1,1,12,0,0.060173," ","integrate(x**4*(b*x**2+a),x)","\frac{a x^{5}}{5} + \frac{b x^{7}}{7}"," ",0,"a*x**5/5 + b*x**7/7","A",0
2,1,12,0,0.058779," ","integrate(x**3*(b*x**2+a),x)","\frac{a x^{4}}{4} + \frac{b x^{6}}{6}"," ",0,"a*x**4/4 + b*x**6/6","A",0
3,1,12,0,0.057685," ","integrate(x**2*(b*x**2+a),x)","\frac{a x^{3}}{3} + \frac{b x^{5}}{5}"," ",0,"a*x**3/3 + b*x**5/5","A",0
4,1,12,0,0.058650," ","integrate(x*(b*x**2+a),x)","\frac{a x^{2}}{2} + \frac{b x^{4}}{4}"," ",0,"a*x**2/2 + b*x**4/4","A",0
5,1,8,0,0.056126," ","integrate(b*x**2+a,x)","a x + \frac{b x^{3}}{3}"," ",0,"a*x + b*x**3/3","A",0
6,1,10,0,0.083205," ","integrate((b*x**2+a)/x,x)","a \log{\left(x \right)} + \frac{b x^{2}}{2}"," ",0,"a*log(x) + b*x**2/2","A",0
7,1,5,0,0.078790," ","integrate((b*x**2+a)/x**2,x)","- \frac{a}{x} + b x"," ",0,"-a/x + b*x","A",0
8,1,10,0,0.106603," ","integrate((b*x**2+a)/x**3,x)","- \frac{a}{2 x^{2}} + b \log{\left(x \right)}"," ",0,"-a/(2*x**2) + b*log(x)","A",0
9,1,14,0,0.114516," ","integrate((b*x**2+a)/x**4,x)","\frac{- a - 3 b x^{2}}{3 x^{3}}"," ",0,"(-a - 3*b*x**2)/(3*x**3)","A",0
10,1,14,0,0.118676," ","integrate((b*x**2+a)/x**5,x)","\frac{- a - 2 b x^{2}}{4 x^{4}}"," ",0,"(-a - 2*b*x**2)/(4*x**4)","A",0
11,1,15,0,0.132590," ","integrate((b*x**2+a)/x**6,x)","\frac{- 3 a - 5 b x^{2}}{15 x^{5}}"," ",0,"(-3*a - 5*b*x**2)/(15*x**5)","A",0
12,1,15,0,0.135067," ","integrate((b*x**2+a)/x**7,x)","\frac{- 2 a - 3 b x^{2}}{12 x^{6}}"," ",0,"(-2*a - 3*b*x**2)/(12*x**6)","A",0
13,1,24,0,0.064730," ","integrate(x**5*(b*x**2+a)**2,x)","\frac{a^{2} x^{6}}{6} + \frac{a b x^{8}}{4} + \frac{b^{2} x^{10}}{10}"," ",0,"a**2*x**6/6 + a*b*x**8/4 + b**2*x**10/10","A",0
14,1,26,0,0.064814," ","integrate(x**4*(b*x**2+a)**2,x)","\frac{a^{2} x^{5}}{5} + \frac{2 a b x^{7}}{7} + \frac{b^{2} x^{9}}{9}"," ",0,"a**2*x**5/5 + 2*a*b*x**7/7 + b**2*x**9/9","A",0
15,1,24,0,0.064257," ","integrate(x**3*(b*x**2+a)**2,x)","\frac{a^{2} x^{4}}{4} + \frac{a b x^{6}}{3} + \frac{b^{2} x^{8}}{8}"," ",0,"a**2*x**4/4 + a*b*x**6/3 + b**2*x**8/8","A",0
16,1,26,0,0.065534," ","integrate(x**2*(b*x**2+a)**2,x)","\frac{a^{2} x^{3}}{3} + \frac{2 a b x^{5}}{5} + \frac{b^{2} x^{7}}{7}"," ",0,"a**2*x**3/3 + 2*a*b*x**5/5 + b**2*x**7/7","A",0
17,1,24,0,0.064605," ","integrate(x*(b*x**2+a)**2,x)","\frac{a^{2} x^{2}}{2} + \frac{a b x^{4}}{2} + \frac{b^{2} x^{6}}{6}"," ",0,"a**2*x**2/2 + a*b*x**4/2 + b**2*x**6/6","B",0
18,1,22,0,0.063684," ","integrate((b*x**2+a)**2,x)","a^{2} x + \frac{2 a b x^{3}}{3} + \frac{b^{2} x^{5}}{5}"," ",0,"a**2*x + 2*a*b*x**3/3 + b**2*x**5/5","A",0
19,1,20,0,0.098110," ","integrate((b*x**2+a)**2/x,x)","a^{2} \log{\left(x \right)} + a b x^{2} + \frac{b^{2} x^{4}}{4}"," ",0,"a**2*log(x) + a*b*x**2 + b**2*x**4/4","A",0
20,1,19,0,0.096685," ","integrate((b*x**2+a)**2/x**2,x)","- \frac{a^{2}}{x} + 2 a b x + \frac{b^{2} x^{3}}{3}"," ",0,"-a**2/x + 2*a*b*x + b**2*x**3/3","A",0
21,1,24,0,0.131061," ","integrate((b*x**2+a)**2/x**3,x)","- \frac{a^{2}}{2 x^{2}} + 2 a b \log{\left(x \right)} + \frac{b^{2} x^{2}}{2}"," ",0,"-a**2/(2*x**2) + 2*a*b*log(x) + b**2*x**2/2","A",0
22,1,22,0,0.139125," ","integrate((b*x**2+a)**2/x**4,x)","b^{2} x + \frac{- a^{2} - 6 a b x^{2}}{3 x^{3}}"," ",0,"b**2*x + (-a**2 - 6*a*b*x**2)/(3*x**3)","A",0
23,1,24,0,0.171914," ","integrate((b*x**2+a)**2/x**5,x)","b^{2} \log{\left(x \right)} + \frac{- a^{2} - 4 a b x^{2}}{4 x^{4}}"," ",0,"b**2*log(x) + (-a**2 - 4*a*b*x**2)/(4*x**4)","A",0
24,1,27,0,0.174543," ","integrate((b*x**2+a)**2/x**6,x)","\frac{- 3 a^{2} - 10 a b x^{2} - 15 b^{2} x^{4}}{15 x^{5}}"," ",0,"(-3*a**2 - 10*a*b*x**2 - 15*b**2*x**4)/(15*x**5)","A",0
25,1,26,0,0.186611," ","integrate((b*x**2+a)**2/x**7,x)","\frac{- a^{2} - 3 a b x^{2} - 3 b^{2} x^{4}}{6 x^{6}}"," ",0,"(-a**2 - 3*a*b*x**2 - 3*b**2*x**4)/(6*x**6)","A",0
26,1,27,0,0.196946," ","integrate((b*x**2+a)**2/x**8,x)","\frac{- 15 a^{2} - 42 a b x^{2} - 35 b^{2} x^{4}}{105 x^{7}}"," ",0,"(-15*a**2 - 42*a*b*x**2 - 35*b**2*x**4)/(105*x**7)","A",0
27,1,27,0,0.208681," ","integrate((b*x**2+a)**2/x**9,x)","\frac{- 3 a^{2} - 8 a b x^{2} - 6 b^{2} x^{4}}{24 x^{8}}"," ",0,"(-3*a**2 - 8*a*b*x**2 - 6*b**2*x**4)/(24*x**8)","A",0
28,1,27,0,0.219575," ","integrate((b*x**2+a)**2/x**10,x)","\frac{- 35 a^{2} - 90 a b x^{2} - 63 b^{2} x^{4}}{315 x^{9}}"," ",0,"(-35*a**2 - 90*a*b*x**2 - 63*b**2*x**4)/(315*x**9)","A",0
29,1,37,0,0.069192," ","integrate(x**9*(b*x**2+a)**3,x)","\frac{a^{3} x^{10}}{10} + \frac{a^{2} b x^{12}}{4} + \frac{3 a b^{2} x^{14}}{14} + \frac{b^{3} x^{16}}{16}"," ",0,"a**3*x**10/10 + a**2*b*x**12/4 + 3*a*b**2*x**14/14 + b**3*x**16/16","A",0
30,1,37,0,0.069507," ","integrate(x**7*(b*x**2+a)**3,x)","\frac{a^{3} x^{8}}{8} + \frac{3 a^{2} b x^{10}}{10} + \frac{a b^{2} x^{12}}{4} + \frac{b^{3} x^{14}}{14}"," ",0,"a**3*x**8/8 + 3*a**2*b*x**10/10 + a*b**2*x**12/4 + b**3*x**14/14","A",0
31,1,39,0,0.068278," ","integrate(x**5*(b*x**2+a)**3,x)","\frac{a^{3} x^{6}}{6} + \frac{3 a^{2} b x^{8}}{8} + \frac{3 a b^{2} x^{10}}{10} + \frac{b^{3} x^{12}}{12}"," ",0,"a**3*x**6/6 + 3*a**2*b*x**8/8 + 3*a*b**2*x**10/10 + b**3*x**12/12","A",0
32,1,37,0,0.068542," ","integrate(x**3*(b*x**2+a)**3,x)","\frac{a^{3} x^{4}}{4} + \frac{a^{2} b x^{6}}{2} + \frac{3 a b^{2} x^{8}}{8} + \frac{b^{3} x^{10}}{10}"," ",0,"a**3*x**4/4 + a**2*b*x**6/2 + 3*a*b**2*x**8/8 + b**3*x**10/10","A",0
33,1,37,0,0.068126," ","integrate(x*(b*x**2+a)**3,x)","\frac{a^{3} x^{2}}{2} + \frac{3 a^{2} b x^{4}}{4} + \frac{a b^{2} x^{6}}{2} + \frac{b^{3} x^{8}}{8}"," ",0,"a**3*x**2/2 + 3*a**2*b*x**4/4 + a*b**2*x**6/2 + b**3*x**8/8","B",0
34,1,37,0,0.109245," ","integrate((b*x**2+a)**3/x,x)","a^{3} \log{\left(x \right)} + \frac{3 a^{2} b x^{2}}{2} + \frac{3 a b^{2} x^{4}}{4} + \frac{b^{3} x^{6}}{6}"," ",0,"a**3*log(x) + 3*a**2*b*x**2/2 + 3*a*b**2*x**4/4 + b**3*x**6/6","A",0
35,1,37,0,0.140315," ","integrate((b*x**2+a)**3/x**3,x)","- \frac{a^{3}}{2 x^{2}} + 3 a^{2} b \log{\left(x \right)} + \frac{3 a b^{2} x^{2}}{2} + \frac{b^{3} x^{4}}{4}"," ",0,"-a**3/(2*x**2) + 3*a**2*b*log(x) + 3*a*b**2*x**2/2 + b**3*x**4/4","A",0
36,1,37,0,0.190286," ","integrate((b*x**2+a)**3/x**5,x)","3 a b^{2} \log{\left(x \right)} + \frac{b^{3} x^{2}}{2} + \frac{- a^{3} - 6 a^{2} b x^{2}}{4 x^{4}}"," ",0,"3*a*b**2*log(x) + b**3*x**2/2 + (-a**3 - 6*a**2*b*x**2)/(4*x**4)","A",0
37,1,37,0,0.241461," ","integrate((b*x**2+a)**3/x**7,x)","b^{3} \log{\left(x \right)} + \frac{- 2 a^{3} - 9 a^{2} b x^{2} - 18 a b^{2} x^{4}}{12 x^{6}}"," ",0,"b**3*log(x) + (-2*a**3 - 9*a**2*b*x**2 - 18*a*b**2*x**4)/(12*x**6)","A",0
38,1,37,0,0.266338," ","integrate((b*x**2+a)**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}}"," ",0,"(-a**3 - 4*a**2*b*x**2 - 6*a*b**2*x**4 - 4*b**3*x**6)/(8*x**8)","B",0
39,1,39,0,0.291954," ","integrate((b*x**2+a)**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}}"," ",0,"(-4*a**3 - 15*a**2*b*x**2 - 20*a*b**2*x**4 - 10*b**3*x**6)/(40*x**10)","A",0
40,1,39,0,0.318928," ","integrate((b*x**2+a)**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}}"," ",0,"(-10*a**3 - 36*a**2*b*x**2 - 45*a*b**2*x**4 - 20*b**3*x**6)/(120*x**12)","A",0
41,1,39,0,0.346428," ","integrate((b*x**2+a)**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}}"," ",0,"(-20*a**3 - 70*a**2*b*x**2 - 84*a*b**2*x**4 - 35*b**3*x**6)/(280*x**14)","A",0
42,1,37,0,0.068292," ","integrate(x**6*(b*x**2+a)**3,x)","\frac{a^{3} x^{7}}{7} + \frac{a^{2} b x^{9}}{3} + \frac{3 a b^{2} x^{11}}{11} + \frac{b^{3} x^{13}}{13}"," ",0,"a**3*x**7/7 + a**2*b*x**9/3 + 3*a*b**2*x**11/11 + b**3*x**13/13","A",0
43,1,37,0,0.068222," ","integrate(x**4*(b*x**2+a)**3,x)","\frac{a^{3} x^{5}}{5} + \frac{3 a^{2} b x^{7}}{7} + \frac{a b^{2} x^{9}}{3} + \frac{b^{3} x^{11}}{11}"," ",0,"a**3*x**5/5 + 3*a**2*b*x**7/7 + a*b**2*x**9/3 + b**3*x**11/11","A",0
44,1,39,0,0.067482," ","integrate(x**2*(b*x**2+a)**3,x)","\frac{a^{3} x^{3}}{3} + \frac{3 a^{2} b x^{5}}{5} + \frac{3 a b^{2} x^{7}}{7} + \frac{b^{3} x^{9}}{9}"," ",0,"a**3*x**3/3 + 3*a**2*b*x**5/5 + 3*a*b**2*x**7/7 + b**3*x**9/9","A",0
45,1,32,0,0.064892," ","integrate((b*x**2+a)**3,x)","a^{3} x + a^{2} b x^{3} + \frac{3 a b^{2} x^{5}}{5} + \frac{b^{3} x^{7}}{7}"," ",0,"a**3*x + a**2*b*x**3 + 3*a*b**2*x**5/5 + b**3*x**7/7","A",0
46,1,29,0,0.105439," ","integrate((b*x**2+a)**3/x**2,x)","- \frac{a^{3}}{x} + 3 a^{2} b x + a b^{2} x^{3} + \frac{b^{3} x^{5}}{5}"," ",0,"-a**3/x + 3*a**2*b*x + a*b**2*x**3 + b**3*x**5/5","A",0
47,1,36,0,0.148414," ","integrate((b*x**2+a)**3/x**4,x)","3 a b^{2} x + \frac{b^{3} x^{3}}{3} + \frac{- a^{3} - 9 a^{2} b x^{2}}{3 x^{3}}"," ",0,"3*a*b**2*x + b**3*x**3/3 + (-a**3 - 9*a**2*b*x**2)/(3*x**3)","A",0
48,1,34,0,0.196671," ","integrate((b*x**2+a)**3/x**6,x)","b^{3} x + \frac{- a^{3} - 5 a^{2} b x^{2} - 15 a b^{2} x^{4}}{5 x^{5}}"," ",0,"b**3*x + (-a**3 - 5*a**2*b*x**2 - 15*a*b**2*x**4)/(5*x**5)","A",0
49,1,39,0,0.256348," ","integrate((b*x**2+a)**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}}"," ",0,"(-5*a**3 - 21*a**2*b*x**2 - 35*a*b**2*x**4 - 35*b**3*x**6)/(35*x**7)","A",0
50,1,39,0,0.273279," ","integrate((b*x**2+a)**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}}"," ",0,"(-35*a**3 - 135*a**2*b*x**2 - 189*a*b**2*x**4 - 105*b**3*x**6)/(315*x**9)","A",0
51,1,39,0,0.302799," ","integrate((b*x**2+a)**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}}"," ",0,"(-105*a**3 - 385*a**2*b*x**2 - 495*a*b**2*x**4 - 231*b**3*x**6)/(1155*x**11)","A",0
52,1,65,0,0.077735," ","integrate(x**13*(b*x**2+a)**5,x)","\frac{a^{5} x^{14}}{14} + \frac{5 a^{4} b x^{16}}{16} + \frac{5 a^{3} b^{2} x^{18}}{9} + \frac{a^{2} b^{3} x^{20}}{2} + \frac{5 a b^{4} x^{22}}{22} + \frac{b^{5} x^{24}}{24}"," ",0,"a**5*x**14/14 + 5*a**4*b*x**16/16 + 5*a**3*b**2*x**18/9 + a**2*b**3*x**20/2 + 5*a*b**4*x**22/22 + b**5*x**24/24","A",0
53,1,65,0,0.078156," ","integrate(x**11*(b*x**2+a)**5,x)","\frac{a^{5} x^{12}}{12} + \frac{5 a^{4} b x^{14}}{14} + \frac{5 a^{3} b^{2} x^{16}}{8} + \frac{5 a^{2} b^{3} x^{18}}{9} + \frac{a b^{4} x^{20}}{4} + \frac{b^{5} x^{22}}{22}"," ",0,"a**5*x**12/12 + 5*a**4*b*x**14/14 + 5*a**3*b**2*x**16/8 + 5*a**2*b**3*x**18/9 + a*b**4*x**20/4 + b**5*x**22/22","A",0
54,1,66,0,0.080144," ","integrate(x**9*(b*x**2+a)**5,x)","\frac{a^{5} x^{10}}{10} + \frac{5 a^{4} b x^{12}}{12} + \frac{5 a^{3} b^{2} x^{14}}{7} + \frac{5 a^{2} b^{3} x^{16}}{8} + \frac{5 a b^{4} x^{18}}{18} + \frac{b^{5} x^{20}}{20}"," ",0,"a**5*x**10/10 + 5*a**4*b*x**12/12 + 5*a**3*b**2*x**14/7 + 5*a**2*b**3*x**16/8 + 5*a*b**4*x**18/18 + b**5*x**20/20","A",0
55,1,65,0,0.092993," ","integrate(x**7*(b*x**2+a)**5,x)","\frac{a^{5} x^{8}}{8} + \frac{a^{4} b x^{10}}{2} + \frac{5 a^{3} b^{2} x^{12}}{6} + \frac{5 a^{2} b^{3} x^{14}}{7} + \frac{5 a b^{4} x^{16}}{16} + \frac{b^{5} x^{18}}{18}"," ",0,"a**5*x**8/8 + a**4*b*x**10/2 + 5*a**3*b**2*x**12/6 + 5*a**2*b**3*x**14/7 + 5*a*b**4*x**16/16 + b**5*x**18/18","A",0
56,1,63,0,0.077372," ","integrate(x**5*(b*x**2+a)**5,x)","\frac{a^{5} x^{6}}{6} + \frac{5 a^{4} b x^{8}}{8} + a^{3} b^{2} x^{10} + \frac{5 a^{2} b^{3} x^{12}}{6} + \frac{5 a b^{4} x^{14}}{14} + \frac{b^{5} x^{16}}{16}"," ",0,"a**5*x**6/6 + 5*a**4*b*x**8/8 + a**3*b**2*x**10 + 5*a**2*b**3*x**12/6 + 5*a*b**4*x**14/14 + b**5*x**16/16","A",0
57,1,63,0,0.076823," ","integrate(x**3*(b*x**2+a)**5,x)","\frac{a^{5} x^{4}}{4} + \frac{5 a^{4} b x^{6}}{6} + \frac{5 a^{3} b^{2} x^{8}}{4} + a^{2} b^{3} x^{10} + \frac{5 a b^{4} x^{12}}{12} + \frac{b^{5} x^{14}}{14}"," ",0,"a**5*x**4/4 + 5*a**4*b*x**6/6 + 5*a**3*b**2*x**8/4 + a**2*b**3*x**10 + 5*a*b**4*x**12/12 + b**5*x**14/14","B",0
58,1,65,0,0.077178," ","integrate(x*(b*x**2+a)**5,x)","\frac{a^{5} x^{2}}{2} + \frac{5 a^{4} b x^{4}}{4} + \frac{5 a^{3} b^{2} x^{6}}{3} + \frac{5 a^{2} b^{3} x^{8}}{4} + \frac{a b^{4} x^{10}}{2} + \frac{b^{5} x^{12}}{12}"," ",0,"a**5*x**2/2 + 5*a**4*b*x**4/4 + 5*a**3*b**2*x**6/3 + 5*a**2*b**3*x**8/4 + a*b**4*x**10/2 + b**5*x**12/12","B",0
59,1,65,0,0.135531," ","integrate((b*x**2+a)**5/x,x)","a^{5} \log{\left(x \right)} + \frac{5 a^{4} b x^{2}}{2} + \frac{5 a^{3} b^{2} x^{4}}{2} + \frac{5 a^{2} b^{3} x^{6}}{3} + \frac{5 a b^{4} x^{8}}{8} + \frac{b^{5} x^{10}}{10}"," ",0,"a**5*log(x) + 5*a**4*b*x**2/2 + 5*a**3*b**2*x**4/2 + 5*a**2*b**3*x**6/3 + 5*a*b**4*x**8/8 + b**5*x**10/10","A",0
60,1,63,0,0.168997," ","integrate((b*x**2+a)**5/x**3,x)","- \frac{a^{5}}{2 x^{2}} + 5 a^{4} b \log{\left(x \right)} + 5 a^{3} b^{2} x^{2} + \frac{5 a^{2} b^{3} x^{4}}{2} + \frac{5 a b^{4} x^{6}}{6} + \frac{b^{5} x^{8}}{8}"," ",0,"-a**5/(2*x**2) + 5*a**4*b*log(x) + 5*a**3*b**2*x**2 + 5*a**2*b**3*x**4/2 + 5*a*b**4*x**6/6 + b**5*x**8/8","A",0
61,1,63,0,0.222685," ","integrate((b*x**2+a)**5/x**5,x)","10 a^{3} b^{2} \log{\left(x \right)} + 5 a^{2} b^{3} x^{2} + \frac{5 a b^{4} x^{4}}{4} + \frac{b^{5} x^{6}}{6} + \frac{- a^{5} - 10 a^{4} b x^{2}}{4 x^{4}}"," ",0,"10*a**3*b**2*log(x) + 5*a**2*b**3*x**2 + 5*a*b**4*x**4/4 + b**5*x**6/6 + (-a**5 - 10*a**4*b*x**2)/(4*x**4)","A",0
62,1,65,0,0.282670," ","integrate((b*x**2+a)**5/x**7,x)","10 a^{2} b^{3} \log{\left(x \right)} + \frac{5 a b^{4} x^{2}}{2} + \frac{b^{5} x^{4}}{4} + \frac{- 2 a^{5} - 15 a^{4} b x^{2} - 60 a^{3} b^{2} x^{4}}{12 x^{6}}"," ",0,"10*a**2*b**3*log(x) + 5*a*b**4*x**2/2 + b**5*x**4/4 + (-2*a**5 - 15*a**4*b*x**2 - 60*a**3*b**2*x**4)/(12*x**6)","A",0
63,1,63,0,0.361771," ","integrate((b*x**2+a)**5/x**9,x)","5 a b^{4} \log{\left(x \right)} + \frac{b^{5} x^{2}}{2} + \frac{- 3 a^{5} - 20 a^{4} b x^{2} - 60 a^{3} b^{2} x^{4} - 120 a^{2} b^{3} x^{6}}{24 x^{8}}"," ",0,"5*a*b**4*log(x) + b**5*x**2/2 + (-3*a**5 - 20*a**4*b*x**2 - 60*a**3*b**2*x**4 - 120*a**2*b**3*x**6)/(24*x**8)","A",0
64,1,61,0,0.440187," ","integrate((b*x**2+a)**5/x**11,x)","b^{5} \log{\left(x \right)} + \frac{- 12 a^{5} - 75 a^{4} b x^{2} - 200 a^{3} b^{2} x^{4} - 300 a^{2} b^{3} x^{6} - 300 a b^{4} x^{8}}{120 x^{10}}"," ",0,"b**5*log(x) + (-12*a**5 - 75*a**4*b*x**2 - 200*a**3*b**2*x**4 - 300*a**2*b**3*x**6 - 300*a*b**4*x**8)/(120*x**10)","A",0
65,1,61,0,0.473627," ","integrate((b*x**2+a)**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}}"," ",0,"(-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",0
66,1,63,0,0.505940," ","integrate((b*x**2+a)**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}}"," ",0,"(-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",0
67,1,63,0,0.550355," ","integrate((b*x**2+a)**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}}"," ",0,"(-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",0
68,1,63,0,0.591389," ","integrate((b*x**2+a)**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}}"," ",0,"(-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",0
69,1,63,0,0.627965," ","integrate((b*x**2+a)**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}}"," ",0,"(-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",0
70,1,66,0,0.077329," ","integrate(x**8*(b*x**2+a)**5,x)","\frac{a^{5} x^{9}}{9} + \frac{5 a^{4} b x^{11}}{11} + \frac{10 a^{3} b^{2} x^{13}}{13} + \frac{2 a^{2} b^{3} x^{15}}{3} + \frac{5 a b^{4} x^{17}}{17} + \frac{b^{5} x^{19}}{19}"," ",0,"a**5*x**9/9 + 5*a**4*b*x**11/11 + 10*a**3*b**2*x**13/13 + 2*a**2*b**3*x**15/3 + 5*a*b**4*x**17/17 + b**5*x**19/19","A",0
71,1,65,0,0.076615," ","integrate(x**6*(b*x**2+a)**5,x)","\frac{a^{5} x^{7}}{7} + \frac{5 a^{4} b x^{9}}{9} + \frac{10 a^{3} b^{2} x^{11}}{11} + \frac{10 a^{2} b^{3} x^{13}}{13} + \frac{a b^{4} x^{15}}{3} + \frac{b^{5} x^{17}}{17}"," ",0,"a**5*x**7/7 + 5*a**4*b*x**9/9 + 10*a**3*b**2*x**11/11 + 10*a**2*b**3*x**13/13 + a*b**4*x**15/3 + b**5*x**17/17","A",0
72,1,66,0,0.075501," ","integrate(x**4*(b*x**2+a)**5,x)","\frac{a^{5} x^{5}}{5} + \frac{5 a^{4} b x^{7}}{7} + \frac{10 a^{3} b^{2} x^{9}}{9} + \frac{10 a^{2} b^{3} x^{11}}{11} + \frac{5 a b^{4} x^{13}}{13} + \frac{b^{5} x^{15}}{15}"," ",0,"a**5*x**5/5 + 5*a**4*b*x**7/7 + 10*a**3*b**2*x**9/9 + 10*a**2*b**3*x**11/11 + 5*a*b**4*x**13/13 + b**5*x**15/15","A",0
73,1,63,0,0.075947," ","integrate(x**2*(b*x**2+a)**5,x)","\frac{a^{5} x^{3}}{3} + a^{4} b x^{5} + \frac{10 a^{3} b^{2} x^{7}}{7} + \frac{10 a^{2} b^{3} x^{9}}{9} + \frac{5 a b^{4} x^{11}}{11} + \frac{b^{5} x^{13}}{13}"," ",0,"a**5*x**3/3 + a**4*b*x**5 + 10*a**3*b**2*x**7/7 + 10*a**2*b**3*x**9/9 + 5*a*b**4*x**11/11 + b**5*x**13/13","A",0
74,1,61,0,0.072483," ","integrate((b*x**2+a)**5,x)","a^{5} x + \frac{5 a^{4} b x^{3}}{3} + 2 a^{3} b^{2} x^{5} + \frac{10 a^{2} b^{3} x^{7}}{7} + \frac{5 a b^{4} x^{9}}{9} + \frac{b^{5} x^{11}}{11}"," ",0,"a**5*x + 5*a**4*b*x**3/3 + 2*a**3*b**2*x**5 + 10*a**2*b**3*x**7/7 + 5*a*b**4*x**9/9 + b**5*x**11/11","A",0
75,1,58,0,0.131927," ","integrate((b*x**2+a)**5/x**2,x)","- \frac{a^{5}}{x} + 5 a^{4} b x + \frac{10 a^{3} b^{2} x^{3}}{3} + 2 a^{2} b^{3} x^{5} + \frac{5 a b^{4} x^{7}}{7} + \frac{b^{5} x^{9}}{9}"," ",0,"-a**5/x + 5*a**4*b*x + 10*a**3*b**2*x**3/3 + 2*a**2*b**3*x**5 + 5*a*b**4*x**7/7 + b**5*x**9/9","A",0
76,1,60,0,0.173707," ","integrate((b*x**2+a)**5/x**4,x)","10 a^{3} b^{2} x + \frac{10 a^{2} b^{3} x^{3}}{3} + a b^{4} x^{5} + \frac{b^{5} x^{7}}{7} + \frac{- a^{5} - 15 a^{4} b x^{2}}{3 x^{3}}"," ",0,"10*a**3*b**2*x + 10*a**2*b**3*x**3/3 + a*b**4*x**5 + b**5*x**7/7 + (-a**5 - 15*a**4*b*x**2)/(3*x**3)","A",0
77,1,63,0,0.226650," ","integrate((b*x**2+a)**5/x**6,x)","10 a^{2} b^{3} x + \frac{5 a b^{4} x^{3}}{3} + \frac{b^{5} x^{5}}{5} + \frac{- 3 a^{5} - 25 a^{4} b x^{2} - 150 a^{3} b^{2} x^{4}}{15 x^{5}}"," ",0,"10*a**2*b**3*x + 5*a*b**4*x**3/3 + b**5*x**5/5 + (-3*a**5 - 25*a**4*b*x**2 - 150*a**3*b**2*x**4)/(15*x**5)","A",0
78,1,61,0,0.293986," ","integrate((b*x**2+a)**5/x**8,x)","5 a b^{4} x + \frac{b^{5} x^{3}}{3} + \frac{- 3 a^{5} - 21 a^{4} b x^{2} - 70 a^{3} b^{2} x^{4} - 210 a^{2} b^{3} x^{6}}{21 x^{7}}"," ",0,"5*a*b**4*x + b**5*x**3/3 + (-3*a**5 - 21*a**4*b*x**2 - 70*a**3*b**2*x**4 - 210*a**2*b**3*x**6)/(21*x**7)","A",0
79,1,60,0,0.361818," ","integrate((b*x**2+a)**5/x**10,x)","b^{5} 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 x^{9}}"," ",0,"b**5*x + (-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*x**9)","A",0
80,1,63,0,0.431474," ","integrate((b*x**2+a)**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}}"," ",0,"(-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",0
81,1,63,0,0.469246," ","integrate((b*x**2+a)**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}}"," ",0,"(-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",0
82,1,63,0,0.505011," ","integrate((b*x**2+a)**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}}"," ",0,"(-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",0
83,1,63,0,0.535823," ","integrate((b*x**2+a)**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}}"," ",0,"(-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",0
84,1,63,0,0.567247," ","integrate((b*x**2+a)**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}}"," ",0,"(-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",0
85,1,105,0,0.088303," ","integrate(x**13*(b*x**2+a)**8,x)","\frac{a^{8} x^{14}}{14} + \frac{a^{7} b x^{16}}{2} + \frac{14 a^{6} b^{2} x^{18}}{9} + \frac{14 a^{5} b^{3} x^{20}}{5} + \frac{35 a^{4} b^{4} x^{22}}{11} + \frac{7 a^{3} b^{5} x^{24}}{3} + \frac{14 a^{2} b^{6} x^{26}}{13} + \frac{2 a b^{7} x^{28}}{7} + \frac{b^{8} x^{30}}{30}"," ",0,"a**8*x**14/14 + a**7*b*x**16/2 + 14*a**6*b**2*x**18/9 + 14*a**5*b**3*x**20/5 + 35*a**4*b**4*x**22/11 + 7*a**3*b**5*x**24/3 + 14*a**2*b**6*x**26/13 + 2*a*b**7*x**28/7 + b**8*x**30/30","A",0
86,1,107,0,0.088457," ","integrate(x**11*(b*x**2+a)**8,x)","\frac{a^{8} x^{12}}{12} + \frac{4 a^{7} b x^{14}}{7} + \frac{7 a^{6} b^{2} x^{16}}{4} + \frac{28 a^{5} b^{3} x^{18}}{9} + \frac{7 a^{4} b^{4} x^{20}}{2} + \frac{28 a^{3} b^{5} x^{22}}{11} + \frac{7 a^{2} b^{6} x^{24}}{6} + \frac{4 a b^{7} x^{26}}{13} + \frac{b^{8} x^{28}}{28}"," ",0,"a**8*x**12/12 + 4*a**7*b*x**14/7 + 7*a**6*b**2*x**16/4 + 28*a**5*b**3*x**18/9 + 7*a**4*b**4*x**20/2 + 28*a**3*b**5*x**22/11 + 7*a**2*b**6*x**24/6 + 4*a*b**7*x**26/13 + b**8*x**28/28","A",0
87,1,104,0,0.087247," ","integrate(x**9*(b*x**2+a)**8,x)","\frac{a^{8} x^{10}}{10} + \frac{2 a^{7} b x^{12}}{3} + 2 a^{6} b^{2} x^{14} + \frac{7 a^{5} b^{3} x^{16}}{2} + \frac{35 a^{4} b^{4} x^{18}}{9} + \frac{14 a^{3} b^{5} x^{20}}{5} + \frac{14 a^{2} b^{6} x^{22}}{11} + \frac{a b^{7} x^{24}}{3} + \frac{b^{8} x^{26}}{26}"," ",0,"a**8*x**10/10 + 2*a**7*b*x**12/3 + 2*a**6*b**2*x**14 + 7*a**5*b**3*x**16/2 + 35*a**4*b**4*x**18/9 + 14*a**3*b**5*x**20/5 + 14*a**2*b**6*x**22/11 + a*b**7*x**24/3 + b**8*x**26/26","A",0
88,1,105,0,0.087005," ","integrate(x**7*(b*x**2+a)**8,x)","\frac{a^{8} x^{8}}{8} + \frac{4 a^{7} b x^{10}}{5} + \frac{7 a^{6} b^{2} x^{12}}{3} + 4 a^{5} b^{3} x^{14} + \frac{35 a^{4} b^{4} x^{16}}{8} + \frac{28 a^{3} b^{5} x^{18}}{9} + \frac{7 a^{2} b^{6} x^{20}}{5} + \frac{4 a b^{7} x^{22}}{11} + \frac{b^{8} x^{24}}{24}"," ",0,"a**8*x**8/8 + 4*a**7*b*x**10/5 + 7*a**6*b**2*x**12/3 + 4*a**5*b**3*x**14 + 35*a**4*b**4*x**16/8 + 28*a**3*b**5*x**18/9 + 7*a**2*b**6*x**20/5 + 4*a*b**7*x**22/11 + b**8*x**24/24","A",0
89,1,102,0,0.087126," ","integrate(x**5*(b*x**2+a)**8,x)","\frac{a^{8} x^{6}}{6} + a^{7} b x^{8} + \frac{14 a^{6} b^{2} x^{10}}{5} + \frac{14 a^{5} b^{3} x^{12}}{3} + 5 a^{4} b^{4} x^{14} + \frac{7 a^{3} b^{5} x^{16}}{2} + \frac{14 a^{2} b^{6} x^{18}}{9} + \frac{2 a b^{7} x^{20}}{5} + \frac{b^{8} x^{22}}{22}"," ",0,"a**8*x**6/6 + a**7*b*x**8 + 14*a**6*b**2*x**10/5 + 14*a**5*b**3*x**12/3 + 5*a**4*b**4*x**14 + 7*a**3*b**5*x**16/2 + 14*a**2*b**6*x**18/9 + 2*a*b**7*x**20/5 + b**8*x**22/22","B",0
90,1,105,0,0.084914," ","integrate(x**3*(b*x**2+a)**8,x)","\frac{a^{8} x^{4}}{4} + \frac{4 a^{7} b x^{6}}{3} + \frac{7 a^{6} b^{2} x^{8}}{2} + \frac{28 a^{5} b^{3} x^{10}}{5} + \frac{35 a^{4} b^{4} x^{12}}{6} + 4 a^{3} b^{5} x^{14} + \frac{7 a^{2} b^{6} x^{16}}{4} + \frac{4 a b^{7} x^{18}}{9} + \frac{b^{8} x^{20}}{20}"," ",0,"a**8*x**4/4 + 4*a**7*b*x**6/3 + 7*a**6*b**2*x**8/2 + 28*a**5*b**3*x**10/5 + 35*a**4*b**4*x**12/6 + 4*a**3*b**5*x**14 + 7*a**2*b**6*x**16/4 + 4*a*b**7*x**18/9 + b**8*x**20/20","B",0
91,1,99,0,0.084448," ","integrate(x*(b*x**2+a)**8,x)","\frac{a^{8} x^{2}}{2} + 2 a^{7} b x^{4} + \frac{14 a^{6} b^{2} x^{6}}{3} + 7 a^{5} b^{3} x^{8} + 7 a^{4} b^{4} x^{10} + \frac{14 a^{3} b^{5} x^{12}}{3} + 2 a^{2} b^{6} x^{14} + \frac{a b^{7} x^{16}}{2} + \frac{b^{8} x^{18}}{18}"," ",0,"a**8*x**2/2 + 2*a**7*b*x**4 + 14*a**6*b**2*x**6/3 + 7*a**5*b**3*x**8 + 7*a**4*b**4*x**10 + 14*a**3*b**5*x**12/3 + 2*a**2*b**6*x**14 + a*b**7*x**16/2 + b**8*x**18/18","B",0
92,1,102,0,0.182932," ","integrate((b*x**2+a)**8/x,x)","a^{8} \log{\left(x \right)} + 4 a^{7} b x^{2} + 7 a^{6} b^{2} x^{4} + \frac{28 a^{5} b^{3} x^{6}}{3} + \frac{35 a^{4} b^{4} x^{8}}{4} + \frac{28 a^{3} b^{5} x^{10}}{5} + \frac{7 a^{2} b^{6} x^{12}}{3} + \frac{4 a b^{7} x^{14}}{7} + \frac{b^{8} x^{16}}{16}"," ",0,"a**8*log(x) + 4*a**7*b*x**2 + 7*a**6*b**2*x**4 + 28*a**5*b**3*x**6/3 + 35*a**4*b**4*x**8/4 + 28*a**3*b**5*x**10/5 + 7*a**2*b**6*x**12/3 + 4*a*b**7*x**14/7 + b**8*x**16/16","A",0
93,1,100,0,0.217247," ","integrate((b*x**2+a)**8/x**3,x)","- \frac{a^{8}}{2 x^{2}} + 8 a^{7} b \log{\left(x \right)} + 14 a^{6} b^{2} x^{2} + 14 a^{5} b^{3} x^{4} + \frac{35 a^{4} b^{4} x^{6}}{3} + 7 a^{3} b^{5} x^{8} + \frac{14 a^{2} b^{6} x^{10}}{5} + \frac{2 a b^{7} x^{12}}{3} + \frac{b^{8} x^{14}}{14}"," ",0,"-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 + 35*a**4*b**4*x**6/3 + 7*a**3*b**5*x**8 + 14*a**2*b**6*x**10/5 + 2*a*b**7*x**12/3 + b**8*x**14/14","A",0
94,1,104,0,0.270547," ","integrate((b*x**2+a)**8/x**5,x)","28 a^{6} b^{2} \log{\left(x \right)} + 28 a^{5} b^{3} x^{2} + \frac{35 a^{4} b^{4} x^{4}}{2} + \frac{28 a^{3} b^{5} x^{6}}{3} + \frac{7 a^{2} b^{6} x^{8}}{2} + \frac{4 a b^{7} x^{10}}{5} + \frac{b^{8} x^{12}}{12} + \frac{- a^{8} - 16 a^{7} b x^{2}}{4 x^{4}}"," ",0,"28*a**6*b**2*log(x) + 28*a**5*b**3*x**2 + 35*a**4*b**4*x**4/2 + 28*a**3*b**5*x**6/3 + 7*a**2*b**6*x**8/2 + 4*a*b**7*x**10/5 + b**8*x**12/12 + (-a**8 - 16*a**7*b*x**2)/(4*x**4)","A",0
95,1,97,0,0.333955," ","integrate((b*x**2+a)**8/x**7,x)","56 a^{5} b^{3} \log{\left(x \right)} + 35 a^{4} b^{4} x^{2} + 14 a^{3} b^{5} x^{4} + \frac{14 a^{2} b^{6} x^{6}}{3} + a b^{7} x^{8} + \frac{b^{8} x^{10}}{10} + \frac{- a^{8} - 12 a^{7} b x^{2} - 84 a^{6} b^{2} x^{4}}{6 x^{6}}"," ",0,"56*a**5*b**3*log(x) + 35*a**4*b**4*x**2 + 14*a**3*b**5*x**4 + 14*a**2*b**6*x**6/3 + a*b**7*x**8 + b**8*x**10/10 + (-a**8 - 12*a**7*b*x**2 - 84*a**6*b**2*x**4)/(6*x**6)","A",0
96,1,100,0,0.416018," ","integrate((b*x**2+a)**8/x**9,x)","70 a^{4} b^{4} \log{\left(x \right)} + 28 a^{3} b^{5} x^{2} + 7 a^{2} b^{6} x^{4} + \frac{4 a b^{7} x^{6}}{3} + \frac{b^{8} x^{8}}{8} + \frac{- 3 a^{8} - 32 a^{7} b x^{2} - 168 a^{6} b^{2} x^{4} - 672 a^{5} b^{3} x^{6}}{24 x^{8}}"," ",0,"70*a**4*b**4*log(x) + 28*a**3*b**5*x**2 + 7*a**2*b**6*x**4 + 4*a*b**7*x**6/3 + b**8*x**8/8 + (-3*a**8 - 32*a**7*b*x**2 - 168*a**6*b**2*x**4 - 672*a**5*b**3*x**6)/(24*x**8)","A",0
97,1,99,0,0.507461," ","integrate((b*x**2+a)**8/x**11,x)","56 a^{3} b^{5} \log{\left(x \right)} + 14 a^{2} b^{6} x^{2} + 2 a b^{7} x^{4} + \frac{b^{8} x^{6}}{6} + \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}}{30 x^{10}}"," ",0,"56*a**3*b**5*log(x) + 14*a**2*b**6*x**2 + 2*a*b**7*x**4 + b**8*x**6/6 + (-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)/(30*x**10)","A",0
98,1,99,0,0.617970," ","integrate((b*x**2+a)**8/x**13,x)","28 a^{2} b^{6} \log{\left(x \right)} + 4 a b^{7} x^{2} + \frac{b^{8} x^{4}}{4} + \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}}{60 x^{12}}"," ",0,"28*a**2*b**6*log(x) + 4*a*b**7*x**2 + b**8*x**4/4 + (-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)/(60*x**12)","A",0
99,1,99,0,0.732779," ","integrate((b*x**2+a)**8/x**15,x)","8 a b^{7} \log{\left(x \right)} + \frac{b^{8} x^{2}}{2} + \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}}{210 x^{14}}"," ",0,"8*a*b**7*log(x) + b**8*x**2/2 + (-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)/(210*x**14)","A",0
100,1,97,0,0.832821," ","integrate((b*x**2+a)**8/x**17,x)","b^{8} \log{\left(x \right)} + \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}}"," ",0,"b**8*log(x) + (-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)","A",0
101,1,97,0,0.895976," ","integrate((b*x**2+a)**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}}"," ",0,"(-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",0
102,1,99,0,0.937201," ","integrate((b*x**2+a)**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}}"," ",0,"(-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",0
103,1,99,0,0.992465," ","integrate((b*x**2+a)**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}}"," ",0,"(-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",0
104,1,99,0,1.077777," ","integrate((b*x**2+a)**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}}"," ",0,"(-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",0
105,1,99,0,1.141332," ","integrate((b*x**2+a)**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}}"," ",0,"(-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",0
106,1,99,0,1.204643," ","integrate((b*x**2+a)**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}}"," ",0,"(-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",0
107,1,99,0,1.280761," ","integrate((b*x**2+a)**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}}"," ",0,"(-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",0
108,1,99,0,1.335754," ","integrate((b*x**2+a)**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}}"," ",0,"(-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",0
109,1,107,0,0.088496," ","integrate(x**8*(b*x**2+a)**8,x)","\frac{a^{8} x^{9}}{9} + \frac{8 a^{7} b x^{11}}{11} + \frac{28 a^{6} b^{2} x^{13}}{13} + \frac{56 a^{5} b^{3} x^{15}}{15} + \frac{70 a^{4} b^{4} x^{17}}{17} + \frac{56 a^{3} b^{5} x^{19}}{19} + \frac{4 a^{2} b^{6} x^{21}}{3} + \frac{8 a b^{7} x^{23}}{23} + \frac{b^{8} x^{25}}{25}"," ",0,"a**8*x**9/9 + 8*a**7*b*x**11/11 + 28*a**6*b**2*x**13/13 + 56*a**5*b**3*x**15/15 + 70*a**4*b**4*x**17/17 + 56*a**3*b**5*x**19/19 + 4*a**2*b**6*x**21/3 + 8*a*b**7*x**23/23 + b**8*x**25/25","A",0
110,1,107,0,0.086909," ","integrate(x**6*(b*x**2+a)**8,x)","\frac{a^{8} x^{7}}{7} + \frac{8 a^{7} b x^{9}}{9} + \frac{28 a^{6} b^{2} x^{11}}{11} + \frac{56 a^{5} b^{3} x^{13}}{13} + \frac{14 a^{4} b^{4} x^{15}}{3} + \frac{56 a^{3} b^{5} x^{17}}{17} + \frac{28 a^{2} b^{6} x^{19}}{19} + \frac{8 a b^{7} x^{21}}{21} + \frac{b^{8} x^{23}}{23}"," ",0,"a**8*x**7/7 + 8*a**7*b*x**9/9 + 28*a**6*b**2*x**11/11 + 56*a**5*b**3*x**13/13 + 14*a**4*b**4*x**15/3 + 56*a**3*b**5*x**17/17 + 28*a**2*b**6*x**19/19 + 8*a*b**7*x**21/21 + b**8*x**23/23","A",0
111,1,107,0,0.086371," ","integrate(x**4*(b*x**2+a)**8,x)","\frac{a^{8} x^{5}}{5} + \frac{8 a^{7} b x^{7}}{7} + \frac{28 a^{6} b^{2} x^{9}}{9} + \frac{56 a^{5} b^{3} x^{11}}{11} + \frac{70 a^{4} b^{4} x^{13}}{13} + \frac{56 a^{3} b^{5} x^{15}}{15} + \frac{28 a^{2} b^{6} x^{17}}{17} + \frac{8 a b^{7} x^{19}}{19} + \frac{b^{8} x^{21}}{21}"," ",0,"a**8*x**5/5 + 8*a**7*b*x**7/7 + 28*a**6*b**2*x**9/9 + 56*a**5*b**3*x**11/11 + 70*a**4*b**4*x**13/13 + 56*a**3*b**5*x**15/15 + 28*a**2*b**6*x**17/17 + 8*a*b**7*x**19/19 + b**8*x**21/21","A",0
112,1,105,0,0.085469," ","integrate(x**2*(b*x**2+a)**8,x)","\frac{a^{8} x^{3}}{3} + \frac{8 a^{7} b x^{5}}{5} + 4 a^{6} b^{2} x^{7} + \frac{56 a^{5} b^{3} x^{9}}{9} + \frac{70 a^{4} b^{4} x^{11}}{11} + \frac{56 a^{3} b^{5} x^{13}}{13} + \frac{28 a^{2} b^{6} x^{15}}{15} + \frac{8 a b^{7} x^{17}}{17} + \frac{b^{8} x^{19}}{19}"," ",0,"a**8*x**3/3 + 8*a**7*b*x**5/5 + 4*a**6*b**2*x**7 + 56*a**5*b**3*x**9/9 + 70*a**4*b**4*x**11/11 + 56*a**3*b**5*x**13/13 + 28*a**2*b**6*x**15/15 + 8*a*b**7*x**17/17 + b**8*x**19/19","A",0
113,1,102,0,0.083296," ","integrate((b*x**2+a)**8,x)","a^{8} x + \frac{8 a^{7} b x^{3}}{3} + \frac{28 a^{6} b^{2} x^{5}}{5} + 8 a^{5} b^{3} x^{7} + \frac{70 a^{4} b^{4} x^{9}}{9} + \frac{56 a^{3} b^{5} x^{11}}{11} + \frac{28 a^{2} b^{6} x^{13}}{13} + \frac{8 a b^{7} x^{15}}{15} + \frac{b^{8} x^{17}}{17}"," ",0,"a**8*x + 8*a**7*b*x**3/3 + 28*a**6*b**2*x**5/5 + 8*a**5*b**3*x**7 + 70*a**4*b**4*x**9/9 + 56*a**3*b**5*x**11/11 + 28*a**2*b**6*x**13/13 + 8*a*b**7*x**15/15 + b**8*x**17/17","A",0
114,1,99,0,0.179123," ","integrate((b*x**2+a)**8/x**2,x)","- \frac{a^{8}}{x} + 8 a^{7} b x + \frac{28 a^{6} b^{2} x^{3}}{3} + \frac{56 a^{5} b^{3} x^{5}}{5} + 10 a^{4} b^{4} x^{7} + \frac{56 a^{3} b^{5} x^{9}}{9} + \frac{28 a^{2} b^{6} x^{11}}{11} + \frac{8 a b^{7} x^{13}}{13} + \frac{b^{8} x^{15}}{15}"," ",0,"-a**8/x + 8*a**7*b*x + 28*a**6*b**2*x**3/3 + 56*a**5*b**3*x**5/5 + 10*a**4*b**4*x**7 + 56*a**3*b**5*x**9/9 + 28*a**2*b**6*x**11/11 + 8*a*b**7*x**13/13 + b**8*x**15/15","A",0
115,1,100,0,0.222509," ","integrate((b*x**2+a)**8/x**4,x)","28 a^{6} b^{2} x + \frac{56 a^{5} b^{3} x^{3}}{3} + 14 a^{4} b^{4} x^{5} + 8 a^{3} b^{5} x^{7} + \frac{28 a^{2} b^{6} x^{9}}{9} + \frac{8 a b^{7} x^{11}}{11} + \frac{b^{8} x^{13}}{13} + \frac{- a^{8} - 24 a^{7} b x^{2}}{3 x^{3}}"," ",0,"28*a**6*b**2*x + 56*a**5*b**3*x**3/3 + 14*a**4*b**4*x**5 + 8*a**3*b**5*x**7 + 28*a**2*b**6*x**9/9 + 8*a*b**7*x**11/11 + b**8*x**13/13 + (-a**8 - 24*a**7*b*x**2)/(3*x**3)","A",0
116,1,102,0,0.275353," ","integrate((b*x**2+a)**8/x**6,x)","56 a^{5} b^{3} x + \frac{70 a^{4} b^{4} x^{3}}{3} + \frac{56 a^{3} b^{5} x^{5}}{5} + 4 a^{2} b^{6} x^{7} + \frac{8 a b^{7} x^{9}}{9} + \frac{b^{8} x^{11}}{11} + \frac{- 3 a^{8} - 40 a^{7} b x^{2} - 420 a^{6} b^{2} x^{4}}{15 x^{5}}"," ",0,"56*a**5*b**3*x + 70*a**4*b**4*x**3/3 + 56*a**3*b**5*x**5/5 + 4*a**2*b**6*x**7 + 8*a*b**7*x**9/9 + b**8*x**11/11 + (-3*a**8 - 40*a**7*b*x**2 - 420*a**6*b**2*x**4)/(15*x**5)","A",0
117,1,102,0,0.332542," ","integrate((b*x**2+a)**8/x**8,x)","70 a^{4} b^{4} x + \frac{56 a^{3} b^{5} x^{3}}{3} + \frac{28 a^{2} b^{6} x^{5}}{5} + \frac{8 a b^{7} x^{7}}{7} + \frac{b^{8} x^{9}}{9} + \frac{- 15 a^{8} - 168 a^{7} b x^{2} - 980 a^{6} b^{2} x^{4} - 5880 a^{5} b^{3} x^{6}}{105 x^{7}}"," ",0,"70*a**4*b**4*x + 56*a**3*b**5*x**3/3 + 28*a**2*b**6*x**5/5 + 8*a*b**7*x**7/7 + b**8*x**9/9 + (-15*a**8 - 168*a**7*b*x**2 - 980*a**6*b**2*x**4 - 5880*a**5*b**3*x**6)/(105*x**7)","A",0
118,1,100,0,0.416819," ","integrate((b*x**2+a)**8/x**10,x)","56 a^{3} b^{5} x + \frac{28 a^{2} b^{6} x^{3}}{3} + \frac{8 a b^{7} x^{5}}{5} + \frac{b^{8} x^{7}}{7} + \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}}{315 x^{9}}"," ",0,"56*a**3*b**5*x + 28*a**2*b**6*x**3/3 + 8*a*b**7*x**5/5 + b**8*x**7/7 + (-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)/(315*x**9)","A",0
119,1,99,0,0.499215," ","integrate((b*x**2+a)**8/x**12,x)","28 a^{2} b^{6} x + \frac{8 a b^{7} x^{3}}{3} + \frac{b^{8} x^{5}}{5} + \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}}{495 x^{11}}"," ",0,"28*a**2*b**6*x + 8*a*b**7*x**3/3 + b**8*x**5/5 + (-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)/(495*x**11)","A",0
120,1,97,0,0.571229," ","integrate((b*x**2+a)**8/x**14,x)","8 a b^{7} x + \frac{b^{8} x^{3}}{3} + \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}}{1287 x^{13}}"," ",0,"8*a*b**7*x + b**8*x**3/3 + (-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)/(1287*x**13)","A",0
121,1,95,0,0.693658," ","integrate((b*x**2+a)**8/x**16,x)","b^{8} 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 x^{15}}"," ",0,"b**8*x + (-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*x**15)","A",0
122,1,99,0,0.788157," ","integrate((b*x**2+a)**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}}"," ",0,"(-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",0
123,1,99,0,0.836225," ","integrate((b*x**2+a)**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}}"," ",0,"(-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",0
124,1,68,0,0.175305," ","integrate(x**11/(b*x**2+a),x)","- \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}"," ",0,"-a**5*log(a + b*x**2)/(2*b**6) + a**4*x**2/(2*b**5) - a**3*x**4/(4*b**4) + a**2*x**6/(6*b**3) - a*x**8/(8*b**2) + x**10/(10*b)","A",0
125,1,119,0,0.199972," ","integrate(x**10/(b*x**2+a),x)","\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{\sqrt{- \frac{a^{9}}{b^{11}}} \log{\left(x - \frac{b^{5} \sqrt{- \frac{a^{9}}{b^{11}}}}{a^{4}} \right)}}{2} - \frac{\sqrt{- \frac{a^{9}}{b^{11}}} \log{\left(x + \frac{b^{5} \sqrt{- \frac{a^{9}}{b^{11}}}}{a^{4}} \right)}}{2} + \frac{x^{9}}{9 b}"," ",0,"a**4*x/b**5 - a**3*x**3/(3*b**4) + a**2*x**5/(5*b**3) - a*x**7/(7*b**2) + sqrt(-a**9/b**11)*log(x - b**5*sqrt(-a**9/b**11)/a**4)/2 - sqrt(-a**9/b**11)*log(x + b**5*sqrt(-a**9/b**11)/a**4)/2 + x**9/(9*b)","A",0
126,1,56,0,0.165724," ","integrate(x**9/(b*x**2+a),x)","\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}"," ",0,"a**4*log(a + b*x**2)/(2*b**5) - a**3*x**2/(2*b**4) + a**2*x**4/(4*b**3) - a*x**6/(6*b**2) + x**8/(8*b)","A",0
127,1,107,0,0.191245," ","integrate(x**8/(b*x**2+a),x)","- \frac{a^{3} x}{b^{4}} + \frac{a^{2} x^{3}}{3 b^{3}} - \frac{a x^{5}}{5 b^{2}} - \frac{\sqrt{- \frac{a^{7}}{b^{9}}} \log{\left(x - \frac{b^{4} \sqrt{- \frac{a^{7}}{b^{9}}}}{a^{3}} \right)}}{2} + \frac{\sqrt{- \frac{a^{7}}{b^{9}}} \log{\left(x + \frac{b^{4} \sqrt{- \frac{a^{7}}{b^{9}}}}{a^{3}} \right)}}{2} + \frac{x^{7}}{7 b}"," ",0,"-a**3*x/b**4 + a**2*x**3/(3*b**3) - a*x**5/(5*b**2) - sqrt(-a**7/b**9)*log(x - b**4*sqrt(-a**7/b**9)/a**3)/2 + sqrt(-a**7/b**9)*log(x + b**4*sqrt(-a**7/b**9)/a**3)/2 + x**7/(7*b)","A",0
128,1,44,0,0.156836," ","integrate(x**7/(b*x**2+a),x)","- \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}"," ",0,"-a**3*log(a + b*x**2)/(2*b**4) + a**2*x**2/(2*b**3) - a*x**4/(4*b**2) + x**6/(6*b)","A",0
129,1,95,0,0.180459," ","integrate(x**6/(b*x**2+a),x)","\frac{a^{2} x}{b^{3}} - \frac{a x^{3}}{3 b^{2}} + \frac{\sqrt{- \frac{a^{5}}{b^{7}}} \log{\left(x - \frac{b^{3} \sqrt{- \frac{a^{5}}{b^{7}}}}{a^{2}} \right)}}{2} - \frac{\sqrt{- \frac{a^{5}}{b^{7}}} \log{\left(x + \frac{b^{3} \sqrt{- \frac{a^{5}}{b^{7}}}}{a^{2}} \right)}}{2} + \frac{x^{5}}{5 b}"," ",0,"a**2*x/b**3 - a*x**3/(3*b**2) + sqrt(-a**5/b**7)*log(x - b**3*sqrt(-a**5/b**7)/a**2)/2 - sqrt(-a**5/b**7)*log(x + b**3*sqrt(-a**5/b**7)/a**2)/2 + x**5/(5*b)","A",0
130,1,32,0,0.150042," ","integrate(x**5/(b*x**2+a),x)","\frac{a^{2} \log{\left(a + b x^{2} \right)}}{2 b^{3}} - \frac{a x^{2}}{2 b^{2}} + \frac{x^{4}}{4 b}"," ",0,"a**2*log(a + b*x**2)/(2*b**3) - a*x**2/(2*b**2) + x**4/(4*b)","A",0
131,1,80,0,0.168087," ","integrate(x**4/(b*x**2+a),x)","- \frac{a x}{b^{2}} - \frac{\sqrt{- \frac{a^{3}}{b^{5}}} \log{\left(x - \frac{b^{2} \sqrt{- \frac{a^{3}}{b^{5}}}}{a} \right)}}{2} + \frac{\sqrt{- \frac{a^{3}}{b^{5}}} \log{\left(x + \frac{b^{2} \sqrt{- \frac{a^{3}}{b^{5}}}}{a} \right)}}{2} + \frac{x^{3}}{3 b}"," ",0,"-a*x/b**2 - sqrt(-a**3/b**5)*log(x - b**2*sqrt(-a**3/b**5)/a)/2 + sqrt(-a**3/b**5)*log(x + b**2*sqrt(-a**3/b**5)/a)/2 + x**3/(3*b)","B",0
132,1,20,0,0.134794," ","integrate(x**3/(b*x**2+a),x)","- \frac{a \log{\left(a + b x^{2} \right)}}{2 b^{2}} + \frac{x^{2}}{2 b}"," ",0,"-a*log(a + b*x**2)/(2*b**2) + x**2/(2*b)","A",0
133,1,56,0,0.145970," ","integrate(x**2/(b*x**2+a),x)","\frac{\sqrt{- \frac{a}{b^{3}}} \log{\left(- b \sqrt{- \frac{a}{b^{3}}} + x \right)}}{2} - \frac{\sqrt{- \frac{a}{b^{3}}} \log{\left(b \sqrt{- \frac{a}{b^{3}}} + x \right)}}{2} + \frac{x}{b}"," ",0,"sqrt(-a/b**3)*log(-b*sqrt(-a/b**3) + x)/2 - sqrt(-a/b**3)*log(b*sqrt(-a/b**3) + x)/2 + x/b","B",0
134,1,10,0,0.108305," ","integrate(x/(b*x**2+a),x)","\frac{\log{\left(a + b x^{2} \right)}}{2 b}"," ",0,"log(a + b*x**2)/(2*b)","A",0
135,1,53,0,0.133679," ","integrate(1/(b*x**2+a),x)","- \frac{\sqrt{- \frac{1}{a b}} \log{\left(- a \sqrt{- \frac{1}{a b}} + x \right)}}{2} + \frac{\sqrt{- \frac{1}{a b}} \log{\left(a \sqrt{- \frac{1}{a b}} + x \right)}}{2}"," ",0,"-sqrt(-1/(a*b))*log(-a*sqrt(-1/(a*b)) + x)/2 + sqrt(-1/(a*b))*log(a*sqrt(-1/(a*b)) + x)/2","B",0
136,1,15,0,0.199736," ","integrate(1/x/(b*x**2+a),x)","\frac{\log{\left(x \right)}}{a} - \frac{\log{\left(\frac{a}{b} + x^{2} \right)}}{2 a}"," ",0,"log(x)/a - log(a/b + x**2)/(2*a)","A",0
137,1,65,0,0.177641," ","integrate(1/x**2/(b*x**2+a),x)","\frac{\sqrt{- \frac{b}{a^{3}}} \log{\left(- \frac{a^{2} \sqrt{- \frac{b}{a^{3}}}}{b} + x \right)}}{2} - \frac{\sqrt{- \frac{b}{a^{3}}} \log{\left(\frac{a^{2} \sqrt{- \frac{b}{a^{3}}}}{b} + x \right)}}{2} - \frac{1}{a x}"," ",0,"sqrt(-b/a**3)*log(-a**2*sqrt(-b/a**3)/b + x)/2 - sqrt(-b/a**3)*log(a**2*sqrt(-b/a**3)/b + x)/2 - 1/(a*x)","B",0
138,1,31,0,0.262854," ","integrate(1/x**3/(b*x**2+a),x)","- \frac{1}{2 a x^{2}} - \frac{b \log{\left(x \right)}}{a^{2}} + \frac{b \log{\left(\frac{a}{b} + x^{2} \right)}}{2 a^{2}}"," ",0,"-1/(2*a*x**2) - b*log(x)/a**2 + b*log(a/b + x**2)/(2*a**2)","A",0
139,1,87,0,0.218477," ","integrate(1/x**4/(b*x**2+a),x)","- \frac{\sqrt{- \frac{b^{3}}{a^{5}}} \log{\left(- \frac{a^{3} \sqrt{- \frac{b^{3}}{a^{5}}}}{b^{2}} + x \right)}}{2} + \frac{\sqrt{- \frac{b^{3}}{a^{5}}} \log{\left(\frac{a^{3} \sqrt{- \frac{b^{3}}{a^{5}}}}{b^{2}} + x \right)}}{2} + \frac{- a + 3 b x^{2}}{3 a^{2} x^{3}}"," ",0,"-sqrt(-b**3/a**5)*log(-a**3*sqrt(-b**3/a**5)/b**2 + x)/2 + sqrt(-b**3/a**5)*log(a**3*sqrt(-b**3/a**5)/b**2 + x)/2 + (-a + 3*b*x**2)/(3*a**2*x**3)","B",0
140,1,42,0,0.303649," ","integrate(1/x**5/(b*x**2+a),x)","\frac{- a + 2 b x^{2}}{4 a^{2} x^{4}} + \frac{b^{2} \log{\left(x \right)}}{a^{3}} - \frac{b^{2} \log{\left(\frac{a}{b} + x^{2} \right)}}{2 a^{3}}"," ",0,"(-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",0
141,1,100,0,0.257059," ","integrate(1/x**6/(b*x**2+a),x)","\frac{\sqrt{- \frac{b^{5}}{a^{7}}} \log{\left(- \frac{a^{4} \sqrt{- \frac{b^{5}}{a^{7}}}}{b^{3}} + x \right)}}{2} - \frac{\sqrt{- \frac{b^{5}}{a^{7}}} \log{\left(\frac{a^{4} \sqrt{- \frac{b^{5}}{a^{7}}}}{b^{3}} + x \right)}}{2} + \frac{- 3 a^{2} + 5 a b x^{2} - 15 b^{2} x^{4}}{15 a^{3} x^{5}}"," ",0,"sqrt(-b**5/a**7)*log(-a**4*sqrt(-b**5/a**7)/b**3 + x)/2 - sqrt(-b**5/a**7)*log(a**4*sqrt(-b**5/a**7)/b**3 + x)/2 + (-3*a**2 + 5*a*b*x**2 - 15*b**2*x**4)/(15*a**3*x**5)","B",0
142,1,56,0,0.347450," ","integrate(1/x**7/(b*x**2+a),x)","\frac{- 2 a^{2} + 3 a b x^{2} - 6 b^{2} x^{4}}{12 a^{3} x^{6}} - \frac{b^{3} \log{\left(x \right)}}{a^{4}} + \frac{b^{3} \log{\left(\frac{a}{b} + x^{2} \right)}}{2 a^{4}}"," ",0,"(-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",0
143,1,112,0,0.296245," ","integrate(1/x**8/(b*x**2+a),x)","- \frac{\sqrt{- \frac{b^{7}}{a^{9}}} \log{\left(- \frac{a^{5} \sqrt{- \frac{b^{7}}{a^{9}}}}{b^{4}} + x \right)}}{2} + \frac{\sqrt{- \frac{b^{7}}{a^{9}}} \log{\left(\frac{a^{5} \sqrt{- \frac{b^{7}}{a^{9}}}}{b^{4}} + x \right)}}{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}}"," ",0,"-sqrt(-b**7/a**9)*log(-a**5*sqrt(-b**7/a**9)/b**4 + x)/2 + sqrt(-b**7/a**9)*log(a**5*sqrt(-b**7/a**9)/b**4 + x)/2 + (-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)","A",0
144,1,68,0,0.385641," ","integrate(1/x**9/(b*x**2+a),x)","\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(x \right)}}{a^{5}} - \frac{b^{4} \log{\left(\frac{a}{b} + x^{2} \right)}}{2 a^{5}}"," ",0,"(-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",0
145,1,88,0,0.312815," ","integrate(x**13/(b*x**2+a)**2,x)","- \frac{a^{6}}{2 a b^{7} + 2 b^{8} x^{2}} - \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}}"," ",0,"-a**6/(2*a*b**7 + 2*b**8*x**2) - 3*a**5*log(a + b*x**2)/b**7 + 5*a**4*x**2/(2*b**6) - a**3*x**4/b**5 + a**2*x**6/(2*b**4) - a*x**8/(4*b**3) + x**10/(10*b**2)","A",0
146,1,151,0,0.340264," ","integrate(x**12/(b*x**2+a)**2,x)","\frac{a^{5} x}{2 a b^{6} + 2 b^{7} x^{2}} + \frac{5 a^{4} x}{b^{6}} - \frac{4 a^{3} x^{3}}{3 b^{5}} + \frac{3 a^{2} x^{5}}{5 b^{4}} - \frac{2 a x^{7}}{7 b^{3}} + \frac{11 \sqrt{- \frac{a^{9}}{b^{13}}} \log{\left(x - \frac{b^{6} \sqrt{- \frac{a^{9}}{b^{13}}}}{a^{4}} \right)}}{4} - \frac{11 \sqrt{- \frac{a^{9}}{b^{13}}} \log{\left(x + \frac{b^{6} \sqrt{- \frac{a^{9}}{b^{13}}}}{a^{4}} \right)}}{4} + \frac{x^{9}}{9 b^{2}}"," ",0,"a**5*x/(2*a*b**6 + 2*b**7*x**2) + 5*a**4*x/b**6 - 4*a**3*x**3/(3*b**5) + 3*a**2*x**5/(5*b**4) - 2*a*x**7/(7*b**3) + 11*sqrt(-a**9/b**13)*log(x - b**6*sqrt(-a**9/b**13)/a**4)/4 - 11*sqrt(-a**9/b**13)*log(x + b**6*sqrt(-a**9/b**13)/a**4)/4 + x**9/(9*b**2)","A",0
147,1,80,0,0.294672," ","integrate(x**11/(b*x**2+a)**2,x)","\frac{a^{5}}{2 a b^{6} + 2 b^{7} x^{2}} + \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}}"," ",0,"a**5/(2*a*b**6 + 2*b**7*x**2) + 5*a**4*log(a + b*x**2)/(2*b**6) - 2*a**3*x**2/b**5 + 3*a**2*x**4/(4*b**4) - a*x**6/(3*b**3) + x**8/(8*b**2)","A",0
148,1,134,0,0.325094," ","integrate(x**10/(b*x**2+a)**2,x)","- \frac{a^{4} x}{2 a b^{5} + 2 b^{6} x^{2}} - \frac{4 a^{3} x}{b^{5}} + \frac{a^{2} x^{3}}{b^{4}} - \frac{2 a x^{5}}{5 b^{3}} - \frac{9 \sqrt{- \frac{a^{7}}{b^{11}}} \log{\left(x - \frac{b^{5} \sqrt{- \frac{a^{7}}{b^{11}}}}{a^{3}} \right)}}{4} + \frac{9 \sqrt{- \frac{a^{7}}{b^{11}}} \log{\left(x + \frac{b^{5} \sqrt{- \frac{a^{7}}{b^{11}}}}{a^{3}} \right)}}{4} + \frac{x^{7}}{7 b^{2}}"," ",0,"-a**4*x/(2*a*b**5 + 2*b**6*x**2) - 4*a**3*x/b**5 + a**2*x**3/b**4 - 2*a*x**5/(5*b**3) - 9*sqrt(-a**7/b**11)*log(x - b**5*sqrt(-a**7/b**11)/a**3)/4 + 9*sqrt(-a**7/b**11)*log(x + b**5*sqrt(-a**7/b**11)/a**3)/4 + x**7/(7*b**2)","A",0
149,1,66,0,0.274296," ","integrate(x**9/(b*x**2+a)**2,x)","- \frac{a^{4}}{2 a b^{5} + 2 b^{6} x^{2}} - \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}}"," ",0,"-a**4/(2*a*b**5 + 2*b**6*x**2) - 2*a**3*log(a + b*x**2)/b**5 + 3*a**2*x**2/(2*b**4) - a*x**4/(2*b**3) + x**6/(6*b**2)","A",0
150,1,124,0,0.307610," ","integrate(x**8/(b*x**2+a)**2,x)","\frac{a^{3} x}{2 a b^{4} + 2 b^{5} x^{2}} + \frac{3 a^{2} x}{b^{4}} - \frac{2 a x^{3}}{3 b^{3}} + \frac{7 \sqrt{- \frac{a^{5}}{b^{9}}} \log{\left(x - \frac{b^{4} \sqrt{- \frac{a^{5}}{b^{9}}}}{a^{2}} \right)}}{4} - \frac{7 \sqrt{- \frac{a^{5}}{b^{9}}} \log{\left(x + \frac{b^{4} \sqrt{- \frac{a^{5}}{b^{9}}}}{a^{2}} \right)}}{4} + \frac{x^{5}}{5 b^{2}}"," ",0,"a**3*x/(2*a*b**4 + 2*b**5*x**2) + 3*a**2*x/b**4 - 2*a*x**3/(3*b**3) + 7*sqrt(-a**5/b**9)*log(x - b**4*sqrt(-a**5/b**9)/a**2)/4 - 7*sqrt(-a**5/b**9)*log(x + b**4*sqrt(-a**5/b**9)/a**2)/4 + x**5/(5*b**2)","A",0
151,1,53,0,0.260251," ","integrate(x**7/(b*x**2+a)**2,x)","\frac{a^{3}}{2 a b^{4} + 2 b^{5} x^{2}} + \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}}"," ",0,"a**3/(2*a*b**4 + 2*b**5*x**2) + 3*a**2*log(a + b*x**2)/(2*b**4) - a*x**2/b**3 + x**4/(4*b**2)","A",0
152,1,107,0,0.286887," ","integrate(x**6/(b*x**2+a)**2,x)","- \frac{a^{2} x}{2 a b^{3} + 2 b^{4} x^{2}} - \frac{2 a x}{b^{3}} - \frac{5 \sqrt{- \frac{a^{3}}{b^{7}}} \log{\left(x - \frac{b^{3} \sqrt{- \frac{a^{3}}{b^{7}}}}{a} \right)}}{4} + \frac{5 \sqrt{- \frac{a^{3}}{b^{7}}} \log{\left(x + \frac{b^{3} \sqrt{- \frac{a^{3}}{b^{7}}}}{a} \right)}}{4} + \frac{x^{3}}{3 b^{2}}"," ",0,"-a**2*x/(2*a*b**3 + 2*b**4*x**2) - 2*a*x/b**3 - 5*sqrt(-a**3/b**7)*log(x - b**3*sqrt(-a**3/b**7)/a)/4 + 5*sqrt(-a**3/b**7)*log(x + b**3*sqrt(-a**3/b**7)/a)/4 + x**3/(3*b**2)","A",0
153,1,39,0,0.232750," ","integrate(x**5/(b*x**2+a)**2,x)","- \frac{a^{2}}{2 a b^{3} + 2 b^{4} x^{2}} - \frac{a \log{\left(a + b x^{2} \right)}}{b^{3}} + \frac{x^{2}}{2 b^{2}}"," ",0,"-a**2/(2*a*b**3 + 2*b**4*x**2) - a*log(a + b*x**2)/b**3 + x**2/(2*b**2)","A",0
154,1,83,0,0.255025," ","integrate(x**4/(b*x**2+a)**2,x)","\frac{a x}{2 a b^{2} + 2 b^{3} x^{2}} + \frac{3 \sqrt{- \frac{a}{b^{5}}} \log{\left(- b^{2} \sqrt{- \frac{a}{b^{5}}} + x \right)}}{4} - \frac{3 \sqrt{- \frac{a}{b^{5}}} \log{\left(b^{2} \sqrt{- \frac{a}{b^{5}}} + x \right)}}{4} + \frac{x}{b^{2}}"," ",0,"a*x/(2*a*b**2 + 2*b**3*x**2) + 3*sqrt(-a/b**5)*log(-b**2*sqrt(-a/b**5) + x)/4 - 3*sqrt(-a/b**5)*log(b**2*sqrt(-a/b**5) + x)/4 + x/b**2","A",0
155,1,29,0,0.192916," ","integrate(x**3/(b*x**2+a)**2,x)","\frac{a}{2 a b^{2} + 2 b^{3} x^{2}} + \frac{\log{\left(a + b x^{2} \right)}}{2 b^{2}}"," ",0,"a/(2*a*b**2 + 2*b**3*x**2) + log(a + b*x**2)/(2*b**2)","A",0
156,1,78,0,0.209239," ","integrate(x**2/(b*x**2+a)**2,x)","- \frac{x}{2 a b + 2 b^{2} x^{2}} - \frac{\sqrt{- \frac{1}{a b^{3}}} \log{\left(- a b \sqrt{- \frac{1}{a b^{3}}} + x \right)}}{4} + \frac{\sqrt{- \frac{1}{a b^{3}}} \log{\left(a b \sqrt{- \frac{1}{a b^{3}}} + x \right)}}{4}"," ",0,"-x/(2*a*b + 2*b**2*x**2) - sqrt(-1/(a*b**3))*log(-a*b*sqrt(-1/(a*b**3)) + x)/4 + sqrt(-1/(a*b**3))*log(a*b*sqrt(-1/(a*b**3)) + x)/4","B",0
157,1,15,0,0.157987," ","integrate(x/(b*x**2+a)**2,x)","- \frac{1}{2 a b + 2 b^{2} x^{2}}"," ",0,"-1/(2*a*b + 2*b**2*x**2)","A",0
158,1,78,0,0.211065," ","integrate(1/(b*x**2+a)**2,x)","\frac{x}{2 a^{2} + 2 a b x^{2}} - \frac{\sqrt{- \frac{1}{a^{3} b}} \log{\left(- a^{2} \sqrt{- \frac{1}{a^{3} b}} + x \right)}}{4} + \frac{\sqrt{- \frac{1}{a^{3} b}} \log{\left(a^{2} \sqrt{- \frac{1}{a^{3} b}} + x \right)}}{4}"," ",0,"x/(2*a**2 + 2*a*b*x**2) - sqrt(-1/(a**3*b))*log(-a**2*sqrt(-1/(a**3*b)) + x)/4 + sqrt(-1/(a**3*b))*log(a**2*sqrt(-1/(a**3*b)) + x)/4","B",0
159,1,34,0,0.295151," ","integrate(1/x/(b*x**2+a)**2,x)","\frac{1}{2 a^{2} + 2 a b x^{2}} + \frac{\log{\left(x \right)}}{a^{2}} - \frac{\log{\left(\frac{a}{b} + x^{2} \right)}}{2 a^{2}}"," ",0,"1/(2*a**2 + 2*a*b*x**2) + log(x)/a**2 - log(a/b + x**2)/(2*a**2)","A",0
160,1,92,0,0.290017," ","integrate(1/x**2/(b*x**2+a)**2,x)","\frac{3 \sqrt{- \frac{b}{a^{5}}} \log{\left(- \frac{a^{3} \sqrt{- \frac{b}{a^{5}}}}{b} + x \right)}}{4} - \frac{3 \sqrt{- \frac{b}{a^{5}}} \log{\left(\frac{a^{3} \sqrt{- \frac{b}{a^{5}}}}{b} + x \right)}}{4} + \frac{- 2 a - 3 b x^{2}}{2 a^{3} x + 2 a^{2} b x^{3}}"," ",0,"3*sqrt(-b/a**5)*log(-a**3*sqrt(-b/a**5)/b + x)/4 - 3*sqrt(-b/a**5)*log(a**3*sqrt(-b/a**5)/b + x)/4 + (-2*a - 3*b*x**2)/(2*a**3*x + 2*a**2*b*x**3)","A",0
161,1,51,0,0.363361," ","integrate(1/x**3/(b*x**2+a)**2,x)","\frac{- a - 2 b x^{2}}{2 a^{3} x^{2} + 2 a^{2} b x^{4}} - \frac{2 b \log{\left(x \right)}}{a^{3}} + \frac{b \log{\left(\frac{a}{b} + x^{2} \right)}}{a^{3}}"," ",0,"(-a - 2*b*x**2)/(2*a**3*x**2 + 2*a**2*b*x**4) - 2*b*log(x)/a**3 + b*log(a/b + x**2)/a**3","A",0
162,1,114,0,0.347466," ","integrate(1/x**4/(b*x**2+a)**2,x)","- \frac{5 \sqrt{- \frac{b^{3}}{a^{7}}} \log{\left(- \frac{a^{4} \sqrt{- \frac{b^{3}}{a^{7}}}}{b^{2}} + x \right)}}{4} + \frac{5 \sqrt{- \frac{b^{3}}{a^{7}}} \log{\left(\frac{a^{4} \sqrt{- \frac{b^{3}}{a^{7}}}}{b^{2}} + x \right)}}{4} + \frac{- 2 a^{2} + 10 a b x^{2} + 15 b^{2} x^{4}}{6 a^{4} x^{3} + 6 a^{3} b x^{5}}"," ",0,"-5*sqrt(-b**3/a**7)*log(-a**4*sqrt(-b**3/a**7)/b**2 + x)/4 + 5*sqrt(-b**3/a**7)*log(a**4*sqrt(-b**3/a**7)/b**2 + x)/4 + (-2*a**2 + 10*a*b*x**2 + 15*b**2*x**4)/(6*a**4*x**3 + 6*a**3*b*x**5)","A",0
163,1,68,0,0.441190," ","integrate(1/x**5/(b*x**2+a)**2,x)","\frac{- a^{2} + 3 a b x^{2} + 6 b^{2} x^{4}}{4 a^{4} x^{4} + 4 a^{3} b x^{6}} + \frac{3 b^{2} \log{\left(x \right)}}{a^{4}} - \frac{3 b^{2} \log{\left(\frac{a}{b} + x^{2} \right)}}{2 a^{4}}"," ",0,"(-a**2 + 3*a*b*x**2 + 6*b**2*x**4)/(4*a**4*x**4 + 4*a**3*b*x**6) + 3*b**2*log(x)/a**4 - 3*b**2*log(a/b + x**2)/(2*a**4)","A",0
164,1,126,0,0.396707," ","integrate(1/x**6/(b*x**2+a)**2,x)","\frac{7 \sqrt{- \frac{b^{5}}{a^{9}}} \log{\left(- \frac{a^{5} \sqrt{- \frac{b^{5}}{a^{9}}}}{b^{3}} + x \right)}}{4} - \frac{7 \sqrt{- \frac{b^{5}}{a^{9}}} \log{\left(\frac{a^{5} \sqrt{- \frac{b^{5}}{a^{9}}}}{b^{3}} + x \right)}}{4} + \frac{- 6 a^{3} + 14 a^{2} b x^{2} - 70 a b^{2} x^{4} - 105 b^{3} x^{6}}{30 a^{5} x^{5} + 30 a^{4} b x^{7}}"," ",0,"7*sqrt(-b**5/a**9)*log(-a**5*sqrt(-b**5/a**9)/b**3 + x)/4 - 7*sqrt(-b**5/a**9)*log(a**5*sqrt(-b**5/a**9)/b**3 + x)/4 + (-6*a**3 + 14*a**2*b*x**2 - 70*a*b**2*x**4 - 105*b**3*x**6)/(30*a**5*x**5 + 30*a**4*b*x**7)","A",0
165,1,78,0,0.466536," ","integrate(1/x**7/(b*x**2+a)**2,x)","\frac{- a^{3} + 2 a^{2} b x^{2} - 6 a b^{2} x^{4} - 12 b^{3} x^{6}}{6 a^{5} x^{6} + 6 a^{4} b x^{8}} - \frac{4 b^{3} \log{\left(x \right)}}{a^{5}} + \frac{2 b^{3} \log{\left(\frac{a}{b} + x^{2} \right)}}{a^{5}}"," ",0,"(-a**3 + 2*a**2*b*x**2 - 6*a*b**2*x**4 - 12*b**3*x**6)/(6*a**5*x**6 + 6*a**4*b*x**8) - 4*b**3*log(x)/a**5 + 2*b**3*log(a/b + x**2)/a**5","A",0
166,1,138,0,0.445830," ","integrate(1/x**8/(b*x**2+a)**2,x)","- \frac{9 \sqrt{- \frac{b^{7}}{a^{11}}} \log{\left(- \frac{a^{6} \sqrt{- \frac{b^{7}}{a^{11}}}}{b^{4}} + x \right)}}{4} + \frac{9 \sqrt{- \frac{b^{7}}{a^{11}}} \log{\left(\frac{a^{6} \sqrt{- \frac{b^{7}}{a^{11}}}}{b^{4}} + x \right)}}{4} + \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^{6} x^{7} + 70 a^{5} b x^{9}}"," ",0,"-9*sqrt(-b**7/a**11)*log(-a**6*sqrt(-b**7/a**11)/b**4 + x)/4 + 9*sqrt(-b**7/a**11)*log(a**6*sqrt(-b**7/a**11)/b**4 + x)/4 + (-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**6*x**7 + 70*a**5*b*x**9)","A",0
167,1,94,0,0.522616," ","integrate(1/x**9/(b*x**2+a)**2,x)","\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^{6} x^{8} + 24 a^{5} b x^{10}} + \frac{5 b^{4} \log{\left(x \right)}}{a^{6}} - \frac{5 b^{4} \log{\left(\frac{a}{b} + x^{2} \right)}}{2 a^{6}}"," ",0,"(-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**6*x**8 + 24*a**5*b*x**10) + 5*b**4*log(x)/a**6 - 5*b**4*log(a/b + x**2)/(2*a**6)","A",0
168,1,119,0,0.482394," ","integrate(x**15/(b*x**2+a)**3,x)","- \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{- 13 a^{7} - 14 a^{6} b x^{2}}{4 a^{2} b^{8} + 8 a b^{9} x^{2} + 4 b^{10} x^{4}} + \frac{x^{10}}{10 b^{3}}"," ",0,"-21*a**5*log(a + b*x**2)/(2*b**8) + 15*a**4*x**2/(2*b**7) - 5*a**3*x**4/(2*b**6) + a**2*x**6/b**5 - 3*a*x**8/(8*b**4) + (-13*a**7 - 14*a**6*b*x**2)/(4*a**2*b**8 + 8*a*b**9*x**2 + 4*b**10*x**4) + x**10/(10*b**3)","A",0
169,1,104,0,0.465860," ","integrate(x**13/(b*x**2+a)**3,x)","\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{11 a^{6} + 12 a^{5} b x^{2}}{4 a^{2} b^{7} + 8 a b^{8} x^{2} + 4 b^{9} x^{4}} + \frac{x^{8}}{8 b^{3}}"," ",0,"15*a**4*log(a + b*x**2)/(2*b**7) - 5*a**3*x**2/b**6 + 3*a**2*x**4/(2*b**5) - a*x**6/(2*b**4) + (11*a**6 + 12*a**5*b*x**2)/(4*a**2*b**7 + 8*a*b**8*x**2 + 4*b**9*x**4) + x**8/(8*b**3)","A",0
170,1,92,0,0.435571," ","integrate(x**11/(b*x**2+a)**3,x)","- \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{- 9 a^{5} - 10 a^{4} b x^{2}}{4 a^{2} b^{6} + 8 a b^{7} x^{2} + 4 b^{8} x^{4}} + \frac{x^{6}}{6 b^{3}}"," ",0,"-5*a**3*log(a + b*x**2)/b**6 + 3*a**2*x**2/b**5 - 3*a*x**4/(4*b**4) + (-9*a**5 - 10*a**4*b*x**2)/(4*a**2*b**6 + 8*a*b**7*x**2 + 4*b**8*x**4) + x**6/(6*b**3)","A",0
171,1,78,0,0.416152," ","integrate(x**9/(b*x**2+a)**3,x)","\frac{3 a^{2} \log{\left(a + b x^{2} \right)}}{b^{5}} - \frac{3 a x^{2}}{2 b^{4}} + \frac{7 a^{4} + 8 a^{3} b x^{2}}{4 a^{2} b^{5} + 8 a b^{6} x^{2} + 4 b^{7} x^{4}} + \frac{x^{4}}{4 b^{3}}"," ",0,"3*a**2*log(a + b*x**2)/b**5 - 3*a*x**2/(2*b**4) + (7*a**4 + 8*a**3*b*x**2)/(4*a**2*b**5 + 8*a*b**6*x**2 + 4*b**7*x**4) + x**4/(4*b**3)","A",0
172,1,68,0,0.379663," ","integrate(x**7/(b*x**2+a)**3,x)","- \frac{3 a \log{\left(a + b x^{2} \right)}}{2 b^{4}} + \frac{- 5 a^{3} - 6 a^{2} b x^{2}}{4 a^{2} b^{4} + 8 a b^{5} x^{2} + 4 b^{6} x^{4}} + \frac{x^{2}}{2 b^{3}}"," ",0,"-3*a*log(a + b*x**2)/(2*b**4) + (-5*a**3 - 6*a**2*b*x**2)/(4*a**2*b**4 + 8*a*b**5*x**2 + 4*b**6*x**4) + x**2/(2*b**3)","A",0
173,1,53,0,0.318644," ","integrate(x**5/(b*x**2+a)**3,x)","\frac{3 a^{2} + 4 a b x^{2}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{\log{\left(a + b x^{2} \right)}}{2 b^{3}}"," ",0,"(3*a**2 + 4*a*b*x**2)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + log(a + b*x**2)/(2*b**3)","A",0
174,1,36,0,0.264913," ","integrate(x**3/(b*x**2+a)**3,x)","\frac{- a - 2 b x^{2}}{4 a^{2} b^{2} + 8 a b^{3} x^{2} + 4 b^{4} x^{4}}"," ",0,"(-a - 2*b*x**2)/(4*a**2*b**2 + 8*a*b**3*x**2 + 4*b**4*x**4)","B",0
175,1,27,0,0.235127," ","integrate(x/(b*x**2+a)**3,x)","- \frac{1}{4 a^{2} b + 8 a b^{2} x^{2} + 4 b^{3} x^{4}}"," ",0,"-1/(4*a**2*b + 8*a*b**2*x**2 + 4*b**3*x**4)","A",0
176,1,56,0,0.406942," ","integrate(1/x/(b*x**2+a)**3,x)","\frac{3 a + 2 b x^{2}}{4 a^{4} + 8 a^{3} b x^{2} + 4 a^{2} b^{2} x^{4}} + \frac{\log{\left(x \right)}}{a^{3}} - \frac{\log{\left(\frac{a}{b} + x^{2} \right)}}{2 a^{3}}"," ",0,"(3*a + 2*b*x**2)/(4*a**4 + 8*a**3*b*x**2 + 4*a**2*b**2*x**4) + log(x)/a**3 - log(a/b + x**2)/(2*a**3)","A",0
177,1,80,0,0.507944," ","integrate(1/x**3/(b*x**2+a)**3,x)","\frac{- 2 a^{2} - 9 a b x^{2} - 6 b^{2} x^{4}}{4 a^{5} x^{2} + 8 a^{4} b x^{4} + 4 a^{3} b^{2} x^{6}} - \frac{3 b \log{\left(x \right)}}{a^{4}} + \frac{3 b \log{\left(\frac{a}{b} + x^{2} \right)}}{2 a^{4}}"," ",0,"(-2*a**2 - 9*a*b*x**2 - 6*b**2*x**4)/(4*a**5*x**2 + 8*a**4*b*x**4 + 4*a**3*b**2*x**6) - 3*b*log(x)/a**4 + 3*b*log(a/b + x**2)/(2*a**4)","A",0
178,1,90,0,0.545552," ","integrate(1/x**5/(b*x**2+a)**3,x)","\frac{- a^{3} + 4 a^{2} b x^{2} + 18 a b^{2} x^{4} + 12 b^{3} x^{6}}{4 a^{6} x^{4} + 8 a^{5} b x^{6} + 4 a^{4} b^{2} x^{8}} + \frac{6 b^{2} \log{\left(x \right)}}{a^{5}} - \frac{3 b^{2} \log{\left(\frac{a}{b} + x^{2} \right)}}{a^{5}}"," ",0,"(-a**3 + 4*a**2*b*x**2 + 18*a*b**2*x**4 + 12*b**3*x**6)/(4*a**6*x**4 + 8*a**5*b*x**6 + 4*a**4*b**2*x**8) + 6*b**2*log(x)/a**5 - 3*b**2*log(a/b + x**2)/a**5","A",0
179,1,104,0,0.594013," ","integrate(1/x**7/(b*x**2+a)**3,x)","\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^{7} x^{6} + 24 a^{6} b x^{8} + 12 a^{5} b^{2} x^{10}} - \frac{10 b^{3} \log{\left(x \right)}}{a^{6}} + \frac{5 b^{3} \log{\left(\frac{a}{b} + x^{2} \right)}}{a^{6}}"," ",0,"(-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**7*x**6 + 24*a**6*b*x**8 + 12*a**5*b**2*x**10) - 10*b**3*log(x)/a**6 + 5*b**3*log(a/b + x**2)/a**6","A",0
180,1,116,0,0.653044," ","integrate(1/x**9/(b*x**2+a)**3,x)","\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^{8} x^{8} + 16 a^{7} b x^{10} + 8 a^{6} b^{2} x^{12}} + \frac{15 b^{4} \log{\left(x \right)}}{a^{7}} - \frac{15 b^{4} \log{\left(\frac{a}{b} + x^{2} \right)}}{2 a^{7}}"," ",0,"(-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**8*x**8 + 16*a**7*b*x**10 + 8*a**6*b**2*x**12) + 15*b**4*log(x)/a**7 - 15*b**4*log(a/b + x**2)/(2*a**7)","A",0
181,1,162,0,0.489108," ","integrate(x**12/(b*x**2+a)**3,x)","- \frac{10 a^{3} x}{b^{6}} + \frac{2 a^{2} x^{3}}{b^{5}} - \frac{3 a x^{5}}{5 b^{4}} - \frac{99 \sqrt{- \frac{a^{7}}{b^{13}}} \log{\left(x - \frac{b^{6} \sqrt{- \frac{a^{7}}{b^{13}}}}{a^{3}} \right)}}{16} + \frac{99 \sqrt{- \frac{a^{7}}{b^{13}}} \log{\left(x + \frac{b^{6} \sqrt{- \frac{a^{7}}{b^{13}}}}{a^{3}} \right)}}{16} + \frac{- 19 a^{5} x - 21 a^{4} b x^{3}}{8 a^{2} b^{6} + 16 a b^{7} x^{2} + 8 b^{8} x^{4}} + \frac{x^{7}}{7 b^{3}}"," ",0,"-10*a**3*x/b**6 + 2*a**2*x**3/b**5 - 3*a*x**5/(5*b**4) - 99*sqrt(-a**7/b**13)*log(x - b**6*sqrt(-a**7/b**13)/a**3)/16 + 99*sqrt(-a**7/b**13)*log(x + b**6*sqrt(-a**7/b**13)/a**3)/16 + (-19*a**5*x - 21*a**4*b*x**3)/(8*a**2*b**6 + 16*a*b**7*x**2 + 8*b**8*x**4) + x**7/(7*b**3)","A",0
182,1,144,0,0.465011," ","integrate(x**10/(b*x**2+a)**3,x)","\frac{6 a^{2} x}{b^{5}} - \frac{a x^{3}}{b^{4}} + \frac{63 \sqrt{- \frac{a^{5}}{b^{11}}} \log{\left(x - \frac{b^{5} \sqrt{- \frac{a^{5}}{b^{11}}}}{a^{2}} \right)}}{16} - \frac{63 \sqrt{- \frac{a^{5}}{b^{11}}} \log{\left(x + \frac{b^{5} \sqrt{- \frac{a^{5}}{b^{11}}}}{a^{2}} \right)}}{16} + \frac{15 a^{4} x + 17 a^{3} b x^{3}}{8 a^{2} b^{5} + 16 a b^{6} x^{2} + 8 b^{7} x^{4}} + \frac{x^{5}}{5 b^{3}}"," ",0,"6*a**2*x/b**5 - a*x**3/b**4 + 63*sqrt(-a**5/b**11)*log(x - b**5*sqrt(-a**5/b**11)/a**2)/16 - 63*sqrt(-a**5/b**11)*log(x + b**5*sqrt(-a**5/b**11)/a**2)/16 + (15*a**4*x + 17*a**3*b*x**3)/(8*a**2*b**5 + 16*a*b**6*x**2 + 8*b**7*x**4) + x**5/(5*b**3)","A",0
183,1,133,0,0.437476," ","integrate(x**8/(b*x**2+a)**3,x)","- \frac{3 a x}{b^{4}} - \frac{35 \sqrt{- \frac{a^{3}}{b^{9}}} \log{\left(x - \frac{b^{4} \sqrt{- \frac{a^{3}}{b^{9}}}}{a} \right)}}{16} + \frac{35 \sqrt{- \frac{a^{3}}{b^{9}}} \log{\left(x + \frac{b^{4} \sqrt{- \frac{a^{3}}{b^{9}}}}{a} \right)}}{16} + \frac{- 11 a^{3} x - 13 a^{2} b x^{3}}{8 a^{2} b^{4} + 16 a b^{5} x^{2} + 8 b^{6} x^{4}} + \frac{x^{3}}{3 b^{3}}"," ",0,"-3*a*x/b**4 - 35*sqrt(-a**3/b**9)*log(x - b**4*sqrt(-a**3/b**9)/a)/16 + 35*sqrt(-a**3/b**9)*log(x + b**4*sqrt(-a**3/b**9)/a)/16 + (-11*a**3*x - 13*a**2*b*x**3)/(8*a**2*b**4 + 16*a*b**5*x**2 + 8*b**6*x**4) + x**3/(3*b**3)","A",0
184,1,107,0,0.397586," ","integrate(x**6/(b*x**2+a)**3,x)","\frac{15 \sqrt{- \frac{a}{b^{7}}} \log{\left(- b^{3} \sqrt{- \frac{a}{b^{7}}} + x \right)}}{16} - \frac{15 \sqrt{- \frac{a}{b^{7}}} \log{\left(b^{3} \sqrt{- \frac{a}{b^{7}}} + x \right)}}{16} + \frac{7 a^{2} x + 9 a b x^{3}}{8 a^{2} b^{3} + 16 a b^{4} x^{2} + 8 b^{5} x^{4}} + \frac{x}{b^{3}}"," ",0,"15*sqrt(-a/b**7)*log(-b**3*sqrt(-a/b**7) + x)/16 - 15*sqrt(-a/b**7)*log(b**3*sqrt(-a/b**7) + x)/16 + (7*a**2*x + 9*a*b*x**3)/(8*a**2*b**3 + 16*a*b**4*x**2 + 8*b**5*x**4) + x/b**3","A",0
185,1,110,0,0.332327," ","integrate(x**4/(b*x**2+a)**3,x)","- \frac{3 \sqrt{- \frac{1}{a b^{5}}} \log{\left(- a b^{2} \sqrt{- \frac{1}{a b^{5}}} + x \right)}}{16} + \frac{3 \sqrt{- \frac{1}{a b^{5}}} \log{\left(a b^{2} \sqrt{- \frac{1}{a b^{5}}} + x \right)}}{16} + \frac{- 3 a x - 5 b x^{3}}{8 a^{2} b^{2} + 16 a b^{3} x^{2} + 8 b^{4} x^{4}}"," ",0,"-3*sqrt(-1/(a*b**5))*log(-a*b**2*sqrt(-1/(a*b**5)) + x)/16 + 3*sqrt(-1/(a*b**5))*log(a*b**2*sqrt(-1/(a*b**5)) + x)/16 + (-3*a*x - 5*b*x**3)/(8*a**2*b**2 + 16*a*b**3*x**2 + 8*b**4*x**4)","A",0
186,1,110,0,0.306164," ","integrate(x**2/(b*x**2+a)**3,x)","- \frac{\sqrt{- \frac{1}{a^{3} b^{3}}} \log{\left(- a^{2} b \sqrt{- \frac{1}{a^{3} b^{3}}} + x \right)}}{16} + \frac{\sqrt{- \frac{1}{a^{3} b^{3}}} \log{\left(a^{2} b \sqrt{- \frac{1}{a^{3} b^{3}}} + x \right)}}{16} + \frac{- a x + b x^{3}}{8 a^{3} b + 16 a^{2} b^{2} x^{2} + 8 a b^{3} x^{4}}"," ",0,"-sqrt(-1/(a**3*b**3))*log(-a**2*b*sqrt(-1/(a**3*b**3)) + x)/16 + sqrt(-1/(a**3*b**3))*log(a**2*b*sqrt(-1/(a**3*b**3)) + x)/16 + (-a*x + b*x**3)/(8*a**3*b + 16*a**2*b**2*x**2 + 8*a*b**3*x**4)","B",0
187,1,105,0,0.319120," ","integrate(1/(b*x**2+a)**3,x)","- \frac{3 \sqrt{- \frac{1}{a^{5} b}} \log{\left(- a^{3} \sqrt{- \frac{1}{a^{5} b}} + x \right)}}{16} + \frac{3 \sqrt{- \frac{1}{a^{5} b}} \log{\left(a^{3} \sqrt{- \frac{1}{a^{5} b}} + x \right)}}{16} + \frac{5 a x + 3 b x^{3}}{8 a^{4} + 16 a^{3} b x^{2} + 8 a^{2} b^{2} x^{4}}"," ",0,"-3*sqrt(-1/(a**5*b))*log(-a**3*sqrt(-1/(a**5*b)) + x)/16 + 3*sqrt(-1/(a**5*b))*log(a**3*sqrt(-1/(a**5*b)) + x)/16 + (5*a*x + 3*b*x**3)/(8*a**4 + 16*a**3*b*x**2 + 8*a**2*b**2*x**4)","A",0
188,1,116,0,0.417916," ","integrate(1/x**2/(b*x**2+a)**3,x)","\frac{15 \sqrt{- \frac{b}{a^{7}}} \log{\left(- \frac{a^{4} \sqrt{- \frac{b}{a^{7}}}}{b} + x \right)}}{16} - \frac{15 \sqrt{- \frac{b}{a^{7}}} \log{\left(\frac{a^{4} \sqrt{- \frac{b}{a^{7}}}}{b} + x \right)}}{16} + \frac{- 8 a^{2} - 25 a b x^{2} - 15 b^{2} x^{4}}{8 a^{5} x + 16 a^{4} b x^{3} + 8 a^{3} b^{2} x^{5}}"," ",0,"15*sqrt(-b/a**7)*log(-a**4*sqrt(-b/a**7)/b + x)/16 - 15*sqrt(-b/a**7)*log(a**4*sqrt(-b/a**7)/b + x)/16 + (-8*a**2 - 25*a*b*x**2 - 15*b**2*x**4)/(8*a**5*x + 16*a**4*b*x**3 + 8*a**3*b**2*x**5)","A",0
189,1,138,0,0.476188," ","integrate(1/x**4/(b*x**2+a)**3,x)","- \frac{35 \sqrt{- \frac{b^{3}}{a^{9}}} \log{\left(- \frac{a^{5} \sqrt{- \frac{b^{3}}{a^{9}}}}{b^{2}} + x \right)}}{16} + \frac{35 \sqrt{- \frac{b^{3}}{a^{9}}} \log{\left(\frac{a^{5} \sqrt{- \frac{b^{3}}{a^{9}}}}{b^{2}} + x \right)}}{16} + \frac{- 8 a^{3} + 56 a^{2} b x^{2} + 175 a b^{2} x^{4} + 105 b^{3} x^{6}}{24 a^{6} x^{3} + 48 a^{5} b x^{5} + 24 a^{4} b^{2} x^{7}}"," ",0,"-35*sqrt(-b**3/a**9)*log(-a**5*sqrt(-b**3/a**9)/b**2 + x)/16 + 35*sqrt(-b**3/a**9)*log(a**5*sqrt(-b**3/a**9)/b**2 + x)/16 + (-8*a**3 + 56*a**2*b*x**2 + 175*a*b**2*x**4 + 105*b**3*x**6)/(24*a**6*x**3 + 48*a**5*b*x**5 + 24*a**4*b**2*x**7)","A",0
190,1,150,0,0.528739," ","integrate(1/x**6/(b*x**2+a)**3,x)","\frac{63 \sqrt{- \frac{b^{5}}{a^{11}}} \log{\left(- \frac{a^{6} \sqrt{- \frac{b^{5}}{a^{11}}}}{b^{3}} + x \right)}}{16} - \frac{63 \sqrt{- \frac{b^{5}}{a^{11}}} \log{\left(\frac{a^{6} \sqrt{- \frac{b^{5}}{a^{11}}}}{b^{3}} + x \right)}}{16} + \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^{7} x^{5} + 80 a^{6} b x^{7} + 40 a^{5} b^{2} x^{9}}"," ",0,"63*sqrt(-b**5/a**11)*log(-a**6*sqrt(-b**5/a**11)/b**3 + x)/16 - 63*sqrt(-b**5/a**11)*log(a**6*sqrt(-b**5/a**11)/b**3 + x)/16 + (-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**7*x**5 + 80*a**6*b*x**7 + 40*a**5*b**2*x**9)","A",0
191,1,162,0,0.578654," ","integrate(1/x**8/(b*x**2+a)**3,x)","- \frac{99 \sqrt{- \frac{b^{7}}{a^{13}}} \log{\left(- \frac{a^{7} \sqrt{- \frac{b^{7}}{a^{13}}}}{b^{4}} + x \right)}}{16} + \frac{99 \sqrt{- \frac{b^{7}}{a^{13}}} \log{\left(\frac{a^{7} \sqrt{- \frac{b^{7}}{a^{13}}}}{b^{4}} + x \right)}}{16} + \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^{8} x^{7} + 560 a^{7} b x^{9} + 280 a^{6} b^{2} x^{11}}"," ",0,"-99*sqrt(-b**7/a**13)*log(-a**7*sqrt(-b**7/a**13)/b**4 + x)/16 + 99*sqrt(-b**7/a**13)*log(a**7*sqrt(-b**7/a**13)/b**4 + x)/16 + (-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**8*x**7 + 560*a**7*b*x**9 + 280*a**6*b**2*x**11)","A",0
192,1,260,0,2.151228," ","integrate(x**25/(b*x**2+a)**10,x)","- \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{- 35201 a^{12} - 296019 a^{11} b x^{2} - 1093356 a^{10} b^{2} x^{4} - 2318316 a^{9} b^{3} x^{6} - 3089394 a^{8} b^{4} x^{8} - 2652804 a^{7} b^{5} x^{10} - 1435896 a^{6} b^{6} x^{12} - 449064 a^{5} b^{7} x^{14} - 62370 a^{4} b^{8} x^{16}}{252 a^{9} b^{13} + 2268 a^{8} b^{14} x^{2} + 9072 a^{7} b^{15} x^{4} + 21168 a^{6} b^{16} x^{6} + 31752 a^{5} b^{17} x^{8} + 31752 a^{4} b^{18} x^{10} + 21168 a^{3} b^{19} x^{12} + 9072 a^{2} b^{20} x^{14} + 2268 a b^{21} x^{16} + 252 b^{22} x^{18}} + \frac{x^{6}}{6 b^{10}}"," ",0,"-110*a**3*log(a + b*x**2)/b**13 + 55*a**2*x**2/(2*b**12) - 5*a*x**4/(2*b**11) + (-35201*a**12 - 296019*a**11*b*x**2 - 1093356*a**10*b**2*x**4 - 2318316*a**9*b**3*x**6 - 3089394*a**8*b**4*x**8 - 2652804*a**7*b**5*x**10 - 1435896*a**6*b**6*x**12 - 449064*a**5*b**7*x**14 - 62370*a**4*b**8*x**16)/(252*a**9*b**13 + 2268*a**8*b**14*x**2 + 9072*a**7*b**15*x**4 + 21168*a**6*b**16*x**6 + 31752*a**5*b**17*x**8 + 31752*a**4*b**18*x**10 + 21168*a**3*b**19*x**12 + 9072*a**2*b**20*x**14 + 2268*a*b**21*x**16 + 252*b**22*x**18) + x**6/(6*b**10)","A",0
193,1,245,0,2.060065," ","integrate(x**23/(b*x**2+a)**10,x)","\frac{55 a^{2} \log{\left(a + b x^{2} \right)}}{2 b^{12}} - \frac{5 a x^{2}}{b^{11}} + \frac{42131 a^{11} + 356499 a^{10} b x^{2} + 1326204 a^{9} b^{2} x^{4} + 2835756 a^{8} b^{3} x^{6} + 3817044 a^{7} b^{4} x^{8} + 3318084 a^{6} b^{5} x^{10} + 1823976 a^{5} b^{6} x^{12} + 582120 a^{4} b^{7} x^{14} + 83160 a^{3} b^{8} x^{16}}{1008 a^{9} b^{12} + 9072 a^{8} b^{13} x^{2} + 36288 a^{7} b^{14} x^{4} + 84672 a^{6} b^{15} x^{6} + 127008 a^{5} b^{16} x^{8} + 127008 a^{4} b^{17} x^{10} + 84672 a^{3} b^{18} x^{12} + 36288 a^{2} b^{19} x^{14} + 9072 a b^{20} x^{16} + 1008 b^{21} x^{18}} + \frac{x^{4}}{4 b^{10}}"," ",0,"55*a**2*log(a + b*x**2)/(2*b**12) - 5*a*x**2/b**11 + (42131*a**11 + 356499*a**10*b*x**2 + 1326204*a**9*b**2*x**4 + 2835756*a**8*b**3*x**6 + 3817044*a**7*b**4*x**8 + 3318084*a**6*b**5*x**10 + 1823976*a**5*b**6*x**12 + 582120*a**4*b**7*x**14 + 83160*a**3*b**8*x**16)/(1008*a**9*b**12 + 9072*a**8*b**13*x**2 + 36288*a**7*b**14*x**4 + 84672*a**6*b**15*x**6 + 127008*a**5*b**16*x**8 + 127008*a**4*b**17*x**10 + 84672*a**3*b**18*x**12 + 36288*a**2*b**19*x**14 + 9072*a*b**20*x**16 + 1008*b**21*x**18) + x**4/(4*b**10)","A",0
194,1,233,0,2.025285," ","integrate(x**21/(b*x**2+a)**10,x)","- \frac{5 a \log{\left(a + b x^{2} \right)}}{b^{11}} + \frac{- 4861 a^{10} - 41481 a^{9} b x^{2} - 155844 a^{8} b^{2} x^{4} - 337176 a^{7} b^{3} x^{6} - 460404 a^{6} b^{4} x^{8} - 407484 a^{5} b^{5} x^{10} - 229320 a^{4} b^{6} x^{12} - 75600 a^{3} b^{7} x^{14} - 11340 a^{2} b^{8} x^{16}}{504 a^{9} b^{11} + 4536 a^{8} b^{12} x^{2} + 18144 a^{7} b^{13} x^{4} + 42336 a^{6} b^{14} x^{6} + 63504 a^{5} b^{15} x^{8} + 63504 a^{4} b^{16} x^{10} + 42336 a^{3} b^{17} x^{12} + 18144 a^{2} b^{18} x^{14} + 4536 a b^{19} x^{16} + 504 b^{20} x^{18}} + \frac{x^{2}}{2 b^{10}}"," ",0,"-5*a*log(a + b*x**2)/b**11 + (-4861*a**10 - 41481*a**9*b*x**2 - 155844*a**8*b**2*x**4 - 337176*a**7*b**3*x**6 - 460404*a**6*b**4*x**8 - 407484*a**5*b**5*x**10 - 229320*a**4*b**6*x**12 - 75600*a**3*b**7*x**14 - 11340*a**2*b**8*x**16)/(504*a**9*b**11 + 4536*a**8*b**12*x**2 + 18144*a**7*b**13*x**4 + 42336*a**6*b**14*x**6 + 63504*a**5*b**15*x**8 + 63504*a**4*b**16*x**10 + 42336*a**3*b**17*x**12 + 18144*a**2*b**18*x**14 + 4536*a*b**19*x**16 + 504*b**20*x**18) + x**2/(2*b**10)","A",0
195,1,219,0,1.835017," ","integrate(x**19/(b*x**2+a)**10,x)","\frac{7129 a^{9} + 61641 a^{8} b x^{2} + 235224 a^{7} b^{2} x^{4} + 518616 a^{6} b^{3} x^{6} + 725004 a^{5} b^{4} x^{8} + 661500 a^{4} b^{5} x^{10} + 388080 a^{3} b^{6} x^{12} + 136080 a^{2} b^{7} x^{14} + 22680 a b^{8} x^{16}}{5040 a^{9} b^{10} + 45360 a^{8} b^{11} x^{2} + 181440 a^{7} b^{12} x^{4} + 423360 a^{6} b^{13} x^{6} + 635040 a^{5} b^{14} x^{8} + 635040 a^{4} b^{15} x^{10} + 423360 a^{3} b^{16} x^{12} + 181440 a^{2} b^{17} x^{14} + 45360 a b^{18} x^{16} + 5040 b^{19} x^{18}} + \frac{\log{\left(a + b x^{2} \right)}}{2 b^{10}}"," ",0,"(7129*a**9 + 61641*a**8*b*x**2 + 235224*a**7*b**2*x**4 + 518616*a**6*b**3*x**6 + 725004*a**5*b**4*x**8 + 661500*a**4*b**5*x**10 + 388080*a**3*b**6*x**12 + 136080*a**2*b**7*x**14 + 22680*a*b**8*x**16)/(5040*a**9*b**10 + 45360*a**8*b**11*x**2 + 181440*a**7*b**12*x**4 + 423360*a**6*b**13*x**6 + 635040*a**5*b**14*x**8 + 635040*a**4*b**15*x**10 + 423360*a**3*b**16*x**12 + 181440*a**2*b**17*x**14 + 45360*a*b**18*x**16 + 5040*b**19*x**18) + log(a + b*x**2)/(2*b**10)","A",0
196,1,202,0,1.699167," ","integrate(x**17/(b*x**2+a)**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 a^{9} b^{9} + 162 a^{8} b^{10} x^{2} + 648 a^{7} b^{11} x^{4} + 1512 a^{6} b^{12} x^{6} + 2268 a^{5} b^{13} x^{8} + 2268 a^{4} b^{14} x^{10} + 1512 a^{3} b^{15} x^{12} + 648 a^{2} b^{16} x^{14} + 162 a b^{17} x^{16} + 18 b^{18} x^{18}}"," ",0,"(-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*a**9*b**9 + 162*a**8*b**10*x**2 + 648*a**7*b**11*x**4 + 1512*a**6*b**12*x**6 + 2268*a**5*b**13*x**8 + 2268*a**4*b**14*x**10 + 1512*a**3*b**15*x**12 + 648*a**2*b**16*x**14 + 162*a*b**17*x**16 + 18*b**18*x**18)","B",0
197,1,190,0,1.418501," ","integrate(x**15/(b*x**2+a)**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 a^{9} b^{8} + 1296 a^{8} b^{9} x^{2} + 5184 a^{7} b^{10} x^{4} + 12096 a^{6} b^{11} x^{6} + 18144 a^{5} b^{12} x^{8} + 18144 a^{4} b^{13} x^{10} + 12096 a^{3} b^{14} x^{12} + 5184 a^{2} b^{15} x^{14} + 1296 a b^{16} x^{16} + 144 b^{17} x^{18}}"," ",0,"(-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*a**9*b**8 + 1296*a**8*b**9*x**2 + 5184*a**7*b**10*x**4 + 12096*a**6*b**11*x**6 + 18144*a**5*b**12*x**8 + 18144*a**4*b**13*x**10 + 12096*a**3*b**14*x**12 + 5184*a**2*b**15*x**14 + 1296*a*b**16*x**16 + 144*b**17*x**18)","B",0
198,1,178,0,1.326792," ","integrate(x**13/(b*x**2+a)**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 a^{9} b^{7} + 4536 a^{8} b^{8} x^{2} + 18144 a^{7} b^{9} x^{4} + 42336 a^{6} b^{10} x^{6} + 63504 a^{5} b^{11} x^{8} + 63504 a^{4} b^{12} x^{10} + 42336 a^{3} b^{13} x^{12} + 18144 a^{2} b^{14} x^{14} + 4536 a b^{15} x^{16} + 504 b^{16} x^{18}}"," ",0,"(-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*a**9*b**7 + 4536*a**8*b**8*x**2 + 18144*a**7*b**9*x**4 + 42336*a**6*b**10*x**6 + 63504*a**5*b**11*x**8 + 63504*a**4*b**12*x**10 + 42336*a**3*b**13*x**12 + 18144*a**2*b**14*x**14 + 4536*a*b**15*x**16 + 504*b**16*x**18)","B",0
199,1,167,0,1.181614," ","integrate(x**11/(b*x**2+a)**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 a^{9} b^{6} + 9072 a^{8} b^{7} x^{2} + 36288 a^{7} b^{8} x^{4} + 84672 a^{6} b^{9} x^{6} + 127008 a^{5} b^{10} x^{8} + 127008 a^{4} b^{11} x^{10} + 84672 a^{3} b^{12} x^{12} + 36288 a^{2} b^{13} x^{14} + 9072 a b^{14} x^{16} + 1008 b^{15} x^{18}}"," ",0,"(-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*a**9*b**6 + 9072*a**8*b**7*x**2 + 36288*a**7*b**8*x**4 + 84672*a**6*b**9*x**6 + 127008*a**5*b**10*x**8 + 127008*a**4*b**11*x**10 + 84672*a**3*b**12*x**12 + 36288*a**2*b**13*x**14 + 9072*a*b**14*x**16 + 1008*b**15*x**18)","B",0
200,1,155,0,1.079243," ","integrate(x**9/(b*x**2+a)**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 a^{9} b^{5} + 11340 a^{8} b^{6} x^{2} + 45360 a^{7} b^{7} x^{4} + 105840 a^{6} b^{8} x^{6} + 158760 a^{5} b^{9} x^{8} + 158760 a^{4} b^{10} x^{10} + 105840 a^{3} b^{11} x^{12} + 45360 a^{2} b^{12} x^{14} + 11340 a b^{13} x^{16} + 1260 b^{14} x^{18}}"," ",0,"(-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*a**9*b**5 + 11340*a**8*b**6*x**2 + 45360*a**7*b**7*x**4 + 105840*a**6*b**8*x**6 + 158760*a**5*b**9*x**8 + 158760*a**4*b**10*x**10 + 105840*a**3*b**11*x**12 + 45360*a**2*b**12*x**14 + 11340*a*b**13*x**16 + 1260*b**14*x**18)","A",0
201,1,143,0,1.007383," ","integrate(x**7/(b*x**2+a)**10,x)","\frac{- a^{3} - 9 a^{2} b x^{2} - 36 a b^{2} x^{4} - 84 b^{3} x^{6}}{1008 a^{9} b^{4} + 9072 a^{8} b^{5} x^{2} + 36288 a^{7} b^{6} x^{4} + 84672 a^{6} b^{7} x^{6} + 127008 a^{5} b^{8} x^{8} + 127008 a^{4} b^{9} x^{10} + 84672 a^{3} b^{10} x^{12} + 36288 a^{2} b^{11} x^{14} + 9072 a b^{12} x^{16} + 1008 b^{13} x^{18}}"," ",0,"(-a**3 - 9*a**2*b*x**2 - 36*a*b**2*x**4 - 84*b**3*x**6)/(1008*a**9*b**4 + 9072*a**8*b**5*x**2 + 36288*a**7*b**6*x**4 + 84672*a**6*b**7*x**6 + 127008*a**5*b**8*x**8 + 127008*a**4*b**9*x**10 + 84672*a**3*b**10*x**12 + 36288*a**2*b**11*x**14 + 9072*a*b**12*x**16 + 1008*b**13*x**18)","B",0
202,1,131,0,0.945462," ","integrate(x**5/(b*x**2+a)**10,x)","\frac{- a^{2} - 9 a b x^{2} - 36 b^{2} x^{4}}{504 a^{9} b^{3} + 4536 a^{8} b^{4} x^{2} + 18144 a^{7} b^{5} x^{4} + 42336 a^{6} b^{6} x^{6} + 63504 a^{5} b^{7} x^{8} + 63504 a^{4} b^{8} x^{10} + 42336 a^{3} b^{9} x^{12} + 18144 a^{2} b^{10} x^{14} + 4536 a b^{11} x^{16} + 504 b^{12} x^{18}}"," ",0,"(-a**2 - 9*a*b*x**2 - 36*b**2*x**4)/(504*a**9*b**3 + 4536*a**8*b**4*x**2 + 18144*a**7*b**5*x**4 + 42336*a**6*b**6*x**6 + 63504*a**5*b**7*x**8 + 63504*a**4*b**8*x**10 + 42336*a**3*b**9*x**12 + 18144*a**2*b**10*x**14 + 4536*a*b**11*x**16 + 504*b**12*x**18)","B",0
203,1,119,0,0.926039," ","integrate(x**3/(b*x**2+a)**10,x)","\frac{- a - 9 b x^{2}}{144 a^{9} b^{2} + 1296 a^{8} b^{3} x^{2} + 5184 a^{7} b^{4} x^{4} + 12096 a^{6} b^{5} x^{6} + 18144 a^{5} b^{6} x^{8} + 18144 a^{4} b^{7} x^{10} + 12096 a^{3} b^{8} x^{12} + 5184 a^{2} b^{9} x^{14} + 1296 a b^{10} x^{16} + 144 b^{11} x^{18}}"," ",0,"(-a - 9*b*x**2)/(144*a**9*b**2 + 1296*a**8*b**3*x**2 + 5184*a**7*b**4*x**4 + 12096*a**6*b**5*x**6 + 18144*a**5*b**6*x**8 + 18144*a**4*b**7*x**10 + 12096*a**3*b**8*x**12 + 5184*a**2*b**9*x**14 + 1296*a*b**10*x**16 + 144*b**11*x**18)","B",0
204,1,110,0,0.893074," ","integrate(x/(b*x**2+a)**10,x)","- \frac{1}{18 a^{9} b + 162 a^{8} b^{2} x^{2} + 648 a^{7} b^{3} x^{4} + 1512 a^{6} b^{4} x^{6} + 2268 a^{5} b^{5} x^{8} + 2268 a^{4} b^{6} x^{10} + 1512 a^{3} b^{7} x^{12} + 648 a^{2} b^{8} x^{14} + 162 a b^{9} x^{16} + 18 b^{10} x^{18}}"," ",0,"-1/(18*a**9*b + 162*a**8*b**2*x**2 + 648*a**7*b**3*x**4 + 1512*a**6*b**4*x**6 + 2268*a**5*b**5*x**8 + 2268*a**4*b**6*x**10 + 1512*a**3*b**7*x**12 + 648*a**2*b**8*x**14 + 162*a*b**9*x**16 + 18*b**10*x**18)","B",0
205,1,223,0,1.308059," ","integrate(1/x/(b*x**2+a)**10,x)","\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^{18} + 45360 a^{17} b x^{2} + 181440 a^{16} b^{2} x^{4} + 423360 a^{15} b^{3} x^{6} + 635040 a^{14} b^{4} x^{8} + 635040 a^{13} b^{5} x^{10} + 423360 a^{12} b^{6} x^{12} + 181440 a^{11} b^{7} x^{14} + 45360 a^{10} b^{8} x^{16} + 5040 a^{9} b^{9} x^{18}} + \frac{\log{\left(x \right)}}{a^{10}} - \frac{\log{\left(\frac{a}{b} + x^{2} \right)}}{2 a^{10}}"," ",0,"(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**18 + 45360*a**17*b*x**2 + 181440*a**16*b**2*x**4 + 423360*a**15*b**3*x**6 + 635040*a**14*b**4*x**8 + 635040*a**13*b**5*x**10 + 423360*a**12*b**6*x**12 + 181440*a**11*b**7*x**14 + 45360*a**10*b**8*x**16 + 5040*a**9*b**9*x**18) + log(x)/a**10 - log(a/b + x**2)/(2*a**10)","A",0
206,1,245,0,1.464043," ","integrate(1/x**3/(b*x**2+a)**10,x)","\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^{19} x^{2} + 4536 a^{18} b x^{4} + 18144 a^{17} b^{2} x^{6} + 42336 a^{16} b^{3} x^{8} + 63504 a^{15} b^{4} x^{10} + 63504 a^{14} b^{5} x^{12} + 42336 a^{13} b^{6} x^{14} + 18144 a^{12} b^{7} x^{16} + 4536 a^{11} b^{8} x^{18} + 504 a^{10} b^{9} x^{20}} - \frac{10 b \log{\left(x \right)}}{a^{11}} + \frac{5 b \log{\left(\frac{a}{b} + x^{2} \right)}}{a^{11}}"," ",0,"(-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**19*x**2 + 4536*a**18*b*x**4 + 18144*a**17*b**2*x**6 + 42336*a**16*b**3*x**8 + 63504*a**15*b**4*x**10 + 63504*a**14*b**5*x**12 + 42336*a**13*b**6*x**14 + 18144*a**12*b**7*x**16 + 4536*a**11*b**8*x**18 + 504*a**10*b**9*x**20) - 10*b*log(x)/a**11 + 5*b*log(a/b + x**2)/a**11","A",0
207,1,260,0,1.548887," ","integrate(1/x**5/(b*x**2+a)**10,x)","\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^{20} x^{4} + 9072 a^{19} b x^{6} + 36288 a^{18} b^{2} x^{8} + 84672 a^{17} b^{3} x^{10} + 127008 a^{16} b^{4} x^{12} + 127008 a^{15} b^{5} x^{14} + 84672 a^{14} b^{6} x^{16} + 36288 a^{13} b^{7} x^{18} + 9072 a^{12} b^{8} x^{20} + 1008 a^{11} b^{9} x^{22}} + \frac{55 b^{2} \log{\left(x \right)}}{a^{12}} - \frac{55 b^{2} \log{\left(\frac{a}{b} + x^{2} \right)}}{2 a^{12}}"," ",0,"(-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**20*x**4 + 9072*a**19*b*x**6 + 36288*a**18*b**2*x**8 + 84672*a**17*b**3*x**10 + 127008*a**16*b**4*x**12 + 127008*a**15*b**5*x**14 + 84672*a**14*b**6*x**16 + 36288*a**13*b**7*x**18 + 9072*a**12*b**8*x**20 + 1008*a**11*b**9*x**22) + 55*b**2*log(x)/a**12 - 55*b**2*log(a/b + x**2)/(2*a**12)","A",0
208,1,270,0,1.604293," ","integrate(1/x**7/(b*x**2+a)**10,x)","\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^{21} x^{6} + 2268 a^{20} b x^{8} + 9072 a^{19} b^{2} x^{10} + 21168 a^{18} b^{3} x^{12} + 31752 a^{17} b^{4} x^{14} + 31752 a^{16} b^{5} x^{16} + 21168 a^{15} b^{6} x^{18} + 9072 a^{14} b^{7} x^{20} + 2268 a^{13} b^{8} x^{22} + 252 a^{12} b^{9} x^{24}} - \frac{220 b^{3} \log{\left(x \right)}}{a^{13}} + \frac{110 b^{3} \log{\left(\frac{a}{b} + x^{2} \right)}}{a^{13}}"," ",0,"(-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**21*x**6 + 2268*a**20*b*x**8 + 9072*a**19*b**2*x**10 + 21168*a**18*b**3*x**12 + 31752*a**17*b**4*x**14 + 31752*a**16*b**5*x**16 + 21168*a**15*b**6*x**18 + 9072*a**14*b**7*x**20 + 2268*a**13*b**8*x**22 + 252*a**12*b**9*x**24) - 220*b**3*log(x)/a**13 + 110*b**3*log(a/b + x**2)/a**13","A",0
209,1,314,0,2.039795," ","integrate(x**24/(b*x**2+a)**10,x)","\frac{55 a^{2} x}{b^{12}} - \frac{10 a x^{3}}{3 b^{11}} + \frac{7436429 \sqrt{- \frac{a^{5}}{b^{25}}} \log{\left(x - \frac{b^{12} \sqrt{- \frac{a^{5}}{b^{25}}}}{a^{2}} \right)}}{131072} - \frac{7436429 \sqrt{- \frac{a^{5}}{b^{25}}} \log{\left(x + \frac{b^{12} \sqrt{- \frac{a^{5}}{b^{25}}}}{a^{2}} \right)}}{131072} + \frac{172437705 a^{11} x + 1450223310 a^{10} b x^{3} + 5358651102 a^{9} b^{2} x^{5} + 11372226678 a^{8} b^{3} x^{7} + 15178104832 a^{7} b^{4} x^{9} + 13066540938 a^{6} b^{5} x^{11} + 7101970722 a^{5} b^{6} x^{13} + 2236176690 a^{4} b^{7} x^{15} + 314167095 a^{3} b^{8} x^{17}}{2949120 a^{9} b^{12} + 26542080 a^{8} b^{13} x^{2} + 106168320 a^{7} b^{14} x^{4} + 247726080 a^{6} b^{15} x^{6} + 371589120 a^{5} b^{16} x^{8} + 371589120 a^{4} b^{17} x^{10} + 247726080 a^{3} b^{18} x^{12} + 106168320 a^{2} b^{19} x^{14} + 26542080 a b^{20} x^{16} + 2949120 b^{21} x^{18}} + \frac{x^{5}}{5 b^{10}}"," ",0,"55*a**2*x/b**12 - 10*a*x**3/(3*b**11) + 7436429*sqrt(-a**5/b**25)*log(x - b**12*sqrt(-a**5/b**25)/a**2)/131072 - 7436429*sqrt(-a**5/b**25)*log(x + b**12*sqrt(-a**5/b**25)/a**2)/131072 + (172437705*a**11*x + 1450223310*a**10*b*x**3 + 5358651102*a**9*b**2*x**5 + 11372226678*a**8*b**3*x**7 + 15178104832*a**7*b**4*x**9 + 13066540938*a**6*b**5*x**11 + 7101970722*a**5*b**6*x**13 + 2236176690*a**4*b**7*x**15 + 314167095*a**3*b**8*x**17)/(2949120*a**9*b**12 + 26542080*a**8*b**13*x**2 + 106168320*a**7*b**14*x**4 + 247726080*a**6*b**15*x**6 + 371589120*a**5*b**16*x**8 + 371589120*a**4*b**17*x**10 + 247726080*a**3*b**18*x**12 + 106168320*a**2*b**19*x**14 + 26542080*a*b**20*x**16 + 2949120*b**21*x**18) + x**5/(5*b**10)","A",0
210,1,299,0,1.919314," ","integrate(x**22/(b*x**2+a)**10,x)","- \frac{10 a x}{b^{11}} - \frac{1616615 \sqrt{- \frac{a^{3}}{b^{23}}} \log{\left(x - \frac{b^{11} \sqrt{- \frac{a^{3}}{b^{23}}}}{a} \right)}}{131072} + \frac{1616615 \sqrt{- \frac{a^{3}}{b^{23}}} \log{\left(x + \frac{b^{11} \sqrt{- \frac{a^{3}}{b^{23}}}}{a} \right)}}{131072} + \frac{- 8651295 a^{10} x - 73208418 a^{9} b x^{3} - 272477394 a^{8} b^{2} x^{5} - 583302906 a^{7} b^{3} x^{7} - 786857984 a^{6} b^{4} x^{9} - 686588166 a^{5} b^{5} x^{11} - 379867950 a^{4} b^{6} x^{13} - 122613150 a^{3} b^{7} x^{15} - 17890785 a^{2} b^{8} x^{17}}{589824 a^{9} b^{11} + 5308416 a^{8} b^{12} x^{2} + 21233664 a^{7} b^{13} x^{4} + 49545216 a^{6} b^{14} x^{6} + 74317824 a^{5} b^{15} x^{8} + 74317824 a^{4} b^{16} x^{10} + 49545216 a^{3} b^{17} x^{12} + 21233664 a^{2} b^{18} x^{14} + 5308416 a b^{19} x^{16} + 589824 b^{20} x^{18}} + \frac{x^{3}}{3 b^{10}}"," ",0,"-10*a*x/b**11 - 1616615*sqrt(-a**3/b**23)*log(x - b**11*sqrt(-a**3/b**23)/a)/131072 + 1616615*sqrt(-a**3/b**23)*log(x + b**11*sqrt(-a**3/b**23)/a)/131072 + (-8651295*a**10*x - 73208418*a**9*b*x**3 - 272477394*a**8*b**2*x**5 - 583302906*a**7*b**3*x**7 - 786857984*a**6*b**4*x**9 - 686588166*a**5*b**5*x**11 - 379867950*a**4*b**6*x**13 - 122613150*a**3*b**7*x**15 - 17890785*a**2*b**8*x**17)/(589824*a**9*b**11 + 5308416*a**8*b**12*x**2 + 21233664*a**7*b**13*x**4 + 49545216*a**6*b**14*x**6 + 74317824*a**5*b**15*x**8 + 74317824*a**4*b**16*x**10 + 49545216*a**3*b**17*x**12 + 21233664*a**2*b**18*x**14 + 5308416*a*b**19*x**16 + 589824*b**20*x**18) + x**3/(3*b**10)","A",0
211,1,274,0,1.815825," ","integrate(x**20/(b*x**2+a)**10,x)","\frac{230945 \sqrt{- \frac{a}{b^{21}}} \log{\left(- b^{10} \sqrt{- \frac{a}{b^{21}}} + x \right)}}{131072} - \frac{230945 \sqrt{- \frac{a}{b^{21}}} \log{\left(b^{10} \sqrt{- \frac{a}{b^{21}}} + x \right)}}{131072} + \frac{10420767 a^{9} x + 88937058 a^{8} b x^{3} + 334408914 a^{7} b^{2} x^{5} + 724860666 a^{6} b^{3} x^{7} + 993296384 a^{5} b^{4} x^{9} + 884769030 a^{4} b^{5} x^{11} + 503730990 a^{3} b^{6} x^{13} + 169799070 a^{2} b^{7} x^{15} + 26738145 a b^{8} x^{17}}{4128768 a^{9} b^{10} + 37158912 a^{8} b^{11} x^{2} + 148635648 a^{7} b^{12} x^{4} + 346816512 a^{6} b^{13} x^{6} + 520224768 a^{5} b^{14} x^{8} + 520224768 a^{4} b^{15} x^{10} + 346816512 a^{3} b^{16} x^{12} + 148635648 a^{2} b^{17} x^{14} + 37158912 a b^{18} x^{16} + 4128768 b^{19} x^{18}} + \frac{x}{b^{10}}"," ",0,"230945*sqrt(-a/b**21)*log(-b**10*sqrt(-a/b**21) + x)/131072 - 230945*sqrt(-a/b**21)*log(b**10*sqrt(-a/b**21) + x)/131072 + (10420767*a**9*x + 88937058*a**8*b*x**3 + 334408914*a**7*b**2*x**5 + 724860666*a**6*b**3*x**7 + 993296384*a**5*b**4*x**9 + 884769030*a**4*b**5*x**11 + 503730990*a**3*b**6*x**13 + 169799070*a**2*b**7*x**15 + 26738145*a*b**8*x**17)/(4128768*a**9*b**10 + 37158912*a**8*b**11*x**2 + 148635648*a**7*b**12*x**4 + 346816512*a**6*b**13*x**6 + 520224768*a**5*b**14*x**8 + 520224768*a**4*b**15*x**10 + 346816512*a**3*b**16*x**12 + 148635648*a**2*b**17*x**14 + 37158912*a*b**18*x**16 + 4128768*b**19*x**18) + x/b**10","A",0
212,1,277,0,1.549637," ","integrate(x**18/(b*x**2+a)**10,x)","- \frac{12155 \sqrt{- \frac{1}{a b^{19}}} \log{\left(- a b^{9} \sqrt{- \frac{1}{a b^{19}}} + x \right)}}{131072} + \frac{12155 \sqrt{- \frac{1}{a b^{19}}} \log{\left(a b^{9} \sqrt{- \frac{1}{a b^{19}}} + x \right)}}{131072} + \frac{- 765765 a^{8} x - 6636630 a^{7} b x^{3} - 25423398 a^{6} b^{2} x^{5} - 56404062 a^{5} b^{3} x^{7} - 79659008 a^{4} b^{4} x^{9} - 73947042 a^{3} b^{5} x^{11} - 44765658 a^{2} b^{6} x^{13} - 16759722 a b^{7} x^{15} - 3363003 b^{8} x^{17}}{4128768 a^{9} b^{9} + 37158912 a^{8} b^{10} x^{2} + 148635648 a^{7} b^{11} x^{4} + 346816512 a^{6} b^{12} x^{6} + 520224768 a^{5} b^{13} x^{8} + 520224768 a^{4} b^{14} x^{10} + 346816512 a^{3} b^{15} x^{12} + 148635648 a^{2} b^{16} x^{14} + 37158912 a b^{17} x^{16} + 4128768 b^{18} x^{18}}"," ",0,"-12155*sqrt(-1/(a*b**19))*log(-a*b**9*sqrt(-1/(a*b**19)) + x)/131072 + 12155*sqrt(-1/(a*b**19))*log(a*b**9*sqrt(-1/(a*b**19)) + x)/131072 + (-765765*a**8*x - 6636630*a**7*b*x**3 - 25423398*a**6*b**2*x**5 - 56404062*a**5*b**3*x**7 - 79659008*a**4*b**4*x**9 - 73947042*a**3*b**5*x**11 - 44765658*a**2*b**6*x**13 - 16759722*a*b**7*x**15 - 3363003*b**8*x**17)/(4128768*a**9*b**9 + 37158912*a**8*b**10*x**2 + 148635648*a**7*b**11*x**4 + 346816512*a**6*b**12*x**6 + 520224768*a**5*b**13*x**8 + 520224768*a**4*b**14*x**10 + 346816512*a**3*b**15*x**12 + 148635648*a**2*b**16*x**14 + 37158912*a*b**17*x**16 + 4128768*b**18*x**18)","A",0
213,1,289,0,1.455999," ","integrate(x**16/(b*x**2+a)**10,x)","- \frac{715 \sqrt{- \frac{1}{a^{3} b^{17}}} \log{\left(- a^{2} b^{8} \sqrt{- \frac{1}{a^{3} b^{17}}} + x \right)}}{131072} + \frac{715 \sqrt{- \frac{1}{a^{3} b^{17}}} \log{\left(a^{2} b^{8} \sqrt{- \frac{1}{a^{3} b^{17}}} + x \right)}}{131072} + \frac{- 45045 a^{8} x - 390390 a^{7} b x^{3} - 1495494 a^{6} b^{2} x^{5} - 3317886 a^{5} b^{3} x^{7} - 4685824 a^{4} b^{4} x^{9} - 4349826 a^{3} b^{5} x^{11} - 2633274 a^{2} b^{6} x^{13} - 985866 a b^{7} x^{15} + 45045 b^{8} x^{17}}{4128768 a^{10} b^{8} + 37158912 a^{9} b^{9} x^{2} + 148635648 a^{8} b^{10} x^{4} + 346816512 a^{7} b^{11} x^{6} + 520224768 a^{6} b^{12} x^{8} + 520224768 a^{5} b^{13} x^{10} + 346816512 a^{4} b^{14} x^{12} + 148635648 a^{3} b^{15} x^{14} + 37158912 a^{2} b^{16} x^{16} + 4128768 a b^{17} x^{18}}"," ",0,"-715*sqrt(-1/(a**3*b**17))*log(-a**2*b**8*sqrt(-1/(a**3*b**17)) + x)/131072 + 715*sqrt(-1/(a**3*b**17))*log(a**2*b**8*sqrt(-1/(a**3*b**17)) + x)/131072 + (-45045*a**8*x - 390390*a**7*b*x**3 - 1495494*a**6*b**2*x**5 - 3317886*a**5*b**3*x**7 - 4685824*a**4*b**4*x**9 - 4349826*a**3*b**5*x**11 - 2633274*a**2*b**6*x**13 - 985866*a*b**7*x**15 + 45045*b**8*x**17)/(4128768*a**10*b**8 + 37158912*a**9*b**9*x**2 + 148635648*a**8*b**10*x**4 + 346816512*a**7*b**11*x**6 + 520224768*a**6*b**12*x**8 + 520224768*a**5*b**13*x**10 + 346816512*a**4*b**14*x**12 + 148635648*a**3*b**15*x**14 + 37158912*a**2*b**16*x**16 + 4128768*a*b**17*x**18)","A",0
214,1,291,0,1.353403," ","integrate(x**14/(b*x**2+a)**10,x)","- \frac{143 \sqrt{- \frac{1}{a^{5} b^{15}}} \log{\left(- a^{3} b^{7} \sqrt{- \frac{1}{a^{5} b^{15}}} + x \right)}}{131072} + \frac{143 \sqrt{- \frac{1}{a^{5} b^{15}}} \log{\left(a^{3} b^{7} \sqrt{- \frac{1}{a^{5} b^{15}}} + x \right)}}{131072} + \frac{- 45045 a^{8} x - 390390 a^{7} b x^{3} - 1495494 a^{6} b^{2} x^{5} - 3317886 a^{5} b^{3} x^{7} - 4685824 a^{4} b^{4} x^{9} - 4349826 a^{3} b^{5} x^{11} - 2633274 a^{2} b^{6} x^{13} + 390390 a b^{7} x^{15} + 45045 b^{8} x^{17}}{20643840 a^{11} b^{7} + 185794560 a^{10} b^{8} x^{2} + 743178240 a^{9} b^{9} x^{4} + 1734082560 a^{8} b^{10} x^{6} + 2601123840 a^{7} b^{11} x^{8} + 2601123840 a^{6} b^{12} x^{10} + 1734082560 a^{5} b^{13} x^{12} + 743178240 a^{4} b^{14} x^{14} + 185794560 a^{3} b^{15} x^{16} + 20643840 a^{2} b^{16} x^{18}}"," ",0,"-143*sqrt(-1/(a**5*b**15))*log(-a**3*b**7*sqrt(-1/(a**5*b**15)) + x)/131072 + 143*sqrt(-1/(a**5*b**15))*log(a**3*b**7*sqrt(-1/(a**5*b**15)) + x)/131072 + (-45045*a**8*x - 390390*a**7*b*x**3 - 1495494*a**6*b**2*x**5 - 3317886*a**5*b**3*x**7 - 4685824*a**4*b**4*x**9 - 4349826*a**3*b**5*x**11 - 2633274*a**2*b**6*x**13 + 390390*a*b**7*x**15 + 45045*b**8*x**17)/(20643840*a**11*b**7 + 185794560*a**10*b**8*x**2 + 743178240*a**9*b**9*x**4 + 1734082560*a**8*b**10*x**6 + 2601123840*a**7*b**11*x**8 + 2601123840*a**6*b**12*x**10 + 1734082560*a**5*b**13*x**12 + 743178240*a**4*b**14*x**14 + 185794560*a**3*b**15*x**16 + 20643840*a**2*b**16*x**18)","A",0
215,1,291,0,1.274494," ","integrate(x**12/(b*x**2+a)**10,x)","- \frac{55 \sqrt{- \frac{1}{a^{7} b^{13}}} \log{\left(- a^{4} b^{6} \sqrt{- \frac{1}{a^{7} b^{13}}} + x \right)}}{131072} + \frac{55 \sqrt{- \frac{1}{a^{7} b^{13}}} \log{\left(a^{4} b^{6} \sqrt{- \frac{1}{a^{7} b^{13}}} + x \right)}}{131072} + \frac{- 3465 a^{8} x - 30030 a^{7} b x^{3} - 115038 a^{6} b^{2} x^{5} - 255222 a^{5} b^{3} x^{7} - 360448 a^{4} b^{4} x^{9} - 334602 a^{3} b^{5} x^{11} + 115038 a^{2} b^{6} x^{13} + 30030 a b^{7} x^{15} + 3465 b^{8} x^{17}}{4128768 a^{12} b^{6} + 37158912 a^{11} b^{7} x^{2} + 148635648 a^{10} b^{8} x^{4} + 346816512 a^{9} b^{9} x^{6} + 520224768 a^{8} b^{10} x^{8} + 520224768 a^{7} b^{11} x^{10} + 346816512 a^{6} b^{12} x^{12} + 148635648 a^{5} b^{13} x^{14} + 37158912 a^{4} b^{14} x^{16} + 4128768 a^{3} b^{15} x^{18}}"," ",0,"-55*sqrt(-1/(a**7*b**13))*log(-a**4*b**6*sqrt(-1/(a**7*b**13)) + x)/131072 + 55*sqrt(-1/(a**7*b**13))*log(a**4*b**6*sqrt(-1/(a**7*b**13)) + x)/131072 + (-3465*a**8*x - 30030*a**7*b*x**3 - 115038*a**6*b**2*x**5 - 255222*a**5*b**3*x**7 - 360448*a**4*b**4*x**9 - 334602*a**3*b**5*x**11 + 115038*a**2*b**6*x**13 + 30030*a*b**7*x**15 + 3465*b**8*x**17)/(4128768*a**12*b**6 + 37158912*a**11*b**7*x**2 + 148635648*a**10*b**8*x**4 + 346816512*a**9*b**9*x**6 + 520224768*a**8*b**10*x**8 + 520224768*a**7*b**11*x**10 + 346816512*a**6*b**12*x**12 + 148635648*a**5*b**13*x**14 + 37158912*a**4*b**14*x**16 + 4128768*a**3*b**15*x**18)","A",0
216,1,291,0,1.189703," ","integrate(x**10/(b*x**2+a)**10,x)","- \frac{35 \sqrt{- \frac{1}{a^{9} b^{11}}} \log{\left(- a^{5} b^{5} \sqrt{- \frac{1}{a^{9} b^{11}}} + x \right)}}{131072} + \frac{35 \sqrt{- \frac{1}{a^{9} b^{11}}} \log{\left(a^{5} b^{5} \sqrt{- \frac{1}{a^{9} b^{11}}} + x \right)}}{131072} + \frac{- 315 a^{8} x - 2730 a^{7} b x^{3} - 10458 a^{6} b^{2} x^{5} - 23202 a^{5} b^{3} x^{7} - 32768 a^{4} b^{4} x^{9} + 23202 a^{3} b^{5} x^{11} + 10458 a^{2} b^{6} x^{13} + 2730 a b^{7} x^{15} + 315 b^{8} x^{17}}{589824 a^{13} b^{5} + 5308416 a^{12} b^{6} x^{2} + 21233664 a^{11} b^{7} x^{4} + 49545216 a^{10} b^{8} x^{6} + 74317824 a^{9} b^{9} x^{8} + 74317824 a^{8} b^{10} x^{10} + 49545216 a^{7} b^{11} x^{12} + 21233664 a^{6} b^{12} x^{14} + 5308416 a^{5} b^{13} x^{16} + 589824 a^{4} b^{14} x^{18}}"," ",0,"-35*sqrt(-1/(a**9*b**11))*log(-a**5*b**5*sqrt(-1/(a**9*b**11)) + x)/131072 + 35*sqrt(-1/(a**9*b**11))*log(a**5*b**5*sqrt(-1/(a**9*b**11)) + x)/131072 + (-315*a**8*x - 2730*a**7*b*x**3 - 10458*a**6*b**2*x**5 - 23202*a**5*b**3*x**7 - 32768*a**4*b**4*x**9 + 23202*a**3*b**5*x**11 + 10458*a**2*b**6*x**13 + 2730*a*b**7*x**15 + 315*b**8*x**17)/(589824*a**13*b**5 + 5308416*a**12*b**6*x**2 + 21233664*a**11*b**7*x**4 + 49545216*a**10*b**8*x**6 + 74317824*a**9*b**9*x**8 + 74317824*a**8*b**10*x**10 + 49545216*a**7*b**11*x**12 + 21233664*a**6*b**12*x**14 + 5308416*a**5*b**13*x**16 + 589824*a**4*b**14*x**18)","A",0
217,1,291,0,1.154174," ","integrate(x**8/(b*x**2+a)**10,x)","- \frac{35 \sqrt{- \frac{1}{a^{11} b^{9}}} \log{\left(- a^{6} b^{4} \sqrt{- \frac{1}{a^{11} b^{9}}} + x \right)}}{131072} + \frac{35 \sqrt{- \frac{1}{a^{11} b^{9}}} \log{\left(a^{6} b^{4} \sqrt{- \frac{1}{a^{11} b^{9}}} + x \right)}}{131072} + \frac{- 315 a^{8} x - 2730 a^{7} b x^{3} - 10458 a^{6} b^{2} x^{5} - 23202 a^{5} b^{3} x^{7} + 32768 a^{4} b^{4} x^{9} + 23202 a^{3} b^{5} x^{11} + 10458 a^{2} b^{6} x^{13} + 2730 a b^{7} x^{15} + 315 b^{8} x^{17}}{589824 a^{14} b^{4} + 5308416 a^{13} b^{5} x^{2} + 21233664 a^{12} b^{6} x^{4} + 49545216 a^{11} b^{7} x^{6} + 74317824 a^{10} b^{8} x^{8} + 74317824 a^{9} b^{9} x^{10} + 49545216 a^{8} b^{10} x^{12} + 21233664 a^{7} b^{11} x^{14} + 5308416 a^{6} b^{12} x^{16} + 589824 a^{5} b^{13} x^{18}}"," ",0,"-35*sqrt(-1/(a**11*b**9))*log(-a**6*b**4*sqrt(-1/(a**11*b**9)) + x)/131072 + 35*sqrt(-1/(a**11*b**9))*log(a**6*b**4*sqrt(-1/(a**11*b**9)) + x)/131072 + (-315*a**8*x - 2730*a**7*b*x**3 - 10458*a**6*b**2*x**5 - 23202*a**5*b**3*x**7 + 32768*a**4*b**4*x**9 + 23202*a**3*b**5*x**11 + 10458*a**2*b**6*x**13 + 2730*a*b**7*x**15 + 315*b**8*x**17)/(589824*a**14*b**4 + 5308416*a**13*b**5*x**2 + 21233664*a**12*b**6*x**4 + 49545216*a**11*b**7*x**6 + 74317824*a**10*b**8*x**8 + 74317824*a**9*b**9*x**10 + 49545216*a**8*b**10*x**12 + 21233664*a**7*b**11*x**14 + 5308416*a**6*b**12*x**16 + 589824*a**5*b**13*x**18)","A",0
218,1,291,0,1.083770," ","integrate(x**6/(b*x**2+a)**10,x)","- \frac{55 \sqrt{- \frac{1}{a^{13} b^{7}}} \log{\left(- a^{7} b^{3} \sqrt{- \frac{1}{a^{13} b^{7}}} + x \right)}}{131072} + \frac{55 \sqrt{- \frac{1}{a^{13} b^{7}}} \log{\left(a^{7} b^{3} \sqrt{- \frac{1}{a^{13} b^{7}}} + x \right)}}{131072} + \frac{- 3465 a^{8} x - 30030 a^{7} b x^{3} - 115038 a^{6} b^{2} x^{5} + 334602 a^{5} b^{3} x^{7} + 360448 a^{4} b^{4} x^{9} + 255222 a^{3} b^{5} x^{11} + 115038 a^{2} b^{6} x^{13} + 30030 a b^{7} x^{15} + 3465 b^{8} x^{17}}{4128768 a^{15} b^{3} + 37158912 a^{14} b^{4} x^{2} + 148635648 a^{13} b^{5} x^{4} + 346816512 a^{12} b^{6} x^{6} + 520224768 a^{11} b^{7} x^{8} + 520224768 a^{10} b^{8} x^{10} + 346816512 a^{9} b^{9} x^{12} + 148635648 a^{8} b^{10} x^{14} + 37158912 a^{7} b^{11} x^{16} + 4128768 a^{6} b^{12} x^{18}}"," ",0,"-55*sqrt(-1/(a**13*b**7))*log(-a**7*b**3*sqrt(-1/(a**13*b**7)) + x)/131072 + 55*sqrt(-1/(a**13*b**7))*log(a**7*b**3*sqrt(-1/(a**13*b**7)) + x)/131072 + (-3465*a**8*x - 30030*a**7*b*x**3 - 115038*a**6*b**2*x**5 + 334602*a**5*b**3*x**7 + 360448*a**4*b**4*x**9 + 255222*a**3*b**5*x**11 + 115038*a**2*b**6*x**13 + 30030*a*b**7*x**15 + 3465*b**8*x**17)/(4128768*a**15*b**3 + 37158912*a**14*b**4*x**2 + 148635648*a**13*b**5*x**4 + 346816512*a**12*b**6*x**6 + 520224768*a**11*b**7*x**8 + 520224768*a**10*b**8*x**10 + 346816512*a**9*b**9*x**12 + 148635648*a**8*b**10*x**14 + 37158912*a**7*b**11*x**16 + 4128768*a**6*b**12*x**18)","A",0
219,1,291,0,1.035949," ","integrate(x**4/(b*x**2+a)**10,x)","- \frac{143 \sqrt{- \frac{1}{a^{15} b^{5}}} \log{\left(- a^{8} b^{2} \sqrt{- \frac{1}{a^{15} b^{5}}} + x \right)}}{131072} + \frac{143 \sqrt{- \frac{1}{a^{15} b^{5}}} \log{\left(a^{8} b^{2} \sqrt{- \frac{1}{a^{15} b^{5}}} + x \right)}}{131072} + \frac{- 45045 a^{8} x - 390390 a^{7} b x^{3} + 2633274 a^{6} b^{2} x^{5} + 4349826 a^{5} b^{3} x^{7} + 4685824 a^{4} b^{4} x^{9} + 3317886 a^{3} b^{5} x^{11} + 1495494 a^{2} b^{6} x^{13} + 390390 a b^{7} x^{15} + 45045 b^{8} x^{17}}{20643840 a^{16} b^{2} + 185794560 a^{15} b^{3} x^{2} + 743178240 a^{14} b^{4} x^{4} + 1734082560 a^{13} b^{5} x^{6} + 2601123840 a^{12} b^{6} x^{8} + 2601123840 a^{11} b^{7} x^{10} + 1734082560 a^{10} b^{8} x^{12} + 743178240 a^{9} b^{9} x^{14} + 185794560 a^{8} b^{10} x^{16} + 20643840 a^{7} b^{11} x^{18}}"," ",0,"-143*sqrt(-1/(a**15*b**5))*log(-a**8*b**2*sqrt(-1/(a**15*b**5)) + x)/131072 + 143*sqrt(-1/(a**15*b**5))*log(a**8*b**2*sqrt(-1/(a**15*b**5)) + x)/131072 + (-45045*a**8*x - 390390*a**7*b*x**3 + 2633274*a**6*b**2*x**5 + 4349826*a**5*b**3*x**7 + 4685824*a**4*b**4*x**9 + 3317886*a**3*b**5*x**11 + 1495494*a**2*b**6*x**13 + 390390*a*b**7*x**15 + 45045*b**8*x**17)/(20643840*a**16*b**2 + 185794560*a**15*b**3*x**2 + 743178240*a**14*b**4*x**4 + 1734082560*a**13*b**5*x**6 + 2601123840*a**12*b**6*x**8 + 2601123840*a**11*b**7*x**10 + 1734082560*a**10*b**8*x**12 + 743178240*a**9*b**9*x**14 + 185794560*a**8*b**10*x**16 + 20643840*a**7*b**11*x**18)","A",0
220,1,286,0,1.026837," ","integrate(x**2/(b*x**2+a)**10,x)","- \frac{715 \sqrt{- \frac{1}{a^{17} b^{3}}} \log{\left(- a^{9} b \sqrt{- \frac{1}{a^{17} b^{3}}} + x \right)}}{131072} + \frac{715 \sqrt{- \frac{1}{a^{17} b^{3}}} \log{\left(a^{9} b \sqrt{- \frac{1}{a^{17} b^{3}}} + x \right)}}{131072} + \frac{- 45045 a^{8} x + 985866 a^{7} b x^{3} + 2633274 a^{6} b^{2} x^{5} + 4349826 a^{5} b^{3} x^{7} + 4685824 a^{4} b^{4} x^{9} + 3317886 a^{3} b^{5} x^{11} + 1495494 a^{2} b^{6} x^{13} + 390390 a b^{7} x^{15} + 45045 b^{8} x^{17}}{4128768 a^{17} b + 37158912 a^{16} b^{2} x^{2} + 148635648 a^{15} b^{3} x^{4} + 346816512 a^{14} b^{4} x^{6} + 520224768 a^{13} b^{5} x^{8} + 520224768 a^{12} b^{6} x^{10} + 346816512 a^{11} b^{7} x^{12} + 148635648 a^{10} b^{8} x^{14} + 37158912 a^{9} b^{9} x^{16} + 4128768 a^{8} b^{10} x^{18}}"," ",0,"-715*sqrt(-1/(a**17*b**3))*log(-a**9*b*sqrt(-1/(a**17*b**3)) + x)/131072 + 715*sqrt(-1/(a**17*b**3))*log(a**9*b*sqrt(-1/(a**17*b**3)) + x)/131072 + (-45045*a**8*x + 985866*a**7*b*x**3 + 2633274*a**6*b**2*x**5 + 4349826*a**5*b**3*x**7 + 4685824*a**4*b**4*x**9 + 3317886*a**3*b**5*x**11 + 1495494*a**2*b**6*x**13 + 390390*a*b**7*x**15 + 45045*b**8*x**17)/(4128768*a**17*b + 37158912*a**16*b**2*x**2 + 148635648*a**15*b**3*x**4 + 346816512*a**14*b**4*x**6 + 520224768*a**13*b**5*x**8 + 520224768*a**12*b**6*x**10 + 346816512*a**11*b**7*x**12 + 148635648*a**10*b**8*x**14 + 37158912*a**9*b**9*x**16 + 4128768*a**8*b**10*x**18)","A",0
221,1,272,0,1.035671," ","integrate(1/(b*x**2+a)**10,x)","- \frac{12155 \sqrt{- \frac{1}{a^{19} b}} \log{\left(- a^{10} \sqrt{- \frac{1}{a^{19} b}} + x \right)}}{131072} + \frac{12155 \sqrt{- \frac{1}{a^{19} b}} \log{\left(a^{10} \sqrt{- \frac{1}{a^{19} b}} + x \right)}}{131072} + \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^{18} + 37158912 a^{17} b x^{2} + 148635648 a^{16} b^{2} x^{4} + 346816512 a^{15} b^{3} x^{6} + 520224768 a^{14} b^{4} x^{8} + 520224768 a^{13} b^{5} x^{10} + 346816512 a^{12} b^{6} x^{12} + 148635648 a^{11} b^{7} x^{14} + 37158912 a^{10} b^{8} x^{16} + 4128768 a^{9} b^{9} x^{18}}"," ",0,"-12155*sqrt(-1/(a**19*b))*log(-a**10*sqrt(-1/(a**19*b)) + x)/131072 + 12155*sqrt(-1/(a**19*b))*log(a**10*sqrt(-1/(a**19*b)) + x)/131072 + (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**18 + 37158912*a**17*b*x**2 + 148635648*a**16*b**2*x**4 + 346816512*a**15*b**3*x**6 + 520224768*a**14*b**4*x**8 + 520224768*a**13*b**5*x**10 + 346816512*a**12*b**6*x**12 + 148635648*a**11*b**7*x**14 + 37158912*a**10*b**8*x**16 + 4128768*a**9*b**9*x**18)","A",0
222,1,282,0,1.347538," ","integrate(1/x**2/(b*x**2+a)**10,x)","\frac{230945 \sqrt{- \frac{b}{a^{21}}} \log{\left(- \frac{a^{11} \sqrt{- \frac{b}{a^{21}}}}{b} + x \right)}}{131072} - \frac{230945 \sqrt{- \frac{b}{a^{21}}} \log{\left(\frac{a^{11} \sqrt{- \frac{b}{a^{21}}}}{b} + x \right)}}{131072} + \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^{19} x + 37158912 a^{18} b x^{3} + 148635648 a^{17} b^{2} x^{5} + 346816512 a^{16} b^{3} x^{7} + 520224768 a^{15} b^{4} x^{9} + 520224768 a^{14} b^{5} x^{11} + 346816512 a^{13} b^{6} x^{13} + 148635648 a^{12} b^{7} x^{15} + 37158912 a^{11} b^{8} x^{17} + 4128768 a^{10} b^{9} x^{19}}"," ",0,"230945*sqrt(-b/a**21)*log(-a**11*sqrt(-b/a**21)/b + x)/131072 - 230945*sqrt(-b/a**21)*log(a**11*sqrt(-b/a**21)/b + x)/131072 + (-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**19*x + 37158912*a**18*b*x**3 + 148635648*a**17*b**2*x**5 + 346816512*a**16*b**3*x**7 + 520224768*a**15*b**4*x**9 + 520224768*a**14*b**5*x**11 + 346816512*a**13*b**6*x**13 + 148635648*a**12*b**7*x**15 + 37158912*a**11*b**8*x**17 + 4128768*a**10*b**9*x**19)","A",0
223,1,304,0,1.454270," ","integrate(1/x**4/(b*x**2+a)**10,x)","- \frac{1616615 \sqrt{- \frac{b^{3}}{a^{23}}} \log{\left(- \frac{a^{12} \sqrt{- \frac{b^{3}}{a^{23}}}}{b^{2}} + x \right)}}{131072} + \frac{1616615 \sqrt{- \frac{b^{3}}{a^{23}}} \log{\left(\frac{a^{12} \sqrt{- \frac{b^{3}}{a^{23}}}}{b^{2}} + x \right)}}{131072} + \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^{20} x^{3} + 5308416 a^{19} b x^{5} + 21233664 a^{18} b^{2} x^{7} + 49545216 a^{17} b^{3} x^{9} + 74317824 a^{16} b^{4} x^{11} + 74317824 a^{15} b^{5} x^{13} + 49545216 a^{14} b^{6} x^{15} + 21233664 a^{13} b^{7} x^{17} + 5308416 a^{12} b^{8} x^{19} + 589824 a^{11} b^{9} x^{21}}"," ",0,"-1616615*sqrt(-b**3/a**23)*log(-a**12*sqrt(-b**3/a**23)/b**2 + x)/131072 + 1616615*sqrt(-b**3/a**23)*log(a**12*sqrt(-b**3/a**23)/b**2 + x)/131072 + (-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**20*x**3 + 5308416*a**19*b*x**5 + 21233664*a**18*b**2*x**7 + 49545216*a**17*b**3*x**9 + 74317824*a**16*b**4*x**11 + 74317824*a**15*b**5*x**13 + 49545216*a**14*b**6*x**15 + 21233664*a**13*b**7*x**17 + 5308416*a**12*b**8*x**19 + 589824*a**11*b**9*x**21)","A",0
224,1,316,0,1.499575," ","integrate(1/x**6/(b*x**2+a)**10,x)","\frac{7436429 \sqrt{- \frac{b^{5}}{a^{25}}} \log{\left(- \frac{a^{13} \sqrt{- \frac{b^{5}}{a^{25}}}}{b^{3}} + x \right)}}{131072} - \frac{7436429 \sqrt{- \frac{b^{5}}{a^{25}}} \log{\left(\frac{a^{13} \sqrt{- \frac{b^{5}}{a^{25}}}}{b^{3}} + x \right)}}{131072} + \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^{21} x^{5} + 26542080 a^{20} b x^{7} + 106168320 a^{19} b^{2} x^{9} + 247726080 a^{18} b^{3} x^{11} + 371589120 a^{17} b^{4} x^{13} + 371589120 a^{16} b^{5} x^{15} + 247726080 a^{15} b^{6} x^{17} + 106168320 a^{14} b^{7} x^{19} + 26542080 a^{13} b^{8} x^{21} + 2949120 a^{12} b^{9} x^{23}}"," ",0,"7436429*sqrt(-b**5/a**25)*log(-a**13*sqrt(-b**5/a**25)/b**3 + x)/131072 - 7436429*sqrt(-b**5/a**25)*log(a**13*sqrt(-b**5/a**25)/b**3 + x)/131072 + (-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**21*x**5 + 26542080*a**20*b*x**7 + 106168320*a**19*b**2*x**9 + 247726080*a**18*b**3*x**11 + 371589120*a**17*b**4*x**13 + 371589120*a**16*b**5*x**15 + 247726080*a**15*b**6*x**17 + 106168320*a**14*b**7*x**19 + 26542080*a**13*b**8*x**21 + 2949120*a**12*b**9*x**23)","A",0
225,1,22,0,0.140768," ","integrate(x**3/(-b*x**2+a),x)","- \frac{a \log{\left(- a + b x^{2} \right)}}{2 b^{2}} - \frac{x^{2}}{2 b}"," ",0,"-a*log(-a + b*x**2)/(2*b**2) - x**2/(2*b)","A",0
226,1,49,0,0.151659," ","integrate(x**2/(-b*x**2+a),x)","- \frac{\sqrt{\frac{a}{b^{3}}} \log{\left(- b \sqrt{\frac{a}{b^{3}}} + x \right)}}{2} + \frac{\sqrt{\frac{a}{b^{3}}} \log{\left(b \sqrt{\frac{a}{b^{3}}} + x \right)}}{2} - \frac{x}{b}"," ",0,"-sqrt(a/b**3)*log(-b*sqrt(a/b**3) + x)/2 + sqrt(a/b**3)*log(b*sqrt(a/b**3) + x)/2 - x/b","A",0
227,1,12,0,0.115381," ","integrate(x/(-b*x**2+a),x)","- \frac{\log{\left(- a + b x^{2} \right)}}{2 b}"," ",0,"-log(-a + b*x**2)/(2*b)","A",0
228,1,46,0,0.140081," ","integrate(1/(-b*x**2+a),x)","- \frac{\sqrt{\frac{1}{a b}} \log{\left(- a \sqrt{\frac{1}{a b}} + x \right)}}{2} + \frac{\sqrt{\frac{1}{a b}} \log{\left(a \sqrt{\frac{1}{a b}} + x \right)}}{2}"," ",0,"-sqrt(1/(a*b))*log(-a*sqrt(1/(a*b)) + x)/2 + sqrt(1/(a*b))*log(a*sqrt(1/(a*b)) + x)/2","B",0
229,1,15,0,0.213916," ","integrate(1/x/(-b*x**2+a),x)","\frac{\log{\left(x \right)}}{a} - \frac{\log{\left(- \frac{a}{b} + x^{2} \right)}}{2 a}"," ",0,"log(x)/a - log(-a/b + x**2)/(2*a)","A",0
230,1,58,0,0.186187," ","integrate(1/x**2/(-b*x**2+a),x)","- \frac{\sqrt{\frac{b}{a^{3}}} \log{\left(- \frac{a^{2} \sqrt{\frac{b}{a^{3}}}}{b} + x \right)}}{2} + \frac{\sqrt{\frac{b}{a^{3}}} \log{\left(\frac{a^{2} \sqrt{\frac{b}{a^{3}}}}{b} + x \right)}}{2} - \frac{1}{a x}"," ",0,"-sqrt(b/a**3)*log(-a**2*sqrt(b/a**3)/b + x)/2 + sqrt(b/a**3)*log(a**2*sqrt(b/a**3)/b + x)/2 - 1/(a*x)","B",0
231,1,31,0,0.272981," ","integrate(1/x**3/(-b*x**2+a),x)","- \frac{1}{2 a x^{2}} + \frac{b \log{\left(x \right)}}{a^{2}} - \frac{b \log{\left(- \frac{a}{b} + x^{2} \right)}}{2 a^{2}}"," ",0,"-1/(2*a*x**2) + b*log(x)/a**2 - b*log(-a/b + x**2)/(2*a**2)","A",0
232,1,29,0,0.196018," ","integrate(x**3/(-b*x**2+a)**2,x)","- \frac{a}{- 2 a b^{2} + 2 b^{3} x^{2}} + \frac{\log{\left(- a + b x^{2} \right)}}{2 b^{2}}"," ",0,"-a/(-2*a*b**2 + 2*b**3*x**2) + log(-a + b*x**2)/(2*b**2)","A",0
233,1,71,0,0.213779," ","integrate(x**2/(-b*x**2+a)**2,x)","- \frac{x}{- 2 a b + 2 b^{2} x^{2}} + \frac{\sqrt{\frac{1}{a b^{3}}} \log{\left(- a b \sqrt{\frac{1}{a b^{3}}} + x \right)}}{4} - \frac{\sqrt{\frac{1}{a b^{3}}} \log{\left(a b \sqrt{\frac{1}{a b^{3}}} + x \right)}}{4}"," ",0,"-x/(-2*a*b + 2*b**2*x**2) + sqrt(1/(a*b**3))*log(-a*b*sqrt(1/(a*b**3)) + x)/4 - sqrt(1/(a*b**3))*log(a*b*sqrt(1/(a*b**3)) + x)/4","A",0
234,1,15,0,0.156267," ","integrate(x/(-b*x**2+a)**2,x)","- \frac{1}{- 2 a b + 2 b^{2} x^{2}}"," ",0,"-1/(-2*a*b + 2*b**2*x**2)","A",0
235,1,71,0,0.220046," ","integrate(1/(-b*x**2+a)**2,x)","- \frac{x}{- 2 a^{2} + 2 a b x^{2}} - \frac{\sqrt{\frac{1}{a^{3} b}} \log{\left(- a^{2} \sqrt{\frac{1}{a^{3} b}} + x \right)}}{4} + \frac{\sqrt{\frac{1}{a^{3} b}} \log{\left(a^{2} \sqrt{\frac{1}{a^{3} b}} + x \right)}}{4}"," ",0,"-x/(-2*a**2 + 2*a*b*x**2) - sqrt(1/(a**3*b))*log(-a**2*sqrt(1/(a**3*b)) + x)/4 + sqrt(1/(a**3*b))*log(a**2*sqrt(1/(a**3*b)) + x)/4","A",0
236,1,34,0,0.299236," ","integrate(1/x/(-b*x**2+a)**2,x)","- \frac{1}{- 2 a^{2} + 2 a b x^{2}} + \frac{\log{\left(x \right)}}{a^{2}} - \frac{\log{\left(- \frac{a}{b} + x^{2} \right)}}{2 a^{2}}"," ",0,"-1/(-2*a**2 + 2*a*b*x**2) + log(x)/a**2 - log(-a/b + x**2)/(2*a**2)","A",0
237,1,83,0,0.297819," ","integrate(1/x**2/(-b*x**2+a)**2,x)","- \frac{3 \sqrt{\frac{b}{a^{5}}} \log{\left(- \frac{a^{3} \sqrt{\frac{b}{a^{5}}}}{b} + x \right)}}{4} + \frac{3 \sqrt{\frac{b}{a^{5}}} \log{\left(\frac{a^{3} \sqrt{\frac{b}{a^{5}}}}{b} + x \right)}}{4} + \frac{2 a - 3 b x^{2}}{- 2 a^{3} x + 2 a^{2} b x^{3}}"," ",0,"-3*sqrt(b/a**5)*log(-a**3*sqrt(b/a**5)/b + x)/4 + 3*sqrt(b/a**5)*log(a**3*sqrt(b/a**5)/b + x)/4 + (2*a - 3*b*x**2)/(-2*a**3*x + 2*a**2*b*x**3)","A",0
238,1,49,0,0.367483," ","integrate(1/x**3/(-b*x**2+a)**2,x)","\frac{a - 2 b x^{2}}{- 2 a^{3} x^{2} + 2 a^{2} b x^{4}} + \frac{2 b \log{\left(x \right)}}{a^{3}} - \frac{b \log{\left(- \frac{a}{b} + x^{2} \right)}}{a^{3}}"," ",0,"(a - 2*b*x**2)/(-2*a**3*x**2 + 2*a**2*b*x**4) + 2*b*log(x)/a**3 - b*log(-a/b + x**2)/a**3","A",0
239,1,36,0,0.274625," ","integrate(x**3/(-b*x**2+a)**3,x)","- \frac{a - 2 b x^{2}}{4 a^{2} b^{2} - 8 a b^{3} x^{2} + 4 b^{4} x^{4}}"," ",0,"-(a - 2*b*x**2)/(4*a**2*b**2 - 8*a*b**3*x**2 + 4*b**4*x**4)","B",0
240,1,105,0,0.315473," ","integrate(x**2/(-b*x**2+a)**3,x)","\frac{\sqrt{\frac{1}{a^{3} b^{3}}} \log{\left(- a^{2} b \sqrt{\frac{1}{a^{3} b^{3}}} + x \right)}}{16} - \frac{\sqrt{\frac{1}{a^{3} b^{3}}} \log{\left(a^{2} b \sqrt{\frac{1}{a^{3} b^{3}}} + x \right)}}{16} - \frac{- a x - b x^{3}}{8 a^{3} b - 16 a^{2} b^{2} x^{2} + 8 a b^{3} x^{4}}"," ",0,"sqrt(1/(a**3*b**3))*log(-a**2*b*sqrt(1/(a**3*b**3)) + x)/16 - sqrt(1/(a**3*b**3))*log(a**2*b*sqrt(1/(a**3*b**3)) + x)/16 - (-a*x - b*x**3)/(8*a**3*b - 16*a**2*b**2*x**2 + 8*a*b**3*x**4)","B",0
241,1,26,0,0.241396," ","integrate(x/(-b*x**2+a)**3,x)","\frac{1}{4 a^{2} b - 8 a b^{2} x^{2} + 4 b^{3} x^{4}}"," ",0,"1/(4*a**2*b - 8*a*b**2*x**2 + 4*b**3*x**4)","B",0
242,1,99,0,0.326582," ","integrate(1/(-b*x**2+a)**3,x)","- \frac{3 \sqrt{\frac{1}{a^{5} b}} \log{\left(- a^{3} \sqrt{\frac{1}{a^{5} b}} + x \right)}}{16} + \frac{3 \sqrt{\frac{1}{a^{5} b}} \log{\left(a^{3} \sqrt{\frac{1}{a^{5} b}} + x \right)}}{16} - \frac{- 5 a x + 3 b x^{3}}{8 a^{4} - 16 a^{3} b x^{2} + 8 a^{2} b^{2} x^{4}}"," ",0,"-3*sqrt(1/(a**5*b))*log(-a**3*sqrt(1/(a**5*b)) + x)/16 + 3*sqrt(1/(a**5*b))*log(a**3*sqrt(1/(a**5*b)) + x)/16 - (-5*a*x + 3*b*x**3)/(8*a**4 - 16*a**3*b*x**2 + 8*a**2*b**2*x**4)","A",0
243,1,56,0,0.419090," ","integrate(1/x/(-b*x**2+a)**3,x)","- \frac{- 3 a + 2 b x^{2}}{4 a^{4} - 8 a^{3} b x^{2} + 4 a^{2} b^{2} x^{4}} + \frac{\log{\left(x \right)}}{a^{3}} - \frac{\log{\left(- \frac{a}{b} + x^{2} \right)}}{2 a^{3}}"," ",0,"-(-3*a + 2*b*x**2)/(4*a**4 - 8*a**3*b*x**2 + 4*a**2*b**2*x**4) + log(x)/a**3 - log(-a/b + x**2)/(2*a**3)","A",0
244,1,107,0,0.426769," ","integrate(1/x**2/(-b*x**2+a)**3,x)","- \frac{15 \sqrt{\frac{b}{a^{7}}} \log{\left(- \frac{a^{4} \sqrt{\frac{b}{a^{7}}}}{b} + x \right)}}{16} + \frac{15 \sqrt{\frac{b}{a^{7}}} \log{\left(\frac{a^{4} \sqrt{\frac{b}{a^{7}}}}{b} + x \right)}}{16} - \frac{8 a^{2} - 25 a b x^{2} + 15 b^{2} x^{4}}{8 a^{5} x - 16 a^{4} b x^{3} + 8 a^{3} b^{2} x^{5}}"," ",0,"-15*sqrt(b/a**7)*log(-a**4*sqrt(b/a**7)/b + x)/16 + 15*sqrt(b/a**7)*log(a**4*sqrt(b/a**7)/b + x)/16 - (8*a**2 - 25*a*b*x**2 + 15*b**2*x**4)/(8*a**5*x - 16*a**4*b*x**3 + 8*a**3*b**2*x**5)","A",0
245,1,78,0,0.514566," ","integrate(1/x**3/(-b*x**2+a)**3,x)","- \frac{2 a^{2} - 9 a b x^{2} + 6 b^{2} x^{4}}{4 a^{5} x^{2} - 8 a^{4} b x^{4} + 4 a^{3} b^{2} x^{6}} + \frac{3 b \log{\left(x \right)}}{a^{4}} - \frac{3 b \log{\left(- \frac{a}{b} + x^{2} \right)}}{2 a^{4}}"," ",0,"-(2*a**2 - 9*a*b*x**2 + 6*b**2*x**4)/(4*a**5*x**2 - 8*a**4*b*x**4 + 4*a**3*b**2*x**6) + 3*b*log(x)/a**4 - 3*b*log(-a/b + x**2)/(2*a**4)","A",0
246,1,60,0,0.435097," ","integrate(x**3/(-b*x**2+a)**5,x)","- \frac{a - 4 b x^{2}}{24 a^{4} b^{2} - 96 a^{3} b^{3} x^{2} + 144 a^{2} b^{4} x^{4} - 96 a b^{5} x^{6} + 24 b^{6} x^{8}}"," ",0,"-(a - 4*b*x**2)/(24*a**4*b**2 - 96*a**3*b**3*x**2 + 144*a**2*b**4*x**4 - 96*a*b**5*x**6 + 24*b**6*x**8)","B",0
247,1,160,0,0.498489," ","integrate(x**2/(-b*x**2+a)**5,x)","\frac{5 \sqrt{\frac{1}{a^{7} b^{3}}} \log{\left(- a^{4} b \sqrt{\frac{1}{a^{7} b^{3}}} + x \right)}}{256} - \frac{5 \sqrt{\frac{1}{a^{7} b^{3}}} \log{\left(a^{4} b \sqrt{\frac{1}{a^{7} b^{3}}} + x \right)}}{256} - \frac{- 15 a^{3} x - 73 a^{2} b x^{3} + 55 a b^{2} x^{5} - 15 b^{3} x^{7}}{384 a^{7} b - 1536 a^{6} b^{2} x^{2} + 2304 a^{5} b^{3} x^{4} - 1536 a^{4} b^{4} x^{6} + 384 a^{3} b^{5} x^{8}}"," ",0,"5*sqrt(1/(a**7*b**3))*log(-a**4*b*sqrt(1/(a**7*b**3)) + x)/256 - 5*sqrt(1/(a**7*b**3))*log(a**4*b*sqrt(1/(a**7*b**3)) + x)/256 - (-15*a**3*x - 73*a**2*b*x**3 + 55*a*b**2*x**5 - 15*b**3*x**7)/(384*a**7*b - 1536*a**6*b**2*x**2 + 2304*a**5*b**3*x**4 - 1536*a**4*b**4*x**6 + 384*a**3*b**5*x**8)","A",0
248,1,49,0,0.404319," ","integrate(x/(-b*x**2+a)**5,x)","\frac{1}{8 a^{4} b - 32 a^{3} b^{2} x^{2} + 48 a^{2} b^{3} x^{4} - 32 a b^{4} x^{6} + 8 b^{5} x^{8}}"," ",0,"1/(8*a**4*b - 32*a**3*b**2*x**2 + 48*a**2*b**3*x**4 - 32*a*b**4*x**6 + 8*b**5*x**8)","B",0
249,1,146,0,0.517549," ","integrate(1/(-b*x**2+a)**5,x)","- \frac{35 \sqrt{\frac{1}{a^{9} b}} \log{\left(- a^{5} \sqrt{\frac{1}{a^{9} b}} + x \right)}}{256} + \frac{35 \sqrt{\frac{1}{a^{9} b}} \log{\left(a^{5} \sqrt{\frac{1}{a^{9} b}} + x \right)}}{256} - \frac{- 279 a^{3} x + 511 a^{2} b x^{3} - 385 a b^{2} x^{5} + 105 b^{3} x^{7}}{384 a^{8} - 1536 a^{7} b x^{2} + 2304 a^{6} b^{2} x^{4} - 1536 a^{5} b^{3} x^{6} + 384 a^{4} b^{4} x^{8}}"," ",0,"-35*sqrt(1/(a**9*b))*log(-a**5*sqrt(1/(a**9*b)) + x)/256 + 35*sqrt(1/(a**9*b))*log(a**5*sqrt(1/(a**9*b)) + x)/256 - (-279*a**3*x + 511*a**2*b*x**3 - 385*a*b**2*x**5 + 105*b**3*x**7)/(384*a**8 - 1536*a**7*b*x**2 + 2304*a**6*b**2*x**4 - 1536*a**5*b**3*x**6 + 384*a**4*b**4*x**8)","A",0
250,1,104,0,0.640191," ","integrate(1/x/(-b*x**2+a)**5,x)","- \frac{- 25 a^{3} + 52 a^{2} b x^{2} - 42 a b^{2} x^{4} + 12 b^{3} x^{6}}{24 a^{8} - 96 a^{7} b x^{2} + 144 a^{6} b^{2} x^{4} - 96 a^{5} b^{3} x^{6} + 24 a^{4} b^{4} x^{8}} + \frac{\log{\left(x \right)}}{a^{5}} - \frac{\log{\left(- \frac{a}{b} + x^{2} \right)}}{2 a^{5}}"," ",0,"-(-25*a**3 + 52*a**2*b*x**2 - 42*a*b**2*x**4 + 12*b**3*x**6)/(24*a**8 - 96*a**7*b*x**2 + 144*a**6*b**2*x**4 - 96*a**5*b**3*x**6 + 24*a**4*b**4*x**8) + log(x)/a**5 - log(-a/b + x**2)/(2*a**5)","A",0
251,1,155,0,0.657095," ","integrate(1/x**2/(-b*x**2+a)**5,x)","- \frac{315 \sqrt{\frac{b}{a^{11}}} \log{\left(- \frac{a^{6} \sqrt{\frac{b}{a^{11}}}}{b} + x \right)}}{256} + \frac{315 \sqrt{\frac{b}{a^{11}}} \log{\left(\frac{a^{6} \sqrt{\frac{b}{a^{11}}}}{b} + x \right)}}{256} - \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^{9} x - 512 a^{8} b x^{3} + 768 a^{7} b^{2} x^{5} - 512 a^{6} b^{3} x^{7} + 128 a^{5} b^{4} x^{9}}"," ",0,"-315*sqrt(b/a**11)*log(-a**6*sqrt(b/a**11)/b + x)/256 + 315*sqrt(b/a**11)*log(a**6*sqrt(b/a**11)/b + x)/256 - (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**9*x - 512*a**8*b*x**3 + 768*a**7*b**2*x**5 - 512*a**6*b**3*x**7 + 128*a**5*b**4*x**9)","A",0
252,1,126,0,0.762588," ","integrate(1/x**3/(-b*x**2+a)**5,x)","- \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^{9} x^{2} - 96 a^{8} b x^{4} + 144 a^{7} b^{2} x^{6} - 96 a^{6} b^{3} x^{8} + 24 a^{5} b^{4} x^{10}} + \frac{5 b \log{\left(x \right)}}{a^{6}} - \frac{5 b \log{\left(- \frac{a}{b} + x^{2} \right)}}{2 a^{6}}"," ",0,"-(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**9*x**2 - 96*a**8*b*x**4 + 144*a**7*b**2*x**6 - 96*a**6*b**3*x**8 + 24*a**5*b**4*x**10) + 5*b*log(x)/a**6 - 5*b*log(-a/b + x**2)/(2*a**6)","A",0
253,1,12,0,0.134691," ","integrate(1/x/(b*x**2+1),x)","\log{\left(x \right)} - \frac{\log{\left(x^{2} + \frac{1}{b} \right)}}{2}"," ",0,"log(x) - log(x**2 + 1/b)/2","A",0
254,1,12,0,0.136806," ","integrate(1/x/(b*x**2-1),x)","- \log{\left(x \right)} + \frac{\log{\left(x^{2} - \frac{1}{b} \right)}}{2}"," ",0,"-log(x) + log(x**2 - 1/b)/2","A",0
255,1,22,0,0.204652," ","integrate(1/x**3/(b*x**2+1),x)","- b \log{\left(x \right)} + \frac{b \log{\left(x^{2} + \frac{1}{b} \right)}}{2} - \frac{1}{2 x^{2}}"," ",0,"-b*log(x) + b*log(x**2 + 1/b)/2 - 1/(2*x**2)","A",0
256,1,22,0,0.209928," ","integrate(1/x**3/(b*x**2-1),x)","- b \log{\left(x \right)} + \frac{b \log{\left(x^{2} - \frac{1}{b} \right)}}{2} + \frac{1}{2 x^{2}}"," ",0,"-b*log(x) + b*log(x**2 - 1/b)/2 + 1/(2*x**2)","A",0
257,1,83,0,0.166239," ","integrate(1/(a*x**2+a-1),x)","- \frac{\sqrt{- \frac{1}{a \left(a - 1\right)}} \log{\left(- a \sqrt{- \frac{1}{a \left(a - 1\right)}} + x + \sqrt{- \frac{1}{a \left(a - 1\right)}} \right)}}{2} + \frac{\sqrt{- \frac{1}{a \left(a - 1\right)}} \log{\left(a \sqrt{- \frac{1}{a \left(a - 1\right)}} + x - \sqrt{- \frac{1}{a \left(a - 1\right)}} \right)}}{2}"," ",0,"-sqrt(-1/(a*(a - 1)))*log(-a*sqrt(-1/(a*(a - 1))) + x + sqrt(-1/(a*(a - 1))))/2 + sqrt(-1/(a*(a - 1)))*log(a*sqrt(-1/(a*(a - 1))) + x - sqrt(-1/(a*(a - 1))))/2","B",0
258,1,87,0,0.227275," ","integrate(1/(-c-d+(c-d)*x**2),x)","\frac{\sqrt{\frac{1}{\left(c - d\right) \left(c + d\right)}} \log{\left(- c \sqrt{\frac{1}{\left(c - d\right) \left(c + d\right)}} - d \sqrt{\frac{1}{\left(c - d\right) \left(c + d\right)}} + x \right)}}{2} - \frac{\sqrt{\frac{1}{\left(c - d\right) \left(c + d\right)}} \log{\left(c \sqrt{\frac{1}{\left(c - d\right) \left(c + d\right)}} + d \sqrt{\frac{1}{\left(c - d\right) \left(c + d\right)}} + x \right)}}{2}"," ",0,"sqrt(1/((c - d)*(c + d)))*log(-c*sqrt(1/((c - d)*(c + d))) - d*sqrt(1/((c - d)*(c + d))) + x)/2 - sqrt(1/((c - d)*(c + d)))*log(c*sqrt(1/((c - d)*(c + d))) + d*sqrt(1/((c - d)*(c + d))) + x)/2","B",0
259,1,22,0,0.204380," ","integrate(1/x/(b*x**2+1)**2,x)","\log{\left(x \right)} - \frac{\log{\left(x^{2} + \frac{1}{b} \right)}}{2} + \frac{1}{2 b x^{2} + 2}"," ",0,"log(x) - log(x**2 + 1/b)/2 + 1/(2*b*x**2 + 2)","A",0
260,1,22,0,0.206458," ","integrate(1/x/(b*x**2-1)**2,x)","\log{\left(x \right)} - \frac{\log{\left(x^{2} - \frac{1}{b} \right)}}{2} - \frac{1}{2 b x^{2} - 2}"," ",0,"log(x) - log(x**2 - 1/b)/2 - 1/(2*b*x**2 - 2)","A",0
261,1,60,0,0.249385," ","integrate(1/(a+(-a*c+b)*x**2),x)","- \frac{\sqrt{\frac{1}{a \left(a c - b\right)}} \log{\left(- a \sqrt{\frac{1}{a \left(a c - b\right)}} + x \right)}}{2} + \frac{\sqrt{\frac{1}{a \left(a c - b\right)}} \log{\left(a \sqrt{\frac{1}{a \left(a c - b\right)}} + x \right)}}{2}"," ",0,"-sqrt(1/(a*(a*c - b)))*log(-a*sqrt(1/(a*(a*c - b))) + x)/2 + sqrt(1/(a*(a*c - b)))*log(a*sqrt(1/(a*(a*c - b))) + x)/2","B",0
262,1,66,0,0.232116," ","integrate(1/(a-(-a*c+b)*x**2),x)","- \frac{\sqrt{- \frac{1}{a \left(a c - b\right)}} \log{\left(- a \sqrt{- \frac{1}{a \left(a c - b\right)}} + x \right)}}{2} + \frac{\sqrt{- \frac{1}{a \left(a c - b\right)}} \log{\left(a \sqrt{- \frac{1}{a \left(a c - b\right)}} + x \right)}}{2}"," ",0,"-sqrt(-1/(a*(a*c - b)))*log(-a*sqrt(-1/(a*(a*c - b))) + x)/2 + sqrt(-1/(a*(a*c - b)))*log(a*sqrt(-1/(a*(a*c - b))) + x)/2","B",0
263,1,104,0,0.319039," ","integrate(1/(c*(a-d)-(b-c)*x**2),x)","- \frac{\sqrt{\frac{1}{c \left(a - d\right) \left(b - c\right)}} \log{\left(- a c \sqrt{\frac{1}{c \left(a - d\right) \left(b - c\right)}} + c d \sqrt{\frac{1}{c \left(a - d\right) \left(b - c\right)}} + x \right)}}{2} + \frac{\sqrt{\frac{1}{c \left(a - d\right) \left(b - c\right)}} \log{\left(a c \sqrt{\frac{1}{c \left(a - d\right) \left(b - c\right)}} - c d \sqrt{\frac{1}{c \left(a - d\right) \left(b - c\right)}} + x \right)}}{2}"," ",0,"-sqrt(1/(c*(a - d)*(b - c)))*log(-a*c*sqrt(1/(c*(a - d)*(b - c))) + c*d*sqrt(1/(c*(a - d)*(b - c))) + x)/2 + sqrt(1/(c*(a - d)*(b - c)))*log(a*c*sqrt(1/(c*(a - d)*(b - c))) - c*d*sqrt(1/(c*(a - d)*(b - c))) + x)/2","B",0
264,1,19,0,5.450006," ","integrate(x**(7/2)*(b*x**2+a),x)","\frac{2 a x^{\frac{9}{2}}}{9} + \frac{2 b x^{\frac{13}{2}}}{13}"," ",0,"2*a*x**(9/2)/9 + 2*b*x**(13/2)/13","A",0
265,1,19,0,2.405840," ","integrate(x**(5/2)*(b*x**2+a),x)","\frac{2 a x^{\frac{7}{2}}}{7} + \frac{2 b x^{\frac{11}{2}}}{11}"," ",0,"2*a*x**(7/2)/7 + 2*b*x**(11/2)/11","A",0
266,1,19,0,0.952449," ","integrate(x**(3/2)*(b*x**2+a),x)","\frac{2 a x^{\frac{5}{2}}}{5} + \frac{2 b x^{\frac{9}{2}}}{9}"," ",0,"2*a*x**(5/2)/5 + 2*b*x**(9/2)/9","A",0
267,1,19,0,1.302817," ","integrate((b*x**2+a)*x**(1/2),x)","\frac{2 a x^{\frac{3}{2}}}{3} + \frac{2 b x^{\frac{7}{2}}}{7}"," ",0,"2*a*x**(3/2)/3 + 2*b*x**(7/2)/7","A",0
268,1,17,0,0.227263," ","integrate((b*x**2+a)/x**(1/2),x)","2 a \sqrt{x} + \frac{2 b x^{\frac{5}{2}}}{5}"," ",0,"2*a*sqrt(x) + 2*b*x**(5/2)/5","A",0
269,1,17,0,0.384146," ","integrate((b*x**2+a)/x**(3/2),x)","- \frac{2 a}{\sqrt{x}} + \frac{2 b x^{\frac{3}{2}}}{3}"," ",0,"-2*a/sqrt(x) + 2*b*x**(3/2)/3","A",0
270,1,17,0,0.559740," ","integrate((b*x**2+a)/x**(5/2),x)","- \frac{2 a}{3 x^{\frac{3}{2}}} + 2 b \sqrt{x}"," ",0,"-2*a/(3*x**(3/2)) + 2*b*sqrt(x)","A",0
271,1,19,0,1.239450," ","integrate((b*x**2+a)/x**(7/2),x)","- \frac{2 a}{5 x^{\frac{5}{2}}} - \frac{2 b}{\sqrt{x}}"," ",0,"-2*a/(5*x**(5/2)) - 2*b/sqrt(x)","A",0
272,1,34,0,10.604907," ","integrate(x**(7/2)*(b*x**2+a)**2,x)","\frac{2 a^{2} x^{\frac{9}{2}}}{9} + \frac{4 a b x^{\frac{13}{2}}}{13} + \frac{2 b^{2} x^{\frac{17}{2}}}{17}"," ",0,"2*a**2*x**(9/2)/9 + 4*a*b*x**(13/2)/13 + 2*b**2*x**(17/2)/17","A",0
273,1,34,0,5.506121," ","integrate(x**(5/2)*(b*x**2+a)**2,x)","\frac{2 a^{2} x^{\frac{7}{2}}}{7} + \frac{4 a b x^{\frac{11}{2}}}{11} + \frac{2 b^{2} x^{\frac{15}{2}}}{15}"," ",0,"2*a**2*x**(7/2)/7 + 4*a*b*x**(11/2)/11 + 2*b**2*x**(15/2)/15","A",0
274,1,34,0,2.545558," ","integrate(x**(3/2)*(b*x**2+a)**2,x)","\frac{2 a^{2} x^{\frac{5}{2}}}{5} + \frac{4 a b x^{\frac{9}{2}}}{9} + \frac{2 b^{2} x^{\frac{13}{2}}}{13}"," ",0,"2*a**2*x**(5/2)/5 + 4*a*b*x**(9/2)/9 + 2*b**2*x**(13/2)/13","A",0
275,1,34,0,1.704989," ","integrate((b*x**2+a)**2*x**(1/2),x)","\frac{2 a^{2} x^{\frac{3}{2}}}{3} + \frac{4 a b x^{\frac{7}{2}}}{7} + \frac{2 b^{2} x^{\frac{11}{2}}}{11}"," ",0,"2*a**2*x**(3/2)/3 + 4*a*b*x**(7/2)/7 + 2*b**2*x**(11/2)/11","A",0
276,1,32,0,0.748399," ","integrate((b*x**2+a)**2/x**(1/2),x)","2 a^{2} \sqrt{x} + \frac{4 a b x^{\frac{5}{2}}}{5} + \frac{2 b^{2} x^{\frac{9}{2}}}{9}"," ",0,"2*a**2*sqrt(x) + 4*a*b*x**(5/2)/5 + 2*b**2*x**(9/2)/9","A",0
277,1,32,0,0.942463," ","integrate((b*x**2+a)**2/x**(3/2),x)","- \frac{2 a^{2}}{\sqrt{x}} + \frac{4 a b x^{\frac{3}{2}}}{3} + \frac{2 b^{2} x^{\frac{7}{2}}}{7}"," ",0,"-2*a**2/sqrt(x) + 4*a*b*x**(3/2)/3 + 2*b**2*x**(7/2)/7","A",0
278,1,32,0,1.110887," ","integrate((b*x**2+a)**2/x**(5/2),x)","- \frac{2 a^{2}}{3 x^{\frac{3}{2}}} + 4 a b \sqrt{x} + \frac{2 b^{2} x^{\frac{5}{2}}}{5}"," ",0,"-2*a**2/(3*x**(3/2)) + 4*a*b*sqrt(x) + 2*b**2*x**(5/2)/5","A",0
279,1,32,0,1.709674," ","integrate((b*x**2+a)**2/x**(7/2),x)","- \frac{2 a^{2}}{5 x^{\frac{5}{2}}} - \frac{4 a b}{\sqrt{x}} + \frac{2 b^{2} x^{\frac{3}{2}}}{3}"," ",0,"-2*a**2/(5*x**(5/2)) - 4*a*b/sqrt(x) + 2*b**2*x**(3/2)/3","A",0
280,1,49,0,19.691053," ","integrate(x**(7/2)*(b*x**2+a)**3,x)","\frac{2 a^{3} x^{\frac{9}{2}}}{9} + \frac{6 a^{2} b x^{\frac{13}{2}}}{13} + \frac{6 a b^{2} x^{\frac{17}{2}}}{17} + \frac{2 b^{3} x^{\frac{21}{2}}}{21}"," ",0,"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",0
281,1,49,0,10.623362," ","integrate(x**(5/2)*(b*x**2+a)**3,x)","\frac{2 a^{3} x^{\frac{7}{2}}}{7} + \frac{6 a^{2} b x^{\frac{11}{2}}}{11} + \frac{2 a b^{2} x^{\frac{15}{2}}}{5} + \frac{2 b^{3} x^{\frac{19}{2}}}{19}"," ",0,"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",0
282,1,49,0,5.733569," ","integrate(x**(3/2)*(b*x**2+a)**3,x)","\frac{2 a^{3} x^{\frac{5}{2}}}{5} + \frac{2 a^{2} b x^{\frac{9}{2}}}{3} + \frac{6 a b^{2} x^{\frac{13}{2}}}{13} + \frac{2 b^{3} x^{\frac{17}{2}}}{17}"," ",0,"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",0
283,1,49,0,2.174745," ","integrate((b*x**2+a)**3*x**(1/2),x)","\frac{2 a^{3} x^{\frac{3}{2}}}{3} + \frac{6 a^{2} b x^{\frac{7}{2}}}{7} + \frac{6 a b^{2} x^{\frac{11}{2}}}{11} + \frac{2 b^{3} x^{\frac{15}{2}}}{15}"," ",0,"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",0
284,1,48,0,2.101174," ","integrate((b*x**2+a)**3/x**(1/2),x)","2 a^{3} \sqrt{x} + \frac{6 a^{2} b x^{\frac{5}{2}}}{5} + \frac{2 a b^{2} x^{\frac{9}{2}}}{3} + \frac{2 b^{3} x^{\frac{13}{2}}}{13}"," ",0,"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",0
285,1,46,0,2.311747," ","integrate((b*x**2+a)**3/x**(3/2),x)","- \frac{2 a^{3}}{\sqrt{x}} + 2 a^{2} b x^{\frac{3}{2}} + \frac{6 a b^{2} x^{\frac{7}{2}}}{7} + \frac{2 b^{3} x^{\frac{11}{2}}}{11}"," ",0,"-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",0
286,1,48,0,2.802248," ","integrate((b*x**2+a)**3/x**(5/2),x)","- \frac{2 a^{3}}{3 x^{\frac{3}{2}}} + 6 a^{2} b \sqrt{x} + \frac{6 a b^{2} x^{\frac{5}{2}}}{5} + \frac{2 b^{3} x^{\frac{9}{2}}}{9}"," ",0,"-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",0
287,1,46,0,3.855108," ","integrate((b*x**2+a)**3/x**(7/2),x)","- \frac{2 a^{3}}{5 x^{\frac{5}{2}}} - \frac{6 a^{2} b}{\sqrt{x}} + 2 a b^{2} x^{\frac{3}{2}} + \frac{2 b^{3} x^{\frac{7}{2}}}{7}"," ",0,"-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",0
288,1,192,0,50.314759," ","integrate(x**(7/2)/(b*x**2+a),x)","\begin{cases} \tilde{\infty} x^{\frac{5}{2}} & \text{for}\: a = 0 \wedge b = 0 \\\frac{2 x^{\frac{5}{2}}}{5 b} & \text{for}\: a = 0 \\\frac{2 x^{\frac{9}{2}}}{9 a} & \text{for}\: b = 0 \\- \frac{\sqrt[4]{-1} a^{\frac{5}{4}} \sqrt[4]{\frac{1}{b}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 b^{2}} + \frac{\sqrt[4]{-1} a^{\frac{5}{4}} \sqrt[4]{\frac{1}{b}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 b^{2}} - \frac{\sqrt[4]{-1} a^{\frac{5}{4}} \sqrt[4]{\frac{1}{b}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{b^{2}} - \frac{2 a \sqrt{x}}{b^{2}} + \frac{2 x^{\frac{5}{2}}}{5 b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x**(5/2), Eq(a, 0) & Eq(b, 0)), (2*x**(5/2)/(5*b), Eq(a, 0)), (2*x**(9/2)/(9*a), Eq(b, 0)), (-(-1)**(1/4)*a**(5/4)*(1/b)**(1/4)*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*b**2) + (-1)**(1/4)*a**(5/4)*(1/b)**(1/4)*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*b**2) - (-1)**(1/4)*a**(5/4)*(1/b)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/b**2 - 2*a*sqrt(x)/b**2 + 2*x**(5/2)/(5*b), True))","A",0
289,1,180,0,15.293266," ","integrate(x**(5/2)/(b*x**2+a),x)","\begin{cases} \tilde{\infty} x^{\frac{3}{2}} & \text{for}\: a = 0 \wedge b = 0 \\\frac{2 x^{\frac{3}{2}}}{3 b} & \text{for}\: a = 0 \\\frac{2 x^{\frac{7}{2}}}{7 a} & \text{for}\: b = 0 \\\frac{\left(-1\right)^{\frac{3}{4}} a^{\frac{3}{4}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 b^{2} \sqrt[4]{\frac{1}{b}}} - \frac{\left(-1\right)^{\frac{3}{4}} a^{\frac{3}{4}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 b^{2} \sqrt[4]{\frac{1}{b}}} - \frac{\left(-1\right)^{\frac{3}{4}} a^{\frac{3}{4}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{b^{2} \sqrt[4]{\frac{1}{b}}} + \frac{2 x^{\frac{3}{2}}}{3 b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x**(3/2), Eq(a, 0) & Eq(b, 0)), (2*x**(3/2)/(3*b), Eq(a, 0)), (2*x**(7/2)/(7*a), Eq(b, 0)), ((-1)**(3/4)*a**(3/4)*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*b**2*(1/b)**(1/4)) - (-1)**(3/4)*a**(3/4)*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*b**2*(1/b)**(1/4)) - (-1)**(3/4)*a**(3/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/(b**2*(1/b)**(1/4)) + 2*x**(3/2)/(3*b), True))","A",0
290,1,172,0,5.891504," ","integrate(x**(3/2)/(b*x**2+a),x)","\begin{cases} \tilde{\infty} \sqrt{x} & \text{for}\: a = 0 \wedge b = 0 \\\frac{2 \sqrt{x}}{b} & \text{for}\: a = 0 \\\frac{2 x^{\frac{5}{2}}}{5 a} & \text{for}\: b = 0 \\\frac{\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 b} - \frac{\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 b} + \frac{\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{b} + \frac{2 \sqrt{x}}{b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*sqrt(x), Eq(a, 0) & Eq(b, 0)), (2*sqrt(x)/b, Eq(a, 0)), (2*x**(5/2)/(5*a), Eq(b, 0)), ((-1)**(1/4)*a**(1/4)*(1/b)**(1/4)*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*b) - (-1)**(1/4)*a**(1/4)*(1/b)**(1/4)*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*b) + (-1)**(1/4)*a**(1/4)*(1/b)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/b + 2*sqrt(x)/b, True))","A",0
291,1,165,0,3.167082," ","integrate(x**(1/2)/(b*x**2+a),x)","\begin{cases} \frac{\tilde{\infty}}{\sqrt{x}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{2}{b \sqrt{x}} & \text{for}\: a = 0 \\\frac{2 x^{\frac{3}{2}}}{3 a} & \text{for}\: b = 0 \\- \frac{\left(-1\right)^{\frac{3}{4}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 \sqrt[4]{a} b \sqrt[4]{\frac{1}{b}}} + \frac{\left(-1\right)^{\frac{3}{4}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 \sqrt[4]{a} b \sqrt[4]{\frac{1}{b}}} + \frac{\left(-1\right)^{\frac{3}{4}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{\sqrt[4]{a} b \sqrt[4]{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/sqrt(x), Eq(a, 0) & Eq(b, 0)), (-2/(b*sqrt(x)), Eq(a, 0)), (2*x**(3/2)/(3*a), Eq(b, 0)), (-(-1)**(3/4)*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*a**(1/4)*b*(1/b)**(1/4)) + (-1)**(3/4)*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*a**(1/4)*b*(1/b)**(1/4)) + (-1)**(3/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/(a**(1/4)*b*(1/b)**(1/4)), True))","A",0
292,1,160,0,5.942055," ","integrate(1/(b*x**2+a)/x**(1/2),x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{3}{2}}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{2}{3 b x^{\frac{3}{2}}} & \text{for}\: a = 0 \\\frac{2 \sqrt{x}}{a} & \text{for}\: b = 0 \\- \frac{\sqrt[4]{-1} \sqrt[4]{\frac{1}{b}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 a^{\frac{3}{4}}} + \frac{\sqrt[4]{-1} \sqrt[4]{\frac{1}{b}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 a^{\frac{3}{4}}} - \frac{\sqrt[4]{-1} \sqrt[4]{\frac{1}{b}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{a^{\frac{3}{4}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(3/2), Eq(a, 0) & Eq(b, 0)), (-2/(3*b*x**(3/2)), Eq(a, 0)), (2*sqrt(x)/a, Eq(b, 0)), (-(-1)**(1/4)*(1/b)**(1/4)*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*a**(3/4)) + (-1)**(1/4)*(1/b)**(1/4)*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*a**(3/4)) - (-1)**(1/4)*(1/b)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/a**(3/4), True))","A",0
293,1,170,0,12.160083," ","integrate(1/x**(3/2)/(b*x**2+a),x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{5}{2}}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{2}{5 b x^{\frac{5}{2}}} & \text{for}\: a = 0 \\- \frac{2}{a \sqrt{x}} & \text{for}\: b = 0 \\- \frac{2}{a \sqrt{x}} + \frac{\left(-1\right)^{\frac{3}{4}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 a^{\frac{5}{4}} \sqrt[4]{\frac{1}{b}}} - \frac{\left(-1\right)^{\frac{3}{4}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 a^{\frac{5}{4}} \sqrt[4]{\frac{1}{b}}} - \frac{\left(-1\right)^{\frac{3}{4}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{a^{\frac{5}{4}} \sqrt[4]{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(5/2), Eq(a, 0) & Eq(b, 0)), (-2/(5*b*x**(5/2)), Eq(a, 0)), (-2/(a*sqrt(x)), Eq(b, 0)), (-2/(a*sqrt(x)) + (-1)**(3/4)*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*a**(5/4)*(1/b)**(1/4)) - (-1)**(3/4)*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*a**(5/4)*(1/b)**(1/4)) - (-1)**(3/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/(a**(5/4)*(1/b)**(1/4)), True))","A",0
294,1,178,0,30.395096," ","integrate(1/x**(5/2)/(b*x**2+a),x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{7}{2}}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{2}{7 b x^{\frac{7}{2}}} & \text{for}\: a = 0 \\- \frac{2}{3 a x^{\frac{3}{2}}} & \text{for}\: b = 0 \\- \frac{2}{3 a x^{\frac{3}{2}}} + \frac{\sqrt[4]{-1} b \sqrt[4]{\frac{1}{b}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 a^{\frac{7}{4}}} - \frac{\sqrt[4]{-1} b \sqrt[4]{\frac{1}{b}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 a^{\frac{7}{4}}} + \frac{\sqrt[4]{-1} b \sqrt[4]{\frac{1}{b}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{a^{\frac{7}{4}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(7/2), Eq(a, 0) & Eq(b, 0)), (-2/(7*b*x**(7/2)), Eq(a, 0)), (-2/(3*a*x**(3/2)), Eq(b, 0)), (-2/(3*a*x**(3/2)) + (-1)**(1/4)*b*(1/b)**(1/4)*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*a**(7/4)) - (-1)**(1/4)*b*(1/b)**(1/4)*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*a**(7/4)) + (-1)**(1/4)*b*(1/b)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/a**(7/4), True))","A",0
295,1,190,0,109.164237," ","integrate(1/x**(7/2)/(b*x**2+a),x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{9}{2}}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{2}{9 b x^{\frac{9}{2}}} & \text{for}\: a = 0 \\- \frac{2}{5 a x^{\frac{5}{2}}} & \text{for}\: b = 0 \\- \frac{2}{5 a x^{\frac{5}{2}}} + \frac{2 b}{a^{2} \sqrt{x}} - \frac{\left(-1\right)^{\frac{3}{4}} b \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 a^{\frac{9}{4}} \sqrt[4]{\frac{1}{b}}} + \frac{\left(-1\right)^{\frac{3}{4}} b \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 a^{\frac{9}{4}} \sqrt[4]{\frac{1}{b}}} + \frac{\left(-1\right)^{\frac{3}{4}} b \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{a^{\frac{9}{4}} \sqrt[4]{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(9/2), Eq(a, 0) & Eq(b, 0)), (-2/(9*b*x**(9/2)), Eq(a, 0)), (-2/(5*a*x**(5/2)), Eq(b, 0)), (-2/(5*a*x**(5/2)) + 2*b/(a**2*sqrt(x)) - (-1)**(3/4)*b*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*a**(9/4)*(1/b)**(1/4)) + (-1)**(3/4)*b*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*a**(9/4)*(1/b)**(1/4)) + (-1)**(3/4)*b*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/(a**(9/4)*(1/b)**(1/4)), True))","A",0
296,-1,0,0,0.000000," ","integrate(x**(7/2)/(b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
297,1,595,0,153.056307," ","integrate(x**(5/2)/(b*x**2+a)**2,x)","\begin{cases} \frac{\tilde{\infty}}{\sqrt{x}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{2}{b^{2} \sqrt{x}} & \text{for}\: a = 0 \\\frac{2 x^{\frac{7}{2}}}{7 a^{2}} & \text{for}\: b = 0 \\- \frac{4 \sqrt[4]{-1} \sqrt[4]{a} b x^{\frac{3}{2}} \sqrt[4]{\frac{1}{b}}}{8 \sqrt[4]{-1} a^{\frac{5}{4}} b^{2} \sqrt[4]{\frac{1}{b}} + 8 \sqrt[4]{-1} \sqrt[4]{a} b^{3} x^{2} \sqrt[4]{\frac{1}{b}}} + \frac{3 a \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{8 \sqrt[4]{-1} a^{\frac{5}{4}} b^{2} \sqrt[4]{\frac{1}{b}} + 8 \sqrt[4]{-1} \sqrt[4]{a} b^{3} x^{2} \sqrt[4]{\frac{1}{b}}} - \frac{3 a \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{8 \sqrt[4]{-1} a^{\frac{5}{4}} b^{2} \sqrt[4]{\frac{1}{b}} + 8 \sqrt[4]{-1} \sqrt[4]{a} b^{3} x^{2} \sqrt[4]{\frac{1}{b}}} - \frac{6 a \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{8 \sqrt[4]{-1} a^{\frac{5}{4}} b^{2} \sqrt[4]{\frac{1}{b}} + 8 \sqrt[4]{-1} \sqrt[4]{a} b^{3} x^{2} \sqrt[4]{\frac{1}{b}}} + \frac{3 b x^{2} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{8 \sqrt[4]{-1} a^{\frac{5}{4}} b^{2} \sqrt[4]{\frac{1}{b}} + 8 \sqrt[4]{-1} \sqrt[4]{a} b^{3} x^{2} \sqrt[4]{\frac{1}{b}}} - \frac{3 b x^{2} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{8 \sqrt[4]{-1} a^{\frac{5}{4}} b^{2} \sqrt[4]{\frac{1}{b}} + 8 \sqrt[4]{-1} \sqrt[4]{a} b^{3} x^{2} \sqrt[4]{\frac{1}{b}}} - \frac{6 b x^{2} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{8 \sqrt[4]{-1} a^{\frac{5}{4}} b^{2} \sqrt[4]{\frac{1}{b}} + 8 \sqrt[4]{-1} \sqrt[4]{a} b^{3} x^{2} \sqrt[4]{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/sqrt(x), Eq(a, 0) & Eq(b, 0)), (-2/(b**2*sqrt(x)), Eq(a, 0)), (2*x**(7/2)/(7*a**2), Eq(b, 0)), (-4*(-1)**(1/4)*a**(1/4)*b*x**(3/2)*(1/b)**(1/4)/(8*(-1)**(1/4)*a**(5/4)*b**2*(1/b)**(1/4) + 8*(-1)**(1/4)*a**(1/4)*b**3*x**2*(1/b)**(1/4)) + 3*a*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(8*(-1)**(1/4)*a**(5/4)*b**2*(1/b)**(1/4) + 8*(-1)**(1/4)*a**(1/4)*b**3*x**2*(1/b)**(1/4)) - 3*a*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(8*(-1)**(1/4)*a**(5/4)*b**2*(1/b)**(1/4) + 8*(-1)**(1/4)*a**(1/4)*b**3*x**2*(1/b)**(1/4)) - 6*a*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/(8*(-1)**(1/4)*a**(5/4)*b**2*(1/b)**(1/4) + 8*(-1)**(1/4)*a**(1/4)*b**3*x**2*(1/b)**(1/4)) + 3*b*x**2*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(8*(-1)**(1/4)*a**(5/4)*b**2*(1/b)**(1/4) + 8*(-1)**(1/4)*a**(1/4)*b**3*x**2*(1/b)**(1/4)) - 3*b*x**2*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(8*(-1)**(1/4)*a**(5/4)*b**2*(1/b)**(1/4) + 8*(-1)**(1/4)*a**(1/4)*b**3*x**2*(1/b)**(1/4)) - 6*b*x**2*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/(8*(-1)**(1/4)*a**(5/4)*b**2*(1/b)**(1/4) + 8*(-1)**(1/4)*a**(1/4)*b**3*x**2*(1/b)**(1/4)), True))","A",0
298,1,440,0,78.160730," ","integrate(x**(3/2)/(b*x**2+a)**2,x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{3}{2}}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{2}{3 b^{2} x^{\frac{3}{2}}} & \text{for}\: a = 0 \\\frac{2 x^{\frac{5}{2}}}{5 a^{2}} & \text{for}\: b = 0 \\- \frac{\sqrt[4]{-1} a^{\frac{5}{4}} \sqrt[4]{\frac{1}{b}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{2} b + 8 a b^{2} x^{2}} + \frac{\sqrt[4]{-1} a^{\frac{5}{4}} \sqrt[4]{\frac{1}{b}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{2} b + 8 a b^{2} x^{2}} - \frac{2 \sqrt[4]{-1} a^{\frac{5}{4}} \sqrt[4]{\frac{1}{b}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{8 a^{2} b + 8 a b^{2} x^{2}} - \frac{\sqrt[4]{-1} \sqrt[4]{a} b x^{2} \sqrt[4]{\frac{1}{b}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{2} b + 8 a b^{2} x^{2}} + \frac{\sqrt[4]{-1} \sqrt[4]{a} b x^{2} \sqrt[4]{\frac{1}{b}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{2} b + 8 a b^{2} x^{2}} - \frac{2 \sqrt[4]{-1} \sqrt[4]{a} b x^{2} \sqrt[4]{\frac{1}{b}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{8 a^{2} b + 8 a b^{2} x^{2}} - \frac{4 a \sqrt{x}}{8 a^{2} b + 8 a b^{2} x^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(3/2), Eq(a, 0) & Eq(b, 0)), (-2/(3*b**2*x**(3/2)), Eq(a, 0)), (2*x**(5/2)/(5*a**2), Eq(b, 0)), (-(-1)**(1/4)*a**(5/4)*(1/b)**(1/4)*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(8*a**2*b + 8*a*b**2*x**2) + (-1)**(1/4)*a**(5/4)*(1/b)**(1/4)*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(8*a**2*b + 8*a*b**2*x**2) - 2*(-1)**(1/4)*a**(5/4)*(1/b)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/(8*a**2*b + 8*a*b**2*x**2) - (-1)**(1/4)*a**(1/4)*b*x**2*(1/b)**(1/4)*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(8*a**2*b + 8*a*b**2*x**2) + (-1)**(1/4)*a**(1/4)*b*x**2*(1/b)**(1/4)*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(8*a**2*b + 8*a*b**2*x**2) - 2*(-1)**(1/4)*a**(1/4)*b*x**2*(1/b)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/(8*a**2*b + 8*a*b**2*x**2) - 4*a*sqrt(x)/(8*a**2*b + 8*a*b**2*x**2), True))","A",0
299,1,578,0,50.141640," ","integrate(x**(1/2)/(b*x**2+a)**2,x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{5}{2}}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{2}{5 b^{2} x^{\frac{5}{2}}} & \text{for}\: a = 0 \\\frac{2 x^{\frac{3}{2}}}{3 a^{2}} & \text{for}\: b = 0 \\\frac{4 \sqrt[4]{-1} \sqrt[4]{a} b x^{\frac{3}{2}} \sqrt[4]{\frac{1}{b}}}{8 \sqrt[4]{-1} a^{\frac{9}{4}} b \sqrt[4]{\frac{1}{b}} + 8 \sqrt[4]{-1} a^{\frac{5}{4}} b^{2} x^{2} \sqrt[4]{\frac{1}{b}}} + \frac{a \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{8 \sqrt[4]{-1} a^{\frac{9}{4}} b \sqrt[4]{\frac{1}{b}} + 8 \sqrt[4]{-1} a^{\frac{5}{4}} b^{2} x^{2} \sqrt[4]{\frac{1}{b}}} - \frac{a \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{8 \sqrt[4]{-1} a^{\frac{9}{4}} b \sqrt[4]{\frac{1}{b}} + 8 \sqrt[4]{-1} a^{\frac{5}{4}} b^{2} x^{2} \sqrt[4]{\frac{1}{b}}} - \frac{2 a \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{8 \sqrt[4]{-1} a^{\frac{9}{4}} b \sqrt[4]{\frac{1}{b}} + 8 \sqrt[4]{-1} a^{\frac{5}{4}} b^{2} x^{2} \sqrt[4]{\frac{1}{b}}} + \frac{b x^{2} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{8 \sqrt[4]{-1} a^{\frac{9}{4}} b \sqrt[4]{\frac{1}{b}} + 8 \sqrt[4]{-1} a^{\frac{5}{4}} b^{2} x^{2} \sqrt[4]{\frac{1}{b}}} - \frac{b x^{2} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{8 \sqrt[4]{-1} a^{\frac{9}{4}} b \sqrt[4]{\frac{1}{b}} + 8 \sqrt[4]{-1} a^{\frac{5}{4}} b^{2} x^{2} \sqrt[4]{\frac{1}{b}}} - \frac{2 b x^{2} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{8 \sqrt[4]{-1} a^{\frac{9}{4}} b \sqrt[4]{\frac{1}{b}} + 8 \sqrt[4]{-1} a^{\frac{5}{4}} b^{2} x^{2} \sqrt[4]{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(5/2), Eq(a, 0) & Eq(b, 0)), (-2/(5*b**2*x**(5/2)), Eq(a, 0)), (2*x**(3/2)/(3*a**2), Eq(b, 0)), (4*(-1)**(1/4)*a**(1/4)*b*x**(3/2)*(1/b)**(1/4)/(8*(-1)**(1/4)*a**(9/4)*b*(1/b)**(1/4) + 8*(-1)**(1/4)*a**(5/4)*b**2*x**2*(1/b)**(1/4)) + a*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(8*(-1)**(1/4)*a**(9/4)*b*(1/b)**(1/4) + 8*(-1)**(1/4)*a**(5/4)*b**2*x**2*(1/b)**(1/4)) - a*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(8*(-1)**(1/4)*a**(9/4)*b*(1/b)**(1/4) + 8*(-1)**(1/4)*a**(5/4)*b**2*x**2*(1/b)**(1/4)) - 2*a*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/(8*(-1)**(1/4)*a**(9/4)*b*(1/b)**(1/4) + 8*(-1)**(1/4)*a**(5/4)*b**2*x**2*(1/b)**(1/4)) + b*x**2*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(8*(-1)**(1/4)*a**(9/4)*b*(1/b)**(1/4) + 8*(-1)**(1/4)*a**(5/4)*b**2*x**2*(1/b)**(1/4)) - b*x**2*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(8*(-1)**(1/4)*a**(9/4)*b*(1/b)**(1/4) + 8*(-1)**(1/4)*a**(5/4)*b**2*x**2*(1/b)**(1/4)) - 2*b*x**2*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/(8*(-1)**(1/4)*a**(9/4)*b*(1/b)**(1/4) + 8*(-1)**(1/4)*a**(5/4)*b**2*x**2*(1/b)**(1/4)), True))","A",0
300,1,434,0,75.794732," ","integrate(1/(b*x**2+a)**2/x**(1/2),x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{7}{2}}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{2}{7 b^{2} x^{\frac{7}{2}}} & \text{for}\: a = 0 \\\frac{2 \sqrt{x}}{a^{2}} & \text{for}\: b = 0 \\- \frac{3 \sqrt[4]{-1} a^{\frac{5}{4}} \sqrt[4]{\frac{1}{b}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{3} + 8 a^{2} b x^{2}} + \frac{3 \sqrt[4]{-1} a^{\frac{5}{4}} \sqrt[4]{\frac{1}{b}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{3} + 8 a^{2} b x^{2}} - \frac{6 \sqrt[4]{-1} a^{\frac{5}{4}} \sqrt[4]{\frac{1}{b}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{8 a^{3} + 8 a^{2} b x^{2}} - \frac{3 \sqrt[4]{-1} \sqrt[4]{a} b x^{2} \sqrt[4]{\frac{1}{b}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{3} + 8 a^{2} b x^{2}} + \frac{3 \sqrt[4]{-1} \sqrt[4]{a} b x^{2} \sqrt[4]{\frac{1}{b}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{3} + 8 a^{2} b x^{2}} - \frac{6 \sqrt[4]{-1} \sqrt[4]{a} b x^{2} \sqrt[4]{\frac{1}{b}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{8 a^{3} + 8 a^{2} b x^{2}} + \frac{4 a \sqrt{x}}{8 a^{3} + 8 a^{2} b x^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(7/2), Eq(a, 0) & Eq(b, 0)), (-2/(7*b**2*x**(7/2)), Eq(a, 0)), (2*sqrt(x)/a**2, Eq(b, 0)), (-3*(-1)**(1/4)*a**(5/4)*(1/b)**(1/4)*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(8*a**3 + 8*a**2*b*x**2) + 3*(-1)**(1/4)*a**(5/4)*(1/b)**(1/4)*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(8*a**3 + 8*a**2*b*x**2) - 6*(-1)**(1/4)*a**(5/4)*(1/b)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/(8*a**3 + 8*a**2*b*x**2) - 3*(-1)**(1/4)*a**(1/4)*b*x**2*(1/b)**(1/4)*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(8*a**3 + 8*a**2*b*x**2) + 3*(-1)**(1/4)*a**(1/4)*b*x**2*(1/b)**(1/4)*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(8*a**3 + 8*a**2*b*x**2) - 6*(-1)**(1/4)*a**(1/4)*b*x**2*(1/b)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/(8*a**3 + 8*a**2*b*x**2) + 4*a*sqrt(x)/(8*a**3 + 8*a**2*b*x**2), True))","A",0
301,1,700,0,150.183912," ","integrate(1/x**(3/2)/(b*x**2+a)**2,x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{9}{2}}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{2}{9 b^{2} x^{\frac{9}{2}}} & \text{for}\: a = 0 \\- \frac{2}{a^{2} \sqrt{x}} & \text{for}\: b = 0 \\- \frac{16 \sqrt[4]{-1} a^{\frac{5}{4}} \sqrt[4]{\frac{1}{b}}}{8 \sqrt[4]{-1} a^{\frac{13}{4}} \sqrt{x} \sqrt[4]{\frac{1}{b}} + 8 \sqrt[4]{-1} a^{\frac{9}{4}} b x^{\frac{5}{2}} \sqrt[4]{\frac{1}{b}}} - \frac{20 \sqrt[4]{-1} \sqrt[4]{a} b x^{2} \sqrt[4]{\frac{1}{b}}}{8 \sqrt[4]{-1} a^{\frac{13}{4}} \sqrt{x} \sqrt[4]{\frac{1}{b}} + 8 \sqrt[4]{-1} a^{\frac{9}{4}} b x^{\frac{5}{2}} \sqrt[4]{\frac{1}{b}}} - \frac{5 a \sqrt{x} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{8 \sqrt[4]{-1} a^{\frac{13}{4}} \sqrt{x} \sqrt[4]{\frac{1}{b}} + 8 \sqrt[4]{-1} a^{\frac{9}{4}} b x^{\frac{5}{2}} \sqrt[4]{\frac{1}{b}}} + \frac{5 a \sqrt{x} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{8 \sqrt[4]{-1} a^{\frac{13}{4}} \sqrt{x} \sqrt[4]{\frac{1}{b}} + 8 \sqrt[4]{-1} a^{\frac{9}{4}} b x^{\frac{5}{2}} \sqrt[4]{\frac{1}{b}}} + \frac{10 a \sqrt{x} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{8 \sqrt[4]{-1} a^{\frac{13}{4}} \sqrt{x} \sqrt[4]{\frac{1}{b}} + 8 \sqrt[4]{-1} a^{\frac{9}{4}} b x^{\frac{5}{2}} \sqrt[4]{\frac{1}{b}}} - \frac{5 b x^{\frac{5}{2}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{8 \sqrt[4]{-1} a^{\frac{13}{4}} \sqrt{x} \sqrt[4]{\frac{1}{b}} + 8 \sqrt[4]{-1} a^{\frac{9}{4}} b x^{\frac{5}{2}} \sqrt[4]{\frac{1}{b}}} + \frac{5 b x^{\frac{5}{2}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{8 \sqrt[4]{-1} a^{\frac{13}{4}} \sqrt{x} \sqrt[4]{\frac{1}{b}} + 8 \sqrt[4]{-1} a^{\frac{9}{4}} b x^{\frac{5}{2}} \sqrt[4]{\frac{1}{b}}} + \frac{10 b x^{\frac{5}{2}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{8 \sqrt[4]{-1} a^{\frac{13}{4}} \sqrt{x} \sqrt[4]{\frac{1}{b}} + 8 \sqrt[4]{-1} a^{\frac{9}{4}} b x^{\frac{5}{2}} \sqrt[4]{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(9/2), Eq(a, 0) & Eq(b, 0)), (-2/(9*b**2*x**(9/2)), Eq(a, 0)), (-2/(a**2*sqrt(x)), Eq(b, 0)), (-16*(-1)**(1/4)*a**(5/4)*(1/b)**(1/4)/(8*(-1)**(1/4)*a**(13/4)*sqrt(x)*(1/b)**(1/4) + 8*(-1)**(1/4)*a**(9/4)*b*x**(5/2)*(1/b)**(1/4)) - 20*(-1)**(1/4)*a**(1/4)*b*x**2*(1/b)**(1/4)/(8*(-1)**(1/4)*a**(13/4)*sqrt(x)*(1/b)**(1/4) + 8*(-1)**(1/4)*a**(9/4)*b*x**(5/2)*(1/b)**(1/4)) - 5*a*sqrt(x)*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(8*(-1)**(1/4)*a**(13/4)*sqrt(x)*(1/b)**(1/4) + 8*(-1)**(1/4)*a**(9/4)*b*x**(5/2)*(1/b)**(1/4)) + 5*a*sqrt(x)*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(8*(-1)**(1/4)*a**(13/4)*sqrt(x)*(1/b)**(1/4) + 8*(-1)**(1/4)*a**(9/4)*b*x**(5/2)*(1/b)**(1/4)) + 10*a*sqrt(x)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/(8*(-1)**(1/4)*a**(13/4)*sqrt(x)*(1/b)**(1/4) + 8*(-1)**(1/4)*a**(9/4)*b*x**(5/2)*(1/b)**(1/4)) - 5*b*x**(5/2)*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(8*(-1)**(1/4)*a**(13/4)*sqrt(x)*(1/b)**(1/4) + 8*(-1)**(1/4)*a**(9/4)*b*x**(5/2)*(1/b)**(1/4)) + 5*b*x**(5/2)*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(8*(-1)**(1/4)*a**(13/4)*sqrt(x)*(1/b)**(1/4) + 8*(-1)**(1/4)*a**(9/4)*b*x**(5/2)*(1/b)**(1/4)) + 10*b*x**(5/2)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/(8*(-1)**(1/4)*a**(13/4)*sqrt(x)*(1/b)**(1/4) + 8*(-1)**(1/4)*a**(9/4)*b*x**(5/2)*(1/b)**(1/4)), True))","A",0
302,-1,0,0,0.000000," ","integrate(1/x**(5/2)/(b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
303,-1,0,0,0.000000," ","integrate(1/x**(7/2)/(b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
304,-1,0,0,0.000000," ","integrate(x**(7/2)/(b*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
305,-1,0,0,0.000000," ","integrate(x**(5/2)/(b*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
306,-1,0,0,0.000000," ","integrate(x**(3/2)/(b*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
307,-1,0,0,0.000000," ","integrate(x**(1/2)/(b*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
308,-1,0,0,0.000000," ","integrate(1/(b*x**2+a)**3/x**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
309,-1,0,0,0.000000," ","integrate(1/x**(3/2)/(b*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
310,-1,0,0,0.000000," ","integrate(1/x**(5/2)/(b*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
311,-1,0,0,0.000000," ","integrate(1/x**(7/2)/(b*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
312,1,122,0,3.102442," ","integrate(x**(1/2)/(-b*x**2+a),x)","\begin{cases} \frac{\tilde{\infty}}{\sqrt{x}} & \text{for}\: a = 0 \wedge b = 0 \\\frac{2}{b \sqrt{x}} & \text{for}\: a = 0 \\\frac{2 x^{\frac{3}{2}}}{3 a} & \text{for}\: b = 0 \\- \frac{\log{\left(- \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 \sqrt[4]{a} b \sqrt[4]{\frac{1}{b}}} + \frac{\log{\left(\sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 \sqrt[4]{a} b \sqrt[4]{\frac{1}{b}}} - \frac{\operatorname{atan}{\left(\frac{\sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{\sqrt[4]{a} b \sqrt[4]{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/sqrt(x), Eq(a, 0) & Eq(b, 0)), (2/(b*sqrt(x)), Eq(a, 0)), (2*x**(3/2)/(3*a), Eq(b, 0)), (-log(-a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*a**(1/4)*b*(1/b)**(1/4)) + log(a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*a**(1/4)*b*(1/b)**(1/4)) - atan(sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/(a**(1/4)*b*(1/b)**(1/4)), True))","A",0
313,1,105,0,4.145645," ","integrate(x**(7/2)/(x**2+1),x)","\frac{2 x^{\frac{5}{2}}}{5} - 2 \sqrt{x} - \frac{\sqrt{2} \log{\left(- 4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{4} + \frac{\sqrt{2} \log{\left(4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{4} + \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{2} + \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{2}"," ",0,"2*x**(5/2)/5 - 2*sqrt(x) - sqrt(2)*log(-4*sqrt(2)*sqrt(x) + 4*x + 4)/4 + sqrt(2)*log(4*sqrt(2)*sqrt(x) + 4*x + 4)/4 + sqrt(2)*atan(sqrt(2)*sqrt(x) - 1)/2 + sqrt(2)*atan(sqrt(2)*sqrt(x) + 1)/2","A",0
314,1,99,0,1.748672," ","integrate(x**(5/2)/(x**2+1),x)","\frac{2 x^{\frac{3}{2}}}{3} - \frac{\sqrt{2} \log{\left(- 4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{4} + \frac{\sqrt{2} \log{\left(4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{4} - \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{2} - \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{2}"," ",0,"2*x**(3/2)/3 - sqrt(2)*log(-4*sqrt(2)*sqrt(x) + 4*x + 4)/4 + sqrt(2)*log(4*sqrt(2)*sqrt(x) + 4*x + 4)/4 - sqrt(2)*atan(sqrt(2)*sqrt(x) - 1)/2 - sqrt(2)*atan(sqrt(2)*sqrt(x) + 1)/2","A",0
315,1,97,0,0.842677," ","integrate(x**(3/2)/(x**2+1),x)","2 \sqrt{x} + \frac{\sqrt{2} \log{\left(- 4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{4} - \frac{\sqrt{2} \log{\left(4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{4} - \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{2} - \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{2}"," ",0,"2*sqrt(x) + sqrt(2)*log(-4*sqrt(2)*sqrt(x) + 4*x + 4)/4 - sqrt(2)*log(4*sqrt(2)*sqrt(x) + 4*x + 4)/4 - sqrt(2)*atan(sqrt(2)*sqrt(x) - 1)/2 - sqrt(2)*atan(sqrt(2)*sqrt(x) + 1)/2","A",0
316,1,90,0,0.546815," ","integrate(x**(1/2)/(x**2+1),x)","\frac{\sqrt{2} \log{\left(- 4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{4} - \frac{\sqrt{2} \log{\left(4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{4} + \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{2} + \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{2}"," ",0,"sqrt(2)*log(-4*sqrt(2)*sqrt(x) + 4*x + 4)/4 - sqrt(2)*log(4*sqrt(2)*sqrt(x) + 4*x + 4)/4 + sqrt(2)*atan(sqrt(2)*sqrt(x) - 1)/2 + sqrt(2)*atan(sqrt(2)*sqrt(x) + 1)/2","A",0
317,1,90,0,0.733890," ","integrate(1/(x**2+1)/x**(1/2),x)","- \frac{\sqrt{2} \log{\left(- 4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{4} + \frac{\sqrt{2} \log{\left(4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{4} + \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{2} + \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{2}"," ",0,"-sqrt(2)*log(-4*sqrt(2)*sqrt(x) + 4*x + 4)/4 + sqrt(2)*log(4*sqrt(2)*sqrt(x) + 4*x + 4)/4 + sqrt(2)*atan(sqrt(2)*sqrt(x) - 1)/2 + sqrt(2)*atan(sqrt(2)*sqrt(x) + 1)/2","A",0
318,1,97,0,1.351360," ","integrate(1/x**(3/2)/(x**2+1),x)","- \frac{\sqrt{2} \log{\left(- 4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{4} + \frac{\sqrt{2} \log{\left(4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{4} - \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{2} - \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{2} - \frac{2}{\sqrt{x}}"," ",0,"-sqrt(2)*log(-4*sqrt(2)*sqrt(x) + 4*x + 4)/4 + sqrt(2)*log(4*sqrt(2)*sqrt(x) + 4*x + 4)/4 - sqrt(2)*atan(sqrt(2)*sqrt(x) - 1)/2 - sqrt(2)*atan(sqrt(2)*sqrt(x) + 1)/2 - 2/sqrt(x)","A",0
319,1,99,0,2.435237," ","integrate(1/x**(5/2)/(x**2+1),x)","\frac{\sqrt{2} \log{\left(- 4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{4} - \frac{\sqrt{2} \log{\left(4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{4} - \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{2} - \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{2} - \frac{2}{3 x^{\frac{3}{2}}}"," ",0,"sqrt(2)*log(-4*sqrt(2)*sqrt(x) + 4*x + 4)/4 - sqrt(2)*log(4*sqrt(2)*sqrt(x) + 4*x + 4)/4 - sqrt(2)*atan(sqrt(2)*sqrt(x) - 1)/2 - sqrt(2)*atan(sqrt(2)*sqrt(x) + 1)/2 - 2/(3*x**(3/2))","A",0
320,1,105,0,5.464554," ","integrate(1/x**(7/2)/(x**2+1),x)","\frac{\sqrt{2} \log{\left(- 4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{4} - \frac{\sqrt{2} \log{\left(4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{4} + \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{2} + \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{2} + \frac{2}{\sqrt{x}} - \frac{2}{5 x^{\frac{5}{2}}}"," ",0,"sqrt(2)*log(-4*sqrt(2)*sqrt(x) + 4*x + 4)/4 - sqrt(2)*log(4*sqrt(2)*sqrt(x) + 4*x + 4)/4 + sqrt(2)*atan(sqrt(2)*sqrt(x) - 1)/2 + sqrt(2)*atan(sqrt(2)*sqrt(x) + 1)/2 + 2/sqrt(x) - 2/(5*x**(5/2))","A",0
321,1,277,0,8.344969," ","integrate(x**(7/2)/(x**2+1)**2,x)","\frac{32 x^{\frac{5}{2}}}{16 x^{2} + 16} + \frac{40 \sqrt{x}}{16 x^{2} + 16} + \frac{5 \sqrt{2} x^{2} \log{\left(- 4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{16 x^{2} + 16} - \frac{5 \sqrt{2} x^{2} \log{\left(4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{16 x^{2} + 16} - \frac{10 \sqrt{2} x^{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{16 x^{2} + 16} - \frac{10 \sqrt{2} x^{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{16 x^{2} + 16} + \frac{5 \sqrt{2} \log{\left(- 4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{16 x^{2} + 16} - \frac{5 \sqrt{2} \log{\left(4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{16 x^{2} + 16} - \frac{10 \sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{16 x^{2} + 16} - \frac{10 \sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{16 x^{2} + 16}"," ",0,"32*x**(5/2)/(16*x**2 + 16) + 40*sqrt(x)/(16*x**2 + 16) + 5*sqrt(2)*x**2*log(-4*sqrt(2)*sqrt(x) + 4*x + 4)/(16*x**2 + 16) - 5*sqrt(2)*x**2*log(4*sqrt(2)*sqrt(x) + 4*x + 4)/(16*x**2 + 16) - 10*sqrt(2)*x**2*atan(sqrt(2)*sqrt(x) - 1)/(16*x**2 + 16) - 10*sqrt(2)*x**2*atan(sqrt(2)*sqrt(x) + 1)/(16*x**2 + 16) + 5*sqrt(2)*log(-4*sqrt(2)*sqrt(x) + 4*x + 4)/(16*x**2 + 16) - 5*sqrt(2)*log(4*sqrt(2)*sqrt(x) + 4*x + 4)/(16*x**2 + 16) - 10*sqrt(2)*atan(sqrt(2)*sqrt(x) - 1)/(16*x**2 + 16) - 10*sqrt(2)*atan(sqrt(2)*sqrt(x) + 1)/(16*x**2 + 16)","B",0
322,1,264,0,5.307977," ","integrate(x**(5/2)/(x**2+1)**2,x)","- \frac{8 x^{\frac{3}{2}}}{16 x^{2} + 16} + \frac{3 \sqrt{2} x^{2} \log{\left(- 4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{16 x^{2} + 16} - \frac{3 \sqrt{2} x^{2} \log{\left(4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{16 x^{2} + 16} + \frac{6 \sqrt{2} x^{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{16 x^{2} + 16} + \frac{6 \sqrt{2} x^{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{16 x^{2} + 16} + \frac{3 \sqrt{2} \log{\left(- 4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{16 x^{2} + 16} - \frac{3 \sqrt{2} \log{\left(4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{16 x^{2} + 16} + \frac{6 \sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{16 x^{2} + 16} + \frac{6 \sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{16 x^{2} + 16}"," ",0,"-8*x**(3/2)/(16*x**2 + 16) + 3*sqrt(2)*x**2*log(-4*sqrt(2)*sqrt(x) + 4*x + 4)/(16*x**2 + 16) - 3*sqrt(2)*x**2*log(4*sqrt(2)*sqrt(x) + 4*x + 4)/(16*x**2 + 16) + 6*sqrt(2)*x**2*atan(sqrt(2)*sqrt(x) - 1)/(16*x**2 + 16) + 6*sqrt(2)*x**2*atan(sqrt(2)*sqrt(x) + 1)/(16*x**2 + 16) + 3*sqrt(2)*log(-4*sqrt(2)*sqrt(x) + 4*x + 4)/(16*x**2 + 16) - 3*sqrt(2)*log(4*sqrt(2)*sqrt(x) + 4*x + 4)/(16*x**2 + 16) + 6*sqrt(2)*atan(sqrt(2)*sqrt(x) - 1)/(16*x**2 + 16) + 6*sqrt(2)*atan(sqrt(2)*sqrt(x) + 1)/(16*x**2 + 16)","B",0
323,1,257,0,3.387160," ","integrate(x**(3/2)/(x**2+1)**2,x)","- \frac{8 \sqrt{x}}{16 x^{2} + 16} - \frac{\sqrt{2} x^{2} \log{\left(- 4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{16 x^{2} + 16} + \frac{\sqrt{2} x^{2} \log{\left(4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{16 x^{2} + 16} + \frac{2 \sqrt{2} x^{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{16 x^{2} + 16} + \frac{2 \sqrt{2} x^{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{16 x^{2} + 16} - \frac{\sqrt{2} \log{\left(- 4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{16 x^{2} + 16} + \frac{\sqrt{2} \log{\left(4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{16 x^{2} + 16} + \frac{2 \sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{16 x^{2} + 16} + \frac{2 \sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{16 x^{2} + 16}"," ",0,"-8*sqrt(x)/(16*x**2 + 16) - sqrt(2)*x**2*log(-4*sqrt(2)*sqrt(x) + 4*x + 4)/(16*x**2 + 16) + sqrt(2)*x**2*log(4*sqrt(2)*sqrt(x) + 4*x + 4)/(16*x**2 + 16) + 2*sqrt(2)*x**2*atan(sqrt(2)*sqrt(x) - 1)/(16*x**2 + 16) + 2*sqrt(2)*x**2*atan(sqrt(2)*sqrt(x) + 1)/(16*x**2 + 16) - sqrt(2)*log(-4*sqrt(2)*sqrt(x) + 4*x + 4)/(16*x**2 + 16) + sqrt(2)*log(4*sqrt(2)*sqrt(x) + 4*x + 4)/(16*x**2 + 16) + 2*sqrt(2)*atan(sqrt(2)*sqrt(x) - 1)/(16*x**2 + 16) + 2*sqrt(2)*atan(sqrt(2)*sqrt(x) + 1)/(16*x**2 + 16)","B",0
324,1,257,0,2.165993," ","integrate(x**(1/2)/(x**2+1)**2,x)","\frac{8 x^{\frac{3}{2}}}{16 x^{2} + 16} + \frac{\sqrt{2} x^{2} \log{\left(- 4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{16 x^{2} + 16} - \frac{\sqrt{2} x^{2} \log{\left(4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{16 x^{2} + 16} + \frac{2 \sqrt{2} x^{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{16 x^{2} + 16} + \frac{2 \sqrt{2} x^{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{16 x^{2} + 16} + \frac{\sqrt{2} \log{\left(- 4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{16 x^{2} + 16} - \frac{\sqrt{2} \log{\left(4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{16 x^{2} + 16} + \frac{2 \sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{16 x^{2} + 16} + \frac{2 \sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{16 x^{2} + 16}"," ",0,"8*x**(3/2)/(16*x**2 + 16) + sqrt(2)*x**2*log(-4*sqrt(2)*sqrt(x) + 4*x + 4)/(16*x**2 + 16) - sqrt(2)*x**2*log(4*sqrt(2)*sqrt(x) + 4*x + 4)/(16*x**2 + 16) + 2*sqrt(2)*x**2*atan(sqrt(2)*sqrt(x) - 1)/(16*x**2 + 16) + 2*sqrt(2)*x**2*atan(sqrt(2)*sqrt(x) + 1)/(16*x**2 + 16) + sqrt(2)*log(-4*sqrt(2)*sqrt(x) + 4*x + 4)/(16*x**2 + 16) - sqrt(2)*log(4*sqrt(2)*sqrt(x) + 4*x + 4)/(16*x**2 + 16) + 2*sqrt(2)*atan(sqrt(2)*sqrt(x) - 1)/(16*x**2 + 16) + 2*sqrt(2)*atan(sqrt(2)*sqrt(x) + 1)/(16*x**2 + 16)","B",0
325,1,264,0,2.988988," ","integrate(1/(x**2+1)**2/x**(1/2),x)","\frac{8 \sqrt{x}}{16 x^{2} + 16} - \frac{3 \sqrt{2} x^{2} \log{\left(- 4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{16 x^{2} + 16} + \frac{3 \sqrt{2} x^{2} \log{\left(4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{16 x^{2} + 16} + \frac{6 \sqrt{2} x^{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{16 x^{2} + 16} + \frac{6 \sqrt{2} x^{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{16 x^{2} + 16} - \frac{3 \sqrt{2} \log{\left(- 4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{16 x^{2} + 16} + \frac{3 \sqrt{2} \log{\left(4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{16 x^{2} + 16} + \frac{6 \sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{16 x^{2} + 16} + \frac{6 \sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{16 x^{2} + 16}"," ",0,"8*sqrt(x)/(16*x**2 + 16) - 3*sqrt(2)*x**2*log(-4*sqrt(2)*sqrt(x) + 4*x + 4)/(16*x**2 + 16) + 3*sqrt(2)*x**2*log(4*sqrt(2)*sqrt(x) + 4*x + 4)/(16*x**2 + 16) + 6*sqrt(2)*x**2*atan(sqrt(2)*sqrt(x) - 1)/(16*x**2 + 16) + 6*sqrt(2)*x**2*atan(sqrt(2)*sqrt(x) + 1)/(16*x**2 + 16) - 3*sqrt(2)*log(-4*sqrt(2)*sqrt(x) + 4*x + 4)/(16*x**2 + 16) + 3*sqrt(2)*log(4*sqrt(2)*sqrt(x) + 4*x + 4)/(16*x**2 + 16) + 6*sqrt(2)*atan(sqrt(2)*sqrt(x) - 1)/(16*x**2 + 16) + 6*sqrt(2)*atan(sqrt(2)*sqrt(x) + 1)/(16*x**2 + 16)","B",0
326,1,366,0,4.563212," ","integrate(1/x**(3/2)/(x**2+1)**2,x)","- \frac{5 \sqrt{2} x^{\frac{5}{2}} \log{\left(- 4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{16 x^{\frac{5}{2}} + 16 \sqrt{x}} + \frac{5 \sqrt{2} x^{\frac{5}{2}} \log{\left(4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{16 x^{\frac{5}{2}} + 16 \sqrt{x}} - \frac{10 \sqrt{2} x^{\frac{5}{2}} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{16 x^{\frac{5}{2}} + 16 \sqrt{x}} - \frac{10 \sqrt{2} x^{\frac{5}{2}} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{16 x^{\frac{5}{2}} + 16 \sqrt{x}} - \frac{5 \sqrt{2} \sqrt{x} \log{\left(- 4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{16 x^{\frac{5}{2}} + 16 \sqrt{x}} + \frac{5 \sqrt{2} \sqrt{x} \log{\left(4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{16 x^{\frac{5}{2}} + 16 \sqrt{x}} - \frac{10 \sqrt{2} \sqrt{x} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{16 x^{\frac{5}{2}} + 16 \sqrt{x}} - \frac{10 \sqrt{2} \sqrt{x} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{16 x^{\frac{5}{2}} + 16 \sqrt{x}} - \frac{40 x^{2}}{16 x^{\frac{5}{2}} + 16 \sqrt{x}} - \frac{32}{16 x^{\frac{5}{2}} + 16 \sqrt{x}}"," ",0,"-5*sqrt(2)*x**(5/2)*log(-4*sqrt(2)*sqrt(x) + 4*x + 4)/(16*x**(5/2) + 16*sqrt(x)) + 5*sqrt(2)*x**(5/2)*log(4*sqrt(2)*sqrt(x) + 4*x + 4)/(16*x**(5/2) + 16*sqrt(x)) - 10*sqrt(2)*x**(5/2)*atan(sqrt(2)*sqrt(x) - 1)/(16*x**(5/2) + 16*sqrt(x)) - 10*sqrt(2)*x**(5/2)*atan(sqrt(2)*sqrt(x) + 1)/(16*x**(5/2) + 16*sqrt(x)) - 5*sqrt(2)*sqrt(x)*log(-4*sqrt(2)*sqrt(x) + 4*x + 4)/(16*x**(5/2) + 16*sqrt(x)) + 5*sqrt(2)*sqrt(x)*log(4*sqrt(2)*sqrt(x) + 4*x + 4)/(16*x**(5/2) + 16*sqrt(x)) - 10*sqrt(2)*sqrt(x)*atan(sqrt(2)*sqrt(x) - 1)/(16*x**(5/2) + 16*sqrt(x)) - 10*sqrt(2)*sqrt(x)*atan(sqrt(2)*sqrt(x) + 1)/(16*x**(5/2) + 16*sqrt(x)) - 40*x**2/(16*x**(5/2) + 16*sqrt(x)) - 32/(16*x**(5/2) + 16*sqrt(x))","B",0
327,1,366,0,8.329983," ","integrate(1/x**(5/2)/(x**2+1)**2,x)","\frac{21 \sqrt{2} x^{\frac{7}{2}} \log{\left(- 4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{48 x^{\frac{7}{2}} + 48 x^{\frac{3}{2}}} - \frac{21 \sqrt{2} x^{\frac{7}{2}} \log{\left(4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{48 x^{\frac{7}{2}} + 48 x^{\frac{3}{2}}} - \frac{42 \sqrt{2} x^{\frac{7}{2}} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{48 x^{\frac{7}{2}} + 48 x^{\frac{3}{2}}} - \frac{42 \sqrt{2} x^{\frac{7}{2}} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{48 x^{\frac{7}{2}} + 48 x^{\frac{3}{2}}} + \frac{21 \sqrt{2} x^{\frac{3}{2}} \log{\left(- 4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{48 x^{\frac{7}{2}} + 48 x^{\frac{3}{2}}} - \frac{21 \sqrt{2} x^{\frac{3}{2}} \log{\left(4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{48 x^{\frac{7}{2}} + 48 x^{\frac{3}{2}}} - \frac{42 \sqrt{2} x^{\frac{3}{2}} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{48 x^{\frac{7}{2}} + 48 x^{\frac{3}{2}}} - \frac{42 \sqrt{2} x^{\frac{3}{2}} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{48 x^{\frac{7}{2}} + 48 x^{\frac{3}{2}}} - \frac{56 x^{2}}{48 x^{\frac{7}{2}} + 48 x^{\frac{3}{2}}} - \frac{32}{48 x^{\frac{7}{2}} + 48 x^{\frac{3}{2}}}"," ",0,"21*sqrt(2)*x**(7/2)*log(-4*sqrt(2)*sqrt(x) + 4*x + 4)/(48*x**(7/2) + 48*x**(3/2)) - 21*sqrt(2)*x**(7/2)*log(4*sqrt(2)*sqrt(x) + 4*x + 4)/(48*x**(7/2) + 48*x**(3/2)) - 42*sqrt(2)*x**(7/2)*atan(sqrt(2)*sqrt(x) - 1)/(48*x**(7/2) + 48*x**(3/2)) - 42*sqrt(2)*x**(7/2)*atan(sqrt(2)*sqrt(x) + 1)/(48*x**(7/2) + 48*x**(3/2)) + 21*sqrt(2)*x**(3/2)*log(-4*sqrt(2)*sqrt(x) + 4*x + 4)/(48*x**(7/2) + 48*x**(3/2)) - 21*sqrt(2)*x**(3/2)*log(4*sqrt(2)*sqrt(x) + 4*x + 4)/(48*x**(7/2) + 48*x**(3/2)) - 42*sqrt(2)*x**(3/2)*atan(sqrt(2)*sqrt(x) - 1)/(48*x**(7/2) + 48*x**(3/2)) - 42*sqrt(2)*x**(3/2)*atan(sqrt(2)*sqrt(x) + 1)/(48*x**(7/2) + 48*x**(3/2)) - 56*x**2/(48*x**(7/2) + 48*x**(3/2)) - 32/(48*x**(7/2) + 48*x**(3/2))","B",0
328,1,384,0,18.732078," ","integrate(1/x**(7/2)/(x**2+1)**2,x)","\frac{45 \sqrt{2} x^{\frac{9}{2}} \log{\left(- 4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{80 x^{\frac{9}{2}} + 80 x^{\frac{5}{2}}} - \frac{45 \sqrt{2} x^{\frac{9}{2}} \log{\left(4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{80 x^{\frac{9}{2}} + 80 x^{\frac{5}{2}}} + \frac{90 \sqrt{2} x^{\frac{9}{2}} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{80 x^{\frac{9}{2}} + 80 x^{\frac{5}{2}}} + \frac{90 \sqrt{2} x^{\frac{9}{2}} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{80 x^{\frac{9}{2}} + 80 x^{\frac{5}{2}}} + \frac{45 \sqrt{2} x^{\frac{5}{2}} \log{\left(- 4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{80 x^{\frac{9}{2}} + 80 x^{\frac{5}{2}}} - \frac{45 \sqrt{2} x^{\frac{5}{2}} \log{\left(4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{80 x^{\frac{9}{2}} + 80 x^{\frac{5}{2}}} + \frac{90 \sqrt{2} x^{\frac{5}{2}} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{80 x^{\frac{9}{2}} + 80 x^{\frac{5}{2}}} + \frac{90 \sqrt{2} x^{\frac{5}{2}} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{80 x^{\frac{9}{2}} + 80 x^{\frac{5}{2}}} + \frac{360 x^{4}}{80 x^{\frac{9}{2}} + 80 x^{\frac{5}{2}}} + \frac{288 x^{2}}{80 x^{\frac{9}{2}} + 80 x^{\frac{5}{2}}} - \frac{32}{80 x^{\frac{9}{2}} + 80 x^{\frac{5}{2}}}"," ",0,"45*sqrt(2)*x**(9/2)*log(-4*sqrt(2)*sqrt(x) + 4*x + 4)/(80*x**(9/2) + 80*x**(5/2)) - 45*sqrt(2)*x**(9/2)*log(4*sqrt(2)*sqrt(x) + 4*x + 4)/(80*x**(9/2) + 80*x**(5/2)) + 90*sqrt(2)*x**(9/2)*atan(sqrt(2)*sqrt(x) - 1)/(80*x**(9/2) + 80*x**(5/2)) + 90*sqrt(2)*x**(9/2)*atan(sqrt(2)*sqrt(x) + 1)/(80*x**(9/2) + 80*x**(5/2)) + 45*sqrt(2)*x**(5/2)*log(-4*sqrt(2)*sqrt(x) + 4*x + 4)/(80*x**(9/2) + 80*x**(5/2)) - 45*sqrt(2)*x**(5/2)*log(4*sqrt(2)*sqrt(x) + 4*x + 4)/(80*x**(9/2) + 80*x**(5/2)) + 90*sqrt(2)*x**(5/2)*atan(sqrt(2)*sqrt(x) - 1)/(80*x**(9/2) + 80*x**(5/2)) + 90*sqrt(2)*x**(5/2)*atan(sqrt(2)*sqrt(x) + 1)/(80*x**(9/2) + 80*x**(5/2)) + 360*x**4/(80*x**(9/2) + 80*x**(5/2)) + 288*x**2/(80*x**(9/2) + 80*x**(5/2)) - 32/(80*x**(9/2) + 80*x**(5/2))","B",0
329,1,481,0,23.353945," ","integrate(x**(7/2)/(x**2+1)**3,x)","- \frac{72 x^{\frac{5}{2}}}{128 x^{4} + 256 x^{2} + 128} - \frac{40 \sqrt{x}}{128 x^{4} + 256 x^{2} + 128} - \frac{5 \sqrt{2} x^{4} \log{\left(- 4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{128 x^{4} + 256 x^{2} + 128} + \frac{5 \sqrt{2} x^{4} \log{\left(4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{128 x^{4} + 256 x^{2} + 128} + \frac{10 \sqrt{2} x^{4} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{128 x^{4} + 256 x^{2} + 128} + \frac{10 \sqrt{2} x^{4} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{128 x^{4} + 256 x^{2} + 128} - \frac{10 \sqrt{2} x^{2} \log{\left(- 4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{128 x^{4} + 256 x^{2} + 128} + \frac{10 \sqrt{2} x^{2} \log{\left(4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{128 x^{4} + 256 x^{2} + 128} + \frac{20 \sqrt{2} x^{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{128 x^{4} + 256 x^{2} + 128} + \frac{20 \sqrt{2} x^{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{128 x^{4} + 256 x^{2} + 128} - \frac{5 \sqrt{2} \log{\left(- 4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{128 x^{4} + 256 x^{2} + 128} + \frac{5 \sqrt{2} \log{\left(4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{128 x^{4} + 256 x^{2} + 128} + \frac{10 \sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{128 x^{4} + 256 x^{2} + 128} + \frac{10 \sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{128 x^{4} + 256 x^{2} + 128}"," ",0,"-72*x**(5/2)/(128*x**4 + 256*x**2 + 128) - 40*sqrt(x)/(128*x**4 + 256*x**2 + 128) - 5*sqrt(2)*x**4*log(-4*sqrt(2)*sqrt(x) + 4*x + 4)/(128*x**4 + 256*x**2 + 128) + 5*sqrt(2)*x**4*log(4*sqrt(2)*sqrt(x) + 4*x + 4)/(128*x**4 + 256*x**2 + 128) + 10*sqrt(2)*x**4*atan(sqrt(2)*sqrt(x) - 1)/(128*x**4 + 256*x**2 + 128) + 10*sqrt(2)*x**4*atan(sqrt(2)*sqrt(x) + 1)/(128*x**4 + 256*x**2 + 128) - 10*sqrt(2)*x**2*log(-4*sqrt(2)*sqrt(x) + 4*x + 4)/(128*x**4 + 256*x**2 + 128) + 10*sqrt(2)*x**2*log(4*sqrt(2)*sqrt(x) + 4*x + 4)/(128*x**4 + 256*x**2 + 128) + 20*sqrt(2)*x**2*atan(sqrt(2)*sqrt(x) - 1)/(128*x**4 + 256*x**2 + 128) + 20*sqrt(2)*x**2*atan(sqrt(2)*sqrt(x) + 1)/(128*x**4 + 256*x**2 + 128) - 5*sqrt(2)*log(-4*sqrt(2)*sqrt(x) + 4*x + 4)/(128*x**4 + 256*x**2 + 128) + 5*sqrt(2)*log(4*sqrt(2)*sqrt(x) + 4*x + 4)/(128*x**4 + 256*x**2 + 128) + 10*sqrt(2)*atan(sqrt(2)*sqrt(x) - 1)/(128*x**4 + 256*x**2 + 128) + 10*sqrt(2)*atan(sqrt(2)*sqrt(x) + 1)/(128*x**4 + 256*x**2 + 128)","B",0
330,1,481,0,15.485965," ","integrate(x**(5/2)/(x**2+1)**3,x)","\frac{24 x^{\frac{7}{2}}}{128 x^{4} + 256 x^{2} + 128} - \frac{8 x^{\frac{3}{2}}}{128 x^{4} + 256 x^{2} + 128} + \frac{3 \sqrt{2} x^{4} \log{\left(- 4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{128 x^{4} + 256 x^{2} + 128} - \frac{3 \sqrt{2} x^{4} \log{\left(4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{128 x^{4} + 256 x^{2} + 128} + \frac{6 \sqrt{2} x^{4} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{128 x^{4} + 256 x^{2} + 128} + \frac{6 \sqrt{2} x^{4} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{128 x^{4} + 256 x^{2} + 128} + \frac{6 \sqrt{2} x^{2} \log{\left(- 4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{128 x^{4} + 256 x^{2} + 128} - \frac{6 \sqrt{2} x^{2} \log{\left(4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{128 x^{4} + 256 x^{2} + 128} + \frac{12 \sqrt{2} x^{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{128 x^{4} + 256 x^{2} + 128} + \frac{12 \sqrt{2} x^{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{128 x^{4} + 256 x^{2} + 128} + \frac{3 \sqrt{2} \log{\left(- 4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{128 x^{4} + 256 x^{2} + 128} - \frac{3 \sqrt{2} \log{\left(4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{128 x^{4} + 256 x^{2} + 128} + \frac{6 \sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{128 x^{4} + 256 x^{2} + 128} + \frac{6 \sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{128 x^{4} + 256 x^{2} + 128}"," ",0,"24*x**(7/2)/(128*x**4 + 256*x**2 + 128) - 8*x**(3/2)/(128*x**4 + 256*x**2 + 128) + 3*sqrt(2)*x**4*log(-4*sqrt(2)*sqrt(x) + 4*x + 4)/(128*x**4 + 256*x**2 + 128) - 3*sqrt(2)*x**4*log(4*sqrt(2)*sqrt(x) + 4*x + 4)/(128*x**4 + 256*x**2 + 128) + 6*sqrt(2)*x**4*atan(sqrt(2)*sqrt(x) - 1)/(128*x**4 + 256*x**2 + 128) + 6*sqrt(2)*x**4*atan(sqrt(2)*sqrt(x) + 1)/(128*x**4 + 256*x**2 + 128) + 6*sqrt(2)*x**2*log(-4*sqrt(2)*sqrt(x) + 4*x + 4)/(128*x**4 + 256*x**2 + 128) - 6*sqrt(2)*x**2*log(4*sqrt(2)*sqrt(x) + 4*x + 4)/(128*x**4 + 256*x**2 + 128) + 12*sqrt(2)*x**2*atan(sqrt(2)*sqrt(x) - 1)/(128*x**4 + 256*x**2 + 128) + 12*sqrt(2)*x**2*atan(sqrt(2)*sqrt(x) + 1)/(128*x**4 + 256*x**2 + 128) + 3*sqrt(2)*log(-4*sqrt(2)*sqrt(x) + 4*x + 4)/(128*x**4 + 256*x**2 + 128) - 3*sqrt(2)*log(4*sqrt(2)*sqrt(x) + 4*x + 4)/(128*x**4 + 256*x**2 + 128) + 6*sqrt(2)*atan(sqrt(2)*sqrt(x) - 1)/(128*x**4 + 256*x**2 + 128) + 6*sqrt(2)*atan(sqrt(2)*sqrt(x) + 1)/(128*x**4 + 256*x**2 + 128)","B",0
331,1,481,0,9.810488," ","integrate(x**(3/2)/(x**2+1)**3,x)","\frac{8 x^{\frac{5}{2}}}{128 x^{4} + 256 x^{2} + 128} - \frac{24 \sqrt{x}}{128 x^{4} + 256 x^{2} + 128} - \frac{3 \sqrt{2} x^{4} \log{\left(- 4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{128 x^{4} + 256 x^{2} + 128} + \frac{3 \sqrt{2} x^{4} \log{\left(4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{128 x^{4} + 256 x^{2} + 128} + \frac{6 \sqrt{2} x^{4} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{128 x^{4} + 256 x^{2} + 128} + \frac{6 \sqrt{2} x^{4} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{128 x^{4} + 256 x^{2} + 128} - \frac{6 \sqrt{2} x^{2} \log{\left(- 4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{128 x^{4} + 256 x^{2} + 128} + \frac{6 \sqrt{2} x^{2} \log{\left(4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{128 x^{4} + 256 x^{2} + 128} + \frac{12 \sqrt{2} x^{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{128 x^{4} + 256 x^{2} + 128} + \frac{12 \sqrt{2} x^{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{128 x^{4} + 256 x^{2} + 128} - \frac{3 \sqrt{2} \log{\left(- 4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{128 x^{4} + 256 x^{2} + 128} + \frac{3 \sqrt{2} \log{\left(4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{128 x^{4} + 256 x^{2} + 128} + \frac{6 \sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{128 x^{4} + 256 x^{2} + 128} + \frac{6 \sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{128 x^{4} + 256 x^{2} + 128}"," ",0,"8*x**(5/2)/(128*x**4 + 256*x**2 + 128) - 24*sqrt(x)/(128*x**4 + 256*x**2 + 128) - 3*sqrt(2)*x**4*log(-4*sqrt(2)*sqrt(x) + 4*x + 4)/(128*x**4 + 256*x**2 + 128) + 3*sqrt(2)*x**4*log(4*sqrt(2)*sqrt(x) + 4*x + 4)/(128*x**4 + 256*x**2 + 128) + 6*sqrt(2)*x**4*atan(sqrt(2)*sqrt(x) - 1)/(128*x**4 + 256*x**2 + 128) + 6*sqrt(2)*x**4*atan(sqrt(2)*sqrt(x) + 1)/(128*x**4 + 256*x**2 + 128) - 6*sqrt(2)*x**2*log(-4*sqrt(2)*sqrt(x) + 4*x + 4)/(128*x**4 + 256*x**2 + 128) + 6*sqrt(2)*x**2*log(4*sqrt(2)*sqrt(x) + 4*x + 4)/(128*x**4 + 256*x**2 + 128) + 12*sqrt(2)*x**2*atan(sqrt(2)*sqrt(x) - 1)/(128*x**4 + 256*x**2 + 128) + 12*sqrt(2)*x**2*atan(sqrt(2)*sqrt(x) + 1)/(128*x**4 + 256*x**2 + 128) - 3*sqrt(2)*log(-4*sqrt(2)*sqrt(x) + 4*x + 4)/(128*x**4 + 256*x**2 + 128) + 3*sqrt(2)*log(4*sqrt(2)*sqrt(x) + 4*x + 4)/(128*x**4 + 256*x**2 + 128) + 6*sqrt(2)*atan(sqrt(2)*sqrt(x) - 1)/(128*x**4 + 256*x**2 + 128) + 6*sqrt(2)*atan(sqrt(2)*sqrt(x) + 1)/(128*x**4 + 256*x**2 + 128)","B",0
332,1,481,0,6.378865," ","integrate(x**(1/2)/(x**2+1)**3,x)","\frac{40 x^{\frac{7}{2}}}{128 x^{4} + 256 x^{2} + 128} + \frac{72 x^{\frac{3}{2}}}{128 x^{4} + 256 x^{2} + 128} + \frac{5 \sqrt{2} x^{4} \log{\left(- 4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{128 x^{4} + 256 x^{2} + 128} - \frac{5 \sqrt{2} x^{4} \log{\left(4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{128 x^{4} + 256 x^{2} + 128} + \frac{10 \sqrt{2} x^{4} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{128 x^{4} + 256 x^{2} + 128} + \frac{10 \sqrt{2} x^{4} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{128 x^{4} + 256 x^{2} + 128} + \frac{10 \sqrt{2} x^{2} \log{\left(- 4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{128 x^{4} + 256 x^{2} + 128} - \frac{10 \sqrt{2} x^{2} \log{\left(4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{128 x^{4} + 256 x^{2} + 128} + \frac{20 \sqrt{2} x^{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{128 x^{4} + 256 x^{2} + 128} + \frac{20 \sqrt{2} x^{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{128 x^{4} + 256 x^{2} + 128} + \frac{5 \sqrt{2} \log{\left(- 4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{128 x^{4} + 256 x^{2} + 128} - \frac{5 \sqrt{2} \log{\left(4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{128 x^{4} + 256 x^{2} + 128} + \frac{10 \sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{128 x^{4} + 256 x^{2} + 128} + \frac{10 \sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{128 x^{4} + 256 x^{2} + 128}"," ",0,"40*x**(7/2)/(128*x**4 + 256*x**2 + 128) + 72*x**(3/2)/(128*x**4 + 256*x**2 + 128) + 5*sqrt(2)*x**4*log(-4*sqrt(2)*sqrt(x) + 4*x + 4)/(128*x**4 + 256*x**2 + 128) - 5*sqrt(2)*x**4*log(4*sqrt(2)*sqrt(x) + 4*x + 4)/(128*x**4 + 256*x**2 + 128) + 10*sqrt(2)*x**4*atan(sqrt(2)*sqrt(x) - 1)/(128*x**4 + 256*x**2 + 128) + 10*sqrt(2)*x**4*atan(sqrt(2)*sqrt(x) + 1)/(128*x**4 + 256*x**2 + 128) + 10*sqrt(2)*x**2*log(-4*sqrt(2)*sqrt(x) + 4*x + 4)/(128*x**4 + 256*x**2 + 128) - 10*sqrt(2)*x**2*log(4*sqrt(2)*sqrt(x) + 4*x + 4)/(128*x**4 + 256*x**2 + 128) + 20*sqrt(2)*x**2*atan(sqrt(2)*sqrt(x) - 1)/(128*x**4 + 256*x**2 + 128) + 20*sqrt(2)*x**2*atan(sqrt(2)*sqrt(x) + 1)/(128*x**4 + 256*x**2 + 128) + 5*sqrt(2)*log(-4*sqrt(2)*sqrt(x) + 4*x + 4)/(128*x**4 + 256*x**2 + 128) - 5*sqrt(2)*log(4*sqrt(2)*sqrt(x) + 4*x + 4)/(128*x**4 + 256*x**2 + 128) + 10*sqrt(2)*atan(sqrt(2)*sqrt(x) - 1)/(128*x**4 + 256*x**2 + 128) + 10*sqrt(2)*atan(sqrt(2)*sqrt(x) + 1)/(128*x**4 + 256*x**2 + 128)","B",0
333,1,481,0,8.459063," ","integrate(1/(x**2+1)**3/x**(1/2),x)","\frac{56 x^{\frac{5}{2}}}{128 x^{4} + 256 x^{2} + 128} + \frac{88 \sqrt{x}}{128 x^{4} + 256 x^{2} + 128} - \frac{21 \sqrt{2} x^{4} \log{\left(- 4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{128 x^{4} + 256 x^{2} + 128} + \frac{21 \sqrt{2} x^{4} \log{\left(4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{128 x^{4} + 256 x^{2} + 128} + \frac{42 \sqrt{2} x^{4} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{128 x^{4} + 256 x^{2} + 128} + \frac{42 \sqrt{2} x^{4} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{128 x^{4} + 256 x^{2} + 128} - \frac{42 \sqrt{2} x^{2} \log{\left(- 4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{128 x^{4} + 256 x^{2} + 128} + \frac{42 \sqrt{2} x^{2} \log{\left(4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{128 x^{4} + 256 x^{2} + 128} + \frac{84 \sqrt{2} x^{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{128 x^{4} + 256 x^{2} + 128} + \frac{84 \sqrt{2} x^{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{128 x^{4} + 256 x^{2} + 128} - \frac{21 \sqrt{2} \log{\left(- 4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{128 x^{4} + 256 x^{2} + 128} + \frac{21 \sqrt{2} \log{\left(4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{128 x^{4} + 256 x^{2} + 128} + \frac{42 \sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{128 x^{4} + 256 x^{2} + 128} + \frac{42 \sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{128 x^{4} + 256 x^{2} + 128}"," ",0,"56*x**(5/2)/(128*x**4 + 256*x**2 + 128) + 88*sqrt(x)/(128*x**4 + 256*x**2 + 128) - 21*sqrt(2)*x**4*log(-4*sqrt(2)*sqrt(x) + 4*x + 4)/(128*x**4 + 256*x**2 + 128) + 21*sqrt(2)*x**4*log(4*sqrt(2)*sqrt(x) + 4*x + 4)/(128*x**4 + 256*x**2 + 128) + 42*sqrt(2)*x**4*atan(sqrt(2)*sqrt(x) - 1)/(128*x**4 + 256*x**2 + 128) + 42*sqrt(2)*x**4*atan(sqrt(2)*sqrt(x) + 1)/(128*x**4 + 256*x**2 + 128) - 42*sqrt(2)*x**2*log(-4*sqrt(2)*sqrt(x) + 4*x + 4)/(128*x**4 + 256*x**2 + 128) + 42*sqrt(2)*x**2*log(4*sqrt(2)*sqrt(x) + 4*x + 4)/(128*x**4 + 256*x**2 + 128) + 84*sqrt(2)*x**2*atan(sqrt(2)*sqrt(x) - 1)/(128*x**4 + 256*x**2 + 128) + 84*sqrt(2)*x**2*atan(sqrt(2)*sqrt(x) + 1)/(128*x**4 + 256*x**2 + 128) - 21*sqrt(2)*log(-4*sqrt(2)*sqrt(x) + 4*x + 4)/(128*x**4 + 256*x**2 + 128) + 21*sqrt(2)*log(4*sqrt(2)*sqrt(x) + 4*x + 4)/(128*x**4 + 256*x**2 + 128) + 42*sqrt(2)*atan(sqrt(2)*sqrt(x) - 1)/(128*x**4 + 256*x**2 + 128) + 42*sqrt(2)*atan(sqrt(2)*sqrt(x) + 1)/(128*x**4 + 256*x**2 + 128)","B",0
334,1,653,0,12.634981," ","integrate(1/x**(3/2)/(x**2+1)**3,x)","- \frac{45 \sqrt{2} x^{\frac{9}{2}} \log{\left(- 4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{128 x^{\frac{9}{2}} + 256 x^{\frac{5}{2}} + 128 \sqrt{x}} + \frac{45 \sqrt{2} x^{\frac{9}{2}} \log{\left(4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{128 x^{\frac{9}{2}} + 256 x^{\frac{5}{2}} + 128 \sqrt{x}} - \frac{90 \sqrt{2} x^{\frac{9}{2}} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{128 x^{\frac{9}{2}} + 256 x^{\frac{5}{2}} + 128 \sqrt{x}} - \frac{90 \sqrt{2} x^{\frac{9}{2}} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{128 x^{\frac{9}{2}} + 256 x^{\frac{5}{2}} + 128 \sqrt{x}} - \frac{90 \sqrt{2} x^{\frac{5}{2}} \log{\left(- 4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{128 x^{\frac{9}{2}} + 256 x^{\frac{5}{2}} + 128 \sqrt{x}} + \frac{90 \sqrt{2} x^{\frac{5}{2}} \log{\left(4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{128 x^{\frac{9}{2}} + 256 x^{\frac{5}{2}} + 128 \sqrt{x}} - \frac{180 \sqrt{2} x^{\frac{5}{2}} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{128 x^{\frac{9}{2}} + 256 x^{\frac{5}{2}} + 128 \sqrt{x}} - \frac{180 \sqrt{2} x^{\frac{5}{2}} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{128 x^{\frac{9}{2}} + 256 x^{\frac{5}{2}} + 128 \sqrt{x}} - \frac{45 \sqrt{2} \sqrt{x} \log{\left(- 4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{128 x^{\frac{9}{2}} + 256 x^{\frac{5}{2}} + 128 \sqrt{x}} + \frac{45 \sqrt{2} \sqrt{x} \log{\left(4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{128 x^{\frac{9}{2}} + 256 x^{\frac{5}{2}} + 128 \sqrt{x}} - \frac{90 \sqrt{2} \sqrt{x} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{128 x^{\frac{9}{2}} + 256 x^{\frac{5}{2}} + 128 \sqrt{x}} - \frac{90 \sqrt{2} \sqrt{x} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{128 x^{\frac{9}{2}} + 256 x^{\frac{5}{2}} + 128 \sqrt{x}} - \frac{360 x^{4}}{128 x^{\frac{9}{2}} + 256 x^{\frac{5}{2}} + 128 \sqrt{x}} - \frac{648 x^{2}}{128 x^{\frac{9}{2}} + 256 x^{\frac{5}{2}} + 128 \sqrt{x}} - \frac{256}{128 x^{\frac{9}{2}} + 256 x^{\frac{5}{2}} + 128 \sqrt{x}}"," ",0,"-45*sqrt(2)*x**(9/2)*log(-4*sqrt(2)*sqrt(x) + 4*x + 4)/(128*x**(9/2) + 256*x**(5/2) + 128*sqrt(x)) + 45*sqrt(2)*x**(9/2)*log(4*sqrt(2)*sqrt(x) + 4*x + 4)/(128*x**(9/2) + 256*x**(5/2) + 128*sqrt(x)) - 90*sqrt(2)*x**(9/2)*atan(sqrt(2)*sqrt(x) - 1)/(128*x**(9/2) + 256*x**(5/2) + 128*sqrt(x)) - 90*sqrt(2)*x**(9/2)*atan(sqrt(2)*sqrt(x) + 1)/(128*x**(9/2) + 256*x**(5/2) + 128*sqrt(x)) - 90*sqrt(2)*x**(5/2)*log(-4*sqrt(2)*sqrt(x) + 4*x + 4)/(128*x**(9/2) + 256*x**(5/2) + 128*sqrt(x)) + 90*sqrt(2)*x**(5/2)*log(4*sqrt(2)*sqrt(x) + 4*x + 4)/(128*x**(9/2) + 256*x**(5/2) + 128*sqrt(x)) - 180*sqrt(2)*x**(5/2)*atan(sqrt(2)*sqrt(x) - 1)/(128*x**(9/2) + 256*x**(5/2) + 128*sqrt(x)) - 180*sqrt(2)*x**(5/2)*atan(sqrt(2)*sqrt(x) + 1)/(128*x**(9/2) + 256*x**(5/2) + 128*sqrt(x)) - 45*sqrt(2)*sqrt(x)*log(-4*sqrt(2)*sqrt(x) + 4*x + 4)/(128*x**(9/2) + 256*x**(5/2) + 128*sqrt(x)) + 45*sqrt(2)*sqrt(x)*log(4*sqrt(2)*sqrt(x) + 4*x + 4)/(128*x**(9/2) + 256*x**(5/2) + 128*sqrt(x)) - 90*sqrt(2)*sqrt(x)*atan(sqrt(2)*sqrt(x) - 1)/(128*x**(9/2) + 256*x**(5/2) + 128*sqrt(x)) - 90*sqrt(2)*sqrt(x)*atan(sqrt(2)*sqrt(x) + 1)/(128*x**(9/2) + 256*x**(5/2) + 128*sqrt(x)) - 360*x**4/(128*x**(9/2) + 256*x**(5/2) + 128*sqrt(x)) - 648*x**2/(128*x**(9/2) + 256*x**(5/2) + 128*sqrt(x)) - 256/(128*x**(9/2) + 256*x**(5/2) + 128*sqrt(x))","B",0
335,1,653,0,22.417421," ","integrate(1/x**(5/2)/(x**2+1)**3,x)","\frac{231 \sqrt{2} x^{\frac{11}{2}} \log{\left(- 4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{384 x^{\frac{11}{2}} + 768 x^{\frac{7}{2}} + 384 x^{\frac{3}{2}}} - \frac{231 \sqrt{2} x^{\frac{11}{2}} \log{\left(4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{384 x^{\frac{11}{2}} + 768 x^{\frac{7}{2}} + 384 x^{\frac{3}{2}}} - \frac{462 \sqrt{2} x^{\frac{11}{2}} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{384 x^{\frac{11}{2}} + 768 x^{\frac{7}{2}} + 384 x^{\frac{3}{2}}} - \frac{462 \sqrt{2} x^{\frac{11}{2}} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{384 x^{\frac{11}{2}} + 768 x^{\frac{7}{2}} + 384 x^{\frac{3}{2}}} + \frac{462 \sqrt{2} x^{\frac{7}{2}} \log{\left(- 4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{384 x^{\frac{11}{2}} + 768 x^{\frac{7}{2}} + 384 x^{\frac{3}{2}}} - \frac{462 \sqrt{2} x^{\frac{7}{2}} \log{\left(4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{384 x^{\frac{11}{2}} + 768 x^{\frac{7}{2}} + 384 x^{\frac{3}{2}}} - \frac{924 \sqrt{2} x^{\frac{7}{2}} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{384 x^{\frac{11}{2}} + 768 x^{\frac{7}{2}} + 384 x^{\frac{3}{2}}} - \frac{924 \sqrt{2} x^{\frac{7}{2}} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{384 x^{\frac{11}{2}} + 768 x^{\frac{7}{2}} + 384 x^{\frac{3}{2}}} + \frac{231 \sqrt{2} x^{\frac{3}{2}} \log{\left(- 4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{384 x^{\frac{11}{2}} + 768 x^{\frac{7}{2}} + 384 x^{\frac{3}{2}}} - \frac{231 \sqrt{2} x^{\frac{3}{2}} \log{\left(4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{384 x^{\frac{11}{2}} + 768 x^{\frac{7}{2}} + 384 x^{\frac{3}{2}}} - \frac{462 \sqrt{2} x^{\frac{3}{2}} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{384 x^{\frac{11}{2}} + 768 x^{\frac{7}{2}} + 384 x^{\frac{3}{2}}} - \frac{462 \sqrt{2} x^{\frac{3}{2}} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{384 x^{\frac{11}{2}} + 768 x^{\frac{7}{2}} + 384 x^{\frac{3}{2}}} - \frac{616 x^{4}}{384 x^{\frac{11}{2}} + 768 x^{\frac{7}{2}} + 384 x^{\frac{3}{2}}} - \frac{968 x^{2}}{384 x^{\frac{11}{2}} + 768 x^{\frac{7}{2}} + 384 x^{\frac{3}{2}}} - \frac{256}{384 x^{\frac{11}{2}} + 768 x^{\frac{7}{2}} + 384 x^{\frac{3}{2}}}"," ",0,"231*sqrt(2)*x**(11/2)*log(-4*sqrt(2)*sqrt(x) + 4*x + 4)/(384*x**(11/2) + 768*x**(7/2) + 384*x**(3/2)) - 231*sqrt(2)*x**(11/2)*log(4*sqrt(2)*sqrt(x) + 4*x + 4)/(384*x**(11/2) + 768*x**(7/2) + 384*x**(3/2)) - 462*sqrt(2)*x**(11/2)*atan(sqrt(2)*sqrt(x) - 1)/(384*x**(11/2) + 768*x**(7/2) + 384*x**(3/2)) - 462*sqrt(2)*x**(11/2)*atan(sqrt(2)*sqrt(x) + 1)/(384*x**(11/2) + 768*x**(7/2) + 384*x**(3/2)) + 462*sqrt(2)*x**(7/2)*log(-4*sqrt(2)*sqrt(x) + 4*x + 4)/(384*x**(11/2) + 768*x**(7/2) + 384*x**(3/2)) - 462*sqrt(2)*x**(7/2)*log(4*sqrt(2)*sqrt(x) + 4*x + 4)/(384*x**(11/2) + 768*x**(7/2) + 384*x**(3/2)) - 924*sqrt(2)*x**(7/2)*atan(sqrt(2)*sqrt(x) - 1)/(384*x**(11/2) + 768*x**(7/2) + 384*x**(3/2)) - 924*sqrt(2)*x**(7/2)*atan(sqrt(2)*sqrt(x) + 1)/(384*x**(11/2) + 768*x**(7/2) + 384*x**(3/2)) + 231*sqrt(2)*x**(3/2)*log(-4*sqrt(2)*sqrt(x) + 4*x + 4)/(384*x**(11/2) + 768*x**(7/2) + 384*x**(3/2)) - 231*sqrt(2)*x**(3/2)*log(4*sqrt(2)*sqrt(x) + 4*x + 4)/(384*x**(11/2) + 768*x**(7/2) + 384*x**(3/2)) - 462*sqrt(2)*x**(3/2)*atan(sqrt(2)*sqrt(x) - 1)/(384*x**(11/2) + 768*x**(7/2) + 384*x**(3/2)) - 462*sqrt(2)*x**(3/2)*atan(sqrt(2)*sqrt(x) + 1)/(384*x**(11/2) + 768*x**(7/2) + 384*x**(3/2)) - 616*x**4/(384*x**(11/2) + 768*x**(7/2) + 384*x**(3/2)) - 968*x**2/(384*x**(11/2) + 768*x**(7/2) + 384*x**(3/2)) - 256/(384*x**(11/2) + 768*x**(7/2) + 384*x**(3/2))","B",0
336,1,678,0,51.156330," ","integrate(1/x**(7/2)/(x**2+1)**3,x)","\frac{585 \sqrt{2} x^{\frac{13}{2}} \log{\left(- 4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{640 x^{\frac{13}{2}} + 1280 x^{\frac{9}{2}} + 640 x^{\frac{5}{2}}} - \frac{585 \sqrt{2} x^{\frac{13}{2}} \log{\left(4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{640 x^{\frac{13}{2}} + 1280 x^{\frac{9}{2}} + 640 x^{\frac{5}{2}}} + \frac{1170 \sqrt{2} x^{\frac{13}{2}} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{640 x^{\frac{13}{2}} + 1280 x^{\frac{9}{2}} + 640 x^{\frac{5}{2}}} + \frac{1170 \sqrt{2} x^{\frac{13}{2}} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{640 x^{\frac{13}{2}} + 1280 x^{\frac{9}{2}} + 640 x^{\frac{5}{2}}} + \frac{1170 \sqrt{2} x^{\frac{9}{2}} \log{\left(- 4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{640 x^{\frac{13}{2}} + 1280 x^{\frac{9}{2}} + 640 x^{\frac{5}{2}}} - \frac{1170 \sqrt{2} x^{\frac{9}{2}} \log{\left(4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{640 x^{\frac{13}{2}} + 1280 x^{\frac{9}{2}} + 640 x^{\frac{5}{2}}} + \frac{2340 \sqrt{2} x^{\frac{9}{2}} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{640 x^{\frac{13}{2}} + 1280 x^{\frac{9}{2}} + 640 x^{\frac{5}{2}}} + \frac{2340 \sqrt{2} x^{\frac{9}{2}} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{640 x^{\frac{13}{2}} + 1280 x^{\frac{9}{2}} + 640 x^{\frac{5}{2}}} + \frac{585 \sqrt{2} x^{\frac{5}{2}} \log{\left(- 4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{640 x^{\frac{13}{2}} + 1280 x^{\frac{9}{2}} + 640 x^{\frac{5}{2}}} - \frac{585 \sqrt{2} x^{\frac{5}{2}} \log{\left(4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{640 x^{\frac{13}{2}} + 1280 x^{\frac{9}{2}} + 640 x^{\frac{5}{2}}} + \frac{1170 \sqrt{2} x^{\frac{5}{2}} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{640 x^{\frac{13}{2}} + 1280 x^{\frac{9}{2}} + 640 x^{\frac{5}{2}}} + \frac{1170 \sqrt{2} x^{\frac{5}{2}} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{640 x^{\frac{13}{2}} + 1280 x^{\frac{9}{2}} + 640 x^{\frac{5}{2}}} + \frac{4680 x^{6}}{640 x^{\frac{13}{2}} + 1280 x^{\frac{9}{2}} + 640 x^{\frac{5}{2}}} + \frac{8424 x^{4}}{640 x^{\frac{13}{2}} + 1280 x^{\frac{9}{2}} + 640 x^{\frac{5}{2}}} + \frac{3328 x^{2}}{640 x^{\frac{13}{2}} + 1280 x^{\frac{9}{2}} + 640 x^{\frac{5}{2}}} - \frac{256}{640 x^{\frac{13}{2}} + 1280 x^{\frac{9}{2}} + 640 x^{\frac{5}{2}}}"," ",0,"585*sqrt(2)*x**(13/2)*log(-4*sqrt(2)*sqrt(x) + 4*x + 4)/(640*x**(13/2) + 1280*x**(9/2) + 640*x**(5/2)) - 585*sqrt(2)*x**(13/2)*log(4*sqrt(2)*sqrt(x) + 4*x + 4)/(640*x**(13/2) + 1280*x**(9/2) + 640*x**(5/2)) + 1170*sqrt(2)*x**(13/2)*atan(sqrt(2)*sqrt(x) - 1)/(640*x**(13/2) + 1280*x**(9/2) + 640*x**(5/2)) + 1170*sqrt(2)*x**(13/2)*atan(sqrt(2)*sqrt(x) + 1)/(640*x**(13/2) + 1280*x**(9/2) + 640*x**(5/2)) + 1170*sqrt(2)*x**(9/2)*log(-4*sqrt(2)*sqrt(x) + 4*x + 4)/(640*x**(13/2) + 1280*x**(9/2) + 640*x**(5/2)) - 1170*sqrt(2)*x**(9/2)*log(4*sqrt(2)*sqrt(x) + 4*x + 4)/(640*x**(13/2) + 1280*x**(9/2) + 640*x**(5/2)) + 2340*sqrt(2)*x**(9/2)*atan(sqrt(2)*sqrt(x) - 1)/(640*x**(13/2) + 1280*x**(9/2) + 640*x**(5/2)) + 2340*sqrt(2)*x**(9/2)*atan(sqrt(2)*sqrt(x) + 1)/(640*x**(13/2) + 1280*x**(9/2) + 640*x**(5/2)) + 585*sqrt(2)*x**(5/2)*log(-4*sqrt(2)*sqrt(x) + 4*x + 4)/(640*x**(13/2) + 1280*x**(9/2) + 640*x**(5/2)) - 585*sqrt(2)*x**(5/2)*log(4*sqrt(2)*sqrt(x) + 4*x + 4)/(640*x**(13/2) + 1280*x**(9/2) + 640*x**(5/2)) + 1170*sqrt(2)*x**(5/2)*atan(sqrt(2)*sqrt(x) - 1)/(640*x**(13/2) + 1280*x**(9/2) + 640*x**(5/2)) + 1170*sqrt(2)*x**(5/2)*atan(sqrt(2)*sqrt(x) + 1)/(640*x**(13/2) + 1280*x**(9/2) + 640*x**(5/2)) + 4680*x**6/(640*x**(13/2) + 1280*x**(9/2) + 640*x**(5/2)) + 8424*x**4/(640*x**(13/2) + 1280*x**(9/2) + 640*x**(5/2)) + 3328*x**2/(640*x**(13/2) + 1280*x**(9/2) + 640*x**(5/2)) - 256/(640*x**(13/2) + 1280*x**(9/2) + 640*x**(5/2))","B",0
337,1,26,0,0.290643," ","integrate(x**(1/2)/(-x**2+1),x)","- \frac{\log{\left(\sqrt{x} - 1 \right)}}{2} + \frac{\log{\left(\sqrt{x} + 1 \right)}}{2} - \operatorname{atan}{\left(\sqrt{x} \right)}"," ",0,"-log(sqrt(x) - 1)/2 + log(sqrt(x) + 1)/2 - atan(sqrt(x))","B",0
338,1,94,0,1.780665," ","integrate(x**(2/3)/(x**2+1),x)","\frac{\sqrt{3} \log{\left(4 x^{\frac{2}{3}} - 4 \sqrt{3} \sqrt[3]{x} + 4 \right)}}{4} - \frac{\sqrt{3} \log{\left(4 x^{\frac{2}{3}} + 4 \sqrt{3} \sqrt[3]{x} + 4 \right)}}{4} + \operatorname{atan}{\left(\sqrt[3]{x} \right)} + \frac{\operatorname{atan}{\left(2 \sqrt[3]{x} - \sqrt{3} \right)}}{2} + \frac{\operatorname{atan}{\left(2 \sqrt[3]{x} + \sqrt{3} \right)}}{2}"," ",0,"sqrt(3)*log(4*x**(2/3) - 4*sqrt(3)*x**(1/3) + 4)/4 - sqrt(3)*log(4*x**(2/3) + 4*sqrt(3)*x**(1/3) + 4)/4 + atan(x**(1/3)) + atan(2*x**(1/3) - sqrt(3))/2 + atan(2*x**(1/3) + sqrt(3))/2","A",0
339,1,1999,0,4.496837," ","integrate(x**m*(b*x**2+a)**5,x)","\begin{cases} - \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{\left(x \right)} & \text{for}\: m = -11 \\- \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{\left(x \right)} + \frac{b^{5} x^{2}}{2} & \text{for}\: m = -9 \\- \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{\left(x \right)} + \frac{5 a b^{4} x^{2}}{2} + \frac{b^{5} x^{4}}{4} & \text{for}\: m = -7 \\- \frac{a^{5}}{4 x^{4}} - \frac{5 a^{4} b}{2 x^{2}} + 10 a^{3} b^{2} \log{\left(x \right)} + 5 a^{2} b^{3} x^{2} + \frac{5 a b^{4} x^{4}}{4} + \frac{b^{5} x^{6}}{6} & \text{for}\: m = -5 \\- \frac{a^{5}}{2 x^{2}} + 5 a^{4} b \log{\left(x \right)} + 5 a^{3} b^{2} x^{2} + \frac{5 a^{2} b^{3} x^{4}}{2} + \frac{5 a b^{4} x^{6}}{6} + \frac{b^{5} x^{8}}{8} & \text{for}\: m = -3 \\a^{5} \log{\left(x \right)} + \frac{5 a^{4} b x^{2}}{2} + \frac{5 a^{3} b^{2} x^{4}}{2} + \frac{5 a^{2} b^{3} x^{6}}{3} + \frac{5 a b^{4} x^{8}}{8} + \frac{b^{5} x^{10}}{10} & \text{for}\: m = -1 \\\frac{a^{5} m^{5} x x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{35 a^{5} m^{4} x x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{470 a^{5} m^{3} x x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{3010 a^{5} m^{2} x x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{9129 a^{5} m x x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{10395 a^{5} x x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{5 a^{4} b m^{5} x^{3} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{165 a^{4} b m^{4} x^{3} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{2030 a^{4} b m^{3} x^{3} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{11310 a^{4} b m^{2} x^{3} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{26765 a^{4} b m x^{3} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{17325 a^{4} b x^{3} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{10 a^{3} b^{2} m^{5} x^{5} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{310 a^{3} b^{2} m^{4} x^{5} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{3500 a^{3} b^{2} m^{3} x^{5} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{17300 a^{3} b^{2} m^{2} x^{5} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{34890 a^{3} b^{2} m x^{5} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{20790 a^{3} b^{2} x^{5} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{10 a^{2} b^{3} m^{5} x^{7} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{290 a^{2} b^{3} m^{4} x^{7} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{3020 a^{2} b^{3} m^{3} x^{7} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{13660 a^{2} b^{3} m^{2} x^{7} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{25770 a^{2} b^{3} m x^{7} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{14850 a^{2} b^{3} x^{7} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{5 a b^{4} m^{5} x^{9} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{135 a b^{4} m^{4} x^{9} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{1310 a b^{4} m^{3} x^{9} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{5610 a b^{4} m^{2} x^{9} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{10205 a b^{4} m x^{9} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{5775 a b^{4} x^{9} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{b^{5} m^{5} x^{11} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{25 b^{5} m^{4} x^{11} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{230 b^{5} m^{3} x^{11} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{950 b^{5} m^{2} x^{11} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{1689 b^{5} m x^{11} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{945 b^{5} x^{11} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**5/(10*x**10) - 5*a**4*b/(8*x**8) - 5*a**3*b**2/(3*x**6) - 5*a**2*b**3/(2*x**4) - 5*a*b**4/(2*x**2) + b**5*log(x), Eq(m, -11)), (-a**5/(8*x**8) - 5*a**4*b/(6*x**6) - 5*a**3*b**2/(2*x**4) - 5*a**2*b**3/x**2 + 5*a*b**4*log(x) + b**5*x**2/2, Eq(m, -9)), (-a**5/(6*x**6) - 5*a**4*b/(4*x**4) - 5*a**3*b**2/x**2 + 10*a**2*b**3*log(x) + 5*a*b**4*x**2/2 + b**5*x**4/4, Eq(m, -7)), (-a**5/(4*x**4) - 5*a**4*b/(2*x**2) + 10*a**3*b**2*log(x) + 5*a**2*b**3*x**2 + 5*a*b**4*x**4/4 + b**5*x**6/6, Eq(m, -5)), (-a**5/(2*x**2) + 5*a**4*b*log(x) + 5*a**3*b**2*x**2 + 5*a**2*b**3*x**4/2 + 5*a*b**4*x**6/6 + b**5*x**8/8, Eq(m, -3)), (a**5*log(x) + 5*a**4*b*x**2/2 + 5*a**3*b**2*x**4/2 + 5*a**2*b**3*x**6/3 + 5*a*b**4*x**8/8 + b**5*x**10/10, Eq(m, -1)), (a**5*m**5*x*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 35*a**5*m**4*x*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 470*a**5*m**3*x*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 3010*a**5*m**2*x*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 9129*a**5*m*x*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 10395*a**5*x*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 5*a**4*b*m**5*x**3*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 165*a**4*b*m**4*x**3*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 2030*a**4*b*m**3*x**3*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 11310*a**4*b*m**2*x**3*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 26765*a**4*b*m*x**3*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 17325*a**4*b*x**3*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 10*a**3*b**2*m**5*x**5*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 310*a**3*b**2*m**4*x**5*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 3500*a**3*b**2*m**3*x**5*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 17300*a**3*b**2*m**2*x**5*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 34890*a**3*b**2*m*x**5*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 20790*a**3*b**2*x**5*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 10*a**2*b**3*m**5*x**7*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 290*a**2*b**3*m**4*x**7*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 3020*a**2*b**3*m**3*x**7*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 13660*a**2*b**3*m**2*x**7*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 25770*a**2*b**3*m*x**7*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 14850*a**2*b**3*x**7*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 5*a*b**4*m**5*x**9*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 135*a*b**4*m**4*x**9*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 1310*a*b**4*m**3*x**9*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 5610*a*b**4*m**2*x**9*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 10205*a*b**4*m*x**9*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 5775*a*b**4*x**9*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + b**5*m**5*x**11*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 25*b**5*m**4*x**11*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 230*b**5*m**3*x**11*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 950*b**5*m**2*x**11*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 1689*b**5*m*x**11*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 945*b**5*x**11*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395), True))","A",0
340,1,1221,0,2.847033," ","integrate(x**m*(b*x**2+a)**4,x)","\begin{cases} - \frac{a^{4}}{8 x^{8}} - \frac{2 a^{3} b}{3 x^{6}} - \frac{3 a^{2} b^{2}}{2 x^{4}} - \frac{2 a b^{3}}{x^{2}} + b^{4} \log{\left(x \right)} & \text{for}\: m = -9 \\- \frac{a^{4}}{6 x^{6}} - \frac{a^{3} b}{x^{4}} - \frac{3 a^{2} b^{2}}{x^{2}} + 4 a b^{3} \log{\left(x \right)} + \frac{b^{4} x^{2}}{2} & \text{for}\: m = -7 \\- \frac{a^{4}}{4 x^{4}} - \frac{2 a^{3} b}{x^{2}} + 6 a^{2} b^{2} \log{\left(x \right)} + 2 a b^{3} x^{2} + \frac{b^{4} x^{4}}{4} & \text{for}\: m = -5 \\- \frac{a^{4}}{2 x^{2}} + 4 a^{3} b \log{\left(x \right)} + 3 a^{2} b^{2} x^{2} + a b^{3} x^{4} + \frac{b^{4} x^{6}}{6} & \text{for}\: m = -3 \\a^{4} \log{\left(x \right)} + 2 a^{3} b x^{2} + \frac{3 a^{2} b^{2} x^{4}}{2} + \frac{2 a b^{3} x^{6}}{3} + \frac{b^{4} x^{8}}{8} & \text{for}\: m = -1 \\\frac{a^{4} m^{4} x x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{24 a^{4} m^{3} x x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{206 a^{4} m^{2} x x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{744 a^{4} m x x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{945 a^{4} x x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{4 a^{3} b m^{4} x^{3} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{88 a^{3} b m^{3} x^{3} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{656 a^{3} b m^{2} x^{3} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{1832 a^{3} b m x^{3} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{1260 a^{3} b x^{3} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{6 a^{2} b^{2} m^{4} x^{5} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{120 a^{2} b^{2} m^{3} x^{5} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{780 a^{2} b^{2} m^{2} x^{5} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{1800 a^{2} b^{2} m x^{5} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{1134 a^{2} b^{2} x^{5} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{4 a b^{3} m^{4} x^{7} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{72 a b^{3} m^{3} x^{7} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{416 a b^{3} m^{2} x^{7} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{888 a b^{3} m x^{7} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{540 a b^{3} x^{7} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{b^{4} m^{4} x^{9} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{16 b^{4} m^{3} x^{9} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{86 b^{4} m^{2} x^{9} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{176 b^{4} m x^{9} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{105 b^{4} x^{9} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**4/(8*x**8) - 2*a**3*b/(3*x**6) - 3*a**2*b**2/(2*x**4) - 2*a*b**3/x**2 + b**4*log(x), Eq(m, -9)), (-a**4/(6*x**6) - a**3*b/x**4 - 3*a**2*b**2/x**2 + 4*a*b**3*log(x) + b**4*x**2/2, Eq(m, -7)), (-a**4/(4*x**4) - 2*a**3*b/x**2 + 6*a**2*b**2*log(x) + 2*a*b**3*x**2 + b**4*x**4/4, Eq(m, -5)), (-a**4/(2*x**2) + 4*a**3*b*log(x) + 3*a**2*b**2*x**2 + a*b**3*x**4 + b**4*x**6/6, Eq(m, -3)), (a**4*log(x) + 2*a**3*b*x**2 + 3*a**2*b**2*x**4/2 + 2*a*b**3*x**6/3 + b**4*x**8/8, Eq(m, -1)), (a**4*m**4*x*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 24*a**4*m**3*x*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 206*a**4*m**2*x*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 744*a**4*m*x*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 945*a**4*x*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 4*a**3*b*m**4*x**3*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 88*a**3*b*m**3*x**3*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 656*a**3*b*m**2*x**3*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 1832*a**3*b*m*x**3*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 1260*a**3*b*x**3*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 6*a**2*b**2*m**4*x**5*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 120*a**2*b**2*m**3*x**5*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 780*a**2*b**2*m**2*x**5*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 1800*a**2*b**2*m*x**5*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 1134*a**2*b**2*x**5*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 4*a*b**3*m**4*x**7*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 72*a*b**3*m**3*x**7*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 416*a*b**3*m**2*x**7*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 888*a*b**3*m*x**7*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 540*a*b**3*x**7*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + b**4*m**4*x**9*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 16*b**4*m**3*x**9*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 86*b**4*m**2*x**9*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 176*b**4*m*x**9*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 105*b**4*x**9*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945), True))","A",0
341,1,683,0,1.664893," ","integrate(x**m*(b*x**2+a)**3,x)","\begin{cases} - \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{\left(x \right)} & \text{for}\: m = -7 \\- \frac{a^{3}}{4 x^{4}} - \frac{3 a^{2} b}{2 x^{2}} + 3 a b^{2} \log{\left(x \right)} + \frac{b^{3} x^{2}}{2} & \text{for}\: m = -5 \\- \frac{a^{3}}{2 x^{2}} + 3 a^{2} b \log{\left(x \right)} + \frac{3 a b^{2} x^{2}}{2} + \frac{b^{3} x^{4}}{4} & \text{for}\: m = -3 \\a^{3} \log{\left(x \right)} + \frac{3 a^{2} b x^{2}}{2} + \frac{3 a b^{2} x^{4}}{4} + \frac{b^{3} x^{6}}{6} & \text{for}\: m = -1 \\\frac{a^{3} m^{3} x x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{15 a^{3} m^{2} x x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{71 a^{3} m x x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{105 a^{3} x x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{3 a^{2} b m^{3} x^{3} x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{39 a^{2} b m^{2} x^{3} x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{141 a^{2} b m x^{3} x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{105 a^{2} b x^{3} x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{3 a b^{2} m^{3} x^{5} x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{33 a b^{2} m^{2} x^{5} x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{93 a b^{2} m x^{5} x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{63 a b^{2} x^{5} x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{b^{3} m^{3} x^{7} x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{9 b^{3} m^{2} x^{7} x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{23 b^{3} m x^{7} x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{15 b^{3} x^{7} x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**3/(6*x**6) - 3*a**2*b/(4*x**4) - 3*a*b**2/(2*x**2) + b**3*log(x), Eq(m, -7)), (-a**3/(4*x**4) - 3*a**2*b/(2*x**2) + 3*a*b**2*log(x) + b**3*x**2/2, Eq(m, -5)), (-a**3/(2*x**2) + 3*a**2*b*log(x) + 3*a*b**2*x**2/2 + b**3*x**4/4, Eq(m, -3)), (a**3*log(x) + 3*a**2*b*x**2/2 + 3*a*b**2*x**4/4 + b**3*x**6/6, Eq(m, -1)), (a**3*m**3*x*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 15*a**3*m**2*x*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 71*a**3*m*x*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 105*a**3*x*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 3*a**2*b*m**3*x**3*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 39*a**2*b*m**2*x**3*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 141*a**2*b*m*x**3*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 105*a**2*b*x**3*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 3*a*b**2*m**3*x**5*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 33*a*b**2*m**2*x**5*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 93*a*b**2*m*x**5*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 63*a*b**2*x**5*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + b**3*m**3*x**7*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 9*b**3*m**2*x**7*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 23*b**3*m*x**7*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 15*b**3*x**7*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105), True))","A",0
342,1,306,0,0.942991," ","integrate(x**m*(b*x**2+a)**2,x)","\begin{cases} - \frac{a^{2}}{4 x^{4}} - \frac{a b}{x^{2}} + b^{2} \log{\left(x \right)} & \text{for}\: m = -5 \\- \frac{a^{2}}{2 x^{2}} + 2 a b \log{\left(x \right)} + \frac{b^{2} x^{2}}{2} & \text{for}\: m = -3 \\a^{2} \log{\left(x \right)} + a b x^{2} + \frac{b^{2} x^{4}}{4} & \text{for}\: m = -1 \\\frac{a^{2} m^{2} x x^{m}}{m^{3} + 9 m^{2} + 23 m + 15} + \frac{8 a^{2} m x x^{m}}{m^{3} + 9 m^{2} + 23 m + 15} + \frac{15 a^{2} x x^{m}}{m^{3} + 9 m^{2} + 23 m + 15} + \frac{2 a b m^{2} x^{3} x^{m}}{m^{3} + 9 m^{2} + 23 m + 15} + \frac{12 a b m x^{3} x^{m}}{m^{3} + 9 m^{2} + 23 m + 15} + \frac{10 a b x^{3} x^{m}}{m^{3} + 9 m^{2} + 23 m + 15} + \frac{b^{2} m^{2} x^{5} x^{m}}{m^{3} + 9 m^{2} + 23 m + 15} + \frac{4 b^{2} m x^{5} x^{m}}{m^{3} + 9 m^{2} + 23 m + 15} + \frac{3 b^{2} x^{5} x^{m}}{m^{3} + 9 m^{2} + 23 m + 15} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2/(4*x**4) - a*b/x**2 + b**2*log(x), Eq(m, -5)), (-a**2/(2*x**2) + 2*a*b*log(x) + b**2*x**2/2, Eq(m, -3)), (a**2*log(x) + a*b*x**2 + b**2*x**4/4, Eq(m, -1)), (a**2*m**2*x*x**m/(m**3 + 9*m**2 + 23*m + 15) + 8*a**2*m*x*x**m/(m**3 + 9*m**2 + 23*m + 15) + 15*a**2*x*x**m/(m**3 + 9*m**2 + 23*m + 15) + 2*a*b*m**2*x**3*x**m/(m**3 + 9*m**2 + 23*m + 15) + 12*a*b*m*x**3*x**m/(m**3 + 9*m**2 + 23*m + 15) + 10*a*b*x**3*x**m/(m**3 + 9*m**2 + 23*m + 15) + b**2*m**2*x**5*x**m/(m**3 + 9*m**2 + 23*m + 15) + 4*b**2*m*x**5*x**m/(m**3 + 9*m**2 + 23*m + 15) + 3*b**2*x**5*x**m/(m**3 + 9*m**2 + 23*m + 15), True))","A",0
343,1,94,0,0.412194," ","integrate(x**m*(b*x**2+a),x)","\begin{cases} - \frac{a}{2 x^{2}} + b \log{\left(x \right)} & \text{for}\: m = -3 \\a \log{\left(x \right)} + \frac{b x^{2}}{2} & \text{for}\: m = -1 \\\frac{a m x x^{m}}{m^{2} + 4 m + 3} + \frac{3 a x x^{m}}{m^{2} + 4 m + 3} + \frac{b m x^{3} x^{m}}{m^{2} + 4 m + 3} + \frac{b x^{3} x^{m}}{m^{2} + 4 m + 3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a/(2*x**2) + b*log(x), Eq(m, -3)), (a*log(x) + b*x**2/2, Eq(m, -1)), (a*m*x*x**m/(m**2 + 4*m + 3) + 3*a*x*x**m/(m**2 + 4*m + 3) + b*m*x**3*x**m/(m**2 + 4*m + 3) + b*x**3*x**m/(m**2 + 4*m + 3), True))","A",0
344,1,88,0,1.246544," ","integrate(x**m/(b*x**2+a),x)","\frac{m x x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{4 a \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{x x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{4 a \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}"," ",0,"m*x*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(4*a*gamma(m/2 + 3/2)) + x*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(4*a*gamma(m/2 + 3/2))","C",0
345,1,374,0,6.223403," ","integrate(x**m/(b*x**2+a)**2,x)","- \frac{a m^{2} x x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{8 a^{3} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 8 a^{2} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{2 a m x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{8 a^{3} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 8 a^{2} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{a x x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{8 a^{3} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 8 a^{2} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{2 a x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{8 a^{3} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 8 a^{2} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} - \frac{b m^{2} x^{3} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{8 a^{3} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 8 a^{2} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{b x^{3} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{8 a^{3} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 8 a^{2} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}"," ",0,"-a*m**2*x*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(8*a**3*gamma(m/2 + 3/2) + 8*a**2*b*x**2*gamma(m/2 + 3/2)) + 2*a*m*x*x**m*gamma(m/2 + 1/2)/(8*a**3*gamma(m/2 + 3/2) + 8*a**2*b*x**2*gamma(m/2 + 3/2)) + a*x*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(8*a**3*gamma(m/2 + 3/2) + 8*a**2*b*x**2*gamma(m/2 + 3/2)) + 2*a*x*x**m*gamma(m/2 + 1/2)/(8*a**3*gamma(m/2 + 3/2) + 8*a**2*b*x**2*gamma(m/2 + 3/2)) - b*m**2*x**3*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(8*a**3*gamma(m/2 + 3/2) + 8*a**2*b*x**2*gamma(m/2 + 3/2)) + b*x**3*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(8*a**3*gamma(m/2 + 3/2) + 8*a**2*b*x**2*gamma(m/2 + 3/2))","C",0
346,1,1556,0,20.437136," ","integrate(x**m/(b*x**2+a)**3,x)","\frac{a^{2} m^{3} x x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} - \frac{3 a^{2} m^{2} x x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} - \frac{2 a^{2} m^{2} x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} - \frac{a^{2} m x x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{8 a^{2} m x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{3 a^{2} x x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{10 a^{2} x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{2 a b m^{3} x^{3} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} - \frac{6 a b m^{2} x^{3} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} - \frac{2 a b m^{2} x^{3} x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} - \frac{2 a b m x^{3} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{4 a b m x^{3} x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{6 a b x^{3} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{6 a b x^{3} x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{b^{2} m^{3} x^{5} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} - \frac{3 b^{2} m^{2} x^{5} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} - \frac{b^{2} m x^{5} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{3 b^{2} x^{5} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}"," ",0,"a**2*m**3*x*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*b*x**2*gamma(m/2 + 3/2) + 32*a**3*b**2*x**4*gamma(m/2 + 3/2)) - 3*a**2*m**2*x*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*b*x**2*gamma(m/2 + 3/2) + 32*a**3*b**2*x**4*gamma(m/2 + 3/2)) - 2*a**2*m**2*x*x**m*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*b*x**2*gamma(m/2 + 3/2) + 32*a**3*b**2*x**4*gamma(m/2 + 3/2)) - a**2*m*x*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*b*x**2*gamma(m/2 + 3/2) + 32*a**3*b**2*x**4*gamma(m/2 + 3/2)) + 8*a**2*m*x*x**m*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*b*x**2*gamma(m/2 + 3/2) + 32*a**3*b**2*x**4*gamma(m/2 + 3/2)) + 3*a**2*x*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*b*x**2*gamma(m/2 + 3/2) + 32*a**3*b**2*x**4*gamma(m/2 + 3/2)) + 10*a**2*x*x**m*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*b*x**2*gamma(m/2 + 3/2) + 32*a**3*b**2*x**4*gamma(m/2 + 3/2)) + 2*a*b*m**3*x**3*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*b*x**2*gamma(m/2 + 3/2) + 32*a**3*b**2*x**4*gamma(m/2 + 3/2)) - 6*a*b*m**2*x**3*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*b*x**2*gamma(m/2 + 3/2) + 32*a**3*b**2*x**4*gamma(m/2 + 3/2)) - 2*a*b*m**2*x**3*x**m*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*b*x**2*gamma(m/2 + 3/2) + 32*a**3*b**2*x**4*gamma(m/2 + 3/2)) - 2*a*b*m*x**3*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*b*x**2*gamma(m/2 + 3/2) + 32*a**3*b**2*x**4*gamma(m/2 + 3/2)) + 4*a*b*m*x**3*x**m*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*b*x**2*gamma(m/2 + 3/2) + 32*a**3*b**2*x**4*gamma(m/2 + 3/2)) + 6*a*b*x**3*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*b*x**2*gamma(m/2 + 3/2) + 32*a**3*b**2*x**4*gamma(m/2 + 3/2)) + 6*a*b*x**3*x**m*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*b*x**2*gamma(m/2 + 3/2) + 32*a**3*b**2*x**4*gamma(m/2 + 3/2)) + b**2*m**3*x**5*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*b*x**2*gamma(m/2 + 3/2) + 32*a**3*b**2*x**4*gamma(m/2 + 3/2)) - 3*b**2*m**2*x**5*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*b*x**2*gamma(m/2 + 3/2) + 32*a**3*b**2*x**4*gamma(m/2 + 3/2)) - b**2*m*x**5*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*b*x**2*gamma(m/2 + 3/2) + 32*a**3*b**2*x**4*gamma(m/2 + 3/2)) + 3*b**2*x**5*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*b*x**2*gamma(m/2 + 3/2) + 32*a**3*b**2*x**4*gamma(m/2 + 3/2))","C",0
347,1,92,0,2.949282," ","integrate((c*x)**(1+m)/(b*x**2+a),x)","\frac{c c^{m} m x^{2} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + 1\right) \Gamma\left(\frac{m}{2} + 1\right)}{4 a \Gamma\left(\frac{m}{2} + 2\right)} + \frac{c c^{m} x^{2} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + 1\right) \Gamma\left(\frac{m}{2} + 1\right)}{2 a \Gamma\left(\frac{m}{2} + 2\right)}"," ",0,"c*c**m*m*x**2*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1)*gamma(m/2 + 1)/(4*a*gamma(m/2 + 2)) + c*c**m*x**2*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1)*gamma(m/2 + 1)/(2*a*gamma(m/2 + 2))","C",0
348,1,95,0,1.249690," ","integrate((c*x)**m/(b*x**2+a),x)","\frac{c^{m} m x x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{4 a \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{c^{m} x x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{4 a \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}"," ",0,"c**m*m*x*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(4*a*gamma(m/2 + 3/2)) + c**m*x*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(4*a*gamma(m/2 + 3/2))","C",0
349,1,39,0,7.150811," ","integrate((c*x)**(-1+m)/(b*x**2+a),x)","\frac{c^{m} m x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2}\right) \Gamma\left(\frac{m}{2}\right)}{4 a c \Gamma\left(\frac{m}{2} + 1\right)}"," ",0,"c**m*m*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2)*gamma(m/2)/(4*a*c*gamma(m/2 + 1))","C",0
350,1,102,0,11.565367," ","integrate((c*x)**(-2+m)/(b*x**2+a),x)","\frac{c^{m} m x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} - \frac{1}{2}\right) \Gamma\left(\frac{m}{2} - \frac{1}{2}\right)}{4 a c^{2} x \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)} - \frac{c^{m} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} - \frac{1}{2}\right) \Gamma\left(\frac{m}{2} - \frac{1}{2}\right)}{4 a c^{2} x \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}"," ",0,"c**m*m*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 - 1/2)*gamma(m/2 - 1/2)/(4*a*c**2*x*gamma(m/2 + 1/2)) - c**m*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 - 1/2)*gamma(m/2 - 1/2)/(4*a*c**2*x*gamma(m/2 + 1/2))","C",0
351,1,92,0,21.423646," ","integrate((c*x)**(-3+m)/(b*x**2+a),x)","\frac{c^{m} m x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} - 1\right) \Gamma\left(\frac{m}{2} - 1\right)}{4 a c^{3} x^{2} \Gamma\left(\frac{m}{2}\right)} - \frac{c^{m} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} - 1\right) \Gamma\left(\frac{m}{2} - 1\right)}{2 a c^{3} x^{2} \Gamma\left(\frac{m}{2}\right)}"," ",0,"c**m*m*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 - 1)*gamma(m/2 - 1)/(4*a*c**3*x**2*gamma(m/2)) - c**m*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 - 1)*gamma(m/2 - 1)/(2*a*c**3*x**2*gamma(m/2))","C",0
352,1,343,0,6.163106," ","integrate(x**m/(1+a*x**2/b)**2,x)","- \frac{a m^{2} x^{3} x^{m} \Phi\left(\frac{a x^{2} e^{i \pi}}{b}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{8 a x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 8 b \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{a x^{3} x^{m} \Phi\left(\frac{a x^{2} e^{i \pi}}{b}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{8 a x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 8 b \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} - \frac{b m^{2} x x^{m} \Phi\left(\frac{a x^{2} e^{i \pi}}{b}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{8 a x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 8 b \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{2 b m x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{8 a x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 8 b \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{b x x^{m} \Phi\left(\frac{a x^{2} e^{i \pi}}{b}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{8 a x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 8 b \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{2 b x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{8 a x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 8 b \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}"," ",0,"-a*m**2*x**3*x**m*lerchphi(a*x**2*exp_polar(I*pi)/b, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(8*a*x**2*gamma(m/2 + 3/2) + 8*b*gamma(m/2 + 3/2)) + a*x**3*x**m*lerchphi(a*x**2*exp_polar(I*pi)/b, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(8*a*x**2*gamma(m/2 + 3/2) + 8*b*gamma(m/2 + 3/2)) - b*m**2*x*x**m*lerchphi(a*x**2*exp_polar(I*pi)/b, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(8*a*x**2*gamma(m/2 + 3/2) + 8*b*gamma(m/2 + 3/2)) + 2*b*m*x*x**m*gamma(m/2 + 1/2)/(8*a*x**2*gamma(m/2 + 3/2) + 8*b*gamma(m/2 + 3/2)) + b*x*x**m*lerchphi(a*x**2*exp_polar(I*pi)/b, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(8*a*x**2*gamma(m/2 + 3/2) + 8*b*gamma(m/2 + 3/2)) + 2*b*x*x**m*gamma(m/2 + 1/2)/(8*a*x**2*gamma(m/2 + 3/2) + 8*b*gamma(m/2 + 3/2))","C",0
353,1,110,0,1.417812," ","integrate(x**7*(b*x**2+a)**(1/2),x)","\begin{cases} - \frac{16 a^{4} \sqrt{a + b x^{2}}}{315 b^{4}} + \frac{8 a^{3} x^{2} \sqrt{a + b x^{2}}}{315 b^{3}} - \frac{2 a^{2} x^{4} \sqrt{a + b x^{2}}}{105 b^{2}} + \frac{a x^{6} \sqrt{a + b x^{2}}}{63 b} + \frac{x^{8} \sqrt{a + b x^{2}}}{9} & \text{for}\: b \neq 0 \\\frac{\sqrt{a} x^{8}}{8} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-16*a**4*sqrt(a + b*x**2)/(315*b**4) + 8*a**3*x**2*sqrt(a + b*x**2)/(315*b**3) - 2*a**2*x**4*sqrt(a + b*x**2)/(105*b**2) + a*x**6*sqrt(a + b*x**2)/(63*b) + x**8*sqrt(a + b*x**2)/9, Ne(b, 0)), (sqrt(a)*x**8/8, True))","A",0
354,1,87,0,0.703630," ","integrate(x**5*(b*x**2+a)**(1/2),x)","\begin{cases} \frac{8 a^{3} \sqrt{a + b x^{2}}}{105 b^{3}} - \frac{4 a^{2} x^{2} \sqrt{a + b x^{2}}}{105 b^{2}} + \frac{a x^{4} \sqrt{a + b x^{2}}}{35 b} + \frac{x^{6} \sqrt{a + b x^{2}}}{7} & \text{for}\: b \neq 0 \\\frac{\sqrt{a} x^{6}}{6} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*a**3*sqrt(a + b*x**2)/(105*b**3) - 4*a**2*x**2*sqrt(a + b*x**2)/(105*b**2) + a*x**4*sqrt(a + b*x**2)/(35*b) + x**6*sqrt(a + b*x**2)/7, Ne(b, 0)), (sqrt(a)*x**6/6, True))","A",0
355,1,63,0,0.318434," ","integrate(x**3*(b*x**2+a)**(1/2),x)","\begin{cases} - \frac{2 a^{2} \sqrt{a + b x^{2}}}{15 b^{2}} + \frac{a x^{2} \sqrt{a + b x^{2}}}{15 b} + \frac{x^{4} \sqrt{a + b x^{2}}}{5} & \text{for}\: b \neq 0 \\\frac{\sqrt{a} x^{4}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*a**2*sqrt(a + b*x**2)/(15*b**2) + a*x**2*sqrt(a + b*x**2)/(15*b) + x**4*sqrt(a + b*x**2)/5, Ne(b, 0)), (sqrt(a)*x**4/4, True))","A",0
356,1,39,0,0.168246," ","integrate(x*(b*x**2+a)**(1/2),x)","\begin{cases} \frac{a \sqrt{a + b x^{2}}}{3 b} + \frac{x^{2} \sqrt{a + b x^{2}}}{3} & \text{for}\: b \neq 0 \\\frac{\sqrt{a} x^{2}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*sqrt(a + b*x**2)/(3*b) + x**2*sqrt(a + b*x**2)/3, Ne(b, 0)), (sqrt(a)*x**2/2, True))","A",0
357,1,56,0,1.409217," ","integrate((b*x**2+a)**(1/2)/x,x)","- \sqrt{a} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)} + \frac{a}{\sqrt{b} x \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{\sqrt{b} x}{\sqrt{\frac{a}{b x^{2}} + 1}}"," ",0,"-sqrt(a)*asinh(sqrt(a)/(sqrt(b)*x)) + a/(sqrt(b)*x*sqrt(a/(b*x**2) + 1)) + sqrt(b)*x/sqrt(a/(b*x**2) + 1)","A",0
358,1,42,0,1.926125," ","integrate((b*x**2+a)**(1/2)/x**3,x)","- \frac{\sqrt{b} \sqrt{\frac{a}{b x^{2}} + 1}}{2 x} - \frac{b \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)}}{2 \sqrt{a}}"," ",0,"-sqrt(b)*sqrt(a/(b*x**2) + 1)/(2*x) - b*asinh(sqrt(a)/(sqrt(b)*x))/(2*sqrt(a))","A",0
359,1,92,0,3.734824," ","integrate((b*x**2+a)**(1/2)/x**5,x)","- \frac{a}{4 \sqrt{b} x^{5} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{3 \sqrt{b}}{8 x^{3} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{b^{\frac{3}{2}}}{8 a x \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{b^{2} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)}}{8 a^{\frac{3}{2}}}"," ",0,"-a/(4*sqrt(b)*x**5*sqrt(a/(b*x**2) + 1)) - 3*sqrt(b)/(8*x**3*sqrt(a/(b*x**2) + 1)) - b**(3/2)/(8*a*x*sqrt(a/(b*x**2) + 1)) + b**2*asinh(sqrt(a)/(sqrt(b)*x))/(8*a**(3/2))","A",0
360,1,117,0,5.907211," ","integrate((b*x**2+a)**(1/2)/x**7,x)","- \frac{a}{6 \sqrt{b} x^{7} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{5 \sqrt{b}}{24 x^{5} \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{b^{\frac{3}{2}}}{48 a x^{3} \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{b^{\frac{5}{2}}}{16 a^{2} x \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{b^{3} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)}}{16 a^{\frac{5}{2}}}"," ",0,"-a/(6*sqrt(b)*x**7*sqrt(a/(b*x**2) + 1)) - 5*sqrt(b)/(24*x**5*sqrt(a/(b*x**2) + 1)) + b**(3/2)/(48*a*x**3*sqrt(a/(b*x**2) + 1)) + b**(5/2)/(16*a**2*x*sqrt(a/(b*x**2) + 1)) - b**3*asinh(sqrt(a)/(sqrt(b)*x))/(16*a**(5/2))","A",0
361,1,117,0,5.772876," ","integrate(x**4*(b*x**2+a)**(1/2),x)","- \frac{a^{\frac{5}{2}} x}{16 b^{2} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{a^{\frac{3}{2}} x^{3}}{48 b \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{5 \sqrt{a} x^{5}}{24 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{a^{3} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{16 b^{\frac{5}{2}}} + \frac{b x^{7}}{6 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"-a**(5/2)*x/(16*b**2*sqrt(1 + b*x**2/a)) - a**(3/2)*x**3/(48*b*sqrt(1 + b*x**2/a)) + 5*sqrt(a)*x**5/(24*sqrt(1 + b*x**2/a)) + a**3*asinh(sqrt(b)*x/sqrt(a))/(16*b**(5/2)) + b*x**7/(6*sqrt(a)*sqrt(1 + b*x**2/a))","A",0
362,1,92,0,3.526839," ","integrate(x**2*(b*x**2+a)**(1/2),x)","\frac{a^{\frac{3}{2}} x}{8 b \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{3 \sqrt{a} x^{3}}{8 \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{a^{2} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{8 b^{\frac{3}{2}}} + \frac{b x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"a**(3/2)*x/(8*b*sqrt(1 + b*x**2/a)) + 3*sqrt(a)*x**3/(8*sqrt(1 + b*x**2/a)) - a**2*asinh(sqrt(b)*x/sqrt(a))/(8*b**(3/2)) + b*x**5/(4*sqrt(a)*sqrt(1 + b*x**2/a))","A",0
363,1,41,0,1.830578," ","integrate((b*x**2+a)**(1/2),x)","\frac{\sqrt{a} x \sqrt{1 + \frac{b x^{2}}{a}}}{2} + \frac{a \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{2 \sqrt{b}}"," ",0,"sqrt(a)*x*sqrt(1 + b*x**2/a)/2 + a*asinh(sqrt(b)*x/sqrt(a))/(2*sqrt(b))","A",0
364,1,56,0,1.417168," ","integrate((b*x**2+a)**(1/2)/x**2,x)","- \frac{\sqrt{a}}{x \sqrt{1 + \frac{b x^{2}}{a}}} + \sqrt{b} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)} - \frac{b x}{\sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"-sqrt(a)/(x*sqrt(1 + b*x**2/a)) + sqrt(b)*asinh(sqrt(b)*x/sqrt(a)) - b*x/(sqrt(a)*sqrt(1 + b*x**2/a))","A",0
365,1,42,0,0.706142," ","integrate((b*x**2+a)**(1/2)/x**4,x)","- \frac{\sqrt{b} \sqrt{\frac{a}{b x^{2}} + 1}}{3 x^{2}} - \frac{b^{\frac{3}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{3 a}"," ",0,"-sqrt(b)*sqrt(a/(b*x**2) + 1)/(3*x**2) - b**(3/2)*sqrt(a/(b*x**2) + 1)/(3*a)","B",0
366,1,68,0,0.911665," ","integrate((b*x**2+a)**(1/2)/x**6,x)","- \frac{\sqrt{b} \sqrt{\frac{a}{b x^{2}} + 1}}{5 x^{4}} - \frac{b^{\frac{3}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{15 a x^{2}} + \frac{2 b^{\frac{5}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{15 a^{2}}"," ",0,"-sqrt(b)*sqrt(a/(b*x**2) + 1)/(5*x**4) - b**(3/2)*sqrt(a/(b*x**2) + 1)/(15*a*x**2) + 2*b**(5/2)*sqrt(a/(b*x**2) + 1)/(15*a**2)","A",0
367,1,359,0,1.297998," ","integrate((b*x**2+a)**(1/2)/x**8,x)","- \frac{15 a^{5} b^{\frac{9}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}} - \frac{33 a^{4} b^{\frac{11}{2}} x^{2} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}} - \frac{17 a^{3} b^{\frac{13}{2}} x^{4} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}} - \frac{3 a^{2} b^{\frac{15}{2}} x^{6} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}} - \frac{12 a b^{\frac{17}{2}} x^{8} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}} - \frac{8 b^{\frac{19}{2}} x^{10} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}}"," ",0,"-15*a**5*b**(9/2)*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10) - 33*a**4*b**(11/2)*x**2*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10) - 17*a**3*b**(13/2)*x**4*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10) - 3*a**2*b**(15/2)*x**6*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10) - 12*a*b**(17/2)*x**8*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10) - 8*b**(19/2)*x**10*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10)","B",0
368,1,575,0,1.742229," ","integrate((b*x**2+a)**(1/2)/x**10,x)","- \frac{35 a^{7} b^{\frac{19}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{315 a^{7} b^{9} x^{8} + 945 a^{6} b^{10} x^{10} + 945 a^{5} b^{11} x^{12} + 315 a^{4} b^{12} x^{14}} - \frac{110 a^{6} b^{\frac{21}{2}} x^{2} \sqrt{\frac{a}{b x^{2}} + 1}}{315 a^{7} b^{9} x^{8} + 945 a^{6} b^{10} x^{10} + 945 a^{5} b^{11} x^{12} + 315 a^{4} b^{12} x^{14}} - \frac{114 a^{5} b^{\frac{23}{2}} x^{4} \sqrt{\frac{a}{b x^{2}} + 1}}{315 a^{7} b^{9} x^{8} + 945 a^{6} b^{10} x^{10} + 945 a^{5} b^{11} x^{12} + 315 a^{4} b^{12} x^{14}} - \frac{40 a^{4} b^{\frac{25}{2}} x^{6} \sqrt{\frac{a}{b x^{2}} + 1}}{315 a^{7} b^{9} x^{8} + 945 a^{6} b^{10} x^{10} + 945 a^{5} b^{11} x^{12} + 315 a^{4} b^{12} x^{14}} + \frac{5 a^{3} b^{\frac{27}{2}} x^{8} \sqrt{\frac{a}{b x^{2}} + 1}}{315 a^{7} b^{9} x^{8} + 945 a^{6} b^{10} x^{10} + 945 a^{5} b^{11} x^{12} + 315 a^{4} b^{12} x^{14}} + \frac{30 a^{2} b^{\frac{29}{2}} x^{10} \sqrt{\frac{a}{b x^{2}} + 1}}{315 a^{7} b^{9} x^{8} + 945 a^{6} b^{10} x^{10} + 945 a^{5} b^{11} x^{12} + 315 a^{4} b^{12} x^{14}} + \frac{40 a b^{\frac{31}{2}} x^{12} \sqrt{\frac{a}{b x^{2}} + 1}}{315 a^{7} b^{9} x^{8} + 945 a^{6} b^{10} x^{10} + 945 a^{5} b^{11} x^{12} + 315 a^{4} b^{12} x^{14}} + \frac{16 b^{\frac{33}{2}} x^{14} \sqrt{\frac{a}{b x^{2}} + 1}}{315 a^{7} b^{9} x^{8} + 945 a^{6} b^{10} x^{10} + 945 a^{5} b^{11} x^{12} + 315 a^{4} b^{12} x^{14}}"," ",0,"-35*a**7*b**(19/2)*sqrt(a/(b*x**2) + 1)/(315*a**7*b**9*x**8 + 945*a**6*b**10*x**10 + 945*a**5*b**11*x**12 + 315*a**4*b**12*x**14) - 110*a**6*b**(21/2)*x**2*sqrt(a/(b*x**2) + 1)/(315*a**7*b**9*x**8 + 945*a**6*b**10*x**10 + 945*a**5*b**11*x**12 + 315*a**4*b**12*x**14) - 114*a**5*b**(23/2)*x**4*sqrt(a/(b*x**2) + 1)/(315*a**7*b**9*x**8 + 945*a**6*b**10*x**10 + 945*a**5*b**11*x**12 + 315*a**4*b**12*x**14) - 40*a**4*b**(25/2)*x**6*sqrt(a/(b*x**2) + 1)/(315*a**7*b**9*x**8 + 945*a**6*b**10*x**10 + 945*a**5*b**11*x**12 + 315*a**4*b**12*x**14) + 5*a**3*b**(27/2)*x**8*sqrt(a/(b*x**2) + 1)/(315*a**7*b**9*x**8 + 945*a**6*b**10*x**10 + 945*a**5*b**11*x**12 + 315*a**4*b**12*x**14) + 30*a**2*b**(29/2)*x**10*sqrt(a/(b*x**2) + 1)/(315*a**7*b**9*x**8 + 945*a**6*b**10*x**10 + 945*a**5*b**11*x**12 + 315*a**4*b**12*x**14) + 40*a*b**(31/2)*x**12*sqrt(a/(b*x**2) + 1)/(315*a**7*b**9*x**8 + 945*a**6*b**10*x**10 + 945*a**5*b**11*x**12 + 315*a**4*b**12*x**14) + 16*b**(33/2)*x**14*sqrt(a/(b*x**2) + 1)/(315*a**7*b**9*x**8 + 945*a**6*b**10*x**10 + 945*a**5*b**11*x**12 + 315*a**4*b**12*x**14)","B",0
369,1,133,0,3.813476," ","integrate(x**7*(b*x**2+a)**(3/2),x)","\begin{cases} - \frac{16 a^{5} \sqrt{a + b x^{2}}}{1155 b^{4}} + \frac{8 a^{4} x^{2} \sqrt{a + b x^{2}}}{1155 b^{3}} - \frac{2 a^{3} x^{4} \sqrt{a + b x^{2}}}{385 b^{2}} + \frac{a^{2} x^{6} \sqrt{a + b x^{2}}}{231 b} + \frac{4 a x^{8} \sqrt{a + b x^{2}}}{33} + \frac{b x^{10} \sqrt{a + b x^{2}}}{11} & \text{for}\: b \neq 0 \\\frac{a^{\frac{3}{2}} x^{8}}{8} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-16*a**5*sqrt(a + b*x**2)/(1155*b**4) + 8*a**4*x**2*sqrt(a + b*x**2)/(1155*b**3) - 2*a**3*x**4*sqrt(a + b*x**2)/(385*b**2) + a**2*x**6*sqrt(a + b*x**2)/(231*b) + 4*a*x**8*sqrt(a + b*x**2)/33 + b*x**10*sqrt(a + b*x**2)/11, Ne(b, 0)), (a**(3/2)*x**8/8, True))","A",0
370,1,109,0,2.239375," ","integrate(x**5*(b*x**2+a)**(3/2),x)","\begin{cases} \frac{8 a^{4} \sqrt{a + b x^{2}}}{315 b^{3}} - \frac{4 a^{3} x^{2} \sqrt{a + b x^{2}}}{315 b^{2}} + \frac{a^{2} x^{4} \sqrt{a + b x^{2}}}{105 b} + \frac{10 a x^{6} \sqrt{a + b x^{2}}}{63} + \frac{b x^{8} \sqrt{a + b x^{2}}}{9} & \text{for}\: b \neq 0 \\\frac{a^{\frac{3}{2}} x^{6}}{6} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*a**4*sqrt(a + b*x**2)/(315*b**3) - 4*a**3*x**2*sqrt(a + b*x**2)/(315*b**2) + a**2*x**4*sqrt(a + b*x**2)/(105*b) + 10*a*x**6*sqrt(a + b*x**2)/63 + b*x**8*sqrt(a + b*x**2)/9, Ne(b, 0)), (a**(3/2)*x**6/6, True))","A",0
371,1,85,0,1.133168," ","integrate(x**3*(b*x**2+a)**(3/2),x)","\begin{cases} - \frac{2 a^{3} \sqrt{a + b x^{2}}}{35 b^{2}} + \frac{a^{2} x^{2} \sqrt{a + b x^{2}}}{35 b} + \frac{8 a x^{4} \sqrt{a + b x^{2}}}{35} + \frac{b x^{6} \sqrt{a + b x^{2}}}{7} & \text{for}\: b \neq 0 \\\frac{a^{\frac{3}{2}} x^{4}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*a**3*sqrt(a + b*x**2)/(35*b**2) + a**2*x**2*sqrt(a + b*x**2)/(35*b) + 8*a*x**4*sqrt(a + b*x**2)/35 + b*x**6*sqrt(a + b*x**2)/7, Ne(b, 0)), (a**(3/2)*x**4/4, True))","A",0
372,1,61,0,0.592480," ","integrate(x*(b*x**2+a)**(3/2),x)","\begin{cases} \frac{a^{2} \sqrt{a + b x^{2}}}{5 b} + \frac{2 a x^{2} \sqrt{a + b x^{2}}}{5} + \frac{b x^{4} \sqrt{a + b x^{2}}}{5} & \text{for}\: b \neq 0 \\\frac{a^{\frac{3}{2}} x^{2}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*sqrt(a + b*x**2)/(5*b) + 2*a*x**2*sqrt(a + b*x**2)/5 + b*x**4*sqrt(a + b*x**2)/5, Ne(b, 0)), (a**(3/2)*x**2/2, True))","A",0
373,1,78,0,1.924109," ","integrate((b*x**2+a)**(3/2)/x,x)","\frac{4 a^{\frac{3}{2}} \sqrt{1 + \frac{b x^{2}}{a}}}{3} + \frac{a^{\frac{3}{2}} \log{\left(\frac{b x^{2}}{a} \right)}}{2} - a^{\frac{3}{2}} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)} + \frac{\sqrt{a} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}}}{3}"," ",0,"4*a**(3/2)*sqrt(1 + b*x**2/a)/3 + a**(3/2)*log(b*x**2/a)/2 - a**(3/2)*log(sqrt(1 + b*x**2/a) + 1) + sqrt(a)*b*x**2*sqrt(1 + b*x**2/a)/3","A",0
374,1,88,0,2.333471," ","integrate((b*x**2+a)**(3/2)/x**3,x)","- \frac{3 \sqrt{a} b \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)}}{2} - \frac{a^{2}}{2 \sqrt{b} x^{3} \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{a \sqrt{b}}{2 x \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{b^{\frac{3}{2}} x}{\sqrt{\frac{a}{b x^{2}} + 1}}"," ",0,"-3*sqrt(a)*b*asinh(sqrt(a)/(sqrt(b)*x))/2 - a**2/(2*sqrt(b)*x**3*sqrt(a/(b*x**2) + 1)) + a*sqrt(b)/(2*x*sqrt(a/(b*x**2) + 1)) + b**(3/2)*x/sqrt(a/(b*x**2) + 1)","A",0
375,1,71,0,2.984386," ","integrate((b*x**2+a)**(3/2)/x**5,x)","- \frac{a \sqrt{b} \sqrt{\frac{a}{b x^{2}} + 1}}{4 x^{3}} - \frac{5 b^{\frac{3}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{8 x} - \frac{3 b^{2} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)}}{8 \sqrt{a}}"," ",0,"-a*sqrt(b)*sqrt(a/(b*x**2) + 1)/(4*x**3) - 5*b**(3/2)*sqrt(a/(b*x**2) + 1)/(8*x) - 3*b**2*asinh(sqrt(a)/(sqrt(b)*x))/(8*sqrt(a))","A",0
376,1,119,0,5.331311," ","integrate((b*x**2+a)**(3/2)/x**7,x)","- \frac{a^{2}}{6 \sqrt{b} x^{7} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{11 a \sqrt{b}}{24 x^{5} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{17 b^{\frac{3}{2}}}{48 x^{3} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{b^{\frac{5}{2}}}{16 a x \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{b^{3} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)}}{16 a^{\frac{3}{2}}}"," ",0,"-a**2/(6*sqrt(b)*x**7*sqrt(a/(b*x**2) + 1)) - 11*a*sqrt(b)/(24*x**5*sqrt(a/(b*x**2) + 1)) - 17*b**(3/2)/(48*x**3*sqrt(a/(b*x**2) + 1)) - b**(5/2)/(16*a*x*sqrt(a/(b*x**2) + 1)) + b**3*asinh(sqrt(a)/(sqrt(b)*x))/(16*a**(3/2))","A",0
377,1,148,0,8.263858," ","integrate((b*x**2+a)**(3/2)/x**9,x)","- \frac{a^{2}}{8 \sqrt{b} x^{9} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{5 a \sqrt{b}}{16 x^{7} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{13 b^{\frac{3}{2}}}{64 x^{5} \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{b^{\frac{5}{2}}}{128 a x^{3} \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{3 b^{\frac{7}{2}}}{128 a^{2} x \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{3 b^{4} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)}}{128 a^{\frac{5}{2}}}"," ",0,"-a**2/(8*sqrt(b)*x**9*sqrt(a/(b*x**2) + 1)) - 5*a*sqrt(b)/(16*x**7*sqrt(a/(b*x**2) + 1)) - 13*b**(3/2)/(64*x**5*sqrt(a/(b*x**2) + 1)) + b**(5/2)/(128*a*x**3*sqrt(a/(b*x**2) + 1)) + 3*b**(7/2)/(128*a**2*x*sqrt(a/(b*x**2) + 1)) - 3*b**4*asinh(sqrt(a)/(sqrt(b)*x))/(128*a**(5/2))","A",0
378,1,148,0,8.195179," ","integrate(x**4*(b*x**2+a)**(3/2),x)","- \frac{3 a^{\frac{7}{2}} x}{128 b^{2} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{a^{\frac{5}{2}} x^{3}}{128 b \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{13 a^{\frac{3}{2}} x^{5}}{64 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{5 \sqrt{a} b x^{7}}{16 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{3 a^{4} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{128 b^{\frac{5}{2}}} + \frac{b^{2} x^{9}}{8 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"-3*a**(7/2)*x/(128*b**2*sqrt(1 + b*x**2/a)) - a**(5/2)*x**3/(128*b*sqrt(1 + b*x**2/a)) + 13*a**(3/2)*x**5/(64*sqrt(1 + b*x**2/a)) + 5*sqrt(a)*b*x**7/(16*sqrt(1 + b*x**2/a)) + 3*a**4*asinh(sqrt(b)*x/sqrt(a))/(128*b**(5/2)) + b**2*x**9/(8*sqrt(a)*sqrt(1 + b*x**2/a))","A",0
379,1,119,0,5.206066," ","integrate(x**2*(b*x**2+a)**(3/2),x)","\frac{a^{\frac{5}{2}} x}{16 b \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{17 a^{\frac{3}{2}} x^{3}}{48 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{11 \sqrt{a} b x^{5}}{24 \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{a^{3} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{16 b^{\frac{3}{2}}} + \frac{b^{2} x^{7}}{6 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"a**(5/2)*x/(16*b*sqrt(1 + b*x**2/a)) + 17*a**(3/2)*x**3/(48*sqrt(1 + b*x**2/a)) + 11*sqrt(a)*b*x**5/(24*sqrt(1 + b*x**2/a)) - a**3*asinh(sqrt(b)*x/sqrt(a))/(16*b**(3/2)) + b**2*x**7/(6*sqrt(a)*sqrt(1 + b*x**2/a))","A",0
380,1,70,0,2.904690," ","integrate((b*x**2+a)**(3/2),x)","\frac{5 a^{\frac{3}{2}} x \sqrt{1 + \frac{b x^{2}}{a}}}{8} + \frac{\sqrt{a} b x^{3} \sqrt{1 + \frac{b x^{2}}{a}}}{4} + \frac{3 a^{2} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{8 \sqrt{b}}"," ",0,"5*a**(3/2)*x*sqrt(1 + b*x**2/a)/8 + sqrt(a)*b*x**3*sqrt(1 + b*x**2/a)/4 + 3*a**2*asinh(sqrt(b)*x/sqrt(a))/(8*sqrt(b))","A",0
381,1,88,0,2.369111," ","integrate((b*x**2+a)**(3/2)/x**2,x)","- \frac{a^{\frac{3}{2}}}{x \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{\sqrt{a} b x}{2 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{3 a \sqrt{b} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{2} + \frac{b^{2} x^{3}}{2 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"-a**(3/2)/(x*sqrt(1 + b*x**2/a)) - sqrt(a)*b*x/(2*sqrt(1 + b*x**2/a)) + 3*a*sqrt(b)*asinh(sqrt(b)*x/sqrt(a))/2 + b**2*x**3/(2*sqrt(a)*sqrt(1 + b*x**2/a))","A",0
382,1,78,0,2.025719," ","integrate((b*x**2+a)**(3/2)/x**4,x)","- \frac{a \sqrt{b} \sqrt{\frac{a}{b x^{2}} + 1}}{3 x^{2}} - \frac{4 b^{\frac{3}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{3} - \frac{b^{\frac{3}{2}} \log{\left(\frac{a}{b x^{2}} \right)}}{2} + b^{\frac{3}{2}} \log{\left(\sqrt{\frac{a}{b x^{2}} + 1} + 1 \right)}"," ",0,"-a*sqrt(b)*sqrt(a/(b*x**2) + 1)/(3*x**2) - 4*b**(3/2)*sqrt(a/(b*x**2) + 1)/3 - b**(3/2)*log(a/(b*x**2))/2 + b**(3/2)*log(sqrt(a/(b*x**2) + 1) + 1)","A",0
383,1,68,0,0.910537," ","integrate((b*x**2+a)**(3/2)/x**6,x)","- \frac{a \sqrt{b} \sqrt{\frac{a}{b x^{2}} + 1}}{5 x^{4}} - \frac{2 b^{\frac{3}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{5 x^{2}} - \frac{b^{\frac{5}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{5 a}"," ",0,"-a*sqrt(b)*sqrt(a/(b*x**2) + 1)/(5*x**4) - 2*b**(3/2)*sqrt(a/(b*x**2) + 1)/(5*x**2) - b**(5/2)*sqrt(a/(b*x**2) + 1)/(5*a)","B",0
384,1,94,0,1.178829," ","integrate((b*x**2+a)**(3/2)/x**8,x)","- \frac{a \sqrt{b} \sqrt{\frac{a}{b x^{2}} + 1}}{7 x^{6}} - \frac{8 b^{\frac{3}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{35 x^{4}} - \frac{b^{\frac{5}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{35 a x^{2}} + \frac{2 b^{\frac{7}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{35 a^{2}}"," ",0,"-a*sqrt(b)*sqrt(a/(b*x**2) + 1)/(7*x**6) - 8*b**(3/2)*sqrt(a/(b*x**2) + 1)/(35*x**4) - b**(5/2)*sqrt(a/(b*x**2) + 1)/(35*a*x**2) + 2*b**(7/2)*sqrt(a/(b*x**2) + 1)/(35*a**2)","B",0
385,1,420,0,1.612654," ","integrate((b*x**2+a)**(3/2)/x**10,x)","- \frac{35 a^{6} b^{\frac{9}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{315 a^{5} b^{4} x^{8} + 630 a^{4} b^{5} x^{10} + 315 a^{3} b^{6} x^{12}} - \frac{120 a^{5} b^{\frac{11}{2}} x^{2} \sqrt{\frac{a}{b x^{2}} + 1}}{315 a^{5} b^{4} x^{8} + 630 a^{4} b^{5} x^{10} + 315 a^{3} b^{6} x^{12}} - \frac{138 a^{4} b^{\frac{13}{2}} x^{4} \sqrt{\frac{a}{b x^{2}} + 1}}{315 a^{5} b^{4} x^{8} + 630 a^{4} b^{5} x^{10} + 315 a^{3} b^{6} x^{12}} - \frac{52 a^{3} b^{\frac{15}{2}} x^{6} \sqrt{\frac{a}{b x^{2}} + 1}}{315 a^{5} b^{4} x^{8} + 630 a^{4} b^{5} x^{10} + 315 a^{3} b^{6} x^{12}} - \frac{3 a^{2} b^{\frac{17}{2}} x^{8} \sqrt{\frac{a}{b x^{2}} + 1}}{315 a^{5} b^{4} x^{8} + 630 a^{4} b^{5} x^{10} + 315 a^{3} b^{6} x^{12}} - \frac{12 a b^{\frac{19}{2}} x^{10} \sqrt{\frac{a}{b x^{2}} + 1}}{315 a^{5} b^{4} x^{8} + 630 a^{4} b^{5} x^{10} + 315 a^{3} b^{6} x^{12}} - \frac{8 b^{\frac{21}{2}} x^{12} \sqrt{\frac{a}{b x^{2}} + 1}}{315 a^{5} b^{4} x^{8} + 630 a^{4} b^{5} x^{10} + 315 a^{3} b^{6} x^{12}}"," ",0,"-35*a**6*b**(9/2)*sqrt(a/(b*x**2) + 1)/(315*a**5*b**4*x**8 + 630*a**4*b**5*x**10 + 315*a**3*b**6*x**12) - 120*a**5*b**(11/2)*x**2*sqrt(a/(b*x**2) + 1)/(315*a**5*b**4*x**8 + 630*a**4*b**5*x**10 + 315*a**3*b**6*x**12) - 138*a**4*b**(13/2)*x**4*sqrt(a/(b*x**2) + 1)/(315*a**5*b**4*x**8 + 630*a**4*b**5*x**10 + 315*a**3*b**6*x**12) - 52*a**3*b**(15/2)*x**6*sqrt(a/(b*x**2) + 1)/(315*a**5*b**4*x**8 + 630*a**4*b**5*x**10 + 315*a**3*b**6*x**12) - 3*a**2*b**(17/2)*x**8*sqrt(a/(b*x**2) + 1)/(315*a**5*b**4*x**8 + 630*a**4*b**5*x**10 + 315*a**3*b**6*x**12) - 12*a*b**(19/2)*x**10*sqrt(a/(b*x**2) + 1)/(315*a**5*b**4*x**8 + 630*a**4*b**5*x**10 + 315*a**3*b**6*x**12) - 8*b**(21/2)*x**12*sqrt(a/(b*x**2) + 1)/(315*a**5*b**4*x**8 + 630*a**4*b**5*x**10 + 315*a**3*b**6*x**12)","B",0
386,1,648,0,2.123714," ","integrate((b*x**2+a)**(3/2)/x**12,x)","- \frac{105 a^{8} b^{\frac{19}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{1155 a^{7} b^{9} x^{10} + 3465 a^{6} b^{10} x^{12} + 3465 a^{5} b^{11} x^{14} + 1155 a^{4} b^{12} x^{16}} - \frac{455 a^{7} b^{\frac{21}{2}} x^{2} \sqrt{\frac{a}{b x^{2}} + 1}}{1155 a^{7} b^{9} x^{10} + 3465 a^{6} b^{10} x^{12} + 3465 a^{5} b^{11} x^{14} + 1155 a^{4} b^{12} x^{16}} - \frac{740 a^{6} b^{\frac{23}{2}} x^{4} \sqrt{\frac{a}{b x^{2}} + 1}}{1155 a^{7} b^{9} x^{10} + 3465 a^{6} b^{10} x^{12} + 3465 a^{5} b^{11} x^{14} + 1155 a^{4} b^{12} x^{16}} - \frac{534 a^{5} b^{\frac{25}{2}} x^{6} \sqrt{\frac{a}{b x^{2}} + 1}}{1155 a^{7} b^{9} x^{10} + 3465 a^{6} b^{10} x^{12} + 3465 a^{5} b^{11} x^{14} + 1155 a^{4} b^{12} x^{16}} - \frac{145 a^{4} b^{\frac{27}{2}} x^{8} \sqrt{\frac{a}{b x^{2}} + 1}}{1155 a^{7} b^{9} x^{10} + 3465 a^{6} b^{10} x^{12} + 3465 a^{5} b^{11} x^{14} + 1155 a^{4} b^{12} x^{16}} + \frac{5 a^{3} b^{\frac{29}{2}} x^{10} \sqrt{\frac{a}{b x^{2}} + 1}}{1155 a^{7} b^{9} x^{10} + 3465 a^{6} b^{10} x^{12} + 3465 a^{5} b^{11} x^{14} + 1155 a^{4} b^{12} x^{16}} + \frac{30 a^{2} b^{\frac{31}{2}} x^{12} \sqrt{\frac{a}{b x^{2}} + 1}}{1155 a^{7} b^{9} x^{10} + 3465 a^{6} b^{10} x^{12} + 3465 a^{5} b^{11} x^{14} + 1155 a^{4} b^{12} x^{16}} + \frac{40 a b^{\frac{33}{2}} x^{14} \sqrt{\frac{a}{b x^{2}} + 1}}{1155 a^{7} b^{9} x^{10} + 3465 a^{6} b^{10} x^{12} + 3465 a^{5} b^{11} x^{14} + 1155 a^{4} b^{12} x^{16}} + \frac{16 b^{\frac{35}{2}} x^{16} \sqrt{\frac{a}{b x^{2}} + 1}}{1155 a^{7} b^{9} x^{10} + 3465 a^{6} b^{10} x^{12} + 3465 a^{5} b^{11} x^{14} + 1155 a^{4} b^{12} x^{16}}"," ",0,"-105*a**8*b**(19/2)*sqrt(a/(b*x**2) + 1)/(1155*a**7*b**9*x**10 + 3465*a**6*b**10*x**12 + 3465*a**5*b**11*x**14 + 1155*a**4*b**12*x**16) - 455*a**7*b**(21/2)*x**2*sqrt(a/(b*x**2) + 1)/(1155*a**7*b**9*x**10 + 3465*a**6*b**10*x**12 + 3465*a**5*b**11*x**14 + 1155*a**4*b**12*x**16) - 740*a**6*b**(23/2)*x**4*sqrt(a/(b*x**2) + 1)/(1155*a**7*b**9*x**10 + 3465*a**6*b**10*x**12 + 3465*a**5*b**11*x**14 + 1155*a**4*b**12*x**16) - 534*a**5*b**(25/2)*x**6*sqrt(a/(b*x**2) + 1)/(1155*a**7*b**9*x**10 + 3465*a**6*b**10*x**12 + 3465*a**5*b**11*x**14 + 1155*a**4*b**12*x**16) - 145*a**4*b**(27/2)*x**8*sqrt(a/(b*x**2) + 1)/(1155*a**7*b**9*x**10 + 3465*a**6*b**10*x**12 + 3465*a**5*b**11*x**14 + 1155*a**4*b**12*x**16) + 5*a**3*b**(29/2)*x**10*sqrt(a/(b*x**2) + 1)/(1155*a**7*b**9*x**10 + 3465*a**6*b**10*x**12 + 3465*a**5*b**11*x**14 + 1155*a**4*b**12*x**16) + 30*a**2*b**(31/2)*x**12*sqrt(a/(b*x**2) + 1)/(1155*a**7*b**9*x**10 + 3465*a**6*b**10*x**12 + 3465*a**5*b**11*x**14 + 1155*a**4*b**12*x**16) + 40*a*b**(33/2)*x**14*sqrt(a/(b*x**2) + 1)/(1155*a**7*b**9*x**10 + 3465*a**6*b**10*x**12 + 3465*a**5*b**11*x**14 + 1155*a**4*b**12*x**16) + 16*b**(35/2)*x**16*sqrt(a/(b*x**2) + 1)/(1155*a**7*b**9*x**10 + 3465*a**6*b**10*x**12 + 3465*a**5*b**11*x**14 + 1155*a**4*b**12*x**16)","B",0
387,1,158,0,9.131271," ","integrate(x**7*(b*x**2+a)**(5/2),x)","\begin{cases} - \frac{16 a^{6} \sqrt{a + b x^{2}}}{3003 b^{4}} + \frac{8 a^{5} x^{2} \sqrt{a + b x^{2}}}{3003 b^{3}} - \frac{2 a^{4} x^{4} \sqrt{a + b x^{2}}}{1001 b^{2}} + \frac{5 a^{3} x^{6} \sqrt{a + b x^{2}}}{3003 b} + \frac{53 a^{2} x^{8} \sqrt{a + b x^{2}}}{429} + \frac{27 a b x^{10} \sqrt{a + b x^{2}}}{143} + \frac{b^{2} x^{12} \sqrt{a + b x^{2}}}{13} & \text{for}\: b \neq 0 \\\frac{a^{\frac{5}{2}} x^{8}}{8} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-16*a**6*sqrt(a + b*x**2)/(3003*b**4) + 8*a**5*x**2*sqrt(a + b*x**2)/(3003*b**3) - 2*a**4*x**4*sqrt(a + b*x**2)/(1001*b**2) + 5*a**3*x**6*sqrt(a + b*x**2)/(3003*b) + 53*a**2*x**8*sqrt(a + b*x**2)/429 + 27*a*b*x**10*sqrt(a + b*x**2)/143 + b**2*x**12*sqrt(a + b*x**2)/13, Ne(b, 0)), (a**(5/2)*x**8/8, True))","A",0
388,1,133,0,6.275192," ","integrate(x**5*(b*x**2+a)**(5/2),x)","\begin{cases} \frac{8 a^{5} \sqrt{a + b x^{2}}}{693 b^{3}} - \frac{4 a^{4} x^{2} \sqrt{a + b x^{2}}}{693 b^{2}} + \frac{a^{3} x^{4} \sqrt{a + b x^{2}}}{231 b} + \frac{113 a^{2} x^{6} \sqrt{a + b x^{2}}}{693} + \frac{23 a b x^{8} \sqrt{a + b x^{2}}}{99} + \frac{b^{2} x^{10} \sqrt{a + b x^{2}}}{11} & \text{for}\: b \neq 0 \\\frac{a^{\frac{5}{2}} x^{6}}{6} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*a**5*sqrt(a + b*x**2)/(693*b**3) - 4*a**4*x**2*sqrt(a + b*x**2)/(693*b**2) + a**3*x**4*sqrt(a + b*x**2)/(231*b) + 113*a**2*x**6*sqrt(a + b*x**2)/693 + 23*a*b*x**8*sqrt(a + b*x**2)/99 + b**2*x**10*sqrt(a + b*x**2)/11, Ne(b, 0)), (a**(5/2)*x**6/6, True))","A",0
389,1,109,0,3.832401," ","integrate(x**3*(b*x**2+a)**(5/2),x)","\begin{cases} - \frac{2 a^{4} \sqrt{a + b x^{2}}}{63 b^{2}} + \frac{a^{3} x^{2} \sqrt{a + b x^{2}}}{63 b} + \frac{5 a^{2} x^{4} \sqrt{a + b x^{2}}}{21} + \frac{19 a b x^{6} \sqrt{a + b x^{2}}}{63} + \frac{b^{2} x^{8} \sqrt{a + b x^{2}}}{9} & \text{for}\: b \neq 0 \\\frac{a^{\frac{5}{2}} x^{4}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*a**4*sqrt(a + b*x**2)/(63*b**2) + a**3*x**2*sqrt(a + b*x**2)/(63*b) + 5*a**2*x**4*sqrt(a + b*x**2)/21 + 19*a*b*x**6*sqrt(a + b*x**2)/63 + b**2*x**8*sqrt(a + b*x**2)/9, Ne(b, 0)), (a**(5/2)*x**4/4, True))","A",0
390,1,85,0,2.100030," ","integrate(x*(b*x**2+a)**(5/2),x)","\begin{cases} \frac{a^{3} \sqrt{a + b x^{2}}}{7 b} + \frac{3 a^{2} x^{2} \sqrt{a + b x^{2}}}{7} + \frac{3 a b x^{4} \sqrt{a + b x^{2}}}{7} + \frac{b^{2} x^{6} \sqrt{a + b x^{2}}}{7} & \text{for}\: b \neq 0 \\\frac{a^{\frac{5}{2}} x^{2}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*sqrt(a + b*x**2)/(7*b) + 3*a**2*x**2*sqrt(a + b*x**2)/7 + 3*a*b*x**4*sqrt(a + b*x**2)/7 + b**2*x**6*sqrt(a + b*x**2)/7, Ne(b, 0)), (a**(5/2)*x**2/2, True))","A",0
391,1,105,0,3.555869," ","integrate((b*x**2+a)**(5/2)/x,x)","\frac{23 a^{\frac{5}{2}} \sqrt{1 + \frac{b x^{2}}{a}}}{15} + \frac{a^{\frac{5}{2}} \log{\left(\frac{b x^{2}}{a} \right)}}{2} - a^{\frac{5}{2}} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)} + \frac{11 a^{\frac{3}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}}}{15} + \frac{\sqrt{a} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}}}{5}"," ",0,"23*a**(5/2)*sqrt(1 + b*x**2/a)/15 + a**(5/2)*log(b*x**2/a)/2 - a**(5/2)*log(sqrt(1 + b*x**2/a) + 1) + 11*a**(3/2)*b*x**2*sqrt(1 + b*x**2/a)/15 + sqrt(a)*b**2*x**4*sqrt(1 + b*x**2/a)/5","A",0
392,1,112,0,3.223333," ","integrate((b*x**2+a)**(5/2)/x**3,x)","- \frac{a^{\frac{5}{2}} \sqrt{1 + \frac{b x^{2}}{a}}}{2 x^{2}} + \frac{7 a^{\frac{3}{2}} b \sqrt{1 + \frac{b x^{2}}{a}}}{3} + \frac{5 a^{\frac{3}{2}} b \log{\left(\frac{b x^{2}}{a} \right)}}{4} - \frac{5 a^{\frac{3}{2}} b \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{2} + \frac{\sqrt{a} b^{2} x^{2} \sqrt{1 + \frac{b x^{2}}{a}}}{3}"," ",0,"-a**(5/2)*sqrt(1 + b*x**2/a)/(2*x**2) + 7*a**(3/2)*b*sqrt(1 + b*x**2/a)/3 + 5*a**(3/2)*b*log(b*x**2/a)/4 - 5*a**(3/2)*b*log(sqrt(1 + b*x**2/a) + 1)/2 + sqrt(a)*b**2*x**2*sqrt(1 + b*x**2/a)/3","A",0
393,1,117,0,3.727081," ","integrate((b*x**2+a)**(5/2)/x**5,x)","- \frac{15 \sqrt{a} b^{2} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)}}{8} - \frac{a^{3}}{4 \sqrt{b} x^{5} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{11 a^{2} \sqrt{b}}{8 x^{3} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{a b^{\frac{3}{2}}}{8 x \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{b^{\frac{5}{2}} x}{\sqrt{\frac{a}{b x^{2}} + 1}}"," ",0,"-15*sqrt(a)*b**2*asinh(sqrt(a)/(sqrt(b)*x))/8 - a**3/(4*sqrt(b)*x**5*sqrt(a/(b*x**2) + 1)) - 11*a**2*sqrt(b)/(8*x**3*sqrt(a/(b*x**2) + 1)) - a*b**(3/2)/(8*x*sqrt(a/(b*x**2) + 1)) + b**(5/2)*x/sqrt(a/(b*x**2) + 1)","A",0
394,1,99,0,4.528002," ","integrate((b*x**2+a)**(5/2)/x**7,x)","- \frac{a^{2} \sqrt{b} \sqrt{\frac{a}{b x^{2}} + 1}}{6 x^{5}} - \frac{13 a b^{\frac{3}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{24 x^{3}} - \frac{11 b^{\frac{5}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{16 x} - \frac{5 b^{3} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)}}{16 \sqrt{a}}"," ",0,"-a**2*sqrt(b)*sqrt(a/(b*x**2) + 1)/(6*x**5) - 13*a*b**(3/2)*sqrt(a/(b*x**2) + 1)/(24*x**3) - 11*b**(5/2)*sqrt(a/(b*x**2) + 1)/(16*x) - 5*b**3*asinh(sqrt(a)/(sqrt(b)*x))/(16*sqrt(a))","A",0
395,1,150,0,7.576264," ","integrate((b*x**2+a)**(5/2)/x**9,x)","- \frac{a^{3}}{8 \sqrt{b} x^{9} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{23 a^{2} \sqrt{b}}{48 x^{7} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{127 a b^{\frac{3}{2}}}{192 x^{5} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{133 b^{\frac{5}{2}}}{384 x^{3} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{5 b^{\frac{7}{2}}}{128 a x \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{5 b^{4} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)}}{128 a^{\frac{3}{2}}}"," ",0,"-a**3/(8*sqrt(b)*x**9*sqrt(a/(b*x**2) + 1)) - 23*a**2*sqrt(b)/(48*x**7*sqrt(a/(b*x**2) + 1)) - 127*a*b**(3/2)/(192*x**5*sqrt(a/(b*x**2) + 1)) - 133*b**(5/2)/(384*x**3*sqrt(a/(b*x**2) + 1)) - 5*b**(7/2)/(128*a*x*sqrt(a/(b*x**2) + 1)) + 5*b**4*asinh(sqrt(a)/(sqrt(b)*x))/(128*a**(3/2))","A",0
396,1,175,0,11.535014," ","integrate((b*x**2+a)**(5/2)/x**11,x)","- \frac{a^{3}}{10 \sqrt{b} x^{11} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{29 a^{2} \sqrt{b}}{80 x^{9} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{73 a b^{\frac{3}{2}}}{160 x^{7} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{129 b^{\frac{5}{2}}}{640 x^{5} \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{b^{\frac{7}{2}}}{256 a x^{3} \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{3 b^{\frac{9}{2}}}{256 a^{2} x \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{3 b^{5} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)}}{256 a^{\frac{5}{2}}}"," ",0,"-a**3/(10*sqrt(b)*x**11*sqrt(a/(b*x**2) + 1)) - 29*a**2*sqrt(b)/(80*x**9*sqrt(a/(b*x**2) + 1)) - 73*a*b**(3/2)/(160*x**7*sqrt(a/(b*x**2) + 1)) - 129*b**(5/2)/(640*x**5*sqrt(a/(b*x**2) + 1)) + b**(7/2)/(256*a*x**3*sqrt(a/(b*x**2) + 1)) + 3*b**(9/2)/(256*a**2*x*sqrt(a/(b*x**2) + 1)) - 3*b**5*asinh(sqrt(a)/(sqrt(b)*x))/(256*a**(5/2))","A",0
397,1,175,0,11.108251," ","integrate(x**4*(b*x**2+a)**(5/2),x)","- \frac{3 a^{\frac{9}{2}} x}{256 b^{2} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{a^{\frac{7}{2}} x^{3}}{256 b \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{129 a^{\frac{5}{2}} x^{5}}{640 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{73 a^{\frac{3}{2}} b x^{7}}{160 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{29 \sqrt{a} b^{2} x^{9}}{80 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{3 a^{5} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{256 b^{\frac{5}{2}}} + \frac{b^{3} x^{11}}{10 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"-3*a**(9/2)*x/(256*b**2*sqrt(1 + b*x**2/a)) - a**(7/2)*x**3/(256*b*sqrt(1 + b*x**2/a)) + 129*a**(5/2)*x**5/(640*sqrt(1 + b*x**2/a)) + 73*a**(3/2)*b*x**7/(160*sqrt(1 + b*x**2/a)) + 29*sqrt(a)*b**2*x**9/(80*sqrt(1 + b*x**2/a)) + 3*a**5*asinh(sqrt(b)*x/sqrt(a))/(256*b**(5/2)) + b**3*x**11/(10*sqrt(a)*sqrt(1 + b*x**2/a))","A",0
398,1,150,0,7.222981," ","integrate(x**2*(b*x**2+a)**(5/2),x)","\frac{5 a^{\frac{7}{2}} x}{128 b \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{133 a^{\frac{5}{2}} x^{3}}{384 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{127 a^{\frac{3}{2}} b x^{5}}{192 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{23 \sqrt{a} b^{2} x^{7}}{48 \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{5 a^{4} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{128 b^{\frac{3}{2}}} + \frac{b^{3} x^{9}}{8 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"5*a**(7/2)*x/(128*b*sqrt(1 + b*x**2/a)) + 133*a**(5/2)*x**3/(384*sqrt(1 + b*x**2/a)) + 127*a**(3/2)*b*x**5/(192*sqrt(1 + b*x**2/a)) + 23*sqrt(a)*b**2*x**7/(48*sqrt(1 + b*x**2/a)) - 5*a**4*asinh(sqrt(b)*x/sqrt(a))/(128*b**(3/2)) + b**3*x**9/(8*sqrt(a)*sqrt(1 + b*x**2/a))","A",0
399,1,97,0,4.213837," ","integrate((b*x**2+a)**(5/2),x)","\frac{11 a^{\frac{5}{2}} x \sqrt{1 + \frac{b x^{2}}{a}}}{16} + \frac{13 a^{\frac{3}{2}} b x^{3} \sqrt{1 + \frac{b x^{2}}{a}}}{24} + \frac{\sqrt{a} b^{2} x^{5} \sqrt{1 + \frac{b x^{2}}{a}}}{6} + \frac{5 a^{3} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{16 \sqrt{b}}"," ",0,"11*a**(5/2)*x*sqrt(1 + b*x**2/a)/16 + 13*a**(3/2)*b*x**3*sqrt(1 + b*x**2/a)/24 + sqrt(a)*b**2*x**5*sqrt(1 + b*x**2/a)/6 + 5*a**3*asinh(sqrt(b)*x/sqrt(a))/(16*sqrt(b))","A",0
400,1,117,0,3.630509," ","integrate((b*x**2+a)**(5/2)/x**2,x)","- \frac{a^{\frac{5}{2}}}{x \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{a^{\frac{3}{2}} b x}{8 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{11 \sqrt{a} b^{2} x^{3}}{8 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{15 a^{2} \sqrt{b} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{8} + \frac{b^{3} x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"-a**(5/2)/(x*sqrt(1 + b*x**2/a)) + a**(3/2)*b*x/(8*sqrt(1 + b*x**2/a)) + 11*sqrt(a)*b**2*x**3/(8*sqrt(1 + b*x**2/a)) + 15*a**2*sqrt(b)*asinh(sqrt(b)*x/sqrt(a))/8 + b**3*x**5/(4*sqrt(a)*sqrt(1 + b*x**2/a))","A",0
401,1,112,0,3.164611," ","integrate((b*x**2+a)**(5/2)/x**4,x)","- \frac{a^{2} \sqrt{b} \sqrt{\frac{a}{b x^{2}} + 1}}{3 x^{2}} - \frac{7 a b^{\frac{3}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{3} - \frac{5 a b^{\frac{3}{2}} \log{\left(\frac{a}{b x^{2}} \right)}}{4} + \frac{5 a b^{\frac{3}{2}} \log{\left(\sqrt{\frac{a}{b x^{2}} + 1} + 1 \right)}}{2} + \frac{b^{\frac{5}{2}} x^{2} \sqrt{\frac{a}{b x^{2}} + 1}}{2}"," ",0,"-a**2*sqrt(b)*sqrt(a/(b*x**2) + 1)/(3*x**2) - 7*a*b**(3/2)*sqrt(a/(b*x**2) + 1)/3 - 5*a*b**(3/2)*log(a/(b*x**2))/4 + 5*a*b**(3/2)*log(sqrt(a/(b*x**2) + 1) + 1)/2 + b**(5/2)*x**2*sqrt(a/(b*x**2) + 1)/2","A",0
402,1,105,0,3.662029," ","integrate((b*x**2+a)**(5/2)/x**6,x)","- \frac{a^{2} \sqrt{b} \sqrt{\frac{a}{b x^{2}} + 1}}{5 x^{4}} - \frac{11 a b^{\frac{3}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{15 x^{2}} - \frac{23 b^{\frac{5}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{15} - \frac{b^{\frac{5}{2}} \log{\left(\frac{a}{b x^{2}} \right)}}{2} + b^{\frac{5}{2}} \log{\left(\sqrt{\frac{a}{b x^{2}} + 1} + 1 \right)}"," ",0,"-a**2*sqrt(b)*sqrt(a/(b*x**2) + 1)/(5*x**4) - 11*a*b**(3/2)*sqrt(a/(b*x**2) + 1)/(15*x**2) - 23*b**(5/2)*sqrt(a/(b*x**2) + 1)/15 - b**(5/2)*log(a/(b*x**2))/2 + b**(5/2)*log(sqrt(a/(b*x**2) + 1) + 1)","A",0
403,1,95,0,1.260448," ","integrate((b*x**2+a)**(5/2)/x**8,x)","- \frac{a^{2} \sqrt{b} \sqrt{\frac{a}{b x^{2}} + 1}}{7 x^{6}} - \frac{3 a b^{\frac{3}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{7 x^{4}} - \frac{3 b^{\frac{5}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{7 x^{2}} - \frac{b^{\frac{7}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{7 a}"," ",0,"-a**2*sqrt(b)*sqrt(a/(b*x**2) + 1)/(7*x**6) - 3*a*b**(3/2)*sqrt(a/(b*x**2) + 1)/(7*x**4) - 3*b**(5/2)*sqrt(a/(b*x**2) + 1)/(7*x**2) - b**(7/2)*sqrt(a/(b*x**2) + 1)/(7*a)","B",0
404,1,121,0,1.591214," ","integrate((b*x**2+a)**(5/2)/x**10,x)","- \frac{a^{2} \sqrt{b} \sqrt{\frac{a}{b x^{2}} + 1}}{9 x^{8}} - \frac{19 a b^{\frac{3}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{63 x^{6}} - \frac{5 b^{\frac{5}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{21 x^{4}} - \frac{b^{\frac{7}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{63 a x^{2}} + \frac{2 b^{\frac{9}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{63 a^{2}}"," ",0,"-a**2*sqrt(b)*sqrt(a/(b*x**2) + 1)/(9*x**8) - 19*a*b**(3/2)*sqrt(a/(b*x**2) + 1)/(63*x**6) - 5*b**(5/2)*sqrt(a/(b*x**2) + 1)/(21*x**4) - b**(7/2)*sqrt(a/(b*x**2) + 1)/(63*a*x**2) + 2*b**(9/2)*sqrt(a/(b*x**2) + 1)/(63*a**2)","B",0
405,1,481,0,2.159619," ","integrate((b*x**2+a)**(5/2)/x**12,x)","- \frac{63 a^{7} b^{\frac{9}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{x^{2} \left(693 a^{5} b^{4} x^{8} + 1386 a^{4} b^{5} x^{10} + 693 a^{3} b^{6} x^{12}\right)} - \frac{287 a^{6} b^{\frac{11}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{693 a^{5} b^{4} x^{8} + 1386 a^{4} b^{5} x^{10} + 693 a^{3} b^{6} x^{12}} - \frac{498 a^{5} b^{\frac{13}{2}} x^{2} \sqrt{\frac{a}{b x^{2}} + 1}}{693 a^{5} b^{4} x^{8} + 1386 a^{4} b^{5} x^{10} + 693 a^{3} b^{6} x^{12}} - \frac{390 a^{4} b^{\frac{15}{2}} x^{4} \sqrt{\frac{a}{b x^{2}} + 1}}{693 a^{5} b^{4} x^{8} + 1386 a^{4} b^{5} x^{10} + 693 a^{3} b^{6} x^{12}} - \frac{115 a^{3} b^{\frac{17}{2}} x^{6} \sqrt{\frac{a}{b x^{2}} + 1}}{693 a^{5} b^{4} x^{8} + 1386 a^{4} b^{5} x^{10} + 693 a^{3} b^{6} x^{12}} - \frac{3 a^{2} b^{\frac{19}{2}} x^{8} \sqrt{\frac{a}{b x^{2}} + 1}}{693 a^{5} b^{4} x^{8} + 1386 a^{4} b^{5} x^{10} + 693 a^{3} b^{6} x^{12}} - \frac{12 a b^{\frac{21}{2}} x^{10} \sqrt{\frac{a}{b x^{2}} + 1}}{693 a^{5} b^{4} x^{8} + 1386 a^{4} b^{5} x^{10} + 693 a^{3} b^{6} x^{12}} - \frac{8 b^{\frac{23}{2}} x^{12} \sqrt{\frac{a}{b x^{2}} + 1}}{693 a^{5} b^{4} x^{8} + 1386 a^{4} b^{5} x^{10} + 693 a^{3} b^{6} x^{12}}"," ",0,"-63*a**7*b**(9/2)*sqrt(a/(b*x**2) + 1)/(x**2*(693*a**5*b**4*x**8 + 1386*a**4*b**5*x**10 + 693*a**3*b**6*x**12)) - 287*a**6*b**(11/2)*sqrt(a/(b*x**2) + 1)/(693*a**5*b**4*x**8 + 1386*a**4*b**5*x**10 + 693*a**3*b**6*x**12) - 498*a**5*b**(13/2)*x**2*sqrt(a/(b*x**2) + 1)/(693*a**5*b**4*x**8 + 1386*a**4*b**5*x**10 + 693*a**3*b**6*x**12) - 390*a**4*b**(15/2)*x**4*sqrt(a/(b*x**2) + 1)/(693*a**5*b**4*x**8 + 1386*a**4*b**5*x**10 + 693*a**3*b**6*x**12) - 115*a**3*b**(17/2)*x**6*sqrt(a/(b*x**2) + 1)/(693*a**5*b**4*x**8 + 1386*a**4*b**5*x**10 + 693*a**3*b**6*x**12) - 3*a**2*b**(19/2)*x**8*sqrt(a/(b*x**2) + 1)/(693*a**5*b**4*x**8 + 1386*a**4*b**5*x**10 + 693*a**3*b**6*x**12) - 12*a*b**(21/2)*x**10*sqrt(a/(b*x**2) + 1)/(693*a**5*b**4*x**8 + 1386*a**4*b**5*x**10 + 693*a**3*b**6*x**12) - 8*b**(23/2)*x**12*sqrt(a/(b*x**2) + 1)/(693*a**5*b**4*x**8 + 1386*a**4*b**5*x**10 + 693*a**3*b**6*x**12)","B",0
406,1,721,0,2.793187," ","integrate((b*x**2+a)**(5/2)/x**14,x)","- \frac{231 a^{9} b^{\frac{19}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{3003 a^{7} b^{9} x^{12} + 9009 a^{6} b^{10} x^{14} + 9009 a^{5} b^{11} x^{16} + 3003 a^{4} b^{12} x^{18}} - \frac{1260 a^{8} b^{\frac{21}{2}} x^{2} \sqrt{\frac{a}{b x^{2}} + 1}}{3003 a^{7} b^{9} x^{12} + 9009 a^{6} b^{10} x^{14} + 9009 a^{5} b^{11} x^{16} + 3003 a^{4} b^{12} x^{18}} - \frac{2765 a^{7} b^{\frac{23}{2}} x^{4} \sqrt{\frac{a}{b x^{2}} + 1}}{3003 a^{7} b^{9} x^{12} + 9009 a^{6} b^{10} x^{14} + 9009 a^{5} b^{11} x^{16} + 3003 a^{4} b^{12} x^{18}} - \frac{3050 a^{6} b^{\frac{25}{2}} x^{6} \sqrt{\frac{a}{b x^{2}} + 1}}{3003 a^{7} b^{9} x^{12} + 9009 a^{6} b^{10} x^{14} + 9009 a^{5} b^{11} x^{16} + 3003 a^{4} b^{12} x^{18}} - \frac{1689 a^{5} b^{\frac{27}{2}} x^{8} \sqrt{\frac{a}{b x^{2}} + 1}}{3003 a^{7} b^{9} x^{12} + 9009 a^{6} b^{10} x^{14} + 9009 a^{5} b^{11} x^{16} + 3003 a^{4} b^{12} x^{18}} - \frac{376 a^{4} b^{\frac{29}{2}} x^{10} \sqrt{\frac{a}{b x^{2}} + 1}}{3003 a^{7} b^{9} x^{12} + 9009 a^{6} b^{10} x^{14} + 9009 a^{5} b^{11} x^{16} + 3003 a^{4} b^{12} x^{18}} + \frac{5 a^{3} b^{\frac{31}{2}} x^{12} \sqrt{\frac{a}{b x^{2}} + 1}}{3003 a^{7} b^{9} x^{12} + 9009 a^{6} b^{10} x^{14} + 9009 a^{5} b^{11} x^{16} + 3003 a^{4} b^{12} x^{18}} + \frac{30 a^{2} b^{\frac{33}{2}} x^{14} \sqrt{\frac{a}{b x^{2}} + 1}}{3003 a^{7} b^{9} x^{12} + 9009 a^{6} b^{10} x^{14} + 9009 a^{5} b^{11} x^{16} + 3003 a^{4} b^{12} x^{18}} + \frac{40 a b^{\frac{35}{2}} x^{16} \sqrt{\frac{a}{b x^{2}} + 1}}{3003 a^{7} b^{9} x^{12} + 9009 a^{6} b^{10} x^{14} + 9009 a^{5} b^{11} x^{16} + 3003 a^{4} b^{12} x^{18}} + \frac{16 b^{\frac{37}{2}} x^{18} \sqrt{\frac{a}{b x^{2}} + 1}}{3003 a^{7} b^{9} x^{12} + 9009 a^{6} b^{10} x^{14} + 9009 a^{5} b^{11} x^{16} + 3003 a^{4} b^{12} x^{18}}"," ",0,"-231*a**9*b**(19/2)*sqrt(a/(b*x**2) + 1)/(3003*a**7*b**9*x**12 + 9009*a**6*b**10*x**14 + 9009*a**5*b**11*x**16 + 3003*a**4*b**12*x**18) - 1260*a**8*b**(21/2)*x**2*sqrt(a/(b*x**2) + 1)/(3003*a**7*b**9*x**12 + 9009*a**6*b**10*x**14 + 9009*a**5*b**11*x**16 + 3003*a**4*b**12*x**18) - 2765*a**7*b**(23/2)*x**4*sqrt(a/(b*x**2) + 1)/(3003*a**7*b**9*x**12 + 9009*a**6*b**10*x**14 + 9009*a**5*b**11*x**16 + 3003*a**4*b**12*x**18) - 3050*a**6*b**(25/2)*x**6*sqrt(a/(b*x**2) + 1)/(3003*a**7*b**9*x**12 + 9009*a**6*b**10*x**14 + 9009*a**5*b**11*x**16 + 3003*a**4*b**12*x**18) - 1689*a**5*b**(27/2)*x**8*sqrt(a/(b*x**2) + 1)/(3003*a**7*b**9*x**12 + 9009*a**6*b**10*x**14 + 9009*a**5*b**11*x**16 + 3003*a**4*b**12*x**18) - 376*a**4*b**(29/2)*x**10*sqrt(a/(b*x**2) + 1)/(3003*a**7*b**9*x**12 + 9009*a**6*b**10*x**14 + 9009*a**5*b**11*x**16 + 3003*a**4*b**12*x**18) + 5*a**3*b**(31/2)*x**12*sqrt(a/(b*x**2) + 1)/(3003*a**7*b**9*x**12 + 9009*a**6*b**10*x**14 + 9009*a**5*b**11*x**16 + 3003*a**4*b**12*x**18) + 30*a**2*b**(33/2)*x**14*sqrt(a/(b*x**2) + 1)/(3003*a**7*b**9*x**12 + 9009*a**6*b**10*x**14 + 9009*a**5*b**11*x**16 + 3003*a**4*b**12*x**18) + 40*a*b**(35/2)*x**16*sqrt(a/(b*x**2) + 1)/(3003*a**7*b**9*x**12 + 9009*a**6*b**10*x**14 + 9009*a**5*b**11*x**16 + 3003*a**4*b**12*x**18) + 16*b**(37/2)*x**18*sqrt(a/(b*x**2) + 1)/(3003*a**7*b**9*x**12 + 9009*a**6*b**10*x**14 + 9009*a**5*b**11*x**16 + 3003*a**4*b**12*x**18)","B",0
407,1,1012,0,3.487784," ","integrate((b*x**2+a)**(5/2)/x**16,x)","- \frac{3003 a^{11} b^{\frac{33}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{45045 a^{9} b^{16} x^{14} + 180180 a^{8} b^{17} x^{16} + 270270 a^{7} b^{18} x^{18} + 180180 a^{6} b^{19} x^{20} + 45045 a^{5} b^{20} x^{22}} - \frac{19173 a^{10} b^{\frac{35}{2}} x^{2} \sqrt{\frac{a}{b x^{2}} + 1}}{45045 a^{9} b^{16} x^{14} + 180180 a^{8} b^{17} x^{16} + 270270 a^{7} b^{18} x^{18} + 180180 a^{6} b^{19} x^{20} + 45045 a^{5} b^{20} x^{22}} - \frac{51135 a^{9} b^{\frac{37}{2}} x^{4} \sqrt{\frac{a}{b x^{2}} + 1}}{45045 a^{9} b^{16} x^{14} + 180180 a^{8} b^{17} x^{16} + 270270 a^{7} b^{18} x^{18} + 180180 a^{6} b^{19} x^{20} + 45045 a^{5} b^{20} x^{22}} - \frac{72905 a^{8} b^{\frac{39}{2}} x^{6} \sqrt{\frac{a}{b x^{2}} + 1}}{45045 a^{9} b^{16} x^{14} + 180180 a^{8} b^{17} x^{16} + 270270 a^{7} b^{18} x^{18} + 180180 a^{6} b^{19} x^{20} + 45045 a^{5} b^{20} x^{22}} - \frac{58585 a^{7} b^{\frac{41}{2}} x^{8} \sqrt{\frac{a}{b x^{2}} + 1}}{45045 a^{9} b^{16} x^{14} + 180180 a^{8} b^{17} x^{16} + 270270 a^{7} b^{18} x^{18} + 180180 a^{6} b^{19} x^{20} + 45045 a^{5} b^{20} x^{22}} - \frac{25151 a^{6} b^{\frac{43}{2}} x^{10} \sqrt{\frac{a}{b x^{2}} + 1}}{45045 a^{9} b^{16} x^{14} + 180180 a^{8} b^{17} x^{16} + 270270 a^{7} b^{18} x^{18} + 180180 a^{6} b^{19} x^{20} + 45045 a^{5} b^{20} x^{22}} - \frac{4501 a^{5} b^{\frac{45}{2}} x^{12} \sqrt{\frac{a}{b x^{2}} + 1}}{45045 a^{9} b^{16} x^{14} + 180180 a^{8} b^{17} x^{16} + 270270 a^{7} b^{18} x^{18} + 180180 a^{6} b^{19} x^{20} + 45045 a^{5} b^{20} x^{22}} - \frac{35 a^{4} b^{\frac{47}{2}} x^{14} \sqrt{\frac{a}{b x^{2}} + 1}}{45045 a^{9} b^{16} x^{14} + 180180 a^{8} b^{17} x^{16} + 270270 a^{7} b^{18} x^{18} + 180180 a^{6} b^{19} x^{20} + 45045 a^{5} b^{20} x^{22}} - \frac{280 a^{3} b^{\frac{49}{2}} x^{16} \sqrt{\frac{a}{b x^{2}} + 1}}{45045 a^{9} b^{16} x^{14} + 180180 a^{8} b^{17} x^{16} + 270270 a^{7} b^{18} x^{18} + 180180 a^{6} b^{19} x^{20} + 45045 a^{5} b^{20} x^{22}} - \frac{560 a^{2} b^{\frac{51}{2}} x^{18} \sqrt{\frac{a}{b x^{2}} + 1}}{45045 a^{9} b^{16} x^{14} + 180180 a^{8} b^{17} x^{16} + 270270 a^{7} b^{18} x^{18} + 180180 a^{6} b^{19} x^{20} + 45045 a^{5} b^{20} x^{22}} - \frac{448 a b^{\frac{53}{2}} x^{20} \sqrt{\frac{a}{b x^{2}} + 1}}{45045 a^{9} b^{16} x^{14} + 180180 a^{8} b^{17} x^{16} + 270270 a^{7} b^{18} x^{18} + 180180 a^{6} b^{19} x^{20} + 45045 a^{5} b^{20} x^{22}} - \frac{128 b^{\frac{55}{2}} x^{22} \sqrt{\frac{a}{b x^{2}} + 1}}{45045 a^{9} b^{16} x^{14} + 180180 a^{8} b^{17} x^{16} + 270270 a^{7} b^{18} x^{18} + 180180 a^{6} b^{19} x^{20} + 45045 a^{5} b^{20} x^{22}}"," ",0,"-3003*a**11*b**(33/2)*sqrt(a/(b*x**2) + 1)/(45045*a**9*b**16*x**14 + 180180*a**8*b**17*x**16 + 270270*a**7*b**18*x**18 + 180180*a**6*b**19*x**20 + 45045*a**5*b**20*x**22) - 19173*a**10*b**(35/2)*x**2*sqrt(a/(b*x**2) + 1)/(45045*a**9*b**16*x**14 + 180180*a**8*b**17*x**16 + 270270*a**7*b**18*x**18 + 180180*a**6*b**19*x**20 + 45045*a**5*b**20*x**22) - 51135*a**9*b**(37/2)*x**4*sqrt(a/(b*x**2) + 1)/(45045*a**9*b**16*x**14 + 180180*a**8*b**17*x**16 + 270270*a**7*b**18*x**18 + 180180*a**6*b**19*x**20 + 45045*a**5*b**20*x**22) - 72905*a**8*b**(39/2)*x**6*sqrt(a/(b*x**2) + 1)/(45045*a**9*b**16*x**14 + 180180*a**8*b**17*x**16 + 270270*a**7*b**18*x**18 + 180180*a**6*b**19*x**20 + 45045*a**5*b**20*x**22) - 58585*a**7*b**(41/2)*x**8*sqrt(a/(b*x**2) + 1)/(45045*a**9*b**16*x**14 + 180180*a**8*b**17*x**16 + 270270*a**7*b**18*x**18 + 180180*a**6*b**19*x**20 + 45045*a**5*b**20*x**22) - 25151*a**6*b**(43/2)*x**10*sqrt(a/(b*x**2) + 1)/(45045*a**9*b**16*x**14 + 180180*a**8*b**17*x**16 + 270270*a**7*b**18*x**18 + 180180*a**6*b**19*x**20 + 45045*a**5*b**20*x**22) - 4501*a**5*b**(45/2)*x**12*sqrt(a/(b*x**2) + 1)/(45045*a**9*b**16*x**14 + 180180*a**8*b**17*x**16 + 270270*a**7*b**18*x**18 + 180180*a**6*b**19*x**20 + 45045*a**5*b**20*x**22) - 35*a**4*b**(47/2)*x**14*sqrt(a/(b*x**2) + 1)/(45045*a**9*b**16*x**14 + 180180*a**8*b**17*x**16 + 270270*a**7*b**18*x**18 + 180180*a**6*b**19*x**20 + 45045*a**5*b**20*x**22) - 280*a**3*b**(49/2)*x**16*sqrt(a/(b*x**2) + 1)/(45045*a**9*b**16*x**14 + 180180*a**8*b**17*x**16 + 270270*a**7*b**18*x**18 + 180180*a**6*b**19*x**20 + 45045*a**5*b**20*x**22) - 560*a**2*b**(51/2)*x**18*sqrt(a/(b*x**2) + 1)/(45045*a**9*b**16*x**14 + 180180*a**8*b**17*x**16 + 270270*a**7*b**18*x**18 + 180180*a**6*b**19*x**20 + 45045*a**5*b**20*x**22) - 448*a*b**(53/2)*x**20*sqrt(a/(b*x**2) + 1)/(45045*a**9*b**16*x**14 + 180180*a**8*b**17*x**16 + 270270*a**7*b**18*x**18 + 180180*a**6*b**19*x**20 + 45045*a**5*b**20*x**22) - 128*b**(55/2)*x**22*sqrt(a/(b*x**2) + 1)/(45045*a**9*b**16*x**14 + 180180*a**8*b**17*x**16 + 270270*a**7*b**18*x**18 + 180180*a**6*b**19*x**20 + 45045*a**5*b**20*x**22)","B",0
408,1,1346,0,4.423176," ","integrate((b*x**2+a)**(5/2)/x**18,x)","- \frac{9009 a^{13} b^{\frac{51}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{153153 a^{11} b^{25} x^{16} + 765765 a^{10} b^{26} x^{18} + 1531530 a^{9} b^{27} x^{20} + 1531530 a^{8} b^{28} x^{22} + 765765 a^{7} b^{29} x^{24} + 153153 a^{6} b^{30} x^{26}} - \frac{66066 a^{12} b^{\frac{53}{2}} x^{2} \sqrt{\frac{a}{b x^{2}} + 1}}{153153 a^{11} b^{25} x^{16} + 765765 a^{10} b^{26} x^{18} + 1531530 a^{9} b^{27} x^{20} + 1531530 a^{8} b^{28} x^{22} + 765765 a^{7} b^{29} x^{24} + 153153 a^{6} b^{30} x^{26}} - \frac{207900 a^{11} b^{\frac{55}{2}} x^{4} \sqrt{\frac{a}{b x^{2}} + 1}}{153153 a^{11} b^{25} x^{16} + 765765 a^{10} b^{26} x^{18} + 1531530 a^{9} b^{27} x^{20} + 1531530 a^{8} b^{28} x^{22} + 765765 a^{7} b^{29} x^{24} + 153153 a^{6} b^{30} x^{26}} - \frac{363888 a^{10} b^{\frac{57}{2}} x^{6} \sqrt{\frac{a}{b x^{2}} + 1}}{153153 a^{11} b^{25} x^{16} + 765765 a^{10} b^{26} x^{18} + 1531530 a^{9} b^{27} x^{20} + 1531530 a^{8} b^{28} x^{22} + 765765 a^{7} b^{29} x^{24} + 153153 a^{6} b^{30} x^{26}} - \frac{382550 a^{9} b^{\frac{59}{2}} x^{8} \sqrt{\frac{a}{b x^{2}} + 1}}{153153 a^{11} b^{25} x^{16} + 765765 a^{10} b^{26} x^{18} + 1531530 a^{9} b^{27} x^{20} + 1531530 a^{8} b^{28} x^{22} + 765765 a^{7} b^{29} x^{24} + 153153 a^{6} b^{30} x^{26}} - \frac{241524 a^{8} b^{\frac{61}{2}} x^{10} \sqrt{\frac{a}{b x^{2}} + 1}}{153153 a^{11} b^{25} x^{16} + 765765 a^{10} b^{26} x^{18} + 1531530 a^{9} b^{27} x^{20} + 1531530 a^{8} b^{28} x^{22} + 765765 a^{7} b^{29} x^{24} + 153153 a^{6} b^{30} x^{26}} - \frac{84780 a^{7} b^{\frac{63}{2}} x^{12} \sqrt{\frac{a}{b x^{2}} + 1}}{153153 a^{11} b^{25} x^{16} + 765765 a^{10} b^{26} x^{18} + 1531530 a^{9} b^{27} x^{20} + 1531530 a^{8} b^{28} x^{22} + 765765 a^{7} b^{29} x^{24} + 153153 a^{6} b^{30} x^{26}} - \frac{12768 a^{6} b^{\frac{65}{2}} x^{14} \sqrt{\frac{a}{b x^{2}} + 1}}{153153 a^{11} b^{25} x^{16} + 765765 a^{10} b^{26} x^{18} + 1531530 a^{9} b^{27} x^{20} + 1531530 a^{8} b^{28} x^{22} + 765765 a^{7} b^{29} x^{24} + 153153 a^{6} b^{30} x^{26}} + \frac{63 a^{5} b^{\frac{67}{2}} x^{16} \sqrt{\frac{a}{b x^{2}} + 1}}{153153 a^{11} b^{25} x^{16} + 765765 a^{10} b^{26} x^{18} + 1531530 a^{9} b^{27} x^{20} + 1531530 a^{8} b^{28} x^{22} + 765765 a^{7} b^{29} x^{24} + 153153 a^{6} b^{30} x^{26}} + \frac{630 a^{4} b^{\frac{69}{2}} x^{18} \sqrt{\frac{a}{b x^{2}} + 1}}{153153 a^{11} b^{25} x^{16} + 765765 a^{10} b^{26} x^{18} + 1531530 a^{9} b^{27} x^{20} + 1531530 a^{8} b^{28} x^{22} + 765765 a^{7} b^{29} x^{24} + 153153 a^{6} b^{30} x^{26}} + \frac{1680 a^{3} b^{\frac{71}{2}} x^{20} \sqrt{\frac{a}{b x^{2}} + 1}}{153153 a^{11} b^{25} x^{16} + 765765 a^{10} b^{26} x^{18} + 1531530 a^{9} b^{27} x^{20} + 1531530 a^{8} b^{28} x^{22} + 765765 a^{7} b^{29} x^{24} + 153153 a^{6} b^{30} x^{26}} + \frac{2016 a^{2} b^{\frac{73}{2}} x^{22} \sqrt{\frac{a}{b x^{2}} + 1}}{153153 a^{11} b^{25} x^{16} + 765765 a^{10} b^{26} x^{18} + 1531530 a^{9} b^{27} x^{20} + 1531530 a^{8} b^{28} x^{22} + 765765 a^{7} b^{29} x^{24} + 153153 a^{6} b^{30} x^{26}} + \frac{1152 a b^{\frac{75}{2}} x^{24} \sqrt{\frac{a}{b x^{2}} + 1}}{153153 a^{11} b^{25} x^{16} + 765765 a^{10} b^{26} x^{18} + 1531530 a^{9} b^{27} x^{20} + 1531530 a^{8} b^{28} x^{22} + 765765 a^{7} b^{29} x^{24} + 153153 a^{6} b^{30} x^{26}} + \frac{256 b^{\frac{77}{2}} x^{26} \sqrt{\frac{a}{b x^{2}} + 1}}{153153 a^{11} b^{25} x^{16} + 765765 a^{10} b^{26} x^{18} + 1531530 a^{9} b^{27} x^{20} + 1531530 a^{8} b^{28} x^{22} + 765765 a^{7} b^{29} x^{24} + 153153 a^{6} b^{30} x^{26}}"," ",0,"-9009*a**13*b**(51/2)*sqrt(a/(b*x**2) + 1)/(153153*a**11*b**25*x**16 + 765765*a**10*b**26*x**18 + 1531530*a**9*b**27*x**20 + 1531530*a**8*b**28*x**22 + 765765*a**7*b**29*x**24 + 153153*a**6*b**30*x**26) - 66066*a**12*b**(53/2)*x**2*sqrt(a/(b*x**2) + 1)/(153153*a**11*b**25*x**16 + 765765*a**10*b**26*x**18 + 1531530*a**9*b**27*x**20 + 1531530*a**8*b**28*x**22 + 765765*a**7*b**29*x**24 + 153153*a**6*b**30*x**26) - 207900*a**11*b**(55/2)*x**4*sqrt(a/(b*x**2) + 1)/(153153*a**11*b**25*x**16 + 765765*a**10*b**26*x**18 + 1531530*a**9*b**27*x**20 + 1531530*a**8*b**28*x**22 + 765765*a**7*b**29*x**24 + 153153*a**6*b**30*x**26) - 363888*a**10*b**(57/2)*x**6*sqrt(a/(b*x**2) + 1)/(153153*a**11*b**25*x**16 + 765765*a**10*b**26*x**18 + 1531530*a**9*b**27*x**20 + 1531530*a**8*b**28*x**22 + 765765*a**7*b**29*x**24 + 153153*a**6*b**30*x**26) - 382550*a**9*b**(59/2)*x**8*sqrt(a/(b*x**2) + 1)/(153153*a**11*b**25*x**16 + 765765*a**10*b**26*x**18 + 1531530*a**9*b**27*x**20 + 1531530*a**8*b**28*x**22 + 765765*a**7*b**29*x**24 + 153153*a**6*b**30*x**26) - 241524*a**8*b**(61/2)*x**10*sqrt(a/(b*x**2) + 1)/(153153*a**11*b**25*x**16 + 765765*a**10*b**26*x**18 + 1531530*a**9*b**27*x**20 + 1531530*a**8*b**28*x**22 + 765765*a**7*b**29*x**24 + 153153*a**6*b**30*x**26) - 84780*a**7*b**(63/2)*x**12*sqrt(a/(b*x**2) + 1)/(153153*a**11*b**25*x**16 + 765765*a**10*b**26*x**18 + 1531530*a**9*b**27*x**20 + 1531530*a**8*b**28*x**22 + 765765*a**7*b**29*x**24 + 153153*a**6*b**30*x**26) - 12768*a**6*b**(65/2)*x**14*sqrt(a/(b*x**2) + 1)/(153153*a**11*b**25*x**16 + 765765*a**10*b**26*x**18 + 1531530*a**9*b**27*x**20 + 1531530*a**8*b**28*x**22 + 765765*a**7*b**29*x**24 + 153153*a**6*b**30*x**26) + 63*a**5*b**(67/2)*x**16*sqrt(a/(b*x**2) + 1)/(153153*a**11*b**25*x**16 + 765765*a**10*b**26*x**18 + 1531530*a**9*b**27*x**20 + 1531530*a**8*b**28*x**22 + 765765*a**7*b**29*x**24 + 153153*a**6*b**30*x**26) + 630*a**4*b**(69/2)*x**18*sqrt(a/(b*x**2) + 1)/(153153*a**11*b**25*x**16 + 765765*a**10*b**26*x**18 + 1531530*a**9*b**27*x**20 + 1531530*a**8*b**28*x**22 + 765765*a**7*b**29*x**24 + 153153*a**6*b**30*x**26) + 1680*a**3*b**(71/2)*x**20*sqrt(a/(b*x**2) + 1)/(153153*a**11*b**25*x**16 + 765765*a**10*b**26*x**18 + 1531530*a**9*b**27*x**20 + 1531530*a**8*b**28*x**22 + 765765*a**7*b**29*x**24 + 153153*a**6*b**30*x**26) + 2016*a**2*b**(73/2)*x**22*sqrt(a/(b*x**2) + 1)/(153153*a**11*b**25*x**16 + 765765*a**10*b**26*x**18 + 1531530*a**9*b**27*x**20 + 1531530*a**8*b**28*x**22 + 765765*a**7*b**29*x**24 + 153153*a**6*b**30*x**26) + 1152*a*b**(75/2)*x**24*sqrt(a/(b*x**2) + 1)/(153153*a**11*b**25*x**16 + 765765*a**10*b**26*x**18 + 1531530*a**9*b**27*x**20 + 1531530*a**8*b**28*x**22 + 765765*a**7*b**29*x**24 + 153153*a**6*b**30*x**26) + 256*b**(77/2)*x**26*sqrt(a/(b*x**2) + 1)/(153153*a**11*b**25*x**16 + 765765*a**10*b**26*x**18 + 1531530*a**9*b**27*x**20 + 1531530*a**8*b**28*x**22 + 765765*a**7*b**29*x**24 + 153153*a**6*b**30*x**26)","B",0
409,1,301,0,103.128589," ","integrate(x**15*(b*x**2+a)**(9/2),x)","\begin{cases} - \frac{2048 a^{12} \sqrt{a + b x^{2}}}{26558675 b^{8}} + \frac{1024 a^{11} x^{2} \sqrt{a + b x^{2}}}{26558675 b^{7}} - \frac{768 a^{10} x^{4} \sqrt{a + b x^{2}}}{26558675 b^{6}} + \frac{128 a^{9} x^{6} \sqrt{a + b x^{2}}}{5311735 b^{5}} - \frac{112 a^{8} x^{8} \sqrt{a + b x^{2}}}{5311735 b^{4}} + \frac{504 a^{7} x^{10} \sqrt{a + b x^{2}}}{26558675 b^{3}} - \frac{42 a^{6} x^{12} \sqrt{a + b x^{2}}}{2414425 b^{2}} + \frac{3 a^{5} x^{14} \sqrt{a + b x^{2}}}{185725 b} + \frac{2321 a^{4} x^{16} \sqrt{a + b x^{2}}}{37145} + \frac{478 a^{3} b x^{18} \sqrt{a + b x^{2}}}{2185} + \frac{168 a^{2} b^{2} x^{20} \sqrt{a + b x^{2}}}{575} + \frac{101 a b^{3} x^{22} \sqrt{a + b x^{2}}}{575} + \frac{b^{4} x^{24} \sqrt{a + b x^{2}}}{25} & \text{for}\: b \neq 0 \\\frac{a^{\frac{9}{2}} x^{16}}{16} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2048*a**12*sqrt(a + b*x**2)/(26558675*b**8) + 1024*a**11*x**2*sqrt(a + b*x**2)/(26558675*b**7) - 768*a**10*x**4*sqrt(a + b*x**2)/(26558675*b**6) + 128*a**9*x**6*sqrt(a + b*x**2)/(5311735*b**5) - 112*a**8*x**8*sqrt(a + b*x**2)/(5311735*b**4) + 504*a**7*x**10*sqrt(a + b*x**2)/(26558675*b**3) - 42*a**6*x**12*sqrt(a + b*x**2)/(2414425*b**2) + 3*a**5*x**14*sqrt(a + b*x**2)/(185725*b) + 2321*a**4*x**16*sqrt(a + b*x**2)/37145 + 478*a**3*b*x**18*sqrt(a + b*x**2)/2185 + 168*a**2*b**2*x**20*sqrt(a + b*x**2)/575 + 101*a*b**3*x**22*sqrt(a + b*x**2)/575 + b**4*x**24*sqrt(a + b*x**2)/25, Ne(b, 0)), (a**(9/2)*x**16/16, True))","A",0
410,1,277,0,79.369527," ","integrate(x**13*(b*x**2+a)**(9/2),x)","\begin{cases} \frac{1024 a^{11} \sqrt{a + b x^{2}}}{7436429 b^{7}} - \frac{512 a^{10} x^{2} \sqrt{a + b x^{2}}}{7436429 b^{6}} + \frac{384 a^{9} x^{4} \sqrt{a + b x^{2}}}{7436429 b^{5}} - \frac{320 a^{8} x^{6} \sqrt{a + b x^{2}}}{7436429 b^{4}} + \frac{40 a^{7} x^{8} \sqrt{a + b x^{2}}}{1062347 b^{3}} - \frac{36 a^{6} x^{10} \sqrt{a + b x^{2}}}{1062347 b^{2}} + \frac{3 a^{5} x^{12} \sqrt{a + b x^{2}}}{96577 b} + \frac{3713 a^{4} x^{14} \sqrt{a + b x^{2}}}{52003} + \frac{12770 a^{3} b x^{16} \sqrt{a + b x^{2}}}{52003} + \frac{990 a^{2} b^{2} x^{18} \sqrt{a + b x^{2}}}{3059} + \frac{31 a b^{3} x^{20} \sqrt{a + b x^{2}}}{161} + \frac{b^{4} x^{22} \sqrt{a + b x^{2}}}{23} & \text{for}\: b \neq 0 \\\frac{a^{\frac{9}{2}} x^{14}}{14} & \text{otherwise} \end{cases}"," ",0,"Piecewise((1024*a**11*sqrt(a + b*x**2)/(7436429*b**7) - 512*a**10*x**2*sqrt(a + b*x**2)/(7436429*b**6) + 384*a**9*x**4*sqrt(a + b*x**2)/(7436429*b**5) - 320*a**8*x**6*sqrt(a + b*x**2)/(7436429*b**4) + 40*a**7*x**8*sqrt(a + b*x**2)/(1062347*b**3) - 36*a**6*x**10*sqrt(a + b*x**2)/(1062347*b**2) + 3*a**5*x**12*sqrt(a + b*x**2)/(96577*b) + 3713*a**4*x**14*sqrt(a + b*x**2)/52003 + 12770*a**3*b*x**16*sqrt(a + b*x**2)/52003 + 990*a**2*b**2*x**18*sqrt(a + b*x**2)/3059 + 31*a*b**3*x**20*sqrt(a + b*x**2)/161 + b**4*x**22*sqrt(a + b*x**2)/23, Ne(b, 0)), (a**(9/2)*x**14/14, True))","A",0
411,1,253,0,62.850326," ","integrate(x**11*(b*x**2+a)**(9/2),x)","\begin{cases} - \frac{256 a^{10} \sqrt{a + b x^{2}}}{969969 b^{6}} + \frac{128 a^{9} x^{2} \sqrt{a + b x^{2}}}{969969 b^{5}} - \frac{32 a^{8} x^{4} \sqrt{a + b x^{2}}}{323323 b^{4}} + \frac{80 a^{7} x^{6} \sqrt{a + b x^{2}}}{969969 b^{3}} - \frac{10 a^{6} x^{8} \sqrt{a + b x^{2}}}{138567 b^{2}} + \frac{3 a^{5} x^{10} \sqrt{a + b x^{2}}}{46189 b} + \frac{1049 a^{4} x^{12} \sqrt{a + b x^{2}}}{12597} + \frac{1898 a^{3} b x^{14} \sqrt{a + b x^{2}}}{6783} + \frac{820 a^{2} b^{2} x^{16} \sqrt{a + b x^{2}}}{2261} + \frac{85 a b^{3} x^{18} \sqrt{a + b x^{2}}}{399} + \frac{b^{4} x^{20} \sqrt{a + b x^{2}}}{21} & \text{for}\: b \neq 0 \\\frac{a^{\frac{9}{2}} x^{12}}{12} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-256*a**10*sqrt(a + b*x**2)/(969969*b**6) + 128*a**9*x**2*sqrt(a + b*x**2)/(969969*b**5) - 32*a**8*x**4*sqrt(a + b*x**2)/(323323*b**4) + 80*a**7*x**6*sqrt(a + b*x**2)/(969969*b**3) - 10*a**6*x**8*sqrt(a + b*x**2)/(138567*b**2) + 3*a**5*x**10*sqrt(a + b*x**2)/(46189*b) + 1049*a**4*x**12*sqrt(a + b*x**2)/12597 + 1898*a**3*b*x**14*sqrt(a + b*x**2)/6783 + 820*a**2*b**2*x**16*sqrt(a + b*x**2)/2261 + 85*a*b**3*x**18*sqrt(a + b*x**2)/399 + b**4*x**20*sqrt(a + b*x**2)/21, Ne(b, 0)), (a**(9/2)*x**12/12, True))","A",0
412,1,230,0,48.284676," ","integrate(x**9*(b*x**2+a)**(9/2),x)","\begin{cases} \frac{128 a^{9} \sqrt{a + b x^{2}}}{230945 b^{5}} - \frac{64 a^{8} x^{2} \sqrt{a + b x^{2}}}{230945 b^{4}} + \frac{48 a^{7} x^{4} \sqrt{a + b x^{2}}}{230945 b^{3}} - \frac{8 a^{6} x^{6} \sqrt{a + b x^{2}}}{46189 b^{2}} + \frac{7 a^{5} x^{8} \sqrt{a + b x^{2}}}{46189 b} + \frac{23063 a^{4} x^{10} \sqrt{a + b x^{2}}}{230945} + \frac{6826 a^{3} b x^{12} \sqrt{a + b x^{2}}}{20995} + \frac{666 a^{2} b^{2} x^{14} \sqrt{a + b x^{2}}}{1615} + \frac{77 a b^{3} x^{16} \sqrt{a + b x^{2}}}{323} + \frac{b^{4} x^{18} \sqrt{a + b x^{2}}}{19} & \text{for}\: b \neq 0 \\\frac{a^{\frac{9}{2}} x^{10}}{10} & \text{otherwise} \end{cases}"," ",0,"Piecewise((128*a**9*sqrt(a + b*x**2)/(230945*b**5) - 64*a**8*x**2*sqrt(a + b*x**2)/(230945*b**4) + 48*a**7*x**4*sqrt(a + b*x**2)/(230945*b**3) - 8*a**6*x**6*sqrt(a + b*x**2)/(46189*b**2) + 7*a**5*x**8*sqrt(a + b*x**2)/(46189*b) + 23063*a**4*x**10*sqrt(a + b*x**2)/230945 + 6826*a**3*b*x**12*sqrt(a + b*x**2)/20995 + 666*a**2*b**2*x**14*sqrt(a + b*x**2)/1615 + 77*a*b**3*x**16*sqrt(a + b*x**2)/323 + b**4*x**18*sqrt(a + b*x**2)/19, Ne(b, 0)), (a**(9/2)*x**10/10, True))","A",0
413,1,204,0,37.198075," ","integrate(x**7*(b*x**2+a)**(9/2),x)","\begin{cases} - \frac{16 a^{8} \sqrt{a + b x^{2}}}{12155 b^{4}} + \frac{8 a^{7} x^{2} \sqrt{a + b x^{2}}}{12155 b^{3}} - \frac{6 a^{6} x^{4} \sqrt{a + b x^{2}}}{12155 b^{2}} + \frac{a^{5} x^{6} \sqrt{a + b x^{2}}}{2431 b} + \frac{303 a^{4} x^{8} \sqrt{a + b x^{2}}}{2431} + \frac{4714 a^{3} b x^{10} \sqrt{a + b x^{2}}}{12155} + \frac{528 a^{2} b^{2} x^{12} \sqrt{a + b x^{2}}}{1105} + \frac{23 a b^{3} x^{14} \sqrt{a + b x^{2}}}{85} + \frac{b^{4} x^{16} \sqrt{a + b x^{2}}}{17} & \text{for}\: b \neq 0 \\\frac{a^{\frac{9}{2}} x^{8}}{8} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-16*a**8*sqrt(a + b*x**2)/(12155*b**4) + 8*a**7*x**2*sqrt(a + b*x**2)/(12155*b**3) - 6*a**6*x**4*sqrt(a + b*x**2)/(12155*b**2) + a**5*x**6*sqrt(a + b*x**2)/(2431*b) + 303*a**4*x**8*sqrt(a + b*x**2)/2431 + 4714*a**3*b*x**10*sqrt(a + b*x**2)/12155 + 528*a**2*b**2*x**12*sqrt(a + b*x**2)/1105 + 23*a*b**3*x**14*sqrt(a + b*x**2)/85 + b**4*x**16*sqrt(a + b*x**2)/17, Ne(b, 0)), (a**(9/2)*x**8/8, True))","A",0
414,1,180,0,27.022150," ","integrate(x**5*(b*x**2+a)**(9/2),x)","\begin{cases} \frac{8 a^{7} \sqrt{a + b x^{2}}}{2145 b^{3}} - \frac{4 a^{6} x^{2} \sqrt{a + b x^{2}}}{2145 b^{2}} + \frac{a^{5} x^{4} \sqrt{a + b x^{2}}}{715 b} + \frac{71 a^{4} x^{6} \sqrt{a + b x^{2}}}{429} + \frac{206 a^{3} b x^{8} \sqrt{a + b x^{2}}}{429} + \frac{406 a^{2} b^{2} x^{10} \sqrt{a + b x^{2}}}{715} + \frac{61 a b^{3} x^{12} \sqrt{a + b x^{2}}}{195} + \frac{b^{4} x^{14} \sqrt{a + b x^{2}}}{15} & \text{for}\: b \neq 0 \\\frac{a^{\frac{9}{2}} x^{6}}{6} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*a**7*sqrt(a + b*x**2)/(2145*b**3) - 4*a**6*x**2*sqrt(a + b*x**2)/(2145*b**2) + a**5*x**4*sqrt(a + b*x**2)/(715*b) + 71*a**4*x**6*sqrt(a + b*x**2)/429 + 206*a**3*b*x**8*sqrt(a + b*x**2)/429 + 406*a**2*b**2*x**10*sqrt(a + b*x**2)/715 + 61*a*b**3*x**12*sqrt(a + b*x**2)/195 + b**4*x**14*sqrt(a + b*x**2)/15, Ne(b, 0)), (a**(9/2)*x**6/6, True))","A",0
415,1,156,0,18.496051," ","integrate(x**3*(b*x**2+a)**(9/2),x)","\begin{cases} - \frac{2 a^{6} \sqrt{a + b x^{2}}}{143 b^{2}} + \frac{a^{5} x^{2} \sqrt{a + b x^{2}}}{143 b} + \frac{35 a^{4} x^{4} \sqrt{a + b x^{2}}}{143} + \frac{90 a^{3} b x^{6} \sqrt{a + b x^{2}}}{143} + \frac{100 a^{2} b^{2} x^{8} \sqrt{a + b x^{2}}}{143} + \frac{53 a b^{3} x^{10} \sqrt{a + b x^{2}}}{143} + \frac{b^{4} x^{12} \sqrt{a + b x^{2}}}{13} & \text{for}\: b \neq 0 \\\frac{a^{\frac{9}{2}} x^{4}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*a**6*sqrt(a + b*x**2)/(143*b**2) + a**5*x**2*sqrt(a + b*x**2)/(143*b) + 35*a**4*x**4*sqrt(a + b*x**2)/143 + 90*a**3*b*x**6*sqrt(a + b*x**2)/143 + 100*a**2*b**2*x**8*sqrt(a + b*x**2)/143 + 53*a*b**3*x**10*sqrt(a + b*x**2)/143 + b**4*x**12*sqrt(a + b*x**2)/13, Ne(b, 0)), (a**(9/2)*x**4/4, True))","A",0
416,1,133,0,12.959875," ","integrate(x*(b*x**2+a)**(9/2),x)","\begin{cases} \frac{a^{5} \sqrt{a + b x^{2}}}{11 b} + \frac{5 a^{4} x^{2} \sqrt{a + b x^{2}}}{11} + \frac{10 a^{3} b x^{4} \sqrt{a + b x^{2}}}{11} + \frac{10 a^{2} b^{2} x^{6} \sqrt{a + b x^{2}}}{11} + \frac{5 a b^{3} x^{8} \sqrt{a + b x^{2}}}{11} + \frac{b^{4} x^{10} \sqrt{a + b x^{2}}}{11} & \text{for}\: b \neq 0 \\\frac{a^{\frac{9}{2}} x^{2}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**5*sqrt(a + b*x**2)/(11*b) + 5*a**4*x**2*sqrt(a + b*x**2)/11 + 10*a**3*b*x**4*sqrt(a + b*x**2)/11 + 10*a**2*b**2*x**6*sqrt(a + b*x**2)/11 + 5*a*b**3*x**8*sqrt(a + b*x**2)/11 + b**4*x**10*sqrt(a + b*x**2)/11, Ne(b, 0)), (a**(9/2)*x**2/2, True))","A",0
417,1,160,0,10.477385," ","integrate((b*x**2+a)**(9/2)/x,x)","\frac{563 a^{\frac{9}{2}} \sqrt{1 + \frac{b x^{2}}{a}}}{315} + \frac{a^{\frac{9}{2}} \log{\left(\frac{b x^{2}}{a} \right)}}{2} - a^{\frac{9}{2}} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)} + \frac{506 a^{\frac{7}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}}}{315} + \frac{136 a^{\frac{5}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}}}{105} + \frac{37 a^{\frac{3}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}}}{63} + \frac{\sqrt{a} b^{4} x^{8} \sqrt{1 + \frac{b x^{2}}{a}}}{9}"," ",0,"563*a**(9/2)*sqrt(1 + b*x**2/a)/315 + a**(9/2)*log(b*x**2/a)/2 - a**(9/2)*log(sqrt(1 + b*x**2/a) + 1) + 506*a**(7/2)*b*x**2*sqrt(1 + b*x**2/a)/315 + 136*a**(5/2)*b**2*x**4*sqrt(1 + b*x**2/a)/105 + 37*a**(3/2)*b**3*x**6*sqrt(1 + b*x**2/a)/63 + sqrt(a)*b**4*x**8*sqrt(1 + b*x**2/a)/9","A",0
418,1,167,0,9.267422," ","integrate((b*x**2+a)**(9/2)/x**3,x)","- \frac{a^{\frac{9}{2}} \sqrt{1 + \frac{b x^{2}}{a}}}{2 x^{2}} + \frac{194 a^{\frac{7}{2}} b \sqrt{1 + \frac{b x^{2}}{a}}}{35} + \frac{9 a^{\frac{7}{2}} b \log{\left(\frac{b x^{2}}{a} \right)}}{4} - \frac{9 a^{\frac{7}{2}} b \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{2} + \frac{78 a^{\frac{5}{2}} b^{2} x^{2} \sqrt{1 + \frac{b x^{2}}{a}}}{35} + \frac{29 a^{\frac{3}{2}} b^{3} x^{4} \sqrt{1 + \frac{b x^{2}}{a}}}{35} + \frac{\sqrt{a} b^{4} x^{6} \sqrt{1 + \frac{b x^{2}}{a}}}{7}"," ",0,"-a**(9/2)*sqrt(1 + b*x**2/a)/(2*x**2) + 194*a**(7/2)*b*sqrt(1 + b*x**2/a)/35 + 9*a**(7/2)*b*log(b*x**2/a)/4 - 9*a**(7/2)*b*log(sqrt(1 + b*x**2/a) + 1)/2 + 78*a**(5/2)*b**2*x**2*sqrt(1 + b*x**2/a)/35 + 29*a**(3/2)*b**3*x**4*sqrt(1 + b*x**2/a)/35 + sqrt(a)*b**4*x**6*sqrt(1 + b*x**2/a)/7","A",0
419,1,175,0,8.727420," ","integrate((b*x**2+a)**(9/2)/x**5,x)","- \frac{63 a^{\frac{5}{2}} b^{2} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)}}{8} - \frac{a^{5}}{4 \sqrt{b} x^{5} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{19 a^{4} \sqrt{b}}{8 x^{3} \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{203 a^{3} b^{\frac{3}{2}}}{40 x \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{43 a^{2} b^{\frac{5}{2}} x}{5 \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{8 a b^{\frac{7}{2}} x^{3}}{5 \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{b^{\frac{9}{2}} x^{5}}{5 \sqrt{\frac{a}{b x^{2}} + 1}}"," ",0,"-63*a**(5/2)*b**2*asinh(sqrt(a)/(sqrt(b)*x))/8 - a**5/(4*sqrt(b)*x**5*sqrt(a/(b*x**2) + 1)) - 19*a**4*sqrt(b)/(8*x**3*sqrt(a/(b*x**2) + 1)) + 203*a**3*b**(3/2)/(40*x*sqrt(a/(b*x**2) + 1)) + 43*a**2*b**(5/2)*x/(5*sqrt(a/(b*x**2) + 1)) + 8*a*b**(7/2)*x**3/(5*sqrt(a/(b*x**2) + 1)) + b**(9/2)*x**5/(5*sqrt(a/(b*x**2) + 1))","A",0
420,1,175,0,7.118423," ","integrate((b*x**2+a)**(9/2)/x**7,x)","- \frac{105 a^{\frac{3}{2}} b^{3} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)}}{16} - \frac{a^{5}}{6 \sqrt{b} x^{7} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{29 a^{4} \sqrt{b}}{24 x^{5} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{215 a^{3} b^{\frac{3}{2}}}{48 x^{3} \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{43 a^{2} b^{\frac{5}{2}}}{48 x \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{14 a b^{\frac{7}{2}} x}{3 \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{b^{\frac{9}{2}} x^{3}}{3 \sqrt{\frac{a}{b x^{2}} + 1}}"," ",0,"-105*a**(3/2)*b**3*asinh(sqrt(a)/(sqrt(b)*x))/16 - a**5/(6*sqrt(b)*x**7*sqrt(a/(b*x**2) + 1)) - 29*a**4*sqrt(b)/(24*x**5*sqrt(a/(b*x**2) + 1)) - 215*a**3*b**(3/2)/(48*x**3*sqrt(a/(b*x**2) + 1)) + 43*a**2*b**(5/2)/(48*x*sqrt(a/(b*x**2) + 1)) + 14*a*b**(7/2)*x/(3*sqrt(a/(b*x**2) + 1)) + b**(9/2)*x**3/(3*sqrt(a/(b*x**2) + 1))","A",0
421,1,173,0,7.741432," ","integrate((b*x**2+a)**(9/2)/x**9,x)","- \frac{315 \sqrt{a} b^{4} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)}}{128} - \frac{a^{5}}{8 \sqrt{b} x^{9} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{13 a^{4} \sqrt{b}}{16 x^{7} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{149 a^{3} b^{\frac{3}{2}}}{64 x^{5} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{535 a^{2} b^{\frac{5}{2}}}{128 x^{3} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{197 a b^{\frac{7}{2}}}{128 x \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{b^{\frac{9}{2}} x}{\sqrt{\frac{a}{b x^{2}} + 1}}"," ",0,"-315*sqrt(a)*b**4*asinh(sqrt(a)/(sqrt(b)*x))/128 - a**5/(8*sqrt(b)*x**9*sqrt(a/(b*x**2) + 1)) - 13*a**4*sqrt(b)/(16*x**7*sqrt(a/(b*x**2) + 1)) - 149*a**3*b**(3/2)/(64*x**5*sqrt(a/(b*x**2) + 1)) - 535*a**2*b**(5/2)/(128*x**3*sqrt(a/(b*x**2) + 1)) - 197*a*b**(7/2)/(128*x*sqrt(a/(b*x**2) + 1)) + b**(9/2)*x/sqrt(a/(b*x**2) + 1)","A",0
422,1,153,0,9.313871," ","integrate((b*x**2+a)**(9/2)/x**11,x)","- \frac{a^{4} \sqrt{b} \sqrt{\frac{a}{b x^{2}} + 1}}{10 x^{9}} - \frac{41 a^{3} b^{\frac{3}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{80 x^{7}} - \frac{171 a^{2} b^{\frac{5}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{160 x^{5}} - \frac{149 a b^{\frac{7}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{128 x^{3}} - \frac{193 b^{\frac{9}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{256 x} - \frac{63 b^{5} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)}}{256 \sqrt{a}}"," ",0,"-a**4*sqrt(b)*sqrt(a/(b*x**2) + 1)/(10*x**9) - 41*a**3*b**(3/2)*sqrt(a/(b*x**2) + 1)/(80*x**7) - 171*a**2*b**(5/2)*sqrt(a/(b*x**2) + 1)/(160*x**5) - 149*a*b**(7/2)*sqrt(a/(b*x**2) + 1)/(128*x**3) - 193*b**(9/2)*sqrt(a/(b*x**2) + 1)/(256*x) - 63*b**5*asinh(sqrt(a)/(sqrt(b)*x))/(256*sqrt(a))","A",0
423,1,204,0,14.979151," ","integrate((b*x**2+a)**(9/2)/x**13,x)","- \frac{a^{5}}{12 \sqrt{b} x^{13} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{59 a^{4} \sqrt{b}}{120 x^{11} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{1151 a^{3} b^{\frac{3}{2}}}{960 x^{9} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{2947 a^{2} b^{\frac{5}{2}}}{1920 x^{7} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{8171 a b^{\frac{7}{2}}}{7680 x^{5} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{1045 b^{\frac{9}{2}}}{3072 x^{3} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{21 b^{\frac{11}{2}}}{1024 a x \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{21 b^{6} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)}}{1024 a^{\frac{3}{2}}}"," ",0,"-a**5/(12*sqrt(b)*x**13*sqrt(a/(b*x**2) + 1)) - 59*a**4*sqrt(b)/(120*x**11*sqrt(a/(b*x**2) + 1)) - 1151*a**3*b**(3/2)/(960*x**9*sqrt(a/(b*x**2) + 1)) - 2947*a**2*b**(5/2)/(1920*x**7*sqrt(a/(b*x**2) + 1)) - 8171*a*b**(7/2)/(7680*x**5*sqrt(a/(b*x**2) + 1)) - 1045*b**(9/2)/(3072*x**3*sqrt(a/(b*x**2) + 1)) - 21*b**(11/2)/(1024*a*x*sqrt(a/(b*x**2) + 1)) + 21*b**6*asinh(sqrt(a)/(sqrt(b)*x))/(1024*a**(3/2))","A",0
424,1,231,0,21.818686," ","integrate((b*x**2+a)**(9/2)/x**15,x)","- \frac{a^{5}}{14 \sqrt{b} x^{15} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{23 a^{4} \sqrt{b}}{56 x^{13} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{541 a^{3} b^{\frac{3}{2}}}{560 x^{11} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{5249 a^{2} b^{\frac{5}{2}}}{4480 x^{9} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{6653 a b^{\frac{7}{2}}}{8960 x^{7} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{1027 b^{\frac{9}{2}}}{5120 x^{5} \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{3 b^{\frac{11}{2}}}{2048 a x^{3} \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{9 b^{\frac{13}{2}}}{2048 a^{2} x \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{9 b^{7} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)}}{2048 a^{\frac{5}{2}}}"," ",0,"-a**5/(14*sqrt(b)*x**15*sqrt(a/(b*x**2) + 1)) - 23*a**4*sqrt(b)/(56*x**13*sqrt(a/(b*x**2) + 1)) - 541*a**3*b**(3/2)/(560*x**11*sqrt(a/(b*x**2) + 1)) - 5249*a**2*b**(5/2)/(4480*x**9*sqrt(a/(b*x**2) + 1)) - 6653*a*b**(7/2)/(8960*x**7*sqrt(a/(b*x**2) + 1)) - 1027*b**(9/2)/(5120*x**5*sqrt(a/(b*x**2) + 1)) + 3*b**(11/2)/(2048*a*x**3*sqrt(a/(b*x**2) + 1)) + 9*b**(13/2)/(2048*a**2*x*sqrt(a/(b*x**2) + 1)) - 9*b**7*asinh(sqrt(a)/(sqrt(b)*x))/(2048*a**(5/2))","A",0
425,1,258,0,30.595290," ","integrate(x**6*(b*x**2+a)**(9/2),x)","\frac{45 a^{\frac{15}{2}} x}{32768 b^{3} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{15 a^{\frac{13}{2}} x^{3}}{32768 b^{2} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{3 a^{\frac{11}{2}} x^{5}}{16384 b \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{4099 a^{\frac{9}{2}} x^{7}}{28672 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{8191 a^{\frac{7}{2}} b x^{9}}{14336 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{1699 a^{\frac{5}{2}} b^{2} x^{11}}{1792 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{725 a^{\frac{3}{2}} b^{3} x^{13}}{896 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{79 \sqrt{a} b^{4} x^{15}}{224 \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{45 a^{8} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{32768 b^{\frac{7}{2}}} + \frac{b^{5} x^{17}}{16 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"45*a**(15/2)*x/(32768*b**3*sqrt(1 + b*x**2/a)) + 15*a**(13/2)*x**3/(32768*b**2*sqrt(1 + b*x**2/a)) - 3*a**(11/2)*x**5/(16384*b*sqrt(1 + b*x**2/a)) + 4099*a**(9/2)*x**7/(28672*sqrt(1 + b*x**2/a)) + 8191*a**(7/2)*b*x**9/(14336*sqrt(1 + b*x**2/a)) + 1699*a**(5/2)*b**2*x**11/(1792*sqrt(1 + b*x**2/a)) + 725*a**(3/2)*b**3*x**13/(896*sqrt(1 + b*x**2/a)) + 79*sqrt(a)*b**4*x**15/(224*sqrt(1 + b*x**2/a)) - 45*a**8*asinh(sqrt(b)*x/sqrt(a))/(32768*b**(7/2)) + b**5*x**17/(16*sqrt(a)*sqrt(1 + b*x**2/a))","A",0
426,1,231,0,20.001201," ","integrate(x**4*(b*x**2+a)**(9/2),x)","- \frac{9 a^{\frac{13}{2}} x}{2048 b^{2} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{3 a^{\frac{11}{2}} x^{3}}{2048 b \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{1027 a^{\frac{9}{2}} x^{5}}{5120 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{6653 a^{\frac{7}{2}} b x^{7}}{8960 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{5249 a^{\frac{5}{2}} b^{2} x^{9}}{4480 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{541 a^{\frac{3}{2}} b^{3} x^{11}}{560 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{23 \sqrt{a} b^{4} x^{13}}{56 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{9 a^{7} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{2048 b^{\frac{5}{2}}} + \frac{b^{5} x^{15}}{14 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"-9*a**(13/2)*x/(2048*b**2*sqrt(1 + b*x**2/a)) - 3*a**(11/2)*x**3/(2048*b*sqrt(1 + b*x**2/a)) + 1027*a**(9/2)*x**5/(5120*sqrt(1 + b*x**2/a)) + 6653*a**(7/2)*b*x**7/(8960*sqrt(1 + b*x**2/a)) + 5249*a**(5/2)*b**2*x**9/(4480*sqrt(1 + b*x**2/a)) + 541*a**(3/2)*b**3*x**11/(560*sqrt(1 + b*x**2/a)) + 23*sqrt(a)*b**4*x**13/(56*sqrt(1 + b*x**2/a)) + 9*a**7*asinh(sqrt(b)*x/sqrt(a))/(2048*b**(5/2)) + b**5*x**15/(14*sqrt(a)*sqrt(1 + b*x**2/a))","A",0
427,1,204,0,13.568438," ","integrate(x**2*(b*x**2+a)**(9/2),x)","\frac{21 a^{\frac{11}{2}} x}{1024 b \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{1045 a^{\frac{9}{2}} x^{3}}{3072 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{8171 a^{\frac{7}{2}} b x^{5}}{7680 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{2947 a^{\frac{5}{2}} b^{2} x^{7}}{1920 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{1151 a^{\frac{3}{2}} b^{3} x^{9}}{960 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{59 \sqrt{a} b^{4} x^{11}}{120 \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{21 a^{6} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{1024 b^{\frac{3}{2}}} + \frac{b^{5} x^{13}}{12 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"21*a**(11/2)*x/(1024*b*sqrt(1 + b*x**2/a)) + 1045*a**(9/2)*x**3/(3072*sqrt(1 + b*x**2/a)) + 8171*a**(7/2)*b*x**5/(7680*sqrt(1 + b*x**2/a)) + 2947*a**(5/2)*b**2*x**7/(1920*sqrt(1 + b*x**2/a)) + 1151*a**(3/2)*b**3*x**9/(960*sqrt(1 + b*x**2/a)) + 59*sqrt(a)*b**4*x**11/(120*sqrt(1 + b*x**2/a)) - 21*a**6*asinh(sqrt(b)*x/sqrt(a))/(1024*b**(3/2)) + b**5*x**13/(12*sqrt(a)*sqrt(1 + b*x**2/a))","A",0
428,1,151,0,8.347919," ","integrate((b*x**2+a)**(9/2),x)","\frac{193 a^{\frac{9}{2}} x \sqrt{1 + \frac{b x^{2}}{a}}}{256} + \frac{149 a^{\frac{7}{2}} b x^{3} \sqrt{1 + \frac{b x^{2}}{a}}}{128} + \frac{171 a^{\frac{5}{2}} b^{2} x^{5} \sqrt{1 + \frac{b x^{2}}{a}}}{160} + \frac{41 a^{\frac{3}{2}} b^{3} x^{7} \sqrt{1 + \frac{b x^{2}}{a}}}{80} + \frac{\sqrt{a} b^{4} x^{9} \sqrt{1 + \frac{b x^{2}}{a}}}{10} + \frac{63 a^{5} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{256 \sqrt{b}}"," ",0,"193*a**(9/2)*x*sqrt(1 + b*x**2/a)/256 + 149*a**(7/2)*b*x**3*sqrt(1 + b*x**2/a)/128 + 171*a**(5/2)*b**2*x**5*sqrt(1 + b*x**2/a)/160 + 41*a**(3/2)*b**3*x**7*sqrt(1 + b*x**2/a)/80 + sqrt(a)*b**4*x**9*sqrt(1 + b*x**2/a)/10 + 63*a**5*asinh(sqrt(b)*x/sqrt(a))/(256*sqrt(b))","A",0
429,1,173,0,7.465033," ","integrate((b*x**2+a)**(9/2)/x**2,x)","- \frac{a^{\frac{9}{2}}}{x \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{197 a^{\frac{7}{2}} b x}{128 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{535 a^{\frac{5}{2}} b^{2} x^{3}}{128 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{149 a^{\frac{3}{2}} b^{3} x^{5}}{64 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{13 \sqrt{a} b^{4} x^{7}}{16 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{315 a^{4} \sqrt{b} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{128} + \frac{b^{5} x^{9}}{8 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"-a**(9/2)/(x*sqrt(1 + b*x**2/a)) + 197*a**(7/2)*b*x/(128*sqrt(1 + b*x**2/a)) + 535*a**(5/2)*b**2*x**3/(128*sqrt(1 + b*x**2/a)) + 149*a**(3/2)*b**3*x**5/(64*sqrt(1 + b*x**2/a)) + 13*sqrt(a)*b**4*x**7/(16*sqrt(1 + b*x**2/a)) + 315*a**4*sqrt(b)*asinh(sqrt(b)*x/sqrt(a))/128 + b**5*x**9/(8*sqrt(a)*sqrt(1 + b*x**2/a))","A",0
430,1,175,0,6.843105," ","integrate((b*x**2+a)**(9/2)/x**4,x)","- \frac{a^{\frac{9}{2}}}{3 x^{3} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{14 a^{\frac{7}{2}} b}{3 x \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{43 a^{\frac{5}{2}} b^{2} x}{48 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{215 a^{\frac{3}{2}} b^{3} x^{3}}{48 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{29 \sqrt{a} b^{4} x^{5}}{24 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{105 a^{3} b^{\frac{3}{2}} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{16} + \frac{b^{5} x^{7}}{6 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"-a**(9/2)/(3*x**3*sqrt(1 + b*x**2/a)) - 14*a**(7/2)*b/(3*x*sqrt(1 + b*x**2/a)) - 43*a**(5/2)*b**2*x/(48*sqrt(1 + b*x**2/a)) + 215*a**(3/2)*b**3*x**3/(48*sqrt(1 + b*x**2/a)) + 29*sqrt(a)*b**4*x**5/(24*sqrt(1 + b*x**2/a)) + 105*a**3*b**(3/2)*asinh(sqrt(b)*x/sqrt(a))/16 + b**5*x**7/(6*sqrt(a)*sqrt(1 + b*x**2/a))","A",0
431,1,175,0,7.822883," ","integrate((b*x**2+a)**(9/2)/x**6,x)","- \frac{a^{\frac{9}{2}}}{5 x^{5} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{8 a^{\frac{7}{2}} b}{5 x^{3} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{43 a^{\frac{5}{2}} b^{2}}{5 x \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{203 a^{\frac{3}{2}} b^{3} x}{40 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{19 \sqrt{a} b^{4} x^{3}}{8 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{63 a^{2} b^{\frac{5}{2}} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{8} + \frac{b^{5} x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"-a**(9/2)/(5*x**5*sqrt(1 + b*x**2/a)) - 8*a**(7/2)*b/(5*x**3*sqrt(1 + b*x**2/a)) - 43*a**(5/2)*b**2/(5*x*sqrt(1 + b*x**2/a)) - 203*a**(3/2)*b**3*x/(40*sqrt(1 + b*x**2/a)) + 19*sqrt(a)*b**4*x**3/(8*sqrt(1 + b*x**2/a)) + 63*a**2*b**(5/2)*asinh(sqrt(b)*x/sqrt(a))/8 + b**5*x**5/(4*sqrt(a)*sqrt(1 + b*x**2/a))","A",0
432,1,167,0,8.787742," ","integrate((b*x**2+a)**(9/2)/x**8,x)","- \frac{a^{4} \sqrt{b} \sqrt{\frac{a}{b x^{2}} + 1}}{7 x^{6}} - \frac{29 a^{3} b^{\frac{3}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{35 x^{4}} - \frac{78 a^{2} b^{\frac{5}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{35 x^{2}} - \frac{194 a b^{\frac{7}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{35} - \frac{9 a b^{\frac{7}{2}} \log{\left(\frac{a}{b x^{2}} \right)}}{4} + \frac{9 a b^{\frac{7}{2}} \log{\left(\sqrt{\frac{a}{b x^{2}} + 1} + 1 \right)}}{2} + \frac{b^{\frac{9}{2}} x^{2} \sqrt{\frac{a}{b x^{2}} + 1}}{2}"," ",0,"-a**4*sqrt(b)*sqrt(a/(b*x**2) + 1)/(7*x**6) - 29*a**3*b**(3/2)*sqrt(a/(b*x**2) + 1)/(35*x**4) - 78*a**2*b**(5/2)*sqrt(a/(b*x**2) + 1)/(35*x**2) - 194*a*b**(7/2)*sqrt(a/(b*x**2) + 1)/35 - 9*a*b**(7/2)*log(a/(b*x**2))/4 + 9*a*b**(7/2)*log(sqrt(a/(b*x**2) + 1) + 1)/2 + b**(9/2)*x**2*sqrt(a/(b*x**2) + 1)/2","A",0
433,1,160,0,9.863020," ","integrate((b*x**2+a)**(9/2)/x**10,x)","- \frac{a^{4} \sqrt{b} \sqrt{\frac{a}{b x^{2}} + 1}}{9 x^{8}} - \frac{37 a^{3} b^{\frac{3}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{63 x^{6}} - \frac{136 a^{2} b^{\frac{5}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{105 x^{4}} - \frac{506 a b^{\frac{7}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{315 x^{2}} - \frac{563 b^{\frac{9}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{315} - \frac{b^{\frac{9}{2}} \log{\left(\frac{a}{b x^{2}} \right)}}{2} + b^{\frac{9}{2}} \log{\left(\sqrt{\frac{a}{b x^{2}} + 1} + 1 \right)}"," ",0,"-a**4*sqrt(b)*sqrt(a/(b*x**2) + 1)/(9*x**8) - 37*a**3*b**(3/2)*sqrt(a/(b*x**2) + 1)/(63*x**6) - 136*a**2*b**(5/2)*sqrt(a/(b*x**2) + 1)/(105*x**4) - 506*a*b**(7/2)*sqrt(a/(b*x**2) + 1)/(315*x**2) - 563*b**(9/2)*sqrt(a/(b*x**2) + 1)/315 - b**(9/2)*log(a/(b*x**2))/2 + b**(9/2)*log(sqrt(a/(b*x**2) + 1) + 1)","A",0
434,1,150,0,2.450257," ","integrate((b*x**2+a)**(9/2)/x**12,x)","- \frac{a^{4} \sqrt{b} \sqrt{\frac{a}{b x^{2}} + 1}}{11 x^{10}} - \frac{5 a^{3} b^{\frac{3}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{11 x^{8}} - \frac{10 a^{2} b^{\frac{5}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{11 x^{6}} - \frac{10 a b^{\frac{7}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{11 x^{4}} - \frac{5 b^{\frac{9}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{11 x^{2}} - \frac{b^{\frac{11}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{11 a}"," ",0,"-a**4*sqrt(b)*sqrt(a/(b*x**2) + 1)/(11*x**10) - 5*a**3*b**(3/2)*sqrt(a/(b*x**2) + 1)/(11*x**8) - 10*a**2*b**(5/2)*sqrt(a/(b*x**2) + 1)/(11*x**6) - 10*a*b**(7/2)*sqrt(a/(b*x**2) + 1)/(11*x**4) - 5*b**(9/2)*sqrt(a/(b*x**2) + 1)/(11*x**2) - b**(11/2)*sqrt(a/(b*x**2) + 1)/(11*a)","B",0
435,1,175,0,2.977525," ","integrate((b*x**2+a)**(9/2)/x**14,x)","- \frac{a^{4} \sqrt{b} \sqrt{\frac{a}{b x^{2}} + 1}}{13 x^{12}} - \frac{53 a^{3} b^{\frac{3}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{143 x^{10}} - \frac{100 a^{2} b^{\frac{5}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{143 x^{8}} - \frac{90 a b^{\frac{7}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{143 x^{6}} - \frac{35 b^{\frac{9}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{143 x^{4}} - \frac{b^{\frac{11}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{143 a x^{2}} + \frac{2 b^{\frac{13}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{143 a^{2}}"," ",0,"-a**4*sqrt(b)*sqrt(a/(b*x**2) + 1)/(13*x**12) - 53*a**3*b**(3/2)*sqrt(a/(b*x**2) + 1)/(143*x**10) - 100*a**2*b**(5/2)*sqrt(a/(b*x**2) + 1)/(143*x**8) - 90*a*b**(7/2)*sqrt(a/(b*x**2) + 1)/(143*x**6) - 35*b**(9/2)*sqrt(a/(b*x**2) + 1)/(143*x**4) - b**(11/2)*sqrt(a/(b*x**2) + 1)/(143*a*x**2) + 2*b**(13/2)*sqrt(a/(b*x**2) + 1)/(143*a**2)","B",0
436,1,604,0,3.928248," ","integrate((b*x**2+a)**(9/2)/x**16,x)","- \frac{143 a^{9} b^{\frac{9}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{x^{6} \left(2145 a^{5} b^{4} x^{8} + 4290 a^{4} b^{5} x^{10} + 2145 a^{3} b^{6} x^{12}\right)} - \frac{957 a^{8} b^{\frac{11}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{x^{4} \left(2145 a^{5} b^{4} x^{8} + 4290 a^{4} b^{5} x^{10} + 2145 a^{3} b^{6} x^{12}\right)} - \frac{2703 a^{7} b^{\frac{13}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{x^{2} \left(2145 a^{5} b^{4} x^{8} + 4290 a^{4} b^{5} x^{10} + 2145 a^{3} b^{6} x^{12}\right)} - \frac{4137 a^{6} b^{\frac{15}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{2145 a^{5} b^{4} x^{8} + 4290 a^{4} b^{5} x^{10} + 2145 a^{3} b^{6} x^{12}} - \frac{3633 a^{5} b^{\frac{17}{2}} x^{2} \sqrt{\frac{a}{b x^{2}} + 1}}{2145 a^{5} b^{4} x^{8} + 4290 a^{4} b^{5} x^{10} + 2145 a^{3} b^{6} x^{12}} - \frac{1743 a^{4} b^{\frac{19}{2}} x^{4} \sqrt{\frac{a}{b x^{2}} + 1}}{2145 a^{5} b^{4} x^{8} + 4290 a^{4} b^{5} x^{10} + 2145 a^{3} b^{6} x^{12}} - \frac{357 a^{3} b^{\frac{21}{2}} x^{6} \sqrt{\frac{a}{b x^{2}} + 1}}{2145 a^{5} b^{4} x^{8} + 4290 a^{4} b^{5} x^{10} + 2145 a^{3} b^{6} x^{12}} - \frac{3 a^{2} b^{\frac{23}{2}} x^{8} \sqrt{\frac{a}{b x^{2}} + 1}}{2145 a^{5} b^{4} x^{8} + 4290 a^{4} b^{5} x^{10} + 2145 a^{3} b^{6} x^{12}} - \frac{12 a b^{\frac{25}{2}} x^{10} \sqrt{\frac{a}{b x^{2}} + 1}}{2145 a^{5} b^{4} x^{8} + 4290 a^{4} b^{5} x^{10} + 2145 a^{3} b^{6} x^{12}} - \frac{8 b^{\frac{27}{2}} x^{12} \sqrt{\frac{a}{b x^{2}} + 1}}{2145 a^{5} b^{4} x^{8} + 4290 a^{4} b^{5} x^{10} + 2145 a^{3} b^{6} x^{12}}"," ",0,"-143*a**9*b**(9/2)*sqrt(a/(b*x**2) + 1)/(x**6*(2145*a**5*b**4*x**8 + 4290*a**4*b**5*x**10 + 2145*a**3*b**6*x**12)) - 957*a**8*b**(11/2)*sqrt(a/(b*x**2) + 1)/(x**4*(2145*a**5*b**4*x**8 + 4290*a**4*b**5*x**10 + 2145*a**3*b**6*x**12)) - 2703*a**7*b**(13/2)*sqrt(a/(b*x**2) + 1)/(x**2*(2145*a**5*b**4*x**8 + 4290*a**4*b**5*x**10 + 2145*a**3*b**6*x**12)) - 4137*a**6*b**(15/2)*sqrt(a/(b*x**2) + 1)/(2145*a**5*b**4*x**8 + 4290*a**4*b**5*x**10 + 2145*a**3*b**6*x**12) - 3633*a**5*b**(17/2)*x**2*sqrt(a/(b*x**2) + 1)/(2145*a**5*b**4*x**8 + 4290*a**4*b**5*x**10 + 2145*a**3*b**6*x**12) - 1743*a**4*b**(19/2)*x**4*sqrt(a/(b*x**2) + 1)/(2145*a**5*b**4*x**8 + 4290*a**4*b**5*x**10 + 2145*a**3*b**6*x**12) - 357*a**3*b**(21/2)*x**6*sqrt(a/(b*x**2) + 1)/(2145*a**5*b**4*x**8 + 4290*a**4*b**5*x**10 + 2145*a**3*b**6*x**12) - 3*a**2*b**(23/2)*x**8*sqrt(a/(b*x**2) + 1)/(2145*a**5*b**4*x**8 + 4290*a**4*b**5*x**10 + 2145*a**3*b**6*x**12) - 12*a*b**(25/2)*x**10*sqrt(a/(b*x**2) + 1)/(2145*a**5*b**4*x**8 + 4290*a**4*b**5*x**10 + 2145*a**3*b**6*x**12) - 8*b**(27/2)*x**12*sqrt(a/(b*x**2) + 1)/(2145*a**5*b**4*x**8 + 4290*a**4*b**5*x**10 + 2145*a**3*b**6*x**12)","B",0
437,1,867,0,4.969194," ","integrate((b*x**2+a)**(9/2)/x**18,x)","- \frac{715 a^{11} b^{\frac{19}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{12155 a^{7} b^{9} x^{16} + 36465 a^{6} b^{10} x^{18} + 36465 a^{5} b^{11} x^{20} + 12155 a^{4} b^{12} x^{22}} - \frac{5434 a^{10} b^{\frac{21}{2}} x^{2} \sqrt{\frac{a}{b x^{2}} + 1}}{12155 a^{7} b^{9} x^{16} + 36465 a^{6} b^{10} x^{18} + 36465 a^{5} b^{11} x^{20} + 12155 a^{4} b^{12} x^{22}} - \frac{17820 a^{9} b^{\frac{23}{2}} x^{4} \sqrt{\frac{a}{b x^{2}} + 1}}{12155 a^{7} b^{9} x^{16} + 36465 a^{6} b^{10} x^{18} + 36465 a^{5} b^{11} x^{20} + 12155 a^{4} b^{12} x^{22}} - \frac{32720 a^{8} b^{\frac{25}{2}} x^{6} \sqrt{\frac{a}{b x^{2}} + 1}}{12155 a^{7} b^{9} x^{16} + 36465 a^{6} b^{10} x^{18} + 36465 a^{5} b^{11} x^{20} + 12155 a^{4} b^{12} x^{22}} - \frac{36370 a^{7} b^{\frac{27}{2}} x^{8} \sqrt{\frac{a}{b x^{2}} + 1}}{12155 a^{7} b^{9} x^{16} + 36465 a^{6} b^{10} x^{18} + 36465 a^{5} b^{11} x^{20} + 12155 a^{4} b^{12} x^{22}} - \frac{24500 a^{6} b^{\frac{29}{2}} x^{10} \sqrt{\frac{a}{b x^{2}} + 1}}{12155 a^{7} b^{9} x^{16} + 36465 a^{6} b^{10} x^{18} + 36465 a^{5} b^{11} x^{20} + 12155 a^{4} b^{12} x^{22}} - \frac{9268 a^{5} b^{\frac{31}{2}} x^{12} \sqrt{\frac{a}{b x^{2}} + 1}}{12155 a^{7} b^{9} x^{16} + 36465 a^{6} b^{10} x^{18} + 36465 a^{5} b^{11} x^{20} + 12155 a^{4} b^{12} x^{22}} - \frac{1520 a^{4} b^{\frac{33}{2}} x^{14} \sqrt{\frac{a}{b x^{2}} + 1}}{12155 a^{7} b^{9} x^{16} + 36465 a^{6} b^{10} x^{18} + 36465 a^{5} b^{11} x^{20} + 12155 a^{4} b^{12} x^{22}} + \frac{5 a^{3} b^{\frac{35}{2}} x^{16} \sqrt{\frac{a}{b x^{2}} + 1}}{12155 a^{7} b^{9} x^{16} + 36465 a^{6} b^{10} x^{18} + 36465 a^{5} b^{11} x^{20} + 12155 a^{4} b^{12} x^{22}} + \frac{30 a^{2} b^{\frac{37}{2}} x^{18} \sqrt{\frac{a}{b x^{2}} + 1}}{12155 a^{7} b^{9} x^{16} + 36465 a^{6} b^{10} x^{18} + 36465 a^{5} b^{11} x^{20} + 12155 a^{4} b^{12} x^{22}} + \frac{40 a b^{\frac{39}{2}} x^{20} \sqrt{\frac{a}{b x^{2}} + 1}}{12155 a^{7} b^{9} x^{16} + 36465 a^{6} b^{10} x^{18} + 36465 a^{5} b^{11} x^{20} + 12155 a^{4} b^{12} x^{22}} + \frac{16 b^{\frac{41}{2}} x^{22} \sqrt{\frac{a}{b x^{2}} + 1}}{12155 a^{7} b^{9} x^{16} + 36465 a^{6} b^{10} x^{18} + 36465 a^{5} b^{11} x^{20} + 12155 a^{4} b^{12} x^{22}}"," ",0,"-715*a**11*b**(19/2)*sqrt(a/(b*x**2) + 1)/(12155*a**7*b**9*x**16 + 36465*a**6*b**10*x**18 + 36465*a**5*b**11*x**20 + 12155*a**4*b**12*x**22) - 5434*a**10*b**(21/2)*x**2*sqrt(a/(b*x**2) + 1)/(12155*a**7*b**9*x**16 + 36465*a**6*b**10*x**18 + 36465*a**5*b**11*x**20 + 12155*a**4*b**12*x**22) - 17820*a**9*b**(23/2)*x**4*sqrt(a/(b*x**2) + 1)/(12155*a**7*b**9*x**16 + 36465*a**6*b**10*x**18 + 36465*a**5*b**11*x**20 + 12155*a**4*b**12*x**22) - 32720*a**8*b**(25/2)*x**6*sqrt(a/(b*x**2) + 1)/(12155*a**7*b**9*x**16 + 36465*a**6*b**10*x**18 + 36465*a**5*b**11*x**20 + 12155*a**4*b**12*x**22) - 36370*a**7*b**(27/2)*x**8*sqrt(a/(b*x**2) + 1)/(12155*a**7*b**9*x**16 + 36465*a**6*b**10*x**18 + 36465*a**5*b**11*x**20 + 12155*a**4*b**12*x**22) - 24500*a**6*b**(29/2)*x**10*sqrt(a/(b*x**2) + 1)/(12155*a**7*b**9*x**16 + 36465*a**6*b**10*x**18 + 36465*a**5*b**11*x**20 + 12155*a**4*b**12*x**22) - 9268*a**5*b**(31/2)*x**12*sqrt(a/(b*x**2) + 1)/(12155*a**7*b**9*x**16 + 36465*a**6*b**10*x**18 + 36465*a**5*b**11*x**20 + 12155*a**4*b**12*x**22) - 1520*a**4*b**(33/2)*x**14*sqrt(a/(b*x**2) + 1)/(12155*a**7*b**9*x**16 + 36465*a**6*b**10*x**18 + 36465*a**5*b**11*x**20 + 12155*a**4*b**12*x**22) + 5*a**3*b**(35/2)*x**16*sqrt(a/(b*x**2) + 1)/(12155*a**7*b**9*x**16 + 36465*a**6*b**10*x**18 + 36465*a**5*b**11*x**20 + 12155*a**4*b**12*x**22) + 30*a**2*b**(37/2)*x**18*sqrt(a/(b*x**2) + 1)/(12155*a**7*b**9*x**16 + 36465*a**6*b**10*x**18 + 36465*a**5*b**11*x**20 + 12155*a**4*b**12*x**22) + 40*a*b**(39/2)*x**20*sqrt(a/(b*x**2) + 1)/(12155*a**7*b**9*x**16 + 36465*a**6*b**10*x**18 + 36465*a**5*b**11*x**20 + 12155*a**4*b**12*x**22) + 16*b**(41/2)*x**22*sqrt(a/(b*x**2) + 1)/(12155*a**7*b**9*x**16 + 36465*a**6*b**10*x**18 + 36465*a**5*b**11*x**20 + 12155*a**4*b**12*x**22)","B",0
438,1,1182,0,6.261583," ","integrate((b*x**2+a)**(9/2)/x**20,x)","- \frac{12155 a^{13} b^{\frac{33}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{230945 a^{9} b^{16} x^{18} + 923780 a^{8} b^{17} x^{20} + 1385670 a^{7} b^{18} x^{22} + 923780 a^{6} b^{19} x^{24} + 230945 a^{5} b^{20} x^{26}} - \frac{103675 a^{12} b^{\frac{35}{2}} x^{2} \sqrt{\frac{a}{b x^{2}} + 1}}{230945 a^{9} b^{16} x^{18} + 923780 a^{8} b^{17} x^{20} + 1385670 a^{7} b^{18} x^{22} + 923780 a^{6} b^{19} x^{24} + 230945 a^{5} b^{20} x^{26}} - \frac{388388 a^{11} b^{\frac{37}{2}} x^{4} \sqrt{\frac{a}{b x^{2}} + 1}}{230945 a^{9} b^{16} x^{18} + 923780 a^{8} b^{17} x^{20} + 1385670 a^{7} b^{18} x^{22} + 923780 a^{6} b^{19} x^{24} + 230945 a^{5} b^{20} x^{26}} - \frac{834988 a^{10} b^{\frac{39}{2}} x^{6} \sqrt{\frac{a}{b x^{2}} + 1}}{230945 a^{9} b^{16} x^{18} + 923780 a^{8} b^{17} x^{20} + 1385670 a^{7} b^{18} x^{22} + 923780 a^{6} b^{19} x^{24} + 230945 a^{5} b^{20} x^{26}} - \frac{1127210 a^{9} b^{\frac{41}{2}} x^{8} \sqrt{\frac{a}{b x^{2}} + 1}}{230945 a^{9} b^{16} x^{18} + 923780 a^{8} b^{17} x^{20} + 1385670 a^{7} b^{18} x^{22} + 923780 a^{6} b^{19} x^{24} + 230945 a^{5} b^{20} x^{26}} - \frac{978810 a^{8} b^{\frac{43}{2}} x^{10} \sqrt{\frac{a}{b x^{2}} + 1}}{230945 a^{9} b^{16} x^{18} + 923780 a^{8} b^{17} x^{20} + 1385670 a^{7} b^{18} x^{22} + 923780 a^{6} b^{19} x^{24} + 230945 a^{5} b^{20} x^{26}} - \frac{534060 a^{7} b^{\frac{45}{2}} x^{12} \sqrt{\frac{a}{b x^{2}} + 1}}{230945 a^{9} b^{16} x^{18} + 923780 a^{8} b^{17} x^{20} + 1385670 a^{7} b^{18} x^{22} + 923780 a^{6} b^{19} x^{24} + 230945 a^{5} b^{20} x^{26}} - \frac{167436 a^{6} b^{\frac{47}{2}} x^{14} \sqrt{\frac{a}{b x^{2}} + 1}}{230945 a^{9} b^{16} x^{18} + 923780 a^{8} b^{17} x^{20} + 1385670 a^{7} b^{18} x^{22} + 923780 a^{6} b^{19} x^{24} + 230945 a^{5} b^{20} x^{26}} - \frac{23091 a^{5} b^{\frac{49}{2}} x^{16} \sqrt{\frac{a}{b x^{2}} + 1}}{230945 a^{9} b^{16} x^{18} + 923780 a^{8} b^{17} x^{20} + 1385670 a^{7} b^{18} x^{22} + 923780 a^{6} b^{19} x^{24} + 230945 a^{5} b^{20} x^{26}} - \frac{35 a^{4} b^{\frac{51}{2}} x^{18} \sqrt{\frac{a}{b x^{2}} + 1}}{230945 a^{9} b^{16} x^{18} + 923780 a^{8} b^{17} x^{20} + 1385670 a^{7} b^{18} x^{22} + 923780 a^{6} b^{19} x^{24} + 230945 a^{5} b^{20} x^{26}} - \frac{280 a^{3} b^{\frac{53}{2}} x^{20} \sqrt{\frac{a}{b x^{2}} + 1}}{230945 a^{9} b^{16} x^{18} + 923780 a^{8} b^{17} x^{20} + 1385670 a^{7} b^{18} x^{22} + 923780 a^{6} b^{19} x^{24} + 230945 a^{5} b^{20} x^{26}} - \frac{560 a^{2} b^{\frac{55}{2}} x^{22} \sqrt{\frac{a}{b x^{2}} + 1}}{230945 a^{9} b^{16} x^{18} + 923780 a^{8} b^{17} x^{20} + 1385670 a^{7} b^{18} x^{22} + 923780 a^{6} b^{19} x^{24} + 230945 a^{5} b^{20} x^{26}} - \frac{448 a b^{\frac{57}{2}} x^{24} \sqrt{\frac{a}{b x^{2}} + 1}}{230945 a^{9} b^{16} x^{18} + 923780 a^{8} b^{17} x^{20} + 1385670 a^{7} b^{18} x^{22} + 923780 a^{6} b^{19} x^{24} + 230945 a^{5} b^{20} x^{26}} - \frac{128 b^{\frac{59}{2}} x^{26} \sqrt{\frac{a}{b x^{2}} + 1}}{230945 a^{9} b^{16} x^{18} + 923780 a^{8} b^{17} x^{20} + 1385670 a^{7} b^{18} x^{22} + 923780 a^{6} b^{19} x^{24} + 230945 a^{5} b^{20} x^{26}}"," ",0,"-12155*a**13*b**(33/2)*sqrt(a/(b*x**2) + 1)/(230945*a**9*b**16*x**18 + 923780*a**8*b**17*x**20 + 1385670*a**7*b**18*x**22 + 923780*a**6*b**19*x**24 + 230945*a**5*b**20*x**26) - 103675*a**12*b**(35/2)*x**2*sqrt(a/(b*x**2) + 1)/(230945*a**9*b**16*x**18 + 923780*a**8*b**17*x**20 + 1385670*a**7*b**18*x**22 + 923780*a**6*b**19*x**24 + 230945*a**5*b**20*x**26) - 388388*a**11*b**(37/2)*x**4*sqrt(a/(b*x**2) + 1)/(230945*a**9*b**16*x**18 + 923780*a**8*b**17*x**20 + 1385670*a**7*b**18*x**22 + 923780*a**6*b**19*x**24 + 230945*a**5*b**20*x**26) - 834988*a**10*b**(39/2)*x**6*sqrt(a/(b*x**2) + 1)/(230945*a**9*b**16*x**18 + 923780*a**8*b**17*x**20 + 1385670*a**7*b**18*x**22 + 923780*a**6*b**19*x**24 + 230945*a**5*b**20*x**26) - 1127210*a**9*b**(41/2)*x**8*sqrt(a/(b*x**2) + 1)/(230945*a**9*b**16*x**18 + 923780*a**8*b**17*x**20 + 1385670*a**7*b**18*x**22 + 923780*a**6*b**19*x**24 + 230945*a**5*b**20*x**26) - 978810*a**8*b**(43/2)*x**10*sqrt(a/(b*x**2) + 1)/(230945*a**9*b**16*x**18 + 923780*a**8*b**17*x**20 + 1385670*a**7*b**18*x**22 + 923780*a**6*b**19*x**24 + 230945*a**5*b**20*x**26) - 534060*a**7*b**(45/2)*x**12*sqrt(a/(b*x**2) + 1)/(230945*a**9*b**16*x**18 + 923780*a**8*b**17*x**20 + 1385670*a**7*b**18*x**22 + 923780*a**6*b**19*x**24 + 230945*a**5*b**20*x**26) - 167436*a**6*b**(47/2)*x**14*sqrt(a/(b*x**2) + 1)/(230945*a**9*b**16*x**18 + 923780*a**8*b**17*x**20 + 1385670*a**7*b**18*x**22 + 923780*a**6*b**19*x**24 + 230945*a**5*b**20*x**26) - 23091*a**5*b**(49/2)*x**16*sqrt(a/(b*x**2) + 1)/(230945*a**9*b**16*x**18 + 923780*a**8*b**17*x**20 + 1385670*a**7*b**18*x**22 + 923780*a**6*b**19*x**24 + 230945*a**5*b**20*x**26) - 35*a**4*b**(51/2)*x**18*sqrt(a/(b*x**2) + 1)/(230945*a**9*b**16*x**18 + 923780*a**8*b**17*x**20 + 1385670*a**7*b**18*x**22 + 923780*a**6*b**19*x**24 + 230945*a**5*b**20*x**26) - 280*a**3*b**(53/2)*x**20*sqrt(a/(b*x**2) + 1)/(230945*a**9*b**16*x**18 + 923780*a**8*b**17*x**20 + 1385670*a**7*b**18*x**22 + 923780*a**6*b**19*x**24 + 230945*a**5*b**20*x**26) - 560*a**2*b**(55/2)*x**22*sqrt(a/(b*x**2) + 1)/(230945*a**9*b**16*x**18 + 923780*a**8*b**17*x**20 + 1385670*a**7*b**18*x**22 + 923780*a**6*b**19*x**24 + 230945*a**5*b**20*x**26) - 448*a*b**(57/2)*x**24*sqrt(a/(b*x**2) + 1)/(230945*a**9*b**16*x**18 + 923780*a**8*b**17*x**20 + 1385670*a**7*b**18*x**22 + 923780*a**6*b**19*x**24 + 230945*a**5*b**20*x**26) - 128*b**(59/2)*x**26*sqrt(a/(b*x**2) + 1)/(230945*a**9*b**16*x**18 + 923780*a**8*b**17*x**20 + 1385670*a**7*b**18*x**22 + 923780*a**6*b**19*x**24 + 230945*a**5*b**20*x**26)","B",0
439,1,1540,0,7.799142," ","integrate((b*x**2+a)**(9/2)/x**22,x)","- \frac{46189 a^{15} b^{\frac{51}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{969969 a^{11} b^{25} x^{20} + 4849845 a^{10} b^{26} x^{22} + 9699690 a^{9} b^{27} x^{24} + 9699690 a^{8} b^{28} x^{26} + 4849845 a^{7} b^{29} x^{28} + 969969 a^{6} b^{30} x^{30}} - \frac{437580 a^{14} b^{\frac{53}{2}} x^{2} \sqrt{\frac{a}{b x^{2}} + 1}}{969969 a^{11} b^{25} x^{20} + 4849845 a^{10} b^{26} x^{22} + 9699690 a^{9} b^{27} x^{24} + 9699690 a^{8} b^{28} x^{26} + 4849845 a^{7} b^{29} x^{28} + 969969 a^{6} b^{30} x^{30}} - \frac{1846845 a^{13} b^{\frac{55}{2}} x^{4} \sqrt{\frac{a}{b x^{2}} + 1}}{969969 a^{11} b^{25} x^{20} + 4849845 a^{10} b^{26} x^{22} + 9699690 a^{9} b^{27} x^{24} + 9699690 a^{8} b^{28} x^{26} + 4849845 a^{7} b^{29} x^{28} + 969969 a^{6} b^{30} x^{30}} - \frac{4558554 a^{12} b^{\frac{57}{2}} x^{6} \sqrt{\frac{a}{b x^{2}} + 1}}{969969 a^{11} b^{25} x^{20} + 4849845 a^{10} b^{26} x^{22} + 9699690 a^{9} b^{27} x^{24} + 9699690 a^{8} b^{28} x^{26} + 4849845 a^{7} b^{29} x^{28} + 969969 a^{6} b^{30} x^{30}} - \frac{7252938 a^{11} b^{\frac{59}{2}} x^{8} \sqrt{\frac{a}{b x^{2}} + 1}}{969969 a^{11} b^{25} x^{20} + 4849845 a^{10} b^{26} x^{22} + 9699690 a^{9} b^{27} x^{24} + 9699690 a^{8} b^{28} x^{26} + 4849845 a^{7} b^{29} x^{28} + 969969 a^{6} b^{30} x^{30}} - \frac{7715232 a^{10} b^{\frac{61}{2}} x^{10} \sqrt{\frac{a}{b x^{2}} + 1}}{969969 a^{11} b^{25} x^{20} + 4849845 a^{10} b^{26} x^{22} + 9699690 a^{9} b^{27} x^{24} + 9699690 a^{8} b^{28} x^{26} + 4849845 a^{7} b^{29} x^{28} + 969969 a^{6} b^{30} x^{30}} - \frac{5487650 a^{9} b^{\frac{63}{2}} x^{12} \sqrt{\frac{a}{b x^{2}} + 1}}{969969 a^{11} b^{25} x^{20} + 4849845 a^{10} b^{26} x^{22} + 9699690 a^{9} b^{27} x^{24} + 9699690 a^{8} b^{28} x^{26} + 4849845 a^{7} b^{29} x^{28} + 969969 a^{6} b^{30} x^{30}} - \frac{2516940 a^{8} b^{\frac{65}{2}} x^{14} \sqrt{\frac{a}{b x^{2}} + 1}}{969969 a^{11} b^{25} x^{20} + 4849845 a^{10} b^{26} x^{22} + 9699690 a^{9} b^{27} x^{24} + 9699690 a^{8} b^{28} x^{26} + 4849845 a^{7} b^{29} x^{28} + 969969 a^{6} b^{30} x^{30}} - \frac{675513 a^{7} b^{\frac{67}{2}} x^{16} \sqrt{\frac{a}{b x^{2}} + 1}}{969969 a^{11} b^{25} x^{20} + 4849845 a^{10} b^{26} x^{22} + 9699690 a^{9} b^{27} x^{24} + 9699690 a^{8} b^{28} x^{26} + 4849845 a^{7} b^{29} x^{28} + 969969 a^{6} b^{30} x^{30}} - \frac{80836 a^{6} b^{\frac{69}{2}} x^{18} \sqrt{\frac{a}{b x^{2}} + 1}}{969969 a^{11} b^{25} x^{20} + 4849845 a^{10} b^{26} x^{22} + 9699690 a^{9} b^{27} x^{24} + 9699690 a^{8} b^{28} x^{26} + 4849845 a^{7} b^{29} x^{28} + 969969 a^{6} b^{30} x^{30}} + \frac{63 a^{5} b^{\frac{71}{2}} x^{20} \sqrt{\frac{a}{b x^{2}} + 1}}{969969 a^{11} b^{25} x^{20} + 4849845 a^{10} b^{26} x^{22} + 9699690 a^{9} b^{27} x^{24} + 9699690 a^{8} b^{28} x^{26} + 4849845 a^{7} b^{29} x^{28} + 969969 a^{6} b^{30} x^{30}} + \frac{630 a^{4} b^{\frac{73}{2}} x^{22} \sqrt{\frac{a}{b x^{2}} + 1}}{969969 a^{11} b^{25} x^{20} + 4849845 a^{10} b^{26} x^{22} + 9699690 a^{9} b^{27} x^{24} + 9699690 a^{8} b^{28} x^{26} + 4849845 a^{7} b^{29} x^{28} + 969969 a^{6} b^{30} x^{30}} + \frac{1680 a^{3} b^{\frac{75}{2}} x^{24} \sqrt{\frac{a}{b x^{2}} + 1}}{969969 a^{11} b^{25} x^{20} + 4849845 a^{10} b^{26} x^{22} + 9699690 a^{9} b^{27} x^{24} + 9699690 a^{8} b^{28} x^{26} + 4849845 a^{7} b^{29} x^{28} + 969969 a^{6} b^{30} x^{30}} + \frac{2016 a^{2} b^{\frac{77}{2}} x^{26} \sqrt{\frac{a}{b x^{2}} + 1}}{969969 a^{11} b^{25} x^{20} + 4849845 a^{10} b^{26} x^{22} + 9699690 a^{9} b^{27} x^{24} + 9699690 a^{8} b^{28} x^{26} + 4849845 a^{7} b^{29} x^{28} + 969969 a^{6} b^{30} x^{30}} + \frac{1152 a b^{\frac{79}{2}} x^{28} \sqrt{\frac{a}{b x^{2}} + 1}}{969969 a^{11} b^{25} x^{20} + 4849845 a^{10} b^{26} x^{22} + 9699690 a^{9} b^{27} x^{24} + 9699690 a^{8} b^{28} x^{26} + 4849845 a^{7} b^{29} x^{28} + 969969 a^{6} b^{30} x^{30}} + \frac{256 b^{\frac{81}{2}} x^{30} \sqrt{\frac{a}{b x^{2}} + 1}}{969969 a^{11} b^{25} x^{20} + 4849845 a^{10} b^{26} x^{22} + 9699690 a^{9} b^{27} x^{24} + 9699690 a^{8} b^{28} x^{26} + 4849845 a^{7} b^{29} x^{28} + 969969 a^{6} b^{30} x^{30}}"," ",0,"-46189*a**15*b**(51/2)*sqrt(a/(b*x**2) + 1)/(969969*a**11*b**25*x**20 + 4849845*a**10*b**26*x**22 + 9699690*a**9*b**27*x**24 + 9699690*a**8*b**28*x**26 + 4849845*a**7*b**29*x**28 + 969969*a**6*b**30*x**30) - 437580*a**14*b**(53/2)*x**2*sqrt(a/(b*x**2) + 1)/(969969*a**11*b**25*x**20 + 4849845*a**10*b**26*x**22 + 9699690*a**9*b**27*x**24 + 9699690*a**8*b**28*x**26 + 4849845*a**7*b**29*x**28 + 969969*a**6*b**30*x**30) - 1846845*a**13*b**(55/2)*x**4*sqrt(a/(b*x**2) + 1)/(969969*a**11*b**25*x**20 + 4849845*a**10*b**26*x**22 + 9699690*a**9*b**27*x**24 + 9699690*a**8*b**28*x**26 + 4849845*a**7*b**29*x**28 + 969969*a**6*b**30*x**30) - 4558554*a**12*b**(57/2)*x**6*sqrt(a/(b*x**2) + 1)/(969969*a**11*b**25*x**20 + 4849845*a**10*b**26*x**22 + 9699690*a**9*b**27*x**24 + 9699690*a**8*b**28*x**26 + 4849845*a**7*b**29*x**28 + 969969*a**6*b**30*x**30) - 7252938*a**11*b**(59/2)*x**8*sqrt(a/(b*x**2) + 1)/(969969*a**11*b**25*x**20 + 4849845*a**10*b**26*x**22 + 9699690*a**9*b**27*x**24 + 9699690*a**8*b**28*x**26 + 4849845*a**7*b**29*x**28 + 969969*a**6*b**30*x**30) - 7715232*a**10*b**(61/2)*x**10*sqrt(a/(b*x**2) + 1)/(969969*a**11*b**25*x**20 + 4849845*a**10*b**26*x**22 + 9699690*a**9*b**27*x**24 + 9699690*a**8*b**28*x**26 + 4849845*a**7*b**29*x**28 + 969969*a**6*b**30*x**30) - 5487650*a**9*b**(63/2)*x**12*sqrt(a/(b*x**2) + 1)/(969969*a**11*b**25*x**20 + 4849845*a**10*b**26*x**22 + 9699690*a**9*b**27*x**24 + 9699690*a**8*b**28*x**26 + 4849845*a**7*b**29*x**28 + 969969*a**6*b**30*x**30) - 2516940*a**8*b**(65/2)*x**14*sqrt(a/(b*x**2) + 1)/(969969*a**11*b**25*x**20 + 4849845*a**10*b**26*x**22 + 9699690*a**9*b**27*x**24 + 9699690*a**8*b**28*x**26 + 4849845*a**7*b**29*x**28 + 969969*a**6*b**30*x**30) - 675513*a**7*b**(67/2)*x**16*sqrt(a/(b*x**2) + 1)/(969969*a**11*b**25*x**20 + 4849845*a**10*b**26*x**22 + 9699690*a**9*b**27*x**24 + 9699690*a**8*b**28*x**26 + 4849845*a**7*b**29*x**28 + 969969*a**6*b**30*x**30) - 80836*a**6*b**(69/2)*x**18*sqrt(a/(b*x**2) + 1)/(969969*a**11*b**25*x**20 + 4849845*a**10*b**26*x**22 + 9699690*a**9*b**27*x**24 + 9699690*a**8*b**28*x**26 + 4849845*a**7*b**29*x**28 + 969969*a**6*b**30*x**30) + 63*a**5*b**(71/2)*x**20*sqrt(a/(b*x**2) + 1)/(969969*a**11*b**25*x**20 + 4849845*a**10*b**26*x**22 + 9699690*a**9*b**27*x**24 + 9699690*a**8*b**28*x**26 + 4849845*a**7*b**29*x**28 + 969969*a**6*b**30*x**30) + 630*a**4*b**(73/2)*x**22*sqrt(a/(b*x**2) + 1)/(969969*a**11*b**25*x**20 + 4849845*a**10*b**26*x**22 + 9699690*a**9*b**27*x**24 + 9699690*a**8*b**28*x**26 + 4849845*a**7*b**29*x**28 + 969969*a**6*b**30*x**30) + 1680*a**3*b**(75/2)*x**24*sqrt(a/(b*x**2) + 1)/(969969*a**11*b**25*x**20 + 4849845*a**10*b**26*x**22 + 9699690*a**9*b**27*x**24 + 9699690*a**8*b**28*x**26 + 4849845*a**7*b**29*x**28 + 969969*a**6*b**30*x**30) + 2016*a**2*b**(77/2)*x**26*sqrt(a/(b*x**2) + 1)/(969969*a**11*b**25*x**20 + 4849845*a**10*b**26*x**22 + 9699690*a**9*b**27*x**24 + 9699690*a**8*b**28*x**26 + 4849845*a**7*b**29*x**28 + 969969*a**6*b**30*x**30) + 1152*a*b**(79/2)*x**28*sqrt(a/(b*x**2) + 1)/(969969*a**11*b**25*x**20 + 4849845*a**10*b**26*x**22 + 9699690*a**9*b**27*x**24 + 9699690*a**8*b**28*x**26 + 4849845*a**7*b**29*x**28 + 969969*a**6*b**30*x**30) + 256*b**(81/2)*x**30*sqrt(a/(b*x**2) + 1)/(969969*a**11*b**25*x**20 + 4849845*a**10*b**26*x**22 + 9699690*a**9*b**27*x**24 + 9699690*a**8*b**28*x**26 + 4849845*a**7*b**29*x**28 + 969969*a**6*b**30*x**30)","B",0
440,1,1950,0,9.066435," ","integrate((b*x**2+a)**(9/2)/x**24,x)","- \frac{323323 a^{17} b^{\frac{73}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{7436429 a^{13} b^{36} x^{22} + 44618574 a^{12} b^{37} x^{24} + 111546435 a^{11} b^{38} x^{26} + 148728580 a^{10} b^{39} x^{28} + 111546435 a^{9} b^{40} x^{30} + 44618574 a^{8} b^{41} x^{32} + 7436429 a^{7} b^{42} x^{34}} - \frac{3371797 a^{16} b^{\frac{75}{2}} x^{2} \sqrt{\frac{a}{b x^{2}} + 1}}{7436429 a^{13} b^{36} x^{22} + 44618574 a^{12} b^{37} x^{24} + 111546435 a^{11} b^{38} x^{26} + 148728580 a^{10} b^{39} x^{28} + 111546435 a^{9} b^{40} x^{30} + 44618574 a^{8} b^{41} x^{32} + 7436429 a^{7} b^{42} x^{34}} - \frac{15847689 a^{15} b^{\frac{77}{2}} x^{4} \sqrt{\frac{a}{b x^{2}} + 1}}{7436429 a^{13} b^{36} x^{22} + 44618574 a^{12} b^{37} x^{24} + 111546435 a^{11} b^{38} x^{26} + 148728580 a^{10} b^{39} x^{28} + 111546435 a^{9} b^{40} x^{30} + 44618574 a^{8} b^{41} x^{32} + 7436429 a^{7} b^{42} x^{34}} - \frac{44210595 a^{14} b^{\frac{79}{2}} x^{6} \sqrt{\frac{a}{b x^{2}} + 1}}{7436429 a^{13} b^{36} x^{22} + 44618574 a^{12} b^{37} x^{24} + 111546435 a^{11} b^{38} x^{26} + 148728580 a^{10} b^{39} x^{28} + 111546435 a^{9} b^{40} x^{30} + 44618574 a^{8} b^{41} x^{32} + 7436429 a^{7} b^{42} x^{34}} - \frac{81074994 a^{13} b^{\frac{81}{2}} x^{8} \sqrt{\frac{a}{b x^{2}} + 1}}{7436429 a^{13} b^{36} x^{22} + 44618574 a^{12} b^{37} x^{24} + 111546435 a^{11} b^{38} x^{26} + 148728580 a^{10} b^{39} x^{28} + 111546435 a^{9} b^{40} x^{30} + 44618574 a^{8} b^{41} x^{32} + 7436429 a^{7} b^{42} x^{34}} - \frac{102129258 a^{12} b^{\frac{83}{2}} x^{10} \sqrt{\frac{a}{b x^{2}} + 1}}{7436429 a^{13} b^{36} x^{22} + 44618574 a^{12} b^{37} x^{24} + 111546435 a^{11} b^{38} x^{26} + 148728580 a^{10} b^{39} x^{28} + 111546435 a^{9} b^{40} x^{30} + 44618574 a^{8} b^{41} x^{32} + 7436429 a^{7} b^{42} x^{34}} - \frac{89502546 a^{11} b^{\frac{85}{2}} x^{12} \sqrt{\frac{a}{b x^{2}} + 1}}{7436429 a^{13} b^{36} x^{22} + 44618574 a^{12} b^{37} x^{24} + 111546435 a^{11} b^{38} x^{26} + 148728580 a^{10} b^{39} x^{28} + 111546435 a^{9} b^{40} x^{30} + 44618574 a^{8} b^{41} x^{32} + 7436429 a^{7} b^{42} x^{34}} - \frac{53885062 a^{10} b^{\frac{87}{2}} x^{14} \sqrt{\frac{a}{b x^{2}} + 1}}{7436429 a^{13} b^{36} x^{22} + 44618574 a^{12} b^{37} x^{24} + 111546435 a^{11} b^{38} x^{26} + 148728580 a^{10} b^{39} x^{28} + 111546435 a^{9} b^{40} x^{30} + 44618574 a^{8} b^{41} x^{32} + 7436429 a^{7} b^{42} x^{34}} - \frac{21329935 a^{9} b^{\frac{89}{2}} x^{16} \sqrt{\frac{a}{b x^{2}} + 1}}{7436429 a^{13} b^{36} x^{22} + 44618574 a^{12} b^{37} x^{24} + 111546435 a^{11} b^{38} x^{26} + 148728580 a^{10} b^{39} x^{28} + 111546435 a^{9} b^{40} x^{30} + 44618574 a^{8} b^{41} x^{32} + 7436429 a^{7} b^{42} x^{34}} - \frac{5012953 a^{8} b^{\frac{91}{2}} x^{18} \sqrt{\frac{a}{b x^{2}} + 1}}{7436429 a^{13} b^{36} x^{22} + 44618574 a^{12} b^{37} x^{24} + 111546435 a^{11} b^{38} x^{26} + 148728580 a^{10} b^{39} x^{28} + 111546435 a^{9} b^{40} x^{30} + 44618574 a^{8} b^{41} x^{32} + 7436429 a^{7} b^{42} x^{34}} - \frac{531157 a^{7} b^{\frac{93}{2}} x^{20} \sqrt{\frac{a}{b x^{2}} + 1}}{7436429 a^{13} b^{36} x^{22} + 44618574 a^{12} b^{37} x^{24} + 111546435 a^{11} b^{38} x^{26} + 148728580 a^{10} b^{39} x^{28} + 111546435 a^{9} b^{40} x^{30} + 44618574 a^{8} b^{41} x^{32} + 7436429 a^{7} b^{42} x^{34}} - \frac{231 a^{6} b^{\frac{95}{2}} x^{22} \sqrt{\frac{a}{b x^{2}} + 1}}{7436429 a^{13} b^{36} x^{22} + 44618574 a^{12} b^{37} x^{24} + 111546435 a^{11} b^{38} x^{26} + 148728580 a^{10} b^{39} x^{28} + 111546435 a^{9} b^{40} x^{30} + 44618574 a^{8} b^{41} x^{32} + 7436429 a^{7} b^{42} x^{34}} - \frac{2772 a^{5} b^{\frac{97}{2}} x^{24} \sqrt{\frac{a}{b x^{2}} + 1}}{7436429 a^{13} b^{36} x^{22} + 44618574 a^{12} b^{37} x^{24} + 111546435 a^{11} b^{38} x^{26} + 148728580 a^{10} b^{39} x^{28} + 111546435 a^{9} b^{40} x^{30} + 44618574 a^{8} b^{41} x^{32} + 7436429 a^{7} b^{42} x^{34}} - \frac{9240 a^{4} b^{\frac{99}{2}} x^{26} \sqrt{\frac{a}{b x^{2}} + 1}}{7436429 a^{13} b^{36} x^{22} + 44618574 a^{12} b^{37} x^{24} + 111546435 a^{11} b^{38} x^{26} + 148728580 a^{10} b^{39} x^{28} + 111546435 a^{9} b^{40} x^{30} + 44618574 a^{8} b^{41} x^{32} + 7436429 a^{7} b^{42} x^{34}} - \frac{14784 a^{3} b^{\frac{101}{2}} x^{28} \sqrt{\frac{a}{b x^{2}} + 1}}{7436429 a^{13} b^{36} x^{22} + 44618574 a^{12} b^{37} x^{24} + 111546435 a^{11} b^{38} x^{26} + 148728580 a^{10} b^{39} x^{28} + 111546435 a^{9} b^{40} x^{30} + 44618574 a^{8} b^{41} x^{32} + 7436429 a^{7} b^{42} x^{34}} - \frac{12672 a^{2} b^{\frac{103}{2}} x^{30} \sqrt{\frac{a}{b x^{2}} + 1}}{7436429 a^{13} b^{36} x^{22} + 44618574 a^{12} b^{37} x^{24} + 111546435 a^{11} b^{38} x^{26} + 148728580 a^{10} b^{39} x^{28} + 111546435 a^{9} b^{40} x^{30} + 44618574 a^{8} b^{41} x^{32} + 7436429 a^{7} b^{42} x^{34}} - \frac{5632 a b^{\frac{105}{2}} x^{32} \sqrt{\frac{a}{b x^{2}} + 1}}{7436429 a^{13} b^{36} x^{22} + 44618574 a^{12} b^{37} x^{24} + 111546435 a^{11} b^{38} x^{26} + 148728580 a^{10} b^{39} x^{28} + 111546435 a^{9} b^{40} x^{30} + 44618574 a^{8} b^{41} x^{32} + 7436429 a^{7} b^{42} x^{34}} - \frac{1024 b^{\frac{107}{2}} x^{34} \sqrt{\frac{a}{b x^{2}} + 1}}{7436429 a^{13} b^{36} x^{22} + 44618574 a^{12} b^{37} x^{24} + 111546435 a^{11} b^{38} x^{26} + 148728580 a^{10} b^{39} x^{28} + 111546435 a^{9} b^{40} x^{30} + 44618574 a^{8} b^{41} x^{32} + 7436429 a^{7} b^{42} x^{34}}"," ",0,"-323323*a**17*b**(73/2)*sqrt(a/(b*x**2) + 1)/(7436429*a**13*b**36*x**22 + 44618574*a**12*b**37*x**24 + 111546435*a**11*b**38*x**26 + 148728580*a**10*b**39*x**28 + 111546435*a**9*b**40*x**30 + 44618574*a**8*b**41*x**32 + 7436429*a**7*b**42*x**34) - 3371797*a**16*b**(75/2)*x**2*sqrt(a/(b*x**2) + 1)/(7436429*a**13*b**36*x**22 + 44618574*a**12*b**37*x**24 + 111546435*a**11*b**38*x**26 + 148728580*a**10*b**39*x**28 + 111546435*a**9*b**40*x**30 + 44618574*a**8*b**41*x**32 + 7436429*a**7*b**42*x**34) - 15847689*a**15*b**(77/2)*x**4*sqrt(a/(b*x**2) + 1)/(7436429*a**13*b**36*x**22 + 44618574*a**12*b**37*x**24 + 111546435*a**11*b**38*x**26 + 148728580*a**10*b**39*x**28 + 111546435*a**9*b**40*x**30 + 44618574*a**8*b**41*x**32 + 7436429*a**7*b**42*x**34) - 44210595*a**14*b**(79/2)*x**6*sqrt(a/(b*x**2) + 1)/(7436429*a**13*b**36*x**22 + 44618574*a**12*b**37*x**24 + 111546435*a**11*b**38*x**26 + 148728580*a**10*b**39*x**28 + 111546435*a**9*b**40*x**30 + 44618574*a**8*b**41*x**32 + 7436429*a**7*b**42*x**34) - 81074994*a**13*b**(81/2)*x**8*sqrt(a/(b*x**2) + 1)/(7436429*a**13*b**36*x**22 + 44618574*a**12*b**37*x**24 + 111546435*a**11*b**38*x**26 + 148728580*a**10*b**39*x**28 + 111546435*a**9*b**40*x**30 + 44618574*a**8*b**41*x**32 + 7436429*a**7*b**42*x**34) - 102129258*a**12*b**(83/2)*x**10*sqrt(a/(b*x**2) + 1)/(7436429*a**13*b**36*x**22 + 44618574*a**12*b**37*x**24 + 111546435*a**11*b**38*x**26 + 148728580*a**10*b**39*x**28 + 111546435*a**9*b**40*x**30 + 44618574*a**8*b**41*x**32 + 7436429*a**7*b**42*x**34) - 89502546*a**11*b**(85/2)*x**12*sqrt(a/(b*x**2) + 1)/(7436429*a**13*b**36*x**22 + 44618574*a**12*b**37*x**24 + 111546435*a**11*b**38*x**26 + 148728580*a**10*b**39*x**28 + 111546435*a**9*b**40*x**30 + 44618574*a**8*b**41*x**32 + 7436429*a**7*b**42*x**34) - 53885062*a**10*b**(87/2)*x**14*sqrt(a/(b*x**2) + 1)/(7436429*a**13*b**36*x**22 + 44618574*a**12*b**37*x**24 + 111546435*a**11*b**38*x**26 + 148728580*a**10*b**39*x**28 + 111546435*a**9*b**40*x**30 + 44618574*a**8*b**41*x**32 + 7436429*a**7*b**42*x**34) - 21329935*a**9*b**(89/2)*x**16*sqrt(a/(b*x**2) + 1)/(7436429*a**13*b**36*x**22 + 44618574*a**12*b**37*x**24 + 111546435*a**11*b**38*x**26 + 148728580*a**10*b**39*x**28 + 111546435*a**9*b**40*x**30 + 44618574*a**8*b**41*x**32 + 7436429*a**7*b**42*x**34) - 5012953*a**8*b**(91/2)*x**18*sqrt(a/(b*x**2) + 1)/(7436429*a**13*b**36*x**22 + 44618574*a**12*b**37*x**24 + 111546435*a**11*b**38*x**26 + 148728580*a**10*b**39*x**28 + 111546435*a**9*b**40*x**30 + 44618574*a**8*b**41*x**32 + 7436429*a**7*b**42*x**34) - 531157*a**7*b**(93/2)*x**20*sqrt(a/(b*x**2) + 1)/(7436429*a**13*b**36*x**22 + 44618574*a**12*b**37*x**24 + 111546435*a**11*b**38*x**26 + 148728580*a**10*b**39*x**28 + 111546435*a**9*b**40*x**30 + 44618574*a**8*b**41*x**32 + 7436429*a**7*b**42*x**34) - 231*a**6*b**(95/2)*x**22*sqrt(a/(b*x**2) + 1)/(7436429*a**13*b**36*x**22 + 44618574*a**12*b**37*x**24 + 111546435*a**11*b**38*x**26 + 148728580*a**10*b**39*x**28 + 111546435*a**9*b**40*x**30 + 44618574*a**8*b**41*x**32 + 7436429*a**7*b**42*x**34) - 2772*a**5*b**(97/2)*x**24*sqrt(a/(b*x**2) + 1)/(7436429*a**13*b**36*x**22 + 44618574*a**12*b**37*x**24 + 111546435*a**11*b**38*x**26 + 148728580*a**10*b**39*x**28 + 111546435*a**9*b**40*x**30 + 44618574*a**8*b**41*x**32 + 7436429*a**7*b**42*x**34) - 9240*a**4*b**(99/2)*x**26*sqrt(a/(b*x**2) + 1)/(7436429*a**13*b**36*x**22 + 44618574*a**12*b**37*x**24 + 111546435*a**11*b**38*x**26 + 148728580*a**10*b**39*x**28 + 111546435*a**9*b**40*x**30 + 44618574*a**8*b**41*x**32 + 7436429*a**7*b**42*x**34) - 14784*a**3*b**(101/2)*x**28*sqrt(a/(b*x**2) + 1)/(7436429*a**13*b**36*x**22 + 44618574*a**12*b**37*x**24 + 111546435*a**11*b**38*x**26 + 148728580*a**10*b**39*x**28 + 111546435*a**9*b**40*x**30 + 44618574*a**8*b**41*x**32 + 7436429*a**7*b**42*x**34) - 12672*a**2*b**(103/2)*x**30*sqrt(a/(b*x**2) + 1)/(7436429*a**13*b**36*x**22 + 44618574*a**12*b**37*x**24 + 111546435*a**11*b**38*x**26 + 148728580*a**10*b**39*x**28 + 111546435*a**9*b**40*x**30 + 44618574*a**8*b**41*x**32 + 7436429*a**7*b**42*x**34) - 5632*a*b**(105/2)*x**32*sqrt(a/(b*x**2) + 1)/(7436429*a**13*b**36*x**22 + 44618574*a**12*b**37*x**24 + 111546435*a**11*b**38*x**26 + 148728580*a**10*b**39*x**28 + 111546435*a**9*b**40*x**30 + 44618574*a**8*b**41*x**32 + 7436429*a**7*b**42*x**34) - 1024*b**(107/2)*x**34*sqrt(a/(b*x**2) + 1)/(7436429*a**13*b**36*x**22 + 44618574*a**12*b**37*x**24 + 111546435*a**11*b**38*x**26 + 148728580*a**10*b**39*x**28 + 111546435*a**9*b**40*x**30 + 44618574*a**8*b**41*x**32 + 7436429*a**7*b**42*x**34)","B",0
441,1,61,0,1.971700," ","integrate(x**5*(4*x**2+9)**(1/2),x)","\frac{x^{6} \sqrt{4 x^{2} + 9}}{7} + \frac{9 x^{4} \sqrt{4 x^{2} + 9}}{140} - \frac{27 x^{2} \sqrt{4 x^{2} + 9}}{140} + \frac{243 \sqrt{4 x^{2} + 9}}{280}"," ",0,"x**6*sqrt(4*x**2 + 9)/7 + 9*x**4*sqrt(4*x**2 + 9)/140 - 27*x**2*sqrt(4*x**2 + 9)/140 + 243*sqrt(4*x**2 + 9)/280","A",0
442,1,75,0,4.564148," ","integrate(x**4*(4*x**2+9)**(1/2),x)","\frac{2 x^{7}}{3 \sqrt{4 x^{2} + 9}} + \frac{15 x^{5}}{8 \sqrt{4 x^{2} + 9}} - \frac{27 x^{3}}{64 \sqrt{4 x^{2} + 9}} - \frac{729 x}{256 \sqrt{4 x^{2} + 9}} + \frac{729 \operatorname{asinh}{\left(\frac{2 x}{3} \right)}}{512}"," ",0,"2*x**7/(3*sqrt(4*x**2 + 9)) + 15*x**5/(8*sqrt(4*x**2 + 9)) - 27*x**3/(64*sqrt(4*x**2 + 9)) - 729*x/(256*sqrt(4*x**2 + 9)) + 729*asinh(2*x/3)/512","A",0
443,1,44,0,0.629218," ","integrate(x**3*(4*x**2+9)**(1/2),x)","\frac{x^{4} \sqrt{4 x^{2} + 9}}{5} + \frac{3 x^{2} \sqrt{4 x^{2} + 9}}{20} - \frac{27 \sqrt{4 x^{2} + 9}}{40}"," ",0,"x**4*sqrt(4*x**2 + 9)/5 + 3*x**2*sqrt(4*x**2 + 9)/20 - 27*sqrt(4*x**2 + 9)/40","A",0
444,1,54,0,2.706965," ","integrate(x**2*(4*x**2+9)**(1/2),x)","\frac{x^{5}}{\sqrt{4 x^{2} + 9}} + \frac{27 x^{3}}{8 \sqrt{4 x^{2} + 9}} + \frac{81 x}{32 \sqrt{4 x^{2} + 9}} - \frac{81 \operatorname{asinh}{\left(\frac{2 x}{3} \right)}}{64}"," ",0,"x**5/sqrt(4*x**2 + 9) + 27*x**3/(8*sqrt(4*x**2 + 9)) + 81*x/(32*sqrt(4*x**2 + 9)) - 81*asinh(2*x/3)/64","A",0
445,1,27,0,0.199782," ","integrate(x*(4*x**2+9)**(1/2),x)","\frac{x^{2} \sqrt{4 x^{2} + 9}}{3} + \frac{3 \sqrt{4 x^{2} + 9}}{4}"," ",0,"x**2*sqrt(4*x**2 + 9)/3 + 3*sqrt(4*x**2 + 9)/4","B",0
446,1,22,0,0.214352," ","integrate((4*x**2+9)**(1/2),x)","\frac{x \sqrt{4 x^{2} + 9}}{2} + \frac{9 \operatorname{asinh}{\left(\frac{2 x}{3} \right)}}{4}"," ",0,"x*sqrt(4*x**2 + 9)/2 + 9*asinh(2*x/3)/4","A",0
447,1,39,0,1.245115," ","integrate((4*x**2+9)**(1/2)/x,x)","\frac{2 x}{\sqrt{1 + \frac{9}{4 x^{2}}}} - 3 \operatorname{asinh}{\left(\frac{3}{2 x} \right)} + \frac{9}{2 x \sqrt{1 + \frac{9}{4 x^{2}}}}"," ",0,"2*x/sqrt(1 + 9/(4*x**2)) - 3*asinh(3/(2*x)) + 9/(2*x*sqrt(1 + 9/(4*x**2)))","A",0
448,1,19,0,0.249307," ","integrate((4*x**2+9)**(1/2)/x**2,x)","2 \operatorname{asinh}{\left(\frac{2 x}{3} \right)} - \frac{\sqrt{4 x^{2} + 9}}{x}"," ",0,"2*asinh(2*x/3) - sqrt(4*x**2 + 9)/x","A",0
449,1,24,0,1.670425," ","integrate((4*x**2+9)**(1/2)/x**3,x)","- \frac{2 \operatorname{asinh}{\left(\frac{3}{2 x} \right)}}{3} - \frac{\sqrt{1 + \frac{9}{4 x^{2}}}}{x}"," ",0,"-2*asinh(3/(2*x))/3 - sqrt(1 + 9/(4*x**2))/x","A",0
450,1,34,0,0.927904," ","integrate((4*x**2+9)**(1/2)/x**4,x)","- \frac{8 \sqrt{1 + \frac{9}{4 x^{2}}}}{27} - \frac{2 \sqrt{1 + \frac{9}{4 x^{2}}}}{3 x^{2}}"," ",0,"-8*sqrt(1 + 9/(4*x**2))/27 - 2*sqrt(1 + 9/(4*x**2))/(3*x**2)","B",0
451,1,63,0,3.197291," ","integrate((4*x**2+9)**(1/2)/x**5,x)","\frac{2 \operatorname{asinh}{\left(\frac{3}{2 x} \right)}}{27} - \frac{1}{9 x \sqrt{1 + \frac{9}{4 x^{2}}}} - \frac{3}{4 x^{3} \sqrt{1 + \frac{9}{4 x^{2}}}} - \frac{9}{8 x^{5} \sqrt{1 + \frac{9}{4 x^{2}}}}"," ",0,"2*asinh(3/(2*x))/27 - 1/(9*x*sqrt(1 + 9/(4*x**2))) - 3/(4*x**3*sqrt(1 + 9/(4*x**2))) - 9/(8*x**5*sqrt(1 + 9/(4*x**2)))","A",0
452,1,61,0,2.008295," ","integrate(x**5*(-4*x**2+9)**(1/2),x)","\frac{x^{6} \sqrt{9 - 4 x^{2}}}{7} - \frac{9 x^{4} \sqrt{9 - 4 x^{2}}}{140} - \frac{27 x^{2} \sqrt{9 - 4 x^{2}}}{140} - \frac{243 \sqrt{9 - 4 x^{2}}}{280}"," ",0,"x**6*sqrt(9 - 4*x**2)/7 - 9*x**4*sqrt(9 - 4*x**2)/140 - 27*x**2*sqrt(9 - 4*x**2)/140 - 243*sqrt(9 - 4*x**2)/280","A",0
453,1,167,0,4.655187," ","integrate(x**4*(-4*x**2+9)**(1/2),x)","\begin{cases} \frac{2 i x^{7}}{3 \sqrt{4 x^{2} - 9}} - \frac{15 i x^{5}}{8 \sqrt{4 x^{2} - 9}} - \frac{27 i x^{3}}{64 \sqrt{4 x^{2} - 9}} + \frac{729 i x}{256 \sqrt{4 x^{2} - 9}} - \frac{729 i \operatorname{acosh}{\left(\frac{2 x}{3} \right)}}{512} & \text{for}\: \frac{4 \left|{x^{2}}\right|}{9} > 1 \\- \frac{2 x^{7}}{3 \sqrt{9 - 4 x^{2}}} + \frac{15 x^{5}}{8 \sqrt{9 - 4 x^{2}}} + \frac{27 x^{3}}{64 \sqrt{9 - 4 x^{2}}} - \frac{729 x}{256 \sqrt{9 - 4 x^{2}}} + \frac{729 \operatorname{asin}{\left(\frac{2 x}{3} \right)}}{512} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*I*x**7/(3*sqrt(4*x**2 - 9)) - 15*I*x**5/(8*sqrt(4*x**2 - 9)) - 27*I*x**3/(64*sqrt(4*x**2 - 9)) + 729*I*x/(256*sqrt(4*x**2 - 9)) - 729*I*acosh(2*x/3)/512, 4*Abs(x**2)/9 > 1), (-2*x**7/(3*sqrt(9 - 4*x**2)) + 15*x**5/(8*sqrt(9 - 4*x**2)) + 27*x**3/(64*sqrt(9 - 4*x**2)) - 729*x/(256*sqrt(9 - 4*x**2)) + 729*asin(2*x/3)/512, True))","A",0
454,1,44,0,0.670514," ","integrate(x**3*(-4*x**2+9)**(1/2),x)","\frac{x^{4} \sqrt{9 - 4 x^{2}}}{5} - \frac{3 x^{2} \sqrt{9 - 4 x^{2}}}{20} - \frac{27 \sqrt{9 - 4 x^{2}}}{40}"," ",0,"x**4*sqrt(9 - 4*x**2)/5 - 3*x**2*sqrt(9 - 4*x**2)/20 - 27*sqrt(9 - 4*x**2)/40","A",0
455,1,124,0,2.684466," ","integrate(x**2*(-4*x**2+9)**(1/2),x)","\begin{cases} \frac{i x^{5}}{\sqrt{4 x^{2} - 9}} - \frac{27 i x^{3}}{8 \sqrt{4 x^{2} - 9}} + \frac{81 i x}{32 \sqrt{4 x^{2} - 9}} - \frac{81 i \operatorname{acosh}{\left(\frac{2 x}{3} \right)}}{64} & \text{for}\: \frac{4 \left|{x^{2}}\right|}{9} > 1 \\- \frac{x^{5}}{\sqrt{9 - 4 x^{2}}} + \frac{27 x^{3}}{8 \sqrt{9 - 4 x^{2}}} - \frac{81 x}{32 \sqrt{9 - 4 x^{2}}} + \frac{81 \operatorname{asin}{\left(\frac{2 x}{3} \right)}}{64} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*x**5/sqrt(4*x**2 - 9) - 27*I*x**3/(8*sqrt(4*x**2 - 9)) + 81*I*x/(32*sqrt(4*x**2 - 9)) - 81*I*acosh(2*x/3)/64, 4*Abs(x**2)/9 > 1), (-x**5/sqrt(9 - 4*x**2) + 27*x**3/(8*sqrt(9 - 4*x**2)) - 81*x/(32*sqrt(9 - 4*x**2)) + 81*asin(2*x/3)/64, True))","A",0
456,1,27,0,0.203368," ","integrate(x*(-4*x**2+9)**(1/2),x)","\frac{x^{2} \sqrt{9 - 4 x^{2}}}{3} - \frac{3 \sqrt{9 - 4 x^{2}}}{4}"," ",0,"x**2*sqrt(9 - 4*x**2)/3 - 3*sqrt(9 - 4*x**2)/4","B",0
457,1,22,0,0.215303," ","integrate((-4*x**2+9)**(1/2),x)","\frac{x \sqrt{9 - 4 x^{2}}}{2} + \frac{9 \operatorname{asin}{\left(\frac{2 x}{3} \right)}}{4}"," ",0,"x*sqrt(9 - 4*x**2)/2 + 9*asin(2*x/3)/4","A",0
458,1,76,0,1.320141," ","integrate((-4*x**2+9)**(1/2)/x,x)","\begin{cases} i \sqrt{4 x^{2} - 9} - 3 \log{\left(x \right)} + \frac{3 \log{\left(x^{2} \right)}}{2} + 3 i \operatorname{asin}{\left(\frac{3}{2 x} \right)} & \text{for}\: \frac{4 \left|{x^{2}}\right|}{9} > 1 \\\sqrt{9 - 4 x^{2}} + \frac{3 \log{\left(x^{2} \right)}}{2} - 3 \log{\left(\sqrt{1 - \frac{4 x^{2}}{9}} + 1 \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*sqrt(4*x**2 - 9) - 3*log(x) + 3*log(x**2)/2 + 3*I*asin(3/(2*x)), 4*Abs(x**2)/9 > 1), (sqrt(9 - 4*x**2) + 3*log(x**2)/2 - 3*log(sqrt(1 - 4*x**2/9) + 1), True))","A",0
459,1,20,0,0.244586," ","integrate((-4*x**2+9)**(1/2)/x**2,x)","- 2 \operatorname{asin}{\left(\frac{2 x}{3} \right)} - \frac{\sqrt{9 - 4 x^{2}}}{x}"," ",0,"-2*asin(2*x/3) - sqrt(9 - 4*x**2)/x","A",0
460,1,97,0,1.733221," ","integrate((-4*x**2+9)**(1/2)/x**3,x)","\begin{cases} \frac{2 \operatorname{acosh}{\left(\frac{3}{2 x} \right)}}{3} + \frac{1}{x \sqrt{-1 + \frac{9}{4 x^{2}}}} - \frac{9}{4 x^{3} \sqrt{-1 + \frac{9}{4 x^{2}}}} & \text{for}\: \frac{9}{4 \left|{x^{2}}\right|} > 1 \\- \frac{2 i \operatorname{asin}{\left(\frac{3}{2 x} \right)}}{3} - \frac{i}{x \sqrt{1 - \frac{9}{4 x^{2}}}} + \frac{9 i}{4 x^{3} \sqrt{1 - \frac{9}{4 x^{2}}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*acosh(3/(2*x))/3 + 1/(x*sqrt(-1 + 9/(4*x**2))) - 9/(4*x**3*sqrt(-1 + 9/(4*x**2))), 9/(4*Abs(x**2)) > 1), (-2*I*asin(3/(2*x))/3 - I/(x*sqrt(1 - 9/(4*x**2))) + 9*I/(4*x**3*sqrt(1 - 9/(4*x**2))), True))","A",0
461,1,76,0,0.965615," ","integrate((-4*x**2+9)**(1/2)/x**4,x)","\begin{cases} \frac{8 \sqrt{-1 + \frac{9}{4 x^{2}}}}{27} - \frac{2 \sqrt{-1 + \frac{9}{4 x^{2}}}}{3 x^{2}} & \text{for}\: \frac{9}{4 \left|{x^{2}}\right|} > 1 \\\frac{8 i \sqrt{1 - \frac{9}{4 x^{2}}}}{27} - \frac{2 i \sqrt{1 - \frac{9}{4 x^{2}}}}{3 x^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*sqrt(-1 + 9/(4*x**2))/27 - 2*sqrt(-1 + 9/(4*x**2))/(3*x**2), 9/(4*Abs(x**2)) > 1), (8*I*sqrt(1 - 9/(4*x**2))/27 - 2*I*sqrt(1 - 9/(4*x**2))/(3*x**2), True))","B",0
462,1,139,0,3.274545," ","integrate((-4*x**2+9)**(1/2)/x**5,x)","\begin{cases} \frac{2 \operatorname{acosh}{\left(\frac{3}{2 x} \right)}}{27} - \frac{1}{9 x \sqrt{-1 + \frac{9}{4 x^{2}}}} + \frac{3}{4 x^{3} \sqrt{-1 + \frac{9}{4 x^{2}}}} - \frac{9}{8 x^{5} \sqrt{-1 + \frac{9}{4 x^{2}}}} & \text{for}\: \frac{9}{4 \left|{x^{2}}\right|} > 1 \\- \frac{2 i \operatorname{asin}{\left(\frac{3}{2 x} \right)}}{27} + \frac{i}{9 x \sqrt{1 - \frac{9}{4 x^{2}}}} - \frac{3 i}{4 x^{3} \sqrt{1 - \frac{9}{4 x^{2}}}} + \frac{9 i}{8 x^{5} \sqrt{1 - \frac{9}{4 x^{2}}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*acosh(3/(2*x))/27 - 1/(9*x*sqrt(-1 + 9/(4*x**2))) + 3/(4*x**3*sqrt(-1 + 9/(4*x**2))) - 9/(8*x**5*sqrt(-1 + 9/(4*x**2))), 9/(4*Abs(x**2)) > 1), (-2*I*asin(3/(2*x))/27 + I/(9*x*sqrt(1 - 9/(4*x**2))) - 3*I/(4*x**3*sqrt(1 - 9/(4*x**2))) + 9*I/(8*x**5*sqrt(1 - 9/(4*x**2))), True))","A",0
463,1,61,0,1.917967," ","integrate(x**5*(4*x**2-9)**(1/2),x)","\frac{x^{6} \sqrt{4 x^{2} - 9}}{7} - \frac{9 x^{4} \sqrt{4 x^{2} - 9}}{140} - \frac{27 x^{2} \sqrt{4 x^{2} - 9}}{140} - \frac{243 \sqrt{4 x^{2} - 9}}{280}"," ",0,"x**6*sqrt(4*x**2 - 9)/7 - 9*x**4*sqrt(4*x**2 - 9)/140 - 27*x**2*sqrt(4*x**2 - 9)/140 - 243*sqrt(4*x**2 - 9)/280","A",0
464,1,167,0,4.563428," ","integrate(x**4*(4*x**2-9)**(1/2),x)","\begin{cases} \frac{2 x^{7}}{3 \sqrt{4 x^{2} - 9}} - \frac{15 x^{5}}{8 \sqrt{4 x^{2} - 9}} - \frac{27 x^{3}}{64 \sqrt{4 x^{2} - 9}} + \frac{729 x}{256 \sqrt{4 x^{2} - 9}} - \frac{729 \operatorname{acosh}{\left(\frac{2 x}{3} \right)}}{512} & \text{for}\: \frac{4 \left|{x^{2}}\right|}{9} > 1 \\- \frac{2 i x^{7}}{3 \sqrt{9 - 4 x^{2}}} + \frac{15 i x^{5}}{8 \sqrt{9 - 4 x^{2}}} + \frac{27 i x^{3}}{64 \sqrt{9 - 4 x^{2}}} - \frac{729 i x}{256 \sqrt{9 - 4 x^{2}}} + \frac{729 i \operatorname{asin}{\left(\frac{2 x}{3} \right)}}{512} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*x**7/(3*sqrt(4*x**2 - 9)) - 15*x**5/(8*sqrt(4*x**2 - 9)) - 27*x**3/(64*sqrt(4*x**2 - 9)) + 729*x/(256*sqrt(4*x**2 - 9)) - 729*acosh(2*x/3)/512, 4*Abs(x**2)/9 > 1), (-2*I*x**7/(3*sqrt(9 - 4*x**2)) + 15*I*x**5/(8*sqrt(9 - 4*x**2)) + 27*I*x**3/(64*sqrt(9 - 4*x**2)) - 729*I*x/(256*sqrt(9 - 4*x**2)) + 729*I*asin(2*x/3)/512, True))","A",0
465,1,44,0,0.655593," ","integrate(x**3*(4*x**2-9)**(1/2),x)","\frac{x^{4} \sqrt{4 x^{2} - 9}}{5} - \frac{3 x^{2} \sqrt{4 x^{2} - 9}}{20} - \frac{27 \sqrt{4 x^{2} - 9}}{40}"," ",0,"x**4*sqrt(4*x**2 - 9)/5 - 3*x**2*sqrt(4*x**2 - 9)/20 - 27*sqrt(4*x**2 - 9)/40","A",0
466,1,124,0,2.799491," ","integrate(x**2*(4*x**2-9)**(1/2),x)","\begin{cases} \frac{x^{5}}{\sqrt{4 x^{2} - 9}} - \frac{27 x^{3}}{8 \sqrt{4 x^{2} - 9}} + \frac{81 x}{32 \sqrt{4 x^{2} - 9}} - \frac{81 \operatorname{acosh}{\left(\frac{2 x}{3} \right)}}{64} & \text{for}\: \frac{4 \left|{x^{2}}\right|}{9} > 1 \\- \frac{i x^{5}}{\sqrt{9 - 4 x^{2}}} + \frac{27 i x^{3}}{8 \sqrt{9 - 4 x^{2}}} - \frac{81 i x}{32 \sqrt{9 - 4 x^{2}}} + \frac{81 i \operatorname{asin}{\left(\frac{2 x}{3} \right)}}{64} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x**5/sqrt(4*x**2 - 9) - 27*x**3/(8*sqrt(4*x**2 - 9)) + 81*x/(32*sqrt(4*x**2 - 9)) - 81*acosh(2*x/3)/64, 4*Abs(x**2)/9 > 1), (-I*x**5/sqrt(9 - 4*x**2) + 27*I*x**3/(8*sqrt(9 - 4*x**2)) - 81*I*x/(32*sqrt(9 - 4*x**2)) + 81*I*asin(2*x/3)/64, True))","A",0
467,1,27,0,0.201717," ","integrate(x*(4*x**2-9)**(1/2),x)","\frac{x^{2} \sqrt{4 x^{2} - 9}}{3} - \frac{3 \sqrt{4 x^{2} - 9}}{4}"," ",0,"x**2*sqrt(4*x**2 - 9)/3 - 3*sqrt(4*x**2 - 9)/4","B",0
468,1,22,0,0.215326," ","integrate((4*x**2-9)**(1/2),x)","\frac{x \sqrt{4 x^{2} - 9}}{2} - \frac{9 \operatorname{acosh}{\left(\frac{2 x}{3} \right)}}{4}"," ",0,"x*sqrt(4*x**2 - 9)/2 - 9*acosh(2*x/3)/4","A",0
469,1,82,0,1.371100," ","integrate((4*x**2-9)**(1/2)/x,x)","\begin{cases} \sqrt{4 x^{2} - 9} - 3 i \log{\left(x \right)} + \frac{3 i \log{\left(x^{2} \right)}}{2} + 3 \operatorname{asin}{\left(\frac{3}{2 x} \right)} & \text{for}\: \frac{4 \left|{x^{2}}\right|}{9} > 1 \\i \sqrt{9 - 4 x^{2}} + \frac{3 i \log{\left(x^{2} \right)}}{2} - 3 i \log{\left(\sqrt{1 - \frac{4 x^{2}}{9}} + 1 \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((sqrt(4*x**2 - 9) - 3*I*log(x) + 3*I*log(x**2)/2 + 3*asin(3/(2*x)), 4*Abs(x**2)/9 > 1), (I*sqrt(9 - 4*x**2) + 3*I*log(x**2)/2 - 3*I*log(sqrt(1 - 4*x**2/9) + 1), True))","C",0
470,1,19,0,0.248569," ","integrate((4*x**2-9)**(1/2)/x**2,x)","2 \operatorname{acosh}{\left(\frac{2 x}{3} \right)} - \frac{\sqrt{4 x^{2} - 9}}{x}"," ",0,"2*acosh(2*x/3) - sqrt(4*x**2 - 9)/x","A",0
471,1,97,0,1.738440," ","integrate((4*x**2-9)**(1/2)/x**3,x)","\begin{cases} \frac{2 i \operatorname{acosh}{\left(\frac{3}{2 x} \right)}}{3} + \frac{i}{x \sqrt{-1 + \frac{9}{4 x^{2}}}} - \frac{9 i}{4 x^{3} \sqrt{-1 + \frac{9}{4 x^{2}}}} & \text{for}\: \frac{9}{4 \left|{x^{2}}\right|} > 1 \\- \frac{2 \operatorname{asin}{\left(\frac{3}{2 x} \right)}}{3} - \frac{1}{x \sqrt{1 - \frac{9}{4 x^{2}}}} + \frac{9}{4 x^{3} \sqrt{1 - \frac{9}{4 x^{2}}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*I*acosh(3/(2*x))/3 + I/(x*sqrt(-1 + 9/(4*x**2))) - 9*I/(4*x**3*sqrt(-1 + 9/(4*x**2))), 9/(4*Abs(x**2)) > 1), (-2*asin(3/(2*x))/3 - 1/(x*sqrt(1 - 9/(4*x**2))) + 9/(4*x**3*sqrt(1 - 9/(4*x**2))), True))","A",0
472,1,76,0,0.975461," ","integrate((4*x**2-9)**(1/2)/x**4,x)","\begin{cases} \frac{8 i \sqrt{-1 + \frac{9}{4 x^{2}}}}{27} - \frac{2 i \sqrt{-1 + \frac{9}{4 x^{2}}}}{3 x^{2}} & \text{for}\: \frac{9}{4 \left|{x^{2}}\right|} > 1 \\\frac{8 \sqrt{1 - \frac{9}{4 x^{2}}}}{27} - \frac{2 \sqrt{1 - \frac{9}{4 x^{2}}}}{3 x^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*I*sqrt(-1 + 9/(4*x**2))/27 - 2*I*sqrt(-1 + 9/(4*x**2))/(3*x**2), 9/(4*Abs(x**2)) > 1), (8*sqrt(1 - 9/(4*x**2))/27 - 2*sqrt(1 - 9/(4*x**2))/(3*x**2), True))","B",0
473,1,139,0,3.359915," ","integrate((4*x**2-9)**(1/2)/x**5,x)","\begin{cases} \frac{2 i \operatorname{acosh}{\left(\frac{3}{2 x} \right)}}{27} - \frac{i}{9 x \sqrt{-1 + \frac{9}{4 x^{2}}}} + \frac{3 i}{4 x^{3} \sqrt{-1 + \frac{9}{4 x^{2}}}} - \frac{9 i}{8 x^{5} \sqrt{-1 + \frac{9}{4 x^{2}}}} & \text{for}\: \frac{9}{4 \left|{x^{2}}\right|} > 1 \\- \frac{2 \operatorname{asin}{\left(\frac{3}{2 x} \right)}}{27} + \frac{1}{9 x \sqrt{1 - \frac{9}{4 x^{2}}}} - \frac{3}{4 x^{3} \sqrt{1 - \frac{9}{4 x^{2}}}} + \frac{9}{8 x^{5} \sqrt{1 - \frac{9}{4 x^{2}}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*I*acosh(3/(2*x))/27 - I/(9*x*sqrt(-1 + 9/(4*x**2))) + 3*I/(4*x**3*sqrt(-1 + 9/(4*x**2))) - 9*I/(8*x**5*sqrt(-1 + 9/(4*x**2))), 9/(4*Abs(x**2)) > 1), (-2*asin(3/(2*x))/27 + 1/(9*x*sqrt(1 - 9/(4*x**2))) - 3/(4*x**3*sqrt(1 - 9/(4*x**2))) + 9/(8*x**5*sqrt(1 - 9/(4*x**2))), True))","A",0
474,1,68,0,2.081021," ","integrate(x**5*(-4*x**2-9)**(1/2),x)","\frac{x^{6} \sqrt{- 4 x^{2} - 9}}{7} + \frac{9 x^{4} \sqrt{- 4 x^{2} - 9}}{140} - \frac{27 x^{2} \sqrt{- 4 x^{2} - 9}}{140} + \frac{243 \sqrt{- 4 x^{2} - 9}}{280}"," ",0,"x**6*sqrt(-4*x**2 - 9)/7 + 9*x**4*sqrt(-4*x**2 - 9)/140 - 27*x**2*sqrt(-4*x**2 - 9)/140 + 243*sqrt(-4*x**2 - 9)/280","A",0
475,1,83,0,4.672299," ","integrate(x**4*(-4*x**2-9)**(1/2),x)","\frac{2 i x^{7}}{3 \sqrt{4 x^{2} + 9}} + \frac{15 i x^{5}}{8 \sqrt{4 x^{2} + 9}} - \frac{27 i x^{3}}{64 \sqrt{4 x^{2} + 9}} - \frac{729 i x}{256 \sqrt{4 x^{2} + 9}} + \frac{729 i \operatorname{asinh}{\left(\frac{2 x}{3} \right)}}{512}"," ",0,"2*I*x**7/(3*sqrt(4*x**2 + 9)) + 15*I*x**5/(8*sqrt(4*x**2 + 9)) - 27*I*x**3/(64*sqrt(4*x**2 + 9)) - 729*I*x/(256*sqrt(4*x**2 + 9)) + 729*I*asinh(2*x/3)/512","C",0
476,1,49,0,0.686364," ","integrate(x**3*(-4*x**2-9)**(1/2),x)","\frac{x^{4} \sqrt{- 4 x^{2} - 9}}{5} + \frac{3 x^{2} \sqrt{- 4 x^{2} - 9}}{20} - \frac{27 \sqrt{- 4 x^{2} - 9}}{40}"," ",0,"x**4*sqrt(-4*x**2 - 9)/5 + 3*x**2*sqrt(-4*x**2 - 9)/20 - 27*sqrt(-4*x**2 - 9)/40","A",0
477,1,61,0,2.759214," ","integrate(x**2*(-4*x**2-9)**(1/2),x)","\frac{i x^{5}}{\sqrt{4 x^{2} + 9}} + \frac{27 i x^{3}}{8 \sqrt{4 x^{2} + 9}} + \frac{81 i x}{32 \sqrt{4 x^{2} + 9}} - \frac{81 i \operatorname{asinh}{\left(\frac{2 x}{3} \right)}}{64}"," ",0,"I*x**5/sqrt(4*x**2 + 9) + 27*I*x**3/(8*sqrt(4*x**2 + 9)) + 81*I*x/(32*sqrt(4*x**2 + 9)) - 81*I*asinh(2*x/3)/64","C",0
478,1,31,0,0.218486," ","integrate(x*(-4*x**2-9)**(1/2),x)","\frac{x^{2} \sqrt{- 4 x^{2} - 9}}{3} + \frac{3 \sqrt{- 4 x^{2} - 9}}{4}"," ",0,"x**2*sqrt(-4*x**2 - 9)/3 + 3*sqrt(-4*x**2 - 9)/4","B",0
479,1,34,0,0.385075," ","integrate((-4*x**2-9)**(1/2),x)","\frac{x \sqrt{- 4 x^{2} - 9}}{2} - \frac{9 \operatorname{atan}{\left(\frac{2 x}{\sqrt{- 4 x^{2} - 9}} \right)}}{4}"," ",0,"x*sqrt(-4*x**2 - 9)/2 - 9*atan(2*x/sqrt(-4*x**2 - 9))/4","A",0
480,1,44,0,1.263619," ","integrate(1/x*(-4*x**2-9)**(1/2),x)","\frac{2 i x}{\sqrt{1 + \frac{9}{4 x^{2}}}} - 3 i \operatorname{asinh}{\left(\frac{3}{2 x} \right)} + \frac{9 i}{2 x \sqrt{1 + \frac{9}{4 x^{2}}}}"," ",0,"2*I*x/sqrt(1 + 9/(4*x**2)) - 3*I*asinh(3/(2*x)) + 9*I/(2*x*sqrt(1 + 9/(4*x**2)))","C",0
481,1,32,0,0.416629," ","integrate((-4*x**2-9)**(1/2)/x**2,x)","- 2 \operatorname{atan}{\left(\frac{2 x}{\sqrt{- 4 x^{2} - 9}} \right)} - \frac{\sqrt{- 4 x^{2} - 9}}{x}"," ",0,"-2*atan(2*x/sqrt(-4*x**2 - 9)) - sqrt(-4*x**2 - 9)/x","A",0
482,1,27,0,1.701144," ","integrate((-4*x**2-9)**(1/2)/x**3,x)","- \frac{2 i \operatorname{asinh}{\left(\frac{3}{2 x} \right)}}{3} - \frac{i \sqrt{1 + \frac{9}{4 x^{2}}}}{x}"," ",0,"-2*I*asinh(3/(2*x))/3 - I*sqrt(1 + 9/(4*x**2))/x","C",0
483,1,37,0,1.000050," ","integrate((-4*x**2-9)**(1/2)/x**4,x)","- \frac{8 i \sqrt{1 + \frac{9}{4 x^{2}}}}{27} - \frac{2 i \sqrt{1 + \frac{9}{4 x^{2}}}}{3 x^{2}}"," ",0,"-8*I*sqrt(1 + 9/(4*x**2))/27 - 2*I*sqrt(1 + 9/(4*x**2))/(3*x**2)","C",0
484,1,68,0,3.366626," ","integrate((-4*x**2-9)**(1/2)/x**5,x)","\frac{2 i \operatorname{asinh}{\left(\frac{3}{2 x} \right)}}{27} - \frac{i}{9 x \sqrt{1 + \frac{9}{4 x^{2}}}} - \frac{3 i}{4 x^{3} \sqrt{1 + \frac{9}{4 x^{2}}}} - \frac{9 i}{8 x^{5} \sqrt{1 + \frac{9}{4 x^{2}}}}"," ",0,"2*I*asinh(3/(2*x))/27 - I/(9*x*sqrt(1 + 9/(4*x**2))) - 3*I/(4*x**3*sqrt(1 + 9/(4*x**2))) - 9*I/(8*x**5*sqrt(1 + 9/(4*x**2)))","C",0
485,1,68,0,0.827033," ","integrate(x**5/(b*x**2+a)**(1/2),x)","\begin{cases} \frac{8 a^{2} \sqrt{a + b x^{2}}}{15 b^{3}} - \frac{4 a x^{2} \sqrt{a + b x^{2}}}{15 b^{2}} + \frac{x^{4} \sqrt{a + b x^{2}}}{5 b} & \text{for}\: b \neq 0 \\\frac{x^{6}}{6 \sqrt{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*a**2*sqrt(a + b*x**2)/(15*b**3) - 4*a*x**2*sqrt(a + b*x**2)/(15*b**2) + x**4*sqrt(a + b*x**2)/(5*b), Ne(b, 0)), (x**6/(6*sqrt(a)), True))","A",0
486,1,95,0,4.030069," ","integrate(x**4/(b*x**2+a)**(1/2),x)","- \frac{3 a^{\frac{3}{2}} x}{8 b^{2} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{\sqrt{a} x^{3}}{8 b \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{3 a^{2} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{8 b^{\frac{5}{2}}} + \frac{x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"-3*a**(3/2)*x/(8*b**2*sqrt(1 + b*x**2/a)) - sqrt(a)*x**3/(8*b*sqrt(1 + b*x**2/a)) + 3*a**2*asinh(sqrt(b)*x/sqrt(a))/(8*b**(5/2)) + x**5/(4*sqrt(a)*sqrt(1 + b*x**2/a))","A",0
487,1,44,0,0.487814," ","integrate(x**3/(b*x**2+a)**(1/2),x)","\begin{cases} - \frac{2 a \sqrt{a + b x^{2}}}{3 b^{2}} + \frac{x^{2} \sqrt{a + b x^{2}}}{3 b} & \text{for}\: b \neq 0 \\\frac{x^{4}}{4 \sqrt{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*a*sqrt(a + b*x**2)/(3*b**2) + x**2*sqrt(a + b*x**2)/(3*b), Ne(b, 0)), (x**4/(4*sqrt(a)), True))","A",0
488,1,42,0,2.253187," ","integrate(x**2/(b*x**2+a)**(1/2),x)","\frac{\sqrt{a} x \sqrt{1 + \frac{b x^{2}}{a}}}{2 b} - \frac{a \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{2 b^{\frac{3}{2}}}"," ",0,"sqrt(a)*x*sqrt(1 + b*x**2/a)/(2*b) - a*asinh(sqrt(b)*x/sqrt(a))/(2*b**(3/2))","A",0
489,1,20,0,0.381636," ","integrate(x/(b*x**2+a)**(1/2),x)","\begin{cases} \frac{\sqrt{a + b x^{2}}}{b} & \text{for}\: b \neq 0 \\\frac{x^{2}}{2 \sqrt{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((sqrt(a + b*x**2)/b, Ne(b, 0)), (x**2/(2*sqrt(a)), True))","A",0
490,1,17,0,1.022727," ","integrate(1/(b*x**2+a)**(1/2),x)","\frac{\operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{\sqrt{b}}"," ",0,"asinh(sqrt(b)*x/sqrt(a))/sqrt(b)","A",0
491,1,19,0,1.061178," ","integrate(1/x/(b*x**2+a)**(1/2),x)","- \frac{\operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)}}{\sqrt{a}}"," ",0,"-asinh(sqrt(a)/(sqrt(b)*x))/sqrt(a)","A",0
492,1,19,0,0.685636," ","integrate(1/x**2/(b*x**2+a)**(1/2),x)","- \frac{\sqrt{b} \sqrt{\frac{a}{b x^{2}} + 1}}{a}"," ",0,"-sqrt(b)*sqrt(a/(b*x**2) + 1)/a","A",0
493,1,42,0,2.251049," ","integrate(1/x**3/(b*x**2+a)**(1/2),x)","- \frac{\sqrt{b} \sqrt{\frac{a}{b x^{2}} + 1}}{2 a x} + \frac{b \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)}}{2 a^{\frac{3}{2}}}"," ",0,"-sqrt(b)*sqrt(a/(b*x**2) + 1)/(2*a*x) + b*asinh(sqrt(a)/(sqrt(b)*x))/(2*a**(3/2))","A",0
494,1,46,0,0.903382," ","integrate(1/x**4/(b*x**2+a)**(1/2),x)","- \frac{\sqrt{b} \sqrt{\frac{a}{b x^{2}} + 1}}{3 a x^{2}} + \frac{2 b^{\frac{3}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{3 a^{2}}"," ",0,"-sqrt(b)*sqrt(a/(b*x**2) + 1)/(3*a*x**2) + 2*b**(3/2)*sqrt(a/(b*x**2) + 1)/(3*a**2)","A",0
495,1,97,0,4.248625," ","integrate(1/x**5/(b*x**2+a)**(1/2),x)","- \frac{1}{4 \sqrt{b} x^{5} \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{\sqrt{b}}{8 a x^{3} \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{3 b^{\frac{3}{2}}}{8 a^{2} x \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{3 b^{2} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)}}{8 a^{\frac{5}{2}}}"," ",0,"-1/(4*sqrt(b)*x**5*sqrt(a/(b*x**2) + 1)) + sqrt(b)/(8*a*x**3*sqrt(a/(b*x**2) + 1)) + 3*b**(3/2)/(8*a**2*x*sqrt(a/(b*x**2) + 1)) - 3*b**2*asinh(sqrt(a)/(sqrt(b)*x))/(8*a**(5/2))","A",0
496,1,68,0,0.941979," ","integrate(x**5/(b*x**2+a)**(3/2),x)","\begin{cases} - \frac{8 a^{2}}{3 b^{3} \sqrt{a + b x^{2}}} - \frac{4 a x^{2}}{3 b^{2} \sqrt{a + b x^{2}}} + \frac{x^{4}}{3 b \sqrt{a + b x^{2}}} & \text{for}\: b \neq 0 \\\frac{x^{6}}{6 a^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-8*a**2/(3*b**3*sqrt(a + b*x**2)) - 4*a*x**2/(3*b**2*sqrt(a + b*x**2)) + x**4/(3*b*sqrt(a + b*x**2)), Ne(b, 0)), (x**6/(6*a**(3/2)), True))","A",0
497,1,71,0,3.256734," ","integrate(x**4/(b*x**2+a)**(3/2),x)","\frac{3 \sqrt{a} x}{2 b^{2} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{3 a \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{2 b^{\frac{5}{2}}} + \frac{x^{3}}{2 \sqrt{a} b \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"3*sqrt(a)*x/(2*b**2*sqrt(1 + b*x**2/a)) - 3*a*asinh(sqrt(b)*x/sqrt(a))/(2*b**(5/2)) + x**3/(2*sqrt(a)*b*sqrt(1 + b*x**2/a))","A",0
498,1,41,0,0.575441," ","integrate(x**3/(b*x**2+a)**(3/2),x)","\begin{cases} \frac{2 a}{b^{2} \sqrt{a + b x^{2}}} + \frac{x^{2}}{b \sqrt{a + b x^{2}}} & \text{for}\: b \neq 0 \\\frac{x^{4}}{4 a^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a/(b**2*sqrt(a + b*x**2)) + x**2/(b*sqrt(a + b*x**2)), Ne(b, 0)), (x**4/(4*a**(3/2)), True))","A",0
499,1,37,0,1.705552," ","integrate(x**2/(b*x**2+a)**(3/2),x)","\frac{\operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{b^{\frac{3}{2}}} - \frac{x}{\sqrt{a} b \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"asinh(sqrt(b)*x/sqrt(a))/b**(3/2) - x/(sqrt(a)*b*sqrt(1 + b*x**2/a))","A",0
500,1,24,0,0.539832," ","integrate(x/(b*x**2+a)**(3/2),x)","\begin{cases} - \frac{1}{b \sqrt{a + b x^{2}}} & \text{for}\: b \neq 0 \\\frac{x^{2}}{2 a^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-1/(b*sqrt(a + b*x**2)), Ne(b, 0)), (x**2/(2*a**(3/2)), True))","A",0
501,1,17,0,0.629436," ","integrate(1/(b*x**2+a)**(3/2),x)","\frac{x}{a^{\frac{3}{2}} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"x/(a**(3/2)*sqrt(1 + b*x**2/a))","A",0
502,1,184,0,1.730712," ","integrate(1/x/(b*x**2+a)**(3/2),x)","\frac{2 a^{3} \sqrt{1 + \frac{b x^{2}}{a}}}{2 a^{\frac{9}{2}} + 2 a^{\frac{7}{2}} b x^{2}} + \frac{a^{3} \log{\left(\frac{b x^{2}}{a} \right)}}{2 a^{\frac{9}{2}} + 2 a^{\frac{7}{2}} b x^{2}} - \frac{2 a^{3} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{2 a^{\frac{9}{2}} + 2 a^{\frac{7}{2}} b x^{2}} + \frac{a^{2} b x^{2} \log{\left(\frac{b x^{2}}{a} \right)}}{2 a^{\frac{9}{2}} + 2 a^{\frac{7}{2}} b x^{2}} - \frac{2 a^{2} b x^{2} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{2 a^{\frac{9}{2}} + 2 a^{\frac{7}{2}} b x^{2}}"," ",0,"2*a**3*sqrt(1 + b*x**2/a)/(2*a**(9/2) + 2*a**(7/2)*b*x**2) + a**3*log(b*x**2/a)/(2*a**(9/2) + 2*a**(7/2)*b*x**2) - 2*a**3*log(sqrt(1 + b*x**2/a) + 1)/(2*a**(9/2) + 2*a**(7/2)*b*x**2) + a**2*b*x**2*log(b*x**2/a)/(2*a**(9/2) + 2*a**(7/2)*b*x**2) - 2*a**2*b*x**2*log(sqrt(1 + b*x**2/a) + 1)/(2*a**(9/2) + 2*a**(7/2)*b*x**2)","B",0
503,1,46,0,0.855926," ","integrate(1/x**2/(b*x**2+a)**(3/2),x)","- \frac{1}{a \sqrt{b} x^{2} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{2 \sqrt{b}}{a^{2} \sqrt{\frac{a}{b x^{2}} + 1}}"," ",0,"-1/(a*sqrt(b)*x**2*sqrt(a/(b*x**2) + 1)) - 2*sqrt(b)/(a**2*sqrt(a/(b*x**2) + 1))","A",0
504,1,73,0,3.386325," ","integrate(1/x**3/(b*x**2+a)**(3/2),x)","- \frac{1}{2 a \sqrt{b} x^{3} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{3 \sqrt{b}}{2 a^{2} x \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{3 b \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)}}{2 a^{\frac{5}{2}}}"," ",0,"-1/(2*a*sqrt(b)*x**3*sqrt(a/(b*x**2) + 1)) - 3*sqrt(b)/(2*a**2*x*sqrt(a/(b*x**2) + 1)) + 3*b*asinh(sqrt(a)/(sqrt(b)*x))/(2*a**(5/2))","A",0
505,1,233,0,1.233138," ","integrate(1/x**4/(b*x**2+a)**(3/2),x)","- \frac{a^{3} b^{\frac{9}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{3 a^{5} b^{4} x^{2} + 6 a^{4} b^{5} x^{4} + 3 a^{3} b^{6} x^{6}} + \frac{3 a^{2} b^{\frac{11}{2}} x^{2} \sqrt{\frac{a}{b x^{2}} + 1}}{3 a^{5} b^{4} x^{2} + 6 a^{4} b^{5} x^{4} + 3 a^{3} b^{6} x^{6}} + \frac{12 a b^{\frac{13}{2}} x^{4} \sqrt{\frac{a}{b x^{2}} + 1}}{3 a^{5} b^{4} x^{2} + 6 a^{4} b^{5} x^{4} + 3 a^{3} b^{6} x^{6}} + \frac{8 b^{\frac{15}{2}} x^{6} \sqrt{\frac{a}{b x^{2}} + 1}}{3 a^{5} b^{4} x^{2} + 6 a^{4} b^{5} x^{4} + 3 a^{3} b^{6} x^{6}}"," ",0,"-a**3*b**(9/2)*sqrt(a/(b*x**2) + 1)/(3*a**5*b**4*x**2 + 6*a**4*b**5*x**4 + 3*a**3*b**6*x**6) + 3*a**2*b**(11/2)*x**2*sqrt(a/(b*x**2) + 1)/(3*a**5*b**4*x**2 + 6*a**4*b**5*x**4 + 3*a**3*b**6*x**6) + 12*a*b**(13/2)*x**4*sqrt(a/(b*x**2) + 1)/(3*a**5*b**4*x**2 + 6*a**4*b**5*x**4 + 3*a**3*b**6*x**6) + 8*b**(15/2)*x**6*sqrt(a/(b*x**2) + 1)/(3*a**5*b**4*x**2 + 6*a**4*b**5*x**4 + 3*a**3*b**6*x**6)","B",0
506,1,367,0,5.121549," ","integrate(x**6/(b*x**2+a)**(5/2),x)","- \frac{15 a^{\frac{81}{2}} b^{22} \sqrt{1 + \frac{b x^{2}}{a}} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{6 a^{\frac{79}{2}} b^{\frac{51}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 6 a^{\frac{77}{2}} b^{\frac{53}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{15 a^{\frac{79}{2}} b^{23} x^{2} \sqrt{1 + \frac{b x^{2}}{a}} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{6 a^{\frac{79}{2}} b^{\frac{51}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 6 a^{\frac{77}{2}} b^{\frac{53}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{15 a^{40} b^{\frac{45}{2}} x}{6 a^{\frac{79}{2}} b^{\frac{51}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 6 a^{\frac{77}{2}} b^{\frac{53}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{20 a^{39} b^{\frac{47}{2}} x^{3}}{6 a^{\frac{79}{2}} b^{\frac{51}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 6 a^{\frac{77}{2}} b^{\frac{53}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{3 a^{38} b^{\frac{49}{2}} x^{5}}{6 a^{\frac{79}{2}} b^{\frac{51}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 6 a^{\frac{77}{2}} b^{\frac{53}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"-15*a**(81/2)*b**22*sqrt(1 + b*x**2/a)*asinh(sqrt(b)*x/sqrt(a))/(6*a**(79/2)*b**(51/2)*sqrt(1 + b*x**2/a) + 6*a**(77/2)*b**(53/2)*x**2*sqrt(1 + b*x**2/a)) - 15*a**(79/2)*b**23*x**2*sqrt(1 + b*x**2/a)*asinh(sqrt(b)*x/sqrt(a))/(6*a**(79/2)*b**(51/2)*sqrt(1 + b*x**2/a) + 6*a**(77/2)*b**(53/2)*x**2*sqrt(1 + b*x**2/a)) + 15*a**40*b**(45/2)*x/(6*a**(79/2)*b**(51/2)*sqrt(1 + b*x**2/a) + 6*a**(77/2)*b**(53/2)*x**2*sqrt(1 + b*x**2/a)) + 20*a**39*b**(47/2)*x**3/(6*a**(79/2)*b**(51/2)*sqrt(1 + b*x**2/a) + 6*a**(77/2)*b**(53/2)*x**2*sqrt(1 + b*x**2/a)) + 3*a**38*b**(49/2)*x**5/(6*a**(79/2)*b**(51/2)*sqrt(1 + b*x**2/a) + 6*a**(77/2)*b**(53/2)*x**2*sqrt(1 + b*x**2/a))","B",0
507,1,138,0,1.091903," ","integrate(x**5/(b*x**2+a)**(5/2),x)","\begin{cases} \frac{8 a^{2}}{3 a b^{3} \sqrt{a + b x^{2}} + 3 b^{4} x^{2} \sqrt{a + b x^{2}}} + \frac{12 a b x^{2}}{3 a b^{3} \sqrt{a + b x^{2}} + 3 b^{4} x^{2} \sqrt{a + b x^{2}}} + \frac{3 b^{2} x^{4}}{3 a b^{3} \sqrt{a + b x^{2}} + 3 b^{4} x^{2} \sqrt{a + b x^{2}}} & \text{for}\: b \neq 0 \\\frac{x^{6}}{6 a^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*a**2/(3*a*b**3*sqrt(a + b*x**2) + 3*b**4*x**2*sqrt(a + b*x**2)) + 12*a*b*x**2/(3*a*b**3*sqrt(a + b*x**2) + 3*b**4*x**2*sqrt(a + b*x**2)) + 3*b**2*x**4/(3*a*b**3*sqrt(a + b*x**2) + 3*b**4*x**2*sqrt(a + b*x**2)), Ne(b, 0)), (x**6/(6*a**(5/2)), True))","A",0
508,1,303,0,2.992092," ","integrate(x**4/(b*x**2+a)**(5/2),x)","\frac{3 a^{\frac{39}{2}} b^{11} \sqrt{1 + \frac{b x^{2}}{a}} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{3 a^{\frac{39}{2}} b^{\frac{27}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 3 a^{\frac{37}{2}} b^{\frac{29}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{3 a^{\frac{37}{2}} b^{12} x^{2} \sqrt{1 + \frac{b x^{2}}{a}} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{3 a^{\frac{39}{2}} b^{\frac{27}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 3 a^{\frac{37}{2}} b^{\frac{29}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{3 a^{19} b^{\frac{23}{2}} x}{3 a^{\frac{39}{2}} b^{\frac{27}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 3 a^{\frac{37}{2}} b^{\frac{29}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{4 a^{18} b^{\frac{25}{2}} x^{3}}{3 a^{\frac{39}{2}} b^{\frac{27}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 3 a^{\frac{37}{2}} b^{\frac{29}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"3*a**(39/2)*b**11*sqrt(1 + b*x**2/a)*asinh(sqrt(b)*x/sqrt(a))/(3*a**(39/2)*b**(27/2)*sqrt(1 + b*x**2/a) + 3*a**(37/2)*b**(29/2)*x**2*sqrt(1 + b*x**2/a)) + 3*a**(37/2)*b**12*x**2*sqrt(1 + b*x**2/a)*asinh(sqrt(b)*x/sqrt(a))/(3*a**(39/2)*b**(27/2)*sqrt(1 + b*x**2/a) + 3*a**(37/2)*b**(29/2)*x**2*sqrt(1 + b*x**2/a)) - 3*a**19*b**(23/2)*x/(3*a**(39/2)*b**(27/2)*sqrt(1 + b*x**2/a) + 3*a**(37/2)*b**(29/2)*x**2*sqrt(1 + b*x**2/a)) - 4*a**18*b**(25/2)*x**3/(3*a**(39/2)*b**(27/2)*sqrt(1 + b*x**2/a) + 3*a**(37/2)*b**(29/2)*x**2*sqrt(1 + b*x**2/a))","B",0
509,1,92,0,1.073246," ","integrate(x**3/(b*x**2+a)**(5/2),x)","\begin{cases} - \frac{2 a}{3 a b^{2} \sqrt{a + b x^{2}} + 3 b^{3} x^{2} \sqrt{a + b x^{2}}} - \frac{3 b x^{2}}{3 a b^{2} \sqrt{a + b x^{2}} + 3 b^{3} x^{2} \sqrt{a + b x^{2}}} & \text{for}\: b \neq 0 \\\frac{x^{4}}{4 a^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*a/(3*a*b**2*sqrt(a + b*x**2) + 3*b**3*x**2*sqrt(a + b*x**2)) - 3*b*x**2/(3*a*b**2*sqrt(a + b*x**2) + 3*b**3*x**2*sqrt(a + b*x**2)), Ne(b, 0)), (x**4/(4*a**(5/2)), True))","A",0
510,1,44,0,0.756170," ","integrate(x**2/(b*x**2+a)**(5/2),x)","\frac{x^{3}}{3 a^{\frac{5}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 3 a^{\frac{3}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"x**3/(3*a**(5/2)*sqrt(1 + b*x**2/a) + 3*a**(3/2)*b*x**2*sqrt(1 + b*x**2/a))","B",0
511,1,46,0,1.001673," ","integrate(x/(b*x**2+a)**(5/2),x)","\begin{cases} - \frac{1}{3 a b \sqrt{a + b x^{2}} + 3 b^{2} x^{2} \sqrt{a + b x^{2}}} & \text{for}\: b \neq 0 \\\frac{x^{2}}{2 a^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-1/(3*a*b*sqrt(a + b*x**2) + 3*b**2*x**2*sqrt(a + b*x**2)), Ne(b, 0)), (x**2/(2*a**(5/2)), True))","A",0
512,1,95,0,0.827926," ","integrate(1/(b*x**2+a)**(5/2),x)","\frac{3 a x}{3 a^{\frac{7}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 3 a^{\frac{5}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{2 b x^{3}}{3 a^{\frac{7}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 3 a^{\frac{5}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"3*a*x/(3*a**(7/2)*sqrt(1 + b*x**2/a) + 3*a**(5/2)*b*x**2*sqrt(1 + b*x**2/a)) + 2*b*x**3/(3*a**(7/2)*sqrt(1 + b*x**2/a) + 3*a**(5/2)*b*x**2*sqrt(1 + b*x**2/a))","B",0
513,1,740,0,2.889296," ","integrate(1/x/(b*x**2+a)**(5/2),x)","\frac{8 a^{7} \sqrt{1 + \frac{b x^{2}}{a}}}{6 a^{\frac{19}{2}} + 18 a^{\frac{17}{2}} b x^{2} + 18 a^{\frac{15}{2}} b^{2} x^{4} + 6 a^{\frac{13}{2}} b^{3} x^{6}} + \frac{3 a^{7} \log{\left(\frac{b x^{2}}{a} \right)}}{6 a^{\frac{19}{2}} + 18 a^{\frac{17}{2}} b x^{2} + 18 a^{\frac{15}{2}} b^{2} x^{4} + 6 a^{\frac{13}{2}} b^{3} x^{6}} - \frac{6 a^{7} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{6 a^{\frac{19}{2}} + 18 a^{\frac{17}{2}} b x^{2} + 18 a^{\frac{15}{2}} b^{2} x^{4} + 6 a^{\frac{13}{2}} b^{3} x^{6}} + \frac{14 a^{6} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}}}{6 a^{\frac{19}{2}} + 18 a^{\frac{17}{2}} b x^{2} + 18 a^{\frac{15}{2}} b^{2} x^{4} + 6 a^{\frac{13}{2}} b^{3} x^{6}} + \frac{9 a^{6} b x^{2} \log{\left(\frac{b x^{2}}{a} \right)}}{6 a^{\frac{19}{2}} + 18 a^{\frac{17}{2}} b x^{2} + 18 a^{\frac{15}{2}} b^{2} x^{4} + 6 a^{\frac{13}{2}} b^{3} x^{6}} - \frac{18 a^{6} b x^{2} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{6 a^{\frac{19}{2}} + 18 a^{\frac{17}{2}} b x^{2} + 18 a^{\frac{15}{2}} b^{2} x^{4} + 6 a^{\frac{13}{2}} b^{3} x^{6}} + \frac{6 a^{5} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}}}{6 a^{\frac{19}{2}} + 18 a^{\frac{17}{2}} b x^{2} + 18 a^{\frac{15}{2}} b^{2} x^{4} + 6 a^{\frac{13}{2}} b^{3} x^{6}} + \frac{9 a^{5} b^{2} x^{4} \log{\left(\frac{b x^{2}}{a} \right)}}{6 a^{\frac{19}{2}} + 18 a^{\frac{17}{2}} b x^{2} + 18 a^{\frac{15}{2}} b^{2} x^{4} + 6 a^{\frac{13}{2}} b^{3} x^{6}} - \frac{18 a^{5} b^{2} x^{4} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{6 a^{\frac{19}{2}} + 18 a^{\frac{17}{2}} b x^{2} + 18 a^{\frac{15}{2}} b^{2} x^{4} + 6 a^{\frac{13}{2}} b^{3} x^{6}} + \frac{3 a^{4} b^{3} x^{6} \log{\left(\frac{b x^{2}}{a} \right)}}{6 a^{\frac{19}{2}} + 18 a^{\frac{17}{2}} b x^{2} + 18 a^{\frac{15}{2}} b^{2} x^{4} + 6 a^{\frac{13}{2}} b^{3} x^{6}} - \frac{6 a^{4} b^{3} x^{6} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{6 a^{\frac{19}{2}} + 18 a^{\frac{17}{2}} b x^{2} + 18 a^{\frac{15}{2}} b^{2} x^{4} + 6 a^{\frac{13}{2}} b^{3} x^{6}}"," ",0,"8*a**7*sqrt(1 + b*x**2/a)/(6*a**(19/2) + 18*a**(17/2)*b*x**2 + 18*a**(15/2)*b**2*x**4 + 6*a**(13/2)*b**3*x**6) + 3*a**7*log(b*x**2/a)/(6*a**(19/2) + 18*a**(17/2)*b*x**2 + 18*a**(15/2)*b**2*x**4 + 6*a**(13/2)*b**3*x**6) - 6*a**7*log(sqrt(1 + b*x**2/a) + 1)/(6*a**(19/2) + 18*a**(17/2)*b*x**2 + 18*a**(15/2)*b**2*x**4 + 6*a**(13/2)*b**3*x**6) + 14*a**6*b*x**2*sqrt(1 + b*x**2/a)/(6*a**(19/2) + 18*a**(17/2)*b*x**2 + 18*a**(15/2)*b**2*x**4 + 6*a**(13/2)*b**3*x**6) + 9*a**6*b*x**2*log(b*x**2/a)/(6*a**(19/2) + 18*a**(17/2)*b*x**2 + 18*a**(15/2)*b**2*x**4 + 6*a**(13/2)*b**3*x**6) - 18*a**6*b*x**2*log(sqrt(1 + b*x**2/a) + 1)/(6*a**(19/2) + 18*a**(17/2)*b*x**2 + 18*a**(15/2)*b**2*x**4 + 6*a**(13/2)*b**3*x**6) + 6*a**5*b**2*x**4*sqrt(1 + b*x**2/a)/(6*a**(19/2) + 18*a**(17/2)*b*x**2 + 18*a**(15/2)*b**2*x**4 + 6*a**(13/2)*b**3*x**6) + 9*a**5*b**2*x**4*log(b*x**2/a)/(6*a**(19/2) + 18*a**(17/2)*b*x**2 + 18*a**(15/2)*b**2*x**4 + 6*a**(13/2)*b**3*x**6) - 18*a**5*b**2*x**4*log(sqrt(1 + b*x**2/a) + 1)/(6*a**(19/2) + 18*a**(17/2)*b*x**2 + 18*a**(15/2)*b**2*x**4 + 6*a**(13/2)*b**3*x**6) + 3*a**4*b**3*x**6*log(b*x**2/a)/(6*a**(19/2) + 18*a**(17/2)*b*x**2 + 18*a**(15/2)*b**2*x**4 + 6*a**(13/2)*b**3*x**6) - 6*a**4*b**3*x**6*log(sqrt(1 + b*x**2/a) + 1)/(6*a**(19/2) + 18*a**(17/2)*b*x**2 + 18*a**(15/2)*b**2*x**4 + 6*a**(13/2)*b**3*x**6)","B",0
514,1,165,0,1.286698," ","integrate(1/x**2/(b*x**2+a)**(5/2),x)","- \frac{3 a^{2} b^{\frac{9}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{3 a^{5} b^{4} + 6 a^{4} b^{5} x^{2} + 3 a^{3} b^{6} x^{4}} - \frac{12 a b^{\frac{11}{2}} x^{2} \sqrt{\frac{a}{b x^{2}} + 1}}{3 a^{5} b^{4} + 6 a^{4} b^{5} x^{2} + 3 a^{3} b^{6} x^{4}} - \frac{8 b^{\frac{13}{2}} x^{4} \sqrt{\frac{a}{b x^{2}} + 1}}{3 a^{5} b^{4} + 6 a^{4} b^{5} x^{2} + 3 a^{3} b^{6} x^{4}}"," ",0,"-3*a**2*b**(9/2)*sqrt(a/(b*x**2) + 1)/(3*a**5*b**4 + 6*a**4*b**5*x**2 + 3*a**3*b**6*x**4) - 12*a*b**(11/2)*x**2*sqrt(a/(b*x**2) + 1)/(3*a**5*b**4 + 6*a**4*b**5*x**2 + 3*a**3*b**6*x**4) - 8*b**(13/2)*x**4*sqrt(a/(b*x**2) + 1)/(3*a**5*b**4 + 6*a**4*b**5*x**2 + 3*a**3*b**6*x**4)","B",0
515,1,864,0,5.168977," ","integrate(1/x**3/(b*x**2+a)**(5/2),x)","- \frac{6 a^{17} \sqrt{1 + \frac{b x^{2}}{a}}}{12 a^{\frac{39}{2}} x^{2} + 36 a^{\frac{37}{2}} b x^{4} + 36 a^{\frac{35}{2}} b^{2} x^{6} + 12 a^{\frac{33}{2}} b^{3} x^{8}} - \frac{46 a^{16} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}}}{12 a^{\frac{39}{2}} x^{2} + 36 a^{\frac{37}{2}} b x^{4} + 36 a^{\frac{35}{2}} b^{2} x^{6} + 12 a^{\frac{33}{2}} b^{3} x^{8}} - \frac{15 a^{16} b x^{2} \log{\left(\frac{b x^{2}}{a} \right)}}{12 a^{\frac{39}{2}} x^{2} + 36 a^{\frac{37}{2}} b x^{4} + 36 a^{\frac{35}{2}} b^{2} x^{6} + 12 a^{\frac{33}{2}} b^{3} x^{8}} + \frac{30 a^{16} b x^{2} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{12 a^{\frac{39}{2}} x^{2} + 36 a^{\frac{37}{2}} b x^{4} + 36 a^{\frac{35}{2}} b^{2} x^{6} + 12 a^{\frac{33}{2}} b^{3} x^{8}} - \frac{70 a^{15} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}}}{12 a^{\frac{39}{2}} x^{2} + 36 a^{\frac{37}{2}} b x^{4} + 36 a^{\frac{35}{2}} b^{2} x^{6} + 12 a^{\frac{33}{2}} b^{3} x^{8}} - \frac{45 a^{15} b^{2} x^{4} \log{\left(\frac{b x^{2}}{a} \right)}}{12 a^{\frac{39}{2}} x^{2} + 36 a^{\frac{37}{2}} b x^{4} + 36 a^{\frac{35}{2}} b^{2} x^{6} + 12 a^{\frac{33}{2}} b^{3} x^{8}} + \frac{90 a^{15} b^{2} x^{4} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{12 a^{\frac{39}{2}} x^{2} + 36 a^{\frac{37}{2}} b x^{4} + 36 a^{\frac{35}{2}} b^{2} x^{6} + 12 a^{\frac{33}{2}} b^{3} x^{8}} - \frac{30 a^{14} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}}}{12 a^{\frac{39}{2}} x^{2} + 36 a^{\frac{37}{2}} b x^{4} + 36 a^{\frac{35}{2}} b^{2} x^{6} + 12 a^{\frac{33}{2}} b^{3} x^{8}} - \frac{45 a^{14} b^{3} x^{6} \log{\left(\frac{b x^{2}}{a} \right)}}{12 a^{\frac{39}{2}} x^{2} + 36 a^{\frac{37}{2}} b x^{4} + 36 a^{\frac{35}{2}} b^{2} x^{6} + 12 a^{\frac{33}{2}} b^{3} x^{8}} + \frac{90 a^{14} b^{3} x^{6} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{12 a^{\frac{39}{2}} x^{2} + 36 a^{\frac{37}{2}} b x^{4} + 36 a^{\frac{35}{2}} b^{2} x^{6} + 12 a^{\frac{33}{2}} b^{3} x^{8}} - \frac{15 a^{13} b^{4} x^{8} \log{\left(\frac{b x^{2}}{a} \right)}}{12 a^{\frac{39}{2}} x^{2} + 36 a^{\frac{37}{2}} b x^{4} + 36 a^{\frac{35}{2}} b^{2} x^{6} + 12 a^{\frac{33}{2}} b^{3} x^{8}} + \frac{30 a^{13} b^{4} x^{8} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{12 a^{\frac{39}{2}} x^{2} + 36 a^{\frac{37}{2}} b x^{4} + 36 a^{\frac{35}{2}} b^{2} x^{6} + 12 a^{\frac{33}{2}} b^{3} x^{8}}"," ",0,"-6*a**17*sqrt(1 + b*x**2/a)/(12*a**(39/2)*x**2 + 36*a**(37/2)*b*x**4 + 36*a**(35/2)*b**2*x**6 + 12*a**(33/2)*b**3*x**8) - 46*a**16*b*x**2*sqrt(1 + b*x**2/a)/(12*a**(39/2)*x**2 + 36*a**(37/2)*b*x**4 + 36*a**(35/2)*b**2*x**6 + 12*a**(33/2)*b**3*x**8) - 15*a**16*b*x**2*log(b*x**2/a)/(12*a**(39/2)*x**2 + 36*a**(37/2)*b*x**4 + 36*a**(35/2)*b**2*x**6 + 12*a**(33/2)*b**3*x**8) + 30*a**16*b*x**2*log(sqrt(1 + b*x**2/a) + 1)/(12*a**(39/2)*x**2 + 36*a**(37/2)*b*x**4 + 36*a**(35/2)*b**2*x**6 + 12*a**(33/2)*b**3*x**8) - 70*a**15*b**2*x**4*sqrt(1 + b*x**2/a)/(12*a**(39/2)*x**2 + 36*a**(37/2)*b*x**4 + 36*a**(35/2)*b**2*x**6 + 12*a**(33/2)*b**3*x**8) - 45*a**15*b**2*x**4*log(b*x**2/a)/(12*a**(39/2)*x**2 + 36*a**(37/2)*b*x**4 + 36*a**(35/2)*b**2*x**6 + 12*a**(33/2)*b**3*x**8) + 90*a**15*b**2*x**4*log(sqrt(1 + b*x**2/a) + 1)/(12*a**(39/2)*x**2 + 36*a**(37/2)*b*x**4 + 36*a**(35/2)*b**2*x**6 + 12*a**(33/2)*b**3*x**8) - 30*a**14*b**3*x**6*sqrt(1 + b*x**2/a)/(12*a**(39/2)*x**2 + 36*a**(37/2)*b*x**4 + 36*a**(35/2)*b**2*x**6 + 12*a**(33/2)*b**3*x**8) - 45*a**14*b**3*x**6*log(b*x**2/a)/(12*a**(39/2)*x**2 + 36*a**(37/2)*b*x**4 + 36*a**(35/2)*b**2*x**6 + 12*a**(33/2)*b**3*x**8) + 90*a**14*b**3*x**6*log(sqrt(1 + b*x**2/a) + 1)/(12*a**(39/2)*x**2 + 36*a**(37/2)*b*x**4 + 36*a**(35/2)*b**2*x**6 + 12*a**(33/2)*b**3*x**8) - 15*a**13*b**4*x**8*log(b*x**2/a)/(12*a**(39/2)*x**2 + 36*a**(37/2)*b*x**4 + 36*a**(35/2)*b**2*x**6 + 12*a**(33/2)*b**3*x**8) + 30*a**13*b**4*x**8*log(sqrt(1 + b*x**2/a) + 1)/(12*a**(39/2)*x**2 + 36*a**(37/2)*b*x**4 + 36*a**(35/2)*b**2*x**6 + 12*a**(33/2)*b**3*x**8)","B",0
516,1,354,0,1.731312," ","integrate(1/x**4/(b*x**2+a)**(5/2),x)","- \frac{a^{4} b^{\frac{19}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{3 a^{7} b^{9} x^{2} + 9 a^{6} b^{10} x^{4} + 9 a^{5} b^{11} x^{6} + 3 a^{4} b^{12} x^{8}} + \frac{5 a^{3} b^{\frac{21}{2}} x^{2} \sqrt{\frac{a}{b x^{2}} + 1}}{3 a^{7} b^{9} x^{2} + 9 a^{6} b^{10} x^{4} + 9 a^{5} b^{11} x^{6} + 3 a^{4} b^{12} x^{8}} + \frac{30 a^{2} b^{\frac{23}{2}} x^{4} \sqrt{\frac{a}{b x^{2}} + 1}}{3 a^{7} b^{9} x^{2} + 9 a^{6} b^{10} x^{4} + 9 a^{5} b^{11} x^{6} + 3 a^{4} b^{12} x^{8}} + \frac{40 a b^{\frac{25}{2}} x^{6} \sqrt{\frac{a}{b x^{2}} + 1}}{3 a^{7} b^{9} x^{2} + 9 a^{6} b^{10} x^{4} + 9 a^{5} b^{11} x^{6} + 3 a^{4} b^{12} x^{8}} + \frac{16 b^{\frac{27}{2}} x^{8} \sqrt{\frac{a}{b x^{2}} + 1}}{3 a^{7} b^{9} x^{2} + 9 a^{6} b^{10} x^{4} + 9 a^{5} b^{11} x^{6} + 3 a^{4} b^{12} x^{8}}"," ",0,"-a**4*b**(19/2)*sqrt(a/(b*x**2) + 1)/(3*a**7*b**9*x**2 + 9*a**6*b**10*x**4 + 9*a**5*b**11*x**6 + 3*a**4*b**12*x**8) + 5*a**3*b**(21/2)*x**2*sqrt(a/(b*x**2) + 1)/(3*a**7*b**9*x**2 + 9*a**6*b**10*x**4 + 9*a**5*b**11*x**6 + 3*a**4*b**12*x**8) + 30*a**2*b**(23/2)*x**4*sqrt(a/(b*x**2) + 1)/(3*a**7*b**9*x**2 + 9*a**6*b**10*x**4 + 9*a**5*b**11*x**6 + 3*a**4*b**12*x**8) + 40*a*b**(25/2)*x**6*sqrt(a/(b*x**2) + 1)/(3*a**7*b**9*x**2 + 9*a**6*b**10*x**4 + 9*a**5*b**11*x**6 + 3*a**4*b**12*x**8) + 16*b**(27/2)*x**8*sqrt(a/(b*x**2) + 1)/(3*a**7*b**9*x**2 + 9*a**6*b**10*x**4 + 9*a**5*b**11*x**6 + 3*a**4*b**12*x**8)","B",0
517,1,3181,0,13.421725," ","integrate(x**10/(b*x**2+a)**(9/2),x)","- \frac{315 a^{\frac{311}{2}} b^{66} \sqrt{1 + \frac{b x^{2}}{a}} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{70 a^{\frac{309}{2}} b^{\frac{143}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{307}{2}} b^{\frac{145}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 1050 a^{\frac{305}{2}} b^{\frac{147}{2}} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 1400 a^{\frac{303}{2}} b^{\frac{149}{2}} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 1050 a^{\frac{301}{2}} b^{\frac{151}{2}} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{299}{2}} b^{\frac{153}{2}} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 70 a^{\frac{297}{2}} b^{\frac{155}{2}} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{1890 a^{\frac{309}{2}} b^{67} x^{2} \sqrt{1 + \frac{b x^{2}}{a}} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{70 a^{\frac{309}{2}} b^{\frac{143}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{307}{2}} b^{\frac{145}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 1050 a^{\frac{305}{2}} b^{\frac{147}{2}} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 1400 a^{\frac{303}{2}} b^{\frac{149}{2}} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 1050 a^{\frac{301}{2}} b^{\frac{151}{2}} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{299}{2}} b^{\frac{153}{2}} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 70 a^{\frac{297}{2}} b^{\frac{155}{2}} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{4725 a^{\frac{307}{2}} b^{68} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{70 a^{\frac{309}{2}} b^{\frac{143}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{307}{2}} b^{\frac{145}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 1050 a^{\frac{305}{2}} b^{\frac{147}{2}} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 1400 a^{\frac{303}{2}} b^{\frac{149}{2}} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 1050 a^{\frac{301}{2}} b^{\frac{151}{2}} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{299}{2}} b^{\frac{153}{2}} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 70 a^{\frac{297}{2}} b^{\frac{155}{2}} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{6300 a^{\frac{305}{2}} b^{69} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{70 a^{\frac{309}{2}} b^{\frac{143}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{307}{2}} b^{\frac{145}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 1050 a^{\frac{305}{2}} b^{\frac{147}{2}} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 1400 a^{\frac{303}{2}} b^{\frac{149}{2}} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 1050 a^{\frac{301}{2}} b^{\frac{151}{2}} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{299}{2}} b^{\frac{153}{2}} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 70 a^{\frac{297}{2}} b^{\frac{155}{2}} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{4725 a^{\frac{303}{2}} b^{70} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{70 a^{\frac{309}{2}} b^{\frac{143}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{307}{2}} b^{\frac{145}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 1050 a^{\frac{305}{2}} b^{\frac{147}{2}} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 1400 a^{\frac{303}{2}} b^{\frac{149}{2}} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 1050 a^{\frac{301}{2}} b^{\frac{151}{2}} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{299}{2}} b^{\frac{153}{2}} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 70 a^{\frac{297}{2}} b^{\frac{155}{2}} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{1890 a^{\frac{301}{2}} b^{71} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{70 a^{\frac{309}{2}} b^{\frac{143}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{307}{2}} b^{\frac{145}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 1050 a^{\frac{305}{2}} b^{\frac{147}{2}} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 1400 a^{\frac{303}{2}} b^{\frac{149}{2}} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 1050 a^{\frac{301}{2}} b^{\frac{151}{2}} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{299}{2}} b^{\frac{153}{2}} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 70 a^{\frac{297}{2}} b^{\frac{155}{2}} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{315 a^{\frac{299}{2}} b^{72} x^{12} \sqrt{1 + \frac{b x^{2}}{a}} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{70 a^{\frac{309}{2}} b^{\frac{143}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{307}{2}} b^{\frac{145}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 1050 a^{\frac{305}{2}} b^{\frac{147}{2}} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 1400 a^{\frac{303}{2}} b^{\frac{149}{2}} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 1050 a^{\frac{301}{2}} b^{\frac{151}{2}} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{299}{2}} b^{\frac{153}{2}} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 70 a^{\frac{297}{2}} b^{\frac{155}{2}} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{315 a^{155} b^{\frac{133}{2}} x}{70 a^{\frac{309}{2}} b^{\frac{143}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{307}{2}} b^{\frac{145}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 1050 a^{\frac{305}{2}} b^{\frac{147}{2}} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 1400 a^{\frac{303}{2}} b^{\frac{149}{2}} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 1050 a^{\frac{301}{2}} b^{\frac{151}{2}} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{299}{2}} b^{\frac{153}{2}} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 70 a^{\frac{297}{2}} b^{\frac{155}{2}} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{1995 a^{154} b^{\frac{135}{2}} x^{3}}{70 a^{\frac{309}{2}} b^{\frac{143}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{307}{2}} b^{\frac{145}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 1050 a^{\frac{305}{2}} b^{\frac{147}{2}} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 1400 a^{\frac{303}{2}} b^{\frac{149}{2}} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 1050 a^{\frac{301}{2}} b^{\frac{151}{2}} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{299}{2}} b^{\frac{153}{2}} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 70 a^{\frac{297}{2}} b^{\frac{155}{2}} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{5313 a^{153} b^{\frac{137}{2}} x^{5}}{70 a^{\frac{309}{2}} b^{\frac{143}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{307}{2}} b^{\frac{145}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 1050 a^{\frac{305}{2}} b^{\frac{147}{2}} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 1400 a^{\frac{303}{2}} b^{\frac{149}{2}} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 1050 a^{\frac{301}{2}} b^{\frac{151}{2}} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{299}{2}} b^{\frac{153}{2}} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 70 a^{\frac{297}{2}} b^{\frac{155}{2}} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{7647 a^{152} b^{\frac{139}{2}} x^{7}}{70 a^{\frac{309}{2}} b^{\frac{143}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{307}{2}} b^{\frac{145}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 1050 a^{\frac{305}{2}} b^{\frac{147}{2}} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 1400 a^{\frac{303}{2}} b^{\frac{149}{2}} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 1050 a^{\frac{301}{2}} b^{\frac{151}{2}} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{299}{2}} b^{\frac{153}{2}} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 70 a^{\frac{297}{2}} b^{\frac{155}{2}} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{6323 a^{151} b^{\frac{141}{2}} x^{9}}{70 a^{\frac{309}{2}} b^{\frac{143}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{307}{2}} b^{\frac{145}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 1050 a^{\frac{305}{2}} b^{\frac{147}{2}} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 1400 a^{\frac{303}{2}} b^{\frac{149}{2}} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 1050 a^{\frac{301}{2}} b^{\frac{151}{2}} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{299}{2}} b^{\frac{153}{2}} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 70 a^{\frac{297}{2}} b^{\frac{155}{2}} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{2907 a^{150} b^{\frac{143}{2}} x^{11}}{70 a^{\frac{309}{2}} b^{\frac{143}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{307}{2}} b^{\frac{145}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 1050 a^{\frac{305}{2}} b^{\frac{147}{2}} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 1400 a^{\frac{303}{2}} b^{\frac{149}{2}} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 1050 a^{\frac{301}{2}} b^{\frac{151}{2}} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{299}{2}} b^{\frac{153}{2}} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 70 a^{\frac{297}{2}} b^{\frac{155}{2}} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{633 a^{149} b^{\frac{145}{2}} x^{13}}{70 a^{\frac{309}{2}} b^{\frac{143}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{307}{2}} b^{\frac{145}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 1050 a^{\frac{305}{2}} b^{\frac{147}{2}} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 1400 a^{\frac{303}{2}} b^{\frac{149}{2}} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 1050 a^{\frac{301}{2}} b^{\frac{151}{2}} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{299}{2}} b^{\frac{153}{2}} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 70 a^{\frac{297}{2}} b^{\frac{155}{2}} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{35 a^{148} b^{\frac{147}{2}} x^{15}}{70 a^{\frac{309}{2}} b^{\frac{143}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{307}{2}} b^{\frac{145}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 1050 a^{\frac{305}{2}} b^{\frac{147}{2}} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 1400 a^{\frac{303}{2}} b^{\frac{149}{2}} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 1050 a^{\frac{301}{2}} b^{\frac{151}{2}} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{299}{2}} b^{\frac{153}{2}} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 70 a^{\frac{297}{2}} b^{\frac{155}{2}} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"-315*a**(311/2)*b**66*sqrt(1 + b*x**2/a)*asinh(sqrt(b)*x/sqrt(a))/(70*a**(309/2)*b**(143/2)*sqrt(1 + b*x**2/a) + 420*a**(307/2)*b**(145/2)*x**2*sqrt(1 + b*x**2/a) + 1050*a**(305/2)*b**(147/2)*x**4*sqrt(1 + b*x**2/a) + 1400*a**(303/2)*b**(149/2)*x**6*sqrt(1 + b*x**2/a) + 1050*a**(301/2)*b**(151/2)*x**8*sqrt(1 + b*x**2/a) + 420*a**(299/2)*b**(153/2)*x**10*sqrt(1 + b*x**2/a) + 70*a**(297/2)*b**(155/2)*x**12*sqrt(1 + b*x**2/a)) - 1890*a**(309/2)*b**67*x**2*sqrt(1 + b*x**2/a)*asinh(sqrt(b)*x/sqrt(a))/(70*a**(309/2)*b**(143/2)*sqrt(1 + b*x**2/a) + 420*a**(307/2)*b**(145/2)*x**2*sqrt(1 + b*x**2/a) + 1050*a**(305/2)*b**(147/2)*x**4*sqrt(1 + b*x**2/a) + 1400*a**(303/2)*b**(149/2)*x**6*sqrt(1 + b*x**2/a) + 1050*a**(301/2)*b**(151/2)*x**8*sqrt(1 + b*x**2/a) + 420*a**(299/2)*b**(153/2)*x**10*sqrt(1 + b*x**2/a) + 70*a**(297/2)*b**(155/2)*x**12*sqrt(1 + b*x**2/a)) - 4725*a**(307/2)*b**68*x**4*sqrt(1 + b*x**2/a)*asinh(sqrt(b)*x/sqrt(a))/(70*a**(309/2)*b**(143/2)*sqrt(1 + b*x**2/a) + 420*a**(307/2)*b**(145/2)*x**2*sqrt(1 + b*x**2/a) + 1050*a**(305/2)*b**(147/2)*x**4*sqrt(1 + b*x**2/a) + 1400*a**(303/2)*b**(149/2)*x**6*sqrt(1 + b*x**2/a) + 1050*a**(301/2)*b**(151/2)*x**8*sqrt(1 + b*x**2/a) + 420*a**(299/2)*b**(153/2)*x**10*sqrt(1 + b*x**2/a) + 70*a**(297/2)*b**(155/2)*x**12*sqrt(1 + b*x**2/a)) - 6300*a**(305/2)*b**69*x**6*sqrt(1 + b*x**2/a)*asinh(sqrt(b)*x/sqrt(a))/(70*a**(309/2)*b**(143/2)*sqrt(1 + b*x**2/a) + 420*a**(307/2)*b**(145/2)*x**2*sqrt(1 + b*x**2/a) + 1050*a**(305/2)*b**(147/2)*x**4*sqrt(1 + b*x**2/a) + 1400*a**(303/2)*b**(149/2)*x**6*sqrt(1 + b*x**2/a) + 1050*a**(301/2)*b**(151/2)*x**8*sqrt(1 + b*x**2/a) + 420*a**(299/2)*b**(153/2)*x**10*sqrt(1 + b*x**2/a) + 70*a**(297/2)*b**(155/2)*x**12*sqrt(1 + b*x**2/a)) - 4725*a**(303/2)*b**70*x**8*sqrt(1 + b*x**2/a)*asinh(sqrt(b)*x/sqrt(a))/(70*a**(309/2)*b**(143/2)*sqrt(1 + b*x**2/a) + 420*a**(307/2)*b**(145/2)*x**2*sqrt(1 + b*x**2/a) + 1050*a**(305/2)*b**(147/2)*x**4*sqrt(1 + b*x**2/a) + 1400*a**(303/2)*b**(149/2)*x**6*sqrt(1 + b*x**2/a) + 1050*a**(301/2)*b**(151/2)*x**8*sqrt(1 + b*x**2/a) + 420*a**(299/2)*b**(153/2)*x**10*sqrt(1 + b*x**2/a) + 70*a**(297/2)*b**(155/2)*x**12*sqrt(1 + b*x**2/a)) - 1890*a**(301/2)*b**71*x**10*sqrt(1 + b*x**2/a)*asinh(sqrt(b)*x/sqrt(a))/(70*a**(309/2)*b**(143/2)*sqrt(1 + b*x**2/a) + 420*a**(307/2)*b**(145/2)*x**2*sqrt(1 + b*x**2/a) + 1050*a**(305/2)*b**(147/2)*x**4*sqrt(1 + b*x**2/a) + 1400*a**(303/2)*b**(149/2)*x**6*sqrt(1 + b*x**2/a) + 1050*a**(301/2)*b**(151/2)*x**8*sqrt(1 + b*x**2/a) + 420*a**(299/2)*b**(153/2)*x**10*sqrt(1 + b*x**2/a) + 70*a**(297/2)*b**(155/2)*x**12*sqrt(1 + b*x**2/a)) - 315*a**(299/2)*b**72*x**12*sqrt(1 + b*x**2/a)*asinh(sqrt(b)*x/sqrt(a))/(70*a**(309/2)*b**(143/2)*sqrt(1 + b*x**2/a) + 420*a**(307/2)*b**(145/2)*x**2*sqrt(1 + b*x**2/a) + 1050*a**(305/2)*b**(147/2)*x**4*sqrt(1 + b*x**2/a) + 1400*a**(303/2)*b**(149/2)*x**6*sqrt(1 + b*x**2/a) + 1050*a**(301/2)*b**(151/2)*x**8*sqrt(1 + b*x**2/a) + 420*a**(299/2)*b**(153/2)*x**10*sqrt(1 + b*x**2/a) + 70*a**(297/2)*b**(155/2)*x**12*sqrt(1 + b*x**2/a)) + 315*a**155*b**(133/2)*x/(70*a**(309/2)*b**(143/2)*sqrt(1 + b*x**2/a) + 420*a**(307/2)*b**(145/2)*x**2*sqrt(1 + b*x**2/a) + 1050*a**(305/2)*b**(147/2)*x**4*sqrt(1 + b*x**2/a) + 1400*a**(303/2)*b**(149/2)*x**6*sqrt(1 + b*x**2/a) + 1050*a**(301/2)*b**(151/2)*x**8*sqrt(1 + b*x**2/a) + 420*a**(299/2)*b**(153/2)*x**10*sqrt(1 + b*x**2/a) + 70*a**(297/2)*b**(155/2)*x**12*sqrt(1 + b*x**2/a)) + 1995*a**154*b**(135/2)*x**3/(70*a**(309/2)*b**(143/2)*sqrt(1 + b*x**2/a) + 420*a**(307/2)*b**(145/2)*x**2*sqrt(1 + b*x**2/a) + 1050*a**(305/2)*b**(147/2)*x**4*sqrt(1 + b*x**2/a) + 1400*a**(303/2)*b**(149/2)*x**6*sqrt(1 + b*x**2/a) + 1050*a**(301/2)*b**(151/2)*x**8*sqrt(1 + b*x**2/a) + 420*a**(299/2)*b**(153/2)*x**10*sqrt(1 + b*x**2/a) + 70*a**(297/2)*b**(155/2)*x**12*sqrt(1 + b*x**2/a)) + 5313*a**153*b**(137/2)*x**5/(70*a**(309/2)*b**(143/2)*sqrt(1 + b*x**2/a) + 420*a**(307/2)*b**(145/2)*x**2*sqrt(1 + b*x**2/a) + 1050*a**(305/2)*b**(147/2)*x**4*sqrt(1 + b*x**2/a) + 1400*a**(303/2)*b**(149/2)*x**6*sqrt(1 + b*x**2/a) + 1050*a**(301/2)*b**(151/2)*x**8*sqrt(1 + b*x**2/a) + 420*a**(299/2)*b**(153/2)*x**10*sqrt(1 + b*x**2/a) + 70*a**(297/2)*b**(155/2)*x**12*sqrt(1 + b*x**2/a)) + 7647*a**152*b**(139/2)*x**7/(70*a**(309/2)*b**(143/2)*sqrt(1 + b*x**2/a) + 420*a**(307/2)*b**(145/2)*x**2*sqrt(1 + b*x**2/a) + 1050*a**(305/2)*b**(147/2)*x**4*sqrt(1 + b*x**2/a) + 1400*a**(303/2)*b**(149/2)*x**6*sqrt(1 + b*x**2/a) + 1050*a**(301/2)*b**(151/2)*x**8*sqrt(1 + b*x**2/a) + 420*a**(299/2)*b**(153/2)*x**10*sqrt(1 + b*x**2/a) + 70*a**(297/2)*b**(155/2)*x**12*sqrt(1 + b*x**2/a)) + 6323*a**151*b**(141/2)*x**9/(70*a**(309/2)*b**(143/2)*sqrt(1 + b*x**2/a) + 420*a**(307/2)*b**(145/2)*x**2*sqrt(1 + b*x**2/a) + 1050*a**(305/2)*b**(147/2)*x**4*sqrt(1 + b*x**2/a) + 1400*a**(303/2)*b**(149/2)*x**6*sqrt(1 + b*x**2/a) + 1050*a**(301/2)*b**(151/2)*x**8*sqrt(1 + b*x**2/a) + 420*a**(299/2)*b**(153/2)*x**10*sqrt(1 + b*x**2/a) + 70*a**(297/2)*b**(155/2)*x**12*sqrt(1 + b*x**2/a)) + 2907*a**150*b**(143/2)*x**11/(70*a**(309/2)*b**(143/2)*sqrt(1 + b*x**2/a) + 420*a**(307/2)*b**(145/2)*x**2*sqrt(1 + b*x**2/a) + 1050*a**(305/2)*b**(147/2)*x**4*sqrt(1 + b*x**2/a) + 1400*a**(303/2)*b**(149/2)*x**6*sqrt(1 + b*x**2/a) + 1050*a**(301/2)*b**(151/2)*x**8*sqrt(1 + b*x**2/a) + 420*a**(299/2)*b**(153/2)*x**10*sqrt(1 + b*x**2/a) + 70*a**(297/2)*b**(155/2)*x**12*sqrt(1 + b*x**2/a)) + 633*a**149*b**(145/2)*x**13/(70*a**(309/2)*b**(143/2)*sqrt(1 + b*x**2/a) + 420*a**(307/2)*b**(145/2)*x**2*sqrt(1 + b*x**2/a) + 1050*a**(305/2)*b**(147/2)*x**4*sqrt(1 + b*x**2/a) + 1400*a**(303/2)*b**(149/2)*x**6*sqrt(1 + b*x**2/a) + 1050*a**(301/2)*b**(151/2)*x**8*sqrt(1 + b*x**2/a) + 420*a**(299/2)*b**(153/2)*x**10*sqrt(1 + b*x**2/a) + 70*a**(297/2)*b**(155/2)*x**12*sqrt(1 + b*x**2/a)) + 35*a**148*b**(147/2)*x**15/(70*a**(309/2)*b**(143/2)*sqrt(1 + b*x**2/a) + 420*a**(307/2)*b**(145/2)*x**2*sqrt(1 + b*x**2/a) + 1050*a**(305/2)*b**(147/2)*x**4*sqrt(1 + b*x**2/a) + 1400*a**(303/2)*b**(149/2)*x**6*sqrt(1 + b*x**2/a) + 1050*a**(301/2)*b**(151/2)*x**8*sqrt(1 + b*x**2/a) + 420*a**(299/2)*b**(153/2)*x**10*sqrt(1 + b*x**2/a) + 70*a**(297/2)*b**(155/2)*x**12*sqrt(1 + b*x**2/a))","B",0
518,1,454,0,6.388554," ","integrate(x**9/(b*x**2+a)**(9/2),x)","\begin{cases} \frac{128 a^{4}}{35 a^{3} b^{5} \sqrt{a + b x^{2}} + 105 a^{2} b^{6} x^{2} \sqrt{a + b x^{2}} + 105 a b^{7} x^{4} \sqrt{a + b x^{2}} + 35 b^{8} x^{6} \sqrt{a + b x^{2}}} + \frac{448 a^{3} b x^{2}}{35 a^{3} b^{5} \sqrt{a + b x^{2}} + 105 a^{2} b^{6} x^{2} \sqrt{a + b x^{2}} + 105 a b^{7} x^{4} \sqrt{a + b x^{2}} + 35 b^{8} x^{6} \sqrt{a + b x^{2}}} + \frac{560 a^{2} b^{2} x^{4}}{35 a^{3} b^{5} \sqrt{a + b x^{2}} + 105 a^{2} b^{6} x^{2} \sqrt{a + b x^{2}} + 105 a b^{7} x^{4} \sqrt{a + b x^{2}} + 35 b^{8} x^{6} \sqrt{a + b x^{2}}} + \frac{280 a b^{3} x^{6}}{35 a^{3} b^{5} \sqrt{a + b x^{2}} + 105 a^{2} b^{6} x^{2} \sqrt{a + b x^{2}} + 105 a b^{7} x^{4} \sqrt{a + b x^{2}} + 35 b^{8} x^{6} \sqrt{a + b x^{2}}} + \frac{35 b^{4} x^{8}}{35 a^{3} b^{5} \sqrt{a + b x^{2}} + 105 a^{2} b^{6} x^{2} \sqrt{a + b x^{2}} + 105 a b^{7} x^{4} \sqrt{a + b x^{2}} + 35 b^{8} x^{6} \sqrt{a + b x^{2}}} & \text{for}\: b \neq 0 \\\frac{x^{10}}{10 a^{\frac{9}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((128*a**4/(35*a**3*b**5*sqrt(a + b*x**2) + 105*a**2*b**6*x**2*sqrt(a + b*x**2) + 105*a*b**7*x**4*sqrt(a + b*x**2) + 35*b**8*x**6*sqrt(a + b*x**2)) + 448*a**3*b*x**2/(35*a**3*b**5*sqrt(a + b*x**2) + 105*a**2*b**6*x**2*sqrt(a + b*x**2) + 105*a*b**7*x**4*sqrt(a + b*x**2) + 35*b**8*x**6*sqrt(a + b*x**2)) + 560*a**2*b**2*x**4/(35*a**3*b**5*sqrt(a + b*x**2) + 105*a**2*b**6*x**2*sqrt(a + b*x**2) + 105*a*b**7*x**4*sqrt(a + b*x**2) + 35*b**8*x**6*sqrt(a + b*x**2)) + 280*a*b**3*x**6/(35*a**3*b**5*sqrt(a + b*x**2) + 105*a**2*b**6*x**2*sqrt(a + b*x**2) + 105*a*b**7*x**4*sqrt(a + b*x**2) + 35*b**8*x**6*sqrt(a + b*x**2)) + 35*b**4*x**8/(35*a**3*b**5*sqrt(a + b*x**2) + 105*a**2*b**6*x**2*sqrt(a + b*x**2) + 105*a*b**7*x**4*sqrt(a + b*x**2) + 35*b**8*x**6*sqrt(a + b*x**2)), Ne(b, 0)), (x**10/(10*a**(9/2)), True))","A",0
519,1,2980,0,9.035655," ","integrate(x**8/(b*x**2+a)**(9/2),x)","\frac{105 a^{\frac{205}{2}} b^{45} \sqrt{1 + \frac{b x^{2}}{a}} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{105 a^{\frac{205}{2}} b^{\frac{99}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 630 a^{\frac{203}{2}} b^{\frac{101}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 1575 a^{\frac{201}{2}} b^{\frac{103}{2}} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 2100 a^{\frac{199}{2}} b^{\frac{105}{2}} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 1575 a^{\frac{197}{2}} b^{\frac{107}{2}} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 630 a^{\frac{195}{2}} b^{\frac{109}{2}} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 105 a^{\frac{193}{2}} b^{\frac{111}{2}} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{630 a^{\frac{203}{2}} b^{46} x^{2} \sqrt{1 + \frac{b x^{2}}{a}} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{105 a^{\frac{205}{2}} b^{\frac{99}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 630 a^{\frac{203}{2}} b^{\frac{101}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 1575 a^{\frac{201}{2}} b^{\frac{103}{2}} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 2100 a^{\frac{199}{2}} b^{\frac{105}{2}} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 1575 a^{\frac{197}{2}} b^{\frac{107}{2}} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 630 a^{\frac{195}{2}} b^{\frac{109}{2}} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 105 a^{\frac{193}{2}} b^{\frac{111}{2}} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{1575 a^{\frac{201}{2}} b^{47} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{105 a^{\frac{205}{2}} b^{\frac{99}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 630 a^{\frac{203}{2}} b^{\frac{101}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 1575 a^{\frac{201}{2}} b^{\frac{103}{2}} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 2100 a^{\frac{199}{2}} b^{\frac{105}{2}} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 1575 a^{\frac{197}{2}} b^{\frac{107}{2}} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 630 a^{\frac{195}{2}} b^{\frac{109}{2}} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 105 a^{\frac{193}{2}} b^{\frac{111}{2}} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{2100 a^{\frac{199}{2}} b^{48} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{105 a^{\frac{205}{2}} b^{\frac{99}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 630 a^{\frac{203}{2}} b^{\frac{101}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 1575 a^{\frac{201}{2}} b^{\frac{103}{2}} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 2100 a^{\frac{199}{2}} b^{\frac{105}{2}} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 1575 a^{\frac{197}{2}} b^{\frac{107}{2}} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 630 a^{\frac{195}{2}} b^{\frac{109}{2}} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 105 a^{\frac{193}{2}} b^{\frac{111}{2}} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{1575 a^{\frac{197}{2}} b^{49} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{105 a^{\frac{205}{2}} b^{\frac{99}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 630 a^{\frac{203}{2}} b^{\frac{101}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 1575 a^{\frac{201}{2}} b^{\frac{103}{2}} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 2100 a^{\frac{199}{2}} b^{\frac{105}{2}} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 1575 a^{\frac{197}{2}} b^{\frac{107}{2}} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 630 a^{\frac{195}{2}} b^{\frac{109}{2}} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 105 a^{\frac{193}{2}} b^{\frac{111}{2}} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{630 a^{\frac{195}{2}} b^{50} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{105 a^{\frac{205}{2}} b^{\frac{99}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 630 a^{\frac{203}{2}} b^{\frac{101}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 1575 a^{\frac{201}{2}} b^{\frac{103}{2}} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 2100 a^{\frac{199}{2}} b^{\frac{105}{2}} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 1575 a^{\frac{197}{2}} b^{\frac{107}{2}} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 630 a^{\frac{195}{2}} b^{\frac{109}{2}} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 105 a^{\frac{193}{2}} b^{\frac{111}{2}} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{105 a^{\frac{193}{2}} b^{51} x^{12} \sqrt{1 + \frac{b x^{2}}{a}} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{105 a^{\frac{205}{2}} b^{\frac{99}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 630 a^{\frac{203}{2}} b^{\frac{101}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 1575 a^{\frac{201}{2}} b^{\frac{103}{2}} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 2100 a^{\frac{199}{2}} b^{\frac{105}{2}} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 1575 a^{\frac{197}{2}} b^{\frac{107}{2}} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 630 a^{\frac{195}{2}} b^{\frac{109}{2}} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 105 a^{\frac{193}{2}} b^{\frac{111}{2}} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{105 a^{102} b^{\frac{91}{2}} x}{105 a^{\frac{205}{2}} b^{\frac{99}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 630 a^{\frac{203}{2}} b^{\frac{101}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 1575 a^{\frac{201}{2}} b^{\frac{103}{2}} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 2100 a^{\frac{199}{2}} b^{\frac{105}{2}} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 1575 a^{\frac{197}{2}} b^{\frac{107}{2}} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 630 a^{\frac{195}{2}} b^{\frac{109}{2}} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 105 a^{\frac{193}{2}} b^{\frac{111}{2}} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{665 a^{101} b^{\frac{93}{2}} x^{3}}{105 a^{\frac{205}{2}} b^{\frac{99}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 630 a^{\frac{203}{2}} b^{\frac{101}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 1575 a^{\frac{201}{2}} b^{\frac{103}{2}} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 2100 a^{\frac{199}{2}} b^{\frac{105}{2}} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 1575 a^{\frac{197}{2}} b^{\frac{107}{2}} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 630 a^{\frac{195}{2}} b^{\frac{109}{2}} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 105 a^{\frac{193}{2}} b^{\frac{111}{2}} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{1771 a^{100} b^{\frac{95}{2}} x^{5}}{105 a^{\frac{205}{2}} b^{\frac{99}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 630 a^{\frac{203}{2}} b^{\frac{101}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 1575 a^{\frac{201}{2}} b^{\frac{103}{2}} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 2100 a^{\frac{199}{2}} b^{\frac{105}{2}} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 1575 a^{\frac{197}{2}} b^{\frac{107}{2}} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 630 a^{\frac{195}{2}} b^{\frac{109}{2}} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 105 a^{\frac{193}{2}} b^{\frac{111}{2}} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{2549 a^{99} b^{\frac{97}{2}} x^{7}}{105 a^{\frac{205}{2}} b^{\frac{99}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 630 a^{\frac{203}{2}} b^{\frac{101}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 1575 a^{\frac{201}{2}} b^{\frac{103}{2}} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 2100 a^{\frac{199}{2}} b^{\frac{105}{2}} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 1575 a^{\frac{197}{2}} b^{\frac{107}{2}} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 630 a^{\frac{195}{2}} b^{\frac{109}{2}} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 105 a^{\frac{193}{2}} b^{\frac{111}{2}} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{2096 a^{98} b^{\frac{99}{2}} x^{9}}{105 a^{\frac{205}{2}} b^{\frac{99}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 630 a^{\frac{203}{2}} b^{\frac{101}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 1575 a^{\frac{201}{2}} b^{\frac{103}{2}} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 2100 a^{\frac{199}{2}} b^{\frac{105}{2}} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 1575 a^{\frac{197}{2}} b^{\frac{107}{2}} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 630 a^{\frac{195}{2}} b^{\frac{109}{2}} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 105 a^{\frac{193}{2}} b^{\frac{111}{2}} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{934 a^{97} b^{\frac{101}{2}} x^{11}}{105 a^{\frac{205}{2}} b^{\frac{99}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 630 a^{\frac{203}{2}} b^{\frac{101}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 1575 a^{\frac{201}{2}} b^{\frac{103}{2}} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 2100 a^{\frac{199}{2}} b^{\frac{105}{2}} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 1575 a^{\frac{197}{2}} b^{\frac{107}{2}} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 630 a^{\frac{195}{2}} b^{\frac{109}{2}} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 105 a^{\frac{193}{2}} b^{\frac{111}{2}} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{176 a^{96} b^{\frac{103}{2}} x^{13}}{105 a^{\frac{205}{2}} b^{\frac{99}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 630 a^{\frac{203}{2}} b^{\frac{101}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 1575 a^{\frac{201}{2}} b^{\frac{103}{2}} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 2100 a^{\frac{199}{2}} b^{\frac{105}{2}} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 1575 a^{\frac{197}{2}} b^{\frac{107}{2}} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 630 a^{\frac{195}{2}} b^{\frac{109}{2}} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 105 a^{\frac{193}{2}} b^{\frac{111}{2}} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"105*a**(205/2)*b**45*sqrt(1 + b*x**2/a)*asinh(sqrt(b)*x/sqrt(a))/(105*a**(205/2)*b**(99/2)*sqrt(1 + b*x**2/a) + 630*a**(203/2)*b**(101/2)*x**2*sqrt(1 + b*x**2/a) + 1575*a**(201/2)*b**(103/2)*x**4*sqrt(1 + b*x**2/a) + 2100*a**(199/2)*b**(105/2)*x**6*sqrt(1 + b*x**2/a) + 1575*a**(197/2)*b**(107/2)*x**8*sqrt(1 + b*x**2/a) + 630*a**(195/2)*b**(109/2)*x**10*sqrt(1 + b*x**2/a) + 105*a**(193/2)*b**(111/2)*x**12*sqrt(1 + b*x**2/a)) + 630*a**(203/2)*b**46*x**2*sqrt(1 + b*x**2/a)*asinh(sqrt(b)*x/sqrt(a))/(105*a**(205/2)*b**(99/2)*sqrt(1 + b*x**2/a) + 630*a**(203/2)*b**(101/2)*x**2*sqrt(1 + b*x**2/a) + 1575*a**(201/2)*b**(103/2)*x**4*sqrt(1 + b*x**2/a) + 2100*a**(199/2)*b**(105/2)*x**6*sqrt(1 + b*x**2/a) + 1575*a**(197/2)*b**(107/2)*x**8*sqrt(1 + b*x**2/a) + 630*a**(195/2)*b**(109/2)*x**10*sqrt(1 + b*x**2/a) + 105*a**(193/2)*b**(111/2)*x**12*sqrt(1 + b*x**2/a)) + 1575*a**(201/2)*b**47*x**4*sqrt(1 + b*x**2/a)*asinh(sqrt(b)*x/sqrt(a))/(105*a**(205/2)*b**(99/2)*sqrt(1 + b*x**2/a) + 630*a**(203/2)*b**(101/2)*x**2*sqrt(1 + b*x**2/a) + 1575*a**(201/2)*b**(103/2)*x**4*sqrt(1 + b*x**2/a) + 2100*a**(199/2)*b**(105/2)*x**6*sqrt(1 + b*x**2/a) + 1575*a**(197/2)*b**(107/2)*x**8*sqrt(1 + b*x**2/a) + 630*a**(195/2)*b**(109/2)*x**10*sqrt(1 + b*x**2/a) + 105*a**(193/2)*b**(111/2)*x**12*sqrt(1 + b*x**2/a)) + 2100*a**(199/2)*b**48*x**6*sqrt(1 + b*x**2/a)*asinh(sqrt(b)*x/sqrt(a))/(105*a**(205/2)*b**(99/2)*sqrt(1 + b*x**2/a) + 630*a**(203/2)*b**(101/2)*x**2*sqrt(1 + b*x**2/a) + 1575*a**(201/2)*b**(103/2)*x**4*sqrt(1 + b*x**2/a) + 2100*a**(199/2)*b**(105/2)*x**6*sqrt(1 + b*x**2/a) + 1575*a**(197/2)*b**(107/2)*x**8*sqrt(1 + b*x**2/a) + 630*a**(195/2)*b**(109/2)*x**10*sqrt(1 + b*x**2/a) + 105*a**(193/2)*b**(111/2)*x**12*sqrt(1 + b*x**2/a)) + 1575*a**(197/2)*b**49*x**8*sqrt(1 + b*x**2/a)*asinh(sqrt(b)*x/sqrt(a))/(105*a**(205/2)*b**(99/2)*sqrt(1 + b*x**2/a) + 630*a**(203/2)*b**(101/2)*x**2*sqrt(1 + b*x**2/a) + 1575*a**(201/2)*b**(103/2)*x**4*sqrt(1 + b*x**2/a) + 2100*a**(199/2)*b**(105/2)*x**6*sqrt(1 + b*x**2/a) + 1575*a**(197/2)*b**(107/2)*x**8*sqrt(1 + b*x**2/a) + 630*a**(195/2)*b**(109/2)*x**10*sqrt(1 + b*x**2/a) + 105*a**(193/2)*b**(111/2)*x**12*sqrt(1 + b*x**2/a)) + 630*a**(195/2)*b**50*x**10*sqrt(1 + b*x**2/a)*asinh(sqrt(b)*x/sqrt(a))/(105*a**(205/2)*b**(99/2)*sqrt(1 + b*x**2/a) + 630*a**(203/2)*b**(101/2)*x**2*sqrt(1 + b*x**2/a) + 1575*a**(201/2)*b**(103/2)*x**4*sqrt(1 + b*x**2/a) + 2100*a**(199/2)*b**(105/2)*x**6*sqrt(1 + b*x**2/a) + 1575*a**(197/2)*b**(107/2)*x**8*sqrt(1 + b*x**2/a) + 630*a**(195/2)*b**(109/2)*x**10*sqrt(1 + b*x**2/a) + 105*a**(193/2)*b**(111/2)*x**12*sqrt(1 + b*x**2/a)) + 105*a**(193/2)*b**51*x**12*sqrt(1 + b*x**2/a)*asinh(sqrt(b)*x/sqrt(a))/(105*a**(205/2)*b**(99/2)*sqrt(1 + b*x**2/a) + 630*a**(203/2)*b**(101/2)*x**2*sqrt(1 + b*x**2/a) + 1575*a**(201/2)*b**(103/2)*x**4*sqrt(1 + b*x**2/a) + 2100*a**(199/2)*b**(105/2)*x**6*sqrt(1 + b*x**2/a) + 1575*a**(197/2)*b**(107/2)*x**8*sqrt(1 + b*x**2/a) + 630*a**(195/2)*b**(109/2)*x**10*sqrt(1 + b*x**2/a) + 105*a**(193/2)*b**(111/2)*x**12*sqrt(1 + b*x**2/a)) - 105*a**102*b**(91/2)*x/(105*a**(205/2)*b**(99/2)*sqrt(1 + b*x**2/a) + 630*a**(203/2)*b**(101/2)*x**2*sqrt(1 + b*x**2/a) + 1575*a**(201/2)*b**(103/2)*x**4*sqrt(1 + b*x**2/a) + 2100*a**(199/2)*b**(105/2)*x**6*sqrt(1 + b*x**2/a) + 1575*a**(197/2)*b**(107/2)*x**8*sqrt(1 + b*x**2/a) + 630*a**(195/2)*b**(109/2)*x**10*sqrt(1 + b*x**2/a) + 105*a**(193/2)*b**(111/2)*x**12*sqrt(1 + b*x**2/a)) - 665*a**101*b**(93/2)*x**3/(105*a**(205/2)*b**(99/2)*sqrt(1 + b*x**2/a) + 630*a**(203/2)*b**(101/2)*x**2*sqrt(1 + b*x**2/a) + 1575*a**(201/2)*b**(103/2)*x**4*sqrt(1 + b*x**2/a) + 2100*a**(199/2)*b**(105/2)*x**6*sqrt(1 + b*x**2/a) + 1575*a**(197/2)*b**(107/2)*x**8*sqrt(1 + b*x**2/a) + 630*a**(195/2)*b**(109/2)*x**10*sqrt(1 + b*x**2/a) + 105*a**(193/2)*b**(111/2)*x**12*sqrt(1 + b*x**2/a)) - 1771*a**100*b**(95/2)*x**5/(105*a**(205/2)*b**(99/2)*sqrt(1 + b*x**2/a) + 630*a**(203/2)*b**(101/2)*x**2*sqrt(1 + b*x**2/a) + 1575*a**(201/2)*b**(103/2)*x**4*sqrt(1 + b*x**2/a) + 2100*a**(199/2)*b**(105/2)*x**6*sqrt(1 + b*x**2/a) + 1575*a**(197/2)*b**(107/2)*x**8*sqrt(1 + b*x**2/a) + 630*a**(195/2)*b**(109/2)*x**10*sqrt(1 + b*x**2/a) + 105*a**(193/2)*b**(111/2)*x**12*sqrt(1 + b*x**2/a)) - 2549*a**99*b**(97/2)*x**7/(105*a**(205/2)*b**(99/2)*sqrt(1 + b*x**2/a) + 630*a**(203/2)*b**(101/2)*x**2*sqrt(1 + b*x**2/a) + 1575*a**(201/2)*b**(103/2)*x**4*sqrt(1 + b*x**2/a) + 2100*a**(199/2)*b**(105/2)*x**6*sqrt(1 + b*x**2/a) + 1575*a**(197/2)*b**(107/2)*x**8*sqrt(1 + b*x**2/a) + 630*a**(195/2)*b**(109/2)*x**10*sqrt(1 + b*x**2/a) + 105*a**(193/2)*b**(111/2)*x**12*sqrt(1 + b*x**2/a)) - 2096*a**98*b**(99/2)*x**9/(105*a**(205/2)*b**(99/2)*sqrt(1 + b*x**2/a) + 630*a**(203/2)*b**(101/2)*x**2*sqrt(1 + b*x**2/a) + 1575*a**(201/2)*b**(103/2)*x**4*sqrt(1 + b*x**2/a) + 2100*a**(199/2)*b**(105/2)*x**6*sqrt(1 + b*x**2/a) + 1575*a**(197/2)*b**(107/2)*x**8*sqrt(1 + b*x**2/a) + 630*a**(195/2)*b**(109/2)*x**10*sqrt(1 + b*x**2/a) + 105*a**(193/2)*b**(111/2)*x**12*sqrt(1 + b*x**2/a)) - 934*a**97*b**(101/2)*x**11/(105*a**(205/2)*b**(99/2)*sqrt(1 + b*x**2/a) + 630*a**(203/2)*b**(101/2)*x**2*sqrt(1 + b*x**2/a) + 1575*a**(201/2)*b**(103/2)*x**4*sqrt(1 + b*x**2/a) + 2100*a**(199/2)*b**(105/2)*x**6*sqrt(1 + b*x**2/a) + 1575*a**(197/2)*b**(107/2)*x**8*sqrt(1 + b*x**2/a) + 630*a**(195/2)*b**(109/2)*x**10*sqrt(1 + b*x**2/a) + 105*a**(193/2)*b**(111/2)*x**12*sqrt(1 + b*x**2/a)) - 176*a**96*b**(103/2)*x**13/(105*a**(205/2)*b**(99/2)*sqrt(1 + b*x**2/a) + 630*a**(203/2)*b**(101/2)*x**2*sqrt(1 + b*x**2/a) + 1575*a**(201/2)*b**(103/2)*x**4*sqrt(1 + b*x**2/a) + 2100*a**(199/2)*b**(105/2)*x**6*sqrt(1 + b*x**2/a) + 1575*a**(197/2)*b**(107/2)*x**8*sqrt(1 + b*x**2/a) + 630*a**(195/2)*b**(109/2)*x**10*sqrt(1 + b*x**2/a) + 105*a**(193/2)*b**(111/2)*x**12*sqrt(1 + b*x**2/a))","B",0
520,1,364,0,6.080858," ","integrate(x**7/(b*x**2+a)**(9/2),x)","\begin{cases} - \frac{16 a^{3}}{35 a^{3} b^{4} \sqrt{a + b x^{2}} + 105 a^{2} b^{5} x^{2} \sqrt{a + b x^{2}} + 105 a b^{6} x^{4} \sqrt{a + b x^{2}} + 35 b^{7} x^{6} \sqrt{a + b x^{2}}} - \frac{56 a^{2} b x^{2}}{35 a^{3} b^{4} \sqrt{a + b x^{2}} + 105 a^{2} b^{5} x^{2} \sqrt{a + b x^{2}} + 105 a b^{6} x^{4} \sqrt{a + b x^{2}} + 35 b^{7} x^{6} \sqrt{a + b x^{2}}} - \frac{70 a b^{2} x^{4}}{35 a^{3} b^{4} \sqrt{a + b x^{2}} + 105 a^{2} b^{5} x^{2} \sqrt{a + b x^{2}} + 105 a b^{6} x^{4} \sqrt{a + b x^{2}} + 35 b^{7} x^{6} \sqrt{a + b x^{2}}} - \frac{35 b^{3} x^{6}}{35 a^{3} b^{4} \sqrt{a + b x^{2}} + 105 a^{2} b^{5} x^{2} \sqrt{a + b x^{2}} + 105 a b^{6} x^{4} \sqrt{a + b x^{2}} + 35 b^{7} x^{6} \sqrt{a + b x^{2}}} & \text{for}\: b \neq 0 \\\frac{x^{8}}{8 a^{\frac{9}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-16*a**3/(35*a**3*b**4*sqrt(a + b*x**2) + 105*a**2*b**5*x**2*sqrt(a + b*x**2) + 105*a*b**6*x**4*sqrt(a + b*x**2) + 35*b**7*x**6*sqrt(a + b*x**2)) - 56*a**2*b*x**2/(35*a**3*b**4*sqrt(a + b*x**2) + 105*a**2*b**5*x**2*sqrt(a + b*x**2) + 105*a*b**6*x**4*sqrt(a + b*x**2) + 35*b**7*x**6*sqrt(a + b*x**2)) - 70*a*b**2*x**4/(35*a**3*b**4*sqrt(a + b*x**2) + 105*a**2*b**5*x**2*sqrt(a + b*x**2) + 105*a*b**6*x**4*sqrt(a + b*x**2) + 35*b**7*x**6*sqrt(a + b*x**2)) - 35*b**3*x**6/(35*a**3*b**4*sqrt(a + b*x**2) + 105*a**2*b**5*x**2*sqrt(a + b*x**2) + 105*a*b**6*x**4*sqrt(a + b*x**2) + 35*b**7*x**6*sqrt(a + b*x**2)), Ne(b, 0)), (x**8/(8*a**(9/2)), True))","A",0
521,1,95,0,1.471519," ","integrate(x**6/(b*x**2+a)**(9/2),x)","\frac{x^{7}}{7 a^{\frac{9}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 21 a^{\frac{7}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 21 a^{\frac{5}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 7 a^{\frac{3}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"x**7/(7*a**(9/2)*sqrt(1 + b*x**2/a) + 21*a**(7/2)*b*x**2*sqrt(1 + b*x**2/a) + 21*a**(5/2)*b**2*x**4*sqrt(1 + b*x**2/a) + 7*a**(3/2)*b**3*x**6*sqrt(1 + b*x**2/a))","B",0
522,1,272,0,5.910593," ","integrate(x**5/(b*x**2+a)**(9/2),x)","\begin{cases} - \frac{8 a^{2}}{105 a^{3} b^{3} \sqrt{a + b x^{2}} + 315 a^{2} b^{4} x^{2} \sqrt{a + b x^{2}} + 315 a b^{5} x^{4} \sqrt{a + b x^{2}} + 105 b^{6} x^{6} \sqrt{a + b x^{2}}} - \frac{28 a b x^{2}}{105 a^{3} b^{3} \sqrt{a + b x^{2}} + 315 a^{2} b^{4} x^{2} \sqrt{a + b x^{2}} + 315 a b^{5} x^{4} \sqrt{a + b x^{2}} + 105 b^{6} x^{6} \sqrt{a + b x^{2}}} - \frac{35 b^{2} x^{4}}{105 a^{3} b^{3} \sqrt{a + b x^{2}} + 315 a^{2} b^{4} x^{2} \sqrt{a + b x^{2}} + 315 a b^{5} x^{4} \sqrt{a + b x^{2}} + 105 b^{6} x^{6} \sqrt{a + b x^{2}}} & \text{for}\: b \neq 0 \\\frac{x^{6}}{6 a^{\frac{9}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-8*a**2/(105*a**3*b**3*sqrt(a + b*x**2) + 315*a**2*b**4*x**2*sqrt(a + b*x**2) + 315*a*b**5*x**4*sqrt(a + b*x**2) + 105*b**6*x**6*sqrt(a + b*x**2)) - 28*a*b*x**2/(105*a**3*b**3*sqrt(a + b*x**2) + 315*a**2*b**4*x**2*sqrt(a + b*x**2) + 315*a*b**5*x**4*sqrt(a + b*x**2) + 105*b**6*x**6*sqrt(a + b*x**2)) - 35*b**2*x**4/(105*a**3*b**3*sqrt(a + b*x**2) + 315*a**2*b**4*x**2*sqrt(a + b*x**2) + 315*a*b**5*x**4*sqrt(a + b*x**2) + 105*b**6*x**6*sqrt(a + b*x**2)), Ne(b, 0)), (x**6/(6*a**(9/2)), True))","A",0
523,1,199,0,1.599044," ","integrate(x**4/(b*x**2+a)**(9/2),x)","\frac{7 a x^{5}}{35 a^{\frac{11}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 105 a^{\frac{9}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 105 a^{\frac{7}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 35 a^{\frac{5}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{2 b x^{7}}{35 a^{\frac{11}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 105 a^{\frac{9}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 105 a^{\frac{7}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 35 a^{\frac{5}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"7*a*x**5/(35*a**(11/2)*sqrt(1 + b*x**2/a) + 105*a**(9/2)*b*x**2*sqrt(1 + b*x**2/a) + 105*a**(7/2)*b**2*x**4*sqrt(1 + b*x**2/a) + 35*a**(5/2)*b**3*x**6*sqrt(1 + b*x**2/a)) + 2*b*x**7/(35*a**(11/2)*sqrt(1 + b*x**2/a) + 105*a**(9/2)*b*x**2*sqrt(1 + b*x**2/a) + 105*a**(7/2)*b**2*x**4*sqrt(1 + b*x**2/a) + 35*a**(5/2)*b**3*x**6*sqrt(1 + b*x**2/a))","B",0
524,1,180,0,5.861000," ","integrate(x**3/(b*x**2+a)**(9/2),x)","\begin{cases} - \frac{2 a}{35 a^{3} b^{2} \sqrt{a + b x^{2}} + 105 a^{2} b^{3} x^{2} \sqrt{a + b x^{2}} + 105 a b^{4} x^{4} \sqrt{a + b x^{2}} + 35 b^{5} x^{6} \sqrt{a + b x^{2}}} - \frac{7 b x^{2}}{35 a^{3} b^{2} \sqrt{a + b x^{2}} + 105 a^{2} b^{3} x^{2} \sqrt{a + b x^{2}} + 105 a b^{4} x^{4} \sqrt{a + b x^{2}} + 35 b^{5} x^{6} \sqrt{a + b x^{2}}} & \text{for}\: b \neq 0 \\\frac{x^{4}}{4 a^{\frac{9}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*a/(35*a**3*b**2*sqrt(a + b*x**2) + 105*a**2*b**3*x**2*sqrt(a + b*x**2) + 105*a*b**4*x**4*sqrt(a + b*x**2) + 35*b**5*x**6*sqrt(a + b*x**2)) - 7*b*x**2/(35*a**3*b**2*sqrt(a + b*x**2) + 105*a**2*b**3*x**2*sqrt(a + b*x**2) + 105*a*b**4*x**4*sqrt(a + b*x**2) + 35*b**5*x**6*sqrt(a + b*x**2)), Ne(b, 0)), (x**4/(4*a**(9/2)), True))","A",0
525,1,517,0,1.870350," ","integrate(x**2/(b*x**2+a)**(9/2),x)","\frac{35 a^{5} x^{3}}{105 a^{\frac{19}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{17}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 630 a^{\frac{15}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{13}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 105 a^{\frac{11}{2}} b^{4} x^{8} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{63 a^{4} b x^{5}}{105 a^{\frac{19}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{17}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 630 a^{\frac{15}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{13}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 105 a^{\frac{11}{2}} b^{4} x^{8} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{36 a^{3} b^{2} x^{7}}{105 a^{\frac{19}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{17}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 630 a^{\frac{15}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{13}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 105 a^{\frac{11}{2}} b^{4} x^{8} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{8 a^{2} b^{3} x^{9}}{105 a^{\frac{19}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{17}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 630 a^{\frac{15}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{13}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 105 a^{\frac{11}{2}} b^{4} x^{8} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"35*a**5*x**3/(105*a**(19/2)*sqrt(1 + b*x**2/a) + 420*a**(17/2)*b*x**2*sqrt(1 + b*x**2/a) + 630*a**(15/2)*b**2*x**4*sqrt(1 + b*x**2/a) + 420*a**(13/2)*b**3*x**6*sqrt(1 + b*x**2/a) + 105*a**(11/2)*b**4*x**8*sqrt(1 + b*x**2/a)) + 63*a**4*b*x**5/(105*a**(19/2)*sqrt(1 + b*x**2/a) + 420*a**(17/2)*b*x**2*sqrt(1 + b*x**2/a) + 630*a**(15/2)*b**2*x**4*sqrt(1 + b*x**2/a) + 420*a**(13/2)*b**3*x**6*sqrt(1 + b*x**2/a) + 105*a**(11/2)*b**4*x**8*sqrt(1 + b*x**2/a)) + 36*a**3*b**2*x**7/(105*a**(19/2)*sqrt(1 + b*x**2/a) + 420*a**(17/2)*b*x**2*sqrt(1 + b*x**2/a) + 630*a**(15/2)*b**2*x**4*sqrt(1 + b*x**2/a) + 420*a**(13/2)*b**3*x**6*sqrt(1 + b*x**2/a) + 105*a**(11/2)*b**4*x**8*sqrt(1 + b*x**2/a)) + 8*a**2*b**3*x**9/(105*a**(19/2)*sqrt(1 + b*x**2/a) + 420*a**(17/2)*b*x**2*sqrt(1 + b*x**2/a) + 630*a**(15/2)*b**2*x**4*sqrt(1 + b*x**2/a) + 420*a**(13/2)*b**3*x**6*sqrt(1 + b*x**2/a) + 105*a**(11/2)*b**4*x**8*sqrt(1 + b*x**2/a))","B",0
526,1,90,0,5.728315," ","integrate(x/(b*x**2+a)**(9/2),x)","\begin{cases} - \frac{1}{7 a^{3} b \sqrt{a + b x^{2}} + 21 a^{2} b^{2} x^{2} \sqrt{a + b x^{2}} + 21 a b^{3} x^{4} \sqrt{a + b x^{2}} + 7 b^{4} x^{6} \sqrt{a + b x^{2}}} & \text{for}\: b \neq 0 \\\frac{x^{2}}{2 a^{\frac{9}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-1/(7*a**3*b*sqrt(a + b*x**2) + 21*a**2*b**2*x**2*sqrt(a + b*x**2) + 21*a*b**3*x**4*sqrt(a + b*x**2) + 7*b**4*x**6*sqrt(a + b*x**2)), Ne(b, 0)), (x**2/(2*a**(9/2)), True))","A",0
527,1,1265,0,2.192399," ","integrate(1/(b*x**2+a)**(9/2),x)","\frac{35 a^{14} x}{35 a^{\frac{37}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{35}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{33}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 700 a^{\frac{31}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{29}{2}} b^{4} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{27}{2}} b^{5} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 35 a^{\frac{25}{2}} b^{6} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{175 a^{13} b x^{3}}{35 a^{\frac{37}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{35}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{33}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 700 a^{\frac{31}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{29}{2}} b^{4} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{27}{2}} b^{5} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 35 a^{\frac{25}{2}} b^{6} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{371 a^{12} b^{2} x^{5}}{35 a^{\frac{37}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{35}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{33}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 700 a^{\frac{31}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{29}{2}} b^{4} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{27}{2}} b^{5} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 35 a^{\frac{25}{2}} b^{6} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{429 a^{11} b^{3} x^{7}}{35 a^{\frac{37}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{35}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{33}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 700 a^{\frac{31}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{29}{2}} b^{4} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{27}{2}} b^{5} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 35 a^{\frac{25}{2}} b^{6} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{286 a^{10} b^{4} x^{9}}{35 a^{\frac{37}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{35}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{33}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 700 a^{\frac{31}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{29}{2}} b^{4} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{27}{2}} b^{5} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 35 a^{\frac{25}{2}} b^{6} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{104 a^{9} b^{5} x^{11}}{35 a^{\frac{37}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{35}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{33}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 700 a^{\frac{31}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{29}{2}} b^{4} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{27}{2}} b^{5} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 35 a^{\frac{25}{2}} b^{6} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{16 a^{8} b^{6} x^{13}}{35 a^{\frac{37}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{35}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{33}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 700 a^{\frac{31}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{29}{2}} b^{4} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{27}{2}} b^{5} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 35 a^{\frac{25}{2}} b^{6} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"35*a**14*x/(35*a**(37/2)*sqrt(1 + b*x**2/a) + 210*a**(35/2)*b*x**2*sqrt(1 + b*x**2/a) + 525*a**(33/2)*b**2*x**4*sqrt(1 + b*x**2/a) + 700*a**(31/2)*b**3*x**6*sqrt(1 + b*x**2/a) + 525*a**(29/2)*b**4*x**8*sqrt(1 + b*x**2/a) + 210*a**(27/2)*b**5*x**10*sqrt(1 + b*x**2/a) + 35*a**(25/2)*b**6*x**12*sqrt(1 + b*x**2/a)) + 175*a**13*b*x**3/(35*a**(37/2)*sqrt(1 + b*x**2/a) + 210*a**(35/2)*b*x**2*sqrt(1 + b*x**2/a) + 525*a**(33/2)*b**2*x**4*sqrt(1 + b*x**2/a) + 700*a**(31/2)*b**3*x**6*sqrt(1 + b*x**2/a) + 525*a**(29/2)*b**4*x**8*sqrt(1 + b*x**2/a) + 210*a**(27/2)*b**5*x**10*sqrt(1 + b*x**2/a) + 35*a**(25/2)*b**6*x**12*sqrt(1 + b*x**2/a)) + 371*a**12*b**2*x**5/(35*a**(37/2)*sqrt(1 + b*x**2/a) + 210*a**(35/2)*b*x**2*sqrt(1 + b*x**2/a) + 525*a**(33/2)*b**2*x**4*sqrt(1 + b*x**2/a) + 700*a**(31/2)*b**3*x**6*sqrt(1 + b*x**2/a) + 525*a**(29/2)*b**4*x**8*sqrt(1 + b*x**2/a) + 210*a**(27/2)*b**5*x**10*sqrt(1 + b*x**2/a) + 35*a**(25/2)*b**6*x**12*sqrt(1 + b*x**2/a)) + 429*a**11*b**3*x**7/(35*a**(37/2)*sqrt(1 + b*x**2/a) + 210*a**(35/2)*b*x**2*sqrt(1 + b*x**2/a) + 525*a**(33/2)*b**2*x**4*sqrt(1 + b*x**2/a) + 700*a**(31/2)*b**3*x**6*sqrt(1 + b*x**2/a) + 525*a**(29/2)*b**4*x**8*sqrt(1 + b*x**2/a) + 210*a**(27/2)*b**5*x**10*sqrt(1 + b*x**2/a) + 35*a**(25/2)*b**6*x**12*sqrt(1 + b*x**2/a)) + 286*a**10*b**4*x**9/(35*a**(37/2)*sqrt(1 + b*x**2/a) + 210*a**(35/2)*b*x**2*sqrt(1 + b*x**2/a) + 525*a**(33/2)*b**2*x**4*sqrt(1 + b*x**2/a) + 700*a**(31/2)*b**3*x**6*sqrt(1 + b*x**2/a) + 525*a**(29/2)*b**4*x**8*sqrt(1 + b*x**2/a) + 210*a**(27/2)*b**5*x**10*sqrt(1 + b*x**2/a) + 35*a**(25/2)*b**6*x**12*sqrt(1 + b*x**2/a)) + 104*a**9*b**5*x**11/(35*a**(37/2)*sqrt(1 + b*x**2/a) + 210*a**(35/2)*b*x**2*sqrt(1 + b*x**2/a) + 525*a**(33/2)*b**2*x**4*sqrt(1 + b*x**2/a) + 700*a**(31/2)*b**3*x**6*sqrt(1 + b*x**2/a) + 525*a**(29/2)*b**4*x**8*sqrt(1 + b*x**2/a) + 210*a**(27/2)*b**5*x**10*sqrt(1 + b*x**2/a) + 35*a**(25/2)*b**6*x**12*sqrt(1 + b*x**2/a)) + 16*a**8*b**6*x**13/(35*a**(37/2)*sqrt(1 + b*x**2/a) + 210*a**(35/2)*b*x**2*sqrt(1 + b*x**2/a) + 525*a**(33/2)*b**2*x**4*sqrt(1 + b*x**2/a) + 700*a**(31/2)*b**3*x**6*sqrt(1 + b*x**2/a) + 525*a**(29/2)*b**4*x**8*sqrt(1 + b*x**2/a) + 210*a**(27/2)*b**5*x**10*sqrt(1 + b*x**2/a) + 35*a**(25/2)*b**6*x**12*sqrt(1 + b*x**2/a))","B",0
528,1,5250,0,7.903798," ","integrate(1/x/(b*x**2+a)**(9/2),x)","\frac{352 a^{32} \sqrt{1 + \frac{b x^{2}}{a}}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{105 a^{32} \log{\left(\frac{b x^{2}}{a} \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} - \frac{210 a^{32} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{2924 a^{31} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{1050 a^{31} b x^{2} \log{\left(\frac{b x^{2}}{a} \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} - \frac{2100 a^{31} b x^{2} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{10852 a^{30} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{4725 a^{30} b^{2} x^{4} \log{\left(\frac{b x^{2}}{a} \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} - \frac{9450 a^{30} b^{2} x^{4} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{23630 a^{29} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{12600 a^{29} b^{3} x^{6} \log{\left(\frac{b x^{2}}{a} \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} - \frac{25200 a^{29} b^{3} x^{6} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{33280 a^{28} b^{4} x^{8} \sqrt{1 + \frac{b x^{2}}{a}}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{22050 a^{28} b^{4} x^{8} \log{\left(\frac{b x^{2}}{a} \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} - \frac{44100 a^{28} b^{4} x^{8} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{31442 a^{27} b^{5} x^{10} \sqrt{1 + \frac{b x^{2}}{a}}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{26460 a^{27} b^{5} x^{10} \log{\left(\frac{b x^{2}}{a} \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} - \frac{52920 a^{27} b^{5} x^{10} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{19924 a^{26} b^{6} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{22050 a^{26} b^{6} x^{12} \log{\left(\frac{b x^{2}}{a} \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} - \frac{44100 a^{26} b^{6} x^{12} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{8162 a^{25} b^{7} x^{14} \sqrt{1 + \frac{b x^{2}}{a}}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{12600 a^{25} b^{7} x^{14} \log{\left(\frac{b x^{2}}{a} \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} - \frac{25200 a^{25} b^{7} x^{14} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{1960 a^{24} b^{8} x^{16} \sqrt{1 + \frac{b x^{2}}{a}}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{4725 a^{24} b^{8} x^{16} \log{\left(\frac{b x^{2}}{a} \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} - \frac{9450 a^{24} b^{8} x^{16} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{210 a^{23} b^{9} x^{18} \sqrt{1 + \frac{b x^{2}}{a}}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{1050 a^{23} b^{9} x^{18} \log{\left(\frac{b x^{2}}{a} \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} - \frac{2100 a^{23} b^{9} x^{18} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{105 a^{22} b^{10} x^{20} \log{\left(\frac{b x^{2}}{a} \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} - \frac{210 a^{22} b^{10} x^{20} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}}"," ",0,"352*a**32*sqrt(1 + b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 105*a**32*log(b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) - 210*a**32*log(sqrt(1 + b*x**2/a) + 1)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 2924*a**31*b*x**2*sqrt(1 + b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 1050*a**31*b*x**2*log(b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) - 2100*a**31*b*x**2*log(sqrt(1 + b*x**2/a) + 1)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 10852*a**30*b**2*x**4*sqrt(1 + b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 4725*a**30*b**2*x**4*log(b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) - 9450*a**30*b**2*x**4*log(sqrt(1 + b*x**2/a) + 1)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 23630*a**29*b**3*x**6*sqrt(1 + b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 12600*a**29*b**3*x**6*log(b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) - 25200*a**29*b**3*x**6*log(sqrt(1 + b*x**2/a) + 1)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 33280*a**28*b**4*x**8*sqrt(1 + b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 22050*a**28*b**4*x**8*log(b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) - 44100*a**28*b**4*x**8*log(sqrt(1 + b*x**2/a) + 1)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 31442*a**27*b**5*x**10*sqrt(1 + b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 26460*a**27*b**5*x**10*log(b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) - 52920*a**27*b**5*x**10*log(sqrt(1 + b*x**2/a) + 1)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 19924*a**26*b**6*x**12*sqrt(1 + b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 22050*a**26*b**6*x**12*log(b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) - 44100*a**26*b**6*x**12*log(sqrt(1 + b*x**2/a) + 1)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 8162*a**25*b**7*x**14*sqrt(1 + b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 12600*a**25*b**7*x**14*log(b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) - 25200*a**25*b**7*x**14*log(sqrt(1 + b*x**2/a) + 1)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 1960*a**24*b**8*x**16*sqrt(1 + b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 4725*a**24*b**8*x**16*log(b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) - 9450*a**24*b**8*x**16*log(sqrt(1 + b*x**2/a) + 1)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 210*a**23*b**9*x**18*sqrt(1 + b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 1050*a**23*b**9*x**18*log(b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) - 2100*a**23*b**9*x**18*log(sqrt(1 + b*x**2/a) + 1)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 105*a**22*b**10*x**20*log(b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) - 210*a**22*b**10*x**20*log(sqrt(1 + b*x**2/a) + 1)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20)","B",0
529,1,400,0,2.928140," ","integrate(1/x**2/(b*x**2+a)**(9/2),x)","- \frac{35 a^{4} b^{\frac{33}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{35 a^{9} b^{16} + 140 a^{8} b^{17} x^{2} + 210 a^{7} b^{18} x^{4} + 140 a^{6} b^{19} x^{6} + 35 a^{5} b^{20} x^{8}} - \frac{280 a^{3} b^{\frac{35}{2}} x^{2} \sqrt{\frac{a}{b x^{2}} + 1}}{35 a^{9} b^{16} + 140 a^{8} b^{17} x^{2} + 210 a^{7} b^{18} x^{4} + 140 a^{6} b^{19} x^{6} + 35 a^{5} b^{20} x^{8}} - \frac{560 a^{2} b^{\frac{37}{2}} x^{4} \sqrt{\frac{a}{b x^{2}} + 1}}{35 a^{9} b^{16} + 140 a^{8} b^{17} x^{2} + 210 a^{7} b^{18} x^{4} + 140 a^{6} b^{19} x^{6} + 35 a^{5} b^{20} x^{8}} - \frac{448 a b^{\frac{39}{2}} x^{6} \sqrt{\frac{a}{b x^{2}} + 1}}{35 a^{9} b^{16} + 140 a^{8} b^{17} x^{2} + 210 a^{7} b^{18} x^{4} + 140 a^{6} b^{19} x^{6} + 35 a^{5} b^{20} x^{8}} - \frac{128 b^{\frac{41}{2}} x^{8} \sqrt{\frac{a}{b x^{2}} + 1}}{35 a^{9} b^{16} + 140 a^{8} b^{17} x^{2} + 210 a^{7} b^{18} x^{4} + 140 a^{6} b^{19} x^{6} + 35 a^{5} b^{20} x^{8}}"," ",0,"-35*a**4*b**(33/2)*sqrt(a/(b*x**2) + 1)/(35*a**9*b**16 + 140*a**8*b**17*x**2 + 210*a**7*b**18*x**4 + 140*a**6*b**19*x**6 + 35*a**5*b**20*x**8) - 280*a**3*b**(35/2)*x**2*sqrt(a/(b*x**2) + 1)/(35*a**9*b**16 + 140*a**8*b**17*x**2 + 210*a**7*b**18*x**4 + 140*a**6*b**19*x**6 + 35*a**5*b**20*x**8) - 560*a**2*b**(37/2)*x**4*sqrt(a/(b*x**2) + 1)/(35*a**9*b**16 + 140*a**8*b**17*x**2 + 210*a**7*b**18*x**4 + 140*a**6*b**19*x**6 + 35*a**5*b**20*x**8) - 448*a*b**(39/2)*x**6*sqrt(a/(b*x**2) + 1)/(35*a**9*b**16 + 140*a**8*b**17*x**2 + 210*a**7*b**18*x**4 + 140*a**6*b**19*x**6 + 35*a**5*b**20*x**8) - 128*b**(41/2)*x**8*sqrt(a/(b*x**2) + 1)/(35*a**9*b**16 + 140*a**8*b**17*x**2 + 210*a**7*b**18*x**4 + 140*a**6*b**19*x**6 + 35*a**5*b**20*x**8)","B",0
530,1,5540,0,12.427970," ","integrate(1/x**3/(b*x**2+a)**(9/2),x)","- \frac{70 a^{49} \sqrt{1 + \frac{b x^{2}}{a}}}{140 a^{\frac{107}{2}} x^{2} + 1400 a^{\frac{105}{2}} b x^{4} + 6300 a^{\frac{103}{2}} b^{2} x^{6} + 16800 a^{\frac{101}{2}} b^{3} x^{8} + 29400 a^{\frac{99}{2}} b^{4} x^{10} + 35280 a^{\frac{97}{2}} b^{5} x^{12} + 29400 a^{\frac{95}{2}} b^{6} x^{14} + 16800 a^{\frac{93}{2}} b^{7} x^{16} + 6300 a^{\frac{91}{2}} b^{8} x^{18} + 1400 a^{\frac{89}{2}} b^{9} x^{20} + 140 a^{\frac{87}{2}} b^{10} x^{22}} - \frac{1476 a^{48} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}}}{140 a^{\frac{107}{2}} x^{2} + 1400 a^{\frac{105}{2}} b x^{4} + 6300 a^{\frac{103}{2}} b^{2} x^{6} + 16800 a^{\frac{101}{2}} b^{3} x^{8} + 29400 a^{\frac{99}{2}} b^{4} x^{10} + 35280 a^{\frac{97}{2}} b^{5} x^{12} + 29400 a^{\frac{95}{2}} b^{6} x^{14} + 16800 a^{\frac{93}{2}} b^{7} x^{16} + 6300 a^{\frac{91}{2}} b^{8} x^{18} + 1400 a^{\frac{89}{2}} b^{9} x^{20} + 140 a^{\frac{87}{2}} b^{10} x^{22}} - \frac{315 a^{48} b x^{2} \log{\left(\frac{b x^{2}}{a} \right)}}{140 a^{\frac{107}{2}} x^{2} + 1400 a^{\frac{105}{2}} b x^{4} + 6300 a^{\frac{103}{2}} b^{2} x^{6} + 16800 a^{\frac{101}{2}} b^{3} x^{8} + 29400 a^{\frac{99}{2}} b^{4} x^{10} + 35280 a^{\frac{97}{2}} b^{5} x^{12} + 29400 a^{\frac{95}{2}} b^{6} x^{14} + 16800 a^{\frac{93}{2}} b^{7} x^{16} + 6300 a^{\frac{91}{2}} b^{8} x^{18} + 1400 a^{\frac{89}{2}} b^{9} x^{20} + 140 a^{\frac{87}{2}} b^{10} x^{22}} + \frac{630 a^{48} b x^{2} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{140 a^{\frac{107}{2}} x^{2} + 1400 a^{\frac{105}{2}} b x^{4} + 6300 a^{\frac{103}{2}} b^{2} x^{6} + 16800 a^{\frac{101}{2}} b^{3} x^{8} + 29400 a^{\frac{99}{2}} b^{4} x^{10} + 35280 a^{\frac{97}{2}} b^{5} x^{12} + 29400 a^{\frac{95}{2}} b^{6} x^{14} + 16800 a^{\frac{93}{2}} b^{7} x^{16} + 6300 a^{\frac{91}{2}} b^{8} x^{18} + 1400 a^{\frac{89}{2}} b^{9} x^{20} + 140 a^{\frac{87}{2}} b^{10} x^{22}} - \frac{9822 a^{47} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}}}{140 a^{\frac{107}{2}} x^{2} + 1400 a^{\frac{105}{2}} b x^{4} + 6300 a^{\frac{103}{2}} b^{2} x^{6} + 16800 a^{\frac{101}{2}} b^{3} x^{8} + 29400 a^{\frac{99}{2}} b^{4} x^{10} + 35280 a^{\frac{97}{2}} b^{5} x^{12} + 29400 a^{\frac{95}{2}} b^{6} x^{14} + 16800 a^{\frac{93}{2}} b^{7} x^{16} + 6300 a^{\frac{91}{2}} b^{8} x^{18} + 1400 a^{\frac{89}{2}} b^{9} x^{20} + 140 a^{\frac{87}{2}} b^{10} x^{22}} - \frac{3150 a^{47} b^{2} x^{4} \log{\left(\frac{b x^{2}}{a} \right)}}{140 a^{\frac{107}{2}} x^{2} + 1400 a^{\frac{105}{2}} b x^{4} + 6300 a^{\frac{103}{2}} b^{2} x^{6} + 16800 a^{\frac{101}{2}} b^{3} x^{8} + 29400 a^{\frac{99}{2}} b^{4} x^{10} + 35280 a^{\frac{97}{2}} b^{5} x^{12} + 29400 a^{\frac{95}{2}} b^{6} x^{14} + 16800 a^{\frac{93}{2}} b^{7} x^{16} + 6300 a^{\frac{91}{2}} b^{8} x^{18} + 1400 a^{\frac{89}{2}} b^{9} x^{20} + 140 a^{\frac{87}{2}} b^{10} x^{22}} + \frac{6300 a^{47} b^{2} x^{4} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{140 a^{\frac{107}{2}} x^{2} + 1400 a^{\frac{105}{2}} b x^{4} + 6300 a^{\frac{103}{2}} b^{2} x^{6} + 16800 a^{\frac{101}{2}} b^{3} x^{8} + 29400 a^{\frac{99}{2}} b^{4} x^{10} + 35280 a^{\frac{97}{2}} b^{5} x^{12} + 29400 a^{\frac{95}{2}} b^{6} x^{14} + 16800 a^{\frac{93}{2}} b^{7} x^{16} + 6300 a^{\frac{91}{2}} b^{8} x^{18} + 1400 a^{\frac{89}{2}} b^{9} x^{20} + 140 a^{\frac{87}{2}} b^{10} x^{22}} - \frac{33956 a^{46} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}}}{140 a^{\frac{107}{2}} x^{2} + 1400 a^{\frac{105}{2}} b x^{4} + 6300 a^{\frac{103}{2}} b^{2} x^{6} + 16800 a^{\frac{101}{2}} b^{3} x^{8} + 29400 a^{\frac{99}{2}} b^{4} x^{10} + 35280 a^{\frac{97}{2}} b^{5} x^{12} + 29400 a^{\frac{95}{2}} b^{6} x^{14} + 16800 a^{\frac{93}{2}} b^{7} x^{16} + 6300 a^{\frac{91}{2}} b^{8} x^{18} + 1400 a^{\frac{89}{2}} b^{9} x^{20} + 140 a^{\frac{87}{2}} b^{10} x^{22}} - \frac{14175 a^{46} b^{3} x^{6} \log{\left(\frac{b x^{2}}{a} \right)}}{140 a^{\frac{107}{2}} x^{2} + 1400 a^{\frac{105}{2}} b x^{4} + 6300 a^{\frac{103}{2}} b^{2} x^{6} + 16800 a^{\frac{101}{2}} b^{3} x^{8} + 29400 a^{\frac{99}{2}} b^{4} x^{10} + 35280 a^{\frac{97}{2}} b^{5} x^{12} + 29400 a^{\frac{95}{2}} b^{6} x^{14} + 16800 a^{\frac{93}{2}} b^{7} x^{16} + 6300 a^{\frac{91}{2}} b^{8} x^{18} + 1400 a^{\frac{89}{2}} b^{9} x^{20} + 140 a^{\frac{87}{2}} b^{10} x^{22}} + \frac{28350 a^{46} b^{3} x^{6} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{140 a^{\frac{107}{2}} x^{2} + 1400 a^{\frac{105}{2}} b x^{4} + 6300 a^{\frac{103}{2}} b^{2} x^{6} + 16800 a^{\frac{101}{2}} b^{3} x^{8} + 29400 a^{\frac{99}{2}} b^{4} x^{10} + 35280 a^{\frac{97}{2}} b^{5} x^{12} + 29400 a^{\frac{95}{2}} b^{6} x^{14} + 16800 a^{\frac{93}{2}} b^{7} x^{16} + 6300 a^{\frac{91}{2}} b^{8} x^{18} + 1400 a^{\frac{89}{2}} b^{9} x^{20} + 140 a^{\frac{87}{2}} b^{10} x^{22}} - \frac{71940 a^{45} b^{4} x^{8} \sqrt{1 + \frac{b x^{2}}{a}}}{140 a^{\frac{107}{2}} x^{2} + 1400 a^{\frac{105}{2}} b x^{4} + 6300 a^{\frac{103}{2}} b^{2} x^{6} + 16800 a^{\frac{101}{2}} b^{3} x^{8} + 29400 a^{\frac{99}{2}} b^{4} x^{10} + 35280 a^{\frac{97}{2}} b^{5} x^{12} + 29400 a^{\frac{95}{2}} b^{6} x^{14} + 16800 a^{\frac{93}{2}} b^{7} x^{16} + 6300 a^{\frac{91}{2}} b^{8} x^{18} + 1400 a^{\frac{89}{2}} b^{9} x^{20} + 140 a^{\frac{87}{2}} b^{10} x^{22}} - \frac{37800 a^{45} b^{4} x^{8} \log{\left(\frac{b x^{2}}{a} \right)}}{140 a^{\frac{107}{2}} x^{2} + 1400 a^{\frac{105}{2}} b x^{4} + 6300 a^{\frac{103}{2}} b^{2} x^{6} + 16800 a^{\frac{101}{2}} b^{3} x^{8} + 29400 a^{\frac{99}{2}} b^{4} x^{10} + 35280 a^{\frac{97}{2}} b^{5} x^{12} + 29400 a^{\frac{95}{2}} b^{6} x^{14} + 16800 a^{\frac{93}{2}} b^{7} x^{16} + 6300 a^{\frac{91}{2}} b^{8} x^{18} + 1400 a^{\frac{89}{2}} b^{9} x^{20} + 140 a^{\frac{87}{2}} b^{10} x^{22}} + \frac{75600 a^{45} b^{4} x^{8} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{140 a^{\frac{107}{2}} x^{2} + 1400 a^{\frac{105}{2}} b x^{4} + 6300 a^{\frac{103}{2}} b^{2} x^{6} + 16800 a^{\frac{101}{2}} b^{3} x^{8} + 29400 a^{\frac{99}{2}} b^{4} x^{10} + 35280 a^{\frac{97}{2}} b^{5} x^{12} + 29400 a^{\frac{95}{2}} b^{6} x^{14} + 16800 a^{\frac{93}{2}} b^{7} x^{16} + 6300 a^{\frac{91}{2}} b^{8} x^{18} + 1400 a^{\frac{89}{2}} b^{9} x^{20} + 140 a^{\frac{87}{2}} b^{10} x^{22}} - \frac{100260 a^{44} b^{5} x^{10} \sqrt{1 + \frac{b x^{2}}{a}}}{140 a^{\frac{107}{2}} x^{2} + 1400 a^{\frac{105}{2}} b x^{4} + 6300 a^{\frac{103}{2}} b^{2} x^{6} + 16800 a^{\frac{101}{2}} b^{3} x^{8} + 29400 a^{\frac{99}{2}} b^{4} x^{10} + 35280 a^{\frac{97}{2}} b^{5} x^{12} + 29400 a^{\frac{95}{2}} b^{6} x^{14} + 16800 a^{\frac{93}{2}} b^{7} x^{16} + 6300 a^{\frac{91}{2}} b^{8} x^{18} + 1400 a^{\frac{89}{2}} b^{9} x^{20} + 140 a^{\frac{87}{2}} b^{10} x^{22}} - \frac{66150 a^{44} b^{5} x^{10} \log{\left(\frac{b x^{2}}{a} \right)}}{140 a^{\frac{107}{2}} x^{2} + 1400 a^{\frac{105}{2}} b x^{4} + 6300 a^{\frac{103}{2}} b^{2} x^{6} + 16800 a^{\frac{101}{2}} b^{3} x^{8} + 29400 a^{\frac{99}{2}} b^{4} x^{10} + 35280 a^{\frac{97}{2}} b^{5} x^{12} + 29400 a^{\frac{95}{2}} b^{6} x^{14} + 16800 a^{\frac{93}{2}} b^{7} x^{16} + 6300 a^{\frac{91}{2}} b^{8} x^{18} + 1400 a^{\frac{89}{2}} b^{9} x^{20} + 140 a^{\frac{87}{2}} b^{10} x^{22}} + \frac{132300 a^{44} b^{5} x^{10} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{140 a^{\frac{107}{2}} x^{2} + 1400 a^{\frac{105}{2}} b x^{4} + 6300 a^{\frac{103}{2}} b^{2} x^{6} + 16800 a^{\frac{101}{2}} b^{3} x^{8} + 29400 a^{\frac{99}{2}} b^{4} x^{10} + 35280 a^{\frac{97}{2}} b^{5} x^{12} + 29400 a^{\frac{95}{2}} b^{6} x^{14} + 16800 a^{\frac{93}{2}} b^{7} x^{16} + 6300 a^{\frac{91}{2}} b^{8} x^{18} + 1400 a^{\frac{89}{2}} b^{9} x^{20} + 140 a^{\frac{87}{2}} b^{10} x^{22}} - \frac{94396 a^{43} b^{6} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}}{140 a^{\frac{107}{2}} x^{2} + 1400 a^{\frac{105}{2}} b x^{4} + 6300 a^{\frac{103}{2}} b^{2} x^{6} + 16800 a^{\frac{101}{2}} b^{3} x^{8} + 29400 a^{\frac{99}{2}} b^{4} x^{10} + 35280 a^{\frac{97}{2}} b^{5} x^{12} + 29400 a^{\frac{95}{2}} b^{6} x^{14} + 16800 a^{\frac{93}{2}} b^{7} x^{16} + 6300 a^{\frac{91}{2}} b^{8} x^{18} + 1400 a^{\frac{89}{2}} b^{9} x^{20} + 140 a^{\frac{87}{2}} b^{10} x^{22}} - \frac{79380 a^{43} b^{6} x^{12} \log{\left(\frac{b x^{2}}{a} \right)}}{140 a^{\frac{107}{2}} x^{2} + 1400 a^{\frac{105}{2}} b x^{4} + 6300 a^{\frac{103}{2}} b^{2} x^{6} + 16800 a^{\frac{101}{2}} b^{3} x^{8} + 29400 a^{\frac{99}{2}} b^{4} x^{10} + 35280 a^{\frac{97}{2}} b^{5} x^{12} + 29400 a^{\frac{95}{2}} b^{6} x^{14} + 16800 a^{\frac{93}{2}} b^{7} x^{16} + 6300 a^{\frac{91}{2}} b^{8} x^{18} + 1400 a^{\frac{89}{2}} b^{9} x^{20} + 140 a^{\frac{87}{2}} b^{10} x^{22}} + \frac{158760 a^{43} b^{6} x^{12} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{140 a^{\frac{107}{2}} x^{2} + 1400 a^{\frac{105}{2}} b x^{4} + 6300 a^{\frac{103}{2}} b^{2} x^{6} + 16800 a^{\frac{101}{2}} b^{3} x^{8} + 29400 a^{\frac{99}{2}} b^{4} x^{10} + 35280 a^{\frac{97}{2}} b^{5} x^{12} + 29400 a^{\frac{95}{2}} b^{6} x^{14} + 16800 a^{\frac{93}{2}} b^{7} x^{16} + 6300 a^{\frac{91}{2}} b^{8} x^{18} + 1400 a^{\frac{89}{2}} b^{9} x^{20} + 140 a^{\frac{87}{2}} b^{10} x^{22}} - \frac{59772 a^{42} b^{7} x^{14} \sqrt{1 + \frac{b x^{2}}{a}}}{140 a^{\frac{107}{2}} x^{2} + 1400 a^{\frac{105}{2}} b x^{4} + 6300 a^{\frac{103}{2}} b^{2} x^{6} + 16800 a^{\frac{101}{2}} b^{3} x^{8} + 29400 a^{\frac{99}{2}} b^{4} x^{10} + 35280 a^{\frac{97}{2}} b^{5} x^{12} + 29400 a^{\frac{95}{2}} b^{6} x^{14} + 16800 a^{\frac{93}{2}} b^{7} x^{16} + 6300 a^{\frac{91}{2}} b^{8} x^{18} + 1400 a^{\frac{89}{2}} b^{9} x^{20} + 140 a^{\frac{87}{2}} b^{10} x^{22}} - \frac{66150 a^{42} b^{7} x^{14} \log{\left(\frac{b x^{2}}{a} \right)}}{140 a^{\frac{107}{2}} x^{2} + 1400 a^{\frac{105}{2}} b x^{4} + 6300 a^{\frac{103}{2}} b^{2} x^{6} + 16800 a^{\frac{101}{2}} b^{3} x^{8} + 29400 a^{\frac{99}{2}} b^{4} x^{10} + 35280 a^{\frac{97}{2}} b^{5} x^{12} + 29400 a^{\frac{95}{2}} b^{6} x^{14} + 16800 a^{\frac{93}{2}} b^{7} x^{16} + 6300 a^{\frac{91}{2}} b^{8} x^{18} + 1400 a^{\frac{89}{2}} b^{9} x^{20} + 140 a^{\frac{87}{2}} b^{10} x^{22}} + \frac{132300 a^{42} b^{7} x^{14} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{140 a^{\frac{107}{2}} x^{2} + 1400 a^{\frac{105}{2}} b x^{4} + 6300 a^{\frac{103}{2}} b^{2} x^{6} + 16800 a^{\frac{101}{2}} b^{3} x^{8} + 29400 a^{\frac{99}{2}} b^{4} x^{10} + 35280 a^{\frac{97}{2}} b^{5} x^{12} + 29400 a^{\frac{95}{2}} b^{6} x^{14} + 16800 a^{\frac{93}{2}} b^{7} x^{16} + 6300 a^{\frac{91}{2}} b^{8} x^{18} + 1400 a^{\frac{89}{2}} b^{9} x^{20} + 140 a^{\frac{87}{2}} b^{10} x^{22}} - \frac{24486 a^{41} b^{8} x^{16} \sqrt{1 + \frac{b x^{2}}{a}}}{140 a^{\frac{107}{2}} x^{2} + 1400 a^{\frac{105}{2}} b x^{4} + 6300 a^{\frac{103}{2}} b^{2} x^{6} + 16800 a^{\frac{101}{2}} b^{3} x^{8} + 29400 a^{\frac{99}{2}} b^{4} x^{10} + 35280 a^{\frac{97}{2}} b^{5} x^{12} + 29400 a^{\frac{95}{2}} b^{6} x^{14} + 16800 a^{\frac{93}{2}} b^{7} x^{16} + 6300 a^{\frac{91}{2}} b^{8} x^{18} + 1400 a^{\frac{89}{2}} b^{9} x^{20} + 140 a^{\frac{87}{2}} b^{10} x^{22}} - \frac{37800 a^{41} b^{8} x^{16} \log{\left(\frac{b x^{2}}{a} \right)}}{140 a^{\frac{107}{2}} x^{2} + 1400 a^{\frac{105}{2}} b x^{4} + 6300 a^{\frac{103}{2}} b^{2} x^{6} + 16800 a^{\frac{101}{2}} b^{3} x^{8} + 29400 a^{\frac{99}{2}} b^{4} x^{10} + 35280 a^{\frac{97}{2}} b^{5} x^{12} + 29400 a^{\frac{95}{2}} b^{6} x^{14} + 16800 a^{\frac{93}{2}} b^{7} x^{16} + 6300 a^{\frac{91}{2}} b^{8} x^{18} + 1400 a^{\frac{89}{2}} b^{9} x^{20} + 140 a^{\frac{87}{2}} b^{10} x^{22}} + \frac{75600 a^{41} b^{8} x^{16} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{140 a^{\frac{107}{2}} x^{2} + 1400 a^{\frac{105}{2}} b x^{4} + 6300 a^{\frac{103}{2}} b^{2} x^{6} + 16800 a^{\frac{101}{2}} b^{3} x^{8} + 29400 a^{\frac{99}{2}} b^{4} x^{10} + 35280 a^{\frac{97}{2}} b^{5} x^{12} + 29400 a^{\frac{95}{2}} b^{6} x^{14} + 16800 a^{\frac{93}{2}} b^{7} x^{16} + 6300 a^{\frac{91}{2}} b^{8} x^{18} + 1400 a^{\frac{89}{2}} b^{9} x^{20} + 140 a^{\frac{87}{2}} b^{10} x^{22}} - \frac{5880 a^{40} b^{9} x^{18} \sqrt{1 + \frac{b x^{2}}{a}}}{140 a^{\frac{107}{2}} x^{2} + 1400 a^{\frac{105}{2}} b x^{4} + 6300 a^{\frac{103}{2}} b^{2} x^{6} + 16800 a^{\frac{101}{2}} b^{3} x^{8} + 29400 a^{\frac{99}{2}} b^{4} x^{10} + 35280 a^{\frac{97}{2}} b^{5} x^{12} + 29400 a^{\frac{95}{2}} b^{6} x^{14} + 16800 a^{\frac{93}{2}} b^{7} x^{16} + 6300 a^{\frac{91}{2}} b^{8} x^{18} + 1400 a^{\frac{89}{2}} b^{9} x^{20} + 140 a^{\frac{87}{2}} b^{10} x^{22}} - \frac{14175 a^{40} b^{9} x^{18} \log{\left(\frac{b x^{2}}{a} \right)}}{140 a^{\frac{107}{2}} x^{2} + 1400 a^{\frac{105}{2}} b x^{4} + 6300 a^{\frac{103}{2}} b^{2} x^{6} + 16800 a^{\frac{101}{2}} b^{3} x^{8} + 29400 a^{\frac{99}{2}} b^{4} x^{10} + 35280 a^{\frac{97}{2}} b^{5} x^{12} + 29400 a^{\frac{95}{2}} b^{6} x^{14} + 16800 a^{\frac{93}{2}} b^{7} x^{16} + 6300 a^{\frac{91}{2}} b^{8} x^{18} + 1400 a^{\frac{89}{2}} b^{9} x^{20} + 140 a^{\frac{87}{2}} b^{10} x^{22}} + \frac{28350 a^{40} b^{9} x^{18} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{140 a^{\frac{107}{2}} x^{2} + 1400 a^{\frac{105}{2}} b x^{4} + 6300 a^{\frac{103}{2}} b^{2} x^{6} + 16800 a^{\frac{101}{2}} b^{3} x^{8} + 29400 a^{\frac{99}{2}} b^{4} x^{10} + 35280 a^{\frac{97}{2}} b^{5} x^{12} + 29400 a^{\frac{95}{2}} b^{6} x^{14} + 16800 a^{\frac{93}{2}} b^{7} x^{16} + 6300 a^{\frac{91}{2}} b^{8} x^{18} + 1400 a^{\frac{89}{2}} b^{9} x^{20} + 140 a^{\frac{87}{2}} b^{10} x^{22}} - \frac{630 a^{39} b^{10} x^{20} \sqrt{1 + \frac{b x^{2}}{a}}}{140 a^{\frac{107}{2}} x^{2} + 1400 a^{\frac{105}{2}} b x^{4} + 6300 a^{\frac{103}{2}} b^{2} x^{6} + 16800 a^{\frac{101}{2}} b^{3} x^{8} + 29400 a^{\frac{99}{2}} b^{4} x^{10} + 35280 a^{\frac{97}{2}} b^{5} x^{12} + 29400 a^{\frac{95}{2}} b^{6} x^{14} + 16800 a^{\frac{93}{2}} b^{7} x^{16} + 6300 a^{\frac{91}{2}} b^{8} x^{18} + 1400 a^{\frac{89}{2}} b^{9} x^{20} + 140 a^{\frac{87}{2}} b^{10} x^{22}} - \frac{3150 a^{39} b^{10} x^{20} \log{\left(\frac{b x^{2}}{a} \right)}}{140 a^{\frac{107}{2}} x^{2} + 1400 a^{\frac{105}{2}} b x^{4} + 6300 a^{\frac{103}{2}} b^{2} x^{6} + 16800 a^{\frac{101}{2}} b^{3} x^{8} + 29400 a^{\frac{99}{2}} b^{4} x^{10} + 35280 a^{\frac{97}{2}} b^{5} x^{12} + 29400 a^{\frac{95}{2}} b^{6} x^{14} + 16800 a^{\frac{93}{2}} b^{7} x^{16} + 6300 a^{\frac{91}{2}} b^{8} x^{18} + 1400 a^{\frac{89}{2}} b^{9} x^{20} + 140 a^{\frac{87}{2}} b^{10} x^{22}} + \frac{6300 a^{39} b^{10} x^{20} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{140 a^{\frac{107}{2}} x^{2} + 1400 a^{\frac{105}{2}} b x^{4} + 6300 a^{\frac{103}{2}} b^{2} x^{6} + 16800 a^{\frac{101}{2}} b^{3} x^{8} + 29400 a^{\frac{99}{2}} b^{4} x^{10} + 35280 a^{\frac{97}{2}} b^{5} x^{12} + 29400 a^{\frac{95}{2}} b^{6} x^{14} + 16800 a^{\frac{93}{2}} b^{7} x^{16} + 6300 a^{\frac{91}{2}} b^{8} x^{18} + 1400 a^{\frac{89}{2}} b^{9} x^{20} + 140 a^{\frac{87}{2}} b^{10} x^{22}} - \frac{315 a^{38} b^{11} x^{22} \log{\left(\frac{b x^{2}}{a} \right)}}{140 a^{\frac{107}{2}} x^{2} + 1400 a^{\frac{105}{2}} b x^{4} + 6300 a^{\frac{103}{2}} b^{2} x^{6} + 16800 a^{\frac{101}{2}} b^{3} x^{8} + 29400 a^{\frac{99}{2}} b^{4} x^{10} + 35280 a^{\frac{97}{2}} b^{5} x^{12} + 29400 a^{\frac{95}{2}} b^{6} x^{14} + 16800 a^{\frac{93}{2}} b^{7} x^{16} + 6300 a^{\frac{91}{2}} b^{8} x^{18} + 1400 a^{\frac{89}{2}} b^{9} x^{20} + 140 a^{\frac{87}{2}} b^{10} x^{22}} + \frac{630 a^{38} b^{11} x^{22} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{140 a^{\frac{107}{2}} x^{2} + 1400 a^{\frac{105}{2}} b x^{4} + 6300 a^{\frac{103}{2}} b^{2} x^{6} + 16800 a^{\frac{101}{2}} b^{3} x^{8} + 29400 a^{\frac{99}{2}} b^{4} x^{10} + 35280 a^{\frac{97}{2}} b^{5} x^{12} + 29400 a^{\frac{95}{2}} b^{6} x^{14} + 16800 a^{\frac{93}{2}} b^{7} x^{16} + 6300 a^{\frac{91}{2}} b^{8} x^{18} + 1400 a^{\frac{89}{2}} b^{9} x^{20} + 140 a^{\frac{87}{2}} b^{10} x^{22}}"," ",0,"-70*a**49*sqrt(1 + b*x**2/a)/(140*a**(107/2)*x**2 + 1400*a**(105/2)*b*x**4 + 6300*a**(103/2)*b**2*x**6 + 16800*a**(101/2)*b**3*x**8 + 29400*a**(99/2)*b**4*x**10 + 35280*a**(97/2)*b**5*x**12 + 29400*a**(95/2)*b**6*x**14 + 16800*a**(93/2)*b**7*x**16 + 6300*a**(91/2)*b**8*x**18 + 1400*a**(89/2)*b**9*x**20 + 140*a**(87/2)*b**10*x**22) - 1476*a**48*b*x**2*sqrt(1 + b*x**2/a)/(140*a**(107/2)*x**2 + 1400*a**(105/2)*b*x**4 + 6300*a**(103/2)*b**2*x**6 + 16800*a**(101/2)*b**3*x**8 + 29400*a**(99/2)*b**4*x**10 + 35280*a**(97/2)*b**5*x**12 + 29400*a**(95/2)*b**6*x**14 + 16800*a**(93/2)*b**7*x**16 + 6300*a**(91/2)*b**8*x**18 + 1400*a**(89/2)*b**9*x**20 + 140*a**(87/2)*b**10*x**22) - 315*a**48*b*x**2*log(b*x**2/a)/(140*a**(107/2)*x**2 + 1400*a**(105/2)*b*x**4 + 6300*a**(103/2)*b**2*x**6 + 16800*a**(101/2)*b**3*x**8 + 29400*a**(99/2)*b**4*x**10 + 35280*a**(97/2)*b**5*x**12 + 29400*a**(95/2)*b**6*x**14 + 16800*a**(93/2)*b**7*x**16 + 6300*a**(91/2)*b**8*x**18 + 1400*a**(89/2)*b**9*x**20 + 140*a**(87/2)*b**10*x**22) + 630*a**48*b*x**2*log(sqrt(1 + b*x**2/a) + 1)/(140*a**(107/2)*x**2 + 1400*a**(105/2)*b*x**4 + 6300*a**(103/2)*b**2*x**6 + 16800*a**(101/2)*b**3*x**8 + 29400*a**(99/2)*b**4*x**10 + 35280*a**(97/2)*b**5*x**12 + 29400*a**(95/2)*b**6*x**14 + 16800*a**(93/2)*b**7*x**16 + 6300*a**(91/2)*b**8*x**18 + 1400*a**(89/2)*b**9*x**20 + 140*a**(87/2)*b**10*x**22) - 9822*a**47*b**2*x**4*sqrt(1 + b*x**2/a)/(140*a**(107/2)*x**2 + 1400*a**(105/2)*b*x**4 + 6300*a**(103/2)*b**2*x**6 + 16800*a**(101/2)*b**3*x**8 + 29400*a**(99/2)*b**4*x**10 + 35280*a**(97/2)*b**5*x**12 + 29400*a**(95/2)*b**6*x**14 + 16800*a**(93/2)*b**7*x**16 + 6300*a**(91/2)*b**8*x**18 + 1400*a**(89/2)*b**9*x**20 + 140*a**(87/2)*b**10*x**22) - 3150*a**47*b**2*x**4*log(b*x**2/a)/(140*a**(107/2)*x**2 + 1400*a**(105/2)*b*x**4 + 6300*a**(103/2)*b**2*x**6 + 16800*a**(101/2)*b**3*x**8 + 29400*a**(99/2)*b**4*x**10 + 35280*a**(97/2)*b**5*x**12 + 29400*a**(95/2)*b**6*x**14 + 16800*a**(93/2)*b**7*x**16 + 6300*a**(91/2)*b**8*x**18 + 1400*a**(89/2)*b**9*x**20 + 140*a**(87/2)*b**10*x**22) + 6300*a**47*b**2*x**4*log(sqrt(1 + b*x**2/a) + 1)/(140*a**(107/2)*x**2 + 1400*a**(105/2)*b*x**4 + 6300*a**(103/2)*b**2*x**6 + 16800*a**(101/2)*b**3*x**8 + 29400*a**(99/2)*b**4*x**10 + 35280*a**(97/2)*b**5*x**12 + 29400*a**(95/2)*b**6*x**14 + 16800*a**(93/2)*b**7*x**16 + 6300*a**(91/2)*b**8*x**18 + 1400*a**(89/2)*b**9*x**20 + 140*a**(87/2)*b**10*x**22) - 33956*a**46*b**3*x**6*sqrt(1 + b*x**2/a)/(140*a**(107/2)*x**2 + 1400*a**(105/2)*b*x**4 + 6300*a**(103/2)*b**2*x**6 + 16800*a**(101/2)*b**3*x**8 + 29400*a**(99/2)*b**4*x**10 + 35280*a**(97/2)*b**5*x**12 + 29400*a**(95/2)*b**6*x**14 + 16800*a**(93/2)*b**7*x**16 + 6300*a**(91/2)*b**8*x**18 + 1400*a**(89/2)*b**9*x**20 + 140*a**(87/2)*b**10*x**22) - 14175*a**46*b**3*x**6*log(b*x**2/a)/(140*a**(107/2)*x**2 + 1400*a**(105/2)*b*x**4 + 6300*a**(103/2)*b**2*x**6 + 16800*a**(101/2)*b**3*x**8 + 29400*a**(99/2)*b**4*x**10 + 35280*a**(97/2)*b**5*x**12 + 29400*a**(95/2)*b**6*x**14 + 16800*a**(93/2)*b**7*x**16 + 6300*a**(91/2)*b**8*x**18 + 1400*a**(89/2)*b**9*x**20 + 140*a**(87/2)*b**10*x**22) + 28350*a**46*b**3*x**6*log(sqrt(1 + b*x**2/a) + 1)/(140*a**(107/2)*x**2 + 1400*a**(105/2)*b*x**4 + 6300*a**(103/2)*b**2*x**6 + 16800*a**(101/2)*b**3*x**8 + 29400*a**(99/2)*b**4*x**10 + 35280*a**(97/2)*b**5*x**12 + 29400*a**(95/2)*b**6*x**14 + 16800*a**(93/2)*b**7*x**16 + 6300*a**(91/2)*b**8*x**18 + 1400*a**(89/2)*b**9*x**20 + 140*a**(87/2)*b**10*x**22) - 71940*a**45*b**4*x**8*sqrt(1 + b*x**2/a)/(140*a**(107/2)*x**2 + 1400*a**(105/2)*b*x**4 + 6300*a**(103/2)*b**2*x**6 + 16800*a**(101/2)*b**3*x**8 + 29400*a**(99/2)*b**4*x**10 + 35280*a**(97/2)*b**5*x**12 + 29400*a**(95/2)*b**6*x**14 + 16800*a**(93/2)*b**7*x**16 + 6300*a**(91/2)*b**8*x**18 + 1400*a**(89/2)*b**9*x**20 + 140*a**(87/2)*b**10*x**22) - 37800*a**45*b**4*x**8*log(b*x**2/a)/(140*a**(107/2)*x**2 + 1400*a**(105/2)*b*x**4 + 6300*a**(103/2)*b**2*x**6 + 16800*a**(101/2)*b**3*x**8 + 29400*a**(99/2)*b**4*x**10 + 35280*a**(97/2)*b**5*x**12 + 29400*a**(95/2)*b**6*x**14 + 16800*a**(93/2)*b**7*x**16 + 6300*a**(91/2)*b**8*x**18 + 1400*a**(89/2)*b**9*x**20 + 140*a**(87/2)*b**10*x**22) + 75600*a**45*b**4*x**8*log(sqrt(1 + b*x**2/a) + 1)/(140*a**(107/2)*x**2 + 1400*a**(105/2)*b*x**4 + 6300*a**(103/2)*b**2*x**6 + 16800*a**(101/2)*b**3*x**8 + 29400*a**(99/2)*b**4*x**10 + 35280*a**(97/2)*b**5*x**12 + 29400*a**(95/2)*b**6*x**14 + 16800*a**(93/2)*b**7*x**16 + 6300*a**(91/2)*b**8*x**18 + 1400*a**(89/2)*b**9*x**20 + 140*a**(87/2)*b**10*x**22) - 100260*a**44*b**5*x**10*sqrt(1 + b*x**2/a)/(140*a**(107/2)*x**2 + 1400*a**(105/2)*b*x**4 + 6300*a**(103/2)*b**2*x**6 + 16800*a**(101/2)*b**3*x**8 + 29400*a**(99/2)*b**4*x**10 + 35280*a**(97/2)*b**5*x**12 + 29400*a**(95/2)*b**6*x**14 + 16800*a**(93/2)*b**7*x**16 + 6300*a**(91/2)*b**8*x**18 + 1400*a**(89/2)*b**9*x**20 + 140*a**(87/2)*b**10*x**22) - 66150*a**44*b**5*x**10*log(b*x**2/a)/(140*a**(107/2)*x**2 + 1400*a**(105/2)*b*x**4 + 6300*a**(103/2)*b**2*x**6 + 16800*a**(101/2)*b**3*x**8 + 29400*a**(99/2)*b**4*x**10 + 35280*a**(97/2)*b**5*x**12 + 29400*a**(95/2)*b**6*x**14 + 16800*a**(93/2)*b**7*x**16 + 6300*a**(91/2)*b**8*x**18 + 1400*a**(89/2)*b**9*x**20 + 140*a**(87/2)*b**10*x**22) + 132300*a**44*b**5*x**10*log(sqrt(1 + b*x**2/a) + 1)/(140*a**(107/2)*x**2 + 1400*a**(105/2)*b*x**4 + 6300*a**(103/2)*b**2*x**6 + 16800*a**(101/2)*b**3*x**8 + 29400*a**(99/2)*b**4*x**10 + 35280*a**(97/2)*b**5*x**12 + 29400*a**(95/2)*b**6*x**14 + 16800*a**(93/2)*b**7*x**16 + 6300*a**(91/2)*b**8*x**18 + 1400*a**(89/2)*b**9*x**20 + 140*a**(87/2)*b**10*x**22) - 94396*a**43*b**6*x**12*sqrt(1 + b*x**2/a)/(140*a**(107/2)*x**2 + 1400*a**(105/2)*b*x**4 + 6300*a**(103/2)*b**2*x**6 + 16800*a**(101/2)*b**3*x**8 + 29400*a**(99/2)*b**4*x**10 + 35280*a**(97/2)*b**5*x**12 + 29400*a**(95/2)*b**6*x**14 + 16800*a**(93/2)*b**7*x**16 + 6300*a**(91/2)*b**8*x**18 + 1400*a**(89/2)*b**9*x**20 + 140*a**(87/2)*b**10*x**22) - 79380*a**43*b**6*x**12*log(b*x**2/a)/(140*a**(107/2)*x**2 + 1400*a**(105/2)*b*x**4 + 6300*a**(103/2)*b**2*x**6 + 16800*a**(101/2)*b**3*x**8 + 29400*a**(99/2)*b**4*x**10 + 35280*a**(97/2)*b**5*x**12 + 29400*a**(95/2)*b**6*x**14 + 16800*a**(93/2)*b**7*x**16 + 6300*a**(91/2)*b**8*x**18 + 1400*a**(89/2)*b**9*x**20 + 140*a**(87/2)*b**10*x**22) + 158760*a**43*b**6*x**12*log(sqrt(1 + b*x**2/a) + 1)/(140*a**(107/2)*x**2 + 1400*a**(105/2)*b*x**4 + 6300*a**(103/2)*b**2*x**6 + 16800*a**(101/2)*b**3*x**8 + 29400*a**(99/2)*b**4*x**10 + 35280*a**(97/2)*b**5*x**12 + 29400*a**(95/2)*b**6*x**14 + 16800*a**(93/2)*b**7*x**16 + 6300*a**(91/2)*b**8*x**18 + 1400*a**(89/2)*b**9*x**20 + 140*a**(87/2)*b**10*x**22) - 59772*a**42*b**7*x**14*sqrt(1 + b*x**2/a)/(140*a**(107/2)*x**2 + 1400*a**(105/2)*b*x**4 + 6300*a**(103/2)*b**2*x**6 + 16800*a**(101/2)*b**3*x**8 + 29400*a**(99/2)*b**4*x**10 + 35280*a**(97/2)*b**5*x**12 + 29400*a**(95/2)*b**6*x**14 + 16800*a**(93/2)*b**7*x**16 + 6300*a**(91/2)*b**8*x**18 + 1400*a**(89/2)*b**9*x**20 + 140*a**(87/2)*b**10*x**22) - 66150*a**42*b**7*x**14*log(b*x**2/a)/(140*a**(107/2)*x**2 + 1400*a**(105/2)*b*x**4 + 6300*a**(103/2)*b**2*x**6 + 16800*a**(101/2)*b**3*x**8 + 29400*a**(99/2)*b**4*x**10 + 35280*a**(97/2)*b**5*x**12 + 29400*a**(95/2)*b**6*x**14 + 16800*a**(93/2)*b**7*x**16 + 6300*a**(91/2)*b**8*x**18 + 1400*a**(89/2)*b**9*x**20 + 140*a**(87/2)*b**10*x**22) + 132300*a**42*b**7*x**14*log(sqrt(1 + b*x**2/a) + 1)/(140*a**(107/2)*x**2 + 1400*a**(105/2)*b*x**4 + 6300*a**(103/2)*b**2*x**6 + 16800*a**(101/2)*b**3*x**8 + 29400*a**(99/2)*b**4*x**10 + 35280*a**(97/2)*b**5*x**12 + 29400*a**(95/2)*b**6*x**14 + 16800*a**(93/2)*b**7*x**16 + 6300*a**(91/2)*b**8*x**18 + 1400*a**(89/2)*b**9*x**20 + 140*a**(87/2)*b**10*x**22) - 24486*a**41*b**8*x**16*sqrt(1 + b*x**2/a)/(140*a**(107/2)*x**2 + 1400*a**(105/2)*b*x**4 + 6300*a**(103/2)*b**2*x**6 + 16800*a**(101/2)*b**3*x**8 + 29400*a**(99/2)*b**4*x**10 + 35280*a**(97/2)*b**5*x**12 + 29400*a**(95/2)*b**6*x**14 + 16800*a**(93/2)*b**7*x**16 + 6300*a**(91/2)*b**8*x**18 + 1400*a**(89/2)*b**9*x**20 + 140*a**(87/2)*b**10*x**22) - 37800*a**41*b**8*x**16*log(b*x**2/a)/(140*a**(107/2)*x**2 + 1400*a**(105/2)*b*x**4 + 6300*a**(103/2)*b**2*x**6 + 16800*a**(101/2)*b**3*x**8 + 29400*a**(99/2)*b**4*x**10 + 35280*a**(97/2)*b**5*x**12 + 29400*a**(95/2)*b**6*x**14 + 16800*a**(93/2)*b**7*x**16 + 6300*a**(91/2)*b**8*x**18 + 1400*a**(89/2)*b**9*x**20 + 140*a**(87/2)*b**10*x**22) + 75600*a**41*b**8*x**16*log(sqrt(1 + b*x**2/a) + 1)/(140*a**(107/2)*x**2 + 1400*a**(105/2)*b*x**4 + 6300*a**(103/2)*b**2*x**6 + 16800*a**(101/2)*b**3*x**8 + 29400*a**(99/2)*b**4*x**10 + 35280*a**(97/2)*b**5*x**12 + 29400*a**(95/2)*b**6*x**14 + 16800*a**(93/2)*b**7*x**16 + 6300*a**(91/2)*b**8*x**18 + 1400*a**(89/2)*b**9*x**20 + 140*a**(87/2)*b**10*x**22) - 5880*a**40*b**9*x**18*sqrt(1 + b*x**2/a)/(140*a**(107/2)*x**2 + 1400*a**(105/2)*b*x**4 + 6300*a**(103/2)*b**2*x**6 + 16800*a**(101/2)*b**3*x**8 + 29400*a**(99/2)*b**4*x**10 + 35280*a**(97/2)*b**5*x**12 + 29400*a**(95/2)*b**6*x**14 + 16800*a**(93/2)*b**7*x**16 + 6300*a**(91/2)*b**8*x**18 + 1400*a**(89/2)*b**9*x**20 + 140*a**(87/2)*b**10*x**22) - 14175*a**40*b**9*x**18*log(b*x**2/a)/(140*a**(107/2)*x**2 + 1400*a**(105/2)*b*x**4 + 6300*a**(103/2)*b**2*x**6 + 16800*a**(101/2)*b**3*x**8 + 29400*a**(99/2)*b**4*x**10 + 35280*a**(97/2)*b**5*x**12 + 29400*a**(95/2)*b**6*x**14 + 16800*a**(93/2)*b**7*x**16 + 6300*a**(91/2)*b**8*x**18 + 1400*a**(89/2)*b**9*x**20 + 140*a**(87/2)*b**10*x**22) + 28350*a**40*b**9*x**18*log(sqrt(1 + b*x**2/a) + 1)/(140*a**(107/2)*x**2 + 1400*a**(105/2)*b*x**4 + 6300*a**(103/2)*b**2*x**6 + 16800*a**(101/2)*b**3*x**8 + 29400*a**(99/2)*b**4*x**10 + 35280*a**(97/2)*b**5*x**12 + 29400*a**(95/2)*b**6*x**14 + 16800*a**(93/2)*b**7*x**16 + 6300*a**(91/2)*b**8*x**18 + 1400*a**(89/2)*b**9*x**20 + 140*a**(87/2)*b**10*x**22) - 630*a**39*b**10*x**20*sqrt(1 + b*x**2/a)/(140*a**(107/2)*x**2 + 1400*a**(105/2)*b*x**4 + 6300*a**(103/2)*b**2*x**6 + 16800*a**(101/2)*b**3*x**8 + 29400*a**(99/2)*b**4*x**10 + 35280*a**(97/2)*b**5*x**12 + 29400*a**(95/2)*b**6*x**14 + 16800*a**(93/2)*b**7*x**16 + 6300*a**(91/2)*b**8*x**18 + 1400*a**(89/2)*b**9*x**20 + 140*a**(87/2)*b**10*x**22) - 3150*a**39*b**10*x**20*log(b*x**2/a)/(140*a**(107/2)*x**2 + 1400*a**(105/2)*b*x**4 + 6300*a**(103/2)*b**2*x**6 + 16800*a**(101/2)*b**3*x**8 + 29400*a**(99/2)*b**4*x**10 + 35280*a**(97/2)*b**5*x**12 + 29400*a**(95/2)*b**6*x**14 + 16800*a**(93/2)*b**7*x**16 + 6300*a**(91/2)*b**8*x**18 + 1400*a**(89/2)*b**9*x**20 + 140*a**(87/2)*b**10*x**22) + 6300*a**39*b**10*x**20*log(sqrt(1 + b*x**2/a) + 1)/(140*a**(107/2)*x**2 + 1400*a**(105/2)*b*x**4 + 6300*a**(103/2)*b**2*x**6 + 16800*a**(101/2)*b**3*x**8 + 29400*a**(99/2)*b**4*x**10 + 35280*a**(97/2)*b**5*x**12 + 29400*a**(95/2)*b**6*x**14 + 16800*a**(93/2)*b**7*x**16 + 6300*a**(91/2)*b**8*x**18 + 1400*a**(89/2)*b**9*x**20 + 140*a**(87/2)*b**10*x**22) - 315*a**38*b**11*x**22*log(b*x**2/a)/(140*a**(107/2)*x**2 + 1400*a**(105/2)*b*x**4 + 6300*a**(103/2)*b**2*x**6 + 16800*a**(101/2)*b**3*x**8 + 29400*a**(99/2)*b**4*x**10 + 35280*a**(97/2)*b**5*x**12 + 29400*a**(95/2)*b**6*x**14 + 16800*a**(93/2)*b**7*x**16 + 6300*a**(91/2)*b**8*x**18 + 1400*a**(89/2)*b**9*x**20 + 140*a**(87/2)*b**10*x**22) + 630*a**38*b**11*x**22*log(sqrt(1 + b*x**2/a) + 1)/(140*a**(107/2)*x**2 + 1400*a**(105/2)*b*x**4 + 6300*a**(103/2)*b**2*x**6 + 16800*a**(101/2)*b**3*x**8 + 29400*a**(99/2)*b**4*x**10 + 35280*a**(97/2)*b**5*x**12 + 29400*a**(95/2)*b**6*x**14 + 16800*a**(93/2)*b**7*x**16 + 6300*a**(91/2)*b**8*x**18 + 1400*a**(89/2)*b**9*x**20 + 140*a**(87/2)*b**10*x**22)","B",0
531,1,668,0,3.836674," ","integrate(1/x**4/(b*x**2+a)**(9/2),x)","- \frac{7 a^{6} b^{\frac{51}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{21 a^{11} b^{25} x^{2} + 105 a^{10} b^{26} x^{4} + 210 a^{9} b^{27} x^{6} + 210 a^{8} b^{28} x^{8} + 105 a^{7} b^{29} x^{10} + 21 a^{6} b^{30} x^{12}} + \frac{63 a^{5} b^{\frac{53}{2}} x^{2} \sqrt{\frac{a}{b x^{2}} + 1}}{21 a^{11} b^{25} x^{2} + 105 a^{10} b^{26} x^{4} + 210 a^{9} b^{27} x^{6} + 210 a^{8} b^{28} x^{8} + 105 a^{7} b^{29} x^{10} + 21 a^{6} b^{30} x^{12}} + \frac{630 a^{4} b^{\frac{55}{2}} x^{4} \sqrt{\frac{a}{b x^{2}} + 1}}{21 a^{11} b^{25} x^{2} + 105 a^{10} b^{26} x^{4} + 210 a^{9} b^{27} x^{6} + 210 a^{8} b^{28} x^{8} + 105 a^{7} b^{29} x^{10} + 21 a^{6} b^{30} x^{12}} + \frac{1680 a^{3} b^{\frac{57}{2}} x^{6} \sqrt{\frac{a}{b x^{2}} + 1}}{21 a^{11} b^{25} x^{2} + 105 a^{10} b^{26} x^{4} + 210 a^{9} b^{27} x^{6} + 210 a^{8} b^{28} x^{8} + 105 a^{7} b^{29} x^{10} + 21 a^{6} b^{30} x^{12}} + \frac{2016 a^{2} b^{\frac{59}{2}} x^{8} \sqrt{\frac{a}{b x^{2}} + 1}}{21 a^{11} b^{25} x^{2} + 105 a^{10} b^{26} x^{4} + 210 a^{9} b^{27} x^{6} + 210 a^{8} b^{28} x^{8} + 105 a^{7} b^{29} x^{10} + 21 a^{6} b^{30} x^{12}} + \frac{1152 a b^{\frac{61}{2}} x^{10} \sqrt{\frac{a}{b x^{2}} + 1}}{21 a^{11} b^{25} x^{2} + 105 a^{10} b^{26} x^{4} + 210 a^{9} b^{27} x^{6} + 210 a^{8} b^{28} x^{8} + 105 a^{7} b^{29} x^{10} + 21 a^{6} b^{30} x^{12}} + \frac{256 b^{\frac{63}{2}} x^{12} \sqrt{\frac{a}{b x^{2}} + 1}}{21 a^{11} b^{25} x^{2} + 105 a^{10} b^{26} x^{4} + 210 a^{9} b^{27} x^{6} + 210 a^{8} b^{28} x^{8} + 105 a^{7} b^{29} x^{10} + 21 a^{6} b^{30} x^{12}}"," ",0,"-7*a**6*b**(51/2)*sqrt(a/(b*x**2) + 1)/(21*a**11*b**25*x**2 + 105*a**10*b**26*x**4 + 210*a**9*b**27*x**6 + 210*a**8*b**28*x**8 + 105*a**7*b**29*x**10 + 21*a**6*b**30*x**12) + 63*a**5*b**(53/2)*x**2*sqrt(a/(b*x**2) + 1)/(21*a**11*b**25*x**2 + 105*a**10*b**26*x**4 + 210*a**9*b**27*x**6 + 210*a**8*b**28*x**8 + 105*a**7*b**29*x**10 + 21*a**6*b**30*x**12) + 630*a**4*b**(55/2)*x**4*sqrt(a/(b*x**2) + 1)/(21*a**11*b**25*x**2 + 105*a**10*b**26*x**4 + 210*a**9*b**27*x**6 + 210*a**8*b**28*x**8 + 105*a**7*b**29*x**10 + 21*a**6*b**30*x**12) + 1680*a**3*b**(57/2)*x**6*sqrt(a/(b*x**2) + 1)/(21*a**11*b**25*x**2 + 105*a**10*b**26*x**4 + 210*a**9*b**27*x**6 + 210*a**8*b**28*x**8 + 105*a**7*b**29*x**10 + 21*a**6*b**30*x**12) + 2016*a**2*b**(59/2)*x**8*sqrt(a/(b*x**2) + 1)/(21*a**11*b**25*x**2 + 105*a**10*b**26*x**4 + 210*a**9*b**27*x**6 + 210*a**8*b**28*x**8 + 105*a**7*b**29*x**10 + 21*a**6*b**30*x**12) + 1152*a*b**(61/2)*x**10*sqrt(a/(b*x**2) + 1)/(21*a**11*b**25*x**2 + 105*a**10*b**26*x**4 + 210*a**9*b**27*x**6 + 210*a**8*b**28*x**8 + 105*a**7*b**29*x**10 + 21*a**6*b**30*x**12) + 256*b**(63/2)*x**12*sqrt(a/(b*x**2) + 1)/(21*a**11*b**25*x**2 + 105*a**10*b**26*x**4 + 210*a**9*b**27*x**6 + 210*a**8*b**28*x**8 + 105*a**7*b**29*x**10 + 21*a**6*b**30*x**12)","B",0
532,1,44,0,1.287130," ","integrate(x**5/(4*x**2+9)**(1/2),x)","\frac{x^{4} \sqrt{4 x^{2} + 9}}{20} - \frac{3 x^{2} \sqrt{4 x^{2} + 9}}{20} + \frac{27 \sqrt{4 x^{2} + 9}}{40}"," ",0,"x**4*sqrt(4*x**2 + 9)/20 - 3*x**2*sqrt(4*x**2 + 9)/20 + 27*sqrt(4*x**2 + 9)/40","A",0
533,1,39,0,0.731129," ","integrate(x**4/(4*x**2+9)**(1/2),x)","\frac{x^{3} \sqrt{4 x^{2} + 9}}{16} - \frac{27 x \sqrt{4 x^{2} + 9}}{128} + \frac{243 \operatorname{asinh}{\left(\frac{2 x}{3} \right)}}{256}"," ",0,"x**3*sqrt(4*x**2 + 9)/16 - 27*x*sqrt(4*x**2 + 9)/128 + 243*asinh(2*x/3)/256","A",0
534,1,27,0,0.378280," ","integrate(x**3/(4*x**2+9)**(1/2),x)","\frac{x^{2} \sqrt{4 x^{2} + 9}}{12} - \frac{3 \sqrt{4 x^{2} + 9}}{8}"," ",0,"x**2*sqrt(4*x**2 + 9)/12 - 3*sqrt(4*x**2 + 9)/8","A",0
535,1,22,0,0.225644," ","integrate(x**2/(4*x**2+9)**(1/2),x)","\frac{x \sqrt{4 x^{2} + 9}}{8} - \frac{9 \operatorname{asinh}{\left(\frac{2 x}{3} \right)}}{16}"," ",0,"x*sqrt(4*x**2 + 9)/8 - 9*asinh(2*x/3)/16","A",0
536,1,10,0,0.151228," ","integrate(x/(4*x**2+9)**(1/2),x)","\frac{\sqrt{4 x^{2} + 9}}{4}"," ",0,"sqrt(4*x**2 + 9)/4","A",0
537,1,7,0,0.152665," ","integrate(1/(4*x**2+9)**(1/2),x)","\frac{\operatorname{asinh}{\left(\frac{2 x}{3} \right)}}{2}"," ",0,"asinh(2*x/3)/2","A",0
538,1,8,0,1.018177," ","integrate(1/x/(4*x**2+9)**(1/2),x)","- \frac{\operatorname{asinh}{\left(\frac{3}{2 x} \right)}}{3}"," ",0,"-asinh(3/(2*x))/3","A",0
539,1,15,0,0.759302," ","integrate(1/x**2/(4*x**2+9)**(1/2),x)","- \frac{2 \sqrt{1 + \frac{9}{4 x^{2}}}}{9}"," ",0,"-2*sqrt(1 + 9/(4*x**2))/9","A",0
540,1,44,0,2.100526," ","integrate(1/x**3/(4*x**2+9)**(1/2),x)","\frac{2 \operatorname{asinh}{\left(\frac{3}{2 x} \right)}}{27} - \frac{1}{9 x \sqrt{1 + \frac{9}{4 x^{2}}}} - \frac{1}{4 x^{3} \sqrt{1 + \frac{9}{4 x^{2}}}}"," ",0,"2*asinh(3/(2*x))/27 - 1/(9*x*sqrt(1 + 9/(4*x**2))) - 1/(4*x**3*sqrt(1 + 9/(4*x**2)))","A",0
541,1,32,0,1.293666," ","integrate(1/x**4/(4*x**2+9)**(1/2),x)","\frac{16 \sqrt{1 + \frac{9}{4 x^{2}}}}{243} - \frac{2 \sqrt{1 + \frac{9}{4 x^{2}}}}{27 x^{2}}"," ",0,"16*sqrt(1 + 9/(4*x**2))/243 - 2*sqrt(1 + 9/(4*x**2))/(27*x**2)","A",0
542,1,63,0,3.890196," ","integrate(1/x**5/(4*x**2+9)**(1/2),x)","- \frac{2 \operatorname{asinh}{\left(\frac{3}{2 x} \right)}}{81} + \frac{1}{27 x \sqrt{1 + \frac{9}{4 x^{2}}}} + \frac{1}{36 x^{3} \sqrt{1 + \frac{9}{4 x^{2}}}} - \frac{1}{8 x^{5} \sqrt{1 + \frac{9}{4 x^{2}}}}"," ",0,"-2*asinh(3/(2*x))/81 + 1/(27*x*sqrt(1 + 9/(4*x**2))) + 1/(36*x**3*sqrt(1 + 9/(4*x**2))) - 1/(8*x**5*sqrt(1 + 9/(4*x**2)))","A",0
543,1,46,0,1.287678," ","integrate(x**5/(-4*x**2+9)**(1/2),x)","- \frac{x^{4} \sqrt{9 - 4 x^{2}}}{20} - \frac{3 x^{2} \sqrt{9 - 4 x^{2}}}{20} - \frac{27 \sqrt{9 - 4 x^{2}}}{40}"," ",0,"-x**4*sqrt(9 - 4*x**2)/20 - 3*x**2*sqrt(9 - 4*x**2)/20 - 27*sqrt(9 - 4*x**2)/40","A",0
544,1,39,0,0.730767," ","integrate(x**4/(-4*x**2+9)**(1/2),x)","- \frac{x^{3} \sqrt{9 - 4 x^{2}}}{16} - \frac{27 x \sqrt{9 - 4 x^{2}}}{128} + \frac{243 \operatorname{asin}{\left(\frac{2 x}{3} \right)}}{256}"," ",0,"-x**3*sqrt(9 - 4*x**2)/16 - 27*x*sqrt(9 - 4*x**2)/128 + 243*asin(2*x/3)/256","A",0
545,1,29,0,0.383409," ","integrate(x**3/(-4*x**2+9)**(1/2),x)","- \frac{x^{2} \sqrt{9 - 4 x^{2}}}{12} - \frac{3 \sqrt{9 - 4 x^{2}}}{8}"," ",0,"-x**2*sqrt(9 - 4*x**2)/12 - 3*sqrt(9 - 4*x**2)/8","A",0
546,1,22,0,0.225830," ","integrate(x**2/(-4*x**2+9)**(1/2),x)","- \frac{x \sqrt{9 - 4 x^{2}}}{8} + \frac{9 \operatorname{asin}{\left(\frac{2 x}{3} \right)}}{16}"," ",0,"-x*sqrt(9 - 4*x**2)/8 + 9*asin(2*x/3)/16","A",0
547,1,12,0,0.149907," ","integrate(x/(-4*x**2+9)**(1/2),x)","- \frac{\sqrt{9 - 4 x^{2}}}{4}"," ",0,"-sqrt(9 - 4*x**2)/4","A",0
548,1,7,0,0.153996," ","integrate(1/(-4*x**2+9)**(1/2),x)","\frac{\operatorname{asin}{\left(\frac{2 x}{3} \right)}}{2}"," ",0,"asin(2*x/3)/2","A",0
549,1,26,0,1.063721," ","integrate(1/x/(-4*x**2+9)**(1/2),x)","\begin{cases} - \frac{\operatorname{acosh}{\left(\frac{3}{2 x} \right)}}{3} & \text{for}\: \frac{9}{4 \left|{x^{2}}\right|} > 1 \\\frac{i \operatorname{asin}{\left(\frac{3}{2 x} \right)}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-acosh(3/(2*x))/3, 9/(4*Abs(x**2)) > 1), (I*asin(3/(2*x))/3, True))","A",0
550,1,41,0,0.795228," ","integrate(1/x**2/(-4*x**2+9)**(1/2),x)","\begin{cases} - \frac{2 \sqrt{-1 + \frac{9}{4 x^{2}}}}{9} & \text{for}\: \frac{9}{4 \left|{x^{2}}\right|} > 1 \\- \frac{2 i \sqrt{1 - \frac{9}{4 x^{2}}}}{9} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*sqrt(-1 + 9/(4*x**2))/9, 9/(4*Abs(x**2)) > 1), (-2*I*sqrt(1 - 9/(4*x**2))/9, True))","A",0
551,1,99,0,2.172413," ","integrate(1/x**3/(-4*x**2+9)**(1/2),x)","\begin{cases} - \frac{2 \operatorname{acosh}{\left(\frac{3}{2 x} \right)}}{27} + \frac{1}{9 x \sqrt{-1 + \frac{9}{4 x^{2}}}} - \frac{1}{4 x^{3} \sqrt{-1 + \frac{9}{4 x^{2}}}} & \text{for}\: \frac{9}{4 \left|{x^{2}}\right|} > 1 \\\frac{2 i \operatorname{asin}{\left(\frac{3}{2 x} \right)}}{27} - \frac{i}{9 x \sqrt{1 - \frac{9}{4 x^{2}}}} + \frac{i}{4 x^{3} \sqrt{1 - \frac{9}{4 x^{2}}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*acosh(3/(2*x))/27 + 1/(9*x*sqrt(-1 + 9/(4*x**2))) - 1/(4*x**3*sqrt(-1 + 9/(4*x**2))), 9/(4*Abs(x**2)) > 1), (2*I*asin(3/(2*x))/27 - I/(9*x*sqrt(1 - 9/(4*x**2))) + I/(4*x**3*sqrt(1 - 9/(4*x**2))), True))","A",0
552,1,80,0,1.328757," ","integrate(1/x**4/(-4*x**2+9)**(1/2),x)","\begin{cases} - \frac{16 \sqrt{-1 + \frac{9}{4 x^{2}}}}{243} - \frac{2 \sqrt{-1 + \frac{9}{4 x^{2}}}}{27 x^{2}} & \text{for}\: \frac{9}{4 \left|{x^{2}}\right|} > 1 \\- \frac{16 i \sqrt{1 - \frac{9}{4 x^{2}}}}{243} - \frac{2 i \sqrt{1 - \frac{9}{4 x^{2}}}}{27 x^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-16*sqrt(-1 + 9/(4*x**2))/243 - 2*sqrt(-1 + 9/(4*x**2))/(27*x**2), 9/(4*Abs(x**2)) > 1), (-16*I*sqrt(1 - 9/(4*x**2))/243 - 2*I*sqrt(1 - 9/(4*x**2))/(27*x**2), True))","A",0
553,1,136,0,3.963444," ","integrate(1/x**5/(-4*x**2+9)**(1/2),x)","\begin{cases} - \frac{2 \operatorname{acosh}{\left(\frac{3}{2 x} \right)}}{81} + \frac{1}{27 x \sqrt{-1 + \frac{9}{4 x^{2}}}} - \frac{1}{36 x^{3} \sqrt{-1 + \frac{9}{4 x^{2}}}} - \frac{1}{8 x^{5} \sqrt{-1 + \frac{9}{4 x^{2}}}} & \text{for}\: \frac{9}{4 \left|{x^{2}}\right|} > 1 \\\frac{2 i \operatorname{asin}{\left(\frac{3}{2 x} \right)}}{81} - \frac{i}{27 x \sqrt{1 - \frac{9}{4 x^{2}}}} + \frac{i}{36 x^{3} \sqrt{1 - \frac{9}{4 x^{2}}}} + \frac{i}{8 x^{5} \sqrt{1 - \frac{9}{4 x^{2}}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*acosh(3/(2*x))/81 + 1/(27*x*sqrt(-1 + 9/(4*x**2))) - 1/(36*x**3*sqrt(-1 + 9/(4*x**2))) - 1/(8*x**5*sqrt(-1 + 9/(4*x**2))), 9/(4*Abs(x**2)) > 1), (2*I*asin(3/(2*x))/81 - I/(27*x*sqrt(1 - 9/(4*x**2))) + I/(36*x**3*sqrt(1 - 9/(4*x**2))) + I/(8*x**5*sqrt(1 - 9/(4*x**2))), True))","A",0
554,1,44,0,1.251944," ","integrate(x**5/(4*x**2-9)**(1/2),x)","\frac{x^{4} \sqrt{4 x^{2} - 9}}{20} + \frac{3 x^{2} \sqrt{4 x^{2} - 9}}{20} + \frac{27 \sqrt{4 x^{2} - 9}}{40}"," ",0,"x**4*sqrt(4*x**2 - 9)/20 + 3*x**2*sqrt(4*x**2 - 9)/20 + 27*sqrt(4*x**2 - 9)/40","A",0
555,1,39,0,0.718222," ","integrate(x**4/(4*x**2-9)**(1/2),x)","\frac{x^{3} \sqrt{4 x^{2} - 9}}{16} + \frac{27 x \sqrt{4 x^{2} - 9}}{128} + \frac{243 \operatorname{acosh}{\left(\frac{2 x}{3} \right)}}{256}"," ",0,"x**3*sqrt(4*x**2 - 9)/16 + 27*x*sqrt(4*x**2 - 9)/128 + 243*acosh(2*x/3)/256","A",0
556,1,27,0,0.365983," ","integrate(x**3/(4*x**2-9)**(1/2),x)","\frac{x^{2} \sqrt{4 x^{2} - 9}}{12} + \frac{3 \sqrt{4 x^{2} - 9}}{8}"," ",0,"x**2*sqrt(4*x**2 - 9)/12 + 3*sqrt(4*x**2 - 9)/8","A",0
557,1,22,0,0.223909," ","integrate(x**2/(4*x**2-9)**(1/2),x)","\frac{x \sqrt{4 x^{2} - 9}}{8} + \frac{9 \operatorname{acosh}{\left(\frac{2 x}{3} \right)}}{16}"," ",0,"x*sqrt(4*x**2 - 9)/8 + 9*acosh(2*x/3)/16","A",0
558,1,10,0,0.152262," ","integrate(x/(4*x**2-9)**(1/2),x)","\frac{\sqrt{4 x^{2} - 9}}{4}"," ",0,"sqrt(4*x**2 - 9)/4","A",0
559,1,7,0,0.155690," ","integrate(1/(4*x**2-9)**(1/2),x)","\frac{\operatorname{acosh}{\left(\frac{2 x}{3} \right)}}{2}"," ",0,"acosh(2*x/3)/2","A",0
560,1,26,0,1.071406," ","integrate(1/x/(4*x**2-9)**(1/2),x)","\begin{cases} \frac{i \operatorname{acosh}{\left(\frac{3}{2 x} \right)}}{3} & \text{for}\: \frac{9}{4 \left|{x^{2}}\right|} > 1 \\- \frac{\operatorname{asin}{\left(\frac{3}{2 x} \right)}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*acosh(3/(2*x))/3, 9/(4*Abs(x**2)) > 1), (-asin(3/(2*x))/3, True))","A",0
561,1,37,0,0.805083," ","integrate(1/x**2/(4*x**2-9)**(1/2),x)","\begin{cases} \frac{2 i \sqrt{-1 + \frac{9}{4 x^{2}}}}{9} & \text{for}\: \frac{9}{4 \left|{x^{2}}\right|} > 1 \\\frac{2 \sqrt{1 - \frac{9}{4 x^{2}}}}{9} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*I*sqrt(-1 + 9/(4*x**2))/9, 9/(4*Abs(x**2)) > 1), (2*sqrt(1 - 9/(4*x**2))/9, True))","A",0
562,1,99,0,2.132641," ","integrate(1/x**3/(4*x**2-9)**(1/2),x)","\begin{cases} \frac{2 i \operatorname{acosh}{\left(\frac{3}{2 x} \right)}}{27} - \frac{i}{9 x \sqrt{-1 + \frac{9}{4 x^{2}}}} + \frac{i}{4 x^{3} \sqrt{-1 + \frac{9}{4 x^{2}}}} & \text{for}\: \frac{9}{4 \left|{x^{2}}\right|} > 1 \\- \frac{2 \operatorname{asin}{\left(\frac{3}{2 x} \right)}}{27} + \frac{1}{9 x \sqrt{1 - \frac{9}{4 x^{2}}}} - \frac{1}{4 x^{3} \sqrt{1 - \frac{9}{4 x^{2}}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*I*acosh(3/(2*x))/27 - I/(9*x*sqrt(-1 + 9/(4*x**2))) + I/(4*x**3*sqrt(-1 + 9/(4*x**2))), 9/(4*Abs(x**2)) > 1), (-2*asin(3/(2*x))/27 + 1/(9*x*sqrt(1 - 9/(4*x**2))) - 1/(4*x**3*sqrt(1 - 9/(4*x**2))), True))","A",0
563,1,76,0,1.348679," ","integrate(1/x**4/(4*x**2-9)**(1/2),x)","\begin{cases} \frac{16 i \sqrt{-1 + \frac{9}{4 x^{2}}}}{243} + \frac{2 i \sqrt{-1 + \frac{9}{4 x^{2}}}}{27 x^{2}} & \text{for}\: \frac{9}{4 \left|{x^{2}}\right|} > 1 \\\frac{16 \sqrt{1 - \frac{9}{4 x^{2}}}}{243} + \frac{2 \sqrt{1 - \frac{9}{4 x^{2}}}}{27 x^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((16*I*sqrt(-1 + 9/(4*x**2))/243 + 2*I*sqrt(-1 + 9/(4*x**2))/(27*x**2), 9/(4*Abs(x**2)) > 1), (16*sqrt(1 - 9/(4*x**2))/243 + 2*sqrt(1 - 9/(4*x**2))/(27*x**2), True))","A",0
564,1,136,0,3.820706," ","integrate(1/x**5/(4*x**2-9)**(1/2),x)","\begin{cases} \frac{2 i \operatorname{acosh}{\left(\frac{3}{2 x} \right)}}{81} - \frac{i}{27 x \sqrt{-1 + \frac{9}{4 x^{2}}}} + \frac{i}{36 x^{3} \sqrt{-1 + \frac{9}{4 x^{2}}}} + \frac{i}{8 x^{5} \sqrt{-1 + \frac{9}{4 x^{2}}}} & \text{for}\: \frac{9}{4 \left|{x^{2}}\right|} > 1 \\- \frac{2 \operatorname{asin}{\left(\frac{3}{2 x} \right)}}{81} + \frac{1}{27 x \sqrt{1 - \frac{9}{4 x^{2}}}} - \frac{1}{36 x^{3} \sqrt{1 - \frac{9}{4 x^{2}}}} - \frac{1}{8 x^{5} \sqrt{1 - \frac{9}{4 x^{2}}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*I*acosh(3/(2*x))/81 - I/(27*x*sqrt(-1 + 9/(4*x**2))) + I/(36*x**3*sqrt(-1 + 9/(4*x**2))) + I/(8*x**5*sqrt(-1 + 9/(4*x**2))), 9/(4*Abs(x**2)) > 1), (-2*asin(3/(2*x))/81 + 1/(27*x*sqrt(1 - 9/(4*x**2))) - 1/(36*x**3*sqrt(1 - 9/(4*x**2))) - 1/(8*x**5*sqrt(1 - 9/(4*x**2))), True))","A",0
565,1,49,0,1.213357," ","integrate(x**5/(-4*x**2-9)**(1/2),x)","- \frac{x^{4} \sqrt{- 4 x^{2} - 9}}{20} + \frac{3 x^{2} \sqrt{- 4 x^{2} - 9}}{20} - \frac{27 \sqrt{- 4 x^{2} - 9}}{40}"," ",0,"-x**4*sqrt(-4*x**2 - 9)/20 + 3*x**2*sqrt(-4*x**2 - 9)/20 - 27*sqrt(-4*x**2 - 9)/40","A",0
566,1,53,0,0.888202," ","integrate(x**4/(-4*x**2-9)**(1/2),x)","- \frac{x^{3} \sqrt{- 4 x^{2} - 9}}{16} + \frac{27 x \sqrt{- 4 x^{2} - 9}}{128} + \frac{243 \operatorname{atan}{\left(\frac{2 x}{\sqrt{- 4 x^{2} - 9}} \right)}}{256}"," ",0,"-x**3*sqrt(-4*x**2 - 9)/16 + 27*x*sqrt(-4*x**2 - 9)/128 + 243*atan(2*x/sqrt(-4*x**2 - 9))/256","A",0
567,1,31,0,0.374536," ","integrate(x**3/(-4*x**2-9)**(1/2),x)","- \frac{x^{2} \sqrt{- 4 x^{2} - 9}}{12} + \frac{3 \sqrt{- 4 x^{2} - 9}}{8}"," ",0,"-x**2*sqrt(-4*x**2 - 9)/12 + 3*sqrt(-4*x**2 - 9)/8","A",0
568,1,36,0,0.391943," ","integrate(x**2/(-4*x**2-9)**(1/2),x)","- \frac{x \sqrt{- 4 x^{2} - 9}}{8} - \frac{9 \operatorname{atan}{\left(\frac{2 x}{\sqrt{- 4 x^{2} - 9}} \right)}}{16}"," ",0,"-x*sqrt(-4*x**2 - 9)/8 - 9*atan(2*x/sqrt(-4*x**2 - 9))/16","A",0
569,1,14,0,0.163907," ","integrate(x/(-4*x**2-9)**(1/2),x)","- \frac{\sqrt{- 4 x^{2} - 9}}{4}"," ",0,"-sqrt(-4*x**2 - 9)/4","A",0
570,1,17,0,0.320361," ","integrate(1/(-4*x**2-9)**(1/2),x)","\frac{\operatorname{atan}{\left(\frac{2 x}{\sqrt{- 4 x^{2} - 9}} \right)}}{2}"," ",0,"atan(2*x/sqrt(-4*x**2 - 9))/2","A",0
571,1,8,0,1.019355," ","integrate(1/x/(-4*x**2-9)**(1/2),x)","\frac{i \operatorname{asinh}{\left(\frac{3}{2 x} \right)}}{3}"," ",0,"I*asinh(3/(2*x))/3","C",0
572,1,15,0,0.765334," ","integrate(1/x**2/(-4*x**2-9)**(1/2),x)","\frac{2 i \sqrt{1 + \frac{9}{4 x^{2}}}}{9}"," ",0,"2*I*sqrt(1 + 9/(4*x**2))/9","C",0
573,1,46,0,2.062206," ","integrate(1/x**3/(-4*x**2-9)**(1/2),x)","- \frac{2 i \operatorname{asinh}{\left(\frac{3}{2 x} \right)}}{27} + \frac{i}{9 x \sqrt{1 + \frac{9}{4 x^{2}}}} + \frac{i}{4 x^{3} \sqrt{1 + \frac{9}{4 x^{2}}}}"," ",0,"-2*I*asinh(3/(2*x))/27 + I/(9*x*sqrt(1 + 9/(4*x**2))) + I/(4*x**3*sqrt(1 + 9/(4*x**2)))","C",0
574,1,36,0,1.285577," ","integrate(1/x**4/(-4*x**2-9)**(1/2),x)","- \frac{16 i \sqrt{1 + \frac{9}{4 x^{2}}}}{243} + \frac{2 i \sqrt{1 + \frac{9}{4 x^{2}}}}{27 x^{2}}"," ",0,"-16*I*sqrt(1 + 9/(4*x**2))/243 + 2*I*sqrt(1 + 9/(4*x**2))/(27*x**2)","C",0
575,1,65,0,3.876260," ","integrate(1/x**5/(-4*x**2-9)**(1/2),x)","\frac{2 i \operatorname{asinh}{\left(\frac{3}{2 x} \right)}}{81} - \frac{i}{27 x \sqrt{1 + \frac{9}{4 x^{2}}}} - \frac{i}{36 x^{3} \sqrt{1 + \frac{9}{4 x^{2}}}} + \frac{i}{8 x^{5} \sqrt{1 + \frac{9}{4 x^{2}}}}"," ",0,"2*I*asinh(3/(2*x))/81 - I/(27*x*sqrt(1 + 9/(4*x**2))) - I/(36*x**3*sqrt(1 + 9/(4*x**2))) + I/(8*x**5*sqrt(1 + 9/(4*x**2)))","C",0
576,1,14,0,0.948486," ","integrate(1/(b*x**2+9)**(1/2),x)","\frac{\operatorname{asinh}{\left(\frac{\sqrt{b} x}{3} \right)}}{\sqrt{b}}"," ",0,"asinh(sqrt(b)*x/3)/sqrt(b)","A",0
577,1,39,0,1.013920," ","integrate(1/(-b*x**2+9)**(1/2),x)","\begin{cases} - \frac{i \operatorname{acosh}{\left(\frac{\sqrt{b} x}{3} \right)}}{\sqrt{b}} & \text{for}\: \frac{\left|{b x^{2}}\right|}{9} > 1 \\\frac{\operatorname{asin}{\left(\frac{\sqrt{b} x}{3} \right)}}{\sqrt{b}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*acosh(sqrt(b)*x/3)/sqrt(b), Abs(b*x**2)/9 > 1), (asin(sqrt(b)*x/3)/sqrt(b), True))","A",0
578,1,39,0,1.025553," ","integrate(1/(b*x**2-9)**(1/2),x)","\begin{cases} \frac{\operatorname{acosh}{\left(\frac{\sqrt{b} x}{3} \right)}}{\sqrt{b}} & \text{for}\: \frac{\left|{b x^{2}}\right|}{9} > 1 \\- \frac{i \operatorname{asin}{\left(\frac{\sqrt{b} x}{3} \right)}}{\sqrt{b}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((acosh(sqrt(b)*x/3)/sqrt(b), Abs(b*x**2)/9 > 1), (-I*asin(sqrt(b)*x/3)/sqrt(b), True))","A",0
579,1,17,0,0.968045," ","integrate(1/(-b*x**2-9)**(1/2),x)","- \frac{i \operatorname{asinh}{\left(\frac{\sqrt{b} x}{3} \right)}}{\sqrt{b}}"," ",0,"-I*asinh(sqrt(b)*x/3)/sqrt(b)","C",0
580,1,17,0,0.980927," ","integrate(1/(b*x**2+pi)**(1/2),x)","\frac{\operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{\pi}} \right)}}{\sqrt{b}}"," ",0,"asinh(sqrt(b)*x/sqrt(pi))/sqrt(b)","A",0
581,1,46,0,1.039802," ","integrate(1/(-b*x**2+pi)**(1/2),x)","\begin{cases} - \frac{i \operatorname{acosh}{\left(\frac{\sqrt{b} x}{\sqrt{\pi}} \right)}}{\sqrt{b}} & \text{for}\: \frac{\left|{b x^{2}}\right|}{\pi} > 1 \\\frac{\operatorname{asin}{\left(\frac{\sqrt{b} x}{\sqrt{\pi}} \right)}}{\sqrt{b}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*acosh(sqrt(b)*x/sqrt(pi))/sqrt(b), Abs(b*x**2)/pi > 1), (asin(sqrt(b)*x/sqrt(pi))/sqrt(b), True))","A",0
582,1,46,0,1.050529," ","integrate(1/(b*x**2-pi)**(1/2),x)","\begin{cases} \frac{\operatorname{acosh}{\left(\frac{\sqrt{b} x}{\sqrt{\pi}} \right)}}{\sqrt{b}} & \text{for}\: \frac{\left|{b x^{2}}\right|}{\pi} > 1 \\- \frac{i \operatorname{asin}{\left(\frac{\sqrt{b} x}{\sqrt{\pi}} \right)}}{\sqrt{b}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((acosh(sqrt(b)*x/sqrt(pi))/sqrt(b), Abs(b*x**2)/pi > 1), (-I*asin(sqrt(b)*x/sqrt(pi))/sqrt(b), True))","A",0
583,1,20,0,0.997058," ","integrate(1/(-b*x**2-pi)**(1/2),x)","- \frac{i \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{\pi}} \right)}}{\sqrt{b}}"," ",0,"-I*asinh(sqrt(b)*x/sqrt(pi))/sqrt(b)","C",0
584,1,17,0,1.014548," ","integrate(1/(b*x**2+a)**(1/2),x)","\frac{\operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{\sqrt{b}}"," ",0,"asinh(sqrt(b)*x/sqrt(a))/sqrt(b)","A",0
585,1,46,0,1.074100," ","integrate(1/(-b*x**2+a)**(1/2),x)","\begin{cases} - \frac{i \operatorname{acosh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{\sqrt{b}} & \text{for}\: \left|{\frac{b x^{2}}{a}}\right| > 1 \\\frac{\operatorname{asin}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{\sqrt{b}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*acosh(sqrt(b)*x/sqrt(a))/sqrt(b), Abs(b*x**2/a) > 1), (asin(sqrt(b)*x/sqrt(a))/sqrt(b), True))","A",0
586,1,46,0,1.090703," ","integrate(1/(b*x**2-a)**(1/2),x)","\begin{cases} \frac{\operatorname{acosh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{\sqrt{b}} & \text{for}\: \left|{\frac{b x^{2}}{a}}\right| > 1 \\- \frac{i \operatorname{asin}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{\sqrt{b}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((acosh(sqrt(b)*x/sqrt(a))/sqrt(b), Abs(b*x**2/a) > 1), (-I*asin(sqrt(b)*x/sqrt(a))/sqrt(b), True))","A",0
587,1,20,0,1.022517," ","integrate(1/(-b*x**2-a)**(1/2),x)","- \frac{i \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{\sqrt{b}}"," ",0,"-I*asinh(sqrt(b)*x/sqrt(a))/sqrt(b)","C",0
588,1,19,0,1.021361," ","integrate(1/(a**2-x**2)**(1/2),x)","\begin{cases} - i \operatorname{acosh}{\left(\frac{x}{a} \right)} & \text{for}\: \left|{\frac{x^{2}}{a^{2}}}\right| > 1 \\\operatorname{asin}{\left(\frac{x}{a} \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*acosh(x/a), Abs(x**2/a**2) > 1), (asin(x/a), True))","A",0
589,1,46,0,27.189389," ","integrate((c*x)**(7/2)*(b*x**2+a)**(1/2),x)","\frac{\sqrt{a} c^{\frac{7}{2}} x^{\frac{9}{2}} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{13}{4}\right)}"," ",0,"sqrt(a)*c**(7/2)*x**(9/2)*gamma(9/4)*hyper((-1/2, 9/4), (13/4,), b*x**2*exp_polar(I*pi)/a)/(2*gamma(13/4))","C",0
590,1,46,0,9.378889," ","integrate((c*x)**(5/2)*(b*x**2+a)**(1/2),x)","\frac{\sqrt{a} c^{\frac{5}{2}} x^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{11}{4}\right)}"," ",0,"sqrt(a)*c**(5/2)*x**(7/2)*gamma(7/4)*hyper((-1/2, 7/4), (11/4,), b*x**2*exp_polar(I*pi)/a)/(2*gamma(11/4))","C",0
591,1,46,0,2.764703," ","integrate((c*x)**(3/2)*(b*x**2+a)**(1/2),x)","\frac{\sqrt{a} c^{\frac{3}{2}} x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{9}{4}\right)}"," ",0,"sqrt(a)*c**(3/2)*x**(5/2)*gamma(5/4)*hyper((-1/2, 5/4), (9/4,), b*x**2*exp_polar(I*pi)/a)/(2*gamma(9/4))","C",0
592,1,46,0,1.071982," ","integrate((c*x)**(1/2)*(b*x**2+a)**(1/2),x)","\frac{\sqrt{a} \sqrt{c} x^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{7}{4}\right)}"," ",0,"sqrt(a)*sqrt(c)*x**(3/2)*gamma(3/4)*hyper((-1/2, 3/4), (7/4,), b*x**2*exp_polar(I*pi)/a)/(2*gamma(7/4))","C",0
593,1,46,0,0.987484," ","integrate((b*x**2+a)**(1/2)/(c*x)**(1/2),x)","\frac{\sqrt{a} \sqrt{x} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{c} \Gamma\left(\frac{5}{4}\right)}"," ",0,"sqrt(a)*sqrt(x)*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), b*x**2*exp_polar(I*pi)/a)/(2*sqrt(c)*gamma(5/4))","C",0
594,1,49,0,1.352739," ","integrate((b*x**2+a)**(1/2)/(c*x)**(3/2),x)","\frac{\sqrt{a} \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 c^{\frac{3}{2}} \sqrt{x} \Gamma\left(\frac{3}{4}\right)}"," ",0,"sqrt(a)*gamma(-1/4)*hyper((-1/2, -1/4), (3/4,), b*x**2*exp_polar(I*pi)/a)/(2*c**(3/2)*sqrt(x)*gamma(3/4))","C",0
595,1,49,0,2.857979," ","integrate((b*x**2+a)**(1/2)/(c*x)**(5/2),x)","\frac{\sqrt{a} \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, - \frac{1}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 c^{\frac{5}{2}} x^{\frac{3}{2}} \Gamma\left(\frac{1}{4}\right)}"," ",0,"sqrt(a)*gamma(-3/4)*hyper((-3/4, -1/2), (1/4,), b*x**2*exp_polar(I*pi)/a)/(2*c**(5/2)*x**(3/2)*gamma(1/4))","C",0
596,1,53,0,9.754966," ","integrate((b*x**2+a)**(1/2)/(c*x)**(7/2),x)","\frac{\sqrt{a} \Gamma\left(- \frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, - \frac{1}{2} \\ - \frac{1}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 c^{\frac{7}{2}} x^{\frac{5}{2}} \Gamma\left(- \frac{1}{4}\right)}"," ",0,"sqrt(a)*gamma(-5/4)*hyper((-5/4, -1/2), (-1/4,), b*x**2*exp_polar(I*pi)/a)/(2*c**(7/2)*x**(5/2)*gamma(-1/4))","C",0
597,1,46,0,50.255955," ","integrate((c*x)**(7/2)*(b*x**2+a)**(3/2),x)","\frac{a^{\frac{3}{2}} c^{\frac{7}{2}} x^{\frac{9}{2}} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{13}{4}\right)}"," ",0,"a**(3/2)*c**(7/2)*x**(9/2)*gamma(9/4)*hyper((-3/2, 9/4), (13/4,), b*x**2*exp_polar(I*pi)/a)/(2*gamma(13/4))","C",0
598,1,46,0,18.194412," ","integrate((c*x)**(5/2)*(b*x**2+a)**(3/2),x)","\frac{a^{\frac{3}{2}} c^{\frac{5}{2}} x^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{11}{4}\right)}"," ",0,"a**(3/2)*c**(5/2)*x**(7/2)*gamma(7/4)*hyper((-3/2, 7/4), (11/4,), b*x**2*exp_polar(I*pi)/a)/(2*gamma(11/4))","C",0
599,1,46,0,6.122805," ","integrate((c*x)**(3/2)*(b*x**2+a)**(3/2),x)","\frac{a^{\frac{3}{2}} c^{\frac{3}{2}} x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{9}{4}\right)}"," ",0,"a**(3/2)*c**(3/2)*x**(5/2)*gamma(5/4)*hyper((-3/2, 5/4), (9/4,), b*x**2*exp_polar(I*pi)/a)/(2*gamma(9/4))","C",0
600,1,46,0,3.398119," ","integrate((c*x)**(1/2)*(b*x**2+a)**(3/2),x)","\frac{a^{\frac{3}{2}} \sqrt{c} x^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{7}{4}\right)}"," ",0,"a**(3/2)*sqrt(c)*x**(3/2)*gamma(3/4)*hyper((-3/2, 3/4), (7/4,), b*x**2*exp_polar(I*pi)/a)/(2*gamma(7/4))","C",0
601,1,46,0,2.626430," ","integrate((b*x**2+a)**(3/2)/(c*x)**(1/2),x)","\frac{a^{\frac{3}{2}} \sqrt{x} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{c} \Gamma\left(\frac{5}{4}\right)}"," ",0,"a**(3/2)*sqrt(x)*gamma(1/4)*hyper((-3/2, 1/4), (5/4,), b*x**2*exp_polar(I*pi)/a)/(2*sqrt(c)*gamma(5/4))","C",0
602,1,49,0,2.483803," ","integrate((b*x**2+a)**(3/2)/(c*x)**(3/2),x)","\frac{a^{\frac{3}{2}} \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 c^{\frac{3}{2}} \sqrt{x} \Gamma\left(\frac{3}{4}\right)}"," ",0,"a**(3/2)*gamma(-1/4)*hyper((-3/2, -1/4), (3/4,), b*x**2*exp_polar(I*pi)/a)/(2*c**(3/2)*sqrt(x)*gamma(3/4))","C",0
603,1,49,0,4.503423," ","integrate((b*x**2+a)**(3/2)/(c*x)**(5/2),x)","\frac{a^{\frac{3}{2}} \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, - \frac{3}{4} \\ \frac{1}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 c^{\frac{5}{2}} x^{\frac{3}{2}} \Gamma\left(\frac{1}{4}\right)}"," ",0,"a**(3/2)*gamma(-3/4)*hyper((-3/2, -3/4), (1/4,), b*x**2*exp_polar(I*pi)/a)/(2*c**(5/2)*x**(3/2)*gamma(1/4))","C",0
604,1,53,0,10.930556," ","integrate((b*x**2+a)**(3/2)/(c*x)**(7/2),x)","\frac{a^{\frac{3}{2}} \Gamma\left(- \frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, - \frac{5}{4} \\ - \frac{1}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 c^{\frac{7}{2}} x^{\frac{5}{2}} \Gamma\left(- \frac{1}{4}\right)}"," ",0,"a**(3/2)*gamma(-5/4)*hyper((-3/2, -5/4), (-1/4,), b*x**2*exp_polar(I*pi)/a)/(2*c**(7/2)*x**(5/2)*gamma(-1/4))","C",0
605,1,53,0,33.123382," ","integrate((b*x**2+a)**(3/2)/(c*x)**(9/2),x)","\frac{a^{\frac{3}{2}} \Gamma\left(- \frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{7}{4}, - \frac{3}{2} \\ - \frac{3}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 c^{\frac{9}{2}} x^{\frac{7}{2}} \Gamma\left(- \frac{3}{4}\right)}"," ",0,"a**(3/2)*gamma(-7/4)*hyper((-7/4, -3/2), (-3/4,), b*x**2*exp_polar(I*pi)/a)/(2*c**(9/2)*x**(7/2)*gamma(-3/4))","C",0
606,1,53,0,83.792109," ","integrate((b*x**2+a)**(3/2)/(c*x)**(11/2),x)","\frac{a^{\frac{3}{2}} \Gamma\left(- \frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{9}{4}, - \frac{3}{2} \\ - \frac{5}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 c^{\frac{11}{2}} x^{\frac{9}{2}} \Gamma\left(- \frac{5}{4}\right)}"," ",0,"a**(3/2)*gamma(-9/4)*hyper((-9/4, -3/2), (-5/4,), b*x**2*exp_polar(I*pi)/a)/(2*c**(11/2)*x**(9/2)*gamma(-5/4))","C",0
607,1,53,0,10.494119," ","integrate((c*x)**(5/2)*(-2*a*x**2+3*a)**(1/2),x)","\frac{\sqrt{3} \sqrt{a} c^{\frac{5}{2}} x^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{2 x^{2} e^{2 i \pi}}{3}} \right)}}{2 \Gamma\left(\frac{11}{4}\right)}"," ",0,"sqrt(3)*sqrt(a)*c**(5/2)*x**(7/2)*gamma(7/4)*hyper((-1/2, 7/4), (11/4,), 2*x**2*exp_polar(2*I*pi)/3)/(2*gamma(11/4))","C",0
608,1,53,0,2.728208," ","integrate((c*x)**(3/2)*(-2*a*x**2+3*a)**(1/2),x)","\frac{\sqrt{3} \sqrt{a} c^{\frac{3}{2}} x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{2 x^{2} e^{2 i \pi}}{3}} \right)}}{2 \Gamma\left(\frac{9}{4}\right)}"," ",0,"sqrt(3)*sqrt(a)*c**(3/2)*x**(5/2)*gamma(5/4)*hyper((-1/2, 5/4), (9/4,), 2*x**2*exp_polar(2*I*pi)/3)/(2*gamma(9/4))","A",0
609,1,53,0,1.045738," ","integrate((c*x)**(1/2)*(-2*a*x**2+3*a)**(1/2),x)","\frac{\sqrt{3} \sqrt{a} \sqrt{c} x^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{2 x^{2} e^{2 i \pi}}{3}} \right)}}{2 \Gamma\left(\frac{7}{4}\right)}"," ",0,"sqrt(3)*sqrt(a)*sqrt(c)*x**(3/2)*gamma(3/4)*hyper((-1/2, 3/4), (7/4,), 2*x**2*exp_polar(2*I*pi)/3)/(2*gamma(7/4))","C",0
610,1,53,0,0.928888," ","integrate((-2*a*x**2+3*a)**(1/2)/(c*x)**(1/2),x)","\frac{\sqrt{3} \sqrt{a} \sqrt{x} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{2 x^{2} e^{2 i \pi}}{3}} \right)}}{2 \sqrt{c} \Gamma\left(\frac{5}{4}\right)}"," ",0,"sqrt(3)*sqrt(a)*sqrt(x)*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), 2*x**2*exp_polar(2*I*pi)/3)/(2*sqrt(c)*gamma(5/4))","A",0
611,1,56,0,1.292892," ","integrate((-2*a*x**2+3*a)**(1/2)/(c*x)**(3/2),x)","\frac{\sqrt{3} \sqrt{a} \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{2 x^{2} e^{2 i \pi}}{3}} \right)}}{2 c^{\frac{3}{2}} \sqrt{x} \Gamma\left(\frac{3}{4}\right)}"," ",0,"sqrt(3)*sqrt(a)*gamma(-1/4)*hyper((-1/2, -1/4), (3/4,), 2*x**2*exp_polar(2*I*pi)/3)/(2*c**(3/2)*sqrt(x)*gamma(3/4))","C",0
612,1,49,0,2.855194," ","integrate((-2*a*x**2+3*a)**(1/2)/(c*x)**(5/2),x)","\frac{\sqrt{2} i \sqrt{a} \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{3}{2 x^{2}}} \right)}}{2 c^{\frac{5}{2}} \sqrt{x} \Gamma\left(\frac{3}{4}\right)}"," ",0,"sqrt(2)*I*sqrt(a)*gamma(-1/4)*hyper((-1/2, 1/4), (5/4,), 3/(2*x**2))/(2*c**(5/2)*sqrt(x)*gamma(3/4))","A",0
613,1,44,0,19.569228," ","integrate((c*x)**(7/2)/(b*x**2+a)**(1/2),x)","\frac{c^{\frac{7}{2}} x^{\frac{9}{2}} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} \Gamma\left(\frac{13}{4}\right)}"," ",0,"c**(7/2)*x**(9/2)*gamma(9/4)*hyper((1/2, 9/4), (13/4,), b*x**2*exp_polar(I*pi)/a)/(2*sqrt(a)*gamma(13/4))","C",0
614,1,44,0,6.833739," ","integrate((c*x)**(5/2)/(b*x**2+a)**(1/2),x)","\frac{c^{\frac{5}{2}} x^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} \Gamma\left(\frac{11}{4}\right)}"," ",0,"c**(5/2)*x**(7/2)*gamma(7/4)*hyper((1/2, 7/4), (11/4,), b*x**2*exp_polar(I*pi)/a)/(2*sqrt(a)*gamma(11/4))","C",0
615,1,44,0,1.927667," ","integrate((c*x)**(3/2)/(b*x**2+a)**(1/2),x)","\frac{c^{\frac{3}{2}} x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} \Gamma\left(\frac{9}{4}\right)}"," ",0,"c**(3/2)*x**(5/2)*gamma(5/4)*hyper((1/2, 5/4), (9/4,), b*x**2*exp_polar(I*pi)/a)/(2*sqrt(a)*gamma(9/4))","C",0
616,1,44,0,0.930229," ","integrate((c*x)**(1/2)/(b*x**2+a)**(1/2),x)","\frac{\sqrt{c} x^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} \Gamma\left(\frac{7}{4}\right)}"," ",0,"sqrt(c)*x**(3/2)*gamma(3/4)*hyper((1/2, 3/4), (7/4,), b*x**2*exp_polar(I*pi)/a)/(2*sqrt(a)*gamma(7/4))","C",0
617,1,44,0,1.089277," ","integrate(1/(c*x)**(1/2)/(b*x**2+a)**(1/2),x)","\frac{\sqrt{x} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} \sqrt{c} \Gamma\left(\frac{5}{4}\right)}"," ",0,"sqrt(x)*gamma(1/4)*hyper((1/4, 1/2), (5/4,), b*x**2*exp_polar(I*pi)/a)/(2*sqrt(a)*sqrt(c)*gamma(5/4))","C",0
618,1,48,0,1.636640," ","integrate(1/(c*x)**(3/2)/(b*x**2+a)**(1/2),x)","\frac{\Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{1}{2} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} c^{\frac{3}{2}} \sqrt{x} \Gamma\left(\frac{3}{4}\right)}"," ",0,"gamma(-1/4)*hyper((-1/4, 1/2), (3/4,), b*x**2*exp_polar(I*pi)/a)/(2*sqrt(a)*c**(3/2)*sqrt(x)*gamma(3/4))","C",0
619,1,48,0,3.894149," ","integrate(1/(c*x)**(5/2)/(b*x**2+a)**(1/2),x)","\frac{\Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{1}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} c^{\frac{5}{2}} x^{\frac{3}{2}} \Gamma\left(\frac{1}{4}\right)}"," ",0,"gamma(-3/4)*hyper((-3/4, 1/2), (1/4,), b*x**2*exp_polar(I*pi)/a)/(2*sqrt(a)*c**(5/2)*x**(3/2)*gamma(1/4))","C",0
620,1,51,0,12.686346," ","integrate(1/(c*x)**(7/2)/(b*x**2+a)**(1/2),x)","\frac{\Gamma\left(- \frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, \frac{1}{2} \\ - \frac{1}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} c^{\frac{7}{2}} x^{\frac{5}{2}} \Gamma\left(- \frac{1}{4}\right)}"," ",0,"gamma(-5/4)*hyper((-5/4, 1/2), (-1/4,), b*x**2*exp_polar(I*pi)/a)/(2*sqrt(a)*c**(7/2)*x**(5/2)*gamma(-1/4))","C",0
621,1,44,0,22.732472," ","integrate((c*x)**(7/2)/(b*x**2+a)**(3/2),x)","\frac{c^{\frac{7}{2}} x^{\frac{9}{2}} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{2}} \Gamma\left(\frac{13}{4}\right)}"," ",0,"c**(7/2)*x**(9/2)*gamma(9/4)*hyper((3/2, 9/4), (13/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(3/2)*gamma(13/4))","C",0
622,1,44,0,7.300730," ","integrate((c*x)**(5/2)/(b*x**2+a)**(3/2),x)","\frac{c^{\frac{5}{2}} x^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{2}} \Gamma\left(\frac{11}{4}\right)}"," ",0,"c**(5/2)*x**(7/2)*gamma(7/4)*hyper((3/2, 7/4), (11/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(3/2)*gamma(11/4))","C",0
623,1,44,0,2.045985," ","integrate((c*x)**(3/2)/(b*x**2+a)**(3/2),x)","\frac{c^{\frac{3}{2}} x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, \frac{3}{2} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{2}} \Gamma\left(\frac{9}{4}\right)}"," ",0,"c**(3/2)*x**(5/2)*gamma(5/4)*hyper((5/4, 3/2), (9/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(3/2)*gamma(9/4))","C",0
624,1,44,0,1.283595," ","integrate((c*x)**(1/2)/(b*x**2+a)**(3/2),x)","\frac{\sqrt{c} x^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{3}{2} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{2}} \Gamma\left(\frac{7}{4}\right)}"," ",0,"sqrt(c)*x**(3/2)*gamma(3/4)*hyper((3/4, 3/2), (7/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(3/2)*gamma(7/4))","C",0
625,1,44,0,1.799959," ","integrate(1/(c*x)**(1/2)/(b*x**2+a)**(3/2),x)","\frac{\sqrt{x} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{3}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{2}} \sqrt{c} \Gamma\left(\frac{5}{4}\right)}"," ",0,"sqrt(x)*gamma(1/4)*hyper((1/4, 3/2), (5/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(3/2)*sqrt(c)*gamma(5/4))","C",0
626,1,48,0,3.162387," ","integrate(1/(c*x)**(3/2)/(b*x**2+a)**(3/2),x)","\frac{\Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{3}{2} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{2}} c^{\frac{3}{2}} \sqrt{x} \Gamma\left(\frac{3}{4}\right)}"," ",0,"gamma(-1/4)*hyper((-1/4, 3/2), (3/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(3/2)*c**(3/2)*sqrt(x)*gamma(3/4))","C",0
627,1,48,0,7.963320," ","integrate(1/(c*x)**(5/2)/(b*x**2+a)**(3/2),x)","\frac{\Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{3}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{2}} c^{\frac{5}{2}} x^{\frac{3}{2}} \Gamma\left(\frac{1}{4}\right)}"," ",0,"gamma(-3/4)*hyper((-3/4, 3/2), (1/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(3/2)*c**(5/2)*x**(3/2)*gamma(1/4))","C",0
628,1,51,0,24.979236," ","integrate(1/(c*x)**(7/2)/(b*x**2+a)**(3/2),x)","\frac{\Gamma\left(- \frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, \frac{3}{2} \\ - \frac{1}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{2}} c^{\frac{7}{2}} x^{\frac{5}{2}} \Gamma\left(- \frac{1}{4}\right)}"," ",0,"gamma(-5/4)*hyper((-5/4, 3/2), (-1/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(3/2)*c**(7/2)*x**(5/2)*gamma(-1/4))","C",0
629,1,44,0,22.872538," ","integrate((c*x)**(7/2)/(b*x**2+a)**(5/2),x)","\frac{c^{\frac{7}{2}} x^{\frac{9}{2}} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{9}{4}, \frac{5}{2} \\ \frac{13}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{5}{2}} \Gamma\left(\frac{13}{4}\right)}"," ",0,"c**(7/2)*x**(9/2)*gamma(9/4)*hyper((9/4, 5/2), (13/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(5/2)*gamma(13/4))","C",0
630,1,44,0,7.328410," ","integrate((c*x)**(5/2)/(b*x**2+a)**(5/2),x)","\frac{c^{\frac{5}{2}} x^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{7}{4}, \frac{5}{2} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{5}{2}} \Gamma\left(\frac{11}{4}\right)}"," ",0,"c**(5/2)*x**(7/2)*gamma(7/4)*hyper((7/4, 5/2), (11/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(5/2)*gamma(11/4))","C",0
631,1,44,0,3.831948," ","integrate((c*x)**(3/2)/(b*x**2+a)**(5/2),x)","\frac{c^{\frac{3}{2}} x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, \frac{5}{2} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{5}{2}} \Gamma\left(\frac{9}{4}\right)}"," ",0,"c**(3/2)*x**(5/2)*gamma(5/4)*hyper((5/4, 5/2), (9/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(5/2)*gamma(9/4))","C",0
632,1,44,0,2.824244," ","integrate((c*x)**(1/2)/(b*x**2+a)**(5/2),x)","\frac{\sqrt{c} x^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{5}{2} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{5}{2}} \Gamma\left(\frac{7}{4}\right)}"," ",0,"sqrt(c)*x**(3/2)*gamma(3/4)*hyper((3/4, 5/2), (7/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(5/2)*gamma(7/4))","C",0
633,1,44,0,4.283826," ","integrate(1/(c*x)**(1/2)/(b*x**2+a)**(5/2),x)","\frac{\sqrt{x} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{5}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{5}{2}} \sqrt{c} \Gamma\left(\frac{5}{4}\right)}"," ",0,"sqrt(x)*gamma(1/4)*hyper((1/4, 5/2), (5/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(5/2)*sqrt(c)*gamma(5/4))","C",0
634,1,48,0,7.658578," ","integrate(1/(c*x)**(3/2)/(b*x**2+a)**(5/2),x)","\frac{\Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{5}{2} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{5}{2}} c^{\frac{3}{2}} \sqrt{x} \Gamma\left(\frac{3}{4}\right)}"," ",0,"gamma(-1/4)*hyper((-1/4, 5/2), (3/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(5/2)*c**(3/2)*sqrt(x)*gamma(3/4))","C",0
635,1,48,0,13.966816," ","integrate(1/(c*x)**(5/2)/(b*x**2+a)**(5/2),x)","\frac{\Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{5}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{5}{2}} c^{\frac{5}{2}} x^{\frac{3}{2}} \Gamma\left(\frac{1}{4}\right)}"," ",0,"gamma(-3/4)*hyper((-3/4, 5/2), (1/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(5/2)*c**(5/2)*x**(3/2)*gamma(1/4))","C",0
636,1,51,0,41.151442," ","integrate(1/(c*x)**(7/2)/(b*x**2+a)**(5/2),x)","\frac{\Gamma\left(- \frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, \frac{5}{2} \\ - \frac{1}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{5}{2}} c^{\frac{7}{2}} x^{\frac{5}{2}} \Gamma\left(- \frac{1}{4}\right)}"," ",0,"gamma(-5/4)*hyper((-5/4, 5/2), (-1/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(5/2)*c**(7/2)*x**(5/2)*gamma(-1/4))","C",0
637,1,51,0,6.444719," ","integrate((c*x)**(5/2)/(-2*a*x**2+3*a)**(1/2),x)","\frac{\sqrt{3} c^{\frac{5}{2}} x^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{2 x^{2} e^{2 i \pi}}{3}} \right)}}{6 \sqrt{a} \Gamma\left(\frac{11}{4}\right)}"," ",0,"sqrt(3)*c**(5/2)*x**(7/2)*gamma(7/4)*hyper((1/2, 7/4), (11/4,), 2*x**2*exp_polar(2*I*pi)/3)/(6*sqrt(a)*gamma(11/4))","C",0
638,1,51,0,1.869972," ","integrate((c*x)**(3/2)/(-2*a*x**2+3*a)**(1/2),x)","\frac{\sqrt{3} c^{\frac{3}{2}} x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{2 x^{2} e^{2 i \pi}}{3}} \right)}}{6 \sqrt{a} \Gamma\left(\frac{9}{4}\right)}"," ",0,"sqrt(3)*c**(3/2)*x**(5/2)*gamma(5/4)*hyper((1/2, 5/4), (9/4,), 2*x**2*exp_polar(2*I*pi)/3)/(6*sqrt(a)*gamma(9/4))","A",0
639,1,51,0,0.858834," ","integrate((c*x)**(1/2)/(-2*a*x**2+3*a)**(1/2),x)","\frac{\sqrt{3} \sqrt{c} x^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{2 x^{2} e^{2 i \pi}}{3}} \right)}}{6 \sqrt{a} \Gamma\left(\frac{7}{4}\right)}"," ",0,"sqrt(3)*sqrt(c)*x**(3/2)*gamma(3/4)*hyper((1/2, 3/4), (7/4,), 2*x**2*exp_polar(2*I*pi)/3)/(6*sqrt(a)*gamma(7/4))","C",0
640,1,51,0,1.036206," ","integrate(1/(c*x)**(1/2)/(-2*a*x**2+3*a)**(1/2),x)","\frac{\sqrt{3} \sqrt{x} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{2 x^{2} e^{2 i \pi}}{3}} \right)}}{6 \sqrt{a} \sqrt{c} \Gamma\left(\frac{5}{4}\right)}"," ",0,"sqrt(3)*sqrt(x)*gamma(1/4)*hyper((1/4, 1/2), (5/4,), 2*x**2*exp_polar(2*I*pi)/3)/(6*sqrt(a)*sqrt(c)*gamma(5/4))","A",0
641,1,54,0,1.584387," ","integrate(1/(c*x)**(3/2)/(-2*a*x**2+3*a)**(1/2),x)","\frac{\sqrt{3} \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{1}{2} \\ \frac{3}{4} \end{matrix}\middle| {\frac{2 x^{2} e^{2 i \pi}}{3}} \right)}}{6 \sqrt{a} c^{\frac{3}{2}} \sqrt{x} \Gamma\left(\frac{3}{4}\right)}"," ",0,"sqrt(3)*gamma(-1/4)*hyper((-1/4, 1/2), (3/4,), 2*x**2*exp_polar(2*I*pi)/3)/(6*sqrt(a)*c**(3/2)*sqrt(x)*gamma(3/4))","C",0
642,1,54,0,3.771441," ","integrate(1/(c*x)**(5/2)/(-2*a*x**2+3*a)**(1/2),x)","\frac{\sqrt{3} \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{1}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{2 x^{2} e^{2 i \pi}}{3}} \right)}}{6 \sqrt{a} c^{\frac{5}{2}} x^{\frac{3}{2}} \Gamma\left(\frac{1}{4}\right)}"," ",0,"sqrt(3)*gamma(-3/4)*hyper((-3/4, 1/2), (1/4,), 2*x**2*exp_polar(2*I*pi)/3)/(6*sqrt(a)*c**(5/2)*x**(3/2)*gamma(1/4))","A",0
643,1,51,0,7.335237," ","integrate((c*x)**(5/2)/(-2*a*x**2+3*a)**(3/2),x)","\frac{\sqrt{3} c^{\frac{5}{2}} x^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{2 x^{2} e^{2 i \pi}}{3}} \right)}}{18 a^{\frac{3}{2}} \Gamma\left(\frac{11}{4}\right)}"," ",0,"sqrt(3)*c**(5/2)*x**(7/2)*gamma(7/4)*hyper((3/2, 7/4), (11/4,), 2*x**2*exp_polar(2*I*pi)/3)/(18*a**(3/2)*gamma(11/4))","C",0
644,1,51,0,2.102862," ","integrate((c*x)**(3/2)/(-2*a*x**2+3*a)**(3/2),x)","\frac{\sqrt{3} c^{\frac{3}{2}} x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, \frac{3}{2} \\ \frac{9}{4} \end{matrix}\middle| {\frac{2 x^{2} e^{2 i \pi}}{3}} \right)}}{18 a^{\frac{3}{2}} \Gamma\left(\frac{9}{4}\right)}"," ",0,"sqrt(3)*c**(3/2)*x**(5/2)*gamma(5/4)*hyper((5/4, 3/2), (9/4,), 2*x**2*exp_polar(2*I*pi)/3)/(18*a**(3/2)*gamma(9/4))","A",0
645,1,51,0,1.273860," ","integrate((c*x)**(1/2)/(-2*a*x**2+3*a)**(3/2),x)","\frac{\sqrt{3} \sqrt{c} x^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{3}{2} \\ \frac{7}{4} \end{matrix}\middle| {\frac{2 x^{2} e^{2 i \pi}}{3}} \right)}}{18 a^{\frac{3}{2}} \Gamma\left(\frac{7}{4}\right)}"," ",0,"sqrt(3)*sqrt(c)*x**(3/2)*gamma(3/4)*hyper((3/4, 3/2), (7/4,), 2*x**2*exp_polar(2*I*pi)/3)/(18*a**(3/2)*gamma(7/4))","C",0
646,1,51,0,1.790567," ","integrate(1/(c*x)**(1/2)/(-2*a*x**2+3*a)**(3/2),x)","\frac{\sqrt{3} \sqrt{x} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{3}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{2 x^{2} e^{2 i \pi}}{3}} \right)}}{18 a^{\frac{3}{2}} \sqrt{c} \Gamma\left(\frac{5}{4}\right)}"," ",0,"sqrt(3)*sqrt(x)*gamma(1/4)*hyper((1/4, 3/2), (5/4,), 2*x**2*exp_polar(2*I*pi)/3)/(18*a**(3/2)*sqrt(c)*gamma(5/4))","A",0
647,1,54,0,3.163402," ","integrate(1/(c*x)**(3/2)/(-2*a*x**2+3*a)**(3/2),x)","\frac{\sqrt{3} \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{3}{2} \\ \frac{3}{4} \end{matrix}\middle| {\frac{2 x^{2} e^{2 i \pi}}{3}} \right)}}{18 a^{\frac{3}{2}} c^{\frac{3}{2}} \sqrt{x} \Gamma\left(\frac{3}{4}\right)}"," ",0,"sqrt(3)*gamma(-1/4)*hyper((-1/4, 3/2), (3/4,), 2*x**2*exp_polar(2*I*pi)/3)/(18*a**(3/2)*c**(3/2)*sqrt(x)*gamma(3/4))","C",0
648,1,54,0,8.112225," ","integrate(1/(c*x)**(5/2)/(-2*a*x**2+3*a)**(3/2),x)","\frac{\sqrt{3} \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{3}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{2 x^{2} e^{2 i \pi}}{3}} \right)}}{18 a^{\frac{3}{2}} c^{\frac{5}{2}} x^{\frac{3}{2}} \Gamma\left(\frac{1}{4}\right)}"," ",0,"sqrt(3)*gamma(-3/4)*hyper((-3/4, 3/2), (1/4,), 2*x**2*exp_polar(2*I*pi)/3)/(18*a**(3/2)*c**(5/2)*x**(3/2)*gamma(1/4))","A",0
649,1,36,0,0.795985," ","integrate(1/x**(1/2)/(-a**2*x**2+1)**(1/2),x)","\frac{\sqrt{x} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {a^{2} x^{2} e^{2 i \pi}} \right)}}{2 \Gamma\left(\frac{5}{4}\right)}"," ",0,"sqrt(x)*gamma(1/4)*hyper((1/4, 1/2), (5/4,), a**2*x**2*exp_polar(2*I*pi))/(2*gamma(5/4))","B",0
650,1,32,0,0.752875," ","integrate(1/x**(1/2)/(a*x**2+1)**(1/2),x)","\frac{\sqrt{x} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {a x^{2} e^{i \pi}} \right)}}{2 \Gamma\left(\frac{5}{4}\right)}"," ",0,"sqrt(x)*gamma(1/4)*hyper((1/4, 1/2), (5/4,), a*x**2*exp_polar(I*pi))/(2*gamma(5/4))","C",0
651,1,54,0,2.847879," ","integrate(x**m*(b*x**2+a)**(3/2),x)","\frac{a^{\frac{3}{2}} x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, \frac{m}{2} + \frac{1}{2} \\ \frac{m}{2} + \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}"," ",0,"a**(3/2)*x*x**m*gamma(m/2 + 1/2)*hyper((-3/2, m/2 + 1/2), (m/2 + 3/2,), b*x**2*exp_polar(I*pi)/a)/(2*gamma(m/2 + 3/2))","C",0
652,1,54,0,1.172985," ","integrate(x**m*(b*x**2+a)**(1/2),x)","\frac{\sqrt{a} x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{m}{2} + \frac{1}{2} \\ \frac{m}{2} + \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}"," ",0,"sqrt(a)*x*x**m*gamma(m/2 + 1/2)*hyper((-1/2, m/2 + 1/2), (m/2 + 3/2,), b*x**2*exp_polar(I*pi)/a)/(2*gamma(m/2 + 3/2))","C",0
653,1,53,0,1.012361," ","integrate(x**m/(b*x**2+a)**(1/2),x)","\frac{x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{m}{2} + \frac{1}{2} \\ \frac{m}{2} + \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}"," ",0,"x*x**m*gamma(m/2 + 1/2)*hyper((1/2, m/2 + 1/2), (m/2 + 3/2,), b*x**2*exp_polar(I*pi)/a)/(2*sqrt(a)*gamma(m/2 + 3/2))","C",0
654,1,53,0,1.393618," ","integrate(x**m/(b*x**2+a)**(3/2),x)","\frac{x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{m}{2} + \frac{1}{2} \\ \frac{m}{2} + \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{2}} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}"," ",0,"x*x**m*gamma(m/2 + 1/2)*hyper((3/2, m/2 + 1/2), (m/2 + 3/2,), b*x**2*exp_polar(I*pi)/a)/(2*a**(3/2)*gamma(m/2 + 3/2))","C",0
655,1,53,0,2.937614," ","integrate(x**m/(b*x**2+a)**(5/2),x)","\frac{x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{2}, \frac{m}{2} + \frac{1}{2} \\ \frac{m}{2} + \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{5}{2}} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}"," ",0,"x*x**m*gamma(m/2 + 1/2)*hyper((5/2, m/2 + 1/2), (m/2 + 3/2,), b*x**2*exp_polar(I*pi)/a)/(2*a**(5/2)*gamma(m/2 + 3/2))","C",0
656,1,54,0,2.643356," ","integrate(x**(2+m)/(b*x**2+a)**(1/2),x)","\frac{x^{3} x^{m} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{m}{2} + \frac{3}{2} \\ \frac{m}{2} + \frac{5}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)}"," ",0,"x**3*x**m*gamma(m/2 + 3/2)*hyper((1/2, m/2 + 3/2), (m/2 + 5/2,), b*x**2*exp_polar(I*pi)/a)/(2*sqrt(a)*gamma(m/2 + 5/2))","C",0
657,1,48,0,1.867908," ","integrate(x**(1+m)/(b*x**2+a)**(1/2),x)","\frac{x^{2} x^{m} \Gamma\left(\frac{m}{2} + 1\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{m}{2} + 1 \\ \frac{m}{2} + 2 \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} \Gamma\left(\frac{m}{2} + 2\right)}"," ",0,"x**2*x**m*gamma(m/2 + 1)*hyper((1/2, m/2 + 1), (m/2 + 2,), b*x**2*exp_polar(I*pi)/a)/(2*sqrt(a)*gamma(m/2 + 2))","C",0
658,1,53,0,1.024633," ","integrate(x**m/(b*x**2+a)**(1/2),x)","\frac{x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{m}{2} + \frac{1}{2} \\ \frac{m}{2} + \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}"," ",0,"x*x**m*gamma(m/2 + 1/2)*hyper((1/2, m/2 + 1/2), (m/2 + 3/2,), b*x**2*exp_polar(I*pi)/a)/(2*sqrt(a)*gamma(m/2 + 3/2))","C",0
659,1,41,0,3.056133," ","integrate(x**(-1+m)/(b*x**2+a)**(1/2),x)","\frac{x^{m} \Gamma\left(\frac{m}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{m}{2} \\ \frac{m}{2} + 1 \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} \Gamma\left(\frac{m}{2} + 1\right)}"," ",0,"x**m*gamma(m/2)*hyper((1/2, m/2), (m/2 + 1,), b*x**2*exp_polar(I*pi)/a)/(2*sqrt(a)*gamma(m/2 + 1))","C",0
660,1,53,0,8.061225," ","integrate(x**(-2+m)/(b*x**2+a)**(1/2),x)","\frac{x^{m} \Gamma\left(\frac{m}{2} - \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{m}{2} - \frac{1}{2} \\ \frac{m}{2} + \frac{1}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} x \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}"," ",0,"x**m*gamma(m/2 - 1/2)*hyper((1/2, m/2 - 1/2), (m/2 + 1/2,), b*x**2*exp_polar(I*pi)/a)/(2*sqrt(a)*x*gamma(m/2 + 1/2))","C",0
661,1,202,0,10.061216," ","integrate(x**(1+m)*(a*(2+m)+b*(3+m)*x**2)/(b*x**2+a)**(1/2),x)","\frac{\sqrt{a} m x^{2} x^{m} \Gamma\left(\frac{m}{2} + 1\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{m}{2} + 1 \\ \frac{m}{2} + 2 \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{m}{2} + 2\right)} + \frac{\sqrt{a} x^{2} x^{m} \Gamma\left(\frac{m}{2} + 1\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{m}{2} + 1 \\ \frac{m}{2} + 2 \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{\Gamma\left(\frac{m}{2} + 2\right)} + \frac{b m x^{4} x^{m} \Gamma\left(\frac{m}{2} + 2\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{m}{2} + 2 \\ \frac{m}{2} + 3 \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} \Gamma\left(\frac{m}{2} + 3\right)} + \frac{3 b x^{4} x^{m} \Gamma\left(\frac{m}{2} + 2\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{m}{2} + 2 \\ \frac{m}{2} + 3 \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} \Gamma\left(\frac{m}{2} + 3\right)}"," ",0,"sqrt(a)*m*x**2*x**m*gamma(m/2 + 1)*hyper((1/2, m/2 + 1), (m/2 + 2,), b*x**2*exp_polar(I*pi)/a)/(2*gamma(m/2 + 2)) + sqrt(a)*x**2*x**m*gamma(m/2 + 1)*hyper((1/2, m/2 + 1), (m/2 + 2,), b*x**2*exp_polar(I*pi)/a)/gamma(m/2 + 2) + b*m*x**4*x**m*gamma(m/2 + 2)*hyper((1/2, m/2 + 2), (m/2 + 3,), b*x**2*exp_polar(I*pi)/a)/(2*sqrt(a)*gamma(m/2 + 3)) + 3*b*x**4*x**m*gamma(m/2 + 2)*hyper((1/2, m/2 + 2), (m/2 + 3,), b*x**2*exp_polar(I*pi)/a)/(2*sqrt(a)*gamma(m/2 + 3))","C",0
662,1,105,0,5.287716," ","integrate(a*(2+m)*x**(1+m)/(b*x**2+a)**(1/2)+b*(3+m)*x**(3+m)/(b*x**2+a)**(1/2),x)","\frac{\sqrt{a} x^{2} x^{m} \left(m + 2\right) \Gamma\left(\frac{m}{2} + 1\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{m}{2} + 1 \\ \frac{m}{2} + 2 \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{m}{2} + 2\right)} + \frac{b x^{4} x^{m} \left(m + 3\right) \Gamma\left(\frac{m}{2} + 2\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{m}{2} + 2 \\ \frac{m}{2} + 3 \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} \Gamma\left(\frac{m}{2} + 3\right)}"," ",0,"sqrt(a)*x**2*x**m*(m + 2)*gamma(m/2 + 1)*hyper((1/2, m/2 + 1), (m/2 + 2,), b*x**2*exp_polar(I*pi)/a)/(2*gamma(m/2 + 2)) + b*x**4*x**m*(m + 3)*gamma(m/2 + 2)*hyper((1/2, m/2 + 2), (m/2 + 3,), b*x**2*exp_polar(I*pi)/a)/(2*sqrt(a)*gamma(m/2 + 3))","C",0
663,1,97,0,52.956555," ","integrate(x**(-1+m)*(a*m+b*(-1+m)*x**2)/(b*x**2+a)**(3/2),x)","\frac{m x^{m} \Gamma\left(\frac{m}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{m}{2} \\ \frac{m}{2} + 1 \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} \Gamma\left(\frac{m}{2} + 1\right)} + \frac{b x^{2} x^{m} \left(m - 1\right) \Gamma\left(\frac{m}{2} + 1\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{m}{2} + 1 \\ \frac{m}{2} + 2 \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{2}} \Gamma\left(\frac{m}{2} + 2\right)}"," ",0,"m*x**m*gamma(m/2)*hyper((3/2, m/2), (m/2 + 1,), b*x**2*exp_polar(I*pi)/a)/(2*sqrt(a)*gamma(m/2 + 1)) + b*x**2*x**m*(m - 1)*gamma(m/2 + 1)*hyper((3/2, m/2 + 1), (m/2 + 2,), b*x**2*exp_polar(I*pi)/a)/(2*a**(3/2)*gamma(m/2 + 2))","C",0
664,1,94,0,5.586477," ","integrate(-b*x**(1+m)/(b*x**2+a)**(3/2)+m*x**(-1+m)/(b*x**2+a)**(1/2),x)","\frac{m x^{m} \Gamma\left(\frac{m}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{m}{2} \\ \frac{m}{2} + 1 \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} \Gamma\left(\frac{m}{2} + 1\right)} - \frac{b x^{2} x^{m} \Gamma\left(\frac{m}{2} + 1\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{m}{2} + 1 \\ \frac{m}{2} + 2 \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{2}} \Gamma\left(\frac{m}{2} + 2\right)}"," ",0,"m*x**m*gamma(m/2)*hyper((1/2, m/2), (m/2 + 1,), b*x**2*exp_polar(I*pi)/a)/(2*sqrt(a)*gamma(m/2 + 1)) - b*x**2*x**m*gamma(m/2 + 1)*hyper((3/2, m/2 + 1), (m/2 + 2,), b*x**2*exp_polar(I*pi)/a)/(2*a**(3/2)*gamma(m/2 + 2))","C",0
665,1,1795,0,2.848102," ","integrate(x**7*(b*x**2+a)**(1/3),x)","- \frac{243 a^{\frac{73}{3}} \sqrt[3]{1 + \frac{b x^{2}}{a}}}{3640 a^{20} b^{4} + 21840 a^{19} b^{5} x^{2} + 54600 a^{18} b^{6} x^{4} + 72800 a^{17} b^{7} x^{6} + 54600 a^{16} b^{8} x^{8} + 21840 a^{15} b^{9} x^{10} + 3640 a^{14} b^{10} x^{12}} + \frac{243 a^{\frac{73}{3}}}{3640 a^{20} b^{4} + 21840 a^{19} b^{5} x^{2} + 54600 a^{18} b^{6} x^{4} + 72800 a^{17} b^{7} x^{6} + 54600 a^{16} b^{8} x^{8} + 21840 a^{15} b^{9} x^{10} + 3640 a^{14} b^{10} x^{12}} - \frac{1377 a^{\frac{70}{3}} b x^{2} \sqrt[3]{1 + \frac{b x^{2}}{a}}}{3640 a^{20} b^{4} + 21840 a^{19} b^{5} x^{2} + 54600 a^{18} b^{6} x^{4} + 72800 a^{17} b^{7} x^{6} + 54600 a^{16} b^{8} x^{8} + 21840 a^{15} b^{9} x^{10} + 3640 a^{14} b^{10} x^{12}} + \frac{1458 a^{\frac{70}{3}} b x^{2}}{3640 a^{20} b^{4} + 21840 a^{19} b^{5} x^{2} + 54600 a^{18} b^{6} x^{4} + 72800 a^{17} b^{7} x^{6} + 54600 a^{16} b^{8} x^{8} + 21840 a^{15} b^{9} x^{10} + 3640 a^{14} b^{10} x^{12}} - \frac{3213 a^{\frac{67}{3}} b^{2} x^{4} \sqrt[3]{1 + \frac{b x^{2}}{a}}}{3640 a^{20} b^{4} + 21840 a^{19} b^{5} x^{2} + 54600 a^{18} b^{6} x^{4} + 72800 a^{17} b^{7} x^{6} + 54600 a^{16} b^{8} x^{8} + 21840 a^{15} b^{9} x^{10} + 3640 a^{14} b^{10} x^{12}} + \frac{3645 a^{\frac{67}{3}} b^{2} x^{4}}{3640 a^{20} b^{4} + 21840 a^{19} b^{5} x^{2} + 54600 a^{18} b^{6} x^{4} + 72800 a^{17} b^{7} x^{6} + 54600 a^{16} b^{8} x^{8} + 21840 a^{15} b^{9} x^{10} + 3640 a^{14} b^{10} x^{12}} - \frac{3927 a^{\frac{64}{3}} b^{3} x^{6} \sqrt[3]{1 + \frac{b x^{2}}{a}}}{3640 a^{20} b^{4} + 21840 a^{19} b^{5} x^{2} + 54600 a^{18} b^{6} x^{4} + 72800 a^{17} b^{7} x^{6} + 54600 a^{16} b^{8} x^{8} + 21840 a^{15} b^{9} x^{10} + 3640 a^{14} b^{10} x^{12}} + \frac{4860 a^{\frac{64}{3}} b^{3} x^{6}}{3640 a^{20} b^{4} + 21840 a^{19} b^{5} x^{2} + 54600 a^{18} b^{6} x^{4} + 72800 a^{17} b^{7} x^{6} + 54600 a^{16} b^{8} x^{8} + 21840 a^{15} b^{9} x^{10} + 3640 a^{14} b^{10} x^{12}} - \frac{2163 a^{\frac{61}{3}} b^{4} x^{8} \sqrt[3]{1 + \frac{b x^{2}}{a}}}{3640 a^{20} b^{4} + 21840 a^{19} b^{5} x^{2} + 54600 a^{18} b^{6} x^{4} + 72800 a^{17} b^{7} x^{6} + 54600 a^{16} b^{8} x^{8} + 21840 a^{15} b^{9} x^{10} + 3640 a^{14} b^{10} x^{12}} + \frac{3645 a^{\frac{61}{3}} b^{4} x^{8}}{3640 a^{20} b^{4} + 21840 a^{19} b^{5} x^{2} + 54600 a^{18} b^{6} x^{4} + 72800 a^{17} b^{7} x^{6} + 54600 a^{16} b^{8} x^{8} + 21840 a^{15} b^{9} x^{10} + 3640 a^{14} b^{10} x^{12}} + \frac{1827 a^{\frac{58}{3}} b^{5} x^{10} \sqrt[3]{1 + \frac{b x^{2}}{a}}}{3640 a^{20} b^{4} + 21840 a^{19} b^{5} x^{2} + 54600 a^{18} b^{6} x^{4} + 72800 a^{17} b^{7} x^{6} + 54600 a^{16} b^{8} x^{8} + 21840 a^{15} b^{9} x^{10} + 3640 a^{14} b^{10} x^{12}} + \frac{1458 a^{\frac{58}{3}} b^{5} x^{10}}{3640 a^{20} b^{4} + 21840 a^{19} b^{5} x^{2} + 54600 a^{18} b^{6} x^{4} + 72800 a^{17} b^{7} x^{6} + 54600 a^{16} b^{8} x^{8} + 21840 a^{15} b^{9} x^{10} + 3640 a^{14} b^{10} x^{12}} + \frac{6573 a^{\frac{55}{3}} b^{6} x^{12} \sqrt[3]{1 + \frac{b x^{2}}{a}}}{3640 a^{20} b^{4} + 21840 a^{19} b^{5} x^{2} + 54600 a^{18} b^{6} x^{4} + 72800 a^{17} b^{7} x^{6} + 54600 a^{16} b^{8} x^{8} + 21840 a^{15} b^{9} x^{10} + 3640 a^{14} b^{10} x^{12}} + \frac{243 a^{\frac{55}{3}} b^{6} x^{12}}{3640 a^{20} b^{4} + 21840 a^{19} b^{5} x^{2} + 54600 a^{18} b^{6} x^{4} + 72800 a^{17} b^{7} x^{6} + 54600 a^{16} b^{8} x^{8} + 21840 a^{15} b^{9} x^{10} + 3640 a^{14} b^{10} x^{12}} + \frac{8787 a^{\frac{52}{3}} b^{7} x^{14} \sqrt[3]{1 + \frac{b x^{2}}{a}}}{3640 a^{20} b^{4} + 21840 a^{19} b^{5} x^{2} + 54600 a^{18} b^{6} x^{4} + 72800 a^{17} b^{7} x^{6} + 54600 a^{16} b^{8} x^{8} + 21840 a^{15} b^{9} x^{10} + 3640 a^{14} b^{10} x^{12}} + \frac{6498 a^{\frac{49}{3}} b^{8} x^{16} \sqrt[3]{1 + \frac{b x^{2}}{a}}}{3640 a^{20} b^{4} + 21840 a^{19} b^{5} x^{2} + 54600 a^{18} b^{6} x^{4} + 72800 a^{17} b^{7} x^{6} + 54600 a^{16} b^{8} x^{8} + 21840 a^{15} b^{9} x^{10} + 3640 a^{14} b^{10} x^{12}} + \frac{2562 a^{\frac{46}{3}} b^{9} x^{18} \sqrt[3]{1 + \frac{b x^{2}}{a}}}{3640 a^{20} b^{4} + 21840 a^{19} b^{5} x^{2} + 54600 a^{18} b^{6} x^{4} + 72800 a^{17} b^{7} x^{6} + 54600 a^{16} b^{8} x^{8} + 21840 a^{15} b^{9} x^{10} + 3640 a^{14} b^{10} x^{12}} + \frac{420 a^{\frac{43}{3}} b^{10} x^{20} \sqrt[3]{1 + \frac{b x^{2}}{a}}}{3640 a^{20} b^{4} + 21840 a^{19} b^{5} x^{2} + 54600 a^{18} b^{6} x^{4} + 72800 a^{17} b^{7} x^{6} + 54600 a^{16} b^{8} x^{8} + 21840 a^{15} b^{9} x^{10} + 3640 a^{14} b^{10} x^{12}}"," ",0,"-243*a**(73/3)*(1 + b*x**2/a)**(1/3)/(3640*a**20*b**4 + 21840*a**19*b**5*x**2 + 54600*a**18*b**6*x**4 + 72800*a**17*b**7*x**6 + 54600*a**16*b**8*x**8 + 21840*a**15*b**9*x**10 + 3640*a**14*b**10*x**12) + 243*a**(73/3)/(3640*a**20*b**4 + 21840*a**19*b**5*x**2 + 54600*a**18*b**6*x**4 + 72800*a**17*b**7*x**6 + 54600*a**16*b**8*x**8 + 21840*a**15*b**9*x**10 + 3640*a**14*b**10*x**12) - 1377*a**(70/3)*b*x**2*(1 + b*x**2/a)**(1/3)/(3640*a**20*b**4 + 21840*a**19*b**5*x**2 + 54600*a**18*b**6*x**4 + 72800*a**17*b**7*x**6 + 54600*a**16*b**8*x**8 + 21840*a**15*b**9*x**10 + 3640*a**14*b**10*x**12) + 1458*a**(70/3)*b*x**2/(3640*a**20*b**4 + 21840*a**19*b**5*x**2 + 54600*a**18*b**6*x**4 + 72800*a**17*b**7*x**6 + 54600*a**16*b**8*x**8 + 21840*a**15*b**9*x**10 + 3640*a**14*b**10*x**12) - 3213*a**(67/3)*b**2*x**4*(1 + b*x**2/a)**(1/3)/(3640*a**20*b**4 + 21840*a**19*b**5*x**2 + 54600*a**18*b**6*x**4 + 72800*a**17*b**7*x**6 + 54600*a**16*b**8*x**8 + 21840*a**15*b**9*x**10 + 3640*a**14*b**10*x**12) + 3645*a**(67/3)*b**2*x**4/(3640*a**20*b**4 + 21840*a**19*b**5*x**2 + 54600*a**18*b**6*x**4 + 72800*a**17*b**7*x**6 + 54600*a**16*b**8*x**8 + 21840*a**15*b**9*x**10 + 3640*a**14*b**10*x**12) - 3927*a**(64/3)*b**3*x**6*(1 + b*x**2/a)**(1/3)/(3640*a**20*b**4 + 21840*a**19*b**5*x**2 + 54600*a**18*b**6*x**4 + 72800*a**17*b**7*x**6 + 54600*a**16*b**8*x**8 + 21840*a**15*b**9*x**10 + 3640*a**14*b**10*x**12) + 4860*a**(64/3)*b**3*x**6/(3640*a**20*b**4 + 21840*a**19*b**5*x**2 + 54600*a**18*b**6*x**4 + 72800*a**17*b**7*x**6 + 54600*a**16*b**8*x**8 + 21840*a**15*b**9*x**10 + 3640*a**14*b**10*x**12) - 2163*a**(61/3)*b**4*x**8*(1 + b*x**2/a)**(1/3)/(3640*a**20*b**4 + 21840*a**19*b**5*x**2 + 54600*a**18*b**6*x**4 + 72800*a**17*b**7*x**6 + 54600*a**16*b**8*x**8 + 21840*a**15*b**9*x**10 + 3640*a**14*b**10*x**12) + 3645*a**(61/3)*b**4*x**8/(3640*a**20*b**4 + 21840*a**19*b**5*x**2 + 54600*a**18*b**6*x**4 + 72800*a**17*b**7*x**6 + 54600*a**16*b**8*x**8 + 21840*a**15*b**9*x**10 + 3640*a**14*b**10*x**12) + 1827*a**(58/3)*b**5*x**10*(1 + b*x**2/a)**(1/3)/(3640*a**20*b**4 + 21840*a**19*b**5*x**2 + 54600*a**18*b**6*x**4 + 72800*a**17*b**7*x**6 + 54600*a**16*b**8*x**8 + 21840*a**15*b**9*x**10 + 3640*a**14*b**10*x**12) + 1458*a**(58/3)*b**5*x**10/(3640*a**20*b**4 + 21840*a**19*b**5*x**2 + 54600*a**18*b**6*x**4 + 72800*a**17*b**7*x**6 + 54600*a**16*b**8*x**8 + 21840*a**15*b**9*x**10 + 3640*a**14*b**10*x**12) + 6573*a**(55/3)*b**6*x**12*(1 + b*x**2/a)**(1/3)/(3640*a**20*b**4 + 21840*a**19*b**5*x**2 + 54600*a**18*b**6*x**4 + 72800*a**17*b**7*x**6 + 54600*a**16*b**8*x**8 + 21840*a**15*b**9*x**10 + 3640*a**14*b**10*x**12) + 243*a**(55/3)*b**6*x**12/(3640*a**20*b**4 + 21840*a**19*b**5*x**2 + 54600*a**18*b**6*x**4 + 72800*a**17*b**7*x**6 + 54600*a**16*b**8*x**8 + 21840*a**15*b**9*x**10 + 3640*a**14*b**10*x**12) + 8787*a**(52/3)*b**7*x**14*(1 + b*x**2/a)**(1/3)/(3640*a**20*b**4 + 21840*a**19*b**5*x**2 + 54600*a**18*b**6*x**4 + 72800*a**17*b**7*x**6 + 54600*a**16*b**8*x**8 + 21840*a**15*b**9*x**10 + 3640*a**14*b**10*x**12) + 6498*a**(49/3)*b**8*x**16*(1 + b*x**2/a)**(1/3)/(3640*a**20*b**4 + 21840*a**19*b**5*x**2 + 54600*a**18*b**6*x**4 + 72800*a**17*b**7*x**6 + 54600*a**16*b**8*x**8 + 21840*a**15*b**9*x**10 + 3640*a**14*b**10*x**12) + 2562*a**(46/3)*b**9*x**18*(1 + b*x**2/a)**(1/3)/(3640*a**20*b**4 + 21840*a**19*b**5*x**2 + 54600*a**18*b**6*x**4 + 72800*a**17*b**7*x**6 + 54600*a**16*b**8*x**8 + 21840*a**15*b**9*x**10 + 3640*a**14*b**10*x**12) + 420*a**(43/3)*b**10*x**20*(1 + b*x**2/a)**(1/3)/(3640*a**20*b**4 + 21840*a**19*b**5*x**2 + 54600*a**18*b**6*x**4 + 72800*a**17*b**7*x**6 + 54600*a**16*b**8*x**8 + 21840*a**15*b**9*x**10 + 3640*a**14*b**10*x**12)","B",0
666,1,700,0,1.877461," ","integrate(x**5*(b*x**2+a)**(1/3),x)","\frac{27 a^{\frac{34}{3}} \sqrt[3]{1 + \frac{b x^{2}}{a}}}{280 a^{8} b^{3} + 840 a^{7} b^{4} x^{2} + 840 a^{6} b^{5} x^{4} + 280 a^{5} b^{6} x^{6}} - \frac{27 a^{\frac{34}{3}}}{280 a^{8} b^{3} + 840 a^{7} b^{4} x^{2} + 840 a^{6} b^{5} x^{4} + 280 a^{5} b^{6} x^{6}} + \frac{72 a^{\frac{31}{3}} b x^{2} \sqrt[3]{1 + \frac{b x^{2}}{a}}}{280 a^{8} b^{3} + 840 a^{7} b^{4} x^{2} + 840 a^{6} b^{5} x^{4} + 280 a^{5} b^{6} x^{6}} - \frac{81 a^{\frac{31}{3}} b x^{2}}{280 a^{8} b^{3} + 840 a^{7} b^{4} x^{2} + 840 a^{6} b^{5} x^{4} + 280 a^{5} b^{6} x^{6}} + \frac{60 a^{\frac{28}{3}} b^{2} x^{4} \sqrt[3]{1 + \frac{b x^{2}}{a}}}{280 a^{8} b^{3} + 840 a^{7} b^{4} x^{2} + 840 a^{6} b^{5} x^{4} + 280 a^{5} b^{6} x^{6}} - \frac{81 a^{\frac{28}{3}} b^{2} x^{4}}{280 a^{8} b^{3} + 840 a^{7} b^{4} x^{2} + 840 a^{6} b^{5} x^{4} + 280 a^{5} b^{6} x^{6}} + \frac{60 a^{\frac{25}{3}} b^{3} x^{6} \sqrt[3]{1 + \frac{b x^{2}}{a}}}{280 a^{8} b^{3} + 840 a^{7} b^{4} x^{2} + 840 a^{6} b^{5} x^{4} + 280 a^{5} b^{6} x^{6}} - \frac{27 a^{\frac{25}{3}} b^{3} x^{6}}{280 a^{8} b^{3} + 840 a^{7} b^{4} x^{2} + 840 a^{6} b^{5} x^{4} + 280 a^{5} b^{6} x^{6}} + \frac{135 a^{\frac{22}{3}} b^{4} x^{8} \sqrt[3]{1 + \frac{b x^{2}}{a}}}{280 a^{8} b^{3} + 840 a^{7} b^{4} x^{2} + 840 a^{6} b^{5} x^{4} + 280 a^{5} b^{6} x^{6}} + \frac{132 a^{\frac{19}{3}} b^{5} x^{10} \sqrt[3]{1 + \frac{b x^{2}}{a}}}{280 a^{8} b^{3} + 840 a^{7} b^{4} x^{2} + 840 a^{6} b^{5} x^{4} + 280 a^{5} b^{6} x^{6}} + \frac{42 a^{\frac{16}{3}} b^{6} x^{12} \sqrt[3]{1 + \frac{b x^{2}}{a}}}{280 a^{8} b^{3} + 840 a^{7} b^{4} x^{2} + 840 a^{6} b^{5} x^{4} + 280 a^{5} b^{6} x^{6}}"," ",0,"27*a**(34/3)*(1 + b*x**2/a)**(1/3)/(280*a**8*b**3 + 840*a**7*b**4*x**2 + 840*a**6*b**5*x**4 + 280*a**5*b**6*x**6) - 27*a**(34/3)/(280*a**8*b**3 + 840*a**7*b**4*x**2 + 840*a**6*b**5*x**4 + 280*a**5*b**6*x**6) + 72*a**(31/3)*b*x**2*(1 + b*x**2/a)**(1/3)/(280*a**8*b**3 + 840*a**7*b**4*x**2 + 840*a**6*b**5*x**4 + 280*a**5*b**6*x**6) - 81*a**(31/3)*b*x**2/(280*a**8*b**3 + 840*a**7*b**4*x**2 + 840*a**6*b**5*x**4 + 280*a**5*b**6*x**6) + 60*a**(28/3)*b**2*x**4*(1 + b*x**2/a)**(1/3)/(280*a**8*b**3 + 840*a**7*b**4*x**2 + 840*a**6*b**5*x**4 + 280*a**5*b**6*x**6) - 81*a**(28/3)*b**2*x**4/(280*a**8*b**3 + 840*a**7*b**4*x**2 + 840*a**6*b**5*x**4 + 280*a**5*b**6*x**6) + 60*a**(25/3)*b**3*x**6*(1 + b*x**2/a)**(1/3)/(280*a**8*b**3 + 840*a**7*b**4*x**2 + 840*a**6*b**5*x**4 + 280*a**5*b**6*x**6) - 27*a**(25/3)*b**3*x**6/(280*a**8*b**3 + 840*a**7*b**4*x**2 + 840*a**6*b**5*x**4 + 280*a**5*b**6*x**6) + 135*a**(22/3)*b**4*x**8*(1 + b*x**2/a)**(1/3)/(280*a**8*b**3 + 840*a**7*b**4*x**2 + 840*a**6*b**5*x**4 + 280*a**5*b**6*x**6) + 132*a**(19/3)*b**5*x**10*(1 + b*x**2/a)**(1/3)/(280*a**8*b**3 + 840*a**7*b**4*x**2 + 840*a**6*b**5*x**4 + 280*a**5*b**6*x**6) + 42*a**(16/3)*b**6*x**12*(1 + b*x**2/a)**(1/3)/(280*a**8*b**3 + 840*a**7*b**4*x**2 + 840*a**6*b**5*x**4 + 280*a**5*b**6*x**6)","B",0
667,1,223,0,1.216127," ","integrate(x**3*(b*x**2+a)**(1/3),x)","- \frac{9 a^{\frac{13}{3}} \sqrt[3]{1 + \frac{b x^{2}}{a}}}{56 a^{2} b^{2} + 56 a b^{3} x^{2}} + \frac{9 a^{\frac{13}{3}}}{56 a^{2} b^{2} + 56 a b^{3} x^{2}} - \frac{6 a^{\frac{10}{3}} b x^{2} \sqrt[3]{1 + \frac{b x^{2}}{a}}}{56 a^{2} b^{2} + 56 a b^{3} x^{2}} + \frac{9 a^{\frac{10}{3}} b x^{2}}{56 a^{2} b^{2} + 56 a b^{3} x^{2}} + \frac{15 a^{\frac{7}{3}} b^{2} x^{4} \sqrt[3]{1 + \frac{b x^{2}}{a}}}{56 a^{2} b^{2} + 56 a b^{3} x^{2}} + \frac{12 a^{\frac{4}{3}} b^{3} x^{6} \sqrt[3]{1 + \frac{b x^{2}}{a}}}{56 a^{2} b^{2} + 56 a b^{3} x^{2}}"," ",0,"-9*a**(13/3)*(1 + b*x**2/a)**(1/3)/(56*a**2*b**2 + 56*a*b**3*x**2) + 9*a**(13/3)/(56*a**2*b**2 + 56*a*b**3*x**2) - 6*a**(10/3)*b*x**2*(1 + b*x**2/a)**(1/3)/(56*a**2*b**2 + 56*a*b**3*x**2) + 9*a**(10/3)*b*x**2/(56*a**2*b**2 + 56*a*b**3*x**2) + 15*a**(7/3)*b**2*x**4*(1 + b*x**2/a)**(1/3)/(56*a**2*b**2 + 56*a*b**3*x**2) + 12*a**(4/3)*b**3*x**6*(1 + b*x**2/a)**(1/3)/(56*a**2*b**2 + 56*a*b**3*x**2)","B",0
668,1,42,0,0.195187," ","integrate(x*(b*x**2+a)**(1/3),x)","\begin{cases} \frac{3 a \sqrt[3]{a + b x^{2}}}{8 b} + \frac{3 x^{2} \sqrt[3]{a + b x^{2}}}{8} & \text{for}\: b \neq 0 \\\frac{\sqrt[3]{a} x^{2}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*a*(a + b*x**2)**(1/3)/(8*b) + 3*x**2*(a + b*x**2)**(1/3)/8, Ne(b, 0)), (a**(1/3)*x**2/2, True))","A",0
669,1,46,0,1.066230," ","integrate((b*x**2+a)**(1/3)/x,x)","- \frac{\sqrt[3]{b} x^{\frac{2}{3}} \Gamma\left(- \frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, - \frac{1}{3} \\ \frac{2}{3} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{2}}} \right)}}{2 \Gamma\left(\frac{2}{3}\right)}"," ",0,"-b**(1/3)*x**(2/3)*gamma(-1/3)*hyper((-1/3, -1/3), (2/3,), a*exp_polar(I*pi)/(b*x**2))/(2*gamma(2/3))","C",0
670,1,42,0,1.195116," ","integrate((b*x**2+a)**(1/3)/x**3,x)","- \frac{\sqrt[3]{b} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{2}}} \right)}}{2 x^{\frac{4}{3}} \Gamma\left(\frac{5}{3}\right)}"," ",0,"-b**(1/3)*gamma(2/3)*hyper((-1/3, 2/3), (5/3,), a*exp_polar(I*pi)/(b*x**2))/(2*x**(4/3)*gamma(5/3))","C",0
671,1,42,0,1.386872," ","integrate((b*x**2+a)**(1/3)/x**5,x)","- \frac{\sqrt[3]{b} \Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{5}{3} \\ \frac{8}{3} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{2}}} \right)}}{2 x^{\frac{10}{3}} \Gamma\left(\frac{8}{3}\right)}"," ",0,"-b**(1/3)*gamma(5/3)*hyper((-1/3, 5/3), (8/3,), a*exp_polar(I*pi)/(b*x**2))/(2*x**(10/3)*gamma(8/3))","C",0
672,1,29,0,0.932604," ","integrate(x**4*(b*x**2+a)**(1/3),x)","\frac{\sqrt[3]{a} x^{5} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{5}"," ",0,"a**(1/3)*x**5*hyper((-1/3, 5/2), (7/2,), b*x**2*exp_polar(I*pi)/a)/5","A",0
673,1,29,0,0.841201," ","integrate(x**2*(b*x**2+a)**(1/3),x)","\frac{\sqrt[3]{a} x^{3} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{3}"," ",0,"a**(1/3)*x**3*hyper((-1/3, 3/2), (5/2,), b*x**2*exp_polar(I*pi)/a)/3","A",0
674,1,26,0,0.784190," ","integrate((b*x**2+a)**(1/3),x)","\sqrt[3]{a} x {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}"," ",0,"a**(1/3)*x*hyper((-1/3, 1/2), (3/2,), b*x**2*exp_polar(I*pi)/a)","A",0
675,1,29,0,0.827072," ","integrate((b*x**2+a)**(1/3)/x**2,x)","- \frac{\sqrt[3]{a} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{3} \\ \frac{1}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{x}"," ",0,"-a**(1/3)*hyper((-1/2, -1/3), (1/2,), b*x**2*exp_polar(I*pi)/a)/x","A",0
676,1,34,0,0.946488," ","integrate((b*x**2+a)**(1/3)/x**4,x)","- \frac{\sqrt[3]{a} {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, - \frac{1}{3} \\ - \frac{1}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{3 x^{3}}"," ",0,"-a**(1/3)*hyper((-3/2, -1/3), (-1/2,), b*x**2*exp_polar(I*pi)/a)/(3*x**3)","A",0
677,1,1795,0,2.940703," ","integrate(x**7*(b*x**2+a)**(2/3),x)","- \frac{243 a^{\frac{74}{3}} \left(1 + \frac{b x^{2}}{a}\right)^{\frac{2}{3}}}{6160 a^{20} b^{4} + 36960 a^{19} b^{5} x^{2} + 92400 a^{18} b^{6} x^{4} + 123200 a^{17} b^{7} x^{6} + 92400 a^{16} b^{8} x^{8} + 36960 a^{15} b^{9} x^{10} + 6160 a^{14} b^{10} x^{12}} + \frac{243 a^{\frac{74}{3}}}{6160 a^{20} b^{4} + 36960 a^{19} b^{5} x^{2} + 92400 a^{18} b^{6} x^{4} + 123200 a^{17} b^{7} x^{6} + 92400 a^{16} b^{8} x^{8} + 36960 a^{15} b^{9} x^{10} + 6160 a^{14} b^{10} x^{12}} - \frac{1296 a^{\frac{71}{3}} b x^{2} \left(1 + \frac{b x^{2}}{a}\right)^{\frac{2}{3}}}{6160 a^{20} b^{4} + 36960 a^{19} b^{5} x^{2} + 92400 a^{18} b^{6} x^{4} + 123200 a^{17} b^{7} x^{6} + 92400 a^{16} b^{8} x^{8} + 36960 a^{15} b^{9} x^{10} + 6160 a^{14} b^{10} x^{12}} + \frac{1458 a^{\frac{71}{3}} b x^{2}}{6160 a^{20} b^{4} + 36960 a^{19} b^{5} x^{2} + 92400 a^{18} b^{6} x^{4} + 123200 a^{17} b^{7} x^{6} + 92400 a^{16} b^{8} x^{8} + 36960 a^{15} b^{9} x^{10} + 6160 a^{14} b^{10} x^{12}} - \frac{2808 a^{\frac{68}{3}} b^{2} x^{4} \left(1 + \frac{b x^{2}}{a}\right)^{\frac{2}{3}}}{6160 a^{20} b^{4} + 36960 a^{19} b^{5} x^{2} + 92400 a^{18} b^{6} x^{4} + 123200 a^{17} b^{7} x^{6} + 92400 a^{16} b^{8} x^{8} + 36960 a^{15} b^{9} x^{10} + 6160 a^{14} b^{10} x^{12}} + \frac{3645 a^{\frac{68}{3}} b^{2} x^{4}}{6160 a^{20} b^{4} + 36960 a^{19} b^{5} x^{2} + 92400 a^{18} b^{6} x^{4} + 123200 a^{17} b^{7} x^{6} + 92400 a^{16} b^{8} x^{8} + 36960 a^{15} b^{9} x^{10} + 6160 a^{14} b^{10} x^{12}} - \frac{3120 a^{\frac{65}{3}} b^{3} x^{6} \left(1 + \frac{b x^{2}}{a}\right)^{\frac{2}{3}}}{6160 a^{20} b^{4} + 36960 a^{19} b^{5} x^{2} + 92400 a^{18} b^{6} x^{4} + 123200 a^{17} b^{7} x^{6} + 92400 a^{16} b^{8} x^{8} + 36960 a^{15} b^{9} x^{10} + 6160 a^{14} b^{10} x^{12}} + \frac{4860 a^{\frac{65}{3}} b^{3} x^{6}}{6160 a^{20} b^{4} + 36960 a^{19} b^{5} x^{2} + 92400 a^{18} b^{6} x^{4} + 123200 a^{17} b^{7} x^{6} + 92400 a^{16} b^{8} x^{8} + 36960 a^{15} b^{9} x^{10} + 6160 a^{14} b^{10} x^{12}} - \frac{1050 a^{\frac{62}{3}} b^{4} x^{8} \left(1 + \frac{b x^{2}}{a}\right)^{\frac{2}{3}}}{6160 a^{20} b^{4} + 36960 a^{19} b^{5} x^{2} + 92400 a^{18} b^{6} x^{4} + 123200 a^{17} b^{7} x^{6} + 92400 a^{16} b^{8} x^{8} + 36960 a^{15} b^{9} x^{10} + 6160 a^{14} b^{10} x^{12}} + \frac{3645 a^{\frac{62}{3}} b^{4} x^{8}}{6160 a^{20} b^{4} + 36960 a^{19} b^{5} x^{2} + 92400 a^{18} b^{6} x^{4} + 123200 a^{17} b^{7} x^{6} + 92400 a^{16} b^{8} x^{8} + 36960 a^{15} b^{9} x^{10} + 6160 a^{14} b^{10} x^{12}} + \frac{4032 a^{\frac{59}{3}} b^{5} x^{10} \left(1 + \frac{b x^{2}}{a}\right)^{\frac{2}{3}}}{6160 a^{20} b^{4} + 36960 a^{19} b^{5} x^{2} + 92400 a^{18} b^{6} x^{4} + 123200 a^{17} b^{7} x^{6} + 92400 a^{16} b^{8} x^{8} + 36960 a^{15} b^{9} x^{10} + 6160 a^{14} b^{10} x^{12}} + \frac{1458 a^{\frac{59}{3}} b^{5} x^{10}}{6160 a^{20} b^{4} + 36960 a^{19} b^{5} x^{2} + 92400 a^{18} b^{6} x^{4} + 123200 a^{17} b^{7} x^{6} + 92400 a^{16} b^{8} x^{8} + 36960 a^{15} b^{9} x^{10} + 6160 a^{14} b^{10} x^{12}} + \frac{11004 a^{\frac{56}{3}} b^{6} x^{12} \left(1 + \frac{b x^{2}}{a}\right)^{\frac{2}{3}}}{6160 a^{20} b^{4} + 36960 a^{19} b^{5} x^{2} + 92400 a^{18} b^{6} x^{4} + 123200 a^{17} b^{7} x^{6} + 92400 a^{16} b^{8} x^{8} + 36960 a^{15} b^{9} x^{10} + 6160 a^{14} b^{10} x^{12}} + \frac{243 a^{\frac{56}{3}} b^{6} x^{12}}{6160 a^{20} b^{4} + 36960 a^{19} b^{5} x^{2} + 92400 a^{18} b^{6} x^{4} + 123200 a^{17} b^{7} x^{6} + 92400 a^{16} b^{8} x^{8} + 36960 a^{15} b^{9} x^{10} + 6160 a^{14} b^{10} x^{12}} + \frac{14352 a^{\frac{53}{3}} b^{7} x^{14} \left(1 + \frac{b x^{2}}{a}\right)^{\frac{2}{3}}}{6160 a^{20} b^{4} + 36960 a^{19} b^{5} x^{2} + 92400 a^{18} b^{6} x^{4} + 123200 a^{17} b^{7} x^{6} + 92400 a^{16} b^{8} x^{8} + 36960 a^{15} b^{9} x^{10} + 6160 a^{14} b^{10} x^{12}} + \frac{10485 a^{\frac{50}{3}} b^{8} x^{16} \left(1 + \frac{b x^{2}}{a}\right)^{\frac{2}{3}}}{6160 a^{20} b^{4} + 36960 a^{19} b^{5} x^{2} + 92400 a^{18} b^{6} x^{4} + 123200 a^{17} b^{7} x^{6} + 92400 a^{16} b^{8} x^{8} + 36960 a^{15} b^{9} x^{10} + 6160 a^{14} b^{10} x^{12}} + \frac{4080 a^{\frac{47}{3}} b^{9} x^{18} \left(1 + \frac{b x^{2}}{a}\right)^{\frac{2}{3}}}{6160 a^{20} b^{4} + 36960 a^{19} b^{5} x^{2} + 92400 a^{18} b^{6} x^{4} + 123200 a^{17} b^{7} x^{6} + 92400 a^{16} b^{8} x^{8} + 36960 a^{15} b^{9} x^{10} + 6160 a^{14} b^{10} x^{12}} + \frac{660 a^{\frac{44}{3}} b^{10} x^{20} \left(1 + \frac{b x^{2}}{a}\right)^{\frac{2}{3}}}{6160 a^{20} b^{4} + 36960 a^{19} b^{5} x^{2} + 92400 a^{18} b^{6} x^{4} + 123200 a^{17} b^{7} x^{6} + 92400 a^{16} b^{8} x^{8} + 36960 a^{15} b^{9} x^{10} + 6160 a^{14} b^{10} x^{12}}"," ",0,"-243*a**(74/3)*(1 + b*x**2/a)**(2/3)/(6160*a**20*b**4 + 36960*a**19*b**5*x**2 + 92400*a**18*b**6*x**4 + 123200*a**17*b**7*x**6 + 92400*a**16*b**8*x**8 + 36960*a**15*b**9*x**10 + 6160*a**14*b**10*x**12) + 243*a**(74/3)/(6160*a**20*b**4 + 36960*a**19*b**5*x**2 + 92400*a**18*b**6*x**4 + 123200*a**17*b**7*x**6 + 92400*a**16*b**8*x**8 + 36960*a**15*b**9*x**10 + 6160*a**14*b**10*x**12) - 1296*a**(71/3)*b*x**2*(1 + b*x**2/a)**(2/3)/(6160*a**20*b**4 + 36960*a**19*b**5*x**2 + 92400*a**18*b**6*x**4 + 123200*a**17*b**7*x**6 + 92400*a**16*b**8*x**8 + 36960*a**15*b**9*x**10 + 6160*a**14*b**10*x**12) + 1458*a**(71/3)*b*x**2/(6160*a**20*b**4 + 36960*a**19*b**5*x**2 + 92400*a**18*b**6*x**4 + 123200*a**17*b**7*x**6 + 92400*a**16*b**8*x**8 + 36960*a**15*b**9*x**10 + 6160*a**14*b**10*x**12) - 2808*a**(68/3)*b**2*x**4*(1 + b*x**2/a)**(2/3)/(6160*a**20*b**4 + 36960*a**19*b**5*x**2 + 92400*a**18*b**6*x**4 + 123200*a**17*b**7*x**6 + 92400*a**16*b**8*x**8 + 36960*a**15*b**9*x**10 + 6160*a**14*b**10*x**12) + 3645*a**(68/3)*b**2*x**4/(6160*a**20*b**4 + 36960*a**19*b**5*x**2 + 92400*a**18*b**6*x**4 + 123200*a**17*b**7*x**6 + 92400*a**16*b**8*x**8 + 36960*a**15*b**9*x**10 + 6160*a**14*b**10*x**12) - 3120*a**(65/3)*b**3*x**6*(1 + b*x**2/a)**(2/3)/(6160*a**20*b**4 + 36960*a**19*b**5*x**2 + 92400*a**18*b**6*x**4 + 123200*a**17*b**7*x**6 + 92400*a**16*b**8*x**8 + 36960*a**15*b**9*x**10 + 6160*a**14*b**10*x**12) + 4860*a**(65/3)*b**3*x**6/(6160*a**20*b**4 + 36960*a**19*b**5*x**2 + 92400*a**18*b**6*x**4 + 123200*a**17*b**7*x**6 + 92400*a**16*b**8*x**8 + 36960*a**15*b**9*x**10 + 6160*a**14*b**10*x**12) - 1050*a**(62/3)*b**4*x**8*(1 + b*x**2/a)**(2/3)/(6160*a**20*b**4 + 36960*a**19*b**5*x**2 + 92400*a**18*b**6*x**4 + 123200*a**17*b**7*x**6 + 92400*a**16*b**8*x**8 + 36960*a**15*b**9*x**10 + 6160*a**14*b**10*x**12) + 3645*a**(62/3)*b**4*x**8/(6160*a**20*b**4 + 36960*a**19*b**5*x**2 + 92400*a**18*b**6*x**4 + 123200*a**17*b**7*x**6 + 92400*a**16*b**8*x**8 + 36960*a**15*b**9*x**10 + 6160*a**14*b**10*x**12) + 4032*a**(59/3)*b**5*x**10*(1 + b*x**2/a)**(2/3)/(6160*a**20*b**4 + 36960*a**19*b**5*x**2 + 92400*a**18*b**6*x**4 + 123200*a**17*b**7*x**6 + 92400*a**16*b**8*x**8 + 36960*a**15*b**9*x**10 + 6160*a**14*b**10*x**12) + 1458*a**(59/3)*b**5*x**10/(6160*a**20*b**4 + 36960*a**19*b**5*x**2 + 92400*a**18*b**6*x**4 + 123200*a**17*b**7*x**6 + 92400*a**16*b**8*x**8 + 36960*a**15*b**9*x**10 + 6160*a**14*b**10*x**12) + 11004*a**(56/3)*b**6*x**12*(1 + b*x**2/a)**(2/3)/(6160*a**20*b**4 + 36960*a**19*b**5*x**2 + 92400*a**18*b**6*x**4 + 123200*a**17*b**7*x**6 + 92400*a**16*b**8*x**8 + 36960*a**15*b**9*x**10 + 6160*a**14*b**10*x**12) + 243*a**(56/3)*b**6*x**12/(6160*a**20*b**4 + 36960*a**19*b**5*x**2 + 92400*a**18*b**6*x**4 + 123200*a**17*b**7*x**6 + 92400*a**16*b**8*x**8 + 36960*a**15*b**9*x**10 + 6160*a**14*b**10*x**12) + 14352*a**(53/3)*b**7*x**14*(1 + b*x**2/a)**(2/3)/(6160*a**20*b**4 + 36960*a**19*b**5*x**2 + 92400*a**18*b**6*x**4 + 123200*a**17*b**7*x**6 + 92400*a**16*b**8*x**8 + 36960*a**15*b**9*x**10 + 6160*a**14*b**10*x**12) + 10485*a**(50/3)*b**8*x**16*(1 + b*x**2/a)**(2/3)/(6160*a**20*b**4 + 36960*a**19*b**5*x**2 + 92400*a**18*b**6*x**4 + 123200*a**17*b**7*x**6 + 92400*a**16*b**8*x**8 + 36960*a**15*b**9*x**10 + 6160*a**14*b**10*x**12) + 4080*a**(47/3)*b**9*x**18*(1 + b*x**2/a)**(2/3)/(6160*a**20*b**4 + 36960*a**19*b**5*x**2 + 92400*a**18*b**6*x**4 + 123200*a**17*b**7*x**6 + 92400*a**16*b**8*x**8 + 36960*a**15*b**9*x**10 + 6160*a**14*b**10*x**12) + 660*a**(44/3)*b**10*x**20*(1 + b*x**2/a)**(2/3)/(6160*a**20*b**4 + 36960*a**19*b**5*x**2 + 92400*a**18*b**6*x**4 + 123200*a**17*b**7*x**6 + 92400*a**16*b**8*x**8 + 36960*a**15*b**9*x**10 + 6160*a**14*b**10*x**12)","B",0
678,1,700,0,1.995959," ","integrate(x**5*(b*x**2+a)**(2/3),x)","\frac{27 a^{\frac{35}{3}} \left(1 + \frac{b x^{2}}{a}\right)^{\frac{2}{3}}}{440 a^{8} b^{3} + 1320 a^{7} b^{4} x^{2} + 1320 a^{6} b^{5} x^{4} + 440 a^{5} b^{6} x^{6}} - \frac{27 a^{\frac{35}{3}}}{440 a^{8} b^{3} + 1320 a^{7} b^{4} x^{2} + 1320 a^{6} b^{5} x^{4} + 440 a^{5} b^{6} x^{6}} + \frac{63 a^{\frac{32}{3}} b x^{2} \left(1 + \frac{b x^{2}}{a}\right)^{\frac{2}{3}}}{440 a^{8} b^{3} + 1320 a^{7} b^{4} x^{2} + 1320 a^{6} b^{5} x^{4} + 440 a^{5} b^{6} x^{6}} - \frac{81 a^{\frac{32}{3}} b x^{2}}{440 a^{8} b^{3} + 1320 a^{7} b^{4} x^{2} + 1320 a^{6} b^{5} x^{4} + 440 a^{5} b^{6} x^{6}} + \frac{42 a^{\frac{29}{3}} b^{2} x^{4} \left(1 + \frac{b x^{2}}{a}\right)^{\frac{2}{3}}}{440 a^{8} b^{3} + 1320 a^{7} b^{4} x^{2} + 1320 a^{6} b^{5} x^{4} + 440 a^{5} b^{6} x^{6}} - \frac{81 a^{\frac{29}{3}} b^{2} x^{4}}{440 a^{8} b^{3} + 1320 a^{7} b^{4} x^{2} + 1320 a^{6} b^{5} x^{4} + 440 a^{5} b^{6} x^{6}} + \frac{78 a^{\frac{26}{3}} b^{3} x^{6} \left(1 + \frac{b x^{2}}{a}\right)^{\frac{2}{3}}}{440 a^{8} b^{3} + 1320 a^{7} b^{4} x^{2} + 1320 a^{6} b^{5} x^{4} + 440 a^{5} b^{6} x^{6}} - \frac{27 a^{\frac{26}{3}} b^{3} x^{6}}{440 a^{8} b^{3} + 1320 a^{7} b^{4} x^{2} + 1320 a^{6} b^{5} x^{4} + 440 a^{5} b^{6} x^{6}} + \frac{207 a^{\frac{23}{3}} b^{4} x^{8} \left(1 + \frac{b x^{2}}{a}\right)^{\frac{2}{3}}}{440 a^{8} b^{3} + 1320 a^{7} b^{4} x^{2} + 1320 a^{6} b^{5} x^{4} + 440 a^{5} b^{6} x^{6}} + \frac{195 a^{\frac{20}{3}} b^{5} x^{10} \left(1 + \frac{b x^{2}}{a}\right)^{\frac{2}{3}}}{440 a^{8} b^{3} + 1320 a^{7} b^{4} x^{2} + 1320 a^{6} b^{5} x^{4} + 440 a^{5} b^{6} x^{6}} + \frac{60 a^{\frac{17}{3}} b^{6} x^{12} \left(1 + \frac{b x^{2}}{a}\right)^{\frac{2}{3}}}{440 a^{8} b^{3} + 1320 a^{7} b^{4} x^{2} + 1320 a^{6} b^{5} x^{4} + 440 a^{5} b^{6} x^{6}}"," ",0,"27*a**(35/3)*(1 + b*x**2/a)**(2/3)/(440*a**8*b**3 + 1320*a**7*b**4*x**2 + 1320*a**6*b**5*x**4 + 440*a**5*b**6*x**6) - 27*a**(35/3)/(440*a**8*b**3 + 1320*a**7*b**4*x**2 + 1320*a**6*b**5*x**4 + 440*a**5*b**6*x**6) + 63*a**(32/3)*b*x**2*(1 + b*x**2/a)**(2/3)/(440*a**8*b**3 + 1320*a**7*b**4*x**2 + 1320*a**6*b**5*x**4 + 440*a**5*b**6*x**6) - 81*a**(32/3)*b*x**2/(440*a**8*b**3 + 1320*a**7*b**4*x**2 + 1320*a**6*b**5*x**4 + 440*a**5*b**6*x**6) + 42*a**(29/3)*b**2*x**4*(1 + b*x**2/a)**(2/3)/(440*a**8*b**3 + 1320*a**7*b**4*x**2 + 1320*a**6*b**5*x**4 + 440*a**5*b**6*x**6) - 81*a**(29/3)*b**2*x**4/(440*a**8*b**3 + 1320*a**7*b**4*x**2 + 1320*a**6*b**5*x**4 + 440*a**5*b**6*x**6) + 78*a**(26/3)*b**3*x**6*(1 + b*x**2/a)**(2/3)/(440*a**8*b**3 + 1320*a**7*b**4*x**2 + 1320*a**6*b**5*x**4 + 440*a**5*b**6*x**6) - 27*a**(26/3)*b**3*x**6/(440*a**8*b**3 + 1320*a**7*b**4*x**2 + 1320*a**6*b**5*x**4 + 440*a**5*b**6*x**6) + 207*a**(23/3)*b**4*x**8*(1 + b*x**2/a)**(2/3)/(440*a**8*b**3 + 1320*a**7*b**4*x**2 + 1320*a**6*b**5*x**4 + 440*a**5*b**6*x**6) + 195*a**(20/3)*b**5*x**10*(1 + b*x**2/a)**(2/3)/(440*a**8*b**3 + 1320*a**7*b**4*x**2 + 1320*a**6*b**5*x**4 + 440*a**5*b**6*x**6) + 60*a**(17/3)*b**6*x**12*(1 + b*x**2/a)**(2/3)/(440*a**8*b**3 + 1320*a**7*b**4*x**2 + 1320*a**6*b**5*x**4 + 440*a**5*b**6*x**6)","B",0
679,1,66,0,0.751292," ","integrate(x**3*(b*x**2+a)**(2/3),x)","\begin{cases} - \frac{9 a^{2} \left(a + b x^{2}\right)^{\frac{2}{3}}}{80 b^{2}} + \frac{3 a x^{2} \left(a + b x^{2}\right)^{\frac{2}{3}}}{40 b} + \frac{3 x^{4} \left(a + b x^{2}\right)^{\frac{2}{3}}}{16} & \text{for}\: b \neq 0 \\\frac{a^{\frac{2}{3}} x^{4}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-9*a**2*(a + b*x**2)**(2/3)/(80*b**2) + 3*a*x**2*(a + b*x**2)**(2/3)/(40*b) + 3*x**4*(a + b*x**2)**(2/3)/16, Ne(b, 0)), (a**(2/3)*x**4/4, True))","A",0
680,1,42,0,0.373510," ","integrate(x*(b*x**2+a)**(2/3),x)","\begin{cases} \frac{3 a \left(a + b x^{2}\right)^{\frac{2}{3}}}{10 b} + \frac{3 x^{2} \left(a + b x^{2}\right)^{\frac{2}{3}}}{10} & \text{for}\: b \neq 0 \\\frac{a^{\frac{2}{3}} x^{2}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*a*(a + b*x**2)**(2/3)/(10*b) + 3*x**2*(a + b*x**2)**(2/3)/10, Ne(b, 0)), (a**(2/3)*x**2/2, True))","A",0
681,1,46,0,1.115609," ","integrate((b*x**2+a)**(2/3)/x,x)","- \frac{b^{\frac{2}{3}} x^{\frac{4}{3}} \Gamma\left(- \frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, - \frac{2}{3} \\ \frac{1}{3} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{2}}} \right)}}{2 \Gamma\left(\frac{1}{3}\right)}"," ",0,"-b**(2/3)*x**(4/3)*gamma(-2/3)*hyper((-2/3, -2/3), (1/3,), a*exp_polar(I*pi)/(b*x**2))/(2*gamma(1/3))","C",0
682,1,42,0,1.219131," ","integrate((b*x**2+a)**(2/3)/x**3,x)","- \frac{b^{\frac{2}{3}} \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{2}}} \right)}}{2 x^{\frac{2}{3}} \Gamma\left(\frac{4}{3}\right)}"," ",0,"-b**(2/3)*gamma(1/3)*hyper((-2/3, 1/3), (4/3,), a*exp_polar(I*pi)/(b*x**2))/(2*x**(2/3)*gamma(4/3))","C",0
683,1,42,0,1.412275," ","integrate((b*x**2+a)**(2/3)/x**5,x)","- \frac{b^{\frac{2}{3}} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{2}}} \right)}}{2 x^{\frac{8}{3}} \Gamma\left(\frac{7}{3}\right)}"," ",0,"-b**(2/3)*gamma(4/3)*hyper((-2/3, 4/3), (7/3,), a*exp_polar(I*pi)/(b*x**2))/(2*x**(8/3)*gamma(7/3))","C",0
684,1,29,0,0.995847," ","integrate(x**4*(b*x**2+a)**(2/3),x)","\frac{a^{\frac{2}{3}} x^{5} {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{5}"," ",0,"a**(2/3)*x**5*hyper((-2/3, 5/2), (7/2,), b*x**2*exp_polar(I*pi)/a)/5","A",0
685,1,29,0,0.906386," ","integrate(x**2*(b*x**2+a)**(2/3),x)","\frac{a^{\frac{2}{3}} x^{3} {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{3}"," ",0,"a**(2/3)*x**3*hyper((-2/3, 3/2), (5/2,), b*x**2*exp_polar(I*pi)/a)/3","A",0
686,1,26,0,0.811662," ","integrate((b*x**2+a)**(2/3),x)","a^{\frac{2}{3}} x {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}"," ",0,"a**(2/3)*x*hyper((-2/3, 1/2), (3/2,), b*x**2*exp_polar(I*pi)/a)","A",0
687,1,29,0,0.887859," ","integrate((b*x**2+a)**(2/3)/x**2,x)","- \frac{a^{\frac{2}{3}} {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, - \frac{1}{2} \\ \frac{1}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{x}"," ",0,"-a**(2/3)*hyper((-2/3, -1/2), (1/2,), b*x**2*exp_polar(I*pi)/a)/x","A",0
688,1,34,0,0.984084," ","integrate((b*x**2+a)**(2/3)/x**4,x)","- \frac{a^{\frac{2}{3}} {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, - \frac{2}{3} \\ - \frac{1}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{3 x^{3}}"," ",0,"-a**(2/3)*hyper((-3/2, -2/3), (-1/2,), b*x**2*exp_polar(I*pi)/a)/(3*x**3)","A",0
689,1,136,0,6.578038," ","integrate(x**7*(b*x**2+a)**(4/3),x)","\begin{cases} - \frac{243 a^{5} \sqrt[3]{a + b x^{2}}}{14560 b^{4}} + \frac{81 a^{4} x^{2} \sqrt[3]{a + b x^{2}}}{14560 b^{3}} - \frac{27 a^{3} x^{4} \sqrt[3]{a + b x^{2}}}{7280 b^{2}} + \frac{3 a^{2} x^{6} \sqrt[3]{a + b x^{2}}}{1040 b} + \frac{51 a x^{8} \sqrt[3]{a + b x^{2}}}{416} + \frac{3 b x^{10} \sqrt[3]{a + b x^{2}}}{32} & \text{for}\: b \neq 0 \\\frac{a^{\frac{4}{3}} x^{8}}{8} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-243*a**5*(a + b*x**2)**(1/3)/(14560*b**4) + 81*a**4*x**2*(a + b*x**2)**(1/3)/(14560*b**3) - 27*a**3*x**4*(a + b*x**2)**(1/3)/(7280*b**2) + 3*a**2*x**6*(a + b*x**2)**(1/3)/(1040*b) + 51*a*x**8*(a + b*x**2)**(1/3)/416 + 3*b*x**10*(a + b*x**2)**(1/3)/32, Ne(b, 0)), (a**(4/3)*x**8/8, True))","A",0
690,1,112,0,3.978782," ","integrate(x**5*(b*x**2+a)**(4/3),x)","\begin{cases} \frac{27 a^{4} \sqrt[3]{a + b x^{2}}}{910 b^{3}} - \frac{9 a^{3} x^{2} \sqrt[3]{a + b x^{2}}}{910 b^{2}} + \frac{3 a^{2} x^{4} \sqrt[3]{a + b x^{2}}}{455 b} + \frac{21 a x^{6} \sqrt[3]{a + b x^{2}}}{130} + \frac{3 b x^{8} \sqrt[3]{a + b x^{2}}}{26} & \text{for}\: b \neq 0 \\\frac{a^{\frac{4}{3}} x^{6}}{6} & \text{otherwise} \end{cases}"," ",0,"Piecewise((27*a**4*(a + b*x**2)**(1/3)/(910*b**3) - 9*a**3*x**2*(a + b*x**2)**(1/3)/(910*b**2) + 3*a**2*x**4*(a + b*x**2)**(1/3)/(455*b) + 21*a*x**6*(a + b*x**2)**(1/3)/130 + 3*b*x**8*(a + b*x**2)**(1/3)/26, Ne(b, 0)), (a**(4/3)*x**6/6, True))","A",0
691,1,88,0,2.540539," ","integrate(x**3*(b*x**2+a)**(4/3),x)","\begin{cases} - \frac{9 a^{3} \sqrt[3]{a + b x^{2}}}{140 b^{2}} + \frac{3 a^{2} x^{2} \sqrt[3]{a + b x^{2}}}{140 b} + \frac{33 a x^{4} \sqrt[3]{a + b x^{2}}}{140} + \frac{3 b x^{6} \sqrt[3]{a + b x^{2}}}{20} & \text{for}\: b \neq 0 \\\frac{a^{\frac{4}{3}} x^{4}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-9*a**3*(a + b*x**2)**(1/3)/(140*b**2) + 3*a**2*x**2*(a + b*x**2)**(1/3)/(140*b) + 33*a*x**4*(a + b*x**2)**(1/3)/140 + 3*b*x**6*(a + b*x**2)**(1/3)/20, Ne(b, 0)), (a**(4/3)*x**4/4, True))","A",0
692,1,65,0,1.368674," ","integrate(x*(b*x**2+a)**(4/3),x)","\begin{cases} \frac{3 a^{2} \sqrt[3]{a + b x^{2}}}{14 b} + \frac{3 a x^{2} \sqrt[3]{a + b x^{2}}}{7} + \frac{3 b x^{4} \sqrt[3]{a + b x^{2}}}{14} & \text{for}\: b \neq 0 \\\frac{a^{\frac{4}{3}} x^{2}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*a**2*(a + b*x**2)**(1/3)/(14*b) + 3*a*x**2*(a + b*x**2)**(1/3)/7 + 3*b*x**4*(a + b*x**2)**(1/3)/14, Ne(b, 0)), (a**(4/3)*x**2/2, True))","A",0
693,1,49,0,1.303274," ","integrate((b*x**2+a)**(4/3)/x,x)","- \frac{b^{\frac{4}{3}} x^{\frac{8}{3}} \Gamma\left(- \frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{4}{3}, - \frac{4}{3} \\ - \frac{1}{3} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{2}}} \right)}}{2 \Gamma\left(- \frac{1}{3}\right)}"," ",0,"-b**(4/3)*x**(8/3)*gamma(-4/3)*hyper((-4/3, -4/3), (-1/3,), a*exp_polar(I*pi)/(b*x**2))/(2*gamma(-1/3))","C",0
694,1,46,0,1.413996," ","integrate((b*x**2+a)**(4/3)/x**3,x)","- \frac{b^{\frac{4}{3}} x^{\frac{2}{3}} \Gamma\left(- \frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{4}{3}, - \frac{1}{3} \\ \frac{2}{3} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{2}}} \right)}}{2 \Gamma\left(\frac{2}{3}\right)}"," ",0,"-b**(4/3)*x**(2/3)*gamma(-1/3)*hyper((-4/3, -1/3), (2/3,), a*exp_polar(I*pi)/(b*x**2))/(2*gamma(2/3))","C",0
695,1,42,0,1.535747," ","integrate((b*x**2+a)**(4/3)/x**5,x)","- \frac{b^{\frac{4}{3}} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{4}{3}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{2}}} \right)}}{2 x^{\frac{4}{3}} \Gamma\left(\frac{5}{3}\right)}"," ",0,"-b**(4/3)*gamma(2/3)*hyper((-4/3, 2/3), (5/3,), a*exp_polar(I*pi)/(b*x**2))/(2*x**(4/3)*gamma(5/3))","C",0
696,1,29,0,1.270920," ","integrate(x**4*(b*x**2+a)**(4/3),x)","\frac{a^{\frac{4}{3}} x^{5} {{}_{2}F_{1}\left(\begin{matrix} - \frac{4}{3}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{5}"," ",0,"a**(4/3)*x**5*hyper((-4/3, 5/2), (7/2,), b*x**2*exp_polar(I*pi)/a)/5","A",0
697,1,29,0,1.137799," ","integrate(x**2*(b*x**2+a)**(4/3),x)","\frac{a^{\frac{4}{3}} x^{3} {{}_{2}F_{1}\left(\begin{matrix} - \frac{4}{3}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{3}"," ",0,"a**(4/3)*x**3*hyper((-4/3, 3/2), (5/2,), b*x**2*exp_polar(I*pi)/a)/3","A",0
698,1,26,0,0.990301," ","integrate((b*x**2+a)**(4/3),x)","a^{\frac{4}{3}} x {{}_{2}F_{1}\left(\begin{matrix} - \frac{4}{3}, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}"," ",0,"a**(4/3)*x*hyper((-4/3, 1/2), (3/2,), b*x**2*exp_polar(I*pi)/a)","A",0
699,1,29,0,1.092640," ","integrate((b*x**2+a)**(4/3)/x**2,x)","- \frac{a^{\frac{4}{3}} {{}_{2}F_{1}\left(\begin{matrix} - \frac{4}{3}, - \frac{1}{2} \\ \frac{1}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{x}"," ",0,"-a**(4/3)*hyper((-4/3, -1/2), (1/2,), b*x**2*exp_polar(I*pi)/a)/x","A",0
700,1,34,0,1.086686," ","integrate((b*x**2+a)**(4/3)/x**4,x)","- \frac{a^{\frac{4}{3}} {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, - \frac{4}{3} \\ - \frac{1}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{3 x^{3}}"," ",0,"-a**(4/3)*hyper((-3/2, -4/3), (-1/2,), b*x**2*exp_polar(I*pi)/a)/(3*x**3)","A",0
701,1,56,0,2.908150," ","integrate(x*(x**2-1)**(7/3),x)","\frac{3 x^{6} \sqrt[3]{x^{2} - 1}}{20} - \frac{9 x^{4} \sqrt[3]{x^{2} - 1}}{20} + \frac{9 x^{2} \sqrt[3]{x^{2} - 1}}{20} - \frac{3 \sqrt[3]{x^{2} - 1}}{20}"," ",0,"3*x**6*(x**2 - 1)**(1/3)/20 - 9*x**4*(x**2 - 1)**(1/3)/20 + 9*x**2*(x**2 - 1)**(1/3)/20 - 3*(x**2 - 1)**(1/3)/20","B",0
702,1,1690,0,2.770846," ","integrate(x**7/(b*x**2+a)**(1/3),x)","- \frac{243 a^{\frac{71}{3}} \left(1 + \frac{b x^{2}}{a}\right)^{\frac{2}{3}}}{880 a^{20} b^{4} + 5280 a^{19} b^{5} x^{2} + 13200 a^{18} b^{6} x^{4} + 17600 a^{17} b^{7} x^{6} + 13200 a^{16} b^{8} x^{8} + 5280 a^{15} b^{9} x^{10} + 880 a^{14} b^{10} x^{12}} + \frac{243 a^{\frac{71}{3}}}{880 a^{20} b^{4} + 5280 a^{19} b^{5} x^{2} + 13200 a^{18} b^{6} x^{4} + 17600 a^{17} b^{7} x^{6} + 13200 a^{16} b^{8} x^{8} + 5280 a^{15} b^{9} x^{10} + 880 a^{14} b^{10} x^{12}} - \frac{1296 a^{\frac{68}{3}} b x^{2} \left(1 + \frac{b x^{2}}{a}\right)^{\frac{2}{3}}}{880 a^{20} b^{4} + 5280 a^{19} b^{5} x^{2} + 13200 a^{18} b^{6} x^{4} + 17600 a^{17} b^{7} x^{6} + 13200 a^{16} b^{8} x^{8} + 5280 a^{15} b^{9} x^{10} + 880 a^{14} b^{10} x^{12}} + \frac{1458 a^{\frac{68}{3}} b x^{2}}{880 a^{20} b^{4} + 5280 a^{19} b^{5} x^{2} + 13200 a^{18} b^{6} x^{4} + 17600 a^{17} b^{7} x^{6} + 13200 a^{16} b^{8} x^{8} + 5280 a^{15} b^{9} x^{10} + 880 a^{14} b^{10} x^{12}} - \frac{2808 a^{\frac{65}{3}} b^{2} x^{4} \left(1 + \frac{b x^{2}}{a}\right)^{\frac{2}{3}}}{880 a^{20} b^{4} + 5280 a^{19} b^{5} x^{2} + 13200 a^{18} b^{6} x^{4} + 17600 a^{17} b^{7} x^{6} + 13200 a^{16} b^{8} x^{8} + 5280 a^{15} b^{9} x^{10} + 880 a^{14} b^{10} x^{12}} + \frac{3645 a^{\frac{65}{3}} b^{2} x^{4}}{880 a^{20} b^{4} + 5280 a^{19} b^{5} x^{2} + 13200 a^{18} b^{6} x^{4} + 17600 a^{17} b^{7} x^{6} + 13200 a^{16} b^{8} x^{8} + 5280 a^{15} b^{9} x^{10} + 880 a^{14} b^{10} x^{12}} - \frac{3120 a^{\frac{62}{3}} b^{3} x^{6} \left(1 + \frac{b x^{2}}{a}\right)^{\frac{2}{3}}}{880 a^{20} b^{4} + 5280 a^{19} b^{5} x^{2} + 13200 a^{18} b^{6} x^{4} + 17600 a^{17} b^{7} x^{6} + 13200 a^{16} b^{8} x^{8} + 5280 a^{15} b^{9} x^{10} + 880 a^{14} b^{10} x^{12}} + \frac{4860 a^{\frac{62}{3}} b^{3} x^{6}}{880 a^{20} b^{4} + 5280 a^{19} b^{5} x^{2} + 13200 a^{18} b^{6} x^{4} + 17600 a^{17} b^{7} x^{6} + 13200 a^{16} b^{8} x^{8} + 5280 a^{15} b^{9} x^{10} + 880 a^{14} b^{10} x^{12}} - \frac{1710 a^{\frac{59}{3}} b^{4} x^{8} \left(1 + \frac{b x^{2}}{a}\right)^{\frac{2}{3}}}{880 a^{20} b^{4} + 5280 a^{19} b^{5} x^{2} + 13200 a^{18} b^{6} x^{4} + 17600 a^{17} b^{7} x^{6} + 13200 a^{16} b^{8} x^{8} + 5280 a^{15} b^{9} x^{10} + 880 a^{14} b^{10} x^{12}} + \frac{3645 a^{\frac{59}{3}} b^{4} x^{8}}{880 a^{20} b^{4} + 5280 a^{19} b^{5} x^{2} + 13200 a^{18} b^{6} x^{4} + 17600 a^{17} b^{7} x^{6} + 13200 a^{16} b^{8} x^{8} + 5280 a^{15} b^{9} x^{10} + 880 a^{14} b^{10} x^{12}} + \frac{72 a^{\frac{56}{3}} b^{5} x^{10} \left(1 + \frac{b x^{2}}{a}\right)^{\frac{2}{3}}}{880 a^{20} b^{4} + 5280 a^{19} b^{5} x^{2} + 13200 a^{18} b^{6} x^{4} + 17600 a^{17} b^{7} x^{6} + 13200 a^{16} b^{8} x^{8} + 5280 a^{15} b^{9} x^{10} + 880 a^{14} b^{10} x^{12}} + \frac{1458 a^{\frac{56}{3}} b^{5} x^{10}}{880 a^{20} b^{4} + 5280 a^{19} b^{5} x^{2} + 13200 a^{18} b^{6} x^{4} + 17600 a^{17} b^{7} x^{6} + 13200 a^{16} b^{8} x^{8} + 5280 a^{15} b^{9} x^{10} + 880 a^{14} b^{10} x^{12}} + \frac{1104 a^{\frac{53}{3}} b^{6} x^{12} \left(1 + \frac{b x^{2}}{a}\right)^{\frac{2}{3}}}{880 a^{20} b^{4} + 5280 a^{19} b^{5} x^{2} + 13200 a^{18} b^{6} x^{4} + 17600 a^{17} b^{7} x^{6} + 13200 a^{16} b^{8} x^{8} + 5280 a^{15} b^{9} x^{10} + 880 a^{14} b^{10} x^{12}} + \frac{243 a^{\frac{53}{3}} b^{6} x^{12}}{880 a^{20} b^{4} + 5280 a^{19} b^{5} x^{2} + 13200 a^{18} b^{6} x^{4} + 17600 a^{17} b^{7} x^{6} + 13200 a^{16} b^{8} x^{8} + 5280 a^{15} b^{9} x^{10} + 880 a^{14} b^{10} x^{12}} + \frac{1152 a^{\frac{50}{3}} b^{7} x^{14} \left(1 + \frac{b x^{2}}{a}\right)^{\frac{2}{3}}}{880 a^{20} b^{4} + 5280 a^{19} b^{5} x^{2} + 13200 a^{18} b^{6} x^{4} + 17600 a^{17} b^{7} x^{6} + 13200 a^{16} b^{8} x^{8} + 5280 a^{15} b^{9} x^{10} + 880 a^{14} b^{10} x^{12}} + \frac{585 a^{\frac{47}{3}} b^{8} x^{16} \left(1 + \frac{b x^{2}}{a}\right)^{\frac{2}{3}}}{880 a^{20} b^{4} + 5280 a^{19} b^{5} x^{2} + 13200 a^{18} b^{6} x^{4} + 17600 a^{17} b^{7} x^{6} + 13200 a^{16} b^{8} x^{8} + 5280 a^{15} b^{9} x^{10} + 880 a^{14} b^{10} x^{12}} + \frac{120 a^{\frac{44}{3}} b^{9} x^{18} \left(1 + \frac{b x^{2}}{a}\right)^{\frac{2}{3}}}{880 a^{20} b^{4} + 5280 a^{19} b^{5} x^{2} + 13200 a^{18} b^{6} x^{4} + 17600 a^{17} b^{7} x^{6} + 13200 a^{16} b^{8} x^{8} + 5280 a^{15} b^{9} x^{10} + 880 a^{14} b^{10} x^{12}}"," ",0,"-243*a**(71/3)*(1 + b*x**2/a)**(2/3)/(880*a**20*b**4 + 5280*a**19*b**5*x**2 + 13200*a**18*b**6*x**4 + 17600*a**17*b**7*x**6 + 13200*a**16*b**8*x**8 + 5280*a**15*b**9*x**10 + 880*a**14*b**10*x**12) + 243*a**(71/3)/(880*a**20*b**4 + 5280*a**19*b**5*x**2 + 13200*a**18*b**6*x**4 + 17600*a**17*b**7*x**6 + 13200*a**16*b**8*x**8 + 5280*a**15*b**9*x**10 + 880*a**14*b**10*x**12) - 1296*a**(68/3)*b*x**2*(1 + b*x**2/a)**(2/3)/(880*a**20*b**4 + 5280*a**19*b**5*x**2 + 13200*a**18*b**6*x**4 + 17600*a**17*b**7*x**6 + 13200*a**16*b**8*x**8 + 5280*a**15*b**9*x**10 + 880*a**14*b**10*x**12) + 1458*a**(68/3)*b*x**2/(880*a**20*b**4 + 5280*a**19*b**5*x**2 + 13200*a**18*b**6*x**4 + 17600*a**17*b**7*x**6 + 13200*a**16*b**8*x**8 + 5280*a**15*b**9*x**10 + 880*a**14*b**10*x**12) - 2808*a**(65/3)*b**2*x**4*(1 + b*x**2/a)**(2/3)/(880*a**20*b**4 + 5280*a**19*b**5*x**2 + 13200*a**18*b**6*x**4 + 17600*a**17*b**7*x**6 + 13200*a**16*b**8*x**8 + 5280*a**15*b**9*x**10 + 880*a**14*b**10*x**12) + 3645*a**(65/3)*b**2*x**4/(880*a**20*b**4 + 5280*a**19*b**5*x**2 + 13200*a**18*b**6*x**4 + 17600*a**17*b**7*x**6 + 13200*a**16*b**8*x**8 + 5280*a**15*b**9*x**10 + 880*a**14*b**10*x**12) - 3120*a**(62/3)*b**3*x**6*(1 + b*x**2/a)**(2/3)/(880*a**20*b**4 + 5280*a**19*b**5*x**2 + 13200*a**18*b**6*x**4 + 17600*a**17*b**7*x**6 + 13200*a**16*b**8*x**8 + 5280*a**15*b**9*x**10 + 880*a**14*b**10*x**12) + 4860*a**(62/3)*b**3*x**6/(880*a**20*b**4 + 5280*a**19*b**5*x**2 + 13200*a**18*b**6*x**4 + 17600*a**17*b**7*x**6 + 13200*a**16*b**8*x**8 + 5280*a**15*b**9*x**10 + 880*a**14*b**10*x**12) - 1710*a**(59/3)*b**4*x**8*(1 + b*x**2/a)**(2/3)/(880*a**20*b**4 + 5280*a**19*b**5*x**2 + 13200*a**18*b**6*x**4 + 17600*a**17*b**7*x**6 + 13200*a**16*b**8*x**8 + 5280*a**15*b**9*x**10 + 880*a**14*b**10*x**12) + 3645*a**(59/3)*b**4*x**8/(880*a**20*b**4 + 5280*a**19*b**5*x**2 + 13200*a**18*b**6*x**4 + 17600*a**17*b**7*x**6 + 13200*a**16*b**8*x**8 + 5280*a**15*b**9*x**10 + 880*a**14*b**10*x**12) + 72*a**(56/3)*b**5*x**10*(1 + b*x**2/a)**(2/3)/(880*a**20*b**4 + 5280*a**19*b**5*x**2 + 13200*a**18*b**6*x**4 + 17600*a**17*b**7*x**6 + 13200*a**16*b**8*x**8 + 5280*a**15*b**9*x**10 + 880*a**14*b**10*x**12) + 1458*a**(56/3)*b**5*x**10/(880*a**20*b**4 + 5280*a**19*b**5*x**2 + 13200*a**18*b**6*x**4 + 17600*a**17*b**7*x**6 + 13200*a**16*b**8*x**8 + 5280*a**15*b**9*x**10 + 880*a**14*b**10*x**12) + 1104*a**(53/3)*b**6*x**12*(1 + b*x**2/a)**(2/3)/(880*a**20*b**4 + 5280*a**19*b**5*x**2 + 13200*a**18*b**6*x**4 + 17600*a**17*b**7*x**6 + 13200*a**16*b**8*x**8 + 5280*a**15*b**9*x**10 + 880*a**14*b**10*x**12) + 243*a**(53/3)*b**6*x**12/(880*a**20*b**4 + 5280*a**19*b**5*x**2 + 13200*a**18*b**6*x**4 + 17600*a**17*b**7*x**6 + 13200*a**16*b**8*x**8 + 5280*a**15*b**9*x**10 + 880*a**14*b**10*x**12) + 1152*a**(50/3)*b**7*x**14*(1 + b*x**2/a)**(2/3)/(880*a**20*b**4 + 5280*a**19*b**5*x**2 + 13200*a**18*b**6*x**4 + 17600*a**17*b**7*x**6 + 13200*a**16*b**8*x**8 + 5280*a**15*b**9*x**10 + 880*a**14*b**10*x**12) + 585*a**(47/3)*b**8*x**16*(1 + b*x**2/a)**(2/3)/(880*a**20*b**4 + 5280*a**19*b**5*x**2 + 13200*a**18*b**6*x**4 + 17600*a**17*b**7*x**6 + 13200*a**16*b**8*x**8 + 5280*a**15*b**9*x**10 + 880*a**14*b**10*x**12) + 120*a**(44/3)*b**9*x**18*(1 + b*x**2/a)**(2/3)/(880*a**20*b**4 + 5280*a**19*b**5*x**2 + 13200*a**18*b**6*x**4 + 17600*a**17*b**7*x**6 + 13200*a**16*b**8*x**8 + 5280*a**15*b**9*x**10 + 880*a**14*b**10*x**12)","B",0
703,1,631,0,1.783905," ","integrate(x**5/(b*x**2+a)**(1/3),x)","\frac{27 a^{\frac{32}{3}} \left(1 + \frac{b x^{2}}{a}\right)^{\frac{2}{3}}}{80 a^{8} b^{3} + 240 a^{7} b^{4} x^{2} + 240 a^{6} b^{5} x^{4} + 80 a^{5} b^{6} x^{6}} - \frac{27 a^{\frac{32}{3}}}{80 a^{8} b^{3} + 240 a^{7} b^{4} x^{2} + 240 a^{6} b^{5} x^{4} + 80 a^{5} b^{6} x^{6}} + \frac{63 a^{\frac{29}{3}} b x^{2} \left(1 + \frac{b x^{2}}{a}\right)^{\frac{2}{3}}}{80 a^{8} b^{3} + 240 a^{7} b^{4} x^{2} + 240 a^{6} b^{5} x^{4} + 80 a^{5} b^{6} x^{6}} - \frac{81 a^{\frac{29}{3}} b x^{2}}{80 a^{8} b^{3} + 240 a^{7} b^{4} x^{2} + 240 a^{6} b^{5} x^{4} + 80 a^{5} b^{6} x^{6}} + \frac{42 a^{\frac{26}{3}} b^{2} x^{4} \left(1 + \frac{b x^{2}}{a}\right)^{\frac{2}{3}}}{80 a^{8} b^{3} + 240 a^{7} b^{4} x^{2} + 240 a^{6} b^{5} x^{4} + 80 a^{5} b^{6} x^{6}} - \frac{81 a^{\frac{26}{3}} b^{2} x^{4}}{80 a^{8} b^{3} + 240 a^{7} b^{4} x^{2} + 240 a^{6} b^{5} x^{4} + 80 a^{5} b^{6} x^{6}} + \frac{18 a^{\frac{23}{3}} b^{3} x^{6} \left(1 + \frac{b x^{2}}{a}\right)^{\frac{2}{3}}}{80 a^{8} b^{3} + 240 a^{7} b^{4} x^{2} + 240 a^{6} b^{5} x^{4} + 80 a^{5} b^{6} x^{6}} - \frac{27 a^{\frac{23}{3}} b^{3} x^{6}}{80 a^{8} b^{3} + 240 a^{7} b^{4} x^{2} + 240 a^{6} b^{5} x^{4} + 80 a^{5} b^{6} x^{6}} + \frac{27 a^{\frac{20}{3}} b^{4} x^{8} \left(1 + \frac{b x^{2}}{a}\right)^{\frac{2}{3}}}{80 a^{8} b^{3} + 240 a^{7} b^{4} x^{2} + 240 a^{6} b^{5} x^{4} + 80 a^{5} b^{6} x^{6}} + \frac{15 a^{\frac{17}{3}} b^{5} x^{10} \left(1 + \frac{b x^{2}}{a}\right)^{\frac{2}{3}}}{80 a^{8} b^{3} + 240 a^{7} b^{4} x^{2} + 240 a^{6} b^{5} x^{4} + 80 a^{5} b^{6} x^{6}}"," ",0,"27*a**(32/3)*(1 + b*x**2/a)**(2/3)/(80*a**8*b**3 + 240*a**7*b**4*x**2 + 240*a**6*b**5*x**4 + 80*a**5*b**6*x**6) - 27*a**(32/3)/(80*a**8*b**3 + 240*a**7*b**4*x**2 + 240*a**6*b**5*x**4 + 80*a**5*b**6*x**6) + 63*a**(29/3)*b*x**2*(1 + b*x**2/a)**(2/3)/(80*a**8*b**3 + 240*a**7*b**4*x**2 + 240*a**6*b**5*x**4 + 80*a**5*b**6*x**6) - 81*a**(29/3)*b*x**2/(80*a**8*b**3 + 240*a**7*b**4*x**2 + 240*a**6*b**5*x**4 + 80*a**5*b**6*x**6) + 42*a**(26/3)*b**2*x**4*(1 + b*x**2/a)**(2/3)/(80*a**8*b**3 + 240*a**7*b**4*x**2 + 240*a**6*b**5*x**4 + 80*a**5*b**6*x**6) - 81*a**(26/3)*b**2*x**4/(80*a**8*b**3 + 240*a**7*b**4*x**2 + 240*a**6*b**5*x**4 + 80*a**5*b**6*x**6) + 18*a**(23/3)*b**3*x**6*(1 + b*x**2/a)**(2/3)/(80*a**8*b**3 + 240*a**7*b**4*x**2 + 240*a**6*b**5*x**4 + 80*a**5*b**6*x**6) - 27*a**(23/3)*b**3*x**6/(80*a**8*b**3 + 240*a**7*b**4*x**2 + 240*a**6*b**5*x**4 + 80*a**5*b**6*x**6) + 27*a**(20/3)*b**4*x**8*(1 + b*x**2/a)**(2/3)/(80*a**8*b**3 + 240*a**7*b**4*x**2 + 240*a**6*b**5*x**4 + 80*a**5*b**6*x**6) + 15*a**(17/3)*b**5*x**10*(1 + b*x**2/a)**(2/3)/(80*a**8*b**3 + 240*a**7*b**4*x**2 + 240*a**6*b**5*x**4 + 80*a**5*b**6*x**6)","B",0
704,1,178,0,1.142220," ","integrate(x**3/(b*x**2+a)**(1/3),x)","- \frac{9 a^{\frac{11}{3}} \left(1 + \frac{b x^{2}}{a}\right)^{\frac{2}{3}}}{20 a^{2} b^{2} + 20 a b^{3} x^{2}} + \frac{9 a^{\frac{11}{3}}}{20 a^{2} b^{2} + 20 a b^{3} x^{2}} - \frac{3 a^{\frac{8}{3}} b x^{2} \left(1 + \frac{b x^{2}}{a}\right)^{\frac{2}{3}}}{20 a^{2} b^{2} + 20 a b^{3} x^{2}} + \frac{9 a^{\frac{8}{3}} b x^{2}}{20 a^{2} b^{2} + 20 a b^{3} x^{2}} + \frac{6 a^{\frac{5}{3}} b^{2} x^{4} \left(1 + \frac{b x^{2}}{a}\right)^{\frac{2}{3}}}{20 a^{2} b^{2} + 20 a b^{3} x^{2}}"," ",0,"-9*a**(11/3)*(1 + b*x**2/a)**(2/3)/(20*a**2*b**2 + 20*a*b**3*x**2) + 9*a**(11/3)/(20*a**2*b**2 + 20*a*b**3*x**2) - 3*a**(8/3)*b*x**2*(1 + b*x**2/a)**(2/3)/(20*a**2*b**2 + 20*a*b**3*x**2) + 9*a**(8/3)*b*x**2/(20*a**2*b**2 + 20*a*b**3*x**2) + 6*a**(5/3)*b**2*x**4*(1 + b*x**2/a)**(2/3)/(20*a**2*b**2 + 20*a*b**3*x**2)","B",0
705,1,24,0,0.396475," ","integrate(x/(b*x**2+a)**(1/3),x)","\begin{cases} \frac{3 \left(a + b x^{2}\right)^{\frac{2}{3}}}{4 b} & \text{for}\: b \neq 0 \\\frac{x^{2}}{2 \sqrt[3]{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*(a + b*x**2)**(2/3)/(4*b), Ne(b, 0)), (x**2/(2*a**(1/3)), True))","A",0
706,1,41,0,1.015373," ","integrate(1/x/(b*x**2+a)**(1/3),x)","- \frac{\Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{2}}} \right)}}{2 \sqrt[3]{b} x^{\frac{2}{3}} \Gamma\left(\frac{4}{3}\right)}"," ",0,"-gamma(1/3)*hyper((1/3, 1/3), (4/3,), a*exp_polar(I*pi)/(b*x**2))/(2*b**(1/3)*x**(2/3)*gamma(4/3))","C",0
707,1,41,0,1.189401," ","integrate(1/x**3/(b*x**2+a)**(1/3),x)","- \frac{\Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{2}}} \right)}}{2 \sqrt[3]{b} x^{\frac{8}{3}} \Gamma\left(\frac{7}{3}\right)}"," ",0,"-gamma(4/3)*hyper((1/3, 4/3), (7/3,), a*exp_polar(I*pi)/(b*x**2))/(2*b**(1/3)*x**(8/3)*gamma(7/3))","C",0
708,1,41,0,1.372218," ","integrate(1/x**5/(b*x**2+a)**(1/3),x)","- \frac{\Gamma\left(\frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{7}{3} \\ \frac{10}{3} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{2}}} \right)}}{2 \sqrt[3]{b} x^{\frac{14}{3}} \Gamma\left(\frac{10}{3}\right)}"," ",0,"-gamma(7/3)*hyper((1/3, 7/3), (10/3,), a*exp_polar(I*pi)/(b*x**2))/(2*b**(1/3)*x**(14/3)*gamma(10/3))","C",0
709,1,27,0,0.824895," ","integrate(x**4/(b*x**2+a)**(1/3),x)","\frac{x^{5} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{5 \sqrt[3]{a}}"," ",0,"x**5*hyper((1/3, 5/2), (7/2,), b*x**2*exp_polar(I*pi)/a)/(5*a**(1/3))","A",0
710,1,27,0,0.776662," ","integrate(x**2/(b*x**2+a)**(1/3),x)","\frac{x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{3 \sqrt[3]{a}}"," ",0,"x**3*hyper((1/3, 3/2), (5/2,), b*x**2*exp_polar(I*pi)/a)/(3*a**(1/3))","A",0
711,1,24,0,0.747587," ","integrate(1/(b*x**2+a)**(1/3),x)","\frac{x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{\sqrt[3]{a}}"," ",0,"x*hyper((1/3, 1/2), (3/2,), b*x**2*exp_polar(I*pi)/a)/a**(1/3)","A",0
712,1,27,0,0.820887," ","integrate(1/x**2/(b*x**2+a)**(1/3),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{3} \\ \frac{1}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{\sqrt[3]{a} x}"," ",0,"-hyper((-1/2, 1/3), (1/2,), b*x**2*exp_polar(I*pi)/a)/(a**(1/3)*x)","A",0
713,1,32,0,0.941255," ","integrate(1/x**4/(b*x**2+a)**(1/3),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, \frac{1}{3} \\ - \frac{1}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{3 \sqrt[3]{a} x^{3}}"," ",0,"-hyper((-3/2, 1/3), (-1/2,), b*x**2*exp_polar(I*pi)/a)/(3*a**(1/3)*x**3)","A",0
714,1,1690,0,2.744101," ","integrate(x**7/(b*x**2+a)**(2/3),x)","- \frac{243 a^{\frac{70}{3}} \sqrt[3]{1 + \frac{b x^{2}}{a}}}{280 a^{20} b^{4} + 1680 a^{19} b^{5} x^{2} + 4200 a^{18} b^{6} x^{4} + 5600 a^{17} b^{7} x^{6} + 4200 a^{16} b^{8} x^{8} + 1680 a^{15} b^{9} x^{10} + 280 a^{14} b^{10} x^{12}} + \frac{243 a^{\frac{70}{3}}}{280 a^{20} b^{4} + 1680 a^{19} b^{5} x^{2} + 4200 a^{18} b^{6} x^{4} + 5600 a^{17} b^{7} x^{6} + 4200 a^{16} b^{8} x^{8} + 1680 a^{15} b^{9} x^{10} + 280 a^{14} b^{10} x^{12}} - \frac{1377 a^{\frac{67}{3}} b x^{2} \sqrt[3]{1 + \frac{b x^{2}}{a}}}{280 a^{20} b^{4} + 1680 a^{19} b^{5} x^{2} + 4200 a^{18} b^{6} x^{4} + 5600 a^{17} b^{7} x^{6} + 4200 a^{16} b^{8} x^{8} + 1680 a^{15} b^{9} x^{10} + 280 a^{14} b^{10} x^{12}} + \frac{1458 a^{\frac{67}{3}} b x^{2}}{280 a^{20} b^{4} + 1680 a^{19} b^{5} x^{2} + 4200 a^{18} b^{6} x^{4} + 5600 a^{17} b^{7} x^{6} + 4200 a^{16} b^{8} x^{8} + 1680 a^{15} b^{9} x^{10} + 280 a^{14} b^{10} x^{12}} - \frac{3213 a^{\frac{64}{3}} b^{2} x^{4} \sqrt[3]{1 + \frac{b x^{2}}{a}}}{280 a^{20} b^{4} + 1680 a^{19} b^{5} x^{2} + 4200 a^{18} b^{6} x^{4} + 5600 a^{17} b^{7} x^{6} + 4200 a^{16} b^{8} x^{8} + 1680 a^{15} b^{9} x^{10} + 280 a^{14} b^{10} x^{12}} + \frac{3645 a^{\frac{64}{3}} b^{2} x^{4}}{280 a^{20} b^{4} + 1680 a^{19} b^{5} x^{2} + 4200 a^{18} b^{6} x^{4} + 5600 a^{17} b^{7} x^{6} + 4200 a^{16} b^{8} x^{8} + 1680 a^{15} b^{9} x^{10} + 280 a^{14} b^{10} x^{12}} - \frac{3927 a^{\frac{61}{3}} b^{3} x^{6} \sqrt[3]{1 + \frac{b x^{2}}{a}}}{280 a^{20} b^{4} + 1680 a^{19} b^{5} x^{2} + 4200 a^{18} b^{6} x^{4} + 5600 a^{17} b^{7} x^{6} + 4200 a^{16} b^{8} x^{8} + 1680 a^{15} b^{9} x^{10} + 280 a^{14} b^{10} x^{12}} + \frac{4860 a^{\frac{61}{3}} b^{3} x^{6}}{280 a^{20} b^{4} + 1680 a^{19} b^{5} x^{2} + 4200 a^{18} b^{6} x^{4} + 5600 a^{17} b^{7} x^{6} + 4200 a^{16} b^{8} x^{8} + 1680 a^{15} b^{9} x^{10} + 280 a^{14} b^{10} x^{12}} - \frac{2583 a^{\frac{58}{3}} b^{4} x^{8} \sqrt[3]{1 + \frac{b x^{2}}{a}}}{280 a^{20} b^{4} + 1680 a^{19} b^{5} x^{2} + 4200 a^{18} b^{6} x^{4} + 5600 a^{17} b^{7} x^{6} + 4200 a^{16} b^{8} x^{8} + 1680 a^{15} b^{9} x^{10} + 280 a^{14} b^{10} x^{12}} + \frac{3645 a^{\frac{58}{3}} b^{4} x^{8}}{280 a^{20} b^{4} + 1680 a^{19} b^{5} x^{2} + 4200 a^{18} b^{6} x^{4} + 5600 a^{17} b^{7} x^{6} + 4200 a^{16} b^{8} x^{8} + 1680 a^{15} b^{9} x^{10} + 280 a^{14} b^{10} x^{12}} - \frac{693 a^{\frac{55}{3}} b^{5} x^{10} \sqrt[3]{1 + \frac{b x^{2}}{a}}}{280 a^{20} b^{4} + 1680 a^{19} b^{5} x^{2} + 4200 a^{18} b^{6} x^{4} + 5600 a^{17} b^{7} x^{6} + 4200 a^{16} b^{8} x^{8} + 1680 a^{15} b^{9} x^{10} + 280 a^{14} b^{10} x^{12}} + \frac{1458 a^{\frac{55}{3}} b^{5} x^{10}}{280 a^{20} b^{4} + 1680 a^{19} b^{5} x^{2} + 4200 a^{18} b^{6} x^{4} + 5600 a^{17} b^{7} x^{6} + 4200 a^{16} b^{8} x^{8} + 1680 a^{15} b^{9} x^{10} + 280 a^{14} b^{10} x^{12}} + \frac{273 a^{\frac{52}{3}} b^{6} x^{12} \sqrt[3]{1 + \frac{b x^{2}}{a}}}{280 a^{20} b^{4} + 1680 a^{19} b^{5} x^{2} + 4200 a^{18} b^{6} x^{4} + 5600 a^{17} b^{7} x^{6} + 4200 a^{16} b^{8} x^{8} + 1680 a^{15} b^{9} x^{10} + 280 a^{14} b^{10} x^{12}} + \frac{243 a^{\frac{52}{3}} b^{6} x^{12}}{280 a^{20} b^{4} + 1680 a^{19} b^{5} x^{2} + 4200 a^{18} b^{6} x^{4} + 5600 a^{17} b^{7} x^{6} + 4200 a^{16} b^{8} x^{8} + 1680 a^{15} b^{9} x^{10} + 280 a^{14} b^{10} x^{12}} + \frac{387 a^{\frac{49}{3}} b^{7} x^{14} \sqrt[3]{1 + \frac{b x^{2}}{a}}}{280 a^{20} b^{4} + 1680 a^{19} b^{5} x^{2} + 4200 a^{18} b^{6} x^{4} + 5600 a^{17} b^{7} x^{6} + 4200 a^{16} b^{8} x^{8} + 1680 a^{15} b^{9} x^{10} + 280 a^{14} b^{10} x^{12}} + \frac{198 a^{\frac{46}{3}} b^{8} x^{16} \sqrt[3]{1 + \frac{b x^{2}}{a}}}{280 a^{20} b^{4} + 1680 a^{19} b^{5} x^{2} + 4200 a^{18} b^{6} x^{4} + 5600 a^{17} b^{7} x^{6} + 4200 a^{16} b^{8} x^{8} + 1680 a^{15} b^{9} x^{10} + 280 a^{14} b^{10} x^{12}} + \frac{42 a^{\frac{43}{3}} b^{9} x^{18} \sqrt[3]{1 + \frac{b x^{2}}{a}}}{280 a^{20} b^{4} + 1680 a^{19} b^{5} x^{2} + 4200 a^{18} b^{6} x^{4} + 5600 a^{17} b^{7} x^{6} + 4200 a^{16} b^{8} x^{8} + 1680 a^{15} b^{9} x^{10} + 280 a^{14} b^{10} x^{12}}"," ",0,"-243*a**(70/3)*(1 + b*x**2/a)**(1/3)/(280*a**20*b**4 + 1680*a**19*b**5*x**2 + 4200*a**18*b**6*x**4 + 5600*a**17*b**7*x**6 + 4200*a**16*b**8*x**8 + 1680*a**15*b**9*x**10 + 280*a**14*b**10*x**12) + 243*a**(70/3)/(280*a**20*b**4 + 1680*a**19*b**5*x**2 + 4200*a**18*b**6*x**4 + 5600*a**17*b**7*x**6 + 4200*a**16*b**8*x**8 + 1680*a**15*b**9*x**10 + 280*a**14*b**10*x**12) - 1377*a**(67/3)*b*x**2*(1 + b*x**2/a)**(1/3)/(280*a**20*b**4 + 1680*a**19*b**5*x**2 + 4200*a**18*b**6*x**4 + 5600*a**17*b**7*x**6 + 4200*a**16*b**8*x**8 + 1680*a**15*b**9*x**10 + 280*a**14*b**10*x**12) + 1458*a**(67/3)*b*x**2/(280*a**20*b**4 + 1680*a**19*b**5*x**2 + 4200*a**18*b**6*x**4 + 5600*a**17*b**7*x**6 + 4200*a**16*b**8*x**8 + 1680*a**15*b**9*x**10 + 280*a**14*b**10*x**12) - 3213*a**(64/3)*b**2*x**4*(1 + b*x**2/a)**(1/3)/(280*a**20*b**4 + 1680*a**19*b**5*x**2 + 4200*a**18*b**6*x**4 + 5600*a**17*b**7*x**6 + 4200*a**16*b**8*x**8 + 1680*a**15*b**9*x**10 + 280*a**14*b**10*x**12) + 3645*a**(64/3)*b**2*x**4/(280*a**20*b**4 + 1680*a**19*b**5*x**2 + 4200*a**18*b**6*x**4 + 5600*a**17*b**7*x**6 + 4200*a**16*b**8*x**8 + 1680*a**15*b**9*x**10 + 280*a**14*b**10*x**12) - 3927*a**(61/3)*b**3*x**6*(1 + b*x**2/a)**(1/3)/(280*a**20*b**4 + 1680*a**19*b**5*x**2 + 4200*a**18*b**6*x**4 + 5600*a**17*b**7*x**6 + 4200*a**16*b**8*x**8 + 1680*a**15*b**9*x**10 + 280*a**14*b**10*x**12) + 4860*a**(61/3)*b**3*x**6/(280*a**20*b**4 + 1680*a**19*b**5*x**2 + 4200*a**18*b**6*x**4 + 5600*a**17*b**7*x**6 + 4200*a**16*b**8*x**8 + 1680*a**15*b**9*x**10 + 280*a**14*b**10*x**12) - 2583*a**(58/3)*b**4*x**8*(1 + b*x**2/a)**(1/3)/(280*a**20*b**4 + 1680*a**19*b**5*x**2 + 4200*a**18*b**6*x**4 + 5600*a**17*b**7*x**6 + 4200*a**16*b**8*x**8 + 1680*a**15*b**9*x**10 + 280*a**14*b**10*x**12) + 3645*a**(58/3)*b**4*x**8/(280*a**20*b**4 + 1680*a**19*b**5*x**2 + 4200*a**18*b**6*x**4 + 5600*a**17*b**7*x**6 + 4200*a**16*b**8*x**8 + 1680*a**15*b**9*x**10 + 280*a**14*b**10*x**12) - 693*a**(55/3)*b**5*x**10*(1 + b*x**2/a)**(1/3)/(280*a**20*b**4 + 1680*a**19*b**5*x**2 + 4200*a**18*b**6*x**4 + 5600*a**17*b**7*x**6 + 4200*a**16*b**8*x**8 + 1680*a**15*b**9*x**10 + 280*a**14*b**10*x**12) + 1458*a**(55/3)*b**5*x**10/(280*a**20*b**4 + 1680*a**19*b**5*x**2 + 4200*a**18*b**6*x**4 + 5600*a**17*b**7*x**6 + 4200*a**16*b**8*x**8 + 1680*a**15*b**9*x**10 + 280*a**14*b**10*x**12) + 273*a**(52/3)*b**6*x**12*(1 + b*x**2/a)**(1/3)/(280*a**20*b**4 + 1680*a**19*b**5*x**2 + 4200*a**18*b**6*x**4 + 5600*a**17*b**7*x**6 + 4200*a**16*b**8*x**8 + 1680*a**15*b**9*x**10 + 280*a**14*b**10*x**12) + 243*a**(52/3)*b**6*x**12/(280*a**20*b**4 + 1680*a**19*b**5*x**2 + 4200*a**18*b**6*x**4 + 5600*a**17*b**7*x**6 + 4200*a**16*b**8*x**8 + 1680*a**15*b**9*x**10 + 280*a**14*b**10*x**12) + 387*a**(49/3)*b**7*x**14*(1 + b*x**2/a)**(1/3)/(280*a**20*b**4 + 1680*a**19*b**5*x**2 + 4200*a**18*b**6*x**4 + 5600*a**17*b**7*x**6 + 4200*a**16*b**8*x**8 + 1680*a**15*b**9*x**10 + 280*a**14*b**10*x**12) + 198*a**(46/3)*b**8*x**16*(1 + b*x**2/a)**(1/3)/(280*a**20*b**4 + 1680*a**19*b**5*x**2 + 4200*a**18*b**6*x**4 + 5600*a**17*b**7*x**6 + 4200*a**16*b**8*x**8 + 1680*a**15*b**9*x**10 + 280*a**14*b**10*x**12) + 42*a**(43/3)*b**9*x**18*(1 + b*x**2/a)**(1/3)/(280*a**20*b**4 + 1680*a**19*b**5*x**2 + 4200*a**18*b**6*x**4 + 5600*a**17*b**7*x**6 + 4200*a**16*b**8*x**8 + 1680*a**15*b**9*x**10 + 280*a**14*b**10*x**12)","B",0
715,1,631,0,1.801034," ","integrate(x**5/(b*x**2+a)**(2/3),x)","\frac{27 a^{\frac{31}{3}} \sqrt[3]{1 + \frac{b x^{2}}{a}}}{28 a^{8} b^{3} + 84 a^{7} b^{4} x^{2} + 84 a^{6} b^{5} x^{4} + 28 a^{5} b^{6} x^{6}} - \frac{27 a^{\frac{31}{3}}}{28 a^{8} b^{3} + 84 a^{7} b^{4} x^{2} + 84 a^{6} b^{5} x^{4} + 28 a^{5} b^{6} x^{6}} + \frac{72 a^{\frac{28}{3}} b x^{2} \sqrt[3]{1 + \frac{b x^{2}}{a}}}{28 a^{8} b^{3} + 84 a^{7} b^{4} x^{2} + 84 a^{6} b^{5} x^{4} + 28 a^{5} b^{6} x^{6}} - \frac{81 a^{\frac{28}{3}} b x^{2}}{28 a^{8} b^{3} + 84 a^{7} b^{4} x^{2} + 84 a^{6} b^{5} x^{4} + 28 a^{5} b^{6} x^{6}} + \frac{60 a^{\frac{25}{3}} b^{2} x^{4} \sqrt[3]{1 + \frac{b x^{2}}{a}}}{28 a^{8} b^{3} + 84 a^{7} b^{4} x^{2} + 84 a^{6} b^{5} x^{4} + 28 a^{5} b^{6} x^{6}} - \frac{81 a^{\frac{25}{3}} b^{2} x^{4}}{28 a^{8} b^{3} + 84 a^{7} b^{4} x^{2} + 84 a^{6} b^{5} x^{4} + 28 a^{5} b^{6} x^{6}} + \frac{18 a^{\frac{22}{3}} b^{3} x^{6} \sqrt[3]{1 + \frac{b x^{2}}{a}}}{28 a^{8} b^{3} + 84 a^{7} b^{4} x^{2} + 84 a^{6} b^{5} x^{4} + 28 a^{5} b^{6} x^{6}} - \frac{27 a^{\frac{22}{3}} b^{3} x^{6}}{28 a^{8} b^{3} + 84 a^{7} b^{4} x^{2} + 84 a^{6} b^{5} x^{4} + 28 a^{5} b^{6} x^{6}} + \frac{9 a^{\frac{19}{3}} b^{4} x^{8} \sqrt[3]{1 + \frac{b x^{2}}{a}}}{28 a^{8} b^{3} + 84 a^{7} b^{4} x^{2} + 84 a^{6} b^{5} x^{4} + 28 a^{5} b^{6} x^{6}} + \frac{6 a^{\frac{16}{3}} b^{5} x^{10} \sqrt[3]{1 + \frac{b x^{2}}{a}}}{28 a^{8} b^{3} + 84 a^{7} b^{4} x^{2} + 84 a^{6} b^{5} x^{4} + 28 a^{5} b^{6} x^{6}}"," ",0,"27*a**(31/3)*(1 + b*x**2/a)**(1/3)/(28*a**8*b**3 + 84*a**7*b**4*x**2 + 84*a**6*b**5*x**4 + 28*a**5*b**6*x**6) - 27*a**(31/3)/(28*a**8*b**3 + 84*a**7*b**4*x**2 + 84*a**6*b**5*x**4 + 28*a**5*b**6*x**6) + 72*a**(28/3)*b*x**2*(1 + b*x**2/a)**(1/3)/(28*a**8*b**3 + 84*a**7*b**4*x**2 + 84*a**6*b**5*x**4 + 28*a**5*b**6*x**6) - 81*a**(28/3)*b*x**2/(28*a**8*b**3 + 84*a**7*b**4*x**2 + 84*a**6*b**5*x**4 + 28*a**5*b**6*x**6) + 60*a**(25/3)*b**2*x**4*(1 + b*x**2/a)**(1/3)/(28*a**8*b**3 + 84*a**7*b**4*x**2 + 84*a**6*b**5*x**4 + 28*a**5*b**6*x**6) - 81*a**(25/3)*b**2*x**4/(28*a**8*b**3 + 84*a**7*b**4*x**2 + 84*a**6*b**5*x**4 + 28*a**5*b**6*x**6) + 18*a**(22/3)*b**3*x**6*(1 + b*x**2/a)**(1/3)/(28*a**8*b**3 + 84*a**7*b**4*x**2 + 84*a**6*b**5*x**4 + 28*a**5*b**6*x**6) - 27*a**(22/3)*b**3*x**6/(28*a**8*b**3 + 84*a**7*b**4*x**2 + 84*a**6*b**5*x**4 + 28*a**5*b**6*x**6) + 9*a**(19/3)*b**4*x**8*(1 + b*x**2/a)**(1/3)/(28*a**8*b**3 + 84*a**7*b**4*x**2 + 84*a**6*b**5*x**4 + 28*a**5*b**6*x**6) + 6*a**(16/3)*b**5*x**10*(1 + b*x**2/a)**(1/3)/(28*a**8*b**3 + 84*a**7*b**4*x**2 + 84*a**6*b**5*x**4 + 28*a**5*b**6*x**6)","B",0
716,1,178,0,1.140078," ","integrate(x**3/(b*x**2+a)**(2/3),x)","- \frac{9 a^{\frac{10}{3}} \sqrt[3]{1 + \frac{b x^{2}}{a}}}{8 a^{2} b^{2} + 8 a b^{3} x^{2}} + \frac{9 a^{\frac{10}{3}}}{8 a^{2} b^{2} + 8 a b^{3} x^{2}} - \frac{6 a^{\frac{7}{3}} b x^{2} \sqrt[3]{1 + \frac{b x^{2}}{a}}}{8 a^{2} b^{2} + 8 a b^{3} x^{2}} + \frac{9 a^{\frac{7}{3}} b x^{2}}{8 a^{2} b^{2} + 8 a b^{3} x^{2}} + \frac{3 a^{\frac{4}{3}} b^{2} x^{4} \sqrt[3]{1 + \frac{b x^{2}}{a}}}{8 a^{2} b^{2} + 8 a b^{3} x^{2}}"," ",0,"-9*a**(10/3)*(1 + b*x**2/a)**(1/3)/(8*a**2*b**2 + 8*a*b**3*x**2) + 9*a**(10/3)/(8*a**2*b**2 + 8*a*b**3*x**2) - 6*a**(7/3)*b*x**2*(1 + b*x**2/a)**(1/3)/(8*a**2*b**2 + 8*a*b**3*x**2) + 9*a**(7/3)*b*x**2/(8*a**2*b**2 + 8*a*b**3*x**2) + 3*a**(4/3)*b**2*x**4*(1 + b*x**2/a)**(1/3)/(8*a**2*b**2 + 8*a*b**3*x**2)","B",0
717,1,24,0,0.413909," ","integrate(x/(b*x**2+a)**(2/3),x)","\begin{cases} \frac{3 \sqrt[3]{a + b x^{2}}}{2 b} & \text{for}\: b \neq 0 \\\frac{x^{2}}{2 a^{\frac{2}{3}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*(a + b*x**2)**(1/3)/(2*b), Ne(b, 0)), (x**2/(2*a**(2/3)), True))","A",0
718,1,41,0,1.058777," ","integrate(1/x/(b*x**2+a)**(2/3),x)","- \frac{\Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{3}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{2}}} \right)}}{2 b^{\frac{2}{3}} x^{\frac{4}{3}} \Gamma\left(\frac{5}{3}\right)}"," ",0,"-gamma(2/3)*hyper((2/3, 2/3), (5/3,), a*exp_polar(I*pi)/(b*x**2))/(2*b**(2/3)*x**(4/3)*gamma(5/3))","C",0
719,1,41,0,1.236508," ","integrate(1/x**3/(b*x**2+a)**(2/3),x)","- \frac{\Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{3}, \frac{5}{3} \\ \frac{8}{3} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{2}}} \right)}}{2 b^{\frac{2}{3}} x^{\frac{10}{3}} \Gamma\left(\frac{8}{3}\right)}"," ",0,"-gamma(5/3)*hyper((2/3, 5/3), (8/3,), a*exp_polar(I*pi)/(b*x**2))/(2*b**(2/3)*x**(10/3)*gamma(8/3))","C",0
720,1,41,0,1.447093," ","integrate(1/x**5/(b*x**2+a)**(2/3),x)","- \frac{\Gamma\left(\frac{8}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{3}, \frac{8}{3} \\ \frac{11}{3} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{2}}} \right)}}{2 b^{\frac{2}{3}} x^{\frac{16}{3}} \Gamma\left(\frac{11}{3}\right)}"," ",0,"-gamma(8/3)*hyper((2/3, 8/3), (11/3,), a*exp_polar(I*pi)/(b*x**2))/(2*b**(2/3)*x**(16/3)*gamma(11/3))","C",0
721,1,27,0,0.847422," ","integrate(x**4/(b*x**2+a)**(2/3),x)","\frac{x^{5} {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{3}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{5 a^{\frac{2}{3}}}"," ",0,"x**5*hyper((2/3, 5/2), (7/2,), b*x**2*exp_polar(I*pi)/a)/(5*a**(2/3))","A",0
722,1,27,0,0.784795," ","integrate(x**2/(b*x**2+a)**(2/3),x)","\frac{x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{3}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{3 a^{\frac{2}{3}}}"," ",0,"x**3*hyper((2/3, 3/2), (5/2,), b*x**2*exp_polar(I*pi)/a)/(3*a**(2/3))","A",0
723,1,24,0,0.757276," ","integrate(1/(b*x**2+a)**(2/3),x)","\frac{x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{a^{\frac{2}{3}}}"," ",0,"x*hyper((1/2, 2/3), (3/2,), b*x**2*exp_polar(I*pi)/a)/a**(2/3)","A",0
724,1,27,0,0.900926," ","integrate(1/x**2/(b*x**2+a)**(2/3),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{2}{3} \\ \frac{1}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{a^{\frac{2}{3}} x}"," ",0,"-hyper((-1/2, 2/3), (1/2,), b*x**2*exp_polar(I*pi)/a)/(a**(2/3)*x)","A",0
725,1,32,0,1.009182," ","integrate(1/x**4/(b*x**2+a)**(2/3),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, \frac{2}{3} \\ - \frac{1}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{3 a^{\frac{2}{3}} x^{3}}"," ",0,"-hyper((-3/2, 2/3), (-1/2,), b*x**2*exp_polar(I*pi)/a)/(3*a**(2/3)*x**3)","A",0
726,1,1584,0,2.841030," ","integrate(x**7/(b*x**2+a)**(4/3),x)","\frac{243 a^{\frac{68}{3}} \left(1 + \frac{b x^{2}}{a}\right)^{\frac{2}{3}}}{80 a^{20} b^{4} + 480 a^{19} b^{5} x^{2} + 1200 a^{18} b^{6} x^{4} + 1600 a^{17} b^{7} x^{6} + 1200 a^{16} b^{8} x^{8} + 480 a^{15} b^{9} x^{10} + 80 a^{14} b^{10} x^{12}} - \frac{243 a^{\frac{68}{3}}}{80 a^{20} b^{4} + 480 a^{19} b^{5} x^{2} + 1200 a^{18} b^{6} x^{4} + 1600 a^{17} b^{7} x^{6} + 1200 a^{16} b^{8} x^{8} + 480 a^{15} b^{9} x^{10} + 80 a^{14} b^{10} x^{12}} + \frac{1296 a^{\frac{65}{3}} b x^{2} \left(1 + \frac{b x^{2}}{a}\right)^{\frac{2}{3}}}{80 a^{20} b^{4} + 480 a^{19} b^{5} x^{2} + 1200 a^{18} b^{6} x^{4} + 1600 a^{17} b^{7} x^{6} + 1200 a^{16} b^{8} x^{8} + 480 a^{15} b^{9} x^{10} + 80 a^{14} b^{10} x^{12}} - \frac{1458 a^{\frac{65}{3}} b x^{2}}{80 a^{20} b^{4} + 480 a^{19} b^{5} x^{2} + 1200 a^{18} b^{6} x^{4} + 1600 a^{17} b^{7} x^{6} + 1200 a^{16} b^{8} x^{8} + 480 a^{15} b^{9} x^{10} + 80 a^{14} b^{10} x^{12}} + \frac{2808 a^{\frac{62}{3}} b^{2} x^{4} \left(1 + \frac{b x^{2}}{a}\right)^{\frac{2}{3}}}{80 a^{20} b^{4} + 480 a^{19} b^{5} x^{2} + 1200 a^{18} b^{6} x^{4} + 1600 a^{17} b^{7} x^{6} + 1200 a^{16} b^{8} x^{8} + 480 a^{15} b^{9} x^{10} + 80 a^{14} b^{10} x^{12}} - \frac{3645 a^{\frac{62}{3}} b^{2} x^{4}}{80 a^{20} b^{4} + 480 a^{19} b^{5} x^{2} + 1200 a^{18} b^{6} x^{4} + 1600 a^{17} b^{7} x^{6} + 1200 a^{16} b^{8} x^{8} + 480 a^{15} b^{9} x^{10} + 80 a^{14} b^{10} x^{12}} + \frac{3120 a^{\frac{59}{3}} b^{3} x^{6} \left(1 + \frac{b x^{2}}{a}\right)^{\frac{2}{3}}}{80 a^{20} b^{4} + 480 a^{19} b^{5} x^{2} + 1200 a^{18} b^{6} x^{4} + 1600 a^{17} b^{7} x^{6} + 1200 a^{16} b^{8} x^{8} + 480 a^{15} b^{9} x^{10} + 80 a^{14} b^{10} x^{12}} - \frac{4860 a^{\frac{59}{3}} b^{3} x^{6}}{80 a^{20} b^{4} + 480 a^{19} b^{5} x^{2} + 1200 a^{18} b^{6} x^{4} + 1600 a^{17} b^{7} x^{6} + 1200 a^{16} b^{8} x^{8} + 480 a^{15} b^{9} x^{10} + 80 a^{14} b^{10} x^{12}} + \frac{1830 a^{\frac{56}{3}} b^{4} x^{8} \left(1 + \frac{b x^{2}}{a}\right)^{\frac{2}{3}}}{80 a^{20} b^{4} + 480 a^{19} b^{5} x^{2} + 1200 a^{18} b^{6} x^{4} + 1600 a^{17} b^{7} x^{6} + 1200 a^{16} b^{8} x^{8} + 480 a^{15} b^{9} x^{10} + 80 a^{14} b^{10} x^{12}} - \frac{3645 a^{\frac{56}{3}} b^{4} x^{8}}{80 a^{20} b^{4} + 480 a^{19} b^{5} x^{2} + 1200 a^{18} b^{6} x^{4} + 1600 a^{17} b^{7} x^{6} + 1200 a^{16} b^{8} x^{8} + 480 a^{15} b^{9} x^{10} + 80 a^{14} b^{10} x^{12}} + \frac{528 a^{\frac{53}{3}} b^{5} x^{10} \left(1 + \frac{b x^{2}}{a}\right)^{\frac{2}{3}}}{80 a^{20} b^{4} + 480 a^{19} b^{5} x^{2} + 1200 a^{18} b^{6} x^{4} + 1600 a^{17} b^{7} x^{6} + 1200 a^{16} b^{8} x^{8} + 480 a^{15} b^{9} x^{10} + 80 a^{14} b^{10} x^{12}} - \frac{1458 a^{\frac{53}{3}} b^{5} x^{10}}{80 a^{20} b^{4} + 480 a^{19} b^{5} x^{2} + 1200 a^{18} b^{6} x^{4} + 1600 a^{17} b^{7} x^{6} + 1200 a^{16} b^{8} x^{8} + 480 a^{15} b^{9} x^{10} + 80 a^{14} b^{10} x^{12}} + \frac{96 a^{\frac{50}{3}} b^{6} x^{12} \left(1 + \frac{b x^{2}}{a}\right)^{\frac{2}{3}}}{80 a^{20} b^{4} + 480 a^{19} b^{5} x^{2} + 1200 a^{18} b^{6} x^{4} + 1600 a^{17} b^{7} x^{6} + 1200 a^{16} b^{8} x^{8} + 480 a^{15} b^{9} x^{10} + 80 a^{14} b^{10} x^{12}} - \frac{243 a^{\frac{50}{3}} b^{6} x^{12}}{80 a^{20} b^{4} + 480 a^{19} b^{5} x^{2} + 1200 a^{18} b^{6} x^{4} + 1600 a^{17} b^{7} x^{6} + 1200 a^{16} b^{8} x^{8} + 480 a^{15} b^{9} x^{10} + 80 a^{14} b^{10} x^{12}} + \frac{48 a^{\frac{47}{3}} b^{7} x^{14} \left(1 + \frac{b x^{2}}{a}\right)^{\frac{2}{3}}}{80 a^{20} b^{4} + 480 a^{19} b^{5} x^{2} + 1200 a^{18} b^{6} x^{4} + 1600 a^{17} b^{7} x^{6} + 1200 a^{16} b^{8} x^{8} + 480 a^{15} b^{9} x^{10} + 80 a^{14} b^{10} x^{12}} + \frac{15 a^{\frac{44}{3}} b^{8} x^{16} \left(1 + \frac{b x^{2}}{a}\right)^{\frac{2}{3}}}{80 a^{20} b^{4} + 480 a^{19} b^{5} x^{2} + 1200 a^{18} b^{6} x^{4} + 1600 a^{17} b^{7} x^{6} + 1200 a^{16} b^{8} x^{8} + 480 a^{15} b^{9} x^{10} + 80 a^{14} b^{10} x^{12}}"," ",0,"243*a**(68/3)*(1 + b*x**2/a)**(2/3)/(80*a**20*b**4 + 480*a**19*b**5*x**2 + 1200*a**18*b**6*x**4 + 1600*a**17*b**7*x**6 + 1200*a**16*b**8*x**8 + 480*a**15*b**9*x**10 + 80*a**14*b**10*x**12) - 243*a**(68/3)/(80*a**20*b**4 + 480*a**19*b**5*x**2 + 1200*a**18*b**6*x**4 + 1600*a**17*b**7*x**6 + 1200*a**16*b**8*x**8 + 480*a**15*b**9*x**10 + 80*a**14*b**10*x**12) + 1296*a**(65/3)*b*x**2*(1 + b*x**2/a)**(2/3)/(80*a**20*b**4 + 480*a**19*b**5*x**2 + 1200*a**18*b**6*x**4 + 1600*a**17*b**7*x**6 + 1200*a**16*b**8*x**8 + 480*a**15*b**9*x**10 + 80*a**14*b**10*x**12) - 1458*a**(65/3)*b*x**2/(80*a**20*b**4 + 480*a**19*b**5*x**2 + 1200*a**18*b**6*x**4 + 1600*a**17*b**7*x**6 + 1200*a**16*b**8*x**8 + 480*a**15*b**9*x**10 + 80*a**14*b**10*x**12) + 2808*a**(62/3)*b**2*x**4*(1 + b*x**2/a)**(2/3)/(80*a**20*b**4 + 480*a**19*b**5*x**2 + 1200*a**18*b**6*x**4 + 1600*a**17*b**7*x**6 + 1200*a**16*b**8*x**8 + 480*a**15*b**9*x**10 + 80*a**14*b**10*x**12) - 3645*a**(62/3)*b**2*x**4/(80*a**20*b**4 + 480*a**19*b**5*x**2 + 1200*a**18*b**6*x**4 + 1600*a**17*b**7*x**6 + 1200*a**16*b**8*x**8 + 480*a**15*b**9*x**10 + 80*a**14*b**10*x**12) + 3120*a**(59/3)*b**3*x**6*(1 + b*x**2/a)**(2/3)/(80*a**20*b**4 + 480*a**19*b**5*x**2 + 1200*a**18*b**6*x**4 + 1600*a**17*b**7*x**6 + 1200*a**16*b**8*x**8 + 480*a**15*b**9*x**10 + 80*a**14*b**10*x**12) - 4860*a**(59/3)*b**3*x**6/(80*a**20*b**4 + 480*a**19*b**5*x**2 + 1200*a**18*b**6*x**4 + 1600*a**17*b**7*x**6 + 1200*a**16*b**8*x**8 + 480*a**15*b**9*x**10 + 80*a**14*b**10*x**12) + 1830*a**(56/3)*b**4*x**8*(1 + b*x**2/a)**(2/3)/(80*a**20*b**4 + 480*a**19*b**5*x**2 + 1200*a**18*b**6*x**4 + 1600*a**17*b**7*x**6 + 1200*a**16*b**8*x**8 + 480*a**15*b**9*x**10 + 80*a**14*b**10*x**12) - 3645*a**(56/3)*b**4*x**8/(80*a**20*b**4 + 480*a**19*b**5*x**2 + 1200*a**18*b**6*x**4 + 1600*a**17*b**7*x**6 + 1200*a**16*b**8*x**8 + 480*a**15*b**9*x**10 + 80*a**14*b**10*x**12) + 528*a**(53/3)*b**5*x**10*(1 + b*x**2/a)**(2/3)/(80*a**20*b**4 + 480*a**19*b**5*x**2 + 1200*a**18*b**6*x**4 + 1600*a**17*b**7*x**6 + 1200*a**16*b**8*x**8 + 480*a**15*b**9*x**10 + 80*a**14*b**10*x**12) - 1458*a**(53/3)*b**5*x**10/(80*a**20*b**4 + 480*a**19*b**5*x**2 + 1200*a**18*b**6*x**4 + 1600*a**17*b**7*x**6 + 1200*a**16*b**8*x**8 + 480*a**15*b**9*x**10 + 80*a**14*b**10*x**12) + 96*a**(50/3)*b**6*x**12*(1 + b*x**2/a)**(2/3)/(80*a**20*b**4 + 480*a**19*b**5*x**2 + 1200*a**18*b**6*x**4 + 1600*a**17*b**7*x**6 + 1200*a**16*b**8*x**8 + 480*a**15*b**9*x**10 + 80*a**14*b**10*x**12) - 243*a**(50/3)*b**6*x**12/(80*a**20*b**4 + 480*a**19*b**5*x**2 + 1200*a**18*b**6*x**4 + 1600*a**17*b**7*x**6 + 1200*a**16*b**8*x**8 + 480*a**15*b**9*x**10 + 80*a**14*b**10*x**12) + 48*a**(47/3)*b**7*x**14*(1 + b*x**2/a)**(2/3)/(80*a**20*b**4 + 480*a**19*b**5*x**2 + 1200*a**18*b**6*x**4 + 1600*a**17*b**7*x**6 + 1200*a**16*b**8*x**8 + 480*a**15*b**9*x**10 + 80*a**14*b**10*x**12) + 15*a**(44/3)*b**8*x**16*(1 + b*x**2/a)**(2/3)/(80*a**20*b**4 + 480*a**19*b**5*x**2 + 1200*a**18*b**6*x**4 + 1600*a**17*b**7*x**6 + 1200*a**16*b**8*x**8 + 480*a**15*b**9*x**10 + 80*a**14*b**10*x**12)","B",0
727,1,561,0,1.822649," ","integrate(x**5/(b*x**2+a)**(4/3),x)","- \frac{27 a^{\frac{29}{3}} \left(1 + \frac{b x^{2}}{a}\right)^{\frac{2}{3}}}{10 a^{8} b^{3} + 30 a^{7} b^{4} x^{2} + 30 a^{6} b^{5} x^{4} + 10 a^{5} b^{6} x^{6}} + \frac{27 a^{\frac{29}{3}}}{10 a^{8} b^{3} + 30 a^{7} b^{4} x^{2} + 30 a^{6} b^{5} x^{4} + 10 a^{5} b^{6} x^{6}} - \frac{63 a^{\frac{26}{3}} b x^{2} \left(1 + \frac{b x^{2}}{a}\right)^{\frac{2}{3}}}{10 a^{8} b^{3} + 30 a^{7} b^{4} x^{2} + 30 a^{6} b^{5} x^{4} + 10 a^{5} b^{6} x^{6}} + \frac{81 a^{\frac{26}{3}} b x^{2}}{10 a^{8} b^{3} + 30 a^{7} b^{4} x^{2} + 30 a^{6} b^{5} x^{4} + 10 a^{5} b^{6} x^{6}} - \frac{42 a^{\frac{23}{3}} b^{2} x^{4} \left(1 + \frac{b x^{2}}{a}\right)^{\frac{2}{3}}}{10 a^{8} b^{3} + 30 a^{7} b^{4} x^{2} + 30 a^{6} b^{5} x^{4} + 10 a^{5} b^{6} x^{6}} + \frac{81 a^{\frac{23}{3}} b^{2} x^{4}}{10 a^{8} b^{3} + 30 a^{7} b^{4} x^{2} + 30 a^{6} b^{5} x^{4} + 10 a^{5} b^{6} x^{6}} - \frac{3 a^{\frac{20}{3}} b^{3} x^{6} \left(1 + \frac{b x^{2}}{a}\right)^{\frac{2}{3}}}{10 a^{8} b^{3} + 30 a^{7} b^{4} x^{2} + 30 a^{6} b^{5} x^{4} + 10 a^{5} b^{6} x^{6}} + \frac{27 a^{\frac{20}{3}} b^{3} x^{6}}{10 a^{8} b^{3} + 30 a^{7} b^{4} x^{2} + 30 a^{6} b^{5} x^{4} + 10 a^{5} b^{6} x^{6}} + \frac{3 a^{\frac{17}{3}} b^{4} x^{8} \left(1 + \frac{b x^{2}}{a}\right)^{\frac{2}{3}}}{10 a^{8} b^{3} + 30 a^{7} b^{4} x^{2} + 30 a^{6} b^{5} x^{4} + 10 a^{5} b^{6} x^{6}}"," ",0,"-27*a**(29/3)*(1 + b*x**2/a)**(2/3)/(10*a**8*b**3 + 30*a**7*b**4*x**2 + 30*a**6*b**5*x**4 + 10*a**5*b**6*x**6) + 27*a**(29/3)/(10*a**8*b**3 + 30*a**7*b**4*x**2 + 30*a**6*b**5*x**4 + 10*a**5*b**6*x**6) - 63*a**(26/3)*b*x**2*(1 + b*x**2/a)**(2/3)/(10*a**8*b**3 + 30*a**7*b**4*x**2 + 30*a**6*b**5*x**4 + 10*a**5*b**6*x**6) + 81*a**(26/3)*b*x**2/(10*a**8*b**3 + 30*a**7*b**4*x**2 + 30*a**6*b**5*x**4 + 10*a**5*b**6*x**6) - 42*a**(23/3)*b**2*x**4*(1 + b*x**2/a)**(2/3)/(10*a**8*b**3 + 30*a**7*b**4*x**2 + 30*a**6*b**5*x**4 + 10*a**5*b**6*x**6) + 81*a**(23/3)*b**2*x**4/(10*a**8*b**3 + 30*a**7*b**4*x**2 + 30*a**6*b**5*x**4 + 10*a**5*b**6*x**6) - 3*a**(20/3)*b**3*x**6*(1 + b*x**2/a)**(2/3)/(10*a**8*b**3 + 30*a**7*b**4*x**2 + 30*a**6*b**5*x**4 + 10*a**5*b**6*x**6) + 27*a**(20/3)*b**3*x**6/(10*a**8*b**3 + 30*a**7*b**4*x**2 + 30*a**6*b**5*x**4 + 10*a**5*b**6*x**6) + 3*a**(17/3)*b**4*x**8*(1 + b*x**2/a)**(2/3)/(10*a**8*b**3 + 30*a**7*b**4*x**2 + 30*a**6*b**5*x**4 + 10*a**5*b**6*x**6)","B",0
728,1,46,0,0.704164," ","integrate(x**3/(b*x**2+a)**(4/3),x)","\begin{cases} \frac{9 a}{4 b^{2} \sqrt[3]{a + b x^{2}}} + \frac{3 x^{2}}{4 b \sqrt[3]{a + b x^{2}}} & \text{for}\: b \neq 0 \\\frac{x^{4}}{4 a^{\frac{4}{3}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((9*a/(4*b**2*(a + b*x**2)**(1/3)) + 3*x**2/(4*b*(a + b*x**2)**(1/3)), Ne(b, 0)), (x**4/(4*a**(4/3)), True))","A",0
729,1,26,0,0.675113," ","integrate(x/(b*x**2+a)**(4/3),x)","\begin{cases} - \frac{3}{2 b \sqrt[3]{a + b x^{2}}} & \text{for}\: b \neq 0 \\\frac{x^{2}}{2 a^{\frac{4}{3}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-3/(2*b*(a + b*x**2)**(1/3)), Ne(b, 0)), (x**2/(2*a**(4/3)), True))","A",0
730,1,41,0,1.134625," ","integrate(1/x/(b*x**2+a)**(4/3),x)","- \frac{\Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{4}{3}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{2}}} \right)}}{2 b^{\frac{4}{3}} x^{\frac{8}{3}} \Gamma\left(\frac{7}{3}\right)}"," ",0,"-gamma(4/3)*hyper((4/3, 4/3), (7/3,), a*exp_polar(I*pi)/(b*x**2))/(2*b**(4/3)*x**(8/3)*gamma(7/3))","C",0
731,1,41,0,1.349720," ","integrate(1/x**3/(b*x**2+a)**(4/3),x)","- \frac{\Gamma\left(\frac{7}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{4}{3}, \frac{7}{3} \\ \frac{10}{3} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{2}}} \right)}}{2 b^{\frac{4}{3}} x^{\frac{14}{3}} \Gamma\left(\frac{10}{3}\right)}"," ",0,"-gamma(7/3)*hyper((4/3, 7/3), (10/3,), a*exp_polar(I*pi)/(b*x**2))/(2*b**(4/3)*x**(14/3)*gamma(10/3))","C",0
732,1,41,0,1.622058," ","integrate(1/x**5/(b*x**2+a)**(4/3),x)","- \frac{\Gamma\left(\frac{10}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{4}{3}, \frac{10}{3} \\ \frac{13}{3} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{2}}} \right)}}{2 b^{\frac{4}{3}} x^{\frac{20}{3}} \Gamma\left(\frac{13}{3}\right)}"," ",0,"-gamma(10/3)*hyper((4/3, 10/3), (13/3,), a*exp_polar(I*pi)/(b*x**2))/(2*b**(4/3)*x**(20/3)*gamma(13/3))","C",0
733,1,27,0,0.884691," ","integrate(x**4/(b*x**2+a)**(4/3),x)","\frac{x^{5} {{}_{2}F_{1}\left(\begin{matrix} \frac{4}{3}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{5 a^{\frac{4}{3}}}"," ",0,"x**5*hyper((4/3, 5/2), (7/2,), b*x**2*exp_polar(I*pi)/a)/(5*a**(4/3))","A",0
734,1,27,0,0.880120," ","integrate(x**2/(b*x**2+a)**(4/3),x)","\frac{x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{4}{3}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{3 a^{\frac{4}{3}}}"," ",0,"x**3*hyper((4/3, 3/2), (5/2,), b*x**2*exp_polar(I*pi)/a)/(3*a**(4/3))","A",0
735,1,24,0,0.818432," ","integrate(1/(b*x**2+a)**(4/3),x)","\frac{x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{4}{3} \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{a^{\frac{4}{3}}}"," ",0,"x*hyper((1/2, 4/3), (3/2,), b*x**2*exp_polar(I*pi)/a)/a**(4/3)","A",0
736,1,27,0,1.018091," ","integrate(1/x**2/(b*x**2+a)**(4/3),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{4}{3} \\ \frac{1}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{a^{\frac{4}{3}} x}"," ",0,"-hyper((-1/2, 4/3), (1/2,), b*x**2*exp_polar(I*pi)/a)/(a**(4/3)*x)","A",0
737,1,32,0,1.146869," ","integrate(1/x**4/(b*x**2+a)**(4/3),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, \frac{4}{3} \\ - \frac{1}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{3 a^{\frac{4}{3}} x^{3}}"," ",0,"-hyper((-3/2, 4/3), (-1/2,), b*x**2*exp_polar(I*pi)/a)/(3*a**(4/3)*x**3)","A",0
738,-1,0,0,0.000000," ","integrate((c*x)**(13/3)*(b*x**2+a)**(1/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
739,1,46,0,33.290316," ","integrate((c*x)**(7/3)*(b*x**2+a)**(1/3),x)","\frac{\sqrt[3]{a} c^{\frac{7}{3}} x^{\frac{10}{3}} \Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{5}{3} \\ \frac{8}{3} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{8}{3}\right)}"," ",0,"a**(1/3)*c**(7/3)*x**(10/3)*gamma(5/3)*hyper((-1/3, 5/3), (8/3,), b*x**2*exp_polar(I*pi)/a)/(2*gamma(8/3))","C",0
740,1,46,0,1.522499," ","integrate((c*x)**(1/3)*(b*x**2+a)**(1/3),x)","\frac{\sqrt[3]{a} \sqrt[3]{c} x^{\frac{4}{3}} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{5}{3}\right)}"," ",0,"a**(1/3)*c**(1/3)*x**(4/3)*gamma(2/3)*hyper((-1/3, 2/3), (5/3,), b*x**2*exp_polar(I*pi)/a)/(2*gamma(5/3))","C",0
741,1,49,0,3.052394," ","integrate((b*x**2+a)**(1/3)/(c*x)**(5/3),x)","\frac{\sqrt[3]{a} \Gamma\left(- \frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, - \frac{1}{3} \\ \frac{2}{3} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 c^{\frac{5}{3}} x^{\frac{2}{3}} \Gamma\left(\frac{2}{3}\right)}"," ",0,"a**(1/3)*gamma(-1/3)*hyper((-1/3, -1/3), (2/3,), b*x**2*exp_polar(I*pi)/a)/(2*c**(5/3)*x**(2/3)*gamma(2/3))","C",0
742,1,78,0,56.585938," ","integrate((b*x**2+a)**(1/3)/(c*x)**(11/3),x)","\frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b x^{2}} + 1} \Gamma\left(- \frac{4}{3}\right)}{2 c^{\frac{11}{3}} x^{2} \Gamma\left(- \frac{1}{3}\right)} + \frac{b^{\frac{4}{3}} \sqrt[3]{\frac{a}{b x^{2}} + 1} \Gamma\left(- \frac{4}{3}\right)}{2 a c^{\frac{11}{3}} \Gamma\left(- \frac{1}{3}\right)}"," ",0,"b**(1/3)*(a/(b*x**2) + 1)**(1/3)*gamma(-4/3)/(2*c**(11/3)*x**2*gamma(-1/3)) + b**(4/3)*(a/(b*x**2) + 1)**(1/3)*gamma(-4/3)/(2*a*c**(11/3)*gamma(-1/3))","B",0
743,-1,0,0,0.000000," ","integrate((b*x**2+a)**(1/3)/(c*x)**(17/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
744,-1,0,0,0.000000," ","integrate((b*x**2+a)**(1/3)/(c*x)**(23/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
745,-1,0,0,0.000000," ","integrate((b*x**2+a)**(1/3)/(c*x)**(29/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
746,1,46,0,127.899066," ","integrate((c*x)**(10/3)*(b*x**2+a)**(1/3),x)","\frac{\sqrt[3]{a} c^{\frac{10}{3}} x^{\frac{13}{3}} \Gamma\left(\frac{13}{6}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{13}{6} \\ \frac{19}{6} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{19}{6}\right)}"," ",0,"a**(1/3)*c**(10/3)*x**(13/3)*gamma(13/6)*hyper((-1/3, 13/6), (19/6,), b*x**2*exp_polar(I*pi)/a)/(2*gamma(19/6))","C",0
747,1,46,0,6.719549," ","integrate((c*x)**(4/3)*(b*x**2+a)**(1/3),x)","\frac{\sqrt[3]{a} c^{\frac{4}{3}} x^{\frac{7}{3}} \Gamma\left(\frac{7}{6}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{7}{6} \\ \frac{13}{6} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{13}{6}\right)}"," ",0,"a**(1/3)*c**(4/3)*x**(7/3)*gamma(7/6)*hyper((-1/3, 7/6), (13/6,), b*x**2*exp_polar(I*pi)/a)/(2*gamma(13/6))","C",0
748,1,46,0,1.312913," ","integrate((b*x**2+a)**(1/3)/(c*x)**(2/3),x)","\frac{\sqrt[3]{a} \sqrt[3]{x} \Gamma\left(\frac{1}{6}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{1}{6} \\ \frac{7}{6} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 c^{\frac{2}{3}} \Gamma\left(\frac{7}{6}\right)}"," ",0,"a**(1/3)*x**(1/3)*gamma(1/6)*hyper((-1/3, 1/6), (7/6,), b*x**2*exp_polar(I*pi)/a)/(2*c**(2/3)*gamma(7/6))","C",0
749,1,32,0,12.230731," ","integrate((b*x**2+a)**(1/3)/(c*x)**(8/3),x)","- \frac{\sqrt[3]{b} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{2}}} \right)}}{c^{\frac{8}{3}} x}"," ",0,"-b**(1/3)*hyper((-1/3, 1/2), (3/2,), a*exp_polar(I*pi)/(b*x**2))/(c**(8/3)*x)","C",0
750,-1,0,0,0.000000," ","integrate((b*x**2+a)**(1/3)/(c*x)**(14/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
751,1,46,0,1.896343," ","integrate((c*x)**(2/3)*(b*x**2+a)**(1/3),x)","\frac{\sqrt[3]{a} c^{\frac{2}{3}} x^{\frac{5}{3}} \Gamma\left(\frac{5}{6}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{5}{6} \\ \frac{11}{6} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{11}{6}\right)}"," ",0,"a**(1/3)*c**(2/3)*x**(5/3)*gamma(5/6)*hyper((-1/3, 5/6), (11/6,), b*x**2*exp_polar(I*pi)/a)/(2*gamma(11/6))","C",0
752,1,46,0,1.092876," ","integrate((b*x**2+a)**(1/3)/(c*x)**(1/3),x)","\frac{\sqrt[3]{a} x^{\frac{2}{3}} \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt[3]{c} \Gamma\left(\frac{4}{3}\right)}"," ",0,"a**(1/3)*x**(2/3)*gamma(1/3)*hyper((-1/3, 1/3), (4/3,), b*x**2*exp_polar(I*pi)/a)/(2*c**(1/3)*gamma(4/3))","C",0
753,1,49,0,2.020820," ","integrate((b*x**2+a)**(1/3)/(c*x)**(4/3),x)","\frac{\sqrt[3]{a} \Gamma\left(- \frac{1}{6}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, - \frac{1}{6} \\ \frac{5}{6} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 c^{\frac{4}{3}} \sqrt[3]{x} \Gamma\left(\frac{5}{6}\right)}"," ",0,"a**(1/3)*gamma(-1/6)*hyper((-1/3, -1/6), (5/6,), b*x**2*exp_polar(I*pi)/a)/(2*c**(4/3)*x**(1/3)*gamma(5/6))","C",0
754,-1,0,0,0.000000," ","integrate((c*x)**(13/3)*(b*x**2+a)**(4/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
755,1,46,0,64.864107," ","integrate((c*x)**(7/3)*(b*x**2+a)**(4/3),x)","\frac{a^{\frac{4}{3}} c^{\frac{7}{3}} x^{\frac{10}{3}} \Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{4}{3}, \frac{5}{3} \\ \frac{8}{3} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{8}{3}\right)}"," ",0,"a**(4/3)*c**(7/3)*x**(10/3)*gamma(5/3)*hyper((-4/3, 5/3), (8/3,), b*x**2*exp_polar(I*pi)/a)/(2*gamma(8/3))","C",0
756,1,46,0,7.090285," ","integrate((c*x)**(1/3)*(b*x**2+a)**(4/3),x)","\frac{a^{\frac{4}{3}} \sqrt[3]{c} x^{\frac{4}{3}} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{4}{3}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{5}{3}\right)}"," ",0,"a**(4/3)*c**(1/3)*x**(4/3)*gamma(2/3)*hyper((-4/3, 2/3), (5/3,), b*x**2*exp_polar(I*pi)/a)/(2*gamma(5/3))","C",0
757,1,49,0,7.232460," ","integrate((b*x**2+a)**(4/3)/(c*x)**(5/3),x)","\frac{a^{\frac{4}{3}} \Gamma\left(- \frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{4}{3}, - \frac{1}{3} \\ \frac{2}{3} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 c^{\frac{5}{3}} x^{\frac{2}{3}} \Gamma\left(\frac{2}{3}\right)}"," ",0,"a**(4/3)*gamma(-1/3)*hyper((-4/3, -1/3), (2/3,), b*x**2*exp_polar(I*pi)/a)/(2*c**(5/3)*x**(2/3)*gamma(2/3))","C",0
758,1,53,0,56.366024," ","integrate((b*x**2+a)**(4/3)/(c*x)**(11/3),x)","\frac{a^{\frac{4}{3}} \Gamma\left(- \frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{4}{3}, - \frac{4}{3} \\ - \frac{1}{3} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 c^{\frac{11}{3}} x^{\frac{8}{3}} \Gamma\left(- \frac{1}{3}\right)}"," ",0,"a**(4/3)*gamma(-4/3)*hyper((-4/3, -4/3), (-1/3,), b*x**2*exp_polar(I*pi)/a)/(2*c**(11/3)*x**(8/3)*gamma(-1/3))","C",0
759,-1,0,0,0.000000," ","integrate((b*x**2+a)**(4/3)/(c*x)**(17/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
760,-1,0,0,0.000000," ","integrate((b*x**2+a)**(4/3)/(c*x)**(23/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
761,-1,0,0,0.000000," ","integrate((b*x**2+a)**(4/3)/(c*x)**(29/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
762,-1,0,0,0.000000," ","integrate((c*x)**(10/3)*(b*x**2+a)**(4/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
763,1,46,0,14.949088," ","integrate((c*x)**(4/3)*(b*x**2+a)**(4/3),x)","\frac{a^{\frac{4}{3}} c^{\frac{4}{3}} x^{\frac{7}{3}} \Gamma\left(\frac{7}{6}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{4}{3}, \frac{7}{6} \\ \frac{13}{6} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{13}{6}\right)}"," ",0,"a**(4/3)*c**(4/3)*x**(7/3)*gamma(7/6)*hyper((-4/3, 7/6), (13/6,), b*x**2*exp_polar(I*pi)/a)/(2*gamma(13/6))","C",0
764,1,46,0,5.039362," ","integrate((b*x**2+a)**(4/3)/(c*x)**(2/3),x)","\frac{a^{\frac{4}{3}} \sqrt[3]{x} \Gamma\left(\frac{1}{6}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{4}{3}, \frac{1}{6} \\ \frac{7}{6} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 c^{\frac{2}{3}} \Gamma\left(\frac{7}{6}\right)}"," ",0,"a**(4/3)*x**(1/3)*gamma(1/6)*hyper((-4/3, 1/6), (7/6,), b*x**2*exp_polar(I*pi)/a)/(2*c**(2/3)*gamma(7/6))","C",0
765,1,32,0,15.928386," ","integrate((b*x**2+a)**(4/3)/(c*x)**(8/3),x)","\frac{b^{\frac{4}{3}} x {{}_{2}F_{1}\left(\begin{matrix} - \frac{4}{3}, - \frac{1}{2} \\ \frac{1}{2} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{2}}} \right)}}{c^{\frac{8}{3}}}"," ",0,"b**(4/3)*x*hyper((-4/3, -1/2), (1/2,), a*exp_polar(I*pi)/(b*x**2))/c**(8/3)","C",0
766,-1,0,0,0.000000," ","integrate((b*x**2+a)**(4/3)/(c*x)**(14/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
767,-1,0,0,0.000000," ","integrate((b*x**2+a)**(4/3)/(c*x)**(20/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
768,1,46,0,8.786951," ","integrate((c*x)**(2/3)*(b*x**2+a)**(4/3),x)","\frac{a^{\frac{4}{3}} c^{\frac{2}{3}} x^{\frac{5}{3}} \Gamma\left(\frac{5}{6}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{4}{3}, \frac{5}{6} \\ \frac{11}{6} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{11}{6}\right)}"," ",0,"a**(4/3)*c**(2/3)*x**(5/3)*gamma(5/6)*hyper((-4/3, 5/6), (11/6,), b*x**2*exp_polar(I*pi)/a)/(2*gamma(11/6))","C",0
769,1,46,0,5.111539," ","integrate((b*x**2+a)**(4/3)/(c*x)**(1/3),x)","\frac{a^{\frac{4}{3}} x^{\frac{2}{3}} \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{4}{3}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt[3]{c} \Gamma\left(\frac{4}{3}\right)}"," ",0,"a**(4/3)*x**(2/3)*gamma(1/3)*hyper((-4/3, 1/3), (4/3,), b*x**2*exp_polar(I*pi)/a)/(2*c**(1/3)*gamma(4/3))","C",0
770,1,49,0,5.071095," ","integrate((b*x**2+a)**(4/3)/(c*x)**(4/3),x)","\frac{a^{\frac{4}{3}} \Gamma\left(- \frac{1}{6}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{4}{3}, - \frac{1}{6} \\ \frac{5}{6} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 c^{\frac{4}{3}} \sqrt[3]{x} \Gamma\left(\frac{5}{6}\right)}"," ",0,"a**(4/3)*gamma(-1/6)*hyper((-4/3, -1/6), (5/6,), b*x**2*exp_polar(I*pi)/a)/(2*c**(4/3)*x**(1/3)*gamma(5/6))","C",0
771,-1,0,0,0.000000," ","integrate((c*x)**(19/3)/(b*x**2+a)**(2/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
772,-1,0,0,0.000000," ","integrate((c*x)**(13/3)/(b*x**2+a)**(2/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
773,1,44,0,30.010564," ","integrate((c*x)**(7/3)/(b*x**2+a)**(2/3),x)","\frac{c^{\frac{7}{3}} x^{\frac{10}{3}} \Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{3}, \frac{5}{3} \\ \frac{8}{3} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{2}{3}} \Gamma\left(\frac{8}{3}\right)}"," ",0,"c**(7/3)*x**(10/3)*gamma(5/3)*hyper((2/3, 5/3), (8/3,), b*x**2*exp_polar(I*pi)/a)/(2*a**(2/3)*gamma(8/3))","C",0
774,1,44,0,1.524629," ","integrate((c*x)**(1/3)/(b*x**2+a)**(2/3),x)","\frac{\sqrt[3]{c} x^{\frac{4}{3}} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{3}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{2}{3}} \Gamma\left(\frac{5}{3}\right)}"," ",0,"c**(1/3)*x**(4/3)*gamma(2/3)*hyper((2/3, 2/3), (5/3,), b*x**2*exp_polar(I*pi)/a)/(2*a**(2/3)*gamma(5/3))","C",0
775,1,36,0,4.166106," ","integrate(1/(c*x)**(5/3)/(b*x**2+a)**(2/3),x)","\frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b x^{2}} + 1} \Gamma\left(- \frac{1}{3}\right)}{2 a c^{\frac{5}{3}} \Gamma\left(\frac{2}{3}\right)}"," ",0,"b**(1/3)*(a/(b*x**2) + 1)**(1/3)*gamma(-1/3)/(2*a*c**(5/3)*gamma(2/3))","A",0
776,1,78,0,109.453966," ","integrate(1/(c*x)**(11/3)/(b*x**2+a)**(2/3),x)","- \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b x^{2}} + 1} \Gamma\left(- \frac{4}{3}\right)}{6 a c^{\frac{11}{3}} x^{2} \Gamma\left(\frac{2}{3}\right)} + \frac{b^{\frac{4}{3}} \sqrt[3]{\frac{a}{b x^{2}} + 1} \Gamma\left(- \frac{4}{3}\right)}{2 a^{2} c^{\frac{11}{3}} \Gamma\left(\frac{2}{3}\right)}"," ",0,"-b**(1/3)*(a/(b*x**2) + 1)**(1/3)*gamma(-4/3)/(6*a*c**(11/3)*x**2*gamma(2/3)) + b**(4/3)*(a/(b*x**2) + 1)**(1/3)*gamma(-4/3)/(2*a**2*c**(11/3)*gamma(2/3))","A",0
777,-1,0,0,0.000000," ","integrate(1/(c*x)**(17/3)/(b*x**2+a)**(2/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
778,-1,0,0,0.000000," ","integrate(1/(c*x)**(23/3)/(b*x**2+a)**(2/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
779,1,44,0,126.930373," ","integrate((c*x)**(10/3)/(b*x**2+a)**(2/3),x)","\frac{c^{\frac{10}{3}} x^{\frac{13}{3}} \Gamma\left(\frac{13}{6}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{3}, \frac{13}{6} \\ \frac{19}{6} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{2}{3}} \Gamma\left(\frac{19}{6}\right)}"," ",0,"c**(10/3)*x**(13/3)*gamma(13/6)*hyper((2/3, 13/6), (19/6,), b*x**2*exp_polar(I*pi)/a)/(2*a**(2/3)*gamma(19/6))","C",0
780,1,44,0,5.435388," ","integrate((c*x)**(4/3)/(b*x**2+a)**(2/3),x)","\frac{c^{\frac{4}{3}} x^{\frac{7}{3}} \Gamma\left(\frac{7}{6}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{3}, \frac{7}{6} \\ \frac{13}{6} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{2}{3}} \Gamma\left(\frac{13}{6}\right)}"," ",0,"c**(4/3)*x**(7/3)*gamma(7/6)*hyper((2/3, 7/6), (13/6,), b*x**2*exp_polar(I*pi)/a)/(2*a**(2/3)*gamma(13/6))","C",0
781,1,31,0,1.786348," ","integrate(1/(c*x)**(2/3)/(b*x**2+a)**(2/3),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{3}{2} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{2}}} \right)}}{b^{\frac{2}{3}} c^{\frac{2}{3}} x}"," ",0,"-hyper((1/2, 2/3), (3/2,), a*exp_polar(I*pi)/(b*x**2))/(b**(2/3)*c**(2/3)*x)","C",0
782,1,48,0,25.884663," ","integrate(1/(c*x)**(8/3)/(b*x**2+a)**(2/3),x)","\frac{\Gamma\left(- \frac{5}{6}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{6}, \frac{2}{3} \\ \frac{1}{6} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{2}{3}} c^{\frac{8}{3}} x^{\frac{5}{3}} \Gamma\left(\frac{1}{6}\right)}"," ",0,"gamma(-5/6)*hyper((-5/6, 2/3), (1/6,), b*x**2*exp_polar(I*pi)/a)/(2*a**(2/3)*c**(8/3)*x**(5/3)*gamma(1/6))","C",0
783,-1,0,0,0.000000," ","integrate(1/(c*x)**(14/3)/(b*x**2+a)**(2/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
784,1,44,0,1.593163," ","integrate((c*x)**(2/3)/(b*x**2+a)**(2/3),x)","\frac{c^{\frac{2}{3}} x^{\frac{5}{3}} \Gamma\left(\frac{5}{6}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{3}, \frac{5}{6} \\ \frac{11}{6} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{2}{3}} \Gamma\left(\frac{11}{6}\right)}"," ",0,"c**(2/3)*x**(5/3)*gamma(5/6)*hyper((2/3, 5/6), (11/6,), b*x**2*exp_polar(I*pi)/a)/(2*a**(2/3)*gamma(11/6))","C",0
785,1,46,0,1.380701," ","integrate(1/(c*x)**(1/3)/(b*x**2+a)**(2/3),x)","\frac{\Gamma\left(- \frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{2}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{2}}} \right)}}{2 b^{\frac{2}{3}} \sqrt[3]{c} x^{\frac{2}{3}} \Gamma\left(\frac{2}{3}\right)}"," ",0,"gamma(-1/3)*hyper((1/3, 2/3), (4/3,), a*exp_polar(I*pi)/(b*x**2))/(2*b**(2/3)*c**(1/3)*x**(2/3)*gamma(2/3))","C",0
786,1,48,0,3.073369," ","integrate(1/(c*x)**(4/3)/(b*x**2+a)**(2/3),x)","\frac{\Gamma\left(- \frac{1}{6}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{6}, \frac{2}{3} \\ \frac{5}{6} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{2}{3}} c^{\frac{4}{3}} \sqrt[3]{x} \Gamma\left(\frac{5}{6}\right)}"," ",0,"gamma(-1/6)*hyper((-1/6, 2/3), (5/6,), b*x**2*exp_polar(I*pi)/a)/(2*a**(2/3)*c**(4/3)*x**(1/3)*gamma(5/6))","C",0
787,1,29,0,0.967127," ","integrate(x**4*(b*x**2+a)**(1/4),x)","\frac{\sqrt[4]{a} x^{5} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{5}"," ",0,"a**(1/4)*x**5*hyper((-1/4, 5/2), (7/2,), b*x**2*exp_polar(I*pi)/a)/5","C",0
788,1,29,0,0.856968," ","integrate(x**2*(b*x**2+a)**(1/4),x)","\frac{\sqrt[4]{a} x^{3} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{3}"," ",0,"a**(1/4)*x**3*hyper((-1/4, 3/2), (5/2,), b*x**2*exp_polar(I*pi)/a)/3","C",0
789,1,26,0,0.811360," ","integrate((b*x**2+a)**(1/4),x)","\sqrt[4]{a} x {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}"," ",0,"a**(1/4)*x*hyper((-1/4, 1/2), (3/2,), b*x**2*exp_polar(I*pi)/a)","C",0
790,1,29,0,0.858586," ","integrate((b*x**2+a)**(1/4)/x**2,x)","- \frac{\sqrt[4]{a} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{1}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{x}"," ",0,"-a**(1/4)*hyper((-1/2, -1/4), (1/2,), b*x**2*exp_polar(I*pi)/a)/x","C",0
791,1,34,0,0.977427," ","integrate((b*x**2+a)**(1/4)/x**4,x)","- \frac{\sqrt[4]{a} {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, - \frac{1}{4} \\ - \frac{1}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{3 x^{3}}"," ",0,"-a**(1/4)*hyper((-3/2, -1/4), (-1/2,), b*x**2*exp_polar(I*pi)/a)/(3*x**3)","C",0
792,1,34,0,1.102179," ","integrate((b*x**2+a)**(1/4)/x**6,x)","- \frac{\sqrt[4]{a} {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{2}, - \frac{1}{4} \\ - \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{5 x^{5}}"," ",0,"-a**(1/4)*hyper((-5/2, -1/4), (-3/2,), b*x**2*exp_polar(I*pi)/a)/(5*x**5)","C",0
793,1,31,0,0.976403," ","integrate(x**4*(-b*x**2+a)**(1/4),x)","\frac{\sqrt[4]{a} x^{5} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{5}"," ",0,"a**(1/4)*x**5*hyper((-1/4, 5/2), (7/2,), b*x**2*exp_polar(2*I*pi)/a)/5","C",0
794,1,31,0,0.900953," ","integrate(x**2*(-b*x**2+a)**(1/4),x)","\frac{\sqrt[4]{a} x^{3} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{3}"," ",0,"a**(1/4)*x**3*hyper((-1/4, 3/2), (5/2,), b*x**2*exp_polar(2*I*pi)/a)/3","C",0
795,1,27,0,0.825973," ","integrate((-b*x**2+a)**(1/4),x)","\sqrt[4]{a} x {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}"," ",0,"a**(1/4)*x*hyper((-1/4, 1/2), (3/2,), b*x**2*exp_polar(2*I*pi)/a)","C",0
796,1,31,0,0.916160," ","integrate((-b*x**2+a)**(1/4)/x**2,x)","- \frac{\sqrt[4]{a} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{1}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{x}"," ",0,"-a**(1/4)*hyper((-1/2, -1/4), (1/2,), b*x**2*exp_polar(2*I*pi)/a)/x","C",0
797,1,36,0,1.005704," ","integrate((-b*x**2+a)**(1/4)/x**4,x)","- \frac{\sqrt[4]{a} {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, - \frac{1}{4} \\ - \frac{1}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{3 x^{3}}"," ",0,"-a**(1/4)*hyper((-3/2, -1/4), (-1/2,), b*x**2*exp_polar(2*I*pi)/a)/(3*x**3)","C",0
798,1,36,0,1.128389," ","integrate((-b*x**2+a)**(1/4)/x**6,x)","- \frac{\sqrt[4]{a} {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{2}, - \frac{1}{4} \\ - \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{5 x^{5}}"," ",0,"-a**(1/4)*hyper((-5/2, -1/4), (-3/2,), b*x**2*exp_polar(2*I*pi)/a)/(5*x**5)","C",0
799,1,29,0,1.196577," ","integrate(x**4*(b*x**2+a)**(3/4),x)","\frac{a^{\frac{3}{4}} x^{5} {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{5}"," ",0,"a**(3/4)*x**5*hyper((-3/4, 5/2), (7/2,), b*x**2*exp_polar(I*pi)/a)/5","C",0
800,1,29,0,1.059245," ","integrate(x**2*(b*x**2+a)**(3/4),x)","\frac{a^{\frac{3}{4}} x^{3} {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{3}"," ",0,"a**(3/4)*x**3*hyper((-3/4, 3/2), (5/2,), b*x**2*exp_polar(I*pi)/a)/3","C",0
801,1,26,0,0.941183," ","integrate((b*x**2+a)**(3/4),x)","a^{\frac{3}{4}} x {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}"," ",0,"a**(3/4)*x*hyper((-3/4, 1/2), (3/2,), b*x**2*exp_polar(I*pi)/a)","C",0
802,1,29,0,1.026809," ","integrate((b*x**2+a)**(3/4)/x**2,x)","- \frac{a^{\frac{3}{4}} {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, - \frac{1}{2} \\ \frac{1}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{x}"," ",0,"-a**(3/4)*hyper((-3/4, -1/2), (1/2,), b*x**2*exp_polar(I*pi)/a)/x","C",0
803,1,34,0,1.087608," ","integrate((b*x**2+a)**(3/4)/x**4,x)","- \frac{a^{\frac{3}{4}} {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, - \frac{3}{4} \\ - \frac{1}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{3 x^{3}}"," ",0,"-a**(3/4)*hyper((-3/2, -3/4), (-1/2,), b*x**2*exp_polar(I*pi)/a)/(3*x**3)","C",0
804,1,34,0,1.233807," ","integrate((b*x**2+a)**(3/4)/x**6,x)","- \frac{a^{\frac{3}{4}} {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{2}, - \frac{3}{4} \\ - \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{5 x^{5}}"," ",0,"-a**(3/4)*hyper((-5/2, -3/4), (-3/2,), b*x**2*exp_polar(I*pi)/a)/(5*x**5)","C",0
805,1,31,0,1.204945," ","integrate(x**4*(-b*x**2+a)**(3/4),x)","\frac{a^{\frac{3}{4}} x^{5} {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{5}"," ",0,"a**(3/4)*x**5*hyper((-3/4, 5/2), (7/2,), b*x**2*exp_polar(2*I*pi)/a)/5","C",0
806,1,31,0,1.078509," ","integrate(x**2*(-b*x**2+a)**(3/4),x)","\frac{a^{\frac{3}{4}} x^{3} {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{3}"," ",0,"a**(3/4)*x**3*hyper((-3/4, 3/2), (5/2,), b*x**2*exp_polar(2*I*pi)/a)/3","C",0
807,1,27,0,0.969932," ","integrate((-b*x**2+a)**(3/4),x)","a^{\frac{3}{4}} x {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}"," ",0,"a**(3/4)*x*hyper((-3/4, 1/2), (3/2,), b*x**2*exp_polar(2*I*pi)/a)","C",0
808,1,31,0,1.047731," ","integrate((-b*x**2+a)**(3/4)/x**2,x)","- \frac{a^{\frac{3}{4}} {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, - \frac{1}{2} \\ \frac{1}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{x}"," ",0,"-a**(3/4)*hyper((-3/4, -1/2), (1/2,), b*x**2*exp_polar(2*I*pi)/a)/x","C",0
809,1,36,0,1.120811," ","integrate((-b*x**2+a)**(3/4)/x**4,x)","- \frac{a^{\frac{3}{4}} {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, - \frac{3}{4} \\ - \frac{1}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{3 x^{3}}"," ",0,"-a**(3/4)*hyper((-3/2, -3/4), (-1/2,), b*x**2*exp_polar(2*I*pi)/a)/(3*x**3)","C",0
810,1,36,0,1.278226," ","integrate((-b*x**2+a)**(3/4)/x**6,x)","- \frac{a^{\frac{3}{4}} {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{2}, - \frac{3}{4} \\ - \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{5 x^{5}}"," ",0,"-a**(3/4)*hyper((-5/2, -3/4), (-3/2,), b*x**2*exp_polar(2*I*pi)/a)/(5*x**5)","C",0
811,1,26,0,1.156292," ","integrate((b*x**2+a)**(5/4),x)","a^{\frac{5}{4}} x {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}"," ",0,"a**(5/4)*x*hyper((-5/4, 1/2), (3/2,), b*x**2*exp_polar(I*pi)/a)","C",0
812,1,27,0,1.185438," ","integrate((-b*x**2+a)**(5/4),x)","a^{\frac{5}{4}} x {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}"," ",0,"a**(5/4)*x*hyper((-5/4, 1/2), (3/2,), b*x**2*exp_polar(2*I*pi)/a)","C",0
813,1,26,0,1.537065," ","integrate((b*x**2+a)**(7/4),x)","a^{\frac{7}{4}} x {{}_{2}F_{1}\left(\begin{matrix} - \frac{7}{4}, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}"," ",0,"a**(7/4)*x*hyper((-7/4, 1/2), (3/2,), b*x**2*exp_polar(I*pi)/a)","C",0
814,1,27,0,1.541621," ","integrate((-b*x**2+a)**(7/4),x)","a^{\frac{7}{4}} x {{}_{2}F_{1}\left(\begin{matrix} - \frac{7}{4}, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}"," ",0,"a**(7/4)*x*hyper((-7/4, 1/2), (3/2,), b*x**2*exp_polar(2*I*pi)/a)","C",0
815,1,27,0,0.972650," ","integrate(x**6/(b*x**2+a)**(1/4),x)","\frac{x^{7} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{7}{2} \\ \frac{9}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{7 \sqrt[4]{a}}"," ",0,"x**7*hyper((1/4, 7/2), (9/2,), b*x**2*exp_polar(I*pi)/a)/(7*a**(1/4))","C",0
816,1,27,0,0.863988," ","integrate(x**4/(b*x**2+a)**(1/4),x)","\frac{x^{5} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{5 \sqrt[4]{a}}"," ",0,"x**5*hyper((1/4, 5/2), (7/2,), b*x**2*exp_polar(I*pi)/a)/(5*a**(1/4))","C",0
817,1,27,0,0.796375," ","integrate(x**2/(b*x**2+a)**(1/4),x)","\frac{x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{3 \sqrt[4]{a}}"," ",0,"x**3*hyper((1/4, 3/2), (5/2,), b*x**2*exp_polar(I*pi)/a)/(3*a**(1/4))","C",0
818,1,24,0,0.775537," ","integrate(1/(b*x**2+a)**(1/4),x)","\frac{x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{\sqrt[4]{a}}"," ",0,"x*hyper((1/4, 1/2), (3/2,), b*x**2*exp_polar(I*pi)/a)/a**(1/4)","C",0
819,1,27,0,0.853554," ","integrate(1/x**2/(b*x**2+a)**(1/4),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{1}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{\sqrt[4]{a} x}"," ",0,"-hyper((-1/2, 1/4), (1/2,), b*x**2*exp_polar(I*pi)/a)/(a**(1/4)*x)","C",0
820,1,32,0,0.998691," ","integrate(1/x**4/(b*x**2+a)**(1/4),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, \frac{1}{4} \\ - \frac{1}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{3 \sqrt[4]{a} x^{3}}"," ",0,"-hyper((-3/2, 1/4), (-1/2,), b*x**2*exp_polar(I*pi)/a)/(3*a**(1/4)*x**3)","C",0
821,1,32,0,1.107276," ","integrate(1/x**6/(b*x**2+a)**(1/4),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{2}, \frac{1}{4} \\ - \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{5 \sqrt[4]{a} x^{5}}"," ",0,"-hyper((-5/2, 1/4), (-3/2,), b*x**2*exp_polar(I*pi)/a)/(5*a**(1/4)*x**5)","C",0
822,1,29,0,1.005778," ","integrate(x**6/(-b*x**2+a)**(1/4),x)","\frac{x^{7} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{7}{2} \\ \frac{9}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{7 \sqrt[4]{a}}"," ",0,"x**7*hyper((1/4, 7/2), (9/2,), b*x**2*exp_polar(2*I*pi)/a)/(7*a**(1/4))","C",0
823,1,29,0,0.912049," ","integrate(x**4/(-b*x**2+a)**(1/4),x)","\frac{x^{5} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{5 \sqrt[4]{a}}"," ",0,"x**5*hyper((1/4, 5/2), (7/2,), b*x**2*exp_polar(2*I*pi)/a)/(5*a**(1/4))","C",0
824,1,29,0,0.823823," ","integrate(x**2/(-b*x**2+a)**(1/4),x)","\frac{x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{3 \sqrt[4]{a}}"," ",0,"x**3*hyper((1/4, 3/2), (5/2,), b*x**2*exp_polar(2*I*pi)/a)/(3*a**(1/4))","C",0
825,1,26,0,0.785679," ","integrate(1/(-b*x**2+a)**(1/4),x)","\frac{x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{\sqrt[4]{a}}"," ",0,"x*hyper((1/4, 1/2), (3/2,), b*x**2*exp_polar(2*I*pi)/a)/a**(1/4)","C",0
826,1,29,0,0.895698," ","integrate(1/x**2/(-b*x**2+a)**(1/4),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{1}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{\sqrt[4]{a} x}"," ",0,"-hyper((-1/2, 1/4), (1/2,), b*x**2*exp_polar(2*I*pi)/a)/(a**(1/4)*x)","C",0
827,1,34,0,1.011669," ","integrate(1/x**4/(-b*x**2+a)**(1/4),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, \frac{1}{4} \\ - \frac{1}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{3 \sqrt[4]{a} x^{3}}"," ",0,"-hyper((-3/2, 1/4), (-1/2,), b*x**2*exp_polar(2*I*pi)/a)/(3*a**(1/4)*x**3)","C",0
828,1,34,0,1.131770," ","integrate(1/x**6/(-b*x**2+a)**(1/4),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{2}, \frac{1}{4} \\ - \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{5 \sqrt[4]{a} x^{5}}"," ",0,"-hyper((-5/2, 1/4), (-3/2,), b*x**2*exp_polar(2*I*pi)/a)/(5*a**(1/4)*x**5)","C",0
829,1,27,0,0.964471," ","integrate(x**6/(b*x**2+a)**(3/4),x)","\frac{x^{7} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{7}{2} \\ \frac{9}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{7 a^{\frac{3}{4}}}"," ",0,"x**7*hyper((3/4, 7/2), (9/2,), b*x**2*exp_polar(I*pi)/a)/(7*a**(3/4))","C",0
830,1,27,0,0.854506," ","integrate(x**4/(b*x**2+a)**(3/4),x)","\frac{x^{5} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{5 a^{\frac{3}{4}}}"," ",0,"x**5*hyper((3/4, 5/2), (7/2,), b*x**2*exp_polar(I*pi)/a)/(5*a**(3/4))","C",0
831,1,27,0,0.819304," ","integrate(x**2/(b*x**2+a)**(3/4),x)","\frac{x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{3 a^{\frac{3}{4}}}"," ",0,"x**3*hyper((3/4, 3/2), (5/2,), b*x**2*exp_polar(I*pi)/a)/(3*a**(3/4))","C",0
832,1,24,0,0.780718," ","integrate(1/(b*x**2+a)**(3/4),x)","\frac{x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{a^{\frac{3}{4}}}"," ",0,"x*hyper((1/2, 3/4), (3/2,), b*x**2*exp_polar(I*pi)/a)/a**(3/4)","C",0
833,1,27,0,0.962941," ","integrate(1/x**2/(b*x**2+a)**(3/4),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{1}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{a^{\frac{3}{4}} x}"," ",0,"-hyper((-1/2, 3/4), (1/2,), b*x**2*exp_polar(I*pi)/a)/(a**(3/4)*x)","C",0
834,1,32,0,1.087271," ","integrate(1/x**4/(b*x**2+a)**(3/4),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, \frac{3}{4} \\ - \frac{1}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{3 a^{\frac{3}{4}} x^{3}}"," ",0,"-hyper((-3/2, 3/4), (-1/2,), b*x**2*exp_polar(I*pi)/a)/(3*a**(3/4)*x**3)","C",0
835,1,32,0,1.229106," ","integrate(1/x**6/(b*x**2+a)**(3/4),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{2}, \frac{3}{4} \\ - \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{5 a^{\frac{3}{4}} x^{5}}"," ",0,"-hyper((-5/2, 3/4), (-3/2,), b*x**2*exp_polar(I*pi)/a)/(5*a**(3/4)*x**5)","C",0
836,1,29,0,0.993071," ","integrate(x**6/(-b*x**2+a)**(3/4),x)","\frac{x^{7} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{7}{2} \\ \frac{9}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{7 a^{\frac{3}{4}}}"," ",0,"x**7*hyper((3/4, 7/2), (9/2,), b*x**2*exp_polar(2*I*pi)/a)/(7*a**(3/4))","C",0
837,1,29,0,0.904760," ","integrate(x**4/(-b*x**2+a)**(3/4),x)","\frac{x^{5} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{5 a^{\frac{3}{4}}}"," ",0,"x**5*hyper((3/4, 5/2), (7/2,), b*x**2*exp_polar(2*I*pi)/a)/(5*a**(3/4))","C",0
838,1,29,0,0.837630," ","integrate(x**2/(-b*x**2+a)**(3/4),x)","\frac{x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{3 a^{\frac{3}{4}}}"," ",0,"x**3*hyper((3/4, 3/2), (5/2,), b*x**2*exp_polar(2*I*pi)/a)/(3*a**(3/4))","C",0
839,1,26,0,0.805312," ","integrate(1/(-b*x**2+a)**(3/4),x)","\frac{x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{a^{\frac{3}{4}}}"," ",0,"x*hyper((1/2, 3/4), (3/2,), b*x**2*exp_polar(2*I*pi)/a)/a**(3/4)","C",0
840,1,29,0,0.982293," ","integrate(1/x**2/(-b*x**2+a)**(3/4),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{1}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{a^{\frac{3}{4}} x}"," ",0,"-hyper((-1/2, 3/4), (1/2,), b*x**2*exp_polar(2*I*pi)/a)/(a**(3/4)*x)","C",0
841,1,34,0,1.102441," ","integrate(1/x**4/(-b*x**2+a)**(3/4),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, \frac{3}{4} \\ - \frac{1}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{3 a^{\frac{3}{4}} x^{3}}"," ",0,"-hyper((-3/2, 3/4), (-1/2,), b*x**2*exp_polar(2*I*pi)/a)/(3*a**(3/4)*x**3)","C",0
842,1,34,0,1.253017," ","integrate(1/x**6/(-b*x**2+a)**(3/4),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{2}, \frac{3}{4} \\ - \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{5 a^{\frac{3}{4}} x^{5}}"," ",0,"-hyper((-5/2, 3/4), (-3/2,), b*x**2*exp_polar(2*I*pi)/a)/(5*a**(3/4)*x**5)","C",0
843,1,27,0,0.973849," ","integrate(x**6/(b*x**2+a)**(5/4),x)","\frac{x^{7} {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, \frac{7}{2} \\ \frac{9}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{7 a^{\frac{5}{4}}}"," ",0,"x**7*hyper((5/4, 7/2), (9/2,), b*x**2*exp_polar(I*pi)/a)/(7*a**(5/4))","C",0
844,1,27,0,0.927563," ","integrate(x**4/(b*x**2+a)**(5/4),x)","\frac{x^{5} {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{5 a^{\frac{5}{4}}}"," ",0,"x**5*hyper((5/4, 5/2), (7/2,), b*x**2*exp_polar(I*pi)/a)/(5*a**(5/4))","C",0
845,1,27,0,0.917419," ","integrate(x**2/(b*x**2+a)**(5/4),x)","\frac{x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{3 a^{\frac{5}{4}}}"," ",0,"x**3*hyper((5/4, 3/2), (5/2,), b*x**2*exp_polar(I*pi)/a)/(3*a**(5/4))","C",0
846,1,24,0,0.889009," ","integrate(1/(b*x**2+a)**(5/4),x)","\frac{x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{5}{4} \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{a^{\frac{5}{4}}}"," ",0,"x*hyper((1/2, 5/4), (3/2,), b*x**2*exp_polar(I*pi)/a)/a**(5/4)","C",0
847,1,27,0,1.066714," ","integrate(1/x**2/(b*x**2+a)**(5/4),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{4} \\ \frac{1}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{a^{\frac{5}{4}} x}"," ",0,"-hyper((-1/2, 5/4), (1/2,), b*x**2*exp_polar(I*pi)/a)/(a**(5/4)*x)","C",0
848,1,32,0,1.227026," ","integrate(1/x**4/(b*x**2+a)**(5/4),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, \frac{5}{4} \\ - \frac{1}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{3 a^{\frac{5}{4}} x^{3}}"," ",0,"-hyper((-3/2, 5/4), (-1/2,), b*x**2*exp_polar(I*pi)/a)/(3*a**(5/4)*x**3)","C",0
849,1,32,0,1.404203," ","integrate(1/x**6/(b*x**2+a)**(5/4),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{2}, \frac{5}{4} \\ - \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{5 a^{\frac{5}{4}} x^{5}}"," ",0,"-hyper((-5/2, 5/4), (-3/2,), b*x**2*exp_polar(I*pi)/a)/(5*a**(5/4)*x**5)","C",0
850,1,29,0,0.986465," ","integrate(x**6/(-b*x**2+a)**(5/4),x)","\frac{x^{7} {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, \frac{7}{2} \\ \frac{9}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{7 a^{\frac{5}{4}}}"," ",0,"x**7*hyper((5/4, 7/2), (9/2,), b*x**2*exp_polar(2*I*pi)/a)/(7*a**(5/4))","C",0
851,1,29,0,0.949160," ","integrate(x**4/(-b*x**2+a)**(5/4),x)","\frac{x^{5} {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{5 a^{\frac{5}{4}}}"," ",0,"x**5*hyper((5/4, 5/2), (7/2,), b*x**2*exp_polar(2*I*pi)/a)/(5*a**(5/4))","C",0
852,1,29,0,0.933652," ","integrate(x**2/(-b*x**2+a)**(5/4),x)","\frac{x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{3 a^{\frac{5}{4}}}"," ",0,"x**3*hyper((5/4, 3/2), (5/2,), b*x**2*exp_polar(2*I*pi)/a)/(3*a**(5/4))","C",0
853,1,26,0,0.892344," ","integrate(1/(-b*x**2+a)**(5/4),x)","\frac{x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{5}{4} \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{a^{\frac{5}{4}}}"," ",0,"x*hyper((1/2, 5/4), (3/2,), b*x**2*exp_polar(2*I*pi)/a)/a**(5/4)","C",0
854,1,29,0,1.089104," ","integrate(1/x**2/(-b*x**2+a)**(5/4),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{4} \\ \frac{1}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{a^{\frac{5}{4}} x}"," ",0,"-hyper((-1/2, 5/4), (1/2,), b*x**2*exp_polar(2*I*pi)/a)/(a**(5/4)*x)","C",0
855,1,34,0,1.246248," ","integrate(1/x**4/(-b*x**2+a)**(5/4),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, \frac{5}{4} \\ - \frac{1}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{3 a^{\frac{5}{4}} x^{3}}"," ",0,"-hyper((-3/2, 5/4), (-1/2,), b*x**2*exp_polar(2*I*pi)/a)/(3*a**(5/4)*x**3)","C",0
856,1,34,0,1.437739," ","integrate(1/x**6/(-b*x**2+a)**(5/4),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{2}, \frac{5}{4} \\ - \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{5 a^{\frac{5}{4}} x^{5}}"," ",0,"-hyper((-5/2, 5/4), (-3/2,), b*x**2*exp_polar(2*I*pi)/a)/(5*a**(5/4)*x**5)","C",0
857,1,24,0,1.042168," ","integrate(1/(b*x**2+a)**(7/4),x)","\frac{x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{7}{4} \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{a^{\frac{7}{4}}}"," ",0,"x*hyper((1/2, 7/4), (3/2,), b*x**2*exp_polar(I*pi)/a)/a**(7/4)","C",0
858,1,24,0,1.357858," ","integrate(1/(b*x**2+a)**(9/4),x)","\frac{x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{9}{4} \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{a^{\frac{9}{4}}}"," ",0,"x*hyper((1/2, 9/4), (3/2,), b*x**2*exp_polar(I*pi)/a)/a**(9/4)","C",0
859,1,24,0,1.813540," ","integrate(1/(b*x**2+a)**(11/4),x)","\frac{x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{11}{4} \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{a^{\frac{11}{4}}}"," ",0,"x*hyper((1/2, 11/4), (3/2,), b*x**2*exp_polar(I*pi)/a)/a**(11/4)","C",0
860,1,26,0,1.061860," ","integrate(1/(-b*x**2+a)**(7/4),x)","\frac{x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{7}{4} \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{a^{\frac{7}{4}}}"," ",0,"x*hyper((1/2, 7/4), (3/2,), b*x**2*exp_polar(2*I*pi)/a)/a**(7/4)","C",0
861,1,26,0,1.363566," ","integrate(1/(-b*x**2+a)**(9/4),x)","\frac{x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{9}{4} \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{a^{\frac{9}{4}}}"," ",0,"x*hyper((1/2, 9/4), (3/2,), b*x**2*exp_polar(2*I*pi)/a)/a**(9/4)","C",0
862,1,26,0,1.840174," ","integrate(1/(-b*x**2+a)**(11/4),x)","\frac{x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{11}{4} \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{a^{\frac{11}{4}}}"," ",0,"x*hyper((1/2, 11/4), (3/2,), b*x**2*exp_polar(2*I*pi)/a)/a**(11/4)","C",0
863,1,27,0,0.829800," ","integrate(x**6/(3*x**2+2)**(1/4),x)","\frac{2^{\frac{3}{4}} x^{7} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{7}{2} \\ \frac{9}{2} \end{matrix}\middle| {\frac{3 x^{2} e^{i \pi}}{2}} \right)}}{14}"," ",0,"2**(3/4)*x**7*hyper((1/4, 7/2), (9/2,), 3*x**2*exp_polar(I*pi)/2)/14","C",0
864,1,27,0,0.754708," ","integrate(x**4/(3*x**2+2)**(1/4),x)","\frac{2^{\frac{3}{4}} x^{5} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{3 x^{2} e^{i \pi}}{2}} \right)}}{10}"," ",0,"2**(3/4)*x**5*hyper((1/4, 5/2), (7/2,), 3*x**2*exp_polar(I*pi)/2)/10","C",0
865,1,27,0,0.695324," ","integrate(x**2/(3*x**2+2)**(1/4),x)","\frac{2^{\frac{3}{4}} x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{3 x^{2} e^{i \pi}}{2}} \right)}}{6}"," ",0,"2**(3/4)*x**3*hyper((1/4, 3/2), (5/2,), 3*x**2*exp_polar(I*pi)/2)/6","C",0
866,1,26,0,0.672271," ","integrate(1/(3*x**2+2)**(1/4),x)","\frac{2^{\frac{3}{4}} x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle| {\frac{3 x^{2} e^{i \pi}}{2}} \right)}}{2}"," ",0,"2**(3/4)*x*hyper((1/4, 1/2), (3/2,), 3*x**2*exp_polar(I*pi)/2)/2","C",0
867,1,29,0,0.740340," ","integrate(1/x**2/(3*x**2+2)**(1/4),x)","- \frac{2^{\frac{3}{4}} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{1}{2} \end{matrix}\middle| {\frac{3 x^{2} e^{i \pi}}{2}} \right)}}{2 x}"," ",0,"-2**(3/4)*hyper((-1/2, 1/4), (1/2,), 3*x**2*exp_polar(I*pi)/2)/(2*x)","C",0
868,1,32,0,0.840993," ","integrate(1/x**4/(3*x**2+2)**(1/4),x)","- \frac{2^{\frac{3}{4}} {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, \frac{1}{4} \\ - \frac{1}{2} \end{matrix}\middle| {\frac{3 x^{2} e^{i \pi}}{2}} \right)}}{6 x^{3}}"," ",0,"-2**(3/4)*hyper((-3/2, 1/4), (-1/2,), 3*x**2*exp_polar(I*pi)/2)/(6*x**3)","C",0
869,1,32,0,0.953254," ","integrate(1/x**6/(3*x**2+2)**(1/4),x)","- \frac{2^{\frac{3}{4}} {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{2}, \frac{1}{4} \\ - \frac{3}{2} \end{matrix}\middle| {\frac{3 x^{2} e^{i \pi}}{2}} \right)}}{10 x^{5}}"," ",0,"-2**(3/4)*hyper((-5/2, 1/4), (-3/2,), 3*x**2*exp_polar(I*pi)/2)/(10*x**5)","C",0
870,1,29,0,0.854953," ","integrate(x**6/(-3*x**2+2)**(1/4),x)","\frac{2^{\frac{3}{4}} x^{7} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{7}{2} \\ \frac{9}{2} \end{matrix}\middle| {\frac{3 x^{2} e^{2 i \pi}}{2}} \right)}}{14}"," ",0,"2**(3/4)*x**7*hyper((1/4, 7/2), (9/2,), 3*x**2*exp_polar(2*I*pi)/2)/14","C",0
871,1,29,0,0.770792," ","integrate(x**4/(-3*x**2+2)**(1/4),x)","\frac{2^{\frac{3}{4}} x^{5} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{3 x^{2} e^{2 i \pi}}{2}} \right)}}{10}"," ",0,"2**(3/4)*x**5*hyper((1/4, 5/2), (7/2,), 3*x**2*exp_polar(2*I*pi)/2)/10","C",0
872,1,29,0,0.715589," ","integrate(x**2/(-3*x**2+2)**(1/4),x)","\frac{2^{\frac{3}{4}} x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{3 x^{2} e^{2 i \pi}}{2}} \right)}}{6}"," ",0,"2**(3/4)*x**3*hyper((1/4, 3/2), (5/2,), 3*x**2*exp_polar(2*I*pi)/2)/6","C",0
873,1,27,0,0.687910," ","integrate(1/(-3*x**2+2)**(1/4),x)","\frac{2^{\frac{3}{4}} x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle| {\frac{3 x^{2} e^{2 i \pi}}{2}} \right)}}{2}"," ",0,"2**(3/4)*x*hyper((1/4, 1/2), (3/2,), 3*x**2*exp_polar(2*I*pi)/2)/2","C",0
874,1,31,0,0.765140," ","integrate(1/x**2/(-3*x**2+2)**(1/4),x)","- \frac{2^{\frac{3}{4}} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{1}{2} \end{matrix}\middle| {\frac{3 x^{2} e^{2 i \pi}}{2}} \right)}}{2 x}"," ",0,"-2**(3/4)*hyper((-1/2, 1/4), (1/2,), 3*x**2*exp_polar(2*I*pi)/2)/(2*x)","C",0
875,1,34,0,0.867392," ","integrate(1/x**4/(-3*x**2+2)**(1/4),x)","- \frac{2^{\frac{3}{4}} {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, \frac{1}{4} \\ - \frac{1}{2} \end{matrix}\middle| {\frac{3 x^{2} e^{2 i \pi}}{2}} \right)}}{6 x^{3}}"," ",0,"-2**(3/4)*hyper((-3/2, 1/4), (-1/2,), 3*x**2*exp_polar(2*I*pi)/2)/(6*x**3)","C",0
876,1,34,0,0.974943," ","integrate(1/x**6/(-3*x**2+2)**(1/4),x)","- \frac{2^{\frac{3}{4}} {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{2}, \frac{1}{4} \\ - \frac{3}{2} \end{matrix}\middle| {\frac{3 x^{2} e^{2 i \pi}}{2}} \right)}}{10 x^{5}}"," ",0,"-2**(3/4)*hyper((-5/2, 1/4), (-3/2,), 3*x**2*exp_polar(2*I*pi)/2)/(10*x**5)","C",0
877,1,27,0,0.815301," ","integrate(x**6/(3*x**2+2)**(3/4),x)","\frac{\sqrt[4]{2} x^{7} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{7}{2} \\ \frac{9}{2} \end{matrix}\middle| {\frac{3 x^{2} e^{i \pi}}{2}} \right)}}{14}"," ",0,"2**(1/4)*x**7*hyper((3/4, 7/2), (9/2,), 3*x**2*exp_polar(I*pi)/2)/14","C",0
878,1,27,0,0.738179," ","integrate(x**4/(3*x**2+2)**(3/4),x)","\frac{\sqrt[4]{2} x^{5} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{3 x^{2} e^{i \pi}}{2}} \right)}}{10}"," ",0,"2**(1/4)*x**5*hyper((3/4, 5/2), (7/2,), 3*x**2*exp_polar(I*pi)/2)/10","C",0
879,1,27,0,0.709423," ","integrate(x**2/(3*x**2+2)**(3/4),x)","\frac{\sqrt[4]{2} x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{3 x^{2} e^{i \pi}}{2}} \right)}}{6}"," ",0,"2**(1/4)*x**3*hyper((3/4, 3/2), (5/2,), 3*x**2*exp_polar(I*pi)/2)/6","C",0
880,1,26,0,0.677728," ","integrate(1/(3*x**2+2)**(3/4),x)","\frac{\sqrt[4]{2} x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{3}{2} \end{matrix}\middle| {\frac{3 x^{2} e^{i \pi}}{2}} \right)}}{2}"," ",0,"2**(1/4)*x*hyper((1/2, 3/4), (3/2,), 3*x**2*exp_polar(I*pi)/2)/2","C",0
881,1,29,0,0.824376," ","integrate(1/x**2/(3*x**2+2)**(3/4),x)","- \frac{\sqrt[4]{2} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{1}{2} \end{matrix}\middle| {\frac{3 x^{2} e^{i \pi}}{2}} \right)}}{2 x}"," ",0,"-2**(1/4)*hyper((-1/2, 3/4), (1/2,), 3*x**2*exp_polar(I*pi)/2)/(2*x)","C",0
882,1,32,0,0.933780," ","integrate(1/x**4/(3*x**2+2)**(3/4),x)","- \frac{\sqrt[4]{2} {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, \frac{3}{4} \\ - \frac{1}{2} \end{matrix}\middle| {\frac{3 x^{2} e^{i \pi}}{2}} \right)}}{6 x^{3}}"," ",0,"-2**(1/4)*hyper((-3/2, 3/4), (-1/2,), 3*x**2*exp_polar(I*pi)/2)/(6*x**3)","C",0
883,1,32,0,1.076592," ","integrate(1/x**6/(3*x**2+2)**(3/4),x)","- \frac{\sqrt[4]{2} {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{2}, \frac{3}{4} \\ - \frac{3}{2} \end{matrix}\middle| {\frac{3 x^{2} e^{i \pi}}{2}} \right)}}{10 x^{5}}"," ",0,"-2**(1/4)*hyper((-5/2, 3/4), (-3/2,), 3*x**2*exp_polar(I*pi)/2)/(10*x**5)","C",0
884,1,29,0,0.839656," ","integrate(x**6/(-3*x**2+2)**(3/4),x)","\frac{\sqrt[4]{2} x^{7} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{7}{2} \\ \frac{9}{2} \end{matrix}\middle| {\frac{3 x^{2} e^{2 i \pi}}{2}} \right)}}{14}"," ",0,"2**(1/4)*x**7*hyper((3/4, 7/2), (9/2,), 3*x**2*exp_polar(2*I*pi)/2)/14","C",0
885,1,29,0,0.766974," ","integrate(x**4/(-3*x**2+2)**(3/4),x)","\frac{\sqrt[4]{2} x^{5} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{3 x^{2} e^{2 i \pi}}{2}} \right)}}{10}"," ",0,"2**(1/4)*x**5*hyper((3/4, 5/2), (7/2,), 3*x**2*exp_polar(2*I*pi)/2)/10","C",0
886,1,29,0,0.732649," ","integrate(x**2/(-3*x**2+2)**(3/4),x)","\frac{\sqrt[4]{2} x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{3 x^{2} e^{2 i \pi}}{2}} \right)}}{6}"," ",0,"2**(1/4)*x**3*hyper((3/4, 3/2), (5/2,), 3*x**2*exp_polar(2*I*pi)/2)/6","C",0
887,1,27,0,0.693395," ","integrate(1/(-3*x**2+2)**(3/4),x)","\frac{\sqrt[4]{2} x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{3}{2} \end{matrix}\middle| {\frac{3 x^{2} e^{2 i \pi}}{2}} \right)}}{2}"," ",0,"2**(1/4)*x*hyper((1/2, 3/4), (3/2,), 3*x**2*exp_polar(2*I*pi)/2)/2","C",0
888,1,31,0,0.841175," ","integrate(1/x**2/(-3*x**2+2)**(3/4),x)","- \frac{\sqrt[4]{2} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{1}{2} \end{matrix}\middle| {\frac{3 x^{2} e^{2 i \pi}}{2}} \right)}}{2 x}"," ",0,"-2**(1/4)*hyper((-1/2, 3/4), (1/2,), 3*x**2*exp_polar(2*I*pi)/2)/(2*x)","C",0
889,1,34,0,0.945225," ","integrate(1/x**4/(-3*x**2+2)**(3/4),x)","- \frac{\sqrt[4]{2} {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, \frac{3}{4} \\ - \frac{1}{2} \end{matrix}\middle| {\frac{3 x^{2} e^{2 i \pi}}{2}} \right)}}{6 x^{3}}"," ",0,"-2**(1/4)*hyper((-3/2, 3/4), (-1/2,), 3*x**2*exp_polar(2*I*pi)/2)/(6*x**3)","C",0
890,1,34,0,1.106339," ","integrate(1/x**6/(-3*x**2+2)**(3/4),x)","- \frac{\sqrt[4]{2} {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{2}, \frac{3}{4} \\ - \frac{3}{2} \end{matrix}\middle| {\frac{3 x^{2} e^{2 i \pi}}{2}} \right)}}{10 x^{5}}"," ",0,"-2**(1/4)*hyper((-5/2, 3/4), (-3/2,), 3*x**2*exp_polar(2*I*pi)/2)/(10*x**5)","C",0
891,1,29,0,0.850588," ","integrate(x**6/(3*x**2-2)**(1/4),x)","\frac{2^{\frac{3}{4}} x^{7} e^{- \frac{i \pi}{4}} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{7}{2} \\ \frac{9}{2} \end{matrix}\middle| {\frac{3 x^{2}}{2}} \right)}}{14}"," ",0,"2**(3/4)*x**7*exp(-I*pi/4)*hyper((1/4, 7/2), (9/2,), 3*x**2/2)/14","C",0
892,1,29,0,0.775669," ","integrate(x**4/(3*x**2-2)**(1/4),x)","\frac{2^{\frac{3}{4}} x^{5} e^{- \frac{i \pi}{4}} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{3 x^{2}}{2}} \right)}}{10}"," ",0,"2**(3/4)*x**5*exp(-I*pi/4)*hyper((1/4, 5/2), (7/2,), 3*x**2/2)/10","C",0
893,1,29,0,0.726573," ","integrate(x**2/(3*x**2-2)**(1/4),x)","\frac{2^{\frac{3}{4}} x^{3} e^{- \frac{i \pi}{4}} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{3 x^{2}}{2}} \right)}}{6}"," ",0,"2**(3/4)*x**3*exp(-I*pi/4)*hyper((1/4, 3/2), (5/2,), 3*x**2/2)/6","C",0
894,1,27,0,0.694649," ","integrate(1/(3*x**2-2)**(1/4),x)","\frac{2^{\frac{3}{4}} x e^{- \frac{i \pi}{4}} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle| {\frac{3 x^{2}}{2}} \right)}}{2}"," ",0,"2**(3/4)*x*exp(-I*pi/4)*hyper((1/4, 1/2), (3/2,), 3*x**2/2)/2","C",0
895,1,31,0,0.759281," ","integrate(1/x**2/(3*x**2-2)**(1/4),x)","\frac{2^{\frac{3}{4}} e^{\frac{3 i \pi}{4}} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{1}{2} \end{matrix}\middle| {\frac{3 x^{2}}{2}} \right)}}{2 x}"," ",0,"2**(3/4)*exp(3*I*pi/4)*hyper((-1/2, 1/4), (1/2,), 3*x**2/2)/(2*x)","C",0
896,1,34,0,0.865682," ","integrate(1/x**4/(3*x**2-2)**(1/4),x)","\frac{2^{\frac{3}{4}} e^{\frac{3 i \pi}{4}} {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, \frac{1}{4} \\ - \frac{1}{2} \end{matrix}\middle| {\frac{3 x^{2}}{2}} \right)}}{6 x^{3}}"," ",0,"2**(3/4)*exp(3*I*pi/4)*hyper((-3/2, 1/4), (-1/2,), 3*x**2/2)/(6*x**3)","C",0
897,1,34,0,0.977344," ","integrate(1/x**6/(3*x**2-2)**(1/4),x)","\frac{2^{\frac{3}{4}} e^{\frac{3 i \pi}{4}} {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{2}, \frac{1}{4} \\ - \frac{3}{2} \end{matrix}\middle| {\frac{3 x^{2}}{2}} \right)}}{10 x^{5}}"," ",0,"2**(3/4)*exp(3*I*pi/4)*hyper((-5/2, 1/4), (-3/2,), 3*x**2/2)/(10*x**5)","C",0
898,1,34,0,0.841421," ","integrate(x**6/(-3*x**2-2)**(1/4),x)","\frac{2^{\frac{3}{4}} x^{7} e^{- \frac{i \pi}{4}} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{7}{2} \\ \frac{9}{2} \end{matrix}\middle| {\frac{3 x^{2} e^{i \pi}}{2}} \right)}}{14}"," ",0,"2**(3/4)*x**7*exp(-I*pi/4)*hyper((1/4, 7/2), (9/2,), 3*x**2*exp_polar(I*pi)/2)/14","C",0
899,1,34,0,0.766985," ","integrate(x**4/(-3*x**2-2)**(1/4),x)","\frac{2^{\frac{3}{4}} x^{5} e^{- \frac{i \pi}{4}} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{3 x^{2} e^{i \pi}}{2}} \right)}}{10}"," ",0,"2**(3/4)*x**5*exp(-I*pi/4)*hyper((1/4, 5/2), (7/2,), 3*x**2*exp_polar(I*pi)/2)/10","C",0
900,1,34,0,0.715611," ","integrate(x**2/(-3*x**2-2)**(1/4),x)","\frac{2^{\frac{3}{4}} x^{3} e^{- \frac{i \pi}{4}} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{3 x^{2} e^{i \pi}}{2}} \right)}}{6}"," ",0,"2**(3/4)*x**3*exp(-I*pi/4)*hyper((1/4, 3/2), (5/2,), 3*x**2*exp_polar(I*pi)/2)/6","C",0
901,1,32,0,0.687222," ","integrate(1/(-3*x**2-2)**(1/4),x)","\frac{2^{\frac{3}{4}} x e^{- \frac{i \pi}{4}} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle| {\frac{3 x^{2} e^{i \pi}}{2}} \right)}}{2}"," ",0,"2**(3/4)*x*exp(-I*pi/4)*hyper((1/4, 1/2), (3/2,), 3*x**2*exp_polar(I*pi)/2)/2","C",0
902,1,36,0,0.758383," ","integrate(1/x**2/(-3*x**2-2)**(1/4),x)","\frac{2^{\frac{3}{4}} e^{\frac{3 i \pi}{4}} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{1}{2} \end{matrix}\middle| {\frac{3 x^{2} e^{i \pi}}{2}} \right)}}{2 x}"," ",0,"2**(3/4)*exp(3*I*pi/4)*hyper((-1/2, 1/4), (1/2,), 3*x**2*exp_polar(I*pi)/2)/(2*x)","C",0
903,1,39,0,0.863476," ","integrate(1/x**4/(-3*x**2-2)**(1/4),x)","\frac{2^{\frac{3}{4}} e^{\frac{3 i \pi}{4}} {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, \frac{1}{4} \\ - \frac{1}{2} \end{matrix}\middle| {\frac{3 x^{2} e^{i \pi}}{2}} \right)}}{6 x^{3}}"," ",0,"2**(3/4)*exp(3*I*pi/4)*hyper((-3/2, 1/4), (-1/2,), 3*x**2*exp_polar(I*pi)/2)/(6*x**3)","C",0
904,1,39,0,0.971231," ","integrate(1/x**6/(-3*x**2-2)**(1/4),x)","\frac{2^{\frac{3}{4}} e^{\frac{3 i \pi}{4}} {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{2}, \frac{1}{4} \\ - \frac{3}{2} \end{matrix}\middle| {\frac{3 x^{2} e^{i \pi}}{2}} \right)}}{10 x^{5}}"," ",0,"2**(3/4)*exp(3*I*pi/4)*hyper((-5/2, 1/4), (-3/2,), 3*x**2*exp_polar(I*pi)/2)/(10*x**5)","C",0
905,1,31,0,0.856032," ","integrate(x**6/(3*x**2-2)**(3/4),x)","\frac{\sqrt[4]{2} x^{7} e^{- \frac{3 i \pi}{4}} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{7}{2} \\ \frac{9}{2} \end{matrix}\middle| {\frac{3 x^{2}}{2}} \right)}}{14}"," ",0,"2**(1/4)*x**7*exp(-3*I*pi/4)*hyper((3/4, 7/2), (9/2,), 3*x**2/2)/14","C",0
906,1,31,0,0.771481," ","integrate(x**4/(3*x**2-2)**(3/4),x)","\frac{\sqrt[4]{2} x^{5} e^{- \frac{3 i \pi}{4}} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{3 x^{2}}{2}} \right)}}{10}"," ",0,"2**(1/4)*x**5*exp(-3*I*pi/4)*hyper((3/4, 5/2), (7/2,), 3*x**2/2)/10","C",0
907,1,31,0,0.742073," ","integrate(x**2/(3*x**2-2)**(3/4),x)","\frac{\sqrt[4]{2} x^{3} e^{- \frac{3 i \pi}{4}} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{3 x^{2}}{2}} \right)}}{6}"," ",0,"2**(1/4)*x**3*exp(-3*I*pi/4)*hyper((3/4, 3/2), (5/2,), 3*x**2/2)/6","C",0
908,1,29,0,0.708661," ","integrate(1/(3*x**2-2)**(3/4),x)","\frac{\sqrt[4]{2} x e^{- \frac{3 i \pi}{4}} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{3}{2} \end{matrix}\middle| {\frac{3 x^{2}}{2}} \right)}}{2}"," ",0,"2**(1/4)*x*exp(-3*I*pi/4)*hyper((1/2, 3/4), (3/2,), 3*x**2/2)/2","C",0
909,1,29,0,0.844970," ","integrate(1/x**2/(3*x**2-2)**(3/4),x)","\frac{\sqrt[4]{2} e^{\frac{i \pi}{4}} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{1}{2} \end{matrix}\middle| {\frac{3 x^{2}}{2}} \right)}}{2 x}"," ",0,"2**(1/4)*exp(I*pi/4)*hyper((-1/2, 3/4), (1/2,), 3*x**2/2)/(2*x)","C",0
910,1,32,0,0.963199," ","integrate(1/x**4/(3*x**2-2)**(3/4),x)","\frac{\sqrt[4]{2} e^{\frac{i \pi}{4}} {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, \frac{3}{4} \\ - \frac{1}{2} \end{matrix}\middle| {\frac{3 x^{2}}{2}} \right)}}{6 x^{3}}"," ",0,"2**(1/4)*exp(I*pi/4)*hyper((-3/2, 3/4), (-1/2,), 3*x**2/2)/(6*x**3)","C",0
911,1,32,0,1.111569," ","integrate(1/x**6/(3*x**2-2)**(3/4),x)","\frac{\sqrt[4]{2} e^{\frac{i \pi}{4}} {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{2}, \frac{3}{4} \\ - \frac{3}{2} \end{matrix}\middle| {\frac{3 x^{2}}{2}} \right)}}{10 x^{5}}"," ",0,"2**(1/4)*exp(I*pi/4)*hyper((-5/2, 3/4), (-3/2,), 3*x**2/2)/(10*x**5)","C",0
912,1,36,0,0.838258," ","integrate(x**6/(-3*x**2-2)**(3/4),x)","\frac{\sqrt[4]{2} x^{7} e^{- \frac{3 i \pi}{4}} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{7}{2} \\ \frac{9}{2} \end{matrix}\middle| {\frac{3 x^{2} e^{i \pi}}{2}} \right)}}{14}"," ",0,"2**(1/4)*x**7*exp(-3*I*pi/4)*hyper((3/4, 7/2), (9/2,), 3*x**2*exp_polar(I*pi)/2)/14","C",0
913,1,36,0,0.763729," ","integrate(x**4/(-3*x**2-2)**(3/4),x)","\frac{\sqrt[4]{2} x^{5} e^{- \frac{3 i \pi}{4}} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{3 x^{2} e^{i \pi}}{2}} \right)}}{10}"," ",0,"2**(1/4)*x**5*exp(-3*I*pi/4)*hyper((3/4, 5/2), (7/2,), 3*x**2*exp_polar(I*pi)/2)/10","C",0
914,1,36,0,0.721097," ","integrate(x**2/(-3*x**2-2)**(3/4),x)","\frac{\sqrt[4]{2} x^{3} e^{- \frac{3 i \pi}{4}} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{3 x^{2} e^{i \pi}}{2}} \right)}}{6}"," ",0,"2**(1/4)*x**3*exp(-3*I*pi/4)*hyper((3/4, 3/2), (5/2,), 3*x**2*exp_polar(I*pi)/2)/6","C",0
915,1,34,0,0.693990," ","integrate(1/(-3*x**2-2)**(3/4),x)","\frac{\sqrt[4]{2} x e^{- \frac{3 i \pi}{4}} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{3}{2} \end{matrix}\middle| {\frac{3 x^{2} e^{i \pi}}{2}} \right)}}{2}"," ",0,"2**(1/4)*x*exp(-3*I*pi/4)*hyper((1/2, 3/4), (3/2,), 3*x**2*exp_polar(I*pi)/2)/2","C",0
916,1,34,0,0.835705," ","integrate(1/x**2/(-3*x**2-2)**(3/4),x)","\frac{\sqrt[4]{2} e^{\frac{i \pi}{4}} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{1}{2} \end{matrix}\middle| {\frac{3 x^{2} e^{i \pi}}{2}} \right)}}{2 x}"," ",0,"2**(1/4)*exp(I*pi/4)*hyper((-1/2, 3/4), (1/2,), 3*x**2*exp_polar(I*pi)/2)/(2*x)","C",0
917,1,37,0,0.940856," ","integrate(1/x**4/(-3*x**2-2)**(3/4),x)","\frac{\sqrt[4]{2} e^{\frac{i \pi}{4}} {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, \frac{3}{4} \\ - \frac{1}{2} \end{matrix}\middle| {\frac{3 x^{2} e^{i \pi}}{2}} \right)}}{6 x^{3}}"," ",0,"2**(1/4)*exp(I*pi/4)*hyper((-3/2, 3/4), (-1/2,), 3*x**2*exp_polar(I*pi)/2)/(6*x**3)","C",0
918,1,37,0,1.118242," ","integrate(1/x**6/(-3*x**2-2)**(3/4),x)","\frac{\sqrt[4]{2} e^{\frac{i \pi}{4}} {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{2}, \frac{3}{4} \\ - \frac{3}{2} \end{matrix}\middle| {\frac{3 x^{2} e^{i \pi}}{2}} \right)}}{10 x^{5}}"," ",0,"2**(1/4)*exp(I*pi/4)*hyper((-5/2, 3/4), (-3/2,), 3*x**2*exp_polar(I*pi)/2)/(10*x**5)","C",0
919,1,46,0,25.910591," ","integrate((c*x)**(7/2)*(b*x**2+a)**(1/4),x)","\frac{\sqrt[4]{a} c^{\frac{7}{2}} x^{\frac{9}{2}} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{13}{4}\right)}"," ",0,"a**(1/4)*c**(7/2)*x**(9/2)*gamma(9/4)*hyper((-1/4, 9/4), (13/4,), b*x**2*exp_polar(I*pi)/a)/(2*gamma(13/4))","C",0
920,1,46,0,2.709130," ","integrate((c*x)**(3/2)*(b*x**2+a)**(1/4),x)","\frac{\sqrt[4]{a} c^{\frac{3}{2}} x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{9}{4}\right)}"," ",0,"a**(1/4)*c**(3/2)*x**(5/2)*gamma(5/4)*hyper((-1/4, 5/4), (9/4,), b*x**2*exp_polar(I*pi)/a)/(2*gamma(9/4))","C",0
921,1,46,0,1.306647," ","integrate((b*x**2+a)**(1/4)/(c*x)**(1/2),x)","\frac{\sqrt[4]{a} \sqrt{x} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{c} \Gamma\left(\frac{5}{4}\right)}"," ",0,"a**(1/4)*sqrt(x)*gamma(1/4)*hyper((-1/4, 1/4), (5/4,), b*x**2*exp_polar(I*pi)/a)/(2*sqrt(c)*gamma(5/4))","C",0
922,1,32,0,3.713198," ","integrate((b*x**2+a)**(1/4)/(c*x)**(5/2),x)","- \frac{\sqrt[4]{b} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{2}}} \right)}}{c^{\frac{5}{2}} x}"," ",0,"-b**(1/4)*hyper((-1/4, 1/2), (3/2,), a*exp_polar(I*pi)/(b*x**2))/(c**(5/2)*x)","C",0
923,1,36,0,27.113496," ","integrate((b*x**2+a)**(1/4)/(c*x)**(9/2),x)","- \frac{\sqrt[4]{b} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{2}}} \right)}}{3 c^{\frac{9}{2}} x^{3}}"," ",0,"-b**(1/4)*hyper((-1/4, 3/2), (5/2,), a*exp_polar(I*pi)/(b*x**2))/(3*c**(9/2)*x**3)","C",0
924,-1,0,0,0.000000," ","integrate((b*x**2+a)**(1/4)/(c*x)**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
925,1,46,0,9.470904," ","integrate((c*x)**(5/2)*(b*x**2+a)**(1/4),x)","\frac{\sqrt[4]{a} c^{\frac{5}{2}} x^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{11}{4}\right)}"," ",0,"a**(1/4)*c**(5/2)*x**(7/2)*gamma(7/4)*hyper((-1/4, 7/4), (11/4,), b*x**2*exp_polar(I*pi)/a)/(2*gamma(11/4))","C",0
926,1,46,0,1.805970," ","integrate((c*x)**(1/2)*(b*x**2+a)**(1/4),x)","\frac{\sqrt[4]{a} \sqrt{c} x^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{7}{4}\right)}"," ",0,"a**(1/4)*sqrt(c)*x**(3/2)*gamma(3/4)*hyper((-1/4, 3/4), (7/4,), b*x**2*exp_polar(I*pi)/a)/(2*gamma(7/4))","C",0
927,1,49,0,2.314727," ","integrate((b*x**2+a)**(1/4)/(c*x)**(3/2),x)","\frac{\sqrt[4]{a} \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 c^{\frac{3}{2}} \sqrt{x} \Gamma\left(\frac{3}{4}\right)}"," ",0,"a**(1/4)*gamma(-1/4)*hyper((-1/4, -1/4), (3/4,), b*x**2*exp_polar(I*pi)/a)/(2*c**(3/2)*sqrt(x)*gamma(3/4))","C",0
928,1,78,0,9.132430," ","integrate((b*x**2+a)**(1/4)/(c*x)**(7/2),x)","\frac{\sqrt[4]{b} \sqrt[4]{\frac{a}{b x^{2}} + 1} \Gamma\left(- \frac{5}{4}\right)}{2 c^{\frac{7}{2}} x^{2} \Gamma\left(- \frac{1}{4}\right)} + \frac{b^{\frac{5}{4}} \sqrt[4]{\frac{a}{b x^{2}} + 1} \Gamma\left(- \frac{5}{4}\right)}{2 a c^{\frac{7}{2}} \Gamma\left(- \frac{1}{4}\right)}"," ",0,"b**(1/4)*(a/(b*x**2) + 1)**(1/4)*gamma(-5/4)/(2*c**(7/2)*x**2*gamma(-1/4)) + b**(5/4)*(a/(b*x**2) + 1)**(1/4)*gamma(-5/4)/(2*a*c**(7/2)*gamma(-1/4))","B",0
929,1,124,0,69.580682," ","integrate((b*x**2+a)**(1/4)/(c*x)**(11/2),x)","- \frac{5 \sqrt[4]{b} \sqrt[4]{\frac{a}{b x^{2}} + 1} \Gamma\left(- \frac{9}{4}\right)}{8 c^{\frac{11}{2}} x^{4} \Gamma\left(- \frac{1}{4}\right)} - \frac{b^{\frac{5}{4}} \sqrt[4]{\frac{a}{b x^{2}} + 1} \Gamma\left(- \frac{9}{4}\right)}{8 a c^{\frac{11}{2}} x^{2} \Gamma\left(- \frac{1}{4}\right)} + \frac{b^{\frac{9}{4}} \sqrt[4]{\frac{a}{b x^{2}} + 1} \Gamma\left(- \frac{9}{4}\right)}{2 a^{2} c^{\frac{11}{2}} \Gamma\left(- \frac{1}{4}\right)}"," ",0,"-5*b**(1/4)*(a/(b*x**2) + 1)**(1/4)*gamma(-9/4)/(8*c**(11/2)*x**4*gamma(-1/4)) - b**(5/4)*(a/(b*x**2) + 1)**(1/4)*gamma(-9/4)/(8*a*c**(11/2)*x**2*gamma(-1/4)) + b**(9/4)*(a/(b*x**2) + 1)**(1/4)*gamma(-9/4)/(2*a**2*c**(11/2)*gamma(-1/4))","B",0
930,-1,0,0,0.000000," ","integrate((b*x**2+a)**(1/4)/(c*x)**(15/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
931,-1,0,0,0.000000," ","integrate((b*x**2+a)**(1/4)/(c*x)**(19/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
932,1,48,0,2.639449," ","integrate((c*x)**(3/2)*(-b*x**2+a)**(1/4),x)","\frac{\sqrt[4]{a} c^{\frac{3}{2}} x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{9}{4}\right)}"," ",0,"a**(1/4)*c**(3/2)*x**(5/2)*gamma(5/4)*hyper((-1/4, 5/4), (9/4,), b*x**2*exp_polar(2*I*pi)/a)/(2*gamma(9/4))","C",0
933,1,39,0,1.335551," ","integrate((-b*x**2+a)**(1/4)/(c*x)**(1/2),x)","- \frac{i \sqrt[4]{b} x e^{\frac{3 i \pi}{4}} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{1}{2} \end{matrix}\middle| {\frac{a}{b x^{2}}} \right)}}{\sqrt{c}}"," ",0,"-I*b**(1/4)*x*exp(3*I*pi/4)*hyper((-1/2, -1/4), (1/2,), a/(b*x**2))/sqrt(c)","C",0
934,1,36,0,3.705082," ","integrate((-b*x**2+a)**(1/4)/(c*x)**(5/2),x)","- \frac{i \sqrt[4]{b} e^{- \frac{i \pi}{4}} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle| {\frac{a}{b x^{2}}} \right)}}{c^{\frac{5}{2}} x}"," ",0,"-I*b**(1/4)*exp(-I*pi/4)*hyper((-1/4, 1/2), (3/2,), a/(b*x**2))/(c**(5/2)*x)","C",0
935,1,39,0,26.578532," ","integrate((-b*x**2+a)**(1/4)/(c*x)**(9/2),x)","\frac{i \sqrt[4]{b} e^{\frac{3 i \pi}{4}} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{a}{b x^{2}}} \right)}}{3 c^{\frac{9}{2}} x^{3}}"," ",0,"I*b**(1/4)*exp(3*I*pi/4)*hyper((-1/4, 3/2), (5/2,), a/(b*x**2))/(3*c**(9/2)*x**3)","C",0
936,-1,0,0,0.000000," ","integrate((-b*x**2+a)**(1/4)/(c*x)**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
937,1,48,0,9.288343," ","integrate((c*x)**(5/2)*(-b*x**2+a)**(1/4),x)","\frac{\sqrt[4]{a} c^{\frac{5}{2}} x^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{11}{4}\right)}"," ",0,"a**(1/4)*c**(5/2)*x**(7/2)*gamma(7/4)*hyper((-1/4, 7/4), (11/4,), b*x**2*exp_polar(2*I*pi)/a)/(2*gamma(11/4))","C",0
938,1,48,0,1.782004," ","integrate((c*x)**(1/2)*(-b*x**2+a)**(1/4),x)","\frac{\sqrt[4]{a} \sqrt{c} x^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{7}{4}\right)}"," ",0,"a**(1/4)*sqrt(c)*x**(3/2)*gamma(3/4)*hyper((-1/4, 3/4), (7/4,), b*x**2*exp_polar(2*I*pi)/a)/(2*gamma(7/4))","C",0
939,1,51,0,2.324111," ","integrate((-b*x**2+a)**(1/4)/(c*x)**(3/2),x)","\frac{\sqrt[4]{a} \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{2 c^{\frac{3}{2}} \sqrt{x} \Gamma\left(\frac{3}{4}\right)}"," ",0,"a**(1/4)*gamma(-1/4)*hyper((-1/4, -1/4), (3/4,), b*x**2*exp_polar(2*I*pi)/a)/(2*c**(3/2)*sqrt(x)*gamma(3/4))","C",0
940,1,178,0,8.763198," ","integrate((-b*x**2+a)**(1/4)/(c*x)**(7/2),x)","\begin{cases} \frac{\sqrt[4]{b} \sqrt[4]{\frac{a}{b x^{2}} - 1} \Gamma\left(- \frac{5}{4}\right)}{2 c^{\frac{7}{2}} x^{2} \Gamma\left(- \frac{1}{4}\right)} - \frac{b^{\frac{5}{4}} \sqrt[4]{\frac{a}{b x^{2}} - 1} \Gamma\left(- \frac{5}{4}\right)}{2 a c^{\frac{7}{2}} \Gamma\left(- \frac{1}{4}\right)} & \text{for}\: \left|{\frac{a}{b x^{2}}}\right| > 1 \\\frac{\sqrt[4]{b} \sqrt[4]{- \frac{a}{b x^{2}} + 1} e^{\frac{i \pi}{4}} \Gamma\left(- \frac{5}{4}\right)}{2 c^{\frac{7}{2}} x^{2} \Gamma\left(- \frac{1}{4}\right)} - \frac{b^{\frac{5}{4}} \sqrt[4]{- \frac{a}{b x^{2}} + 1} e^{\frac{i \pi}{4}} \Gamma\left(- \frac{5}{4}\right)}{2 a c^{\frac{7}{2}} \Gamma\left(- \frac{1}{4}\right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((b**(1/4)*(a/(b*x**2) - 1)**(1/4)*gamma(-5/4)/(2*c**(7/2)*x**2*gamma(-1/4)) - b**(5/4)*(a/(b*x**2) - 1)**(1/4)*gamma(-5/4)/(2*a*c**(7/2)*gamma(-1/4)), Abs(a/(b*x**2)) > 1), (b**(1/4)*(-a/(b*x**2) + 1)**(1/4)*exp(I*pi/4)*gamma(-5/4)/(2*c**(7/2)*x**2*gamma(-1/4)) - b**(5/4)*(-a/(b*x**2) + 1)**(1/4)*exp(I*pi/4)*gamma(-5/4)/(2*a*c**(7/2)*gamma(-1/4)), True))","B",0
941,1,462,0,68.247322," ","integrate((-b*x**2+a)**(1/4)/(c*x)**(11/2),x)","\begin{cases} - \frac{5 \sqrt[4]{b} \sqrt[4]{\frac{a}{b x^{2}} - 1} \Gamma\left(- \frac{9}{4}\right)}{8 c^{\frac{11}{2}} x^{4} \Gamma\left(- \frac{1}{4}\right)} + \frac{b^{\frac{5}{4}} \sqrt[4]{\frac{a}{b x^{2}} - 1} \Gamma\left(- \frac{9}{4}\right)}{8 a c^{\frac{11}{2}} x^{2} \Gamma\left(- \frac{1}{4}\right)} + \frac{b^{\frac{9}{4}} \sqrt[4]{\frac{a}{b x^{2}} - 1} \Gamma\left(- \frac{9}{4}\right)}{2 a^{2} c^{\frac{11}{2}} \Gamma\left(- \frac{1}{4}\right)} & \text{for}\: \left|{\frac{a}{b x^{2}}}\right| > 1 \\\frac{5 a^{3} b^{\frac{5}{4}} \sqrt[4]{- \frac{a}{b x^{2}} + 1} e^{\frac{i \pi}{4}} \Gamma\left(- \frac{9}{4}\right)}{x^{2} \left(- 8 a^{3} b c^{\frac{11}{2}} x^{2} \Gamma\left(- \frac{1}{4}\right) + 8 a^{2} b^{2} c^{\frac{11}{2}} x^{4} \Gamma\left(- \frac{1}{4}\right)\right)} - \frac{6 a^{2} b^{\frac{9}{4}} \sqrt[4]{- \frac{a}{b x^{2}} + 1} e^{\frac{i \pi}{4}} \Gamma\left(- \frac{9}{4}\right)}{- 8 a^{3} b c^{\frac{11}{2}} x^{2} \Gamma\left(- \frac{1}{4}\right) + 8 a^{2} b^{2} c^{\frac{11}{2}} x^{4} \Gamma\left(- \frac{1}{4}\right)} - \frac{3 a b^{\frac{13}{4}} x^{2} \sqrt[4]{- \frac{a}{b x^{2}} + 1} e^{\frac{i \pi}{4}} \Gamma\left(- \frac{9}{4}\right)}{- 8 a^{3} b c^{\frac{11}{2}} x^{2} \Gamma\left(- \frac{1}{4}\right) + 8 a^{2} b^{2} c^{\frac{11}{2}} x^{4} \Gamma\left(- \frac{1}{4}\right)} + \frac{4 b^{\frac{17}{4}} x^{4} \sqrt[4]{- \frac{a}{b x^{2}} + 1} e^{\frac{i \pi}{4}} \Gamma\left(- \frac{9}{4}\right)}{- 8 a^{3} b c^{\frac{11}{2}} x^{2} \Gamma\left(- \frac{1}{4}\right) + 8 a^{2} b^{2} c^{\frac{11}{2}} x^{4} \Gamma\left(- \frac{1}{4}\right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-5*b**(1/4)*(a/(b*x**2) - 1)**(1/4)*gamma(-9/4)/(8*c**(11/2)*x**4*gamma(-1/4)) + b**(5/4)*(a/(b*x**2) - 1)**(1/4)*gamma(-9/4)/(8*a*c**(11/2)*x**2*gamma(-1/4)) + b**(9/4)*(a/(b*x**2) - 1)**(1/4)*gamma(-9/4)/(2*a**2*c**(11/2)*gamma(-1/4)), Abs(a/(b*x**2)) > 1), (5*a**3*b**(5/4)*(-a/(b*x**2) + 1)**(1/4)*exp(I*pi/4)*gamma(-9/4)/(x**2*(-8*a**3*b*c**(11/2)*x**2*gamma(-1/4) + 8*a**2*b**2*c**(11/2)*x**4*gamma(-1/4))) - 6*a**2*b**(9/4)*(-a/(b*x**2) + 1)**(1/4)*exp(I*pi/4)*gamma(-9/4)/(-8*a**3*b*c**(11/2)*x**2*gamma(-1/4) + 8*a**2*b**2*c**(11/2)*x**4*gamma(-1/4)) - 3*a*b**(13/4)*x**2*(-a/(b*x**2) + 1)**(1/4)*exp(I*pi/4)*gamma(-9/4)/(-8*a**3*b*c**(11/2)*x**2*gamma(-1/4) + 8*a**2*b**2*c**(11/2)*x**4*gamma(-1/4)) + 4*b**(17/4)*x**4*(-a/(b*x**2) + 1)**(1/4)*exp(I*pi/4)*gamma(-9/4)/(-8*a**3*b*c**(11/2)*x**2*gamma(-1/4) + 8*a**2*b**2*c**(11/2)*x**4*gamma(-1/4)), True))","B",0
942,-1,0,0,0.000000," ","integrate((-b*x**2+a)**(1/4)/(c*x)**(15/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
943,-1,0,0,0.000000," ","integrate((-b*x**2+a)**(1/4)/(c*x)**(19/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
944,1,44,0,2.175421," ","integrate((c*x)**(3/2)/(b*x**2+a)**(1/4),x)","\frac{c^{\frac{3}{2}} x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt[4]{a} \Gamma\left(\frac{9}{4}\right)}"," ",0,"c**(3/2)*x**(5/2)*gamma(5/4)*hyper((1/4, 5/4), (9/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(1/4)*gamma(9/4))","C",0
945,1,44,0,1.505381," ","integrate(1/(c*x)**(1/2)/(b*x**2+a)**(1/4),x)","\frac{\sqrt{x} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt[4]{a} \sqrt{c} \Gamma\left(\frac{5}{4}\right)}"," ",0,"sqrt(x)*gamma(1/4)*hyper((1/4, 1/4), (5/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(1/4)*sqrt(c)*gamma(5/4))","C",0
946,1,36,0,3.583125," ","integrate(1/(c*x)**(5/2)/(b*x**2+a)**(1/4),x)","\frac{b^{\frac{3}{4}} \left(\frac{a}{b x^{2}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{3}{4}\right)}{2 a c^{\frac{5}{2}} \Gamma\left(\frac{1}{4}\right)}"," ",0,"b**(3/4)*(a/(b*x**2) + 1)**(3/4)*gamma(-3/4)/(2*a*c**(5/2)*gamma(1/4))","A",0
947,1,80,0,34.720002," ","integrate(1/(c*x)**(9/2)/(b*x**2+a)**(1/4),x)","- \frac{3 b^{\frac{3}{4}} \left(\frac{a}{b x^{2}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{7}{4}\right)}{8 a c^{\frac{9}{2}} x^{2} \Gamma\left(\frac{1}{4}\right)} + \frac{b^{\frac{7}{4}} \left(\frac{a}{b x^{2}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{7}{4}\right)}{2 a^{2} c^{\frac{9}{2}} \Gamma\left(\frac{1}{4}\right)}"," ",0,"-3*b**(3/4)*(a/(b*x**2) + 1)**(3/4)*gamma(-7/4)/(8*a*c**(9/2)*x**2*gamma(1/4)) + b**(7/4)*(a/(b*x**2) + 1)**(3/4)*gamma(-7/4)/(2*a**2*c**(9/2)*gamma(1/4))","A",0
948,-1,0,0,0.000000," ","integrate(1/(c*x)**(13/2)/(b*x**2+a)**(1/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
949,1,44,0,51.813025," ","integrate((c*x)**(9/2)/(b*x**2+a)**(1/4),x)","\frac{c^{\frac{9}{2}} x^{\frac{11}{2}} \Gamma\left(\frac{11}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{11}{4} \\ \frac{15}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt[4]{a} \Gamma\left(\frac{15}{4}\right)}"," ",0,"c**(9/2)*x**(11/2)*gamma(11/4)*hyper((1/4, 11/4), (15/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(1/4)*gamma(15/4))","C",0
950,1,44,0,6.737337," ","integrate((c*x)**(5/2)/(b*x**2+a)**(1/4),x)","\frac{c^{\frac{5}{2}} x^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt[4]{a} \Gamma\left(\frac{11}{4}\right)}"," ",0,"c**(5/2)*x**(7/2)*gamma(7/4)*hyper((1/4, 7/4), (11/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(1/4)*gamma(11/4))","C",0
951,1,44,0,1.008116," ","integrate((c*x)**(1/2)/(b*x**2+a)**(1/4),x)","\frac{\sqrt{c} x^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt[4]{a} \Gamma\left(\frac{7}{4}\right)}"," ",0,"sqrt(c)*x**(3/2)*gamma(3/4)*hyper((1/4, 3/4), (7/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(1/4)*gamma(7/4))","C",0
952,1,31,0,2.037671," ","integrate(1/(c*x)**(3/2)/(b*x**2+a)**(1/4),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{2}}} \right)}}{\sqrt[4]{b} c^{\frac{3}{2}} x}"," ",0,"-hyper((1/4, 1/2), (3/2,), a*exp_polar(I*pi)/(b*x**2))/(b**(1/4)*c**(3/2)*x)","C",0
953,1,34,0,12.232944," ","integrate(1/(c*x)**(7/2)/(b*x**2+a)**(1/4),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{2}}} \right)}}{3 \sqrt[4]{b} c^{\frac{7}{2}} x^{3}}"," ",0,"-hyper((1/4, 3/2), (5/2,), a*exp_polar(I*pi)/(b*x**2))/(3*b**(1/4)*c**(7/2)*x**3)","C",0
954,1,34,0,89.345029," ","integrate(1/(c*x)**(11/2)/(b*x**2+a)**(1/4),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{2}}} \right)}}{5 \sqrt[4]{b} c^{\frac{11}{2}} x^{5}}"," ",0,"-hyper((1/4, 5/2), (7/2,), a*exp_polar(I*pi)/(b*x**2))/(5*b**(1/4)*c**(11/2)*x**5)","C",0
955,1,46,0,2.204989," ","integrate((c*x)**(3/2)/(-b*x**2+a)**(1/4),x)","\frac{c^{\frac{3}{2}} x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{2 \sqrt[4]{a} \Gamma\left(\frac{9}{4}\right)}"," ",0,"c**(3/2)*x**(5/2)*gamma(5/4)*hyper((1/4, 5/4), (9/4,), b*x**2*exp_polar(2*I*pi)/a)/(2*a**(1/4)*gamma(9/4))","C",0
956,1,46,0,1.523069," ","integrate(1/(c*x)**(1/2)/(-b*x**2+a)**(1/4),x)","\frac{\sqrt{x} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{2 \sqrt[4]{a} \sqrt{c} \Gamma\left(\frac{5}{4}\right)}"," ",0,"sqrt(x)*gamma(1/4)*hyper((1/4, 1/4), (5/4,), b*x**2*exp_polar(2*I*pi)/a)/(2*a**(1/4)*sqrt(c)*gamma(5/4))","C",0
957,1,88,0,3.617159," ","integrate(1/(c*x)**(5/2)/(-b*x**2+a)**(1/4),x)","\begin{cases} \frac{b^{\frac{3}{4}} \left(\frac{a}{b x^{2}} - 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{3}{4}\right)}{2 a c^{\frac{5}{2}} \Gamma\left(\frac{1}{4}\right)} & \text{for}\: \left|{\frac{a}{b x^{2}}}\right| > 1 \\- \frac{b^{\frac{3}{4}} \left(- \frac{a}{b x^{2}} + 1\right)^{\frac{3}{4}} e^{- \frac{i \pi}{4}} \Gamma\left(- \frac{3}{4}\right)}{2 a c^{\frac{5}{2}} \Gamma\left(\frac{1}{4}\right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((b**(3/4)*(a/(b*x**2) - 1)**(3/4)*gamma(-3/4)/(2*a*c**(5/2)*gamma(1/4)), Abs(a/(b*x**2)) > 1), (-b**(3/4)*(-a/(b*x**2) + 1)**(3/4)*exp(-I*pi/4)*gamma(-3/4)/(2*a*c**(5/2)*gamma(1/4)), True))","A",0
958,1,343,0,34.343261," ","integrate(1/(c*x)**(9/2)/(-b*x**2+a)**(1/4),x)","\begin{cases} - \frac{3 b^{\frac{3}{4}} \left(\frac{a}{b x^{2}} - 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{7}{4}\right)}{8 a c^{\frac{9}{2}} x^{2} \Gamma\left(\frac{1}{4}\right)} - \frac{b^{\frac{7}{4}} \left(\frac{a}{b x^{2}} - 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{7}{4}\right)}{2 a^{2} c^{\frac{9}{2}} \Gamma\left(\frac{1}{4}\right)} & \text{for}\: \left|{\frac{a}{b x^{2}}}\right| > 1 \\- \frac{3 a^{2} b^{\frac{7}{4}} \left(- \frac{a}{b x^{2}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{7}{4}\right)}{- 8 a^{3} b c^{\frac{9}{2}} x^{2} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 8 a^{2} b^{2} c^{\frac{9}{2}} x^{4} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right)} - \frac{a b^{\frac{11}{4}} x^{2} \left(- \frac{a}{b x^{2}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{7}{4}\right)}{- 8 a^{3} b c^{\frac{9}{2}} x^{2} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 8 a^{2} b^{2} c^{\frac{9}{2}} x^{4} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right)} + \frac{4 b^{\frac{15}{4}} x^{4} \left(- \frac{a}{b x^{2}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{7}{4}\right)}{- 8 a^{3} b c^{\frac{9}{2}} x^{2} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) + 8 a^{2} b^{2} c^{\frac{9}{2}} x^{4} e^{\frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-3*b**(3/4)*(a/(b*x**2) - 1)**(3/4)*gamma(-7/4)/(8*a*c**(9/2)*x**2*gamma(1/4)) - b**(7/4)*(a/(b*x**2) - 1)**(3/4)*gamma(-7/4)/(2*a**2*c**(9/2)*gamma(1/4)), Abs(a/(b*x**2)) > 1), (-3*a**2*b**(7/4)*(-a/(b*x**2) + 1)**(3/4)*gamma(-7/4)/(-8*a**3*b*c**(9/2)*x**2*exp(I*pi/4)*gamma(1/4) + 8*a**2*b**2*c**(9/2)*x**4*exp(I*pi/4)*gamma(1/4)) - a*b**(11/4)*x**2*(-a/(b*x**2) + 1)**(3/4)*gamma(-7/4)/(-8*a**3*b*c**(9/2)*x**2*exp(I*pi/4)*gamma(1/4) + 8*a**2*b**2*c**(9/2)*x**4*exp(I*pi/4)*gamma(1/4)) + 4*b**(15/4)*x**4*(-a/(b*x**2) + 1)**(3/4)*gamma(-7/4)/(-8*a**3*b*c**(9/2)*x**2*exp(I*pi/4)*gamma(1/4) + 8*a**2*b**2*c**(9/2)*x**4*exp(I*pi/4)*gamma(1/4)), True))","A",0
959,-1,0,0,0.000000," ","integrate(1/(c*x)**(13/2)/(-b*x**2+a)**(1/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
960,1,46,0,6.784529," ","integrate((c*x)**(5/2)/(-b*x**2+a)**(1/4),x)","\frac{c^{\frac{5}{2}} x^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{2 \sqrt[4]{a} \Gamma\left(\frac{11}{4}\right)}"," ",0,"c**(5/2)*x**(7/2)*gamma(7/4)*hyper((1/4, 7/4), (11/4,), b*x**2*exp_polar(2*I*pi)/a)/(2*a**(1/4)*gamma(11/4))","C",0
961,1,46,0,1.035868," ","integrate((c*x)**(1/2)/(-b*x**2+a)**(1/4),x)","\frac{\sqrt{c} x^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{2 \sqrt[4]{a} \Gamma\left(\frac{7}{4}\right)}"," ",0,"sqrt(c)*x**(3/2)*gamma(3/4)*hyper((1/4, 3/4), (7/4,), b*x**2*exp_polar(2*I*pi)/a)/(2*a**(1/4)*gamma(7/4))","C",0
962,1,32,0,2.063342," ","integrate(1/(c*x)**(3/2)/(-b*x**2+a)**(1/4),x)","\frac{i e^{\frac{i \pi}{4}} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle| {\frac{a}{b x^{2}}} \right)}}{\sqrt[4]{b} c^{\frac{3}{2}} x}"," ",0,"I*exp(I*pi/4)*hyper((1/4, 1/2), (3/2,), a/(b*x**2))/(b**(1/4)*c**(3/2)*x)","C",0
963,1,39,0,12.195046," ","integrate(1/(c*x)**(7/2)/(-b*x**2+a)**(1/4),x)","- \frac{i e^{- \frac{3 i \pi}{4}} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{a}{b x^{2}}} \right)}}{3 \sqrt[4]{b} c^{\frac{7}{2}} x^{3}}"," ",0,"-I*exp(-3*I*pi/4)*hyper((1/4, 3/2), (5/2,), a/(b*x**2))/(3*b**(1/4)*c**(7/2)*x**3)","C",0
964,1,36,0,87.775302," ","integrate(1/(c*x)**(11/2)/(-b*x**2+a)**(1/4),x)","\frac{i e^{\frac{i \pi}{4}} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{a}{b x^{2}}} \right)}}{5 \sqrt[4]{b} c^{\frac{11}{2}} x^{5}}"," ",0,"I*exp(I*pi/4)*hyper((1/4, 5/2), (7/2,), a/(b*x**2))/(5*b**(1/4)*c**(11/2)*x**5)","C",0
965,1,44,0,2.029761," ","integrate((c*x)**(3/2)/(b*x**2+a)**(3/4),x)","\frac{c^{\frac{3}{2}} x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{4}} \Gamma\left(\frac{9}{4}\right)}"," ",0,"c**(3/2)*x**(5/2)*gamma(5/4)*hyper((3/4, 5/4), (9/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(3/4)*gamma(9/4))","C",0
966,1,31,0,1.713643," ","integrate(1/(c*x)**(1/2)/(b*x**2+a)**(3/4),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{3}{2} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{2}}} \right)}}{b^{\frac{3}{4}} \sqrt{c} x}"," ",0,"-hyper((1/2, 3/4), (3/2,), a*exp_polar(I*pi)/(b*x**2))/(b**(3/4)*sqrt(c)*x)","C",0
967,1,48,0,7.834820," ","integrate(1/(c*x)**(5/2)/(b*x**2+a)**(3/4),x)","\frac{\Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{3}{4} \\ \frac{1}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{4}} c^{\frac{5}{2}} x^{\frac{3}{2}} \Gamma\left(\frac{1}{4}\right)}"," ",0,"gamma(-3/4)*hyper((-3/4, 3/4), (1/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(3/4)*c**(5/2)*x**(3/2)*gamma(1/4))","C",0
968,1,34,0,66.188036," ","integrate(1/(c*x)**(9/2)/(b*x**2+a)**(3/4),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{2}}} \right)}}{5 b^{\frac{3}{4}} c^{\frac{9}{2}} x^{5}}"," ",0,"-hyper((3/4, 5/2), (7/2,), a*exp_polar(I*pi)/(b*x**2))/(5*b**(3/4)*c**(9/2)*x**5)","C",0
969,-1,0,0,0.000000," ","integrate(1/(c*x)**(13/2)/(b*x**2+a)**(3/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
970,1,44,0,7.779185," ","integrate((c*x)**(5/2)/(b*x**2+a)**(3/4),x)","\frac{c^{\frac{5}{2}} x^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{4}} \Gamma\left(\frac{11}{4}\right)}"," ",0,"c**(5/2)*x**(7/2)*gamma(7/4)*hyper((3/4, 7/4), (11/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(3/4)*gamma(11/4))","C",0
971,1,44,0,1.501323," ","integrate((c*x)**(1/2)/(b*x**2+a)**(3/4),x)","\frac{\sqrt{c} x^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{4}} \Gamma\left(\frac{7}{4}\right)}"," ",0,"sqrt(c)*x**(3/2)*gamma(3/4)*hyper((3/4, 3/4), (7/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(3/4)*gamma(7/4))","C",0
972,1,36,0,2.924130," ","integrate(1/(c*x)**(3/2)/(b*x**2+a)**(3/4),x)","\frac{\sqrt[4]{b} \sqrt[4]{\frac{a}{b x^{2}} + 1} \Gamma\left(- \frac{1}{4}\right)}{2 a c^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right)}"," ",0,"b**(1/4)*(a/(b*x**2) + 1)**(1/4)*gamma(-1/4)/(2*a*c**(3/2)*gamma(3/4))","A",0
973,1,78,0,24.761563," ","integrate(1/(c*x)**(7/2)/(b*x**2+a)**(3/4),x)","- \frac{\sqrt[4]{b} \sqrt[4]{\frac{a}{b x^{2}} + 1} \Gamma\left(- \frac{5}{4}\right)}{8 a c^{\frac{7}{2}} x^{2} \Gamma\left(\frac{3}{4}\right)} + \frac{b^{\frac{5}{4}} \sqrt[4]{\frac{a}{b x^{2}} + 1} \Gamma\left(- \frac{5}{4}\right)}{2 a^{2} c^{\frac{7}{2}} \Gamma\left(\frac{3}{4}\right)}"," ",0,"-b**(1/4)*(a/(b*x**2) + 1)**(1/4)*gamma(-5/4)/(8*a*c**(7/2)*x**2*gamma(3/4)) + b**(5/4)*(a/(b*x**2) + 1)**(1/4)*gamma(-5/4)/(2*a**2*c**(7/2)*gamma(3/4))","A",0
974,1,483,0,172.060130," ","integrate(1/(c*x)**(11/2)/(b*x**2+a)**(3/4),x)","\frac{5 a^{4} b^{\frac{17}{4}} \sqrt[4]{\frac{a}{b x^{2}} + 1} \Gamma\left(- \frac{9}{4}\right)}{32 a^{5} b^{4} c^{\frac{11}{2}} x^{4} \Gamma\left(\frac{3}{4}\right) + 64 a^{4} b^{5} c^{\frac{11}{2}} x^{6} \Gamma\left(\frac{3}{4}\right) + 32 a^{3} b^{6} c^{\frac{11}{2}} x^{8} \Gamma\left(\frac{3}{4}\right)} + \frac{2 a^{3} b^{\frac{21}{4}} x^{2} \sqrt[4]{\frac{a}{b x^{2}} + 1} \Gamma\left(- \frac{9}{4}\right)}{32 a^{5} b^{4} c^{\frac{11}{2}} x^{4} \Gamma\left(\frac{3}{4}\right) + 64 a^{4} b^{5} c^{\frac{11}{2}} x^{6} \Gamma\left(\frac{3}{4}\right) + 32 a^{3} b^{6} c^{\frac{11}{2}} x^{8} \Gamma\left(\frac{3}{4}\right)} + \frac{21 a^{2} b^{\frac{25}{4}} x^{4} \sqrt[4]{\frac{a}{b x^{2}} + 1} \Gamma\left(- \frac{9}{4}\right)}{32 a^{5} b^{4} c^{\frac{11}{2}} x^{4} \Gamma\left(\frac{3}{4}\right) + 64 a^{4} b^{5} c^{\frac{11}{2}} x^{6} \Gamma\left(\frac{3}{4}\right) + 32 a^{3} b^{6} c^{\frac{11}{2}} x^{8} \Gamma\left(\frac{3}{4}\right)} + \frac{56 a b^{\frac{29}{4}} x^{6} \sqrt[4]{\frac{a}{b x^{2}} + 1} \Gamma\left(- \frac{9}{4}\right)}{32 a^{5} b^{4} c^{\frac{11}{2}} x^{4} \Gamma\left(\frac{3}{4}\right) + 64 a^{4} b^{5} c^{\frac{11}{2}} x^{6} \Gamma\left(\frac{3}{4}\right) + 32 a^{3} b^{6} c^{\frac{11}{2}} x^{8} \Gamma\left(\frac{3}{4}\right)} + \frac{32 b^{\frac{33}{4}} x^{8} \sqrt[4]{\frac{a}{b x^{2}} + 1} \Gamma\left(- \frac{9}{4}\right)}{32 a^{5} b^{4} c^{\frac{11}{2}} x^{4} \Gamma\left(\frac{3}{4}\right) + 64 a^{4} b^{5} c^{\frac{11}{2}} x^{6} \Gamma\left(\frac{3}{4}\right) + 32 a^{3} b^{6} c^{\frac{11}{2}} x^{8} \Gamma\left(\frac{3}{4}\right)}"," ",0,"5*a**4*b**(17/4)*(a/(b*x**2) + 1)**(1/4)*gamma(-9/4)/(32*a**5*b**4*c**(11/2)*x**4*gamma(3/4) + 64*a**4*b**5*c**(11/2)*x**6*gamma(3/4) + 32*a**3*b**6*c**(11/2)*x**8*gamma(3/4)) + 2*a**3*b**(21/4)*x**2*(a/(b*x**2) + 1)**(1/4)*gamma(-9/4)/(32*a**5*b**4*c**(11/2)*x**4*gamma(3/4) + 64*a**4*b**5*c**(11/2)*x**6*gamma(3/4) + 32*a**3*b**6*c**(11/2)*x**8*gamma(3/4)) + 21*a**2*b**(25/4)*x**4*(a/(b*x**2) + 1)**(1/4)*gamma(-9/4)/(32*a**5*b**4*c**(11/2)*x**4*gamma(3/4) + 64*a**4*b**5*c**(11/2)*x**6*gamma(3/4) + 32*a**3*b**6*c**(11/2)*x**8*gamma(3/4)) + 56*a*b**(29/4)*x**6*(a/(b*x**2) + 1)**(1/4)*gamma(-9/4)/(32*a**5*b**4*c**(11/2)*x**4*gamma(3/4) + 64*a**4*b**5*c**(11/2)*x**6*gamma(3/4) + 32*a**3*b**6*c**(11/2)*x**8*gamma(3/4)) + 32*b**(33/4)*x**8*(a/(b*x**2) + 1)**(1/4)*gamma(-9/4)/(32*a**5*b**4*c**(11/2)*x**4*gamma(3/4) + 64*a**4*b**5*c**(11/2)*x**6*gamma(3/4) + 32*a**3*b**6*c**(11/2)*x**8*gamma(3/4))","B",0
975,1,46,0,2.198847," ","integrate((c*x)**(3/2)/(-b*x**2+a)**(3/4),x)","\frac{c^{\frac{3}{2}} x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{2 a^{\frac{3}{4}} \Gamma\left(\frac{9}{4}\right)}"," ",0,"c**(3/2)*x**(5/2)*gamma(5/4)*hyper((3/4, 5/4), (9/4,), b*x**2*exp_polar(2*I*pi)/a)/(2*a**(3/4)*gamma(9/4))","C",0
976,1,32,0,1.893772," ","integrate(1/(c*x)**(1/2)/(-b*x**2+a)**(3/4),x)","\frac{i e^{- \frac{i \pi}{4}} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{3}{2} \end{matrix}\middle| {\frac{a}{b x^{2}}} \right)}}{b^{\frac{3}{4}} \sqrt{c} x}"," ",0,"I*exp(-I*pi/4)*hyper((1/2, 3/4), (3/2,), a/(b*x**2))/(b**(3/4)*sqrt(c)*x)","C",0
977,1,39,0,8.314949," ","integrate(1/(c*x)**(5/2)/(-b*x**2+a)**(3/4),x)","- \frac{i e^{\frac{3 i \pi}{4}} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{a}{b x^{2}}} \right)}}{3 b^{\frac{3}{4}} c^{\frac{5}{2}} x^{3}}"," ",0,"-I*exp(3*I*pi/4)*hyper((3/4, 3/2), (5/2,), a/(b*x**2))/(3*b**(3/4)*c**(5/2)*x**3)","C",0
978,1,36,0,68.933852," ","integrate(1/(c*x)**(9/2)/(-b*x**2+a)**(3/4),x)","\frac{i e^{- \frac{i \pi}{4}} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{a}{b x^{2}}} \right)}}{5 b^{\frac{3}{4}} c^{\frac{9}{2}} x^{5}}"," ",0,"I*exp(-I*pi/4)*hyper((3/4, 5/2), (7/2,), a/(b*x**2))/(5*b**(3/4)*c**(9/2)*x**5)","C",0
979,-1,0,0,0.000000," ","integrate(1/(c*x)**(13/2)/(-b*x**2+a)**(3/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
980,1,46,0,7.817184," ","integrate((c*x)**(5/2)/(-b*x**2+a)**(3/4),x)","\frac{c^{\frac{5}{2}} x^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{2 a^{\frac{3}{4}} \Gamma\left(\frac{11}{4}\right)}"," ",0,"c**(5/2)*x**(7/2)*gamma(7/4)*hyper((3/4, 7/4), (11/4,), b*x**2*exp_polar(2*I*pi)/a)/(2*a**(3/4)*gamma(11/4))","C",0
981,1,46,0,1.563657," ","integrate((c*x)**(1/2)/(-b*x**2+a)**(3/4),x)","\frac{\sqrt{c} x^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{2 a^{\frac{3}{4}} \Gamma\left(\frac{7}{4}\right)}"," ",0,"sqrt(c)*x**(3/2)*gamma(3/4)*hyper((3/4, 3/4), (7/4,), b*x**2*exp_polar(2*I*pi)/a)/(2*a**(3/4)*gamma(7/4))","C",0
982,1,90,0,3.001490," ","integrate(1/(c*x)**(3/2)/(-b*x**2+a)**(3/4),x)","\begin{cases} \frac{\sqrt[4]{b} \sqrt[4]{\frac{a}{b x^{2}} - 1} \Gamma\left(- \frac{1}{4}\right)}{2 a c^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right)} & \text{for}\: \left|{\frac{a}{b x^{2}}}\right| > 1 \\- \frac{\sqrt[4]{b} \sqrt[4]{- \frac{a}{b x^{2}} + 1} e^{- \frac{3 i \pi}{4}} \Gamma\left(- \frac{1}{4}\right)}{2 a c^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((b**(1/4)*(a/(b*x**2) - 1)**(1/4)*gamma(-1/4)/(2*a*c**(3/2)*gamma(3/4)), Abs(a/(b*x**2)) > 1), (-b**(1/4)*(-a/(b*x**2) + 1)**(1/4)*exp(-3*I*pi/4)*gamma(-1/4)/(2*a*c**(3/2)*gamma(3/4)), True))","A",0
983,1,352,0,25.445455," ","integrate(1/(c*x)**(7/2)/(-b*x**2+a)**(3/4),x)","\begin{cases} - \frac{\sqrt[4]{b} \sqrt[4]{\frac{a}{b x^{2}} - 1} \Gamma\left(- \frac{5}{4}\right)}{8 a c^{\frac{7}{2}} x^{2} \Gamma\left(\frac{3}{4}\right)} - \frac{b^{\frac{5}{4}} \sqrt[4]{\frac{a}{b x^{2}} - 1} \Gamma\left(- \frac{5}{4}\right)}{2 a^{2} c^{\frac{7}{2}} \Gamma\left(\frac{3}{4}\right)} & \text{for}\: \left|{\frac{a}{b x^{2}}}\right| > 1 \\- \frac{a^{2} b^{\frac{5}{4}} \sqrt[4]{- \frac{a}{b x^{2}} + 1} \Gamma\left(- \frac{5}{4}\right)}{- 8 a^{3} b c^{\frac{7}{2}} x^{2} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 8 a^{2} b^{2} c^{\frac{7}{2}} x^{4} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right)} - \frac{3 a b^{\frac{9}{4}} x^{2} \sqrt[4]{- \frac{a}{b x^{2}} + 1} \Gamma\left(- \frac{5}{4}\right)}{- 8 a^{3} b c^{\frac{7}{2}} x^{2} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 8 a^{2} b^{2} c^{\frac{7}{2}} x^{4} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right)} + \frac{4 b^{\frac{13}{4}} x^{4} \sqrt[4]{- \frac{a}{b x^{2}} + 1} \Gamma\left(- \frac{5}{4}\right)}{- 8 a^{3} b c^{\frac{7}{2}} x^{2} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 8 a^{2} b^{2} c^{\frac{7}{2}} x^{4} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-b**(1/4)*(a/(b*x**2) - 1)**(1/4)*gamma(-5/4)/(8*a*c**(7/2)*x**2*gamma(3/4)) - b**(5/4)*(a/(b*x**2) - 1)**(1/4)*gamma(-5/4)/(2*a**2*c**(7/2)*gamma(3/4)), Abs(a/(b*x**2)) > 1), (-a**2*b**(5/4)*(-a/(b*x**2) + 1)**(1/4)*gamma(-5/4)/(-8*a**3*b*c**(7/2)*x**2*exp(3*I*pi/4)*gamma(3/4) + 8*a**2*b**2*c**(7/2)*x**4*exp(3*I*pi/4)*gamma(3/4)) - 3*a*b**(9/4)*x**2*(-a/(b*x**2) + 1)**(1/4)*gamma(-5/4)/(-8*a**3*b*c**(7/2)*x**2*exp(3*I*pi/4)*gamma(3/4) + 8*a**2*b**2*c**(7/2)*x**4*exp(3*I*pi/4)*gamma(3/4)) + 4*b**(13/4)*x**4*(-a/(b*x**2) + 1)**(1/4)*gamma(-5/4)/(-8*a**3*b*c**(7/2)*x**2*exp(3*I*pi/4)*gamma(3/4) + 8*a**2*b**2*c**(7/2)*x**4*exp(3*I*pi/4)*gamma(3/4)), True))","A",0
984,1,1263,0,171.233987," ","integrate(1/(c*x)**(11/2)/(-b*x**2+a)**(3/4),x)","\begin{cases} - \frac{5 a^{4} b^{\frac{17}{4}} \sqrt[4]{\frac{a}{b x^{2}} - 1} e^{- \frac{i \pi}{4}} \Gamma\left(- \frac{9}{4}\right)}{32 a^{5} b^{4} c^{\frac{11}{2}} x^{4} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) - 64 a^{4} b^{5} c^{\frac{11}{2}} x^{6} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 32 a^{3} b^{6} c^{\frac{11}{2}} x^{8} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right)} + \frac{2 a^{3} b^{\frac{21}{4}} x^{2} \sqrt[4]{\frac{a}{b x^{2}} - 1} e^{- \frac{i \pi}{4}} \Gamma\left(- \frac{9}{4}\right)}{32 a^{5} b^{4} c^{\frac{11}{2}} x^{4} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) - 64 a^{4} b^{5} c^{\frac{11}{2}} x^{6} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 32 a^{3} b^{6} c^{\frac{11}{2}} x^{8} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right)} - \frac{21 a^{2} b^{\frac{25}{4}} x^{4} \sqrt[4]{\frac{a}{b x^{2}} - 1} e^{- \frac{i \pi}{4}} \Gamma\left(- \frac{9}{4}\right)}{32 a^{5} b^{4} c^{\frac{11}{2}} x^{4} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) - 64 a^{4} b^{5} c^{\frac{11}{2}} x^{6} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 32 a^{3} b^{6} c^{\frac{11}{2}} x^{8} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right)} + \frac{56 a b^{\frac{29}{4}} x^{6} \sqrt[4]{\frac{a}{b x^{2}} - 1} e^{- \frac{i \pi}{4}} \Gamma\left(- \frac{9}{4}\right)}{32 a^{5} b^{4} c^{\frac{11}{2}} x^{4} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) - 64 a^{4} b^{5} c^{\frac{11}{2}} x^{6} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 32 a^{3} b^{6} c^{\frac{11}{2}} x^{8} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right)} - \frac{32 b^{\frac{33}{4}} x^{8} \sqrt[4]{\frac{a}{b x^{2}} - 1} e^{- \frac{i \pi}{4}} \Gamma\left(- \frac{9}{4}\right)}{32 a^{5} b^{4} c^{\frac{11}{2}} x^{4} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) - 64 a^{4} b^{5} c^{\frac{11}{2}} x^{6} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 32 a^{3} b^{6} c^{\frac{11}{2}} x^{8} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right)} & \text{for}\: \left|{\frac{a}{b x^{2}}}\right| > 1 \\- \frac{5 a^{4} b^{\frac{17}{4}} \sqrt[4]{- \frac{a}{b x^{2}} + 1} \Gamma\left(- \frac{9}{4}\right)}{32 a^{5} b^{4} c^{\frac{11}{2}} x^{4} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) - 64 a^{4} b^{5} c^{\frac{11}{2}} x^{6} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 32 a^{3} b^{6} c^{\frac{11}{2}} x^{8} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right)} + \frac{2 a^{3} b^{\frac{21}{4}} x^{2} \sqrt[4]{- \frac{a}{b x^{2}} + 1} \Gamma\left(- \frac{9}{4}\right)}{32 a^{5} b^{4} c^{\frac{11}{2}} x^{4} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) - 64 a^{4} b^{5} c^{\frac{11}{2}} x^{6} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 32 a^{3} b^{6} c^{\frac{11}{2}} x^{8} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right)} - \frac{21 a^{2} b^{\frac{25}{4}} x^{4} \sqrt[4]{- \frac{a}{b x^{2}} + 1} \Gamma\left(- \frac{9}{4}\right)}{32 a^{5} b^{4} c^{\frac{11}{2}} x^{4} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) - 64 a^{4} b^{5} c^{\frac{11}{2}} x^{6} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 32 a^{3} b^{6} c^{\frac{11}{2}} x^{8} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right)} + \frac{56 a b^{\frac{29}{4}} x^{6} \sqrt[4]{- \frac{a}{b x^{2}} + 1} \Gamma\left(- \frac{9}{4}\right)}{32 a^{5} b^{4} c^{\frac{11}{2}} x^{4} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) - 64 a^{4} b^{5} c^{\frac{11}{2}} x^{6} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 32 a^{3} b^{6} c^{\frac{11}{2}} x^{8} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right)} - \frac{32 b^{\frac{33}{4}} x^{8} \sqrt[4]{- \frac{a}{b x^{2}} + 1} \Gamma\left(- \frac{9}{4}\right)}{32 a^{5} b^{4} c^{\frac{11}{2}} x^{4} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) - 64 a^{4} b^{5} c^{\frac{11}{2}} x^{6} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) + 32 a^{3} b^{6} c^{\frac{11}{2}} x^{8} e^{\frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-5*a**4*b**(17/4)*(a/(b*x**2) - 1)**(1/4)*exp(-I*pi/4)*gamma(-9/4)/(32*a**5*b**4*c**(11/2)*x**4*exp(3*I*pi/4)*gamma(3/4) - 64*a**4*b**5*c**(11/2)*x**6*exp(3*I*pi/4)*gamma(3/4) + 32*a**3*b**6*c**(11/2)*x**8*exp(3*I*pi/4)*gamma(3/4)) + 2*a**3*b**(21/4)*x**2*(a/(b*x**2) - 1)**(1/4)*exp(-I*pi/4)*gamma(-9/4)/(32*a**5*b**4*c**(11/2)*x**4*exp(3*I*pi/4)*gamma(3/4) - 64*a**4*b**5*c**(11/2)*x**6*exp(3*I*pi/4)*gamma(3/4) + 32*a**3*b**6*c**(11/2)*x**8*exp(3*I*pi/4)*gamma(3/4)) - 21*a**2*b**(25/4)*x**4*(a/(b*x**2) - 1)**(1/4)*exp(-I*pi/4)*gamma(-9/4)/(32*a**5*b**4*c**(11/2)*x**4*exp(3*I*pi/4)*gamma(3/4) - 64*a**4*b**5*c**(11/2)*x**6*exp(3*I*pi/4)*gamma(3/4) + 32*a**3*b**6*c**(11/2)*x**8*exp(3*I*pi/4)*gamma(3/4)) + 56*a*b**(29/4)*x**6*(a/(b*x**2) - 1)**(1/4)*exp(-I*pi/4)*gamma(-9/4)/(32*a**5*b**4*c**(11/2)*x**4*exp(3*I*pi/4)*gamma(3/4) - 64*a**4*b**5*c**(11/2)*x**6*exp(3*I*pi/4)*gamma(3/4) + 32*a**3*b**6*c**(11/2)*x**8*exp(3*I*pi/4)*gamma(3/4)) - 32*b**(33/4)*x**8*(a/(b*x**2) - 1)**(1/4)*exp(-I*pi/4)*gamma(-9/4)/(32*a**5*b**4*c**(11/2)*x**4*exp(3*I*pi/4)*gamma(3/4) - 64*a**4*b**5*c**(11/2)*x**6*exp(3*I*pi/4)*gamma(3/4) + 32*a**3*b**6*c**(11/2)*x**8*exp(3*I*pi/4)*gamma(3/4)), Abs(a/(b*x**2)) > 1), (-5*a**4*b**(17/4)*(-a/(b*x**2) + 1)**(1/4)*gamma(-9/4)/(32*a**5*b**4*c**(11/2)*x**4*exp(3*I*pi/4)*gamma(3/4) - 64*a**4*b**5*c**(11/2)*x**6*exp(3*I*pi/4)*gamma(3/4) + 32*a**3*b**6*c**(11/2)*x**8*exp(3*I*pi/4)*gamma(3/4)) + 2*a**3*b**(21/4)*x**2*(-a/(b*x**2) + 1)**(1/4)*gamma(-9/4)/(32*a**5*b**4*c**(11/2)*x**4*exp(3*I*pi/4)*gamma(3/4) - 64*a**4*b**5*c**(11/2)*x**6*exp(3*I*pi/4)*gamma(3/4) + 32*a**3*b**6*c**(11/2)*x**8*exp(3*I*pi/4)*gamma(3/4)) - 21*a**2*b**(25/4)*x**4*(-a/(b*x**2) + 1)**(1/4)*gamma(-9/4)/(32*a**5*b**4*c**(11/2)*x**4*exp(3*I*pi/4)*gamma(3/4) - 64*a**4*b**5*c**(11/2)*x**6*exp(3*I*pi/4)*gamma(3/4) + 32*a**3*b**6*c**(11/2)*x**8*exp(3*I*pi/4)*gamma(3/4)) + 56*a*b**(29/4)*x**6*(-a/(b*x**2) + 1)**(1/4)*gamma(-9/4)/(32*a**5*b**4*c**(11/2)*x**4*exp(3*I*pi/4)*gamma(3/4) - 64*a**4*b**5*c**(11/2)*x**6*exp(3*I*pi/4)*gamma(3/4) + 32*a**3*b**6*c**(11/2)*x**8*exp(3*I*pi/4)*gamma(3/4)) - 32*b**(33/4)*x**8*(-a/(b*x**2) + 1)**(1/4)*gamma(-9/4)/(32*a**5*b**4*c**(11/2)*x**4*exp(3*I*pi/4)*gamma(3/4) - 64*a**4*b**5*c**(11/2)*x**6*exp(3*I*pi/4)*gamma(3/4) + 32*a**3*b**6*c**(11/2)*x**8*exp(3*I*pi/4)*gamma(3/4)), True))","C",0
985,1,44,0,24.493506," ","integrate((c*x)**(7/2)/(b*x**2+a)**(5/4),x)","\frac{c^{\frac{7}{2}} x^{\frac{9}{2}} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{5}{4}} \Gamma\left(\frac{13}{4}\right)}"," ",0,"c**(7/2)*x**(9/2)*gamma(9/4)*hyper((5/4, 9/4), (13/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(5/4)*gamma(13/4))","C",0
986,1,44,0,4.257117," ","integrate((c*x)**(3/2)/(b*x**2+a)**(5/4),x)","\frac{c^{\frac{3}{2}} x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{5}{4}} \Gamma\left(\frac{9}{4}\right)}"," ",0,"c**(3/2)*x**(5/2)*gamma(5/4)*hyper((5/4, 5/4), (9/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(5/4)*gamma(9/4))","C",0
987,1,34,0,3.140831," ","integrate(1/(c*x)**(1/2)/(b*x**2+a)**(5/4),x)","\frac{\Gamma\left(\frac{1}{4}\right)}{2 a \sqrt[4]{b} \sqrt{c} \sqrt[4]{\frac{a}{b x^{2}} + 1} \Gamma\left(\frac{5}{4}\right)}"," ",0,"gamma(1/4)/(2*a*b**(1/4)*sqrt(c)*(a/(b*x**2) + 1)**(1/4)*gamma(5/4))","A",0
988,1,78,0,14.989436," ","integrate(1/(c*x)**(5/2)/(b*x**2+a)**(5/4),x)","\frac{\Gamma\left(- \frac{3}{4}\right)}{8 a \sqrt[4]{b} c^{\frac{5}{2}} x^{2} \sqrt[4]{\frac{a}{b x^{2}} + 1} \Gamma\left(\frac{5}{4}\right)} + \frac{b^{\frac{3}{4}} \Gamma\left(- \frac{3}{4}\right)}{2 a^{2} c^{\frac{5}{2}} \sqrt[4]{\frac{a}{b x^{2}} + 1} \Gamma\left(\frac{5}{4}\right)}"," ",0,"gamma(-3/4)/(8*a*b**(1/4)*c**(5/2)*x**2*(a/(b*x**2) + 1)**(1/4)*gamma(5/4)) + b**(3/4)*gamma(-3/4)/(2*a**2*c**(5/2)*(a/(b*x**2) + 1)**(1/4)*gamma(5/4))","A",0
989,1,384,0,109.043893," ","integrate(1/(c*x)**(9/2)/(b*x**2+a)**(5/4),x)","- \frac{3 a^{3} b^{\frac{19}{4}} \left(\frac{a}{b x^{2}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{7}{4}\right)}{32 a^{5} b^{4} c^{\frac{9}{2}} x^{2} \Gamma\left(\frac{5}{4}\right) + 64 a^{4} b^{5} c^{\frac{9}{2}} x^{4} \Gamma\left(\frac{5}{4}\right) + 32 a^{3} b^{6} c^{\frac{9}{2}} x^{6} \Gamma\left(\frac{5}{4}\right)} + \frac{5 a^{2} b^{\frac{23}{4}} x^{2} \left(\frac{a}{b x^{2}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{7}{4}\right)}{32 a^{5} b^{4} c^{\frac{9}{2}} x^{2} \Gamma\left(\frac{5}{4}\right) + 64 a^{4} b^{5} c^{\frac{9}{2}} x^{4} \Gamma\left(\frac{5}{4}\right) + 32 a^{3} b^{6} c^{\frac{9}{2}} x^{6} \Gamma\left(\frac{5}{4}\right)} + \frac{40 a b^{\frac{27}{4}} x^{4} \left(\frac{a}{b x^{2}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{7}{4}\right)}{32 a^{5} b^{4} c^{\frac{9}{2}} x^{2} \Gamma\left(\frac{5}{4}\right) + 64 a^{4} b^{5} c^{\frac{9}{2}} x^{4} \Gamma\left(\frac{5}{4}\right) + 32 a^{3} b^{6} c^{\frac{9}{2}} x^{6} \Gamma\left(\frac{5}{4}\right)} + \frac{32 b^{\frac{31}{4}} x^{6} \left(\frac{a}{b x^{2}} + 1\right)^{\frac{3}{4}} \Gamma\left(- \frac{7}{4}\right)}{32 a^{5} b^{4} c^{\frac{9}{2}} x^{2} \Gamma\left(\frac{5}{4}\right) + 64 a^{4} b^{5} c^{\frac{9}{2}} x^{4} \Gamma\left(\frac{5}{4}\right) + 32 a^{3} b^{6} c^{\frac{9}{2}} x^{6} \Gamma\left(\frac{5}{4}\right)}"," ",0,"-3*a**3*b**(19/4)*(a/(b*x**2) + 1)**(3/4)*gamma(-7/4)/(32*a**5*b**4*c**(9/2)*x**2*gamma(5/4) + 64*a**4*b**5*c**(9/2)*x**4*gamma(5/4) + 32*a**3*b**6*c**(9/2)*x**6*gamma(5/4)) + 5*a**2*b**(23/4)*x**2*(a/(b*x**2) + 1)**(3/4)*gamma(-7/4)/(32*a**5*b**4*c**(9/2)*x**2*gamma(5/4) + 64*a**4*b**5*c**(9/2)*x**4*gamma(5/4) + 32*a**3*b**6*c**(9/2)*x**6*gamma(5/4)) + 40*a*b**(27/4)*x**4*(a/(b*x**2) + 1)**(3/4)*gamma(-7/4)/(32*a**5*b**4*c**(9/2)*x**2*gamma(5/4) + 64*a**4*b**5*c**(9/2)*x**4*gamma(5/4) + 32*a**3*b**6*c**(9/2)*x**6*gamma(5/4)) + 32*b**(31/4)*x**6*(a/(b*x**2) + 1)**(3/4)*gamma(-7/4)/(32*a**5*b**4*c**(9/2)*x**2*gamma(5/4) + 64*a**4*b**5*c**(9/2)*x**4*gamma(5/4) + 32*a**3*b**6*c**(9/2)*x**6*gamma(5/4))","B",0
990,-1,0,0,0.000000," ","integrate(1/(c*x)**(13/2)/(b*x**2+a)**(5/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
991,-1,0,0,0.000000," ","integrate((c*x)**(13/2)/(b*x**2+a)**(5/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
992,1,44,0,64.024319," ","integrate((c*x)**(9/2)/(b*x**2+a)**(5/4),x)","\frac{c^{\frac{9}{2}} x^{\frac{11}{2}} \Gamma\left(\frac{11}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, \frac{11}{4} \\ \frac{15}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{5}{4}} \Gamma\left(\frac{15}{4}\right)}"," ",0,"c**(9/2)*x**(11/2)*gamma(11/4)*hyper((5/4, 11/4), (15/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(5/4)*gamma(15/4))","C",0
993,1,44,0,7.776453," ","integrate((c*x)**(5/2)/(b*x**2+a)**(5/4),x)","\frac{c^{\frac{5}{2}} x^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{5}{4}} \Gamma\left(\frac{11}{4}\right)}"," ",0,"c**(5/2)*x**(7/2)*gamma(7/4)*hyper((5/4, 7/4), (11/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(5/4)*gamma(11/4))","C",0
994,1,44,0,2.101823," ","integrate((c*x)**(1/2)/(b*x**2+a)**(5/4),x)","\frac{\sqrt{c} x^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{5}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{5}{4}} \Gamma\left(\frac{7}{4}\right)}"," ",0,"sqrt(c)*x**(3/2)*gamma(3/4)*hyper((3/4, 5/4), (7/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(5/4)*gamma(7/4))","C",0
995,1,48,0,6.012585," ","integrate(1/(c*x)**(3/2)/(b*x**2+a)**(5/4),x)","\frac{\Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{5}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{5}{4}} c^{\frac{3}{2}} \sqrt{x} \Gamma\left(\frac{3}{4}\right)}"," ",0,"gamma(-1/4)*hyper((-1/4, 5/4), (3/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(5/4)*c**(3/2)*sqrt(x)*gamma(3/4))","C",0
996,1,34,0,41.485727," ","integrate(1/(c*x)**(7/2)/(b*x**2+a)**(5/4),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{2}}} \right)}}{5 b^{\frac{5}{4}} c^{\frac{7}{2}} x^{5}}"," ",0,"-hyper((5/4, 5/2), (7/2,), a*exp_polar(I*pi)/(b*x**2))/(5*b**(5/4)*c**(7/2)*x**5)","C",0
997,-1,0,0,0.000000," ","integrate(1/(c*x)**(11/2)/(b*x**2+a)**(5/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
998,1,44,0,12.122856," ","integrate((c*x)**(5/4)/(b*x**2+a)**(1/4),x)","\frac{c^{\frac{5}{4}} x^{\frac{9}{4}} \Gamma\left(\frac{9}{8}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{9}{8} \\ \frac{17}{8} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt[4]{a} \Gamma\left(\frac{17}{8}\right)}"," ",0,"c**(5/4)*x**(9/4)*gamma(9/8)*hyper((1/4, 9/8), (17/8,), b*x**2*exp_polar(I*pi)/a)/(2*a**(1/4)*gamma(17/8))","C",0
999,1,44,0,3.689919," ","integrate((c*x)**(3/4)/(b*x**2+a)**(1/4),x)","\frac{c^{\frac{3}{4}} x^{\frac{7}{4}} \Gamma\left(\frac{7}{8}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{7}{8} \\ \frac{15}{8} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt[4]{a} \Gamma\left(\frac{15}{8}\right)}"," ",0,"c**(3/4)*x**(7/4)*gamma(7/8)*hyper((1/4, 7/8), (15/8,), b*x**2*exp_polar(I*pi)/a)/(2*a**(1/4)*gamma(15/8))","C",0
1000,1,44,0,1.228645," ","integrate((c*x)**(1/4)/(b*x**2+a)**(1/4),x)","\frac{\sqrt[4]{c} x^{\frac{5}{4}} \Gamma\left(\frac{5}{8}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{5}{8} \\ \frac{13}{8} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt[4]{a} \Gamma\left(\frac{13}{8}\right)}"," ",0,"c**(1/4)*x**(5/4)*gamma(5/8)*hyper((1/4, 5/8), (13/8,), b*x**2*exp_polar(I*pi)/a)/(2*a**(1/4)*gamma(13/8))","C",0
1001,1,44,0,1.299631," ","integrate(1/(c*x)**(1/4)/(b*x**2+a)**(1/4),x)","\frac{x^{\frac{3}{4}} \Gamma\left(\frac{3}{8}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{3}{8} \\ \frac{11}{8} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt[4]{a} \sqrt[4]{c} \Gamma\left(\frac{11}{8}\right)}"," ",0,"x**(3/4)*gamma(3/8)*hyper((1/4, 3/8), (11/8,), b*x**2*exp_polar(I*pi)/a)/(2*a**(1/4)*c**(1/4)*gamma(11/8))","C",0
1002,1,44,0,2.086336," ","integrate(1/(c*x)**(3/4)/(b*x**2+a)**(1/4),x)","\frac{\sqrt[4]{x} \Gamma\left(\frac{1}{8}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{8}, \frac{1}{4} \\ \frac{9}{8} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt[4]{a} c^{\frac{3}{4}} \Gamma\left(\frac{9}{8}\right)}"," ",0,"x**(1/4)*gamma(1/8)*hyper((1/8, 1/4), (9/8,), b*x**2*exp_polar(I*pi)/a)/(2*a**(1/4)*c**(3/4)*gamma(9/8))","C",0
1003,1,48,0,3.764595," ","integrate(1/(c*x)**(5/4)/(b*x**2+a)**(1/4),x)","\frac{\Gamma\left(- \frac{1}{8}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{8}, \frac{1}{4} \\ \frac{7}{8} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt[4]{a} c^{\frac{5}{4}} \sqrt[4]{x} \Gamma\left(\frac{7}{8}\right)}"," ",0,"gamma(-1/8)*hyper((-1/8, 1/4), (7/8,), b*x**2*exp_polar(I*pi)/a)/(2*a**(1/4)*c**(5/4)*x**(1/4)*gamma(7/8))","C",0
1004,1,44,0,23.695095," ","integrate((c*x)**(5/4)/(b*x**2+a)**(7/4),x)","\frac{c^{\frac{5}{4}} x^{\frac{9}{4}} \Gamma\left(\frac{9}{8}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{9}{8}, \frac{7}{4} \\ \frac{17}{8} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{7}{4}} \Gamma\left(\frac{17}{8}\right)}"," ",0,"c**(5/4)*x**(9/4)*gamma(9/8)*hyper((9/8, 7/4), (17/8,), b*x**2*exp_polar(I*pi)/a)/(2*a**(7/4)*gamma(17/8))","C",0
1005,1,44,0,13.712475," ","integrate((c*x)**(3/4)/(b*x**2+a)**(7/4),x)","\frac{c^{\frac{3}{4}} x^{\frac{7}{4}} \Gamma\left(\frac{7}{8}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{7}{8}, \frac{7}{4} \\ \frac{15}{8} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{7}{4}} \Gamma\left(\frac{15}{8}\right)}"," ",0,"c**(3/4)*x**(7/4)*gamma(7/8)*hyper((7/8, 7/4), (15/8,), b*x**2*exp_polar(I*pi)/a)/(2*a**(7/4)*gamma(15/8))","C",0
1006,1,44,0,7.478427," ","integrate((c*x)**(1/4)/(b*x**2+a)**(7/4),x)","\frac{\sqrt[4]{c} x^{\frac{5}{4}} \Gamma\left(\frac{5}{8}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{8}, \frac{7}{4} \\ \frac{13}{8} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{7}{4}} \Gamma\left(\frac{13}{8}\right)}"," ",0,"c**(1/4)*x**(5/4)*gamma(5/8)*hyper((5/8, 7/4), (13/8,), b*x**2*exp_polar(I*pi)/a)/(2*a**(7/4)*gamma(13/8))","C",0
1007,1,44,0,8.138483," ","integrate(1/(c*x)**(1/4)/(b*x**2+a)**(7/4),x)","\frac{x^{\frac{3}{4}} \Gamma\left(\frac{3}{8}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{8}, \frac{7}{4} \\ \frac{11}{8} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{7}{4}} \sqrt[4]{c} \Gamma\left(\frac{11}{8}\right)}"," ",0,"x**(3/4)*gamma(3/8)*hyper((3/8, 7/4), (11/8,), b*x**2*exp_polar(I*pi)/a)/(2*a**(7/4)*c**(1/4)*gamma(11/8))","C",0
1008,1,44,0,14.678087," ","integrate(1/(c*x)**(3/4)/(b*x**2+a)**(7/4),x)","\frac{\sqrt[4]{x} \Gamma\left(\frac{1}{8}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{8}, \frac{7}{4} \\ \frac{9}{8} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{7}{4}} c^{\frac{3}{4}} \Gamma\left(\frac{9}{8}\right)}"," ",0,"x**(1/4)*gamma(1/8)*hyper((1/8, 7/4), (9/8,), b*x**2*exp_polar(I*pi)/a)/(2*a**(7/4)*c**(3/4)*gamma(9/8))","C",0
1009,1,48,0,25.454157," ","integrate(1/(c*x)**(5/4)/(b*x**2+a)**(7/4),x)","\frac{\Gamma\left(- \frac{1}{8}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{8}, \frac{7}{4} \\ \frac{7}{8} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{7}{4}} c^{\frac{5}{4}} \sqrt[4]{x} \Gamma\left(\frac{7}{8}\right)}"," ",0,"gamma(-1/8)*hyper((-1/8, 7/4), (7/8,), b*x**2*exp_polar(I*pi)/a)/(2*a**(7/4)*c**(5/4)*x**(1/4)*gamma(7/8))","C",0
1010,1,29,0,1.189178," ","integrate(x**6*(b*x**2+a)**(1/6),x)","\frac{\sqrt[6]{a} x^{7} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{6}, \frac{7}{2} \\ \frac{9}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{7}"," ",0,"a**(1/6)*x**7*hyper((-1/6, 7/2), (9/2,), b*x**2*exp_polar(I*pi)/a)/7","A",0
1011,1,29,0,1.060959," ","integrate(x**4*(b*x**2+a)**(1/6),x)","\frac{\sqrt[6]{a} x^{5} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{6}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{5}"," ",0,"a**(1/6)*x**5*hyper((-1/6, 5/2), (7/2,), b*x**2*exp_polar(I*pi)/a)/5","A",0
1012,1,29,0,0.977367," ","integrate(x**2*(b*x**2+a)**(1/6),x)","\frac{\sqrt[6]{a} x^{3} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{6}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{3}"," ",0,"a**(1/6)*x**3*hyper((-1/6, 3/2), (5/2,), b*x**2*exp_polar(I*pi)/a)/3","A",0
1013,1,26,0,0.893300," ","integrate((b*x**2+a)**(1/6),x)","\sqrt[6]{a} x {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{6}, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}"," ",0,"a**(1/6)*x*hyper((-1/6, 1/2), (3/2,), b*x**2*exp_polar(I*pi)/a)","A",0
1014,1,29,0,0.984755," ","integrate((b*x**2+a)**(1/6)/x**2,x)","- \frac{\sqrt[6]{a} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{6} \\ \frac{1}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{x}"," ",0,"-a**(1/6)*hyper((-1/2, -1/6), (1/2,), b*x**2*exp_polar(I*pi)/a)/x","A",0
1015,1,34,0,1.107758," ","integrate((b*x**2+a)**(1/6)/x**4,x)","- \frac{\sqrt[6]{a} {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, - \frac{1}{6} \\ - \frac{1}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{3 x^{3}}"," ",0,"-a**(1/6)*hyper((-3/2, -1/6), (-1/2,), b*x**2*exp_polar(I*pi)/a)/(3*x**3)","A",0
1016,1,34,0,1.292814," ","integrate((b*x**2+a)**(1/6)/x**6,x)","- \frac{\sqrt[6]{a} {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{2}, - \frac{1}{6} \\ - \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{5 x^{5}}"," ",0,"-a**(1/6)*hyper((-5/2, -1/6), (-3/2,), b*x**2*exp_polar(I*pi)/a)/(5*x**5)","A",0
1017,1,34,0,1.462917," ","integrate((b*x**2+a)**(1/6)/x**8,x)","- \frac{\sqrt[6]{a} {{}_{2}F_{1}\left(\begin{matrix} - \frac{7}{2}, - \frac{1}{6} \\ - \frac{5}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{7 x^{7}}"," ",0,"-a**(1/6)*hyper((-7/2, -1/6), (-5/2,), b*x**2*exp_polar(I*pi)/a)/(7*x**7)","A",0
1018,1,27,0,1.106245," ","integrate(x**6/(b*x**2+a)**(1/6),x)","\frac{x^{7} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{6}, \frac{7}{2} \\ \frac{9}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{7 \sqrt[6]{a}}"," ",0,"x**7*hyper((1/6, 7/2), (9/2,), b*x**2*exp_polar(I*pi)/a)/(7*a**(1/6))","A",0
1019,1,27,0,0.960882," ","integrate(x**4/(b*x**2+a)**(1/6),x)","\frac{x^{5} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{6}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{5 \sqrt[6]{a}}"," ",0,"x**5*hyper((1/6, 5/2), (7/2,), b*x**2*exp_polar(I*pi)/a)/(5*a**(1/6))","A",0
1020,1,27,0,0.843431," ","integrate(x**2/(b*x**2+a)**(1/6),x)","\frac{x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{6}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{3 \sqrt[6]{a}}"," ",0,"x**3*hyper((1/6, 3/2), (5/2,), b*x**2*exp_polar(I*pi)/a)/(3*a**(1/6))","A",0
1021,1,24,0,0.848645," ","integrate(1/(b*x**2+a)**(1/6),x)","\frac{x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{6}, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{\sqrt[6]{a}}"," ",0,"x*hyper((1/6, 1/2), (3/2,), b*x**2*exp_polar(I*pi)/a)/a**(1/6)","A",0
1022,1,27,0,0.974133," ","integrate(1/x**2/(b*x**2+a)**(1/6),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{6} \\ \frac{1}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{\sqrt[6]{a} x}"," ",0,"-hyper((-1/2, 1/6), (1/2,), b*x**2*exp_polar(I*pi)/a)/(a**(1/6)*x)","A",0
1023,1,32,0,1.121009," ","integrate(1/x**4/(b*x**2+a)**(1/6),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, \frac{1}{6} \\ - \frac{1}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{3 \sqrt[6]{a} x^{3}}"," ",0,"-hyper((-3/2, 1/6), (-1/2,), b*x**2*exp_polar(I*pi)/a)/(3*a**(1/6)*x**3)","A",0
1024,1,32,0,1.301467," ","integrate(1/x**6/(b*x**2+a)**(1/6),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{2}, \frac{1}{6} \\ - \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{5 \sqrt[6]{a} x^{5}}"," ",0,"-hyper((-5/2, 1/6), (-3/2,), b*x**2*exp_polar(I*pi)/a)/(5*a**(1/6)*x**5)","A",0
1025,1,27,0,0.991687," ","integrate(x**6/(b*x**2+a)**(5/6),x)","\frac{x^{7} {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{6}, \frac{7}{2} \\ \frac{9}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{7 a^{\frac{5}{6}}}"," ",0,"x**7*hyper((5/6, 7/2), (9/2,), b*x**2*exp_polar(I*pi)/a)/(7*a**(5/6))","A",0
1026,1,27,0,0.919305," ","integrate(x**4/(b*x**2+a)**(5/6),x)","\frac{x^{5} {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{6}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{5 a^{\frac{5}{6}}}"," ",0,"x**5*hyper((5/6, 5/2), (7/2,), b*x**2*exp_polar(I*pi)/a)/(5*a**(5/6))","A",0
1027,1,27,0,0.937149," ","integrate(x**2/(b*x**2+a)**(5/6),x)","\frac{x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{6}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{3 a^{\frac{5}{6}}}"," ",0,"x**3*hyper((5/6, 3/2), (5/2,), b*x**2*exp_polar(I*pi)/a)/(3*a**(5/6))","A",0
1028,1,24,0,0.869663," ","integrate(1/(b*x**2+a)**(5/6),x)","\frac{x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{5}{6} \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{a^{\frac{5}{6}}}"," ",0,"x*hyper((1/2, 5/6), (3/2,), b*x**2*exp_polar(I*pi)/a)/a**(5/6)","A",0
1029,1,27,0,1.150662," ","integrate(1/x**2/(b*x**2+a)**(5/6),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{6} \\ \frac{1}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{a^{\frac{5}{6}} x}"," ",0,"-hyper((-1/2, 5/6), (1/2,), b*x**2*exp_polar(I*pi)/a)/(a**(5/6)*x)","A",0
1030,1,32,0,1.463211," ","integrate(1/x**4/(b*x**2+a)**(5/6),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, \frac{5}{6} \\ - \frac{1}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{3 a^{\frac{5}{6}} x^{3}}"," ",0,"-hyper((-3/2, 5/6), (-1/2,), b*x**2*exp_polar(I*pi)/a)/(3*a**(5/6)*x**3)","A",0
1031,1,32,0,1.489925," ","integrate(1/x**6/(b*x**2+a)**(5/6),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{2}, \frac{5}{6} \\ - \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{5 a^{\frac{5}{6}} x^{5}}"," ",0,"-hyper((-5/2, 5/6), (-3/2,), b*x**2*exp_polar(I*pi)/a)/(5*a**(5/6)*x**5)","A",0
1032,1,27,0,1.052223," ","integrate(x**6/(b*x**2+a)**(7/6),x)","\frac{x^{7} {{}_{2}F_{1}\left(\begin{matrix} \frac{7}{6}, \frac{7}{2} \\ \frac{9}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{7 a^{\frac{7}{6}}}"," ",0,"x**7*hyper((7/6, 7/2), (9/2,), b*x**2*exp_polar(I*pi)/a)/(7*a**(7/6))","A",0
1033,1,27,0,1.039463," ","integrate(x**4/(b*x**2+a)**(7/6),x)","\frac{x^{5} {{}_{2}F_{1}\left(\begin{matrix} \frac{7}{6}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{5 a^{\frac{7}{6}}}"," ",0,"x**5*hyper((7/6, 5/2), (7/2,), b*x**2*exp_polar(I*pi)/a)/(5*a**(7/6))","A",0
1034,1,27,0,1.025784," ","integrate(x**2/(b*x**2+a)**(7/6),x)","\frac{x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{7}{6}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{3 a^{\frac{7}{6}}}"," ",0,"x**3*hyper((7/6, 3/2), (5/2,), b*x**2*exp_polar(I*pi)/a)/(3*a**(7/6))","A",0
1035,1,24,0,0.977186," ","integrate(1/(b*x**2+a)**(7/6),x)","\frac{x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{7}{6} \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{a^{\frac{7}{6}}}"," ",0,"x*hyper((1/2, 7/6), (3/2,), b*x**2*exp_polar(I*pi)/a)/a**(7/6)","A",0
1036,1,27,0,1.240070," ","integrate(1/x**2/(b*x**2+a)**(7/6),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{7}{6} \\ \frac{1}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{a^{\frac{7}{6}} x}"," ",0,"-hyper((-1/2, 7/6), (1/2,), b*x**2*exp_polar(I*pi)/a)/(a**(7/6)*x)","A",0
1037,1,32,0,1.446886," ","integrate(1/x**4/(b*x**2+a)**(7/6),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, \frac{7}{6} \\ - \frac{1}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{3 a^{\frac{7}{6}} x^{3}}"," ",0,"-hyper((-3/2, 7/6), (-1/2,), b*x**2*exp_polar(I*pi)/a)/(3*a**(7/6)*x**3)","A",0
1038,1,32,0,1.703589," ","integrate(1/x**6/(b*x**2+a)**(7/6),x)","- \frac{{{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{2}, \frac{7}{6} \\ - \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{5 a^{\frac{7}{6}} x^{5}}"," ",0,"-hyper((-5/2, 7/6), (-3/2,), b*x**2*exp_polar(I*pi)/a)/(5*a**(7/6)*x**5)","A",0
1039,1,2025,0,11.064778," ","integrate(x**7*(b*x**2+a)**p,x)","\begin{cases} \frac{a^{p} x^{8}}{8} & \text{for}\: b = 0 \\\frac{6 a^{3} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} + \frac{6 a^{3} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} + \frac{11 a^{3}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} + \frac{18 a^{2} b x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} + \frac{18 a^{2} b x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} + \frac{27 a^{2} b x^{2}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} + \frac{18 a b^{2} x^{4} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} + \frac{18 a b^{2} x^{4} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} + \frac{18 a b^{2} x^{4}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} + \frac{6 b^{3} x^{6} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} + \frac{6 b^{3} x^{6} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} & \text{for}\: p = -4 \\- \frac{6 a^{3} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{4} + 8 a b^{5} x^{2} + 4 b^{6} x^{4}} - \frac{6 a^{3} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{4} + 8 a b^{5} x^{2} + 4 b^{6} x^{4}} - \frac{9 a^{3}}{4 a^{2} b^{4} + 8 a b^{5} x^{2} + 4 b^{6} x^{4}} - \frac{12 a^{2} b x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{4} + 8 a b^{5} x^{2} + 4 b^{6} x^{4}} - \frac{12 a^{2} b x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{4} + 8 a b^{5} x^{2} + 4 b^{6} x^{4}} - \frac{12 a^{2} b x^{2}}{4 a^{2} b^{4} + 8 a b^{5} x^{2} + 4 b^{6} x^{4}} - \frac{6 a b^{2} x^{4} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{4} + 8 a b^{5} x^{2} + 4 b^{6} x^{4}} - \frac{6 a b^{2} x^{4} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{4} + 8 a b^{5} x^{2} + 4 b^{6} x^{4}} + \frac{2 b^{3} x^{6}}{4 a^{2} b^{4} + 8 a b^{5} x^{2} + 4 b^{6} x^{4}} & \text{for}\: p = -3 \\\frac{6 a^{3} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a b^{4} + 4 b^{5} x^{2}} + \frac{6 a^{3} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a b^{4} + 4 b^{5} x^{2}} + \frac{6 a^{3}}{4 a b^{4} + 4 b^{5} x^{2}} + \frac{6 a^{2} b x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a b^{4} + 4 b^{5} x^{2}} + \frac{6 a^{2} b x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a b^{4} + 4 b^{5} x^{2}} - \frac{3 a b^{2} x^{4}}{4 a b^{4} + 4 b^{5} x^{2}} + \frac{b^{3} x^{6}}{4 a b^{4} + 4 b^{5} x^{2}} & \text{for}\: p = -2 \\- \frac{a^{3} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 b^{4}} - \frac{a^{3} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 b^{4}} + \frac{a^{2} x^{2}}{2 b^{3}} - \frac{a x^{4}}{4 b^{2}} + \frac{x^{6}}{6 b} & \text{for}\: p = -1 \\- \frac{6 a^{4} \left(a + b x^{2}\right)^{p}}{2 b^{4} p^{4} + 20 b^{4} p^{3} + 70 b^{4} p^{2} + 100 b^{4} p + 48 b^{4}} + \frac{6 a^{3} b p x^{2} \left(a + b x^{2}\right)^{p}}{2 b^{4} p^{4} + 20 b^{4} p^{3} + 70 b^{4} p^{2} + 100 b^{4} p + 48 b^{4}} - \frac{3 a^{2} b^{2} p^{2} x^{4} \left(a + b x^{2}\right)^{p}}{2 b^{4} p^{4} + 20 b^{4} p^{3} + 70 b^{4} p^{2} + 100 b^{4} p + 48 b^{4}} - \frac{3 a^{2} b^{2} p x^{4} \left(a + b x^{2}\right)^{p}}{2 b^{4} p^{4} + 20 b^{4} p^{3} + 70 b^{4} p^{2} + 100 b^{4} p + 48 b^{4}} + \frac{a b^{3} p^{3} x^{6} \left(a + b x^{2}\right)^{p}}{2 b^{4} p^{4} + 20 b^{4} p^{3} + 70 b^{4} p^{2} + 100 b^{4} p + 48 b^{4}} + \frac{3 a b^{3} p^{2} x^{6} \left(a + b x^{2}\right)^{p}}{2 b^{4} p^{4} + 20 b^{4} p^{3} + 70 b^{4} p^{2} + 100 b^{4} p + 48 b^{4}} + \frac{2 a b^{3} p x^{6} \left(a + b x^{2}\right)^{p}}{2 b^{4} p^{4} + 20 b^{4} p^{3} + 70 b^{4} p^{2} + 100 b^{4} p + 48 b^{4}} + \frac{b^{4} p^{3} x^{8} \left(a + b x^{2}\right)^{p}}{2 b^{4} p^{4} + 20 b^{4} p^{3} + 70 b^{4} p^{2} + 100 b^{4} p + 48 b^{4}} + \frac{6 b^{4} p^{2} x^{8} \left(a + b x^{2}\right)^{p}}{2 b^{4} p^{4} + 20 b^{4} p^{3} + 70 b^{4} p^{2} + 100 b^{4} p + 48 b^{4}} + \frac{11 b^{4} p x^{8} \left(a + b x^{2}\right)^{p}}{2 b^{4} p^{4} + 20 b^{4} p^{3} + 70 b^{4} p^{2} + 100 b^{4} p + 48 b^{4}} + \frac{6 b^{4} x^{8} \left(a + b x^{2}\right)^{p}}{2 b^{4} p^{4} + 20 b^{4} p^{3} + 70 b^{4} p^{2} + 100 b^{4} p + 48 b^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**p*x**8/8, Eq(b, 0)), (6*a**3*log(-I*sqrt(a)*sqrt(1/b) + x)/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6) + 6*a**3*log(I*sqrt(a)*sqrt(1/b) + x)/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6) + 11*a**3/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6) + 18*a**2*b*x**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6) + 18*a**2*b*x**2*log(I*sqrt(a)*sqrt(1/b) + x)/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6) + 27*a**2*b*x**2/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6) + 18*a*b**2*x**4*log(-I*sqrt(a)*sqrt(1/b) + x)/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6) + 18*a*b**2*x**4*log(I*sqrt(a)*sqrt(1/b) + x)/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6) + 18*a*b**2*x**4/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6) + 6*b**3*x**6*log(-I*sqrt(a)*sqrt(1/b) + x)/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6) + 6*b**3*x**6*log(I*sqrt(a)*sqrt(1/b) + x)/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6), Eq(p, -4)), (-6*a**3*log(-I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**4 + 8*a*b**5*x**2 + 4*b**6*x**4) - 6*a**3*log(I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**4 + 8*a*b**5*x**2 + 4*b**6*x**4) - 9*a**3/(4*a**2*b**4 + 8*a*b**5*x**2 + 4*b**6*x**4) - 12*a**2*b*x**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**4 + 8*a*b**5*x**2 + 4*b**6*x**4) - 12*a**2*b*x**2*log(I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**4 + 8*a*b**5*x**2 + 4*b**6*x**4) - 12*a**2*b*x**2/(4*a**2*b**4 + 8*a*b**5*x**2 + 4*b**6*x**4) - 6*a*b**2*x**4*log(-I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**4 + 8*a*b**5*x**2 + 4*b**6*x**4) - 6*a*b**2*x**4*log(I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**4 + 8*a*b**5*x**2 + 4*b**6*x**4) + 2*b**3*x**6/(4*a**2*b**4 + 8*a*b**5*x**2 + 4*b**6*x**4), Eq(p, -3)), (6*a**3*log(-I*sqrt(a)*sqrt(1/b) + x)/(4*a*b**4 + 4*b**5*x**2) + 6*a**3*log(I*sqrt(a)*sqrt(1/b) + x)/(4*a*b**4 + 4*b**5*x**2) + 6*a**3/(4*a*b**4 + 4*b**5*x**2) + 6*a**2*b*x**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(4*a*b**4 + 4*b**5*x**2) + 6*a**2*b*x**2*log(I*sqrt(a)*sqrt(1/b) + x)/(4*a*b**4 + 4*b**5*x**2) - 3*a*b**2*x**4/(4*a*b**4 + 4*b**5*x**2) + b**3*x**6/(4*a*b**4 + 4*b**5*x**2), Eq(p, -2)), (-a**3*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*b**4) - a**3*log(I*sqrt(a)*sqrt(1/b) + x)/(2*b**4) + a**2*x**2/(2*b**3) - a*x**4/(4*b**2) + x**6/(6*b), Eq(p, -1)), (-6*a**4*(a + b*x**2)**p/(2*b**4*p**4 + 20*b**4*p**3 + 70*b**4*p**2 + 100*b**4*p + 48*b**4) + 6*a**3*b*p*x**2*(a + b*x**2)**p/(2*b**4*p**4 + 20*b**4*p**3 + 70*b**4*p**2 + 100*b**4*p + 48*b**4) - 3*a**2*b**2*p**2*x**4*(a + b*x**2)**p/(2*b**4*p**4 + 20*b**4*p**3 + 70*b**4*p**2 + 100*b**4*p + 48*b**4) - 3*a**2*b**2*p*x**4*(a + b*x**2)**p/(2*b**4*p**4 + 20*b**4*p**3 + 70*b**4*p**2 + 100*b**4*p + 48*b**4) + a*b**3*p**3*x**6*(a + b*x**2)**p/(2*b**4*p**4 + 20*b**4*p**3 + 70*b**4*p**2 + 100*b**4*p + 48*b**4) + 3*a*b**3*p**2*x**6*(a + b*x**2)**p/(2*b**4*p**4 + 20*b**4*p**3 + 70*b**4*p**2 + 100*b**4*p + 48*b**4) + 2*a*b**3*p*x**6*(a + b*x**2)**p/(2*b**4*p**4 + 20*b**4*p**3 + 70*b**4*p**2 + 100*b**4*p + 48*b**4) + b**4*p**3*x**8*(a + b*x**2)**p/(2*b**4*p**4 + 20*b**4*p**3 + 70*b**4*p**2 + 100*b**4*p + 48*b**4) + 6*b**4*p**2*x**8*(a + b*x**2)**p/(2*b**4*p**4 + 20*b**4*p**3 + 70*b**4*p**2 + 100*b**4*p + 48*b**4) + 11*b**4*p*x**8*(a + b*x**2)**p/(2*b**4*p**4 + 20*b**4*p**3 + 70*b**4*p**2 + 100*b**4*p + 48*b**4) + 6*b**4*x**8*(a + b*x**2)**p/(2*b**4*p**4 + 20*b**4*p**3 + 70*b**4*p**2 + 100*b**4*p + 48*b**4), True))","A",0
1040,1,981,0,5.045032," ","integrate(x**5*(b*x**2+a)**p,x)","\begin{cases} \frac{a^{p} x^{6}}{6} & \text{for}\: b = 0 \\\frac{2 a^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{2 a^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{3 a^{2}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{4 a b x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{4 a b x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{4 a b x^{2}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{2 b^{2} x^{4} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{2 b^{2} x^{4} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} & \text{for}\: p = -3 \\- \frac{2 a^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{3} + 2 b^{4} x^{2}} - \frac{2 a^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{3} + 2 b^{4} x^{2}} - \frac{2 a^{2}}{2 a b^{3} + 2 b^{4} x^{2}} - \frac{2 a b x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{3} + 2 b^{4} x^{2}} - \frac{2 a b x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{3} + 2 b^{4} x^{2}} + \frac{b^{2} x^{4}}{2 a b^{3} + 2 b^{4} x^{2}} & \text{for}\: p = -2 \\\frac{a^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 b^{3}} + \frac{a^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 b^{3}} - \frac{a x^{2}}{2 b^{2}} + \frac{x^{4}}{4 b} & \text{for}\: p = -1 \\\frac{2 a^{3} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} - \frac{2 a^{2} b p x^{2} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} + \frac{a b^{2} p^{2} x^{4} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} + \frac{a b^{2} p x^{4} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} + \frac{b^{3} p^{2} x^{6} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} + \frac{3 b^{3} p x^{6} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} + \frac{2 b^{3} x^{6} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**p*x**6/6, Eq(b, 0)), (2*a**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 2*a**2*log(I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 3*a**2/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 4*a*b*x**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 4*a*b*x**2*log(I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 4*a*b*x**2/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 2*b**2*x**4*log(-I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 2*b**2*x**4*log(I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4), Eq(p, -3)), (-2*a**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**3 + 2*b**4*x**2) - 2*a**2*log(I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**3 + 2*b**4*x**2) - 2*a**2/(2*a*b**3 + 2*b**4*x**2) - 2*a*b*x**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**3 + 2*b**4*x**2) - 2*a*b*x**2*log(I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**3 + 2*b**4*x**2) + b**2*x**4/(2*a*b**3 + 2*b**4*x**2), Eq(p, -2)), (a**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*b**3) + a**2*log(I*sqrt(a)*sqrt(1/b) + x)/(2*b**3) - a*x**2/(2*b**2) + x**4/(4*b), Eq(p, -1)), (2*a**3*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) - 2*a**2*b*p*x**2*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) + a*b**2*p**2*x**4*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) + a*b**2*p*x**4*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) + b**3*p**2*x**6*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) + 3*b**3*p*x**6*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) + 2*b**3*x**6*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3), True))","A",0
1041,1,364,0,2.003152," ","integrate(x**3*(b*x**2+a)**p,x)","\begin{cases} \frac{a^{p} x^{4}}{4} & \text{for}\: b = 0 \\\frac{a \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{2} + 2 b^{3} x^{2}} + \frac{a \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{2} + 2 b^{3} x^{2}} + \frac{a}{2 a b^{2} + 2 b^{3} x^{2}} + \frac{b x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{2} + 2 b^{3} x^{2}} + \frac{b x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{2} + 2 b^{3} x^{2}} & \text{for}\: p = -2 \\- \frac{a \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 b^{2}} - \frac{a \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 b^{2}} + \frac{x^{2}}{2 b} & \text{for}\: p = -1 \\- \frac{a^{2} \left(a + b x^{2}\right)^{p}}{2 b^{2} p^{2} + 6 b^{2} p + 4 b^{2}} + \frac{a b p x^{2} \left(a + b x^{2}\right)^{p}}{2 b^{2} p^{2} + 6 b^{2} p + 4 b^{2}} + \frac{b^{2} p x^{4} \left(a + b x^{2}\right)^{p}}{2 b^{2} p^{2} + 6 b^{2} p + 4 b^{2}} + \frac{b^{2} x^{4} \left(a + b x^{2}\right)^{p}}{2 b^{2} p^{2} + 6 b^{2} p + 4 b^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**p*x**4/4, Eq(b, 0)), (a*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**2 + 2*b**3*x**2) + a*log(I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**2 + 2*b**3*x**2) + a/(2*a*b**2 + 2*b**3*x**2) + b*x**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**2 + 2*b**3*x**2) + b*x**2*log(I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**2 + 2*b**3*x**2), Eq(p, -2)), (-a*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*b**2) - a*log(I*sqrt(a)*sqrt(1/b) + x)/(2*b**2) + x**2/(2*b), Eq(p, -1)), (-a**2*(a + b*x**2)**p/(2*b**2*p**2 + 6*b**2*p + 4*b**2) + a*b*p*x**2*(a + b*x**2)**p/(2*b**2*p**2 + 6*b**2*p + 4*b**2) + b**2*p*x**4*(a + b*x**2)**p/(2*b**2*p**2 + 6*b**2*p + 4*b**2) + b**2*x**4*(a + b*x**2)**p/(2*b**2*p**2 + 6*b**2*p + 4*b**2), True))","A",0
1042,1,97,0,0.732047," ","integrate(x*(b*x**2+a)**p,x)","\begin{cases} \frac{x^{2}}{2 a} & \text{for}\: b = 0 \wedge p = -1 \\\frac{a^{p} x^{2}}{2} & \text{for}\: b = 0 \\\frac{\log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 b} + \frac{\log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 b} & \text{for}\: p = -1 \\\frac{a \left(a + b x^{2}\right)^{p}}{2 b p + 2 b} + \frac{b x^{2} \left(a + b x^{2}\right)^{p}}{2 b p + 2 b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x**2/(2*a), Eq(b, 0) & Eq(p, -1)), (a**p*x**2/2, Eq(b, 0)), (log(-I*sqrt(a)*sqrt(1/b) + x)/(2*b) + log(I*sqrt(a)*sqrt(1/b) + x)/(2*b), Eq(p, -1)), (a*(a + b*x**2)**p/(2*b*p + 2*b) + b*x**2*(a + b*x**2)**p/(2*b*p + 2*b), True))","A",0
1043,1,39,0,2.486843," ","integrate((b*x**2+a)**p/x,x)","- \frac{b^{p} x^{2 p} \Gamma\left(- p\right) {{}_{2}F_{1}\left(\begin{matrix} - p, - p \\ 1 - p \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{2}}} \right)}}{2 \Gamma\left(1 - p\right)}"," ",0,"-b**p*x**(2*p)*gamma(-p)*hyper((-p, -p), (1 - p,), a*exp_polar(I*pi)/(b*x**2))/(2*gamma(1 - p))","C",0
1044,1,42,0,5.132639," ","integrate((b*x**2+a)**p/x**3,x)","- \frac{b^{p} x^{2 p} \Gamma\left(1 - p\right) {{}_{2}F_{1}\left(\begin{matrix} - p, 1 - p \\ 2 - p \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{2}}} \right)}}{2 x^{2} \Gamma\left(2 - p\right)}"," ",0,"-b**p*x**(2*p)*gamma(1 - p)*hyper((-p, 1 - p), (2 - p,), a*exp_polar(I*pi)/(b*x**2))/(2*x**2*gamma(2 - p))","C",0
1045,1,26,0,11.851248," ","integrate(x**6*(b*x**2+a)**p,x)","\frac{a^{p} x^{7} {{}_{2}F_{1}\left(\begin{matrix} \frac{7}{2}, - p \\ \frac{9}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{7}"," ",0,"a**p*x**7*hyper((7/2, -p), (9/2,), b*x**2*exp_polar(I*pi)/a)/7","C",0
1046,1,26,0,6.608043," ","integrate(x**4*(b*x**2+a)**p,x)","\frac{a^{p} x^{5} {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{2}, - p \\ \frac{7}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{5}"," ",0,"a**p*x**5*hyper((5/2, -p), (7/2,), b*x**2*exp_polar(I*pi)/a)/5","C",0
1047,1,26,0,3.813275," ","integrate(x**2*(b*x**2+a)**p,x)","\frac{a^{p} x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, - p \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{3}"," ",0,"a**p*x**3*hyper((3/2, -p), (5/2,), b*x**2*exp_polar(I*pi)/a)/3","C",0
1048,1,22,0,2.324718," ","integrate((b*x**2+a)**p,x)","a^{p} x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, - p \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}"," ",0,"a**p*x*hyper((1/2, -p), (3/2,), b*x**2*exp_polar(I*pi)/a)","C",0
1049,1,26,0,3.745823," ","integrate((b*x**2+a)**p/x**2,x)","- \frac{a^{p} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - p \\ \frac{1}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{x}"," ",0,"-a**p*hyper((-1/2, -p), (1/2,), b*x**2*exp_polar(I*pi)/a)/x","C",0
1050,-1,0,0,0.000000," ","integrate(x**(7/2)*(b*x**2+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1051,-1,0,0,0.000000," ","integrate(x**(5/2)*(b*x**2+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1052,-1,0,0,0.000000," ","integrate(x**(3/2)*(b*x**2+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1053,1,37,0,57.086586," ","integrate(x**(1/2)*(b*x**2+a)**p,x)","\frac{a^{p} x^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, - p \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{7}{4}\right)}"," ",0,"a**p*x**(3/2)*gamma(3/4)*hyper((3/4, -p), (7/4,), b*x**2*exp_polar(I*pi)/a)/(2*gamma(7/4))","C",0
1054,1,37,0,38.996693," ","integrate((b*x**2+a)**p/x**(1/2),x)","\frac{a^{p} \sqrt{x} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, - p \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{5}{4}\right)}"," ",0,"a**p*sqrt(x)*gamma(1/4)*hyper((1/4, -p), (5/4,), b*x**2*exp_polar(I*pi)/a)/(2*gamma(5/4))","C",0
1055,-1,0,0,0.000000," ","integrate((b*x**2+a)**p/x**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1056,-1,0,0,0.000000," ","integrate((b*x**2+a)**p/x**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1057,-1,0,0,0.000000," ","integrate((b*x**2+a)**p/x**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1058,1,51,0,21.283791," ","integrate(x**m*(b*x**2+a)**p,x)","\frac{a^{p} x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} - p, \frac{m}{2} + \frac{1}{2} \\ \frac{m}{2} + \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}"," ",0,"a**p*x*x**m*gamma(m/2 + 1/2)*hyper((-p, m/2 + 1/2), (m/2 + 3/2,), b*x**2*exp_polar(I*pi)/a)/(2*gamma(m/2 + 3/2))","C",0
1059,1,54,0,21.457144," ","integrate((c*x)**m*(b*x**2+a)**p,x)","\frac{a^{p} c^{m} x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} - p, \frac{m}{2} + \frac{1}{2} \\ \frac{m}{2} + \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}"," ",0,"a**p*c**m*x*x**m*gamma(m/2 + 1/2)*hyper((-p, m/2 + 1/2), (m/2 + 3/2,), b*x**2*exp_polar(I*pi)/a)/(2*gamma(m/2 + 3/2))","C",0
1060,-1,0,0,0.000000," ","integrate(x**(-8-2*p)*(b*x**2+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1061,-1,0,0,0.000000," ","integrate(x**(-7-2*p)*(b*x**2+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1062,-2,0,0,0.000000," ","integrate(x**(-6-2*p)*(b*x**2+a)**p,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
1063,-1,0,0,0.000000," ","integrate(x**(-5-2*p)*(b*x**2+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1064,-1,0,0,0.000000," ","integrate(x**(-4-2*p)*(b*x**2+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1065,-1,0,0,0.000000," ","integrate(x**(-3-2*p)*(b*x**2+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1066,-1,0,0,0.000000," ","integrate(x**(-2-2*p)*(b*x**2+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1067,-1,0,0,0.000000," ","integrate(x**(-1-2*p)*(b*x**2+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1068,1,24,0,15.080415," ","integrate((b*x**2+a)**p/(x**(2*p)),x)","b^{p} x {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - p \\ \frac{1}{2} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{2}}} \right)}"," ",0,"b**p*x*hyper((-1/2, -p), (1/2,), a*exp_polar(I*pi)/(b*x**2))","C",0
1069,-1,0,0,0.000000," ","integrate(x**(1-2*p)*(b*x**2+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1070,-1,0,0,0.000000," ","integrate(x**(2-2*p)*(b*x**2+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1071,-1,0,0,0.000000," ","integrate(x**(3-2*p)*(b*x**2+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
