010938,"\int x^{7/2} \left(a+b x^2\right)^2 \, dx","IntegrateAlgebraic[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",1
273,1,36,36,0.0107543,"\int x^{5/2} \left(a+b x^2\right)^2 \, dx","IntegrateAlgebraic[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",1
274,1,36,36,0.0109767,"\int x^{3/2} \left(a+b x^2\right)^2 \, dx","IntegrateAlgebraic[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",1
275,1,36,36,0.0103899,"\int \sqrt{x} \left(a+b x^2\right)^2 \, dx","IntegrateAlgebraic[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",1
276,1,34,34,0.0111246,"\int \frac{\left(a+b x^2\right)^2}{\sqrt{x}} \, dx","IntegrateAlgebraic[(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",1
277,1,34,34,0.0132179,"\int \frac{\left(a+b x^2\right)^2}{x^{3/2}} \, dx","IntegrateAlgebraic[(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",1
278,1,34,34,0.0128826,"\int \frac{\left(a+b x^2\right)^2}{x^{5/2}} \, dx","IntegrateAlgebraic[(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",1
279,1,34,34,0.0137179,"\int \frac{\left(a+b x^2\right)^2}{x^{7/2}} \, dx","IntegrateAlgebraic[(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",1
280,1,51,51,0.014795,"\int x^{7/2} \left(a+b x^2\right)^3 \, dx","IntegrateAlgebraic[x^(7/2)*(a + b*x^2)^3,x]","\frac{2}{9} a^3 x^{9/2}+\frac{6}{13} a^2 b x^{13/2}+\frac{6}{17} a b^2 x^{17/2}+\frac{2}{21} b^3 x^{21/2}","\frac{2}{9} a^3 x^{9/2}+\frac{6}{13} a^2 b x^{13/2}+\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",1
281,1,51,51,0.014367,"\int x^{5/2} \left(a+b x^2\right)^3 \, dx","IntegrateAlgebraic[x^(5/2)*(a + b*x^2)^3,x]","\frac{2}{7} a^3 x^{7/2}+\frac{6}{11} a^2 b x^{11/2}+\frac{2}{5} a b^2 x^{15/2}+\frac{2}{19} b^3 x^{19/2}","\frac{2}{7} a^3 x^{7/2}+\frac{6}{11} a^2 b x^{11/2}+\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",1
282,1,51,51,0.0139136,"\int x^{3/2} \left(a+b x^2\right)^3 \, dx","IntegrateAlgebraic[x^(3/2)*(a + b*x^2)^3,x]","\frac{2}{5} a^3 x^{5/2}+\frac{2}{3} a^2 b x^{9/2}+\frac{6}{13} a b^2 x^{13/2}+\frac{2}{17} b^3 x^{17/2}","\frac{2}{5} a^3 x^{5/2}+\frac{2}{3} a^2 b x^{9/2}+\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",1
283,1,51,51,0.0137063,"\int \sqrt{x} \left(a+b x^2\right)^3 \, dx","IntegrateAlgebraic[Sqrt[x]*(a + b*x^2)^3,x]","\frac{2}{3} a^3 x^{3/2}+\frac{6}{7} a^2 b x^{7/2}+\frac{6}{11} a b^2 x^{11/2}+\frac{2}{15} b^3 x^{15/2}","\frac{2}{3} a^3 x^{3/2}+\frac{6}{7} a^2 b x^{7/2}+\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",1
284,1,49,49,0.0135567,"\int \frac{\left(a+b x^2\right)^3}{\sqrt{x}} \, dx","IntegrateAlgebraic[(a + b*x^2)^3/Sqrt[x],x]","2 a^3 \sqrt{x}+\frac{6}{5} a^2 b x^{5/2}+\frac{2}{3} a b^2 x^{9/2}+\frac{2}{13} b^3 x^{13/2}","2 a^3 \sqrt{x}+\frac{6}{5} a^2 b x^{5/2}+\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",1
285,1,47,47,0.0183328,"\int \frac{\left(a+b x^2\right)^3}{x^{3/2}} \, dx","IntegrateAlgebraic[(a + b*x^2)^3/x^(3/2),x]","-\frac{2 a^3}{\sqrt{x}}+2 a^2 b x^{3/2}+\frac{6}{7} a b^2 x^{7/2}+\frac{2}{11} b^3 x^{11/2}","-\frac{2 a^3}{\sqrt{x}}+2 a^2 b x^{3/2}+\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",1
286,1,49,49,0.0188548,"\int \frac{\left(a+b x^2\right)^3}{x^{5/2}} \, dx","IntegrateAlgebraic[(a + b*x^2)^3/x^(5/2),x]","-\frac{2 a^3}{3 x^{3/2}}+6 a^2 b \sqrt{x}+\frac{6}{5} a b^2 x^{5/2}+\frac{2}{9} b^3 x^{9/2}","-\frac{2 a^3}{3 x^{3/2}}+6 a^2 b \sqrt{x}+\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",1
287,1,47,47,0.0205766,"\int \frac{\left(a+b x^2\right)^3}{x^{7/2}} \, dx","IntegrateAlgebraic[(a + b*x^2)^3/x^(7/2),x]","-\frac{2 a^3}{5 x^{5/2}}-\frac{6 a^2 b}{\sqrt{x}}+2 a b^2 x^{3/2}+\frac{2}{7} b^3 x^{7/2}","-\frac{2 a^3}{5 x^{5/2}}-\frac{6 a^2 b}{\sqrt{x}}+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",1
288,1,136,215,0.138476,"\int \frac{x^{7/2}}{a+b x^2} \, dx","IntegrateAlgebraic[x^(7/2)/(a + b*x^2),x]","-\frac{a^{5/4} \tan ^{-1}\left(\frac{\frac{\sqrt[4]{a}}{\sqrt{2} \sqrt[4]{b}}-\frac{\sqrt[4]{b} x}{\sqrt{2} \sqrt[4]{a}}}{\sqrt{x}}\right)}{\sqrt{2} b^{9/4}}+\frac{a^{5/4} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}}{\sqrt{a}+\sqrt{b} x}\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[(a^(1/4)/(Sqrt[2]*b^(1/4)) - (b^(1/4)*x)/(Sqrt[2]*a^(1/4)))/Sqrt[x]])/(Sqrt[2]*b^(9/4)) + (a^(5/4)*ArcTanh[(Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x])/(Sqrt[a] + Sqrt[b]*x)])/(Sqrt[2]*b^(9/4))","A",1
289,1,124,204,0.1034272,"\int \frac{x^{5/2}}{a+b x^2} \, dx","IntegrateAlgebraic[x^(5/2)/(a + b*x^2),x]","\frac{a^{3/4} \tan ^{-1}\left(\frac{\frac{\sqrt[4]{a}}{\sqrt{2} \sqrt[4]{b}}-\frac{\sqrt[4]{b} x}{\sqrt{2} \sqrt[4]{a}}}{\sqrt{x}}\right)}{\sqrt{2} b^{7/4}}+\frac{a^{3/4} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}}{\sqrt{a}+\sqrt{b} x}\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[(a^(1/4)/(Sqrt[2]*b^(1/4)) - (b^(1/4)*x)/(Sqrt[2]*a^(1/4)))/Sqrt[x]])/(Sqrt[2]*b^(7/4)) + (a^(3/4)*ArcTanh[(Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x])/(Sqrt[a] + Sqrt[b]*x)])/(Sqrt[2]*b^(7/4))","A",1
290,1,123,202,0.0979803,"\int \frac{x^{3/2}}{a+b x^2} \, dx","IntegrateAlgebraic[x^(3/2)/(a + b*x^2),x]","\frac{\sqrt[4]{a} \tan ^{-1}\left(\frac{\frac{\sqrt[4]{a}}{\sqrt{2} \sqrt[4]{b}}-\frac{\sqrt[4]{b} x}{\sqrt{2} \sqrt[4]{a}}}{\sqrt{x}}\right)}{\sqrt{2} b^{5/4}}-\frac{\sqrt[4]{a} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}}{\sqrt{a}+\sqrt{b} x}\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[(a^(1/4)/(Sqrt[2]*b^(1/4)) - (b^(1/4)*x)/(Sqrt[2]*a^(1/4)))/Sqrt[x]])/(Sqrt[2]*b^(5/4)) - (a^(1/4)*ArcTanh[(Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x])/(Sqrt[a] + Sqrt[b]*x)])/(Sqrt[2]*b^(5/4))","A",1
291,1,114,192,0.0924244,"\int \frac{\sqrt{x}}{a+b x^2} \, dx","IntegrateAlgebraic[Sqrt[x]/(a + b*x^2),x]","-\frac{\tan ^{-1}\left(\frac{\frac{\sqrt[4]{a}}{\sqrt{2} \sqrt[4]{b}}-\frac{\sqrt[4]{b} x}{\sqrt{2} \sqrt[4]{a}}}{\sqrt{x}}\right)}{\sqrt{2} \sqrt[4]{a} b^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}}{\sqrt{a}+\sqrt{b} x}\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[(a^(1/4)/(Sqrt[2]*b^(1/4)) - (b^(1/4)*x)/(Sqrt[2]*a^(1/4)))/Sqrt[x]]/(Sqrt[2]*a^(1/4)*b^(3/4))) - ArcTanh[(Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x])/(Sqrt[a] + Sqrt[b]*x)]/(Sqrt[2]*a^(1/4)*b^(3/4))","A",1
292,1,113,192,0.0879213,"\int \frac{1}{\sqrt{x} \left(a+b x^2\right)} \, dx","IntegrateAlgebraic[1/(Sqrt[x]*(a + b*x^2)),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}}{\sqrt{a}+\sqrt{b} x}\right)}{\sqrt{2} a^{3/4} \sqrt[4]{b}}-\frac{\tan ^{-1}\left(\frac{\frac{\sqrt[4]{a}}{\sqrt{2} \sqrt[4]{b}}-\frac{\sqrt[4]{b} x}{\sqrt{2} \sqrt[4]{a}}}{\sqrt{x}}\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[(a^(1/4)/(Sqrt[2]*b^(1/4)) - (b^(1/4)*x)/(Sqrt[2]*a^(1/4)))/Sqrt[x]]/(Sqrt[2]*a^(3/4)*b^(1/4))) + ArcTanh[(Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x])/(Sqrt[a] + Sqrt[b]*x)]/(Sqrt[2]*a^(3/4)*b^(1/4))","A",1
293,1,122,202,0.1042713,"\int \frac{1}{x^{3/2} \left(a+b x^2\right)} \, dx","IntegrateAlgebraic[1/(x^(3/2)*(a + b*x^2)),x]","\frac{\sqrt[4]{b} \tan ^{-1}\left(\frac{\frac{\sqrt[4]{a}}{\sqrt{2} \sqrt[4]{b}}-\frac{\sqrt[4]{b} x}{\sqrt{2} \sqrt[4]{a}}}{\sqrt{x}}\right)}{\sqrt{2} a^{5/4}}+\frac{\sqrt[4]{b} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}}{\sqrt{a}+\sqrt{b} x}\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[(a^(1/4)/(Sqrt[2]*b^(1/4)) - (b^(1/4)*x)/(Sqrt[2]*a^(1/4)))/Sqrt[x]])/(Sqrt[2]*a^(5/4)) + (b^(1/4)*ArcTanh[(Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x])/(Sqrt[a] + Sqrt[b]*x)])/(Sqrt[2]*a^(5/4))","A",1
294,1,125,204,0.1084742,"\int \frac{1}{x^{5/2} \left(a+b x^2\right)} \, dx","IntegrateAlgebraic[1/(x^(5/2)*(a + b*x^2)),x]","\frac{b^{3/4} \tan ^{-1}\left(\frac{\frac{\sqrt[4]{a}}{\sqrt{2} \sqrt[4]{b}}-\frac{\sqrt[4]{b} x}{\sqrt{2} \sqrt[4]{a}}}{\sqrt{x}}\right)}{\sqrt{2} a^{7/4}}-\frac{b^{3/4} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}}{\sqrt{a}+\sqrt{b} x}\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[(a^(1/4)/(Sqrt[2]*b^(1/4)) - (b^(1/4)*x)/(Sqrt[2]*a^(1/4)))/Sqrt[x]])/(Sqrt[2]*a^(7/4)) - (b^(3/4)*ArcTanh[(Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x])/(Sqrt[a] + Sqrt[b]*x)])/(Sqrt[2]*a^(7/4))","A",1
295,1,137,215,0.1229973,"\int \frac{1}{x^{7/2} \left(a+b x^2\right)} \, dx","IntegrateAlgebraic[1/(x^(7/2)*(a + b*x^2)),x]","-\frac{b^{5/4} \tan ^{-1}\left(\frac{\frac{\sqrt[4]{a}}{\sqrt{2} \sqrt[4]{b}}-\frac{\sqrt[4]{b} x}{\sqrt{2} \sqrt[4]{a}}}{\sqrt{x}}\right)}{\sqrt{2} a^{9/4}}-\frac{b^{5/4} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}}{\sqrt{a}+\sqrt{b} x}\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[(a^(1/4)/(Sqrt[2]*b^(1/4)) - (b^(1/4)*x)/(Sqrt[2]*a^(1/4)))/Sqrt[x]])/(Sqrt[2]*a^(9/4)) - (b^(5/4)*ArcTanh[(Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x])/(Sqrt[a] + Sqrt[b]*x)])/(Sqrt[2]*a^(9/4))","A",1
296,1,150,230,0.1905596,"\int \frac{x^{7/2}}{\left(a+b x^2\right)^2} \, dx","IntegrateAlgebraic[x^(7/2)/(a + b*x^2)^2,x]","\frac{5 \sqrt[4]{a} \tan ^{-1}\left(\frac{\frac{\sqrt[4]{a}}{\sqrt{2} \sqrt[4]{b}}-\frac{\sqrt[4]{b} x}{\sqrt{2} \sqrt[4]{a}}}{\sqrt{x}}\right)}{4 \sqrt{2} b^{9/4}}-\frac{5 \sqrt[4]{a} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}}{\sqrt{a}+\sqrt{b} x}\right)}{4 \sqrt{2} b^{9/4}}+\frac{a \sqrt{x}}{2 b^2 \left(a+b x^2\right)}+\frac{2 \sqrt{x}}{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,"(2*Sqrt[x])/b^2 + (a*Sqrt[x])/(2*b^2*(a + b*x^2)) + (5*a^(1/4)*ArcTan[(a^(1/4)/(Sqrt[2]*b^(1/4)) - (b^(1/4)*x)/(Sqrt[2]*a^(1/4)))/Sqrt[x]])/(4*Sqrt[2]*b^(9/4)) - (5*a^(1/4)*ArcTanh[(Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x])/(Sqrt[a] + Sqrt[b]*x)])/(4*Sqrt[2]*b^(9/4))","A",1
297,1,139,218,0.1892868,"\int \frac{x^{5/2}}{\left(a+b x^2\right)^2} \, dx","IntegrateAlgebraic[x^(5/2)/(a + b*x^2)^2,x]","-\frac{3 \tan ^{-1}\left(\frac{\frac{\sqrt[4]{a}}{\sqrt{2} \sqrt[4]{b}}-\frac{\sqrt[4]{b} x}{\sqrt{2} \sqrt[4]{a}}}{\sqrt{x}}\right)}{4 \sqrt{2} \sqrt[4]{a} b^{7/4}}-\frac{3 \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}}{\sqrt{a}+\sqrt{b} x}\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,"-1/2*x^(3/2)/(b*(a + b*x^2)) - (3*ArcTan[(a^(1/4)/(Sqrt[2]*b^(1/4)) - (b^(1/4)*x)/(Sqrt[2]*a^(1/4)))/Sqrt[x]])/(4*Sqrt[2]*a^(1/4)*b^(7/4)) - (3*ArcTanh[(Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x])/(Sqrt[a] + Sqrt[b]*x)])/(4*Sqrt[2]*a^(1/4)*b^(7/4))","A",1
298,1,139,218,0.1857676,"\int \frac{x^{3/2}}{\left(a+b x^2\right)^2} \, dx","IntegrateAlgebraic[x^(3/2)/(a + b*x^2)^2,x]","-\frac{\tan ^{-1}\left(\frac{\frac{\sqrt[4]{a}}{\sqrt{2} \sqrt[4]{b}}-\frac{\sqrt[4]{b} x}{\sqrt{2} \sqrt[4]{a}}}{\sqrt{x}}\right)}{4 \sqrt{2} a^{3/4} b^{5/4}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}}{\sqrt{a}+\sqrt{b} x}\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,"-1/2*Sqrt[x]/(b*(a + b*x^2)) - ArcTan[(a^(1/4)/(Sqrt[2]*b^(1/4)) - (b^(1/4)*x)/(Sqrt[2]*a^(1/4)))/Sqrt[x]]/(4*Sqrt[2]*a^(3/4)*b^(5/4)) + ArcTanh[(Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x])/(Sqrt[a] + Sqrt[b]*x)]/(4*Sqrt[2]*a^(3/4)*b^(5/4))","A",1
299,1,139,218,0.1851413,"\int \frac{\sqrt{x}}{\left(a+b x^2\right)^2} \, dx","IntegrateAlgebraic[Sqrt[x]/(a + b*x^2)^2,x]","-\frac{\tan ^{-1}\left(\frac{\frac{\sqrt[4]{a}}{\sqrt{2} \sqrt[4]{b}}-\frac{\sqrt[4]{b} x}{\sqrt{2} \sqrt[4]{a}}}{\sqrt{x}}\right)}{4 \sqrt{2} a^{5/4} b^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}}{\sqrt{a}+\sqrt{b} x}\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[(a^(1/4)/(Sqrt[2]*b^(1/4)) - (b^(1/4)*x)/(Sqrt[2]*a^(1/4)))/Sqrt[x]]/(4*Sqrt[2]*a^(5/4)*b^(3/4)) - ArcTanh[(Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x])/(Sqrt[a] + Sqrt[b]*x)]/(4*Sqrt[2]*a^(5/4)*b^(3/4))","A",1
300,1,139,218,0.1808386,"\int \frac{1}{\sqrt{x} \left(a+b x^2\right)^2} \, dx","IntegrateAlgebraic[1/(Sqrt[x]*(a + b*x^2)^2),x]","-\frac{3 \tan ^{-1}\left(\frac{\frac{\sqrt[4]{a}}{\sqrt{2} \sqrt[4]{b}}-\frac{\sqrt[4]{b} x}{\sqrt{2} \sqrt[4]{a}}}{\sqrt{x}}\right)}{4 \sqrt{2} a^{7/4} \sqrt[4]{b}}+\frac{3 \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}}{\sqrt{a}+\sqrt{b} x}\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[(a^(1/4)/(Sqrt[2]*b^(1/4)) - (b^(1/4)*x)/(Sqrt[2]*a^(1/4)))/Sqrt[x]])/(4*Sqrt[2]*a^(7/4)*b^(1/4)) + (3*ArcTanh[(Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x])/(Sqrt[a] + Sqrt[b]*x)])/(4*Sqrt[2]*a^(7/4)*b^(1/4))","A",1
301,1,150,230,0.2090235,"\int \frac{1}{x^{3/2} \left(a+b x^2\right)^2} \, dx","IntegrateAlgebraic[1/(x^(3/2)*(a + b*x^2)^2),x]","\frac{5 \sqrt[4]{b} \tan ^{-1}\left(\frac{\frac{\sqrt[4]{a}}{\sqrt{2} \sqrt[4]{b}}-\frac{\sqrt[4]{b} x}{\sqrt{2} \sqrt[4]{a}}}{\sqrt{x}}\right)}{4 \sqrt{2} a^{9/4}}+\frac{5 \sqrt[4]{b} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}}{\sqrt{a}+\sqrt{b} x}\right)}{4 \sqrt{2} a^{9/4}}-\frac{b x^{3/2}}{2 a^2 \left(a+b x^2\right)}-\frac{2}{a^2 \sqrt{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)}",1,"-2/(a^2*Sqrt[x]) - (b*x^(3/2))/(2*a^2*(a + b*x^2)) + (5*b^(1/4)*ArcTan[(a^(1/4)/(Sqrt[2]*b^(1/4)) - (b^(1/4)*x)/(Sqrt[2]*a^(1/4)))/Sqrt[x]])/(4*Sqrt[2]*a^(9/4)) + (5*b^(1/4)*ArcTanh[(Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x])/(Sqrt[a] + Sqrt[b]*x)])/(4*Sqrt[2]*a^(9/4))","A",1
302,1,152,230,0.2164233,"\int \frac{1}{x^{5/2} \left(a+b x^2\right)^2} \, dx","IntegrateAlgebraic[1/(x^(5/2)*(a + b*x^2)^2),x]","\frac{7 b^{3/4} \tan ^{-1}\left(\frac{\frac{\sqrt[4]{a}}{\sqrt{2} \sqrt[4]{b}}-\frac{\sqrt[4]{b} x}{\sqrt{2} \sqrt[4]{a}}}{\sqrt{x}}\right)}{4 \sqrt{2} a^{11/4}}-\frac{7 b^{3/4} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}}{\sqrt{a}+\sqrt{b} x}\right)}{4 \sqrt{2} a^{11/4}}-\frac{b \sqrt{x}}{2 a^2 \left(a+b x^2\right)}-\frac{2}{3 a^2 x^{3/2}}","\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,"-2/(3*a^2*x^(3/2)) - (b*Sqrt[x])/(2*a^2*(a + b*x^2)) + (7*b^(3/4)*ArcTan[(a^(1/4)/(Sqrt[2]*b^(1/4)) - (b^(1/4)*x)/(Sqrt[2]*a^(1/4)))/Sqrt[x]])/(4*Sqrt[2]*a^(11/4)) - (7*b^(3/4)*ArcTanh[(Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x])/(Sqrt[a] + Sqrt[b]*x)])/(4*Sqrt[2]*a^(11/4))","A",1
303,1,164,243,0.2349718,"\int \frac{1}{x^{7/2} \left(a+b x^2\right)^2} \, dx","IntegrateAlgebraic[1/(x^(7/2)*(a + b*x^2)^2),x]","-\frac{9 b^{5/4} \tan ^{-1}\left(\frac{\frac{\sqrt[4]{a}}{\sqrt{2} \sqrt[4]{b}}-\frac{\sqrt[4]{b} x}{\sqrt{2} \sqrt[4]{a}}}{\sqrt{x}}\right)}{4 \sqrt{2} a^{13/4}}-\frac{9 b^{5/4} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}}{\sqrt{a}+\sqrt{b} x}\right)}{4 \sqrt{2} a^{13/4}}+\frac{-4 a^2+36 a b x^2+45 b^2 x^4}{10 a^4 x^{5/2}+10 a^3 b x^{9/2}}","\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,"(-4*a^2 + 36*a*b*x^2 + 45*b^2*x^4)/(10*a^4*x^(5/2) + 10*a^3*b*x^(9/2)) - (9*b^(5/4)*ArcTan[(a^(1/4)/(Sqrt[2]*b^(1/4)) - (b^(1/4)*x)/(Sqrt[2]*a^(1/4)))/Sqrt[x]])/(4*Sqrt[2]*a^(13/4)) - (9*b^(5/4)*ArcTanh[(Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x])/(Sqrt[a] + Sqrt[b]*x)])/(4*Sqrt[2]*a^(13/4))","A",1
304,1,151,239,0.1723212,"\int \frac{x^{7/2}}{\left(a+b x^2\right)^3} \, dx","IntegrateAlgebraic[x^(7/2)/(a + b*x^2)^3,x]","-\frac{5 \tan ^{-1}\left(\frac{\frac{\sqrt[4]{a}}{\sqrt{2} \sqrt[4]{b}}-\frac{\sqrt[4]{b} x}{\sqrt{2} \sqrt[4]{a}}}{\sqrt{x}}\right)}{32 \sqrt{2} a^{3/4} b^{9/4}}+\frac{5 \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}}{\sqrt{a}+\sqrt{b} x}\right)}{32 \sqrt{2} a^{3/4} b^{9/4}}+\frac{-5 a \sqrt{x}-9 b x^{5/2}}{16 b^2 \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,"(-5*a*Sqrt[x] - 9*b*x^(5/2))/(16*b^2*(a + b*x^2)^2) - (5*ArcTan[(a^(1/4)/(Sqrt[2]*b^(1/4)) - (b^(1/4)*x)/(Sqrt[2]*a^(1/4)))/Sqrt[x]])/(32*Sqrt[2]*a^(3/4)*b^(9/4)) + (5*ArcTanh[(Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x])/(Sqrt[a] + Sqrt[b]*x)])/(32*Sqrt[2]*a^(3/4)*b^(9/4))","A",1
305,1,154,242,0.1806349,"\int \frac{x^{5/2}}{\left(a+b x^2\right)^3} \, dx","IntegrateAlgebraic[x^(5/2)/(a + b*x^2)^3,x]","-\frac{3 \tan ^{-1}\left(\frac{\frac{\sqrt[4]{a}}{\sqrt{2} \sqrt[4]{b}}-\frac{\sqrt[4]{b} x}{\sqrt{2} \sqrt[4]{a}}}{\sqrt{x}}\right)}{32 \sqrt{2} a^{5/4} b^{7/4}}-\frac{3 \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}}{\sqrt{a}+\sqrt{b} x}\right)}{32 \sqrt{2} a^{5/4} b^{7/4}}+\frac{3 b x^{7/2}-a x^{3/2}}{16 a 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,"(-(a*x^(3/2)) + 3*b*x^(7/2))/(16*a*b*(a + b*x^2)^2) - (3*ArcTan[(a^(1/4)/(Sqrt[2]*b^(1/4)) - (b^(1/4)*x)/(Sqrt[2]*a^(1/4)))/Sqrt[x]])/(32*Sqrt[2]*a^(5/4)*b^(7/4)) - (3*ArcTanh[(Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x])/(Sqrt[a] + Sqrt[b]*x)])/(32*Sqrt[2]*a^(5/4)*b^(7/4))","A",1
306,1,153,242,0.1667902,"\int \frac{x^{3/2}}{\left(a+b x^2\right)^3} \, dx","IntegrateAlgebraic[x^(3/2)/(a + b*x^2)^3,x]","-\frac{3 \tan ^{-1}\left(\frac{\frac{\sqrt[4]{a}}{\sqrt{2} \sqrt[4]{b}}-\frac{\sqrt[4]{b} x}{\sqrt{2} \sqrt[4]{a}}}{\sqrt{x}}\right)}{32 \sqrt{2} a^{7/4} b^{5/4}}+\frac{3 \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}}{\sqrt{a}+\sqrt{b} x}\right)}{32 \sqrt{2} a^{7/4} b^{5/4}}+\frac{b x^{5/2}-3 a \sqrt{x}}{16 a 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,"(-3*a*Sqrt[x] + b*x^(5/2))/(16*a*b*(a + b*x^2)^2) - (3*ArcTan[(a^(1/4)/(Sqrt[2]*b^(1/4)) - (b^(1/4)*x)/(Sqrt[2]*a^(1/4)))/Sqrt[x]])/(32*Sqrt[2]*a^(7/4)*b^(5/4)) + (3*ArcTanh[(Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x])/(Sqrt[a] + Sqrt[b]*x)])/(32*Sqrt[2]*a^(7/4)*b^(5/4))","A",1
307,1,151,239,0.1694161,"\int \frac{\sqrt{x}}{\left(a+b x^2\right)^3} \, dx","IntegrateAlgebraic[Sqrt[x]/(a + b*x^2)^3,x]","-\frac{5 \tan ^{-1}\left(\frac{\frac{\sqrt[4]{a}}{\sqrt{2} \sqrt[4]{b}}-\frac{\sqrt[4]{b} x}{\sqrt{2} \sqrt[4]{a}}}{\sqrt{x}}\right)}{32 \sqrt{2} a^{9/4} b^{3/4}}-\frac{5 \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}}{\sqrt{a}+\sqrt{b} x}\right)}{32 \sqrt{2} a^{9/4} b^{3/4}}+\frac{9 a x^{3/2}+5 b x^{7/2}}{16 a^2 \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,"(9*a*x^(3/2) + 5*b*x^(7/2))/(16*a^2*(a + b*x^2)^2) - (5*ArcTan[(a^(1/4)/(Sqrt[2]*b^(1/4)) - (b^(1/4)*x)/(Sqrt[2]*a^(1/4)))/Sqrt[x]])/(32*Sqrt[2]*a^(9/4)*b^(3/4)) - (5*ArcTanh[(Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x])/(Sqrt[a] + Sqrt[b]*x)])/(32*Sqrt[2]*a^(9/4)*b^(3/4))","A",1
308,1,151,239,0.1613571,"\int \frac{1}{\sqrt{x} \left(a+b x^2\right)^3} \, dx","IntegrateAlgebraic[1/(Sqrt[x]*(a + b*x^2)^3),x]","-\frac{21 \tan ^{-1}\left(\frac{\frac{\sqrt[4]{a}}{\sqrt{2} \sqrt[4]{b}}-\frac{\sqrt[4]{b} x}{\sqrt{2} \sqrt[4]{a}}}{\sqrt{x}}\right)}{32 \sqrt{2} a^{11/4} \sqrt[4]{b}}+\frac{21 \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}}{\sqrt{a}+\sqrt{b} x}\right)}{32 \sqrt{2} a^{11/4} \sqrt[4]{b}}+\frac{11 a \sqrt{x}+7 b x^{5/2}}{16 a^2 \left(a+b x^2\right)^2}","-\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{7 \sqrt{x}}{16 a^2 \left(a+b x^2\right)}+\frac{\sqrt{x}}{4 a \left(a+b x^2\right)^2}",1,"(11*a*Sqrt[x] + 7*b*x^(5/2))/(16*a^2*(a + b*x^2)^2) - (21*ArcTan[(a^(1/4)/(Sqrt[2]*b^(1/4)) - (b^(1/4)*x)/(Sqrt[2]*a^(1/4)))/Sqrt[x]])/(32*Sqrt[2]*a^(11/4)*b^(1/4)) + (21*ArcTanh[(Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x])/(Sqrt[a] + Sqrt[b]*x)])/(32*Sqrt[2]*a^(11/4)*b^(1/4))","A",1
309,1,172,251,0.1721032,"\int \frac{1}{x^{3/2} \left(a+b x^2\right)^3} \, dx","IntegrateAlgebraic[1/(x^(3/2)*(a + b*x^2)^3),x]","\frac{45 \sqrt[4]{b} \tan ^{-1}\left(\frac{\frac{\sqrt[4]{a}}{\sqrt{2} \sqrt[4]{b}}-\frac{\sqrt[4]{b} x}{\sqrt{2} \sqrt[4]{a}}}{\sqrt{x}}\right)}{32 \sqrt{2} a^{13/4}}+\frac{45 \sqrt[4]{b} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}}{\sqrt{a}+\sqrt{b} x}\right)}{32 \sqrt{2} a^{13/4}}-\frac{13 b x^{3/2}}{16 a^3 \left(a+b x^2\right)}-\frac{2}{a^3 \sqrt{x}}-\frac{b x^{3/2}}{4 a^2 \left(a+b x^2\right)^2}","-\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{9}{16 a^2 \sqrt{x} \left(a+b x^2\right)}+\frac{1}{4 a \sqrt{x} \left(a+b x^2\right)^2}",1,"-2/(a^3*Sqrt[x]) - (b*x^(3/2))/(4*a^2*(a + b*x^2)^2) - (13*b*x^(3/2))/(16*a^3*(a + b*x^2)) + (45*b^(1/4)*ArcTan[(a^(1/4)/(Sqrt[2]*b^(1/4)) - (b^(1/4)*x)/(Sqrt[2]*a^(1/4)))/Sqrt[x]])/(32*Sqrt[2]*a^(13/4)) + (45*b^(1/4)*ArcTanh[(Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x])/(Sqrt[a] + Sqrt[b]*x)])/(32*Sqrt[2]*a^(13/4))","A",1
310,1,174,251,0.1783882,"\int \frac{1}{x^{5/2} \left(a+b x^2\right)^3} \, dx","IntegrateAlgebraic[1/(x^(5/2)*(a + b*x^2)^3),x]","\frac{77 b^{3/4} \tan ^{-1}\left(\frac{\frac{\sqrt[4]{a}}{\sqrt{2} \sqrt[4]{b}}-\frac{\sqrt[4]{b} x}{\sqrt{2} \sqrt[4]{a}}}{\sqrt{x}}\right)}{32 \sqrt{2} a^{15/4}}-\frac{77 b^{3/4} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}}{\sqrt{a}+\sqrt{b} x}\right)}{32 \sqrt{2} a^{15/4}}-\frac{15 b \sqrt{x}}{16 a^3 \left(a+b x^2\right)}-\frac{2}{3 a^3 x^{3/2}}-\frac{b \sqrt{x}}{4 a^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{77}{48 a^3 x^{3/2}}+\frac{11}{16 a^2 x^{3/2} \left(a+b x^2\right)}+\frac{1}{4 a x^{3/2} \left(a+b x^2\right)^2}",1,"-2/(3*a^3*x^(3/2)) - (b*Sqrt[x])/(4*a^2*(a + b*x^2)^2) - (15*b*Sqrt[x])/(16*a^3*(a + b*x^2)) + (77*b^(3/4)*ArcTan[(a^(1/4)/(Sqrt[2]*b^(1/4)) - (b^(1/4)*x)/(Sqrt[2]*a^(1/4)))/Sqrt[x]])/(32*Sqrt[2]*a^(15/4)) - (77*b^(3/4)*ArcTanh[(Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x])/(Sqrt[a] + Sqrt[b]*x)])/(32*Sqrt[2]*a^(15/4))","A",1
311,1,188,264,0.1939406,"\int \frac{1}{x^{7/2} \left(a+b x^2\right)^3} \, dx","IntegrateAlgebraic[1/(x^(7/2)*(a + b*x^2)^3),x]","-\frac{117 b^{5/4} \tan ^{-1}\left(\frac{\frac{\sqrt[4]{a}}{\sqrt{2} \sqrt[4]{b}}-\frac{\sqrt[4]{b} x}{\sqrt{2} \sqrt[4]{a}}}{\sqrt{x}}\right)}{32 \sqrt{2} a^{17/4}}-\frac{117 b^{5/4} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}}{\sqrt{a}+\sqrt{b} x}\right)}{32 \sqrt{2} a^{17/4}}+\frac{-32 a^3+416 a^2 b x^2+1053 a b^2 x^4+585 b^3 x^6}{80 a^6 x^{5/2}+160 a^5 b x^{9/2}+80 a^4 b^2 x^{13/2}}","\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{117 b}{16 a^4 \sqrt{x}}-\frac{117}{80 a^3 x^{5/2}}+\frac{13}{16 a^2 x^{5/2} \left(a+b x^2\right)}+\frac{1}{4 a x^{5/2} \left(a+b x^2\right)^2}",1,"(-32*a^3 + 416*a^2*b*x^2 + 1053*a*b^2*x^4 + 585*b^3*x^6)/(80*a^6*x^(5/2) + 160*a^5*b*x^(9/2) + 80*a^4*b^2*x^(13/2)) - (117*b^(5/4)*ArcTan[(a^(1/4)/(Sqrt[2]*b^(1/4)) - (b^(1/4)*x)/(Sqrt[2]*a^(1/4)))/Sqrt[x]])/(32*Sqrt[2]*a^(17/4)) - (117*b^(5/4)*ArcTanh[(Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x])/(Sqrt[a] + Sqrt[b]*x)])/(32*Sqrt[2]*a^(17/4))","A",1
312,1,58,58,0.0297073,"\int \frac{\sqrt{x}}{a-b x^2} \, dx","IntegrateAlgebraic[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",1
313,1,71,108,0.0614607,"\int \frac{x^{7/2}}{1+x^2} \, dx","IntegrateAlgebraic[x^(7/2)/(1 + x^2),x]","\frac{2 x^{5/2}}{5}-2 \sqrt{x}+\frac{\tan ^{-1}\left(\frac{\frac{x}{\sqrt{2}}-\frac{1}{\sqrt{2}}}{\sqrt{x}}\right)}{\sqrt{2}}+\frac{\tanh ^{-1}\left(\frac{\frac{x}{\sqrt{2}}+\frac{1}{\sqrt{2}}}{\sqrt{x}}\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]) + x/Sqrt[2])/Sqrt[x]]/Sqrt[2] + ArcTanh[(1/Sqrt[2] + x/Sqrt[2])/Sqrt[x]]/Sqrt[2]","A",1
314,1,65,101,0.05046,"\int \frac{x^{5/2}}{1+x^2} \, dx","IntegrateAlgebraic[x^(5/2)/(1 + x^2),x]","\frac{2 x^{3/2}}{3}-\frac{\tan ^{-1}\left(\frac{\frac{x}{\sqrt{2}}-\frac{1}{\sqrt{2}}}{\sqrt{x}}\right)}{\sqrt{2}}+\frac{\tanh ^{-1}\left(\frac{\frac{x}{\sqrt{2}}+\frac{1}{\sqrt{2}}}{\sqrt{x}}\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]) + x/Sqrt[2])/Sqrt[x]]/Sqrt[2] + ArcTanh[(1/Sqrt[2] + x/Sqrt[2])/Sqrt[x]]/Sqrt[2]","A",1
315,1,64,99,0.0481197,"\int \frac{x^{3/2}}{1+x^2} \, dx","IntegrateAlgebraic[x^(3/2)/(1 + x^2),x]","2 \sqrt{x}-\frac{\tan ^{-1}\left(\frac{\frac{x}{\sqrt{2}}-\frac{1}{\sqrt{2}}}{\sqrt{x}}\right)}{\sqrt{2}}-\frac{\tanh ^{-1}\left(\frac{\frac{x}{\sqrt{2}}+\frac{1}{\sqrt{2}}}{\sqrt{x}}\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]) + x/Sqrt[2])/Sqrt[x]]/Sqrt[2] - ArcTanh[(1/Sqrt[2] + x/Sqrt[2])/Sqrt[x]]/Sqrt[2]","A",1
316,1,56,92,0.0449812,"\int \frac{\sqrt{x}}{1+x^2} \, dx","IntegrateAlgebraic[Sqrt[x]/(1 + x^2),x]","\frac{\tan ^{-1}\left(\frac{\frac{x}{\sqrt{2}}-\frac{1}{\sqrt{2}}}{\sqrt{x}}\right)}{\sqrt{2}}-\frac{\tanh ^{-1}\left(\frac{\frac{x}{\sqrt{2}}+\frac{1}{\sqrt{2}}}{\sqrt{x}}\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]) + x/Sqrt[2])/Sqrt[x]]/Sqrt[2] - ArcTanh[(1/Sqrt[2] + x/Sqrt[2])/Sqrt[x]]/Sqrt[2]","A",1
317,1,55,92,0.0403089,"\int \frac{1}{\sqrt{x} \left(1+x^2\right)} \, dx","IntegrateAlgebraic[1/(Sqrt[x]*(1 + x^2)),x]","\frac{\tan ^{-1}\left(\frac{\frac{x}{\sqrt{2}}-\frac{1}{\sqrt{2}}}{\sqrt{x}}\right)}{\sqrt{2}}+\frac{\tanh ^{-1}\left(\frac{\frac{x}{\sqrt{2}}+\frac{1}{\sqrt{2}}}{\sqrt{x}}\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]) + x/Sqrt[2])/Sqrt[x]]/Sqrt[2] + ArcTanh[(1/Sqrt[2] + x/Sqrt[2])/Sqrt[x]]/Sqrt[2]","A",1
318,1,63,99,0.0518323,"\int \frac{1}{x^{3/2} \left(1+x^2\right)} \, dx","IntegrateAlgebraic[1/(x^(3/2)*(1 + x^2)),x]","-\frac{2}{\sqrt{x}}-\frac{\tan ^{-1}\left(\frac{\frac{x}{\sqrt{2}}-\frac{1}{\sqrt{2}}}{\sqrt{x}}\right)}{\sqrt{2}}+\frac{\tanh ^{-1}\left(\frac{\frac{x}{\sqrt{2}}+\frac{1}{\sqrt{2}}}{\sqrt{x}}\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]) + x/Sqrt[2])/Sqrt[x]]/Sqrt[2] + ArcTanh[(1/Sqrt[2] + x/Sqrt[2])/Sqrt[x]]/Sqrt[2]","A",1
319,1,66,101,0.0625331,"\int \frac{1}{x^{5/2} \left(1+x^2\right)} \, dx","IntegrateAlgebraic[1/(x^(5/2)*(1 + x^2)),x]","-\frac{2}{3 x^{3/2}}-\frac{\tan ^{-1}\left(\frac{\frac{x}{\sqrt{2}}-\frac{1}{\sqrt{2}}}{\sqrt{x}}\right)}{\sqrt{2}}-\frac{\tanh ^{-1}\left(\frac{\frac{x}{\sqrt{2}}+\frac{1}{\sqrt{2}}}{\sqrt{x}}\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]) + x/Sqrt[2])/Sqrt[x]]/Sqrt[2] - ArcTanh[(1/Sqrt[2] + x/Sqrt[2])/Sqrt[x]]/Sqrt[2]","A",1
320,1,72,108,0.0675359,"\int \frac{1}{x^{7/2} \left(1+x^2\right)} \, dx","IntegrateAlgebraic[1/(x^(7/2)*(1 + x^2)),x]","-\frac{2}{5 x^{5/2}}+\frac{2}{\sqrt{x}}+\frac{\tan ^{-1}\left(\frac{\frac{x}{\sqrt{2}}-\frac{1}{\sqrt{2}}}{\sqrt{x}}\right)}{\sqrt{2}}-\frac{\tanh ^{-1}\left(\frac{\frac{x}{\sqrt{2}}+\frac{1}{\sqrt{2}}}{\sqrt{x}}\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]) + x/Sqrt[2])/Sqrt[x]]/Sqrt[2] - ArcTanh[(1/Sqrt[2] + x/Sqrt[2])/Sqrt[x]]/Sqrt[2]","A",1
321,1,84,122,0.0907083,"\int \frac{x^{7/2}}{\left(1+x^2\right)^2} \, dx","IntegrateAlgebraic[x^(7/2)/(1 + x^2)^2,x]","\frac{\sqrt{x}}{2 \left(x^2+1\right)}+2 \sqrt{x}-\frac{5 \tan ^{-1}\left(\frac{\frac{x}{\sqrt{2}}-\frac{1}{\sqrt{2}}}{\sqrt{x}}\right)}{4 \sqrt{2}}-\frac{5 \tanh ^{-1}\left(\frac{\frac{x}{\sqrt{2}}+\frac{1}{\sqrt{2}}}{\sqrt{x}}\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,"2*Sqrt[x] + Sqrt[x]/(2*(1 + x^2)) - (5*ArcTan[(-(1/Sqrt[2]) + x/Sqrt[2])/Sqrt[x]])/(4*Sqrt[2]) - (5*ArcTanh[(1/Sqrt[2] + x/Sqrt[2])/Sqrt[x]])/(4*Sqrt[2])","A",1
322,1,77,113,0.0884126,"\int \frac{x^{5/2}}{\left(1+x^2\right)^2} \, dx","IntegrateAlgebraic[x^(5/2)/(1 + x^2)^2,x]","-\frac{x^{3/2}}{2 \left(x^2+1\right)}+\frac{3 \tan ^{-1}\left(\frac{\frac{x}{\sqrt{2}}-\frac{1}{\sqrt{2}}}{\sqrt{x}}\right)}{4 \sqrt{2}}-\frac{3 \tanh ^{-1}\left(\frac{\frac{x}{\sqrt{2}}+\frac{1}{\sqrt{2}}}{\sqrt{x}}\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,"-1/2*x^(3/2)/(1 + x^2) + (3*ArcTan[(-(1/Sqrt[2]) + x/Sqrt[2])/Sqrt[x]])/(4*Sqrt[2]) - (3*ArcTanh[(1/Sqrt[2] + x/Sqrt[2])/Sqrt[x]])/(4*Sqrt[2])","A",1
323,1,77,113,0.0881193,"\int \frac{x^{3/2}}{\left(1+x^2\right)^2} \, dx","IntegrateAlgebraic[x^(3/2)/(1 + x^2)^2,x]","-\frac{\sqrt{x}}{2 \left(x^2+1\right)}+\frac{\tan ^{-1}\left(\frac{\frac{x}{\sqrt{2}}-\frac{1}{\sqrt{2}}}{\sqrt{x}}\right)}{4 \sqrt{2}}+\frac{\tanh ^{-1}\left(\frac{\frac{x}{\sqrt{2}}+\frac{1}{\sqrt{2}}}{\sqrt{x}}\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,"-1/2*Sqrt[x]/(1 + x^2) + ArcTan[(-(1/Sqrt[2]) + x/Sqrt[2])/Sqrt[x]]/(4*Sqrt[2]) + ArcTanh[(1/Sqrt[2] + x/Sqrt[2])/Sqrt[x]]/(4*Sqrt[2])","A",1
324,1,77,113,0.0758075,"\int \frac{\sqrt{x}}{\left(1+x^2\right)^2} \, dx","IntegrateAlgebraic[Sqrt[x]/(1 + x^2)^2,x]","\frac{x^{3/2}}{2 \left(x^2+1\right)}+\frac{\tan ^{-1}\left(\frac{\frac{x}{\sqrt{2}}-\frac{1}{\sqrt{2}}}{\sqrt{x}}\right)}{4 \sqrt{2}}-\frac{\tanh ^{-1}\left(\frac{\frac{x}{\sqrt{2}}+\frac{1}{\sqrt{2}}}{\sqrt{x}}\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]) + x/Sqrt[2])/Sqrt[x]]/(4*Sqrt[2]) - ArcTanh[(1/Sqrt[2] + x/Sqrt[2])/Sqrt[x]]/(4*Sqrt[2])","A",1
325,1,77,113,0.0740444,"\int \frac{1}{\sqrt{x} \left(1+x^2\right)^2} \, dx","IntegrateAlgebraic[1/(Sqrt[x]*(1 + x^2)^2),x]","\frac{\sqrt{x}}{2 \left(x^2+1\right)}+\frac{3 \tan ^{-1}\left(\frac{\frac{x}{\sqrt{2}}-\frac{1}{\sqrt{2}}}{\sqrt{x}}\right)}{4 \sqrt{2}}+\frac{3 \tanh ^{-1}\left(\frac{\frac{x}{\sqrt{2}}+\frac{1}{\sqrt{2}}}{\sqrt{x}}\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]) + x/Sqrt[2])/Sqrt[x]])/(4*Sqrt[2]) + (3*ArcTanh[(1/Sqrt[2] + x/Sqrt[2])/Sqrt[x]])/(4*Sqrt[2])","A",1
326,1,84,122,0.1011662,"\int \frac{1}{x^{3/2} \left(1+x^2\right)^2} \, dx","IntegrateAlgebraic[1/(x^(3/2)*(1 + x^2)^2),x]","-\frac{x^{3/2}}{2 \left(x^2+1\right)}-\frac{2}{\sqrt{x}}-\frac{5 \tan ^{-1}\left(\frac{\frac{x}{\sqrt{2}}-\frac{1}{\sqrt{2}}}{\sqrt{x}}\right)}{4 \sqrt{2}}+\frac{5 \tanh ^{-1}\left(\frac{\frac{x}{\sqrt{2}}+\frac{1}{\sqrt{2}}}{\sqrt{x}}\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,"-2/Sqrt[x] - x^(3/2)/(2*(1 + x^2)) - (5*ArcTan[(-(1/Sqrt[2]) + x/Sqrt[2])/Sqrt[x]])/(4*Sqrt[2]) + (5*ArcTanh[(1/Sqrt[2] + x/Sqrt[2])/Sqrt[x]])/(4*Sqrt[2])","A",1
327,1,86,122,0.1042576,"\int \frac{1}{x^{5/2} \left(1+x^2\right)^2} \, dx","IntegrateAlgebraic[1/(x^(5/2)*(1 + x^2)^2),x]","\frac{-7 x^2-4}{6 x^{7/2}+6 x^{3/2}}-\frac{7 \tan ^{-1}\left(\frac{\frac{x}{\sqrt{2}}-\frac{1}{\sqrt{2}}}{\sqrt{x}}\right)}{4 \sqrt{2}}-\frac{7 \tanh ^{-1}\left(\frac{\frac{x}{\sqrt{2}}+\frac{1}{\sqrt{2}}}{\sqrt{x}}\right)}{4 \sqrt{2}}","-\frac{7}{6 x^{3/2}}+\frac{1}{2 x^{3/2} \left(x^2+1\right)}+\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,"(-4 - 7*x^2)/(6*x^(3/2) + 6*x^(7/2)) - (7*ArcTan[(-(1/Sqrt[2]) + x/Sqrt[2])/Sqrt[x]])/(4*Sqrt[2]) - (7*ArcTanh[(1/Sqrt[2] + x/Sqrt[2])/Sqrt[x]])/(4*Sqrt[2])","A",1
328,1,91,131,0.1207336,"\int \frac{1}{x^{7/2} \left(1+x^2\right)^2} \, dx","IntegrateAlgebraic[1/(x^(7/2)*(1 + x^2)^2),x]","\frac{45 x^4+36 x^2-4}{10 x^{9/2}+10 x^{5/2}}+\frac{9 \tan ^{-1}\left(\frac{\frac{x}{\sqrt{2}}-\frac{1}{\sqrt{2}}}{\sqrt{x}}\right)}{4 \sqrt{2}}-\frac{9 \tanh ^{-1}\left(\frac{\frac{x}{\sqrt{2}}+\frac{1}{\sqrt{2}}}{\sqrt{x}}\right)}{4 \sqrt{2}}","-\frac{9}{10 x^{5/2}}+\frac{1}{2 x^{5/2} \left(x^2+1\right)}+\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,"(-4 + 36*x^2 + 45*x^4)/(10*x^(5/2) + 10*x^(9/2)) + (9*ArcTan[(-(1/Sqrt[2]) + x/Sqrt[2])/Sqrt[x]])/(4*Sqrt[2]) - (9*ArcTanh[(1/Sqrt[2] + x/Sqrt[2])/Sqrt[x]])/(4*Sqrt[2])","A",1
329,1,87,129,0.076233,"\int \frac{x^{7/2}}{\left(1+x^2\right)^3} \, dx","IntegrateAlgebraic[x^(7/2)/(1 + x^2)^3,x]","\frac{-9 x^{5/2}-5 \sqrt{x}}{16 \left(x^2+1\right)^2}+\frac{5 \tan ^{-1}\left(\frac{\frac{x}{\sqrt{2}}-\frac{1}{\sqrt{2}}}{\sqrt{x}}\right)}{32 \sqrt{2}}+\frac{5 \tanh ^{-1}\left(\frac{\frac{x}{\sqrt{2}}+\frac{1}{\sqrt{2}}}{\sqrt{x}}\right)}{32 \sqrt{2}}","-\frac{5 \sqrt{x}}{16 \left(x^2+1\right)}-\frac{x^{5/2}}{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,"(-5*Sqrt[x] - 9*x^(5/2))/(16*(1 + x^2)^2) + (5*ArcTan[(-(1/Sqrt[2]) + x/Sqrt[2])/Sqrt[x]])/(32*Sqrt[2]) + (5*ArcTanh[(1/Sqrt[2] + x/Sqrt[2])/Sqrt[x]])/(32*Sqrt[2])","A",1
330,1,87,129,0.0747867,"\int \frac{x^{5/2}}{\left(1+x^2\right)^3} \, dx","IntegrateAlgebraic[x^(5/2)/(1 + x^2)^3,x]","\frac{3 x^{7/2}-x^{3/2}}{16 \left(x^2+1\right)^2}+\frac{3 \tan ^{-1}\left(\frac{\frac{x}{\sqrt{2}}-\frac{1}{\sqrt{2}}}{\sqrt{x}}\right)}{32 \sqrt{2}}-\frac{3 \tanh ^{-1}\left(\frac{\frac{x}{\sqrt{2}}+\frac{1}{\sqrt{2}}}{\sqrt{x}}\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) + 3*x^(7/2))/(16*(1 + x^2)^2) + (3*ArcTan[(-(1/Sqrt[2]) + x/Sqrt[2])/Sqrt[x]])/(32*Sqrt[2]) - (3*ArcTanh[(1/Sqrt[2] + x/Sqrt[2])/Sqrt[x]])/(32*Sqrt[2])","A",1
331,1,85,129,0.0677401,"\int \frac{x^{3/2}}{\left(1+x^2\right)^3} \, dx","IntegrateAlgebraic[x^(3/2)/(1 + x^2)^3,x]","\frac{x^{5/2}-3 \sqrt{x}}{16 \left(x^2+1\right)^2}+\frac{3 \tan ^{-1}\left(\frac{\frac{x}{\sqrt{2}}-\frac{1}{\sqrt{2}}}{\sqrt{x}}\right)}{32 \sqrt{2}}+\frac{3 \tanh ^{-1}\left(\frac{\frac{x}{\sqrt{2}}+\frac{1}{\sqrt{2}}}{\sqrt{x}}\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,"(-3*Sqrt[x] + x^(5/2))/(16*(1 + x^2)^2) + (3*ArcTan[(-(1/Sqrt[2]) + x/Sqrt[2])/Sqrt[x]])/(32*Sqrt[2]) + (3*ArcTanh[(1/Sqrt[2] + x/Sqrt[2])/Sqrt[x]])/(32*Sqrt[2])","A",1
332,1,87,129,0.0701811,"\int \frac{\sqrt{x}}{\left(1+x^2\right)^3} \, dx","IntegrateAlgebraic[Sqrt[x]/(1 + x^2)^3,x]","\frac{5 x^{7/2}+9 x^{3/2}}{16 \left(x^2+1\right)^2}+\frac{5 \tan ^{-1}\left(\frac{\frac{x}{\sqrt{2}}-\frac{1}{\sqrt{2}}}{\sqrt{x}}\right)}{32 \sqrt{2}}-\frac{5 \tanh ^{-1}\left(\frac{\frac{x}{\sqrt{2}}+\frac{1}{\sqrt{2}}}{\sqrt{x}}\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,"(9*x^(3/2) + 5*x^(7/2))/(16*(1 + x^2)^2) + (5*ArcTan[(-(1/Sqrt[2]) + x/Sqrt[2])/Sqrt[x]])/(32*Sqrt[2]) - (5*ArcTanh[(1/Sqrt[2] + x/Sqrt[2])/Sqrt[x]])/(32*Sqrt[2])","A",1
333,1,87,129,0.0721111,"\int \frac{1}{\sqrt{x} \left(1+x^2\right)^3} \, dx","IntegrateAlgebraic[1/(Sqrt[x]*(1 + x^2)^3),x]","\frac{7 x^{5/2}+11 \sqrt{x}}{16 \left(x^2+1\right)^2}+\frac{21 \tan ^{-1}\left(\frac{\frac{x}{\sqrt{2}}-\frac{1}{\sqrt{2}}}{\sqrt{x}}\right)}{32 \sqrt{2}}+\frac{21 \tanh ^{-1}\left(\frac{\frac{x}{\sqrt{2}}+\frac{1}{\sqrt{2}}}{\sqrt{x}}\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,"(11*Sqrt[x] + 7*x^(5/2))/(16*(1 + x^2)^2) + (21*ArcTan[(-(1/Sqrt[2]) + x/Sqrt[2])/Sqrt[x]])/(32*Sqrt[2]) + (21*ArcTanh[(1/Sqrt[2] + x/Sqrt[2])/Sqrt[x]])/(32*Sqrt[2])","A",1
334,1,98,138,0.0802622,"\int \frac{1}{x^{3/2} \left(1+x^2\right)^3} \, dx","IntegrateAlgebraic[1/(x^(3/2)*(1 + x^2)^3),x]","\frac{-45 x^4-81 x^2-32}{16 x^{9/2}+32 x^{5/2}+16 \sqrt{x}}-\frac{45 \tan ^{-1}\left(\frac{\frac{x}{\sqrt{2}}-\frac{1}{\sqrt{2}}}{\sqrt{x}}\right)}{32 \sqrt{2}}+\frac{45 \tanh ^{-1}\left(\frac{\frac{x}{\sqrt{2}}+\frac{1}{\sqrt{2}}}{\sqrt{x}}\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,"(-32 - 81*x^2 - 45*x^4)/(16*Sqrt[x] + 32*x^(5/2) + 16*x^(9/2)) - (45*ArcTan[(-(1/Sqrt[2]) + x/Sqrt[2])/Sqrt[x]])/(32*Sqrt[2]) + (45*ArcTanh[(1/Sqrt[2] + x/Sqrt[2])/Sqrt[x]])/(32*Sqrt[2])","A",1
335,1,98,138,0.0818851,"\int \frac{1}{x^{5/2} \left(1+x^2\right)^3} \, dx","IntegrateAlgebraic[1/(x^(5/2)*(1 + x^2)^3),x]","\frac{-77 x^4-121 x^2-32}{48 x^{11/2}+96 x^{7/2}+48 x^{3/2}}-\frac{77 \tan ^{-1}\left(\frac{\frac{x}{\sqrt{2}}-\frac{1}{\sqrt{2}}}{\sqrt{x}}\right)}{32 \sqrt{2}}-\frac{77 \tanh ^{-1}\left(\frac{\frac{x}{\sqrt{2}}+\frac{1}{\sqrt{2}}}{\sqrt{x}}\right)}{32 \sqrt{2}}","-\frac{77}{48 x^{3/2}}+\frac{11}{16 x^{3/2} \left(x^2+1\right)}+\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,"(-32 - 121*x^2 - 77*x^4)/(48*x^(3/2) + 96*x^(7/2) + 48*x^(11/2)) - (77*ArcTan[(-(1/Sqrt[2]) + x/Sqrt[2])/Sqrt[x]])/(32*Sqrt[2]) - (77*ArcTanh[(1/Sqrt[2] + x/Sqrt[2])/Sqrt[x]])/(32*Sqrt[2])","A",1
336,1,103,147,0.0884823,"\int \frac{1}{x^{7/2} \left(1+x^2\right)^3} \, dx","IntegrateAlgebraic[1/(x^(7/2)*(1 + x^2)^3),x]","\frac{585 x^6+1053 x^4+416 x^2-32}{80 x^{13/2}+160 x^{9/2}+80 x^{5/2}}+\frac{117 \tan ^{-1}\left(\frac{\frac{x}{\sqrt{2}}-\frac{1}{\sqrt{2}}}{\sqrt{x}}\right)}{32 \sqrt{2}}-\frac{117 \tanh ^{-1}\left(\frac{\frac{x}{\sqrt{2}}+\frac{1}{\sqrt{2}}}{\sqrt{x}}\right)}{32 \sqrt{2}}","-\frac{117}{80 x^{5/2}}+\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}{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,"(-32 + 416*x^2 + 1053*x^4 + 585*x^6)/(80*x^(5/2) + 160*x^(9/2) + 80*x^(13/2)) + (117*ArcTan[(-(1/Sqrt[2]) + x/Sqrt[2])/Sqrt[x]])/(32*Sqrt[2]) - (117*ArcTanh[(1/Sqrt[2] + x/Sqrt[2])/Sqrt[x]])/(32*Sqrt[2])","A",1
337,1,15,15,0.0117649,"\int \frac{\sqrt{x}}{1-x^2} \, dx","IntegrateAlgebraic[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",1
338,1,55,73,0.0462696,"\int \frac{x^{2/3}}{1+x^2} \, dx","IntegrateAlgebraic[x^(2/3)/(1 + x^2),x]","\frac{1}{2} \tan ^{-1}\left(\frac{x^{2/3}-1}{\sqrt[3]{x}}\right)-\frac{1}{2} \sqrt{3} \tanh ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{x}}{x^{2/3}+1}\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[(-1 + x^(2/3))/x^(1/3)]/2 + ArcTan[x^(1/3)] - (Sqrt[3]*ArcTanh[(Sqrt[3]*x^(1/3))/(1 + x^(2/3))])/2","A",1
339,0,0,97,0.0839613,"\int x^m \left(a+b x^2\right)^5 \, dx","IntegrateAlgebraic[x^m*(a + b*x^2)^5,x]","\int x^m \left(a+b x^2\right)^5 \, dx","\frac{a^5 x^{m+1}}{m+1}+\frac{5 a^4 b x^{m+3}}{m+3}+\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 b^4 x^{m+9}}{m+9}+\frac{b^5 x^{m+11}}{m+11}",1,"Could not integrate","F",-1
340,0,0,79,0.0346647,"\int x^m \left(a+b x^2\right)^4 \, dx","IntegrateAlgebraic[x^m*(a + b*x^2)^4,x]","\int x^m \left(a+b x^2\right)^4 \, dx","\frac{a^4 x^{m+1}}{m+1}+\frac{4 a^3 b x^{m+3}}{m+3}+\frac{6 a^2 b^2 x^{m+5}}{m+5}+\frac{4 a b^3 x^{m+7}}{m+7}+\frac{b^4 x^{m+9}}{m+9}",1,"Could not integrate","F",-1
341,0,0,61,0.0172588,"\int x^m \left(a+b x^2\right)^3 \, dx","IntegrateAlgebraic[x^m*(a + b*x^2)^3,x]","\int x^m \left(a+b x^2\right)^3 \, dx","\frac{a^3 x^{m+1}}{m+1}+\frac{3 a^2 b x^{m+3}}{m+3}+\frac{3 a b^2 x^{m+5}}{m+5}+\frac{b^3 x^{m+7}}{m+7}",1,"Could not integrate","F",-1
342,0,0,43,0.012389,"\int x^m \left(a+b x^2\right)^2 \, dx","IntegrateAlgebraic[x^m*(a + b*x^2)^2,x]","\int x^m \left(a+b x^2\right)^2 \, dx","\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,"Could not integrate","F",-1
343,0,0,25,0.0078486,"\int x^m \left(a+b x^2\right) \, dx","IntegrateAlgebraic[x^m*(a + b*x^2),x]","\int x^m \left(a+b x^2\right) \, dx","\frac{a x^{m+1}}{m+1}+\frac{b x^{m+3}}{m+3}",1,"Could not integrate","F",-1
344,0,0,39,0.0122784,"\int \frac{x^m}{a+b x^2} \, dx","IntegrateAlgebraic[x^m/(a + b*x^2),x]","\int \frac{x^m}{a+b x^2} \, dx","\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,"Could not integrate","F",-1
345,0,0,39,0.0136255,"\int \frac{x^m}{\left(a+b x^2\right)^2} \, dx","IntegrateAlgebraic[x^m/(a + b*x^2)^2,x]","\int \frac{x^m}{\left(a+b x^2\right)^2} \, dx","\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,"Could not integrate","F",-1
346,0,0,39,0.0145592,"\int \frac{x^m}{\left(a+b x^2\right)^3} \, dx","IntegrateAlgebraic[x^m/(a + b*x^2)^3,x]","\int \frac{x^m}{\left(a+b x^2\right)^3} \, dx","\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,"Could not integrate","F",-1
347,0,0,44,0.0145846,"\int \frac{(c x)^{1+m}}{a+b x^2} \, dx","IntegrateAlgebraic[(c*x)^(1 + m)/(a + b*x^2),x]","\int \frac{(c x)^{1+m}}{a+b x^2} \, dx","\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,"Could not integrate","F",-1
348,0,0,44,0.0131554,"\int \frac{(c x)^m}{a+b x^2} \, dx","IntegrateAlgebraic[(c*x)^m/(a + b*x^2),x]","\int \frac{(c x)^m}{a+b x^2} \, dx","\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,"Could not integrate","F",-1
349,0,0,38,0.0165826,"\int \frac{(c x)^{-1+m}}{a+b x^2} \, dx","IntegrateAlgebraic[(c*x)^(-1 + m)/(a + b*x^2),x]","\int \frac{(c x)^{-1+m}}{a+b x^2} \, dx","\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,"Could not integrate","F",-1
350,0,0,47,0.0170909,"\int \frac{(c x)^{-2+m}}{a+b x^2} \, dx","IntegrateAlgebraic[(c*x)^(-2 + m)/(a + b*x^2),x]","\int \frac{(c x)^{-2+m}}{a+b x^2} \, dx","-\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,"Could not integrate","F",-1
351,0,0,45,0.0171681,"\int \frac{(c x)^{-3+m}}{a+b x^2} \, dx","IntegrateAlgebraic[(c*x)^(-3 + m)/(a + b*x^2),x]","\int \frac{(c x)^{-3+m}}{a+b x^2} \, dx","-\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,"Could not integrate","F",-1
352,0,0,36,0.0175531,"\int \frac{x^m}{\left(1+\frac{a x^2}{b}\right)^2} \, dx","IntegrateAlgebraic[x^m/(1 + (a*x^2)/b)^2,x]","\int \frac{x^m}{\left(1+\frac{a x^2}{b}\right)^2} \, dx","\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,"Could not integrate","F",-1
353,1,61,80,0.0371196,"\int x^7 \sqrt{a+b x^2} \, dx","IntegrateAlgebraic[x^7*Sqrt[a + b*x^2],x]","\frac{\sqrt{a+b x^2} \left(-16 a^4+8 a^3 b x^2-6 a^2 b^2 x^4+5 a b^3 x^6+35 b^4 x^8\right)}{315 b^4}","-\frac{a^3 \left(a+b x^2\right)^{3/2}}{3 b^4}+\frac{3 a^2 \left(a+b x^2\right)^{5/2}}{5 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,"(Sqrt[a + b*x^2]*(-16*a^4 + 8*a^3*b*x^2 - 6*a^2*b^2*x^4 + 5*a*b^3*x^6 + 35*b^4*x^8))/(315*b^4)","A",1
354,1,50,59,0.1106323,"\int x^5 \sqrt{a+b x^2} \, dx","IntegrateAlgebraic[x^5*Sqrt[a + b*x^2],x]","\frac{\sqrt{a+b x^2} \left(8 a^3-4 a^2 b x^2+3 a b^2 x^4+15 b^3 x^6\right)}{105 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,"(Sqrt[a + b*x^2]*(8*a^3 - 4*a^2*b*x^2 + 3*a*b^2*x^4 + 15*b^3*x^6))/(105*b^3)","A",1
355,1,38,38,0.0308569,"\int x^3 \sqrt{a+b x^2} \, dx","IntegrateAlgebraic[x^3*Sqrt[a + b*x^2],x]","\frac{\sqrt{a+b x^2} \left(-2 a^2+a b x^2+3 b^2 x^4\right)}{15 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,"(Sqrt[a + b*x^2]*(-2*a^2 + a*b*x^2 + 3*b^2*x^4))/(15*b^2)","A",1
356,1,18,18,0.0215937,"\int x \sqrt{a+b x^2} \, dx","IntegrateAlgebraic[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
357,1,37,37,0.0415407,"\int \frac{\sqrt{a+b x^2}}{x} \, dx","IntegrateAlgebraic[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",1
358,1,47,47,0.1323433,"\int \frac{\sqrt{a+b x^2}}{x^3} \, dx","IntegrateAlgebraic[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,"-1/2*Sqrt[a + b*x^2]/x^2 - (b*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(2*Sqrt[a])","A",1
359,1,62,71,0.0791676,"\int \frac{\sqrt{a+b x^2}}{x^5} \, dx","IntegrateAlgebraic[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{\left(-2 a-b x^2\right) \sqrt{a+b x^2}}{8 a 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,"((-2*a - b*x^2)*Sqrt[a + b*x^2])/(8*a*x^4) + (b^2*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(8*a^(3/2))","A",1
360,1,73,95,0.152619,"\int \frac{\sqrt{a+b x^2}}{x^7} \, dx","IntegrateAlgebraic[Sqrt[a + b*x^2]/x^7,x]","\frac{\sqrt{a+b x^2} \left(-8 a^2-2 a b x^2+3 b^2 x^4\right)}{48 a^2 x^6}-\frac{b^3 \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{16 a^{5/2}}","-\frac{b^3 \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{16 a^{5/2}}+\frac{b^2 \sqrt{a+b x^2}}{16 a^2 x^2}-\frac{\sqrt{a+b x^2}}{6 x^6}-\frac{b \sqrt{a+b x^2}}{24 a x^4}",1,"(Sqrt[a + b*x^2]*(-8*a^2 - 2*a*b*x^2 + 3*b^2*x^4))/(48*a^2*x^6) - (b^3*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(16*a^(5/2))","A",1
361,1,72,94,0.2353207,"\int x^4 \sqrt{a+b x^2} \, dx","IntegrateAlgebraic[x^4*Sqrt[a + b*x^2],x]","\frac{a^3 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{16 b^{5/2}}+\frac{\sqrt{a+b x^2} \left(-3 a^2 x+2 a b x^3+8 b^2 x^5\right)}{48 b^2}","\frac{a^3 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{16 b^{5/2}}-\frac{a^2 x \sqrt{a+b x^2}}{16 b^2}+\frac{1}{6} x^5 \sqrt{a+b x^2}+\frac{a x^3 \sqrt{a+b x^2}}{24 b}",1,"(Sqrt[a + b*x^2]*(-3*a^2*x + 2*a*b*x^3 + 8*b^2*x^5))/(48*b^2) + (a^3*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(16*b^(5/2))","A",1
362,1,60,70,0.1303713,"\int x^2 \sqrt{a+b x^2} \, dx","IntegrateAlgebraic[x^2*Sqrt[a + b*x^2],x]","\frac{\sqrt{a+b x^2} \left(a x+2 b x^3\right)}{8 b}-\frac{a^2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{8 b^{3/2}}","-\frac{a^2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{8 b^{3/2}}+\frac{a x \sqrt{a+b x^2}}{8 b}+\frac{1}{4} x^3 \sqrt{a+b x^2}",1,"(Sqrt[a + b*x^2]*(a*x + 2*b*x^3))/(8*b) - (a^2*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(8*b^(3/2))","A",1
363,1,46,46,0.1041769,"\int \sqrt{a+b x^2} \, dx","IntegrateAlgebraic[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",1
364,1,42,42,0.0879006,"\int \frac{\sqrt{a+b x^2}}{x^2} \, dx","IntegrateAlgebraic[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",1
365,1,21,21,0.0559194,"\int \frac{\sqrt{a+b x^2}}{x^4} \, dx","IntegrateAlgebraic[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,"-1/3*(a + b*x^2)^(3/2)/(a*x^3)","A",1
366,1,42,44,0.0705642,"\int \frac{\sqrt{a+b x^2}}{x^6} \, dx","IntegrateAlgebraic[Sqrt[a + b*x^2]/x^6,x]","\frac{\sqrt{a+b x^2} \left(-3 a^2-a b x^2+2 b^2 x^4\right)}{15 a^2 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,"(Sqrt[a + b*x^2]*(-3*a^2 - a*b*x^2 + 2*b^2*x^4))/(15*a^2*x^5)","A",1
367,1,53,68,0.0814846,"\int \frac{\sqrt{a+b x^2}}{x^8} \, dx","IntegrateAlgebraic[Sqrt[a + b*x^2]/x^8,x]","\frac{\sqrt{a+b x^2} \left(-15 a^3-3 a^2 b x^2+4 a b^2 x^4-8 b^3 x^6\right)}{105 a^3 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,"(Sqrt[a + b*x^2]*(-15*a^3 - 3*a^2*b*x^2 + 4*a*b^2*x^4 - 8*b^3*x^6))/(105*a^3*x^7)","A",1
368,1,64,92,0.0940602,"\int \frac{\sqrt{a+b x^2}}{x^{10}} \, dx","IntegrateAlgebraic[Sqrt[a + b*x^2]/x^10,x]","\frac{\sqrt{a+b x^2} \left(-35 a^4-5 a^3 b x^2+6 a^2 b^2 x^4-8 a b^3 x^6+16 b^4 x^8\right)}{315 a^4 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,"(Sqrt[a + b*x^2]*(-35*a^4 - 5*a^3*b*x^2 + 6*a^2*b^2*x^4 - 8*a*b^3*x^6 + 16*b^4*x^8))/(315*a^4*x^9)","A",1
369,1,72,80,0.0392127,"\int x^7 \left(a+b x^2\right)^{3/2} \, dx","IntegrateAlgebraic[x^7*(a + b*x^2)^(3/2),x]","\frac{\sqrt{a+b x^2} \left(-16 a^5+8 a^4 b x^2-6 a^3 b^2 x^4+5 a^2 b^3 x^6+140 a b^4 x^8+105 b^5 x^{10}\right)}{1155 b^4}","-\frac{a^3 \left(a+b x^2\right)^{5/2}}{5 b^4}+\frac{3 a^2 \left(a+b x^2\right)^{7/2}}{7 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,"(Sqrt[a + b*x^2]*(-16*a^5 + 8*a^4*b*x^2 - 6*a^3*b^2*x^4 + 5*a^2*b^3*x^6 + 140*a*b^4*x^8 + 105*b^5*x^10))/(1155*b^4)","A",1
370,1,61,59,0.0367254,"\int x^5 \left(a+b x^2\right)^{3/2} \, dx","IntegrateAlgebraic[x^5*(a + b*x^2)^(3/2),x]","\frac{\sqrt{a+b x^2} \left(8 a^4-4 a^3 b x^2+3 a^2 b^2 x^4+50 a b^3 x^6+35 b^4 x^8\right)}{315 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,"(Sqrt[a + b*x^2]*(8*a^4 - 4*a^3*b*x^2 + 3*a^2*b^2*x^4 + 50*a*b^3*x^6 + 35*b^4*x^8))/(315*b^3)","A",1
371,1,49,38,0.0330975,"\int x^3 \left(a+b x^2\right)^{3/2} \, dx","IntegrateAlgebraic[x^3*(a + b*x^2)^(3/2),x]","\frac{\sqrt{a+b x^2} \left(-2 a^3+a^2 b x^2+8 a b^2 x^4+5 b^3 x^6\right)}{35 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,"(Sqrt[a + b*x^2]*(-2*a^3 + a^2*b*x^2 + 8*a*b^2*x^4 + 5*b^3*x^6))/(35*b^2)","A",1
372,1,18,18,0.0217157,"\int x \left(a+b x^2\right)^{3/2} \, dx","IntegrateAlgebraic[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
373,1,50,54,0.0524397,"\int \frac{\left(a+b x^2\right)^{3/2}}{x} \, dx","IntegrateAlgebraic[(a + b*x^2)^(3/2)/x,x]","\frac{1}{3} \sqrt{a+b x^2} \left(4 a+b x^2\right)-a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)","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,"(Sqrt[a + b*x^2]*(4*a + b*x^2))/3 - a^(3/2)*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]]","A",1
374,1,57,63,0.0715681,"\int \frac{\left(a+b x^2\right)^{3/2}}{x^3} \, dx","IntegrateAlgebraic[(a + b*x^2)^(3/2)/x^3,x]","\frac{\sqrt{a+b x^2} \left(2 b x^2-a\right)}{2 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,"(Sqrt[a + b*x^2]*(-a + 2*b*x^2))/(2*x^2) - (3*Sqrt[a]*b*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/2","A",1
375,1,59,68,0.0920032,"\int \frac{\left(a+b x^2\right)^{3/2}}{x^5} \, dx","IntegrateAlgebraic[(a + b*x^2)^(3/2)/x^5,x]","\frac{\left(-2 a-5 b x^2\right) \sqrt{a+b x^2}}{8 x^4}-\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{8 \sqrt{a}}","-\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,"((-2*a - 5*b*x^2)*Sqrt[a + b*x^2])/(8*x^4) - (3*b^2*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(8*Sqrt[a])","A",1
376,1,73,92,0.0938463,"\int \frac{\left(a+b x^2\right)^{3/2}}{x^7} \, dx","IntegrateAlgebraic[(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{\sqrt{a+b x^2} \left(-8 a^2-14 a b x^2-3 b^2 x^4\right)}{48 a 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{\left(a+b x^2\right)^{3/2}}{6 x^6}-\frac{b \sqrt{a+b x^2}}{8 x^4}",1,"(Sqrt[a + b*x^2]*(-8*a^2 - 14*a*b*x^2 - 3*b^2*x^4))/(48*a*x^6) + (b^3*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(16*a^(3/2))","A",1
377,1,84,116,0.1080157,"\int \frac{\left(a+b x^2\right)^{3/2}}{x^9} \, dx","IntegrateAlgebraic[(a + b*x^2)^(3/2)/x^9,x]","\frac{\sqrt{a+b x^2} \left(-16 a^3-24 a^2 b x^2-2 a b^2 x^4+3 b^3 x^6\right)}{128 a^2 x^8}-\frac{3 b^4 \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{128 a^{5/2}}","-\frac{3 b^4 \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{128 a^{5/2}}+\frac{3 b^3 \sqrt{a+b x^2}}{128 a^2 x^2}-\frac{b^2 \sqrt{a+b x^2}}{64 a x^4}-\frac{\left(a+b x^2\right)^{3/2}}{8 x^8}-\frac{b \sqrt{a+b x^2}}{16 x^6}",1,"(Sqrt[a + b*x^2]*(-16*a^3 - 24*a^2*b*x^2 - 2*a*b^2*x^4 + 3*b^3*x^6))/(128*a^2*x^8) - (3*b^4*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(128*a^(5/2))","A",1
378,1,83,115,0.1743559,"\int x^4 \left(a+b x^2\right)^{3/2} \, dx","IntegrateAlgebraic[x^4*(a + b*x^2)^(3/2),x]","\frac{3 a^4 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{128 b^{5/2}}+\frac{\sqrt{a+b x^2} \left(-3 a^3 x+2 a^2 b x^3+24 a b^2 x^5+16 b^3 x^7\right)}{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{3 a^3 x \sqrt{a+b x^2}}{128 b^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,"(Sqrt[a + b*x^2]*(-3*a^3*x + 2*a^2*b*x^3 + 24*a*b^2*x^5 + 16*b^3*x^7))/(128*b^2) + (3*a^4*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(128*b^(5/2))","A",1
379,1,72,91,0.1455184,"\int x^2 \left(a+b x^2\right)^{3/2} \, dx","IntegrateAlgebraic[x^2*(a + b*x^2)^(3/2),x]","\frac{\sqrt{a+b x^2} \left(3 a^2 x+14 a b x^3+8 b^2 x^5\right)}{48 b}-\frac{a^3 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{16 b^{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,"(Sqrt[a + b*x^2]*(3*a^2*x + 14*a*b*x^3 + 8*b^2*x^5))/(48*b) - (a^3*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(16*b^(3/2))","A",1
380,1,58,65,0.1344701,"\int \left(a+b x^2\right)^{3/2} \, dx","IntegrateAlgebraic[(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{1}{8} \sqrt{a+b x^2} \left(5 a x+2 b x^3\right)","\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,"(Sqrt[a + b*x^2]*(5*a*x + 2*b*x^3))/8 + (3*a^2*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(8*Sqrt[b])","A",1
381,1,57,63,0.1209811,"\int \frac{\left(a+b x^2\right)^{3/2}}{x^2} \, dx","IntegrateAlgebraic[(a + b*x^2)^(3/2)/x^2,x]","\frac{\sqrt{a+b x^2} \left(b x^2-2 a\right)}{2 x}+\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,"((-2*a + b*x^2)*Sqrt[a + b*x^2])/(2*x) + (3*a*Sqrt[b]*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/2","A",1
382,1,54,61,0.1039129,"\int \frac{\left(a+b x^2\right)^{3/2}}{x^4} \, dx","IntegrateAlgebraic[(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{\left(-a-4 b x^2\right) \sqrt{a+b x^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,"((-a - 4*b*x^2)*Sqrt[a + b*x^2])/(3*x^3) + b^(3/2)*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]]","A",1
383,1,21,21,0.0570195,"\int \frac{\left(a+b x^2\right)^{3/2}}{x^6} \, dx","IntegrateAlgebraic[(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,"-1/5*(a + b*x^2)^(5/2)/(a*x^5)","A",1
384,1,53,44,0.0799394,"\int \frac{\left(a+b x^2\right)^{3/2}}{x^8} \, dx","IntegrateAlgebraic[(a + b*x^2)^(3/2)/x^8,x]","\frac{\sqrt{a+b x^2} \left(-5 a^3-8 a^2 b x^2-a b^2 x^4+2 b^3 x^6\right)}{35 a^2 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,"(Sqrt[a + b*x^2]*(-5*a^3 - 8*a^2*b*x^2 - a*b^2*x^4 + 2*b^3*x^6))/(35*a^2*x^7)","A",1
385,1,64,68,0.09139,"\int \frac{\left(a+b x^2\right)^{3/2}}{x^{10}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(3/2)/x^10,x]","\frac{\sqrt{a+b x^2} \left(-35 a^4-50 a^3 b x^2-3 a^2 b^2 x^4+4 a b^3 x^6-8 b^4 x^8\right)}{315 a^3 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,"(Sqrt[a + b*x^2]*(-35*a^4 - 50*a^3*b*x^2 - 3*a^2*b^2*x^4 + 4*a*b^3*x^6 - 8*b^4*x^8))/(315*a^3*x^9)","A",1
386,1,75,92,0.1049498,"\int \frac{\left(a+b x^2\right)^{3/2}}{x^{12}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(3/2)/x^12,x]","\frac{\sqrt{a+b x^2} \left(-105 a^5-140 a^4 b x^2-5 a^3 b^2 x^4+6 a^2 b^3 x^6-8 a b^4 x^8+16 b^5 x^{10}\right)}{1155 a^4 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,"(Sqrt[a + b*x^2]*(-105*a^5 - 140*a^4*b*x^2 - 5*a^3*b^2*x^4 + 6*a^2*b^3*x^6 - 8*a*b^4*x^8 + 16*b^5*x^10))/(1155*a^4*x^11)","A",1
387,1,83,80,0.0412246,"\int x^7 \left(a+b x^2\right)^{5/2} \, dx","IntegrateAlgebraic[x^7*(a + b*x^2)^(5/2),x]","\frac{\sqrt{a+b x^2} \left(-16 a^6+8 a^5 b x^2-6 a^4 b^2 x^4+5 a^3 b^3 x^6+371 a^2 b^4 x^8+567 a b^5 x^{10}+231 b^6 x^{12}\right)}{3003 b^4}","-\frac{a^3 \left(a+b x^2\right)^{7/2}}{7 b^4}+\frac{a^2 \left(a+b x^2\right)^{9/2}}{3 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,"(Sqrt[a + b*x^2]*(-16*a^6 + 8*a^5*b*x^2 - 6*a^4*b^2*x^4 + 5*a^3*b^3*x^6 + 371*a^2*b^4*x^8 + 567*a*b^5*x^10 + 231*b^6*x^12))/(3003*b^4)","A",1
388,1,72,59,0.0373687,"\int x^5 \left(a+b x^2\right)^{5/2} \, dx","IntegrateAlgebraic[x^5*(a + b*x^2)^(5/2),x]","\frac{\sqrt{a+b x^2} \left(8 a^5-4 a^4 b x^2+3 a^3 b^2 x^4+113 a^2 b^3 x^6+161 a b^4 x^8+63 b^5 x^{10}\right)}{693 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,"(Sqrt[a + b*x^2]*(8*a^5 - 4*a^4*b*x^2 + 3*a^3*b^2*x^4 + 113*a^2*b^3*x^6 + 161*a*b^4*x^8 + 63*b^5*x^10))/(693*b^3)","A",1
389,1,60,38,0.0345261,"\int x^3 \left(a+b x^2\right)^{5/2} \, dx","IntegrateAlgebraic[x^3*(a + b*x^2)^(5/2),x]","\frac{\sqrt{a+b x^2} \left(-2 a^4+a^3 b x^2+15 a^2 b^2 x^4+19 a b^3 x^6+7 b^4 x^8\right)}{63 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,"(Sqrt[a + b*x^2]*(-2*a^4 + a^3*b*x^2 + 15*a^2*b^2*x^4 + 19*a*b^3*x^6 + 7*b^4*x^8))/(63*b^2)","A",1
390,1,18,18,0.0213871,"\int x \left(a+b x^2\right)^{5/2} \, dx","IntegrateAlgebraic[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
391,1,62,72,0.0595346,"\int \frac{\left(a+b x^2\right)^{5/2}}{x} \, dx","IntegrateAlgebraic[(a + b*x^2)^(5/2)/x,x]","\frac{1}{15} \sqrt{a+b x^2} \left(23 a^2+11 a b x^2+3 b^2 x^4\right)-a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)","a^{5/2} \left(-\tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)\right)+a^2 \sqrt{a+b x^2}+\frac{1}{3} a \left(a+b x^2\right)^{3/2}+\frac{1}{5} \left(a+b x^2\right)^{5/2}",1,"(Sqrt[a + b*x^2]*(23*a^2 + 11*a*b*x^2 + 3*b^2*x^4))/15 - a^(5/2)*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]]","A",1
392,1,68,80,0.0861864,"\int \frac{\left(a+b x^2\right)^{5/2}}{x^3} \, dx","IntegrateAlgebraic[(a + b*x^2)^(5/2)/x^3,x]","\frac{\sqrt{a+b x^2} \left(-3 a^2+14 a b x^2+2 b^2 x^4\right)}{6 x^2}-\frac{5}{2} a^{3/2} b \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)","-\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,"(Sqrt[a + b*x^2]*(-3*a^2 + 14*a*b*x^2 + 2*b^2*x^4))/(6*x^2) - (5*a^(3/2)*b*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/2","A",1
393,1,70,86,0.1055675,"\int \frac{\left(a+b x^2\right)^{5/2}}{x^5} \, dx","IntegrateAlgebraic[(a + b*x^2)^(5/2)/x^5,x]","\frac{\sqrt{a+b x^2} \left(-2 a^2-9 a b x^2+8 b^2 x^4\right)}{8 x^4}-\frac{15}{8} \sqrt{a} b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)","\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{5 b \left(a+b x^2\right)^{3/2}}{8 x^2}-\frac{\left(a+b x^2\right)^{5/2}}{4 x^4}",1,"(Sqrt[a + b*x^2]*(-2*a^2 - 9*a*b*x^2 + 8*b^2*x^4))/(8*x^4) - (15*Sqrt[a]*b^2*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/8","A",1
394,1,70,89,0.0953552,"\int \frac{\left(a+b x^2\right)^{5/2}}{x^7} \, dx","IntegrateAlgebraic[(a + b*x^2)^(5/2)/x^7,x]","\frac{\sqrt{a+b x^2} \left(-8 a^2-26 a b x^2-33 b^2 x^4\right)}{48 x^6}-\frac{5 b^3 \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{16 \sqrt{a}}","-\frac{5 b^3 \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{16 \sqrt{a}}-\frac{5 b^2 \sqrt{a+b x^2}}{16 x^2}-\frac{\left(a+b x^2\right)^{5/2}}{6 x^6}-\frac{5 b \left(a+b x^2\right)^{3/2}}{24 x^4}",1,"(Sqrt[a + b*x^2]*(-8*a^2 - 26*a*b*x^2 - 33*b^2*x^4))/(48*x^6) - (5*b^3*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(16*Sqrt[a])","A",1
395,1,84,113,0.1129922,"\int \frac{\left(a+b x^2\right)^{5/2}}{x^9} \, dx","IntegrateAlgebraic[(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{\sqrt{a+b x^2} \left(-48 a^3-136 a^2 b x^2-118 a b^2 x^4-15 b^3 x^6\right)}{384 a 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{\left(a+b x^2\right)^{5/2}}{8 x^8}-\frac{5 b \left(a+b x^2\right)^{3/2}}{48 x^6}",1,"(Sqrt[a + b*x^2]*(-48*a^3 - 136*a^2*b*x^2 - 118*a*b^2*x^4 - 15*b^3*x^6))/(384*a*x^8) + (5*b^4*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(128*a^(3/2))","A",1
396,1,95,137,0.1183794,"\int \frac{\left(a+b x^2\right)^{5/2}}{x^{11}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(5/2)/x^11,x]","\frac{\sqrt{a+b x^2} \left(-128 a^4-336 a^3 b x^2-248 a^2 b^2 x^4-10 a b^3 x^6+15 b^4 x^8\right)}{1280 a^2 x^{10}}-\frac{3 b^5 \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{256 a^{5/2}}","-\frac{3 b^5 \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{256 a^{5/2}}+\frac{3 b^4 \sqrt{a+b x^2}}{256 a^2 x^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{\left(a+b x^2\right)^{5/2}}{10 x^{10}}-\frac{b \left(a+b x^2\right)^{3/2}}{16 x^8}",1,"(Sqrt[a + b*x^2]*(-128*a^4 - 336*a^3*b*x^2 - 248*a^2*b^2*x^4 - 10*a*b^3*x^6 + 15*b^4*x^8))/(1280*a^2*x^10) - (3*b^5*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(256*a^(5/2))","A",1
397,1,94,136,0.1974303,"\int x^4 \left(a+b x^2\right)^{5/2} \, dx","IntegrateAlgebraic[x^4*(a + b*x^2)^(5/2),x]","\frac{3 a^5 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{256 b^{5/2}}+\frac{\sqrt{a+b x^2} \left(-15 a^4 x+10 a^3 b x^3+248 a^2 b^2 x^5+336 a b^3 x^7+128 b^4 x^9\right)}{1280 b^2}","\frac{3 a^5 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{256 b^{5/2}}-\frac{3 a^4 x \sqrt{a+b x^2}}{256 b^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,"(Sqrt[a + b*x^2]*(-15*a^4*x + 10*a^3*b*x^3 + 248*a^2*b^2*x^5 + 336*a*b^3*x^7 + 128*b^4*x^9))/(1280*b^2) + (3*a^5*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(256*b^(5/2))","A",1
398,1,83,112,0.1707906,"\int x^2 \left(a+b x^2\right)^{5/2} \, dx","IntegrateAlgebraic[x^2*(a + b*x^2)^(5/2),x]","\frac{\sqrt{a+b x^2} \left(15 a^3 x+118 a^2 b x^3+136 a b^2 x^5+48 b^3 x^7\right)}{384 b}-\frac{5 a^4 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{128 b^{3/2}}","-\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,"(Sqrt[a + b*x^2]*(15*a^3*x + 118*a^2*b*x^3 + 136*a*b^2*x^5 + 48*b^3*x^7))/(384*b) - (5*a^4*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(128*b^(3/2))","A",1
399,1,69,84,0.1408525,"\int \left(a+b x^2\right)^{5/2} \, dx","IntegrateAlgebraic[(a + b*x^2)^(5/2),x]","\frac{5 a^3 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{16 \sqrt{b}}+\frac{1}{48} \sqrt{a+b x^2} \left(33 a^2 x+26 a b x^3+8 b^2 x^5\right)","\frac{5 a^3 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{16 \sqrt{b}}+\frac{5}{16} a^2 x \sqrt{a+b x^2}+\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,"(Sqrt[a + b*x^2]*(33*a^2*x + 26*a*b*x^3 + 8*b^2*x^5))/48 + (5*a^3*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(16*Sqrt[b])","A",1
400,1,71,83,0.159875,"\int \frac{\left(a+b x^2\right)^{5/2}}{x^2} \, dx","IntegrateAlgebraic[(a + b*x^2)^(5/2)/x^2,x]","\frac{\sqrt{a+b x^2} \left(-8 a^2+9 a b x^2+2 b^2 x^4\right)}{8 x}+\frac{15}{8} a^2 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)","\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,"(Sqrt[a + b*x^2]*(-8*a^2 + 9*a*b*x^2 + 2*b^2*x^4))/(8*x) + (15*a^2*Sqrt[b]*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/8","A",1
401,1,69,86,0.1459556,"\int \frac{\left(a+b x^2\right)^{5/2}}{x^4} \, dx","IntegrateAlgebraic[(a + b*x^2)^(5/2)/x^4,x]","\frac{\sqrt{a+b x^2} \left(-2 a^2-14 a b x^2+3 b^2 x^4\right)}{6 x^3}+\frac{5}{2} a b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)","\frac{5}{2} a b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)+\frac{5}{2} b^2 x \sqrt{a+b x^2}-\frac{5 b \left(a+b x^2\right)^{3/2}}{3 x}-\frac{\left(a+b x^2\right)^{5/2}}{3 x^3}",1,"(Sqrt[a + b*x^2]*(-2*a^2 - 14*a*b*x^2 + 3*b^2*x^4))/(6*x^3) + (5*a*b^(3/2)*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/2","A",1
402,1,65,82,0.1170086,"\int \frac{\left(a+b x^2\right)^{5/2}}{x^6} \, dx","IntegrateAlgebraic[(a + b*x^2)^(5/2)/x^6,x]","\frac{\sqrt{a+b x^2} \left(-3 a^2-11 a b x^2-23 b^2 x^4\right)}{15 x^5}+b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)","b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)-\frac{b^2 \sqrt{a+b x^2}}{x}-\frac{\left(a+b x^2\right)^{5/2}}{5 x^5}-\frac{b \left(a+b x^2\right)^{3/2}}{3 x^3}",1,"(Sqrt[a + b*x^2]*(-3*a^2 - 11*a*b*x^2 - 23*b^2*x^4))/(15*x^5) + b^(5/2)*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]]","A",1
403,1,21,21,0.0579535,"\int \frac{\left(a+b x^2\right)^{5/2}}{x^8} \, dx","IntegrateAlgebraic[(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,"-1/7*(a + b*x^2)^(7/2)/(a*x^7)","A",1
404,1,64,44,0.0869769,"\int \frac{\left(a+b x^2\right)^{5/2}}{x^{10}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(5/2)/x^10,x]","\frac{\sqrt{a+b x^2} \left(-7 a^4-19 a^3 b x^2-15 a^2 b^2 x^4-a b^3 x^6+2 b^4 x^8\right)}{63 a^2 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,"(Sqrt[a + b*x^2]*(-7*a^4 - 19*a^3*b*x^2 - 15*a^2*b^2*x^4 - a*b^3*x^6 + 2*b^4*x^8))/(63*a^2*x^9)","A",1
405,1,75,68,0.1011453,"\int \frac{\left(a+b x^2\right)^{5/2}}{x^{12}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(5/2)/x^12,x]","\frac{\sqrt{a+b x^2} \left(-63 a^5-161 a^4 b x^2-113 a^3 b^2 x^4-3 a^2 b^3 x^6+4 a b^4 x^8-8 b^5 x^{10}\right)}{693 a^3 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,"(Sqrt[a + b*x^2]*(-63*a^5 - 161*a^4*b*x^2 - 113*a^3*b^2*x^4 - 3*a^2*b^3*x^6 + 4*a*b^4*x^8 - 8*b^5*x^10))/(693*a^3*x^11)","A",1
406,1,86,92,0.118301,"\int \frac{\left(a+b x^2\right)^{5/2}}{x^{14}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(5/2)/x^14,x]","\frac{\sqrt{a+b x^2} \left(-231 a^6-567 a^5 b x^2-371 a^4 b^2 x^4-5 a^3 b^3 x^6+6 a^2 b^4 x^8-8 a b^5 x^{10}+16 b^6 x^{12}\right)}{3003 a^4 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,"(Sqrt[a + b*x^2]*(-231*a^6 - 567*a^5*b*x^2 - 371*a^4*b^2*x^4 - 5*a^3*b^3*x^6 + 6*a^2*b^4*x^8 - 8*a*b^5*x^10 + 16*b^6*x^12))/(3003*a^4*x^13)","A",1
407,1,97,116,0.1409149,"\int \frac{\left(a+b x^2\right)^{5/2}}{x^{16}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(5/2)/x^16,x]","\frac{\sqrt{a+b x^2} \left(-3003 a^7-7161 a^6 b x^2-4473 a^5 b^2 x^4-35 a^4 b^3 x^6+40 a^3 b^4 x^8-48 a^2 b^5 x^{10}+64 a b^6 x^{12}-128 b^7 x^{14}\right)}{45045 a^5 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,"(Sqrt[a + b*x^2]*(-3003*a^7 - 7161*a^6*b*x^2 - 4473*a^5*b^2*x^4 - 35*a^4*b^3*x^6 + 40*a^3*b^4*x^8 - 48*a^2*b^5*x^10 + 64*a*b^6*x^12 - 128*b^7*x^14))/(45045*a^5*x^15)","A",1
408,1,108,140,0.1629262,"\int \frac{\left(a+b x^2\right)^{5/2}}{x^{18}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(5/2)/x^18,x]","\frac{\sqrt{a+b x^2} \left(-9009 a^8-21021 a^7 b x^2-12705 a^6 b^2 x^4-63 a^5 b^3 x^6+70 a^4 b^4 x^8-80 a^3 b^5 x^{10}+96 a^2 b^6 x^{12}-128 a b^7 x^{14}+256 b^8 x^{16}\right)}{153153 a^6 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,"(Sqrt[a + b*x^2]*(-9009*a^8 - 21021*a^7*b*x^2 - 12705*a^6*b^2*x^4 - 63*a^5*b^3*x^6 + 70*a^4*b^4*x^8 - 80*a^3*b^5*x^10 + 96*a^2*b^6*x^12 - 128*a*b^7*x^14 + 256*b^8*x^16))/(153153*a^6*x^17)","A",1
409,1,149,161,0.0572145,"\int x^{15} \left(a+b x^2\right)^{9/2} \, dx","IntegrateAlgebraic[x^15*(a + b*x^2)^(9/2),x]","\frac{\sqrt{a+b x^2} \left(-2048 a^{12}+1024 a^{11} b x^2-768 a^{10} b^2 x^4+640 a^9 b^3 x^6-560 a^8 b^4 x^8+504 a^7 b^5 x^{10}-462 a^6 b^6 x^{12}+429 a^5 b^7 x^{14}+1659515 a^4 b^8 x^{16}+5810090 a^3 b^9 x^{18}+7759752 a^2 b^{10} x^{20}+4665089 a b^{11} x^{22}+1062347 b^{12} x^{24}\right)}{26558675 b^8}","-\frac{a^7 \left(a+b x^2\right)^{11/2}}{11 b^8}+\frac{7 a^6 \left(a+b x^2\right)^{13/2}}{13 b^8}-\frac{7 a^5 \left(a+b x^2\right)^{15/2}}{5 b^8}+\frac{35 a^4 \left(a+b x^2\right)^{17/2}}{17 b^8}-\frac{35 a^3 \left(a+b x^2\right)^{19/2}}{19 b^8}+\frac{a^2 \left(a+b x^2\right)^{21/2}}{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,"(Sqrt[a + b*x^2]*(-2048*a^12 + 1024*a^11*b*x^2 - 768*a^10*b^2*x^4 + 640*a^9*b^3*x^6 - 560*a^8*b^4*x^8 + 504*a^7*b^5*x^10 - 462*a^6*b^6*x^12 + 429*a^5*b^7*x^14 + 1659515*a^4*b^8*x^16 + 5810090*a^3*b^9*x^18 + 7759752*a^2*b^10*x^20 + 4665089*a*b^11*x^22 + 1062347*b^12*x^24))/(26558675*b^8)","A",1
410,1,138,140,0.0547091,"\int x^{13} \left(a+b x^2\right)^{9/2} \, dx","IntegrateAlgebraic[x^13*(a + b*x^2)^(9/2),x]","\frac{\sqrt{a+b x^2} \left(1024 a^{11}-512 a^{10} b x^2+384 a^9 b^2 x^4-320 a^8 b^3 x^6+280 a^7 b^4 x^8-252 a^6 b^5 x^{10}+231 a^5 b^6 x^{12}+530959 a^4 b^7 x^{14}+1826110 a^3 b^8 x^{16}+2406690 a^2 b^9 x^{18}+1431859 a b^{10} x^{20}+323323 b^{11} x^{22}\right)}{7436429 b^7}","\frac{a^6 \left(a+b x^2\right)^{11/2}}{11 b^7}-\frac{6 a^5 \left(a+b x^2\right)^{13/2}}{13 b^7}+\frac{a^4 \left(a+b x^2\right)^{15/2}}{b^7}-\frac{20 a^3 \left(a+b x^2\right)^{17/2}}{17 b^7}+\frac{15 a^2 \left(a+b x^2\right)^{19/2}}{19 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,"(Sqrt[a + b*x^2]*(1024*a^11 - 512*a^10*b*x^2 + 384*a^9*b^2*x^4 - 320*a^8*b^3*x^6 + 280*a^7*b^4*x^8 - 252*a^6*b^5*x^10 + 231*a^5*b^6*x^12 + 530959*a^4*b^7*x^14 + 1826110*a^3*b^8*x^16 + 2406690*a^2*b^9*x^18 + 1431859*a*b^10*x^20 + 323323*b^11*x^22))/(7436429*b^7)","A",1
411,1,127,122,0.0526017,"\int x^{11} \left(a+b x^2\right)^{9/2} \, dx","IntegrateAlgebraic[x^11*(a + b*x^2)^(9/2),x]","\frac{\sqrt{a+b x^2} \left(-256 a^{10}+128 a^9 b x^2-96 a^8 b^2 x^4+80 a^7 b^3 x^6-70 a^6 b^4 x^8+63 a^5 b^5 x^{10}+80773 a^4 b^6 x^{12}+271414 a^3 b^7 x^{14}+351780 a^2 b^8 x^{16}+206635 a b^9 x^{18}+46189 b^{10} x^{20}\right)}{969969 b^6}","-\frac{a^5 \left(a+b x^2\right)^{11/2}}{11 b^6}+\frac{5 a^4 \left(a+b x^2\right)^{13/2}}{13 b^6}-\frac{2 a^3 \left(a+b x^2\right)^{15/2}}{3 b^6}+\frac{10 a^2 \left(a+b x^2\right)^{17/2}}{17 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,"(Sqrt[a + b*x^2]*(-256*a^10 + 128*a^9*b*x^2 - 96*a^8*b^2*x^4 + 80*a^7*b^3*x^6 - 70*a^6*b^4*x^8 + 63*a^5*b^5*x^10 + 80773*a^4*b^6*x^12 + 271414*a^3*b^7*x^14 + 351780*a^2*b^8*x^16 + 206635*a*b^9*x^18 + 46189*b^10*x^20))/(969969*b^6)","A",1
412,1,116,101,0.0473725,"\int x^9 \left(a+b x^2\right)^{9/2} \, dx","IntegrateAlgebraic[x^9*(a + b*x^2)^(9/2),x]","\frac{\sqrt{a+b x^2} \left(128 a^9-64 a^8 b x^2+48 a^7 b^2 x^4-40 a^6 b^3 x^6+35 a^5 b^4 x^8+23063 a^4 b^5 x^{10}+75086 a^3 b^6 x^{12}+95238 a^2 b^7 x^{14}+55055 a b^8 x^{16}+12155 b^9 x^{18}\right)}{230945 b^5}","\frac{a^4 \left(a+b x^2\right)^{11/2}}{11 b^5}-\frac{4 a^3 \left(a+b x^2\right)^{13/2}}{13 b^5}+\frac{2 a^2 \left(a+b x^2\right)^{15/2}}{5 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,"(Sqrt[a + b*x^2]*(128*a^9 - 64*a^8*b*x^2 + 48*a^7*b^2*x^4 - 40*a^6*b^3*x^6 + 35*a^5*b^4*x^8 + 23063*a^4*b^5*x^10 + 75086*a^3*b^6*x^12 + 95238*a^2*b^7*x^14 + 55055*a*b^8*x^16 + 12155*b^9*x^18))/(230945*b^5)","A",1
413,1,105,80,0.0439447,"\int x^7 \left(a+b x^2\right)^{9/2} \, dx","IntegrateAlgebraic[x^7*(a + b*x^2)^(9/2),x]","\frac{\sqrt{a+b x^2} \left(-16 a^8+8 a^7 b x^2-6 a^6 b^2 x^4+5 a^5 b^3 x^6+1515 a^4 b^4 x^8+4714 a^3 b^5 x^{10}+5808 a^2 b^6 x^{12}+3289 a b^7 x^{14}+715 b^8 x^{16}\right)}{12155 b^4}","-\frac{a^3 \left(a+b x^2\right)^{11/2}}{11 b^4}+\frac{3 a^2 \left(a+b x^2\right)^{13/2}}{13 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,"(Sqrt[a + b*x^2]*(-16*a^8 + 8*a^7*b*x^2 - 6*a^6*b^2*x^4 + 5*a^5*b^3*x^6 + 1515*a^4*b^4*x^8 + 4714*a^3*b^5*x^10 + 5808*a^2*b^6*x^12 + 3289*a*b^7*x^14 + 715*b^8*x^16))/(12155*b^4)","A",1
414,1,94,59,0.041364,"\int x^5 \left(a+b x^2\right)^{9/2} \, dx","IntegrateAlgebraic[x^5*(a + b*x^2)^(9/2),x]","\frac{\sqrt{a+b x^2} \left(8 a^7-4 a^6 b x^2+3 a^5 b^2 x^4+355 a^4 b^3 x^6+1030 a^3 b^4 x^8+1218 a^2 b^5 x^{10}+671 a b^6 x^{12}+143 b^7 x^{14}\right)}{2145 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,"(Sqrt[a + b*x^2]*(8*a^7 - 4*a^6*b*x^2 + 3*a^5*b^2*x^4 + 355*a^4*b^3*x^6 + 1030*a^3*b^4*x^8 + 1218*a^2*b^5*x^10 + 671*a*b^6*x^12 + 143*b^7*x^14))/(2145*b^3)","A",1
415,1,82,38,0.0375539,"\int x^3 \left(a+b x^2\right)^{9/2} \, dx","IntegrateAlgebraic[x^3*(a + b*x^2)^(9/2),x]","\frac{\sqrt{a+b x^2} \left(-2 a^6+a^5 b x^2+35 a^4 b^2 x^4+90 a^3 b^3 x^6+100 a^2 b^4 x^8+53 a b^5 x^{10}+11 b^6 x^{12}\right)}{143 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,"(Sqrt[a + b*x^2]*(-2*a^6 + a^5*b*x^2 + 35*a^4*b^2*x^4 + 90*a^3*b^3*x^6 + 100*a^2*b^4*x^8 + 53*a*b^5*x^10 + 11*b^6*x^12))/(143*b^2)","B",1
416,1,18,18,0.0213973,"\int x \left(a+b x^2\right)^{9/2} \, dx","IntegrateAlgebraic[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
417,1,84,108,0.0704107,"\int \frac{\left(a+b x^2\right)^{9/2}}{x} \, dx","IntegrateAlgebraic[(a + b*x^2)^(9/2)/x,x]","\frac{1}{315} \sqrt{a+b x^2} \left(563 a^4+506 a^3 b x^2+408 a^2 b^2 x^4+185 a b^3 x^6+35 b^4 x^8\right)-a^{9/2} \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)","a^{9/2} \left(-\tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)\right)+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{1}{7} a \left(a+b x^2\right)^{7/2}+\frac{1}{9} \left(a+b x^2\right)^{9/2}",1,"(Sqrt[a + b*x^2]*(563*a^4 + 506*a^3*b*x^2 + 408*a^2*b^2*x^4 + 185*a*b^3*x^6 + 35*b^4*x^8))/315 - a^(9/2)*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]]","A",1
418,1,90,118,0.1031083,"\int \frac{\left(a+b x^2\right)^{9/2}}{x^3} \, dx","IntegrateAlgebraic[(a + b*x^2)^(9/2)/x^3,x]","\frac{\sqrt{a+b x^2} \left(-35 a^4+388 a^3 b x^2+156 a^2 b^2 x^4+58 a b^3 x^6+10 b^4 x^8\right)}{70 x^2}-\frac{9}{2} a^{7/2} b \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)","-\frac{9}{2} a^{7/2} b \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)+\frac{9}{2} a^3 b \sqrt{a+b x^2}+\frac{3}{2} a^2 b \left(a+b x^2\right)^{3/2}-\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,"(Sqrt[a + b*x^2]*(-35*a^4 + 388*a^3*b*x^2 + 156*a^2*b^2*x^4 + 58*a*b^3*x^6 + 10*b^4*x^8))/(70*x^2) - (9*a^(7/2)*b*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/2","A",1
419,1,92,126,0.1139859,"\int \frac{\left(a+b x^2\right)^{9/2}}{x^5} \, dx","IntegrateAlgebraic[(a + b*x^2)^(9/2)/x^5,x]","\frac{\sqrt{a+b x^2} \left(-10 a^4-85 a^3 b x^2+288 a^2 b^2 x^4+56 a b^3 x^6+8 b^4 x^8\right)}{40 x^4}-\frac{63}{8} a^{5/2} b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)","-\frac{63}{8} a^{5/2} b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)+\frac{63}{8} a^2 b^2 \sqrt{a+b x^2}+\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{9 b \left(a+b x^2\right)^{7/2}}{8 x^2}-\frac{\left(a+b x^2\right)^{9/2}}{4 x^4}",1,"(Sqrt[a + b*x^2]*(-10*a^4 - 85*a^3*b*x^2 + 288*a^2*b^2*x^4 + 56*a*b^3*x^6 + 8*b^4*x^8))/(40*x^4) - (63*a^(5/2)*b^2*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/8","A",1
420,1,92,126,0.1085974,"\int \frac{\left(a+b x^2\right)^{9/2}}{x^7} \, dx","IntegrateAlgebraic[(a + b*x^2)^(9/2)/x^7,x]","\frac{\sqrt{a+b x^2} \left(-8 a^4-50 a^3 b x^2-165 a^2 b^2 x^4+208 a b^3 x^6+16 b^4 x^8\right)}{48 x^6}-\frac{105}{16} a^{3/2} b^3 \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)","-\frac{105}{16} a^{3/2} b^3 \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)+\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{21 b^2 \left(a+b x^2\right)^{5/2}}{16 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,"(Sqrt[a + b*x^2]*(-8*a^4 - 50*a^3*b*x^2 - 165*a^2*b^2*x^4 + 208*a*b^3*x^6 + 16*b^4*x^8))/(48*x^6) - (105*a^(3/2)*b^3*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/16","A",1
421,1,92,128,0.1039352,"\int \frac{\left(a+b x^2\right)^{9/2}}{x^9} \, dx","IntegrateAlgebraic[(a + b*x^2)^(9/2)/x^9,x]","\frac{\sqrt{a+b x^2} \left(-16 a^4-88 a^3 b x^2-210 a^2 b^2 x^4-325 a b^3 x^6+128 b^4 x^8\right)}{128 x^8}-\frac{315}{128} \sqrt{a} b^4 \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)","\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{105 b^3 \left(a+b x^2\right)^{3/2}}{128 x^2}-\frac{21 b^2 \left(a+b x^2\right)^{5/2}}{64 x^4}-\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,"(Sqrt[a + b*x^2]*(-16*a^4 - 88*a^3*b*x^2 - 210*a^2*b^2*x^4 - 325*a*b^3*x^6 + 128*b^4*x^8))/(128*x^8) - (315*Sqrt[a]*b^4*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/128","A",1
422,1,92,131,0.112563,"\int \frac{\left(a+b x^2\right)^{9/2}}{x^{11}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(9/2)/x^11,x]","\frac{\sqrt{a+b x^2} \left(-128 a^4-656 a^3 b x^2-1368 a^2 b^2 x^4-1490 a b^3 x^6-965 b^4 x^8\right)}{1280 x^{10}}-\frac{63 b^5 \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{256 \sqrt{a}}","-\frac{63 b^5 \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{256 \sqrt{a}}-\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{\left(a+b x^2\right)^{9/2}}{10 x^{10}}-\frac{9 b \left(a+b x^2\right)^{7/2}}{80 x^8}",1,"(Sqrt[a + b*x^2]*(-128*a^4 - 656*a^3*b*x^2 - 1368*a^2*b^2*x^4 - 1490*a*b^3*x^6 - 965*b^4*x^8))/(1280*x^10) - (63*b^5*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(256*Sqrt[a])","A",1
423,1,106,155,0.1274858,"\int \frac{\left(a+b x^2\right)^{9/2}}{x^{13}} \, dx","IntegrateAlgebraic[(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{\sqrt{a+b x^2} \left(-1280 a^5-6272 a^4 b x^2-12144 a^3 b^2 x^4-11432 a^2 b^3 x^6-4910 a b^4 x^8-315 b^5 x^{10}\right)}{15360 a 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{\left(a+b x^2\right)^{9/2}}{12 x^{12}}-\frac{3 b \left(a+b x^2\right)^{7/2}}{40 x^{10}}",1,"(Sqrt[a + b*x^2]*(-1280*a^5 - 6272*a^4*b*x^2 - 12144*a^3*b^2*x^4 - 11432*a^2*b^3*x^6 - 4910*a*b^4*x^8 - 315*b^5*x^10))/(15360*a*x^12) + (21*b^6*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(1024*a^(3/2))","A",1
424,1,117,179,0.1349532,"\int \frac{\left(a+b x^2\right)^{9/2}}{x^{15}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(9/2)/x^15,x]","\frac{\sqrt{a+b x^2} \left(-5120 a^6-24320 a^5 b x^2-44928 a^4 b^2 x^4-39056 a^3 b^3 x^6-14168 a^2 b^4 x^8-210 a b^5 x^{10}+315 b^6 x^{12}\right)}{71680 a^2 x^{14}}-\frac{9 b^7 \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{2048 a^{5/2}}","-\frac{9 b^7 \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{2048 a^{5/2}}+\frac{9 b^6 \sqrt{a+b x^2}}{2048 a^2 x^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{\left(a+b x^2\right)^{9/2}}{14 x^{14}}-\frac{3 b \left(a+b x^2\right)^{7/2}}{56 x^{12}}",1,"(Sqrt[a + b*x^2]*(-5120*a^6 - 24320*a^5*b*x^2 - 44928*a^4*b^2*x^4 - 39056*a^3*b^3*x^6 - 14168*a^2*b^4*x^8 - 210*a*b^5*x^10 + 315*b^6*x^12))/(71680*a^2*x^14) - (9*b^7*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(2048*a^(5/2))","A",1
425,1,127,202,0.287795,"\int x^6 \left(a+b x^2\right)^{9/2} \, dx","IntegrateAlgebraic[x^6*(a + b*x^2)^(9/2),x]","\frac{\sqrt{a+b x^2} \left(315 a^7 x-210 a^6 b x^3+168 a^5 b^2 x^5+32624 a^4 b^3 x^7+98432 a^3 b^4 x^9+119040 a^2 b^5 x^{11}+66560 a b^6 x^{13}+14336 b^7 x^{15}\right)}{229376 b^3}-\frac{45 a^8 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{32768 b^{7/2}}","-\frac{45 a^8 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{32768 b^{7/2}}+\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{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,"(Sqrt[a + b*x^2]*(315*a^7*x - 210*a^6*b*x^3 + 168*a^5*b^2*x^5 + 32624*a^4*b^3*x^7 + 98432*a^3*b^4*x^9 + 119040*a^2*b^5*x^11 + 66560*a*b^6*x^13 + 14336*b^7*x^15))/(229376*b^3) - (45*a^8*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(32768*b^(7/2))","A",1
426,1,116,178,0.2471273,"\int x^4 \left(a+b x^2\right)^{9/2} \, dx","IntegrateAlgebraic[x^4*(a + b*x^2)^(9/2),x]","\frac{9 a^7 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{2048 b^{5/2}}+\frac{\sqrt{a+b x^2} \left(-315 a^6 x+210 a^5 b x^3+14168 a^4 b^2 x^5+39056 a^3 b^3 x^7+44928 a^2 b^4 x^9+24320 a b^5 x^{11}+5120 b^6 x^{13}\right)}{71680 b^2}","\frac{9 a^7 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{2048 b^{5/2}}-\frac{9 a^6 x \sqrt{a+b x^2}}{2048 b^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,"(Sqrt[a + b*x^2]*(-315*a^6*x + 210*a^5*b*x^3 + 14168*a^4*b^2*x^5 + 39056*a^3*b^3*x^7 + 44928*a^2*b^4*x^9 + 24320*a*b^5*x^11 + 5120*b^6*x^13))/(71680*b^2) + (9*a^7*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(2048*b^(5/2))","A",1
427,1,105,154,0.2130517,"\int x^2 \left(a+b x^2\right)^{9/2} \, dx","IntegrateAlgebraic[x^2*(a + b*x^2)^(9/2),x]","\frac{\sqrt{a+b x^2} \left(315 a^5 x+4910 a^4 b x^3+11432 a^3 b^2 x^5+12144 a^2 b^3 x^7+6272 a b^4 x^9+1280 b^5 x^{11}\right)}{15360 b}-\frac{21 a^6 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{1024 b^{3/2}}","-\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,"(Sqrt[a + b*x^2]*(315*a^5*x + 4910*a^4*b*x^3 + 11432*a^3*b^2*x^5 + 12144*a^2*b^3*x^7 + 6272*a*b^4*x^9 + 1280*b^5*x^11))/(15360*b) - (21*a^6*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(1024*b^(3/2))","A",1
428,1,91,122,0.1830243,"\int \left(a+b x^2\right)^{9/2} \, dx","IntegrateAlgebraic[(a + b*x^2)^(9/2),x]","\frac{63 a^5 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{256 \sqrt{b}}+\frac{\sqrt{a+b x^2} \left(965 a^4 x+1490 a^3 b x^3+1368 a^2 b^2 x^5+656 a b^3 x^7+128 b^4 x^9\right)}{1280}","\frac{63 a^5 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{256 \sqrt{b}}+\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{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,"(Sqrt[a + b*x^2]*(965*a^4*x + 1490*a^3*b*x^3 + 1368*a^2*b^2*x^5 + 656*a*b^3*x^7 + 128*b^4*x^9))/1280 + (63*a^5*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(256*Sqrt[b])","A",1
429,1,93,123,0.1815594,"\int \frac{\left(a+b x^2\right)^{9/2}}{x^2} \, dx","IntegrateAlgebraic[(a + b*x^2)^(9/2)/x^2,x]","\frac{315}{128} a^4 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)+\frac{\sqrt{a+b x^2} \left(-128 a^4+325 a^3 b x^2+210 a^2 b^2 x^4+88 a b^3 x^6+16 b^4 x^8\right)}{128 x}","\frac{315}{128} a^4 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)+\frac{315}{128} a^3 b x \sqrt{a+b x^2}+\frac{105}{64} a^2 b x \left(a+b x^2\right)^{3/2}-\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,"(Sqrt[a + b*x^2]*(-128*a^4 + 325*a^3*b*x^2 + 210*a^2*b^2*x^4 + 88*a*b^3*x^6 + 16*b^4*x^8))/(128*x) + (315*a^4*Sqrt[b]*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/128","A",1
430,1,93,128,0.1811356,"\int \frac{\left(a+b x^2\right)^{9/2}}{x^4} \, dx","IntegrateAlgebraic[(a + b*x^2)^(9/2)/x^4,x]","\frac{105}{16} a^3 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)+\frac{\sqrt{a+b x^2} \left(-16 a^4-208 a^3 b x^2+165 a^2 b^2 x^4+50 a b^3 x^6+8 b^4 x^8\right)}{48 x^3}","\frac{105}{16} a^3 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)+\frac{105}{16} a^2 b^2 x \sqrt{a+b x^2}+\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{3 b \left(a+b x^2\right)^{7/2}}{x}-\frac{\left(a+b x^2\right)^{9/2}}{3 x^3}",1,"(Sqrt[a + b*x^2]*(-16*a^4 - 208*a^3*b*x^2 + 165*a^2*b^2*x^4 + 50*a*b^3*x^6 + 8*b^4*x^8))/(48*x^3) + (105*a^3*b^(3/2)*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/16","A",1
431,1,93,129,0.180758,"\int \frac{\left(a+b x^2\right)^{9/2}}{x^6} \, dx","IntegrateAlgebraic[(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{\sqrt{a+b x^2} \left(-8 a^4-56 a^3 b x^2-288 a^2 b^2 x^4+85 a b^3 x^6+10 b^4 x^8\right)}{40 x^5}","\frac{63}{8} a^2 b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)+\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{21 b^2 \left(a+b x^2\right)^{5/2}}{5 x}-\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,"(Sqrt[a + b*x^2]*(-8*a^4 - 56*a^3*b*x^2 - 288*a^2*b^2*x^4 + 85*a*b^3*x^6 + 10*b^4*x^8))/(40*x^5) + (63*a^2*b^(5/2)*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/8","A",1
432,1,91,126,0.177689,"\int \frac{\left(a+b x^2\right)^{9/2}}{x^8} \, dx","IntegrateAlgebraic[(a + b*x^2)^(9/2)/x^8,x]","\frac{\sqrt{a+b x^2} \left(-10 a^4-58 a^3 b x^2-156 a^2 b^2 x^4-388 a b^3 x^6+35 b^4 x^8\right)}{70 x^7}+\frac{9}{2} a b^{7/2} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)","\frac{9}{2} a b^{7/2} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)+\frac{9}{2} b^4 x \sqrt{a+b x^2}-\frac{3 b^3 \left(a+b x^2\right)^{3/2}}{x}-\frac{3 b^2 \left(a+b x^2\right)^{5/2}}{5 x^3}-\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,"(Sqrt[a + b*x^2]*(-10*a^4 - 58*a^3*b*x^2 - 156*a^2*b^2*x^4 - 388*a*b^3*x^6 + 35*b^4*x^8))/(70*x^7) + (9*a*b^(7/2)*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/2","A",1
433,1,87,124,0.1480352,"\int \frac{\left(a+b x^2\right)^{9/2}}{x^{10}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(9/2)/x^10,x]","\frac{\sqrt{a+b x^2} \left(-35 a^4-185 a^3 b x^2-408 a^2 b^2 x^4-506 a b^3 x^6-563 b^4 x^8\right)}{315 x^9}+b^{9/2} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)","b^{9/2} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)-\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}-\frac{\left(a+b x^2\right)^{9/2}}{9 x^9}-\frac{b \left(a+b x^2\right)^{7/2}}{7 x^7}",1,"(Sqrt[a + b*x^2]*(-35*a^4 - 185*a^3*b*x^2 - 408*a^2*b^2*x^4 - 506*a*b^3*x^6 - 563*b^4*x^8))/(315*x^9) + b^(9/2)*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]]","A",1
434,1,21,21,0.0618995,"\int \frac{\left(a+b x^2\right)^{9/2}}{x^{12}} \, dx","IntegrateAlgebraic[(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,"-1/11*(a + b*x^2)^(11/2)/(a*x^11)","A",1
435,1,86,44,0.1131737,"\int \frac{\left(a+b x^2\right)^{9/2}}{x^{14}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(9/2)/x^14,x]","\frac{\sqrt{a+b x^2} \left(-11 a^6-53 a^5 b x^2-100 a^4 b^2 x^4-90 a^3 b^3 x^6-35 a^2 b^4 x^8-a b^5 x^{10}+2 b^6 x^{12}\right)}{143 a^2 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,"(Sqrt[a + b*x^2]*(-11*a^6 - 53*a^5*b*x^2 - 100*a^4*b^2*x^4 - 90*a^3*b^3*x^6 - 35*a^2*b^4*x^8 - a*b^5*x^10 + 2*b^6*x^12))/(143*a^2*x^13)","A",1
436,1,97,68,0.1327979,"\int \frac{\left(a+b x^2\right)^{9/2}}{x^{16}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(9/2)/x^16,x]","\frac{\sqrt{a+b x^2} \left(-143 a^7-671 a^6 b x^2-1218 a^5 b^2 x^4-1030 a^4 b^3 x^6-355 a^3 b^4 x^8-3 a^2 b^5 x^{10}+4 a b^6 x^{12}-8 b^7 x^{14}\right)}{2145 a^3 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,"(Sqrt[a + b*x^2]*(-143*a^7 - 671*a^6*b*x^2 - 1218*a^5*b^2*x^4 - 1030*a^4*b^3*x^6 - 355*a^3*b^4*x^8 - 3*a^2*b^5*x^10 + 4*a*b^6*x^12 - 8*b^7*x^14))/(2145*a^3*x^15)","A",1
437,1,108,92,0.1550582,"\int \frac{\left(a+b x^2\right)^{9/2}}{x^{18}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(9/2)/x^18,x]","\frac{\sqrt{a+b x^2} \left(-715 a^8-3289 a^7 b x^2-5808 a^6 b^2 x^4-4714 a^5 b^3 x^6-1515 a^4 b^4 x^8-5 a^3 b^5 x^{10}+6 a^2 b^6 x^{12}-8 a b^7 x^{14}+16 b^8 x^{16}\right)}{12155 a^4 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,"(Sqrt[a + b*x^2]*(-715*a^8 - 3289*a^7*b*x^2 - 5808*a^6*b^2*x^4 - 4714*a^5*b^3*x^6 - 1515*a^4*b^4*x^8 - 5*a^3*b^5*x^10 + 6*a^2*b^6*x^12 - 8*a*b^7*x^14 + 16*b^8*x^16))/(12155*a^4*x^17)","A",1
438,1,119,116,0.1809122,"\int \frac{\left(a+b x^2\right)^{9/2}}{x^{20}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(9/2)/x^20,x]","\frac{\sqrt{a+b x^2} \left(-12155 a^9-55055 a^8 b x^2-95238 a^7 b^2 x^4-75086 a^6 b^3 x^6-23063 a^5 b^4 x^8-35 a^4 b^5 x^{10}+40 a^3 b^6 x^{12}-48 a^2 b^7 x^{14}+64 a b^8 x^{16}-128 b^9 x^{18}\right)}{230945 a^5 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,"(Sqrt[a + b*x^2]*(-12155*a^9 - 55055*a^8*b*x^2 - 95238*a^7*b^2*x^4 - 75086*a^6*b^3*x^6 - 23063*a^5*b^4*x^8 - 35*a^4*b^5*x^10 + 40*a^3*b^6*x^12 - 48*a^2*b^7*x^14 + 64*a*b^8*x^16 - 128*b^9*x^18))/(230945*a^5*x^19)","A",1
439,1,130,140,0.2127978,"\int \frac{\left(a+b x^2\right)^{9/2}}{x^{22}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(9/2)/x^22,x]","\frac{\sqrt{a+b x^2} \left(-46189 a^{10}-206635 a^9 b x^2-351780 a^8 b^2 x^4-271414 a^7 b^3 x^6-80773 a^6 b^4 x^8-63 a^5 b^5 x^{10}+70 a^4 b^6 x^{12}-80 a^3 b^7 x^{14}+96 a^2 b^8 x^{16}-128 a b^9 x^{18}+256 b^{10} x^{20}\right)}{969969 a^6 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,"(Sqrt[a + b*x^2]*(-46189*a^10 - 206635*a^9*b*x^2 - 351780*a^8*b^2*x^4 - 271414*a^7*b^3*x^6 - 80773*a^6*b^4*x^8 - 63*a^5*b^5*x^10 + 70*a^4*b^6*x^12 - 80*a^3*b^7*x^14 + 96*a^2*b^8*x^16 - 128*a*b^9*x^18 + 256*b^10*x^20))/(969969*a^6*x^21)","A",1
440,1,141,164,0.248322,"\int \frac{\left(a+b x^2\right)^{9/2}}{x^{24}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(9/2)/x^24,x]","\frac{\sqrt{a+b x^2} \left(-323323 a^{11}-1431859 a^{10} b x^2-2406690 a^9 b^2 x^4-1826110 a^8 b^3 x^6-530959 a^7 b^4 x^8-231 a^6 b^5 x^{10}+252 a^5 b^6 x^{12}-280 a^4 b^7 x^{14}+320 a^3 b^8 x^{16}-384 a^2 b^9 x^{18}+512 a b^{10} x^{20}-1024 b^{11} x^{22}\right)}{7436429 a^7 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,"(Sqrt[a + b*x^2]*(-323323*a^11 - 1431859*a^10*b*x^2 - 2406690*a^9*b^2*x^4 - 1826110*a^8*b^3*x^6 - 530959*a^7*b^4*x^8 - 231*a^6*b^5*x^10 + 252*a^5*b^6*x^12 - 280*a^4*b^7*x^14 + 320*a^3*b^8*x^16 - 384*a^2*b^9*x^18 + 512*a*b^10*x^20 - 1024*b^11*x^22))/(7436429*a^7*x^23)","A",1
441,1,32,46,0.0185209,"\int x^5 \sqrt{9+4 x^2} \, dx","IntegrateAlgebraic[x^5*Sqrt[9 + 4*x^2],x]","\frac{1}{280} \sqrt{4 x^2+9} \left(40 x^6+18 x^4-54 x^2+243\right)","\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,"(Sqrt[9 + 4*x^2]*(243 - 54*x^2 + 18*x^4 + 40*x^6))/280","A",1
442,1,50,63,0.0429246,"\int x^4 \sqrt{9+4 x^2} \, dx","IntegrateAlgebraic[x^4*Sqrt[9 + 4*x^2],x]","\frac{1}{768} \sqrt{4 x^2+9} \left(128 x^5+72 x^3-243 x\right)-\frac{729}{512} \log \left(\sqrt{4 x^2+9}-2 x\right)","-\frac{81}{256} \sqrt{4 x^2+9} x+\frac{1}{6} \sqrt{4 x^2+9} x^5+\frac{3}{32} \sqrt{4 x^2+9} x^3+\frac{729}{512} \sinh ^{-1}\left(\frac{2 x}{3}\right)",1,"(Sqrt[9 + 4*x^2]*(-243*x + 72*x^3 + 128*x^5))/768 - (729*Log[-2*x + Sqrt[9 + 4*x^2]])/512","A",1
443,1,27,31,0.0158358,"\int x^3 \sqrt{9+4 x^2} \, dx","IntegrateAlgebraic[x^3*Sqrt[9 + 4*x^2],x]","\frac{1}{40} \sqrt{4 x^2+9} \left(8 x^4+6 x^2-27\right)","\frac{1}{80} \left(4 x^2+9\right)^{5/2}-\frac{3}{16} \left(4 x^2+9\right)^{3/2}",1,"(Sqrt[9 + 4*x^2]*(-27 + 6*x^2 + 8*x^4))/40","A",1
444,1,45,45,0.0232211,"\int x^2 \sqrt{9+4 x^2} \, dx","IntegrateAlgebraic[x^2*Sqrt[9 + 4*x^2],x]","\frac{81}{64} \log \left(\sqrt{4 x^2+9}-2 x\right)+\frac{1}{32} \sqrt{4 x^2+9} \left(8 x^3+9 x\right)","\frac{9}{32} \sqrt{4 x^2+9} x+\frac{1}{4} \sqrt{4 x^2+9} x^3-\frac{81}{64} \sinh ^{-1}\left(\frac{2 x}{3}\right)",1,"(Sqrt[9 + 4*x^2]*(9*x + 8*x^3))/32 + (81*Log[-2*x + Sqrt[9 + 4*x^2]])/64","A",1
445,1,15,15,0.0114359,"\int x \sqrt{9+4 x^2} \, dx","IntegrateAlgebraic[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
446,1,37,27,0.0223599,"\int \sqrt{9+4 x^2} \, dx","IntegrateAlgebraic[Sqrt[9 + 4*x^2],x]","\frac{1}{2} x \sqrt{4 x^2+9}-\frac{9}{4} \log \left(\sqrt{4 x^2+9}-2 x\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*Log[-2*x + Sqrt[9 + 4*x^2]])/4","A",1
447,1,30,30,0.0257026,"\int \frac{\sqrt{9+4 x^2}}{x} \, dx","IntegrateAlgebraic[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",1
448,1,35,25,0.0321582,"\int \frac{\sqrt{9+4 x^2}}{x^2} \, dx","IntegrateAlgebraic[Sqrt[9 + 4*x^2]/x^2,x]","-\frac{\sqrt{4 x^2+9}}{x}-2 \log \left(\sqrt{4 x^2+9}-2 x\right)","2 \sinh ^{-1}\left(\frac{2 x}{3}\right)-\frac{\sqrt{4 x^2+9}}{x}",1,"-(Sqrt[9 + 4*x^2]/x) - 2*Log[-2*x + Sqrt[9 + 4*x^2]]","A",1
449,1,39,39,0.0380455,"\int \frac{\sqrt{9+4 x^2}}{x^3} \, dx","IntegrateAlgebraic[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,"-1/2*Sqrt[9 + 4*x^2]/x^2 - (2*ArcTanh[Sqrt[9 + 4*x^2]/3])/3","A",1
450,1,25,18,0.03207,"\int \frac{\sqrt{9+4 x^2}}{x^4} \, dx","IntegrateAlgebraic[Sqrt[9 + 4*x^2]/x^4,x]","\frac{\left(-4 x^2-9\right) \sqrt{4 x^2+9}}{27 x^3}","-\frac{\left(4 x^2+9\right)^{3/2}}{27 x^3}",1,"((-9 - 4*x^2)*Sqrt[9 + 4*x^2])/(27*x^3)","A",1
451,1,46,57,0.0526811,"\int \frac{\sqrt{9+4 x^2}}{x^5} \, dx","IntegrateAlgebraic[Sqrt[9 + 4*x^2]/x^5,x]","\frac{2}{27} \tanh ^{-1}\left(\frac{1}{3} \sqrt{4 x^2+9}\right)+\frac{\sqrt{4 x^2+9} \left(-2 x^2-9\right)}{36 x^4}","-\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}}{4 x^4}",1,"((-9 - 2*x^2)*Sqrt[9 + 4*x^2])/(36*x^4) + (2*ArcTanh[Sqrt[9 + 4*x^2]/3])/27","A",1
452,1,32,46,0.0447998,"\int x^5 \sqrt{9-4 x^2} \, dx","IntegrateAlgebraic[x^5*Sqrt[9 - 4*x^2],x]","\frac{1}{280} \sqrt{9-4 x^2} \left(40 x^6-18 x^4-54 x^2-243\right)","-\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,"(Sqrt[9 - 4*x^2]*(-243 - 54*x^2 - 18*x^4 + 40*x^6))/280","A",1
453,1,53,63,0.0769711,"\int x^4 \sqrt{9-4 x^2} \, dx","IntegrateAlgebraic[x^4*Sqrt[9 - 4*x^2],x]","\frac{729}{256} \tan ^{-1}\left(\frac{2 x}{\sqrt{9-4 x^2}-3}\right)+\frac{1}{768} \sqrt{9-4 x^2} \left(128 x^5-72 x^3-243 x\right)","-\frac{81}{256} \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{729}{512} \sin ^{-1}\left(\frac{2 x}{3}\right)",1,"(Sqrt[9 - 4*x^2]*(-243*x - 72*x^3 + 128*x^5))/768 + (729*ArcTan[(2*x)/(-3 + Sqrt[9 - 4*x^2])])/256","A",1
454,1,27,31,0.0439692,"\int x^3 \sqrt{9-4 x^2} \, dx","IntegrateAlgebraic[x^3*Sqrt[9 - 4*x^2],x]","\frac{1}{40} \sqrt{9-4 x^2} \left(8 x^4-6 x^2-27\right)","\frac{1}{80} \left(9-4 x^2\right)^{5/2}-\frac{3}{16} \left(9-4 x^2\right)^{3/2}",1,"(Sqrt[9 - 4*x^2]*(-27 - 6*x^2 + 8*x^4))/40","A",1
455,1,48,45,0.0594472,"\int x^2 \sqrt{9-4 x^2} \, dx","IntegrateAlgebraic[x^2*Sqrt[9 - 4*x^2],x]","\frac{81}{32} \tan ^{-1}\left(\frac{2 x}{\sqrt{9-4 x^2}-3}\right)+\frac{1}{32} \sqrt{9-4 x^2} \left(8 x^3-9 x\right)","-\frac{9}{32} \sqrt{9-4 x^2} x+\frac{1}{4} \sqrt{9-4 x^2} x^3+\frac{81}{64} \sin ^{-1}\left(\frac{2 x}{3}\right)",1,"(Sqrt[9 - 4*x^2]*(-9*x + 8*x^3))/32 + (81*ArcTan[(2*x)/(-3 + Sqrt[9 - 4*x^2])])/32","A",1
456,1,15,15,0.0184182,"\int x \sqrt{9-4 x^2} \, dx","IntegrateAlgebraic[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,"-1/12*(9 - 4*x^2)^(3/2)","A",1
457,1,41,27,0.0440399,"\int \sqrt{9-4 x^2} \, dx","IntegrateAlgebraic[Sqrt[9 - 4*x^2],x]","\frac{1}{2} x \sqrt{9-4 x^2}-\frac{9}{2} \tan ^{-1}\left(\frac{\sqrt{9-4 x^2}}{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*ArcTan[Sqrt[9 - 4*x^2]/(3 + 2*x)])/2","A",1
458,1,30,30,0.0344557,"\int \frac{\sqrt{9-4 x^2}}{x} \, dx","IntegrateAlgebraic[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",1
459,1,39,25,0.0445902,"\int \frac{\sqrt{9-4 x^2}}{x^2} \, dx","IntegrateAlgebraic[Sqrt[9 - 4*x^2]/x^2,x]","4 \tan ^{-1}\left(\frac{\sqrt{9-4 x^2}}{2 x+3}\right)-\frac{\sqrt{9-4 x^2}}{x}","-\frac{\sqrt{9-4 x^2}}{x}-2 \sin ^{-1}\left(\frac{2 x}{3}\right)",1,"-(Sqrt[9 - 4*x^2]/x) + 4*ArcTan[Sqrt[9 - 4*x^2]/(3 + 2*x)]","A",1
460,1,39,39,0.0455805,"\int \frac{\sqrt{9-4 x^2}}{x^3} \, dx","IntegrateAlgebraic[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,"-1/2*Sqrt[9 - 4*x^2]/x^2 + (2*ArcTanh[Sqrt[9 - 4*x^2]/3])/3","A",1
461,1,25,18,0.0285292,"\int \frac{\sqrt{9-4 x^2}}{x^4} \, dx","IntegrateAlgebraic[Sqrt[9 - 4*x^2]/x^4,x]","\frac{\sqrt{9-4 x^2} \left(4 x^2-9\right)}{27 x^3}","-\frac{\left(9-4 x^2\right)^{3/2}}{27 x^3}",1,"(Sqrt[9 - 4*x^2]*(-9 + 4*x^2))/(27*x^3)","A",1
462,1,46,57,0.0459958,"\int \frac{\sqrt{9-4 x^2}}{x^5} \, dx","IntegrateAlgebraic[Sqrt[9 - 4*x^2]/x^5,x]","\frac{2}{27} \tanh ^{-1}\left(\frac{1}{3} \sqrt{9-4 x^2}\right)+\frac{\sqrt{9-4 x^2} \left(2 x^2-9\right)}{36 x^4}","\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}}{4 x^4}",1,"(Sqrt[9 - 4*x^2]*(-9 + 2*x^2))/(36*x^4) + (2*ArcTanh[Sqrt[9 - 4*x^2]/3])/27","A",1
463,1,32,46,0.0246578,"\int x^5 \sqrt{-9+4 x^2} \, dx","IntegrateAlgebraic[x^5*Sqrt[-9 + 4*x^2],x]","\frac{1}{280} \sqrt{4 x^2-9} \left(40 x^6-18 x^4-54 x^2-243\right)","\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,"(Sqrt[-9 + 4*x^2]*(-243 - 54*x^2 - 18*x^4 + 40*x^6))/280","A",1
464,1,50,72,0.0420109,"\int x^4 \sqrt{-9+4 x^2} \, dx","IntegrateAlgebraic[x^4*Sqrt[-9 + 4*x^2],x]","\frac{729}{512} \log \left(\sqrt{4 x^2-9}-2 x\right)+\frac{1}{768} \sqrt{4 x^2-9} \left(128 x^5-72 x^3-243 x\right)","-\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",1,"(Sqrt[-9 + 4*x^2]*(-243*x - 72*x^3 + 128*x^5))/768 + (729*Log[-2*x + Sqrt[-9 + 4*x^2]])/512","A",1
465,1,27,31,0.0229494,"\int x^3 \sqrt{-9+4 x^2} \, dx","IntegrateAlgebraic[x^3*Sqrt[-9 + 4*x^2],x]","\frac{1}{40} \sqrt{4 x^2-9} \left(8 x^4-6 x^2-27\right)","\frac{1}{80} \left(4 x^2-9\right)^{5/2}+\frac{3}{16} \left(4 x^2-9\right)^{3/2}",1,"(Sqrt[-9 + 4*x^2]*(-27 - 6*x^2 + 8*x^4))/40","A",1
466,1,45,54,0.0291676,"\int x^2 \sqrt{-9+4 x^2} \, dx","IntegrateAlgebraic[x^2*Sqrt[-9 + 4*x^2],x]","\frac{81}{64} \log \left(\sqrt{4 x^2-9}-2 x\right)+\frac{1}{32} \sqrt{4 x^2-9} \left(8 x^3-9 x\right)","-\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",1,"(Sqrt[-9 + 4*x^2]*(-9*x + 8*x^3))/32 + (81*Log[-2*x + Sqrt[-9 + 4*x^2]])/64","A",1
467,1,15,15,0.0182516,"\int x \sqrt{-9+4 x^2} \, dx","IntegrateAlgebraic[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
468,1,37,36,0.0267334,"\int \sqrt{-9+4 x^2} \, dx","IntegrateAlgebraic[Sqrt[-9 + 4*x^2],x]","\frac{1}{2} \sqrt{4 x^2-9} x+\frac{9}{4} \log \left(\sqrt{4 x^2-9}-2 x\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*Log[-2*x + Sqrt[-9 + 4*x^2]])/4","A",1
469,1,30,30,0.0310895,"\int \frac{\sqrt{-9+4 x^2}}{x} \, dx","IntegrateAlgebraic[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",1
470,1,35,34,0.0380697,"\int \frac{\sqrt{-9+4 x^2}}{x^2} \, dx","IntegrateAlgebraic[Sqrt[-9 + 4*x^2]/x^2,x]","-\frac{\sqrt{4 x^2-9}}{x}-2 \log \left(\sqrt{4 x^2-9}-2 x\right)","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*Log[-2*x + Sqrt[-9 + 4*x^2]]","A",1
471,1,39,39,0.0411324,"\int \frac{\sqrt{-9+4 x^2}}{x^3} \, dx","IntegrateAlgebraic[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,"-1/2*Sqrt[-9 + 4*x^2]/x^2 + (2*ArcTan[Sqrt[-9 + 4*x^2]/3])/3","A",1
472,1,18,18,0.0366547,"\int \frac{\sqrt{-9+4 x^2}}{x^4} \, dx","IntegrateAlgebraic[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
473,1,46,57,0.0483922,"\int \frac{\sqrt{-9+4 x^2}}{x^5} \, dx","IntegrateAlgebraic[Sqrt[-9 + 4*x^2]/x^5,x]","\frac{2}{27} \tan ^{-1}\left(\frac{1}{3} \sqrt{4 x^2-9}\right)+\frac{\sqrt{4 x^2-9} \left(2 x^2-9\right)}{36 x^4}","\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}}{4 x^4}",1,"((-9 + 2*x^2)*Sqrt[-9 + 4*x^2])/(36*x^4) + (2*ArcTan[Sqrt[-9 + 4*x^2]/3])/27","A",1
474,1,32,46,0.0235846,"\int x^5 \sqrt{-9-4 x^2} \, dx","IntegrateAlgebraic[x^5*Sqrt[-9 - 4*x^2],x]","\frac{1}{280} \sqrt{-4 x^2-9} \left(40 x^6+18 x^4-54 x^2+243\right)","-\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,"(Sqrt[-9 - 4*x^2]*(243 - 54*x^2 + 18*x^4 + 40*x^6))/280","A",1
475,1,58,72,0.0838068,"\int x^4 \sqrt{-9-4 x^2} \, dx","IntegrateAlgebraic[x^4*Sqrt[-9 - 4*x^2],x]","\frac{729}{512} \tan ^{-1}\left(\frac{2 x \sqrt{-4 x^2-9}}{4 x^2+9}\right)+\frac{1}{768} \sqrt{-4 x^2-9} \left(128 x^5+72 x^3-243 x\right)","-\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",1,"(Sqrt[-9 - 4*x^2]*(-243*x + 72*x^3 + 128*x^5))/768 + (729*ArcTan[(2*x*Sqrt[-9 - 4*x^2])/(9 + 4*x^2)])/512","A",1
476,1,27,31,0.0215279,"\int x^3 \sqrt{-9-4 x^2} \, dx","IntegrateAlgebraic[x^3*Sqrt[-9 - 4*x^2],x]","\frac{1}{40} \sqrt{-4 x^2-9} \left(8 x^4+6 x^2-27\right)","\frac{1}{80} \left(-4 x^2-9\right)^{5/2}+\frac{3}{16} \left(-4 x^2-9\right)^{3/2}",1,"(Sqrt[-9 - 4*x^2]*(-27 + 6*x^2 + 8*x^4))/40","A",1
477,1,53,54,0.0760575,"\int x^2 \sqrt{-9-4 x^2} \, dx","IntegrateAlgebraic[x^2*Sqrt[-9 - 4*x^2],x]","\frac{1}{32} \sqrt{-4 x^2-9} \left(8 x^3+9 x\right)-\frac{81}{64} \tan ^{-1}\left(\frac{2 x \sqrt{-4 x^2-9}}{4 x^2+9}\right)","\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",1,"(Sqrt[-9 - 4*x^2]*(9*x + 8*x^3))/32 - (81*ArcTan[(2*x*Sqrt[-9 - 4*x^2])/(9 + 4*x^2)])/64","A",1
478,1,15,15,0.0170999,"\int x \sqrt{-9-4 x^2} \, dx","IntegrateAlgebraic[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,"-1/12*(-9 - 4*x^2)^(3/2)","A",1
479,1,45,36,0.0700897,"\int \sqrt{-9-4 x^2} \, dx","IntegrateAlgebraic[Sqrt[-9 - 4*x^2],x]","\frac{1}{2} \sqrt{-4 x^2-9} x+\frac{9}{4} \tan ^{-1}\left(\frac{2 x \sqrt{-4 x^2-9}}{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])/(9 + 4*x^2)])/4","A",1
480,1,30,30,0.0287122,"\int \frac{\sqrt{-9-4 x^2}}{x} \, dx","IntegrateAlgebraic[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",1
481,1,43,34,0.0616484,"\int \frac{\sqrt{-9-4 x^2}}{x^2} \, dx","IntegrateAlgebraic[Sqrt[-9 - 4*x^2]/x^2,x]","2 \tan ^{-1}\left(\frac{2 x \sqrt{-4 x^2-9}}{4 x^2+9}\right)-\frac{\sqrt{-4 x^2-9}}{x}","-\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])/(9 + 4*x^2)]","A",1
482,1,39,39,0.03565,"\int \frac{\sqrt{-9-4 x^2}}{x^3} \, dx","IntegrateAlgebraic[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,"-1/2*Sqrt[-9 - 4*x^2]/x^2 - (2*ArcTan[Sqrt[-9 - 4*x^2]/3])/3","A",1
483,1,18,18,0.0457129,"\int \frac{\sqrt{-9-4 x^2}}{x^4} \, dx","IntegrateAlgebraic[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
484,1,46,57,0.0405688,"\int \frac{\sqrt{-9-4 x^2}}{x^5} \, dx","IntegrateAlgebraic[Sqrt[-9 - 4*x^2]/x^5,x]","\frac{2}{27} \tan ^{-1}\left(\frac{1}{3} \sqrt{-4 x^2-9}\right)+\frac{\sqrt{-4 x^2-9} \left(-2 x^2-9\right)}{36 x^4}","-\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}}{4 x^4}",1,"(Sqrt[-9 - 4*x^2]*(-9 - 2*x^2))/(36*x^4) + (2*ArcTan[Sqrt[-9 - 4*x^2]/3])/27","A",1
485,1,39,56,0.034001,"\int \frac{x^5}{\sqrt{a+b x^2}} \, dx","IntegrateAlgebraic[x^5/Sqrt[a + b*x^2],x]","\frac{\sqrt{a+b x^2} \left(8 a^2-4 a b x^2+3 b^2 x^4\right)}{15 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,"(Sqrt[a + b*x^2]*(8*a^2 - 4*a*b*x^2 + 3*b^2*x^4))/(15*b^3)","A",1
486,1,61,73,0.1531448,"\int \frac{x^4}{\sqrt{a+b x^2}} \, dx","IntegrateAlgebraic[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{\sqrt{a+b x^2} \left(2 b x^3-3 a x\right)}{8 b^2}","\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,"(Sqrt[a + b*x^2]*(-3*a*x + 2*b*x^3))/(8*b^2) + (3*a^2*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(8*b^(5/2))","A",1
487,1,27,36,0.0301683,"\int \frac{x^3}{\sqrt{a+b x^2}} \, dx","IntegrateAlgebraic[x^3/Sqrt[a + b*x^2],x]","\frac{\left(b x^2-2 a\right) \sqrt{a+b x^2}}{3 b^2}","\frac{\left(a+b x^2\right)^{3/2}}{3 b^2}-\frac{a \sqrt{a+b x^2}}{b^2}",1,"((-2*a + b*x^2)*Sqrt[a + b*x^2])/(3*b^2)","A",1
488,1,49,49,0.122644,"\int \frac{x^2}{\sqrt{a+b x^2}} \, dx","IntegrateAlgebraic[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",1
489,1,15,15,0.0210136,"\int \frac{x}{\sqrt{a+b x^2}} \, dx","IntegrateAlgebraic[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
490,1,25,25,0.0803668,"\int \frac{1}{\sqrt{a+b x^2}} \, dx","IntegrateAlgebraic[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",1
491,1,25,25,0.0337311,"\int \frac{1}{x \sqrt{a+b x^2}} \, dx","IntegrateAlgebraic[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",1
492,1,19,19,0.0630896,"\int \frac{1}{x^2 \sqrt{a+b x^2}} \, dx","IntegrateAlgebraic[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
493,1,50,50,0.06978,"\int \frac{1}{x^3 \sqrt{a+b x^2}} \, dx","IntegrateAlgebraic[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,"-1/2*Sqrt[a + b*x^2]/(a*x^2) + (b*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(2*a^(3/2))","A",1
494,1,31,44,0.0745455,"\int \frac{1}{x^4 \sqrt{a+b x^2}} \, dx","IntegrateAlgebraic[1/(x^4*Sqrt[a + b*x^2]),x]","\frac{\sqrt{a+b x^2} \left(2 b x^2-a\right)}{3 a^2 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]*(-a + 2*b*x^2))/(3*a^2*x^3)","A",1
495,1,62,74,0.0895909,"\int \frac{1}{x^5 \sqrt{a+b x^2}} \, dx","IntegrateAlgebraic[1/(x^5*Sqrt[a + b*x^2]),x]","\frac{\sqrt{a+b x^2} \left(3 b x^2-2 a\right)}{8 a^2 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^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]*(-2*a + 3*b*x^2))/(8*a^2*x^4) - (3*b^2*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(8*a^(5/2))","A",1
496,1,38,55,0.0389639,"\int \frac{x^5}{\left(a+b x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[x^5/(a + b*x^2)^(3/2),x]","\frac{-8 a^2-4 a b x^2+b^2 x^4}{3 b^3 \sqrt{a+b x^2}}","-\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,"(-8*a^2 - 4*a*b*x^2 + b^2*x^4)/(3*b^3*Sqrt[a + b*x^2])","A",1
497,1,58,68,0.1607081,"\int \frac{x^4}{\left(a+b x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[x^4/(a + b*x^2)^(3/2),x]","\frac{3 a x+b x^3}{2 b^2 \sqrt{a+b x^2}}-\frac{3 a \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{2 b^{5/2}}","-\frac{3 a \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{2 b^{5/2}}+\frac{3 x \sqrt{a+b x^2}}{2 b^2}-\frac{x^3}{b \sqrt{a+b x^2}}",1,"(3*a*x + b*x^3)/(2*b^2*Sqrt[a + b*x^2]) - (3*a*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(2*b^(5/2))","A",1
498,1,24,32,0.0350335,"\int \frac{x^3}{\left(a+b x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[x^3/(a + b*x^2)^(3/2),x]","\frac{2 a+b x^2}{b^2 \sqrt{a+b x^2}}","\frac{a}{b^2 \sqrt{a+b x^2}}+\frac{\sqrt{a+b x^2}}{b^2}",1,"(2*a + b*x^2)/(b^2*Sqrt[a + b*x^2])","A",1
499,1,43,43,0.1202495,"\int \frac{x^2}{\left(a+b x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[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",1
500,1,16,16,0.0267459,"\int \frac{x}{\left(a+b x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[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
501,1,16,16,0.0714501,"\int \frac{1}{\left(a+b x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[(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
502,1,41,41,0.0528811,"\int \frac{1}{x \left(a+b x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[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",1
503,1,28,38,0.0853798,"\int \frac{1}{x^2 \left(a+b x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[1/(x^2*(a + b*x^2)^(3/2)),x]","\frac{-a-2 b x^2}{a^2 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,"(-a - 2*b*x^2)/(a^2*x*Sqrt[a + b*x^2])","A",1
504,1,60,69,0.0973746,"\int \frac{1}{x^3 \left(a+b x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[1/(x^3*(a + b*x^2)^(3/2)),x]","\frac{3 b \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{2 a^{5/2}}+\frac{-a-3 b x^2}{2 a^2 x^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{3 b}{2 a^2 \sqrt{a+b x^2}}-\frac{1}{2 a x^2 \sqrt{a+b x^2}}",1,"(-a - 3*b*x^2)/(2*a^2*x^2*Sqrt[a + b*x^2]) + (3*b*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(2*a^(5/2))","A",1
505,1,42,66,0.1126827,"\int \frac{1}{x^4 \left(a+b x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[1/(x^4*(a + b*x^2)^(3/2)),x]","\frac{-a^2+4 a b x^2+8 b^2 x^4}{3 a^3 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,"(-a^2 + 4*a*b*x^2 + 8*b^2*x^4)/(3*a^3*x^3*Sqrt[a + b*x^2])","A",1
506,1,70,91,0.20896,"\int \frac{x^6}{\left(a+b x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[x^6/(a + b*x^2)^(5/2),x]","\frac{15 a^2 x+20 a b x^3+3 b^2 x^5}{6 b^3 \left(a+b x^2\right)^{3/2}}-\frac{5 a \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{2 b^{7/2}}","-\frac{5 a \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{2 b^{7/2}}+\frac{5 x \sqrt{a+b x^2}}{2 b^3}-\frac{5 x^3}{3 b^2 \sqrt{a+b x^2}}-\frac{x^5}{3 b \left(a+b x^2\right)^{3/2}}",1,"(15*a^2*x + 20*a*b*x^3 + 3*b^2*x^5)/(6*b^3*(a + b*x^2)^(3/2)) - (5*a*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(2*b^(7/2))","A",1
507,1,39,54,0.0408525,"\int \frac{x^5}{\left(a+b x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[x^5/(a + b*x^2)^(5/2),x]","\frac{8 a^2+12 a b x^2+3 b^2 x^4}{3 b^3 \left(a+b x^2\right)^{3/2}}","-\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,"(8*a^2 + 12*a*b*x^2 + 3*b^2*x^4)/(3*b^3*(a + b*x^2)^(3/2))","A",1
508,1,55,64,0.1562709,"\int \frac{x^4}{\left(a+b x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[x^4/(a + b*x^2)^(5/2),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{b^{5/2}}+\frac{-3 a x-4 b x^3}{3 b^2 \left(a+b x^2\right)^{3/2}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{b^{5/2}}-\frac{x}{b^2 \sqrt{a+b x^2}}-\frac{x^3}{3 b \left(a+b x^2\right)^{3/2}}",1,"(-3*a*x - 4*b*x^3)/(3*b^2*(a + b*x^2)^(3/2)) + ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]]/b^(5/2)","A",1
509,1,28,36,0.036249,"\int \frac{x^3}{\left(a+b x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[x^3/(a + b*x^2)^(5/2),x]","\frac{-2 a-3 b x^2}{3 b^2 \left(a+b x^2\right)^{3/2}}","\frac{a}{3 b^2 \left(a+b x^2\right)^{3/2}}-\frac{1}{b^2 \sqrt{a+b x^2}}",1,"(-2*a - 3*b*x^2)/(3*b^2*(a + b*x^2)^(3/2))","A",1
510,1,21,21,0.0815985,"\int \frac{x^2}{\left(a+b x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[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
511,1,18,18,0.0253491,"\int \frac{x}{\left(a+b x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[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*1/(b*(a + b*x^2)^(3/2))","A",1
512,1,29,39,0.0877278,"\int \frac{1}{\left(a+b x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(-5/2),x]","\frac{x \left(3 a+2 b x^2\right)}{3 a^2 \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 + 2*b*x^2))/(3*a^2*(a + b*x^2)^(3/2))","A",1
513,1,54,59,0.0772969,"\int \frac{1}{x \left(a+b x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[1/(x*(a + b*x^2)^(5/2)),x]","\frac{4 a+3 b x^2}{3 a^2 \left(a+b x^2\right)^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{a^{5/2}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{a^{5/2}}+\frac{1}{a^2 \sqrt{a+b x^2}}+\frac{1}{3 a \left(a+b x^2\right)^{3/2}}",1,"(4*a + 3*b*x^2)/(3*a^2*(a + b*x^2)^(3/2)) - ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]]/a^(5/2)","A",1
514,1,42,60,0.1081405,"\int \frac{1}{x^2 \left(a+b x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[1/(x^2*(a + b*x^2)^(5/2)),x]","\frac{-3 a^2-12 a b x^2-8 b^2 x^4}{3 a^3 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,"(-3*a^2 - 12*a*b*x^2 - 8*b^2*x^4)/(3*a^3*x*(a + b*x^2)^(3/2))","A",1
515,1,71,88,0.1306458,"\int \frac{1}{x^3 \left(a+b x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[1/(x^3*(a + b*x^2)^(5/2)),x]","\frac{5 b \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{2 a^{7/2}}+\frac{-3 a^2-20 a b x^2-15 b^2 x^4}{6 a^3 x^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{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{1}{2 a x^2 \left(a+b x^2\right)^{3/2}}",1,"(-3*a^2 - 20*a*b*x^2 - 15*b^2*x^4)/(6*a^3*x^2*(a + b*x^2)^(3/2)) + (5*b*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(2*a^(7/2))","A",1
516,1,53,86,0.1562915,"\int \frac{1}{x^4 \left(a+b x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[1/(x^4*(a + b*x^2)^(5/2)),x]","\frac{-a^3+6 a^2 b x^2+24 a b^2 x^4+16 b^3 x^6}{3 a^4 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,"(-a^3 + 6*a^2*b*x^2 + 24*a*b^2*x^4 + 16*b^3*x^6)/(3*a^4*x^3*(a + b*x^2)^(3/2))","A",1
517,1,92,131,0.3284802,"\int \frac{x^{10}}{\left(a+b x^2\right)^{9/2}} \, dx","IntegrateAlgebraic[x^10/(a + b*x^2)^(9/2),x]","\frac{315 a^4 x+1050 a^3 b x^3+1218 a^2 b^2 x^5+528 a b^3 x^7+35 b^4 x^9}{70 b^5 \left(a+b x^2\right)^{7/2}}-\frac{9 a \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{2 b^{11/2}}","-\frac{9 a \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{2 b^{11/2}}+\frac{9 x \sqrt{a+b x^2}}{2 b^5}-\frac{3 x^3}{b^4 \sqrt{a+b x^2}}-\frac{3 x^5}{5 b^3 \left(a+b x^2\right)^{3/2}}-\frac{9 x^7}{35 b^2 \left(a+b x^2\right)^{5/2}}-\frac{x^9}{7 b \left(a+b x^2\right)^{7/2}}",1,"(315*a^4*x + 1050*a^3*b*x^3 + 1218*a^2*b^2*x^5 + 528*a*b^3*x^7 + 35*b^4*x^9)/(70*b^5*(a + b*x^2)^(7/2)) - (9*a*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(2*b^(11/2))","A",1
518,1,61,94,0.0650723,"\int \frac{x^9}{\left(a+b x^2\right)^{9/2}} \, dx","IntegrateAlgebraic[x^9/(a + b*x^2)^(9/2),x]","\frac{128 a^4+448 a^3 b x^2+560 a^2 b^2 x^4+280 a b^3 x^6+35 b^4 x^8}{35 b^5 \left(a+b x^2\right)^{7/2}}","-\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,"(128*a^4 + 448*a^3*b*x^2 + 560*a^2*b^2*x^4 + 280*a*b^3*x^6 + 35*b^4*x^8)/(35*b^5*(a + b*x^2)^(7/2))","A",1
519,1,77,106,0.2571048,"\int \frac{x^8}{\left(a+b x^2\right)^{9/2}} \, dx","IntegrateAlgebraic[x^8/(a + b*x^2)^(9/2),x]","\frac{-105 a^3 x-350 a^2 b x^3-406 a b^2 x^5-176 b^3 x^7}{105 b^4 \left(a+b x^2\right)^{7/2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{b^{9/2}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{b^{9/2}}-\frac{x}{b^4 \sqrt{a+b x^2}}-\frac{x^3}{3 b^3 \left(a+b x^2\right)^{3/2}}-\frac{x^5}{5 b^2 \left(a+b x^2\right)^{5/2}}-\frac{x^7}{7 b \left(a+b x^2\right)^{7/2}}",1,"(-105*a^3*x - 350*a^2*b*x^3 - 406*a*b^2*x^5 - 176*b^3*x^7)/(105*b^4*(a + b*x^2)^(7/2)) + ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]]/b^(9/2)","A",1
520,1,50,75,0.0558546,"\int \frac{x^7}{\left(a+b x^2\right)^{9/2}} \, dx","IntegrateAlgebraic[x^7/(a + b*x^2)^(9/2),x]","\frac{-16 a^3-56 a^2 b x^2-70 a b^2 x^4-35 b^3 x^6}{35 b^4 \left(a+b x^2\right)^{7/2}}","\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,"(-16*a^3 - 56*a^2*b*x^2 - 70*a*b^2*x^4 - 35*b^3*x^6)/(35*b^4*(a + b*x^2)^(7/2))","A",1
521,1,21,21,0.1352725,"\int \frac{x^6}{\left(a+b x^2\right)^{9/2}} \, dx","IntegrateAlgebraic[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
522,1,39,59,0.0462701,"\int \frac{x^5}{\left(a+b x^2\right)^{9/2}} \, dx","IntegrateAlgebraic[x^5/(a + b*x^2)^(9/2),x]","\frac{-8 a^2-28 a b x^2-35 b^2 x^4}{105 b^3 \left(a+b x^2\right)^{7/2}}","-\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,"(-8*a^2 - 28*a*b*x^2 - 35*b^2*x^4)/(105*b^3*(a + b*x^2)^(7/2))","A",1
523,1,31,44,0.1345202,"\int \frac{x^4}{\left(a+b x^2\right)^{9/2}} \, dx","IntegrateAlgebraic[x^4/(a + b*x^2)^(9/2),x]","\frac{x^5 \left(7 a+2 b x^2\right)}{35 a^2 \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*(7*a + 2*b*x^2))/(35*a^2*(a + b*x^2)^(7/2))","A",1
524,1,28,38,0.0391218,"\int \frac{x^3}{\left(a+b x^2\right)^{9/2}} \, dx","IntegrateAlgebraic[x^3/(a + b*x^2)^(9/2),x]","\frac{-2 a-7 b x^2}{35 b^2 \left(a+b x^2\right)^{7/2}}","\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,"(-2*a - 7*b*x^2)/(35*b^2*(a + b*x^2)^(7/2))","A",1
525,1,42,68,0.1287621,"\int \frac{x^2}{\left(a+b x^2\right)^{9/2}} \, dx","IntegrateAlgebraic[x^2/(a + b*x^2)^(9/2),x]","\frac{x^3 \left(35 a^2+28 a b x^2+8 b^2 x^4\right)}{105 a^3 \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*(35*a^2 + 28*a*b*x^2 + 8*b^2*x^4))/(105*a^3*(a + b*x^2)^(7/2))","A",1
526,1,18,18,0.0279954,"\int \frac{x}{\left(a+b x^2\right)^{9/2}} \, dx","IntegrateAlgebraic[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*1/(b*(a + b*x^2)^(7/2))","A",1
527,1,51,77,0.1330499,"\int \frac{1}{\left(a+b x^2\right)^{9/2}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(-9/2),x]","\frac{x \left(35 a^3+70 a^2 b x^2+56 a b^2 x^4+16 b^3 x^6\right)}{35 a^4 \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*(35*a^3 + 70*a^2*b*x^2 + 56*a*b^2*x^4 + 16*b^3*x^6))/(35*a^4*(a + b*x^2)^(7/2))","A",1
528,1,76,95,0.1066367,"\int \frac{1}{x \left(a+b x^2\right)^{9/2}} \, dx","IntegrateAlgebraic[1/(x*(a + b*x^2)^(9/2)),x]","\frac{176 a^3+406 a^2 b x^2+350 a b^2 x^4+105 b^3 x^6}{105 a^4 \left(a+b x^2\right)^{7/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{a^{9/2}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{a^{9/2}}+\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{1}{7 a \left(a+b x^2\right)^{7/2}}",1,"(176*a^3 + 406*a^2*b*x^2 + 350*a*b^2*x^4 + 105*b^3*x^6)/(105*a^4*(a + b*x^2)^(7/2)) - ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]]/a^(9/2)","A",1
529,1,64,100,0.1746048,"\int \frac{1}{x^2 \left(a+b x^2\right)^{9/2}} \, dx","IntegrateAlgebraic[1/(x^2*(a + b*x^2)^(9/2)),x]","\frac{-35 a^4-280 a^3 b x^2-560 a^2 b^2 x^4-448 a b^3 x^6-128 b^4 x^8}{35 a^5 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,"(-35*a^4 - 280*a^3*b*x^2 - 560*a^2*b^2*x^4 - 448*a*b^3*x^6 - 128*b^4*x^8)/(35*a^5*x*(a + b*x^2)^(7/2))","A",1
530,1,93,126,0.1891289,"\int \frac{1}{x^3 \left(a+b x^2\right)^{9/2}} \, dx","IntegrateAlgebraic[1/(x^3*(a + b*x^2)^(9/2)),x]","\frac{9 b \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{2 a^{11/2}}+\frac{-35 a^4-528 a^3 b x^2-1218 a^2 b^2 x^4-1050 a b^3 x^6-315 b^4 x^8}{70 a^5 x^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{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{1}{2 a x^2 \left(a+b x^2\right)^{7/2}}",1,"(-35*a^4 - 528*a^3*b*x^2 - 1218*a^2*b^2*x^4 - 1050*a*b^3*x^6 - 315*b^4*x^8)/(70*a^5*x^2*(a + b*x^2)^(7/2)) + (9*b*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(2*a^(11/2))","A",1
531,1,75,132,0.2781774,"\int \frac{1}{x^4 \left(a+b x^2\right)^{9/2}} \, dx","IntegrateAlgebraic[1/(x^4*(a + b*x^2)^(9/2)),x]","\frac{-7 a^5+70 a^4 b x^2+560 a^3 b^2 x^4+1120 a^2 b^3 x^6+896 a b^4 x^8+256 b^5 x^{10}}{21 a^6 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,"(-7*a^5 + 70*a^4*b*x^2 + 560*a^3*b^2*x^4 + 1120*a^2*b^3*x^6 + 896*a*b^4*x^8 + 256*b^5*x^10)/(21*a^6*x^3*(a + b*x^2)^(7/2))","A",1
532,1,27,46,0.0304845,"\int \frac{x^5}{\sqrt{9+4 x^2}} \, dx","IntegrateAlgebraic[x^5/Sqrt[9 + 4*x^2],x]","\frac{1}{40} \sqrt{4 x^2+9} \left(2 x^4-6 x^2+27\right)","\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,"(Sqrt[9 + 4*x^2]*(27 - 6*x^2 + 2*x^4))/40","A",1
533,1,45,45,0.0472865,"\int \frac{x^4}{\sqrt{9+4 x^2}} \, dx","IntegrateAlgebraic[x^4/Sqrt[9 + 4*x^2],x]","\frac{1}{128} \sqrt{4 x^2+9} \left(8 x^3-27 x\right)-\frac{243}{256} \log \left(\sqrt{4 x^2+9}-2 x\right)","-\frac{27}{128} \sqrt{4 x^2+9} x+\frac{1}{16} \sqrt{4 x^2+9} x^3+\frac{243}{256} \sinh ^{-1}\left(\frac{2 x}{3}\right)",1,"(Sqrt[9 + 4*x^2]*(-27*x + 8*x^3))/128 - (243*Log[-2*x + Sqrt[9 + 4*x^2]])/256","A",1
534,1,22,31,0.0248284,"\int \frac{x^3}{\sqrt{9+4 x^2}} \, dx","IntegrateAlgebraic[x^3/Sqrt[9 + 4*x^2],x]","\frac{1}{24} \left(2 x^2-9\right) \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 + 2*x^2)*Sqrt[9 + 4*x^2])/24","A",1
535,1,37,27,0.035654,"\int \frac{x^2}{\sqrt{9+4 x^2}} \, dx","IntegrateAlgebraic[x^2/Sqrt[9 + 4*x^2],x]","\frac{1}{8} \sqrt{4 x^2+9} x+\frac{9}{16} \log \left(\sqrt{4 x^2+9}-2 x\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*Log[-2*x + Sqrt[9 + 4*x^2]])/16","A",1
536,1,15,15,0.0119226,"\int \frac{x}{\sqrt{9+4 x^2}} \, dx","IntegrateAlgebraic[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
537,1,20,10,0.013366,"\int \frac{1}{\sqrt{9+4 x^2}} \, dx","IntegrateAlgebraic[1/Sqrt[9 + 4*x^2],x]","-\frac{1}{2} \log \left(\sqrt{4 x^2+9}-2 x\right)","\frac{1}{2} \sinh ^{-1}\left(\frac{2 x}{3}\right)",1,"-1/2*Log[-2*x + Sqrt[9 + 4*x^2]]","A",1
538,1,20,20,0.023029,"\int \frac{1}{x \sqrt{9+4 x^2}} \, dx","IntegrateAlgebraic[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,"-1/3*ArcTanh[Sqrt[9 + 4*x^2]/3]","A",1
539,1,18,18,0.0228158,"\int \frac{1}{x^2 \sqrt{9+4 x^2}} \, dx","IntegrateAlgebraic[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,"-1/9*Sqrt[9 + 4*x^2]/x","A",1
540,1,39,39,0.0378054,"\int \frac{1}{x^3 \sqrt{9+4 x^2}} \, dx","IntegrateAlgebraic[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,"-1/18*Sqrt[9 + 4*x^2]/x^2 + (2*ArcTanh[Sqrt[9 + 4*x^2]/3])/27","A",1
541,1,25,37,0.030795,"\int \frac{1}{x^4 \sqrt{9+4 x^2}} \, dx","IntegrateAlgebraic[1/(x^4*Sqrt[9 + 4*x^2]),x]","\frac{\sqrt{4 x^2+9} \left(8 x^2-9\right)}{243 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]*(-9 + 8*x^2))/(243*x^3)","A",1
542,1,46,57,0.0500617,"\int \frac{1}{x^5 \sqrt{9+4 x^2}} \, dx","IntegrateAlgebraic[1/(x^5*Sqrt[9 + 4*x^2]),x]","\frac{\left(2 x^2-3\right) \sqrt{4 x^2+9}}{108 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{2}{81} \tanh ^{-1}\left(\frac{1}{3} \sqrt{4 x^2+9}\right)-\frac{\sqrt{4 x^2+9}}{36 x^4}",1,"((-3 + 2*x^2)*Sqrt[9 + 4*x^2])/(108*x^4) - (2*ArcTanh[Sqrt[9 + 4*x^2]/3])/81","A",1
543,1,27,46,0.0316899,"\int \frac{x^5}{\sqrt{9-4 x^2}} \, dx","IntegrateAlgebraic[x^5/Sqrt[9 - 4*x^2],x]","\frac{1}{40} \sqrt{9-4 x^2} \left(-2 x^4-6 x^2-27\right)","-\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,"(Sqrt[9 - 4*x^2]*(-27 - 6*x^2 - 2*x^4))/40","A",1
544,1,48,45,0.0599861,"\int \frac{x^4}{\sqrt{9-4 x^2}} \, dx","IntegrateAlgebraic[x^4/Sqrt[9 - 4*x^2],x]","\frac{243}{128} \tan ^{-1}\left(\frac{2 x}{\sqrt{9-4 x^2}-3}\right)+\frac{1}{128} \sqrt{9-4 x^2} \left(-8 x^3-27 x\right)","-\frac{27}{128} \sqrt{9-4 x^2} x-\frac{1}{16} \sqrt{9-4 x^2} x^3+\frac{243}{256} \sin ^{-1}\left(\frac{2 x}{3}\right)",1,"(Sqrt[9 - 4*x^2]*(-27*x - 8*x^3))/128 + (243*ArcTan[(2*x)/(-3 + Sqrt[9 - 4*x^2])])/128","A",1
545,1,22,31,0.0287435,"\int \frac{x^3}{\sqrt{9-4 x^2}} \, dx","IntegrateAlgebraic[x^3/Sqrt[9 - 4*x^2],x]","\frac{1}{24} \sqrt{9-4 x^2} \left(-2 x^2-9\right)","\frac{1}{48} \left(9-4 x^2\right)^{3/2}-\frac{9}{16} \sqrt{9-4 x^2}",1,"(Sqrt[9 - 4*x^2]*(-9 - 2*x^2))/24","A",1
546,1,40,27,0.0497563,"\int \frac{x^2}{\sqrt{9-4 x^2}} \, dx","IntegrateAlgebraic[x^2/Sqrt[9 - 4*x^2],x]","\frac{9}{8} \tan ^{-1}\left(\frac{2 x}{\sqrt{9-4 x^2}-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,"-1/8*(x*Sqrt[9 - 4*x^2]) + (9*ArcTan[(2*x)/(-3 + Sqrt[9 - 4*x^2])])/8","A",1
547,1,15,15,0.0234968,"\int \frac{x}{\sqrt{9-4 x^2}} \, dx","IntegrateAlgebraic[x/Sqrt[9 - 4*x^2],x]","-\frac{1}{4} \sqrt{9-4 x^2}","-\frac{1}{4} \sqrt{9-4 x^2}",1,"-1/4*Sqrt[9 - 4*x^2]","A",1
548,1,19,10,0.038258,"\int \frac{1}{\sqrt{9-4 x^2}} \, dx","IntegrateAlgebraic[1/Sqrt[9 - 4*x^2],x]","\tan ^{-1}\left(\frac{2 x}{\sqrt{9-4 x^2}-3}\right)","\frac{1}{2} \sin ^{-1}\left(\frac{2 x}{3}\right)",1,"ArcTan[(2*x)/(-3 + Sqrt[9 - 4*x^2])]","A",1
549,1,25,20,0.0393155,"\int \frac{1}{x \sqrt{9-4 x^2}} \, dx","IntegrateAlgebraic[1/(x*Sqrt[9 - 4*x^2]),x]","\frac{1}{3} \log \left(\sqrt{9-4 x^2}-3\right)-\frac{\log (x)}{3}","-\frac{1}{3} \tanh ^{-1}\left(\frac{1}{3} \sqrt{9-4 x^2}\right)",1,"-1/3*Log[x] + Log[-3 + Sqrt[9 - 4*x^2]]/3","A",1
550,1,18,18,0.0370115,"\int \frac{1}{x^2 \sqrt{9-4 x^2}} \, dx","IntegrateAlgebraic[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,"-1/9*Sqrt[9 - 4*x^2]/x","A",1
551,1,43,39,0.0449784,"\int \frac{1}{x^3 \sqrt{9-4 x^2}} \, dx","IntegrateAlgebraic[1/(x^3*Sqrt[9 - 4*x^2]),x]","-\frac{\sqrt{9-4 x^2}}{18 x^2}+\frac{2}{27} \log \left(\sqrt{9-4 x^2}-3\right)-\frac{2 \log (x)}{27}","-\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,"-1/18*Sqrt[9 - 4*x^2]/x^2 - (2*Log[x])/27 + (2*Log[-3 + Sqrt[9 - 4*x^2]])/27","A",1
552,1,25,37,0.0422123,"\int \frac{1}{x^4 \sqrt{9-4 x^2}} \, dx","IntegrateAlgebraic[1/(x^4*Sqrt[9 - 4*x^2]),x]","\frac{\left(-8 x^2-9\right) \sqrt{9-4 x^2}}{243 x^3}","-\frac{8 \sqrt{9-4 x^2}}{243 x}-\frac{\sqrt{9-4 x^2}}{27 x^3}",1,"((-9 - 8*x^2)*Sqrt[9 - 4*x^2])/(243*x^3)","A",1
553,1,50,57,0.0516795,"\int \frac{1}{x^5 \sqrt{9-4 x^2}} \, dx","IntegrateAlgebraic[1/(x^5*Sqrt[9 - 4*x^2]),x]","\frac{2}{81} \log \left(\sqrt{9-4 x^2}-3\right)+\frac{\sqrt{9-4 x^2} \left(-2 x^2-3\right)}{108 x^4}-\frac{2 \log (x)}{81}","-\frac{\sqrt{9-4 x^2}}{54 x^2}-\frac{2}{81} \tanh ^{-1}\left(\frac{1}{3} \sqrt{9-4 x^2}\right)-\frac{\sqrt{9-4 x^2}}{36 x^4}",1,"(Sqrt[9 - 4*x^2]*(-3 - 2*x^2))/(108*x^4) - (2*Log[x])/81 + (2*Log[-3 + Sqrt[9 - 4*x^2]])/81","A",1
554,1,27,46,0.0410162,"\int \frac{x^5}{\sqrt{-9+4 x^2}} \, dx","IntegrateAlgebraic[x^5/Sqrt[-9 + 4*x^2],x]","\frac{1}{40} \sqrt{4 x^2-9} \left(2 x^4+6 x^2+27\right)","\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,"(Sqrt[-9 + 4*x^2]*(27 + 6*x^2 + 2*x^4))/40","A",1
555,1,45,54,0.0503778,"\int \frac{x^4}{\sqrt{-9+4 x^2}} \, dx","IntegrateAlgebraic[x^4/Sqrt[-9 + 4*x^2],x]","\frac{1}{128} \sqrt{4 x^2-9} \left(8 x^3+27 x\right)-\frac{243}{256} \log \left(\sqrt{4 x^2-9}-2 x\right)","\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",1,"(Sqrt[-9 + 4*x^2]*(27*x + 8*x^3))/128 - (243*Log[-2*x + Sqrt[-9 + 4*x^2]])/256","A",1
556,1,22,31,0.0371339,"\int \frac{x^3}{\sqrt{-9+4 x^2}} \, dx","IntegrateAlgebraic[x^3/Sqrt[-9 + 4*x^2],x]","\frac{1}{24} \left(2 x^2+9\right) \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 + 2*x^2)*Sqrt[-9 + 4*x^2])/24","A",1
557,1,37,36,0.0392171,"\int \frac{x^2}{\sqrt{-9+4 x^2}} \, dx","IntegrateAlgebraic[x^2/Sqrt[-9 + 4*x^2],x]","\frac{1}{8} x \sqrt{4 x^2-9}-\frac{9}{16} \log \left(\sqrt{4 x^2-9}-2 x\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*Log[-2*x + Sqrt[-9 + 4*x^2]])/16","A",1
558,1,15,15,0.0236549,"\int \frac{x}{\sqrt{-9+4 x^2}} \, dx","IntegrateAlgebraic[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
559,1,20,19,0.0242313,"\int \frac{1}{\sqrt{-9+4 x^2}} \, dx","IntegrateAlgebraic[1/Sqrt[-9 + 4*x^2],x]","-\frac{1}{2} \log \left(\sqrt{4 x^2-9}-2 x\right)","\frac{1}{2} \tanh ^{-1}\left(\frac{2 x}{\sqrt{4 x^2-9}}\right)",1,"-1/2*Log[-2*x + Sqrt[-9 + 4*x^2]]","A",1
560,1,20,20,0.0311039,"\int \frac{1}{x \sqrt{-9+4 x^2}} \, dx","IntegrateAlgebraic[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",1
561,1,18,18,0.0295321,"\int \frac{1}{x^2 \sqrt{-9+4 x^2}} \, dx","IntegrateAlgebraic[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
562,1,39,39,0.0437109,"\int \frac{1}{x^3 \sqrt{-9+4 x^2}} \, dx","IntegrateAlgebraic[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",1
563,1,25,37,0.0369978,"\int \frac{1}{x^4 \sqrt{-9+4 x^2}} \, dx","IntegrateAlgebraic[1/(x^4*Sqrt[-9 + 4*x^2]),x]","\frac{\sqrt{4 x^2-9} \left(8 x^2+9\right)}{243 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]*(9 + 8*x^2))/(243*x^3)","A",1
564,1,46,57,0.0528163,"\int \frac{1}{x^5 \sqrt{-9+4 x^2}} \, dx","IntegrateAlgebraic[1/(x^5*Sqrt[-9 + 4*x^2]),x]","\frac{2}{81} \tan ^{-1}\left(\frac{1}{3} \sqrt{4 x^2-9}\right)+\frac{\sqrt{4 x^2-9} \left(2 x^2+3\right)}{108 x^4}","\frac{\sqrt{4 x^2-9}}{54 x^2}+\frac{2}{81} \tan ^{-1}\left(\frac{1}{3} \sqrt{4 x^2-9}\right)+\frac{\sqrt{4 x^2-9}}{36 x^4}",1,"((3 + 2*x^2)*Sqrt[-9 + 4*x^2])/(108*x^4) + (2*ArcTan[Sqrt[-9 + 4*x^2]/3])/81","A",1
565,1,27,46,0.0236748,"\int \frac{x^5}{\sqrt{-9-4 x^2}} \, dx","IntegrateAlgebraic[x^5/Sqrt[-9 - 4*x^2],x]","\frac{1}{40} \sqrt{-4 x^2-9} \left(-2 x^4+6 x^2-27\right)","-\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,"(Sqrt[-9 - 4*x^2]*(-27 + 6*x^2 - 2*x^4))/40","A",1
566,1,53,54,0.0804567,"\int \frac{x^4}{\sqrt{-9-4 x^2}} \, dx","IntegrateAlgebraic[x^4/Sqrt[-9 - 4*x^2],x]","\frac{1}{128} \sqrt{-4 x^2-9} \left(27 x-8 x^3\right)-\frac{243}{256} \tan ^{-1}\left(\frac{2 x \sqrt{-4 x^2-9}}{4 x^2+9}\right)","\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",1,"(Sqrt[-9 - 4*x^2]*(27*x - 8*x^3))/128 - (243*ArcTan[(2*x*Sqrt[-9 - 4*x^2])/(9 + 4*x^2)])/256","A",1
567,1,22,31,0.0219907,"\int \frac{x^3}{\sqrt{-9-4 x^2}} \, dx","IntegrateAlgebraic[x^3/Sqrt[-9 - 4*x^2],x]","\frac{1}{24} \sqrt{-4 x^2-9} \left(9-2 x^2\right)","\frac{1}{48} \left(-4 x^2-9\right)^{3/2}+\frac{9}{16} \sqrt{-4 x^2-9}",1,"(Sqrt[-9 - 4*x^2]*(9 - 2*x^2))/24","A",1
568,1,45,36,0.0703126,"\int \frac{x^2}{\sqrt{-9-4 x^2}} \, dx","IntegrateAlgebraic[x^2/Sqrt[-9 - 4*x^2],x]","\frac{9}{16} \tan ^{-1}\left(\frac{2 x \sqrt{-4 x^2-9}}{4 x^2+9}\right)-\frac{1}{8} x \sqrt{-4 x^2-9}","-\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,"-1/8*(x*Sqrt[-9 - 4*x^2]) + (9*ArcTan[(2*x*Sqrt[-9 - 4*x^2])/(9 + 4*x^2)])/16","A",1
569,1,15,15,0.0179388,"\int \frac{x}{\sqrt{-9-4 x^2}} \, dx","IntegrateAlgebraic[x/Sqrt[-9 - 4*x^2],x]","-\frac{1}{4} \sqrt{-4 x^2-9}","-\frac{1}{4} \sqrt{-4 x^2-9}",1,"-1/4*Sqrt[-9 - 4*x^2]","A",1
570,1,28,19,0.0586515,"\int \frac{1}{\sqrt{-9-4 x^2}} \, dx","IntegrateAlgebraic[1/Sqrt[-9 - 4*x^2],x]","-\frac{1}{2} \tan ^{-1}\left(\frac{2 x \sqrt{-4 x^2-9}}{4 x^2+9}\right)","\frac{1}{2} \tan ^{-1}\left(\frac{2 x}{\sqrt{-4 x^2-9}}\right)",1,"-1/2*ArcTan[(2*x*Sqrt[-9 - 4*x^2])/(9 + 4*x^2)]","A",1
571,1,20,20,0.0250599,"\int \frac{1}{x \sqrt{-9-4 x^2}} \, dx","IntegrateAlgebraic[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",1
572,1,18,18,0.0500914,"\int \frac{1}{x^2 \sqrt{-9-4 x^2}} \, dx","IntegrateAlgebraic[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
573,1,39,39,0.0353384,"\int \frac{1}{x^3 \sqrt{-9-4 x^2}} \, dx","IntegrateAlgebraic[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",1
574,1,25,37,0.0560351,"\int \frac{1}{x^4 \sqrt{-9-4 x^2}} \, dx","IntegrateAlgebraic[1/(x^4*Sqrt[-9 - 4*x^2]),x]","\frac{\left(9-8 x^2\right) \sqrt{-4 x^2-9}}{243 x^3}","\frac{\sqrt{-4 x^2-9}}{27 x^3}-\frac{8 \sqrt{-4 x^2-9}}{243 x}",1,"((9 - 8*x^2)*Sqrt[-9 - 4*x^2])/(243*x^3)","A",1
575,1,46,57,0.0407662,"\int \frac{1}{x^5 \sqrt{-9-4 x^2}} \, dx","IntegrateAlgebraic[1/(x^5*Sqrt[-9 - 4*x^2]),x]","\frac{2}{81} \tan ^{-1}\left(\frac{1}{3} \sqrt{-4 x^2-9}\right)+\frac{\sqrt{-4 x^2-9} \left(3-2 x^2\right)}{108 x^4}","-\frac{\sqrt{-4 x^2-9}}{54 x^2}+\frac{2}{81} \tan ^{-1}\left(\frac{1}{3} \sqrt{-4 x^2-9}\right)+\frac{\sqrt{-4 x^2-9}}{36 x^4}",1,"(Sqrt[-9 - 4*x^2]*(3 - 2*x^2))/(108*x^4) + (2*ArcTan[Sqrt[-9 - 4*x^2]/3])/81","A",1
576,1,25,17,0.0757331,"\int \frac{1}{\sqrt{9+b x^2}} \, dx","IntegrateAlgebraic[1/Sqrt[9 + b*x^2],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+9}}\right)}{\sqrt{b}}","\frac{\sinh ^{-1}\left(\frac{\sqrt{b} x}{3}\right)}{\sqrt{b}}",1,"ArcTanh[(Sqrt[b]*x)/Sqrt[9 + b*x^2]]/Sqrt[b]","A",1
577,1,26,17,0.0784828,"\int \frac{1}{\sqrt{9-b x^2}} \, dx","IntegrateAlgebraic[1/Sqrt[9 - b*x^2],x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{9-b x^2}}\right)}{\sqrt{b}}","\frac{\sin ^{-1}\left(\frac{\sqrt{b} x}{3}\right)}{\sqrt{b}}",1,"ArcTan[(Sqrt[b]*x)/Sqrt[9 - b*x^2]]/Sqrt[b]","A",1
578,1,25,25,0.0766285,"\int \frac{1}{\sqrt{-9+b x^2}} \, dx","IntegrateAlgebraic[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",1
579,1,36,26,0.0789284,"\int \frac{1}{\sqrt{-9-b x^2}} \, dx","IntegrateAlgebraic[1/Sqrt[-9 - b*x^2],x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{b} x \sqrt{-b x^2-9}}{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])/(9 + b*x^2)]/Sqrt[b])","A",1
580,1,25,19,0.0833446,"\int \frac{1}{\sqrt{\pi +b x^2}} \, dx","IntegrateAlgebraic[1/Sqrt[Pi + b*x^2],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+\pi }}\right)}{\sqrt{b}}","\frac{\sinh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{\pi }}\right)}{\sqrt{b}}",1,"ArcTanh[(Sqrt[b]*x)/Sqrt[Pi + b*x^2]]/Sqrt[b]","A",1
581,1,26,19,0.0806502,"\int \frac{1}{\sqrt{\pi -b x^2}} \, dx","IntegrateAlgebraic[1/Sqrt[Pi - b*x^2],x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{\pi -b x^2}}\right)}{\sqrt{b}}","\frac{\sin ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{\pi }}\right)}{\sqrt{b}}",1,"ArcTan[(Sqrt[b]*x)/Sqrt[Pi - b*x^2]]/Sqrt[b]","A",1
582,1,38,27,0.0824854,"\int \frac{1}{\sqrt{-\pi +b x^2}} \, dx","IntegrateAlgebraic[1/Sqrt[-Pi + b*x^2],x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x \sqrt{b x^2-\pi }}{\pi -b x^2}\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])/(Pi - b*x^2)]/Sqrt[b])","A",1
583,1,38,28,0.0828079,"\int \frac{1}{\sqrt{-\pi -b x^2}} \, dx","IntegrateAlgebraic[1/Sqrt[-Pi - b*x^2],x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{b} x \sqrt{-b x^2-\pi }}{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])/(Pi + b*x^2)]/Sqrt[b])","A",1
584,1,25,25,0.0005614,"\int \frac{1}{\sqrt{a+b x^2}} \, dx","IntegrateAlgebraic[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",1
585,1,38,26,0.0859739,"\int \frac{1}{\sqrt{a-b x^2}} \, dx","IntegrateAlgebraic[1/Sqrt[a - b*x^2],x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{b} x \sqrt{a-b x^2}}{b x^2-a}\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])/(-a + b*x^2)]/Sqrt[b])","A",1
586,1,27,27,0.0819776,"\int \frac{1}{\sqrt{-a+b x^2}} \, dx","IntegrateAlgebraic[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",1
587,1,38,28,0.088183,"\int \frac{1}{\sqrt{-a-b x^2}} \, dx","IntegrateAlgebraic[1/Sqrt[-a - b*x^2],x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{b} x \sqrt{-a-b x^2}}{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])/(a + b*x^2)]/Sqrt[b])","A",1
588,1,16,16,0.0691005,"\int \frac{1}{\sqrt{a^2-x^2}} \, dx","IntegrateAlgebraic[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",1
589,0,0,184,11.1722211,"\int (c x)^{7/2} \sqrt{a+b x^2} \, dx","IntegrateAlgebraic[(c*x)^(7/2)*Sqrt[a + b*x^2],x]","\int (c x)^{7/2} \sqrt{a+b x^2} \, dx","\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{20 a^2 c^3 \sqrt{c x} \sqrt{a+b x^2}}{231 b^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,"Could not integrate","F",-1
590,0,0,301,10.938286,"\int (c x)^{5/2} \sqrt{a+b x^2} \, dx","IntegrateAlgebraic[(c*x)^(5/2)*Sqrt[a + b*x^2],x]","\int (c x)^{5/2} \sqrt{a+b x^2} \, dx","-\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{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 (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,"Could not integrate","F",-1
591,0,0,153,9.8298006,"\int (c x)^{3/2} \sqrt{a+b x^2} \, dx","IntegrateAlgebraic[(c*x)^(3/2)*Sqrt[a + b*x^2],x]","\int (c x)^{3/2} \sqrt{a+b x^2} \, dx","-\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,"Could not integrate","F",-1
592,0,0,269,5.8765871,"\int \sqrt{c x} \sqrt{a+b x^2} \, dx","IntegrateAlgebraic[Sqrt[c*x]*Sqrt[a + b*x^2],x]","\int \sqrt{c x} \sqrt{a+b x^2} \, dx","\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,"Could not integrate","F",-1
593,0,0,126,4.7568179,"\int \frac{\sqrt{a+b x^2}}{\sqrt{c x}} \, dx","IntegrateAlgebraic[Sqrt[a + b*x^2]/Sqrt[c*x],x]","\int \frac{\sqrt{a+b x^2}}{\sqrt{c x}} \, dx","\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,"Could not integrate","F",-1
594,0,0,263,8.3640539,"\int \frac{\sqrt{a+b x^2}}{(c x)^{3/2}} \, dx","IntegrateAlgebraic[Sqrt[a + b*x^2]/(c*x)^(3/2),x]","\int \frac{\sqrt{a+b x^2}}{(c x)^{3/2}} \, dx","\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{4 \sqrt{b} \sqrt{c x} \sqrt{a+b x^2}}{c^2 \left(\sqrt{a}+\sqrt{b} x\right)}-\frac{2 \sqrt{a+b x^2}}{c \sqrt{c x}}",1,"Could not integrate","F",-1
595,0,0,126,13.9862272,"\int \frac{\sqrt{a+b x^2}}{(c x)^{5/2}} \, dx","IntegrateAlgebraic[Sqrt[a + b*x^2]/(c*x)^(5/2),x]","\int \frac{\sqrt{a+b x^2}}{(c x)^{5/2}} \, dx","\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,"Could not integrate","F",-1
596,0,0,303,18.9601186,"\int \frac{\sqrt{a+b x^2}}{(c x)^{7/2}} \, dx","IntegrateAlgebraic[Sqrt[a + b*x^2]/(c*x)^(7/2),x]","\int \frac{\sqrt{a+b x^2}}{(c x)^{7/2}} \, dx","\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,"Could not integrate","F",-1
597,0,0,212,12.7347999,"\int (c x)^{7/2} \left(a+b x^2\right)^{3/2} \, dx","IntegrateAlgebraic[(c*x)^(7/2)*(a + b*x^2)^(3/2),x]","\int (c x)^{7/2} \left(a+b x^2\right)^{3/2} \, dx","\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^3 c^3 \sqrt{c x} \sqrt{a+b x^2}}{231 b^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,"Could not integrate","F",-1
598,0,0,329,11.9128419,"\int (c x)^{5/2} \left(a+b x^2\right)^{3/2} \, dx","IntegrateAlgebraic[(c*x)^(5/2)*(a + b*x^2)^(3/2),x]","\int (c x)^{5/2} \left(a+b x^2\right)^{3/2} \, dx","-\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^3 c^2 \sqrt{c x} \sqrt{a+b x^2}}{65 b^{3/2} \left(\sqrt{a}+\sqrt{b} x\right)}+\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,"Could not integrate","F",-1
599,0,0,181,11.4145524,"\int (c x)^{3/2} \left(a+b x^2\right)^{3/2} \, dx","IntegrateAlgebraic[(c*x)^(3/2)*(a + b*x^2)^(3/2),x]","\int (c x)^{3/2} \left(a+b x^2\right)^{3/2} \, dx","-\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,"Could not integrate","F",-1
600,0,0,297,10.738624,"\int \sqrt{c x} \left(a+b x^2\right)^{3/2} \, dx","IntegrateAlgebraic[Sqrt[c*x]*(a + b*x^2)^(3/2),x]","\int \sqrt{c x} \left(a+b x^2\right)^{3/2} \, dx","\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,"Could not integrate","F",-1
601,0,0,152,6.6405804,"\int \frac{\left(a+b x^2\right)^{3/2}}{\sqrt{c x}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(3/2)/Sqrt[c*x],x]","\int \frac{\left(a+b x^2\right)^{3/2}}{\sqrt{c x}} \, dx","\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,"Could not integrate","F",-1
602,0,0,296,9.6365961,"\int \frac{\left(a+b x^2\right)^{3/2}}{(c x)^{3/2}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(3/2)/(c*x)^(3/2),x]","\int \frac{\left(a+b x^2\right)^{3/2}}{(c x)^{3/2}} \, dx","\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,"Could not integrate","F",-1
603,0,0,152,13.8492121,"\int \frac{\left(a+b x^2\right)^{3/2}}{(c x)^{5/2}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(3/2)/(c*x)^(5/2),x]","\int \frac{\left(a+b x^2\right)^{3/2}}{(c x)^{5/2}} \, dx","\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,"Could not integrate","F",-1
604,0,0,297,17.2476911,"\int \frac{\left(a+b x^2\right)^{3/2}}{(c x)^{7/2}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(3/2)/(c*x)^(7/2),x]","\int \frac{\left(a+b x^2\right)^{3/2}}{(c x)^{7/2}} \, dx","\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{24 b^{3/2} \sqrt{c x} \sqrt{a+b x^2}}{5 c^4 \left(\sqrt{a}+\sqrt{b} x\right)}-\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,"Could not integrate","F",-1
605,0,0,152,19.6906672,"\int \frac{\left(a+b x^2\right)^{3/2}}{(c x)^{9/2}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(3/2)/(c*x)^(9/2),x]","\int \frac{\left(a+b x^2\right)^{3/2}}{(c x)^{9/2}} \, dx","\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,"Could not integrate","F",-1
606,0,0,331,22.6467364,"\int \frac{\left(a+b x^2\right)^{3/2}}{(c x)^{11/2}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(3/2)/(c*x)^(11/2),x]","\int \frac{\left(a+b x^2\right)^{3/2}}{(c x)^{11/2}} \, dx","\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,"Could not integrate","F",-1
607,0,0,128,13.1887751,"\int (c x)^{5/2} \sqrt{3 a-2 a x^2} \, dx","IntegrateAlgebraic[(c*x)^(5/2)*Sqrt[3*a - 2*a*x^2],x]","\int (c x)^{5/2} \sqrt{3 a-2 a x^2} \, dx","-\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,"Could not integrate","F",-1
608,0,0,117,12.1689689,"\int (c x)^{3/2} \sqrt{3 a-2 a x^2} \, dx","IntegrateAlgebraic[(c*x)^(3/2)*Sqrt[3*a - 2*a*x^2],x]","\int (c x)^{3/2} \sqrt{3 a-2 a x^2} \, dx","\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,"Could not integrate","F",-1
609,0,0,99,10.8579805,"\int \sqrt{c x} \sqrt{3 a-2 a x^2} \, dx","IntegrateAlgebraic[Sqrt[c*x]*Sqrt[3*a - 2*a*x^2],x]","\int \sqrt{c x} \sqrt{3 a-2 a x^2} \, dx","\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,"Could not integrate","F",-1
610,0,0,94,6.9316906,"\int \frac{\sqrt{3 a-2 a x^2}}{\sqrt{c x}} \, dx","IntegrateAlgebraic[Sqrt[3*a - 2*a*x^2]/Sqrt[c*x],x]","\int \frac{\sqrt{3 a-2 a x^2}}{\sqrt{c x}} \, dx","\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,"Could not integrate","F",-1
611,0,0,98,9.2113656,"\int \frac{\sqrt{3 a-2 a x^2}}{(c x)^{3/2}} \, dx","IntegrateAlgebraic[Sqrt[3*a - 2*a*x^2]/(c*x)^(3/2),x]","\int \frac{\sqrt{3 a-2 a x^2}}{(c x)^{3/2}} \, dx","\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,"Could not integrate","F",-1
612,0,0,96,17.59917,"\int \frac{\sqrt{3 a-2 a x^2}}{(c x)^{5/2}} \, dx","IntegrateAlgebraic[Sqrt[3*a - 2*a*x^2]/(c*x)^(5/2),x]","\int \frac{\sqrt{3 a-2 a x^2}}{(c x)^{5/2}} \, dx","-\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,"Could not integrate","F",-1
613,0,0,156,20.8773282,"\int \frac{(c x)^{7/2}}{\sqrt{a+b x^2}} \, dx","IntegrateAlgebraic[(c*x)^(7/2)/Sqrt[a + b*x^2],x]","\int \frac{(c x)^{7/2}}{\sqrt{a+b x^2}} \, dx","\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,"Could not integrate","F",-1
614,0,0,273,19.9546214,"\int \frac{(c x)^{5/2}}{\sqrt{a+b x^2}} \, dx","IntegrateAlgebraic[(c*x)^(5/2)/Sqrt[a + b*x^2],x]","\int \frac{(c x)^{5/2}}{\sqrt{a+b x^2}} \, dx","-\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,"Could not integrate","F",-1
615,0,0,127,19.3367875,"\int \frac{(c x)^{3/2}}{\sqrt{a+b x^2}} \, dx","IntegrateAlgebraic[(c*x)^(3/2)/Sqrt[a + b*x^2],x]","\int \frac{(c x)^{3/2}}{\sqrt{a+b x^2}} \, dx","\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,"Could not integrate","F",-1
616,0,0,236,15.5717383,"\int \frac{\sqrt{c x}}{\sqrt{a+b x^2}} \, dx","IntegrateAlgebraic[Sqrt[c*x]/Sqrt[a + b*x^2],x]","\int \frac{\sqrt{c x}}{\sqrt{a+b x^2}} \, dx","\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,"Could not integrate","F",-1
617,0,0,97,14.5227418,"\int \frac{1}{\sqrt{c x} \sqrt{a+b x^2}} \, dx","IntegrateAlgebraic[1/(Sqrt[c*x]*Sqrt[a + b*x^2]),x]","\int \frac{1}{\sqrt{c x} \sqrt{a+b x^2}} \, dx","\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,"Could not integrate","F",-1
618,0,0,268,20.4602352,"\int \frac{1}{(c x)^{3/2} \sqrt{a+b x^2}} \, dx","IntegrateAlgebraic[1/((c*x)^(3/2)*Sqrt[a + b*x^2]),x]","\int \frac{1}{(c x)^{3/2} \sqrt{a+b x^2}} \, dx","\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,"Could not integrate","F",-1
619,0,0,129,30.0165909,"\int \frac{1}{(c x)^{5/2} \sqrt{a+b x^2}} \, dx","IntegrateAlgebraic[1/((c*x)^(5/2)*Sqrt[a + b*x^2]),x]","\int \frac{1}{(c x)^{5/2} \sqrt{a+b x^2}} \, dx","-\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,"Could not integrate","F",-1
620,0,0,306,32.9540425,"\int \frac{1}{(c x)^{7/2} \sqrt{a+b x^2}} \, dx","IntegrateAlgebraic[1/((c*x)^(7/2)*Sqrt[a + b*x^2]),x]","\int \frac{1}{(c x)^{7/2} \sqrt{a+b x^2}} \, dx","-\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^{3/2} \sqrt{c x} \sqrt{a+b x^2}}{5 a^2 c^4 \left(\sqrt{a}+\sqrt{b} x\right)}+\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,"Could not integrate","F",-1
621,0,0,153,17.1855829,"\int \frac{(c x)^{7/2}}{\left(a+b x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[(c*x)^(7/2)/(a + b*x^2)^(3/2),x]","\int \frac{(c x)^{7/2}}{\left(a+b x^2\right)^{3/2}} \, dx","-\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,"Could not integrate","F",-1
622,0,0,266,14.0642564,"\int \frac{(c x)^{5/2}}{\left(a+b x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[(c*x)^(5/2)/(a + b*x^2)^(3/2),x]","\int \frac{(c x)^{5/2}}{\left(a+b x^2\right)^{3/2}} \, dx","\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{3 c^2 \sqrt{c x} \sqrt{a+b x^2}}{b^{3/2} \left(\sqrt{a}+\sqrt{b} x\right)}-\frac{c (c x)^{3/2}}{b \sqrt{a+b x^2}}",1,"Could not integrate","F",-1
623,0,0,125,13.6004111,"\int \frac{(c x)^{3/2}}{\left(a+b x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[(c*x)^(3/2)/(a + b*x^2)^(3/2),x]","\int \frac{(c x)^{3/2}}{\left(a+b x^2\right)^{3/2}} \, dx","\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,"Could not integrate","F",-1
624,0,0,266,12.0766379,"\int \frac{\sqrt{c x}}{\left(a+b x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[Sqrt[c*x]/(a + b*x^2)^(3/2),x]","\int \frac{\sqrt{c x}}{\left(a+b x^2\right)^{3/2}} \, dx","-\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,"Could not integrate","F",-1
625,0,0,126,13.3592288,"\int \frac{1}{\sqrt{c x} \left(a+b x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[1/(Sqrt[c*x]*(a + b*x^2)^(3/2)),x]","\int \frac{1}{\sqrt{c x} \left(a+b x^2\right)^{3/2}} \, dx","\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,"Could not integrate","F",-1
626,0,0,296,17.5276431,"\int \frac{1}{(c x)^{3/2} \left(a+b x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[1/((c*x)^(3/2)*(a + b*x^2)^(3/2)),x]","\int \frac{1}{(c x)^{3/2} \left(a+b x^2\right)^{3/2}} \, dx","\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{b} \sqrt{c x} \sqrt{a+b x^2}}{a^2 c^2 \left(\sqrt{a}+\sqrt{b} x\right)}-\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,"Could not integrate","F",-1
627,0,0,154,24.4664973,"\int \frac{1}{(c x)^{5/2} \left(a+b x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[1/((c*x)^(5/2)*(a + b*x^2)^(3/2)),x]","\int \frac{1}{(c x)^{5/2} \left(a+b x^2\right)^{3/2}} \, dx","-\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,"Could not integrate","F",-1
628,0,0,331,27.9600423,"\int \frac{1}{(c x)^{7/2} \left(a+b x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[1/((c*x)^(7/2)*(a + b*x^2)^(3/2)),x]","\int \frac{1}{(c x)^{7/2} \left(a+b x^2\right)^{3/2}} \, dx","-\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^{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 \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,"Could not integrate","F",-1
629,0,0,155,21.2856636,"\int \frac{(c x)^{7/2}}{\left(a+b x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[(c*x)^(7/2)/(a + b*x^2)^(5/2),x]","\int \frac{(c x)^{7/2}}{\left(a+b x^2\right)^{5/2}} \, dx","\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{5 c^3 \sqrt{c x}}{6 b^2 \sqrt{a+b x^2}}-\frac{c (c x)^{5/2}}{3 b \left(a+b x^2\right)^{3/2}}",1,"Could not integrate","F",-1
630,0,0,304,20.1411527,"\int \frac{(c x)^{5/2}}{\left(a+b x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[(c*x)^(5/2)/(a + b*x^2)^(5/2),x]","\int \frac{(c x)^{5/2}}{\left(a+b x^2\right)^{5/2}} \, dx","-\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,"Could not integrate","F",-1
631,0,0,156,19.6566043,"\int \frac{(c x)^{3/2}}{\left(a+b x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[(c*x)^(3/2)/(a + b*x^2)^(5/2),x]","\int \frac{(c x)^{3/2}}{\left(a+b x^2\right)^{5/2}} \, dx","\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,"Could not integrate","F",-1
632,0,0,302,19.1284403,"\int \frac{\sqrt{c x}}{\left(a+b x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[Sqrt[c*x]/(a + b*x^2)^(5/2),x]","\int \frac{\sqrt{c x}}{\left(a+b x^2\right)^{5/2}} \, dx","-\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,"Could not integrate","F",-1
633,0,0,157,19.2943461,"\int \frac{1}{\sqrt{c x} \left(a+b x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[1/(Sqrt[c*x]*(a + b*x^2)^(5/2)),x]","\int \frac{1}{\sqrt{c x} \left(a+b x^2\right)^{5/2}} \, dx","\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{5 \sqrt{c x}}{6 a^2 c \sqrt{a+b x^2}}+\frac{\sqrt{c x}}{3 a c \left(a+b x^2\right)^{3/2}}",1,"Could not integrate","F",-1
634,0,0,333,23.2737336,"\int \frac{1}{(c x)^{3/2} \left(a+b x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[1/((c*x)^(3/2)*(a + b*x^2)^(5/2)),x]","\int \frac{1}{(c x)^{3/2} \left(a+b x^2\right)^{5/2}} \, dx","\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{b} \sqrt{c x} \sqrt{a+b x^2}}{2 a^3 c^2 \left(\sqrt{a}+\sqrt{b} x\right)}-\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,"Could not integrate","F",-1
635,0,0,185,28.4867289,"\int \frac{1}{(c x)^{5/2} \left(a+b x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[1/((c*x)^(5/2)*(a + b*x^2)^(5/2)),x]","\int \frac{1}{(c x)^{5/2} \left(a+b x^2\right)^{5/2}} \, dx","-\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,"Could not integrate","F",-1
636,0,0,362,31.8152252,"\int \frac{1}{(c x)^{7/2} \left(a+b x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[1/((c*x)^(7/2)*(a + b*x^2)^(5/2)),x]","\int \frac{1}{(c x)^{7/2} \left(a+b x^2\right)^{5/2}} \, dx","-\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^{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 \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,"Could not integrate","F",-1
637,0,0,107,21.0751481,"\int \frac{(c x)^{5/2}}{\sqrt{3 a-2 a x^2}} \, dx","IntegrateAlgebraic[(c*x)^(5/2)/Sqrt[3*a - 2*a*x^2],x]","\int \frac{(c x)^{5/2}}{\sqrt{3 a-2 a x^2}} \, dx","-\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,"Could not integrate","F",-1
638,0,0,88,21.5942998,"\int \frac{(c x)^{3/2}}{\sqrt{3 a-2 a x^2}} \, dx","IntegrateAlgebraic[(c*x)^(3/2)/Sqrt[3*a - 2*a*x^2],x]","\int \frac{(c x)^{3/2}}{\sqrt{3 a-2 a x^2}} \, dx","\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,"Could not integrate","F",-1
639,0,0,67,19.3330457,"\int \frac{\sqrt{c x}}{\sqrt{3 a-2 a x^2}} \, dx","IntegrateAlgebraic[Sqrt[c*x]/Sqrt[3*a - 2*a*x^2],x]","\int \frac{\sqrt{c x}}{\sqrt{3 a-2 a x^2}} \, dx","-\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,"Could not integrate","F",-1
640,0,0,63,17.6691941,"\int \frac{1}{\sqrt{c x} \sqrt{3 a-2 a x^2}} \, dx","IntegrateAlgebraic[1/(Sqrt[c*x]*Sqrt[3*a - 2*a*x^2]),x]","\int \frac{1}{\sqrt{c x} \sqrt{3 a-2 a x^2}} \, dx","\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,"Could not integrate","F",-1
641,0,0,107,23.744646,"\int \frac{1}{(c x)^{3/2} \sqrt{3 a-2 a x^2}} \, dx","IntegrateAlgebraic[1/((c*x)^(3/2)*Sqrt[3*a - 2*a*x^2]),x]","\int \frac{1}{(c x)^{3/2} \sqrt{3 a-2 a x^2}} \, dx","\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,"Could not integrate","F",-1
642,0,0,98,30.0272855,"\int \frac{1}{(c x)^{5/2} \sqrt{3 a-2 a x^2}} \, dx","IntegrateAlgebraic[1/((c*x)^(5/2)*Sqrt[3*a - 2*a*x^2]),x]","\int \frac{1}{(c x)^{5/2} \sqrt{3 a-2 a x^2}} \, dx","\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,"Could not integrate","F",-1
643,0,0,110,16.3627703,"\int \frac{(c x)^{5/2}}{\left(3 a-2 a x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[(c*x)^(5/2)/(3*a - 2*a*x^2)^(3/2),x]","\int \frac{(c x)^{5/2}}{\left(3 a-2 a x^2\right)^{3/2}} \, dx","\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,"Could not integrate","F",-1
644,0,0,94,18.7917072,"\int \frac{(c x)^{3/2}}{\left(3 a-2 a x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[(c*x)^(3/2)/(3*a - 2*a*x^2)^(3/2),x]","\int \frac{(c x)^{3/2}}{\left(3 a-2 a x^2\right)^{3/2}} \, dx","\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,"Could not integrate","F",-1
645,0,0,101,16.8469392,"\int \frac{\sqrt{c x}}{\left(3 a-2 a x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[Sqrt[c*x]/(3*a - 2*a*x^2)^(3/2),x]","\int \frac{\sqrt{c x}}{\left(3 a-2 a x^2\right)^{3/2}} \, dx","\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,"Could not integrate","F",-1
646,0,0,96,19.6270881,"\int \frac{1}{\sqrt{c x} \left(3 a-2 a x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[1/(Sqrt[c*x]*(3*a - 2*a*x^2)^(3/2)),x]","\int \frac{1}{\sqrt{c x} \left(3 a-2 a x^2\right)^{3/2}} \, dx","\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,"Could not integrate","F",-1
647,0,0,140,23.2166662,"\int \frac{1}{(c x)^{3/2} \left(3 a-2 a x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[1/((c*x)^(3/2)*(3*a - 2*a*x^2)^(3/2)),x]","\int \frac{1}{(c x)^{3/2} \left(3 a-2 a x^2\right)^{3/2}} \, dx","-\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,"Could not integrate","F",-1
648,0,0,132,30.8106391,"\int \frac{1}{(c x)^{5/2} \left(3 a-2 a x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[1/((c*x)^(5/2)*(3*a - 2*a*x^2)^(3/2)),x]","\int \frac{1}{(c x)^{5/2} \left(3 a-2 a x^2\right)^{3/2}} \, dx","-\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,"Could not integrate","F",-1
649,0,0,21,14.1733009,"\int \frac{1}{\sqrt{x} \sqrt{1-a^2 x^2}} \, dx","IntegrateAlgebraic[1/(Sqrt[x]*Sqrt[1 - a^2*x^2]),x]","\int \frac{1}{\sqrt{x} \sqrt{1-a^2 x^2}} \, dx","\frac{2 F\left(\left.\sin ^{-1}\left(\sqrt{a} \sqrt{x}\right)\right|-1\right)}{\sqrt{a}}",1,"Could not integrate","F",-1
650,0,0,67,13.9840503,"\int \frac{1}{\sqrt{x} \sqrt{1+a x^2}} \, dx","IntegrateAlgebraic[1/(Sqrt[x]*Sqrt[1 + a*x^2]),x]","\int \frac{1}{\sqrt{x} \sqrt{1+a x^2}} \, dx","\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,"Could not integrate","F",-1
651,0,0,50,0.0234164,"\int x^m \left(a+b x^2\right)^{3/2} \, dx","IntegrateAlgebraic[x^m*(a + b*x^2)^(3/2),x]","\int x^m \left(a+b x^2\right)^{3/2} \, dx","\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,"Could not integrate","F",-1
652,0,0,50,0.0178565,"\int x^m \sqrt{a+b x^2} \, dx","IntegrateAlgebraic[x^m*Sqrt[a + b*x^2],x]","\int x^m \sqrt{a+b x^2} \, dx","\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,"Could not integrate","F",-1
653,0,0,50,0.0188874,"\int \frac{x^m}{\sqrt{a+b x^2}} \, dx","IntegrateAlgebraic[x^m/Sqrt[a + b*x^2],x]","\int \frac{x^m}{\sqrt{a+b x^2}} \, dx","\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,"Could not integrate","F",-1
654,0,0,48,0.0277886,"\int \frac{x^m}{\left(a+b x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[x^m/(a + b*x^2)^(3/2),x]","\int \frac{x^m}{\left(a+b x^2\right)^{3/2}} \, dx","\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,"Could not integrate","F",-1
655,0,0,50,0.0988178,"\int \frac{x^m}{\left(a+b x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[x^m/(a + b*x^2)^(5/2),x]","\int \frac{x^m}{\left(a+b x^2\right)^{5/2}} \, dx","\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,"Could not integrate","F",-1
656,0,0,50,0.0890439,"\int \frac{x^{2+m}}{\sqrt{a+b x^2}} \, dx","IntegrateAlgebraic[x^(2 + m)/Sqrt[a + b*x^2],x]","\int \frac{x^{2+m}}{\sqrt{a+b x^2}} \, dx","\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,"Could not integrate","F",-1
657,0,0,50,0.0200815,"\int \frac{x^{1+m}}{\sqrt{a+b x^2}} \, dx","IntegrateAlgebraic[x^(1 + m)/Sqrt[a + b*x^2],x]","\int \frac{x^{1+m}}{\sqrt{a+b x^2}} \, dx","\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,"Could not integrate","F",-1
658,0,0,50,0.0005645,"\int \frac{x^m}{\sqrt{a+b x^2}} \, dx","IntegrateAlgebraic[x^m/Sqrt[a + b*x^2],x]","\int \frac{x^m}{\sqrt{a+b x^2}} \, dx","\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,"Could not integrate","F",-1
659,0,0,46,0.0210143,"\int \frac{x^{-1+m}}{\sqrt{a+b x^2}} \, dx","IntegrateAlgebraic[x^(-1 + m)/Sqrt[a + b*x^2],x]","\int \frac{x^{-1+m}}{\sqrt{a+b x^2}} \, dx","\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,"Could not integrate","F",-1
660,0,0,51,0.0211257,"\int \frac{x^{-2+m}}{\sqrt{a+b x^2}} \, dx","IntegrateAlgebraic[x^(-2 + m)/Sqrt[a + b*x^2],x]","\int \frac{x^{-2+m}}{\sqrt{a+b x^2}} \, dx","-\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,"Could not integrate","F",-1
661,0,0,17,0.0353144,"\int \frac{x^{1+m} \left(a (2+m)+b (3+m) x^2\right)}{\sqrt{a+b x^2}} \, dx","IntegrateAlgebraic[(x^(1 + m)*(a*(2 + m) + b*(3 + m)*x^2))/Sqrt[a + b*x^2],x]","\int \frac{x^{1+m} \left(a (2+m)+b (3+m) x^2\right)}{\sqrt{a+b x^2}} \, dx","x^{m+2} \sqrt{a+b x^2}",1,"Could not integrate","F",-1
662,0,0,17,0.0986783,"\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","IntegrateAlgebraic[(a*(2 + m)*x^(1 + m))/Sqrt[a + b*x^2] + (b*(3 + m)*x^(3 + m))/Sqrt[a + b*x^2],x]","\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","x^{m+2} \sqrt{a+b x^2}",1,"Could not integrate","F",-1
663,0,0,15,0.050915,"\int \frac{x^{-1+m} \left(a m+b (-1+m) x^2\right)}{\left(a+b x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[(x^(-1 + m)*(a*m + b*(-1 + m)*x^2))/(a + b*x^2)^(3/2),x]","\int \frac{x^{-1+m} \left(a m+b (-1+m) x^2\right)}{\left(a+b x^2\right)^{3/2}} \, dx","\frac{x^m}{\sqrt{a+b x^2}}",1,"Could not integrate","F",-1
664,0,0,15,0.0575234,"\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","IntegrateAlgebraic[-((b*x^(1 + m))/(a + b*x^2)^(3/2)) + (m*x^(-1 + m))/Sqrt[a + b*x^2],x]","\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","\frac{x^m}{\sqrt{a+b x^2}}",1,"Could not integrate","F",-1
665,1,61,80,0.0977998,"\int x^7 \sqrt[3]{a+b x^2} \, dx","IntegrateAlgebraic[x^7*(a + b*x^2)^(1/3),x]","-\frac{3 \sqrt[3]{a+b x^2} \left(81 a^4-27 a^3 b x^2+18 a^2 b^2 x^4-14 a b^3 x^6-140 b^4 x^8\right)}{3640 b^4}","-\frac{3 a^3 \left(a+b x^2\right)^{4/3}}{8 b^4}+\frac{9 a^2 \left(a+b x^2\right)^{7/3}}{14 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 + b*x^2)^(1/3)*(81*a^4 - 27*a^3*b*x^2 + 18*a^2*b^2*x^4 - 14*a*b^3*x^6 - 140*b^4*x^8))/(3640*b^4)","A",1
666,1,50,59,0.0373398,"\int x^5 \sqrt[3]{a+b x^2} \, dx","IntegrateAlgebraic[x^5*(a + b*x^2)^(1/3),x]","\frac{3 \sqrt[3]{a+b x^2} \left(9 a^3-3 a^2 b x^2+2 a b^2 x^4+14 b^3 x^6\right)}{280 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 + b*x^2)^(1/3)*(9*a^3 - 3*a^2*b*x^2 + 2*a*b^2*x^4 + 14*b^3*x^6))/(280*b^3)","A",1
667,1,39,38,0.0324602,"\int x^3 \sqrt[3]{a+b x^2} \, dx","IntegrateAlgebraic[x^3*(a + b*x^2)^(1/3),x]","-\frac{3 \sqrt[3]{a+b x^2} \left(3 a^2-a b x^2-4 b^2 x^4\right)}{56 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 + b*x^2)^(1/3)*(3*a^2 - a*b*x^2 - 4*b^2*x^4))/(56*b^2)","A",1
668,1,18,18,0.0224783,"\int x \sqrt[3]{a+b x^2} \, dx","IntegrateAlgebraic[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
669,1,133,101,0.228146,"\int \frac{\sqrt[3]{a+b x^2}}{x} \, dx","IntegrateAlgebraic[(a + b*x^2)^(1/3)/x,x]","-\frac{1}{4} \sqrt[3]{a} \log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}\right)+\frac{3}{2} \sqrt[3]{a+b x^2}+\frac{1}{2} \sqrt[3]{a} \log \left(\sqrt[3]{a+b x^2}-\sqrt[3]{a}\right)-\frac{1}{2} \sqrt{3} \sqrt[3]{a} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}}{\sqrt{3} \sqrt[3]{a}}+\frac{1}{\sqrt{3}}\right)","\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[1/Sqrt[3] + (2*(a + b*x^2)^(1/3))/(Sqrt[3]*a^(1/3))])/2 + (a^(1/3)*Log[-a^(1/3) + (a + b*x^2)^(1/3)])/2 - (a^(1/3)*Log[a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3)])/4","A",1
670,1,139,107,0.4463262,"\int \frac{\sqrt[3]{a+b x^2}}{x^3} \, dx","IntegrateAlgebraic[(a + b*x^2)^(1/3)/x^3,x]","\frac{b \log \left(\sqrt[3]{a+b x^2}-\sqrt[3]{a}\right)}{6 a^{2/3}}-\frac{b \log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}\right)}{12 a^{2/3}}-\frac{b \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}}{\sqrt{3} \sqrt[3]{a}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} 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,"-1/2*(a + b*x^2)^(1/3)/x^2 - (b*ArcTan[1/Sqrt[3] + (2*(a + b*x^2)^(1/3))/(Sqrt[3]*a^(1/3))])/(2*Sqrt[3]*a^(2/3)) + (b*Log[-a^(1/3) + (a + b*x^2)^(1/3)])/(6*a^(2/3)) - (b*Log[a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3)])/(12*a^(2/3))","A",1
671,1,158,135,0.189308,"\int \frac{\sqrt[3]{a+b x^2}}{x^5} \, dx","IntegrateAlgebraic[(a + b*x^2)^(1/3)/x^5,x]","-\frac{b^2 \log \left(\sqrt[3]{a+b x^2}-\sqrt[3]{a}\right)}{18 a^{5/3}}+\frac{b^2 \log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}\right)}{36 a^{5/3}}+\frac{b^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}}{\sqrt{3} \sqrt[3]{a}}+\frac{1}{\sqrt{3}}\right)}{6 \sqrt{3} a^{5/3}}+\frac{\left(-3 a-b x^2\right) \sqrt[3]{a+b x^2}}{12 a 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,"((-3*a - b*x^2)*(a + b*x^2)^(1/3))/(12*a*x^4) + (b^2*ArcTan[1/Sqrt[3] + (2*(a + b*x^2)^(1/3))/(Sqrt[3]*a^(1/3))])/(6*Sqrt[3]*a^(5/3)) - (b^2*Log[-a^(1/3) + (a + b*x^2)^(1/3)])/(18*a^(5/3)) + (b^2*Log[a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3)])/(36*a^(5/3))","A",1
672,0,0,314,4.1652916,"\int x^4 \sqrt[3]{a+b x^2} \, dx","IntegrateAlgebraic[x^4*(a + b*x^2)^(1/3),x]","\int x^4 \sqrt[3]{a+b x^2} \, dx","-\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,"Could not integrate","F",-1
673,0,0,290,3.8699979,"\int x^2 \sqrt[3]{a+b x^2} \, dx","IntegrateAlgebraic[x^2*(a + b*x^2)^(1/3),x]","\int x^2 \sqrt[3]{a+b x^2} \, dx","\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{6 a x \sqrt[3]{a+b x^2}}{55 b}+\frac{3}{11} x^3 \sqrt[3]{a+b x^2}",1,"Could not integrate","F",-1
674,0,0,266,3.7765467,"\int \sqrt[3]{a+b x^2} \, dx","IntegrateAlgebraic[(a + b*x^2)^(1/3),x]","\int \sqrt[3]{a+b x^2} \, dx","\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,"Could not integrate","F",-1
675,0,0,260,4.0045766,"\int \frac{\sqrt[3]{a+b x^2}}{x^2} \, dx","IntegrateAlgebraic[(a + b*x^2)^(1/3)/x^2,x]","\int \frac{\sqrt[3]{a+b x^2}}{x^2} \, dx","-\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,"Could not integrate","F",-1
676,0,0,290,8.844187,"\int \frac{\sqrt[3]{a+b x^2}}{x^4} \, dx","IntegrateAlgebraic[(a + b*x^2)^(1/3)/x^4,x]","\int \frac{\sqrt[3]{a+b x^2}}{x^4} \, dx","\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,"Could not integrate","F",-1
677,1,61,80,0.0424592,"\int x^7 \left(a+b x^2\right)^{2/3} \, dx","IntegrateAlgebraic[x^7*(a + b*x^2)^(2/3),x]","-\frac{3 \left(a+b x^2\right)^{2/3} \left(81 a^4-54 a^3 b x^2+45 a^2 b^2 x^4-40 a b^3 x^6-220 b^4 x^8\right)}{6160 b^4}","-\frac{3 a^3 \left(a+b x^2\right)^{5/3}}{10 b^4}+\frac{9 a^2 \left(a+b x^2\right)^{8/3}}{16 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 + b*x^2)^(2/3)*(81*a^4 - 54*a^3*b*x^2 + 45*a^2*b^2*x^4 - 40*a*b^3*x^6 - 220*b^4*x^8))/(6160*b^4)","A",1
678,1,50,59,0.037876,"\int x^5 \left(a+b x^2\right)^{2/3} \, dx","IntegrateAlgebraic[x^5*(a + b*x^2)^(2/3),x]","\frac{3 \left(a+b x^2\right)^{2/3} \left(9 a^3-6 a^2 b x^2+5 a b^2 x^4+20 b^3 x^6\right)}{440 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 + b*x^2)^(2/3)*(9*a^3 - 6*a^2*b*x^2 + 5*a*b^2*x^4 + 20*b^3*x^6))/(440*b^3)","A",1
679,1,39,38,0.0342313,"\int x^3 \left(a+b x^2\right)^{2/3} \, dx","IntegrateAlgebraic[x^3*(a + b*x^2)^(2/3),x]","-\frac{3 \left(a+b x^2\right)^{2/3} \left(3 a^2-2 a b x^2-5 b^2 x^4\right)}{80 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 + b*x^2)^(2/3)*(3*a^2 - 2*a*b*x^2 - 5*b^2*x^4))/(80*b^2)","A",1
680,1,18,18,0.0227377,"\int x \left(a+b x^2\right)^{2/3} \, dx","IntegrateAlgebraic[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
681,1,133,101,0.1219973,"\int \frac{\left(a+b x^2\right)^{2/3}}{x} \, dx","IntegrateAlgebraic[(a + b*x^2)^(2/3)/x,x]","\frac{1}{2} a^{2/3} \log \left(\sqrt[3]{a+b x^2}-\sqrt[3]{a}\right)-\frac{1}{4} a^{2/3} \log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}\right)+\frac{1}{2} \sqrt{3} a^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}}{\sqrt{3} \sqrt[3]{a}}+\frac{1}{\sqrt{3}}\right)+\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[1/Sqrt[3] + (2*(a + b*x^2)^(1/3))/(Sqrt[3]*a^(1/3))])/2 + (a^(2/3)*Log[-a^(1/3) + (a + b*x^2)^(1/3)])/2 - (a^(2/3)*Log[a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3)])/4","A",1
682,1,136,104,0.1677943,"\int \frac{\left(a+b x^2\right)^{2/3}}{x^3} \, dx","IntegrateAlgebraic[(a + b*x^2)^(2/3)/x^3,x]","-\frac{b \log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}\right)}{6 \sqrt[3]{a}}-\frac{\left(a+b x^2\right)^{2/3}}{2 x^2}+\frac{b \log \left(\sqrt[3]{a+b x^2}-\sqrt[3]{a}\right)}{3 \sqrt[3]{a}}+\frac{b \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}}{\sqrt{3} \sqrt[3]{a}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{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,"-1/2*(a + b*x^2)^(2/3)/x^2 + (b*ArcTan[1/Sqrt[3] + (2*(a + b*x^2)^(1/3))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(1/3)) + (b*Log[-a^(1/3) + (a + b*x^2)^(1/3)])/(3*a^(1/3)) - (b*Log[a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3)])/(6*a^(1/3))","A",1
683,1,158,135,0.2104602,"\int \frac{\left(a+b x^2\right)^{2/3}}{x^5} \, dx","IntegrateAlgebraic[(a + b*x^2)^(2/3)/x^5,x]","-\frac{b^2 \log \left(\sqrt[3]{a+b x^2}-\sqrt[3]{a}\right)}{18 a^{4/3}}+\frac{b^2 \log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}\right)}{36 a^{4/3}}-\frac{b^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}}{\sqrt{3} \sqrt[3]{a}}+\frac{1}{\sqrt{3}}\right)}{6 \sqrt{3} a^{4/3}}+\frac{\left(-3 a-2 b x^2\right) \left(a+b x^2\right)^{2/3}}{12 a 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,"((-3*a - 2*b*x^2)*(a + b*x^2)^(2/3))/(12*a*x^4) - (b^2*ArcTan[1/Sqrt[3] + (2*(a + b*x^2)^(1/3))/(Sqrt[3]*a^(1/3))])/(6*Sqrt[3]*a^(4/3)) - (b^2*Log[-a^(1/3) + (a + b*x^2)^(1/3)])/(18*a^(4/3)) + (b^2*Log[a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3)])/(36*a^(4/3))","A",1
684,0,0,601,4.7553651,"\int x^4 \left(a+b x^2\right)^{2/3} \, dx","IntegrateAlgebraic[x^4*(a + b*x^2)^(2/3),x]","\int x^4 \left(a+b x^2\right)^{2/3} \, dx","-\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{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 a^2 x \left(a+b x^2\right)^{2/3}}{1729 b^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,"Could not integrate","F",-1
685,0,0,577,4.285811,"\int x^2 \left(a+b x^2\right)^{2/3} \, dx","IntegrateAlgebraic[x^2*(a + b*x^2)^(2/3),x]","\int x^2 \left(a+b x^2\right)^{2/3} \, dx","\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{12 a x \left(a+b x^2\right)^{2/3}}{91 b}+\frac{3}{13} x^3 \left(a+b x^2\right)^{2/3}",1,"Could not integrate","F",-1
686,0,0,550,4.0963315,"\int \left(a+b x^2\right)^{2/3} \, dx","IntegrateAlgebraic[(a + b*x^2)^(2/3),x]","\int \left(a+b x^2\right)^{2/3} \, dx","-\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,"Could not integrate","F",-1
687,0,0,538,4.6473281,"\int \frac{\left(a+b x^2\right)^{2/3}}{x^2} \, dx","IntegrateAlgebraic[(a + b*x^2)^(2/3)/x^2,x]","\int \frac{\left(a+b x^2\right)^{2/3}}{x^2} \, dx","-\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,"Could not integrate","F",-1
688,0,0,575,9.2840696,"\int \frac{\left(a+b x^2\right)^{2/3}}{x^4} \, dx","IntegrateAlgebraic[(a + b*x^2)^(2/3)/x^4,x]","\int \frac{\left(a+b x^2\right)^{2/3}}{x^4} \, dx","-\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,"Could not integrate","F",-1
689,1,72,80,0.042068,"\int x^7 \left(a+b x^2\right)^{4/3} \, dx","IntegrateAlgebraic[x^7*(a + b*x^2)^(4/3),x]","-\frac{3 \sqrt[3]{a+b x^2} \left(81 a^5-27 a^4 b x^2+18 a^3 b^2 x^4-14 a^2 b^3 x^6-595 a b^4 x^8-455 b^5 x^{10}\right)}{14560 b^4}","-\frac{3 a^3 \left(a+b x^2\right)^{7/3}}{14 b^4}+\frac{9 a^2 \left(a+b x^2\right)^{10/3}}{20 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 + b*x^2)^(1/3)*(81*a^5 - 27*a^4*b*x^2 + 18*a^3*b^2*x^4 - 14*a^2*b^3*x^6 - 595*a*b^4*x^8 - 455*b^5*x^10))/(14560*b^4)","A",1
690,1,61,59,0.0374236,"\int x^5 \left(a+b x^2\right)^{4/3} \, dx","IntegrateAlgebraic[x^5*(a + b*x^2)^(4/3),x]","\frac{3 \sqrt[3]{a+b x^2} \left(9 a^4-3 a^3 b x^2+2 a^2 b^2 x^4+49 a b^3 x^6+35 b^4 x^8\right)}{910 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 + b*x^2)^(1/3)*(9*a^4 - 3*a^3*b*x^2 + 2*a^2*b^2*x^4 + 49*a*b^3*x^6 + 35*b^4*x^8))/(910*b^3)","A",1
691,1,50,38,0.0338147,"\int x^3 \left(a+b x^2\right)^{4/3} \, dx","IntegrateAlgebraic[x^3*(a + b*x^2)^(4/3),x]","-\frac{3 \sqrt[3]{a+b x^2} \left(3 a^3-a^2 b x^2-11 a b^2 x^4-7 b^3 x^6\right)}{140 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 + b*x^2)^(1/3)*(3*a^3 - a^2*b*x^2 - 11*a*b^2*x^4 - 7*b^3*x^6))/(140*b^2)","A",1
692,1,18,18,0.0223873,"\int x \left(a+b x^2\right)^{4/3} \, dx","IntegrateAlgebraic[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
693,1,142,117,0.1302209,"\int \frac{\left(a+b x^2\right)^{4/3}}{x} \, dx","IntegrateAlgebraic[(a + b*x^2)^(4/3)/x,x]","\frac{1}{2} a^{4/3} \log \left(\sqrt[3]{a+b x^2}-\sqrt[3]{a}\right)-\frac{1}{4} a^{4/3} \log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}\right)-\frac{1}{2} \sqrt{3} a^{4/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}}{\sqrt{3} \sqrt[3]{a}}+\frac{1}{\sqrt{3}}\right)+\frac{3}{8} \sqrt[3]{a+b x^2} \left(5 a+b x^2\right)","\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 + b*x^2)^(1/3)*(5*a + b*x^2))/8 - (Sqrt[3]*a^(4/3)*ArcTan[1/Sqrt[3] + (2*(a + b*x^2)^(1/3))/(Sqrt[3]*a^(1/3))])/2 + (a^(4/3)*Log[-a^(1/3) + (a + b*x^2)^(1/3)])/2 - (a^(4/3)*Log[a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3)])/4","A",1
694,1,147,116,0.1832113,"\int \frac{\left(a+b x^2\right)^{4/3}}{x^3} \, dx","IntegrateAlgebraic[(a + b*x^2)^(4/3)/x^3,x]","-\frac{1}{3} \sqrt[3]{a} b \log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}\right)+\frac{\sqrt[3]{a+b x^2} \left(3 b x^2-a\right)}{2 x^2}+\frac{2}{3} \sqrt[3]{a} b \log \left(\sqrt[3]{a+b x^2}-\sqrt[3]{a}\right)-\frac{2 \sqrt[3]{a} b \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}}{\sqrt{3} \sqrt[3]{a}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3}}","-\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,"((a + b*x^2)^(1/3)*(-a + 3*b*x^2))/(2*x^2) - (2*a^(1/3)*b*ArcTan[1/Sqrt[3] + (2*(a + b*x^2)^(1/3))/(Sqrt[3]*a^(1/3))])/Sqrt[3] + (2*a^(1/3)*b*Log[-a^(1/3) + (a + b*x^2)^(1/3)])/3 - (a^(1/3)*b*Log[a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3)])/3","A",1
695,1,155,132,0.2786064,"\int \frac{\left(a+b x^2\right)^{4/3}}{x^5} \, dx","IntegrateAlgebraic[(a + b*x^2)^(4/3)/x^5,x]","\frac{b^2 \log \left(\sqrt[3]{a+b x^2}-\sqrt[3]{a}\right)}{9 a^{2/3}}-\frac{b^2 \log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}\right)}{18 a^{2/3}}-\frac{b^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}}{\sqrt{3} \sqrt[3]{a}}+\frac{1}{\sqrt{3}}\right)}{3 \sqrt{3} a^{2/3}}+\frac{\left(-3 a-7 b x^2\right) \sqrt[3]{a+b x^2}}{12 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,"((-3*a - 7*b*x^2)*(a + b*x^2)^(1/3))/(12*x^4) - (b^2*ArcTan[1/Sqrt[3] + (2*(a + b*x^2)^(1/3))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(2/3)) + (b^2*Log[-a^(1/3) + (a + b*x^2)^(1/3)])/(9*a^(2/3)) - (b^2*Log[a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3)])/(18*a^(2/3))","A",1
696,0,0,335,4.9532714,"\int x^4 \left(a+b x^2\right)^{4/3} \, dx","IntegrateAlgebraic[x^4*(a + b*x^2)^(4/3),x]","\int x^4 \left(a+b x^2\right)^{4/3} \, dx","-\frac{432 a^3 x \sqrt[3]{a+b x^2}}{21505 b^2}+\frac{48 a^2 x^3 \sqrt[3]{a+b x^2}}{4301 b}-\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{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,"Could not integrate","F",-1
697,0,0,311,4.7147046,"\int x^2 \left(a+b x^2\right)^{4/3} \, dx","IntegrateAlgebraic[x^2*(a + b*x^2)^(4/3),x]","\int x^2 \left(a+b x^2\right)^{4/3} \, dx","\frac{48 a^2 x \sqrt[3]{a+b x^2}}{935 b}+\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{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,"Could not integrate","F",-1
698,0,0,285,4.3649297,"\int \left(a+b x^2\right)^{4/3} \, dx","IntegrateAlgebraic[(a + b*x^2)^(4/3),x]","\int \left(a+b x^2\right)^{4/3} \, dx","-\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,"Could not integrate","F",-1
699,0,0,280,4.7313382,"\int \frac{\left(a+b x^2\right)^{4/3}}{x^2} \, dx","IntegrateAlgebraic[(a + b*x^2)^(4/3)/x^2,x]","\int \frac{\left(a+b x^2\right)^{4/3}}{x^2} \, dx","-\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,"Could not integrate","F",-1
700,0,0,284,8.9962998,"\int \frac{\left(a+b x^2\right)^{4/3}}{x^4} \, dx","IntegrateAlgebraic[(a + b*x^2)^(4/3)/x^4,x]","\int \frac{\left(a+b x^2\right)^{4/3}}{x^4} \, dx","-\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{8 b \sqrt[3]{a+b x^2}}{9 x}-\frac{\left(a+b x^2\right)^{4/3}}{3 x^3}",1,"Could not integrate","F",-1
701,1,13,13,0.0179289,"\int x \left(-1+x^2\right)^{7/3} \, dx","IntegrateAlgebraic[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
702,1,50,80,0.0426419,"\int \frac{x^7}{\sqrt[3]{a+b x^2}} \, dx","IntegrateAlgebraic[x^7/(a + b*x^2)^(1/3),x]","-\frac{3 \left(a+b x^2\right)^{2/3} \left(81 a^3-54 a^2 b x^2+45 a b^2 x^4-40 b^3 x^6\right)}{880 b^4}","-\frac{3 a^3 \left(a+b x^2\right)^{2/3}}{4 b^4}+\frac{9 a^2 \left(a+b x^2\right)^{5/3}}{10 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 + b*x^2)^(2/3)*(81*a^3 - 54*a^2*b*x^2 + 45*a*b^2*x^4 - 40*b^3*x^6))/(880*b^4)","A",1
703,1,39,59,0.0386348,"\int \frac{x^5}{\sqrt[3]{a+b x^2}} \, dx","IntegrateAlgebraic[x^5/(a + b*x^2)^(1/3),x]","\frac{3 \left(a+b x^2\right)^{2/3} \left(9 a^2-6 a b x^2+5 b^2 x^4\right)}{80 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 + b*x^2)^(2/3)*(9*a^2 - 6*a*b*x^2 + 5*b^2*x^4))/(80*b^3)","A",1
704,1,28,38,0.0337874,"\int \frac{x^3}{\sqrt[3]{a+b x^2}} \, dx","IntegrateAlgebraic[x^3/(a + b*x^2)^(1/3),x]","-\frac{3 \left(3 a-2 b x^2\right) \left(a+b x^2\right)^{2/3}}{20 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*(3*a - 2*b*x^2)*(a + b*x^2)^(2/3))/(20*b^2)","A",1
705,1,18,18,0.0236964,"\int \frac{x}{\sqrt[3]{a+b x^2}} \, dx","IntegrateAlgebraic[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
706,1,118,86,0.1082762,"\int \frac{1}{x \sqrt[3]{a+b x^2}} \, dx","IntegrateAlgebraic[1/(x*(a + b*x^2)^(1/3)),x]","-\frac{\log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}\right)}{4 \sqrt[3]{a}}+\frac{\log \left(\sqrt[3]{a+b x^2}-\sqrt[3]{a}\right)}{2 \sqrt[3]{a}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}}{\sqrt{3} \sqrt[3]{a}}+\frac{1}{\sqrt{3}}\right)}{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[1/Sqrt[3] + (2*(a + b*x^2)^(1/3))/(Sqrt[3]*a^(1/3))])/(2*a^(1/3)) + Log[-a^(1/3) + (a + b*x^2)^(1/3)]/(2*a^(1/3)) - Log[a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3)]/(4*a^(1/3))","A",1
707,1,142,110,0.1887987,"\int \frac{1}{x^3 \sqrt[3]{a+b x^2}} \, dx","IntegrateAlgebraic[1/(x^3*(a + b*x^2)^(1/3)),x]","-\frac{b \log \left(\sqrt[3]{a+b x^2}-\sqrt[3]{a}\right)}{6 a^{4/3}}+\frac{b \log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}\right)}{12 a^{4/3}}-\frac{b \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}}{\sqrt{3} \sqrt[3]{a}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} 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,"-1/2*(a + b*x^2)^(2/3)/(a*x^2) - (b*ArcTan[1/Sqrt[3] + (2*(a + b*x^2)^(1/3))/(Sqrt[3]*a^(1/3))])/(2*Sqrt[3]*a^(4/3)) - (b*Log[-a^(1/3) + (a + b*x^2)^(1/3)])/(6*a^(4/3)) + (b*Log[a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3)])/(12*a^(4/3))","A",1
708,1,158,138,0.2960966,"\int \frac{1}{x^5 \sqrt[3]{a+b x^2}} \, dx","IntegrateAlgebraic[1/(x^5*(a + b*x^2)^(1/3)),x]","\frac{b^2 \log \left(\sqrt[3]{a+b x^2}-\sqrt[3]{a}\right)}{9 a^{7/3}}-\frac{b^2 \log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}\right)}{18 a^{7/3}}+\frac{b^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}}{\sqrt{3} \sqrt[3]{a}}+\frac{1}{\sqrt{3}}\right)}{3 \sqrt{3} a^{7/3}}+\frac{\left(a+b x^2\right)^{2/3} \left(4 b x^2-3 a\right)}{12 a^2 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)*(-3*a + 4*b*x^2))/(12*a^2*x^4) + (b^2*ArcTan[1/Sqrt[3] + (2*(a + b*x^2)^(1/3))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(7/3)) + (b^2*Log[-a^(1/3) + (a + b*x^2)^(1/3)])/(9*a^(7/3)) - (b^2*Log[a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3)])/(18*a^(7/3))","A",1
709,0,0,580,3.8502996,"\int \frac{x^4}{\sqrt[3]{a+b x^2}} \, dx","IntegrateAlgebraic[x^4/(a + b*x^2)^(1/3),x]","\int \frac{x^4}{\sqrt[3]{a+b x^2}} \, dx","-\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{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 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,"Could not integrate","F",-1
710,0,0,556,3.5979593,"\int \frac{x^2}{\sqrt[3]{a+b x^2}} \, dx","IntegrateAlgebraic[x^2/(a + b*x^2)^(1/3),x]","\int \frac{x^2}{\sqrt[3]{a+b x^2}} \, dx","\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,"Could not integrate","F",-1
711,0,0,529,3.5503537,"\int \frac{1}{\sqrt[3]{a+b x^2}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(-1/3),x]","\int \frac{1}{\sqrt[3]{a+b x^2}} \, dx","-\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,"Could not integrate","F",-1
712,0,0,546,3.9490504,"\int \frac{1}{x^2 \sqrt[3]{a+b x^2}} \, dx","IntegrateAlgebraic[1/(x^2*(a + b*x^2)^(1/3)),x]","\int \frac{1}{x^2 \sqrt[3]{a+b x^2}} \, dx","-\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,"Could not integrate","F",-1
713,0,0,578,8.5649193,"\int \frac{1}{x^4 \sqrt[3]{a+b x^2}} \, dx","IntegrateAlgebraic[1/(x^4*(a + b*x^2)^(1/3)),x]","\int \frac{1}{x^4 \sqrt[3]{a+b x^2}} \, dx","\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{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{\left(a+b x^2\right)^{2/3}}{3 a x^3}",1,"Could not integrate","F",-1
714,1,50,80,0.0413236,"\int \frac{x^7}{\left(a+b x^2\right)^{2/3}} \, dx","IntegrateAlgebraic[x^7/(a + b*x^2)^(2/3),x]","-\frac{3 \sqrt[3]{a+b x^2} \left(81 a^3-27 a^2 b x^2+18 a b^2 x^4-14 b^3 x^6\right)}{280 b^4}","-\frac{3 a^3 \sqrt[3]{a+b x^2}}{2 b^4}+\frac{9 a^2 \left(a+b x^2\right)^{4/3}}{8 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 + b*x^2)^(1/3)*(81*a^3 - 27*a^2*b*x^2 + 18*a*b^2*x^4 - 14*b^3*x^6))/(280*b^4)","A",1
715,1,39,59,0.0371498,"\int \frac{x^5}{\left(a+b x^2\right)^{2/3}} \, dx","IntegrateAlgebraic[x^5/(a + b*x^2)^(2/3),x]","\frac{3 \sqrt[3]{a+b x^2} \left(9 a^2-3 a b x^2+2 b^2 x^4\right)}{28 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 + b*x^2)^(1/3)*(9*a^2 - 3*a*b*x^2 + 2*b^2*x^4))/(28*b^3)","A",1
716,1,28,38,0.0327323,"\int \frac{x^3}{\left(a+b x^2\right)^{2/3}} \, dx","IntegrateAlgebraic[x^3/(a + b*x^2)^(2/3),x]","-\frac{3 \left(3 a-b x^2\right) \sqrt[3]{a+b x^2}}{8 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*(3*a - b*x^2)*(a + b*x^2)^(1/3))/(8*b^2)","A",1
717,1,18,18,0.0233225,"\int \frac{x}{\left(a+b x^2\right)^{2/3}} \, dx","IntegrateAlgebraic[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
718,1,118,86,0.1102772,"\int \frac{1}{x \left(a+b x^2\right)^{2/3}} \, dx","IntegrateAlgebraic[1/(x*(a + b*x^2)^(2/3)),x]","\frac{\log \left(\sqrt[3]{a+b x^2}-\sqrt[3]{a}\right)}{2 a^{2/3}}-\frac{\log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}\right)}{4 a^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}}{\sqrt{3} \sqrt[3]{a}}+\frac{1}{\sqrt{3}}\right)}{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,"-1/2*(Sqrt[3]*ArcTan[1/Sqrt[3] + (2*(a + b*x^2)^(1/3))/(Sqrt[3]*a^(1/3))])/a^(2/3) + Log[-a^(1/3) + (a + b*x^2)^(1/3)]/(2*a^(2/3)) - Log[a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3)]/(4*a^(2/3))","A",1
719,1,139,107,0.1899984,"\int \frac{1}{x^3 \left(a+b x^2\right)^{2/3}} \, dx","IntegrateAlgebraic[1/(x^3*(a + b*x^2)^(2/3)),x]","-\frac{b \log \left(\sqrt[3]{a+b x^2}-\sqrt[3]{a}\right)}{3 a^{5/3}}+\frac{b \log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}\right)}{6 a^{5/3}}+\frac{b \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}}{\sqrt{3} \sqrt[3]{a}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{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,"-1/2*(a + b*x^2)^(1/3)/(a*x^2) + (b*ArcTan[1/Sqrt[3] + (2*(a + b*x^2)^(1/3))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(5/3)) - (b*Log[-a^(1/3) + (a + b*x^2)^(1/3)])/(3*a^(5/3)) + (b*Log[a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3)])/(6*a^(5/3))","A",1
720,1,158,138,0.1912094,"\int \frac{1}{x^5 \left(a+b x^2\right)^{2/3}} \, dx","IntegrateAlgebraic[1/(x^5*(a + b*x^2)^(2/3)),x]","\frac{5 b^2 \log \left(\sqrt[3]{a+b x^2}-\sqrt[3]{a}\right)}{18 a^{8/3}}-\frac{5 b^2 \log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}\right)}{36 a^{8/3}}-\frac{5 b^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}}{\sqrt{3} \sqrt[3]{a}}+\frac{1}{\sqrt{3}}\right)}{6 \sqrt{3} a^{8/3}}+\frac{\sqrt[3]{a+b x^2} \left(5 b x^2-3 a\right)}{12 a^2 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)*(-3*a + 5*b*x^2))/(12*a^2*x^4) - (5*b^2*ArcTan[1/Sqrt[3] + (2*(a + b*x^2)^(1/3))/(Sqrt[3]*a^(1/3))])/(6*Sqrt[3]*a^(8/3)) + (5*b^2*Log[-a^(1/3) + (a + b*x^2)^(1/3)])/(18*a^(8/3)) - (5*b^2*Log[a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3)])/(36*a^(8/3))","A",1
721,0,0,293,4.0101351,"\int \frac{x^4}{\left(a+b x^2\right)^{2/3}} \, dx","IntegrateAlgebraic[x^4/(a + b*x^2)^(2/3),x]","\int \frac{x^4}{\left(a+b x^2\right)^{2/3}} \, dx","-\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,"Could not integrate","F",-1
722,0,0,269,3.5896821,"\int \frac{x^2}{\left(a+b x^2\right)^{2/3}} \, dx","IntegrateAlgebraic[x^2/(a + b*x^2)^(2/3),x]","\int \frac{x^2}{\left(a+b x^2\right)^{2/3}} \, dx","\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,"Could not integrate","F",-1
723,0,0,246,3.4945176,"\int \frac{1}{\left(a+b x^2\right)^{2/3}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(-2/3),x]","\int \frac{1}{\left(a+b x^2\right)^{2/3}} \, dx","-\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,"Could not integrate","F",-1
724,0,0,265,4.1380476,"\int \frac{1}{x^2 \left(a+b x^2\right)^{2/3}} \, dx","IntegrateAlgebraic[1/(x^2*(a + b*x^2)^(2/3)),x]","\int \frac{1}{x^2 \left(a+b x^2\right)^{2/3}} \, dx","\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,"Could not integrate","F",-1
725,0,0,293,8.9089806,"\int \frac{1}{x^4 \left(a+b x^2\right)^{2/3}} \, dx","IntegrateAlgebraic[1/(x^4*(a + b*x^2)^(2/3)),x]","\int \frac{1}{x^4 \left(a+b x^2\right)^{2/3}} \, dx","\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,"Could not integrate","F",-1
726,1,50,80,0.0499335,"\int \frac{x^7}{\left(a+b x^2\right)^{4/3}} \, dx","IntegrateAlgebraic[x^7/(a + b*x^2)^(4/3),x]","\frac{3 \left(81 a^3+27 a^2 b x^2-9 a b^2 x^4+5 b^3 x^6\right)}{80 b^4 \sqrt[3]{a+b x^2}}","\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*(81*a^3 + 27*a^2*b*x^2 - 9*a*b^2*x^4 + 5*b^3*x^6))/(80*b^4*(a + b*x^2)^(1/3))","A",1
727,1,39,59,0.0425382,"\int \frac{x^5}{\left(a+b x^2\right)^{4/3}} \, dx","IntegrateAlgebraic[x^5/(a + b*x^2)^(4/3),x]","-\frac{3 \left(9 a^2+3 a b x^2-b^2 x^4\right)}{10 b^3 \sqrt[3]{a+b x^2}}","-\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*(9*a^2 + 3*a*b*x^2 - b^2*x^4))/(10*b^3*(a + b*x^2)^(1/3))","A",1
728,1,27,38,0.037758,"\int \frac{x^3}{\left(a+b x^2\right)^{4/3}} \, dx","IntegrateAlgebraic[x^3/(a + b*x^2)^(4/3),x]","\frac{3 \left(3 a+b x^2\right)}{4 b^2 \sqrt[3]{a+b x^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*(3*a + b*x^2))/(4*b^2*(a + b*x^2)^(1/3))","A",1
729,1,18,18,0.0266781,"\int \frac{x}{\left(a+b x^2\right)^{4/3}} \, dx","IntegrateAlgebraic[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
730,1,136,104,0.1390603,"\int \frac{1}{x \left(a+b x^2\right)^{4/3}} \, dx","IntegrateAlgebraic[1/(x*(a + b*x^2)^(4/3)),x]","\frac{\log \left(\sqrt[3]{a+b x^2}-\sqrt[3]{a}\right)}{2 a^{4/3}}-\frac{\log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}\right)}{4 a^{4/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}}{\sqrt{3} \sqrt[3]{a}}+\frac{1}{\sqrt{3}}\right)}{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[1/Sqrt[3] + (2*(a + b*x^2)^(1/3))/(Sqrt[3]*a^(1/3))])/(2*a^(4/3)) + Log[-a^(1/3) + (a + b*x^2)^(1/3)]/(2*a^(4/3)) - Log[a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3)]/(4*a^(4/3))","A",1
731,1,150,123,0.230673,"\int \frac{1}{x^3 \left(a+b x^2\right)^{4/3}} \, dx","IntegrateAlgebraic[1/(x^3*(a + b*x^2)^(4/3)),x]","-\frac{2 b \log \left(\sqrt[3]{a+b x^2}-\sqrt[3]{a}\right)}{3 a^{7/3}}+\frac{b \log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}\right)}{3 a^{7/3}}-\frac{2 b \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}}{\sqrt{3} \sqrt[3]{a}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} a^{7/3}}+\frac{-a-4 b x^2}{2 a^2 x^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{2 b}{a^2 \sqrt[3]{a+b x^2}}-\frac{1}{2 a x^2 \sqrt[3]{a+b x^2}}",1,"(-a - 4*b*x^2)/(2*a^2*x^2*(a + b*x^2)^(1/3)) - (2*b*ArcTan[1/Sqrt[3] + (2*(a + b*x^2)^(1/3))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(7/3)) - (2*b*Log[-a^(1/3) + (a + b*x^2)^(1/3)])/(3*a^(7/3)) + (b*Log[a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3)])/(3*a^(7/3))","A",1
732,1,169,159,0.3430991,"\int \frac{1}{x^5 \left(a+b x^2\right)^{4/3}} \, dx","IntegrateAlgebraic[1/(x^5*(a + b*x^2)^(4/3)),x]","\frac{7 b^2 \log \left(\sqrt[3]{a+b x^2}-\sqrt[3]{a}\right)}{9 a^{10/3}}-\frac{7 b^2 \log \left(a^{2/3}+\sqrt[3]{a} \sqrt[3]{a+b x^2}+\left(a+b x^2\right)^{2/3}\right)}{18 a^{10/3}}+\frac{7 b^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^2}}{\sqrt{3} \sqrt[3]{a}}+\frac{1}{\sqrt{3}}\right)}{3 \sqrt{3} a^{10/3}}+\frac{-3 a^2+7 a b x^2+28 b^2 x^4}{12 a^3 x^4 \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^2}{3 a^3 \sqrt[3]{a+b x^2}}+\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*a^2 + 7*a*b*x^2 + 28*b^2*x^4)/(12*a^3*x^4*(a + b*x^2)^(1/3)) + (7*b^2*ArcTan[1/Sqrt[3] + (2*(a + b*x^2)^(1/3))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(10/3)) + (7*b^2*Log[-a^(1/3) + (a + b*x^2)^(1/3)])/(9*a^(10/3)) - (7*b^2*Log[a^(2/3) + a^(1/3)*(a + b*x^2)^(1/3) + (a + b*x^2)^(2/3)])/(18*a^(10/3))","A",1
733,0,0,577,4.3581894,"\int \frac{x^4}{\left(a+b x^2\right)^{4/3}} \, dx","IntegrateAlgebraic[x^4/(a + b*x^2)^(4/3),x]","\int \frac{x^4}{\left(a+b x^2\right)^{4/3}} \, dx","\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,"Could not integrate","F",-1
734,0,0,553,4.07887,"\int \frac{x^2}{\left(a+b x^2\right)^{4/3}} \, dx","IntegrateAlgebraic[x^2/(a + b*x^2)^(4/3),x]","\int \frac{x^2}{\left(a+b x^2\right)^{4/3}} \, dx","-\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,"Could not integrate","F",-1
735,0,0,552,3.7904952,"\int \frac{1}{\left(a+b x^2\right)^{4/3}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(-4/3),x]","\int \frac{1}{\left(a+b x^2\right)^{4/3}} \, dx","\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,"Could not integrate","F",-1
736,0,0,571,4.5665407,"\int \frac{1}{x^2 \left(a+b x^2\right)^{4/3}} \, dx","IntegrateAlgebraic[1/(x^2*(a + b*x^2)^(4/3)),x]","\int \frac{1}{x^2 \left(a+b x^2\right)^{4/3}} \, dx","-\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{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{3}{2 a x \sqrt[3]{a+b x^2}}",1,"Could not integrate","F",-1
737,0,0,599,9.050249,"\int \frac{1}{x^4 \left(a+b x^2\right)^{4/3}} \, dx","IntegrateAlgebraic[1/(x^4*(a + b*x^2)^(4/3)),x]","\int \frac{1}{x^4 \left(a+b x^2\right)^{4/3}} \, dx","\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{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{3}{2 a x^3 \sqrt[3]{a+b x^2}}",1,"Could not integrate","F",-1
738,1,267,195,7.1796398,"\int (c x)^{13/3} \sqrt[3]{a+b x^2} \, dx","IntegrateAlgebraic[(c*x)^(13/3)*(a + b*x^2)^(1/3),x]","-\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)}{162 b^{8/3}}+\frac{5 a^3 c^{13/3} \log \left(c^{4/3} \left(a+b x^2\right)^{2/3}+\sqrt[3]{b} c^{2/3} (c x)^{2/3} \sqrt[3]{a+b x^2}+b^{2/3} (c x)^{4/3}\right)}{324 b^{8/3}}-\frac{5 a^3 c^{13/3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{b} (c x)^{2/3}}{2 c^{2/3} \sqrt[3]{a+b x^2}+\sqrt[3]{b} (c x)^{2/3}}\right)}{54 \sqrt{3} b^{8/3}}+\frac{\sqrt[3]{a+b x^2} \left(-5 a^2 c^4 (c x)^{4/3}+3 a b c^2 (c x)^{10/3}+18 b^2 (c x)^{16/3}\right)}{108 b^2 c}","-\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{5 a^2 c^3 (c x)^{4/3} \sqrt[3]{a+b x^2}}{108 b^2}+\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,"((a + b*x^2)^(1/3)*(-5*a^2*c^4*(c*x)^(4/3) + 3*a*b*c^2*(c*x)^(10/3) + 18*b^2*(c*x)^(16/3)))/(108*b^2*c) - (5*a^3*c^(13/3)*ArcTan[(Sqrt[3]*b^(1/3)*(c*x)^(2/3))/(b^(1/3)*(c*x)^(2/3) + 2*c^(2/3)*(a + b*x^2)^(1/3))])/(54*Sqrt[3]*b^(8/3)) - (5*a^3*c^(13/3)*Log[b^(1/3)*(c*x)^(2/3) - c^(2/3)*(a + b*x^2)^(1/3)])/(162*b^(8/3)) + (5*a^3*c^(13/3)*Log[b^(2/3)*(c*x)^(4/3) + b^(1/3)*c^(2/3)*(c*x)^(2/3)*(a + b*x^2)^(1/3) + c^(4/3)*(a + b*x^2)^(2/3)])/(324*b^(8/3))","A",1
739,1,248,164,7.0404865,"\int (c x)^{7/3} \sqrt[3]{a+b x^2} \, dx","IntegrateAlgebraic[(c*x)^(7/3)*(a + b*x^2)^(1/3),x]","\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)}{18 b^{5/3}}-\frac{a^2 c^{7/3} \log \left(c^{4/3} \left(a+b x^2\right)^{2/3}+\sqrt[3]{b} c^{2/3} (c x)^{2/3} \sqrt[3]{a+b x^2}+b^{2/3} (c x)^{4/3}\right)}{36 b^{5/3}}+\frac{a^2 c^{7/3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{b} (c x)^{2/3}}{2 c^{2/3} \sqrt[3]{a+b x^2}+\sqrt[3]{b} (c x)^{2/3}}\right)}{6 \sqrt{3} b^{5/3}}+\frac{\sqrt[3]{a+b x^2} \left(a c^2 (c x)^{4/3}+3 b (c x)^{10/3}\right)}{12 b c}","\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 + b*x^2)^(1/3)*(a*c^2*(c*x)^(4/3) + 3*b*(c*x)^(10/3)))/(12*b*c) + (a^2*c^(7/3)*ArcTan[(Sqrt[3]*b^(1/3)*(c*x)^(2/3))/(b^(1/3)*(c*x)^(2/3) + 2*c^(2/3)*(a + b*x^2)^(1/3))])/(6*Sqrt[3]*b^(5/3)) + (a^2*c^(7/3)*Log[b^(1/3)*(c*x)^(2/3) - c^(2/3)*(a + b*x^2)^(1/3)])/(18*b^(5/3)) - (a^2*c^(7/3)*Log[b^(2/3)*(c*x)^(4/3) + b^(1/3)*c^(2/3)*(c*x)^(2/3)*(a + b*x^2)^(1/3) + c^(4/3)*(a + b*x^2)^(2/3)])/(36*b^(5/3))","A",1
740,1,223,133,1.9322983,"\int \sqrt[3]{c x} \sqrt[3]{a+b x^2} \, dx","IntegrateAlgebraic[(c*x)^(1/3)*(a + b*x^2)^(1/3),x]","-\frac{a \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 \sqrt[3]{c} \log \left(c^{4/3} \left(a+b x^2\right)^{2/3}+\sqrt[3]{b} c^{2/3} (c x)^{2/3} \sqrt[3]{a+b x^2}+b^{2/3} (c x)^{4/3}\right)}{12 b^{2/3}}-\frac{a \sqrt[3]{c} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{b} (c x)^{2/3}}{2 c^{2/3} \sqrt[3]{a+b x^2}+\sqrt[3]{b} (c x)^{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[(Sqrt[3]*b^(1/3)*(c*x)^(2/3))/(b^(1/3)*(c*x)^(2/3) + 2*c^(2/3)*(a + b*x^2)^(1/3))])/(2*Sqrt[3]*b^(2/3)) - (a*c^(1/3)*Log[b^(1/3)*(c*x)^(2/3) - c^(2/3)*(a + b*x^2)^(1/3)])/(6*b^(2/3)) + (a*c^(1/3)*Log[b^(2/3)*(c*x)^(4/3) + b^(1/3)*c^(2/3)*(c*x)^(2/3)*(a + b*x^2)^(1/3) + c^(4/3)*(a + b*x^2)^(2/3)])/(12*b^(2/3))","A",1
741,1,220,131,1.3116226,"\int \frac{\sqrt[3]{a+b x^2}}{(c x)^{5/3}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(1/3)/(c*x)^(5/3),x]","\frac{\sqrt[3]{b} \log \left(c^{4/3} \left(a+b x^2\right)^{2/3}+\sqrt[3]{b} c^{2/3} (c x)^{2/3} \sqrt[3]{a+b x^2}+b^{2/3} (c x)^{4/3}\right)}{4 c^{5/3}}-\frac{\sqrt[3]{b} \log \left(\sqrt[3]{b} (c x)^{2/3}-c^{2/3} \sqrt[3]{a+b x^2}\right)}{2 c^{5/3}}-\frac{\sqrt{3} \sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{b} (c x)^{2/3}}{2 c^{2/3} \sqrt[3]{a+b x^2}+\sqrt[3]{b} (c x)^{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[(Sqrt[3]*b^(1/3)*(c*x)^(2/3))/(b^(1/3)*(c*x)^(2/3) + 2*c^(2/3)*(a + b*x^2)^(1/3))])/(2*c^(5/3)) - (b^(1/3)*Log[b^(1/3)*(c*x)^(2/3) - c^(2/3)*(a + b*x^2)^(1/3)])/(2*c^(5/3)) + (b^(1/3)*Log[b^(2/3)*(c*x)^(4/3) + b^(1/3)*c^(2/3)*(c*x)^(2/3)*(a + b*x^2)^(1/3) + c^(4/3)*(a + b*x^2)^(2/3)])/(4*c^(5/3))","A",1
742,1,28,28,5.3142784,"\int \frac{\sqrt[3]{a+b x^2}}{(c x)^{11/3}} \, dx","IntegrateAlgebraic[(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
743,0,0,57,0.9008809,"\int \frac{\sqrt[3]{a+b x^2}}{(c x)^{17/3}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(1/3)/(c*x)^(17/3),x]","\int \frac{\sqrt[3]{a+b x^2}}{(c x)^{17/3}} \, dx","\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,"Could not integrate","F",-1
744,0,0,85,0.9784404,"\int \frac{\sqrt[3]{a+b x^2}}{(c x)^{23/3}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(1/3)/(c*x)^(23/3),x]","\int \frac{\sqrt[3]{a+b x^2}}{(c x)^{23/3}} \, dx","-\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,"Could not integrate","F",-1
745,0,0,113,1.0813569,"\int \frac{\sqrt[3]{a+b x^2}}{(c x)^{29/3}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(1/3)/(c*x)^(29/3),x]","\int \frac{\sqrt[3]{a+b x^2}}{(c x)^{29/3}} \, dx","\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,"Could not integrate","F",-1
746,0,0,451,11.9065717,"\int (c x)^{10/3} \sqrt[3]{a+b x^2} \, dx","IntegrateAlgebraic[(c*x)^(10/3)*(a + b*x^2)^(1/3),x]","\int (c x)^{10/3} \sqrt[3]{a+b x^2} \, dx","-\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,"Could not integrate","F",-1
747,0,0,418,8.5625826,"\int (c x)^{4/3} \sqrt[3]{a+b x^2} \, dx","IntegrateAlgebraic[(c*x)^(4/3)*(a + b*x^2)^(1/3),x]","\int (c x)^{4/3} \sqrt[3]{a+b x^2} \, dx","-\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,"Could not integrate","F",-1
748,0,0,381,10.3254696,"\int \frac{\sqrt[3]{a+b x^2}}{(c x)^{2/3}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(1/3)/(c*x)^(2/3),x]","\int \frac{\sqrt[3]{a+b x^2}}{(c x)^{2/3}} \, dx","\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,"Could not integrate","F",-1
749,0,0,391,18.1700412,"\int \frac{\sqrt[3]{a+b x^2}}{(c x)^{8/3}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(1/3)/(c*x)^(8/3),x]","\int \frac{\sqrt[3]{a+b x^2}}{(c x)^{8/3}} \, dx","\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,"Could not integrate","F",-1
750,0,0,422,24.1627038,"\int \frac{\sqrt[3]{a+b x^2}}{(c x)^{14/3}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(1/3)/(c*x)^(14/3),x]","\int \frac{\sqrt[3]{a+b x^2}}{(c x)^{14/3}} \, dx","-\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,"Could not integrate","F",-1
751,0,0,58,5.7897435,"\int (c x)^{2/3} \sqrt[3]{a+b x^2} \, dx","IntegrateAlgebraic[(c*x)^(2/3)*(a + b*x^2)^(1/3),x]","\int (c x)^{2/3} \sqrt[3]{a+b x^2} \, dx","\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,"Could not integrate","F",-1
752,0,0,58,7.3382288,"\int \frac{\sqrt[3]{a+b x^2}}{\sqrt[3]{c x}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(1/3)/(c*x)^(1/3),x]","\int \frac{\sqrt[3]{a+b x^2}}{\sqrt[3]{c x}} \, dx","\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,"Could not integrate","F",-1
753,0,0,56,14.5908492,"\int \frac{\sqrt[3]{a+b x^2}}{(c x)^{4/3}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(1/3)/(c*x)^(4/3),x]","\int \frac{\sqrt[3]{a+b x^2}}{(c x)^{4/3}} \, dx","-\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,"Could not integrate","F",-1
754,1,285,223,7.241209,"\int (c x)^{13/3} \left(a+b x^2\right)^{4/3} \, dx","IntegrateAlgebraic[(c*x)^(13/3)*(a + b*x^2)^(4/3),x]","-\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)}{486 b^{8/3}}+\frac{5 a^4 c^{13/3} \log \left(c^{4/3} \left(a+b x^2\right)^{2/3}+\sqrt[3]{b} c^{2/3} (c x)^{2/3} \sqrt[3]{a+b x^2}+b^{2/3} (c x)^{4/3}\right)}{972 b^{8/3}}-\frac{5 a^4 c^{13/3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{b} (c x)^{2/3}}{2 c^{2/3} \sqrt[3]{a+b x^2}+\sqrt[3]{b} (c x)^{2/3}}\right)}{162 \sqrt{3} b^{8/3}}+\frac{\sqrt[3]{a+b x^2} \left(-10 a^3 c^6 (c x)^{4/3}+6 a^2 b c^4 (c x)^{10/3}+117 a b^2 c^2 (c x)^{16/3}+81 b^3 (c x)^{22/3}\right)}{648 b^2 c^3}","-\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{5 a^3 c^3 (c x)^{4/3} \sqrt[3]{a+b x^2}}{324 b^2}+\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,"((a + b*x^2)^(1/3)*(-10*a^3*c^6*(c*x)^(4/3) + 6*a^2*b*c^4*(c*x)^(10/3) + 117*a*b^2*c^2*(c*x)^(16/3) + 81*b^3*(c*x)^(22/3)))/(648*b^2*c^3) - (5*a^4*c^(13/3)*ArcTan[(Sqrt[3]*b^(1/3)*(c*x)^(2/3))/(b^(1/3)*(c*x)^(2/3) + 2*c^(2/3)*(a + b*x^2)^(1/3))])/(162*Sqrt[3]*b^(8/3)) - (5*a^4*c^(13/3)*Log[b^(1/3)*(c*x)^(2/3) - c^(2/3)*(a + b*x^2)^(1/3)])/(486*b^(8/3)) + (5*a^4*c^(13/3)*Log[b^(2/3)*(c*x)^(4/3) + b^(1/3)*c^(2/3)*(c*x)^(2/3)*(a + b*x^2)^(1/3) + c^(4/3)*(a + b*x^2)^(2/3)])/(972*b^(8/3))","A",1
755,1,267,192,7.1175174,"\int (c x)^{7/3} \left(a+b x^2\right)^{4/3} \, dx","IntegrateAlgebraic[(c*x)^(7/3)*(a + b*x^2)^(4/3),x]","\frac{2 a^3 c^{7/3} \log \left(\sqrt[3]{b} (c x)^{2/3}-c^{2/3} \sqrt[3]{a+b x^2}\right)}{81 b^{5/3}}-\frac{a^3 c^{7/3} \log \left(c^{4/3} \left(a+b x^2\right)^{2/3}+\sqrt[3]{b} c^{2/3} (c x)^{2/3} \sqrt[3]{a+b x^2}+b^{2/3} (c x)^{4/3}\right)}{81 b^{5/3}}+\frac{2 a^3 c^{7/3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{b} (c x)^{2/3}}{2 c^{2/3} \sqrt[3]{a+b x^2}+\sqrt[3]{b} (c x)^{2/3}}\right)}{27 \sqrt{3} b^{5/3}}+\frac{\sqrt[3]{a+b x^2} \left(2 a^2 c^4 (c x)^{4/3}+15 a b c^2 (c x)^{10/3}+9 b^2 (c x)^{16/3}\right)}{54 b c^3}","\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 + b*x^2)^(1/3)*(2*a^2*c^4*(c*x)^(4/3) + 15*a*b*c^2*(c*x)^(10/3) + 9*b^2*(c*x)^(16/3)))/(54*b*c^3) + (2*a^3*c^(7/3)*ArcTan[(Sqrt[3]*b^(1/3)*(c*x)^(2/3))/(b^(1/3)*(c*x)^(2/3) + 2*c^(2/3)*(a + b*x^2)^(1/3))])/(27*Sqrt[3]*b^(5/3)) + (2*a^3*c^(7/3)*Log[b^(1/3)*(c*x)^(2/3) - c^(2/3)*(a + b*x^2)^(1/3)])/(81*b^(5/3)) - (a^3*c^(7/3)*Log[b^(2/3)*(c*x)^(4/3) + b^(1/3)*c^(2/3)*(c*x)^(2/3)*(a + b*x^2)^(1/3) + c^(4/3)*(a + b*x^2)^(2/3)])/(81*b^(5/3))","A",1
756,1,246,163,4.2032119,"\int \sqrt[3]{c x} \left(a+b x^2\right)^{4/3} \, dx","IntegrateAlgebraic[(c*x)^(1/3)*(a + b*x^2)^(4/3),x]","-\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)}{9 b^{2/3}}+\frac{a^2 \sqrt[3]{c} \log \left(c^{4/3} \left(a+b x^2\right)^{2/3}+\sqrt[3]{b} c^{2/3} (c x)^{2/3} \sqrt[3]{a+b x^2}+b^{2/3} (c x)^{4/3}\right)}{18 b^{2/3}}-\frac{a^2 \sqrt[3]{c} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{b} (c x)^{2/3}}{2 c^{2/3} \sqrt[3]{a+b x^2}+\sqrt[3]{b} (c x)^{2/3}}\right)}{3 \sqrt{3} b^{2/3}}+\frac{\sqrt[3]{a+b x^2} \left(7 a c^2 (c x)^{4/3}+3 b (c x)^{10/3}\right)}{12 c^3}","-\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 + b*x^2)^(1/3)*(7*a*c^2*(c*x)^(4/3) + 3*b*(c*x)^(10/3)))/(12*c^3) - (a^2*c^(1/3)*ArcTan[(Sqrt[3]*b^(1/3)*(c*x)^(2/3))/(b^(1/3)*(c*x)^(2/3) + 2*c^(2/3)*(a + b*x^2)^(1/3))])/(3*Sqrt[3]*b^(2/3)) - (a^2*c^(1/3)*Log[b^(1/3)*(c*x)^(2/3) - c^(2/3)*(a + b*x^2)^(1/3)])/(9*b^(2/3)) + (a^2*c^(1/3)*Log[b^(2/3)*(c*x)^(4/3) + b^(1/3)*c^(2/3)*(c*x)^(2/3)*(a + b*x^2)^(1/3) + c^(4/3)*(a + b*x^2)^(2/3)])/(18*b^(2/3))","A",1
757,1,236,153,1.4840415,"\int \frac{\left(a+b x^2\right)^{4/3}}{(c x)^{5/3}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(4/3)/(c*x)^(5/3),x]","\frac{a \sqrt[3]{b} \log \left(c^{4/3} \left(a+b x^2\right)^{2/3}+\sqrt[3]{b} c^{2/3} (c x)^{2/3} \sqrt[3]{a+b x^2}+b^{2/3} (c x)^{4/3}\right)}{3 c^{5/3}}-\frac{2 a \sqrt[3]{b} \log \left(\sqrt[3]{b} (c x)^{2/3}-c^{2/3} \sqrt[3]{a+b x^2}\right)}{3 c^{5/3}}-\frac{2 a \sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{b} (c x)^{2/3}}{2 c^{2/3} \sqrt[3]{a+b x^2}+\sqrt[3]{b} (c x)^{2/3}}\right)}{\sqrt{3} c^{5/3}}+\frac{\sqrt[3]{a+b x^2} \left(b c^2 x^2-3 a c^2\right)}{2 c^3 (c x)^{2/3}}","-\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{2 b (c x)^{4/3} \sqrt[3]{a+b x^2}}{c^3}-\frac{3 \left(a+b x^2\right)^{4/3}}{2 c (c x)^{2/3}}",1,"((a + b*x^2)^(1/3)*(-3*a*c^2 + b*c^2*x^2))/(2*c^3*(c*x)^(2/3)) - (2*a*b^(1/3)*ArcTan[(Sqrt[3]*b^(1/3)*(c*x)^(2/3))/(b^(1/3)*(c*x)^(2/3) + 2*c^(2/3)*(a + b*x^2)^(1/3))])/(Sqrt[3]*c^(5/3)) - (2*a*b^(1/3)*Log[b^(1/3)*(c*x)^(2/3) - c^(2/3)*(a + b*x^2)^(1/3)])/(3*c^(5/3)) + (a*b^(1/3)*Log[b^(2/3)*(c*x)^(4/3) + b^(1/3)*c^(2/3)*(c*x)^(2/3)*(a + b*x^2)^(1/3) + c^(4/3)*(a + b*x^2)^(2/3)])/(3*c^(5/3))","A",1
758,1,235,157,1.8862908,"\int \frac{\left(a+b x^2\right)^{4/3}}{(c x)^{11/3}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(4/3)/(c*x)^(11/3),x]","-\frac{b^{4/3} \log \left(\sqrt[3]{b} (c x)^{2/3}-c^{2/3} \sqrt[3]{a+b x^2}\right)}{2 c^{11/3}}+\frac{b^{4/3} \log \left(c^{4/3} \left(a+b x^2\right)^{2/3}+\sqrt[3]{b} c^{2/3} (c x)^{2/3} \sqrt[3]{a+b x^2}+b^{2/3} (c x)^{4/3}\right)}{4 c^{11/3}}-\frac{\sqrt{3} b^{4/3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{b} (c x)^{2/3}}{2 c^{2/3} \sqrt[3]{a+b x^2}+\sqrt[3]{b} (c x)^{2/3}}\right)}{2 c^{11/3}}-\frac{3 \sqrt[3]{a+b x^2} \left(a c^2+5 b c^2 x^2\right)}{8 c^3 (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*(a + b*x^2)^(1/3)*(a*c^2 + 5*b*c^2*x^2))/(8*c^3*(c*x)^(8/3)) - (Sqrt[3]*b^(4/3)*ArcTan[(Sqrt[3]*b^(1/3)*(c*x)^(2/3))/(b^(1/3)*(c*x)^(2/3) + 2*c^(2/3)*(a + b*x^2)^(1/3))])/(2*c^(11/3)) - (b^(4/3)*Log[b^(1/3)*(c*x)^(2/3) - c^(2/3)*(a + b*x^2)^(1/3)])/(2*c^(11/3)) + (b^(4/3)*Log[b^(2/3)*(c*x)^(4/3) + b^(1/3)*c^(2/3)*(c*x)^(2/3)*(a + b*x^2)^(1/3) + c^(4/3)*(a + b*x^2)^(2/3)])/(4*c^(11/3))","A",1
759,0,0,28,1.258308,"\int \frac{\left(a+b x^2\right)^{4/3}}{(c x)^{17/3}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(4/3)/(c*x)^(17/3),x]","\int \frac{\left(a+b x^2\right)^{4/3}}{(c x)^{17/3}} \, dx","-\frac{3 \left(a+b x^2\right)^{7/3}}{14 a c (c x)^{14/3}}",1,"Could not integrate","F",-1
760,0,0,57,1.4017256,"\int \frac{\left(a+b x^2\right)^{4/3}}{(c x)^{23/3}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(4/3)/(c*x)^(23/3),x]","\int \frac{\left(a+b x^2\right)^{4/3}}{(c x)^{23/3}} \, dx","\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,"Could not integrate","F",-1
761,0,0,85,1.4408922,"\int \frac{\left(a+b x^2\right)^{4/3}}{(c x)^{29/3}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(4/3)/(c*x)^(29/3),x]","\int \frac{\left(a+b x^2\right)^{4/3}}{(c x)^{29/3}} \, dx","-\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,"Could not integrate","F",-1
762,0,0,479,12.7037579,"\int (c x)^{10/3} \left(a+b x^2\right)^{4/3} \, dx","IntegrateAlgebraic[(c*x)^(10/3)*(a + b*x^2)^(4/3),x]","\int (c x)^{10/3} \left(a+b x^2\right)^{4/3} \, dx","-\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,"Could not integrate","F",-1
763,0,0,448,12.2768417,"\int (c x)^{4/3} \left(a+b x^2\right)^{4/3} \, dx","IntegrateAlgebraic[(c*x)^(4/3)*(a + b*x^2)^(4/3),x]","\int (c x)^{4/3} \left(a+b x^2\right)^{4/3} \, dx","-\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,"Could not integrate","F",-1
764,0,0,414,11.5797583,"\int \frac{\left(a+b x^2\right)^{4/3}}{(c x)^{2/3}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(4/3)/(c*x)^(2/3),x]","\int \frac{\left(a+b x^2\right)^{4/3}}{(c x)^{2/3}} \, dx","\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,"Could not integrate","F",-1
765,0,0,414,18.2764155,"\int \frac{\left(a+b x^2\right)^{4/3}}{(c x)^{8/3}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(4/3)/(c*x)^(8/3),x]","\int \frac{\left(a+b x^2\right)^{4/3}}{(c x)^{8/3}} \, dx","\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,"Could not integrate","F",-1
766,0,0,419,22.8009073,"\int \frac{\left(a+b x^2\right)^{4/3}}{(c x)^{14/3}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(4/3)/(c*x)^(14/3),x]","\int \frac{\left(a+b x^2\right)^{4/3}}{(c x)^{14/3}} \, dx","\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,"Could not integrate","F",-1
767,0,0,450,1.6312151,"\int \frac{\left(a+b x^2\right)^{4/3}}{(c x)^{20/3}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(4/3)/(c*x)^(20/3),x]","\int \frac{\left(a+b x^2\right)^{4/3}}{(c x)^{20/3}} \, dx","-\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,"Could not integrate","F",-1
768,0,0,59,6.9436464,"\int (c x)^{2/3} \left(a+b x^2\right)^{4/3} \, dx","IntegrateAlgebraic[(c*x)^(2/3)*(a + b*x^2)^(4/3),x]","\int (c x)^{2/3} \left(a+b x^2\right)^{4/3} \, dx","\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,"Could not integrate","F",-1
769,0,0,59,8.2816075,"\int \frac{\left(a+b x^2\right)^{4/3}}{\sqrt[3]{c x}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(4/3)/(c*x)^(1/3),x]","\int \frac{\left(a+b x^2\right)^{4/3}}{\sqrt[3]{c x}} \, dx","\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,"Could not integrate","F",-1
770,0,0,57,15.5521686,"\int \frac{\left(a+b x^2\right)^{4/3}}{(c x)^{4/3}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(4/3)/(c*x)^(4/3),x]","\int \frac{\left(a+b x^2\right)^{4/3}}{(c x)^{4/3}} \, dx","-\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,"Could not integrate","F",-1
771,0,0,198,1.3518524,"\int \frac{(c x)^{19/3}}{\left(a+b x^2\right)^{2/3}} \, dx","IntegrateAlgebraic[(c*x)^(19/3)/(a + b*x^2)^(2/3),x]","\int \frac{(c x)^{19/3}}{\left(a+b x^2\right)^{2/3}} \, dx","\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{10 a^2 c^5 (c x)^{4/3} \sqrt[3]{a+b x^2}}{27 b^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,"Could not integrate","F",-1
772,1,247,167,7.6526382,"\int \frac{(c x)^{13/3}}{\left(a+b x^2\right)^{2/3}} \, dx","IntegrateAlgebraic[(c*x)^(13/3)/(a + b*x^2)^(2/3),x]","-\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)}{18 b^{8/3}}+\frac{5 a^2 c^{13/3} \log \left(c^{4/3} \left(a+b x^2\right)^{2/3}+\sqrt[3]{b} c^{2/3} (c x)^{2/3} \sqrt[3]{a+b x^2}+b^{2/3} (c x)^{4/3}\right)}{36 b^{8/3}}-\frac{5 a^2 c^{13/3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{b} (c x)^{2/3}}{2 c^{2/3} \sqrt[3]{a+b x^2}+\sqrt[3]{b} (c x)^{2/3}}\right)}{6 \sqrt{3} b^{8/3}}+\frac{\sqrt[3]{a+b x^2} \left(3 b c (c x)^{10/3}-5 a c^3 (c x)^{4/3}\right)}{12 b^2}","-\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,"((a + b*x^2)^(1/3)*(-5*a*c^3*(c*x)^(4/3) + 3*b*c*(c*x)^(10/3)))/(12*b^2) - (5*a^2*c^(13/3)*ArcTan[(Sqrt[3]*b^(1/3)*(c*x)^(2/3))/(b^(1/3)*(c*x)^(2/3) + 2*c^(2/3)*(a + b*x^2)^(1/3))])/(6*Sqrt[3]*b^(8/3)) - (5*a^2*c^(13/3)*Log[b^(1/3)*(c*x)^(2/3) - c^(2/3)*(a + b*x^2)^(1/3)])/(18*b^(8/3)) + (5*a^2*c^(13/3)*Log[b^(2/3)*(c*x)^(4/3) + b^(1/3)*c^(2/3)*(c*x)^(2/3)*(a + b*x^2)^(1/3) + c^(4/3)*(a + b*x^2)^(2/3)])/(36*b^(8/3))","A",1
773,1,221,131,5.2123024,"\int \frac{(c x)^{7/3}}{\left(a+b x^2\right)^{2/3}} \, dx","IntegrateAlgebraic[(c*x)^(7/3)/(a + b*x^2)^(2/3),x]","\frac{a c^{7/3} \log \left(\sqrt[3]{b} (c x)^{2/3}-c^{2/3} \sqrt[3]{a+b x^2}\right)}{3 b^{5/3}}-\frac{a c^{7/3} \log \left(c^{4/3} \left(a+b x^2\right)^{2/3}+\sqrt[3]{b} c^{2/3} (c x)^{2/3} \sqrt[3]{a+b x^2}+b^{2/3} (c x)^{4/3}\right)}{6 b^{5/3}}+\frac{a c^{7/3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{b} (c x)^{2/3}}{2 c^{2/3} \sqrt[3]{a+b x^2}+\sqrt[3]{b} (c x)^{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[(Sqrt[3]*b^(1/3)*(c*x)^(2/3))/(b^(1/3)*(c*x)^(2/3) + 2*c^(2/3)*(a + b*x^2)^(1/3))])/(Sqrt[3]*b^(5/3)) + (a*c^(7/3)*Log[b^(1/3)*(c*x)^(2/3) - c^(2/3)*(a + b*x^2)^(1/3)])/(3*b^(5/3)) - (a*c^(7/3)*Log[b^(2/3)*(c*x)^(4/3) + b^(1/3)*c^(2/3)*(c*x)^(2/3)*(a + b*x^2)^(1/3) + c^(4/3)*(a + b*x^2)^(2/3)])/(6*b^(5/3))","A",1
774,1,195,106,1.7539989,"\int \frac{\sqrt[3]{c x}}{\left(a+b x^2\right)^{2/3}} \, dx","IntegrateAlgebraic[(c*x)^(1/3)/(a + b*x^2)^(2/3),x]","-\frac{\sqrt[3]{c} \log \left(\sqrt[3]{b} (c x)^{2/3}-c^{2/3} \sqrt[3]{a+b x^2}\right)}{2 b^{2/3}}+\frac{\sqrt[3]{c} \log \left(c^{4/3} \left(a+b x^2\right)^{2/3}+\sqrt[3]{b} c^{2/3} (c x)^{2/3} \sqrt[3]{a+b x^2}+b^{2/3} (c x)^{4/3}\right)}{4 b^{2/3}}-\frac{\sqrt{3} \sqrt[3]{c} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[3]{b} (c x)^{2/3}}{2 c^{2/3} \sqrt[3]{a+b x^2}+\sqrt[3]{b} (c x)^{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,"-1/2*(Sqrt[3]*c^(1/3)*ArcTan[(Sqrt[3]*b^(1/3)*(c*x)^(2/3))/(b^(1/3)*(c*x)^(2/3) + 2*c^(2/3)*(a + b*x^2)^(1/3))])/b^(2/3) - (c^(1/3)*Log[b^(1/3)*(c*x)^(2/3) - c^(2/3)*(a + b*x^2)^(1/3)])/(2*b^(2/3)) + (c^(1/3)*Log[b^(2/3)*(c*x)^(4/3) + b^(1/3)*c^(2/3)*(c*x)^(2/3)*(a + b*x^2)^(1/3) + c^(4/3)*(a + b*x^2)^(2/3)])/(4*b^(2/3))","A",1
775,1,28,28,2.0788627,"\int \frac{1}{(c x)^{5/3} \left(a+b x^2\right)^{2/3}} \, dx","IntegrateAlgebraic[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
776,1,44,57,7.2291089,"\int \frac{1}{(c x)^{11/3} \left(a+b x^2\right)^{2/3}} \, dx","IntegrateAlgebraic[1/((c*x)^(11/3)*(a + b*x^2)^(2/3)),x]","\frac{3 \sqrt[3]{a+b x^2} \left(3 b c^2 x^2-a c^2\right)}{8 a^2 c^3 (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)*(-(a*c^2) + 3*b*c^2*x^2))/(8*a^2*c^3*(c*x)^(8/3))","A",1
777,0,0,85,1.4473456,"\int \frac{1}{(c x)^{17/3} \left(a+b x^2\right)^{2/3}} \, dx","IntegrateAlgebraic[1/((c*x)^(17/3)*(a + b*x^2)^(2/3)),x]","\int \frac{1}{(c x)^{17/3} \left(a+b x^2\right)^{2/3}} \, dx","-\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,"Could not integrate","F",-1
778,0,0,113,1.639008,"\int \frac{1}{(c x)^{23/3} \left(a+b x^2\right)^{2/3}} \, dx","IntegrateAlgebraic[1/((c*x)^(23/3)*(a + b*x^2)^(2/3)),x]","\int \frac{1}{(c x)^{23/3} \left(a+b x^2\right)^{2/3}} \, dx","\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,"Could not integrate","F",-1
779,0,0,421,16.8548565,"\int \frac{(c x)^{10/3}}{\left(a+b x^2\right)^{2/3}} \, dx","IntegrateAlgebraic[(c*x)^(10/3)/(a + b*x^2)^(2/3),x]","\int \frac{(c x)^{10/3}}{\left(a+b x^2\right)^{2/3}} \, dx","-\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,"Could not integrate","F",-1
780,0,0,388,9.4799458,"\int \frac{(c x)^{4/3}}{\left(a+b x^2\right)^{2/3}} \, dx","IntegrateAlgebraic[(c*x)^(4/3)/(a + b*x^2)^(2/3),x]","\int \frac{(c x)^{4/3}}{\left(a+b x^2\right)^{2/3}} \, dx","\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,"Could not integrate","F",-1
781,0,0,364,11.4412115,"\int \frac{1}{(c x)^{2/3} \left(a+b x^2\right)^{2/3}} \, dx","IntegrateAlgebraic[1/((c*x)^(2/3)*(a + b*x^2)^(2/3)),x]","\int \frac{1}{(c x)^{2/3} \left(a+b x^2\right)^{2/3}} \, dx","\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,"Could not integrate","F",-1
782,0,0,394,22.7849595,"\int \frac{1}{(c x)^{8/3} \left(a+b x^2\right)^{2/3}} \, dx","IntegrateAlgebraic[1/((c*x)^(8/3)*(a + b*x^2)^(2/3)),x]","\int \frac{1}{(c x)^{8/3} \left(a+b x^2\right)^{2/3}} \, dx","-\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,"Could not integrate","F",-1
783,0,0,425,28.0462908,"\int \frac{1}{(c x)^{14/3} \left(a+b x^2\right)^{2/3}} \, dx","IntegrateAlgebraic[1/((c*x)^(14/3)*(a + b*x^2)^(2/3)),x]","\int \frac{1}{(c x)^{14/3} \left(a+b x^2\right)^{2/3}} \, dx","\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,"Could not integrate","F",-1
784,0,0,58,7.9521566,"\int \frac{(c x)^{2/3}}{\left(a+b x^2\right)^{2/3}} \, dx","IntegrateAlgebraic[(c*x)^(2/3)/(a + b*x^2)^(2/3),x]","\int \frac{(c x)^{2/3}}{\left(a+b x^2\right)^{2/3}} \, dx","\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,"Could not integrate","F",-1
785,0,0,58,8.4999966,"\int \frac{1}{\sqrt[3]{c x} \left(a+b x^2\right)^{2/3}} \, dx","IntegrateAlgebraic[1/((c*x)^(1/3)*(a + b*x^2)^(2/3)),x]","\int \frac{1}{\sqrt[3]{c x} \left(a+b x^2\right)^{2/3}} \, dx","\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,"Could not integrate","F",-1
786,0,0,56,17.676331,"\int \frac{1}{(c x)^{4/3} \left(a+b x^2\right)^{2/3}} \, dx","IntegrateAlgebraic[1/((c*x)^(4/3)*(a + b*x^2)^(2/3)),x]","\int \frac{1}{(c x)^{4/3} \left(a+b x^2\right)^{2/3}} \, dx","-\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,"Could not integrate","F",-1
787,0,0,121,4.7810997,"\int x^4 \sqrt[4]{a+b x^2} \, dx","IntegrateAlgebraic[x^4*(a + b*x^2)^(1/4),x]","\int x^4 \sqrt[4]{a+b x^2} \, dx","\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{4 a^2 x \sqrt[4]{a+b x^2}}{77 b^2}+\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,"Could not integrate","F",-1
788,0,0,97,4.5894332,"\int x^2 \sqrt[4]{a+b x^2} \, dx","IntegrateAlgebraic[x^2*(a + b*x^2)^(1/4),x]","\int x^2 \sqrt[4]{a+b x^2} \, dx","-\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 a x \sqrt[4]{a+b x^2}}{21 b}+\frac{2}{7} x^3 \sqrt[4]{a+b x^2}",1,"Could not integrate","F",-1
789,0,0,75,4.4986574,"\int \sqrt[4]{a+b x^2} \, dx","IntegrateAlgebraic[(a + b*x^2)^(1/4),x]","\int \sqrt[4]{a+b x^2} \, dx","\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,"Could not integrate","F",-1
790,0,0,72,4.6725462,"\int \frac{\sqrt[4]{a+b x^2}}{x^2} \, dx","IntegrateAlgebraic[(a + b*x^2)^(1/4)/x^2,x]","\int \frac{\sqrt[4]{a+b x^2}}{x^2} \, dx","\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,"Could not integrate","F",-1
791,0,0,99,9.3872103,"\int \frac{\sqrt[4]{a+b x^2}}{x^4} \, dx","IntegrateAlgebraic[(a + b*x^2)^(1/4)/x^4,x]","\int \frac{\sqrt[4]{a+b x^2}}{x^4} \, dx","-\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,"Could not integrate","F",-1
792,0,0,123,14.7532564,"\int \frac{\sqrt[4]{a+b x^2}}{x^6} \, dx","IntegrateAlgebraic[(a + b*x^2)^(1/4)/x^6,x]","\int \frac{\sqrt[4]{a+b x^2}}{x^6} \, dx","\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^2 \sqrt[4]{a+b x^2}}{12 a^2 x}-\frac{\sqrt[4]{a+b x^2}}{5 x^5}-\frac{b \sqrt[4]{a+b x^2}}{30 a x^3}",1,"Could not integrate","F",-1
793,0,0,126,4.8002124,"\int x^4 \sqrt[4]{a-b x^2} \, dx","IntegrateAlgebraic[x^4*(a - b*x^2)^(1/4),x]","\int x^4 \sqrt[4]{a-b x^2} \, dx","\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{4 a^2 x \sqrt[4]{a-b x^2}}{77 b^2}+\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,"Could not integrate","F",-1
794,0,0,101,4.5959213,"\int x^2 \sqrt[4]{a-b x^2} \, dx","IntegrateAlgebraic[x^2*(a - b*x^2)^(1/4),x]","\int x^2 \sqrt[4]{a-b x^2} \, dx","\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 a x \sqrt[4]{a-b x^2}}{21 b}+\frac{2}{7} x^3 \sqrt[4]{a-b x^2}",1,"Could not integrate","F",-1
795,0,0,78,4.5042759,"\int \sqrt[4]{a-b x^2} \, dx","IntegrateAlgebraic[(a - b*x^2)^(1/4),x]","\int \sqrt[4]{a-b x^2} \, dx","\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,"Could not integrate","F",-1
796,0,0,76,4.6610953,"\int \frac{\sqrt[4]{a-b x^2}}{x^2} \, dx","IntegrateAlgebraic[(a - b*x^2)^(1/4)/x^2,x]","\int \frac{\sqrt[4]{a-b x^2}}{x^2} \, dx","-\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,"Could not integrate","F",-1
797,0,0,103,9.4278633,"\int \frac{\sqrt[4]{a-b x^2}}{x^4} \, dx","IntegrateAlgebraic[(a - b*x^2)^(1/4)/x^4,x]","\int \frac{\sqrt[4]{a-b x^2}}{x^4} \, dx","-\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,"Could not integrate","F",-1
798,0,0,128,14.7171637,"\int \frac{\sqrt[4]{a-b x^2}}{x^6} \, dx","IntegrateAlgebraic[(a - b*x^2)^(1/4)/x^6,x]","\int \frac{\sqrt[4]{a-b x^2}}{x^6} \, dx","-\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^2 \sqrt[4]{a-b x^2}}{12 a^2 x}-\frac{\sqrt[4]{a-b x^2}}{5 x^5}+\frac{b \sqrt[4]{a-b x^2}}{30 a x^3}",1,"Could not integrate","F",-1
799,0,0,143,5.3799283,"\int x^4 \left(a+b x^2\right)^{3/4} \, dx","IntegrateAlgebraic[x^4*(a + b*x^2)^(3/4),x]","\int x^4 \left(a+b x^2\right)^{3/4} \, dx","-\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{8 a^3 x}{65 b^2 \sqrt[4]{a+b x^2}}-\frac{4 a^2 x \left(a+b x^2\right)^{3/4}}{65 b^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,"Could not integrate","F",-1
800,0,0,119,5.0997925,"\int x^2 \left(a+b x^2\right)^{3/4} \, dx","IntegrateAlgebraic[x^2*(a + b*x^2)^(3/4),x]","\int x^2 \left(a+b x^2\right)^{3/4} \, dx","\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 a x \left(a+b x^2\right)^{3/4}}{15 b}+\frac{2}{9} x^3 \left(a+b x^2\right)^{3/4}",1,"Could not integrate","F",-1
801,0,0,92,4.7461849,"\int \left(a+b x^2\right)^{3/4} \, dx","IntegrateAlgebraic[(a + b*x^2)^(3/4),x]","\int \left(a+b x^2\right)^{3/4} \, dx","-\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,"Could not integrate","F",-1
802,0,0,88,5.175519,"\int \frac{\left(a+b x^2\right)^{3/4}}{x^2} \, dx","IntegrateAlgebraic[(a + b*x^2)^(3/4)/x^2,x]","\int \frac{\left(a+b x^2\right)^{3/4}}{x^2} \, dx","\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,"Could not integrate","F",-1
803,0,0,121,9.9191548,"\int \frac{\left(a+b x^2\right)^{3/4}}{x^4} \, dx","IntegrateAlgebraic[(a + b*x^2)^(3/4)/x^4,x]","\int \frac{\left(a+b x^2\right)^{3/4}}{x^4} \, dx","-\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^2 x}{2 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,"Could not integrate","F",-1
804,0,0,145,15.2716896,"\int \frac{\left(a+b x^2\right)^{3/4}}{x^6} \, dx","IntegrateAlgebraic[(a + b*x^2)^(3/4)/x^6,x]","\int \frac{\left(a+b x^2\right)^{3/4}}{x^6} \, dx","\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{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{\left(a+b x^2\right)^{3/4}}{5 x^5}-\frac{b \left(a+b x^2\right)^{3/4}}{10 a x^3}",1,"Could not integrate","F",-1
805,0,0,126,5.4315586,"\int x^4 \left(a-b x^2\right)^{3/4} \, dx","IntegrateAlgebraic[x^4*(a - b*x^2)^(3/4),x]","\int x^4 \left(a-b x^2\right)^{3/4} \, dx","\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{4 a^2 x \left(a-b x^2\right)^{3/4}}{65 b^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,"Could not integrate","F",-1
806,0,0,101,5.1215471,"\int x^2 \left(a-b x^2\right)^{3/4} \, dx","IntegrateAlgebraic[x^2*(a - b*x^2)^(3/4),x]","\int x^2 \left(a-b x^2\right)^{3/4} \, dx","\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 a x \left(a-b x^2\right)^{3/4}}{15 b}+\frac{2}{9} x^3 \left(a-b x^2\right)^{3/4}",1,"Could not integrate","F",-1
807,0,0,78,4.7779824,"\int \left(a-b x^2\right)^{3/4} \, dx","IntegrateAlgebraic[(a - b*x^2)^(3/4),x]","\int \left(a-b x^2\right)^{3/4} \, dx","\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,"Could not integrate","F",-1
808,0,0,76,5.1837744,"\int \frac{\left(a-b x^2\right)^{3/4}}{x^2} \, dx","IntegrateAlgebraic[(a - b*x^2)^(3/4)/x^2,x]","\int \frac{\left(a-b x^2\right)^{3/4}}{x^2} \, dx","-\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,"Could not integrate","F",-1
809,0,0,103,9.9301882,"\int \frac{\left(a-b x^2\right)^{3/4}}{x^4} \, dx","IntegrateAlgebraic[(a - b*x^2)^(3/4)/x^4,x]","\int \frac{\left(a-b x^2\right)^{3/4}}{x^4} \, dx","\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,"Could not integrate","F",-1
810,0,0,128,15.2594457,"\int \frac{\left(a-b x^2\right)^{3/4}}{x^6} \, dx","IntegrateAlgebraic[(a - b*x^2)^(3/4)/x^6,x]","\int \frac{\left(a-b x^2\right)^{3/4}}{x^6} \, dx","\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{3 b^2 \left(a-b x^2\right)^{3/4}}{20 a^2 x}-\frac{\left(a-b x^2\right)^{3/4}}{5 x^5}+\frac{b \left(a-b x^2\right)^{3/4}}{10 a x^3}",1,"Could not integrate","F",-1
811,0,0,92,5.2096715,"\int \left(a+b x^2\right)^{5/4} \, dx","IntegrateAlgebraic[(a + b*x^2)^(5/4),x]","\int \left(a+b x^2\right)^{5/4} \, dx","\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,"Could not integrate","F",-1
812,0,0,96,5.2510126,"\int \left(a-b x^2\right)^{5/4} \, dx","IntegrateAlgebraic[(a - b*x^2)^(5/4),x]","\int \left(a-b x^2\right)^{5/4} \, dx","\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,"Could not integrate","F",-1
813,0,0,111,5.19074,"\int \left(a+b x^2\right)^{7/4} \, dx","IntegrateAlgebraic[(a + b*x^2)^(7/4),x]","\int \left(a+b x^2\right)^{7/4} \, dx","-\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 a^2 x}{15 \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,"Could not integrate","F",-1
814,0,0,96,5.185752,"\int \left(a-b x^2\right)^{7/4} \, dx","IntegrateAlgebraic[(a - b*x^2)^(7/4),x]","\int \left(a-b x^2\right)^{7/4} \, dx","\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,"Could not integrate","F",-1
815,0,0,146,4.6736931,"\int \frac{x^6}{\sqrt[4]{a+b x^2}} \, dx","IntegrateAlgebraic[x^6/(a + b*x^2)^(1/4),x]","\int \frac{x^6}{\sqrt[4]{a+b x^2}} \, dx","\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{16 a^3 x}{39 b^3 \sqrt[4]{a+b x^2}}+\frac{8 a^2 x \left(a+b x^2\right)^{3/4}}{39 b^3}-\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,"Could not integrate","F",-1
816,0,0,122,4.5890813,"\int \frac{x^4}{\sqrt[4]{a+b x^2}} \, dx","IntegrateAlgebraic[x^4/(a + b*x^2)^(1/4),x]","\int \frac{x^4}{\sqrt[4]{a+b x^2}} \, dx","-\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{8 a^2 x}{15 b^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,"Could not integrate","F",-1
817,0,0,98,4.3481934,"\int \frac{x^2}{\sqrt[4]{a+b x^2}} \, dx","IntegrateAlgebraic[x^2/(a + b*x^2)^(1/4),x]","\int \frac{x^2}{\sqrt[4]{a+b x^2}} \, dx","\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,"Could not integrate","F",-1
818,0,0,71,4.302671,"\int \frac{1}{\sqrt[4]{a+b x^2}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(-1/4),x]","\int \frac{1}{\sqrt[4]{a+b x^2}} \, dx","\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,"Could not integrate","F",-1
819,0,0,93,4.5171464,"\int \frac{1}{x^2 \sqrt[4]{a+b x^2}} \, dx","IntegrateAlgebraic[1/(x^2*(a + b*x^2)^(1/4)),x]","\int \frac{1}{x^2 \sqrt[4]{a+b x^2}} \, dx","\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,"Could not integrate","F",-1
820,0,0,124,9.4088077,"\int \frac{1}{x^4 \sqrt[4]{a+b x^2}} \, dx","IntegrateAlgebraic[1/(x^4*(a + b*x^2)^(1/4)),x]","\int \frac{1}{x^4 \sqrt[4]{a+b x^2}} \, dx","\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^2 x}{2 a^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,"Could not integrate","F",-1
821,0,0,148,14.6934136,"\int \frac{1}{x^6 \sqrt[4]{a+b x^2}} \, dx","IntegrateAlgebraic[1/(x^6*(a + b*x^2)^(1/4)),x]","\int \frac{1}{x^6 \sqrt[4]{a+b x^2}} \, dx","-\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^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 \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,"Could not integrate","F",-1
822,0,0,129,4.6927486,"\int \frac{x^6}{\sqrt[4]{a-b x^2}} \, dx","IntegrateAlgebraic[x^6/(a - b*x^2)^(1/4),x]","\int \frac{x^6}{\sqrt[4]{a-b x^2}} \, dx","\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{8 a^2 x \left(a-b x^2\right)^{3/4}}{39 b^3}-\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,"Could not integrate","F",-1
823,0,0,104,4.5315564,"\int \frac{x^4}{\sqrt[4]{a-b x^2}} \, dx","IntegrateAlgebraic[x^4/(a - b*x^2)^(1/4),x]","\int \frac{x^4}{\sqrt[4]{a-b x^2}} \, dx","\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,"Could not integrate","F",-1
824,0,0,81,4.3728801,"\int \frac{x^2}{\sqrt[4]{a-b x^2}} \, dx","IntegrateAlgebraic[x^2/(a - b*x^2)^(1/4),x]","\int \frac{x^2}{\sqrt[4]{a-b x^2}} \, dx","\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,"Could not integrate","F",-1
825,0,0,58,4.3296172,"\int \frac{1}{\sqrt[4]{a-b x^2}} \, dx","IntegrateAlgebraic[(a - b*x^2)^(-1/4),x]","\int \frac{1}{\sqrt[4]{a-b x^2}} \, dx","\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,"Could not integrate","F",-1
826,0,0,79,4.4839945,"\int \frac{1}{x^2 \sqrt[4]{a-b x^2}} \, dx","IntegrateAlgebraic[1/(x^2*(a - b*x^2)^(1/4)),x]","\int \frac{1}{x^2 \sqrt[4]{a-b x^2}} \, dx","-\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,"Could not integrate","F",-1
827,0,0,106,9.319399,"\int \frac{1}{x^4 \sqrt[4]{a-b x^2}} \, dx","IntegrateAlgebraic[1/(x^4*(a - b*x^2)^(1/4)),x]","\int \frac{1}{x^4 \sqrt[4]{a-b x^2}} \, dx","-\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,"Could not integrate","F",-1
828,0,0,131,14.7446678,"\int \frac{1}{x^6 \sqrt[4]{a-b x^2}} \, dx","IntegrateAlgebraic[1/(x^6*(a - b*x^2)^(1/4)),x]","\int \frac{1}{x^6 \sqrt[4]{a-b x^2}} \, dx","-\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^2 \left(a-b x^2\right)^{3/4}}{20 a^3 x}-\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,"Could not integrate","F",-1
829,0,0,124,4.9323426,"\int \frac{x^6}{\left(a+b x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[x^6/(a + b*x^2)^(3/4),x]","\int \frac{x^6}{\left(a+b x^2\right)^{3/4}} \, dx","-\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{40 a^2 x \sqrt[4]{a+b x^2}}{77 b^3}-\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,"Could not integrate","F",-1
830,0,0,100,4.8853254,"\int \frac{x^4}{\left(a+b x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[x^4/(a + b*x^2)^(3/4),x]","\int \frac{x^4}{\left(a+b x^2\right)^{3/4}} \, dx","\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,"Could not integrate","F",-1
831,0,0,78,4.5874285,"\int \frac{x^2}{\left(a+b x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[x^2/(a + b*x^2)^(3/4),x]","\int \frac{x^2}{\left(a+b x^2\right)^{3/4}} \, dx","\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,"Could not integrate","F",-1
832,0,0,56,4.348739,"\int \frac{1}{\left(a+b x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(-3/4),x]","\int \frac{1}{\left(a+b x^2\right)^{3/4}} \, dx","\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,"Could not integrate","F",-1
833,0,0,76,4.7745536,"\int \frac{1}{x^2 \left(a+b x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[1/(x^2*(a + b*x^2)^(3/4)),x]","\int \frac{1}{x^2 \left(a+b x^2\right)^{3/4}} \, dx","-\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,"Could not integrate","F",-1
834,0,0,102,9.6290429,"\int \frac{1}{x^4 \left(a+b x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[1/(x^4*(a + b*x^2)^(3/4)),x]","\int \frac{1}{x^4 \left(a+b x^2\right)^{3/4}} \, dx","\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,"Could not integrate","F",-1
835,0,0,126,14.8842529,"\int \frac{1}{x^6 \left(a+b x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[1/(x^6*(a + b*x^2)^(3/4)),x]","\int \frac{1}{x^6 \left(a+b x^2\right)^{3/4}} \, dx","-\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^2 \sqrt[4]{a+b x^2}}{4 a^3 x}+\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,"Could not integrate","F",-1
836,0,0,129,4.9094909,"\int \frac{x^6}{\left(a-b x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[x^6/(a - b*x^2)^(3/4),x]","\int \frac{x^6}{\left(a-b x^2\right)^{3/4}} \, dx","\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{40 a^2 x \sqrt[4]{a-b x^2}}{77 b^3}-\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,"Could not integrate","F",-1
837,0,0,104,4.897832,"\int \frac{x^4}{\left(a-b x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[x^4/(a - b*x^2)^(3/4),x]","\int \frac{x^4}{\left(a-b x^2\right)^{3/4}} \, dx","\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,"Could not integrate","F",-1
838,0,0,81,4.5513628,"\int \frac{x^2}{\left(a-b x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[x^2/(a - b*x^2)^(3/4),x]","\int \frac{x^2}{\left(a-b x^2\right)^{3/4}} \, dx","\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,"Could not integrate","F",-1
839,0,0,58,4.3202888,"\int \frac{1}{\left(a-b x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[(a - b*x^2)^(-3/4),x]","\int \frac{1}{\left(a-b x^2\right)^{3/4}} \, dx","\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,"Could not integrate","F",-1
840,0,0,78,4.7473571,"\int \frac{1}{x^2 \left(a-b x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[1/(x^2*(a - b*x^2)^(3/4)),x]","\int \frac{1}{x^2 \left(a-b x^2\right)^{3/4}} \, dx","\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,"Could not integrate","F",-1
841,0,0,106,9.5749721,"\int \frac{1}{x^4 \left(a-b x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[1/(x^4*(a - b*x^2)^(3/4)),x]","\int \frac{1}{x^4 \left(a-b x^2\right)^{3/4}} \, dx","\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,"Could not integrate","F",-1
842,0,0,131,14.9471178,"\int \frac{1}{x^6 \left(a-b x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[1/(x^6*(a - b*x^2)^(3/4)),x]","\int \frac{1}{x^6 \left(a-b x^2\right)^{3/4}} \, dx","\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^2 \sqrt[4]{a-b x^2}}{4 a^3 x}-\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,"Could not integrate","F",-1
843,0,0,124,5.2017577,"\int \frac{x^6}{\left(a+b x^2\right)^{5/4}} \, dx","IntegrateAlgebraic[x^6/(a + b*x^2)^(5/4),x]","\int \frac{x^6}{\left(a+b x^2\right)^{5/4}} \, dx","-\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{8 a^2 x}{3 b^3 \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,"Could not integrate","F",-1
844,0,0,100,5.0976013,"\int \frac{x^4}{\left(a+b x^2\right)^{5/4}} \, dx","IntegrateAlgebraic[x^4/(a + b*x^2)^(5/4),x]","\int \frac{x^4}{\left(a+b x^2\right)^{5/4}} \, dx","\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,"Could not integrate","F",-1
845,0,0,74,4.6738324,"\int \frac{x^2}{\left(a+b x^2\right)^{5/4}} \, dx","IntegrateAlgebraic[x^2/(a + b*x^2)^(5/4),x]","\int \frac{x^2}{\left(a+b x^2\right)^{5/4}} \, dx","\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,"Could not integrate","F",-1
846,0,0,56,4.616103,"\int \frac{1}{\left(a+b x^2\right)^{5/4}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(-5/4),x]","\int \frac{1}{\left(a+b x^2\right)^{5/4}} \, dx","\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,"Could not integrate","F",-1
847,0,0,76,5.0499807,"\int \frac{1}{x^2 \left(a+b x^2\right)^{5/4}} \, dx","IntegrateAlgebraic[1/(x^2*(a + b*x^2)^(5/4)),x]","\int \frac{1}{x^2 \left(a+b x^2\right)^{5/4}} \, dx","-\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,"Could not integrate","F",-1
848,0,0,102,9.9473776,"\int \frac{1}{x^4 \left(a+b x^2\right)^{5/4}} \, dx","IntegrateAlgebraic[1/(x^4*(a + b*x^2)^(5/4)),x]","\int \frac{1}{x^4 \left(a+b x^2\right)^{5/4}} \, dx","\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,"Could not integrate","F",-1
849,0,0,126,15.3398892,"\int \frac{1}{x^6 \left(a+b x^2\right)^{5/4}} \, dx","IntegrateAlgebraic[1/(x^6*(a + b*x^2)^(5/4)),x]","\int \frac{1}{x^6 \left(a+b x^2\right)^{5/4}} \, dx","-\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{77 b^2}{60 a^3 x \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,"Could not integrate","F",-1
850,0,0,124,5.184567,"\int \frac{x^6}{\left(a-b x^2\right)^{5/4}} \, dx","IntegrateAlgebraic[x^6/(a - b*x^2)^(5/4),x]","\int \frac{x^6}{\left(a-b x^2\right)^{5/4}} \, dx","-\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{8 a x \left(a-b x^2\right)^{3/4}}{3 b^3}+\frac{20 x^3 \left(a-b x^2\right)^{3/4}}{9 b^2}+\frac{2 x^5}{b \sqrt[4]{a-b x^2}}",1,"Could not integrate","F",-1
851,0,0,101,5.0780056,"\int \frac{x^4}{\left(a-b x^2\right)^{5/4}} \, dx","IntegrateAlgebraic[x^4/(a - b*x^2)^(5/4),x]","\int \frac{x^4}{\left(a-b x^2\right)^{5/4}} \, dx","-\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,"Could not integrate","F",-1
852,0,0,77,4.6368504,"\int \frac{x^2}{\left(a-b x^2\right)^{5/4}} \, dx","IntegrateAlgebraic[x^2/(a - b*x^2)^(5/4),x]","\int \frac{x^2}{\left(a-b x^2\right)^{5/4}} \, dx","\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,"Could not integrate","F",-1
853,0,0,77,4.5898818,"\int \frac{1}{\left(a-b x^2\right)^{5/4}} \, dx","IntegrateAlgebraic[(a - b*x^2)^(-5/4),x]","\int \frac{1}{\left(a-b x^2\right)^{5/4}} \, dx","\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,"Could not integrate","F",-1
854,0,0,99,4.9805176,"\int \frac{1}{x^2 \left(a-b x^2\right)^{5/4}} \, dx","IntegrateAlgebraic[1/(x^2*(a - b*x^2)^(5/4)),x]","\int \frac{1}{x^2 \left(a-b x^2\right)^{5/4}} \, dx","-\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{3 \left(a-b x^2\right)^{3/4}}{a^2 x}+\frac{2}{a x \sqrt[4]{a-b x^2}}",1,"Could not integrate","F",-1
855,0,0,126,10.0040497,"\int \frac{1}{x^4 \left(a-b x^2\right)^{5/4}} \, dx","IntegrateAlgebraic[1/(x^4*(a - b*x^2)^(5/4)),x]","\int \frac{1}{x^4 \left(a-b x^2\right)^{5/4}} \, dx","-\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,"Could not integrate","F",-1
856,0,0,151,15.3463511,"\int \frac{1}{x^6 \left(a-b x^2\right)^{5/4}} \, dx","IntegrateAlgebraic[1/(x^6*(a - b*x^2)^(5/4)),x]","\int \frac{1}{x^6 \left(a-b x^2\right)^{5/4}} \, dx","-\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^2 \left(a-b x^2\right)^{3/4}}{20 a^4 x}-\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,"Could not integrate","F",-1
857,0,0,78,4.8141981,"\int \frac{1}{\left(a+b x^2\right)^{7/4}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(-7/4),x]","\int \frac{1}{\left(a+b x^2\right)^{7/4}} \, dx","\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,"Could not integrate","F",-1
858,0,0,78,5.239008,"\int \frac{1}{\left(a+b x^2\right)^{9/4}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(-9/4),x]","\int \frac{1}{\left(a+b x^2\right)^{9/4}} \, dx","\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,"Could not integrate","F",-1
859,0,0,97,5.1729284,"\int \frac{1}{\left(a+b x^2\right)^{11/4}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(-11/4),x]","\int \frac{1}{\left(a+b x^2\right)^{11/4}} \, dx","\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{10 x}{21 a^2 \left(a+b x^2\right)^{3/4}}+\frac{2 x}{7 a \left(a+b x^2\right)^{7/4}}",1,"Could not integrate","F",-1
860,0,0,81,4.8158279,"\int \frac{1}{\left(a-b x^2\right)^{7/4}} \, dx","IntegrateAlgebraic[(a - b*x^2)^(-7/4),x]","\int \frac{1}{\left(a-b x^2\right)^{7/4}} \, dx","\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,"Could not integrate","F",-1
861,0,0,101,5.2338364,"\int \frac{1}{\left(a-b x^2\right)^{9/4}} \, dx","IntegrateAlgebraic[(a - b*x^2)^(-9/4),x]","\int \frac{1}{\left(a-b x^2\right)^{9/4}} \, dx","-\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{6 x}{5 a^2 \sqrt[4]{a-b x^2}}+\frac{2 x}{5 a \left(a-b x^2\right)^{5/4}}",1,"Could not integrate","F",-1
862,0,0,101,5.1924509,"\int \frac{1}{\left(a-b x^2\right)^{11/4}} \, dx","IntegrateAlgebraic[(a - b*x^2)^(-11/4),x]","\int \frac{1}{\left(a-b x^2\right)^{11/4}} \, dx","\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{10 x}{21 a^2 \left(a-b x^2\right)^{3/4}}+\frac{2 x}{7 a \left(a-b x^2\right)^{7/4}}",1,"Could not integrate","F",-1
863,0,0,99,4.2597759,"\int \frac{x^6}{\sqrt[4]{2+3 x^2}} \, dx","IntegrateAlgebraic[x^6/(2 + 3*x^2)^(1/4),x]","\int \frac{x^6}{\sqrt[4]{2+3 x^2}} \, dx","\frac{32 \left(3 x^2+2\right)^{3/4} x}{1053}-\frac{128 x}{1053 \sqrt[4]{3 x^2+2}}+\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{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,"Could not integrate","F",-1
864,0,0,81,4.103761,"\int \frac{x^4}{\sqrt[4]{2+3 x^2}} \, dx","IntegrateAlgebraic[x^4/(2 + 3*x^2)^(1/4),x]","\int \frac{x^4}{\sqrt[4]{2+3 x^2}} \, dx","-\frac{8}{135} \left(3 x^2+2\right)^{3/4} x+\frac{32 x}{135 \sqrt[4]{3 x^2+2}}+\frac{2}{27} \left(3 x^2+2\right)^{3/4} x^3-\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,"Could not integrate","F",-1
865,0,0,63,3.9785121,"\int \frac{x^2}{\sqrt[4]{2+3 x^2}} \, dx","IntegrateAlgebraic[x^2/(2 + 3*x^2)^(1/4),x]","\int \frac{x^2}{\sqrt[4]{2+3 x^2}} \, dx","\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,"Could not integrate","F",-1
866,0,0,43,3.9603789,"\int \frac{1}{\sqrt[4]{2+3 x^2}} \, dx","IntegrateAlgebraic[(2 + 3*x^2)^(-1/4),x]","\int \frac{1}{\sqrt[4]{2+3 x^2}} \, dx","\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,"Could not integrate","F",-1
867,0,0,63,4.050489,"\int \frac{1}{x^2 \sqrt[4]{2+3 x^2}} \, dx","IntegrateAlgebraic[1/(x^2*(2 + 3*x^2)^(1/4)),x]","\int \frac{1}{x^2 \sqrt[4]{2+3 x^2}} \, dx","\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,"Could not integrate","F",-1
868,0,0,83,8.8277812,"\int \frac{1}{x^4 \sqrt[4]{2+3 x^2}} \, dx","IntegrateAlgebraic[1/(x^4*(2 + 3*x^2)^(1/4)),x]","\int \frac{1}{x^4 \sqrt[4]{2+3 x^2}} \, dx","-\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,"Could not integrate","F",-1
869,0,0,101,13.9083144,"\int \frac{1}{x^6 \sqrt[4]{2+3 x^2}} \, dx","IntegrateAlgebraic[1/(x^6*(2 + 3*x^2)^(1/4)),x]","\int \frac{1}{x^6 \sqrt[4]{2+3 x^2}} \, dx","\frac{189 x}{160 \sqrt[4]{3 x^2+2}}-\frac{63 \left(3 x^2+2\right)^{3/4}}{160 x}-\frac{\left(3 x^2+2\right)^{3/4}}{10 x^5}+\frac{7 \left(3 x^2+2\right)^{3/4}}{40 x^3}-\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,"Could not integrate","F",-1
870,0,0,83,4.3304717,"\int \frac{x^6}{\sqrt[4]{2-3 x^2}} \, dx","IntegrateAlgebraic[x^6/(2 - 3*x^2)^(1/4),x]","\int \frac{x^6}{\sqrt[4]{2-3 x^2}} \, dx","-\frac{32 \left(2-3 x^2\right)^{3/4} x}{1053}-\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{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,"Could not integrate","F",-1
871,0,0,65,4.1658753,"\int \frac{x^4}{\sqrt[4]{2-3 x^2}} \, dx","IntegrateAlgebraic[x^4/(2 - 3*x^2)^(1/4),x]","\int \frac{x^4}{\sqrt[4]{2-3 x^2}} \, dx","-\frac{8}{135} \left(2-3 x^2\right)^{3/4} x-\frac{2}{27} \left(2-3 x^2\right)^{3/4} x^3+\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,"Could not integrate","F",-1
872,0,0,47,4.0766724,"\int \frac{x^2}{\sqrt[4]{2-3 x^2}} \, dx","IntegrateAlgebraic[x^2/(2 - 3*x^2)^(1/4),x]","\int \frac{x^2}{\sqrt[4]{2-3 x^2}} \, dx","\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,"Could not integrate","F",-1
873,0,0,28,4.020162,"\int \frac{1}{\sqrt[4]{2-3 x^2}} \, dx","IntegrateAlgebraic[(2 - 3*x^2)^(-1/4),x]","\int \frac{1}{\sqrt[4]{2-3 x^2}} \, dx","\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,"Could not integrate","F",-1
874,0,0,47,4.1722529,"\int \frac{1}{x^2 \sqrt[4]{2-3 x^2}} \, dx","IntegrateAlgebraic[1/(x^2*(2 - 3*x^2)^(1/4)),x]","\int \frac{1}{x^2 \sqrt[4]{2-3 x^2}} \, dx","-\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,"Could not integrate","F",-1
875,0,0,67,8.9370401,"\int \frac{1}{x^4 \sqrt[4]{2-3 x^2}} \, dx","IntegrateAlgebraic[1/(x^4*(2 - 3*x^2)^(1/4)),x]","\int \frac{1}{x^4 \sqrt[4]{2-3 x^2}} \, dx","-\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,"Could not integrate","F",-1
876,0,0,85,14.0369474,"\int \frac{1}{x^6 \sqrt[4]{2-3 x^2}} \, dx","IntegrateAlgebraic[1/(x^6*(2 - 3*x^2)^(1/4)),x]","\int \frac{1}{x^6 \sqrt[4]{2-3 x^2}} \, dx","-\frac{63 \left(2-3 x^2\right)^{3/4}}{160 x}-\frac{\left(2-3 x^2\right)^{3/4}}{10 x^5}-\frac{7 \left(2-3 x^2\right)^{3/4}}{40 x^3}-\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,"Could not integrate","F",-1
877,0,0,83,4.5030621,"\int \frac{x^6}{\left(2+3 x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[x^6/(2 + 3*x^2)^(3/4),x]","\int \frac{x^6}{\left(2+3 x^2\right)^{3/4}} \, dx","\frac{160 \sqrt[4]{3 x^2+2} x}{2079}+\frac{2}{33} \sqrt[4]{3 x^2+2} x^5-\frac{40}{693} \sqrt[4]{3 x^2+2} x^3-\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,"Could not integrate","F",-1
878,0,0,65,4.4894464,"\int \frac{x^4}{\left(2+3 x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[x^4/(2 + 3*x^2)^(3/4),x]","\int \frac{x^4}{\left(2+3 x^2\right)^{3/4}} \, dx","-\frac{8}{63} \sqrt[4]{3 x^2+2} x+\frac{2}{21} \sqrt[4]{3 x^2+2} x^3+\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,"Could not integrate","F",-1
879,0,0,47,4.1119335,"\int \frac{x^2}{\left(2+3 x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[x^2/(2 + 3*x^2)^(3/4),x]","\int \frac{x^2}{\left(2+3 x^2\right)^{3/4}} \, dx","\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,"Could not integrate","F",-1
880,0,0,27,3.9507292,"\int \frac{1}{\left(2+3 x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[(2 + 3*x^2)^(-3/4),x]","\int \frac{1}{\left(2+3 x^2\right)^{3/4}} \, dx","\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,"Could not integrate","F",-1
881,0,0,49,4.2938337,"\int \frac{1}{x^2 \left(2+3 x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[1/(x^2*(2 + 3*x^2)^(3/4)),x]","\int \frac{1}{x^2 \left(2+3 x^2\right)^{3/4}} \, dx","-\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,"Could not integrate","F",-1
882,0,0,67,9.0046453,"\int \frac{1}{x^4 \left(2+3 x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[1/(x^4*(2 + 3*x^2)^(3/4)),x]","\int \frac{1}{x^4 \left(2+3 x^2\right)^{3/4}} \, dx","\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,"Could not integrate","F",-1
883,0,0,85,14.3010289,"\int \frac{1}{x^6 \left(2+3 x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[1/(x^6*(2 + 3*x^2)^(3/4)),x]","\int \frac{1}{x^6 \left(2+3 x^2\right)^{3/4}} \, dx","-\frac{27 \sqrt[4]{3 x^2+2}}{32 x}-\frac{\sqrt[4]{3 x^2+2}}{10 x^5}+\frac{9 \sqrt[4]{3 x^2+2}}{40 x^3}-\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,"Could not integrate","F",-1
884,0,0,83,4.521598,"\int \frac{x^6}{\left(2-3 x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[x^6/(2 - 3*x^2)^(3/4),x]","\int \frac{x^6}{\left(2-3 x^2\right)^{3/4}} \, dx","-\frac{160 \sqrt[4]{2-3 x^2} x}{2079}-\frac{2}{33} \sqrt[4]{2-3 x^2} x^5-\frac{40}{693} \sqrt[4]{2-3 x^2} x^3+\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,"Could not integrate","F",-1
885,0,0,65,4.5271022,"\int \frac{x^4}{\left(2-3 x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[x^4/(2 - 3*x^2)^(3/4),x]","\int \frac{x^4}{\left(2-3 x^2\right)^{3/4}} \, dx","-\frac{8}{63} \sqrt[4]{2-3 x^2} x-\frac{2}{21} \sqrt[4]{2-3 x^2} x^3+\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,"Could not integrate","F",-1
886,0,0,47,4.1643815,"\int \frac{x^2}{\left(2-3 x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[x^2/(2 - 3*x^2)^(3/4),x]","\int \frac{x^2}{\left(2-3 x^2\right)^{3/4}} \, dx","\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,"Could not integrate","F",-1
887,0,0,27,4.0016288,"\int \frac{1}{\left(2-3 x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[(2 - 3*x^2)^(-3/4),x]","\int \frac{1}{\left(2-3 x^2\right)^{3/4}} \, dx","\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,"Could not integrate","F",-1
888,0,0,49,4.3622052,"\int \frac{1}{x^2 \left(2-3 x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[1/(x^2*(2 - 3*x^2)^(3/4)),x]","\int \frac{1}{x^2 \left(2-3 x^2\right)^{3/4}} \, dx","\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,"Could not integrate","F",-1
889,0,0,67,9.057014,"\int \frac{1}{x^4 \left(2-3 x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[1/(x^4*(2 - 3*x^2)^(3/4)),x]","\int \frac{1}{x^4 \left(2-3 x^2\right)^{3/4}} \, dx","-\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,"Could not integrate","F",-1
890,0,0,85,14.1151641,"\int \frac{1}{x^6 \left(2-3 x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[1/(x^6*(2 - 3*x^2)^(3/4)),x]","\int \frac{1}{x^6 \left(2-3 x^2\right)^{3/4}} \, dx","-\frac{27 \sqrt[4]{2-3 x^2}}{32 x}-\frac{\sqrt[4]{2-3 x^2}}{10 x^5}-\frac{9 \sqrt[4]{2-3 x^2}}{40 x^3}+\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,"Could not integrate","F",-1
891,0,0,258,4.2573256,"\int \frac{x^6}{\sqrt[4]{-2+3 x^2}} \, dx","IntegrateAlgebraic[x^6/(-2 + 3*x^2)^(1/4),x]","\int \frac{x^6}{\sqrt[4]{-2+3 x^2}} \, dx","\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}",1,"Could not integrate","F",-1
892,0,0,240,4.113842,"\int \frac{x^4}{\sqrt[4]{-2+3 x^2}} \, dx","IntegrateAlgebraic[x^4/(-2 + 3*x^2)^(1/4),x]","\int \frac{x^4}{\sqrt[4]{-2+3 x^2}} \, dx","\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",1,"Could not integrate","F",-1
893,0,0,222,4.0036442,"\int \frac{x^2}{\sqrt[4]{-2+3 x^2}} \, dx","IntegrateAlgebraic[x^2/(-2 + 3*x^2)^(1/4),x]","\int \frac{x^2}{\sqrt[4]{-2+3 x^2}} \, dx","\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,"Could not integrate","F",-1
894,0,0,199,3.9772374,"\int \frac{1}{\sqrt[4]{-2+3 x^2}} \, dx","IntegrateAlgebraic[(-2 + 3*x^2)^(-1/4),x]","\int \frac{1}{\sqrt[4]{-2+3 x^2}} \, dx","\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,"Could not integrate","F",-1
895,0,0,221,4.0679561,"\int \frac{1}{x^2 \sqrt[4]{-2+3 x^2}} \, dx","IntegrateAlgebraic[1/(x^2*(-2 + 3*x^2)^(1/4)),x]","\int \frac{1}{x^2 \sqrt[4]{-2+3 x^2}} \, dx","-\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,"Could not integrate","F",-1
896,0,0,242,8.8021739,"\int \frac{1}{x^4 \sqrt[4]{-2+3 x^2}} \, dx","IntegrateAlgebraic[1/(x^4*(-2 + 3*x^2)^(1/4)),x]","\int \frac{1}{x^4 \sqrt[4]{-2+3 x^2}} \, dx","-\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{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{\left(3 x^2-2\right)^{3/4}}{6 x^3}",1,"Could not integrate","F",-1
897,0,0,260,13.9189868,"\int \frac{1}{x^6 \sqrt[4]{-2+3 x^2}} \, dx","IntegrateAlgebraic[1/(x^6*(-2 + 3*x^2)^(1/4)),x]","\int \frac{1}{x^6 \sqrt[4]{-2+3 x^2}} \, dx","-\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{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{\left(3 x^2-2\right)^{3/4}}{10 x^5}+\frac{7 \left(3 x^2-2\right)^{3/4}}{40 x^3}",1,"Could not integrate","F",-1
898,0,0,260,4.2842126,"\int \frac{x^6}{\sqrt[4]{-2-3 x^2}} \, dx","IntegrateAlgebraic[x^6/(-2 - 3*x^2)^(1/4),x]","\int \frac{x^6}{\sqrt[4]{-2-3 x^2}} \, dx","-\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}",1,"Could not integrate","F",-1
899,0,0,242,4.1400946,"\int \frac{x^4}{\sqrt[4]{-2-3 x^2}} \, dx","IntegrateAlgebraic[x^4/(-2 - 3*x^2)^(1/4),x]","\int \frac{x^4}{\sqrt[4]{-2-3 x^2}} \, dx","\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",1,"Could not integrate","F",-1
900,0,0,224,4.0303831,"\int \frac{x^2}{\sqrt[4]{-2-3 x^2}} \, dx","IntegrateAlgebraic[x^2/(-2 - 3*x^2)^(1/4),x]","\int \frac{x^2}{\sqrt[4]{-2-3 x^2}} \, dx","-\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,"Could not integrate","F",-1
901,0,0,202,3.9810259,"\int \frac{1}{\sqrt[4]{-2-3 x^2}} \, dx","IntegrateAlgebraic[(-2 - 3*x^2)^(-1/4),x]","\int \frac{1}{\sqrt[4]{-2-3 x^2}} \, dx","\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,"Could not integrate","F",-1
902,0,0,223,4.1215097,"\int \frac{1}{x^2 \sqrt[4]{-2-3 x^2}} \, dx","IntegrateAlgebraic[1/(x^2*(-2 - 3*x^2)^(1/4)),x]","\int \frac{1}{x^2 \sqrt[4]{-2-3 x^2}} \, dx","\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,"Could not integrate","F",-1
903,0,0,244,8.9137704,"\int \frac{1}{x^4 \sqrt[4]{-2-3 x^2}} \, dx","IntegrateAlgebraic[1/(x^4*(-2 - 3*x^2)^(1/4)),x]","\int \frac{1}{x^4 \sqrt[4]{-2-3 x^2}} \, dx","-\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{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{\left(-3 x^2-2\right)^{3/4}}{6 x^3}",1,"Could not integrate","F",-1
904,0,0,262,13.9786984,"\int \frac{1}{x^6 \sqrt[4]{-2-3 x^2}} \, dx","IntegrateAlgebraic[1/(x^6*(-2 - 3*x^2)^(1/4)),x]","\int \frac{1}{x^6 \sqrt[4]{-2-3 x^2}} \, dx","\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{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{\left(-3 x^2-2\right)^{3/4}}{10 x^5}-\frac{7 \left(-3 x^2-2\right)^{3/4}}{40 x^3}",1,"Could not integrate","F",-1
905,0,0,138,4.5101187,"\int \frac{x^6}{\left(-2+3 x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[x^6/(-2 + 3*x^2)^(3/4),x]","\int \frac{x^6}{\left(-2+3 x^2\right)^{3/4}} \, dx","\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",1,"Could not integrate","F",-1
906,0,0,120,4.4765422,"\int \frac{x^4}{\left(-2+3 x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[x^4/(-2 + 3*x^2)^(3/4),x]","\int \frac{x^4}{\left(-2+3 x^2\right)^{3/4}} \, dx","\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",1,"Could not integrate","F",-1
907,0,0,102,4.0628321,"\int \frac{x^2}{\left(-2+3 x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[x^2/(-2 + 3*x^2)^(3/4),x]","\int \frac{x^2}{\left(-2+3 x^2\right)^{3/4}} \, dx","\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,"Could not integrate","F",-1
908,0,0,82,3.9238093,"\int \frac{1}{\left(-2+3 x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[(-2 + 3*x^2)^(-3/4),x]","\int \frac{1}{\left(-2+3 x^2\right)^{3/4}} \, dx","\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,"Could not integrate","F",-1
909,0,0,104,4.2921494,"\int \frac{1}{x^2 \left(-2+3 x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[1/(x^2*(-2 + 3*x^2)^(3/4)),x]","\int \frac{1}{x^2 \left(-2+3 x^2\right)^{3/4}} \, dx","\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,"Could not integrate","F",-1
910,0,0,122,9.0004993,"\int \frac{1}{x^4 \left(-2+3 x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[1/(x^4*(-2 + 3*x^2)^(3/4)),x]","\int \frac{1}{x^4 \left(-2+3 x^2\right)^{3/4}} \, dx","\frac{5 \sqrt[4]{3 x^2-2}}{8 x}+\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{\sqrt[4]{3 x^2-2}}{6 x^3}",1,"Could not integrate","F",-1
911,0,0,140,14.068375,"\int \frac{1}{x^6 \left(-2+3 x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[1/(x^6*(-2 + 3*x^2)^(3/4)),x]","\int \frac{1}{x^6 \left(-2+3 x^2\right)^{3/4}} \, dx","\frac{27 \sqrt[4]{3 x^2-2}}{32 x}+\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{\sqrt[4]{3 x^2-2}}{10 x^5}+\frac{9 \sqrt[4]{3 x^2-2}}{40 x^3}",1,"Could not integrate","F",-1
912,0,0,139,4.5097041,"\int \frac{x^6}{\left(-2-3 x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[x^6/(-2 - 3*x^2)^(3/4),x]","\int \frac{x^6}{\left(-2-3 x^2\right)^{3/4}} \, dx","-\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",1,"Could not integrate","F",-1
913,0,0,121,4.4975172,"\int \frac{x^4}{\left(-2-3 x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[x^4/(-2 - 3*x^2)^(3/4),x]","\int \frac{x^4}{\left(-2-3 x^2\right)^{3/4}} \, dx","\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",1,"Could not integrate","F",-1
914,0,0,103,4.1488261,"\int \frac{x^2}{\left(-2-3 x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[x^2/(-2 - 3*x^2)^(3/4),x]","\int \frac{x^2}{\left(-2-3 x^2\right)^{3/4}} \, dx","\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,"Could not integrate","F",-1
915,0,0,84,3.9910646,"\int \frac{1}{\left(-2-3 x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[(-2 - 3*x^2)^(-3/4),x]","\int \frac{1}{\left(-2-3 x^2\right)^{3/4}} \, dx","-\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,"Could not integrate","F",-1
916,0,0,105,4.3614081,"\int \frac{1}{x^2 \left(-2-3 x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[1/(x^2*(-2 - 3*x^2)^(3/4)),x]","\int \frac{1}{x^2 \left(-2-3 x^2\right)^{3/4}} \, dx","\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,"Could not integrate","F",-1
917,0,0,123,9.0557285,"\int \frac{1}{x^4 \left(-2-3 x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[1/(x^4*(-2 - 3*x^2)^(3/4)),x]","\int \frac{1}{x^4 \left(-2-3 x^2\right)^{3/4}} \, dx","-\frac{5 \sqrt[4]{-3 x^2-2}}{8 x}-\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{\sqrt[4]{-3 x^2-2}}{6 x^3}",1,"Could not integrate","F",-1
918,0,0,141,14.0936646,"\int \frac{1}{x^6 \left(-2-3 x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[1/(x^6*(-2 - 3*x^2)^(3/4)),x]","\int \frac{1}{x^6 \left(-2-3 x^2\right)^{3/4}} \, dx","\frac{27 \sqrt[4]{-3 x^2-2}}{32 x}+\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{\sqrt[4]{-3 x^2-2}}{10 x^5}-\frac{9 \sqrt[4]{-3 x^2-2}}{40 x^3}",1,"Could not integrate","F",-1
919,0,0,152,6.1248068,"\int (c x)^{7/2} \sqrt[4]{a+b x^2} \, dx","IntegrateAlgebraic[(c*x)^(7/2)*(a + b*x^2)^(1/4),x]","\int (c x)^{7/2} \sqrt[4]{a+b x^2} \, dx","-\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{a^2 c^3 \sqrt{c x} \sqrt[4]{a+b x^2}}{12 b^2}+\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,"Could not integrate","F",-1
920,0,0,118,5.7253282,"\int (c x)^{3/2} \sqrt[4]{a+b x^2} \, dx","IntegrateAlgebraic[(c*x)^(3/2)*(a + b*x^2)^(1/4),x]","\int (c x)^{3/2} \sqrt[4]{a+b x^2} \, dx","\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,"Could not integrate","F",-1
921,0,0,89,5.8313207,"\int \frac{\sqrt[4]{a+b x^2}}{\sqrt{c x}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(1/4)/Sqrt[c*x],x]","\int \frac{\sqrt[4]{a+b x^2}}{\sqrt{c x}} \, dx","\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,"Could not integrate","F",-1
922,0,0,94,15.7370131,"\int \frac{\sqrt[4]{a+b x^2}}{(c x)^{5/2}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(1/4)/(c*x)^(5/2),x]","\int \frac{\sqrt[4]{a+b x^2}}{(c x)^{5/2}} \, dx","-\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,"Could not integrate","F",-1
923,0,0,123,18.5060417,"\int \frac{\sqrt[4]{a+b x^2}}{(c x)^{9/2}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(1/4)/(c*x)^(9/2),x]","\int \frac{\sqrt[4]{a+b x^2}}{(c x)^{9/2}} \, dx","\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,"Could not integrate","F",-1
924,0,0,154,19.2765933,"\int \frac{\sqrt[4]{a+b x^2}}{(c x)^{13/2}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(1/4)/(c*x)^(13/2),x]","\int \frac{\sqrt[4]{a+b x^2}}{(c x)^{13/2}} \, dx","-\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{4 b^2 \sqrt[4]{a+b x^2}}{77 a^2 c^5 (c x)^{3/2}}-\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,"Could not integrate","F",-1
925,1,171,147,0.5324325,"\int (c x)^{5/2} \sqrt[4]{a+b x^2} \, dx","IntegrateAlgebraic[(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} c^{3/2} \sqrt{c x} \left(a+b x^2\right)^{3/4}}{a c^2+b c^2 x^2}\right)}{32 b^{7/4}}-\frac{3 a^2 c^{5/2} \tanh ^{-1}\left(\frac{\sqrt[4]{b} c^{3/2} \sqrt{c x} \left(a+b x^2\right)^{3/4}}{a c^2+b c^2 x^2}\right)}{32 b^{7/4}}+\frac{\sqrt[4]{a+b x^2} \left(a c^2 (c x)^{3/2}+4 b (c x)^{7/2}\right)}{16 b c}","\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 + b*x^2)^(1/4)*(a*c^2*(c*x)^(3/2) + 4*b*(c*x)^(7/2)))/(16*b*c) + (3*a^2*c^(5/2)*ArcTan[(b^(1/4)*c^(3/2)*Sqrt[c*x]*(a + b*x^2)^(3/4))/(a*c^2 + b*c^2*x^2)])/(32*b^(7/4)) - (3*a^2*c^(5/2)*ArcTanh[(b^(1/4)*c^(3/2)*Sqrt[c*x]*(a + b*x^2)^(3/4))/(a*c^2 + b*c^2*x^2)])/(32*b^(7/4))","A",1
926,1,148,116,0.4739936,"\int \sqrt{c x} \sqrt[4]{a+b x^2} \, dx","IntegrateAlgebraic[Sqrt[c*x]*(a + b*x^2)^(1/4),x]","-\frac{a \sqrt{c} \tan ^{-1}\left(\frac{\sqrt[4]{b} c^{3/2} \sqrt{c x} \left(a+b x^2\right)^{3/4}}{a c^2+b c^2 x^2}\right)}{4 b^{3/4}}+\frac{a \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt[4]{b} c^{3/2} \sqrt{c x} \left(a+b x^2\right)^{3/4}}{a c^2+b c^2 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)*c^(3/2)*Sqrt[c*x]*(a + b*x^2)^(3/4))/(a*c^2 + b*c^2*x^2)])/(4*b^(3/4)) + (a*Sqrt[c]*ArcTanh[(b^(1/4)*c^(3/2)*Sqrt[c*x]*(a + b*x^2)^(3/4))/(a*c^2 + b*c^2*x^2)])/(4*b^(3/4))","A",1
927,1,139,107,0.3980023,"\int \frac{\sqrt[4]{a+b x^2}}{(c x)^{3/2}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(1/4)/(c*x)^(3/2),x]","-\frac{\sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt[4]{b} c^{3/2} \sqrt{c x} \left(a+b x^2\right)^{3/4}}{a c^2+b c^2 x^2}\right)}{c^{3/2}}+\frac{\sqrt[4]{b} \tanh ^{-1}\left(\frac{\sqrt[4]{b} c^{3/2} \sqrt{c x} \left(a+b x^2\right)^{3/4}}{a c^2+b c^2 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)*c^(3/2)*Sqrt[c*x]*(a + b*x^2)^(3/4))/(a*c^2 + b*c^2*x^2)])/c^(3/2) + (b^(1/4)*ArcTanh[(b^(1/4)*c^(3/2)*Sqrt[c*x]*(a + b*x^2)^(3/4))/(a*c^2 + b*c^2*x^2)])/c^(3/2)","A",1
928,1,28,28,0.234476,"\int \frac{\sqrt[4]{a+b x^2}}{(c x)^{7/2}} \, dx","IntegrateAlgebraic[(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
929,1,58,57,0.2902858,"\int \frac{\sqrt[4]{a+b x^2}}{(c x)^{11/2}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(1/4)/(c*x)^(11/2),x]","\frac{2 \sqrt[4]{a+b x^2} \left(-5 a^2 c^4-a b c^4 x^2+4 b^2 c^4 x^4\right)}{45 a^2 c^5 (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)^(1/4)*(-5*a^2*c^4 - a*b*c^4*x^2 + 4*b^2*c^4*x^4))/(45*a^2*c^5*(c*x)^(9/2))","A",1
930,1,72,85,0.3500239,"\int \frac{\sqrt[4]{a+b x^2}}{(c x)^{15/2}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(1/4)/(c*x)^(15/2),x]","-\frac{2 \sqrt[4]{a+b x^2} \left(45 a^3 c^6+5 a^2 b c^6 x^2-8 a b^2 c^6 x^4+32 b^3 c^6 x^6\right)}{585 a^3 c^7 (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)^(1/4)*(45*a^3*c^6 + 5*a^2*b*c^6*x^2 - 8*a*b^2*c^6*x^4 + 32*b^3*c^6*x^6))/(585*a^3*c^7*(c*x)^(13/2))","A",1
931,0,0,113,1.2796191,"\int \frac{\sqrt[4]{a+b x^2}}{(c x)^{19/2}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(1/4)/(c*x)^(19/2),x]","\int \frac{\sqrt[4]{a+b x^2}}{(c x)^{19/2}} \, dx","\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,"Could not integrate","F",-1
932,0,0,122,5.6006755,"\int (c x)^{3/2} \sqrt[4]{a-b x^2} \, dx","IntegrateAlgebraic[(c*x)^(3/2)*(a - b*x^2)^(1/4),x]","\int (c x)^{3/2} \sqrt[4]{a-b x^2} \, dx","-\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,"Could not integrate","F",-1
933,0,0,92,5.7693134,"\int \frac{\sqrt[4]{a-b x^2}}{\sqrt{c x}} \, dx","IntegrateAlgebraic[(a - b*x^2)^(1/4)/Sqrt[c*x],x]","\int \frac{\sqrt[4]{a-b x^2}}{\sqrt{c x}} \, dx","\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,"Could not integrate","F",-1
934,0,0,97,15.5522762,"\int \frac{\sqrt[4]{a-b x^2}}{(c x)^{5/2}} \, dx","IntegrateAlgebraic[(a - b*x^2)^(1/4)/(c*x)^(5/2),x]","\int \frac{\sqrt[4]{a-b x^2}}{(c x)^{5/2}} \, dx","\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,"Could not integrate","F",-1
935,0,0,127,18.5783421,"\int \frac{\sqrt[4]{a-b x^2}}{(c x)^{9/2}} \, dx","IntegrateAlgebraic[(a - b*x^2)^(1/4)/(c*x)^(9/2),x]","\int \frac{\sqrt[4]{a-b x^2}}{(c x)^{9/2}} \, dx","\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,"Could not integrate","F",-1
936,0,0,159,19.3386008,"\int \frac{\sqrt[4]{a-b x^2}}{(c x)^{13/2}} \, dx","IntegrateAlgebraic[(a - b*x^2)^(1/4)/(c*x)^(13/2),x]","\int \frac{\sqrt[4]{a-b x^2}}{(c x)^{13/2}} \, dx","\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{4 b^2 \sqrt[4]{a-b x^2}}{77 a^2 c^5 (c x)^{3/2}}+\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,"Could not integrate","F",-1
937,0,0,343,8.5513937,"\int (c x)^{5/2} \sqrt[4]{a-b x^2} \, dx","IntegrateAlgebraic[(c*x)^(5/2)*(a - b*x^2)^(1/4),x]","\int (c x)^{5/2} \sqrt[4]{a-b x^2} \, dx","\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,"Could not integrate","F",-1
938,0,0,307,8.2737502,"\int \sqrt{c x} \sqrt[4]{a-b x^2} \, dx","IntegrateAlgebraic[Sqrt[c*x]*(a - b*x^2)^(1/4),x]","\int \sqrt{c x} \sqrt[4]{a-b x^2} \, dx","\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,"Could not integrate","F",-1
939,0,0,296,12.843276,"\int \frac{\sqrt[4]{a-b x^2}}{(c x)^{3/2}} \, dx","IntegrateAlgebraic[(a - b*x^2)^(1/4)/(c*x)^(3/2),x]","\int \frac{\sqrt[4]{a-b x^2}}{(c x)^{3/2}} \, dx","-\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,"Could not integrate","F",-1
940,1,29,29,0.2442322,"\int \frac{\sqrt[4]{a-b x^2}}{(c x)^{7/2}} \, dx","IntegrateAlgebraic[(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
941,1,58,59,0.2998781,"\int \frac{\sqrt[4]{a-b x^2}}{(c x)^{11/2}} \, dx","IntegrateAlgebraic[(a - b*x^2)^(1/4)/(c*x)^(11/2),x]","\frac{2 \sqrt[4]{a-b x^2} \left(-5 a^2 c^4+a b c^4 x^2+4 b^2 c^4 x^4\right)}{45 a^2 c^5 (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)^(1/4)*(-5*a^2*c^4 + a*b*c^4*x^2 + 4*b^2*c^4*x^4))/(45*a^2*c^5*(c*x)^(9/2))","A",1
942,1,73,88,0.3580767,"\int \frac{\sqrt[4]{a-b x^2}}{(c x)^{15/2}} \, dx","IntegrateAlgebraic[(a - b*x^2)^(1/4)/(c*x)^(15/2),x]","\frac{2 \sqrt[4]{a-b x^2} \left(-45 a^3 c^6+5 a^2 b c^6 x^2+8 a b^2 c^6 x^4+32 b^3 c^6 x^6\right)}{585 a^3 c^7 (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)^(1/4)*(-45*a^3*c^6 + 5*a^2*b*c^6*x^2 + 8*a*b^2*c^6*x^4 + 32*b^3*c^6*x^6))/(585*a^3*c^7*(c*x)^(13/2))","A",1
943,0,0,117,1.3376888,"\int \frac{\sqrt[4]{a-b x^2}}{(c x)^{19/2}} \, dx","IntegrateAlgebraic[(a - b*x^2)^(1/4)/(c*x)^(19/2),x]","\int \frac{\sqrt[4]{a-b x^2}}{(c x)^{19/2}} \, dx","\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,"Could not integrate","F",-1
944,1,149,117,0.5590219,"\int \frac{(c x)^{3/2}}{\sqrt[4]{a+b x^2}} \, dx","IntegrateAlgebraic[(c*x)^(3/2)/(a + b*x^2)^(1/4),x]","-\frac{a c^{3/2} \tan ^{-1}\left(\frac{\sqrt[4]{b} c^{3/2} \sqrt{c x} \left(a+b x^2\right)^{3/4}}{a c^2+b c^2 x^2}\right)}{4 b^{5/4}}-\frac{a c^{3/2} \tanh ^{-1}\left(\frac{\sqrt[4]{b} c^{3/2} \sqrt{c x} \left(a+b x^2\right)^{3/4}}{a c^2+b c^2 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)*c^(3/2)*Sqrt[c*x]*(a + b*x^2)^(3/4))/(a*c^2 + b*c^2*x^2)])/(4*b^(5/4)) - (a*c^(3/2)*ArcTanh[(b^(1/4)*c^(3/2)*Sqrt[c*x]*(a + b*x^2)^(3/4))/(a*c^2 + b*c^2*x^2)])/(4*b^(5/4))","A",1
945,1,115,83,0.4351817,"\int \frac{1}{\sqrt{c x} \sqrt[4]{a+b x^2}} \, dx","IntegrateAlgebraic[1/(Sqrt[c*x]*(a + b*x^2)^(1/4)),x]","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{b} c^{3/2} \sqrt{c x} \left(a+b x^2\right)^{3/4}}{a c^2+b c^2 x^2}\right)}{\sqrt[4]{b} \sqrt{c}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{b} c^{3/2} \sqrt{c x} \left(a+b x^2\right)^{3/4}}{a c^2+b c^2 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)*c^(3/2)*Sqrt[c*x]*(a + b*x^2)^(3/4))/(a*c^2 + b*c^2*x^2)]/(b^(1/4)*Sqrt[c]) + ArcTanh[(b^(1/4)*c^(3/2)*Sqrt[c*x]*(a + b*x^2)^(3/4))/(a*c^2 + b*c^2*x^2)]/(b^(1/4)*Sqrt[c])","A",1
946,1,28,28,0.3179596,"\int \frac{1}{(c x)^{5/2} \sqrt[4]{a+b x^2}} \, dx","IntegrateAlgebraic[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
947,1,44,57,0.3935391,"\int \frac{1}{(c x)^{9/2} \sqrt[4]{a+b x^2}} \, dx","IntegrateAlgebraic[1/((c*x)^(9/2)*(a + b*x^2)^(1/4)),x]","\frac{2 \left(a+b x^2\right)^{3/4} \left(4 b c^2 x^2-3 a c^2\right)}{21 a^2 c^3 (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^2 + 4*b*c^2*x^2))/(21*a^2*c^3*(c*x)^(7/2))","A",1
948,1,58,85,0.6491237,"\int \frac{1}{(c x)^{13/2} \sqrt[4]{a+b x^2}} \, dx","IntegrateAlgebraic[1/((c*x)^(13/2)*(a + b*x^2)^(1/4)),x]","-\frac{2 \left(a+b x^2\right)^{3/4} \left(21 a^2 c^4-24 a b c^4 x^2+32 b^2 c^4 x^4\right)}{231 a^3 c^5 (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)*(21*a^2*c^4 - 24*a*b*c^4*x^2 + 32*b^2*c^4*x^4))/(231*a^3*c^5*(c*x)^(11/2))","A",1
949,0,0,156,6.6685957,"\int \frac{(c x)^{9/2}}{\sqrt[4]{a+b x^2}} \, dx","IntegrateAlgebraic[(c*x)^(9/2)/(a + b*x^2)^(1/4),x]","\int \frac{(c x)^{9/2}}{\sqrt[4]{a+b x^2}} \, dx","\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^2 c^4 x \sqrt{c x}}{20 b^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,"Could not integrate","F",-1
950,0,0,125,6.1309152,"\int \frac{(c x)^{5/2}}{\sqrt[4]{a+b x^2}} \, dx","IntegrateAlgebraic[(c*x)^(5/2)/(a + b*x^2)^(1/4),x]","\int \frac{(c x)^{5/2}}{\sqrt[4]{a+b x^2}} \, dx","-\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,"Could not integrate","F",-1
951,0,0,83,5.9611618,"\int \frac{\sqrt{c x}}{\sqrt[4]{a+b x^2}} \, dx","IntegrateAlgebraic[Sqrt[c*x]/(a + b*x^2)^(1/4),x]","\int \frac{\sqrt{c x}}{\sqrt[4]{a+b x^2}} \, dx","\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,"Could not integrate","F",-1
952,0,0,90,10.6935206,"\int \frac{1}{(c x)^{3/2} \sqrt[4]{a+b x^2}} \, dx","IntegrateAlgebraic[1/((c*x)^(3/2)*(a + b*x^2)^(1/4)),x]","\int \frac{1}{(c x)^{3/2} \sqrt[4]{a+b x^2}} \, dx","\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,"Could not integrate","F",-1
953,0,0,126,18.4703379,"\int \frac{1}{(c x)^{7/2} \sqrt[4]{a+b x^2}} \, dx","IntegrateAlgebraic[1/((c*x)^(7/2)*(a + b*x^2)^(1/4)),x]","\int \frac{1}{(c x)^{7/2} \sqrt[4]{a+b x^2}} \, dx","-\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,"Could not integrate","F",-1
954,0,0,157,19.4136979,"\int \frac{1}{(c x)^{11/2} \sqrt[4]{a+b x^2}} \, dx","IntegrateAlgebraic[1/((c*x)^(11/2)*(a + b*x^2)^(1/4)),x]","\int \frac{1}{(c x)^{11/2} \sqrt[4]{a+b x^2}} \, dx","\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{8 b^2}{15 a^2 c^5 \sqrt{c x} \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,"Could not integrate","F",-1
955,0,0,308,8.0388503,"\int \frac{(c x)^{3/2}}{\sqrt[4]{a-b x^2}} \, dx","IntegrateAlgebraic[(c*x)^(3/2)/(a - b*x^2)^(1/4),x]","\int \frac{(c x)^{3/2}}{\sqrt[4]{a-b x^2}} \, dx","-\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,"Could not integrate","F",-1
956,1,163,272,3.0282781,"\int \frac{1}{\sqrt{c x} \sqrt[4]{a-b x^2}} \, dx","IntegrateAlgebraic[1/(Sqrt[c*x]*(a - b*x^2)^(1/4)),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c} \sqrt{c x} \sqrt[4]{a-b x^2}}{c \sqrt{a-b x^2}+\sqrt{b} c x}\right)}{\sqrt{2} \sqrt[4]{b} \sqrt{c}}-\frac{\tan ^{-1}\left(\frac{\frac{\sqrt{c} \sqrt{a-b x^2}}{\sqrt{2} \sqrt[4]{b}}-\frac{\sqrt[4]{b} \sqrt{c} x}{\sqrt{2}}}{\sqrt{c x} \sqrt[4]{a-b x^2}}\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[(-((b^(1/4)*Sqrt[c]*x)/Sqrt[2]) + (Sqrt[c]*Sqrt[a - b*x^2])/(Sqrt[2]*b^(1/4)))/(Sqrt[c*x]*(a - b*x^2)^(1/4))]/(Sqrt[2]*b^(1/4)*Sqrt[c])) + ArcTanh[(Sqrt[2]*b^(1/4)*Sqrt[c]*Sqrt[c*x]*(a - b*x^2)^(1/4))/(Sqrt[b]*c*x + c*Sqrt[a - b*x^2])]/(Sqrt[2]*b^(1/4)*Sqrt[c])","A",1
957,1,29,29,0.3098409,"\int \frac{1}{(c x)^{5/2} \sqrt[4]{a-b x^2}} \, dx","IntegrateAlgebraic[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
958,1,45,59,0.3926729,"\int \frac{1}{(c x)^{9/2} \sqrt[4]{a-b x^2}} \, dx","IntegrateAlgebraic[1/((c*x)^(9/2)*(a - b*x^2)^(1/4)),x]","-\frac{2 \left(a-b x^2\right)^{3/4} \left(3 a c^2+4 b c^2 x^2\right)}{21 a^2 c^3 (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^2 + 4*b*c^2*x^2))/(21*a^2*c^3*(c*x)^(7/2))","A",1
959,1,59,88,0.654491,"\int \frac{1}{(c x)^{13/2} \sqrt[4]{a-b x^2}} \, dx","IntegrateAlgebraic[1/((c*x)^(13/2)*(a - b*x^2)^(1/4)),x]","-\frac{2 \left(a-b x^2\right)^{3/4} \left(21 a^2 c^4+24 a b c^4 x^2+32 b^2 c^4 x^4\right)}{231 a^3 c^5 (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)*(21*a^2*c^4 + 24*a*b*c^4*x^2 + 32*b^2*c^4*x^4))/(231*a^3*c^5*(c*x)^(11/2))","A",1
960,0,0,128,6.0347853,"\int \frac{(c x)^{5/2}}{\sqrt[4]{a-b x^2}} \, dx","IntegrateAlgebraic[(c*x)^(5/2)/(a - b*x^2)^(1/4),x]","\int \frac{(c x)^{5/2}}{\sqrt[4]{a-b x^2}} \, dx","\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,"Could not integrate","F",-1
961,0,0,90,5.91065,"\int \frac{\sqrt{c x}}{\sqrt[4]{a-b x^2}} \, dx","IntegrateAlgebraic[Sqrt[c*x]/(a - b*x^2)^(1/4),x]","\int \frac{\sqrt{c x}}{\sqrt[4]{a-b x^2}} \, dx","\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,"Could not integrate","F",-1
962,0,0,68,10.6348475,"\int \frac{1}{(c x)^{3/2} \sqrt[4]{a-b x^2}} \, dx","IntegrateAlgebraic[1/((c*x)^(3/2)*(a - b*x^2)^(1/4)),x]","\int \frac{1}{(c x)^{3/2} \sqrt[4]{a-b x^2}} \, dx","-\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,"Could not integrate","F",-1
963,0,0,100,18.4656745,"\int \frac{1}{(c x)^{7/2} \sqrt[4]{a-b x^2}} \, dx","IntegrateAlgebraic[1/((c*x)^(7/2)*(a - b*x^2)^(1/4)),x]","\int \frac{1}{(c x)^{7/2} \sqrt[4]{a-b x^2}} \, dx","-\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,"Could not integrate","F",-1
964,0,0,130,19.3963256,"\int \frac{1}{(c x)^{11/2} \sqrt[4]{a-b x^2}} \, dx","IntegrateAlgebraic[1/((c*x)^(11/2)*(a - b*x^2)^(1/4)),x]","\int \frac{1}{(c x)^{11/2} \sqrt[4]{a-b x^2}} \, dx","-\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,"Could not integrate","F",-1
965,0,0,86,7.4357695,"\int \frac{(c x)^{3/2}}{\left(a+b x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[(c*x)^(3/2)/(a + b*x^2)^(3/4),x]","\int \frac{(c x)^{3/2}}{\left(a+b x^2\right)^{3/4}} \, dx","\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,"Could not integrate","F",-1
966,0,0,66,6.6592884,"\int \frac{1}{\sqrt{c x} \left(a+b x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[1/(Sqrt[c*x]*(a + b*x^2)^(3/4)),x]","\int \frac{1}{\sqrt{c x} \left(a+b x^2\right)^{3/4}} \, dx","-\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,"Could not integrate","F",-1
967,0,0,97,16.5929986,"\int \frac{1}{(c x)^{5/2} \left(a+b x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[1/((c*x)^(5/2)*(a + b*x^2)^(3/4)),x]","\int \frac{1}{(c x)^{5/2} \left(a+b x^2\right)^{3/4}} \, dx","\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,"Could not integrate","F",-1
968,0,0,126,19.8746853,"\int \frac{1}{(c x)^{9/2} \left(a+b x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[1/((c*x)^(9/2)*(a + b*x^2)^(3/4)),x]","\int \frac{1}{(c x)^{9/2} \left(a+b x^2\right)^{3/4}} \, dx","-\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,"Could not integrate","F",-1
969,0,0,157,21.3885375,"\int \frac{1}{(c x)^{13/2} \left(a+b x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[1/((c*x)^(13/2)*(a + b*x^2)^(3/4)),x]","\int \frac{1}{(c x)^{13/2} \left(a+b x^2\right)^{3/4}} \, dx","\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{40 b^2 \sqrt[4]{a+b x^2}}{77 a^3 c^5 (c x)^{3/2}}+\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,"Could not integrate","F",-1
970,1,149,117,0.8818323,"\int \frac{(c x)^{5/2}}{\left(a+b x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[(c*x)^(5/2)/(a + b*x^2)^(3/4),x]","\frac{3 a c^{5/2} \tan ^{-1}\left(\frac{\sqrt[4]{b} c^{3/2} \sqrt{c x} \left(a+b x^2\right)^{3/4}}{a c^2+b c^2 x^2}\right)}{4 b^{7/4}}-\frac{3 a c^{5/2} \tanh ^{-1}\left(\frac{\sqrt[4]{b} c^{3/2} \sqrt{c x} \left(a+b x^2\right)^{3/4}}{a c^2+b c^2 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)*c^(3/2)*Sqrt[c*x]*(a + b*x^2)^(3/4))/(a*c^2 + b*c^2*x^2)])/(4*b^(7/4)) - (3*a*c^(5/2)*ArcTanh[(b^(1/4)*c^(3/2)*Sqrt[c*x]*(a + b*x^2)^(3/4))/(a*c^2 + b*c^2*x^2)])/(4*b^(7/4))","A",1
971,1,116,84,0.564896,"\int \frac{\sqrt{c x}}{\left(a+b x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[Sqrt[c*x]/(a + b*x^2)^(3/4),x]","\frac{\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt[4]{b} c^{3/2} \sqrt{c x} \left(a+b x^2\right)^{3/4}}{a c^2+b c^2 x^2}\right)}{b^{3/4}}-\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt[4]{b} c^{3/2} \sqrt{c x} \left(a+b x^2\right)^{3/4}}{a c^2+b c^2 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)*c^(3/2)*Sqrt[c*x]*(a + b*x^2)^(3/4))/(a*c^2 + b*c^2*x^2)])/b^(3/4)) + (Sqrt[c]*ArcTanh[(b^(1/4)*c^(3/2)*Sqrt[c*x]*(a + b*x^2)^(3/4))/(a*c^2 + b*c^2*x^2)])/b^(3/4)","A",1
972,1,26,26,0.3800008,"\int \frac{1}{(c x)^{3/2} \left(a+b x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[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
973,1,44,55,0.5454995,"\int \frac{1}{(c x)^{7/2} \left(a+b x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[1/((c*x)^(7/2)*(a + b*x^2)^(3/4)),x]","\frac{2 \sqrt[4]{a+b x^2} \left(4 b c^2 x^2-a c^2\right)}{5 a^2 c^3 (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^2) + 4*b*c^2*x^2))/(5*a^2*c^3*(c*x)^(5/2))","A",1
974,1,58,83,0.9800942,"\int \frac{1}{(c x)^{11/2} \left(a+b x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[1/((c*x)^(11/2)*(a + b*x^2)^(3/4)),x]","-\frac{2 \sqrt[4]{a+b x^2} \left(5 a^2 c^4-8 a b c^4 x^2+32 b^2 c^4 x^4\right)}{45 a^3 c^5 (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)*(5*a^2*c^4 - 8*a*b*c^4*x^2 + 32*b^2*c^4*x^4))/(45*a^3*c^5*(c*x)^(9/2))","A",1
975,0,0,91,7.1975785,"\int \frac{(c x)^{3/2}}{\left(a-b x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[(c*x)^(3/2)/(a - b*x^2)^(3/4),x]","\int \frac{(c x)^{3/2}}{\left(a-b x^2\right)^{3/4}} \, dx","-\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,"Could not integrate","F",-1
976,0,0,68,6.5601168,"\int \frac{1}{\sqrt{c x} \left(a-b x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[1/(Sqrt[c*x]*(a - b*x^2)^(3/4)),x]","\int \frac{1}{\sqrt{c x} \left(a-b x^2\right)^{3/4}} \, dx","-\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,"Could not integrate","F",-1
977,0,0,100,16.4478862,"\int \frac{1}{(c x)^{5/2} \left(a-b x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[1/((c*x)^(5/2)*(a - b*x^2)^(3/4)),x]","\int \frac{1}{(c x)^{5/2} \left(a-b x^2\right)^{3/4}} \, dx","-\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,"Could not integrate","F",-1
978,0,0,130,19.7521278,"\int \frac{1}{(c x)^{9/2} \left(a-b x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[1/((c*x)^(9/2)*(a - b*x^2)^(3/4)),x]","\int \frac{1}{(c x)^{9/2} \left(a-b x^2\right)^{3/4}} \, dx","-\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,"Could not integrate","F",-1
979,0,0,162,21.2870968,"\int \frac{1}{(c x)^{13/2} \left(a-b x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[1/((c*x)^(13/2)*(a - b*x^2)^(3/4)),x]","\int \frac{1}{(c x)^{13/2} \left(a-b x^2\right)^{3/4}} \, dx","-\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{40 b^2 \sqrt[4]{a-b x^2}}{77 a^3 c^5 (c x)^{3/2}}-\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,"Could not integrate","F",-1
980,0,0,308,9.6941952,"\int \frac{(c x)^{5/2}}{\left(a-b x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[(c*x)^(5/2)/(a - b*x^2)^(3/4),x]","\int \frac{(c x)^{5/2}}{\left(a-b x^2\right)^{3/4}} \, dx","\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,"Could not integrate","F",-1
981,1,164,272,5.6156809,"\int \frac{\sqrt{c x}}{\left(a-b x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[Sqrt[c*x]/(a - b*x^2)^(3/4),x]","-\frac{\sqrt{c} \tan ^{-1}\left(\frac{\frac{\sqrt{c} \sqrt{a-b x^2}}{\sqrt{2} \sqrt[4]{b}}-\frac{\sqrt[4]{b} \sqrt{c} x}{\sqrt{2}}}{\sqrt{c x} \sqrt[4]{a-b x^2}}\right)}{\sqrt{2} b^{3/4}}-\frac{\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{c} \sqrt{c x} \sqrt[4]{a-b x^2}}{c \sqrt{a-b x^2}+\sqrt{b} c x}\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[(-((b^(1/4)*Sqrt[c]*x)/Sqrt[2]) + (Sqrt[c]*Sqrt[a - b*x^2])/(Sqrt[2]*b^(1/4)))/(Sqrt[c*x]*(a - b*x^2)^(1/4))])/(Sqrt[2]*b^(3/4))) - (Sqrt[c]*ArcTanh[(Sqrt[2]*b^(1/4)*Sqrt[c]*Sqrt[c*x]*(a - b*x^2)^(1/4))/(Sqrt[b]*c*x + c*Sqrt[a - b*x^2])])/(Sqrt[2]*b^(3/4))","A",1
982,1,27,27,0.3766097,"\int \frac{1}{(c x)^{3/2} \left(a-b x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[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
983,1,44,57,0.5473947,"\int \frac{1}{(c x)^{7/2} \left(a-b x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[1/((c*x)^(7/2)*(a - b*x^2)^(3/4)),x]","-\frac{2 \sqrt[4]{a-b x^2} \left(a c^2+4 b c^2 x^2\right)}{5 a^2 c^3 (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^2 + 4*b*c^2*x^2))/(5*a^2*c^3*(c*x)^(5/2))","A",1
984,1,59,86,0.9895447,"\int \frac{1}{(c x)^{11/2} \left(a-b x^2\right)^{3/4}} \, dx","IntegrateAlgebraic[1/((c*x)^(11/2)*(a - b*x^2)^(3/4)),x]","-\frac{2 \sqrt[4]{a-b x^2} \left(5 a^2 c^4+8 a b c^4 x^2+32 b^2 c^4 x^4\right)}{45 a^3 c^5 (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)*(5*a^2*c^4 + 8*a*b*c^4*x^2 + 32*b^2*c^4*x^4))/(45*a^3*c^5*(c*x)^(9/2))","A",1
985,0,0,146,11.3657814,"\int \frac{(c x)^{7/2}}{\left(a+b x^2\right)^{5/4}} \, dx","IntegrateAlgebraic[(c*x)^(7/2)/(a + b*x^2)^(5/4),x]","\int \frac{(c x)^{7/2}}{\left(a+b x^2\right)^{5/4}} \, dx","-\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{5 a c^3 \sqrt{c x}}{2 b^2 \sqrt[4]{a+b x^2}}+\frac{c (c x)^{5/2}}{2 b \sqrt[4]{a+b x^2}}",1,"Could not integrate","F",-1
986,1,157,107,1.3156729,"\int \frac{(c x)^{3/2}}{\left(a+b x^2\right)^{5/4}} \, dx","IntegrateAlgebraic[(c*x)^(3/2)/(a + b*x^2)^(5/4),x]","\frac{c^{3/2} \tan ^{-1}\left(\frac{\sqrt[4]{b} c^{3/2} \sqrt{c x} \left(a+b x^2\right)^{3/4}}{a c^2+b c^2 x^2}\right)}{b^{5/4}}+\frac{c^{3/2} \tanh ^{-1}\left(\frac{\sqrt[4]{b} c^{3/2} \sqrt{c x} \left(a+b x^2\right)^{3/4}}{a c^2+b c^2 x^2}\right)}{b^{5/4}}-\frac{2 c^3 \sqrt{c x} \left(a+b x^2\right)^{3/4}}{b \left(a c^2+b c^2 x^2\right)}","\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^3*Sqrt[c*x]*(a + b*x^2)^(3/4))/(b*(a*c^2 + b*c^2*x^2)) + (c^(3/2)*ArcTan[(b^(1/4)*c^(3/2)*Sqrt[c*x]*(a + b*x^2)^(3/4))/(a*c^2 + b*c^2*x^2)])/b^(5/4) + (c^(3/2)*ArcTanh[(b^(1/4)*c^(3/2)*Sqrt[c*x]*(a + b*x^2)^(3/4))/(a*c^2 + b*c^2*x^2)])/b^(5/4)","A",1
987,1,40,26,0.5715767,"\int \frac{1}{\sqrt{c x} \left(a+b x^2\right)^{5/4}} \, dx","IntegrateAlgebraic[1/(Sqrt[c*x]*(a + b*x^2)^(5/4)),x]","\frac{2 c \sqrt{c x} \left(a+b x^2\right)^{3/4}}{a \left(a c^2+b c^2 x^2\right)}","\frac{2 \sqrt{c x}}{a c \sqrt[4]{a+b x^2}}",1,"(2*c*Sqrt[c*x]*(a + b*x^2)^(3/4))/(a*(a*c^2 + b*c^2*x^2))","A",1
988,1,59,55,0.7301794,"\int \frac{1}{(c x)^{5/2} \left(a+b x^2\right)^{5/4}} \, dx","IntegrateAlgebraic[1/((c*x)^(5/2)*(a + b*x^2)^(5/4)),x]","-\frac{2 \left(a+b x^2\right)^{3/4} \left(a c^2+4 b c^2 x^2\right)}{3 a^2 c (c x)^{3/2} \left(a c^2+b c^2 x^2\right)}","\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 + b*x^2)^(3/4)*(a*c^2 + 4*b*c^2*x^2))/(3*a^2*c*(c*x)^(3/2)*(a*c^2 + b*c^2*x^2))","A",1
989,1,74,83,1.3697233,"\int \frac{1}{(c x)^{9/2} \left(a+b x^2\right)^{5/4}} \, dx","IntegrateAlgebraic[1/((c*x)^(9/2)*(a + b*x^2)^(5/4)),x]","\frac{2 \left(a+b x^2\right)^{3/4} \left(-3 a^2 c^4+8 a b c^4 x^2+32 b^2 c^4 x^4\right)}{21 a^3 c^3 (c x)^{7/2} \left(a c^2+b c^2 x^2\right)}","\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 + b*x^2)^(3/4)*(-3*a^2*c^4 + 8*a*b*c^4*x^2 + 32*b^2*c^4*x^4))/(21*a^3*c^3*(c*x)^(7/2)*(a*c^2 + b*c^2*x^2))","A",1
990,1,88,109,3.534963,"\int \frac{1}{(c x)^{13/2} \left(a+b x^2\right)^{5/4}} \, dx","IntegrateAlgebraic[1/((c*x)^(13/2)*(a + b*x^2)^(5/4)),x]","-\frac{2 \left(a+b x^2\right)^{3/4} \left(7 a^3 c^6-12 a^2 b c^6 x^2+32 a b^2 c^6 x^4+128 b^3 c^6 x^6\right)}{77 a^4 c^5 (c x)^{11/2} \left(a c^2+b c^2 x^2\right)}","-\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 + b*x^2)^(3/4)*(7*a^3*c^6 - 12*a^2*b*c^6*x^2 + 32*a*b^2*c^6*x^4 + 128*b^3*c^6*x^6))/(77*a^4*c^5*(c*x)^(11/2)*(a*c^2 + b*c^2*x^2))","A",1
991,0,0,155,11.6059615,"\int \frac{(c x)^{13/2}}{\left(a+b x^2\right)^{5/4}} \, dx","IntegrateAlgebraic[(c*x)^(13/2)/(a + b*x^2)^(5/4),x]","\int \frac{(c x)^{13/2}}{\left(a+b x^2\right)^{5/4}} \, dx","\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{77 a^2 c^5 (c x)^{3/2}}{60 b^3 \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,"Could not integrate","F",-1
992,0,0,124,11.2111509,"\int \frac{(c x)^{9/2}}{\left(a+b x^2\right)^{5/4}} \, dx","IntegrateAlgebraic[(c*x)^(9/2)/(a + b*x^2)^(5/4),x]","\int \frac{(c x)^{9/2}}{\left(a+b x^2\right)^{5/4}} \, dx","-\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,"Could not integrate","F",-1
993,0,0,90,10.6418228,"\int \frac{(c x)^{5/2}}{\left(a+b x^2\right)^{5/4}} \, dx","IntegrateAlgebraic[(c*x)^(5/2)/(a + b*x^2)^(5/4),x]","\int \frac{(c x)^{5/2}}{\left(a+b x^2\right)^{5/4}} \, dx","\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,"Could not integrate","F",-1
994,0,0,63,9.8076293,"\int \frac{\sqrt{c x}}{\left(a+b x^2\right)^{5/4}} \, dx","IntegrateAlgebraic[Sqrt[c*x]/(a + b*x^2)^(5/4),x]","\int \frac{\sqrt{c x}}{\left(a+b x^2\right)^{5/4}} \, dx","-\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,"Could not integrate","F",-1
995,0,0,93,13.198807,"\int \frac{1}{(c x)^{3/2} \left(a+b x^2\right)^{5/4}} \, dx","IntegrateAlgebraic[1/((c*x)^(3/2)*(a + b*x^2)^(5/4)),x]","\int \frac{1}{(c x)^{3/2} \left(a+b x^2\right)^{5/4}} \, dx","\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,"Could not integrate","F",-1
996,0,0,126,21.3105525,"\int \frac{1}{(c x)^{7/2} \left(a+b x^2\right)^{5/4}} \, dx","IntegrateAlgebraic[1/((c*x)^(7/2)*(a + b*x^2)^(5/4)),x]","\int \frac{1}{(c x)^{7/2} \left(a+b x^2\right)^{5/4}} \, dx","-\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,"Could not integrate","F",-1
997,0,0,157,23.5049434,"\int \frac{1}{(c x)^{11/2} \left(a+b x^2\right)^{5/4}} \, dx","IntegrateAlgebraic[1/((c*x)^(11/2)*(a + b*x^2)^(5/4)),x]","\int \frac{1}{(c x)^{11/2} \left(a+b x^2\right)^{5/4}} \, dx","\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{8 b^2}{3 a^3 c^5 \sqrt{c x} \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,"Could not integrate","F",-1
998,0,0,58,10.2894928,"\int \frac{(c x)^{5/4}}{\sqrt[4]{a+b x^2}} \, dx","IntegrateAlgebraic[(c*x)^(5/4)/(a + b*x^2)^(1/4),x]","\int \frac{(c x)^{5/4}}{\sqrt[4]{a+b x^2}} \, dx","\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,"Could not integrate","F",-1
999,0,0,58,10.3221743,"\int \frac{(c x)^{3/4}}{\sqrt[4]{a+b x^2}} \, dx","IntegrateAlgebraic[(c*x)^(3/4)/(a + b*x^2)^(1/4),x]","\int \frac{(c x)^{3/4}}{\sqrt[4]{a+b x^2}} \, dx","\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,"Could not integrate","F",-1
1000,0,0,58,9.0689154,"\int \frac{\sqrt[4]{c x}}{\sqrt[4]{a+b x^2}} \, dx","IntegrateAlgebraic[(c*x)^(1/4)/(a + b*x^2)^(1/4),x]","\int \frac{\sqrt[4]{c x}}{\sqrt[4]{a+b x^2}} \, dx","\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,"Could not integrate","F",-1
1001,0,0,58,13.6675953,"\int \frac{1}{\sqrt[4]{c x} \sqrt[4]{a+b x^2}} \, dx","IntegrateAlgebraic[1/((c*x)^(1/4)*(a + b*x^2)^(1/4)),x]","\int \frac{1}{\sqrt[4]{c x} \sqrt[4]{a+b x^2}} \, dx","\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,"Could not integrate","F",-1
1002,0,0,56,18.2126622,"\int \frac{1}{(c x)^{3/4} \sqrt[4]{a+b x^2}} \, dx","IntegrateAlgebraic[1/((c*x)^(3/4)*(a + b*x^2)^(1/4)),x]","\int \frac{1}{(c x)^{3/4} \sqrt[4]{a+b x^2}} \, dx","\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,"Could not integrate","F",-1
1003,0,0,56,21.3215064,"\int \frac{1}{(c x)^{5/4} \sqrt[4]{a+b x^2}} \, dx","IntegrateAlgebraic[1/((c*x)^(5/4)*(a + b*x^2)^(1/4)),x]","\int \frac{1}{(c x)^{5/4} \sqrt[4]{a+b x^2}} \, dx","-\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,"Could not integrate","F",-1
1004,0,0,61,18.3538277,"\int \frac{(c x)^{5/4}}{\left(a+b x^2\right)^{7/4}} \, dx","IntegrateAlgebraic[(c*x)^(5/4)/(a + b*x^2)^(7/4),x]","\int \frac{(c x)^{5/4}}{\left(a+b x^2\right)^{7/4}} \, dx","\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,"Could not integrate","F",-1
1005,0,0,61,17.1555521,"\int \frac{(c x)^{3/4}}{\left(a+b x^2\right)^{7/4}} \, dx","IntegrateAlgebraic[(c*x)^(3/4)/(a + b*x^2)^(7/4),x]","\int \frac{(c x)^{3/4}}{\left(a+b x^2\right)^{7/4}} \, dx","\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,"Could not integrate","F",-1
1006,0,0,61,17.6876794,"\int \frac{\sqrt[4]{c x}}{\left(a+b x^2\right)^{7/4}} \, dx","IntegrateAlgebraic[(c*x)^(1/4)/(a + b*x^2)^(7/4),x]","\int \frac{\sqrt[4]{c x}}{\left(a+b x^2\right)^{7/4}} \, dx","\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,"Could not integrate","F",-1
1007,0,0,61,23.0011848,"\int \frac{1}{\sqrt[4]{c x} \left(a+b x^2\right)^{7/4}} \, dx","IntegrateAlgebraic[1/((c*x)^(1/4)*(a + b*x^2)^(7/4)),x]","\int \frac{1}{\sqrt[4]{c x} \left(a+b x^2\right)^{7/4}} \, dx","\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,"Could not integrate","F",-1
1008,0,0,59,28.2918726,"\int \frac{1}{(c x)^{3/4} \left(a+b x^2\right)^{7/4}} \, dx","IntegrateAlgebraic[1/((c*x)^(3/4)*(a + b*x^2)^(7/4)),x]","\int \frac{1}{(c x)^{3/4} \left(a+b x^2\right)^{7/4}} \, dx","\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,"Could not integrate","F",-1
1009,0,0,59,30.5939653,"\int \frac{1}{(c x)^{5/4} \left(a+b x^2\right)^{7/4}} \, dx","IntegrateAlgebraic[1/((c*x)^(5/4)*(a + b*x^2)^(7/4)),x]","\int \frac{1}{(c x)^{5/4} \left(a+b x^2\right)^{7/4}} \, dx","-\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,"Could not integrate","F",-1
1010,0,0,345,5.7341095,"\int x^6 \sqrt[6]{a+b x^2} \, dx","IntegrateAlgebraic[x^6*(a + b*x^2)^(1/6),x]","\int x^6 \sqrt[6]{a+b x^2} \, dx","-\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{81 a^3 x \sqrt[6]{a+b x^2}}{2816 b^3}-\frac{9 a^2 x^3 \sqrt[6]{a+b x^2}}{704 b^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,"Could not integrate","F",-1
1011,0,0,321,5.684881,"\int x^4 \sqrt[6]{a+b x^2} \, dx","IntegrateAlgebraic[x^4*(a + b*x^2)^(1/6),x]","\int x^4 \sqrt[6]{a+b x^2} \, dx","\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{27 a^2 x \sqrt[6]{a+b x^2}}{640 b^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,"Could not integrate","F",-1
1012,0,0,297,5.3750646,"\int x^2 \sqrt[6]{a+b x^2} \, dx","IntegrateAlgebraic[x^2*(a + b*x^2)^(1/6),x]","\int x^2 \sqrt[6]{a+b x^2} \, dx","-\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 a x \sqrt[6]{a+b x^2}}{40 b}+\frac{3}{10} x^3 \sqrt[6]{a+b x^2}",1,"Could not integrate","F",-1
1013,0,0,273,5.282948,"\int \sqrt[6]{a+b x^2} \, dx","IntegrateAlgebraic[(a + b*x^2)^(1/6),x]","\int \sqrt[6]{a+b x^2} \, dx","\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,"Could not integrate","F",-1
1014,0,0,266,5.4293485,"\int \frac{\sqrt[6]{a+b x^2}}{x^2} \, dx","IntegrateAlgebraic[(a + b*x^2)^(1/6)/x^2,x]","\int \frac{\sqrt[6]{a+b x^2}}{x^2} \, dx","\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,"Could not integrate","F",-1
1015,0,0,297,10.4439243,"\int \frac{\sqrt[6]{a+b x^2}}{x^4} \, dx","IntegrateAlgebraic[(a + b*x^2)^(1/6)/x^4,x]","\int \frac{\sqrt[6]{a+b x^2}}{x^4} \, dx","-\frac{b \sqrt[6]{a+b x^2}}{9 a x}-\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{\sqrt[6]{a+b x^2}}{3 x^3}",1,"Could not integrate","F",-1
1016,0,0,323,15.7580009,"\int \frac{\sqrt[6]{a+b x^2}}{x^6} \, dx","IntegrateAlgebraic[(a + b*x^2)^(1/6)/x^6,x]","\int \frac{\sqrt[6]{a+b x^2}}{x^6} \, dx","\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{\sqrt[6]{a+b x^2}}{5 x^5}-\frac{b \sqrt[6]{a+b x^2}}{45 a x^3}",1,"Could not integrate","F",-1
1017,0,0,347,18.3035338,"\int \frac{\sqrt[6]{a+b x^2}}{x^8} \, dx","IntegrateAlgebraic[(a + b*x^2)^(1/6)/x^8,x]","\int \frac{\sqrt[6]{a+b x^2}}{x^8} \, dx","-\frac{16 b^3 \sqrt[6]{a+b x^2}}{405 a^3 x}-\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{2 b^2 \sqrt[6]{a+b x^2}}{135 a^2 x^3}-\frac{\sqrt[6]{a+b x^2}}{7 x^7}-\frac{b \sqrt[6]{a+b x^2}}{105 a x^5}",1,"Could not integrate","F",-1
1018,0,0,659,5.7053113,"\int \frac{x^6}{\sqrt[6]{a+b x^2}} \, dx","IntegrateAlgebraic[x^6/(a + b*x^2)^(1/6),x]","\int \frac{x^6}{\sqrt[6]{a+b x^2}} \, dx","\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{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{243 a^3 x}{896 b^3 \sqrt[6]{a+b x^2}}+\frac{81 a^2 x \left(a+b x^2\right)^{5/6}}{448 b^3}-\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,"Could not integrate","F",-1
1019,0,0,635,5.6317941,"\int \frac{x^4}{\sqrt[6]{a+b x^2}} \, dx","IntegrateAlgebraic[x^4/(a + b*x^2)^(1/6),x]","\int \frac{x^4}{\sqrt[6]{a+b x^2}} \, dx","-\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{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 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,"Could not integrate","F",-1
1020,0,0,611,5.3593012,"\int \frac{x^2}{\sqrt[6]{a+b x^2}} \, dx","IntegrateAlgebraic[x^2/(a + b*x^2)^(1/6),x]","\int \frac{x^2}{\sqrt[6]{a+b x^2}} \, dx","\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,"Could not integrate","F",-1
1021,0,0,577,5.3063522,"\int \frac{1}{\sqrt[6]{a+b x^2}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(-1/6),x]","\int \frac{1}{\sqrt[6]{a+b x^2}} \, dx","\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,"Could not integrate","F",-1
1022,0,0,586,5.4331789,"\int \frac{1}{x^2 \sqrt[6]{a+b x^2}} \, dx","IntegrateAlgebraic[1/(x^2*(a + b*x^2)^(1/6)),x]","\int \frac{1}{x^2 \sqrt[6]{a+b x^2}} \, dx","\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,"Could not integrate","F",-1
1023,0,0,633,10.4800755,"\int \frac{1}{x^4 \sqrt[6]{a+b x^2}} \, dx","IntegrateAlgebraic[1/(x^4*(a + b*x^2)^(1/6)),x]","\int \frac{1}{x^4 \sqrt[6]{a+b x^2}} \, dx","-\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{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{\left(a+b x^2\right)^{5/6}}{3 a x^3}",1,"Could not integrate","F",-1
1024,0,0,661,15.6416587,"\int \frac{1}{x^6 \sqrt[6]{a+b x^2}} \, dx","IntegrateAlgebraic[1/(x^6*(a + b*x^2)^(1/6)),x]","\int \frac{1}{x^6 \sqrt[6]{a+b x^2}} \, dx","\frac{8 b^3 x}{27 a^3 \sqrt[6]{a+b x^2}}-\frac{8 b^2 \left(a+b x^2\right)^{5/6}}{27 a^3 x}+\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 \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,"Could not integrate","F",-1
1025,0,0,324,5.8714083,"\int \frac{x^6}{\left(a+b x^2\right)^{5/6}} \, dx","IntegrateAlgebraic[x^6/(a + b*x^2)^(5/6),x]","\int \frac{x^6}{\left(a+b x^2\right)^{5/6}} \, dx","-\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{81 a^2 x \sqrt[6]{a+b x^2}}{128 b^3}-\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,"Could not integrate","F",-1
1026,0,0,300,5.8095748,"\int \frac{x^4}{\left(a+b x^2\right)^{5/6}} \, dx","IntegrateAlgebraic[x^4/(a + b*x^2)^(5/6),x]","\int \frac{x^4}{\left(a+b x^2\right)^{5/6}} \, dx","\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,"Could not integrate","F",-1
1027,0,0,276,5.3061669,"\int \frac{x^2}{\left(a+b x^2\right)^{5/6}} \, dx","IntegrateAlgebraic[x^2/(a + b*x^2)^(5/6),x]","\int \frac{x^2}{\left(a+b x^2\right)^{5/6}} \, dx","\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,"Could not integrate","F",-1
1028,0,0,252,5.2449998,"\int \frac{1}{\left(a+b x^2\right)^{5/6}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(-5/6),x]","\int \frac{1}{\left(a+b x^2\right)^{5/6}} \, dx","\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,"Could not integrate","F",-1
1029,0,0,273,5.5766343,"\int \frac{1}{x^2 \left(a+b x^2\right)^{5/6}} \, dx","IntegrateAlgebraic[1/(x^2*(a + b*x^2)^(5/6)),x]","\int \frac{1}{x^2 \left(a+b x^2\right)^{5/6}} \, dx","-\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,"Could not integrate","F",-1
1030,0,0,300,10.6594367,"\int \frac{1}{x^4 \left(a+b x^2\right)^{5/6}} \, dx","IntegrateAlgebraic[1/(x^4*(a + b*x^2)^(5/6)),x]","\int \frac{1}{x^4 \left(a+b x^2\right)^{5/6}} \, dx","\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,"Could not integrate","F",-1
1031,0,0,326,15.739778,"\int \frac{1}{x^6 \left(a+b x^2\right)^{5/6}} \, dx","IntegrateAlgebraic[1/(x^6*(a + b*x^2)^(5/6)),x]","\int \frac{1}{x^6 \left(a+b x^2\right)^{5/6}} \, dx","-\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,"Could not integrate","F",-1
1032,0,0,654,5.9041863,"\int \frac{x^6}{\left(a+b x^2\right)^{7/6}} \, dx","IntegrateAlgebraic[x^6/(a + b*x^2)^(7/6),x]","\int \frac{x^6}{\left(a+b x^2\right)^{7/6}} \, dx","-\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{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{1215 a^2 x}{224 b^3 \sqrt[6]{a+b x^2}}-\frac{405 a x \left(a+b x^2\right)^{5/6}}{112 b^3}+\frac{45 x^3 \left(a+b x^2\right)^{5/6}}{14 b^2}-\frac{3 x^5}{b \sqrt[6]{a+b x^2}}",1,"Could not integrate","F",-1
1033,0,0,630,5.8674015,"\int \frac{x^4}{\left(a+b x^2\right)^{7/6}} \, dx","IntegrateAlgebraic[x^4/(a + b*x^2)^(7/6),x]","\int \frac{x^4}{\left(a+b x^2\right)^{7/6}} \, dx","\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{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 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,"Could not integrate","F",-1
1034,0,0,583,5.3565015,"\int \frac{x^2}{\left(a+b x^2\right)^{7/6}} \, dx","IntegrateAlgebraic[x^2/(a + b*x^2)^(7/6),x]","\int \frac{x^2}{\left(a+b x^2\right)^{7/6}} \, dx","-\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,"Could not integrate","F",-1
1035,0,0,555,5.2713508,"\int \frac{1}{\left(a+b x^2\right)^{7/6}} \, dx","IntegrateAlgebraic[(a + b*x^2)^(-7/6),x]","\int \frac{1}{\left(a+b x^2\right)^{7/6}} \, dx","-\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,"Could not integrate","F",-1
1036,0,0,614,5.7483143,"\int \frac{1}{x^2 \left(a+b x^2\right)^{7/6}} \, dx","IntegrateAlgebraic[1/(x^2*(a + b*x^2)^(7/6)),x]","\int \frac{1}{x^2 \left(a+b x^2\right)^{7/6}} \, dx","\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,"Could not integrate","F",-1
1037,0,0,652,10.7272918,"\int \frac{1}{x^4 \left(a+b x^2\right)^{7/6}} \, dx","IntegrateAlgebraic[1/(x^4*(a + b*x^2)^(7/6)),x]","\int \frac{1}{x^4 \left(a+b x^2\right)^{7/6}} \, dx","-\frac{40 b^2 x}{9 a^3 \sqrt[6]{a+b x^2}}+\frac{40 b \left(a+b x^2\right)^{5/6}}{9 a^3 x}-\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 \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{10 \left(a+b x^2\right)^{5/6}}{3 a^2 x^3}+\frac{3}{a x^3 \sqrt[6]{a+b x^2}}",1,"Could not integrate","F",-1
1038,0,0,680,15.9465501,"\int \frac{1}{x^6 \left(a+b x^2\right)^{7/6}} \, dx","IntegrateAlgebraic[1/(x^6*(a + b*x^2)^(7/6)),x]","\int \frac{1}{x^6 \left(a+b x^2\right)^{7/6}} \, dx","\frac{128 b^3 x}{27 a^4 \sqrt[6]{a+b x^2}}-\frac{128 b^2 \left(a+b x^2\right)^{5/6}}{27 a^4 x}+\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 \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,"Could not integrate","F",-1
1039,0,0,100,0.0292695,"\int x^7 \left(a+b x^2\right)^p \, dx","IntegrateAlgebraic[x^7*(a + b*x^2)^p,x]","\int x^7 \left(a+b x^2\right)^p \, dx","-\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,"Could not integrate","F",-1
1040,0,0,72,0.0270459,"\int x^5 \left(a+b x^2\right)^p \, dx","IntegrateAlgebraic[x^5*(a + b*x^2)^p,x]","\int x^5 \left(a+b x^2\right)^p \, dx","\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,"Could not integrate","F",-1
1041,0,0,48,0.0243411,"\int x^3 \left(a+b x^2\right)^p \, dx","IntegrateAlgebraic[x^3*(a + b*x^2)^p,x]","\int x^3 \left(a+b x^2\right)^p \, dx","\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,"Could not integrate","F",-1
1042,0,0,23,0.0162598,"\int x \left(a+b x^2\right)^p \, dx","IntegrateAlgebraic[x*(a + b*x^2)^p,x]","\int x \left(a+b x^2\right)^p \, dx","\frac{\left(a+b x^2\right)^{p+1}}{2 b (p+1)}",1,"Could not integrate","F",-1
1043,0,0,41,0.0221976,"\int \frac{\left(a+b x^2\right)^p}{x} \, dx","IntegrateAlgebraic[(a + b*x^2)^p/x,x]","\int \frac{\left(a+b x^2\right)^p}{x} \, dx","-\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,"Could not integrate","F",-1
1044,0,0,42,0.0253365,"\int \frac{\left(a+b x^2\right)^p}{x^3} \, dx","IntegrateAlgebraic[(a + b*x^2)^p/x^3,x]","\int \frac{\left(a+b x^2\right)^p}{x^3} \, dx","\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,"Could not integrate","F",-1
1045,0,0,40,0.0405831,"\int x^6 \left(a+b x^2\right)^p \, dx","IntegrateAlgebraic[x^6*(a + b*x^2)^p,x]","\int x^6 \left(a+b x^2\right)^p \, dx","\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,"Could not integrate","F",-1
1046,0,0,40,0.0384594,"\int x^4 \left(a+b x^2\right)^p \, dx","IntegrateAlgebraic[x^4*(a + b*x^2)^p,x]","\int x^4 \left(a+b x^2\right)^p \, dx","\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,"Could not integrate","F",-1
1047,0,0,40,0.0287766,"\int x^2 \left(a+b x^2\right)^p \, dx","IntegrateAlgebraic[x^2*(a + b*x^2)^p,x]","\int x^2 \left(a+b x^2\right)^p \, dx","\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,"Could not integrate","F",-1
1048,0,0,35,0.028662,"\int \left(a+b x^2\right)^p \, dx","IntegrateAlgebraic[(a + b*x^2)^p,x]","\int \left(a+b x^2\right)^p \, dx","\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,"Could not integrate","F",-1
1049,0,0,38,0.1034119,"\int \frac{\left(a+b x^2\right)^p}{x^2} \, dx","IntegrateAlgebraic[(a + b*x^2)^p/x^2,x]","\int \frac{\left(a+b x^2\right)^p}{x^2} \, dx","-\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,"Could not integrate","F",-1
1050,0,0,42,0.1672699,"\int x^{7/2} \left(a+b x^2\right)^p \, dx","IntegrateAlgebraic[x^(7/2)*(a + b*x^2)^p,x]","\int x^{7/2} \left(a+b x^2\right)^p \, dx","\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,"Could not integrate","F",-1
1051,0,0,42,0.0946504,"\int x^{5/2} \left(a+b x^2\right)^p \, dx","IntegrateAlgebraic[x^(5/2)*(a + b*x^2)^p,x]","\int x^{5/2} \left(a+b x^2\right)^p \, dx","\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,"Could not integrate","F",-1
1052,0,0,42,0.0797768,"\int x^{3/2} \left(a+b x^2\right)^p \, dx","IntegrateAlgebraic[x^(3/2)*(a + b*x^2)^p,x]","\int x^{3/2} \left(a+b x^2\right)^p \, dx","\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,"Could not integrate","F",-1
1053,0,0,42,0.1332483,"\int \sqrt{x} \left(a+b x^2\right)^p \, dx","IntegrateAlgebraic[Sqrt[x]*(a + b*x^2)^p,x]","\int \sqrt{x} \left(a+b x^2\right)^p \, dx","\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,"Could not integrate","F",-1
1054,0,0,40,0.088704,"\int \frac{\left(a+b x^2\right)^p}{\sqrt{x}} \, dx","IntegrateAlgebraic[(a + b*x^2)^p/Sqrt[x],x]","\int \frac{\left(a+b x^2\right)^p}{\sqrt{x}} \, dx","\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,"Could not integrate","F",-1
1055,0,0,40,0.0807155,"\int \frac{\left(a+b x^2\right)^p}{x^{3/2}} \, dx","IntegrateAlgebraic[(a + b*x^2)^p/x^(3/2),x]","\int \frac{\left(a+b x^2\right)^p}{x^{3/2}} \, dx","-\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,"Could not integrate","F",-1
1056,0,0,42,0.1394713,"\int \frac{\left(a+b x^2\right)^p}{x^{5/2}} \, dx","IntegrateAlgebraic[(a + b*x^2)^p/x^(5/2),x]","\int \frac{\left(a+b x^2\right)^p}{x^{5/2}} \, dx","-\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,"Could not integrate","F",-1
1057,0,0,42,0.1431704,"\int \frac{\left(a+b x^2\right)^p}{x^{7/2}} \, dx","IntegrateAlgebraic[(a + b*x^2)^p/x^(7/2),x]","\int \frac{\left(a+b x^2\right)^p}{x^{7/2}} \, dx","-\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,"Could not integrate","F",-1
1058,0,0,53,0.013271,"\int x^m \left(a+b x^2\right)^p \, dx","IntegrateAlgebraic[x^m*(a + b*x^2)^p,x]","\int x^m \left(a+b x^2\right)^p \, dx","\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,"Could not integrate","F",-1
1059,0,0,66,0.0138278,"\int (c x)^m \left(a+b x^2\right)^p \, dx","IntegrateAlgebraic[(c*x)^m*(a + b*x^2)^p,x]","\int (c x)^m \left(a+b x^2\right)^p \, dx","\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,"Could not integrate","F",-1
1060,0,0,53,0.0155161,"\int x^{-8-2 p} \left(a+b x^2\right)^p \, dx","IntegrateAlgebraic[x^(-8 - 2*p)*(a + b*x^2)^p,x]","\int x^{-8-2 p} \left(a+b x^2\right)^p \, dx","-\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,"Could not integrate","F",-1
1061,0,0,105,0.0156264,"\int x^{-7-2 p} \left(a+b x^2\right)^p \, dx","IntegrateAlgebraic[x^(-7 - 2*p)*(a + b*x^2)^p,x]","\int x^{-7-2 p} \left(a+b x^2\right)^p \, dx","-\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,"Could not integrate","F",-1
1062,0,0,53,0.0151169,"\int x^{-6-2 p} \left(a+b x^2\right)^p \, dx","IntegrateAlgebraic[x^(-6 - 2*p)*(a + b*x^2)^p,x]","\int x^{-6-2 p} \left(a+b x^2\right)^p \, dx","-\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,"Could not integrate","F",-1
1063,0,0,67,0.0157581,"\int x^{-5-2 p} \left(a+b x^2\right)^p \, dx","IntegrateAlgebraic[x^(-5 - 2*p)*(a + b*x^2)^p,x]","\int x^{-5-2 p} \left(a+b x^2\right)^p \, dx","\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,"Could not integrate","F",-1
1064,0,0,53,0.015804,"\int x^{-4-2 p} \left(a+b x^2\right)^p \, dx","IntegrateAlgebraic[x^(-4 - 2*p)*(a + b*x^2)^p,x]","\int x^{-4-2 p} \left(a+b x^2\right)^p \, dx","-\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,"Could not integrate","F",-1
1065,0,0,30,0.126204,"\int x^{-3-2 p} \left(a+b x^2\right)^p \, dx","IntegrateAlgebraic[x^(-3 - 2*p)*(a + b*x^2)^p,x]","\int x^{-3-2 p} \left(a+b x^2\right)^p \, dx","-\frac{x^{-2 (p+1)} \left(a+b x^2\right)^{p+1}}{2 a (p+1)}",1,"Could not integrate","F",-1
1066,0,0,53,0.0149946,"\int x^{-2-2 p} \left(a+b x^2\right)^p \, dx","IntegrateAlgebraic[x^(-2 - 2*p)*(a + b*x^2)^p,x]","\int x^{-2-2 p} \left(a+b x^2\right)^p \, dx","-\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,"Could not integrate","F",-1
1067,0,0,43,0.0151086,"\int x^{-1-2 p} \left(a+b x^2\right)^p \, dx","IntegrateAlgebraic[x^(-1 - 2*p)*(a + b*x^2)^p,x]","\int x^{-1-2 p} \left(a+b x^2\right)^p \, dx","-\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,"Could not integrate","F",-1
1068,0,0,52,0.0139803,"\int x^{-2 p} \left(a+b x^2\right)^p \, dx","IntegrateAlgebraic[(a + b*x^2)^p/x^(2*p),x]","\int x^{-2 p} \left(a+b x^2\right)^p \, dx","\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,"Could not integrate","F",-1
1069,0,0,49,0.0139394,"\int x^{1-2 p} \left(a+b x^2\right)^p \, dx","IntegrateAlgebraic[x^(1 - 2*p)*(a + b*x^2)^p,x]","\int x^{1-2 p} \left(a+b x^2\right)^p \, dx","\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,"Could not integrate","F",-1
1070,0,0,52,0.0153414,"\int x^{2-2 p} \left(a+b x^2\right)^p \, dx","IntegrateAlgebraic[x^(2 - 2*p)*(a + b*x^2)^p,x]","\int x^{2-2 p} \left(a+b x^2\right)^p \, dx","\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,"Could not integrate","F",-1
1071,0,0,49,0.0150024,"\int x^{3-2 p} \left(a+b x^2\right)^p \, dx","IntegrateAlgebraic[x^(3 - 2*p)*(a + b*x^2)^p,x]","\int x^{3-2 p} \left(a+b x^2\right)^p \, dx","\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,"Could not integrate","F",-1