1,0,0,0,0.000000," ","integrate((b*x**6+a*x**3)**(5/3),x)","\int \left(a x^{3} + b x^{6}\right)^{\frac{5}{3}}\, dx"," ",0,"Integral((a*x**3 + b*x**6)**(5/3), x)","F",0
2,0,0,0,0.000000," ","integrate((b*x**6+a*x**3)**(2/3),x)","\int \left(a x^{3} + b x^{6}\right)^{\frac{2}{3}}\, dx"," ",0,"Integral((a*x**3 + b*x**6)**(2/3), x)","F",0
3,0,0,0,0.000000," ","integrate(1/(b*x**6+a*x**3)**(2/3),x)","\int \frac{1}{\left(a x^{3} + b x^{6}\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral((a*x**3 + b*x**6)**(-2/3), x)","F",0
4,0,0,0,0.000000," ","integrate(1/(b*x**6+a*x**3)**(5/3),x)","\int \frac{1}{\left(a x^{3} + b x^{6}\right)^{\frac{5}{3}}}\, dx"," ",0,"Integral((a*x**3 + b*x**6)**(-5/3), x)","F",0
5,1,48,0,0.147399," ","integrate(1/(x**6-x**3),x)","\frac{\log{\left(x - 1 \right)}}{3} - \frac{\log{\left(x^{2} + x + 1 \right)}}{6} - \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{3} + \frac{1}{2 x^{2}}"," ",0,"log(x - 1)/3 - log(x**2 + x + 1)/6 - sqrt(3)*atan(2*sqrt(3)*x/3 + sqrt(3)/3)/3 + 1/(2*x**2)","A",0
6,1,12,0,0.107011," ","integrate(x**5*((b*x**3+a)**2)**(1/2),x)","\frac{a x^{6}}{6} + \frac{b x^{9}}{9}"," ",0,"a*x**6/6 + b*x**9/9","A",0
7,1,12,0,0.109142," ","integrate(x**4*((b*x**3+a)**2)**(1/2),x)","\frac{a x^{5}}{5} + \frac{b x^{8}}{8}"," ",0,"a*x**5/5 + b*x**8/8","A",0
8,1,12,0,0.106488," ","integrate(x**3*((b*x**3+a)**2)**(1/2),x)","\frac{a x^{4}}{4} + \frac{b x^{7}}{7}"," ",0,"a*x**4/4 + b*x**7/7","A",0
9,1,12,0,0.105381," ","integrate(x**2*((b*x**3+a)**2)**(1/2),x)","\frac{a x^{3}}{3} + \frac{b x^{6}}{6}"," ",0,"a*x**3/3 + b*x**6/6","A",0
10,1,12,0,0.104556," ","integrate(x*((b*x**3+a)**2)**(1/2),x)","\frac{a x^{2}}{2} + \frac{b x^{5}}{5}"," ",0,"a*x**2/2 + b*x**5/5","A",0
11,1,8,0,0.102730," ","integrate(((b*x**3+a)**2)**(1/2),x)","a x + \frac{b x^{4}}{4}"," ",0,"a*x + b*x**4/4","A",0
12,1,10,0,0.129258," ","integrate(((b*x**3+a)**2)**(1/2)/x,x)","a \log{\left(x \right)} + \frac{b x^{3}}{3}"," ",0,"a*log(x) + b*x**3/3","A",0
13,1,8,0,0.125324," ","integrate(((b*x**3+a)**2)**(1/2)/x**2,x)","- \frac{a}{x} + \frac{b x^{2}}{2}"," ",0,"-a/x + b*x**2/2","A",0
14,1,8,0,0.133595," ","integrate(((b*x**3+a)**2)**(1/2)/x**3,x)","- \frac{a}{2 x^{2}} + b x"," ",0,"-a/(2*x**2) + b*x","A",0
15,1,10,0,0.161779," ","integrate(((b*x**3+a)**2)**(1/2)/x**4,x)","- \frac{a}{3 x^{3}} + b \log{\left(x \right)}"," ",0,"-a/(3*x**3) + b*log(x)","A",0
16,1,14,0,0.168284," ","integrate(((b*x**3+a)**2)**(1/2)/x**5,x)","\frac{- a - 4 b x^{3}}{4 x^{4}}"," ",0,"(-a - 4*b*x**3)/(4*x**4)","A",0
17,1,15,0,0.178614," ","integrate(((b*x**3+a)**2)**(1/2)/x**6,x)","\frac{- 2 a - 5 b x^{3}}{10 x^{5}}"," ",0,"(-2*a - 5*b*x**3)/(10*x**5)","A",0
18,1,14,0,0.185084," ","integrate(((b*x**3+a)**2)**(1/2)/x**7,x)","\frac{- a - 2 b x^{3}}{6 x^{6}}"," ",0,"(-a - 2*b*x**3)/(6*x**6)","A",0
19,1,15,0,0.193035," ","integrate(((b*x**3+a)**2)**(1/2)/x**8,x)","\frac{- 4 a - 7 b x^{3}}{28 x^{7}}"," ",0,"(-4*a - 7*b*x**3)/(28*x**7)","A",0
20,1,15,0,0.197387," ","integrate(((b*x**3+a)**2)**(1/2)/x**9,x)","\frac{- 5 a - 8 b x^{3}}{40 x^{8}}"," ",0,"(-5*a - 8*b*x**3)/(40*x**8)","A",0
21,1,15,0,0.209070," ","integrate(((b*x**3+a)**2)**(1/2)/x**10,x)","\frac{- 2 a - 3 b x^{3}}{18 x^{9}}"," ",0,"(-2*a - 3*b*x**3)/(18*x**9)","A",0
22,1,15,0,0.217061," ","integrate(((b*x**3+a)**2)**(1/2)/x**11,x)","\frac{- 7 a - 10 b x^{3}}{70 x^{10}}"," ",0,"(-7*a - 10*b*x**3)/(70*x**10)","A",0
23,0,0,0,0.000000," ","integrate(x**9*(b**2*x**6+2*a*b*x**3+a**2)**(3/2),x)","\int x^{9} \left(\left(a + b x^{3}\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**9*((a + b*x**3)**2)**(3/2), x)","F",0
24,0,0,0,0.000000," ","integrate(x**8*(b**2*x**6+2*a*b*x**3+a**2)**(3/2),x)","\int x^{8} \left(\left(a + b x^{3}\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**8*((a + b*x**3)**2)**(3/2), x)","F",0
25,0,0,0,0.000000," ","integrate(x**7*(b**2*x**6+2*a*b*x**3+a**2)**(3/2),x)","\int x^{7} \left(\left(a + b x^{3}\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**7*((a + b*x**3)**2)**(3/2), x)","F",0
26,0,0,0,0.000000," ","integrate(x**6*(b**2*x**6+2*a*b*x**3+a**2)**(3/2),x)","\int x^{6} \left(\left(a + b x^{3}\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**6*((a + b*x**3)**2)**(3/2), x)","F",0
27,0,0,0,0.000000," ","integrate(x**5*(b**2*x**6+2*a*b*x**3+a**2)**(3/2),x)","\int x^{5} \left(\left(a + b x^{3}\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**5*((a + b*x**3)**2)**(3/2), x)","F",0
28,0,0,0,0.000000," ","integrate(x**4*(b**2*x**6+2*a*b*x**3+a**2)**(3/2),x)","\int x^{4} \left(\left(a + b x^{3}\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**4*((a + b*x**3)**2)**(3/2), x)","F",0
29,0,0,0,0.000000," ","integrate(x**3*(b**2*x**6+2*a*b*x**3+a**2)**(3/2),x)","\int x^{3} \left(\left(a + b x^{3}\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**3*((a + b*x**3)**2)**(3/2), x)","F",0
30,0,0,0,0.000000," ","integrate(x**2*(b**2*x**6+2*a*b*x**3+a**2)**(3/2),x)","\int x^{2} \left(\left(a + b x^{3}\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**2*((a + b*x**3)**2)**(3/2), x)","F",0
31,0,0,0,0.000000," ","integrate(x*(b**2*x**6+2*a*b*x**3+a**2)**(3/2),x)","\int x \left(\left(a + b x^{3}\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x*((a + b*x**3)**2)**(3/2), x)","F",0
32,0,0,0,0.000000," ","integrate((b**2*x**6+2*a*b*x**3+a**2)**(3/2),x)","\int \left(a^{2} + 2 a b x^{3} + b^{2} x^{6}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a**2 + 2*a*b*x**3 + b**2*x**6)**(3/2), x)","F",0
33,0,0,0,0.000000," ","integrate((b**2*x**6+2*a*b*x**3+a**2)**(3/2)/x,x)","\int \frac{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{3}{2}}}{x}\, dx"," ",0,"Integral(((a + b*x**3)**2)**(3/2)/x, x)","F",0
34,0,0,0,0.000000," ","integrate((b**2*x**6+2*a*b*x**3+a**2)**(3/2)/x**2,x)","\int \frac{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{3}{2}}}{x^{2}}\, dx"," ",0,"Integral(((a + b*x**3)**2)**(3/2)/x**2, x)","F",0
35,0,0,0,0.000000," ","integrate((b**2*x**6+2*a*b*x**3+a**2)**(3/2)/x**3,x)","\int \frac{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{3}{2}}}{x^{3}}\, dx"," ",0,"Integral(((a + b*x**3)**2)**(3/2)/x**3, x)","F",0
36,0,0,0,0.000000," ","integrate((b**2*x**6+2*a*b*x**3+a**2)**(3/2)/x**4,x)","\int \frac{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{3}{2}}}{x^{4}}\, dx"," ",0,"Integral(((a + b*x**3)**2)**(3/2)/x**4, x)","F",0
37,0,0,0,0.000000," ","integrate((b**2*x**6+2*a*b*x**3+a**2)**(3/2)/x**5,x)","\int \frac{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{3}{2}}}{x^{5}}\, dx"," ",0,"Integral(((a + b*x**3)**2)**(3/2)/x**5, x)","F",0
38,0,0,0,0.000000," ","integrate((b**2*x**6+2*a*b*x**3+a**2)**(3/2)/x**6,x)","\int \frac{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{3}{2}}}{x^{6}}\, dx"," ",0,"Integral(((a + b*x**3)**2)**(3/2)/x**6, x)","F",0
39,0,0,0,0.000000," ","integrate((b**2*x**6+2*a*b*x**3+a**2)**(3/2)/x**7,x)","\int \frac{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{3}{2}}}{x^{7}}\, dx"," ",0,"Integral(((a + b*x**3)**2)**(3/2)/x**7, x)","F",0
40,0,0,0,0.000000," ","integrate((b**2*x**6+2*a*b*x**3+a**2)**(3/2)/x**8,x)","\int \frac{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{3}{2}}}{x^{8}}\, dx"," ",0,"Integral(((a + b*x**3)**2)**(3/2)/x**8, x)","F",0
41,0,0,0,0.000000," ","integrate((b**2*x**6+2*a*b*x**3+a**2)**(3/2)/x**9,x)","\int \frac{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{3}{2}}}{x^{9}}\, dx"," ",0,"Integral(((a + b*x**3)**2)**(3/2)/x**9, x)","F",0
42,0,0,0,0.000000," ","integrate((b**2*x**6+2*a*b*x**3+a**2)**(3/2)/x**10,x)","\int \frac{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{3}{2}}}{x^{10}}\, dx"," ",0,"Integral(((a + b*x**3)**2)**(3/2)/x**10, x)","F",0
43,0,0,0,0.000000," ","integrate((b**2*x**6+2*a*b*x**3+a**2)**(3/2)/x**11,x)","\int \frac{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{3}{2}}}{x^{11}}\, dx"," ",0,"Integral(((a + b*x**3)**2)**(3/2)/x**11, x)","F",0
44,0,0,0,0.000000," ","integrate((b**2*x**6+2*a*b*x**3+a**2)**(3/2)/x**12,x)","\int \frac{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{3}{2}}}{x^{12}}\, dx"," ",0,"Integral(((a + b*x**3)**2)**(3/2)/x**12, x)","F",0
45,0,0,0,0.000000," ","integrate((b**2*x**6+2*a*b*x**3+a**2)**(3/2)/x**13,x)","\int \frac{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{3}{2}}}{x^{13}}\, dx"," ",0,"Integral(((a + b*x**3)**2)**(3/2)/x**13, x)","F",0
46,0,0,0,0.000000," ","integrate((b**2*x**6+2*a*b*x**3+a**2)**(3/2)/x**14,x)","\int \frac{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{3}{2}}}{x^{14}}\, dx"," ",0,"Integral(((a + b*x**3)**2)**(3/2)/x**14, x)","F",0
47,0,0,0,0.000000," ","integrate((b**2*x**6+2*a*b*x**3+a**2)**(3/2)/x**15,x)","\int \frac{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{3}{2}}}{x^{15}}\, dx"," ",0,"Integral(((a + b*x**3)**2)**(3/2)/x**15, x)","F",0
48,0,0,0,0.000000," ","integrate((b**2*x**6+2*a*b*x**3+a**2)**(3/2)/x**16,x)","\int \frac{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{3}{2}}}{x^{16}}\, dx"," ",0,"Integral(((a + b*x**3)**2)**(3/2)/x**16, x)","F",0
49,0,0,0,0.000000," ","integrate((b**2*x**6+2*a*b*x**3+a**2)**(3/2)/x**17,x)","\int \frac{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{3}{2}}}{x^{17}}\, dx"," ",0,"Integral(((a + b*x**3)**2)**(3/2)/x**17, x)","F",0
50,0,0,0,0.000000," ","integrate(x**13*(b**2*x**6+2*a*b*x**3+a**2)**(5/2),x)","\int x^{13} \left(\left(a + b x^{3}\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(x**13*((a + b*x**3)**2)**(5/2), x)","F",0
51,0,0,0,0.000000," ","integrate(x**12*(b**2*x**6+2*a*b*x**3+a**2)**(5/2),x)","\int x^{12} \left(\left(a + b x^{3}\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(x**12*((a + b*x**3)**2)**(5/2), x)","F",0
52,0,0,0,0.000000," ","integrate(x**11*(b**2*x**6+2*a*b*x**3+a**2)**(5/2),x)","\int x^{11} \left(\left(a + b x^{3}\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(x**11*((a + b*x**3)**2)**(5/2), x)","F",0
53,0,0,0,0.000000," ","integrate(x**10*(b**2*x**6+2*a*b*x**3+a**2)**(5/2),x)","\int x^{10} \left(\left(a + b x^{3}\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(x**10*((a + b*x**3)**2)**(5/2), x)","F",0
54,0,0,0,0.000000," ","integrate(x**9*(b**2*x**6+2*a*b*x**3+a**2)**(5/2),x)","\int x^{9} \left(\left(a + b x^{3}\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(x**9*((a + b*x**3)**2)**(5/2), x)","F",0
55,0,0,0,0.000000," ","integrate(x**8*(b**2*x**6+2*a*b*x**3+a**2)**(5/2),x)","\int x^{8} \left(\left(a + b x^{3}\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(x**8*((a + b*x**3)**2)**(5/2), x)","F",0
56,0,0,0,0.000000," ","integrate(x**7*(b**2*x**6+2*a*b*x**3+a**2)**(5/2),x)","\int x^{7} \left(\left(a + b x^{3}\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(x**7*((a + b*x**3)**2)**(5/2), x)","F",0
57,0,0,0,0.000000," ","integrate(x**6*(b**2*x**6+2*a*b*x**3+a**2)**(5/2),x)","\int x^{6} \left(\left(a + b x^{3}\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(x**6*((a + b*x**3)**2)**(5/2), x)","F",0
58,0,0,0,0.000000," ","integrate(x**5*(b**2*x**6+2*a*b*x**3+a**2)**(5/2),x)","\int x^{5} \left(\left(a + b x^{3}\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(x**5*((a + b*x**3)**2)**(5/2), x)","F",0
59,0,0,0,0.000000," ","integrate(x**4*(b**2*x**6+2*a*b*x**3+a**2)**(5/2),x)","\int x^{4} \left(\left(a + b x^{3}\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(x**4*((a + b*x**3)**2)**(5/2), x)","F",0
60,0,0,0,0.000000," ","integrate(x**3*(b**2*x**6+2*a*b*x**3+a**2)**(5/2),x)","\int x^{3} \left(\left(a + b x^{3}\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(x**3*((a + b*x**3)**2)**(5/2), x)","F",0
61,0,0,0,0.000000," ","integrate(x**2*(b**2*x**6+2*a*b*x**3+a**2)**(5/2),x)","\int x^{2} \left(\left(a + b x^{3}\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(x**2*((a + b*x**3)**2)**(5/2), x)","F",0
62,0,0,0,0.000000," ","integrate(x*(b**2*x**6+2*a*b*x**3+a**2)**(5/2),x)","\int x \left(\left(a + b x^{3}\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(x*((a + b*x**3)**2)**(5/2), x)","F",0
63,0,0,0,0.000000," ","integrate((b**2*x**6+2*a*b*x**3+a**2)**(5/2),x)","\int \left(a^{2} + 2 a b x^{3} + b^{2} x^{6}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((a**2 + 2*a*b*x**3 + b**2*x**6)**(5/2), x)","F",0
64,0,0,0,0.000000," ","integrate((b**2*x**6+2*a*b*x**3+a**2)**(5/2)/x,x)","\int \frac{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{5}{2}}}{x}\, dx"," ",0,"Integral(((a + b*x**3)**2)**(5/2)/x, x)","F",0
65,0,0,0,0.000000," ","integrate((b**2*x**6+2*a*b*x**3+a**2)**(5/2)/x**2,x)","\int \frac{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{5}{2}}}{x^{2}}\, dx"," ",0,"Integral(((a + b*x**3)**2)**(5/2)/x**2, x)","F",0
66,0,0,0,0.000000," ","integrate((b**2*x**6+2*a*b*x**3+a**2)**(5/2)/x**3,x)","\int \frac{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{5}{2}}}{x^{3}}\, dx"," ",0,"Integral(((a + b*x**3)**2)**(5/2)/x**3, x)","F",0
67,0,0,0,0.000000," ","integrate((b**2*x**6+2*a*b*x**3+a**2)**(5/2)/x**4,x)","\int \frac{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{5}{2}}}{x^{4}}\, dx"," ",0,"Integral(((a + b*x**3)**2)**(5/2)/x**4, x)","F",0
68,0,0,0,0.000000," ","integrate((b**2*x**6+2*a*b*x**3+a**2)**(5/2)/x**5,x)","\int \frac{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{5}{2}}}{x^{5}}\, dx"," ",0,"Integral(((a + b*x**3)**2)**(5/2)/x**5, x)","F",0
69,0,0,0,0.000000," ","integrate((b**2*x**6+2*a*b*x**3+a**2)**(5/2)/x**6,x)","\int \frac{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{5}{2}}}{x^{6}}\, dx"," ",0,"Integral(((a + b*x**3)**2)**(5/2)/x**6, x)","F",0
70,0,0,0,0.000000," ","integrate((b**2*x**6+2*a*b*x**3+a**2)**(5/2)/x**7,x)","\int \frac{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{5}{2}}}{x^{7}}\, dx"," ",0,"Integral(((a + b*x**3)**2)**(5/2)/x**7, x)","F",0
71,0,0,0,0.000000," ","integrate((b**2*x**6+2*a*b*x**3+a**2)**(5/2)/x**8,x)","\int \frac{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{5}{2}}}{x^{8}}\, dx"," ",0,"Integral(((a + b*x**3)**2)**(5/2)/x**8, x)","F",0
72,0,0,0,0.000000," ","integrate((b**2*x**6+2*a*b*x**3+a**2)**(5/2)/x**9,x)","\int \frac{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{5}{2}}}{x^{9}}\, dx"," ",0,"Integral(((a + b*x**3)**2)**(5/2)/x**9, x)","F",0
73,0,0,0,0.000000," ","integrate((b**2*x**6+2*a*b*x**3+a**2)**(5/2)/x**10,x)","\int \frac{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{5}{2}}}{x^{10}}\, dx"," ",0,"Integral(((a + b*x**3)**2)**(5/2)/x**10, x)","F",0
74,0,0,0,0.000000," ","integrate((b**2*x**6+2*a*b*x**3+a**2)**(5/2)/x**11,x)","\int \frac{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{5}{2}}}{x^{11}}\, dx"," ",0,"Integral(((a + b*x**3)**2)**(5/2)/x**11, x)","F",0
75,0,0,0,0.000000," ","integrate((b**2*x**6+2*a*b*x**3+a**2)**(5/2)/x**12,x)","\int \frac{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{5}{2}}}{x^{12}}\, dx"," ",0,"Integral(((a + b*x**3)**2)**(5/2)/x**12, x)","F",0
76,0,0,0,0.000000," ","integrate((b**2*x**6+2*a*b*x**3+a**2)**(5/2)/x**13,x)","\int \frac{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{5}{2}}}{x^{13}}\, dx"," ",0,"Integral(((a + b*x**3)**2)**(5/2)/x**13, x)","F",0
77,0,0,0,0.000000," ","integrate((b**2*x**6+2*a*b*x**3+a**2)**(5/2)/x**14,x)","\int \frac{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{5}{2}}}{x^{14}}\, dx"," ",0,"Integral(((a + b*x**3)**2)**(5/2)/x**14, x)","F",0
78,0,0,0,0.000000," ","integrate((b**2*x**6+2*a*b*x**3+a**2)**(5/2)/x**15,x)","\int \frac{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{5}{2}}}{x^{15}}\, dx"," ",0,"Integral(((a + b*x**3)**2)**(5/2)/x**15, x)","F",0
79,0,0,0,0.000000," ","integrate((b**2*x**6+2*a*b*x**3+a**2)**(5/2)/x**16,x)","\int \frac{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{5}{2}}}{x^{16}}\, dx"," ",0,"Integral(((a + b*x**3)**2)**(5/2)/x**16, x)","F",0
80,0,0,0,0.000000," ","integrate((b**2*x**6+2*a*b*x**3+a**2)**(5/2)/x**17,x)","\int \frac{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{5}{2}}}{x^{17}}\, dx"," ",0,"Integral(((a + b*x**3)**2)**(5/2)/x**17, x)","F",0
81,0,0,0,0.000000," ","integrate((b**2*x**6+2*a*b*x**3+a**2)**(5/2)/x**18,x)","\int \frac{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{5}{2}}}{x^{18}}\, dx"," ",0,"Integral(((a + b*x**3)**2)**(5/2)/x**18, x)","F",0
82,0,0,0,0.000000," ","integrate((b**2*x**6+2*a*b*x**3+a**2)**(5/2)/x**19,x)","\int \frac{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{5}{2}}}{x^{19}}\, dx"," ",0,"Integral(((a + b*x**3)**2)**(5/2)/x**19, x)","F",0
83,0,0,0,0.000000," ","integrate((b**2*x**6+2*a*b*x**3+a**2)**(5/2)/x**20,x)","\int \frac{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{5}{2}}}{x^{20}}\, dx"," ",0,"Integral(((a + b*x**3)**2)**(5/2)/x**20, x)","F",0
84,0,0,0,0.000000," ","integrate((b**2*x**6+2*a*b*x**3+a**2)**(5/2)/x**21,x)","\int \frac{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{5}{2}}}{x^{21}}\, dx"," ",0,"Integral(((a + b*x**3)**2)**(5/2)/x**21, x)","F",0
85,0,0,0,0.000000," ","integrate((b**2*x**6+2*a*b*x**3+a**2)**(5/2)/x**22,x)","\int \frac{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{5}{2}}}{x^{22}}\, dx"," ",0,"Integral(((a + b*x**3)**2)**(5/2)/x**22, x)","F",0
86,0,0,0,0.000000," ","integrate((b**2*x**6+2*a*b*x**3+a**2)**(5/2)/x**23,x)","\int \frac{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{5}{2}}}{x^{23}}\, dx"," ",0,"Integral(((a + b*x**3)**2)**(5/2)/x**23, x)","F",0
87,0,0,0,0.000000," ","integrate((b**2*x**6+2*a*b*x**3+a**2)**(5/2)/x**24,x)","\int \frac{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{5}{2}}}{x^{24}}\, dx"," ",0,"Integral(((a + b*x**3)**2)**(5/2)/x**24, x)","F",0
88,0,0,0,0.000000," ","integrate((b**2*x**6+2*a*b*x**3+a**2)**(5/2)/x**25,x)","\int \frac{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{5}{2}}}{x^{25}}\, dx"," ",0,"Integral(((a + b*x**3)**2)**(5/2)/x**25, x)","F",0
89,1,32,0,0.211742," ","integrate(x**4/((b*x**3+a)**2)**(1/2),x)","\operatorname{RootSum} {\left(27 t^{3} b^{5} - a^{2}, \left( t \mapsto t \log{\left(\frac{9 t^{2} b^{3}}{a} + x \right)} \right)\right)} + \frac{x^{2}}{2 b}"," ",0,"RootSum(27*_t**3*b**5 - a**2, Lambda(_t, _t*log(9*_t**2*b**3/a + x))) + x**2/(2*b)","A",0
90,1,22,0,0.202733," ","integrate(x**3/((b*x**3+a)**2)**(1/2),x)","\operatorname{RootSum} {\left(27 t^{3} b^{4} + a, \left( t \mapsto t \log{\left(- 3 t b + x \right)} \right)\right)} + \frac{x}{b}"," ",0,"RootSum(27*_t**3*b**4 + a, Lambda(_t, _t*log(-3*_t*b + x))) + x/b","A",0
91,1,10,0,0.173062," ","integrate(x**2/((b*x**3+a)**2)**(1/2),x)","\frac{\log{\left(a + b x^{3} \right)}}{3 b}"," ",0,"log(a + b*x**3)/(3*b)","A",0
92,1,24,0,0.178700," ","integrate(x/((b*x**3+a)**2)**(1/2),x)","\operatorname{RootSum} {\left(27 t^{3} a b^{2} + 1, \left( t \mapsto t \log{\left(9 t^{2} a b + x \right)} \right)\right)}"," ",0,"RootSum(27*_t**3*a*b**2 + 1, Lambda(_t, _t*log(9*_t**2*a*b + x)))","A",0
93,1,20,0,0.190319," ","integrate(1/((b*x**3+a)**2)**(1/2),x)","\operatorname{RootSum} {\left(27 t^{3} a^{2} b - 1, \left( t \mapsto t \log{\left(3 t a + x \right)} \right)\right)}"," ",0,"RootSum(27*_t**3*a**2*b - 1, Lambda(_t, _t*log(3*_t*a + x)))","A",0
94,1,15,0,0.275510," ","integrate(1/x/((b*x**3+a)**2)**(1/2),x)","\frac{\log{\left(x \right)}}{a} - \frac{\log{\left(\frac{a}{b} + x^{3} \right)}}{3 a}"," ",0,"log(x)/a - log(a/b + x**3)/(3*a)","A",0
95,1,29,0,0.234313," ","integrate(1/x**2/((b*x**3+a)**2)**(1/2),x)","\operatorname{RootSum} {\left(27 t^{3} a^{4} - b, \left( t \mapsto t \log{\left(\frac{9 t^{2} a^{3}}{b} + x \right)} \right)\right)} - \frac{1}{a x}"," ",0,"RootSum(27*_t**3*a**4 - b, Lambda(_t, _t*log(9*_t**2*a**3/b + x))) - 1/(a*x)","A",0
96,1,32,0,0.261034," ","integrate(1/x**3/((b*x**3+a)**2)**(1/2),x)","\operatorname{RootSum} {\left(27 t^{3} a^{5} + b^{2}, \left( t \mapsto t \log{\left(- \frac{3 t a^{2}}{b} + x \right)} \right)\right)} - \frac{1}{2 a x^{2}}"," ",0,"RootSum(27*_t**3*a**5 + b**2, Lambda(_t, _t*log(-3*_t*a**2/b + x))) - 1/(2*a*x**2)","A",0
97,1,31,0,0.362184," ","integrate(1/x**4/((b*x**3+a)**2)**(1/2),x)","- \frac{1}{3 a x^{3}} - \frac{b \log{\left(x \right)}}{a^{2}} + \frac{b \log{\left(\frac{a}{b} + x^{3} \right)}}{3 a^{2}}"," ",0,"-1/(3*a*x**3) - b*log(x)/a**2 + b*log(a/b + x**3)/(3*a**2)","A",0
98,0,0,0,0.000000," ","integrate(x**4/(b**2*x**6+2*a*b*x**3+a**2)**(3/2),x)","\int \frac{x^{4}}{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**4/((a + b*x**3)**2)**(3/2), x)","F",0
99,0,0,0,0.000000," ","integrate(x**3/(b**2*x**6+2*a*b*x**3+a**2)**(3/2),x)","\int \frac{x^{3}}{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**3/((a + b*x**3)**2)**(3/2), x)","F",0
100,0,0,0,0.000000," ","integrate(x**2/(b**2*x**6+2*a*b*x**3+a**2)**(3/2),x)","\int \frac{x^{2}}{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**2/((a + b*x**3)**2)**(3/2), x)","F",0
101,0,0,0,0.000000," ","integrate(x/(b**2*x**6+2*a*b*x**3+a**2)**(3/2),x)","\int \frac{x}{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x/((a + b*x**3)**2)**(3/2), x)","F",0
102,0,0,0,0.000000," ","integrate(1/(b**2*x**6+2*a*b*x**3+a**2)**(3/2),x)","\int \frac{1}{\left(a^{2} + 2 a b x^{3} + b^{2} x^{6}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a**2 + 2*a*b*x**3 + b**2*x**6)**(-3/2), x)","F",0
103,0,0,0,0.000000," ","integrate(1/x/(b**2*x**6+2*a*b*x**3+a**2)**(3/2),x)","\int \frac{1}{x \left(\left(a + b x^{3}\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x*((a + b*x**3)**2)**(3/2)), x)","F",0
104,0,0,0,0.000000," ","integrate(1/x**2/(b**2*x**6+2*a*b*x**3+a**2)**(3/2),x)","\int \frac{1}{x^{2} \left(\left(a + b x^{3}\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**2*((a + b*x**3)**2)**(3/2)), x)","F",0
105,0,0,0,0.000000," ","integrate(1/x**3/(b**2*x**6+2*a*b*x**3+a**2)**(3/2),x)","\int \frac{1}{x^{3} \left(\left(a + b x^{3}\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**3*((a + b*x**3)**2)**(3/2)), x)","F",0
106,0,0,0,0.000000," ","integrate(1/x**4/(b**2*x**6+2*a*b*x**3+a**2)**(3/2),x)","\int \frac{1}{x^{4} \left(\left(a + b x^{3}\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**4*((a + b*x**3)**2)**(3/2)), x)","F",0
107,0,0,0,0.000000," ","integrate(x**6/(b**2*x**6+2*a*b*x**3+a**2)**(5/2),x)","\int \frac{x^{6}}{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**6/((a + b*x**3)**2)**(5/2), x)","F",0
108,0,0,0,0.000000," ","integrate(x**5/(b**2*x**6+2*a*b*x**3+a**2)**(5/2),x)","\int \frac{x^{5}}{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**5/((a + b*x**3)**2)**(5/2), x)","F",0
109,0,0,0,0.000000," ","integrate(x**4/(b**2*x**6+2*a*b*x**3+a**2)**(5/2),x)","\int \frac{x^{4}}{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**4/((a + b*x**3)**2)**(5/2), x)","F",0
110,0,0,0,0.000000," ","integrate(x**3/(b**2*x**6+2*a*b*x**3+a**2)**(5/2),x)","\int \frac{x^{3}}{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**3/((a + b*x**3)**2)**(5/2), x)","F",0
111,0,0,0,0.000000," ","integrate(x**2/(b**2*x**6+2*a*b*x**3+a**2)**(5/2),x)","\int \frac{x^{2}}{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**2/((a + b*x**3)**2)**(5/2), x)","F",0
112,0,0,0,0.000000," ","integrate(x/(b**2*x**6+2*a*b*x**3+a**2)**(5/2),x)","\int \frac{x}{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x/((a + b*x**3)**2)**(5/2), x)","F",0
113,0,0,0,0.000000," ","integrate(1/(b**2*x**6+2*a*b*x**3+a**2)**(5/2),x)","\int \frac{1}{\left(a^{2} + 2 a b x^{3} + b^{2} x^{6}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a**2 + 2*a*b*x**3 + b**2*x**6)**(-5/2), x)","F",0
114,0,0,0,0.000000," ","integrate(1/x/(b**2*x**6+2*a*b*x**3+a**2)**(5/2),x)","\int \frac{1}{x \left(\left(a + b x^{3}\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/(x*((a + b*x**3)**2)**(5/2)), x)","F",0
115,0,0,0,0.000000," ","integrate(1/x**2/(b**2*x**6+2*a*b*x**3+a**2)**(5/2),x)","\int \frac{1}{x^{2} \left(\left(a + b x^{3}\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/(x**2*((a + b*x**3)**2)**(5/2)), x)","F",0
116,0,0,0,0.000000," ","integrate(1/x**3/(b**2*x**6+2*a*b*x**3+a**2)**(5/2),x)","\int \frac{1}{x^{3} \left(\left(a + b x^{3}\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/(x**3*((a + b*x**3)**2)**(5/2)), x)","F",0
117,0,0,0,0.000000," ","integrate(1/x**4/(b**2*x**6+2*a*b*x**3+a**2)**(5/2),x)","\int \frac{1}{x^{4} \left(\left(a + b x^{3}\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/(x**4*((a + b*x**3)**2)**(5/2)), x)","F",0
118,0,0,0,0.000000," ","integrate((d*x)**m*(b**2*x**6+2*a*b*x**3+a**2)**(5/2),x)","\int \left(d x\right)^{m} \left(\left(a + b x^{3}\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((d*x)**m*((a + b*x**3)**2)**(5/2), x)","F",0
119,0,0,0,0.000000," ","integrate((d*x)**m*(b**2*x**6+2*a*b*x**3+a**2)**(3/2),x)","\int \left(d x\right)^{m} \left(\left(a + b x^{3}\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((d*x)**m*((a + b*x**3)**2)**(3/2), x)","F",0
120,0,0,0,0.000000," ","integrate((d*x)**m*(b**2*x**6+2*a*b*x**3+a**2)**(1/2),x)","\int \left(d x\right)^{m} \sqrt{\left(a + b x^{3}\right)^{2}}\, dx"," ",0,"Integral((d*x)**m*sqrt((a + b*x**3)**2), x)","F",0
121,0,0,0,0.000000," ","integrate((d*x)**m/(b**2*x**6+2*a*b*x**3+a**2)**(1/2),x)","\int \frac{\left(d x\right)^{m}}{\sqrt{\left(a + b x^{3}\right)^{2}}}\, dx"," ",0,"Integral((d*x)**m/sqrt((a + b*x**3)**2), x)","F",0
122,0,0,0,0.000000," ","integrate((d*x)**m/(b**2*x**6+2*a*b*x**3+a**2)**(3/2),x)","\int \frac{\left(d x\right)^{m}}{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d*x)**m/((a + b*x**3)**2)**(3/2), x)","F",0
123,0,0,0,0.000000," ","integrate((d*x)**m/(b**2*x**6+2*a*b*x**3+a**2)**(5/2),x)","\int \frac{\left(d x\right)^{m}}{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((d*x)**m/((a + b*x**3)**2)**(5/2), x)","F",0
124,-1,0,0,0.000000," ","integrate((d*x)**m*(b**2*x**6+2*a*b*x**3+a**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
125,0,0,0,0.000000," ","integrate(x**11*(b**2*x**6+2*a*b*x**3+a**2)**p,x)","\begin{cases} \frac{x^{12} \left(a^{2}\right)^{p}}{12} & \text{for}\: b = 0 \\\frac{6 a^{3} \log{\left(- \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{\frac{1}{b}} + x \right)}}{18 a^{3} b^{4} + 54 a^{2} b^{5} x^{3} + 54 a b^{6} x^{6} + 18 b^{7} x^{9}} + \frac{6 a^{3} \log{\left(4 \left(-1\right)^{\frac{2}{3}} a^{\frac{2}{3}} \left(\frac{1}{b}\right)^{\frac{2}{3}} + 4 \sqrt[3]{-1} \sqrt[3]{a} x \sqrt[3]{\frac{1}{b}} + 4 x^{2} \right)}}{18 a^{3} b^{4} + 54 a^{2} b^{5} x^{3} + 54 a b^{6} x^{6} + 18 b^{7} x^{9}} - \frac{12 a^{3} \log{\left(2 \right)}}{18 a^{3} b^{4} + 54 a^{2} b^{5} x^{3} + 54 a b^{6} x^{6} + 18 b^{7} x^{9}} + \frac{11 a^{3}}{18 a^{3} b^{4} + 54 a^{2} b^{5} x^{3} + 54 a b^{6} x^{6} + 18 b^{7} x^{9}} + \frac{18 a^{2} b x^{3} \log{\left(- \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{\frac{1}{b}} + x \right)}}{18 a^{3} b^{4} + 54 a^{2} b^{5} x^{3} + 54 a b^{6} x^{6} + 18 b^{7} x^{9}} + \frac{18 a^{2} b x^{3} \log{\left(4 \left(-1\right)^{\frac{2}{3}} a^{\frac{2}{3}} \left(\frac{1}{b}\right)^{\frac{2}{3}} + 4 \sqrt[3]{-1} \sqrt[3]{a} x \sqrt[3]{\frac{1}{b}} + 4 x^{2} \right)}}{18 a^{3} b^{4} + 54 a^{2} b^{5} x^{3} + 54 a b^{6} x^{6} + 18 b^{7} x^{9}} - \frac{36 a^{2} b x^{3} \log{\left(2 \right)}}{18 a^{3} b^{4} + 54 a^{2} b^{5} x^{3} + 54 a b^{6} x^{6} + 18 b^{7} x^{9}} + \frac{27 a^{2} b x^{3}}{18 a^{3} b^{4} + 54 a^{2} b^{5} x^{3} + 54 a b^{6} x^{6} + 18 b^{7} x^{9}} + \frac{18 a b^{2} x^{6} \log{\left(- \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{\frac{1}{b}} + x \right)}}{18 a^{3} b^{4} + 54 a^{2} b^{5} x^{3} + 54 a b^{6} x^{6} + 18 b^{7} x^{9}} + \frac{18 a b^{2} x^{6} \log{\left(4 \left(-1\right)^{\frac{2}{3}} a^{\frac{2}{3}} \left(\frac{1}{b}\right)^{\frac{2}{3}} + 4 \sqrt[3]{-1} \sqrt[3]{a} x \sqrt[3]{\frac{1}{b}} + 4 x^{2} \right)}}{18 a^{3} b^{4} + 54 a^{2} b^{5} x^{3} + 54 a b^{6} x^{6} + 18 b^{7} x^{9}} - \frac{36 a b^{2} x^{6} \log{\left(2 \right)}}{18 a^{3} b^{4} + 54 a^{2} b^{5} x^{3} + 54 a b^{6} x^{6} + 18 b^{7} x^{9}} + \frac{18 a b^{2} x^{6}}{18 a^{3} b^{4} + 54 a^{2} b^{5} x^{3} + 54 a b^{6} x^{6} + 18 b^{7} x^{9}} + \frac{6 b^{3} x^{9} \log{\left(- \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{\frac{1}{b}} + x \right)}}{18 a^{3} b^{4} + 54 a^{2} b^{5} x^{3} + 54 a b^{6} x^{6} + 18 b^{7} x^{9}} + \frac{6 b^{3} x^{9} \log{\left(4 \left(-1\right)^{\frac{2}{3}} a^{\frac{2}{3}} \left(\frac{1}{b}\right)^{\frac{2}{3}} + 4 \sqrt[3]{-1} \sqrt[3]{a} x \sqrt[3]{\frac{1}{b}} + 4 x^{2} \right)}}{18 a^{3} b^{4} + 54 a^{2} b^{5} x^{3} + 54 a b^{6} x^{6} + 18 b^{7} x^{9}} - \frac{12 b^{3} x^{9} \log{\left(2 \right)}}{18 a^{3} b^{4} + 54 a^{2} b^{5} x^{3} + 54 a b^{6} x^{6} + 18 b^{7} x^{9}} & \text{for}\: p = -2 \\\int \frac{x^{11}}{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{3}{2}}}\, dx & \text{for}\: p = - \frac{3}{2} \\\frac{6 a^{3} \log{\left(- \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{\frac{1}{b}} + x \right)}}{6 a b^{4} + 6 b^{5} x^{3}} + \frac{6 a^{3} \log{\left(4 \left(-1\right)^{\frac{2}{3}} a^{\frac{2}{3}} \left(\frac{1}{b}\right)^{\frac{2}{3}} + 4 \sqrt[3]{-1} \sqrt[3]{a} x \sqrt[3]{\frac{1}{b}} + 4 x^{2} \right)}}{6 a b^{4} + 6 b^{5} x^{3}} - \frac{12 a^{3} \log{\left(2 \right)}}{6 a b^{4} + 6 b^{5} x^{3}} + \frac{6 a^{3}}{6 a b^{4} + 6 b^{5} x^{3}} + \frac{6 a^{2} b x^{3} \log{\left(- \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{\frac{1}{b}} + x \right)}}{6 a b^{4} + 6 b^{5} x^{3}} + \frac{6 a^{2} b x^{3} \log{\left(4 \left(-1\right)^{\frac{2}{3}} a^{\frac{2}{3}} \left(\frac{1}{b}\right)^{\frac{2}{3}} + 4 \sqrt[3]{-1} \sqrt[3]{a} x \sqrt[3]{\frac{1}{b}} + 4 x^{2} \right)}}{6 a b^{4} + 6 b^{5} x^{3}} - \frac{12 a^{2} b x^{3} \log{\left(2 \right)}}{6 a b^{4} + 6 b^{5} x^{3}} - \frac{3 a b^{2} x^{6}}{6 a b^{4} + 6 b^{5} x^{3}} + \frac{b^{3} x^{9}}{6 a b^{4} + 6 b^{5} x^{3}} & \text{for}\: p = -1 \\\int \frac{x^{11}}{\sqrt{\left(a + b x^{3}\right)^{2}}}\, dx & \text{for}\: p = - \frac{1}{2} \\- \frac{3 a^{4} \left(a^{2} + 2 a b x^{3} + b^{2} x^{6}\right)^{p}}{24 b^{4} p^{4} + 120 b^{4} p^{3} + 210 b^{4} p^{2} + 150 b^{4} p + 36 b^{4}} + \frac{6 a^{3} b p x^{3} \left(a^{2} + 2 a b x^{3} + b^{2} x^{6}\right)^{p}}{24 b^{4} p^{4} + 120 b^{4} p^{3} + 210 b^{4} p^{2} + 150 b^{4} p + 36 b^{4}} - \frac{6 a^{2} b^{2} p^{2} x^{6} \left(a^{2} + 2 a b x^{3} + b^{2} x^{6}\right)^{p}}{24 b^{4} p^{4} + 120 b^{4} p^{3} + 210 b^{4} p^{2} + 150 b^{4} p + 36 b^{4}} - \frac{3 a^{2} b^{2} p x^{6} \left(a^{2} + 2 a b x^{3} + b^{2} x^{6}\right)^{p}}{24 b^{4} p^{4} + 120 b^{4} p^{3} + 210 b^{4} p^{2} + 150 b^{4} p + 36 b^{4}} + \frac{4 a b^{3} p^{3} x^{9} \left(a^{2} + 2 a b x^{3} + b^{2} x^{6}\right)^{p}}{24 b^{4} p^{4} + 120 b^{4} p^{3} + 210 b^{4} p^{2} + 150 b^{4} p + 36 b^{4}} + \frac{6 a b^{3} p^{2} x^{9} \left(a^{2} + 2 a b x^{3} + b^{2} x^{6}\right)^{p}}{24 b^{4} p^{4} + 120 b^{4} p^{3} + 210 b^{4} p^{2} + 150 b^{4} p + 36 b^{4}} + \frac{2 a b^{3} p x^{9} \left(a^{2} + 2 a b x^{3} + b^{2} x^{6}\right)^{p}}{24 b^{4} p^{4} + 120 b^{4} p^{3} + 210 b^{4} p^{2} + 150 b^{4} p + 36 b^{4}} + \frac{4 b^{4} p^{3} x^{12} \left(a^{2} + 2 a b x^{3} + b^{2} x^{6}\right)^{p}}{24 b^{4} p^{4} + 120 b^{4} p^{3} + 210 b^{4} p^{2} + 150 b^{4} p + 36 b^{4}} + \frac{12 b^{4} p^{2} x^{12} \left(a^{2} + 2 a b x^{3} + b^{2} x^{6}\right)^{p}}{24 b^{4} p^{4} + 120 b^{4} p^{3} + 210 b^{4} p^{2} + 150 b^{4} p + 36 b^{4}} + \frac{11 b^{4} p x^{12} \left(a^{2} + 2 a b x^{3} + b^{2} x^{6}\right)^{p}}{24 b^{4} p^{4} + 120 b^{4} p^{3} + 210 b^{4} p^{2} + 150 b^{4} p + 36 b^{4}} + \frac{3 b^{4} x^{12} \left(a^{2} + 2 a b x^{3} + b^{2} x^{6}\right)^{p}}{24 b^{4} p^{4} + 120 b^{4} p^{3} + 210 b^{4} p^{2} + 150 b^{4} p + 36 b^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x**12*(a**2)**p/12, Eq(b, 0)), (6*a**3*log(-(-1)**(1/3)*a**(1/3)*(1/b)**(1/3) + x)/(18*a**3*b**4 + 54*a**2*b**5*x**3 + 54*a*b**6*x**6 + 18*b**7*x**9) + 6*a**3*log(4*(-1)**(2/3)*a**(2/3)*(1/b)**(2/3) + 4*(-1)**(1/3)*a**(1/3)*x*(1/b)**(1/3) + 4*x**2)/(18*a**3*b**4 + 54*a**2*b**5*x**3 + 54*a*b**6*x**6 + 18*b**7*x**9) - 12*a**3*log(2)/(18*a**3*b**4 + 54*a**2*b**5*x**3 + 54*a*b**6*x**6 + 18*b**7*x**9) + 11*a**3/(18*a**3*b**4 + 54*a**2*b**5*x**3 + 54*a*b**6*x**6 + 18*b**7*x**9) + 18*a**2*b*x**3*log(-(-1)**(1/3)*a**(1/3)*(1/b)**(1/3) + x)/(18*a**3*b**4 + 54*a**2*b**5*x**3 + 54*a*b**6*x**6 + 18*b**7*x**9) + 18*a**2*b*x**3*log(4*(-1)**(2/3)*a**(2/3)*(1/b)**(2/3) + 4*(-1)**(1/3)*a**(1/3)*x*(1/b)**(1/3) + 4*x**2)/(18*a**3*b**4 + 54*a**2*b**5*x**3 + 54*a*b**6*x**6 + 18*b**7*x**9) - 36*a**2*b*x**3*log(2)/(18*a**3*b**4 + 54*a**2*b**5*x**3 + 54*a*b**6*x**6 + 18*b**7*x**9) + 27*a**2*b*x**3/(18*a**3*b**4 + 54*a**2*b**5*x**3 + 54*a*b**6*x**6 + 18*b**7*x**9) + 18*a*b**2*x**6*log(-(-1)**(1/3)*a**(1/3)*(1/b)**(1/3) + x)/(18*a**3*b**4 + 54*a**2*b**5*x**3 + 54*a*b**6*x**6 + 18*b**7*x**9) + 18*a*b**2*x**6*log(4*(-1)**(2/3)*a**(2/3)*(1/b)**(2/3) + 4*(-1)**(1/3)*a**(1/3)*x*(1/b)**(1/3) + 4*x**2)/(18*a**3*b**4 + 54*a**2*b**5*x**3 + 54*a*b**6*x**6 + 18*b**7*x**9) - 36*a*b**2*x**6*log(2)/(18*a**3*b**4 + 54*a**2*b**5*x**3 + 54*a*b**6*x**6 + 18*b**7*x**9) + 18*a*b**2*x**6/(18*a**3*b**4 + 54*a**2*b**5*x**3 + 54*a*b**6*x**6 + 18*b**7*x**9) + 6*b**3*x**9*log(-(-1)**(1/3)*a**(1/3)*(1/b)**(1/3) + x)/(18*a**3*b**4 + 54*a**2*b**5*x**3 + 54*a*b**6*x**6 + 18*b**7*x**9) + 6*b**3*x**9*log(4*(-1)**(2/3)*a**(2/3)*(1/b)**(2/3) + 4*(-1)**(1/3)*a**(1/3)*x*(1/b)**(1/3) + 4*x**2)/(18*a**3*b**4 + 54*a**2*b**5*x**3 + 54*a*b**6*x**6 + 18*b**7*x**9) - 12*b**3*x**9*log(2)/(18*a**3*b**4 + 54*a**2*b**5*x**3 + 54*a*b**6*x**6 + 18*b**7*x**9), Eq(p, -2)), (Integral(x**11/((a + b*x**3)**2)**(3/2), x), Eq(p, -3/2)), (6*a**3*log(-(-1)**(1/3)*a**(1/3)*(1/b)**(1/3) + x)/(6*a*b**4 + 6*b**5*x**3) + 6*a**3*log(4*(-1)**(2/3)*a**(2/3)*(1/b)**(2/3) + 4*(-1)**(1/3)*a**(1/3)*x*(1/b)**(1/3) + 4*x**2)/(6*a*b**4 + 6*b**5*x**3) - 12*a**3*log(2)/(6*a*b**4 + 6*b**5*x**3) + 6*a**3/(6*a*b**4 + 6*b**5*x**3) + 6*a**2*b*x**3*log(-(-1)**(1/3)*a**(1/3)*(1/b)**(1/3) + x)/(6*a*b**4 + 6*b**5*x**3) + 6*a**2*b*x**3*log(4*(-1)**(2/3)*a**(2/3)*(1/b)**(2/3) + 4*(-1)**(1/3)*a**(1/3)*x*(1/b)**(1/3) + 4*x**2)/(6*a*b**4 + 6*b**5*x**3) - 12*a**2*b*x**3*log(2)/(6*a*b**4 + 6*b**5*x**3) - 3*a*b**2*x**6/(6*a*b**4 + 6*b**5*x**3) + b**3*x**9/(6*a*b**4 + 6*b**5*x**3), Eq(p, -1)), (Integral(x**11/sqrt((a + b*x**3)**2), x), Eq(p, -1/2)), (-3*a**4*(a**2 + 2*a*b*x**3 + b**2*x**6)**p/(24*b**4*p**4 + 120*b**4*p**3 + 210*b**4*p**2 + 150*b**4*p + 36*b**4) + 6*a**3*b*p*x**3*(a**2 + 2*a*b*x**3 + b**2*x**6)**p/(24*b**4*p**4 + 120*b**4*p**3 + 210*b**4*p**2 + 150*b**4*p + 36*b**4) - 6*a**2*b**2*p**2*x**6*(a**2 + 2*a*b*x**3 + b**2*x**6)**p/(24*b**4*p**4 + 120*b**4*p**3 + 210*b**4*p**2 + 150*b**4*p + 36*b**4) - 3*a**2*b**2*p*x**6*(a**2 + 2*a*b*x**3 + b**2*x**6)**p/(24*b**4*p**4 + 120*b**4*p**3 + 210*b**4*p**2 + 150*b**4*p + 36*b**4) + 4*a*b**3*p**3*x**9*(a**2 + 2*a*b*x**3 + b**2*x**6)**p/(24*b**4*p**4 + 120*b**4*p**3 + 210*b**4*p**2 + 150*b**4*p + 36*b**4) + 6*a*b**3*p**2*x**9*(a**2 + 2*a*b*x**3 + b**2*x**6)**p/(24*b**4*p**4 + 120*b**4*p**3 + 210*b**4*p**2 + 150*b**4*p + 36*b**4) + 2*a*b**3*p*x**9*(a**2 + 2*a*b*x**3 + b**2*x**6)**p/(24*b**4*p**4 + 120*b**4*p**3 + 210*b**4*p**2 + 150*b**4*p + 36*b**4) + 4*b**4*p**3*x**12*(a**2 + 2*a*b*x**3 + b**2*x**6)**p/(24*b**4*p**4 + 120*b**4*p**3 + 210*b**4*p**2 + 150*b**4*p + 36*b**4) + 12*b**4*p**2*x**12*(a**2 + 2*a*b*x**3 + b**2*x**6)**p/(24*b**4*p**4 + 120*b**4*p**3 + 210*b**4*p**2 + 150*b**4*p + 36*b**4) + 11*b**4*p*x**12*(a**2 + 2*a*b*x**3 + b**2*x**6)**p/(24*b**4*p**4 + 120*b**4*p**3 + 210*b**4*p**2 + 150*b**4*p + 36*b**4) + 3*b**4*x**12*(a**2 + 2*a*b*x**3 + b**2*x**6)**p/(24*b**4*p**4 + 120*b**4*p**3 + 210*b**4*p**2 + 150*b**4*p + 36*b**4), True))","F",0
126,0,0,0,0.000000," ","integrate(x**8*(b**2*x**6+2*a*b*x**3+a**2)**p,x)","\begin{cases} \frac{x^{9} \left(a^{2}\right)^{p}}{9} & \text{for}\: b = 0 \\\int \frac{x^{8}}{\left(\left(a + b x^{3}\right)^{2}\right)^{\frac{3}{2}}}\, dx & \text{for}\: p = - \frac{3}{2} \\- \frac{2 a^{2} \log{\left(- \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{\frac{1}{b}} + x \right)}}{3 a b^{3} + 3 b^{4} x^{3}} - \frac{2 a^{2} \log{\left(4 \left(-1\right)^{\frac{2}{3}} a^{\frac{2}{3}} \left(\frac{1}{b}\right)^{\frac{2}{3}} + 4 \sqrt[3]{-1} \sqrt[3]{a} x \sqrt[3]{\frac{1}{b}} + 4 x^{2} \right)}}{3 a b^{3} + 3 b^{4} x^{3}} - \frac{2 a^{2}}{3 a b^{3} + 3 b^{4} x^{3}} + \frac{4 a^{2} \log{\left(2 \right)}}{3 a b^{3} + 3 b^{4} x^{3}} - \frac{2 a b x^{3} \log{\left(- \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{\frac{1}{b}} + x \right)}}{3 a b^{3} + 3 b^{4} x^{3}} - \frac{2 a b x^{3} \log{\left(4 \left(-1\right)^{\frac{2}{3}} a^{\frac{2}{3}} \left(\frac{1}{b}\right)^{\frac{2}{3}} + 4 \sqrt[3]{-1} \sqrt[3]{a} x \sqrt[3]{\frac{1}{b}} + 4 x^{2} \right)}}{3 a b^{3} + 3 b^{4} x^{3}} + \frac{4 a b x^{3} \log{\left(2 \right)}}{3 a b^{3} + 3 b^{4} x^{3}} + \frac{b^{2} x^{6}}{3 a b^{3} + 3 b^{4} x^{3}} & \text{for}\: p = -1 \\\int \frac{x^{8}}{\sqrt{\left(a + b x^{3}\right)^{2}}}\, dx & \text{for}\: p = - \frac{1}{2} \\\frac{a^{3} \left(a^{2} + 2 a b x^{3} + b^{2} x^{6}\right)^{p}}{12 b^{3} p^{3} + 36 b^{3} p^{2} + 33 b^{3} p + 9 b^{3}} - \frac{2 a^{2} b p x^{3} \left(a^{2} + 2 a b x^{3} + b^{2} x^{6}\right)^{p}}{12 b^{3} p^{3} + 36 b^{3} p^{2} + 33 b^{3} p + 9 b^{3}} + \frac{2 a b^{2} p^{2} x^{6} \left(a^{2} + 2 a b x^{3} + b^{2} x^{6}\right)^{p}}{12 b^{3} p^{3} + 36 b^{3} p^{2} + 33 b^{3} p + 9 b^{3}} + \frac{a b^{2} p x^{6} \left(a^{2} + 2 a b x^{3} + b^{2} x^{6}\right)^{p}}{12 b^{3} p^{3} + 36 b^{3} p^{2} + 33 b^{3} p + 9 b^{3}} + \frac{2 b^{3} p^{2} x^{9} \left(a^{2} + 2 a b x^{3} + b^{2} x^{6}\right)^{p}}{12 b^{3} p^{3} + 36 b^{3} p^{2} + 33 b^{3} p + 9 b^{3}} + \frac{3 b^{3} p x^{9} \left(a^{2} + 2 a b x^{3} + b^{2} x^{6}\right)^{p}}{12 b^{3} p^{3} + 36 b^{3} p^{2} + 33 b^{3} p + 9 b^{3}} + \frac{b^{3} x^{9} \left(a^{2} + 2 a b x^{3} + b^{2} x^{6}\right)^{p}}{12 b^{3} p^{3} + 36 b^{3} p^{2} + 33 b^{3} p + 9 b^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x**9*(a**2)**p/9, Eq(b, 0)), (Integral(x**8/((a + b*x**3)**2)**(3/2), x), Eq(p, -3/2)), (-2*a**2*log(-(-1)**(1/3)*a**(1/3)*(1/b)**(1/3) + x)/(3*a*b**3 + 3*b**4*x**3) - 2*a**2*log(4*(-1)**(2/3)*a**(2/3)*(1/b)**(2/3) + 4*(-1)**(1/3)*a**(1/3)*x*(1/b)**(1/3) + 4*x**2)/(3*a*b**3 + 3*b**4*x**3) - 2*a**2/(3*a*b**3 + 3*b**4*x**3) + 4*a**2*log(2)/(3*a*b**3 + 3*b**4*x**3) - 2*a*b*x**3*log(-(-1)**(1/3)*a**(1/3)*(1/b)**(1/3) + x)/(3*a*b**3 + 3*b**4*x**3) - 2*a*b*x**3*log(4*(-1)**(2/3)*a**(2/3)*(1/b)**(2/3) + 4*(-1)**(1/3)*a**(1/3)*x*(1/b)**(1/3) + 4*x**2)/(3*a*b**3 + 3*b**4*x**3) + 4*a*b*x**3*log(2)/(3*a*b**3 + 3*b**4*x**3) + b**2*x**6/(3*a*b**3 + 3*b**4*x**3), Eq(p, -1)), (Integral(x**8/sqrt((a + b*x**3)**2), x), Eq(p, -1/2)), (a**3*(a**2 + 2*a*b*x**3 + b**2*x**6)**p/(12*b**3*p**3 + 36*b**3*p**2 + 33*b**3*p + 9*b**3) - 2*a**2*b*p*x**3*(a**2 + 2*a*b*x**3 + b**2*x**6)**p/(12*b**3*p**3 + 36*b**3*p**2 + 33*b**3*p + 9*b**3) + 2*a*b**2*p**2*x**6*(a**2 + 2*a*b*x**3 + b**2*x**6)**p/(12*b**3*p**3 + 36*b**3*p**2 + 33*b**3*p + 9*b**3) + a*b**2*p*x**6*(a**2 + 2*a*b*x**3 + b**2*x**6)**p/(12*b**3*p**3 + 36*b**3*p**2 + 33*b**3*p + 9*b**3) + 2*b**3*p**2*x**9*(a**2 + 2*a*b*x**3 + b**2*x**6)**p/(12*b**3*p**3 + 36*b**3*p**2 + 33*b**3*p + 9*b**3) + 3*b**3*p*x**9*(a**2 + 2*a*b*x**3 + b**2*x**6)**p/(12*b**3*p**3 + 36*b**3*p**2 + 33*b**3*p + 9*b**3) + b**3*x**9*(a**2 + 2*a*b*x**3 + b**2*x**6)**p/(12*b**3*p**3 + 36*b**3*p**2 + 33*b**3*p + 9*b**3), True))","F",0
127,0,0,0,0.000000," ","integrate(x**5*(b**2*x**6+2*a*b*x**3+a**2)**p,x)","\begin{cases} \frac{x^{6} \left(a^{2}\right)^{p}}{6} & \text{for}\: b = 0 \\\frac{a \log{\left(- \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{\frac{1}{b}} + x \right)}}{3 a b^{2} + 3 b^{3} x^{3}} + \frac{a \log{\left(4 \left(-1\right)^{\frac{2}{3}} a^{\frac{2}{3}} \left(\frac{1}{b}\right)^{\frac{2}{3}} + 4 \sqrt[3]{-1} \sqrt[3]{a} x \sqrt[3]{\frac{1}{b}} + 4 x^{2} \right)}}{3 a b^{2} + 3 b^{3} x^{3}} - \frac{2 a \log{\left(2 \right)}}{3 a b^{2} + 3 b^{3} x^{3}} + \frac{a}{3 a b^{2} + 3 b^{3} x^{3}} + \frac{b x^{3} \log{\left(- \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{\frac{1}{b}} + x \right)}}{3 a b^{2} + 3 b^{3} x^{3}} + \frac{b x^{3} \log{\left(4 \left(-1\right)^{\frac{2}{3}} a^{\frac{2}{3}} \left(\frac{1}{b}\right)^{\frac{2}{3}} + 4 \sqrt[3]{-1} \sqrt[3]{a} x \sqrt[3]{\frac{1}{b}} + 4 x^{2} \right)}}{3 a b^{2} + 3 b^{3} x^{3}} - \frac{2 b x^{3} \log{\left(2 \right)}}{3 a b^{2} + 3 b^{3} x^{3}} & \text{for}\: p = -1 \\\int \frac{x^{5}}{\sqrt{\left(a + b x^{3}\right)^{2}}}\, dx & \text{for}\: p = - \frac{1}{2} \\- \frac{a^{2} \left(a^{2} + 2 a b x^{3} + b^{2} x^{6}\right)^{p}}{12 b^{2} p^{2} + 18 b^{2} p + 6 b^{2}} + \frac{2 a b p x^{3} \left(a^{2} + 2 a b x^{3} + b^{2} x^{6}\right)^{p}}{12 b^{2} p^{2} + 18 b^{2} p + 6 b^{2}} + \frac{2 b^{2} p x^{6} \left(a^{2} + 2 a b x^{3} + b^{2} x^{6}\right)^{p}}{12 b^{2} p^{2} + 18 b^{2} p + 6 b^{2}} + \frac{b^{2} x^{6} \left(a^{2} + 2 a b x^{3} + b^{2} x^{6}\right)^{p}}{12 b^{2} p^{2} + 18 b^{2} p + 6 b^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x**6*(a**2)**p/6, Eq(b, 0)), (a*log(-(-1)**(1/3)*a**(1/3)*(1/b)**(1/3) + x)/(3*a*b**2 + 3*b**3*x**3) + a*log(4*(-1)**(2/3)*a**(2/3)*(1/b)**(2/3) + 4*(-1)**(1/3)*a**(1/3)*x*(1/b)**(1/3) + 4*x**2)/(3*a*b**2 + 3*b**3*x**3) - 2*a*log(2)/(3*a*b**2 + 3*b**3*x**3) + a/(3*a*b**2 + 3*b**3*x**3) + b*x**3*log(-(-1)**(1/3)*a**(1/3)*(1/b)**(1/3) + x)/(3*a*b**2 + 3*b**3*x**3) + b*x**3*log(4*(-1)**(2/3)*a**(2/3)*(1/b)**(2/3) + 4*(-1)**(1/3)*a**(1/3)*x*(1/b)**(1/3) + 4*x**2)/(3*a*b**2 + 3*b**3*x**3) - 2*b*x**3*log(2)/(3*a*b**2 + 3*b**3*x**3), Eq(p, -1)), (Integral(x**5/sqrt((a + b*x**3)**2), x), Eq(p, -1/2)), (-a**2*(a**2 + 2*a*b*x**3 + b**2*x**6)**p/(12*b**2*p**2 + 18*b**2*p + 6*b**2) + 2*a*b*p*x**3*(a**2 + 2*a*b*x**3 + b**2*x**6)**p/(12*b**2*p**2 + 18*b**2*p + 6*b**2) + 2*b**2*p*x**6*(a**2 + 2*a*b*x**3 + b**2*x**6)**p/(12*b**2*p**2 + 18*b**2*p + 6*b**2) + b**2*x**6*(a**2 + 2*a*b*x**3 + b**2*x**6)**p/(12*b**2*p**2 + 18*b**2*p + 6*b**2), True))","F",0
128,0,0,0,0.000000," ","integrate(x**4*(b**2*x**6+2*a*b*x**3+a**2)**p,x)","\int x^{4} \left(\left(a + b x^{3}\right)^{2}\right)^{p}\, dx"," ",0,"Integral(x**4*((a + b*x**3)**2)**p, x)","F",0
129,0,0,0,0.000000," ","integrate(x**3*(b**2*x**6+2*a*b*x**3+a**2)**p,x)","\int x^{3} \left(\left(a + b x^{3}\right)^{2}\right)^{p}\, dx"," ",0,"Integral(x**3*((a + b*x**3)**2)**p, x)","F",0
130,0,0,0,0.000000," ","integrate(x**2*(b**2*x**6+2*a*b*x**3+a**2)**p,x)","\begin{cases} \frac{x^{3}}{3 \sqrt{a^{2}}} & \text{for}\: b = 0 \wedge p = - \frac{1}{2} \\\frac{x^{3} \left(a^{2}\right)^{p}}{3} & \text{for}\: b = 0 \\\int \frac{x^{2}}{\sqrt{\left(a + b x^{3}\right)^{2}}}\, dx & \text{for}\: p = - \frac{1}{2} \\\frac{a \left(a^{2} + 2 a b x^{3} + b^{2} x^{6}\right)^{p}}{6 b p + 3 b} + \frac{b x^{3} \left(a^{2} + 2 a b x^{3} + b^{2} x^{6}\right)^{p}}{6 b p + 3 b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x**3/(3*sqrt(a**2)), Eq(b, 0) & Eq(p, -1/2)), (x**3*(a**2)**p/3, Eq(b, 0)), (Integral(x**2/sqrt((a + b*x**3)**2), x), Eq(p, -1/2)), (a*(a**2 + 2*a*b*x**3 + b**2*x**6)**p/(6*b*p + 3*b) + b*x**3*(a**2 + 2*a*b*x**3 + b**2*x**6)**p/(6*b*p + 3*b), True))","F",0
131,0,0,0,0.000000," ","integrate(x*(b**2*x**6+2*a*b*x**3+a**2)**p,x)","\int x \left(\left(a + b x^{3}\right)^{2}\right)^{p}\, dx"," ",0,"Integral(x*((a + b*x**3)**2)**p, x)","F",0
132,0,0,0,0.000000," ","integrate((b**2*x**6+2*a*b*x**3+a**2)**p,x)","\int \left(a^{2} + 2 a b x^{3} + b^{2} x^{6}\right)^{p}\, dx"," ",0,"Integral((a**2 + 2*a*b*x**3 + b**2*x**6)**p, x)","F",0
133,0,0,0,0.000000," ","integrate((b**2*x**6+2*a*b*x**3+a**2)**p/x,x)","\int \frac{\left(\left(a + b x^{3}\right)^{2}\right)^{p}}{x}\, dx"," ",0,"Integral(((a + b*x**3)**2)**p/x, x)","F",0
134,0,0,0,0.000000," ","integrate((b**2*x**6+2*a*b*x**3+a**2)**p/x**2,x)","\int \frac{\left(\left(a + b x^{3}\right)^{2}\right)^{p}}{x^{2}}\, dx"," ",0,"Integral(((a + b*x**3)**2)**p/x**2, x)","F",0
135,0,0,0,0.000000," ","integrate((b**2*x**6+2*a*b*x**3+a**2)**p/x**3,x)","\int \frac{\left(\left(a + b x^{3}\right)^{2}\right)^{p}}{x^{3}}\, dx"," ",0,"Integral(((a + b*x**3)**2)**p/x**3, x)","F",0
136,0,0,0,0.000000," ","integrate((b**2*x**6+2*a*b*x**3+a**2)**p/x**4,x)","\int \frac{\left(\left(a + b x^{3}\right)^{2}\right)^{p}}{x^{4}}\, dx"," ",0,"Integral(((a + b*x**3)**2)**p/x**4, x)","F",0
137,0,0,0,0.000000," ","integrate((b**2*x**6+2*a*b*x**3+a**2)**p/x**5,x)","\int \frac{\left(\left(a + b x^{3}\right)^{2}\right)^{p}}{x^{5}}\, dx"," ",0,"Integral(((a + b*x**3)**2)**p/x**5, x)","F",0
138,1,316,0,2.695006," ","integrate(x**8/(c*x**6+b*x**3+a),x)","\left(- \frac{b}{6 c^{2}} - \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{6 c^{2} \left(4 a c - b^{2}\right)}\right) \log{\left(x^{3} + \frac{- a b - 12 a c^{2} \left(- \frac{b}{6 c^{2}} - \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{6 c^{2} \left(4 a c - b^{2}\right)}\right) + 3 b^{2} c \left(- \frac{b}{6 c^{2}} - \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{6 c^{2} \left(4 a c - b^{2}\right)}\right)}{2 a c - b^{2}} \right)} + \left(- \frac{b}{6 c^{2}} + \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{6 c^{2} \left(4 a c - b^{2}\right)}\right) \log{\left(x^{3} + \frac{- a b - 12 a c^{2} \left(- \frac{b}{6 c^{2}} + \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{6 c^{2} \left(4 a c - b^{2}\right)}\right) + 3 b^{2} c \left(- \frac{b}{6 c^{2}} + \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{6 c^{2} \left(4 a c - b^{2}\right)}\right)}{2 a c - b^{2}} \right)} + \frac{x^{3}}{3 c}"," ",0,"(-b/(6*c**2) - sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(6*c**2*(4*a*c - b**2)))*log(x**3 + (-a*b - 12*a*c**2*(-b/(6*c**2) - sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(6*c**2*(4*a*c - b**2))) + 3*b**2*c*(-b/(6*c**2) - sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(6*c**2*(4*a*c - b**2))))/(2*a*c - b**2)) + (-b/(6*c**2) + sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(6*c**2*(4*a*c - b**2)))*log(x**3 + (-a*b - 12*a*c**2*(-b/(6*c**2) + sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(6*c**2*(4*a*c - b**2))) + 3*b**2*c*(-b/(6*c**2) + sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(6*c**2*(4*a*c - b**2))))/(2*a*c - b**2)) + x**3/(3*c)","B",0
139,1,223,0,1.369417," ","integrate(x**5/(c*x**6+b*x**3+a),x)","\left(- \frac{b \sqrt{- 4 a c + b^{2}}}{6 c \left(4 a c - b^{2}\right)} + \frac{1}{6 c}\right) \log{\left(x^{3} + \frac{- 12 a c \left(- \frac{b \sqrt{- 4 a c + b^{2}}}{6 c \left(4 a c - b^{2}\right)} + \frac{1}{6 c}\right) + 2 a + 3 b^{2} \left(- \frac{b \sqrt{- 4 a c + b^{2}}}{6 c \left(4 a c - b^{2}\right)} + \frac{1}{6 c}\right)}{b} \right)} + \left(\frac{b \sqrt{- 4 a c + b^{2}}}{6 c \left(4 a c - b^{2}\right)} + \frac{1}{6 c}\right) \log{\left(x^{3} + \frac{- 12 a c \left(\frac{b \sqrt{- 4 a c + b^{2}}}{6 c \left(4 a c - b^{2}\right)} + \frac{1}{6 c}\right) + 2 a + 3 b^{2} \left(\frac{b \sqrt{- 4 a c + b^{2}}}{6 c \left(4 a c - b^{2}\right)} + \frac{1}{6 c}\right)}{b} \right)}"," ",0,"(-b*sqrt(-4*a*c + b**2)/(6*c*(4*a*c - b**2)) + 1/(6*c))*log(x**3 + (-12*a*c*(-b*sqrt(-4*a*c + b**2)/(6*c*(4*a*c - b**2)) + 1/(6*c)) + 2*a + 3*b**2*(-b*sqrt(-4*a*c + b**2)/(6*c*(4*a*c - b**2)) + 1/(6*c)))/b) + (b*sqrt(-4*a*c + b**2)/(6*c*(4*a*c - b**2)) + 1/(6*c))*log(x**3 + (-12*a*c*(b*sqrt(-4*a*c + b**2)/(6*c*(4*a*c - b**2)) + 1/(6*c)) + 2*a + 3*b**2*(b*sqrt(-4*a*c + b**2)/(6*c*(4*a*c - b**2)) + 1/(6*c)))/b)","B",0
140,1,131,0,0.637774," ","integrate(x**2/(c*x**6+b*x**3+a),x)","- \frac{\sqrt{- \frac{1}{4 a c - b^{2}}} \log{\left(x^{3} + \frac{- 4 a c \sqrt{- \frac{1}{4 a c - b^{2}}} + b^{2} \sqrt{- \frac{1}{4 a c - b^{2}}} + b}{2 c} \right)}}{3} + \frac{\sqrt{- \frac{1}{4 a c - b^{2}}} \log{\left(x^{3} + \frac{4 a c \sqrt{- \frac{1}{4 a c - b^{2}}} - b^{2} \sqrt{- \frac{1}{4 a c - b^{2}}} + b}{2 c} \right)}}{3}"," ",0,"-sqrt(-1/(4*a*c - b**2))*log(x**3 + (-4*a*c*sqrt(-1/(4*a*c - b**2)) + b**2*sqrt(-1/(4*a*c - b**2)) + b)/(2*c))/3 + sqrt(-1/(4*a*c - b**2))*log(x**3 + (4*a*c*sqrt(-1/(4*a*c - b**2)) - b**2*sqrt(-1/(4*a*c - b**2)) + b)/(2*c))/3","B",0
141,1,253,0,6.730884," ","integrate(1/x/(c*x**6+b*x**3+a),x)","\left(- \frac{b \sqrt{- 4 a c + b^{2}}}{6 a \left(4 a c - b^{2}\right)} - \frac{1}{6 a}\right) \log{\left(x^{3} + \frac{- 12 a^{2} c \left(- \frac{b \sqrt{- 4 a c + b^{2}}}{6 a \left(4 a c - b^{2}\right)} - \frac{1}{6 a}\right) + 3 a b^{2} \left(- \frac{b \sqrt{- 4 a c + b^{2}}}{6 a \left(4 a c - b^{2}\right)} - \frac{1}{6 a}\right) - 2 a c + b^{2}}{b c} \right)} + \left(\frac{b \sqrt{- 4 a c + b^{2}}}{6 a \left(4 a c - b^{2}\right)} - \frac{1}{6 a}\right) \log{\left(x^{3} + \frac{- 12 a^{2} c \left(\frac{b \sqrt{- 4 a c + b^{2}}}{6 a \left(4 a c - b^{2}\right)} - \frac{1}{6 a}\right) + 3 a b^{2} \left(\frac{b \sqrt{- 4 a c + b^{2}}}{6 a \left(4 a c - b^{2}\right)} - \frac{1}{6 a}\right) - 2 a c + b^{2}}{b c} \right)} + \frac{\log{\left(x \right)}}{a}"," ",0,"(-b*sqrt(-4*a*c + b**2)/(6*a*(4*a*c - b**2)) - 1/(6*a))*log(x**3 + (-12*a**2*c*(-b*sqrt(-4*a*c + b**2)/(6*a*(4*a*c - b**2)) - 1/(6*a)) + 3*a*b**2*(-b*sqrt(-4*a*c + b**2)/(6*a*(4*a*c - b**2)) - 1/(6*a)) - 2*a*c + b**2)/(b*c)) + (b*sqrt(-4*a*c + b**2)/(6*a*(4*a*c - b**2)) - 1/(6*a))*log(x**3 + (-12*a**2*c*(b*sqrt(-4*a*c + b**2)/(6*a*(4*a*c - b**2)) - 1/(6*a)) + 3*a*b**2*(b*sqrt(-4*a*c + b**2)/(6*a*(4*a*c - b**2)) - 1/(6*a)) - 2*a*c + b**2)/(b*c)) + log(x)/a","B",0
142,1,345,0,113.787086," ","integrate(1/x**4/(c*x**6+b*x**3+a),x)","\left(\frac{b}{6 a^{2}} - \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{6 a^{2} \left(4 a c - b^{2}\right)}\right) \log{\left(x^{3} + \frac{- 12 a^{3} c \left(\frac{b}{6 a^{2}} - \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{6 a^{2} \left(4 a c - b^{2}\right)}\right) + 3 a^{2} b^{2} \left(\frac{b}{6 a^{2}} - \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{6 a^{2} \left(4 a c - b^{2}\right)}\right) + 3 a b c - b^{3}}{2 a c^{2} - b^{2} c} \right)} + \left(\frac{b}{6 a^{2}} + \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{6 a^{2} \left(4 a c - b^{2}\right)}\right) \log{\left(x^{3} + \frac{- 12 a^{3} c \left(\frac{b}{6 a^{2}} + \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{6 a^{2} \left(4 a c - b^{2}\right)}\right) + 3 a^{2} b^{2} \left(\frac{b}{6 a^{2}} + \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{6 a^{2} \left(4 a c - b^{2}\right)}\right) + 3 a b c - b^{3}}{2 a c^{2} - b^{2} c} \right)} - \frac{1}{3 a x^{3}} - \frac{b \log{\left(x \right)}}{a^{2}}"," ",0,"(b/(6*a**2) - sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(6*a**2*(4*a*c - b**2)))*log(x**3 + (-12*a**3*c*(b/(6*a**2) - sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(6*a**2*(4*a*c - b**2))) + 3*a**2*b**2*(b/(6*a**2) - sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(6*a**2*(4*a*c - b**2))) + 3*a*b*c - b**3)/(2*a*c**2 - b**2*c)) + (b/(6*a**2) + sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(6*a**2*(4*a*c - b**2)))*log(x**3 + (-12*a**3*c*(b/(6*a**2) + sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(6*a**2*(4*a*c - b**2))) + 3*a**2*b**2*(b/(6*a**2) + sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(6*a**2*(4*a*c - b**2))) + 3*a*b*c - b**3)/(2*a*c**2 - b**2*c)) - 1/(3*a*x**3) - b*log(x)/a**2","B",0
143,1,279,0,14.581420," ","integrate(x**7/(c*x**6+b*x**3+a),x)","\operatorname{RootSum} {\left(t^{6} \left(46656 a^{3} c^{8} - 34992 a^{2} b^{2} c^{7} + 8748 a b^{4} c^{6} - 729 b^{6} c^{5}\right) + t^{3} \left(432 a^{4} c^{4} - 1512 a^{3} b^{2} c^{3} + 1107 a^{2} b^{4} c^{2} - 297 a b^{6} c + 27 b^{8}\right) + a^{5}, \left( t \mapsto t \log{\left(x + \frac{- 15552 t^{5} a^{4} c^{9} + 27216 t^{5} a^{3} b^{2} c^{8} - 14580 t^{5} a^{2} b^{4} c^{7} + 3159 t^{5} a b^{6} c^{6} - 243 t^{5} b^{8} c^{5} - 72 t^{2} a^{5} c^{5} + 594 t^{2} a^{4} b^{2} c^{4} - 864 t^{2} a^{3} b^{4} c^{3} + 468 t^{2} a^{2} b^{6} c^{2} - 108 t^{2} a b^{8} c + 9 t^{2} b^{10}}{5 a^{5} b c^{2} - 5 a^{4} b^{3} c + a^{3} b^{5}} \right)} \right)\right)} + \frac{x^{2}}{2 c}"," ",0,"RootSum(_t**6*(46656*a**3*c**8 - 34992*a**2*b**2*c**7 + 8748*a*b**4*c**6 - 729*b**6*c**5) + _t**3*(432*a**4*c**4 - 1512*a**3*b**2*c**3 + 1107*a**2*b**4*c**2 - 297*a*b**6*c + 27*b**8) + a**5, Lambda(_t, _t*log(x + (-15552*_t**5*a**4*c**9 + 27216*_t**5*a**3*b**2*c**8 - 14580*_t**5*a**2*b**4*c**7 + 3159*_t**5*a*b**6*c**6 - 243*_t**5*b**8*c**5 - 72*_t**2*a**5*c**5 + 594*_t**2*a**4*b**2*c**4 - 864*_t**2*a**3*b**4*c**3 + 468*_t**2*a**2*b**6*c**2 - 108*_t**2*a*b**8*c + 9*_t**2*b**10)/(5*a**5*b*c**2 - 5*a**4*b**3*c + a**3*b**5)))) + x**2/(2*c)","A",0
144,1,196,0,6.903018," ","integrate(x**6/(c*x**6+b*x**3+a),x)","\operatorname{RootSum} {\left(t^{6} \left(46656 a^{3} c^{7} - 34992 a^{2} b^{2} c^{6} + 8748 a b^{4} c^{5} - 729 b^{6} c^{4}\right) + t^{3} \left(864 a^{3} b c^{3} - 864 a^{2} b^{3} c^{2} + 270 a b^{5} c - 27 b^{7}\right) + a^{4}, \left( t \mapsto t \log{\left(x + \frac{1296 t^{4} a^{2} b c^{6} - 648 t^{4} a b^{3} c^{5} + 81 t^{4} b^{5} c^{4} - 12 t a^{3} c^{3} + 39 t a^{2} b^{2} c^{2} - 21 t a b^{4} c + 3 t b^{6}}{2 a^{3} c^{2} - 4 a^{2} b^{2} c + a b^{4}} \right)} \right)\right)} + \frac{x}{c}"," ",0,"RootSum(_t**6*(46656*a**3*c**7 - 34992*a**2*b**2*c**6 + 8748*a*b**4*c**5 - 729*b**6*c**4) + _t**3*(864*a**3*b*c**3 - 864*a**2*b**3*c**2 + 270*a*b**5*c - 27*b**7) + a**4, Lambda(_t, _t*log(x + (1296*_t**4*a**2*b*c**6 - 648*_t**4*a*b**3*c**5 + 81*_t**4*b**5*c**4 - 12*_t*a**3*c**3 + 39*_t*a**2*b**2*c**2 - 21*_t*a*b**4*c + 3*_t*b**6)/(2*a**3*c**2 - 4*a**2*b**2*c + a*b**4)))) + x/c","A",0
145,1,175,0,2.181566," ","integrate(x**4/(c*x**6+b*x**3+a),x)","\operatorname{RootSum} {\left(t^{6} \left(46656 a^{3} c^{5} - 34992 a^{2} b^{2} c^{4} + 8748 a b^{4} c^{3} - 729 b^{6} c^{2}\right) + t^{3} \left(- 432 a^{2} b c^{2} + 216 a b^{3} c - 27 b^{5}\right) + a^{2}, \left( t \mapsto t \log{\left(x + \frac{15552 t^{5} a^{3} c^{5} - 11664 t^{5} a^{2} b^{2} c^{4} + 2916 t^{5} a b^{4} c^{3} - 243 t^{5} b^{6} c^{2} - 108 t^{2} a^{2} b c^{2} + 63 t^{2} a b^{3} c - 9 t^{2} b^{5}}{2 a^{2} c - a b^{2}} \right)} \right)\right)}"," ",0,"RootSum(_t**6*(46656*a**3*c**5 - 34992*a**2*b**2*c**4 + 8748*a*b**4*c**3 - 729*b**6*c**2) + _t**3*(-432*a**2*b*c**2 + 216*a*b**3*c - 27*b**5) + a**2, Lambda(_t, _t*log(x + (15552*_t**5*a**3*c**5 - 11664*_t**5*a**2*b**2*c**4 + 2916*_t**5*a*b**4*c**3 - 243*_t**5*b**6*c**2 - 108*_t**2*a**2*b*c**2 + 63*_t**2*a*b**3*c - 9*_t**2*b**5)/(2*a**2*c - a*b**2))))","A",0
146,1,122,0,1.800413," ","integrate(x**3/(c*x**6+b*x**3+a),x)","\operatorname{RootSum} {\left(t^{6} \left(46656 a^{3} c^{4} - 34992 a^{2} b^{2} c^{3} + 8748 a b^{4} c^{2} - 729 b^{6} c\right) + t^{3} \left(432 a^{2} c^{2} - 216 a b^{2} c + 27 b^{4}\right) + a, \left( t \mapsto t \log{\left(x + \frac{2592 t^{4} a^{2} c^{3} - 1296 t^{4} a b^{2} c^{2} + 162 t^{4} b^{4} c + 12 t a c - 3 t b^{2}}{b} \right)} \right)\right)}"," ",0,"RootSum(_t**6*(46656*a**3*c**4 - 34992*a**2*b**2*c**3 + 8748*a*b**4*c**2 - 729*b**6*c) + _t**3*(432*a**2*c**2 - 216*a*b**2*c + 27*b**4) + a, Lambda(_t, _t*log(x + (2592*_t**4*a**2*c**3 - 1296*_t**4*a*b**2*c**2 + 162*_t**4*b**4*c + 12*_t*a*c - 3*_t*b**2)/b)))","A",0
147,1,158,0,1.528274," ","integrate(x/(c*x**6+b*x**3+a),x)","\operatorname{RootSum} {\left(t^{6} \left(46656 a^{4} c^{3} - 34992 a^{3} b^{2} c^{2} + 8748 a^{2} b^{4} c - 729 a b^{6}\right) + t^{3} \left(- 432 a^{2} c^{2} + 216 a b^{2} c - 27 b^{4}\right) + c, \left( t \mapsto t \log{\left(x + \frac{- 15552 t^{5} a^{4} c^{3} + 11664 t^{5} a^{3} b^{2} c^{2} - 2916 t^{5} a^{2} b^{4} c + 243 t^{5} a b^{6} + 72 t^{2} a^{2} c^{2} - 54 t^{2} a b^{2} c + 9 t^{2} b^{4}}{b c} \right)} \right)\right)}"," ",0,"RootSum(_t**6*(46656*a**4*c**3 - 34992*a**3*b**2*c**2 + 8748*a**2*b**4*c - 729*a*b**6) + _t**3*(-432*a**2*c**2 + 216*a*b**2*c - 27*b**4) + c, Lambda(_t, _t*log(x + (-15552*_t**5*a**4*c**3 + 11664*_t**5*a**3*b**2*c**2 - 2916*_t**5*a**2*b**4*c + 243*_t**5*a*b**6 + 72*_t**2*a**2*c**2 - 54*_t**2*a*b**2*c + 9*_t**2*b**4)/(b*c))))","A",0
148,1,155,0,4.352986," ","integrate(1/(c*x**6+b*x**3+a),x)","\operatorname{RootSum} {\left(t^{6} \left(46656 a^{5} c^{3} - 34992 a^{4} b^{2} c^{2} + 8748 a^{3} b^{4} c - 729 a^{2} b^{6}\right) + t^{3} \left(432 a^{2} b c^{2} - 216 a b^{3} c + 27 b^{5}\right) + c^{2}, \left( t \mapsto t \log{\left(x + \frac{- 1296 t^{4} a^{4} b c^{2} + 648 t^{4} a^{3} b^{3} c - 81 t^{4} a^{2} b^{5} + 12 t a^{2} c^{2} - 15 t a b^{2} c + 3 t b^{4}}{2 a c^{2} - b^{2} c} \right)} \right)\right)}"," ",0,"RootSum(_t**6*(46656*a**5*c**3 - 34992*a**4*b**2*c**2 + 8748*a**3*b**4*c - 729*a**2*b**6) + _t**3*(432*a**2*b*c**2 - 216*a*b**3*c + 27*b**5) + c**2, Lambda(_t, _t*log(x + (-1296*_t**4*a**4*b*c**2 + 648*_t**4*a**3*b**3*c - 81*_t**4*a**2*b**5 + 12*_t*a**2*c**2 - 15*_t*a*b**2*c + 3*_t*b**4)/(2*a*c**2 - b**2*c))))","A",0
149,1,252,0,3.187691," ","integrate(1/x**2/(c*x**6+b*x**3+a),x)","\operatorname{RootSum} {\left(t^{6} \left(46656 a^{7} c^{3} - 34992 a^{6} b^{2} c^{2} + 8748 a^{5} b^{4} c - 729 a^{4} b^{6}\right) + t^{3} \left(- 864 a^{3} b c^{3} + 864 a^{2} b^{3} c^{2} - 270 a b^{5} c + 27 b^{7}\right) + c^{4}, \left( t \mapsto t \log{\left(x + \frac{- 15552 t^{5} a^{8} c^{4} + 27216 t^{5} a^{7} b^{2} c^{3} - 14580 t^{5} a^{6} b^{4} c^{2} + 3159 t^{5} a^{5} b^{6} c - 243 t^{5} a^{4} b^{8} + 252 t^{2} a^{4} b c^{4} - 567 t^{2} a^{3} b^{3} c^{3} + 378 t^{2} a^{2} b^{5} c^{2} - 99 t^{2} a b^{7} c + 9 t^{2} b^{9}}{2 a^{2} c^{5} - 4 a b^{2} c^{4} + b^{4} c^{3}} \right)} \right)\right)} - \frac{1}{a x}"," ",0,"RootSum(_t**6*(46656*a**7*c**3 - 34992*a**6*b**2*c**2 + 8748*a**5*b**4*c - 729*a**4*b**6) + _t**3*(-864*a**3*b*c**3 + 864*a**2*b**3*c**2 - 270*a*b**5*c + 27*b**7) + c**4, Lambda(_t, _t*log(x + (-15552*_t**5*a**8*c**4 + 27216*_t**5*a**7*b**2*c**3 - 14580*_t**5*a**6*b**4*c**2 + 3159*_t**5*a**5*b**6*c - 243*_t**5*a**4*b**8 + 252*_t**2*a**4*b*c**4 - 567*_t**2*a**3*b**3*c**3 + 378*_t**2*a**2*b**5*c**2 - 99*_t**2*a*b**7*c + 9*_t**2*b**9)/(2*a**2*c**5 - 4*a*b**2*c**4 + b**4*c**3)))) - 1/(a*x)","A",0
150,1,241,0,52.501050," ","integrate(1/x**3/(c*x**6+b*x**3+a),x)","\operatorname{RootSum} {\left(t^{6} \left(46656 a^{8} c^{3} - 34992 a^{7} b^{2} c^{2} + 8748 a^{6} b^{4} c - 729 a^{5} b^{6}\right) + t^{3} \left(- 432 a^{4} c^{4} + 1512 a^{3} b^{2} c^{3} - 1107 a^{2} b^{4} c^{2} + 297 a b^{6} c - 27 b^{8}\right) + c^{5}, \left( t \mapsto t \log{\left(x + \frac{- 2592 t^{4} a^{8} c^{3} + 2592 t^{4} a^{7} b^{2} c^{2} - 810 t^{4} a^{6} b^{4} c + 81 t^{4} a^{5} b^{6} + 12 t a^{4} c^{4} - 75 t a^{3} b^{2} c^{3} + 78 t a^{2} b^{4} c^{2} - 27 t a b^{6} c + 3 t b^{8}}{5 a^{2} b c^{4} - 5 a b^{3} c^{3} + b^{5} c^{2}} \right)} \right)\right)} - \frac{1}{2 a x^{2}}"," ",0,"RootSum(_t**6*(46656*a**8*c**3 - 34992*a**7*b**2*c**2 + 8748*a**6*b**4*c - 729*a**5*b**6) + _t**3*(-432*a**4*c**4 + 1512*a**3*b**2*c**3 - 1107*a**2*b**4*c**2 + 297*a*b**6*c - 27*b**8) + c**5, Lambda(_t, _t*log(x + (-2592*_t**4*a**8*c**3 + 2592*_t**4*a**7*b**2*c**2 - 810*_t**4*a**6*b**4*c + 81*_t**4*a**5*b**6 + 12*_t*a**4*c**4 - 75*_t*a**3*b**2*c**3 + 78*_t*a**2*b**4*c**2 - 27*_t*a*b**6*c + 3*_t*b**8)/(5*a**2*b*c**4 - 5*a*b**3*c**3 + b**5*c**2)))) - 1/(2*a*x**2)","A",0
151,1,29,0,0.126122," ","integrate(x**11/(x**6+4*x**3+3),x)","\frac{x^{6}}{6} - \frac{4 x^{3}}{3} - \frac{\log{\left(x^{3} + 1 \right)}}{6} + \frac{9 \log{\left(x^{3} + 3 \right)}}{2}"," ",0,"x**6/6 - 4*x**3/3 - log(x**3 + 1)/6 + 9*log(x**3 + 3)/2","A",0
152,1,22,0,0.123978," ","integrate(x**8/(x**6+4*x**3+3),x)","\frac{x^{3}}{3} + \frac{\log{\left(x^{3} + 1 \right)}}{6} - \frac{3 \log{\left(x^{3} + 3 \right)}}{2}"," ",0,"x**3/3 + log(x**3 + 1)/6 - 3*log(x**3 + 3)/2","A",0
153,1,15,0,0.115646," ","integrate(x**5/(x**6+4*x**3+3),x)","- \frac{\log{\left(x^{3} + 1 \right)}}{6} + \frac{\log{\left(x^{3} + 3 \right)}}{2}"," ",0,"-log(x**3 + 1)/6 + log(x**3 + 3)/2","A",0
154,1,15,0,0.107894," ","integrate(x**2/(x**6+4*x**3+3),x)","\frac{\log{\left(x^{3} + 1 \right)}}{6} - \frac{\log{\left(x^{3} + 3 \right)}}{6}"," ",0,"log(x**3 + 1)/6 - log(x**3 + 3)/6","A",0
155,1,20,0,0.140972," ","integrate(1/x/(x**6+4*x**3+3),x)","\frac{\log{\left(x \right)}}{3} - \frac{\log{\left(x^{3} + 1 \right)}}{6} + \frac{\log{\left(x^{3} + 3 \right)}}{18}"," ",0,"log(x)/3 - log(x**3 + 1)/6 + log(x**3 + 3)/18","A",0
156,1,29,0,0.169760," ","integrate(1/x**4/(x**6+4*x**3+3),x)","- \frac{4 \log{\left(x \right)}}{9} + \frac{\log{\left(x^{3} + 1 \right)}}{6} - \frac{\log{\left(x^{3} + 3 \right)}}{54} - \frac{1}{9 x^{3}}"," ",0,"-4*log(x)/9 + log(x**3 + 1)/6 - log(x**3 + 3)/54 - 1/(9*x**3)","A",0
157,1,34,0,0.188148," ","integrate(1/x**7/(x**6+4*x**3+3),x)","\frac{13 \log{\left(x \right)}}{27} - \frac{\log{\left(x^{3} + 1 \right)}}{6} + \frac{\log{\left(x^{3} + 3 \right)}}{162} + \frac{8 x^{3} - 3}{54 x^{6}}"," ",0,"13*log(x)/27 - log(x**3 + 1)/6 + log(x**3 + 3)/162 + (8*x**3 - 3)/(54*x**6)","A",0
158,1,144,0,0.619082," ","integrate(x**10/(x**6+4*x**3+3),x)","\frac{x^{5}}{5} - 2 x^{2} + \frac{\log{\left(x + 1 \right)}}{6} + \left(- \frac{1}{12} - \frac{\sqrt{3} i}{12}\right) \log{\left(x + \frac{3872 \left(- \frac{1}{12} - \frac{\sqrt{3} i}{12}\right)^{5}}{3281} + \frac{3188648 \left(- \frac{1}{12} - \frac{\sqrt{3} i}{12}\right)^{2}}{88587} \right)} + \left(- \frac{1}{12} + \frac{\sqrt{3} i}{12}\right) \log{\left(x + \frac{3188648 \left(- \frac{1}{12} + \frac{\sqrt{3} i}{12}\right)^{2}}{88587} + \frac{3872 \left(- \frac{1}{12} + \frac{\sqrt{3} i}{12}\right)^{5}}{3281} \right)} + \operatorname{RootSum} {\left(8 t^{3} + 243, \left( t \mapsto t \log{\left(\frac{3872 t^{5}}{3281} + \frac{3188648 t^{2}}{88587} + x \right)} \right)\right)}"," ",0,"x**5/5 - 2*x**2 + log(x + 1)/6 + (-1/12 - sqrt(3)*I/12)*log(x + 3872*(-1/12 - sqrt(3)*I/12)**5/3281 + 3188648*(-1/12 - sqrt(3)*I/12)**2/88587) + (-1/12 + sqrt(3)*I/12)*log(x + 3188648*(-1/12 + sqrt(3)*I/12)**2/88587 + 3872*(-1/12 + sqrt(3)*I/12)**5/3281) + RootSum(8*_t**3 + 243, Lambda(_t, _t*log(3872*_t**5/3281 + 3188648*_t**2/88587 + x)))","C",0
159,1,129,0,0.610798," ","integrate(x**9/(x**6+4*x**3+3),x)","\frac{x^{4}}{4} - 4 x - \frac{\log{\left(x + 1 \right)}}{6} + \left(\frac{1}{12} + \frac{\sqrt{3} i}{12}\right) \log{\left(x - \frac{9841}{19692} - \frac{9841 \sqrt{3} i}{19692} + \frac{360 \left(\frac{1}{12} + \frac{\sqrt{3} i}{12}\right)^{4}}{547} \right)} + \left(\frac{1}{12} - \frac{\sqrt{3} i}{12}\right) \log{\left(x - \frac{9841}{19692} + \frac{360 \left(\frac{1}{12} - \frac{\sqrt{3} i}{12}\right)^{4}}{547} + \frac{9841 \sqrt{3} i}{19692} \right)} + \operatorname{RootSum} {\left(8 t^{3} - 81, \left( t \mapsto t \log{\left(\frac{360 t^{4}}{547} - \frac{9841 t}{1641} + x \right)} \right)\right)}"," ",0,"x**4/4 - 4*x - log(x + 1)/6 + (1/12 + sqrt(3)*I/12)*log(x - 9841/19692 - 9841*sqrt(3)*I/19692 + 360*(1/12 + sqrt(3)*I/12)**4/547) + (1/12 - sqrt(3)*I/12)*log(x - 9841/19692 + 360*(1/12 - sqrt(3)*I/12)**4/547 + 9841*sqrt(3)*I/19692) + RootSum(8*_t**3 - 81, Lambda(_t, _t*log(360*_t**4/547 - 9841*_t/1641 + x)))","C",0
160,1,134,0,0.607244," ","integrate(x**7/(x**6+4*x**3+3),x)","\frac{x^{2}}{2} - \frac{\log{\left(x + 1 \right)}}{6} + \left(\frac{1}{12} - \frac{\sqrt{3} i}{12}\right) \log{\left(x + \frac{6562 \left(\frac{1}{12} - \frac{\sqrt{3} i}{12}\right)^{2}}{183} - \frac{1872 \left(\frac{1}{12} - \frac{\sqrt{3} i}{12}\right)^{5}}{61} \right)} + \left(\frac{1}{12} + \frac{\sqrt{3} i}{12}\right) \log{\left(x - \frac{1872 \left(\frac{1}{12} + \frac{\sqrt{3} i}{12}\right)^{5}}{61} + \frac{6562 \left(\frac{1}{12} + \frac{\sqrt{3} i}{12}\right)^{2}}{183} \right)} + \operatorname{RootSum} {\left(8 t^{3} - 9, \left( t \mapsto t \log{\left(- \frac{1872 t^{5}}{61} + \frac{6562 t^{2}}{183} + x \right)} \right)\right)}"," ",0,"x**2/2 - log(x + 1)/6 + (1/12 - sqrt(3)*I/12)*log(x + 6562*(1/12 - sqrt(3)*I/12)**2/183 - 1872*(1/12 - sqrt(3)*I/12)**5/61) + (1/12 + sqrt(3)*I/12)*log(x - 1872*(1/12 + sqrt(3)*I/12)**5/61 + 6562*(1/12 + sqrt(3)*I/12)**2/183) + RootSum(8*_t**3 - 9, Lambda(_t, _t*log(-1872*_t**5/61 + 6562*_t**2/183 + x)))","C",0
161,1,126,0,0.614892," ","integrate(x**6/(x**6+4*x**3+3),x)","x + \frac{\log{\left(x + 1 \right)}}{6} + \left(- \frac{1}{12} - \frac{\sqrt{3} i}{12}\right) \log{\left(x - \frac{121}{246} - \frac{121 \sqrt{3} i}{246} + \frac{864 \left(- \frac{1}{12} - \frac{\sqrt{3} i}{12}\right)^{4}}{41} \right)} + \left(- \frac{1}{12} + \frac{\sqrt{3} i}{12}\right) \log{\left(x - \frac{121}{246} + \frac{864 \left(- \frac{1}{12} + \frac{\sqrt{3} i}{12}\right)^{4}}{41} + \frac{121 \sqrt{3} i}{246} \right)} + \operatorname{RootSum} {\left(8 t^{3} + 3, \left( t \mapsto t \log{\left(\frac{864 t^{4}}{41} + \frac{242 t}{41} + x \right)} \right)\right)}"," ",0,"x + log(x + 1)/6 + (-1/12 - sqrt(3)*I/12)*log(x - 121/246 - 121*sqrt(3)*I/246 + 864*(-1/12 - sqrt(3)*I/12)**4/41) + (-1/12 + sqrt(3)*I/12)*log(x - 121/246 + 864*(-1/12 + sqrt(3)*I/12)**4/41 + 121*sqrt(3)*I/246) + RootSum(8*_t**3 + 3, Lambda(_t, _t*log(864*_t**4/41 + 242*_t/41 + x)))","C",0
162,1,134,0,0.600145," ","integrate(x**4/(x**6+4*x**3+3),x)","\frac{\log{\left(x + 1 \right)}}{6} + \left(- \frac{1}{12} - \frac{\sqrt{3} i}{12}\right) \log{\left(x + \frac{2592 \left(- \frac{1}{12} - \frac{\sqrt{3} i}{12}\right)^{5}}{5} + \frac{168 \left(- \frac{1}{12} - \frac{\sqrt{3} i}{12}\right)^{2}}{5} \right)} + \left(- \frac{1}{12} + \frac{\sqrt{3} i}{12}\right) \log{\left(x + \frac{168 \left(- \frac{1}{12} + \frac{\sqrt{3} i}{12}\right)^{2}}{5} + \frac{2592 \left(- \frac{1}{12} + \frac{\sqrt{3} i}{12}\right)^{5}}{5} \right)} + \operatorname{RootSum} {\left(24 t^{3} + 1, \left( t \mapsto t \log{\left(\frac{2592 t^{5}}{5} + \frac{168 t^{2}}{5} + x \right)} \right)\right)}"," ",0,"log(x + 1)/6 + (-1/12 - sqrt(3)*I/12)*log(x + 2592*(-1/12 - sqrt(3)*I/12)**5/5 + 168*(-1/12 - sqrt(3)*I/12)**2/5) + (-1/12 + sqrt(3)*I/12)*log(x + 168*(-1/12 + sqrt(3)*I/12)**2/5 + 2592*(-1/12 + sqrt(3)*I/12)**5/5) + RootSum(24*_t**3 + 1, Lambda(_t, _t*log(2592*_t**5/5 + 168*_t**2/5 + x)))","C",0
163,1,110,0,0.588997," ","integrate(x**3/(x**6+4*x**3+3),x)","- \frac{\log{\left(x + 1 \right)}}{6} + \left(\frac{1}{12} - \frac{\sqrt{3} i}{12}\right) \log{\left(x - \frac{1}{4} + 648 \left(\frac{1}{12} - \frac{\sqrt{3} i}{12}\right)^{4} + \frac{\sqrt{3} i}{4} \right)} + \left(\frac{1}{12} + \frac{\sqrt{3} i}{12}\right) \log{\left(x - \frac{1}{4} + 648 \left(\frac{1}{12} + \frac{\sqrt{3} i}{12}\right)^{4} - \frac{\sqrt{3} i}{4} \right)} + \operatorname{RootSum} {\left(72 t^{3} - 1, \left( t \mapsto t \log{\left(648 t^{4} - 3 t + x \right)} \right)\right)}"," ",0,"-log(x + 1)/6 + (1/12 - sqrt(3)*I/12)*log(x - 1/4 + 648*(1/12 - sqrt(3)*I/12)**4 + sqrt(3)*I/4) + (1/12 + sqrt(3)*I/12)*log(x - 1/4 + 648*(1/12 + sqrt(3)*I/12)**4 - sqrt(3)*I/4) + RootSum(72*_t**3 - 1, Lambda(_t, _t*log(648*_t**4 - 3*_t + x)))","C",0
164,1,119,0,1.856531," ","integrate(x/(x**6+4*x**3+3),x)","- \frac{\log{\left(x + 1 \right)}}{6} + \left(\frac{1}{12} - \frac{\sqrt{3} i}{12}\right) \log{\left(x + 90 \left(\frac{1}{12} - \frac{\sqrt{3} i}{12}\right)^{2} + 11664 \left(\frac{1}{12} - \frac{\sqrt{3} i}{12}\right)^{5} \right)} + \left(\frac{1}{12} + \frac{\sqrt{3} i}{12}\right) \log{\left(x + 11664 \left(\frac{1}{12} + \frac{\sqrt{3} i}{12}\right)^{5} + 90 \left(\frac{1}{12} + \frac{\sqrt{3} i}{12}\right)^{2} \right)} + \operatorname{RootSum} {\left(648 t^{3} - 1, \left( t \mapsto t \log{\left(11664 t^{5} + 90 t^{2} + x \right)} \right)\right)}"," ",0,"-log(x + 1)/6 + (1/12 - sqrt(3)*I/12)*log(x + 90*(1/12 - sqrt(3)*I/12)**2 + 11664*(1/12 - sqrt(3)*I/12)**5) + (1/12 + sqrt(3)*I/12)*log(x + 11664*(1/12 + sqrt(3)*I/12)**5 + 90*(1/12 + sqrt(3)*I/12)**2) + RootSum(648*_t**3 - 1, Lambda(_t, _t*log(11664*_t**5 + 90*_t**2 + x)))","C",0
165,1,124,0,1.819486," ","integrate(1/(x**6+4*x**3+3),x)","\frac{\log{\left(x + 1 \right)}}{6} + \left(- \frac{1}{12} + \frac{\sqrt{3} i}{12}\right) \log{\left(x + \frac{13}{10} - \frac{13 \sqrt{3} i}{10} + \frac{23328 \left(- \frac{1}{12} + \frac{\sqrt{3} i}{12}\right)^{4}}{5} \right)} + \left(- \frac{1}{12} - \frac{\sqrt{3} i}{12}\right) \log{\left(x + \frac{13}{10} + \frac{23328 \left(- \frac{1}{12} - \frac{\sqrt{3} i}{12}\right)^{4}}{5} + \frac{13 \sqrt{3} i}{10} \right)} + \operatorname{RootSum} {\left(1944 t^{3} + 1, \left( t \mapsto t \log{\left(\frac{23328 t^{4}}{5} - \frac{78 t}{5} + x \right)} \right)\right)}"," ",0,"log(x + 1)/6 + (-1/12 + sqrt(3)*I/12)*log(x + 13/10 - 13*sqrt(3)*I/10 + 23328*(-1/12 + sqrt(3)*I/12)**4/5) + (-1/12 - sqrt(3)*I/12)*log(x + 13/10 + 23328*(-1/12 - sqrt(3)*I/12)**4/5 + 13*sqrt(3)*I/10) + RootSum(1944*_t**3 + 1, Lambda(_t, _t*log(23328*_t**4/5 - 78*_t/5 + x)))","C",0
166,1,139,0,1.830154," ","integrate(1/x**2/(x**6+4*x**3+3),x)","\frac{\log{\left(x + 1 \right)}}{6} + \left(- \frac{1}{12} - \frac{\sqrt{3} i}{12}\right) \log{\left(x - \frac{8188128 \left(- \frac{1}{12} - \frac{\sqrt{3} i}{12}\right)^{5}}{41} + \frac{39384 \left(- \frac{1}{12} - \frac{\sqrt{3} i}{12}\right)^{2}}{41} \right)} + \left(- \frac{1}{12} + \frac{\sqrt{3} i}{12}\right) \log{\left(x + \frac{39384 \left(- \frac{1}{12} + \frac{\sqrt{3} i}{12}\right)^{2}}{41} - \frac{8188128 \left(- \frac{1}{12} + \frac{\sqrt{3} i}{12}\right)^{5}}{41} \right)} + \operatorname{RootSum} {\left(17496 t^{3} + 1, \left( t \mapsto t \log{\left(- \frac{8188128 t^{5}}{41} + \frac{39384 t^{2}}{41} + x \right)} \right)\right)} - \frac{1}{3 x}"," ",0,"log(x + 1)/6 + (-1/12 - sqrt(3)*I/12)*log(x - 8188128*(-1/12 - sqrt(3)*I/12)**5/41 + 39384*(-1/12 - sqrt(3)*I/12)**2/41) + (-1/12 + sqrt(3)*I/12)*log(x + 39384*(-1/12 + sqrt(3)*I/12)**2/41 - 8188128*(-1/12 + sqrt(3)*I/12)**5/41) + RootSum(17496*_t**3 + 1, Lambda(_t, _t*log(-8188128*_t**5/41 + 39384*_t**2/41 + x))) - 1/(3*x)","C",0
167,1,128,0,1.742126," ","integrate(1/x**3/(x**6+4*x**3+3),x)","- \frac{\log{\left(x + 1 \right)}}{6} + \left(\frac{1}{12} - \frac{\sqrt{3} i}{12}\right) \log{\left(x + \frac{1093}{244} - \frac{1093 \sqrt{3} i}{244} + \frac{787320 \left(\frac{1}{12} - \frac{\sqrt{3} i}{12}\right)^{4}}{61} \right)} + \left(\frac{1}{12} + \frac{\sqrt{3} i}{12}\right) \log{\left(x + \frac{1093}{244} + \frac{787320 \left(\frac{1}{12} + \frac{\sqrt{3} i}{12}\right)^{4}}{61} + \frac{1093 \sqrt{3} i}{244} \right)} + \operatorname{RootSum} {\left(52488 t^{3} - 1, \left( t \mapsto t \log{\left(\frac{787320 t^{4}}{61} + \frac{3279 t}{61} + x \right)} \right)\right)} - \frac{1}{6 x^{2}}"," ",0,"-log(x + 1)/6 + (1/12 - sqrt(3)*I/12)*log(x + 1093/244 - 1093*sqrt(3)*I/244 + 787320*(1/12 - sqrt(3)*I/12)**4/61) + (1/12 + sqrt(3)*I/12)*log(x + 1093/244 + 787320*(1/12 + sqrt(3)*I/12)**4/61 + 1093*sqrt(3)*I/244) + RootSum(52488*_t**3 - 1, Lambda(_t, _t*log(787320*_t**4/61 + 3279*_t/61 + x))) - 1/(6*x**2)","C",0
168,1,141,0,1.835584," ","integrate(1/x**5/(x**6+4*x**3+3),x)","- \frac{\log{\left(x + 1 \right)}}{6} + \left(\frac{1}{12} - \frac{\sqrt{3} i}{12}\right) \log{\left(x + \frac{4782978 \left(\frac{1}{12} - \frac{\sqrt{3} i}{12}\right)^{2}}{547} + \frac{1028869776 \left(\frac{1}{12} - \frac{\sqrt{3} i}{12}\right)^{5}}{547} \right)} + \left(\frac{1}{12} + \frac{\sqrt{3} i}{12}\right) \log{\left(x + \frac{1028869776 \left(\frac{1}{12} + \frac{\sqrt{3} i}{12}\right)^{5}}{547} + \frac{4782978 \left(\frac{1}{12} + \frac{\sqrt{3} i}{12}\right)^{2}}{547} \right)} + \operatorname{RootSum} {\left(472392 t^{3} - 1, \left( t \mapsto t \log{\left(\frac{1028869776 t^{5}}{547} + \frac{4782978 t^{2}}{547} + x \right)} \right)\right)} + \frac{16 x^{3} - 3}{36 x^{4}}"," ",0,"-log(x + 1)/6 + (1/12 - sqrt(3)*I/12)*log(x + 4782978*(1/12 - sqrt(3)*I/12)**2/547 + 1028869776*(1/12 - sqrt(3)*I/12)**5/547) + (1/12 + sqrt(3)*I/12)*log(x + 1028869776*(1/12 + sqrt(3)*I/12)**5/547 + 4782978*(1/12 + sqrt(3)*I/12)**2/547) + RootSum(472392*_t**3 - 1, Lambda(_t, _t*log(1028869776*_t**5/547 + 4782978*_t**2/547 + x))) + (16*x**3 - 3)/(36*x**4)","C",0
169,1,136,0,1.776183," ","integrate(1/x**6/(x**6+4*x**3+3),x)","\frac{\log{\left(x + 1 \right)}}{6} + \left(- \frac{1}{12} + \frac{\sqrt{3} i}{12}\right) \log{\left(x + \frac{88573}{6562} - \frac{88573 \sqrt{3} i}{6562} + \frac{119042784 \left(- \frac{1}{12} + \frac{\sqrt{3} i}{12}\right)^{4}}{3281} \right)} + \left(- \frac{1}{12} - \frac{\sqrt{3} i}{12}\right) \log{\left(x + \frac{88573}{6562} + \frac{119042784 \left(- \frac{1}{12} - \frac{\sqrt{3} i}{12}\right)^{4}}{3281} + \frac{88573 \sqrt{3} i}{6562} \right)} + \operatorname{RootSum} {\left(1417176 t^{3} + 1, \left( t \mapsto t \log{\left(\frac{119042784 t^{4}}{3281} - \frac{531438 t}{3281} + x \right)} \right)\right)} + \frac{10 x^{3} - 3}{45 x^{5}}"," ",0,"log(x + 1)/6 + (-1/12 + sqrt(3)*I/12)*log(x + 88573/6562 - 88573*sqrt(3)*I/6562 + 119042784*(-1/12 + sqrt(3)*I/12)**4/3281) + (-1/12 - sqrt(3)*I/12)*log(x + 88573/6562 + 119042784*(-1/12 - sqrt(3)*I/12)**4/3281 + 88573*sqrt(3)*I/6562) + RootSum(1417176*_t**3 + 1, Lambda(_t, _t*log(119042784*_t**4/3281 - 531438*_t/3281 + x))) + (10*x**3 - 3)/(45*x**5)","C",0
170,1,26,0,0.180496," ","integrate(x**6/(x**6-x**3+1),x)","x + \operatorname{RootSum} {\left(19683 t^{6} - 243 t^{3} + 1, \left( t \mapsto t \log{\left(729 t^{4} - 9 t + x \right)} \right)\right)}"," ",0,"x + RootSum(19683*_t**6 - 243*_t**3 + 1, Lambda(_t, _t*log(729*_t**4 - 9*_t + x)))","A",0
171,1,37,0,0.128107," ","integrate(x**5/(x**6-x**3+1),x)","\frac{\log{\left(x^{6} - x^{3} + 1 \right)}}{6} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x^{3}}{3} - \frac{\sqrt{3}}{3} \right)}}{9}"," ",0,"log(x**6 - x**3 + 1)/6 + sqrt(3)*atan(2*sqrt(3)*x**3/3 - sqrt(3)/3)/9","A",0
172,1,26,0,0.180753," ","integrate(x**4/(x**6-x**3+1),x)","\operatorname{RootSum} {\left(19683 t^{6} + 243 t^{3} + 1, \left( t \mapsto t \log{\left(6561 t^{5} + 54 t^{2} + x \right)} \right)\right)}"," ",0,"RootSum(19683*_t**6 + 243*_t**3 + 1, Lambda(_t, _t*log(6561*_t**5 + 54*_t**2 + x)))","A",0
173,1,24,0,0.178748," ","integrate(x**3/(x**6-x**3+1),x)","\operatorname{RootSum} {\left(19683 t^{6} + 243 t^{3} + 1, \left( t \mapsto t \log{\left(- 1458 t^{4} - 9 t + x \right)} \right)\right)}"," ",0,"RootSum(19683*_t**6 + 243*_t**3 + 1, Lambda(_t, _t*log(-1458*_t**4 - 9*_t + x)))","A",0
174,1,27,0,0.115536," ","integrate(x**2/(x**6-x**3+1),x)","\frac{2 \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x^{3}}{3} - \frac{\sqrt{3}}{3} \right)}}{9}"," ",0,"2*sqrt(3)*atan(2*sqrt(3)*x**3/3 - sqrt(3)/3)/9","A",0
175,1,26,0,0.180064," ","integrate(x/(x**6-x**3+1),x)","\operatorname{RootSum} {\left(19683 t^{6} - 243 t^{3} + 1, \left( t \mapsto t \log{\left(6561 t^{5} - 27 t^{2} + x \right)} \right)\right)}"," ",0,"RootSum(19683*_t**6 - 243*_t**3 + 1, Lambda(_t, _t*log(6561*_t**5 - 27*_t**2 + x)))","A",0
176,1,20,0,0.183652," ","integrate(1/(x**6-x**3+1),x)","\operatorname{RootSum} {\left(19683 t^{6} - 243 t^{3} + 1, \left( t \mapsto t \log{\left(729 t^{4} + x \right)} \right)\right)}"," ",0,"RootSum(19683*_t**6 - 243*_t**3 + 1, Lambda(_t, _t*log(729*_t**4 + x)))","A",0
177,1,41,0,0.148277," ","integrate(1/x/(x**6-x**3+1),x)","\log{\left(x \right)} - \frac{\log{\left(x^{6} - x^{3} + 1 \right)}}{6} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x^{3}}{3} - \frac{\sqrt{3}}{3} \right)}}{9}"," ",0,"log(x) - log(x**6 - x**3 + 1)/6 + sqrt(3)*atan(2*sqrt(3)*x**3/3 - sqrt(3)/3)/9","A",0
178,1,24,0,0.198349," ","integrate(1/x**2/(x**6-x**3+1),x)","\operatorname{RootSum} {\left(19683 t^{6} + 243 t^{3} + 1, \left( t \mapsto t \log{\left(- 27 t^{2} + x \right)} \right)\right)} - \frac{1}{x}"," ",0,"RootSum(19683*_t**6 + 243*_t**3 + 1, Lambda(_t, _t*log(-27*_t**2 + x))) - 1/x","A",0
179,1,31,0,0.205787," ","integrate(1/x**3/(x**6-x**3+1),x)","\operatorname{RootSum} {\left(19683 t^{6} + 243 t^{3} + 1, \left( t \mapsto t \log{\left(729 t^{4} + 9 t + x \right)} \right)\right)} - \frac{1}{2 x^{2}}"," ",0,"RootSum(19683*_t**6 + 243*_t**3 + 1, Lambda(_t, _t*log(729*_t**4 + 9*_t + x))) - 1/(2*x**2)","A",0
180,1,48,0,0.172004," ","integrate(1/x**4/(x**6-x**3+1),x)","\log{\left(x \right)} - \frac{\log{\left(x^{6} - x^{3} + 1 \right)}}{6} - \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x^{3}}{3} - \frac{\sqrt{3}}{3} \right)}}{9} - \frac{1}{3 x^{3}}"," ",0,"log(x) - log(x**6 - x**3 + 1)/6 - sqrt(3)*atan(2*sqrt(3)*x**3/3 - sqrt(3)/3)/9 - 1/(3*x**3)","A",0
181,1,39,0,0.218312," ","integrate(1/x**5/(x**6-x**3+1),x)","\operatorname{RootSum} {\left(19683 t^{6} - 243 t^{3} + 1, \left( t \mapsto t \log{\left(- 6561 t^{5} + 54 t^{2} + x \right)} \right)\right)} + \frac{- 4 x^{3} - 1}{4 x^{4}}"," ",0,"RootSum(19683*_t**6 - 243*_t**3 + 1, Lambda(_t, _t*log(-6561*_t**5 + 54*_t**2 + x))) + (-4*x**3 - 1)/(4*x**4)","A",0
182,1,24,0,0.153959," ","integrate(1/(x**6+x**3+2),x)","\operatorname{RootSum} {\left(1000188 t^{6} + 1323 t^{3} + 1, \left( t \mapsto t \log{\left(- 5292 t^{4} + 7 t + x \right)} \right)\right)}"," ",0,"RootSum(1000188*_t**6 + 1323*_t**3 + 1, Lambda(_t, _t*log(-5292*_t**4 + 7*_t + x)))","A",0
183,1,27,0,0.113181," ","integrate(x**2/(x**6+x**3+2),x)","\frac{2 \sqrt{7} \operatorname{atan}{\left(\frac{2 \sqrt{7} x^{3}}{7} + \frac{\sqrt{7}}{7} \right)}}{21}"," ",0,"2*sqrt(7)*atan(2*sqrt(7)*x**3/7 + sqrt(7)/7)/21","A",0
184,1,24,0,0.147811," ","integrate(x**3/(x**6+x**3+2),x)","\operatorname{RootSum} {\left(250047 t^{6} + 1323 t^{3} + 2, \left( t \mapsto t \log{\left(7938 t^{4} + 21 t + x \right)} \right)\right)}"," ",0,"RootSum(250047*_t**6 + 1323*_t**3 + 2, Lambda(_t, _t*log(7938*_t**4 + 21*_t + x)))","A",0
185,0,0,0,0.000000," ","integrate(x**14*(c*x**6+b*x**3+a)**(1/2),x)","\int x^{14} \sqrt{a + b x^{3} + c x^{6}}\, dx"," ",0,"Integral(x**14*sqrt(a + b*x**3 + c*x**6), x)","F",0
186,0,0,0,0.000000," ","integrate(x**11*(c*x**6+b*x**3+a)**(1/2),x)","\int x^{11} \sqrt{a + b x^{3} + c x^{6}}\, dx"," ",0,"Integral(x**11*sqrt(a + b*x**3 + c*x**6), x)","F",0
187,0,0,0,0.000000," ","integrate(x**8*(c*x**6+b*x**3+a)**(1/2),x)","\int x^{8} \sqrt{a + b x^{3} + c x^{6}}\, dx"," ",0,"Integral(x**8*sqrt(a + b*x**3 + c*x**6), x)","F",0
188,0,0,0,0.000000," ","integrate(x**5*(c*x**6+b*x**3+a)**(1/2),x)","\int x^{5} \sqrt{a + b x^{3} + c x^{6}}\, dx"," ",0,"Integral(x**5*sqrt(a + b*x**3 + c*x**6), x)","F",0
189,0,0,0,0.000000," ","integrate(x**2*(c*x**6+b*x**3+a)**(1/2),x)","\int x^{2} \sqrt{a + b x^{3} + c x^{6}}\, dx"," ",0,"Integral(x**2*sqrt(a + b*x**3 + c*x**6), x)","F",0
190,0,0,0,0.000000," ","integrate((c*x**6+b*x**3+a)**(1/2)/x,x)","\int \frac{\sqrt{a + b x^{3} + c x^{6}}}{x}\, dx"," ",0,"Integral(sqrt(a + b*x**3 + c*x**6)/x, x)","F",0
191,0,0,0,0.000000," ","integrate((c*x**6+b*x**3+a)**(1/2)/x**4,x)","\int \frac{\sqrt{a + b x^{3} + c x^{6}}}{x^{4}}\, dx"," ",0,"Integral(sqrt(a + b*x**3 + c*x**6)/x**4, x)","F",0
192,0,0,0,0.000000," ","integrate((c*x**6+b*x**3+a)**(1/2)/x**7,x)","\int \frac{\sqrt{a + b x^{3} + c x^{6}}}{x^{7}}\, dx"," ",0,"Integral(sqrt(a + b*x**3 + c*x**6)/x**7, x)","F",0
193,0,0,0,0.000000," ","integrate((c*x**6+b*x**3+a)**(1/2)/x**10,x)","\int \frac{\sqrt{a + b x^{3} + c x^{6}}}{x^{10}}\, dx"," ",0,"Integral(sqrt(a + b*x**3 + c*x**6)/x**10, x)","F",0
194,0,0,0,0.000000," ","integrate((c*x**6+b*x**3+a)**(1/2)/x**13,x)","\int \frac{\sqrt{a + b x^{3} + c x^{6}}}{x^{13}}\, dx"," ",0,"Integral(sqrt(a + b*x**3 + c*x**6)/x**13, x)","F",0
195,0,0,0,0.000000," ","integrate((c*x**6+b*x**3+a)**(1/2)/x**16,x)","\int \frac{\sqrt{a + b x^{3} + c x^{6}}}{x^{16}}\, dx"," ",0,"Integral(sqrt(a + b*x**3 + c*x**6)/x**16, x)","F",0
196,0,0,0,0.000000," ","integrate(x**3*(c*x**6+b*x**3+a)**(1/2),x)","\int x^{3} \sqrt{a + b x^{3} + c x^{6}}\, dx"," ",0,"Integral(x**3*sqrt(a + b*x**3 + c*x**6), x)","F",0
197,0,0,0,0.000000," ","integrate(x*(c*x**6+b*x**3+a)**(1/2),x)","\int x \sqrt{a + b x^{3} + c x^{6}}\, dx"," ",0,"Integral(x*sqrt(a + b*x**3 + c*x**6), x)","F",0
198,0,0,0,0.000000," ","integrate((c*x**6+b*x**3+a)**(1/2),x)","\int \sqrt{a + b x^{3} + c x^{6}}\, dx"," ",0,"Integral(sqrt(a + b*x**3 + c*x**6), x)","F",0
199,0,0,0,0.000000," ","integrate((c*x**6+b*x**3+a)**(1/2)/x**2,x)","\int \frac{\sqrt{a + b x^{3} + c x^{6}}}{x^{2}}\, dx"," ",0,"Integral(sqrt(a + b*x**3 + c*x**6)/x**2, x)","F",0
200,0,0,0,0.000000," ","integrate((c*x**6+b*x**3+a)**(1/2)/x**3,x)","\int \frac{\sqrt{a + b x^{3} + c x^{6}}}{x^{3}}\, dx"," ",0,"Integral(sqrt(a + b*x**3 + c*x**6)/x**3, x)","F",0
201,0,0,0,0.000000," ","integrate(x**14*(c*x**6+b*x**3+a)**(3/2),x)","\int x^{14} \left(a + b x^{3} + c x^{6}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**14*(a + b*x**3 + c*x**6)**(3/2), x)","F",0
202,0,0,0,0.000000," ","integrate(x**11*(c*x**6+b*x**3+a)**(3/2),x)","\int x^{11} \left(a + b x^{3} + c x^{6}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**11*(a + b*x**3 + c*x**6)**(3/2), x)","F",0
203,0,0,0,0.000000," ","integrate(x**8*(c*x**6+b*x**3+a)**(3/2),x)","\int x^{8} \left(a + b x^{3} + c x^{6}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**8*(a + b*x**3 + c*x**6)**(3/2), x)","F",0
204,0,0,0,0.000000," ","integrate(x**5*(c*x**6+b*x**3+a)**(3/2),x)","\int x^{5} \left(a + b x^{3} + c x^{6}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**5*(a + b*x**3 + c*x**6)**(3/2), x)","F",0
205,0,0,0,0.000000," ","integrate(x**2*(c*x**6+b*x**3+a)**(3/2),x)","\int x^{2} \left(a + b x^{3} + c x^{6}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**2*(a + b*x**3 + c*x**6)**(3/2), x)","F",0
206,0,0,0,0.000000," ","integrate((c*x**6+b*x**3+a)**(3/2)/x,x)","\int \frac{\left(a + b x^{3} + c x^{6}\right)^{\frac{3}{2}}}{x}\, dx"," ",0,"Integral((a + b*x**3 + c*x**6)**(3/2)/x, x)","F",0
207,0,0,0,0.000000," ","integrate((c*x**6+b*x**3+a)**(3/2)/x**4,x)","\int \frac{\left(a + b x^{3} + c x^{6}\right)^{\frac{3}{2}}}{x^{4}}\, dx"," ",0,"Integral((a + b*x**3 + c*x**6)**(3/2)/x**4, x)","F",0
208,0,0,0,0.000000," ","integrate((c*x**6+b*x**3+a)**(3/2)/x**7,x)","\int \frac{\left(a + b x^{3} + c x^{6}\right)^{\frac{3}{2}}}{x^{7}}\, dx"," ",0,"Integral((a + b*x**3 + c*x**6)**(3/2)/x**7, x)","F",0
209,0,0,0,0.000000," ","integrate((c*x**6+b*x**3+a)**(3/2)/x**10,x)","\int \frac{\left(a + b x^{3} + c x^{6}\right)^{\frac{3}{2}}}{x^{10}}\, dx"," ",0,"Integral((a + b*x**3 + c*x**6)**(3/2)/x**10, x)","F",0
210,0,0,0,0.000000," ","integrate((c*x**6+b*x**3+a)**(3/2)/x**13,x)","\int \frac{\left(a + b x^{3} + c x^{6}\right)^{\frac{3}{2}}}{x^{13}}\, dx"," ",0,"Integral((a + b*x**3 + c*x**6)**(3/2)/x**13, x)","F",0
211,0,0,0,0.000000," ","integrate((c*x**6+b*x**3+a)**(3/2)/x**16,x)","\int \frac{\left(a + b x^{3} + c x^{6}\right)^{\frac{3}{2}}}{x^{16}}\, dx"," ",0,"Integral((a + b*x**3 + c*x**6)**(3/2)/x**16, x)","F",0
212,0,0,0,0.000000," ","integrate((c*x**6+b*x**3+a)**(3/2)/x**19,x)","\int \frac{\left(a + b x^{3} + c x^{6}\right)^{\frac{3}{2}}}{x^{19}}\, dx"," ",0,"Integral((a + b*x**3 + c*x**6)**(3/2)/x**19, x)","F",0
213,0,0,0,0.000000," ","integrate((c*x**6+b*x**3+a)**(3/2)/x**22,x)","\int \frac{\left(a + b x^{3} + c x^{6}\right)^{\frac{3}{2}}}{x^{22}}\, dx"," ",0,"Integral((a + b*x**3 + c*x**6)**(3/2)/x**22, x)","F",0
214,0,0,0,0.000000," ","integrate(x**3*(c*x**6+b*x**3+a)**(3/2),x)","\int x^{3} \left(a + b x^{3} + c x^{6}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**3*(a + b*x**3 + c*x**6)**(3/2), x)","F",0
215,0,0,0,0.000000," ","integrate(x*(c*x**6+b*x**3+a)**(3/2),x)","\int x \left(a + b x^{3} + c x^{6}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x*(a + b*x**3 + c*x**6)**(3/2), x)","F",0
216,0,0,0,0.000000," ","integrate((c*x**6+b*x**3+a)**(3/2),x)","\int \left(a + b x^{3} + c x^{6}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b*x**3 + c*x**6)**(3/2), x)","F",0
217,0,0,0,0.000000," ","integrate((c*x**6+b*x**3+a)**(3/2)/x**2,x)","\int \frac{\left(a + b x^{3} + c x^{6}\right)^{\frac{3}{2}}}{x^{2}}\, dx"," ",0,"Integral((a + b*x**3 + c*x**6)**(3/2)/x**2, x)","F",0
218,0,0,0,0.000000," ","integrate((c*x**6+b*x**3+a)**(3/2)/x**3,x)","\int \frac{\left(a + b x^{3} + c x^{6}\right)^{\frac{3}{2}}}{x^{3}}\, dx"," ",0,"Integral((a + b*x**3 + c*x**6)**(3/2)/x**3, x)","F",0
219,0,0,0,0.000000," ","integrate(x**14/(c*x**6+b*x**3+a)**(1/2),x)","\int \frac{x^{14}}{\sqrt{a + b x^{3} + c x^{6}}}\, dx"," ",0,"Integral(x**14/sqrt(a + b*x**3 + c*x**6), x)","F",0
220,0,0,0,0.000000," ","integrate(x**11/(c*x**6+b*x**3+a)**(1/2),x)","\int \frac{x^{11}}{\sqrt{a + b x^{3} + c x^{6}}}\, dx"," ",0,"Integral(x**11/sqrt(a + b*x**3 + c*x**6), x)","F",0
221,0,0,0,0.000000," ","integrate(x**8/(c*x**6+b*x**3+a)**(1/2),x)","\int \frac{x^{8}}{\sqrt{a + b x^{3} + c x^{6}}}\, dx"," ",0,"Integral(x**8/sqrt(a + b*x**3 + c*x**6), x)","F",0
222,0,0,0,0.000000," ","integrate(x**5/(c*x**6+b*x**3+a)**(1/2),x)","\int \frac{x^{5}}{\sqrt{a + b x^{3} + c x^{6}}}\, dx"," ",0,"Integral(x**5/sqrt(a + b*x**3 + c*x**6), x)","F",0
223,0,0,0,0.000000," ","integrate(x**2/(c*x**6+b*x**3+a)**(1/2),x)","\int \frac{x^{2}}{\sqrt{a + b x^{3} + c x^{6}}}\, dx"," ",0,"Integral(x**2/sqrt(a + b*x**3 + c*x**6), x)","F",0
224,0,0,0,0.000000," ","integrate(1/x/(c*x**6+b*x**3+a)**(1/2),x)","\int \frac{1}{x \sqrt{a + b x^{3} + c x^{6}}}\, dx"," ",0,"Integral(1/(x*sqrt(a + b*x**3 + c*x**6)), x)","F",0
225,0,0,0,0.000000," ","integrate(1/x**4/(c*x**6+b*x**3+a)**(1/2),x)","\int \frac{1}{x^{4} \sqrt{a + b x^{3} + c x^{6}}}\, dx"," ",0,"Integral(1/(x**4*sqrt(a + b*x**3 + c*x**6)), x)","F",0
226,0,0,0,0.000000," ","integrate(1/x**7/(c*x**6+b*x**3+a)**(1/2),x)","\int \frac{1}{x^{7} \sqrt{a + b x^{3} + c x^{6}}}\, dx"," ",0,"Integral(1/(x**7*sqrt(a + b*x**3 + c*x**6)), x)","F",0
227,0,0,0,0.000000," ","integrate(1/x**10/(c*x**6+b*x**3+a)**(1/2),x)","\int \frac{1}{x^{10} \sqrt{a + b x^{3} + c x^{6}}}\, dx"," ",0,"Integral(1/(x**10*sqrt(a + b*x**3 + c*x**6)), x)","F",0
228,0,0,0,0.000000," ","integrate(1/x**13/(c*x**6+b*x**3+a)**(1/2),x)","\int \frac{1}{x^{13} \sqrt{a + b x^{3} + c x^{6}}}\, dx"," ",0,"Integral(1/(x**13*sqrt(a + b*x**3 + c*x**6)), x)","F",0
229,0,0,0,0.000000," ","integrate(x**3/(c*x**6+b*x**3+a)**(1/2),x)","\int \frac{x^{3}}{\sqrt{a + b x^{3} + c x^{6}}}\, dx"," ",0,"Integral(x**3/sqrt(a + b*x**3 + c*x**6), x)","F",0
230,0,0,0,0.000000," ","integrate(x/(c*x**6+b*x**3+a)**(1/2),x)","\int \frac{x}{\sqrt{a + b x^{3} + c x^{6}}}\, dx"," ",0,"Integral(x/sqrt(a + b*x**3 + c*x**6), x)","F",0
231,0,0,0,0.000000," ","integrate(1/(c*x**6+b*x**3+a)**(1/2),x)","\int \frac{1}{\sqrt{a + b x^{3} + c x^{6}}}\, dx"," ",0,"Integral(1/sqrt(a + b*x**3 + c*x**6), x)","F",0
232,0,0,0,0.000000," ","integrate(1/x**2/(c*x**6+b*x**3+a)**(1/2),x)","\int \frac{1}{x^{2} \sqrt{a + b x^{3} + c x^{6}}}\, dx"," ",0,"Integral(1/(x**2*sqrt(a + b*x**3 + c*x**6)), x)","F",0
233,0,0,0,0.000000," ","integrate(1/x**3/(c*x**6+b*x**3+a)**(1/2),x)","\int \frac{1}{x^{3} \sqrt{a + b x^{3} + c x^{6}}}\, dx"," ",0,"Integral(1/(x**3*sqrt(a + b*x**3 + c*x**6)), x)","F",0
234,0,0,0,0.000000," ","integrate(x**14/(c*x**6+b*x**3+a)**(3/2),x)","\int \frac{x^{14}}{\left(a + b x^{3} + c x^{6}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**14/(a + b*x**3 + c*x**6)**(3/2), x)","F",0
235,0,0,0,0.000000," ","integrate(x**11/(c*x**6+b*x**3+a)**(3/2),x)","\int \frac{x^{11}}{\left(a + b x^{3} + c x^{6}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**11/(a + b*x**3 + c*x**6)**(3/2), x)","F",0
236,0,0,0,0.000000," ","integrate(x**8/(c*x**6+b*x**3+a)**(3/2),x)","\int \frac{x^{8}}{\left(a + b x^{3} + c x^{6}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**8/(a + b*x**3 + c*x**6)**(3/2), x)","F",0
237,0,0,0,0.000000," ","integrate(x**5/(c*x**6+b*x**3+a)**(3/2),x)","\int \frac{x^{5}}{\left(a + b x^{3} + c x^{6}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**5/(a + b*x**3 + c*x**6)**(3/2), x)","F",0
238,0,0,0,0.000000," ","integrate(x**2/(c*x**6+b*x**3+a)**(3/2),x)","\int \frac{x^{2}}{\left(a + b x^{3} + c x^{6}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**2/(a + b*x**3 + c*x**6)**(3/2), x)","F",0
239,0,0,0,0.000000," ","integrate(1/x/(c*x**6+b*x**3+a)**(3/2),x)","\int \frac{1}{x \left(a + b x^{3} + c x^{6}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x*(a + b*x**3 + c*x**6)**(3/2)), x)","F",0
240,0,0,0,0.000000," ","integrate(1/x**4/(c*x**6+b*x**3+a)**(3/2),x)","\int \frac{1}{x^{4} \left(a + b x^{3} + c x^{6}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**4*(a + b*x**3 + c*x**6)**(3/2)), x)","F",0
241,0,0,0,0.000000," ","integrate(1/x**7/(c*x**6+b*x**3+a)**(3/2),x)","\int \frac{1}{x^{7} \left(a + b x^{3} + c x^{6}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**7*(a + b*x**3 + c*x**6)**(3/2)), x)","F",0
242,0,0,0,0.000000," ","integrate(1/x**10/(c*x**6+b*x**3+a)**(3/2),x)","\int \frac{1}{x^{10} \left(a + b x^{3} + c x^{6}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**10*(a + b*x**3 + c*x**6)**(3/2)), x)","F",0
243,0,0,0,0.000000," ","integrate(x**3/(c*x**6+b*x**3+a)**(3/2),x)","\int \frac{x^{3}}{\left(a + b x^{3} + c x^{6}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**3/(a + b*x**3 + c*x**6)**(3/2), x)","F",0
244,0,0,0,0.000000," ","integrate(x/(c*x**6+b*x**3+a)**(3/2),x)","\int \frac{x}{\left(a + b x^{3} + c x^{6}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x/(a + b*x**3 + c*x**6)**(3/2), x)","F",0
245,0,0,0,0.000000," ","integrate(1/(c*x**6+b*x**3+a)**(3/2),x)","\int \frac{1}{\left(a + b x^{3} + c x^{6}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*x**3 + c*x**6)**(-3/2), x)","F",0
246,0,0,0,0.000000," ","integrate(1/x**2/(c*x**6+b*x**3+a)**(3/2),x)","\int \frac{1}{x^{2} \left(a + b x^{3} + c x^{6}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**2*(a + b*x**3 + c*x**6)**(3/2)), x)","F",0
247,0,0,0,0.000000," ","integrate(1/x**3/(c*x**6+b*x**3+a)**(3/2),x)","\int \frac{1}{x^{3} \left(a + b x^{3} + c x^{6}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**3*(a + b*x**3 + c*x**6)**(3/2)), x)","F",0
248,1,1510,0,5.824153," ","integrate((d*x)**m*(c*x**6+b*x**3+a)**2,x)","\begin{cases} \frac{- \frac{a^{2}}{12 x^{12}} - \frac{2 a b}{9 x^{9}} - \frac{a c}{3 x^{6}} - \frac{b^{2}}{6 x^{6}} - \frac{2 b c}{3 x^{3}} + c^{2} \log{\left(x \right)}}{d^{13}} & \text{for}\: m = -13 \\\frac{- \frac{a^{2}}{9 x^{9}} - \frac{a b}{3 x^{6}} - \frac{2 a c}{3 x^{3}} - \frac{b^{2}}{3 x^{3}} + 2 b c \log{\left(x \right)} + \frac{c^{2} x^{3}}{3}}{d^{10}} & \text{for}\: m = -10 \\\frac{- \frac{a^{2}}{6 x^{6}} - \frac{2 a b}{3 x^{3}} + 2 a c \log{\left(x \right)} + b^{2} \log{\left(x \right)} + \frac{2 b c x^{3}}{3} + \frac{c^{2} x^{6}}{6}}{d^{7}} & \text{for}\: m = -7 \\\frac{- \frac{a^{2}}{3 x^{3}} + 2 a b \log{\left(x \right)} + \frac{2 a c x^{3}}{3} + \frac{b^{2} x^{3}}{3} + \frac{b c x^{6}}{3} + \frac{c^{2} x^{9}}{9}}{d^{4}} & \text{for}\: m = -4 \\\frac{a^{2} \log{\left(x \right)} + \frac{2 a b x^{3}}{3} + \frac{a c x^{6}}{3} + \frac{b^{2} x^{6}}{6} + \frac{2 b c x^{9}}{9} + \frac{c^{2} x^{12}}{12}}{d} & \text{for}\: m = -1 \\\frac{a^{2} d^{m} m^{4} x x^{m}}{m^{5} + 35 m^{4} + 445 m^{3} + 2485 m^{2} + 5714 m + 3640} + \frac{34 a^{2} d^{m} m^{3} x x^{m}}{m^{5} + 35 m^{4} + 445 m^{3} + 2485 m^{2} + 5714 m + 3640} + \frac{411 a^{2} d^{m} m^{2} x x^{m}}{m^{5} + 35 m^{4} + 445 m^{3} + 2485 m^{2} + 5714 m + 3640} + \frac{2074 a^{2} d^{m} m x x^{m}}{m^{5} + 35 m^{4} + 445 m^{3} + 2485 m^{2} + 5714 m + 3640} + \frac{3640 a^{2} d^{m} x x^{m}}{m^{5} + 35 m^{4} + 445 m^{3} + 2485 m^{2} + 5714 m + 3640} + \frac{2 a b d^{m} m^{4} x^{4} x^{m}}{m^{5} + 35 m^{4} + 445 m^{3} + 2485 m^{2} + 5714 m + 3640} + \frac{62 a b d^{m} m^{3} x^{4} x^{m}}{m^{5} + 35 m^{4} + 445 m^{3} + 2485 m^{2} + 5714 m + 3640} + \frac{642 a b d^{m} m^{2} x^{4} x^{m}}{m^{5} + 35 m^{4} + 445 m^{3} + 2485 m^{2} + 5714 m + 3640} + \frac{2402 a b d^{m} m x^{4} x^{m}}{m^{5} + 35 m^{4} + 445 m^{3} + 2485 m^{2} + 5714 m + 3640} + \frac{1820 a b d^{m} x^{4} x^{m}}{m^{5} + 35 m^{4} + 445 m^{3} + 2485 m^{2} + 5714 m + 3640} + \frac{2 a c d^{m} m^{4} x^{7} x^{m}}{m^{5} + 35 m^{4} + 445 m^{3} + 2485 m^{2} + 5714 m + 3640} + \frac{56 a c d^{m} m^{3} x^{7} x^{m}}{m^{5} + 35 m^{4} + 445 m^{3} + 2485 m^{2} + 5714 m + 3640} + \frac{498 a c d^{m} m^{2} x^{7} x^{m}}{m^{5} + 35 m^{4} + 445 m^{3} + 2485 m^{2} + 5714 m + 3640} + \frac{1484 a c d^{m} m x^{7} x^{m}}{m^{5} + 35 m^{4} + 445 m^{3} + 2485 m^{2} + 5714 m + 3640} + \frac{1040 a c d^{m} x^{7} x^{m}}{m^{5} + 35 m^{4} + 445 m^{3} + 2485 m^{2} + 5714 m + 3640} + \frac{b^{2} d^{m} m^{4} x^{7} x^{m}}{m^{5} + 35 m^{4} + 445 m^{3} + 2485 m^{2} + 5714 m + 3640} + \frac{28 b^{2} d^{m} m^{3} x^{7} x^{m}}{m^{5} + 35 m^{4} + 445 m^{3} + 2485 m^{2} + 5714 m + 3640} + \frac{249 b^{2} d^{m} m^{2} x^{7} x^{m}}{m^{5} + 35 m^{4} + 445 m^{3} + 2485 m^{2} + 5714 m + 3640} + \frac{742 b^{2} d^{m} m x^{7} x^{m}}{m^{5} + 35 m^{4} + 445 m^{3} + 2485 m^{2} + 5714 m + 3640} + \frac{520 b^{2} d^{m} x^{7} x^{m}}{m^{5} + 35 m^{4} + 445 m^{3} + 2485 m^{2} + 5714 m + 3640} + \frac{2 b c d^{m} m^{4} x^{10} x^{m}}{m^{5} + 35 m^{4} + 445 m^{3} + 2485 m^{2} + 5714 m + 3640} + \frac{50 b c d^{m} m^{3} x^{10} x^{m}}{m^{5} + 35 m^{4} + 445 m^{3} + 2485 m^{2} + 5714 m + 3640} + \frac{390 b c d^{m} m^{2} x^{10} x^{m}}{m^{5} + 35 m^{4} + 445 m^{3} + 2485 m^{2} + 5714 m + 3640} + \frac{1070 b c d^{m} m x^{10} x^{m}}{m^{5} + 35 m^{4} + 445 m^{3} + 2485 m^{2} + 5714 m + 3640} + \frac{728 b c d^{m} x^{10} x^{m}}{m^{5} + 35 m^{4} + 445 m^{3} + 2485 m^{2} + 5714 m + 3640} + \frac{c^{2} d^{m} m^{4} x^{13} x^{m}}{m^{5} + 35 m^{4} + 445 m^{3} + 2485 m^{2} + 5714 m + 3640} + \frac{22 c^{2} d^{m} m^{3} x^{13} x^{m}}{m^{5} + 35 m^{4} + 445 m^{3} + 2485 m^{2} + 5714 m + 3640} + \frac{159 c^{2} d^{m} m^{2} x^{13} x^{m}}{m^{5} + 35 m^{4} + 445 m^{3} + 2485 m^{2} + 5714 m + 3640} + \frac{418 c^{2} d^{m} m x^{13} x^{m}}{m^{5} + 35 m^{4} + 445 m^{3} + 2485 m^{2} + 5714 m + 3640} + \frac{280 c^{2} d^{m} x^{13} x^{m}}{m^{5} + 35 m^{4} + 445 m^{3} + 2485 m^{2} + 5714 m + 3640} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-a**2/(12*x**12) - 2*a*b/(9*x**9) - a*c/(3*x**6) - b**2/(6*x**6) - 2*b*c/(3*x**3) + c**2*log(x))/d**13, Eq(m, -13)), ((-a**2/(9*x**9) - a*b/(3*x**6) - 2*a*c/(3*x**3) - b**2/(3*x**3) + 2*b*c*log(x) + c**2*x**3/3)/d**10, Eq(m, -10)), ((-a**2/(6*x**6) - 2*a*b/(3*x**3) + 2*a*c*log(x) + b**2*log(x) + 2*b*c*x**3/3 + c**2*x**6/6)/d**7, Eq(m, -7)), ((-a**2/(3*x**3) + 2*a*b*log(x) + 2*a*c*x**3/3 + b**2*x**3/3 + b*c*x**6/3 + c**2*x**9/9)/d**4, Eq(m, -4)), ((a**2*log(x) + 2*a*b*x**3/3 + a*c*x**6/3 + b**2*x**6/6 + 2*b*c*x**9/9 + c**2*x**12/12)/d, Eq(m, -1)), (a**2*d**m*m**4*x*x**m/(m**5 + 35*m**4 + 445*m**3 + 2485*m**2 + 5714*m + 3640) + 34*a**2*d**m*m**3*x*x**m/(m**5 + 35*m**4 + 445*m**3 + 2485*m**2 + 5714*m + 3640) + 411*a**2*d**m*m**2*x*x**m/(m**5 + 35*m**4 + 445*m**3 + 2485*m**2 + 5714*m + 3640) + 2074*a**2*d**m*m*x*x**m/(m**5 + 35*m**4 + 445*m**3 + 2485*m**2 + 5714*m + 3640) + 3640*a**2*d**m*x*x**m/(m**5 + 35*m**4 + 445*m**3 + 2485*m**2 + 5714*m + 3640) + 2*a*b*d**m*m**4*x**4*x**m/(m**5 + 35*m**4 + 445*m**3 + 2485*m**2 + 5714*m + 3640) + 62*a*b*d**m*m**3*x**4*x**m/(m**5 + 35*m**4 + 445*m**3 + 2485*m**2 + 5714*m + 3640) + 642*a*b*d**m*m**2*x**4*x**m/(m**5 + 35*m**4 + 445*m**3 + 2485*m**2 + 5714*m + 3640) + 2402*a*b*d**m*m*x**4*x**m/(m**5 + 35*m**4 + 445*m**3 + 2485*m**2 + 5714*m + 3640) + 1820*a*b*d**m*x**4*x**m/(m**5 + 35*m**4 + 445*m**3 + 2485*m**2 + 5714*m + 3640) + 2*a*c*d**m*m**4*x**7*x**m/(m**5 + 35*m**4 + 445*m**3 + 2485*m**2 + 5714*m + 3640) + 56*a*c*d**m*m**3*x**7*x**m/(m**5 + 35*m**4 + 445*m**3 + 2485*m**2 + 5714*m + 3640) + 498*a*c*d**m*m**2*x**7*x**m/(m**5 + 35*m**4 + 445*m**3 + 2485*m**2 + 5714*m + 3640) + 1484*a*c*d**m*m*x**7*x**m/(m**5 + 35*m**4 + 445*m**3 + 2485*m**2 + 5714*m + 3640) + 1040*a*c*d**m*x**7*x**m/(m**5 + 35*m**4 + 445*m**3 + 2485*m**2 + 5714*m + 3640) + b**2*d**m*m**4*x**7*x**m/(m**5 + 35*m**4 + 445*m**3 + 2485*m**2 + 5714*m + 3640) + 28*b**2*d**m*m**3*x**7*x**m/(m**5 + 35*m**4 + 445*m**3 + 2485*m**2 + 5714*m + 3640) + 249*b**2*d**m*m**2*x**7*x**m/(m**5 + 35*m**4 + 445*m**3 + 2485*m**2 + 5714*m + 3640) + 742*b**2*d**m*m*x**7*x**m/(m**5 + 35*m**4 + 445*m**3 + 2485*m**2 + 5714*m + 3640) + 520*b**2*d**m*x**7*x**m/(m**5 + 35*m**4 + 445*m**3 + 2485*m**2 + 5714*m + 3640) + 2*b*c*d**m*m**4*x**10*x**m/(m**5 + 35*m**4 + 445*m**3 + 2485*m**2 + 5714*m + 3640) + 50*b*c*d**m*m**3*x**10*x**m/(m**5 + 35*m**4 + 445*m**3 + 2485*m**2 + 5714*m + 3640) + 390*b*c*d**m*m**2*x**10*x**m/(m**5 + 35*m**4 + 445*m**3 + 2485*m**2 + 5714*m + 3640) + 1070*b*c*d**m*m*x**10*x**m/(m**5 + 35*m**4 + 445*m**3 + 2485*m**2 + 5714*m + 3640) + 728*b*c*d**m*x**10*x**m/(m**5 + 35*m**4 + 445*m**3 + 2485*m**2 + 5714*m + 3640) + c**2*d**m*m**4*x**13*x**m/(m**5 + 35*m**4 + 445*m**3 + 2485*m**2 + 5714*m + 3640) + 22*c**2*d**m*m**3*x**13*x**m/(m**5 + 35*m**4 + 445*m**3 + 2485*m**2 + 5714*m + 3640) + 159*c**2*d**m*m**2*x**13*x**m/(m**5 + 35*m**4 + 445*m**3 + 2485*m**2 + 5714*m + 3640) + 418*c**2*d**m*m*x**13*x**m/(m**5 + 35*m**4 + 445*m**3 + 2485*m**2 + 5714*m + 3640) + 280*c**2*d**m*x**13*x**m/(m**5 + 35*m**4 + 445*m**3 + 2485*m**2 + 5714*m + 3640), True))","A",0
249,1,314,0,1.467674," ","integrate((d*x)**m*(c*x**6+b*x**3+a),x)","\begin{cases} \frac{- \frac{a}{6 x^{6}} - \frac{b}{3 x^{3}} + c \log{\left(x \right)}}{d^{7}} & \text{for}\: m = -7 \\\frac{- \frac{a}{3 x^{3}} + b \log{\left(x \right)} + \frac{c x^{3}}{3}}{d^{4}} & \text{for}\: m = -4 \\\frac{a \log{\left(x \right)} + \frac{b x^{3}}{3} + \frac{c x^{6}}{6}}{d} & \text{for}\: m = -1 \\\frac{a d^{m} m^{2} x x^{m}}{m^{3} + 12 m^{2} + 39 m + 28} + \frac{11 a d^{m} m x x^{m}}{m^{3} + 12 m^{2} + 39 m + 28} + \frac{28 a d^{m} x x^{m}}{m^{3} + 12 m^{2} + 39 m + 28} + \frac{b d^{m} m^{2} x^{4} x^{m}}{m^{3} + 12 m^{2} + 39 m + 28} + \frac{8 b d^{m} m x^{4} x^{m}}{m^{3} + 12 m^{2} + 39 m + 28} + \frac{7 b d^{m} x^{4} x^{m}}{m^{3} + 12 m^{2} + 39 m + 28} + \frac{c d^{m} m^{2} x^{7} x^{m}}{m^{3} + 12 m^{2} + 39 m + 28} + \frac{5 c d^{m} m x^{7} x^{m}}{m^{3} + 12 m^{2} + 39 m + 28} + \frac{4 c d^{m} x^{7} x^{m}}{m^{3} + 12 m^{2} + 39 m + 28} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-a/(6*x**6) - b/(3*x**3) + c*log(x))/d**7, Eq(m, -7)), ((-a/(3*x**3) + b*log(x) + c*x**3/3)/d**4, Eq(m, -4)), ((a*log(x) + b*x**3/3 + c*x**6/6)/d, Eq(m, -1)), (a*d**m*m**2*x*x**m/(m**3 + 12*m**2 + 39*m + 28) + 11*a*d**m*m*x*x**m/(m**3 + 12*m**2 + 39*m + 28) + 28*a*d**m*x*x**m/(m**3 + 12*m**2 + 39*m + 28) + b*d**m*m**2*x**4*x**m/(m**3 + 12*m**2 + 39*m + 28) + 8*b*d**m*m*x**4*x**m/(m**3 + 12*m**2 + 39*m + 28) + 7*b*d**m*x**4*x**m/(m**3 + 12*m**2 + 39*m + 28) + c*d**m*m**2*x**7*x**m/(m**3 + 12*m**2 + 39*m + 28) + 5*c*d**m*m*x**7*x**m/(m**3 + 12*m**2 + 39*m + 28) + 4*c*d**m*x**7*x**m/(m**3 + 12*m**2 + 39*m + 28), True))","A",0
250,-1,0,0,0.000000," ","integrate((d*x)**m/(c*x**6+b*x**3+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
251,-1,0,0,0.000000," ","integrate((d*x)**m/(c*x**6+b*x**3+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
252,0,0,0,0.000000," ","integrate((d*x)**m*(c*x**6+b*x**3+a)**(3/2),x)","\int \left(d x\right)^{m} \left(a + b x^{3} + c x^{6}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((d*x)**m*(a + b*x**3 + c*x**6)**(3/2), x)","F",0
253,0,0,0,0.000000," ","integrate((d*x)**m*(c*x**6+b*x**3+a)**(1/2),x)","\int \left(d x\right)^{m} \sqrt{a + b x^{3} + c x^{6}}\, dx"," ",0,"Integral((d*x)**m*sqrt(a + b*x**3 + c*x**6), x)","F",0
254,0,0,0,0.000000," ","integrate((d*x)**m/(c*x**6+b*x**3+a)**(1/2),x)","\int \frac{\left(d x\right)^{m}}{\sqrt{a + b x^{3} + c x^{6}}}\, dx"," ",0,"Integral((d*x)**m/sqrt(a + b*x**3 + c*x**6), x)","F",0
255,0,0,0,0.000000," ","integrate((d*x)**m/(c*x**6+b*x**3+a)**(3/2),x)","\int \frac{\left(d x\right)^{m}}{\left(a + b x^{3} + c x^{6}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d*x)**m/(a + b*x**3 + c*x**6)**(3/2), x)","F",0
256,-1,0,0,0.000000," ","integrate((d*x)**m*(c*x**6+b*x**3+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
257,-1,0,0,0.000000," ","integrate(x**8*(c*x**6+b*x**3+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
258,-1,0,0,0.000000," ","integrate(x**5*(c*x**6+b*x**3+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
259,-1,0,0,0.000000," ","integrate(x**2*(c*x**6+b*x**3+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
260,-1,0,0,0.000000," ","integrate(x**4*(c*x**6+b*x**3+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
261,-1,0,0,0.000000," ","integrate(x**3*(c*x**6+b*x**3+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
262,-1,0,0,0.000000," ","integrate(x*(c*x**6+b*x**3+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
263,-1,0,0,0.000000," ","integrate((c*x**6+b*x**3+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
264,-1,0,0,0.000000," ","integrate((c*x**6+b*x**3+a)**p/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
265,-1,0,0,0.000000," ","integrate((c*x**6+b*x**3+a)**p/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
266,-1,0,0,0.000000," ","integrate((c*x**6+b*x**3+a)**p/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
267,-1,0,0,0.000000," ","integrate((c*x**6+b*x**3+a)**p/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
268,-1,0,0,0.000000," ","integrate((c*x**6+b*x**3+a)**p/x**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
269,-1,0,0,0.000000," ","integrate((c*x**6+b*x**3+a)**p/x**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
270,-1,0,0,0.000000," ","integrate((c*x**6+b*x**3+a)**p/x**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
271,0,0,0,0.000000," ","integrate(x**m/(x**8+2*x**4+1),x)","\int \frac{x^{m}}{\left(x^{4} + 1\right)^{2}}\, dx"," ",0,"Integral(x**m/(x**4 + 1)**2, x)","F",0
272,1,22,0,0.126066," ","integrate(x**9/(x**8+2*x**4+1),x)","\frac{x^{2}}{2} + \frac{x^{2}}{4 x^{4} + 4} - \frac{3 \operatorname{atan}{\left(x^{2} \right)}}{4}"," ",0,"x**2/2 + x**2/(4*x**4 + 4) - 3*atan(x**2)/4","A",0
273,1,15,0,0.106317," ","integrate(x**7/(x**8+2*x**4+1),x)","\frac{\log{\left(x^{4} + 1 \right)}}{4} + \frac{1}{4 x^{4} + 4}"," ",0,"log(x**4 + 1)/4 + 1/(4*x**4 + 4)","A",0
274,1,15,0,0.117702," ","integrate(x**5/(x**8+2*x**4+1),x)","- \frac{x^{2}}{4 x^{4} + 4} + \frac{\operatorname{atan}{\left(x^{2} \right)}}{4}"," ",0,"-x**2/(4*x**4 + 4) + atan(x**2)/4","A",0
275,1,8,0,0.093512," ","integrate(x**3/(x**8+2*x**4+1),x)","- \frac{1}{4 x^{4} + 4}"," ",0,"-1/(4*x**4 + 4)","A",0
276,1,15,0,0.115663," ","integrate(x/(x**8+2*x**4+1),x)","\frac{x^{2}}{4 x^{4} + 4} + \frac{\operatorname{atan}{\left(x^{2} \right)}}{4}"," ",0,"x**2/(4*x**4 + 4) + atan(x**2)/4","A",0
277,1,19,0,0.125274," ","integrate(1/x/(x**8+2*x**4+1),x)","\log{\left(x \right)} - \frac{\log{\left(x^{4} + 1 \right)}}{4} + \frac{1}{4 x^{4} + 4}"," ",0,"log(x) - log(x**4 + 1)/4 + 1/(4*x**4 + 4)","A",0
278,1,26,0,0.146588," ","integrate(1/x**3/(x**8+2*x**4+1),x)","\frac{- 3 x^{4} - 2}{4 x^{6} + 4 x^{2}} - \frac{3 \operatorname{atan}{\left(x^{2} \right)}}{4}"," ",0,"(-3*x**4 - 2)/(4*x**6 + 4*x**2) - 3*atan(x**2)/4","A",0
279,1,31,0,0.152879," ","integrate(1/x**5/(x**8+2*x**4+1),x)","\frac{- 2 x^{4} - 1}{4 x^{8} + 4 x^{4}} - 2 \log{\left(x \right)} + \frac{\log{\left(x^{4} + 1 \right)}}{2}"," ",0,"(-2*x**4 - 1)/(4*x**8 + 4*x**4) - 2*log(x) + log(x**4 + 1)/2","A",0
280,1,29,0,0.170458," ","integrate(1/x**7/(x**8+2*x**4+1),x)","\frac{5 \operatorname{atan}{\left(x^{2} \right)}}{4} + \frac{15 x^{8} + 10 x^{4} - 2}{12 x^{10} + 12 x^{6}}"," ",0,"5*atan(x**2)/4 + (15*x**8 + 10*x**4 - 2)/(12*x**10 + 12*x**6)","A",0
281,1,90,0,0.175525," ","integrate(x**8/(x**8+2*x**4+1),x)","x + \frac{x}{4 x^{4} + 4} + \frac{5 \sqrt{2} \log{\left(x^{2} - \sqrt{2} x + 1 \right)}}{32} - \frac{5 \sqrt{2} \log{\left(x^{2} + \sqrt{2} x + 1 \right)}}{32} - \frac{5 \sqrt{2} \operatorname{atan}{\left(\sqrt{2} x - 1 \right)}}{16} - \frac{5 \sqrt{2} \operatorname{atan}{\left(\sqrt{2} x + 1 \right)}}{16}"," ",0,"x + x/(4*x**4 + 4) + 5*sqrt(2)*log(x**2 - sqrt(2)*x + 1)/32 - 5*sqrt(2)*log(x**2 + sqrt(2)*x + 1)/32 - 5*sqrt(2)*atan(sqrt(2)*x - 1)/16 - 5*sqrt(2)*atan(sqrt(2)*x + 1)/16","A",0
282,1,90,0,0.178641," ","integrate(x**6/(x**8+2*x**4+1),x)","- \frac{x^{3}}{4 x^{4} + 4} + \frac{3 \sqrt{2} \log{\left(x^{2} - \sqrt{2} x + 1 \right)}}{32} - \frac{3 \sqrt{2} \log{\left(x^{2} + \sqrt{2} x + 1 \right)}}{32} + \frac{3 \sqrt{2} \operatorname{atan}{\left(\sqrt{2} x - 1 \right)}}{16} + \frac{3 \sqrt{2} \operatorname{atan}{\left(\sqrt{2} x + 1 \right)}}{16}"," ",0,"-x**3/(4*x**4 + 4) + 3*sqrt(2)*log(x**2 - sqrt(2)*x + 1)/32 - 3*sqrt(2)*log(x**2 + sqrt(2)*x + 1)/32 + 3*sqrt(2)*atan(sqrt(2)*x - 1)/16 + 3*sqrt(2)*atan(sqrt(2)*x + 1)/16","A",0
283,1,82,0,0.170186," ","integrate(x**4/(x**8+2*x**4+1),x)","- \frac{x}{4 x^{4} + 4} - \frac{\sqrt{2} \log{\left(x^{2} - \sqrt{2} x + 1 \right)}}{32} + \frac{\sqrt{2} \log{\left(x^{2} + \sqrt{2} x + 1 \right)}}{32} + \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} x - 1 \right)}}{16} + \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} x + 1 \right)}}{16}"," ",0,"-x/(4*x**4 + 4) - sqrt(2)*log(x**2 - sqrt(2)*x + 1)/32 + sqrt(2)*log(x**2 + sqrt(2)*x + 1)/32 + sqrt(2)*atan(sqrt(2)*x - 1)/16 + sqrt(2)*atan(sqrt(2)*x + 1)/16","A",0
284,1,83,0,0.173999," ","integrate(x**2/(x**8+2*x**4+1),x)","\frac{x^{3}}{4 x^{4} + 4} + \frac{\sqrt{2} \log{\left(x^{2} - \sqrt{2} x + 1 \right)}}{32} - \frac{\sqrt{2} \log{\left(x^{2} + \sqrt{2} x + 1 \right)}}{32} + \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} x - 1 \right)}}{16} + \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} x + 1 \right)}}{16}"," ",0,"x**3/(4*x**4 + 4) + sqrt(2)*log(x**2 - sqrt(2)*x + 1)/32 - sqrt(2)*log(x**2 + sqrt(2)*x + 1)/32 + sqrt(2)*atan(sqrt(2)*x - 1)/16 + sqrt(2)*atan(sqrt(2)*x + 1)/16","A",0
285,1,88,0,0.200290," ","integrate(1/(x**8+2*x**4+1),x)","\frac{x}{4 x^{4} + 4} - \frac{3 \sqrt{2} \log{\left(x^{2} - \sqrt{2} x + 1 \right)}}{32} + \frac{3 \sqrt{2} \log{\left(x^{2} + \sqrt{2} x + 1 \right)}}{32} + \frac{3 \sqrt{2} \operatorname{atan}{\left(\sqrt{2} x - 1 \right)}}{16} + \frac{3 \sqrt{2} \operatorname{atan}{\left(\sqrt{2} x + 1 \right)}}{16}"," ",0,"x/(4*x**4 + 4) - 3*sqrt(2)*log(x**2 - sqrt(2)*x + 1)/32 + 3*sqrt(2)*log(x**2 + sqrt(2)*x + 1)/32 + 3*sqrt(2)*atan(sqrt(2)*x - 1)/16 + 3*sqrt(2)*atan(sqrt(2)*x + 1)/16","A",0
286,1,97,0,0.207155," ","integrate(1/x**2/(x**8+2*x**4+1),x)","\frac{- 5 x^{4} - 4}{4 x^{5} + 4 x} - \frac{5 \sqrt{2} \log{\left(x^{2} - \sqrt{2} x + 1 \right)}}{32} + \frac{5 \sqrt{2} \log{\left(x^{2} + \sqrt{2} x + 1 \right)}}{32} - \frac{5 \sqrt{2} \operatorname{atan}{\left(\sqrt{2} x - 1 \right)}}{16} - \frac{5 \sqrt{2} \operatorname{atan}{\left(\sqrt{2} x + 1 \right)}}{16}"," ",0,"(-5*x**4 - 4)/(4*x**5 + 4*x) - 5*sqrt(2)*log(x**2 - sqrt(2)*x + 1)/32 + 5*sqrt(2)*log(x**2 + sqrt(2)*x + 1)/32 - 5*sqrt(2)*atan(sqrt(2)*x - 1)/16 - 5*sqrt(2)*atan(sqrt(2)*x + 1)/16","A",0
287,1,99,0,0.224123," ","integrate(1/x**4/(x**8+2*x**4+1),x)","\frac{- 7 x^{4} - 4}{12 x^{7} + 12 x^{3}} + \frac{7 \sqrt{2} \log{\left(x^{2} - \sqrt{2} x + 1 \right)}}{32} - \frac{7 \sqrt{2} \log{\left(x^{2} + \sqrt{2} x + 1 \right)}}{32} - \frac{7 \sqrt{2} \operatorname{atan}{\left(\sqrt{2} x - 1 \right)}}{16} - \frac{7 \sqrt{2} \operatorname{atan}{\left(\sqrt{2} x + 1 \right)}}{16}"," ",0,"(-7*x**4 - 4)/(12*x**7 + 12*x**3) + 7*sqrt(2)*log(x**2 - sqrt(2)*x + 1)/32 - 7*sqrt(2)*log(x**2 + sqrt(2)*x + 1)/32 - 7*sqrt(2)*atan(sqrt(2)*x - 1)/16 - 7*sqrt(2)*atan(sqrt(2)*x + 1)/16","A",0
288,1,102,0,0.232183," ","integrate(1/x**6/(x**8+2*x**4+1),x)","\frac{9 \sqrt{2} \log{\left(x^{2} - \sqrt{2} x + 1 \right)}}{32} - \frac{9 \sqrt{2} \log{\left(x^{2} + \sqrt{2} x + 1 \right)}}{32} + \frac{9 \sqrt{2} \operatorname{atan}{\left(\sqrt{2} x - 1 \right)}}{16} + \frac{9 \sqrt{2} \operatorname{atan}{\left(\sqrt{2} x + 1 \right)}}{16} + \frac{45 x^{8} + 36 x^{4} - 4}{20 x^{9} + 20 x^{5}}"," ",0,"9*sqrt(2)*log(x**2 - sqrt(2)*x + 1)/32 - 9*sqrt(2)*log(x**2 + sqrt(2)*x + 1)/32 + 9*sqrt(2)*atan(sqrt(2)*x - 1)/16 + 9*sqrt(2)*atan(sqrt(2)*x + 1)/16 + (45*x**8 + 36*x**4 - 4)/(20*x**9 + 20*x**5)","A",0
289,1,102,0,0.234333," ","integrate(1/x**8/(x**8+2*x**4+1),x)","- \frac{11 \sqrt{2} \log{\left(x^{2} - \sqrt{2} x + 1 \right)}}{32} + \frac{11 \sqrt{2} \log{\left(x^{2} + \sqrt{2} x + 1 \right)}}{32} + \frac{11 \sqrt{2} \operatorname{atan}{\left(\sqrt{2} x - 1 \right)}}{16} + \frac{11 \sqrt{2} \operatorname{atan}{\left(\sqrt{2} x + 1 \right)}}{16} + \frac{77 x^{8} + 44 x^{4} - 12}{84 x^{11} + 84 x^{7}}"," ",0,"-11*sqrt(2)*log(x**2 - sqrt(2)*x + 1)/32 + 11*sqrt(2)*log(x**2 + sqrt(2)*x + 1)/32 + 11*sqrt(2)*atan(sqrt(2)*x - 1)/16 + 11*sqrt(2)*atan(sqrt(2)*x + 1)/16 + (77*x**8 + 44*x**4 - 12)/(84*x**11 + 84*x**7)","A",0
290,0,0,0,0.000000," ","integrate(x**m/(x**8-2*x**4+1),x)","\int \frac{x^{m}}{\left(x - 1\right)^{2} \left(x + 1\right)^{2} \left(x^{2} + 1\right)^{2}}\, dx"," ",0,"Integral(x**m/((x - 1)**2*(x + 1)**2*(x**2 + 1)**2), x)","F",0
291,1,34,0,0.122020," ","integrate(x**9/(x**8-2*x**4+1),x)","\frac{x^{2}}{2} - \frac{x^{2}}{4 x^{4} - 4} + \frac{3 \log{\left(x^{2} - 1 \right)}}{8} - \frac{3 \log{\left(x^{2} + 1 \right)}}{8}"," ",0,"x**2/2 - x**2/(4*x**4 - 4) + 3*log(x**2 - 1)/8 - 3*log(x**2 + 1)/8","A",0
292,1,15,0,0.103581," ","integrate(x**7/(x**8-2*x**4+1),x)","\frac{\log{\left(x^{4} - 1 \right)}}{4} - \frac{1}{4 x^{4} - 4}"," ",0,"log(x**4 - 1)/4 - 1/(4*x**4 - 4)","A",0
293,1,26,0,0.118418," ","integrate(x**5/(x**8-2*x**4+1),x)","- \frac{x^{2}}{4 x^{4} - 4} + \frac{\log{\left(x^{2} - 1 \right)}}{8} - \frac{\log{\left(x^{2} + 1 \right)}}{8}"," ",0,"-x**2/(4*x**4 - 4) + log(x**2 - 1)/8 - log(x**2 + 1)/8","A",0
294,1,8,0,0.095228," ","integrate(x**3/(x**8-2*x**4+1),x)","- \frac{1}{4 x^{4} - 4}"," ",0,"-1/(4*x**4 - 4)","A",0
295,1,26,0,0.118722," ","integrate(x/(x**8-2*x**4+1),x)","- \frac{x^{2}}{4 x^{4} - 4} - \frac{\log{\left(x^{2} - 1 \right)}}{8} + \frac{\log{\left(x^{2} + 1 \right)}}{8}"," ",0,"-x**2/(4*x**4 - 4) - log(x**2 - 1)/8 + log(x**2 + 1)/8","A",0
296,1,19,0,0.125915," ","integrate(1/x/(x**8-2*x**4+1),x)","\log{\left(x \right)} - \frac{\log{\left(x^{4} - 1 \right)}}{4} - \frac{1}{4 x^{4} - 4}"," ",0,"log(x) - log(x**4 - 1)/4 - 1/(4*x**4 - 4)","A",0
297,1,36,0,0.149556," ","integrate(1/x**3/(x**8-2*x**4+1),x)","\frac{2 - 3 x^{4}}{4 x^{6} - 4 x^{2}} - \frac{3 \log{\left(x^{2} - 1 \right)}}{8} + \frac{3 \log{\left(x^{2} + 1 \right)}}{8}"," ",0,"(2 - 3*x**4)/(4*x**6 - 4*x**2) - 3*log(x**2 - 1)/8 + 3*log(x**2 + 1)/8","A",0
298,1,29,0,0.151554," ","integrate(1/x**5/(x**8-2*x**4+1),x)","\frac{1 - 2 x^{4}}{4 x^{8} - 4 x^{4}} + 2 \log{\left(x \right)} - \frac{\log{\left(x^{4} - 1 \right)}}{2}"," ",0,"(1 - 2*x**4)/(4*x**8 - 4*x**4) + 2*log(x) - log(x**4 - 1)/2","A",0
299,1,41,0,0.175545," ","integrate(1/x**7/(x**8-2*x**4+1),x)","- \frac{5 \log{\left(x^{2} - 1 \right)}}{8} + \frac{5 \log{\left(x^{2} + 1 \right)}}{8} + \frac{- 15 x^{8} + 10 x^{4} + 2}{12 x^{10} - 12 x^{6}}"," ",0,"-5*log(x**2 - 1)/8 + 5*log(x**2 + 1)/8 + (-15*x**8 + 10*x**4 + 2)/(12*x**10 - 12*x**6)","A",0
300,1,32,0,0.151488," ","integrate(x**8/(x**8-2*x**4+1),x)","x - \frac{x}{4 x^{4} - 4} + \frac{5 \log{\left(x - 1 \right)}}{16} - \frac{5 \log{\left(x + 1 \right)}}{16} - \frac{5 \operatorname{atan}{\left(x \right)}}{8}"," ",0,"x - x/(4*x**4 - 4) + 5*log(x - 1)/16 - 5*log(x + 1)/16 - 5*atan(x)/8","A",0
301,1,32,0,0.152730," ","integrate(x**6/(x**8-2*x**4+1),x)","- \frac{x^{3}}{4 x^{4} - 4} + \frac{3 \log{\left(x - 1 \right)}}{16} - \frac{3 \log{\left(x + 1 \right)}}{16} + \frac{3 \operatorname{atan}{\left(x \right)}}{8}"," ",0,"-x**3/(4*x**4 - 4) + 3*log(x - 1)/16 - 3*log(x + 1)/16 + 3*atan(x)/8","A",0
302,1,26,0,0.146870," ","integrate(x**4/(x**8-2*x**4+1),x)","- \frac{x}{4 x^{4} - 4} + \frac{\log{\left(x - 1 \right)}}{16} - \frac{\log{\left(x + 1 \right)}}{16} - \frac{\operatorname{atan}{\left(x \right)}}{8}"," ",0,"-x/(4*x**4 - 4) + log(x - 1)/16 - log(x + 1)/16 - atan(x)/8","A",0
303,1,27,0,0.149252," ","integrate(x**2/(x**8-2*x**4+1),x)","- \frac{x^{3}}{4 x^{4} - 4} - \frac{\log{\left(x - 1 \right)}}{16} + \frac{\log{\left(x + 1 \right)}}{16} - \frac{\operatorname{atan}{\left(x \right)}}{8}"," ",0,"-x**3/(4*x**4 - 4) - log(x - 1)/16 + log(x + 1)/16 - atan(x)/8","A",0
304,1,31,0,0.155960," ","integrate(1/(x**8-2*x**4+1),x)","- \frac{x}{4 x^{4} - 4} - \frac{3 \log{\left(x - 1 \right)}}{16} + \frac{3 \log{\left(x + 1 \right)}}{16} + \frac{3 \operatorname{atan}{\left(x \right)}}{8}"," ",0,"-x/(4*x**4 - 4) - 3*log(x - 1)/16 + 3*log(x + 1)/16 + 3*atan(x)/8","A",0
305,1,37,0,0.179119," ","integrate(1/x**2/(x**8-2*x**4+1),x)","\frac{4 - 5 x^{4}}{4 x^{5} - 4 x} - \frac{5 \log{\left(x - 1 \right)}}{16} + \frac{5 \log{\left(x + 1 \right)}}{16} - \frac{5 \operatorname{atan}{\left(x \right)}}{8}"," ",0,"(4 - 5*x**4)/(4*x**5 - 4*x) - 5*log(x - 1)/16 + 5*log(x + 1)/16 - 5*atan(x)/8","A",0
306,1,39,0,0.184437," ","integrate(1/x**4/(x**8-2*x**4+1),x)","\frac{4 - 7 x^{4}}{12 x^{7} - 12 x^{3}} - \frac{7 \log{\left(x - 1 \right)}}{16} + \frac{7 \log{\left(x + 1 \right)}}{16} + \frac{7 \operatorname{atan}{\left(x \right)}}{8}"," ",0,"(4 - 7*x**4)/(12*x**7 - 12*x**3) - 7*log(x - 1)/16 + 7*log(x + 1)/16 + 7*atan(x)/8","A",0
307,1,44,0,0.200809," ","integrate(1/x**6/(x**8-2*x**4+1),x)","- \frac{9 \log{\left(x - 1 \right)}}{16} + \frac{9 \log{\left(x + 1 \right)}}{16} - \frac{9 \operatorname{atan}{\left(x \right)}}{8} + \frac{- 45 x^{8} + 36 x^{4} + 4}{20 x^{9} - 20 x^{5}}"," ",0,"-9*log(x - 1)/16 + 9*log(x + 1)/16 - 9*atan(x)/8 + (-45*x**8 + 36*x**4 + 4)/(20*x**9 - 20*x**5)","A",0
308,1,44,0,0.210539," ","integrate(1/x**8/(x**8-2*x**4+1),x)","- \frac{11 \log{\left(x - 1 \right)}}{16} + \frac{11 \log{\left(x + 1 \right)}}{16} + \frac{11 \operatorname{atan}{\left(x \right)}}{8} + \frac{- 77 x^{8} + 44 x^{4} + 12}{84 x^{11} - 84 x^{7}}"," ",0,"-11*log(x - 1)/16 + 11*log(x + 1)/16 + 11*atan(x)/8 + (-77*x**8 + 44*x**4 + 12)/(84*x**11 - 84*x**7)","A",0
309,-1,0,0,0.000000," ","integrate(x**m/(c*x**8+b*x**4+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
310,1,316,0,4.113355," ","integrate(x**11/(c*x**8+b*x**4+a),x)","\left(- \frac{b}{8 c^{2}} - \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{8 c^{2} \left(4 a c - b^{2}\right)}\right) \log{\left(x^{4} + \frac{- a b - 16 a c^{2} \left(- \frac{b}{8 c^{2}} - \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{8 c^{2} \left(4 a c - b^{2}\right)}\right) + 4 b^{2} c \left(- \frac{b}{8 c^{2}} - \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{8 c^{2} \left(4 a c - b^{2}\right)}\right)}{2 a c - b^{2}} \right)} + \left(- \frac{b}{8 c^{2}} + \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{8 c^{2} \left(4 a c - b^{2}\right)}\right) \log{\left(x^{4} + \frac{- a b - 16 a c^{2} \left(- \frac{b}{8 c^{2}} + \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{8 c^{2} \left(4 a c - b^{2}\right)}\right) + 4 b^{2} c \left(- \frac{b}{8 c^{2}} + \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{8 c^{2} \left(4 a c - b^{2}\right)}\right)}{2 a c - b^{2}} \right)} + \frac{x^{4}}{4 c}"," ",0,"(-b/(8*c**2) - sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(8*c**2*(4*a*c - b**2)))*log(x**4 + (-a*b - 16*a*c**2*(-b/(8*c**2) - sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(8*c**2*(4*a*c - b**2))) + 4*b**2*c*(-b/(8*c**2) - sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(8*c**2*(4*a*c - b**2))))/(2*a*c - b**2)) + (-b/(8*c**2) + sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(8*c**2*(4*a*c - b**2)))*log(x**4 + (-a*b - 16*a*c**2*(-b/(8*c**2) + sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(8*c**2*(4*a*c - b**2))) + 4*b**2*c*(-b/(8*c**2) + sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(8*c**2*(4*a*c - b**2))))/(2*a*c - b**2)) + x**4/(4*c)","B",0
311,1,134,0,4.419220," ","integrate(x**9/(c*x**8+b*x**4+a),x)","\operatorname{RootSum} {\left(t^{4} \left(4096 a^{2} c^{5} - 2048 a b^{2} c^{4} + 256 b^{4} c^{3}\right) + t^{2} \left(192 a^{2} b c^{2} - 112 a b^{3} c + 16 b^{5}\right) + a^{3}, \left( t \mapsto t \log{\left(x^{2} + \frac{256 t^{3} a b c^{4} - 64 t^{3} b^{3} c^{3} - 8 t a^{2} c^{2} + 16 t a b^{2} c - 4 t b^{4}}{a^{2} c - a b^{2}} \right)} \right)\right)} + \frac{x^{2}}{2 c}"," ",0,"RootSum(_t**4*(4096*a**2*c**5 - 2048*a*b**2*c**4 + 256*b**4*c**3) + _t**2*(192*a**2*b*c**2 - 112*a*b**3*c + 16*b**5) + a**3, Lambda(_t, _t*log(x**2 + (256*_t**3*a*b*c**4 - 64*_t**3*b**3*c**3 - 8*_t*a**2*c**2 + 16*_t*a*b**2*c - 4*_t*b**4)/(a**2*c - a*b**2)))) + x**2/(2*c)","A",0
312,1,223,0,2.179801," ","integrate(x**7/(c*x**8+b*x**4+a),x)","\left(- \frac{b \sqrt{- 4 a c + b^{2}}}{8 c \left(4 a c - b^{2}\right)} + \frac{1}{8 c}\right) \log{\left(x^{4} + \frac{- 16 a c \left(- \frac{b \sqrt{- 4 a c + b^{2}}}{8 c \left(4 a c - b^{2}\right)} + \frac{1}{8 c}\right) + 2 a + 4 b^{2} \left(- \frac{b \sqrt{- 4 a c + b^{2}}}{8 c \left(4 a c - b^{2}\right)} + \frac{1}{8 c}\right)}{b} \right)} + \left(\frac{b \sqrt{- 4 a c + b^{2}}}{8 c \left(4 a c - b^{2}\right)} + \frac{1}{8 c}\right) \log{\left(x^{4} + \frac{- 16 a c \left(\frac{b \sqrt{- 4 a c + b^{2}}}{8 c \left(4 a c - b^{2}\right)} + \frac{1}{8 c}\right) + 2 a + 4 b^{2} \left(\frac{b \sqrt{- 4 a c + b^{2}}}{8 c \left(4 a c - b^{2}\right)} + \frac{1}{8 c}\right)}{b} \right)}"," ",0,"(-b*sqrt(-4*a*c + b**2)/(8*c*(4*a*c - b**2)) + 1/(8*c))*log(x**4 + (-16*a*c*(-b*sqrt(-4*a*c + b**2)/(8*c*(4*a*c - b**2)) + 1/(8*c)) + 2*a + 4*b**2*(-b*sqrt(-4*a*c + b**2)/(8*c*(4*a*c - b**2)) + 1/(8*c)))/b) + (b*sqrt(-4*a*c + b**2)/(8*c*(4*a*c - b**2)) + 1/(8*c))*log(x**4 + (-16*a*c*(b*sqrt(-4*a*c + b**2)/(8*c*(4*a*c - b**2)) + 1/(8*c)) + 2*a + 4*b**2*(b*sqrt(-4*a*c + b**2)/(8*c*(4*a*c - b**2)) + 1/(8*c)))/b)","B",0
313,1,76,0,2.509162," ","integrate(x**5/(c*x**8+b*x**4+a),x)","\operatorname{RootSum} {\left(t^{4} \left(4096 a^{2} c^{3} - 2048 a b^{2} c^{2} + 256 b^{4} c\right) + t^{2} \left(- 64 a b c + 16 b^{3}\right) + a, \left( t \mapsto t \log{\left(512 t^{3} a c^{2} - 128 t^{3} b^{2} c - 4 t b + x^{2} \right)} \right)\right)}"," ",0,"RootSum(_t**4*(4096*a**2*c**3 - 2048*a*b**2*c**2 + 256*b**4*c) + _t**2*(-64*a*b*c + 16*b**3) + a, Lambda(_t, _t*log(512*_t**3*a*c**2 - 128*_t**3*b**2*c - 4*_t*b + x**2)))","A",0
314,1,131,0,0.769880," ","integrate(x**3/(c*x**8+b*x**4+a),x)","- \frac{\sqrt{- \frac{1}{4 a c - b^{2}}} \log{\left(x^{4} + \frac{- 4 a c \sqrt{- \frac{1}{4 a c - b^{2}}} + b^{2} \sqrt{- \frac{1}{4 a c - b^{2}}} + b}{2 c} \right)}}{4} + \frac{\sqrt{- \frac{1}{4 a c - b^{2}}} \log{\left(x^{4} + \frac{4 a c \sqrt{- \frac{1}{4 a c - b^{2}}} - b^{2} \sqrt{- \frac{1}{4 a c - b^{2}}} + b}{2 c} \right)}}{4}"," ",0,"-sqrt(-1/(4*a*c - b**2))*log(x**4 + (-4*a*c*sqrt(-1/(4*a*c - b**2)) + b**2*sqrt(-1/(4*a*c - b**2)) + b)/(2*c))/4 + sqrt(-1/(4*a*c - b**2))*log(x**4 + (4*a*c*sqrt(-1/(4*a*c - b**2)) - b**2*sqrt(-1/(4*a*c - b**2)) + b)/(2*c))/4","B",0
315,1,88,0,3.358922," ","integrate(x/(c*x**8+b*x**4+a),x)","\operatorname{RootSum} {\left(t^{4} \left(4096 a^{3} c^{2} - 2048 a^{2} b^{2} c + 256 a b^{4}\right) + t^{2} \left(- 64 a b c + 16 b^{3}\right) + c, \left( t \mapsto t \log{\left(x^{2} + \frac{256 t^{3} a^{2} b c - 64 t^{3} a b^{3} + 8 t a c - 4 t b^{2}}{c} \right)} \right)\right)}"," ",0,"RootSum(_t**4*(4096*a**3*c**2 - 2048*a**2*b**2*c + 256*a*b**4) + _t**2*(-64*a*b*c + 16*b**3) + c, Lambda(_t, _t*log(x**2 + (256*_t**3*a**2*b*c - 64*_t**3*a*b**3 + 8*_t*a*c - 4*_t*b**2)/c)))","A",0
316,1,253,0,14.469485," ","integrate(1/x/(c*x**8+b*x**4+a),x)","\left(- \frac{b \sqrt{- 4 a c + b^{2}}}{8 a \left(4 a c - b^{2}\right)} - \frac{1}{8 a}\right) \log{\left(x^{4} + \frac{- 16 a^{2} c \left(- \frac{b \sqrt{- 4 a c + b^{2}}}{8 a \left(4 a c - b^{2}\right)} - \frac{1}{8 a}\right) + 4 a b^{2} \left(- \frac{b \sqrt{- 4 a c + b^{2}}}{8 a \left(4 a c - b^{2}\right)} - \frac{1}{8 a}\right) - 2 a c + b^{2}}{b c} \right)} + \left(\frac{b \sqrt{- 4 a c + b^{2}}}{8 a \left(4 a c - b^{2}\right)} - \frac{1}{8 a}\right) \log{\left(x^{4} + \frac{- 16 a^{2} c \left(\frac{b \sqrt{- 4 a c + b^{2}}}{8 a \left(4 a c - b^{2}\right)} - \frac{1}{8 a}\right) + 4 a b^{2} \left(\frac{b \sqrt{- 4 a c + b^{2}}}{8 a \left(4 a c - b^{2}\right)} - \frac{1}{8 a}\right) - 2 a c + b^{2}}{b c} \right)} + \frac{\log{\left(x \right)}}{a}"," ",0,"(-b*sqrt(-4*a*c + b**2)/(8*a*(4*a*c - b**2)) - 1/(8*a))*log(x**4 + (-16*a**2*c*(-b*sqrt(-4*a*c + b**2)/(8*a*(4*a*c - b**2)) - 1/(8*a)) + 4*a*b**2*(-b*sqrt(-4*a*c + b**2)/(8*a*(4*a*c - b**2)) - 1/(8*a)) - 2*a*c + b**2)/(b*c)) + (b*sqrt(-4*a*c + b**2)/(8*a*(4*a*c - b**2)) - 1/(8*a))*log(x**4 + (-16*a**2*c*(b*sqrt(-4*a*c + b**2)/(8*a*(4*a*c - b**2)) - 1/(8*a)) + 4*a*b**2*(b*sqrt(-4*a*c + b**2)/(8*a*(4*a*c - b**2)) - 1/(8*a)) - 2*a*c + b**2)/(b*c)) + log(x)/a","B",0
317,1,153,0,15.343715," ","integrate(1/x**3/(c*x**8+b*x**4+a),x)","\operatorname{RootSum} {\left(t^{4} \left(4096 a^{5} c^{2} - 2048 a^{4} b^{2} c + 256 a^{3} b^{4}\right) + t^{2} \left(192 a^{2} b c^{2} - 112 a b^{3} c + 16 b^{5}\right) + c^{3}, \left( t \mapsto t \log{\left(x^{2} + \frac{- 512 t^{3} a^{5} c^{2} + 384 t^{3} a^{4} b^{2} c - 64 t^{3} a^{3} b^{4} - 20 t a^{2} b c^{2} + 20 t a b^{3} c - 4 t b^{5}}{a c^{3} - b^{2} c^{2}} \right)} \right)\right)} - \frac{1}{2 a x^{2}}"," ",0,"RootSum(_t**4*(4096*a**5*c**2 - 2048*a**4*b**2*c + 256*a**3*b**4) + _t**2*(192*a**2*b*c**2 - 112*a*b**3*c + 16*b**5) + c**3, Lambda(_t, _t*log(x**2 + (-512*_t**3*a**5*c**2 + 384*_t**3*a**4*b**2*c - 64*_t**3*a**3*b**4 - 20*_t*a**2*b*c**2 + 20*_t*a*b**3*c - 4*_t*b**5)/(a*c**3 - b**2*c**2)))) - 1/(2*a*x**2)","A",0
318,-1,0,0,0.000000," ","integrate(1/x**5/(c*x**8+b*x**4+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
319,-1,0,0,0.000000," ","integrate(x**10/(c*x**8+b*x**4+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
320,-1,0,0,0.000000," ","integrate(x**8/(c*x**8+b*x**4+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
321,1,230,0,61.576859," ","integrate(x**6/(c*x**8+b*x**4+a),x)","\operatorname{RootSum} {\left(t^{8} \left(16777216 a^{4} c^{7} - 16777216 a^{3} b^{2} c^{6} + 6291456 a^{2} b^{4} c^{5} - 1048576 a b^{6} c^{4} + 65536 b^{8} c^{3}\right) + t^{4} \left(- 12288 a^{3} b c^{3} + 10240 a^{2} b^{3} c^{2} - 2816 a b^{5} c + 256 b^{7}\right) + a^{3}, \left( t \mapsto t \log{\left(x + \frac{2097152 t^{7} a^{4} c^{7} - 2621440 t^{7} a^{3} b^{2} c^{6} + 1179648 t^{7} a^{2} b^{4} c^{5} - 229376 t^{7} a b^{6} c^{4} + 16384 t^{7} b^{8} c^{3} - 1280 t^{3} a^{3} b c^{3} + 1600 t^{3} a^{2} b^{3} c^{2} - 576 t^{3} a b^{5} c + 64 t^{3} b^{7}}{a^{3} c - a^{2} b^{2}} \right)} \right)\right)}"," ",0,"RootSum(_t**8*(16777216*a**4*c**7 - 16777216*a**3*b**2*c**6 + 6291456*a**2*b**4*c**5 - 1048576*a*b**6*c**4 + 65536*b**8*c**3) + _t**4*(-12288*a**3*b*c**3 + 10240*a**2*b**3*c**2 - 2816*a*b**5*c + 256*b**7) + a**3, Lambda(_t, _t*log(x + (2097152*_t**7*a**4*c**7 - 2621440*_t**7*a**3*b**2*c**6 + 1179648*_t**7*a**2*b**4*c**5 - 229376*_t**7*a*b**6*c**4 + 16384*_t**7*b**8*c**3 - 1280*_t**3*a**3*b*c**3 + 1600*_t**3*a**2*b**3*c**2 - 576*_t**3*a*b**5*c + 64*_t**3*b**7)/(a**3*c - a**2*b**2))))","A",0
322,1,126,0,2.917305," ","integrate(x**4/(c*x**8+b*x**4+a),x)","\operatorname{RootSum} {\left(t^{8} \left(16777216 a^{4} c^{5} - 16777216 a^{3} b^{2} c^{4} + 6291456 a^{2} b^{4} c^{3} - 1048576 a b^{6} c^{2} + 65536 b^{8} c\right) + t^{4} \left(4096 a^{2} b c^{2} - 2048 a b^{3} c + 256 b^{5}\right) + a, \left( t \mapsto t \log{\left(- 32768 t^{5} a^{2} c^{3} + 16384 t^{5} a b^{2} c^{2} - 2048 t^{5} b^{4} c - 4 t b + x \right)} \right)\right)}"," ",0,"RootSum(_t**8*(16777216*a**4*c**5 - 16777216*a**3*b**2*c**4 + 6291456*a**2*b**4*c**3 - 1048576*a*b**6*c**2 + 65536*b**8*c) + _t**4*(4096*a**2*b*c**2 - 2048*a*b**3*c + 256*b**5) + a, Lambda(_t, _t*log(-32768*_t**5*a**2*c**3 + 16384*_t**5*a*b**2*c**2 - 2048*_t**5*b**4*c - 4*_t*b + x)))","A",0
323,1,172,0,4.098754," ","integrate(x**2/(c*x**8+b*x**4+a),x)","\operatorname{RootSum} {\left(t^{8} \left(16777216 a^{5} c^{4} - 16777216 a^{4} b^{2} c^{3} + 6291456 a^{3} b^{4} c^{2} - 1048576 a^{2} b^{6} c + 65536 a b^{8}\right) + t^{4} \left(4096 a^{2} b c^{2} - 2048 a b^{3} c + 256 b^{5}\right) + c, \left( t \mapsto t \log{\left(x + \frac{1048576 t^{7} a^{4} b c^{3} - 786432 t^{7} a^{3} b^{3} c^{2} + 196608 t^{7} a^{2} b^{5} c - 16384 t^{7} a b^{7} - 512 t^{3} a^{2} c^{2} + 384 t^{3} a b^{2} c - 64 t^{3} b^{4}}{c} \right)} \right)\right)}"," ",0,"RootSum(_t**8*(16777216*a**5*c**4 - 16777216*a**4*b**2*c**3 + 6291456*a**3*b**4*c**2 - 1048576*a**2*b**6*c + 65536*a*b**8) + _t**4*(4096*a**2*b*c**2 - 2048*a*b**3*c + 256*b**5) + c, Lambda(_t, _t*log(x + (1048576*_t**7*a**4*b*c**3 - 786432*_t**7*a**3*b**3*c**2 + 196608*_t**7*a**2*b**5*c - 16384*_t**7*a*b**7 - 512*_t**3*a**2*c**2 + 384*_t**3*a*b**2*c - 64*_t**3*b**4)/c)))","A",0
324,1,177,0,19.791984," ","integrate(1/(c*x**8+b*x**4+a),x)","\operatorname{RootSum} {\left(t^{8} \left(16777216 a^{7} c^{4} - 16777216 a^{6} b^{2} c^{3} + 6291456 a^{5} b^{4} c^{2} - 1048576 a^{4} b^{6} c + 65536 a^{3} b^{8}\right) + t^{4} \left(- 12288 a^{3} b c^{3} + 10240 a^{2} b^{3} c^{2} - 2816 a b^{5} c + 256 b^{7}\right) + c^{3}, \left( t \mapsto t \log{\left(x + \frac{16384 t^{5} a^{5} b c^{2} - 8192 t^{5} a^{4} b^{3} c + 1024 t^{5} a^{3} b^{5} + 8 t a^{2} c^{2} - 16 t a b^{2} c + 4 t b^{4}}{a c^{2} - b^{2} c} \right)} \right)\right)}"," ",0,"RootSum(_t**8*(16777216*a**7*c**4 - 16777216*a**6*b**2*c**3 + 6291456*a**5*b**4*c**2 - 1048576*a**4*b**6*c + 65536*a**3*b**8) + _t**4*(-12288*a**3*b*c**3 + 10240*a**2*b**3*c**2 - 2816*a*b**5*c + 256*b**7) + c**3, Lambda(_t, _t*log(x + (16384*_t**5*a**5*b*c**2 - 8192*_t**5*a**4*b**3*c + 1024*_t**5*a**3*b**5 + 8*_t*a**2*c**2 - 16*_t*a*b**2*c + 4*_t*b**4)/(a*c**2 - b**2*c))))","A",0
325,-1,0,0,0.000000," ","integrate(1/x**2/(c*x**8+b*x**4+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
326,-1,0,0,0.000000," ","integrate(1/x**4/(c*x**8+b*x**4+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
327,0,0,0,0.000000," ","integrate(x**m/(x**8+x**4+1),x)","\int \frac{x^{m}}{\left(x^{2} - x + 1\right) \left(x^{2} + x + 1\right) \left(x^{4} - x^{2} + 1\right)}\, dx"," ",0,"Integral(x**m/((x**2 - x + 1)*(x**2 + x + 1)*(x**4 - x**2 + 1)), x)","F",0
328,1,42,0,0.138634," ","integrate(x**11/(x**8+x**4+1),x)","\frac{x^{4}}{4} - \frac{\log{\left(x^{8} + x^{4} + 1 \right)}}{8} - \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x^{4}}{3} + \frac{\sqrt{3}}{3} \right)}}{12}"," ",0,"x**4/4 - log(x**8 + x**4 + 1)/8 - sqrt(3)*atan(2*sqrt(3)*x**4/3 + sqrt(3)/3)/12","A",0
329,1,51,0,0.139545," ","integrate(x**9/(x**8+x**4+1),x)","\frac{x^{2}}{2} + \frac{\sqrt{3} \left(- 2 \operatorname{atan}{\left(\frac{\sqrt{3} x^{2}}{3} \right)} - 2 \operatorname{atan}{\left(\frac{\sqrt{3} x^{6}}{3} + \frac{2 \sqrt{3} x^{2}}{3} \right)}\right)}{12}"," ",0,"x**2/2 + sqrt(3)*(-2*atan(sqrt(3)*x**2/3) - 2*atan(sqrt(3)*x**6/3 + 2*sqrt(3)*x**2/3))/12","A",0
330,1,37,0,0.133264," ","integrate(x**7/(x**8+x**4+1),x)","\frac{\log{\left(x^{8} + x^{4} + 1 \right)}}{8} - \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x^{4}}{3} + \frac{\sqrt{3}}{3} \right)}}{12}"," ",0,"log(x**8 + x**4 + 1)/8 - sqrt(3)*atan(2*sqrt(3)*x**4/3 + sqrt(3)/3)/12","A",0
331,1,76,0,0.205899," ","integrate(x**5/(x**8+x**4+1),x)","\frac{\log{\left(x^{4} - x^{2} + 1 \right)}}{8} - \frac{\log{\left(x^{4} + x^{2} + 1 \right)}}{8} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x^{2}}{3} - \frac{\sqrt{3}}{3} \right)}}{12} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x^{2}}{3} + \frac{\sqrt{3}}{3} \right)}}{12}"," ",0,"log(x**4 - x**2 + 1)/8 - log(x**4 + x**2 + 1)/8 + sqrt(3)*atan(2*sqrt(3)*x**2/3 - sqrt(3)/3)/12 + sqrt(3)*atan(2*sqrt(3)*x**2/3 + sqrt(3)/3)/12","A",0
332,1,26,0,0.118444," ","integrate(x**3/(x**8+x**4+1),x)","\frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x^{4}}{3} + \frac{\sqrt{3}}{3} \right)}}{6}"," ",0,"sqrt(3)*atan(2*sqrt(3)*x**4/3 + sqrt(3)/3)/6","A",0
333,1,76,0,0.202157," ","integrate(x/(x**8+x**4+1),x)","- \frac{\log{\left(x^{4} - x^{2} + 1 \right)}}{8} + \frac{\log{\left(x^{4} + x^{2} + 1 \right)}}{8} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x^{2}}{3} - \frac{\sqrt{3}}{3} \right)}}{12} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x^{2}}{3} + \frac{\sqrt{3}}{3} \right)}}{12}"," ",0,"-log(x**4 - x**2 + 1)/8 + log(x**4 + x**2 + 1)/8 + sqrt(3)*atan(2*sqrt(3)*x**2/3 - sqrt(3)/3)/12 + sqrt(3)*atan(2*sqrt(3)*x**2/3 + sqrt(3)/3)/12","A",0
334,1,41,0,0.154658," ","integrate(1/x/(x**8+x**4+1),x)","\log{\left(x \right)} - \frac{\log{\left(x^{8} + x^{4} + 1 \right)}}{8} - \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x^{4}}{3} + \frac{\sqrt{3}}{3} \right)}}{12}"," ",0,"log(x) - log(x**8 + x**4 + 1)/8 - sqrt(3)*atan(2*sqrt(3)*x**4/3 + sqrt(3)/3)/12","A",0
335,1,53,0,0.163802," ","integrate(1/x**3/(x**8+x**4+1),x)","\frac{\sqrt{3} \left(- 2 \operatorname{atan}{\left(\frac{\sqrt{3} x^{2}}{3} \right)} - 2 \operatorname{atan}{\left(\frac{\sqrt{3} x^{6}}{3} + \frac{2 \sqrt{3} x^{2}}{3} \right)}\right)}{12} - \frac{1}{2 x^{2}}"," ",0,"sqrt(3)*(-2*atan(sqrt(3)*x**2/3) - 2*atan(sqrt(3)*x**6/3 + 2*sqrt(3)*x**2/3))/12 - 1/(2*x**2)","A",0
336,1,48,0,0.184107," ","integrate(1/x**5/(x**8+x**4+1),x)","- \log{\left(x \right)} + \frac{\log{\left(x^{8} + x^{4} + 1 \right)}}{8} - \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x^{4}}{3} + \frac{\sqrt{3}}{3} \right)}}{12} - \frac{1}{4 x^{4}}"," ",0,"-log(x) + log(x**8 + x**4 + 1)/8 - sqrt(3)*atan(2*sqrt(3)*x**4/3 + sqrt(3)/3)/12 - 1/(4*x**4)","A",0
337,1,88,0,0.248634," ","integrate(1/x**7/(x**8+x**4+1),x)","\frac{\log{\left(x^{4} - x^{2} + 1 \right)}}{8} - \frac{\log{\left(x^{4} + x^{2} + 1 \right)}}{8} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x^{2}}{3} - \frac{\sqrt{3}}{3} \right)}}{12} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x^{2}}{3} + \frac{\sqrt{3}}{3} \right)}}{12} + \frac{3 x^{4} - 1}{6 x^{6}}"," ",0,"log(x**4 - x**2 + 1)/8 - log(x**4 + x**2 + 1)/8 + sqrt(3)*atan(2*sqrt(3)*x**2/3 - sqrt(3)/3)/12 + sqrt(3)*atan(2*sqrt(3)*x**2/3 + sqrt(3)/3)/12 + (3*x**4 - 1)/(6*x**6)","A",0
338,1,192,0,0.708910," ","integrate(x**8/(x**8+x**4+1),x)","x + \left(\frac{1}{8} + \frac{\sqrt{3} i}{24}\right) \log{\left(x - 1 - \frac{\sqrt{3} i}{3} - 9216 \left(\frac{1}{8} + \frac{\sqrt{3} i}{24}\right)^{5} \right)} + \left(\frac{1}{8} - \frac{\sqrt{3} i}{24}\right) \log{\left(x - 1 - 9216 \left(\frac{1}{8} - \frac{\sqrt{3} i}{24}\right)^{5} + \frac{\sqrt{3} i}{3} \right)} + \left(- \frac{1}{8} + \frac{\sqrt{3} i}{24}\right) \log{\left(x + 1 - \frac{\sqrt{3} i}{3} - 9216 \left(- \frac{1}{8} + \frac{\sqrt{3} i}{24}\right)^{5} \right)} + \left(- \frac{1}{8} - \frac{\sqrt{3} i}{24}\right) \log{\left(x + 1 - 9216 \left(- \frac{1}{8} - \frac{\sqrt{3} i}{24}\right)^{5} + \frac{\sqrt{3} i}{3} \right)} + \operatorname{RootSum} {\left(2304 t^{4} + 48 t^{2} + 1, \left( t \mapsto t \log{\left(- 9216 t^{5} - 8 t + x \right)} \right)\right)}"," ",0,"x + (1/8 + sqrt(3)*I/24)*log(x - 1 - sqrt(3)*I/3 - 9216*(1/8 + sqrt(3)*I/24)**5) + (1/8 - sqrt(3)*I/24)*log(x - 1 - 9216*(1/8 - sqrt(3)*I/24)**5 + sqrt(3)*I/3) + (-1/8 + sqrt(3)*I/24)*log(x + 1 - sqrt(3)*I/3 - 9216*(-1/8 + sqrt(3)*I/24)**5) + (-1/8 - sqrt(3)*I/24)*log(x + 1 - 9216*(-1/8 - sqrt(3)*I/24)**5 + sqrt(3)*I/3) + RootSum(2304*_t**4 + 48*_t**2 + 1, Lambda(_t, _t*log(-9216*_t**5 - 8*_t + x)))","C",0
339,1,82,0,0.178694," ","integrate(x**6/(x**8+x**4+1),x)","\frac{\sqrt{3} \left(2 \operatorname{atan}{\left(\frac{\sqrt{3} x}{3} \right)} + 2 \operatorname{atan}{\left(\frac{\sqrt{3} x^{3}}{3} + \frac{2 \sqrt{3} x}{3} \right)}\right)}{12} + \frac{\sqrt{3} \log{\left(x^{2} - \sqrt{3} x + 1 \right)}}{12} - \frac{\sqrt{3} \log{\left(x^{2} + \sqrt{3} x + 1 \right)}}{12}"," ",0,"sqrt(3)*(2*atan(sqrt(3)*x/3) + 2*atan(sqrt(3)*x**3/3 + 2*sqrt(3)*x/3))/12 + sqrt(3)*log(x**2 - sqrt(3)*x + 1)/12 - sqrt(3)*log(x**2 + sqrt(3)*x + 1)/12","A",0
340,1,197,0,0.724693," ","integrate(x**4/(x**8+x**4+1),x)","\left(\frac{1}{8} - \frac{\sqrt{3} i}{24}\right) \log{\left(x - \frac{1}{2} + \frac{\sqrt{3} i}{6} - 18432 \left(\frac{1}{8} - \frac{\sqrt{3} i}{24}\right)^{5} \right)} + \left(\frac{1}{8} + \frac{\sqrt{3} i}{24}\right) \log{\left(x - \frac{1}{2} - 18432 \left(\frac{1}{8} + \frac{\sqrt{3} i}{24}\right)^{5} - \frac{\sqrt{3} i}{6} \right)} + \left(- \frac{1}{8} - \frac{\sqrt{3} i}{24}\right) \log{\left(x + \frac{1}{2} + \frac{\sqrt{3} i}{6} - 18432 \left(- \frac{1}{8} - \frac{\sqrt{3} i}{24}\right)^{5} \right)} + \left(- \frac{1}{8} + \frac{\sqrt{3} i}{24}\right) \log{\left(x + \frac{1}{2} - 18432 \left(- \frac{1}{8} + \frac{\sqrt{3} i}{24}\right)^{5} - \frac{\sqrt{3} i}{6} \right)} + \operatorname{RootSum} {\left(2304 t^{4} + 48 t^{2} + 1, \left( t \mapsto t \log{\left(- 18432 t^{5} - 4 t + x \right)} \right)\right)}"," ",0,"(1/8 - sqrt(3)*I/24)*log(x - 1/2 + sqrt(3)*I/6 - 18432*(1/8 - sqrt(3)*I/24)**5) + (1/8 + sqrt(3)*I/24)*log(x - 1/2 - 18432*(1/8 + sqrt(3)*I/24)**5 - sqrt(3)*I/6) + (-1/8 - sqrt(3)*I/24)*log(x + 1/2 + sqrt(3)*I/6 - 18432*(-1/8 - sqrt(3)*I/24)**5) + (-1/8 + sqrt(3)*I/24)*log(x + 1/2 - 18432*(-1/8 + sqrt(3)*I/24)**5 - sqrt(3)*I/6) + RootSum(2304*_t**4 + 48*_t**2 + 1, Lambda(_t, _t*log(-18432*_t**5 - 4*_t + x)))","C",0
341,1,214,0,0.712780," ","integrate(x**2/(x**8+x**4+1),x)","\left(- \frac{1}{8} - \frac{\sqrt{3} i}{24}\right) \log{\left(x + 442368 \left(- \frac{1}{8} - \frac{\sqrt{3} i}{24}\right)^{7} - 192 \left(- \frac{1}{8} - \frac{\sqrt{3} i}{24}\right)^{3} \right)} + \left(- \frac{1}{8} + \frac{\sqrt{3} i}{24}\right) \log{\left(x - 192 \left(- \frac{1}{8} + \frac{\sqrt{3} i}{24}\right)^{3} + 442368 \left(- \frac{1}{8} + \frac{\sqrt{3} i}{24}\right)^{7} \right)} + \left(\frac{1}{8} - \frac{\sqrt{3} i}{24}\right) \log{\left(x + 442368 \left(\frac{1}{8} - \frac{\sqrt{3} i}{24}\right)^{7} - 192 \left(\frac{1}{8} - \frac{\sqrt{3} i}{24}\right)^{3} \right)} + \left(\frac{1}{8} + \frac{\sqrt{3} i}{24}\right) \log{\left(x - 192 \left(\frac{1}{8} + \frac{\sqrt{3} i}{24}\right)^{3} + 442368 \left(\frac{1}{8} + \frac{\sqrt{3} i}{24}\right)^{7} \right)} + \operatorname{RootSum} {\left(2304 t^{4} + 48 t^{2} + 1, \left( t \mapsto t \log{\left(442368 t^{7} - 192 t^{3} + x \right)} \right)\right)}"," ",0,"(-1/8 - sqrt(3)*I/24)*log(x + 442368*(-1/8 - sqrt(3)*I/24)**7 - 192*(-1/8 - sqrt(3)*I/24)**3) + (-1/8 + sqrt(3)*I/24)*log(x - 192*(-1/8 + sqrt(3)*I/24)**3 + 442368*(-1/8 + sqrt(3)*I/24)**7) + (1/8 - sqrt(3)*I/24)*log(x + 442368*(1/8 - sqrt(3)*I/24)**7 - 192*(1/8 - sqrt(3)*I/24)**3) + (1/8 + sqrt(3)*I/24)*log(x - 192*(1/8 + sqrt(3)*I/24)**3 + 442368*(1/8 + sqrt(3)*I/24)**7) + RootSum(2304*_t**4 + 48*_t**2 + 1, Lambda(_t, _t*log(442368*_t**7 - 192*_t**3 + x)))","C",0
342,1,82,0,0.181687," ","integrate(1/(x**8+x**4+1),x)","\frac{\sqrt{3} \left(2 \operatorname{atan}{\left(\frac{\sqrt{3} x}{3} \right)} + 2 \operatorname{atan}{\left(\frac{\sqrt{3} x^{3}}{3} + \frac{2 \sqrt{3} x}{3} \right)}\right)}{12} - \frac{\sqrt{3} \log{\left(x^{2} - \sqrt{3} x + 1 \right)}}{12} + \frac{\sqrt{3} \log{\left(x^{2} + \sqrt{3} x + 1 \right)}}{12}"," ",0,"sqrt(3)*(2*atan(sqrt(3)*x/3) + 2*atan(sqrt(3)*x**3/3 + 2*sqrt(3)*x/3))/12 - sqrt(3)*log(x**2 - sqrt(3)*x + 1)/12 + sqrt(3)*log(x**2 + sqrt(3)*x + 1)/12","A",0
343,1,218,0,0.738240," ","integrate(1/x**2/(x**8+x**4+1),x)","\left(- \frac{1}{8} - \frac{\sqrt{3} i}{24}\right) \log{\left(x - 442368 \left(- \frac{1}{8} - \frac{\sqrt{3} i}{24}\right)^{7} - 384 \left(- \frac{1}{8} - \frac{\sqrt{3} i}{24}\right)^{3} \right)} + \left(- \frac{1}{8} + \frac{\sqrt{3} i}{24}\right) \log{\left(x - 384 \left(- \frac{1}{8} + \frac{\sqrt{3} i}{24}\right)^{3} - 442368 \left(- \frac{1}{8} + \frac{\sqrt{3} i}{24}\right)^{7} \right)} + \left(\frac{1}{8} - \frac{\sqrt{3} i}{24}\right) \log{\left(x - 442368 \left(\frac{1}{8} - \frac{\sqrt{3} i}{24}\right)^{7} - 384 \left(\frac{1}{8} - \frac{\sqrt{3} i}{24}\right)^{3} \right)} + \left(\frac{1}{8} + \frac{\sqrt{3} i}{24}\right) \log{\left(x - 384 \left(\frac{1}{8} + \frac{\sqrt{3} i}{24}\right)^{3} - 442368 \left(\frac{1}{8} + \frac{\sqrt{3} i}{24}\right)^{7} \right)} + \operatorname{RootSum} {\left(2304 t^{4} + 48 t^{2} + 1, \left( t \mapsto t \log{\left(- 442368 t^{7} - 384 t^{3} + x \right)} \right)\right)} - \frac{1}{x}"," ",0,"(-1/8 - sqrt(3)*I/24)*log(x - 442368*(-1/8 - sqrt(3)*I/24)**7 - 384*(-1/8 - sqrt(3)*I/24)**3) + (-1/8 + sqrt(3)*I/24)*log(x - 384*(-1/8 + sqrt(3)*I/24)**3 - 442368*(-1/8 + sqrt(3)*I/24)**7) + (1/8 - sqrt(3)*I/24)*log(x - 442368*(1/8 - sqrt(3)*I/24)**7 - 384*(1/8 - sqrt(3)*I/24)**3) + (1/8 + sqrt(3)*I/24)*log(x - 384*(1/8 + sqrt(3)*I/24)**3 - 442368*(1/8 + sqrt(3)*I/24)**7) + RootSum(2304*_t**4 + 48*_t**2 + 1, Lambda(_t, _t*log(-442368*_t**7 - 384*_t**3 + x))) - 1/x","C",0
344,1,197,0,0.747536," ","integrate(1/x**4/(x**8+x**4+1),x)","\left(\frac{1}{8} + \frac{\sqrt{3} i}{24}\right) \log{\left(x - 1 - \frac{\sqrt{3} i}{3} - 9216 \left(\frac{1}{8} + \frac{\sqrt{3} i}{24}\right)^{5} \right)} + \left(\frac{1}{8} - \frac{\sqrt{3} i}{24}\right) \log{\left(x - 1 - 9216 \left(\frac{1}{8} - \frac{\sqrt{3} i}{24}\right)^{5} + \frac{\sqrt{3} i}{3} \right)} + \left(- \frac{1}{8} + \frac{\sqrt{3} i}{24}\right) \log{\left(x + 1 - \frac{\sqrt{3} i}{3} - 9216 \left(- \frac{1}{8} + \frac{\sqrt{3} i}{24}\right)^{5} \right)} + \left(- \frac{1}{8} - \frac{\sqrt{3} i}{24}\right) \log{\left(x + 1 - 9216 \left(- \frac{1}{8} - \frac{\sqrt{3} i}{24}\right)^{5} + \frac{\sqrt{3} i}{3} \right)} + \operatorname{RootSum} {\left(2304 t^{4} + 48 t^{2} + 1, \left( t \mapsto t \log{\left(- 9216 t^{5} - 8 t + x \right)} \right)\right)} - \frac{1}{3 x^{3}}"," ",0,"(1/8 + sqrt(3)*I/24)*log(x - 1 - sqrt(3)*I/3 - 9216*(1/8 + sqrt(3)*I/24)**5) + (1/8 - sqrt(3)*I/24)*log(x - 1 - 9216*(1/8 - sqrt(3)*I/24)**5 + sqrt(3)*I/3) + (-1/8 + sqrt(3)*I/24)*log(x + 1 - sqrt(3)*I/3 - 9216*(-1/8 + sqrt(3)*I/24)**5) + (-1/8 - sqrt(3)*I/24)*log(x + 1 - 9216*(-1/8 - sqrt(3)*I/24)**5 + sqrt(3)*I/3) + RootSum(2304*_t**4 + 48*_t**2 + 1, Lambda(_t, _t*log(-9216*_t**5 - 8*_t + x))) - 1/(3*x**3)","C",0
345,1,94,0,0.217184," ","integrate(1/x**6/(x**8+x**4+1),x)","\frac{\sqrt{3} \left(2 \operatorname{atan}{\left(\frac{\sqrt{3} x}{3} \right)} + 2 \operatorname{atan}{\left(\frac{\sqrt{3} x^{3}}{3} + \frac{2 \sqrt{3} x}{3} \right)}\right)}{12} + \frac{\sqrt{3} \log{\left(x^{2} - \sqrt{3} x + 1 \right)}}{12} - \frac{\sqrt{3} \log{\left(x^{2} + \sqrt{3} x + 1 \right)}}{12} + \frac{5 x^{4} - 1}{5 x^{5}}"," ",0,"sqrt(3)*(2*atan(sqrt(3)*x/3) + 2*atan(sqrt(3)*x**3/3 + 2*sqrt(3)*x/3))/12 + sqrt(3)*log(x**2 - sqrt(3)*x + 1)/12 - sqrt(3)*log(x**2 + sqrt(3)*x + 1)/12 + (5*x**4 - 1)/(5*x**5)","A",0
346,1,209,0,0.763508," ","integrate(1/x**8/(x**8+x**4+1),x)","\left(\frac{1}{8} - \frac{\sqrt{3} i}{24}\right) \log{\left(x - \frac{1}{2} + \frac{\sqrt{3} i}{6} - 18432 \left(\frac{1}{8} - \frac{\sqrt{3} i}{24}\right)^{5} \right)} + \left(\frac{1}{8} + \frac{\sqrt{3} i}{24}\right) \log{\left(x - \frac{1}{2} - 18432 \left(\frac{1}{8} + \frac{\sqrt{3} i}{24}\right)^{5} - \frac{\sqrt{3} i}{6} \right)} + \left(- \frac{1}{8} - \frac{\sqrt{3} i}{24}\right) \log{\left(x + \frac{1}{2} + \frac{\sqrt{3} i}{6} - 18432 \left(- \frac{1}{8} - \frac{\sqrt{3} i}{24}\right)^{5} \right)} + \left(- \frac{1}{8} + \frac{\sqrt{3} i}{24}\right) \log{\left(x + \frac{1}{2} - 18432 \left(- \frac{1}{8} + \frac{\sqrt{3} i}{24}\right)^{5} - \frac{\sqrt{3} i}{6} \right)} + \operatorname{RootSum} {\left(2304 t^{4} + 48 t^{2} + 1, \left( t \mapsto t \log{\left(- 18432 t^{5} - 4 t + x \right)} \right)\right)} + \frac{7 x^{4} - 3}{21 x^{7}}"," ",0,"(1/8 - sqrt(3)*I/24)*log(x - 1/2 + sqrt(3)*I/6 - 18432*(1/8 - sqrt(3)*I/24)**5) + (1/8 + sqrt(3)*I/24)*log(x - 1/2 - 18432*(1/8 + sqrt(3)*I/24)**5 - sqrt(3)*I/6) + (-1/8 - sqrt(3)*I/24)*log(x + 1/2 + sqrt(3)*I/6 - 18432*(-1/8 - sqrt(3)*I/24)**5) + (-1/8 + sqrt(3)*I/24)*log(x + 1/2 - 18432*(-1/8 + sqrt(3)*I/24)**5 - sqrt(3)*I/6) + RootSum(2304*_t**4 + 48*_t**2 + 1, Lambda(_t, _t*log(-18432*_t**5 - 4*_t + x))) + (7*x**4 - 3)/(21*x**7)","C",0
347,0,0,0,0.000000," ","integrate(x**m/(x**8-x**4+1),x)","\int \frac{x^{m}}{x^{8} - x^{4} + 1}\, dx"," ",0,"Integral(x**m/(x**8 - x**4 + 1), x)","F",0
348,1,42,0,0.140164," ","integrate(x**11/(x**8-x**4+1),x)","\frac{x^{4}}{4} + \frac{\log{\left(x^{8} - x^{4} + 1 \right)}}{8} - \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x^{4}}{3} - \frac{\sqrt{3}}{3} \right)}}{12}"," ",0,"x**4/4 + log(x**8 - x**4 + 1)/8 - sqrt(3)*atan(2*sqrt(3)*x**4/3 - sqrt(3)/3)/12","A",0
349,1,48,0,0.127205," ","integrate(x**9/(x**8-x**4+1),x)","\frac{x^{2}}{2} + \frac{\sqrt{3} \log{\left(x^{4} - \sqrt{3} x^{2} + 1 \right)}}{12} - \frac{\sqrt{3} \log{\left(x^{4} + \sqrt{3} x^{2} + 1 \right)}}{12}"," ",0,"x**2/2 + sqrt(3)*log(x**4 - sqrt(3)*x**2 + 1)/12 - sqrt(3)*log(x**4 + sqrt(3)*x**2 + 1)/12","A",0
350,1,37,0,0.137259," ","integrate(x**7/(x**8-x**4+1),x)","\frac{\log{\left(x^{8} - x^{4} + 1 \right)}}{8} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x^{4}}{3} - \frac{\sqrt{3}}{3} \right)}}{12}"," ",0,"log(x**8 - x**4 + 1)/8 + sqrt(3)*atan(2*sqrt(3)*x**4/3 - sqrt(3)/3)/12","A",0
351,1,70,0,0.209116," ","integrate(x**5/(x**8-x**4+1),x)","\frac{\sqrt{3} \log{\left(x^{4} - \sqrt{3} x^{2} + 1 \right)}}{24} - \frac{\sqrt{3} \log{\left(x^{4} + \sqrt{3} x^{2} + 1 \right)}}{24} + \frac{\operatorname{atan}{\left(2 x^{2} - \sqrt{3} \right)}}{4} + \frac{\operatorname{atan}{\left(2 x^{2} + \sqrt{3} \right)}}{4}"," ",0,"sqrt(3)*log(x**4 - sqrt(3)*x**2 + 1)/24 - sqrt(3)*log(x**4 + sqrt(3)*x**2 + 1)/24 + atan(2*x**2 - sqrt(3))/4 + atan(2*x**2 + sqrt(3))/4","A",0
352,1,26,0,0.122396," ","integrate(x**3/(x**8-x**4+1),x)","\frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x^{4}}{3} - \frac{\sqrt{3}}{3} \right)}}{6}"," ",0,"sqrt(3)*atan(2*sqrt(3)*x**4/3 - sqrt(3)/3)/6","A",0
353,1,70,0,0.208006," ","integrate(x/(x**8-x**4+1),x)","- \frac{\sqrt{3} \log{\left(x^{4} - \sqrt{3} x^{2} + 1 \right)}}{24} + \frac{\sqrt{3} \log{\left(x^{4} + \sqrt{3} x^{2} + 1 \right)}}{24} + \frac{\operatorname{atan}{\left(2 x^{2} - \sqrt{3} \right)}}{4} + \frac{\operatorname{atan}{\left(2 x^{2} + \sqrt{3} \right)}}{4}"," ",0,"-sqrt(3)*log(x**4 - sqrt(3)*x**2 + 1)/24 + sqrt(3)*log(x**4 + sqrt(3)*x**2 + 1)/24 + atan(2*x**2 - sqrt(3))/4 + atan(2*x**2 + sqrt(3))/4","A",0
354,1,41,0,0.156509," ","integrate(1/x/(x**8-x**4+1),x)","\log{\left(x \right)} - \frac{\log{\left(x^{8} - x^{4} + 1 \right)}}{8} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x^{4}}{3} - \frac{\sqrt{3}}{3} \right)}}{12}"," ",0,"log(x) - log(x**8 - x**4 + 1)/8 + sqrt(3)*atan(2*sqrt(3)*x**4/3 - sqrt(3)/3)/12","A",0
355,1,49,0,0.152852," ","integrate(1/x**3/(x**8-x**4+1),x)","- \frac{\sqrt{3} \log{\left(x^{4} - \sqrt{3} x^{2} + 1 \right)}}{12} + \frac{\sqrt{3} \log{\left(x^{4} + \sqrt{3} x^{2} + 1 \right)}}{12} - \frac{1}{2 x^{2}}"," ",0,"-sqrt(3)*log(x**4 - sqrt(3)*x**2 + 1)/12 + sqrt(3)*log(x**4 + sqrt(3)*x**2 + 1)/12 - 1/(2*x**2)","A",0
356,1,48,0,0.190187," ","integrate(1/x**5/(x**8-x**4+1),x)","\log{\left(x \right)} - \frac{\log{\left(x^{8} - x^{4} + 1 \right)}}{8} - \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x^{4}}{3} - \frac{\sqrt{3}}{3} \right)}}{12} - \frac{1}{4 x^{4}}"," ",0,"log(x) - log(x**8 - x**4 + 1)/8 - sqrt(3)*atan(2*sqrt(3)*x**4/3 - sqrt(3)/3)/12 - 1/(4*x**4)","A",0
357,1,83,0,0.261486," ","integrate(1/x**7/(x**8-x**4+1),x)","- \frac{\sqrt{3} \log{\left(x^{4} - \sqrt{3} x^{2} + 1 \right)}}{24} + \frac{\sqrt{3} \log{\left(x^{4} + \sqrt{3} x^{2} + 1 \right)}}{24} - \frac{\operatorname{atan}{\left(2 x^{2} - \sqrt{3} \right)}}{4} - \frac{\operatorname{atan}{\left(2 x^{2} + \sqrt{3} \right)}}{4} + \frac{- 3 x^{4} - 1}{6 x^{6}}"," ",0,"-sqrt(3)*log(x**4 - sqrt(3)*x**2 + 1)/24 + sqrt(3)*log(x**4 + sqrt(3)*x**2 + 1)/24 - atan(2*x**2 - sqrt(3))/4 - atan(2*x**2 + sqrt(3))/4 + (-3*x**4 - 1)/(6*x**6)","A",0
358,1,26,0,3.202004," ","integrate(x**8/(x**8-x**4+1),x)","x + \operatorname{RootSum} {\left(5308416 t^{8} - 2304 t^{4} + 1, \left( t \mapsto t \log{\left(9216 t^{5} - 8 t + x \right)} \right)\right)}"," ",0,"x + RootSum(5308416*_t**8 - 2304*_t**4 + 1, Lambda(_t, _t*log(9216*_t**5 - 8*_t + x)))","A",0
359,1,165,0,0.218596," ","integrate(x**6/(x**8-x**4+1),x)","\frac{\sqrt{6} \left(2 \operatorname{atan}{\left(\frac{\sqrt{6} x}{3} - \frac{1}{3} \right)} + 2 \operatorname{atan}{\left(\sqrt{6} x^{3} - 4 x^{2} + 2 \sqrt{6} x - 3 \right)}\right)}{24} + \frac{\sqrt{6} \left(2 \operatorname{atan}{\left(\frac{\sqrt{6} x}{3} + \frac{1}{3} \right)} + 2 \operatorname{atan}{\left(\sqrt{6} x^{3} + 4 x^{2} + 2 \sqrt{6} x + 3 \right)}\right)}{24} + \frac{\sqrt{6} \log{\left(x^{4} - \sqrt{6} x^{3} + 3 x^{2} - \sqrt{6} x + 1 \right)}}{24} - \frac{\sqrt{6} \log{\left(x^{4} + \sqrt{6} x^{3} + 3 x^{2} + \sqrt{6} x + 1 \right)}}{24}"," ",0,"sqrt(6)*(2*atan(sqrt(6)*x/3 - 1/3) + 2*atan(sqrt(6)*x**3 - 4*x**2 + 2*sqrt(6)*x - 3))/24 + sqrt(6)*(2*atan(sqrt(6)*x/3 + 1/3) + 2*atan(sqrt(6)*x**3 + 4*x**2 + 2*sqrt(6)*x + 3))/24 + sqrt(6)*log(x**4 - sqrt(6)*x**3 + 3*x**2 - sqrt(6)*x + 1)/24 - sqrt(6)*log(x**4 + sqrt(6)*x**3 + 3*x**2 + sqrt(6)*x + 1)/24","A",0
360,1,24,0,3.186931," ","integrate(x**4/(x**8-x**4+1),x)","\operatorname{RootSum} {\left(5308416 t^{8} - 2304 t^{4} + 1, \left( t \mapsto t \log{\left(- 18432 t^{5} + 4 t + x \right)} \right)\right)}"," ",0,"RootSum(5308416*_t**8 - 2304*_t**4 + 1, Lambda(_t, _t*log(-18432*_t**5 + 4*_t + x)))","A",0
361,1,26,0,3.280807," ","integrate(x**2/(x**8-x**4+1),x)","\operatorname{RootSum} {\left(5308416 t^{8} - 2304 t^{4} + 1, \left( t \mapsto t \log{\left(- 442368 t^{7} - 192 t^{3} + x \right)} \right)\right)}"," ",0,"RootSum(5308416*_t**8 - 2304*_t**4 + 1, Lambda(_t, _t*log(-442368*_t**7 - 192*_t**3 + x)))","A",0
362,1,165,0,0.220473," ","integrate(1/(x**8-x**4+1),x)","\frac{\sqrt{6} \left(2 \operatorname{atan}{\left(\frac{\sqrt{6} x}{3} - \frac{1}{3} \right)} + 2 \operatorname{atan}{\left(\sqrt{6} x^{3} - 4 x^{2} + 2 \sqrt{6} x - 3 \right)}\right)}{24} + \frac{\sqrt{6} \left(2 \operatorname{atan}{\left(\frac{\sqrt{6} x}{3} + \frac{1}{3} \right)} + 2 \operatorname{atan}{\left(\sqrt{6} x^{3} + 4 x^{2} + 2 \sqrt{6} x + 3 \right)}\right)}{24} - \frac{\sqrt{6} \log{\left(x^{4} - \sqrt{6} x^{3} + 3 x^{2} - \sqrt{6} x + 1 \right)}}{24} + \frac{\sqrt{6} \log{\left(x^{4} + \sqrt{6} x^{3} + 3 x^{2} + \sqrt{6} x + 1 \right)}}{24}"," ",0,"sqrt(6)*(2*atan(sqrt(6)*x/3 - 1/3) + 2*atan(sqrt(6)*x**3 - 4*x**2 + 2*sqrt(6)*x - 3))/24 + sqrt(6)*(2*atan(sqrt(6)*x/3 + 1/3) + 2*atan(sqrt(6)*x**3 + 4*x**2 + 2*sqrt(6)*x + 3))/24 - sqrt(6)*log(x**4 - sqrt(6)*x**3 + 3*x**2 - sqrt(6)*x + 1)/24 + sqrt(6)*log(x**4 + sqrt(6)*x**3 + 3*x**2 + sqrt(6)*x + 1)/24","A",0
363,1,29,0,3.292913," ","integrate(1/x**2/(x**8-x**4+1),x)","\operatorname{RootSum} {\left(5308416 t^{8} - 2304 t^{4} + 1, \left( t \mapsto t \log{\left(- 442368 t^{7} + 384 t^{3} + x \right)} \right)\right)} - \frac{1}{x}"," ",0,"RootSum(5308416*_t**8 - 2304*_t**4 + 1, Lambda(_t, _t*log(-442368*_t**7 + 384*_t**3 + x))) - 1/x","A",0
364,1,31,0,3.251713," ","integrate(1/x**4/(x**8-x**4+1),x)","\operatorname{RootSum} {\left(5308416 t^{8} - 2304 t^{4} + 1, \left( t \mapsto t \log{\left(- 9216 t^{5} + 8 t + x \right)} \right)\right)} - \frac{1}{3 x^{3}}"," ",0,"RootSum(5308416*_t**8 - 2304*_t**4 + 1, Lambda(_t, _t*log(-9216*_t**5 + 8*_t + x))) - 1/(3*x**3)","A",0
365,1,182,0,0.272993," ","integrate(1/x**6/(x**8-x**4+1),x)","\frac{\sqrt{6} \left(- 2 \operatorname{atan}{\left(\frac{\sqrt{6} x}{3} - \frac{1}{3} \right)} - 2 \operatorname{atan}{\left(\sqrt{6} x^{3} - 4 x^{2} + 2 \sqrt{6} x - 3 \right)}\right)}{24} + \frac{\sqrt{6} \left(- 2 \operatorname{atan}{\left(\frac{\sqrt{6} x}{3} + \frac{1}{3} \right)} - 2 \operatorname{atan}{\left(\sqrt{6} x^{3} + 4 x^{2} + 2 \sqrt{6} x + 3 \right)}\right)}{24} - \frac{\sqrt{6} \log{\left(x^{4} - \sqrt{6} x^{3} + 3 x^{2} - \sqrt{6} x + 1 \right)}}{24} + \frac{\sqrt{6} \log{\left(x^{4} + \sqrt{6} x^{3} + 3 x^{2} + \sqrt{6} x + 1 \right)}}{24} + \frac{- 5 x^{4} - 1}{5 x^{5}}"," ",0,"sqrt(6)*(-2*atan(sqrt(6)*x/3 - 1/3) - 2*atan(sqrt(6)*x**3 - 4*x**2 + 2*sqrt(6)*x - 3))/24 + sqrt(6)*(-2*atan(sqrt(6)*x/3 + 1/3) - 2*atan(sqrt(6)*x**3 + 4*x**2 + 2*sqrt(6)*x + 3))/24 - sqrt(6)*log(x**4 - sqrt(6)*x**3 + 3*x**2 - sqrt(6)*x + 1)/24 + sqrt(6)*log(x**4 + sqrt(6)*x**3 + 3*x**2 + sqrt(6)*x + 1)/24 + (-5*x**4 - 1)/(5*x**5)","A",0
366,1,37,0,3.365546," ","integrate(1/x**8/(x**8-x**4+1),x)","\operatorname{RootSum} {\left(5308416 t^{8} - 2304 t^{4} + 1, \left( t \mapsto t \log{\left(18432 t^{5} - 4 t + x \right)} \right)\right)} + \frac{- 7 x^{4} - 3}{21 x^{7}}"," ",0,"RootSum(5308416*_t**8 - 2304*_t**4 + 1, Lambda(_t, _t*log(18432*_t**5 - 4*_t + x))) + (-7*x**4 - 3)/(21*x**7)","A",0
367,0,0,0,0.000000," ","integrate(x**m/(x**8+3*x**4+1),x)","\int \frac{x^{m}}{x^{8} + 3 x^{4} + 1}\, dx"," ",0,"Integral(x**m/(x**8 + 3*x**4 + 1), x)","F",0
368,1,60,0,0.144980," ","integrate(x**11/(x**8+3*x**4+1),x)","\frac{x^{4}}{4} + \left(- \frac{3}{8} + \frac{7 \sqrt{5}}{40}\right) \log{\left(x^{4} - \frac{\sqrt{5}}{2} + \frac{3}{2} \right)} + \left(- \frac{7 \sqrt{5}}{40} - \frac{3}{8}\right) \log{\left(x^{4} + \frac{\sqrt{5}}{2} + \frac{3}{2} \right)}"," ",0,"x**4/4 + (-3/8 + 7*sqrt(5)/40)*log(x**4 - sqrt(5)/2 + 3/2) + (-7*sqrt(5)/40 - 3/8)*log(x**4 + sqrt(5)/2 + 3/2)","A",0
369,1,54,0,0.207111," ","integrate(x**9/(x**8+3*x**4+1),x)","\frac{x^{2}}{2} + 2 \left(\frac{1}{4} - \frac{\sqrt{5}}{10}\right) \operatorname{atan}{\left(\frac{2 x^{2}}{-1 + \sqrt{5}} \right)} - 2 \left(\frac{\sqrt{5}}{10} + \frac{1}{4}\right) \operatorname{atan}{\left(\frac{2 x^{2}}{1 + \sqrt{5}} \right)}"," ",0,"x**2/2 + 2*(1/4 - sqrt(5)/10)*atan(2*x**2/(-1 + sqrt(5))) - 2*(sqrt(5)/10 + 1/4)*atan(2*x**2/(1 + sqrt(5)))","A",0
370,1,53,0,0.135172," ","integrate(x**7/(x**8+3*x**4+1),x)","\left(\frac{1}{8} - \frac{3 \sqrt{5}}{40}\right) \log{\left(x^{4} - \frac{\sqrt{5}}{2} + \frac{3}{2} \right)} + \left(\frac{1}{8} + \frac{3 \sqrt{5}}{40}\right) \log{\left(x^{4} + \frac{\sqrt{5}}{2} + \frac{3}{2} \right)}"," ",0,"(1/8 - 3*sqrt(5)/40)*log(x**4 - sqrt(5)/2 + 3/2) + (1/8 + 3*sqrt(5)/40)*log(x**4 + sqrt(5)/2 + 3/2)","A",0
371,1,49,0,0.201303," ","integrate(x**5/(x**8+3*x**4+1),x)","- 2 \left(\frac{1}{8} - \frac{\sqrt{5}}{40}\right) \operatorname{atan}{\left(\frac{2 x^{2}}{-1 + \sqrt{5}} \right)} + 2 \left(\frac{\sqrt{5}}{40} + \frac{1}{8}\right) \operatorname{atan}{\left(\frac{2 x^{2}}{1 + \sqrt{5}} \right)}"," ",0,"-2*(1/8 - sqrt(5)/40)*atan(2*x**2/(-1 + sqrt(5))) + 2*(sqrt(5)/40 + 1/8)*atan(2*x**2/(1 + sqrt(5)))","A",0
372,1,42,0,0.118309," ","integrate(x**3/(x**8+3*x**4+1),x)","\frac{\sqrt{5} \log{\left(x^{4} - \frac{\sqrt{5}}{2} + \frac{3}{2} \right)}}{20} - \frac{\sqrt{5} \log{\left(x^{4} + \frac{\sqrt{5}}{2} + \frac{3}{2} \right)}}{20}"," ",0,"sqrt(5)*log(x**4 - sqrt(5)/2 + 3/2)/20 - sqrt(5)*log(x**4 + sqrt(5)/2 + 3/2)/20","A",0
373,1,49,0,0.203928," ","integrate(x/(x**8+3*x**4+1),x)","2 \left(\frac{\sqrt{5}}{40} + \frac{1}{8}\right) \operatorname{atan}{\left(\frac{2 x^{2}}{-1 + \sqrt{5}} \right)} - 2 \left(\frac{1}{8} - \frac{\sqrt{5}}{40}\right) \operatorname{atan}{\left(\frac{2 x^{2}}{1 + \sqrt{5}} \right)}"," ",0,"2*(sqrt(5)/40 + 1/8)*atan(2*x**2/(-1 + sqrt(5))) - 2*(1/8 - sqrt(5)/40)*atan(2*x**2/(1 + sqrt(5)))","A",0
374,1,58,0,0.158441," ","integrate(1/x/(x**8+3*x**4+1),x)","\log{\left(x \right)} + \left(- \frac{3 \sqrt{5}}{40} - \frac{1}{8}\right) \log{\left(x^{4} - \frac{\sqrt{5}}{2} + \frac{3}{2} \right)} + \left(- \frac{1}{8} + \frac{3 \sqrt{5}}{40}\right) \log{\left(x^{4} + \frac{\sqrt{5}}{2} + \frac{3}{2} \right)}"," ",0,"log(x) + (-3*sqrt(5)/40 - 1/8)*log(x**4 - sqrt(5)/2 + 3/2) + (-1/8 + 3*sqrt(5)/40)*log(x**4 + sqrt(5)/2 + 3/2)","A",0
375,1,56,0,0.237966," ","integrate(1/x**3/(x**8+3*x**4+1),x)","- 2 \left(\frac{\sqrt{5}}{10} + \frac{1}{4}\right) \operatorname{atan}{\left(\frac{2 x^{2}}{-1 + \sqrt{5}} \right)} + 2 \left(\frac{1}{4} - \frac{\sqrt{5}}{10}\right) \operatorname{atan}{\left(\frac{2 x^{2}}{1 + \sqrt{5}} \right)} - \frac{1}{2 x^{2}}"," ",0,"-2*(sqrt(5)/10 + 1/4)*atan(2*x**2/(-1 + sqrt(5))) + 2*(1/4 - sqrt(5)/10)*atan(2*x**2/(1 + sqrt(5))) - 1/(2*x**2)","A",0
376,1,65,0,0.188257," ","integrate(1/x**5/(x**8+3*x**4+1),x)","- 3 \log{\left(x \right)} + \left(\frac{3}{8} + \frac{7 \sqrt{5}}{40}\right) \log{\left(x^{4} - \frac{\sqrt{5}}{2} + \frac{3}{2} \right)} + \left(\frac{3}{8} - \frac{7 \sqrt{5}}{40}\right) \log{\left(x^{4} + \frac{\sqrt{5}}{2} + \frac{3}{2} \right)} - \frac{1}{4 x^{4}}"," ",0,"-3*log(x) + (3/8 + 7*sqrt(5)/40)*log(x**4 - sqrt(5)/2 + 3/2) + (3/8 - 7*sqrt(5)/40)*log(x**4 + sqrt(5)/2 + 3/2) - 1/(4*x**4)","A",0
377,1,65,0,0.271082," ","integrate(1/x**7/(x**8+3*x**4+1),x)","2 \left(\frac{11 \sqrt{5}}{40} + \frac{5}{8}\right) \operatorname{atan}{\left(\frac{2 x^{2}}{-1 + \sqrt{5}} \right)} - 2 \left(\frac{5}{8} - \frac{11 \sqrt{5}}{40}\right) \operatorname{atan}{\left(\frac{2 x^{2}}{1 + \sqrt{5}} \right)} + \frac{9 x^{4} - 1}{6 x^{6}}"," ",0,"2*(11*sqrt(5)/40 + 5/8)*atan(2*x**2/(-1 + sqrt(5))) - 2*(5/8 - 11*sqrt(5)/40)*atan(2*x**2/(1 + sqrt(5))) + (9*x**4 - 1)/(6*x**6)","A",0
378,1,29,0,1.591228," ","integrate(x**8/(x**8+3*x**4+1),x)","x + \operatorname{RootSum} {\left(40960000 t^{8} + 787200 t^{4} + 1, \left( t \mapsto t \log{\left(\frac{15360 t^{5}}{11} + \frac{1288 t}{55} + x \right)} \right)\right)}"," ",0,"x + RootSum(40960000*_t**8 + 787200*_t**4 + 1, Lambda(_t, _t*log(15360*_t**5/11 + 1288*_t/55 + x)))","A",0
379,1,26,0,1.530448," ","integrate(x**6/(x**8+3*x**4+1),x)","\operatorname{RootSum} {\left(40960000 t^{8} + 115200 t^{4} + 1, \left( t \mapsto t \log{\left(- 1792000 t^{7} - 4920 t^{3} + x \right)} \right)\right)}"," ",0,"RootSum(40960000*_t**8 + 115200*_t**4 + 1, Lambda(_t, _t*log(-1792000*_t**7 - 4920*_t**3 + x)))","A",0
380,1,24,0,1.482208," ","integrate(x**4/(x**8+3*x**4+1),x)","\operatorname{RootSum} {\left(40960000 t^{8} + 19200 t^{4} + 1, \left( t \mapsto t \log{\left(- 51200 t^{5} - 12 t + x \right)} \right)\right)}"," ",0,"RootSum(40960000*_t**8 + 19200*_t**4 + 1, Lambda(_t, _t*log(-51200*_t**5 - 12*_t + x)))","A",0
381,1,26,0,1.510216," ","integrate(x**2/(x**8+3*x**4+1),x)","\operatorname{RootSum} {\left(40960000 t^{8} + 19200 t^{4} + 1, \left( t \mapsto t \log{\left(- 6144000 t^{7} - 2240 t^{3} + x \right)} \right)\right)}"," ",0,"RootSum(40960000*_t**8 + 19200*_t**4 + 1, Lambda(_t, _t*log(-6144000*_t**7 - 2240*_t**3 + x)))","A",0
382,1,26,0,1.518543," ","integrate(1/(x**8+3*x**4+1),x)","\operatorname{RootSum} {\left(40960000 t^{8} + 115200 t^{4} + 1, \left( t \mapsto t \log{\left(- 9600 t^{5} - \frac{47 t}{2} + x \right)} \right)\right)}"," ",0,"RootSum(40960000*_t**8 + 115200*_t**4 + 1, Lambda(_t, _t*log(-9600*_t**5 - 47*_t/2 + x)))","A",0
383,1,32,0,1.609436," ","integrate(1/x**2/(x**8+3*x**4+1),x)","\operatorname{RootSum} {\left(40960000 t^{8} + 787200 t^{4} + 1, \left( t \mapsto t \log{\left(\frac{19251200 t^{7}}{11} + \frac{369792 t^{3}}{11} + x \right)} \right)\right)} - \frac{1}{x}"," ",0,"RootSum(40960000*_t**8 + 787200*_t**4 + 1, Lambda(_t, _t*log(19251200*_t**7/11 + 369792*_t**3/11 + x))) - 1/x","A",0
384,1,34,0,1.624297," ","integrate(1/x**4/(x**8+3*x**4+1),x)","\operatorname{RootSum} {\left(40960000 t^{8} + 5395200 t^{4} + 1, \left( t \mapsto t \log{\left(\frac{179200 t^{5}}{377} + \frac{23112 t}{377} + x \right)} \right)\right)} - \frac{1}{3 x^{3}}"," ",0,"RootSum(40960000*_t**8 + 5395200*_t**4 + 1, Lambda(_t, _t*log(179200*_t**5/377 + 23112*_t/377 + x))) - 1/(3*x**3)","A",0
385,0,0,0,0.000000," ","integrate(x**m/(x**8-3*x**4+1),x)","\int \frac{x^{m}}{\left(x^{4} - x^{2} - 1\right) \left(x^{4} + x^{2} - 1\right)}\, dx"," ",0,"Integral(x**m/((x**4 - x**2 - 1)*(x**4 + x**2 - 1)), x)","F",0
386,1,58,0,0.142759," ","integrate(x**11/(x**8-3*x**4+1),x)","\frac{x^{4}}{4} + \left(\frac{3}{8} + \frac{7 \sqrt{5}}{40}\right) \log{\left(x^{4} - \frac{3}{2} - \frac{\sqrt{5}}{2} \right)} + \left(\frac{3}{8} - \frac{7 \sqrt{5}}{40}\right) \log{\left(x^{4} - \frac{3}{2} + \frac{\sqrt{5}}{2} \right)}"," ",0,"x**4/4 + (3/8 + 7*sqrt(5)/40)*log(x**4 - 3/2 - sqrt(5)/2) + (3/8 - 7*sqrt(5)/40)*log(x**4 - 3/2 + sqrt(5)/2)","A",0
387,1,170,0,0.379559," ","integrate(x**9/(x**8-3*x**4+1),x)","\frac{x^{2}}{2} + \left(- \frac{1}{4} - \frac{\sqrt{5}}{10}\right) \log{\left(x^{2} - \frac{47}{8} - \frac{47 \sqrt{5}}{20} - 120 \left(- \frac{1}{4} - \frac{\sqrt{5}}{10}\right)^{3} \right)} + \left(- \frac{1}{4} + \frac{\sqrt{5}}{10}\right) \log{\left(x^{2} - \frac{47}{8} - 120 \left(- \frac{1}{4} + \frac{\sqrt{5}}{10}\right)^{3} + \frac{47 \sqrt{5}}{20} \right)} + \left(\frac{1}{4} - \frac{\sqrt{5}}{10}\right) \log{\left(x^{2} - \frac{47 \sqrt{5}}{20} - 120 \left(\frac{1}{4} - \frac{\sqrt{5}}{10}\right)^{3} + \frac{47}{8} \right)} + \left(\frac{\sqrt{5}}{10} + \frac{1}{4}\right) \log{\left(x^{2} - 120 \left(\frac{\sqrt{5}}{10} + \frac{1}{4}\right)^{3} + \frac{47 \sqrt{5}}{20} + \frac{47}{8} \right)}"," ",0,"x**2/2 + (-1/4 - sqrt(5)/10)*log(x**2 - 47/8 - 47*sqrt(5)/20 - 120*(-1/4 - sqrt(5)/10)**3) + (-1/4 + sqrt(5)/10)*log(x**2 - 47/8 - 120*(-1/4 + sqrt(5)/10)**3 + 47*sqrt(5)/20) + (1/4 - sqrt(5)/10)*log(x**2 - 47*sqrt(5)/20 - 120*(1/4 - sqrt(5)/10)**3 + 47/8) + (sqrt(5)/10 + 1/4)*log(x**2 - 120*(sqrt(5)/10 + 1/4)**3 + 47*sqrt(5)/20 + 47/8)","B",0
388,1,53,0,0.135388," ","integrate(x**7/(x**8-3*x**4+1),x)","\left(\frac{1}{8} + \frac{3 \sqrt{5}}{40}\right) \log{\left(x^{4} - \frac{3}{2} - \frac{\sqrt{5}}{2} \right)} + \left(\frac{1}{8} - \frac{3 \sqrt{5}}{40}\right) \log{\left(x^{4} - \frac{3}{2} + \frac{\sqrt{5}}{2} \right)}"," ",0,"(1/8 + 3*sqrt(5)/40)*log(x**4 - 3/2 - sqrt(5)/2) + (1/8 - 3*sqrt(5)/40)*log(x**4 - 3/2 + sqrt(5)/2)","A",0
389,1,165,0,0.371056," ","integrate(x**5/(x**8-3*x**4+1),x)","\left(- \frac{1}{8} - \frac{\sqrt{5}}{40}\right) \log{\left(x^{2} - \frac{3}{2} - \frac{3 \sqrt{5}}{10} - 640 \left(- \frac{1}{8} - \frac{\sqrt{5}}{40}\right)^{3} \right)} + \left(- \frac{1}{8} + \frac{\sqrt{5}}{40}\right) \log{\left(x^{2} - \frac{3}{2} - 640 \left(- \frac{1}{8} + \frac{\sqrt{5}}{40}\right)^{3} + \frac{3 \sqrt{5}}{10} \right)} + \left(\frac{1}{8} - \frac{\sqrt{5}}{40}\right) \log{\left(x^{2} - \frac{3 \sqrt{5}}{10} - 640 \left(\frac{1}{8} - \frac{\sqrt{5}}{40}\right)^{3} + \frac{3}{2} \right)} + \left(\frac{\sqrt{5}}{40} + \frac{1}{8}\right) \log{\left(x^{2} - 640 \left(\frac{\sqrt{5}}{40} + \frac{1}{8}\right)^{3} + \frac{3 \sqrt{5}}{10} + \frac{3}{2} \right)}"," ",0,"(-1/8 - sqrt(5)/40)*log(x**2 - 3/2 - 3*sqrt(5)/10 - 640*(-1/8 - sqrt(5)/40)**3) + (-1/8 + sqrt(5)/40)*log(x**2 - 3/2 - 640*(-1/8 + sqrt(5)/40)**3 + 3*sqrt(5)/10) + (1/8 - sqrt(5)/40)*log(x**2 - 3*sqrt(5)/10 - 640*(1/8 - sqrt(5)/40)**3 + 3/2) + (sqrt(5)/40 + 1/8)*log(x**2 - 640*(sqrt(5)/40 + 1/8)**3 + 3*sqrt(5)/10 + 3/2)","B",0
390,1,42,0,0.117606," ","integrate(x**3/(x**8-3*x**4+1),x)","\frac{\sqrt{5} \log{\left(x^{4} - \frac{3}{2} - \frac{\sqrt{5}}{2} \right)}}{20} - \frac{\sqrt{5} \log{\left(x^{4} - \frac{3}{2} + \frac{\sqrt{5}}{2} \right)}}{20}"," ",0,"sqrt(5)*log(x**4 - 3/2 - sqrt(5)/2)/20 - sqrt(5)*log(x**4 - 3/2 + sqrt(5)/2)/20","A",0
391,1,165,0,0.365604," ","integrate(x/(x**8-3*x**4+1),x)","\left(\frac{\sqrt{5}}{40} + \frac{1}{8}\right) \log{\left(x^{2} - \frac{7}{2} - \frac{7 \sqrt{5}}{10} + 960 \left(\frac{\sqrt{5}}{40} + \frac{1}{8}\right)^{3} \right)} + \left(\frac{1}{8} - \frac{\sqrt{5}}{40}\right) \log{\left(x^{2} - \frac{7}{2} + 960 \left(\frac{1}{8} - \frac{\sqrt{5}}{40}\right)^{3} + \frac{7 \sqrt{5}}{10} \right)} + \left(- \frac{1}{8} + \frac{\sqrt{5}}{40}\right) \log{\left(x^{2} - \frac{7 \sqrt{5}}{10} + 960 \left(- \frac{1}{8} + \frac{\sqrt{5}}{40}\right)^{3} + \frac{7}{2} \right)} + \left(- \frac{1}{8} - \frac{\sqrt{5}}{40}\right) \log{\left(x^{2} + 960 \left(- \frac{1}{8} - \frac{\sqrt{5}}{40}\right)^{3} + \frac{7 \sqrt{5}}{10} + \frac{7}{2} \right)}"," ",0,"(sqrt(5)/40 + 1/8)*log(x**2 - 7/2 - 7*sqrt(5)/10 + 960*(sqrt(5)/40 + 1/8)**3) + (1/8 - sqrt(5)/40)*log(x**2 - 7/2 + 960*(1/8 - sqrt(5)/40)**3 + 7*sqrt(5)/10) + (-1/8 + sqrt(5)/40)*log(x**2 - 7*sqrt(5)/10 + 960*(-1/8 + sqrt(5)/40)**3 + 7/2) + (-1/8 - sqrt(5)/40)*log(x**2 + 960*(-1/8 - sqrt(5)/40)**3 + 7*sqrt(5)/10 + 7/2)","B",0
392,1,58,0,0.158489," ","integrate(1/x/(x**8-3*x**4+1),x)","\log{\left(x \right)} + \left(- \frac{1}{8} + \frac{3 \sqrt{5}}{40}\right) \log{\left(x^{4} - \frac{3}{2} - \frac{\sqrt{5}}{2} \right)} + \left(- \frac{3 \sqrt{5}}{40} - \frac{1}{8}\right) \log{\left(x^{4} - \frac{3}{2} + \frac{\sqrt{5}}{2} \right)}"," ",0,"log(x) + (-1/8 + 3*sqrt(5)/40)*log(x**4 - 3/2 - sqrt(5)/2) + (-3*sqrt(5)/40 - 1/8)*log(x**4 - 3/2 + sqrt(5)/2)","A",0
393,1,172,0,0.405605," ","integrate(1/x**3/(x**8-3*x**4+1),x)","\left(\frac{\sqrt{5}}{10} + \frac{1}{4}\right) \log{\left(x^{2} - \frac{123}{8} - \frac{123 \sqrt{5}}{20} + 280 \left(\frac{\sqrt{5}}{10} + \frac{1}{4}\right)^{3} \right)} + \left(\frac{1}{4} - \frac{\sqrt{5}}{10}\right) \log{\left(x^{2} - \frac{123}{8} + 280 \left(\frac{1}{4} - \frac{\sqrt{5}}{10}\right)^{3} + \frac{123 \sqrt{5}}{20} \right)} + \left(- \frac{1}{4} + \frac{\sqrt{5}}{10}\right) \log{\left(x^{2} - \frac{123 \sqrt{5}}{20} + 280 \left(- \frac{1}{4} + \frac{\sqrt{5}}{10}\right)^{3} + \frac{123}{8} \right)} + \left(- \frac{1}{4} - \frac{\sqrt{5}}{10}\right) \log{\left(x^{2} + 280 \left(- \frac{1}{4} - \frac{\sqrt{5}}{10}\right)^{3} + \frac{123 \sqrt{5}}{20} + \frac{123}{8} \right)} - \frac{1}{2 x^{2}}"," ",0,"(sqrt(5)/10 + 1/4)*log(x**2 - 123/8 - 123*sqrt(5)/20 + 280*(sqrt(5)/10 + 1/4)**3) + (1/4 - sqrt(5)/10)*log(x**2 - 123/8 + 280*(1/4 - sqrt(5)/10)**3 + 123*sqrt(5)/20) + (-1/4 + sqrt(5)/10)*log(x**2 - 123*sqrt(5)/20 + 280*(-1/4 + sqrt(5)/10)**3 + 123/8) + (-1/4 - sqrt(5)/10)*log(x**2 + 280*(-1/4 - sqrt(5)/10)**3 + 123*sqrt(5)/20 + 123/8) - 1/(2*x**2)","B",0
394,1,66,0,0.190218," ","integrate(1/x**5/(x**8-3*x**4+1),x)","3 \log{\left(x \right)} + \left(- \frac{3}{8} + \frac{7 \sqrt{5}}{40}\right) \log{\left(x^{4} - \frac{3}{2} - \frac{\sqrt{5}}{2} \right)} + \left(- \frac{7 \sqrt{5}}{40} - \frac{3}{8}\right) \log{\left(x^{4} - \frac{3}{2} + \frac{\sqrt{5}}{2} \right)} - \frac{1}{4 x^{4}}"," ",0,"3*log(x) + (-3/8 + 7*sqrt(5)/40)*log(x**4 - 3/2 - sqrt(5)/2) + (-7*sqrt(5)/40 - 3/8)*log(x**4 - 3/2 + sqrt(5)/2) - 1/(4*x**4)","A",0
395,1,199,0,0.439112," ","integrate(1/x**7/(x**8-3*x**4+1),x)","\left(\frac{11 \sqrt{5}}{40} + \frac{5}{8}\right) \log{\left(x^{2} - \frac{2207}{22} - \frac{2207 \sqrt{5}}{50} + \frac{1152 \left(\frac{11 \sqrt{5}}{40} + \frac{5}{8}\right)^{3}}{11} \right)} + \left(\frac{5}{8} - \frac{11 \sqrt{5}}{40}\right) \log{\left(x^{2} - \frac{2207}{22} + \frac{1152 \left(\frac{5}{8} - \frac{11 \sqrt{5}}{40}\right)^{3}}{11} + \frac{2207 \sqrt{5}}{50} \right)} + \left(- \frac{5}{8} + \frac{11 \sqrt{5}}{40}\right) \log{\left(x^{2} - \frac{2207 \sqrt{5}}{50} + \frac{1152 \left(- \frac{5}{8} + \frac{11 \sqrt{5}}{40}\right)^{3}}{11} + \frac{2207}{22} \right)} + \left(- \frac{5}{8} - \frac{11 \sqrt{5}}{40}\right) \log{\left(x^{2} + \frac{1152 \left(- \frac{5}{8} - \frac{11 \sqrt{5}}{40}\right)^{3}}{11} + \frac{2207 \sqrt{5}}{50} + \frac{2207}{22} \right)} + \frac{- 9 x^{4} - 1}{6 x^{6}}"," ",0,"(11*sqrt(5)/40 + 5/8)*log(x**2 - 2207/22 - 2207*sqrt(5)/50 + 1152*(11*sqrt(5)/40 + 5/8)**3/11) + (5/8 - 11*sqrt(5)/40)*log(x**2 - 2207/22 + 1152*(5/8 - 11*sqrt(5)/40)**3/11 + 2207*sqrt(5)/50) + (-5/8 + 11*sqrt(5)/40)*log(x**2 - 2207*sqrt(5)/50 + 1152*(-5/8 + 11*sqrt(5)/40)**3/11 + 2207/22) + (-5/8 - 11*sqrt(5)/40)*log(x**2 + 1152*(-5/8 - 11*sqrt(5)/40)**3/11 + 2207*sqrt(5)/50 + 2207/22) + (-9*x**4 - 1)/(6*x**6)","B",0
396,1,58,0,1.244766," ","integrate(x**8/(x**8-3*x**4+1),x)","x + \operatorname{RootSum} {\left(6400 t^{4} - 880 t^{2} - 1, \left( t \mapsto t \log{\left(- \frac{15360 t^{5}}{11} + \frac{1288 t}{55} + x \right)} \right)\right)} + \operatorname{RootSum} {\left(6400 t^{4} + 880 t^{2} - 1, \left( t \mapsto t \log{\left(- \frac{15360 t^{5}}{11} + \frac{1288 t}{55} + x \right)} \right)\right)}"," ",0,"x + RootSum(6400*_t**4 - 880*_t**2 - 1, Lambda(_t, _t*log(-15360*_t**5/11 + 1288*_t/55 + x))) + RootSum(6400*_t**4 + 880*_t**2 - 1, Lambda(_t, _t*log(-15360*_t**5/11 + 1288*_t/55 + x)))","A",0
397,1,53,0,1.221576," ","integrate(x**6/(x**8-3*x**4+1),x)","\operatorname{RootSum} {\left(6400 t^{4} - 320 t^{2} - 1, \left( t \mapsto t \log{\left(- 1792000 t^{7} + 4920 t^{3} + x \right)} \right)\right)} + \operatorname{RootSum} {\left(6400 t^{4} + 320 t^{2} - 1, \left( t \mapsto t \log{\left(- 1792000 t^{7} + 4920 t^{3} + x \right)} \right)\right)}"," ",0,"RootSum(6400*_t**4 - 320*_t**2 - 1, Lambda(_t, _t*log(-1792000*_t**7 + 4920*_t**3 + x))) + RootSum(6400*_t**4 + 320*_t**2 - 1, Lambda(_t, _t*log(-1792000*_t**7 + 4920*_t**3 + x)))","A",0
398,1,49,0,1.202961," ","integrate(x**4/(x**8-3*x**4+1),x)","\operatorname{RootSum} {\left(6400 t^{4} - 80 t^{2} - 1, \left( t \mapsto t \log{\left(- 51200 t^{5} + 12 t + x \right)} \right)\right)} + \operatorname{RootSum} {\left(6400 t^{4} + 80 t^{2} - 1, \left( t \mapsto t \log{\left(- 51200 t^{5} + 12 t + x \right)} \right)\right)}"," ",0,"RootSum(6400*_t**4 - 80*_t**2 - 1, Lambda(_t, _t*log(-51200*_t**5 + 12*_t + x))) + RootSum(6400*_t**4 + 80*_t**2 - 1, Lambda(_t, _t*log(-51200*_t**5 + 12*_t + x)))","A",0
399,1,53,0,1.185135," ","integrate(x**2/(x**8-3*x**4+1),x)","\operatorname{RootSum} {\left(6400 t^{4} - 80 t^{2} - 1, \left( t \mapsto t \log{\left(6144000 t^{7} - 2240 t^{3} + x \right)} \right)\right)} + \operatorname{RootSum} {\left(6400 t^{4} + 80 t^{2} - 1, \left( t \mapsto t \log{\left(6144000 t^{7} - 2240 t^{3} + x \right)} \right)\right)}"," ",0,"RootSum(6400*_t**4 - 80*_t**2 - 1, Lambda(_t, _t*log(6144000*_t**7 - 2240*_t**3 + x))) + RootSum(6400*_t**4 + 80*_t**2 - 1, Lambda(_t, _t*log(6144000*_t**7 - 2240*_t**3 + x)))","A",0
400,1,53,0,1.212038," ","integrate(1/(x**8-3*x**4+1),x)","\operatorname{RootSum} {\left(6400 t^{4} - 320 t^{2} - 1, \left( t \mapsto t \log{\left(9600 t^{5} - \frac{47 t}{2} + x \right)} \right)\right)} + \operatorname{RootSum} {\left(6400 t^{4} + 320 t^{2} - 1, \left( t \mapsto t \log{\left(9600 t^{5} - \frac{47 t}{2} + x \right)} \right)\right)}"," ",0,"RootSum(6400*_t**4 - 320*_t**2 - 1, Lambda(_t, _t*log(9600*_t**5 - 47*_t/2 + x))) + RootSum(6400*_t**4 + 320*_t**2 - 1, Lambda(_t, _t*log(9600*_t**5 - 47*_t/2 + x)))","A",0
401,1,63,0,1.250350," ","integrate(1/x**2/(x**8-3*x**4+1),x)","\operatorname{RootSum} {\left(6400 t^{4} - 880 t^{2} - 1, \left( t \mapsto t \log{\left(\frac{19251200 t^{7}}{11} - \frac{369792 t^{3}}{11} + x \right)} \right)\right)} + \operatorname{RootSum} {\left(6400 t^{4} + 880 t^{2} - 1, \left( t \mapsto t \log{\left(\frac{19251200 t^{7}}{11} - \frac{369792 t^{3}}{11} + x \right)} \right)\right)} - \frac{1}{x}"," ",0,"RootSum(6400*_t**4 - 880*_t**2 - 1, Lambda(_t, _t*log(19251200*_t**7/11 - 369792*_t**3/11 + x))) + RootSum(6400*_t**4 + 880*_t**2 - 1, Lambda(_t, _t*log(19251200*_t**7/11 - 369792*_t**3/11 + x))) - 1/x","A",0
402,1,63,0,1.280600," ","integrate(1/x**4/(x**8-3*x**4+1),x)","\operatorname{RootSum} {\left(6400 t^{4} - 2320 t^{2} - 1, \left( t \mapsto t \log{\left(\frac{179200 t^{5}}{377} - \frac{23112 t}{377} + x \right)} \right)\right)} + \operatorname{RootSum} {\left(6400 t^{4} + 2320 t^{2} - 1, \left( t \mapsto t \log{\left(\frac{179200 t^{5}}{377} - \frac{23112 t}{377} + x \right)} \right)\right)} - \frac{1}{3 x^{3}}"," ",0,"RootSum(6400*_t**4 - 2320*_t**2 - 1, Lambda(_t, _t*log(179200*_t**5/377 - 23112*_t/377 + x))) + RootSum(6400*_t**4 + 2320*_t**2 - 1, Lambda(_t, _t*log(179200*_t**5/377 - 23112*_t/377 + x))) - 1/(3*x**3)","A",0
403,1,73,0,1.289721," ","integrate(1/x**6/(x**8-3*x**4+1),x)","\operatorname{RootSum} {\left(6400 t^{4} - 6080 t^{2} - 1, \left( t \mapsto t \log{\left(\frac{215808000 t^{7}}{323} - \frac{194833880 t^{3}}{323} + x \right)} \right)\right)} + \operatorname{RootSum} {\left(6400 t^{4} + 6080 t^{2} - 1, \left( t \mapsto t \log{\left(\frac{215808000 t^{7}}{323} - \frac{194833880 t^{3}}{323} + x \right)} \right)\right)} + \frac{- 15 x^{4} - 1}{5 x^{5}}"," ",0,"RootSum(6400*_t**4 - 6080*_t**2 - 1, Lambda(_t, _t*log(215808000*_t**7/323 - 194833880*_t**3/323 + x))) + RootSum(6400*_t**4 + 6080*_t**2 - 1, Lambda(_t, _t*log(215808000*_t**7/323 - 194833880*_t**3/323 + x))) + (-15*x**4 - 1)/(5*x**5)","A",0
404,1,70,0,1.297935," ","integrate(1/x**8/(x**8-3*x**4+1),x)","\operatorname{RootSum} {\left(6400 t^{4} - 15920 t^{2} - 1, \left( t \mapsto t \log{\left(\frac{460800 t^{5}}{17711} - \frac{2842588 t}{17711} + x \right)} \right)\right)} + \operatorname{RootSum} {\left(6400 t^{4} + 15920 t^{2} - 1, \left( t \mapsto t \log{\left(\frac{460800 t^{5}}{17711} - \frac{2842588 t}{17711} + x \right)} \right)\right)} + \frac{- 7 x^{4} - 1}{7 x^{7}}"," ",0,"RootSum(6400*_t**4 - 15920*_t**2 - 1, Lambda(_t, _t*log(460800*_t**5/17711 - 2842588*_t/17711 + x))) + RootSum(6400*_t**4 + 15920*_t**2 - 1, Lambda(_t, _t*log(460800*_t**5/17711 - 2842588*_t/17711 + x))) + (-7*x**4 - 1)/(7*x**7)","A",0
405,1,15,0,0.116472," ","integrate(x**3/(x**8+3*x**4+2),x)","\frac{\log{\left(x^{4} + 1 \right)}}{4} - \frac{\log{\left(x^{4} + 2 \right)}}{4}"," ",0,"log(x**4 + 1)/4 - log(x**4 + 2)/4","A",0
406,1,19,0,0.129737," ","integrate(x**11/(x**8+3*x**4+2),x)","\frac{x^{4}}{4} + \frac{\log{\left(x^{4} + 1 \right)}}{4} - \log{\left(x^{4} + 2 \right)}"," ",0,"x**4/4 + log(x**4 + 1)/4 - log(x**4 + 2)","A",0
407,1,37,0,0.142931," ","integrate(x**9/(x**10+x**5+2),x)","\frac{\log{\left(x^{10} + x^{5} + 2 \right)}}{10} - \frac{\sqrt{7} \operatorname{atan}{\left(\frac{2 \sqrt{7} x^{5}}{7} + \frac{\sqrt{7}}{7} \right)}}{35}"," ",0,"log(x**10 + x**5 + 2)/10 - sqrt(7)*atan(2*sqrt(7)*x**5/7 + sqrt(7)/7)/35","A",0
408,1,27,0,0.130561," ","integrate(x**4/(x**10+x**5+2),x)","\frac{2 \sqrt{7} \operatorname{atan}{\left(\frac{2 \sqrt{7} x^{5}}{7} + \frac{\sqrt{7}}{7} \right)}}{35}"," ",0,"2*sqrt(7)*atan(2*sqrt(7)*x**5/7 + sqrt(7)/7)/35","A",0
409,1,41,0,0.165099," ","integrate(1/x/(x**10+x**5+1),x)","\log{\left(x \right)} - \frac{\log{\left(x^{10} + x^{5} + 1 \right)}}{10} - \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x^{5}}{3} + \frac{\sqrt{3}}{3} \right)}}{15}"," ",0,"log(x) - log(x**10 + x**5 + 1)/10 - sqrt(3)*atan(2*sqrt(3)*x**5/3 + sqrt(3)/3)/15","A",0
410,1,48,0,0.202041," ","integrate(1/x**6/(x**10+x**5+1),x)","- \log{\left(x \right)} + \frac{\log{\left(x^{10} + x^{5} + 1 \right)}}{10} - \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x^{5}}{3} + \frac{\sqrt{3}}{3} \right)}}{15} - \frac{1}{5 x^{5}}"," ",0,"-log(x) + log(x**10 + x**5 + 1)/10 - sqrt(3)*atan(2*sqrt(3)*x**5/3 + sqrt(3)/3)/15 - 1/(5*x**5)","A",0
411,1,41,0,0.165653," ","integrate(1/(x**11+x**6+x),x)","\log{\left(x \right)} - \frac{\log{\left(x^{10} + x^{5} + 1 \right)}}{10} - \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x^{5}}{3} + \frac{\sqrt{3}}{3} \right)}}{15}"," ",0,"log(x) - log(x**10 + x**5 + 1)/10 - sqrt(3)*atan(2*sqrt(3)*x**5/3 + sqrt(3)/3)/15","A",0
412,1,605,0,1.249186," ","integrate(x**3/(c+a/x**2+b/x),x)","- \frac{b x^{3}}{3 c^{2}} + x^{2} \left(- \frac{a}{2 c^{2}} + \frac{b^{2}}{2 c^{3}}\right) + x \left(\frac{2 a b}{c^{3}} - \frac{b^{3}}{c^{4}}\right) + \left(- \frac{b \sqrt{- 4 a c + b^{2}} \left(5 a^{2} c^{2} - 5 a b^{2} c + b^{4}\right)}{2 c^{5} \left(4 a c - b^{2}\right)} + \frac{a^{2} c^{2} - 3 a b^{2} c + b^{4}}{2 c^{5}}\right) \log{\left(x + \frac{2 a^{3} c^{2} - 4 a^{2} b^{2} c + a b^{4} - 4 a c^{5} \left(- \frac{b \sqrt{- 4 a c + b^{2}} \left(5 a^{2} c^{2} - 5 a b^{2} c + b^{4}\right)}{2 c^{5} \left(4 a c - b^{2}\right)} + \frac{a^{2} c^{2} - 3 a b^{2} c + b^{4}}{2 c^{5}}\right) + b^{2} c^{4} \left(- \frac{b \sqrt{- 4 a c + b^{2}} \left(5 a^{2} c^{2} - 5 a b^{2} c + b^{4}\right)}{2 c^{5} \left(4 a c - b^{2}\right)} + \frac{a^{2} c^{2} - 3 a b^{2} c + b^{4}}{2 c^{5}}\right)}{5 a^{2} b c^{2} - 5 a b^{3} c + b^{5}} \right)} + \left(\frac{b \sqrt{- 4 a c + b^{2}} \left(5 a^{2} c^{2} - 5 a b^{2} c + b^{4}\right)}{2 c^{5} \left(4 a c - b^{2}\right)} + \frac{a^{2} c^{2} - 3 a b^{2} c + b^{4}}{2 c^{5}}\right) \log{\left(x + \frac{2 a^{3} c^{2} - 4 a^{2} b^{2} c + a b^{4} - 4 a c^{5} \left(\frac{b \sqrt{- 4 a c + b^{2}} \left(5 a^{2} c^{2} - 5 a b^{2} c + b^{4}\right)}{2 c^{5} \left(4 a c - b^{2}\right)} + \frac{a^{2} c^{2} - 3 a b^{2} c + b^{4}}{2 c^{5}}\right) + b^{2} c^{4} \left(\frac{b \sqrt{- 4 a c + b^{2}} \left(5 a^{2} c^{2} - 5 a b^{2} c + b^{4}\right)}{2 c^{5} \left(4 a c - b^{2}\right)} + \frac{a^{2} c^{2} - 3 a b^{2} c + b^{4}}{2 c^{5}}\right)}{5 a^{2} b c^{2} - 5 a b^{3} c + b^{5}} \right)} + \frac{x^{4}}{4 c}"," ",0,"-b*x**3/(3*c**2) + x**2*(-a/(2*c**2) + b**2/(2*c**3)) + x*(2*a*b/c**3 - b**3/c**4) + (-b*sqrt(-4*a*c + b**2)*(5*a**2*c**2 - 5*a*b**2*c + b**4)/(2*c**5*(4*a*c - b**2)) + (a**2*c**2 - 3*a*b**2*c + b**4)/(2*c**5))*log(x + (2*a**3*c**2 - 4*a**2*b**2*c + a*b**4 - 4*a*c**5*(-b*sqrt(-4*a*c + b**2)*(5*a**2*c**2 - 5*a*b**2*c + b**4)/(2*c**5*(4*a*c - b**2)) + (a**2*c**2 - 3*a*b**2*c + b**4)/(2*c**5)) + b**2*c**4*(-b*sqrt(-4*a*c + b**2)*(5*a**2*c**2 - 5*a*b**2*c + b**4)/(2*c**5*(4*a*c - b**2)) + (a**2*c**2 - 3*a*b**2*c + b**4)/(2*c**5)))/(5*a**2*b*c**2 - 5*a*b**3*c + b**5)) + (b*sqrt(-4*a*c + b**2)*(5*a**2*c**2 - 5*a*b**2*c + b**4)/(2*c**5*(4*a*c - b**2)) + (a**2*c**2 - 3*a*b**2*c + b**4)/(2*c**5))*log(x + (2*a**3*c**2 - 4*a**2*b**2*c + a*b**4 - 4*a*c**5*(b*sqrt(-4*a*c + b**2)*(5*a**2*c**2 - 5*a*b**2*c + b**4)/(2*c**5*(4*a*c - b**2)) + (a**2*c**2 - 3*a*b**2*c + b**4)/(2*c**5)) + b**2*c**4*(b*sqrt(-4*a*c + b**2)*(5*a**2*c**2 - 5*a*b**2*c + b**4)/(2*c**5*(4*a*c - b**2)) + (a**2*c**2 - 3*a*b**2*c + b**4)/(2*c**5)))/(5*a**2*b*c**2 - 5*a*b**3*c + b**5)) + x**4/(4*c)","B",0
413,1,498,0,1.011683," ","integrate(x**2/(c+a/x**2+b/x),x)","- \frac{b x^{2}}{2 c^{2}} + x \left(- \frac{a}{c^{2}} + \frac{b^{2}}{c^{3}}\right) + \left(\frac{b \left(2 a c - b^{2}\right)}{2 c^{4}} - \frac{\sqrt{- 4 a c + b^{2}} \left(2 a^{2} c^{2} - 4 a b^{2} c + b^{4}\right)}{2 c^{4} \left(4 a c - b^{2}\right)}\right) \log{\left(x + \frac{- 3 a^{2} b c + a b^{3} + 4 a c^{4} \left(\frac{b \left(2 a c - b^{2}\right)}{2 c^{4}} - \frac{\sqrt{- 4 a c + b^{2}} \left(2 a^{2} c^{2} - 4 a b^{2} c + b^{4}\right)}{2 c^{4} \left(4 a c - b^{2}\right)}\right) - b^{2} c^{3} \left(\frac{b \left(2 a c - b^{2}\right)}{2 c^{4}} - \frac{\sqrt{- 4 a c + b^{2}} \left(2 a^{2} c^{2} - 4 a b^{2} c + b^{4}\right)}{2 c^{4} \left(4 a c - b^{2}\right)}\right)}{2 a^{2} c^{2} - 4 a b^{2} c + b^{4}} \right)} + \left(\frac{b \left(2 a c - b^{2}\right)}{2 c^{4}} + \frac{\sqrt{- 4 a c + b^{2}} \left(2 a^{2} c^{2} - 4 a b^{2} c + b^{4}\right)}{2 c^{4} \left(4 a c - b^{2}\right)}\right) \log{\left(x + \frac{- 3 a^{2} b c + a b^{3} + 4 a c^{4} \left(\frac{b \left(2 a c - b^{2}\right)}{2 c^{4}} + \frac{\sqrt{- 4 a c + b^{2}} \left(2 a^{2} c^{2} - 4 a b^{2} c + b^{4}\right)}{2 c^{4} \left(4 a c - b^{2}\right)}\right) - b^{2} c^{3} \left(\frac{b \left(2 a c - b^{2}\right)}{2 c^{4}} + \frac{\sqrt{- 4 a c + b^{2}} \left(2 a^{2} c^{2} - 4 a b^{2} c + b^{4}\right)}{2 c^{4} \left(4 a c - b^{2}\right)}\right)}{2 a^{2} c^{2} - 4 a b^{2} c + b^{4}} \right)} + \frac{x^{3}}{3 c}"," ",0,"-b*x**2/(2*c**2) + x*(-a/c**2 + b**2/c**3) + (b*(2*a*c - b**2)/(2*c**4) - sqrt(-4*a*c + b**2)*(2*a**2*c**2 - 4*a*b**2*c + b**4)/(2*c**4*(4*a*c - b**2)))*log(x + (-3*a**2*b*c + a*b**3 + 4*a*c**4*(b*(2*a*c - b**2)/(2*c**4) - sqrt(-4*a*c + b**2)*(2*a**2*c**2 - 4*a*b**2*c + b**4)/(2*c**4*(4*a*c - b**2))) - b**2*c**3*(b*(2*a*c - b**2)/(2*c**4) - sqrt(-4*a*c + b**2)*(2*a**2*c**2 - 4*a*b**2*c + b**4)/(2*c**4*(4*a*c - b**2))))/(2*a**2*c**2 - 4*a*b**2*c + b**4)) + (b*(2*a*c - b**2)/(2*c**4) + sqrt(-4*a*c + b**2)*(2*a**2*c**2 - 4*a*b**2*c + b**4)/(2*c**4*(4*a*c - b**2)))*log(x + (-3*a**2*b*c + a*b**3 + 4*a*c**4*(b*(2*a*c - b**2)/(2*c**4) + sqrt(-4*a*c + b**2)*(2*a**2*c**2 - 4*a*b**2*c + b**4)/(2*c**4*(4*a*c - b**2))) - b**2*c**3*(b*(2*a*c - b**2)/(2*c**4) + sqrt(-4*a*c + b**2)*(2*a**2*c**2 - 4*a*b**2*c + b**4)/(2*c**4*(4*a*c - b**2))))/(2*a**2*c**2 - 4*a*b**2*c + b**4)) + x**3/(3*c)","B",0
414,1,381,0,0.835335," ","integrate(x/(c+a/x**2+b/x),x)","- \frac{b x}{c^{2}} + \left(- \frac{b \sqrt{- 4 a c + b^{2}} \left(3 a c - b^{2}\right)}{2 c^{3} \left(4 a c - b^{2}\right)} - \frac{a c - b^{2}}{2 c^{3}}\right) \log{\left(x + \frac{2 a^{2} c - a b^{2} + 4 a c^{3} \left(- \frac{b \sqrt{- 4 a c + b^{2}} \left(3 a c - b^{2}\right)}{2 c^{3} \left(4 a c - b^{2}\right)} - \frac{a c - b^{2}}{2 c^{3}}\right) - b^{2} c^{2} \left(- \frac{b \sqrt{- 4 a c + b^{2}} \left(3 a c - b^{2}\right)}{2 c^{3} \left(4 a c - b^{2}\right)} - \frac{a c - b^{2}}{2 c^{3}}\right)}{3 a b c - b^{3}} \right)} + \left(\frac{b \sqrt{- 4 a c + b^{2}} \left(3 a c - b^{2}\right)}{2 c^{3} \left(4 a c - b^{2}\right)} - \frac{a c - b^{2}}{2 c^{3}}\right) \log{\left(x + \frac{2 a^{2} c - a b^{2} + 4 a c^{3} \left(\frac{b \sqrt{- 4 a c + b^{2}} \left(3 a c - b^{2}\right)}{2 c^{3} \left(4 a c - b^{2}\right)} - \frac{a c - b^{2}}{2 c^{3}}\right) - b^{2} c^{2} \left(\frac{b \sqrt{- 4 a c + b^{2}} \left(3 a c - b^{2}\right)}{2 c^{3} \left(4 a c - b^{2}\right)} - \frac{a c - b^{2}}{2 c^{3}}\right)}{3 a b c - b^{3}} \right)} + \frac{x^{2}}{2 c}"," ",0,"-b*x/c**2 + (-b*sqrt(-4*a*c + b**2)*(3*a*c - b**2)/(2*c**3*(4*a*c - b**2)) - (a*c - b**2)/(2*c**3))*log(x + (2*a**2*c - a*b**2 + 4*a*c**3*(-b*sqrt(-4*a*c + b**2)*(3*a*c - b**2)/(2*c**3*(4*a*c - b**2)) - (a*c - b**2)/(2*c**3)) - b**2*c**2*(-b*sqrt(-4*a*c + b**2)*(3*a*c - b**2)/(2*c**3*(4*a*c - b**2)) - (a*c - b**2)/(2*c**3)))/(3*a*b*c - b**3)) + (b*sqrt(-4*a*c + b**2)*(3*a*c - b**2)/(2*c**3*(4*a*c - b**2)) - (a*c - b**2)/(2*c**3))*log(x + (2*a**2*c - a*b**2 + 4*a*c**3*(b*sqrt(-4*a*c + b**2)*(3*a*c - b**2)/(2*c**3*(4*a*c - b**2)) - (a*c - b**2)/(2*c**3)) - b**2*c**2*(b*sqrt(-4*a*c + b**2)*(3*a*c - b**2)/(2*c**3*(4*a*c - b**2)) - (a*c - b**2)/(2*c**3)))/(3*a*b*c - b**3)) + x**2/(2*c)","B",0
415,1,306,0,0.596650," ","integrate(1/(c+a/x**2+b/x),x)","\left(- \frac{b}{2 c^{2}} - \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{2 c^{2} \left(4 a c - b^{2}\right)}\right) \log{\left(x + \frac{- a b - 4 a c^{2} \left(- \frac{b}{2 c^{2}} - \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{2 c^{2} \left(4 a c - b^{2}\right)}\right) + b^{2} c \left(- \frac{b}{2 c^{2}} - \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{2 c^{2} \left(4 a c - b^{2}\right)}\right)}{2 a c - b^{2}} \right)} + \left(- \frac{b}{2 c^{2}} + \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{2 c^{2} \left(4 a c - b^{2}\right)}\right) \log{\left(x + \frac{- a b - 4 a c^{2} \left(- \frac{b}{2 c^{2}} + \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{2 c^{2} \left(4 a c - b^{2}\right)}\right) + b^{2} c \left(- \frac{b}{2 c^{2}} + \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{2 c^{2} \left(4 a c - b^{2}\right)}\right)}{2 a c - b^{2}} \right)} + \frac{x}{c}"," ",0,"(-b/(2*c**2) - sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(2*c**2*(4*a*c - b**2)))*log(x + (-a*b - 4*a*c**2*(-b/(2*c**2) - sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(2*c**2*(4*a*c - b**2))) + b**2*c*(-b/(2*c**2) - sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(2*c**2*(4*a*c - b**2))))/(2*a*c - b**2)) + (-b/(2*c**2) + sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(2*c**2*(4*a*c - b**2)))*log(x + (-a*b - 4*a*c**2*(-b/(2*c**2) + sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(2*c**2*(4*a*c - b**2))) + b**2*c*(-b/(2*c**2) + sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(2*c**2*(4*a*c - b**2))))/(2*a*c - b**2)) + x/c","B",0
416,1,216,0,0.318162," ","integrate(1/(c+a/x**2+b/x)/x,x)","\left(- \frac{b \sqrt{- 4 a c + b^{2}}}{2 c \left(4 a c - b^{2}\right)} + \frac{1}{2 c}\right) \log{\left(x + \frac{- 4 a c \left(- \frac{b \sqrt{- 4 a c + b^{2}}}{2 c \left(4 a c - b^{2}\right)} + \frac{1}{2 c}\right) + 2 a + b^{2} \left(- \frac{b \sqrt{- 4 a c + b^{2}}}{2 c \left(4 a c - b^{2}\right)} + \frac{1}{2 c}\right)}{b} \right)} + \left(\frac{b \sqrt{- 4 a c + b^{2}}}{2 c \left(4 a c - b^{2}\right)} + \frac{1}{2 c}\right) \log{\left(x + \frac{- 4 a c \left(\frac{b \sqrt{- 4 a c + b^{2}}}{2 c \left(4 a c - b^{2}\right)} + \frac{1}{2 c}\right) + 2 a + b^{2} \left(\frac{b \sqrt{- 4 a c + b^{2}}}{2 c \left(4 a c - b^{2}\right)} + \frac{1}{2 c}\right)}{b} \right)}"," ",0,"(-b*sqrt(-4*a*c + b**2)/(2*c*(4*a*c - b**2)) + 1/(2*c))*log(x + (-4*a*c*(-b*sqrt(-4*a*c + b**2)/(2*c*(4*a*c - b**2)) + 1/(2*c)) + 2*a + b**2*(-b*sqrt(-4*a*c + b**2)/(2*c*(4*a*c - b**2)) + 1/(2*c)))/b) + (b*sqrt(-4*a*c + b**2)/(2*c*(4*a*c - b**2)) + 1/(2*c))*log(x + (-4*a*c*(b*sqrt(-4*a*c + b**2)/(2*c*(4*a*c - b**2)) + 1/(2*c)) + 2*a + b**2*(b*sqrt(-4*a*c + b**2)/(2*c*(4*a*c - b**2)) + 1/(2*c)))/b)","B",0
417,1,124,0,0.218376," ","integrate(1/(c+a/x**2+b/x)/x**2,x)","- \sqrt{- \frac{1}{4 a c - b^{2}}} \log{\left(x + \frac{- 4 a c \sqrt{- \frac{1}{4 a c - b^{2}}} + b^{2} \sqrt{- \frac{1}{4 a c - b^{2}}} + b}{2 c} \right)} + \sqrt{- \frac{1}{4 a c - b^{2}}} \log{\left(x + \frac{4 a c \sqrt{- \frac{1}{4 a c - b^{2}}} - b^{2} \sqrt{- \frac{1}{4 a c - b^{2}}} + b}{2 c} \right)}"," ",0,"-sqrt(-1/(4*a*c - b**2))*log(x + (-4*a*c*sqrt(-1/(4*a*c - b**2)) + b**2*sqrt(-1/(4*a*c - b**2)) + b)/(2*c)) + sqrt(-1/(4*a*c - b**2))*log(x + (4*a*c*sqrt(-1/(4*a*c - b**2)) - b**2*sqrt(-1/(4*a*c - b**2)) + b)/(2*c))","B",0
418,1,564,0,4.080482," ","integrate(1/(c+a/x**2+b/x)/x**3,x)","\left(- \frac{b \sqrt{- 4 a c + b^{2}}}{2 a \left(4 a c - b^{2}\right)} - \frac{1}{2 a}\right) \log{\left(x + \frac{24 a^{4} c^{2} \left(- \frac{b \sqrt{- 4 a c + b^{2}}}{2 a \left(4 a c - b^{2}\right)} - \frac{1}{2 a}\right)^{2} - 14 a^{3} b^{2} c \left(- \frac{b \sqrt{- 4 a c + b^{2}}}{2 a \left(4 a c - b^{2}\right)} - \frac{1}{2 a}\right)^{2} - 12 a^{3} c^{2} \left(- \frac{b \sqrt{- 4 a c + b^{2}}}{2 a \left(4 a c - b^{2}\right)} - \frac{1}{2 a}\right) + 2 a^{2} b^{4} \left(- \frac{b \sqrt{- 4 a c + b^{2}}}{2 a \left(4 a c - b^{2}\right)} - \frac{1}{2 a}\right)^{2} + 3 a^{2} b^{2} c \left(- \frac{b \sqrt{- 4 a c + b^{2}}}{2 a \left(4 a c - b^{2}\right)} - \frac{1}{2 a}\right) - 12 a^{2} c^{2} + 11 a b^{2} c - 2 b^{4}}{9 a b c^{2} - 2 b^{3} c} \right)} + \left(\frac{b \sqrt{- 4 a c + b^{2}}}{2 a \left(4 a c - b^{2}\right)} - \frac{1}{2 a}\right) \log{\left(x + \frac{24 a^{4} c^{2} \left(\frac{b \sqrt{- 4 a c + b^{2}}}{2 a \left(4 a c - b^{2}\right)} - \frac{1}{2 a}\right)^{2} - 14 a^{3} b^{2} c \left(\frac{b \sqrt{- 4 a c + b^{2}}}{2 a \left(4 a c - b^{2}\right)} - \frac{1}{2 a}\right)^{2} - 12 a^{3} c^{2} \left(\frac{b \sqrt{- 4 a c + b^{2}}}{2 a \left(4 a c - b^{2}\right)} - \frac{1}{2 a}\right) + 2 a^{2} b^{4} \left(\frac{b \sqrt{- 4 a c + b^{2}}}{2 a \left(4 a c - b^{2}\right)} - \frac{1}{2 a}\right)^{2} + 3 a^{2} b^{2} c \left(\frac{b \sqrt{- 4 a c + b^{2}}}{2 a \left(4 a c - b^{2}\right)} - \frac{1}{2 a}\right) - 12 a^{2} c^{2} + 11 a b^{2} c - 2 b^{4}}{9 a b c^{2} - 2 b^{3} c} \right)} + \frac{\log{\left(x \right)}}{a}"," ",0,"(-b*sqrt(-4*a*c + b**2)/(2*a*(4*a*c - b**2)) - 1/(2*a))*log(x + (24*a**4*c**2*(-b*sqrt(-4*a*c + b**2)/(2*a*(4*a*c - b**2)) - 1/(2*a))**2 - 14*a**3*b**2*c*(-b*sqrt(-4*a*c + b**2)/(2*a*(4*a*c - b**2)) - 1/(2*a))**2 - 12*a**3*c**2*(-b*sqrt(-4*a*c + b**2)/(2*a*(4*a*c - b**2)) - 1/(2*a)) + 2*a**2*b**4*(-b*sqrt(-4*a*c + b**2)/(2*a*(4*a*c - b**2)) - 1/(2*a))**2 + 3*a**2*b**2*c*(-b*sqrt(-4*a*c + b**2)/(2*a*(4*a*c - b**2)) - 1/(2*a)) - 12*a**2*c**2 + 11*a*b**2*c - 2*b**4)/(9*a*b*c**2 - 2*b**3*c)) + (b*sqrt(-4*a*c + b**2)/(2*a*(4*a*c - b**2)) - 1/(2*a))*log(x + (24*a**4*c**2*(b*sqrt(-4*a*c + b**2)/(2*a*(4*a*c - b**2)) - 1/(2*a))**2 - 14*a**3*b**2*c*(b*sqrt(-4*a*c + b**2)/(2*a*(4*a*c - b**2)) - 1/(2*a))**2 - 12*a**3*c**2*(b*sqrt(-4*a*c + b**2)/(2*a*(4*a*c - b**2)) - 1/(2*a)) + 2*a**2*b**4*(b*sqrt(-4*a*c + b**2)/(2*a*(4*a*c - b**2)) - 1/(2*a))**2 + 3*a**2*b**2*c*(b*sqrt(-4*a*c + b**2)/(2*a*(4*a*c - b**2)) - 1/(2*a)) - 12*a**2*c**2 + 11*a*b**2*c - 2*b**4)/(9*a*b*c**2 - 2*b**3*c)) + log(x)/a","B",0
419,-1,0,0,0.000000," ","integrate(1/(c+a/x**2+b/x)/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
420,-1,0,0,0.000000," ","integrate(1/(c+a/x**2+b/x)/x**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
421,-1,0,0,0.000000," ","integrate(1/(c+a/x**2+b/x)/x**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
422,1,1012,0,2.369300," ","integrate(x/(c+a/x**2+b/x)**2,x)","- \frac{2 b x}{c^{3}} + \left(- \frac{b \sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(30 a^{2} c^{2} - 20 a b^{2} c + 3 b^{4}\right)}{2 c^{4} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)} - \frac{2 a c - 3 b^{2}}{2 c^{4}}\right) \log{\left(x + \frac{16 a^{3} c^{2} - 17 a^{2} b^{2} c + 16 a^{2} c^{5} \left(- \frac{b \sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(30 a^{2} c^{2} - 20 a b^{2} c + 3 b^{4}\right)}{2 c^{4} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)} - \frac{2 a c - 3 b^{2}}{2 c^{4}}\right) + 3 a b^{4} - 8 a b^{2} c^{4} \left(- \frac{b \sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(30 a^{2} c^{2} - 20 a b^{2} c + 3 b^{4}\right)}{2 c^{4} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)} - \frac{2 a c - 3 b^{2}}{2 c^{4}}\right) + b^{4} c^{3} \left(- \frac{b \sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(30 a^{2} c^{2} - 20 a b^{2} c + 3 b^{4}\right)}{2 c^{4} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)} - \frac{2 a c - 3 b^{2}}{2 c^{4}}\right)}{30 a^{2} b c^{2} - 20 a b^{3} c + 3 b^{5}} \right)} + \left(\frac{b \sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(30 a^{2} c^{2} - 20 a b^{2} c + 3 b^{4}\right)}{2 c^{4} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)} - \frac{2 a c - 3 b^{2}}{2 c^{4}}\right) \log{\left(x + \frac{16 a^{3} c^{2} - 17 a^{2} b^{2} c + 16 a^{2} c^{5} \left(\frac{b \sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(30 a^{2} c^{2} - 20 a b^{2} c + 3 b^{4}\right)}{2 c^{4} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)} - \frac{2 a c - 3 b^{2}}{2 c^{4}}\right) + 3 a b^{4} - 8 a b^{2} c^{4} \left(\frac{b \sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(30 a^{2} c^{2} - 20 a b^{2} c + 3 b^{4}\right)}{2 c^{4} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)} - \frac{2 a c - 3 b^{2}}{2 c^{4}}\right) + b^{4} c^{3} \left(\frac{b \sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(30 a^{2} c^{2} - 20 a b^{2} c + 3 b^{4}\right)}{2 c^{4} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)} - \frac{2 a c - 3 b^{2}}{2 c^{4}}\right)}{30 a^{2} b c^{2} - 20 a b^{3} c + 3 b^{5}} \right)} + \frac{- 2 a^{3} c^{2} + 4 a^{2} b^{2} c - a b^{4} + x \left(- 5 a^{2} b c^{2} + 5 a b^{3} c - b^{5}\right)}{4 a^{2} c^{5} - a b^{2} c^{4} + x^{2} \left(4 a c^{6} - b^{2} c^{5}\right) + x \left(4 a b c^{5} - b^{3} c^{4}\right)} + \frac{x^{2}}{2 c^{2}}"," ",0,"-2*b*x/c**3 + (-b*sqrt(-(4*a*c - b**2)**3)*(30*a**2*c**2 - 20*a*b**2*c + 3*b**4)/(2*c**4*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)) - (2*a*c - 3*b**2)/(2*c**4))*log(x + (16*a**3*c**2 - 17*a**2*b**2*c + 16*a**2*c**5*(-b*sqrt(-(4*a*c - b**2)**3)*(30*a**2*c**2 - 20*a*b**2*c + 3*b**4)/(2*c**4*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)) - (2*a*c - 3*b**2)/(2*c**4)) + 3*a*b**4 - 8*a*b**2*c**4*(-b*sqrt(-(4*a*c - b**2)**3)*(30*a**2*c**2 - 20*a*b**2*c + 3*b**4)/(2*c**4*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)) - (2*a*c - 3*b**2)/(2*c**4)) + b**4*c**3*(-b*sqrt(-(4*a*c - b**2)**3)*(30*a**2*c**2 - 20*a*b**2*c + 3*b**4)/(2*c**4*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)) - (2*a*c - 3*b**2)/(2*c**4)))/(30*a**2*b*c**2 - 20*a*b**3*c + 3*b**5)) + (b*sqrt(-(4*a*c - b**2)**3)*(30*a**2*c**2 - 20*a*b**2*c + 3*b**4)/(2*c**4*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)) - (2*a*c - 3*b**2)/(2*c**4))*log(x + (16*a**3*c**2 - 17*a**2*b**2*c + 16*a**2*c**5*(b*sqrt(-(4*a*c - b**2)**3)*(30*a**2*c**2 - 20*a*b**2*c + 3*b**4)/(2*c**4*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)) - (2*a*c - 3*b**2)/(2*c**4)) + 3*a*b**4 - 8*a*b**2*c**4*(b*sqrt(-(4*a*c - b**2)**3)*(30*a**2*c**2 - 20*a*b**2*c + 3*b**4)/(2*c**4*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)) - (2*a*c - 3*b**2)/(2*c**4)) + b**4*c**3*(b*sqrt(-(4*a*c - b**2)**3)*(30*a**2*c**2 - 20*a*b**2*c + 3*b**4)/(2*c**4*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)) - (2*a*c - 3*b**2)/(2*c**4)))/(30*a**2*b*c**2 - 20*a*b**3*c + 3*b**5)) + (-2*a**3*c**2 + 4*a**2*b**2*c - a*b**4 + x*(-5*a**2*b*c**2 + 5*a*b**3*c - b**5))/(4*a**2*c**5 - a*b**2*c**4 + x**2*(4*a*c**6 - b**2*c**5) + x*(4*a*b*c**5 - b**3*c**4)) + x**2/(2*c**2)","B",0
423,1,842,0,1.726698," ","integrate(1/(c+a/x**2+b/x)**2,x)","\left(- \frac{b}{c^{3}} - \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(6 a^{2} c^{2} - 6 a b^{2} c + b^{4}\right)}{c^{3} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right) \log{\left(x + \frac{- 10 a^{2} b c - 16 a^{2} c^{4} \left(- \frac{b}{c^{3}} - \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(6 a^{2} c^{2} - 6 a b^{2} c + b^{4}\right)}{c^{3} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right) + 2 a b^{3} + 8 a b^{2} c^{3} \left(- \frac{b}{c^{3}} - \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(6 a^{2} c^{2} - 6 a b^{2} c + b^{4}\right)}{c^{3} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right) - b^{4} c^{2} \left(- \frac{b}{c^{3}} - \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(6 a^{2} c^{2} - 6 a b^{2} c + b^{4}\right)}{c^{3} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right)}{12 a^{2} c^{2} - 12 a b^{2} c + 2 b^{4}} \right)} + \left(- \frac{b}{c^{3}} + \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(6 a^{2} c^{2} - 6 a b^{2} c + b^{4}\right)}{c^{3} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right) \log{\left(x + \frac{- 10 a^{2} b c - 16 a^{2} c^{4} \left(- \frac{b}{c^{3}} + \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(6 a^{2} c^{2} - 6 a b^{2} c + b^{4}\right)}{c^{3} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right) + 2 a b^{3} + 8 a b^{2} c^{3} \left(- \frac{b}{c^{3}} + \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(6 a^{2} c^{2} - 6 a b^{2} c + b^{4}\right)}{c^{3} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right) - b^{4} c^{2} \left(- \frac{b}{c^{3}} + \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(6 a^{2} c^{2} - 6 a b^{2} c + b^{4}\right)}{c^{3} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right)}{12 a^{2} c^{2} - 12 a b^{2} c + 2 b^{4}} \right)} + \frac{- 3 a^{2} b c + a b^{3} + x \left(2 a^{2} c^{2} - 4 a b^{2} c + b^{4}\right)}{4 a^{2} c^{4} - a b^{2} c^{3} + x^{2} \left(4 a c^{5} - b^{2} c^{4}\right) + x \left(4 a b c^{4} - b^{3} c^{3}\right)} + \frac{x}{c^{2}}"," ",0,"(-b/c**3 - sqrt(-(4*a*c - b**2)**3)*(6*a**2*c**2 - 6*a*b**2*c + b**4)/(c**3*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)))*log(x + (-10*a**2*b*c - 16*a**2*c**4*(-b/c**3 - sqrt(-(4*a*c - b**2)**3)*(6*a**2*c**2 - 6*a*b**2*c + b**4)/(c**3*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6))) + 2*a*b**3 + 8*a*b**2*c**3*(-b/c**3 - sqrt(-(4*a*c - b**2)**3)*(6*a**2*c**2 - 6*a*b**2*c + b**4)/(c**3*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6))) - b**4*c**2*(-b/c**3 - sqrt(-(4*a*c - b**2)**3)*(6*a**2*c**2 - 6*a*b**2*c + b**4)/(c**3*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6))))/(12*a**2*c**2 - 12*a*b**2*c + 2*b**4)) + (-b/c**3 + sqrt(-(4*a*c - b**2)**3)*(6*a**2*c**2 - 6*a*b**2*c + b**4)/(c**3*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)))*log(x + (-10*a**2*b*c - 16*a**2*c**4*(-b/c**3 + sqrt(-(4*a*c - b**2)**3)*(6*a**2*c**2 - 6*a*b**2*c + b**4)/(c**3*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6))) + 2*a*b**3 + 8*a*b**2*c**3*(-b/c**3 + sqrt(-(4*a*c - b**2)**3)*(6*a**2*c**2 - 6*a*b**2*c + b**4)/(c**3*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6))) - b**4*c**2*(-b/c**3 + sqrt(-(4*a*c - b**2)**3)*(6*a**2*c**2 - 6*a*b**2*c + b**4)/(c**3*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6))))/(12*a**2*c**2 - 12*a*b**2*c + 2*b**4)) + (-3*a**2*b*c + a*b**3 + x*(2*a**2*c**2 - 4*a*b**2*c + b**4))/(4*a**2*c**4 - a*b**2*c**3 + x**2*(4*a*c**5 - b**2*c**4) + x*(4*a*b*c**4 - b**3*c**3)) + x/c**2","B",0
424,1,729,0,1.322791," ","integrate(1/(c+a/x**2+b/x)**2/x,x)","\left(- \frac{b \sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(6 a c - b^{2}\right)}{2 c^{2} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)} + \frac{1}{2 c^{2}}\right) \log{\left(x + \frac{- 16 a^{2} c^{3} \left(- \frac{b \sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(6 a c - b^{2}\right)}{2 c^{2} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)} + \frac{1}{2 c^{2}}\right) + 8 a^{2} c + 8 a b^{2} c^{2} \left(- \frac{b \sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(6 a c - b^{2}\right)}{2 c^{2} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)} + \frac{1}{2 c^{2}}\right) - a b^{2} - b^{4} c \left(- \frac{b \sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(6 a c - b^{2}\right)}{2 c^{2} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)} + \frac{1}{2 c^{2}}\right)}{6 a b c - b^{3}} \right)} + \left(\frac{b \sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(6 a c - b^{2}\right)}{2 c^{2} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)} + \frac{1}{2 c^{2}}\right) \log{\left(x + \frac{- 16 a^{2} c^{3} \left(\frac{b \sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(6 a c - b^{2}\right)}{2 c^{2} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)} + \frac{1}{2 c^{2}}\right) + 8 a^{2} c + 8 a b^{2} c^{2} \left(\frac{b \sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(6 a c - b^{2}\right)}{2 c^{2} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)} + \frac{1}{2 c^{2}}\right) - a b^{2} - b^{4} c \left(\frac{b \sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(6 a c - b^{2}\right)}{2 c^{2} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)} + \frac{1}{2 c^{2}}\right)}{6 a b c - b^{3}} \right)} + \frac{2 a^{2} c - a b^{2} + x \left(3 a b c - b^{3}\right)}{4 a^{2} c^{3} - a b^{2} c^{2} + x^{2} \left(4 a c^{4} - b^{2} c^{3}\right) + x \left(4 a b c^{3} - b^{3} c^{2}\right)}"," ",0,"(-b*sqrt(-(4*a*c - b**2)**3)*(6*a*c - b**2)/(2*c**2*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)) + 1/(2*c**2))*log(x + (-16*a**2*c**3*(-b*sqrt(-(4*a*c - b**2)**3)*(6*a*c - b**2)/(2*c**2*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)) + 1/(2*c**2)) + 8*a**2*c + 8*a*b**2*c**2*(-b*sqrt(-(4*a*c - b**2)**3)*(6*a*c - b**2)/(2*c**2*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)) + 1/(2*c**2)) - a*b**2 - b**4*c*(-b*sqrt(-(4*a*c - b**2)**3)*(6*a*c - b**2)/(2*c**2*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)) + 1/(2*c**2)))/(6*a*b*c - b**3)) + (b*sqrt(-(4*a*c - b**2)**3)*(6*a*c - b**2)/(2*c**2*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)) + 1/(2*c**2))*log(x + (-16*a**2*c**3*(b*sqrt(-(4*a*c - b**2)**3)*(6*a*c - b**2)/(2*c**2*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)) + 1/(2*c**2)) + 8*a**2*c + 8*a*b**2*c**2*(b*sqrt(-(4*a*c - b**2)**3)*(6*a*c - b**2)/(2*c**2*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)) + 1/(2*c**2)) - a*b**2 - b**4*c*(b*sqrt(-(4*a*c - b**2)**3)*(6*a*c - b**2)/(2*c**2*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)) + 1/(2*c**2)))/(6*a*b*c - b**3)) + (2*a**2*c - a*b**2 + x*(3*a*b*c - b**3))/(4*a**2*c**3 - a*b**2*c**2 + x**2*(4*a*c**4 - b**2*c**3) + x*(4*a*b*c**3 - b**3*c**2))","B",0
425,1,280,0,0.597321," ","integrate(1/(c+a/x**2+b/x)**2/x**2,x)","- 2 a \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \log{\left(x + \frac{- 32 a^{3} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + 16 a^{2} b^{2} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} - 2 a b^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + 2 a b}{4 a c} \right)} + 2 a \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \log{\left(x + \frac{32 a^{3} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} - 16 a^{2} b^{2} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + 2 a b^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + 2 a b}{4 a c} \right)} + \frac{a b + x \left(- 2 a c + b^{2}\right)}{4 a^{2} c^{2} - a b^{2} c + x^{2} \left(4 a c^{3} - b^{2} c^{2}\right) + x \left(4 a b c^{2} - b^{3} c\right)}"," ",0,"-2*a*sqrt(-1/(4*a*c - b**2)**3)*log(x + (-32*a**3*c**2*sqrt(-1/(4*a*c - b**2)**3) + 16*a**2*b**2*c*sqrt(-1/(4*a*c - b**2)**3) - 2*a*b**4*sqrt(-1/(4*a*c - b**2)**3) + 2*a*b)/(4*a*c)) + 2*a*sqrt(-1/(4*a*c - b**2)**3)*log(x + (32*a**3*c**2*sqrt(-1/(4*a*c - b**2)**3) - 16*a**2*b**2*c*sqrt(-1/(4*a*c - b**2)**3) + 2*a*b**4*sqrt(-1/(4*a*c - b**2)**3) + 2*a*b)/(4*a*c)) + (a*b + x*(-2*a*c + b**2))/(4*a**2*c**2 - a*b**2*c + x**2*(4*a*c**3 - b**2*c**2) + x*(4*a*b*c**2 - b**3*c))","B",0
426,1,253,0,0.562058," ","integrate(1/(c+a/x**2+b/x)**2/x**3,x)","b \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \log{\left(x + \frac{- 16 a^{2} b c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + 8 a b^{3} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} - b^{5} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + b^{2}}{2 b c} \right)} - b \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \log{\left(x + \frac{16 a^{2} b c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} - 8 a b^{3} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + b^{5} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + b^{2}}{2 b c} \right)} + \frac{- 2 a - b x}{4 a^{2} c - a b^{2} + x^{2} \left(4 a c^{2} - b^{2} c\right) + x \left(4 a b c - b^{3}\right)}"," ",0,"b*sqrt(-1/(4*a*c - b**2)**3)*log(x + (-16*a**2*b*c**2*sqrt(-1/(4*a*c - b**2)**3) + 8*a*b**3*c*sqrt(-1/(4*a*c - b**2)**3) - b**5*sqrt(-1/(4*a*c - b**2)**3) + b**2)/(2*b*c)) - b*sqrt(-1/(4*a*c - b**2)**3)*log(x + (16*a**2*b*c**2*sqrt(-1/(4*a*c - b**2)**3) - 8*a*b**3*c*sqrt(-1/(4*a*c - b**2)**3) + b**5*sqrt(-1/(4*a*c - b**2)**3) + b**2)/(2*b*c)) + (-2*a - b*x)/(4*a**2*c - a*b**2 + x**2*(4*a*c**2 - b**2*c) + x*(4*a*b*c - b**3))","B",0
427,1,265,0,0.579449," ","integrate(1/(c+a/x**2+b/x)**2/x**4,x)","- 2 c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \log{\left(x + \frac{- 32 a^{2} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + 16 a b^{2} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} - 2 b^{4} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + 2 b c}{4 c^{2}} \right)} + 2 c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \log{\left(x + \frac{32 a^{2} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} - 16 a b^{2} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + 2 b^{4} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + 2 b c}{4 c^{2}} \right)} + \frac{b + 2 c x}{4 a^{2} c - a b^{2} + x^{2} \left(4 a c^{2} - b^{2} c\right) + x \left(4 a b c - b^{3}\right)}"," ",0,"-2*c*sqrt(-1/(4*a*c - b**2)**3)*log(x + (-32*a**2*c**3*sqrt(-1/(4*a*c - b**2)**3) + 16*a*b**2*c**2*sqrt(-1/(4*a*c - b**2)**3) - 2*b**4*c*sqrt(-1/(4*a*c - b**2)**3) + 2*b*c)/(4*c**2)) + 2*c*sqrt(-1/(4*a*c - b**2)**3)*log(x + (32*a**2*c**3*sqrt(-1/(4*a*c - b**2)**3) - 16*a*b**2*c**2*sqrt(-1/(4*a*c - b**2)**3) + 2*b**4*c*sqrt(-1/(4*a*c - b**2)**3) + 2*b*c)/(4*c**2)) + (b + 2*c*x)/(4*a**2*c - a*b**2 + x**2*(4*a*c**2 - b**2*c) + x*(4*a*b*c - b**3))","B",0
428,-1,0,0,0.000000," ","integrate(1/(c+a/x**2+b/x)**2/x**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
429,-1,0,0,0.000000," ","integrate(1/(c+a/x**2+b/x)**2/x**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
430,-1,0,0,0.000000," ","integrate(1/(c+a/x**2+b/x)**2/x**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
431,1,1714,0,4.195955," ","integrate(1/(c+a/x**2+b/x)**3,x)","\left(- \frac{3 b}{2 c^{4}} - \frac{3 \sqrt{- \left(4 a c - b^{2}\right)^{5}} \left(20 a^{3} c^{3} - 30 a^{2} b^{2} c^{2} + 10 a b^{4} c - b^{6}\right)}{2 c^{4} \left(1024 a^{5} c^{5} - 1280 a^{4} b^{2} c^{4} + 640 a^{3} b^{4} c^{3} - 160 a^{2} b^{6} c^{2} + 20 a b^{8} c - b^{10}\right)}\right) \log{\left(x + \frac{- 66 a^{3} b c^{2} - 64 a^{3} c^{6} \left(- \frac{3 b}{2 c^{4}} - \frac{3 \sqrt{- \left(4 a c - b^{2}\right)^{5}} \left(20 a^{3} c^{3} - 30 a^{2} b^{2} c^{2} + 10 a b^{4} c - b^{6}\right)}{2 c^{4} \left(1024 a^{5} c^{5} - 1280 a^{4} b^{2} c^{4} + 640 a^{3} b^{4} c^{3} - 160 a^{2} b^{6} c^{2} + 20 a b^{8} c - b^{10}\right)}\right) + 27 a^{2} b^{3} c + 48 a^{2} b^{2} c^{5} \left(- \frac{3 b}{2 c^{4}} - \frac{3 \sqrt{- \left(4 a c - b^{2}\right)^{5}} \left(20 a^{3} c^{3} - 30 a^{2} b^{2} c^{2} + 10 a b^{4} c - b^{6}\right)}{2 c^{4} \left(1024 a^{5} c^{5} - 1280 a^{4} b^{2} c^{4} + 640 a^{3} b^{4} c^{3} - 160 a^{2} b^{6} c^{2} + 20 a b^{8} c - b^{10}\right)}\right) - 3 a b^{5} - 12 a b^{4} c^{4} \left(- \frac{3 b}{2 c^{4}} - \frac{3 \sqrt{- \left(4 a c - b^{2}\right)^{5}} \left(20 a^{3} c^{3} - 30 a^{2} b^{2} c^{2} + 10 a b^{4} c - b^{6}\right)}{2 c^{4} \left(1024 a^{5} c^{5} - 1280 a^{4} b^{2} c^{4} + 640 a^{3} b^{4} c^{3} - 160 a^{2} b^{6} c^{2} + 20 a b^{8} c - b^{10}\right)}\right) + b^{6} c^{3} \left(- \frac{3 b}{2 c^{4}} - \frac{3 \sqrt{- \left(4 a c - b^{2}\right)^{5}} \left(20 a^{3} c^{3} - 30 a^{2} b^{2} c^{2} + 10 a b^{4} c - b^{6}\right)}{2 c^{4} \left(1024 a^{5} c^{5} - 1280 a^{4} b^{2} c^{4} + 640 a^{3} b^{4} c^{3} - 160 a^{2} b^{6} c^{2} + 20 a b^{8} c - b^{10}\right)}\right)}{60 a^{3} c^{3} - 90 a^{2} b^{2} c^{2} + 30 a b^{4} c - 3 b^{6}} \right)} + \left(- \frac{3 b}{2 c^{4}} + \frac{3 \sqrt{- \left(4 a c - b^{2}\right)^{5}} \left(20 a^{3} c^{3} - 30 a^{2} b^{2} c^{2} + 10 a b^{4} c - b^{6}\right)}{2 c^{4} \left(1024 a^{5} c^{5} - 1280 a^{4} b^{2} c^{4} + 640 a^{3} b^{4} c^{3} - 160 a^{2} b^{6} c^{2} + 20 a b^{8} c - b^{10}\right)}\right) \log{\left(x + \frac{- 66 a^{3} b c^{2} - 64 a^{3} c^{6} \left(- \frac{3 b}{2 c^{4}} + \frac{3 \sqrt{- \left(4 a c - b^{2}\right)^{5}} \left(20 a^{3} c^{3} - 30 a^{2} b^{2} c^{2} + 10 a b^{4} c - b^{6}\right)}{2 c^{4} \left(1024 a^{5} c^{5} - 1280 a^{4} b^{2} c^{4} + 640 a^{3} b^{4} c^{3} - 160 a^{2} b^{6} c^{2} + 20 a b^{8} c - b^{10}\right)}\right) + 27 a^{2} b^{3} c + 48 a^{2} b^{2} c^{5} \left(- \frac{3 b}{2 c^{4}} + \frac{3 \sqrt{- \left(4 a c - b^{2}\right)^{5}} \left(20 a^{3} c^{3} - 30 a^{2} b^{2} c^{2} + 10 a b^{4} c - b^{6}\right)}{2 c^{4} \left(1024 a^{5} c^{5} - 1280 a^{4} b^{2} c^{4} + 640 a^{3} b^{4} c^{3} - 160 a^{2} b^{6} c^{2} + 20 a b^{8} c - b^{10}\right)}\right) - 3 a b^{5} - 12 a b^{4} c^{4} \left(- \frac{3 b}{2 c^{4}} + \frac{3 \sqrt{- \left(4 a c - b^{2}\right)^{5}} \left(20 a^{3} c^{3} - 30 a^{2} b^{2} c^{2} + 10 a b^{4} c - b^{6}\right)}{2 c^{4} \left(1024 a^{5} c^{5} - 1280 a^{4} b^{2} c^{4} + 640 a^{3} b^{4} c^{3} - 160 a^{2} b^{6} c^{2} + 20 a b^{8} c - b^{10}\right)}\right) + b^{6} c^{3} \left(- \frac{3 b}{2 c^{4}} + \frac{3 \sqrt{- \left(4 a c - b^{2}\right)^{5}} \left(20 a^{3} c^{3} - 30 a^{2} b^{2} c^{2} + 10 a b^{4} c - b^{6}\right)}{2 c^{4} \left(1024 a^{5} c^{5} - 1280 a^{4} b^{2} c^{4} + 640 a^{3} b^{4} c^{3} - 160 a^{2} b^{6} c^{2} + 20 a b^{8} c - b^{10}\right)}\right)}{60 a^{3} c^{3} - 90 a^{2} b^{2} c^{2} + 30 a b^{4} c - 3 b^{6}} \right)} + \frac{- 58 a^{4} b c^{2} + 36 a^{3} b^{3} c - 5 a^{2} b^{5} + x^{3} \left(36 a^{3} c^{4} - 102 a^{2} b^{2} c^{3} + 48 a b^{4} c^{2} - 6 b^{6} c\right) + x^{2} \left(- 42 a^{3} b c^{3} - 41 a^{2} b^{3} c^{2} + 34 a b^{5} c - 5 b^{7}\right) + x \left(28 a^{4} c^{3} - 142 a^{3} b^{2} c^{2} + 76 a^{2} b^{4} c - 10 a b^{6}\right)}{32 a^{4} c^{6} - 16 a^{3} b^{2} c^{5} + 2 a^{2} b^{4} c^{4} + x^{4} \left(32 a^{2} c^{8} - 16 a b^{2} c^{7} + 2 b^{4} c^{6}\right) + x^{3} \left(64 a^{2} b c^{7} - 32 a b^{3} c^{6} + 4 b^{5} c^{5}\right) + x^{2} \left(64 a^{3} c^{7} - 12 a b^{4} c^{5} + 2 b^{6} c^{4}\right) + x \left(64 a^{3} b c^{6} - 32 a^{2} b^{3} c^{5} + 4 a b^{5} c^{4}\right)} + \frac{x}{c^{3}}"," ",0,"(-3*b/(2*c**4) - 3*sqrt(-(4*a*c - b**2)**5)*(20*a**3*c**3 - 30*a**2*b**2*c**2 + 10*a*b**4*c - b**6)/(2*c**4*(1024*a**5*c**5 - 1280*a**4*b**2*c**4 + 640*a**3*b**4*c**3 - 160*a**2*b**6*c**2 + 20*a*b**8*c - b**10)))*log(x + (-66*a**3*b*c**2 - 64*a**3*c**6*(-3*b/(2*c**4) - 3*sqrt(-(4*a*c - b**2)**5)*(20*a**3*c**3 - 30*a**2*b**2*c**2 + 10*a*b**4*c - b**6)/(2*c**4*(1024*a**5*c**5 - 1280*a**4*b**2*c**4 + 640*a**3*b**4*c**3 - 160*a**2*b**6*c**2 + 20*a*b**8*c - b**10))) + 27*a**2*b**3*c + 48*a**2*b**2*c**5*(-3*b/(2*c**4) - 3*sqrt(-(4*a*c - b**2)**5)*(20*a**3*c**3 - 30*a**2*b**2*c**2 + 10*a*b**4*c - b**6)/(2*c**4*(1024*a**5*c**5 - 1280*a**4*b**2*c**4 + 640*a**3*b**4*c**3 - 160*a**2*b**6*c**2 + 20*a*b**8*c - b**10))) - 3*a*b**5 - 12*a*b**4*c**4*(-3*b/(2*c**4) - 3*sqrt(-(4*a*c - b**2)**5)*(20*a**3*c**3 - 30*a**2*b**2*c**2 + 10*a*b**4*c - b**6)/(2*c**4*(1024*a**5*c**5 - 1280*a**4*b**2*c**4 + 640*a**3*b**4*c**3 - 160*a**2*b**6*c**2 + 20*a*b**8*c - b**10))) + b**6*c**3*(-3*b/(2*c**4) - 3*sqrt(-(4*a*c - b**2)**5)*(20*a**3*c**3 - 30*a**2*b**2*c**2 + 10*a*b**4*c - b**6)/(2*c**4*(1024*a**5*c**5 - 1280*a**4*b**2*c**4 + 640*a**3*b**4*c**3 - 160*a**2*b**6*c**2 + 20*a*b**8*c - b**10))))/(60*a**3*c**3 - 90*a**2*b**2*c**2 + 30*a*b**4*c - 3*b**6)) + (-3*b/(2*c**4) + 3*sqrt(-(4*a*c - b**2)**5)*(20*a**3*c**3 - 30*a**2*b**2*c**2 + 10*a*b**4*c - b**6)/(2*c**4*(1024*a**5*c**5 - 1280*a**4*b**2*c**4 + 640*a**3*b**4*c**3 - 160*a**2*b**6*c**2 + 20*a*b**8*c - b**10)))*log(x + (-66*a**3*b*c**2 - 64*a**3*c**6*(-3*b/(2*c**4) + 3*sqrt(-(4*a*c - b**2)**5)*(20*a**3*c**3 - 30*a**2*b**2*c**2 + 10*a*b**4*c - b**6)/(2*c**4*(1024*a**5*c**5 - 1280*a**4*b**2*c**4 + 640*a**3*b**4*c**3 - 160*a**2*b**6*c**2 + 20*a*b**8*c - b**10))) + 27*a**2*b**3*c + 48*a**2*b**2*c**5*(-3*b/(2*c**4) + 3*sqrt(-(4*a*c - b**2)**5)*(20*a**3*c**3 - 30*a**2*b**2*c**2 + 10*a*b**4*c - b**6)/(2*c**4*(1024*a**5*c**5 - 1280*a**4*b**2*c**4 + 640*a**3*b**4*c**3 - 160*a**2*b**6*c**2 + 20*a*b**8*c - b**10))) - 3*a*b**5 - 12*a*b**4*c**4*(-3*b/(2*c**4) + 3*sqrt(-(4*a*c - b**2)**5)*(20*a**3*c**3 - 30*a**2*b**2*c**2 + 10*a*b**4*c - b**6)/(2*c**4*(1024*a**5*c**5 - 1280*a**4*b**2*c**4 + 640*a**3*b**4*c**3 - 160*a**2*b**6*c**2 + 20*a*b**8*c - b**10))) + b**6*c**3*(-3*b/(2*c**4) + 3*sqrt(-(4*a*c - b**2)**5)*(20*a**3*c**3 - 30*a**2*b**2*c**2 + 10*a*b**4*c - b**6)/(2*c**4*(1024*a**5*c**5 - 1280*a**4*b**2*c**4 + 640*a**3*b**4*c**3 - 160*a**2*b**6*c**2 + 20*a*b**8*c - b**10))))/(60*a**3*c**3 - 90*a**2*b**2*c**2 + 30*a*b**4*c - 3*b**6)) + (-58*a**4*b*c**2 + 36*a**3*b**3*c - 5*a**2*b**5 + x**3*(36*a**3*c**4 - 102*a**2*b**2*c**3 + 48*a*b**4*c**2 - 6*b**6*c) + x**2*(-42*a**3*b*c**3 - 41*a**2*b**3*c**2 + 34*a*b**5*c - 5*b**7) + x*(28*a**4*c**3 - 142*a**3*b**2*c**2 + 76*a**2*b**4*c - 10*a*b**6))/(32*a**4*c**6 - 16*a**3*b**2*c**5 + 2*a**2*b**4*c**4 + x**4*(32*a**2*c**8 - 16*a*b**2*c**7 + 2*b**4*c**6) + x**3*(64*a**2*b*c**7 - 32*a*b**3*c**6 + 4*b**5*c**5) + x**2*(64*a**3*c**7 - 12*a*b**4*c**5 + 2*b**6*c**4) + x*(64*a**3*b*c**6 - 32*a**2*b**3*c**5 + 4*a*b**5*c**4)) + x/c**3","B",0
432,1,1510,0,3.207857," ","integrate(1/(c+a/x**2+b/x)**3/x,x)","\left(- \frac{b \sqrt{- \left(4 a c - b^{2}\right)^{5}} \left(30 a^{2} c^{2} - 10 a b^{2} c + b^{4}\right)}{2 c^{3} \left(1024 a^{5} c^{5} - 1280 a^{4} b^{2} c^{4} + 640 a^{3} b^{4} c^{3} - 160 a^{2} b^{6} c^{2} + 20 a b^{8} c - b^{10}\right)} + \frac{1}{2 c^{3}}\right) \log{\left(x + \frac{- 64 a^{3} c^{5} \left(- \frac{b \sqrt{- \left(4 a c - b^{2}\right)^{5}} \left(30 a^{2} c^{2} - 10 a b^{2} c + b^{4}\right)}{2 c^{3} \left(1024 a^{5} c^{5} - 1280 a^{4} b^{2} c^{4} + 640 a^{3} b^{4} c^{3} - 160 a^{2} b^{6} c^{2} + 20 a b^{8} c - b^{10}\right)} + \frac{1}{2 c^{3}}\right) + 32 a^{3} c^{2} + 48 a^{2} b^{2} c^{4} \left(- \frac{b \sqrt{- \left(4 a c - b^{2}\right)^{5}} \left(30 a^{2} c^{2} - 10 a b^{2} c + b^{4}\right)}{2 c^{3} \left(1024 a^{5} c^{5} - 1280 a^{4} b^{2} c^{4} + 640 a^{3} b^{4} c^{3} - 160 a^{2} b^{6} c^{2} + 20 a b^{8} c - b^{10}\right)} + \frac{1}{2 c^{3}}\right) - 9 a^{2} b^{2} c - 12 a b^{4} c^{3} \left(- \frac{b \sqrt{- \left(4 a c - b^{2}\right)^{5}} \left(30 a^{2} c^{2} - 10 a b^{2} c + b^{4}\right)}{2 c^{3} \left(1024 a^{5} c^{5} - 1280 a^{4} b^{2} c^{4} + 640 a^{3} b^{4} c^{3} - 160 a^{2} b^{6} c^{2} + 20 a b^{8} c - b^{10}\right)} + \frac{1}{2 c^{3}}\right) + a b^{4} + b^{6} c^{2} \left(- \frac{b \sqrt{- \left(4 a c - b^{2}\right)^{5}} \left(30 a^{2} c^{2} - 10 a b^{2} c + b^{4}\right)}{2 c^{3} \left(1024 a^{5} c^{5} - 1280 a^{4} b^{2} c^{4} + 640 a^{3} b^{4} c^{3} - 160 a^{2} b^{6} c^{2} + 20 a b^{8} c - b^{10}\right)} + \frac{1}{2 c^{3}}\right)}{30 a^{2} b c^{2} - 10 a b^{3} c + b^{5}} \right)} + \left(\frac{b \sqrt{- \left(4 a c - b^{2}\right)^{5}} \left(30 a^{2} c^{2} - 10 a b^{2} c + b^{4}\right)}{2 c^{3} \left(1024 a^{5} c^{5} - 1280 a^{4} b^{2} c^{4} + 640 a^{3} b^{4} c^{3} - 160 a^{2} b^{6} c^{2} + 20 a b^{8} c - b^{10}\right)} + \frac{1}{2 c^{3}}\right) \log{\left(x + \frac{- 64 a^{3} c^{5} \left(\frac{b \sqrt{- \left(4 a c - b^{2}\right)^{5}} \left(30 a^{2} c^{2} - 10 a b^{2} c + b^{4}\right)}{2 c^{3} \left(1024 a^{5} c^{5} - 1280 a^{4} b^{2} c^{4} + 640 a^{3} b^{4} c^{3} - 160 a^{2} b^{6} c^{2} + 20 a b^{8} c - b^{10}\right)} + \frac{1}{2 c^{3}}\right) + 32 a^{3} c^{2} + 48 a^{2} b^{2} c^{4} \left(\frac{b \sqrt{- \left(4 a c - b^{2}\right)^{5}} \left(30 a^{2} c^{2} - 10 a b^{2} c + b^{4}\right)}{2 c^{3} \left(1024 a^{5} c^{5} - 1280 a^{4} b^{2} c^{4} + 640 a^{3} b^{4} c^{3} - 160 a^{2} b^{6} c^{2} + 20 a b^{8} c - b^{10}\right)} + \frac{1}{2 c^{3}}\right) - 9 a^{2} b^{2} c - 12 a b^{4} c^{3} \left(\frac{b \sqrt{- \left(4 a c - b^{2}\right)^{5}} \left(30 a^{2} c^{2} - 10 a b^{2} c + b^{4}\right)}{2 c^{3} \left(1024 a^{5} c^{5} - 1280 a^{4} b^{2} c^{4} + 640 a^{3} b^{4} c^{3} - 160 a^{2} b^{6} c^{2} + 20 a b^{8} c - b^{10}\right)} + \frac{1}{2 c^{3}}\right) + a b^{4} + b^{6} c^{2} \left(\frac{b \sqrt{- \left(4 a c - b^{2}\right)^{5}} \left(30 a^{2} c^{2} - 10 a b^{2} c + b^{4}\right)}{2 c^{3} \left(1024 a^{5} c^{5} - 1280 a^{4} b^{2} c^{4} + 640 a^{3} b^{4} c^{3} - 160 a^{2} b^{6} c^{2} + 20 a b^{8} c - b^{10}\right)} + \frac{1}{2 c^{3}}\right)}{30 a^{2} b c^{2} - 10 a b^{3} c + b^{5}} \right)} + \frac{24 a^{4} c^{2} - 21 a^{3} b^{2} c + 3 a^{2} b^{4} + x^{3} \left(50 a^{2} b c^{3} - 30 a b^{3} c^{2} + 4 b^{5} c\right) + x^{2} \left(32 a^{3} c^{3} + 11 a^{2} b^{2} c^{2} - 19 a b^{4} c + 3 b^{6}\right) + x \left(62 a^{3} b c^{2} - 44 a^{2} b^{3} c + 6 a b^{5}\right)}{32 a^{4} c^{5} - 16 a^{3} b^{2} c^{4} + 2 a^{2} b^{4} c^{3} + x^{4} \left(32 a^{2} c^{7} - 16 a b^{2} c^{6} + 2 b^{4} c^{5}\right) + x^{3} \left(64 a^{2} b c^{6} - 32 a b^{3} c^{5} + 4 b^{5} c^{4}\right) + x^{2} \left(64 a^{3} c^{6} - 12 a b^{4} c^{4} + 2 b^{6} c^{3}\right) + x \left(64 a^{3} b c^{5} - 32 a^{2} b^{3} c^{4} + 4 a b^{5} c^{3}\right)}"," ",0,"(-b*sqrt(-(4*a*c - b**2)**5)*(30*a**2*c**2 - 10*a*b**2*c + b**4)/(2*c**3*(1024*a**5*c**5 - 1280*a**4*b**2*c**4 + 640*a**3*b**4*c**3 - 160*a**2*b**6*c**2 + 20*a*b**8*c - b**10)) + 1/(2*c**3))*log(x + (-64*a**3*c**5*(-b*sqrt(-(4*a*c - b**2)**5)*(30*a**2*c**2 - 10*a*b**2*c + b**4)/(2*c**3*(1024*a**5*c**5 - 1280*a**4*b**2*c**4 + 640*a**3*b**4*c**3 - 160*a**2*b**6*c**2 + 20*a*b**8*c - b**10)) + 1/(2*c**3)) + 32*a**3*c**2 + 48*a**2*b**2*c**4*(-b*sqrt(-(4*a*c - b**2)**5)*(30*a**2*c**2 - 10*a*b**2*c + b**4)/(2*c**3*(1024*a**5*c**5 - 1280*a**4*b**2*c**4 + 640*a**3*b**4*c**3 - 160*a**2*b**6*c**2 + 20*a*b**8*c - b**10)) + 1/(2*c**3)) - 9*a**2*b**2*c - 12*a*b**4*c**3*(-b*sqrt(-(4*a*c - b**2)**5)*(30*a**2*c**2 - 10*a*b**2*c + b**4)/(2*c**3*(1024*a**5*c**5 - 1280*a**4*b**2*c**4 + 640*a**3*b**4*c**3 - 160*a**2*b**6*c**2 + 20*a*b**8*c - b**10)) + 1/(2*c**3)) + a*b**4 + b**6*c**2*(-b*sqrt(-(4*a*c - b**2)**5)*(30*a**2*c**2 - 10*a*b**2*c + b**4)/(2*c**3*(1024*a**5*c**5 - 1280*a**4*b**2*c**4 + 640*a**3*b**4*c**3 - 160*a**2*b**6*c**2 + 20*a*b**8*c - b**10)) + 1/(2*c**3)))/(30*a**2*b*c**2 - 10*a*b**3*c + b**5)) + (b*sqrt(-(4*a*c - b**2)**5)*(30*a**2*c**2 - 10*a*b**2*c + b**4)/(2*c**3*(1024*a**5*c**5 - 1280*a**4*b**2*c**4 + 640*a**3*b**4*c**3 - 160*a**2*b**6*c**2 + 20*a*b**8*c - b**10)) + 1/(2*c**3))*log(x + (-64*a**3*c**5*(b*sqrt(-(4*a*c - b**2)**5)*(30*a**2*c**2 - 10*a*b**2*c + b**4)/(2*c**3*(1024*a**5*c**5 - 1280*a**4*b**2*c**4 + 640*a**3*b**4*c**3 - 160*a**2*b**6*c**2 + 20*a*b**8*c - b**10)) + 1/(2*c**3)) + 32*a**3*c**2 + 48*a**2*b**2*c**4*(b*sqrt(-(4*a*c - b**2)**5)*(30*a**2*c**2 - 10*a*b**2*c + b**4)/(2*c**3*(1024*a**5*c**5 - 1280*a**4*b**2*c**4 + 640*a**3*b**4*c**3 - 160*a**2*b**6*c**2 + 20*a*b**8*c - b**10)) + 1/(2*c**3)) - 9*a**2*b**2*c - 12*a*b**4*c**3*(b*sqrt(-(4*a*c - b**2)**5)*(30*a**2*c**2 - 10*a*b**2*c + b**4)/(2*c**3*(1024*a**5*c**5 - 1280*a**4*b**2*c**4 + 640*a**3*b**4*c**3 - 160*a**2*b**6*c**2 + 20*a*b**8*c - b**10)) + 1/(2*c**3)) + a*b**4 + b**6*c**2*(b*sqrt(-(4*a*c - b**2)**5)*(30*a**2*c**2 - 10*a*b**2*c + b**4)/(2*c**3*(1024*a**5*c**5 - 1280*a**4*b**2*c**4 + 640*a**3*b**4*c**3 - 160*a**2*b**6*c**2 + 20*a*b**8*c - b**10)) + 1/(2*c**3)))/(30*a**2*b*c**2 - 10*a*b**3*c + b**5)) + (24*a**4*c**2 - 21*a**3*b**2*c + 3*a**2*b**4 + x**3*(50*a**2*b*c**3 - 30*a*b**3*c**2 + 4*b**5*c) + x**2*(32*a**3*c**3 + 11*a**2*b**2*c**2 - 19*a*b**4*c + 3*b**6) + x*(62*a**3*b*c**2 - 44*a**2*b**3*c + 6*a*b**5))/(32*a**4*c**5 - 16*a**3*b**2*c**4 + 2*a**2*b**4*c**3 + x**4*(32*a**2*c**7 - 16*a*b**2*c**6 + 2*b**4*c**5) + x**3*(64*a**2*b*c**6 - 32*a*b**3*c**5 + 4*b**5*c**4) + x**2*(64*a**3*c**6 - 12*a*b**4*c**4 + 2*b**6*c**3) + x*(64*a**3*b*c**5 - 32*a**2*b**3*c**4 + 4*a*b**5*c**3))","B",0
433,1,547,0,1.410720," ","integrate(1/(c+a/x**2+b/x)**3/x**2,x)","- 6 a^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \log{\left(x + \frac{- 384 a^{5} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 288 a^{4} b^{2} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} - 72 a^{3} b^{4} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 6 a^{2} b^{6} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 6 a^{2} b}{12 a^{2} c} \right)} + 6 a^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \log{\left(x + \frac{384 a^{5} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} - 288 a^{4} b^{2} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 72 a^{3} b^{4} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} - 6 a^{2} b^{6} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 6 a^{2} b}{12 a^{2} c} \right)} + \frac{10 a^{3} b c - a^{2} b^{3} + x^{3} \left(- 20 a^{2} c^{3} + 16 a b^{2} c^{2} - 2 b^{4} c\right) + x^{2} \left(2 a^{2} b c^{2} + 8 a b^{3} c - b^{5}\right) + x \left(- 12 a^{3} c^{2} + 20 a^{2} b^{2} c - 2 a b^{4}\right)}{32 a^{4} c^{4} - 16 a^{3} b^{2} c^{3} + 2 a^{2} b^{4} c^{2} + x^{4} \left(32 a^{2} c^{6} - 16 a b^{2} c^{5} + 2 b^{4} c^{4}\right) + x^{3} \left(64 a^{2} b c^{5} - 32 a b^{3} c^{4} + 4 b^{5} c^{3}\right) + x^{2} \left(64 a^{3} c^{5} - 12 a b^{4} c^{3} + 2 b^{6} c^{2}\right) + x \left(64 a^{3} b c^{4} - 32 a^{2} b^{3} c^{3} + 4 a b^{5} c^{2}\right)}"," ",0,"-6*a**2*sqrt(-1/(4*a*c - b**2)**5)*log(x + (-384*a**5*c**3*sqrt(-1/(4*a*c - b**2)**5) + 288*a**4*b**2*c**2*sqrt(-1/(4*a*c - b**2)**5) - 72*a**3*b**4*c*sqrt(-1/(4*a*c - b**2)**5) + 6*a**2*b**6*sqrt(-1/(4*a*c - b**2)**5) + 6*a**2*b)/(12*a**2*c)) + 6*a**2*sqrt(-1/(4*a*c - b**2)**5)*log(x + (384*a**5*c**3*sqrt(-1/(4*a*c - b**2)**5) - 288*a**4*b**2*c**2*sqrt(-1/(4*a*c - b**2)**5) + 72*a**3*b**4*c*sqrt(-1/(4*a*c - b**2)**5) - 6*a**2*b**6*sqrt(-1/(4*a*c - b**2)**5) + 6*a**2*b)/(12*a**2*c)) + (10*a**3*b*c - a**2*b**3 + x**3*(-20*a**2*c**3 + 16*a*b**2*c**2 - 2*b**4*c) + x**2*(2*a**2*b*c**2 + 8*a*b**3*c - b**5) + x*(-12*a**3*c**2 + 20*a**2*b**2*c - 2*a*b**4))/(32*a**4*c**4 - 16*a**3*b**2*c**3 + 2*a**2*b**4*c**2 + x**4*(32*a**2*c**6 - 16*a*b**2*c**5 + 2*b**4*c**4) + x**3*(64*a**2*b*c**5 - 32*a*b**3*c**4 + 4*b**5*c**3) + x**2*(64*a**3*c**5 - 12*a*b**4*c**3 + 2*b**6*c**2) + x*(64*a**3*b*c**4 - 32*a**2*b**3*c**3 + 4*a*b**5*c**2))","B",0
434,1,513,0,1.208711," ","integrate(1/(c+a/x**2+b/x)**3/x**3,x)","3 a b \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \log{\left(x + \frac{- 192 a^{4} b c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 144 a^{3} b^{3} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} - 36 a^{2} b^{5} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 3 a b^{7} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 3 a b^{2}}{6 a b c} \right)} - 3 a b \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \log{\left(x + \frac{192 a^{4} b c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} - 144 a^{3} b^{3} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 36 a^{2} b^{5} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} - 3 a b^{7} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 3 a b^{2}}{6 a b c} \right)} + \frac{- 8 a^{3} c - a^{2} b^{2} - 6 a b c^{2} x^{3} + x^{2} \left(- 16 a^{2} c^{2} - a b^{2} c - b^{4}\right) + x \left(- 10 a^{2} b c - 2 a b^{3}\right)}{32 a^{4} c^{3} - 16 a^{3} b^{2} c^{2} + 2 a^{2} b^{4} c + x^{4} \left(32 a^{2} c^{5} - 16 a b^{2} c^{4} + 2 b^{4} c^{3}\right) + x^{3} \left(64 a^{2} b c^{4} - 32 a b^{3} c^{3} + 4 b^{5} c^{2}\right) + x^{2} \left(64 a^{3} c^{4} - 12 a b^{4} c^{2} + 2 b^{6} c\right) + x \left(64 a^{3} b c^{3} - 32 a^{2} b^{3} c^{2} + 4 a b^{5} c\right)}"," ",0,"3*a*b*sqrt(-1/(4*a*c - b**2)**5)*log(x + (-192*a**4*b*c**3*sqrt(-1/(4*a*c - b**2)**5) + 144*a**3*b**3*c**2*sqrt(-1/(4*a*c - b**2)**5) - 36*a**2*b**5*c*sqrt(-1/(4*a*c - b**2)**5) + 3*a*b**7*sqrt(-1/(4*a*c - b**2)**5) + 3*a*b**2)/(6*a*b*c)) - 3*a*b*sqrt(-1/(4*a*c - b**2)**5)*log(x + (192*a**4*b*c**3*sqrt(-1/(4*a*c - b**2)**5) - 144*a**3*b**3*c**2*sqrt(-1/(4*a*c - b**2)**5) + 36*a**2*b**5*c*sqrt(-1/(4*a*c - b**2)**5) - 3*a*b**7*sqrt(-1/(4*a*c - b**2)**5) + 3*a*b**2)/(6*a*b*c)) + (-8*a**3*c - a**2*b**2 - 6*a*b*c**2*x**3 + x**2*(-16*a**2*c**2 - a*b**2*c - b**4) + x*(-10*a**2*b*c - 2*a*b**3))/(32*a**4*c**3 - 16*a**3*b**2*c**2 + 2*a**2*b**4*c + x**4*(32*a**2*c**5 - 16*a*b**2*c**4 + 2*b**4*c**3) + x**3*(64*a**2*b*c**4 - 32*a*b**3*c**3 + 4*b**5*c**2) + x**2*(64*a**3*c**4 - 12*a*b**4*c**2 + 2*b**6*c) + x*(64*a**3*b*c**3 - 32*a**2*b**3*c**2 + 4*a*b**5*c))","B",0
435,1,570,0,1.281816," ","integrate(1/(c+a/x**2+b/x)**3/x**4,x)","- \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(2 a c + b^{2}\right) \log{\left(x + \frac{- 64 a^{3} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(2 a c + b^{2}\right) + 48 a^{2} b^{2} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(2 a c + b^{2}\right) - 12 a b^{4} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(2 a c + b^{2}\right) + 2 a b c + b^{6} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(2 a c + b^{2}\right) + b^{3}}{4 a c^{2} + 2 b^{2} c} \right)} + \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(2 a c + b^{2}\right) \log{\left(x + \frac{64 a^{3} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(2 a c + b^{2}\right) - 48 a^{2} b^{2} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(2 a c + b^{2}\right) + 12 a b^{4} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(2 a c + b^{2}\right) + 2 a b c - b^{6} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(2 a c + b^{2}\right) + b^{3}}{4 a c^{2} + 2 b^{2} c} \right)} + \frac{6 a^{2} b + x^{3} \left(4 a c^{2} + 2 b^{2} c\right) + x^{2} \left(6 a b c + 3 b^{3}\right) + x \left(- 4 a^{2} c + 10 a b^{2}\right)}{32 a^{4} c^{2} - 16 a^{3} b^{2} c + 2 a^{2} b^{4} + x^{4} \left(32 a^{2} c^{4} - 16 a b^{2} c^{3} + 2 b^{4} c^{2}\right) + x^{3} \left(64 a^{2} b c^{3} - 32 a b^{3} c^{2} + 4 b^{5} c\right) + x^{2} \left(64 a^{3} c^{3} - 12 a b^{4} c + 2 b^{6}\right) + x \left(64 a^{3} b c^{2} - 32 a^{2} b^{3} c + 4 a b^{5}\right)}"," ",0,"-sqrt(-1/(4*a*c - b**2)**5)*(2*a*c + b**2)*log(x + (-64*a**3*c**3*sqrt(-1/(4*a*c - b**2)**5)*(2*a*c + b**2) + 48*a**2*b**2*c**2*sqrt(-1/(4*a*c - b**2)**5)*(2*a*c + b**2) - 12*a*b**4*c*sqrt(-1/(4*a*c - b**2)**5)*(2*a*c + b**2) + 2*a*b*c + b**6*sqrt(-1/(4*a*c - b**2)**5)*(2*a*c + b**2) + b**3)/(4*a*c**2 + 2*b**2*c)) + sqrt(-1/(4*a*c - b**2)**5)*(2*a*c + b**2)*log(x + (64*a**3*c**3*sqrt(-1/(4*a*c - b**2)**5)*(2*a*c + b**2) - 48*a**2*b**2*c**2*sqrt(-1/(4*a*c - b**2)**5)*(2*a*c + b**2) + 12*a*b**4*c*sqrt(-1/(4*a*c - b**2)**5)*(2*a*c + b**2) + 2*a*b*c - b**6*sqrt(-1/(4*a*c - b**2)**5)*(2*a*c + b**2) + b**3)/(4*a*c**2 + 2*b**2*c)) + (6*a**2*b + x**3*(4*a*c**2 + 2*b**2*c) + x**2*(6*a*b*c + 3*b**3) + x*(-4*a**2*c + 10*a*b**2))/(32*a**4*c**2 - 16*a**3*b**2*c + 2*a**2*b**4 + x**4*(32*a**2*c**4 - 16*a*b**2*c**3 + 2*b**4*c**2) + x**3*(64*a**2*b*c**3 - 32*a*b**3*c**2 + 4*b**5*c) + x**2*(64*a**3*c**3 - 12*a*b**4*c + 2*b**6) + x*(64*a**3*b*c**2 - 32*a**2*b**3*c + 4*a*b**5))","B",0
436,1,481,0,1.092219," ","integrate(1/(c+a/x**2+b/x)**3/x**5,x)","3 b c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \log{\left(x + \frac{- 192 a^{3} b c^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 144 a^{2} b^{3} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} - 36 a b^{5} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 3 b^{7} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 3 b^{2} c}{6 b c^{2}} \right)} - 3 b c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \log{\left(x + \frac{192 a^{3} b c^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} - 144 a^{2} b^{3} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 36 a b^{5} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} - 3 b^{7} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 3 b^{2} c}{6 b c^{2}} \right)} + \frac{- 8 a^{2} c - a b^{2} - 9 b^{2} c x^{2} - 6 b c^{2} x^{3} + x \left(- 10 a b c - 2 b^{3}\right)}{32 a^{4} c^{2} - 16 a^{3} b^{2} c + 2 a^{2} b^{4} + x^{4} \left(32 a^{2} c^{4} - 16 a b^{2} c^{3} + 2 b^{4} c^{2}\right) + x^{3} \left(64 a^{2} b c^{3} - 32 a b^{3} c^{2} + 4 b^{5} c\right) + x^{2} \left(64 a^{3} c^{3} - 12 a b^{4} c + 2 b^{6}\right) + x \left(64 a^{3} b c^{2} - 32 a^{2} b^{3} c + 4 a b^{5}\right)}"," ",0,"3*b*c*sqrt(-1/(4*a*c - b**2)**5)*log(x + (-192*a**3*b*c**4*sqrt(-1/(4*a*c - b**2)**5) + 144*a**2*b**3*c**3*sqrt(-1/(4*a*c - b**2)**5) - 36*a*b**5*c**2*sqrt(-1/(4*a*c - b**2)**5) + 3*b**7*c*sqrt(-1/(4*a*c - b**2)**5) + 3*b**2*c)/(6*b*c**2)) - 3*b*c*sqrt(-1/(4*a*c - b**2)**5)*log(x + (192*a**3*b*c**4*sqrt(-1/(4*a*c - b**2)**5) - 144*a**2*b**3*c**3*sqrt(-1/(4*a*c - b**2)**5) + 36*a*b**5*c**2*sqrt(-1/(4*a*c - b**2)**5) - 3*b**7*c*sqrt(-1/(4*a*c - b**2)**5) + 3*b**2*c)/(6*b*c**2)) + (-8*a**2*c - a*b**2 - 9*b**2*c*x**2 - 6*b*c**2*x**3 + x*(-10*a*b*c - 2*b**3))/(32*a**4*c**2 - 16*a**3*b**2*c + 2*a**2*b**4 + x**4*(32*a**2*c**4 - 16*a*b**2*c**3 + 2*b**4*c**2) + x**3*(64*a**2*b*c**3 - 32*a*b**3*c**2 + 4*b**5*c) + x**2*(64*a**3*c**3 - 12*a*b**4*c + 2*b**6) + x*(64*a**3*b*c**2 - 32*a**2*b**3*c + 4*a*b**5))","B",0
437,1,474,0,1.111298," ","integrate(1/(c+a/x**2+b/x)**3/x**6,x)","- 6 c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \log{\left(x + \frac{- 384 a^{3} c^{5} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 288 a^{2} b^{2} c^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} - 72 a b^{4} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 6 b^{6} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 6 b c^{2}}{12 c^{3}} \right)} + 6 c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \log{\left(x + \frac{384 a^{3} c^{5} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} - 288 a^{2} b^{2} c^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 72 a b^{4} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} - 6 b^{6} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 6 b c^{2}}{12 c^{3}} \right)} + \frac{10 a b c - b^{3} + 18 b c^{2} x^{2} + 12 c^{3} x^{3} + x \left(20 a c^{2} + 4 b^{2} c\right)}{32 a^{4} c^{2} - 16 a^{3} b^{2} c + 2 a^{2} b^{4} + x^{4} \left(32 a^{2} c^{4} - 16 a b^{2} c^{3} + 2 b^{4} c^{2}\right) + x^{3} \left(64 a^{2} b c^{3} - 32 a b^{3} c^{2} + 4 b^{5} c\right) + x^{2} \left(64 a^{3} c^{3} - 12 a b^{4} c + 2 b^{6}\right) + x \left(64 a^{3} b c^{2} - 32 a^{2} b^{3} c + 4 a b^{5}\right)}"," ",0,"-6*c**2*sqrt(-1/(4*a*c - b**2)**5)*log(x + (-384*a**3*c**5*sqrt(-1/(4*a*c - b**2)**5) + 288*a**2*b**2*c**4*sqrt(-1/(4*a*c - b**2)**5) - 72*a*b**4*c**3*sqrt(-1/(4*a*c - b**2)**5) + 6*b**6*c**2*sqrt(-1/(4*a*c - b**2)**5) + 6*b*c**2)/(12*c**3)) + 6*c**2*sqrt(-1/(4*a*c - b**2)**5)*log(x + (384*a**3*c**5*sqrt(-1/(4*a*c - b**2)**5) - 288*a**2*b**2*c**4*sqrt(-1/(4*a*c - b**2)**5) + 72*a*b**4*c**3*sqrt(-1/(4*a*c - b**2)**5) - 6*b**6*c**2*sqrt(-1/(4*a*c - b**2)**5) + 6*b*c**2)/(12*c**3)) + (10*a*b*c - b**3 + 18*b*c**2*x**2 + 12*c**3*x**3 + x*(20*a*c**2 + 4*b**2*c))/(32*a**4*c**2 - 16*a**3*b**2*c + 2*a**2*b**4 + x**4*(32*a**2*c**4 - 16*a*b**2*c**3 + 2*b**4*c**2) + x**3*(64*a**2*b*c**3 - 32*a*b**3*c**2 + 4*b**5*c) + x**2*(64*a**3*c**3 - 12*a*b**4*c + 2*b**6) + x*(64*a**3*b*c**2 - 32*a**2*b**3*c + 4*a*b**5))","B",0
438,-1,0,0,0.000000," ","integrate(1/(c+a/x**2+b/x)**3/x**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
439,-1,0,0,0.000000," ","integrate(1/(c+a/x**2+b/x)**3/x**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
440,1,34,0,0.120505," ","integrate(x**2/(15+2/x**2+13/x),x)","\frac{x^{3}}{45} - \frac{13 x^{2}}{450} + \frac{139 x}{3375} + \frac{\log{\left(x + \frac{1}{5} \right)}}{4375} - \frac{16 \log{\left(x + \frac{2}{3} \right)}}{567}"," ",0,"x**3/45 - 13*x**2/450 + 139*x/3375 + log(x + 1/5)/4375 - 16*log(x + 2/3)/567","A",0
441,1,27,0,0.118917," ","integrate(x/(15+2/x**2+13/x),x)","\frac{x^{2}}{30} - \frac{13 x}{225} - \frac{\log{\left(x + \frac{1}{5} \right)}}{875} + \frac{8 \log{\left(x + \frac{2}{3} \right)}}{189}"," ",0,"x**2/30 - 13*x/225 - log(x + 1/5)/875 + 8*log(x + 2/3)/189","A",0
442,1,20,0,0.116155," ","integrate(1/(15+2/x**2+13/x),x)","\frac{x}{15} + \frac{\log{\left(x + \frac{1}{5} \right)}}{175} - \frac{4 \log{\left(x + \frac{2}{3} \right)}}{63}"," ",0,"x/15 + log(x + 1/5)/175 - 4*log(x + 2/3)/63","A",0
443,1,17,0,0.111001," ","integrate(1/(15+2/x**2+13/x)/x,x)","- \frac{\log{\left(x + \frac{1}{5} \right)}}{35} + \frac{2 \log{\left(x + \frac{2}{3} \right)}}{21}"," ",0,"-log(x + 1/5)/35 + 2*log(x + 2/3)/21","A",0
444,1,15,0,0.110934," ","integrate(1/(15+2/x**2+13/x)/x**2,x)","\frac{\log{\left(x + \frac{1}{5} \right)}}{7} - \frac{\log{\left(x + \frac{2}{3} \right)}}{7}"," ",0,"log(x + 1/5)/7 - log(x + 2/3)/7","A",0
445,1,24,0,0.149135," ","integrate(1/(15+2/x**2+13/x)/x**3,x)","\frac{\log{\left(x \right)}}{2} - \frac{5 \log{\left(x + \frac{1}{5} \right)}}{7} + \frac{3 \log{\left(x + \frac{2}{3} \right)}}{14}"," ",0,"log(x)/2 - 5*log(x + 1/5)/7 + 3*log(x + 2/3)/14","A",0
446,1,31,0,0.163294," ","integrate(1/(15+2/x**2+13/x)/x**4,x)","- \frac{13 \log{\left(x \right)}}{4} + \frac{25 \log{\left(x + \frac{1}{5} \right)}}{7} - \frac{9 \log{\left(x + \frac{2}{3} \right)}}{28} - \frac{1}{2 x}"," ",0,"-13*log(x)/4 + 25*log(x + 1/5)/7 - 9*log(x + 2/3)/28 - 1/(2*x)","A",0
447,1,36,0,0.172668," ","integrate(1/(15+2/x**2+13/x)/x**5,x)","\frac{139 \log{\left(x \right)}}{8} - \frac{125 \log{\left(x + \frac{1}{5} \right)}}{7} + \frac{27 \log{\left(x + \frac{2}{3} \right)}}{56} + \frac{13 x - 1}{4 x^{2}}"," ",0,"139*log(x)/8 - 125*log(x + 1/5)/7 + 27*log(x + 2/3)/56 + (13*x - 1)/(4*x**2)","A",0
448,1,41,0,0.184539," ","integrate(1/(15+2/x**2+13/x)/x**6,x)","- \frac{1417 \log{\left(x \right)}}{16} + \frac{625 \log{\left(x + \frac{1}{5} \right)}}{7} - \frac{81 \log{\left(x + \frac{2}{3} \right)}}{112} + \frac{- 417 x^{2} + 39 x - 4}{24 x^{3}}"," ",0,"-1417*log(x)/16 + 625*log(x + 1/5)/7 - 81*log(x + 2/3)/112 + (-417*x**2 + 39*x - 4)/(24*x**3)","A",0
449,0,0,0,0.000000," ","integrate((a+c/x**2+b/x)**(5/2),x)","\int \left(a + \frac{b}{x} + \frac{c}{x^{2}}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((a + b/x + c/x**2)**(5/2), x)","F",0
450,0,0,0,0.000000," ","integrate((a+c/x**2+b/x)**(3/2),x)","\int \left(a + \frac{b}{x} + \frac{c}{x^{2}}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b/x + c/x**2)**(3/2), x)","F",0
451,0,0,0,0.000000," ","integrate((a+c/x**2+b/x)**(1/2),x)","\int \sqrt{a + \frac{b}{x} + \frac{c}{x^{2}}}\, dx"," ",0,"Integral(sqrt(a + b/x + c/x**2), x)","F",0
452,0,0,0,0.000000," ","integrate(1/(a+c/x**2+b/x)**(1/2),x)","\int \frac{1}{\sqrt{a + \frac{b}{x} + \frac{c}{x^{2}}}}\, dx"," ",0,"Integral(1/sqrt(a + b/x + c/x**2), x)","F",0
453,0,0,0,0.000000," ","integrate(1/(a+c/x**2+b/x)**(3/2),x)","\int \frac{1}{\left(a + \frac{b}{x} + \frac{c}{x^{2}}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b/x + c/x**2)**(-3/2), x)","F",0
454,0,0,0,0.000000," ","integrate(1/(a+c/x**2+b/x)**(5/2),x)","\int \frac{1}{\left(a + \frac{b}{x} + \frac{c}{x^{2}}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b/x + c/x**2)**(-5/2), x)","F",0
455,0,0,0,0.000000," ","integrate((a**2+b**2/x**2+2*a*b/x)**(1/2),x)","\int \sqrt{a^{2} + \frac{2 a b}{x} + \frac{b^{2}}{x^{2}}}\, dx"," ",0,"Integral(sqrt(a**2 + 2*a*b/x + b**2/x**2), x)","F",0
456,1,129,0,2.119197," ","integrate(1/(c+a/x**4+b/x**2),x)","\operatorname{RootSum} {\left(t^{4} \left(256 a^{2} c^{5} - 128 a b^{2} c^{4} + 16 b^{4} c^{3}\right) + t^{2} \left(48 a^{2} b c^{2} - 28 a b^{3} c + 4 b^{5}\right) + a^{3}, \left( t \mapsto t \log{\left(x + \frac{32 t^{3} a b c^{4} - 8 t^{3} b^{3} c^{3} - 4 t a^{2} c^{2} + 8 t a b^{2} c - 2 t b^{4}}{a^{2} c - a b^{2}} \right)} \right)\right)} + \frac{x}{c}"," ",0,"RootSum(_t**4*(256*a**2*c**5 - 128*a*b**2*c**4 + 16*b**4*c**3) + _t**2*(48*a**2*b*c**2 - 28*a*b**3*c + 4*b**5) + a**3, Lambda(_t, _t*log(x + (32*_t**3*a*b*c**4 - 8*_t**3*b**3*c**3 - 4*_t*a**2*c**2 + 8*_t*a*b**2*c - 2*_t*b**4)/(a**2*c - a*b**2)))) + x/c","A",0
457,1,196,0,6.965219," ","integrate(1/(c+a/x**6+b/x**3),x)","\operatorname{RootSum} {\left(t^{6} \left(46656 a^{3} c^{7} - 34992 a^{2} b^{2} c^{6} + 8748 a b^{4} c^{5} - 729 b^{6} c^{4}\right) + t^{3} \left(864 a^{3} b c^{3} - 864 a^{2} b^{3} c^{2} + 270 a b^{5} c - 27 b^{7}\right) + a^{4}, \left( t \mapsto t \log{\left(x + \frac{1296 t^{4} a^{2} b c^{6} - 648 t^{4} a b^{3} c^{5} + 81 t^{4} b^{5} c^{4} - 12 t a^{3} c^{3} + 39 t a^{2} b^{2} c^{2} - 21 t a b^{4} c + 3 t b^{6}}{2 a^{3} c^{2} - 4 a^{2} b^{2} c + a b^{4}} \right)} \right)\right)} + \frac{x}{c}"," ",0,"RootSum(_t**6*(46656*a**3*c**7 - 34992*a**2*b**2*c**6 + 8748*a*b**4*c**5 - 729*b**6*c**4) + _t**3*(864*a**3*b*c**3 - 864*a**2*b**3*c**2 + 270*a*b**5*c - 27*b**7) + a**4, Lambda(_t, _t*log(x + (1296*_t**4*a**2*b*c**6 - 648*_t**4*a*b**3*c**5 + 81*_t**4*b**5*c**4 - 12*_t*a**3*c**3 + 39*_t*a**2*b**2*c**2 - 21*_t*a*b**4*c + 3*_t*b**6)/(2*a**3*c**2 - 4*a**2*b**2*c + a*b**4)))) + x/c","A",0
458,-1,0,0,0.000000," ","integrate(1/(c+a/x**8+b/x**4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
459,0,0,0,0.000000," ","integrate((a+c*x+b*x**(1/2))**(1/2)/x,x)","\int \frac{\sqrt{a + b \sqrt{x} + c x}}{x}\, dx"," ",0,"Integral(sqrt(a + b*sqrt(x) + c*x)/x, x)","F",0
460,1,51,0,0.329735," ","integrate((1/4/c*b**2+c*x+b*x**(1/2))**2,x)","\frac{b^{4} x}{16 c^{2}} + \frac{b^{3} x^{\frac{3}{2}}}{3 c} + \frac{3 b^{2} x^{2}}{4} + \frac{4 b c x^{\frac{5}{2}}}{5} + \frac{c^{2} x^{3}}{3}"," ",0,"b**4*x/(16*c**2) + b**3*x**(3/2)/(3*c) + 3*b**2*x**2/4 + 4*b*c*x**(5/2)/5 + c**2*x**3/3","A",0
461,0,0,0,0.000000," ","integrate(1/(a**2+b**2*x+2*a*b*x**(1/2))**(1/2),x)","\int \frac{1}{\sqrt{a^{2} + 2 a b \sqrt{x} + b^{2} x}}\, dx"," ",0,"Integral(1/sqrt(a**2 + 2*a*b*sqrt(x) + b**2*x), x)","F",0
462,0,0,0,0.000000," ","integrate((a**2+2*a*b*x**(1/3)+b**2*x**(2/3))**(7/2),x)","\int \left(a^{2} + 2 a b \sqrt[3]{x} + b^{2} x^{\frac{2}{3}}\right)^{\frac{7}{2}}\, dx"," ",0,"Integral((a**2 + 2*a*b*x**(1/3) + b**2*x**(2/3))**(7/2), x)","F",0
463,0,0,0,0.000000," ","integrate((a**2+2*a*b*x**(1/3)+b**2*x**(2/3))**(5/2),x)","\int \left(a^{2} + 2 a b \sqrt[3]{x} + b^{2} x^{\frac{2}{3}}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((a**2 + 2*a*b*x**(1/3) + b**2*x**(2/3))**(5/2), x)","F",0
464,0,0,0,0.000000," ","integrate((a**2+2*a*b*x**(1/3)+b**2*x**(2/3))**(3/2),x)","\int \left(a^{2} + 2 a b \sqrt[3]{x} + b^{2} x^{\frac{2}{3}}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a**2 + 2*a*b*x**(1/3) + b**2*x**(2/3))**(3/2), x)","F",0
465,0,0,0,0.000000," ","integrate((a**2+2*a*b*x**(1/3)+b**2*x**(2/3))**(1/2),x)","\int \sqrt{a^{2} + 2 a b \sqrt[3]{x} + b^{2} x^{\frac{2}{3}}}\, dx"," ",0,"Integral(sqrt(a**2 + 2*a*b*x**(1/3) + b**2*x**(2/3)), x)","F",0
466,0,0,0,0.000000," ","integrate(1/(a**2+2*a*b*x**(1/3)+b**2*x**(2/3))**(1/2),x)","\int \frac{1}{\sqrt{a^{2} + 2 a b \sqrt[3]{x} + b^{2} x^{\frac{2}{3}}}}\, dx"," ",0,"Integral(1/sqrt(a**2 + 2*a*b*x**(1/3) + b**2*x**(2/3)), x)","F",0
467,0,0,0,0.000000," ","integrate(1/(a**2+2*a*b*x**(1/3)+b**2*x**(2/3))**(3/2),x)","\int \frac{1}{\left(a^{2} + 2 a b \sqrt[3]{x} + b^{2} x^{\frac{2}{3}}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a**2 + 2*a*b*x**(1/3) + b**2*x**(2/3))**(-3/2), x)","F",0
468,0,0,0,0.000000," ","integrate(1/(a**2+2*a*b*x**(1/3)+b**2*x**(2/3))**(5/2),x)","\int \frac{1}{\left(a^{2} + 2 a b \sqrt[3]{x} + b^{2} x^{\frac{2}{3}}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a**2 + 2*a*b*x**(1/3) + b**2*x**(2/3))**(-5/2), x)","F",0
469,0,0,0,0.000000," ","integrate(1/(a**2+2*a*b*x**(1/3)+b**2*x**(2/3))**(7/2),x)","\int \frac{1}{\left(a^{2} + 2 a b \sqrt[3]{x} + b^{2} x^{\frac{2}{3}}\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((a**2 + 2*a*b*x**(1/3) + b**2*x**(2/3))**(-7/2), x)","F",0
470,0,0,0,0.000000," ","integrate(1/(a**2+2*a*b*x**(1/3)+b**2*x**(2/3))**(9/2),x)","\int \frac{1}{\left(a^{2} + 2 a b \sqrt[3]{x} + b^{2} x^{\frac{2}{3}}\right)^{\frac{9}{2}}}\, dx"," ",0,"Integral((a**2 + 2*a*b*x**(1/3) + b**2*x**(2/3))**(-9/2), x)","F",0
471,0,0,0,0.000000," ","integrate(1/(a**2+2*a*b*x**(1/3)+b**2*x**(2/3))**(11/2),x)","\int \frac{1}{\left(a^{2} + 2 a b \sqrt[3]{x} + b^{2} x^{\frac{2}{3}}\right)^{\frac{11}{2}}}\, dx"," ",0,"Integral((a**2 + 2*a*b*x**(1/3) + b**2*x**(2/3))**(-11/2), x)","F",0
472,-1,0,0,0.000000," ","integrate((a**2+2*a*b*x**(1/3)+b**2*x**(2/3))**p*(d*x)**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
473,-2,0,0,0.000000," ","integrate((a**2+2*a*b*x**(1/3)+b**2*x**(2/3))**p*x**2,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
474,-2,0,0,0.000000," ","integrate((a**2+2*a*b*x**(1/3)+b**2*x**(2/3))**p*x,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
475,0,0,0,0.000000," ","integrate((a**2+2*a*b*x**(1/3)+b**2*x**(2/3))**p,x)","\int \left(a^{2} + 2 a b \sqrt[3]{x} + b^{2} x^{\frac{2}{3}}\right)^{p}\, dx"," ",0,"Integral((a**2 + 2*a*b*x**(1/3) + b**2*x**(2/3))**p, x)","F",0
476,0,0,0,0.000000," ","integrate((a**2+2*a*b*x**(1/3)+b**2*x**(2/3))**p/x,x)","\int \frac{\left(\left(a + b \sqrt[3]{x}\right)^{2}\right)^{p}}{x}\, dx"," ",0,"Integral(((a + b*x**(1/3))**2)**p/x, x)","F",0
477,0,0,0,0.000000," ","integrate((a**2+2*a*b*x**(1/3)+b**2*x**(2/3))**p/x**2,x)","\int \frac{\left(\left(a + b \sqrt[3]{x}\right)^{2}\right)^{p}}{x^{2}}\, dx"," ",0,"Integral(((a + b*x**(1/3))**2)**p/x**2, x)","F",0
478,0,0,0,0.000000," ","integrate((a**2+2*a*b*x**(1/3)+b**2*x**(2/3))**p/x**2-2/3*b**3*(1-2*p)*(1-p)*p*(a**2+2*a*b*x**(1/3)+b**2*x**(2/3))**p/a**3/x,x)","- \frac{\int \left(- \frac{3 a^{3} \left(a^{2} + 2 a b \sqrt[3]{x} + b^{2} x^{\frac{2}{3}}\right)^{p}}{x^{2}}\right)\, dx + \int \frac{2 b^{3} p \left(a^{2} + 2 a b \sqrt[3]{x} + b^{2} x^{\frac{2}{3}}\right)^{p}}{x}\, dx + \int \left(- \frac{6 b^{3} p^{2} \left(a^{2} + 2 a b \sqrt[3]{x} + b^{2} x^{\frac{2}{3}}\right)^{p}}{x}\right)\, dx + \int \frac{4 b^{3} p^{3} \left(a^{2} + 2 a b \sqrt[3]{x} + b^{2} x^{\frac{2}{3}}\right)^{p}}{x}\, dx}{3 a^{3}}"," ",0,"-(Integral(-3*a**3*(a**2 + 2*a*b*x**(1/3) + b**2*x**(2/3))**p/x**2, x) + Integral(2*b**3*p*(a**2 + 2*a*b*x**(1/3) + b**2*x**(2/3))**p/x, x) + Integral(-6*b**3*p**2*(a**2 + 2*a*b*x**(1/3) + b**2*x**(2/3))**p/x, x) + Integral(4*b**3*p**3*(a**2 + 2*a*b*x**(1/3) + b**2*x**(2/3))**p/x, x))/(3*a**3)","F",0
479,0,0,0,0.000000," ","integrate(1/(a**2+2*a*b*x**(1/4)+b**2*x**(1/2))**(3/2),x)","\int \frac{1}{\left(a^{2} + 2 a b \sqrt[4]{x} + b^{2} \sqrt{x}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a**2 + 2*a*b*x**(1/4) + b**2*sqrt(x))**(-3/2), x)","F",0
480,-1,0,0,0.000000," ","integrate(1/(a**2+2*a*b*x**(1/6)+b**2*x**(1/3))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
481,0,0,0,0.000000," ","integrate((a**2+b**2/x+2*a*b/x**(1/2))**(3/2),x)","\int \left(a^{2} + \frac{2 a b}{\sqrt{x}} + \frac{b^{2}}{x}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a**2 + 2*a*b/sqrt(x) + b**2/x)**(3/2), x)","F",0
482,0,0,0,0.000000," ","integrate((a**2+b**2/x**(2/3)+2*a*b/x**(1/3))**(7/2),x)","\int \left(a^{2} + \frac{2 a b}{\sqrt[3]{x}} + \frac{b^{2}}{x^{\frac{2}{3}}}\right)^{\frac{7}{2}}\, dx"," ",0,"Integral((a**2 + 2*a*b/x**(1/3) + b**2/x**(2/3))**(7/2), x)","F",0
483,0,0,0,0.000000," ","integrate((a**2+b**2/x**(2/3)+2*a*b/x**(1/3))**(5/2),x)","\int \left(a^{2} + \frac{2 a b}{\sqrt[3]{x}} + \frac{b^{2}}{x^{\frac{2}{3}}}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((a**2 + 2*a*b/x**(1/3) + b**2/x**(2/3))**(5/2), x)","F",0
484,0,0,0,0.000000," ","integrate((a**2+b**2/x**(2/3)+2*a*b/x**(1/3))**(3/2),x)","\int \left(a^{2} + \frac{2 a b}{\sqrt[3]{x}} + \frac{b^{2}}{x^{\frac{2}{3}}}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a**2 + 2*a*b/x**(1/3) + b**2/x**(2/3))**(3/2), x)","F",0
485,0,0,0,0.000000," ","integrate((a**2+b**2/x**(2/3)+2*a*b/x**(1/3))**(1/2),x)","\int \sqrt{a^{2} + \frac{2 a b}{\sqrt[3]{x}} + \frac{b^{2}}{x^{\frac{2}{3}}}}\, dx"," ",0,"Integral(sqrt(a**2 + 2*a*b/x**(1/3) + b**2/x**(2/3)), x)","F",0
486,0,0,0,0.000000," ","integrate(1/(a**2+b**2/x**(2/3)+2*a*b/x**(1/3))**(1/2),x)","\int \frac{1}{\sqrt{a^{2} + \frac{2 a b}{\sqrt[3]{x}} + \frac{b^{2}}{x^{\frac{2}{3}}}}}\, dx"," ",0,"Integral(1/sqrt(a**2 + 2*a*b/x**(1/3) + b**2/x**(2/3)), x)","F",0
487,0,0,0,0.000000," ","integrate(1/(a**2+b**2/x**(2/3)+2*a*b/x**(1/3))**(3/2),x)","\int \frac{1}{\left(a^{2} + \frac{2 a b}{\sqrt[3]{x}} + \frac{b^{2}}{x^{\frac{2}{3}}}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a**2 + 2*a*b/x**(1/3) + b**2/x**(2/3))**(-3/2), x)","F",0
488,0,0,0,0.000000," ","integrate(1/(a**2+b**2/x**(2/3)+2*a*b/x**(1/3))**(5/2),x)","\int \frac{1}{\left(a^{2} + \frac{2 a b}{\sqrt[3]{x}} + \frac{b^{2}}{x^{\frac{2}{3}}}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a**2 + 2*a*b/x**(1/3) + b**2/x**(2/3))**(-5/2), x)","F",0
489,-1,0,0,0.000000," ","integrate((a**2+2*a*b/x**(1/4)+b**2/x**(1/2))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
490,0,0,0,0.000000," ","integrate((a**2+b**2/x**(2/5)+2*a*b/x**(1/5))**(5/2),x)","\int \left(a^{2} + \frac{2 a b}{\sqrt[5]{x}} + \frac{b^{2}}{x^{\frac{2}{5}}}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((a**2 + 2*a*b/x**(1/5) + b**2/x**(2/5))**(5/2), x)","F",0
491,0,0,0,0.000000," ","integrate(1/(a**2+2*a*b*x**(1/5)+b**2*x**(2/5))**(5/2),x)","\int \frac{1}{\left(a^{2} + 2 a b \sqrt[5]{x} + b^{2} x^{\frac{2}{5}}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a**2 + 2*a*b*x**(1/5) + b**2*x**(2/5))**(-5/2), x)","F",0
492,-1,0,0,0.000000," ","integrate((a**2+b**2/x**(1/3)+2*a*b/x**(1/6))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
493,1,42,0,19.825723," ","integrate(x**(-1+4*n)/(b*x**n+c*x**(2*n)),x)","\frac{b^{2} \left(\begin{cases} \frac{x^{n}}{b} & \text{for}\: c = 0 \\\frac{\log{\left(b + c x^{n} \right)}}{c} & \text{otherwise} \end{cases}\right)}{c^{2} n} - \frac{b x^{n}}{c^{2} n} + \frac{x^{2 n}}{2 c n}"," ",0,"b**2*Piecewise((x**n/b, Eq(c, 0)), (log(b + c*x**n)/c, True))/(c**2*n) - b*x**n/(c**2*n) + x**(2*n)/(2*c*n)","A",0
494,1,26,0,13.889823," ","integrate(x**(-1+3*n)/(b*x**n+c*x**(2*n)),x)","- \frac{b \left(\begin{cases} \frac{x^{n}}{b} & \text{for}\: c = 0 \\\frac{\log{\left(b + c x^{n} \right)}}{c} & \text{otherwise} \end{cases}\right)}{c n} + \frac{x^{n}}{c n}"," ",0,"-b*Piecewise((x**n/b, Eq(c, 0)), (log(b + c*x**n)/c, True))/(c*n) + x**n/(c*n)","A",0
495,1,37,0,11.279796," ","integrate(x**(-1+2*n)/(b*x**n+c*x**(2*n)),x)","\begin{cases} \frac{\log{\left(x \right)}}{b} & \text{for}\: c = 0 \wedge n = 0 \\\frac{\log{\left(x \right)}}{b + c} & \text{for}\: n = 0 \\\frac{x^{n}}{b n} & \text{for}\: c = 0 \\- \frac{\log{\left(x \right)}}{c} + \frac{\log{\left(\frac{b x^{n}}{c} + x^{2 n} \right)}}{c n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(x)/b, Eq(c, 0) & Eq(n, 0)), (log(x)/(b + c), Eq(n, 0)), (x**n/(b*n), Eq(c, 0)), (-log(x)/c + log(b*x**n/c + x**(2*n))/(c*n), True))","A",0
496,1,66,0,16.485329," ","integrate(x**(-1+n)/(b*x**n+c*x**(2*n)),x)","\begin{cases} \tilde{\infty} \log{\left(x \right)} & \text{for}\: b = 0 \wedge c = 0 \wedge n = 0 \\- \frac{x^{- n}}{c n} & \text{for}\: b = 0 \\\frac{\log{\left(x \right)}}{b + c} & \text{for}\: n = 0 \\\frac{\frac{n^{2} \log{\left(x \right)}}{n^{2} - n} - \frac{n \log{\left(x \right)}}{n^{2} - n}}{b} & \text{for}\: c = 0 \\\frac{2 \log{\left(x \right)}}{b} - \frac{\log{\left(\frac{b x^{n}}{c} + x^{2 n} \right)}}{b n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*log(x), Eq(b, 0) & Eq(c, 0) & Eq(n, 0)), (-x**(-n)/(c*n), Eq(b, 0)), (log(x)/(b + c), Eq(n, 0)), ((n**2*log(x)/(n**2 - n) - n*log(x)/(n**2 - n))/b, Eq(c, 0)), (2*log(x)/b - log(b*x**n/c + x**(2*n))/(b*n), True))","A",0
497,-2,0,0,0.000000," ","integrate(x**(-1-n)/(b*x**n+c*x**(2*n)),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
498,1,73,0,52.911122," ","integrate(x**(-1-2*n)/(b*x**n+c*x**(2*n)),x)","- \frac{x^{- 3 n}}{3 b n} + \frac{c x^{- 2 n}}{2 b^{2} n} - \frac{c^{2} x^{- n}}{b^{3} n} + \frac{c^{4} \left(\begin{cases} \frac{x^{n}}{b} & \text{for}\: c = 0 \\\frac{\log{\left(b + c x^{n} \right)}}{c} & \text{otherwise} \end{cases}\right)}{b^{4} n} - \frac{c^{3} \log{\left(x^{n} \right)}}{b^{4} n}"," ",0,"-x**(-3*n)/(3*b*n) + c*x**(-2*n)/(2*b**2*n) - c**2*x**(-n)/(b**3*n) + c**4*Piecewise((x**n/b, Eq(c, 0)), (log(b + c*x**n)/c, True))/(b**4*n) - c**3*log(x**n)/(b**4*n)","A",0
499,1,88,0,105.733987," ","integrate(x**(-1-3*n)/(b*x**n+c*x**(2*n)),x)","- \frac{x^{- 4 n}}{4 b n} + \frac{c x^{- 3 n}}{3 b^{2} n} - \frac{c^{2} x^{- 2 n}}{2 b^{3} n} + \frac{c^{3} x^{- n}}{b^{4} n} - \frac{c^{5} \left(\begin{cases} \frac{x^{n}}{b} & \text{for}\: c = 0 \\\frac{\log{\left(b + c x^{n} \right)}}{c} & \text{otherwise} \end{cases}\right)}{b^{5} n} + \frac{c^{4} \log{\left(x^{n} \right)}}{b^{5} n}"," ",0,"-x**(-4*n)/(4*b*n) + c*x**(-3*n)/(3*b**2*n) - c**2*x**(-2*n)/(2*b**3*n) + c**3*x**(-n)/(b**4*n) - c**5*Piecewise((x**n/b, Eq(c, 0)), (log(b + c*x**n)/c, True))/(b**5*n) + c**4*log(x**n)/(b**5*n)","A",0
500,0,0,0,0.000000," ","integrate(x**(-1+1/4*n)/(b*x**n+c*x**(2*n)),x)","\int \frac{x^{- n} x^{\frac{n}{4} - 1}}{b + c x^{n}}\, dx"," ",0,"Integral(x**(-n)*x**(n/4 - 1)/(b + c*x**n), x)","F",0
501,-1,0,0,0.000000," ","integrate(x**(-1+1/3*n)/(b*x**n+c*x**(2*n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
502,1,36,0,12.998809," ","integrate(x**(-1+1/2*n)/(b*x**n+c*x**(2*n)),x)","- \frac{2 \operatorname{atan}{\left(\frac{x^{\frac{n}{2}}}{\sqrt{\frac{b}{c}}} \right)}}{b n \sqrt{\frac{b}{c}}} - \frac{2 x^{- \frac{n}{2}}}{b n}"," ",0,"-2*atan(x**(n/2)/sqrt(b/c))/(b*n*sqrt(b/c)) - 2*x**(-n/2)/(b*n)","A",0
503,1,58,0,24.919274," ","integrate(x**(-1-1/2*n)/(b*x**n+c*x**(2*n)),x)","- \frac{2 x^{- \frac{3 n}{2}}}{3 b n} + \frac{2 c x^{- \frac{n}{2}}}{b^{2} n} - \frac{2 c^{2} \operatorname{atan}{\left(\frac{x^{- \frac{n}{2}}}{\sqrt{\frac{c}{b}}} \right)}}{b^{3} n \sqrt{\frac{c}{b}}}"," ",0,"-2*x**(-3*n/2)/(3*b*n) + 2*c*x**(-n/2)/(b**2*n) - 2*c**2*atan(x**(-n/2)/sqrt(c/b))/(b**3*n*sqrt(c/b))","A",0
504,-1,0,0,0.000000," ","integrate(x**(-1-1/3*n)/(b*x**n+c*x**(2*n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
505,-1,0,0,0.000000," ","integrate(x**(-1-1/4*n)/(b*x**n+c*x**(2*n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
506,-1,0,0,0.000000," ","integrate(x**(-1-n*(-1+p))*(b*x**n+c*x**(2*n))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
507,-1,0,0,0.000000," ","integrate(x**(-1-n*(1+2*p))*(b*x**n+c*x**(2*n))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
508,-1,0,0,0.000000," ","integrate(x**(-1+2*n)*(a**2+2*a*b*x**n+b**2*x**(2*n))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
509,-1,0,0,0.000000," ","integrate(x**(-1+2*n)*(a**2+2*a*b*x**n+b**2*x**(2*n))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
510,0,0,0,0.000000," ","integrate(x**(-1+2*n)*(a**2+2*a*b*x**n+b**2*x**(2*n))**(1/2),x)","\int x^{2 n - 1} \sqrt{\left(a + b x^{n}\right)^{2}}\, dx"," ",0,"Integral(x**(2*n - 1)*sqrt((a + b*x**n)**2), x)","F",0
511,0,0,0,0.000000," ","integrate(x**(-1+2*n)/(a**2+2*a*b*x**n+b**2*x**(2*n))**(1/2),x)","\int \frac{x^{2 n - 1}}{\sqrt{\left(a + b x^{n}\right)^{2}}}\, dx"," ",0,"Integral(x**(2*n - 1)/sqrt((a + b*x**n)**2), x)","F",0
512,0,0,0,0.000000," ","integrate(x**(-1+2*n)/(a**2+2*a*b*x**n+b**2*x**(2*n))**(3/2),x)","\int \frac{x^{2 n - 1}}{\left(\left(a + b x^{n}\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**(2*n - 1)/((a + b*x**n)**2)**(3/2), x)","F",0
513,-1,0,0,0.000000," ","integrate(x**(-1+2*n)/(a**2+2*a*b*x**n+b**2*x**(2*n))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
514,-1,0,0,0.000000," ","integrate(x**(-1+2*n)/(a**2+2*a*b*x**n+b**2*x**(2*n))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
515,0,0,0,0.000000," ","integrate((d*x)**m*(a**2+2*a*b*x**n+b**2*x**(2*n))**(1/2),x)","\int \left(d x\right)^{m} \sqrt{\left(a + b x^{n}\right)^{2}}\, dx"," ",0,"Integral((d*x)**m*sqrt((a + b*x**n)**2), x)","F",0
516,0,0,0,0.000000," ","integrate(x**2*(a**2+2*a*b*x**n+b**2*x**(2*n))**(1/2),x)","\int x^{2} \sqrt{\left(a + b x^{n}\right)^{2}}\, dx"," ",0,"Integral(x**2*sqrt((a + b*x**n)**2), x)","F",0
517,0,0,0,0.000000," ","integrate(x*(a**2+2*a*b*x**n+b**2*x**(2*n))**(1/2),x)","\int x \sqrt{\left(a + b x^{n}\right)^{2}}\, dx"," ",0,"Integral(x*sqrt((a + b*x**n)**2), x)","F",0
518,0,0,0,0.000000," ","integrate((a**2+2*a*b*x**n+b**2*x**(2*n))**(1/2),x)","\int \sqrt{a^{2} + 2 a b x^{n} + b^{2} x^{2 n}}\, dx"," ",0,"Integral(sqrt(a**2 + 2*a*b*x**n + b**2*x**(2*n)), x)","F",0
519,0,0,0,0.000000," ","integrate((a**2+2*a*b*x**n+b**2*x**(2*n))**(1/2)/x,x)","\int \frac{\sqrt{\left(a + b x^{n}\right)^{2}}}{x}\, dx"," ",0,"Integral(sqrt((a + b*x**n)**2)/x, x)","F",0
520,0,0,0,0.000000," ","integrate((a**2+2*a*b*x**n+b**2*x**(2*n))**(1/2)/x**2,x)","\int \frac{\sqrt{\left(a + b x^{n}\right)^{2}}}{x^{2}}\, dx"," ",0,"Integral(sqrt((a + b*x**n)**2)/x**2, x)","F",0
521,0,0,0,0.000000," ","integrate((a**2+2*a*b*x**n+b**2*x**(2*n))**(1/2)/x**3,x)","\int \frac{\sqrt{\left(a + b x^{n}\right)^{2}}}{x^{3}}\, dx"," ",0,"Integral(sqrt((a + b*x**n)**2)/x**3, x)","F",0
522,0,0,0,0.000000," ","integrate((d*x)**m*(a**2+2*a*b*x**n+b**2*x**(2*n))**(3/2),x)","\int \left(d x\right)^{m} \left(\left(a + b x^{n}\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((d*x)**m*((a + b*x**n)**2)**(3/2), x)","F",0
523,0,0,0,0.000000," ","integrate(x**2*(a**2+2*a*b*x**n+b**2*x**(2*n))**(3/2),x)","\int x^{2} \left(\left(a + b x^{n}\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**2*((a + b*x**n)**2)**(3/2), x)","F",0
524,0,0,0,0.000000," ","integrate(x*(a**2+2*a*b*x**n+b**2*x**(2*n))**(3/2),x)","\int x \left(\left(a + b x^{n}\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x*((a + b*x**n)**2)**(3/2), x)","F",0
525,0,0,0,0.000000," ","integrate((a**2+2*a*b*x**n+b**2*x**(2*n))**(3/2),x)","\int \left(a^{2} + 2 a b x^{n} + b^{2} x^{2 n}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a**2 + 2*a*b*x**n + b**2*x**(2*n))**(3/2), x)","F",0
526,0,0,0,0.000000," ","integrate((a**2+2*a*b*x**n+b**2*x**(2*n))**(3/2)/x,x)","\int \frac{\left(\left(a + b x^{n}\right)^{2}\right)^{\frac{3}{2}}}{x}\, dx"," ",0,"Integral(((a + b*x**n)**2)**(3/2)/x, x)","F",0
527,0,0,0,0.000000," ","integrate((a**2+2*a*b*x**n+b**2*x**(2*n))**(3/2)/x**2,x)","\int \frac{\left(\left(a + b x^{n}\right)^{2}\right)^{\frac{3}{2}}}{x^{2}}\, dx"," ",0,"Integral(((a + b*x**n)**2)**(3/2)/x**2, x)","F",0
528,0,0,0,0.000000," ","integrate((a**2+2*a*b*x**n+b**2*x**(2*n))**(3/2)/x**3,x)","\int \frac{\left(\left(a + b x^{n}\right)^{2}\right)^{\frac{3}{2}}}{x^{3}}\, dx"," ",0,"Integral(((a + b*x**n)**2)**(3/2)/x**3, x)","F",0
529,0,0,0,0.000000," ","integrate((d*x)**m/(a**2+2*a*b*x**n+b**2*x**(2*n))**(1/2),x)","\int \frac{\left(d x\right)^{m}}{\sqrt{\left(a + b x^{n}\right)^{2}}}\, dx"," ",0,"Integral((d*x)**m/sqrt((a + b*x**n)**2), x)","F",0
530,0,0,0,0.000000," ","integrate(x**2/(a**2+2*a*b*x**n+b**2*x**(2*n))**(1/2),x)","\int \frac{x^{2}}{\sqrt{\left(a + b x^{n}\right)^{2}}}\, dx"," ",0,"Integral(x**2/sqrt((a + b*x**n)**2), x)","F",0
531,0,0,0,0.000000," ","integrate(x/(a**2+2*a*b*x**n+b**2*x**(2*n))**(1/2),x)","\int \frac{x}{\sqrt{\left(a + b x^{n}\right)^{2}}}\, dx"," ",0,"Integral(x/sqrt((a + b*x**n)**2), x)","F",0
532,0,0,0,0.000000," ","integrate(1/(a**2+2*a*b*x**n+b**2*x**(2*n))**(1/2),x)","\int \frac{1}{\sqrt{a^{2} + 2 a b x^{n} + b^{2} x^{2 n}}}\, dx"," ",0,"Integral(1/sqrt(a**2 + 2*a*b*x**n + b**2*x**(2*n)), x)","F",0
533,0,0,0,0.000000," ","integrate(1/x/(a**2+2*a*b*x**n+b**2*x**(2*n))**(1/2),x)","\int \frac{1}{x \sqrt{\left(a + b x^{n}\right)^{2}}}\, dx"," ",0,"Integral(1/(x*sqrt((a + b*x**n)**2)), x)","F",0
534,0,0,0,0.000000," ","integrate(1/x**2/(a**2+2*a*b*x**n+b**2*x**(2*n))**(1/2),x)","\int \frac{1}{x^{2} \sqrt{\left(a + b x^{n}\right)^{2}}}\, dx"," ",0,"Integral(1/(x**2*sqrt((a + b*x**n)**2)), x)","F",0
535,0,0,0,0.000000," ","integrate(1/x**3/(a**2+2*a*b*x**n+b**2*x**(2*n))**(1/2),x)","\int \frac{1}{x^{3} \sqrt{\left(a + b x^{n}\right)^{2}}}\, dx"," ",0,"Integral(1/(x**3*sqrt((a + b*x**n)**2)), x)","F",0
536,0,0,0,0.000000," ","integrate((d*x)**m/(a**2+2*a*b*x**n+b**2*x**(2*n))**(3/2),x)","\int \frac{\left(d x\right)^{m}}{\left(\left(a + b x^{n}\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d*x)**m/((a + b*x**n)**2)**(3/2), x)","F",0
537,0,0,0,0.000000," ","integrate(x**2/(a**2+2*a*b*x**n+b**2*x**(2*n))**(3/2),x)","\int \frac{x^{2}}{\left(\left(a + b x^{n}\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**2/((a + b*x**n)**2)**(3/2), x)","F",0
538,0,0,0,0.000000," ","integrate(x/(a**2+2*a*b*x**n+b**2*x**(2*n))**(3/2),x)","\int \frac{x}{\left(\left(a + b x^{n}\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x/((a + b*x**n)**2)**(3/2), x)","F",0
539,0,0,0,0.000000," ","integrate(1/(a**2+2*a*b*x**n+b**2*x**(2*n))**(3/2),x)","\int \frac{1}{\left(a^{2} + 2 a b x^{n} + b^{2} x^{2 n}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a**2 + 2*a*b*x**n + b**2*x**(2*n))**(-3/2), x)","F",0
540,0,0,0,0.000000," ","integrate(1/x/(a**2+2*a*b*x**n+b**2*x**(2*n))**(3/2),x)","\int \frac{1}{x \left(\left(a + b x^{n}\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x*((a + b*x**n)**2)**(3/2)), x)","F",0
541,0,0,0,0.000000," ","integrate(1/x**2/(a**2+2*a*b*x**n+b**2*x**(2*n))**(3/2),x)","\int \frac{1}{x^{2} \left(\left(a + b x^{n}\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**2*((a + b*x**n)**2)**(3/2)), x)","F",0
542,0,0,0,0.000000," ","integrate(1/x**3/(a**2+2*a*b*x**n+b**2*x**(2*n))**(3/2),x)","\int \frac{1}{x^{3} \left(\left(a + b x^{n}\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**3*((a + b*x**n)**2)**(3/2)), x)","F",0
543,-1,0,0,0.000000," ","integrate((a**2+b**2/(x**(2/(1+2*p)))+2*a*b/(x**(1/(1+2*p))))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
544,0,0,0,0.000000," ","integrate(1/((a**2+2*a*b*x**n+b**2*x**(2*n))**(1/2*(1+n)/n)),x)","\int \left(a^{2} + 2 a b x^{n} + b^{2} x^{2 n}\right)^{- \frac{\frac{n}{2} + \frac{1}{2}}{n}}\, dx"," ",0,"Integral((a**2 + 2*a*b*x**n + b**2*x**(2*n))**(-(n/2 + 1/2)/n), x)","F",0
545,-1,0,0,0.000000," ","integrate((a**2+b**2/(x**(1/(1+p)))+2*a*b/(x**(1/2/(1+p))))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
546,-1,0,0,0.000000," ","integrate(1/((a**2+2*a*b*x**n+b**2*x**(2*n))**(1/2*(1+2*n)/n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
547,-1,0,0,0.000000," ","integrate((d*x)**(-1-2*n*(1+p))*(a**2+2*a*b*x**n+b**2*x**(2*n))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
548,-1,0,0,0.000000," ","integrate(x**(-1+2*n)*(a**2+2*a*b*x**n+b**2*x**(2*n))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
549,-1,0,0,0.000000," ","integrate(x**(-1+4*n)/(a+b*x**n+c*x**(2*n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
550,-1,0,0,0.000000," ","integrate(x**(-1+3*n)/(a+b*x**n+c*x**(2*n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
551,-1,0,0,0.000000," ","integrate(x**(-1+2*n)/(a+b*x**n+c*x**(2*n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
552,-1,0,0,0.000000," ","integrate(x**(-1+n)/(a+b*x**n+c*x**(2*n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
553,-1,0,0,0.000000," ","integrate(x**(-1-n)/(a+b*x**n+c*x**(2*n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
554,-1,0,0,0.000000," ","integrate(x**(-1-2*n)/(a+b*x**n+c*x**(2*n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
555,-1,0,0,0.000000," ","integrate(x**(-1-3*n)/(a+b*x**n+c*x**(2*n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
556,0,0,0,0.000000," ","integrate(x**(-1+1/4*n)/(a+b*x**n+c*x**(2*n)),x)","\int \frac{x^{\frac{n}{4} - 1}}{a + b x^{n} + c x^{2 n}}\, dx"," ",0,"Integral(x**(n/4 - 1)/(a + b*x**n + c*x**(2*n)), x)","F",0
557,-1,0,0,0.000000," ","integrate(x**(-1+1/3*n)/(a+b*x**n+c*x**(2*n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
558,0,0,0,0.000000," ","integrate(x**(-1+1/2*n)/(a+b*x**n+c*x**(2*n)),x)","\int \frac{x^{\frac{n}{2} - 1}}{a + b x^{n} + c x^{2 n}}\, dx"," ",0,"Integral(x**(n/2 - 1)/(a + b*x**n + c*x**(2*n)), x)","F",0
559,0,0,0,0.000000," ","integrate(x**(-1-1/2*n)/(a+b*x**n+c*x**(2*n)),x)","\int \frac{x^{- \frac{n}{2} - 1}}{a + b x^{n} + c x^{2 n}}\, dx"," ",0,"Integral(x**(-n/2 - 1)/(a + b*x**n + c*x**(2*n)), x)","F",0
560,-1,0,0,0.000000," ","integrate(x**(-1-1/3*n)/(a+b*x**n+c*x**(2*n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
561,-1,0,0,0.000000," ","integrate(x**(-1-1/4*n)/(a+b*x**n+c*x**(2*n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
562,0,0,0,0.000000," ","integrate(x**2/(a+b*x**n+c*x**(2*n)),x)","\int \frac{x^{2}}{a + b x^{n} + c x^{2 n}}\, dx"," ",0,"Integral(x**2/(a + b*x**n + c*x**(2*n)), x)","F",0
563,0,0,0,0.000000," ","integrate(x/(a+b*x**n+c*x**(2*n)),x)","\int \frac{x}{a + b x^{n} + c x^{2 n}}\, dx"," ",0,"Integral(x/(a + b*x**n + c*x**(2*n)), x)","F",0
564,0,0,0,0.000000," ","integrate(1/(a+b*x**n+c*x**(2*n)),x)","\int \frac{1}{a + b x^{n} + c x^{2 n}}\, dx"," ",0,"Integral(1/(a + b*x**n + c*x**(2*n)), x)","F",0
565,-1,0,0,0.000000," ","integrate(1/x/(a+b*x**n+c*x**(2*n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
566,-1,0,0,0.000000," ","integrate(1/x**2/(a+b*x**n+c*x**(2*n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
567,-1,0,0,0.000000," ","integrate(1/x**3/(a+b*x**n+c*x**(2*n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
568,0,0,0,0.000000," ","integrate(x**3*(a+b*x**n+c*x**(2*n))**(1/2),x)","\int x^{3} \sqrt{a + b x^{n} + c x^{2 n}}\, dx"," ",0,"Integral(x**3*sqrt(a + b*x**n + c*x**(2*n)), x)","F",0
569,0,0,0,0.000000," ","integrate(x**2*(a+b*x**n+c*x**(2*n))**(1/2),x)","\int x^{2} \sqrt{a + b x^{n} + c x^{2 n}}\, dx"," ",0,"Integral(x**2*sqrt(a + b*x**n + c*x**(2*n)), x)","F",0
570,0,0,0,0.000000," ","integrate(x*(a+b*x**n+c*x**(2*n))**(1/2),x)","\int x \sqrt{a + b x^{n} + c x^{2 n}}\, dx"," ",0,"Integral(x*sqrt(a + b*x**n + c*x**(2*n)), x)","F",0
571,0,0,0,0.000000," ","integrate((a+b*x**n+c*x**(2*n))**(1/2),x)","\int \sqrt{a + b x^{n} + c x^{2 n}}\, dx"," ",0,"Integral(sqrt(a + b*x**n + c*x**(2*n)), x)","F",0
572,0,0,0,0.000000," ","integrate((a+b*x**n+c*x**(2*n))**(1/2)/x,x)","\int \frac{\sqrt{a + b x^{n} + c x^{2 n}}}{x}\, dx"," ",0,"Integral(sqrt(a + b*x**n + c*x**(2*n))/x, x)","F",0
573,0,0,0,0.000000," ","integrate((a+b*x**n+c*x**(2*n))**(1/2)/x**2,x)","\int \frac{\sqrt{a + b x^{n} + c x^{2 n}}}{x^{2}}\, dx"," ",0,"Integral(sqrt(a + b*x**n + c*x**(2*n))/x**2, x)","F",0
574,0,0,0,0.000000," ","integrate((a+b*x**n+c*x**(2*n))**(1/2)/x**3,x)","\int \frac{\sqrt{a + b x^{n} + c x^{2 n}}}{x^{3}}\, dx"," ",0,"Integral(sqrt(a + b*x**n + c*x**(2*n))/x**3, x)","F",0
575,0,0,0,0.000000," ","integrate(x**3*(a+b*x**n+c*x**(2*n))**(3/2),x)","\int x^{3} \left(a + b x^{n} + c x^{2 n}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**3*(a + b*x**n + c*x**(2*n))**(3/2), x)","F",0
576,0,0,0,0.000000," ","integrate(x**2*(a+b*x**n+c*x**(2*n))**(3/2),x)","\int x^{2} \left(a + b x^{n} + c x^{2 n}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**2*(a + b*x**n + c*x**(2*n))**(3/2), x)","F",0
577,0,0,0,0.000000," ","integrate(x*(a+b*x**n+c*x**(2*n))**(3/2),x)","\int x \left(a + b x^{n} + c x^{2 n}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x*(a + b*x**n + c*x**(2*n))**(3/2), x)","F",0
578,0,0,0,0.000000," ","integrate((a+b*x**n+c*x**(2*n))**(3/2),x)","\int \left(a + b x^{n} + c x^{2 n}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b*x**n + c*x**(2*n))**(3/2), x)","F",0
579,0,0,0,0.000000," ","integrate((a+b*x**n+c*x**(2*n))**(3/2)/x,x)","\int \frac{\left(a + b x^{n} + c x^{2 n}\right)^{\frac{3}{2}}}{x}\, dx"," ",0,"Integral((a + b*x**n + c*x**(2*n))**(3/2)/x, x)","F",0
580,0,0,0,0.000000," ","integrate((a+b*x**n+c*x**(2*n))**(3/2)/x**2,x)","\int \frac{\left(a + b x^{n} + c x^{2 n}\right)^{\frac{3}{2}}}{x^{2}}\, dx"," ",0,"Integral((a + b*x**n + c*x**(2*n))**(3/2)/x**2, x)","F",0
581,0,0,0,0.000000," ","integrate((a+b*x**n+c*x**(2*n))**(3/2)/x**3,x)","\int \frac{\left(a + b x^{n} + c x^{2 n}\right)^{\frac{3}{2}}}{x^{3}}\, dx"," ",0,"Integral((a + b*x**n + c*x**(2*n))**(3/2)/x**3, x)","F",0
582,0,0,0,0.000000," ","integrate(x**3/(a+b*x**n+c*x**(2*n))**(1/2),x)","\int \frac{x^{3}}{\sqrt{a + b x^{n} + c x^{2 n}}}\, dx"," ",0,"Integral(x**3/sqrt(a + b*x**n + c*x**(2*n)), x)","F",0
583,0,0,0,0.000000," ","integrate(x**2/(a+b*x**n+c*x**(2*n))**(1/2),x)","\int \frac{x^{2}}{\sqrt{a + b x^{n} + c x^{2 n}}}\, dx"," ",0,"Integral(x**2/sqrt(a + b*x**n + c*x**(2*n)), x)","F",0
584,0,0,0,0.000000," ","integrate(x/(a+b*x**n+c*x**(2*n))**(1/2),x)","\int \frac{x}{\sqrt{a + b x^{n} + c x^{2 n}}}\, dx"," ",0,"Integral(x/sqrt(a + b*x**n + c*x**(2*n)), x)","F",0
585,0,0,0,0.000000," ","integrate(1/(a+b*x**n+c*x**(2*n))**(1/2),x)","\int \frac{1}{\sqrt{a + b x^{n} + c x^{2 n}}}\, dx"," ",0,"Integral(1/sqrt(a + b*x**n + c*x**(2*n)), x)","F",0
586,0,0,0,0.000000," ","integrate(1/x/(a+b*x**n+c*x**(2*n))**(1/2),x)","\int \frac{1}{x \sqrt{a + b x^{n} + c x^{2 n}}}\, dx"," ",0,"Integral(1/(x*sqrt(a + b*x**n + c*x**(2*n))), x)","F",0
587,0,0,0,0.000000," ","integrate(1/x**2/(a+b*x**n+c*x**(2*n))**(1/2),x)","\int \frac{1}{x^{2} \sqrt{a + b x^{n} + c x^{2 n}}}\, dx"," ",0,"Integral(1/(x**2*sqrt(a + b*x**n + c*x**(2*n))), x)","F",0
588,0,0,0,0.000000," ","integrate(1/x**3/(a+b*x**n+c*x**(2*n))**(1/2),x)","\int \frac{1}{x^{3} \sqrt{a + b x^{n} + c x^{2 n}}}\, dx"," ",0,"Integral(1/(x**3*sqrt(a + b*x**n + c*x**(2*n))), x)","F",0
589,0,0,0,0.000000," ","integrate(x**3/(a+b*x**n+c*x**(2*n))**(3/2),x)","\int \frac{x^{3}}{\left(a + b x^{n} + c x^{2 n}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**3/(a + b*x**n + c*x**(2*n))**(3/2), x)","F",0
590,0,0,0,0.000000," ","integrate(x**2/(a+b*x**n+c*x**(2*n))**(3/2),x)","\int \frac{x^{2}}{\left(a + b x^{n} + c x^{2 n}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**2/(a + b*x**n + c*x**(2*n))**(3/2), x)","F",0
591,0,0,0,0.000000," ","integrate(x/(a+b*x**n+c*x**(2*n))**(3/2),x)","\int \frac{x}{\left(a + b x^{n} + c x^{2 n}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x/(a + b*x**n + c*x**(2*n))**(3/2), x)","F",0
592,0,0,0,0.000000," ","integrate(1/(a+b*x**n+c*x**(2*n))**(3/2),x)","\int \frac{1}{\left(a + b x^{n} + c x^{2 n}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*x**n + c*x**(2*n))**(-3/2), x)","F",0
593,0,0,0,0.000000," ","integrate(1/x/(a+b*x**n+c*x**(2*n))**(3/2),x)","\int \frac{1}{x \left(a + b x^{n} + c x^{2 n}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x*(a + b*x**n + c*x**(2*n))**(3/2)), x)","F",0
594,0,0,0,0.000000," ","integrate(1/x**2/(a+b*x**n+c*x**(2*n))**(3/2),x)","\int \frac{1}{x^{2} \left(a + b x^{n} + c x^{2 n}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**2*(a + b*x**n + c*x**(2*n))**(3/2)), x)","F",0
595,0,0,0,0.000000," ","integrate(1/x**3/(a+b*x**n+c*x**(2*n))**(3/2),x)","\int \frac{1}{x^{3} \left(a + b x^{n} + c x^{2 n}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**3*(a + b*x**n + c*x**(2*n))**(3/2)), x)","F",0
596,-1,0,0,0.000000," ","integrate((d*x)**m*(a+b*x**n+c*x**(2*n))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
597,-1,0,0,0.000000," ","integrate((d*x)**m*(a+b*x**n+c*x**(2*n))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
598,1,1239,0,42.998639," ","integrate((d*x)**m*(a+b*x**n+c*x**(2*n)),x)","\begin{cases} \frac{\left(a + b + c\right) \log{\left(x \right)}}{d} & \text{for}\: m = -1 \wedge n = 0 \\\frac{a \log{\left(x \right)} + \frac{b x^{n}}{n} + \frac{c x^{2 n}}{2 n}}{d} & \text{for}\: m = -1 \\\frac{a \left(\begin{cases} \log{\left(x \right)} & \text{for}\: n = 0 \\- \frac{x^{- 2 n} \left(0^{\frac{1}{n}}\right)^{- 2 n}}{2 n} & \text{for}\: d = 0^{\frac{1}{n}} \\- \frac{d^{- 2 n} x^{- 2 n}}{2 n} & \text{otherwise} \end{cases}\right)}{d} + \frac{b \left(\begin{cases} \log{\left(x \right)} & \text{for}\: n = 0 \\- \frac{x^{n}}{2 \cdot 0^{\frac{1}{n}} \tilde{\infty}^{\frac{1}{n}} n x^{2 n} \left(0^{\frac{1}{n}}\right)^{2 n} - n x^{2 n} \left(0^{\frac{1}{n}}\right)^{2 n}} & \text{for}\: d = 0^{\frac{1}{n}} \\- \frac{d^{- 2 n} x^{- n}}{n} & \text{otherwise} \end{cases}\right)}{d} + \frac{c \left(\begin{cases} d^{- 2 n} \log{\left(x \right)} & \text{for}\: \left|{x}\right| < 1 \\- d^{- 2 n} \log{\left(\frac{1}{x} \right)} & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- d^{- 2 n} {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} + d^{- 2 n} {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} & \text{otherwise} \end{cases}\right)}{d} & \text{for}\: m = - 2 n - 1 \\\frac{a \left(\begin{cases} \log{\left(x \right)} & \text{for}\: n = 0 \\- \frac{x^{- n} \left(0^{\frac{1}{n}}\right)^{- n}}{n} & \text{for}\: d = 0^{\frac{1}{n}} \\- \frac{d^{- n} x^{- n}}{n} & \text{otherwise} \end{cases}\right)}{d} + \frac{b \left(\begin{cases} d^{- n} \log{\left(x \right)} & \text{for}\: \left|{x}\right| < 1 \\- d^{- n} \log{\left(\frac{1}{x} \right)} & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- d^{- n} {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} + d^{- n} {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} & \text{otherwise} \end{cases}\right)}{d} + \frac{c \left(\begin{cases} \log{\left(x \right)} & \text{for}\: n = 0 \\- \frac{x^{2 n}}{0^{\frac{1}{n}} \tilde{\infty}^{\frac{1}{n}} n x^{n} \left(0^{\frac{1}{n}}\right)^{n} - 2 n x^{n} \left(0^{\frac{1}{n}}\right)^{n}} & \text{for}\: d = 0^{\frac{1}{n}} \\\frac{d^{- n} x^{n}}{n} & \text{otherwise} \end{cases}\right)}{d} & \text{for}\: m = - n - 1 \\\frac{a d^{m} m^{2} x x^{m}}{m^{3} + 3 m^{2} n + 3 m^{2} + 2 m n^{2} + 6 m n + 3 m + 2 n^{2} + 3 n + 1} + \frac{3 a d^{m} m n x x^{m}}{m^{3} + 3 m^{2} n + 3 m^{2} + 2 m n^{2} + 6 m n + 3 m + 2 n^{2} + 3 n + 1} + \frac{2 a d^{m} m x x^{m}}{m^{3} + 3 m^{2} n + 3 m^{2} + 2 m n^{2} + 6 m n + 3 m + 2 n^{2} + 3 n + 1} + \frac{2 a d^{m} n^{2} x x^{m}}{m^{3} + 3 m^{2} n + 3 m^{2} + 2 m n^{2} + 6 m n + 3 m + 2 n^{2} + 3 n + 1} + \frac{3 a d^{m} n x x^{m}}{m^{3} + 3 m^{2} n + 3 m^{2} + 2 m n^{2} + 6 m n + 3 m + 2 n^{2} + 3 n + 1} + \frac{a d^{m} x x^{m}}{m^{3} + 3 m^{2} n + 3 m^{2} + 2 m n^{2} + 6 m n + 3 m + 2 n^{2} + 3 n + 1} + \frac{b d^{m} m^{2} x x^{m} x^{n}}{m^{3} + 3 m^{2} n + 3 m^{2} + 2 m n^{2} + 6 m n + 3 m + 2 n^{2} + 3 n + 1} + \frac{2 b d^{m} m n x x^{m} x^{n}}{m^{3} + 3 m^{2} n + 3 m^{2} + 2 m n^{2} + 6 m n + 3 m + 2 n^{2} + 3 n + 1} + \frac{2 b d^{m} m x x^{m} x^{n}}{m^{3} + 3 m^{2} n + 3 m^{2} + 2 m n^{2} + 6 m n + 3 m + 2 n^{2} + 3 n + 1} + \frac{2 b d^{m} n x x^{m} x^{n}}{m^{3} + 3 m^{2} n + 3 m^{2} + 2 m n^{2} + 6 m n + 3 m + 2 n^{2} + 3 n + 1} + \frac{b d^{m} x x^{m} x^{n}}{m^{3} + 3 m^{2} n + 3 m^{2} + 2 m n^{2} + 6 m n + 3 m + 2 n^{2} + 3 n + 1} + \frac{c d^{m} m^{2} x x^{m} x^{2 n}}{m^{3} + 3 m^{2} n + 3 m^{2} + 2 m n^{2} + 6 m n + 3 m + 2 n^{2} + 3 n + 1} + \frac{c d^{m} m n x x^{m} x^{2 n}}{m^{3} + 3 m^{2} n + 3 m^{2} + 2 m n^{2} + 6 m n + 3 m + 2 n^{2} + 3 n + 1} + \frac{2 c d^{m} m x x^{m} x^{2 n}}{m^{3} + 3 m^{2} n + 3 m^{2} + 2 m n^{2} + 6 m n + 3 m + 2 n^{2} + 3 n + 1} + \frac{c d^{m} n x x^{m} x^{2 n}}{m^{3} + 3 m^{2} n + 3 m^{2} + 2 m n^{2} + 6 m n + 3 m + 2 n^{2} + 3 n + 1} + \frac{c d^{m} x x^{m} x^{2 n}}{m^{3} + 3 m^{2} n + 3 m^{2} + 2 m n^{2} + 6 m n + 3 m + 2 n^{2} + 3 n + 1} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((a + b + c)*log(x)/d, Eq(m, -1) & Eq(n, 0)), ((a*log(x) + b*x**n/n + c*x**(2*n)/(2*n))/d, Eq(m, -1)), (a*Piecewise((log(x), Eq(n, 0)), (-x**(-2*n)*(0**(1/n))**(-2*n)/(2*n), Eq(d, 0**(1/n))), (-d**(-2*n)*x**(-2*n)/(2*n), True))/d + b*Piecewise((log(x), Eq(n, 0)), (-x**n/(2*0**(1/n)*zoo**(1/n)*n*x**(2*n)*(0**(1/n))**(2*n) - n*x**(2*n)*(0**(1/n))**(2*n)), Eq(d, 0**(1/n))), (-d**(-2*n)*x**(-n)/n, True))/d + c*Piecewise((d**(-2*n)*log(x), Abs(x) < 1), (-d**(-2*n)*log(1/x), 1/Abs(x) < 1), (-d**(-2*n)*meijerg(((), (1, 1)), ((0, 0), ()), x) + d**(-2*n)*meijerg(((1, 1), ()), ((), (0, 0)), x), True))/d, Eq(m, -2*n - 1)), (a*Piecewise((log(x), Eq(n, 0)), (-x**(-n)*(0**(1/n))**(-n)/n, Eq(d, 0**(1/n))), (-d**(-n)*x**(-n)/n, True))/d + b*Piecewise((d**(-n)*log(x), Abs(x) < 1), (-d**(-n)*log(1/x), 1/Abs(x) < 1), (-d**(-n)*meijerg(((), (1, 1)), ((0, 0), ()), x) + d**(-n)*meijerg(((1, 1), ()), ((), (0, 0)), x), True))/d + c*Piecewise((log(x), Eq(n, 0)), (-x**(2*n)/(0**(1/n)*zoo**(1/n)*n*x**n*(0**(1/n))**n - 2*n*x**n*(0**(1/n))**n), Eq(d, 0**(1/n))), (d**(-n)*x**n/n, True))/d, Eq(m, -n - 1)), (a*d**m*m**2*x*x**m/(m**3 + 3*m**2*n + 3*m**2 + 2*m*n**2 + 6*m*n + 3*m + 2*n**2 + 3*n + 1) + 3*a*d**m*m*n*x*x**m/(m**3 + 3*m**2*n + 3*m**2 + 2*m*n**2 + 6*m*n + 3*m + 2*n**2 + 3*n + 1) + 2*a*d**m*m*x*x**m/(m**3 + 3*m**2*n + 3*m**2 + 2*m*n**2 + 6*m*n + 3*m + 2*n**2 + 3*n + 1) + 2*a*d**m*n**2*x*x**m/(m**3 + 3*m**2*n + 3*m**2 + 2*m*n**2 + 6*m*n + 3*m + 2*n**2 + 3*n + 1) + 3*a*d**m*n*x*x**m/(m**3 + 3*m**2*n + 3*m**2 + 2*m*n**2 + 6*m*n + 3*m + 2*n**2 + 3*n + 1) + a*d**m*x*x**m/(m**3 + 3*m**2*n + 3*m**2 + 2*m*n**2 + 6*m*n + 3*m + 2*n**2 + 3*n + 1) + b*d**m*m**2*x*x**m*x**n/(m**3 + 3*m**2*n + 3*m**2 + 2*m*n**2 + 6*m*n + 3*m + 2*n**2 + 3*n + 1) + 2*b*d**m*m*n*x*x**m*x**n/(m**3 + 3*m**2*n + 3*m**2 + 2*m*n**2 + 6*m*n + 3*m + 2*n**2 + 3*n + 1) + 2*b*d**m*m*x*x**m*x**n/(m**3 + 3*m**2*n + 3*m**2 + 2*m*n**2 + 6*m*n + 3*m + 2*n**2 + 3*n + 1) + 2*b*d**m*n*x*x**m*x**n/(m**3 + 3*m**2*n + 3*m**2 + 2*m*n**2 + 6*m*n + 3*m + 2*n**2 + 3*n + 1) + b*d**m*x*x**m*x**n/(m**3 + 3*m**2*n + 3*m**2 + 2*m*n**2 + 6*m*n + 3*m + 2*n**2 + 3*n + 1) + c*d**m*m**2*x*x**m*x**(2*n)/(m**3 + 3*m**2*n + 3*m**2 + 2*m*n**2 + 6*m*n + 3*m + 2*n**2 + 3*n + 1) + c*d**m*m*n*x*x**m*x**(2*n)/(m**3 + 3*m**2*n + 3*m**2 + 2*m*n**2 + 6*m*n + 3*m + 2*n**2 + 3*n + 1) + 2*c*d**m*m*x*x**m*x**(2*n)/(m**3 + 3*m**2*n + 3*m**2 + 2*m*n**2 + 6*m*n + 3*m + 2*n**2 + 3*n + 1) + c*d**m*n*x*x**m*x**(2*n)/(m**3 + 3*m**2*n + 3*m**2 + 2*m*n**2 + 6*m*n + 3*m + 2*n**2 + 3*n + 1) + c*d**m*x*x**m*x**(2*n)/(m**3 + 3*m**2*n + 3*m**2 + 2*m*n**2 + 6*m*n + 3*m + 2*n**2 + 3*n + 1), True))","A",0
599,0,0,0,0.000000," ","integrate((d*x)**m/(a+b*x**n+c*x**(2*n)),x)","\int \frac{\left(d x\right)^{m}}{a + b x^{n} + c x^{2 n}}\, dx"," ",0,"Integral((d*x)**m/(a + b*x**n + c*x**(2*n)), x)","F",0
600,-1,0,0,0.000000," ","integrate((d*x)**m/(a+b*x**n+c*x**(2*n))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
601,-1,0,0,0.000000," ","integrate((d*x)**m/(a+b*x**n+c*x**(2*n))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
602,0,0,0,0.000000," ","integrate((d*x)**m*(a+b*x**n+c*x**(2*n))**(3/2),x)","\int \left(d x\right)^{m} \left(a + b x^{n} + c x^{2 n}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((d*x)**m*(a + b*x**n + c*x**(2*n))**(3/2), x)","F",0
603,0,0,0,0.000000," ","integrate((d*x)**m*(a+b*x**n+c*x**(2*n))**(1/2),x)","\int \left(d x\right)^{m} \sqrt{a + b x^{n} + c x^{2 n}}\, dx"," ",0,"Integral((d*x)**m*sqrt(a + b*x**n + c*x**(2*n)), x)","F",0
604,0,0,0,0.000000," ","integrate((d*x)**m/(a+b*x**n+c*x**(2*n))**(1/2),x)","\int \frac{\left(d x\right)^{m}}{\sqrt{a + b x^{n} + c x^{2 n}}}\, dx"," ",0,"Integral((d*x)**m/sqrt(a + b*x**n + c*x**(2*n)), x)","F",0
605,0,0,0,0.000000," ","integrate((d*x)**m/(a+b*x**n+c*x**(2*n))**(3/2),x)","\int \frac{\left(d x\right)^{m}}{\left(a + b x^{n} + c x^{2 n}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d*x)**m/(a + b*x**n + c*x**(2*n))**(3/2), x)","F",0
606,-1,0,0,0.000000," ","integrate((d*x)**m*(a+b*x**n+c*x**(2*n))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
607,1,178,0,0.106277," ","integrate((e*x+d)**3*(a+b*(e*x+d)**2+c*(e*x+d)**4),x)","c d e^{6} x^{7} + \frac{c e^{7} x^{8}}{8} + x^{6} \left(\frac{b e^{5}}{6} + \frac{7 c d^{2} e^{5}}{2}\right) + x^{5} \left(b d e^{4} + 7 c d^{3} e^{4}\right) + x^{4} \left(\frac{a e^{3}}{4} + \frac{5 b d^{2} e^{3}}{2} + \frac{35 c d^{4} e^{3}}{4}\right) + x^{3} \left(a d e^{2} + \frac{10 b d^{3} e^{2}}{3} + 7 c d^{5} e^{2}\right) + x^{2} \left(\frac{3 a d^{2} e}{2} + \frac{5 b d^{4} e}{2} + \frac{7 c d^{6} e}{2}\right) + x \left(a d^{3} + b d^{5} + c d^{7}\right)"," ",0,"c*d*e**6*x**7 + c*e**7*x**8/8 + x**6*(b*e**5/6 + 7*c*d**2*e**5/2) + x**5*(b*d*e**4 + 7*c*d**3*e**4) + x**4*(a*e**3/4 + 5*b*d**2*e**3/2 + 35*c*d**4*e**3/4) + x**3*(a*d*e**2 + 10*b*d**3*e**2/3 + 7*c*d**5*e**2) + x**2*(3*a*d**2*e/2 + 5*b*d**4*e/2 + 7*c*d**6*e/2) + x*(a*d**3 + b*d**5 + c*d**7)","B",0
608,1,559,0,0.193851," ","integrate((e*x+d)**3*(a+b*(e*x+d)**2+c*(e*x+d)**4)**2,x)","c^{2} d e^{10} x^{11} + \frac{c^{2} e^{11} x^{12}}{12} + x^{10} \left(\frac{b c e^{9}}{5} + \frac{11 c^{2} d^{2} e^{9}}{2}\right) + x^{9} \left(2 b c d e^{8} + \frac{55 c^{2} d^{3} e^{8}}{3}\right) + x^{8} \left(\frac{a c e^{7}}{4} + \frac{b^{2} e^{7}}{8} + 9 b c d^{2} e^{7} + \frac{165 c^{2} d^{4} e^{7}}{4}\right) + x^{7} \left(2 a c d e^{6} + b^{2} d e^{6} + 24 b c d^{3} e^{6} + 66 c^{2} d^{5} e^{6}\right) + x^{6} \left(\frac{a b e^{5}}{3} + 7 a c d^{2} e^{5} + \frac{7 b^{2} d^{2} e^{5}}{2} + 42 b c d^{4} e^{5} + 77 c^{2} d^{6} e^{5}\right) + x^{5} \left(2 a b d e^{4} + 14 a c d^{3} e^{4} + 7 b^{2} d^{3} e^{4} + \frac{252 b c d^{5} e^{4}}{5} + 66 c^{2} d^{7} e^{4}\right) + x^{4} \left(\frac{a^{2} e^{3}}{4} + 5 a b d^{2} e^{3} + \frac{35 a c d^{4} e^{3}}{2} + \frac{35 b^{2} d^{4} e^{3}}{4} + 42 b c d^{6} e^{3} + \frac{165 c^{2} d^{8} e^{3}}{4}\right) + x^{3} \left(a^{2} d e^{2} + \frac{20 a b d^{3} e^{2}}{3} + 14 a c d^{5} e^{2} + 7 b^{2} d^{5} e^{2} + 24 b c d^{7} e^{2} + \frac{55 c^{2} d^{9} e^{2}}{3}\right) + x^{2} \left(\frac{3 a^{2} d^{2} e}{2} + 5 a b d^{4} e + 7 a c d^{6} e + \frac{7 b^{2} d^{6} e}{2} + 9 b c d^{8} e + \frac{11 c^{2} d^{10} e}{2}\right) + x \left(a^{2} d^{3} + 2 a b d^{5} + 2 a c d^{7} + b^{2} d^{7} + 2 b c d^{9} + c^{2} d^{11}\right)"," ",0,"c**2*d*e**10*x**11 + c**2*e**11*x**12/12 + x**10*(b*c*e**9/5 + 11*c**2*d**2*e**9/2) + x**9*(2*b*c*d*e**8 + 55*c**2*d**3*e**8/3) + x**8*(a*c*e**7/4 + b**2*e**7/8 + 9*b*c*d**2*e**7 + 165*c**2*d**4*e**7/4) + x**7*(2*a*c*d*e**6 + b**2*d*e**6 + 24*b*c*d**3*e**6 + 66*c**2*d**5*e**6) + x**6*(a*b*e**5/3 + 7*a*c*d**2*e**5 + 7*b**2*d**2*e**5/2 + 42*b*c*d**4*e**5 + 77*c**2*d**6*e**5) + x**5*(2*a*b*d*e**4 + 14*a*c*d**3*e**4 + 7*b**2*d**3*e**4 + 252*b*c*d**5*e**4/5 + 66*c**2*d**7*e**4) + x**4*(a**2*e**3/4 + 5*a*b*d**2*e**3 + 35*a*c*d**4*e**3/2 + 35*b**2*d**4*e**3/4 + 42*b*c*d**6*e**3 + 165*c**2*d**8*e**3/4) + x**3*(a**2*d*e**2 + 20*a*b*d**3*e**2/3 + 14*a*c*d**5*e**2 + 7*b**2*d**5*e**2 + 24*b*c*d**7*e**2 + 55*c**2*d**9*e**2/3) + x**2*(3*a**2*d**2*e/2 + 5*a*b*d**4*e + 7*a*c*d**6*e + 7*b**2*d**6*e/2 + 9*b*c*d**8*e + 11*c**2*d**10*e/2) + x*(a**2*d**3 + 2*a*b*d**5 + 2*a*c*d**7 + b**2*d**7 + 2*b*c*d**9 + c**2*d**11)","B",0
609,1,1314,0,0.356482," ","integrate((e*x+d)**3*(a+b*(e*x+d)**2+c*(e*x+d)**4)**3,x)","c^{3} d e^{14} x^{15} + \frac{c^{3} e^{15} x^{16}}{16} + x^{14} \left(\frac{3 b c^{2} e^{13}}{14} + \frac{15 c^{3} d^{2} e^{13}}{2}\right) + x^{13} \left(3 b c^{2} d e^{12} + 35 c^{3} d^{3} e^{12}\right) + x^{12} \left(\frac{a c^{2} e^{11}}{4} + \frac{b^{2} c e^{11}}{4} + \frac{39 b c^{2} d^{2} e^{11}}{2} + \frac{455 c^{3} d^{4} e^{11}}{4}\right) + x^{11} \left(3 a c^{2} d e^{10} + 3 b^{2} c d e^{10} + 78 b c^{2} d^{3} e^{10} + 273 c^{3} d^{5} e^{10}\right) + x^{10} \left(\frac{3 a b c e^{9}}{5} + \frac{33 a c^{2} d^{2} e^{9}}{2} + \frac{b^{3} e^{9}}{10} + \frac{33 b^{2} c d^{2} e^{9}}{2} + \frac{429 b c^{2} d^{4} e^{9}}{2} + \frac{1001 c^{3} d^{6} e^{9}}{2}\right) + x^{9} \left(6 a b c d e^{8} + 55 a c^{2} d^{3} e^{8} + b^{3} d e^{8} + 55 b^{2} c d^{3} e^{8} + 429 b c^{2} d^{5} e^{8} + 715 c^{3} d^{7} e^{8}\right) + x^{8} \left(\frac{3 a^{2} c e^{7}}{8} + \frac{3 a b^{2} e^{7}}{8} + 27 a b c d^{2} e^{7} + \frac{495 a c^{2} d^{4} e^{7}}{4} + \frac{9 b^{3} d^{2} e^{7}}{2} + \frac{495 b^{2} c d^{4} e^{7}}{4} + \frac{1287 b c^{2} d^{6} e^{7}}{2} + \frac{6435 c^{3} d^{8} e^{7}}{8}\right) + x^{7} \left(3 a^{2} c d e^{6} + 3 a b^{2} d e^{6} + 72 a b c d^{3} e^{6} + 198 a c^{2} d^{5} e^{6} + 12 b^{3} d^{3} e^{6} + 198 b^{2} c d^{5} e^{6} + \frac{5148 b c^{2} d^{7} e^{6}}{7} + 715 c^{3} d^{9} e^{6}\right) + x^{6} \left(\frac{a^{2} b e^{5}}{2} + \frac{21 a^{2} c d^{2} e^{5}}{2} + \frac{21 a b^{2} d^{2} e^{5}}{2} + 126 a b c d^{4} e^{5} + 231 a c^{2} d^{6} e^{5} + 21 b^{3} d^{4} e^{5} + 231 b^{2} c d^{6} e^{5} + \frac{1287 b c^{2} d^{8} e^{5}}{2} + \frac{1001 c^{3} d^{10} e^{5}}{2}\right) + x^{5} \left(3 a^{2} b d e^{4} + 21 a^{2} c d^{3} e^{4} + 21 a b^{2} d^{3} e^{4} + \frac{756 a b c d^{5} e^{4}}{5} + 198 a c^{2} d^{7} e^{4} + \frac{126 b^{3} d^{5} e^{4}}{5} + 198 b^{2} c d^{7} e^{4} + 429 b c^{2} d^{9} e^{4} + 273 c^{3} d^{11} e^{4}\right) + x^{4} \left(\frac{a^{3} e^{3}}{4} + \frac{15 a^{2} b d^{2} e^{3}}{2} + \frac{105 a^{2} c d^{4} e^{3}}{4} + \frac{105 a b^{2} d^{4} e^{3}}{4} + 126 a b c d^{6} e^{3} + \frac{495 a c^{2} d^{8} e^{3}}{4} + 21 b^{3} d^{6} e^{3} + \frac{495 b^{2} c d^{8} e^{3}}{4} + \frac{429 b c^{2} d^{10} e^{3}}{2} + \frac{455 c^{3} d^{12} e^{3}}{4}\right) + x^{3} \left(a^{3} d e^{2} + 10 a^{2} b d^{3} e^{2} + 21 a^{2} c d^{5} e^{2} + 21 a b^{2} d^{5} e^{2} + 72 a b c d^{7} e^{2} + 55 a c^{2} d^{9} e^{2} + 12 b^{3} d^{7} e^{2} + 55 b^{2} c d^{9} e^{2} + 78 b c^{2} d^{11} e^{2} + 35 c^{3} d^{13} e^{2}\right) + x^{2} \left(\frac{3 a^{3} d^{2} e}{2} + \frac{15 a^{2} b d^{4} e}{2} + \frac{21 a^{2} c d^{6} e}{2} + \frac{21 a b^{2} d^{6} e}{2} + 27 a b c d^{8} e + \frac{33 a c^{2} d^{10} e}{2} + \frac{9 b^{3} d^{8} e}{2} + \frac{33 b^{2} c d^{10} e}{2} + \frac{39 b c^{2} d^{12} e}{2} + \frac{15 c^{3} d^{14} e}{2}\right) + x \left(a^{3} d^{3} + 3 a^{2} b d^{5} + 3 a^{2} c d^{7} + 3 a b^{2} d^{7} + 6 a b c d^{9} + 3 a c^{2} d^{11} + b^{3} d^{9} + 3 b^{2} c d^{11} + 3 b c^{2} d^{13} + c^{3} d^{15}\right)"," ",0,"c**3*d*e**14*x**15 + c**3*e**15*x**16/16 + x**14*(3*b*c**2*e**13/14 + 15*c**3*d**2*e**13/2) + x**13*(3*b*c**2*d*e**12 + 35*c**3*d**3*e**12) + x**12*(a*c**2*e**11/4 + b**2*c*e**11/4 + 39*b*c**2*d**2*e**11/2 + 455*c**3*d**4*e**11/4) + x**11*(3*a*c**2*d*e**10 + 3*b**2*c*d*e**10 + 78*b*c**2*d**3*e**10 + 273*c**3*d**5*e**10) + x**10*(3*a*b*c*e**9/5 + 33*a*c**2*d**2*e**9/2 + b**3*e**9/10 + 33*b**2*c*d**2*e**9/2 + 429*b*c**2*d**4*e**9/2 + 1001*c**3*d**6*e**9/2) + x**9*(6*a*b*c*d*e**8 + 55*a*c**2*d**3*e**8 + b**3*d*e**8 + 55*b**2*c*d**3*e**8 + 429*b*c**2*d**5*e**8 + 715*c**3*d**7*e**8) + x**8*(3*a**2*c*e**7/8 + 3*a*b**2*e**7/8 + 27*a*b*c*d**2*e**7 + 495*a*c**2*d**4*e**7/4 + 9*b**3*d**2*e**7/2 + 495*b**2*c*d**4*e**7/4 + 1287*b*c**2*d**6*e**7/2 + 6435*c**3*d**8*e**7/8) + x**7*(3*a**2*c*d*e**6 + 3*a*b**2*d*e**6 + 72*a*b*c*d**3*e**6 + 198*a*c**2*d**5*e**6 + 12*b**3*d**3*e**6 + 198*b**2*c*d**5*e**6 + 5148*b*c**2*d**7*e**6/7 + 715*c**3*d**9*e**6) + x**6*(a**2*b*e**5/2 + 21*a**2*c*d**2*e**5/2 + 21*a*b**2*d**2*e**5/2 + 126*a*b*c*d**4*e**5 + 231*a*c**2*d**6*e**5 + 21*b**3*d**4*e**5 + 231*b**2*c*d**6*e**5 + 1287*b*c**2*d**8*e**5/2 + 1001*c**3*d**10*e**5/2) + x**5*(3*a**2*b*d*e**4 + 21*a**2*c*d**3*e**4 + 21*a*b**2*d**3*e**4 + 756*a*b*c*d**5*e**4/5 + 198*a*c**2*d**7*e**4 + 126*b**3*d**5*e**4/5 + 198*b**2*c*d**7*e**4 + 429*b*c**2*d**9*e**4 + 273*c**3*d**11*e**4) + x**4*(a**3*e**3/4 + 15*a**2*b*d**2*e**3/2 + 105*a**2*c*d**4*e**3/4 + 105*a*b**2*d**4*e**3/4 + 126*a*b*c*d**6*e**3 + 495*a*c**2*d**8*e**3/4 + 21*b**3*d**6*e**3 + 495*b**2*c*d**8*e**3/4 + 429*b*c**2*d**10*e**3/2 + 455*c**3*d**12*e**3/4) + x**3*(a**3*d*e**2 + 10*a**2*b*d**3*e**2 + 21*a**2*c*d**5*e**2 + 21*a*b**2*d**5*e**2 + 72*a*b*c*d**7*e**2 + 55*a*c**2*d**9*e**2 + 12*b**3*d**7*e**2 + 55*b**2*c*d**9*e**2 + 78*b*c**2*d**11*e**2 + 35*c**3*d**13*e**2) + x**2*(3*a**3*d**2*e/2 + 15*a**2*b*d**4*e/2 + 21*a**2*c*d**6*e/2 + 21*a*b**2*d**6*e/2 + 27*a*b*c*d**8*e + 33*a*c**2*d**10*e/2 + 9*b**3*d**8*e/2 + 33*b**2*c*d**10*e/2 + 39*b*c**2*d**12*e/2 + 15*c**3*d**14*e/2) + x*(a**3*d**3 + 3*a**2*b*d**5 + 3*a**2*c*d**7 + 3*a*b**2*d**7 + 6*a*b*c*d**9 + 3*a*c**2*d**11 + b**3*d**9 + 3*b**2*c*d**11 + 3*b*c**2*d**13 + c**3*d**15)","B",0
610,1,240,0,0.112040," ","integrate((e*f*x+d*f)**3*(a+b*(e*x+d)**2+c*(e*x+d)**4),x)","c d e^{6} f^{3} x^{7} + \frac{c e^{7} f^{3} x^{8}}{8} + x^{6} \left(\frac{b e^{5} f^{3}}{6} + \frac{7 c d^{2} e^{5} f^{3}}{2}\right) + x^{5} \left(b d e^{4} f^{3} + 7 c d^{3} e^{4} f^{3}\right) + x^{4} \left(\frac{a e^{3} f^{3}}{4} + \frac{5 b d^{2} e^{3} f^{3}}{2} + \frac{35 c d^{4} e^{3} f^{3}}{4}\right) + x^{3} \left(a d e^{2} f^{3} + \frac{10 b d^{3} e^{2} f^{3}}{3} + 7 c d^{5} e^{2} f^{3}\right) + x^{2} \left(\frac{3 a d^{2} e f^{3}}{2} + \frac{5 b d^{4} e f^{3}}{2} + \frac{7 c d^{6} e f^{3}}{2}\right) + x \left(a d^{3} f^{3} + b d^{5} f^{3} + c d^{7} f^{3}\right)"," ",0,"c*d*e**6*f**3*x**7 + c*e**7*f**3*x**8/8 + x**6*(b*e**5*f**3/6 + 7*c*d**2*e**5*f**3/2) + x**5*(b*d*e**4*f**3 + 7*c*d**3*e**4*f**3) + x**4*(a*e**3*f**3/4 + 5*b*d**2*e**3*f**3/2 + 35*c*d**4*e**3*f**3/4) + x**3*(a*d*e**2*f**3 + 10*b*d**3*e**2*f**3/3 + 7*c*d**5*e**2*f**3) + x**2*(3*a*d**2*e*f**3/2 + 5*b*d**4*e*f**3/2 + 7*c*d**6*e*f**3/2) + x*(a*d**3*f**3 + b*d**5*f**3 + c*d**7*f**3)","B",0
611,1,722,0,0.212335," ","integrate((e*f*x+d*f)**3*(a+b*(e*x+d)**2+c*(e*x+d)**4)**2,x)","c^{2} d e^{10} f^{3} x^{11} + \frac{c^{2} e^{11} f^{3} x^{12}}{12} + x^{10} \left(\frac{b c e^{9} f^{3}}{5} + \frac{11 c^{2} d^{2} e^{9} f^{3}}{2}\right) + x^{9} \left(2 b c d e^{8} f^{3} + \frac{55 c^{2} d^{3} e^{8} f^{3}}{3}\right) + x^{8} \left(\frac{a c e^{7} f^{3}}{4} + \frac{b^{2} e^{7} f^{3}}{8} + 9 b c d^{2} e^{7} f^{3} + \frac{165 c^{2} d^{4} e^{7} f^{3}}{4}\right) + x^{7} \left(2 a c d e^{6} f^{3} + b^{2} d e^{6} f^{3} + 24 b c d^{3} e^{6} f^{3} + 66 c^{2} d^{5} e^{6} f^{3}\right) + x^{6} \left(\frac{a b e^{5} f^{3}}{3} + 7 a c d^{2} e^{5} f^{3} + \frac{7 b^{2} d^{2} e^{5} f^{3}}{2} + 42 b c d^{4} e^{5} f^{3} + 77 c^{2} d^{6} e^{5} f^{3}\right) + x^{5} \left(2 a b d e^{4} f^{3} + 14 a c d^{3} e^{4} f^{3} + 7 b^{2} d^{3} e^{4} f^{3} + \frac{252 b c d^{5} e^{4} f^{3}}{5} + 66 c^{2} d^{7} e^{4} f^{3}\right) + x^{4} \left(\frac{a^{2} e^{3} f^{3}}{4} + 5 a b d^{2} e^{3} f^{3} + \frac{35 a c d^{4} e^{3} f^{3}}{2} + \frac{35 b^{2} d^{4} e^{3} f^{3}}{4} + 42 b c d^{6} e^{3} f^{3} + \frac{165 c^{2} d^{8} e^{3} f^{3}}{4}\right) + x^{3} \left(a^{2} d e^{2} f^{3} + \frac{20 a b d^{3} e^{2} f^{3}}{3} + 14 a c d^{5} e^{2} f^{3} + 7 b^{2} d^{5} e^{2} f^{3} + 24 b c d^{7} e^{2} f^{3} + \frac{55 c^{2} d^{9} e^{2} f^{3}}{3}\right) + x^{2} \left(\frac{3 a^{2} d^{2} e f^{3}}{2} + 5 a b d^{4} e f^{3} + 7 a c d^{6} e f^{3} + \frac{7 b^{2} d^{6} e f^{3}}{2} + 9 b c d^{8} e f^{3} + \frac{11 c^{2} d^{10} e f^{3}}{2}\right) + x \left(a^{2} d^{3} f^{3} + 2 a b d^{5} f^{3} + 2 a c d^{7} f^{3} + b^{2} d^{7} f^{3} + 2 b c d^{9} f^{3} + c^{2} d^{11} f^{3}\right)"," ",0,"c**2*d*e**10*f**3*x**11 + c**2*e**11*f**3*x**12/12 + x**10*(b*c*e**9*f**3/5 + 11*c**2*d**2*e**9*f**3/2) + x**9*(2*b*c*d*e**8*f**3 + 55*c**2*d**3*e**8*f**3/3) + x**8*(a*c*e**7*f**3/4 + b**2*e**7*f**3/8 + 9*b*c*d**2*e**7*f**3 + 165*c**2*d**4*e**7*f**3/4) + x**7*(2*a*c*d*e**6*f**3 + b**2*d*e**6*f**3 + 24*b*c*d**3*e**6*f**3 + 66*c**2*d**5*e**6*f**3) + x**6*(a*b*e**5*f**3/3 + 7*a*c*d**2*e**5*f**3 + 7*b**2*d**2*e**5*f**3/2 + 42*b*c*d**4*e**5*f**3 + 77*c**2*d**6*e**5*f**3) + x**5*(2*a*b*d*e**4*f**3 + 14*a*c*d**3*e**4*f**3 + 7*b**2*d**3*e**4*f**3 + 252*b*c*d**5*e**4*f**3/5 + 66*c**2*d**7*e**4*f**3) + x**4*(a**2*e**3*f**3/4 + 5*a*b*d**2*e**3*f**3 + 35*a*c*d**4*e**3*f**3/2 + 35*b**2*d**4*e**3*f**3/4 + 42*b*c*d**6*e**3*f**3 + 165*c**2*d**8*e**3*f**3/4) + x**3*(a**2*d*e**2*f**3 + 20*a*b*d**3*e**2*f**3/3 + 14*a*c*d**5*e**2*f**3 + 7*b**2*d**5*e**2*f**3 + 24*b*c*d**7*e**2*f**3 + 55*c**2*d**9*e**2*f**3/3) + x**2*(3*a**2*d**2*e*f**3/2 + 5*a*b*d**4*e*f**3 + 7*a*c*d**6*e*f**3 + 7*b**2*d**6*e*f**3/2 + 9*b*c*d**8*e*f**3 + 11*c**2*d**10*e*f**3/2) + x*(a**2*d**3*f**3 + 2*a*b*d**5*f**3 + 2*a*c*d**7*f**3 + b**2*d**7*f**3 + 2*b*c*d**9*f**3 + c**2*d**11*f**3)","B",0
612,1,1654,0,0.392375," ","integrate((e*f*x+d*f)**3*(a+b*(e*x+d)**2+c*(e*x+d)**4)**3,x)","c^{3} d e^{14} f^{3} x^{15} + \frac{c^{3} e^{15} f^{3} x^{16}}{16} + x^{14} \left(\frac{3 b c^{2} e^{13} f^{3}}{14} + \frac{15 c^{3} d^{2} e^{13} f^{3}}{2}\right) + x^{13} \left(3 b c^{2} d e^{12} f^{3} + 35 c^{3} d^{3} e^{12} f^{3}\right) + x^{12} \left(\frac{a c^{2} e^{11} f^{3}}{4} + \frac{b^{2} c e^{11} f^{3}}{4} + \frac{39 b c^{2} d^{2} e^{11} f^{3}}{2} + \frac{455 c^{3} d^{4} e^{11} f^{3}}{4}\right) + x^{11} \left(3 a c^{2} d e^{10} f^{3} + 3 b^{2} c d e^{10} f^{3} + 78 b c^{2} d^{3} e^{10} f^{3} + 273 c^{3} d^{5} e^{10} f^{3}\right) + x^{10} \left(\frac{3 a b c e^{9} f^{3}}{5} + \frac{33 a c^{2} d^{2} e^{9} f^{3}}{2} + \frac{b^{3} e^{9} f^{3}}{10} + \frac{33 b^{2} c d^{2} e^{9} f^{3}}{2} + \frac{429 b c^{2} d^{4} e^{9} f^{3}}{2} + \frac{1001 c^{3} d^{6} e^{9} f^{3}}{2}\right) + x^{9} \left(6 a b c d e^{8} f^{3} + 55 a c^{2} d^{3} e^{8} f^{3} + b^{3} d e^{8} f^{3} + 55 b^{2} c d^{3} e^{8} f^{3} + 429 b c^{2} d^{5} e^{8} f^{3} + 715 c^{3} d^{7} e^{8} f^{3}\right) + x^{8} \left(\frac{3 a^{2} c e^{7} f^{3}}{8} + \frac{3 a b^{2} e^{7} f^{3}}{8} + 27 a b c d^{2} e^{7} f^{3} + \frac{495 a c^{2} d^{4} e^{7} f^{3}}{4} + \frac{9 b^{3} d^{2} e^{7} f^{3}}{2} + \frac{495 b^{2} c d^{4} e^{7} f^{3}}{4} + \frac{1287 b c^{2} d^{6} e^{7} f^{3}}{2} + \frac{6435 c^{3} d^{8} e^{7} f^{3}}{8}\right) + x^{7} \left(3 a^{2} c d e^{6} f^{3} + 3 a b^{2} d e^{6} f^{3} + 72 a b c d^{3} e^{6} f^{3} + 198 a c^{2} d^{5} e^{6} f^{3} + 12 b^{3} d^{3} e^{6} f^{3} + 198 b^{2} c d^{5} e^{6} f^{3} + \frac{5148 b c^{2} d^{7} e^{6} f^{3}}{7} + 715 c^{3} d^{9} e^{6} f^{3}\right) + x^{6} \left(\frac{a^{2} b e^{5} f^{3}}{2} + \frac{21 a^{2} c d^{2} e^{5} f^{3}}{2} + \frac{21 a b^{2} d^{2} e^{5} f^{3}}{2} + 126 a b c d^{4} e^{5} f^{3} + 231 a c^{2} d^{6} e^{5} f^{3} + 21 b^{3} d^{4} e^{5} f^{3} + 231 b^{2} c d^{6} e^{5} f^{3} + \frac{1287 b c^{2} d^{8} e^{5} f^{3}}{2} + \frac{1001 c^{3} d^{10} e^{5} f^{3}}{2}\right) + x^{5} \left(3 a^{2} b d e^{4} f^{3} + 21 a^{2} c d^{3} e^{4} f^{3} + 21 a b^{2} d^{3} e^{4} f^{3} + \frac{756 a b c d^{5} e^{4} f^{3}}{5} + 198 a c^{2} d^{7} e^{4} f^{3} + \frac{126 b^{3} d^{5} e^{4} f^{3}}{5} + 198 b^{2} c d^{7} e^{4} f^{3} + 429 b c^{2} d^{9} e^{4} f^{3} + 273 c^{3} d^{11} e^{4} f^{3}\right) + x^{4} \left(\frac{a^{3} e^{3} f^{3}}{4} + \frac{15 a^{2} b d^{2} e^{3} f^{3}}{2} + \frac{105 a^{2} c d^{4} e^{3} f^{3}}{4} + \frac{105 a b^{2} d^{4} e^{3} f^{3}}{4} + 126 a b c d^{6} e^{3} f^{3} + \frac{495 a c^{2} d^{8} e^{3} f^{3}}{4} + 21 b^{3} d^{6} e^{3} f^{3} + \frac{495 b^{2} c d^{8} e^{3} f^{3}}{4} + \frac{429 b c^{2} d^{10} e^{3} f^{3}}{2} + \frac{455 c^{3} d^{12} e^{3} f^{3}}{4}\right) + x^{3} \left(a^{3} d e^{2} f^{3} + 10 a^{2} b d^{3} e^{2} f^{3} + 21 a^{2} c d^{5} e^{2} f^{3} + 21 a b^{2} d^{5} e^{2} f^{3} + 72 a b c d^{7} e^{2} f^{3} + 55 a c^{2} d^{9} e^{2} f^{3} + 12 b^{3} d^{7} e^{2} f^{3} + 55 b^{2} c d^{9} e^{2} f^{3} + 78 b c^{2} d^{11} e^{2} f^{3} + 35 c^{3} d^{13} e^{2} f^{3}\right) + x^{2} \left(\frac{3 a^{3} d^{2} e f^{3}}{2} + \frac{15 a^{2} b d^{4} e f^{3}}{2} + \frac{21 a^{2} c d^{6} e f^{3}}{2} + \frac{21 a b^{2} d^{6} e f^{3}}{2} + 27 a b c d^{8} e f^{3} + \frac{33 a c^{2} d^{10} e f^{3}}{2} + \frac{9 b^{3} d^{8} e f^{3}}{2} + \frac{33 b^{2} c d^{10} e f^{3}}{2} + \frac{39 b c^{2} d^{12} e f^{3}}{2} + \frac{15 c^{3} d^{14} e f^{3}}{2}\right) + x \left(a^{3} d^{3} f^{3} + 3 a^{2} b d^{5} f^{3} + 3 a^{2} c d^{7} f^{3} + 3 a b^{2} d^{7} f^{3} + 6 a b c d^{9} f^{3} + 3 a c^{2} d^{11} f^{3} + b^{3} d^{9} f^{3} + 3 b^{2} c d^{11} f^{3} + 3 b c^{2} d^{13} f^{3} + c^{3} d^{15} f^{3}\right)"," ",0,"c**3*d*e**14*f**3*x**15 + c**3*e**15*f**3*x**16/16 + x**14*(3*b*c**2*e**13*f**3/14 + 15*c**3*d**2*e**13*f**3/2) + x**13*(3*b*c**2*d*e**12*f**3 + 35*c**3*d**3*e**12*f**3) + x**12*(a*c**2*e**11*f**3/4 + b**2*c*e**11*f**3/4 + 39*b*c**2*d**2*e**11*f**3/2 + 455*c**3*d**4*e**11*f**3/4) + x**11*(3*a*c**2*d*e**10*f**3 + 3*b**2*c*d*e**10*f**3 + 78*b*c**2*d**3*e**10*f**3 + 273*c**3*d**5*e**10*f**3) + x**10*(3*a*b*c*e**9*f**3/5 + 33*a*c**2*d**2*e**9*f**3/2 + b**3*e**9*f**3/10 + 33*b**2*c*d**2*e**9*f**3/2 + 429*b*c**2*d**4*e**9*f**3/2 + 1001*c**3*d**6*e**9*f**3/2) + x**9*(6*a*b*c*d*e**8*f**3 + 55*a*c**2*d**3*e**8*f**3 + b**3*d*e**8*f**3 + 55*b**2*c*d**3*e**8*f**3 + 429*b*c**2*d**5*e**8*f**3 + 715*c**3*d**7*e**8*f**3) + x**8*(3*a**2*c*e**7*f**3/8 + 3*a*b**2*e**7*f**3/8 + 27*a*b*c*d**2*e**7*f**3 + 495*a*c**2*d**4*e**7*f**3/4 + 9*b**3*d**2*e**7*f**3/2 + 495*b**2*c*d**4*e**7*f**3/4 + 1287*b*c**2*d**6*e**7*f**3/2 + 6435*c**3*d**8*e**7*f**3/8) + x**7*(3*a**2*c*d*e**6*f**3 + 3*a*b**2*d*e**6*f**3 + 72*a*b*c*d**3*e**6*f**3 + 198*a*c**2*d**5*e**6*f**3 + 12*b**3*d**3*e**6*f**3 + 198*b**2*c*d**5*e**6*f**3 + 5148*b*c**2*d**7*e**6*f**3/7 + 715*c**3*d**9*e**6*f**3) + x**6*(a**2*b*e**5*f**3/2 + 21*a**2*c*d**2*e**5*f**3/2 + 21*a*b**2*d**2*e**5*f**3/2 + 126*a*b*c*d**4*e**5*f**3 + 231*a*c**2*d**6*e**5*f**3 + 21*b**3*d**4*e**5*f**3 + 231*b**2*c*d**6*e**5*f**3 + 1287*b*c**2*d**8*e**5*f**3/2 + 1001*c**3*d**10*e**5*f**3/2) + x**5*(3*a**2*b*d*e**4*f**3 + 21*a**2*c*d**3*e**4*f**3 + 21*a*b**2*d**3*e**4*f**3 + 756*a*b*c*d**5*e**4*f**3/5 + 198*a*c**2*d**7*e**4*f**3 + 126*b**3*d**5*e**4*f**3/5 + 198*b**2*c*d**7*e**4*f**3 + 429*b*c**2*d**9*e**4*f**3 + 273*c**3*d**11*e**4*f**3) + x**4*(a**3*e**3*f**3/4 + 15*a**2*b*d**2*e**3*f**3/2 + 105*a**2*c*d**4*e**3*f**3/4 + 105*a*b**2*d**4*e**3*f**3/4 + 126*a*b*c*d**6*e**3*f**3 + 495*a*c**2*d**8*e**3*f**3/4 + 21*b**3*d**6*e**3*f**3 + 495*b**2*c*d**8*e**3*f**3/4 + 429*b*c**2*d**10*e**3*f**3/2 + 455*c**3*d**12*e**3*f**3/4) + x**3*(a**3*d*e**2*f**3 + 10*a**2*b*d**3*e**2*f**3 + 21*a**2*c*d**5*e**2*f**3 + 21*a*b**2*d**5*e**2*f**3 + 72*a*b*c*d**7*e**2*f**3 + 55*a*c**2*d**9*e**2*f**3 + 12*b**3*d**7*e**2*f**3 + 55*b**2*c*d**9*e**2*f**3 + 78*b*c**2*d**11*e**2*f**3 + 35*c**3*d**13*e**2*f**3) + x**2*(3*a**3*d**2*e*f**3/2 + 15*a**2*b*d**4*e*f**3/2 + 21*a**2*c*d**6*e*f**3/2 + 21*a*b**2*d**6*e*f**3/2 + 27*a*b*c*d**8*e*f**3 + 33*a*c**2*d**10*e*f**3/2 + 9*b**3*d**8*e*f**3/2 + 33*b**2*c*d**10*e*f**3/2 + 39*b*c**2*d**12*e*f**3/2 + 15*c**3*d**14*e*f**3/2) + x*(a**3*d**3*f**3 + 3*a**2*b*d**5*f**3 + 3*a**2*c*d**7*f**3 + 3*a*b**2*d**7*f**3 + 6*a*b*c*d**9*f**3 + 3*a*c**2*d**11*f**3 + b**3*d**9*f**3 + 3*b**2*c*d**11*f**3 + 3*b*c**2*d**13*f**3 + c**3*d**15*f**3)","B",0
613,1,178,0,3.065034," ","integrate((e*x+d)**4/(a+b*(e*x+d)**2+c*(e*x+d)**4),x)","\operatorname{RootSum} {\left(t^{4} \left(256 a^{2} c^{5} e^{4} - 128 a b^{2} c^{4} e^{4} + 16 b^{4} c^{3} e^{4}\right) + t^{2} \left(48 a^{2} b c^{2} e^{2} - 28 a b^{3} c e^{2} + 4 b^{5} e^{2}\right) + a^{3}, \left( t \mapsto t \log{\left(x + \frac{32 t^{3} a b c^{4} e^{3} - 8 t^{3} b^{3} c^{3} e^{3} - 4 t a^{2} c^{2} e + 8 t a b^{2} c e - 2 t b^{4} e + a^{2} c d - a b^{2} d}{a^{2} c e - a b^{2} e} \right)} \right)\right)} + \frac{x}{c}"," ",0,"RootSum(_t**4*(256*a**2*c**5*e**4 - 128*a*b**2*c**4*e**4 + 16*b**4*c**3*e**4) + _t**2*(48*a**2*b*c**2*e**2 - 28*a*b**3*c*e**2 + 4*b**5*e**2) + a**3, Lambda(_t, _t*log(x + (32*_t**3*a*b*c**4*e**3 - 8*_t**3*b**3*c**3*e**3 - 4*_t*a**2*c**2*e + 8*_t*a*b**2*c*e - 2*_t*b**4*e + a**2*c*d - a*b**2*d)/(a**2*c*e - a*b**2*e)))) + x/c","A",0
614,1,280,0,1.637668," ","integrate((e*x+d)**3/(a+b*(e*x+d)**2+c*(e*x+d)**4),x)","\left(- \frac{b \sqrt{- 4 a c + b^{2}}}{4 c e \left(4 a c - b^{2}\right)} + \frac{1}{4 c e}\right) \log{\left(\frac{2 d x}{e} + x^{2} + \frac{- 8 a c e \left(- \frac{b \sqrt{- 4 a c + b^{2}}}{4 c e \left(4 a c - b^{2}\right)} + \frac{1}{4 c e}\right) + 2 a + 2 b^{2} e \left(- \frac{b \sqrt{- 4 a c + b^{2}}}{4 c e \left(4 a c - b^{2}\right)} + \frac{1}{4 c e}\right) + b d^{2}}{b e^{2}} \right)} + \left(\frac{b \sqrt{- 4 a c + b^{2}}}{4 c e \left(4 a c - b^{2}\right)} + \frac{1}{4 c e}\right) \log{\left(\frac{2 d x}{e} + x^{2} + \frac{- 8 a c e \left(\frac{b \sqrt{- 4 a c + b^{2}}}{4 c e \left(4 a c - b^{2}\right)} + \frac{1}{4 c e}\right) + 2 a + 2 b^{2} e \left(\frac{b \sqrt{- 4 a c + b^{2}}}{4 c e \left(4 a c - b^{2}\right)} + \frac{1}{4 c e}\right) + b d^{2}}{b e^{2}} \right)}"," ",0,"(-b*sqrt(-4*a*c + b**2)/(4*c*e*(4*a*c - b**2)) + 1/(4*c*e))*log(2*d*x/e + x**2 + (-8*a*c*e*(-b*sqrt(-4*a*c + b**2)/(4*c*e*(4*a*c - b**2)) + 1/(4*c*e)) + 2*a + 2*b**2*e*(-b*sqrt(-4*a*c + b**2)/(4*c*e*(4*a*c - b**2)) + 1/(4*c*e)) + b*d**2)/(b*e**2)) + (b*sqrt(-4*a*c + b**2)/(4*c*e*(4*a*c - b**2)) + 1/(4*c*e))*log(2*d*x/e + x**2 + (-8*a*c*e*(b*sqrt(-4*a*c + b**2)/(4*c*e*(4*a*c - b**2)) + 1/(4*c*e)) + 2*a + 2*b**2*e*(b*sqrt(-4*a*c + b**2)/(4*c*e*(4*a*c - b**2)) + 1/(4*c*e)) + b*d**2)/(b*e**2))","B",0
615,1,104,0,1.350067," ","integrate((e*x+d)**2/(a+b*(e*x+d)**2+c*(e*x+d)**4),x)","\operatorname{RootSum} {\left(t^{4} \left(256 a^{2} c^{3} e^{4} - 128 a b^{2} c^{2} e^{4} + 16 b^{4} c e^{4}\right) + t^{2} \left(- 16 a b c e^{2} + 4 b^{3} e^{2}\right) + a, \left( t \mapsto t \log{\left(x + \frac{64 t^{3} a c^{2} e^{3} - 16 t^{3} b^{2} c e^{3} - 2 t b e + d}{e} \right)} \right)\right)}"," ",0,"RootSum(_t**4*(256*a**2*c**3*e**4 - 128*a*b**2*c**2*e**4 + 16*b**4*c*e**4) + _t**2*(-16*a*b*c*e**2 + 4*b**3*e**2) + a, Lambda(_t, _t*log(x + (64*_t**3*a*c**2*e**3 - 16*_t**3*b**2*c*e**3 - 2*_t*b*e + d)/e)))","A",0
616,1,168,0,1.036490," ","integrate((e*x+d)/(a+b*(e*x+d)**2+c*(e*x+d)**4),x)","- \frac{\sqrt{- \frac{1}{4 a c - b^{2}}} \log{\left(\frac{2 d x}{e} + x^{2} + \frac{- 4 a c \sqrt{- \frac{1}{4 a c - b^{2}}} + b^{2} \sqrt{- \frac{1}{4 a c - b^{2}}} + b + 2 c d^{2}}{2 c e^{2}} \right)}}{2 e} + \frac{\sqrt{- \frac{1}{4 a c - b^{2}}} \log{\left(\frac{2 d x}{e} + x^{2} + \frac{4 a c \sqrt{- \frac{1}{4 a c - b^{2}}} - b^{2} \sqrt{- \frac{1}{4 a c - b^{2}}} + b + 2 c d^{2}}{2 c e^{2}} \right)}}{2 e}"," ",0,"-sqrt(-1/(4*a*c - b**2))*log(2*d*x/e + x**2 + (-4*a*c*sqrt(-1/(4*a*c - b**2)) + b**2*sqrt(-1/(4*a*c - b**2)) + b + 2*c*d**2)/(2*c*e**2))/(2*e) + sqrt(-1/(4*a*c - b**2))*log(2*d*x/e + x**2 + (4*a*c*sqrt(-1/(4*a*c - b**2)) - b**2*sqrt(-1/(4*a*c - b**2)) + b + 2*c*d**2)/(2*c*e**2))/(2*e)","B",0
617,1,320,0,6.044279," ","integrate(1/(e*x+d)/(a+b*(e*x+d)**2+c*(e*x+d)**4),x)","\left(- \frac{b \sqrt{- 4 a c + b^{2}}}{4 a e \left(4 a c - b^{2}\right)} - \frac{1}{4 a e}\right) \log{\left(\frac{2 d x}{e} + x^{2} + \frac{- 8 a^{2} c e \left(- \frac{b \sqrt{- 4 a c + b^{2}}}{4 a e \left(4 a c - b^{2}\right)} - \frac{1}{4 a e}\right) + 2 a b^{2} e \left(- \frac{b \sqrt{- 4 a c + b^{2}}}{4 a e \left(4 a c - b^{2}\right)} - \frac{1}{4 a e}\right) - 2 a c + b^{2} + b c d^{2}}{b c e^{2}} \right)} + \left(\frac{b \sqrt{- 4 a c + b^{2}}}{4 a e \left(4 a c - b^{2}\right)} - \frac{1}{4 a e}\right) \log{\left(\frac{2 d x}{e} + x^{2} + \frac{- 8 a^{2} c e \left(\frac{b \sqrt{- 4 a c + b^{2}}}{4 a e \left(4 a c - b^{2}\right)} - \frac{1}{4 a e}\right) + 2 a b^{2} e \left(\frac{b \sqrt{- 4 a c + b^{2}}}{4 a e \left(4 a c - b^{2}\right)} - \frac{1}{4 a e}\right) - 2 a c + b^{2} + b c d^{2}}{b c e^{2}} \right)} + \frac{\log{\left(\frac{d}{e} + x \right)}}{a e}"," ",0,"(-b*sqrt(-4*a*c + b**2)/(4*a*e*(4*a*c - b**2)) - 1/(4*a*e))*log(2*d*x/e + x**2 + (-8*a**2*c*e*(-b*sqrt(-4*a*c + b**2)/(4*a*e*(4*a*c - b**2)) - 1/(4*a*e)) + 2*a*b**2*e*(-b*sqrt(-4*a*c + b**2)/(4*a*e*(4*a*c - b**2)) - 1/(4*a*e)) - 2*a*c + b**2 + b*c*d**2)/(b*c*e**2)) + (b*sqrt(-4*a*c + b**2)/(4*a*e*(4*a*c - b**2)) - 1/(4*a*e))*log(2*d*x/e + x**2 + (-8*a**2*c*e*(b*sqrt(-4*a*c + b**2)/(4*a*e*(4*a*c - b**2)) - 1/(4*a*e)) + 2*a*b**2*e*(b*sqrt(-4*a*c + b**2)/(4*a*e*(4*a*c - b**2)) - 1/(4*a*e)) - 2*a*c + b**2 + b*c*d**2)/(b*c*e**2)) + log(d/e + x)/(a*e)","B",0
618,1,211,0,4.268833," ","integrate(1/(e*x+d)**2/(a+b*(e*x+d)**2+c*(e*x+d)**4),x)","\operatorname{RootSum} {\left(t^{4} \left(256 a^{5} c^{2} e^{4} - 128 a^{4} b^{2} c e^{4} + 16 a^{3} b^{4} e^{4}\right) + t^{2} \left(48 a^{2} b c^{2} e^{2} - 28 a b^{3} c e^{2} + 4 b^{5} e^{2}\right) + c^{3}, \left( t \mapsto t \log{\left(x + \frac{- 64 t^{3} a^{5} c^{2} e^{3} + 48 t^{3} a^{4} b^{2} c e^{3} - 8 t^{3} a^{3} b^{4} e^{3} - 10 t a^{2} b c^{2} e + 10 t a b^{3} c e - 2 t b^{5} e + a c^{3} d - b^{2} c^{2} d}{a c^{3} e - b^{2} c^{2} e} \right)} \right)\right)} - \frac{1}{a d e + a e^{2} x}"," ",0,"RootSum(_t**4*(256*a**5*c**2*e**4 - 128*a**4*b**2*c*e**4 + 16*a**3*b**4*e**4) + _t**2*(48*a**2*b*c**2*e**2 - 28*a*b**3*c*e**2 + 4*b**5*e**2) + c**3, Lambda(_t, _t*log(x + (-64*_t**3*a**5*c**2*e**3 + 48*_t**3*a**4*b**2*c*e**3 - 8*_t**3*a**3*b**4*e**3 - 10*_t*a**2*b*c**2*e + 10*_t*a*b**3*c*e - 2*_t*b**5*e + a*c**3*d - b**2*c**2*d)/(a*c**3*e - b**2*c**2*e)))) - 1/(a*d*e + a*e**2*x)","A",0
619,1,464,0,146.463611," ","integrate(1/(e*x+d)**3/(a+b*(e*x+d)**2+c*(e*x+d)**4),x)","\left(\frac{b}{4 a^{2} e} - \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{4 a^{2} e \left(4 a c - b^{2}\right)}\right) \log{\left(\frac{2 d x}{e} + x^{2} + \frac{- 8 a^{3} c e \left(\frac{b}{4 a^{2} e} - \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{4 a^{2} e \left(4 a c - b^{2}\right)}\right) + 2 a^{2} b^{2} e \left(\frac{b}{4 a^{2} e} - \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{4 a^{2} e \left(4 a c - b^{2}\right)}\right) + 3 a b c + 2 a c^{2} d^{2} - b^{3} - b^{2} c d^{2}}{2 a c^{2} e^{2} - b^{2} c e^{2}} \right)} + \left(\frac{b}{4 a^{2} e} + \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{4 a^{2} e \left(4 a c - b^{2}\right)}\right) \log{\left(\frac{2 d x}{e} + x^{2} + \frac{- 8 a^{3} c e \left(\frac{b}{4 a^{2} e} + \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{4 a^{2} e \left(4 a c - b^{2}\right)}\right) + 2 a^{2} b^{2} e \left(\frac{b}{4 a^{2} e} + \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{4 a^{2} e \left(4 a c - b^{2}\right)}\right) + 3 a b c + 2 a c^{2} d^{2} - b^{3} - b^{2} c d^{2}}{2 a c^{2} e^{2} - b^{2} c e^{2}} \right)} - \frac{1}{2 a d^{2} e + 4 a d e^{2} x + 2 a e^{3} x^{2}} - \frac{b \log{\left(\frac{d}{e} + x \right)}}{a^{2} e}"," ",0,"(b/(4*a**2*e) - sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(4*a**2*e*(4*a*c - b**2)))*log(2*d*x/e + x**2 + (-8*a**3*c*e*(b/(4*a**2*e) - sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(4*a**2*e*(4*a*c - b**2))) + 2*a**2*b**2*e*(b/(4*a**2*e) - sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(4*a**2*e*(4*a*c - b**2))) + 3*a*b*c + 2*a*c**2*d**2 - b**3 - b**2*c*d**2)/(2*a*c**2*e**2 - b**2*c*e**2)) + (b/(4*a**2*e) + sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(4*a**2*e*(4*a*c - b**2)))*log(2*d*x/e + x**2 + (-8*a**3*c*e*(b/(4*a**2*e) + sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(4*a**2*e*(4*a*c - b**2))) + 2*a**2*b**2*e*(b/(4*a**2*e) + sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(4*a**2*e*(4*a*c - b**2))) + 3*a*b*c + 2*a*c**2*d**2 - b**3 - b**2*c*d**2)/(2*a*c**2*e**2 - b**2*c*e**2)) - 1/(2*a*d**2*e + 4*a*d*e**2*x + 2*a*e**3*x**2) - b*log(d/e + x)/(a**2*e)","B",0
620,1,347,0,12.774375," ","integrate(1/(e*x+d)**4/(a+b*(e*x+d)**2+c*(e*x+d)**4),x)","\frac{- a + 3 b d^{2} + 6 b d e x + 3 b e^{2} x^{2}}{3 a^{2} d^{3} e + 9 a^{2} d^{2} e^{2} x + 9 a^{2} d e^{3} x^{2} + 3 a^{2} e^{4} x^{3}} + \operatorname{RootSum} {\left(t^{4} \left(256 a^{7} c^{2} e^{4} - 128 a^{6} b^{2} c e^{4} + 16 a^{5} b^{4} e^{4}\right) + t^{2} \left(- 80 a^{3} b c^{3} e^{2} + 100 a^{2} b^{3} c^{2} e^{2} - 36 a b^{5} c e^{2} + 4 b^{7} e^{2}\right) + c^{5}, \left( t \mapsto t \log{\left(x + \frac{- 96 t^{3} a^{7} b c^{2} e^{3} + 56 t^{3} a^{6} b^{3} c e^{3} - 8 t^{3} a^{5} b^{5} e^{3} - 4 t a^{4} c^{4} e + 32 t a^{3} b^{2} c^{3} e - 40 t a^{2} b^{4} c^{2} e + 16 t a b^{6} c e - 2 t b^{8} e + a^{2} c^{5} d - 3 a b^{2} c^{4} d + b^{4} c^{3} d}{a^{2} c^{5} e - 3 a b^{2} c^{4} e + b^{4} c^{3} e} \right)} \right)\right)}"," ",0,"(-a + 3*b*d**2 + 6*b*d*e*x + 3*b*e**2*x**2)/(3*a**2*d**3*e + 9*a**2*d**2*e**2*x + 9*a**2*d*e**3*x**2 + 3*a**2*e**4*x**3) + RootSum(_t**4*(256*a**7*c**2*e**4 - 128*a**6*b**2*c*e**4 + 16*a**5*b**4*e**4) + _t**2*(-80*a**3*b*c**3*e**2 + 100*a**2*b**3*c**2*e**2 - 36*a*b**5*c*e**2 + 4*b**7*e**2) + c**5, Lambda(_t, _t*log(x + (-96*_t**3*a**7*b*c**2*e**3 + 56*_t**3*a**6*b**3*c*e**3 - 8*_t**3*a**5*b**5*e**3 - 4*_t*a**4*c**4*e + 32*_t*a**3*b**2*c**3*e - 40*_t*a**2*b**4*c**2*e + 16*_t*a*b**6*c*e - 2*_t*b**8*e + a**2*c**5*d - 3*a*b**2*c**4*d + b**4*c**3*d)/(a**2*c**5*e - 3*a*b**2*c**4*e + b**4*c**3*e))))","A",0
621,1,573,0,8.966100," ","integrate((e*x+d)**4/(a+b*(e*x+d)**2+c*(e*x+d)**4)**2,x)","\frac{- 2 a d - b d^{3} - 3 b d e^{2} x^{2} - b e^{3} x^{3} + x \left(- 2 a e - 3 b d^{2} e\right)}{8 a^{2} c e - 2 a b^{2} e + 8 a b c d^{2} e + 8 a c^{2} d^{4} e - 2 b^{3} d^{2} e - 2 b^{2} c d^{4} e + x^{4} \left(8 a c^{2} e^{5} - 2 b^{2} c e^{5}\right) + x^{3} \left(32 a c^{2} d e^{4} - 8 b^{2} c d e^{4}\right) + x^{2} \left(8 a b c e^{3} + 48 a c^{2} d^{2} e^{3} - 2 b^{3} e^{3} - 12 b^{2} c d^{2} e^{3}\right) + x \left(16 a b c d e^{2} + 32 a c^{2} d^{3} e^{2} - 4 b^{3} d e^{2} - 8 b^{2} c d^{3} e^{2}\right)} + \operatorname{RootSum} {\left(t^{4} \left(1048576 a^{6} c^{7} e^{4} - 1572864 a^{5} b^{2} c^{6} e^{4} + 983040 a^{4} b^{4} c^{5} e^{4} - 327680 a^{3} b^{6} c^{4} e^{4} + 61440 a^{2} b^{8} c^{3} e^{4} - 6144 a b^{10} c^{2} e^{4} + 256 b^{12} c e^{4}\right) + t^{2} \left(- 12288 a^{4} b c^{4} e^{2} + 8192 a^{3} b^{3} c^{3} e^{2} - 1536 a^{2} b^{5} c^{2} e^{2} + 16 b^{9} e^{2}\right) + 16 a^{3} c^{2} + 24 a^{2} b^{2} c + 9 a b^{4}, \left( t \mapsto t \log{\left(x + \frac{16384 t^{3} a^{3} b c^{4} e^{3} - 12288 t^{3} a^{2} b^{3} c^{3} e^{3} + 3072 t^{3} a b^{5} c^{2} e^{3} - 256 t^{3} b^{7} c e^{3} + 64 t a^{2} c^{2} e - 128 t a b^{2} c e - 4 t b^{4} e + 4 a c d + 3 b^{2} d}{4 a c e + 3 b^{2} e} \right)} \right)\right)}"," ",0,"(-2*a*d - b*d**3 - 3*b*d*e**2*x**2 - b*e**3*x**3 + x*(-2*a*e - 3*b*d**2*e))/(8*a**2*c*e - 2*a*b**2*e + 8*a*b*c*d**2*e + 8*a*c**2*d**4*e - 2*b**3*d**2*e - 2*b**2*c*d**4*e + x**4*(8*a*c**2*e**5 - 2*b**2*c*e**5) + x**3*(32*a*c**2*d*e**4 - 8*b**2*c*d*e**4) + x**2*(8*a*b*c*e**3 + 48*a*c**2*d**2*e**3 - 2*b**3*e**3 - 12*b**2*c*d**2*e**3) + x*(16*a*b*c*d*e**2 + 32*a*c**2*d**3*e**2 - 4*b**3*d*e**2 - 8*b**2*c*d**3*e**2)) + RootSum(_t**4*(1048576*a**6*c**7*e**4 - 1572864*a**5*b**2*c**6*e**4 + 983040*a**4*b**4*c**5*e**4 - 327680*a**3*b**6*c**4*e**4 + 61440*a**2*b**8*c**3*e**4 - 6144*a*b**10*c**2*e**4 + 256*b**12*c*e**4) + _t**2*(-12288*a**4*b*c**4*e**2 + 8192*a**3*b**3*c**3*e**2 - 1536*a**2*b**5*c**2*e**2 + 16*b**9*e**2) + 16*a**3*c**2 + 24*a**2*b**2*c + 9*a*b**4, Lambda(_t, _t*log(x + (16384*_t**3*a**3*b*c**4*e**3 - 12288*_t**3*a**2*b**3*c**3*e**3 + 3072*_t**3*a*b**5*c**2*e**3 - 256*_t**3*b**7*c*e**3 + 64*_t*a**2*c**2*e - 128*_t*a*b**2*c*e - 4*_t*b**4*e + 4*a*c*d + 3*b**2*d)/(4*a*c*e + 3*b**2*e))))","B",0
622,1,495,0,4.875396," ","integrate((e*x+d)**3/(a+b*(e*x+d)**2+c*(e*x+d)**4)**2,x)","\frac{b \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \log{\left(\frac{2 d x}{e} + x^{2} + \frac{- 16 a^{2} b c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + 8 a b^{3} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} - b^{5} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + b^{2} + 2 b c d^{2}}{2 b c e^{2}} \right)}}{2 e} - \frac{b \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \log{\left(\frac{2 d x}{e} + x^{2} + \frac{16 a^{2} b c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} - 8 a b^{3} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + b^{5} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + b^{2} + 2 b c d^{2}}{2 b c e^{2}} \right)}}{2 e} + \frac{- 2 a - b d^{2} - 2 b d e x - b e^{2} x^{2}}{8 a^{2} c e - 2 a b^{2} e + 8 a b c d^{2} e + 8 a c^{2} d^{4} e - 2 b^{3} d^{2} e - 2 b^{2} c d^{4} e + x^{4} \left(8 a c^{2} e^{5} - 2 b^{2} c e^{5}\right) + x^{3} \left(32 a c^{2} d e^{4} - 8 b^{2} c d e^{4}\right) + x^{2} \left(8 a b c e^{3} + 48 a c^{2} d^{2} e^{3} - 2 b^{3} e^{3} - 12 b^{2} c d^{2} e^{3}\right) + x \left(16 a b c d e^{2} + 32 a c^{2} d^{3} e^{2} - 4 b^{3} d e^{2} - 8 b^{2} c d^{3} e^{2}\right)}"," ",0,"b*sqrt(-1/(4*a*c - b**2)**3)*log(2*d*x/e + x**2 + (-16*a**2*b*c**2*sqrt(-1/(4*a*c - b**2)**3) + 8*a*b**3*c*sqrt(-1/(4*a*c - b**2)**3) - b**5*sqrt(-1/(4*a*c - b**2)**3) + b**2 + 2*b*c*d**2)/(2*b*c*e**2))/(2*e) - b*sqrt(-1/(4*a*c - b**2)**3)*log(2*d*x/e + x**2 + (16*a**2*b*c**2*sqrt(-1/(4*a*c - b**2)**3) - 8*a*b**3*c*sqrt(-1/(4*a*c - b**2)**3) + b**5*sqrt(-1/(4*a*c - b**2)**3) + b**2 + 2*b*c*d**2)/(2*b*c*e**2))/(2*e) + (-2*a - b*d**2 - 2*b*d*e*x - b*e**2*x**2)/(8*a**2*c*e - 2*a*b**2*e + 8*a*b*c*d**2*e + 8*a*c**2*d**4*e - 2*b**3*d**2*e - 2*b**2*c*d**4*e + x**4*(8*a*c**2*e**5 - 2*b**2*c*e**5) + x**3*(32*a*c**2*d*e**4 - 8*b**2*c*d*e**4) + x**2*(8*a*b*c*e**3 + 48*a*c**2*d**2*e**3 - 2*b**3*e**3 - 12*b**2*c*d**2*e**3) + x*(16*a*b*c*d*e**2 + 32*a*c**2*d**3*e**2 - 4*b**3*d*e**2 - 8*b**2*c*d**3*e**2))","B",0
623,1,578,0,18.532361," ","integrate((e*x+d)**2/(a+b*(e*x+d)**2+c*(e*x+d)**4)**2,x)","\frac{b d + 2 c d^{3} + 6 c d e^{2} x^{2} + 2 c e^{3} x^{3} + x \left(b e + 6 c d^{2} e\right)}{8 a^{2} c e - 2 a b^{2} e + 8 a b c d^{2} e + 8 a c^{2} d^{4} e - 2 b^{3} d^{2} e - 2 b^{2} c d^{4} e + x^{4} \left(8 a c^{2} e^{5} - 2 b^{2} c e^{5}\right) + x^{3} \left(32 a c^{2} d e^{4} - 8 b^{2} c d e^{4}\right) + x^{2} \left(8 a b c e^{3} + 48 a c^{2} d^{2} e^{3} - 2 b^{3} e^{3} - 12 b^{2} c d^{2} e^{3}\right) + x \left(16 a b c d e^{2} + 32 a c^{2} d^{3} e^{2} - 4 b^{3} d e^{2} - 8 b^{2} c d^{3} e^{2}\right)} + \operatorname{RootSum} {\left(t^{4} \left(1048576 a^{7} c^{6} e^{4} - 1572864 a^{6} b^{2} c^{5} e^{4} + 983040 a^{5} b^{4} c^{4} e^{4} - 327680 a^{4} b^{6} c^{3} e^{4} + 61440 a^{3} b^{8} c^{2} e^{4} - 6144 a^{2} b^{10} c e^{4} + 256 a b^{12} e^{4}\right) + t^{2} \left(- 12288 a^{4} b c^{4} e^{2} + 8192 a^{3} b^{3} c^{3} e^{2} - 1536 a^{2} b^{5} c^{2} e^{2} + 16 b^{9} e^{2}\right) + 16 a^{2} c^{3} + 24 a b^{2} c^{2} + 9 b^{4} c, \left( t \mapsto t \log{\left(x + \frac{16384 t^{3} a^{5} c^{4} e^{3} - 8192 t^{3} a^{4} b^{2} c^{3} e^{3} + 512 t^{3} a^{2} b^{6} c e^{3} - 64 t^{3} a b^{8} e^{3} - 128 t a^{2} b c^{2} e - 16 t a b^{3} c e - 4 t b^{5} e + 4 a c^{2} d + 3 b^{2} c d}{4 a c^{2} e + 3 b^{2} c e} \right)} \right)\right)}"," ",0,"(b*d + 2*c*d**3 + 6*c*d*e**2*x**2 + 2*c*e**3*x**3 + x*(b*e + 6*c*d**2*e))/(8*a**2*c*e - 2*a*b**2*e + 8*a*b*c*d**2*e + 8*a*c**2*d**4*e - 2*b**3*d**2*e - 2*b**2*c*d**4*e + x**4*(8*a*c**2*e**5 - 2*b**2*c*e**5) + x**3*(32*a*c**2*d*e**4 - 8*b**2*c*d*e**4) + x**2*(8*a*b*c*e**3 + 48*a*c**2*d**2*e**3 - 2*b**3*e**3 - 12*b**2*c*d**2*e**3) + x*(16*a*b*c*d*e**2 + 32*a*c**2*d**3*e**2 - 4*b**3*d*e**2 - 8*b**2*c*d**3*e**2)) + RootSum(_t**4*(1048576*a**7*c**6*e**4 - 1572864*a**6*b**2*c**5*e**4 + 983040*a**5*b**4*c**4*e**4 - 327680*a**4*b**6*c**3*e**4 + 61440*a**3*b**8*c**2*e**4 - 6144*a**2*b**10*c*e**4 + 256*a*b**12*e**4) + _t**2*(-12288*a**4*b*c**4*e**2 + 8192*a**3*b**3*c**3*e**2 - 1536*a**2*b**5*c**2*e**2 + 16*b**9*e**2) + 16*a**2*c**3 + 24*a*b**2*c**2 + 9*b**4*c, Lambda(_t, _t*log(x + (16384*_t**3*a**5*c**4*e**3 - 8192*_t**3*a**4*b**2*c**3*e**3 + 512*_t**3*a**2*b**6*c*e**3 - 64*_t**3*a*b**8*e**3 - 128*_t*a**2*b*c**2*e - 16*_t*a*b**3*c*e - 4*_t*b**5*e + 4*a*c**2*d + 3*b**2*c*d)/(4*a*c**2*e + 3*b**2*c*e))))","B",0
624,1,495,0,4.675241," ","integrate((e*x+d)/(a+b*(e*x+d)**2+c*(e*x+d)**4)**2,x)","- \frac{c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \log{\left(\frac{2 d x}{e} + x^{2} + \frac{- 16 a^{2} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + 8 a b^{2} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} - b^{4} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + b c + 2 c^{2} d^{2}}{2 c^{2} e^{2}} \right)}}{e} + \frac{c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \log{\left(\frac{2 d x}{e} + x^{2} + \frac{16 a^{2} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} - 8 a b^{2} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + b^{4} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + b c + 2 c^{2} d^{2}}{2 c^{2} e^{2}} \right)}}{e} + \frac{b + 2 c d^{2} + 4 c d e x + 2 c e^{2} x^{2}}{8 a^{2} c e - 2 a b^{2} e + 8 a b c d^{2} e + 8 a c^{2} d^{4} e - 2 b^{3} d^{2} e - 2 b^{2} c d^{4} e + x^{4} \left(8 a c^{2} e^{5} - 2 b^{2} c e^{5}\right) + x^{3} \left(32 a c^{2} d e^{4} - 8 b^{2} c d e^{4}\right) + x^{2} \left(8 a b c e^{3} + 48 a c^{2} d^{2} e^{3} - 2 b^{3} e^{3} - 12 b^{2} c d^{2} e^{3}\right) + x \left(16 a b c d e^{2} + 32 a c^{2} d^{3} e^{2} - 4 b^{3} d e^{2} - 8 b^{2} c d^{3} e^{2}\right)}"," ",0,"-c*sqrt(-1/(4*a*c - b**2)**3)*log(2*d*x/e + x**2 + (-16*a**2*c**3*sqrt(-1/(4*a*c - b**2)**3) + 8*a*b**2*c**2*sqrt(-1/(4*a*c - b**2)**3) - b**4*c*sqrt(-1/(4*a*c - b**2)**3) + b*c + 2*c**2*d**2)/(2*c**2*e**2))/e + c*sqrt(-1/(4*a*c - b**2)**3)*log(2*d*x/e + x**2 + (16*a**2*c**3*sqrt(-1/(4*a*c - b**2)**3) - 8*a*b**2*c**2*sqrt(-1/(4*a*c - b**2)**3) + b**4*c*sqrt(-1/(4*a*c - b**2)**3) + b*c + 2*c**2*d**2)/(2*c**2*e**2))/e + (b + 2*c*d**2 + 4*c*d*e*x + 2*c*e**2*x**2)/(8*a**2*c*e - 2*a*b**2*e + 8*a*b*c*d**2*e + 8*a*c**2*d**4*e - 2*b**3*d**2*e - 2*b**2*c*d**4*e + x**4*(8*a*c**2*e**5 - 2*b**2*c*e**5) + x**3*(32*a*c**2*d*e**4 - 8*b**2*c*d*e**4) + x**2*(8*a*b*c*e**3 + 48*a*c**2*d**2*e**3 - 2*b**3*e**3 - 12*b**2*c*d**2*e**3) + x*(16*a*b*c*d*e**2 + 32*a*c**2*d**3*e**2 - 4*b**3*d*e**2 - 8*b**2*c*d**3*e**2))","B",0
625,-1,0,0,0.000000," ","integrate(1/(a+b*(e*x+d)**2+c*(e*x+d)**4)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
626,-1,0,0,0.000000," ","integrate(1/(e*x+d)/(a+b*(e*x+d)**2+c*(e*x+d)**4)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
627,-1,0,0,0.000000," ","integrate(1/(e*x+d)**2/(a+b*(e*x+d)**2+c*(e*x+d)**4)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
628,-1,0,0,0.000000," ","integrate(1/(e*x+d)**3/(a+b*(e*x+d)**2+c*(e*x+d)**4)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
629,-1,0,0,0.000000," ","integrate(1/(e*x+d)**4/(a+b*(e*x+d)**2+c*(e*x+d)**4)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
630,-1,0,0,0.000000," ","integrate((e*x+d)**4/(a+b*(e*x+d)**2+c*(e*x+d)**4)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
631,1,1671,0,14.452744," ","integrate((e*x+d)**3/(a+b*(e*x+d)**2+c*(e*x+d)**4)**3,x)","\frac{3 b c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \log{\left(\frac{2 d x}{e} + x^{2} + \frac{- 192 a^{3} b c^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 144 a^{2} b^{3} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} - 36 a b^{5} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 3 b^{7} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 3 b^{2} c + 6 b c^{2} d^{2}}{6 b c^{2} e^{2}} \right)}}{2 e} - \frac{3 b c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \log{\left(\frac{2 d x}{e} + x^{2} + \frac{192 a^{3} b c^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} - 144 a^{2} b^{3} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 36 a b^{5} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} - 3 b^{7} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 3 b^{2} c + 6 b c^{2} d^{2}}{6 b c^{2} e^{2}} \right)}}{2 e} + \frac{- 8 a^{2} c - a b^{2} - 10 a b c d^{2} - 2 b^{3} d^{2} - 9 b^{2} c d^{4} - 6 b c^{2} d^{6} - 36 b c^{2} d e^{5} x^{5} - 6 b c^{2} e^{6} x^{6} + x^{4} \left(- 9 b^{2} c e^{4} - 90 b c^{2} d^{2} e^{4}\right) + x^{3} \left(- 36 b^{2} c d e^{3} - 120 b c^{2} d^{3} e^{3}\right) + x^{2} \left(- 10 a b c e^{2} - 2 b^{3} e^{2} - 54 b^{2} c d^{2} e^{2} - 90 b c^{2} d^{4} e^{2}\right) + x \left(- 20 a b c d e - 4 b^{3} d e - 36 b^{2} c d^{3} e - 36 b c^{2} d^{5} e\right)}{64 a^{4} c^{2} e - 32 a^{3} b^{2} c e + 128 a^{3} b c^{2} d^{2} e + 128 a^{3} c^{3} d^{4} e + 4 a^{2} b^{4} e - 64 a^{2} b^{3} c d^{2} e + 128 a^{2} b c^{3} d^{6} e + 64 a^{2} c^{4} d^{8} e + 8 a b^{5} d^{2} e - 24 a b^{4} c d^{4} e - 64 a b^{3} c^{2} d^{6} e - 32 a b^{2} c^{3} d^{8} e + 4 b^{6} d^{4} e + 8 b^{5} c d^{6} e + 4 b^{4} c^{2} d^{8} e + x^{8} \left(64 a^{2} c^{4} e^{9} - 32 a b^{2} c^{3} e^{9} + 4 b^{4} c^{2} e^{9}\right) + x^{7} \left(512 a^{2} c^{4} d e^{8} - 256 a b^{2} c^{3} d e^{8} + 32 b^{4} c^{2} d e^{8}\right) + x^{6} \left(128 a^{2} b c^{3} e^{7} + 1792 a^{2} c^{4} d^{2} e^{7} - 64 a b^{3} c^{2} e^{7} - 896 a b^{2} c^{3} d^{2} e^{7} + 8 b^{5} c e^{7} + 112 b^{4} c^{2} d^{2} e^{7}\right) + x^{5} \left(768 a^{2} b c^{3} d e^{6} + 3584 a^{2} c^{4} d^{3} e^{6} - 384 a b^{3} c^{2} d e^{6} - 1792 a b^{2} c^{3} d^{3} e^{6} + 48 b^{5} c d e^{6} + 224 b^{4} c^{2} d^{3} e^{6}\right) + x^{4} \left(128 a^{3} c^{3} e^{5} + 1920 a^{2} b c^{3} d^{2} e^{5} + 4480 a^{2} c^{4} d^{4} e^{5} - 24 a b^{4} c e^{5} - 960 a b^{3} c^{2} d^{2} e^{5} - 2240 a b^{2} c^{3} d^{4} e^{5} + 4 b^{6} e^{5} + 120 b^{5} c d^{2} e^{5} + 280 b^{4} c^{2} d^{4} e^{5}\right) + x^{3} \left(512 a^{3} c^{3} d e^{4} + 2560 a^{2} b c^{3} d^{3} e^{4} + 3584 a^{2} c^{4} d^{5} e^{4} - 96 a b^{4} c d e^{4} - 1280 a b^{3} c^{2} d^{3} e^{4} - 1792 a b^{2} c^{3} d^{5} e^{4} + 16 b^{6} d e^{4} + 160 b^{5} c d^{3} e^{4} + 224 b^{4} c^{2} d^{5} e^{4}\right) + x^{2} \left(128 a^{3} b c^{2} e^{3} + 768 a^{3} c^{3} d^{2} e^{3} - 64 a^{2} b^{3} c e^{3} + 1920 a^{2} b c^{3} d^{4} e^{3} + 1792 a^{2} c^{4} d^{6} e^{3} + 8 a b^{5} e^{3} - 144 a b^{4} c d^{2} e^{3} - 960 a b^{3} c^{2} d^{4} e^{3} - 896 a b^{2} c^{3} d^{6} e^{3} + 24 b^{6} d^{2} e^{3} + 120 b^{5} c d^{4} e^{3} + 112 b^{4} c^{2} d^{6} e^{3}\right) + x \left(256 a^{3} b c^{2} d e^{2} + 512 a^{3} c^{3} d^{3} e^{2} - 128 a^{2} b^{3} c d e^{2} + 768 a^{2} b c^{3} d^{5} e^{2} + 512 a^{2} c^{4} d^{7} e^{2} + 16 a b^{5} d e^{2} - 96 a b^{4} c d^{3} e^{2} - 384 a b^{3} c^{2} d^{5} e^{2} - 256 a b^{2} c^{3} d^{7} e^{2} + 16 b^{6} d^{3} e^{2} + 48 b^{5} c d^{5} e^{2} + 32 b^{4} c^{2} d^{7} e^{2}\right)}"," ",0,"3*b*c*sqrt(-1/(4*a*c - b**2)**5)*log(2*d*x/e + x**2 + (-192*a**3*b*c**4*sqrt(-1/(4*a*c - b**2)**5) + 144*a**2*b**3*c**3*sqrt(-1/(4*a*c - b**2)**5) - 36*a*b**5*c**2*sqrt(-1/(4*a*c - b**2)**5) + 3*b**7*c*sqrt(-1/(4*a*c - b**2)**5) + 3*b**2*c + 6*b*c**2*d**2)/(6*b*c**2*e**2))/(2*e) - 3*b*c*sqrt(-1/(4*a*c - b**2)**5)*log(2*d*x/e + x**2 + (192*a**3*b*c**4*sqrt(-1/(4*a*c - b**2)**5) - 144*a**2*b**3*c**3*sqrt(-1/(4*a*c - b**2)**5) + 36*a*b**5*c**2*sqrt(-1/(4*a*c - b**2)**5) - 3*b**7*c*sqrt(-1/(4*a*c - b**2)**5) + 3*b**2*c + 6*b*c**2*d**2)/(6*b*c**2*e**2))/(2*e) + (-8*a**2*c - a*b**2 - 10*a*b*c*d**2 - 2*b**3*d**2 - 9*b**2*c*d**4 - 6*b*c**2*d**6 - 36*b*c**2*d*e**5*x**5 - 6*b*c**2*e**6*x**6 + x**4*(-9*b**2*c*e**4 - 90*b*c**2*d**2*e**4) + x**3*(-36*b**2*c*d*e**3 - 120*b*c**2*d**3*e**3) + x**2*(-10*a*b*c*e**2 - 2*b**3*e**2 - 54*b**2*c*d**2*e**2 - 90*b*c**2*d**4*e**2) + x*(-20*a*b*c*d*e - 4*b**3*d*e - 36*b**2*c*d**3*e - 36*b*c**2*d**5*e))/(64*a**4*c**2*e - 32*a**3*b**2*c*e + 128*a**3*b*c**2*d**2*e + 128*a**3*c**3*d**4*e + 4*a**2*b**4*e - 64*a**2*b**3*c*d**2*e + 128*a**2*b*c**3*d**6*e + 64*a**2*c**4*d**8*e + 8*a*b**5*d**2*e - 24*a*b**4*c*d**4*e - 64*a*b**3*c**2*d**6*e - 32*a*b**2*c**3*d**8*e + 4*b**6*d**4*e + 8*b**5*c*d**6*e + 4*b**4*c**2*d**8*e + x**8*(64*a**2*c**4*e**9 - 32*a*b**2*c**3*e**9 + 4*b**4*c**2*e**9) + x**7*(512*a**2*c**4*d*e**8 - 256*a*b**2*c**3*d*e**8 + 32*b**4*c**2*d*e**8) + x**6*(128*a**2*b*c**3*e**7 + 1792*a**2*c**4*d**2*e**7 - 64*a*b**3*c**2*e**7 - 896*a*b**2*c**3*d**2*e**7 + 8*b**5*c*e**7 + 112*b**4*c**2*d**2*e**7) + x**5*(768*a**2*b*c**3*d*e**6 + 3584*a**2*c**4*d**3*e**6 - 384*a*b**3*c**2*d*e**6 - 1792*a*b**2*c**3*d**3*e**6 + 48*b**5*c*d*e**6 + 224*b**4*c**2*d**3*e**6) + x**4*(128*a**3*c**3*e**5 + 1920*a**2*b*c**3*d**2*e**5 + 4480*a**2*c**4*d**4*e**5 - 24*a*b**4*c*e**5 - 960*a*b**3*c**2*d**2*e**5 - 2240*a*b**2*c**3*d**4*e**5 + 4*b**6*e**5 + 120*b**5*c*d**2*e**5 + 280*b**4*c**2*d**4*e**5) + x**3*(512*a**3*c**3*d*e**4 + 2560*a**2*b*c**3*d**3*e**4 + 3584*a**2*c**4*d**5*e**4 - 96*a*b**4*c*d*e**4 - 1280*a*b**3*c**2*d**3*e**4 - 1792*a*b**2*c**3*d**5*e**4 + 16*b**6*d*e**4 + 160*b**5*c*d**3*e**4 + 224*b**4*c**2*d**5*e**4) + x**2*(128*a**3*b*c**2*e**3 + 768*a**3*c**3*d**2*e**3 - 64*a**2*b**3*c*e**3 + 1920*a**2*b*c**3*d**4*e**3 + 1792*a**2*c**4*d**6*e**3 + 8*a*b**5*e**3 - 144*a*b**4*c*d**2*e**3 - 960*a*b**3*c**2*d**4*e**3 - 896*a*b**2*c**3*d**6*e**3 + 24*b**6*d**2*e**3 + 120*b**5*c*d**4*e**3 + 112*b**4*c**2*d**6*e**3) + x*(256*a**3*b*c**2*d*e**2 + 512*a**3*c**3*d**3*e**2 - 128*a**2*b**3*c*d*e**2 + 768*a**2*b*c**3*d**5*e**2 + 512*a**2*c**4*d**7*e**2 + 16*a*b**5*d*e**2 - 96*a*b**4*c*d**3*e**2 - 384*a*b**3*c**2*d**5*e**2 - 256*a*b**2*c**3*d**7*e**2 + 16*b**6*d**3*e**2 + 48*b**5*c*d**5*e**2 + 32*b**4*c**2*d**7*e**2))","B",0
632,-1,0,0,0.000000," ","integrate((e*x+d)**2/(a+b*(e*x+d)**2+c*(e*x+d)**4)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
633,1,1646,0,13.928452," ","integrate((e*x+d)/(a+b*(e*x+d)**2+c*(e*x+d)**4)**3,x)","- \frac{3 c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \log{\left(\frac{2 d x}{e} + x^{2} + \frac{- 192 a^{3} c^{5} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 144 a^{2} b^{2} c^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} - 36 a b^{4} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 3 b^{6} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 3 b c^{2} + 6 c^{3} d^{2}}{6 c^{3} e^{2}} \right)}}{e} + \frac{3 c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \log{\left(\frac{2 d x}{e} + x^{2} + \frac{192 a^{3} c^{5} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} - 144 a^{2} b^{2} c^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 36 a b^{4} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} - 3 b^{6} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 3 b c^{2} + 6 c^{3} d^{2}}{6 c^{3} e^{2}} \right)}}{e} + \frac{10 a b c + 20 a c^{2} d^{2} - b^{3} + 4 b^{2} c d^{2} + 18 b c^{2} d^{4} + 12 c^{3} d^{6} + 72 c^{3} d e^{5} x^{5} + 12 c^{3} e^{6} x^{6} + x^{4} \left(18 b c^{2} e^{4} + 180 c^{3} d^{2} e^{4}\right) + x^{3} \left(72 b c^{2} d e^{3} + 240 c^{3} d^{3} e^{3}\right) + x^{2} \left(20 a c^{2} e^{2} + 4 b^{2} c e^{2} + 108 b c^{2} d^{2} e^{2} + 180 c^{3} d^{4} e^{2}\right) + x \left(40 a c^{2} d e + 8 b^{2} c d e + 72 b c^{2} d^{3} e + 72 c^{3} d^{5} e\right)}{64 a^{4} c^{2} e - 32 a^{3} b^{2} c e + 128 a^{3} b c^{2} d^{2} e + 128 a^{3} c^{3} d^{4} e + 4 a^{2} b^{4} e - 64 a^{2} b^{3} c d^{2} e + 128 a^{2} b c^{3} d^{6} e + 64 a^{2} c^{4} d^{8} e + 8 a b^{5} d^{2} e - 24 a b^{4} c d^{4} e - 64 a b^{3} c^{2} d^{6} e - 32 a b^{2} c^{3} d^{8} e + 4 b^{6} d^{4} e + 8 b^{5} c d^{6} e + 4 b^{4} c^{2} d^{8} e + x^{8} \left(64 a^{2} c^{4} e^{9} - 32 a b^{2} c^{3} e^{9} + 4 b^{4} c^{2} e^{9}\right) + x^{7} \left(512 a^{2} c^{4} d e^{8} - 256 a b^{2} c^{3} d e^{8} + 32 b^{4} c^{2} d e^{8}\right) + x^{6} \left(128 a^{2} b c^{3} e^{7} + 1792 a^{2} c^{4} d^{2} e^{7} - 64 a b^{3} c^{2} e^{7} - 896 a b^{2} c^{3} d^{2} e^{7} + 8 b^{5} c e^{7} + 112 b^{4} c^{2} d^{2} e^{7}\right) + x^{5} \left(768 a^{2} b c^{3} d e^{6} + 3584 a^{2} c^{4} d^{3} e^{6} - 384 a b^{3} c^{2} d e^{6} - 1792 a b^{2} c^{3} d^{3} e^{6} + 48 b^{5} c d e^{6} + 224 b^{4} c^{2} d^{3} e^{6}\right) + x^{4} \left(128 a^{3} c^{3} e^{5} + 1920 a^{2} b c^{3} d^{2} e^{5} + 4480 a^{2} c^{4} d^{4} e^{5} - 24 a b^{4} c e^{5} - 960 a b^{3} c^{2} d^{2} e^{5} - 2240 a b^{2} c^{3} d^{4} e^{5} + 4 b^{6} e^{5} + 120 b^{5} c d^{2} e^{5} + 280 b^{4} c^{2} d^{4} e^{5}\right) + x^{3} \left(512 a^{3} c^{3} d e^{4} + 2560 a^{2} b c^{3} d^{3} e^{4} + 3584 a^{2} c^{4} d^{5} e^{4} - 96 a b^{4} c d e^{4} - 1280 a b^{3} c^{2} d^{3} e^{4} - 1792 a b^{2} c^{3} d^{5} e^{4} + 16 b^{6} d e^{4} + 160 b^{5} c d^{3} e^{4} + 224 b^{4} c^{2} d^{5} e^{4}\right) + x^{2} \left(128 a^{3} b c^{2} e^{3} + 768 a^{3} c^{3} d^{2} e^{3} - 64 a^{2} b^{3} c e^{3} + 1920 a^{2} b c^{3} d^{4} e^{3} + 1792 a^{2} c^{4} d^{6} e^{3} + 8 a b^{5} e^{3} - 144 a b^{4} c d^{2} e^{3} - 960 a b^{3} c^{2} d^{4} e^{3} - 896 a b^{2} c^{3} d^{6} e^{3} + 24 b^{6} d^{2} e^{3} + 120 b^{5} c d^{4} e^{3} + 112 b^{4} c^{2} d^{6} e^{3}\right) + x \left(256 a^{3} b c^{2} d e^{2} + 512 a^{3} c^{3} d^{3} e^{2} - 128 a^{2} b^{3} c d e^{2} + 768 a^{2} b c^{3} d^{5} e^{2} + 512 a^{2} c^{4} d^{7} e^{2} + 16 a b^{5} d e^{2} - 96 a b^{4} c d^{3} e^{2} - 384 a b^{3} c^{2} d^{5} e^{2} - 256 a b^{2} c^{3} d^{7} e^{2} + 16 b^{6} d^{3} e^{2} + 48 b^{5} c d^{5} e^{2} + 32 b^{4} c^{2} d^{7} e^{2}\right)}"," ",0,"-3*c**2*sqrt(-1/(4*a*c - b**2)**5)*log(2*d*x/e + x**2 + (-192*a**3*c**5*sqrt(-1/(4*a*c - b**2)**5) + 144*a**2*b**2*c**4*sqrt(-1/(4*a*c - b**2)**5) - 36*a*b**4*c**3*sqrt(-1/(4*a*c - b**2)**5) + 3*b**6*c**2*sqrt(-1/(4*a*c - b**2)**5) + 3*b*c**2 + 6*c**3*d**2)/(6*c**3*e**2))/e + 3*c**2*sqrt(-1/(4*a*c - b**2)**5)*log(2*d*x/e + x**2 + (192*a**3*c**5*sqrt(-1/(4*a*c - b**2)**5) - 144*a**2*b**2*c**4*sqrt(-1/(4*a*c - b**2)**5) + 36*a*b**4*c**3*sqrt(-1/(4*a*c - b**2)**5) - 3*b**6*c**2*sqrt(-1/(4*a*c - b**2)**5) + 3*b*c**2 + 6*c**3*d**2)/(6*c**3*e**2))/e + (10*a*b*c + 20*a*c**2*d**2 - b**3 + 4*b**2*c*d**2 + 18*b*c**2*d**4 + 12*c**3*d**6 + 72*c**3*d*e**5*x**5 + 12*c**3*e**6*x**6 + x**4*(18*b*c**2*e**4 + 180*c**3*d**2*e**4) + x**3*(72*b*c**2*d*e**3 + 240*c**3*d**3*e**3) + x**2*(20*a*c**2*e**2 + 4*b**2*c*e**2 + 108*b*c**2*d**2*e**2 + 180*c**3*d**4*e**2) + x*(40*a*c**2*d*e + 8*b**2*c*d*e + 72*b*c**2*d**3*e + 72*c**3*d**5*e))/(64*a**4*c**2*e - 32*a**3*b**2*c*e + 128*a**3*b*c**2*d**2*e + 128*a**3*c**3*d**4*e + 4*a**2*b**4*e - 64*a**2*b**3*c*d**2*e + 128*a**2*b*c**3*d**6*e + 64*a**2*c**4*d**8*e + 8*a*b**5*d**2*e - 24*a*b**4*c*d**4*e - 64*a*b**3*c**2*d**6*e - 32*a*b**2*c**3*d**8*e + 4*b**6*d**4*e + 8*b**5*c*d**6*e + 4*b**4*c**2*d**8*e + x**8*(64*a**2*c**4*e**9 - 32*a*b**2*c**3*e**9 + 4*b**4*c**2*e**9) + x**7*(512*a**2*c**4*d*e**8 - 256*a*b**2*c**3*d*e**8 + 32*b**4*c**2*d*e**8) + x**6*(128*a**2*b*c**3*e**7 + 1792*a**2*c**4*d**2*e**7 - 64*a*b**3*c**2*e**7 - 896*a*b**2*c**3*d**2*e**7 + 8*b**5*c*e**7 + 112*b**4*c**2*d**2*e**7) + x**5*(768*a**2*b*c**3*d*e**6 + 3584*a**2*c**4*d**3*e**6 - 384*a*b**3*c**2*d*e**6 - 1792*a*b**2*c**3*d**3*e**6 + 48*b**5*c*d*e**6 + 224*b**4*c**2*d**3*e**6) + x**4*(128*a**3*c**3*e**5 + 1920*a**2*b*c**3*d**2*e**5 + 4480*a**2*c**4*d**4*e**5 - 24*a*b**4*c*e**5 - 960*a*b**3*c**2*d**2*e**5 - 2240*a*b**2*c**3*d**4*e**5 + 4*b**6*e**5 + 120*b**5*c*d**2*e**5 + 280*b**4*c**2*d**4*e**5) + x**3*(512*a**3*c**3*d*e**4 + 2560*a**2*b*c**3*d**3*e**4 + 3584*a**2*c**4*d**5*e**4 - 96*a*b**4*c*d*e**4 - 1280*a*b**3*c**2*d**3*e**4 - 1792*a*b**2*c**3*d**5*e**4 + 16*b**6*d*e**4 + 160*b**5*c*d**3*e**4 + 224*b**4*c**2*d**5*e**4) + x**2*(128*a**3*b*c**2*e**3 + 768*a**3*c**3*d**2*e**3 - 64*a**2*b**3*c*e**3 + 1920*a**2*b*c**3*d**4*e**3 + 1792*a**2*c**4*d**6*e**3 + 8*a*b**5*e**3 - 144*a*b**4*c*d**2*e**3 - 960*a*b**3*c**2*d**4*e**3 - 896*a*b**2*c**3*d**6*e**3 + 24*b**6*d**2*e**3 + 120*b**5*c*d**4*e**3 + 112*b**4*c**2*d**6*e**3) + x*(256*a**3*b*c**2*d*e**2 + 512*a**3*c**3*d**3*e**2 - 128*a**2*b**3*c*d*e**2 + 768*a**2*b*c**3*d**5*e**2 + 512*a**2*c**4*d**7*e**2 + 16*a*b**5*d*e**2 - 96*a*b**4*c*d**3*e**2 - 384*a*b**3*c**2*d**5*e**2 - 256*a*b**2*c**3*d**7*e**2 + 16*b**6*d**3*e**2 + 48*b**5*c*d**5*e**2 + 32*b**4*c**2*d**7*e**2))","B",0
634,-1,0,0,0.000000," ","integrate(1/(a+b*(e*x+d)**2+c*(e*x+d)**4)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
635,-1,0,0,0.000000," ","integrate(1/(e*x+d)/(a+b*(e*x+d)**2+c*(e*x+d)**4)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
636,-1,0,0,0.000000," ","integrate(1/(e*x+d)**2/(a+b*(e*x+d)**2+c*(e*x+d)**4)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
637,-1,0,0,0.000000," ","integrate(1/(e*x+d)**3/(a+b*(e*x+d)**2+c*(e*x+d)**4)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
638,1,219,0,3.623171," ","integrate((e*f*x+d*f)**4/(a+b*(e*x+d)**2+c*(e*x+d)**4),x)","\operatorname{RootSum} {\left(t^{4} \left(256 a^{2} c^{5} e^{4} - 128 a b^{2} c^{4} e^{4} + 16 b^{4} c^{3} e^{4}\right) + t^{2} \left(48 a^{2} b c^{2} e^{2} f^{8} - 28 a b^{3} c e^{2} f^{8} + 4 b^{5} e^{2} f^{8}\right) + a^{3} f^{16}, \left( t \mapsto t \log{\left(x + \frac{32 t^{3} a b c^{4} e^{3} - 8 t^{3} b^{3} c^{3} e^{3} - 4 t a^{2} c^{2} e f^{8} + 8 t a b^{2} c e f^{8} - 2 t b^{4} e f^{8} + a^{2} c d f^{12} - a b^{2} d f^{12}}{a^{2} c e f^{12} - a b^{2} e f^{12}} \right)} \right)\right)} + \frac{f^{4} x}{c}"," ",0,"RootSum(_t**4*(256*a**2*c**5*e**4 - 128*a*b**2*c**4*e**4 + 16*b**4*c**3*e**4) + _t**2*(48*a**2*b*c**2*e**2*f**8 - 28*a*b**3*c*e**2*f**8 + 4*b**5*e**2*f**8) + a**3*f**16, Lambda(_t, _t*log(x + (32*_t**3*a*b*c**4*e**3 - 8*_t**3*b**3*c**3*e**3 - 4*_t*a**2*c**2*e*f**8 + 8*_t*a*b**2*c*e*f**8 - 2*_t*b**4*e*f**8 + a**2*c*d*f**12 - a*b**2*d*f**12)/(a**2*c*e*f**12 - a*b**2*e*f**12)))) + f**4*x/c","A",0
639,1,332,0,1.949892," ","integrate((e*f*x+d*f)**3/(a+b*(e*x+d)**2+c*(e*x+d)**4),x)","\left(- \frac{b f^{3} \sqrt{- 4 a c + b^{2}}}{4 c e \left(4 a c - b^{2}\right)} + \frac{f^{3}}{4 c e}\right) \log{\left(\frac{2 d x}{e} + x^{2} + \frac{- 8 a c e \left(- \frac{b f^{3} \sqrt{- 4 a c + b^{2}}}{4 c e \left(4 a c - b^{2}\right)} + \frac{f^{3}}{4 c e}\right) + 2 a f^{3} + 2 b^{2} e \left(- \frac{b f^{3} \sqrt{- 4 a c + b^{2}}}{4 c e \left(4 a c - b^{2}\right)} + \frac{f^{3}}{4 c e}\right) + b d^{2} f^{3}}{b e^{2} f^{3}} \right)} + \left(\frac{b f^{3} \sqrt{- 4 a c + b^{2}}}{4 c e \left(4 a c - b^{2}\right)} + \frac{f^{3}}{4 c e}\right) \log{\left(\frac{2 d x}{e} + x^{2} + \frac{- 8 a c e \left(\frac{b f^{3} \sqrt{- 4 a c + b^{2}}}{4 c e \left(4 a c - b^{2}\right)} + \frac{f^{3}}{4 c e}\right) + 2 a f^{3} + 2 b^{2} e \left(\frac{b f^{3} \sqrt{- 4 a c + b^{2}}}{4 c e \left(4 a c - b^{2}\right)} + \frac{f^{3}}{4 c e}\right) + b d^{2} f^{3}}{b e^{2} f^{3}} \right)}"," ",0,"(-b*f**3*sqrt(-4*a*c + b**2)/(4*c*e*(4*a*c - b**2)) + f**3/(4*c*e))*log(2*d*x/e + x**2 + (-8*a*c*e*(-b*f**3*sqrt(-4*a*c + b**2)/(4*c*e*(4*a*c - b**2)) + f**3/(4*c*e)) + 2*a*f**3 + 2*b**2*e*(-b*f**3*sqrt(-4*a*c + b**2)/(4*c*e*(4*a*c - b**2)) + f**3/(4*c*e)) + b*d**2*f**3)/(b*e**2*f**3)) + (b*f**3*sqrt(-4*a*c + b**2)/(4*c*e*(4*a*c - b**2)) + f**3/(4*c*e))*log(2*d*x/e + x**2 + (-8*a*c*e*(b*f**3*sqrt(-4*a*c + b**2)/(4*c*e*(4*a*c - b**2)) + f**3/(4*c*e)) + 2*a*f**3 + 2*b**2*e*(b*f**3*sqrt(-4*a*c + b**2)/(4*c*e*(4*a*c - b**2)) + f**3/(4*c*e)) + b*d**2*f**3)/(b*e**2*f**3))","B",0
640,1,124,0,1.594779," ","integrate((e*f*x+d*f)**2/(a+b*(e*x+d)**2+c*(e*x+d)**4),x)","\operatorname{RootSum} {\left(t^{4} \left(256 a^{2} c^{3} e^{4} - 128 a b^{2} c^{2} e^{4} + 16 b^{4} c e^{4}\right) + t^{2} \left(- 16 a b c e^{2} f^{4} + 4 b^{3} e^{2} f^{4}\right) + a f^{8}, \left( t \mapsto t \log{\left(x + \frac{64 t^{3} a c^{2} e^{3} - 16 t^{3} b^{2} c e^{3} - 2 t b e f^{4} + d f^{6}}{e f^{6}} \right)} \right)\right)}"," ",0,"RootSum(_t**4*(256*a**2*c**3*e**4 - 128*a*b**2*c**2*e**4 + 16*b**4*c*e**4) + _t**2*(-16*a*b*c*e**2*f**4 + 4*b**3*e**2*f**4) + a*f**8, Lambda(_t, _t*log(x + (64*_t**3*a*c**2*e**3 - 16*_t**3*b**2*c*e**3 - 2*_t*b*e*f**4 + d*f**6)/(e*f**6))))","A",0
641,1,189,0,1.187284," ","integrate((e*f*x+d*f)/(a+b*(e*x+d)**2+c*(e*x+d)**4),x)","- \frac{f \sqrt{- \frac{1}{4 a c - b^{2}}} \log{\left(\frac{2 d x}{e} + x^{2} + \frac{- 4 a c f \sqrt{- \frac{1}{4 a c - b^{2}}} + b^{2} f \sqrt{- \frac{1}{4 a c - b^{2}}} + b f + 2 c d^{2} f}{2 c e^{2} f} \right)}}{2 e} + \frac{f \sqrt{- \frac{1}{4 a c - b^{2}}} \log{\left(\frac{2 d x}{e} + x^{2} + \frac{4 a c f \sqrt{- \frac{1}{4 a c - b^{2}}} - b^{2} f \sqrt{- \frac{1}{4 a c - b^{2}}} + b f + 2 c d^{2} f}{2 c e^{2} f} \right)}}{2 e}"," ",0,"-f*sqrt(-1/(4*a*c - b**2))*log(2*d*x/e + x**2 + (-4*a*c*f*sqrt(-1/(4*a*c - b**2)) + b**2*f*sqrt(-1/(4*a*c - b**2)) + b*f + 2*c*d**2*f)/(2*c*e**2*f))/(2*e) + f*sqrt(-1/(4*a*c - b**2))*log(2*d*x/e + x**2 + (4*a*c*f*sqrt(-1/(4*a*c - b**2)) - b**2*f*sqrt(-1/(4*a*c - b**2)) + b*f + 2*c*d**2*f)/(2*c*e**2*f))/(2*e)","B",0
642,1,348,0,7.157460," ","integrate(1/(e*f*x+d*f)/(a+b*(e*x+d)**2+c*(e*x+d)**4),x)","\left(- \frac{b \sqrt{- 4 a c + b^{2}}}{4 a e f \left(4 a c - b^{2}\right)} - \frac{1}{4 a e f}\right) \log{\left(\frac{2 d x}{e} + x^{2} + \frac{- 8 a^{2} c e f \left(- \frac{b \sqrt{- 4 a c + b^{2}}}{4 a e f \left(4 a c - b^{2}\right)} - \frac{1}{4 a e f}\right) + 2 a b^{2} e f \left(- \frac{b \sqrt{- 4 a c + b^{2}}}{4 a e f \left(4 a c - b^{2}\right)} - \frac{1}{4 a e f}\right) - 2 a c + b^{2} + b c d^{2}}{b c e^{2}} \right)} + \left(\frac{b \sqrt{- 4 a c + b^{2}}}{4 a e f \left(4 a c - b^{2}\right)} - \frac{1}{4 a e f}\right) \log{\left(\frac{2 d x}{e} + x^{2} + \frac{- 8 a^{2} c e f \left(\frac{b \sqrt{- 4 a c + b^{2}}}{4 a e f \left(4 a c - b^{2}\right)} - \frac{1}{4 a e f}\right) + 2 a b^{2} e f \left(\frac{b \sqrt{- 4 a c + b^{2}}}{4 a e f \left(4 a c - b^{2}\right)} - \frac{1}{4 a e f}\right) - 2 a c + b^{2} + b c d^{2}}{b c e^{2}} \right)} + \frac{\log{\left(\frac{d}{e} + x \right)}}{a e f}"," ",0,"(-b*sqrt(-4*a*c + b**2)/(4*a*e*f*(4*a*c - b**2)) - 1/(4*a*e*f))*log(2*d*x/e + x**2 + (-8*a**2*c*e*f*(-b*sqrt(-4*a*c + b**2)/(4*a*e*f*(4*a*c - b**2)) - 1/(4*a*e*f)) + 2*a*b**2*e*f*(-b*sqrt(-4*a*c + b**2)/(4*a*e*f*(4*a*c - b**2)) - 1/(4*a*e*f)) - 2*a*c + b**2 + b*c*d**2)/(b*c*e**2)) + (b*sqrt(-4*a*c + b**2)/(4*a*e*f*(4*a*c - b**2)) - 1/(4*a*e*f))*log(2*d*x/e + x**2 + (-8*a**2*c*e*f*(b*sqrt(-4*a*c + b**2)/(4*a*e*f*(4*a*c - b**2)) - 1/(4*a*e*f)) + 2*a*b**2*e*f*(b*sqrt(-4*a*c + b**2)/(4*a*e*f*(4*a*c - b**2)) - 1/(4*a*e*f)) - 2*a*c + b**2 + b*c*d**2)/(b*c*e**2)) + log(d/e + x)/(a*e*f)","B",0
643,1,258,0,4.899042," ","integrate(1/(e*f*x+d*f)**2/(a+b*(e*x+d)**2+c*(e*x+d)**4),x)","\operatorname{RootSum} {\left(t^{4} \left(256 a^{5} c^{2} e^{4} f^{8} - 128 a^{4} b^{2} c e^{4} f^{8} + 16 a^{3} b^{4} e^{4} f^{8}\right) + t^{2} \left(48 a^{2} b c^{2} e^{2} f^{4} - 28 a b^{3} c e^{2} f^{4} + 4 b^{5} e^{2} f^{4}\right) + c^{3}, \left( t \mapsto t \log{\left(x + \frac{- 64 t^{3} a^{5} c^{2} e^{3} f^{6} + 48 t^{3} a^{4} b^{2} c e^{3} f^{6} - 8 t^{3} a^{3} b^{4} e^{3} f^{6} - 10 t a^{2} b c^{2} e f^{2} + 10 t a b^{3} c e f^{2} - 2 t b^{5} e f^{2} + a c^{3} d - b^{2} c^{2} d}{a c^{3} e - b^{2} c^{2} e} \right)} \right)\right)} - \frac{1}{a d e f^{2} + a e^{2} f^{2} x}"," ",0,"RootSum(_t**4*(256*a**5*c**2*e**4*f**8 - 128*a**4*b**2*c*e**4*f**8 + 16*a**3*b**4*e**4*f**8) + _t**2*(48*a**2*b*c**2*e**2*f**4 - 28*a*b**3*c*e**2*f**4 + 4*b**5*e**2*f**4) + c**3, Lambda(_t, _t*log(x + (-64*_t**3*a**5*c**2*e**3*f**6 + 48*_t**3*a**4*b**2*c*e**3*f**6 - 8*_t**3*a**3*b**4*e**3*f**6 - 10*_t*a**2*b*c**2*e*f**2 + 10*_t*a*b**3*c*e*f**2 - 2*_t*b**5*e*f**2 + a*c**3*d - b**2*c**2*d)/(a*c**3*e - b**2*c**2*e)))) - 1/(a*d*e*f**2 + a*e**2*f**2*x)","A",0
644,1,532,0,156.627980," ","integrate(1/(e*f*x+d*f)**3/(a+b*(e*x+d)**2+c*(e*x+d)**4),x)","\left(\frac{b}{4 a^{2} e f^{3}} - \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{4 a^{2} e f^{3} \left(4 a c - b^{2}\right)}\right) \log{\left(\frac{2 d x}{e} + x^{2} + \frac{- 8 a^{3} c e f^{3} \left(\frac{b}{4 a^{2} e f^{3}} - \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{4 a^{2} e f^{3} \left(4 a c - b^{2}\right)}\right) + 2 a^{2} b^{2} e f^{3} \left(\frac{b}{4 a^{2} e f^{3}} - \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{4 a^{2} e f^{3} \left(4 a c - b^{2}\right)}\right) + 3 a b c + 2 a c^{2} d^{2} - b^{3} - b^{2} c d^{2}}{2 a c^{2} e^{2} - b^{2} c e^{2}} \right)} + \left(\frac{b}{4 a^{2} e f^{3}} + \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{4 a^{2} e f^{3} \left(4 a c - b^{2}\right)}\right) \log{\left(\frac{2 d x}{e} + x^{2} + \frac{- 8 a^{3} c e f^{3} \left(\frac{b}{4 a^{2} e f^{3}} + \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{4 a^{2} e f^{3} \left(4 a c - b^{2}\right)}\right) + 2 a^{2} b^{2} e f^{3} \left(\frac{b}{4 a^{2} e f^{3}} + \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{4 a^{2} e f^{3} \left(4 a c - b^{2}\right)}\right) + 3 a b c + 2 a c^{2} d^{2} - b^{3} - b^{2} c d^{2}}{2 a c^{2} e^{2} - b^{2} c e^{2}} \right)} - \frac{1}{2 a d^{2} e f^{3} + 4 a d e^{2} f^{3} x + 2 a e^{3} f^{3} x^{2}} - \frac{b \log{\left(\frac{d}{e} + x \right)}}{a^{2} e f^{3}}"," ",0,"(b/(4*a**2*e*f**3) - sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(4*a**2*e*f**3*(4*a*c - b**2)))*log(2*d*x/e + x**2 + (-8*a**3*c*e*f**3*(b/(4*a**2*e*f**3) - sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(4*a**2*e*f**3*(4*a*c - b**2))) + 2*a**2*b**2*e*f**3*(b/(4*a**2*e*f**3) - sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(4*a**2*e*f**3*(4*a*c - b**2))) + 3*a*b*c + 2*a*c**2*d**2 - b**3 - b**2*c*d**2)/(2*a*c**2*e**2 - b**2*c*e**2)) + (b/(4*a**2*e*f**3) + sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(4*a**2*e*f**3*(4*a*c - b**2)))*log(2*d*x/e + x**2 + (-8*a**3*c*e*f**3*(b/(4*a**2*e*f**3) + sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(4*a**2*e*f**3*(4*a*c - b**2))) + 2*a**2*b**2*e*f**3*(b/(4*a**2*e*f**3) + sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(4*a**2*e*f**3*(4*a*c - b**2))) + 3*a*b*c + 2*a*c**2*d**2 - b**3 - b**2*c*d**2)/(2*a*c**2*e**2 - b**2*c*e**2)) - 1/(2*a*d**2*e*f**3 + 4*a*d*e**2*f**3*x + 2*a*e**3*f**3*x**2) - b*log(d/e + x)/(a**2*e*f**3)","B",0
645,1,411,0,14.012003," ","integrate(1/(e*f*x+d*f)**4/(a+b*(e*x+d)**2+c*(e*x+d)**4),x)","\frac{- a + 3 b d^{2} + 6 b d e x + 3 b e^{2} x^{2}}{3 a^{2} d^{3} e f^{4} + 9 a^{2} d^{2} e^{2} f^{4} x + 9 a^{2} d e^{3} f^{4} x^{2} + 3 a^{2} e^{4} f^{4} x^{3}} + \operatorname{RootSum} {\left(t^{4} \left(256 a^{7} c^{2} e^{4} f^{16} - 128 a^{6} b^{2} c e^{4} f^{16} + 16 a^{5} b^{4} e^{4} f^{16}\right) + t^{2} \left(- 80 a^{3} b c^{3} e^{2} f^{8} + 100 a^{2} b^{3} c^{2} e^{2} f^{8} - 36 a b^{5} c e^{2} f^{8} + 4 b^{7} e^{2} f^{8}\right) + c^{5}, \left( t \mapsto t \log{\left(x + \frac{- 96 t^{3} a^{7} b c^{2} e^{3} f^{12} + 56 t^{3} a^{6} b^{3} c e^{3} f^{12} - 8 t^{3} a^{5} b^{5} e^{3} f^{12} - 4 t a^{4} c^{4} e f^{4} + 32 t a^{3} b^{2} c^{3} e f^{4} - 40 t a^{2} b^{4} c^{2} e f^{4} + 16 t a b^{6} c e f^{4} - 2 t b^{8} e f^{4} + a^{2} c^{5} d - 3 a b^{2} c^{4} d + b^{4} c^{3} d}{a^{2} c^{5} e - 3 a b^{2} c^{4} e + b^{4} c^{3} e} \right)} \right)\right)}"," ",0,"(-a + 3*b*d**2 + 6*b*d*e*x + 3*b*e**2*x**2)/(3*a**2*d**3*e*f**4 + 9*a**2*d**2*e**2*f**4*x + 9*a**2*d*e**3*f**4*x**2 + 3*a**2*e**4*f**4*x**3) + RootSum(_t**4*(256*a**7*c**2*e**4*f**16 - 128*a**6*b**2*c*e**4*f**16 + 16*a**5*b**4*e**4*f**16) + _t**2*(-80*a**3*b*c**3*e**2*f**8 + 100*a**2*b**3*c**2*e**2*f**8 - 36*a*b**5*c*e**2*f**8 + 4*b**7*e**2*f**8) + c**5, Lambda(_t, _t*log(x + (-96*_t**3*a**7*b*c**2*e**3*f**12 + 56*_t**3*a**6*b**3*c*e**3*f**12 - 8*_t**3*a**5*b**5*e**3*f**12 - 4*_t*a**4*c**4*e*f**4 + 32*_t*a**3*b**2*c**3*e*f**4 - 40*_t*a**2*b**4*c**2*e*f**4 + 16*_t*a*b**6*c*e*f**4 - 2*_t*b**8*e*f**4 + a**2*c**5*d - 3*a*b**2*c**4*d + b**4*c**3*d)/(a**2*c**5*e - 3*a*b**2*c**4*e + b**4*c**3*e))))","A",0
646,1,641,0,9.821481," ","integrate((e*f*x+d*f)**4/(a+b*(e*x+d)**2+c*(e*x+d)**4)**2,x)","\frac{- 2 a d f^{4} - b d^{3} f^{4} - 3 b d e^{2} f^{4} x^{2} - b e^{3} f^{4} x^{3} + x \left(- 2 a e f^{4} - 3 b d^{2} e f^{4}\right)}{8 a^{2} c e - 2 a b^{2} e + 8 a b c d^{2} e + 8 a c^{2} d^{4} e - 2 b^{3} d^{2} e - 2 b^{2} c d^{4} e + x^{4} \left(8 a c^{2} e^{5} - 2 b^{2} c e^{5}\right) + x^{3} \left(32 a c^{2} d e^{4} - 8 b^{2} c d e^{4}\right) + x^{2} \left(8 a b c e^{3} + 48 a c^{2} d^{2} e^{3} - 2 b^{3} e^{3} - 12 b^{2} c d^{2} e^{3}\right) + x \left(16 a b c d e^{2} + 32 a c^{2} d^{3} e^{2} - 4 b^{3} d e^{2} - 8 b^{2} c d^{3} e^{2}\right)} + \operatorname{RootSum} {\left(t^{4} \left(1048576 a^{6} c^{7} e^{4} - 1572864 a^{5} b^{2} c^{6} e^{4} + 983040 a^{4} b^{4} c^{5} e^{4} - 327680 a^{3} b^{6} c^{4} e^{4} + 61440 a^{2} b^{8} c^{3} e^{4} - 6144 a b^{10} c^{2} e^{4} + 256 b^{12} c e^{4}\right) + t^{2} \left(- 12288 a^{4} b c^{4} e^{2} f^{8} + 8192 a^{3} b^{3} c^{3} e^{2} f^{8} - 1536 a^{2} b^{5} c^{2} e^{2} f^{8} + 16 b^{9} e^{2} f^{8}\right) + 16 a^{3} c^{2} f^{16} + 24 a^{2} b^{2} c f^{16} + 9 a b^{4} f^{16}, \left( t \mapsto t \log{\left(x + \frac{16384 t^{3} a^{3} b c^{4} e^{3} - 12288 t^{3} a^{2} b^{3} c^{3} e^{3} + 3072 t^{3} a b^{5} c^{2} e^{3} - 256 t^{3} b^{7} c e^{3} + 64 t a^{2} c^{2} e f^{8} - 128 t a b^{2} c e f^{8} - 4 t b^{4} e f^{8} + 4 a c d f^{12} + 3 b^{2} d f^{12}}{4 a c e f^{12} + 3 b^{2} e f^{12}} \right)} \right)\right)}"," ",0,"(-2*a*d*f**4 - b*d**3*f**4 - 3*b*d*e**2*f**4*x**2 - b*e**3*f**4*x**3 + x*(-2*a*e*f**4 - 3*b*d**2*e*f**4))/(8*a**2*c*e - 2*a*b**2*e + 8*a*b*c*d**2*e + 8*a*c**2*d**4*e - 2*b**3*d**2*e - 2*b**2*c*d**4*e + x**4*(8*a*c**2*e**5 - 2*b**2*c*e**5) + x**3*(32*a*c**2*d*e**4 - 8*b**2*c*d*e**4) + x**2*(8*a*b*c*e**3 + 48*a*c**2*d**2*e**3 - 2*b**3*e**3 - 12*b**2*c*d**2*e**3) + x*(16*a*b*c*d*e**2 + 32*a*c**2*d**3*e**2 - 4*b**3*d*e**2 - 8*b**2*c*d**3*e**2)) + RootSum(_t**4*(1048576*a**6*c**7*e**4 - 1572864*a**5*b**2*c**6*e**4 + 983040*a**4*b**4*c**5*e**4 - 327680*a**3*b**6*c**4*e**4 + 61440*a**2*b**8*c**3*e**4 - 6144*a*b**10*c**2*e**4 + 256*b**12*c*e**4) + _t**2*(-12288*a**4*b*c**4*e**2*f**8 + 8192*a**3*b**3*c**3*e**2*f**8 - 1536*a**2*b**5*c**2*e**2*f**8 + 16*b**9*e**2*f**8) + 16*a**3*c**2*f**16 + 24*a**2*b**2*c*f**16 + 9*a*b**4*f**16, Lambda(_t, _t*log(x + (16384*_t**3*a**3*b*c**4*e**3 - 12288*_t**3*a**2*b**3*c**3*e**3 + 3072*_t**3*a*b**5*c**2*e**3 - 256*_t**3*b**7*c*e**3 + 64*_t*a**2*c**2*e*f**8 - 128*_t*a*b**2*c*e*f**8 - 4*_t*b**4*e*f**8 + 4*a*c*d*f**12 + 3*b**2*d*f**12)/(4*a*c*e*f**12 + 3*b**2*e*f**12))))","B",0
647,1,556,0,5.285553," ","integrate((e*f*x+d*f)**3/(a+b*(e*x+d)**2+c*(e*x+d)**4)**2,x)","\frac{b f^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \log{\left(\frac{2 d x}{e} + x^{2} + \frac{- 16 a^{2} b c^{2} f^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + 8 a b^{3} c f^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} - b^{5} f^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + b^{2} f^{3} + 2 b c d^{2} f^{3}}{2 b c e^{2} f^{3}} \right)}}{2 e} - \frac{b f^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \log{\left(\frac{2 d x}{e} + x^{2} + \frac{16 a^{2} b c^{2} f^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} - 8 a b^{3} c f^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + b^{5} f^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + b^{2} f^{3} + 2 b c d^{2} f^{3}}{2 b c e^{2} f^{3}} \right)}}{2 e} + \frac{- 2 a f^{3} - b d^{2} f^{3} - 2 b d e f^{3} x - b e^{2} f^{3} x^{2}}{8 a^{2} c e - 2 a b^{2} e + 8 a b c d^{2} e + 8 a c^{2} d^{4} e - 2 b^{3} d^{2} e - 2 b^{2} c d^{4} e + x^{4} \left(8 a c^{2} e^{5} - 2 b^{2} c e^{5}\right) + x^{3} \left(32 a c^{2} d e^{4} - 8 b^{2} c d e^{4}\right) + x^{2} \left(8 a b c e^{3} + 48 a c^{2} d^{2} e^{3} - 2 b^{3} e^{3} - 12 b^{2} c d^{2} e^{3}\right) + x \left(16 a b c d e^{2} + 32 a c^{2} d^{3} e^{2} - 4 b^{3} d e^{2} - 8 b^{2} c d^{3} e^{2}\right)}"," ",0,"b*f**3*sqrt(-1/(4*a*c - b**2)**3)*log(2*d*x/e + x**2 + (-16*a**2*b*c**2*f**3*sqrt(-1/(4*a*c - b**2)**3) + 8*a*b**3*c*f**3*sqrt(-1/(4*a*c - b**2)**3) - b**5*f**3*sqrt(-1/(4*a*c - b**2)**3) + b**2*f**3 + 2*b*c*d**2*f**3)/(2*b*c*e**2*f**3))/(2*e) - b*f**3*sqrt(-1/(4*a*c - b**2)**3)*log(2*d*x/e + x**2 + (16*a**2*b*c**2*f**3*sqrt(-1/(4*a*c - b**2)**3) - 8*a*b**3*c*f**3*sqrt(-1/(4*a*c - b**2)**3) + b**5*f**3*sqrt(-1/(4*a*c - b**2)**3) + b**2*f**3 + 2*b*c*d**2*f**3)/(2*b*c*e**2*f**3))/(2*e) + (-2*a*f**3 - b*d**2*f**3 - 2*b*d*e*f**3*x - b*e**2*f**3*x**2)/(8*a**2*c*e - 2*a*b**2*e + 8*a*b*c*d**2*e + 8*a*c**2*d**4*e - 2*b**3*d**2*e - 2*b**2*c*d**4*e + x**4*(8*a*c**2*e**5 - 2*b**2*c*e**5) + x**3*(32*a*c**2*d*e**4 - 8*b**2*c*d*e**4) + x**2*(8*a*b*c*e**3 + 48*a*c**2*d**2*e**3 - 2*b**3*e**3 - 12*b**2*c*d**2*e**3) + x*(16*a*b*c*d*e**2 + 32*a*c**2*d**3*e**2 - 4*b**3*d*e**2 - 8*b**2*c*d**3*e**2))","B",0
648,1,646,0,19.757112," ","integrate((e*f*x+d*f)**2/(a+b*(e*x+d)**2+c*(e*x+d)**4)**2,x)","\frac{b d f^{2} + 2 c d^{3} f^{2} + 6 c d e^{2} f^{2} x^{2} + 2 c e^{3} f^{2} x^{3} + x \left(b e f^{2} + 6 c d^{2} e f^{2}\right)}{8 a^{2} c e - 2 a b^{2} e + 8 a b c d^{2} e + 8 a c^{2} d^{4} e - 2 b^{3} d^{2} e - 2 b^{2} c d^{4} e + x^{4} \left(8 a c^{2} e^{5} - 2 b^{2} c e^{5}\right) + x^{3} \left(32 a c^{2} d e^{4} - 8 b^{2} c d e^{4}\right) + x^{2} \left(8 a b c e^{3} + 48 a c^{2} d^{2} e^{3} - 2 b^{3} e^{3} - 12 b^{2} c d^{2} e^{3}\right) + x \left(16 a b c d e^{2} + 32 a c^{2} d^{3} e^{2} - 4 b^{3} d e^{2} - 8 b^{2} c d^{3} e^{2}\right)} + \operatorname{RootSum} {\left(t^{4} \left(1048576 a^{7} c^{6} e^{4} - 1572864 a^{6} b^{2} c^{5} e^{4} + 983040 a^{5} b^{4} c^{4} e^{4} - 327680 a^{4} b^{6} c^{3} e^{4} + 61440 a^{3} b^{8} c^{2} e^{4} - 6144 a^{2} b^{10} c e^{4} + 256 a b^{12} e^{4}\right) + t^{2} \left(- 12288 a^{4} b c^{4} e^{2} f^{4} + 8192 a^{3} b^{3} c^{3} e^{2} f^{4} - 1536 a^{2} b^{5} c^{2} e^{2} f^{4} + 16 b^{9} e^{2} f^{4}\right) + 16 a^{2} c^{3} f^{8} + 24 a b^{2} c^{2} f^{8} + 9 b^{4} c f^{8}, \left( t \mapsto t \log{\left(x + \frac{16384 t^{3} a^{5} c^{4} e^{3} - 8192 t^{3} a^{4} b^{2} c^{3} e^{3} + 512 t^{3} a^{2} b^{6} c e^{3} - 64 t^{3} a b^{8} e^{3} - 128 t a^{2} b c^{2} e f^{4} - 16 t a b^{3} c e f^{4} - 4 t b^{5} e f^{4} + 4 a c^{2} d f^{6} + 3 b^{2} c d f^{6}}{4 a c^{2} e f^{6} + 3 b^{2} c e f^{6}} \right)} \right)\right)}"," ",0,"(b*d*f**2 + 2*c*d**3*f**2 + 6*c*d*e**2*f**2*x**2 + 2*c*e**3*f**2*x**3 + x*(b*e*f**2 + 6*c*d**2*e*f**2))/(8*a**2*c*e - 2*a*b**2*e + 8*a*b*c*d**2*e + 8*a*c**2*d**4*e - 2*b**3*d**2*e - 2*b**2*c*d**4*e + x**4*(8*a*c**2*e**5 - 2*b**2*c*e**5) + x**3*(32*a*c**2*d*e**4 - 8*b**2*c*d*e**4) + x**2*(8*a*b*c*e**3 + 48*a*c**2*d**2*e**3 - 2*b**3*e**3 - 12*b**2*c*d**2*e**3) + x*(16*a*b*c*d*e**2 + 32*a*c**2*d**3*e**2 - 4*b**3*d*e**2 - 8*b**2*c*d**3*e**2)) + RootSum(_t**4*(1048576*a**7*c**6*e**4 - 1572864*a**6*b**2*c**5*e**4 + 983040*a**5*b**4*c**4*e**4 - 327680*a**4*b**6*c**3*e**4 + 61440*a**3*b**8*c**2*e**4 - 6144*a**2*b**10*c*e**4 + 256*a*b**12*e**4) + _t**2*(-12288*a**4*b*c**4*e**2*f**4 + 8192*a**3*b**3*c**3*e**2*f**4 - 1536*a**2*b**5*c**2*e**2*f**4 + 16*b**9*e**2*f**4) + 16*a**2*c**3*f**8 + 24*a*b**2*c**2*f**8 + 9*b**4*c*f**8, Lambda(_t, _t*log(x + (16384*_t**3*a**5*c**4*e**3 - 8192*_t**3*a**4*b**2*c**3*e**3 + 512*_t**3*a**2*b**6*c*e**3 - 64*_t**3*a*b**8*e**3 - 128*_t*a**2*b*c**2*e*f**4 - 16*_t*a*b**3*c*e*f**4 - 4*_t*b**5*e*f**4 + 4*a*c**2*d*f**6 + 3*b**2*c*d*f**6)/(4*a*c**2*e*f**6 + 3*b**2*c*e*f**6))))","B",0
649,1,525,0,5.067774," ","integrate((e*f*x+d*f)/(a+b*(e*x+d)**2+c*(e*x+d)**4)**2,x)","- \frac{c f \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \log{\left(\frac{2 d x}{e} + x^{2} + \frac{- 16 a^{2} c^{3} f \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + 8 a b^{2} c^{2} f \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} - b^{4} c f \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + b c f + 2 c^{2} d^{2} f}{2 c^{2} e^{2} f} \right)}}{e} + \frac{c f \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \log{\left(\frac{2 d x}{e} + x^{2} + \frac{16 a^{2} c^{3} f \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} - 8 a b^{2} c^{2} f \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + b^{4} c f \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + b c f + 2 c^{2} d^{2} f}{2 c^{2} e^{2} f} \right)}}{e} + \frac{b f + 2 c d^{2} f + 4 c d e f x + 2 c e^{2} f x^{2}}{8 a^{2} c e - 2 a b^{2} e + 8 a b c d^{2} e + 8 a c^{2} d^{4} e - 2 b^{3} d^{2} e - 2 b^{2} c d^{4} e + x^{4} \left(8 a c^{2} e^{5} - 2 b^{2} c e^{5}\right) + x^{3} \left(32 a c^{2} d e^{4} - 8 b^{2} c d e^{4}\right) + x^{2} \left(8 a b c e^{3} + 48 a c^{2} d^{2} e^{3} - 2 b^{3} e^{3} - 12 b^{2} c d^{2} e^{3}\right) + x \left(16 a b c d e^{2} + 32 a c^{2} d^{3} e^{2} - 4 b^{3} d e^{2} - 8 b^{2} c d^{3} e^{2}\right)}"," ",0,"-c*f*sqrt(-1/(4*a*c - b**2)**3)*log(2*d*x/e + x**2 + (-16*a**2*c**3*f*sqrt(-1/(4*a*c - b**2)**3) + 8*a*b**2*c**2*f*sqrt(-1/(4*a*c - b**2)**3) - b**4*c*f*sqrt(-1/(4*a*c - b**2)**3) + b*c*f + 2*c**2*d**2*f)/(2*c**2*e**2*f))/e + c*f*sqrt(-1/(4*a*c - b**2)**3)*log(2*d*x/e + x**2 + (16*a**2*c**3*f*sqrt(-1/(4*a*c - b**2)**3) - 8*a*b**2*c**2*f*sqrt(-1/(4*a*c - b**2)**3) + b**4*c*f*sqrt(-1/(4*a*c - b**2)**3) + b*c*f + 2*c**2*d**2*f)/(2*c**2*e**2*f))/e + (b*f + 2*c*d**2*f + 4*c*d*e*f*x + 2*c*e**2*f*x**2)/(8*a**2*c*e - 2*a*b**2*e + 8*a*b*c*d**2*e + 8*a*c**2*d**4*e - 2*b**3*d**2*e - 2*b**2*c*d**4*e + x**4*(8*a*c**2*e**5 - 2*b**2*c*e**5) + x**3*(32*a*c**2*d*e**4 - 8*b**2*c*d*e**4) + x**2*(8*a*b*c*e**3 + 48*a*c**2*d**2*e**3 - 2*b**3*e**3 - 12*b**2*c*d**2*e**3) + x*(16*a*b*c*d*e**2 + 32*a*c**2*d**3*e**2 - 4*b**3*d*e**2 - 8*b**2*c*d**3*e**2))","B",0
650,-1,0,0,0.000000," ","integrate(1/(e*f*x+d*f)/(a+b*(e*x+d)**2+c*(e*x+d)**4)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
651,-1,0,0,0.000000," ","integrate(1/(e*f*x+d*f)**2/(a+b*(e*x+d)**2+c*(e*x+d)**4)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
652,-1,0,0,0.000000," ","integrate(1/(e*f*x+d*f)**3/(a+b*(e*x+d)**2+c*(e*x+d)**4)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
653,-1,0,0,0.000000," ","integrate(1/(e*f*x+d*f)**4/(a+b*(e*x+d)**2+c*(e*x+d)**4)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
654,-1,0,0,0.000000," ","integrate((e*f*x+d*f)**4/(a+b*(e*x+d)**2+c*(e*x+d)**4)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
655,1,1794,0,14.582601," ","integrate((e*f*x+d*f)**3/(a+b*(e*x+d)**2+c*(e*x+d)**4)**3,x)","\frac{3 b c f^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \log{\left(\frac{2 d x}{e} + x^{2} + \frac{- 192 a^{3} b c^{4} f^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 144 a^{2} b^{3} c^{3} f^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} - 36 a b^{5} c^{2} f^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 3 b^{7} c f^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 3 b^{2} c f^{3} + 6 b c^{2} d^{2} f^{3}}{6 b c^{2} e^{2} f^{3}} \right)}}{2 e} - \frac{3 b c f^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \log{\left(\frac{2 d x}{e} + x^{2} + \frac{192 a^{3} b c^{4} f^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} - 144 a^{2} b^{3} c^{3} f^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 36 a b^{5} c^{2} f^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} - 3 b^{7} c f^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 3 b^{2} c f^{3} + 6 b c^{2} d^{2} f^{3}}{6 b c^{2} e^{2} f^{3}} \right)}}{2 e} + \frac{- 8 a^{2} c f^{3} - a b^{2} f^{3} - 10 a b c d^{2} f^{3} - 2 b^{3} d^{2} f^{3} - 9 b^{2} c d^{4} f^{3} - 6 b c^{2} d^{6} f^{3} - 36 b c^{2} d e^{5} f^{3} x^{5} - 6 b c^{2} e^{6} f^{3} x^{6} + x^{4} \left(- 9 b^{2} c e^{4} f^{3} - 90 b c^{2} d^{2} e^{4} f^{3}\right) + x^{3} \left(- 36 b^{2} c d e^{3} f^{3} - 120 b c^{2} d^{3} e^{3} f^{3}\right) + x^{2} \left(- 10 a b c e^{2} f^{3} - 2 b^{3} e^{2} f^{3} - 54 b^{2} c d^{2} e^{2} f^{3} - 90 b c^{2} d^{4} e^{2} f^{3}\right) + x \left(- 20 a b c d e f^{3} - 4 b^{3} d e f^{3} - 36 b^{2} c d^{3} e f^{3} - 36 b c^{2} d^{5} e f^{3}\right)}{64 a^{4} c^{2} e - 32 a^{3} b^{2} c e + 128 a^{3} b c^{2} d^{2} e + 128 a^{3} c^{3} d^{4} e + 4 a^{2} b^{4} e - 64 a^{2} b^{3} c d^{2} e + 128 a^{2} b c^{3} d^{6} e + 64 a^{2} c^{4} d^{8} e + 8 a b^{5} d^{2} e - 24 a b^{4} c d^{4} e - 64 a b^{3} c^{2} d^{6} e - 32 a b^{2} c^{3} d^{8} e + 4 b^{6} d^{4} e + 8 b^{5} c d^{6} e + 4 b^{4} c^{2} d^{8} e + x^{8} \left(64 a^{2} c^{4} e^{9} - 32 a b^{2} c^{3} e^{9} + 4 b^{4} c^{2} e^{9}\right) + x^{7} \left(512 a^{2} c^{4} d e^{8} - 256 a b^{2} c^{3} d e^{8} + 32 b^{4} c^{2} d e^{8}\right) + x^{6} \left(128 a^{2} b c^{3} e^{7} + 1792 a^{2} c^{4} d^{2} e^{7} - 64 a b^{3} c^{2} e^{7} - 896 a b^{2} c^{3} d^{2} e^{7} + 8 b^{5} c e^{7} + 112 b^{4} c^{2} d^{2} e^{7}\right) + x^{5} \left(768 a^{2} b c^{3} d e^{6} + 3584 a^{2} c^{4} d^{3} e^{6} - 384 a b^{3} c^{2} d e^{6} - 1792 a b^{2} c^{3} d^{3} e^{6} + 48 b^{5} c d e^{6} + 224 b^{4} c^{2} d^{3} e^{6}\right) + x^{4} \left(128 a^{3} c^{3} e^{5} + 1920 a^{2} b c^{3} d^{2} e^{5} + 4480 a^{2} c^{4} d^{4} e^{5} - 24 a b^{4} c e^{5} - 960 a b^{3} c^{2} d^{2} e^{5} - 2240 a b^{2} c^{3} d^{4} e^{5} + 4 b^{6} e^{5} + 120 b^{5} c d^{2} e^{5} + 280 b^{4} c^{2} d^{4} e^{5}\right) + x^{3} \left(512 a^{3} c^{3} d e^{4} + 2560 a^{2} b c^{3} d^{3} e^{4} + 3584 a^{2} c^{4} d^{5} e^{4} - 96 a b^{4} c d e^{4} - 1280 a b^{3} c^{2} d^{3} e^{4} - 1792 a b^{2} c^{3} d^{5} e^{4} + 16 b^{6} d e^{4} + 160 b^{5} c d^{3} e^{4} + 224 b^{4} c^{2} d^{5} e^{4}\right) + x^{2} \left(128 a^{3} b c^{2} e^{3} + 768 a^{3} c^{3} d^{2} e^{3} - 64 a^{2} b^{3} c e^{3} + 1920 a^{2} b c^{3} d^{4} e^{3} + 1792 a^{2} c^{4} d^{6} e^{3} + 8 a b^{5} e^{3} - 144 a b^{4} c d^{2} e^{3} - 960 a b^{3} c^{2} d^{4} e^{3} - 896 a b^{2} c^{3} d^{6} e^{3} + 24 b^{6} d^{2} e^{3} + 120 b^{5} c d^{4} e^{3} + 112 b^{4} c^{2} d^{6} e^{3}\right) + x \left(256 a^{3} b c^{2} d e^{2} + 512 a^{3} c^{3} d^{3} e^{2} - 128 a^{2} b^{3} c d e^{2} + 768 a^{2} b c^{3} d^{5} e^{2} + 512 a^{2} c^{4} d^{7} e^{2} + 16 a b^{5} d e^{2} - 96 a b^{4} c d^{3} e^{2} - 384 a b^{3} c^{2} d^{5} e^{2} - 256 a b^{2} c^{3} d^{7} e^{2} + 16 b^{6} d^{3} e^{2} + 48 b^{5} c d^{5} e^{2} + 32 b^{4} c^{2} d^{7} e^{2}\right)}"," ",0,"3*b*c*f**3*sqrt(-1/(4*a*c - b**2)**5)*log(2*d*x/e + x**2 + (-192*a**3*b*c**4*f**3*sqrt(-1/(4*a*c - b**2)**5) + 144*a**2*b**3*c**3*f**3*sqrt(-1/(4*a*c - b**2)**5) - 36*a*b**5*c**2*f**3*sqrt(-1/(4*a*c - b**2)**5) + 3*b**7*c*f**3*sqrt(-1/(4*a*c - b**2)**5) + 3*b**2*c*f**3 + 6*b*c**2*d**2*f**3)/(6*b*c**2*e**2*f**3))/(2*e) - 3*b*c*f**3*sqrt(-1/(4*a*c - b**2)**5)*log(2*d*x/e + x**2 + (192*a**3*b*c**4*f**3*sqrt(-1/(4*a*c - b**2)**5) - 144*a**2*b**3*c**3*f**3*sqrt(-1/(4*a*c - b**2)**5) + 36*a*b**5*c**2*f**3*sqrt(-1/(4*a*c - b**2)**5) - 3*b**7*c*f**3*sqrt(-1/(4*a*c - b**2)**5) + 3*b**2*c*f**3 + 6*b*c**2*d**2*f**3)/(6*b*c**2*e**2*f**3))/(2*e) + (-8*a**2*c*f**3 - a*b**2*f**3 - 10*a*b*c*d**2*f**3 - 2*b**3*d**2*f**3 - 9*b**2*c*d**4*f**3 - 6*b*c**2*d**6*f**3 - 36*b*c**2*d*e**5*f**3*x**5 - 6*b*c**2*e**6*f**3*x**6 + x**4*(-9*b**2*c*e**4*f**3 - 90*b*c**2*d**2*e**4*f**3) + x**3*(-36*b**2*c*d*e**3*f**3 - 120*b*c**2*d**3*e**3*f**3) + x**2*(-10*a*b*c*e**2*f**3 - 2*b**3*e**2*f**3 - 54*b**2*c*d**2*e**2*f**3 - 90*b*c**2*d**4*e**2*f**3) + x*(-20*a*b*c*d*e*f**3 - 4*b**3*d*e*f**3 - 36*b**2*c*d**3*e*f**3 - 36*b*c**2*d**5*e*f**3))/(64*a**4*c**2*e - 32*a**3*b**2*c*e + 128*a**3*b*c**2*d**2*e + 128*a**3*c**3*d**4*e + 4*a**2*b**4*e - 64*a**2*b**3*c*d**2*e + 128*a**2*b*c**3*d**6*e + 64*a**2*c**4*d**8*e + 8*a*b**5*d**2*e - 24*a*b**4*c*d**4*e - 64*a*b**3*c**2*d**6*e - 32*a*b**2*c**3*d**8*e + 4*b**6*d**4*e + 8*b**5*c*d**6*e + 4*b**4*c**2*d**8*e + x**8*(64*a**2*c**4*e**9 - 32*a*b**2*c**3*e**9 + 4*b**4*c**2*e**9) + x**7*(512*a**2*c**4*d*e**8 - 256*a*b**2*c**3*d*e**8 + 32*b**4*c**2*d*e**8) + x**6*(128*a**2*b*c**3*e**7 + 1792*a**2*c**4*d**2*e**7 - 64*a*b**3*c**2*e**7 - 896*a*b**2*c**3*d**2*e**7 + 8*b**5*c*e**7 + 112*b**4*c**2*d**2*e**7) + x**5*(768*a**2*b*c**3*d*e**6 + 3584*a**2*c**4*d**3*e**6 - 384*a*b**3*c**2*d*e**6 - 1792*a*b**2*c**3*d**3*e**6 + 48*b**5*c*d*e**6 + 224*b**4*c**2*d**3*e**6) + x**4*(128*a**3*c**3*e**5 + 1920*a**2*b*c**3*d**2*e**5 + 4480*a**2*c**4*d**4*e**5 - 24*a*b**4*c*e**5 - 960*a*b**3*c**2*d**2*e**5 - 2240*a*b**2*c**3*d**4*e**5 + 4*b**6*e**5 + 120*b**5*c*d**2*e**5 + 280*b**4*c**2*d**4*e**5) + x**3*(512*a**3*c**3*d*e**4 + 2560*a**2*b*c**3*d**3*e**4 + 3584*a**2*c**4*d**5*e**4 - 96*a*b**4*c*d*e**4 - 1280*a*b**3*c**2*d**3*e**4 - 1792*a*b**2*c**3*d**5*e**4 + 16*b**6*d*e**4 + 160*b**5*c*d**3*e**4 + 224*b**4*c**2*d**5*e**4) + x**2*(128*a**3*b*c**2*e**3 + 768*a**3*c**3*d**2*e**3 - 64*a**2*b**3*c*e**3 + 1920*a**2*b*c**3*d**4*e**3 + 1792*a**2*c**4*d**6*e**3 + 8*a*b**5*e**3 - 144*a*b**4*c*d**2*e**3 - 960*a*b**3*c**2*d**4*e**3 - 896*a*b**2*c**3*d**6*e**3 + 24*b**6*d**2*e**3 + 120*b**5*c*d**4*e**3 + 112*b**4*c**2*d**6*e**3) + x*(256*a**3*b*c**2*d*e**2 + 512*a**3*c**3*d**3*e**2 - 128*a**2*b**3*c*d*e**2 + 768*a**2*b*c**3*d**5*e**2 + 512*a**2*c**4*d**7*e**2 + 16*a*b**5*d*e**2 - 96*a*b**4*c*d**3*e**2 - 384*a*b**3*c**2*d**5*e**2 - 256*a*b**2*c**3*d**7*e**2 + 16*b**6*d**3*e**2 + 48*b**5*c*d**5*e**2 + 32*b**4*c**2*d**7*e**2))","B",0
656,-1,0,0,0.000000," ","integrate((e*f*x+d*f)**2/(a+b*(e*x+d)**2+c*(e*x+d)**4)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
657,1,1707,0,13.965017," ","integrate((e*f*x+d*f)/(a+b*(e*x+d)**2+c*(e*x+d)**4)**3,x)","- \frac{3 c^{2} f \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \log{\left(\frac{2 d x}{e} + x^{2} + \frac{- 192 a^{3} c^{5} f \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 144 a^{2} b^{2} c^{4} f \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} - 36 a b^{4} c^{3} f \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 3 b^{6} c^{2} f \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 3 b c^{2} f + 6 c^{3} d^{2} f}{6 c^{3} e^{2} f} \right)}}{e} + \frac{3 c^{2} f \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \log{\left(\frac{2 d x}{e} + x^{2} + \frac{192 a^{3} c^{5} f \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} - 144 a^{2} b^{2} c^{4} f \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 36 a b^{4} c^{3} f \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} - 3 b^{6} c^{2} f \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 3 b c^{2} f + 6 c^{3} d^{2} f}{6 c^{3} e^{2} f} \right)}}{e} + \frac{10 a b c f + 20 a c^{2} d^{2} f - b^{3} f + 4 b^{2} c d^{2} f + 18 b c^{2} d^{4} f + 12 c^{3} d^{6} f + 72 c^{3} d e^{5} f x^{5} + 12 c^{3} e^{6} f x^{6} + x^{4} \left(18 b c^{2} e^{4} f + 180 c^{3} d^{2} e^{4} f\right) + x^{3} \left(72 b c^{2} d e^{3} f + 240 c^{3} d^{3} e^{3} f\right) + x^{2} \left(20 a c^{2} e^{2} f + 4 b^{2} c e^{2} f + 108 b c^{2} d^{2} e^{2} f + 180 c^{3} d^{4} e^{2} f\right) + x \left(40 a c^{2} d e f + 8 b^{2} c d e f + 72 b c^{2} d^{3} e f + 72 c^{3} d^{5} e f\right)}{64 a^{4} c^{2} e - 32 a^{3} b^{2} c e + 128 a^{3} b c^{2} d^{2} e + 128 a^{3} c^{3} d^{4} e + 4 a^{2} b^{4} e - 64 a^{2} b^{3} c d^{2} e + 128 a^{2} b c^{3} d^{6} e + 64 a^{2} c^{4} d^{8} e + 8 a b^{5} d^{2} e - 24 a b^{4} c d^{4} e - 64 a b^{3} c^{2} d^{6} e - 32 a b^{2} c^{3} d^{8} e + 4 b^{6} d^{4} e + 8 b^{5} c d^{6} e + 4 b^{4} c^{2} d^{8} e + x^{8} \left(64 a^{2} c^{4} e^{9} - 32 a b^{2} c^{3} e^{9} + 4 b^{4} c^{2} e^{9}\right) + x^{7} \left(512 a^{2} c^{4} d e^{8} - 256 a b^{2} c^{3} d e^{8} + 32 b^{4} c^{2} d e^{8}\right) + x^{6} \left(128 a^{2} b c^{3} e^{7} + 1792 a^{2} c^{4} d^{2} e^{7} - 64 a b^{3} c^{2} e^{7} - 896 a b^{2} c^{3} d^{2} e^{7} + 8 b^{5} c e^{7} + 112 b^{4} c^{2} d^{2} e^{7}\right) + x^{5} \left(768 a^{2} b c^{3} d e^{6} + 3584 a^{2} c^{4} d^{3} e^{6} - 384 a b^{3} c^{2} d e^{6} - 1792 a b^{2} c^{3} d^{3} e^{6} + 48 b^{5} c d e^{6} + 224 b^{4} c^{2} d^{3} e^{6}\right) + x^{4} \left(128 a^{3} c^{3} e^{5} + 1920 a^{2} b c^{3} d^{2} e^{5} + 4480 a^{2} c^{4} d^{4} e^{5} - 24 a b^{4} c e^{5} - 960 a b^{3} c^{2} d^{2} e^{5} - 2240 a b^{2} c^{3} d^{4} e^{5} + 4 b^{6} e^{5} + 120 b^{5} c d^{2} e^{5} + 280 b^{4} c^{2} d^{4} e^{5}\right) + x^{3} \left(512 a^{3} c^{3} d e^{4} + 2560 a^{2} b c^{3} d^{3} e^{4} + 3584 a^{2} c^{4} d^{5} e^{4} - 96 a b^{4} c d e^{4} - 1280 a b^{3} c^{2} d^{3} e^{4} - 1792 a b^{2} c^{3} d^{5} e^{4} + 16 b^{6} d e^{4} + 160 b^{5} c d^{3} e^{4} + 224 b^{4} c^{2} d^{5} e^{4}\right) + x^{2} \left(128 a^{3} b c^{2} e^{3} + 768 a^{3} c^{3} d^{2} e^{3} - 64 a^{2} b^{3} c e^{3} + 1920 a^{2} b c^{3} d^{4} e^{3} + 1792 a^{2} c^{4} d^{6} e^{3} + 8 a b^{5} e^{3} - 144 a b^{4} c d^{2} e^{3} - 960 a b^{3} c^{2} d^{4} e^{3} - 896 a b^{2} c^{3} d^{6} e^{3} + 24 b^{6} d^{2} e^{3} + 120 b^{5} c d^{4} e^{3} + 112 b^{4} c^{2} d^{6} e^{3}\right) + x \left(256 a^{3} b c^{2} d e^{2} + 512 a^{3} c^{3} d^{3} e^{2} - 128 a^{2} b^{3} c d e^{2} + 768 a^{2} b c^{3} d^{5} e^{2} + 512 a^{2} c^{4} d^{7} e^{2} + 16 a b^{5} d e^{2} - 96 a b^{4} c d^{3} e^{2} - 384 a b^{3} c^{2} d^{5} e^{2} - 256 a b^{2} c^{3} d^{7} e^{2} + 16 b^{6} d^{3} e^{2} + 48 b^{5} c d^{5} e^{2} + 32 b^{4} c^{2} d^{7} e^{2}\right)}"," ",0,"-3*c**2*f*sqrt(-1/(4*a*c - b**2)**5)*log(2*d*x/e + x**2 + (-192*a**3*c**5*f*sqrt(-1/(4*a*c - b**2)**5) + 144*a**2*b**2*c**4*f*sqrt(-1/(4*a*c - b**2)**5) - 36*a*b**4*c**3*f*sqrt(-1/(4*a*c - b**2)**5) + 3*b**6*c**2*f*sqrt(-1/(4*a*c - b**2)**5) + 3*b*c**2*f + 6*c**3*d**2*f)/(6*c**3*e**2*f))/e + 3*c**2*f*sqrt(-1/(4*a*c - b**2)**5)*log(2*d*x/e + x**2 + (192*a**3*c**5*f*sqrt(-1/(4*a*c - b**2)**5) - 144*a**2*b**2*c**4*f*sqrt(-1/(4*a*c - b**2)**5) + 36*a*b**4*c**3*f*sqrt(-1/(4*a*c - b**2)**5) - 3*b**6*c**2*f*sqrt(-1/(4*a*c - b**2)**5) + 3*b*c**2*f + 6*c**3*d**2*f)/(6*c**3*e**2*f))/e + (10*a*b*c*f + 20*a*c**2*d**2*f - b**3*f + 4*b**2*c*d**2*f + 18*b*c**2*d**4*f + 12*c**3*d**6*f + 72*c**3*d*e**5*f*x**5 + 12*c**3*e**6*f*x**6 + x**4*(18*b*c**2*e**4*f + 180*c**3*d**2*e**4*f) + x**3*(72*b*c**2*d*e**3*f + 240*c**3*d**3*e**3*f) + x**2*(20*a*c**2*e**2*f + 4*b**2*c*e**2*f + 108*b*c**2*d**2*e**2*f + 180*c**3*d**4*e**2*f) + x*(40*a*c**2*d*e*f + 8*b**2*c*d*e*f + 72*b*c**2*d**3*e*f + 72*c**3*d**5*e*f))/(64*a**4*c**2*e - 32*a**3*b**2*c*e + 128*a**3*b*c**2*d**2*e + 128*a**3*c**3*d**4*e + 4*a**2*b**4*e - 64*a**2*b**3*c*d**2*e + 128*a**2*b*c**3*d**6*e + 64*a**2*c**4*d**8*e + 8*a*b**5*d**2*e - 24*a*b**4*c*d**4*e - 64*a*b**3*c**2*d**6*e - 32*a*b**2*c**3*d**8*e + 4*b**6*d**4*e + 8*b**5*c*d**6*e + 4*b**4*c**2*d**8*e + x**8*(64*a**2*c**4*e**9 - 32*a*b**2*c**3*e**9 + 4*b**4*c**2*e**9) + x**7*(512*a**2*c**4*d*e**8 - 256*a*b**2*c**3*d*e**8 + 32*b**4*c**2*d*e**8) + x**6*(128*a**2*b*c**3*e**7 + 1792*a**2*c**4*d**2*e**7 - 64*a*b**3*c**2*e**7 - 896*a*b**2*c**3*d**2*e**7 + 8*b**5*c*e**7 + 112*b**4*c**2*d**2*e**7) + x**5*(768*a**2*b*c**3*d*e**6 + 3584*a**2*c**4*d**3*e**6 - 384*a*b**3*c**2*d*e**6 - 1792*a*b**2*c**3*d**3*e**6 + 48*b**5*c*d*e**6 + 224*b**4*c**2*d**3*e**6) + x**4*(128*a**3*c**3*e**5 + 1920*a**2*b*c**3*d**2*e**5 + 4480*a**2*c**4*d**4*e**5 - 24*a*b**4*c*e**5 - 960*a*b**3*c**2*d**2*e**5 - 2240*a*b**2*c**3*d**4*e**5 + 4*b**6*e**5 + 120*b**5*c*d**2*e**5 + 280*b**4*c**2*d**4*e**5) + x**3*(512*a**3*c**3*d*e**4 + 2560*a**2*b*c**3*d**3*e**4 + 3584*a**2*c**4*d**5*e**4 - 96*a*b**4*c*d*e**4 - 1280*a*b**3*c**2*d**3*e**4 - 1792*a*b**2*c**3*d**5*e**4 + 16*b**6*d*e**4 + 160*b**5*c*d**3*e**4 + 224*b**4*c**2*d**5*e**4) + x**2*(128*a**3*b*c**2*e**3 + 768*a**3*c**3*d**2*e**3 - 64*a**2*b**3*c*e**3 + 1920*a**2*b*c**3*d**4*e**3 + 1792*a**2*c**4*d**6*e**3 + 8*a*b**5*e**3 - 144*a*b**4*c*d**2*e**3 - 960*a*b**3*c**2*d**4*e**3 - 896*a*b**2*c**3*d**6*e**3 + 24*b**6*d**2*e**3 + 120*b**5*c*d**4*e**3 + 112*b**4*c**2*d**6*e**3) + x*(256*a**3*b*c**2*d*e**2 + 512*a**3*c**3*d**3*e**2 - 128*a**2*b**3*c*d*e**2 + 768*a**2*b*c**3*d**5*e**2 + 512*a**2*c**4*d**7*e**2 + 16*a*b**5*d*e**2 - 96*a*b**4*c*d**3*e**2 - 384*a*b**3*c**2*d**5*e**2 - 256*a*b**2*c**3*d**7*e**2 + 16*b**6*d**3*e**2 + 48*b**5*c*d**5*e**2 + 32*b**4*c**2*d**7*e**2))","B",0
658,-1,0,0,0.000000," ","integrate(1/(e*f*x+d*f)/(a+b*(e*x+d)**2+c*(e*x+d)**4)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
659,-1,0,0,0.000000," ","integrate(1/(e*f*x+d*f)**2/(a+b*(e*x+d)**2+c*(e*x+d)**4)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
660,-1,0,0,0.000000," ","integrate(1/(e*f*x+d*f)**3/(a+b*(e*x+d)**2+c*(e*x+d)**4)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
661,0,0,0,0.000000," ","integrate(x/(a+b*(e*x+d)**3+c*(e*x+d)**6)**(1/2),x)","\int \frac{x}{\sqrt{a + b d^{3} + 3 b d^{2} e x + 3 b d e^{2} x^{2} + b e^{3} x^{3} + c d^{6} + 6 c d^{5} e x + 15 c d^{4} e^{2} x^{2} + 20 c d^{3} e^{3} x^{3} + 15 c d^{2} e^{4} x^{4} + 6 c d e^{5} x^{5} + c e^{6} x^{6}}}\, dx"," ",0,"Integral(x/sqrt(a + b*d**3 + 3*b*d**2*e*x + 3*b*d*e**2*x**2 + b*e**3*x**3 + c*d**6 + 6*c*d**5*e*x + 15*c*d**4*e**2*x**2 + 20*c*d**3*e**3*x**3 + 15*c*d**2*e**4*x**4 + 6*c*d*e**5*x**5 + c*e**6*x**6), x)","F",0
662,0,0,0,0.000000," ","integrate(x**2/(a+b*(e*x+d)**3+c*(e*x+d)**6)**(1/2),x)","\int \frac{x^{2}}{\sqrt{a + b d^{3} + 3 b d^{2} e x + 3 b d e^{2} x^{2} + b e^{3} x^{3} + c d^{6} + 6 c d^{5} e x + 15 c d^{4} e^{2} x^{2} + 20 c d^{3} e^{3} x^{3} + 15 c d^{2} e^{4} x^{4} + 6 c d e^{5} x^{5} + c e^{6} x^{6}}}\, dx"," ",0,"Integral(x**2/sqrt(a + b*d**3 + 3*b*d**2*e*x + 3*b*d*e**2*x**2 + b*e**3*x**3 + c*d**6 + 6*c*d**5*e*x + 15*c*d**4*e**2*x**2 + 20*c*d**3*e**3*x**3 + 15*c*d**2*e**4*x**4 + 6*c*d*e**5*x**5 + c*e**6*x**6), x)","F",0
663,1,107,0,0.101302," ","integrate((2+3*x)**6*(1+(2+3*x)**7+(2+3*x)**14),x)","\frac{1162261467 x^{21}}{7} + 2324522934 x^{20} + 15496819560 x^{19} + 65431015920 x^{18} + 196293047760 x^{17} + 444930908256 x^{16} + 790988281344 x^{15} + \frac{15819767221203 x^{14}}{14} + 1318314865122 x^{13} + 1269491970942 x^{12} + 1015602174288 x^{11} + 677082445416 x^{10} + 376174427616 x^{9} + 173635132896 x^{8} + 66158154783 x^{7} + 20588764518 x^{6} + 5149786572 x^{5} + 1010576952 x^{4} + 149902032 x^{3} + 15808800 x^{2} + 1056832 x"," ",0,"1162261467*x**21/7 + 2324522934*x**20 + 15496819560*x**19 + 65431015920*x**18 + 196293047760*x**17 + 444930908256*x**16 + 790988281344*x**15 + 15819767221203*x**14/14 + 1318314865122*x**13 + 1269491970942*x**12 + 1015602174288*x**11 + 677082445416*x**10 + 376174427616*x**9 + 173635132896*x**8 + 66158154783*x**7 + 20588764518*x**6 + 5149786572*x**5 + 1010576952*x**4 + 149902032*x**3 + 15808800*x**2 + 1056832*x","B",0
664,1,187,0,0.150084," ","integrate((2+3*x)**6*(1+(2+3*x)**7+(2+3*x)**14)**2,x)","\frac{16677181699666569 x^{35}}{35} + 11118121133111046 x^{34} + 126005372841925188 x^{33} + 924039400840784712 x^{32} + 4928210137817518464 x^{31} + \frac{101849676181562048256 x^{30}}{5} + 67899784121041365504 x^{29} + \frac{2625458326972530284475 x^{28}}{14} + 437576396725285446564 x^{27} + 875152864622814086340 x^{26} + \frac{7584660010542711771792 x^{25}}{5} + 2298383223254096766840 x^{24} + 3064515076512846852480 x^{23} + 3614565944605222108800 x^{22} + \frac{26506949038858918036881 x^{21}}{7} + 3534290697929473864098 x^{20} + 2945285062308448290360 x^{19} + 2194577166014752240080 x^{18} + 1463104032160519033200 x^{17} + 872775774067455498528 x^{16} + 465517091041681015296 x^{15} + 221699757548270194389 x^{14} + 94069263918929616324 x^{13} + 35454069480572048124 x^{12} + 11821487501620716192 x^{11} + \frac{17344958593049772048 x^{10}}{5} + 889942562270387136 x^{9} + 197897276851452864 x^{8} + 37727143432895007 x^{7} + 6077684727888102 x^{6} + \frac{4057390785756924 x^{5}}{5} + 87406679578680 x^{4} + 7299544818384 x^{3} + 443569828128 x^{2} + 17451466816 x"," ",0,"16677181699666569*x**35/35 + 11118121133111046*x**34 + 126005372841925188*x**33 + 924039400840784712*x**32 + 4928210137817518464*x**31 + 101849676181562048256*x**30/5 + 67899784121041365504*x**29 + 2625458326972530284475*x**28/14 + 437576396725285446564*x**27 + 875152864622814086340*x**26 + 7584660010542711771792*x**25/5 + 2298383223254096766840*x**24 + 3064515076512846852480*x**23 + 3614565944605222108800*x**22 + 26506949038858918036881*x**21/7 + 3534290697929473864098*x**20 + 2945285062308448290360*x**19 + 2194577166014752240080*x**18 + 1463104032160519033200*x**17 + 872775774067455498528*x**16 + 465517091041681015296*x**15 + 221699757548270194389*x**14 + 94069263918929616324*x**13 + 35454069480572048124*x**12 + 11821487501620716192*x**11 + 17344958593049772048*x**10/5 + 889942562270387136*x**9 + 197897276851452864*x**8 + 37727143432895007*x**7 + 6077684727888102*x**6 + 4057390785756924*x**5/5 + 87406679578680*x**4 + 7299544818384*x**3 + 443569828128*x**2 + 17451466816*x","B",0
